Finite Group Databasebeta

← #7660759

Subgroups — #7660759

Order 512.

4274 conjugacy classes of subgroups.

The subgroup lattice has 1378 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#52279C211yesmaximal, characteristic
2#52267C212yesmaximal, complemented
3#42772C212yesmaximal, complemented
4#42710C212yesmaximal, complemented
5#42451C212yesmaximal, complemented
6#42320C214yesmaximal, complemented
7#41577C214yesmaximal, complemented
8#40860C214yesmaximal, complemented
9#40071C212yesmaximal, complemented
10#40065C214yesmaximal, complemented
11#39656C212yesmaximal, complemented
12#39640C211yesmaximal, characteristic, complemented
13#39637C212yesmaximal, complemented
14#39632C211yesmaximal, characteristic
15#38520C214yesmaximal
16#38472C212yesmaximal, complemented
17#37398C212yesmaximal, complemented
18#37323C211yesmaximal, characteristic, complemented
19#37146C212yesmaximal, complemented
20#36834C214yesmaximal, complemented
21#36552C212yesmaximal, complemented
22#36481C211yesmaximal, characteristic, complemented
23#36272C211yesmaximal, characteristic
24#36256C212yesmaximal, complemented
25#35997C212yesmaximal, complemented
26#35919C212yesmaximal, complemented
27#35870C212yesmaximal, complemented
28#34304C212yesmaximal, complemented
29#34254C211yesmaximal, characteristic, complemented
30C2×#552C2212yes—
31C2×#519C2211yescharacteristic
32#2863C2212yes—
33#2859C2212yes—
34#2857C2212yes—
35#2857C2211yescharacteristic
36#2857C2211yescharacteristic
37#2855C2212yes—
38#2851C2214yes—
39#2851C2214yes—
40#2839C2214yes—
41#2839C2214yes—
42#2834C2214yes—
43#2810C2211yescharacteristic
44#2810C2212yes—
45#2809C2211yescharacteristic
46#2809C2212yes—
47#2807C2214yes—
48#2806C2212yes—
49#2806C2212yes—
50#2805C2214yes—
51#2805C2212yes—
52#2805C2212yes—
53#2804C2212yes—
54#2802C2214yes—
55#2794C2214yes—
56#2791C2214yes—
57#2790C2214yes—
58#2788C2214yes—
59#2788C2214yes—
60#2787C2212yes—
61#2787C2212yes—
62#2787C2214yes—
63#2780C2214yes—
64#2776C2214yes—
65#2774C2214yes—
66#2774C2214yes—
67#2771C2214yes—
68#2771C2212yes—
69#2770C2214yes—
70#2770C2214yes—
71#2768C2214yes—
72#2768C2214yes—
73#2767C2214yes—
74#2766C2214yes—
75#2766C2214yes—
76#2765C2214yes—
77#2762C2214yes—
78#2750C2214yes—
79#2750C2212yes—
80#2747C2214yes—
81#2745C2214yes—
82#2743C2214yes—
83#2732C2211yescharacteristic
84#2729C2214yes—
85#2728C2212yes—
86#2726C2212yes—
87#2726C2214yes—
88#2724C2211yescharacteristic
89#2719C2214yes—
90#2719C2214yes—
91#2708C2212yes—
92#2690C2214yes—
93#2667C2214yes—
94#2655C2214yes—
95#2655C2214yes—
96#2655C2214yes—
97#2655C2214yes—
98#2655C2214yes—
99#2652C2214yes—
100#2652C2214yes—
101#2647C2214yes—
102#2646C2212yes—
103#2646C2212yes—
104#2645C2212yes—
105#2642C2212yes—
106#2634C2214yes—
107#2633C2214yes—
108#2625C2212yes—
109#2611C2214yes—
110#2606C2214yes—
111#2599C2214yes—
112#2590C2214yes—
113#2590C2214yes—
114#2590C2214yes—
115#2588C2214yes—
116#2585C2214yes—
117#2585C2214yes—
118#2584C2214yes—
119#2575C2214yes—
120#2573C2214yes—
121#2568C2212yes—
122#2565C2212yes—
123#2553C2214yes—
124#2552C2211yescharacteristic
125#2552C2211yescharacteristic
126#2552C2212yes—
127#2546C2212yes—
128#2546C2211yescharacteristic
129#2542C2211yescharacteristic
130#2533C2214yes—
131#2533C2214yes—
132#2530C2214yes—
133#2528C2214yes—
134#2528C2214yes—
135#2528C2214yes—
136#2527C2214yes—
137#2527C2214yes—
138#2524C2214yes—
139#2522C2214yes—
140#2522C2214yes—
