Finite Group Databasebeta

← #7632362

Subgroups — #7632362

Order 512.

5346 conjugacy classes of subgroups.

The subgroup lattice has 1320 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#36588C213yesmaximal, complemented
2#36576C211yesmaximal, characteristic
3#36486C213yesmaximal, complemented
4#36483C211yesmaximal, characteristic, complemented
5#36483C211yesmaximal, characteristic, complemented
6#36435C211yesmaximal, characteristic, complemented
7#36118C213yesmaximal, complemented
8#36117C213yesmaximal, complemented
9#36049C211yesmaximal, characteristic, complemented
10#35968C213yesmaximal, complemented
11#35945C213yesmaximal, complemented
12#35898C211yesmaximal, characteristic, complemented
13#35898C211yesmaximal, characteristic, complemented
14#35895C213yesmaximal, complemented
15#35884C213yesmaximal, complemented
16#35868C211yesmaximal, characteristic, complemented
17#35609C213yesmaximal, complemented
18#35605C213yesmaximal, complemented
19#35593C213yesmaximal, complemented
20#35587C213yesmaximal, complemented
21#35271C213yesmaximal, complemented
22#35229C213yesmaximal, complemented
23#34811C213yesmaximal, complemented
24#34763C213yesmaximal, complemented
25#34337C211yesmaximal, characteristic, complemented
26#34295C211yesmaximal, characteristic, complemented
27#34294C211yesmaximal, characteristic, complemented
28#34263C211yesmaximal, characteristic, complemented
29#34193C211yesmaximal, characteristic, complemented
30C4×#548C211yesmaximal, characteristic, complemented
31C2×#2276C211yesmaximal, characteristic, complemented
32C2×#557C2211yescharacteristic
33C2×#550C2211yescharacteristic
34C2×#548C2211yescharacteristic
35C2×#548C2211yescharacteristic
36C2×#529C2216yes—
37C2×#520C2211yescharacteristic
38C2×C4×#41C2211yescharacteristic
39C22×C4×Q8C2211yescharacteristic
40C22×C4×Q8C2211yescharacteristic
41C22×C4×Q8C2211yescharacteristic
42#2856C2213yes—
43#2854C2216yes—
44#2854C2213yes—
45#2854C2213yes—
46#2853C2216yes—
47#2851C2213yes—
48#2654C2216yes—
49#2651C2216yes—
50#2647C2213yes—
51#2644C2213yes—
52#2644C2213yes—
53#2641C2213yes—
54#2597C2216yes—
55#2595C2216yes—
56#2594C2216yes—
57#2594C2216yes—
58#2593C2216yes—
59#2590C2216yes—
60#2581C2213yes—
61#2577C2216yes—
62#2573C2216yes—
63#2570C2213yes—
64#2565C2213yes—
65#2562C2213yes—
66#2552C2213yes—
67#2548C2213yes—
68#2548C2213yes—
69#2538C2213yes—
70#2533C2213yes—
71#2532C2213yes—
72#2531C2216yes—
73#2531C2216yes—
74#2531C2213yes—
75#2530C2213yes—
76#2529C2213yes—
77#2528C2213yes—
78#2527C2213yes—
79#2526C2216yes—
80#2526C2213yes—
81#2526C2216yes—
82#2522C2216yes—
83#2521C2216yes—
84#2519C2216yes—
85#2516C2216yes—
86#2513C2213yes—
87#2513C2213yes—
88#2512C2213yes—
89#2512C2213yes—
90#2512C2213yes—
91#2512C2213yes—
92#2510C2213yes—
93#2509C2213yes—
94#2507C2213yes—
95#2506C2213yes—
96#2506C2213yes—
97#2505C2211yescharacteristic
98#2501C2213yes—
99#2501C2213yes—
100#2497C2213yes—
101#2497C2213yes—
102#2496C2213yes—
103#2496C2213yes—
104#2494C2213yes—
105#2494C2213yes—
106#2493C2213yes—
107#2491C2213yes—
108#2491C2213yes—
109#2490C2213yes—
110#2490C2213yes—
111#2488C2213yes—
112#2486C2213yes—
113#2486C2213yes—
114#2479C2216yes—
115#2479C2216yes—
116#2475C2216yes—
117#2474C2216yes—
118#2469C2216yes—
119#2468C2216yes—
120#2454C2216yes—
121#2453C2213yes—
122#2451C2213yes—
123#2450C2213yes—
124#2448C2213yes—
125#2448C2216yes—
126#2448C2213yes—
127#2448C2213yes—
128#2448C2213yes—
