Finite Group Databasebeta

← #7652246

Subgroups — #7652246

Order 512.

6400 conjugacy classes of subgroups.

The subgroup lattice has 1466 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#3523C212yesmaximal, complemented
2#42980C211yesmaximal, characteristic, complemented
3#42929C211yesmaximal, characteristic, complemented
4#42811C212yesmaximal, complemented
5#42808C212yesmaximal, complemented
6#42807C211yesmaximal, characteristic, complemented
7#42807C211yesmaximal, characteristic, complemented
8#42315C214yesmaximal, complemented
9#42313C214yesmaximal, complemented
10#42306C214yesmaximal, complemented
11#42300C214yesmaximal, complemented
12#39959C212yesmaximal, complemented
13#39955C212yesmaximal, complemented
14#39851C214yesmaximal, complemented
15#39616C212yesmaximal, complemented
16#39615C212yesmaximal, complemented
17#39591C214yesmaximal, complemented
18#38380C214yesmaximal, complemented
19#38374C214yesmaximal, complemented
20#35671C212yesmaximal, complemented
21#35665C212yesmaximal, complemented
22#35635C212yesmaximal, complemented
23#35319C211yesmaximal, characteristic, complemented
24#35244C212yesmaximal, complemented
25#34880C211yesmaximal, characteristic
26#34691C212yesmaximal, complemented
27#34254C211yesmaximal, characteristic, complemented
28#3523—232no—
29C2×#557C2212yes—
30C2×#557C2212yes—
31C2×#557C2214yes—
32C2×#556C2212yes—
33C2×#556C2214yes—
34C2×#552C2212yes—
35C2×#552C2212yes—
36C2×#552C2214yes—
37C2×#552C2214yes—
38C2×D4×Q8C2212yes—
39C2×D4×Q8C2212yes—
40C2×D4×Q8C2212yes—
41C2×#541C2212yes—
42C2×#541C2214yes—
43C2×#541C2214yes—
44C2×#541C2212yes—
45C2×#533C2212yes—
46C2×#533C2214yes—
47C2×#529C2212yes—
48C2×#529C2214yes—
49C2×#519C2212yes—
50C2×#519C2211yescharacteristic
51C22×C4×Q8C2212yes—
52#2868C2211yescharacteristic
53#2859C2211yescharacteristic
54#2857C2212yes—
55#2852C2214yes—
56#2851C2214yes—
57#2823C2212yes—
58#2822C2214yes—
59#2822C2212yes—
60#2821C2214yes—
61#2817C2212yes—
62#2817C2212yes—
63#2734C2212yes—
64#2734C2212yes—
65#2734C2214yes—
66#2732C2214yes—
67#2729C2214yes—
68#2729C2214yes—
69#2729C2214yes—
70#2729C2214yes—
71#2728C2212yes—
72#2728C2212yes—
73#2722C2214yes—
74#2722C2212yes—
75#2722C2212yes—
76#2720C2214yes—
77#2720C2214yes—
78#2720C2214yes—
79#2720C2214yes—
80#2720C2214yes—
81#2720C2214yes—
82#2719C2214yes—
83#2719C2214yes—
84#2719C2214yes—
85#2715C2214yes—
86#2715C2214yes—
87#2713C2214yes—
88#2713C2214yes—
89#2713C2214yes—
90#2712C2212yes—
91#2696C2214yes—
92#2696C2214yes—
93#2695C2214yes—
94#2695C2214yes—
95#2694C2214yes—
96#2693C2212yes—
97#2674C2214yes—
98#2672C2214yes—
99#2664C2214yes—
100#2664C2214yes—
101#2660C2214yes—
102#2659C2214yes—
103#2642C2212yes—
104#2638C2214yes—
105#2638C2214yes—
106#2637C2214yes—
107#2637C2214yes—
108#2636C2214yes—
109#2634C2214yes—
110#2634C2214yes—
111#2634C2214yes—
112#2629C2214yes—
113#2628C2214yes—
114#2621C2211yescharacteristic
115#2621C2211yescharacteristic
116#2611C2214yes—
117#2611C2214yes—
118#2609C2214yes—
119#2609C2212yes—
120#2604C2214yes—
121#2604C2214yes—
122#2601C2214yes—
123#2601C2214yes—
124#2600C2212yes—
125#2600C2212yes—
126#2599C2214yes—
127#2599C2214yes—
128#2598C2214yes—
129#2584C2212yes—
130#2584C2214yes—
131#2584C2214yes—
132#2582C2212yes—
133#2581C2214yes—
134#2581C2214yes—
135#2568C2212yes—
136#2567C2214yes—
137#2566C2214yes—
138#2564C2214yes—
139#2564C2214yes—
140#2562C2212yes—
141#2559C2214yes—
142#2558C2214yes—
143#2556C2214yes—
144#2556C2212yes—
145#2555C2212yes—
146#2554C2212yes—
147#2553C2214yes—
148#2553C2212yes—
149#2542C2212yes—
