Finite Group Databasebeta

← #8726338

Subgroups — #8726338

Order 512.

4799 conjugacy classes of subgroups.

The subgroup lattice has 1514 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#59827C211yesmaximal, characteristic, complemented
2#59502C212yesmaximal, complemented
3#59381C212yesmaximal, complemented
4#59317C212yesmaximal, complemented
5#59308C212yesmaximal, complemented
6#58343C212yesmaximal, complemented
7#57903C214yesmaximal, complemented
8#57902C214yesmaximal, complemented
9#55015C214yesmaximal, complemented
10#53017C211yesmaximal, characteristic, complemented
11#52963C212yesmaximal, complemented
12#52297C211yesmaximal, characteristic, complemented
13#47800C212yesmaximal, complemented
14#46555C214yesmaximal, complemented
15#45251C211yesmaximal, characteristic, complemented
16#44913C212yesmaximal, complemented
17#44657C212yesmaximal, complemented
18#43920C214yesmaximal, complemented
19#42989C212yesmaximal, complemented
20#42985C211yesmaximal, characteristic, complemented
21#42252C212yesmaximal, complemented
22#41156C214yesmaximal, complemented
23#39789C212yesmaximal, complemented
24#39410C212yesmaximal, complemented
25#39222C212yesmaximal, complemented
26#39169C211yesmaximal, characteristic, complemented
27#39145C212yesmaximal, complemented
28#36076C211yesmaximal, characteristic, complemented
29#35772C212yesmaximal, complemented
30C2×#559C2212yes—
31C2×#554C2211yescharacteristic
32C2×#552C2212yes—
33C2×#550C2211yescharacteristic
34C2×#540C2214yes—
35C2×#537C2211yescharacteristic
36C2×#520C2211yescharacteristic
37#2858C2211yescharacteristic
38#2854C2212yes—
39#2841C2212yes—
40#2831C2214yes—
41#2831C2214yes—
42#2829C2214yes—
43#2827C2214yes—
44#2827C2214yes—
45#2826C2214yes—
46#2822C2212yes—
47#2815C2212yes—
48#2803C2212yes—
49#2800C2214yes—
50#2797C2214yes—
51#2795C2211yescharacteristic
52#2792C2211yescharacteristic
53#2789C2212yes—
54#2788C2214yes—
55#2784C2211yescharacteristic
56#2783C2214yes—
57#2782C2214yes—
58#2781C2214yes—
59#2778C2214yes—
60#2772C2214yes—
61#2769C2212yes—
62#2765C2214yes—
63#2764C2212yes—
64#2762C2214yes—
65#2761C2214yes—
66#2760C2212yes—
67#2756C2212yes—
68#2753C2214yes—
69#2751C2214yes—
70#2745C2214yes—
71#2737C2212yes—
72#2732C2214yes—
73#2730C2214yes—
74#2724C2212yes—
75#2724C2212yes—
76#2723C2214yes—
77#2719C2214yes—
78#2714C2212yes—
79#2712C2214yes—
80#2711C2214yes—
81#2710C2214yes—
82#2709C2214yes—
83#2708C2214yes—
84#2708C2214yes—
85#2707C2214yes—
86#2707C2214yes—
87#2705C2212yes—
88#2704C2214yes—
89#2701C2214yes—
90#2700C2214yes—
91#2699C2214yes—
92#2699C2211yescharacteristic
93#2698C2214yes—
94#2691C2214yes—
95#2688C2214yes—
96#2688C2214yes—
97#2688C2214yes—
98#2676C2214yes—
99#2676C2214yes—
100#2676C2214yes—
101#2676C2214yes—
102#2673C2214yes—
103#2673C2212yes—
104#2672C2214yes—
105#2671C2214yes—
106#2665C2214yes—
107#2662C2214yes—
108#2653C2214yes—
109#2651C2214yes—
110#2643C2214yes—
111#2641C2212yes—
112#2639C2212yes—
113#2638C2212yes—
114#2636C2214yes—
115#2630C2214yes—
116#2629C2212yes—
117#2624C2212yes—
118#2624C2211yescharacteristic
119#2615C2211yescharacteristic
120#2611C2214yes—
121#2609C2214yes—
122#2609C2212yes—
123#2607C2212yes—
124#2601C2214yes—
125#2595C2214yes—
126#2590C2214yes—
127#2582C2212yes—
128#2578C2214yes—
129#2576C2214yes—
130#2576C2214yes—
131#2575C2214yes—
132#2570C2212yes—
133#2566C2212yes—
134#2566C2212yes—
135#2563C2211yescharacteristic
136#2559C2214yes—
137#2557C2214yes—
138#2555C2214yes—
139#2555C2214yes—
140#2550C2212yes—
141#2547C2212yes—
142#2547C2212yes—
143#2543C2212yes—
144#2543C2214yes—
145#2541C2212yes—
146#2541C2211yescharacteristic
147#2537C2212yes—
148#2536C2212yes—
149#2535C2212yes—
