Finite Group Databasebeta

← #7630844

Subgroups — #7630844

Order 512.

4742 conjugacy classes of subgroups.

The subgroup lattice has 1268 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#36050C213yesmaximal, complemented
2#36017C213yesmaximal
3#35971C211yesmaximal, characteristic, complemented
4#35910C211yesmaximal, characteristic, complemented
5#35901C213yesmaximal, complemented
6#35899C213yesmaximal, complemented
7#35883C211yesmaximal, characteristic, complemented
8#35883C211yesmaximal, characteristic, complemented
9#35870C213yesmaximal, complemented
10#35804C213yesmaximal, complemented
11#35803C213yesmaximal, complemented
12#35789C213yesmaximal, complemented
13#35786C211yesmaximal, characteristic, complemented
14#35723C211yesmaximal, characteristic, complemented
15#35723C211yesmaximal, characteristic, complemented
16#35700C211yesmaximal, characteristic
17#35217C213yesmaximal, complemented
18#35204C213yesmaximal, complemented
19#35187C213yesmaximal, complemented
20#35183C213yesmaximal, complemented
21#35163C213yesmaximal, complemented
22#35162C213yesmaximal, complemented
23#34640C213yesmaximal
24#34629C213yesmaximal, complemented
25#34336C211yesmaximal, characteristic, complemented
26#34311C211yesmaximal, characteristic, complemented
27#34291C211yesmaximal, characteristic, complemented
28#34291C211yesmaximal, characteristic, complemented
29#34262C211yesmaximal, characteristic, complemented
30#34262C211yesmaximal, characteristic, complemented
31C4×#519C211yesmaximal, characteristic, complemented
32C2×#557C2211yescharacteristic
33C2×D4×Q8C2211yescharacteristic
34C2×D4×Q8C2211yescharacteristic
35C2×D4×Q8C2211yescharacteristic
36C2×#519C2211yescharacteristic
37C2×#519C2211yescharacteristic
38C2×#519C2211yescharacteristic
39C2×#519C2211yescharacteristic
40C22×C4×Q8C2211yescharacteristic
41#2866C2216yes—
42#2865C2216yes—
43#2864C2216yes—
44#2863C2216yes—
45#2655C2213yes—
46#2655C2216yes—
47#2655C2216yes—
48#2655C2213yes—
49#2654C2213yes—
50#2654C2213yes—
51#2653C2213yes—
52#2653C2213yes—
53#2652C2213yes—
54#2652C2216yes—
55#2652C2213yes—
56#2651C2213yes—
57#2651C2213yes—
58#2650C2213yes—
59#2650C2213yes—
60#2649C2213yes—
61#2649C2213yes—
62#2648C2211yescharacteristic
63#2648C2213yes—
64#2647C2213yes—
65#2645C2213yes—
66#2645C2213yes—
67#2642C2213yes—
68#2629C2213yes—
69#2625C2213yes—
70#2625C2213yes—
71#2621C2213yes—
72#2596C2216yes—
73#2596C2216yes—
74#2594C2216yes—
75#2594C2216yes—
76#2593C2216yes—
77#2590C2216yes—
78#2588C2216yes—
79#2585C2216yes—
80#2582C2213yes—
81#2571C2213yes—
82#2570C2213yes—
83#2568C2213yes—
84#2565C2213yes—
85#2562C2213yes—
86#2546C2213yes—
87#2536C2213yes—
88#2533C2216yes—
89#2533C2216yes—
90#2532C2216yes—
91#2532C2216yes—
92#2529C2216yes—
93#2529C2216yes—
94#2528C2216yes—
95#2528C2216yes—
96#2524C2216yes—
97#2524C2216yes—
98#2523C2216yes—
99#2518C2216yes—
100#2518C2216yes—
101#2517C2216yes—
102#2514C2213yes—
103#2514C2213yes—
104#2514C2213yes—
105#2514C2213yes—
106#2514C2216yes—
107#2511C2213yes—
108#2511C2213yes—
109#2509C2213yes—
110#2508C2216yes—
111#2508C2213yes—
112#2508C2213yes—
113#2507C2213yes—
114#2499C2213yes—
115#2499C2213yes—
116#2497C2213yes—
117#2497C2213yes—