150#2521C2214yes—
151#2521C2212yes—
152#2519C2214yes—
153#2519C2212yes—
154#2506C2214yes—
155#2506C2214yes—
156#2506C2214yes—
157#2496C2214yes—
158#2496C2214yes—
159#2496C2214yes—
160#2481C2214yes—
161#2479C2214yes—
162#2477C2214yes—
163#2475C2214yes—
164#2475C2214yes—
165#2473C2214yes—
166#2473C2214yes—
167#2469C2214yes—
168#2469C2214yes—
169#2465C2214yes—
170#2465C2214yes—
171#2464C2212yes—
172#2462C2214yes—
173#2462C2214yes—
174#2462C2214yes—
175#2462C2214yes—
176#2461C2212yes—
177#2453C2212yes—
178#2453C2212yes—
179#2451C2212yes—
180#2451C2212yes—
181#2449C2214yes—
182#2446C2212yes—
183#2446C2212yes—
184#2446C2212yes—
185#2446C2212yes—
186#2442C2212yes—
187#2441C2212yes—
188#2440C2212yes—
189#2439C2212yes—
190#2434C2212yes—
191#2434C2212yes—
192#2434C2212yes—
193#2434C2212yes—
194#2429C2212yes—
195#2429C2212yes—
196#2429C2212yes—
197#2429C2212yes—
198#2423C2212yes—
199#2423C2212yes—
200#2421C2212yes—
201#2421C2212yes—
202#2417C2212yes—
203#2417C2212yes—
204#2417C2212yes—
205#2417C2212yes—
206#2415C2212yes—
207#2415C2212yes—
208#2415C2212yes—
209#2415C2212yes—
210#2409C2212yes—
211#2409C2212yes—
212#2409C2212yes—
213#2409C2212yes—
214#2399C2211yescharacteristic
215#2399C2214yes—
216#2397C2211yescharacteristic
217#2396C2214yes—
218#2392C2211yescharacteristic
219#2392C2211yescharacteristic
220#2356C2214yes—
221#2355C2214yes—
222#2343C2214yes—
223#2343C2214yes—
224#2327C2211yescharacteristic
225#2327C2211yescharacteristic
226#2326C2214yes—
227#2325C2214yes—
228#2323C2214yes—
229#2323C2214yes—
230#2323C2212yes—
231#2323C2212yes—
232#2320C2212yes—
233#2320C2212yes—
234#2317C2211yescharacteristic
235#2310C2211yescharacteristic
236C4×C4⋊Q8C2212yes—
237C4×#124C2212yes—
238C4×C22⋊Q8C2212yes—
239C4×C22⋊Q8C2212yes—
240C4×C22⋊Q8C2214yes—
241C4×#121C2212yes—
242#2296C2211yescharacteristic
243#2295C2212yes—
244#2295C2212yes—
245C2×#391C2211yescharacteristic
246#2293C2211yescharacteristic
247#2290C2212yes—
248#2290C2214yes—
249#2274C2211yescharacteristic
250C42×D4C2211yescharacteristic
251C4×#117C2211yescharacteristic
252C23×Q8C2312yes—
253C23×Q8C2312yes—
254C23×Q8C2311yescharacteristic
255#557—216no—
256#557—232no—
257#557—216no—
258#556—232no—
259#556—216no—
260#552—232no—
261#552—216no—
262#552—232no—
263#552—216no—
264D4×Q8—216no—
265D4×Q8—216no—
266D4×Q8—216no—
267#541—216no—
268#541—232no—
269#541—216no—
270#541—232no—
271#533—216no—
272#533—232no—
273C2×C4⋊Q8C2314yes—
274C2×C4⋊Q8C2312yes—
275C2×C4⋊Q8C2314yes—
276C2×C4⋊Q8C2312yes—
277C2×C4⋊Q8C2312yes—
278C2×C4⋊Q8C2314yes—
279C2×C4⋊Q8C2312yes—
280C2×C4⋊Q8C2314yes—
281C2×C4⋊Q8C2312yes—
282C2×C4⋊Q8C2311yescharacteristic
283C2×C4⋊Q8C2311yescharacteristic
284#529—216no—
285#529—232no—
286C2×#126C2314yes—
287C2×#126C2314yes—
288C2×#126C2314yes—
289C2×#126C2314yes—
290C2×#126C2312yes—
291C2×#126C2314yes—
292C2×#126C2312yes—
293C2×#126C2314yes—
294C2×#126C2314yes—
295C2×#126C2314yes—
296C2×#125C2312yes—
297C2×#125C2314yes—
298C2×#125C2314yes—
299C2×#125C2314yes—
300C2×#125C2314yes—
301C2×#125C2314yes—
302C2×#125C2312yes—
303C2×#125C2314yes—
304C2×#125C2314yes—
305C2×#125C2314yes—
306C2×#125C2314yes—
307C2×#125C2312yes—
308C2×#125C2314yes—
309C2×#125C2314yes—
310C2×#125C2314yes—
311C2×#124C2312yes—
312C2×#124C2314yes—
313C2×#124C2312yes—
314C2×#123C2314yes—
315C2×#123C2314yes—
316C2×#123C2312yes—
317C2×#123C2312yes—
318C2×C22⋊Q8C2314yes—
319C2×C22⋊Q8C2314yes—
320C2×C22⋊Q8C2314yes—
321C2×C22⋊Q8C2312yes—
322C2×C22⋊Q8C2312yes—
323C2×C22⋊Q8C2312yes—
324C2×C22⋊Q8C2312yes—
325C2×C22⋊Q8C2312yes—
326C2×C22⋊Q8C2312yes—
327C2×C22⋊Q8C2314yes—
