Finite Group Databasebeta

← #7674353

Subgroups — #7674353

Order 512.

4245 conjugacy classes of subgroups.

The subgroup lattice has 1225 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#45414C212yesmaximal, complemented
2#45411C212yesmaximal, complemented
3#45343C212yesmaximal
4#45334C211yesmaximal, characteristic, complemented
5#45324C212yesmaximal
6#45304C212yesmaximal
7#45277C211yesmaximal, characteristic, complemented
8#45164C211yesmaximal, characteristic, complemented
9#45152C211yesmaximal, characteristic, complemented
10#45124C212yesmaximal
11#40475C214yesmaximal
12#40466C214yesmaximal, complemented
13#40107C214yesmaximal, complemented
14#40087C214yesmaximal
15#38815C214yesmaximal
16#38809C214yesmaximal, complemented
17#38623C214yesmaximal
18#38614C214yesmaximal, complemented
19#35646C212yesmaximal
20#35645C212yesmaximal
21#35221C212yesmaximal, complemented
22#35187C212yesmaximal, complemented
23#34644C211yesmaximal, characteristic
24#34336C212yesmaximal, complemented
25#34328C212yesmaximal, complemented
26C4×#541C211yesmaximal, characteristic
27C4×#541C211yesmaximal, characteristic
28C2×#557C2212yes—
29C2×#557C2212yes—
30C2×#541C2211yescharacteristic
31C2×#541C2211yescharacteristic
32#2864C2214yes—
33#2864C2214yes—
34#2863C2214yes—
35#2863C2214yes—
36#2805C2214yes—
37#2805C2214yes—
38#2791C2214yes—
39#2789C2214yes—
40#2789C2214yes—
41#2777C2214yes—
42#2775C2214yes—
43#2774C2214yes—
44#2774C2214yes—
45#2773C2214yes—
46#2769C2214yes—
47#2769C2214yes—
48#2767C2214yes—
49#2766C2214yes—
50#2766C2214yes—
51#2766C2214yes—
52#2762C2214yes—
53#2762C2214yes—
54#2759C2214yes—
55#2758C2214yes—
56#2726C2214yes—
57#2726C2214yes—
58#2725C2214yes—
59#2725C2214yes—
60#2721C2214yes—
61#2719C2214yes—
62#2719C2214yes—
63#2719C2214yes—
64#2719C2214yes—
65#2719C2214yes—
66#2716C2214yes—
67#2713C2214yes—
68#2667C2212yes—
69#2667C2212yes—
70#2666C2212yes—
71#2666C2212yes—
72#2666C2212yes—
73#2666C2212yes—
74#2666C2214yes—
75#2666C2214yes—
76#2665C2212yes—
77#2665C2212yes—
78#2655C2214yes—
79#2655C2214yes—
80#2606C2214yes—
81#2606C2214yes—
82#2596C2214yes—
83#2594C2214yes—
84#2590C2214yes—
85#2590C2214yes—
86#2588C2214yes—
87#2588C2214yes—
88#2586C2214yes—
89#2585C2214yes—
90#2584C2212yes—
91#2582C2212yes—
92#2581C2212yes—
93#2577C2214yes—
94#2575C2214yes—
95#2574C2214yes—
96#2573C2214yes—
97#2571C2212yes—
98#2570C2214yes—
99#2568C2212yes—
100#2565C2212yes—
101#2550C2214yes—
102#2550C2212yes—
103#2546C2212yes—
104#2533C2214yes—
105#2533C2214yes—
106#2533C2214yes—
107#2533C2214yes—
108#2532C2214yes—
109#2530C2214yes—
110#2529C2214yes—
111#2528C2214yes—
112#2528C2214yes—
113#2527C2214yes—
114#2524C2214yes—
115#2524C2214yes—
116#2524C2214yes—
117#2524C2214yes—
118#2524C2214yes—
119#2524C2214yes—
120#2524C2214yes—
121#2524C2214yes—
122#2524C2214yes—
123#2522C2214yes—
124#2520C2214yes—
125#2519C2214yes—
126#2519C2214yes—
127#2515C2214yes—
128#2514C2214yes—
129#2514C2212yes—
130#2514C2214yes—
131#2514C2212yes—
