Finite Group Databasebeta

← #8935143

Subgroups — #8935143

Order 512.

5630 conjugacy classes of subgroups.

The subgroup lattice has 1393 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#58802C212yesmaximal, complemented
2#58801C212yesmaximal, complemented
3#54956C214yesmaximal, complemented
4#54950C214yesmaximal, complemented
5#51934C214yesmaximal, complemented
6#51427C212yesmaximal, complemented
7#49592C212yesmaximal, complemented
8#48682C214yesmaximal, complemented
9#47833C214yesmaximal, complemented
10#47831C212yesmaximal, complemented
11#47068C214yesmaximal, complemented
12#44649C214yesmaximal, complemented
13#43379C214yesmaximal, complemented
14#42107C214yesmaximal, complemented
15#41242C214yesmaximal, complemented
16#40505C212yesmaximal, complemented
17#37769C212yesmaximal, complemented
18#37752C212yesmaximal, complemented
19#36719C211yesmaximal, characteristic, complemented
20#35944C212yesmaximal, complemented
21#35757C212yesmaximal, complemented
22#35659C211yesmaximal, characteristic, complemented
23#35377C211yesmaximal, characteristic, complemented
24C22×2−1+4C2211yescharacteristic, complemented
25C2×#550C2212yes—
26C2×#548C2214yescomplemented
27C2×#543C2212yescomplemented
28C2×#539C2211yescharacteristic, complemented
29C2×#538C2212yescomplemented
30C2×#534C2211yescharacteristic
31C2×#525C2212yes—
32C22×C22⋊Q8C2211yescharacteristic
33#2848C2211yescharacteristic
34#2847C2211yescharacteristic
35#2829C2214yescomplemented
36#2828C2212yescomplemented
37#2825C2214yes—
38#2825C2214yescomplemented
39#2819C2212yescomplemented
40#2818C2212yescomplemented
41#2813C2212yescomplemented
42#2803C2214yescomplemented
43#2803C2214yescomplemented
44#2799C2214yescomplemented
45#2789C2212yescomplemented
46#2789C2214yescomplemented
47#2785C2212yescomplemented
48#2779C2214yescomplemented
49#2778C2214yes—
50#2768C2214yescomplemented
51#2761C2214yescomplemented
52#2760C2214yescomplemented
53#2759C2214yescomplemented
54#2742C2214yescomplemented
55#2741C2214yescomplemented
56#2741C2214yescomplemented
57#2733C2214yescomplemented
58#2730C2214yes—
59#2730C2214yescomplemented
60#2728C2214yes—
61#2710C2214yescomplemented
62#2709C2214yescomplemented
63#2705C2214yescomplemented
64#2704C2214yescomplemented
65#2703C2214yescomplemented
66#2703C2214yescomplemented
67#2702C2214yescomplemented
68#2700C2214yescomplemented
69#2700C2214yescomplemented
70#2699C2214yes—
71#2699C2212yescomplemented
72#2699C2214yescomplemented
73#2698C2214yescomplemented
74#2696C2214yescomplemented
75#2692C2214yes—
76#2692C2214yescomplemented
77#2688C2214yescomplemented
78#2686C2214yescomplemented
79#2683C2214yescomplemented
80#2683C2212yescomplemented
81#2681C2214yescomplemented
82#2681C2214yescomplemented
83#2676C2214yes—
84#2676C2214yes—
85#2676C2214yescomplemented
86#2673C2214yes—
87#2673C2214yes—
88#2673C2214yes—
89#2673C2214yes—
90#2673C2214yescomplemented
91#2672C2214yescomplemented
92#2672C2214yescomplemented
93#2671C2214yes—
94#2670C2214yescomplemented
95#2669C2214yes—
96#2669C2214yes—
97#2668C2214yescomplemented
98#2665C2212yescomplemented
99#2661C2214yescomplemented
100#2656C2212yescomplemented
101#2653C2214yescomplemented
102#2648C2214yescomplemented
103#2648C2214yescomplemented
104#2641C2212yescomplemented
105#2639C2212yescomplemented
106#2639C2212yescomplemented
107#2638C2214yescomplemented
108#2635C2212yes—
109#2634C2212yescomplemented
110#2627C2211yescharacteristic, complemented
111#2618C2211yescharacteristic, complemented
112#2617C2212yescomplemented
113#2617C2212yescomplemented
114#2616C2212yescomplemented
115#2615C2212yes—
116#2615C2214yescomplemented
117#2612C2212yescomplemented
118#2610C2214yescomplemented
119#2607C2214yescomplemented
120#2604C2214yescomplemented
121#2604C2212yescomplemented
122#2603C2214yescomplemented
123#2591C2212yes—
124#2591C2212yes—
125#2578C2214yescomplemented
126#2576C2214yescomplemented
