Finite Group Databasebeta

← #8701658

Subgroups — #8701658

Order 512.

4354 conjugacy classes of subgroups.

The subgroup lattice has 1399 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#59938C212yesmaximal, complemented
2#59828C212yesmaximal, complemented
3#59697C212yesmaximal, complemented
4#59479C212yesmaximal, complemented
5#58390C212yesmaximal, complemented
6#58292C214yesmaximal, complemented
7#57359C214yesmaximal, complemented
8#56663C212yesmaximal, complemented
9#52300C211yesmaximal, characteristic, complemented
10#51594C214yesmaximal, complemented
11#49087C214yesmaximal, complemented
12#48289C214yesmaximal, complemented
13#45675C212yesmaximal, complemented
14#45503C211yesmaximal, characteristic, complemented
15#45419C211yesmaximal, characteristic, complemented
16#45345C211yesmaximal, characteristic, complemented
17#45323C212yesmaximal, complemented
18#44994C212yesmaximal, complemented
19#42912C211yesmaximal, characteristic
20#42840C212yesmaximal, complemented
21#42815C211yesmaximal, characteristic
22#42702C212yesmaximal, complemented
23#39663C212yesmaximal, complemented
24#39663C212yesmaximal, complemented
25#39200C212yesmaximal, complemented
26#37058C212yesmaximal, complemented
27#36954C214yesmaximal, complemented
28#36545C212yesmaximal, complemented
29#36483C211yesmaximal, characteristic
30C2×#557C2212yes—
31C2×#557C2211yescharacteristic
32C2×#548C2211yescharacteristic
33C2×#536C2211yescharacteristic
34C22×C4×Q8C2211yescharacteristic
35#2862C2212yes—
36#2857C2212yes—
37#2854C2212yes—
38#2854C2211yescharacteristic
39#2851C2214yes—
40#2841C2212yes—
41#2839C2214yes—
42#2836C2214yes—
43#2836C2214yes—
44#2820C2212yes—
45#2817C2212yes—
46#2807C2214yes—
47#2806C2214yes—
48#2806C2214yes—
49#2798C2214yes—
50#2798C2214yes—
51#2798C2214yes—
52#2794C2212yes—
53#2794C2214yes—
54#2792C2214yes—
55#2791C2212yes—
56#2791C2214yes—
57#2788C2214yes—
58#2788C2214yes—
59#2777C2212yes—
60#2777C2214yes—
61#2777C2214yes—
62#2774C2214yes—
63#2774C2214yes—
64#2773C2214yes—
65#2773C2214yes—
66#2773C2214yes—
67#2771C2211yescharacteristic
68#2771C2212yes—
69#2768C2214yes—
70#2768C2214yes—
71#2768C2214yes—
72#2767C2214yes—
73#2764C2212yes—
74#2764C2211yescharacteristic
75#2758C2214yes—
76#2758C2212yes—
77#2755C2214yes—
78#2754C2214yes—
79#2754C2214yes—
80#2748C2212yes—
81#2742C2212yes—
82#2741C2214yes—
83#2738C2214yes—
84#2738C2214yes—
85#2726C2214yes—
86#2726C2214yes—
87#2726C2214yes—
88#2723C2214yes—
89#2722C2212yes—
90#2722C2211yescharacteristic
91#2721C2214yes—
92#2720C2214yes—
93#2719C2214yes—
94#2718C2214yes—
95#2718C2212yes—
96#2717C2214yes—
97#2716C2212yes—
98#2711C2214yes—
99#2708C2214yes—
100#2707C2214yes—
101#2704C2214yes—
102#2704C2214yes—
103#2702C2212yes—
104#2694C2214yes—
105#2694C2214yes—
106#2692C2214yes—
107#2690C2214yes—
108#2687C2214yes—
109#2677C2211yescharacteristic
110#2667C2214yes—
111#2666C2214yes—
112#2666C2214yes—
113#2664C2214yes—
114#2659C2212yes—
115#2658C2211yescharacteristic
116#2654C2214yes—
117#2654C2214yes—
118#2638C2212yes—
119#2633C2212yes—
120#2632C2212yes—
121#2625C2214yes—
122#2625C2211yescharacteristic
123#2607C2212yes—
124#2607C2212yes—
125#2596C2214yes—
126#2592C2212yes—
127#2592C2211yescharacteristic
128#2589C2214yes—
129#2589C2214yes—
130#2588C2214yes—
