Finite Group Databasebeta

← #7688583

Subgroups — #7688583

Order 512.

4779 conjugacy classes of subgroups.

The subgroup lattice has 1128 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#59871C211yesmaximal, characteristic, complemented
2#59432C214yesmaximal, complemented
3#59297C214yesmaximal, complemented
4#59228C212yesmaximal, complemented
5#59211C212yesmaximal, complemented
6#59034C212yesmaximal, complemented
7#45406C214yesmaximal, complemented
8#44521C218yesmaximal, complemented
9#39915C214yesmaximal, complemented
10#39002C214yesmaximal, complemented
11#38932C212yesmaximal, complemented
12#38931C212yesmaximal, complemented
13#36459C212yesmaximal, complemented
14#36459C212yesmaximal, complemented
15#36411C212yesmaximal, complemented
16#36194C211yesmaximal, characteristic, complemented
17#36194C211yesmaximal, characteristic, complemented
18#36176C212yesmaximal, complemented
19#36134C211yesmaximal, characteristic, complemented
20#36050C214yesmaximal, complemented
21#34948C212yesmaximal, complemented
22#34943C211yesmaximal, characteristic, complemented
23#34231C212yesmaximal, complemented
24#34193C212yesmaximal, complemented
25C4×#555C211yesmaximal, characteristic, complemented
26C4×#547C211yesmaximal, characteristic, complemented
27C2×#555C2211yescharacteristic
28C2×#547C2211yescharacteristic
29C2×#533C2212yes—
30C2×C4×#41C2212yes—
31#2868C2211yescharacteristic
32#2860C2214yes—
33#2857C2212yes—
34#2857C2212yes—
35#2857C2212yes—
36#2854C2214yes—
37#2806C2214yes—
38#2779C2218yes—
39#2764C2218yes—
40#2761C2218yes—
41#2758C2218yes—
42#2756C2218yes—
43#2740C2218yes—
44#2705C2218yes—
45#2698C2218yes—
46#2696C2218yes—
47#2687C2218yes—
48#2651C2218yes—
49#2647C2214yes—
50#2596C2218yes—
51#2593C2218yes—
52#2584C2214yes—
53#2582C2214yes—
54#2573C2218yes—
55#2572C2214yes—
56#2571C2212yes—
57#2571C2212yes—
58#2571C2211yescharacteristic
59#2570C2214yes—
60#2570C2214yes—
61#2569C2218yes—
62#2567C2212yes—
63#2563C2212yes—
64#2563C2211yescharacteristic
65#2563C2212yes—
66#2563C2211yescharacteristic
67#2562C2214yes—
68#2560C2218yes—
69#2560C2218yes—
70#2552C2212yes—
71#2552C2212yes—
72#2552C2212yes—
73#2542C2212yes—
74#2538C2212yes—
75#2538C2212yes—
76#2538C2212yes—
77#2537C2211yescharacteristic
78#2536C2214yes—
79#2532C2218yes—
80#2532C2218yes—
81#2532C2218yes—
82#2529C2218yes—
83#2525C2218yes—
84#2524C2218yes—
85#2513C2214yes—
86#2508C2214yes—
87#2507C2214yes—
88#2500C2214yes—
89#2497C2214yes—
90#2497C2214yes—
91#2496C2214yes—
92#2496C2214yes—
93#2495C2214yes—
94#2495C2214yes—
95#2495C2214yes—
96#2495C2212yes—
97#2495C2214yes—
98#2495C2212yes—
99#2492C2214yes—
100#2492C2214yes—
101#2490C2214yes—
102#2490C2214yes—
103#2488C2218yes—
104#2486C2214yes—
105#2485C2214yes—
106#2485C2214yes—
107#2474C2218yes—
108#2461C2218yes—
109#2458C2218yes—
110#2442C2214yes—
111#2442C2214yes—
