Finite Group Databasebeta

← #8096434

Subgroups — #8096434

Order 512.

4222 conjugacy classes of subgroups.

The subgroup lattice has 1360 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#53146C212yesmaximal, complemented
2#53032C211yesmaximal, characteristic
3#53013C212yesmaximal, complemented
4#53008C211yesmaximal, characteristic
5#52954C214yesmaximal, complemented
6#52929C212yesmaximal, complemented
7#52896C212yesmaximal, complemented
8#52812C214yesmaximal, complemented
9#52300C211yesmaximal, characteristic
10#52289C212yesmaximal, complemented
11#46344C212yesmaximal, complemented
12#46009C214yesmaximal, complemented
13#46002C212yesmaximal, complemented
14#46002C212yesmaximal, complemented
15#45931C214yesmaximal, complemented
16#45861C214yesmaximal
17#45759C212yesmaximal, complemented
18#45634C212yesmaximal, complemented
19#45630C214yesmaximal
20#45503C211yesmaximal, characteristic
21#36560C212yesmaximal, complemented
22#36545C212yesmaximal, complemented
23#36491C212yesmaximal, complemented
24#36423C211yesmaximal, characteristic
25#36408C212yesmaximal, complemented
26#35997C211yesmaximal, characteristic
27#35949C211yesmaximal, characteristic
28#35870C212yesmaximal, complemented
29#35749C212yesmaximal, complemented
30C2×#557C2211yescharacteristic
31C2×#557C2212yes—
32C2×#552C2211yescharacteristic
33C2×#519C2211yescharacteristic
34C22×C4×Q8C2211yescharacteristic
35#2868C2212yes—
36#2866C2214yes—
37#2864C2214yes—
38#2863C2212yes—
39#2863C2212yes—
40#2859C2214yes—
41#2857C2212yes—
42#2855C2211yescharacteristic
43#2853C2212yes—
44#2851C2214yes—
45#2845C2214yes—
46#2844C2214yes—
47#2843C2212yes—
48#2843C2214yes—
49#2843C2214yes—
50#2841C2212yes—
51#2839C2214yes—
52#2839C2214yes—
53#2839C2214yes—
54#2839C2214yes—
55#2839C2214yes—
56#2839C2214yes—
57#2839C2214yes—
58#2838C2214yes—
59#2836C2214yes—
60#2836C2214yes—
61#2835C2212yes—
62#2835C2212yes—
63#2834C2212yes—
64#2807C2212yes—
65#2807C2214yes—
66#2802C2214yes—
67#2802C2214yes—
68#2802C2214yes—
69#2802C2214yes—
70#2802C2214yes—
71#2802C2214yes—
72#2792C2212yes—
73#2792C2214yes—
74#2792C2214yes—
75#2792C2214yes—
76#2792C2214yes—
77#2792C2214yes—
78#2792C2214yes—
79#2792C2214yes—
80#2791C2214yes—
81#2791C2212yes—
82#2790C2214yes—
83#2790C2214yes—
84#2790C2214yes—
85#2790C2214yes—
86#2790C2214yes—
87#2790C2214yes—
88#2783C2214yes—
89#2782C2214yes—
90#2777C2212yes—
91#2776C2214yes—
92#2771C2211yescharacteristic
93#2769C2214yes—
94#2764C2211yescharacteristic
95#2763C2212yes—
96#2763C2212yes—
97#2762C2214yes—
98#2758C2214yes—
99#2758C2212yes—
100#2757C2214yes—
101#2755C2214yes—
102#2755C2214yes—
103#2754C2214yes—
104#2748C2212yes—
105#2747C2214yes—
106#2744C2214yes—
107#2742C2212yes—
108#2739C2214yes—
109#2722C2211yescharacteristic
110#2718C2212yes—
111#2716C2212yes—
112#2713C2214yes—
113#2704C2214yes—
114#2702C2212yes—
115#2677C2211yescharacteristic
116#2664C2212yes—
117#2655C2214yes—
118#2642C2212yes—
119#2642C2211yescharacteristic
120#2634C2212yes—
121#2634C2214yes—
122#2625C2211yescharacteristic
123#2621C2212yes—
124#2611C2214yes—
125#2611C2212yes—
126#2604C2212yes—
127#2599C2214yes—
128#2599C2212yes—
129#2596C2214yes—
130#2590C2214yes—