131#2586C2214yes—
132#2586C2214yes—
133#2584C2214yes—
134#2582C2212yes—
135#2582C2212yes—
136#2582C2212yes—
137#2582C2212yes—
138#2581C2214yes—
139#2580C2212yes—
140#2575C2214yes—
141#2565C2214yes—
142#2564C2212yes—
143#2560C2214yes—
144#2558C2214yes—
145#2558C2214yes—
146#2556C2214yes—
147#2553C2214yes—
148#2552C2214yes—
149#2547C2212yes—
150#2546C2212yes—
151#2546C2212yes—
152#2546C2212yes—
153#2546C2212yes—
154#2545C2212yes—
155#2545C2212yes—
156#2542C2212yes—
157#2542C2211yescharacteristic
158#2524C2214yes—
159#2523C2212yes—
160#2522C2214yes—
161#2522C2214yes—
162#2520C2214yes—
163#2516C2214yes—
164#2511C2212yes—
165#2511C2212yes—
166#2511C2212yes—
167#2506C2214yes—
168#2506C2212yes—
169#2506C2212yes—
170#2506C2214yes—
171#2501C2211yescharacteristic
172#2501C2212yes—
173#2496C2212yes—
174#2492C2214yes—
175#2492C2212yes—
176#2492C2212yes—
177#2486C2212yes—
178#2486C2211yescharacteristic
179#2479C2214yes—
180#2473C2214yes—
181#2473C2214yes—
182#2470C2214yes—
183#2465C2214yes—
184#2462C2214yes—
185#2462C2214yes—
186#2462C2214yes—
187#2458C2214yes—
188#2458C2214yes—
189#2453C2214yes—
190#2453C2214yes—
191#2451C2212yes—
192#2451C2212yes—
193#2448C2212yes—
194#2448C2214yes—
195#2448C2212yes—
196#2447C2212yes—
197#2446C2212yes—
198#2446C2212yes—
199#2446C2212yes—
200#2446C2212yes—
201#2446C2212yes—
202#2446C2212yes—
203#2441C2214yes—
204#2438C2214yes—
205#2434C2212yes—
206#2434C2212yes—
207#2434C2212yes—
208#2434C2211yescharacteristic
209#2432C2212yes—
210#2429C2212yes—
211#2429C2212yes—
212#2427C2212yes—
213#2426C2212yes—
214#2423C2214yes—
215#2423C2212yes—
216#2423C2212yes—
217#2423C2212yes—
218#2423C2214yes—
219#2409C2211yescharacteristic
220#2402C2212yes—
221#2398C2211yescharacteristic
222#2396C2212yes—
223#2395C2211yescharacteristic
224#2378C2214yes—
225#2376C2212yes—
226#2374C2214yes—
227#2368C2214yes—
228#2367C2212yes—
229#2365C2212yes—
230#2365C2212yes—
231#2365C2212yes—
232#2365C2214yes—
233#2365C2212yes—
234#2360C2212yes—
235#2360C2212yes—
236#2355C2212yes—
237Q8×C4⋊C4C2212yes—
238Q8×C4⋊C4C2212yes—
239#2341C2212yes—
240Q8×C22⋊C4C2212yes—
241Q8×C22⋊C4C2211yescharacteristic
242#2339C2211yescharacteristic
243#2334C2214yes—
244#2334C2214yes—
245#2323C2212yes—
246#2323C2214yes—
247#2320C2211yescharacteristic
248#2320C2212yes—
249C4×C4⋊Q8C2212yes—
250C4×C4⋊Q8C2212yes—
251C4×C4⋊Q8C2212yes—
252C4×#126C2212yes—
253C4×#126C2212yes—
254C4×C22⋊Q8C2214yes—
255C4×C22⋊Q8C2212yes—
256C4×#123C2212yes—
257C4×#123C2211yescharacteristic
258#2293C2212yes—
259C22×#41C2311yescharacteristic
260C23×Q8C2311yescharacteristic
261C23×Q8C2311yescharacteristic
262#557—48no—
263#557—44no—
264#548—44no—
265#536—44no—
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×#126C2314yes—
278C2×#125C2312yes—
279C2×#125C2314yes—
280C2×#125C2314yes—
281C2×#125C2314yes—
282C2×#125C2314yes—
283C2×#125C2314yes—
284C2×#125C2314yes—
285C2×#124C2312yes—
286C2×#124C2311yescharacteristic
287C2×#124C2312yes—
288C2×#124C2312yes—
289C2×#123C2312yes—
290C2×#123C2311yescharacteristic
291C2×#123C2314yes—
292C2×#123C2312yes—
293C2×#123C2312yes—
294C2×#123C2312yes—
295C2×C22⋊Q8C2314yes—
296C2×C22⋊Q8C2312yes—
297C2×C22⋊Q8C2312yes—
298C2×C22⋊Q8C2312yes—
299C2×C22⋊Q8C2312yes—
300C2×C22⋊Q8C2312yes—
301C2×C22⋊Q8C2312yes—
