Finite Group Databasebeta

← #7687502

Subgroups — #7687502

Order 512.

4726 conjugacy classes of subgroups.

The subgroup lattice has 1256 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#59563C213yesmaximal, complemented
2#59509C213yesmaximal, complemented
3#59500C213yesmaximal, complemented
4#59448C213yesmaximal, complemented
5#59289C213yesmaximal, complemented
6#45383C213yesmaximal, complemented
7#45050C213yesmaximal, complemented
8#45017C213yesmaximal, complemented
9#44956C213yesmaximal, complemented
10#39547C213yesmaximal, complemented
11#39082C213yesmaximal, complemented
12#38274C213yesmaximal, complemented
13#37982C213yesmaximal, complemented
14#36584C211yesmaximal, characteristic, complemented
15Q8×#126C211yesmaximal, characteristic, complemented
16Q8×#125C211yesmaximal, characteristic, complemented
17#36448C211yesmaximal, characteristic, complemented
18#36432C211yesmaximal, characteristic
19#36299C213yesmaximal, complemented
20#36280C213yesmaximal, complemented
21#35996C211yesmaximal, characteristic
22#35868C211yesmaximal, characteristic, complemented
23#35816C211yesmaximal, characteristic, complemented
24#35786C211yesmaximal, characteristic, complemented
25#34866C213yesmaximal, complemented
26#34312C211yesmaximal, characteristic
27#34263C211yesmaximal, characteristic, complemented
28#34262C211yesmaximal, characteristic, complemented
29#34250C211yesmaximal, characteristic, complemented
30C4×#557C211yesmaximal, characteristic, complemented
31#34129C211yesmaximal, characteristic, complemented
32C2×#557C2211yescharacteristic
33C2×#548C2211yescharacteristic
34C2×#520C2211yescharacteristic
35C2×#520C2211yescharacteristic
36C2×#519C2211yescharacteristic
37C2×C4×#41C2211yescharacteristic
38#2863C2213yes—
39#2863C2213yes—
40#2859C2213yes—
41#2859C2213yes—
42#2855C2213yes—
43#2787C2216yes—
44#2781C2216yes—
45#2772C2216yes—
46#2767C2216yes—
47#2766C2216yes—
48#2765C2216yes—
49#2764C2216yes—
50#2747C2216yes—
51#2744C2216yes—
52#2739C2216yes—
53#2739C2216yes—
54#2719C2216yes—
55#2707C2216yes—
56#2702C2216yes—
57#2647C2213yes—
58#2629C2213yes—
59#2629C2213yes—
60#2625C2213yes—
61#2612C2216yes—
62#2611C2216yes—
63#2606C2213yes—
64#2606C2216yes—
65#2604C2213yes—
66#2601C2213yes—
67#2599C2213yes—
68#2596C2213yes—
69#2590C2213yes—
70#2585C2216yes—
71#2582C2213yes—
72#2577C2216yes—
73#2575C2213yes—
74#2571C2213yes—
75#2571C2213yes—
76#2570C2213yes—
77#2566C2213yes—
78#2565C2213yes—
79#2558C2213yes—
80#2558C2216yes—
81#2552C2213yes—
82#2552C2213yes—
83#2552C2213yes—
84#2538C2213yes—
85#2533C2213yes—
86#2530C2216yes—
87#2529C2213yes—
88#2519C2211yescharacteristic
89#2515C2213yes—
90#2515C2216yes—
91#2514C2213yes—
92#2514C2213yes—
93#2511C2213yes—
94#2511C2213yes—
95#2511C2213yes—
96#2511C2213yes—
97#2509C2213yes—
98#2509C2213yes—
99#2509C2213yes—
100#2509C2213yes—
101#2509C2213yes—
102#2507C2213yes—
103#2507C2213yes—
104#2507C2213yes—
105#2507C2213yes—
106#2507C2213yes—
107#2506C2213yes—
108#2506C2213yes—
109#2502C2213yes—
110#2499C2213yes—
111#2498C2216yes—
112#2497C2213yes—
113#2497C2213yes—
114#2497C2213yes—
115#2496C2213yes—
116#2495C2213yes—
117#2495C2216yes—
118#2494C2213yes—
119#2493C2216yes—
