Finite Group Databasebeta

← #3532×D73 #33993099

Subgroups — #3532×D73 #33993099

Order 18688.

9542 conjugacy classes of subgroups.

The subgroup lattice has 1676 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#22624088C211yesmaximal, characteristic, complemented
2#22624087C213yesmaximal, complemented
3#22624086C213yesmaximal, complemented
4#22624085C213yesmaximal, complemented
5#22624084C213yesmaximal, complemented
6#22624083C213yesmaximal, complemented
7#22624082C216yesmaximal, complemented
8#22624081C213yesmaximal, complemented
9#22624080C216yesmaximal, complemented
10H(3,𝔽4)×D73C211yesmaximal, characteristic, complemented
11#560×D73C213yesmaximal, complemented
12#551×D73C213yesmaximal, complemented
13#546×D73C216yesmaximal, complemented
14D42×D73C213yesmaximal, complemented
15#538×D73C216yesmaximal, complemented
16#535×D73C213yesmaximal, complemented
17#534×D73C213yesmaximal, complemented
18C2×#120×D73C213yesmaximal, complemented
19C73×#3532C211yesmaximal, characteristic, complemented
20C25×D73C2211yescharacteristic, complemented
21C2×#41×D73C2213yescomplemented
22C22×D4×D73C2213yescomplemented
23C22×D4×D73C2216yescomplemented
24C22×D4×D73C2213yescomplemented
25#17989330C2213yescomplemented
26#17989330C2213yescomplemented
27#17989329C2216yescomplemented
28#17989329C2213yescomplemented
29#17989328C2216yescomplemented
30#17989327C2216yescomplemented
31#17989327C2213yescomplemented
32#17989326C2216yescomplemented
33#17989326C2213yescomplemented
34#17989325C2216yescomplemented
35#17989325C2216yescomplemented
36#17989325C2216yescomplemented
37#17989324C2213yescomplemented
38#17989268C2213yescomplemented
39#17989267C2213yescomplemented
40#17989266C2216yescomplemented
41#17989265C2213yescomplemented
42#17989264C2216yescomplemented
43#17989263C2216yescomplemented
44#17989262C2216yescomplemented
45#17989261C2216yescomplemented
46#17989260C2216yescomplemented
47#17989234C2216yescomplemented
48#17989233C2216yescomplemented
49#17989232C2216yescomplemented
50#17989231C2216yescomplemented
51#17989230C2216yescomplemented
52#17989229C2216yescomplemented
53#17989229C2216yescomplemented
54#17989228C2216yescomplemented
55#17989227C2216yescomplemented
56#17989227C2216yescomplemented
57#17989226C2216yescomplemented
58#17989226C2216yescomplemented
59#17989225C2216yescomplemented
60#17989224C2216yescomplemented
61#17989224C2216yescomplemented
62D4×D292C2216yescomplemented
63#17989222C2213yescomplemented
64#17989221C2216yescomplemented
65#17989221C2216yescomplemented
66D4×C22⋊D73C2216yescomplemented
67D4×C22⋊D73C2216yescomplemented
68#17989219C2213yescomplemented
69#17989219C2213yescomplemented
70#17989219C2216yescomplemented
71#17989177C2216yescomplemented
72#17989176C2216yescomplemented
73#17989176C2216yescomplemented
74#17989175C2216yescomplemented
75#17989174C2216yescomplemented
76#17989173C2216yescomplemented
77#17989173C2216yescomplemented
78#17989172C2216yescomplemented
79#17989172C2216yescomplemented
80#17989171C2216yescomplemented
81#17989171C2216yescomplemented
82#17989170C2216yescomplemented
83#17989170C2216yescomplemented
84#17989169C2216yescomplemented
85#17989169C2216yescomplemented
86#17989156C2213yescomplemented
87#17989155C2213yescomplemented
88#17989155C2213yescomplemented
89#17989154C2213yescomplemented
90#17989153C2216yescomplemented
91#17989153C2216yescomplemented
92#17989152C2216yescomplemented
93#17989152C2216yescomplemented
94#17989151C2213yescomplemented
95#17989150C2213yescomplemented
96#17989150C2213yescomplemented
97#17989149C2213yescomplemented
98#17989148C2216yescomplemented
99#17989148C2213yescomplemented
100#17989148C2213yescomplemented
101#17989147C2213yescomplemented
102#17989147C2216yescomplemented
103#17989147C2213yescomplemented
104#17989146C2213yescomplemented
105#17989146C2213yescomplemented
106#17989145C2216yescomplemented
107#17989145C2216yescomplemented
108#127×D73C2211yescharacteristic, complemented
109#127×D73C2213yescomplemented
110#126×D73C2212yescomplemented
111#126×D73C2216yescomplemented
112#124×D73C2213yescomplemented
113#124×D73C2213yescomplemented
114#124×D73C2216yescomplemented
115#123×D73C2213yescomplemented
116#123×D73C2216yescomplemented
117#123×D73C2213yescomplemented
118#123×D73C2216yescomplemented
119C22⋊Q8×D73C2216yescomplemented
120#121×D73C2216yescomplemented
121#121×D73C2216yescomplemented
122#121×D73C2216yescomplemented
123#121×D73C2216yescomplemented
124#121×D73C2216yescomplemented
125C2×#14556561C2216yescomplemented
126C2×#14556561C2213yescomplemented
127C2×#14556560C2213yescomplemented
128C2×#14556559C2216yescomplemented
129C2×#14556559C2213yescomplemented
130#120×D73C2213yes—
131#120×D73C2213yescomplemented
132#120×D73C2216yescomplemented
133#120×D73C2216yescomplemented
134#120×D73C2213yescomplemented
135#120×D73C2213yescomplemented
136#120×D73C2213yescomplemented
137#120×D73C2216yescomplemented
138#120×D73C2216yescomplemented
139#120×D73C2213yescomplemented
140#120×D73C2213yescomplemented
141#120×D73C2216yescomplemented
142#120×D73C2213yescomplemented
143#120×D73C2213yescomplemented
144#120×D73C2211yescharacteristic, complemented
145C4×D4×D73C2216yescomplemented
146C4×D4×D73C2216yescomplemented
147#117×D73C2213yescomplemented
148C2×C22⋊C4×D73C2213yescomplemented
149C2×C22⋊C4×D73C2216yescomplemented
150C2×C22⋊C4×D73C2213yescomplemented
151H(3,𝔽4)×C73C2211yescharacteristic, complemented
152#560×C73C2213yescomplemented
153#551×C73C2213yescomplemented
154#546×C73C2216yescomplemented
155D42×C73C2213yescomplemented
156#538×C73C2216yescomplemented
157#535×C73C2213yescomplemented
158#534×C73C2213yescomplemented
159C2×#120×C73C2213yescomplemented
160C24×D73—412no—
161C24×D73C2313yes—
162C24×D73C2313yes—
163C24×D73C2313yes—
164C24×D73C2311yescharacteristic
165C24×D73C2311yescharacteristic, complemented
166C24×D73C2313yescomplemented
167C24×D73C2313yescomplemented
168C24×D73C2311yescharacteristic, complemented
169C2×#11924029C2313yescomplemented
170C2×#11924028C2313yescomplemented
171C2×#11924028C2316yescomplemented
172C2×#11924027C2316yescomplemented
173C2×#11924027C2313yescomplemented
174#41×D73—412no—
175C2×Q8×D73C2313yescomplemented
176C22×D292C2313yescomplemented
177C22×D292C2316yescomplemented
178C22×D292C2313yescomplemented
179C22×C22⋊D73C2313yescomplemented
180C22×C22⋊D73C2313yescomplemented
181C22×C22⋊D73C2316yescomplemented
182C22×C22⋊D73C2316yescomplemented
183C22×C22⋊D73C2313yescomplemented
184C22×C22⋊D73C2313yescomplemented
185C2×D4×D73—412no—
186C2×D4×D73—424no—
187C2×D4×D73—412no—
188C2×D4×D73C2316yes—
189C2×D4×D73C2316yes—
190C2×D4×D73C2313yes—
191C2×D4×D73C2316yes—
192C2×D4×D73C2313yes—
193C2×D4×D73C2313yes—
194C2×D4×D73C2316yes—
195C2×D4×D73C2313yes—
196C2×D4×D73C2313yescomplemented
197C2×D4×D73C2313yescomplemented
198C2×D4×D73C2313yescomplemented
