Finite Group Databasebeta

← #7687697

Subgroups — #7687697

Order 512.

5106 conjugacy classes of subgroups.

The subgroup lattice has 1356 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#59865C213yesmaximal, complemented
2#59645C213yesmaximal, complemented
3#59644C213yesmaximal, complemented
4#59627C213yesmaximal, complemented
5#59592C213yesmaximal, complemented
6#45302C213yesmaximal, complemented
7#45222C213yesmaximal, complemented
8#45076C213yesmaximal, complemented
9#45043C213yesmaximal, complemented
10#39766C213yesmaximal, complemented
11#39274C213yesmaximal, complemented
12#39270C213yesmaximal, complemented
13#39197C213yesmaximal, complemented
14#36591C213yesmaximal, complemented
15#36578C211yesmaximal, characteristic, complemented
16#36499C213yesmaximal, complemented
17#36467C211yesmaximal, characteristic, complemented
18#36467C211yesmaximal, characteristic, complemented
19#36465C211yesmaximal, characteristic
20#36432C211yesmaximal, characteristic, complemented
21#36049C211yesmaximal, characteristic, complemented
22#35996C211yesmaximal, characteristic, complemented
23#35910C211yesmaximal, characteristic, complemented
24#35801C211yesmaximal, characteristic, complemented
25#34918C213yesmaximal, complemented
26#34336C211yesmaximal, characteristic, complemented
27#34312C211yesmaximal, characteristic, complemented
28#34295C211yesmaximal, characteristic, complemented
29#34291C211yesmaximal, characteristic, complemented
30C4×#557C211yesmaximal, characteristic, complemented
31C4×#548C211yesmaximal, characteristic, complemented
32C2×#557C2211yescharacteristic
33C2×#557C2211yescharacteristic
34C2×#550C2211yescharacteristic
35C2×D4×Q8C2211yescharacteristic
36C2×#548C2211yescharacteristic
37C2×#548C2211yescharacteristic
38C2×#548C2211yescharacteristic
39C2×#548C2211yescharacteristic
40C2×#520C2211yescharacteristic
41C2×#519C2211yescharacteristic
42C2×C4×#41C2211yescharacteristic
43C22×C4×Q8C2211yescharacteristic
44#2861C2213yes—
45#2861C2213yes—
46#2858C2213yes—
47#2855C2213yes—
48#2854C2213yes—
49#2803C2216yes—
50#2798C2216yes—
51#2797C2216yes—
52#2797C2216yes—
53#2796C2216yes—
54#2796C2216yes—
55#2794C2216yes—
56#2773C2216yes—
57#2771C2216yes—
58#2754C2216yes—
59#2751C2216yes—
60#2751C2216yes—
61#2712C2216yes—
62#2709C2216yes—
63#2642C2213yes—
64#2641C2213yes—
65#2625C2213yes—
66#2624C2213yes—
67#2602C2216yes—
68#2597C2213yes—
69#2597C2213yes—
70#2596C2216yes—
71#2595C2213yes—
72#2595C2216yes—
73#2595C2213yes—
74#2595C2216yes—
75#2595C2216yes—
76#2595C2216yes—
77#2593C2216yes—
78#2592C2213yes—
79#2592C2213yes—
80#2592C2213yes—
81#2589C2216yes—
82#2589C2216yes—
83#2580C2213yes—
84#2570C2213yes—
85#2568C2213yes—
86#2562C2213yes—
87#2562C2213yes—
88#2562C2213yes—
89#2562C2213yes—
90#2557C2216yes—
91#2548C2213yes—
92#2544C2213yes—
93#2542C2213yes—
94#2541C2213yes—
95#2540C2213yes—
96#2540C2213yes—
97#2540C2213yes—
98#2540C2213yes—
99#2517C2216yes—
100#2516C2216yes—
101#2516C2216yes—
102#2516C2216yes—
103#2516C2211yescharacteristic
104#2516C2213yes—
105#2513C2216yes—
106#2513C2213yes—
107#2511C2213yes—
108#2504C2213yes—
109#2502C2213yes—
110#2500C2213yes—
111#2499C2213yes—
112#2492C2213yes—
113#2492C2213yes—
114#2492C2213yes—
115#2492C2213yes—
116#2491C2213yes—
117#2491C2213yes—
118#2491C2213yes—
119#2491C2213yes—
120#2490C2213yes—
121#2490C2213yes—
122#2490C2213yes—
123#2490C2213yes—
124#2489C2213yes—
125#2489C2213yes—
126#2489C2213yes—
