Finite Group Databasebeta

← #7652740

Subgroups — #7652740

Order 512.

6814 conjugacy classes of subgroups.

The subgroup lattice has 1580 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#3524C212yesmaximal, complemented
2#42971C211yesmaximal, characteristic, complemented
3#42952C211yesmaximal, characteristic, complemented
4#42886C212yesmaximal, complemented
5#42885C212yesmaximal, complemented
6#42883C211yesmaximal, characteristic, complemented
7#42883C211yesmaximal, characteristic, complemented
8#41961C214yesmaximal, complemented
9#41956C214yesmaximal, complemented
10#41945C214yesmaximal, complemented
11#41942C214yesmaximal, complemented
12#39958C212yesmaximal, complemented
13#39955C212yesmaximal, complemented
14#39850C214yesmaximal, complemented
15#39745C212yesmaximal, complemented
16#39743C212yesmaximal, complemented
17#39130C214yesmaximal, complemented
18#38381C214yesmaximal, complemented
19#38378C214yesmaximal, complemented
20#35567C212yesmaximal, complemented
21#35539C212yesmaximal, complemented
22#35525C212yesmaximal, complemented
23#35278C211yesmaximal, characteristic, complemented
24#35195C212yesmaximal, complemented
25#34880C211yesmaximal, characteristic, complemented
26#34727C212yesmaximal, complemented
27#34254C211yesmaximal, characteristic, complemented
28#3524—232no—
29C2×#559C2212yes—
30C2×#559C2214yes—
31C2×#557C2212yes—
32C2×#555C2212yes—
33C2×#555C2214yes—
34C2×#553C2212yes—
35C2×#553C2214yes—
36C2×#552C2212yes—
37C2×#552C2214yes—
38C2×#550C2212yes—
39C2×#548C2212yes—
40C2×#548C2212yes—
41C2×#542C2212yes—
42C2×#542C2214yes—
43C2×#540C2212yes—
44C2×#540C2214yes—
45C2×#529C2212yes—
46C2×#529C2212yes—
47C2×#529C2214yes—
48C2×#529C2214yes—
49C2×#520C2212yes—
50C2×#519C2211yescharacteristic
51C2×C4×#41C2212yes—
52#2867C2211yescharacteristic
53#2859C2211yescharacteristic
54#2856C2212yes—
55#2852C2214yes—
56#2850C2214yes—
57#2823C2212yes—
58#2820C2214yes—
59#2819C2212yes—
60#2818C2214yes—
61#2815C2212yes—
62#2815C2212yes—
63#2733C2214yes—
64#2733C2212yes—
65#2733C2212yes—
66#2732C2214yes—
67#2730C2214yes—
68#2730C2214yes—
69#2730C2214yes—
70#2730C2214yes—
71#2728C2212yes—
72#2728C2212yes—
73#2719C2214yes—
74#2713C2214yes—
75#2712C2212yes—
76#2711C2214yes—
77#2711C2214yes—
78#2694C2214yes—
79#2694C2214yes—
80#2694C2214yes—
81#2693C2212yes—
82#2676C2214yes—
83#2676C2214yes—
84#2675C2214yes—
85#2675C2212yes—
86#2675C2212yes—
87#2674C2214yes—
88#2674C2214yes—
89#2674C2214yes—
90#2673C2214yes—
91#2673C2214yes—
92#2673C2214yes—
93#2673C2214yes—
94#2673C2214yes—
95#2673C2214yes—
96#2672C2214yes—
97#2671C2214yes—
98#2671C2214yes—
99#2664C2214yes—
100#2662C2214yes—
101#2657C2214yes—
102#2656C2214yes—
103#2641C2212yes—
104#2636C2214yes—
105#2636C2214yes—
106#2636C2214yes—
107#2635C2214yes—
108#2635C2214yes—
109#2633C2214yes—
110#2632C2214yes—
111#2631C2214yes—
112#2620C2214yes—
113#2619C2211yescharacteristic
114#2619C2211yescharacteristic
115#2619C2214yes—
116#2611C2214yes—
117#2610C2214yes—
118#2609C2214yes—
119#2609C2212yes—
120#2604C2214yes—
121#2603C2214yes—
122#2601C2214yes—
123#2601C2214yes—
124#2600C2212yes—
125#2600C2212yes—
126#2598C2214yes—
127#2598C2214yes—
128#2598C2214yes—
129#2584C2212yes—
130#2562C2212yes—
131#2559C2214yes—
132#2558C2214yes—
133#2556C2212yes—
134#2555C2212yes—
135#2555C2214yes—
136#2554C2212yes—
137#2554C2214yes—
138#2553C2212yes—
139#2548C2212yes—
140#2544C2214yes—
141#2543C2214yes—
142#2543C2214yes—
143#2541C2212yes—
144#2541C2214yes—
145#2540C2214yes—
146#2540C2214yes—
147#2537C2212yes—
148#2536C2214yes—
149#2535C2214yes—
150#2521C2212yes—
151#2519C2212yes—
152#2481C2214yes—
153#2479C2214yes—
154#2477C2214yes—
155#2471C2214yes—
156#2471C2214yes—
157#2467C2214yes—
158#2467C2214yes—
159#2464C2212yes—
160#2464C2214yes—
161#2463C2214yes—