302C2×C22⋊Q8C2311yescharacteristic
303C2×C22⋊Q8C2312yes—
304C2×C22⋊Q8C2314yes—
305C2×#121C2311yescharacteristic
306C2×#121C2312yes—
307C2×C4×Q8—44no—
308C2×C4×Q8C2311yescharacteristic
309C2×C4×Q8C2312yes—
310C2×C4×Q8C2311yescharacteristic
311C2×C4×Q8C2312yes—
312C2×C4×Q8C2312yes—
313C2×C4×Q8C2312yes—
314C2×C4×Q8C2312yes—
315C2×C4×Q8C2312yes—
316C2×C4×Q8C2312yes—
317C2×C4×Q8C2312yes—
318C2×C4×Q8C2312yes—
319C2×C4×Q8C2314yes—
320C2×C4×Q8C2314yes—
321C2×C4×Q8C2312yes—
322C2×C4×Q8C2314yes—
323C2×C4×D4C2312yes—
324C2×C4×D4C2312yes—
325C2×C4×D4C2311yescharacteristic
326C2×#117C2311yescharacteristic
327C2×#117C2314yes—
328C22×C4⋊C4C2311yescharacteristic
329C22×C4⋊C4C2312yes—
330C22×C42C2312yes—
331C22×C42C2311yescharacteristic
332#400C2311yescharacteristic
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#400C2314yes—
348#400C2314yes—
349#400C2314yes—
350#400C2314yes—
351#400C2312yes—
352#400C2312yes—
353#400C2312yes—
354#400C2312yes—
355#400C2314yes—
356#400C2314yes—
357#399C2311yescharacteristic
358#399C2312yes—
359#399C2312yes—
360#399C2314yes—
361#399C2312yes—
362#399C2314yes—
363#399C2314yes—
364#399C2314yes—
365#399C2312yes—
366#399C2312yes—
367#399C2314yes—
368#399C2314yes—
369#399C2314yes—
370#399C2314yes—
371#399C2314yes—
372#398C2314yes—
373#398C2312yes—
374#398C2314yes—
375#398C2314yes—
376#398C2314yes—
377#398C2314yes—
378#398C2314yes—
379#398C2314yes—
380#398C2314yes—
381#398C2314yes—
382#398C2314yes—
383#398C2314yes—
384#398C2314yes—
385#398C2311yescharacteristic
386#398C2314yes—
387#398C2314yes—
388#398C2314yes—
389#398C2314yes—
390#398C2314yes—
391#398C2312yes—
392#398C2314yes—
393#398C2314yes—
394#398C2314yes—
395#398C2314yes—
396#398C2314yes—
397#398C2314yes—
398#398C2314yes—
399#398C2312yes—
400#398C2312yes—
401#398C2312yes—
402#398C2314yes—
403#398C2312yes—
404#398C2312yes—
405#398C2312yes—
406#398C2314yes—
407#398C2314yes—
408#398C2314yes—
409#398C2314yes—
410#397C2314yes—
411#397C2314yes—
412#397C2314yes—
413#397C2311yescharacteristic
414#397C2312yes—
415#397C2314yes—
416#397C2314yes—
417#397C2314yes—
418#397C2314yes—
419#397C2314yes—
420#397C2314yes—
421#397C2311yescharacteristic
422#397C2311yescharacteristic
423#397C2312yes—
424#397C2314yes—
425#397C2312yes—
426#396C2314yes—
427#396C2314yes—
428#396C2314yes—
429#396C2314yes—
430#396C2314yes—
431#396C2314yes—
432#396C2312yes—
433#396C2312yes—
434#396C2314yes—
435#395C2314yes—
436#395C2312yes—
437#395C2312yes—
438#395C2312yes—
439#395C2314yes—
440#395C2314yes—
441#395C2314yes—
442#395C2314yes—
443#395C2314yes—
444#395C2314yes—
445#395C2314yes—
446#395C2312yes—
447#394C2314yes—
448#394C2314yes—
449#394C2314yes—
450#394C2314yes—
451#394C2312yes—
452#394C2312yes—
453#393C2314yes—
454#393C2312yes—
455#393C2311yescharacteristic
456#393C2312yes—
457#393C2314yes—
458#393C2314yes—
459#393C2311yescharacteristic
460#393C2312yes—
461#391C2314yes—
462#391C2312yes—
463#391C2312yes—
464#391C2312yes—
465#391C2312yes—
466#391C2312yes—
467#391C2312yes—
468#391C2314yes—
469#391C2312yes—
470#391C2312yes—
471#391C2312yes—
472#391C2312yes—
473#391C2314yes—
474#391C2312yes—
475#391C2314yes—
476#391C2314yes—
477#391C2314yes—
478#391C2314yes—
479#391C2312yes—
480#391C2312yes—
481#391C2312yes—
482#391C2314yes—
483#391C2312yes—
484#391C2314yes—
485#391C2314yes—