328C2×C22⋊Q8C2312yes—
329C2×C22⋊Q8C2314yes—
330C2×C22⋊Q8C2314yes—
331C2×C22⋊Q8C2314yes—
332C2×C22⋊Q8C2314yes—
333C2×C22⋊Q8C2312yes—
334C2×C22⋊Q8C2312yes—
335C2×C22⋊Q8C2312yes—
336C2×C22⋊Q8C2312yes—
337C2×#121C2312yes—
338C2×#121C2312yes—
339#519—216no—
340#519D4116yescomplemented
341C2×C4×Q8—216no—
342C2×C4×Q8C2312yes—
343C2×C4×Q8C2312yes—
344C2×C4×Q8C2314yes—
345C2×C4×Q8C2312yes—
346C2×C4×Q8C2314yes—
347C2×C4×Q8C2314yes—
348C2×C4×Q8C2314yes—
349C2×C4×Q8C2314yes—
350C2×C4×Q8C2314yes—
351C2×C4×Q8C2312yes—
352C2×C4×Q8C2312yes—
353C2×C4×Q8C2314yes—
354C2×C4×Q8C2312yes—
355C2×C4×Q8C2312yes—
356C2×C4×Q8C2314yes—
357C2×C4×Q8C2312yes—
358C2×C4×Q8C2312yes—
359C2×C4×Q8C2314yes—
360C2×C4×D4C2312yes—
361C2×C4×D4C2314yes—
362C2×C4×D4C2314yes—
363C2×C4×D4C2314yes—
364C2×C4×D4C2312yes—
365C2×C4×D4C2312yes—
366C2×C4×D4C2312yes—
367C2×C4×D4C2311yescharacteristic
368C2×C4×D4C2311yescharacteristic
369C2×C4×D4C2312yes—
370C2×#117C2312yes—
371C2×#117C2314yes—
372C2×#117C2314yes—
373C2×#117C2314yes—
374C2×#117C2314yes—
375C2×#117C2312yes—
376C2×#117C2314yes—
377C2×#117C2311yescharacteristic
378C2×#117C2311yescharacteristic
379C2×#117C2311yescharacteristic
380C2×#117C2314yes—
381C2×#117C2311yescharacteristic
382C22×C4⋊C4C2312yes—
383C22×C4⋊C4C2314yes—
384C22×C4⋊C4C2311yescharacteristic
385C22×C42C2314yes—
386C22×C42C2312yes—
387C22×C42C2311yescharacteristic
388#400C2314yes—
389#400C2314yes—
390#400C2314yes—
391#400C2314yes—
392#400C2314yes—
393#400C2314yes—
394#400C2314yes—
395#400C2314yes—
396#400C2314yes—
397#400C2314yes—
398#400C2314yes—
399#400C2314yes—
400#400C2314yes—
401#400C2314yes—
402#400C2314yes—
403#400C2314yes—
404#399C2314yes—
405#399C2314yes—
406#399C2312yes—
407#399C2314yes—
408#399C2314yes—
409#399C2314yes—
410#399C2312yes—
411#398C2314yes—
412#398C2314yes—
413#398C2311yescharacteristic
414#398C2312yes—
415#398C2314yes—
416#398C2314yes—
417#398C2314yes—
418#398C2314yes—
419#398C2314yes—
420#398C2314yes—
421#398C2314yes—
422#398C2312yes—
423#398C2314yes—
424#398C2314yes—
425#398C2312yes—
426#398C2311yescharacteristic
427#398C2314yes—
428#398C2314yes—
429#398C2314yes—
430#398C2312yes—
431#398C2312yes—
432#398C2314yes—
433#398C2312yes—
434#398C2314yes—
435#398C2314yes—
436#398C2314yes—
437#398C2314yes—
438#398C2314yes—
439#398C2314yes—
440#397C2311yescharacteristic
441#397C2311yescharacteristic
442#397C2312yes—
443#397C2312yes—
444#397C2314yes—
445#397C2314yes—
446#397C2314yes—
447#397C2314yes—
448#397C2314yes—
449#397C2312yes—
450#397C2312yes—
451#397C2314yes—
452#396C2314yes—
453#396C2314yes—
454#396C2314yes—
455#396C2314yes—
456#396C2314yes—
457#396C2314yes—
458#396C2314yes—
459#396C2314yes—
460#396C2312yes—
461#396C2314yes—
462#396C2314yes—
463#396C2312yes—
464#395C2314yes—
465#395C2314yes—
466#395C2314yes—
467#395C2314yes—
468#395C2314yes—
469#395C2314yes—
470#395C2314yes—
471#395C2314yes—
472#395C2314yes—
473#395C2312yes—
474#395C2314yes—
475#395C2314yes—
476#395C2314yes—
477#395C2314yes—
478#395C2312yes—
479#395C2314yes—
480#395C2314yes—
481#395C2314yes—
482#394C2314yes—
483#394C2311yescharacteristic
484#394C2314yes—
485#394C2314yes—
486#394C2314yes—
487#394C2314yes—
488#394C2311yescharacteristic
489#394C2312yes—
490#394C2312yes—
491#393C2314yes—
492#393C2314yes—
493#393C2314yes—
494#393C2314yes—
495#393C2314yes—
496#392C2312yes—
497#392C2311yescharacteristic
498#392C2311yescharacteristic
499#392C2312yes—
500#391C2312yes—
501#391C2312yes—
502#391C2312yes—
503#391C2312yes—
504#391C2312yes—
505#391C2312yes—
506#391C2312yes—
507#391C2314yes—
508#391C2312yes—
