Finite Group Databasebeta

← #7711066

Subgroups — #7711066

Order 512.

4368 conjugacy classes of subgroups.

The subgroup lattice has 1474 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#59872C212yesmaximal, complemented
2#59865C212yesmaximal, complemented
3#59431C212yesmaximal, complemented
4#59430C212yesmaximal, complemented
5#45810C214yesmaximal, complemented
6#45809C212yesmaximal, complemented
7#45808C212yesmaximal
8#40005C212yesmaximal, complemented
9#40004C212yesmaximal, complemented
10#39839C212yesmaximal, complemented
11#39837C212yesmaximal, complemented
12#39824C214yesmaximal, complemented
13#39545C212yesmaximal, complemented
14#39544C212yesmaximal, complemented
15#39509C211yesmaximal, characteristic, complemented
16#39509C211yesmaximal, characteristic, complemented
17#39493C211yesmaximal, characteristic, complemented
18#39493C211yesmaximal, characteristic, complemented
19#38493C212yesmaximal, complemented
20#38492C212yesmaximal, complemented
21#37560C212yesmaximal, complemented
22#37146C212yesmaximal, complemented
23#37145C212yesmaximal, complemented
24#36635C211yesmaximal, characteristic, complemented
25#36631C211yesmaximal, characteristic
26#36514C212yesmaximal, complemented
27#36417C212yesmaximal, complemented
28#36398C214yesmaximal, complemented
29#35112C214yesmaximal, complemented
30#34385C212yesmaximal, complemented
31C4×#533C211yesmaximal, characteristic, complemented
32C2×#533C2211yescharacteristic
33C2×#529C2212yes—
34#2866C2214yes—
35#2865C2214yes—
36#2864C2212yes—
37#2863C2212yes—
38#2863C2212yes—
39#2862C2211yescharacteristic
40#2861C2212yes—
41#2860C2212yes—
42#2860C2211yescharacteristic
43#2860C2211yescharacteristic
44#2859C2211yescharacteristic
45#2859C2211yescharacteristic
46#2858C2211yescharacteristic
47#2857C2211yescharacteristic
48#2857C2211yescharacteristic
49#2857C2211yescharacteristic
50#2856C2211yescharacteristic
51#2855C2212yes—
52#2855C2212yes—
53#2854C2212yes—
54#2854C2211yescharacteristic
55#2854C2211yescharacteristic
56#2851C2212yes—
57#2850C2212yes—
58#2817C2214yes—
59#2816C2214yes—
60#2810C2212yes—
61#2810C2212yes—
62#2808C2212yes—
63#2808C2212yes—
64#2806C2212yes—
65#2806C2212yes—
66#2805C2212yes—
67#2805C2212yes—
68#2805C2212yes—
69#2805C2212yes—
70#2804C2212yes—
71#2804C2212yes—
72#2794C2214yes—
73#2791C2214yes—
74#2786C2214yes—
75#2776C2214yes—
76#2775C2214yes—
77#2774C2214yes—
78#2773C2214yes—
79#2771C2214yes—
80#2767C2214yes—
81#2762C2214yes—
82#2751C2214yes—
83#2750C2214yes—
84#2747C2214yes—
85#2745C2214yes—
86#2732C2212yes—
87#2732C2212yes—
88#2728C2214yes—
89#2727C2212yes—
90#2727C2212yes—
91#2723C2214yes—
92#2715C2214yes—
93#2713C2214yes—
94#2709C2214yes—
95#2700C2214yes—
96#2694C2214yes—
97#2691C2214yes—
98#2690C2214yes—
99#2681C2214yes—
100#2663C2214yes—
101#2663C2214yes—
102#2654C2214yes—
103#2650C2214yes—
104#2634C2214yes—
105#2632C2214yes—
106#2628C2212yes—
107#2628C2212yes—
108#2628C2212yes—
109#2628C2212yes—
110#2605C2214yes—
111#2604C2214yes—
112#2604C2214yes—
113#2604C2214yes—
114#2601C2214yes—
115#2599C2214yes—
116#2597C2214yes—
117#2596C2214yes—
118#2596C2214yes—
119#2596C2214yes—
120#2595C2214yes—
121#2595C2214yes—
122#2595C2214yes—
123#2594C2214yes—
124#2593C2214yes—
125#2590C2214yes—
126#2589C2214yes—
127#2589C2214yes—
128#2588C2214yes—
129#2588C2214yes—
130#2588C2214yes—
131#2585C2214yes—
132#2585C2214yes—
133#2584C2212yes—
134#2584C2212yes—
135#2578C2214yes—
136#2577C2214yes—
137#2576C2214yes—
138#2575C2214yes—
139#2573C2214yes—
140#2570C2212yes—
141#2570C2212yes—
142#2562C2212yes—
143#2562C2212yes—
144#2562C2212yes—
145#2562C2212yes—
146#2560C2214yes—
147#2560C2214yes—
148#2559C2214yes—
149#2558C2214yes—
150#2533C2214yes—