141#2515C2214yes—
142#2514C2212yes—
143#2511C2212yes—
144#2511C2212yes—
145#2511C2212yes—
146#2511C2212yes—
147#2508C2214yes—
148#2507C2214yes—
149#2507C2212yes—
150#2506C2212yes—
151#2506C2214yes—
152#2506C2212yes—
153#2505C2214yes—
154#2505C2214yes—
155#2505C2214yes—
156#2502C2212yes—
157#2502C2212yes—
158#2496C2212yes—
159#2494C2212yes—
160#2493C2214yes—
161#2492C2212yes—
162#2489C2212yes—
163#2489C2212yes—
164#2478C2214yes—
165#2478C2214yes—
166#2475C2214yes—
167#2475C2214yes—
168#2470C2214yes—
169#2470C2214yes—
170#2460C2214yes—
171#2453C2212yes—
172#2453C2214yes—
173#2453C2214yes—
174#2453C2212yes—
175#2451C2212yes—
176#2450C2214yes—
177#2446C2212yes—
178#2446C2212yes—
179#2446C2212yes—
180#2442C2212yes—
181#2441C2212yes—
182#2434C2212yes—
183#2429C2212yes—
184#2429C2212yes—
185#2429C2212yes—
186#2429C2212yes—
187#2423C2212yes—
188#2423C2212yes—
189#2422C2212yes—
190#2419C2214yes—
191#2417C2212yes—
192#2415C2212yes—
193#2409C2212yes—
194#2402C2214yes—
195#2402C2212yes—
196#2401C2212yes—
197#2396C2214yes—
198#2396C2214yes—
199#2395C2212yes—
200#2373C2214yes—
201#2370C2214yes—
202#2370C2212yes—
203#2370C2212yes—
204#2365C2211yescharacteristic
205#2365C2212yes—
206#2365C2212yes—
207#2365C2211yescharacteristic
208#2360C2212yes—
209#2360C2212yes—
210#2360C2212yes—
211#2360C2212yes—
212#2360C2212yes—
213#2359C2214yes—
214#2356C2212yes—
215#2356C2212yes—
216#2355C2212yes—
217#2355C2212yes—
218#2355C2212yes—
219Q8×C4⋊C4C2211yescharacteristic
220D4×C4⋊C4C2212yes—
221D4×C4⋊C4C2211yescharacteristic
222#2347C2212yes—
223#2344C2212yes—
224#2343C2214yes—
225#2343C2214yes—
226#2343C2214yes—
227#2336C2214yes—
228#2335C2214yes—
229#2334C2214yes—
230#2331C2214yes—
231#2330C2212yes—
232#2329C2212yes—
233#2325C2212yes—
234#2323C2212yes—
235#2320C2212yes—
236#2320C2212yes—
237#2317C2211yescharacteristic
238#2310C2211yescharacteristic
239C4×C4⋊Q8C2212yes—
240C4×C22⋊Q8C2212yes—
241C4×C22⋊Q8C2214yes—
242C4×C22⋊Q8C2211yescharacteristic
243C4×C22⋊Q8C2212yes—
244C4×#123C2214yes—
245C4×#123C2212yes—
246C4×#121C2211yescharacteristic
247#2296C2214yes—
248#2296C2211yescharacteristic
249#2295C2212yes—
250#2295C2212yes—
251C2×#391C2211yescharacteristic
252#2293C2212yes—
253#2290C2212yes—
254#2290C2214yes—
255#2276C2212yes—
256#2274C2211yescharacteristic
257C4×#117C2211yescharacteristic
258C2×C4×C4⋊C4C2212yes—
259C23×Q8C2311yescharacteristic
260#552—216no—
261C2×C4⋊Q8C2312yes—
262C2×C4⋊Q8C2312yes—
263C2×C4⋊Q8C2311yescharacteristic
264C2×C4⋊Q8C2311yescharacteristic
265C2×C4⋊Q8C2312yes—
266C2×#126C2314yes—
267C2×#125C2314yes—
268C2×#125C2312yes—
269C2×#125C2312yes—
270C2×#125C2314yes—
271C2×#125C2314yes—
272C2×#125C2314yes—
273C2×#123C2312yes—
274C2×#123C2314yes—
275C2×C22⋊Q8C2312yes—
276C2×C22⋊Q8C2311yescharacteristic
277C2×C22⋊Q8C2312yes—
278C2×C22⋊Q8C2312yes—
279C2×C22⋊Q8C2312yes—
280C2×C22⋊Q8C2312yes—
281C2×C22⋊Q8C2312yes—
282C2×C22⋊Q8C2312yes—
283C2×#121C2311yescharacteristic
284#519—28no—
285C2×C4×Q8C2312yes—
286C2×C4×Q8C2312yes—
287C2×C4×Q8C2312yes—
288C2×C4×Q8C2312yes—
289C2×C4×Q8C2312yes—
290C2×C4×Q8C2312yes—
291C2×C4×Q8C2311yescharacteristic
292C2×C4×Q8C2312yes—
293C2×C4×Q8C2312yes—
294C2×C4×Q8C2312yes—
295C2×C4×D4C2312yes—
296C2×C4×D4C2312yes—
297C2×C4×D4C2311yescharacteristic
298C2×C4×D4C2314yes—
299C2×#117C2311yescharacteristic
300C2×#117C2314yes—
301C2×#117C2314yes—
302C2×#117C2311yescharacteristic
303C2×#117C2311yescharacteristic