131#2590C2214yes—
132#2585C2214yes—
133#2585C2214yes—
134#2584C2211yescharacteristic
135#2584C2214yes—
136#2584C2212yes—
137#2582C2212yes—
138#2581C2212yes—
139#2581C2214yes—
140#2573C2214yes—
141#2568C2212yes—
142#2568C2212yes—
143#2565C2212yes—
144#2565C2214yes—
145#2565C2214yes—
146#2558C2214yes—
147#2546C2212yes—
148#2546C2212yes—
149#2546C2212yes—
150#2546C2212yes—
151#2546C2212yes—
152#2546C2212yes—
153#2546C2212yes—
154#2542C2211yescharacteristic
155#2533C2214yes—
156#2533C2214yes—
157#2533C2214yes—
158#2528C2214yes—
159#2525C2214yes—
160#2524C2214yes—
161#2524C2214yes—
162#2524C2214yes—
163#2524C2214yes—
164#2519C2214yes—
165#2515C2214yes—
166#2514C2212yes—
167#2511C2212yes—
168#2508C2212yes—
169#2506C2212yes—
170#2506C2214yes—
171#2506C2214yes—
172#2506C2214yes—
173#2506C2214yes—
174#2506C2214yes—
175#2489C2212yes—
176#2489C2212yes—
177#2484C2212yes—
178#2478C2214yes—
179#2478C2214yes—
180#2475C2214yes—
181#2475C2214yes—
182#2473C2214yes—
183#2473C2214yes—
184#2470C2214yes—
185#2469C2214yes—
186#2462C2214yes—
187#2462C2214yes—
188#2462C2214yes—
189#2462C2214yes—
190#2462C2214yes—
191#2453C2212yes—
192#2453C2212yes—
193#2453C2212yes—
194#2453C2212yes—
195#2446C2212yes—
196#2446C2212yes—
197#2446C2212yes—
198#2446C2212yes—
199#2446C2212yes—
200#2446C2212yes—
201#2446C2212yes—
202#2446C2212yes—
203#2434C2212yes—
204#2434C2212yes—
205#2434C2212yes—
206#2434C2211yescharacteristic
207#2434C2211yescharacteristic
208#2434C2212yes—
209#2429C2212yes—
210#2429C2212yes—
211#2429C2212yes—
212#2429C2212yes—
213#2429C2212yes—
214#2429C2212yes—
215#2423C2212yes—
216#2421C2212yes—
217#2413C2212yes—
218#2409C2211yescharacteristic
219#2409C2211yescharacteristic
220#2402C2214yes—
221#2402C2212yes—
222#2399C2214yes—
223#2398C2211yescharacteristic
224#2396C2212yes—
225#2396C2212yes—
226#2396C2212yes—
227#2395C2211yescharacteristic
228#2383C2214yes—
229#2383C2214yes—
230#2382C2214yes—
231#2382C2214yes—
232#2376C2212yes—
233#2370C2212yes—
234#2365C2212yes—
235#2365C2212yes—
236#2365C2212yes—
237#2365C2212yes—
238#2365C2212yes—
239#2362C2212yes—
240#2362C2212yes—
241#2360C2212yes—
242#2360C2212yes—
243#2356C2212yes—
244#2355C2212yes—
245#2347C2211yescharacteristic
246#2344C2211yescharacteristic
247C4×C4⋊Q8C2212yes—
248C4×C4⋊Q8C2214yes—
249C4×#125C2214yes—
250C4×#126C2212yes—
251C4×#126C2212yes—
252C4×C22⋊Q8C2214yes—
253C4×C22⋊Q8C2212yes—
254C4×#123C2211yescharacteristic
255#2298C2214yes—
256#2296C2212yes—
257#2276C2211yescharacteristic
258C42×Q8C2212yes—
259C23×Q8C2311yescharacteristic
260C23×Q8C2311yescharacteristic
261#557—48no—
262#557—44no—
263#552—44no—
264C2×C4⋊Q8C2312yes—
265C2×C4⋊Q8C2312yes—
266C2×C4⋊Q8C2312yes—
267C2×C4⋊Q8C2312yes—
268C2×C4⋊Q8C2312yes—
269C2×C4⋊Q8C2312yes—
270C2×C4⋊Q8C2312yes—
271C2×C4⋊Q8C2312yes—
272C2×C4⋊Q8C2312yes—
273C2×C4⋊Q8C2312yes—
274C2×C4⋊Q8C2311yescharacteristic
275C2×#126C2312yes—
276C2×#126C2312yes—
277C2×#126C2312yes—
278C2×#125C2314yes—
279C2×#125C2314yes—
280C2×#125C2314yes—
281C2×#125C2312yes—
282C2×#125C2314yes—
283C2×#125C2312yes—
284C2×#125C2311yescharacteristic
285C2×#125C2314yes—
286C2×#125C2312yes—
287C2×#123C2311yescharacteristic
288C2×#123C2312yes—
