Finite Group Databasebeta

← #8943233

Subgroups — #8943233

Order 512.

5080 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#58030C214yesmaximal, complemented
2#57954C214yesmaximal, complemented
3#56283C214yesmaximal, complemented
4#51945C212yesmaximal, complemented
5#51895C212yesmaximal, complemented
6#50800C214yesmaximal, complemented
7#50661C212yesmaximal, complemented
8#50182C212yesmaximal, complemented
9#49382C214yesmaximal, complemented
10#48777C212yesmaximal, complemented
11#46512C214yesmaximal, complemented
12#43270C214yesmaximal, complemented
13#43040C214yesmaximal, complemented
14#41442C212yesmaximal, complemented
15#41261C214yesmaximal, complemented
16#40705C214yesmaximal, complemented
17#37948C212yesmaximal, complemented
18#37768C212yesmaximal, complemented
19#36717C211yesmaximal, characteristic, complemented
20#36011C212yesmaximal, complemented
21#36004C212yesmaximal, complemented
22#35563C211yesmaximal, characteristic, complemented
23#35351C211yesmaximal, characteristic, complemented
24C2×#555C2212yes—
25C2×#551C2212yescomplemented
26C2×#539C2212yescomplemented
27C2×#535C2211yescharacteristic
28C2×#534C2211yescharacteristic
29C2×#525C2211yescharacteristic, complemented
30C22×#121C2211yescharacteristic
31C2×#520C2211yescharacteristic, complemented
32C2×#518C2211yescharacteristic, complemented
33#2847C2212yes—
34#2837C2214yescomplemented
35#2830C2214yescomplemented
36#2828C2214yescomplemented
37#2825C2214yescomplemented
38#2816C2214yescomplemented
39#2807C2214yescomplemented
40#2803C2214yescomplemented
41#2784C2214yescomplemented
42#2781C2214yescomplemented
43#2773C2214yescomplemented
44#2772C2214yescomplemented
45#2766C2214yescomplemented
46#2761C2214yescomplemented
47#2757C2214yescomplemented
48#2753C2214yescomplemented
49#2752C2214yescomplemented
50#2746C2214yescomplemented
51#2744C2214yescomplemented
52#2740C2214yescomplemented
53#2735C2214yes—
54#2732C2214yescomplemented
55#2732C2214yescomplemented
56#2730C2214yescomplemented
57#2730C2214yescomplemented
58#2714C2214yescomplemented
59#2709C2212yescomplemented
60#2707C2214yescomplemented
61#2706C2214yescomplemented
62#2706C2214yescomplemented
63#2705C2214yescomplemented
64#2705C2214yescomplemented
65#2703C2214yes—
66#2703C2214yes—
67#2699C2214yescomplemented
68#2699C2214yescomplemented
69#2697C2212yescomplemented
70#2696C2214yescomplemented
71#2694C2214yescomplemented
72#2691C2214yescomplemented
73#2691C2214yescomplemented
74#2689C2214yescomplemented
75#2688C2214yescomplemented
76#2686C2214yes—
77#2685C2214yes—
78#2685C2214yescomplemented
79#2685C2214yescomplemented
80#2683C2212yescomplemented
81#2682C2214yes—
82#2678C2214yescomplemented
83#2678C2214yescomplemented
84#2676C2214yescomplemented
85#2674C2214yescomplemented
86#2673C2214yescomplemented
87#2672C2214yescomplemented
88#2671C2214yescomplemented
89#2670C2214yescomplemented
90#2669C2214yes—
91#2669C2214yes—
92#2669C2212yescomplemented
93#2668C2214yescomplemented
94#2668C2214yescomplemented
95#2667C2212yescomplemented
96#2662C2214yescomplemented
97#2659C2212yescomplemented
98#2656C2212yescomplemented
99#2654C2214yescomplemented
100#2653C2214yescomplemented
101#2651C2214yescomplemented
102#2648C2214yescomplemented
103#2635C2212yes—
104#2635C2212yescomplemented
105#2631C2214yescomplemented
106#2628C2212yescomplemented
107#2624C2212yes—
108#2619C2214yescomplemented
109#2618C2212yescomplemented
110#2618C2212yescomplemented
111#2617C2212yes—
112#2609C2214yescomplemented
113#2602C2214yescomplemented
114#2598C2214yescomplemented
115#2594C2214yescomplemented
116#2591C2212yes—
117#2591C2212yescomplemented
118#2590C2214yescomplemented
119#2576C2214yescomplemented
120#2576C2214yescomplemented
121#2574C2214yescomplemented
