Finite Group Databasebeta

← #7662386

Subgroups — #7662386

Order 512.

5224 conjugacy classes of subgroups.

The subgroup lattice has 1414 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#52282C213yesmaximal, complemented
2#42726C213yesmaximal, complemented
3#42664C213yesmaximal, complemented
4#42629C213yesmaximal, complemented
5#42617C213yesmaximal, complemented
6#42570C213yesmaximal, complemented
7#42454C213yesmaximal, complemented
8#40217C213yesmaximal, complemented
9#40170C213yesmaximal, complemented
10#40046C213yesmaximal, complemented
11#40026C213yesmaximal, complemented
12#39246C213yesmaximal, complemented
13#39191C213yesmaximal, complemented
14#37372C213yesmaximal, complemented
15#37372C213yesmaximal, complemented
16#37329C213yesmaximal, complemented
17#36584C211yesmaximal, characteristic, complemented
18#36578C211yesmaximal, characteristic, complemented
19#36465C211yesmaximal, characteristic, complemented
20#36434C211yesmaximal, characteristic, complemented
21#36433C211yesmaximal, characteristic, complemented
22#36430C211yesmaximal, characteristic, complemented
23#36029C211yesmaximal, characteristic, complemented
24#36018C211yesmaximal, characteristic, complemented
25#35983C211yesmaximal, characteristic, complemented
26#35831C211yesmaximal, characteristic, complemented
27#35831C211yesmaximal, characteristic, complemented
28#35723C211yesmaximal, characteristic, complemented
29#34294C211yesmaximal, characteristic, complemented
30#34293C211yesmaximal, characteristic, complemented
31#34263C211yesmaximal, characteristic, complemented
32C2×#550C2211yescharacteristic
33C2×#550C2211yescharacteristic
34C2×#550C2211yescharacteristic
35C2×D4×Q8C2211yescharacteristic
36C2×#548C2211yescharacteristic
37C2×#548C2211yescharacteristic
38C2×#548C2211yescharacteristic
39C2×#548C2211yescharacteristic
40C2×#548C2211yescharacteristic
41C2×#548C2211yescharacteristic
42C2×#520C2211yescharacteristic
43C2×#520C2211yescharacteristic
44C2×#519C2211yescharacteristic
45C2×C4×#41C2211yescharacteristic
46C22×C4×Q8C2211yescharacteristic
47#2859C2213yes—
48#2858C2213yes—
49#2854C2213yes—
50#2854C2213yes—
51#2850C2213yes—
52#2850C2213yes—
53#2836C2216yes—
54#2828C2216yes—
55#2803C2213yes—
56#2803C2216yes—
57#2803C2216yes—
58#2800C2213yes—
59#2800C2216yes—
60#2797C2213yes—
61#2793C2213yes—
62#2791C2213yes—
63#2786C2213yes—
64#2780C2213yes—
65#2780C2216yes—
66#2761C2211yescharacteristic
67#2761C2216yes—
68#2753C2216yes—
69#2753C2216yes—
70#2753C2213yes—
71#2753C2216yes—
72#2752C2213yes—
73#2743C2216yes—
74#2743C2216yes—
75#2741C2216yes—
76#2741C2216yes—
77#2740C2213yes—
78#2711C2213yes—
79#2711C2216yes—
80#2709C2213yes—
81#2707C2213yes—
82#2703C2216yes—
83#2703C2216yes—
84#2701C2216yes—
85#2701C2213yes—
86#2701C2216yes—
87#2688C2216yes—
88#2688C2216yes—
89#2673C2213yes—
90#2654C2216yes—
91#2649C2216yes—
92#2648C2216yes—
93#2648C2216yes—
94#2635C2216yes—
95#2625C2213yes—
96#2625C2213yes—
97#2624C2216yes—
98#2620C2213yes—
99#2620C2213yes—
100#2619C2213yes—
101#2619C2213yes—
102#2571C2213yes—
103#2571C2213yes—
104#2548C2213yes—
105#2545C2213yes—
106#2544C2213yes—
107#2544C2213yes—
108#2544C2213yes—
109#2542C2213yes—
110#2541C2213yes—
111#2541C2213yes—
112#2540C2213yes—
113#2540C2213yes—
114#2540C2213yes—
115#2540C2213yes—
116#2537C2213yes—
117#2537C2213yes—
118#2536C2213yes—
119#2536C2213yes—
120#2535C2213yes—
121#2535C2213yes—
122#2516C2216yes—
123#2509C2213yes—
124#2509C2213yes—
125#2509C2213yes—
126#2509C2213yes—
127#2504C2213yes—
128#2503C2213yes—
129#2500C2213yes—
130#2499C2213yes—
131#2497C2216yes—
