Finite Group Databasebeta

← #7699042

Subgroups — #7699042

Order 512.

5286 conjugacy classes of subgroups.

The subgroup lattice has 1371 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#59856C213yesmaximal, complemented
2#59696C213yesmaximal, complemented
3#59683C213yesmaximal, complemented
4#52262C213yesmaximal, complemented
5#45224C213yesmaximal, complemented
6#45069C213yesmaximal, complemented
7#45046C213yesmaximal, complemented
8#45035C213yesmaximal, complemented
9#44975C213yesmaximal, complemented
10#44974C213yesmaximal, complemented
11#39817C213yesmaximal, complemented
12#39555C213yesmaximal, complemented
13#39280C213yesmaximal, complemented
14#39191C213yesmaximal, complemented
15#38218C213yesmaximal, complemented
16#38123C213yesmaximal, complemented
17Q8×#126C211yesmaximal, characteristic, complemented
18Q8×#125C211yesmaximal, characteristic, complemented
19#36455C211yesmaximal, characteristic, complemented
20#36005C211yesmaximal, characteristic, complemented
21#35898C211yesmaximal, characteristic, complemented
22#35831C211yesmaximal, characteristic, complemented
23#35831C211yesmaximal, characteristic, complemented
24#35831C211yesmaximal, characteristic, complemented
25#35801C211yesmaximal, characteristic, complemented
26#34313C211yesmaximal, characteristic, complemented
27#34313C211yesmaximal, characteristic, complemented
28#34312C211yesmaximal, characteristic, complemented
29#34293C211yesmaximal, characteristic, complemented
30#34263C211yesmaximal, characteristic, complemented
31#34250C211yesmaximal, characteristic, complemented
32C2×#550C2211yescharacteristic
33C2×#550C2211yescharacteristic
34C2×#550C2211yescharacteristic
35C2×#548C2211yescharacteristic
36C2×#548C2211yescharacteristic
37C2×#548C2211yescharacteristic
38C2×#520C2211yescharacteristic
39C2×#520C2211yescharacteristic
40C2×#520C2211yescharacteristic
41C2×#520C2211yescharacteristic
42C2×#519C2211yescharacteristic
43C2×C4×#41C2211yescharacteristic
44#2863C2213yes—
45#2859C2213yes—
46#2856C2213yes—
47#2803C2213yes—
48#2802C2213yes—
49#2801C2213yes—
50#2800C2213yes—
51#2800C2213yes—
52#2800C2216yes—
53#2797C2213yes—
54#2796C2213yes—
55#2787C2213yes—
56#2786C2216yes—
57#2780C2216yes—
58#2779C2213yes—
59#2779C2216yes—
60#2777C2213yes—
61#2772C2213yes—
62#2757C2213yes—
63#2756C2216yes—
64#2753C2213yes—
65#2753C2216yes—
66#2746C2216yes—
67#2741C2216yes—
68#2725C2211yescharacteristic
69#2714C2213yes—
70#2711C2216yes—
71#2711C2216yes—
72#2711C2213yes—
73#2708C2216yes—
74#2701C2216yes—
75#2691C2216yes—
76#2644C2213yes—
77#2624C2213yes—
78#2624C2213yes—
79#2620C2213yes—
80#2620C2213yes—
81#2620C2213yes—
82#2602C2216yes—
83#2602C2216yes—
84#2601C2216yes—
85#2587C2216yes—
86#2579C2216yes—
87#2569C2216yes—
88#2559C2216yes—
89#2558C2216yes—
90#2552C2213yes—
91#2552C2213yes—
92#2544C2213yes—
93#2544C2213yes—
94#2544C2213yes—
95#2543C2216yes—
96#2541C2213yes—
97#2537C2213yes—
98#2537C2213yes—
99#2537C2213yes—
100#2537C2213yes—
101#2522C2216yes—
102#2513C2213yes—
103#2512C2213yes—
104#2512C2213yes—
105#2511C2213yes—
106#2511C2213yes—
107#2511C2213yes—
108#2507C2213yes—
109#2507C2213yes—
110#2507C2213yes—
111#2507C2213yes—
112#2501C2213yes—
113#2500C2213yes—
114#2497C2213yes—
115#2497C2213yes—
116#2497C2213yes—
117#2497C2213yes—
118#2496C2213yes—
119#2494C2213yes—
120#2487C2216yes—
121#2487C2213yes—
122#2485C2216yes—
123#2485C2213yes—
124#2476C2216yes—
125#2467C2216yes—
126#2464C2216yes—
127#2460C2216yes—
128#2457C2216yes—
129#2448C2213yes—