122#2568C2212yescomplemented
123#2560C2214yescomplemented
124#2557C2214yescomplemented
125#2554C2214yescomplemented
126#2554C2214yescomplemented
127#2540C2214yescomplemented
128#2539C2214yescomplemented
129#2536C2212yescomplemented
130#2534C2212yes—
131#2534C2214yescomplemented
132#2534C2212yescomplemented
133#2525C2214yescomplemented
134#2519C2214yescomplemented
135#2519C2214yescomplemented
136#2518C2214yescomplemented
137#2516C2214yescomplemented
138#2516C2214yescomplemented
139#2488C2214yescomplemented
140#2484C2212yescomplemented
141#2484C2212yescomplemented
142#2483C2212yescomplemented
143#2482C2212yes—
144#2479C2214yescomplemented
145#2479C2214yescomplemented
146#2478C2214yescomplemented
147#2476C2214yescomplemented
148#2474C2214yescomplemented
149#2474C2214yescomplemented
150#2472C2214yescomplemented
151#2472C2214yescomplemented
152#2471C2214yescomplemented
153#2470C2214yescomplemented
154#2467C2214yescomplemented
155#2464C2214yescomplemented
156#2464C2214yescomplemented
157#2460C2214yescomplemented
158#2459C2214yescomplemented
159#2459C2214yescomplemented
160#2456C2214yescomplemented
161#2456C2214yescomplemented
162#2454C2214yescomplemented
163#2452C2214yescomplemented
164#2445C2214yescomplemented
165#2444C2214yescomplemented
166#2444C2214yescomplemented
167#2443C2214yescomplemented
168#2443C2214yescomplemented
169#2435C2214yes—
170#2433C2212yes—
171#2428C2214yescomplemented
172#2428C2214yescomplemented
173#2426C2214yescomplemented
174#2425C2214yescomplemented
175#2424C2214yescomplemented
176#2424C2214yescomplemented
177#2424C2214yescomplemented
178#2420C2214yescomplemented
179#2418C2214yescomplemented
180#2418C2214yescomplemented
181#2416C2214yescomplemented
182#2414C2214yescomplemented
183#2411C2214yescomplemented
184#2410C2214yes—
185#2408C2212yes—
186#2408C2212yescomplemented
187#2407C2214yescomplemented
188#2405C2212yes—
189#2403C2212yes—
190#2403C2212yes—
191#2395C2212yescomplemented
192#2395C2212yescomplemented
193#2392C2214yescomplemented
194#2392C2212yescomplemented
195#2379C2212yescomplemented
196#2377C2212yes—
197#2375C2212yescomplemented
198#2374C2212yescomplemented
199#2366C2214yescomplemented
200#2363C2214yescomplemented
201#2362C2214yescomplemented
202#2361C2214yescomplemented
203#2357C2212yescomplemented
204#2352C2214yescomplemented
205#2352C2214yescomplemented
206#2347C2212yescomplemented
207#2333C2214yescomplemented
208#2329C2212yescomplemented
209#2325C2212yescomplemented
210#2321C2214yescomplemented
211#2316C2211yescharacteristic, complemented
212#2313C2212yescomplemented
213#2312C2211yescharacteristic
214#2309C2211yescharacteristic
215#2308C2212yes—
216#2308C2211yescharacteristic, complemented
217C2×#385C2212yescomplemented
218#2280C2211yescharacteristic, complemented
219C22×#41C2311yescharacteristic
220C23×D4C2311yescharacteristic
221C23×D4C2311yescharacteristic
222C23×D4C2311yescharacteristic
223C23×D4C2312yes—
224C24×C4C2311yescharacteristic
225#555—48no—
226#551—48no—
227#539—48no—
228#535—44no—
229#534—44no—
230C2×C4⋊Q8C2312yes—
231C2×#127C2312yes—
232C2×#127C2314yes—
233C2×#126C2314yes—
234C2×#126C2314yes—
235C2×#126C2314yes—
236C2×#125C2314yes—
237C2×#124C2312yes—
238C2×#124C2314yes—
239C2×#124C2314yes—
240C2×#124C2314yes—
241#525—44no—
242C2×#123C2314yes—
243C2×#123C2312yes—
244C2×#123C2312yes—
245C2×#123C2312yes—
246C2×#123C2314yes—
247C2×#123C2314yes—
248C2×#123C2314yes—
249C2×#123C2314yes—
250C2×#123C2314yes—
251C2×C22⋊Q8C2312yes—
252C2×C22⋊Q8C2314yes—
253C2×C22⋊Q8C2314yes—
254C2×C22⋊Q8C2314yes—
255C2×C22⋊Q8C2314yes—
256C2×#121—44no—
257C2×#121C2312yes—
258C2×#121C2312yes—
259C2×#121C2314yes—
260C2×#121C2312yes—
261C2×#121C2312yes—
262C2×#121C2312yes—
263C2×#121C2314yes—
264C2×#121C2312yes—