120#2486C2213yes—
121#2485C2213yes—
122#2479C2213yes—
123#2475C2213yes—
124#2475C2216yes—
125#2475C2216yes—
126#2475C2216yes—
127#2473C2216yes—
128#2462C2213yes—
129#2458C2213yes—
130#2454C2213yes—
131#2453C2213yes—
132#2452C2213yes—
133#2451C2213yes—
134#2447C2213yes—
135#2447C2213yes—
136#2447C2213yes—
137#2447C2213yes—
138#2442C2213yes—
139#2441C2213yes—
140#2440C2213yes—
141#2439C2213yes—
142#2438C2216yes—
143#2422C2213yes—
144#2422C2213yes—
145#2422C2213yes—
146#2421C2216yes—
147#2420C2213yes—
148#2413C2216yes—
149#2402C2213yes—
150#2396C2213yes—
151#2396C2213yes—
152#2395C2213yes—
153#2370C2213yes—
154#2370C2213yes—
155#2367C2213yes—
156#2365C2213yes—
157#2363C2213yes—
158#2360C2213yes—
159#2360C2216yes—
160#2357C2213yes—
161#2356C2213yes—
162#2355C2213yes—
163#2355C2213yes—
164#2354C2213yes—
165#2354C2213yes—
166#2354C2213yes—
167#2352C2213yes—
168#2351C2211yescharacteristic
169#2351C2211yescharacteristic
170#2351C2211yescharacteristic
171#2351C2211yescharacteristic
172#2351C2211yescharacteristic
173#2351C2211yescharacteristic
174Q8×C4⋊C4C2211yescharacteristic
175Q8×C4⋊C4C2211yescharacteristic
176Q8×C4⋊C4C2211yescharacteristic
177Q8×C4⋊C4C2211yescharacteristic
178Q8×C4⋊C4C2211yescharacteristic
179Q8×C4⋊C4C2211yescharacteristic
180Q8×C4⋊C4C2211yescharacteristic
181Q8×C4⋊C4C2211yescharacteristic
182Q8×C4⋊C4C2211yescharacteristic
183Q8×C4⋊C4C2211yescharacteristic
184#2349C2213yes—
185#2349C2213yes—
186D4×C4⋊C4C2213yes—
187D4×C4⋊C4C2213yes—
188#2347C2213yes—
189#2346C2213yes—
190#2346C2213yes—
191#2346C2213yes—
192#2345C2213yes—
193#2344C2213yes—
194#2344C2216yes—
195#2343C2216yes—
196#2341C2211yescharacteristic
197#2341C2211yescharacteristic
198#2341C2211yescharacteristic
199Q8×C22⋊C4C2211yescharacteristic
200Q8×C22⋊C4C2211yescharacteristic
201Q8×C22⋊C4C2211yescharacteristic
202Q8×C22⋊C4C2211yescharacteristic
203Q8×C22⋊C4C2211yescharacteristic
204#2324C2213yes—
205#2323C2213yes—
206#2320C2213yes—
207#2319C2213yes—
208#2317C2213yes—
209#2316C2213yes—
210#2314C2213yes—
211#2314C2213yes—
212C4×C4⋊Q8C2213yes—
213C4×#125C2213yes—
214C4×#125C2213yes—
215C4×#125C2213yes—
216C4×#125C2213yes—
217C4×#126C2213yes—
218C4×#126C2213yes—
219C4×#124C2213yes—
220C4×#123C2213yes—
221#2298C2213yes—
222#2298C2213yes—
223#2296C2213yes—
224#2295C2213yes—
225#2293C2213yes—
226#2293C2213yes—
227#2293C2213yes—
228#2293C2213yes—
229C2×#389C2213yes—
230#2285C2213yes—
231#2276C2211yescharacteristic
232C42×Q8C2211yescharacteristic
233C42×Q8C2213yes—
234C42×Q8C2211yescharacteristic
235C42×Q8C2211yescharacteristic
236C42×Q8C2211yescharacteristic
237C4×#117C2213yes—
238C22×#41C2311yescharacteristic
239C23×Q8C2311yescharacteristic
240#557—28no—
241#548—28no—
242C2×C4⋊Q8C2313yes—
243C2×#126C2311yescharacteristic
244C2×#126C2313yes—
245C2×#125C2311yescharacteristic
246C2×#125C2313yes—
247C2×#125C2313yes—
248C2×#125C2313yes—
249C2×#125C2316yes—
250C2×#125C2316yes—
251C2×#124C2313yes—
252C2×#123C2313yes—
253C2×#123C2316yes—
254C2×C22⋊Q8C2313yes—
255C2×C22⋊Q8C2316yes—
256C2×#121C2313yes—
257#520—28no—
258#520—28no—
259#519—28no—
260C4×#41—28no—
261C2×C4×Q8C2313yes—
262C2×C4×Q8C2313yes—
263C2×C4×Q8C2313yes—
