Finite Group Databasebeta

← #33993297

Subgroups — #33993297

Order 18688.

7346 conjugacy classes of subgroups.

The subgroup lattice has 1530 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#22624247C214yesmaximal, complemented
2#22624224C214yesmaximal, complemented
3#22624206C212yesmaximal, complemented
4#22624191C212yesmaximal, complemented
5#22624180C211yesmaximal, characteristic, complemented
6#22624170C211yesmaximal, characteristic, complemented
7#22624158C212yesmaximal, complemented
8#22624140C214yesmaximal, complemented
9#22624121C214yesmaximal, complemented
10#22624102C214yesmaximal, complemented
11#22624086C214yesmaximal, complemented
12#22624069C214yesmaximal, complemented
13#22623533C214yesmaximal, complemented
14#22623489C214yesmaximal, complemented
15D4×#11924028C214yesmaximal, complemented
16#22623349C214yesmaximal, complemented
17#22623338C214yesmaximal, complemented
18#22623321C212yesmaximal, complemented
19#22623260C212yesmaximal, complemented
20C2×#17989098C212yesmaximal, complemented
21C2×#525×C73C211yesmaximal, characteristic, complemented
22C22×#11924028C2212yescomplemented
23C22×#11924028C2212yescomplemented
24#17989340C2214yescomplemented
25#17989338C2218yescomplemented
26#17989334C2218yescomplemented
27#17989333C2218yescomplemented
28#17989332C2218yescomplemented
29#17989330C2214yescomplemented
30#17989327C2214yescomplemented
31#17989326C2218yescomplemented
32#17989326C2214yescomplemented
33#17989325C2218yescomplemented
34#17989321C2214yescomplemented
35#17989307C2214yescomplemented
36#17989302C2214yescomplemented
37#17989294C2214yescomplemented
38#17989291C2218yescomplemented
39#17989283C2214yescomplemented
40#17989283C2214yescomplemented
41#17989282C2218yescomplemented
42#17989280C2218yescomplemented
43#17989277C2214yescomplemented
44#17989277C2214yescomplemented
45#17989272C2218yescomplemented
46#17989268C2214yescomplemented
47#17989265C2214yescomplemented
48#17989264C2218yescomplemented
49#17989263C2218yescomplemented
50#17989263C2218yescomplemented
51#17989258C2214yescomplemented
52D4×Dic146C2214yescomplemented
53#17989246C2214yescomplemented
54#17989246C2214yescomplemented
55#17989242C2214yescomplemented
56#17989241C2214yescomplemented
57#17989238C2218yescomplemented
58#17989233C2214yescomplemented
59#17989233C2214yescomplemented
60#17989231C2218yescomplemented
61#17989227C2218yescomplemented
62#17989227C2218yescomplemented
63#17989226C2218yescomplemented
64#17989224C2218yescomplemented
65D4×D292C2214yescomplemented
66D4×C22⋊D73C2218yescomplemented
67#17989219C2214yescomplemented
68#17989216C2214yescomplemented
69#17989212C2214yescomplemented
70#17989208C2214yescomplemented
71#17989208C2214yescomplemented
72#17989207C2218yescomplemented
73#17989205C2218yescomplemented
74#17989199C2212yescomplemented
75#17989199C2212yescomplemented
76#17989192C2212yescomplemented
77#17989192C2212yescomplemented
78#17989189C2218yescomplemented
79#17989187C2218yescomplemented
80#17989186C2214yescomplemented
81#17989184C2218yescomplemented
82#17989183C2218yescomplemented
83#17989182C2214yescomplemented
84#17989180C2218yescomplemented
85#17989177C2214yescomplemented
86#17989175C2218yescomplemented
87#17989174C2214yescomplemented
88#17989173C2218yescomplemented
89#17989172C2218yescomplemented
90#17989172C2218yescomplemented
91#17989169C2218yescomplemented
92#17989165C2214yescomplemented
93#17989165C2214yescomplemented
94#17989164C2214yescomplemented
95#17989161C2214yescomplemented
96#17989158C2212yescomplemented
97#17989158C2212yescomplemented
98#17989154C2214yescomplemented
99#17989152C2218yescomplemented
100#17989151C2212yescomplemented
101#17989151C2212yescomplemented
102#17989147C2218yescomplemented
103#17989146C2214yescomplemented
104#17989146C2214yescomplemented
105#17989145C2214yescomplemented
106#17989144C2212yescomplemented
107#17989137C2212yescomplemented
108#17989134C2218yescomplemented
109#17989133C2214yescomplemented
110#17989133C2214yescomplemented
111#17989119C2218yescomplemented
112#17989117C2218yescomplemented
113#17989117C2218yescomplemented
114#17989115C2218yescomplemented
115#17989115C2218yescomplemented
116#17989098C2214yescomplemented
117#17989098C2214yescomplemented
118#17989098C2214yescomplemented
119#17989098C2214yescomplemented
120#17989098C2214yescomplemented
121#17989098C2214yescomplemented
122#17989098C2214yescomplemented
123#17989098C2214yescomplemented
124#17989098C2214yescomplemented
125#17989096C2218yescomplemented
126#17989096C2218yescomplemented
127#17989094C2214yescomplemented
128#17989094C2214yescomplemented
129C2×#14556574C2214yescomplemented
130C2×#14556570C2212yescomplemented
131C2×#14556570C2212yescomplemented
132C2×#14556565C2212yescomplemented
133C2×#14556565C2212yescomplemented
134C2×#14556560C2214yescomplemented
135C4×#11924028C2214yescomplemented
136C4×#11924027C2218yescomplemented
137C2×C4×C22⋊D73C2214yescomplemented
138C2×C4×C22⋊D73C2214yescomplemented
139C4×D4×D73C2218yescomplemented
140C2×#14556550C2212yescomplemented
141C2×#14556550C2212yescomplemented
142C22×#41×C73C2211yescharacteristic, complemented
143C24×C4×C73C2211yescharacteristic, complemented
144#525×C73C2211yescharacteristic
145#525×C73C2212yescomplemented
146#525×C73C2212yescomplemented