304C2×#117C2314yes—
305C2×#117C2311yescharacteristic
306C22×C4⋊C4C2312yes—
307C22×C4⋊C4C2311yescharacteristic
308C22×C4⋊C4C2312yes—
309C22×C42C2312yes—
310C22×C42C2311yescharacteristic
311C22×C42C2314yes—
312#401C2314yes—
313#401C2314yes—
314#401C2314yes—
315#401C2312yes—
316#400C2314yes—
317#400C2314yes—
318#400C2314yes—
319#400C2314yes—
320#400C2314yes—
321#400C2314yes—
322#400C2312yes—
323#400C2312yes—
324#400C2314yes—
325#400C2314yes—
326#400C2314yes—
327#400C2314yes—
328#400C2314yes—
329#400C2314yes—
330#400C2314yes—
331#400C2314yes—
332#400C2314yes—
333#400C2312yes—
334#400C2314yes—
335#400C2314yes—
336#400C2314yes—
337#400C2312yes—
338#400C2314yes—
339#400C2314yes—
340#400C2314yes—
341#400C2314yes—
342#400C2314yes—
343#400C2312yes—
344#400C2314yes—
345#400C2314yes—
346#400C2314yes—
347#400C2312yes—
348#400C2312yes—
349#400C2314yes—
350#400C2314yes—
351#400C2314yes—
352#400C2314yes—
353#400C2312yes—
354#399C2314yes—
355#399C2314yes—
356#399C2314yes—
357#399C2312yes—
358#398C2314yes—
359#398C2314yes—
360#398C2314yes—
361#398C2314yes—
362#398C2314yes—
363#398C2314yes—
364#398C2314yes—
365#398C2314yes—
366#398C2314yes—
367#398C2314yes—
368#398C2314yes—
369#398C2314yes—
370#398C2314yes—
371#398C2314yes—
372#398C2312yes—
373#398C2314yes—
374#398C2312yes—
375#398C2314yes—
376#398C2314yes—
377#398C2314yes—
378#398C2314yes—
379#398C2312yes—
380#398C2314yes—
381#398C2314yes—
382#398C2314yes—
383#398C2314yes—
384#398C2314yes—
385#398C2314yes—
386#398C2314yes—
387#398C2314yes—
388#398C2314yes—
389#398C2314yes—
390#398C2312yes—
391#398C2314yes—
392#398C2312yes—
393#397C2314yes—
394#397C2312yes—
395#397C2312yes—
396#397C2314yes—
397#397C2314yes—
398#397C2312yes—
399#397C2314yes—
400#397C2314yes—
401#397C2314yes—
402#397C2312yes—
403#397C2312yes—
404#397C2312yes—
405#396C2314yes—
406#396C2312yes—
407#396C2314yes—
408#396C2314yes—
409#396C2314yes—
410#396C2314yes—
411#395C2314yes—
412#395C2314yes—
413#395C2314yes—
414#395C2314yes—
415#394C2312yes—
416#394C2314yes—
417#394C2312yes—
418#393C2314yes—
419#393C2314yes—
420#391C2311yescharacteristic
421#391C2312yes—
422#391C2312yes—
423#391C2312yes—
424#391C2312yes—
425#391C2312yes—
426#391C2312yes—
427#391C2312yes—
428#391C2314yes—
429#391C2312yes—
430#391C2312yes—
431#391C2312yes—
432#391C2312yes—
433#391C2312yes—
434#391C2312yes—
435#391C2312yes—
436#391C2314yes—
437#391C2314yes—
438#391C2312yes—
439#391C2312yes—
440#391C2312yes—
441#391C2312yes—
442#391C2312yes—
443#391C2312yes—
444#391C2312yes—
445#391C2312yes—
446#390C2312yes—
447#390C2311yescharacteristic
448#389C2314yes—
449#389C2314yes—
450#389C2312yes—
451#389C2312yes—
452#389C2314yes—
453#389C2311yescharacteristic
454#389C2311yescharacteristic
455#389C2314yes—
456#389C2312yes—
457#389C2314yes—
458#389C2314yes—
459#389C2314yes—
460#389C2314yes—
461#389C2314yes—
462#389C2314yes—
463#389C2314yes—
464#389C2314yes—
465#389C2314yes—
466#389C2314yes—
467#389C2314yes—
468#389C2312yes—
469#389C2312yes—
470#389C2314yes—
471#389C2312yes—
472#389C2312yes—
473#389C2314yes—
474#389C2314yes—
475#389C2312yes—
476#389C2314yes—
477#389C2314yes—
478#389C2314yes—
479#389C2312yes—
480#389C2312yes—
481#389C2312yes—
482#389C2312yes—
483#389C2312yes—
484#389C2314yes—
485#389C2312yes—
486#389C2311yescharacteristic
487#389C2314yes—
488#389C2311yescharacteristic
489#389C2312yes—
490#389C2312yes—
491#389C2312yes—
492#389C2314yes—
493#389C2312yes—
