Finite Group Databasebeta

← #7710088

Subgroups — #7710088

Order 512.

4390 conjugacy classes of subgroups.

The subgroup lattice has 1483 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#59872C212yesmaximal, complemented
2#59865C212yesmaximal, complemented
3#59433C212yesmaximal, complemented
4#59432C212yesmaximal, complemented
5#46245C212yesmaximal, complemented
6#46244C212yesmaximal, complemented
7#46160C212yesmaximal, complemented
8#46018C212yesmaximal, complemented
9#39842C214yesmaximal, complemented
10#39775C214yesmaximal, complemented
11#39547C212yesmaximal, complemented
12#39546C212yesmaximal, complemented
13#39510C212yesmaximal, complemented
14#39494C212yesmaximal, complemented
15#39190C212yesmaximal, complemented
16#38973C212yesmaximal, complemented
17#38127C214yesmaximal, complemented
18#37549C211yesmaximal, characteristic, complemented
19#37549C211yesmaximal, characteristic, complemented
20#36762C212yesmaximal, complemented
21#36761C212yesmaximal
22#36640C211yesmaximal, characteristic, complemented
23#36631C211yesmaximal, characteristic
24#36486C212yesmaximal, complemented
25#36353C214yesmaximal, complemented
26#36254C212yesmaximal, complemented
27#35098C212yesmaximal, complemented
28#35035C212yesmaximal, complemented
29#34382C211yesmaximal, characteristic, complemented
30#34382C211yesmaximal, characteristic, complemented
31C2×C4×#125C211yesmaximal, characteristic, complemented
32C2×#529C2211yescharacteristic
33C2×#529C2211yescharacteristic
34C22×#125C2211yescharacteristic
35#2864C2212yes—
36#2864C2212yes—
37#2861C2211yescharacteristic
38#2861C2211yescharacteristic
39#2860C2212yes—
40#2860C2212yes—
41#2859C2211yescharacteristic
42#2859C2211yescharacteristic
43#2859C2211yescharacteristic
44#2859C2211yescharacteristic
45#2859C2211yescharacteristic
46#2858C2211yescharacteristic
47#2857C2211yescharacteristic
48#2856C2211yescharacteristic
49#2854C2212yes—
50#2854C2212yes—
51#2853C2214yes—
52#2852C2214yes—
53#2851C2212yes—
54#2851C2212yes—
55#2851C2212yes—
56#2851C2212yes—
57#2850C2211yescharacteristic
58#2850C2211yescharacteristic
59#2822C2212yes—
60#2822C2212yes—
61#2820C2212yes—
62#2820C2212yes—
63#2802C2214yes—
64#2802C2214yes—
65#2802C2214yes—
66#2800C2214yes—
67#2800C2214yes—
68#2796C2214yes—
69#2794C2214yes—
70#2791C2214yes—
71#2789C2214yes—
72#2787C2214yes—
73#2786C2214yes—
74#2780C2214yes—
75#2780C2214yes—
76#2777C2214yes—
77#2777C2214yes—
78#2776C2214yes—
79#2776C2214yes—
80#2776C2214yes—
81#2773C2214yes—
82#2772C2214yes—
83#2771C2214yes—
84#2766C2214yes—
85#2765C2214yes—
86#2761C2214yes—
87#2758C2214yes—
88#2740C2214yes—
89#2739C2214yes—
90#2719C2214yes—
91#2713C2214yes—
92#2709C2214yes—
93#2707C2214yes—
94#2694C2214yes—
95#2664C2214yes—
96#2664C2214yes—
97#2643C2214yes—
98#2629C2212yes—
99#2629C2212yes—
100#2629C2212yes—
101#2629C2212yes—
102#2627C2212yes—
103#2627C2212yes—
104#2623C2214yes—
105#2618C2212yes—
106#2618C2212yes—
107#2606C2214yes—
108#2601C2214yes—
109#2597C2214yes—
110#2596C2214yes—
111#2596C2214yes—
112#2596C2214yes—
113#2595C2214yes—
114#2595C2214yes—
115#2594C2214yes—
116#2594C2214yes—
117#2594C2214yes—
118#2594C2214yes—
119#2593C2214yes—
120#2590C2214yes—
121#2590C2214yes—
122#2588C2214yes—
123#2587C2214yes—
124#2587C2214yes—
125#2585C2214yes—
126#2585C2214yes—
127#2584C2212yes—
128#2584C2212yes—
129#2577C2214yes—
130#2575C2214yes—
131#2573C2214yes—
132#2570C2212yes—
133#2570C2212yes—
134#2562C2212yes—
135#2562C2212yes—
136#2562C2212yes—
137#2562C2212yes—
138#2558C2214yes—
139#2533C2214yes—
140#2529C2214yes—
141#2528C2214yes—