129#2444C2216yes—
130#2444C2213yes—
131#2442C2213yes—
132#2440C2213yes—
133#2426C2213yes—
134#2426C2213yes—
135#2425C2213yes—
136#2425C2216yes—
137#2425C2216yes—
138#2423C2213yes—
139#2423C2213yes—
140#2423C2213yes—
141#2423C2213yes—
142#2419C2213yes—
143#2416C2213yes—
144#2416C2213yes—
145#2402C2213yes—
146#2401C2213yes—
147#2401C2213yes—
148#2398C2213yes—
149#2396C2216yes—
150#2395C2216yes—
151#2370C2213yes—
152#2370C2213yes—
153#2367C2213yes—
154#2367C2213yes—
155#2366C2213yes—
156#2365C2213yes—
157#2363C2213yes—
158#2362C2213yes—
159#2361C2213yes—
160#2361C2213yes—
161#2361C2213yes—
162#2360C2213yes—
163#2357C2213yes—
164#2354C2213yes—
165#2354C2213yes—
166#2354C2213yes—
167#2352C2213yes—
168#2352C2213yes—
169#2351C2211yescharacteristic
170#2351C2211yescharacteristic
171#2351C2211yescharacteristic
172Q8×C4⋊C4C2213yes—
173Q8×C4⋊C4C2211yescharacteristic
174Q8×C4⋊C4C2211yescharacteristic
175Q8×C4⋊C4C2211yescharacteristic
176Q8×C4⋊C4C2211yescharacteristic
177Q8×C4⋊C4C2211yescharacteristic
178Q8×C4⋊C4C2211yescharacteristic
179Q8×C4⋊C4C2211yescharacteristic
180D4×C4⋊C4C2213yes—
181#2347C2213yes—
182#2347C2213yes—
183#2345C2213yes—
184#2344C2213yes—
185#2341C2211yescharacteristic
186#2341C2211yescharacteristic
187#2341C2211yescharacteristic
188#2341C2211yescharacteristic
189#2341C2211yescharacteristic
190#2341C2211yescharacteristic
191#2341C2211yescharacteristic
192#2341C2211yescharacteristic
193Q8×C22⋊C4C2211yescharacteristic
194Q8×C22⋊C4C2211yescharacteristic
195#2330C2213yes—
196#2330C2213yes—
197#2328C2213yes—
198#2326C2213yes—
199#2324C2213yes—
200#2323C2213yes—
201#2319C2213yes—
202#2319C2213yes—
203#2319C2213yes—
204#2314C2213yes—
205C4×C4⋊Q8C2213yes—
206C4×#124C2213yes—
207C4×C22⋊Q8C2213yes—
208C4×C22⋊Q8C2213yes—
209C4×#123C2213yes—
210C4×#123C2213yes—
211C4×#123C2216yes—
212C4×#121C2213yes—
213C4×#121C2213yes—
214C4×#121C2213yes—
215C4×#121C2213yes—
216#2298C2213yes—
217#2295C2213yes—
218#2293C2213yes—
219#2290C2213yes—
220#2290C2213yes—
221#2285C2213yes—
222#2283C2213yes—
223#2276C2213yes—
224#2276C2213yes—
225#2276C2211yescharacteristic
226#2276C2211yescharacteristic
227#2276C2211yescharacteristic
228#2276C2213yes—
229#2276C2211yescharacteristic
230#2276C2213yes—
231#2276C2211yescharacteristic
232C42×Q8C2211yescharacteristic
233C42×D4C2213yes—
234C2×C4×C4⋊C4C2213yes—
235C2×C4×C4⋊C4C2213yes—
236C2×C4×C4⋊C4C2213yes—
237C2×#376C2213yes—
238C22×#41C2311yescharacteristic
239C22×#41C2311yescharacteristic
240C23×Q8C2311yescharacteristic
241#557—28no—
242#550—28no—
243#548—28no—
244#548—28no—
245C2×C4⋊Q8C2313yes—
246C2×#127C2313yes—
247#529—424no—
248C2×#126C2316yes—
249C2×#126C2316yes—
250C2×#125C2313yes—
251C2×#125C2313yes—
252C2×#125C2316yes—
253C2×#124C2313yes—
254C2×#124C2313yes—
255C2×#124C2316yes—
256C2×#123C2313yes—
257C2×#123C2316yes—
258C2×#123C2313yes—
259C2×#123C2316yes—
260C2×C22⋊Q8C2313yes—
261C2×C22⋊Q8C2313yes—
262C2×C22⋊Q8C2313yes—
263C2×#121C2313yes—
264C2×#121C2313yes—
265C2×#121C2313yes—
266C2×#121C2313yes—
267C2×#121C2316yes—
268C2×#121C2313yes—
269#520—28no—
270C4×#41—28no—
271C2×C4×Q8—28no—
272C2×C4×Q8—28no—
273C2×C4×Q8—28no—
274C2×C4×Q8C2313yes—
275C2×C4×Q8C2313yes—
276C2×C4×Q8C2313yes—
277C2×C4×Q8C2311yescharacteristic
278C2×C4×Q8C2311yescharacteristic
279C2×C4×Q8C2311yescharacteristic
280C2×C4×Q8C2311yescharacteristic
281C2×C4×Q8C2311yescharacteristic
282C2×C4×Q8C2311yescharacteristic
283C2×C4×Q8C2311yescharacteristic