151#2533C2214yes—
152#2531C2214yes—
153#2530C2214yes—
154#2528C2214yes—
155#2526C2214yes—
156#2525C2214yes—
157#2520C2214yes—
158#2516C2214yes—
159#2516C2214yes—
160#2509C2212yes—
161#2509C2214yes—
162#2508C2212yes—
163#2507C2212yes—
164#2506C2212yes—
165#2497C2212yes—
166#2497C2212yes—
167#2497C2212yes—
168#2496C2212yes—
169#2496C2212yes—
170#2496C2212yes—
171#2495C2212yes—
172#2494C2212yes—
173#2487C2212yes—
174#2486C2212yes—
175#2485C2212yes—
176#2485C2212yes—
177#2485C2212yes—
178#2485C2212yes—
179#2485C2212yes—
180#2485C2212yes—
181#2479C2214yes—
182#2476C2214yes—
183#2469C2214yes—
184#2469C2214yes—
185#2469C2214yes—
186#2469C2214yes—
187#2465C2214yes—
188#2465C2214yes—
189#2462C2214yes—
190#2458C2214yes—
191#2440C2212yes—
192#2440C2212yes—
193#2439C2212yes—
194#2439C2212yes—
195#2421C2214yes—
196#2378C2214yes—
197#2377C2214yes—
198#2374C2214yes—
199#2373C2214yes—
200#2373C2214yes—
201#2373C2214yes—
202#2370C2214yes—
203#2370C2212yes—
204#2370C2212yes—
205#2362C2214yes—
206#2355C2212yes—
207#2355C2212yes—
208#2354C2212yes—
209#2354C2212yes—
210#2352C2212yes—
211#2352C2212yes—
212#2352C2212yes—
213#2352C2212yes—
214#2352C2212yes—
215#2352C2212yes—
216#2347C2212yes—
217#2346C2212yes—
218#2345C2212yes—
219#2344C2212yes—
220#2337C2214yes—
221#2336C2214yes—
222#2335C2214yes—
223#2335C2214yes—
224#2334C2214yes—
225#2332C2214yes—
226#2317C2212yes—
227#2317C2212yes—
228#2314C2212yes—
229#2314C2212yes—
230C4×C4⋊Q8C2211yescharacteristic
231C4×C4⋊Q8C2211yescharacteristic
232C4×C4⋊Q8C2211yescharacteristic
233C4×C4⋊Q8C2211yescharacteristic
234C4×C4⋊Q8C2211yescharacteristic
235C4×C4⋊Q8C2211yescharacteristic
236C4×C4⋊Q8C2211yescharacteristic
237C4×#127C2211yescharacteristic
238C4×#125C2212yes—
239C4×#125C2212yes—
240C4×#125C2212yes—
241C4×#126C2214yes—
242C4×#124C2212yes—
243C4×C22⋊Q8C2212yes—
244C4×C22⋊Q8C2212yes—
245C4×C22⋊Q8C2212yes—
246C4×C22⋊Q8C2212yes—
247C4×C22⋊Q8C2212yes—
248C4×C22⋊Q8C2212yes—
249C4×#121C2211yescharacteristic
250C4×#121C2212yes—
251C4×#121C2211yescharacteristic
252#2298C2214yes—
253#2296C2212yes—
254#2295C2212yes—
255#2295C2212yes—
256#2295C2212yes—
257#2295C2212yes—
258#2293C2211yescharacteristic
259#2293C2211yescharacteristic
260#2293C2212yes—
261#2285C2211yescharacteristic
262#2283C2212yes—
263C42×Q8C2212yes—
264C42×Q8C2212yes—
265C4×#117C2212yes—
266C2×C43C2211yescharacteristic
267#533—28no—
268C2×C4⋊Q8C2311yescharacteristic
269C2×C4⋊Q8C2311yescharacteristic
270C2×C4⋊Q8C2311yescharacteristic
271C2×C4⋊Q8C2311yescharacteristic
272C2×C4⋊Q8C2311yescharacteristic
273C2×#127C2311yescharacteristic
274#529—216no—
275C2×#126C2312yes—
276C2×#126C2312yes—
277C2×#126C2314yes—
278C2×#126C2314yes—
279C2×#126C2314yes—
280C2×#125C2312yes—
281C2×#125C2312yes—
282C2×#125C2312yes—
283C2×#125C2314yes—
284C2×#124C2312yes—
285C2×#124C2312yes—
286C2×#123C2312yes—
287C2×#123C2312yes—
288C2×#123C2314yes—
289C2×C22⋊Q8C2312yes—
290C2×C22⋊Q8C2312yes—
291C2×C22⋊Q8C2312yes—
292C2×C22⋊Q8C2314yes—
293C2×C22⋊Q8C2314yes—
294C2×C22⋊Q8C2312yes—
295C2×C22⋊Q8C2312yes—
296C2×#121C2312yes—
297C2×#121C2312yes—
298C2×#121C2311yescharacteristic
299C2×#121C2311yescharacteristic
300C2×C4×Q8C2312yes—
301C2×C4×Q8C2312yes—
302C2×C4×Q8C2312yes—
303C2×C4×Q8C2312yes—
304C2×C4×Q8C2312yes—
305C2×C4×Q8C2312yes—
306C2×C4×Q8C2312yes—
307C2×C4×Q8C2312yes—
308C2×C4×Q8C2312yes—
309C2×C4×D4C2312yes—
310C2×C4×D4C2311yescharacteristic
311C2×C4×D4C2311yescharacteristic
312C2×C4×D4C2312yes—
313C2×C4×D4C2312yes—
314C2×C4×D4C2312yes—
315C2×#117C2312yes—
316C2×#117C2312yes—
317C2×#117C2312yes—
318C2×#117C2312yes—
319C2×#117C2312yes—
320C2×#117C2314yes—
321C2×#117C2312yes—
322C22×C4⋊C4C2312yes—
323C22×C4⋊C4C2312yes—
324C22×C42C2311yescharacteristic
