Finite Group Databasebeta

← #7688710

Subgroups — #7688710

Order 512.

5287 conjugacy classes of subgroups.

The subgroup lattice has 1511 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#60046C212yesmaximal, complemented
2#59946C211yesmaximal, characteristic, complemented
3#59782C214yesmaximal, complemented
4#59721C214yesmaximal, complemented
5#59700C212yesmaximal, complemented
6#59104C212yesmaximal, complemented
7#45315C211yesmaximal, characteristic, complemented
8#45244C211yesmaximal, characteristic, complemented
9#45190C212yesmaximal, complemented
10#44834C212yesmaximal, complemented
11#44193C214yesmaximal, complemented
12#43442C212yesmaximal, complemented
13#38865C214yesmaximal, complemented
14#38841C214yesmaximal, complemented
15#38214C212yesmaximal, complemented
16#37785C212yesmaximal, complemented
17#36589C212yesmaximal, complemented
18#36588C212yesmaximal, complemented
19#36412C211yesmaximal, characteristic, complemented
20#36399C212yesmaximal, complemented
21#36369C214yesmaximal, complemented
22#36077C211yesmaximal, characteristic, complemented
23#35756C211yesmaximal, characteristic, complemented
24#35704C212yesmaximal, complemented
25#34962C212yesmaximal, complemented
26#34871C211yesmaximal, characteristic, complemented
27#34312C212yesmaximal, complemented
28#34274C212yesmaximal, complemented
29#34153C212yesmaximal, complemented
30C2×#555C2211yescharacteristic
31C2×#550C2211yescharacteristic
32C2×#548C2212yes—
33C2×#537C2212yes—
34C2×#529C2212yes—
35C2×#520C2212yes—
36C2×#520C2211yescharacteristic
37C2×#519C2211yescharacteristic
38#2860C2214yes—
39#2860C2212yes—
40#2858C2211yescharacteristic
41#2856C2212yes—
42#2854C2214yes—
43#2854C2212yes—
44#2805C2214yes—
45#2803C2214yes—
46#2801C2214yes—
47#2800C2214yes—
48#2797C2214yes—
49#2789C2212yes—
50#2788C2214yes—
51#2778C2214yes—
52#2774C2214yes—
53#2753C2214yes—
54#2752C2212yes—
55#2742C2214yes—
56#2724C2212yes—
57#2717C2212yes—
58#2714C2214yes—
59#2710C2214yes—
60#2703C2214yes—
61#2703C2214yes—
62#2703C2214yes—
63#2703C2214yes—
64#2702C2214yes—
65#2683C2212yes—
66#2676C2214yes—
67#2675C2212yes—
68#2635C2214yes—
69#2632C2212yes—
70#2631C2212yes—
71#2624C2211yescharacteristic
72#2619C2212yes—
73#2615C2211yescharacteristic
74#2612C2211yescharacteristic
75#2610C2214yes—
76#2610C2212yes—
77#2609C2211yescharacteristic
78#2602C2214yes—
79#2600C2212yes—
80#2599C2212yes—
81#2599C2212yes—
82#2597C2214yes—
83#2596C2214yes—
84#2595C2214yes—
85#2595C2214yes—
86#2594C2214yes—
87#2593C2212yes—
88#2593C2214yes—
89#2593C2214yes—
90#2592C2212yes—
91#2592C2212yes—
92#2591C2214yes—
93#2588C2214yes—
94#2586C2212yes—
95#2586C2211yescharacteristic
96#2581C2212yes—
97#2574C2214yes—
98#2573C2214yes—
99#2573C2214yes—
100#2572C2211yescharacteristic
101#2567C2211yescharacteristic
102#2560C2214yes—
103#2559C2214yes—
104#2559C2214yes—
105#2557C2214yes—
106#2555C2214yes—
107#2555C2214yes—
108#2555C2212yes—
109#2554C2212yes—
110#2554C2214yes—
111#2548C2212yes—
112#2541C2211yescharacteristic
113#2532C2212yes—
114#2531C2214yes—
115#2530C2214yes—
116#2527C2214yes—
117#2526C2212yes—
118#2525C2214yes—
119#2521C2214yes—
120#2518C2214yes—
121#2516C2214yes—
122#2513C2212yes—
123#2510C2214yes—
124#2509C2212yes—
125#2509C2212yes—
126#2507C2214yes—
127#2504C2211yescharacteristic
128#2500C2212yes—
129#2497C2214yes—
130#2494C2212yes—
131#2490C2212yes—
132#2490C2212yes—
133#2486C2211yescharacteristic
134#2479C2212yes—
135#2477C2214yes—
136#2477C2214yes—
137#2476C2214yes—
138#2476C2214yes—
139#2476C2214yes—
140#2474C2214yes—
141#2471C2214yes—
142#2471C2212yes—
143#2470C2214yes—
144#2470C2214yes—
145#2467C2214yes—
146#2467C2214yes—
147#2464C2214yes—
148#2464C2214yes—
149#2463C2212yes—
150#2459C2214yes—