284C2×C4×Q8C2311yescharacteristic
285C2×C4×Q8C2311yescharacteristic
286C2×C4×Q8C2311yescharacteristic
287C2×C4×Q8C2313yes—
288C2×C4×Q8C2313yes—
289C2×C4×Q8C2313yes—
290C2×C4×Q8C2313yes—
291C2×C4×Q8C2316yes—
292C2×C4×Q8C2311yescharacteristic
293C2×C4×Q8C2311yescharacteristic
294C2×C4×D4C2313yes—
295C2×C4×D4C2313yes—
296C2×C4×D4C2313yes—
297C2×C4×D4C2313yes—
298C2×C4×D4C2313yes—
299C2×C4×D4C2313yes—
300C2×C4×D4C2313yes—
301C2×C4×D4C2313yes—
302C2×C4×D4C2316yes—
303C2×C4×D4C2316yes—
304C2×C4×D4C2313yes—
305C2×#117C2313yes—
306C2×#117C2313yes—
307C2×#117C2316yes—
308C2×#117C2316yes—
309C22×C4⋊C4C2313yes—
310C22×C4⋊C4C2313yes—
311C22×C4⋊C4C2313yes—
312C22×C4⋊C4C2313yes—
313C22×C42C2313yes—
314C22×C42C2313yes—
315C22×C42C2313yes—
316C22×C42C2313yes—
317C22×C42C2316yes—
318#401C2313yes—
319#401C2313yes—
320#400C2313yes—
321#400C2313yes—
322#400C2316yes—
323#400C2316yes—
324#400C2313yes—
325#400C2313yes—
326#400C2313yes—
327#400C2313yes—
328#400C2313yes—
329#400C2311yescharacteristic
330#400C2313yes—
331#400C2311yescharacteristic
332#400C2311yescharacteristic
333#400C2313yes—
334#399C2316yes—
335#399C2316yes—
336#399C2316yes—
337#399C2316yes—
338#398C2316yes—
339#398C2316yes—
340#398C2316yes—
341#398C2316yes—
342#398C2316yes—
343#398C2316yes—
344#398C2313yes—
345#398C2311yescharacteristic
346#398C2313yes—
347#398C2313yes—
348#397C2313yes—
349#397C2316yes—
350#397C2316yes—
351#397C2316yes—
352#397C2316yes—
353#397C2313yes—
354#397C2316yes—
355#397C2313yes—
356#397C2313yes—
357#397C2316yes—
358#397C2313yes—
359#397C2313yes—
360#397C2313yes—
361#397C2313yes—
362#396C2316yes—
363#396C2316yes—
364#396C2316yes—
365#396C2316yes—
366#396C2313yes—
367#396C2313yes—
368#395C2316yes—
369#394C2316yes—
370#394C2316yes—
371#394C2316yes—
372#394C2313yes—
373#394C2316yes—
374#394C2316yes—
375#394C2313yes—
376#393C2313yes—
377#393C2313yes—
378#391C2313yes—
379#391C2313yes—
380#391C2313yes—
381#391C2313yes—
382#391C2313yes—
383#391C2313yes—
384#391C2313yes—
385#390C2313yes—
386#390C2313yes—
387#390C2313yes—
388#390C2313yes—
389#390C2313yes—
390#390C2313yes—
391#390C2316yes—
392#390C2313yes—
393#390C2313yes—
394#390C2313yes—
395#390C2313yes—
396#390C2316yes—
397#390C2313yes—
398#390C2313yes—
399#390C2313yes—
400#390C2313yes—
401#390C2313yes—
402#390C2313yes—
403#390C2313yes—
404#390C2316yes—
405#390C2316yes—
406#389C2316yes—
407#389C2313yes—
408#389C2313yes—
409#389C2313yes—
410#389C2313yes—
411#389C2316yes—
412#389C2313yes—
413#389C2313yes—
414#389C2313yes—
415#389C2313yes—
416#389C2313yes—
417#389C2316yes—
418#389C2313yes—
419#389C2313yes—
420#389C2313yes—
421#389C2316yes—
422#389C2313yes—
423#389C2313yes—
424#389C2313yes—
425#389C2313yes—
426#389C2313yes—
427#389C2316yes—
428#389C2313yes—
429#389C2313yes—
430#389C2313yes—
431#389C2313yes—
432#389C2313yes—
433#389C2313yes—
434#389C2311yescharacteristic
435#388C2316yes—
436#388C2316yes—
437#388C2316yes—
438#388C2316yes—
439#388C2316yes—
440#388C2316yes—
441#388C2313yes—
442#388C2316yes—
443#388C2316yes—
444#388C2316yes—
445#388C2316yes—
446#388C2313yes—
447#388C2316yes—
448#388C2316yes—
449#388C2316yes—
450#388C2313yes—
451#388C2313yes—
452#388C2313yes—
453#388C2316yes—
454#388C2316yes—
455#388C2316yes—
456#388C2313yes—
457#388C2313yes—
458#388C2316yes—
459#388C2313yes—
460#388C2316yes—
461#388C2316yes—
462#388C2316yes—
463#388C2313yes—
464#388C2316yes—
465#388C2316yes—
466#388C2313yes—
467#388C2313yes—