162#2463C2214yes—
163#2461C2212yes—
164#2461C2214yes—
165#2456C2214yes—
166#2456C2214yes—
167#2456C2214yes—
168#2456C2214yes—
169#2454C2212yes—
170#2454C2212yes—
171#2452C2212yes—
172#2452C2212yes—
173#2449C2214yes—
174#2448C2212yes—
175#2448C2212yes—
176#2448C2212yes—
177#2448C2212yes—
178#2445C2214yes—
179#2445C2214yes—
180#2445C2214yes—
181#2443C2214yes—
182#2443C2214yes—
183#2442C2212yes—
184#2441C2212yes—
185#2440C2212yes—
186#2439C2212yes—
187#2431C2212yes—
188#2431C2212yes—
189#2431C2212yes—
190#2431C2212yes—
191#2428C2212yes—
192#2428C2212yes—
193#2428C2212yes—
194#2428C2212yes—
195#2428C2214yes—
196#2428C2214yes—
197#2428C2214yes—
198#2423C2212yes—
199#2423C2212yes—
200#2421C2212yes—
201#2421C2212yes—
202#2416C2212yes—
203#2416C2212yes—
204#2416C2212yes—
205#2416C2212yes—
206#2414C2212yes—
207#2414C2212yes—
208#2414C2212yes—
209#2414C2212yes—
210#2407C2212yes—
211#2407C2212yes—
212#2407C2212yes—
213#2407C2212yes—
214#2399C2211yescharacteristic
215#2397C2211yescharacteristic
216#2397C2214yes—
217#2392C2211yescharacteristic
218#2392C2211yescharacteristic
219#2392C2214yes—
220#2356C2214yes—
221#2355C2214yes—
222#2343C2214yes—
223#2343C2214yes—
224#2328C2214yes—
225#2328C2211yescharacteristic
226#2328C2211yescharacteristic
227#2325C2214yes—
228#2324C2214yes—
229#2324C2212yes—
230#2324C2212yes—
231#2323C2214yes—
232#2320C2212yes—
233#2320C2212yes—
234#2317C2211yescharacteristic
235#2310C2211yescharacteristic
236C4×#127C2212yes—
237C4×#124C2212yes—
238C4×#121C2212yes—
239C4×#121C2212yes—
240C4×#121C2214yes—
241C4×#121C2212yes—
242#2296C2211yescharacteristic
243#2295C2212yes—
244#2295C2212yes—
245C2×#391C2211yescharacteristic
246#2293C2211yescharacteristic
247#2290C2212yes—
248#2290C2214yes—
249#2274C2211yescharacteristic
250C42×D4C2211yescharacteristic
251C4×#117C2211yescharacteristic
252C22×#41C2312yes—
253C22×#41C2312yes—
254C23×Q8C2311yescharacteristic
255#559—232no—
256#559—216no—
257#557—216no—
258#555—232no—
259#555—216no—
260#553—232no—
261#553—216no—
262#552—232no—
263#552—216no—
264#550—216no—
265#548—216no—
266#548—216no—
267#542—216no—
268#542—232no—
269#540—216no—
270#540—232no—
271C2×C4⋊Q8C2314yes—
272C2×C4⋊Q8C2312yes—
273C2×#127C2314yes—
274C2×#127C2312yes—
275C2×#127C2312yes—
276C2×#127C2311yescharacteristic
277C2×#127C2311yescharacteristic
278C2×#127C2314yes—
279C2×#127C2314yes—
280C2×#127C2314yes—
281#529—216no—
282#529—232no—
283#529—216no—
284#529—232no—
285C2×#126C2314yes—
286C2×#126C2314yes—
287C2×#126C2314yes—
288C2×#126C2314yes—
289C2×#126C2312yes—
290C2×#126C2312yes—
291C2×#125C2312yes—
292C2×#125C2314yes—
293C2×#125C2314yes—
294C2×#125C2312yes—
295C2×#125C2314yes—
296C2×#125C2312yes—
297C2×#124C2314yes—
298C2×#124C2314yes—
299C2×#124C2314yes—
300C2×#124C2314yes—
301C2×#124C2312yes—
302C2×#124C2314yes—
303C2×#124C2312yes—
304C2×#124C2312yes—
305C2×#124C2314yes—
306C2×#124C2312yes—
307C2×#124C2314yes—
308C2×#123C2314yes—
309C2×#123C2314yes—
310C2×#123C2314yes—
311C2×#123C2314yes—
312C2×#123C2314yes—
313C2×#123C2312yes—
314C2×#123C2312yes—
315C2×#123C2314yes—
316C2×#123C2314yes—
317C2×#123C2314yes—
318C2×C22⋊Q8C2312yes—
319C2×C22⋊Q8C2312yes—
320C2×C22⋊Q8C2314yes—
321C2×C22⋊Q8C2312yes—
322C2×C22⋊Q8C2314yes—
323C2×C22⋊Q8C2314yes—
324C2×C22⋊Q8C2314yes—
325C2×C22⋊Q8C2314yes—
326C2×C22⋊Q8C2314yes—
327C2×#121C2312yes—
328C2×#121C2312yes—
329C2×#121C2314yes—
330C2×#121C2314yes—
331C2×#121C2312yes—
332C2×#121C2312yes—
333C2×#121C2314yes—
334C2×#121C2314yes—
335C2×#121C2314yes—
336C2×#121C2312yes—
337C2×#121C2314yes—
338C2×#121C2314yes—
339C2×#121C2314yes—
340C2×#121C2312yes—
341C2×#121C2312yes—
342C2×#121C2314yes—
343C2×#121C2314yes—
344C2×#121C2312yes—
345C2×#121C2312yes—
346C2×#121C2312yes—
347C2×#121C2314yes—
348C2×#121C2314yes—
349C2×#121C2314yes—