325C22×C42C2311yescharacteristic
326C22×C42C2311yescharacteristic
327C22×C42C2311yescharacteristic
328C22×C42C2311yescharacteristic
329C22×C42C2311yescharacteristic
330C22×C42C2311yescharacteristic
331#401C2314yes—
332#400C2314yes—
333#400C2314yes—
334#400C2314yes—
335#400C2314yes—
336#400C2314yes—
337#400C2314yes—
338#400C2314yes—
339#400C2314yes—
340#400C2314yes—
341#400C2314yes—
342#400C2314yes—
343#400C2314yes—
344#400C2314yes—
345#400C2314yes—
346#400C2314yes—
347#400C2314yes—
348#400C2314yes—
349#400C2314yes—
350#400C2314yes—
351#400C2314yes—
352#400C2314yes—
353#400C2314yes—
354#399C2314yes—
355#399C2314yes—
356#399C2314yes—
357#399C2314yes—
358#399C2314yes—
359#398C2314yes—
360#398C2314yes—
361#398C2314yes—
362#398C2314yes—
363#398C2314yes—
364#398C2314yes—
365#398C2314yes—
366#398C2314yes—
367#398C2314yes—
368#398C2314yes—
369#398C2314yes—
370#397C2314yes—
371#397C2314yes—
372#397C2314yes—
373#397C2314yes—
374#397C2314yes—
375#397C2314yes—
376#397C2314yes—
377#397C2314yes—
378#397C2314yes—
379#397C2314yes—
380#397C2314yes—
381#397C2314yes—
382#396C2314yes—
383#396C2314yes—
384#396C2314yes—
385#396C2314yes—
386#396C2314yes—
387#395C2314yes—
388#395C2314yes—
389#395C2314yes—
390#395C2314yes—
391#395C2314yes—
392#395C2314yes—
393#395C2314yes—
394#395C2314yes—
395#394C2314yes—
396#394C2314yes—
397#394C2314yes—
398#394C2314yes—
399#394C2314yes—
400#394C2314yes—
401#394C2314yes—
402#394C2314yes—
403#394C2314yes—
404#394C2314yes—
405#393C2314yes—
406#393C2314yes—
407#393C2314yes—
408#393C2314yes—
409#393C2314yes—
410#393C2314yes—
411#391C2312yes—
412#391C2312yes—
413#391C2312yes—
414#391C2312yes—
415#391C2312yes—
416#391C2312yes—
417#391C2312yes—
418#391C2312yes—
419#391C2312yes—
420#391C2314yes—
421#391C2312yes—
422#391C2314yes—
423#391C2314yes—
424#391C2314yes—
425#391C2312yes—
426#391C2312yes—
427#391C2312yes—
428#391C2312yes—
429#390C2312yes—
430#390C2312yes—
431#390C2312yes—
432#390C2312yes—
433#390C2311yescharacteristic
434#390C2311yescharacteristic
435#390C2314yes—
436#390C2314yes—
437#390C2312yes—
438#390C2311yescharacteristic
439#390C2311yescharacteristic
440#390C2312yes—
441#390C2311yescharacteristic
442#390C2311yescharacteristic
443#390C2311yescharacteristic
444#390C2311yescharacteristic
445#389C2312yes—
446#389C2312yes—
447#389C2312yes—
448#389C2312yes—
449#389C2312yes—
450#389C2312yes—
451#389C2311yescharacteristic
452#389C2312yes—
453#389C2312yes—
454#389C2312yes—
455#389C2312yes—
456#389C2311yescharacteristic
457#389C2312yes—
458#389C2312yes—
459#389C2312yes—
460#389C2312yes—
461#389C2312yes—
462#389C2312yes—
463#389C2312yes—
464#389C2312yes—
465#389C2312yes—
466#389C2314yes—
467#389C2314yes—
468#389C2314yes—
469#389C2314yes—
470#389C2314yes—
471#389C2314yes—
472#389C2314yes—
473#389C2314yes—
474#389C2312yes—
475#389C2312yes—
476#389C2312yes—
477#389C2312yes—
478#389C2312yes—
479#389C2314yes—
480#389C2312yes—
481#389C2312yes—
482#389C2314yes—
483#389C2312yes—
484#389C2312yes—
485#389C2312yes—
486#389C2311yescharacteristic
487#389C2311yescharacteristic
488#389C2312yes—
489#389C2312yes—
490#389C2311yescharacteristic
491#389C2311yescharacteristic
492#389C2311yescharacteristic
493#389C2311yescharacteristic
494#389C2312yes—
495#389C2314yes—
496#389C2314yes—
497#388C2312yes—
498#388C2314yes—
499#388C2314yes—
500#388C2314yes—
501#388C2314yes—
502#388C2314yes—
503#388C2314yes—
504#388C2314yes—
505#388C2314yes—
506#388C2314yes—
507#388C2314yes—
508#388C2314yes—
509#388C2314yes—
510#388C2314yes—
511#388C2314yes—
512#388C2314yes—
513#388C2314yes—
514#388C2314yes—
515#388C2314yes—
516#388C2312yes—
517#388C2312yes—
518#388C2314yes—
519#388C2314yes—
520#388C2314yes—
521#388C2314yes—
522#388C2312yes—
