Finite Group Databasebeta

← #3538×D73 #33993224

Subgroups — #3538×D73 #33993224

Order 18688.

7162 conjugacy classes of subgroups.

The subgroup lattice has 1490 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#22624180C211yesmaximal, characteristic, complemented
2#22624179C212yesmaximal, complemented
3#22624178C214yesmaximal, complemented
4#22624177C214yesmaximal, complemented
5#22624176C212yesmaximal, complemented
6#22624175C214yesmaximal, complemented
7#22624174C212yesmaximal, complemented
8#22624173C214yesmaximal, complemented
9#22624172C214yesmaximal, complemented
10#22624171C214yesmaximal, complemented
11#563×D73C214yesmaximal, complemented
12#552×D73C214yesmaximal, complemented
13#551×D73C214yesmaximal, complemented
14D4×Q8×D73C214yesmaximal, complemented
15#544×D73C214yesmaximal, complemented
16#541×D73C212yesmaximal, complemented
17#539×D73C214yesmaximal, complemented
18#536×D73C212yesmaximal, complemented
19#525×D73C211yesmaximal, characteristic
20C2×C22⋊Q8×D73C212yesmaximal, complemented
21C73×#3538C211yesmaximal, characteristic, complemented
22C2×#41×D73C2211yescharacteristic
23C22×Q8×D73C2212yes—
24C22×Q8×D73C2212yescomplemented
25C23×C4×D73C2211yescharacteristic
26#17989341C2218yescomplemented
27#17989340C2214yescomplemented
28#17989340C2214yescomplemented
29#17989339C2218yescomplemented
30#17989339C2218yescomplemented
31#17989338C2218yescomplemented
32#17989338C2218yescomplemented
33#17989337C2214yescomplemented
34#17989336C2218yescomplemented
35#17989279C2214yescomplemented
36#17989278C2214yescomplemented
37#17989277C2214yescomplemented
38#17989276C2214yescomplemented
39#17989275C2214yescomplemented
40#17989274C2218yescomplemented
41#17989273C2218yescomplemented
42#17989272C2214yescomplemented
43#17989271C2214yescomplemented
44#17989270C2218yescomplemented
45#17989269C2218yescomplemented
46#17989268C2214yescomplemented
47#17989267C2214yescomplemented
48#17989266C2218yescomplemented
49#17989265C2214yescomplemented
50#17989264C2218yescomplemented
51#17989263C2218yescomplemented
52#17989262C2218yescomplemented
53#17989261C2218yescomplemented
54#17989260C2218yescomplemented
55Q8×D292C2214yescomplemented
56D4×Dic146C2218yescomplemented
57D4×Dic146C2214yescomplemented
58#17989252C2214yescomplemented
59#17989252C2218yescomplemented
60Q8×C22⋊D73C2214yescomplemented
61Q8×C22⋊D73C2214yescomplemented
62#17989250C2218yescomplemented
63#17989250C2214yescomplemented
64#17989250C2214yescomplemented
65#17989250C2218yescomplemented
66#17989218C2214yescomplemented
67#17989217C2218yescomplemented
68#17989217C2218yescomplemented
69#17989216C2218yescomplemented
70#17989216C2214yescomplemented
71#17989216C2214yescomplemented
72#17989215C2218yescomplemented
73#17989214C2218yescomplemented
74#17989214C2218yescomplemented
75#17989200C2212yescomplemented
76#17989199C2212yescomplemented
77#17989198C2212yescomplemented
78#17989197C2214yescomplemented
79#17989196C2218yescomplemented
80#17989195C2214yescomplemented
81#17989194C2218yescomplemented
82#17989186C2214yescomplemented
83#17989185C2218yescomplemented
84#17989184C2214yescomplemented
85#17989183C2218yescomplemented
86#17989182C2214yescomplemented
87#17989181C2218yescomplemented
88#17989180C2218yescomplemented
89#17989179C2218yescomplemented
90#17989178C2218yescomplemented
91#17989163C2212yescomplemented
92#17989162C2214yescomplemented
93#17989161C2212yescomplemented
94#17989160C2214yescomplemented
95#17989160C2214yescomplemented
96#17989159C2214yescomplemented
97#17989159C2214yescomplemented
98#17989158C2212yescomplemented
99#17989157C2214yescomplemented
100C4⋊Q8×D73C2214yescomplemented
101C4⋊Q8×D73C2218yescomplemented
102C4⋊Q8×D73C2212yescomplemented
103#126×D73C2218yes—
104#126×D73C2218yescomplemented
105#125×D73C2218yescomplemented
106#125×D73C2218yescomplemented
107#125×D73C2212yescomplemented
108#124×D73C2214yes—
109#17989100C2212yes—
110#17989099C2211yescharacteristic
111#17989098C2211yescharacteristic
112#17989097C2212yes—
113#17989096C2214yes—
114#17989095C2212yes—
115#17989094C2211yescharacteristic
116#17989093C2212yes—
117#123×D73C2214yes—
118#123×D73C2218yes—
119#123×D73C2212yes—
120#123×D73C2214yescomplemented
121C2×#14556571C2212yescomplemented
122C2×#14556570C2212yescomplemented
123C2×#14556569C2214yescomplemented
124C2×#14556568C2214yescomplemented
125C2×#14556567C2212yescomplemented
126C22⋊Q8×D73C2214yes—
127C22⋊Q8×D73C2214yes—
128C22⋊Q8×D73C2214yes—
129C22⋊Q8×D73C2212yes—
130C22⋊Q8×D73C2218yes—
131C22⋊Q8×D73C2214yes—
132C22⋊Q8×D73C2214yescomplemented
133C22⋊Q8×D73C2214yescomplemented
134C22⋊Q8×D73C2214yescomplemented
135C22⋊Q8×D73C2214yescomplemented
136C22⋊Q8×D73C2214yescomplemented
137C22⋊Q8×D73C2218yescomplemented
138#121×D73C2212yes—
139#120×D73C2212yes—
140C4×Q8×D73C2214yescomplemented
141C4×D4×D73C2218yes—
142C4×D4×D73C2214yes—
143#117×D73C2211yescharacteristic
144#117×D73C2218yes—
145#117×D73C2212yescomplemented
146C2×C4⋊C4×D73C2214yes—
147C2×C4⋊C4×D73C2212yes—
