Finite Group Databasebeta

← #7985703

Subgroups — #7985703

Order 512.

5453 conjugacy classes of subgroups.

The subgroup lattice has 1187 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#59815C211yesmaximal, characteristic, complemented
2#59654C212yesmaximal, complemented
3#59640C212yesmaximal, complemented
4#59219C212yesmaximal, complemented
5#49768C218yesmaximal, complemented
6#45653C214yesmaximal, complemented
7#45417C214yesmaximal, complemented
8#44888C214yesmaximal, complemented
9#42839C214yesmaximal, complemented
10#42618C214yesmaximal, complemented
11#39378C212yesmaximal, complemented
12#39221C214yesmaximal, complemented
13#39194C212yesmaximal, complemented
14#38965C212yesmaximal, complemented
15#38909C212yesmaximal, complemented
16#36576C212yesmaximal, complemented
17#36563C211yesmaximal, characteristic, complemented
18#36559C211yesmaximal, characteristic, complemented
19#36453C212yesmaximal, complemented
20#36187C211yesmaximal, characteristic, complemented
21#35247C212yesmaximal, complemented
22#35171C212yesmaximal, complemented
23#34954C211yesmaximal, characteristic, complemented
24#34934C211yesmaximal, characteristic, complemented
25#34480C212yesmaximal, complemented
26C4×D4×Q8C211yesmaximal, characteristic, complemented
27C2×#555C2212yes—
28C2×#554C2212yes—
29C2×#550C2212yes—
30C2×D4×Q8C2211yescharacteristic
31C2×#548C2214yes—
32C2×#547C2212yes—
33C2×#540C2214yes—
34C2×#529C2212yes—
35C22×C4×Q8C2212yes—
36#2868C2211yescharacteristic
37#2859C2212yes—
38#2859C2212yes—
39#2856C2214yes—
40#2856C2212yes—
41#2855C2214yes—
42#2854C2214yes—
43#2830C2218yes—
44#2803C2218yes—
45#2801C2218yes—
46#2800C2218yes—
47#2768C2218yes—
48#2765C2218yes—
49#2710C2218yes—
50#2704C2218yes—
51#2701C2218yes—
52#2701C2218yes—
53#2700C2218yes—
54#2692C2218yes—
55#2691C2218yes—
56#2686C2218yes—
57#2682C2214yes—
58#2681C2218yes—
59#2672C2218yes—
60#2671C2218yes—
61#2661C2218yes—
62#2653C2218yes—
63#2637C2218yes—
64#2629C2214yes—
65#2624C2214yes—
66#2593C2214yes—
67#2592C2214yes—
68#2584C2214yes—
69#2582C2211yescharacteristic
70#2582C2212yes—
71#2576C2218yes—
72#2571C2211yescharacteristic
73#2567C2212yes—
74#2566C2214yes—
75#2563C2212yes—
76#2563C2212yes—
77#2554C2214yes—
78#2552C2211yescharacteristic
79#2552C2212yes—
80#2550C2214yes—
81#2548C2214yes—
82#2548C2211yescharacteristic
83#2548C2211yescharacteristic
84#2548C2211yescharacteristic
85#2544C2214yes—
86#2541C2211yescharacteristic
87#2541C2212yes—
88#2538C2212yes—
89#2538C2214yes—
90#2538C2212yes—
91#2538C2211yescharacteristic
92#2538C2212yes—
93#2537C2212yes—
94#2537C2212yes—
95#2537C2212yes—
96#2536C2214yes—
97#2513C2212yes—
98#2513C2212yes—
99#2512C2212yes—
100#2507C2214yes—
101#2507C2214yes—
102#2500C2214yes—
103#2500C2214yes—
104#2494C2214yes—
105#2494C2214yes—
106#2494C2214yes—
107#2491C2214yes—
108#2491C2214yes—
109#2491C2214yes—
110#2490C2214yes—
111#2490C2212yes—
112#2486C2214yes—
113#2486C2214yes—
114#2470C2218yes—
115#2464C2218yes—
116#2461C2218yes—