523#388C2314yes—
524#388C2314yes—
525#388C2314yes—
526#388C2312yes—
527#388C2312yes—
528#388C2314yes—
529#388C2314yes—
530#388C2312yes—
531#388C2314yes—
532#388C2314yes—
533#388C2314yes—
534#388C2314yes—
535#388C2314yes—
536#388C2312yes—
537#388C2314yes—
538#388C2312yes—
539#388C2312yes—
540#388C2312yes—
541#388C2312yes—
542#388C2312yes—
543#388C2314yes—
544#388C2314yes—
545#388C2314yes—
546#388C2312yes—
547#388C2312yes—
548#388C2314yes—
549#388C2312yes—
550#387C2314yes—
551#387C2314yes—
552#387C2314yes—
553#387C2314yes—
554#387C2314yes—
555#387C2314yes—
556#387C2314yes—
557#387C2314yes—
558#387C2314yes—
559#387C2314yes—
560#387C2314yes—
561#387C2314yes—
562#387C2314yes—
563#387C2314yes—
564#387C2314yes—
565#387C2314yes—
566#387C2314yes—
567#387C2314yes—
568#387C2314yes—
569#387C2314yes—
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#387C2314yes—
591#387C2314yes—
592#387C2314yes—
593#387C2314yes—
594#387C2314yes—
595#387C2314yes—
596#387C2314yes—
597#387C2314yes—
598#387C2314yes—
599#387C2314yes—
600#387C2314yes—
601#387C2314yes—
602#387C2314yes—
603#387C2314yes—
604#387C2314yes—
605#387C2314yes—
606#387C2314yes—
607#386C2314yes—
608#386C2314yes—
609#386C2312yes—
610#386C2314yes—
611#386C2312yes—
612#386C2314yes—
613#386C2314yes—
614#386C2312yes—
615#386C2312yes—
616#386C2314yes—
617#386C2314yes—
618#385C2314yes—
619#385C2314yes—
620#385C2314yes—
621#385C2314yes—
622#385C2314yes—
623#385C2314yes—
624#385C2314yes—
625#385C2314yes—
626#385C2314yes—
627#385C2314yes—
628#385C2314yes—
629#384C2311yescharacteristic
630#384C2311yescharacteristic
631#384C2311yescharacteristic
632#384C2311yescharacteristic
633#384C2311yescharacteristic
634#384C2311yescharacteristic
635#384C2312yes—
636#384C2312yes—
637#383C2314yes—
638#383C2314yes—
639#383C2314yes—
640#382C2312yes—
641#382C2312yes—
642#382C2312yes—
643#382C2312yes—
644#382C2312yes—
645#382C2312yes—
646#382C2314yes—
647#382C2314yes—
648#382C2312yes—
649#381C2314yes—
650#381C2314yes—
651#381C2314yes—
652#380C2312yes—
653#380C2312yes—
654#380C2312yes—
655#380C2312yes—
656#380C2312yes—
657#380C2312yes—
658#380C2312yes—
659#380C2312yes—
660#380C2312yes—
661#380C2312yes—
662#380C2312yes—
663#380C2312yes—
664#380C2311yescharacteristic
665#380C2314yes—
666#380C2312yes—
667#380C2312yes—
668#380C2312yes—
669#380C2312yes—
670#380C2311yescharacteristic
671#380C2312yes—
672#380C2312yes—
673#380C2312yes—
674C4×C4⋊C4C2314yes—
675C4×C4⋊C4C2314yes—
676C4×C4⋊C4C2314yes—
677C4×C4⋊C4C2314yes—
678C4×C4⋊C4C2314yes—
679C4×C4⋊C4C2312yes—
680C4×C4⋊C4C2312yes—
681C4×C4⋊C4C2312yes—
682C4×C4⋊C4C2312yes—
683C4×C4⋊C4C2312yes—
684C4×C4⋊C4C2312yes—
685C4×C4⋊C4C2314yes—
686C4×C4⋊C4C2314yes—
687C4×C4⋊C4C2314yes—
688C4×C4⋊C4C2314yes—
689C4×C4⋊C4C2314yes—
690C4×C4⋊C4C2311yescharacteristic
691C4×C4⋊C4C2311yescharacteristic
692C4×C4⋊C4C2312yes—
693C4×C4⋊C4C2312yes—
694C4×C4⋊C4C2312yes—
695C4×C4⋊C4C2312yes—
696C4×C4⋊C4C2312yes—
697C4×C4⋊C4C2312yes—
698C4×C4⋊C4C2312yes—
699C4×C4⋊C4C2312yes—
700C4×C4⋊C4C2312yes—
701C4×C4⋊C4C2312yes—
702C4×C4⋊C4C2312yes—
703C4×C4⋊C4C2314yes—
704C4×C4⋊C4C2314yes—
705C4×C4⋊C4C2314yes—
706C4×C4⋊C4C2314yes—
707C4×C4⋊C4C2314yes—
708C4×C4⋊C4C2312yes—
709C4×C4⋊C4C2312yes—
710C4×C22⋊C4C2314yes—
711C4×C22⋊C4C2314yes—
712C4×C22⋊C4C2314yes—
713C4×C22⋊C4C2314yes—
714C4×C22⋊C4C2314yes—
715C4×C22⋊C4C2314yes—
716C4×C22⋊C4C2314yes—
717C4×C22⋊C4C2314yes—
718C4×C22⋊C4C2314yes—
719C4×C22⋊C4C2314yes—
720C4×C22⋊C4C2312yes—
721C4×C22⋊C4C2312yes—
722C4×C22⋊C4C2312yes—
723C4×C22⋊C4C2312yes—
724#376C2314yes—
725#376C2314yes—
726#376C2314yes—
727C43C2314yes—
728C43C2311yescharacteristic
729C43C2311yescharacteristic
730C43C2311yescharacteristic
731C43C2311yescharacteristic