148C2×C22⋊C4×D73C2214yes—
149#563×C73C2214yescomplemented
150#552×C73C2214yescomplemented
151#551×C73C2214yescomplemented
152D4×Q8×C73C2214yescomplemented
153#544×C73C2214yescomplemented
154#541×C73C2212yescomplemented
155#539×C73C2214yescomplemented
156#536×C73C2212yescomplemented
157#525×C73C2211yescharacteristic
158C2×C22⋊Q8×C73C2212yescomplemented
159C24×D73C2311yescharacteristic
160C2×#11924029C2311yescharacteristic
161C2×#11924028C2311yescharacteristic
162C2×#11924028C2312yes—
163C2×#11924027C2312yes—
164C2×#11924027C2311yescharacteristic
165#41×D73—44no—
166C22×Dic146C2314yes—
167C22×Dic146C2312yes—
168C22×Dic146C2312yescomplemented
169C22×Dic146C2314yescomplemented
170C2×Q8×D73—48no—
171C2×Q8×D73—48no—
172C2×Q8×D73C2314yes—
173C2×Q8×D73C2311yescharacteristic
174C2×Q8×D73C2314yes—
175C2×Q8×D73C2314yes—
176C2×Q8×D73C2314yes—
177C2×Q8×D73C2314yes—
178C2×Q8×D73C2314yescomplemented
179C2×Q8×D73C2314yescomplemented
180C2×D4×D73C2314yes—
181C2×D4×D73C2312yes—
182C2×D4×D73C2311yescharacteristic
183C23×Dic73C2311yescharacteristic
184C22×C4×D73—44no—
185C22×C4×D73C2312yes—
186C22×C4×D73C2311yescharacteristic
187C22×C4×D73C2312yes—
188C22×C4×D73C2314yes—
189C22×C4×D73C2312yes—
190C22×C4×D73C2311yescharacteristic
191C22×C4×D73C2311yescharacteristic
192C22×C4×D73C2311yescharacteristic
193C22×C4×D73C2312yes—
194C22×C4×D73C2312yes—
195C22×C4×D73C2314yes—
196C22×C4×D73C2314yes—
197#14556591C2314yescomplemented
198#14556591C2312yescomplemented
199#14556591C2318yescomplemented
200#14556590C2318yescomplemented
201#14556590C2318yescomplemented
202#14556590C2318yescomplemented
203#14556590C2318yescomplemented
204#14556590C2318yescomplemented
205#14556590C2318yescomplemented
206#14556590C2318yescomplemented
207#14556589C2314yescomplemented
208#14556589C2314yescomplemented
209#14556589C2314yescomplemented
210#14556589C2318yescomplemented
211#14556589C2318yescomplemented
212#14556586C2318yes—
213#14556586C2318yes—
214#14556586C2318yes—
215#14556586C2318yescomplemented
216#14556586C2318yescomplemented
217#14556586C2318yescomplemented
218#14556585C2318yes—
219#14556585C2318yescomplemented
220#14556584C2318yes—
221#14556584C2318yes—
222#14556584C2318yes—
223#14556584C2318yescomplemented
224#14556584C2318yescomplemented
225#14556584C2318yescomplemented
226#14556583C2318yescomplemented
227#14556583C2312yescomplemented
228#14556583C2318yescomplemented
229#14556582C2318yescomplemented
230#14556582C2318yescomplemented
231#14556582C2314yescomplemented
232#14556582C2318yescomplemented
233#14556582C2318yescomplemented
234#14556581C2318yescomplemented
235#14556581C2318yescomplemented
236#14556581C2318yescomplemented
237#14556581C2318yescomplemented
238#14556581C2318yescomplemented
239#14556581C2318yescomplemented
240#14556581C2318yescomplemented
241#14556581C2318yescomplemented
242#14556581C2318yescomplemented
243#14556580C2314yes—
244#14556579C2314yes—
245#14556578C2314yes—
246#14556577C2318yes—
247#14556577C2318yes—
248#14556576C2318yes—
249#14556576C2318yes—
250#14556576C2318yes—
251#14556576C2314yes—
252#14556576C2318yescomplemented
253#14556575C2314yes—
254#14556575C2318yes—
255#14556575C2312yes—
256#14556575C2314yescomplemented
257#14556574C2314yes—
258#14556574C2318yes—
259#14556574C2312yes—
260#14556574C2314yescomplemented
261#14556573C2318yes—
262#14556573C2318yes—
263#14556573C2318yes—
264#14556573C2314yes—
265#14556573C2318yescomplemented
266#14556572C2314yes—
267#14556572C2318yes—
268#14556572C2312yes—
269#14556572C2314yescomplemented
270#14556571C2314yes—
271#14556571C2314yes—
272#14556571C2312yes—
273#14556571C2318yes—
274#14556571C2314yes—
275#14556571C2314yes—
276#14556571C2314yescomplemented
277#14556571C2318yescomplemented
278#14556570C2314yes—
279#14556570C2314yes—
280#14556570C2312yes—
281#14556570C2318yes—
282#14556570C2314yes—
283#14556570C2314yes—
284#14556570C2314yescomplemented
285#14556570C2318yescomplemented
286#14556569C2318yes—
287#14556569C2318yes—
288#14556569C2314yes—
289#14556569C2318yes—
290#14556569C2318yes—
291#14556569C2318yes—
292#14556569C2318yes—
293#14556569C2318yescomplemented
294#14556569C2318yescomplemented
295#14556569C2318yescomplemented
296#14556568C2318yes—
297#14556568C2318yes—
298#14556568C2314yes—
299#14556568C2318yes—
300#14556568C2318yes—
301#14556568C2318yes—
302#14556568C2318yes—
303#14556568C2318yescomplemented
304#14556568C2318yescomplemented
305#14556568C2318yescomplemented
306#14556567C2314yes—
307#14556567C2314yes—
308#14556567C2312yes—
309#14556567C2318yes—
310#14556567C2314yes—
311#14556567C2314yes—
312#14556567C2314yescomplemented
313#14556567C2318yescomplemented
314#14556566C2312yes—
315#14556565C2312yes—
316#14556564C2314yes—
317#14556563C2314yes—
318#14556562C2312yes—
319#14556561C2314yes—
320#14556561C2312yes—
321#14556560C2312yes—
322#14556559C2314yes—
323#14556559C2312yes—
324Q8×Dic73C2314yescomplemented
325C4×Dic146C2318yescomplemented
326C4×Dic146C2314yescomplemented
327#14556556C2318yescomplemented
