Finite Group Databasebeta

← #8726252

Subgroups — #8726252

Order 512.

4284 conjugacy classes of subgroups.

The subgroup lattice has 1388 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#59828C212yesmaximal, complemented
2#59694C212yesmaximal, complemented
3#59631C211yesmaximal, characteristic, complemented
4#59481C212yesmaximal, complemented
5#59144C212yesmaximal, complemented
6#58931C214yesmaximal, complemented
7#55843C214yesmaximal, complemented
8#55138C214yesmaximal, complemented
9#53886C212yesmaximal, complemented
10#53013C212yesmaximal, complemented
11#53008C211yesmaximal, characteristic, complemented
12#52300C211yesmaximal, characteristic, complemented
13#47737C214yesmaximal, complemented
14#47183C212yesmaximal, complemented
15#45419C211yesmaximal, characteristic, complemented
16#45411C212yesmaximal, complemented
17#44671C212yesmaximal, complemented
18#44371C214yesmaximal, complemented
19#42815C211yesmaximal, characteristic
20#42702C212yesmaximal, complemented
21#41769C212yesmaximal, complemented
22#41190C214yesmaximal, complemented
23#40225C212yesmaximal, complemented
24#40200C212yesmaximal, complemented
25#40022C212yesmaximal, complemented
26#39721C211yesmaximal, characteristic
27#39245C212yesmaximal, complemented
28#35996C211yesmaximal, characteristic
29#35712C212yesmaximal, complemented
30C2×#557C2212yes—
31C2×#557C2211yescharacteristic
32C2×#548C2211yescharacteristic
33C22×C4⋊Q8C2211yescharacteristic
34C2×#520C2211yescharacteristic
35#2861C2212yes—
36#2854C2211yescharacteristic
37#2845C2214yes—
38#2843C2212yes—
39#2839C2214yes—
40#2838C2214yes—
41#2836C2214yes—
42#2836C2214yes—
43#2836C2214yes—
44#2834C2212yes—
45#2820C2212yes—
46#2807C2212yes—
47#2802C2214yes—
48#2802C2214yes—
49#2800C2214yes—
50#2798C2214yes—
51#2792C2212yes—
52#2791C2214yes—
53#2791C2212yes—
54#2790C2214yes—
55#2790C2214yes—
56#2790C2214yes—
57#2788C2214yes—
58#2783C2214yes—
59#2779C2214yes—
60#2777C2214yes—
61#2777C2212yes—
62#2777C2214yes—
63#2775C2214yes—
64#2773C2214yes—
65#2771C2211yescharacteristic
66#2771C2212yes—
67#2770C2214yes—
68#2769C2214yes—
69#2768C2214yes—
70#2768C2214yes—
71#2766C2214yes—
72#2766C2214yes—
73#2765C2214yes—
74#2764C2211yescharacteristic
75#2764C2212yes—
76#2758C2212yes—
77#2758C2214yes—
78#2757C2214yes—
79#2755C2214yes—
80#2755C2214yes—
81#2754C2214yes—
82#2738C2214yes—
83#2731C2214yes—
84#2729C2214yes—
85#2727C2214yes—
86#2726C2214yes—
87#2726C2214yes—
88#2724C2212yes—
89#2724C2214yes—
90#2722C2214yes—
91#2722C2212yes—
92#2722C2211yescharacteristic
93#2720C2214yes—
94#2718C2212yes—
95#2718C2214yes—
96#2716C2212yes—
97#2716C2214yes—
98#2713C2214yes—
99#2713C2214yes—
100#2711C2214yes—
101#2702C2212yes—
102#2695C2214yes—
103#2677C2211yescharacteristic
104#2667C2214yes—
105#2658C2211yescharacteristic
106#2654C2214yes—
107#2654C2214yes—
108#2654C2214yes—
109#2651C2214yes—
110#2650C2214yes—
111#2633C2214yes—
112#2633C2212yes—
113#2632C2212yes—
114#2625C2211yescharacteristic
115#2625C2212yes—
116#2621C2212yes—
117#2618C2212yes—
118#2612C2214yes—
119#2611C2214yes—
120#2607C2212yes—
121#2606C2214yes—
122#2599C2214yes—
123#2595C2214yes—
124#2593C2214yes—
125#2592C2211yescharacteristic
126#2591C2212yes—
127#2588C2214yes—
128#2587C2214yes—
129#2587C2214yes—
130#2587C2214yes—
131#2585C2214yes—
132#2582C2212yes—
133#2582C2212yes—
134#2580C2212yes—
135#2580C2212yes—