142#2525C2214yes—
143#2525C2214yes—
144#2525C2214yes—
145#2524C2214yes—
146#2522C2214yes—
147#2522C2214yes—
148#2521C2214yes—
149#2520C2214yes—
150#2519C2214yes—
151#2516C2214yes—
152#2516C2214yes—
153#2515C2214yes—
154#2509C2212yes—
155#2509C2214yes—
156#2508C2212yes—
157#2507C2212yes—
158#2506C2212yes—
159#2505C2214yes—
160#2497C2212yes—
161#2496C2212yes—
162#2495C2212yes—
163#2495C2212yes—
164#2495C2212yes—
165#2494C2212yes—
166#2494C2212yes—
167#2494C2212yes—
168#2494C2214yes—
169#2493C2214yes—
170#2493C2214yes—
171#2487C2212yes—
172#2487C2212yes—
173#2487C2212yes—
174#2486C2212yes—
175#2486C2212yes—
176#2486C2212yes—
177#2485C2212yes—
178#2485C2212yes—
179#2479C2214yes—
180#2475C2214yes—
181#2474C2214yes—
182#2473C2214yes—
183#2444C2214yes—
184#2443C2214yes—
185#2442C2212yes—
186#2442C2212yes—
187#2441C2212yes—
188#2441C2212yes—
189#2425C2214yes—
190#2425C2214yes—
191#2413C2214yes—
192#2413C2214yes—
193#2382C2212yes—
194#2382C2212yes—
195#2379C2212yes—
196#2379C2212yes—
197#2374C2214yes—
198#2373C2214yes—
199#2370C2214yes—
200#2370C2212yes—
201#2370C2212yes—
202#2359C2214yes—
203#2359C2214yes—
204#2355C2212yes—
205#2355C2212yes—
206#2352C2212yes—
207#2352C2212yes—
208#2352C2212yes—
209#2352C2212yes—
210#2352C2212yes—
211#2352C2212yes—
212D4×C4⋊C4C2212yes—
213D4×C4⋊C4C2212yes—
214#2347C2214yes—
215#2347C2212yes—
216#2346C2212yes—
217#2345C2212yes—
218#2344C2212yes—
219#2334C2214yes—
220#2334C2214yes—
221#2329C2212yes—
222#2329C2212yes—
223#2325C2212yes—
224#2325C2212yes—
225#2322C2214yes—
226#2318C2214yes—
227#2317C2212yes—
228#2317C2212yes—
229#2314C2212yes—
230#2314C2212yes—
231C4×C4⋊Q8C2211yescharacteristic
232C4×#127C2211yescharacteristic
233C4×#125C2212yes—
234C4×#125C2212yes—
235C4×#125C2212yes—
236C4×#125C2212yes—
237C4×#125C2212yes—
238C4×#125C2212yes—
239C4×#125C2212yes—
240C4×#125C2212yes—
241C4×#125C2212yes—
242C4×#125C2212yes—
243C4×#125C2212yes—
244C4×#125C2212yes—
245C4×#124C2211yescharacteristic
246C4×#124C2211yescharacteristic
247C4×#123C2214yes—
248C4×#121C2212yes—
249C4×#121C2212yes—
250#2296C2212yes—
251#2296C2212yes—
252#2293C2212yes—
253#2293C2212yes—
254C2×#389C2211yescharacteristic
255C2×#389C2211yescharacteristic
256#2290C2214yes—
257C2×#387C2212yes—
258C2×#387C2212yes—
259#2285C2211yescharacteristic
260#2285C2211yescharacteristic
261C2×#382C2211yescharacteristic
262C2×C4×C4⋊C4C2212yes—
263C2×C4×C4⋊C4C2212yes—
264C2×C4×C4⋊C4C2211yescharacteristic
265C2×C4×C4⋊C4C2211yescharacteristic
266C2×C43C2211yescharacteristic
267C2×C4⋊Q8C2311yescharacteristic
268C2×#127C2311yescharacteristic
269#529—28no—
270#529—28no—
271C2×#126C2312yes—
272C2×#126C2312yes—
273C2×#126C2314yes—
274C2×#125—28no—
275C2×#125C2312yes—
276C2×#125C2312yes—
277C2×#125C2312yes—
278C2×#125C2312yes—
279C2×#125C2312yes—
280C2×#125C2311yescharacteristic
281C2×#125C2311yescharacteristic
282C2×#125C2312yes—
283C2×#125C2312yes—
284C2×#125C2312yes—
285C2×#125C2314yes—
286C2×#124C2311yescharacteristic
287C2×#124C2311yescharacteristic
288C2×#124C2311yescharacteristic
289C2×#124C2311yescharacteristic
290C2×#123C2312yes—
291C2×#123C2312yes—
292C2×#123C2314yes—
293C2×#123C2314yes—
294C2×#123C2314yes—
295C2×C22⋊Q8C2311yescharacteristic
296C2×C22⋊Q8C2311yescharacteristic
297C2×#121C2311yescharacteristic
298C2×#121C2311yescharacteristic
299C2×#121C2312yes—
300C2×#121C2312yes—
301C2×C4×Q8C2311yescharacteristic
302C2×C4×Q8C2311yescharacteristic
303C2×C4×D4C2311yescharacteristic
304C2×C4×D4C2311yescharacteristic
305C2×C4×D4C2312yes—
306C2×C4×D4C2312yes—
307C2×C4×D4C2312yes—
308C2×C4×D4C2312yes—