127#2489C2213yes—
128#2487C2213yes—
129#2486C2213yes—
130#2485C2213yes—
131#2485C2213yes—
132#2459C2216yes—
133#2458C2213yes—
134#2458C2213yes—
135#2455C2216yes—
136#2448C2213yes—
137#2448C2216yes—
138#2448C2213yes—
139#2448C2213yes—
140#2448C2213yes—
141#2447C2213yes—
142#2447C2213yes—
143#2447C2213yes—
144#2447C2213yes—
145#2447C2213yes—
146#2445C2213yes—
147#2423C2213yes—
148#2422C2213yes—
149#2422C2213yes—
150#2422C2213yes—
151#2421C2213yes—
152#2421C2213yes—
153#2421C2213yes—
154#2420C2213yes—
155#2398C2213yes—
156#2398C2213yes—
157#2395C2213yes—
158#2395C2213yes—
159#2374C2216yes—
160#2370C2213yes—
161#2370C2213yes—
162#2370C2213yes—
163#2370C2213yes—
164#2369C2213yes—
165#2367C2213yes—
166#2367C2213yes—
167#2367C2216yes—
168#2366C2213yes—
169#2365C2213yes—
170#2365C2213yes—
171#2363C2213yes—
172#2363C2213yes—
173#2362C2213yes—
174#2362C2213yes—
175#2361C2213yes—
176#2361C2213yes—
177#2360C2213yes—
178#2360C2213yes—
179#2357C2216yes—
180#2355C2213yes—
181#2355C2213yes—
182#2352C2213yes—
183#2352C2213yes—
184#2352C2213yes—
185#2352C2213yes—
186#2351C2211yescharacteristic
187#2351C2211yescharacteristic
188#2351C2211yescharacteristic
189#2351C2211yescharacteristic
190Q8×C4⋊C4C2211yescharacteristic
191Q8×C4⋊C4C2211yescharacteristic
192#2341C2211yescharacteristic
193#2341C2211yescharacteristic
194#2341C2211yescharacteristic
195#2341C2211yescharacteristic
196#2341C2211yescharacteristic
197#2341C2211yescharacteristic
198Q8×C22⋊C4C2211yescharacteristic
199Q8×C22⋊C4C2211yescharacteristic
200Q8×C22⋊C4C2211yescharacteristic
201Q8×C22⋊C4C2211yescharacteristic
202Q8×C22⋊C4C2211yescharacteristic
203Q8×C22⋊C4C2211yescharacteristic
204#2331C2213yes—
205#2330C2213yes—
206#2328C2213yes—
207#2327C2213yes—
208#2324C2213yes—
209#2324C2213yes—
210#2323C2213yes—
211#2323C2213yes—
212C4×C4⋊Q8C2213yes—
213C4×#127C2213yes—
214C4×#125C2213yes—
215C4×#125C2213yes—
216C4×#125C2213yes—
217C4×#124C2213yes—
218C4×#124C2213yes—
219C4×#124C2213yes—
220C4×#124C2213yes—
221C4×C22⋊Q8C2213yes—
222C4×C22⋊Q8C2213yes—
223C4×#123C2213yes—
224C4×#123C2213yes—
225C4×#121C2213yes—
226C4×#121C2213yes—
227#2295C2213yes—
228#2293C2213yes—
229#2290C2213yes—
230#2290C2213yes—
231#2276C2211yescharacteristic
232#2276C2211yescharacteristic
233C42×Q8C2211yescharacteristic
234C42×Q8C2211yescharacteristic
235C42×Q8C2213yes—
236C42×Q8C2211yescharacteristic
237C42×D4C2213yes—
238C22×#41C2311yescharacteristic
239C22×#41C2311yescharacteristic
240C23×Q8C2311yescharacteristic
241C23×Q8C2311yescharacteristic
242#557—28no—
243#557—28no—
244#550—28no—
245D4×Q8—28no—
246#548—28no—
247#548—28no—
248#548—44no—
249#548—44no—
250C2×C4⋊Q8C2313yes—
251C2×C4⋊Q8C2313yes—
252C2×C4⋊Q8C2313yes—
253C2×#127C2313yes—
254C2×#127C2313yes—
255C2×#125C2313yes—
256C2×#125C2313yes—
257C2×#125C2313yes—
258C2×#125C2313yes—
259C2×#124C2313yes—
260C2×#124C2313yes—
261C2×#124C2313yes—
262C2×#124C2313yes—
263C2×#124C2313yes—
264C2×#124C2316yes—
265C2×#124C2313yes—
266C2×#123C2313yes—
267C2×#123C2313yes—
268C2×#123C2316yes—
269C2×C22⋊Q8C2313yes—
270C2×C22⋊Q8C2313yes—
271C2×C22⋊Q8C2313yes—
272C2×C22⋊Q8C2313yes—
273C2×C22⋊Q8C2313yes—
274C2×C22⋊Q8C2313yes—
275C2×#121C2313yes—
276C2×#121C2313yes—
277C2×#121C2313yes—
278C2×#121C2313yes—
279C2×#121C2313yes—
280C2×#121C2313yes—
281#520—44no—
282#519—44no—
283C4×#41—44no—
284C2×C4×Q8—44no—
285C2×C4×Q8C2313yes—
286C2×C4×Q8C2313yes—
287C2×C4×Q8C2311yescharacteristic
288C2×C4×Q8C2311yescharacteristic