509#391C2312yes—
510#391C2312yes—
511#391C2312yes—
512#391C2312yes—
513#391C2314yes—
514#391C2314yes—
515#391C2314yes—
516#391C2312yes—
517#391C2312yes—
518#391C2314yes—
519#391C2312yes—
520#390C2312yes—
521#390C2314yes—
522#390C2312yes—
523#390C2312yes—
524#389C2314yes—
525#389C2314yes—
526#389C2314yes—
527#389C2314yes—
528#389C2314yes—
529#389C2314yes—
530#389C2312yes—
531#389C2312yes—
532#389C2312yes—
533#389C2314yes—
534#389C2314yes—
535#389C2314yes—
536#389C2314yes—
537#389C2312yes—
538#389C2314yes—
539#389C2312yes—
540#389C2314yes—
541#389C2314yes—
542#389C2314yes—
543#389C2314yes—
544#389C2314yes—
545#389C2314yes—
546#389C2312yes—
547#389C2312yes—
548#389C2314yes—
549#389C2314yes—
550#389C2314yes—
551#389C2312yes—
552#389C2312yes—
553#389C2314yes—
554#389C2312yes—
555#388C2314yes—
556#388C2314yes—
557#388C2312yes—
558#388C2312yes—
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#388C2314yes—
573#388C2314yes—
574#388C2312yes—
575#388C2314yes—
576#388C2312yes—
577#388C2312yes—
578#388C2312yes—
579#388C2312yes—
580#388C2312yes—
581#388C2312yes—
582#388C2312yes—
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#387C2312yes—
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#387C2312yes—
616#387C2314yes—
617#387C2314yes—
618#387C2314yes—
619#386C2312yes—
620#386C2312yes—
621#386C2314yes—
622#386C2314yes—
623#386C2314yes—
624#386C2314yes—
625#386C2312yes—
626#386C2314yes—
627#386C2314yes—
628#386C2314yes—
629#386C2314yes—
630#386C2312yes—
631#385C2314yes—
632#385C2314yes—
633#385C2314yes—
634#385C2314yes—
635#385C2314yes—
636#385C2314yes—
637#385C2314yes—
638#385C2312yes—
639#385C2312yes—
640#385C2314yes—
641#385C2314yes—
642#385C2314yes—
643#385C2312yes—
644#385C2314yes—
645#385C2314yes—
646#385C2314yes—
647#385C2314yes—
648#385C2312yes—
649#385C2314yes—
650#385C2314yes—
651#385C2314yes—
652#384C2312yes—
653#384C2314yes—
654#384C2314yes—
655#384C2312yes—
656#384C2314yes—
657#383C2314yes—
658#383C2314yes—
659#382C2314yes—
660#382C2312yes—
661#382C2314yes—
662#382C2314yes—
663#382C2311yescharacteristic
664#382C2311yescharacteristic
665#382C2312yes—
666#381C2312yes—
667#381C2312yes—
668#380C2312yes—
669#380C2312yes—
670#380C2312yes—
671#380C2312yes—
672#380C2314yes—
673#380C2314yes—
674#380C2314yes—
675#380C2314yes—
676#380C2314yes—
677#380C2314yes—
678#380C2314yes—
679#380C2312yes—
680C4×C4⋊C4C2312yes—
681C4×C4⋊C4C2314yes—
682C4×C4⋊C4C2314yes—
683C4×C4⋊C4C2314yes—
684C4×C4⋊C4C2312yes—
685C4×C4⋊C4C2314yes—
686C4×C4⋊C4C2314yes—
687C4×C4⋊C4C2312yes—
688C4×C4⋊C4C2314yes—
689C4×C4⋊C4C2312yes—
690C4×C4⋊C4C2311yescharacteristic
691C4×C4⋊C4C2311yescharacteristic
692C4×C4⋊C4C2314yes—
693C4×C4⋊C4C2312yes—
694C4×C4⋊C4C2312yes—
695C4×C4⋊C4C2314yes—
696C4×C22⋊C4C2312yes—
697C4×C22⋊C4C2312yes—
698C4×C22⋊C4C2314yes—
699C4×C22⋊C4C2312yes—
700C4×C22⋊C4C2312yes—
701C4×C22⋊C4C2312yes—
702C4×C22⋊C4C2314yes—
703C4×C22⋊C4C2312yes—
704C4×C22⋊C4C2312yes—
705C4×C22⋊C4C2312yes—
706C4×C22⋊C4C2314yes—
707#376C2311yescharacteristic
708#376C2311yescharacteristic
709#376C2314yes—
710#376C2314yes—
711C2×#95C2314yes—
712C43C2311yescharacteristic
713C43C2311yescharacteristic
714C22×Q8—28no—
715C22×Q8—28no—
716C22×Q8—42no—
717C22×Q8—42no—
718C22×Q8—44no—
719C22×Q8—44no—
720C22×Q8—44no—
721C22×Q8—44no—
722C22×Q8C2×D418yes—
723C22×Q8C2412yes—
724C22×Q8C2412yes—
725C22×Q8C2414yes—
726C22×Q8C2412yes—
727C22×Q8C2412yes—
728C22×Q8C2414yes—
729C22×Q8C2414yes—
730C22×Q8C2412yes—
731C22×D4C2412yes—
732C22×D4C2412yes—
733C22×D4C2412yes—
734C22×D4C2411yescharacteristic
735C22×D4C2412yes—