130#2448C2213yes—
131#2445C2213yes—
132#2445C2213yes—
133#2444C2216yes—
134#2443C2216yes—
135#2428C2213yes—
136#2428C2213yes—
137#2428C2213yes—
138#2428C2213yes—
139#2428C2213yes—
140#2427C2213yes—
141#2427C2213yes—
142#2427C2213yes—
143#2423C2213yes—
144#2422C2213yes—
145#2422C2213yes—
146#2421C2213yes—
147#2417C2213yes—
148#2417C2213yes—
149#2417C2213yes—
150#2416C2216yes—
151#2416C2213yes—
152#2416C2213yes—
153#2416C2213yes—
154#2414C2216yes—
155#2414C2213yes—
156#2414C2213yes—
157#2401C2213yes—
158#2395C2213yes—
159#2395C2213yes—
160#2392C2213yes—
161#2392C2213yes—
162#2392C2213yes—
163#2367C2213yes—
164#2367C2213yes—
165#2366C2213yes—
166#2366C2213yes—
167#2364C2216yes—
168#2363C2213yes—
169#2363C2213yes—
170#2362C2213yes—
171#2361C2213yes—
172#2361C2213yes—
173#2361C2213yes—
174#2361C2213yes—
175#2360C2213yes—
176#2357C2213yes—
177#2354C2213yes—
178#2354C2213yes—
179#2352C2213yes—
180#2351C2211yescharacteristic
181#2351C2211yescharacteristic
182Q8×C4⋊C4C2211yescharacteristic
183Q8×C4⋊C4C2211yescharacteristic
184Q8×C4⋊C4C2211yescharacteristic
185Q8×C4⋊C4C2211yescharacteristic
186Q8×C4⋊C4C2211yescharacteristic
187Q8×C4⋊C4C2211yescharacteristic
188Q8×C4⋊C4C2211yescharacteristic
189Q8×C4⋊C4C2211yescharacteristic
190#2349C2213yes—
191#2349C2213yes—
192D4×C4⋊C4C2213yes—
193D4×C4⋊C4C2213yes—
194D4×C4⋊C4C2213yes—
195D4×C4⋊C4C2213yes—
196#2345C2213yes—
197#2344C2213yes—
198#2341C2211yescharacteristic
199#2341C2211yescharacteristic
200#2341C2211yescharacteristic
201#2341C2211yescharacteristic
202#2341C2211yescharacteristic
203#2341C2211yescharacteristic
204#2341C2211yescharacteristic
205Q8×C22⋊C4C2211yescharacteristic
206Q8×C22⋊C4C2211yescharacteristic
207Q8×C22⋊C4C2211yescharacteristic
208#2326C2213yes—
209#2324C2213yes—
210#2324C2213yes—
211#2324C2213yes—
212#2324C2213yes—
213#2324C2213yes—
214#2324C2213yes—
215#2323C2213yes—
216#2319C2213yes—
217#2317C2213yes—
218#2316C2213yes—
219#2314C2213yes—
220C4×#127C2213yes—
221C4×#127C2213yes—
222C4×#125C2213yes—
223C4×#126C2213yes—
224C4×#124C2213yes—
225C4×C22⋊Q8C2213yes—
226C4×#121C2213yes—
227#2298C2213yes—
228#2296C2213yes—
229#2293C2213yes—
230#2293C2213yes—
231#2293C2213yes—
232#2293C2213yes—
233C2×#389C2213yes—
234#2290C2213yes—
235#2276C2211yescharacteristic
236C42×Q8C2211yescharacteristic
237C42×Q8C2211yescharacteristic
238C22×#41C2311yescharacteristic
239C22×#41C2311yescharacteristic
240C22×#41C2311yescharacteristic
241C23×Q8C2311yescharacteristic
242#550—28no—
243#550—28no—
244#550—44no—
245#548—28no—
246#548—28no—
247#548—44no—
248C2×#127C2313yes—
249C2×#127C2313yes—
250C2×#127C2313yes—
251C2×#126C2311yescharacteristic
252C2×#126C2316yes—
253C2×#125C2311yescharacteristic
254C2×#125C2316yes—
255C2×#124C2313yes—
256C2×#124C2313yes—
257C2×#124C2313yes—
258C2×#123C2316yes—
259C2×#123C2316yes—
260C2×C22⋊Q8C2313yes—
261C2×C22⋊Q8C2313yes—
262C2×C22⋊Q8C2313yes—
263C2×#121C2313yes—
264C2×#121C2313yes—
265C2×#121C2313yes—
266C2×#121C2313yes—
267C2×#121C2313yes—
268C2×#121C2313yes—
269C2×#121C2313yes—
270C2×#121C2313yes—
271C2×#121C2313yes—
272C2×#121C2313yes—
273C2×#121C2316yes—
274C2×#121C2316yes—
275C2×#121C2316yes—
276C2×#121C2316yes—
277C2×#121C2316yes—
278#520—28no—
279#520—28no—
280#520—44no—
281#520—44no—
282#519—44no—
283C4×#41—44no—
284C2×C4×Q8C2311yescharacteristic
285C2×C4×Q8C2311yescharacteristic
286C2×C4×Q8C2311yescharacteristic
287C2×C4×Q8C2311yescharacteristic
288C2×C4×Q8C2311yescharacteristic
289C2×C4×Q8C2311yescharacteristic
290C2×C4×Q8C2311yescharacteristic