132#2514C2212yes—
133#2514C2214yes—
134#2514C2214yes—
135#2511C2212yes—
136#2509C2212yes—
137#2509C2212yes—
138#2508C2214yes—
139#2508C2214yes—
140#2508C2212yes—
141#2508C2214yes—
142#2507C2212yes—
143#2506C2214yes—
144#2495C2212yes—
145#2494C2212yes—
146#2492C2212yes—
147#2489C2212yes—
148#2469C2214yes—
149#2469C2214yes—
150#2462C2214yes—
151#2462C2214yes—
152#2462C2214yes—
153#2462C2214yes—
154#2453C2212yes—
155#2453C2214yes—
156#2453C2212yes—
157#2451C2212yes—
158#2451C2212yes—
159#2451C2214yes—
160#2446C2212yes—
161#2446C2212yes—
162#2446C2212yes—
163#2446C2212yes—
164#2429C2212yes—
165#2429C2212yes—
166#2423C2212yes—
167#2421C2212yes—
168#2402C2211yescharacteristic
169#2402C2211yescharacteristic
170#2399C2211yescharacteristic
171#2399C2211yescharacteristic
172#2396C2212yes—
173#2396C2212yes—
174#2371C2214yes—
175#2371C2214yes—
176#2370C2214yes—
177#2370C2212yes—
178#2370C2212yes—
179#2370C2214yes—
180#2370C2214yes—
181#2369C2212yes—
182#2369C2214yes—
183#2365C2212yes—
184#2365C2212yes—
185#2365C2212yes—
186#2356C2212yes—
187#2356C2212yes—
188#2356C2214yes—
189#2355C2212yes—
190#2355C2212yes—
191#2355C2212yes—
192#2355C2214yes—
193#2351C2212yes—
194#2351C2212yes—
195Q8×C4⋊C4C2212yes—
196#2336C2214yes—
197#2336C2214yes—
198#2336C2214yes—
199#2336C2214yes—
200#2334C2214yes—
201#2334C2214yes—
202#2331C2214yes—
203#2331C2212yes—
204#2330C2214yes—
205#2330C2212yes—
206#2330C2211yescharacteristic
207#2330C2211yescharacteristic
208#2327C2211yescharacteristic
209#2327C2211yescharacteristic
210#2327C2212yes—
211#2327C2212yes—
212#2323C2212yes—
213#2323C2212yes—
214#2320C2212yes—
215#2320C2212yes—
216#2320C2212yes—
217#2320C2212yes—
218#2314C2211yescharacteristic
219#2314C2211yescharacteristic
220C4×C4⋊Q8C2211yescharacteristic
221C4×C4⋊Q8C2211yescharacteristic
222C4×#125C2214yes—
223C4×#125C2214yes—
224C4×#125C2214yes—
225C4×#125C2211yescharacteristic
226C4×#125C2211yescharacteristic
227C4×#125C2214yes—
228C4×#126C2214yes—
229C4×#126C2214yes—
230C4×C22⋊Q8C2212yes—
231C4×C22⋊Q8C2212yes—
232#2295C2212yes—
233#2295C2214yes—
234#2295C2212yes—
235#2295C2214yes—
236#2283C2211yescharacteristic
237#2283C2211yescharacteristic
238#2276C2212yes—
239#2276C2212yes—
240C42×Q8C2212yes—
241C42×Q8C2212yes—
242C4×#117C2211yescharacteristic
243#557—216no—
244#557—216no—
245#541—28no—
246#541—28no—
247C2×C4⋊Q8C2311yescharacteristic
248C2×C4⋊Q8C2312yes—
249C2×C4⋊Q8C2312yes—
250C2×C4⋊Q8C2312yes—
251C2×C4⋊Q8C2314yes—
252C2×C4⋊Q8C2311yescharacteristic
253C2×#126C2314yes—
254C2×#126C2314yes—
255C2×#125C2311yescharacteristic
256C2×#125C2314yes—
257C2×#125C2314yes—
258C2×#125C2314yes—
259C2×#125C2314yes—
260C2×#125C2312yes—
261C2×#125C2314yes—
262C2×#125C2314yes—
263C2×#125C2314yes—
264C2×#125C2311yescharacteristic
265C2×C22⋊Q8C2312yes—
266C2×C22⋊Q8C2312yes—
267C2×C4×Q8C2312yes—
268C2×C4×Q8C2312yes—
269C2×C4×Q8C2312yes—
270C2×C4×Q8C2312yes—
271C2×C4×Q8C2312yes—
272C2×C4×Q8C2312yes—
273C2×C4×Q8C2312yes—
274C2×C4×Q8C2312yes—
275C2×C4×Q8C2312yes—