199C2×D4×D73C2313yescomplemented
200C2×D4×D73C2316yescomplemented
201C2×D4×D73C2316yescomplemented
202C2×D4×D73C2316yescomplemented
203C2×D4×D73C2316yescomplemented
204C2×D4×D73C2316yescomplemented
205C2×D4×D73C2313yescomplemented
206C2×D4×D73C2316yescomplemented
207C2×D4×D73C2316yescomplemented
208C22×C4×D73C2313yes—
209C22×C4×D73C2316yes—
210C22×C4×D73C2313yescomplemented
211C22×C4×D73C2316yescomplemented
212#14556588C2311yescharacteristic, complemented
213#14556588C2313yescomplemented
214#14556587C2313yescomplemented
215#14556587C2316yescomplemented
216#14556587C2313yescomplemented
217#14556587C2313yescomplemented
218#14556587C2313yescomplemented
219#14556587C2316yescomplemented
220#14556586C2316yescomplemented
221#14556586C2316yescomplemented
222#14556586C2316yescomplemented
223#14556586C2316yescomplemented
224#14556585C2312yescomplemented
225#14556585C2316yescomplemented
226#14556584C2316yescomplemented
227#14556584C2316yescomplemented
228#14556584C2316yescomplemented
229#14556584C2316yescomplemented
230#14556580C2313yescomplemented
231#14556580C2313yescomplemented
232#14556580C2316yescomplemented
233#14556579C2313yescomplemented
234#14556579C2313yescomplemented
235#14556579C2316yescomplemented
236#14556578C2313yescomplemented
237#14556578C2313yescomplemented
238#14556578C2316yescomplemented
239#14556577C2316yescomplemented
240#14556577C2316yescomplemented
241#14556577C2316yescomplemented
242#14556577C2316yescomplemented
243#14556577C2316yescomplemented
244#14556577C2316yescomplemented
245#14556577C2316yescomplemented
246#14556577C2316yescomplemented
247#14556576C2316yescomplemented
248#14556576C2316yescomplemented
249#14556576C2316yescomplemented
250#14556576C2316yescomplemented
251#14556576C2316yescomplemented
252#14556576C2316yescomplemented
253#14556575C2316yescomplemented
254#14556575C2313yescomplemented
255#14556575C2313yescomplemented
256#14556575C2316yescomplemented
257#14556574C2316yescomplemented
258#14556574C2313yescomplemented
259#14556574C2313yescomplemented
260#14556574C2316yescomplemented
261#14556573C2316yescomplemented
262#14556573C2316yescomplemented
263#14556573C2316yescomplemented
264#14556573C2316yescomplemented
265#14556573C2316yescomplemented
266#14556573C2316yescomplemented
267#14556572C2313yescomplemented
268#14556572C2313yescomplemented
269#14556572C2316yescomplemented
270#14556572C2316yescomplemented
271#14556571C2316yescomplemented
272#14556570C2316yescomplemented
273#14556569C2316yescomplemented
274#14556569C2316yescomplemented
275#14556568C2316yescomplemented
276#14556568C2316yescomplemented
277#14556567C2316yescomplemented
278#14556566C2316yescomplemented
279#14556566C2316yescomplemented
280#14556566C2316yescomplemented
281#14556566C2316yescomplemented
282#14556566C2316yescomplemented
283#14556565C2316yescomplemented
284#14556565C2316yescomplemented
285#14556565C2316yescomplemented
286#14556565C2316yescomplemented
287#14556565C2316yescomplemented
288#14556564C2316yescomplemented
289#14556564C2316yescomplemented
290#14556564C2316yescomplemented
291#14556564C2316yescomplemented
292#14556564C2316yescomplemented
293#14556564C2316yescomplemented
294#14556564C2316yescomplemented
295#14556564C2316yescomplemented
296#14556564C2316yescomplemented
297#14556564C2316yescomplemented
298#14556563C2316yescomplemented
299#14556563C2316yescomplemented
300#14556563C2316yescomplemented
301#14556563C2316yescomplemented
302#14556563C2316yescomplemented
303#14556563C2316yescomplemented
304#14556563C2316yescomplemented
305#14556563C2316yescomplemented
306#14556563C2316yescomplemented
307#14556563C2316yescomplemented
308#14556562C2316yescomplemented
309#14556562C2316yescomplemented
310#14556562C2316yescomplemented
311#14556562C2316yescomplemented
312#14556562C2316yescomplemented
313#14556561C2316yes—
314#14556561C2313yes—
315#14556561C2316yescomplemented
316#14556561C2316yescomplemented
317#14556561C2316yescomplemented
318#14556561C2316yescomplemented
319#14556561C2316yescomplemented
320#14556561C2316yescomplemented
321#14556561C2316yescomplemented
322#14556561C2313yescomplemented
323#14556561C2313yescomplemented
324#14556561C2316yescomplemented
325#14556561C2316yescomplemented
326#14556561C2313yescomplemented
327#14556561C2316yescomplemented
328#14556561C2316yescomplemented
329#14556561C2316yescomplemented
330#14556561C2313yescomplemented
331#14556561C2316yescomplemented
332#14556561C2313yescomplemented
333#14556560C2313yes—
334#14556560C2316yescomplemented
335#14556560C2316yescomplemented
336#14556560C2313yescomplemented
337#14556560C2313yescomplemented
338#14556560C2313yescomplemented
339#14556560C2316yescomplemented
340#14556560C2311yescharacteristic, complemented
341#14556560C2313yescomplemented
342#14556559C2313yes—
343#14556559C2316yes—
344#14556559C2316yescomplemented
345#14556559C2316yescomplemented
346#14556559C2316yescomplemented
347#14556559C2316yescomplemented
348#14556559C2316yescomplemented
349#14556559C2316yescomplemented
350#14556559C2316yescomplemented
351#14556559C2313yescomplemented
352#14556559C2316yescomplemented
353#14556559C2313yescomplemented
354#14556559C2313yescomplemented
355#14556559C2316yescomplemented
356#14556559C2316yescomplemented
357#14556559C2313yescomplemented
358#14556559C2316yescomplemented
359#14556559C2313yescomplemented
360#14556559C2316yescomplemented
361#14556559C2316yescomplemented
362C4×D292C2316yescomplemented
363C4×D292C2316yescomplemented
364D4×Dic73C2316yescomplemented
365D4×Dic73C2316yescomplemented
366#14556553C2316yescomplemented
367#14556553C2316yescomplemented
368C4×C22⋊D73C2316yescomplemented
369C4×C22⋊D73C2316yescomplemented
370C4×C22⋊D73C2316yescomplemented
371C4×C22⋊D73C2316yescomplemented
372#14556551C2316yescomplemented
373#14556551C2316yescomplemented
374#14556551C2316yescomplemented
375#14556551C2316yescomplemented
376#14556550C2313yescomplemented
377#14556549C2316yescomplemented
378#14556548C2313yescomplemented
379#14556548C2313yescomplemented
380#14556547C2316yescomplemented
381C4⋊C4×D73C2316yescomplemented
382C4⋊C4×D73C2316yescomplemented
383C4⋊C4×D73C2316yescomplemented
384C2×C22⋊Dic73C2313yescomplemented
385C2×C22⋊Dic73C2316yescomplemented
386C2×C22⋊Dic73C2313yescomplemented
387C2×#11924005C2316yescomplemented
388C2×#11924005C2316yescomplemented
389C2×#11924005C2316yescomplemented
390C2×#11924005C2316yescomplemented
391C22⋊C4×D73C2316yes—
392C22⋊C4×D73C2316yes—
393C22⋊C4×D73C2313yes—
394C22⋊C4×D73C2316yes—
395C22⋊C4×D73C2316yes—
396C22⋊C4×D73C2316yes—
397C22⋊C4×D73C2313yes—
398C22⋊C4×D73C2313yescomplemented
399C22⋊C4×D73C2316yescomplemented
400C22⋊C4×D73C2313yescomplemented
401C22⋊C4×D73C2316yescomplemented
402C22⋊C4×D73C2316yescomplemented
403C22⋊C4×D73C2316yescomplemented
404C22⋊C4×D73C2316yescomplemented