289C2×C22⋊Q8C2312yes—
290C2×C22⋊Q8C2311yescharacteristic
291C2×C22⋊Q8C2312yes—
292C2×C22⋊Q8C2312yes—
293C2×C22⋊Q8C2312yes—
294C2×C22⋊Q8C2312yes—
295C2×C22⋊Q8C2311yescharacteristic
296#519—44no—
297C2×C4×Q8—44no—
298C2×C4×Q8C2312yes—
299C2×C4×Q8C2312yes—
300C2×C4×Q8C2312yes—
301C2×C4×Q8C2311yescharacteristic
302C2×C4×Q8C2312yes—
303C2×C4×Q8C2311yescharacteristic
304C2×C4×Q8C2314yes—
305C2×C4×Q8C2312yes—
306C2×C4×Q8C2312yes—
307C2×C4×Q8C2314yes—
308C2×C4×Q8C2312yes—
309C2×C4×Q8C2312yes—
310C2×C4×Q8C2312yes—
311C2×C4×Q8C2312yes—
312C2×C4×Q8C2312yes—
313C2×C4×Q8C2312yes—
314C2×C4×D4C2311yescharacteristic
315C2×#117C2312yes—
316C2×#117C2311yescharacteristic
317C2×#117C2312yes—
318C2×#117C2314yes—
319C2×#117C2311yescharacteristic
320C22×C4⋊C4C2311yescharacteristic
321C22×C4⋊C4C2312yes—
322C22×C42C2312yes—
323C22×C42C2311yescharacteristic
324#401C2314yes—
325#400C2314yes—
326#400C2314yes—
327#400C2314yes—
328#400C2314yes—
329#400C2314yes—
330#400C2314yes—
331#400C2314yes—
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#400C2312yes—
346#400C2312yes—
347#400C2312yes—
348#400C2314yes—
349#400C2314yes—
350#400C2312yes—
351#400C2314yes—
352#400C2312yes—
353#400C2312yes—
354#400C2312yes—
355#400C2312yes—
356#400C2314yes—
357#400C2314yes—
358#400C2314yes—
359#400C2314yes—
360#400C2314yes—
361#400C2314yes—
362#400C2311yescharacteristic
363#400C2312yes—
364#400C2314yes—
365#399C2312yes—
366#399C2312yes—
367#399C2314yes—
368#399C2312yes—
369#399C2311yescharacteristic
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#398C2314yes—
387#398C2314yes—
388#398C2312yes—
389#398C2314yes—
390#398C2314yes—
391#398C2314yes—
392#398C2314yes—
393#398C2314yes—
394#398C2314yes—
395#398C2314yes—
396#398C2314yes—
397#398C2314yes—
398#398C2314yes—
399#398C2314yes—
400#398C2314yes—
401#398C2314yes—
402#398C2314yes—
403#398C2314yes—
404#398C2314yes—
405#398C2314yes—
406#398C2311yescharacteristic
407#398C2312yes—
408#398C2312yes—
409#398C2314yes—
410#398C2314yes—
411#398C2314yes—
412#398C2314yes—
413#398C2312yes—
414#398C2312yes—
415#398C2314yes—
416#398C2312yes—
417#398C2314yes—
418#398C2312yes—
419#398C2312yes—
420#397C2314yes—
421#397C2311yescharacteristic
422#397C2314yes—
423#397C2311yescharacteristic
424#397C2311yescharacteristic
425#397C2314yes—
426#397C2314yes—
427#397C2314yes—
428#397C2314yes—
429#397C2312yes—
430#396C2314yes—
431#396C2312yes—
432#396C2314yes—
433#396C2314yes—
434#396C2314yes—
435#396C2314yes—
436#396C2314yes—
437#396C2312yes—
438#395C2314yes—
439#395C2314yes—
440#395C2314yes—
441#395C2314yes—
442#395C2314yes—
443#395C2314yes—
444#395C2312yes—
445#395C2312yes—
446#395C2312yes—
447#395C2314yes—
448#395C2312yes—
449#395C2312yes—
450#395C2314yes—
451#395C2314yes—
452#395C2312yes—
453#395C2314yes—
454#394C2312yes—
455#394C2312yes—
456#393C2312yes—
457#393C2312yes—
458#393C2312yes—
459#393C2311yescharacteristic
460#393C2311yescharacteristic
461#391C2312yes—
462#391C2312yes—
463#391C2314yes—
464#391C2314yes—
465#391C2312yes—
466#391C2312yes—
467#391C2312yes—
468#391C2312yes—
469#391C2312yes—
470#391C2312yes—
471#391C2312yes—
472#391C2312yes—
473#391C2312yes—
474#391C2314yes—
475#391C2312yes—
