Finite Group Databasebeta

← #8639890

Subgroups — #8639890

Order 512.

4386 conjugacy classes of subgroups.

The subgroup lattice has 1402 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#59152C212yesmaximal, complemented
2#58647C214yesmaximal, complemented
3#58045C212yesmaximal, complemented
4#57925C214yesmaximal, complemented
5#52991C211yesmaximal, characteristic, complemented
6#51669C214yesmaximal, complemented
7#48594C214yesmaximal, complemented
8#47890C214yesmaximal, complemented
9#47147C214yesmaximal, complemented
10#47003C212yesmaximal, complemented
11#46060C212yesmaximal, complemented
12#45502C211yesmaximal, characteristic, complemented
13#45253C212yesmaximal, complemented
14#45251C211yesmaximal, characteristic
15#43814C212yesmaximal, complemented
16#42948C212yesmaximal, complemented
17#42888C211yesmaximal, characteristic, complemented
18#42818C212yesmaximal, complemented
19#39788C212yesmaximal, complemented
20#39563C212yesmaximal, complemented
21#39496C212yesmaximal, complemented
22#39465C211yesmaximal, characteristic, complemented
23#39077C212yesmaximal, complemented
24#37314C212yesmaximal, complemented
25#36129C212yesmaximal, complemented
26#36080C211yesmaximal, characteristic
27#35519C212yesmaximal, complemented
28#35017C212yesmaximal, complemented
29#34906C211yesmaximal, characteristic
30C2×#557C2211yescharacteristic
31C2×#552C2211yescharacteristic
32C2×#533C2212yes—
33C22×C4⋊Q8C2211yescharacteristic
34C2×#520C2211yescharacteristic
35#2863C2212yes—
36#2862C2212yes—
37#2859C2212yes—
38#2857C2212yes—
39#2857C2212yes—
40#2855C2211yescharacteristic
41#2841C2212yes—
42#2841C2212yes—
43#2839C2214yes—
44#2839C2214yes—
45#2835C2212yes—
46#2833C2214yes—
47#2821C2212yes—
48#2809C2214yes—
49#2806C2214yes—
50#2806C2214yes—
51#2805C2214yes—
52#2802C2214yes—
53#2802C2214yes—
54#2799C2214yes—
55#2794C2214yes—
56#2791C2214yes—
57#2789C2212yes—
58#2788C2214yes—
59#2786C2214yes—
60#2776C2214yes—
61#2774C2214yes—
62#2774C2214yes—
63#2771C2212yes—
64#2771C2214yes—
65#2770C2214yes—
66#2767C2214yes—
67#2765C2214yes—
68#2764C2214yes—
69#2764C2214yes—
70#2763C2214yes—
71#2762C2214yes—
72#2762C2214yes—
73#2762C2214yes—
74#2760C2212yes—
75#2758C2214yes—
76#2755C2214yes—
77#2754C2214yes—
78#2751C2214yes—
79#2751C2214yes—
80#2750C2214yes—
81#2750C2214yes—
82#2747C2214yes—
83#2746C2214yes—
84#2745C2214yes—
85#2743C2214yes—
86#2729C2214yes—
87#2729C2214yes—
88#2725C2214yes—
89#2722C2212yes—
90#2719C2214yes—
91#2716C2214yes—
92#2713C2214yes—
93#2713C2214yes—
94#2704C2214yes—
95#2704C2214yes—
96#2698C2214yes—
97#2695C2214yes—
98#2694C2214yes—
99#2683C2212yes—
100#2677C2214yes—
101#2677C2212yes—
102#2667C2214yes—
103#2667C2214yes—
104#2666C2214yes—
105#2664C2214yes—
106#2660C2211yescharacteristic
107#2655C2214yes—
108#2647C2212yes—
109#2637C2212yes—
110#2634C2212yes—
111#2628C2212yes—
112#2627C2214yes—
113#2625C2212yes—
114#2616C2211yescharacteristic
115#2614C2212yes—
116#2609C2212yes—
117#2609C2214yes—
118#2607C2212yes—
119#2607C2211yescharacteristic
120#2602C2212yes—
121#2601C2214yes—
122#2600C2211yescharacteristic
123#2599C2214yes—
124#2599C2212yes—
125#2598C2212yes—
126#2595C2212yes—
127#2588C2212yes—
128#2588C2214yes—
129#2585C2214yes—
130#2584C2212yes—
131#2584C2211yescharacteristic
132#2582C2214yes—
133#2581C2214yes—
134#2580C2214yes—
135#2578C2212yes—
136#2575C2214yes—
137#2573C2214yes—
138#2571C2212yes—