147#525×C73C2212yescomplemented
148#525×C73C2212yescomplemented
149#525×C73C2211yescharacteristic, complemented
150#525×C73C2211yescharacteristic, complemented
151#525×C73C2211yescharacteristic, complemented
152#525×C73C2214yescomplemented
153C2×#123×C73C2212yescomplemented
154C2×C22⋊Q8×C73C2212yescomplemented
155C2×#121×C73C2212yescomplemented
156C2×#120×C73C2212yescomplemented
157C2×C4×D4×C73C2214yescomplemented
158C2×#117×C73C2211yescharacteristic, complemented
159C2×#11924028—48no—
160C2×#11924028—48no—
161C2×#11924028C2314yes—
162C2×#11924028C2314yes—
163C2×#11924028C2314yes—
164C2×#11924028C2314yes—
165C2×#11924028C2314yes—
166C2×#11924028C2314yescomplemented
167C2×#11924028C2314yescomplemented
168C2×#11924027C2318yes—
169C22×Dic146C2312yes—
170C22×Dic146C2312yescomplemented
171C22×D292C2312yes—
172C22×D292C2312yescomplemented
173C22×C22⋊D73C2314yes—
174C22×C22⋊D73C2314yes—
175C22×C22⋊D73C2314yes—
176C22×C22⋊D73C2314yes—
177C2×D4×D73C2318yes—
178C22×C4×D73C2314yes—
179C22×C4×D73C2314yescomplemented
180#14556591C2312yescomplemented
181#14556591C2314yescomplemented
182#14556590C2318yescomplemented
183#14556589C2314yescomplemented
184#14556589C2314yescomplemented
185#14556588C2312yescomplemented
186#14556587C2314yes—
187#14556587C2314yes—
188#14556587C2318yes—
189#14556586C2318yescomplemented
190#14556586C2318yescomplemented
191#14556586C2318yescomplemented
192#14556586C2318yescomplemented
193#14556584C2318yes—
194#14556584C2318yes—
195#14556584C2318yes—
196#14556584C2318yes—
197#14556584C2318yescomplemented
198#14556584C2318yescomplemented
199#14556583C2312yescomplemented
200#14556583C2312yescomplemented
201#14556582C2318yescomplemented
202#14556581C2318yescomplemented
203#14556581C2318yescomplemented
204#14556581C2318yescomplemented
205#14556581C2318yescomplemented
206#14556580C2314yescomplemented
207#14556580C2314yescomplemented
208#14556579C2314yescomplemented
209#14556578C2314yes—
210#14556578C2314yes—
211#14556578C2318yes—
212#14556577C2318yes—
213#14556577C2318yes—
214#14556577C2318yes—
215#14556577C2318yes—
216#14556577C2318yescomplemented
217#14556577C2318yescomplemented
218#14556576C2318yescomplemented
219#14556576C2318yescomplemented
220#14556576C2318yescomplemented
221#14556576C2318yescomplemented
222#14556575C2318yes—
223#14556575C2318yescomplemented
224#14556574C2318yes—
225#14556574C2318yes—
226#14556574C2318yes—
227#14556574C2318yes—
228#14556574C2318yes—
229#14556573C2318yes—
230#14556573C2318yes—
231#14556573C2318yes—
232#14556573C2318yes—
233#14556573C2318yescomplemented
234#14556573C2318yescomplemented
235#14556572C2314yes—
236#14556572C2314yes—
237#14556572C2318yes—
238#14556572C2318yes—
239#14556572C2314yescomplemented
240#14556572C2314yescomplemented
241#14556571C2318yescomplemented
242#14556570C2318yes—
243#14556570C2314yes—
244#14556570C2314yes—
245#14556570C2314yes—
246#14556570C2314yes—
247#14556570C2314yes—
248#14556570C2314yes—
249#14556570C2314yes—
250#14556570C2314yes—
251#14556570C2314yescomplemented
252#14556570C2314yescomplemented
253#14556569C2318yescomplemented
254#14556569C2318yescomplemented
255#14556569C2318yescomplemented
256#14556569C2318yescomplemented
257#14556568C2318yes—
258#14556568C2318yes—
259#14556568C2318yescomplemented
260#14556568C2318yescomplemented
261#14556567C2318yescomplemented
262#14556567C2318yescomplemented
263#14556566C2318yescomplemented
264#14556565C2318yes—
265#14556565C2314yes—
266#14556565C2314yes—
267#14556565C2314yes—
268#14556565C2314yes—
269#14556565C2314yes—
270#14556565C2314yes—
271#14556565C2314yes—
272#14556565C2314yes—
273#14556565C2314yescomplemented
274#14556565C2314yescomplemented
275#14556564C2318yes—
276#14556564C2318yes—
277#14556564C2318yes—
278#14556564C2318yes—
279#14556564C2318yescomplemented
280#14556564C2318yescomplemented
281#14556563C2318yes—
282#14556563C2318yes—
283#14556563C2318yes—
284#14556563C2318yes—
285#14556563C2318yes—
286#14556563C2318yes—
287#14556563C2318yescomplemented
288#14556563C2318yescomplemented
289#14556562C2318yes—
290#14556562C2318yes—
291#14556562C2318yes—
292#14556562C2318yes—
293#14556561C2318yes—
294#14556561C2318yescomplemented
295#14556560C2318yes—
296#14556560C2318yes—
297#14556560C2318yes—
298#14556560C2318yes—
299#14556560C2318yes—
300#14556559C2314yes—
301#14556559C2314yes—
302#14556559C2318yes—
303#14556559C2318yes—
304#14556559C2314yescomplemented
305#14556559C2314yescomplemented
306C4×Dic146C2318yescomplemented
307C4×Dic146C2314yescomplemented
308C4×Dic146C2314yescomplemented
309#14556556C2318yescomplemented
310C4×D292C2318yescomplemented
311C4×D292C2314yescomplemented
312C4×D292C2314yescomplemented
313D4×Dic73C2318yes—
314D4×Dic73C2318yes—
315#14556553C2318yescomplemented
316C4×C22⋊D73C2318yes—
317C4×C22⋊D73C2318yes—
318C4×C22⋊D73C2318yes—
319C4×C22⋊D73C2318yes—
320C4×C22⋊D73C2318yes—
321C4×C22⋊D73C2318yes—
322C4×C22⋊D73C2318yes—
323C4×C22⋊D73C2318yes—
324C4×C22⋊D73C2318yes—
325C4×C22⋊D73C2318yes—
326C4×C22⋊D73C2318yescomplemented
327C4×C22⋊D73C2318yescomplemented
328#14556551C2318yes—
329#14556551C2318yes—
330#14556551C2318yescomplemented
331#14556551C2318yescomplemented
332#14556550C2314yes—
333#14556550C2314yes—
334#14556550C2314yes—
335#14556550C2314yes—
336#14556550C2314yes—
337#14556550C2312yescomplemented