151#2459C2214yes—
152#2456C2214yes—
153#2456C2214yes—
154#2456C2214yes—
155#2456C2214yes—
156#2453C2212yes—
157#2451C2212yes—
158#2448C2212yes—
159#2445C2214yes—
160#2445C2212yes—
161#2445C2212yes—
162#2444C2214yes—
163#2442C2212yes—
164#2439C2212yes—
165#2436C2211yescharacteristic
166#2431C2212yes—
167#2431C2212yes—
168#2431C2212yes—
169#2428C2214yes—
170#2428C2212yes—
171#2428C2212yes—
172#2426C2212yes—
173#2426C2212yes—
174#2421C2212yes—
175#2416C2212yes—
176#2414C2214yes—
177#2414C2214yes—
178#2414C2212yes—
179#2409C2211yescharacteristic
180#2406C2214yes—
181#2396C2212yes—
182#2396C2212yes—
183#2395C2211yescharacteristic
184#2392C2212yes—
185#2388C2211yescharacteristic
186#2388C2214yes—
187#2374C2212yes—
188#2374C2214yes—
189#2373C2214yes—
190#2373C2214yes—
191#2372C2214yes—
192#2370C2212yes—
193#2370C2212yes—
194#2367C2214yes—
195#2367C2212yes—
196#2367C2212yes—
197#2367C2212yes—
198#2363C2214yes—
199#2363C2212yes—
200#2363C2214yes—
201#2363C2214yes—
202#2363C2214yes—
203#2363C2212yes—
204#2363C2212yes—
205#2362C2214yes—
206#2362C2212yes—
207#2362C2212yes—
208#2361C2212yes—
209#2361C2212yes—
210#2361C2214yes—
211#2361C2212yes—
212#2361C2212yes—
213#2360C2214yes—
214#2360C2212yes—
215#2360C2212yes—
216#2360C2212yes—
217#2360C2214yes—
218#2359C2214yes—
219#2359C2214yes—
220#2357C2212yes—
221#2352C2214yes—
222#2352C2212yes—
223#2351C2212yes—
224#2347C2211yescharacteristic
225#2347C2211yescharacteristic
226#2341C2212yes—
227Q8×C22⋊C4C2212yes—
228#2325C2214yes—
229#2325C2214yes—
230#2324C2212yes—
231#2324C2214yes—
232#2323C2214yes—
233#2323C2212yes—
234#2316C2212yes—
235C4×#126C2212yes—
236C4×#126C2214yes—
237C4×#124C2212yes—
238C4×#124C2214yes—
239C4×#124C2211yescharacteristic
240C4×#123C2212yes—
241C4×#123C2214yes—
242C4×#121C2214yes—
243C4×#121C2214yes—
244#2298C2214yes—
245#2297C2212yes—
246#2297C2212yes—
247#2297C2212yes—
248#2296C2214yes—
249#2295C2212yes—
250#2293C2214yes—
251#2293C2212yes—
252#2293C2212yes—
253#2290C2214yes—
254C42×Q8C2212yes—
255C42×D4C2214yes—
256C42×D4C2211yescharacteristic
257C4×#117C2212yes—
258C2×C4×C4⋊C4C2212yes—
259C22×#41C2312yes—
260C22×#41C2311yescharacteristic
261C22×#41C2312yes—
262C23×Q8C2311yescharacteristic
263#555—44no—
264#550—44no—
265#548—216no—
266#537—216no—
267C2×C4⋊Q8C2311yescharacteristic
268C2×#127C2311yescharacteristic
269C2×#127C2312yes—
270C2×#127C2312yes—
271#529—216no—
272C2×#126C2314yes—
273C2×#126C2314yes—
274C2×#126C2312yes—
275C2×#125C2312yes—
276C2×#124C2312yes—
277C2×#124C2314yes—
278C2×#124C2312yes—
279C2×#124C2312yes—
280C2×#124C2312yes—
281C2×#124C2314yes—
282C2×#124C2311yescharacteristic
283C2×#123C2314yes—
284C2×#123C2314yes—
285C2×#123C2312yes—
286C2×#123C2314yes—
287C2×#123C2312yes—
288C2×#123C2314yes—
289C2×C22⋊Q8C2314yes—
290C2×C22⋊Q8C2312yes—
291C2×C22⋊Q8C2314yes—
292C2×C22⋊Q8C2312yes—
293C2×#121C2312yes—
294C2×#121C2314yes—
295C2×#121C2314yes—
296C2×#121C2314yes—
297C2×#121C2312yes—
298C2×#121C2312yes—
299C2×#121C2314yes—
300C2×#121C2312yes—
301C2×#121C2314yes—
302C2×#121C2314yes—
303C2×#121C2314yes—
304C2×#121C2312yes—
305C2×#121C2312yes—
306C2×#121C2311yescharacteristic
307C2×#121C2311yescharacteristic
308C2×#121C2314yes—
309#520—44no—
310#520—48no—
311#519—44no—
312C2×C4×Q8C2312yes—
313C2×C4×Q8C2312yes—
314C2×C4×Q8C2312yes—
315C2×C4×Q8C2311yescharacteristic
316C2×C4×Q8C2312yes—
317C2×C4×Q8C2312yes—
318C2×C4×Q8C2312yes—
319C2×C4×Q8C2312yes—
320C2×C4×Q8C2312yes—
321C2×C4×D4C2314yes—
322C2×C4×D4C2312yes—
323C2×C4×D4C2312yes—
324C2×C4×D4C2311yescharacteristic
325C2×C4×D4C2312yes—
326C2×C4×D4C2314yes—
327C2×C4×D4C2314yes—
328C2×C4×D4C2312yes—
329C2×C4×D4C2312yes—
330C2×C4×D4C2314yes—
331C2×C4×D4C2314yes—
332C2×C4×D4C2314yes—
333C2×C4×D4C2314yes—