264C2×C4×Q8C2311yescharacteristic
265C2×C4×Q8C2311yescharacteristic
266C2×C4×Q8C2311yescharacteristic
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×Q8C2313yes—
277C2×C4×Q8C2313yes—
278C2×C4×Q8C2311yescharacteristic
279C2×C4×D4C2313yes—
280C2×C4×D4C2313yes—
281C2×C4×D4C2313yes—
282C2×C4×D4C2313yes—
283C2×C4×D4C2313yes—
284C2×C4×D4C2313yes—
285C2×C4×D4C2313yes—
286C2×#117C2313yes—
287C2×#117C2313yes—
288C2×#117C2313yes—
289C2×#117C2313yes—
290C2×#117C2313yes—
291C2×#117C2313yes—
292C2×#117C2313yes—
293C2×#117C2316yes—
294C2×#117C2316yes—
295C22×C4⋊C4C2313yes—
296C22×C4⋊C4C2313yes—
297C22×C4⋊C4C2316yes—
298C22×C42C2313yes—
299#401C2316yes—
300#400C2313yes—
301#400C2316yes—
302#400C2316yes—
303#400C2316yes—
304#400C2316yes—
305#400C2313yes—
306#400C2313yes—
307#400C2316yes—
308#400C2313yes—
309#400C2313yes—
310#400C2313yes—
311#400C2316yes—
312#400C2316yes—
313#400C2313yes—
314#400C2316yes—
315#400C2316yes—
316#400C2316yes—
317#399C2313yes—
318#399C2313yes—
319#399C2311yescharacteristic
320#398C2313yes—
321#398C2316yes—
322#398C2316yes—
323#398C2313yes—
324#398C2316yes—
325#398C2316yes—
326#398C2316yes—
327#398C2313yes—
328#398C2313yes—
329#398C2311yescharacteristic
330#398C2313yes—
331#398C2311yescharacteristic
332#398C2313yes—
333#398C2316yes—
334#398C2316yes—
335#398C2313yes—
336#398C2316yes—
337#398C2316yes—
338#398C2316yes—
339#397C2313yes—
340#397C2316yes—
341#397C2316yes—
342#397C2313yes—
343#397C2313yes—
344#397C2316yes—
345#397C2316yes—
346#397C2316yes—
347#397C2316yes—
348#396C2313yes—
349#396C2316yes—
350#396C2311yescharacteristic
351#396C2313yes—
352#396C2313yes—
353#396C2316yes—
354#396C2316yes—
355#396C2316yes—
356#395C2313yes—
357#395C2313yes—
358#394C2313yes—
359#394C2313yes—
360#394C2316yes—
361#393C2313yes—
362#393C2313yes—
363#391C2316yes—
364#391C2313yes—
365#391C2313yes—
366#391C2313yes—
367#391C2313yes—
368#391C2313yes—
369#391C2313yes—
370#391C2313yes—
371#391C2316yes—
372#391C2313yes—
373#391C2313yes—
374#391C2313yes—
375#390C2313yes—
376#390C2313yes—
377#390C2313yes—
378#390C2313yes—
379#390C2313yes—
380#390C2313yes—
381#390C2313yes—
382#390C2313yes—
383#389C2313yes—
384#389C2313yes—
385#389C2313yes—
386#389C2313yes—
387#389C2313yes—
388#389C2313yes—
389#389C2313yes—
390#389C2313yes—
391#389C2316yes—
392#389C2313yes—
393#389C2313yes—
394#389C2313yes—
395#389C2313yes—
396#389C2313yes—
397#389C2313yes—
398#389C2313yes—
399#389C2316yes—
400#389C2313yes—
401#389C2313yes—
402#389C2313yes—
403#389C2313yes—
404#389C2313yes—
405#389C2313yes—
406#389C2313yes—
407#389C2313yes—
408#389C2316yes—
409#389C2313yes—
410#389C2313yes—
411#389C2316yes—
412#389C2311yescharacteristic
413#389C2313yes—
414#389C2316yes—
415#389C2313yes—
416#389C2313yes—
417#389C2313yes—
418#389C2313yes—
419#389C2313yes—
420#389C2313yes—
421#389C2313yes—
422#389C2313yes—
423#389C2316yes—
424#389C2316yes—
425#389C2313yes—
426#389C2313yes—
427#389C2313yes—
428#389C2313yes—
429#389C2313yes—
430#389C2313yes—
431#389C2313yes—
432#389C2316yes—
433#388C2311yescharacteristic
434#388C2313yes—
435#388C2313yes—
436#388C2313yes—
437#388C2313yes—
438#388C2313yes—
439#388C2313yes—
440#388C2316yes—
441#388C2316yes—