476#391C2312yes—
477#391C2312yes—
478#391C2312yes—
479#391C2312yes—
480#391C2312yes—
481#391C2312yes—
482#391C2312yes—
483#391C2312yes—
484#391C2312yes—
485#390C2312yes—
486#389C2314yes—
487#389C2314yes—
488#389C2314yes—
489#389C2312yes—
490#389C2312yes—
491#389C2314yes—
492#389C2312yes—
493#389C2312yes—
494#389C2314yes—
495#389C2314yes—
496#389C2314yes—
497#389C2314yes—
498#389C2314yes—
499#389C2314yes—
500#389C2314yes—
501#389C2312yes—
502#389C2312yes—
503#389C2312yes—
504#389C2312yes—
505#389C2314yes—
506#389C2314yes—
507#389C2314yes—
508#389C2314yes—
509#389C2312yes—
510#389C2314yes—
511#389C2314yes—
512#389C2314yes—
513#389C2314yes—
514#389C2314yes—
515#389C2314yes—
516#389C2314yes—
517#389C2314yes—
518#389C2314yes—
519#389C2314yes—
520#389C2314yes—
521#389C2312yes—
522#389C2314yes—
523#389C2312yes—
524#389C2314yes—
525#389C2314yes—
526#389C2314yes—
527#389C2312yes—
528#389C2312yes—
529#389C2314yes—
530#389C2314yes—
531#389C2314yes—
532#389C2314yes—
533#389C2314yes—
534#389C2314yes—
535#388C2312yes—
536#388C2312yes—
537#388C2312yes—
538#388C2312yes—
539#388C2312yes—
540#388C2312yes—
541#388C2314yes—
542#388C2314yes—
543#388C2314yes—
544#388C2314yes—
545#388C2314yes—
546#388C2314yes—
547#388C2314yes—
548#388C2314yes—
549#388C2314yes—
550#388C2314yes—
551#388C2314yes—
552#388C2314yes—
553#388C2314yes—
554#388C2314yes—
555#388C2314yes—
556#388C2312yes—
557#387C2312yes—
558#387C2312yes—
559#387C2312yes—
560#387C2312yes—
561#387C2312yes—
562#387C2312yes—
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#387C2312yes—
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#387C2314yes—
608#387C2314yes—
609#387C2314yes—
610#387C2314yes—
611#387C2314yes—
612#387C2314yes—
613#387C2314yes—
614#387C2314yes—
615#387C2314yes—
616#387C2314yes—
617#387C2314yes—
618#387C2314yes—
619#387C2314yes—
620#387C2312yes—
621#387C2314yes—
622#387C2314yes—
623#387C2314yes—
624#387C2312yes—
625#386C2311yescharacteristic
626#386C2312yes—
627#386C2312yes—
628#385C2314yes—
629#385C2312yes—
630#385C2314yes—
631#385C2314yes—
632#385C2314yes—
633#385C2312yes—
634#385C2314yes—
635#385C2312yes—
636#385C2312yes—
637#385C2314yes—
638#385C2314yes—
639#385C2314yes—
640#385C2312yes—
641#385C2314yes—
642#385C2311yescharacteristic
643#385C2314yes—
644#385C2314yes—
645#385C2312yes—
646#385C2312yes—
647#384C2312yes—
648#384C2314yes—
649#384C2314yes—
650#384C2312yes—
651#384C2314yes—
652#384C2312yes—
653#384C2314yes—
654#383C2312yes—
655#383C2312yes—
656#383C2314yes—
657#383C2314yes—
658#383C2314yes—
659#383C2314yes—
660#383C2312yes—
661#382C2314yes—
662#382C2314yes—
663#382C2314yes—
664#382C2312yes—
665#382C2314yes—
666#382C2314yes—
667#382C2314yes—
668#381C2312yes—
669#381C2311yescharacteristic
670#381C2312yes—
671#380C2314yes—
672#380C2312yes—
673#380C2314yes—
674#380C2311yescharacteristic
675#380C2311yescharacteristic
676C4×C4⋊C4C2312yes—
677C4×C4⋊C4C2312yes—
678C4×C4⋊C4C2312yes—
679C4×C4⋊C4C2312yes—
680C4×C4⋊C4C2312yes—
681C4×C4⋊C4C2312yes—
682C4×C4⋊C4C2314yes—
683C4×C4⋊C4C2314yes—
684C4×C4⋊C4C2314yes—
685C4×C4⋊C4C2314yes—
686C4×C4⋊C4C2314yes—
687C4×C4⋊C4C2312yes—
688C4×C4⋊C4C2314yes—
689C4×C4⋊C4C2314yes—