494#389C2312yes—
495#389C2314yes—
496#389C2314yes—
497#389C2312yes—
498#389C2312yes—
499#389C2314yes—
500#389C2311yescharacteristic
501#389C2311yescharacteristic
502#388C2312yes—
503#388C2314yes—
504#388C2314yes—
505#388C2314yes—
506#388C2314yes—
507#388C2314yes—
508#388C2312yes—
509#388C2314yes—
510#388C2314yes—
511#388C2314yes—
512#388C2314yes—
513#388C2314yes—
514#388C2312yes—
515#388C2314yes—
516#388C2312yes—
517#388C2314yes—
518#388C2312yes—
519#388C2314yes—
520#387C2314yes—
521#387C2314yes—
522#387C2314yes—
523#387C2314yes—
524#387C2314yes—
525#387C2314yes—
526#387C2314yes—
527#387C2314yes—
528#387C2314yes—
529#387C2314yes—
530#387C2314yes—
531#387C2314yes—
532#387C2314yes—
533#387C2314yes—
534#387C2314yes—
535#387C2314yes—
536#387C2314yes—
537#387C2314yes—
538#387C2314yes—
539#387C2312yes—
540#387C2314yes—
541#387C2314yes—
542#387C2314yes—
543#387C2314yes—
544#387C2314yes—
545#387C2314yes—
546#387C2314yes—
547#387C2314yes—
548#387C2314yes—
549#387C2314yes—
550#387C2314yes—
551#387C2312yes—
552#387C2312yes—
553#387C2314yes—
554#387C2314yes—
555#387C2314yes—
556#387C2314yes—
557#387C2314yes—
558#387C2314yes—
559#387C2314yes—
560#387C2314yes—
561#387C2314yes—
562#387C2314yes—
563#387C2314yes—
564#387C2314yes—
565#387C2314yes—
566#387C2312yes—
567#387C2314yes—
568#387C2314yes—
569#387C2314yes—
570#387C2314yes—
571#387C2314yes—
572#387C2314yes—
573#387C2314yes—
574#387C2314yes—
575#387C2314yes—
576#387C2312yes—
577#387C2314yes—
578#387C2314yes—
579#387C2314yes—
580#387C2312yes—
581#387C2314yes—
582#387C2314yes—
583#387C2314yes—
584#387C2314yes—
585#387C2312yes—
586#386C2314yes—
587#386C2314yes—
588#386C2312yes—
589#386C2312yes—
590#386C2312yes—
591#386C2312yes—
592#385C2314yes—
593#385C2314yes—
594#385C2314yes—
595#385C2314yes—
596#385C2314yes—
597#385C2314yes—
598#385C2314yes—
599#385C2314yes—
600#385C2312yes—
601#385C2314yes—
602#385C2314yes—
603#385C2314yes—
604#385C2312yes—
605#385C2312yes—
606#385C2312yes—
607#385C2314yes—
608#385C2314yes—
609#385C2314yes—
610#385C2314yes—
611#385C2314yes—
612#385C2314yes—
613#385C2312yes—
614#385C2312yes—
615#385C2314yes—
616#385C2312yes—
617#385C2314yes—
618#385C2312yes—
619#384C2312yes—
620#384C2312yes—
621#384C2312yes—
622#384C2311yescharacteristic
623#384C2312yes—
624#384C2311yescharacteristic
625#384C2312yes—
626#384C2312yes—
627#383C2314yes—
628#383C2314yes—
629#383C2314yes—
630#383C2314yes—
631#382C2312yes—
632#382C2314yes—
633#382C2314yes—
634#382C2314yes—
635#382C2314yes—
636#382C2314yes—
637#382C2314yes—
638#381C2314yes—
639#381C2314yes—
640#381C2314yes—
641#381C2312yes—
642#380C2312yes—
643#380C2312yes—
644#380C2312yes—
645#380C2314yes—
646#380C2312yes—
647#380C2314yes—
648#380C2314yes—
649#380C2314yes—
650#380C2312yes—
651#380C2312yes—
652#380C2312yes—
653#380C2311yescharacteristic
654#380C2311yescharacteristic
655C4×C4⋊C4C2314yes—
656C4×C4⋊C4C2314yes—
657C4×C4⋊C4C2312yes—
658C4×C4⋊C4C2312yes—
659C4×C4⋊C4C2314yes—
660C4×C4⋊C4C2314yes—
661C4×C4⋊C4C2312yes—
662C4×C4⋊C4C2312yes—
663C4×C4⋊C4C2312yes—
664C4×C4⋊C4C2312yes—
665C4×C4⋊C4C2314yes—
666C4×C4⋊C4C2314yes—
667C4×C4⋊C4C2314yes—
668C4×C4⋊C4C2314yes—
669C4×C4⋊C4C2314yes—
670C4×C4⋊C4C2314yes—
671C4×C4⋊C4C2314yes—
672C4×C4⋊C4C2314yes—
673C4×C4⋊C4C2312yes—
674C4×C4⋊C4C2312yes—
675C4×C4⋊C4C2312yes—
676C4×C4⋊C4C2311yescharacteristic
677C4×C4⋊C4C2312yes—
678C4×C4⋊C4C2311yescharacteristic
679C4×C4⋊C4C2311yescharacteristic