350C2×#121C2314yes—
351C2×#121C2314yes—
352C2×#121C2314yes—
353C2×#121C2314yes—
354C2×#121C2314yes—
355#520—216no—
356#519D4116yescomplemented
357C4×#41—216no—
358C2×C4×Q8C2314yes—
359C2×C4×Q8C2312yes—
360C2×C4×Q8C2312yes—
361C2×C4×Q8C2312yes—
362C2×C4×Q8C2312yes—
363C2×C4×Q8C2312yes—
364C2×C4×Q8C2314yes—
365C2×C4×D4C2312yes—
366C2×C4×D4C2312yes—
367C2×C4×D4C2312yes—
368C2×C4×D4C2314yes—
369C2×C4×D4C2314yes—
370C2×C4×D4C2314yes—
371C2×C4×D4C2314yes—
372C2×C4×D4C2314yes—
373C2×C4×D4C2314yes—
374C2×C4×D4C2314yes—
375C2×C4×D4C2314yes—
376C2×C4×D4C2312yes—
377C2×C4×D4C2312yes—
378C2×C4×D4C2312yes—
379C2×C4×D4C2314yes—
380C2×C4×D4C2312yes—
381C2×C4×D4C2314yes—
382C2×C4×D4C2314yes—
383C2×C4×D4C2311yescharacteristic
384C2×C4×D4C2311yescharacteristic
385C2×C4×D4C2312yes—
386C2×C4×D4C2312yes—
387C2×C4×D4C2314yes—
388C2×C4×D4C2314yes—
389C2×C4×D4C2314yes—
390C2×#117C2314yes—
391C2×#117C2312yes—
392C2×#117C2314yes—
393C2×#117C2314yes—
394C2×#117C2314yes—
395C2×#117C2312yes—
396C2×#117C2314yes—
397C2×#117C2311yescharacteristic
398C2×#117C2311yescharacteristic
399C2×#117C2311yescharacteristic
400C2×#117C2314yes—
401C2×#117C2311yescharacteristic
402C22×C4⋊C4C2312yes—
403C22×C4⋊C4C2314yes—
404C22×C4⋊C4C2311yescharacteristic
405C22×C42C2314yes—
406C22×C42C2312yes—
407C22×C42C2311yescharacteristic
408#400C2314yes—
409#400C2314yes—
410#400C2314yes—
411#400C2314yes—
412#399C2314yes—
413#399C2314yes—
414#399C2312yes—
415#399C2314yes—
416#399C2314yes—
417#399C2314yes—
418#399C2314yes—
419#399C2314yes—
420#399C2314yes—
421#399C2312yes—
422#399C2314yes—
423#398C2311yescharacteristic
424#398C2314yes—
425#398C2314yes—
426#398C2314yes—
427#398C2314yes—
428#398C2311yescharacteristic
429#398C2314yes—
430#398C2312yes—
431#398C2312yes—
432#397C2314yes—
433#397C2314yes—
434#397C2311yescharacteristic
435#397C2311yescharacteristic
436#397C2314yes—
437#397C2314yes—
438#397C2314yes—
439#397C2314yes—
440#396C2314yes—
441#396C2314yes—
442#396C2314yes—
443#396C2314yes—
444#396C2314yes—
445#396C2314yes—
446#396C2314yes—
447#396C2314yes—
448#396C2312yes—
449#396C2314yes—
450#396C2312yes—
451#396C2314yes—
452#395C2312yes—
453#395C2314yes—
454#395C2314yes—
455#395C2312yes—
456#394C2314yes—
457#394C2314yes—
458#394C2314yes—
459#394C2314yes—
460#394C2314yes—
461#394C2314yes—
462#394C2311yescharacteristic
463#394C2312yes—
464#394C2314yes—
465#394C2314yes—
466#394C2314yes—
467#394C2312yes—
468#394C2314yes—
469#394C2314yes—
470#394C2314yes—
471#394C2314yes—
472#394C2314yes—
473#394C2314yes—
474#394C2314yes—
475#394C2312yes—
476#394C2314yes—
477#394C2312yes—
478#394C2314yes—
479#394C2314yes—
480#394C2314yes—
481#394C2314yes—
482#394C2312yes—
483#394C2312yes—
484#394C2314yes—
485#394C2314yes—
486#394C2311yescharacteristic
487#393C2314yes—
488#393C2314yes—
489#393C2314yes—
490#392C2312yes—
491#392C2314yes—
492#392C2314yes—
493#392C2314yes—
494#392C2314yes—
495#392C2314yes—
496#392C2314yes—
497#392C2314yes—
498#392C2314yes—
499#392C2312yes—
500#392C2312yes—
501#392C2314yes—
502#392C2314yes—
503#392C2312yes—
504#392C2314yes—
505#392C2312yes—
506#392C2312yes—
507#392C2314yes—
508#392C2314yes—
509#392C2314yes—
510#392C2314yes—
511#392C2314yes—
512#392C2314yes—
513#392C2314yes—
514#392C2314yes—
515#392C2311yescharacteristic
516#392C2311yescharacteristic
517#392C2314yes—
518#392C2314yes—
519#392C2314yes—
520#391C2312yes—
521#391C2312yes—
522#391C2312yes—
523#391C2312yes—
524#391C2312yes—
525#391C2314yes—
526#391C2314yes—
527#391C2312yes—
528#391C2312yes—
529#390C2314yes—
530#390C2314yes—
531#390C2312yes—
532#390C2312yes—
533#390C2314yes—
534#390C2314yes—
535#390C2314yes—
536#390C2314yes—
537#390C2312yes—
538#390C2314yes—
539#390C2312yes—
540#390C2312yes—
541#390C2312yes—
542#390C2314yes—
543#390C2314yes—
544#390C2314yes—