405C22⋊C4×D73C2316yescomplemented
406C22⋊C4×D73C2313yescomplemented
407C22⋊C4×D73C2313yescomplemented
408C22⋊C4×D73C2313yescomplemented
409C22⋊C4×D73C2313yescomplemented
410C22⋊C4×D73C2316yescomplemented
411C22⋊C4×D73C2316yescomplemented
412C42×D73C2311yescharacteristic, complemented
413C42×D73C2313yescomplemented
414C42×D73C2312yescomplemented
415C25×C73C2311yescharacteristic, complemented
416C2×#41×C73C2313yescomplemented
417C22×D4×C73C2313yescomplemented
418C22×D4×C73C2316yescomplemented
419C22×D4×C73C2313yescomplemented
420#127×C73C2311yescharacteristic, complemented
421#127×C73C2313yescomplemented
422#126×C73C2312yescomplemented
423#126×C73C2316yescomplemented
424#124×C73C2313yescomplemented
425#124×C73C2313yescomplemented
426#124×C73C2316yescomplemented
427#123×C73C2313yescomplemented
428#123×C73C2313yescomplemented
429#123×C73C2316yescomplemented
430#123×C73C2316yescomplemented
431C22⋊Q8×C73C2316yescomplemented
432#121×C73C2316yescomplemented
433#121×C73C2316yescomplemented
434#121×C73C2316yescomplemented
435#121×C73C2316yescomplemented
436#121×C73C2316yescomplemented
437#120×C73C2313yes—
438#120×C73C2316yescomplemented
439#120×C73C2316yescomplemented
440#120×C73C2313yescomplemented
441#120×C73C2313yescomplemented
442#120×C73C2313yescomplemented
443#120×C73C2316yescomplemented
444#120×C73C2311yescharacteristic, complemented
445#120×C73C2313yescomplemented
446C4×D4×C73C2316yescomplemented
447C4×D4×C73C2316yescomplemented
448#117×C73C2313yescomplemented
449C2×C22⋊C4×C73C2313yescomplemented
450C2×C22⋊C4×C73C2316yescomplemented
451C2×C22⋊C4×C73C2313yescomplemented
452C23×D73—224no—
453C23×D73—212no—
454C23×D73—212no—
455C23×D73—46no—
456C23×D73—412no—
457C23×D73—46no—
458C23×D73—46no—
459C23×D73—412no—
460C23×D73—46no—
461C23×D73—412no—
462C23×D73—46no—
463C23×D73—46no—
464C23×D73—412no—
465C23×D73—464no—
466C23×D73C2413yes—
467C23×D73C2411yescharacteristic
468C23×D73C2413yes—
469C23×D73C2413yes—
470C23×D73C2413yes—
471C23×D73C2416yes—
472C23×D73C2413yes—
473C23×D73C2413yes—
474C23×D73C2413yes—
475C23×D73C2413yes—
476C23×D73C2413yes—
477C23×D73C2413yes—
478C23×D73C2413yes—
479C23×D73C2413yes—
480C23×D73C2413yescomplemented
481#11924029—46no—
482#11924028—412no—
483#11924028—46no—
484#11924027—46no—
485#11924027—412no—
486C2×Dic146C2413yescomplemented
487C2×Dic146C2416yescomplemented
488Q8×D73—46no—
489C2×D292—46no—
490C2×D292—412no—
491C2×D292—46no—
492C2×D292C2416yes—
493C2×D292C2416yes—
494C2×D292C2413yes—
495C2×D292C2416yes—
496C2×D292C2413yes—
497C2×D292C2413yes—
498C2×D292C2413yes—
499C2×D292C2416yes—
500C2×D292C2413yescomplemented
501C2×D292C2416yescomplemented
502C2×C22⋊D73—46no—
503C2×C22⋊D73—46no—
504C2×C22⋊D73—412no—
505C2×C22⋊D73—46no—
506C2×C22⋊D73—412no—
507C2×C22⋊D73—46no—
508C2×C22⋊D73C2416yes—
509C2×C22⋊D73C2416yes—
510C2×C22⋊D73C2416yes—
511C2×C22⋊D73C2416yes—
512C2×C22⋊D73C2413yes—
513C2×C22⋊D73C2413yes—
514C2×C22⋊D73C2416yes—
515C2×C22⋊D73C2413yes—
516C2×C22⋊D73C2416yes—
517C2×C22⋊D73C2413yes—
518C2×C22⋊D73C2413yes—
519C2×C22⋊D73C2416yes—
520C2×C22⋊D73C2413yes—
521C2×C22⋊D73C2413yes—
522C2×C22⋊D73C2413yes—
523C2×C22⋊D73C2416yes—
524C2×C22⋊D73C2416yescomplemented
525C2×C22⋊D73C2416yescomplemented
526C2×C22⋊D73C2416yescomplemented
527D4×D73—224no—
528D4×D73—224no—
529D4×D73—46no—
530D4×D73—46no—
531D4×D73—46no—
532D4×D73—46no—
533D4×D73—412no—
534D4×D73—412no—
535D4×D73—46no—
536D4×D73—46no—
537D4×D73—46no—
538D4×D73—46no—
539D4×D73—412no—
540D4×D73—46no—
541D4×D73—412no—
542D4×D73—412no—
543D4×D73—412no—
544D4×D73—412no—
545D4×D73—412no—
546D4×D73—412no—
547C22×Dic73C2413yes—
548C22×Dic73C2416yes—
549C22×Dic73C2416yescomplemented
550C22×Dic73C2413yescomplemented
551C2×C4×D73—212no—
552C2×C4×D73—412no—
553C2×C4×D73—46no—
554C2×C4×D73—412no—
555C2×C4×D73C2413yes—
556C2×C4×D73C2416yes—
557C2×C4×D73C2416yes—
558C2×C4×D73C2413yes—
559C2×C4×D73C2413yes—
560C2×C4×D73C2413yes—
561C2×C4×D73C2416yes—
562C2×C4×D73C2416yes—
563C2×C4×D73C2416yescomplemented
564C2×C4×D73C2416yescomplemented
565C2×C4×D73C2416yescomplemented
566C4⋊Dic73C2416yescomplemented
567C4⋊Dic73C2416yescomplemented
568C4⋊Dic73C2416yescomplemented
569#11924007C2416yescomplemented
570#11924007C2416yescomplemented
571#11924007C2416yescomplemented
572#11924007C2416yescomplemented
573#11924007C2416yescomplemented
574#11924007C2416yescomplemented
575C22⋊Dic73C2416yes—
576C22⋊Dic73C2416yes—
577C22⋊Dic73C2413yes—
578C22⋊Dic73C2416yes—
579C22⋊Dic73C2416yes—
580C22⋊Dic73C2416yes—
581C22⋊Dic73C2413yes—
582C22⋊Dic73C2413yescomplemented
583C22⋊Dic73C2413yescomplemented
584C22⋊Dic73C2416yescomplemented
585C22⋊Dic73C2416yescomplemented
586#11924005C2416yes—
587#11924005C2416yes—
588#11924005C2416yes—
589#11924005C2416yes—
590#11924005C2416yes—
591#11924005C2416yes—
592#11924005C2416yes—
593#11924005C2416yes—
594#11924005C2416yes—
595#11924005C2416yes—
596#11924005C2416yes—
597#11924005C2416yes—
598#11924005C2416yescomplemented
599#11924005C2416yescomplemented
600#11924005C2416yescomplemented
601#11924005C2416yescomplemented
602#11924005C2416yescomplemented
603#11924005C2416yescomplemented
604C4×Dic73C2413yescomplemented
605C4×Dic73C2416yescomplemented
606C4×Dic73C2413yescomplemented
607C4×Dic73C2416yescomplemented
608C24×C73—46no—
609C24×C73C2413yes—
610C24×C73C2413yes—
611C24×C73C2413yes—
612C24×C73C2411yescharacteristic
613C24×C73C2411yescharacteristic, complemented
614#41×C73—46no—
615C2×Q8×C73C2413yescomplemented
616C2×D4×C73—46no—
617C2×D4×C73—412no—
618C2×D4×C73—46no—
619C2×D4×C73C2416yes—
620C2×D4×C73C2416yes—
621C2×D4×C73C2413yes—
622C2×D4×C73C2413yes—
623C2×D4×C73C2416yes—
624C2×D4×C73C2413yes—
625C2×D4×C73C2416yes—
626C2×D4×C73C2413yes—
627C2×D4×C73C2413yescomplemented
628C2×D4×C73C2416yescomplemented
629C22×C4×C73C2413yes—
630C22×C4×C73C2416yes—
631C22×C4×C73C2416yescomplemented
632C22×C4×C73C2413yescomplemented
633C4⋊C4×C73C2416yescomplemented
634C4⋊C4×C73C2416yescomplemented
635C4⋊C4×C73C2416yescomplemented
636C22⋊C4×C73C2416yes—
637C22⋊C4×C73C2416yes—
638C22⋊C4×C73C2413yes—
639C22⋊C4×C73C2416yes—
640C22⋊C4×C73C2416yes—
641C22⋊C4×C73C2416yes—
642C22⋊C4×C73C2413yes—
643C22⋊C4×C73C2413yescomplemented
644C22⋊C4×C73C2413yescomplemented
645C22⋊C4×C73C2416yescomplemented
646C22⋊C4×C73C2416yescomplemented
647C42×C73C2411yescharacteristic, complemented
648C42×C73C2413yescomplemented
649C42×C73C2412yescomplemented
650C23×C73—212no—
651C23×C73—26no—
652C23×C73—26no—
653C23×C73—43no—
654C23×C73—46no—
655C23×C73—43no—
656C23×C73—46no—
657C23×C73—43no—
658C23×C73—416no—
659C23×C73C2513yes—
660C23×C73C2511yescharacteristic
661C23×C73C2513yes—
662C23×C73C2513yes—
663C23×C73C2513yes—
664C22×D73—212no—
665C22×D73—212no—
666C22×D73—26no—
667C22×D73—26no—
668C22×D73—212no—
669C22×D73—26no—
670C22×D73—212no—
671C22×D73—26no—
672C22×D73—212no—