309C2×C4×D4C2314yes—
310C2×C4×D4C2314yes—
311C2×#117C2312yes—
312C2×#117C2312yes—
313C2×#117C2312yes—
314C2×#117C2312yes—
315C2×#117C2314yes—
316C2×#117C2312yes—
317C2×#117C2312yes—
318C22×C4⋊C4C2312yes—
319C22×C4⋊C4C2312yes—
320C22×C4⋊C4C2311yescharacteristic
321C22×C4⋊C4C2311yescharacteristic
322C22×C4⋊C4C2312yes—
323C22×C4⋊C4C2312yes—
324C22×C4⋊C4C2312yes—
325C22×C4⋊C4C2311yescharacteristic
326C22×C4⋊C4C2311yescharacteristic
327C22×C4⋊C4C2312yes—
328C22×C42C2311yescharacteristic
329C22×C42C2311yescharacteristic
330C22×C42C2311yescharacteristic
331C22×C42C2311yescharacteristic
332C22×C42C2312yes—
333C22×C42C2312yes—
334C22×C42C2311yescharacteristic
335C22×C42C2311yescharacteristic
336C22×C42C2311yescharacteristic
337#401C2314yes—
338#401C2314yes—
339#401C2314yes—
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#400C2314yes—
355#400C2314yes—
356#400C2314yes—
357#400C2314yes—
358#400C2314yes—
359#400C2314yes—
360#399C2314yes—
361#399C2314yes—
362#399C2314yes—
363#399C2314yes—
364#399C2314yes—
365#398C2314yes—
366#398C2314yes—
367#398C2314yes—
368#398C2314yes—
369#398C2314yes—
370#398C2314yes—
371#398C2314yes—
372#398C2314yes—
373#398C2314yes—
374#398C2314yes—
375#398C2314yes—
376#398C2314yes—
377#398C2314yes—
378#398C2314yes—
379#398C2314yes—
380#398C2314yes—
381#398C2314yes—
382#398C2314yes—
383#398C2314yes—
384#398C2314yes—
385#398C2314yes—
386#397C2314yes—
387#397C2314yes—
388#397C2314yes—
389#397C2314yes—
390#397C2314yes—
391#397C2314yes—
392#397C2314yes—
393#397C2314yes—
394#397C2314yes—
395#397C2314yes—
396#397C2314yes—
397#397C2314yes—
398#396C2314yes—
399#396C2314yes—
400#396C2314yes—
401#396C2314yes—
402#396C2314yes—
403#396C2314yes—
404#396C2314yes—
405#396C2314yes—
406#396C2314yes—
407#396C2314yes—
408#396C2314yes—
409#395C2314yes—
410#395C2314yes—
411#394C2314yes—
412#394C2314yes—
413#394C2314yes—
414#394C2314yes—
415#394C2314yes—
416#394C2314yes—
417#391C2311yescharacteristic
418#391C2311yescharacteristic
419#391C2314yes—
420#391C2314yes—
421#391C2311yescharacteristic
422#391C2311yescharacteristic
423#390C2312yes—
424#390C2311yescharacteristic
425#390C2311yescharacteristic
426#390C2312yes—
427#390C2312yes—
428#390C2312yes—
429#390C2312yes—
430#390C2312yes—
431#390C2312yes—
432#390C2311yescharacteristic
433#390C2311yescharacteristic
434#390C2312yes—
435#389C2312yes—
436#389C2312yes—
437#389C2312yes—
438#389C2312yes—
439#389C2312yes—
440#389C2312yes—
441#389C2312yes—
442#389C2312yes—
443#389C2312yes—
444#389C2312yes—
445#389C2312yes—
446#389C2312yes—
447#389C2312yes—
448#389C2312yes—
449#389C2312yes—
450#389C2312yes—
451#389C2312yes—
452#389C2312yes—
453#389C2312yes—
454#389C2312yes—
455#389C2312yes—
456#389C2312yes—
457#389C2314yes—
458#389C2314yes—
459#389C2314yes—
460#389C2314yes—
461#389C2314yes—
462#389C2314yes—
463#389C2314yes—
464#389C2314yes—
465#389C2314yes—
466#389C2314yes—
467#389C2312yes—
468#389C2312yes—
469#389C2312yes—
470#389C2312yes—
471#389C2312yes—
472#389C2314yes—
473#389C2314yes—
474#389C2314yes—
475#389C2312yes—
476#389C2312yes—
477#389C2312yes—
478#389C2314yes—
479#389C2312yes—
480#389C2312yes—
481#389C2312yes—
482#389C2312yes—
483#389C2312yes—
484#389C2312yes—
485#389C2312yes—
486#389C2312yes—
487#389C2312yes—
488#389C2312yes—
489#389C2314yes—
490#389C2314yes—
491#388C2314yes—
492#388C2314yes—
493#388C2314yes—
494#388C2314yes—
495#388C2314yes—
496#388C2314yes—
497#388C2314yes—
498#388C2314yes—
499#388C2314yes—
500#388C2314yes—
501#388C2314yes—
502#388C2314yes—
503#388C2312yes—
504#388C2314yes—
505#388C2314yes—
506#388C2312yes—