139#2570C2212yes—
140#2565C2212yes—
141#2565C2214yes—
142#2563C2211yescharacteristic
143#2562C2212yes—
144#2560C2214yes—
145#2560C2212yes—
146#2556C2214yes—
147#2556C2214yes—
148#2551C2212yes—
149#2550C2212yes—
150#2550C2212yes—
151#2550C2212yes—
152#2538C2214yes—
153#2524C2214yes—
154#2523C2211yescharacteristic
155#2514C2212yes—
156#2509C2212yes—
157#2509C2212yes—
158#2507C2212yes—
159#2507C2212yes—
160#2506C2212yes—
161#2503C2211yescharacteristic
162#2503C2211yescharacteristic
163#2502C2212yes—
164#2497C2212yes—
165#2497C2212yes—
166#2497C2212yes—
167#2496C2212yes—
168#2494C2212yes—
169#2492C2214yes—
170#2492C2212yes—
171#2487C2211yescharacteristic
172#2487C2212yes—
173#2486C2211yescharacteristic
174#2484C2212yes—
175#2477C2214yes—
176#2475C2214yes—
177#2475C2214yes—
178#2473C2214yes—
179#2471C2214yes—
180#2469C2214yes—
181#2468C2214yes—
182#2467C2212yes—
183#2465C2214yes—
184#2463C2211yescharacteristic
185#2462C2214yes—
186#2462C2214yes—
187#2457C2214yes—
188#2453C2214yes—
189#2451C2212yes—
190#2451C2214yes—
191#2451C2212yes—
192#2451C2214yes—
193#2450C2214yes—
194#2450C2214yes—
195#2449C2214yes—
196#2449C2214yes—
197#2449C2214yes—
198#2446C2214yes—
199#2442C2212yes—
200#2442C2212yes—
201#2442C2212yes—
202#2442C2212yes—
203#2442C2212yes—
204#2441C2212yes—
205#2441C2214yes—
206#2441C2212yes—
207#2440C2212yes—
208#2440C2212yes—
209#2439C2212yes—
210#2439C2212yes—
211#2439C2212yes—
212#2439C2212yes—
213#2438C2214yes—
214#2438C2214yes—
215#2429C2214yes—
216#2423C2212yes—
217#2421C2212yes—
218#2417C2214yes—
219#2417C2212yes—
220#2413C2212yes—
221#2409C2214yes—
222#2398C2211yescharacteristic
223#2396C2212yes—
224#2395C2212yes—
225#2388C2211yescharacteristic
226#2378C2214yes—
227#2376C2212yes—
228#2370C2212yes—
229#2365C2214yes—
230#2362C2212yes—
231#2362C2212yes—
232#2360C2214yes—
233#2352C2212yes—
234#2352C2212yes—
235#2347C2211yescharacteristic
236#2344C2211yescharacteristic
237#2344C2212yes—
238#2344C2212yes—
239Q8×C22⋊C4C2214yes—
240#2336C2214yes—
241#2329C2214yes—
242#2320C2211yescharacteristic
243#2318C2214yes—
244#2317C2212yes—
245#2317C2212yes—
246#2316C2214yes—
247#2314C2212yes—
248#2311C2212yes—
249#2310C2212yes—
250C4×C4⋊Q8C2212yes—
251C4×#126C2212yes—
252C4×C22⋊Q8C2212yes—
253C4×C22⋊Q8C2212yes—
254C4×#123C2211yescharacteristic
255#2298C2212yes—
256#2297C2212yes—
257C2×#389C2212yes—
258C42×D4C2212yes—
259C22×#41C2311yescharacteristic
260C23×Q8C2312yes—
261#557—44no—
262#552—44no—
263#533—48no—
264C2×C4⋊Q8—44no—
265C2×C4⋊Q8C2312yes—
266C2×C4⋊Q8C2311yescharacteristic
267C2×C4⋊Q8C2312yes—
268C2×C4⋊Q8C2312yes—
269C2×C4⋊Q8C2312yes—
270C2×C4⋊Q8C2314yes—
271C2×C4⋊Q8C2314yes—
272C2×#126C2312yes—
273C2×#126C2312yes—
274C2×#126C2314yes—
275C2×#125C2312yes—
276C2×#125C2312yes—
277C2×#125C2312yes—
278C2×#125C2311yescharacteristic
279C2×#125C2314yes—
280C2×#125C2314yes—
281C2×#125C2314yes—
282C2×#123C2311yescharacteristic
283C2×#123C2312yes—
284C2×#123C2312yes—
285C2×C22⋊Q8C2312yes—
286C2×C22⋊Q8C2312yes—
287C2×C22⋊Q8C2314yes—
288C2×C22⋊Q8C2311yescharacteristic
289C2×C22⋊Q8C2314yes—
290C2×C22⋊Q8C2311yescharacteristic
291C2×C22⋊Q8C2314yes—
292C2×C22⋊Q8C2314yes—
293C2×C22⋊Q8C2314yes—
294C2×C22⋊Q8C2314yes—
295#520—44no—
296C2×C4×Q8C2311yescharacteristic
297C2×C4×Q8C2312yes—
298C2×C4×Q8C2314yes—
299C2×C4×Q8C2312yes—
300C2×C4×Q8C2314yes—
301C2×C4×Q8C2311yescharacteristic
302C2×C4×Q8C2312yes—