442#388C2316yes—
443#388C2313yes—
444#388C2313yes—
445#388C2313yes—
446#388C2313yes—
447#388C2316yes—
448#388C2316yes—
449#388C2316yes—
450#388C2311yescharacteristic
451#388C2313yes—
452#388C2313yes—
453#388C2313yes—
454#388C2316yes—
455#388C2316yes—
456#388C2316yes—
457#388C2313yes—
458#388C2313yes—
459#388C2313yes—
460#388C2311yescharacteristic
461#388C2311yescharacteristic
462#387C2313yes—
463#387C2313yes—
464#387C2313yes—
465#387C2313yes—
466#387C2313yes—
467#387C2313yes—
468#387C2313yes—
469#387C2313yes—
470#387C2313yes—
471#387C2313yes—
472#387C2313yes—
473#387C2313yes—
474#387C2313yes—
475#387C2313yes—
476#387C2316yes—
477#387C2316yes—
478#387C2316yes—
479#387C2316yes—
480#387C2316yes—
481#387C2316yes—
482#387C2313yes—
483#387C2316yes—
484#387C2316yes—
485#387C2316yes—
486#387C2316yes—
487#387C2316yes—
488#387C2313yes—
489#387C2313yes—
490#387C2316yes—
491#387C2316yes—
492#387C2313yes—
493#387C2316yes—
494#387C2313yes—
495#387C2313yes—
496#387C2316yes—
497#387C2316yes—
498#387C2313yes—
499#387C2313yes—
500#387C2313yes—
501#387C2316yes—
502#387C2316yes—
503#387C2311yescharacteristic
504#386C2316yes—
505#386C2313yes—
506#385C2316yes—
507#385C2316yes—
508#385C2316yes—
509#385C2316yes—
510#385C2313yes—
511#385C2316yes—
512#385C2316yes—
513#385C2313yes—
514#385C2313yes—
515#385C2316yes—
516#385C2313yes—
517#385C2313yes—
518#385C2316yes—
519#384C2313yes—
520#384C2313yes—
521#384C2313yes—
522#384C2313yes—
523#384C2313yes—
524#384C2313yes—
525#384C2313yes—
526#384C2313yes—
527#384C2313yes—
528#384C2313yes—
529#383C2313yes—
530#383C2313yes—
531#383C2316yes—
532#383C2316yes—
533#382C2311yescharacteristic
534#382C2313yes—
535#382C2313yes—
536#382C2313yes—
537#382C2313yes—
538#382C2313yes—
539#382C2313yes—
540#382C2316yes—
541#382C2313yes—
542#382C2316yes—
543#382C2316yes—
544#381C2316yes—
545#381C2313yes—
546#381C2316yes—
547#381C2316yes—
548#380C2313yes—
549#380C2313yes—
550#380C2313yes—
551#380C2313yes—
552#380C2316yes—
553#380C2316yes—
554#380C2316yes—
555#380C2313yes—
556#380C2313yes—
557#380C2313yes—
558#380C2313yes—
559#380C2316yes—
560#380C2316yes—
561C4×C4⋊C4C2313yes—
562C4×C4⋊C4C2313yes—
563C4×C4⋊C4C2313yes—
564C4×C4⋊C4C2313yes—
565C4×C4⋊C4C2313yes—
566C4×C4⋊C4C2313yes—
567C4×C4⋊C4C2316yes—
568C4×C4⋊C4C2313yes—
569C4×C4⋊C4C2313yes—
570C4×C4⋊C4C2313yes—
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⋊C4C2313yes—
589C4×C4⋊C4C2316yes—
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⋊C4C2311yescharacteristic
601C4×C4⋊C4C2311yescharacteristic
602C4×C22⋊C4C2313yes—
603C4×C22⋊C4C2313yes—
604C4×C22⋊C4C2313yes—
605C4×C22⋊C4C2313yes—
606C4×C22⋊C4C2313yes—
607C4×C22⋊C4C2313yes—
608C4×C22⋊C4C2316yes—
609C4×C22⋊C4C2313yes—
610C4×C22⋊C4C2313yes—
611C4×C22⋊C4C2313yes—
612C4×C22⋊C4C2316yes—
613C4×C22⋊C4C2316yes—
614C4×C22⋊C4C2313yes—
615#376C2313yes—
616#376C2316yes—
617#376C2313yes—
618#376C2313yes—
619C2×#95C2316yes—
620C43C2313yes—
621C43C2313yes—
622C43C2313yes—
623C43C2313yes—
624C2×#41—24no—
625C2×#41—24no—
626C2×#41#4118yes—
627C22×Q8—24no—
628C22×Q8—24no—
629C22×Q8—24no—
630C22×Q8C2413yes—
631C22×Q8C2413yes—
632C22×Q8C2411yescharacteristic
633C22×D4C2413yes—
634C22×D4C2413yes—