486#391C2314yes—
487#391C2312yes—
488#391C2312yes—
489#391C2314yes—
490#391C2312yes—
491#391C2314yes—
492#390C2314yes—
493#390C2314yes—
494#390C2312yes—
495#390C2312yes—
496#390C2314yes—
497#390C2312yes—
498#390C2312yes—
499#389C2312yes—
500#389C2312yes—
501#389C2314yes—
502#389C2314yes—
503#389C2314yes—
504#389C2312yes—
505#389C2314yes—
506#389C2312yes—
507#389C2312yes—
508#389C2312yes—
509#389C2312yes—
510#389C2314yes—
511#389C2312yes—
512#389C2314yes—
513#389C2314yes—
514#389C2314yes—
515#389C2314yes—
516#389C2314yes—
517#389C2314yes—
518#389C2312yes—
519#389C2314yes—
520#389C2312yes—
521#389C2312yes—
522#389C2314yes—
523#389C2314yes—
524#389C2312yes—
525#389C2314yes—
526#389C2314yes—
527#389C2314yes—
528#389C2314yes—
529#389C2314yes—
530#389C2314yes—
531#389C2314yes—
532#389C2314yes—
533#389C2314yes—
534#389C2314yes—
535#389C2314yes—
536#389C2314yes—
537#389C2314yes—
538#389C2314yes—
539#389C2314yes—
540#389C2312yes—
541#388C2312yes—
542#388C2312yes—
543#388C2312yes—
544#388C2312yes—
545#388C2312yes—
546#388C2312yes—
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#388C2314yes—
566#388C2314yes—
567#388C2314yes—
568#388C2314yes—
569#388C2314yes—
570#388C2314yes—
571#388C2314yes—
572#388C2312yes—
573#388C2314yes—
574#387C2312yes—
575#387C2312yes—
576#387C2312yes—
577#387C2312yes—
578#387C2312yes—
579#387C2312yes—
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#387C2312yes—
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#387C2312yes—
620#387C2314yes—
621#387C2314yes—
622#387C2314yes—
623#387C2312yes—
624#387C2314yes—
625#386C2314yes—
626#386C2314yes—
627#386C2312yes—
628#386C2311yescharacteristic
629#386C2312yes—
630#385C2314yes—
631#385C2314yes—
632#385C2314yes—
633#385C2314yes—
634#385C2314yes—
635#385C2314yes—
636#385C2314yes—
637#385C2314yes—
638#385C2314yes—
639#385C2314yes—
640#385C2314yes—
641#385C2314yes—
642#385C2314yes—
643#385C2312yes—
644#385C2311yescharacteristic
645#385C2312yes—
646#385C2312yes—
647#384C2312yes—
648#384C2312yes—
649#384C2312yes—
650#384C2314yes—
651#384C2312yes—
652#384C2312yes—
653#384C2314yes—
654#383C2312yes—
655#383C2312yes—
656#383C2312yes—
657#383C2314yes—
658#382C2312yes—
659#382C2314yes—
660#382C2314yes—
661#382C2314yes—
662#382C2314yes—
663#381C2312yes—
664#381C2311yescharacteristic
665#381C2312yes—
666#381C2314yes—
667#380C2314yes—
668#380C2312yes—
669#380C2314yes—
670#380C2314yes—
671#380C2311yescharacteristic
672#380C2312yes—
673#380C2314yes—
674#380C2311yescharacteristic
675#380C2312yes—
676#380C2314yes—
677#380C2314yes—
678#380C2314yes—
679C4×C4⋊C4C2312yes—
680C4×C4⋊C4C2312yes—
681C4×C4⋊C4C2312yes—
682C4×C4⋊C4C2312yes—
683C4×C4⋊C4C2312yes—
684C4×C4⋊C4C2314yes—
685C4×C4⋊C4C2314yes—
686C4×C4⋊C4C2314yes—
687C4×C4⋊C4C2314yes—
688C4×C4⋊C4C2312yes—
689C4×C4⋊C4C2312yes—
690C4×C4⋊C4C2314yes—
691C4×C4⋊C4C2311yescharacteristic
692C4×C4⋊C4C2312yes—
693C4×C4⋊C4C2314yes—
694C4×C4⋊C4C2312yes—
695C4×C4⋊C4C2314yes—
696C4×C4⋊C4C2314yes—
697C4×C4⋊C4C2314yes—
698C4×C4⋊C4C2314yes—
699C4×C4⋊C4C2312yes—
700C4×C4⋊C4C2312yes—
701C4×C22⋊C4C2311yescharacteristic
702C4×C22⋊C4C2311yescharacteristic
703C4×C22⋊C4C2312yes—
704C4×C22⋊C4C2312yes—
705C4×C22⋊C4C2312yes—
706C4×C22⋊C4C2312yes—
707C4×C22⋊C4C2314yes—
708C4×C22⋊C4C2314yes—
709C4×C22⋊C4C2312yes—