289C2×C4×Q8C2311yescharacteristic
290C2×C4×Q8C2311yescharacteristic
291C2×C4×Q8C2311yescharacteristic
292C2×C4×Q8C2311yescharacteristic
293C2×C4×Q8C2311yescharacteristic
294C2×C4×Q8C2311yescharacteristic
295C2×C4×Q8C2311yescharacteristic
296C2×C4×Q8C2313yes—
297C2×C4×Q8C2313yes—
298C2×C4×Q8C2313yes—
299C2×C4×Q8C2313yes—
300C2×C4×Q8C2313yes—
301C2×C4×Q8C2313yes—
302C2×C4×Q8C2311yescharacteristic
303C2×C4×Q8C2311yescharacteristic
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×D4C2313yes—
314C2×C4×D4C2316yes—
315C2×C4×D4C2313yes—
316C2×C4×D4C2313yes—
317C2×#117C2313yes—
318C2×#117C2313yes—
319C2×#117C2313yes—
320C2×#117C2313yes—
321C22×C4⋊C4C2313yes—
322C22×C4⋊C4C2313yes—
323C22×C42C2313yes—
324C22×C42C2313yes—
325#400C2313yes—
326#400C2316yes—
327#400C2316yes—
328#400C2316yes—
329#400C2313yes—
330#400C2311yescharacteristic
331#400C2316yes—
332#400C2316yes—
333#400C2313yes—
334#400C2316yes—
335#400C2313yes—
336#400C2313yes—
337#399C2311yescharacteristic
338#399C2313yes—
339#399C2316yes—
340#399C2316yes—
341#399C2316yes—
342#399C2316yes—
343#398C2313yes—
344#398C2313yes—
345#398C2316yes—
346#397C2311yescharacteristic
347#397C2316yes—
348#397C2313yes—
349#397C2316yes—
350#397C2313yes—
351#397C2316yes—
352#397C2316yes—
353#397C2313yes—
354#397C2313yes—
355#397C2313yes—
356#397C2316yes—
357#397C2316yes—
358#397C2316yes—
359#397C2316yes—
360#397C2316yes—
361#397C2316yes—
362#397C2313yes—
363#397C2313yes—
364#397C2313yes—
365#397C2313yes—
366#394C2313yes—
367#394C2316yes—
368#394C2316yes—
369#394C2316yes—
370#394C2316yes—
371#394C2316yes—
372#394C2313yes—
373#394C2316yes—
374#394C2313yes—
375#394C2313yes—
376#394C2313yes—
377#394C2316yes—
378#394C2313yes—
379#394C2313yes—
380#394C2311yescharacteristic
381#393C2313yes—
382#393C2313yes—
383#393C2313yes—
384#393C2316yes—
385#393C2313yes—
386#393C2316yes—
387#392C2316yes—
388#392C2316yes—
389#391C2316yes—
390#391C2316yes—
391#391C2313yes—
392#391C2313yes—
393#391C2313yes—
394#391C2313yes—
395#391C2313yes—
396#391C2313yes—
397#391C2313yes—
398#391C2313yes—
399#391C2313yes—
400#391C2316yes—
401#391C2313yes—
402#391C2313yes—
403#391C2313yes—
404#391C2313yes—
405#391C2313yes—
406#391C2313yes—
407#391C2313yes—
408#390C2311yescharacteristic
409#390C2313yes—
410#390C2313yes—
411#390C2313yes—
412#390C2313yes—
413#390C2313yes—
414#390C2313yes—
415#390C2313yes—
416#390C2313yes—
417#390C2316yes—
418#390C2313yes—
419#390C2313yes—
420#390C2313yes—
421#390C2313yes—
422#390C2313yes—
423#390C2316yes—
424#390C2316yes—
425#390C2313yes—
426#390C2313yes—
427#390C2313yes—
428#390C2313yes—
429#390C2313yes—
430#390C2313yes—
431#390C2313yes—
432#390C2316yes—
433#390C2316yes—
434#390C2313yes—
435#389C2313yes—
436#389C2313yes—
437#389C2313yes—
438#389C2313yes—
439#389C2313yes—
440#389C2313yes—
441#389C2316yes—
442#389C2313yes—
443#389C2313yes—
444#389C2313yes—
445#389C2313yes—
446#389C2313yes—
447#389C2313yes—
448#389C2316yes—
449#389C2313yes—
450#389C2313yes—
451#389C2316yes—
452#389C2313yes—
453#389C2313yes—
454#388C2313yes—
455#388C2313yes—
456#388C2316yes—
457#388C2316yes—
458#388C2316yes—
459#388C2316yes—
460#388C2316yes—
461#388C2316yes—
462#388C2313yes—
463#388C2316yes—
464#388C2316yes—
465#388C2316yes—
466#388C2316yes—
467#388C2316yes—
468#388C2316yes—
469#388C2316yes—
470#388C2313yes—
471#388C2313yes—
472#388C2313yes—
473#388C2313yes—
474#388C2313yes—
475#388C2313yes—
476#388C2316yes—
477#388C2316yes—
478#388C2316yes—