276C2×C4×Q8C2312yes—
277C2×C4×Q8C2312yes—
278C2×C4×Q8C2312yes—
279C2×C4×Q8C2314yes—
280C2×C4×Q8C2314yes—
281C2×#117C2311yescharacteristic
282C2×#117C2311yescharacteristic
283C22×C42C2311yescharacteristic
284#401C2314yes—
285#401C2314yes—
286#401C2314yes—
287#401C2314yes—
288#400C2314yes—
289#400C2314yes—
290#400C2314yes—
291#400C2314yes—
292#400C2314yes—
293#400C2314yes—
294#400C2314yes—
295#400C2314yes—
296#400C2314yes—
297#400C2314yes—
298#400C2314yes—
299#400C2314yes—
300#400C2314yes—
301#400C2314yes—
302#400C2314yes—
303#400C2314yes—
304#400C2312yes—
305#400C2312yes—
306#400C2314yes—
307#400C2314yes—
308#400C2312yes—
309#400C2312yes—
310#400C2312yes—
311#400C2312yes—
312#400C2314yes—
313#400C2314yes—
314#400C2314yes—
315#400C2314yes—
316#400C2314yes—
317#400C2314yes—
318#400C2314yes—
319#399C2314yes—
320#399C2312yes—
321#399C2312yes—
322#398C2314yes—
323#398C2314yes—
324#398C2312yes—
325#398C2314yes—
326#398C2314yes—
327#398C2314yes—
328#398C2314yes—
329#398C2314yes—
330#398C2314yes—
331#398C2314yes—
332#398C2314yes—
333#398C2312yes—
334#398C2314yes—
335#398C2314yes—
336#398C2312yes—
337#398C2312yes—
338#398C2314yes—
339#398C2314yes—
340#398C2314yes—
341#398C2312yes—
342#398C2312yes—
343#398C2312yes—
344#398C2312yes—
345#398C2312yes—
346#398C2312yes—
347#398C2314yes—
348#398C2314yes—
349#398C2314yes—
350#398C2312yes—
351#398C2312yes—
352#398C2314yes—
353#398C2314yes—
354#398C2314yes—
355#398C2314yes—
356#397C2314yes—
357#397C2314yes—
358#397C2314yes—
359#397C2314yes—
360#396C2314yes—
361#396C2314yes—
362#396C2312yes—
363#396C2312yes—
364#396C2312yes—
365#396C2312yes—
366#395C2314yes—
367#395C2314yes—
368#395C2314yes—
369#395C2314yes—
370#395C2312yes—
371#395C2314yes—
372#395C2312yes—
373#395C2312yes—
374#395C2312yes—
375#395C2312yes—
376#395C2312yes—
377#393C2314yes—
378#393C2312yes—
379#393C2312yes—
380#391C2312yes—
381#391C2312yes—
382#391C2312yes—
383#391C2312yes—
384#391C2312yes—
385#391C2312yes—
386#391C2314yes—
387#391C2314yes—
388#391C2312yes—
389#391C2312yes—
390#391C2312yes—
391#391C2312yes—
392#391C2312yes—
393#391C2312yes—
394#391C2314yes—
395#391C2312yes—
396#391C2314yes—
397#391C2314yes—
398#391C2312yes—
399#391C2314yes—
400#391C2314yes—
401#391C2314yes—
402#391C2314yes—
403#391C2312yes—
404#391C2314yes—
405#391C2312yes—
406#391C2314yes—
407#391C2314yes—
408#389C2312yes—
409#389C2314yes—
410#389C2312yes—
411#389C2312yes—
412#389C2314yes—
413#389C2314yes—
414#389C2314yes—
415#389C2314yes—
416#389C2314yes—
417#389C2314yes—
418#389C2314yes—
419#389C2314yes—
420#389C2314yes—
421#389C2312yes—
422#389C2312yes—
423#389C2314yes—
424#389C2314yes—
425#389C2312yes—
426#389C2312yes—
427#389C2312yes—
428#389C2312yes—
429#389C2312yes—
430#389C2312yes—
431#389C2314yes—
432#389C2312yes—
433#389C2312yes—
434#389C2314yes—
435#389C2314yes—
436#389C2312yes—
437#389C2314yes—
438#389C2314yes—
439#389C2312yes—
440#389C2314yes—
441#389C2314yes—
442#389C2314yes—
443#389C2314yes—
444#389C2314yes—