338#14556550C2312yescomplemented
339#14556550C2314yescomplemented
340#14556549C2318yescomplemented
341#14556548C2318yescomplemented
342#14556547C2318yes—
343#14556547C2318yescomplemented
344C2×C4⋊Dic73C2312yes—
345C2×C4⋊Dic73C2312yes—
346C2×C4⋊Dic73C2314yescomplemented
347C2×#11924007C2314yes—
348C2×#11924007C2314yes—
349C4⋊C4×D73C2318yescomplemented
350C2×C22⋊Dic73C2314yes—
351C2×C22⋊Dic73C2314yes—
352C2×C22⋊Dic73C2314yes—
353C2×C22⋊Dic73C2314yes—
354C2×#11924005C2314yes—
355C2×#11924005C2314yes—
356C22⋊C4×D73C2318yes—
357C22⋊C4×D73C2318yescomplemented
358C2×C4×Dic73C2314yes—
359C2×C4×Dic73C2314yescomplemented
360C42×D73C2318yescomplemented
361C25×C73C2311yescharacteristic
362C2×#41×C73—44no—
363C2×#41×C73C2311yescharacteristic
364C2×#41×C73C2312yes—
365C2×#41×C73C2311yescharacteristic
366C2×#41×C73C2312yes—
367C2×#41×C73C2311yescharacteristic
368C2×#41×C73C2311yescharacteristic
369C22×Q8×C73C2311yescharacteristic
370C22×D4×C73C2311yescharacteristic
371C22×D4×C73C2312yes—
372C22×D4×C73C2314yes—
373C23×C4×C73—44no—
374C23×C4×C73C2312yes—
375C23×C4×C73C2312yes—
376C23×C4×C73C2311yescharacteristic
377C23×C4×C73C2312yes—
378C23×C4×C73C2311yescharacteristic
379C23×C4×C73C2311yescharacteristic
380C23×C4×C73C2311yescharacteristic
381C23×C4×C73C2312yes—
382C23×C4×C73C2312yes—
383C23×C4×C73C2311yescharacteristic
384C23×C4×C73C2311yescharacteristic
385#123×C73C2314yes—
386#123×C73C2314yes—
387#123×C73C2312yes—
388#123×C73C2312yes—
389#123×C73C2312yes—
390#123×C73C2312yes—
391C22⋊Q8×C73C2312yes—
392C22⋊Q8×C73C2312yes—
393C22⋊Q8×C73C2312yes—
394C22⋊Q8×C73C2312yes—
395C22⋊Q8×C73C2314yes—
396C22⋊Q8×C73C2314yes—
397#121×C73C2312yes—
398#121×C73C2312yes—
399#121×C73C2312yes—
400#121×C73C2312yes—
401#121×C73C2314yes—
402#121×C73C2314yes—
403#120×C73C2314yes—
404#120×C73C2314yes—
405#120×C73C2312yes—
406#120×C73C2312yes—
407#120×C73C2312yes—
408#120×C73C2312yes—
409C4×D4×C73C2314yes—
410C4×D4×C73C2314yes—
411C4×D4×C73C2314yes—
412C4×D4×C73C2314yes—
413C4×D4×C73C2314yes—
414C4×D4×C73C2314yes—
415C4×D4×C73C2314yes—
416C4×D4×C73C2314yes—
417#117×C73C2311yescharacteristic
418#117×C73C2312yes—
419#117×C73C2311yescharacteristic
420#117×C73C2312yes—
421#117×C73C2312yes—
422C2×C4⋊C4×C73C2312yes—
423C2×C4⋊C4×C73C2314yes—
424C2×C22⋊C4×C73C2312yes—
425C2×C22⋊C4×C73C2314yes—
426C2×C22⋊C4×C73C2314yes—
427C2×C42×C73C2312yes—
428C23×D73C2414yes—
429C23×D73C2414yes—
430#11924028—216no—
431#11924028—48no—
432#11924028—48no—
433#11924028—48no—
434#11924028—48no—
435#11924028—48no—
436#11924028—48no—
437#11924027—416no—
438C2×Dic146—44no—
439C2×Dic146—44no—
440C2×Dic146C2414yes—
441C2×Dic146C2418yes—
442C2×Dic146C2414yes—
443C2×Dic146C2414yes—
444C2×D292—44no—
445C2×D292—44no—
446C2×D292C2414yes—
447C2×D292C2418yes—
448C2×D292C2414yes—
449C2×D292C2414yes—
450C2×C22⋊D73—48no—
451C2×C22⋊D73—48no—
452C2×C22⋊D73—48no—
453C2×C22⋊D73—48no—
454C2×C22⋊D73C2418yes—
455C2×C22⋊D73C2418yes—
456C2×C22⋊D73C2418yes—
457C2×C22⋊D73C2418yes—
458C2×C22⋊D73C2418yes—
459C2×C22⋊D73C2418yes—
460C2×C22⋊D73C2418yes—
461C2×C22⋊D73C2418yes—
462C2×C22⋊D73C2418yes—
463D4×D73—416no—
464C22×Dic73C2414yes—
465C22×Dic73C2414yes—
466C22×Dic73C2418yes—
467C22×Dic73C2414yes—
468C22×Dic73C2414yes—
469C2×C4×D73—48no—
470C2×C4×D73—48no—
471C2×C4×D73C2418yes—
472C2×C4×D73C2418yes—
473C2×C4×D73C2418yes—
474C2×C4×D73C2418yes—
475C2×C4×D73C2418yes—
476C4⋊Dic73C2418yes—
477C4⋊Dic73C2414yes—
478C4⋊Dic73C2414yes—
479C4⋊Dic73C2414yes—
480C4⋊Dic73C2414yes—
481C4⋊Dic73C2418yes—
482C4⋊Dic73C2418yes—
483#11924007C2418yes—
484#11924007C2418yes—
485#11924007C2418yes—
486#11924007C2418yes—
487#11924007C2418yes—
488#11924007C2418yes—
489#11924007C2418yes—
490#11924007C2418yes—
491#11924007C2418yes—
492#11924007C2418yes—
493C22⋊Dic73C2418yes—
494C22⋊Dic73C2418yes—
495C22⋊Dic73C2418yes—
496C22⋊Dic73C2418yes—
497C22⋊Dic73C2414yes—
498C22⋊Dic73C2414yes—
499C22⋊Dic73C2418yes—
500C22⋊Dic73C2418yes—
501C22⋊Dic73C2418yes—
502C22⋊Dic73C2418yes—
503#11924005C2418yes—
504#11924005C2418yes—
505#11924005C2418yes—
506#11924005C2418yes—
507#11924005C2418yes—
508#11924005C2418yes—
509#11924005C2418yes—
510#11924005C2418yes—
511#11924005C2418yes—
512#11924005C2418yes—
513C4×Dic73C2418yes—
514C4×Dic73C2418yes—
515C4×Dic73C2418yes—
516C4×Dic73C2418yes—
517C4×Dic73C2414yes—
518C4×Dic73C2414yes—
519C24×C73—42no—
520C24×C73—44no—
521C24×C73C2412yes—
522C24×C73C2411yescharacteristic
523C24×C73C2411yescharacteristic
524C24×C73C2412yes—
525C24×C73C2412yes—
526C24×C73C2411yescharacteristic
527#41×C73—42no—
528#41×C73—44no—
529#41×C73—42no—
530#41×C73—44no—
531#41×C73—42no—
532#41×C73—42no—
533C2×Q8×C73—42no—
534C2×Q8×C73C2411yescharacteristic
535C2×Q8×C73C2412yes—
536C2×Q8×C73C2411yescharacteristic
537C2×D4×C73—42no—
538C2×D4×C73—44no—
539C2×D4×C73—48no—
540C2×D4×C73C2414yes—
541C2×D4×C73C2414yes—
542C2×D4×C73C2414yes—
543C2×D4×C73C2414yes—
544C2×D4×C73C2412yes—
545C2×D4×C73C2412yes—
546C2×D4×C73C2412yes—
547C2×D4×C73C2412yes—
548C2×D4×C73C2411yescharacteristic
549C2×D4×C73C2412yes—
550C2×D4×C73C2411yescharacteristic
551C22×C4×C73—24no—
552C22×C4×C73—28no—
553C22×C4×C73—28no—
554C22×C4×C73—42no—
555C22×C4×C73—44no—
556C22×C4×C73—42no—
557C22×C4×C73—44no—
558C22×C4×C73—42no—
559C22×C4×C73—42no—
560C22×C4×C73—44no—
561C22×C4×C73—42no—