673C22×D73—26no—
674C22×D73—26no—
675C22×D73—212no—
676C22×D73—26no—
677C22×D73—26no—
678C22×D73—212no—
679C22×D73—26no—
680C22×D73—26no—
681C22×D73—43no—
682C22×D73—46no—
683C22×D73—46no—
684C22×D73—46no—
685C22×D73—46no—
686C22×D73—43no—
687C22×D73—46no—
688C22×D73—448no—
689C22×D73—46no—
690C22×D73—46no—
691C22×D73—46no—
692C22×D73—46no—
693C22×D73—43no—
694C22×D73—448no—
695C22×D73—416no—
696C22×D73—448no—
697C22×D73—448no—
698C22×D73—416no—
699C22×D73—824no—
700C22×D73—88no—
701C22×D73H(5,𝔽2)112yes—
702C22×D73C2513yes—
703C22×D73C2511yescharacteristic
704C22×D73C2513yes—
705C22×D73C2513yes—
706C22×D73C2513yes—
707C22×D73C2511yescharacteristic
708Q8×C73—43no—
709D4×C73—212no—
710D4×C73—212no—
711D4×C73—43no—
712D4×C73—43no—
713D4×C73—46no—
714D4×C73—43no—
715D4×C73—43no—
716D4×C73—46no—
717D4×C73—46no—
718D4×C73—43no—
719C2×C4×C73—26no—
720C2×C4×C73—46no—
721C2×C4×C73—43no—
722C2×C4×C73—46no—
723C2×C4×C73C2513yes—
724C2×C4×C73C2516yes—
725C2×C4×C73C2516yes—
726C2×C4×C73C2513yes—
727C22⋊D73—212no—
728C22⋊D73—212no—
729C22⋊D73—212no—
730C22⋊D73—212no—
731C22⋊D73—43no—
732C22⋊D73—43no—
733C22⋊D73—43no—
734C22⋊D73—43no—
735C22⋊D73—46no—
736C22⋊D73—46no—
737C22⋊D73—43no—
738C22⋊D73—43no—
739C22⋊D73—43no—
740C22⋊D73—43no—
741C22⋊D73—46no—
742C22⋊D73—46no—
743C22⋊D73—46no—
744C22⋊D73—46no—
745C22⋊D73—46no—
746C2×Dic73—26no—
747C2×Dic73—46no—
748C2×Dic73—43no—
749C2×Dic73—46no—
750C2×Dic73C2513yes—
751C2×Dic73C2516yes—
752C2×Dic73C2516yes—
753C2×Dic73C2513yes—
754D292—212no—
755D292—212no—
756D292—43no—
757D292—43no—
758D292—46no—
759D292—43no—
760D292—43no—
761D292—46no—
762D292—46no—
763D292—43no—
764C4×D73—26no—
765C4×D73—26no—
766C4×D73—26no—
767C4×D73—26no—
768C4×D73—212no—
769C4×D73—212no—
770C4×D73—46no—
771C4×D73—46no—
772C4×D73—46no—
773C4×D73—46no—
774C4×D73—46no—
775Dic146—46no—
776Dic146—43no—
777C22×C73—26no—
778C22×C73—26no—
779C22×C73—23no—
780C22×C73—26no—
781C22×C73—23no—
782C22×C73—23no—
783C22×C73—26no—
784C22×C73—23no—
785C22×C73—412no—
786C22×C73—412no—
787C22×C73—44no—
788C22×C73—86no—
789C22×C73—82no—
790C22×C73C2×H(5,𝔽2)16yes—
791C22×C73C2611yescharacteristic
792C2×D73—26no—
793C2×D73—224no—
794C2×D73—26no—
795C2×D73—23no—
796C2×D73—26no—
797C2×D73—23no—
798C2×D73—26no—
799C2×D73—23no—
800C2×D73—23no—
801C2×D73—412no—
802C2×D73—424no—
803C2×D73—412no—
804C2×D73—412no—
805C2×D73—412no—
806C2×D73—412no—
807C2×D73—412no—
808C2×D73—44no—
809C2×D73—412no—
810C2×D73—412no—
811C2×D73—86no—
812C2×D73—86no—
813C2×D73—86no—
814C2×D73—86no—
815C2×D73C2×H(5,𝔽2)16yes—
816C2×D73C2×H(5,𝔽2)16yes—
817C4×C73—23no—
818C4×C73—26no—
819C4×C73—23no—
820C4×C73—26no—
821Dic73—23no—
822Dic73—26no—
823Dic73—23no—
824Dic73—26no—
825C2×#3532—731nomaximal, Sylow
826C2×C73—26no—
827C2×C73—43no—
828C2×C73—41no—
829C2×C73—43no—
830C2×C73—43no—
831C2×C73C22×H(5,𝔽2)13yes—
832D73—26no—
833D73—43no—
834D73—41no—
835D73—43no—
836D73—43no—
837D73#353214yesdirect product factor
838#3532—731no—
839#3532—733no—
840#3532—733no—
841#3532—736no—
842#3532—733no—
843#3532—736no—
844#3532—733no—
845#3532—733no—
846#3532—733no—
847#3532D7311yescharacteristic, direct product factor
848C2×H(3,𝔽4)—731no—
849C2×#560—733no—
850C2×#551—733no—
851C2×#546—736no—
852C2×D42—733no—
853C2×#538—736no—
854C2×#535—733no—
855C2×#534—733no—
856C22×#120—733no—
857C73C2×#353211yescharacteristic, complemented, Sylow
858C26—731no—
859C22×#41—733no—
860C23×D4—733no—
861C23×D4—736no—
862C23×D4—733no—
863H(3,𝔽4)—736no—
864H(3,𝔽4)—733no—
865H(3,𝔽4)—733no—
866H(3,𝔽4)—733no—
867H(3,𝔽4)C2×D7311yescharacteristic, complemented
868#560—733no—
869#560—736no—
870#560—736no—
871#560—733no—
872#560—736no—
873#560—736no—
874#560—736no—
875#560—733no—
876#560—736no—
877#560C2×D7313yescomplemented
878#551—736no—
879#551—733no—
880#551—736no—
881#551—733no—
882#551—736no—
883#551—733no—
884#551—736no—
885#551—736no—
886#551—736no—
887#551C2×D7313yescomplemented
888#546—736no—
889#546—736no—
890#546—736no—
891#546—736no—
892#546—736no—
893#546—736no—
894#546—736no—
895#546—736no—
896#546—736no—
897#546—736no—
898#546—736no—
899#546—736no—
900#546—736no—
901#546—736no—
902#546—736no—
903#546C2×D7316yescomplemented
904D42—736no—
905D42—736no—
906D42—733no—
907D42—736no—
908D42—736no—
909D42—733no—
910D42—736no—
911D42—733no—
912D42—736no—
913D42C2×D7313yescomplemented
914#538—736no—
915#538—736no—
916#538—736no—
917#538—736no—
918#538—736no—
919#538—736no—
920#538—736no—
921#538—736no—
922#538—736no—
923#538—736no—
924#538—736no—
925#538—736no—
926#538—736no—
927#538—736no—
928#538—736no—
929#538C2×D7316yescomplemented
930#535—733no—
931#535—733no—
932#535—733no—
933#535—733no—
934#535—733no—
935#535—733no—
936#535—736no—
937#535—736no—
938#535—736no—
939#535—736no—
940#535—733no—
941#535C2×D7313yescomplemented
942#534—733no—
943#534—733no—
944#534—736no—
945#534—733no—
946#534—733no—
947#534—736no—
948#534—736no—
949#534—736no—
950#534—733no—
951#534—733no—
952#534—733no—
953#534C2×D7313yescomplemented
954C2×#127—731no—
955C2×#127—733no—
956C2×#126—732no—
957C2×#126—736no—
958C2×#124—733no—
959C2×#124—733no—
960C2×#124—736no—
961C2×#123—733no—
962C2×#123—736no—
963C2×#123—733no—
964C2×#123—736no—
965C2×C22⋊Q8—736no—
966C2×#121—736no—
967C2×#121—736no—
968C2×#121—736no—
969C2×#121—736no—
970C2×#121—736no—
971C2×#120—733no—
972C2×#120—733no—
973C2×#120—736no—
974C2×#120—733no—
975C2×#120—733no—
976C2×#120—736no—
977C2×#120—736no—
978C2×#120—733no—
979C2×#120—733no—
980C2×#120—733no—
981C2×#120—736no—
982C2×#120—736no—
983C2×#120—733no—
984C2×#120—733no—
985C2×#120—733no—
986C2×#120—731no—
987C2×#120—733no—
988C2×#120—736no—
989C2×#120—736no—
990C2×#120—733no—
991C2×#120C2×D7313yescomplemented
992C2×C4×D4—736no—
993C2×C4×D4—736no—
994C2×#117—733no—
995C22×C22⋊C4—733no—
996C22×C22⋊C4—736no—
997C22×C22⋊C4—733no—
998C25—29212no—
999C25—731no—
1000C25—733no—
1001C25—733no—
1002C25—731no—
1003C25—731no—
1004C25—733no—
1005C25—733no—
1006C25—733no—
1007C25C22×D7311yescharacteristic, complemented
1008C2×#41—29212no—
1009C2×#41—733no—
1010C2×#41—736no—
1011C2×#41—733no—
1012C2×#41—733no—
1013C2×#41—736no—
1014C2×#41C22×D7313yescomplemented
1015C22×Q8—733no—
1016C22×D4—29212no—
1017C22×D4—29224no—
1018C22×D4—29212no—
1019C22×D4—733no—
1020C22×D4—733no—
1021C22×D4—736no—
1022C22×D4—736no—
1023C22×D4—733no—
1024C22×D4—733no—
1025C22×D4—733no—
1026C22×D4—736no—
1027C22×D4—733no—
1028C22×D4—733no—
1029C22×D4—736no—
1030C22×D4—733no—
1031C22×D4—733no—
1032C22×D4—733no—
1033C22×D4—733no—
1034C22×D4—733no—
1035C22×D4—736no—
1036C22×D4—736no—
1037C22×D4—736no—
1038C22×D4—736no—
1039C22×D4—736no—
1040C22×D4—733no—
1041C22×D4—736no—
1042C22×D4—736no—
1043C22×D4—736no—
1044C22×D4—736no—
1045C22×D4—733no—
1046C22×D4—736no—
1047C22×D4—733no—
1048C22×D4C22×D7313yescomplemented