112#2441C2214yes—
113#2439C2214yes—
114#2439C2214yes—
115#2429C2214yes—
116#2423C2214yes—
117#2422C2214yes—
118#2421C2214yes—
119#2420C2212yes—
120#2420C2212yes—
121#2414C2214yes—
122#2414C2214yes—
123#2407C2214yes—
124#2402C2218yes—
125#2398C2214yes—
126#2372C2214yes—
127#2369C2211yescharacteristic
128#2369C2212yes—
129#2369C2212yes—
130#2369C2212yes—
131#2365C2212yes—
132#2365C2211yescharacteristic
133#2365C2212yes—
134#2363C2212yes—
135#2363C2212yes—
136#2362C2214yes—
137#2362C2214yes—
138#2362C2212yes—
139#2361C2212yes—
140#2359C2214yes—
141#2356C2218yes—
142#2355C2212yes—
143#2355C2212yes—
144#2354C2212yes—
145#2354C2212yes—
146#2354C2214yes—
147#2354C2211yescharacteristic
148#2354C2212yes—
149#2354C2214yes—
150#2354C2211yescharacteristic
151#2354C2214yes—
152#2354C2211yescharacteristic
153#2352C2214yes—
154Q8×C4⋊C4C2212yes—
155Q8×C4⋊C4C2212yes—
156D4×C4⋊C4C2211yescharacteristic
157#2347C2214yes—
158#2347C2218yes—
159#2347C2214yes—
160#2347C2214yes—
161#2346C2214yes—
162#2346C2212yes—
163#2346C2212yes—
164#2344C2212yes—
165#2341C2214yes—
166#2339C2212yes—
167#2332C2218yes—
168#2320C2214yes—
169#2319C2214yes—
170#2319C2218yes—
171C4×C4⋊Q8C2211yescharacteristic
172C4×C4⋊Q8C2211yescharacteristic
173C4×C4⋊Q8C2211yescharacteristic
174C4×#125C2214yes—
175C4×#125C2214yes—
176C4×#125C2214yes—
177C4×#124C2214yes—
178C4×C22⋊Q8C2212yes—
179C4×#123C2214yes—
180C4×#121C2212yes—
181C4×#121C2212yes—
182C4×#121C2212yes—
183C4×#121C2212yes—
184C4×#121C2212yes—
185#2296C2214yes—
186#2285C2212yes—
187#2285C2212yes—
188#2285C2214yes—
189#2283C2212yes—
190#2283C2212yes—
191#2283C2214yes—
192#2276C2214yes—
193C42×D4C2211yescharacteristic
194C42×D4C2211yescharacteristic
195C42×D4C2211yescharacteristic
196C4×#117C2212yes—
197C4×#117C2212yes—
198C2×C4×C4⋊C4C2212yes—
199C22×#41C2312yes—
200#555—28no—
201#547—28no—
202#533—216no—
203C2×C4⋊Q8C2311yescharacteristic
204C2×C4⋊Q8C2311yescharacteristic
205C2×C4⋊Q8C2312yes—
206C2×C4⋊Q8C2312yes—
207C2×C4⋊Q8C2312yes—
208C2×C4⋊Q8C2311yescharacteristic
209C2×#126C2318yes—
210C2×#125C2314yes—
211C2×#125C2314yes—
212C2×#124C2314yes—
213C2×#123C2314yes—
214C2×#123C2318yes—
215C2×C22⋊Q8C2314yes—
216C2×C22⋊Q8C2314yes—
217C2×C22⋊Q8C2312yes—
218C2×C22⋊Q8C2314yes—
219C2×C22⋊Q8C2314yes—
220C2×C22⋊Q8C2314yes—
221C2×#121C2312yes—
222C2×#121C2312yes—
223C2×#121C2312yes—
224C2×#121C2312yes—
225C2×#121C2312yes—
226C4×#41—216no—
227C2×C4×Q8C2312yes—
228C2×C4×Q8C2314yes—
229C2×C4×Q8C2314yes—
230C2×C4×Q8C2312yes—
231C2×C4×Q8C2312yes—
232C2×C4×Q8C2312yes—
233C2×C4×Q8C2314yes—
234C2×C4×D4C2311yescharacteristic
235C2×C4×D4C2311yescharacteristic
236C2×C4×D4C2311yescharacteristic
237C2×C4×D4C2311yescharacteristic
238C2×C4×D4C2312yes—
239C2×C4×D4C2314yes—
240C2×C4×D4C2314yes—
241C2×C4×D4C2311yescharacteristic
242C2×C4×D4C2314yes—
243C2×C4×D4C2311yescharacteristic
244C2×C4×D4C2314yes—