150#2528C2214yes—
151#2519C2214yes—
152#2518C2214yes—
153#2513C2212yes—
154#2510C2214yes—
155#2509C2212yes—
156#2506C2212yes—
157#2504C2211yescharacteristic
158#2504C2212yes—
159#2504C2211yescharacteristic
160#2500C2212yes—
161#2497C2212yes—
162#2495C2212yes—
163#2494C2212yes—
164#2494C2212yes—
165#2491C2212yes—
166#2490C2212yes—
167#2489C2214yes—
168#2488C2214yes—
169#2487C2212yes—
170#2487C2212yes—
171#2486C2211yescharacteristic
172#2486C2212yes—
173#2486C2211yescharacteristic
174#2486C2212yes—
175#2477C2214yes—
176#2476C2214yes—
177#2473C2214yes—
178#2471C2214yes—
179#2464C2214yes—
180#2462C2214yes—
181#2461C2214yes—
182#2460C2214yes—
183#2458C2214yes—
184#2457C2214yes—
185#2456C2214yes—
186#2452C2212yes—
187#2451C2212yes—
188#2447C2214yes—
189#2447C2214yes—
190#2445C2214yes—
191#2445C2212yes—
192#2444C2214yes—
193#2443C2214yes—
194#2442C2212yes—
195#2442C2212yes—
196#2440C2212yes—
197#2439C2212yes—
198#2438C2214yes—
199#2428C2212yes—
200#2426C2214yes—
201#2425C2214yes—
202#2425C2214yes—
203#2423C2212yes—
204#2422C2212yes—
205#2421C2212yes—
206#2421C2212yes—
207#2420C2214yes—
208#2420C2212yes—
209#2419C2214yes—
210#2419C2214yes—
211#2416C2212yes—
212#2416C2212yes—
213#2416C2212yes—
214#2416C2212yes—
215#2416C2212yes—
216#2414C2214yes—
217#2407C2212yes—
218#2407C2212yes—
219#2407C2212yes—
220#2395C2212yes—
221#2395C2211yescharacteristic
222#2392C2212yes—
223#2392C2214yes—
224#2388C2212yes—
225#2388C2211yescharacteristic
226#2368C2214yes—
227#2364C2214yes—
228#2363C2212yes—
229#2362C2214yes—
230#2361C2212yes—
231#2360C2212yes—
232#2359C2214yes—
233#2357C2212yes—
234#2355C2212yes—
235#2352C2212yes—
236#2352C2212yes—
237#2351C2212yes—
238D4×C4⋊C4C2212yes—
239D4×C4⋊C4C2212yes—
240#2344C2212yes—
241#2341C2211yescharacteristic
242#2341C2212yes—
243#2339C2211yescharacteristic
244#2337C2214yes—
245#2337C2214yes—
246#2328C2212yes—
247#2325C2214yes—
248#2311C2212yes—
249C4×C4⋊Q8C2212yes—
250C4×#127C2211yescharacteristic
251C4×#126C2212yes—
252C4×C22⋊Q8C2212yes—
253C4×#123C2212yes—
254C4×#121C2212yes—
255C4×#121C2212yes—
256C4×#121C2212yes—
257#2295C2211yescharacteristic
258C2×#382C2212yes—
259C22×#41C2311yescharacteristic
260C22×#41C2311yescharacteristic
261C22×#41C2311yescharacteristic
262#559—48no—
263#554—44no—
264#552—48no—
265#550—44no—
266#540—416no—
267#537—44no—
268C2×C4⋊Q8C2312yes—
269C2×C4⋊Q8C2311yescharacteristic
270C2×#127C2311yescharacteristic
271C2×#127C2312yes—
272C2×#127C2311yescharacteristic
273C2×#127C2312yes—
274C2×#126C2312yes—
275C2×#126C2314yes—
276C2×#125C2312yes—
277C2×#125C2312yes—
278C2×#125C2314yes—
279C2×#125C2314yes—
280C2×#124C2314yes—
281C2×#124C2314yes—
282C2×#124C2314yes—
283C2×#124C2314yes—
284C2×#123C2314yes—
285C2×#123C2314yes—
286C2×#123C2314yes—
287C2×#123C2314yes—
288C2×#123C2312yes—
289C2×#123C2312yes—
290C2×#123C2314yes—
291C2×#123C2312yes—
292C2×C22⋊Q8C2312yes—
293C2×C22⋊Q8C2312yes—
294C2×C22⋊Q8C2314yes—
295C2×C22⋊Q8C2314yes—
296C2×C22⋊Q8C2312yes—
297C2×C22⋊Q8C2314yes—
298C2×#121C2312yes—
299C2×#121C2314yes—
300C2×#121C2312yes—
301C2×#121C2312yes—
302C2×#121C2311yescharacteristic
303C2×#121C2314yes—
304C2×#121C2311yescharacteristic
305C2×#121C2312yes—
306C2×#121C2312yes—
307C2×#121C2312yes—
308C2×#121C2314yes—
309C2×#121C2314yes—
310C2×#121C2312yes—
311C2×#121C2314yes—
312C2×#121C2312yes—
313C2×#121C2314yes—
314C2×#121C2314yes—
315C2×#121C2312yes—
316C2×#121C2314yes—
317#520—44no—
318C2×C4×Q8C2312yes—
319C2×C4×Q8C2311yescharacteristic
320C2×C4×Q8C2314yes—
321C2×C4×Q8C2312yes—
322C2×C4×D4C2311yescharacteristic
323C2×C4×D4C2312yes—
324C2×C4×D4C2312yes—
325C2×C4×D4C2311yescharacteristic
326C2×C4×D4C2312yes—
327C2×C4×D4C2312yes—