468#388C2313yes—
469#388C2313yes—
470#388C2313yes—
471#387C2313yes—
472#387C2316yes—
473#387C2313yes—
474#387C2316yes—
475#387C2316yes—
476#387C2316yes—
477#387C2313yes—
478#387C2316yes—
479#387C2316yes—
480#387C2316yes—
481#387C2316yes—
482#387C2313yes—
483#387C2313yes—
484#387C2313yes—
485#387C2313yes—
486#387C2316yes—
487#387C2313yes—
488#387C2316yes—
489#387C2313yes—
490#387C2313yes—
491#387C2313yes—
492#387C2313yes—
493#387C2313yes—
494#387C2313yes—
495#387C2313yes—
496#387C2313yes—
497#387C2311yescharacteristic
498#387C2311yescharacteristic
499#386C2316yes—
500#386C2313yes—
501#386C2316yes—
502#386C2316yes—
503#386C2313yes—
504#386C2316yes—
505#386C2313yes—
506#386C2313yes—
507#386C2313yes—
508#386C2313yes—
509#386C2313yes—
510#386C2313yes—
511#385C2316yes—
512#385C2316yes—
513#385C2313yes—
514#385C2313yes—
515#385C2316yes—
516#385C2313yes—
517#385C2313yes—
518#385C2316yes—
519#385C2311yescharacteristic
520#385C2311yescharacteristic
521#385C2311yescharacteristic
522#385C2311yescharacteristic
523#384C2313yes—
524#384C2313yes—
525#384C2313yes—
526#384C2313yes—
527#384C2313yes—
528#384C2313yes—
529#384C2313yes—
530#383C2313yes—
531#383C2313yes—
532#382C2313yes—
533#382C2313yes—
534#382C2313yes—
535#382C2313yes—
536#382C2311yescharacteristic
537#381C2316yes—
538#381C2313yes—
539#381C2313yes—
540#381C2313yes—
541#381C2313yes—
542#380C2313yes—
543#380C2313yes—
544#380C2313yes—
545#380C2313yes—
546#380C2313yes—
547#380C2316yes—
548#380C2316yes—
549#380C2313yes—
550#380C2313yes—
551#380C2313yes—
552#380C2313yes—
553#380C2313yes—
554#380C2313yes—
555#380C2313yes—
556#380C2313yes—
557#380C2311yescharacteristic
558C4×C4⋊C4C2313yes—
559C4×C4⋊C4C2313yes—
560C4×C4⋊C4C2313yes—
561C4×C4⋊C4C2316yes—
562C4×C4⋊C4C2313yes—
563C4×C4⋊C4C2313yes—
564C4×C4⋊C4C2313yes—
565C4×C4⋊C4C2313yes—
566C4×C4⋊C4C2316yes—
567C4×C4⋊C4C2316yes—
568C4×C4⋊C4C2316yes—
569C4×C4⋊C4C2316yes—
570C4×C4⋊C4C2316yes—
571C4×C4⋊C4C2313yes—
572C4×C4⋊C4C2313yes—
573C4×C4⋊C4C2313yes—
574C4×C4⋊C4C2313yes—
575C4×C4⋊C4C2313yes—
576C4×C4⋊C4C2313yes—
577C4×C4⋊C4C2313yes—
578C4×C4⋊C4C2313yes—
579C4×C4⋊C4C2313yes—
580C4×C4⋊C4C2313yes—
581C4×C4⋊C4C2313yes—
582C4×C4⋊C4C2313yes—
583C4×C4⋊C4C2313yes—
584C4×C4⋊C4C2313yes—
585C4×C4⋊C4C2313yes—
586C4×C4⋊C4C2313yes—
587C4×C4⋊C4C2313yes—
588C4×C4⋊C4C2316yes—
589C4×C4⋊C4C2313yes—
590C4×C4⋊C4C2313yes—
591C4×C4⋊C4C2313yes—
592C4×C4⋊C4C2313yes—
593C4×C4⋊C4C2313yes—
594C4×C4⋊C4C2316yes—
595C4×C4⋊C4C2313yes—
596C4×C22⋊C4C2316yes—
597C4×C22⋊C4C2316yes—
598C4×C22⋊C4C2313yes—
599C4×C22⋊C4C2313yes—
600C4×C22⋊C4C2313yes—
601C4×C22⋊C4C2313yes—
602C4×C22⋊C4C2313yes—
603C4×C22⋊C4C2313yes—
604C4×C22⋊C4C2313yes—
605C4×C22⋊C4C2313yes—
606C4×C22⋊C4C2313yes—
607C4×C22⋊C4C2313yes—
608C4×C22⋊C4C2313yes—
609C4×C22⋊C4C2316yes—
610C4×C22⋊C4C2313yes—
611C4×C22⋊C4C2311yescharacteristic
612C4×C22⋊C4C2316yes—
613C4×C22⋊C4C2313yes—
614#376C2313yes—
615#376C2313yes—
616#376C2313yes—
617#376C2313yes—
618#376C2313yes—
619#376C2313yes—
620#376C2313yes—
621#376C2313yes—
622#376C2313yes—
623C2×#95C2313yes—
624C2×#95C2313yes—
625C2×#95C2311yescharacteristic
626C2×#95C2313yes—
627C43C2313yes—
628C2×#41—24no—
629C2×#41—24no—
630C2×#41—24no—
631C2×#41—24no—
632C2×#41—24no—
633C2×#41—24no—
634C22×Q8—24no—
635C22×Q8—24no—
636C22×Q8#4118yes—
637C22×Q8C2413yes—
638C22×Q8C2413yes—
639C22×Q8C2411yescharacteristic
640C22×D4C2413yes—
641C22×D4C2413yes—
642C22×D4C2413yes—
643C22×D4C2413yes—
644C22×D4C2416yes—