507#388C2312yes—
508#388C2314yes—
509#388C2314yes—
510#388C2312yes—
511#388C2312yes—
512#388C2314yes—
513#388C2314yes—
514#388C2314yes—
515#388C2314yes—
516#388C2314yes—
517#388C2314yes—
518#388C2312yes—
519#388C2312yes—
520#388C2314yes—
521#388C2314yes—
522#388C2314yes—
523#388C2314yes—
524#388C2312yes—
525#388C2312yes—
526#388C2312yes—
527#388C2312yes—
528#388C2312yes—
529#388C2314yes—
530#388C2314yes—
531#388C2314yes—
532#388C2314yes—
533#388C2312yes—
534#388C2312yes—
535#388C2312yes—
536#388C2312yes—
537#388C2314yes—
538#387C2314yes—
539#387C2314yes—
540#387C2314yes—
541#387C2314yes—
542#387C2314yes—
543#387C2314yes—
544#387C2314yes—
545#387C2314yes—
546#387C2314yes—
547#387C2314yes—
548#387C2314yes—
549#387C2314yes—
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#386C2312yes—
594#386C2314yes—
595#386C2312yes—
596#386C2314yes—
597#386C2314yes—
598#386C2314yes—
599#386C2314yes—
600#386C2312yes—
601#386C2312yes—
602#386C2314yes—
603#386C2314yes—
604#386C2314yes—
605#386C2314yes—
606#385C2314yes—
607#385C2314yes—
608#385C2314yes—
609#385C2314yes—
610#385C2314yes—
611#385C2314yes—
612#385C2314yes—
613#385C2314yes—
614#385C2314yes—
615#385C2314yes—
616#385C2314yes—
617#385C2314yes—
618#385C2314yes—
619#385C2314yes—
620#385C2314yes—
621#385C2314yes—
622#385C2314yes—
623#384C2311yescharacteristic
624#384C2311yescharacteristic
625#384C2311yescharacteristic
626#384C2311yescharacteristic
627#384C2312yes—
628#384C2312yes—
629#384C2311yescharacteristic
630#384C2311yescharacteristic
631#383C2314yes—
632#383C2314yes—
633#383C2314yes—
634#383C2314yes—
635#382C2312yes—
636#382C2312yes—
637#382C2312yes—
638#382C2312yes—
639#382C2312yes—
640#382C2312yes—
641#382C2312yes—
642#382C2312yes—
643#382C2312yes—
644#382C2312yes—
645#382C2312yes—
646#382C2312yes—
647#382C2314yes—
648#382C2314yes—
649#382C2311yescharacteristic
650#382C2311yescharacteristic
651#381C2314yes—
652#381C2314yes—
653#381C2314yes—
654#381C2314yes—
655#380C2312yes—
656#380C2312yes—
657#380C2312yes—
658#380C2312yes—
659#380C2312yes—
660#380C2312yes—
661#380C2312yes—
662#380C2312yes—
663#380C2312yes—
664#380C2312yes—
665#380C2312yes—
666#380C2312yes—
667#380C2314yes—
668#380C2314yes—
669#380C2312yes—
670#380C2312yes—
671#380C2312yes—
672#380C2312yes—
673#380C2312yes—
674#380C2312yes—
675#380C2314yes—
676C4×C4⋊C4C2312yes—
677C4×C4⋊C4C2312yes—
678C4×C4⋊C4C2312yes—
679C4×C4⋊C4C2312yes—
680C4×C4⋊C4C2314yes—
681C4×C4⋊C4C2312yes—
682C4×C4⋊C4C2312yes—
683C4×C4⋊C4C2314yes—
684C4×C4⋊C4C2314yes—
685C4×C4⋊C4C2314yes—
686C4×C4⋊C4C2314yes—
687C4×C4⋊C4C2314yes—
688C4×C4⋊C4C2314yes—
689C4×C4⋊C4C2312yes—
690C4×C4⋊C4C2312yes—
691C4×C4⋊C4C2312yes—
692C4×C4⋊C4C2314yes—
693C4×C4⋊C4C2314yes—
694C4×C4⋊C4C2314yes—
695C4×C4⋊C4C2312yes—
696C4×C4⋊C4C2312yes—
697C4×C4⋊C4C2314yes—
698C4×C4⋊C4C2314yes—
699C4×C4⋊C4C2312yes—
700C4×C4⋊C4C2312yes—
701C4×C4⋊C4C2312yes—
702C4×C4⋊C4C2312yes—
703C4×C4⋊C4C2312yes—
704C4×C4⋊C4C2312yes—
705C4×C4⋊C4C2312yes—
706C4×C4⋊C4C2314yes—
707C4×C4⋊C4C2314yes—
708C4×C4⋊C4C2314yes—
709C4×C4⋊C4C2314yes—
710C4×C4⋊C4C2314yes—
711C4×C22⋊C4C2314yes—
712C4×C22⋊C4C2314yes—
713C4×C22⋊C4C2314yes—
714C4×C22⋊C4C2314yes—
715C4×C22⋊C4C2314yes—
716C4×C22⋊C4C2314yes—
717C4×C22⋊C4C2314yes—
718C4×C22⋊C4C2312yes—
719C4×C22⋊C4C2312yes—
720C4×C22⋊C4C2312yes—
721C4×C22⋊C4C2312yes—
722#376C2314yes—
723C2×#95C2312yes—
724C2×#95C2312yes—
725C2×#95C2312yes—
726C2×#95C2312yes—
727C2×#95C2312yes—
728C2×#95C2312yes—
729C43C2311yescharacteristic
730C43C2311yescharacteristic
731C43C2311yescharacteristic
732C43C2311yescharacteristic