445#389C2314yes—
446#389C2314yes—
447#389C2314yes—
448#389C2314yes—
449#389C2314yes—
450#389C2314yes—
451#389C2314yes—
452#389C2314yes—
453#389C2314yes—
454#389C2312yes—
455#389C2314yes—
456#389C2314yes—
457#389C2314yes—
458#388C2314yes—
459#388C2314yes—
460#388C2314yes—
461#388C2314yes—
462#388C2314yes—
463#388C2314yes—
464#388C2314yes—
465#388C2314yes—
466#388C2314yes—
467#388C2314yes—
468#388C2314yes—
469#388C2314yes—
470#388C2314yes—
471#388C2314yes—
472#387C2314yes—
473#387C2314yes—
474#387C2314yes—
475#387C2314yes—
476#387C2314yes—
477#387C2314yes—
478#387C2314yes—
479#387C2312yes—
480#387C2314yes—
481#387C2314yes—
482#387C2314yes—
483#387C2314yes—
484#387C2314yes—
485#387C2314yes—
486#387C2314yes—
487#387C2314yes—
488#387C2314yes—
489#387C2314yes—
490#387C2314yes—
491#387C2314yes—
492#387C2314yes—
493#387C2314yes—
494#387C2314yes—
495#387C2314yes—
496#387C2314yes—
497#387C2314yes—
498#387C2314yes—
499#387C2314yes—
500#387C2314yes—
501#387C2314yes—
502#387C2314yes—
503#387C2314yes—
504#387C2314yes—
505#387C2314yes—
506#387C2314yes—
507#387C2314yes—
508#387C2314yes—
509#387C2314yes—
510#387C2314yes—
511#387C2314yes—
512#387C2314yes—
513#387C2314yes—
514#387C2314yes—
515#387C2314yes—
516#387C2314yes—
517#387C2314yes—
518#387C2314yes—
519#387C2314yes—
520#387C2314yes—
521#387C2314yes—
522#387C2314yes—
523#387C2314yes—
524#387C2314yes—
525#387C2314yes—
526#387C2314yes—
527#387C2314yes—
528#387C2314yes—
529#387C2314yes—
530#387C2312yes—
531#387C2314yes—
532#387C2312yes—
533#387C2314yes—
534#387C2312yes—
535#387C2312yes—
536#387C2314yes—
537#387C2314yes—
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#387C2312yes—
554#387C2314yes—
555#387C2314yes—
556#387C2314yes—
557#387C2312yes—
558#387C2314yes—
559#387C2312yes—
560#387C2314yes—
561#387C2314yes—
562#385C2314yes—
563#385C2314yes—
564#384C2311yescharacteristic
565#384C2311yescharacteristic
566#384C2312yes—
567#384C2314yes—
568#383C2314yes—
569#383C2314yes—
570#383C2314yes—
571#383C2314yes—
572#383C2314yes—
573#383C2314yes—
574#383C2314yes—
575#383C2314yes—
576#383C2314yes—
577#383C2314yes—
578#383C2311yescharacteristic
579#383C2311yescharacteristic
580#383C2311yescharacteristic
581#383C2311yescharacteristic
582#382C2311yescharacteristic
583#382C2311yescharacteristic
584#382C2314yes—
585#382C2314yes—
586#382C2314yes—
587#382C2314yes—
588#382C2312yes—
589#382C2314yes—
590#382C2314yes—
591#382C2312yes—
592#382C2312yes—
593#382C2314yes—
594#382C2314yes—
595#382C2314yes—
596#382C2314yes—
597#382C2312yes—
598#382C2312yes—
599#382C2314yes—
600#381C2311yescharacteristic
601#381C2311yescharacteristic
602#381C2311yescharacteristic
603#381C2311yescharacteristic
604#380C2312yes—
605#380C2312yes—
606#380C2312yes—
607#380C2312yes—
608C4×C4⋊C4C2314yes—
609C4×C4⋊C4C2314yes—
610C4×C4⋊C4C2314yes—
611C4×C4⋊C4C2314yes—
612C4×C4⋊C4C2314yes—
613C4×C4⋊C4C2314yes—
614C4×C4⋊C4C2312yes—
615C4×C4⋊C4C2312yes—
616C4×C4⋊C4C2314yes—
617C4×C4⋊C4C2314yes—
618C4×C4⋊C4C2314yes—