479#388C2316yes—
480#388C2316yes—
481#388C2316yes—
482#388C2316yes—
483#388C2313yes—
484#388C2316yes—
485#388C2313yes—
486#388C2311yescharacteristic
487#388C2311yescharacteristic
488#388C2313yes—
489#388C2313yes—
490#388C2313yes—
491#388C2313yes—
492#388C2313yes—
493#388C2316yes—
494#388C2311yescharacteristic
495#388C2311yescharacteristic
496#387C2313yes—
497#387C2316yes—
498#387C2316yes—
499#387C2316yes—
500#387C2316yes—
501#387C2316yes—
502#387C2313yes—
503#387C2313yes—
504#387C2313yes—
505#387C2313yes—
506#387C2316yes—
507#387C2316yes—
508#387C2316yes—
509#387C2316yes—
510#387C2316yes—
511#387C2316yes—
512#387C2313yes—
513#387C2316yes—
514#387C2311yescharacteristic
515#387C2313yes—
516#387C2313yes—
517#387C2313yes—
518#387C2316yes—
519#387C2313yes—
520#387C2316yes—
521#387C2311yescharacteristic
522#386C2316yes—
523#386C2316yes—
524#386C2313yes—
525#386C2316yes—
526#386C2316yes—
527#386C2313yes—
528#386C2313yes—
529#386C2316yes—
530#386C2313yes—
531#386C2313yes—
532#386C2316yes—
533#386C2311yescharacteristic
534#385C2313yes—
535#385C2316yes—
536#385C2313yes—
537#385C2313yes—
538#385C2313yes—
539#385C2313yes—
540#385C2316yes—
541#385C2316yes—
542#385C2316yes—
543#385C2316yes—
544#385C2313yes—
545#384C2313yes—
546#384C2313yes—
547#384C2313yes—
548#382C2313yes—
549#382C2313yes—
550#382C2313yes—
551#382C2316yes—
552#382C2313yes—
553#382C2313yes—
554#382C2313yes—
555#381C2316yes—
556#381C2313yes—
557#381C2316yes—
558#381C2311yescharacteristic
559#380C2313yes—
560#380C2313yes—
561#380C2313yes—
562#380C2313yes—
563#380C2313yes—
564#380C2313yes—
565#380C2313yes—
566#380C2313yes—
567#380C2313yes—
568#380C2313yes—
569#380C2313yes—
570#380C2313yes—
571C4×C4⋊C4C2313yes—
572C4×C4⋊C4C2316yes—
573C4×C4⋊C4C2313yes—
574C4×C4⋊C4C2313yes—
575C4×C4⋊C4C2313yes—
576C4×C4⋊C4C2313yes—
577C4×C4⋊C4C2313yes—
578C4×C4⋊C4C2313yes—
579C4×C4⋊C4C2316yes—
580C4×C4⋊C4C2316yes—
581C4×C4⋊C4C2313yes—
582C4×C4⋊C4C2313yes—
583C4×C4⋊C4C2313yes—
584C4×C4⋊C4C2313yes—
585C4×C4⋊C4C2313yes—
586C4×C4⋊C4C2313yes—
587C4×C4⋊C4C2316yes—
588C4×C4⋊C4C2313yes—
589C4×C4⋊C4C2313yes—
590C4×C4⋊C4C2313yes—
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×C4⋊C4C2313yes—
601C4×C4⋊C4C2313yes—
602C4×C4⋊C4C2313yes—
603C4×C4⋊C4C2311yescharacteristic
604C4×C22⋊C4C2316yes—
605C4×C22⋊C4C2316yes—
606C4×C22⋊C4C2313yes—
607C4×C22⋊C4C2313yes—
608C4×C22⋊C4C2316yes—
609C4×C22⋊C4C2316yes—
610C4×C22⋊C4C2316yes—
611C4×C22⋊C4C2313yes—
612C4×C22⋊C4C2313yes—
613C4×C22⋊C4C2313yes—
614C4×C22⋊C4C2313yes—
615C4×C22⋊C4C2313yes—
616C4×C22⋊C4C2313yes—
617C4×C22⋊C4C2313yes—
618C4×C22⋊C4C2313yes—
619C4×C22⋊C4C2313yes—
620C4×C22⋊C4C2313yes—
621C4×C22⋊C4C2313yes—
622C4×C22⋊C4C2313yes—
623C4×C22⋊C4C2313yes—
624C4×C22⋊C4C2311yescharacteristic
625#376C2313yes—
626#376C2313yes—
627C43C2313yes—
628C43C2313yes—
629C43C2313yes—
630C2×#41—24no—
631C2×#41—24no—
632C2×#41—24no—
633C2×#41—24no—
634C2×#41—24no—
635C2×#41—24no—
636C22×Q8—24no—
637C22×Q8—24no—
638C22×Q8—24no—
639C22×Q8—24no—
640C22×Q8—24no—
641C22×Q8—24no—
642C22×Q8C2413yes—
643C22×Q8C2413yes—
644C22×Q8C2413yes—
645C22×Q8C2413yes—
646C22×Q8C2411yescharacteristic
647C22×D4C2413yes—
648C22×D4C2413yes—
649C22×D4C2413yes—
650C22×D4C2411yescharacteristic
651C22×D4C2413yes—
652C22×D4C2413yes—
653C22×D4C2416yes—
654C22×D4C2413yes—
655C22×D4C2413yes—
656C23×C4C2413yes—
657C23×C4C2413yes—
658C23×C4C2413yes—
659C23×C4C2413yes—
660C23×C4C2411yescharacteristic
661C23×C4C2413yes—