562C22×C4×C73C2412yes—
563C22×C4×C73C2412yes—
564C22×C4×C73C2411yescharacteristic
565C22×C4×C73C2411yescharacteristic
566C22×C4×C73C2411yescharacteristic
567C22×C4×C73C2411yescharacteristic
568C22×C4×C73C2411yescharacteristic
569C22×C4×C73C2412yes—
570C22×C4×C73C2412yes—
571C22×C4×C73C2412yes—
572C22×C4×C73C2412yes—
573C22×C4×C73C2412yes—
574C22×C4×C73C2412yes—
575C22×C4×C73C2412yes—
576C22×C4×C73C2412yes—
577C22×C4×C73C2414yes—
578C22×C4×C73C2412yes—
579C22×C4×C73C2412yes—
580C22×C4×C73C2412yes—
581C22×C4×C73C2412yes—
582C22×C4×C73C2411yescharacteristic
583C22×C4×C73C2412yes—
584C22×C4×C73C2411yescharacteristic
585C22×C4×C73C2411yescharacteristic
586C4⋊C4×C73C2412yes—
587C4⋊C4×C73C2414yes—
588C4⋊C4×C73C2412yes—
589C4⋊C4×C73C2414yes—
590C4⋊C4×C73C2414yes—
591C4⋊C4×C73C2414yes—
592C4⋊C4×C73C2414yes—
593C22⋊C4×C73C2412yes—
594C22⋊C4×C73C2414yes—
595C22⋊C4×C73C2412yes—
596C22⋊C4×C73C2414yes—
597C22⋊C4×C73C2414yes—
598C22⋊C4×C73C2414yes—
599C22⋊C4×C73C2414yes—
600C22⋊C4×C73C2414yes—
601C22⋊C4×C73C2414yes—
602C22⋊C4×C73C2414yes—
603C22⋊C4×C73C2414yes—
604C42×C73C2414yes—
605C42×C73C2412yes—
606C42×C73C2412yes—
607C23×C73—22no—
608C23×C73—24no—
609C23×C73—24no—
610C23×C73—24no—
611C23×C73—24no—
612C23×C73—24no—
613C23×C73—41no—
614C23×C73—42no—
615C23×C73—41no—
616C23×C73—42no—
617C23×C73—42no—
618C23×C73—42no—
619C23×C73—42no—
620C23×C73—44no—
621C23×C73—416no—
622C23×C73C2512yes—
623C23×C73C2511yescharacteristic
624C23×C73C2511yescharacteristic
625C23×C73C2512yes—
626C23×C73C2512yes—
627C23×C73C2511yescharacteristic
628C23×C73C2512yes—
629C22×D73—28no—
630C22×D73—44no—
631C22×D73—44no—
632C22×D73—48no—
633C22×D73—44no—
634C22×D73C2518yes—
635Q8×C73—41no—
636Q8×C73—42no—
637Q8×C73—41no—
638D4×C73—28no—
639D4×C73—28no—
640D4×C73—44no—
641D4×C73—44no—
642D4×C73—42no—
643D4×C73—42no—
644D4×C73—42no—
645D4×C73—42no—
646D4×C73—41no—
647D4×C73—42no—
648D4×C73—41no—
649C2×C4×C73—22no—
650C2×C4×C73—24no—
651C2×C4×C73—24no—
652C2×C4×C73—22no—
653C2×C4×C73—22no—
654C2×C4×C73—22no—
655C2×C4×C73—22no—
656C2×C4×C73—24no—
657C2×C4×C73—24no—
658C2×C4×C73—24no—
659C2×C4×C73—24no—
660C2×C4×C73—24no—
661C2×C4×C73—24no—
662C2×C4×C73—24no—
663C2×C4×C73—24no—
664C2×C4×C73—41no—
665C2×C4×C73—42no—
666C2×C4×C73—42no—
667C2×C4×C73—42no—
668C2×C4×C73—41no—
669C2×C4×C73—42no—
670C2×C4×C73—42no—
671C2×C4×C73—44no—
672C2×C4×C73H(5,𝔽2)14yes—
673C2×C4×C73C2514yes—
674C2×C4×C73C2514yes—
675C2×C4×C73C2512yes—
676C2×C4×C73C2512yes—
677C2×C4×C73C2512yes—
678C2×C4×C73C2512yes—
679C2×C4×C73C2511yescharacteristic
680C2×C4×C73C2511yescharacteristic
681C2×C4×C73C2511yescharacteristic
682C2×C4×C73C2511yescharacteristic
683C22⋊D73—216no—
684C22⋊D73—216no—
685C22⋊D73—48no—
686C22⋊D73—48no—
687C22⋊D73—48no—
688C22⋊D73—48no—
689C22⋊D73—48no—
690C22⋊D73—48no—
691C22⋊D73—48no—
692C2×Dic73—28no—
693C2×Dic73—44no—
694C2×Dic73—44no—
695C2×Dic73—44no—
696C2×Dic73—48no—
697C2×Dic73C2518yes—
698C2×Dic73C2518yes—
699C2×Dic73C2518yes—
700D292—28no—
701D292—48no—
702D292—44no—
703D292—44no—
704C4×D73—216no—
705C4×D73—48no—
706C4×D73—48no—
707C4×D73—48no—
708C4×D73—48no—
709Dic146—28no—
710Dic146—44no—
711Dic146—44no—
712Dic146—48no—
713C22×C73—22no—
714C22×C73—22no—
715C22×C73—22no—
716C22×C73—22no—
717C22×C73—22no—
718C22×C73—22no—
719C22×C73—21no—
720C22×C73—21no—
721C22×C73—24no—
722C22×C73—22no—
723C22×C73—22no—
724C22×C73—22no—
725C22×C73—24no—
726C22×C73—22no—
727C22×C73—44no—
728C22×C73—48no—
729C22×C73—48no—
730C22×C73—44no—
731C22×C73—44no—
732C22×C73—84no—
733C22×C73C2×H(5,𝔽2)12yes—
734C22×C73#58514yes—
735C22×C73C2611yescharacteristic
736C2×D73—28no—
737C2×D73—28no—
738C2×D73—28no—
739C2×D73—88no—
740C2×D73—88no—
741C4×C73—22no—
742C4×C73—22no—
743C4×C73—22no—
744C4×C73—22no—
745C4×C73—21no—
746C4×C73—21no—
747C4×C73—24no—
748C4×C73—24no—
749C4×C73C2×H(5,𝔽2)12yes—
750C4×C73C2×H(5,𝔽2)12yes—
751Dic73—28no—
752Dic73—28no—
753Dic73—28no—
754#62729—731nomaximal, Sylow
755C2×C73—24no—
756C2×C73—22no—
757C2×C73—42no—
758C2×C73—42no—
759C2×C73—41no—
760C2×C73—41no—
761C2×C73—42no—
762C2×C73C22×H(5,𝔽2)11yescharacteristic
763C2×C73C2×#58512yes—
764D73—48no—
765#3542—734no—
766#3541—734no—
767#3540—732no—
768#3539—732no—
769#3538—731no—
770#3537—731no—
771#3536—732no—
772#3535—734no—
773#3534—734no—
774#3533—734no—
775#3532—734no—
776#3529—734no—
777#3481—734no—
778#3475—734no—
779D4×#41—734no—
780#3460—734no—
781#3459—734no—
782#3455—732no—
783#3449—732no—
784C2×#525—732no—
785C2×#525D7311yescharacteristic, complemented
786C73#6272911yescharacteristic, complemented, Sylow
787C22×#41—732no—
788C22×#41—732no—
789C22×#41C2×D7311yescharacteristic, complemented
790C24×C4C2×D7311yescharacteristic, complemented
791#563—734no—
792#563—738no—
793#562—738no—
794#562—738no—
795#562—738no—
796H(3,𝔽4)—734no—
797#560—734no—
798#560—738no—
799#560—738no—
800#560—734no—
801#559—734no—
802#556—734no—
803#555—734no—
804#554—738no—
805#554—734no—
806#553—738no—
807#553—738no—
808#553—734no—
809#553—734no—
810#552—734no—
811#552—734no—
812#552—738no—
813#551—734no—
814#551—738no—
815#551—734no—
816#551—738no—
817#551—738no—
818#550—734no—
819D4×Q8—734no—
820#548—734no—
821#548—734no—
822#547—734no—
823#547—734no—
824#547—738no—
825#546—738no—
826#546—738no—
827#546—738no—
828#546—734no—
829#546—734no—