732C43C2311yescharacteristic
733C43C2311yescharacteristic
734C43C2311yescharacteristic
735C43C2311yescharacteristic
736C22×Q8C2412yes—
737C22×Q8C2412yes—
738C22×Q8C2412yes—
739C22×Q8C2412yes—
740C22×Q8C2412yes—
741C22×D4C2412yes—
742C22×D4C2412yes—
743C22×D4C2412yes—
744C22×D4C2412yes—
745C22×D4C2411yescharacteristic
746C22×D4C2411yescharacteristic
747C23×C4C2412yes—
748C23×C4C2412yes—
749C23×C4C2411yescharacteristic
750C23×C4C2411yescharacteristic
751C23×C4C2411yescharacteristic
752C23×C4C2411yescharacteristic
753C23×C4C2411yescharacteristic
754C23×C4C2414yes—
755C23×C4C2414yes—
756C23×C4C2411yescharacteristic
757C23×C4C2411yescharacteristic
758C4⋊Q8—24no—
759C4⋊Q8—24no—
760C4⋊Q8—42no—
761C4⋊Q8—42no—
762C4⋊Q8—42no—
763#127—42no—
764#126—28no—
765#126—28no—
766#126—48no—
767#126—48no—
768#126—48no—
769#125—28no—
770#125—28no—
771#125—28no—
772#125—48no—
773#124—28no—
774#124—44no—
775#123—28no—
776#123—28no—
777#123—48no—
778C22⋊Q8—28no—
779C22⋊Q8—28no—
780C22⋊Q8—28no—
781C22⋊Q8—48no—
782C22⋊Q8—48no—
783C22⋊Q8—44no—
784C22⋊Q8—44no—
785#121—28no—
786#121—42no—
787#121—44no—
788#121—42no—
789C4×Q8—28no—
790C4×Q8—28no—
791C4×Q8—28no—
792C4×Q8—44no—
793C4×Q8—44no—
794C4×Q8—44no—
795C4×Q8—44no—
796C4×Q8—44no—
797C4×Q8—44no—
798C4×D4—28no—
799C4×D4—28no—
800C4×D4—28no—
801C4×D4—24no—
802C4×D4—24no—
803C4×D4—44no—
804#117—28no—
805#117—28no—
806#117—28no—
807#117—48no—
808#117—44no—
809#117—44no—
810#117—44no—
811C2×C4⋊C4—44no—
812C2×C4⋊C4—44no—
813C2×C4⋊C4C2412yes—
814C2×C4⋊C4C2412yes—
815C2×C4⋊C4C2412yes—
816C2×C4⋊C4C2412yes—
817C2×C4⋊C4C2414yes—
818C2×C4⋊C4C2412yes—
819C2×C4⋊C4C2412yes—
820C2×C4⋊C4C2412yes—
821C2×C4⋊C4C2412yes—
822C2×C4⋊C4C2412yes—
823C2×C4⋊C4C2412yes—
824C2×C4⋊C4C2412yes—
825C2×C4⋊C4C2412yes—
826C2×C4⋊C4C2412yes—
827C2×C4⋊C4C2411yescharacteristic
828C2×C4⋊C4C2411yescharacteristic
829C2×C4⋊C4C2412yes—
830C2×C4⋊C4C2414yes—
831C2×C4⋊C4C2414yes—
832C2×C4⋊C4C2414yes—
833C2×C4⋊C4C2414yes—
834C2×C4⋊C4C2412yes—
835C2×C4⋊C4C2412yes—
836C2×C4⋊C4C2414yes—
837C2×C4⋊C4C2412yes—
838C2×C4⋊C4C2412yes—
839C2×C4⋊C4C2412yes—
840C2×C4⋊C4C2414yes—
841C2×C4⋊C4C2412yes—
842C2×C4⋊C4C2412yes—
843C2×C4⋊C4C2412yes—
844C2×C4⋊C4C2412yes—
845C2×C4⋊C4C2414yes—
846C2×C4⋊C4C2414yes—
847C2×C4⋊C4C2414yes—
848C2×C4⋊C4C2414yes—
849C2×C4⋊C4C2414yes—
850C2×C4⋊C4C2412yes—
851C2×C4⋊C4C2412yes—
852C2×C4⋊C4C2412yes—
853C2×C4⋊C4C2412yes—
854C2×C4⋊C4C2412yes—
855C2×C4⋊C4C2414yes—
856C2×C4⋊C4C2414yes—
857C2×C4⋊C4C2412yes—
858C2×C4⋊C4C2411yescharacteristic
859C2×C4⋊C4C2412yes—
860C2×C4⋊C4C2411yescharacteristic
861C2×C4⋊C4C2414yes—
862C2×C4⋊C4C2414yes—
863C2×C4⋊C4C2414yes—
864C2×C4⋊C4C2412yes—
865C2×C4⋊C4C2414yes—
866C2×C4⋊C4C2414yes—
867C2×C4⋊C4C2414yes—
868C2×C4⋊C4C2414yes—
869C2×C4⋊C4C2414yes—
870C2×C4⋊C4C2414yes—
871C2×C4⋊C4C2414yes—
872C2×C4⋊C4C2414yes—
873C2×C4⋊C4C2414yes—
874C2×C4⋊C4C2412yes—
875C2×C4⋊C4C2412yes—
876C2×C4⋊C4C2411yescharacteristic
877C2×C4⋊C4C2411yescharacteristic
878C2×C22⋊C4C2412yes—
879C2×C22⋊C4C2412yes—
880C2×C22⋊C4C2412yes—
881C2×C22⋊C4C2414yes—
882C2×C22⋊C4C2412yes—
883C2×C22⋊C4C2412yes—
884C2×C22⋊C4C2412yes—
885C2×C22⋊C4C2412yes—
886C2×C22⋊C4C2412yes—
887C2×C22⋊C4C2412yes—
888C2×C22⋊C4C2412yes—
889C2×C22⋊C4C2412yes—
890C2×C22⋊C4C2412yes—
891C2×C22⋊C4C2412yes—
892C2×C22⋊C4C2412yes—
893C2×C22⋊C4C2412yes—
894C2×C22⋊C4C2412yes—
895C2×C22⋊C4C2412yes—
896C2×C22⋊C4C2412yes—
897C2×C22⋊C4C2414yes—
898C2×C22⋊C4C2414yes—
899C2×C22⋊C4C2414yes—
900C2×C22⋊C4C2414yes—
901C2×C22⋊C4C2412yes—
902C2×C22⋊C4C2412yes—
903C2×C22⋊C4C2414yes—
904C2×C22⋊C4C2414yes—
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⋊C4C2414yes—
917C2×C22⋊C4C2414yes—
918C2×C42—24no—
919C2×C42—42no—
920C2×C42—42no—
921C2×C42—42no—
922C2×C42—42no—
923C2×C42—42no—