662C23×C4C2413yes—
663C23×C4C2416yes—
664C23×C4C2413yes—
665C4⋊Q8—212no—
666C4⋊Q8—212no—
667C4⋊Q8—212no—
668#127—212no—
669#127—46no—
670#125—212no—
671#125—212no—
672#125—212no—
673#125—212no—
674#124—212no—
675#124—212no—
676#124—46no—
677#124—46no—
678#124—46no—
679#124—46no—
680#124—412no—
681#123—412no—
682#123—46no—
683#123—46no—
684C22⋊Q8—212no—
685C22⋊Q8—212no—
686C22⋊Q8—212no—
687C22⋊Q8—212no—
688C22⋊Q8—46no—
689C22⋊Q8—46no—
690#121—212no—
691#121—212no—
692#121—212no—
693#121—212no—
694#121—46no—
695#121—46no—
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—212no—
706C4×Q8—212no—
707C4×Q8—46no—
708C4×Q8—46no—
709C4×Q8—46no—
710C4×Q8—46no—
711C4×Q8—46no—
712C4×Q8—46no—
713C4×Q8#4118yes—
714C4×Q8#4118yes—
715C4×D4—212no—
716C4×D4—212no—
717C4×D4—212no—
718C4×D4—212no—
719C4×D4—46no—
720C4×D4—46no—
721C4×D4—46no—
722C4×D4—46no—
723C4×D4—46no—
724C4×D4—46no—
725C4×D4—46no—
726C4×D4—412no—
727C4×D4—46no—
728#117—46no—
729#117—46no—
730#117—46no—
731#117—46no—
732C2×C4⋊C4—46no—
733C2×C4⋊C4—46no—
734C2×C4⋊C4C2413yes—
735C2×C4⋊C4C2413yes—
736C2×C4⋊C4C2413yes—
737C2×C4⋊C4C2413yes—
738C2×C4⋊C4C2411yescharacteristic
739C2×C4⋊C4C2413yes—
740C2×C4⋊C4C2413yes—
741C2×C4⋊C4C2413yes—
742C2×C4⋊C4C2413yes—
743C2×C4⋊C4C2411yescharacteristic
744C2×C4⋊C4C2411yescharacteristic
745C2×C4⋊C4C2411yescharacteristic
746C2×C4⋊C4C2413yes—
747C2×C4⋊C4C2413yes—
748C2×C4⋊C4C2413yes—
749C2×C4⋊C4C2413yes—
750C2×C4⋊C4C2413yes—
751C2×C4⋊C4C2413yes—
752C2×C4⋊C4C2413yes—
753C2×C4⋊C4C2413yes—
754C2×C4⋊C4C2413yes—
755C2×C4⋊C4C2413yes—
756C2×C4⋊C4C2416yes—
757C2×C4⋊C4C2416yes—
758C2×C4⋊C4C2416yes—
759C2×C4⋊C4C2413yes—
760C2×C4⋊C4C2416yes—
761C2×C4⋊C4C2411yescharacteristic
762C2×C4⋊C4C2413yes—
763C2×C4⋊C4C2413yes—
764C2×C4⋊C4C2413yes—
765C2×C4⋊C4C2413yes—
766C2×C4⋊C4C2413yes—
767C2×C4⋊C4C2413yes—
768C2×C4⋊C4C2413yes—
769C2×C4⋊C4C2413yes—
770C2×C4⋊C4C2413yes—
771C2×C4⋊C4C2413yes—
772C2×C4⋊C4C2416yes—
773C2×C4⋊C4C2416yes—
774C2×C4⋊C4C2413yes—
775C2×C4⋊C4C2411yescharacteristic
776C2×C4⋊C4C2413yes—
777C2×C4⋊C4C2413yes—
778C2×C4⋊C4C2413yes—
779C2×C22⋊C4C2411yescharacteristic
780C2×C22⋊C4C2411yescharacteristic
781C2×C22⋊C4C2411yescharacteristic
782C2×C22⋊C4C2413yes—
783C2×C22⋊C4C2413yes—
784C2×C22⋊C4C2413yes—
785C2×C22⋊C4C2413yes—
786C2×C22⋊C4C2413yes—
787C2×C22⋊C4C2413yes—
788C2×C22⋊C4C2413yes—
789C2×C22⋊C4C2413yes—
790C2×C22⋊C4C2413yes—
791C2×C22⋊C4C2416yes—
792C2×C22⋊C4C2416yes—
793C2×C22⋊C4C2411yescharacteristic
794C2×C22⋊C4C2413yes—
795C2×C22⋊C4C2411yescharacteristic
796C2×C22⋊C4C2411yescharacteristic
797C2×C22⋊C4C2413yes—
798C2×C22⋊C4C2413yes—
799C2×C22⋊C4C2411yescharacteristic
800C2×C22⋊C4C2413yes—
801C2×C22⋊C4C2416yes—
802C2×C22⋊C4C2413yes—
803C2×C22⋊C4C2411yescharacteristic
804C2×C22⋊C4C2411yescharacteristic
805C2×C22⋊C4C2413yes—
806C2×C22⋊C4C2413yes—
807C2×C22⋊C4C2413yes—
808C2×C22⋊C4C2416yes—
809C2×C22⋊C4C2416yes—
810C2×C22⋊C4C2416yes—
811C2×C22⋊C4C2413yes—
812C2×C22⋊C4C2413yes—
813C2×C22⋊C4C2413yes—
814C2×C22⋊C4C2413yes—
815C2×C22⋊C4C2416yes—
816C2×C22⋊C4C2413yes—
817C2×C22⋊C4C2416yes—
818C2×C22⋊C4C2413yes—
819C2×C22⋊C4C2413yes—
820C2×C22⋊C4C2413yes—
821C2×C22⋊C4C2416yes—
822C2×C22⋊C4C2411yescharacteristic
823C2×C22⋊C4C2411yescharacteristic
824C2×C22⋊C4C2413yes—
825C2×C22⋊C4C2413yes—
826C2×C22⋊C4C2416yes—
827C2×C22⋊C4C2416yes—
828C2×C22⋊C4C2413yes—
829C2×C22⋊C4C2413yes—
830C2×C42—46no—
831C2×C42—46no—
832C2×C42C2413yes—
833C2×C42C2413yes—
834C2×C42C2413yes—