118#2495C2213yes—
119#2495C2213yes—
120#2494C2213yes—
121#2494C2213yes—
122#2492C2213yes—
123#2492C2213yes—
124#2489C2213yes—
125#2489C2213yes—
126#2485C2213yes—
127#2485C2213yes—
128#2453C2213yes—
129#2451C2213yes—
130#2446C2213yes—
131#2446C2213yes—
132#2446C2213yes—
133#2446C2213yes—
134#2441C2213yes—
135#2439C2213yes—
136#2429C2213yes—
137#2429C2213yes—
138#2423C2213yes—
139#2423C2213yes—
140#2421C2213yes—
141#2421C2213yes—
142#2415C2213yes—
143#2415C2213yes—
144#2402C2216yes—
145#2402C2213yes—
146#2402C2216yes—
147#2401C2213yes—
148#2401C2213yes—
149#2401C2216yes—
150#2401C2216yes—
151#2398C2213yes—
152#2396C2213yes—
153#2395C2213yes—
154#2395C2213yes—
155#2392C2213yes—
156#2370C2213yes—
157#2370C2213yes—
158#2369C2213yes—
159#2365C2213yes—
160#2365C2213yes—
161#2365C2213yes—
162#2362C2213yes—
163#2362C2213yes—
164#2362C2213yes—
165#2362C2213yes—
166#2360C2213yes—
167#2360C2213yes—
168#2356C2213yes—
169#2356C2213yes—
170#2355C2213yes—
171#2355C2213yes—
172#2355C2213yes—
173#2354C2213yes—
174#2352C2213yes—
175#2352C2213yes—
176#2351C2211yescharacteristic
177#2351C2211yescharacteristic
178#2351C2211yescharacteristic
179#2351C2211yescharacteristic
180#2351C2211yescharacteristic
181#2351C2211yescharacteristic
182Q8×C4⋊C4C2211yescharacteristic
183Q8×C4⋊C4C2211yescharacteristic
184Q8×C4⋊C4C2211yescharacteristic
185Q8×C4⋊C4C2211yescharacteristic
186#2347C2213yes—
187#2347C2213yes—
188#2346C2213yes—
189#2346C2213yes—
190Q8×C22⋊C4C2211yescharacteristic
191Q8×C22⋊C4C2211yescharacteristic
192Q8×C22⋊C4C2211yescharacteristic
193Q8×C22⋊C4C2211yescharacteristic
194Q8×C22⋊C4C2211yescharacteristic
195Q8×C22⋊C4C2211yescharacteristic
196Q8×C22⋊C4C2211yescharacteristic
197Q8×C22⋊C4C2211yescharacteristic
198Q8×C22⋊C4C2211yescharacteristic
199Q8×C22⋊C4C2211yescharacteristic
200#2331C2213yes—
201#2330C2213yes—
202#2327C2213yes—
203#2327C2213yes—
204#2323C2213yes—
205#2323C2213yes—
206#2323C2213yes—
207#2323C2213yes—
208#2320C2213yes—
209#2320C2213yes—
210#2314C2213yes—
211#2314C2213yes—
212C4×C4⋊Q8C2213yes—
213C4×#125C2213yes—
214C4×C22⋊Q8C2213yes—
215C4×C22⋊Q8C2213yes—
216#2298C2213yes—
217#2298C2213yes—
218#2295C2213yes—
219#2295C2213yes—
220#2295C2213yes—
221#2293C2213yes—
222#2290C2213yes—
223#2290C2213yes—
224#2276C2213yes—
225#2276C2211yescharacteristic
226#2276C2211yescharacteristic
227#2276C2211yescharacteristic
228#2276C2213yes—
229#2276C2211yescharacteristic
230#2274C2213yes—
231#2274C2213yes—
232C42×Q8C2211yescharacteristic
233C42×Q8C2213yes—
234C42×Q8C2213yes—
235C42×Q8C2211yescharacteristic
236C4×#117C2213yes—
237C4×#117C2213yes—
238C23×Q8C2311yescharacteristic
239C23×Q8C2311yescharacteristic
240C23×Q8C2311yescharacteristic
241#557—28no—
242D4×Q8—28no—
243D4×Q8—28no—
244D4×Q8—28no—
245C2×C4⋊Q8C2313yes—
246C2×C4⋊Q8C2313yes—
247C2×C4⋊Q8C2313yes—
248C2×C4⋊Q8C2313yes—
249C2×#125C2313yes—
250C2×#125C2313yes—
251C2×C22⋊Q8C2313yes—
252C2×C22⋊Q8C2313yes—
253C2×C22⋊Q8C2313yes—
254C2×C22⋊Q8C2313yes—
255C2×C22⋊Q8C2313yes—
256C2×C22⋊Q8C2313yes—
257#519—28no—
258#519—28no—
259#519—28no—
260#519—28no—
261C2×C4×Q8—28no—
262C2×C4×Q8C2313yes—
263C2×C4×Q8C2313yes—
264C2×C4×Q8C2313yes—
265C2×C4×Q8C2313yes—
266C2×C4×Q8C2313yes—
