Finite Group Databasebeta

← #7710984

Subgroups — #7710984

Order 512.

4750 conjugacy classes of subgroups.

The subgroup lattice has 1144 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#59871C211yesmaximal, characteristic, complemented
2#59870C211yesmaximal, characteristic, complemented
3#59864C211yesmaximal, characteristic, complemented
4#59863C211yesmaximal, characteristic, complemented
5#59436C212yesmaximal, complemented
6#59435C212yesmaximal, complemented
7#46332C214yesmaximal, complemented
8#46285C214yesmaximal, complemented
9#39801C214yesmaximal, complemented
10#39771C212yesmaximal, complemented
11#39754C212yesmaximal, complemented
12#39545C214yesmaximal, complemented
13#39515C212yesmaximal, complemented
14#39498C212yesmaximal, complemented
15#39199C214yesmaximal, complemented
16#39190C214yesmaximal, complemented
17#37632C212yesmaximal, complemented
18#37140C214yesmaximal, complemented
19#36635C211yesmaximal, characteristic, complemented
20#36631C211yesmaximal, characteristic
21#36177C212yesmaximal, complemented
22#36176C212yesmaximal, complemented
23#36117C212yesmaximal
24#36116C212yesmaximal, complemented
25#35111C214yesmaximal, complemented
26#34384C212yesmaximal, complemented
27C2×C4×C4⋊Q8C211yesmaximal, characteristic, complemented
28C22×C4⋊Q8C2211yescharacteristic
29C2×#529C2212yes—
30C2×#529C2214yes—
31C22×C4×Q8C2212yes—
32#2864C2212yes—
33#2863C2212yes—
34#2863C2212yes—
35#2862C2211yescharacteristic
36#2861C2212yes—
37#2860C2212yes—
38#2860C2212yes—
39#2859C2211yescharacteristic
40#2859C2211yescharacteristic
41#2858C2211yescharacteristic
42#2857C2211yescharacteristic
43#2857C2211yescharacteristic
44#2857C2211yescharacteristic
45#2856C2211yescharacteristic
46#2855C2214yes—
47#2855C2212yes—
48#2855C2212yes—
49#2854C2212yes—
50#2854C2214yes—
51#2854C2212yes—
52#2851C2212yes—
53#2850C2212yes—
54#2821C2218yes—
55#2808C2214yes—
56#2807C2218yes—
57#2806C2214yes—
58#2805C2214yes—
59#2804C2214yes—
60#2802C2218yes—
61#2798C2218yes—
62#2796C2218yes—
63#2788C2218yes—
64#2787C2218yes—
65#2777C2218yes—
66#2775C2218yes—
67#2774C2218yes—
68#2773C2218yes—
69#2771C2218yes—
70#2759C2218yes—
71#2751C2218yes—
72#2745C2218yes—
73#2660C2214yes—
74#2640C2214yes—
75#2628C2214yes—
76#2628C2214yes—
77#2623C2218yes—
78#2614C2218yes—
79#2604C2218yes—
80#2604C2218yes—
81#2599C2218yes—
82#2599C2218yes—
83#2592C2214yes—
84#2592C2214yes—
85#2584C2214yes—
86#2584C2214yes—
87#2582C2214yes—
88#2581C2214yes—
89#2581C2214yes—
90#2580C2214yes—
91#2580C2214yes—
92#2580C2214yes—
93#2571C2214yes—
94#2571C2212yes—
95#2571C2212yes—
96#2570C2214yes—
97#2568C2212yes—
98#2567C2212yes—
99#2567C2212yes—
100#2563C2212yes—
101#2563C2212yes—
102#2563C2212yes—
103#2552C2212yes—