710C4×C22⋊C4C2314yes—
711C4×C22⋊C4C2314yes—
712C4×C22⋊C4C2314yes—
713C4×C22⋊C4C2314yes—
714#376C2311yescharacteristic
715C2×#95C2312yes—
716C43C2312yes—
717C2×#41—24no—
718C2×#41—44no—
719C22×Q8—24no—
720C22×Q8—44no—
721C22×Q8—42no—
722C22×Q8—44no—
723C22×Q8C2412yes—
724C22×Q8C2411yescharacteristic
725C22×Q8C2412yes—
726C22×Q8C2412yes—
727C22×Q8C2411yescharacteristic
728C22×Q8C2411yescharacteristic
729C22×Q8C2412yes—
730C22×Q8C2414yes—
731C22×Q8C2412yes—
732C22×D4C2411yescharacteristic
733C22×D4C2412yes—
734C22×D4C2411yescharacteristic
735C22×D4C2412yes—
736C23×C4C2411yescharacteristic
737C23×C4C2411yescharacteristic
738C23×C4C2411yescharacteristic
739C23×C4C2412yes—
740C23×C4C2411yescharacteristic
741C23×C4C2412yes—
742C23×C4C2414yes—
743C23×C4C2412yes—
744C23×C4C2412yes—
745C4⋊Q8—28no—
746C4⋊Q8—28no—
747C4⋊Q8—28no—
748C4⋊Q8—44no—
749C4⋊Q8—44no—
750C4⋊Q8—44no—
751C4⋊Q8—44no—
752C4⋊Q8—44no—
753C4⋊Q8—42no—
754#126—28no—
755#126—28no—
756#126—84no—
757#125—48no—
758#125—44no—
759#125—48no—
760#125—48no—
761#125—48no—
762#125—84no—
763#125—84no—
764#124—44no—
765#124—44no—
766#124—44no—
767#124—42no—
768#123—28no—
769#123—24no—
770#123—48no—
771#123—82no—
772#123—82no—
773#123—82no—
774C22⋊Q8—28no—
775C22⋊Q8—216no—
776C22⋊Q8—44no—
777C22⋊Q8—44no—
778C22⋊Q8—44no—
779C22⋊Q8—44no—
780C22⋊Q8—44no—
781C22⋊Q8—42no—
782C22⋊Q8—44no—
783C22⋊Q8—84no—
784#121—42no—
785#121—44no—
786C4×Q8—28no—
787C4×Q8—24no—
788C4×Q8—44no—
789C4×Q8—42no—
790C4×Q8—48no—
791C4×Q8—44no—
792C4×Q8—48no—
793C4×Q8—44no—
794C4×Q8—44no—
795C4×Q8—44no—
796C4×Q8—44no—
797C4×Q8—44no—
798C4×Q8—44no—
799C4×Q8—44no—
800C4×Q8—84no—
801C4×D4—44no—
802C4×D4—44no—
803C4×D4—42no—
804#117—42no—
805#117—84no—
806C2×C4⋊C4—42no—
807C2×C4⋊C4—44no—
808C2×C4⋊C4C2412yes—
809C2×C4⋊C4C2414yes—
810C2×C4⋊C4C2412yes—
811C2×C4⋊C4C2411yescharacteristic
812C2×C4⋊C4C2414yes—
813C2×C4⋊C4C2412yes—
814C2×C4⋊C4C2412yes—
815C2×C4⋊C4C2414yes—
816C2×C4⋊C4C2412yes—
817C2×C4⋊C4C2414yes—
818C2×C4⋊C4C2412yes—
819C2×C4⋊C4C2412yes—
820C2×C4⋊C4C2414yes—
821C2×C4⋊C4C2414yes—
822C2×C4⋊C4C2414yes—
823C2×C4⋊C4C2412yes—
824C2×C4⋊C4C2414yes—
825C2×C4⋊C4C2412yes—
826C2×C4⋊C4C2412yes—
827C2×C4⋊C4C2412yes—
828C2×C4⋊C4C2412yes—
829C2×C4⋊C4C2412yes—
830C2×C4⋊C4C2412yes—
831C2×C4⋊C4C2412yes—
832C2×C4⋊C4C2412yes—
833C2×C4⋊C4C2412yes—
834C2×C4⋊C4C2414yes—
835C2×C4⋊C4C2411yescharacteristic
836C2×C4⋊C4C2411yescharacteristic
837C2×C4⋊C4C2414yes—
838C2×C4⋊C4C2414yes—
839C2×C4⋊C4C2411yescharacteristic
840C2×C4⋊C4C2412yes—
841C2×C4⋊C4C2412yes—
842C2×C4⋊C4C2414yes—
843C2×C4⋊C4C2414yes—
844C2×C4⋊C4C2412yes—
845C2×C4⋊C4C2412yes—
846C2×C4⋊C4C2414yes—
847C2×C4⋊C4C2412yes—
848C2×C4⋊C4C2414yes—
849C2×C4⋊C4C2412yes—
850C2×C4⋊C4C2411yescharacteristic
851C2×C4⋊C4C2414yes—
852C2×C4⋊C4C2412yes—
853C2×C4⋊C4C2414yes—
854C2×C4⋊C4C2414yes—
855C2×C4⋊C4C2414yes—
856C2×C4⋊C4C2414yes—
857C2×C4⋊C4C2412yes—
858C2×C4⋊C4C2414yes—
859C2×C4⋊C4C2414yes—
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⋊C4C2414yes—
871C2×C4⋊C4C2414yes—
872C2×C4⋊C4C2414yes—
873C2×C4⋊C4C2414yes—
874C2×C4⋊C4C2414yes—
875C2×C4⋊C4C2414yes—
876C2×C4⋊C4C2414yes—
877C2×C4⋊C4C2414yes—
878C2×C4⋊C4C2414yes—
879C2×C4⋊C4C2412yes—
880C2×C22⋊C4C2412yes—
881C2×C22⋊C4C2412yes—
882C2×C22⋊C4C2414yes—
883C2×C22⋊C4C2414yes—