334C2×C4×D4C2311yescharacteristic
335C2×C4×D4C2314yes—
336C2×C4×D4C2314yes—
337C2×#117C2311yescharacteristic
338C2×#117C2311yescharacteristic
339C2×#117C2314yes—
340C2×#117C2312yes—
341C2×#117C2312yes—
342C2×#117C2314yes—
343C2×#117C2311yescharacteristic
344C2×#117C2314yes—
345C2×#117C2312yes—
346C2×#117C2312yes—
347C2×#117C2312yes—
348C2×#117C2314yes—
349C22×C4⋊C4C2312yes—
350C22×C4⋊C4C2312yes—
351C22×C4⋊C4C2314yes—
352C22×C4⋊C4C2311yescharacteristic
353C22×C42C2312yes—
354C22×C42C2314yes—
355C22×C42C2312yes—
356#401C2314yes—
357#400C2311yescharacteristic
358#400C2314yes—
359#400C2314yes—
360#400C2314yes—
361#400C2314yes—
362#400C2314yes—
363#400C2312yes—
364#400C2314yes—
365#400C2314yes—
366#400C2314yes—
367#399C2314yes—
368#399C2312yes—
369#399C2311yescharacteristic
370#399C2312yes—
371#398C2314yes—
372#398C2314yes—
373#398C2312yes—
374#398C2311yescharacteristic
375#398C2314yes—
376#398C2312yes—
377#398C2312yes—
378#397C2314yes—
379#397C2314yes—
380#397C2314yes—
381#397C2311yescharacteristic
382#397C2312yes—
383#397C2312yes—
384#397C2312yes—
385#397C2314yes—
386#397C2314yes—
387#397C2314yes—
388#397C2314yes—
389#397C2312yes—
390#397C2312yes—
391#396C2314yes—
392#396C2314yes—
393#396C2314yes—
394#396C2312yes—
395#396C2314yes—
396#396C2312yes—
397#395C2314yes—
398#395C2314yes—
399#395C2311yescharacteristic
400#395C2312yes—
401#395C2312yes—
402#395C2314yes—
403#394C2314yes—
404#394C2311yescharacteristic
405#394C2314yes—
406#394C2314yes—
407#394C2314yes—
408#394C2314yes—
409#394C2314yes—
410#394C2314yes—
411#394C2314yes—
412#394C2314yes—
413#394C2314yes—
414#394C2312yes—
415#394C2314yes—
416#394C2314yes—
417#394C2314yes—
418#394C2314yes—
419#394C2314yes—
420#394C2312yes—
421#394C2314yes—
422#394C2314yes—
423#393C2312yes—
424#393C2312yes—
425#393C2311yescharacteristic
426#393C2312yes—
427#393C2312yes—
428#393C2312yes—
429#393C2314yes—
430#392C2312yes—
431#392C2314yes—
432#392C2314yes—
433#392C2312yes—
434#392C2312yes—
435#392C2314yes—
436#392C2314yes—
437#392C2314yes—
438#392C2311yescharacteristic
439#392C2314yes—
440#392C2314yes—
441#392C2314yes—
442#392C2314yes—
443#392C2312yes—
444#392C2314yes—
445#391C2314yes—
446#391C2312yes—
447#391C2311yescharacteristic
448#391C2312yes—
449#391C2312yes—
450#391C2314yes—
451#391C2312yes—
452#391C2314yes—
453#391C2314yes—
454#391C2312yes—
455#391C2312yes—
456#391C2312yes—
457#390C2314yes—
458#390C2312yes—
459#390C2314yes—
460#390C2312yes—
461#390C2314yes—
462#390C2314yes—
463#390C2314yes—
464#390C2314yes—
465#390C2314yes—
466#390C2312yes—
467#390C2314yes—
468#390C2314yes—
469#390C2312yes—
470#390C2314yes—
471#390C2314yes—
472#390C2312yes—
473#390C2311yescharacteristic
474#390C2312yes—
475#390C2312yes—
476#390C2312yes—
477#390C2312yes—
478#390C2314yes—
479#390C2312yes—
480#390C2314yes—
481#390C2312yes—
482#390C2312yes—
483#390C2312yes—
484#390C2312yes—
485#390C2312yes—
486#389C2312yes—
487#389C2312yes—
488#389C2312yes—
489#389C2312yes—
490#389C2314yes—
491#389C2312yes—
492#389C2314yes—
493#389C2314yes—
494#389C2312yes—
495#389C2314yes—
496#389C2314yes—
497#389C2314yes—
498#389C2312yes—
499#389C2312yes—
500#389C2314yes—
501#389C2314yes—
502#389C2314yes—
503#389C2312yes—
504#389C2312yes—
505#389C2312yes—
506#389C2314yes—
507#389C2314yes—
508#389C2314yes—
509#389C2312yes—
510#389C2314yes—
511#388C2312yes—
512#388C2314yes—
513#388C2314yes—
514#388C2314yes—
515#388C2312yes—
516#388C2312yes—
517#388C2314yes—
518#388C2314yes—
519#388C2314yes—
520#388C2312yes—
521#388C2314yes—
522#388C2314yes—
523#388C2314yes—
524#388C2314yes—
525#388C2314yes—
526#388C2314yes—
527#388C2314yes—
528#388C2314yes—
529#388C2314yes—
530#388C2314yes—
531#388C2314yes—
532#388C2314yes—
533#388C2314yes—
534#388C2314yes—