117#2460C2218yes—
118#2459C2218yes—
119#2454C2214yes—
120#2452C2214yes—
121#2452C2214yes—
122#2451C2214yes—
123#2448C2212yes—
124#2448C2212yes—
125#2445C2214yes—
126#2445C2212yes—
127#2441C2214yes—
128#2440C2214yes—
129#2428C2214yes—
130#2428C2214yes—
131#2427C2218yes—
132#2427C2214yes—
133#2426C2214yes—
134#2426C2212yes—
135#2426C2218yes—
136#2422C2214yes—
137#2420C2214yes—
138#2420C2214yes—
139#2416C2214yes—
140#2416C2218yes—
141#2416C2214yes—
142#2416C2214yes—
143#2413C2218yes—
144#2409C2214yes—
145#2407C2214yes—
146#2407C2214yes—
147#2395C2214yes—
148#2392C2214yes—
149#2376C2218yes—
150#2369C2212yes—
151#2365C2212yes—
152#2365C2211yescharacteristic
153#2363C2214yes—
154#2361C2214yes—
155#2360C2214yes—
156#2360C2212yes—
157#2360C2214yes—
158#2357C2214yes—
159#2355C2212yes—
160#2354C2212yes—
161#2354C2212yes—
162Q8×C4⋊C4C2211yescharacteristic
163Q8×C4⋊C4C2212yes—
164D4×C4⋊C4C2212yes—
165D4×C4⋊C4C2212yes—
166D4×C4⋊C4C2212yes—
167D4×C4⋊C4C2211yescharacteristic
168D4×C4⋊C4C2212yes—
169#2345C2214yes—
170#2341C2214yes—
171Q8×C22⋊C4C2212yes—
172#2335C2218yes—
173#2324C2214yes—
174#2323C2214yes—
175#2323C2214yes—
176#2316C2214yes—
177#2311C2214yes—
178C4×C4⋊Q8C2212yes—
179C4×C4⋊Q8C2212yes—
180C4×C4⋊Q8C2211yescharacteristic
181C4×#127C2212yes—
182C4×#127C2211yescharacteristic
183C4×#127C2212yes—
184C4×#127C2211yescharacteristic
185C4×#124C2212yes—
186C4×#124C2212yes—
187C4×C22⋊Q8C2214yes—
188C4×C22⋊Q8C2212yes—
189C4×#121C2214yes—
190C4×#121C2212yes—
191#2293C2212yes—
192#2293C2212yes—
193#2293C2212yes—
194#2285C2212yes—
195C42×Q8C2211yescharacteristic
196C42×Q8C2211yescharacteristic
197C42×D4C2211yescharacteristic
198C42×D4C2212yes—
199C22×#41C2314yes—
200C23×Q8C2312yes—
201#555—48no—
202#554—48no—
203#550—48no—
204D4×Q8—28no—
205#548—416no—
206#547—216no—
207#540—416no—
208C2×C4⋊Q8C2312yes—
209C2×C4⋊Q8C2312yes—
210C2×C4⋊Q8C2312yes—
211C2×C4⋊Q8C2312yes—
212C2×C4⋊Q8C2311yescharacteristic
213C2×#127C2311yescharacteristic
214C2×#127C2311yescharacteristic
215C2×#127C2312yes—
216C2×#127C2314yes—
217#529—48no—
218C2×#126C2314yes—
219C2×#125C2314yes—
220C2×#125C2312yes—
221C2×#125C2314yes—
222C2×#124C2312yes—
223C2×#124C2312yes—
224C2×#124C2318yes—
225C2×#124C2318yes—
226C2×#124C2312yes—
227C2×#123C2318yes—
228C2×#123C2318yes—
229C2×#123C2314yes—
230C2×#123C2318yes—
231C2×C22⋊Q8C2314yes—
232C2×C22⋊Q8C2314yes—
233C2×C22⋊Q8C2312yes—
234C2×C22⋊Q8C2314yes—
235C2×C22⋊Q8C2312yes—
236C2×C22⋊Q8C2318yes—
237C2×C22⋊Q8C2318yes—
238C2×#121C2314yes—
239C2×#121C2314yes—
240C2×#121C2312yes—
241C2×#121C2312yes—
242C2×#121C2314yes—
243C2×#121C2318yes—
244C2×#121C2314yes—
245C2×#121C2314yes—
246C2×#121C2318yes—
247C2×#121C2314yes—
248C2×#121C2318yes—
249C2×#121C2318yes—
250C2×#121C2314yes—
251C2×C4×Q8—48no—
252C2×C4×Q8C2312yes—
253C2×C4×Q8C2311yescharacteristic
254C2×C4×Q8C2311yescharacteristic
255C2×C4×Q8C2311yescharacteristic
256C2×C4×Q8C2311yescharacteristic
257C2×C4×Q8C2311yescharacteristic
258C2×C4×Q8C2314yes—
259C2×C4×Q8C2314yes—