328#14556556C2314yescomplemented
329C4×D292C2318yes—
330C4×D292C2314yes—
331D4×Dic73C2318yes—
332D4×Dic73C2314yes—
333#14556553C2318yes—
334#14556553C2314yes—
335C4×C22⋊D73C2318yes—
336C4×C22⋊D73C2318yes—
337C4×C22⋊D73C2314yes—
338C4×C22⋊D73C2314yes—
339#14556551C2318yes—
340#14556551C2318yes—
341#14556551C2314yes—
342#14556551C2314yes—
343#14556550C2311yescharacteristic
344#14556550C2318yes—
345#14556550C2312yescomplemented
346#14556549C2312yes—
347#14556549C2318yes—
348#14556549C2318yes—
349#14556549C2314yescomplemented
350#14556548C2312yes—
351#14556548C2318yes—
352#14556548C2318yes—
353#14556548C2314yescomplemented
354#14556547C2312yes—
355#14556547C2318yes—
356#14556547C2318yes—
357#14556547C2314yescomplemented
358C2×C4⋊Dic73C2314yes—
359C2×C4⋊Dic73C2312yes—
360C2×#11924007C2314yes—
361C2×#11924007C2314yes—
362C2×#11924007C2314yes—
363C4⋊C4×D73C2318yes—
364C4⋊C4×D73C2318yes—
365C4⋊C4×D73C2314yes—
366C4⋊C4×D73C2318yes—
367C4⋊C4×D73C2318yes—
368C4⋊C4×D73C2318yes—
369C4⋊C4×D73C2318yes—
370C4⋊C4×D73C2314yes—
371C4⋊C4×D73C2314yes—
372C4⋊C4×D73C2314yes—
373C4⋊C4×D73C2314yes—
374C4⋊C4×D73C2312yes—
375C4⋊C4×D73C2318yes—
376C4⋊C4×D73C2318yes—
377C2×C22⋊Dic73C2314yes—
378C2×#11924005C2314yes—
379C2×#11924005C2314yes—
380C22⋊C4×D73C2318yes—
381C22⋊C4×D73C2318yes—
382C22⋊C4×D73C2318yes—
383C22⋊C4×D73C2318yes—
384C22⋊C4×D73C2314yes—
385C22⋊C4×D73C2312yes—
386C22⋊C4×D73C2314yes—
387C22⋊C4×D73C2314yes—
388C22⋊C4×D73C2318yes—
389C42×D73C2314yes—
390C42×D73C2312yes—
391C42×D73C2318yes—
392C2×#41×C73C2311yescharacteristic
393C22×Q8×C73C2312yes—
394C22×Q8×C73C2312yescomplemented
395C23×C4×C73C2311yescharacteristic
396C4⋊Q8×C73C2314yescomplemented
397C4⋊Q8×C73C2312yescomplemented
398C4⋊Q8×C73C2318yescomplemented
399#126×C73C2318yes—
400#126×C73C2318yescomplemented
401#125×C73C2318yescomplemented
402#125×C73C2312yescomplemented
403#125×C73C2318yescomplemented
404#124×C73C2314yes—
405#123×C73C2314yes—
406#123×C73C2318yes—
407#123×C73C2312yes—
408#123×C73C2314yescomplemented
409C22⋊Q8×C73C2314yes—
410C22⋊Q8×C73C2314yes—
411C22⋊Q8×C73C2312yes—
412C22⋊Q8×C73C2318yes—
413C22⋊Q8×C73C2314yes—
414C22⋊Q8×C73C2314yes—
415C22⋊Q8×C73C2314yescomplemented
416C22⋊Q8×C73C2318yescomplemented
417#121×C73C2312yes—
418#120×C73C2312yes—
419C4×Q8×C73C2314yescomplemented
420C4×D4×C73C2318yes—
421C4×D4×C73C2314yes—
422#117×C73C2311yescharacteristic
423#117×C73C2318yes—
424#117×C73C2312yescomplemented
425C2×C4⋊C4×C73C2314yes—
426C2×C4⋊C4×C73C2312yes—
427C2×C22⋊C4×C73C2314yes—
428C23×D73—28no—
429C23×D73—42no—
430C23×D73C2411yescharacteristic
431C23×D73C2412yes—
432C23×D73C2411yescharacteristic
433C23×D73C2412yes—
434C23×D73C2412yes—
435#11924029—42no—
436#11924028—44no—
437#11924028—42no—
438#11924027—42no—
439#11924027—44no—
440C2×Dic146—48no—
441C2×Dic146—48no—
442C2×Dic146—44no—
443C2×Dic146—44no—
444C2×Dic146C2418yes—
445C2×Dic146C2414yes—
446C2×Dic146C2418yes—
447C2×Dic146C2414yes—
448C2×Dic146C2412yes—
449C2×Dic146C2418yes—
450C2×Dic146C2414yes—
451C2×Dic146C2411yescharacteristic
452Q8×D73—216no—
453Q8×D73—48no—
454Q8×D73—48no—
455Q8×D73—48no—
456Q8×D73—48no—
457Q8×D73—48no—
458Q8×D73—48no—
459Q8×D73—42no—
460C2×D292C2414yes—
461C2×D292C2412yes—
462C2×D292C2411yescharacteristic
463C2×C22⋊D73C2414yes—
464C2×C22⋊D73C2414yes—
465C2×C22⋊D73C2412yes—
466C2×C22⋊D73C2412yes—
467C2×C22⋊D73C2412yes—
468D4×D73—216no—
469D4×D73—42no—
470D4×D73—44no—
471C22×Dic73—42no—
472C22×Dic73C2414yes—
473C22×Dic73C2412yes—
474C22×Dic73C2411yescharacteristic
475C22×Dic73C2412yes—
476C22×Dic73C2414yes—
477C22×Dic73C2412yes—
478C22×Dic73C2414yes—
479C22×Dic73C2411yescharacteristic
480C2×C4×D73—216no—
481C2×C4×D73—28no—
482C2×C4×D73—24no—
483C2×C4×D73—28no—
484C2×C4×D73—42no—
485C2×C4×D73—44no—
486C2×C4×D73—42no—
487C2×C4×D73—44no—
488C2×C4×D73—44no—
489C2×C4×D73—42no—
490C2×C4×D73—48no—
491C2×C4×D73—48no—
492C2×C4×D73C2414yes—
493C2×C4×D73C2418yes—
494C2×C4×D73C2412yes—
495C2×C4×D73C2418yes—
496C2×C4×D73C2412yes—
497C2×C4×D73C2418yes—
498C2×C4×D73C2411yescharacteristic
499C2×C4×D73C2412yes—
500C2×C4×D73C2412yes—
501C2×C4×D73C2411yescharacteristic
502C2×C4×D73C2412yes—
503C2×C4×D73C2411yescharacteristic
504C2×C4×D73C2412yes—
505C2×C4×D73C2418yes—
506C2×C4×D73C2412yes—
507C2×C4×D73C2412yes—
508C2×C4×D73C2418yes—
509C2×C4×D73C2412yes—
510C2×C4×D73C2411yescharacteristic
511C4⋊Dic73C2414yes—
512C4⋊Dic73C2414yes—
513C4⋊Dic73C2418yes—
514C4⋊Dic73C2418yes—
515C4⋊Dic73C2412yes—
516C4⋊Dic73C2418yes—
517C4⋊Dic73C2418yes—
518C4⋊Dic73C2418yes—
519C4⋊Dic73C2414yes—
520C4⋊Dic73C2418yes—
521#11924007C2418yes—
522#11924007C2418yes—
523#11924007C2418yes—
524#11924007C2418yes—
525#11924007C2418yes—
526#11924007C2418yes—
527#11924007C2414yes—
528#11924007C2418yes—
529#11924007C2418yes—
530#11924007C2418yes—
531#11924007C2418yes—
532#11924007C2418yes—
533#11924007C2414yes—
534#11924007C2418yes—
535#11924007C2414yes—
536#11924007C2418yes—
537#11924007C2418yes—
538C22⋊Dic73C2418yes—
539C22⋊Dic73C2418yes—
540C22⋊Dic73C2414yes—