245C2×C4×D4C2311yescharacteristic
246C2×C4×D4C2311yescharacteristic
247C2×C4×D4C2311yescharacteristic
248C2×#117C2314yes—
249C2×#117C2314yes—
250C2×#117C2312yes—
251C2×#117C2312yes—
252C2×#117C2312yes—
253C2×#117C2314yes—
254C2×#117C2312yes—
255C2×#117C2314yes—
256C2×#117C2312yes—
257C22×C4⋊C4C2312yes—
258C22×C4⋊C4C2312yes—
259C22×C42C2314yes—
260C22×C42C2312yes—
261C22×C42C2312yes—
262C22×C42C2312yes—
263#400C2318yes—
264#400C2314yes—
265#400C2318yes—
266#400C2318yes—
267#400C2318yes—
268#400C2318yes—
269#400C2314yes—
270#400C2318yes—
271#400C2318yes—
272#399C2318yes—
273#398C2318yes—
274#398C2318yes—
275#398C2318yes—
276#398C2318yes—
277#398C2318yes—
278#398C2318yes—
279#398C2318yes—
280#397C2318yes—
281#397C2318yes—
282#397C2314yes—
283#397C2318yes—
284#397C2318yes—
285#397C2314yes—
286#397C2318yes—
287#396C2318yes—
288#396C2318yes—
289#396C2318yes—
290#395C2318yes—
291#394C2318yes—
292#394C2318yes—
293#394C2318yes—
294#394C2314yes—
295#394C2318yes—
296#394C2314yes—
297#393C2314yes—
298#393C2318yes—
299#393C2314yes—
300#393C2318yes—
301#392C2318yes—
302#391C2318yes—
303#391C2318yes—
304#391C2312yes—
305#391C2312yes—
306#391C2312yes—
307#391C2314yes—
308#391C2312yes—
309#391C2318yes—
310#391C2314yes—
311#391C2314yes—
312#391C2314yes—
313#391C2314yes—
314#390C2318yes—
315#390C2318yes—
316#390C2314yes—
317#390C2312yes—
318#390C2312yes—
319#390C2314yes—
320#390C2312yes—
321#390C2318yes—
322#390C2314yes—
323#390C2312yes—
324#390C2312yes—
325#390C2314yes—
326#389C2312yes—
327#389C2312yes—
328#389C2314yes—
329#389C2314yes—
330#389C2314yes—
331#389C2314yes—
332#389C2312yes—
333#389C2312yes—
334#389C2312yes—
335#389C2312yes—
336#389C2312yes—
337#389C2312yes—
338#389C2314yes—
339#389C2314yes—
340#389C2312yes—
341#389C2314yes—
342#389C2314yes—
343#389C2314yes—
344#389C2314yes—
345#389C2318yes—
346#389C2314yes—
347#389C2318yes—
348#389C2314yes—
349#389C2318yes—
350#389C2314yes—
351#389C2314yes—
352#389C2312yes—
353#389C2312yes—
354#389C2312yes—
355#388C2314yes—
356#388C2318yes—
357#388C2318yes—
358#388C2318yes—
359#388C2318yes—
360#388C2318yes—
361#388C2318yes—
362#388C2318yes—
363#388C2314yes—
364#388C2314yes—
365#388C2314yes—
366#388C2314yes—
367#388C2318yes—
368#388C2318yes—
369#388C2318yes—
370#388C2318yes—
371#388C2318yes—
372#388C2318yes—
373#388C2314yes—
374#388C2314yes—
375#388C2318yes—
376#388C2318yes—
377#388C2314yes—
378#388C2318yes—
379#388C2314yes—
380#388C2318yes—
381#388C2318yes—
382#388C2314yes—
383#388C2314yes—
384#387C2318yes—
385#387C2318yes—
386#387C2318yes—
387#387C2318yes—
388#387C2318yes—
389#387C2318yes—
390#387C2318yes—
391#387C2318yes—
392#387C2314yes—
393#387C2318yes—
394#387C2314yes—
395#387C2318yes—
396#387C2314yes—
397#387C2318yes—
398#386C2314yes—
399#386C2314yes—
400#386C2314yes—
401#386C2314yes—
402#386C2318yes—
403#386C2314yes—
404#386C2314yes—