328C2×C4×D4C2314yes—
329C2×C4×D4C2314yes—
330C2×C4×D4C2312yes—
331C2×C4×D4C2312yes—
332C2×C4×D4C2314yes—
333C2×C4×D4C2312yes—
334C2×C4×D4C2312yes—
335C2×C4×D4C2314yes—
336C2×C4×D4C2314yes—
337C2×C4×D4C2312yes—
338C2×#117C2312yes—
339C2×#117C2314yes—
340C2×#117C2312yes—
341C2×#117C2314yes—
342C2×#117C2311yescharacteristic
343C22×C4⋊C4C2312yes—
344C22×C4⋊C4C2311yescharacteristic
345C22×C4⋊C4C2312yes—
346C22×C4⋊C4C2311yescharacteristic
347C22×C4⋊C4C2312yes—
348C22×C4⋊C4C2312yes—
349C22×C42C2312yes—
350#401C2314yes—
351#401C2314yes—
352#400C2314yes—
353#400C2314yes—
354#400C2314yes—
355#400C2314yes—
356#400C2314yes—
357#400C2314yes—
358#400C2314yes—
359#400C2314yes—
360#400C2314yes—
361#400C2314yes—
362#400C2314yes—
363#400C2314yes—
364#400C2311yescharacteristic
365#399C2314yes—
366#399C2312yes—
367#399C2314yes—
368#399C2314yes—
369#399C2311yescharacteristic
370#398C2311yescharacteristic
371#398C2314yes—
372#398C2314yes—
373#398C2312yes—
374#398C2314yes—
375#398C2314yes—
376#398C2314yes—
377#398C2314yes—
378#398C2314yes—
379#398C2312yes—
380#398C2314yes—
381#398C2312yes—
382#398C2314yes—
383#398C2314yes—
384#398C2314yes—
385#398C2314yes—
386#397C2314yes—
387#397C2314yes—
388#397C2312yes—
389#397C2314yes—
390#397C2314yes—
391#397C2314yes—
392#397C2314yes—
393#397C2314yes—
394#397C2314yes—
395#397C2312yes—
396#397C2312yes—
397#397C2312yes—
398#397C2314yes—
399#397C2314yes—
400#397C2314yes—
401#397C2312yes—
402#397C2312yes—
403#397C2314yes—
404#397C2312yes—
405#397C2312yes—
406#397C2314yes—
407#397C2314yes—
408#397C2311yescharacteristic
409#397C2312yes—
410#397C2314yes—
411#397C2314yes—
412#396C2314yes—
413#396C2314yes—
414#396C2314yes—
415#396C2314yes—
416#396C2314yes—
417#396C2314yes—
418#396C2312yes—
419#396C2314yes—
420#396C2314yes—
421#396C2314yes—
422#396C2314yes—
423#396C2314yes—
424#396C2312yes—
425#396C2314yes—
426#395C2314yes—
427#395C2314yes—
428#395C2311yescharacteristic
429#395C2312yes—
430#395C2314yes—
431#394C2312yes—
432#394C2314yes—
433#394C2314yes—
434#394C2314yes—
435#394C2314yes—
436#394C2314yes—
437#394C2312yes—
438#394C2314yes—
439#394C2314yes—
440#394C2314yes—
441#394C2314yes—
442#394C2314yes—
443#394C2314yes—
444#394C2311yescharacteristic
445#394C2314yes—
446#394C2314yes—
447#394C2314yes—
448#394C2314yes—
449#394C2314yes—
450#394C2312yes—
451#394C2312yes—
452#394C2312yes—
453#394C2312yes—
454#394C2312yes—
455#394C2312yes—
456#394C2314yes—
457#394C2314yes—
458#394C2314yes—
459#394C2314yes—
460#394C2314yes—
461#393C2312yes—
462#393C2312yes—
463#393C2314yes—
464#393C2311yescharacteristic
465#393C2312yes—
466#393C2312yes—
467#393C2314yes—
468#393C2314yes—
469#392C2314yes—
470#392C2314yes—
471#392C2312yes—
472#392C2314yes—
473#392C2314yes—
474#392C2312yes—
475#392C2312yes—
476#392C2312yes—
477#392C2312yes—
478#392C2311yescharacteristic
479#392C2314yes—
480#392C2312yes—
481#392C2314yes—
482#392C2314yes—
483#391C2314yes—
484#391C2314yes—
485#391C2314yes—
486#391C2314yes—
487#391C2314yes—
488#391C2314yes—
489#391C2314yes—
490#391C2312yes—
491#391C2312yes—
492#390C2311yescharacteristic
493#390C2311yescharacteristic
494#390C2312yes—
495#390C2312yes—
496#390C2312yes—
497#390C2312yes—
498#390C2312yes—
499#390C2312yes—
500#390C2312yes—
501#390C2314yes—
502#390C2312yes—
503#390C2314yes—
504#390C2312yes—
505#390C2312yes—
506#390C2314yes—
507#390C2312yes—
508#390C2314yes—
509#390C2314yes—
510#390C2312yes—
511#390C2314yes—
512#390C2312yes—
513#390C2312yes—
514#389C2312yes—
515#389C2314yes—
516#389C2312yes—
517#389C2312yes—
518#389C2312yes—
519#389C2314yes—
520#389C2314yes—
521#389C2314yes—
522#389C2314yes—
523#389C2314yes—
524#389C2312yes—
525#389C2314yes—
526#389C2312yes—