541C22⋊Dic73C2412yes—
542C22⋊Dic73C2414yes—
543C22⋊Dic73C2414yes—
544C22⋊Dic73C2418yes—
545#11924005C2418yes—
546#11924005C2418yes—
547#11924005C2418yes—
548#11924005C2418yes—
549#11924005C2414yes—
550#11924005C2414yes—
551#11924005C2414yes—
552#11924005C2418yes—
553#11924005C2414yes—
554#11924005C2418yes—
555#11924005C2414yes—
556#11924005C2418yes—
557C4×Dic73C2414yes—
558C4×Dic73C2418yes—
559C4×Dic73C2414yes—
560C4×Dic73C2418yes—
561C4×Dic73C2418yes—
562C4×Dic73C2418yes—
563C4×Dic73C2412yes—
564C24×C73C2411yescharacteristic
565#41×C73—42no—
566C2×Q8×C73—44no—
567C2×Q8×C73—44no—
568C2×Q8×C73C2414yes—
569C2×Q8×C73C2414yes—
570C2×Q8×C73C2414yes—
571C2×Q8×C73C2411yescharacteristic
572C2×D4×C73C2414yes—
573C2×D4×C73C2412yes—
574C2×D4×C73C2411yescharacteristic
575C22×C4×C73—42no—
576C22×C4×C73C2414yes—
577C22×C4×C73C2412yes—
578C22×C4×C73C2411yescharacteristic
579C22×C4×C73C2412yes—
580C22×C4×C73C2414yes—
581C22×C4×C73C2412yes—
582C22×C4×C73C2414yes—
583C22×C4×C73C2411yescharacteristic
584C4⋊C4×C73C2414yes—
585C4⋊C4×C73C2418yes—
586C4⋊C4×C73C2418yes—
587C4⋊C4×C73C2414yes—
588C4⋊C4×C73C2412yes—
589C4⋊C4×C73C2418yes—
590C4⋊C4×C73C2418yes—
591C4⋊C4×C73C2418yes—
592C4⋊C4×C73C2414yes—
593C4⋊C4×C73C2418yes—
594C22⋊C4×C73C2418yes—
595C22⋊C4×C73C2418yes—
596C22⋊C4×C73C2414yes—
597C22⋊C4×C73C2412yes—
598C22⋊C4×C73C2414yes—
599C22⋊C4×C73C2414yes—
600C22⋊C4×C73C2418yes—
601C42×C73C2414yes—
602C42×C73C2412yes—
603C42×C73C2418yes—
604C23×C73—24no—
605C23×C73—41no—
606C23×C73C2511yescharacteristic
607C23×C73C2512yes—
608C23×C73C2512yes—
609C22×D73—24no—
610C22×D73—24no—
611C22×D73—24no—
612C22×D73—24no—
613C22×D73—22no—
614C22×D73—28no—
615C22×D73—24no—
616C22×D73—24no—
617C22×D73—24no—
618C22×D73—41no—
619C22×D73—42no—
620C22×D73—416no—
621C22×D732−1+418yes—
622C22×D73C2511yescharacteristic
623C22×D73C2512yes—
624C22×D73C2512yes—
625C22×D73C2511yescharacteristic
626Q8×C73—28no—
627Q8×C73—44no—
628Q8×C73—44no—
629Q8×C73—41no—
630D4×C73—28no—
631D4×C73—42no—
632D4×C73—41no—
633C2×C4×C73—28no—
634C2×C4×C73—24no—
635C2×C4×C73—22no—
636C2×C4×C73—24no—
637C2×C4×C73—41no—
638C2×C4×C73—42no—
639C2×C4×C73—44no—
640C2×C4×C73—44no—
641C2×C4×C73C2514yes—
642C2×C4×C73C2518yes—
643C2×C4×C73C2512yes—
644C2×C4×C73C2518yes—
645C2×C4×C73C2512yes—
646C2×C4×C73C2511yescharacteristic
647C2×C4×C73C2511yescharacteristic
648C22⋊D73—28no—
649C22⋊D73—28no—
650C22⋊D73—42no—
651C22⋊D73—42no—
652C22⋊D73—42no—
653C2×Dic73—28no—
654C2×Dic73—24no—
655C2×Dic73—22no—
656C2×Dic73—24no—
657C2×Dic73—41no—
658C2×Dic73—42no—
659C2×Dic73—44no—
660C2×Dic73—44no—
661C2×Dic73C2514yes—
662C2×Dic73C2518yes—
663C2×Dic73C2512yes—
664C2×Dic73C2518yes—
665C2×Dic73C2512yes—
666C2×Dic73C2511yescharacteristic
667C2×Dic73C2511yescharacteristic
668D292—28no—
669D292—42no—
670D292—41no—
671C4×D73—22no—
672C4×D73—24no—
673C4×D73—24no—
674C4×D73—216no—
675C4×D73—216no—
676C4×D73—216no—
677C4×D73—28no—
678C4×D73—24no—
679C4×D73—22no—
680C4×D73—24no—
681C4×D73—24no—
682C4×D73—22no—
683C4×D73—24no—
684C4×D73—42no—
685C4×D73—42no—
686C4×D73—42no—
687C4×D73—48no—
688C4×D73—48no—
689C4×D73H(5,𝔽2)14yes—
690Dic146—28no—
691Dic146—216no—
692Dic146—44no—
693Dic146—44no—
694Dic146—48no—
695Dic146—48no—
696Dic146—41no—
697Dic146—42no—
698C22×C73—22no—
699C22×C73—22no—
700C22×C73—22no—
701C22×C73—21no—
702C22×C73—24no—
703C22×C73—22no—
704C22×C73—44no—
705C22×C73C2×2−1+414yes—
706C22×C73C2611yescharacteristic
707C2×D73—22no—
708C2×D73—22no—
709C2×D73—216no—
710C2×D73—22no—
711C2×D73—21no—
712C2×D73—24no—
713C2×D73—22no—
714C2×D73—44no—
715C2×D73—48no—
716C2×D73—48no—
717C2×D73—44no—
718C2×D73C2×H(5,𝔽2)12yes—
719C2×D73C2×2−1+414yes—
720C2×D73C2×2−1+414yes—
721C4×C73—28no—
722C4×C73—22no—
723C4×C73—22no—
724C4×C73—21no—
725C4×C73—28no—
726C4×C73—24no—
727C4×C73C2×H(5,𝔽2)12yes—
728Dic73—28no—
729Dic73—22no—
730Dic73—22no—
731Dic73—21no—
732Dic73—28no—
733Dic73—24no—
734Dic73C2×H(5,𝔽2)12yes—
735C2×#3538—731nomaximal, Sylow
736C2×C73—24no—
737C2×C73—41no—
738C2×C73—42no—
739C2×C73C22×H(5,𝔽2)11yescharacteristic
740C2×C73C22×2−1+412yes—
741D73—24no—
742D73—42no—
743D73—41no—
744D73#353814yesdirect product factor
745#3538—734no—
746#3538—734no—
747#3538—734no—
748#3538—734no—
749#3538—734no—
750#3538—732no—
751#3538—734no—
752#3538—732no—
753#3538—731no—
754#3538—732no—
755#3538D7311yescharacteristic, direct product factor
756C2×#563—734no—
757C2×#552—734no—
758C2×#551—734no—
759C2×D4×Q8—734no—
760C2×#544—734no—
761C2×#541—732no—
762C2×#539—734no—
763C2×#536—732no—
764C2×#525—731no—
765C22×C22⋊Q8—732no—
766C73C2×#353811yescharacteristic, complemented, Sylow
767C22×#41—731no—
768C23×Q8—732no—
769C23×Q8—732no—
770C24×C4—731no—
771#563—738no—
772#563—738no—
773#563—738no—
774#563—738no—
775#563—734no—
776#563—734no—
777#563—734no—
778#563—738no—
779#563—738no—
780#563C2×D7314yescomplemented
781#552—738no—
782#552—738no—
783#552—734no—
784#552—738no—
785#552—734no—
786#552—734no—
787#552—734no—
788#552—734no—
789#552—738no—