267C2×C4×Q8C2311yescharacteristic
268C2×C4×Q8C2311yescharacteristic
269C2×C4×Q8C2311yescharacteristic
270C2×C4×Q8C2311yescharacteristic
271C2×C4×Q8C2311yescharacteristic
272C2×C4×Q8C2311yescharacteristic
273C2×C4×Q8C2311yescharacteristic
274C2×C4×Q8C2311yescharacteristic
275C2×C4×Q8C2311yescharacteristic
276C2×C4×Q8C2311yescharacteristic
277C2×C4×Q8C2313yes—
278C2×C4×Q8C2313yes—
279C2×C4×Q8C2313yes—
280C2×C4×Q8C2313yes—
281C2×C4×Q8C2313yes—
282C2×C4×Q8C2313yes—
283C2×C4×Q8C2311yescharacteristic
284C2×C4×Q8C2311yescharacteristic
285C2×C4×D4C2313yes—
286C2×C4×D4C2313yes—
287C2×C4×D4C2313yes—
288C2×#117C2313yes—
289C2×#117C2313yes—
290C2×#117C2313yes—
291C2×#117C2313yes—
292C2×#117C2313yes—
293C2×#117C2313yes—
294C2×#117C2313yes—
295C2×#117C2313yes—
296C22×C4⋊C4C2313yes—
297C22×C42C2313yes—
298#401C2316yes—
299#401C2316yes—
300#401C2313yes—
301#401C2313yes—
302#400C2316yes—
303#400C2313yes—
304#400C2316yes—
305#400C2313yes—
306#400C2313yes—
307#400C2316yes—
308#400C2316yes—
309#400C2316yes—
310#400C2316yes—
311#400C2316yes—
312#400C2316yes—
313#400C2313yes—
314#400C2316yes—
315#400C2313yes—
316#400C2313yes—
317#400C2316yes—
318#400C2316yes—
319#400C2311yescharacteristic
320#400C2313yes—
321#400C2313yes—
322#400C2313yes—
323#400C2313yes—
324#400C2313yes—
325#400C2313yes—
326#400C2313yes—
327#400C2313yes—
328#399C2313yes—
329#399C2313yes—
330#399C2313yes—
331#398C2313yes—
332#398C2316yes—
333#398C2313yes—
334#398C2313yes—
335#398C2316yes—
336#398C2316yes—
337#398C2313yes—
338#398C2313yes—
339#398C2316yes—
340#398C2316yes—
341#398C2316yes—
342#398C2313yes—
343#398C2316yes—
344#398C2313yes—
345#398C2313yes—
346#398C2313yes—
347#397C2313yes—
348#397C2313yes—
349#397C2313yes—
350#397C2313yes—
351#397C2313yes—
352#397C2316yes—
353#397C2313yes—
354#397C2313yes—
355#397C2316yes—
356#397C2316yes—
357#397C2311yescharacteristic
358#397C2311yescharacteristic
359#397C2313yes—
360#397C2313yes—
361#397C2313yes—
362#397C2313yes—
363#397C2313yes—
364#397C2313yes—
365#396C2313yes—
366#396C2313yes—
367#396C2313yes—
368#396C2316yes—
369#396C2313yes—
370#396C2311yescharacteristic
371#396C2313yes—
372#395C2313yes—
373#394C2313yes—
374#394C2313yes—
375#394C2313yes—
376#394C2313yes—
377#394C2311yescharacteristic
378#394C2313yes—
379#394C2311yescharacteristic
380#394C2313yes—
381#394C2311yescharacteristic
382#393C2313yes—
383#393C2313yes—
384#393C2313yes—
385#392C2311yescharacteristic
386#391C2313yes—
387#391C2313yes—
388#391C2313yes—
389#391C2313yes—
390#391C2313yes—
391#391C2313yes—
392#391C2313yes—
393#391C2313yes—
394#391C2316yes—
395#391C2313yes—
396#391C2313yes—
397#391C2313yes—
398#391C2313yes—
399#391C2313yes—
400#391C2313yes—
401#391C2316yes—
402#391C2313yes—
403#391C2316yes—
404#391C2313yes—
405#391C2313yes—
406#391C2313yes—
407#391C2313yes—
408#391C2313yes—
409#391C2313yes—
410#391C2313yes—
411#390C2313yes—
412#390C2311yescharacteristic
413#389C2313yes—
414#389C2313yes—
415#389C2313yes—
416#389C2316yes—
417#389C2313yes—
418#389C2313yes—
419#389C2313yes—
420#389C2313yes—
421#389C2316yes—
422#389C2313yes—
423#389C2313yes—
424#389C2316yes—
425#389C2316yes—
426#389C2313yes—
427#389C2313yes—
428#389C2316yes—
429#389C2313yes—