835C2×C42C2413yes—
836C2×C42C2413yes—
837C2×C42C2413yes—
838C2×C42C2411yescharacteristic
839C2×C42C2413yes—
840C2×C42C2413yes—
841C2×C42C2413yes—
842C2×C42C2413yes—
843C2×C42C2413yes—
844C2×C42C2416yes—
845C2×C42C2413yes—
846C2×C42C2416yes—
847C2×C42C2413yes—
848C2×C42C2413yes—
849C2×C42C2413yes—
850C2×C42C2413yes—
851C2×C42C2413yes—
852C2×C42C2413yes—
853C2×C42C2413yes—
854C2×C42C2416yes—
855C2×C42C2413yes—
856C2×C42C2411yescharacteristic
857C2×C42C2411yescharacteristic
858C2×C42C2413yes—
859C2×C42C2411yescharacteristic
860C2×C42C2413yes—
861C2×C42C2413yes—
862#95C2411yescharacteristic
863#95C2411yescharacteristic
864#95C2413yes—
865#95C2413yes—
866#95C2413yes—
867#95C2413yes—
868#95C2413yes—
869#95C2413yes—
870#95C2413yes—
871#95C2411yescharacteristic
872#95C2411yescharacteristic
873#95C2413yes—
874#95C2413yes—
875#95C2411yescharacteristic
876#95C2411yescharacteristic
877#95C2411yescharacteristic
878#95C2411yescharacteristic
879#95C2411yescharacteristic
880#95C2413yes—
881#95C2416yes—
882#95C2416yes—
883#95C2413yes—
884#95C2413yes—
885#95C2413yes—
886#95C2413yes—
887#95C2413yes—
888#95C2413yes—
889#95C2413yes—
890#95C2416yes—
891#95C2416yes—
892#95C2416yes—
893#95C2413yes—
894#95C2413yes—
895#95C2413yes—
896#95C2413yes—
897#95C2413yes—
898#95C2413yes—
899#95C2413yes—
900#95C2413yes—
901#95C2411yescharacteristic
902#95C2411yescharacteristic
903#95C2413yes—
904#95C2413yes—
905#95C2411yescharacteristic
906#95C2413yes—
907#95C2413yes—
908#95C2416yes—
909#95C2416yes—
910#95C2416yes—
911#95C2413yes—
912#95C2416yes—
913#95C2413yes—
914#95C2416yes—
915#95C2413yes—
916#95C2416yes—
917#95C2416yes—
918#95C2416yes—
919C24C2511yescharacteristic
920C24C2513yes—
921C24C2513yes—
922C24C2511yescharacteristic
923#41—416no—
924#41—416no—
925C2×Q8—26no—
926C2×Q8—26no—
927C2×Q8—26no—
928C2×Q8—26no—
929C2×Q8—26no—
930C2×Q8—26no—
931C2×Q8—26no—
932C2×Q8—26no—
933C2×Q8—26no—
934C2×Q8—43no—
935C2×Q8—43no—
936C2×Q8—43no—
937C2×Q8—416no—
938C2×Q8—416no—
939C2×Q8C2×#4114yes—
940C2×Q8C2×#4114yes—
941C2×Q8H(5,𝔽2)14yes—
942C2×D4—26no—
943C2×D4—22no—
944C2×D4—26no—
945C2×D4—22no—
946C2×D4—26no—
947C2×D4—26no—
948C2×D4—26no—
949C2×D4—26no—
950C2×D4—26no—
951C2×D4—26no—
952C2×D4—26no—
953C2×D4—212no—
954C2×D4—26no—
955C2×D4—26no—
956C2×D4—43no—
957C2×D4—41no—
958C2×D4—43no—
959C2×D4—43no—
960C2×D4—46no—
961C2×D4—43no—
962C2×D4—43no—
963C2×D4—43no—
964C2×D4—46no—
965C2×D4—43no—
966C2×D4—43no—
967C2×D4—43no—
968C2×D4—43no—
969C22×C4—22no—
970C22×C4—26no—
971C22×C4—26no—
972C22×C4—26no—
973C22×C4—26no—
974C22×C4—26no—
975C22×C4—26no—
976C22×C4—26no—
977C22×C4—26no—
978C22×C4—26no—
979C22×C4—26no—
980C22×C4—26no—
981C22×C4—26no—
982C22×C4—22no—
983C22×C4—26no—
984C22×C4—41no—
985C22×C4—43no—
986C22×C4—43no—
987C22×C4—43no—
988C22×C4—43no—
989C22×C4—43no—
990C22×C4—43no—
991C22×C4—43no—
992C22×C4—43no—
993C22×C4—46no—
994C22×C4—46no—
995C22×C4—46no—
996C22×C4C2511yescharacteristic
997C22×C4C2511yescharacteristic
998C22×C4C2511yescharacteristic
999C22×C4C2513yes—
1000C22×C4C2511yescharacteristic
1001C22×C4C2513yes—
1002C22×C4C2511yescharacteristic
1003C22×C4C2513yes—
1004C22×C4C2513yes—
1005C22×C4C2513yes—
1006C22×C4C2513yes—
1007C22×C4C2513yes—
1008C22×C4C2513yes—
1009C22×C4C2511yescharacteristic
1010C22×C4C2513yes—
1011C22×C4C2513yes—
1012C22×C4C2513yes—
1013C22×C4C2511yescharacteristic
1014C22×C4C2511yescharacteristic
1015C22×C4C2511yescharacteristic
1016C22×C4C2511yescharacteristic