132#2487C2213yes—
133#2487C2213yes—
134#2485C2213yes—
135#2485C2213yes—
136#2476C2216yes—
137#2471C2216yes—
138#2457C2216yes—
139#2448C2213yes—
140#2448C2213yes—
141#2447C2213yes—
142#2447C2213yes—
143#2446C2213yes—
144#2446C2213yes—
145#2445C2213yes—
146#2445C2213yes—
147#2429C2213yes—
148#2428C2216yes—
149#2428C2213yes—
150#2428C2213yes—
151#2428C2213yes—
152#2428C2213yes—
153#2428C2213yes—
154#2427C2213yes—
155#2427C2213yes—
156#2427C2213yes—
157#2426C2213yes—
158#2426C2213yes—
159#2426C2213yes—
160#2423C2213yes—
161#2422C2213yes—
162#2421C2213yes—
163#2421C2213yes—
164#2421C2213yes—
165#2420C2213yes—
166#2420C2213yes—
167#2420C2213yes—
168#2417C2213yes—
169#2417C2213yes—
170#2417C2213yes—
171#2416C2213yes—
172#2416C2213yes—
173#2416C2213yes—
174#2416C2213yes—
175#2416C2213yes—
176#2415C2213yes—
177#2414C2213yes—
178#2414C2213yes—
179#2414C2213yes—
180#2395C2213yes—
181#2395C2213yes—
182#2392C2213yes—
183#2392C2213yes—
184#2392C2213yes—
185#2392C2213yes—
186#2367C2213yes—
187#2367C2213yes—
188#2363C2213yes—
189#2362C2213yes—
190#2361C2213yes—
191#2360C2213yes—
192#2357C2213yes—
193#2354C2213yes—
194#2354C2213yes—
195#2351C2211yescharacteristic
196#2351C2211yescharacteristic
197#2351C2211yescharacteristic
198#2351C2211yescharacteristic
199#2351C2211yescharacteristic
200Q8×C4⋊C4C2211yescharacteristic
201Q8×C4⋊C4C2211yescharacteristic
202Q8×C4⋊C4C2211yescharacteristic
203D4×C4⋊C4C2213yes—
204#2345C2213yes—
205#2344C2213yes—
206#2341C2211yescharacteristic
207#2341C2211yescharacteristic
208#2341C2211yescharacteristic
209#2341C2211yescharacteristic
210#2341C2211yescharacteristic
211#2341C2211yescharacteristic
212Q8×C22⋊C4C2211yescharacteristic
213Q8×C22⋊C4C2211yescharacteristic
214Q8×C22⋊C4C2211yescharacteristic
215Q8×C22⋊C4C2211yescharacteristic
216#2333C2216yes—
217#2326C2213yes—
218#2326C2213yes—
219#2324C2216yes—
220#2324C2213yes—
221#2323C2213yes—
222#2319C2213yes—
223#2314C2213yes—
224C4×#127C2213yes—
225C4×#125C2213yes—
226C4×C22⋊Q8C2213yes—
227C4×#123C2213yes—
228C4×#123C2213yes—
229C4×#121C2213yes—
230C4×#121C2213yes—
231C4×#121C2213yes—
232#2298C2213yes—
233#2293C2213yes—
234#2290C2213yes—
235#2290C2213yes—
236#2276C2211yescharacteristic
237C42×Q8C2211yescharacteristic
238C22×#41C2311yescharacteristic
239C22×#41C2311yescharacteristic
240C22×#41C2311yescharacteristic
241C23×Q8C2311yescharacteristic
242C23×Q8C2311yescharacteristic
243#550—44no—
244#550—44no—
245#550—44no—
246D4×Q8—44no—
247#548—28no—
248#548—28no—
249#548—44no—
250#548—44no—
251#548—44no—
252#548—44no—
253C2×C4⋊Q8C2313yes—
254C2×#127C2313yes—
255C2×#127C2313yes—
256C2×#127C2313yes—
257C2×#127C2313yes—
258C2×#125C2313yes—
259C2×#124C2313yes—
260C2×#124C2313yes—
261C2×#124C2313yes—
262C2×#124C2313yes—
263C2×#124C2313yes—
264C2×#124C2313yes—
265C2×#123C2313yes—
266C2×#123C2313yes—
267C2×#123C2316yes—
268C2×C22⋊Q8C2313yes—
269C2×C22⋊Q8C2313yes—
270C2×C22⋊Q8C2313yes—
271C2×C22⋊Q8C2313yes—
272C2×C22⋊Q8C2313yes—
273C2×C22⋊Q8C2313yes—
274C2×C22⋊Q8C2313yes—
275C2×C22⋊Q8C2313yes—
276C2×#121C2313yes—
277C2×#121C2313yes—
278C2×#121C2316yes—
279C2×#121C2316yes—
280C2×#121C2313yes—
281C2×#121C2313yes—
282C2×#121C2313yes—
283C2×#121C2313yes—
284C2×#121C2313yes—
285C2×#121C2313yes—
286C2×#121C2313yes—
287C2×#121C2313yes—
288C2×#121C2313yes—
289C2×#121C2313yes—
290C2×#121C2313yes—
291C2×#121C2313yes—
292C2×#121C2316yes—
293C2×#121C2316yes—
294#520—28no—
295#520—44no—
296#519—44no—
297C4×#41—44no—
298C2×C4×Q8—44no—
299C2×C4×Q8C2311yescharacteristic
300C2×C4×Q8C2311yescharacteristic
301C2×C4×Q8C2311yescharacteristic