924C2×C42#4118yes—
925C2×C42C2412yes—
926C2×C42C2412yes—
927C2×C42C2414yes—
928C2×C42C2414yes—
929C2×C42C2411yescharacteristic
930C2×C42C2411yescharacteristic
931C2×C42C2411yescharacteristic
932C2×C42C2411yescharacteristic
933C2×C42C2411yescharacteristic
934C2×C42C2411yescharacteristic
935C2×C42C2411yescharacteristic
936C2×C42C2411yescharacteristic
937C2×C42C2411yescharacteristic
938C2×C42C2411yescharacteristic
939C2×C42C2411yescharacteristic
940C2×C42C2411yescharacteristic
941C2×C42C2411yescharacteristic
942C2×C42C2414yes—
943C2×C42C2414yes—
944C2×C42C2414yes—
945C2×C42C2414yes—
946C2×C42C2414yes—
947C2×C42C2414yes—
948C2×C42C2414yes—
949C2×C42C2414yes—
950C2×C42C2414yes—
951C2×C42C2414yes—
952C2×C42C2414yes—
953C2×C42C2414yes—
954C2×C42C2411yescharacteristic
955C2×C42C2411yescharacteristic
956C2×C42C2411yescharacteristic
957C2×C42C2411yescharacteristic
958C2×C42C2411yescharacteristic
959C2×C42C2411yescharacteristic
960C2×C42C2411yescharacteristic
961C2×C42C2411yescharacteristic
962C2×C42C2411yescharacteristic
963C2×C42C2411yescharacteristic
964C2×C42C2411yescharacteristic
965C2×C42C2411yescharacteristic
966C2×C42C2411yescharacteristic
967C2×C42C2411yescharacteristic
968C2×C42C2411yescharacteristic
969#95C2412yes—
970#95C2414yes—
971#95C2414yes—
972#95C2414yes—
973#95C2414yes—
974#95C2414yes—
975#95C2414yes—
976#95C2414yes—
977#95C2414yes—
978#95C2414yes—
979#95C2414yes—
980#95C2414yes—
981#95C2414yes—
982#95C2414yes—
983#95C2412yes—
984#95C2414yes—
985#95C2414yes—
986#95C2414yes—
987#95C2412yes—
988#95C2414yes—
989#95C2412yes—
990#95C2412yes—
991#95C2414yes—
992#95C2412yes—
993#95C2414yes—
994#95C2414yes—
995#95C2414yes—
996#95C2412yes—
997#95C2412yes—
998#95C2414yes—
999#95C2414yes—
1000#95C2414yes—
1001#95C2414yes—
1002#95C2414yes—
1003#95C2414yes—
1004#95C2412yes—
1005#95C2412yes—
1006#95C2414yes—
1007#95C2414yes—
1008#95C2414yes—
1009#95C2414yes—
1010#95C2414yes—
1011#95C2414yes—
1012#95C2414yes—
1013#95C2414yes—
1014#95C2414yes—
1015#95C2414yes—
1016#95C2412yes—
1017#95C2414yes—
1018#95C2414yes—
1019#95C2414yes—
1020#95C2414yes—
1021#95C2414yes—
1022#95C2414yes—
1023#95C2412yes—
1024#95C2414yes—
1025#95C2414yes—
1026#95C2414yes—
1027#95C2414yes—
1028#95C2414yes—
1029#95C2414yes—
1030#95C2414yes—
1031#95C2414yes—
1032#95C2414yes—
1033C24C2512yes—
1034C24C2512yes—
1035C24C2511yescharacteristic
1036C2×Q8—24no—
1037C2×Q8—24no—
1038C2×Q8—24no—
1039C2×Q8—24no—
1040C2×Q8—24no—
1041C2×Q8—42no—
1042C2×Q8—42no—
1043C2×Q8—42no—
1044C2×Q8—42no—
1045C2×Q8—42no—
1046C2×Q8—42no—
1047C2×Q8—42no—
1048C2×Q8—42no—
1049C2×Q8—42no—
1050C2×Q8—42no—
1051C2×D4—24no—
1052C2×D4—24no—
1053C2×D4—24no—
1054C2×D4—22no—
1055C2×D4—22no—
1056C2×D4—24no—
1057C2×D4—42no—
1058C2×D4—41no—
1059C2×D4—42no—
1060C2×D4—41no—
1061C2×D4—42no—
1062C2×D4—42no—
1063C2×D4—42no—
1064C2×D4—42no—
1065C2×D4—42no—
1066C2×D4—41no—
1067C2×D4—41no—
1068C2×D4—42no—
1069C22×C4—22no—
1070C22×C4—22no—
1071C22×C4—24no—
1072C22×C4—24no—
1073C22×C4—22no—
1074C22×C4—22no—
1075C22×C4—24no—
1076C22×C4—24no—
1077C22×C4—22no—
1078C22×C4—22no—
1079C22×C4—22no—
1080C22×C4—22no—
1081C22×C4—24no—
1082C22×C4—24no—
1083C22×C4—41no—
1084C22×C4—41no—
1085C22×C4—41no—
1086C22×C4—41no—
1087C22×C4—41no—
1088C22×C4—41no—
1089C22×C4—41no—
1090C22×C4—41no—
1091C22×C4—41no—
1092C22×C4—41no—
1093C22×C4—44no—
1094C22×C4—44no—
1095C22×C4—44no—
1096C22×C4—44no—
1097C22×C4—44no—
1098C22×C4—44no—
1099C22×C4C2×#4114yes—
1100C22×C4C2×#4114yes—
1101C22×C4C2×#4114yes—
1102C22×C4C2511yescharacteristic
1103C22×C4C2512yes—
1104C22×C4C2512yes—
1105C22×C4C2514yes—
1106C22×C4C2514yes—
1107C22×C4C2514yes—
1108C22×C4C2514yes—
1109C22×C4C2511yescharacteristic
1110C22×C4C2514yes—