535#388C2314yes—
536#388C2314yes—
537#388C2314yes—
538#388C2314yes—
539#388C2314yes—
540#388C2314yes—
541#388C2314yes—
542#388C2312yes—
543#388C2314yes—
544#388C2314yes—
545#388C2314yes—
546#388C2314yes—
547#388C2314yes—
548#388C2314yes—
549#388C2314yes—
550#388C2314yes—
551#388C2314yes—
552#388C2312yes—
553#388C2314yes—
554#388C2314yes—
555#388C2314yes—
556#388C2314yes—
557#388C2314yes—
558#388C2312yes—
559#388C2312yes—
560#388C2314yes—
561#388C2314yes—
562#388C2314yes—
563#388C2312yes—
564#388C2312yes—
565#388C2314yes—
566#388C2312yes—
567#387C2312yes—
568#387C2314yes—
569#387C2314yes—
570#387C2314yes—
571#387C2312yes—
572#387C2312yes—
573#387C2312yes—
574#387C2312yes—
575#387C2314yes—
576#387C2314yes—
577#387C2314yes—
578#387C2314yes—
579#387C2314yes—
580#387C2314yes—
581#387C2314yes—
582#387C2314yes—
583#387C2314yes—
584#387C2314yes—
585#387C2314yes—
586#387C2314yes—
587#387C2314yes—
588#387C2314yes—
589#387C2314yes—
590#387C2314yes—
591#387C2314yes—
592#387C2314yes—
593#387C2314yes—
594#386C2314yes—
595#386C2312yes—
596#386C2314yes—
597#386C2314yes—
598#386C2314yes—
599#386C2312yes—
600#386C2312yes—
601#386C2314yes—
602#386C2314yes—
603#386C2314yes—
604#386C2314yes—
605#386C2314yes—
606#386C2314yes—
607#386C2314yes—
608#386C2314yes—
609#386C2314yes—
610#386C2314yes—
611#386C2312yes—
612#386C2314yes—
613#386C2314yes—
614#386C2314yes—
615#386C2314yes—
616#386C2312yes—
617#386C2314yes—
618#386C2314yes—
619#386C2314yes—
620#386C2314yes—
621#386C2314yes—
622#386C2312yes—
623#385C2314yes—
624#385C2314yes—
625#385C2314yes—
626#385C2314yes—
627#385C2314yes—
628#385C2314yes—
629#385C2314yes—
630#385C2314yes—
631#385C2314yes—
632#385C2312yes—
633#385C2314yes—
634#385C2314yes—
635#385C2314yes—
636#385C2312yes—
637#384C2312yes—
638#383C2312yes—
639#383C2312yes—
640#383C2312yes—
641#382C2314yes—
642#382C2312yes—
643#382C2312yes—
644#382C2311yescharacteristic
645#381C2312yes—
646#381C2314yes—
647#381C2312yes—
648#380C2314yes—
649#380C2314yes—
650#380C2312yes—
651#380C2314yes—
652#380C2312yes—
653#380C2314yes—
654#380C2314yes—
655#380C2311yescharacteristic
656#380C2311yescharacteristic
657C4×C4⋊C4C2312yes—
658C4×C4⋊C4C2314yes—
659C4×C4⋊C4C2312yes—
660C4×C4⋊C4C2312yes—
661C4×C4⋊C4C2314yes—
662C4×C4⋊C4C2312yes—
663C4×C4⋊C4C2314yes—
664C4×C4⋊C4C2311yescharacteristic
665C4×C4⋊C4C2314yes—
666C4×C4⋊C4C2314yes—
667C4×C4⋊C4C2314yes—
668C4×C4⋊C4C2314yes—
669C4×C4⋊C4C2312yes—
670C4×C4⋊C4C2312yes—
671C4×C4⋊C4C2314yes—
672C4×C4⋊C4C2314yes—
673C4×C4⋊C4C2312yes—
674C4×C4⋊C4C2314yes—
675C4×C4⋊C4C2314yes—
676C4×C4⋊C4C2312yes—
677C4×C4⋊C4C2312yes—
678C4×C4⋊C4C2312yes—
679C4×C4⋊C4C2312yes—
680C4×C4⋊C4C2312yes—
681C4×C4⋊C4C2312yes—
682C4×C4⋊C4C2312yes—
683C4×C22⋊C4C2311yescharacteristic
684C4×C22⋊C4C2314yes—
685C4×C22⋊C4C2314yes—
686C4×C22⋊C4C2314yes—
687C4×C22⋊C4C2312yes—
688C4×C22⋊C4C2312yes—
689C4×C22⋊C4C2314yes—
690C4×C22⋊C4C2312yes—
691C4×C22⋊C4C2314yes—
692C4×C22⋊C4C2314yes—
693C4×C22⋊C4C2314yes—
694C4×C22⋊C4C2314yes—
695C4×C22⋊C4C2312yes—
696C4×C22⋊C4C2312yes—
697C4×C22⋊C4C2314yes—
698C4×C22⋊C4C2311yescharacteristic
699C4×C22⋊C4C2314yes—
700C4×C22⋊C4C2312yes—
701C4×C22⋊C4C2314yes—
702C4×C22⋊C4C2314yes—
703C4×C22⋊C4C2312yes—
704C4×C22⋊C4C2314yes—
705C4×C22⋊C4C2314yes—
706C4×C22⋊C4C2314yes—
707C4×C22⋊C4C2314yes—
708C4×C22⋊C4C2312yes—
709C4×C22⋊C4C2314yes—
710C4×C22⋊C4C2314yes—
711C4×C22⋊C4C2314yes—
712C4×C22⋊C4C2312yes—
713#376C2312yes—
714#376C2314yes—
715#376C2312yes—
716C2×#95C2314yes—
717C43C2312yes—
718C43C2314yes—
719C43C2311yescharacteristic
720C2×#41—28no—
721C2×#41—28no—
722C2×#41—28no—
723C2×#41—42no—
724C2×#41—44no—
725C2×#41—44no—
726C2×#41—44no—
727C2×#41—82no—
728C22×Q8—28no—
729C22×Q8—42no—
730C22×Q8C2411yescharacteristic
731C22×Q8C2412yes—