733C43C2311yescharacteristic
734C43C2311yescharacteristic
735C43C2311yescharacteristic
736C43C2311yescharacteristic
737C22×Q8C2411yescharacteristic
738C22×Q8C2411yescharacteristic
739C22×D4C2412yes—
740C22×D4C2412yes—
741C22×D4C2412yes—
742C22×D4C2411yescharacteristic
743C22×D4C2411yescharacteristic
744C22×D4C2412yes—
745C23×C4C2412yes—
746C23×C4C2412yes—
747C23×C4C2412yes—
748C23×C4C2411yescharacteristic
749C23×C4C2411yescharacteristic
750C23×C4C2411yescharacteristic
751C23×C4C2411yescharacteristic
752C23×C4C2411yescharacteristic
753C23×C4C2412yes—
754C23×C4C2412yes—
755C23×C4C2412yes—
756C23×C4C2411yescharacteristic
757C23×C4C2414yes—
758C23×C4C2414yes—
759C23×C4C2411yescharacteristic
760C4⋊Q8—42no—
761#127—42no—
762#126—28no—
763#126—28no—
764#126—48no—
765#125—28no—
766#125—28no—
767#125—28no—
768#125—28no—
769#125—24no—
770#125—24no—
771#125—28no—
772#125—44no—
773#125—44no—
774#125—44no—
775#125—48no—
776#124—24no—
777#124—24no—
778#124—42no—
779#124—42no—
780#123—28no—
781#123—28no—
782#123—48no—
783#123—48no—
784#123—48no—
785C22⋊Q8—24no—
786C22⋊Q8—24no—
787#121—24no—
788#121—24no—
789#121—44no—
790#121—44no—
791C4×Q8—24no—
792C4×Q8—24no—
793C4×D4—28no—
794C4×D4—28no—
795C4×D4—24no—
796C4×D4—24no—
797C4×D4—28no—
798C4×D4—44no—
799C4×D4—48no—
800C4×D4—48no—
801#117—28no—
802#117—28no—
803#117—48no—
804#117—44no—
805#117—44no—
806#117—44no—
807#117—44no—
808C2×C4⋊C4—24no—
809C2×C4⋊C4—24no—
810C2×C4⋊C4—28no—
811C2×C4⋊C4—28no—
812C2×C4⋊C4—42no—
813C2×C4⋊C4—42no—
814C2×C4⋊C4—44no—
815C2×C4⋊C4—44no—
816C2×C4⋊C4—44no—
817C2×C4⋊C4—44no—
818C2×C4⋊C4C2412yes—
819C2×C4⋊C4C2412yes—
820C2×C4⋊C4C2412yes—
821C2×C4⋊C4C2412yes—
822C2×C4⋊C4C2414yes—
823C2×C4⋊C4C2412yes—
824C2×C4⋊C4C2412yes—
825C2×C4⋊C4C2414yes—
826C2×C4⋊C4C2414yes—
827C2×C4⋊C4C2414yes—
828C2×C4⋊C4C2414yes—
829C2×C4⋊C4C2412yes—
830C2×C4⋊C4C2412yes—
831C2×C4⋊C4C2412yes—
832C2×C4⋊C4C2412yes—
833C2×C4⋊C4C2412yes—
834C2×C4⋊C4C2412yes—
835C2×C4⋊C4C2414yes—
836C2×C4⋊C4C2411yescharacteristic
837C2×C4⋊C4C2411yescharacteristic
838C2×C4⋊C4C2412yes—
839C2×C4⋊C4C2412yes—
840C2×C4⋊C4C2412yes—
841C2×C4⋊C4C2411yescharacteristic
842C2×C4⋊C4C2411yescharacteristic
843C2×C4⋊C4C2412yes—
844C2×C4⋊C4C2412yes—
845C2×C4⋊C4C2414yes—
846C2×C4⋊C4C2412yes—
847C2×C4⋊C4C2412yes—
848C2×C4⋊C4C2412yes—
849C2×C4⋊C4C2414yes—
850C2×C4⋊C4C2414yes—
851C2×C4⋊C4C2412yes—
852C2×C4⋊C4C2412yes—
853C2×C4⋊C4C2414yes—
854C2×C4⋊C4C2414yes—
855C2×C4⋊C4C2414yes—
856C2×C4⋊C4C2414yes—
857C2×C4⋊C4C2414yes—
858C2×C4⋊C4C2412yes—
859C2×C4⋊C4C2412yes—
860C2×C4⋊C4C2412yes—
861C2×C4⋊C4C2412yes—
862C2×C4⋊C4C2414yes—
863C2×C4⋊C4C2412yes—
864C2×C4⋊C4C2414yes—
865C2×C4⋊C4C2414yes—
866C2×C4⋊C4C2412yes—
867C2×C4⋊C4C2412yes—
868C2×C4⋊C4C2414yes—
869C2×C4⋊C4C2414yes—
870C2×C4⋊C4C2414yes—
871C2×C4⋊C4C2414yes—
872C2×C4⋊C4C2412yes—
873C2×C4⋊C4C2412yes—
874C2×C4⋊C4C2412yes—
875C2×C4⋊C4C2412yes—
876C2×C4⋊C4C2414yes—
877C2×C4⋊C4C2414yes—
878C2×C4⋊C4C2414yes—
879C2×C4⋊C4C2414yes—
880C2×C4⋊C4C2414yes—
881C2×C4⋊C4C2414yes—
882C2×C4⋊C4C2414yes—
883C2×C4⋊C4C2414yes—
884C2×C4⋊C4C2414yes—
885C2×C4⋊C4C2412yes—
886C2×C22⋊C4C2412yes—
887C2×C22⋊C4C2414yes—
888C2×C22⋊C4C2414yes—
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⋊C4C2412yes—
898C2×C22⋊C4C2412yes—
899C2×C22⋊C4C2412yes—
900C2×C22⋊C4C2412yes—
901C2×C22⋊C4C2412yes—
902C2×C22⋊C4C2414yes—
903C2×C22⋊C4C2414yes—
904C2×C22⋊C4C2414yes—
905C2×C22⋊C4C2414yes—
906C2×C22⋊C4C2414yes—
907C2×C22⋊C4C2412yes—
908C2×C22⋊C4C2412yes—
909C2×C22⋊C4C2412yes—
910C2×C22⋊C4C2412yes—
911C2×C22⋊C4C2412yes—
912C2×C22⋊C4C2412yes—
913C2×C22⋊C4C2414yes—
914C2×C22⋊C4C2414yes—