265C2×#121C2314yes—
266C2×#121C2314yes—
267C2×#121C2314yes—
268C2×#121C2314yes—
269C2×#121C2314yes—
270C2×#121C2314yes—
271C2×#121C2314yes—
272C2×#121C2314yes—
273C2×#121C2314yes—
274C2×#120C2314yes—
275C2×#120C2312yes—
276C2×#120C2312yes—
277C2×#120C2312yes—
278C2×#120C2312yes—
279C2×#120C2312yes—
280C2×#120C2314yes—
281C2×#120C2314yes—
282C2×#120C2314yes—
283C2×#120C2314yes—
284#520—44no—
285#518—44no—
286C2×C4×Q8C2312yes—
287C2×C4×D4C2312yes—
288C2×C4×D4C2314yes—
289C2×C4×D4C2314yes—
290C2×C4×D4C2314yes—
291C2×C4×D4C2314yes—
292C2×C4×D4C2314yes—
293C2×C4×D4C2314yes—
294C2×C4×D4C2314yes—
295C2×C4×D4C2312yes—
296C2×C4×D4C2312yes—
297C2×C4×D4C2312yes—
298C2×#117C2312yes—
299C2×#117C2311yescharacteristic
300C2×#117C2311yescharacteristic
301C2×#117C2311yescharacteristic
302C2×#117C2314yes—
303C2×#117C2314yes—
304C2×#117C2312yes—
305C2×#117C2312yes—
306C22×C4⋊C4C2311yescharacteristic
307C22×C4⋊C4C2312yes—
308C22×C4⋊C4C2312yes—
309C22×C4⋊C4C2312yes—
310C22×C22⋊C4C2311yescharacteristic
311C22×C22⋊C4C2312yes—
312C22×C22⋊C4C2312yes—
313C22×C22⋊C4C2314yes—
314C22×C22⋊C4C2311yescharacteristic
315C22×C22⋊C4C2312yes—
316#401C2314yes—
317#400C2312yes—
318#400C2312yes—
319#400C2312yes—
320#400C2312yes—
321#400C2314yes—
322#400C2312yes—
323#400C2312yes—
324#400C2314yes—
325#400C2314yes—
326#399C2314yes—
327#399C2314yes—
328#399C2312yes—
329#399C2314yes—
330#399C2312yes—
331#399C2314yes—
332#399C2314yes—
333#399C2314yes—
334#399C2314yes—
335#399C2314yes—
336#398C2314yes—
337#398C2314yes—
338#398C2314yes—
339#398C2314yes—
340#398C2314yes—
341#398C2314yes—
342#398C2314yes—
343#398C2312yes—
344#398C2312yes—
345#398C2312yes—
346#398C2314yes—
347#398C2314yes—
348#397C2314yes—
349#397C2314yes—
350#397C2314yes—
351#397C2314yes—
352#397C2314yes—
353#397C2314yes—
354#397C2314yes—
355#397C2314yes—
356#397C2314yes—
357#397C2314yes—
358#397C2314yes—
359#397C2312yes—
360#397C2314yes—
361#397C2314yes—
362#397C2314yes—
363#397C2314yes—
364#396C2314yes—
365#396C2314yes—
366#396C2314yes—
367#396C2314yes—
368#396C2314yes—
369#396C2314yes—
370#396C2314yes—
371#396C2314yes—
372#396C2314yes—
373#396C2314yes—
374#396C2314yes—
375#396C2314yes—
376#396C2314yes—
377#396C2314yes—
378#395C2314yes—
379#395C2314yes—
380#394C2314yes—
381#394C2314yes—
382#394C2314yes—
383#394C2314yes—
384#394C2314yes—
385#394C2314yes—
386#394C2314yes—
387#394C2314yes—
388#394C2314yes—
389#394C2314yes—
390#394C2314yes—
391#394C2314yes—
392#394C2314yes—
393#394C2314yes—
394#394C2314yes—
395#394C2314yes—
396#394C2314yes—
397#394C2312yes—
398#394C2312yes—
399#394C2312yes—
400#394C2314yes—
401#394C2314yes—
402#394C2314yes—
403#394C2314yes—
404#394C2314yes—
405#394C2314yes—
406#394C2314yes—
407#394C2314yes—
408#394C2314yes—
409#394C2314yes—
410#394C2314yes—
411#394C2314yes—
412#394C2314yes—
413#394C2314yes—
414#393C2314yes—
415#393C2314yes—
416#393C2314yes—
417#393C2314yes—
418#392C2314yes—
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#392C2312yes—
432#392C2314yes—
433#392C2314yes—
434#392C2314yes—
435#392C2314yes—
436#391C2314yes—
437#391C2314yes—
438#391C2314yes—
439#390C2314yes—
440#390C2312yes—
441#390C2312yes—
442#390C2314yes—
443#390C2314yes—
444#390C2314yes—
445#390C2314yes—
446#390C2314yes—
447#390C2314yes—
448#390C2314yes—
449#390C2314yes—
450#390C2314yes—
451#390C2314yes—
452#390C2314yes—
453#390C2314yes—
454#390C2314yes—
455#390C2314yes—
456#390C2314yes—
457#390C2314yes—
458#390C2314yes—
459#389C2314yes—
460#389C2314yes—
461#389C2314yes—
462#389C2314yes—
463#389C2314yes—
464#389C2314yes—
465#389C2314yes—
466#389C2314yes—
467#389C2314yes—
468#388C2314yes—
469#388C2314yes—
470#388C2314yes—
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#388C2314yes—
503#388C2314yes—
504#388C2314yes—