405#385C2318yes—
406#385C2318yes—
407#385C2314yes—
408#385C2314yes—
409#384C2311yescharacteristic
410#384C2311yescharacteristic
411#384C2311yescharacteristic
412#384C2314yes—
413#384C2314yes—
414#384C2314yes—
415#384C2312yes—
416#384C2312yes—
417#384C2312yes—
418#384C2312yes—
419#383C2314yes—
420#383C2314yes—
421#383C2318yes—
422#383C2318yes—
423#383C2318yes—
424#382C2312yes—
425#382C2312yes—
426#382C2314yes—
427#382C2314yes—
428#382C2312yes—
429#382C2312yes—
430#382C2314yes—
431#382C2314yes—
432#382C2318yes—
433#382C2314yes—
434#381C2314yes—
435#381C2314yes—
436#381C2314yes—
437#381C2318yes—
438#380C2312yes—
439#380C2312yes—
440#380C2314yes—
441#380C2314yes—
442#380C2314yes—
443#380C2314yes—
444#380C2314yes—
445#380C2312yes—
446#380C2312yes—
447#380C2312yes—
448#380C2312yes—
449#380C2314yes—
450#380C2318yes—
451#380C2318yes—
452#380C2314yes—
453#380C2312yes—
454#380C2314yes—
455#380C2314yes—
456#380C2314yes—
457#380C2312yes—
458#380C2312yes—
459#380C2312yes—
460C4×C4⋊C4C2318yes—
461C4×C4⋊C4C2318yes—
462C4×C4⋊C4C2312yes—
463C4×C4⋊C4C2312yes—
464C4×C4⋊C4C2314yes—
465C4×C4⋊C4C2314yes—
466C4×C4⋊C4C2318yes—
467C4×C4⋊C4C2314yes—
468C4×C4⋊C4C2318yes—
469C4×C4⋊C4C2318yes—
470C4×C4⋊C4C2318yes—
471C4×C4⋊C4C2312yes—
472C4×C4⋊C4C2312yes—
473C4×C4⋊C4C2312yes—
474C4×C4⋊C4C2312yes—
475C4×C4⋊C4C2312yes—
476C4×C4⋊C4C2312yes—
477C4×C4⋊C4C2311yescharacteristic
478C4×C4⋊C4C2311yescharacteristic
479C4×C4⋊C4C2312yes—
480C4×C4⋊C4C2312yes—
481C4×C4⋊C4C2314yes—
482C4×C4⋊C4C2311yescharacteristic
483C4×C4⋊C4C2314yes—
484C4×C4⋊C4C2312yes—
485C4×C4⋊C4C2314yes—
486C4×C4⋊C4C2318yes—
487C4×C4⋊C4C2311yescharacteristic
488C4×C4⋊C4C2311yescharacteristic
489C4×C4⋊C4C2311yescharacteristic
490C4×C4⋊C4C2312yes—
491C4×C4⋊C4C2314yes—
492C4×C4⋊C4C2314yes—
493C4×C4⋊C4C2314yes—
494C4×C4⋊C4C2311yescharacteristic
495C4×C4⋊C4C2311yescharacteristic
496C4×C4⋊C4C2314yes—
497C4×C4⋊C4C2311yescharacteristic
498C4×C4⋊C4C2314yes—
499C4×C22⋊C4C2314yes—
500C4×C22⋊C4C2314yes—
501C4×C22⋊C4C2312yes—
502C4×C22⋊C4C2312yes—
503C4×C22⋊C4C2318yes—
504C4×C22⋊C4C2312yes—
505C4×C22⋊C4C2314yes—
506C4×C22⋊C4C2312yes—
507C4×C22⋊C4C2314yes—
508C4×C22⋊C4C2312yes—
509C4×C22⋊C4C2312yes—
510C4×C22⋊C4C2314yes—
511C4×C22⋊C4C2312yes—
512C4×C22⋊C4C2314yes—
513C4×C22⋊C4C2312yes—
514C4×C22⋊C4C2312yes—
515C4×C22⋊C4C2314yes—
516#376C2314yes—
517#376C2318yes—
518#376C2314yes—
519#376C2314yes—
520C2×#95C2314yes—
521C43C2314yes—
522C43C2311yescharacteristic
523C2×#41—28no—
524C2×#41—28no—
525C2×#41—44no—
526C22×Q8C2412yes—
527C22×Q8C2412yes—
528C22×Q8C2414yes—
529C22×Q8C2412yes—
530C22×D4C2411yescharacteristic
531C22×D4C2411yescharacteristic
532C22×D4C2414yes—
533C22×D4C2411yescharacteristic
534C22×D4C2414yes—
535C22×D4C2414yes—
536C23×C4C2412yes—
537C23×C4C2412yes—
538C23×C4C2412yes—
539C23×C4C2412yes—
540C23×C4C2412yes—
541C23×C4C2414yes—
542C23×C4C2412yes—