884C2×C22⋊C4C2414yes—
885C2×C22⋊C4C2412yes—
886C2×C22⋊C4C2412yes—
887C2×C22⋊C4C2412yes—
888C2×C22⋊C4C2412yes—
889C2×C22⋊C4C2412yes—
890C2×C22⋊C4C2412yes—
891C2×C22⋊C4C2414yes—
892C2×C22⋊C4C2412yes—
893C2×C22⋊C4C2414yes—
894C2×C22⋊C4C2411yescharacteristic
895C2×C22⋊C4C2412yes—
896C2×C22⋊C4C2411yescharacteristic
897C2×C22⋊C4C2414yes—
898C2×C22⋊C4C2412yes—
899C2×C22⋊C4C2412yes—
900C2×C22⋊C4C2412yes—
901C2×C22⋊C4C2414yes—
902C2×C22⋊C4C2414yes—
903C2×C22⋊C4C2414yes—
904C2×C22⋊C4C2414yes—
905C2×C22⋊C4C2414yes—
906C2×C22⋊C4C2414yes—
907C2×C22⋊C4C2412yes—
908C2×C22⋊C4C2411yescharacteristic
909C2×C22⋊C4C2414yes—
910C2×C22⋊C4C2414yes—
911C2×C22⋊C4C2414yes—
912C2×C22⋊C4C2412yes—
913C2×C22⋊C4C2412yes—
914C2×C22⋊C4C2411yescharacteristic
915C2×C42—44no—
916C2×C42—42no—
917C2×C42C2412yes—
918C2×C42C2412yes—
919C2×C42C2411yescharacteristic
920C2×C42C2412yes—
921C2×C42C2412yes—
922C2×C42C2414yes—
923C2×C42C2412yes—
924C2×C42C2412yes—
925C2×C42C2412yes—
926C2×C42C2412yes—
927C2×C42C2412yes—
928C2×C42C2412yes—
929C2×C42C2412yes—
930C2×C42C2414yes—
931C2×C42C2414yes—
932C2×C42C2414yes—
933C2×C42C2414yes—
934C2×C42C2414yes—
935C2×C42C2412yes—
936C2×C42C2412yes—
937C2×C42C2414yes—
938C2×C42C2414yes—
939C2×C42C2414yes—
940C2×C42C2414yes—
941C2×C42C2414yes—
942#95C2411yescharacteristic
943#95C2414yes—
944#95C2412yes—
945#95C2411yescharacteristic
946#95C2412yes—
947#95C2411yescharacteristic
948#95C2412yes—
949#95C2414yes—
950#95C2412yes—
951#95C2414yes—
952#95C2412yes—
953#95C2414yes—
954#95C2412yes—
955#95C2414yes—
956#95C2411yescharacteristic
957#95C2414yes—
958#95C2414yes—
959#95C2412yes—
960#95C2414yes—
961#95C2412yes—
962#95C2412yes—
963#95C2412yes—
964#95C2412yes—
965#95C2412yes—
966#95C2414yes—
967#95C2414yes—
968#95C2414yes—
969#95C2414yes—
970#95C2414yes—
971#95C2414yes—
972#95C2412yes—
973#95C2412yes—
974#95C2412yes—
975#95C2414yes—
976#95C2414yes—
977#95C2414yes—
978#95C2412yes—
979#95C2414yes—
980#95C2414yes—
981#95C2412yes—
982#95C2414yes—
983#95C2414yes—
984#95C2414yes—
985#95C2414yes—
986#95C2412yes—
987#95C2412yes—
988#95C2412yes—
989#95C2412yes—
990#95C2412yes—
991#95C2414yes—
992#95C2414yes—
993#95C2412yes—
994#95C2414yes—
995#95C2412yes—
996#95C2414yes—
997#95C2414yes—
998#95C2412yes—
999#95C2412yes—
1000#95C2412yes—
1001#95C2412yes—
1002#95C2414yes—
1003#95C2414yes—
1004#95C2414yes—
1005#95C2414yes—
1006#95C2414yes—
1007#95C2414yes—
1008#95C2414yes—
1009#95C2414yes—
1010#95C2412yes—
1011#95C2414yes—
1012#95C2414yes—
1013#95C2414yes—
1014#95C2414yes—
1015#95C2414yes—
1016#95C2414yes—
1017C24C2512yes—
1018C24C2511yescharacteristic
1019C24C2511yescharacteristic
1020#41—88no—
1021C2×Q8—24no—
1022C2×Q8—22no—
1023C2×Q8—24no—
1024C2×Q8—24no—
1025C2×Q8—24no—
1026C2×Q8—24no—
1027C2×Q8—24no—
1028C2×Q8—28no—
1029C2×Q8—24no—
1030C2×Q8—24no—
1031C2×Q8—24no—
1032C2×Q8—24no—
1033C2×Q8—24no—
1034C2×Q8—24no—
1035C2×Q8—42no—
1036C2×Q8—41no—
1037C2×Q8—44no—
1038C2×Q8—44no—
1039C2×Q8—42no—
1040C2×Q8—44no—
1041C2×Q8—44no—
1042C2×Q8—416no—
1043C2×Q8—88no—
1044C2×Q8H(5,𝔽2)14yes—
1045C2×D4—24no—
1046C2×D4—22no—
1047C2×D4—22no—
1048C2×D4—24no—
1049C2×D4—24no—
1050C2×D4—42no—
1051C2×D4—41no—
1052C2×D4—41no—
1053C2×D4—42no—
1054C2×D4—44no—
1055C22×C4—24no—
1056C22×C4—22no—
1057C22×C4—24no—
1058C22×C4—22no—
1059C22×C4—22no—