690C4×C4⋊C4C2312yes—
691C4×C4⋊C4C2314yes—
692C4×C4⋊C4C2314yes—
693C4×C4⋊C4C2312yes—
694C4×C4⋊C4C2312yes—
695C4×C4⋊C4C2314yes—
696C4×C4⋊C4C2311yescharacteristic
697C4×C4⋊C4C2314yes—
698C4×C4⋊C4C2312yes—
699C4×C4⋊C4C2312yes—
700C4×C4⋊C4C2312yes—
701C4×C4⋊C4C2314yes—
702C4×C4⋊C4C2312yes—
703C4×C4⋊C4C2314yes—
704C4×C22⋊C4C2311yescharacteristic
705C4×C22⋊C4C2311yescharacteristic
706C4×C22⋊C4C2312yes—
707C4×C22⋊C4C2312yes—
708C4×C22⋊C4C2312yes—
709C4×C22⋊C4C2312yes—
710C4×C22⋊C4C2314yes—
711C4×C22⋊C4C2314yes—
712#376C2312yes—
713#376C2314yes—
714#376C2311yescharacteristic
715C43C2312yes—
716C43C2314yes—
717C22×Q8—42no—
718C22×Q8—42no—
719C22×Q8—44no—
720C22×Q8—44no—
721C22×Q8C2411yescharacteristic
722C22×Q8C2412yes—
723C22×Q8C2412yes—
724C22×Q8C2412yes—
725C22×Q8C2412yes—
726C22×Q8C2411yescharacteristic
727C22×Q8C2412yes—
728C22×Q8C2412yes—
729C22×D4C2411yescharacteristic
730C23×C4C2411yescharacteristic
731C23×C4C2411yescharacteristic
732C23×C4C2412yes—
733C23×C4C2411yescharacteristic
734C23×C4C2411yescharacteristic
735C23×C4C2412yes—
736C23×C4C2412yes—
737C4⋊Q8—28no—
738C4⋊Q8—44no—
739C4⋊Q8—44no—
740C4⋊Q8—44no—
741C4⋊Q8—44no—
742C4⋊Q8—44no—
743C4⋊Q8—44no—
744C4⋊Q8—44no—
745C4⋊Q8—42no—
746C4⋊Q8—44no—
747C4⋊Q8—44no—
748#126—28no—
749#126—28no—
750#126—44no—
751#125—216no—
752#125—44no—
753#125—44no—
754#125—42no—
755#125—48no—
756#125—48no—
757#125—44no—
758#125—48no—
759#125—48no—
760#123—24no—
761#123—44no—
762C22⋊Q8—28no—
763C22⋊Q8—44no—
764C22⋊Q8—44no—
765C22⋊Q8—44no—
766C22⋊Q8—44no—
767C22⋊Q8—42no—
768C22⋊Q8—42no—
769C4×Q8—28no—
770C4×Q8—28no—
771C4×Q8—24no—
772C4×Q8—28no—
773C4×Q8—44no—
774C4×Q8—48no—
775C4×Q8—44no—
776C4×Q8—44no—
777C4×Q8—42no—
778C4×Q8—48no—
779C4×Q8—44no—
780C4×Q8—44no—
781C4×Q8—44no—
782C4×Q8—44no—
783C4×Q8—44no—
784C4×Q8—44no—
785C4×D4—42no—
786#117—24no—
787#117—28no—
788#117—42no—
789#117—44no—
790#117—48no—
791C2×C4⋊C4—24no—
792C2×C4⋊C4—44no—
793C2×C4⋊C4C2411yescharacteristic
794C2×C4⋊C4C2414yes—
795C2×C4⋊C4C2412yes—
796C2×C4⋊C4C2411yescharacteristic
797C2×C4⋊C4C2414yes—
798C2×C4⋊C4C2414yes—
799C2×C4⋊C4C2412yes—
800C2×C4⋊C4C2412yes—
801C2×C4⋊C4C2412yes—
802C2×C4⋊C4C2412yes—
803C2×C4⋊C4C2414yes—
804C2×C4⋊C4C2412yes—
805C2×C4⋊C4C2412yes—
806C2×C4⋊C4C2412yes—
807C2×C4⋊C4C2414yes—
808C2×C4⋊C4C2414yes—
809C2×C4⋊C4C2414yes—
810C2×C4⋊C4C2414yes—
811C2×C4⋊C4C2414yes—
812C2×C4⋊C4C2412yes—
813C2×C4⋊C4C2412yes—
814C2×C4⋊C4C2412yes—
815C2×C4⋊C4C2412yes—
816C2×C4⋊C4C2412yes—
817C2×C4⋊C4C2412yes—
818C2×C4⋊C4C2412yes—
819C2×C4⋊C4C2412yes—
820C2×C4⋊C4C2414yes—
821C2×C4⋊C4C2411yescharacteristic
822C2×C4⋊C4C2414yes—
823C2×C4⋊C4C2411yescharacteristic
824C2×C4⋊C4C2412yes—
825C2×C4⋊C4C2412yes—
826C2×C4⋊C4C2411yescharacteristic
827C2×C4⋊C4C2412yes—
828C2×C4⋊C4C2412yes—
829C2×C4⋊C4C2412yes—
830C2×C4⋊C4C2412yes—
831C2×C4⋊C4C2411yescharacteristic
832C2×C4⋊C4C2414yes—
833C2×C4⋊C4C2414yes—
834C2×C4⋊C4C2414yes—
835C2×C4⋊C4C2414yes—
836C2×C4⋊C4C2412yes—
837C2×C4⋊C4C2414yes—
838C2×C4⋊C4C2414yes—
839C2×C4⋊C4C2414yes—
840C2×C4⋊C4C2412yes—
841C2×C4⋊C4C2414yes—
842C2×C4⋊C4C2414yes—
843C2×C4⋊C4C2414yes—
844C2×C4⋊C4C2414yes—
845C2×C4⋊C4C2412yes—
846C2×C4⋊C4C2414yes—
847C2×C4⋊C4C2414yes—
848C2×C4⋊C4C2414yes—