430#389C2313yes—
431#389C2316yes—
432#389C2313yes—
433#389C2313yes—
434#389C2313yes—
435#389C2313yes—
436#389C2316yes—
437#389C2313yes—
438#389C2313yes—
439#389C2313yes—
440#389C2313yes—
441#389C2313yes—
442#389C2313yes—
443#389C2316yes—
444#389C2313yes—
445#388C2316yes—
446#388C2316yes—
447#388C2313yes—
448#388C2313yes—
449#388C2316yes—
450#388C2316yes—
451#388C2313yes—
452#388C2313yes—
453#388C2313yes—
454#388C2313yes—
455#388C2316yes—
456#388C2316yes—
457#388C2316yes—
458#388C2316yes—
459#388C2316yes—
460#388C2316yes—
461#388C2316yes—
462#388C2316yes—
463#388C2313yes—
464#388C2313yes—
465#388C2316yes—
466#388C2313yes—
467#388C2313yes—
468#388C2316yes—
469#388C2313yes—
470#388C2313yes—
471#388C2313yes—
472#388C2313yes—
473#388C2311yescharacteristic
474#388C2311yescharacteristic
475#387C2313yes—
476#387C2316yes—
477#387C2316yes—
478#387C2316yes—
479#387C2316yes—
480#387C2316yes—
481#387C2316yes—
482#387C2316yes—
483#387C2316yes—
484#387C2316yes—
485#387C2313yes—
486#387C2313yes—
487#387C2316yes—
488#387C2316yes—
489#387C2316yes—
490#387C2316yes—
491#387C2313yes—
492#387C2313yes—
493#387C2316yes—
494#387C2316yes—
495#387C2316yes—
496#387C2316yes—
497#387C2316yes—
498#387C2316yes—
499#387C2316yes—
500#387C2316yes—
501#387C2316yes—
502#387C2316yes—
503#387C2313yes—
504#387C2316yes—
505#387C2313yes—
506#387C2316yes—
507#387C2316yes—
508#387C2316yes—
509#387C2316yes—
510#387C2316yes—
511#387C2313yes—
512#387C2313yes—
513#387C2313yes—
514#387C2313yes—
515#387C2313yes—
516#387C2313yes—
517#387C2311yescharacteristic
518#387C2313yes—
519#387C2313yes—
520#386C2313yes—
521#386C2313yes—
522#386C2311yescharacteristic
523#386C2311yescharacteristic
524#385C2313yes—
525#385C2313yes—
526#385C2313yes—
527#385C2313yes—
528#384C2313yes—
529#384C2313yes—
530#384C2313yes—
531#384C2313yes—
532#383C2316yes—
533#383C2316yes—
534#383C2316yes—
535#383C2316yes—
536#382C2313yes—
537#382C2313yes—
538#382C2316yes—
539#382C2313yes—
540#382C2313yes—
541#382C2313yes—
542#382C2316yes—
543#382C2316yes—
544#382C2316yes—
545#382C2313yes—
546#380C2313yes—
547#380C2313yes—
548#380C2313yes—
549#380C2313yes—
550#380C2313yes—
551#380C2313yes—
552#380C2313yes—
553#380C2313yes—
554#380C2313yes—
555#380C2313yes—
556C4×C4⋊C4C2313yes—
557C4×C4⋊C4C2313yes—
558C4×C4⋊C4C2316yes—
559C4×C4⋊C4C2316yes—
560C4×C4⋊C4C2313yes—
561C4×C4⋊C4C2316yes—
562C4×C4⋊C4C2316yes—
563C4×C4⋊C4C2313yes—
564C4×C4⋊C4C2313yes—
565C4×C4⋊C4C2313yes—
566C4×C4⋊C4C2313yes—
567C4×C4⋊C4C2316yes—
568C4×C4⋊C4C2316yes—
569C4×C4⋊C4C2316yes—
570C4×C4⋊C4C2316yes—
571C4×C4⋊C4C2316yes—
572C4×C4⋊C4C2316yes—
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⋊C4C2313yes—
589C4×C4⋊C4C2316yes—
590C4×C4⋊C4C2316yes—
591C4×C4⋊C4C2313yes—
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×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⋊C4C2313yes—
610C4×C22⋊C4C2316yes—
611C4×C22⋊C4C2316yes—
612C4×C22⋊C4C2311yescharacteristic
613C4×C22⋊C4C2313yes—
614C4×C22⋊C4C2313yes—
615C4×C22⋊C4C2313yes—
616C4×C22⋊C4C2316yes—
617#376C2313yes—
618#376C2313yes—
619#376C2316yes—
620#376C2316yes—
621#376C2313yes—
622#376C2313yes—
623#376C2316yes—
624C43C2313yes—
625C43C2316yes—
626C43C2313yes—
627C22×Q8—24no—