1017C22×C4C2513yes—
1018C22×C4C2513yes—
1019C22×C4C2511yescharacteristic
1020C22×C4C2511yescharacteristic
1021C22×C4C2511yescharacteristic
1022C22×C4C2513yes—
1023C4⋊C4—22no—
1024C4⋊C4—26no—
1025C4⋊C4—26no—
1026C4⋊C4—26no—
1027C4⋊C4—22no—
1028C4⋊C4—22no—
1029C4⋊C4—26no—
1030C4⋊C4—26no—
1031C4⋊C4—26no—
1032C4⋊C4—26no—
1033C4⋊C4—26no—
1034C4⋊C4—26no—
1035C4⋊C4—26no—
1036C4⋊C4—26no—
1037C4⋊C4—212no—
1038C4⋊C4—212no—
1039C4⋊C4—212no—
1040C4⋊C4—26no—
1041C4⋊C4—26no—
1042C4⋊C4—26no—
1043C4⋊C4—26no—
1044C4⋊C4—26no—
1045C4⋊C4—26no—
1046C4⋊C4—22no—
1047C4⋊C4—26no—
1048C4⋊C4—43no—
1049C4⋊C4—46no—
1050C4⋊C4—43no—
1051C4⋊C4—41no—
1052C4⋊C4—41no—
1053C4⋊C4—43no—
1054C4⋊C4—43no—
1055C4⋊C4—43no—
1056C4⋊C4—43no—
1057C4⋊C4—43no—
1058C4⋊C4—43no—
1059C4⋊C4—43no—
1060C4⋊C4—43no—
1061C4⋊C4—43no—
1062C4⋊C4—43no—
1063C4⋊C4—43no—
1064C4⋊C4—46no—
1065C4⋊C4—46no—
1066C4⋊C4C2×#41112yes—
1067C4⋊C4C2×#41112yes—
1068C22⋊C4—26no—
1069C22⋊C4—26no—
1070C22⋊C4—22no—
1071C22⋊C4—22no—
1072C22⋊C4—22no—
1073C22⋊C4—26no—
1074C22⋊C4—26no—
1075C22⋊C4—26no—
1076C22⋊C4—26no—
1077C22⋊C4—26no—
1078C22⋊C4—26no—
1079C22⋊C4—212no—
1080C22⋊C4—212no—
1081C22⋊C4—22no—
1082C22⋊C4—26no—
1083C22⋊C4—26no—
1084C22⋊C4—22no—
1085C22⋊C4—26no—
1086C22⋊C4—22no—
1087C22⋊C4—41no—
1088C22⋊C4—43no—
1089C22⋊C4—43no—
1090C22⋊C4—43no—
1091C22⋊C4—43no—
1092C22⋊C4—46no—
1093C22⋊C4—41no—
1094C22⋊C4—46no—
1095C22⋊C4—41no—
1096C22⋊C4—43no—
1097C22⋊C4—43no—
1098C22⋊C4—43no—
1099C22⋊C4—46no—
1100C22⋊C4—46no—
1101C22⋊C4—43no—
1102C22⋊C4—41no—
1103C22⋊C4—41no—
1104C22⋊C4—43no—
1105C22⋊C4—43no—
1106C22⋊C4—46no—
1107C22⋊C4—46no—
1108C22⋊C4—43no—
1109C22⋊C4—43no—
1110C22⋊C4—46no—
1111C22⋊C4—43no—
1112C22⋊C4—43no—
1113C22⋊C4—43no—
1114C22⋊C4—43no—
1115C22⋊C4—43no—
1116C22⋊C4—46no—
1117C22⋊C4—46no—
1118C22⋊C4—43no—
1119C42—26no—
1120C42—26no—
1121C42—26no—
1122C42—26no—
1123C42—26no—
1124C42—26no—
1125C42—26no—
1126C42—26no—
1127C42—26no—
1128C42—26no—
1129C42—22no—
1130C42—41no—
1131C42—43no—
1132C42—43no—
1133C42—43no—
1134C42—41no—
1135C42—41no—
1136C42—43no—
1137C42—46no—
1138C42—46no—
1139C42—43no—
1140C42—43no—
1141C42—43no—
1142C42—43no—
1143C42—43no—
1144C42—43no—
1145C42—46no—
1146C42—43no—
1147C42C2×#41112yes—
1148C42C2×#41112yes—
1149C23—21no—
1150C23—21no—
1151C23—21no—
1152C23—21no—
1153C23—21no—
1154C23—21no—
1155C23—21no—
1156C23—23no—
1157C23—23no—
1158C23—21no—
1159C23—23no—
1160C23—23no—
1161C23—21no—
1162C23—23no—
1163C23—23no—
1164C23—21no—
1165C23—23no—
1166C23—21no—
1167C23—23no—
1168C23—23no—
1169C23—23no—
1170C23—23no—
1171C23—23no—
1172C23—21no—
1173C23—21no—
1174C23—23no—
1175C23—23no—
1176C23#58512yes—
1177C23C2611yescharacteristic
1178Q8—412no—
1179Q8—412no—
1180Q8—412no—
1181Q8—86no—
1182Q8#559116yes—
1183D4—44no—
1184D4—412no—
1185D4—412no—
1186D4—412no—
1187D4—86no—
1188D4—812no—
1189D4—86no—
1190D4—86no—
1191D4—86no—
1192C2×C4—21no—
1193C2×C4—21no—
1194C2×C4—21no—
1195C2×C4—23no—
1196C2×C4—21no—
1197C2×C4—23no—
1198C2×C4—23no—
1199C2×C4—23no—
1200C2×C4—21no—
1201C2×C4—21no—
1202C2×C4—21no—
1203C2×C4—21no—
1204C2×C4—21no—
1205C2×C4—21no—
1206C2×C4—21no—
1207C2×C4—23no—
1208C2×C4—23no—
1209C2×C4—23no—
1210C2×C4—23no—
1211C2×C4—21no—
1212C2×C4—21no—
1213C2×C4—23no—
1214C2×C4—23no—
1215C2×C4—21no—
1216C2×C4—21no—
1217C2×C4—23no—
1218C2×C4—23no—
1219C2×C4—21no—
1220C2×C4—21no—
1221C2×C4—21no—
1222C2×C4—21no—
1223C2×C4—23no—
1224C2×C4—23no—
1225C2×C4—23no—
1226C2×C4—23no—
1227C2×C4—23no—
1228C2×C4—21no—