849C2×C4⋊C4C2412yes—
850C2×C4⋊C4C2414yes—
851C2×C4⋊C4C2414yes—
852C2×C4⋊C4C2414yes—
853C2×C4⋊C4C2414yes—
854C2×C4⋊C4C2414yes—
855C2×C4⋊C4C2414yes—
856C2×C4⋊C4C2414yes—
857C2×C4⋊C4C2414yes—
858C2×C4⋊C4C2414yes—
859C2×C4⋊C4C2414yes—
860C2×C4⋊C4C2414yes—
861C2×C4⋊C4C2414yes—
862C2×C4⋊C4C2414yes—
863C2×C4⋊C4C2412yes—
864C2×C4⋊C4C2412yes—
865C2×C4⋊C4C2412yes—
866C2×C4⋊C4C2412yes—
867C2×C4⋊C4C2414yes—
868C2×C4⋊C4C2414yes—
869C2×C4⋊C4C2414yes—
870C2×C4⋊C4C2414yes—
871C2×C4⋊C4C2411yescharacteristic
872C2×C4⋊C4C2412yes—
873C2×C22⋊C4C2412yes—
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⋊C4C2412yes—
884C2×C22⋊C4C2411yescharacteristic
885C2×C22⋊C4C2412yes—
886C2×C22⋊C4C2411yescharacteristic
887C2×C22⋊C4C2412yes—
888C2×C22⋊C4C2414yes—
889C2×C22⋊C4C2414yes—
890C2×C22⋊C4C2414yes—
891C2×C22⋊C4C2414yes—
892C2×C22⋊C4C2411yescharacteristic
893C2×C22⋊C4C2412yes—
894C2×C22⋊C4C2412yes—
895C2×C22⋊C4C2411yescharacteristic
896C2×C42—44no—
897C2×C42—42no—
898C2×C42C2412yes—
899C2×C42C2414yes—
900C2×C42C2412yes—
901C2×C42C2412yes—
902C2×C42C2414yes—
903C2×C42C2411yescharacteristic
904C2×C42C2414yes—
905C2×C42C2414yes—
906C2×C42C2412yes—
907C2×C42C2412yes—
908C2×C42C2412yes—
909C2×C42C2412yes—
910C2×C42C2412yes—
911C2×C42C2414yes—
912C2×C42C2412yes—
913C2×C42C2412yes—
914C2×C42C2412yes—
915C2×C42C2414yes—
916C2×C42C2412yes—
917C2×C42C2414yes—
918C2×C42C2414yes—
919C2×C42C2414yes—
920C2×C42C2414yes—
921C2×C42C2414yes—
922C2×C42C2412yes—
923C2×C42C2414yes—
924C2×C42C2412yes—
925#95C2411yescharacteristic
926#95C2412yes—
927#95C2414yes—
928#95C2411yescharacteristic
929#95C2412yes—
930#95C2412yes—
931#95C2414yes—
932#95C2414yes—
933#95C2414yes—
934#95C2412yes—
935#95C2412yes—
936#95C2411yescharacteristic
937#95C2412yes—
938#95C2412yes—
939#95C2414yes—
940#95C2411yescharacteristic
941#95C2412yes—
942#95C2412yes—
943#95C2412yes—
944#95C2414yes—
945#95C2412yes—
946#95C2412yes—
947#95C2414yes—
948#95C2414yes—
949#95C2414yes—
950#95C2414yes—
951#95C2412yes—
952#95C2414yes—
953#95C2412yes—
954#95C2414yes—
955#95C2412yes—
956#95C2412yes—
957#95C2414yes—
958#95C2412yes—
959#95C2412yes—
960#95C2414yes—
961#95C2414yes—
962#95C2414yes—
963#95C2412yes—
964#95C2412yes—
965#95C2412yes—
966#95C2414yes—
967#95C2412yes—
968#95C2412yes—
969#95C2414yes—
970#95C2414yes—
971#95C2412yes—
972#95C2412yes—
973#95C2414yes—
974#95C2414yes—
975#95C2412yes—
976#95C2414yes—
977#95C2414yes—
978#95C2412yes—
979#95C2412yes—
980#95C2414yes—
981#95C2414yes—
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#95C2414yes—
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—
1008C24C2511yescharacteristic
1009C24C2511yescharacteristic
1010C2×Q8—24no—
1011C2×Q8—24no—
1012C2×Q8—22no—
1013C2×Q8—24no—
1014C2×Q8—24no—
1015C2×Q8—24no—
1016C2×Q8—24no—
1017C2×Q8—24no—
1018C2×Q8—24no—
1019C2×Q8—24no—
1020C2×Q8—24no—
1021C2×Q8—24no—
1022C2×Q8—24no—
1023C2×Q8—24no—
1024C2×Q8—42no—
1025C2×Q8—41no—
1026C2×Q8—42no—
1027C2×Q8—42no—
1028C2×Q8—44no—
1029C2×Q8—44no—
1030C2×Q8—416no—
1031C2×Q8—416no—
1032C2×D4—22no—
1033C2×D4—41no—
1034C2×D4—41no—
1035C22×C4—24no—
1036C22×C4—22no—
1037C22×C4—24no—
1038C22×C4—22no—
1039C22×C4—22no—
1040C22×C4—24no—