260C2×C4×Q8C2311yescharacteristic
261C2×C4×Q8C2312yes—
262C2×C4×Q8C2312yes—
263C2×C4×Q8C2314yes—
264C2×C4×D4C2312yes—
265C2×C4×D4C2311yescharacteristic
266C2×C4×D4C2312yes—
267C2×C4×D4C2312yes—
268C2×C4×D4C2312yes—
269C2×C4×D4C2312yes—
270C2×C4×D4C2311yescharacteristic
271C2×C4×D4C2312yes—
272C2×C4×D4C2311yescharacteristic
273C2×C4×D4C2312yes—
274C2×C4×D4C2312yes—
275C2×C4×D4C2314yes—
276C2×C4×D4C2314yes—
277C2×C4×D4C2314yes—
278C2×C4×D4C2314yes—
279C2×C4×D4C2314yes—
280C2×C4×D4C2314yes—
281C2×C4×D4C2318yes—
282C2×#117C2314yes—
283C2×#117C2314yes—
284C2×#117C2314yes—
285C2×#117C2314yes—
286C22×C4⋊C4C2314yes—
287C22×C4⋊C4C2314yes—
288C22×C4⋊C4C2314yes—
289C22×C4⋊C4C2312yes—
290C22×C42C2312yes—
291C22×C42C2314yes—
292#401C2318yes—
293#400C2314yes—
294#399C2318yes—
295#399C2314yes—
296#398C2318yes—
297#398C2314yes—
298#398C2318yes—
299#398C2318yes—
300#398C2318yes—
301#398C2314yes—
302#398C2318yes—
303#397C2314yes—
304#397C2318yes—
305#397C2318yes—
306#397C2318yes—
307#397C2314yes—
308#397C2314yes—
309#397C2314yes—
310#397C2318yes—
311#396C2318yes—
312#396C2318yes—
313#396C2314yes—
314#396C2318yes—
315#396C2314yes—
316#396C2318yes—
317#396C2318yes—
318#396C2318yes—
319#395C2318yes—
320#395C2318yes—
321#394C2318yes—
322#394C2318yes—
323#394C2318yes—
324#394C2314yes—
325#394C2314yes—
326#394C2318yes—
327#394C2318yes—
328#394C2314yes—
329#394C2314yes—
330#394C2314yes—
331#394C2318yes—
332#394C2318yes—
333#394C2318yes—
334#394C2318yes—
335#394C2318yes—
336#394C2318yes—
337#393C2318yes—
338#393C2318yes—
339#393C2318yes—
340#392C2314yes—
341#392C2318yes—
342#392C2318yes—
343#391C2314yes—
344#391C2312yes—
345#391C2314yes—
346#391C2312yes—
347#391C2314yes—
348#391C2312yes—
349#391C2312yes—
350#391C2314yes—
351#391C2318yes—
352#390C2314yes—
353#390C2312yes—
354#390C2314yes—
355#390C2312yes—
356#390C2312yes—
357#390C2312yes—
358#390C2312yes—
359#390C2312yes—
360#390C2314yes—
361#390C2312yes—
362#390C2314yes—
363#390C2312yes—
364#390C2314yes—
365#390C2314yes—
366#390C2312yes—
367#390C2314yes—
368#390C2318yes—
369#390C2312yes—
370#390C2318yes—
371#390C2314yes—
372#390C2312yes—
373#390C2312yes—
374#390C2314yes—
375#390C2318yes—
376#390C2312yes—
377#390C2312yes—
378#390C2312yes—
379#390C2312yes—
380#390C2312yes—
381#389C2314yes—
382#389C2312yes—
383#389C2314yes—
384#389C2312yes—
385#389C2312yes—
386#389C2312yes—
387#389C2314yes—
388#389C2314yes—
389#389C2312yes—
390#389C2312yes—
391#389C2312yes—
392#389C2318yes—
393#389C2314yes—
394#389C2318yes—
395#389C2312yes—
396#389C2314yes—
397#389C2318yes—
398#389C2312yes—
399#389C2314yes—
400#389C2314yes—
401#389C2314yes—
402#389C2312yes—
403#389C2314yes—
404#389C2314yes—
405#389C2314yes—
406#389C2314yes—
407#389C2312yes—
408#389C2314yes—
409#389C2318yes—
410#389C2312yes—
411#388C2314yes—
412#388C2318yes—
413#388C2318yes—
414#388C2318yes—
415#388C2318yes—
416#388C2318yes—
417#388C2314yes—
418#388C2314yes—
419#388C2318yes—
420#388C2314yes—
421#388C2314yes—
422#388C2314yes—