545#390C2314yes—
546#390C2314yes—
547#390C2312yes—
548#390C2312yes—
549#390C2312yes—
550#390C2312yes—
551#390C2312yes—
552#389C2312yes—
553#389C2312yes—
554#389C2312yes—
555#389C2314yes—
556#389C2314yes—
557#389C2314yes—
558#389C2312yes—
559#389C2312yes—
560#389C2314yes—
561#389C2312yes—
562#389C2312yes—
563#389C2312yes—
564#389C2312yes—
565#389C2314yes—
566#389C2312yes—
567#388C2314yes—
568#388C2314yes—
569#388C2312yes—
570#388C2314yes—
571#388C2314yes—
572#388C2312yes—
573#388C2314yes—
574#388C2314yes—
575#388C2314yes—
576#388C2314yes—
577#388C2314yes—
578#388C2312yes—
579#388C2314yes—
580#388C2314yes—
581#388C2314yes—
582#388C2312yes—
583#388C2314yes—
584#388C2314yes—
585#388C2314yes—
586#388C2314yes—
587#388C2314yes—
588#388C2314yes—
589#388C2314yes—
590#388C2312yes—
591#388C2312yes—
592#388C2314yes—
593#388C2314yes—
594#388C2312yes—
595#388C2312yes—
596#388C2314yes—
597#388C2312yes—
598#388C2312yes—
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#387C2314yes—
614#387C2312yes—
615#386C2314yes—
616#386C2314yes—
617#386C2314yes—
618#386C2314yes—
619#386C2314yes—
620#386C2314yes—
621#386C2314yes—
622#386C2314yes—
623#386C2314yes—
624#386C2314yes—
625#386C2314yes—
626#386C2314yes—
627#386C2314yes—
628#386C2314yes—
629#386C2314yes—
630#386C2314yes—
631#386C2314yes—
632#386C2314yes—
633#386C2314yes—
634#386C2314yes—
635#386C2314yes—
636#386C2314yes—
637#386C2314yes—
638#386C2314yes—
639#386C2314yes—
640#386C2312yes—
641#386C2314yes—
642#386C2314yes—
643#386C2312yes—
644#386C2314yes—
645#386C2312yes—
646#386C2312yes—
647#385C2312yes—
648#385C2312yes—
649#385C2314yes—
650#385C2314yes—
651#385C2314yes—
652#385C2314yes—
653#385C2314yes—
654#385C2314yes—
655#385C2312yes—
656#385C2314yes—
657#385C2314yes—
658#385C2314yes—
659#385C2314yes—
660#385C2314yes—
661#385C2314yes—
662#385C2314yes—
663#385C2312yes—
664#384C2312yes—
665#384C2312yes—
666#383C2314yes—
667#383C2314yes—
668#382C2312yes—
669#382C2314yes—
670#382C2314yes—
671#382C2312yes—
672#382C2311yescharacteristic
673#382C2311yescharacteristic
674#381C2312yes—
675#381C2312yes—
676#380C2312yes—
677#380C2312yes—
678#380C2312yes—
679#380C2312yes—
680#380C2314yes—
681#380C2314yes—
682#380C2312yes—
683#380C2314yes—
684C4×C4⋊C4C2312yes—
685C4×C4⋊C4C2312yes—
686C4×C4⋊C4C2314yes—
687C4×C4⋊C4C2314yes—
688C4×C4⋊C4C2314yes—
689C4×C4⋊C4C2312yes—
690C4×C4⋊C4C2314yes—
691C4×C4⋊C4C2312yes—
692C4×C4⋊C4C2311yescharacteristic
693C4×C4⋊C4C2311yescharacteristic
694C4×C4⋊C4C2312yes—
695C4×C4⋊C4C2312yes—
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
714C2×#41—28no—
715C2×#41—28no—
716C2×#41—44no—
717C2×#41—44no—
718C2×#41—44no—
719C2×#41—44no—
720C22×Q8—42no—
721C22×Q8—42no—
722C22×Q8C2×D418yes—
723C22×Q8C2412yes—
724C22×Q8C2414yes—
725C22×Q8C2412yes—
726C22×Q8C2412yes—
727C22×D4C2412yes—
728C22×D4C2412yes—
729C22×D4C2414yes—
730C22×D4C2414yes—
731C22×D4C2414yes—
732C22×D4C2412yes—
733C22×D4C2414yes—
734C22×D4C2412yes—
735C22×D4C2414yes—
736C22×D4C2414yes—
737C22×D4C2414yes—
738C22×D4C2414yes—
739C22×D4C2414yes—
740C22×D4C2412yes—
741C22×D4C2414yes—
742C22×D4C2411yescharacteristic
743C22×D4C2411yescharacteristic
744C22×D4C2414yes—
745C22×D4C2412yes—
746C22×D4C2414yes—
747C22×D4C2414yes—
748C22×D4C2414yes—
749C22×D4C2412yes—
750C22×D4C2412yes—
751C22×D4C2412yes—
752C22×D4C2412yes—
753C23×C4C2412yes—
754C23×C4C2412yes—
755C23×C4C2411yescharacteristic
756C23×C4C2414yes—
757C23×C4C2414yes—
758C23×C4C2414yes—
759C23×C4C2414yes—
760C23×C4C2414yes—
761C23×C4C2412yes—
762C23×C4C2414yes—
763C23×C4C2412yes—
764C23×C4C2414yes—
765C23×C4C2412yes—
766C23×C4C2412yes—
767C23×C4C2412yes—
768C4⋊Q8—28no—
769C4⋊Q8—216no—
770#127—216no—
771#127—28no—
772#127—44no—
773#127—42no—
774#127—42no—
775#127—48no—
776#127—84no—
777#127—84no—
778#126—216no—