527#389C2314yes—
528#389C2312yes—
529#389C2312yes—
530#389C2312yes—
531#389C2312yes—
532#389C2312yes—
533#389C2312yes—
534#388C2312yes—
535#388C2312yes—
536#388C2312yes—
537#388C2314yes—
538#388C2314yes—
539#388C2314yes—
540#388C2314yes—
541#388C2312yes—
542#388C2314yes—
543#388C2314yes—
544#388C2314yes—
545#388C2314yes—
546#388C2314yes—
547#388C2314yes—
548#388C2314yes—
549#388C2312yes—
550#388C2314yes—
551#388C2314yes—
552#388C2312yes—
553#388C2314yes—
554#388C2314yes—
555#388C2314yes—
556#388C2314yes—
557#388C2314yes—
558#388C2314yes—
559#388C2314yes—
560#388C2314yes—
561#388C2314yes—
562#388C2314yes—
563#388C2314yes—
564#388C2312yes—
565#388C2312yes—
566#388C2312yes—
567#387C2312yes—
568#387C2312yes—
569#387C2312yes—
570#387C2314yes—
571#387C2314yes—
572#387C2314yes—
573#387C2314yes—
574#387C2314yes—
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#387C2312yes—
591#387C2312yes—
592#387C2314yes—
593#386C2314yes—
594#386C2314yes—
595#386C2314yes—
596#386C2314yes—
597#386C2314yes—
598#386C2314yes—
599#386C2314yes—
600#386C2314yes—
601#386C2314yes—
602#386C2314yes—
603#386C2314yes—
604#386C2312yes—
605#386C2314yes—
606#386C2314yes—
607#386C2314yes—
608#386C2314yes—
609#386C2314yes—
610#386C2314yes—
611#386C2314yes—
612#386C2314yes—
613#386C2314yes—
614#386C2314yes—
615#386C2314yes—
616#386C2312yes—
617#386C2314yes—
618#386C2312yes—
619#386C2314yes—
620#386C2314yes—
621#386C2312yes—
622#386C2314yes—
623#386C2312yes—
624#385C2314yes—
625#385C2314yes—
626#385C2314yes—
627#385C2314yes—
628#385C2314yes—
629#385C2314yes—
630#385C2314yes—
631#385C2314yes—
632#385C2314yes—
633#385C2312yes—
634#385C2314yes—
635#385C2314yes—
636#385C2314yes—
637#385C2314yes—
638#385C2314yes—
639#385C2314yes—
640#385C2314yes—
641#385C2314yes—
642#385C2314yes—
643#385C2314yes—
644#384C2311yescharacteristic
645#384C2312yes—
646#384C2312yes—
647#383C2312yes—
648#383C2314yes—
649#382C2312yes—
650#382C2312yes—
651#382C2312yes—
652#382C2312yes—
653#382C2314yes—
654#382C2314yes—
655#382C2314yes—
656#382C2312yes—
657#382C2314yes—
658#381C2314yes—
659#381C2312yes—
660#381C2314yes—
661#381C2312yes—
662#381C2312yes—
663#381C2314yes—
664#381C2312yes—
665#381C2314yes—
666#380C2312yes—
667#380C2312yes—
668#380C2312yes—
669#380C2312yes—
670#380C2312yes—
671#380C2312yes—
672#380C2314yes—
673#380C2314yes—
674#380C2311yescharacteristic
675#380C2312yes—
676#380C2311yescharacteristic
677#380C2314yes—
678#380C2312yes—
679#380C2312yes—
680#380C2312yes—
681#380C2312yes—
682#380C2312yes—
683#380C2314yes—
684#380C2312yes—
685C4×C4⋊C4C2312yes—
686C4×C4⋊C4C2312yes—
687C4×C4⋊C4C2312yes—
688C4×C4⋊C4C2314yes—
689C4×C4⋊C4C2312yes—
690C4×C4⋊C4C2312yes—
691C4×C4⋊C4C2311yescharacteristic
692C4×C4⋊C4C2312yes—
693C4×C4⋊C4C2312yes—
694C4×C4⋊C4C2314yes—
695C4×C4⋊C4C2314yes—
696C4×C4⋊C4C2314yes—
697C4×C4⋊C4C2312yes—
698C4×C22⋊C4C2312yes—
699C4×C22⋊C4C2312yes—
700C4×C22⋊C4C2312yes—
701C4×C22⋊C4C2314yes—
702C4×C22⋊C4C2314yes—
703C4×C22⋊C4C2314yes—
704C4×C22⋊C4C2314yes—
705C4×C22⋊C4C2314yes—
706C4×C22⋊C4C2312yes—
707C4×C22⋊C4C2314yes—
708C4×C22⋊C4C2314yes—
709C4×C22⋊C4C2311yescharacteristic
710C4×C22⋊C4C2312yes—
711C4×C22⋊C4C2311yescharacteristic
712C4×C22⋊C4C2314yes—
713C4×C22⋊C4C2312yes—
714#376C2312yes—
715C2×#95C2314yes—
716C2×#95C2312yes—
717C2×#95C2314yes—
718C43C2311yescharacteristic
719C2×#41—24no—
720C2×#41—24no—
721C2×#41—42no—
722C2×#41—44no—
723C2×#41—44no—
724C2×#41—44no—
725C22×Q8C2411yescharacteristic
726C22×Q8C2414yes—
727C22×Q8C2412yes—
728C22×Q8C2411yescharacteristic
729C22×D4C2411yescharacteristic
730C22×D4C2411yescharacteristic
731C22×D4C2412yes—
732C22×D4C2412yes—
733C22×D4C2412yes—
734C22×D4C2412yes—
735C22×D4C2412yes—