303C2×C4×Q8C2314yes—
304C2×C4×D4C2312yes—
305C2×C4×D4C2312yes—
306C2×C4×D4C2312yes—
307C2×C4×D4C2311yescharacteristic
308C2×C4×D4C2314yes—
309C2×C4×D4C2312yes—
310C2×#117C2312yes—
311C2×#117C2312yes—
312C2×#117C2311yescharacteristic
313C2×#117C2312yes—
314C2×#117C2312yes—
315C2×#117C2312yes—
316C2×#117C2314yes—
317C2×#117C2314yes—
318C22×C4⋊C4C2312yes—
319C22×C4⋊C4C2311yescharacteristic
320C22×C4⋊C4C2314yes—
321C22×C4⋊C4C2312yes—
322C22×C4⋊C4C2311yescharacteristic
323C22×C4⋊C4C2312yes—
324C22×C4⋊C4C2311yescharacteristic
325C22×C42C2311yescharacteristic
326C22×C42C2312yes—
327#401C2314yes—
328#401C2314yes—
329#400C2312yes—
330#400C2312yes—
331#400C2314yes—
332#400C2314yes—
333#400C2314yes—
334#400C2314yes—
335#400C2314yes—
336#400C2314yes—
337#400C2314yes—
338#400C2312yes—
339#400C2314yes—
340#400C2314yes—
341#400C2314yes—
342#400C2312yes—
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#400C2312yes—
356#400C2314yes—
357#400C2314yes—
358#400C2314yes—
359#399C2314yes—
360#399C2314yes—
361#399C2314yes—
362#399C2312yes—
363#399C2312yes—
364#399C2314yes—
365#398C2314yes—
366#398C2312yes—
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#398C2312yes—
380#398C2314yes—
381#398C2314yes—
382#398C2314yes—
383#398C2314yes—
384#398C2312yes—
385#398C2314yes—
386#398C2314yes—
387#398C2314yes—
388#398C2314yes—
389#398C2314yes—
390#398C2314yes—
391#398C2314yes—
392#398C2314yes—
393#398C2314yes—
394#398C2314yes—
395#398C2314yes—
396#398C2314yes—
397#397C2312yes—
398#397C2314yes—
399#397C2314yes—
400#397C2312yes—
401#397C2312yes—
402#397C2314yes—
403#397C2312yes—
404#397C2311yescharacteristic
405#397C2311yescharacteristic
406#397C2314yes—
407#397C2314yes—
408#396C2314yes—
409#396C2314yes—
410#396C2314yes—
411#396C2314yes—
412#396C2314yes—
413#396C2314yes—
414#396C2314yes—
415#396C2314yes—
416#396C2314yes—
417#396C2314yes—
418#395C2312yes—
419#395C2312yes—
420#395C2314yes—
421#395C2314yes—
422#395C2314yes—
423#395C2314yes—
424#395C2314yes—
425#395C2312yes—
426#395C2311yescharacteristic
427#395C2314yes—
428#395C2314yes—
429#395C2312yes—
430#395C2314yes—
431#395C2314yes—
432#395C2314yes—
433#394C2312yes—
434#394C2314yes—
435#394C2311yescharacteristic
436#394C2312yes—
437#394C2312yes—
438#394C2312yes—
439#394C2312yes—
440#393C2311yescharacteristic
441#393C2314yes—
442#393C2312yes—
443#393C2312yes—
444#393C2314yes—
445#393C2314yes—
446#393C2311yescharacteristic
447#393C2311yescharacteristic
448#393C2314yes—
449#393C2314yes—
450#392C2311yescharacteristic
451#392C2312yes—
452#391C2314yes—
453#391C2312yes—
454#391C2314yes—
455#391C2314yes—
456#391C2314yes—
457#391C2312yes—
458#391C2312yes—
459#391C2314yes—
460#391C2314yes—
461#391C2314yes—
462#391C2314yes—
463#391C2312yes—
464#391C2314yes—
465#391C2312yes—
466#391C2312yes—
467#391C2314yes—
468#391C2314yes—
469#391C2314yes—
470#391C2314yes—
471#391C2314yes—
472#391C2314yes—
473#391C2312yes—
474#391C2314yes—
475#391C2314yes—
476#391C2314yes—
477#390C2314yes—
478#390C2312yes—
479#390C2312yes—
480#390C2312yes—
481#389C2312yes—
482#389C2312yes—
483#389C2314yes—
484#389C2312yes—
485#389C2312yes—
486#389C2312yes—
487#389C2314yes—
488#389C2314yes—
489#389C2314yes—
490#389C2314yes—
491#389C2314yes—
492#389C2314yes—
493#389C2314yes—
494#389C2314yes—
495#389C2314yes—
496#389C2314yes—
497#389C2314yes—
498#389C2312yes—
499#389C2312yes—
500#389C2314yes—
501#389C2314yes—
502#389C2314yes—