136#2579C2212yes—
137#2577C2214yes—
138#2575C2214yes—
139#2574C2214yes—
140#2570C2214yes—
141#2570C2214yes—
142#2568C2212yes—
143#2565C2212yes—
144#2560C2214yes—
145#2553C2214yes—
146#2553C2214yes—
147#2552C2214yes—
148#2550C2214yes—
149#2547C2212yes—
150#2546C2212yes—
151#2546C2212yes—
152#2546C2212yes—
153#2546C2212yes—
154#2545C2212yes—
155#2545C2212yes—
156#2542C2211yescharacteristic
157#2533C2214yes—
158#2533C2214yes—
159#2532C2214yes—
160#2530C2214yes—
161#2527C2214yes—
162#2524C2214yes—
163#2523C2212yes—
164#2522C2214yes—
165#2520C2214yes—
166#2517C2212yes—
167#2514C2212yes—
168#2512C2212yes—
169#2511C2212yes—
170#2508C2212yes—
171#2507C2214yes—
172#2507C2212yes—
173#2506C2214yes—
174#2506C2214yes—
175#2502C2211yescharacteristic
176#2502C2212yes—
177#2496C2212yes—
178#2489C2212yes—
179#2489C2212yes—
180#2486C2212yes—
181#2486C2211yescharacteristic
182#2473C2214yes—
183#2473C2214yes—
184#2473C2214yes—
185#2473C2214yes—
186#2460C2214yes—
187#2460C2214yes—
188#2453C2212yes—
189#2453C2212yes—
190#2453C2214yes—
191#2453C2214yes—
192#2451C2214yes—
193#2448C2212yes—
194#2447C2212yes—
195#2447C2214yes—
196#2446C2212yes—
197#2446C2212yes—
198#2446C2212yes—
199#2446C2212yes—
200#2446C2212yes—
201#2446C2212yes—
202#2446C2212yes—
203#2442C2214yes—
204#2436C2211yescharacteristic
205#2434C2212yes—
206#2434C2212yes—
207#2432C2212yes—
208#2432C2212yes—
209#2429C2212yes—
210#2429C2212yes—
211#2429C2212yes—
212#2426C2212yes—
213#2423C2212yes—
214#2422C2212yes—
215#2422C2214yes—
216#2421C2212yes—
217#2409C2211yescharacteristic
218#2402C2212yes—
219#2398C2211yescharacteristic
220#2398C2214yes—
221#2396C2212yes—
222#2395C2211yescharacteristic
223#2395C2212yes—
224#2374C2212yes—
225#2373C2214yes—
226#2373C2214yes—
227#2370C2212yes—
228#2367C2212yes—
229#2367C2212yes—
230#2365C2212yes—
231#2365C2212yes—
232#2365C2214yes—
233#2360C2214yes—
234#2360C2212yes—
235#2360C2212yes—
236#2356C2212yes—
237Q8×C4⋊C4C2212yes—
238Q8×C4⋊C4C2212yes—
239#2341C2211yescharacteristic
240Q8×C22⋊C4C2212yes—
241Q8×C22⋊C4C2212yes—
242Q8×C22⋊C4C2211yescharacteristic
243#2335C2214yes—
244#2334C2214yes—
245#2334C2214yes—
246#2334C2214yes—
247#2322C2212yes—
248#2320C2211yescharacteristic
249#2320C2212yes—
250C4×C4⋊Q8C2212yes—
251C4×C4⋊Q8C2212yes—
252C4×C4⋊Q8C2212yes—
253C4×#126C2212yes—
254C4×#126C2212yes—
255C4×C22⋊Q8C2212yes—
256C4×C22⋊Q8C2212yes—
257C4×#123C2211yescharacteristic
258#2295C2212yes—
259C22×#41C2311yescharacteristic
260C23×Q8C2311yescharacteristic
261C23×Q8C2311yescharacteristic
262#557—48no—
263#557—44no—
264#548—44no—
265C2×C4⋊Q8—44no—
266C2×C4⋊Q8C2312yes—
267C2×C4⋊Q8C2312yes—
268C2×C4⋊Q8C2312yes—
269C2×C4⋊Q8C2312yes—
270C2×C4⋊Q8C2312yes—
271C2×C4⋊Q8C2312yes—
272C2×C4⋊Q8C2312yes—
273C2×C4⋊Q8C2311yescharacteristic
274C2×C4⋊Q8C2314yes—
275C2×#126C2312yes—
276C2×#126C2314yes—
277C2×#126C2312yes—
278C2×#126C2314yes—
279C2×#125C2312yes—
280C2×#125C2312yes—
281C2×#125C2314yes—
282C2×#125C2314yes—
283C2×#125C2314yes—
284C2×#125C2314yes—
285C2×#124C2312yes—
286C2×#124C2311yescharacteristic
287C2×#124C2312yes—
288C2×#124C2312yes—
289C2×#123C2312yes—
290C2×#123C2314yes—
291C2×#123C2311yescharacteristic
292C2×#123C2312yes—
293C2×C22⋊Q8C2312yes—
294C2×C22⋊Q8C2312yes—
295C2×C22⋊Q8C2312yes—
296C2×C22⋊Q8C2311yescharacteristic
297C2×C22⋊Q8C2312yes—
298C2×C22⋊Q8C2312yes—
299C2×#121C2312yes—
300C2×#121C2311yescharacteristic