619C4×C4⋊C4C2314yes—
620C4×C4⋊C4C2314yes—
621C4×C4⋊C4C2312yes—
622C4×C4⋊C4C2314yes—
623C4×C4⋊C4C2312yes—
624C4×C4⋊C4C2314yes—
625C4×C4⋊C4C2314yes—
626C4×C4⋊C4C2314yes—
627C4×C4⋊C4C2314yes—
628C4×C4⋊C4C2314yes—
629C4×C4⋊C4C2314yes—
630C4×C4⋊C4C2314yes—
631C4×C4⋊C4C2314yes—
632C4×C4⋊C4C2312yes—
633C4×C4⋊C4C2312yes—
634C4×C4⋊C4C2312yes—
635C4×C4⋊C4C2312yes—
636C4×C4⋊C4C2312yes—
637C4×C4⋊C4C2314yes—
638C4×C4⋊C4C2314yes—
639C4×C4⋊C4C2312yes—
640C4×C4⋊C4C2314yes—
641C4×C4⋊C4C2314yes—
642C4×C4⋊C4C2314yes—
643C4×C4⋊C4C2314yes—
644C4×C4⋊C4C2314yes—
645C4×C4⋊C4C2312yes—
646C4×C4⋊C4C2314yes—
647C4×C4⋊C4C2312yes—
648C4×C4⋊C4C2314yes—
649C4×C4⋊C4C2314yes—
650C4×C4⋊C4C2312yes—
651C4×C4⋊C4C2312yes—
652C4×C4⋊C4C2312yes—
653C4×C4⋊C4C2312yes—
654C4×C4⋊C4C2312yes—
655C4×C4⋊C4C2312yes—
656C4×C4⋊C4C2311yescharacteristic
657C4×C4⋊C4C2311yescharacteristic
658C4×C4⋊C4C2311yescharacteristic
659C4×C4⋊C4C2311yescharacteristic
660C4×C22⋊C4C2314yes—
661C4×C22⋊C4C2312yes—
662C4×C22⋊C4C2312yes—
663C4×C22⋊C4C2314yes—
664C4×C22⋊C4C2312yes—
665C4×C22⋊C4C2312yes—
666#376C2311yescharacteristic
667#376C2312yes—
668#376C2312yes—
669#376C2311yescharacteristic
670#376C2314yes—
671#376C2314yes—
672#376C2314yes—
673#376C2314yes—
674C43C2314yes—
675C43C2314yes—
676C43C2311yescharacteristic
677C43C2311yescharacteristic
678C22×Q8C2412yes—
679C22×Q8C2412yes—
680C22×Q8C2412yes—
681C22×Q8C2412yes—
682C22×Q8C2414yes—
683C23×C4C2411yescharacteristic
684C23×C4C2411yescharacteristic
685C23×C4C2411yescharacteristic
686C4⋊Q8—28no—
687C4⋊Q8—28no—
688C4⋊Q8—216no—
689C4⋊Q8—28no—
690C4⋊Q8—24no—
691C4⋊Q8#4118yes—
692#126—216no—
693#126—216no—
694#125—216no—
695#125—216no—
696#125—216no—
697#125—216no—
698#125—216no—
699#125—216no—
700#125—28no—
701#125—216no—
702#125—24no—
703#125#4118yes—
704C22⋊Q8—28no—
705C22⋊Q8—28no—
706C4×Q8—28no—
707C4×Q8—28no—
708C4×Q8—28no—
709C4×Q8—28no—
710C4×Q8—28no—
711C4×Q8—216no—
712C4×Q8—216no—
713C4×Q8—28no—
714C4×Q8—28no—
715C4×Q8—28no—
716C4×Q8—28no—
717C4×Q8—28no—
718C4×Q8—28no—
719C4×Q8—28no—
720#117—24no—
721#117—24no—
722C2×C4⋊C4C2412yes—
723C2×C4⋊C4C2412yes—
724C2×C4⋊C4C2412yes—
725C2×C4⋊C4C2412yes—
726C2×C4⋊C4C2412yes—
727C2×C4⋊C4C2414yes—
728C2×C4⋊C4C2414yes—
729C2×C4⋊C4C2414yes—
730C2×C4⋊C4C2414yes—
731C2×C4⋊C4C2412yes—
732C2×C4⋊C4C2412yes—
733C2×C4⋊C4C2412yes—
734C2×C4⋊C4C2412yes—
735C2×C4⋊C4C2412yes—
736C2×C4⋊C4C2414yes—
737C2×C4⋊C4C2414yes—
738C2×C4⋊C4C2414yes—
739C2×C4⋊C4C2412yes—
740C2×C4⋊C4C2414yes—
741C2×C4⋊C4C2414yes—
742C2×C4⋊C4C2414yes—
743C2×C4⋊C4C2414yes—
744C2×C4⋊C4C2412yes—
745C2×C4⋊C4C2414yes—
746C2×C4⋊C4C2412yes—
747C2×C4⋊C4C2414yes—
748C2×C4⋊C4C2414yes—
749C2×C4⋊C4C2414yes—
750C2×C4⋊C4C2414yes—
751C2×C4⋊C4C2414yes—
752C2×C4⋊C4C2414yes—
753C2×C4⋊C4C2414yes—
754C2×C4⋊C4C2414yes—
755C2×C4⋊C4C2414yes—
756C2×C4⋊C4C2412yes—
757C2×C4⋊C4C2414yes—
758C2×C4⋊C4C2414yes—
759C2×C4⋊C4C2412yes—
760C2×C4⋊C4C2412yes—
761C2×C4⋊C4C2412yes—
762C2×C4⋊C4C2412yes—
763C2×C4⋊C4C2412yes—
764C2×C4⋊C4C2412yes—
765C2×C4⋊C4C2412yes—