302C2×C4×Q8C2311yescharacteristic
303C2×C4×Q8C2311yescharacteristic
304C2×C4×Q8C2311yescharacteristic
305C2×C4×Q8C2311yescharacteristic
306C2×C4×Q8C2311yescharacteristic
307C2×C4×Q8C2311yescharacteristic
308C2×C4×Q8C2313yes—
309C2×C4×Q8C2313yes—
310C2×C4×Q8C2313yes—
311C2×C4×Q8C2313yes—
312C2×C4×Q8C2311yescharacteristic
313C2×C4×D4C2313yes—
314C2×C4×D4C2313yes—
315C2×C4×D4C2313yes—
316C2×C4×D4C2313yes—
317C2×C4×D4C2313yes—
318C2×C4×D4C2313yes—
319C2×C4×D4C2313yes—
320C2×C4×D4C2313yes—
321C2×C4×D4C2313yes—
322C2×C4×D4C2313yes—
323C2×C4×D4C2313yes—
324C2×C4×D4C2313yes—
325C2×C4×D4C2313yes—
326C2×C4×D4C2313yes—
327C2×C4×D4C2313yes—
328C2×C4×D4C2313yes—
329C2×C4×D4C2316yes—
330C2×#117C2313yes—
331C2×#117C2313yes—
332C2×#117C2313yes—
333C2×#117C2313yes—
334C2×#117C2313yes—
335C2×#117C2316yes—
336C22×C4⋊C4C2313yes—
337C22×C4⋊C4C2313yes—
338C22×C4⋊C4C2313yes—
339C22×C42C2313yes—
340C22×C42C2313yes—
341#400C2316yes—
342#400C2316yes—
343#400C2316yes—
344#400C2316yes—
345#400C2316yes—
346#400C2316yes—
347#400C2313yes—
348#400C2313yes—
349#400C2316yes—
350#399C2316yes—
351#399C2313yes—
352#399C2316yes—
353#399C2313yes—
354#399C2316yes—
355#398C2313yes—
356#398C2313yes—
357#398C2316yes—
358#398C2316yes—
359#398C2313yes—
360#398C2311yescharacteristic
361#398C2313yes—
362#398C2313yes—
363#397C2313yes—
364#397C2316yes—
365#397C2316yes—
366#397C2316yes—
367#397C2316yes—
368#397C2316yes—
369#397C2313yes—
370#397C2316yes—
371#397C2316yes—
372#397C2311yescharacteristic
373#397C2313yes—
374#397C2313yes—
375#397C2313yes—
376#397C2311yescharacteristic
377#397C2313yes—
378#397C2313yes—
379#397C2313yes—
380#396C2313yes—
381#396C2316yes—
382#396C2313yes—
383#396C2313yes—
384#396C2316yes—
385#396C2311yescharacteristic
386#396C2311yescharacteristic
387#396C2313yes—
388#396C2313yes—
389#396C2313yes—
390#396C2316yes—
391#396C2316yes—
392#394C2313yes—
393#394C2316yes—
394#394C2316yes—
395#394C2316yes—
396#394C2316yes—
397#394C2313yes—
398#394C2316yes—
399#394C2316yes—
400#394C2316yes—
401#394C2316yes—
402#394C2316yes—
403#394C2316yes—
404#394C2313yes—
405#394C2316yes—
406#394C2313yes—
407#394C2313yes—
408#394C2313yes—
409#394C2313yes—
410#394C2313yes—
411#394C2313yes—
412#394C2313yes—
413#394C2313yes—
414#394C2313yes—
415#394C2313yes—
416#394C2316yes—
417#394C2316yes—
418#394C2311yescharacteristic
419#394C2313yes—
420#394C2313yes—
421#392C2313yes—
422#392C2316yes—
423#392C2316yes—
424#392C2316yes—
425#392C2313yes—
426#392C2316yes—
427#392C2313yes—
428#392C2316yes—
429#392C2316yes—
430#392C2313yes—
431#391C2313yes—
432#391C2313yes—
433#391C2313yes—
434#391C2313yes—
435#391C2313yes—
436#391C2313yes—
437#391C2313yes—
438#391C2313yes—
439#390C2311yescharacteristic
440#390C2313yes—
441#390C2313yes—
442#390C2313yes—
443#390C2313yes—
444#390C2313yes—
445#390C2316yes—
446#390C2313yes—
447#390C2313yes—
448#390C2313yes—
449#390C2313yes—
450#390C2316yes—
451#390C2313yes—
452#390C2313yes—
453#390C2316yes—
454#390C2316yes—
455#390C2313yes—
456#390C2313yes—
457#390C2313yes—
458#390C2313yes—
459#390C2313yes—
460#390C2313yes—
461#390C2313yes—
462#390C2316yes—
463#390C2316yes—
464#390C2313yes—
465#389C2313yes—
466#389C2313yes—
467#389C2313yes—
468#389C2313yes—
469#389C2313yes—
470#389C2313yes—
471#389C2313yes—
472#389C2313yes—
473#389C2316yes—
474#389C2313yes—
475#389C2316yes—
476#389C2313yes—
477#389C2313yes—
478#389C2313yes—
479#389C2313yes—
480#389C2313yes—
481#389C2313yes—
482#389C2313yes—
483#389C2316yes—
484#389C2313yes—
485#389C2313yes—
486#389C2313yes—
487#389C2313yes—
488#388C2316yes—
489#388C2316yes—
490#388C2316yes—