1041C22×C4—24no—
1042C22×C4—24no—
1043C22×C4—41no—
1044C22×C4—42no—
1045C22×C4—42no—
1046C22×C4—42no—
1047C22×C4—44no—
1048C22×C4—44no—
1049C22×C4—41no—
1050C22×C4—41no—
1051C22×C4C2512yes—
1052C22×C4C2514yes—
1053C22×C4C2512yes—
1054C22×C4C2512yes—
1055C22×C4C2514yes—
1056C22×C4C2512yes—
1057C22×C4C2514yes—
1058C22×C4C2511yescharacteristic
1059C22×C4C2512yes—
1060C22×C4C2512yes—
1061C22×C4C2511yescharacteristic
1062C22×C4C2512yes—
1063C22×C4C2512yes—
1064C22×C4C2512yes—
1065C22×C4C2512yes—
1066C22×C4C2511yescharacteristic
1067C22×C4C2514yes—
1068C22×C4C2514yes—
1069C22×C4C2511yescharacteristic
1070C22×C4C2512yes—
1071C22×C4C2514yes—
1072C22×C4C2512yes—
1073C22×C4C2512yes—
1074C22×C4C2512yes—
1075C22×C4C2512yes—
1076C22×C4C2512yes—
1077C22×C4C2511yescharacteristic
1078C4⋊C4—22no—
1079C4⋊C4—24no—
1080C4⋊C4—28no—
1081C4⋊C4—22no—
1082C4⋊C4—28no—
1083C4⋊C4—24no—
1084C4⋊C4—28no—
1085C4⋊C4—28no—
1086C4⋊C4—24no—
1087C4⋊C4—24no—
1088C4⋊C4—24no—
1089C4⋊C4—28no—
1090C4⋊C4—28no—
1091C4⋊C4—28no—
1092C4⋊C4—28no—
1093C4⋊C4—28no—
1094C4⋊C4—24no—
1095C4⋊C4—24no—
1096C4⋊C4—24no—
1097C4⋊C4—24no—
1098C4⋊C4—24no—
1099C4⋊C4—24no—
1100C4⋊C4—24no—
1101C4⋊C4—24no—
1102C4⋊C4—24no—
1103C4⋊C4—24no—
1104C4⋊C4—24no—
1105C4⋊C4—44no—
1106C4⋊C4—42no—
1107C4⋊C4—42no—
1108C4⋊C4—42no—
1109C4⋊C4—42no—
1110C4⋊C4—44no—
1111C4⋊C4—44no—
1112C4⋊C4—44no—
1113C4⋊C4—44no—
1114C4⋊C4—41no—
1115C4⋊C4—44no—
1116C4⋊C4—41no—
1117C4⋊C4—42no—
1118C4⋊C4—42no—
1119C4⋊C4—41no—
1120C4⋊C4—44no—
1121C4⋊C4—44no—
1122C4⋊C4—44no—
1123C4⋊C4—42no—
1124C4⋊C4—42no—
1125C4⋊C4—42no—
1126C4⋊C4—41no—
1127C4⋊C4—42no—
1128C4⋊C4—44no—
1129C4⋊C4—44no—
1130C4⋊C4—44no—
1131C4⋊C4—42no—
1132C4⋊C4—44no—
1133C4⋊C4—44no—
1134C4⋊C4—44no—
1135C4⋊C4—44no—
1136C4⋊C4—44no—
1137C4⋊C4—42no—
1138C4⋊C4—42no—
1139C4⋊C4—44no—
1140C4⋊C4—44no—
1141C4⋊C4—44no—
1142C4⋊C4—44no—
1143C4⋊C4—44no—
1144C4⋊C4—44no—
1145C4⋊C4—42no—
1146C4⋊C4—44no—
1147C4⋊C4—44no—
1148C4⋊C4—44no—
1149C4⋊C4—44no—
1150C4⋊C4—44no—
1151C4⋊C4—44no—
1152C4⋊C4—44no—
1153C4⋊C4—44no—
1154C4⋊C4—44no—
1155C4⋊C4—44no—
1156C4⋊C4H(5,𝔽2)14yes—
1157C4⋊C42−1+418yes—
1158C22⋊C4—24no—
1159C22⋊C4—24no—
1160C22⋊C4—24no—
1161C22⋊C4—24no—
1162C22⋊C4—24no—
1163C22⋊C4—24no—
1164C22⋊C4—24no—
1165C22⋊C4—24no—
1166C22⋊C4—24no—
1167C22⋊C4—24no—
1168C22⋊C4—42no—
1169C22⋊C4—41no—
1170C22⋊C4—42no—
1171C22⋊C4—42no—
1172C22⋊C4—41no—
1173C22⋊C4—42no—
1174C22⋊C4—41no—
1175C22⋊C4—44no—
1176C22⋊C4—44no—
1177C22⋊C4—44no—
1178C22⋊C4—44no—
1179C22⋊C4—42no—
1180C22⋊C42−1+414yes—
1181C42—28no—
1182C42—24no—
1183C42—24no—
1184C42—28no—
1185C42—24no—
1186C42—24no—
1187C42—22no—
1188C42—28no—
1189C42—24no—
1190C42—28no—
1191C42—28no—
1192C42—24no—
1193C42—24no—
1194C42—24no—
1195C42—24no—
1196C42—24no—
1197C42—24no—
1198C42—42no—
1199C42—44no—
1200C42—44no—
1201C42—44no—
1202C42—42no—
1203C42—42no—
1204C42—44no—
1205C42—44no—
1206C42—44no—
1207C42—44no—
1208C23—21no—
1209C23—22no—
1210C23—22no—
1211C23—21no—
1212C23—21no—
1213C23—22no—
1214C23—21no—
1215C23—22no—
1216C23—21no—
1217C23C2×2−1+412yes—
1218C23C2611yescharacteristic
1219Q8—48no—
1220Q8—44no—
1221Q8—48no—
1222Q8—48no—
1223Q8—44no—
1224Q8—48no—
1225Q8—48no—
1226Q8—48no—
1227D4—82no—
1228C2×C4—22no—