1060C22×C4—24no—
1061C22×C4—24no—
1062C22×C4—24no—
1063C22×C4—24no—
1064C22×C4—28no—
1065C22×C4—41no—
1066C22×C4—44no—
1067C22×C4—42no—
1068C22×C4—41no—
1069C22×C4—44no—
1070C22×C4—44no—
1071C22×C4—42no—
1072C22×C4—42no—
1073C22×C4—41no—
1074C22×C4—44no—
1075C22×C4—44no—
1076C22×C4C2512yes—
1077C22×C4C2512yes—
1078C22×C4C2511yescharacteristic
1079C22×C4C2512yes—
1080C22×C4C2511yescharacteristic
1081C22×C4C2514yes—
1082C22×C4C2514yes—
1083C22×C4C2514yes—
1084C22×C4C2512yes—
1085C22×C4C2512yes—
1086C22×C4C2511yescharacteristic
1087C22×C4C2512yes—
1088C22×C4C2514yes—
1089C22×C4C2514yes—
1090C22×C4C2512yes—
1091C22×C4C2511yescharacteristic
1092C22×C4C2512yes—
1093C22×C4C2512yes—
1094C22×C4C2512yes—
1095C22×C4C2514yes—
1096C22×C4C2512yes—
1097C22×C4C2512yes—
1098C22×C4C2512yes—
1099C22×C4C2512yes—
1100C22×C4C2512yes—
1101C22×C4C2511yescharacteristic
1102C4⋊C4—24no—
1103C4⋊C4—28no—
1104C4⋊C4—22no—
1105C4⋊C4—24no—
1106C4⋊C4—28no—
1107C4⋊C4—28no—
1108C4⋊C4—28no—
1109C4⋊C4—28no—
1110C4⋊C4—24no—
1111C4⋊C4—24no—
1112C4⋊C4—28no—
1113C4⋊C4—28no—
1114C4⋊C4—28no—
1115C4⋊C4—24no—
1116C4⋊C4—24no—
1117C4⋊C4—24no—
1118C4⋊C4—24no—
1119C4⋊C4—24no—
1120C4⋊C4—24no—
1121C4⋊C4—24no—
1122C4⋊C4—24no—
1123C4⋊C4—24no—
1124C4⋊C4—24no—
1125C4⋊C4—24no—
1126C4⋊C4—24no—
1127C4⋊C4—42no—
1128C4⋊C4—44no—
1129C4⋊C4—41no—
1130C4⋊C4—41no—
1131C4⋊C4—44no—
1132C4⋊C4—44no—
1133C4⋊C4—42no—
1134C4⋊C4—41no—
1135C4⋊C4—44no—
1136C4⋊C4—44no—
1137C4⋊C4—44no—
1138C4⋊C4—42no—
1139C4⋊C4—42no—
1140C4⋊C4—42no—
1141C4⋊C4—41no—
1142C4⋊C4—44no—
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⋊C4—44no—
1152C4⋊C4—44no—
1153C4⋊C4—44no—
1154C4⋊C4—42no—
1155C4⋊C4—44no—
1156C4⋊C4—44no—
1157C4⋊C4—44no—
1158C4⋊C4—44no—
1159C4⋊C4—44no—
1160C4⋊C4—42no—
1161C4⋊C4—44no—
1162C4⋊C4—42no—
1163C4⋊C4—42no—
1164C4⋊C4—44no—
1165C4⋊C4—44no—
1166C4⋊C4—44no—
1167C4⋊C4—44no—
1168C4⋊C4—44no—
1169C4⋊C4—44no—
1170C4⋊C4—44no—
1171C4⋊C4—44no—
1172C4⋊C4—44no—
1173C4⋊C42−1+418yes—
1174C22⋊C4—24no—
1175C22⋊C4—24no—
1176C22⋊C4—24no—
1177C22⋊C4—28no—
1178C22⋊C4—24no—
1179C22⋊C4—28no—
1180C22⋊C4—28no—
1181C22⋊C4—24no—
1182C22⋊C4—24no—
1183C22⋊C4—24no—
1184C22⋊C4—24no—
1185C22⋊C4—42no—
1186C22⋊C4—44no—
1187C22⋊C4—44no—
1188C22⋊C4—44no—
1189C22⋊C4—41no—
1190C22⋊C4—42no—
1191C22⋊C4—41no—
1192C22⋊C4—42no—
1193C22⋊C4—42no—
1194C22⋊C4—42no—
1195C22⋊C4—44no—
1196C22⋊C4—44no—
1197C22⋊C4—44no—
1198C22⋊C4—44no—
1199C22⋊C4—44no—
1200C22⋊C4—44no—
1201C22⋊C4—41no—
1202C22⋊C4—42no—
1203C22⋊C4—44no—
1204C22⋊C4—44no—
1205C22⋊C4—44no—
1206C22⋊C4—42no—
1207C22⋊C4—42no—
1208C22⋊C42−1+414yes—
1209C42—28no—
1210C42—24no—
1211C42—24no—
1212C42—24no—
1213C42—22no—
1214C42—24no—
1215C42—24no—
1216C42—24no—
1217C42—24no—
1218C42—24no—
1219C42—24no—
1220C42—24no—
1221C42—44no—
1222C42—42no—
1223C42—42no—
1224C42—44no—
1225C42—44no—
1226C42—44no—
1227C42—44no—
1228C42—44no—
1229C42—44no—
1230C42—44no—
1231C42—42no—
1232C42—44no—
1233C42—44no—
1234C23—21no—
1235C23—22no—
1236C23—22no—
1237C23—21no—
1238C23—22no—
1239C23—21no—
1240C23—22no—
1241C23—24no—
1242C23—21no—
1243C23—22no—
1244C23—24no—
1245C23—22no—
1246C23—21no—
1247C23—22no—
1248C23C2×2−1+412yes—
1249C23C2611yescharacteristic
1250Q8—28no—
1251Q8—48no—
1252Q8—44no—
1253Q8—48no—
1254Q8—48no—
1255Q8—44no—
1256Q8—48no—
1257Q8—88no—
1258Q8—84no—