779#126—28no—
780#126—28no—
781#126—216no—
782#126—216no—
783#126—216no—
784#125—216no—
785#125—28no—
786#125—28no—
787#125—216no—
788#125—216no—
789#125—28no—
790#124—28no—
791#124—216no—
792#124—28no—
793#124—216no—
794#124—28no—
795#124—216no—
796#124—216no—
797#124—216no—
798#124—216no—
799#124—44no—
800#124—84no—
801#123—216no—
802#123—216no—
803#123—216no—
804#123—216no—
805#123—28no—
806#123—216no—
807#123—216no—
808#123—216no—
809#123—28no—
810#123—216no—
811C22⋊Q8—28no—
812C22⋊Q8—216no—
813C22⋊Q8—28no—
814C22⋊Q8—216no—
815C22⋊Q8—216no—
816C22⋊Q8—28no—
817C22⋊Q8—48no—
818C22⋊Q8—84no—
819C22⋊Q8—84no—
820#121—28no—
821#121—216no—
822#121—28no—
823#121—216no—
824#121—28no—
825#121—216no—
826#121—28no—
827#121—216no—
828#121—28no—
829#121—216no—
830#121—216no—
831#121—216no—
832#121—216no—
833#121—44no—
834#121—48no—
835#121—48no—
836#121—44no—
837#121—44no—
838#121—44no—
839#121—44no—
840#121—48no—
841#121—84no—
842#121—84no—
843#121—84no—
844#121—84no—
845#121—84no—
846#121—84no—
847#121—84no—
848C4×Q8—28no—
849C4×Q8—28no—
850C4×Q8—216no—
851C4×Q8—28no—
852C4×Q8C2×D4116yes—
853C4×Q8C2×D4132yes—
854C4×Q8C2×D4116yes—
855C4×D4—28no—
856C4×D4—216no—
857C4×D4—28no—
858C4×D4—216no—
859C4×D4—28no—
860C4×D4—216no—
861C4×D4—28no—
862C4×D4—216no—
863C4×D4—28no—
864C4×D4—216no—
865C4×D4—28no—
866C4×D4—216no—
867C4×D4—216no—
868C4×D4—28no—
869C4×D4—216no—
870C4×D4—216no—
871C4×D4—216no—
872C4×D4—44no—
873C4×D4—48no—
874C4×D4—44no—
875C4×D4—42no—
876C4×D4—42no—
877C4×D4—84no—
878C4×D4—84no—
879C4×D4—84no—
880#117—28no—
881#117—216no—
882#117—28no—
883#117—216no—
884#117—216no—
885#117—216no—
886#117—216no—
887#117—42no—
888#117—42no—
889#117C2×D418yes—
890#117C2×D4132yes—
891#117C2×D418yes—
892C2×C4⋊C4—28no—
893C2×C4⋊C4—216no—
894C2×C4⋊C4—42no—
895C2×C4⋊C4C2412yes—
896C2×C4⋊C4C2414yes—
897C2×C4⋊C4C2412yes—
898C2×C4⋊C4C2414yes—
899C2×C4⋊C4C2412yes—
900C2×C4⋊C4C2412yes—
901C2×C4⋊C4C2414yes—
902C2×C4⋊C4C2412yes—
903C2×C4⋊C4C2412yes—
904C2×C4⋊C4C2414yes—
905C2×C4⋊C4C2412yes—
906C2×C4⋊C4C2414yes—
907C2×C4⋊C4C2414yes—
908C2×C4⋊C4C2414yes—
909C2×C4⋊C4C2412yes—
910C2×C4⋊C4C2414yes—
911C2×C4⋊C4C2412yes—
912C2×C4⋊C4C2414yes—
913C2×C4⋊C4C2414yes—
914C2×C4⋊C4C2412yes—
915C2×C4⋊C4C2412yes—
916C2×C4⋊C4C2414yes—
917C2×C4⋊C4C2412yes—
918C2×C4⋊C4C2414yes—
919C2×C4⋊C4C2412yes—
920C2×C4⋊C4C2411yescharacteristic
921C2×C4⋊C4C2411yescharacteristic
922C2×C4⋊C4C2414yes—
923C2×C4⋊C4C2414yes—
924C2×C4⋊C4C2414yes—
925C2×C4⋊C4C2411yescharacteristic
926C2×C4⋊C4C2412yes—
927C2×C4⋊C4C2412yes—
928C2×C4⋊C4C2411yescharacteristic
929C2×C4⋊C4C2414yes—
930C2×C4⋊C4C2414yes—
931C2×C4⋊C4C2414yes—
932C2×C4⋊C4C2414yes—
933C2×C4⋊C4C2412yes—
934C2×C4⋊C4C2412yes—
935C2×C4⋊C4C2412yes—
936C2×C4⋊C4C2414yes—
937C2×C4⋊C4C2412yes—
938C2×C4⋊C4C2414yes—
939C2×C4⋊C4C2414yes—
940C2×C4⋊C4C2412yes—
941C2×C22⋊C4C2414yes—
942C2×C22⋊C4C2412yes—
943C2×C22⋊C4C2412yes—
944C2×C22⋊C4C2414yes—
945C2×C22⋊C4C2414yes—
946C2×C22⋊C4C2414yes—
947C2×C22⋊C4C2414yes—
948C2×C22⋊C4C2412yes—
949C2×C22⋊C4C2414yes—
950C2×C22⋊C4C2414yes—
951C2×C22⋊C4C2414yes—
952C2×C22⋊C4C2414yes—
953C2×C22⋊C4C2412yes—
954C2×C22⋊C4C2414yes—
955C2×C22⋊C4C2412yes—
956C2×C22⋊C4C2412yes—
957C2×C22⋊C4C2414yes—
958C2×C22⋊C4C2412yes—
959C2×C22⋊C4C2412yes—
960C2×C22⋊C4C2414yes—
961C2×C22⋊C4C2414yes—
962C2×C22⋊C4C2414yes—
963C2×C22⋊C4C2412yes—
964C2×C22⋊C4C2414yes—
965C2×C22⋊C4C2412yes—
966C2×C22⋊C4C2412yes—
967C2×C22⋊C4C2412yes—
968C2×C22⋊C4C2411yescharacteristic
969C2×C22⋊C4C2411yescharacteristic
970C2×C22⋊C4C2412yes—
971C2×C22⋊C4C2414yes—
972C2×C22⋊C4C2414yes—
973C2×C22⋊C4C2414yes—
974C2×C22⋊C4C2414yes—
975C2×C22⋊C4C2414yes—
976C2×C22⋊C4C2414yes—
977C2×C22⋊C4C2412yes—
978C2×C22⋊C4C2412yes—
979C2×C22⋊C4C2414yes—
980C2×C22⋊C4C2414yes—
981C2×C22⋊C4C2412yes—
982C2×C22⋊C4C2412yes—