766C2×C4⋊C4C2412yes—
767C2×C4⋊C4C2412yes—
768C2×C4⋊C4C2414yes—
769C2×C4⋊C4C2412yes—
770C2×C4⋊C4C2414yes—
771C2×C4⋊C4C2414yes—
772C2×C4⋊C4C2414yes—
773C2×C4⋊C4C2414yes—
774C2×C4⋊C4C2412yes—
775C2×C4⋊C4C2414yes—
776C2×C4⋊C4C2414yes—
777C2×C4⋊C4C2412yes—
778C2×C4⋊C4C2412yes—
779C2×C4⋊C4C2412yes—
780C2×C4⋊C4C2414yes—
781C2×C4⋊C4C2414yes—
782C2×C4⋊C4C2412yes—
783C2×C4⋊C4C2414yes—
784C2×C4⋊C4C2414yes—
785C2×C4⋊C4C2414yes—
786C2×C4⋊C4C2414yes—
787C2×C4⋊C4C2414yes—
788C2×C4⋊C4C2412yes—
789C2×C4⋊C4C2414yes—
790C2×C4⋊C4C2414yes—
791C2×C22⋊C4C2412yes—
792C2×C22⋊C4C2412yes—
793C2×C22⋊C4C2414yes—
794C2×C22⋊C4C2414yes—
795C2×C22⋊C4C2412yes—
796C2×C22⋊C4C2412yes—
797C2×C22⋊C4C2412yes—
798C2×C22⋊C4C2412yes—
799C2×C22⋊C4C2414yes—
800C2×C22⋊C4C2414yes—
801C2×C42—24no—
802C2×C42C2411yescharacteristic
803C2×C42C2411yescharacteristic
804C2×C42C2414yes—
805C2×C42C2414yes—
806C2×C42C2414yes—
807C2×C42C2414yes—
808C2×C42C2412yes—
809C2×C42C2414yes—
810C2×C42C2412yes—
811C2×C42C2412yes—
812C2×C42C2412yes—
813C2×C42C2414yes—
814C2×C42C2414yes—
815C2×C42C2414yes—
816C2×C42C2414yes—
817C2×C42C2414yes—
818C2×C42C2411yescharacteristic
819C2×C42C2411yescharacteristic
820C2×C42C2411yescharacteristic
821C2×C42C2412yes—
822C2×C42C2412yes—
823C2×C42C2414yes—
824C2×C42C2414yes—
825C2×C42C2412yes—
826C2×C42C2412yes—
827C2×C42C2414yes—
828C2×C42C2414yes—
829C2×C42C2414yes—
830C2×C42C2414yes—
831C2×C42C2414yes—
832C2×C42C2414yes—
833C2×C42C2414yes—
834C2×C42C2414yes—
835C2×C42C2411yescharacteristic
836C2×C42C2411yescharacteristic
837C2×C42C2411yescharacteristic
838#95C2412yes—
839#95C2412yes—
840#95C2414yes—
841#95C2412yes—
842#95C2412yes—
843#95C2412yes—
844#95C2412yes—
845#95C2412yes—
846#95C2412yes—
847#95C2412yes—
848#95C2412yes—
849#95C2412yes—
850#95C2412yes—
851#95C2412yes—
852#95C2412yes—
853#95C2414yes—
854#95C2414yes—
855#95C2414yes—
856#95C2414yes—
857#95C2414yes—
858#95C2414yes—
859#95C2414yes—
860#95C2414yes—
861#95C2414yes—
862#95C2414yes—
863#95C2412yes—
864#95C2414yes—
865#95C2412yes—
866#95C2412yes—
867#95C2412yes—
868#95C2414yes—
869#95C2414yes—
870#95C2414yes—
871#95C2414yes—
872#95C2414yes—
873#95C2412yes—
874#95C2414yes—
875#95C2414yes—
876#95C2414yes—
877#95C2414yes—
878#95C2414yes—
879#95C2412yes—
880#95C2412yes—
881#95C2412yes—
882#95C2414yes—
883#95C2414yes—
884#95C2411yescharacteristic
885#95C2411yescharacteristic
886#95C2411yescharacteristic
887#95C2411yescharacteristic
888#95C2411yescharacteristic
889#95C2411yescharacteristic
890#95C2411yescharacteristic
891#95C2411yescharacteristic
892#95C2414yes—
893#95C2412yes—
894#95C2414yes—
895#95C2414yes—
896#95C2414yes—
897#95C2414yes—
898#95C2414yes—
899#95C2414yes—
900#95C2414yes—
901#95C2414yes—
902#95C2414yes—
903#95C2414yes—
904#95C2414yes—
905#95C2414yes—
906#95C2414yes—
907#95C2414yes—
908#95C2412yes—
909#95C2412yes—
910#95C2412yes—
911#95C2414yes—
912#95C2414yes—
913#95C2414yes—
914#95C2414yes—
915#95C2412yes—
916#95C2412yes—
917#95C2414yes—
918#95C2414yes—