680C4×C4⋊C4C2312yes—
681C4×C4⋊C4C2312yes—
682C4×C4⋊C4C2312yes—
683C4×C4⋊C4C2311yescharacteristic
684C4×C4⋊C4C2312yes—
685C4×C4⋊C4C2314yes—
686C4×C4⋊C4C2314yes—
687C4×C4⋊C4C2311yescharacteristic
688C4×C4⋊C4C2312yes—
689C4×C4⋊C4C2311yescharacteristic
690C4×C4⋊C4C2312yes—
691C4×C22⋊C4C2314yes—
692C4×C22⋊C4C2314yes—
693C4×C22⋊C4C2314yes—
694C4×C22⋊C4C2314yes—
695C4×C22⋊C4C2314yes—
696C4×C22⋊C4C2314yes—
697C4×C22⋊C4C2312yes—
698C4×C22⋊C4C2312yes—
699C4×C22⋊C4C2312yes—
700C4×C22⋊C4C2312yes—
701C4×C22⋊C4C2312yes—
702C4×C22⋊C4C2312yes—
703C4×C22⋊C4C2314yes—
704C4×C22⋊C4C2312yes—
705#376C2312yes—
706#376C2312yes—
707#376C2314yes—
708#376C2314yes—
709#376C2314yes—
710C2×#95C2312yes—
711C2×#95C2312yes—
712C2×#95C2314yes—
713C43C2312yes—
714C22×Q8—24no—
715C22×Q8—42no—
716C22×Q8—42no—
717C22×Q8C2412yes—
718C22×Q8C2412yes—
719C22×Q8C2412yes—
720C22×Q8C2412yes—
721C22×Q8C2411yescharacteristic
722C22×D4C2412yes—
723C22×D4C2411yescharacteristic
724C23×C4C2412yes—
725C23×C4C2414yes—
726C23×C4C2411yescharacteristic
727C23×C4C2412yes—
728C23×C4C2411yescharacteristic
729C23×C4C2411yescharacteristic
730C23×C4C2412yes—
731C23×C4C2412yes—
732C23×C4C2412yes—
733C23×C4C2414yes—
734C4⋊Q8—28no—
735C4⋊Q8—42no—
736C4⋊Q8—42no—
737C4⋊Q8—44no—
738C4⋊Q8—44no—
739#126—216no—
740#125—28no—
741#125—216no—
742#125—44no—
743#125—84no—
744#125—84no—
745#125—84no—
746#123—28no—
747#123—216no—
748C22⋊Q8—28no—
749C22⋊Q8—24no—
750C22⋊Q8—28no—
751C22⋊Q8—28no—
752C22⋊Q8—44no—
753C22⋊Q8—44no—
754C22⋊Q8—44no—
755C22⋊Q8—82no—
756#121—24no—
757C4×Q8—28no—
758C4×Q8—28no—
759C4×Q8—28no—
760C4×Q8—28no—
761C4×Q8—28no—
762C4×Q8—42no—
763C4×Q8—44no—
764C4×Q8—44no—
765C4×Q8—82no—
766C4×Q8—82no—
767C4×D4—28no—
768C4×D4—28no—
769C4×D4—42no—
770C4×D4—84no—
771#117—24no—
772#117—216no—
773#117—216no—
774#117—42no—
775#117—42no—
776#117—84no—
777#117#4118yes—
778C2×C4⋊C4—28no—
779C2×C4⋊C4—42no—
780C2×C4⋊C4—44no—
781C2×C4⋊C4C2412yes—
782C2×C4⋊C4C2412yes—
783C2×C4⋊C4C2412yes—
784C2×C4⋊C4C2414yes—
785C2×C4⋊C4C2414yes—
786C2×C4⋊C4C2414yes—
787C2×C4⋊C4C2411yescharacteristic
788C2×C4⋊C4C2411yescharacteristic
789C2×C4⋊C4C2411yescharacteristic
790C2×C4⋊C4C2414yes—
791C2×C4⋊C4C2411yescharacteristic
792C2×C4⋊C4C2414yes—
793C2×C4⋊C4C2412yes—
794C2×C4⋊C4C2412yes—
795C2×C4⋊C4C2412yes—
796C2×C4⋊C4C2414yes—
797C2×C4⋊C4C2411yescharacteristic
798C2×C4⋊C4C2414yes—
799C2×C4⋊C4C2412yes—
800C2×C4⋊C4C2412yes—
801C2×C4⋊C4C2412yes—
802C2×C4⋊C4C2412yes—
803C2×C4⋊C4C2411yescharacteristic
804C2×C4⋊C4C2414yes—
805C2×C4⋊C4C2412yes—
806C2×C4⋊C4C2412yes—
807C2×C4⋊C4C2414yes—
808C2×C4⋊C4C2414yes—
809C2×C4⋊C4C2412yes—
810C2×C4⋊C4C2414yes—
811C2×C4⋊C4C2414yes—
812C2×C4⋊C4C2414yes—
813C2×C4⋊C4C2411yescharacteristic
814C2×C4⋊C4C2411yescharacteristic
815C2×C4⋊C4C2414yes—
816C2×C4⋊C4C2411yescharacteristic
817C2×C4⋊C4C2411yescharacteristic
818C2×C4⋊C4C2412yes—
819C2×C4⋊C4C2414yes—
820C2×C4⋊C4C2414yes—
821C2×C4⋊C4C2414yes—
822C2×C4⋊C4C2414yes—
823C2×C4⋊C4C2412yes—
824C2×C4⋊C4C2411yescharacteristic
825C2×C4⋊C4C2414yes—
826C2×C4⋊C4C2414yes—
827C2×C4⋊C4C2414yes—
828C2×C4⋊C4C2414yes—
829C2×C4⋊C4C2412yes—
830C2×C4⋊C4C2412yes—
831C2×C4⋊C4C2414yes—
832C2×C4⋊C4C2412yes—
833C2×C4⋊C4C2412yes—
834C2×C4⋊C4C2414yes—
835C2×C4⋊C4C2414yes—
836C2×C4⋊C4C2414yes—
837C2×C4⋊C4C2414yes—
838C2×C4⋊C4C2414yes—
839C2×C4⋊C4C2414yes—
840C2×C4⋊C4C2412yes—
841C2×C4⋊C4C2414yes—
842C2×C4⋊C4C2414yes—
843C2×C4⋊C4C2412yes—
844C2×C4⋊C4C2412yes—