983C2×C22⋊C4C2412yes—
984C2×C22⋊C4C2412yes—
985C2×C22⋊C4C2414yes—
986C2×C22⋊C4C2414yes—
987C2×C22⋊C4C2414yes—
988C2×C22⋊C4C2414yes—
989C2×C22⋊C4C2414yes—
990C2×C22⋊C4C2414yes—
991C2×C22⋊C4C2414yes—
992C2×C22⋊C4C2414yes—
993C2×C22⋊C4C2414yes—
994C2×C22⋊C4C2414yes—
995C2×C22⋊C4C2414yes—
996C2×C22⋊C4C2414yes—
997C2×C22⋊C4C2414yes—
998C2×C22⋊C4C2414yes—
999C2×C22⋊C4C2414yes—
1000C2×C22⋊C4C2414yes—
1001C2×C22⋊C4C2412yes—
1002C2×C22⋊C4C2412yes—
1003C2×C22⋊C4C2412yes—
1004C2×C22⋊C4C2412yes—
1005C2×C42—28no—
1006C2×C42—216no—
1007C2×C42—42no—
1008C2×C42C2412yes—
1009C2×C42C2414yes—
1010C2×C42C2412yes—
1011C2×C42C2414yes—
1012C2×C42C2411yescharacteristic
1013C2×C42C2411yescharacteristic
1014C2×C42C2412yes—
1015C2×C42C2412yes—
1016C2×C42C2414yes—
1017C2×C42C2411yescharacteristic
1018C2×C42C2412yes—
1019C2×C42C2412yes—
1020C2×C42C2411yescharacteristic
1021C2×C42C2412yes—
1022C2×C42C2412yes—
1023C2×C42C2414yes—
1024C2×C42C2414yes—
1025C2×C42C2412yes—
1026C2×C42C2412yes—
1027C2×C42C2411yescharacteristic
1028C2×C42C2414yes—
1029C2×C42C2412yes—
1030C2×C42C2414yes—
1031C2×C42C2411yescharacteristic
1032#95C2414yes—
1033#95C2414yes—
1034#95C2414yes—
1035#95C2414yes—
1036#95C2414yes—
1037#95C2412yes—
1038#95C2412yes—
1039#95C2412yes—
1040#95C2412yes—
1041#95C2414yes—
1042#95C2414yes—
1043#95C2414yes—
1044#95C2414yes—
1045#95C2411yescharacteristic
1046#95C2412yes—
1047#95C2412yes—
1048#95C2411yescharacteristic
1049#95C2414yes—
1050#95C2414yes—
1051#95C2414yes—
1052#95C2414yes—
1053#95C2414yes—
1054#95C2412yes—
1055#95C2412yes—
1056#95C2412yes—
1057#95C2412yes—
1058#95C2412yes—
1059#95C2412yes—
1060#95C2414yes—
1061#95C2412yes—
1062#95C2414yes—
1063#95C2414yes—
1064#95C2414yes—
1065#95C2411yescharacteristic
1066#95C2412yes—
1067#95C2411yescharacteristic
1068#95C2412yes—
1069#95C2414yes—
1070#95C2414yes—
1071#95C2414yes—
1072#95C2412yes—
1073#95C2412yes—
1074#95C2412yes—
1075#95C2414yes—
1076C24C2512yes—
1077C24C2512yes—
1078C24C2514yes—
1079C24C2514yes—
1080C24C2511yescharacteristic
1081#41—432no—
1082#41—432no—
1083C2×Q8—28no—
1084C2×Q8—24no—
1085C2×Q8—24no—
1086C2×Q8—24no—
1087C2×Q8—42no—
1088C2×Q8—42no—
1089C2×Q8—44no—
1090C2×Q8—44no—
1091C2×Q8—42no—
1092C2×Q8—42no—
1093C2×Q8—416no—
1094C2×Q8C22×D418yes—
1095C2×Q8C22×D418yes—
1096C2×D4—24no—
1097C2×D4—28no—
1098C2×D4—24no—
1099C2×D4—28no—
1100C2×D4—28no—
1101C2×D4—28no—
1102C2×D4—24no—
1103C2×D4—24no—
1104C2×D4—28no—
1105C2×D4—28no—
1106C2×D4—28no—
1107C2×D4—24no—
1108C2×D4—28no—
1109C2×D4—24no—
1110C2×D4—24no—
1111C2×D4—24no—
1112C2×D4—24no—
1113C2×D4—28no—
1114C2×D4—28no—
1115C2×D4—42no—
1116C2×D4—41no—
1117C2×D4—44no—
1118C2×D4—44no—
1119C2×D4—44no—
1120C2×D4—44no—
1121C2×D4—42no—
1122C2×D4—41no—
1123C2×D4—44no—
1124C2×D4—44no—
1125C2×D4—44no—
1126C2×D4—44no—
1127C2×D4—44no—
1128C2×D4—44no—
1129C2×D4—42no—
1130C2×D4—42no—
1131C2×D4—42no—
1132C2×D4—44no—
1133C2×D4—44no—
1134C2×D4—44no—
1135C2×D4—44no—
1136C2×D4—44no—
1137C2×D4—44no—
1138C2×D4—42no—
1139C2×D4—42no—
1140C2×D4—44no—
1141C2×D4—42no—
1142C2×D4—42no—
1143C2×D4—44no—
1144C2×D4—44no—
1145C2×D4—44no—
1146C2×D4—42no—
1147C2×D4—44no—
1148C2×D4—44no—
1149C2×D4—44no—
1150C2×D4—44no—
1151C2×D4—44no—
1152C2×D4—44no—
1153C2×D4—42no—
1154C2×D4—44no—
1155C2×D4—44no—
1156C2×D4—44no—
1157C2×D4—44no—
1158C2×D4—44no—
1159C2×D4—44no—
1160C2×D4—44no—
1161C2×D4—44no—
1162C2×D4—44no—
1163C2×D4—44no—
1164C2×D4—42no—
1165C2×D4—42no—
1166C2×D4—42no—
1167C2×D4—42no—
1168C22×C4—22no—
1169C22×C4—22no—
1170C22×C4—28no—
1171C22×C4—24no—
1172C22×C4—28no—
1173C22×C4—24no—
1174C22×C4—24no—
1175C22×C4—24no—
1176C22×C4—24no—
1177C22×C4—24no—
1178C22×C4—24no—
1179C22×C4—28no—
1180C22×C4—24no—
1181C22×C4—28no—
1182C22×C4—28no—
1183C22×C4—28no—
1184C22×C4—28no—
1185C22×C4—24no—
1186C22×C4—42no—
1187C22×C4—42no—
1188C22×C4—44no—