1049C22×D4C22×D7316yescomplemented
1050C22×D4C22×D7313yescomplemented
1051C23×C4—736no—
1052C23×C4—736no—
1053C23×C4—733no—
1054C23×C4—733no—
1055#127—733no—
1056#127—736no—
1057#127—733no—
1058#127—733no—
1059#127—736no—
1060#127—733no—
1061#127—731no—
1062#127—733no—
1063#127C22×D7311yescharacteristic, complemented
1064#127C22×D7313yescomplemented
1065#126—736no—
1066#126—736no—
1067#126—736no—
1068#126—736no—
1069#126—736no—
1070#126—736no—
1071#126—736no—
1072#126—736no—
1073#126—732no—
1074#126—736no—
1075#126C22×D7312yescomplemented
1076#126C22×D7316yescomplemented
1077#124—733no—
1078#124—733no—
1079#124—736no—
1080#124—733no—
1081#124—733no—
1082#124—736no—
1083#124—736no—
1084#124—736no—
1085#124—736no—
1086#124—736no—
1087#124—736no—
1088#124—736no—
1089#124—736no—
1090#124—736no—
1091#124—733no—
1092#124—733no—
1093#124—736no—
1094#124C22×D7313yescomplemented
1095#124C22×D7313yescomplemented
1096#124C22×D7316yescomplemented
1097#123—733no—
1098#123—736no—
1099#123—733no—
1100#123—736no—
1101#123—736no—
1102#123—733no—
1103#123—733no—
1104#123—736no—
1105#123—736no—
1106#123—736no—
1107#123—736no—
1108#123—736no—
1109#123—736no—
1110#123—736no—
1111#123—736no—
1112#123—736no—
1113#123—736no—
1114#123—736no—
1115#123—736no—
1116#123—733no—
1117#123—736no—
1118#123—736no—
1119#123—733no—
1120#123—736no—
1121#123C22×D7313yescomplemented
1122#123C22×D7313yescomplemented
1123#123C22×D7316yescomplemented
1124#123C22×D7316yescomplemented
1125C22⋊Q8—736no—
1126C22⋊Q8—736no—
1127C22⋊Q8—736no—
1128C22⋊Q8—736no—
1129C22⋊Q8—736no—
1130C22⋊Q8—736no—
1131C22⋊Q8—736no—
1132C22⋊Q8C22×D7316yescomplemented
1133#121—736no—
1134#121—736no—
1135#121—736no—
1136#121—736no—
1137#121—736no—
1138#121—736no—
1139#121—736no—
1140#121—736no—
1141#121—736no—
1142#121—736no—
1143#121—736no—
1144#121—736no—
1145#121—736no—
1146#121—736no—
1147#121—736no—
1148#121—736no—
1149#121—736no—
1150#121—736no—
1151#121—736no—
1152#121—736no—
1153#121—736no—
1154#121—736no—
1155#121—736no—
1156#121—736no—
1157#121—736no—
1158#121—736no—
1159#121—736no—
1160#121—736no—
1161#121—736no—
1162#121—736no—
1163#121—736no—
1164#121—736no—
1165#121—736no—
1166#121—736no—
1167#121—736no—
1168#121C22×D7316yescomplemented
1169#121C22×D7316yescomplemented
1170#121C22×D7316yescomplemented
1171#121C22×D7316yescomplemented
1172#121C22×D7316yescomplemented
1173#120—736no—
1174#120—736no—
1175#120—733no—
1176#120—733no—
1177#120—733no—
1178#120—733no—
1179#120—736no—
1180#120—731no—
1181#120—733no—
1182#120—736no—
1183#120—736no—
1184#120—736no—
1185#120—736no—
1186#120—736no—
1187#120—736no—
1188#120—736no—
1189#120—733no—
1190#120—736no—
1191#120—733no—
1192#120—733no—
1193#120—736no—
1194#120—736no—
1195#120—733no—
1196#120—733no—
1197#120—733no—
1198#120—736no—
1199#120—736no—
1200#120—736no—
1201#120—736no—
1202#120—736no—
1203#120—736no—
1204#120—736no—
1205#120—736no—
1206#120—736no—
1207#120—736no—
1208#120—733no—
1209#120—736no—
1210#120—733no—
1211#120—736no—
1212#120—736no—
1213#120—733no—
1214#120—733no—
1215#120—736no—
1216#120—736no—
1217#120—733no—
1218#120—736no—
1219#120—733no—
1220#120—736no—
1221#120—736no—
1222#120C22×D7313yes—
1223#120C22×D7316yescomplemented
1224#120C22×D7316yescomplemented
1225#120C22×D7313yescomplemented
1226#120C22×D7313yescomplemented
1227#120C22×D7313yescomplemented
1228#120C22×D7316yescomplemented
1229#120C22×D7311yescharacteristic, complemented
1230#120C22×D7313yescomplemented
1231C4×D4—736no—
1232C4×D4—736no—
1233C4×D4—736no—
1234C4×D4—736no—
1235C4×D4—736no—
1236C4×D4—736no—
1237C4×D4—736no—
1238C4×D4—736no—
1239C4×D4—736no—
1240C4×D4—736no—
1241C4×D4—736no—
1242C4×D4—736no—
1243C4×D4—736no—
1244C4×D4—736no—
1245C4×D4C22×D7316yescomplemented
1246C4×D4C22×D7316yescomplemented
1247#117—733no—
1248#117—736no—
1249#117—736no—
1250#117—733no—
1251#117—733no—
1252#117C22×D7313yescomplemented
1253C2×C4⋊C4—736no—
1254C2×C4⋊C4—736no—
1255C2×C4⋊C4—736no—
1256C2×C22⋊C4—733no—
1257C2×C22⋊C4—736no—
1258C2×C22⋊C4—733no—
1259C2×C22⋊C4—736no—
1260C2×C22⋊C4—736no—
1261C2×C22⋊C4—736no—
1262C2×C22⋊C4—736no—
1263C2×C22⋊C4—736no—
1264C2×C22⋊C4—736no—
1265C2×C22⋊C4—733no—
1266C2×C22⋊C4—736no—
1267C2×C22⋊C4—736no—
1268C2×C22⋊C4—736no—
1269C2×C22⋊C4—733no—
1270C2×C22⋊C4—733no—
1271C2×C22⋊C4—736no—
1272C2×C22⋊C4—733no—
1273C2×C22⋊C4—736no—
1274C2×C22⋊C4—736no—
1275C2×C22⋊C4—736no—
1276C2×C22⋊C4—736no—
1277C2×C22⋊C4—736no—
1278C2×C22⋊C4—733no—
1279C2×C22⋊C4—733no—
1280C2×C22⋊C4—733no—
1281C2×C22⋊C4—733no—
1282C2×C22⋊C4—736no—
1283C2×C22⋊C4—736no—
1284C2×C22⋊C4C22×D7313yescomplemented
1285C2×C22⋊C4C22×D7316yescomplemented
1286C2×C22⋊C4C22×D7313yescomplemented
1287C2×C42—731no—
1288C2×C42—733no—
1289C2×C42—732no—
1290C24—46no—
1291C24—29212no—
1292C24—2926no—
1293C24—29264no—
1294C24—2926no—
1295C24—2926no—
1296C24—29212no—
1297C24—2926no—
1298C24—29212no—
1299C24—2926no—
1300C24—29212no—
1301C24—2926no—
1302C24—733no—
1303C24—733no—
1304C24—733no—
1305C24—733no—
1306C24—733no—
1307C24—733no—
1308C24—733no—
1309C24—733no—
1310C24—733no—
1311C24—736no—
1312C24—733no—
1313C24—733no—
1314C24—731no—
1315C24—733no—
1316C24—733no—
1317C24—14612no—
1318C24—14624no—
1319C24—14612no—
1320C24C23×D7313yes—
1321C24C23×D7313yes—
1322C24C23×D7313yes—
1323C24C23×D7311yescharacteristic
1324C24C23×D7311yescharacteristic, complemented
1325#41—46no—
1326#41—2926no—
1327#41—29212no—
1328#41—29212no—
1329#41—2926no—
1330#41—2926no—
1331C2×Q8—2926no—
1332C2×Q8—736no—
1333C2×Q8—733no—
1334C2×Q8C23×D7313yescomplemented
1335C2×D4—46no—
1336C2×D4—412no—
1337C2×D4—46no—
1338C2×D4—2926no—
1339C2×D4—29212no—
1340C2×D4—2926no—
1341C2×D4—29212no—
1342C2×D4—29212no—
1343C2×D4—29212no—
1344C2×D4—29212no—
1345C2×D4—29212no—
1346C2×D4—29212no—
1347C2×D4—2926no—
1348C2×D4—29212no—
1349C2×D4—2926no—
1350C2×D4—29212no—
1351C2×D4—2926no—
1352C2×D4—2926no—
1353C2×D4—29212no—
1354C2×D4—29212no—
1355C2×D4—29212no—
1356C2×D4—2926no—
1357C2×D4—2926no—
1358C2×D4—2926no—
1359C2×D4—2926no—
1360C2×D4—2926no—
1361C2×D4—2926no—
1362C2×D4—2926no—
1363C2×D4—2926no—
1364C2×D4—2926no—
1365C2×D4—733no—
1366C2×D4—733no—
1367C2×D4—736no—
1368C2×D4—736no—
1369C2×D4—733no—
1370C2×D4—733no—
1371C2×D4—733no—
1372C2×D4—733no—
1373C2×D4—736no—
1374C2×D4—736no—
1375C2×D4—733no—
1376C2×D4—733no—
1377C2×D4—736no—
1378C2×D4—736no—
1379C2×D4—736no—
1380C2×D4—736no—
1381C2×D4—736no—
1382C2×D4—736no—
1383C2×D4—736no—
1384C2×D4—733no—
1385C2×D4—736no—
1386C2×D4—733no—
1387C2×D4—733no—
1388C2×D4—736no—
1389C2×D4—733no—
1390C2×D4—733no—
1391C2×D4—736no—
1392C2×D4—736no—
1393C2×D4—736no—
1394C2×D4—14624no—
1395C2×D4—14624no—
1396C2×D4C23×D7316yes—
1397C2×D4C23×D7316yes—
1398C2×D4C23×D7313yes—
1399C2×D4C23×D7313yes—
1400C2×D4C23×D7316yes—
1401C2×D4C23×D7313yes—
1402C2×D4C23×D7316yes—
1403C2×D4C23×D7313yes—