1111C22×C4C2514yes—
1112C22×C4C2512yes—
1113C22×C4C2512yes—
1114C22×C4C2514yes—
1115C22×C4C2514yes—
1116C22×C4C2512yes—
1117C22×C4C2512yes—
1118C22×C4C2511yescharacteristic
1119C22×C4C2511yescharacteristic
1120C22×C4C2511yescharacteristic
1121C22×C4C2511yescharacteristic
1122C22×C4C2511yescharacteristic
1123C22×C4C2511yescharacteristic
1124C22×C4C2511yescharacteristic
1125C22×C4C2511yescharacteristic
1126C22×C4C2511yescharacteristic
1127C22×C4C2511yescharacteristic
1128C22×C4C2511yescharacteristic
1129C22×C4C2511yescharacteristic
1130C4⋊C4—24no—
1131C4⋊C4—24no—
1132C4⋊C4—24no—
1133C4⋊C4—24no—
1134C4⋊C4—24no—
1135C4⋊C4—24no—
1136C4⋊C4—24no—
1137C4⋊C4—24no—
1138C4⋊C4—24no—
1139C4⋊C4—24no—
1140C4⋊C4—28no—
1141C4⋊C4—28no—
1142C4⋊C4—24no—
1143C4⋊C4—24no—
1144C4⋊C4—24no—
1145C4⋊C4—24no—
1146C4⋊C4—22no—
1147C4⋊C4—22no—
1148C4⋊C4—28no—
1149C4⋊C4—28no—
1150C4⋊C4—24no—
1151C4⋊C4—24no—
1152C4⋊C4—24no—
1153C4⋊C4—24no—
1154C4⋊C4—24no—
1155C4⋊C4—24no—
1156C4⋊C4—28no—
1157C4⋊C4—28no—
1158C4⋊C4—28no—
1159C4⋊C4—28no—
1160C4⋊C4—24no—
1161C4⋊C4—28no—
1162C4⋊C4—24no—
1163C4⋊C4—24no—
1164C4⋊C4—44no—
1165C4⋊C4—44no—
1166C4⋊C4—44no—
1167C4⋊C4—42no—
1168C4⋊C4—42no—
1169C4⋊C4—42no—
1170C4⋊C4—42no—
1171C4⋊C4—42no—
1172C4⋊C4—42no—
1173C4⋊C4—44no—
1174C4⋊C4—44no—
1175C4⋊C4—41no—
1176C4⋊C4—42no—
1177C4⋊C4—41no—
1178C4⋊C4—42no—
1179C4⋊C4—44no—
1180C4⋊C4—44no—
1181C4⋊C4—44no—
1182C4⋊C4—44no—
1183C4⋊C4—44no—
1184C4⋊C4—44no—
1185C4⋊C4—44no—
1186C4⋊C4—44no—
1187C4⋊C4—44no—
1188C4⋊C4—44no—
1189C4⋊C4—44no—
1190C4⋊C4—44no—
1191C4⋊C4—41no—
1192C4⋊C4—41no—
1193C4⋊C4—42no—
1194C4⋊C4—42no—
1195C22⋊C4—28no—
1196C22⋊C4—24no—
1197C22⋊C4—24no—
1198C22⋊C4—24no—
1199C22⋊C4—24no—
1200C22⋊C4—24no—
1201C22⋊C4—24no—
1202C22⋊C4—24no—
1203C22⋊C4—24no—
1204C22⋊C4—24no—
1205C22⋊C4—24no—
1206C22⋊C4—24no—
1207C22⋊C4—24no—
1208C22⋊C4—24no—
1209C22⋊C4—24no—
1210C22⋊C4—24no—
1211C22⋊C4—24no—
1212C22⋊C4—24no—
1213C22⋊C4—24no—
1214C22⋊C4—44no—
1215C22⋊C4—44no—
1216C22⋊C4—44no—
1217C22⋊C4—44no—
1218C22⋊C4—42no—
1219C22⋊C4—42no—
1220C22⋊C4—44no—
1221C22⋊C4—44no—
1222C22⋊C4—44no—
1223C22⋊C4—44no—
1224C22⋊C4—44no—
1225C22⋊C4—44no—
1226C22⋊C4—44no—
1227C22⋊C4—42no—
1228C22⋊C4—42no—
1229C22⋊C4—44no—
1230C22⋊C4—44no—
1231C22⋊C4—44no—
1232C22⋊C4—44no—
1233C22⋊C4—44no—
1234C22⋊C4—44no—
1235C42—24no—
1236C42—24no—
1237C42—28no—
1238C42—22no—
1239C42—22no—
1240C42—22no—
1241C42—22no—
1242C42—22no—
1243C42—22no—
1244C42—22no—
1245C42—22no—
1246C42—22no—
1247C42—22no—
1248C42—22no—
1249C42—22no—
1250C42—22no—
1251C42—28no—
1252C42—41no—
1253C42—41no—
1254C42—41no—
1255C42—41no—
1256C42—41no—
1257C42—41no—
1258C42—41no—
1259C42—41no—
1260C42—41no—
1261C42—41no—
1262C42—44no—
1263C42—44no—
1264C42—44no—
1265C42—44no—
1266C42—44no—
1267C42—44no—
1268C42—44no—
1269C42—44no—
1270C42—44no—
1271C42—44no—
1272C42—44no—
1273C42—44no—
1274C42C2×#4114yes—
1275C42C2×#4114yes—
1276C42C2×#4114yes—
1277C42C2×#4114yes—
1278C422−1+414yes—
1279C23—21no—
1280C23—21no—
1281C23—21no—
1282C23—21no—
1283C23—21no—
1284C23—21no—
1285C23—22no—
1286C23—22no—
1287C23—22no—
1288C23—22no—
1289C23—22no—
1290C23—22no—
1291C23—22no—
1292C23—22no—
1293C23—22no—
1294C23—22no—
1295C23—22no—
1296C23—22no—
1297C23—22no—
1298C23—22no—
1299C23C22×#4112yes—
1300C23C2611yescharacteristic
1301Q8—48no—
1302Q8—48no—
1303Q8—84no—
1304Q8—84no—
1305Q8—84no—
1306D4—82no—
1307D4—82no—
1308D4—84no—
1309D4—84no—
1310D4—84no—
1311D4—84no—
1312C2×C4—21no—
1313C2×C4—21no—
1314C2×C4—21no—
1315C2×C4—21no—
1316C2×C4—21no—
1317C2×C4—21no—
1318C2×C4—21no—
1319C2×C4—21no—
1320C2×C4—21no—
1321C2×C4—21no—
1322C2×C4—21no—
1323C2×C4—21no—
1324C2×C4—21no—
1325C2×C4—21no—
1326C2×C4—21no—
1327C2×C4—21no—
1328C2×C4—21no—
1329C2×C4—21no—
1330C2×C4—21no—