635C23×C4C2413yes—
636C23×C4C2413yes—
637C23×C4C2413yes—
638C23×C4C2413yes—
639C23×C4C2416yes—
640C23×C4C2416yes—
641C4⋊Q8—212no—
642#126—24no—
643#126—46no—
644#125—212no—
645#125—24no—
646#125—212no—
647#125—46no—
648#125—86no—
649#125—86no—
650#124—212no—
651#123—46no—
652#123—86no—
653C22⋊Q8—212no—
654C22⋊Q8—412no—
655#121—212no—
656C4×Q8—24no—
657C4×Q8—24no—
658C4×Q8—24no—
659C4×Q8—24no—
660C4×Q8—24no—
661C4×Q8—24no—
662C4×Q8—24no—
663C4×Q8—24no—
664C4×Q8—24no—
665C4×Q8—24no—
666C4×Q8—24no—
667C4×Q8—24no—
668C4×Q8—212no—
669C4×Q8—212no—
670C4×Q8—212no—
671C4×Q8—46no—
672C4×Q8—46no—
673C4×Q8#4118yes—
674C4×D4—212no—
675C4×D4—212no—
676C4×D4—212no—
677C4×D4—212no—
678C4×D4—212no—
679C4×D4—212no—
680C4×D4—212no—
681#117—212no—
682#117—212no—
683#117—212no—
684#117—212no—
685#117—212no—
686#117—212no—
687#117—46no—
688#117—86no—
689#117—86no—
690C2×C4⋊C4—212no—
691C2×C4⋊C4—212no—
692C2×C4⋊C4—412no—
693C2×C4⋊C4C2413yes—
694C2×C4⋊C4C2413yes—
695C2×C4⋊C4C2413yes—
696C2×C4⋊C4C2413yes—
697C2×C4⋊C4C2413yes—
698C2×C4⋊C4C2413yes—
699C2×C4⋊C4C2413yes—
700C2×C4⋊C4C2411yescharacteristic
701C2×C4⋊C4C2411yescharacteristic
702C2×C4⋊C4C2411yescharacteristic
703C2×C4⋊C4C2413yes—
704C2×C4⋊C4C2413yes—
705C2×C4⋊C4C2413yes—
706C2×C4⋊C4C2413yes—
707C2×C4⋊C4C2413yes—
708C2×C4⋊C4C2413yes—
709C2×C4⋊C4C2413yes—
710C2×C4⋊C4C2411yescharacteristic
711C2×C4⋊C4C2411yescharacteristic
712C2×C4⋊C4C2413yes—
713C2×C4⋊C4C2413yes—
714C2×C4⋊C4C2413yes—
715C2×C4⋊C4C2413yes—
716C2×C4⋊C4C2413yes—
717C2×C4⋊C4C2413yes—
718C2×C4⋊C4C2413yes—
719C2×C4⋊C4C2413yes—
720C2×C4⋊C4C2413yes—
721C2×C4⋊C4C2413yes—
722C2×C4⋊C4C2416yes—
723C2×C4⋊C4C2411yescharacteristic
724C2×C4⋊C4C2411yescharacteristic
725C2×C4⋊C4C2411yescharacteristic
726C2×C4⋊C4C2411yescharacteristic
727C2×C4⋊C4C2411yescharacteristic
728C2×C4⋊C4C2411yescharacteristic
729C2×C4⋊C4C2411yescharacteristic
730C2×C4⋊C4C2416yes—
731C2×C4⋊C4C2416yes—
732C2×C4⋊C4C2413yes—
733C2×C4⋊C4C2416yes—
734C2×C4⋊C4C2416yes—
735C2×C4⋊C4C2416yes—
736C2×C4⋊C4C2413yes—
737C2×C4⋊C4C2413yes—
738C2×C4⋊C4C2413yes—
739C2×C4⋊C4C2413yes—
740C2×C4⋊C4C2416yes—
741C2×C4⋊C4C2416yes—
742C2×C4⋊C4C2416yes—
743C2×C4⋊C4C2416yes—
744C2×C4⋊C4C2413yes—
745C2×C4⋊C4C2413yes—
746C2×C4⋊C4C2413yes—
747C2×C4⋊C4C2413yes—
748C2×C4⋊C4C2413yes—
749C2×C4⋊C4C2413yes—
750C2×C4⋊C4C2416yes—
751C2×C4⋊C4C2413yes—
752C2×C4⋊C4C2413yes—
753C2×C4⋊C4C2413yes—
754C2×C4⋊C4C2413yes—
755C2×C4⋊C4C2413yes—
756C2×C4⋊C4C2413yes—
757C2×C4⋊C4C2413yes—
758C2×C4⋊C4C2411yescharacteristic
759C2×C22⋊C4C2413yes—
760C2×C22⋊C4C2411yescharacteristic
761C2×C22⋊C4C2416yes—
762C2×C22⋊C4C2413yes—
763C2×C22⋊C4C2413yes—
764C2×C22⋊C4C2413yes—
765C2×C22⋊C4C2413yes—
766C2×C22⋊C4C2413yes—
767C2×C22⋊C4C2413yes—
768C2×C22⋊C4C2413yes—
769C2×C22⋊C4C2411yescharacteristic
770C2×C22⋊C4C2413yes—
771C2×C22⋊C4C2416yes—
772C2×C22⋊C4C2411yescharacteristic
773C2×C22⋊C4C2411yescharacteristic
774C2×C22⋊C4C2411yescharacteristic
775C2×C22⋊C4C2411yescharacteristic
776C2×C22⋊C4C2411yescharacteristic
777C2×C22⋊C4C2416yes—
778C2×C22⋊C4C2413yes—
779C2×C22⋊C4C2416yes—
780C2×C22⋊C4C2413yes—
781C2×C22⋊C4C2416yes—
782C2×C22⋊C4C2413yes—
783C2×C22⋊C4C2413yes—
784C2×C22⋊C4C2413yes—
785C2×C22⋊C4C2413yes—