736C22×D4C2414yes—
737C22×D4C2414yes—
738C22×D4C2412yes—
739C22×D4C2411yescharacteristic
740C22×D4C2412yes—
741C22×D4C2412yes—
742C22×D4C2414yes—
743C22×D4C2414yes—
744C22×D4C2412yes—
745C22×D4C2412yes—
746C22×D4C2412yes—
747C22×D4C2411yescharacteristic
748C22×D4C2412yes—
749C22×D4C2411yescharacteristic
750C23×C4C2412yes—
751C23×C4C2411yescharacteristic
752C23×C4C2412yes—
753C23×C4C2411yescharacteristic
754C23×C4C2414yes—
755C23×C4C2412yes—
756C23×C4C2412yes—
757C23×C4C2412yes—
758C23×C4C2414yes—
759C23×C4C2412yes—
760C23×C4C2414yes—
761C23×C4C2412yes—
762C23×C4C2414yes—
763C23×C4C2414yes—
764C23×C4C2412yes—
765C4⋊Q8—44no—
766C4⋊Q8—42no—
767#127—28no—
768#127—24no—
769#127—44no—
770#127—42no—
771#126—44no—
772#126—48no—
773#125—48no—
774#125—44no—
775#125—44no—
776#125—48no—
777#124—48no—
778#124—48no—
779#124—48no—
780#124—48no—
781#123—216no—
782#123—48no—
783#123—48no—
784#123—48no—
785#123—44no—
786#123—48no—
787#123—44no—
788#123—44no—
789C22⋊Q8—28no—
790C22⋊Q8—28no—
791C22⋊Q8—48no—
792C22⋊Q8—48no—
793C22⋊Q8—48no—
794C22⋊Q8—44no—
795#121—28no—
796#121—44no—
797#121—48no—
798#121—48no—
799#121—44no—
800#121—48no—
801#121—48no—
802#121—48no—
803#121—48no—
804#121—48no—
805#121—44no—
806#121—44no—
807#121—44no—
808#121—44no—
809#121—42no—
810#121—42no—
811#121—44no—
812#121—44no—
813#121—48no—
814C4×Q8—28no—
815C4×Q8—24no—
816C4×Q8—48no—
817C4×Q8—44no—
818C4×D4—44no—
819C4×D4—44no—
820C4×D4—48no—
821C4×D4—44no—
822C4×D4—44no—
823C4×D4—44no—
824C4×D4—44no—
825C4×D4—44no—
826C4×D4—44no—
827C4×D4—42no—
828C4×D4—44no—
829C4×D4—42no—
830C4×D4—48no—
831C4×D4—48no—
832C4×D4—48no—
833C4×D4—48no—
834#117—44no—
835#117—42no—
836#117—48no—
837#117—48no—
838#117—44no—
839C2×C4⋊C4—44no—
840C2×C4⋊C4—42no—
841C2×C4⋊C4—44no—
842C2×C4⋊C4—42no—
843C2×C4⋊C4—44no—
844C2×C4⋊C4—44no—
845C2×C4⋊C4C2412yes—
846C2×C4⋊C4C2411yescharacteristic
847C2×C4⋊C4C2412yes—
848C2×C4⋊C4C2412yes—
849C2×C4⋊C4C2414yes—
850C2×C4⋊C4C2412yes—
851C2×C4⋊C4C2412yes—
852C2×C4⋊C4C2414yes—
853C2×C4⋊C4C2414yes—
854C2×C4⋊C4C2412yes—
855C2×C4⋊C4C2412yes—
856C2×C4⋊C4C2414yes—
857C2×C4⋊C4C2414yes—
858C2×C4⋊C4C2412yes—
859C2×C4⋊C4C2412yes—
860C2×C4⋊C4C2412yes—
861C2×C4⋊C4C2414yes—
862C2×C4⋊C4C2412yes—
863C2×C4⋊C4C2411yescharacteristic
864C2×C4⋊C4C2412yes—
865C2×C4⋊C4C2414yes—
866C2×C4⋊C4C2414yes—
867C2×C4⋊C4C2414yes—
868C2×C4⋊C4C2411yescharacteristic
869C2×C4⋊C4C2414yes—
870C2×C4⋊C4C2414yes—
871C2×C4⋊C4C2411yescharacteristic
872C2×C4⋊C4C2414yes—
873C2×C4⋊C4C2414yes—
874C2×C4⋊C4C2414yes—
875C2×C4⋊C4C2412yes—
876C2×C4⋊C4C2411yescharacteristic
877C2×C4⋊C4C2412yes—
878C2×C4⋊C4C2412yes—
879C2×C4⋊C4C2412yes—
880C2×C4⋊C4C2412yes—
881C2×C4⋊C4C2412yes—
882C2×C4⋊C4C2414yes—
883C2×C4⋊C4C2414yes—
884C2×C4⋊C4C2414yes—
885C2×C4⋊C4C2414yes—
886C2×C4⋊C4C2414yes—
887C2×C4⋊C4C2414yes—
888C2×C4⋊C4C2414yes—
889C2×C4⋊C4C2414yes—
890C2×C4⋊C4C2412yes—
891C2×C4⋊C4C2412yes—
892C2×C4⋊C4C2414yes—
893C2×C4⋊C4C2412yes—
894C2×C4⋊C4C2414yes—
895C2×C22⋊C4C2412yes—
896C2×C22⋊C4C2414yes—
897C2×C22⋊C4C2412yes—
898C2×C22⋊C4C2414yes—
899C2×C22⋊C4C2414yes—
900C2×C22⋊C4C2414yes—
901C2×C22⋊C4C2414yes—
902C2×C22⋊C4C2414yes—
903C2×C22⋊C4C2412yes—
904C2×C22⋊C4C2414yes—
905C2×C22⋊C4C2412yes—
906C2×C22⋊C4C2412yes—
907C2×C22⋊C4C2414yes—
908C2×C22⋊C4C2412yes—
909C2×C22⋊C4C2414yes—
910C2×C22⋊C4C2414yes—
911C2×C22⋊C4C2412yes—
912C2×C22⋊C4C2411yescharacteristic
913C2×C22⋊C4C2411yescharacteristic
914C2×C22⋊C4C2412yes—
915C2×C22⋊C4C2414yes—
916C2×C22⋊C4C2414yes—
917C2×C22⋊C4C2412yes—
918C2×C22⋊C4C2414yes—
919C2×C22⋊C4C2414yes—
920C2×C22⋊C4C2412yes—
921C2×C22⋊C4C2412yes—
922C2×C22⋊C4C2412yes—
923C2×C22⋊C4C2412yes—
924C2×C22⋊C4C2412yes—
925C2×C22⋊C4C2414yes—
926C2×C22⋊C4C2412yes—