301#520—44no—
302C2×C4×Q8C2311yescharacteristic
303C2×C4×Q8C2312yes—
304C2×C4×Q8C2311yescharacteristic
305C2×C4×Q8C2312yes—
306C2×C4×Q8C2312yes—
307C2×C4×Q8C2312yes—
308C2×C4×Q8C2312yes—
309C2×C4×Q8C2312yes—
310C2×C4×Q8C2312yes—
311C2×C4×Q8C2312yes—
312C2×C4×Q8C2312yes—
313C2×C4×Q8C2314yes—
314C2×C4×Q8C2312yes—
315C2×C4×D4C2312yes—
316C2×C4×D4C2312yes—
317C2×C4×D4C2314yes—
318C2×C4×D4C2311yescharacteristic
319C2×#117C2312yes—
320C2×#117C2311yescharacteristic
321C22×C4⋊C4C2312yes—
322C22×C4⋊C4C2312yes—
323C22×C4⋊C4C2311yescharacteristic
324C22×C4⋊C4C2312yes—
325C22×C42C2311yescharacteristic
326#401C2314yes—
327#400C2314yes—
328#400C2314yes—
329#400C2314yes—
330#400C2314yes—
331#400C2314yes—
332#400C2314yes—
333#400C2314yes—
334#400C2314yes—
335#400C2312yes—
336#400C2314yes—
337#400C2314yes—
338#400C2314yes—
339#400C2312yes—
340#400C2312yes—
341#400C2314yes—
342#400C2314yes—
343#400C2314yes—
344#400C2314yes—
345#400C2314yes—
346#400C2311yescharacteristic
347#400C2314yes—
348#400C2314yes—
349#400C2312yes—
350#400C2312yes—
351#400C2314yes—
352#400C2312yes—
353#400C2312yes—
354#399C2312yes—
355#399C2312yes—
356#399C2312yes—
357#399C2314yes—
358#399C2312yes—
359#399C2314yes—
360#399C2314yes—
361#399C2312yes—
362#399C2311yescharacteristic
363#399C2314yes—
364#398C2314yes—
365#398C2314yes—
366#398C2314yes—
367#398C2312yes—
368#398C2312yes—
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#398C2314yes—
387#398C2314yes—
388#398C2312yes—
389#398C2314yes—
390#398C2312yes—
391#398C2312yes—
392#398C2314yes—
393#398C2314yes—
394#398C2312yes—
395#398C2314yes—
396#398C2314yes—
397#398C2314yes—
398#398C2314yes—
399#398C2314yes—
400#398C2311yescharacteristic
401#398C2314yes—
402#398C2312yes—
403#398C2314yes—
404#398C2312yes—
405#398C2312yes—
406#398C2312yes—
407#397C2314yes—
408#397C2311yescharacteristic
409#397C2312yes—
410#397C2314yes—
411#397C2314yes—
412#397C2311yescharacteristic
413#397C2314yes—
414#397C2314yes—
415#397C2314yes—
416#397C2314yes—
417#397C2314yes—
418#397C2314yes—
419#397C2314yes—
420#397C2312yes—
421#397C2314yes—
422#397C2314yes—
423#397C2311yescharacteristic
424#397C2314yes—
425#397C2312yes—
426#397C2314yes—
427#396C2314yes—
428#396C2314yes—
429#396C2314yes—
430#396C2314yes—
431#396C2314yes—
432#396C2312yes—
433#396C2314yes—
434#396C2314yes—
435#396C2314yes—
436#396C2314yes—
437#396C2312yes—
438#395C2314yes—
439#395C2314yes—
440#395C2314yes—
441#395C2312yes—
442#395C2314yes—
443#395C2312yes—
444#394C2314yes—
445#394C2314yes—
446#394C2314yes—
447#394C2314yes—
448#394C2314yes—
449#394C2314yes—
450#394C2312yes—
451#394C2312yes—
452#393C2314yes—
453#393C2314yes—
454#393C2311yescharacteristic
455#393C2312yes—
456#393C2312yes—
457#393C2311yescharacteristic
458#393C2312yes—
459#391C2314yes—
460#391C2312yes—
461#391C2312yes—
462#391C2312yes—
463#391C2312yes—
464#391C2312yes—
465#391C2312yes—
466#391C2312yes—
467#391C2312yes—
468#391C2312yes—
469#391C2314yes—
470#391C2312yes—
471#391C2314yes—
472#391C2312yes—
473#391C2312yes—
474#391C2312yes—
475#391C2314yes—
476#391C2312yes—
477#391C2312yes—
478#391C2314yes—
479#391C2314yes—
480#391C2314yes—
481#391C2312yes—
482#391C2314yes—
483#391C2312yes—
484#391C2312yes—
485#390C2314yes—
486#390C2312yes—
487#390C2312yes—
488#390C2314yes—
489#390C2312yes—
490#390C2312yes—
491#389C2314yes—
492#389C2312yes—
493#389C2314yes—