786C2×C22⋊C4C2413yes—
787C2×C22⋊C4C2413yes—
788C2×C42—212no—
789C2×C42C2413yes—
790C2×C42C2413yes—
791C2×C42C2413yes—
792C2×C42C2413yes—
793C2×C42C2413yes—
794C2×C42C2416yes—
795C2×C42C2413yes—
796C2×C42C2413yes—
797C2×C42C2413yes—
798C2×C42C2413yes—
799C2×C42C2413yes—
800C2×C42C2413yes—
801C2×C42C2411yescharacteristic
802C2×C42C2413yes—
803C2×C42C2413yes—
804C2×C42C2413yes—
805C2×C42C2413yes—
806C2×C42C2413yes—
807C2×C42C2411yescharacteristic
808C2×C42C2411yescharacteristic
809C2×C42C2411yescharacteristic
810C2×C42C2411yescharacteristic
811C2×C42C2413yes—
812C2×C42C2413yes—
813C2×C42C2413yes—
814C2×C42C2416yes—
815C2×C42C2413yes—
816C2×C42C2413yes—
817C2×C42C2413yes—
818C2×C42C2413yes—
819C2×C42C2413yes—
820C2×C42C2413yes—
821C2×C42C2413yes—
822#95C2413yes—
823#95C2413yes—
824#95C2416yes—
825#95C2416yes—
826#95C2411yescharacteristic
827#95C2411yescharacteristic
828#95C2411yescharacteristic
829#95C2413yes—
830#95C2413yes—
831#95C2413yes—
832#95C2413yes—
833#95C2413yes—
834#95C2413yes—
835#95C2413yes—
836#95C2413yes—
837#95C2413yes—
838#95C2413yes—
839#95C2413yes—
840#95C2416yes—
841#95C2413yes—
842#95C2411yescharacteristic
843#95C2413yes—
844#95C2413yes—
845#95C2413yes—
846#95C2413yes—
847#95C2416yes—
848#95C2413yes—
849#95C2416yes—
850#95C2413yes—
851#95C2413yes—
852#95C2416yes—
853#95C2413yes—
854#95C2413yes—
855#95C2413yes—
856#95C2413yes—
857#95C2411yescharacteristic
858#95C2411yescharacteristic
859#95C2416yes—
860#95C2416yes—
861#95C2416yes—
862#95C2413yes—
863#95C2413yes—
864#95C2413yes—
865#95C2411yescharacteristic
866#95C2411yescharacteristic
867#95C2411yescharacteristic
868#95C2411yescharacteristic
869#95C2416yes—
870#95C2413yes—
871#95C2413yes—
872#95C2413yes—
873#95C2413yes—
874#95C2416yes—
875#95C2413yes—
876#95C2413yes—
877#95C2413yes—
878#95C2416yes—
879#95C2413yes—
880#95C2413yes—
881#95C2413yes—
882#95C2413yes—
883#95C2413yes—
884#95C2413yes—
885#95C2413yes—
886#95C2416yes—
887#95C2416yes—
888#95C2416yes—
889C24C2511yescharacteristic
890C24C2513yes—
891#41—232no—
892C2×Q8—26no—
893C2×Q8—26no—
894C2×Q8—26no—
895C2×Q8—26no—
896C2×Q8—26no—
897C2×Q8—43no—
898C2×Q8—416no—
899C2×Q8C2×#4114yes—
900C2×Q8C2×#4114yes—
901C2×Q82−1+414yes—
902C2×D4—26no—
903C2×D4—26no—
904C2×D4—26no—
905C2×D4—43no—
906C2×D4—43no—
907C2×D4C2×#41112yes—
908C22×C4—26no—
909C22×C4—26no—
910C22×C4—26no—
911C22×C4—26no—
912C22×C4—212no—
913C22×C4—26no—
914C22×C4—26no—
915C22×C4—26no—
916C22×C4—26no—
917C22×C4—26no—
918C22×C4—212no—
919C22×C4—43no—
920C22×C4—43no—
921C22×C4—46no—
922C22×C4—46no—
923C22×C4—46no—
924C22×C4—46no—
925C22×C4C2×#41112yes—
926C22×C4C2513yes—
927C22×C4C2511yescharacteristic
928C22×C4C2513yes—
929C22×C4C2511yescharacteristic
930C22×C4C2511yescharacteristic
931C22×C4C2511yescharacteristic
932C22×C4C2513yes—
933C22×C4C2513yes—
934C22×C4C2511yescharacteristic
935C22×C4C2513yes—
936C22×C4C2513yes—
937C22×C4C2511yescharacteristic
938C22×C4C2513yes—
939C22×C4C2513yes—
940C22×C4C2513yes—
941C22×C4C2513yes—
942C22×C4C2513yes—
943C22×C4C2511yescharacteristic
944C22×C4C2513yes—
945C22×C4C2513yes—
946C22×C4C2511yescharacteristic
947C22×C4C2513yes—
948C22×C4C2511yescharacteristic