927C2×C22⋊C4C2412yes—
928C2×C22⋊C4C2412yes—
929C2×C22⋊C4C2412yes—
930C2×C22⋊C4C2414yes—
931C2×C22⋊C4C2414yes—
932C2×C22⋊C4C2414yes—
933C2×C22⋊C4C2414yes—
934C2×C22⋊C4C2414yes—
935C2×C22⋊C4C2414yes—
936C2×C22⋊C4C2412yes—
937C2×C22⋊C4C2414yes—
938C2×C22⋊C4C2414yes—
939C2×C22⋊C4C2414yes—
940C2×C22⋊C4C2414yes—
941C2×C22⋊C4C2412yes—
942C2×C22⋊C4C2412yes—
943C2×C22⋊C4C2412yes—
944C2×C22⋊C4C2412yes—
945C2×C22⋊C4C2412yes—
946C2×C22⋊C4C2414yes—
947C2×C22⋊C4C2414yes—
948C2×C22⋊C4C2414yes—
949C2×C22⋊C4C2414yes—
950C2×C22⋊C4C2412yes—
951C2×C22⋊C4C2412yes—
952C2×C22⋊C4C2414yes—
953C2×C22⋊C4C2412yes—
954C2×C22⋊C4C2412yes—
955C2×C22⋊C4C2414yes—
956C2×C42—44no—
957C2×C42C2414yes—
958C2×C42C2412yes—
959C2×C42C2412yes—
960C2×C42C2412yes—
961C2×C42C2411yescharacteristic
962C2×C42C2412yes—
963C2×C42C2412yes—
964C2×C42C2412yes—
965C2×C42C2411yescharacteristic
966C2×C42C2412yes—
967C2×C42C2414yes—
968C2×C42C2414yes—
969C2×C42C2414yes—
970C2×C42C2414yes—
971C2×C42C2414yes—
972C2×C42C2414yes—
973C2×C42C2411yescharacteristic
974C2×C42C2412yes—
975C2×C42C2412yes—
976#95C2411yescharacteristic
977#95C2414yes—
978#95C2414yes—
979#95C2414yes—
980#95C2412yes—
981#95C2414yes—
982#95C2414yes—
983#95C2414yes—
984#95C2414yes—
985#95C2414yes—
986#95C2414yes—
987#95C2414yes—
988#95C2414yes—
989#95C2411yescharacteristic
990#95C2412yes—
991#95C2412yes—
992#95C2412yes—
993#95C2414yes—
994#95C2412yes—
995#95C2414yes—
996#95C2414yes—
997#95C2412yes—
998#95C2414yes—
999#95C2411yescharacteristic
1000#95C2412yes—
1001#95C2412yes—
1002#95C2412yes—
1003#95C2414yes—
1004#95C2411yescharacteristic
1005#95C2414yes—
1006#95C2414yes—
1007#95C2414yes—
1008#95C2412yes—
1009#95C2414yes—
1010#95C2414yes—
1011#95C2412yes—
1012#95C2412yes—
1013#95C2412yes—
1014#95C2412yes—
1015#95C2414yes—
1016#95C2414yes—
1017#95C2412yes—
1018#95C2414yes—
1019#95C2412yes—
1020#95C2414yes—
1021#95C2414yes—
1022#95C2412yes—
1023#95C2414yes—
1024#95C2412yes—
1025#95C2414yes—
1026#95C2412yes—
1027#95C2414yes—
1028#95C2414yes—
1029#95C2414yes—
1030#95C2414yes—
1031#95C2414yes—
1032#95C2414yes—
1033#95C2414yes—
1034#95C2414yes—
1035C24C2512yes—
1036C24C2511yescharacteristic
1037C24C2511yescharacteristic
1038C24C2512yes—
1039C24C2512yes—
1040C24C2512yes—
1041#41—416no—
1042#41—88no—
1043#41—88no—
1044C2×Q8—24no—
1045C2×Q8—28no—
1046C2×Q8—44no—
1047C2×Q8—41no—
1048C2×Q8—44no—
1049C2×Q8—42no—
1050C2×Q8—42no—
1051C2×Q8—44no—
1052C2×Q8H(5,𝔽2)14yes—
1053C2×D4—24no—
1054C2×D4—24no—
1055C2×D4—28no—
1056C2×D4—28no—
1057C2×D4—24no—
1058C2×D4—24no—
1059C2×D4—24no—
1060C2×D4—22no—
1061C2×D4—22no—
1062C2×D4—24no—
1063C2×D4—24no—
1064C2×D4—22no—
1065C2×D4—24no—
1066C2×D4—24no—
1067C2×D4—24no—
1068C2×D4—24no—
1069C2×D4—41no—
1070C2×D4—42no—
1071C2×D4—42no—
1072C2×D4—41no—
1073C2×D4—44no—
1074C2×D4—42no—
1075C2×D4—42no—
1076C2×D4—41no—
1077C2×D4—42no—
1078C2×D4—42no—
1079C2×D4—42no—
1080C2×D4—41no—
1081C2×D4—42no—
1082C2×D4—42no—
1083C2×D4—44no—
1084C2×D4—44no—
1085C2×D4—44no—
1086C2×D4—44no—
1087C2×D4—42no—
1088C2×D4—41no—
1089C2×D4—42no—
1090C2×D4—42no—
1091C2×D4—44no—
1092C2×D4—42no—
1093C2×D4—42no—
1094C2×D4—42no—
1095C2×D4—44no—
1096C2×D4—44no—
1097C2×D4—44no—
1098C2×D4—42no—
1099C2×D4—42no—
1100C2×D4—42no—
1101C2×D4—44no—
1102C2×D4—44no—
1103C2×D4—44no—
1104C2×D4—44no—
1105C2×D4—44no—
1106C2×D4—44no—
1107C2×D4H(5,𝔽2)14yes—
1108C22×C4—28no—
1109C22×C4—24no—
1110C22×C4—24no—
1111C22×C4—24no—
1112C22×C4—22no—
1113C22×C4—22no—
1114C22×C4—24no—
1115C22×C4—24no—
1116C22×C4—24no—
1117C22×C4—24no—
1118C22×C4—24no—
1119C22×C4—24no—
1120C22×C4—24no—
1121C22×C4—24no—
1122C22×C4—44no—
1123C22×C4—42no—
1124C22×C4—42no—
1125C22×C4—44no—
1126C22×C4—44no—
1127C22×C4—44no—