491#388C2313yes—
492#388C2316yes—
493#388C2316yes—
494#388C2316yes—
495#388C2316yes—
496#388C2313yes—
497#388C2316yes—
498#388C2316yes—
499#388C2313yes—
500#388C2316yes—
501#388C2313yes—
502#388C2316yes—
503#388C2316yes—
504#388C2316yes—
505#388C2313yes—
506#388C2316yes—
507#388C2313yes—
508#388C2313yes—
509#388C2313yes—
510#388C2313yes—
511#388C2313yes—
512#388C2316yes—
513#388C2316yes—
514#388C2313yes—
515#388C2313yes—
516#388C2313yes—
517#388C2313yes—
518#388C2311yescharacteristic
519#388C2311yescharacteristic
520#387C2313yes—
521#387C2313yes—
522#387C2313yes—
523#387C2313yes—
524#387C2313yes—
525#387C2316yes—
526#387C2313yes—
527#387C2316yes—
528#387C2313yes—
529#387C2313yes—
530#387C2313yes—
531#387C2313yes—
532#387C2316yes—
533#387C2316yes—
534#387C2313yes—
535#387C2313yes—
536#387C2311yescharacteristic
537#387C2313yes—
538#387C2313yes—
539#387C2311yescharacteristic
540#386C2313yes—
541#386C2316yes—
542#386C2316yes—
543#386C2313yes—
544#386C2316yes—
545#386C2316yes—
546#386C2316yes—
547#386C2313yes—
548#386C2316yes—
549#386C2316yes—
550#386C2316yes—
551#386C2313yes—
552#386C2313yes—
553#386C2313yes—
554#386C2316yes—
555#386C2316yes—
556#386C2316yes—
557#386C2316yes—
558#386C2313yes—
559#386C2311yescharacteristic
560#386C2313yes—
561#386C2313yes—
562#385C2313yes—
563#385C2316yes—
564#385C2316yes—
565#385C2313yes—
566#385C2316yes—
567#385C2316yes—
568#385C2313yes—
569#385C2313yes—
570#385C2313yes—
571#385C2311yescharacteristic
572#384C2313yes—
573#384C2313yes—
574#384C2313yes—
575#384C2313yes—
576#382C2311yescharacteristic
577#382C2313yes—
578#382C2316yes—
579#382C2313yes—
580#382C2313yes—
581#382C2313yes—
582#382C2313yes—
583#381C2316yes—
584#381C2316yes—
585#381C2316yes—
586#381C2313yes—
587#381C2311yescharacteristic
588#380C2313yes—
589#380C2313yes—
590#380C2316yes—
591#380C2313yes—
592#380C2313yes—
593#380C2316yes—
594#380C2313yes—
595#380C2313yes—
596#380C2313yes—
597#380C2313yes—
598#380C2313yes—
599#380C2313yes—
600#380C2316yes—
601#380C2313yes—
602#380C2313yes—
603C4×C4⋊C4C2313yes—
604C4×C4⋊C4C2313yes—
605C4×C4⋊C4C2313yes—
606C4×C4⋊C4C2313yes—
607C4×C4⋊C4C2313yes—
608C4×C4⋊C4C2313yes—
609C4×C4⋊C4C2313yes—
610C4×C4⋊C4C2313yes—
611C4×C4⋊C4C2313yes—
612C4×C4⋊C4C2313yes—
613C4×C4⋊C4C2316yes—
614C4×C4⋊C4C2313yes—
615C4×C4⋊C4C2313yes—
616C4×C4⋊C4C2313yes—
617C4×C4⋊C4C2313yes—
618C4×C22⋊C4C2316yes—
619C4×C22⋊C4C2316yes—
620C4×C22⋊C4C2316yes—
621C4×C22⋊C4C2313yes—
622C4×C22⋊C4C2313yes—
623C4×C22⋊C4C2313yes—
624C4×C22⋊C4C2313yes—
625C4×C22⋊C4C2313yes—
626C4×C22⋊C4C2313yes—
627C4×C22⋊C4C2313yes—
628C4×C22⋊C4C2313yes—
629C4×C22⋊C4C2313yes—
630C4×C22⋊C4C2313yes—
631#376C2313yes—
632C43C2313yes—
633C2×#41—24no—
634C2×#41—24no—
635C2×#41—24no—
636C2×#41—24no—
637C2×#41—24no—
638C2×#41—24no—
639C2×#41—24no—
640C2×#41—24no—
641C2×#41—24no—
642C22×Q8—24no—
643C22×Q8—24no—
644C22×Q8—24no—
645C22×Q8—24no—
646C22×Q8—24no—
647C22×Q8—24no—
648C22×Q8C2413yes—
649C22×Q8C2413yes—
650C22×Q8C2411yescharacteristic
651C22×D4C2413yes—
652C22×D4C2413yes—
653C22×D4C2413yes—
654C22×D4C2413yes—
655C22×D4C2411yescharacteristic
656C22×D4C2413yes—
657C22×D4C2413yes—
658C22×D4C2413yes—
659C22×D4C2413yes—
660C22×D4C2413yes—
661C22×D4C2413yes—
662C22×D4C2413yes—
663C22×D4C2413yes—
664C22×D4C2416yes—
665C22×D4C2416yes—
666C22×D4C2416yes—
667C23×C4C2413yes—
668C23×C4C2413yes—
669C23×C4C2413yes—
670C23×C4C2413yes—
671C23×C4C2413yes—
672C23×C4C2416yes—
673C23×C4C2411yescharacteristic
674C23×C4C2413yes—
675C23×C4C2416yes—
676C23×C4C2413yes—
677C23×C4C2413yes—
678C4⋊Q8—46no—
679#127—46no—
680#127—46no—