645C22×D4C2413yes—
646C23×C4C2413yes—
647C23×C4C2413yes—
648C23×C4C2413yes—
649C23×C4C2413yes—
650C23×C4C2413yes—
651C23×C4C2413yes—
652C23×C4C2411yescharacteristic
653C23×C4C2411yescharacteristic
654C23×C4C2413yes—
655C23×C4C2416yes—
656C23×C4C2413yes—
657C23×C4C2411yescharacteristic
658C4⋊Q8—212no—
659#127—212no—
660#126—412no—
661#126—412no—
662#125—212no—
663#125—212no—
664#125—412no—
665#124—212no—
666#124—212no—
667#124—412no—
668#123—212no—
669#123—412no—
670#123—46no—
671#123—412no—
672C22⋊Q8—212no—
673C22⋊Q8—212no—
674C22⋊Q8—212no—
675#121—212no—
676#121—212no—
677#121—212no—
678#121—212no—
679#121—46no—
680#121—412no—
681C4×Q8—212no—
682C4×Q8—212no—
683C4×Q8—24no—
684C4×Q8—24no—
685C4×Q8—24no—
686C4×Q8—24no—
687C4×Q8—24no—
688C4×Q8—24no—
689C4×Q8—24no—
690C4×Q8—24no—
691C4×Q8—24no—
692C4×Q8—24no—
693C4×Q8—212no—
694C4×Q8—212no—
695C4×Q8—212no—
696C4×Q8—212no—
697C4×Q8—212no—
698C4×Q8—412no—
699C4×Q8#4118yes—
700C4×Q8#4118yes—
701C4×D4—212no—
702C4×D4—212no—
703C4×D4—212no—
704C4×D4—212no—
705C4×D4—212no—
706C4×D4—212no—
707C4×D4—212no—
708C4×D4—212no—
709C4×D4—412no—
710C4×D4—46no—
711C4×D4—412no—
712#117—212no—
713#117—212no—
714#117—412no—
715#117—412no—
716C2×C4⋊C4—212no—
717C2×C4⋊C4—212no—
718C2×C4⋊C4—212no—
719C2×C4⋊C4—212no—
720C2×C4⋊C4C2413yes—
721C2×C4⋊C4C2413yes—
722C2×C4⋊C4C2413yes—
723C2×C4⋊C4C2413yes—
724C2×C4⋊C4C2413yes—
725C2×C4⋊C4C2413yes—
726C2×C4⋊C4C2416yes—
727C2×C4⋊C4C2416yes—
728C2×C4⋊C4C2416yes—
729C2×C4⋊C4C2411yescharacteristic
730C2×C4⋊C4C2413yes—
731C2×C4⋊C4C2413yes—
732C2×C4⋊C4C2413yes—
733C2×C4⋊C4C2413yes—
734C2×C4⋊C4C2411yescharacteristic
735C2×C4⋊C4C2413yes—
736C2×C4⋊C4C2413yes—
737C2×C4⋊C4C2413yes—
738C2×C4⋊C4C2413yes—
739C2×C4⋊C4C2411yescharacteristic
740C2×C4⋊C4C2413yes—
741C2×C4⋊C4C2413yes—
742C2×C4⋊C4C2413yes—
743C2×C4⋊C4C2413yes—
744C2×C4⋊C4C2413yes—
745C2×C4⋊C4C2413yes—
746C2×C4⋊C4C2413yes—
747C2×C4⋊C4C2416yes—
748C2×C4⋊C4C2416yes—
749C2×C4⋊C4C2416yes—
750C2×C4⋊C4C2413yes—
751C2×C4⋊C4C2416yes—
752C2×C4⋊C4C2416yes—
753C2×C4⋊C4C2413yes—
754C2×C4⋊C4C2416yes—
755C2×C4⋊C4C2413yes—
756C2×C4⋊C4C2413yes—
757C2×C4⋊C4C2416yes—
758C2×C4⋊C4C2411yescharacteristic
759C2×C4⋊C4C2411yescharacteristic
760C2×C4⋊C4C2411yescharacteristic
761C2×C4⋊C4C2411yescharacteristic
762C2×C4⋊C4C2411yescharacteristic
763C2×C4⋊C4C2411yescharacteristic
764C2×C4⋊C4C2411yescharacteristic
765C2×C4⋊C4C2413yes—
766C2×C4⋊C4C2416yes—
767C2×C4⋊C4C2413yes—
768C2×C4⋊C4C2413yes—
769C2×C4⋊C4C2413yes—
770C2×C4⋊C4C2413yes—
771C2×C22⋊C4C2413yes—
772C2×C22⋊C4C2413yes—
773C2×C22⋊C4C2416yes—
774C2×C22⋊C4C2413yes—
775C2×C22⋊C4C2411yescharacteristic
776C2×C22⋊C4C2411yescharacteristic
777C2×C22⋊C4C2413yes—
778C2×C22⋊C4C2413yes—
779C2×C22⋊C4C2413yes—
780C2×C22⋊C4C2413yes—
781C2×C22⋊C4C2413yes—
782C2×C22⋊C4C2413yes—
783C2×C22⋊C4C2413yes—
784C2×C22⋊C4C2413yes—
785C2×C22⋊C4C2416yes—
786C2×C22⋊C4C2416yes—
787C2×C22⋊C4C2411yescharacteristic
788C2×C22⋊C4C2416yes—
789C2×C22⋊C4C2416yes—
790C2×C22⋊C4C2416yes—
791C2×C22⋊C4C2416yes—
792C2×C22⋊C4C2416yes—
793C2×C22⋊C4C2413yes—
794C2×C22⋊C4C2413yes—
795C2×C22⋊C4C2413yes—
796C2×C22⋊C4C2416yes—
797C2×C22⋊C4C2413yes—
798C2×C22⋊C4C2416yes—
799C2×C22⋊C4C2413yes—
800C2×C22⋊C4C2413yes—
801C2×C22⋊C4C2413yes—
802C2×C22⋊C4C2413yes—
803C2×C22⋊C4C2413yes—
804C2×C22⋊C4C2416yes—
805C2×C22⋊C4C2413yes—
806C2×C22⋊C4C2413yes—
807C2×C22⋊C4C2413yes—
808C2×C22⋊C4C2413yes—
809C2×C22⋊C4C2411yescharacteristic
810C2×C42—212no—