503#389C2314yes—
504#389C2312yes—
505#389C2312yes—
506#389C2312yes—
507#389C2312yes—
508#389C2314yes—
509#389C2312yes—
510#389C2312yes—
511#389C2314yes—
512#389C2314yes—
513#389C2314yes—
514#389C2314yes—
515#389C2312yes—
516#389C2314yes—
517#389C2312yes—
518#389C2312yes—
519#389C2312yes—
520#389C2312yes—
521#389C2312yes—
522#389C2314yes—
523#389C2314yes—
524#388C2312yes—
525#388C2312yes—
526#388C2312yes—
527#388C2314yes—
528#388C2312yes—
529#388C2312yes—
530#388C2314yes—
531#388C2314yes—
532#388C2314yes—
533#388C2314yes—
534#388C2314yes—
535#388C2314yes—
536#388C2314yes—
537#388C2314yes—
538#388C2312yes—
539#388C2312yes—
540#388C2312yes—
541#388C2314yes—
542#388C2314yes—
543#388C2314yes—
544#388C2314yes—
545#388C2314yes—
546#388C2314yes—
547#388C2314yes—
548#387C2312yes—
549#387C2312yes—
550#387C2312yes—
551#387C2314yes—
552#387C2312yes—
553#387C2312yes—
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#387C2312yes—
571#387C2314yes—
572#387C2314yes—
573#387C2314yes—
574#387C2314yes—
575#387C2314yes—
576#387C2314yes—
577#387C2314yes—
578#387C2314yes—
579#387C2314yes—
580#387C2314yes—
581#387C2314yes—
582#387C2312yes—
583#387C2314yes—
584#387C2312yes—
585#387C2312yes—
586#387C2314yes—
587#387C2312yes—
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#386C2312yes—
603#386C2312yes—
604#386C2314yes—
605#386C2314yes—
606#386C2314yes—
607#386C2314yes—
608#386C2312yes—
609#386C2312yes—
610#386C2314yes—
611#386C2314yes—
612#386C2312yes—
613#386C2311yescharacteristic
614#385C2314yes—
615#385C2314yes—
616#385C2314yes—
617#385C2314yes—
618#385C2314yes—
619#385C2314yes—
620#385C2314yes—
621#385C2314yes—
622#385C2312yes—
623#385C2314yes—
624#385C2312yes—
625#385C2314yes—
626#385C2314yes—
627#385C2314yes—
628#385C2314yes—
629#385C2312yes—
630#385C2314yes—
631#385C2312yes—
632#385C2311yescharacteristic
633#385C2314yes—
634#384C2312yes—
635#384C2312yes—
636#384C2314yes—
637#384C2312yes—
638#384C2312yes—
639#383C2312yes—
640#383C2312yes—
641#383C2314yes—
642#383C2314yes—
643#383C2312yes—
644#382C2312yes—
645#382C2312yes—
646#382C2312yes—
647#382C2312yes—
648#382C2312yes—
649#382C2312yes—
650#382C2314yes—
651#382C2314yes—
652#382C2312yes—
653#382C2314yes—
654#381C2311yescharacteristic
655#381C2312yes—
656#381C2312yes—
657#381C2312yes—
658#381C2312yes—
659#381C2312yes—
660#381C2314yes—
661#381C2314yes—
662#381C2314yes—
663#380C2314yes—
664#380C2314yes—
665#380C2312yes—
666#380C2312yes—
667#380C2312yes—
668#380C2312yes—
669#380C2312yes—
670#380C2312yes—
671#380C2312yes—
672#380C2314yes—
673#380C2314yes—
674#380C2314yes—
675#380C2314yes—
676#380C2314yes—
677#380C2311yescharacteristic
678#380C2312yes—
679#380C2311yescharacteristic
680#380C2314yes—
681C4×C4⋊C4C2312yes—
682C4×C4⋊C4C2312yes—
683C4×C4⋊C4C2312yes—
684C4×C4⋊C4C2314yes—
685C4×C4⋊C4C2312yes—
686C4×C4⋊C4C2312yes—
687C4×C4⋊C4C2314yes—
688C4×C4⋊C4C2312yes—
689C4×C4⋊C4C2312yes—
690C4×C4⋊C4C2311yescharacteristic
691C4×C4⋊C4C2314yes—
692C4×C4⋊C4C2312yes—
693C4×C4⋊C4C2312yes—
694C4×C4⋊C4C2314yes—
695C4×C4⋊C4C2312yes—
696C4×C4⋊C4C2312yes—
697C4×C4⋊C4C2314yes—
698C4×C4⋊C4C2312yes—
699C4×C22⋊C4C2311yescharacteristic
700C4×C22⋊C4C2312yes—
701C4×C22⋊C4C2312yes—
702C4×C22⋊C4C2314yes—
703C4×C22⋊C4C2312yes—
704C4×C22⋊C4C2314yes—
705C4×C22⋊C4C2314yes—
706C4×C22⋊C4C2312yes—
707C4×C22⋊C4C2312yes—
708C4×C22⋊C4C2312yes—
709C4×C22⋊C4C2312yes—
710C4×C22⋊C4C2311yescharacteristic