127#2576C2214yescomplemented
128#2559C2214yescomplemented
129#2559C2214yescomplemented
130#2557C2214yescomplemented
131#2557C2214yescomplemented
132#2555C2214yescomplemented
133#2555C2212yescomplemented
134#2534C2212yes—
135#2534C2214yescomplemented
136#2531C2214yescomplemented
137#2530C2214yescomplemented
138#2530C2214yescomplemented
139#2527C2214yescomplemented
140#2527C2214yescomplemented
141#2526C2214yescomplemented
142#2504C2212yes—
143#2488C2214yes—
144#2488C2214yes—
145#2488C2214yescomplemented
146#2477C2214yescomplemented
147#2472C2214yes—
148#2472C2214yes—
149#2472C2214yes—
150#2472C2214yescomplemented
151#2471C2214yescomplemented
152#2471C2214yescomplemented
153#2467C2214yes—
154#2465C2214yescomplemented
155#2465C2214yescomplemented
156#2464C2214yescomplemented
157#2463C2214yes—
158#2463C2214yescomplemented
159#2460C2214yescomplemented
160#2459C2214yes—
161#2458C2214yes—
162#2457C2214yes—
163#2457C2214yescomplemented
164#2450C2214yescomplemented
165#2436C2212yes—
166#2436C2214yescomplemented
167#2433C2214yes—
168#2431C2214yescomplemented
169#2431C2214yescomplemented
170#2431C2214yescomplemented
171#2430C2212yescomplemented
172#2428C2214yes—
173#2427C2214yes—
174#2427C2214yescomplemented
175#2427C2214yescomplemented
176#2424C2214yes—
177#2424C2214yes—
178#2424C2214yescomplemented
179#2413C2212yescomplemented
180#2411C2212yes—
181#2410C2214yes—
182#2409C2214yescomplemented
183#2409C2214yescomplemented
184#2409C2214yescomplemented
185#2409C2212yescomplemented
186#2407C2214yescomplemented
187#2407C2214yescomplemented
188#2407C2214yescomplemented
189#2407C2214yescomplemented
190#2407C2214yescomplemented
191#2406C2212yescomplemented
192#2406C2212yescomplemented
193#2404C2212yes—
194#2404C2212yes—
195#2404C2214yes—
196#2398C2214yescomplemented
197#2388C2214yescomplemented
198#2388C2212yescomplemented
199#2378C2214yescomplemented
200#2377C2212yes—
201#2372C2214yescomplemented
202#2372C2214yescomplemented
203#2364C2214yescomplemented
204#2364C2214yescomplemented
205#2358C2214yescomplemented
206#2353C2212yescomplemented
207#2341C2212yescomplemented
208Q8×C22⋊C4C2214yescomplemented
209#2333C2214yes—
210#2329C2212yescomplemented
211#2329C2212yescomplemented
212#2328C2214yes—
213#2316C2211yescharacteristic, complemented
214#2311C2212yescomplemented
215#2310C2211yescharacteristic, complemented
216#2308C2212yes—
217C2×#386C2212yes—
218#2273C2211yescharacteristic
219C2×2−1+4—48no—
220C2×2−1+4—44no—
221C22×#41C2312yes—
222C22×#41C2312yes—
223C22×#41C2314yes—
224C22×#41C2312yes—
225C22×#41C2312yes—
226C23×Q8C2311yescharacteristic
227C23×Q8C2314yes—
228C23×D4C2312yes—
229C24×C4C2311yescharacteristic
230#550—48no—
231#548—416no—
232#543—48no—
233#539—44no—
234#538—48no—
235#534—44no—
236C2×#127C2312yes—
237C2×#127C2314yes—
238C2×#127C2314yes—
239C2×#126C2312yes—
240C2×#126C2314yes—
241C2×#125C2312yes—
242C2×#124C2314yes—
243C2×#124C2314yes—
244C2×#124C2314yes—
245C2×#124C2314yes—
246C2×#124C2314yes—
247C2×#124C2314yes—
248#525—48no—
249C2×#123C2314yes—
250C2×#123C2312yes—
251C2×#123C2314yes—
252C2×#123C2314yes—
253C2×#123C2312yes—
254C2×#123C2312yes—
255C2×#123C2314yes—
256C2×C22⋊Q8—44no—
257C2×C22⋊Q8C2312yes—
258C2×C22⋊Q8C2312yes—
259C2×C22⋊Q8C2314yes—
260C2×C22⋊Q8C2311yescharacteristic
261C2×C22⋊Q8C2312yes—
262C2×C22⋊Q8C2314yes—
263C2×C22⋊Q8C2312yes—
264C2×C22⋊Q8C2314yes—
265C2×C22⋊Q8C2314yes—
266C2×C22⋊Q8C2314yes—
267C2×C22⋊Q8C2314yes—
268C2×C22⋊Q8C2314yes—
269C2×C22⋊Q8C2314yes—
270C2×C22⋊Q8C2314yes—
271C2×#121C2312yes—
272C2×#121C2314yes—
273C2×#121C2312yes—
274C2×#121C2311yescharacteristic
275C2×#121C2312yes—
276C2×#121C2314yes—
277C2×#121C2314yes—
278C2×#121C2314yes—
279C2×#121C2314yes—
280C2×#121C2312yes—
281C2×#121C2312yes—
282C2×#121C2314yes—
283C2×#121C2314yes—
284C2×#121C2312yes—
285C2×#121C2314yes—
286C2×#121C2314yes—
287C2×#121C2314yes—
288C2×#121C2314yes—
289C2×#120C2314yes—
290C2×#120C2314yes—