423#388C2314yes—
424#388C2314yes—
425#388C2314yes—
426#388C2318yes—
427#388C2318yes—
428#388C2318yes—
429#388C2314yes—
430#388C2318yes—
431#388C2314yes—
432#387C2314yes—
433#387C2318yes—
434#387C2318yes—
435#387C2318yes—
436#387C2314yes—
437#387C2318yes—
438#387C2314yes—
439#387C2318yes—
440#386C2318yes—
441#386C2318yes—
442#386C2318yes—
443#386C2318yes—
444#386C2318yes—
445#386C2318yes—
446#386C2314yes—
447#386C2318yes—
448#385C2318yes—
449#385C2318yes—
450#385C2318yes—
451#385C2318yes—
452#385C2318yes—
453#385C2314yes—
454#385C2314yes—
455#385C2314yes—
456#385C2318yes—
457#384C2311yescharacteristic
458#384C2311yescharacteristic
459#384C2312yes—
460#384C2312yes—
461#384C2311yescharacteristic
462#384C2312yes—
463#384C2312yes—
464#384C2312yes—
465#384C2314yes—
466#384C2312yes—
467#382C2314yes—
468#382C2314yes—
469#382C2312yes—
470#382C2312yes—
471#382C2314yes—
472#381C2318yes—
473#381C2318yes—
474#380C2314yes—
475#380C2314yes—
476#380C2314yes—
477#380C2314yes—
478#380C2318yes—
479#380C2318yes—
480#380C2318yes—
481#380C2314yes—
482#380C2312yes—
483#380C2314yes—
484#380C2314yes—
485#380C2314yes—
486#380C2314yes—
487#380C2312yes—
488C4×C4⋊C4C2312yes—
489C4×C4⋊C4C2311yescharacteristic
490C4×C4⋊C4C2312yes—
491C4×C4⋊C4C2314yes—
492C4×C4⋊C4C2314yes—
493C4×C4⋊C4C2314yes—
494C4×C4⋊C4C2311yescharacteristic
495C4×C4⋊C4C2311yescharacteristic
496C4×C4⋊C4C2312yes—
497C4×C4⋊C4C2311yescharacteristic
498C4×C4⋊C4C2311yescharacteristic
499C4×C4⋊C4C2314yes—
500C4×C4⋊C4C2312yes—
501C4×C4⋊C4C2314yes—
502C4×C4⋊C4C2312yes—
503C4×C4⋊C4C2311yescharacteristic
504C4×C4⋊C4C2312yes—
505C4×C4⋊C4C2311yescharacteristic
506C4×C4⋊C4C2314yes—
507C4×C4⋊C4C2312yes—
508C4×C4⋊C4C2311yescharacteristic
509C4×C4⋊C4C2312yes—
510C4×C4⋊C4C2312yes—
511C4×C4⋊C4C2312yes—
512C4×C4⋊C4C2311yescharacteristic
513C4×C22⋊C4C2314yes—
514C4×C22⋊C4C2318yes—
515C4×C22⋊C4C2318yes—
516C4×C22⋊C4C2312yes—
517C4×C22⋊C4C2314yes—
518C4×C22⋊C4C2314yes—
519C4×C22⋊C4C2314yes—
520C4×C22⋊C4C2312yes—
521C4×C22⋊C4C2314yes—
522C4×C22⋊C4C2314yes—
523C4×C22⋊C4C2314yes—
524C4×C22⋊C4C2312yes—
525C43C2311yescharacteristic
526C43C2312yes—
527C43C2312yes—
528C2×#41—216no—
529C2×#41—48no—
530C2×#41—48no—
531C22×Q8—28no—
532C22×Q8—28no—
533C22×Q8—44no—
534C22×Q8C2411yescharacteristic
535C22×Q8C2414yes—
536C22×Q8C2412yes—
537C22×Q8C2411yescharacteristic
538C22×Q8C2414yes—
539C22×D4C2412yes—
540C22×D4C2412yes—
541C22×D4C2412yes—
542C22×D4C2412yes—
543C22×D4C2411yescharacteristic
544C22×D4C2412yes—
545C22×D4C2418yes—
546C22×D4C2412yes—
547C22×D4C2414yes—
548C22×D4C2414yes—
549C22×D4C2418yes—
550C22×D4C2418yes—
551C23×C4C2414yes—
552C23×C4C2414yes—
553C23×C4C2412yes—
554C23×C4C2412yes—
555C23×C4C2412yes—
556C23×C4C2414yes—
557C23×C4C2414yes—
558C23×C4C2418yes—
559C23×C4C2418yes—
560C4⋊Q8—28no—
561C4⋊Q8—44no—
562C4⋊Q8—44no—
563C4⋊Q8—44no—
564C4⋊Q8#4118yes—
565#127—28no—
566#127—24no—
567#127—24no—
568#127—48no—
569#126—48no—
570#125—44no—
571#125—48no—
572#125—48no—
573#124—28no—