291C2×C4×Q8C2311yescharacteristic
292C2×C4×Q8C2311yescharacteristic
293C2×C4×Q8C2311yescharacteristic
294C2×C4×Q8C2313yes—
295C2×C4×Q8C2313yes—
296C2×C4×Q8C2311yescharacteristic
297C2×C4×D4C2313yes—
298C2×C4×D4C2313yes—
299C2×C4×D4C2313yes—
300C2×C4×D4C2313yes—
301C2×C4×D4C2313yes—
302C2×C4×D4C2313yes—
303C2×C4×D4C2313yes—
304C2×C4×D4C2313yes—
305C2×C4×D4C2313yes—
306C2×C4×D4C2313yes—
307C2×C4×D4C2313yes—
308C2×C4×D4C2313yes—
309C2×C4×D4C2313yes—
310C2×C4×D4C2313yes—
311C2×C4×D4C2313yes—
312C2×C4×D4C2313yes—
313C2×C4×D4C2316yes—
314C2×C4×D4C2316yes—
315C2×C4×D4C2316yes—
316C2×C4×D4C2316yes—
317C2×#117C2313yes—
318C2×#117C2313yes—
319C2×#117C2313yes—
320C2×#117C2313yes—
321C2×#117C2313yes—
322C2×#117C2313yes—
323C2×#117C2313yes—
324C2×#117C2316yes—
325C22×C4⋊C4C2313yes—
326C22×C4⋊C4C2313yes—
327C22×C4⋊C4C2313yes—
328C22×C4⋊C4C2313yes—
329C22×C4⋊C4C2316yes—
330C22×C42C2313yes—
331#401C2313yes—
332#400C2313yes—
333#400C2316yes—
334#400C2316yes—
335#400C2313yes—
336#400C2311yescharacteristic
337#400C2313yes—
338#400C2313yes—
339#400C2316yes—
340#399C2316yes—
341#399C2316yes—
342#399C2313yes—
343#399C2313yes—
344#398C2313yes—
345#398C2316yes—
346#398C2313yes—
347#398C2316yes—
348#398C2313yes—
349#398C2316yes—
350#398C2313yes—
351#398C2311yescharacteristic
352#398C2316yes—
353#397C2313yes—
354#397C2316yes—
355#397C2313yes—
356#397C2316yes—
357#397C2313yes—
358#397C2316yes—
359#397C2313yes—
360#397C2313yes—
361#397C2313yes—
362#397C2311yescharacteristic
363#397C2313yes—
364#397C2313yes—
365#397C2313yes—
366#397C2313yes—
367#397C2313yes—
368#396C2316yes—
369#396C2316yes—
370#396C2316yes—
371#396C2313yes—
372#396C2313yes—
373#396C2313yes—
374#396C2316yes—
375#396C2311yescharacteristic
376#396C2311yescharacteristic
377#396C2311yescharacteristic
378#396C2313yes—
379#396C2316yes—
380#394C2316yes—
381#394C2313yes—
382#394C2316yes—
383#394C2316yes—
384#394C2316yes—
385#394C2316yes—
386#394C2316yes—
387#394C2316yes—
388#394C2313yes—
389#394C2316yes—
390#394C2316yes—
391#394C2313yes—
392#394C2313yes—
393#394C2313yes—
394#394C2313yes—
395#394C2313yes—
396#394C2313yes—
397#394C2313yes—
398#394C2313yes—
399#394C2313yes—
400#394C2313yes—
401#394C2313yes—
402#394C2316yes—
403#394C2316yes—
404#392C2316yes—
405#392C2316yes—
406#392C2313yes—
407#392C2313yes—
408#392C2313yes—
409#391C2313yes—
410#391C2313yes—
411#391C2313yes—
412#391C2313yes—
413#391C2313yes—
414#391C2313yes—
415#390C2313yes—
416#390C2313yes—
417#390C2313yes—
418#390C2316yes—
419#390C2316yes—
420#390C2313yes—
421#390C2313yes—
422#390C2313yes—
423#390C2313yes—
424#390C2313yes—
425#390C2313yes—
426#390C2313yes—
427#390C2313yes—
428#390C2313yes—
429#390C2316yes—
430#390C2313yes—
431#390C2313yes—
432#390C2313yes—
433#390C2313yes—
434#390C2313yes—
435#390C2313yes—
436#390C2316yes—
437#390C2313yes—
438#390C2313yes—
439#390C2313yes—
440#389C2313yes—
441#389C2313yes—
442#389C2313yes—
443#389C2316yes—
444#389C2313yes—
445#389C2313yes—
446#389C2313yes—
447#389C2313yes—
448#389C2313yes—
449#389C2313yes—
450#389C2313yes—
451#389C2313yes—
452#389C2313yes—
453#389C2313yes—
454#389C2313yes—
455#389C2313yes—
456#389C2313yes—
457#389C2313yes—
458#389C2316yes—
459#389C2313yes—
460#389C2313yes—
461#389C2313yes—
462#389C2316yes—
463#389C2313yes—
464#389C2313yes—
465#389C2313yes—
466#389C2313yes—
467#389C2313yes—
468#389C2313yes—
469#389C2313yes—
470#389C2313yes—
471#389C2311yescharacteristic
472#389C2311yescharacteristic
473#389C2311yescharacteristic
474#389C2311yescharacteristic