628C22×Q8—24no—
629C22×Q8—24no—
630C22×Q8—24no—
631C22×Q8—24no—
632C22×Q8—24no—
633C22×Q8—24no—
634C22×Q8—24no—
635C22×Q8#4118yes—
636C22×Q8C2413yes—
637C22×Q8C2413yes—
638C22×Q8C2413yes—
639C22×Q8C2413yes—
640C22×Q8C2411yescharacteristic
641C22×D4C2411yescharacteristic
642C22×D4C2411yescharacteristic
643C22×D4C2411yescharacteristic
644C23×C4C2413yes—
645C23×C4C2413yes—
646C23×C4C2413yes—
647C23×C4C2413yes—
648C23×C4C2411yescharacteristic
649C4⋊Q8—212no—
650C4⋊Q8—212no—
651C4⋊Q8—212no—
652C4⋊Q8—212no—
653#125—212no—
654#125—212no—
655C22⋊Q8—212no—
656C22⋊Q8—212no—
657C22⋊Q8—212no—
658C22⋊Q8—212no—
659C22⋊Q8—212no—
660C22⋊Q8—212no—
661C4×Q8—24no—
662C4×Q8—212no—
663C4×Q8—212no—
664C4×Q8—24no—
665C4×Q8—24no—
666C4×Q8—24no—
667C4×Q8—24no—
668C4×Q8—24no—
669C4×Q8—24no—
670C4×Q8—24no—
671C4×Q8—24no—
672C4×Q8—24no—
673C4×Q8—212no—
674C4×Q8—212no—
675C4×Q8—212no—
676C4×Q8—212no—
677C4×Q8—212no—
678C4×Q8—212no—
679C4×Q8—212no—
680C4×Q8—212no—
681C4×Q8—212no—
682C4×Q8#4118yes—
683C4×Q8#4118yes—
684C4×D4—212no—
685C4×D4—212no—
686C4×D4—212no—
687#117—212no—
688#117—212no—
689#117—212no—
690#117—212no—
691#117—212no—
692#117—212no—
693#117—212no—
694#117—212no—
695C2×C4⋊C4—212no—
696C2×C4⋊C4C2413yes—
697C2×C4⋊C4C2416yes—
698C2×C4⋊C4C2413yes—
699C2×C4⋊C4C2413yes—
700C2×C4⋊C4C2413yes—
701C2×C4⋊C4C2413yes—
702C2×C4⋊C4C2413yes—
703C2×C4⋊C4C2413yes—
704C2×C4⋊C4C2413yes—
705C2×C4⋊C4C2413yes—
706C2×C4⋊C4C2413yes—
707C2×C4⋊C4C2413yes—
708C2×C4⋊C4C2413yes—
709C2×C4⋊C4C2413yes—
710C2×C4⋊C4C2413yes—
711C2×C4⋊C4C2413yes—
712C2×C4⋊C4C2413yes—
713C2×C4⋊C4C2413yes—
714C2×C4⋊C4C2411yescharacteristic
715C2×C4⋊C4C2413yes—
716C2×C4⋊C4C2413yes—
717C2×C4⋊C4C2413yes—
718C2×C4⋊C4C2413yes—
719C2×C4⋊C4C2413yes—
720C2×C4⋊C4C2413yes—
721C2×C4⋊C4C2416yes—
722C2×C4⋊C4C2416yes—
723C2×C4⋊C4C2416yes—
724C2×C4⋊C4C2416yes—
725C2×C4⋊C4C2413yes—
726C2×C4⋊C4C2413yes—
727C2×C4⋊C4C2413yes—
728C2×C4⋊C4C2411yescharacteristic
729C2×C4⋊C4C2411yescharacteristic
730C2×C4⋊C4C2413yes—
731C2×C4⋊C4C2413yes—
732C2×C4⋊C4C2411yescharacteristic
733C2×C4⋊C4C2413yes—
734C2×C4⋊C4C2411yescharacteristic
735C2×C4⋊C4C2413yes—
736C2×C4⋊C4C2413yes—
737C2×C4⋊C4C2413yes—
738C2×C4⋊C4C2416yes—
739C2×C4⋊C4C2416yes—
740C2×C4⋊C4C2416yes—
741C2×C4⋊C4C2413yes—
742C2×C4⋊C4C2413yes—
743C2×C4⋊C4C2413yes—
744C2×C4⋊C4C2416yes—
745C2×C4⋊C4C2413yes—
746C2×C4⋊C4C2413yes—
747C2×C4⋊C4C2413yes—
748C2×C4⋊C4C2413yes—
749C2×C4⋊C4C2413yes—
750C2×C4⋊C4C2413yes—
751C2×C22⋊C4C2411yescharacteristic
752C2×C22⋊C4C2413yes—
753C2×C22⋊C4C2411yescharacteristic
754C2×C22⋊C4C2413yes—
755C2×C22⋊C4C2411yescharacteristic
756C2×C22⋊C4C2411yescharacteristic
757C2×C22⋊C4C2413yes—
758C2×C22⋊C4C2413yes—
759C2×C22⋊C4C2413yes—
760C2×C22⋊C4C2413yes—
761C2×C22⋊C4C2413yes—
762C2×C22⋊C4C2413yes—
763C2×C22⋊C4C2413yes—
764C2×C22⋊C4C2413yes—
765C2×C22⋊C4C2413yes—
766C2×C22⋊C4C2413yes—
767C2×C22⋊C4C2411yescharacteristic
768C2×C22⋊C4C2411yescharacteristic
769C2×C22⋊C4C2411yescharacteristic
770C2×C22⋊C4C2411yescharacteristic
771C2×C22⋊C4C2411yescharacteristic
772C2×C22⋊C4C2411yescharacteristic
773C2×C22⋊C4C2411yescharacteristic
774C2×C22⋊C4C2411yescharacteristic
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×C42—212no—