1128C22×C4—42no—
1129C22×C4—44no—
1130C22×C4—42no—
1131C22×C4—42no—
1132C22×C4—44no—
1133C22×C4—44no—
1134C22×C4—42no—
1135C22×C4—44no—
1136C22×C4—44no—
1137C22×C4—42no—
1138C22×C4—42no—
1139C22×C4—42no—
1140C22×C4—44no—
1141C22×C4—44no—
1142C22×C4—44no—
1143C22×C4—44no—
1144C22×C4—44no—
1145C22×C4—44no—
1146C22×C4—44no—
1147C22×C4—42no—
1148C22×C4—42no—
1149C22×C4C2512yes—
1150C22×C4C2511yescharacteristic
1151C22×C4C2512yes—
1152C22×C4C2511yescharacteristic
1153C22×C4C2512yes—
1154C22×C4C2512yes—
1155C22×C4C2512yes—
1156C22×C4C2512yes—
1157C22×C4C2514yes—
1158C22×C4C2514yes—
1159C22×C4C2511yescharacteristic
1160C22×C4C2514yes—
1161C22×C4C2514yes—
1162C22×C4C2514yes—
1163C22×C4C2512yes—
1164C22×C4C2512yes—
1165C22×C4C2514yes—
1166C22×C4C2512yes—
1167C22×C4C2512yes—
1168C22×C4C2512yes—
1169C22×C4C2511yescharacteristic
1170C22×C4C2512yes—
1171C22×C4C2511yescharacteristic
1172C4⋊C4—24no—
1173C4⋊C4—22no—
1174C4⋊C4—24no—
1175C4⋊C4—24no—
1176C4⋊C4—28no—
1177C4⋊C4—28no—
1178C4⋊C4—28no—
1179C4⋊C4—24no—
1180C4⋊C4—28no—
1181C4⋊C4—24no—
1182C4⋊C4—28no—
1183C4⋊C4—24no—
1184C4⋊C4—24no—
1185C4⋊C4—24no—
1186C4⋊C4—28no—
1187C4⋊C4—24no—
1188C4⋊C4—24no—
1189C4⋊C4—42no—
1190C4⋊C4—41no—
1191C4⋊C4—44no—
1192C4⋊C4—42no—
1193C4⋊C4—44no—
1194C4⋊C4—44no—
1195C4⋊C4—42no—
1196C4⋊C4—44no—
1197C4⋊C4—41no—
1198C4⋊C4—44no—
1199C4⋊C4—44no—
1200C4⋊C4—42no—
1201C4⋊C4—42no—
1202C4⋊C4—42no—
1203C4⋊C4—42no—
1204C4⋊C4—41no—
1205C4⋊C4—44no—
1206C4⋊C4—44no—
1207C4⋊C4—44no—
1208C4⋊C4—41no—
1209C4⋊C4—42no—
1210C4⋊C4—42no—
1211C4⋊C4—44no—
1212C4⋊C4—44no—
1213C4⋊C4—44no—
1214C4⋊C4—44no—
1215C4⋊C4—44no—
1216C4⋊C4—44no—
1217C4⋊C4—44no—
1218C4⋊C4—44no—
1219C4⋊C4—42no—
1220C4⋊C4—42no—
1221C4⋊C4—44no—
1222C22⋊C4—24no—
1223C22⋊C4—28no—
1224C22⋊C4—28no—
1225C22⋊C4—28no—
1226C22⋊C4—24no—
1227C22⋊C4—28no—
1228C22⋊C4—28no—
1229C22⋊C4—28no—
1230C22⋊C4—24no—
1231C22⋊C4—28no—
1232C22⋊C4—24no—
1233C22⋊C4—42no—
1234C22⋊C4—42no—
1235C22⋊C4—44no—
1236C22⋊C4—44no—
1237C22⋊C4—42no—
1238C22⋊C4—44no—
1239C22⋊C4—42no—
1240C22⋊C4—44no—
1241C22⋊C4—44no—
1242C22⋊C4—42no—
1243C22⋊C4—42no—
1244C22⋊C4—44no—
1245C22⋊C4—42no—
1246C22⋊C4—42no—
1247C22⋊C4—42no—
1248C22⋊C4—42no—
1249C22⋊C4—42no—
1250C22⋊C4—42no—
1251C22⋊C4—41no—
1252C22⋊C4—41no—
1253C22⋊C4—42no—
1254C22⋊C4—42no—
1255C22⋊C4—44no—
1256C22⋊C4—44no—
1257C22⋊C4—42no—
1258C22⋊C4—44no—
1259C22⋊C4—44no—
1260C22⋊C4—42no—
1261C22⋊C4—42no—
1262C22⋊C4—44no—
1263C22⋊C4—44no—
1264C22⋊C4—44no—
1265C22⋊C4—44no—
1266C22⋊C4—44no—
1267C22⋊C4—44no—
1268C22⋊C4—44no—
1269C22⋊C4—44no—
1270C22⋊C4—44no—
1271C22⋊C4—44no—
1272C22⋊C4—42no—
1273C22⋊C4—42no—
1274C22⋊C4—42no—
1275C22⋊C4—42no—
1276C22⋊C4—42no—
1277C22⋊C4—44no—
1278C22⋊C4—44no—
1279C22⋊C4—44no—
1280C22⋊C4—44no—
1281C22⋊C4—42no—
1282C22⋊C4—42no—
1283C42—28no—
1284C42—24no—
1285C42—24no—
1286C42—24no—
1287C42—22no—
1288C42—22no—
1289C42—24no—
1290C42—24no—
1291C42—24no—
1292C42—24no—
1293C42—42no—
1294C42—42no—
1295C42—41no—
1296C42—44no—
1297C42—44no—
1298C42—44no—
1299C42—44no—
1300C42—44no—
1301C42—44no—
1302C23—22no—
1303C23—22no—
1304C23—22no—
1305C23—22no—
1306C23—22no—
1307C23—22no—
1308C23—22no—
1309C23—22no—
1310C23—21no—
1311C23—21no—
1312C23—22no—
1313C23—22no—
1314C23—22no—
1315C23—21no—
1316C23—22no—
1317C23—21no—
1318C23—22no—
1319C23—24no—
1320C23—22no—
1321C23—24no—
1322C23—22no—
1323C23—22no—
1324C23—22no—
1325C23—24no—
1326C23—24no—
1327C23—22no—
1328C23—22no—
1329C23—22no—
1330C23—21no—
1331C23—22no—
1332C23—22no—
1333C23—22no—
1334C23—21no—
1335C23C2×H(5,𝔽2)14yes—
1336C23C2611yescharacteristic
1337Q8—28no—
1338Q8—88no—
1339Q8—82no—
1340Q8—162no—
1341D4—44no—
1342D4—48no—
1343D4—48no—
1344D4—48no—
1345D4—44no—
1346D4—44no—