475#389C2313yes—
476#388C2313yes—
477#388C2313yes—
478#388C2313yes—
479#388C2316yes—
480#388C2316yes—
481#388C2313yes—
482#388C2316yes—
483#388C2316yes—
484#388C2313yes—
485#388C2313yes—
486#388C2313yes—
487#388C2313yes—
488#388C2316yes—
489#388C2316yes—
490#388C2316yes—
491#388C2313yes—
492#388C2316yes—
493#388C2316yes—
494#388C2313yes—
495#388C2316yes—
496#388C2316yes—
497#388C2313yes—
498#388C2313yes—
499#388C2313yes—
500#388C2313yes—
501#388C2313yes—
502#388C2313yes—
503#388C2313yes—
504#388C2313yes—
505#388C2313yes—
506#388C2313yes—
507#388C2313yes—
508#388C2316yes—
509#388C2311yescharacteristic
510#388C2311yescharacteristic
511#387C2313yes—
512#387C2313yes—
513#387C2313yes—
514#387C2313yes—
515#387C2313yes—
516#387C2313yes—
517#387C2313yes—
518#387C2316yes—
519#387C2316yes—
520#387C2316yes—
521#387C2316yes—
522#387C2313yes—
523#387C2313yes—
524#387C2316yes—
525#387C2313yes—
526#387C2316yes—
527#387C2316yes—
528#387C2313yes—
529#387C2311yescharacteristic
530#387C2313yes—
531#386C2313yes—
532#386C2316yes—
533#386C2313yes—
534#386C2316yes—
535#386C2316yes—
536#386C2316yes—
537#386C2316yes—
538#386C2316yes—
539#386C2316yes—
540#386C2316yes—
541#386C2316yes—
542#386C2313yes—
543#386C2316yes—
544#386C2316yes—
545#386C2316yes—
546#386C2313yes—
547#385C2316yes—
548#385C2316yes—
549#385C2316yes—
550#385C2316yes—
551#385C2316yes—
552#385C2316yes—
553#385C2316yes—
554#385C2316yes—
555#385C2316yes—
556#385C2313yes—
557#385C2313yes—
558#385C2313yes—
559#385C2313yes—
560#385C2313yes—
561#385C2313yes—
562#384C2313yes—
563#384C2313yes—
564#384C2313yes—
565#384C2313yes—
566#384C2313yes—
567#384C2313yes—
568#384C2313yes—
569#384C2313yes—
570#383C2313yes—
571#382C2313yes—
572#382C2313yes—
573#382C2313yes—
574#381C2316yes—
575#380C2313yes—
576#380C2316yes—
577#380C2316yes—
578#380C2313yes—
579#380C2313yes—
580#380C2316yes—
581#380C2316yes—
582#380C2316yes—
583#380C2313yes—
584#380C2313yes—
585#380C2313yes—
586#380C2313yes—
587#380C2313yes—
588#380C2313yes—
589#380C2313yes—
590#380C2313yes—
591#380C2316yes—
592C4×C4⋊C4C2313yes—
593C4×C4⋊C4C2313yes—
594C4×C4⋊C4C2313yes—
595C4×C4⋊C4C2313yes—
596C4×C4⋊C4C2313yes—
597C4×C4⋊C4C2313yes—
598C4×C4⋊C4C2313yes—
599C4×C4⋊C4C2313yes—
600C4×C4⋊C4C2313yes—
601C4×C4⋊C4C2313yes—
602C4×C4⋊C4C2313yes—
603C4×C4⋊C4C2313yes—
604C4×C4⋊C4C2313yes—
605C4×C4⋊C4C2313yes—
606C4×C4⋊C4C2316yes—
607C4×C4⋊C4C2313yes—
608C4×C4⋊C4C2313yes—
609C4×C4⋊C4C2313yes—
610C4×C4⋊C4C2313yes—
611C4×C4⋊C4C2313yes—
612C4×C22⋊C4C2313yes—
613C4×C22⋊C4C2313yes—
614C4×C22⋊C4C2313yes—
615C4×C22⋊C4C2316yes—
616C4×C22⋊C4C2316yes—
617C4×C22⋊C4C2313yes—
618C4×C22⋊C4C2313yes—
619C4×C22⋊C4C2313yes—
620C4×C22⋊C4C2313yes—
621C4×C22⋊C4C2313yes—
622C4×C22⋊C4C2313yes—
623C4×C22⋊C4C2313yes—
624C4×C22⋊C4C2316yes—
625C4×C22⋊C4C2316yes—
626#376C2313yes—
627C2×#95C2316yes—
628C43C2313yes—
629C43C2313yes—
630C2×#41—24no—
631C2×#41—24no—
632C2×#41—24no—
633C2×#41—24no—
634C2×#41—24no—
635C2×#41—24no—
636C2×#41—24no—
637C2×#41—24no—
638C2×#41#4118yes—
639C22×Q8—24no—
640C22×Q8—24no—
641C22×Q8—24no—
642C22×Q8C2413yes—
643C22×Q8C2411yescharacteristic
644C22×D4C2413yes—
645C22×D4C2413yes—
646C22×D4C2413yes—
647C22×D4C2413yes—
648C22×D4C2413yes—
649C22×D4C2413yes—
650C22×D4C2413yes—
651C22×D4C2416yes—
652C22×D4C2416yes—
653C22×D4C2413yes—
654C22×D4C2413yes—
655C22×D4C2416yes—
656C23×C4C2413yes—
657C23×C4C2413yes—
658C23×C4C2413yes—
659C23×C4C2413yes—
660C23×C4C2416yes—
661C23×C4C2416yes—
662C23×C4C2413yes—
663C23×C4C2416yes—