494#389C2312yes—
495#389C2314yes—
496#389C2312yes—
497#389C2314yes—
498#389C2312yes—
499#389C2314yes—
500#389C2314yes—
501#389C2314yes—
502#389C2314yes—
503#389C2312yes—
504#389C2312yes—
505#389C2312yes—
506#389C2314yes—
507#389C2312yes—
508#389C2314yes—
509#389C2312yes—
510#389C2314yes—
511#389C2314yes—
512#389C2314yes—
513#389C2314yes—
514#389C2312yes—
515#389C2312yes—
516#389C2314yes—
517#389C2314yes—
518#389C2314yes—
519#389C2314yes—
520#389C2314yes—
521#389C2314yes—
522#389C2314yes—
523#389C2314yes—
524#389C2314yes—
525#389C2314yes—
526#389C2314yes—
527#389C2314yes—
528#389C2314yes—
529#389C2314yes—
530#389C2312yes—
531#389C2314yes—
532#389C2312yes—
533#388C2312yes—
534#388C2312yes—
535#388C2312yes—
536#388C2312yes—
537#388C2312yes—
538#388C2312yes—
539#388C2314yes—
540#388C2314yes—
541#388C2314yes—
542#388C2314yes—
543#388C2314yes—
544#388C2312yes—
545#388C2314yes—
546#388C2314yes—
547#388C2314yes—
548#388C2314yes—
549#388C2314yes—
550#388C2314yes—
551#388C2314yes—
552#388C2314yes—
553#388C2314yes—
554#388C2314yes—
555#388C2314yes—
556#388C2314yes—
557#388C2314yes—
558#388C2314yes—
559#388C2314yes—
560#388C2314yes—
561#388C2314yes—
562#388C2314yes—
563#388C2314yes—
564#388C2314yes—
565#387C2312yes—
566#387C2312yes—
567#387C2312yes—
568#387C2312yes—
569#387C2312yes—
570#387C2312yes—
571#387C2314yes—
572#387C2314yes—
573#387C2314yes—
574#387C2312yes—
575#387C2314yes—
576#387C2314yes—
577#387C2314yes—
578#387C2314yes—
579#387C2314yes—
580#387C2314yes—
581#387C2314yes—
582#387C2314yes—
583#387C2314yes—
584#387C2314yes—
585#387C2314yes—
586#387C2314yes—
587#387C2314yes—
588#387C2314yes—
589#387C2314yes—
590#387C2314yes—
591#387C2314yes—
592#387C2314yes—
593#387C2314yes—
594#387C2314yes—
595#387C2314yes—
596#387C2314yes—
597#387C2314yes—
598#387C2314yes—
599#387C2314yes—
600#387C2314yes—
601#387C2314yes—
602#387C2314yes—
603#387C2314yes—
604#387C2314yes—
605#387C2314yes—
606#387C2312yes—
607#387C2314yes—
608#387C2314yes—
609#387C2314yes—
610#387C2314yes—
611#387C2314yes—
612#387C2314yes—
613#387C2312yes—
614#387C2314yes—
615#387C2314yes—
616#386C2312yes—
617#386C2312yes—
618#386C2312yes—
619#386C2311yescharacteristic
620#386C2312yes—
621#385C2314yes—
622#385C2314yes—
623#385C2314yes—
624#385C2312yes—
625#385C2314yes—
626#385C2314yes—
627#385C2311yescharacteristic
628#385C2314yes—
629#385C2314yes—
630#385C2314yes—
631#385C2314yes—
632#385C2314yes—
633#385C2314yes—
634#385C2314yes—
635#385C2314yes—
636#385C2314yes—
637#385C2314yes—
638#385C2314yes—
639#385C2314yes—
640#385C2312yes—
641#385C2312yes—
642#385C2314yes—
643#384C2312yes—
644#384C2312yes—
645#384C2312yes—
646#384C2312yes—
647#384C2314yes—
648#384C2314yes—
649#383C2312yes—
650#383C2312yes—
651#383C2312yes—
652#383C2314yes—
653#383C2314yes—
654#383C2314yes—
655#382C2312yes—
656#382C2312yes—
657#382C2314yes—
658#382C2314yes—
659#382C2314yes—
660#382C2314yes—
661#382C2314yes—
662#381C2312yes—
663#381C2311yescharacteristic
664#381C2314yes—
665#380C2314yes—
666#380C2312yes—
667#380C2314yes—
668#380C2312yes—
669#380C2311yescharacteristic
670#380C2314yes—
671#380C2314yes—
672#380C2311yescharacteristic
673#380C2312yes—
674#380C2312yes—
675C4×C4⋊C4C2312yes—
676C4×C4⋊C4C2312yes—
677C4×C4⋊C4C2312yes—
678C4×C4⋊C4C2312yes—
679C4×C4⋊C4C2312yes—
680C4×C4⋊C4C2314yes—
681C4×C4⋊C4C2314yes—
682C4×C4⋊C4C2314yes—
683C4×C4⋊C4C2314yes—