543C23×C4C2414yes—
544C23×C4C2412yes—
545C23×C4C2412yes—
546C23×C4C2412yes—
547C4⋊Q8—28no—
548C4⋊Q8—24no—
549C4⋊Q8—24no—
550C4⋊Q8—44no—
551C4⋊Q8—82no—
552C4⋊Q8#4118yes—
553#126—88no—
554#125—216no—
555#125—48no—
556#124—216no—
557#123—216no—
558#123—88no—
559C22⋊Q8—216no—
560C22⋊Q8—28no—
561C22⋊Q8—216no—
562C22⋊Q8—84no—
563C22⋊Q8—84no—
564C22⋊Q8—84no—
565#121—28no—
566#121—28no—
567#121—28no—
568#121—44no—
569#121—44no—
570C4×Q8—216no—
571C4×Q8—28no—
572C4×Q8—216no—
573C4×Q8—28no—
574C4×Q8—44no—
575C4×Q8—44no—
576C4×Q8—48no—
577C4×D4—28no—
578C4×D4—216no—
579C4×D4—216no—
580C4×D4—24no—
581C4×D4—24no—
582C4×D4—24no—
583C4×D4—24no—
584C4×D4—24no—
585C4×D4—42no—
586C4×D4—42no—
587C4×D4—42no—
588C4×D4—48no—
589C4×D4—48no—
590C4×D4#4118yes—
591#117—28no—
592#117—28no—
593#117—216no—
594#117—28no—
595#117—216no—
596#117—44no—
597#117—48no—
598#117—44no—
599#117—48no—
600C2×C4⋊C4—28no—
601C2×C4⋊C4—44no—
602C2×C4⋊C4C2411yescharacteristic
603C2×C4⋊C4C2411yescharacteristic
604C2×C4⋊C4C2414yes—
605C2×C4⋊C4C2412yes—
606C2×C4⋊C4C2412yes—
607C2×C4⋊C4C2411yescharacteristic
608C2×C4⋊C4C2411yescharacteristic
609C2×C4⋊C4C2411yescharacteristic
610C2×C4⋊C4C2412yes—
611C2×C4⋊C4C2414yes—
612C2×C4⋊C4C2414yes—
613C2×C4⋊C4C2412yes—
614C2×C4⋊C4C2414yes—
615C2×C4⋊C4C2412yes—
616C2×C4⋊C4C2412yes—
617C2×C4⋊C4C2412yes—
618C2×C4⋊C4C2414yes—
619C2×C4⋊C4C2411yescharacteristic
620C2×C4⋊C4C2411yescharacteristic
621C2×C4⋊C4C2411yescharacteristic
622C2×C4⋊C4C2418yes—
623C2×C4⋊C4C2418yes—
624C2×C4⋊C4C2414yes—
625C2×C4⋊C4C2412yes—
626C2×C4⋊C4C2412yes—
627C2×C4⋊C4C2412yes—
628C2×C4⋊C4C2414yes—
629C2×C4⋊C4C2414yes—
630C2×C4⋊C4C2414yes—
631C2×C4⋊C4C2412yes—
632C2×C4⋊C4C2412yes—
633C2×C4⋊C4C2418yes—
634C2×C4⋊C4C2414yes—
635C2×C4⋊C4C2414yes—
636C2×C4⋊C4C2412yes—
637C2×C4⋊C4C2418yes—
638C2×C4⋊C4C2418yes—
639C2×C4⋊C4C2418yes—
640C2×C4⋊C4C2414yes—
641C2×C4⋊C4C2414yes—
642C2×C4⋊C4C2418yes—
643C2×C4⋊C4C2418yes—
644C2×C4⋊C4C2418yes—
645C2×C4⋊C4C2414yes—
646C2×C4⋊C4C2412yes—
647C2×C4⋊C4C2411yescharacteristic
648C2×C4⋊C4C2412yes—
649C2×C22⋊C4C2414yes—
650C2×C22⋊C4C2414yes—
651C2×C22⋊C4C2414yes—
652C2×C22⋊C4C2414yes—
653C2×C22⋊C4C2418yes—
654C2×C22⋊C4C2412yes—
655C2×C22⋊C4C2412yes—
656C2×C22⋊C4C2412yes—
657C2×C22⋊C4C2412yes—
658C2×C22⋊C4C2412yes—
659C2×C22⋊C4C2414yes—
660C2×C22⋊C4C2414yes—
661C2×C22⋊C4C2414yes—
662C2×C22⋊C4C2418yes—
663C2×C22⋊C4C2418yes—
664C2×C22⋊C4C2414yes—
665C2×C22⋊C4C2412yes—
666C2×C22⋊C4C2412yes—
667C2×C22⋊C4C2412yes—
668C2×C22⋊C4C2414yes—
669C2×C22⋊C4C2414yes—
670C2×C22⋊C4C2414yes—
671C2×C22⋊C4C2414yes—
672C2×C22⋊C4C2414yes—
673C2×C22⋊C4C2418yes—
674C2×C22⋊C4C2418yes—
675C2×C22⋊C4C2418yes—
676C2×C22⋊C4C2414yes—
677C2×C22⋊C4C2414yes—
678C2×C22⋊C4C2414yes—
679C2×C22⋊C4C2412yes—
680C2×C42—216no—
681C2×C42—28no—
682C2×C42—28no—
683C2×C42—28no—
684C2×C42C2414yes—
685C2×C42C2412yes—
686C2×C42C2414yes—