1404C2×D4C23×D7313yescomplemented
1405C2×D4C23×D7316yescomplemented
1406C22×C4—29212no—
1407C22×C4—2926no—
1408C22×C4—29212no—
1409C22×C4—736no—
1410C22×C4—736no—
1411C22×C4—733no—
1412C22×C4—736no—
1413C22×C4—736no—
1414C22×C4—736no—
1415C22×C4—736no—
1416C22×C4—736no—
1417C22×C4—733no—
1418C22×C4—733no—
1419C22×C4—736no—
1420C22×C4—736no—
1421C22×C4—733no—
1422C22×C4—733no—
1423C22×C4—733no—
1424C22×C4—14612no—
1425C22×C4C23×D7313yes—
1426C22×C4C23×D7316yes—
1427C22×C4C23×D7316yescomplemented
1428C22×C4C23×D7313yescomplemented
1429C4⋊C4—736no—
1430C4⋊C4—736no—
1431C4⋊C4—736no—
1432C4⋊C4—736no—
1433C4⋊C4—736no—
1434C4⋊C4—736no—
1435C4⋊C4—736no—
1436C4⋊C4—736no—
1437C4⋊C4—736no—
1438C4⋊C4C23×D7316yescomplemented
1439C4⋊C4C23×D7316yescomplemented
1440C4⋊C4C23×D7316yescomplemented
1441C22⋊C4—736no—
1442C22⋊C4—736no—
1443C22⋊C4—733no—
1444C22⋊C4—736no—
1445C22⋊C4—736no—
1446C22⋊C4—736no—
1447C22⋊C4—733no—
1448C22⋊C4—733no—
1449C22⋊C4—733no—
1450C22⋊C4—736no—
1451C22⋊C4—736no—
1452C22⋊C4—736no—
1453C22⋊C4—736no—
1454C22⋊C4—736no—
1455C22⋊C4—736no—
1456C22⋊C4—736no—
1457C22⋊C4—736no—
1458C22⋊C4—736no—
1459C22⋊C4—736no—
1460C22⋊C4—736no—
1461C22⋊C4—736no—
1462C22⋊C4—736no—
1463C22⋊C4—736no—
1464C22⋊C4—736no—
1465C22⋊C4—736no—
1466C22⋊C4—736no—
1467C22⋊C4—736no—
1468C22⋊C4—736no—
1469C22⋊C4—736no—
1470C22⋊C4C23×D7316yes—
1471C22⋊C4C23×D7316yes—
1472C22⋊C4C23×D7313yes—
1473C22⋊C4C23×D7316yes—
1474C22⋊C4C23×D7316yes—
1475C22⋊C4C23×D7316yes—
1476C22⋊C4C23×D7313yes—
1477C22⋊C4C23×D7313yescomplemented
1478C22⋊C4C23×D7313yescomplemented
1479C22⋊C4C23×D7316yescomplemented
1480C22⋊C4C23×D7316yescomplemented
1481C42—733no—
1482C42—736no—
1483C42—733no—
1484C42—736no—
1485C42C23×D7311yescharacteristic, complemented
1486C42C23×D7313yescomplemented
1487C42C23×D7312yescomplemented
1488C23—212no—
1489C23—26no—
1490C23—26no—
1491C23—43no—
1492C23—46no—
1493C23—43no—
1494C23—46no—
1495C23—43no—
1496C23—416no—
1497C23—2926no—
1498C23—2926no—
1499C23—2923no—
1500C23—2926no—
1501C23—2926no—
1502C23—2926no—
1503C23—2923no—
1504C23—2926no—
1505C23—2926no—
1506C23—2923no—
1507C23—2926no—
1508C23—2926no—
1509C23—29248no—
1510C23—29248no—
1511C23—29216no—
1512C23—29216no—
1513C23—29248no—
1514C23—29248no—
1515C23—5848no—
1516C23—58424no—
1517C23—731no—
1518C23—7312no—
1519C23—733no—
1520C23—733no—
1521C23—731no—
1522C23—733no—
1523C23—733no—
1524C23—14612no—
1525C23—1466no—
1526C23—1466no—
1527C23—14612no—
1528C23—14612no—
1529C23—1466no—
1530C23—14612no—
1531C23—1466no—
1532C23—1466no—
1533C23—1466no—
1534C23—14612no—
1535C23—1466no—
1536C23—1466no—
1537C23—14612no—
1538C23—1466no—
1539C23—14612no—
1540C23—1466no—
1541C23C24×D7313yes—
1542C23C24×D7311yescharacteristic
1543C23C24×D7313yes—
1544C23C24×D7313yes—
1545C23C24×D7313yes—
1546Q8—43no—
1547Q8—2923no—
1548Q8—2926no—
1549D4—212no—
1550D4—212no—
1551D4—43no—
1552D4—43no—
1553D4—43no—
1554D4—43no—
1555D4—46no—
1556D4—46no—
1557D4—46no—
1558D4—43no—
1559D4—2923no—
1560D4—2923no—
1561D4—2923no—
1562D4—2923no—
1563D4—2926no—
1564D4—2926no—
1565D4—2926no—
1566D4—2923no—
1567D4—2923no—
1568D4—2923no—
1569D4—2923no—
1570D4—2923no—
1571D4—2926no—
1572D4—2926no—
1573D4—2926no—
1574D4—2926no—
1575D4—2926no—
1576D4—2926no—
1577D4—2923no—
1578D4—2923no—
1579D4—2923no—
1580D4—2923no—
1581D4—2926no—
1582D4—14612no—
1583D4—14612no—
1584D4—14612no—
1585D4—14612no—
1586D4—14612no—
1587D4—14612no—
1588C2×C4—26no—
1589C2×C4—46no—
1590C2×C4—43no—
1591C2×C4—46no—
1592C2×C4—2926no—
1593C2×C4—2926no—
1594C2×C4—2926no—
1595C2×C4—2926no—
1596C2×C4—2926no—
1597C2×C4—2923no—
1598C2×C4—2926no—
1599C2×C4—2926no—
1600C2×C4—733no—
1601C2×C4—736no—
1602C2×C4—736no—
1603C2×C4—733no—
1604C2×C4—1466no—
1605C2×C4—14612no—
1606C2×C4—14612no—
1607C2×C4—1466no—
1608C2×C4—1466no—
1609C2×C4—1466no—
1610C2×C4—1466no—
1611C2×C4C24×D7313yes—
1612C2×C4C24×D7316yes—
1613C2×C4C24×D7316yes—
1614C2×C4C24×D7313yes—
1615C22—26no—
1616C22—26no—
1617C22—23no—
1618C22—26no—
1619C22—23no—
1620C22—23no—
1621C22—26no—
1622C22—23no—
1623C22—412no—
1624C22—412no—
1625C22—44no—
1626C22—86no—
1627C22—82no—
1628C22—29212no—
1629C22—29224no—
1630C22—29212no—
1631C22—29212no—
1632C22—2924no—
1633C22—29212no—
1634C22—29212no—
1635C22—29212no—
1636C22—29212no—
1637C22—29212no—
1638C22—5846no—
1639C22—5846no—
1640C22—5846no—
1641C22—5846no—
1642C22—736no—
1643C22—736no—
1644C22—14624no—
1645C22—1466no—
1646C22—1463no—
1647C22—1463no—
1648C22—1466no—
1649C22—1463no—
1650C22—1463no—
1651C22—1466no—
1652C22—1466no—
1653C22H(5,𝔽2)×D7316yes—
1654C22C25×D7311yescharacteristic
1655C4—23no—
1656C4—23no—
1657C4—26no—
1658C4—26no—
1659C4—1463no—
1660C4—1466no—
1661C4—1466no—
1662C4—1463no—
1663C2—26no—
1664C2—43no—
1665C2—41no—
1666C2—43no—
1667C2—43no—
1668C2—2921no—
1669C2—2923no—
1670C2—2923no—
1671C2—2923no—
1672C2—734no—
1673C2—1466no—
1674C2C2×H(5,𝔽2)×D7313yes—
subgroupG/H
center, FrattiniC22C25×D73
commutator, socle, cosocleC22×C73C26
FittingC73×#3532C2
hypercenter#3532D73
hypocenterC73C2×#3532
LCSG ▷ C22×C73 ▷ C73
UCSC1 ◁ C22 ◁ #3532

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
1. #22624088C2semidirect
2. #22624087C2semidirect
3. #22624086C2semidirect
4. #22624085C2semidirect
5. #22624084C2semidirect
6. #22624083C2semidirect
7. #22624082C2semidirect
8. #22624081C2semidirect
9. #22624080C2semidirect
10. H(3,𝔽4)×D73C2semidirect
11. #560×D73C2semidirect
12. #551×D73C2semidirect
13. #546×D73C2semidirect
14. D42×D73C2semidirect
15. #538×D73C2semidirect
16. #535×D73C2semidirect
17. #534×D73C2semidirect
18. C2×#120×D73C2semidirect
19. C73×#3532C2semidirect
20. C25×D73C22semidirect
21. C2×#41×D73C22semidirect
22. C22×D4×D73C22semidirect
23. C22×D4×D73C22semidirect
24. C22×D4×D73C22semidirect
25. #17989330C22semidirect
26. #17989330C22semidirect
27. #17989329C22semidirect
28. #17989329C22semidirect
29. #17989328C22semidirect
30. #17989327C22semidirect
31. #17989327C22semidirect
32. #17989326C22semidirect
33. #17989326C22semidirect
34. #17989325C22semidirect
35. #17989325C22semidirect
36. #17989325C22semidirect
37. #17989324C22semidirect
38. #17989268C22semidirect
39. #17989267C22semidirect
40. #17989266C22semidirect
41. #17989265C22semidirect
42. #17989264C22semidirect
43. #17989263C22semidirect
44. #17989262C22semidirect
45. #17989261C22semidirect
46. #17989260C22semidirect
47. #17989234C22semidirect
48. #17989233C22semidirect
49. #17989232C22semidirect
50. #17989231C22semidirect
51. #17989230C22semidirect
52. #17989229C22semidirect
53. #17989229C22semidirect
54. #17989228C22semidirect
55. #17989227C22semidirect
56. #17989227C22semidirect
57. #17989226C22semidirect
58. #17989226C22semidirect
59. #17989225C22semidirect
60. #17989224C22semidirect
61. #17989224C22semidirect
62. D4×D292C22semidirect
63. #17989222C22semidirect