830#546—738no—
831#546—738no—
832D42—738no—
833D42—734no—
834D42—734no—
835#544—734no—
836#543—734no—
837#542—738no—
838#542—738no—
839#542—734no—
840#542—734no—
841#541—732no—
842#541—732no—
843#540—738no—
844#540—738no—
845#540—732no—
846#540—732no—
847#539—738no—
848#539—738no—
849#539—734no—
850#539—734no—
851#539—738no—
852#538—738no—
853#538—734no—
854#538—738no—
855#538—734no—
856#538—738no—
857#538—738no—
858#538—738no—
859#537—734no—
860#537—734no—
861#537—734no—
862#536—732no—
863#536—732no—
864#536—734no—
865#535—732no—
866#535—732no—
867#535—734no—
868#535—738no—
869#534—734no—
870#534—734no—
871#534—734no—
872#534—738no—
873#533—732no—
874#532—734no—
875#532—734no—
876#532—738no—
877#532—732no—
878#529—738no—
879#529—738no—
880#529—738no—
881#529—738no—
882#529—738no—
883#525—734no—
884#525—734no—
885#525—734no—
886#525—734no—
887#525—734no—
888#525—734no—
889#525—734no—
890#525—734no—
891#525—734no—
892#525—734no—
893#525—734no—
894#525—738no—
895#525—738no—
896#525C2×D7311yescharacteristic
897#525C2×D7312yescomplemented
898#525C2×D7312yescomplemented
899#525C2×D7312yescomplemented
900#525C2×D7312yescomplemented
901#525C2×D7311yescharacteristic, complemented
902#525C2×D7311yescharacteristic, complemented
903#525C2×D7311yescharacteristic, complemented
904#525C2×D7314yescomplemented
905C2×#123—734no—
906C2×#123C2×D7312yescomplemented
907C2×C22⋊Q8—732no—
908C2×C22⋊Q8—732no—
909C2×C22⋊Q8C2×D7312yescomplemented
910C2×#121—732no—
911C2×#121—732no—
912C2×#121C2×D7312yescomplemented
913C2×#120—734no—
914C2×#120C2×D7312yescomplemented
915C4×#41—738no—
916C4×#41—734no—
917C2×C4×D4—734no—
918C2×C4×D4—734no—
919C2×C4×D4—738no—
920C2×C4×D4C2×D7314yescomplemented
921C2×#117—732no—
922C2×#117—732no—
923C2×#117C2×D7311yescharacteristic, complemented
924C25C22×D7311yescharacteristic
925C2×#41—44no—
926C2×#41—2928no—
927C2×#41—2928no—
928C2×#41—738no—
929C2×#41—734no—
930C2×#41—734no—
931C2×#41—734no—
932C2×#41—734no—
933C2×#41—734no—
934C2×#41—734no—
935C2×#41—734no—
936C2×#41C22×D7311yescharacteristic
937C2×#41C22×D7312yes—
938C2×#41C22×D7311yescharacteristic
939C2×#41C22×D7311yescharacteristic
940C2×#41C22×D7312yes—
941C2×#41C22×D7311yescharacteristic
942C22×Q8—732no—
943C22×Q8—732no—
944C22×Q8C22×D7311yescharacteristic
945C22×D4—734no—
946C22×D4—734no—
947C22×D4—734no—
948C22×D4—734no—
949C22×D4—738no—
950C22×D4—732no—
951C22×D4—732no—
952C22×D4C22×D7314yes—
953C22×D4C22×D7312yes—
954C22×D4C22×D7311yescharacteristic
955C23×C4—44no—
956C23×C4—734no—
957C23×C4—734no—
958C23×C4C22×D7312yes—
959C23×C4C22×D7312yes—
960C23×C4C22×D7311yescharacteristic
961C23×C4C22×D7311yescharacteristic
962C23×C4C22×D7312yes—
963C23×C4C22×D7311yescharacteristic
964C23×C4C22×D7312yes—
965C23×C4C22×D7312yes—
966C23×C4C22×D7311yescharacteristic
967C23×C4C22×D7311yescharacteristic
968C23×C4C22×D7311yescharacteristic
969C4⋊Q8—734no—
970C4⋊Q8—734no—
971C4⋊Q8—738no—
972C4⋊Q8—732no—
973C4⋊Q8—734no—
974#127—734no—
975#127—734no—
976#127—738no—
977#127—732no—
978#126—738no—
979#126—738no—
980#126—738no—
981#126—738no—
982#126—738no—
983#126—738no—
984#126—738no—
985#126—738no—
986#126—738no—
987#126—738no—
988#125—738no—
989#125—738no—
990#125—738no—
991#125—738no—
992#125—738no—
993#125—732no—
994#125—732no—
995#124—734no—
996#124—734no—
997#124—738no—
998#124—734no—
999#124—734no—
1000#124—738no—
1001#124—738no—
1002#124—738no—
1003#124—738no—
1004#124—738no—
1005#124—738no—
1006#124—734no—
1007#123—734no—
1008#123—734no—
1009#123—734no—
1010#123—734no—
1011#123—738no—
1012#123—738no—
1013#123—738no—
1014#123—738no—
1015#123—738no—
1016#123—738no—
1017#123—738no—
1018#123—738no—
1019#123—738no—
1020#123—738no—
1021#123—738no—
1022#123—738no—
1023#123—738no—
1024#123—738no—
1025#123—738no—
1026#123—738no—
1027#123—738no—
1028#123—738no—
1029#123—738no—
1030#123C22×D7312yes—
1031#123C22×D7314yes—
1032#123C22×D7314yes—
1033#123C22×D7312yes—
1034#123C22×D7312yes—
1035#123C22×D7312yes—
1036C22⋊Q8—738no—
1037C22⋊Q8—738no—
1038C22⋊Q8—734no—
1039C22⋊Q8—734no—
1040C22⋊Q8—734no—
1041C22⋊Q8—734no—
1042C22⋊Q8—734no—
1043C22⋊Q8—734no—
1044C22⋊Q8—734no—
1045C22⋊Q8—734no—
1046C22⋊Q8—734no—
1047C22⋊Q8—734no—
1048C22⋊Q8—738no—
1049C22⋊Q8—738no—
1050C22⋊Q8—738no—
1051C22⋊Q8—738no—
1052C22⋊Q8—738no—
1053C22⋊Q8—738no—
1054C22⋊Q8—738no—
1055C22⋊Q8—738no—
1056C22⋊Q8—738no—
1057C22⋊Q8—738no—
1058C22⋊Q8C22×D7312yes—
1059C22⋊Q8C22×D7312yes—
1060C22⋊Q8C22×D7312yes—
1061C22⋊Q8C22×D7312yes—
1062C22⋊Q8C22×D7314yes—
1063C22⋊Q8C22×D7314yes—
1064#121—738no—
1065#121—738no—
1066#121—738no—
1067#121—738no—
1068#121—738no—
1069#121—738no—
1070#121—738no—
1071#121—738no—
1072#121—738no—
1073#121—738no—
1074#121—738no—
1075#121—738no—
1076#121—734no—
1077#121—734no—
1078#121—734no—
1079#121—734no—
1080#121—734no—
1081#121—734no—
1082#121—734no—
1083#121—734no—
1084#121—734no—
1085#121—734no—
1086#121—738no—
1087#121—738no—
1088#121—738no—
1089#121—738no—
1090#121—738no—
1091#121—738no—
1092#121—738no—
1093#121—738no—
1094#121C22×D7312yes—
1095#121C22×D7312yes—
1096#121C22×D7312yes—
1097#121C22×D7312yes—
1098#121C22×D7314yes—
1099#121C22×D7314yes—
1100#120—738no—
1101#120—738no—
1102#120—738no—
1103#120—738no—
1104#120—738no—
1105#120—734no—
1106#120—734no—
1107#120—734no—
1108#120—734no—
1109#120—738no—