1229C2×C4—22no—
1230C2×C4—22no—
1231C2×C4—22no—
1232C2×C4—22no—
1233C2×C4—22no—
1234C2×C4—22no—
1235C2×C4—22no—
1236C2×C4—22no—
1237C2×C4—22no—
1238C2×C4—21no—
1239C2×C4—22no—
1240C2×C4—21no—
1241C2×C4—22no—
1242C2×C4—22no—
1243C2×C4—22no—
1244C2×C4—24no—
1245C2×C4—24no—
1246C2×C4—22no—
1247C2×C4—22no—
1248C2×C4—21no—
1249C2×C4—24no—
1250C2×C4—22no—
1251C2×C4—21no—
1252C2×C4—22no—
1253C2×C4—24no—
1254C2×C4—22no—
1255C2×C4—22no—
1256C2×C4—22no—
1257C2×C4—24no—
1258C2×C4—24no—
1259C2×C4—22no—
1260C2×C4—22no—
1261C2×C4—22no—
1262C2×C4—22no—
1263C2×C4—22no—
1264C2×C4—22no—
1265C2×C4—24no—
1266C2×C4—24no—
1267C2×C4—22no—
1268C2×C4—21no—
1269C2×C4—22no—
1270C2×C4—22no—
1271C2×C4—22no—
1272C2×C4—22no—
1273C2×C4—22no—
1274C2×C4—22no—
1275C2×C4—24no—
1276C2×C4—24no—
1277C2×C4—24no—
1278C2×C4—24no—
1279C2×C4—24no—
1280C2×C4—24no—
1281C2×C4—24no—
1282C2×C4—24no—
1283C2×C4—22no—
1284C2×C4—22no—
1285C2×C4—24no—
1286C2×C4—24no—
1287C2×C4—22no—
1288C2×C4—24no—
1289C2×C4—21no—
1290C2×C4—22no—
1291C2×C4—22no—
1292C2×C4—24no—
1293C2×C4—22no—
1294C2×C4—22no—
1295C2×C4—22no—
1296C2×C4—44no—
1297C2×C4—48no—
1298C2×C4—48no—
1299C2×C4—48no—
1300C2×C4—44no—
1301C2×C4—44no—
1302C2×C4—82no—
1303C2×C4C2×H(5,𝔽2)14yes—
1304C2×C4C2×H(5,𝔽2)12yes—
1305C2×C4C2×2−1+414yes—
1306C2×C4C2×2−1+414yes—
1307C2×C4C2×2−1+414yes—
1308C2×C4C2×2−1+414yes—
1309C2×C4#58514yes—
1310C22—24no—
1311C22—22no—
1312C22—41no—
1313C22—41no—
1314C22—42no—
1315C22—41no—
1316C22—42no—
1317C22—41no—
1318C22—41no—
1319C22—42no—
1320C22C22×H(5,𝔽2)11yescharacteristic
1321C22C22×2−1+412yes—
1322C22C22×2−1+411yescharacteristic
1323C22C2×#58512yes—
1324C222−1+611yescharacteristic
1325C4—24no—
1326C4—24no—
1327C4—24no—
1328C4—24no—
1329C4—24no—
1330C4—42no—
1331C4—41no—
1332C4—42no—
1333C4—42no—
1334C4—44no—
1335C4—42no—
1336C4—42no—
1337C4—42no—
1338C4—42no—
1339C4—42no—
1340C4—41no—
1341C4—41no—
1342C4—44no—
1343C4—44no—
1344C4—41no—
1345C4—42no—
1346C4—44no—
1347C4—42no—
1348C4—44no—
1349C4—42no—
1350C4—44no—
1351C4#352914yes—
1352C2—42no—
1353C2—81no—
1354C2C2×#352911yescharacteristic
1355C2#6291511yescharacteristic
1356C2#6295612yes—
1357C2#6301611yescharacteristic
1358C2#6303212yes—
subgroupG/H
center, commutator, Frattini, socle, cosocleC23C26
prime radicalC22×D4C24
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23 ◁ G
LECSG ▷ C23 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #53146C2semidirect
3. #53013C2semidirect
5. #52954C2semidirect
6. #52929C2semidirect
7. #52896C2semidirect
8. #52812C2semidirect
10. #52289C2semidirect
11. #46344C2semidirect
12. #46009C2semidirect
13. #46002C2semidirect
14. #46002C2semidirect
15. #45931C2semidirect
17. #45759C2semidirect
18. #45634C2semidirect
21. #36560C2semidirect
22. #36545C2semidirect
23. #36491C2semidirect
25. #36408C2semidirect
28. #35870C2semidirect
29. #35749C2semidirect

Maximal subgroups

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

subgroupindex
#531462
#530322
#530132
#530082
#529542
#529292
#528962
#528122
#523002
#522892
#463442
#460092
#460022
#459312
#458612
#457592
#456342
#456302
#455032
#365602
#365452
#364912
#364232
#364082
#359972
#359492
#358702
#357492