64. #17989221C22semidirect
65. #17989221C22semidirect
66. D4×C22⋊D73C22semidirect
67. D4×C22⋊D73C22semidirect
68. #17989219C22semidirect
69. #17989219C22semidirect
70. #17989219C22semidirect
71. #17989177C22semidirect
72. #17989176C22semidirect
73. #17989176C22semidirect
74. #17989175C22semidirect
75. #17989174C22semidirect
76. #17989173C22semidirect
77. #17989173C22semidirect
78. #17989172C22semidirect
79. #17989172C22semidirect
80. #17989171C22semidirect
81. #17989171C22semidirect
82. #17989170C22semidirect
83. #17989170C22semidirect
84. #17989169C22semidirect
85. #17989169C22semidirect
86. #17989156C22semidirect
87. #17989155C22semidirect
88. #17989155C22semidirect
89. #17989154C22semidirect
90. #17989153C22semidirect
91. #17989153C22semidirect
92. #17989152C22semidirect
93. #17989152C22semidirect
94. #17989151C22semidirect
95. #17989150C22semidirect
96. #17989150C22semidirect
97. #17989149C22semidirect
98. #17989148C22semidirect
99. #17989148C22semidirect
100. #17989148C22semidirect
101. #17989147C22semidirect
102. #17989147C22semidirect
103. #17989147C22semidirect
104. #17989146C22semidirect
105. #17989146C22semidirect
106. #17989145C22semidirect
107. #17989145C22semidirect
108. #127×D73C22semidirect
109. #127×D73C22semidirect
110. #126×D73C22semidirect
111. #126×D73C22semidirect
112. #124×D73C22semidirect
113. #124×D73C22semidirect
114. #124×D73C22semidirect
115. #123×D73C22semidirect
116. #123×D73C22semidirect
117. #123×D73C22semidirect
118. #123×D73C22semidirect
119. C22⋊Q8×D73C22semidirect
120. #121×D73C22semidirect
121. #121×D73C22semidirect
122. #121×D73C22semidirect
123. #121×D73C22semidirect
124. #121×D73C22semidirect
125. C2×#14556561C22semidirect
126. C2×#14556561C22semidirect
127. C2×#14556560C22semidirect
128. C2×#14556559C22semidirect
129. C2×#14556559C22semidirect
131. #120×D73C22semidirect
132. #120×D73C22semidirect
133. #120×D73C22semidirect
134. #120×D73C22semidirect
135. #120×D73C22semidirect
136. #120×D73C22semidirect
137. #120×D73C22semidirect
138. #120×D73C22semidirect
139. #120×D73C22semidirect
140. #120×D73C22semidirect
141. #120×D73C22semidirect
142. #120×D73C22semidirect
143. #120×D73C22semidirect
144. #120×D73C22semidirect
145. C4×D4×D73C22semidirect
146. C4×D4×D73C22semidirect
147. #117×D73C22semidirect
148. C2×C22⋊C4×D73C22semidirect
149. C2×C22⋊C4×D73C22semidirect
150. C2×C22⋊C4×D73C22semidirect
151. H(3,𝔽4)×C73C22semidirect
152. #560×C73C22semidirect
153. #551×C73C22semidirect
154. #546×C73C22semidirect
155. D42×C73C22semidirect
156. #538×C73C22semidirect
157. #535×C73C22semidirect
158. #534×C73C22semidirect
159. C2×#120×C73C22semidirect
165. C24×D73C23semidirect
166. C24×D73C23semidirect
167. C24×D73C23semidirect
168. C24×D73C23semidirect
169. C2×#11924029C23semidirect
170. C2×#11924028C23semidirect
171. C2×#11924028C23semidirect
172. C2×#11924027C23semidirect
173. C2×#11924027C23semidirect
175. C2×Q8×D73C23semidirect
176. C22×D292C23semidirect
177. C22×D292C23semidirect
178. C22×D292C23semidirect
179. C22×C22⋊D73C23semidirect
180. C22×C22⋊D73C23semidirect
181. C22×C22⋊D73C23semidirect
182. C22×C22⋊D73C23semidirect
183. C22×C22⋊D73C23semidirect
184. C22×C22⋊D73C23semidirect
196. C2×D4×D73C23semidirect
197. C2×D4×D73C23semidirect
198. C2×D4×D73C23semidirect
199. C2×D4×D73C23semidirect
200. C2×D4×D73C23semidirect
201. C2×D4×D73C23semidirect
202. C2×D4×D73C23semidirect
203. C2×D4×D73C23semidirect
204. C2×D4×D73C23semidirect
205. C2×D4×D73C23semidirect
206. C2×D4×D73C23semidirect
207. C2×D4×D73C23semidirect
210. C22×C4×D73C23semidirect
211. C22×C4×D73C23semidirect
212. #14556588C23semidirect
213. #14556588C23semidirect
214. #14556587C23semidirect
215. #14556587C23semidirect
216. #14556587C23semidirect
217. #14556587C23semidirect
218. #14556587C23semidirect
219. #14556587C23semidirect
220. #14556586C23semidirect
221. #14556586C23semidirect
222. #14556586C23semidirect
223. #14556586C23semidirect
224. #14556585C23semidirect
225. #14556585C23semidirect
226. #14556584C23semidirect
227. #14556584C23semidirect
228. #14556584C23semidirect
229. #14556584C23semidirect
230. #14556580C23semidirect
231. #14556580C23semidirect
232. #14556580C23semidirect
233. #14556579C23semidirect
234. #14556579C23semidirect
235. #14556579C23semidirect
236. #14556578C23semidirect
237. #14556578C23semidirect
238. #14556578C23semidirect
239. #14556577C23semidirect
240. #14556577C23semidirect
241. #14556577C23semidirect
242. #14556577C23semidirect
243. #14556577C23semidirect
244. #14556577C23semidirect
245. #14556577C23semidirect
246. #14556577C23semidirect
247. #14556576C23semidirect
248. #14556576C23semidirect
249. #14556576C23semidirect
250. #14556576C23semidirect
251. #14556576C23semidirect
252. #14556576C23semidirect
253. #14556575C23semidirect
254. #14556575C23semidirect
255. #14556575C23semidirect
256. #14556575C23semidirect
257. #14556574C23semidirect
258. #14556574C23semidirect
259. #14556574C23semidirect
260. #14556574C23semidirect
261. #14556573C23semidirect
262. #14556573C23semidirect
263. #14556573C23semidirect
264. #14556573C23semidirect
265. #14556573C23semidirect
266. #14556573C23semidirect
267. #14556572C23semidirect
268. #14556572C23semidirect
269. #14556572C23semidirect
270. #14556572C23semidirect
271. #14556571C23semidirect
272. #14556570C23semidirect
273. #14556569C23semidirect
274. #14556569C23semidirect
275. #14556568C23semidirect
276. #14556568C23semidirect
277. #14556567C23semidirect
278. #14556566C23semidirect
279. #14556566C23semidirect
280. #14556566C23semidirect
281. #14556566C23semidirect
282. #14556566C23semidirect
283. #14556565C23semidirect
284. #14556565C23semidirect
285. #14556565C23semidirect
286. #14556565C23semidirect
287. #14556565C23semidirect
288. #14556564C23semidirect
289. #14556564C23semidirect
290. #14556564C23semidirect
291. #14556564C23semidirect
292. #14556564C23semidirect
293. #14556564C23semidirect
294. #14556564C23semidirect
295. #14556564C23semidirect
296. #14556564C23semidirect
297. #14556564C23semidirect
298. #14556563C23semidirect
299. #14556563C23semidirect
300. #14556563C23semidirect
301. #14556563C23semidirect
302. #14556563C23semidirect
303. #14556563C23semidirect
304. #14556563C23semidirect
305. #14556563C23semidirect
306. #14556563C23semidirect
307. #14556563C23semidirect
308. #14556562C23semidirect
309. #14556562C23semidirect
310. #14556562C23semidirect
311. #14556562C23semidirect
312. #14556562C23semidirect
315. #14556561C23semidirect
316. #14556561C23semidirect
317. #14556561C23semidirect
318. #14556561C23semidirect
319. #14556561C23semidirect
320. #14556561C23semidirect
321. #14556561C23semidirect
322. #14556561C23semidirect
323. #14556561C23semidirect
324. #14556561C23semidirect
325. #14556561C23semidirect
326. #14556561C23semidirect