291C2×#120C2314yes—
292C2×#120C2314yes—
293C2×#120C2312yes—
294C2×#120C2314yes—
295C2×C4×Q8C2312yes—
296C2×C4×Q8C2314yes—
297C2×C4×D4C2312yes—
298C2×C4×D4C2314yes—
299C2×C4×D4C2314yes—
300C2×C4×D4C2314yes—
301C2×C4×D4C2314yes—
302C2×C4×D4C2314yes—
303C2×C4×D4C2314yes—
304C2×C4×D4C2314yes—
305C2×#117C2312yes—
306C2×#117C2312yes—
307C22×C4⋊C4C2311yescharacteristic
308C22×C4⋊C4C2311yescharacteristic
309C22×C4⋊C4C2311yescharacteristic
310C22×C22⋊C4C2311yescharacteristic
311C22×C22⋊C4C2311yescharacteristic
312C22×C22⋊C4C2312yes—
313C22×C22⋊C4C2312yes—
314C22×C22⋊C4C2314yes—
315C22×C22⋊C4C2312yes—
316#401C2314yes—
317#401C2314yes—
318#400C2312yes—
319#400C2314yes—
320#400C2312yes—
321#400C2312yes—
322#400C2314yes—
323#400C2314yes—
324#400C2312yes—
325#400C2314yes—
326#400C2314yes—
327#400C2314yes—
328#399C2314yes—
329#399C2312yes—
330#399C2314yes—
331#399C2314yes—
332#398C2314yes—
333#398C2314yes—
334#398C2312yes—
335#398C2314yes—
336#398C2314yes—
337#398C2314yes—
338#397C2314yes—
339#397C2314yes—
340#397C2314yes—
341#397C2314yes—
342#397C2314yes—
343#397C2314yes—
344#397C2314yes—
345#397C2314yes—
346#397C2314yes—
347#397C2314yes—
348#397C2314yes—
349#397C2314yes—
350#397C2314yes—
351#396C2314yes—
352#396C2314yes—
353#396C2314yes—
354#396C2314yes—
355#396C2314yes—
356#396C2314yes—
357#396C2314yes—
358#396C2314yes—
359#395C2312yes—
360#395C2312yes—
361#395C2314yes—
362#395C2312yes—
363#395C2312yes—
364#395C2312yes—
365#395C2314yes—
366#395C2312yes—
367#395C2314yes—
368#394C2314yes—
369#394C2312yes—
370#394C2312yes—
371#394C2314yes—
372#394C2312yes—
373#394C2314yes—
374#394C2312yes—
375#394C2314yes—
376#394C2314yes—
377#394C2314yes—
378#394C2312yes—
379#394C2314yes—
380#394C2314yes—
381#394C2314yes—
382#394C2314yes—
383#394C2314yes—
384#394C2314yes—
385#394C2314yes—
386#394C2312yes—
387#394C2314yes—
388#394C2312yes—
389#394C2314yes—
390#394C2314yes—
391#394C2314yes—
392#394C2314yes—
393#394C2312yes—
394#394C2314yes—
395#394C2312yes—
396#394C2314yes—
397#394C2314yes—
398#394C2314yes—
399#394C2314yes—
400#394C2314yes—
401#394C2314yes—
402#394C2314yes—
403#394C2314yes—
404#393C2314yes—
405#393C2314yes—
406#393C2314yes—
407#393C2312yes—
408#393C2314yes—
409#393C2314yes—
410#393C2314yes—
411#393C2314yes—
412#393C2314yes—
413#393C2314yes—
414#393C2314yes—
415#393C2314yes—
416#392C2314yes—
417#392C2312yes—
418#392C2312yes—
419#392C2314yes—
420#392C2314yes—
421#392C2314yes—
422#392C2314yes—
423#392C2314yes—
424#392C2314yes—
425#392C2314yes—
426#392C2314yes—
427#392C2314yes—
428#392C2314yes—
429#392C2314yes—
430#392C2314yes—
431#392C2314yes—
432#392C2314yes—
433#392C2314yes—
434#392C2314yes—
435#392C2314yes—
436#392C2314yes—
437#392C2314yes—
438#392C2314yes—
439#392C2314yes—
440#391C2314yes—
441#391C2314yes—
442#391C2314yes—
443#391C2314yes—
444#391C2314yes—
445#391C2314yes—
446#391C2314yes—
447#391C2314yes—
448#391C2314yes—
449#391C2314yes—
450#391C2314yes—
451#391C2314yes—
452#390C2314yes—
453#390C2312yes—
454#390C2314yes—
455#390C2314yes—
456#390C2314yes—
457#390C2314yes—
458#390C2314yes—
459#390C2314yes—
460#390C2314yes—
461#390C2314yes—
462#390C2312yes—
463#390C2314yes—
464#390C2314yes—
465#389C2314yes—
466#389C2314yes—
467#389C2314yes—
468#389C2314yes—
469#389C2314yes—
470#389C2314yes—
471#388C2314yes—
472#388C2314yes—
473#388C2314yes—
474#388C2314yes—
475#388C2314yes—
476#388C2314yes—
477#388C2314yes—
478#388C2314yes—
479#388C2314yes—
480#388C2314yes—
481#388C2314yes—
482#388C2314yes—
483#388C2314yes—
484#388C2314yes—
485#388C2314yes—
486#388C2314yes—
487#388C2314yes—
488#388C2314yes—
489#388C2314yes—
490#388C2314yes—
491#388C2314yes—
492#388C2314yes—
493#388C2314yes—
494#388C2314yes—
495#388C2314yes—
496#388C2314yes—
497#388C2314yes—
498#388C2314yes—
499#388C2314yes—
500#388C2314yes—
501#388C2314yes—
502#387C2314yes—
503#387C2314yes—
504#387C2314yes—
505#387C2314yes—
506#387C2314yes—
507#387C2314yes—