919#95C2414yes—
920#95C2414yes—
921#95C2414yes—
922#95C2414yes—
923#95C2414yes—
924#95C2414yes—
925#95C2414yes—
926#95C2414yes—
927#95C2414yes—
928#95C2414yes—
929#95C2414yes—
930C24C2511yescharacteristic
931C2×Q8—24no—
932C2×Q8—24no—
933C2×Q8—24no—
934C2×Q8—24no—
935C2×Q8—28no—
936C2×Q8—24no—
937C2×Q8—24no—
938C2×Q8—24no—
939C2×Q8—42no—
940C2×Q8—42no—
941C2×Q8—42no—
942C2×Q8—44no—
943C2×Q8—44no—
944C2×Q8—42no—
945C2×Q8C2×#4118yes—
946C22×C4—22no—
947C22×C4—22no—
948C22×C4—22no—
949C22×C4—22no—
950C22×C4—22no—
951C22×C4—42no—
952C22×C4—42no—
953C22×C4C2512yes—
954C22×C4C2511yescharacteristic
955C22×C4C2511yescharacteristic
956C22×C4C2514yes—
957C22×C4C2514yes—
958C22×C4C2512yes—
959C22×C4C2512yes—
960C22×C4C2514yes—
961C22×C4C2512yes—
962C22×C4C2514yes—
963C22×C4C2511yescharacteristic
964C22×C4C2512yes—
965C22×C4C2512yes—
966C22×C4C2514yes—
967C22×C4C2512yes—
968C22×C4C2514yes—
969C22×C4C2512yes—
970C22×C4C2512yes—
971C22×C4C2512yes—
972C22×C4C2514yes—
973C22×C4C2514yes—
974C22×C4C2512yes—
975C22×C4C2512yes—
976C22×C4C2511yescharacteristic
977C22×C4C2511yescharacteristic
978C22×C4C2511yescharacteristic
979C4⋊C4—24no—
980C4⋊C4—24no—
981C4⋊C4—24no—
982C4⋊C4—24no—
983C4⋊C4—24no—
984C4⋊C4—28no—
985C4⋊C4—28no—
986C4⋊C4—28no—
987C4⋊C4—24no—
988C4⋊C4—28no—
989C4⋊C4—28no—
990C4⋊C4—24no—
991C4⋊C4—24no—
992C4⋊C4—24no—
993C4⋊C4—24no—
994C4⋊C4—28no—
995C4⋊C4—28no—
996C4⋊C4—28no—
997C4⋊C4—28no—
998C4⋊C4—28no—
999C4⋊C4—28no—
1000C4⋊C4—24no—
1001C4⋊C4—28no—
1002C4⋊C4—28no—
1003C4⋊C4—28no—
1004C4⋊C4—28no—
1005C4⋊C4—28no—
1006C4⋊C4—28no—
1007C4⋊C4—28no—
1008C4⋊C4—28no—
1009C4⋊C4—28no—
1010C4⋊C4—24no—
1011C4⋊C4—24no—
1012C4⋊C4—28no—
1013C4⋊C4—42no—
1014C4⋊C4—44no—
1015C4⋊C4—42no—
1016C4⋊C4—44no—
1017C4⋊C4—44no—
1018C4⋊C4—44no—
1019C4⋊C4—44no—
1020C4⋊C4—44no—
1021C4⋊C4—42no—
1022C4⋊C4—42no—
1023C4⋊C4—42no—
1024C4⋊C4—42no—
1025C4⋊C4—44no—
1026C4⋊C4—44no—
1027C4⋊C4—44no—
1028C4⋊C4—42no—
1029C4⋊C4—42no—
1030C4⋊C4—42no—
1031C4⋊C4—42no—
1032C4⋊C4—42no—
1033C4⋊C4—42no—
1034C4⋊C4—44no—
1035C4⋊C4—44no—
1036C4⋊C4—44no—
1037C4⋊C4—44no—
1038C4⋊C4—44no—
1039C4⋊C4—44no—
1040C4⋊C4—44no—
1041C4⋊C4—42no—
1042C4⋊C4—42no—
1043C4⋊C4—42no—
1044C4⋊C4—42no—
1045C4⋊C4C2×#4118yes—
1046C4⋊C4C2×#41116yes—
1047C4⋊C4C2×#41116yes—
1048C22⋊C4—24no—
1049C22⋊C4—24no—
1050C22⋊C4—28no—
1051C22⋊C4—28no—
1052C22⋊C4—44no—
1053C22⋊C4—42no—
1054C22⋊C4—42no—
1055C22⋊C4—44no—
1056C22⋊C4—42no—
1057C22⋊C4—42no—
1058C42—22no—
1059C42—22no—
1060C42—28no—
1061C42—28no—
1062C42—28no—
1063C42—28no—
1064C42—28no—
1065C42—24no—
1066C42—28no—
1067C42—24no—
1068C42—24no—
1069C42—24no—
1070C42—28no—
1071C42—28no—
1072C42—22no—
1073C42—22no—
1074C42—22no—
1075C42—28no—
1076C42—28no—
1077C42—42no—
1078C42—44no—
1079C42—42no—
1080C42—42no—
1081C42—42no—
1082C42—44no—
1083C42—44no—
1084C42—44no—
1085C42—44no—
1086C42—44no—
1087C42—44no—
1088C42—44no—
1089C42—44no—
1090C42—44no—
1091C42C2×#4114yes—
1092C42C2×#4114yes—
1093C422−1+414yes—
1094C23—21no—
1095C23—21no—