664C23×C4C2413yes—
665C23×C4C2416yes—
666#127—212no—
667#127—212no—
668#127—46no—
669#126—24no—
670#126—86no—
671#125—24no—
672#125—86no—
673#124—212no—
674#124—212no—
675#124—46no—
676#123—86no—
677#123—86no—
678C22⋊Q8—212no—
679C22⋊Q8—212no—
680C22⋊Q8—46no—
681#121—212no—
682#121—212no—
683#121—212no—
684#121—212no—
685#121—212no—
686#121—212no—
687#121—212no—
688#121—46no—
689#121—46no—
690#121—46no—
691#121—86no—
692#121—86no—
693#121—86no—
694#121—86no—
695#121—86no—
696C4×Q8—24no—
697C4×Q8—24no—
698C4×Q8—24no—
699C4×Q8—24no—
700C4×Q8—24no—
701C4×Q8—24no—
702C4×Q8—24no—
703C4×Q8—24no—
704C4×Q8—24no—
705C4×Q8—24no—
706C4×Q8—46no—
707C4×Q8—46no—
708C4×Q8#4118yes—
709C4×D4—212no—
710C4×D4—212no—
711C4×D4—212no—
712C4×D4—212no—
713C4×D4—212no—
714C4×D4—212no—
715C4×D4—212no—
716C4×D4—212no—
717C4×D4—46no—
718C4×D4—46no—
719C4×D4—46no—
720C4×D4—46no—
721C4×D4—46no—
722C4×D4—46no—
723C4×D4—46no—
724C4×D4—46no—
725C4×D4—86no—
726C4×D4—86no—
727C4×D4—86no—
728C4×D4—86no—
729#117—212no—
730#117—212no—
731#117—46no—
732#117—46no—
733#117—46no—
734#117—46no—
735#117—46no—
736#117—86no—
737C2×C4⋊C4—212no—
738C2×C4⋊C4—212no—
739C2×C4⋊C4—46no—
740C2×C4⋊C4—46no—
741C2×C4⋊C4—86no—
742C2×C4⋊C4C2413yes—
743C2×C4⋊C4C2413yes—
744C2×C4⋊C4C2413yes—
745C2×C4⋊C4C2413yes—
746C2×C4⋊C4C2413yes—
747C2×C4⋊C4C2413yes—
748C2×C4⋊C4C2413yes—
749C2×C4⋊C4C2411yescharacteristic
750C2×C4⋊C4C2411yescharacteristic
751C2×C4⋊C4C2413yes—
752C2×C4⋊C4C2413yes—
753C2×C4⋊C4C2411yescharacteristic
754C2×C4⋊C4C2411yescharacteristic
755C2×C4⋊C4C2413yes—
756C2×C4⋊C4C2413yes—
757C2×C4⋊C4C2413yes—
758C2×C4⋊C4C2413yes—
759C2×C4⋊C4C2413yes—
760C2×C4⋊C4C2411yescharacteristic
761C2×C4⋊C4C2411yescharacteristic
762C2×C4⋊C4C2411yescharacteristic
763C2×C4⋊C4C2411yescharacteristic
764C2×C4⋊C4C2411yescharacteristic
765C2×C4⋊C4C2411yescharacteristic
766C2×C4⋊C4C2411yescharacteristic
767C2×C4⋊C4C2413yes—
768C2×C4⋊C4C2413yes—
769C2×C4⋊C4C2413yes—
770C2×C4⋊C4C2413yes—
771C2×C4⋊C4C2416yes—
772C2×C4⋊C4C2416yes—
773C2×C4⋊C4C2411yescharacteristic
774C2×C4⋊C4C2411yescharacteristic
775C2×C4⋊C4C2413yes—
776C2×C4⋊C4C2413yes—
777C2×C4⋊C4C2413yes—
778C2×C4⋊C4C2416yes—
779C2×C4⋊C4C2411yescharacteristic
780C2×C4⋊C4C2413yes—
781C2×C4⋊C4C2413yes—
782C2×C4⋊C4C2413yes—
783C2×C4⋊C4C2416yes—
784C2×C4⋊C4C2416yes—
785C2×C4⋊C4C2413yes—
786C2×C4⋊C4C2416yes—
787C2×C4⋊C4C2416yes—
788C2×C4⋊C4C2413yes—
789C2×C4⋊C4C2413yes—
790C2×C4⋊C4C2416yes—
791C2×C4⋊C4C2413yes—
792C2×C4⋊C4C2413yes—
793C2×C4⋊C4C2413yes—
794C2×C4⋊C4C2413yes—
795C2×C4⋊C4C2413yes—
796C2×C4⋊C4C2411yescharacteristic
797C2×C22⋊C4C2413yes—
798C2×C22⋊C4C2413yes—
799C2×C22⋊C4C2413yes—
800C2×C22⋊C4C2413yes—
801C2×C22⋊C4C2411yescharacteristic
802C2×C22⋊C4C2411yescharacteristic
803C2×C22⋊C4C2413yes—
804C2×C22⋊C4C2413yes—
805C2×C22⋊C4C2413yes—
806C2×C22⋊C4C2413yes—
807C2×C22⋊C4C2413yes—
808C2×C22⋊C4C2413yes—
809C2×C22⋊C4C2416yes—
810C2×C22⋊C4C2416yes—
811C2×C22⋊C4C2413yes—
812C2×C22⋊C4C2413yes—
813C2×C22⋊C4C2411yescharacteristic
814C2×C22⋊C4C2411yescharacteristic
815C2×C22⋊C4C2411yescharacteristic
816C2×C22⋊C4C2413yes—
817C2×C22⋊C4C2411yescharacteristic
818C2×C22⋊C4C2413yes—
819C2×C22⋊C4C2413yes—
820C2×C22⋊C4C2416yes—
821C2×C22⋊C4C2413yes—
822C2×C22⋊C4C2413yes—
823C2×C22⋊C4C2413yes—
824C2×C22⋊C4C2416yes—
825C2×C22⋊C4C2411yescharacteristic
826C2×C22⋊C4C2416yes—
827C2×C22⋊C4C2413yes—
828C2×C22⋊C4C2413yes—
829C2×C22⋊C4C2413yes—
830C2×C22⋊C4C2413yes—
831C2×C22⋊C4C2413yes—
832C2×C22⋊C4C2413yes—
833C2×C22⋊C4C2416yes—
834C2×C22⋊C4C2416yes—