845C2×C4⋊C4C2414yes—
846C2×C4⋊C4C2411yescharacteristic
847C2×C4⋊C4C2412yes—
848C2×C4⋊C4C2412yes—
849C2×C4⋊C4C2412yes—
850C2×C4⋊C4C2414yes—
851C2×C4⋊C4C2414yes—
852C2×C4⋊C4C2414yes—
853C2×C4⋊C4C2412yes—
854C2×C4⋊C4C2414yes—
855C2×C4⋊C4C2411yescharacteristic
856C2×C4⋊C4C2411yescharacteristic
857C2×C22⋊C4C2412yes—
858C2×C22⋊C4C2412yes—
859C2×C22⋊C4C2414yes—
860C2×C22⋊C4C2412yes—
861C2×C22⋊C4C2414yes—
862C2×C22⋊C4C2412yes—
863C2×C22⋊C4C2414yes—
864C2×C22⋊C4C2412yes—
865C2×C22⋊C4C2412yes—
866C2×C22⋊C4C2412yes—
867C2×C22⋊C4C2412yes—
868C2×C22⋊C4C2412yes—
869C2×C22⋊C4C2412yes—
870C2×C22⋊C4C2412yes—
871C2×C22⋊C4C2414yes—
872C2×C22⋊C4C2412yes—
873C2×C22⋊C4C2412yes—
874C2×C22⋊C4C2414yes—
875C2×C22⋊C4C2412yes—
876C2×C22⋊C4C2414yes—
877C2×C22⋊C4C2414yes—
878C2×C22⋊C4C2414yes—
879C2×C22⋊C4C2412yes—
880C2×C22⋊C4C2412yes—
881C2×C22⋊C4C2412yes—
882C2×C42—44no—
883C2×C42—42no—
884C2×C42—84no—
885C2×C42C2414yes—
886C2×C42C2414yes—
887C2×C42C2412yes—
888C2×C42C2414yes—
889C2×C42C2412yes—
890C2×C42C2412yes—
891C2×C42C2411yescharacteristic
892C2×C42C2412yes—
893C2×C42C2412yes—
894C2×C42C2412yes—
895C2×C42C2411yescharacteristic
896C2×C42C2412yes—
897C2×C42C2414yes—
898C2×C42C2412yes—
899C2×C42C2414yes—
900C2×C42C2414yes—
901C2×C42C2412yes—
902C2×C42C2414yes—
903C2×C42C2414yes—
904C2×C42C2414yes—
905C2×C42C2414yes—
906C2×C42C2414yes—
907C2×C42C2411yescharacteristic
908C2×C42C2412yes—
909C2×C42C2411yescharacteristic
910C2×C42C2414yes—
911C2×C42C2412yes—
912C2×C42C2412yes—
913C2×C42C2412yes—
914#95C2414yes—
915#95C2414yes—
916#95C2414yes—
917#95C2414yes—
918#95C2414yes—
919#95C2414yes—
920#95C2414yes—
921#95C2414yes—
922#95C2412yes—
923#95C2412yes—
924#95C2412yes—
925#95C2412yes—
926#95C2412yes—
927#95C2412yes—
928#95C2412yes—
929#95C2414yes—
930#95C2414yes—
931#95C2412yes—
932#95C2412yes—
933#95C2412yes—
934#95C2414yes—
935#95C2414yes—
936#95C2414yes—
937#95C2414yes—
938#95C2414yes—
939#95C2414yes—
940#95C2412yes—
941#95C2414yes—
942#95C2414yes—
943#95C2414yes—
944#95C2412yes—
945#95C2412yes—
946#95C2412yes—
947#95C2414yes—
948#95C2412yes—
949#95C2412yes—
950#95C2412yes—
951#95C2414yes—
952#95C2414yes—
953#95C2414yes—
954#95C2412yes—
955#95C2414yes—
956#95C2414yes—
957#95C2412yes—
958#95C2414yes—
959#95C2414yes—
960#95C2412yes—
961#95C2412yes—
962#95C2412yes—
963#95C2414yes—
964#95C2414yes—
965#95C2414yes—
966#95C2412yes—
967#95C2412yes—
968#95C2414yes—
969#95C2414yes—
970#95C2412yes—
971#95C2414yes—
972#95C2414yes—
973#95C2412yes—
974#95C2412yes—
975#95C2414yes—
976#95C2414yes—
977#95C2412yes—
978#95C2412yes—
979#95C2414yes—
980#95C2414yes—
981#95C2412yes—
982#95C2412yes—
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—
996C24C2511yescharacteristic
997C24C2512yes—
998C2×Q8—24no—
999C2×Q8—24no—
1000C2×Q8—24no—
1001C2×Q8—24no—
1002C2×Q8—24no—
1003C2×Q8—24no—
1004C2×Q8—24no—
1005C2×Q8—24no—
1006C2×Q8—41no—
1007C2×Q8—41no—
1008C2×Q8—42no—
1009C2×Q8—42no—
1010C2×Q8—42no—
1011C2×Q8—42no—
1012C2×Q8—416no—
1013C2×Q82−1+414yes—
1014C2×D4—24no—
1015C2×D4—24no—
1016C2×D4—41no—
1017C2×D4—42no—
1018C2×D4—41no—
1019C2×D42−1+414yes—
1020C22×C4—22no—
1021C22×C4—22no—
1022C22×C4—24no—
1023C22×C4—28no—
1024C22×C4—24no—
1025C22×C4—28no—
1026C22×C4—24no—
1027C22×C4—24no—
1028C22×C4—24no—
1029C22×C4—24no—
1030C22×C4—22no—
1031C22×C4—22no—
1032C22×C4—42no—
1033C22×C4—42no—
1034C22×C4—44no—
1035C22×C4—42no—
1036C22×C4—42no—
1037C22×C4—41no—
1038C22×C4—41no—