508#387C2314yes—
509#387C2314yes—
510#387C2314yes—
511#387C2314yes—
512#387C2314yes—
513#387C2314yes—
514#387C2314yes—
515#387C2314yes—
516#387C2314yes—
517#387C2314yes—
518#387C2314yes—
519#387C2314yes—
520#387C2314yes—
521#386C2314yes—
522#386C2314yes—
523#386C2314yes—
524#386C2314yes—
525#386C2314yes—
526#386C2314yes—
527#386C2314yes—
528#386C2314yes—
529#386C2314yes—
530#386C2314yes—
531#386C2314yes—
532#386C2314yes—
533#386C2314yes—
534#386C2314yes—
535#386C2314yes—
536#386C2314yes—
537#386C2314yes—
538#386C2314yes—
539#386C2314yes—
540#386C2314yes—
541#386C2314yes—
542#386C2314yes—
543#386C2314yes—
544#386C2314yes—
545#386C2312yes—
546#386C2314yes—
547#386C2314yes—
548#386C2314yes—
549#386C2314yes—
550#386C2312yes—
551#386C2314yes—
552#386C2314yes—
553#386C2314yes—
554#386C2314yes—
555#386C2314yes—
556#386C2314yes—
557#386C2314yes—
558#386C2314yes—
559#386C2314yes—
560#386C2314yes—
561#386C2314yes—
562#386C2314yes—
563#386C2314yes—
564#385C2314yes—
565#385C2314yes—
566#385C2314yes—
567#385C2314yes—
568#385C2314yes—
569#385C2312yes—
570#385C2314yes—
571#385C2314yes—
572#385C2312yes—
573#385C2314yes—
574#385C2314yes—
575#385C2314yes—
576#385C2314yes—
577#383C2312yes—
578#382C2312yes—
579#382C2312yes—
580#382C2314yes—
581#381C2314yes—
582#381C2312yes—
583#381C2312yes—
584#381C2314yes—
585#381C2314yes—
586#381C2312yes—
587#381C2314yes—
588#380C2314yes—
589#380C2314yes—
590#380C2311yescharacteristic
591#380C2311yescharacteristic
592#380C2312yes—
593#380C2314yes—
594#380C2312yes—
595#380C2312yes—
596#380C2314yes—
597#380C2314yes—
598#380C2314yes—
599#380C2312yes—
600#380C2314yes—
601#379C2314yes—
602#379C2312yes—
603C4×C22⋊C4C2314yes—
604C4×C22⋊C4C2314yes—
605C4×C22⋊C4C2314yes—
606C4×C22⋊C4C2314yes—
607C4×C22⋊C4C2314yes—
608C4×C22⋊C4C2314yes—
609C4×C22⋊C4C2314yes—
610C4×C22⋊C4C2312yes—
611C4×C22⋊C4C2312yes—
612C4×C22⋊C4C2314yes—
613C4×C22⋊C4C2314yes—
614C4×C22⋊C4C2314yes—
615C4×C22⋊C4C2314yes—
616C4×C22⋊C4C2314yes—
617C4×C22⋊C4C2314yes—
618#376C2314yes—
619#376C2314yes—
620#376C2312yes—
621C2×#95C2312yes—
622C2×#95C2312yes—
623C2×#95C2312yes—
624C25C2411yescharacteristic
625C25C2412yes—
6262−1+4—464no—
627C2×#41—28no—
628C2×#41—28no—
629C2×#41—44no—
630C2×#41—48no—
631C2×#41—44no—
632C2×#41—44no—
633C2×#41—48no—
634C2×#41—48no—
635C2×#41—48no—
636C2×#41—48no—
637C2×#41—48no—
638C2×#41—44no—
639C22×Q8—216no—
640C22×Q8—24no—
641C22×Q8—44no—
642C22×Q8—48no—
643C22×Q8—48no—
644C22×Q8C2412yes—
645C22×Q8C2414yes—
646C22×Q8C2412yes—
647C22×Q8C2411yescharacteristic
648C22×Q8C2414yes—
649C22×Q8C2412yes—
650C22×D4—44no—
651C22×D4—44no—
652C22×D4—44no—
653C22×D4C2414yes—
654C22×D4C2414yes—
655C22×D4C2414yes—
656C22×D4C2414yes—
657C22×D4C2412yes—
658C22×D4C2412yes—
659C22×D4C2414yes—
660C22×D4C2414yes—
661C22×D4C2414yes—
662C22×D4C2412yes—
663C22×D4C2412yes—
664C22×D4C2414yes—
665C22×D4C2414yes—
666C22×D4C2414yes—
667C22×D4C2414yes—
668C22×D4C2412yes—
669C22×D4C2414yes—
670C22×D4C2414yes—
671C22×D4C2411yescharacteristic
672C22×D4C2414yes—
673C22×D4C2412yes—
674C23×C4—44no—
675C23×C4—42no—
676C23×C4C2411yescharacteristic
677C23×C4C2414yes—
678C23×C4C2414yes—
679C23×C4C2411yescharacteristic
680C23×C4C2411yescharacteristic
681C23×C4C2411yescharacteristic
682C23×C4C2414yes—
683C23×C4C2412yes—
684C23×C4C2412yes—
685C23×C4C2411yescharacteristic
686C23×C4C2412yes—
687C23×C4C2414yes—
688C23×C4C2412yes—
689C23×C4C2412yes—
690C23×C4C2412yes—
691C23×C4C2414yes—
692C23×C4C2414yes—
693C23×C4C2411yescharacteristic
694#127—44no—
695#127—48no—
696#127—48no—
697#126—48no—
698#126—44no—
699#125—44no—
700#124—216no—
701#124—48no—
702#124—48no—
703#124—48no—
704#124—84no—
705#124—84no—
706#123—48no—
707#123—48no—
708#123—44no—
709#123—44no—
710#123—48no—
711#123—82no—
712#123—84no—
713C22⋊Q8—28no—
714C22⋊Q8—28no—
715C22⋊Q8—216no—
716C22⋊Q8—42no—
717C22⋊Q8—48no—
718C22⋊Q8—48no—
719C22⋊Q8—48no—
720C22⋊Q8—48no—
721C22⋊Q8—48no—