835C2×C22⋊C4C2413yes—
836C2×C22⋊C4C2413yes—
837C2×C22⋊C4C2413yes—
838C2×C22⋊C4C2413yes—
839C2×C22⋊C4C2413yes—
840C2×C22⋊C4C2413yes—
841C2×C22⋊C4C2416yes—
842C2×C22⋊C4C2416yes—
843C2×C22⋊C4C2416yes—
844C2×C22⋊C4C2416yes—
845C2×C22⋊C4C2413yes—
846C2×C22⋊C4C2413yes—
847C2×C22⋊C4C2413yes—
848C2×C22⋊C4C2413yes—
849C2×C22⋊C4C2413yes—
850C2×C42—46no—
851C2×C42C2413yes—
852C2×C42C2413yes—
853C2×C42C2413yes—
854C2×C42C2413yes—
855C2×C42C2413yes—
856C2×C42C2413yes—
857C2×C42C2413yes—
858C2×C42C2413yes—
859C2×C42C2413yes—
860C2×C42C2413yes—
861C2×C42C2411yescharacteristic
862C2×C42C2411yescharacteristic
863C2×C42C2413yes—
864C2×C42C2413yes—
865C2×C42C2416yes—
866C2×C42C2416yes—
867C2×C42C2413yes—
868C2×C42C2413yes—
869C2×C42C2413yes—
870C2×C42C2413yes—
871C2×C42C2413yes—
872C2×C42C2411yescharacteristic
873C2×C42C2413yes—
874#95C2413yes—
875#95C2413yes—
876#95C2416yes—
877#95C2416yes—
878#95C2411yescharacteristic
879#95C2413yes—
880#95C2413yes—
881#95C2413yes—
882#95C2413yes—
883#95C2411yescharacteristic
884#95C2411yescharacteristic
885#95C2413yes—
886#95C2411yescharacteristic
887#95C2411yescharacteristic
888#95C2411yescharacteristic
889#95C2411yescharacteristic
890#95C2411yescharacteristic
891#95C2413yes—
892#95C2413yes—
893#95C2413yes—
894#95C2413yes—
895#95C2413yes—
896#95C2413yes—
897#95C2413yes—
898#95C2413yes—
899#95C2413yes—
900#95C2413yes—
901#95C2416yes—
902#95C2413yes—
903#95C2413yes—
904#95C2413yes—
905#95C2413yes—
906#95C2416yes—
907#95C2416yes—
908#95C2411yescharacteristic
909#95C2411yescharacteristic
910#95C2413yes—
911#95C2413yes—
912#95C2416yes—
913#95C2413yes—
914#95C2413yes—
915#95C2413yes—
916#95C2413yes—
917#95C2413yes—
918#95C2413yes—
919#95C2413yes—
920#95C2413yes—
921#95C2413yes—
922#95C2413yes—
923#95C2413yes—
924#95C2416yes—
925C24C2513yes—
926C24C2513yes—
927C24C2511yescharacteristic
928C24C2513yes—
929#41—232no—
930#41—416no—
931#41—416no—
932C2×Q8—26no—
933C2×Q8—26no—
934C2×Q8—26no—
935C2×Q8—416no—
936C2×Q8C2×#4114yes—
937C2×Q8C2×#4114yes—
938C2×Q8H(5,𝔽2)14yes—
939C2×D4—26no—
940C2×D4—26no—
941C2×D4—26no—
942C2×D4—212no—
943C2×D4—212no—
944C2×D4—26no—
945C2×D4—26no—
946C2×D4—26no—
947C2×D4—26no—
948C2×D4—26no—
949C2×D4—26no—
950C2×D4—26no—
951C2×D4—26no—
952C2×D4—26no—
953C2×D4—26no—
954C2×D4—26no—
955C2×D4—26no—
956C2×D4—43no—
957C2×D4—43no—
958C2×D4—43no—
959C2×D4—43no—
960C2×D4—46no—
961C2×D4—46no—
962C2×D4—43no—
963C2×D4—43no—
964C2×D4—43no—
965C2×D4—43no—
966C2×D4—46no—
967C2×D4—46no—
968C2×D4—43no—
969C2×D4—43no—
970C2×D4—43no—
971C2×D4—46no—
972C2×D4—46no—
973C2×D4—46no—
974C2×D4C2×#41112yes—
975C22×C4—26no—
976C22×C4—26no—
977C22×C4—26no—
978C22×C4—26no—
979C22×C4—26no—
980C22×C4—26no—
981C22×C4—26no—
982C22×C4—26no—
983C22×C4—26no—
984C22×C4—26no—
985C22×C4—26no—
986C22×C4—212no—
987C22×C4—212no—
988C22×C4—26no—
989C22×C4—43no—
990C22×C4—43no—
991C22×C4—43no—
992C22×C4—46no—
993C22×C4—46no—
994C22×C4—46no—
995C22×C4—46no—
996C22×C4—43no—
997C22×C4—43no—
998C22×C4—46no—
999C22×C4—46no—
1000C22×C4—46no—
1001C22×C4—46no—
1002C22×C4—46no—
1003C22×C4—46no—
1004C22×C4C2×#41112yes—
1005C22×C4C2511yescharacteristic
1006C22×C4C2511yescharacteristic
1007C22×C4C2511yescharacteristic
1008C22×C4C2513yes—
1009C22×C4C2511yescharacteristic
1010C22×C4C2511yescharacteristic
1011C22×C4C2513yes—
1012C22×C4C2513yes—
1013C22×C4C2513yes—
1014C22×C4C2513yes—
1015C22×C4C2513yes—
1016C22×C4C2513yes—
1017C22×C4C2511yescharacteristic
1018C22×C4C2511yescharacteristic
1019C22×C4C2511yescharacteristic