736C22×D4C2411yescharacteristic
737C23×C4C2412yes—
738C23×C4C2412yes—
739C23×C4C2412yes—
740C23×C4C2414yes—
741C23×C4C2412yes—
742C23×C4C2411yescharacteristic
743C23×C4C2414yes—
744C23×C4C2414yes—
745C23×C4C2412yes—
746C23×C4C2412yes—
747C23×C4C2412yes—
748C4⋊Q8—28no—
749C4⋊Q8—216no—
750C4⋊Q8—28no—
751C4⋊Q8—216no—
752C4⋊Q8—28no—
753C4⋊Q8—216no—
754C4⋊Q8—216no—
755C4⋊Q8—28no—
756C4⋊Q8—44no—
757C4⋊Q8—42no—
758C4⋊Q8—42no—
759#126—216no—
760#126—28no—
761#126—28no—
762#126—216no—
763#126—216no—
764#126—216no—
765#126—216no—
766#126—216no—
767#126—216no—
768#126—216no—
769#125—216no—
770#125—28no—
771#125—216no—
772#125—216no—
773#125—216no—
774#125—216no—
775#125—216no—
776#125—216no—
777#125—28no—
778#125—216no—
779#125—216no—
780#125—216no—
781#125—216no—
782#125—216no—
783#125—28no—
784#124—28no—
785#124—216no—
786#124—28no—
787#123—216no—
788#123—28no—
789#123—28no—
790#123—216no—
791C22⋊Q8—28no—
792C22⋊Q8—216no—
793C22⋊Q8—28no—
794C22⋊Q8—216no—
795C22⋊Q8—28no—
796C22⋊Q8—216no—
797C22⋊Q8—28no—
798C22⋊Q8—216no—
799C22⋊Q8—216no—
800C22⋊Q8—28no—
801C22⋊Q8—28no—
802C22⋊Q8—216no—
803C22⋊Q8—28no—
804C22⋊Q8—216no—
805C22⋊Q8—216no—
806C22⋊Q8—44no—
807C22⋊Q8—44no—
808C22⋊Q8—44no—
809C22⋊Q8—44no—
810#121—28no—
811#121—28no—
812C4×Q8—28no—
813C4×Q8—28no—
814C4×Q8—28no—
815C4×Q8—216no—
816C4×Q8—28no—
817C4×Q8—216no—
818C4×Q8—28no—
819C4×Q8—216no—
820C4×Q8—28no—
821C4×Q8—216no—
822C4×Q8—216no—
823C4×Q8—28no—
824C4×Q8—216no—
825C4×Q8—216no—
826C4×Q8—216no—
827C4×Q8C2×D4116yes—
828C4×Q8C2×D4132yes—
829C4×Q8C2×D4116yes—
830C4×D4—28no—
831C4×D4—216no—
832C4×D4—28no—
833C4×D4—216no—
834C4×D4—28no—
835C4×D4—216no—
836C4×D4—28no—
837C4×D4—44no—
838C4×D4—42no—
839C4×D4—42no—
840#117—28no—
841#117—216no—
842#117—28no—
843#117—216no—
844#117—216no—
845#117—216no—
846#117—216no—
847#117—42no—
848#117—42no—
849#117C2×D418yes—
850#117C2×D4132yes—
851#117C2×D418yes—
852C2×C4⋊C4—28no—
853C2×C4⋊C4—216no—
854C2×C4⋊C4—42no—
855C2×C4⋊C4C2412yes—
856C2×C4⋊C4C2414yes—
857C2×C4⋊C4C2414yes—
858C2×C4⋊C4C2414yes—
859C2×C4⋊C4C2414yes—
860C2×C4⋊C4C2412yes—
861C2×C4⋊C4C2412yes—
862C2×C4⋊C4C2414yes—
863C2×C4⋊C4C2412yes—
864C2×C4⋊C4C2414yes—
865C2×C4⋊C4C2412yes—
866C2×C4⋊C4C2414yes—
867C2×C4⋊C4C2414yes—
868C2×C4⋊C4C2414yes—
869C2×C4⋊C4C2414yes—
870C2×C4⋊C4C2412yes—
871C2×C4⋊C4C2414yes—
872C2×C4⋊C4C2414yes—
873C2×C4⋊C4C2414yes—
874C2×C4⋊C4C2414yes—
875C2×C4⋊C4C2412yes—
876C2×C4⋊C4C2412yes—
877C2×C4⋊C4C2414yes—
878C2×C4⋊C4C2414yes—
879C2×C4⋊C4C2412yes—
880C2×C4⋊C4C2412yes—
881C2×C4⋊C4C2412yes—
882C2×C4⋊C4C2414yes—
883C2×C4⋊C4C2414yes—
884C2×C4⋊C4C2414yes—
885C2×C4⋊C4C2414yes—
886C2×C4⋊C4C2414yes—
887C2×C4⋊C4C2414yes—
888C2×C4⋊C4C2414yes—
889C2×C4⋊C4C2412yes—
890C2×C4⋊C4C2412yes—
891C2×C4⋊C4C2414yes—
892C2×C4⋊C4C2412yes—
893C2×C4⋊C4C2414yes—
894C2×C4⋊C4C2414yes—
895C2×C4⋊C4C2414yes—
896C2×C4⋊C4C2412yes—
897C2×C4⋊C4C2411yescharacteristic
898C2×C4⋊C4C2411yescharacteristic
899C2×C4⋊C4C2411yescharacteristic
900C2×C4⋊C4C2412yes—
901C2×C4⋊C4C2411yescharacteristic
902C2×C4⋊C4C2414yes—
903C2×C4⋊C4C2414yes—
904C2×C4⋊C4C2414yes—
905C2×C4⋊C4C2414yes—
906C2×C4⋊C4C2414yes—
907C2×C4⋊C4C2414yes—
908C2×C4⋊C4C2412yes—
909C2×C4⋊C4C2412yes—
910C2×C4⋊C4C2412yes—
911C2×C4⋊C4C2412yes—
912C2×C4⋊C4C2414yes—
913C2×C4⋊C4C2414yes—
914C2×C4⋊C4C2414yes—
915C2×C4⋊C4C2414yes—
916C2×C4⋊C4C2412yes—
917C2×C4⋊C4C2414yes—
918C2×C4⋊C4C2412yes—
919C2×C4⋊C4C2414yes—
920C2×C4⋊C4C2414yes—
921C2×C4⋊C4C2412yes—
922C2×C4⋊C4C2414yes—
923C2×C4⋊C4C2414yes—
924C2×C4⋊C4C2412yes—
925C2×C22⋊C4C2412yes—
926C2×C22⋊C4C2412yes—
927C2×C22⋊C4C2414yes—
928C2×C22⋊C4C2414yes—