811C2×C42—212no—
812C2×C42—212no—
813C2×C42—212no—
814C2×C42—412no—
815C2×C42C2413yes—
816C2×C42C2413yes—
817C2×C42C2413yes—
818C2×C42C2413yes—
819C2×C42C2413yes—
820C2×C42C2413yes—
821C2×C42C2413yes—
822C2×C42C2413yes—
823C2×C42C2413yes—
824C2×C42C2413yes—
825C2×C42C2413yes—
826C2×C42C2413yes—
827C2×C42C2413yes—
828C2×C42C2413yes—
829C2×C42C2413yes—
830C2×C42C2413yes—
831C2×C42C2413yes—
832C2×C42C2413yes—
833C2×C42C2411yescharacteristic
834C2×C42C2416yes—
835C2×C42C2416yes—
836C2×C42C2416yes—
837C2×C42C2413yes—
838C2×C42C2416yes—
839C2×C42C2416yes—
840C2×C42C2411yescharacteristic
841C2×C42C2413yes—
842C2×C42C2413yes—
843C2×C42C2413yes—
844#95C2411yescharacteristic
845#95C2411yescharacteristic
846#95C2411yescharacteristic
847#95C2411yescharacteristic
848#95C2413yes—
849#95C2413yes—
850#95C2413yes—
851#95C2413yes—
852#95C2413yes—
853#95C2413yes—
854#95C2413yes—
855#95C2413yes—
856#95C2413yes—
857#95C2413yes—
858#95C2413yes—
859#95C2413yes—
860#95C2411yescharacteristic
861#95C2413yes—
862#95C2413yes—
863#95C2413yes—
864#95C2411yescharacteristic
865#95C2411yescharacteristic
866#95C2413yes—
867#95C2411yescharacteristic
868#95C2411yescharacteristic
869#95C2411yescharacteristic
870#95C2411yescharacteristic
871#95C2411yescharacteristic
872#95C2411yescharacteristic
873#95C2411yescharacteristic
874#95C2413yes—
875#95C2413yes—
876#95C2413yes—
877#95C2413yes—
878#95C2413yes—
879#95C2413yes—
880#95C2413yes—
881#95C2413yes—
882#95C2413yes—
883#95C2413yes—
884#95C2413yes—
885#95C2413yes—
886#95C2416yes—
887#95C2416yes—
888#95C2416yes—
889#95C2416yes—
890#95C2416yes—
891#95C2413yes—
892#95C2413yes—
893#95C2416yes—
894#95C2413yes—
895#95C2411yescharacteristic
896#95C2411yescharacteristic
897#95C2413yes—
898#95C2413yes—
899#95C2413yes—
900#95C2413yes—
901#95C2413yes—
902#95C2413yes—
903#95C2413yes—
904#95C2413yes—
905#95C2413yes—
906#95C2413yes—
907#95C2413yes—
908#95C2413yes—
909#95C2413yes—
910C24C2513yes—
911C24C2513yes—
912C24C2511yescharacteristic
913#41—416no—
914#41—416no—
915C2×Q8—232no—
916C2×Q8—26no—
917C2×Q8—26no—
918C2×Q8—26no—
919C2×Q8—26no—
920C2×Q8—43no—
921C2×Q8C2×#41112yes—
922C2×Q8C2×#4114yes—
923C2×Q8C2×#4114yes—
924C2×Q8C2×#4114yes—
925C2×D4—26no—
926C2×D4—26no—
927C2×D4—26no—
928C2×D4—26no—
929C2×D4—26no—
930C2×D4—26no—
931C2×D4—26no—
932C2×D4—26no—
933C2×D4—26no—
934C2×D4—26no—
935C2×D4—26no—
936C2×D4—26no—
937C2×D4—26no—
938C2×D4—212no—
939C2×D4—46no—
940C2×D4—43no—
941C2×D4—43no—
942C2×D4—46no—
943C22×C4—26no—
944C22×C4—26no—
945C22×C4—22no—
946C22×C4—26no—
947C22×C4—26no—
948C22×C4—26no—
949C22×C4—26no—
950C22×C4—22no—
951C22×C4—22no—
952C22×C4—26no—
953C22×C4—22no—
954C22×C4—22no—
955C22×C4—26no—
956C22×C4—26no—
957C22×C4—26no—
958C22×C4—26no—
959C22×C4—26no—
960C22×C4—26no—
961C22×C4—26no—
962C22×C4—26no—
963C22×C4—26no—
964C22×C4—26no—
965C22×C4—26no—
966C22×C4—212no—
967C22×C4—43no—
968C22×C4—43no—
969C22×C4—41no—
970C22×C4—41no—
971C22×C4—43no—
972C22×C4—41no—
973C22×C4—41no—
974C22×C4—46no—
975C22×C4—43no—
976C22×C4—43no—
977C22×C4—46no—
978C22×C4C2×#41112yes—
979C22×C4C2511yescharacteristic
980C22×C4C2511yescharacteristic
981C22×C4C2511yescharacteristic
982C22×C4C2511yescharacteristic
983C22×C4C2511yescharacteristic
984C22×C4C2511yescharacteristic
985C22×C4C2511yescharacteristic
986C22×C4C2511yescharacteristic
987C22×C4C2513yes—
988C22×C4C2511yescharacteristic
989C22×C4C2511yescharacteristic
990C22×C4C2513yes—
991C22×C4C2513yes—