1020C22×C4C2511yescharacteristic
1021C22×C4C2513yes—
1022C22×C4C2513yes—
1023C22×C4C2513yes—
1024C22×C4C2513yes—
1025C22×C4C2513yes—
1026C22×C4C2511yescharacteristic
1027C22×C4C2511yescharacteristic
1028C22×C4C2511yescharacteristic
1029C22×C4C2511yescharacteristic
1030C22×C4C2511yescharacteristic
1031C22×C4C2513yes—
1032C4⋊C4—26no—
1033C4⋊C4—26no—
1034C4⋊C4—26no—
1035C4⋊C4—26no—
1036C4⋊C4—22no—
1037C4⋊C4—22no—
1038C4⋊C4—22no—
1039C4⋊C4—22no—
1040C4⋊C4—26no—
1041C4⋊C4—26no—
1042C4⋊C4—26no—
1043C4⋊C4—26no—
1044C4⋊C4—26no—
1045C4⋊C4—26no—
1046C4⋊C4—26no—
1047C4⋊C4—26no—
1048C4⋊C4—26no—
1049C4⋊C4—26no—
1050C4⋊C4—22no—
1051C4⋊C4—22no—
1052C4⋊C4—22no—
1053C4⋊C4—22no—
1054C4⋊C4—22no—
1055C4⋊C4—22no—
1056C4⋊C4—22no—
1057C4⋊C4—43no—
1058C4⋊C4—43no—
1059C4⋊C4—43no—
1060C4⋊C4—43no—
1061C4⋊C4—46no—
1062C4⋊C4—46no—
1063C4⋊C4—41no—
1064C4⋊C4—41no—
1065C4⋊C4—43no—
1066C4⋊C4—43no—
1067C4⋊C4—43no—
1068C4⋊C4—46no—
1069C4⋊C4—41no—
1070C4⋊C4—43no—
1071C4⋊C4—43no—
1072C4⋊C4—43no—
1073C4⋊C4—46no—
1074C4⋊C4—46no—
1075C4⋊C4—43no—
1076C4⋊C4—46no—
1077C4⋊C4—46no—
1078C4⋊C4—43no—
1079C4⋊C4—43no—
1080C4⋊C4—46no—
1081C4⋊C4—43no—
1082C4⋊C4—43no—
1083C4⋊C4—43no—
1084C4⋊C4—43no—
1085C4⋊C4C2×#41112yes—
1086C4⋊C42−1+414yes—
1087C22⋊C4—26no—
1088C22⋊C4—26no—
1089C22⋊C4—26no—
1090C22⋊C4—212no—
1091C22⋊C4—26no—
1092C22⋊C4—26no—
1093C22⋊C4—26no—
1094C22⋊C4—26no—
1095C22⋊C4—22no—
1096C22⋊C4—22no—
1097C22⋊C4—26no—
1098C22⋊C4—26no—
1099C22⋊C4—26no—
1100C22⋊C4—212no—
1101C22⋊C4—26no—
1102C22⋊C4—26no—
1103C22⋊C4—22no—
1104C22⋊C4—22no—
1105C22⋊C4—22no—
1106C22⋊C4—41no—
1107C22⋊C4—43no—
1108C22⋊C4—43no—
1109C22⋊C4—43no—
1110C22⋊C4—43no—
1111C22⋊C4—43no—
1112C22⋊C4—46no—
1113C22⋊C4—43no—
1114C22⋊C4—46no—
1115C22⋊C4—41no—
1116C22⋊C4—43no—
1117C22⋊C4—43no—
1118C22⋊C4—43no—
1119C22⋊C4—43no—
1120C22⋊C4—43no—
1121C22⋊C4—43no—
1122C22⋊C4—43no—
1123C22⋊C4—46no—
1124C22⋊C4—46no—
1125C22⋊C4—46no—
1126C22⋊C4—46no—
1127C22⋊C4—43no—
1128C22⋊C4—43no—
1129C22⋊C4—43no—
1130C22⋊C4—43no—
1131C22⋊C4—43no—
1132C22⋊C4—46no—
1133C22⋊C4—46no—
1134C22⋊C4—46no—
1135C22⋊C4—43no—
1136C22⋊C4—43no—
1137C22⋊C4—43no—
1138C22⋊C4—43no—
1139C22⋊C4—43no—
1140C42—26no—
1141C42—26no—
1142C42—26no—
1143C42—26no—
1144C42—26no—
1145C42—26no—
1146C42—26no—
1147C42—26no—
1148C42—26no—
1149C42—26no—
1150C42—22no—
1151C42—22no—
1152C42—41no—
1153C42—43no—
1154C42—46no—
1155C42—43no—
1156C42—46no—
1157C42—43no—
1158C42—43no—
1159C42—43no—
1160C42—43no—
1161C42—43no—
1162C42C2×#41112yes—
1163C23—23no—
1164C23—23no—
1165C23—23no—
1166C23—23no—
1167C23—23no—
1168C23—23no—
1169C23—23no—
1170C23—23no—
1171C23—21no—
1172C23—21no—
1173C23—23no—
1174C23—23no—
1175C23—21no—
1176C23—23no—
1177C23—23no—
1178C23—21no—
1179C23—23no—
1180C23—23no—
1181C23—23no—
1182C23—23no—
1183C23—23no—
1184C23—23no—
1185C23—23no—
1186C23—23no—
1187C23—21no—
1188C23—21no—
1189C23—21no—
1190C23C22×#4116yes—
1191C23C2611yescharacteristic
1192Q8—412no—
1193Q8#553116yes—
1194D4—224no—
1195D4—412no—
1196D4—412no—
1197D4—412no—
1198D4—412no—
1199D4—86no—
1200D4—86no—
1201D4—86no—
1202D4—812no—
1203D4—812no—
1204D4—86no—
1205D4—166no—
1206C2×C4—21no—
1207C2×C4—21no—
1208C2×C4—21no—
1209C2×C4—21no—
1210C2×C4—21no—
1211C2×C4—21no—
1212C2×C4—21no—
1213C2×C4—21no—
1214C2×C4—21no—
1215C2×C4—23no—
1216C2×C4—23no—
1217C2×C4—21no—
1218C2×C4—224no—
1219C2×C4—21no—
1220C2×C4—21no—
1221C2×C4—21no—
1222C2×C4—23no—
1223C2×C4—23no—
1224C2×C4—23no—
1225C2×C4—23no—
1226C2×C4—23no—
1227C2×C4—21no—
1228C2×C4—21no—
1229C2×C4—23no—
1230C2×C4—23no—
1231C2×C4—21no—