929C2×C22⋊C4C2414yes—
930C2×C22⋊C4C2412yes—
931C2×C22⋊C4C2412yes—
932C2×C22⋊C4C2414yes—
933C2×C22⋊C4C2412yes—
934C2×C22⋊C4C2414yes—
935C2×C22⋊C4C2412yes—
936C2×C22⋊C4C2414yes—
937C2×C22⋊C4C2412yes—
938C2×C22⋊C4C2414yes—
939C2×C22⋊C4C2412yes—
940C2×C22⋊C4C2412yes—
941C2×C22⋊C4C2412yes—
942C2×C22⋊C4C2414yes—
943C2×C22⋊C4C2412yes—
944C2×C22⋊C4C2412yes—
945C2×C22⋊C4C2412yes—
946C2×C22⋊C4C2411yescharacteristic
947C2×C22⋊C4C2411yescharacteristic
948C2×C22⋊C4C2412yes—
949C2×C22⋊C4C2412yes—
950C2×C22⋊C4C2412yes—
951C2×C22⋊C4C2412yes—
952C2×C22⋊C4C2412yes—
953C2×C22⋊C4C2414yes—
954C2×C22⋊C4C2414yes—
955C2×C22⋊C4C2414yes—
956C2×C22⋊C4C2414yes—
957C2×C22⋊C4C2414yes—
958C2×C22⋊C4C2412yes—
959C2×C22⋊C4C2412yes—
960C2×C22⋊C4C2414yes—
961C2×C22⋊C4C2414yes—
962C2×C22⋊C4C2412yes—
963C2×C22⋊C4C2412yes—
964C2×C22⋊C4C2412yes—
965C2×C42—28no—
966C2×C42—216no—
967C2×C42—42no—
968C2×C42C2414yes—
969C2×C42C2414yes—
970C2×C42C2414yes—
971C2×C42C2411yescharacteristic
972C2×C42C2412yes—
973C2×C42C2414yes—
974C2×C42C2411yescharacteristic
975C2×C42C2411yescharacteristic
976C2×C42C2412yes—
977C2×C42C2414yes—
978C2×C42C2412yes—
979C2×C42C2412yes—
980C2×C42C2414yes—
981C2×C42C2414yes—
982C2×C42C2412yes—
983C2×C42C2412yes—
984C2×C42C2411yescharacteristic
985C2×C42C2412yes—
986C2×C42C2412yes—
987C2×C42C2412yes—
988C2×C42C2414yes—
989C2×C42C2414yes—
990C2×C42C2412yes—
991C2×C42C2411yescharacteristic
992C2×C42C2414yes—
993C2×C42C2412yes—
994C2×C42C2414yes—
995C2×C42C2411yescharacteristic
996#95C2414yes—
997#95C2414yes—
998#95C2414yes—
999#95C2414yes—
1000#95C2414yes—
1001#95C2412yes—
1002#95C2412yes—
1003#95C2412yes—
1004#95C2412yes—
1005#95C2414yes—
1006#95C2414yes—
1007#95C2414yes—
1008#95C2414yes—
1009#95C2412yes—
1010#95C2412yes—
1011#95C2411yescharacteristic
1012#95C2411yescharacteristic
1013#95C2414yes—
1014#95C2414yes—
1015#95C2414yes—
1016#95C2412yes—
1017#95C2412yes—
1018#95C2412yes—
1019#95C2412yes—
1020#95C2412yes—
1021#95C2414yes—
1022#95C2414yes—
1023#95C2414yes—
1024#95C2412yes—
1025#95C2414yes—
1026#95C2414yes—
1027#95C2414yes—
1028#95C2414yes—
1029#95C2414yes—
1030#95C2414yes—
1031#95C2414yes—
1032#95C2414yes—
1033#95C2414yes—
1034#95C2414yes—
1035#95C2412yes—
1036#95C2412yes—
1037#95C2414yes—
1038#95C2411yescharacteristic
1039#95C2411yescharacteristic
1040#95C2412yes—
1041#95C2414yes—
1042#95C2414yes—
1043#95C2414yes—
1044#95C2414yes—
1045#95C2414yes—
1046#95C2414yes—
1047#95C2414yes—
1048#95C2414yes—
1049#95C2412yes—
1050#95C2414yes—
1051#95C2414yes—
1052#95C2412yes—
1053#95C2412yes—
1054#95C2414yes—
1055#95C2414yes—
1056C24C2512yes—
1057C24C2511yescharacteristic
1058C24C2512yes—
1059C2×Q8—28no—
1060C2×Q8—24no—
1061C2×Q8—28no—
1062C2×Q8—28no—
1063C2×Q8—24no—
1064C2×Q8—24no—
1065C2×Q8—28no—
1066C2×Q8—24no—
1067C2×Q8—24no—
1068C2×Q8—24no—
1069C2×Q8—24no—
1070C2×Q8—24no—
1071C2×Q8—24no—
1072C2×Q8—24no—
1073C2×Q8—42no—
1074C2×Q8—42no—
1075C2×Q8—44no—
1076C2×Q8—44no—
1077C2×Q8—44no—
1078C2×Q8—44no—
1079C2×Q8—42no—
1080C2×Q8—44no—
1081C2×Q8—416no—
1082C2×Q8—432no—
1083C2×Q8—432no—
1084C2×Q8C22×D418yes—
1085C2×Q8C22×D418yes—
1086C2×D4—24no—
1087C2×D4—24no—
1088C2×D4—24no—
1089C2×D4—24no—
1090C2×D4—24no—
1091C2×D4—24no—
1092C2×D4—24no—
1093C2×D4—24no—
1094C2×D4—41no—
1095C2×D4—42no—
1096C2×D4—42no—
1097C2×D4—42no—
1098C2×D4—42no—
1099C2×D4—41no—
1100C2×D4—42no—
1101C2×D4—42no—
1102C22×C4—22no—
1103C22×C4—22no—
1104C22×C4—24no—
1105C22×C4—28no—
1106C22×C4—24no—
1107C22×C4—24no—
1108C22×C4—28no—
1109C22×C4—28no—
1110C22×C4—24no—
1111C22×C4—28no—
1112C22×C4—24no—
1113C22×C4—24no—
1114C22×C4—24no—