327. #14556561C23semidirect
328. #14556561C23semidirect
329. #14556561C23semidirect
330. #14556561C23semidirect
331. #14556561C23semidirect
332. #14556561C23semidirect
334. #14556560C23semidirect
335. #14556560C23semidirect
336. #14556560C23semidirect
337. #14556560C23semidirect
338. #14556560C23semidirect
339. #14556560C23semidirect
340. #14556560C23semidirect
341. #14556560C23semidirect
344. #14556559C23semidirect
345. #14556559C23semidirect
346. #14556559C23semidirect
347. #14556559C23semidirect
348. #14556559C23semidirect
349. #14556559C23semidirect
350. #14556559C23semidirect
351. #14556559C23semidirect
352. #14556559C23semidirect
353. #14556559C23semidirect
354. #14556559C23semidirect
355. #14556559C23semidirect
356. #14556559C23semidirect
357. #14556559C23semidirect
358. #14556559C23semidirect
359. #14556559C23semidirect
360. #14556559C23semidirect
361. #14556559C23semidirect
362. C4×D292C23semidirect
363. C4×D292C23semidirect
364. D4×Dic73C23semidirect
365. D4×Dic73C23semidirect
366. #14556553C23semidirect
367. #14556553C23semidirect
368. C4×C22⋊D73C23semidirect
369. C4×C22⋊D73C23semidirect
370. C4×C22⋊D73C23semidirect
371. C4×C22⋊D73C23semidirect
372. #14556551C23semidirect
373. #14556551C23semidirect
374. #14556551C23semidirect
375. #14556551C23semidirect
376. #14556550C23semidirect
377. #14556549C23semidirect
378. #14556548C23semidirect
379. #14556548C23semidirect
380. #14556547C23semidirect
381. C4⋊C4×D73C23semidirect
382. C4⋊C4×D73C23semidirect
383. C4⋊C4×D73C23semidirect
384. C2×C22⋊Dic73C23semidirect
385. C2×C22⋊Dic73C23semidirect
386. C2×C22⋊Dic73C23semidirect
387. C2×#11924005C23semidirect
388. C2×#11924005C23semidirect
389. C2×#11924005C23semidirect
390. C2×#11924005C23semidirect
398. C22⋊C4×D73C23semidirect
399. C22⋊C4×D73C23semidirect
400. C22⋊C4×D73C23semidirect
401. C22⋊C4×D73C23semidirect
402. C22⋊C4×D73C23semidirect
403. C22⋊C4×D73C23semidirect
404. C22⋊C4×D73C23semidirect
405. C22⋊C4×D73C23semidirect
406. C22⋊C4×D73C23semidirect
407. C22⋊C4×D73C23semidirect
408. C22⋊C4×D73C23semidirect
409. C22⋊C4×D73C23semidirect
410. C22⋊C4×D73C23semidirect
411. C22⋊C4×D73C23semidirect
412. C42×D73C23semidirect
413. C42×D73C23semidirect
414. C42×D73C23semidirect
415. C25×C73C23semidirect
416. C2×#41×C73C23semidirect
417. C22×D4×C73C23semidirect
418. C22×D4×C73C23semidirect
419. C22×D4×C73C23semidirect
420. #127×C73C23semidirect
421. #127×C73C23semidirect
422. #126×C73C23semidirect
423. #126×C73C23semidirect
424. #124×C73C23semidirect
425. #124×C73C23semidirect
426. #124×C73C23semidirect
427. #123×C73C23semidirect
428. #123×C73C23semidirect
429. #123×C73C23semidirect
430. #123×C73C23semidirect
431. C22⋊Q8×C73C23semidirect
432. #121×C73C23semidirect
433. #121×C73C23semidirect
434. #121×C73C23semidirect
435. #121×C73C23semidirect
436. #121×C73C23semidirect
438. #120×C73C23semidirect
439. #120×C73C23semidirect
440. #120×C73C23semidirect
441. #120×C73C23semidirect
442. #120×C73C23semidirect
443. #120×C73C23semidirect
444. #120×C73C23semidirect
445. #120×C73C23semidirect
446. C4×D4×C73C23semidirect
447. C4×D4×C73C23semidirect
448. #117×C73C23semidirect
449. C2×C22⋊C4×C73C23semidirect
450. C2×C22⋊C4×C73C23semidirect
451. C2×C22⋊C4×C73C23semidirect
480. C23×D73C24semidirect
486. C2×Dic146C24semidirect
487. C2×Dic146C24semidirect
500. C2×D292C24semidirect
501. C2×D292C24semidirect
524. C2×C22⋊D73C24semidirect
525. C2×C22⋊D73C24semidirect
526. C2×C22⋊D73C24semidirect
549. C22×Dic73C24semidirect
550. C22×Dic73C24semidirect
563. C2×C4×D73C24semidirect
564. C2×C4×D73C24semidirect
565. C2×C4×D73C24semidirect
566. C4⋊Dic73C24semidirect
567. C4⋊Dic73C24semidirect
568. C4⋊Dic73C24semidirect
569. #11924007C24semidirect
570. #11924007C24semidirect
571. #11924007C24semidirect
572. #11924007C24semidirect
573. #11924007C24semidirect
574. #11924007C24semidirect
582. C22⋊Dic73C24semidirect
583. C22⋊Dic73C24semidirect
584. C22⋊Dic73C24semidirect
585. C22⋊Dic73C24semidirect
598. #11924005C24semidirect
599. #11924005C24semidirect
600. #11924005C24semidirect
601. #11924005C24semidirect
602. #11924005C24semidirect
603. #11924005C24semidirect
604. C4×Dic73C24semidirect
605. C4×Dic73C24semidirect
606. C4×Dic73C24semidirect
607. C4×Dic73C24semidirect
613. C24×C73C24semidirect
615. C2×Q8×C73C24semidirect
627. C2×D4×C73C24semidirect
628. C2×D4×C73C24semidirect
631. C22×C4×C73C24semidirect
632. C22×C4×C73C24semidirect
633. C4⋊C4×C73C24semidirect
634. C4⋊C4×C73C24semidirect
635. C4⋊C4×C73C24semidirect
643. C22⋊C4×C73C24semidirect
644. C22⋊C4×C73C24semidirect
645. C22⋊C4×C73C24semidirect
646. C22⋊C4×C73C24semidirect
647. C42×C73C24semidirect
648. C42×C73C24semidirect
649. C42×C73C24semidirect
837. D73#3532direct (N × H)
847. #3532D73direct (N × H)
857. C73C2×#3532semidirect
867. H(3,𝔽4)C2×D73semidirect
877. #560C2×D73semidirect
887. #551C2×D73semidirect
903. #546C2×D73semidirect
913. D42C2×D73semidirect
929. #538C2×D73semidirect
941. #535C2×D73semidirect
953. #534C2×D73semidirect
991. C2×#120C2×D73semidirect
1007. C25C22×D73semidirect
1014. C2×#41C22×D73semidirect
1048. C22×D4C22×D73semidirect
1049. C22×D4C22×D73semidirect
1050. C22×D4C22×D73semidirect
1063. #127C22×D73semidirect
1064. #127C22×D73semidirect
1075. #126C22×D73semidirect
1076. #126C22×D73semidirect
1094. #124C22×D73semidirect
1095. #124C22×D73semidirect
1096. #124C22×D73semidirect
1121. #123C22×D73semidirect
1122. #123C22×D73semidirect
1123. #123C22×D73semidirect
1124. #123C22×D73semidirect
1132. C22⋊Q8C22×D73semidirect
1168. #121C22×D73semidirect
1169. #121C22×D73semidirect
1170. #121C22×D73semidirect
1171. #121C22×D73semidirect
1172. #121C22×D73semidirect
1223. #120C22×D73semidirect
1224. #120C22×D73semidirect
1225. #120C22×D73semidirect
1226. #120C22×D73semidirect
1227. #120C22×D73semidirect
1228. #120C22×D73semidirect
1229. #120C22×D73semidirect
1230. #120C22×D73semidirect
1245. C4×D4C22×D73semidirect
1246. C4×D4C22×D73semidirect
1252. #117C22×D73semidirect
1284. C2×C22⋊C4C22×D73semidirect
1285. C2×C22⋊C4C22×D73semidirect
1286. C2×C22⋊C4C22×D73semidirect
1324. C24C23×D73semidirect
1334. C2×Q8C23×D73semidirect
1404. C2×D4C23×D73semidirect
1405. C2×D4C23×D73semidirect
1427. C22×C4C23×D73semidirect
1428. C22×C4C23×D73semidirect
1438. C4⋊C4C23×D73semidirect
1439. C4⋊C4C23×D73semidirect
1440. C4⋊C4C23×D73semidirect
1477. C22⋊C4C23×D73semidirect
1478. C22⋊C4C23×D73semidirect
1479. C22⋊C4C23×D73semidirect
1480. C22⋊C4C23×D73semidirect
1485. C42C23×D73semidirect
1486. C42C23×D73semidirect
1487. C42C23×D73semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
#226240882
#226240872
#226240862
#226240852
#226240842
#226240832
#226240822
#226240812
#226240802
H(3,𝔽4)×D732
#560×D732
#551×D732
#546×D732
D42×D732
#538×D732
#535×D732
#534×D732
C2×#120×D732
C73×#35322
C2×#353273