687C2×C42C2418yes—
688C2×C42C2411yescharacteristic
689C2×C42C2411yescharacteristic
690C2×C42C2414yes—
691C2×C42C2414yes—
692C2×C42C2412yes—
693C2×C42C2414yes—
694C2×C42C2414yes—
695C2×C42C2411yescharacteristic
696C2×C42C2412yes—
697C2×C42C2412yes—
698C2×C42C2412yes—
699C2×C42C2412yes—
700C2×C42C2412yes—
701C2×C42C2412yes—
702C2×C42C2412yes—
703C2×C42C2414yes—
704C2×C42C2414yes—
705C2×C42C2418yes—
706C2×C42C2418yes—
707C2×C42C2418yes—
708C2×C42C2414yes—
709C2×C42C2411yescharacteristic
710C2×C42C2411yescharacteristic
711C2×C42C2411yescharacteristic
712C2×C42C2411yescharacteristic
713#95C2412yes—
714#95C2414yes—
715#95C2414yes—
716#95C2414yes—
717#95C2414yes—
718#95C2414yes—
719#95C2412yes—
720#95C2412yes—
721#95C2414yes—
722#95C2414yes—
723#95C2414yes—
724#95C2414yes—
725#95C2414yes—
726#95C2414yes—
727#95C2418yes—
728#95C2414yes—
729#95C2414yes—
730#95C2418yes—
731#95C2414yes—
732#95C2412yes—
733#95C2412yes—
734#95C2412yes—
735#95C2412yes—
736#95C2412yes—
737#95C2412yes—
738#95C2418yes—
739#95C2414yes—
740#95C2414yes—
741#95C2414yes—
742#95C2414yes—
743#95C2414yes—
744#95C2418yes—
745#95C2418yes—
746#95C2418yes—
747#95C2418yes—
748#95C2418yes—
749#95C2418yes—
750#95C2418yes—
751#95C2414yes—
752#95C2414yes—
753#95C2414yes—
754#95C2418yes—
755#95C2418yes—
756#95C2418yes—
757C24C2512yes—
758C24C2512yes—
759C24C2512yes—
760#41—432no—
761C2×Q8—24no—
762C2×Q8—28no—
763C2×Q8—24no—
764C2×Q8—24no—
765C2×Q8—24no—
766C2×Q8—42no—
767C2×Q8—42no—
768C2×Q8—42no—
769C2×Q8—42no—
770C2×Q8—44no—
771C2×Q8—44no—
772C2×Q8C2×#4118yes—
773C2×D4—28no—
774C2×D4—28no—
775C2×D4—22no—
776C2×D4—22no—
777C2×D4—22no—
778C2×D4—28no—
779C2×D4—22no—
780C2×D4—22no—
781C2×D4—22no—
782C2×D4—22no—
783C2×D4—22no—
784C2×D4—44no—
785C2×D4—44no—
786C2×D4—44no—
787C2×D4—44no—
788C2×D4—44no—
789C2×D4—44no—
790C2×D4C2×#4114yes—
791C22×C4—24no—
792C22×C4—24no—
793C22×C4—28no—
794C22×C4—28no—
795C22×C4—24no—
796C22×C4—24no—
797C22×C4—24no—
798C22×C4—24no—
799C22×C4—24no—
800C22×C4—28no—
801C22×C4—24no—
802C22×C4—24no—
803C22×C4—24no—
804C22×C4—24no—
805C22×C4—24no—
806C22×C4—24no—
807C22×C4—24no—
808C22×C4—24no—
809C22×C4—24no—
810C22×C4—24no—
811C22×C4—24no—
812C22×C4—24no—
813C22×C4—24no—
814C22×C4—44no—
815C22×C4—44no—
816C22×C4—42no—
817C22×C4—42no—
818C22×C4—42no—
819C22×C4—42no—
820C22×C4—42no—
821C22×C4—42no—
822C22×C4—44no—
823C22×C4C2×#4118yes—
824C22×C4C2512yes—
825C22×C4C2512yes—
826C22×C4C2512yes—
827C22×C4C2512yes—
828C22×C4C2512yes—
829C22×C4C2512yes—
830C22×C4C2514yes—
831C22×C4C2512yes—
832C22×C4C2514yes—
833C22×C4C2514yes—
834C22×C4C2514yes—
835C22×C4C2512yes—
836C22×C4C2511yescharacteristic
837C22×C4C2518yes—
838C22×C4C2514yes—
839C22×C4C2511yescharacteristic
840C22×C4C2512yes—
841C22×C4C2514yes—
842C22×C4C2511yescharacteristic
843C22×C4C2511yescharacteristic
844C22×C4C2511yescharacteristic