1110#120—738no—
1111#120—738no—
1112#120—738no—
1113#120C22×D7312yes—
1114#120C22×D7314yes—
1115#120C22×D7314yes—
1116#120C22×D7312yes—
1117#120C22×D7312yes—
1118#120C22×D7312yes—
1119C4×Q8—738no—
1120C4×Q8—738no—
1121C4×Q8—734no—
1122C4×Q8—734no—
1123C4×D4—738no—
1124C4×D4—738no—
1125C4×D4—738no—
1126C4×D4—738no—
1127C4×D4—738no—
1128C4×D4—738no—
1129C4×D4—738no—
1130C4×D4—738no—
1131C4×D4—738no—
1132C4×D4—738no—
1133C4×D4—738no—
1134C4×D4—738no—
1135C4×D4—738no—
1136C4×D4—738no—
1137C4×D4—738no—
1138C4×D4—738no—
1139C4×D4—738no—
1140C4×D4—738no—
1141C4×D4—738no—
1142C4×D4—738no—
1143C4×D4—734no—
1144C4×D4—734no—
1145C4×D4C22×D7314yes—
1146C4×D4C22×D7314yes—
1147C4×D4C22×D7314yes—
1148C4×D4C22×D7314yes—
1149C4×D4C22×D7314yes—
1150C4×D4C22×D7314yes—
1151C4×D4C22×D7314yes—
1152C4×D4C22×D7314yes—
1153#117—734no—
1154#117—734no—
1155#117—734no—
1156#117—734no—
1157#117—734no—
1158#117—734no—
1159#117—732no—
1160#117—732no—
1161#117—738no—
1162#117—738no—
1163#117—738no—
1164#117—738no—
1165#117C22×D7311yescharacteristic
1166#117C22×D7312yes—
1167#117C22×D7312yes—
1168#117C22×D7312yes—
1169#117C22×D7311yescharacteristic
1170C2×C4⋊C4—732no—
1171C2×C4⋊C4—732no—
1172C2×C4⋊C4—734no—
1173C2×C4⋊C4—734no—
1174C2×C4⋊C4—734no—
1175C2×C4⋊C4—738no—
1176C2×C4⋊C4C22×D7312yes—
1177C2×C4⋊C4C22×D7314yes—
1178C2×C22⋊C4—734no—
1179C2×C22⋊C4—734no—
1180C2×C22⋊C4—734no—
1181C2×C22⋊C4—734no—
1182C2×C22⋊C4—734no—
1183C2×C22⋊C4—734no—
1184C2×C22⋊C4—738no—
1185C2×C22⋊C4—738no—
1186C2×C22⋊C4C22×D7312yes—
1187C2×C22⋊C4C22×D7314yes—
1188C2×C22⋊C4C22×D7314yes—
1189C2×C42—734no—
1190C2×C42—734no—
1191C2×C42—738no—
1192C2×C42C22×D7312yes—
1193C24—42no—
1194C24—44no—
1195C24—734no—
1196C24—734no—
1197C24C23×D7311yescharacteristic
1198C24C23×D7312yes—
1199C24C23×D7312yes—
1200C24C23×D7312yes—
1201C24C23×D7311yescharacteristic
1202C24C23×D7311yescharacteristic
1203#41—42no—
1204#41—44no—
1205#41—42no—
1206#41—44no—
1207#41—42no—
1208#41—42no—
1209#41—2928no—
1210#41—2928no—
1211#41—2928no—
1212#41—2928no—
1213#41—2928no—
1214#41—2928no—
1215#41—29216no—
1216#41—14616no—
1217C2×Q8—42no—
1218C2×Q8—2924no—
1219C2×Q8—2924no—
1220C2×Q8—738no—
1221C2×Q8—734no—
1222C2×Q8—734no—
1223C2×Q8—734no—
1224C2×Q8C23×D7311yescharacteristic
1225C2×Q8C23×D7312yes—
1226C2×Q8C23×D7311yescharacteristic
1227C2×D4—42no—
1228C2×D4—44no—
1229C2×D4—48no—
1230C2×D4—2924no—
1231C2×D4—2924no—
1232C2×D4—29216no—
1233C2×D4—2928no—
1234C2×D4—2928no—
1235C2×D4—2928no—
1236C2×D4—2928no—
1237C2×D4—738no—
1238C2×D4—738no—
1239C2×D4—738no—
1240C2×D4—738no—
1241C2×D4—738no—
1242C2×D4—738no—
1243C2×D4—738no—
1244C2×D4—738no—
1245C2×D4—738no—
1246C2×D4—738no—
1247C2×D4—734no—
1248C2×D4—734no—
1249C2×D4—734no—
1250C2×D4C23×D7314yes—
1251C2×D4C23×D7314yes—
1252C2×D4C23×D7314yes—
1253C2×D4C23×D7314yes—
1254C2×D4C23×D7311yescharacteristic
1255C2×D4C23×D7312yes—
1256C2×D4C23×D7312yes—
1257C2×D4C23×D7312yes—
1258C2×D4C23×D7312yes—
1259C2×D4C23×D7312yes—
1260C2×D4C23×D7311yescharacteristic
1261C22×C4—24no—
1262C22×C4—28no—
1263C22×C4—28no—
1264C22×C4—42no—
1265C22×C4—44no—
1266C22×C4—42no—
1267C22×C4—44no—
1268C22×C4—42no—
1269C22×C4—42no—
1270C22×C4—44no—
1271C22×C4—42no—
1272C22×C4—2928no—
1273C22×C4—2928no—
1274C22×C4—734no—
1275C22×C4—738no—
1276C22×C4—734no—
1277C22×C4—734no—
1278C22×C4—738no—
1279C22×C4—738no—
1280C22×C4—738no—
1281C22×C4—738no—
1282C22×C4—734no—
1283C22×C4—738no—
1284C22×C4C23×D7312yes—
1285C22×C4C23×D7312yes—
1286C22×C4C23×D7312yes—
1287C22×C4C23×D7312yes—
1288C22×C4C23×D7311yescharacteristic
1289C22×C4C23×D7312yes—
1290C22×C4C23×D7312yes—
1291C22×C4C23×D7311yescharacteristic
1292C22×C4C23×D7311yescharacteristic
1293C22×C4C23×D7312yes—
1294C22×C4C23×D7312yes—
1295C22×C4C23×D7312yes—
1296C22×C4C23×D7312yes—
1297C22×C4C23×D7311yescharacteristic
1298C22×C4C23×D7311yescharacteristic
1299C22×C4C23×D7314yes—
1300C22×C4C23×D7312yes—
1301C22×C4C23×D7312yes—
1302C22×C4C23×D7311yescharacteristic
1303C22×C4C23×D7312yes—
1304C22×C4C23×D7312yes—
1305C22×C4C23×D7311yescharacteristic
1306C22×C4C23×D7312yes—
1307C22×C4C23×D7311yescharacteristic
1308C4⋊C4—738no—
1309C4⋊C4—738no—
1310C4⋊C4—738no—
1311C4⋊C4—738no—
1312C4⋊C4—738no—
1313C4⋊C4—738no—
1314C4⋊C4—738no—
1315C4⋊C4—738no—
1316C4⋊C4—738no—
1317C4⋊C4—738no—
1318C4⋊C4—734no—
1319C4⋊C4—734no—
1320C4⋊C4—738no—
1321C4⋊C4—734no—
1322C4⋊C4—734no—
1323C4⋊C4—738no—
1324C4⋊C4—738no—
1325C4⋊C4C23×D7314yes—
1326C4⋊C4C23×D7314yes—
1327C4⋊C4C23×D7312yes—
1328C4⋊C4C23×D7314yes—
1329C4⋊C4C23×D7312yes—
1330C4⋊C4C23×D7314yes—
1331C4⋊C4C23×D7314yes—
1332C22⋊C4—738no—
1333C22⋊C4—738no—
1334C22⋊C4—734no—
1335C22⋊C4—734no—
1336C22⋊C4—738no—
1337C22⋊C4—738no—
1338C22⋊C4—738no—
1339C22⋊C4—738no—
1340C22⋊C4—738no—
1341C22⋊C4—738no—
1342C22⋊C4—738no—
1343C22⋊C4—738no—
1344C22⋊C4—738no—
1345C22⋊C4—738no—
1346C22⋊C4—738no—
1347C22⋊C4—738no—
1348C22⋊C4—738no—
1349C22⋊C4—738no—
1350C22⋊C4—738no—
1351C22⋊C4—738no—
1352C22⋊C4C23×D7314yes—
1353C22⋊C4C23×D7314yes—
1354C22⋊C4C23×D7314yes—
1355C22⋊C4C23×D7314yes—
1356C22⋊C4C23×D7312yes—
1357C22⋊C4C23×D7314yes—
1358C22⋊C4C23×D7312yes—
1359C22⋊C4C23×D7314yes—
1360C22⋊C4C23×D7314yes—
1361C22⋊C4C23×D7314yes—
1362C22⋊C4C23×D7314yes—
1363C42—734no—
1364C42—738no—
1365C42—738no—
1366C42—734no—
1367C42—738no—
1368C42—738no—