505#388C2314yes—
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#387C2314yes—
522#387C2314yes—
523#387C2314yes—
524#386C2312yes—
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#386C2314yes—
546#386C2314yes—
547#386C2314yes—
548#386C2314yes—
549#386C2314yes—
550#386C2314yes—
551#386C2314yes—
552#386C2314yes—
553#386C2312yes—
554#386C2312yes—
555#386C2314yes—
556#386C2312yes—
557#386C2314yes—
558#386C2314yes—
559#385C2314yes—
560#385C2314yes—
561#385C2314yes—
562#385C2314yes—
563#385C2314yes—
564#385C2314yes—
565#385C2314yes—
566#385C2314yes—
567#385C2314yes—
568#385C2314yes—
569#385C2314yes—
570#385C2314yes—
571#385C2314yes—
572#385C2314yes—
573#383C2314yes—
574#382C2314yes—
575#382C2314yes—
576#382C2314yes—
577#382C2312yes—
578#381C2314yes—
579#381C2314yes—
580#381C2312yes—
581#381C2314yes—
582#381C2314yes—
583#381C2312yes—
584#381C2312yes—
585#380C2312yes—
586#380C2312yes—
587#380C2312yes—
588#380C2312yes—
589#380C2312yes—
590#380C2312yes—
591#380C2314yes—
592#380C2314yes—
593#380C2314yes—
594#380C2314yes—
595#380C2312yes—
596#379C2314yes—
597#379C2312yes—
598#379C2312yes—
599#379C2312yes—
600#379C2312yes—
601#379C2314yes—
602#379C2314yes—
603#379C2312yes—
604C4×C4⋊C4C2314yes—
605C4×C4⋊C4C2312yes—
606C4×C4⋊C4C2314yes—
607C4×C4⋊C4C2314yes—
608C4×C4⋊C4C2314yes—
609C4×C4⋊C4C2314yes—
610C4×C4⋊C4C2314yes—
611C4×C22⋊C4C2314yes—
612C4×C22⋊C4C2312yes—
613C4×C22⋊C4C2314yes—
614C4×C22⋊C4C2314yes—
615C4×C22⋊C4C2314yes—
616C4×C22⋊C4C2314yes—
617C4×C22⋊C4C2314yes—
618C4×C22⋊C4C2314yes—
619C4×C22⋊C4C2312yes—
620C4×C22⋊C4C2314yes—
621C2×#95C2312yes—
622C2×#95C2312yes—
623C25C2411yescharacteristic
624C25C2411yescharacteristic
625C25C2411yescharacteristic
626C25C2412yes—
627C2×#41—24no—
628C2×#41—42no—
629C2×#41—42no—
630C22×Q8C2414yes—
631C22×Q8C2411yescharacteristic
632C22×D4—24no—
633C22×D4—42no—
634C22×D4—42no—
635C22×D4—42no—
636C22×D4—42no—
637C22×D4—44no—
638C22×D4—44no—
639C22×D4—44no—
640C22×D4—84no—
641C22×D4C2412yes—
642C22×D4C2414yes—
643C22×D4C2411yescharacteristic
644C22×D4C2414yes—
645C22×D4C2412yes—
646C22×D4C2414yes—
647C22×D4C2414yes—
648C22×D4C2414yes—
649C22×D4C2412yes—
650C22×D4C2414yes—
651C22×D4C2412yes—
652C22×D4C2414yes—
653C22×D4C2414yes—
654C22×D4C2412yes—
655C22×D4C2414yes—
656C22×D4C2414yes—
657C22×D4C2414yes—
658C22×D4C2414yes—
659C22×D4C2414yes—
660C23×C4—42no—
661C23×C4—42no—
662C23×C4—42no—
663C23×C4C2411yescharacteristic
664C23×C4C2412yes—
665C23×C4C2411yescharacteristic
666C23×C4C2412yes—
667C23×C4C2411yescharacteristic
668C23×C4C2412yes—
669C23×C4C2414yes—
670C23×C4C2412yes—
671C23×C4C2412yes—
672C23×C4C2412yes—
673C23×C4C2412yes—
674C23×C4C2414yes—
675C23×C4C2412yes—
676C23×C4C2412yes—
677C23×C4C2412yes—
678C23×C4C2412yes—
679C23×C4C2412yes—
680C23×C4C2411yescharacteristic
681C4⋊Q8—44no—
682#127—44no—
683#127—48no—
684#126—48no—
685#126—48no—
686#126—84no—
687#125—48no—
688#124—28no—
689#124—48no—
690#124—48no—
691#124—84no—
692#123—48no—
693#123—48no—
694#123—48no—
695#123—48no—
696#123—44no—
697#123—44no—
698#123—44no—
699#123—84no—
700#123—84no—
701C22⋊Q8—28no—
702C22⋊Q8—216no—
703C22⋊Q8—84no—
704C22⋊Q8—84no—
705C22⋊Q8—84no—
706#121—28no—
707#121—44no—
708#121—48no—
709#121—44no—
710#121—48no—
711#121—48no—
712#121—48no—
713#121—48no—
714#121—48no—
715#121—44no—
716#121—44no—
717#121—48no—
718#121—44no—
719#121—84no—
720#121—84no—
721#121—84no—
722#121—84no—
723#120—44no—
724#120—44no—
725#120—48no—
726#120—44no—
727#120—44no—
728#120—44no—
729#120—48no—
730#120—84no—
731#120—84no—
732#120—84no—
733C4×Q8—44no—
734C4×D4—28no—
735C4×D4—48no—
736C4×D4—48no—
737C4×D4—44no—
738C4×D4—48no—
739C4×D4—44no—
740C4×D4—48no—
741C4×D4—48no—
742C4×D4—48no—
743C4×D4—48no—
744C4×D4—44no—
745#117—28no—
746#117—42no—