681#127—46no—
682#127—46no—
683#125—46no—
684#124—212no—
685#124—212no—
686#124—46no—
687#124—46no—
688#124—46no—
689#124—46no—
690#123—46no—
691#123—46no—
692#123—86no—
693C22⋊Q8—212no—
694C22⋊Q8—212no—
695C22⋊Q8—46no—
696C22⋊Q8—46no—
697C22⋊Q8—46no—
698C22⋊Q8—46no—
699C22⋊Q8—46no—
700C22⋊Q8—46no—
701#121—212no—
702#121—212no—
703#121—412no—
704#121—46no—
705#121—46no—
706#121—412no—
707#121—46no—
708#121—46no—
709#121—46no—
710#121—46no—
711#121—46no—
712#121—46no—
713#121—46no—
714#121—46no—
715#121—46no—
716#121—46no—
717#121—86no—
718#121—86no—
719C4×Q8—24no—
720C4×Q8—24no—
721C4×Q8—24no—
722C4×Q8—24no—
723C4×Q8—24no—
724C4×Q8—24no—
725C4×Q8—24no—
726C4×Q8—24no—
727C4×Q8—24no—
728C4×Q8—46no—
729C4×Q8—46no—
730C4×Q8—46no—
731C4×Q8—46no—
732C4×Q8#4118yes—
733C4×D4—212no—
734C4×D4—212no—
735C4×D4—212no—
736C4×D4—212no—
737C4×D4—46no—
738C4×D4—46no—
739C4×D4—46no—
740C4×D4—46no—
741C4×D4—46no—
742C4×D4—46no—
743C4×D4—46no—
744C4×D4—46no—
745C4×D4—46no—
746C4×D4—46no—
747C4×D4—46no—
748C4×D4—46no—
749C4×D4—86no—
750#117—212no—
751#117—46no—
752#117—46no—
753#117—46no—
754#117—46no—
755#117—86no—
756C2×C4⋊C4—212no—
757C2×C4⋊C4—46no—
758C2×C4⋊C4—46no—
759C2×C4⋊C4C2413yes—
760C2×C4⋊C4C2413yes—
761C2×C4⋊C4C2413yes—
762C2×C4⋊C4C2413yes—
763C2×C4⋊C4C2413yes—
764C2×C4⋊C4C2411yescharacteristic
765C2×C4⋊C4C2413yes—
766C2×C4⋊C4C2413yes—
767C2×C4⋊C4C2413yes—
768C2×C4⋊C4C2413yes—
769C2×C4⋊C4C2413yes—
770C2×C4⋊C4C2413yes—
771C2×C4⋊C4C2413yes—
772C2×C4⋊C4C2413yes—
773C2×C4⋊C4C2413yes—
774C2×C4⋊C4C2411yescharacteristic
775C2×C4⋊C4C2413yes—
776C2×C4⋊C4C2416yes—
777C2×C4⋊C4C2411yescharacteristic
778C2×C4⋊C4C2413yes—
779C2×C4⋊C4C2413yes—
780C2×C4⋊C4C2413yes—
781C2×C4⋊C4C2416yes—
782C2×C4⋊C4C2411yescharacteristic
783C2×C4⋊C4C2411yescharacteristic
784C2×C4⋊C4C2411yescharacteristic
785C2×C4⋊C4C2416yes—
786C2×C4⋊C4C2413yes—
787C2×C4⋊C4C2413yes—
788C2×C4⋊C4C2413yes—
789C2×C4⋊C4C2413yes—
790C2×C4⋊C4C2413yes—
791C2×C4⋊C4C2413yes—
792C2×C4⋊C4C2416yes—
793C2×C4⋊C4C2413yes—
794C2×C4⋊C4C2416yes—
795C2×C4⋊C4C2413yes—
796C2×C4⋊C4C2413yes—
797C2×C4⋊C4C2413yes—
798C2×C4⋊C4C2413yes—
799C2×C4⋊C4C2413yes—
800C2×C4⋊C4C2413yes—
801C2×C4⋊C4C2413yes—
802C2×C4⋊C4C2411yescharacteristic
803C2×C4⋊C4C2411yescharacteristic
804C2×C4⋊C4C2413yes—
805C2×C4⋊C4C2413yes—
806C2×C22⋊C4C2413yes—
807C2×C22⋊C4C2413yes—
808C2×C22⋊C4C2411yescharacteristic
809C2×C22⋊C4C2411yescharacteristic
810C2×C22⋊C4C2413yes—
811C2×C22⋊C4C2413yes—
812C2×C22⋊C4C2411yescharacteristic
813C2×C22⋊C4C2413yes—
814C2×C22⋊C4C2413yes—
815C2×C22⋊C4C2416yes—
816C2×C22⋊C4C2416yes—
817C2×C22⋊C4C2411yescharacteristic
818C2×C22⋊C4C2413yes—
819C2×C22⋊C4C2413yes—
820C2×C22⋊C4C2413yes—
821C2×C22⋊C4C2413yes—
822C2×C22⋊C4C2416yes—
823C2×C22⋊C4C2416yes—
824C2×C22⋊C4C2411yescharacteristic
825C2×C22⋊C4C2411yescharacteristic
826C2×C22⋊C4C2411yescharacteristic
827C2×C22⋊C4C2411yescharacteristic
828C2×C22⋊C4C2413yes—
829C2×C22⋊C4C2413yes—
830C2×C22⋊C4C2413yes—
831C2×C22⋊C4C2413yes—
832C2×C22⋊C4C2413yes—
833C2×C22⋊C4C2413yes—
834C2×C22⋊C4C2413yes—
835C2×C22⋊C4C2413yes—
836C2×C22⋊C4C2413yes—
837C2×C22⋊C4C2416yes—
838C2×C22⋊C4C2413yes—
839C2×C22⋊C4C2413yes—
840C2×C22⋊C4C2413yes—
841C2×C22⋊C4C2413yes—
842C2×C22⋊C4C2413yes—
843C2×C22⋊C4C2413yes—
844C2×C22⋊C4C2416yes—
845C2×C22⋊C4C2416yes—
846C2×C22⋊C4C2416yes—
847C2×C22⋊C4C2416yes—
848C2×C22⋊C4C2416yes—
849C2×C22⋊C4C2413yes—
850C2×C22⋊C4C2416yes—
851C2×C22⋊C4C2413yes—
852C2×C22⋊C4C2416yes—
853C2×C22⋊C4C2413yes—
854C2×C22⋊C4C2413yes—
855C2×C22⋊C4C2413yes—
856C2×C22⋊C4C2413yes—
857C2×C22⋊C4C2413yes—
858C2×C22⋊C4C2413yes—