1039C22×C4—42no—
1040C22×C4—44no—
1041C22×C4—44no—
1042C22×C4—41no—
1043C22×C4—41no—
1044C22×C4—42no—
1045C22×C4—44no—
1046C22×C4—42no—
1047C22×C4—42no—
1048C22×C4—42no—
1049C22×C4C2×#4114yes—
1050C22×C4C2512yes—
1051C22×C4C2512yes—
1052C22×C4C2512yes—
1053C22×C4C2511yescharacteristic
1054C22×C4C2512yes—
1055C22×C4C2512yes—
1056C22×C4C2512yes—
1057C22×C4C2514yes—
1058C22×C4C2512yes—
1059C22×C4C2514yes—
1060C22×C4C2514yes—
1061C22×C4C2512yes—
1062C22×C4C2514yes—
1063C22×C4C2511yescharacteristic
1064C22×C4C2512yes—
1065C22×C4C2514yes—
1066C22×C4C2512yes—
1067C22×C4C2514yes—
1068C22×C4C2512yes—
1069C22×C4C2512yes—
1070C22×C4C2512yes—
1071C22×C4C2512yes—
1072C22×C4C2511yescharacteristic
1073C22×C4C2511yescharacteristic
1074C22×C4C2511yescharacteristic
1075C22×C4C2512yes—
1076C22×C4C2511yescharacteristic
1077C4⋊C4—24no—
1078C4⋊C4—28no—
1079C4⋊C4—22no—
1080C4⋊C4—22no—
1081C4⋊C4—28no—
1082C4⋊C4—28no—
1083C4⋊C4—28no—
1084C4⋊C4—28no—
1085C4⋊C4—24no—
1086C4⋊C4—28no—
1087C4⋊C4—28no—
1088C4⋊C4—28no—
1089C4⋊C4—24no—
1090C4⋊C4—22no—
1091C4⋊C4—22no—
1092C4⋊C4—24no—
1093C4⋊C4—24no—
1094C4⋊C4—24no—
1095C4⋊C4—24no—
1096C4⋊C4—24no—
1097C4⋊C4—24no—
1098C4⋊C4—28no—
1099C4⋊C4—28no—
1100C4⋊C4—24no—
1101C4⋊C4—24no—
1102C4⋊C4—22no—
1103C4⋊C4—22no—
1104C4⋊C4—24no—
1105C4⋊C4—42no—
1106C4⋊C4—44no—
1107C4⋊C4—44no—
1108C4⋊C4—41no—
1109C4⋊C4—42no—
1110C4⋊C4—42no—
1111C4⋊C4—44no—
1112C4⋊C4—44no—
1113C4⋊C4—44no—
1114C4⋊C4—42no—
1115C4⋊C4—42no—
1116C4⋊C4—41no—
1117C4⋊C4—41no—
1118C4⋊C4—44no—
1119C4⋊C4—44no—
1120C4⋊C4—41no—
1121C4⋊C4—44no—
1122C4⋊C4—42no—
1123C4⋊C4—41no—
1124C4⋊C4—44no—
1125C4⋊C4—44no—
1126C4⋊C4—41no—
1127C4⋊C4—42no—
1128C4⋊C4—44no—
1129C4⋊C4—44no—
1130C4⋊C4—44no—
1131C4⋊C4—44no—
1132C4⋊C4—44no—
1133C4⋊C4—44no—
1134C4⋊C4—44no—
1135C4⋊C4—44no—
1136C4⋊C4—42no—
1137C4⋊C4—42no—
1138C4⋊C4—44no—
1139C4⋊C4—44no—
1140C4⋊C4—42no—
1141C4⋊C4—44no—
1142C4⋊C4—42no—
1143C4⋊C4—44no—
1144C4⋊C4—42no—
1145C4⋊C4—44no—
1146C4⋊C4—44no—
1147C4⋊C4—42no—
1148C4⋊C4—42no—
1149C4⋊C4—44no—
1150C4⋊C4—44no—
1151C4⋊C4C2×#4114yes—
1152C4⋊C4C2×#4114yes—
1153C22⋊C4—24no—
1154C22⋊C4—24no—
1155C22⋊C4—28no—
1156C22⋊C4—28no—
1157C22⋊C4—24no—
1158C22⋊C4—24no—
1159C22⋊C4—24no—
1160C22⋊C4—24no—
1161C22⋊C4—24no—
1162C22⋊C4—28no—
1163C22⋊C4—24no—
1164C22⋊C4—24no—
1165C22⋊C4—24no—
1166C22⋊C4—42no—
1167C22⋊C4—42no—
1168C22⋊C4—42no—
1169C22⋊C4—42no—
1170C22⋊C4—42no—
1171C22⋊C4—44no—
1172C22⋊C4—42no—
1173C22⋊C4—44no—
1174C22⋊C4—44no—
1175C22⋊C4—44no—
1176C22⋊C4—44no—
1177C22⋊C4C2×#4118yes—
1178C42—24no—
1179C42—28no—
1180C42—28no—
1181C42—28no—
1182C42—24no—
1183C42—24no—
1184C42—24no—
1185C42—24no—
1186C42—22no—
1187C42—24no—
1188C42—22no—
1189C42—24no—
1190C42—41no—
1191C42—42no—
1192C42—41no—
1193C42—42no—
1194C42—44no—
1195C42—44no—
1196C42—44no—
1197C42—44no—
1198C42—42no—
1199C42—44no—
1200C42—42no—
1201C42—44no—
1202C42—44no—
1203C42—44no—
1204C42—44no—
1205C42—42no—
1206C42C2×#4118yes—
1207C23—22no—
1208C23—21no—
1209C23—22no—
1210C23—21no—
1211C23—22no—
1212C23—22no—
1213C23—21no—
1214C23—21no—
1215C23—21no—
1216C23—22no—
1217C23—21no—
1218C23—22no—
1219C23C22×#4112yes—
1220C23C2×2−1+414yes—
1221C23C2611yescharacteristic
1222Q8—44no—
1223Q8—48no—
1224Q8—48no—
1225Q8—48no—
1226Q8—84no—
1227D4—44no—
1228D4—48no—
1229C2×C4—22no—
1230C2×C4—22no—
1231C2×C4—21no—
1232C2×C4—22no—
1233C2×C4—21no—
1234C2×C4—21no—
1235C2×C4—21no—
1236C2×C4—22no—
1237C2×C4—22no—
1238C2×C4—21no—