915C2×C22⋊C4C2414yes—
916C2×C22⋊C4C2414yes—
917C2×C22⋊C4C2414yes—
918C2×C22⋊C4C2414yes—
919C2×C22⋊C4C2414yes—
920C2×C22⋊C4C2412yes—
921C2×C22⋊C4C2412yes—
922C2×C22⋊C4C2414yes—
923C2×C22⋊C4C2414yes—
924C2×C42—24no—
925C2×C42—44no—
926C2×C42—42no—
927C2×C42—42no—
928C2×C42—42no—
929C2×C42—42no—
930C2×C42—44no—
931C2×C42—42no—
932C2×C42#4118yes—
933C2×C42C2412yes—
934C2×C42C2412yes—
935C2×C42C2414yes—
936C2×C42C2411yescharacteristic
937C2×C42C2411yescharacteristic
938C2×C42C2411yescharacteristic
939C2×C42C2411yescharacteristic
940C2×C42C2411yescharacteristic
941C2×C42C2411yescharacteristic
942C2×C42C2411yescharacteristic
943C2×C42C2411yescharacteristic
944C2×C42C2411yescharacteristic
945C2×C42C2414yes—
946C2×C42C2414yes—
947C2×C42C2414yes—
948C2×C42C2414yes—
949C2×C42C2414yes—
950C2×C42C2414yes—
951C2×C42C2414yes—
952C2×C42C2414yes—
953C2×C42C2411yescharacteristic
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×C42C2414yes—
968C2×C42C2414yes—
969C2×C42C2414yes—
970C2×C42C2411yescharacteristic
971C2×C42C2411yescharacteristic
972C2×C42C2411yescharacteristic
973C2×C42C2411yescharacteristic
974C2×C42C2411yescharacteristic
975#95C2414yes—
976#95C2414yes—
977#95C2414yes—
978#95C2414yes—
979#95C2414yes—
980#95C2414yes—
981#95C2414yes—
982#95C2414yes—
983#95C2414yes—
984#95C2414yes—
985#95C2414yes—
986#95C2414yes—
987#95C2412yes—
988#95C2414yes—
989#95C2414yes—
990#95C2414yes—
991#95C2414yes—
992#95C2412yes—
993#95C2414yes—
994#95C2414yes—
995#95C2414yes—
996#95C2412yes—
997#95C2414yes—
998#95C2412yes—
999#95C2412yes—
1000#95C2414yes—
1001#95C2414yes—
1002#95C2414yes—
1003#95C2412yes—
1004#95C2414yes—
1005#95C2412yes—
1006#95C2414yes—
1007#95C2412yes—
1008#95C2412yes—
1009#95C2412yes—
1010#95C2414yes—
1011#95C2414yes—
1012#95C2414yes—
1013#95C2414yes—
1014#95C2414yes—
1015#95C2414yes—
1016#95C2414yes—
1017#95C2414yes—
1018#95C2414yes—
1019#95C2414yes—
1020#95C2414yes—
1021#95C2412yes—
1022#95C2414yes—
1023#95C2414yes—
1024#95C2414yes—
1025#95C2414yes—
1026#95C2414yes—
1027#95C2414yes—
1028#95C2414yes—
1029#95C2414yes—
1030#95C2412yes—
1031#95C2414yes—
1032#95C2414yes—
1033#95C2414yes—
1034#95C2414yes—
1035#95C2414yes—
1036#95C2414yes—
1037#95C2414yes—
1038#95C2414yes—
1039C24C2512yes—
1040C24C2512yes—
1041C24C2511yescharacteristic
1042C2×Q8—22no—
1043C2×Q8—22no—
1044C2×Q8—41no—
1045C2×Q8—41no—
1046C2×Q8—41no—
1047C2×Q8—41no—
1048C2×D4—24no—
1049C2×D4—24no—
1050C2×D4—24no—
1051C2×D4—24no—
1052C2×D4—24no—
1053C2×D4—24no—
1054C2×D4—22no—
1055C2×D4—22no—
1056C2×D4—24no—
1057C2×D4—24no—
1058C2×D4—42no—
1059C2×D4—42no—
1060C2×D4—42no—
1061C2×D4—41no—
1062C2×D4—41no—
1063C2×D4—42no—
1064C2×D4—41no—
1065C2×D4—41no—
1066C22×C4—22no—
1067C22×C4—22no—
1068C22×C4—22no—
1069C22×C4—22no—
1070C22×C4—22no—
1071C22×C4—22no—
1072C22×C4—22no—
1073C22×C4—24no—
1074C22×C4—24no—
1075C22×C4—22no—
1076C22×C4—22no—
1077C22×C4—22no—
1078C22×C4—24no—
1079C22×C4—24no—
1080C22×C4—24no—
1081C22×C4—24no—
1082C22×C4—24no—
1083C22×C4—24no—
1084C22×C4—22no—
1085C22×C4—24no—
1086C22×C4—24no—
1087C22×C4—22no—
1088C22×C4—24no—
1089C22×C4—24no—
1090C22×C4—41no—
1091C22×C4—41no—
1092C22×C4—41no—
1093C22×C4—41no—
1094C22×C4—41no—
1095C22×C4—41no—
1096C22×C4—42no—
1097C22×C4—42no—
1098C22×C4—42no—
1099C22×C4—44no—
1100C22×C4—42no—
1101C22×C4—42no—
1102C22×C4—42no—
1103C22×C4—44no—
1104C22×C4—44no—
1105C22×C4—44no—
1106C22×C4—44no—
1107C22×C4—44no—
1108C22×C4C2×#4114yes—
1109C22×C4C2×#4114yes—
1110C22×C4C2×#4114yes—
1111C22×C4C2511yescharacteristic
1112C22×C4C2512yes—
1113C22×C4C2512yes—
1114C22×C4C2514yes—