747#117—44no—
748#117—48no—
749#117—48no—
750#117—42no—
751#117—42no—
752#117—44no—
753C2×C4⋊C4—24no—
754C2×C4⋊C4—44no—
755C2×C4⋊C4—44no—
756C2×C4⋊C4—44no—
757C2×C4⋊C4C2412yes—
758C2×C4⋊C4C2412yes—
759C2×C4⋊C4C2414yes—
760C2×C4⋊C4C2412yes—
761C2×C4⋊C4C2414yes—
762C2×C4⋊C4C2412yes—
763C2×C4⋊C4C2412yes—
764C2×C4⋊C4C2412yes—
765C2×C4⋊C4C2412yes—
766C2×C4⋊C4C2414yes—
767C2×C4⋊C4C2414yes—
768C2×C4⋊C4C2414yes—
769C2×C4⋊C4C2411yescharacteristic
770C2×C4⋊C4C2412yes—
771C2×C4⋊C4C2414yes—
772C2×C4⋊C4C2414yes—
773C2×C4⋊C4C2411yescharacteristic
774C2×C4⋊C4C2412yes—
775C2×C4⋊C4C2414yes—
776C2×C4⋊C4C2414yes—
777C2×C4⋊C4C2414yes—
778C2×C4⋊C4C2414yes—
779C2×C4⋊C4C2414yes—
780C2×C4⋊C4C2414yes—
781C2×C4⋊C4C2412yes—
782C2×C4⋊C4C2414yes—
783C2×C4⋊C4C2412yes—
784C2×C4⋊C4C2414yes—
785C2×C4⋊C4C2414yes—
786C2×C4⋊C4C2412yes—
787C2×C4⋊C4C2414yes—
788C2×C4⋊C4C2414yes—
789C2×C4⋊C4C2414yes—
790C2×C4⋊C4C2414yes—
791C2×C4⋊C4C2414yes—
792C2×C4⋊C4C2414yes—
793C2×C4⋊C4C2414yes—
794C2×C4⋊C4C2414yes—
795C2×C22⋊C4—24no—
796C2×C22⋊C4—48no—
797C2×C22⋊C4—44no—
798C2×C22⋊C4—44no—
799C2×C22⋊C4—44no—
800C2×C22⋊C4—42no—
801C2×C22⋊C4C2414yes—
802C2×C22⋊C4C2414yes—
803C2×C22⋊C4C2414yes—
804C2×C22⋊C4C2414yes—
805C2×C22⋊C4C2412yes—
806C2×C22⋊C4C2412yes—
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⋊C4C2414yes—
816C2×C22⋊C4C2414yes—
817C2×C22⋊C4C2414yes—
818C2×C22⋊C4C2414yes—
819C2×C22⋊C4C2414yes—
820C2×C22⋊C4C2412yes—
821C2×C22⋊C4C2412yes—
822C2×C22⋊C4C2412yes—
823C2×C22⋊C4C2414yes—
824C2×C22⋊C4C2414yes—
825C2×C22⋊C4C2414yes—
826C2×C22⋊C4C2414yes—
827C2×C22⋊C4C2414yes—
828C2×C22⋊C4C2414yes—
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⋊C4C2412yes—
839C2×C22⋊C4C2414yes—
840C2×C22⋊C4C2414yes—
841C2×C22⋊C4C2412yes—
842C2×C22⋊C4C2414yes—
843C2×C22⋊C4C2414yes—
844C2×C22⋊C4C2414yes—
845C2×C22⋊C4C2414yes—
846C2×C22⋊C4C2414yes—
847C2×C22⋊C4C2414yes—
848C2×C22⋊C4C2414yes—
849C2×C22⋊C4C2414yes—
850C2×C22⋊C4C2414yes—
851C2×C22⋊C4C2414yes—
852C2×C22⋊C4C2414yes—
853C2×C22⋊C4C2414yes—
854C2×C22⋊C4C2414yes—
855C2×C22⋊C4C2414yes—
856C2×C22⋊C4C2414yes—
857C2×C22⋊C4C2412yes—
858C2×C22⋊C4C2414yes—
859C2×C22⋊C4C2414yes—
860C2×C22⋊C4C2414yes—
861C2×C22⋊C4C2412yes—
862C2×C42C2412yes—
863C2×C42C2414yes—
864C2×C42C2412yes—
865C2×C42C2414yes—
866C2×C42C2412yes—
867C2×C42C2412yes—
868C2×C42C2412yes—
869C2×C42C2414yes—
870C2×C42C2414yes—
871C2×C42C2414yes—
872C2×C42C2414yes—
873C2×C42C2414yes—
874C2×C42C2414yes—
875#95C2414yes—
876#95C2414yes—
877#95C2414yes—
878#95C2414yes—
879#95C2414yes—
880#95C2412yes—
881#95C2414yes—
882#95C2412yes—
883#95C2414yes—
884#95C2414yes—
885#95C2414yes—
886#95C2414yes—
887#95C2414yes—
888#95C2414yes—
889#95C2414yes—
890#95C2412yes—
891#95C2414yes—
892#95C2414yes—
893#95C2414yes—
894#95C2414yes—
895#95C2414yes—
896#95C2414yes—
897#95C2414yes—
898#95C2412yes—
899#95C2414yes—
900#95C2414yes—
901#95C2414yes—
902#95C2414yes—
903#95C2414yes—
904#95C2414yes—
905#95C2414yes—
906#95C2414yes—
907#95C2414yes—
908#95C2414yes—
909#95C2414yes—
910#95C2414yes—
911#95C2414yes—
912#95C2414yes—
913#95C2414yes—
914#95C2414yes—
915C24—22no—
916C24—24no—
917C24—22no—
918C24—22no—
919C24—42no—
920C24—42no—
921C24—41no—
922C24—42no—
923C24—41no—
924C24—42no—
925C24—44no—
926C24—41no—
927C24—41no—
928C24—42no—
929C24—44no—
930C24—42no—
931C24—42no—
932C24—41no—
933C24—41no—
934C24—42no—
935C24C2512yes—
936C24C2514yes—
937C24C2512yes—
938C24C2512yes—
939C24C2511yescharacteristic
940C24C2512yes—
941#41—416no—
942C2×Q8—41no—
943C2×Q8—41no—
944C2×Q8—44no—
945C2×Q8—44no—
946C2×Q8—44no—
947C2×Q8H(5,𝔽2)14yes—
948C2×D4—24no—
949C2×D4—28no—
950C2×D4—28no—
951C2×D4—28no—
952C2×D4—28no—
953C2×D4—28no—
954C2×D4—28no—
955C2×D4—28no—
956C2×D4—24no—
957C2×D4—22no—
958C2×D4—24no—
959C2×D4—24no—