1229C2×C4—23no—
1230C2×C4—23no—
1231C2×C4—21no—
1232C2×C4—23no—
1233C2×C4—21no—
1234C2×C4—21no—
1235C2×C4—21no—
1236C2×C4—23no—
1237C2×C4—23no—
1238C2×C4—23no—
1239C2×C4—23no—
1240C2×C4—23no—
1241C2×C4—23no—
1242C2×C4—23no—
1243C2×C4—23no—
1244C2×C4—23no—
1245C2×C4—23no—
1246C2×C4—23no—
1247C2×C4—21no—
1248C2×C4—23no—
1249C2×C4—21no—
1250C2×C4—21no—
1251C2×C4—23no—
1252C2×C4—21no—
1253C2×C4—21no—
1254C2×C4—21no—
1255C2×C4—21no—
1256C2×C4—23no—
1257C2×C4—21no—
1258C2×C4—23no—
1259C2×C4—21no—
1260C2×C4—21no—
1261C2×C4—23no—
1262C2×C4—23no—
1263C2×C4—21no—
1264C2×C4—44no—
1265C2×C4—412no—
1266C2×C4—412no—
1267C2×C4—412no—
1268C2×C4—412no—
1269C2×C4—86no—
1270C2×C4—86no—
1271C2×C4—86no—
1272C2×C4—166no—
1273C2×C4C22×#4112yes—
1274C2×C4C22×#4112yes—
1275C2×C4C22×#4116yes—
1276C2×C4C22×#4116yes—
1277C2×C4C22×#4116yes—
1278C2×C4C22×#4116yes—
1279C2×C4C2×H(5,𝔽2)16yes—
1280C2×C4#58512yes—
1281C2×C4#58512yes—
1282C22—22no—
1283C22—22no—
1284C22—22no—
1285C22—41no—
1286C22—41no—
1287C22—41no—
1288C22—41no—
1289C22—41no—
1290C22—43no—
1291C22—43no—
1292C22—43no—
1293C22—43no—
1294C22—41no—
1295C22—43no—
1296C22—43no—
1297C22—41no—
1298C22—43no—
1299C22—43no—
1300C22—41no—
1301C22—43no—
1302C22—41no—
1303C22—43no—
1304C22—43no—
1305C22—41no—
1306C22—43no—
1307C22—41no—
1308C22—43no—
1309C22—43no—
1310C22C23×#4111yescharacteristic
1311C22C23×#4111yescharacteristic
1312C22C22×H(5,𝔽2)11yescharacteristic
1313C22C2×#58511yescharacteristic
1314C22C2×#58511yescharacteristic
1315C22C2×#58511yescharacteristic
1316C222−1+611yescharacteristic
1317C4—22no—
1318C4—22no—
1319C4—22no—
1320C4—26no—
1321C4—22no—
1322C4—26no—
1323C4—41no—
1324C4—43no—
1325C4—41no—
1326C4—43no—
1327C4—41no—
1328C4—43no—
1329C4—43no—
1330C4—43no—
1331C4—43no—
1332C4—43no—
1333C4—41no—
1334C4—41no—
1335C4—41no—
1336C4—43no—
1337C4—43no—
1338C4—41no—
1339C4—41no—
1340C4—41no—
1341C4—43no—
1342C4—43no—
1343C4C2×#559112yes—
1344C2—42no—
1345C2—81no—
1346C2—83no—
1347C2—83no—
1348C2C22×#55911yescharacteristic
1349C2#6281011yescharacteristic
1350C2#6281611yescharacteristic
1351C2#6292211yescharacteristic
1352C2#6300511yescharacteristic
1353C2#6300711yescharacteristic
1354C2#6302011yescharacteristic
subgroupG/H
center, commutator, Frattini, socle, cosocleC23C26
prime radical#36465C2
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23 ◁ G
LECSG ▷ C23 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #59865C2semidirect
2. #59645C2semidirect
3. #59644C2semidirect
4. #59627C2semidirect
5. #59592C2semidirect
6. #45302C2semidirect
7. #45222C2semidirect
8. #45076C2semidirect
9. #45043C2semidirect
10. #39766C2semidirect
11. #39274C2semidirect
12. #39270C2semidirect
13. #39197C2semidirect
14. #36591C2semidirect
15. #36578C2semidirect
16. #36499C2semidirect
17. #36467C2semidirect
18. #36467C2semidirect
20. #36432C2semidirect
21. #36049C2semidirect
22. #35996C2semidirect
23. #35910C2semidirect
24. #35801C2semidirect
25. #34918C2semidirect
26. #34336C2semidirect
27. #34312C2semidirect
28. #34295C2semidirect
29. #34291C2semidirect
30. C4×#557C2semidirect
31. C4×#548C2semidirect

Maximal subgroups

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

subgroupindex
#598652
#596452
#596442
#596272
#595922
#453022
#452222
#450762
#450432
#397662
#392742
#392702
#391972
#365912
#365782
#364992
#364672
#364652
#364322
#360492
#359962
#359102
#358012
#349182
#343362
#343122
#342952
#342912
C4×#5572
C4×#5482