1096C23—21no—
1097C23—22no—
1098C23—22no—
1099C23C2611yescharacteristic
1100Q8—216no—
1101Q8—48no—
1102Q8—48no—
1103Q8—88no—
1104Q8—84no—
1105C2×C4—24no—
1106C2×C4—24no—
1107C2×C4—22no—
1108C2×C4—22no—
1109C2×C4—22no—
1110C2×C4—24no—
1111C2×C4—22no—
1112C2×C4—22no—
1113C2×C4—24no—
1114C2×C4—22no—
1115C2×C4—22no—
1116C2×C4—22no—
1117C2×C4—24no—
1118C2×C4—22no—
1119C2×C4—22no—
1120C2×C4—22no—
1121C2×C4—22no—
1122C2×C4—24no—
1123C2×C4—24no—
1124C2×C4—22no—
1125C2×C4—22no—
1126C2×C4—22no—
1127C2×C4—22no—
1128C2×C4—24no—
1129C2×C4—24no—
1130C2×C4—21no—
1131C2×C4—21no—
1132C2×C4—21no—
1133C2×C4—21no—
1134C2×C4—21no—
1135C2×C4—24no—
1136C2×C4—24no—
1137C2×C4—24no—
1138C2×C4—24no—
1139C2×C4—22no—
1140C2×C4—24no—
1141C2×C4—22no—
1142C2×C4—24no—
1143C2×C4—22no—
1144C2×C4—22no—
1145C2×C4—22no—
1146C2×C4—22no—
1147C2×C4—24no—
1148C2×C4—24no—
1149C2×C4—24no—
1150C2×C4—22no—
1151C2×C4—24no—
1152C2×C4—24no—
1153C2×C4—22no—
1154C2×C4—24no—
1155C2×C4—24no—
1156C2×C4—22no—
1157C2×C4—22no—
1158C2×C4—22no—
1159C2×C4—22no—
1160C2×C4—22no—
1161C2×C4—22no—
1162C2×C4—22no—
1163C2×C4—22no—
1164C2×C4—22no—
1165C2×C4—22no—
1166C2×C4—22no—
1167C2×C4—22no—
1168C2×C4—22no—
1169C2×C4—22no—
1170C2×C4—44no—
1171C2×C4—82no—
1172C2×C4—82no—
1173C2×C4C22×#4118yes—
1174C2×C4C22×#4118yes—
1175C2×C4C22×#4114yes—
1176C2×C4C22×#4114yes—
1177C2×C4C22×#4112yes—
1178C2×C4C22×#4112yes—
1179C2×C4C2×2−1+412yes—
1180C2×C4C2×2−1+412yes—
1181C2×C4C2×2−1+412yes—
1182C22—42no—
1183C22—42no—
1184C22—41no—
1185C22—41no—
1186C22—41no—
1187C22C23×#4111yescharacteristic
1188C22C23×#4111yescharacteristic
1189C22C22×2−1+411yescharacteristic
1190C222−1+612yes—
1191C222−1+612yes—
1192C4—24no—
1193C4—28no—
1194C4—24no—
1195C4—22no—
1196C4—22no—
1197C4—28no—
1198C4—42no—
1199C4—44no—
1200C4—44no—
1201C4—42no—
1202C4—42no—
1203C4—42no—
1204C4—42no—
1205C4—42no—
1206C4—42no—
1207C4—42no—
1208C4—42no—
1209C4—44no—
1210C4—42no—
1211C4—44no—
1212C4—44no—
1213C4—41no—
1214C4—41no—
1215C4—41no—
1216C4—44no—
1217C4#348214yes—
1218C2—81no—
1219C2C2×#348211yescharacteristic
1220C2#6285012yes—
1221C2#6286112yes—
1222C2#6288911yescharacteristic
1223C2#6288911yescharacteristic
subgroupG/H
center, commutator, Frattini, socle, cosocleC23C26
prime radicalC24C25
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23 ◁ G
LECSG ▷ C23 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #45414C2semidirect
2. #45411C2semidirect
4. #45334C2semidirect
7. #45277C2semidirect
8. #45164C2semidirect
9. #45152C2semidirect
12. #40466C2semidirect
13. #40107C2semidirect
16. #38809C2semidirect
18. #38614C2semidirect
21. #35221C2semidirect
22. #35187C2semidirect
24. #34336C2semidirect
25. #34328C2semidirect

Maximal subgroups

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

subgroupindex
#454142
#454112
#453432
#453342
#453242
#453042
#452772
#451642
#451522
#451242
#404752
#404662
#401072
#400872
#388152
#388092
#386232
#386142
#356462
#356452
#352212
#351872
#346442
#343362
#343282
C4×#5412