722C22⋊Q8—48no—
723C22⋊Q8—48no—
724C22⋊Q8—44no—
725C22⋊Q8—44no—
726C22⋊Q8—48no—
727#121—28no—
728#121—44no—
729#121—48no—
730#121—48no—
731#121—48no—
732#121—48no—
733#121—48no—
734#121—48no—
735#121—48no—
736#121—44no—
737#121—44no—
738#121—48no—
739#121—44no—
740#121—48no—
741#121—44no—
742#121—42no—
743#121—84no—
744#121—84no—
745#120—48no—
746#120—48no—
747#120—48no—
748#120—48no—
749#120—82no—
750#120—84no—
751C4×Q8—48no—
752C4×Q8—44no—
753C4×D4—28no—
754C4×D4—48no—
755C4×D4—48no—
756C4×D4—48no—
757C4×D4—48no—
758C4×D4—48no—
759C4×D4—48no—
760C4×D4—48no—
761#117—44no—
762#117—82no—
763C2×C4⋊C4—24no—
764C2×C4⋊C4—42no—
765C2×C4⋊C4—42no—
766C2×C4⋊C4C2412yes—
767C2×C4⋊C4C2412yes—
768C2×C4⋊C4C2412yes—
769C2×C4⋊C4C2412yes—
770C2×C4⋊C4C2412yes—
771C2×C4⋊C4C2414yes—
772C2×C4⋊C4C2414yes—
773C2×C4⋊C4C2414yes—
774C2×C4⋊C4C2414yes—
775C2×C4⋊C4C2412yes—
776C2×C4⋊C4C2414yes—
777C2×C4⋊C4C2414yes—
778C2×C4⋊C4C2412yes—
779C2×C4⋊C4C2412yes—
780C2×C4⋊C4C2414yes—
781C2×C4⋊C4C2414yes—
782C2×C4⋊C4C2414yes—
783C2×C4⋊C4C2414yes—
784C2×C4⋊C4C2414yes—
785C2×C4⋊C4C2414yes—
786C2×C4⋊C4C2412yes—
787C2×C4⋊C4C2414yes—
788C2×C4⋊C4C2414yes—
789C2×C4⋊C4C2411yescharacteristic
790C2×C4⋊C4C2412yes—
791C2×C4⋊C4C2414yes—
792C2×C4⋊C4C2414yes—
793C2×C4⋊C4C2414yes—
794C2×C4⋊C4C2414yes—
795C2×C4⋊C4C2412yes—
796C2×C4⋊C4C2412yes—
797C2×C4⋊C4C2412yes—
798C2×C4⋊C4C2411yescharacteristic
799C2×C4⋊C4C2412yes—
800C2×C22⋊C4—24no—
801C2×C22⋊C4—44no—
802C2×C22⋊C4—48no—
803C2×C22⋊C4—44no—
804C2×C22⋊C4—44no—
805C2×C22⋊C4—42no—
806C2×C22⋊C4C2414yes—
807C2×C22⋊C4C2414yes—
808C2×C22⋊C4C2414yes—
809C2×C22⋊C4C2414yes—
810C2×C22⋊C4C2414yes—
811C2×C22⋊C4C2414yes—
812C2×C22⋊C4C2414yes—
813C2×C22⋊C4C2414yes—
814C2×C22⋊C4C2414yes—
815C2×C22⋊C4C2412yes—
816C2×C22⋊C4C2412yes—
817C2×C22⋊C4C2414yes—
818C2×C22⋊C4C2414yes—
819C2×C22⋊C4C2414yes—
820C2×C22⋊C4C2414yes—
821C2×C22⋊C4C2414yes—
822C2×C22⋊C4C2414yes—
823C2×C22⋊C4C2414yes—
824C2×C22⋊C4C2414yes—
825C2×C22⋊C4C2414yes—
826C2×C22⋊C4C2414yes—
827C2×C22⋊C4C2412yes—
828C2×C22⋊C4C2412yes—
829C2×C22⋊C4C2414yes—
830C2×C22⋊C4C2414yes—
831C2×C22⋊C4C2414yes—
832C2×C22⋊C4C2414yes—
833C2×C22⋊C4C2414yes—
834C2×C22⋊C4C2414yes—
835C2×C22⋊C4C2414yes—
836C2×C22⋊C4C2414yes—
837C2×C22⋊C4C2414yes—
838C2×C22⋊C4C2414yes—
839C2×C22⋊C4C2414yes—
840C2×C22⋊C4C2414yes—
841C2×C22⋊C4C2414yes—
842C2×C22⋊C4C2414yes—
843C2×C22⋊C4C2412yes—
844C2×C22⋊C4C2414yes—
845C2×C22⋊C4C2414yes—
846C2×C22⋊C4C2414yes—
847C2×C22⋊C4C2414yes—
848C2×C22⋊C4C2414yes—
849C2×C22⋊C4C2414yes—
850C2×C22⋊C4C2414yes—
851C2×C22⋊C4C2412yes—
852C2×C22⋊C4C2412yes—
853C2×C22⋊C4C2414yes—
854C2×C22⋊C4C2414yes—
855C2×C22⋊C4C2414yes—
856C2×C22⋊C4C2414yes—
857C2×C22⋊C4C2414yes—
858C2×C22⋊C4C2414yes—
859C2×C22⋊C4C2414yes—
860C2×C22⋊C4C2414yes—
861C2×C22⋊C4C2414yes—
862C2×C22⋊C4C2414yes—
863C2×C42C2414yes—
864C2×C42C2412yes—
865C2×C42C2414yes—
866C2×C42C2414yes—
867C2×C42C2414yes—
868C2×C42C2414yes—
869C2×C42C2414yes—
870C2×C42C2412yes—
871C2×C42C2414yes—
872C2×C42C2414yes—
873C2×C42C2412yes—
874#95C2412yes—
875#95C2414yes—
876#95C2414yes—
877#95C2412yes—
878#95C2414yes—
879#95C2414yes—
880#95C2414yes—
881#95C2414yes—
882#95C2414yes—
883#95C2414yes—
884#95C2412yes—
885#95C2414yes—
886#95C2414yes—
887#95C2414yes—
888#95C2414yes—
889#95C2414yes—
890#95C2414yes—
891#95C2412yes—
892#95C2414yes—
893#95C2414yes—
894#95C2414yes—
895#95C2414yes—
896#95C2414yes—
897#95C2414yes—
898#95C2414yes—
899#95C2414yes—
900#95C2414yes—
901#95C2414yes—
902#95C2414yes—
903#95C2414yes—
904#95C2414yes—
905#95C2414yes—
906#95C2414yes—
907#95C2412yes—
908#95C2414yes—
909#95C2412yes—
910#95C2412yes—
911#95C2414yes—
912#95C2414yes—
913#95C2412yes—
914#95C2414yes—
915#95C2414yes—
916#95C2414yes—
917#95C2414yes—
918#95C2414yes—
919#95C2414yes—
920C24—22no—
921C24—24no—
922C24—24no—
923C24—42no—
924C24—42no—
925C24—42no—
926C24—41no—
927C24—41no—
928C24—42no—
929C24—42no—
930C24—42no—
931C24—42no—