684C4×C4⋊C4C2314yes—
685C4×C4⋊C4C2312yes—
686C4×C4⋊C4C2312yes—
687C4×C4⋊C4C2312yes—
688C4×C4⋊C4C2314yes—
689C4×C4⋊C4C2314yes—
690C4×C4⋊C4C2314yes—
691C4×C4⋊C4C2311yescharacteristic
692C4×C4⋊C4C2312yes—
693C4×C4⋊C4C2314yes—
694C4×C4⋊C4C2314yes—
695C4×C4⋊C4C2314yes—
696C4×C4⋊C4C2312yes—
697C4×C4⋊C4C2312yes—
698C4×C22⋊C4C2311yescharacteristic
699C4×C22⋊C4C2311yescharacteristic
700C4×C22⋊C4C2312yes—
701C4×C22⋊C4C2312yes—
702C4×C22⋊C4C2312yes—
703C4×C22⋊C4C2312yes—
704C4×C22⋊C4C2314yes—
705C4×C22⋊C4C2314yes—
706C4×C22⋊C4C2314yes—
707C4×C22⋊C4C2314yes—
708C4×C22⋊C4C2312yes—
709C4×C22⋊C4C2312yes—
710C4×C22⋊C4C2314yes—
711C4×C22⋊C4C2314yes—
712C4×C22⋊C4C2314yes—
713#376C2311yescharacteristic
714#376C2314yes—
715#376C2314yes—
716C43C2312yes—
717C2×#41—24no—
718C2×#41—44no—
719C22×Q8—24no—
720C22×Q8—42no—
721C22×Q8—44no—
722C22×Q8—44no—
723C22×Q8C2412yes—
724C22×Q8C2412yes—
725C22×Q8C2411yescharacteristic
726C22×Q8C2412yes—
727C22×Q8C2411yescharacteristic
728C22×Q8C2411yescharacteristic
729C22×Q8C2412yes—
730C22×Q8C2412yes—
731C22×D4C2411yescharacteristic
732C22×D4C2412yes—
733C22×D4C2412yes—
734C22×D4C2411yescharacteristic
735C23×C4C2411yescharacteristic
736C23×C4C2411yescharacteristic
737C23×C4C2411yescharacteristic
738C23×C4C2412yes—
739C23×C4C2411yescharacteristic
740C23×C4C2412yes—
741C23×C4C2412yes—
742C23×C4C2412yes—
743C23×C4C2414yes—
744C4⋊Q8—28no—
745C4⋊Q8—28no—
746C4⋊Q8—28no—
747C4⋊Q8—44no—
748C4⋊Q8—44no—
749C4⋊Q8—44no—
750C4⋊Q8—44no—
751C4⋊Q8—42no—
752C4⋊Q8—48no—
753#126—28no—
754#126—216no—
755#126—44no—
756#126—48no—
757#125—44no—
758#125—48no—
759#125—44no—
760#125—48no—
761#125—48no—
762#125—48no—
763#124—44no—
764#124—44no—
765#124—44no—
766#124—42no—
767#123—48no—
768#123—44no—
769#123—44no—
770#123—42no—
771C22⋊Q8—28no—
772C22⋊Q8—44no—
773C22⋊Q8—44no—
774C22⋊Q8—44no—
775C22⋊Q8—42no—
776C22⋊Q8—44no—
777#121—42no—
778#121—44no—
779C4×Q8—28no—
780C4×Q8—24no—
781C4×Q8—44no—
782C4×Q8—42no—
783C4×Q8—48no—
784C4×Q8—44no—
785C4×Q8—44no—
786C4×Q8—44no—
787C4×Q8—44no—
788C4×Q8—44no—
789C4×Q8—44no—
790C4×Q8—44no—
791C4×Q8—44no—
792C4×D4—48no—
793C4×D4—44no—
794C4×D4—44no—
795C4×D4—42no—
796#117—44no—
797#117—42no—
798C2×C4⋊C4—42no—
799C2×C4⋊C4—44no—
800C2×C4⋊C4—44no—
801C2×C4⋊C4—44no—
802C2×C4⋊C4C2412yes—
803C2×C4⋊C4C2414yes—
804C2×C4⋊C4C2414yes—
805C2×C4⋊C4C2414yes—
806C2×C4⋊C4C2411yescharacteristic
807C2×C4⋊C4C2412yes—
808C2×C4⋊C4C2414yes—
809C2×C4⋊C4C2412yes—
810C2×C4⋊C4C2412yes—
811C2×C4⋊C4C2412yes—
812C2×C4⋊C4C2412yes—
813C2×C4⋊C4C2412yes—
814C2×C4⋊C4C2414yes—
815C2×C4⋊C4C2412yes—
816C2×C4⋊C4C2412yes—
817C2×C4⋊C4C2414yes—
818C2×C4⋊C4C2414yes—
819C2×C4⋊C4C2412yes—
820C2×C4⋊C4C2412yes—
821C2×C4⋊C4C2412yes—
822C2×C4⋊C4C2412yes—
823C2×C4⋊C4C2411yescharacteristic
824C2×C4⋊C4C2414yes—
825C2×C4⋊C4C2414yes—
826C2×C4⋊C4C2411yescharacteristic
827C2×C4⋊C4C2411yescharacteristic
828C2×C4⋊C4C2412yes—
829C2×C4⋊C4C2412yes—
830C2×C4⋊C4C2414yes—
831C2×C4⋊C4C2414yes—
832C2×C4⋊C4C2412yes—
833C2×C4⋊C4C2412yes—
834C2×C4⋊C4C2414yes—
835C2×C4⋊C4C2412yes—
836C2×C4⋊C4C2411yescharacteristic
837C2×C4⋊C4C2414yes—
838C2×C4⋊C4C2412yes—
839C2×C4⋊C4C2414yes—
840C2×C4⋊C4C2414yes—
841C2×C4⋊C4C2414yes—
842C2×C4⋊C4C2414yes—
843C2×C4⋊C4C2414yes—
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⋊C4C2412yes—
858C2×C4⋊C4C2414yes—
859C2×C4⋊C4C2412yes—
860C2×C4⋊C4C2414yes—
861C2×C4⋊C4C2414yes—