1259D4—44no—
1260D4—84no—
1261D4—84no—
1262D4—82no—
1263C2×C4—22no—
1264C2×C4—22no—
1265C2×C4—22no—
1266C2×C4—22no—
1267C2×C4—22no—
1268C2×C4—22no—
1269C2×C4—22no—
1270C2×C4—24no—
1271C2×C4—22no—
1272C2×C4—21no—
1273C2×C4—24no—
1274C2×C4—22no—
1275C2×C4—22no—
1276C2×C4—22no—
1277C2×C4—22no—
1278C2×C4—21no—
1279C2×C4—22no—
1280C2×C4—21no—
1281C2×C4—22no—
1282C2×C4—24no—
1283C2×C4—24no—
1284C2×C4—21no—
1285C2×C4—22no—
1286C2×C4—22no—
1287C2×C4—22no—
1288C2×C4—22no—
1289C2×C4—22no—
1290C2×C4—22no—
1291C2×C4—22no—
1292C2×C4—22no—
1293C2×C4—24no—
1294C2×C4—22no—
1295C2×C4—22no—
1296C2×C4—24no—
1297C2×C4—24no—
1298C2×C4—24no—
1299C2×C4—22no—
1300C2×C4—21no—
1301C2×C4—22no—
1302C2×C4—22no—
1303C2×C4—22no—
1304C2×C4—22no—
1305C2×C4—22no—
1306C2×C4—22no—
1307C2×C4—24no—
1308C2×C4—24no—
1309C2×C4—24no—
1310C2×C4—24no—
1311C2×C4—24no—
1312C2×C4—24no—
1313C2×C4—22no—
1314C2×C4—24no—
1315C2×C4—24no—
1316C2×C4—22no—
1317C2×C4—24no—
1318C2×C4—24no—
1319C2×C4—22no—
1320C2×C4—22no—
1321C2×C4—21no—
1322C2×C4—22no—
1323C2×C4—22no—
1324C2×C4—24no—
1325C2×C4—24no—
1326C2×C4—22no—
1327C2×C4—22no—
1328C2×C4—44no—
1329C2×C4—48no—
1330C2×C4—44no—
1331C2×C4—44no—
1332C2×C4—88no—
1333C2×C4—84no—
1334C2×C4—84no—
1335C2×C4—82no—
1336C2×C4—84no—
1337C2×C4C2×H(5,𝔽2)14yes—
1338C2×C4C2×H(5,𝔽2)12yes—
1339C2×C4C2×2−1+414yes—
1340C2×C4C2×2−1+414yes—
1341C2×C4C2×2−1+414yes—
1342C2×C4C2×2−1+414yes—
1343C2×C4#58514yes—
1344C22—24no—
1345C22—22no—
1346C22—41no—
1347C22—41no—
1348C22—42no—
1349C22—41no—
1350C22—42no—
1351C22—42no—
1352C22—41no—
1353C22—42no—
1354C22—44no—
1355C22—42no—
1356C22—41no—
1357C22—44no—
1358C22—42no—
1359C22C22×H(5,𝔽2)11yescharacteristic
1360C22C22×2−1+412yes—
1361C22C22×2−1+411yescharacteristic
1362C22C2×#58512yes—
1363C22H(7,𝔽2)11yescharacteristic
1364C4—24no—
1365C4—24no—
1366C4—24no—
1367C4—24no—
1368C4—24no—
1369C4—41no—
1370C4—41no—
1371C4—42no—
1372C4—44no—
1373C4—44no—
1374C4—41no—
1375C4—42no—
1376C4—42no—
1377C4—42no—
1378C4—42no—
1379C4—42no—
1380C4—44no—
1381C4—42no—
1382C4—42no—
1383C4—41no—
1384C4—42no—
1385C4—42no—
1386C4—44no—
1387C4—44no—
1388C4—44no—
1389C4#353314yes—
1390C2—42no—
1391C2—81no—
1392C2—82no—
1393C2C2×#353311yescharacteristic
1394C2#6291711yescharacteristic
1395C2#6296212yes—
1396C2#6301611yescharacteristic
1397C2#6303212yes—
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. #59938C2semidirect
2. #59828C2semidirect
3. #59697C2semidirect
4. #59479C2semidirect
5. #58390C2semidirect
6. #58292C2semidirect
7. #57359C2semidirect
8. #56663C2semidirect
9. #52300C2semidirect
10. #51594C2semidirect
11. #49087C2semidirect
12. #48289C2semidirect
13. #45675C2semidirect
14. #45503C2semidirect
15. #45419C2semidirect
16. #45345C2semidirect
17. #45323C2semidirect
18. #44994C2semidirect
20. #42840C2semidirect
22. #42702C2semidirect
23. #39663C2semidirect
24. #39663C2semidirect
25. #39200C2semidirect
26. #37058C2semidirect
27. #36954C2semidirect
28. #36545C2semidirect

Maximal subgroups

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

subgroupindex
#599382
#598282
#596972
#594792
#583902
#582922
#573592
#566632
#523002
#515942
#490872
#482892
#456752
#455032
#454192
#453452
#453232
#449942
#429122
#428402
#428152
#427022
#396632
#392002
#370582
#369542
#365452
#364832