932C24C2514yes—
933C24C2512yes—
934C24C2514yes—
935C24C2511yescharacteristic
936C24C2512yes—
937#41—432no—
938#41—432no—
939#41—464no—
940#41—432no—
941#41—816no—
942C2×Q8—28no—
943C2×Q8—24no—
944C2×Q8—28no—
945C2×Q8—28no—
946C2×Q8—28no—
947C2×Q8—42no—
948C2×Q8—44no—
949C2×Q8—42no—
950C2×Q8—42no—
951C2×Q8—44no—
952C2×Q8—41no—
953C2×Q8—42no—
954C2×Q8—44no—
955C2×Q8—44no—
956C2×Q8—416no—
957C2×Q8—464no—
958C2×Q8H(5,𝔽2)18yes—
959C2×D4—28no—
960C2×D4—24no—
961C2×D4—28no—
962C2×D4—28no—
963C2×D4—28no—
964C2×D4—28no—
965C2×D4—28no—
966C2×D4—28no—
967C2×D4—24no—
968C2×D4—24no—
969C2×D4—24no—
970C2×D4—28no—
971C2×D4—42no—
972C2×D4—44no—
973C2×D4—44no—
974C2×D4—42no—
975C2×D4—44no—
976C2×D4—42no—
977C2×D4—44no—
978C2×D4—44no—
979C2×D4—44no—
980C2×D4—44no—
981C2×D4—44no—
982C2×D4—44no—
983C2×D4—44no—
984C2×D4—44no—
985C2×D4—44no—
986C2×D4—44no—
987C2×D4—44no—
988C2×D4—44no—
989C2×D4—44no—
990C2×D4—42no—
991C2×D4—44no—
992C2×D4—44no—
993C2×D4—44no—
994C2×D4—44no—
995C2×D4—44no—
996C2×D4—44no—
997C2×D4—44no—
998C2×D4—44no—
999C2×D4—44no—
1000C2×D4—44no—
1001C2×D4—44no—
1002C2×D4—42no—
1003C2×D4—44no—
1004C2×D4—42no—
1005C2×D4—44no—
1006C2×D4—44no—
1007C2×D4—42no—
1008C2×D4—44no—
1009C2×D4—44no—
1010C2×D4—41no—
1011C2×D4—44no—
1012C2×D4—44no—
1013C2×D4—42no—
1014C2×D4—44no—
1015C2×D4—44no—
1016C2×D4—42no—
1017C2×D4—44no—
1018C2×D4—816no—
1019C22×C4—22no—
1020C22×C4—24no—
1021C22×C4—22no—
1022C22×C4—22no—
1023C22×C4—22no—
1024C22×C4—22no—
1025C22×C4—24no—
1026C22×C4—28no—
1027C22×C4—28no—
1028C22×C4—28no—
1029C22×C4—28no—
1030C22×C4—28no—
1031C22×C4—28no—
1032C22×C4—24no—
1033C22×C4—24no—
1034C22×C4—24no—
1035C22×C4—41no—
1036C22×C4—41no—
1037C22×C4—44no—
1038C22×C4—44no—
1039C22×C4—42no—
1040C22×C4—44no—
1041C22×C4—44no—
1042C22×C4—42no—
1043C22×C4—42no—
1044C22×C4—42no—
1045C22×C4—44no—
1046C22×C4—44no—
1047C22×C4—44no—
1048C22×C4—42no—
1049C22×C4—42no—
1050C22×C4—42no—
1051C22×C4—42no—
1052C22×C4—41no—
1053C22×C4—41no—
1054C22×C4—42no—
1055C22×C4—42no—
1056C22×C4—44no—
1057C22×C4—42no—
1058C22×C4—42no—
1059C22×C4—42no—
1060C22×C4—44no—
1061C22×C4—44no—
1062C22×C4—44no—
1063C22×C4—42no—
1064C22×C4—44no—
1065C22×C4—42no—
1066C22×C4—44no—
1067C22×C4—88no—
1068C22×C4H(5,𝔽2)14yes—
1069C22×C4C2514yes—
1070C22×C4C2514yes—
1071C22×C4C2514yes—
1072C22×C4C2512yes—
1073C22×C4C2512yes—
1074C22×C4C2512yes—
1075C22×C4C2512yes—
1076C22×C4C2514yes—
1077C22×C4C2514yes—
1078C22×C4C2514yes—
1079C22×C4C2514yes—
1080C22×C4C2512yes—
1081C22×C4C2512yes—
1082C22×C4C2511yescharacteristic
1083C22×C4C2511yescharacteristic
1084C22×C4C2514yes—
1085C22×C4C2512yes—
1086C22×C4C2512yes—
1087C4⋊C4—24no—
1088C4⋊C4—24no—
1089C4⋊C4—24no—
1090C4⋊C4—24no—
1091C4⋊C4—24no—
1092C4⋊C4—28no—
1093C4⋊C4—28no—
1094C4⋊C4—28no—
1095C4⋊C4—28no—
1096C4⋊C4—24no—
1097C4⋊C4—28no—
1098C4⋊C4—44no—
1099C4⋊C4—42no—
1100C4⋊C4—42no—
1101C4⋊C4—44no—
1102C4⋊C4—44no—
1103C4⋊C4—44no—
1104C4⋊C4—44no—
1105C4⋊C4—44no—
1106C4⋊C4—44no—
1107C4⋊C4—44no—
1108C4⋊C4—44no—
1109C4⋊C4—44no—
1110C4⋊C4—42no—
1111C4⋊C4—41no—
1112C4⋊C4—42no—
1113C4⋊C4—44no—
1114C4⋊C4—44no—
1115C4⋊C4—44no—
1116C4⋊C4—42no—
1117C4⋊C4—42no—
1118C4⋊C4—42no—
1119C4⋊C4—41no—
1120C4⋊C4—42no—
1121C22⋊C4—24no—
1122C22⋊C4—28no—
1123C22⋊C4—28no—
1124C22⋊C4—28no—
1125C22⋊C4—28no—
1126C22⋊C4—28no—
1127C22⋊C4—28no—
1128C22⋊C4—28no—
1129C22⋊C4—24no—
1130C22⋊C4—28no—
1131C22⋊C4—28no—
1132C22⋊C4—28no—
1133C22⋊C4—28no—
1134C22⋊C4—28no—
1135C22⋊C4—44no—
1136C22⋊C4—44no—
1137C22⋊C4—44no—
1138C22⋊C4—44no—
1139C22⋊C4—44no—
1140C22⋊C4—44no—
1141C22⋊C4—44no—
1142C22⋊C4—44no—
1143C22⋊C4—44no—
1144C22⋊C4—44no—
1145C22⋊C4—44no—
1146C22⋊C4—42no—
1147C22⋊C4—42no—
1148C22⋊C4—44no—
1149C22⋊C4—44no—
1150C22⋊C4—44no—
1151C22⋊C4—44no—
1152C22⋊C4—44no—
1153C22⋊C4—44no—
1154C22⋊C4—44no—
1155C22⋊C4—44no—
1156C22⋊C4—44no—
1157C22⋊C4—44no—
1158C22⋊C4—44no—
1159C22⋊C4—44no—
1160C22⋊C4—44no—
1161C22⋊C4—44no—
1162C22⋊C4—44no—
1163C22⋊C4—44no—