711C4×C22⋊C4C2312yes—
712C4×C22⋊C4C2312yes—
713C4×C22⋊C4C2312yes—
714#376C2311yescharacteristic
715C2×#95C2314yes—
716C43C2312yes—
717C2×#41—28no—
718C2×#41—42no—
719C22×Q8—28no—
720C22×Q8—44no—
721C22×Q8—82no—
722C22×Q8C2411yescharacteristic
723C22×Q8C2414yes—
724C22×Q8C2411yescharacteristic
725C22×Q8C2414yes—
726C22×Q8C2414yes—
727C22×Q8C2411yescharacteristic
728C22×Q8C2412yes—
729C22×D4C2412yes—
730C22×D4C2411yescharacteristic
731C22×D4C2412yes—
732C22×D4C2411yescharacteristic
733C23×C4C2411yescharacteristic
734C23×C4C2411yescharacteristic
735C23×C4C2412yes—
736C23×C4C2411yescharacteristic
737C23×C4C2412yes—
738C23×C4C2414yes—
739C23×C4C2412yes—
740C23×C4C2412yes—
741C23×C4C2412yes—
742C23×C4C2414yes—
743C23×C4C2412yes—
744C23×C4C2411yescharacteristic
745C4⋊Q8—28no—
746C4⋊Q8—44no—
747C4⋊Q8—44no—
748C4⋊Q8—44no—
749C4⋊Q8—42no—
750C4⋊Q8—48no—
751C4⋊Q8—48no—
752#126—44no—
753#126—44no—
754#126—84no—
755#125—28no—
756#125—48no—
757#125—44no—
758#125—44no—
759#125—42no—
760#125—48no—
761#125—84no—
762#123—24no—
763#123—44no—
764#123—82no—
765C22⋊Q8—28no—
766C22⋊Q8—48no—
767C22⋊Q8—48no—
768C22⋊Q8—48no—
769C22⋊Q8—48no—
770C22⋊Q8—48no—
771C22⋊Q8—44no—
772C22⋊Q8—42no—
773C22⋊Q8—42no—
774C22⋊Q8—84no—
775C4×Q8—24no—
776C4×Q8—44no—
777C4×Q8—42no—
778C4×Q8—48no—
779C4×Q8—44no—
780C4×Q8—48no—
781C4×Q8—44no—
782C4×Q8—84no—
783C4×D4—28no—
784C4×D4—28no—
785C4×D4—44no—
786C4×D4—48no—
787C4×D4—42no—
788C4×D4—44no—
789#117—28no—
790#117—28no—
791#117—24no—
792#117—44no—
793#117—44no—
794#117—82no—
795#117—84no—
796#117—84no—
797C2×C4⋊C4—28no—
798C2×C4⋊C4—24no—
799C2×C4⋊C4—48no—
800C2×C4⋊C4—44no—
801C2×C4⋊C4—42no—
802C2×C4⋊C4—42no—
803C2×C4⋊C4—44no—
804C2×C4⋊C4C2411yescharacteristic
805C2×C4⋊C4C2412yes—
806C2×C4⋊C4C2412yes—
807C2×C4⋊C4C2414yes—
808C2×C4⋊C4C2414yes—
809C2×C4⋊C4C2411yescharacteristic
810C2×C4⋊C4C2414yes—
811C2×C4⋊C4C2412yes—
812C2×C4⋊C4C2412yes—
813C2×C4⋊C4C2412yes—
814C2×C4⋊C4C2414yes—
815C2×C4⋊C4C2412yes—
816C2×C4⋊C4C2412yes—
817C2×C4⋊C4C2412yes—
818C2×C4⋊C4C2412yes—
819C2×C4⋊C4C2412yes—
820C2×C4⋊C4C2412yes—
821C2×C4⋊C4C2414yes—
822C2×C4⋊C4C2414yes—
823C2×C4⋊C4C2412yes—
824C2×C4⋊C4C2414yes—
825C2×C4⋊C4C2412yes—
826C2×C4⋊C4C2412yes—
827C2×C4⋊C4C2414yes—
828C2×C4⋊C4C2412yes—
829C2×C4⋊C4C2414yes—
830C2×C4⋊C4C2412yes—
831C2×C4⋊C4C2414yes—
832C2×C4⋊C4C2412yes—
833C2×C4⋊C4C2414yes—
834C2×C4⋊C4C2414yes—
835C2×C4⋊C4C2412yes—
836C2×C4⋊C4C2414yes—
837C2×C4⋊C4C2414yes—
838C2×C4⋊C4C2412yes—
839C2×C4⋊C4C2414yes—
840C2×C4⋊C4C2414yes—
841C2×C4⋊C4C2414yes—
842C2×C4⋊C4C2411yescharacteristic
843C2×C4⋊C4C2411yescharacteristic
844C2×C4⋊C4C2414yes—
845C2×C4⋊C4C2414yes—
846C2×C4⋊C4C2414yes—
847C2×C4⋊C4C2414yes—
848C2×C4⋊C4C2412yes—
849C2×C4⋊C4C2414yes—
850C2×C4⋊C4C2414yes—
851C2×C4⋊C4C2414yes—
852C2×C4⋊C4C2412yes—
853C2×C4⋊C4C2414yes—
854C2×C4⋊C4C2414yes—
855C2×C4⋊C4C2412yes—
856C2×C4⋊C4C2414yes—
857C2×C4⋊C4C2414yes—
858C2×C4⋊C4C2414yes—
859C2×C4⋊C4C2414yes—
860C2×C4⋊C4C2412yes—
861C2×C4⋊C4C2412yes—
862C2×C4⋊C4C2412yes—
863C2×C4⋊C4C2414yes—
864C2×C4⋊C4C2414yes—
865C2×C4⋊C4C2414yes—
866C2×C4⋊C4C2414yes—
867C2×C4⋊C4C2414yes—
868C2×C4⋊C4C2412yes—
869C2×C4⋊C4C2412yes—
870C2×C4⋊C4C2414yes—
871C2×C4⋊C4C2414yes—
872C2×C4⋊C4C2411yescharacteristic
873C2×C22⋊C4C2414yes—
874C2×C22⋊C4C2412yes—
875C2×C22⋊C4C2412yes—
876C2×C22⋊C4C2412yes—
877C2×C22⋊C4C2412yes—
878C2×C22⋊C4C2412yes—
879C2×C22⋊C4C2412yes—
880C2×C22⋊C4C2412yes—