786C2×C42C2413yes—
787C2×C42C2413yes—
788C2×C42C2413yes—
789C2×C42C2416yes—
790C2×C42C2416yes—
791C2×C42C2416yes—
792C2×C42C2416yes—
793C2×C42C2413yes—
794C2×C42C2413yes—
795C2×C42C2413yes—
796C2×C42C2413yes—
797C2×C42C2413yes—
798C2×C42C2413yes—
799C2×C42C2413yes—
800C2×C42C2413yes—
801C2×C42C2413yes—
802C2×C42C2413yes—
803C2×C42C2411yescharacteristic
804C2×C42C2411yescharacteristic
805C2×C42C2413yes—
806C2×C42C2413yes—
807C2×C42C2413yes—
808C2×C42C2413yes—
809C2×C42C2413yes—
810C2×C42C2416yes—
811C2×C42C2416yes—
812C2×C42C2416yes—
813C2×C42C2416yes—
814C2×C42C2413yes—
815C2×C42C2413yes—
816#95C2413yes—
817#95C2411yescharacteristic
818#95C2413yes—
819#95C2411yescharacteristic
820#95C2411yescharacteristic
821#95C2411yescharacteristic
822#95C2413yes—
823#95C2413yes—
824#95C2413yes—
825#95C2413yes—
826#95C2416yes—
827#95C2416yes—
828#95C2413yes—
829#95C2413yes—
830#95C2413yes—
831#95C2413yes—
832#95C2413yes—
833#95C2413yes—
834#95C2413yes—
835#95C2413yes—
836#95C2413yes—
837#95C2413yes—
838#95C2416yes—
839#95C2416yes—
840#95C2416yes—
841#95C2416yes—
842#95C2413yes—
843#95C2413yes—
844#95C2413yes—
845#95C2413yes—
846#95C2413yes—
847#95C2413yes—
848#95C2416yes—
849#95C2416yes—
850#95C2413yes—
851#95C2413yes—
852#95C2413yes—
853#95C2416yes—
854#95C2416yes—
855#95C2413yes—
856#95C2413yes—
857#95C2413yes—
858#95C2413yes—
859#95C2413yes—
860#95C2413yes—
861#95C2413yes—
862#95C2413yes—
863#95C2413yes—
864#95C2413yes—
865#95C2411yescharacteristic
866#95C2411yescharacteristic
867#95C2411yescharacteristic
868#95C2411yescharacteristic
869#95C2411yescharacteristic
870#95C2413yes—
871#95C2411yescharacteristic
872#95C2416yes—
873#95C2416yes—
874#95C2416yes—
875#95C2416yes—
876#95C2416yes—
877#95C2416yes—
878#95C2413yes—
879#95C2413yes—
880#95C2413yes—
881#95C2413yes—
882#95C2413yes—
883#95C2413yes—
884#95C2416yes—
885#95C2416yes—
886#95C2413yes—
887#95C2413yes—
888#95C2413yes—
889#95C2413yes—
890C24C2511yescharacteristic
891C24C2511yescharacteristic
892C24C2511yescharacteristic
893C2×Q8—232no—
894C2×Q8—26no—
895C2×Q8—26no—
896C2×Q8—26no—
897C2×Q8—26no—
898C2×Q8—26no—
899C2×Q8—26no—
900C2×Q8—26no—
901C2×Q8—26no—
902C2×Q8—26no—
903C2×Q8—43no—
904C2×Q8—43no—
905C2×Q8—416no—
906C2×Q8—416no—
907C2×Q8C2×#41112yes—
908C2×Q8C2×#4114yes—
909C2×Q8C2×#4114yes—
910C2×Q8C2×#4114yes—
911C2×D4—22no—
912C2×D4—22no—
913C2×D4—22no—
914C2×D4—41no—
915C2×D4—41no—
916C2×D4—41no—
917C2×D4—41no—
918C2×D4—41no—
919C2×D4—41no—
920C22×C4—26no—
921C22×C4—26no—
922C22×C4—22no—
923C22×C4—26no—
924C22×C4—26no—
925C22×C4—26no—
926C22×C4—26no—
927C22×C4—26no—
928C22×C4—26no—
929C22×C4—26no—
930C22×C4—41no—
931C22×C4—41no—
932C22×C4—43no—
933C22×C4—43no—
934C22×C4C2×#41112yes—
935C22×C4C2511yescharacteristic
936C22×C4C2511yescharacteristic
937C22×C4C2513yes—
938C22×C4C2513yes—
939C22×C4C2511yescharacteristic
940C22×C4C2511yescharacteristic
941C22×C4C2513yes—
942C22×C4C2513yes—
943C22×C4C2511yescharacteristic
944C22×C4C2513yes—
945C22×C4C2511yescharacteristic
946C22×C4C2513yes—
947C22×C4C2511yescharacteristic
948C22×C4C2513yes—
949C22×C4C2513yes—
950C22×C4C2511yescharacteristic
951C22×C4C2513yes—
952C22×C4C2511yescharacteristic
953C22×C4C2511yescharacteristic