1115C22×C4C2514yes—
1116C22×C4C2514yes—
1117C22×C4C2514yes—
1118C22×C4C2511yescharacteristic
1119C22×C4C2511yescharacteristic
1120C22×C4C2511yescharacteristic
1121C22×C4C2512yes—
1122C22×C4C2512yes—
1123C22×C4C2512yes—
1124C22×C4C2512yes—
1125C22×C4C2514yes—
1126C22×C4C2514yes—
1127C22×C4C2514yes—
1128C22×C4C2514yes—
1129C22×C4C2511yescharacteristic
1130C22×C4C2511yescharacteristic
1131C22×C4C2511yescharacteristic
1132C22×C4C2511yescharacteristic
1133C22×C4C2511yescharacteristic
1134C22×C4C2511yescharacteristic
1135C22×C4C2511yescharacteristic
1136C22×C4C2511yescharacteristic
1137C22×C4C2511yescharacteristic
1138C22×C4C2511yescharacteristic
1139C4⋊C4—28no—
1140C4⋊C4—28no—
1141C4⋊C4—28no—
1142C4⋊C4—24no—
1143C4⋊C4—24no—
1144C4⋊C4—28no—
1145C4⋊C4—24no—
1146C4⋊C4—24no—
1147C4⋊C4—24no—
1148C4⋊C4—24no—
1149C4⋊C4—24no—
1150C4⋊C4—24no—
1151C4⋊C4—22no—
1152C4⋊C4—22no—
1153C4⋊C4—24no—
1154C4⋊C4—24no—
1155C4⋊C4—22no—
1156C4⋊C4—22no—
1157C4⋊C4—24no—
1158C4⋊C4—24no—
1159C4⋊C4—24no—
1160C4⋊C4—28no—
1161C4⋊C4—28no—
1162C4⋊C4—24no—
1163C4⋊C4—24no—
1164C4⋊C4—24no—
1165C4⋊C4—24no—
1166C4⋊C4—24no—
1167C4⋊C4—24no—
1168C4⋊C4—28no—
1169C4⋊C4—28no—
1170C4⋊C4—28no—
1171C4⋊C4—24no—
1172C4⋊C4—42no—
1173C4⋊C4—42no—
1174C4⋊C4—44no—
1175C4⋊C4—44no—
1176C4⋊C4—44no—
1177C4⋊C4—44no—
1178C4⋊C4—44no—
1179C4⋊C4—42no—
1180C4⋊C4—42no—
1181C4⋊C4—42no—
1182C4⋊C4—42no—
1183C4⋊C4—44no—
1184C4⋊C4—42no—
1185C4⋊C4—44no—
1186C4⋊C4—44no—
1187C4⋊C4—42no—
1188C4⋊C4—42no—
1189C4⋊C4—44no—
1190C4⋊C4—44no—
1191C4⋊C4—44no—
1192C4⋊C4—44no—
1193C4⋊C4—42no—
1194C4⋊C4—42no—
1195C4⋊C4—42no—
1196C4⋊C4—42no—
1197C4⋊C4—44no—
1198C4⋊C4—44no—
1199C4⋊C4—44no—
1200C4⋊C4—44no—
1201C4⋊C4—44no—
1202C4⋊C4—44no—
1203C4⋊C4—44no—
1204C4⋊C4—44no—
1205C4⋊C4—44no—
1206C4⋊C4—42no—
1207C22⋊C4—24no—
1208C22⋊C4—24no—
1209C22⋊C4—28no—
1210C22⋊C4—28no—
1211C22⋊C4—24no—
1212C22⋊C4—24no—
1213C22⋊C4—24no—
1214C22⋊C4—24no—
1215C22⋊C4—24no—
1216C22⋊C4—24no—
1217C22⋊C4—24no—
1218C22⋊C4—24no—
1219C22⋊C4—24no—
1220C22⋊C4—24no—
1221C22⋊C4—24no—
1222C22⋊C4—24no—
1223C22⋊C4—44no—
1224C22⋊C4—44no—
1225C22⋊C4—44no—
1226C22⋊C4—42no—
1227C22⋊C4—42no—
1228C22⋊C4—44no—
1229C22⋊C4—44no—
1230C22⋊C4—42no—
1231C22⋊C4—42no—
1232C22⋊C4—42no—
1233C22⋊C4—42no—
1234C22⋊C4—44no—
1235C22⋊C4—44no—
1236C22⋊C4—44no—
1237C22⋊C4—44no—
1238C22⋊C4—44no—
1239C22⋊C4—44no—
1240C22⋊C4—44no—
1241C22⋊C4—42no—
1242C22⋊C4—42no—
1243C22⋊C4—44no—
1244C22⋊C4—44no—
1245C42—24no—
1246C42—24no—
1247C42—22no—
1248C42—22no—
1249C42—22no—
1250C42—28no—
1251C42—22no—
1252C42—22no—
1253C42—22no—
1254C42—22no—
1255C42—22no—
1256C42—22no—
1257C42—41no—
1258C42—41no—
1259C42—41no—
1260C42—41no—
1261C42—41no—
1262C42—41no—
1263C42—41no—
1264C42—41no—
1265C42—41no—
1266C42—41no—
1267C42—44no—
1268C42—44no—
1269C42—44no—
1270C42—41no—
1271C42—41no—
1272C42—41no—
1273C42—41no—
1274C42—44no—
1275C42—44no—
1276C42—44no—
1277C42—44no—
1278C42—44no—
1279C42—44no—
1280C42—44no—
1281C42—44no—
1282C42C2×#4114yes—
1283C42C2×#4114yes—
1284C42C2×#4114yes—
1285C42C2×#4114yes—
1286C422−1+414yes—
1287C23—21no—
1288C23—21no—
1289C23—21no—
1290C23—21no—
1291C23—22no—
1292C23—22no—
1293C23—22no—
1294C23—22no—
1295C23—22no—
1296C23—22no—
1297C23—22no—
1298C23—22no—
1299C23—22no—
1300C23—22no—
1301C23—22no—
1302C23—22no—
1303C23—22no—
1304C23—22no—
1305C23C22×#4112yes—
1306C23#58512yes—
1307C23#58512yes—
1308C23C2611yescharacteristic
1309Q8—82no—
1310Q8—82no—
1311D4—48no—
1312D4—48no—
1313D4—84no—
1314D4—82no—
1315D4—82no—
1316D4—84no—
1317C2×C4—28no—
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—21no—
1335C2×C4—21no—