960C2×D4—24no—
961C2×D4—41no—
962C2×D4—44no—
963C2×D4—42no—
964C2×D4—41no—
965C2×D4—44no—
966C2×D4—44no—
967C2×D4—44no—
968C2×D4—44no—
969C2×D4—44no—
970C2×D4—44no—
971C2×D4—44no—
972C2×D4—44no—
973C2×D4—44no—
974C2×D4—44no—
975C2×D4—44no—
976C2×D4—42no—
977C2×D4—42no—
978C2×D4—42no—
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—42no—
988C2×D4—44no—
989C2×D4—42no—
990C2×D4—44no—
991C2×D4—44no—
992C2×D4—44no—
993C2×D4—44no—
994C2×D4—44no—
995C2×D4—44no—
996C2×D4—44no—
997C2×D4—42no—
998C2×D4—44no—
999C2×D4—44no—
1000C2×D4—42no—
1001C2×D4—44no—
1002C2×D4—44no—
1003C2×D4—44no—
1004C2×D4—416no—
1005C2×D4—88no—
1006C2×D4—88no—
1007C2×D4—816no—
1008C22×C4—22no—
1009C22×C4—22no—
1010C22×C4—22no—
1011C22×C4—22no—
1012C22×C4—22no—
1013C22×C4—24no—
1014C22×C4—24no—
1015C22×C4—24no—
1016C22×C4—24no—
1017C22×C4—28no—
1018C22×C4—24no—
1019C22×C4—24no—
1020C22×C4—24no—
1021C22×C4—42no—
1022C22×C4—42no—
1023C22×C4—44no—
1024C22×C4—42no—
1025C22×C4—42no—
1026C22×C4—44no—
1027C22×C4—42no—
1028C22×C4—44no—
1029C22×C4—44no—
1030C22×C4—42no—
1031C22×C4—42no—
1032C22×C4—44no—
1033C22×C4—44no—
1034C22×C4—44no—
1035C22×C4—41no—
1036C22×C4—42no—
1037C22×C4—42no—
1038C22×C4—42no—
1039C22×C4—42no—
1040C22×C4—41no—
1041C22×C4—42no—
1042C22×C4—42no—
1043C22×C4—42no—
1044C22×C4—42no—
1045C22×C4—42no—
1046C22×C4—42no—
1047C22×C4—42no—
1048C22×C4—42no—
1049C22×C4—42no—
1050C22×C4—44no—
1051C22×C4—42no—
1052C22×C4—44no—
1053C22×C4—42no—
1054C22×C4—42no—
1055C22×C4—88no—
1056C22×C4H(5,𝔽2)14yes—
1057C22×C4C2512yes—
1058C22×C4C2514yes—
1059C22×C4C2514yes—
1060C22×C4C2512yes—
1061C22×C4C2514yes—
1062C22×C4C2514yes—
1063C22×C4C2514yes—
1064C22×C4C2512yes—
1065C22×C4C2514yes—
1066C22×C4C2514yes—
1067C22×C4C2514yes—
1068C22×C4C2512yes—
1069C22×C4C2514yes—
1070C22×C4C2512yes—
1071C22×C4C2511yescharacteristic
1072C22×C4C2512yes—
1073C22×C4C2511yescharacteristic
1074C4⋊C4—24no—
1075C4⋊C4—24no—
1076C4⋊C4—24no—
1077C4⋊C4—28no—
1078C4⋊C4—24no—
1079C4⋊C4—24no—
1080C4⋊C4—24no—
1081C4⋊C4—24no—
1082C4⋊C4—28no—
1083C4⋊C4—28no—
1084C4⋊C4—28no—
1085C4⋊C4—28no—
1086C4⋊C4—41no—
1087C4⋊C4—44no—
1088C4⋊C4—42no—
1089C4⋊C4—44no—
1090C4⋊C4—41no—
1091C4⋊C4—42no—
1092C4⋊C4—44no—
1093C4⋊C4—44no—
1094C4⋊C4—44no—
1095C4⋊C4—44no—
1096C4⋊C4—42no—
1097C4⋊C4—44no—
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—44no—
1111C4⋊C4—44no—
1112C22⋊C4—28no—
1113C22⋊C4—24no—
1114C22⋊C4—28no—
1115C22⋊C4—28no—
1116C22⋊C4—28no—
1117C22⋊C4—28no—
1118C22⋊C4—24no—
1119C22⋊C4—28no—
1120C22⋊C4—28no—
1121C22⋊C4—28no—
1122C22⋊C4—28no—
1123C22⋊C4—28no—
1124C22⋊C4—44no—
1125C22⋊C4—44no—
1126C22⋊C4—44no—
1127C22⋊C4—44no—
1128C22⋊C4—44no—
1129C22⋊C4—44no—
1130C22⋊C4—44no—
1131C22⋊C4—42no—
1132C22⋊C4—42no—
1133C22⋊C4—42no—
1134C22⋊C4—44no—
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—42no—
1144C22⋊C4—44no—
1145C22⋊C4—44no—
1146C22⋊C4—42no—
1147C22⋊C4—44no—
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—44no—
1167C22⋊C4—44no—
1168C22⋊C4—42no—
1169C22⋊C4—44no—
1170C22⋊C4—42no—
1171C22⋊C4—44no—
1172C22⋊C4—44no—
1173C42—28no—
1174C42—24no—
1175C42—24no—
1176C42—44no—
1177C42—42no—
1178C42—42no—
1179C42—42no—
1180C42—44no—
1181C42—44no—
1182C42—44no—
1183C42—44no—
1184C42—44no—
1185C42—44no—
1186C23—28no—
1187C23—22no—
1188C23—21no—
1189C23—22no—
1190C23—22no—
1191C23—22no—
1192C23—22no—
1193C23—21no—
1194C23—22no—
1195C23—22no—
1196C23—22no—
1197C23—24no—
1198C23—22no—
1199C23—22no—
1200C23—22no—
1201C23—22no—
1202C23—24no—
1203C23—22no—
1204C23—22no—
1205C23—24no—
1206C23—22no—
1207C23—22no—
1208C23—24no—
1209C23—24no—
1210C23—24no—
1211C23—24no—
1212C23—22no—
1213C23—24no—
1214C23—24no—
1215C23—24no—
1216C23—24no—
1217C23—24no—
1218C23—24no—
1219C23—44no—
1220C23—44no—
1221C23—82no—
1222C23—82no—