732C22×Q8C2412yes—
733C22×Q8C2411yescharacteristic
734C22×Q8C2412yes—
735C22×D4C2411yescharacteristic
736C22×D4C2412yes—
737C22×D4C2411yescharacteristic
738C22×D4C2412yes—
739C22×D4C2414yes—
740C22×D4C2414yes—
741C22×D4C2414yes—
742C22×D4C2412yes—
743C22×D4C2414yes—
744C22×D4C2414yes—
745C22×D4C2411yescharacteristic
746C22×D4C2412yes—
747C22×D4C2412yes—
748C22×D4C2412yes—
749C22×D4C2414yes—
750C22×D4C2412yes—
751C22×D4C2414yes—
752C23×C4C2411yescharacteristic
753C23×C4C2411yescharacteristic
754C23×C4C2414yes—
755C23×C4C2414yes—
756C23×C4C2412yes—
757C23×C4C2412yes—
758C23×C4C2412yes—
759C23×C4C2412yes—
760C23×C4C2414yes—
761C23×C4C2414yes—
762C23×C4C2414yes—
763C23×C4C2412yes—
764C23×C4C2412yes—
765C23×C4C2414yes—
766C4⋊Q8—42no—
767#127—44no—
768#127—42no—
769#127—82no—
770#126—216no—
771#126—44no—
772#126—48no—
773#125—28no—
774#124—28no—
775#124—28no—
776#124—216no—
777#124—48no—
778#124—44no—
779#124—44no—
780#124—42no—
781#123—216no—
782#123—44no—
783#123—48no—
784#123—48no—
785#123—44no—
786#123—84no—
787C22⋊Q8—28no—
788C22⋊Q8—216no—
789C22⋊Q8—216no—
790C22⋊Q8#41116yescomplemented
791#121—28no—
792#121—28no—
793#121—28no—
794#121—216no—
795#121—28no—
796#121—216no—
797#121—216no—
798#121—216no—
799#121—48no—
800#121—48no—
801#121—44no—
802#121—48no—
803#121—44no—
804#121—42no—
805#121—42no—
806#121—84no—
807C4×Q8—28no—
808C4×Q8—28no—
809C4×Q8—28no—
810C4×Q8—44no—
811C4×Q8—42no—
812C4×Q8—44no—
813C4×Q8—44no—
814C4×Q8—44no—
815C4×Q8—44no—
816C4×D4—28no—
817C4×D4—28no—
818C4×D4—216no—
819C4×D4—28no—
820C4×D4—24no—
821C4×D4—216no—
822C4×D4—44no—
823C4×D4—44no—
824C4×D4—48no—
825C4×D4—42no—
826C4×D4—48no—
827C4×D4—48no—
828C4×D4—48no—
829C4×D4—48no—
830C4×D4—84no—
831C4×D4—84no—
832#117—216no—
833#117—24no—
834#117—24no—
835#117—42no—
836#117—44no—
837#117—44no—
838#117—44no—
839#117—44no—
840#117—48no—
841#117—48no—
842#117—44no—
843#117—84no—
844C2×C4⋊C4—28no—
845C2×C4⋊C4—28no—
846C2×C4⋊C4—42no—
847C2×C4⋊C4—48no—
848C2×C4⋊C4C2412yes—
849C2×C4⋊C4C2414yes—
850C2×C4⋊C4C2414yes—
851C2×C4⋊C4C2412yes—
852C2×C4⋊C4C2414yes—
853C2×C4⋊C4C2411yescharacteristic
854C2×C4⋊C4C2411yescharacteristic
855C2×C4⋊C4C2412yes—
856C2×C4⋊C4C2414yes—
857C2×C4⋊C4C2412yes—
858C2×C4⋊C4C2412yes—
859C2×C4⋊C4C2414yes—
860C2×C4⋊C4C2414yes—
861C2×C4⋊C4C2414yes—
862C2×C4⋊C4C2414yes—
863C2×C4⋊C4C2412yes—
864C2×C4⋊C4C2414yes—
865C2×C4⋊C4C2414yes—
866C2×C4⋊C4C2412yes—
867C2×C4⋊C4C2414yes—
868C2×C4⋊C4C2412yes—
869C2×C4⋊C4C2412yes—
870C2×C4⋊C4C2411yescharacteristic
871C2×C4⋊C4C2414yes—
872C2×C4⋊C4C2414yes—
873C2×C4⋊C4C2411yescharacteristic
874C2×C4⋊C4C2411yescharacteristic
875C2×C4⋊C4C2412yes—
876C2×C4⋊C4C2414yes—
877C2×C4⋊C4C2412yes—
878C2×C4⋊C4C2412yes—
879C2×C4⋊C4C2414yes—
880C2×C4⋊C4C2411yescharacteristic
881C2×C4⋊C4C2412yes—
882C2×C4⋊C4C2414yes—
883C2×C4⋊C4C2414yes—
884C2×C4⋊C4C2412yes—
885C2×C4⋊C4C2414yes—
886C2×C4⋊C4C2412yes—
887C2×C4⋊C4C2414yes—
888C2×C4⋊C4C2412yes—
889C2×C4⋊C4C2414yes—
890C2×C4⋊C4C2412yes—
891C2×C4⋊C4C2412yes—
892C2×C4⋊C4C2414yes—
893C2×C4⋊C4C2411yescharacteristic
894C2×C22⋊C4C2412yes—
895C2×C22⋊C4C2414yes—
896C2×C22⋊C4C2412yes—
897C2×C22⋊C4C2412yes—
898C2×C22⋊C4C2412yes—
899C2×C22⋊C4C2414yes—
900C2×C22⋊C4C2414yes—
901C2×C22⋊C4C2412yes—
902C2×C22⋊C4C2412yes—
903C2×C22⋊C4C2414yes—
904C2×C22⋊C4C2412yes—
905C2×C22⋊C4C2414yes—
906C2×C22⋊C4C2414yes—
907C2×C22⋊C4C2414yes—
908C2×C22⋊C4C2414yes—
909C2×C22⋊C4C2414yes—
910C2×C22⋊C4C2412yes—
911C2×C22⋊C4C2412yes—
912C2×C22⋊C4C2414yes—
913C2×C22⋊C4C2414yes—
914C2×C22⋊C4C2414yes—
915C2×C22⋊C4C2414yes—
916C2×C22⋊C4C2412yes—
917C2×C22⋊C4C2414yes—
918C2×C22⋊C4C2412yes—
919C2×C22⋊C4C2412yes—
920C2×C22⋊C4C2414yes—
921C2×C22⋊C4C2412yes—
922C2×C22⋊C4C2412yes—
923C2×C22⋊C4C2414yes—
924C2×C22⋊C4C2414yes—