1369C42C23×D7312yes—
1370C42C23×D7312yes—
1371C42C23×D7314yes—
1372C23—22no—
1373C23—24no—
1374C23—24no—
1375C23—24no—
1376C23—24no—
1377C23—24no—
1378C23—41no—
1379C23—42no—
1380C23—41no—
1381C23—42no—
1382C23—42no—
1383C23—42no—
1384C23—42no—
1385C23—44no—
1386C23—416no—
1387C23—2924no—
1388C23—2924no—
1389C23—2924no—
1390C23—2928no—
1391C23—738no—
1392C23—1468no—
1393C23C24×D7312yes—
1394C23C24×D7311yescharacteristic
1395C23C24×D7311yescharacteristic
1396C23C24×D7312yes—
1397C23C24×D7312yes—
1398C23C24×D7311yescharacteristic
1399C23C24×D7312yes—
1400Q8—41no—
1401Q8—42no—
1402Q8—41no—
1403Q8—2924no—
1404Q8—2924no—
1405Q8—2928no—
1406Q8—1468no—
1407D4—28no—
1408D4—28no—
1409D4—41no—
1410D4—42no—
1411D4—41no—
1412D4—42no—
1413D4—42no—
1414D4—42no—
1415D4—42no—
1416D4—44no—
1417D4—44no—
1418D4—2924no—
1419D4—2924no—
1420D4—2928no—
1421D4—2928no—
1422D4—2928no—
1423D4—2928no—
1424D4—2928no—
1425D4—2928no—
1426D4—2928no—
1427D4—2928no—
1428D4—14616no—
1429D4—14616no—
1430D4—1468no—
1431C2×C4—22no—
1432C2×C4—24no—
1433C2×C4—24no—
1434C2×C4—24no—
1435C2×C4—24no—
1436C2×C4—22no—
1437C2×C4—22no—
1438C2×C4—22no—
1439C2×C4—22no—
1440C2×C4—24no—
1441C2×C4—24no—
1442C2×C4—24no—
1443C2×C4—24no—
1444C2×C4—24no—
1445C2×C4—24no—
1446C2×C4—41no—
1447C2×C4—42no—
1448C2×C4—42no—
1449C2×C4—42no—
1450C2×C4—42no—
1451C2×C4—42no—
1452C2×C4—41no—
1453C2×C4—44no—
1454C2×C4—2928no—
1455C2×C4—2928no—
1456C2×C4—2928no—
1457C2×C4—2928no—
1458C2×C4—2924no—
1459C2×C4—2924no—
1460C2×C4—2924no—
1461C2×C4—2928no—
1462C2×C4—738no—
1463C2×C4—738no—
1464C2×C4—738no—
1465C2×C4—1468no—
1466C2×C4—14616no—
1467C2×C4#1455663614yes—
1468C2×C4C24×D7312yes—
1469C2×C4C24×D7312yes—
1470C2×C4C24×D7314yes—
1471C2×C4C24×D7314yes—
1472C2×C4C24×D7311yescharacteristic
1473C2×C4C24×D7311yescharacteristic
1474C2×C4C24×D7312yes—
1475C2×C4C24×D7312yes—
1476C2×C4C24×D7311yescharacteristic
1477C2×C4C24×D7311yescharacteristic
1478C22—22no—
1479C22—22no—
1480C22—22no—
1481C22—21no—
1482C22—21no—
1483C22—22no—
1484C22—22no—
1485C22—22no—
1486C22—24no—
1487C22—24no—
1488C22—22no—
1489C22—22no—
1490C22—22no—
1491C22—22no—
1492C22—48no—
1493C22—44no—
1494C22—44no—
1495C22—48no—
1496C22—44no—
1497C22—84no—
1498C22—5848no—
1499C22—5848no—
1500C22—1468no—
1501C22—1468no—
1502C22—1468no—
1503C22C2×#1455663612yes—
1504C22#1798942314yes—
1505C22C25×D7311yescharacteristic
1506C4—22no—
1507C4—21no—
1508C4—21no—
1509C4—22no—
1510C4—22no—
1511C4—22no—
1512C4—24no—
1513C4—24no—
1514C4—1468no—
1515C4—1468no—
1516C4—1468no—
1517C4C2×#1455663612yes—
1518C4C2×#1455663612yes—
1519C2—22no—
1520C2—24no—
1521C2—41no—
1522C2—41no—
1523C2—42no—
1524C2—42no—
1525C2—42no—
1526C2—2928no—
1527C2C22×#1455663611yescharacteristic
1528C2C2×#1798942312yes—
subgroupG/H
centerC2×C4C24×D73
commutator, socle, cosocleC22×C73C26
FrattiniC22C25×D73
FittingC2×#525×C73C2
hypercenterC2×#525D73
hypocenterC73#62729
LCSG ▷ C22×C73 ▷ C73
UCSC1 ◁ C2×C4 ◁ C2×#525

Complements

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

NH ≅ G/Ntype
1. #22624247C2semidirect
2. #22624224C2semidirect
3. #22624206C2semidirect
4. #22624191C2semidirect
5. #22624180C2semidirect
6. #22624170C2semidirect
7. #22624158C2semidirect
8. #22624140C2semidirect
9. #22624121C2semidirect
10. #22624102C2semidirect
11. #22624086C2semidirect
12. #22624069C2semidirect
13. #22623533C2semidirect
14. #22623489C2semidirect
15. D4×#11924028C2semidirect
16. #22623349C2semidirect
17. #22623338C2semidirect
18. #22623321C2semidirect
19. #22623260C2semidirect
20. C2×#17989098C2semidirect
21. C2×#525×C73C2semidirect
22. C22×#11924028C22semidirect
23. C22×#11924028C22semidirect
24. #17989340C22semidirect
25. #17989338C22semidirect
26. #17989334C22semidirect
27. #17989333C22semidirect
28. #17989332C22semidirect
29. #17989330C22semidirect
30. #17989327C22semidirect
31. #17989326C22semidirect
32. #17989326C22semidirect
33. #17989325C22semidirect
34. #17989321C22semidirect
35. #17989307C22semidirect
36. #17989302C22semidirect
37. #17989294C22semidirect
38. #17989291C22semidirect
39. #17989283C22semidirect
40. #17989283C22semidirect
41. #17989282C22semidirect
42. #17989280C22semidirect
43. #17989277C22semidirect
44. #17989277C22semidirect
45. #17989272C22semidirect
46. #17989268C22semidirect
47. #17989265C22semidirect
48. #17989264C22semidirect
49. #17989263C22semidirect
50. #17989263C22semidirect
51. #17989258C22semidirect
52. D4×Dic146C22semidirect
53. #17989246C22semidirect
54. #17989246C22semidirect
55. #17989242C22semidirect
56. #17989241C22semidirect
57. #17989238C22semidirect
58. #17989233C22semidirect
59. #17989233C22semidirect
60. #17989231C22semidirect
61. #17989227C22semidirect
62. #17989227C22semidirect
63. #17989226C22semidirect
64. #17989224C22semidirect
65. D4×D292C22semidirect
66. D4×C22⋊D73C22semidirect
67. #17989219C22semidirect
68. #17989216C22semidirect
69. #17989212C22semidirect
70. #17989208C22semidirect
71. #17989208C22semidirect
72. #17989207C22semidirect
73. #17989205C22semidirect
74. #17989199C22semidirect
75. #17989199C22semidirect
76. #17989192C22semidirect
77. #17989192C22semidirect
78. #17989189C22semidirect
79. #17989187C22semidirect
80. #17989186C22semidirect
81. #17989184C22semidirect
82. #17989183C22semidirect
83. #17989182C22semidirect