862C2×C4⋊C4C2414yes—
863C2×C4⋊C4C2414yes—
864C2×C4⋊C4C2414yes—
865C2×C4⋊C4C2414yes—
866C2×C4⋊C4C2412yes—
867C2×C4⋊C4C2412yes—
868C2×C4⋊C4C2412yes—
869C2×C4⋊C4C2414yes—
870C2×C4⋊C4C2412yes—
871C2×C4⋊C4C2414yes—
872C2×C4⋊C4C2412yes—
873C2×C22⋊C4C2412yes—
874C2×C22⋊C4C2412yes—
875C2×C22⋊C4C2414yes—
876C2×C22⋊C4C2412yes—
877C2×C22⋊C4C2412yes—
878C2×C22⋊C4C2411yescharacteristic
879C2×C22⋊C4C2412yes—
880C2×C22⋊C4C2412yes—
881C2×C22⋊C4C2412yes—
882C2×C22⋊C4C2414yes—
883C2×C22⋊C4C2414yes—
884C2×C22⋊C4C2412yes—
885C2×C22⋊C4C2414yes—
886C2×C22⋊C4C2414yes—
887C2×C22⋊C4C2412yes—
888C2×C22⋊C4C2411yescharacteristic
889C2×C22⋊C4C2411yescharacteristic
890C2×C22⋊C4C2412yes—
891C2×C22⋊C4C2412yes—
892C2×C22⋊C4C2412yes—
893C2×C22⋊C4C2412yes—
894C2×C22⋊C4C2414yes—
895C2×C22⋊C4C2414yes—
896C2×C22⋊C4C2414yes—
897C2×C22⋊C4C2412yes—
898C2×C22⋊C4C2414yes—
899C2×C22⋊C4C2412yes—
900C2×C22⋊C4C2414yes—
901C2×C22⋊C4C2414yes—
902C2×C22⋊C4C2414yes—
903C2×C22⋊C4C2414yes—
904C2×C22⋊C4C2414yes—
905C2×C22⋊C4C2411yescharacteristic
906C2×C22⋊C4C2412yes—
907C2×C22⋊C4C2414yes—
908C2×C42—42no—
909C2×C42C2414yes—
910C2×C42C2412yes—
911C2×C42C2412yes—
912C2×C42C2411yescharacteristic
913C2×C42C2412yes—
914C2×C42C2412yes—
915C2×C42C2412yes—
916C2×C42C2412yes—
917C2×C42C2412yes—
918C2×C42C2412yes—
919C2×C42C2414yes—
920C2×C42C2412yes—
921C2×C42C2414yes—
922C2×C42C2414yes—
923C2×C42C2414yes—
924C2×C42C2414yes—
925C2×C42C2414yes—
926C2×C42C2414yes—
927C2×C42C2414yes—
928C2×C42C2412yes—
929C2×C42C2414yes—
930C2×C42C2412yes—
931C2×C42C2412yes—
932C2×C42C2414yes—
933C2×C42C2412yes—
934#95C2412yes—
935#95C2414yes—
936#95C2414yes—
937#95C2414yes—
938#95C2411yescharacteristic
939#95C2412yes—
940#95C2414yes—
941#95C2411yescharacteristic
942#95C2414yes—
943#95C2414yes—
944#95C2414yes—
945#95C2411yescharacteristic
946#95C2412yes—
947#95C2414yes—
948#95C2412yes—
949#95C2414yes—
950#95C2414yes—
951#95C2412yes—
952#95C2414yes—
953#95C2411yescharacteristic
954#95C2414yes—
955#95C2412yes—
956#95C2412yes—
957#95C2412yes—
958#95C2414yes—
959#95C2414yes—
960#95C2412yes—
961#95C2412yes—
962#95C2412yes—
963#95C2412yes—
964#95C2412yes—
965#95C2414yes—
966#95C2412yes—
967#95C2414yes—
968#95C2414yes—
969#95C2412yes—
970#95C2414yes—
971#95C2414yes—
972#95C2414yes—
973#95C2412yes—
974#95C2414yes—
975#95C2412yes—
976#95C2412yes—
977#95C2414yes—
978#95C2414yes—
979#95C2412yes—
980#95C2414yes—
981#95C2414yes—
982#95C2414yes—
983#95C2414yes—
984#95C2412yes—
985#95C2412yes—
986#95C2412yes—
987#95C2414yes—
988#95C2412yes—
989#95C2412yes—
990#95C2412yes—
991#95C2412yes—
992#95C2414yes—
993#95C2414yes—
994#95C2412yes—
995#95C2414yes—
996#95C2414yes—
997#95C2414yes—
998#95C2412yes—
999#95C2414yes—
1000#95C2414yes—
1001#95C2414yes—
1002#95C2412yes—
1003#95C2414yes—
1004#95C2414yes—
1005#95C2414yes—
1006#95C2414yes—
1007#95C2414yes—
1008#95C2414yes—
1009#95C2414yes—
1010#95C2414yes—
1011C24C2511yescharacteristic
1012C24C2512yes—
1013C24C2511yescharacteristic
1014#41—416no—
1015C2×Q8—24no—
1016C2×Q8—24no—
1017C2×Q8—22no—
1018C2×Q8—24no—
1019C2×Q8—24no—
1020C2×Q8—24no—
1021C2×Q8—24no—
1022C2×Q8—24no—
1023C2×Q8—24no—
1024C2×Q8—24no—
1025C2×Q8—24no—
1026C2×Q8—24no—
1027C2×Q8—24no—
1028C2×Q8—41no—
1029C2×Q8—42no—
1030C2×Q8—42no—
1031C2×Q8—44no—
1032C2×Q8—44no—
1033C2×Q8—88no—
1034C2×Q8—88no—
1035C2×Q8H(5,𝔽2)14yes—
1036C2×D4—24no—
1037C2×D4—22no—
1038C2×D4—24no—