574#124—44no—
575#124—44no—
576#124—416no—
577#124—416no—
578#123—232no—
579#123—416no—
580#123—48no—
581#123—416no—
582C22⋊Q8—216no—
583C22⋊Q8—28no—
584C22⋊Q8—216no—
585C22⋊Q8—216no—
586C22⋊Q8—416no—
587C22⋊Q8—416no—
588C22⋊Q8—44no—
589#121—216no—
590#121—216no—
591#121—416no—
592#121—416no—
593#121—416no—
594#121—48no—
595#121—44no—
596#121—44no—
597#121—48no—
598#121—48no—
599#121—48no—
600#121—416no—
601#121—48no—
602C4×Q8—24no—
603C4×Q8—24no—
604C4×Q8—24no—
605C4×Q8—28no—
606C4×Q8—24no—
607C4×Q8—24no—
608C4×Q8—48no—
609C4×Q8—48no—
610C4×Q8—44no—
611C4×Q8—44no—
612C4×Q8—42no—
613C4×Q8—48no—
614C4×D4—28no—
615C4×D4—24no—
616C4×D4—28no—
617C4×D4—28no—
618C4×D4—28no—
619C4×D4—24no—
620C4×D4—28no—
621C4×D4—24no—
622C4×D4—28no—
623C4×D4—48no—
624C4×D4—48no—
625C4×D4—48no—
626C4×D4—48no—
627C4×D4—48no—
628C4×D4—48no—
629C4×D4—44no—
630C4×D4—44no—
631C4×D4—416no—
632#117—48no—
633#117—48no—
634#117—48no—
635#117—48no—
636C2×C4⋊C4—216no—
637C2×C4⋊C4—48no—
638C2×C4⋊C4—44no—
639C2×C4⋊C4—48no—
640C2×C4⋊C4C2411yescharacteristic
641C2×C4⋊C4C2412yes—
642C2×C4⋊C4C2411yescharacteristic
643C2×C4⋊C4C2412yes—
644C2×C4⋊C4C2412yes—
645C2×C4⋊C4C2414yes—
646C2×C4⋊C4C2414yes—
647C2×C4⋊C4C2418yes—
648C2×C4⋊C4C2411yescharacteristic
649C2×C4⋊C4C2414yes—
650C2×C4⋊C4C2412yes—
651C2×C4⋊C4C2412yes—
652C2×C4⋊C4C2414yes—
653C2×C4⋊C4C2418yes—
654C2×C4⋊C4C2412yes—
655C2×C4⋊C4C2411yescharacteristic
656C2×C4⋊C4C2411yescharacteristic
657C2×C4⋊C4C2412yes—
658C2×C4⋊C4C2411yescharacteristic
659C2×C4⋊C4C2411yescharacteristic
660C2×C4⋊C4C2412yes—
661C2×C4⋊C4C2411yescharacteristic
662C2×C4⋊C4C2412yes—
663C2×C4⋊C4C2412yes—
664C2×C4⋊C4C2411yescharacteristic
665C2×C4⋊C4C2412yes—
666C2×C4⋊C4C2414yes—
667C2×C4⋊C4C2414yes—
668C2×C4⋊C4C2414yes—
669C2×C4⋊C4C2414yes—
670C2×C4⋊C4C2418yes—
671C2×C4⋊C4C2412yes—
672C2×C4⋊C4C2414yes—
673C2×C4⋊C4C2414yes—
674C2×C4⋊C4C2414yes—
675C2×C4⋊C4C2414yes—
676C2×C4⋊C4C2414yes—
677C2×C4⋊C4C2414yes—
678C2×C4⋊C4C2412yes—
679C2×C4⋊C4C2414yes—
680C2×C4⋊C4C2414yes—
681C2×C4⋊C4C2418yes—
682C2×C4⋊C4C2412yes—
683C2×C4⋊C4C2418yes—
684C2×C4⋊C4C2418yes—
685C2×C4⋊C4C2414yes—
686C2×C4⋊C4C2414yes—
687C2×C4⋊C4C2412yes—
688C2×C4⋊C4C2412yes—
689C2×C4⋊C4C2412yes—
690C2×C22⋊C4C2418yes—
691C2×C22⋊C4C2414yes—
692C2×C22⋊C4C2414yes—
693C2×C22⋊C4C2414yes—
694C2×C22⋊C4C2418yes—
695C2×C22⋊C4C2414yes—
696C2×C22⋊C4C2412yes—
697C2×C22⋊C4C2414yes—
698C2×C22⋊C4C2414yes—
699C2×C22⋊C4C2412yes—
700C2×C22⋊C4C2412yes—
701C2×C22⋊C4C2414yes—
702C2×C22⋊C4C2414yes—
703C2×C22⋊C4C2418yes—
704C2×C22⋊C4C2414yes—
705C2×C22⋊C4C2414yes—
706C2×C22⋊C4C2418yes—
707C2×C22⋊C4C2414yes—
708C2×C22⋊C4C2414yes—
709C2×C22⋊C4C2414yes—
710C2×C22⋊C4C2418yes—
711C2×C22⋊C4C2418yes—
712C2×C22⋊C4C2414yes—
713C2×C22⋊C4C2414yes—
714C2×C22⋊C4C2414yes—
715C2×C22⋊C4C2414yes—
716C2×C22⋊C4C2414yes—
717C2×C22⋊C4C2418yes—
718C2×C22⋊C4C2418yes—
719C2×C22⋊C4C2418yes—
720C2×C22⋊C4C2418yes—
721C2×C22⋊C4C2414yes—
722C2×C22⋊C4C2414yes—
723C2×C22⋊C4C2414yes—
724C2×C22⋊C4C2414yes—
725C2×C22⋊C4C2414yes—