949C22×C4C2511yescharacteristic
950C22×C4C2511yescharacteristic
951C22×C4C2511yescharacteristic
952C22×C4C2511yescharacteristic
953C22×C4C2511yescharacteristic
954C22×C4C2513yes—
955C4⋊C4—26no—
956C4⋊C4—26no—
957C4⋊C4—26no—
958C4⋊C4—26no—
959C4⋊C4—26no—
960C4⋊C4—22no—
961C4⋊C4—22no—
962C4⋊C4—26no—
963C4⋊C4—26no—
964C4⋊C4—26no—
965C4⋊C4—26no—
966C4⋊C4—26no—
967C4⋊C4—26no—
968C4⋊C4—22no—
969C4⋊C4—26no—
970C4⋊C4—26no—
971C4⋊C4—26no—
972C4⋊C4—26no—
973C4⋊C4—26no—
974C4⋊C4—212no—
975C4⋊C4—26no—
976C4⋊C4—26no—
977C4⋊C4—26no—
978C4⋊C4—26no—
979C4⋊C4—22no—
980C4⋊C4—22no—
981C4⋊C4—22no—
982C4⋊C4—22no—
983C4⋊C4—22no—
984C4⋊C4—22no—
985C4⋊C4—22no—
986C4⋊C4—26no—
987C4⋊C4—26no—
988C4⋊C4—22no—
989C4⋊C4—22no—
990C4⋊C4—26no—
991C4⋊C4—26no—
992C4⋊C4—46no—
993C4⋊C4—46no—
994C4⋊C4—43no—
995C4⋊C4—43no—
996C4⋊C4—46no—
997C4⋊C4—46no—
998C4⋊C4—46no—
999C4⋊C4—43no—
1000C4⋊C4—43no—
1001C4⋊C4—43no—
1002C4⋊C4—46no—
1003C4⋊C4—46no—
1004C4⋊C4—43no—
1005C4⋊C4—46no—
1006C4⋊C4—46no—
1007C4⋊C4—43no—
1008C4⋊C4—43no—
1009C4⋊C4—43no—
1010C4⋊C4—43no—
1011C4⋊C4—43no—
1012C4⋊C4—43no—
1013C4⋊C4—43no—
1014C4⋊C4—43no—
1015C4⋊C4—43no—
1016C4⋊C4—46no—
1017C4⋊C4—43no—
1018C4⋊C4—43no—
1019C4⋊C4C2×#41112yes—
1020C4⋊C42−1+414yes—
1021C22⋊C4—26no—
1022C22⋊C4—26no—
1023C22⋊C4—212no—
1024C22⋊C4—26no—
1025C22⋊C4—212no—
1026C22⋊C4—26no—
1027C22⋊C4—22no—
1028C22⋊C4—26no—
1029C22⋊C4—26no—
1030C22⋊C4—22no—
1031C22⋊C4—26no—
1032C22⋊C4—26no—
1033C22⋊C4—22no—
1034C22⋊C4—22no—
1035C22⋊C4—22no—
1036C22⋊C4—26no—
1037C22⋊C4—22no—
1038C22⋊C4—22no—
1039C22⋊C4—43no—
1040C22⋊C4—43no—
1041C22⋊C4—46no—
1042C22⋊C4—46no—
1043C22⋊C4—46no—
1044C22⋊C4—43no—
1045C22⋊C4—43no—
1046C22⋊C4—43no—
1047C22⋊C4—43no—
1048C22⋊C4—43no—
1049C22⋊C4—43no—
1050C42—22no—
1051C42—26no—
1052C42—26no—
1053C42—26no—
1054C42—26no—
1055C42—26no—
1056C42—26no—
1057C42—26no—
1058C42—212no—
1059C42—26no—
1060C42—26no—
1061C42—26no—
1062C42—26no—
1063C42—26no—
1064C42—26no—
1065C42—26no—
1066C42—26no—
1067C42—22no—
1068C42—22no—
1069C42—26no—
1070C42—22no—
1071C42—22no—
1072C42—43no—
1073C42—43no—
1074C42—43no—
1075C42—43no—
1076C42—46no—
1077C42—43no—
1078C42—43no—
1079C42—43no—
1080C42—43no—
1081C42—43no—
1082C42C2×#41112yes—
1083C23—23no—
1084C23—23no—
1085C23—23no—
1086C23—23no—
1087C23—23no—
1088C23—23no—
1089C23—21no—
1090C23—21no—
1091C23—21no—
1092C23—21no—
1093C23—21no—
1094C23—21no—
1095C23—21no—
1096C23C22×#4116yes—
1097C23C2611yescharacteristic
1098Q8—412no—
1099Q8—412no—
1100Q8#552116yes—
1101D4—224no—
1102D4—86no—
1103C2×C4—21no—
1104C2×C4—21no—
1105C2×C4—21no—
1106C2×C4—21no—
1107C2×C4—21no—
1108C2×C4—21no—
1109C2×C4—21no—
1110C2×C4—21no—
1111C2×C4—21no—
1112C2×C4—21no—
1113C2×C4—21no—
1114C2×C4—23no—
1115C2×C4—23no—
1116C2×C4—21no—
1117C2×C4—21no—
1118C2×C4—21no—
1119C2×C4—224no—
1120C2×C4—21no—
1121C2×C4—21no—
1122C2×C4—21no—
1123C2×C4—21no—
1124C2×C4—23no—
1125C2×C4—21no—
1126C2×C4—21no—
1127C2×C4—23no—
1128C2×C4—23no—
1129C2×C4—23no—
1130C2×C4—23no—
1131C2×C4—23no—
1132C2×C4—23no—
1133C2×C4—23no—
1134C2×C4—23no—
1135C2×C4—23no—
1136C2×C4—23no—
1137C2×C4—21no—
1138C2×C4—23no—
1139C2×C4—23no—
1140C2×C4—23no—
1141C2×C4—21no—
1142C2×C4—21no—
1143C2×C4—21no—
1144C2×C4—23no—
1145C2×C4—23no—