1039C2×D4—22no—
1040C2×D4—24no—
1041C2×D4—44no—
1042C2×D4—42no—
1043C2×D4—41no—
1044C2×D4—41no—
1045C2×D4—42no—
1046C22×C4—22no—
1047C22×C4—22no—
1048C22×C4—24no—
1049C22×C4—22no—
1050C22×C4—24no—
1051C22×C4—24no—
1052C22×C4—24no—
1053C22×C4—24no—
1054C22×C4—41no—
1055C22×C4—41no—
1056C22×C4—41no—
1057C22×C4—44no—
1058C22×C4—42no—
1059C22×C4—44no—
1060C22×C4—44no—
1061C22×C4—42no—
1062C22×C4—44no—
1063C22×C4—42no—
1064C22×C4—44no—
1065C22×C4—42no—
1066C22×C4—44no—
1067C22×C4C2512yes—
1068C22×C4C2514yes—
1069C22×C4C2512yes—
1070C22×C4C2511yescharacteristic
1071C22×C4C2512yes—
1072C22×C4C2511yescharacteristic
1073C22×C4C2512yes—
1074C22×C4C2514yes—
1075C22×C4C2512yes—
1076C22×C4C2512yes—
1077C22×C4C2514yes—
1078C22×C4C2514yes—
1079C22×C4C2514yes—
1080C22×C4C2512yes—
1081C22×C4C2512yes—
1082C22×C4C2511yescharacteristic
1083C22×C4C2512yes—
1084C22×C4C2511yescharacteristic
1085C22×C4C2512yes—
1086C22×C4C2512yes—
1087C22×C4C2514yes—
1088C22×C4C2512yes—
1089C22×C4C2512yes—
1090C22×C4C2512yes—
1091C22×C4C2512yes—
1092C22×C4C2511yescharacteristic
1093C4⋊C4—24no—
1094C4⋊C4—28no—
1095C4⋊C4—28no—
1096C4⋊C4—28no—
1097C4⋊C4—22no—
1098C4⋊C4—24no—
1099C4⋊C4—28no—
1100C4⋊C4—28no—
1101C4⋊C4—24no—
1102C4⋊C4—24no—
1103C4⋊C4—24no—
1104C4⋊C4—24no—
1105C4⋊C4—28no—
1106C4⋊C4—28no—
1107C4⋊C4—24no—
1108C4⋊C4—24no—
1109C4⋊C4—24no—
1110C4⋊C4—24no—
1111C4⋊C4—24no—
1112C4⋊C4—24no—
1113C4⋊C4—42no—
1114C4⋊C4—41no—
1115C4⋊C4—44no—
1116C4⋊C4—44no—
1117C4⋊C4—42no—
1118C4⋊C4—42no—
1119C4⋊C4—44no—
1120C4⋊C4—42no—
1121C4⋊C4—44no—
1122C4⋊C4—44no—
1123C4⋊C4—42no—
1124C4⋊C4—41no—
1125C4⋊C4—42no—
1126C4⋊C4—41no—
1127C4⋊C4—44no—
1128C4⋊C4—44no—
1129C4⋊C4—44no—
1130C4⋊C4—44no—
1131C4⋊C4—42no—
1132C4⋊C4—42no—
1133C4⋊C4—42no—
1134C4⋊C4—41no—
1135C4⋊C4—42no—
1136C4⋊C4—44no—
1137C4⋊C4—44no—
1138C4⋊C4—44no—
1139C4⋊C4—42no—
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—42no—
1152C4⋊C4—44no—
1153C4⋊C4—42no—
1154C4⋊C4—44no—
1155C4⋊C4—42no—
1156C4⋊C4—44no—
1157C4⋊C4—44no—
1158C4⋊C4—42no—
1159C4⋊C4—44no—
1160C4⋊C4—44no—
1161C4⋊C4—44no—
1162C4⋊C4—44no—
1163C4⋊C42−1+418yes—
1164C22⋊C4—24no—
1165C22⋊C4—28no—
1166C22⋊C4—24no—
1167C22⋊C4—22no—
1168C22⋊C4—24no—
1169C22⋊C4—24no—
1170C22⋊C4—24no—
1171C22⋊C4—24no—
1172C22⋊C4—24no—
1173C22⋊C4—28no—
1174C22⋊C4—28no—
1175C22⋊C4—28no—
1176C22⋊C4—24no—
1177C22⋊C4—41no—
1178C22⋊C4—44no—
1179C22⋊C4—42no—
1180C22⋊C4—44no—
1181C22⋊C4—42no—
1182C22⋊C4—41no—
1183C22⋊C4—41no—
1184C22⋊C4—42no—
1185C22⋊C4—42no—
1186C22⋊C4—42no—
1187C22⋊C4—42no—
1188C22⋊C4—44no—
1189C22⋊C4—44no—
1190C22⋊C4—44no—
1191C22⋊C4—44no—
1192C22⋊C4—42no—
1193C22⋊C4—44no—
1194C22⋊C4—42no—
1195C22⋊C4—44no—
1196C22⋊C4—44no—
1197C22⋊C4—44no—
1198C22⋊C4—44no—
1199C42—24no—
1200C42—28no—
1201C42—24no—
1202C42—24no—
1203C42—22no—
1204C42—24no—
1205C42—28no—
1206C42—24no—
1207C42—24no—
1208C42—24no—
1209C42—24no—
1210C42—24no—
1211C42—42no—
1212C42—42no—
1213C42—44no—
1214C42—42no—
1215C42—44no—
1216C42—44no—
1217C42—44no—
1218C42—44no—
1219C42—44no—
1220C42—44no—
1221C42—44no—
1222C42—44no—
1223C42—42no—
1224C23—21no—
1225C23—22no—
1226C23—22no—
1227C23—21no—
1228C23—22no—
1229C23—21no—
1230C23—22no—
1231C23—24no—
1232C23—22no—
1233C23—21no—
1234C23—22no—
1235C23—24no—
1236C23—21no—
1237C23—22no—
1238C23#58512yes—
1239C23C2611yescharacteristic
1240Q8—28no—
1241Q8—48no—
1242Q8—44no—
1243Q8—48no—
1244Q8—48no—
1245Q8—44no—