925C2×C22⋊C4C2412yes—
926C2×C22⋊C4C2412yes—
927C2×C22⋊C4C2412yes—
928C2×C22⋊C4C2414yes—
929C2×C22⋊C4C2412yes—
930C2×C22⋊C4C2411yescharacteristic
931C2×C22⋊C4C2411yescharacteristic
932C2×C22⋊C4C2414yes—
933C2×C22⋊C4C2414yes—
934C2×C22⋊C4C2412yes—
935C2×C22⋊C4C2414yes—
936C2×C22⋊C4C2412yes—
937C2×C22⋊C4C2414yes—
938C2×C22⋊C4C2414yes—
939C2×C22⋊C4C2414yes—
940C2×C22⋊C4C2414yes—
941C2×C22⋊C4C2412yes—
942C2×C22⋊C4C2414yes—
943C2×C22⋊C4C2412yes—
944C2×C22⋊C4C2414yes—
945C2×C22⋊C4C2412yes—
946C2×C22⋊C4C2414yes—
947C2×C22⋊C4C2412yes—
948C2×C22⋊C4C2414yes—
949C2×C22⋊C4C2414yes—
950C2×C22⋊C4C2414yes—
951C2×C22⋊C4C2412yes—
952C2×C22⋊C4C2412yes—
953C2×C22⋊C4C2414yes—
954C2×C42—28no—
955C2×C42—82no—
956C2×C42—84no—
957C2×C42C2414yes—
958C2×C42C2412yes—
959C2×C42C2412yes—
960C2×C42C2412yes—
961C2×C42C2411yescharacteristic
962C2×C42C2412yes—
963C2×C42C2412yes—
964C2×C42C2414yes—
965C2×C42C2412yes—
966C2×C42C2411yescharacteristic
967C2×C42C2412yes—
968C2×C42C2414yes—
969C2×C42C2412yes—
970C2×C42C2412yes—
971C2×C42C2412yes—
972C2×C42C2412yes—
973C2×C42C2412yes—
974C2×C42C2414yes—
975C2×C42C2414yes—
976C2×C42C2414yes—
977C2×C42C2412yes—
978C2×C42C2412yes—
979C2×C42C2414yes—
980C2×C42C2414yes—
981C2×C42C2414yes—
982C2×C42C2414yes—
983C2×C42C2414yes—
984C2×C42C2412yes—
985C2×C42C2414yes—
986C2×C42C2411yescharacteristic
987#95C2414yes—
988#95C2414yes—
989#95C2414yes—
990#95C2414yes—
991#95C2412yes—
992#95C2412yes—
993#95C2412yes—
994#95C2414yes—
995#95C2412yes—
996#95C2412yes—
997#95C2412yes—
998#95C2412yes—
999#95C2412yes—
1000#95C2414yes—
1001#95C2414yes—
1002#95C2414yes—
1003#95C2414yes—
1004#95C2412yes—
1005#95C2412yes—
1006#95C2414yes—
1007#95C2412yes—
1008#95C2412yes—
1009#95C2414yes—
1010#95C2412yes—
1011#95C2414yes—
1012#95C2414yes—
1013#95C2411yescharacteristic
1014#95C2411yescharacteristic
1015#95C2412yes—
1016#95C2412yes—
1017#95C2414yes—
1018#95C2414yes—
1019#95C2414yes—
1020#95C2414yes—
1021#95C2414yes—
1022#95C2414yes—
1023#95C2414yes—
1024#95C2414yes—
1025#95C2414yes—
1026#95C2412yes—
1027#95C2414yes—
1028#95C2412yes—
1029#95C2411yescharacteristic
1030#95C2411yescharacteristic
1031#95C2412yes—
1032#95C2412yes—
1033#95C2414yes—
1034#95C2414yes—
1035#95C2414yes—
1036#95C2414yes—
1037#95C2412yes—
1038#95C2412yes—
1039#95C2412yes—
1040#95C2412yes—
1041#95C2414yes—
1042#95C2414yes—
1043#95C2414yes—
1044C24C2512yes—
1045C24C2514yes—
1046C24C2511yescharacteristic
1047C24C2511yescharacteristic
1048C24C2512yes—
1049#41—416no—
1050#41—432no—
1051#41—816no—
1052C2×Q8—24no—
1053C2×Q8—24no—
1054C2×Q8—28no—
1055C2×Q8—24no—
1056C2×Q8—22no—
1057C2×Q8—42no—
1058C2×Q8—41no—
1059C2×Q8—41no—
1060C2×Q8—41no—
1061C2×Q8—42no—
1062C2×Q8—44no—
1063C2×Q8—416no—
1064C2×Q8C2×#4118yes—
1065C2×D4—28no—
1066C2×D4—24no—
1067C2×D4—24no—
1068C2×D4—28no—
1069C2×D4—24no—
1070C2×D4—28no—
1071C2×D4—24no—
1072C2×D4—24no—
1073C2×D4—28no—
1074C2×D4—24no—
1075C2×D4—24no—
1076C2×D4—28no—
1077C2×D4—28no—
1078C2×D4—24no—
1079C2×D4—22no—
1080C2×D4—22no—
1081C2×D4—24no—
1082C2×D4—44no—
1083C2×D4—42no—
1084C2×D4—41no—
1085C2×D4—44no—
1086C2×D4—44no—
1087C2×D4—41no—
1088C2×D4—44no—
1089C2×D4—44no—
1090C2×D4—42no—
1091C2×D4—44no—
1092C2×D4—44no—
1093C2×D4—44no—
1094C2×D4—42no—
1095C2×D4—44no—
1096C2×D4—42no—
1097C2×D4—44no—
1098C2×D4—44no—
1099C2×D4—41no—
1100C2×D4—42no—
1101C2×D4—44no—
1102C2×D4—42no—
1103C2×D4—42no—
1104C2×D4—44no—
1105C2×D4—42no—
1106C2×D4—44no—
1107C2×D4—44no—
1108C2×D4—44no—
1109C2×D4—44no—
1110C2×D4—44no—
1111C22×C4—24no—
1112C22×C4—24no—
1113C22×C4—24no—
1114C22×C4—24no—
1115C22×C4—28no—
1116C22×C4—28no—
1117C22×C4—24no—
1118C22×C4—28no—
1119C22×C4—28no—
1120C22×C4—24no—
1121C22×C4—22no—
1122C22×C4—22no—
1123C22×C4—24no—
1124C22×C4—24no—