726C2×C22⋊C4C2414yes—
727C2×C42—28no—
728C2×C42—48no—
729C2×C42C2412yes—
730C2×C42C2412yes—
731C2×C42C2412yes—
732C2×C42C2412yes—
733C2×C42C2411yescharacteristic
734C2×C42C2412yes—
735C2×C42C2412yes—
736C2×C42C2411yescharacteristic
737C2×C42C2412yes—
738C2×C42C2414yes—
739C2×C42C2412yes—
740C2×C42C2412yes—
741C2×C42C2412yes—
742C2×C42C2412yes—
743C2×C42C2411yescharacteristic
744C2×C42C2412yes—
745C2×C42C2418yes—
746C2×C42C2418yes—
747C2×C42C2414yes—
748C2×C42C2414yes—
749C2×C42C2412yes—
750C2×C42C2411yescharacteristic
751C2×C42C2412yes—
752C2×C42C2412yes—
753C2×C42C2411yescharacteristic
754C2×C42C2411yescharacteristic
755C2×C42C2411yescharacteristic
756#95C2414yes—
757#95C2414yes—
758#95C2414yes—
759#95C2414yes—
760#95C2414yes—
761#95C2412yes—
762#95C2414yes—
763#95C2412yes—
764#95C2412yes—
765#95C2418yes—
766#95C2414yes—
767#95C2414yes—
768#95C2414yes—
769#95C2414yes—
770#95C2414yes—
771#95C2414yes—
772#95C2412yes—
773#95C2412yes—
774#95C2412yes—
775#95C2412yes—
776#95C2412yes—
777#95C2412yes—
778#95C2418yes—
779#95C2418yes—
780#95C2414yes—
781#95C2418yes—
782#95C2414yes—
783#95C2418yes—
784#95C2418yes—
785#95C2418yes—
786#95C2418yes—
787#95C2418yes—
788C24C2514yes—
789C24C2514yes—
790C24C2512yes—
791#41—832no—
792C2×Q8—22no—
793C2×Q8—28no—
794C2×Q8—22no—
795C2×Q8—24no—
796C2×Q8—24no—
797C2×Q8—22no—
798C2×Q8—28no—
799C2×Q8—22no—
800C2×Q8—22no—
801C2×Q8—44no—
802C2×Q8—44no—
803C2×Q8—44no—
804C2×Q8—44no—
805C2×Q8—432no—
806C2×Q8C2×#4118yes—
807C2×Q8H(5,𝔽2)14yes—
808C2×D4—216no—
809C2×D4—28no—
810C2×D4—28no—
811C2×D4—22no—
812C2×D4—24no—
813C2×D4—24no—
814C2×D4—216no—
815C2×D4—24no—
816C2×D4—24no—
817C2×D4—24no—
818C2×D4—24no—
819C2×D4—24no—
820C2×D4—24no—
821C2×D4—22no—
822C2×D4—24no—
823C2×D4—24no—
824C2×D4—24no—
825C2×D4—24no—
826C2×D4—24no—
827C2×D4—24no—
828C2×D4—42no—
829C2×D4—42no—
830C2×D4—42no—
831C2×D4—44no—
832C2×D4—48no—
833C2×D4—44no—
834C2×D4—48no—
835C2×D4—48no—
836C2×D4—44no—
837C2×D4—48no—
838C2×D4—42no—
839C2×D4—44no—
840C2×D4—48no—
841C2×D4—48no—
842C2×D4—48no—
843C2×D4H(5,𝔽2)14yes—
844C22×C4—24no—
845C22×C4—28no—
846C22×C4—28no—
847C22×C4—28no—
848C22×C4—24no—
849C22×C4—28no—
850C22×C4—24no—
851C22×C4—24no—
852C22×C4—24no—
853C22×C4—28no—
854C22×C4—28no—
855C22×C4—28no—
856C22×C4—28no—
857C22×C4—24no—
858C22×C4—28no—
859C22×C4—24no—
860C22×C4—24no—
861C22×C4—216no—
862C22×C4—44no—
863C22×C4—42no—
864C22×C4—44no—
865C22×C4—48no—
866C22×C4—48no—
867C22×C4—44no—
868C22×C4—48no—
869C22×C4—48no—
870C22×C4—48no—
871C22×C4C2512yes—
872C22×C4C2512yes—
873C22×C4C2512yes—
874C22×C4C2512yes—
875C22×C4C2514yes—
876C22×C4C2511yescharacteristic
877C22×C4C2512yes—
878C22×C4C2514yes—
879C22×C4C2512yes—
880C22×C4C2512yes—
881C22×C4C2512yes—
882C22×C4C2518yes—
883C22×C4C2514yes—
884C22×C4C2512yes—
885C22×C4C2512yes—
886C22×C4C2514yes—
887C22×C4C2511yescharacteristic
888C22×C4C2512yes—
889C22×C4C2511yescharacteristic
890C22×C4C2511yescharacteristic
891C22×C4C2511yescharacteristic
892C22×C4C2511yescharacteristic