954C22×C4C2513yes—
955C22×C4C2513yes—
956C22×C4C2513yes—
957C22×C4C2513yes—
958C22×C4C2511yescharacteristic
959C22×C4C2513yes—
960C22×C4C2511yescharacteristic
961C22×C4C2513yes—
962C22×C4C2513yes—
963C4⋊C4—212no—
964C4⋊C4—26no—
965C4⋊C4—26no—
966C4⋊C4—26no—
967C4⋊C4—26no—
968C4⋊C4—26no—
969C4⋊C4—26no—
970C4⋊C4—26no—
971C4⋊C4—26no—
972C4⋊C4—26no—
973C4⋊C4—26no—
974C4⋊C4—26no—
975C4⋊C4—26no—
976C4⋊C4—26no—
977C4⋊C4—26no—
978C4⋊C4—26no—
979C4⋊C4—26no—
980C4⋊C4—26no—
981C4⋊C4—22no—
982C4⋊C4—26no—
983C4⋊C4—26no—
984C4⋊C4—26no—
985C4⋊C4—26no—
986C4⋊C4—26no—
987C4⋊C4—26no—
988C4⋊C4—212no—
989C4⋊C4—212no—
990C4⋊C4—212no—
991C4⋊C4—212no—
992C4⋊C4—41no—
993C4⋊C4—43no—
994C4⋊C4—43no—
995C4⋊C4—46no—
996C4⋊C4—43no—
997C4⋊C4—43no—
998C4⋊C4—43no—
999C4⋊C4—41no—
1000C4⋊C4—41no—
1001C4⋊C4—43no—
1002C4⋊C4—43no—
1003C4⋊C4—43no—
1004C4⋊C4—43no—
1005C4⋊C4—46no—
1006C4⋊C4—43no—
1007C4⋊C4—46no—
1008C4⋊C4—43no—
1009C4⋊C4—46no—
1010C4⋊C4—43no—
1011C4⋊C4—43no—
1012C4⋊C4—43no—
1013C4⋊C4—41no—
1014C4⋊C4—43no—
1015C4⋊C4—43no—
1016C4⋊C4C2×#41112yes—
1017C4⋊C4C2×#41112yes—
1018C22⋊C4—22no—
1019C22⋊C4—26no—
1020C22⋊C4—26no—
1021C22⋊C4—26no—
1022C22⋊C4—26no—
1023C22⋊C4—26no—
1024C22⋊C4—22no—
1025C22⋊C4—22no—
1026C22⋊C4—26no—
1027C22⋊C4—22no—
1028C22⋊C4—26no—
1029C22⋊C4—26no—
1030C22⋊C4—26no—
1031C22⋊C4—26no—
1032C22⋊C4—41no—
1033C22⋊C4—41no—
1034C22⋊C4—43no—
1035C22⋊C4—43no—
1036C22⋊C4—41no—
1037C22⋊C4—41no—
1038C22⋊C4—43no—
1039C22⋊C4—43no—
1040C22⋊C4—43no—
1041C22⋊C4—43no—
1042C22⋊C4—43no—
1043C22⋊C4—41no—
1044C22⋊C4—43no—
1045C22⋊C4—41no—
1046C22⋊C4—43no—
1047C22⋊C4—41no—
1048C22⋊C4—43no—
1049C22⋊C4—41no—
1050C22⋊C4—41no—
1051C22⋊C4—41no—
1052C42—26no—
1053C42—26no—
1054C42—26no—
1055C42—212no—
1056C42—212no—
1057C42—26no—
1058C42—26no—
1059C42—26no—
1060C42—26no—
1061C42—26no—
1062C42—212no—
1063C42—212no—
1064C42—26no—
1065C42—26no—
1066C42—26no—
1067C42—26no—
1068C42—43no—
1069C42—43no—
1070C42—41no—
1071C42—43no—
1072C42—43no—
1073C42—43no—
1074C42—46no—
1075C42—46no—
1076C42—43no—
1077C42—41no—
1078C42—46no—
1079C42—46no—
1080C42C2×#41112yes—
1081C42C2×#41112yes—
1082C23—21no—
1083C23—21no—
1084C23—21no—
1085C23—21no—
1086C23—21no—
1087C23—21no—
1088C23—21no—
1089C23—21no—
1090C23—21no—
1091C23—21no—
1092C23—21no—
1093C23—21no—
1094C23—21no—
1095C23—21no—
1096C23—21no—
1097C23—21no—
1098C23—21no—
1099C23—21no—
1100C23—21no—
1101C23—21no—
1102C23C22×#4112yes—
1103C23C2611yescharacteristic
1104Q8—224no—
1105Q8—412no—
1106Q8—412no—
1107Q8—86no—
1108Q8#529116yes—
1109D4—44no—
1110D4—44no—
1111D4—44no—
1112C2×C4—23no—
1113C2×C4—23no—
1114C2×C4—21no—
1115C2×C4—21no—
1116C2×C4—23no—
1117C2×C4—23no—
1118C2×C4—21no—
1119C2×C4—23no—
1120C2×C4—21no—
1121C2×C4—23no—
1122C2×C4—224no—
1123C2×C4—21no—
1124C2×C4—21no—
1125C2×C4—23no—
1126C2×C4—21no—
1127C2×C4—23no—
1128C2×C4—23no—
1129C2×C4—23no—
1130C2×C4—23no—
1131C2×C4—21no—
1132C2×C4—21no—
1133C2×C4—21no—
1134C2×C4—21no—
1135C2×C4—21no—
1136C2×C4—21no—
1137C2×C4—21no—
1138C2×C4—23no—
1139C2×C4—23no—
1140C2×C4—23no—
1141C2×C4—23no—
1142C2×C4—23no—
1143C2×C4—23no—
1144C2×C4—23no—
1145C2×C4—23no—
1146C2×C4—23no—
1147C2×C4—23no—
1148C2×C4—23no—
1149C2×C4—21no—
1150C2×C4—23no—