1125C22×C4—28no—
1126C22×C4—24no—
1127C22×C4—28no—
1128C22×C4—28no—
1129C22×C4—28no—
1130C22×C4—42no—
1131C22×C4—44no—
1132C22×C4—42no—
1133C22×C4—44no—
1134C22×C4—42no—
1135C22×C4—42no—
1136C22×C4—42no—
1137C22×C4—44no—
1138C22×C4—44no—
1139C22×C4—44no—
1140C22×C4—44no—
1141C22×C4—44no—
1142C22×C4—44no—
1143C22×C4—44no—
1144C22×C4—42no—
1145C22×C4—42no—
1146C22×C4—44no—
1147C22×C4—44no—
1148C22×C4—42no—
1149C22×C4C2×#4118yes—
1150C22×C4C2511yescharacteristic
1151C22×C4C2512yes—
1152C22×C4C2512yes—
1153C22×C4C2514yes—
1154C22×C4C2512yes—
1155C22×C4C2511yescharacteristic
1156C22×C4C2514yes—
1157C22×C4C2511yescharacteristic
1158C22×C4C2512yes—
1159C22×C4C2512yes—
1160C22×C4C2514yes—
1161C22×C4C2512yes—
1162C22×C4C2512yes—
1163C22×C4C2512yes—
1164C22×C4C2512yes—
1165C22×C4C2512yes—
1166C22×C4C2512yes—
1167C22×C4C2514yes—
1168C22×C4C2514yes—
1169C22×C4C2512yes—
1170C22×C4C2512yes—
1171C22×C4C2511yescharacteristic
1172C22×C4C2512yes—
1173C22×C4C2511yescharacteristic
1174C4⋊C4—28no—
1175C4⋊C4—24no—
1176C4⋊C4—28no—
1177C4⋊C4—24no—
1178C4⋊C4—28no—
1179C4⋊C4—28no—
1180C4⋊C4—24no—
1181C4⋊C4—28no—
1182C4⋊C4—28no—
1183C4⋊C4—28no—
1184C4⋊C4—24no—
1185C4⋊C4—28no—
1186C4⋊C4—22no—
1187C4⋊C4—22no—
1188C4⋊C4—24no—
1189C4⋊C4—24no—
1190C4⋊C4—28no—
1191C4⋊C4—28no—
1192C4⋊C4—42no—
1193C4⋊C4—44no—
1194C4⋊C4—42no—
1195C4⋊C4—42no—
1196C4⋊C4—42no—
1197C4⋊C4—42no—
1198C4⋊C4—41no—
1199C4⋊C4—44no—
1200C4⋊C4—41no—
1201C4⋊C4—41no—
1202C4⋊C4—42no—
1203C4⋊C4—44no—
1204C4⋊C4—44no—
1205C4⋊C4—44no—
1206C4⋊C4—41no—
1207C4⋊C4—42no—
1208C4⋊C4—44no—
1209C4⋊C4—44no—
1210C4⋊C4—42no—
1211C4⋊C4—44no—
1212C4⋊C4—42no—
1213C4⋊C4—44no—
1214C4⋊C4—42no—
1215C4⋊C4—44no—
1216C4⋊C4—42no—
1217C4⋊C4C2×#4118yes—
1218C4⋊C4C2×#41116yes—
1219C4⋊C4H(5,𝔽2)14yes—
1220C22⋊C4—24no—
1221C22⋊C4—28no—
1222C22⋊C4—28no—
1223C22⋊C4—24no—
1224C22⋊C4—28no—
1225C22⋊C4—28no—
1226C22⋊C4—28no—
1227C22⋊C4—28no—
1228C22⋊C4—28no—
1229C22⋊C4—28no—
1230C22⋊C4—28no—
1231C22⋊C4—28no—
1232C22⋊C4—24no—
1233C22⋊C4—24no—
1234C22⋊C4—28no—
1235C22⋊C4—24no—
1236C22⋊C4—24no—
1237C22⋊C4—24no—
1238C22⋊C4—24no—
1239C22⋊C4—24no—
1240C22⋊C4—28no—
1241C22⋊C4—28no—
1242C22⋊C4—42no—
1243C22⋊C4—42no—
1244C22⋊C4—42no—
1245C22⋊C4—42no—
1246C22⋊C4—44no—
1247C22⋊C4—42no—
1248C22⋊C4—44no—
1249C22⋊C4—42no—
1250C22⋊C4—42no—
1251C22⋊C4—44no—
1252C22⋊C4—44no—
1253C22⋊C4—44no—
1254C22⋊C4—44no—
1255C22⋊C4—41no—
1256C22⋊C4—41no—
1257C22⋊C4—44no—
1258C22⋊C4—42no—
1259C22⋊C4—42no—
1260C22⋊C4—42no—
1261C22⋊C4—44no—
1262C22⋊C4—42no—
1263C22⋊C4—44no—
1264C22⋊C4—44no—
1265C22⋊C4—44no—
1266C22⋊C4—44no—
1267C22⋊C4—44no—
1268C22⋊C4—42no—
1269C22⋊C4—44no—
1270C22⋊C4—42no—
1271C22⋊C4—44no—
1272C22⋊C4—44no—
1273C22⋊C4—42no—
1274C22⋊C4—42no—
1275C22⋊C4—44no—
1276C22⋊C4—42no—
1277C22⋊C4—42no—
1278C22⋊C4—44no—
1279C22⋊C4C2×#41116yes—
1280C42—24no—
1281C42—24no—
1282C42—24no—
1283C42—24no—
1284C42—28no—
1285C42—28no—
1286C42—24no—
1287C42—24no—
1288C42—24no—
1289C42—28no—
1290C42—24no—
1291C42—24no—
1292C42—22no—
1293C42—22no—
1294C42—24no—
1295C42—24no—
1296C42—41no—
1297C42—44no—
1298C42—44no—
1299C42—44no—
1300C42—44no—
1301C42—42no—
1302C42—42no—
1303C42—42no—
1304C42—44no—
1305C42—44no—
1306C42—44no—
1307C42—42no—
1308C42—44no—
1309C42—44no—
1310C23—22no—
1311C23—22no—
1312C23—22no—
1313C23—22no—
1314C23—22no—
1315C23—22no—
1316C23—24no—
1317C23—24no—
1318C23—22no—
1319C23—24no—
1320C23—22no—
1321C23—21no—
1322C23—21no—
1323C23—22no—
1324C23—24no—
1325C23—24no—
1326C23—22no—
1327C23—24no—
1328C23—22no—
1329C23—21no—
1330C23—21no—
1331C23—24no—
1332C23—22no—
1333C23—24no—
1334C23—22no—
1335C23—21no—
1336C23—24no—
1337C23—21no—
1338C23C22×#4114yes—
1339C23C2611yescharacteristic
1340Q8—216no—
1341Q8—48no—
1342Q8—44no—
1343Q8—44no—
1344Q8—162no—
1345D4—48no—