104#2552C2212yes—
105#2548C2212yes—
106#2547C2212yes—
107#2533C2218yes—
108#2532C2218yes—
109#2514C2214yes—
110#2514C2214yes—
111#2513C2214yes—
112#2513C2214yes—
113#2512C2214yes—
114#2511C2214yes—
115#2509C2214yes—
116#2509C2214yes—
117#2508C2214yes—
118#2507C2214yes—
119#2503C2214yes—
120#2501C2214yes—
121#2496C2214yes—
122#2495C2214yes—
123#2495C2214yes—
124#2494C2214yes—
125#2493C2218yes—
126#2488C2218yes—
127#2487C2214yes—
128#2486C2214yes—
129#2486C2214yes—
130#2485C2214yes—
131#2479C2218yes—
132#2478C2218yes—
133#2454C2214yes—
134#2453C2214yes—
135#2448C2214yes—
136#2448C2214yes—
137#2447C2214yes—
138#2447C2214yes—
139#2442C2214yes—
140#2441C2214yes—
141#2425C2218yes—
142#2419C2218yes—
143#2383C2218yes—
144#2369C2212yes—
145#2366C2212yes—
146#2365C2212yes—
147#2365C2212yes—
148#2361C2214yes—
149#2360C2214yes—
150#2356C2214yes—
151#2355C2212yes—
152#2355C2212yes—
153#2354C2214yes—
154#2354C2212yes—
155#2354C2212yes—
156#2352C2214yes—
157Q8×C4⋊C4C2212yes—
158Q8×C4⋊C4C2212yes—
159D4×C4⋊C4C2214yes—
160D4×C4⋊C4C2212yes—
161D4×C4⋊C4C2212yes—
162#2346C2214yes—
163#2344C2214yes—
164#2330C2214yes—
165#2326C2214yes—
166#2322C2218yes—
167#2322C2218yes—
168#2317C2214yes—
169#2314C2214yes—
170C4×C4⋊Q8C2211yescharacteristic
171C4×C4⋊Q8C2211yescharacteristic
172C4×C4⋊Q8C2211yescharacteristic
173C4×C4⋊Q8C2211yescharacteristic
174C4×C4⋊Q8C2211yescharacteristic
175C4×C4⋊Q8C2212yes—
176C4×C4⋊Q8C2212yes—
177C4×C4⋊Q8C2212yes—
178C4×C4⋊Q8C2212yes—
179C4×C4⋊Q8C2212yes—
180C4×C4⋊Q8C2211yescharacteristic
181C4×C4⋊Q8C2211yescharacteristic
182C4×C4⋊Q8C2212yes—
183C4×#127C2211yescharacteristic
184C4×#125C2212yes—
185C4×#124C2212yes—
186C4×C22⋊Q8C2212yes—
187C4×C22⋊Q8C2212yes—
188C4×#121C2212yes—
189C4×#121C2212yes—
190#2295C2212yes—
191#2295C2212yes—
192C2×#391C2212yes—
193#2293C2212yes—
194#2293C2212yes—
195C2×#389C2212yes—
196C2×#389C2212yes—
197C2×#384C2211yescharacteristic
198#2283C2212yes—
199#2283C2214yes—
200C2×C4×C4⋊C4C2212yes—
201C2×C4×C4⋊C4C2212yes—
202C2×C43C2211yescharacteristic
203C23×Q8C2312yes—
204C2×C4⋊Q8—28no—
205C2×C4⋊Q8C2311yescharacteristic
206C2×C4⋊Q8C2311yescharacteristic
207C2×C4⋊Q8C2312yes—
208C2×C4⋊Q8C2312yes—
209C2×C4⋊Q8C2312yes—
210C2×C4⋊Q8C2311yescharacteristic
211C2×C4⋊Q8C2311yescharacteristic
212C2×C4⋊Q8C2311yescharacteristic
213C2×#127C2311yescharacteristic
214#529—216no—
215#529—416no—
216C2×#126C2314yes—
217C2×#126C2318yes—
218C2×#125C2312yes—
219C2×#125C2312yes—
220C2×#125C2314yes—
221C2×#124C2312yes—
222C2×#124C2314yes—
223C2×#124C2312yes—
224C2×#123C2314yes—
225C2×#123C2318yes—
226C2×#123C2318yes—
227C2×C22⋊Q8C2312yes—
228C2×C22⋊Q8C2312yes—
229C2×C22⋊Q8C2312yes—
230C2×#121C2312yes—
231C2×#121C2312yes—
232C2×#121C2312yes—
233C2×C4×Q8—48no—