1115C22×C4—24no—
1116C22×C4—24no—
1117C22×C4—24no—
1118C22×C4—24no—
1119C22×C4—42no—
1120C22×C4—42no—
1121C22×C4—44no—
1122C22×C4—42no—
1123C22×C4—42no—
1124C22×C4—44no—
1125C22×C4—44no—
1126C22×C4—44no—
1127C22×C4—44no—
1128C22×C4—42no—
1129C22×C4—42no—
1130C22×C4—42no—
1131C22×C4—44no—
1132C22×C4C22×D414yes—
1133C22×C4C22×D418yes—
1134C22×C4C2511yescharacteristic
1135C22×C4C2512yes—
1136C22×C4C2511yescharacteristic
1137C22×C4C2514yes—
1138C22×C4C2511yescharacteristic
1139C22×C4C2514yes—
1140C22×C4C2511yescharacteristic
1141C22×C4C2512yes—
1142C22×C4C2514yes—
1143C22×C4C2512yes—
1144C22×C4C2512yes—
1145C22×C4C2514yes—
1146C22×C4C2512yes—
1147C22×C4C2512yes—
1148C22×C4C2514yes—
1149C22×C4C2514yes—
1150C22×C4C2514yes—
1151C22×C4C2512yes—
1152C22×C4C2512yes—
1153C22×C4C2514yes—
1154C22×C4C2511yescharacteristic
1155C22×C4C2512yes—
1156C22×C4C2512yes—
1157C22×C4C2511yescharacteristic
1158C4⋊C4—28no—
1159C4⋊C4—24no—
1160C4⋊C4—28no—
1161C4⋊C4—28no—
1162C4⋊C4—28no—
1163C4⋊C4—28no—
1164C4⋊C4—24no—
1165C4⋊C4—24no—
1166C4⋊C4—28no—
1167C4⋊C4—24no—
1168C4⋊C4—28no—
1169C4⋊C4—28no—
1170C4⋊C4—28no—
1171C4⋊C4—28no—
1172C4⋊C4—28no—
1173C4⋊C4—28no—
1174C4⋊C4—28no—
1175C4⋊C4—28no—
1176C4⋊C4—24no—
1177C4⋊C4—28no—
1178C4⋊C4—24no—
1179C4⋊C4—24no—
1180C4⋊C4—28no—
1181C4⋊C4—24no—
1182C4⋊C4—28no—
1183C4⋊C4—28no—
1184C4⋊C4—28no—
1185C4⋊C4—28no—
1186C4⋊C4—28no—
1187C4⋊C4—28no—
1188C4⋊C4—24no—
1189C4⋊C4—28no—
1190C4⋊C4—28no—
1191C4⋊C4—24no—
1192C4⋊C4—24no—
1193C4⋊C4—24no—
1194C4⋊C4—28no—
1195C4⋊C4—28no—
1196C4⋊C4—28no—
1197C4⋊C4—24no—
1198C4⋊C4—24no—
1199C4⋊C4—42no—
1200C4⋊C4—44no—
1201C4⋊C4—44no—
1202C4⋊C4—44no—
1203C4⋊C4—44no—
1204C4⋊C4—44no—
1205C4⋊C4—44no—
1206C4⋊C4—44no—
1207C4⋊C4—42no—
1208C4⋊C4—42no—
1209C4⋊C4—41no—
1210C4⋊C4—41no—
1211C4⋊C4—42no—
1212C4⋊C4—41no—
1213C4⋊C4—41no—
1214C4⋊C4—44no—
1215C4⋊C4—44no—
1216C4⋊C4—44no—
1217C4⋊C4—44no—
1218C4⋊C4—44no—
1219C4⋊C4—44no—
1220C4⋊C4—42no—
1221C4⋊C4—42no—
1222C4⋊C4—42no—
1223C4⋊C4—42no—
1224C4⋊C4C22×D418yes—
1225C4⋊C4C22×D4116yes—
1226C4⋊C4C22×D4116yes—
1227C4⋊C4C22×D418yes—
1228C22⋊C4—28no—
1229C22⋊C4—24no—
1230C22⋊C4—28no—
1231C22⋊C4—24no—
1232C22⋊C4—28no—
1233C22⋊C4—24no—
1234C22⋊C4—24no—
1235C22⋊C4—24no—
1236C22⋊C4—28no—
1237C22⋊C4—28no—
1238C22⋊C4—24no—
1239C22⋊C4—28no—
1240C22⋊C4—24no—
1241C22⋊C4—28no—
1242C22⋊C4—24no—
1243C22⋊C4—28no—
1244C22⋊C4—24no—
1245C22⋊C4—24no—
1246C22⋊C4—24no—
1247C22⋊C4—24no—
1248C22⋊C4—24no—
1249C22⋊C4—44no—
1250C22⋊C4—42no—
1251C22⋊C4—42no—
1252C22⋊C4—44no—
1253C22⋊C4—44no—
1254C22⋊C4—41no—
1255C22⋊C4—41no—
1256C22⋊C4—42no—
1257C22⋊C4—42no—
1258C22⋊C4—42no—
1259C22⋊C4—42no—
1260C22⋊C4—42no—
1261C22⋊C4—44no—
1262C22⋊C4—44no—
1263C22⋊C4—44no—
1264C22⋊C4—44no—
1265C22⋊C4C22×D418yes—
1266C22⋊C4C22×D418yes—
1267C22⋊C42−1+418yes—
1268C42—28no—
1269C42—24no—
1270C42—24no—
1271C42—28no—
1272C42—24no—
1273C42—28no—
1274C42—28no—
1275C42—28no—
1276C42—28no—
1277C42—28no—
1278C42—24no—
1279C42—24no—
1280C42—24no—
1281C42—22no—
1282C42—22no—
1283C42—22no—
1284C42—22no—
1285C42—42no—
1286C42—42no—
1287C42—44no—
1288C42—42no—
1289C42—44no—
1290C42—42no—
1291C42C22×D414yes—
1292C42C22×D4116yes—
1293C42C22×D418yes—
1294C42C22×D4116yes—
1295C42C22×D414yes—
1296C23—22no—
1297C23—22no—
1298C23—22no—
1299C23—22no—
1300C23—22no—
1301C23—21no—
1302C23—21no—
1303C23—22no—
1304C23—22no—
1305C23—22no—
1306C23—22no—
1307C23—22no—
1308C23—22no—
1309C23—22no—
1310C23—22no—
1311C23—22no—
1312C23—22no—
1313C23C23×D412yes—
1314C23C2×2−1+414yes—
1315C23C2611yescharacteristic
1316Q8—216no—
1317Q8—48no—
1318Q8—416no—