84. #17989180C22semidirect
85. #17989177C22semidirect
86. #17989175C22semidirect
87. #17989174C22semidirect
88. #17989173C22semidirect
89. #17989172C22semidirect
90. #17989172C22semidirect
91. #17989169C22semidirect
92. #17989165C22semidirect
93. #17989165C22semidirect
94. #17989164C22semidirect
95. #17989161C22semidirect
96. #17989158C22semidirect
97. #17989158C22semidirect
98. #17989154C22semidirect
99. #17989152C22semidirect
100. #17989151C22semidirect
101. #17989151C22semidirect
102. #17989147C22semidirect
103. #17989146C22semidirect
104. #17989146C22semidirect
105. #17989145C22semidirect
106. #17989144C22semidirect
107. #17989137C22semidirect
108. #17989134C22semidirect
109. #17989133C22semidirect
110. #17989133C22semidirect
111. #17989119C22semidirect
112. #17989117C22semidirect
113. #17989117C22semidirect
114. #17989115C22semidirect
115. #17989115C22semidirect
116. #17989098C22semidirect
117. #17989098C22semidirect
118. #17989098C22semidirect
119. #17989098C22semidirect
120. #17989098C22semidirect
121. #17989098C22semidirect
122. #17989098C22semidirect
123. #17989098C22semidirect
124. #17989098C22semidirect
125. #17989096C22semidirect
126. #17989096C22semidirect
127. #17989094C22semidirect
128. #17989094C22semidirect
129. C2×#14556574C22semidirect
130. C2×#14556570C22semidirect
131. C2×#14556570C22semidirect
132. C2×#14556565C22semidirect
133. C2×#14556565C22semidirect
134. C2×#14556560C22semidirect
135. C4×#11924028C22semidirect
136. C4×#11924027C22semidirect
137. C2×C4×C22⋊D73C22semidirect
138. C2×C4×C22⋊D73C22semidirect
139. C4×D4×D73C22semidirect
140. C2×#14556550C22semidirect
141. C2×#14556550C22semidirect
142. C22×#41×C73C22semidirect
143. C24×C4×C73C22semidirect
145. #525×C73C22semidirect
146. #525×C73C22semidirect
147. #525×C73C22semidirect
148. #525×C73C22semidirect
149. #525×C73C22semidirect
150. #525×C73C22semidirect
151. #525×C73C22semidirect
152. #525×C73C22semidirect
153. C2×#123×C73C22semidirect
154. C2×C22⋊Q8×C73C22semidirect
155. C2×#121×C73C22semidirect
156. C2×#120×C73C22semidirect
157. C2×C4×D4×C73C22semidirect
158. C2×#117×C73C22semidirect
166. C2×#11924028C23semidirect
167. C2×#11924028C23semidirect
170. C22×Dic146C23semidirect
172. C22×D292C23semidirect
179. C22×C4×D73C23semidirect
180. #14556591C23semidirect
181. #14556591C23semidirect
182. #14556590C23semidirect
183. #14556589C23semidirect
184. #14556589C23semidirect
185. #14556588C23semidirect
189. #14556586C23semidirect
190. #14556586C23semidirect
191. #14556586C23semidirect
192. #14556586C23semidirect
197. #14556584C23semidirect
198. #14556584C23semidirect
199. #14556583C23semidirect
200. #14556583C23semidirect
201. #14556582C23semidirect
202. #14556581C23semidirect
203. #14556581C23semidirect
204. #14556581C23semidirect
205. #14556581C23semidirect
206. #14556580C23semidirect
207. #14556580C23semidirect
208. #14556579C23semidirect
216. #14556577C23semidirect
217. #14556577C23semidirect
218. #14556576C23semidirect
219. #14556576C23semidirect
220. #14556576C23semidirect
221. #14556576C23semidirect
223. #14556575C23semidirect
233. #14556573C23semidirect
234. #14556573C23semidirect
239. #14556572C23semidirect
240. #14556572C23semidirect
241. #14556571C23semidirect
251. #14556570C23semidirect
252. #14556570C23semidirect
253. #14556569C23semidirect
254. #14556569C23semidirect
255. #14556569C23semidirect
256. #14556569C23semidirect
259. #14556568C23semidirect
260. #14556568C23semidirect
261. #14556567C23semidirect
262. #14556567C23semidirect
263. #14556566C23semidirect
273. #14556565C23semidirect
274. #14556565C23semidirect
279. #14556564C23semidirect
280. #14556564C23semidirect
287. #14556563C23semidirect
288. #14556563C23semidirect
294. #14556561C23semidirect
304. #14556559C23semidirect
305. #14556559C23semidirect
306. C4×Dic146C23semidirect
307. C4×Dic146C23semidirect
308. C4×Dic146C23semidirect
309. #14556556C23semidirect
310. C4×D292C23semidirect
311. C4×D292C23semidirect
312. C4×D292C23semidirect
315. #14556553C23semidirect
326. C4×C22⋊D73C23semidirect
327. C4×C22⋊D73C23semidirect
330. #14556551C23semidirect
331. #14556551C23semidirect
337. #14556550C23semidirect
338. #14556550C23semidirect
339. #14556550C23semidirect
340. #14556549C23semidirect
341. #14556548C23semidirect
343. #14556547C23semidirect
346. C2×C4⋊Dic73C23semidirect
349. C4⋊C4×D73C23semidirect
357. C22⋊C4×D73C23semidirect
359. C2×C4×Dic73C23semidirect
360. C42×D73C23semidirect
785. C2×#525D73semidirect
786. C73#62729semidirect
789. C22×#41C2×D73semidirect
790. C24×C4C2×D73semidirect
897. #525C2×D73semidirect
898. #525C2×D73semidirect
899. #525C2×D73semidirect
900. #525C2×D73semidirect
901. #525C2×D73semidirect
902. #525C2×D73semidirect
903. #525C2×D73semidirect
904. #525C2×D73semidirect
906. C2×#123C2×D73semidirect
909. C2×C22⋊Q8C2×D73semidirect
912. C2×#121C2×D73semidirect
914. C2×#120C2×D73semidirect
920. C2×C4×D4C2×D73semidirect
923. C2×#117C2×D73semidirect

Maximal subgroups

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

subgroupindex
#226242472
#226242242
#226242062
#226241912
#226241802
#226241702
#226241582
#226241402
#226241212
#226241022
#226240862
#226240692
#226235332
#226234892
D4×#119240282
#226233492
#226233382
#226233212
#226232602
C2×#179890982
C2×#525×C732
#6272973