893C22×C4C2511yescharacteristic
894C4⋊C4—24no—
895C4⋊C4—216no—
896C4⋊C4—24no—
897C4⋊C4—22no—
898C4⋊C4—24no—
899C4⋊C4—22no—
900C4⋊C4—28no—
901C4⋊C4—22no—
902C4⋊C4—24no—
903C4⋊C4—22no—
904C4⋊C4—28no—
905C4⋊C4—24no—
906C4⋊C4—28no—
907C4⋊C4—22no—
908C4⋊C4—28no—
909C4⋊C4—24no—
910C4⋊C4—24no—
911C4⋊C4—216no—
912C4⋊C4—22no—
913C4⋊C4—24no—
914C4⋊C4—24no—
915C4⋊C4—22no—
916C4⋊C4—24no—
917C4⋊C4—22no—
918C4⋊C4—24no—
919C4⋊C4—28no—
920C4⋊C4—22no—
921C4⋊C4—44no—
922C4⋊C4—44no—
923C4⋊C4—44no—
924C4⋊C4—48no—
925C4⋊C4—42no—
926C4⋊C4—44no—
927C4⋊C4—42no—
928C4⋊C4—44no—
929C4⋊C4—44no—
930C4⋊C4—44no—
931C4⋊C4—44no—
932C4⋊C4—44no—
933C4⋊C4—44no—
934C4⋊C4—42no—
935C4⋊C4—44no—
936C4⋊C4—44no—
937C4⋊C4—42no—
938C4⋊C4—48no—
939C4⋊C4—48no—
940C4⋊C4—48no—
941C4⋊C4—44no—
942C4⋊C4C2×#4118yes—
943C4⋊C4C2×#4118yes—
944C22⋊C4—216no—
945C22⋊C4—28no—
946C22⋊C4—24no—
947C22⋊C4—28no—
948C22⋊C4—24no—
949C22⋊C4—28no—
950C22⋊C4—28no—
951C22⋊C4—216no—
952C22⋊C4—28no—
953C22⋊C4—28no—
954C22⋊C4—216no—
955C22⋊C4—28no—
956C22⋊C4—24no—
957C22⋊C4—28no—
958C22⋊C4—44no—
959C22⋊C4—44no—
960C22⋊C4—44no—
961C22⋊C4—44no—
962C22⋊C4—44no—
963C22⋊C4—48no—
964C22⋊C4—44no—
965C22⋊C4—44no—
966C22⋊C4—48no—
967C22⋊C4—44no—
968C22⋊C4—48no—
969C22⋊C4—48no—
970C22⋊C4—44no—
971C22⋊C4—44no—
972C22⋊C4—44no—
973C22⋊C4—44no—
974C22⋊C4—44no—
975C22⋊C4—44no—
976C22⋊C4—48no—
977C22⋊C4—48no—
978C22⋊C4—48no—
979C22⋊C4—44no—
980C22⋊C4—44no—
981C42—24no—
982C42—24no—
983C42—24no—
984C42—24no—
985C42—24no—
986C42—28no—
987C42—24no—
988C42—24no—
989C42—24no—
990C42—22no—
991C42—24no—
992C42—22no—
993C42—24no—
994C42—24no—
995C42—24no—
996C42—22no—
997C42—44no—
998C42—44no—
999C42—41no—
1000C42—42no—
1001C42—42no—
1002C42—48no—
1003C42—48no—
1004C42—42no—
1005C42C2×#4114yes—
1006C42H(5,𝔽2)14yes—
1007C422−1+414yes—
1008C23—22no—
1009C23—22no—
1010C23—22no—
1011C23—22no—
1012C23—22no—
1013C23—22no—
1014C23—24no—
1015C23—24no—
1016C23—24no—
1017C23—24no—
1018C23—24no—
1019C23—24no—
1020C23—24no—
1021C23—24no—
1022C23—24no—
1023C23—24no—
1024C23—24no—
1025C23—24no—
1026C23—24no—
1027C23—24no—
1028C23C2×H(5,𝔽2)14yes—
1029C23C2611yescharacteristic
1030Q8—28no—
1031Q8—216no—
1032Q8—416no—
1033Q8—44no—
1034Q8—164no—
1035D4—28no—
1036D4—48no—
1037D4—48no—
1038D4—48no—
1039D4—48no—
1040D4—48no—
1041D4—84no—
1042D4—816no—
1043D4—816no—
1044D4—88no—
1045D4—88no—
1046D4—168no—
1047C2×C4—22no—
1048C2×C4—21no—
1049C2×C4—22no—
1050C2×C4—24no—
1051C2×C4—21no—
1052C2×C4—24no—
1053C2×C4—21no—
1054C2×C4—21no—
1055C2×C4—21no—
1056C2×C4—21no—
1057C2×C4—22no—
1058C2×C4—24no—
1059C2×C4—24no—
1060C2×C4—22no—
1061C2×C4—22no—
1062C2×C4—22no—
1063C2×C4—22no—
1064C2×C4—22no—
1065C2×C4—22no—
1066C2×C4—24no—
1067C2×C4—21no—
1068C2×C4—22no—
1069C2×C4—22no—
1070C2×C4—22no—
1071C2×C4—22no—
1072C2×C4—21no—
1073C2×C4—22no—
1074C2×C4—22no—
1075C2×C4—22no—
1076C2×C4—22no—
1077C2×C4—22no—
1078C2×C4—24no—
1079C2×C4—28no—
1080C2×C4—28no—
1081C2×C4—24no—
1082C2×C4—24no—
1083C2×C4—22no—
1084C2×C4—24no—