1246Q8—84no—
1247Q8—84no—
1248D4—48no—
1249D4—44no—
1250D4—84no—
1251D4—82no—
1252C2×C4—22no—
1253C2×C4—22no—
1254C2×C4—22no—
1255C2×C4—22no—
1256C2×C4—22no—
1257C2×C4—24no—
1258C2×C4—22no—
1259C2×C4—21no—
1260C2×C4—22no—
1261C2×C4—22no—
1262C2×C4—24no—
1263C2×C4—22no—
1264C2×C4—21no—
1265C2×C4—22no—
1266C2×C4—22no—
1267C2×C4—21no—
1268C2×C4—24no—
1269C2×C4—24no—
1270C2×C4—22no—
1271C2×C4—21no—
1272C2×C4—22no—
1273C2×C4—24no—
1274C2×C4—22no—
1275C2×C4—24no—
1276C2×C4—22no—
1277C2×C4—22no—
1278C2×C4—24no—
1279C2×C4—22no—
1280C2×C4—22no—
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—24no—
1290C2×C4—24no—
1291C2×C4—22no—
1292C2×C4—22no—
1293C2×C4—24no—
1294C2×C4—22no—
1295C2×C4—24no—
1296C2×C4—24no—
1297C2×C4—24no—
1298C2×C4—24no—
1299C2×C4—24no—
1300C2×C4—22no—
1301C2×C4—22no—
1302C2×C4—24no—
1303C2×C4—24no—
1304C2×C4—24no—
1305C2×C4—22no—
1306C2×C4—21no—
1307C2×C4—22no—
1308C2×C4—22no—
1309C2×C4—22no—
1310C2×C4—24no—
1311C2×C4—21no—
1312C2×C4—22no—
1313C2×C4—24no—
1314C2×C4—22no—
1315C2×C4—22no—
1316C2×C4—22no—
1317C2×C4—22no—
1318C2×C4—44no—
1319C2×C4—48no—
1320C2×C4—44no—
1321C2×C4—44no—
1322C2×C4—44no—
1323C2×C4—84no—
1324C2×C4—84no—
1325C2×C4—162no—
1326C2×C4—164no—
1327C2×C4C2×H(5,𝔽2)14yes—
1328C2×C4C2×H(5,𝔽2)12yes—
1329C2×C4C2×2−1+414yes—
1330C2×C4C2×2−1+414yes—
1331C2×C4C2×2−1+414yes—
1332C2×C4#58514yes—
1333C22—24no—
1334C22—22no—
1335C22—41no—
1336C22—41no—
1337C22—42no—
1338C22—42no—
1339C22—41no—
1340C22—42no—
1341C22—41no—
1342C22—42no—
1343C22—44no—
1344C22—42no—
1345C22—41no—
1346C22—42no—
1347C22—44no—
1348C22C22×H(5,𝔽2)11yescharacteristic
1349C22C22×2−1+412yes—
1350C22C2×#58512yes—
1351C22C2×#58511yescharacteristic
1352C222−1+611yescharacteristic
1353C4—24no—
1354C4—24no—
1355C4—24no—
1356C4—24no—
1357C4—41no—
1358C4—41no—
1359C4—44no—
1360C4—42no—
1361C4—44no—
1362C4—41no—
1363C4—42no—
1364C4—42no—
1365C4—44no—
1366C4—42no—
1367C4—42no—
1368C4—44no—
1369C4—42no—
1370C4—42no—
1371C4—44no—
1372C4—42no—
1373C4—42no—
1374C4—41no—
1375C4—42no—
1376C4—44no—
1377C4—42no—
1378C4#353314yes—
1379C2—42no—
1380C2—82no—
1381C2—81no—
1382C2C2×#353311yescharacteristic
1383C2#6291911yescharacteristic
1384C2#6295612yes—
1385C2#6301611yescharacteristic
1386C2#6303312yes—
subgroupG/H
center, commutator, Frattini, socle, cosocleC23C26
prime radicalC2×#548C22
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23 ◁ G
LECSG ▷ C23 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #59828C2semidirect
2. #59694C2semidirect
3. #59631C2semidirect
4. #59481C2semidirect
5. #59144C2semidirect
6. #58931C2semidirect
7. #55843C2semidirect
8. #55138C2semidirect
9. #53886C2semidirect
10. #53013C2semidirect
11. #53008C2semidirect
12. #52300C2semidirect
13. #47737C2semidirect
14. #47183C2semidirect
15. #45419C2semidirect
16. #45411C2semidirect
17. #44671C2semidirect
18. #44371C2semidirect
20. #42702C2semidirect
21. #41769C2semidirect
22. #41190C2semidirect
23. #40225C2semidirect
24. #40200C2semidirect
25. #40022C2semidirect
27. #39245C2semidirect
29. #35712C2semidirect

Maximal subgroups

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

subgroupindex
#598282
#596942
#596312
#594812
#591442
#589312
#558432
#551382
#538862
#530132
#530082
#523002
#477372
#471832
#454192
#454112
#446712
#443712
#428152
#427022
#417692
#411902
#402252
#402002
#400222
#397212
#392452
#359962
#357122