859C2×C22⋊C4C2411yescharacteristic
860C2×C22⋊C4C2411yescharacteristic
861C2×C22⋊C4C2413yes—
862C2×C22⋊C4C2411yescharacteristic
863C2×C22⋊C4C2416yes—
864C2×C22⋊C4C2413yes—
865C2×C42—46no—
866C2×C42—46no—
867C2×C42C2413yes—
868C2×C42C2413yes—
869C2×C42C2413yes—
870C2×C42C2413yes—
871C2×C42C2413yes—
872C2×C42C2413yes—
873C2×C42C2413yes—
874C2×C42C2413yes—
875C2×C42C2413yes—
876C2×C42C2411yescharacteristic
877C2×C42C2413yes—
878C2×C42C2413yes—
879C2×C42C2416yes—
880C2×C42C2416yes—
881C2×C42C2413yes—
882C2×C42C2413yes—
883C2×C42C2413yes—
884C2×C42C2413yes—
885C2×C42C2411yescharacteristic
886C2×C42C2413yes—
887#95C2411yescharacteristic
888#95C2413yes—
889#95C2413yes—
890#95C2413yes—
891#95C2411yescharacteristic
892#95C2413yes—
893#95C2411yescharacteristic
894#95C2411yescharacteristic
895#95C2411yescharacteristic
896#95C2411yescharacteristic
897#95C2411yescharacteristic
898#95C2413yes—
899#95C2413yes—
900#95C2413yes—
901#95C2413yes—
902#95C2413yes—
903#95C2413yes—
904#95C2413yes—
905#95C2413yes—
906#95C2413yes—
907#95C2413yes—
908#95C2416yes—
909#95C2416yes—
910#95C2413yes—
911#95C2413yes—
912#95C2413yes—
913#95C2413yes—
914#95C2413yes—
915#95C2413yes—
916#95C2416yes—
917#95C2411yescharacteristic
918#95C2411yescharacteristic
919#95C2411yescharacteristic
920#95C2411yescharacteristic
921#95C2411yescharacteristic
922#95C2416yes—
923#95C2413yes—
924#95C2413yes—
925#95C2413yes—
926#95C2413yes—
927#95C2413yes—
928#95C2413yes—
929#95C2413yes—
930#95C2413yes—
931#95C2416yes—
932#95C2416yes—
933#95C2416yes—
934#95C2416yes—
935#95C2416yes—
936#95C2416yes—
937C24C2513yes—
938C24C2513yes—
939C24C2513yes—
940C24C2511yescharacteristic
941C24C2511yescharacteristic
942#41—416no—
943#41—416no—
944#41—416no—
945C2×Q8—26no—
946C2×Q8—26no—
947C2×Q8—26no—
948C2×Q8—26no—
949C2×Q8—26no—
950C2×Q8—26no—
951C2×Q8—416no—
952C2×Q8—416no—
953C2×Q8C2×#4114yes—
954C2×Q8H(5,𝔽2)14yes—
955C2×Q8H(5,𝔽2)14yes—
956C2×D4—26no—
957C2×D4—22no—
958C2×D4—26no—
959C2×D4—26no—
960C2×D4—26no—
961C2×D4—26no—
962C2×D4—26no—
963C2×D4—26no—
964C2×D4—26no—
965C2×D4—26no—
966C2×D4—26no—
967C2×D4—26no—
968C2×D4—26no—
969C2×D4—26no—
970C2×D4—26no—
971C2×D4—22no—
972C2×D4—26no—
973C2×D4—41no—
974C2×D4—43no—
975C2×D4—43no—
976C2×D4—43no—
977C2×D4—43no—
978C2×D4—43no—
979C2×D4—43no—
980C2×D4—43no—
981C2×D4—43no—
982C2×D4—43no—
983C2×D4—43no—
984C2×D4—43no—
985C2×D4—43no—
986C2×D4—43no—
987C2×D4—43no—
988C2×D4—43no—
989C2×D4—43no—
990C2×D4—43no—
991C2×D4—43no—
992C2×D4—43no—
993C2×D4—43no—
994C2×D4—43no—
995C2×D4—46no—
996C2×D4—46no—
997C2×D4—46no—
998C2×D4—46no—
999C2×D4—46no—
1000C2×D4—46no—
1001C2×D4—46no—
1002C2×D4—46no—
1003C2×D4—46no—
1004C22×C4—22no—
1005C22×C4—26no—
1006C22×C4—26no—
1007C22×C4—26no—
1008C22×C4—26no—
1009C22×C4—26no—
1010C22×C4—26no—
1011C22×C4—26no—
1012C22×C4—26no—
1013C22×C4—26no—
1014C22×C4—26no—
1015C22×C4—26no—
1016C22×C4—26no—
1017C22×C4—26no—
1018C22×C4—26no—
1019C22×C4—26no—
1020C22×C4—212no—
1021C22×C4—41no—
1022C22×C4—41no—
1023C22×C4—43no—
1024C22×C4—43no—
1025C22×C4—43no—
1026C22×C4—46no—
1027C22×C4—43no—
1028C22×C4—46no—
1029C22×C4—43no—
1030C22×C4—43no—
1031C22×C4—43no—
1032C22×C4—43no—
1033C22×C4—43no—
1034C22×C4—46no—
1035C22×C4—46no—
1036C22×C4—46no—
1037C22×C4C2511yescharacteristic
1038C22×C4C2511yescharacteristic
1039C22×C4C2511yescharacteristic
1040C22×C4C2511yescharacteristic
1041C22×C4C2513yes—
1042C22×C4C2511yescharacteristic
1043C22×C4C2513yes—
1044C22×C4C2513yes—
1045C22×C4C2511yescharacteristic
1046C22×C4C2511yescharacteristic
1047C22×C4C2513yes—
1048C22×C4C2513yes—
1049C22×C4C2513yes—
1050C22×C4C2513yes—