790#552—734no—
791#552—734no—
792#552C2×D7314yescomplemented
793#551—738no—
794#551—734no—
795#551—738no—
796#551—734no—
797#551—738no—
798#551—734no—
799#551—738no—
800#551—738no—
801#551—738no—
802#551C2×D7314yescomplemented
803D4×Q8—734no—
804D4×Q8—734no—
805D4×Q8—738no—
806D4×Q8—734no—
807D4×Q8—734no—
808D4×Q8—738no—
809D4×Q8—734no—
810D4×Q8—738no—
811D4×Q8—734no—
812D4×Q8—738no—
813D4×Q8—734no—
814D4×Q8C2×D7314yescomplemented
815#544—738no—
816#544—738no—
817#544—738no—
818#544—738no—
819#544—734no—
820#544—734no—
821#544—738no—
822#544—738no—
823#544—734no—
824#544C2×D7314yescomplemented
825#541—732no—
826#541—738no—
827#541—738no—
828#541—732no—
829#541—734no—
830#541—734no—
831#541—732no—
832#541C2×D7312yescomplemented
833#539—738no—
834#539—738no—
835#539—738no—
836#539—738no—
837#539—734no—
838#539—738no—
839#539—734no—
840#539—738no—
841#539—734no—
842#539C2×D7314yescomplemented
843#536—732no—
844#536—732no—
845#536—734no—
846#536—734no—
847#536—734no—
848#536—734no—
849#536—734no—
850#536—734no—
851#536—732no—
852#536C2×D7312yescomplemented
853C2×C4⋊Q8—734no—
854C2×C4⋊Q8—732no—
855C2×C4⋊Q8—738no—
856C2×#126—738no—
857C2×#126—738no—
858C2×#125—738no—
859C2×#125—732no—
860C2×#125—738no—
861C2×#124—734no—
862#525—731no—
863#525—731no—
864#525—732no—
865#525—732no—
866#525—732no—
867#525—732no—
868#525—734no—
869#525—731no—
870#525C2×D7311yescharacteristic
871C2×#123—732no—
872C2×#123—734no—
873C2×#123—738no—
874C2×#123—734no—
875C2×C22⋊Q8—732no—
876C2×C22⋊Q8—732no—
877C2×C22⋊Q8—734no—
878C2×C22⋊Q8—734no—
879C2×C22⋊Q8—734no—
880C2×C22⋊Q8—734no—
881C2×C22⋊Q8—734no—
882C2×C22⋊Q8—734no—
883C2×C22⋊Q8—734no—
884C2×C22⋊Q8—734no—
885C2×C22⋊Q8—732no—
886C2×C22⋊Q8—738no—
887C2×C22⋊Q8—734no—
888C2×C22⋊Q8—738no—
889C2×C22⋊Q8—734no—
890C2×C22⋊Q8—732no—
891C2×C22⋊Q8—734no—
892C2×C22⋊Q8C2×D7312yescomplemented
893C2×#121—732no—
894C2×#120—732no—
895C2×C4×Q8—734no—
896C2×C4×D4—734no—
897C2×C4×D4—738no—
898C2×#117—731no—
899C2×#117—738no—
900C2×#117—732no—
901C22×C4⋊C4—734no—
902C22×C4⋊C4—732no—
903C22×C22⋊C4—734no—
904C25—731no—
905C2×#41—2924no—
906C2×#41—731no—
907C2×#41—731no—
908C2×#41—732no—
909C2×#41—731no—
910C2×#41—732no—
911C2×#41C22×D7311yescharacteristic
912C22×Q8—2928no—
913C22×Q8—2928no—
914C22×Q8—734no—
915C22×Q8—734no—
916C22×Q8—731no—
917C22×Q8—734no—
918C22×Q8—734no—
919C22×Q8—734no—
920C22×Q8—734no—
921C22×Q8—734no—
922C22×Q8—732no—
923C22×Q8—734no—
924C22×Q8—732no—
925C22×Q8—734no—
926C22×Q8C22×D7312yes—
927C22×Q8C22×D7312yescomplemented
928C22×D4—732no—
929C22×D4—731no—
930C22×D4—734no—
931C23×C4—2924no—
932C23×C4—731no—
933C23×C4—734no—
934C23×C4—732no—
935C23×C4—734no—
936C23×C4—731no—
937C23×C4—732no—
938C23×C4—731no—
939C23×C4—731no—
940C23×C4—732no—
941C23×C4—734no—
942C23×C4—732no—
943C23×C4—732no—
944C23×C4—731no—
945C23×C4C22×D7311yescharacteristic
946C4⋊Q8—734no—
947C4⋊Q8—734no—
948C4⋊Q8—734no—
949C4⋊Q8—738no—
950C4⋊Q8—738no—
951C4⋊Q8—738no—
952C4⋊Q8—738no—
953C4⋊Q8—738no—
954C4⋊Q8—738no—
955C4⋊Q8—738no—
956C4⋊Q8—738no—
957C4⋊Q8—738no—
958C4⋊Q8—734no—
959C4⋊Q8—732no—
960C4⋊Q8—738no—
961C4⋊Q8C22×D7314yescomplemented
962C4⋊Q8C22×D7312yescomplemented
963C4⋊Q8C22×D7318yescomplemented
964#126—738no—
965#126—738no—
966#126—738no—
967#126—738no—
968#126—738no—
969#126—738no—
970#126—738no—
971#126—738no—
972#126—738no—
973#126—738no—
974#126—738no—
975#126—738no—
976#126—738no—
977#126—738no—
978#126C22×D7318yes—
979#126C22×D7318yescomplemented
980#125—738no—
981#125—738no—
982#125—738no—
983#125—738no—
984#125—738no—
985#125—738no—
986#125—738no—
987#125—734no—
988#125—738no—
989#125—738no—
990#125—738no—
991#125—738no—
992#125—738no—
993#125—738no—
994#125—738no—
995#125—732no—
996#125—738no—
997#125C22×D7318yescomplemented
998#125C22×D7312yescomplemented
999#125C22×D7318yescomplemented
1000#124—734no—
1001#124—734no—
1002#124—738no—
1003#124—738no—
1004#124—734no—
1005#124C22×D7314yes—
1006#123—732no—
1007#123—734no—
1008#123—734no—
1009#123—738no—
1010#123—732no—
1011#123—734no—
1012#123—734no—
1013#123—738no—
1014#123—734no—
1015#123—738no—
1016#123—738no—
1017#123—738no—
1018#123—738no—
1019#123—734no—
1020#123—732no—
1021#123—738no—
1022#123—734no—
1023#123—738no—
1024#123—734no—
1025#123—738no—
1026#123—738no—
1027#123—738no—
1028#123C22×D7312yes—
1029#123C22×D7314yes—
1030#123C22×D7318yes—
1031#123C22×D7314yescomplemented
1032C22⋊Q8—734no—
1033C22⋊Q8—734no—
1034C22⋊Q8—734no—
1035C22⋊Q8—734no—
1036C22⋊Q8—732no—
1037C22⋊Q8—734no—
1038C22⋊Q8—738no—
1039C22⋊Q8—738no—
1040C22⋊Q8—734no—
1041C22⋊Q8—734no—
1042C22⋊Q8—734no—
1043C22⋊Q8—734no—
1044C22⋊Q8—732no—
1045C22⋊Q8—734no—
1046C22⋊Q8—738no—
1047C22⋊Q8—738no—
1048C22⋊Q8—738no—
1049C22⋊Q8—734no—
1050C22⋊Q8—738no—
1051C22⋊Q8—734no—
1052C22⋊Q8—738no—
1053C22⋊Q8—734no—
1054C22⋊Q8—738no—
1055C22⋊Q8—734no—
1056C22⋊Q8—734no—
1057C22⋊Q8—732no—
1058C22⋊Q8—738no—
1059C22⋊Q8—734no—
1060C22⋊Q8—738no—
1061C22⋊Q8—738no—
1062C22⋊Q8—738no—
1063C22⋊Q8—738no—
1064C22⋊Q8—738no—
1065C22⋊Q8—738no—