1164C22⋊C4—44no—
1165C22⋊C4—44no—
1166C22⋊C4—42no—
1167C22⋊C4—44no—
1168C22⋊C4—44no—
1169C22⋊C4—44no—
1170C22⋊C4—42no—
1171C22⋊C4—42no—
1172C22⋊C4—44no—
1173C22⋊C4—44no—
1174C22⋊C4—44no—
1175C22⋊C4—44no—
1176C22⋊C4—44no—
1177C22⋊C4—44no—
1178C42—24no—
1179C42—28no—
1180C42—42no—
1181C42—44no—
1182C42—44no—
1183C42—44no—
1184C42—44no—
1185C42—44no—
1186C42—44no—
1187C42—42no—
1188C42—44no—
1189C23—28no—
1190C23—22no—
1191C23—22no—
1192C23—22no—
1193C23—22no—
1194C23—22no—
1195C23—22no—
1196C23—21no—
1197C23—22no—
1198C23—21no—
1199C23—22no—
1200C23—24no—
1201C23—24no—
1202C23—24no—
1203C23—22no—
1204C23—24no—
1205C23—24no—
1206C23—24no—
1207C23—24no—
1208C23—24no—
1209C23—24no—
1210C23—24no—
1211C23—24no—
1212C23—24no—
1213C23—24no—
1214C23—22no—
1215C23—24no—
1216C23—24no—
1217C23—24no—
1218C23—22no—
1219C23—48no—
1220C23—82no—
1221C23—82no—
1222C23—84no—
1223C23—84no—
1224C23—84no—
1225C23—84no—
1226C23—162no—
1227C23—162no—
1228C23—162no—
1229C23—162no—
1230C23C2×H(5,𝔽2)12yes—
1231C23#58514yes—
1232C23C2611yescharacteristic
1233Q8—216no—
1234Q8—48no—
1235Q8—416no—
1236Q8—48no—
1237Q8—161no—
1238Q8—164no—
1239D4—416no—
1240D4—48no—
1241D4—48no—
1242D4—48no—
1243D4—88no—
1244D4—84no—
1245D4—84no—
1246D4—88no—
1247D4—88no—
1248D4—88no—
1249D4—88no—
1250D4—88no—
1251D4—88no—
1252D4—88no—
1253D4—88no—
1254D4—88no—
1255D4—161no—
1256D4—164no—
1257D4—164no—
1258D4—162no—
1259D4—164no—
1260C2×C4—28no—
1261C2×C4—22no—
1262C2×C4—24no—
1263C2×C4—24no—
1264C2×C4—24no—
1265C2×C4—22no—
1266C2×C4—24no—
1267C2×C4—22no—
1268C2×C4—22no—
1269C2×C4—24no—
1270C2×C4—24no—
1271C2×C4—24no—
1272C2×C4—24no—
1273C2×C4—24no—
1274C2×C4—24no—
1275C2×C4—22no—
1276C2×C4—22no—
1277C2×C4—22no—
1278C2×C4—22no—
1279C2×C4—22no—
1280C2×C4—24no—
1281C2×C4—24no—
1282C2×C4—21no—
1283C2×C4—22no—
1284C2×C4—21no—
1285C2×C4—24no—
1286C2×C4—24no—
1287C2×C4—24no—
1288C2×C4—24no—
1289C2×C4—24no—
1290C2×C4—24no—
1291C2×C4—24no—
1292C2×C4—24no—
1293C2×C4—24no—
1294C2×C4—22no—
1295C2×C4—22no—
1296C2×C4—24no—
1297C2×C4—24no—
1298C2×C4—24no—
1299C2×C4—24no—
1300C2×C4—22no—
1301C2×C4—24no—
1302C2×C4—22no—
1303C2×C4—22no—
1304C2×C4—24no—
1305C2×C4—22no—
1306C2×C4—44no—
1307C2×C4—416no—
1308C2×C4—416no—
1309C2×C4—416no—
1310C2×C4—44no—
1311C2×C4—44no—
1312C2×C4—84no—
1313C2×C4—84no—
1314C2×C4—84no—
1315C2×C4—88no—
1316C2×C4—82no—
1317C2×C4—82no—
1318C2×C4—84no—
1319C2×C4—162no—
1320C2×C4—164no—
1321C2×C4—162no—
1322C2×C4—164no—
1323C2×C4C2×H(5,𝔽2)18yes—
1324C2×C4C2×H(5,𝔽2)14yes—
1325C2×C4C2×H(5,𝔽2)14yes—
1326C22—22no—
1327C22—24no—
1328C22—22no—
1329C22—22no—
1330C22—24no—
1331C22—24no—
1332C22—42no—
1333C22—42no—
1334C22—42no—
1335C22—42no—
1336C22—42no—
1337C22—42no—
1338C22—44no—
1339C22—42no—
1340C22—44no—
1341C22—44no—
1342C22—42no—
1343C22—44no—
1344C22—44no—
1345C22—42no—
1346C22—44no—
1347C22—44no—
1348C22—44no—
1349C22—44no—
1350C22—44no—
1351C22—44no—
1352C22—44no—
1353C22—44no—
1354C22—44no—
1355C22—44no—
1356C22—44no—
1357C22—88no—
1358C22—168no—
1359C22C22×H(5,𝔽2)11yescharacteristic
1360C22C22×H(5,𝔽2)12yes—
1361C22C2×#58512yes—
1362C22H(7,𝔽2)11yescharacteristic
1363C222−1+611yescharacteristic
1364C4—24no—
1365C4—28no—
1366C4—24no—
1367C4—42no—
1368C4—41no—
1369C4—42no—
1370C4—41no—
1371C4—44no—
1372C4—42no—
1373C4—42no—
1374C4—42no—
1375C4—42no—
1376C4—44no—
1377C4—44no—
1378C4—44no—
1379C4—44no—
1380C4—44no—
1381C4—44no—
1382C2—42no—
1383C2—44no—
1384C2—84no—
1385C2—82no—
1386C2—84no—
1387C2#6281711yescharacteristic
1388C2#6282411yescharacteristic
1389C2#6287511yescharacteristic
1390C2#6289912yes—
1391C2#6291912yes—
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. #58802C2semidirect
2. #58801C2semidirect
3. #54956C2semidirect
4. #54950C2semidirect
5. #51934C2semidirect
6. #51427C2semidirect
7. #49592C2semidirect
8. #48682C2semidirect
9. #47833C2semidirect
10. #47831C2semidirect
11. #47068C2semidirect
12. #44649C2semidirect