1189C22×C4—44no—
1190C22×C4—44no—
1191C22×C4—44no—
1192C22×C4—42no—
1193C22×C4—42no—
1194C22×C4—42no—
1195C22×C4—44no—
1196C22×C4—44no—
1197C22×C4—44no—
1198C22×C4—42no—
1199C22×C4—42no—
1200C22×C4—44no—
1201C22×C4—44no—
1202C22×C4—44no—
1203C22×C4—42no—
1204C22×C4—44no—
1205C22×C4—44no—
1206C22×C4—44no—
1207C22×C4—44no—
1208C22×C4—42no—
1209C22×C4—44no—
1210C22×C4C22×D414yes—
1211C22×C4C22×D418yes—
1212C22×C4C2511yescharacteristic
1213C22×C4C2511yescharacteristic
1214C22×C4C2511yescharacteristic
1215C22×C4C2514yes—
1216C22×C4C2512yes—
1217C22×C4C2514yes—
1218C22×C4C2512yes—
1219C22×C4C2511yescharacteristic
1220C22×C4C2512yes—
1221C22×C4C2512yes—
1222C22×C4C2512yes—
1223C22×C4C2512yes—
1224C22×C4C2514yes—
1225C22×C4C2512yes—
1226C22×C4C2514yes—
1227C22×C4C2514yes—
1228C22×C4C2512yes—
1229C22×C4C2512yes—
1230C22×C4C2514yes—
1231C22×C4C2511yescharacteristic
1232C22×C4C2512yes—
1233C22×C4C2511yescharacteristic
1234C4⋊C4—24no—
1235C4⋊C4—28no—
1236C4⋊C4—28no—
1237C4⋊C4—24no—
1238C4⋊C4—24no—
1239C4⋊C4—28no—
1240C4⋊C4—24no—
1241C4⋊C4—28no—
1242C4⋊C4—24no—
1243C4⋊C4—28no—
1244C4⋊C4—28no—
1245C4⋊C4—28no—
1246C4⋊C4—24no—
1247C4⋊C4—28no—
1248C4⋊C4—24no—
1249C4⋊C4—28no—
1250C4⋊C4—24no—
1251C4⋊C4—24no—
1252C4⋊C4—28no—
1253C4⋊C4—24no—
1254C4⋊C4—24no—
1255C4⋊C4—24no—
1256C4⋊C4—28no—
1257C4⋊C4—28no—
1258C4⋊C4—42no—
1259C4⋊C4—41no—
1260C4⋊C4—41no—
1261C4⋊C4—42no—
1262C4⋊C4—42no—
1263C4⋊C4—41no—
1264C4⋊C4—41no—
1265C4⋊C4—44no—
1266C4⋊C4—44no—
1267C4⋊C4—44no—
1268C4⋊C4—42no—
1269C4⋊C4—44no—
1270C4⋊C4—44no—
1271C4⋊C4—44no—
1272C4⋊C4—44no—
1273C4⋊C4—44no—
1274C4⋊C4—42no—
1275C4⋊C4—42no—
1276C4⋊C4C22×D418yes—
1277C4⋊C4C22×D4116yes—
1278C4⋊C4C22×D4116yes—
1279C4⋊C4C22×D418yes—
1280C22⋊C4—24no—
1281C22⋊C4—24no—
1282C22⋊C4—28no—
1283C22⋊C4—24no—
1284C22⋊C4—24no—
1285C22⋊C4—28no—
1286C22⋊C4—28no—
1287C22⋊C4—28no—
1288C22⋊C4—28no—
1289C22⋊C4—24no—
1290C22⋊C4—28no—
1291C22⋊C4—28no—
1292C22⋊C4—28no—
1293C22⋊C4—28no—
1294C22⋊C4—28no—
1295C22⋊C4—24no—
1296C22⋊C4—28no—
1297C22⋊C4—24no—
1298C22⋊C4—28no—
1299C22⋊C4—28no—
1300C22⋊C4—28no—
1301C22⋊C4—28no—
1302C22⋊C4—24no—
1303C22⋊C4—24no—
1304C22⋊C4—24no—
1305C22⋊C4—24no—
1306C22⋊C4—24no—
1307C22⋊C4—41no—
1308C22⋊C4—41no—
1309C22⋊C4—42no—
1310C22⋊C4—42no—
1311C22⋊C4—42no—
1312C22⋊C4—44no—
1313C22⋊C4—44no—
1314C22⋊C4—42no—
1315C22⋊C4—42no—
1316C22⋊C4—44no—
1317C22⋊C4—44no—
1318C22⋊C4—44no—
1319C22⋊C4—44no—
1320C22⋊C4—44no—
1321C22⋊C4—44no—
1322C22⋊C4—44no—
1323C22⋊C4—44no—
1324C22⋊C4—44no—
1325C22⋊C4—44no—
1326C22⋊C4—44no—
1327C22⋊C4—44no—
1328C22⋊C4—44no—
1329C22⋊C4—44no—
1330C22⋊C4—44no—
1331C22⋊C4—44no—
1332C22⋊C4—42no—
1333C22⋊C4—42no—
1334C22⋊C4—44no—
1335C22⋊C4—44no—
1336C22⋊C4—44no—
1337C22⋊C4—44no—
1338C22⋊C4—44no—
1339C22⋊C4—44no—
1340C22⋊C4—42no—
1341C22⋊C4—42no—
1342C22⋊C4C22×D418yes—
1343C22⋊C4C22×D418yes—
1344C42—24no—
1345C42—24no—
1346C42—28no—
1347C42—28no—
1348C42—24no—
1349C42—28no—
1350C42—24no—
1351C42—22no—
1352C42—22no—
1353C42—22no—
1354C42—22no—
1355C42—24no—
1356C42—24no—
1357C42—42no—
1358C42—42no—
1359C42—42no—
1360C42—44no—
1361C42—44no—
1362C42—42no—
1363C42C22×D414yes—
1364C42C22×D4116yes—
1365C42C22×D418yes—
1366C42C22×D4116yes—
1367C42C22×D414yes—
1368C23—21no—
1369C23—21no—
1370C23—22no—
1371C23—22no—
1372C23—22no—
1373C23—24no—
1374C23—22no—
1375C23—24no—
1376C23—22no—
1377C23—22no—
1378C23—22no—
1379C23—22no—
1380C23—24no—
1381C23—24no—
1382C23—22no—
1383C23—22no—
1384C23—22no—
1385C23—22no—
1386C23—24no—
1387C23—24no—
1388C23—24no—
1389C23—24no—
1390C23—24no—
1391C23—24no—
1392C23—24no—
1393C23—22no—
1394C23—24no—
1395C23—22no—
1396C23—22no—
1397C23—24no—
1398C23—24no—
1399C23—22no—
1400C23C23×D412yes—
1401C23C2611yescharacteristic
1402Q8—216no—
1403Q8—48no—
1404Q8—88no—
1405Q8—84no—
1406D4—416no—
1407D4—416no—