1085C2×C4—22no—
1086C2×C4—22no—
1087C2×C4—22no—
1088C2×C4—24no—
1089C2×C4—22no—
1090C2×C4—22no—
1091C2×C4—21no—
1092C2×C4—22no—
1093C2×C4—22no—
1094C2×C4—22no—
1095C2×C4—28no—
1096C2×C4—22no—
1097C2×C4—22no—
1098C2×C4—22no—
1099C2×C4—22no—
1100C2×C4—22no—
1101C2×C4—24no—
1102C2×C4—416no—
1103C2×C4—48no—
1104C2×C4—48no—
1105C2×C4—416no—
1106C2×C4—416no—
1107C2×C4—48no—
1108C2×C4—816no—
1109C2×C4—88no—
1110C2×C4—168no—
1111C2×C4C22×#4112yes—
1112C2×C4C22×#4118yes—
1113C2×C4C22×#4112yes—
1114C2×C4C22×#4112yes—
1115C2×C4C2×H(5,𝔽2)12yes—
1116C2×C4C2×H(5,𝔽2)14yes—
1117C2×C4C2×H(5,𝔽2)12yes—
1118C2×C4C2×H(5,𝔽2)12yes—
1119C2×C4C2×H(5,𝔽2)12yes—
1120C2×C4C2×H(5,𝔽2)12yes—
1121C2×C4C2×2−1+412yes—
1122C2×C4C2×2−1+412yes—
1123C2×C4C2×2−1+412yes—
1124C2×C4#58512yes—
1125C22—24no—
1126C22—24no—
1127C22—24no—
1128C22—42no—
1129C22—42no—
1130C22—42no—
1131C22—42no—
1132C22—44no—
1133C22—44no—
1134C22—44no—
1135C22—44no—
1136C22—44no—
1137C22—44no—
1138C22—44no—
1139C22—44no—
1140C22—44no—
1141C22—44no—
1142C22—44no—
1143C22—44no—
1144C22—44no—
1145C22—44no—
1146C22C23×#4111yescharacteristic
1147C22C22×H(5,𝔽2)11yescharacteristic
1148C22C22×H(5,𝔽2)11yescharacteristic
1149C22C22×H(5,𝔽2)11yescharacteristic
1150C22C22×2−1+411yescharacteristic
1151C22C2×#58511yescharacteristic
1152C222−1+611yescharacteristic
1153C4—22no—
1154C4—24no—
1155C4—28no—
1156C4—22no—
1157C4—22no—
1158C4—42no—
1159C4—42no—
1160C4—42no—
1161C4—42no—
1162C4—48no—
1163C4—42no—
1164C4—41no—
1165C4—44no—
1166C4—42no—
1167C4—44no—
1168C4—42no—
1169C4—42no—
1170C4—42no—
1171C4—44no—
1172C4—42no—
1173C4#351914yes—
1174C4#352214yes—
1175C4#354714yes—
1176C2—44no—
1177C2—84no—
1178C2—84no—
1179C2C2×#354711yescharacteristic
1180C2C2×#351911yescharacteristic
1181C2C2×#352211yescharacteristic
1182C2#6291311yescharacteristic
1183C2#6291411yescharacteristic
1184C2#6300711yescharacteristic
1185C2#6301411yescharacteristic
subgroupG/H
center, commutator, Frattini, socle, cosocleC23C26
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23 ◁ G
LECSG ▷ C23 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #59815C2semidirect
2. #59654C2semidirect
3. #59640C2semidirect
4. #59219C2semidirect
5. #49768C2semidirect
6. #45653C2semidirect
7. #45417C2semidirect
8. #44888C2semidirect
9. #42839C2semidirect
10. #42618C2semidirect
11. #39378C2semidirect
12. #39221C2semidirect
13. #39194C2semidirect
14. #38965C2semidirect
15. #38909C2semidirect
16. #36576C2semidirect
17. #36563C2semidirect
18. #36559C2semidirect
19. #36453C2semidirect
20. #36187C2semidirect
21. #35247C2semidirect
22. #35171C2semidirect
23. #34954C2semidirect
24. #34934C2semidirect
25. #34480C2semidirect
26. C4×D4×Q8C2semidirect

Maximal subgroups

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

subgroupindex
#598152
#596542
#596402
#592192
#497682
#456532
#454172
#448882
#428392
#426182
#393782
#392212
#391942
#389652
#389092
#365762
#365632
#365592
#364532
#361872
#352472
#351712
#349542
#349342
#344802
C4×D4×Q82