992C22×C4C2513yes—
993C22×C4C2513yes—
994C22×C4C2513yes—
995C22×C4C2513yes—
996C22×C4C2513yes—
997C22×C4C2513yes—
998C22×C4C2513yes—
999C22×C4C2511yescharacteristic
1000C22×C4C2511yescharacteristic
1001C22×C4C2513yes—
1002C22×C4C2513yes—
1003C22×C4C2513yes—
1004C22×C4C2511yescharacteristic
1005C22×C4C2511yescharacteristic
1006C22×C4C2513yes—
1007C4⋊C4—26no—
1008C4⋊C4—26no—
1009C4⋊C4—212no—
1010C4⋊C4—212no—
1011C4⋊C4—212no—
1012C4⋊C4—26no—
1013C4⋊C4—26no—
1014C4⋊C4—26no—
1015C4⋊C4—26no—
1016C4⋊C4—22no—
1017C4⋊C4—26no—
1018C4⋊C4—22no—
1019C4⋊C4—26no—
1020C4⋊C4—26no—
1021C4⋊C4—22no—
1022C4⋊C4—26no—
1023C4⋊C4—26no—
1024C4⋊C4—26no—
1025C4⋊C4—26no—
1026C4⋊C4—26no—
1027C4⋊C4—26no—
1028C4⋊C4—212no—
1029C4⋊C4—26no—
1030C4⋊C4—26no—
1031C4⋊C4—26no—
1032C4⋊C4—26no—
1033C4⋊C4—26no—
1034C4⋊C4—26no—
1035C4⋊C4—41no—
1036C4⋊C4—41no—
1037C4⋊C4—41no—
1038C4⋊C4—41no—
1039C4⋊C4—43no—
1040C4⋊C4—41no—
1041C4⋊C4—41no—
1042C4⋊C4—43no—
1043C4⋊C4—41no—
1044C4⋊C4—43no—
1045C4⋊C4—46no—
1046C4⋊C4—46no—
1047C4⋊C4—43no—
1048C4⋊C4—46no—
1049C4⋊C4—46no—
1050C4⋊C4—46no—
1051C4⋊C4—43no—
1052C4⋊C4—46no—
1053C4⋊C4—43no—
1054C4⋊C4—43no—
1055C4⋊C4—46no—
1056C4⋊C4C2×#41112yes—
1057C4⋊C4C2×#41112yes—
1058C22⋊C4—22no—
1059C22⋊C4—22no—
1060C22⋊C4—26no—
1061C22⋊C4—26no—
1062C22⋊C4—22no—
1063C22⋊C4—26no—
1064C22⋊C4—212no—
1065C22⋊C4—26no—
1066C22⋊C4—26no—
1067C22⋊C4—26no—
1068C22⋊C4—26no—
1069C22⋊C4—26no—
1070C22⋊C4—212no—
1071C22⋊C4—212no—
1072C22⋊C4—26no—
1073C22⋊C4—26no—
1074C22⋊C4—26no—
1075C22⋊C4—46no—
1076C22⋊C4—43no—
1077C22⋊C4—43no—
1078C22⋊C4—43no—
1079C22⋊C4—43no—
1080C22⋊C4—43no—
1081C22⋊C4—43no—
1082C22⋊C4—43no—
1083C22⋊C4—43no—
1084C22⋊C4—46no—
1085C22⋊C4—46no—
1086C22⋊C4—46no—
1087C22⋊C4—43no—
1088C22⋊C4—46no—
1089C22⋊C4—46no—
1090C22⋊C4—43no—
1091C22⋊C4—43no—
1092C22⋊C4—46no—
1093C22⋊C4—43no—
1094C22⋊C4—43no—
1095C22⋊C4—46no—
1096C22⋊C4H(5,𝔽2)14yes—
1097C42—22no—
1098C42—26no—
1099C42—26no—
1100C42—26no—
1101C42—26no—
1102C42—26no—
1103C42—26no—
1104C42—26no—
1105C42—26no—
1106C42—26no—
1107C42—26no—
1108C42—26no—
1109C42—26no—
1110C42—26no—
1111C42—26no—
1112C42—26no—
1113C42—26no—
1114C42—26no—
1115C42—26no—
1116C42—46no—
1117C42—46no—
1118C42—46no—
1119C42—46no—
1120C42—41no—
1121C42—43no—
1122C42—46no—
1123C42—43no—
1124C42C2×#41112yes—
1125C42C2×#41112yes—
1126C23—21no—
1127C23—21no—
1128C23—21no—
1129C23—21no—
1130C23—23no—
1131C23—23no—
1132C23—23no—
1133C23—23no—
1134C23—23no—
1135C23—23no—
1136C23—23no—
1137C23—23no—
1138C23—23no—
1139C23—23no—
1140C23—23no—
1141C23—23no—
1142C23—23no—
1143C23—23no—
1144C23C22×#4112yes—
1145C23C2×H(5,𝔽2)12yes—
1146C23#58512yes—
1147C23C2611yescharacteristic
1148Q8—224no—
1149Q8—412no—
1150Q8#529116yescomplemented
1151D4—412no—
1152D4—412no—
1153D4—412no—
1154D4—412no—
1155D4—812no—
1156D4—86no—
1157C2×C4—21no—
1158C2×C4—21no—
1159C2×C4—23no—
1160C2×C4—23no—
1161C2×C4—23no—
1162C2×C4—23no—
1163C2×C4—21no—
1164C2×C4—21no—
1165C2×C4—21no—
1166C2×C4—23no—
1167C2×C4—21no—
1168C2×C4—21no—
1169C2×C4—21no—
1170C2×C4—23no—
1171C2×C4—224no—
1172C2×C4—21no—
1173C2×C4—21no—
1174C2×C4—21no—
1175C2×C4—21no—
1176C2×C4—21no—
1177C2×C4—21no—
1178C2×C4—21no—
1179C2×C4—21no—
1180C2×C4—21no—
1181C2×C4—23no—
1182C2×C4—23no—
1183C2×C4—23no—
1184C2×C4—23no—
1185C2×C4—23no—
1186C2×C4—23no—
1187C2×C4—23no—
1188C2×C4—23no—
1189C2×C4—23no—
1190C2×C4—23no—
1191C2×C4—21no—
1192C2×C4—21no—
1193C2×C4—21no—
1194C2×C4—21no—
1195C2×C4—21no—
1196C2×C4—23no—