881C2×C22⋊C4C2412yes—
882C2×C22⋊C4C2412yes—
883C2×C22⋊C4C2414yes—
884C2×C22⋊C4C2411yescharacteristic
885C2×C22⋊C4C2412yes—
886C2×C22⋊C4C2411yescharacteristic
887C2×C22⋊C4C2412yes—
888C2×C22⋊C4C2412yes—
889C2×C22⋊C4C2411yescharacteristic
890C2×C22⋊C4C2414yes—
891C2×C22⋊C4C2412yes—
892C2×C22⋊C4C2414yes—
893C2×C22⋊C4C2414yes—
894C2×C22⋊C4C2412yes—
895C2×C22⋊C4C2411yescharacteristic
896C2×C22⋊C4C2412yes—
897C2×C22⋊C4C2412yes—
898C2×C22⋊C4C2414yes—
899C2×C22⋊C4C2414yes—
900C2×C22⋊C4C2414yes—
901C2×C22⋊C4C2412yes—
902C2×C22⋊C4C2412yes—
903C2×C22⋊C4C2414yes—
904C2×C22⋊C4C2414yes—
905C2×C22⋊C4C2412yes—
906C2×C22⋊C4C2412yes—
907C2×C22⋊C4C2412yes—
908C2×C22⋊C4C2412yes—
909C2×C42—42no—
910C2×C42—44no—
911C2×C42C2412yes—
912C2×C42C2414yes—
913C2×C42C2412yes—
914C2×C42C2412yes—
915C2×C42C2412yes—
916C2×C42C2411yescharacteristic
917C2×C42C2412yes—
918C2×C42C2412yes—
919C2×C42C2412yes—
920C2×C42C2412yes—
921C2×C42C2412yes—
922C2×C42C2412yes—
923C2×C42C2414yes—
924C2×C42C2414yes—
925C2×C42C2414yes—
926C2×C42C2414yes—
927C2×C42C2412yes—
928C2×C42C2414yes—
929C2×C42C2412yes—
930C2×C42C2412yes—
931C2×C42C2412yes—
932C2×C42C2414yes—
933C2×C42C2412yes—
934C2×C42C2414yes—
935#95C2414yes—
936#95C2414yes—
937#95C2414yes—
938#95C2414yes—
939#95C2411yescharacteristic
940#95C2411yescharacteristic
941#95C2412yes—
942#95C2412yes—
943#95C2412yes—
944#95C2412yes—
945#95C2412yes—
946#95C2412yes—
947#95C2412yes—
948#95C2411yescharacteristic
949#95C2412yes—
950#95C2412yes—
951#95C2414yes—
952#95C2414yes—
953#95C2414yes—
954#95C2414yes—
955#95C2414yes—
956#95C2412yes—
957#95C2414yes—
958#95C2411yescharacteristic
959#95C2412yes—
960#95C2412yes—
961#95C2412yes—
962#95C2412yes—
963#95C2412yes—
964#95C2412yes—
965#95C2412yes—
966#95C2414yes—
967#95C2412yes—
968#95C2414yes—
969#95C2412yes—
970#95C2412yes—
971#95C2414yes—
972#95C2414yes—
973#95C2414yes—
974#95C2414yes—
975#95C2412yes—
976#95C2414yes—
977#95C2414yes—
978#95C2412yes—
979#95C2414yes—
980#95C2414yes—
981#95C2412yes—
982#95C2414yes—
983#95C2412yes—
984#95C2414yes—
985#95C2414yes—
986#95C2414yes—
987#95C2414yes—
988#95C2414yes—
989#95C2414yes—
990#95C2414yes—
991#95C2414yes—
992#95C2414yes—
993#95C2414yes—
994#95C2412yes—
995#95C2414yes—
996#95C2414yes—
997#95C2414yes—
998#95C2414yes—
999#95C2414yes—
1000#95C2414yes—
1001#95C2414yes—
1002#95C2414yes—
1003#95C2414yes—
1004#95C2414yes—
1005#95C2414yes—
1006#95C2414yes—
1007#95C2414yes—
1008#95C2414yes—
1009#95C2414yes—
1010#95C2414yes—
1011#95C2414yes—
1012C24C2511yescharacteristic
1013C24C2512yes—
1014C24C2511yescharacteristic
1015#41—416no—
1016C2×Q8—22no—
1017C2×Q8—28no—
1018C2×Q8—24no—
1019C2×Q8—28no—
1020C2×Q8—24no—
1021C2×Q8—28no—
1022C2×Q8—28no—
1023C2×Q8—41no—
1024C2×Q8—44no—
1025C2×Q8—44no—
1026C2×Q8—41no—
1027C2×Q8—42no—
1028C2×Q8—44no—
1029C2×Q8—42no—
1030C2×Q8—44no—
1031C2×Q8—44no—
1032C2×Q8—44no—
1033C2×Q8—816no—
1034C2×D4—24no—
1035C2×D4—24no—
1036C2×D4—24no—
1037C2×D4—24no—
1038C2×D4—22no—
1039C2×D4—24no—
1040C2×D4—42no—
1041C2×D4—41no—
1042C2×D4—42no—
1043C2×D4—41no—
1044C2×D4—41no—
1045C22×C4—24no—
1046C22×C4—24no—
1047C22×C4—28no—
1048C22×C4—24no—
1049C22×C4—24no—
1050C22×C4—22no—
1051C22×C4—24no—
1052C22×C4—22no—
1053C22×C4—24no—
1054C22×C4—24no—
1055C22×C4—24no—
1056C22×C4—24no—
1057C22×C4—24no—
1058C22×C4—41no—
1059C22×C4—41no—
1060C22×C4—44no—
1061C22×C4—44no—
1062C22×C4—42no—
1063C22×C4—41no—
1064C22×C4—42no—