1051C22×C4C2513yes—
1052C22×C4C2511yescharacteristic
1053C22×C4C2513yes—
1054C22×C4C2513yes—
1055C22×C4C2513yes—
1056C22×C4C2511yescharacteristic
1057C22×C4C2511yescharacteristic
1058C22×C4C2511yescharacteristic
1059C22×C4C2513yes—
1060C22×C4C2511yescharacteristic
1061C22×C4C2511yescharacteristic
1062C22×C4C2513yes—
1063C4⋊C4—26no—
1064C4⋊C4—26no—
1065C4⋊C4—22no—
1066C4⋊C4—26no—
1067C4⋊C4—26no—
1068C4⋊C4—26no—
1069C4⋊C4—26no—
1070C4⋊C4—26no—
1071C4⋊C4—26no—
1072C4⋊C4—26no—
1073C4⋊C4—26no—
1074C4⋊C4—26no—
1075C4⋊C4—26no—
1076C4⋊C4—26no—
1077C4⋊C4—26no—
1078C4⋊C4—22no—
1079C4⋊C4—43no—
1080C4⋊C4—46no—
1081C4⋊C4—41no—
1082C4⋊C4—41no—
1083C4⋊C4—43no—
1084C4⋊C4—41no—
1085C4⋊C4—43no—
1086C4⋊C4—43no—
1087C4⋊C4—43no—
1088C4⋊C4—46no—
1089C4⋊C4—41no—
1090C4⋊C4—41no—
1091C4⋊C4—41no—
1092C4⋊C4—43no—
1093C4⋊C4—43no—
1094C4⋊C4—43no—
1095C4⋊C4—43no—
1096C4⋊C4—43no—
1097C4⋊C4—46no—
1098C4⋊C4—46no—
1099C4⋊C4—43no—
1100C4⋊C4—43no—
1101C4⋊C4—46no—
1102C4⋊C4—43no—
1103C4⋊C4—43no—
1104C4⋊C4—43no—
1105C4⋊C4—43no—
1106C4⋊C4—43no—
1107C4⋊C4—43no—
1108C4⋊C4—43no—
1109C4⋊C4C2×#41112yes—
1110C22⋊C4—22no—
1111C22⋊C4—26no—
1112C22⋊C4—26no—
1113C22⋊C4—26no—
1114C22⋊C4—22no—
1115C22⋊C4—22no—
1116C22⋊C4—26no—
1117C22⋊C4—26no—
1118C22⋊C4—212no—
1119C22⋊C4—212no—
1120C22⋊C4—26no—
1121C22⋊C4—46no—
1122C22⋊C4—43no—
1123C22⋊C4—41no—
1124C22⋊C4—43no—
1125C22⋊C4—41no—
1126C22⋊C4—41no—
1127C22⋊C4—41no—
1128C22⋊C4—43no—
1129C22⋊C4—43no—
1130C22⋊C4—43no—
1131C22⋊C4—46no—
1132C22⋊C4—43no—
1133C22⋊C4—46no—
1134C22⋊C4—41no—
1135C22⋊C4—41no—
1136C22⋊C4—41no—
1137C22⋊C4—41no—
1138C22⋊C4—43no—
1139C22⋊C4—43no—
1140C22⋊C4—43no—
1141C22⋊C4—43no—
1142C22⋊C4—43no—
1143C22⋊C4—43no—
1144C22⋊C4—43no—
1145C22⋊C4—43no—
1146C22⋊C4—43no—
1147C22⋊C4—43no—
1148C22⋊C4—43no—
1149C22⋊C4—43no—
1150C22⋊C4—43no—
1151C22⋊C4—46no—
1152C22⋊C4—43no—
1153C22⋊C4—46no—
1154C22⋊C4—43no—
1155C22⋊C4—46no—
1156C22⋊C4—46no—
1157C22⋊C4—46no—
1158C22⋊C4—46no—
1159C22⋊C4—46no—
1160C22⋊C4—43no—
1161C22⋊C4—43no—
1162C22⋊C4—46no—
1163C22⋊C4—43no—
1164C22⋊C4—43no—
1165C22⋊C4—43no—
1166C22⋊C4—43no—
1167C22⋊C4—43no—
1168C22⋊C4—43no—
1169C42—26no—
1170C42—26no—
1171C42—26no—
1172C42—26no—
1173C42—26no—
1174C42—26no—
1175C42—26no—
1176C42—26no—
1177C42—26no—
1178C42—22no—
1179C42—41no—
1180C42—43no—
1181C42—43no—
1182C42—43no—
1183C42—43no—
1184C42—46no—
1185C42—43no—
1186C42—46no—
1187C42—43no—
1188C42C2×#41112yes—
1189C23—21no—
1190C23—21no—
1191C23—21no—
1192C23—21no—
1193C23—21no—
1194C23—21no—
1195C23—23no—
1196C23—23no—
1197C23—23no—
1198C23—21no—
1199C23—21no—
1200C23—23no—
1201C23—23no—
1202C23—23no—
1203C23—23no—
1204C23—23no—
1205C23—21no—
1206C23—23no—
1207C23—23no—
1208C23—23no—
1209C23—21no—
1210C23—23no—
1211C23—23no—
1212C23—23no—
1213C23—23no—
1214C23—21no—
1215C23—23no—
1216C23—23no—
1217C23—23no—
1218C23—21no—
1219C23—23no—
1220C23—21no—
1221C23—23no—
1222C23—23no—
1223C23#58512yes—
1224C23C2611yescharacteristic
1225Q8—412no—
1226Q8—412no—
1227Q8#540116yes—
1228D4—412no—
1229D4—44no—
1230D4—412no—
1231D4—412no—
1232D4—412no—
1233D4—86no—
1234D4—86no—
1235D4—86no—
1236D4—86no—
1237D4—86no—
1238D4—86no—
1239D4—86no—
1240D4—86no—
1241D4—166no—
1242D4—166no—
1243D4—166no—
1244C2×C4—21no—
1245C2×C4—21no—
1246C2×C4—21no—
1247C2×C4—23no—
1248C2×C4—23no—
1249C2×C4—21no—
1250C2×C4—21no—
1251C2×C4—23no—
1252C2×C4—23no—
1253C2×C4—23no—
1254C2×C4—21no—
1255C2×C4—21no—
1256C2×C4—21no—
1257C2×C4—21no—
1258C2×C4—21no—
1259C2×C4—21no—
1260C2×C4—21no—
1261C2×C4—21no—
1262C2×C4—21no—
1263C2×C4—21no—
1264C2×C4—23no—
1265C2×C4—23no—
1266C2×C4—23no—
1267C2×C4—23no—