1066C22⋊Q8—738no—
1067C22⋊Q8—738no—
1068C22⋊Q8—738no—
1069C22⋊Q8—738no—
1070C22⋊Q8—734no—
1071C22⋊Q8—738no—
1072C22⋊Q8—738no—
1073C22⋊Q8—738no—
1074C22⋊Q8—738no—
1075C22⋊Q8—738no—
1076C22⋊Q8C22×D7314yes—
1077C22⋊Q8C22×D7314yes—
1078C22⋊Q8C22×D7314yes—
1079C22⋊Q8C22×D7314yes—
1080C22⋊Q8C22×D7312yes—
1081C22⋊Q8C22×D7318yes—
1082C22⋊Q8C22×D7314yescomplemented
1083C22⋊Q8C22×D7318yescomplemented
1084#121—732no—
1085#121—734no—
1086#121—732no—
1087#121—732no—
1088#121—734no—
1089#121C22×D7312yes—
1090#120—732no—
1091#120—734no—
1092#120—732no—
1093#120—732no—
1094#120—734no—
1095#120C22×D7312yes—
1096C4×Q8—734no—
1097C4×Q8—738no—
1098C4×Q8—734no—
1099C4×Q8—738no—
1100C4×Q8—734no—
1101C4×Q8C22×D7314yescomplemented
1102C4×D4—734no—
1103C4×D4—738no—
1104C4×D4—734no—
1105C4×D4—734no—
1106C4×D4—738no—
1107C4×D4—738no—
1108C4×D4—734no—
1109C4×D4—738no—
1110C4×D4—734no—
1111C4×D4—734no—
1112C4×D4—738no—
1113C4×D4—738no—
1114C4×D4—734no—
1115C4×D4—738no—
1116C4×D4C22×D7314yes—
1117C4×D4C22×D7318yes—
1118#117—731no—
1119#117—732no—
1120#117—738no—
1121#117—732no—
1122#117—734no—
1123#117—738no—
1124#117—738no—
1125#117—732no—
1126#117—734no—
1127#117—738no—
1128#117—738no—
1129#117—732no—
1130#117—734no—
1131#117—738no—
1132#117—738no—
1133#117C22×D7311yescharacteristic
1134#117C22×D7318yes—
1135#117C22×D7312yescomplemented
1136C2×C4⋊C4—734no—
1137C2×C4⋊C4—734no—
1138C2×C4⋊C4—734no—
1139C2×C4⋊C4—734no—
1140C2×C4⋊C4—732no—
1141C2×C4⋊C4—734no—
1142C2×C4⋊C4—738no—
1143C2×C4⋊C4—738no—
1144C2×C4⋊C4—734no—
1145C2×C4⋊C4—738no—
1146C2×C4⋊C4—738no—
1147C2×C4⋊C4—734no—
1148C2×C4⋊C4—734no—
1149C2×C4⋊C4—732no—
1150C2×C4⋊C4—738no—
1151C2×C4⋊C4—738no—
1152C2×C4⋊C4—738no—
1153C2×C4⋊C4—734no—
1154C2×C4⋊C4—738no—
1155C2×C4⋊C4C22×D7314yes—
1156C2×C4⋊C4C22×D7312yes—
1157C2×C22⋊C4—734no—
1158C2×C22⋊C4—734no—
1159C2×C22⋊C4—734no—
1160C2×C22⋊C4—738no—
1161C2×C22⋊C4—738no—
1162C2×C22⋊C4—738no—
1163C2×C22⋊C4—738no—
1164C2×C22⋊C4—734no—
1165C2×C22⋊C4—732no—
1166C2×C22⋊C4—734no—
1167C2×C22⋊C4—734no—
1168C2×C22⋊C4—738no—
1169C2×C22⋊C4C22×D7314yes—
1170C2×C42—734no—
1171C2×C42—732no—
1172C2×C42—738no—
1173C24—2922no—
1174C24—731no—
1175C24—732no—
1176C24—732no—
1177C24—731no—
1178C24—732no—
1179C24—1468no—
1180C24C23×D7311yescharacteristic
1181#41—42no—
1182#41—2922no—
1183#41—2924no—
1184#41—2922no—
1185#41—2924no—
1186#41—2922no—
1187C2×Q8—44no—
1188C2×Q8—44no—
1189C2×Q8—2924no—
1190C2×Q8—2924no—
1191C2×Q8—2928no—
1192C2×Q8—2928no—
1193C2×Q8—2928no—
1194C2×Q8—2928no—
1195C2×Q8—2928no—
1196C2×Q8—2928no—
1197C2×Q8—2928no—
1198C2×Q8—2928no—
1199C2×Q8—2922no—
1200C2×Q8—734no—
1201C2×Q8—738no—
1202C2×Q8—738no—
1203C2×Q8—734no—
1204C2×Q8—731no—
1205C2×Q8—732no—
1206C2×Q8—738no—
1207C2×Q8—734no—
1208C2×Q8—14616no—
1209C2×Q8C23×D7314yes—
1210C2×Q8C23×D7314yes—
1211C2×Q8C23×D7314yes—
1212C2×Q8C23×D7311yescharacteristic
1213C2×D4—2922no—
1214C2×D4—2924no—
1215C2×D4—732no—
1216C2×D4—732no—
1217C2×D4—732no—
1218C2×D4—734no—
1219C2×D4—734no—
1220C2×D4—732no—
1221C2×D4—731no—
1222C2×D4—734no—
1223C2×D4—14616no—
1224C2×D4C23×D7314yes—
1225C2×D4C23×D7312yes—
1226C2×D4C23×D7311yescharacteristic
1227C22×C4—42no—
1228C22×C4—2924no—
1229C22×C4—2922no—
1230C22×C4—2924no—
1231C22×C4—2922no—
1232C22×C4—2928no—
1233C22×C4—2928no—
1234C22×C4—2922no—
1235C22×C4—2924no—
1236C22×C4—2922no—
1237C22×C4—734no—
1238C22×C4—732no—
1239C22×C4—734no—
1240C22×C4—731no—
1241C22×C4—738no—
1242C22×C4—732no—
1243C22×C4—732no—
1244C22×C4—738no—
1245C22×C4—732no—
1246C22×C4—731no—
1247C22×C4—734no—
1248C22×C4—732no—
1249C22×C4—732no—
1250C22×C4—731no—
1251C22×C4—734no—
1252C22×C4—738no—
1253C22×C4—732no—
1254C22×C4—738no—
1255C22×C4—732no—
1256C22×C4—738no—
1257C22×C4—731no—
1258C22×C4—732no—
1259C22×C4—732no—
1260C22×C4—732no—
1261C22×C4—732no—
1262C22×C4—731no—
1263C22×C4—731no—
1264C22×C4—1468no—
1265C22×C4—1464no—
1266C22×C4—1468no—
1267C22×C4—14616no—
1268C22×C4C23×D7314yes—
1269C22×C4C23×D7312yes—
1270C22×C4C23×D7311yescharacteristic
1271C22×C4C23×D7312yes—
1272C22×C4C23×D7314yes—
1273C22×C4C23×D7312yes—
1274C22×C4C23×D7314yes—
1275C22×C4C23×D7311yescharacteristic
1276C4⋊C4—738no—
1277C4⋊C4—738no—
1278C4⋊C4—738no—
1279C4⋊C4—738no—
1280C4⋊C4—738no—
1281C4⋊C4—738no—
1282C4⋊C4—734no—
1283C4⋊C4—738no—
1284C4⋊C4—738no—
1285C4⋊C4—738no—
1286C4⋊C4—738no—
1287C4⋊C4—738no—
1288C4⋊C4—738no—
1289C4⋊C4—734no—
1290C4⋊C4—734no—
1291C4⋊C4—738no—
1292C4⋊C4—738no—
1293C4⋊C4—734no—
1294C4⋊C4—738no—
1295C4⋊C4—738no—
1296C4⋊C4—734no—
1297C4⋊C4—732no—
1298C4⋊C4—738no—
1299C4⋊C4—738no—
1300C4⋊C4—738no—
1301C4⋊C4—734no—
1302C4⋊C4—738no—
1303C4⋊C4C23×D7314yes—
1304C4⋊C4C23×D7318yes—
1305C4⋊C4C23×D7318yes—
1306C4⋊C4C23×D7314yes—
1307C4⋊C4C23×D7312yes—
1308C4⋊C4C23×D7318yes—
1309C4⋊C4C23×D7318yes—
1310C4⋊C4C23×D7318yes—
1311C4⋊C4C23×D7314yes—
1312C4⋊C4C23×D7318yes—
1313C22⋊C4—738no—
1314C22⋊C4—738no—
1315C22⋊C4—734no—
1316C22⋊C4—732no—
1317C22⋊C4—734no—
1318C22⋊C4—734no—
1319C22⋊C4—738no—
1320C22⋊C4—738no—
1321C22⋊C4—738no—