1197C2×C4—23no—
1198C2×C4—23no—
1199C2×C4—23no—
1200C2×C4—23no—
1201C2×C4—23no—
1202C2×C4—23no—
1203C2×C4—23no—
1204C2×C4—23no—
1205C2×C4—23no—
1206C2×C4—21no—
1207C2×C4—21no—
1208C2×C4—23no—
1209C2×C4—21no—
1210C2×C4—21no—
1211C2×C4—23no—
1212C2×C4—23no—
1213C2×C4—23no—
1214C2×C4—21no—
1215C2×C4—23no—
1216C2×C4—21no—
1217C2×C4—21no—
1218C2×C4—21no—
1219C2×C4—23no—
1220C2×C4—21no—
1221C2×C4—21no—
1222C2×C4—21no—
1223C2×C4—21no—
1224C2×C4—21no—
1225C2×C4—23no—
1226C2×C4—23no—
1227C2×C4—23no—
1228C2×C4—23no—
1229C2×C4—21no—
1230C2×C4—21no—
1231C2×C4—21no—
1232C2×C4—412no—
1233C2×C4—412no—
1234C2×C4—412no—
1235C2×C4—44no—
1236C2×C4—44no—
1237C2×C4—44no—
1238C2×C4—412no—
1239C2×C4—412no—
1240C2×C4—412no—
1241C2×C4—812no—
1242C2×C4—86no—
1243C2×C4C22×#4112yes—
1244C2×C4C22×#4112yes—
1245C2×C4C22×#4116yes—
1246C2×C4C22×#4116yes—
1247C2×C4C22×#4116yes—
1248C2×C4C22×#4116yes—
1249C2×C4C22×#4116yes—
1250C2×C4C22×#4116yes—
1251C2×C4C2×H(5,𝔽2)12yes—
1252C2×C4C2×H(5,𝔽2)12yes—
1253C22—22no—
1254C22—22no—
1255C22—22no—
1256C22—22no—
1257C22—22no—
1258C22—22no—
1259C22—43no—
1260C22—43no—
1261C22—43no—
1262C22—43no—
1263C22—43no—
1264C22—43no—
1265C22—43no—
1266C22—43no—
1267C22—43no—
1268C22—43no—
1269C22—43no—
1270C22—43no—
1271C22—43no—
1272C22—43no—
1273C22#351714yes—
1274C22C23×#4111yescharacteristic
1275C22C23×#4111yescharacteristic
1276C22C23×#4111yescharacteristic
1277C22C22×H(5,𝔽2)11yescharacteristic
1278C22C2×#58511yescharacteristic
1279C222−1+611yescharacteristic
1280C222−1+611yescharacteristic
1281C4—22no—
1282C4—26no—
1283C4—26no—
1284C4—22no—
1285C4—22no—
1286C4—22no—
1287C4—26no—
1288C4—43no—
1289C4—43no—
1290C4—43no—
1291C4—43no—
1292C4—41no—
1293C4—41no—
1294C4—43no—
1295C4—41no—
1296C4—41no—
1297C4—43no—
1298C4—43no—
1299C4—43no—
1300C4—43no—
1301C4—43no—
1302C4—41no—
1303C4—41no—
1304C4—41no—
1305C4—41no—
1306C4—41no—
1307C4—41no—
1308C4C2×#529112yes—
1309C2—24no—
1310C2—83no—
1311C2—83no—
1312C2C22×#52911yescharacteristic
1313C2C2×#351711yescharacteristic
1314C2#6285011yescharacteristic
1315C2#6298511yescharacteristic
1316C2#6298511yescharacteristic
1317C2#6300511yescharacteristic
1318C2#6300511yescharacteristic
subgroupG/H
center, commutator, Frattini, socle, cosocleC23C26
prime radical#36576C2
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23 ◁ G
LECSG ▷ C23 ▷ C1

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
1. #36588C2semidirect
3. #36486C2semidirect
4. #36483C2semidirect
5. #36483C2semidirect
6. #36435C2semidirect
7. #36118C2semidirect
8. #36117C2semidirect
9. #36049C2semidirect
10. #35968C2semidirect
11. #35945C2semidirect
12. #35898C2semidirect
13. #35898C2semidirect
14. #35895C2semidirect
15. #35884C2semidirect
16. #35868C2semidirect
17. #35609C2semidirect
18. #35605C2semidirect
19. #35593C2semidirect
20. #35587C2semidirect
21. #35271C2semidirect
22. #35229C2semidirect
23. #34811C2semidirect
24. #34763C2semidirect
25. #34337C2semidirect
26. #34295C2semidirect
27. #34294C2semidirect
28. #34263C2semidirect
29. #34193C2semidirect
30. C4×#548C2semidirect
31. C2×#2276C2semidirect
1150. Q8#529semidirect

Maximal subgroups

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

subgroupindex
#365882
#365762
#364862
#364832
#364352
#361182
#361172
#360492
#359682
#359452
#358982
#358952
#358842
#358682
#356092
#356052
#355932
#355872
#352712
#352292
#348112
#347632
#343372
#342952
#342942
#342632
#341932
C4×#5482
C2×#22762