1151C2×C4—21no—
1152C2×C4—23no—
1153C2×C4—21no—
1154C2×C4—23no—
1155C2×C4—23no—
1156C2×C4—23no—
1157C2×C4—23no—
1158C2×C4—23no—
1159C2×C4—23no—
1160C2×C4—23no—
1161C2×C4—23no—
1162C2×C4—23no—
1163C2×C4—23no—
1164C2×C4—21no—
1165C2×C4—21no—
1166C2×C4—21no—
1167C2×C4—23no—
1168C2×C4—23no—
1169C2×C4—21no—
1170C2×C4—21no—
1171C2×C4—21no—
1172C2×C4—23no—
1173C2×C4—21no—
1174C2×C4—23no—
1175C2×C4—23no—
1176C2×C4—21no—
1177C2×C4—21no—
1178C2×C4—21no—
1179C2×C4—21no—
1180C2×C4—21no—
1181C2×C4—21no—
1182C2×C4—23no—
1183C2×C4—21no—
1184C2×C4—23no—
1185C2×C4—23no—
1186C2×C4—21no—
1187C2×C4—21no—
1188C2×C4—21no—
1189C2×C4—44no—
1190C2×C4—412no—
1191C2×C4—412no—
1192C2×C4—86no—
1193C2×C4C22×#4116yes—
1194C2×C4C22×#4112yes—
1195C2×C4C22×#4116yes—
1196C2×C4C22×#4116yes—
1197C2×C4C22×#4112yes—
1198C2×C4C22×#4116yes—
1199C2×C4C22×#4116yes—
1200C2×C4C22×#4116yes—
1201C22—22no—
1202C22—22no—
1203C22—22no—
1204C22—41no—
1205C22—41no—
1206C22—41no—
1207C22—41no—
1208C22—41no—
1209C22—41no—
1210C22—41no—
1211C22—41no—
1212C22—41no—
1213C22—41no—
1214C22—41no—
1215C22—41no—
1216C22—41no—
1217C22—41no—
1218C22—41no—
1219C22—41no—
1220C22—41no—
1221C22—41no—
1222C22C23×#4111yescharacteristic
1223C22C23×#4111yescharacteristic
1224C22C23×#4111yescharacteristic
1225C222−1+611yescharacteristic
1226C222−1+611yescharacteristic
1227C222−1+611yescharacteristic
1228C222−1+611yescharacteristic
1229C4—22no—
1230C4—22no—
1231C4—26no—
1232C4—26no—
1233C4—26no—
1234C4—43no—
1235C4—43no—
1236C4—43no—
1237C4—41no—
1238C4—43no—
1239C4—41no—
1240C4—43no—
1241C4—41no—
1242C4—43no—
1243C4—43no—
1244C4—43no—
1245C4—41no—
1246C4—41no—
1247C4—41no—
1248C4—41no—
1249C4—41no—
1250C4—41no—
1251C4—43no—
1252C4—43no—
1253C4—41no—
1254C4—43no—
1255C4—43no—
1256C4C2×#529112yes—
1257C2—42no—
1258C2—81no—
1259C2—81no—
1260C2C22×#52911yescharacteristic
1261C2#6285011yescharacteristic
1262C2#6285011yescharacteristic
1263C2#6285011yescharacteristic
1264C2#6285011yescharacteristic
1265C2#6286111yescharacteristic
1266C2#6286111yescharacteristic
subgroupG/H
center, commutator, Frattini, socle, cosocleC23C26
prime radical#392C23
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23 ◁ G
LECSG ▷ C23 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #36050C2semidirect
3. #35971C2semidirect
4. #35910C2semidirect
5. #35901C2semidirect
6. #35899C2semidirect
7. #35883C2semidirect
8. #35883C2semidirect
9. #35870C2semidirect
10. #35804C2semidirect
11. #35803C2semidirect
12. #35789C2semidirect
13. #35786C2semidirect
14. #35723C2semidirect
15. #35723C2semidirect
17. #35217C2semidirect
18. #35204C2semidirect
19. #35187C2semidirect
20. #35183C2semidirect
21. #35163C2semidirect
22. #35162C2semidirect
24. #34629C2semidirect
25. #34336C2semidirect
26. #34311C2semidirect
27. #34291C2semidirect
28. #34291C2semidirect
29. #34262C2semidirect
30. #34262C2semidirect
31. C4×#519C2semidirect

Maximal subgroups

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

subgroupindex
#360502
#360172
#359712
#359102
#359012
#358992
#358832
#358702
#358042
#358032
#357892
#357862
#357232
#357002
#352172
#352042
#351872
#351832
#351632
#351622
#346402
#346292
#343362
#343112
#342912
#342622
C4×#5192