1223C23—84no—
1224C23—84no—
1225C23—82no—
1226C23—82no—
1227C23—82no—
1228C23—82no—
1229C23—84no—
1230C23—88no—
1231C23—162no—
1232C23—162no—
1233C23—162no—
1234C23—162no—
1235C23—162no—
1236C23—162no—
1237C23—164no—
1238C23C2×H(5,𝔽2)12yes—
1239C23#58514yes—
1240C23C2611yescharacteristic
1241Q8—44no—
1242Q8—164no—
1243D4—416no—
1244D4—48no—
1245D4—44no—
1246D4—84no—
1247D4—84no—
1248D4—84no—
1249D4—88no—
1250D4—88no—
1251D4—88no—
1252D4—88no—
1253D4—88no—
1254D4—88no—
1255D4—88no—
1256D4—88no—
1257D4—162no—
1258D4—164no—
1259D4—164no—
1260D4—164no—
1261D4—164no—
1262C2×C4—28no—
1263C2×C4—22no—
1264C2×C4—21no—
1265C2×C4—21no—
1266C2×C4—21no—
1267C2×C4—22no—
1268C2×C4—24no—
1269C2×C4—21no—
1270C2×C4—22no—
1271C2×C4—24no—
1272C2×C4—24no—
1273C2×C4—24no—
1274C2×C4—22no—
1275C2×C4—24no—
1276C2×C4—24no—
1277C2×C4—24no—
1278C2×C4—24no—
1279C2×C4—22no—
1280C2×C4—22no—
1281C2×C4—24no—
1282C2×C4—22no—
1283C2×C4—24no—
1284C2×C4—24no—
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—24no—
1296C2×C4—24no—
1297C2×C4—24no—
1298C2×C4—24no—
1299C2×C4—24no—
1300C2×C4—24no—
1301C2×C4—24no—
1302C2×C4—24no—
1303C2×C4—24no—
1304C2×C4—24no—
1305C2×C4—24no—
1306C2×C4—44no—
1307C2×C4—48no—
1308C2×C4—88no—
1309C2×C4—84no—
1310C2×C4—84no—
1311C2×C4—84no—
1312C2×C4—84no—
1313C2×C4—84no—
1314C2×C4—82no—
1315C2×C4—82no—
1316C2×C4—88no—
1317C2×C4—84no—
1318C2×C4—162no—
1319C2×C4—162no—
1320C2×C4—162no—
1321C2×C4—162no—
1322C2×C4—162no—
1323C2×C4C2×H(5,𝔽2)14yes—
1324C2×C4C2×H(5,𝔽2)12yes—
1325C2×C4C2×H(5,𝔽2)14yes—
1326C2×C4#58512yes—
1327C22—22no—
1328C22—22no—
1329C22—24no—
1330C22—22no—
1331C22—24no—
1332C22—24no—
1333C22—42no—
1334C22—42no—
1335C22—42no—
1336C22—42no—
1337C22—42no—
1338C22—42no—
1339C22—42no—
1340C22—44no—
1341C22—42no—
1342C22—42no—
1343C22—42no—
1344C22—42no—
1345C22—42no—
1346C22—44no—
1347C22—42no—
1348C22—42no—
1349C22—44no—
1350C22—42no—
1351C22—44no—
1352C22—44no—
1353C22—44no—
1354C22—44no—
1355C22—44no—
1356C22—44no—
1357C22—44no—
1358C22—44no—
1359C22—44no—
1360C22—44no—
1361C22—88no—
1362C22—164no—
1363C22—164no—
1364C22—168no—
1365C22C22×H(5,𝔽2)11yescharacteristic
1366C22C22×H(5,𝔽2)11yescharacteristic
1367C22C2×#58511yescharacteristic
1368C22C2×#58512yes—
1369C22H(7,𝔽2)12yes—
1370C4—22no—
1371C4—22no—
1372C4—24no—
1373C4—24no—
1374C4—42no—
1375C4—44no—
1376C4—42no—
1377C4—42no—
1378C4—44no—
1379C4—44no—
1380C4—42no—
1381C4—44no—
1382C4—44no—
1383C4—44no—
1384C4—44no—
1385C4—44no—
1386C4—44no—
1387C2—44no—
1388C2—42no—
1389C2—82no—
1390C2—84no—
1391C2—82no—
1392C2—82no—
1393C2#6281811yescharacteristic
1394C2#6282011yescharacteristic
1395C2#6287611yescharacteristic
1396C2#6289912yes—
1397C2#6291012yes—
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. #58030C2semidirect
2. #57954C2semidirect
3. #56283C2semidirect
4. #51945C2semidirect
5. #51895C2semidirect
6. #50800C2semidirect
7. #50661C2semidirect
8. #50182C2semidirect
9. #49382C2semidirect
10. #48777C2semidirect
11. #46512C2semidirect
12. #43270C2semidirect
13. #43040C2semidirect
14. #41442C2semidirect
15. #41261C2semidirect
16. #40705C2semidirect
17. #37948C2semidirect
18. #37768C2semidirect
19. #36717C2semidirect
20. #36011C2semidirect
21. #36004C2semidirect
22. #35563C2semidirect
23. #35351C2semidirect
25. C2×#551C22semidirect
26. C2×#539C22semidirect
29. C2×#525C22semidirect
31. C2×#520C22semidirect
32. C2×#518C22semidirect
34. #2837C22semidirect
35. #2830C22semidirect
36. #2828C22semidirect
37. #2825C22semidirect
38. #2816C22semidirect
39. #2807C22semidirect
40. #2803C22semidirect
41. #2784C22semidirect
42. #2781C22semidirect
43. #2773C22semidirect
44. #2772C22semidirect
45. #2766C22semidirect
46. #2761C22semidirect
47. #2757C22semidirect
48. #2753C22semidirect