1322C22⋊C4—738no—
1323C22⋊C4—738no—
1324C22⋊C4—734no—
1325C22⋊C4—734no—
1326C22⋊C4—734no—
1327C22⋊C4—738no—
1328C22⋊C4—734no—
1329C22⋊C4—734no—
1330C22⋊C4—738no—
1331C22⋊C4—738no—
1332C22⋊C4C23×D7318yes—
1333C22⋊C4C23×D7318yes—
1334C22⋊C4C23×D7314yes—
1335C22⋊C4C23×D7312yes—
1336C22⋊C4C23×D7314yes—
1337C22⋊C4C23×D7314yes—
1338C22⋊C4C23×D7318yes—
1339C42—734no—
1340C42—738no—
1341C42—734no—
1342C42—732no—
1343C42—738no—
1344C42—738no—
1345C42—738no—
1346C42C23×D7314yes—
1347C42C23×D7312yes—
1348C42C23×D7318yes—
1349C23—24no—
1350C23—41no—
1351C23—2922no—
1352C23—2921no—
1353C23—29216no—
1354C23—731no—
1355C23—738no—
1356C23—732no—
1357C23—731no—
1358C23—732no—
1359C23—1464no—
1360C23—1462no—
1361C23—1468no—
1362C23—1464no—
1363C23—1464no—
1364C23—1464no—
1365C23—1464no—
1366C23—1464no—
1367C23—1464no—
1368C23C24×D7311yescharacteristic
1369C23C24×D7312yes—
1370C23C24×D7312yes—
1371Q8—28no—
1372Q8—44no—
1373Q8—44no—
1374Q8—41no—
1375Q8—2924no—
1376Q8—2924no—
1377Q8—2928no—
1378Q8—2928no—
1379Q8—2921no—
1380Q8—2922no—
1381Q8—14616no—
1382Q8—1468no—
1383D4—28no—
1384D4—41no—
1385D4—42no—
1386D4—2921no—
1387D4—2922no—
1388D4—2922no—
1389D4—2922no—
1390D4—2922no—
1391D4—1468no—
1392D4—1468no—
1393D4—1468no—
1394C2×C4—28no—
1395C2×C4—24no—
1396C2×C4—22no—
1397C2×C4—24no—
1398C2×C4—42no—
1399C2×C4—41no—
1400C2×C4—44no—
1401C2×C4—44no—
1402C2×C4—2922no—
1403C2×C4—2922no—
1404C2×C4—2922no—
1405C2×C4—2928no—
1406C2×C4—2928no—
1407C2×C4—2922no—
1408C2×C4—2921no—
1409C2×C4—2924no—
1410C2×C4—2924no—
1411C2×C4—731no—
1412C2×C4—734no—
1413C2×C4—734no—
1414C2×C4—738no—
1415C2×C4—732no—
1416C2×C4—738no—
1417C2×C4—732no—
1418C2×C4—731no—
1419C2×C4—1464no—
1420C2×C4—1462no—
1421C2×C4—1464no—
1422C2×C4—1462no—
1423C2×C4—1464no—
1424C2×C4—14616no—
1425C2×C4—1464no—
1426C2×C4—14616no—
1427C2×C4—14616no—
1428C2×C4—1468no—
1429C2×C4—1464no—
1430C2×C4—1462no—
1431C2×C4—1464no—
1432C2×C4—1468no—
1433C2×C4—1464no—
1434C2×C4—1462no—
1435C2×C4—1464no—
1436C2×C4C24×D7314yes—
1437C2×C4C24×D7318yes—
1438C2×C4C24×D7312yes—
1439C2×C4C24×D7318yes—
1440C2×C4C24×D7312yes—
1441C2×C4C24×D7311yescharacteristic
1442C2×C4C24×D7311yescharacteristic
1443C22—22no—
1444C22—22no—
1445C22—22no—
1446C22—21no—
1447C22—24no—
1448C22—22no—
1449C22—44no—
1450C22—2928no—
1451C22—2924no—
1452C22—2928no—
1453C22—2924no—
1454C22—732no—
1455C22—734no—
1456C22—734no—
1457C22—14616no—
1458C22—1462no—
1459C22—1461no—
1460C22—1464no—
1461C22—1462no—
1462C22—1462no—
1463C22—1462no—
1464C222−1+4×D7314yes—
1465C22C25×D7311yescharacteristic
1466C4—21no—
1467C4—22no—
1468C4—22no—
1469C4—28no—
1470C4—28no—
1471C4—24no—
1472C4—732no—
1473C4—1461no—
1474C4—1462no—
1475C4—1468no—
1476C4—1462no—
1477C4—1468no—
1478C4—1464no—
1479C4H(5,𝔽2)×D7312yes—
1480C2—24no—
1481C2—41no—
1482C2—42no—
1483C2—2921no—
1484C2—2922no—
1485C2—734no—
1486C2—1464no—
1487C2C2×H(5,𝔽2)×D7311yescharacteristic
1488C2C2×2−1+4×D7312yes—
subgroupG/H
center, FrattiniC22C25×D73
commutator, socle, cosocleC22×C73C26
FittingC73×#3538C2
prime radical#525×D73C2
hypercenter#3538D73
hypocenterC73C2×#3538
LCSG ▷ C22×C73 ▷ C73
UCSC1 ◁ C22 ◁ #3538

Complements

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

NH ≅ G/Ntype
1. #22624180C2semidirect
2. #22624179C2semidirect
3. #22624178C2semidirect
4. #22624177C2semidirect
5. #22624176C2semidirect
6. #22624175C2semidirect
7. #22624174C2semidirect
8. #22624173C2semidirect
9. #22624172C2semidirect
10. #22624171C2semidirect
11. #563×D73C2semidirect
12. #552×D73C2semidirect
13. #551×D73C2semidirect
14. D4×Q8×D73C2semidirect
15. #544×D73C2semidirect
16. #541×D73C2semidirect
17. #539×D73C2semidirect
18. #536×D73C2semidirect
20. C2×C22⋊Q8×D73C2semidirect
21. C73×#3538C2semidirect
24. C22×Q8×D73C22semidirect
26. #17989341C22semidirect
27. #17989340C22semidirect
28. #17989340C22semidirect
29. #17989339C22semidirect
30. #17989339C22semidirect
31. #17989338C22semidirect
32. #17989338C22semidirect
33. #17989337C22semidirect
34. #17989336C22semidirect
35. #17989279C22semidirect
36. #17989278C22semidirect
37. #17989277C22semidirect
38. #17989276C22semidirect
39. #17989275C22semidirect
40. #17989274C22semidirect
41. #17989273C22semidirect
42. #17989272C22semidirect
43. #17989271C22semidirect
44. #17989270C22semidirect
45. #17989269C22semidirect
46. #17989268C22semidirect
47. #17989267C22semidirect
48. #17989266C22semidirect
49. #17989265C22semidirect
50. #17989264C22semidirect
51. #17989263C22semidirect
52. #17989262C22semidirect
53. #17989261C22semidirect
54. #17989260C22semidirect
55. Q8×D292C22semidirect
56. D4×Dic146C22semidirect
57. D4×Dic146C22semidirect
58. #17989252C22semidirect
59. #17989252C22semidirect
60. Q8×C22⋊D73C22semidirect
61. Q8×C22⋊D73C22semidirect
62. #17989250C22semidirect
63. #17989250C22semidirect
64. #17989250C22semidirect
65. #17989250C22semidirect
66. #17989218C22semidirect
67. #17989217C22semidirect
68. #17989217C22semidirect
69. #17989216C22semidirect
70. #17989216C22semidirect
71. #17989216C22semidirect