13. #43379C2semidirect
14. #42107C2semidirect
15. #41242C2semidirect
16. #40505C2semidirect
17. #37769C2semidirect
18. #37752C2semidirect
19. #36719C2semidirect
20. #35944C2semidirect
21. #35757C2semidirect
22. #35659C2semidirect
23. #35377C2semidirect
24. C22×2−1+4C22semidirect
26. C2×#548C22semidirect
27. C2×#543C22semidirect
28. C2×#539C22semidirect
29. C2×#538C22semidirect
35. #2829C22semidirect
36. #2828C22semidirect
38. #2825C22semidirect
39. #2819C22semidirect
40. #2818C22semidirect
41. #2813C22semidirect
42. #2803C22semidirect
43. #2803C22semidirect
44. #2799C22semidirect
45. #2789C22semidirect
46. #2789C22semidirect
47. #2785C22semidirect
48. #2779C22semidirect
50. #2768C22semidirect
51. #2761C22semidirect
52. #2760C22semidirect
53. #2759C22semidirect
54. #2742C22semidirect
55. #2741C22semidirect
56. #2741C22semidirect
57. #2733C22semidirect
59. #2730C22semidirect
61. #2710C22semidirect
62. #2709C22semidirect
63. #2705C22semidirect
64. #2704C22semidirect
65. #2703C22semidirect
66. #2703C22semidirect
67. #2702C22semidirect
68. #2700C22semidirect
69. #2700C22semidirect
71. #2699C22semidirect
72. #2699C22semidirect
73. #2698C22semidirect
74. #2696C22semidirect
76. #2692C22semidirect
77. #2688C22semidirect
78. #2686C22semidirect
79. #2683C22semidirect
80. #2683C22semidirect
81. #2681C22semidirect
82. #2681C22semidirect
85. #2676C22semidirect
90. #2673C22semidirect
91. #2672C22semidirect
92. #2672C22semidirect
94. #2670C22semidirect
97. #2668C22semidirect
98. #2665C22semidirect
99. #2661C22semidirect
100. #2656C22semidirect
101. #2653C22semidirect
102. #2648C22semidirect
103. #2648C22semidirect
104. #2641C22semidirect
105. #2639C22semidirect
106. #2639C22semidirect
107. #2638C22semidirect
109. #2634C22semidirect
110. #2627C22semidirect
111. #2618C22semidirect
112. #2617C22semidirect
113. #2617C22semidirect
114. #2616C22semidirect
116. #2615C22semidirect
117. #2612C22semidirect
118. #2610C22semidirect
119. #2607C22semidirect
120. #2604C22semidirect
121. #2604C22semidirect
122. #2603C22semidirect
125. #2578C22semidirect
126. #2576C22semidirect
127. #2576C22semidirect
128. #2559C22semidirect
129. #2559C22semidirect
130. #2557C22semidirect
131. #2557C22semidirect
132. #2555C22semidirect
133. #2555C22semidirect
135. #2534C22semidirect
136. #2531C22semidirect
137. #2530C22semidirect
138. #2530C22semidirect
139. #2527C22semidirect
140. #2527C22semidirect
141. #2526C22semidirect
145. #2488C22semidirect
146. #2477C22semidirect
150. #2472C22semidirect
151. #2471C22semidirect
152. #2471C22semidirect
154. #2465C22semidirect
155. #2465C22semidirect
156. #2464C22semidirect
158. #2463C22semidirect
159. #2460C22semidirect
163. #2457C22semidirect
164. #2450C22semidirect
166. #2436C22semidirect
168. #2431C22semidirect
169. #2431C22semidirect
170. #2431C22semidirect
171. #2430C22semidirect
174. #2427C22semidirect
175. #2427C22semidirect
178. #2424C22semidirect
179. #2413C22semidirect
182. #2409C22semidirect
183. #2409C22semidirect
184. #2409C22semidirect
185. #2409C22semidirect
186. #2407C22semidirect
187. #2407C22semidirect
188. #2407C22semidirect
189. #2407C22semidirect
190. #2407C22semidirect
191. #2406C22semidirect
192. #2406C22semidirect
196. #2398C22semidirect
197. #2388C22semidirect
198. #2388C22semidirect
199. #2378C22semidirect
201. #2372C22semidirect
202. #2372C22semidirect
203. #2364C22semidirect
204. #2364C22semidirect
205. #2358C22semidirect
206. #2353C22semidirect
207. #2341C22semidirect
208. Q8×C22⋊C4C22semidirect
210. #2329C22semidirect
211. #2329C22semidirect
213. #2316C22semidirect
214. #2311C22semidirect
215. #2310C22semidirect

Maximal subgroups

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

subgroupindex
#588022
#588012
#549562
#549502
#519342
#514272
#495922
#486822
#478332
#478312
#470682
#446492
#433792
#421072
#412422
#405052
#377692
#377522
#367192
#359442
#357572
#356592
#353772