845C22×C4C2511yescharacteristic
846C22×C4C2511yescharacteristic
847C4⋊C4—22no—
848C4⋊C4—28no—
849C4⋊C4—22no—
850C4⋊C4—28no—
851C4⋊C4—28no—
852C4⋊C4—24no—
853C4⋊C4—24no—
854C4⋊C4—24no—
855C4⋊C4—28no—
856C4⋊C4—22no—
857C4⋊C4—216no—
858C4⋊C4—216no—
859C4⋊C4—28no—
860C4⋊C4—22no—
861C4⋊C4—22no—
862C4⋊C4—24no—
863C4⋊C4—24no—
864C4⋊C4—22no—
865C4⋊C4—24no—
866C4⋊C4—24no—
867C4⋊C4—22no—
868C4⋊C4—22no—
869C4⋊C4—24no—
870C4⋊C4—28no—
871C4⋊C4—24no—
872C4⋊C4—24no—
873C4⋊C4—44no—
874C4⋊C4—44no—
875C4⋊C4—44no—
876C4⋊C4—42no—
877C4⋊C4—42no—
878C4⋊C4—48no—
879C4⋊C4—44no—
880C4⋊C4—44no—
881C4⋊C4—42no—
882C4⋊C4—48no—
883C4⋊C4—48no—
884C4⋊C4—48no—
885C4⋊C4—44no—
886C4⋊C4—44no—
887C4⋊C4—48no—
888C4⋊C4—48no—
889C4⋊C4—48no—
890C4⋊C4—44no—
891C4⋊C4C2×#4118yes—
892C4⋊C4C2×#4114yes—
893C4⋊C4C2×#4118yes—
894C22⋊C4—28no—
895C22⋊C4—28no—
896C22⋊C4—28no—
897C22⋊C4—28no—
898C22⋊C4—216no—
899C22⋊C4—24no—
900C22⋊C4—24no—
901C22⋊C4—24no—
902C22⋊C4—28no—
903C22⋊C4—24no—
904C22⋊C4—24no—
905C22⋊C4—44no—
906C22⋊C4—48no—
907C22⋊C4—44no—
908C22⋊C4—48no—
909C22⋊C4—44no—
910C22⋊C4—44no—
911C22⋊C4—42no—
912C22⋊C4—42no—
913C22⋊C4—44no—
914C22⋊C4—44no—
915C22⋊C4—42no—
916C22⋊C4—44no—
917C22⋊C4—44no—
918C22⋊C4—48no—
919C22⋊C4—48no—
920C22⋊C4—48no—
921C22⋊C4—44no—
922C22⋊C4—44no—
923C22⋊C4—44no—
924C22⋊C4C2×#4118yes—
925C42—24no—
926C42—28no—
927C42—24no—
928C42—28no—
929C42—28no—
930C42—24no—
931C42—24no—
932C42—24no—
933C42—24no—
934C42—28no—
935C42—216no—
936C42—24no—
937C42—24no—
938C42—24no—
939C42—22no—
940C42—22no—
941C42—28no—
942C42—28no—
943C42—22no—
944C42—44no—
945C42—48no—
946C42—48no—
947C42—44no—
948C42—48no—
949C42—44no—
950C42—41no—
951C42C2×#4114yes—
952C42C2×#4114yes—
953C422−1+414yes—
954C23—22no—
955C23—22no—
956C23—22no—
957C23—22no—
958C23—22no—
959C23—22no—
960C23—22no—
961C23—22no—
962C23—22no—
963C23—22no—
964C23—22no—
965C23—22no—
966C23—22no—
967C23—22no—
968C23—22no—
969C23—22no—
970C23—22no—
971C23—22no—
972C23—22no—
973C23—22no—
974C23C22×#4114yes—
975C23C2611yescharacteristic
976Q8—216no—
977Q8—84no—
978Q8—88no—
979Q8—84no—
980D4—28no—
981D4—416no—
982D4—44no—
983D4—44no—
984D4—88no—
985D4—88no—
986C2×C4—24no—
987C2×C4—22no—
988C2×C4—21no—
989C2×C4—21no—
990C2×C4—21no—
991C2×C4—22no—
992C2×C4—24no—
993C2×C4—21no—
994C2×C4—21no—
995C2×C4—21no—
996C2×C4—216no—
997C2×C4—22no—
998C2×C4—22no—
999C2×C4—22no—
1000C2×C4—22no—
1001C2×C4—24no—
1002C2×C4—22no—
1003C2×C4—22no—
1004C2×C4—22no—
1005C2×C4—24no—
1006C2×C4—28no—
1007C2×C4—22no—
1008C2×C4—22no—
1009C2×C4—22no—
1010C2×C4—22no—
1011C2×C4—22no—
1012C2×C4—22no—
1013C2×C4—24no—
1014C2×C4—24no—
1015C2×C4—21no—
1016C2×C4—24no—
1017C2×C4—21no—
1018C2×C4—21no—
1019C2×C4—24no—
1020C2×C4—24no—
1021C2×C4—22no—
1022C2×C4—24no—
1023C2×C4—24no—
1024C2×C4—22no—
1025C2×C4—22no—
1026C2×C4—24no—
1027C2×C4—28no—
1028C2×C4—22no—
1029C2×C4—22no—
1030C2×C4—22no—