72. #17989215C22semidirect
73. #17989214C22semidirect
74. #17989214C22semidirect
75. #17989200C22semidirect
76. #17989199C22semidirect
77. #17989198C22semidirect
78. #17989197C22semidirect
79. #17989196C22semidirect
80. #17989195C22semidirect
81. #17989194C22semidirect
82. #17989186C22semidirect
83. #17989185C22semidirect
84. #17989184C22semidirect
85. #17989183C22semidirect
86. #17989182C22semidirect
87. #17989181C22semidirect
88. #17989180C22semidirect
89. #17989179C22semidirect
90. #17989178C22semidirect
91. #17989163C22semidirect
92. #17989162C22semidirect
93. #17989161C22semidirect
94. #17989160C22semidirect
95. #17989160C22semidirect
96. #17989159C22semidirect
97. #17989159C22semidirect
98. #17989158C22semidirect
99. #17989157C22semidirect
100. C4⋊Q8×D73C22semidirect
101. C4⋊Q8×D73C22semidirect
102. C4⋊Q8×D73C22semidirect
104. #126×D73C22semidirect
105. #125×D73C22semidirect
106. #125×D73C22semidirect
107. #125×D73C22semidirect
120. #123×D73C22semidirect
121. C2×#14556571C22semidirect
122. C2×#14556570C22semidirect
123. C2×#14556569C22semidirect
124. C2×#14556568C22semidirect
125. C2×#14556567C22semidirect
132. C22⋊Q8×D73C22semidirect
133. C22⋊Q8×D73C22semidirect
134. C22⋊Q8×D73C22semidirect
135. C22⋊Q8×D73C22semidirect
136. C22⋊Q8×D73C22semidirect
137. C22⋊Q8×D73C22semidirect
140. C4×Q8×D73C22semidirect
145. #117×D73C22semidirect
149. #563×C73C22semidirect
150. #552×C73C22semidirect
151. #551×C73C22semidirect
152. D4×Q8×C73C22semidirect
153. #544×C73C22semidirect
154. #541×C73C22semidirect
155. #539×C73C22semidirect
156. #536×C73C22semidirect
158. C2×C22⋊Q8×C73C22semidirect
168. C22×Dic146C23semidirect
169. C22×Dic146C23semidirect
178. C2×Q8×D73C23semidirect
179. C2×Q8×D73C23semidirect
197. #14556591C23semidirect
198. #14556591C23semidirect
199. #14556591C23semidirect
200. #14556590C23semidirect
201. #14556590C23semidirect
202. #14556590C23semidirect
203. #14556590C23semidirect
204. #14556590C23semidirect
205. #14556590C23semidirect
206. #14556590C23semidirect
207. #14556589C23semidirect
208. #14556589C23semidirect
209. #14556589C23semidirect
210. #14556589C23semidirect
211. #14556589C23semidirect
215. #14556586C23semidirect
216. #14556586C23semidirect
217. #14556586C23semidirect
219. #14556585C23semidirect
223. #14556584C23semidirect
224. #14556584C23semidirect
225. #14556584C23semidirect
226. #14556583C23semidirect
227. #14556583C23semidirect
228. #14556583C23semidirect
229. #14556582C23semidirect
230. #14556582C23semidirect
231. #14556582C23semidirect
232. #14556582C23semidirect
233. #14556582C23semidirect
234. #14556581C23semidirect
235. #14556581C23semidirect
236. #14556581C23semidirect
237. #14556581C23semidirect
238. #14556581C23semidirect
239. #14556581C23semidirect
240. #14556581C23semidirect
241. #14556581C23semidirect
242. #14556581C23semidirect
252. #14556576C23semidirect
256. #14556575C23semidirect
260. #14556574C23semidirect
265. #14556573C23semidirect
269. #14556572C23semidirect
276. #14556571C23semidirect
277. #14556571C23semidirect
284. #14556570C23semidirect
285. #14556570C23semidirect
293. #14556569C23semidirect
294. #14556569C23semidirect
295. #14556569C23semidirect
303. #14556568C23semidirect
304. #14556568C23semidirect
305. #14556568C23semidirect
312. #14556567C23semidirect
313. #14556567C23semidirect
324. Q8×Dic73C23semidirect
325. C4×Dic146C23semidirect
326. C4×Dic146C23semidirect
327. #14556556C23semidirect
328. #14556556C23semidirect
345. #14556550C23semidirect
349. #14556549C23semidirect
353. #14556548C23semidirect
357. #14556547C23semidirect
394. C22×Q8×C73C23semidirect
396. C4⋊Q8×C73C23semidirect
397. C4⋊Q8×C73C23semidirect
398. C4⋊Q8×C73C23semidirect
400. #126×C73C23semidirect
401. #125×C73C23semidirect
402. #125×C73C23semidirect
403. #125×C73C23semidirect
408. #123×C73C23semidirect
415. C22⋊Q8×C73C23semidirect
416. C22⋊Q8×C73C23semidirect
419. C4×Q8×C73C23semidirect
424. #117×C73C23semidirect
744. D73#3538direct (N × H)
755. #3538D73direct (N × H)
766. C73C2×#3538semidirect
780. #563C2×D73semidirect
792. #552C2×D73semidirect
802. #551C2×D73semidirect
814. D4×Q8C2×D73semidirect
824. #544C2×D73semidirect
832. #541C2×D73semidirect
842. #539C2×D73semidirect
852. #536C2×D73semidirect
892. C2×C22⋊Q8C2×D73semidirect
927. C22×Q8C22×D73semidirect
961. C4⋊Q8C22×D73semidirect
962. C4⋊Q8C22×D73semidirect
963. C4⋊Q8C22×D73semidirect
979. #126C22×D73semidirect
997. #125C22×D73semidirect
998. #125C22×D73semidirect
999. #125C22×D73semidirect
1031. #123C22×D73semidirect
1082. C22⋊Q8C22×D73semidirect
1083. C22⋊Q8C22×D73semidirect
1101. C4×Q8C22×D73semidirect
1135. #117C22×D73semidirect

Maximal subgroups

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

subgroupindex
#226241802
#226241792
#226241782
#226241772
#226241762
#226241752
#226241742
#226241732
#226241722
#226241712
#563×D732
#552×D732
#551×D732
D4×Q8×D732
#544×D732
#541×D732
#539×D732
#536×D732
#525×D732
C2×C22⋊Q8×D732
C73×#35382
C2×#353873