1319Q8—48no—
1320Q8—416no—
1321Q8—416no—
1322Q8—48no—
1323Q8—48no—
1324D4—48no—
1325D4—48no—
1326D4—48no—
1327D4—44no—
1328D4—84no—
1329D4—82no—
1330C2×C4—22no—
1331C2×C4—22no—
1332C2×C4—22no—
1333C2×C4—24no—
1334C2×C4—22no—
1335C2×C4—21no—
1336C2×C4—21no—
1337C2×C4—24no—
1338C2×C4—24no—
1339C2×C4—22no—
1340C2×C4—22no—
1341C2×C4—22no—
1342C2×C4—24no—
1343C2×C4—22no—
1344C2×C4—28no—
1345C2×C4—22no—
1346C2×C4—24no—
1347C2×C4—22no—
1348C2×C4—22no—
1349C2×C4—24no—
1350C2×C4—22no—
1351C2×C4—24no—
1352C2×C4—22no—
1353C2×C4—24no—
1354C2×C4—22no—
1355C2×C4—22no—
1356C2×C4—22no—
1357C2×C4—24no—
1358C2×C4—22no—
1359C2×C4—22no—
1360C2×C4—24no—
1361C2×C4—24no—
1362C2×C4—22no—
1363C2×C4—22no—
1364C2×C4—21no—
1365C2×C4—21no—
1366C2×C4—21no—
1367C2×C4—21no—
1368C2×C4—24no—
1369C2×C4—24no—
1370C2×C4—22no—
1371C2×C4—22no—
1372C2×C4—22no—
1373C2×C4—22no—
1374C2×C4—24no—
1375C2×C4—24no—
1376C2×C4—24no—
1377C2×C4—24no—
1378C2×C4—24no—
1379C2×C4—22no—
1380C2×C4—24no—
1381C2×C4—24no—
1382C2×C4—22no—
1383C2×C4—24no—
1384C2×C4—22no—
1385C2×C4—22no—
1386C2×C4—24no—
1387C2×C4—22no—
1388C2×C4—22no—
1389C2×C4—48no—
1390C2×C4—48no—
1391C2×C4—48no—
1392C2×C4—416no—
1393C2×C4—416no—
1394C2×C4—416no—
1395C2×C4—48no—
1396C2×C4—48no—
1397C2×C4—84no—
1398C2×C4—162no—
1399C2×C4C23×D414yes—
1400C2×C4C23×D418yes—
1401C2×C4C23×D418yes—
1402C2×C4C23×D414yes—
1403C2×C4C23×D412yes—
1404C2×C4C23×D412yes—
1405C2×C4C2×2−1+414yes—
1406C2×C4C2×2−1+414yes—
1407C2×C4#58512yes—
1408C2×C4#58512yes—
1409C22—24no—
1410C22—24no—
1411C22—24no—
1412C22—22no—
1413C22—24no—
1414C22—42no—
1415C22—41no—
1416C22—41no—
1417C22—42no—
1418C22—42no—
1419C22—42no—
1420C22—42no—
1421C22—42no—
1422C22—42no—
1423C22—42no—
1424C22—42no—
1425C22—42no—
1426C22—42no—
1427C22—42no—
1428C22C24×D411yescharacteristic
1429C22C22×2−1+412yes—
1430C22C2×#58511yescharacteristic
1431C22C2×#58511yescharacteristic
1432C222−1+612yes—
1433C4—24no—
1434C4—28no—
1435C4—24no—
1436C4—24no—
1437C4—22no—
1438C4—28no—
1439C4—24no—
1440C4—42no—
1441C4—44no—
1442C4—42no—
1443C4—42no—
1444C4—44no—
1445C4—41no—
1446C4—41no—
1447C4—41no—
1448C4—44no—
1449C4—41no—
1450C4—42no—
1451C4—42no—
1452C4—44no—
1453C4—44no—
1454C4—44no—
1455C4—42no—
1456C4#344914yes—
1457C2—44no—
1458C2—42no—
1459C2—82no—
1460C2C2×#344911yescharacteristic
1461C2#6283711yescharacteristic
1462C2#6289111yescharacteristic
1463C2#6295012yes—
1464C2D4×2−1+412yes—
subgroupG/H
center, commutator, Frattini, socle, cosocleC23C26
prime radical#34880C2
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23 ◁ G
LECSG ▷ C23 ▷ C1

Complements

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

NH ≅ G/Ntype
1. C2×#3523C2semidirect
2. #42980C2semidirect
3. #42929C2semidirect
4. #42811C2semidirect
5. #42808C2semidirect
6. #42807C2semidirect
7. #42807C2semidirect
8. #42315C2semidirect
9. #42313C2semidirect
10. #42306C2semidirect
11. #42300C2semidirect
12. #39959C2semidirect
13. #39955C2semidirect
14. #39851C2semidirect
15. #39616C2semidirect
16. #39615C2semidirect
17. #39591C2semidirect
18. #38380C2semidirect
19. #38374C2semidirect
20. #35671C2semidirect
21. #35665C2semidirect
22. #35635C2semidirect
23. #35319C2semidirect
24. #35244C2semidirect
26. #34691C2semidirect
27. #34254C2semidirect
340. #519D4semidirect

Maximal subgroups

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

subgroupindex
C2×#35232
#429802
#429292
#428112
#428082
#428072
#423152
#423132
#423062
#423002
#399592
#399552
#398512
#396162
#396152
#395912
#383802
#383742
#356712
#356652
#356352
#353192
#352442
#348802
#346912
#342542