1031C2×C4—22no—
1032C2×C4—24no—
1033C2×C4—22no—
1034C2×C4—24no—
1035C2×C4—22no—
1036C2×C4—22no—
1037C2×C4—24no—
1038C2×C4—24no—
1039C2×C4—24no—
1040C2×C4—28no—
1041C2×C4—22no—
1042C2×C4—416no—
1043C2×C4—48no—
1044C2×C4—48no—
1045C2×C4—48no—
1046C2×C4—48no—
1047C2×C4—48no—
1048C2×C4—84no—
1049C2×C4—84no—
1050C2×C4—84no—
1051C2×C4—88no—
1052C2×C4C22×#4114yes—
1053C2×C4C22×#4112yes—
1054C2×C4C22×#4112yes—
1055C2×C4C22×#4118yes—
1056C2×C4C22×#4112yes—
1057C2×C4C22×#4112yes—
1058C2×C4C22×#4112yes—
1059C2×C4C22×#4112yes—
1060C2×C4C2×2−1+412yes—
1061C2×C4C2×2−1+412yes—
1062C2×C4C2×2−1+412yes—
1063C2×C4#58512yes—
1064C2×C4#58512yes—
1065C2×C4#58512yes—
1066C22—24no—
1067C22—24no—
1068C22—24no—
1069C22—42no—
1070C22—42no—
1071C22—42no—
1072C22—42no—
1073C22—42no—
1074C22—42no—
1075C22—42no—
1076C22—42no—
1077C22—42no—
1078C22—42no—
1079C22—42no—
1080C22—42no—
1081C22—42no—
1082C22—42no—
1083C22—42no—
1084C22—42no—
1085C22—42no—
1086C22—42no—
1087C22C23×#4111yescharacteristic
1088C22C23×#4111yescharacteristic
1089C22C22×2−1+411yescharacteristic
1090C22C2×#58511yescharacteristic
1091C22C2×#58511yescharacteristic
1092C22C2×#58511yescharacteristic
1093C22H(7,𝔽2)11yescharacteristic
1094C4—22no—
1095C4—22no—
1096C4—24no—
1097C4—22no—
1098C4—28no—
1099C4—44no—
1100C4—42no—
1101C4—44no—
1102C4—42no—
1103C4—48no—
1104C4—41no—
1105C4—44no—
1106C4—44no—
1107C4—42no—
1108C4—42no—
1109C4—42no—
1110C4—42no—
1111C4—44no—
1112C4—42no—
1113C4—42no—
1114C4#347514yes—
1115C4#351514yes—
1116C4#351814yes—
1117C2—44no—
1118C2—82no—
1119C2—82no—
1120C2C2×#347511yescharacteristic
1121C2C2×#351511yescharacteristic
1122C2C2×#351811yescharacteristic
1123C2#6292911yescharacteristic
1124C2#6299411yescharacteristic
1125C2#6300611yescharacteristic
1126C2#6303111yescharacteristic
subgroupG/H
center, commutator, Frattini, socle, cosocleC23C26
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23 ◁ G
LECSG ▷ C23 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #59871C2semidirect
2. #59432C2semidirect
3. #59297C2semidirect
4. #59228C2semidirect
5. #59211C2semidirect
6. #59034C2semidirect
7. #45406C2semidirect
8. #44521C2semidirect
9. #39915C2semidirect
10. #39002C2semidirect
11. #38932C2semidirect
12. #38931C2semidirect
13. #36459C2semidirect
14. #36459C2semidirect
15. #36411C2semidirect
16. #36194C2semidirect
17. #36194C2semidirect
18. #36176C2semidirect
19. #36134C2semidirect
20. #36050C2semidirect
21. #34948C2semidirect
22. #34943C2semidirect
23. #34231C2semidirect
24. #34193C2semidirect
25. C4×#555C2semidirect
26. C4×#547C2semidirect

Maximal subgroups

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

subgroupindex
#598712
#594322
#592972
#592282
#592112
#590342
#454062
#445212
#399152
#390022
#389322
#389312
#364592
#364112
#361942
#361762
#361342
#360502
#349482
#349432
#342312
#341932
C4×#5552
C4×#5472