49. #2752C22semidirect
50. #2746C22semidirect
51. #2744C22semidirect
52. #2740C22semidirect
54. #2732C22semidirect
55. #2732C22semidirect
56. #2730C22semidirect
57. #2730C22semidirect
58. #2714C22semidirect
59. #2709C22semidirect
60. #2707C22semidirect
61. #2706C22semidirect
62. #2706C22semidirect
63. #2705C22semidirect
64. #2705C22semidirect
67. #2699C22semidirect
68. #2699C22semidirect
69. #2697C22semidirect
70. #2696C22semidirect
71. #2694C22semidirect
72. #2691C22semidirect
73. #2691C22semidirect
74. #2689C22semidirect
75. #2688C22semidirect
78. #2685C22semidirect
79. #2685C22semidirect
80. #2683C22semidirect
82. #2678C22semidirect
83. #2678C22semidirect
84. #2676C22semidirect
85. #2674C22semidirect
86. #2673C22semidirect
87. #2672C22semidirect
88. #2671C22semidirect
89. #2670C22semidirect
92. #2669C22semidirect
93. #2668C22semidirect
94. #2668C22semidirect
95. #2667C22semidirect
96. #2662C22semidirect
97. #2659C22semidirect
98. #2656C22semidirect
99. #2654C22semidirect
100. #2653C22semidirect
101. #2651C22semidirect
102. #2648C22semidirect
104. #2635C22semidirect
105. #2631C22semidirect
106. #2628C22semidirect
108. #2619C22semidirect
109. #2618C22semidirect
110. #2618C22semidirect
112. #2609C22semidirect
113. #2602C22semidirect
114. #2598C22semidirect
115. #2594C22semidirect
117. #2591C22semidirect
118. #2590C22semidirect
119. #2576C22semidirect
120. #2576C22semidirect
121. #2574C22semidirect
122. #2568C22semidirect
123. #2560C22semidirect
124. #2557C22semidirect
125. #2554C22semidirect
126. #2554C22semidirect
127. #2540C22semidirect
128. #2539C22semidirect
129. #2536C22semidirect
131. #2534C22semidirect
132. #2534C22semidirect
133. #2525C22semidirect
134. #2519C22semidirect
135. #2519C22semidirect
136. #2518C22semidirect
137. #2516C22semidirect
138. #2516C22semidirect
139. #2488C22semidirect
140. #2484C22semidirect
141. #2484C22semidirect
142. #2483C22semidirect
144. #2479C22semidirect
145. #2479C22semidirect
146. #2478C22semidirect
147. #2476C22semidirect
148. #2474C22semidirect
149. #2474C22semidirect
150. #2472C22semidirect
151. #2472C22semidirect
152. #2471C22semidirect
153. #2470C22semidirect
154. #2467C22semidirect
155. #2464C22semidirect
156. #2464C22semidirect
157. #2460C22semidirect
158. #2459C22semidirect
159. #2459C22semidirect
160. #2456C22semidirect
161. #2456C22semidirect
162. #2454C22semidirect
163. #2452C22semidirect
164. #2445C22semidirect
165. #2444C22semidirect
166. #2444C22semidirect
167. #2443C22semidirect
168. #2443C22semidirect
171. #2428C22semidirect
172. #2428C22semidirect
173. #2426C22semidirect
174. #2425C22semidirect
175. #2424C22semidirect
176. #2424C22semidirect
177. #2424C22semidirect
178. #2420C22semidirect
179. #2418C22semidirect
180. #2418C22semidirect
181. #2416C22semidirect
182. #2414C22semidirect
183. #2411C22semidirect
186. #2408C22semidirect
187. #2407C22semidirect
191. #2395C22semidirect
192. #2395C22semidirect
193. #2392C22semidirect
194. #2392C22semidirect
195. #2379C22semidirect
197. #2375C22semidirect
198. #2374C22semidirect
199. #2366C22semidirect
200. #2363C22semidirect
201. #2362C22semidirect
202. #2361C22semidirect
203. #2357C22semidirect
204. #2352C22semidirect
205. #2352C22semidirect
206. #2347C22semidirect
207. #2333C22semidirect
208. #2329C22semidirect
209. #2325C22semidirect
210. #2321C22semidirect
211. #2316C22semidirect
212. #2313C22semidirect
216. #2308C22semidirect
217. C2×#385C22semidirect
218. #2280C22semidirect

Maximal subgroups

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

subgroupindex
#580302
#579542
#562832
#519452
#518952
#508002
#506612
#501822
#493822
#487772
#465122
#432702
#430402
#414422
#412612
#407052
#379482
#377682
#367172
#360112
#360042
#355632
#353512