1331C2×C4—21no—
1332C2×C4—21no—
1333C2×C4—21no—
1334C2×C4—28no—
1335C2×C4—22no—
1336C2×C4—22no—
1337C2×C4—22no—
1338C2×C4—22no—
1339C2×C4—24no—
1340C2×C4—24no—
1341C2×C4—22no—
1342C2×C4—22no—
1343C2×C4—21no—
1344C2×C4—22no—
1345C2×C4—22no—
1346C2×C4—24no—
1347C2×C4—24no—
1348C2×C4—21no—
1349C2×C4—21no—
1350C2×C4—24no—
1351C2×C4—21no—
1352C2×C4—21no—
1353C2×C4—24no—
1354C2×C4—22no—
1355C2×C4—22no—
1356C2×C4—22no—
1357C2×C4—24no—
1358C2×C4—24no—
1359C2×C4—24no—
1360C2×C4—24no—
1361C2×C4—24no—
1362C2×C4—24no—
1363C2×C4—24no—
1364C2×C4—22no—
1365C2×C4—22no—
1366C2×C4—22no—
1367C2×C4—21no—
1368C2×C4—24no—
1369C2×C4—24no—
1370C2×C4—24no—
1371C2×C4—24no—
1372C2×C4—24no—
1373C2×C4—24no—
1374C2×C4—24no—
1375C2×C4—24no—
1376C2×C4—24no—
1377C2×C4—22no—
1378C2×C4—22no—
1379C2×C4—22no—
1380C2×C4—24no—
1381C2×C4—24no—
1382C2×C4—22no—
1383C2×C4—44no—
1384C2×C4—44no—
1385C2×C4—44no—
1386C2×C4—44no—
1387C2×C4—44no—
1388C2×C4—44no—
1389C2×C4—48no—
1390C2×C4—48no—
1391C2×C4—88no—
1392C2×C4—164no—
1393C2×C4C22×#4112yes—
1394C2×C4C22×#4112yes—
1395C2×C4C22×#4112yes—
1396C2×C4C22×#4112yes—
1397C2×C4C22×#4112yes—
1398C2×C4C22×#4112yes—
1399C2×C4C2×2−1+412yes—
1400C2×C4C2×2−1+412yes—
1401C2×C4C2×2−1+412yes—
1402C2×C4#58512yes—
1403C2×C4#58512yes—
1404C2×C4#58512yes—
1405C2×C4#58512yes—
1406C2×C4#58512yes—
1407C22—22no—
1408C22—22no—
1409C22—22no—
1410C22—41no—
1411C22—41no—
1412C22—41no—
1413C22—41no—
1414C22—42no—
1415C22—42no—
1416C22—42no—
1417C22—42no—
1418C22—42no—
1419C22—42no—
1420C22—42no—
1421C22—42no—
1422C22—42no—
1423C22—42no—
1424C22—42no—
1425C22—42no—
1426C22—42no—
1427C22—42no—
1428C22C23×#4111yescharacteristic
1429C22C22×2−1+411yescharacteristic
1430C22C2×#58511yescharacteristic
1431C22C2×#58511yescharacteristic
1432C22C2×#58511yescharacteristic
1433C22C2×#58511yescharacteristic
1434C22C2×#58511yescharacteristic
1435C4—22no—
1436C4—22no—
1437C4—22no—
1438C4—22no—
1439C4—22no—
1440C4—22no—
1441C4—22no—
1442C4—22no—
1443C4—22no—
1444C4—22no—
1445C4—22no—
1446C4—41no—
1447C4—44no—
1448C4—44no—
1449C4—44no—
1450C4—42no—
1451C4—42no—
1452C4—42no—
1453C4—42no—
1454C4—44no—
1455C4—44no—
1456C4—42no—
1457C4—42no—
1458C4—44no—
1459C4—44no—
1460C4—44no—
1461C4—41no—
1462C4#350714yes—
1463C2—42no—
1464C2—82no—
1465C2—82no—
1466C2#6274311yescharacteristic
1467C2#6275211yescharacteristic
1468C2C2×#350711yescharacteristic
1469C2#6281511yescharacteristic
1470C2#6281511yescharacteristic
1471C2#6282811yescharacteristic
1472C2#6283811yescharacteristic
subgroupG/H
center, commutator, Frattini, socle, cosocleC23C26
prime radical#2856C22
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23 ◁ G
LECSG ▷ C23 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #59872C2semidirect
2. #59865C2semidirect
3. #59431C2semidirect
4. #59430C2semidirect
5. #45810C2semidirect
6. #45809C2semidirect
8. #40005C2semidirect
9. #40004C2semidirect
10. #39839C2semidirect
11. #39837C2semidirect
12. #39824C2semidirect
13. #39545C2semidirect
14. #39544C2semidirect
15. #39509C2semidirect
16. #39509C2semidirect
17. #39493C2semidirect
18. #39493C2semidirect
19. #38493C2semidirect
20. #38492C2semidirect
21. #37560C2semidirect
22. #37146C2semidirect
23. #37145C2semidirect
24. #36635C2semidirect
26. #36514C2semidirect
27. #36417C2semidirect
28. #36398C2semidirect
29. #35112C2semidirect
30. #34385C2semidirect
31. C4×#533C2semidirect

Maximal subgroups

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

subgroupindex
#598722
#598652
#594312
#594302
#458102
#458092
#458082
#400052
#400042
#398392
#398372
#398242
#395452
#395442
#395092
#394932
#384932
#384922
#375602
#371462
#371452
#366352
#366312
#365142
#364172
#363982
#351122
#343852
C4×#5332