1268C2×C4—23no—
1269C2×C4—23no—
1270C2×C4—23no—
1271C2×C4—23no—
1272C2×C4—21no—
1273C2×C4—23no—
1274C2×C4—23no—
1275C2×C4—21no—
1276C2×C4—23no—
1277C2×C4—21no—
1278C2×C4—21no—
1279C2×C4—21no—
1280C2×C4—23no—
1281C2×C4—21no—
1282C2×C4—21no—
1283C2×C4—23no—
1284C2×C4—23no—
1285C2×C4—21no—
1286C2×C4—23no—
1287C2×C4—23no—
1288C2×C4—21no—
1289C2×C4—21no—
1290C2×C4—21no—
1291C2×C4—21no—
1292C2×C4—21no—
1293C2×C4—23no—
1294C2×C4—23no—
1295C2×C4—23no—
1296C2×C4—23no—
1297C2×C4—23no—
1298C2×C4—21no—
1299C2×C4—23no—
1300C2×C4—23no—
1301C2×C4—23no—
1302C2×C4—23no—
1303C2×C4—23no—
1304C2×C4—21no—
1305C2×C4—21no—
1306C2×C4—23no—
1307C2×C4—23no—
1308C2×C4—23no—
1309C2×C4—21no—
1310C2×C4—23no—
1311C2×C4—21no—
1312C2×C4—21no—
1313C2×C4—21no—
1314C2×C4—21no—
1315C2×C4—21no—
1316C2×C4—44no—
1317C2×C4—412no—
1318C2×C4—412no—
1319C2×C4—412no—
1320C2×C4—412no—
1321C2×C4—412no—
1322C2×C4—812no—
1323C2×C4—86no—
1324C2×C4—86no—
1325C2×C4—86no—
1326C2×C4—166no—
1327C2×C4C22×#4112yes—
1328C2×C4C22×#4116yes—
1329C2×C4C22×#4116yes—
1330C2×C4C2×H(5,𝔽2)16yes—
1331C2×C4C2×H(5,𝔽2)16yes—
1332C2×C4#58512yes—
1333C22—22no—
1334C22—22no—
1335C22—22no—
1336C22—41no—
1337C22—41no—
1338C22—41no—
1339C22—41no—
1340C22—43no—
1341C22—43no—
1342C22—43no—
1343C22—41no—
1344C22—43no—
1345C22—43no—
1346C22—41no—
1347C22—43no—
1348C22—43no—
1349C22—41no—
1350C22—43no—
1351C22—43no—
1352C22—43no—
1353C22—43no—
1354C22—43no—
1355C22—41no—
1356C22—41no—
1357C22—43no—
1358C22—43no—
1359C22—43no—
1360C22—43no—
1361C22—41no—
1362C22—43no—
1363C22—43no—
1364C22—41no—
1365C22—43no—
1366C22—43no—
1367C22—43no—
1368C22C23×#4111yescharacteristic
1369C22C22×H(5,𝔽2)11yescharacteristic
1370C22C22×H(5,𝔽2)11yescharacteristic
1371C22C2×#58511yescharacteristic
1372C22C2×#58511yescharacteristic
1373C22H(7,𝔽2)11yescharacteristic
1374C222−1+611yescharacteristic
1375C4—22no—
1376C4—26no—
1377C4—22no—
1378C4—41no—
1379C4—43no—
1380C4—41no—
1381C4—43no—
1382C4—43no—
1383C4—43no—
1384C4—41no—
1385C4—41no—
1386C4—43no—
1387C4—41no—
1388C4—41no—
1389C4—43no—
1390C4—41no—
1391C4—41no—
1392C4—43no—
1393C4—43no—
1394C4—43no—
1395C4—41no—
1396C4—41no—
1397C4—41no—
1398C4—43no—
1399C4—43no—
1400C4C2×#540112yes—
1401C2—42no—
1402C2—83no—
1403C2—83no—
1404C2—81no—
1405C2—83no—
1406C2C22×#54011yescharacteristic
1407C2#6289711yescharacteristic
1408C2#6292311yescharacteristic
1409C2#6300711yescharacteristic
1410C2#6300811yescharacteristic
1411C2#6302011yescharacteristic
1412C2#6305211yescharacteristic
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. #52282C2semidirect
2. #42726C2semidirect
3. #42664C2semidirect
4. #42629C2semidirect
5. #42617C2semidirect
6. #42570C2semidirect
7. #42454C2semidirect
8. #40217C2semidirect
9. #40170C2semidirect
10. #40046C2semidirect
11. #40026C2semidirect
12. #39246C2semidirect
13. #39191C2semidirect
14. #37372C2semidirect
15. #37372C2semidirect
16. #37329C2semidirect
17. #36584C2semidirect
18. #36578C2semidirect
19. #36465C2semidirect
20. #36434C2semidirect
21. #36433C2semidirect
22. #36430C2semidirect
23. #36029C2semidirect
24. #36018C2semidirect
25. #35983C2semidirect
26. #35831C2semidirect
27. #35831C2semidirect
28. #35723C2semidirect
29. #34294C2semidirect
30. #34293C2semidirect
31. #34263C2semidirect

Maximal subgroups

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

subgroupindex
#522822
#427262
#426642
#426292
#426172
#425702
#424542
#402172
#401702
#400462
#400262
#392462
#391912
#373722
#373292
#365842
#365782
#364652
#364342
#364332
#364302
#360292
#360182
#359832
#358312
#357232
#342942
#342932
#342632