1408D4—44no—
1409D4—48no—
1410D4—48no—
1411D4—88no—
1412D4—88no—
1413D4—84no—
1414D4—88no—
1415D4—88no—
1416D4—88no—
1417D4—88no—
1418D4—84no—
1419D4—88no—
1420D4—84no—
1421D4—88no—
1422D4—88no—
1423D4—82no—
1424D4—84no—
1425D4—88no—
1426D4—162no—
1427D4—162no—
1428D4—164no—
1429D4—162no—
1430D4—162no—
1431D4—164no—
1432C2×C4—22no—
1433C2×C4—22no—
1434C2×C4—22no—
1435C2×C4—21no—
1436C2×C4—24no—
1437C2×C4—21no—
1438C2×C4—24no—
1439C2×C4—24no—
1440C2×C4—22no—
1441C2×C4—22no—
1442C2×C4—22no—
1443C2×C4—24no—
1444C2×C4—28no—
1445C2×C4—22no—
1446C2×C4—22no—
1447C2×C4—22no—
1448C2×C4—22no—
1449C2×C4—24no—
1450C2×C4—22no—
1451C2×C4—24no—
1452C2×C4—22no—
1453C2×C4—22no—
1454C2×C4—22no—
1455C2×C4—21no—
1456C2×C4—21no—
1457C2×C4—22no—
1458C2×C4—21no—
1459C2×C4—21no—
1460C2×C4—24no—
1461C2×C4—22no—
1462C2×C4—22no—
1463C2×C4—22no—
1464C2×C4—22no—
1465C2×C4—22no—
1466C2×C4—24no—
1467C2×C4—24no—
1468C2×C4—22no—
1469C2×C4—22no—
1470C2×C4—22no—
1471C2×C4—22no—
1472C2×C4—24no—
1473C2×C4—24no—
1474C2×C4—24no—
1475C2×C4—22no—
1476C2×C4—24no—
1477C2×C4—24no—
1478C2×C4—22no—
1479C2×C4—22no—
1480C2×C4—24no—
1481C2×C4—22no—
1482C2×C4—22no—
1483C2×C4—22no—
1484C2×C4—22no—
1485C2×C4—24no—
1486C2×C4—48no—
1487C2×C4—416no—
1488C2×C4—416no—
1489C2×C4—48no—
1490C2×C4—48no—
1491C2×C4—84no—
1492C2×C4—88no—
1493C2×C4—84no—
1494C2×C4—88no—
1495C2×C4—88no—
1496C2×C4—88no—
1497C2×C4—88no—
1498C2×C4—84no—
1499C2×C4—162no—
1500C2×C4C23×D414yes—
1501C2×C4C23×D418yes—
1502C2×C4C23×D418yes—
1503C2×C4C23×D414yes—
1504C2×C4C23×D412yes—
1505C2×C4C23×D412yes—
1506C2×C4#58514yes—
1507C2×C4#58512yes—
1508C2×C4#58512yes—
1509C22—24no—
1510C22—22no—
1511C22—41no—
1512C22—41no—
1513C22—42no—
1514C22—42no—
1515C22—44no—
1516C22—42no—
1517C22—44no—
1518C22—42no—
1519C22—44no—
1520C22—42no—
1521C22—44no—
1522C22—42no—
1523C22—44no—
1524C22—44no—
1525C22—42no—
1526C22—42no—
1527C22—42no—
1528C22—44no—
1529C22—44no—
1530C22—44no—
1531C22—44no—
1532C22—42no—
1533C22—42no—
1534C22—44no—
1535C22—42no—
1536C22—42no—
1537C22—44no—
1538C22—44no—
1539C22—44no—
1540C22—42no—
1541C22—42no—
1542C22C24×D411yescharacteristic
1543C22C2×#58512yes—
1544C22C2×#58511yescharacteristic
1545C22C2×#58511yescharacteristic
1546C22H(7,𝔽2)12yes—
1547C4—24no—
1548C4—28no—
1549C4—24no—
1550C4—22no—
1551C4—28no—
1552C4—24no—
1553C4—42no—
1554C4—42no—
1555C4—44no—
1556C4—42no—
1557C4—44no—
1558C4—42no—
1559C4—41no—
1560C4—41no—
1561C4—44no—
1562C4—41no—
1563C4—41no—
1564C4—42no—
1565C4—42no—
1566C4—42no—
1567C4—44no—
1568C4#344914yes—
1569C2—42no—
1570C2—84no—
1571C2—82no—
1572C2—82no—
1573C2—84no—
1574C2C2×#344911yescharacteristic
1575C2#6283911yescharacteristic
1576C2#6288511yescharacteristic
1577C2#6294112yes—
1578C2#6300312yes—
subgroupG/H
center, commutator, Frattini, socle, cosocleC23C26
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×#3524C2semidirect
2. #42971C2semidirect
3. #42952C2semidirect
4. #42886C2semidirect
5. #42885C2semidirect
6. #42883C2semidirect
7. #42883C2semidirect
8. #41961C2semidirect
9. #41956C2semidirect
10. #41945C2semidirect
11. #41942C2semidirect
12. #39958C2semidirect
13. #39955C2semidirect
14. #39850C2semidirect
15. #39745C2semidirect
16. #39743C2semidirect
17. #39130C2semidirect
18. #38381C2semidirect
19. #38378C2semidirect
20. #35567C2semidirect
21. #35539C2semidirect
22. #35525C2semidirect
23. #35278C2semidirect
24. #35195C2semidirect
25. #34880C2semidirect
26. #34727C2semidirect
27. #34254C2semidirect
356. #519D4semidirect

Maximal subgroups

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

subgroupindex
C2×#35242
#429712
#429522
#428862
#428852
#428832
#419612
#419562
#419452
#419422
#399582
#399552
#398502
#397452
#397432
#391302
#383812
#383782
#355672
#355392
#355252
#352782
#351952
#348802
#347272
#342542