1239C2×C4—22no—
1240C2×C4—21no—
1241C2×C4—28no—
1242C2×C4—22no—
1243C2×C4—22no—
1244C2×C4—22no—
1245C2×C4—24no—
1246C2×C4—24no—
1247C2×C4—22no—
1248C2×C4—24no—
1249C2×C4—22no—
1250C2×C4—22no—
1251C2×C4—22no—
1252C2×C4—22no—
1253C2×C4—22no—
1254C2×C4—21no—
1255C2×C4—22no—
1256C2×C4—22no—
1257C2×C4—22no—
1258C2×C4—24no—
1259C2×C4—22no—
1260C2×C4—22no—
1261C2×C4—22no—
1262C2×C4—22no—
1263C2×C4—21no—
1264C2×C4—24no—
1265C2×C4—22no—
1266C2×C4—22no—
1267C2×C4—21no—
1268C2×C4—22no—
1269C2×C4—21no—
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—22no—
1283C2×C4—22no—
1284C2×C4—24no—
1285C2×C4—24no—
1286C2×C4—22no—
1287C2×C4—24no—
1288C2×C4—24no—
1289C2×C4—22no—
1290C2×C4—22no—
1291C2×C4—22no—
1292C2×C4—21no—
1293C2×C4—22no—
1294C2×C4—22no—
1295C2×C4—24no—
1296C2×C4—22no—
1297C2×C4—22no—
1298C2×C4—22no—
1299C2×C4—22no—
1300C2×C4—24no—
1301C2×C4—21no—
1302C2×C4—416no—
1303C2×C4—48no—
1304C2×C4—48no—
1305C2×C4—48no—
1306C2×C4—82no—
1307C2×C4—82no—
1308C2×C4—84no—
1309C2×C4—88no—
1310C2×C4—162no—
1311C2×C4C22×#4114yes—
1312C2×C4C22×#4114yes—
1313C2×C4C22×#4112yes—
1314C2×C4C22×#4112yes—
1315C2×C4C2×2−1+412yes—
1316C2×C4C2×2−1+412yes—
1317C2×C4C2×2−1+414yes—
1318C2×C4#58512yes—
1319C2×C4#58512yes—
1320C22—24no—
1321C22—22no—
1322C22—22no—
1323C22—24no—
1324C22—24no—
1325C22—22no—
1326C22—42no—
1327C22—41no—
1328C22—42no—
1329C22—41no—
1330C22—42no—
1331C22—41no—
1332C22—41no—
1333C22—42no—
1334C22C23×#4111yescharacteristic
1335C22C22×2−1+411yescharacteristic
1336C22C22×2−1+411yescharacteristic
1337C22C2×#58511yescharacteristic
1338C22C2×#58511yescharacteristic
1339C22H(7,𝔽2)11yescharacteristic
1340C222−1+611yescharacteristic
1341C4—24no—
1342C4—24no—
1343C4—24no—
1344C4—22no—
1345C4—22no—
1346C4—22no—
1347C4—42no—
1348C4—44no—
1349C4—42no—
1350C4—42no—
1351C4—42no—
1352C4—42no—
1353C4—42no—
1354C4—42no—
1355C4—42no—
1356C4—44no—
1357C4—44no—
1358C4—42no—
1359C4—41no—
1360C4—44no—
1361C4—41no—
1362C4—42no—
1363C4—42no—
1364C4—42no—
1365C4—44no—
1366C4—44no—
1367C4#345514yes—
1368C2—44no—
1369C2—42no—
1370C2C2×#345511yescharacteristic
1371C2#6290211yescharacteristic
1372C2#6290411yescharacteristic
1373C2#6300011yescharacteristic
1374C2#6300111yescharacteristic
1375C2#6303211yescharacteristic
1376C2#6305611yescharacteristic
subgroupG/H
center, commutator, Frattini, socle, cosocleC23C26
prime radicalC2×#121C23
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23 ◁ G
LECSG ▷ C23 ▷ C1

Complements

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

NH ≅ G/Ntype
2. #52267C2semidirect
3. #42772C2semidirect
4. #42710C2semidirect
5. #42451C2semidirect
6. #42320C2semidirect
7. #41577C2semidirect
8. #40860C2semidirect
9. #40071C2semidirect
10. #40065C2semidirect
11. #39656C2semidirect
12. #39640C2semidirect
13. #39637C2semidirect
16. #38472C2semidirect
17. #37398C2semidirect
18. #37323C2semidirect
19. #37146C2semidirect
20. #36834C2semidirect
21. #36552C2semidirect
22. #36481C2semidirect
24. #36256C2semidirect
25. #35997C2semidirect
26. #35919C2semidirect
27. #35870C2semidirect
28. #34304C2semidirect
29. #34254C2semidirect

Maximal subgroups

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

subgroupindex
#522792
#522672
#427722
#427102
#424512
#423202
#415772
#408602
#400712
#400652
#396562
#396402
#396372
#396322
#385202
#384722
#373982
#373232
#371462
#368342
#365522
#364812
#362722
#362562
#359972
#359192
#358702
#343042
#342542