1336C2×C4—28no—
1337C2×C4—28no—
1338C2×C4—22no—
1339C2×C4—22no—
1340C2×C4—22no—
1341C2×C4—22no—
1342C2×C4—22no—
1343C2×C4—22no—
1344C2×C4—24no—
1345C2×C4—24no—
1346C2×C4—21no—
1347C2×C4—22no—
1348C2×C4—22no—
1349C2×C4—24no—
1350C2×C4—24no—
1351C2×C4—24no—
1352C2×C4—21no—
1353C2×C4—21no—
1354C2×C4—24no—
1355C2×C4—21no—
1356C2×C4—21no—
1357C2×C4—21no—
1358C2×C4—21no—
1359C2×C4—24no—
1360C2×C4—24no—
1361C2×C4—24no—
1362C2×C4—22no—
1363C2×C4—21no—
1364C2×C4—21no—
1365C2×C4—24no—
1366C2×C4—22no—
1367C2×C4—22no—
1368C2×C4—22no—
1369C2×C4—22no—
1370C2×C4—22no—
1371C2×C4—21no—
1372C2×C4—21no—
1373C2×C4—21no—
1374C2×C4—24no—
1375C2×C4—24no—
1376C2×C4—24no—
1377C2×C4—24no—
1378C2×C4—24no—
1379C2×C4—24no—
1380C2×C4—24no—
1381C2×C4—24no—
1382C2×C4—24no—
1383C2×C4—24no—
1384C2×C4—22no—
1385C2×C4—24no—
1386C2×C4—24no—
1387C2×C4—24no—
1388C2×C4—24no—
1389C2×C4—22no—
1390C2×C4—22no—
1391C2×C4—22no—
1392C2×C4—44no—
1393C2×C4—44no—
1394C2×C4—44no—
1395C2×C4—44no—
1396C2×C4—48no—
1397C2×C4—48no—
1398C2×C4—48no—
1399C2×C4—48no—
1400C2×C4—84no—
1401C2×C4—84no—
1402C2×C4—88no—
1403C2×C4—164no—
1404C2×C4C22×#4112yes—
1405C2×C4C22×#4112yes—
1406C2×C4C22×#4112yes—
1407C2×C4C22×#4112yes—
1408C2×C4C22×#4112yes—
1409C2×C4C22×#4112yes—
1410C2×C4C2×2−1+412yes—
1411C2×C4C2×2−1+412yes—
1412C2×C4C2×2−1+412yes—
1413C2×C4#58512yes—
1414C2×C4#58512yes—
1415C2×C4#58512yes—
1416C22—22no—
1417C22—22no—
1418C22—22no—
1419C22—22no—
1420C22—22no—
1421C22—22no—
1422C22—42no—
1423C22—42no—
1424C22—42no—
1425C22—42no—
1426C22—42no—
1427C22—42no—
1428C22—42no—
1429C22—42no—
1430C22—42no—
1431C22—42no—
1432C22—42no—
1433C22—42no—
1434C22—42no—
1435C22—42no—
1436C22#351214yes—
1437C22C23×#4111yescharacteristic
1438C22C22×2−1+411yescharacteristic
1439C22C2×#58511yescharacteristic
1440C22C2×#58511yescharacteristic
1441C22C2×#58511yescharacteristic
1442C22C2×#58511yescharacteristic
1443C22C2×#58511yescharacteristic
1444C4—22no—
1445C4—22no—
1446C4—22no—
1447C4—22no—
1448C4—22no—
1449C4—22no—
1450C4—22no—
1451C4—22no—
1452C4—22no—
1453C4—41no—
1454C4—41no—
1455C4—44no—
1456C4—44no—
1457C4—44no—
1458C4—41no—
1459C4—42no—
1460C4—42no—
1461C4—44no—
1462C4—42no—
1463C4—42no—
1464C4—44no—
1465C4—42no—
1466C4—42no—
1467C4—44no—
1468C4—41no—
1469C4—44no—
1470C4—44no—
1471C4#350714yes—
1472C2—24no—
1473C2—82no—
1474C2—82no—
1475C2#6274311yescharacteristic
1476C2#6275211yescharacteristic
1477C2C2×#350711yescharacteristic
1478C2C2×#351211yescharacteristic
1479C2#6281511yescharacteristic
1480C2#6282511yescharacteristic
1481C2#6282811yescharacteristic
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. #59433C2semidirect
4. #59432C2semidirect
5. #46245C2semidirect
6. #46244C2semidirect
7. #46160C2semidirect
8. #46018C2semidirect
9. #39842C2semidirect
10. #39775C2semidirect
11. #39547C2semidirect
12. #39546C2semidirect
13. #39510C2semidirect
14. #39494C2semidirect
15. #39190C2semidirect
16. #38973C2semidirect
17. #38127C2semidirect
18. #37549C2semidirect
19. #37549C2semidirect
20. #36762C2semidirect
22. #36640C2semidirect
24. #36486C2semidirect
25. #36353C2semidirect
26. #36254C2semidirect
27. #35098C2semidirect
28. #35035C2semidirect
29. #34382C2semidirect
30. #34382C2semidirect
31. C2×C4×#125C2semidirect

Maximal subgroups

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

subgroupindex
#598722
#598652
#594332
#594322
#462452
#462442
#461602
#460182
#398422
#397752
#395472
#395462
#395102
#394942
#391902
#389732
#381272
#375492
#367622
#367612
#366402
#366312
#364862
#363532
#362542
#350982
#350352
#343822
C2×C4×#1252