1065C22×C4—42no—
1066C22×C4—42no—
1067C22×C4—42no—
1068C22×C4—42no—
1069C22×C4—42no—
1070C22×C4—44no—
1071C22×C4—42no—
1072C22×C4—44no—
1073C22×C4—44no—
1074C22×C4—44no—
1075C22×C42−1+418yes—
1076C22×C42−1+414yes—
1077C22×C4C2512yes—
1078C22×C4C2511yescharacteristic
1079C22×C4C2512yes—
1080C22×C4C2512yes—
1081C22×C4C2512yes—
1082C22×C4C2511yescharacteristic
1083C22×C4C2514yes—
1084C22×C4C2514yes—
1085C22×C4C2514yes—
1086C22×C4C2512yes—
1087C22×C4C2512yes—
1088C22×C4C2512yes—
1089C22×C4C2512yes—
1090C22×C4C2514yes—
1091C22×C4C2511yescharacteristic
1092C22×C4C2514yes—
1093C22×C4C2512yes—
1094C22×C4C2514yes—
1095C22×C4C2511yescharacteristic
1096C22×C4C2512yes—
1097C22×C4C2512yes—
1098C22×C4C2512yes—
1099C22×C4C2512yes—
1100C22×C4C2512yes—
1101C22×C4C2512yes—
1102C22×C4C2511yescharacteristic
1103C4⋊C4—22no—
1104C4⋊C4—24no—
1105C4⋊C4—22no—
1106C4⋊C4—24no—
1107C4⋊C4—24no—
1108C4⋊C4—28no—
1109C4⋊C4—24no—
1110C4⋊C4—24no—
1111C4⋊C4—28no—
1112C4⋊C4—28no—
1113C4⋊C4—28no—
1114C4⋊C4—24no—
1115C4⋊C4—24no—
1116C4⋊C4—24no—
1117C4⋊C4—24no—
1118C4⋊C4—24no—
1119C4⋊C4—24no—
1120C4⋊C4—24no—
1121C4⋊C4—28no—
1122C4⋊C4—24no—
1123C4⋊C4—28no—
1124C4⋊C4—28no—
1125C4⋊C4—24no—
1126C4⋊C4—28no—
1127C4⋊C4—24no—
1128C4⋊C4—44no—
1129C4⋊C4—44no—
1130C4⋊C4—44no—
1131C4⋊C4—42no—
1132C4⋊C4—44no—
1133C4⋊C4—42no—
1134C4⋊C4—42no—
1135C4⋊C4—42no—
1136C4⋊C4—44no—
1137C4⋊C4—44no—
1138C4⋊C4—44no—
1139C4⋊C4—44no—
1140C4⋊C4—44no—
1141C4⋊C4—41no—
1142C4⋊C4—41no—
1143C4⋊C4—44no—
1144C4⋊C4—44no—
1145C4⋊C4—44no—
1146C4⋊C4—42no—
1147C4⋊C4—44no—
1148C4⋊C4—44no—
1149C4⋊C4—44no—
1150C4⋊C4—44no—
1151C4⋊C4—44no—
1152C4⋊C4—42no—
1153C4⋊C4—44no—
1154C4⋊C4—44no—
1155C4⋊C4—44no—
1156C4⋊C4—44no—
1157C4⋊C4—42no—
1158C4⋊C4—44no—
1159C4⋊C4—42no—
1160C4⋊C4—44no—
1161C4⋊C4—44no—
1162C4⋊C4—44no—
1163C4⋊C4—44no—
1164C4⋊C4—42no—
1165C4⋊C4—42no—
1166C4⋊C4—44no—
1167C4⋊C4—42no—
1168C4⋊C4—42no—
1169C4⋊C4—44no—
1170C4⋊C4—44no—
1171C4⋊C4H(5,𝔽2)14yes—
1172C22⋊C4—24no—
1173C22⋊C4—24no—
1174C22⋊C4—24no—
1175C22⋊C4—24no—
1176C22⋊C4—28no—
1177C22⋊C4—22no—
1178C22⋊C4—28no—
1179C22⋊C4—24no—
1180C22⋊C4—24no—
1181C22⋊C4—24no—
1182C22⋊C4—24no—
1183C22⋊C4—24no—
1184C22⋊C4—24no—
1185C22⋊C4—41no—
1186C22⋊C4—44no—
1187C22⋊C4—42no—
1188C22⋊C4—42no—
1189C22⋊C4—41no—
1190C22⋊C4—42no—
1191C22⋊C4—44no—
1192C22⋊C4—44no—
1193C22⋊C4—42no—
1194C22⋊C4—42no—
1195C22⋊C4—41no—
1196C22⋊C4—42no—
1197C22⋊C4—42no—
1198C22⋊C4—44no—
1199C22⋊C4—44no—
1200C22⋊C4—44no—
1201C22⋊C4—44no—
1202C22⋊C4—42no—
1203C22⋊C4—44no—
1204C22⋊C4—42no—
1205C22⋊C4—42no—
1206C22⋊C4—42no—
1207C22⋊C4—42no—
1208C42—24no—
1209C42—24no—
1210C42—24no—
1211C42—28no—
1212C42—24no—
1213C42—22no—
1214C42—24no—
1215C42—24no—
1216C42—24no—
1217C42—24no—
1218C42—24no—
1219C42—42no—
1220C42—42no—
1221C42—42no—
1222C42—44no—
1223C42—44no—
1224C42—42no—
1225C42—44no—
1226C42—44no—
1227C42—42no—
1228C42—44no—
1229C42—42no—
1230C42—44no—
1231C42—44no—
1232C23—22no—
1233C23—21no—
1234C23—22no—
1235C23—22no—
1236C23—22no—
1237C23—22no—
1238C23—22no—
1239C23—22no—
1240C23—22no—
1241C23—21no—
1242C23—21no—
1243C23—21no—
1244C23—22no—
1245C23—22no—
1246C23—21no—
1247C23C2×2−1+414yes—
1248C23C2×2−1+412yes—
1249C23C2611yescharacteristic
1250Q8—416no—
1251Q8—44no—
1252Q8—44no—
1253Q8—88no—
1254Q8—88no—
1255Q8—82no—
1256Q8—84no—
1257D4—48no—
1258D4—48no—
1259D4—44no—
1260D4—82no—
1261C2×C4—22no—
1262C2×C4—22no—
1263C2×C4—22no—
1264C2×C4—22no—