1346D4—416no—
1347D4—44no—
1348D4—416no—
1349D4—44no—
1350D4—48no—
1351D4—88no—
1352D4—88no—
1353D4—82no—
1354D4—84no—
1355D4—88no—
1356D4—84no—
1357D4—88no—
1358D4—164no—
1359D4—162no—
1360D4—162no—
1361D4—162no—
1362C2×C4—22no—
1363C2×C4—24no—
1364C2×C4—22no—
1365C2×C4—24no—
1366C2×C4—21no—
1367C2×C4—22no—
1368C2×C4—22no—
1369C2×C4—24no—
1370C2×C4—22no—
1371C2×C4—22no—
1372C2×C4—24no—
1373C2×C4—21no—
1374C2×C4—216no—
1375C2×C4—22no—
1376C2×C4—22no—
1377C2×C4—22no—
1378C2×C4—22no—
1379C2×C4—22no—
1380C2×C4—24no—
1381C2×C4—22no—
1382C2×C4—24no—
1383C2×C4—22no—
1384C2×C4—22no—
1385C2×C4—21no—
1386C2×C4—21no—
1387C2×C4—22no—
1388C2×C4—22no—
1389C2×C4—22no—
1390C2×C4—22no—
1391C2×C4—21no—
1392C2×C4—22no—
1393C2×C4—24no—
1394C2×C4—22no—
1395C2×C4—22no—
1396C2×C4—22no—
1397C2×C4—22no—
1398C2×C4—22no—
1399C2×C4—22no—
1400C2×C4—22no—
1401C2×C4—24no—
1402C2×C4—24no—
1403C2×C4—22no—
1404C2×C4—22no—
1405C2×C4—24no—
1406C2×C4—22no—
1407C2×C4—24no—
1408C2×C4—22no—
1409C2×C4—22no—
1410C2×C4—22no—
1411C2×C4—24no—
1412C2×C4—22no—
1413C2×C4—24no—
1414C2×C4—22no—
1415C2×C4—22no—
1416C2×C4—24no—
1417C2×C4—24no—
1418C2×C4—22no—
1419C2×C4—22no—
1420C2×C4—22no—
1421C2×C4—416no—
1422C2×C4—48no—
1423C2×C4—416no—
1424C2×C4—48no—
1425C2×C4—48no—
1426C2×C4—48no—
1427C2×C4—44no—
1428C2×C4—44no—
1429C2×C4—88no—
1430C2×C4—88no—
1431C2×C4—88no—
1432C2×C4—162no—
1433C2×C4—164no—
1434C2×C4C22×#4114yes—
1435C2×C4C22×#4118yes—
1436C2×C4C22×#4118yes—
1437C2×C4C22×#4114yes—
1438C2×C4C2×H(5,𝔽2)14yes—
1439C2×C4C2×H(5,𝔽2)12yes—
1440C2×C4#58514yes—
1441C2×C4#58512yes—
1442C22—24no—
1443C22—24no—
1444C22—24no—
1445C22—42no—
1446C22—42no—
1447C22—42no—
1448C22—42no—
1449C22—44no—
1450C22—42no—
1451C22—42no—
1452C22—44no—
1453C22—44no—
1454C22—42no—
1455C22—41no—
1456C22—41no—
1457C22—44no—
1458C22—44no—
1459C22—44no—
1460C22—44no—
1461C22—42no—
1462C22—42no—
1463C22—42no—
1464C22—44no—
1465C22—41no—
1466C22—41no—
1467C22—41no—
1468C22—44no—
1469C22—41no—
1470C22—42no—
1471C22C23×#4112yes—
1472C22C22×H(5,𝔽2)11yescharacteristic
1473C22C2×#58512yes—
1474C22C2×#58511yescharacteristic
1475C22H(7,𝔽2)11yescharacteristic
1476C4—24no—
1477C4—28no—
1478C4—22no—
1479C4—24no—
1480C4—24no—
1481C4—28no—
1482C4—42no—
1483C4—44no—
1484C4—42no—
1485C4—42no—
1486C4—42no—
1487C4—41no—
1488C4—42no—
1489C4—42no—
1490C4—42no—
1491C4—42no—
1492C4—42no—
1493C4—44no—
1494C4—42no—
1495C4—44no—
1496C4—42no—
1497C4—41no—
1498C4—41no—
1499C4#348114yes—
1500C2—44no—
1501C2—82no—
1502C2—81no—
1503C2—81no—
1504C2—84no—
1505C2C2×#348111yescharacteristic
1506C2#6279312yes—
1507C2#6291811yescharacteristic
1508C2#6300812yes—
1509C2#6303511yescharacteristic
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. #60046C2semidirect
2. #59946C2semidirect
3. #59782C2semidirect
4. #59721C2semidirect
5. #59700C2semidirect
6. #59104C2semidirect
7. #45315C2semidirect
8. #45244C2semidirect
9. #45190C2semidirect
10. #44834C2semidirect
11. #44193C2semidirect
12. #43442C2semidirect
13. #38865C2semidirect
14. #38841C2semidirect
15. #38214C2semidirect
16. #37785C2semidirect
17. #36589C2semidirect
18. #36588C2semidirect
19. #36412C2semidirect
20. #36399C2semidirect
21. #36369C2semidirect
22. #36077C2semidirect
23. #35756C2semidirect
24. #35704C2semidirect
25. #34962C2semidirect
26. #34871C2semidirect
27. #34312C2semidirect
28. #34274C2semidirect
29. #34153C2semidirect
790. C22⋊Q8#41semidirect

Maximal subgroups

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

subgroupindex
#600462
#599462
#597822
#597212
#597002
#591042
#453152
#452442
#451902
#448342
#441932
#434422
#388652
#388412
#382142
#377852
#365892
#365882
#364122
#363992
#363692
#360772
#357562
#357042
#349622
#348712
#343122
#342742
#341532