1347D4—82no—
1348D4—84no—
1349D4—84no—
1350D4—84no—
1351D4—88no—
1352D4—88no—
1353D4—84no—
1354D4—84no—
1355D4—82no—
1356D4—84no—
1357D4—164no—
1358D4—162no—
1359D4—162no—
1360D4—162no—
1361D4—164no—
1362C2×C4—21no—
1363C2×C4—22no—
1364C2×C4—22no—
1365C2×C4—24no—
1366C2×C4—21no—
1367C2×C4—22no—
1368C2×C4—24no—
1369C2×C4—24no—
1370C2×C4—21no—
1371C2×C4—22no—
1372C2×C4—22no—
1373C2×C4—22no—
1374C2×C4—24no—
1375C2×C4—22no—
1376C2×C4—24no—
1377C2×C4—24no—
1378C2×C4—24no—
1379C2×C4—24no—
1380C2×C4—22no—
1381C2×C4—24no—
1382C2×C4—22no—
1383C2×C4—21no—
1384C2×C4—21no—
1385C2×C4—22no—
1386C2×C4—22no—
1387C2×C4—22no—
1388C2×C4—22no—
1389C2×C4—22no—
1390C2×C4—22no—
1391C2×C4—22no—
1392C2×C4—22no—
1393C2×C4—22no—
1394C2×C4—22no—
1395C2×C4—24no—
1396C2×C4—24no—
1397C2×C4—24no—
1398C2×C4—24no—
1399C2×C4—22no—
1400C2×C4—22no—
1401C2×C4—22no—
1402C2×C4—22no—
1403C2×C4—22no—
1404C2×C4—24no—
1405C2×C4—22no—
1406C2×C4—24no—
1407C2×C4—24no—
1408C2×C4—24no—
1409C2×C4—22no—
1410C2×C4—22no—
1411C2×C4—24no—
1412C2×C4—22no—
1413C2×C4—22no—
1414C2×C4—22no—
1415C2×C4—22no—
1416C2×C4—22no—
1417C2×C4—22no—
1418C2×C4—24no—
1419C2×C4—24no—
1420C2×C4—48no—
1421C2×C4—48no—
1422C2×C4—44no—
1423C2×C4—48no—
1424C2×C4—44no—
1425C2×C4—84no—
1426C2×C4—84no—
1427C2×C4—88no—
1428C2×C4—88no—
1429C2×C4—84no—
1430C2×C4—164no—
1431C2×C4—164no—
1432C2×C4—162no—
1433C2×C4—164no—
1434C2×C4—162no—
1435C2×C4C2×H(5,𝔽2)14yes—
1436C2×C4C2×H(5,𝔽2)12yes—
1437C2×C4C2×H(5,𝔽2)12yes—
1438C2×C4#58514yes—
1439C2×C4#58514yes—
1440C22—24no—
1441C22—24no—
1442C22—24no—
1443C22—42no—
1444C22—42no—
1445C22—42no—
1446C22—42no—
1447C22—42no—
1448C22—41no—
1449C22—41no—
1450C22—42no—
1451C22—42no—
1452C22—42no—
1453C22—44no—
1454C22—42no—
1455C22—42no—
1456C22—42no—
1457C22—44no—
1458C22—42no—
1459C22—41no—
1460C22—42no—
1461C22—41no—
1462C22—42no—
1463C22—41no—
1464C22—41no—
1465C22—42no—
1466C22—42no—
1467C22—42no—
1468C22—42no—
1469C22—42no—
1470C22—42no—
1471C22—44no—
1472C22—44no—
1473C22—42no—
1474C22C22×H(5,𝔽2)11yescharacteristic
1475C22C22×H(5,𝔽2)11yescharacteristic
1476C22C2×#58512yes—
1477C22C2×#58512yes—
1478C222−1+611yescharacteristic
1479C4—24no—
1480C4—24no—
1481C4—22no—
1482C4—42no—
1483C4—41no—
1484C4—41no—
1485C4—42no—
1486C4—42no—
1487C4—42no—
1488C4—44no—
1489C4—44no—
1490C4—44no—
1491C4—42no—
1492C4—42no—
1493C4—44no—
1494C4—41no—
1495C4—44no—
1496C4—44no—
1497C4—42no—
1498C4—42no—
1499C4—42no—
1500C4—42no—
1501C4#353314yes—
1502C2—44no—
1503C2—81no—
1504C2—82no—
1505C2—81no—
1506C2—82no—
1507C2—82no—
1508C2C2×#353311yescharacteristic
1509C2#6289511yescharacteristic
1510C2#6293912yes—
1511C2#6301812yes—
1512C2#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. #59827C2semidirect
2. #59502C2semidirect
3. #59381C2semidirect
4. #59317C2semidirect
5. #59308C2semidirect
6. #58343C2semidirect
7. #57903C2semidirect
8. #57902C2semidirect
9. #55015C2semidirect
10. #53017C2semidirect
11. #52963C2semidirect
12. #52297C2semidirect
13. #47800C2semidirect
14. #46555C2semidirect
15. #45251C2semidirect
16. #44913C2semidirect
17. #44657C2semidirect
18. #43920C2semidirect
19. #42989C2semidirect
20. #42985C2semidirect
21. #42252C2semidirect
22. #41156C2semidirect
23. #39789C2semidirect
24. #39410C2semidirect
25. #39222C2semidirect
26. #39169C2semidirect
27. #39145C2semidirect
28. #36076C2semidirect
29. #35772C2semidirect

Maximal subgroups

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

subgroupindex
#598272
#595022
#593812
#593172
#593082
#583432
#579032
#579022
#550152
#530172
#529632
#522972
#478002
#465552
#452512
#449132
#446572
#439202
#429892
#429852
#422522
#411562
#397892
#394102
#392222
#391692
#391452
#360762
#357722