1265C2×C4—22no—
1266C2×C4—22no—
1267C2×C4—22no—
1268C2×C4—22no—
1269C2×C4—216no—
1270C2×C4—21no—
1271C2×C4—21no—
1272C2×C4—22no—
1273C2×C4—22no—
1274C2×C4—22no—
1275C2×C4—22no—
1276C2×C4—24no—
1277C2×C4—21no—
1278C2×C4—24no—
1279C2×C4—21no—
1280C2×C4—24no—
1281C2×C4—22no—
1282C2×C4—22no—
1283C2×C4—22no—
1284C2×C4—22no—
1285C2×C4—22no—
1286C2×C4—22no—
1287C2×C4—22no—
1288C2×C4—22no—
1289C2×C4—22no—
1290C2×C4—22no—
1291C2×C4—24no—
1292C2×C4—22no—
1293C2×C4—22no—
1294C2×C4—24no—
1295C2×C4—24no—
1296C2×C4—24no—
1297C2×C4—21no—
1298C2×C4—22no—
1299C2×C4—22no—
1300C2×C4—24no—
1301C2×C4—22no—
1302C2×C4—22no—
1303C2×C4—22no—
1304C2×C4—22no—
1305C2×C4—22no—
1306C2×C4—24no—
1307C2×C4—24no—
1308C2×C4—22no—
1309C2×C4—22no—
1310C2×C4—24no—
1311C2×C4—24no—
1312C2×C4—24no—
1313C2×C4—24no—
1314C2×C4—22no—
1315C2×C4—24no—
1316C2×C4—22no—
1317C2×C4—24no—
1318C2×C4—22no—
1319C2×C4—22no—
1320C2×C4—24no—
1321C2×C4—22no—
1322C2×C4—24no—
1323C2×C4—21no—
1324C2×C4—22no—
1325C2×C4—24no—
1326C2×C4—24no—
1327C2×C4—22no—
1328C2×C4—44no—
1329C2×C4—44no—
1330C2×C4—48no—
1331C2×C4—416no—
1332C2×C4—44no—
1333C2×C4—44no—
1334C2×C4—84no—
1335C2×C4—84no—
1336C2×C4—84no—
1337C2×C4—164no—
1338C2×C4—162no—
1339C2×C4C2×H(5,𝔽2)14yes—
1340C2×C4C2×H(5,𝔽2)12yes—
1341C2×C4C2×2−1+414yes—
1342C2×C4C2×2−1+414yes—
1343C2×C4C2×2−1+414yes—
1344C2×C4#58514yes—
1345C22—24no—
1346C22—24no—
1347C22—24no—
1348C22—22no—
1349C22—24no—
1350C22—41no—
1351C22—41no—
1352C22—42no—
1353C22—42no—
1354C22—42no—
1355C22—42no—
1356C22—42no—
1357C22—41no—
1358C22—41no—
1359C22—42no—
1360C22—41no—
1361C22—42no—
1362C22C22×H(5,𝔽2)11yescharacteristic
1363C22C22×2−1+412yes—
1364C22C22×2−1+411yescharacteristic
1365C22C2×#58512yes—
1366C22H(7,𝔽2)11yescharacteristic
1367C4—24no—
1368C4—24no—
1369C4—24no—
1370C4—24no—
1371C4—41no—
1372C4—41no—
1373C4—42no—
1374C4—42no—
1375C4—42no—
1376C4—44no—
1377C4—44no—
1378C4—41no—
1379C4—42no—
1380C4—42no—
1381C4—42no—
1382C4—42no—
1383C4—42no—
1384C4—44no—
1385C4—41no—
1386C4—42no—
1387C4—42no—
1388C4—42no—
1389C4—44no—
1390C4—44no—
1391C4—44no—
1392C4#353814yes—
1393C2—44no—
1394C2—42no—
1395C2—81no—
1396C2C2×#353811yescharacteristic
1397C2#6283712yes—
1398C2#6289411yescharacteristic
1399C2#6292612yes—
1400C2#6302011yescharacteristic
subgroupG/H
center, commutator, Frattini, socle, cosocleC23C26
prime radical#2388C22
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23 ◁ G
LECSG ▷ C23 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #59152C2semidirect
2. #58647C2semidirect
3. #58045C2semidirect
4. #57925C2semidirect
5. #52991C2semidirect
6. #51669C2semidirect
7. #48594C2semidirect
8. #47890C2semidirect
9. #47147C2semidirect
10. #47003C2semidirect
11. #46060C2semidirect
12. #45502C2semidirect
13. #45253C2semidirect
15. #43814C2semidirect
16. #42948C2semidirect
17. #42888C2semidirect
18. #42818C2semidirect
19. #39788C2semidirect
20. #39563C2semidirect
21. #39496C2semidirect
22. #39465C2semidirect
23. #39077C2semidirect
24. #37314C2semidirect
25. #36129C2semidirect
27. #35519C2semidirect
28. #35017C2semidirect

Maximal subgroups

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

subgroupindex
#591522
#586472
#580452
#579252
#529912
#516692
#485942
#478902
#471472
#470032
#460602
#455022
#452532
#452512
#438142
#429482
#428882
#428182
#397882
#395632
#394962
#394652
#390772
#373142
#361292
#360802
#355192
#350172
#349062