1146C2×C4—23no—
1147C2×C4—21no—
1148C2×C4—21no—
1149C2×C4—21no—
1150C2×C4—23no—
1151C2×C4—23no—
1152C2×C4—23no—
1153C2×C4—21no—
1154C2×C4—21no—
1155C2×C4—21no—
1156C2×C4—21no—
1157C2×C4—23no—
1158C2×C4—23no—
1159C2×C4—23no—
1160C2×C4—23no—
1161C2×C4—23no—
1162C2×C4—21no—
1163C2×C4—21no—
1164C2×C4—23no—
1165C2×C4—23no—
1166C2×C4—23no—
1167C2×C4—23no—
1168C2×C4—23no—
1169C2×C4—21no—
1170C2×C4—23no—
1171C2×C4—23no—
1172C2×C4—23no—
1173C2×C4—23no—
1174C2×C4—23no—
1175C2×C4—23no—
1176C2×C4—23no—
1177C2×C4—23no—
1178C2×C4—21no—
1179C2×C4—23no—
1180C2×C4—412no—
1181C2×C4—412no—
1182C2×C4—412no—
1183C2×C4—812no—
1184C2×C4—812no—
1185C2×C4C22×#4112yes—
1186C2×C4C22×#4116yes—
1187C2×C4C22×#4112yes—
1188C2×C4C22×#4116yes—
1189C2×C4C22×#4116yes—
1190C2×C4C2×2−1+412yes—
1191C2×C4C2×2−1+412yes—
1192C2×C4C2×2−1+412yes—
1193C2×C4C2×2−1+416yes—
1194C2×C4#58512yes—
1195C2×C4#58512yes—
1196C22—26no—
1197C22—26no—
1198C22—26no—
1199C22—43no—
1200C22—43no—
1201C22—43no—
1202C22—43no—
1203C22—41no—
1204C22—41no—
1205C22—41no—
1206C22—41no—
1207C22—41no—
1208C22—41no—
1209C22—41no—
1210C22C23×#4111yescharacteristic
1211C22C23×#4111yescharacteristic
1212C22C22×2−1+411yescharacteristic
1213C22C22×2−1+411yescharacteristic
1214C22C2×#58511yescharacteristic
1215C22C2×#58511yescharacteristic
1216C22H(7,𝔽2)11yescharacteristic
1217C4—22no—
1218C4—22no—
1219C4—22no—
1220C4—22no—
1221C4—22no—
1222C4—26no—
1223C4—22no—
1224C4—22no—
1225C4—41no—
1226C4—43no—
1227C4—41no—
1228C4—43no—
1229C4—43no—
1230C4—43no—
1231C4—43no—
1232C4—43no—
1233C4—41no—
1234C4—41no—
1235C4—41no—
1236C4—41no—
1237C4—43no—
1238C4—41no—
1239C4—43no—
1240C4—43no—
1241C4—43no—
1242C4—43no—
1243C4—43no—
1244C4—43no—
1245C4C2×#552112yes—
1246C2—46no—
1247C2—81no—
1248C2C22×#55211yescharacteristic
1249C2#6280511yescharacteristic
1250C2#6281011yescharacteristic
1251C2#6295211yescharacteristic
1252C2#6299911yescharacteristic
1253C2#6300811yescharacteristic
1254C2#6303211yescharacteristic
subgroupG/H
center, commutator, Frattini, socle, cosocleC23C26
prime radicalC2×#548C22
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23 ◁ G
LECSG ▷ C23 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #59563C2semidirect
2. #59509C2semidirect
3. #59500C2semidirect
4. #59448C2semidirect
5. #59289C2semidirect
6. #45383C2semidirect
7. #45050C2semidirect
8. #45017C2semidirect
9. #44956C2semidirect
10. #39547C2semidirect
11. #39082C2semidirect
12. #38274C2semidirect
13. #37982C2semidirect
14. #36584C2semidirect
15. Q8×#126C2semidirect
16. Q8×#125C2semidirect
17. #36448C2semidirect
19. #36299C2semidirect
20. #36280C2semidirect
22. #35868C2semidirect
23. #35816C2semidirect
24. #35786C2semidirect
25. #34866C2semidirect
27. #34263C2semidirect
28. #34262C2semidirect
29. #34250C2semidirect
30. C4×#557C2semidirect
31. #34129C2semidirect

Maximal subgroups

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

subgroupindex
#595632
#595092
#595002
#594482
#592892
#453832
#450502
#450172
#449562
#395472
#390822
#382742
#379822
#365842
Q8×#1262
Q8×#1252
#364482
#364322
#362992
#362802
#359962
#358682
#358162
#357862
#348662
#343122
#342632
#342622
#342502
C4×#5572
#341292