1232C2×C4—21no—
1233C2×C4—21no—
1234C2×C4—21no—
1235C2×C4—21no—
1236C2×C4—21no—
1237C2×C4—23no—
1238C2×C4—23no—
1239C2×C4—23no—
1240C2×C4—23no—
1241C2×C4—23no—
1242C2×C4—23no—
1243C2×C4—21no—
1244C2×C4—21no—
1245C2×C4—21no—
1246C2×C4—21no—
1247C2×C4—21no—
1248C2×C4—23no—
1249C2×C4—21no—
1250C2×C4—21no—
1251C2×C4—21no—
1252C2×C4—21no—
1253C2×C4—21no—
1254C2×C4—21no—
1255C2×C4—23no—
1256C2×C4—23no—
1257C2×C4—23no—
1258C2×C4—23no—
1259C2×C4—23no—
1260C2×C4—23no—
1261C2×C4—23no—
1262C2×C4—23no—
1263C2×C4—23no—
1264C2×C4—23no—
1265C2×C4—23no—
1266C2×C4—23no—
1267C2×C4—21no—
1268C2×C4—21no—
1269C2×C4—21no—
1270C2×C4—23no—
1271C2×C4—21no—
1272C2×C4—23no—
1273C2×C4—23no—
1274C2×C4—23no—
1275C2×C4—23no—
1276C2×C4—23no—
1277C2×C4—21no—
1278C2×C4—23no—
1279C2×C4—412no—
1280C2×C4—412no—
1281C2×C4—412no—
1282C2×C4—812no—
1283C2×C4—812no—
1284C2×C4—86no—
1285C2×C4—86no—
1286C2×C4—166no—
1287C2×C4—166no—
1288C2×C4C22×#4112yes—
1289C2×C4C22×#4116yes—
1290C2×C4C22×#4112yes—
1291C2×C4C22×#4116yes—
1292C2×C4C22×#4116yes—
1293C2×C4C2×H(5,𝔽2)16yes—
1294C2×C4C2×2−1+412yes—
1295C2×C4C2×2−1+412yes—
1296C2×C4C2×2−1+412yes—
1297C22—26no—
1298C22—26no—
1299C22—26no—
1300C22—43no—
1301C22—43no—
1302C22—43no—
1303C22—43no—
1304C22—43no—
1305C22—43no—
1306C22—41no—
1307C22—43no—
1308C22—43no—
1309C22—41no—
1310C22—43no—
1311C22—41no—
1312C22—43no—
1313C22—43no—
1314C22—41no—
1315C22—41no—
1316C22—43no—
1317C22—43no—
1318C22—43no—
1319C22—43no—
1320C22—43no—
1321C22—41no—
1322C22—41no—
1323C22—43no—
1324C22—43no—
1325C22C23×#4111yescharacteristic
1326C22C23×#4111yescharacteristic
1327C22C22×H(5,𝔽2)11yescharacteristic
1328C22C22×2−1+411yescharacteristic
1329C22H(7,𝔽2)11yescharacteristic
1330C22H(7,𝔽2)11yescharacteristic
1331C22H(7,𝔽2)11yescharacteristic
1332C4—22no—
1333C4—22no—
1334C4—22no—
1335C4—26no—
1336C4—22no—
1337C4—22no—
1338C4—41no—
1339C4—41no—
1340C4—41no—
1341C4—41no—
1342C4—43no—
1343C4—43no—
1344C4—43no—
1345C4—43no—
1346C4—43no—
1347C4—43no—
1348C4—43no—
1349C4—43no—
1350C4—43no—
1351C4—41no—
1352C4—41no—
1353C4—41no—
1354C4—43no—
1355C4—41no—
1356C4—41no—
1357C4—43no—
1358C4C2×#553112yes—
1359C2—46no—
1360C2—83no—
1361C2—83no—
1362C2—81no—
1363C2C22×#55311yescharacteristic
1364C2#6285811yescharacteristic
1365C2#6285811yescharacteristic
1366C2#6291711yescharacteristic
1367C2#6299911yescharacteristic
1368C2#6300011yescharacteristic
1369C2#6306611yescharacteristic
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. #59856C2semidirect
2. #59696C2semidirect
3. #59683C2semidirect
4. #52262C2semidirect
5. #45224C2semidirect
6. #45069C2semidirect
7. #45046C2semidirect
8. #45035C2semidirect
9. #44975C2semidirect
10. #44974C2semidirect
11. #39817C2semidirect
12. #39555C2semidirect
13. #39280C2semidirect
14. #39191C2semidirect
15. #38218C2semidirect
16. #38123C2semidirect
17. Q8×#126C2semidirect
18. Q8×#125C2semidirect
19. #36455C2semidirect
20. #36005C2semidirect
21. #35898C2semidirect
22. #35831C2semidirect
23. #35831C2semidirect
24. #35831C2semidirect
25. #35801C2semidirect
26. #34313C2semidirect
27. #34313C2semidirect
28. #34312C2semidirect
29. #34293C2semidirect
30. #34263C2semidirect
31. #34250C2semidirect

Maximal subgroups

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

subgroupindex
#598562
#596962
#596832
#522622
#452242
#450692
#450462
#450352
#449752
#449742
#398172
#395552
#392802
#391912
#382182
#381232
Q8×#1262
Q8×#1252
#364552
#360052
#358982
#358312
#358012
#343132
#343122
#342932
#342632
#342502