234C2×C4×Q8C2312yes—
235C2×C4×Q8C2312yes—
236C2×C4×Q8C2312yes—
237C2×C4×Q8C2314yes—
238C2×C4×Q8C2312yes—
239C2×C4×Q8C2312yes—
240C2×C4×Q8C2314yes—
241C2×C4×Q8C2312yes—
242C2×C4×Q8C2312yes—
243C2×C4×Q8C2314yes—
244C2×C4×Q8C2314yes—
245C2×C4×D4C2312yes—
246C2×C4×D4C2312yes—
247C2×C4×D4C2314yes—
248C2×C4×D4C2312yes—
249C2×C4×D4C2318yes—
250C2×C4×D4C2314yes—
251C2×C4×D4C2314yes—
252C2×#117C2314yes—
253C2×#117C2314yes—
254C2×#117C2318yes—
255C22×C4⋊C4C2312yes—
256C22×C4⋊C4C2312yes—
257C22×C4⋊C4C2314yes—
258C22×C4⋊C4C2312yes—
259C22×C4⋊C4C2314yes—
260C22×C4⋊C4C2312yes—
261C22×C4⋊C4C2312yes—
262C22×C42C2311yescharacteristic
263C22×C42C2314yes—
264C22×C42C2311yescharacteristic
265C22×C42C2311yescharacteristic
266C22×C42C2311yescharacteristic
267C22×C42C2311yescharacteristic
268C22×C42C2311yescharacteristic
269C22×C42C2311yescharacteristic
270#401C2318yes—
271#400C2318yes—
272#400C2318yes—
273#400C2318yes—
274#400C2318yes—
275#400C2318yes—
276#400C2318yes—
277#400C2318yes—
278#400C2318yes—
279#400C2318yes—
280#400C2318yes—
281#399C2318yes—
282#399C2318yes—
283#399C2318yes—
284#399C2318yes—
285#398C2318yes—
286#398C2318yes—
287#398C2318yes—
288#398C2318yes—
289#398C2318yes—
290#398C2318yes—
291#397C2318yes—
292#397C2318yes—
293#397C2318yes—
294#397C2318yes—
295#397C2318yes—
296#397C2318yes—
297#397C2318yes—
298#397C2318yes—
299#396C2318yes—
300#395C2318yes—
301#395C2318yes—
302#395C2318yes—
303#395C2318yes—
304#394C2318yes—
305#393C2318yes—
306#393C2318yes—
307#393C2318yes—
308#393C2318yes—
309#393C2318yes—
310#391C2312yes—
311#391C2314yes—
312#391C2314yes—
313#391C2312yes—
314#391C2312yes—
315#391C2312yes—
316#391C2312yes—
317#391C2312yes—
318#391C2312yes—
319#391C2314yes—
320#391C2314yes—
321#391C2314yes—
322#391C2314yes—
323#391C2312yes—
324#391C2314yes—
325#391C2318yes—
326#391C2312yes—
327#391C2312yes—
328#391C2312yes—
329#391C2312yes—
330#391C2312yes—
331#391C2312yes—
332#390C2312yes—
333#390C2312yes—
334#390C2312yes—
335#390C2314yes—
336#390C2314yes—
337#390C2314yes—
338#390C2312yes—
339#390C2314yes—
340#390C2314yes—
341#390C2312yes—
342#390C2312yes—
343#390C2312yes—
344#390C2312yes—
345#390C2312yes—
346#390C2312yes—
347#389C2312yes—
348#389C2312yes—
349#389C2312yes—
350#389C2312yes—
351#389C2312yes—
352#389C2312yes—
353#389C2312yes—
354#389C2312yes—
355#389C2312yes—
356#389C2312yes—
357#389C2314yes—
358#389C2314yes—
359#389C2314yes—
360#389C2314yes—
361#389C2312yes—
362#389C2312yes—
363#389C2312yes—
364#389C2312yes—
365#389C2312yes—
366#389C2312yes—
367#389C2314yes—
368#389C2314yes—
369#389C2314yes—
370#389C2314yes—
371#389C2314yes—
372#389C2318yes—
373#389C2314yes—
374#389C2314yes—
375#389C2314yes—
376#389C2318yes—
377#389C2318yes—
378#389C2318yes—
379#389C2318yes—
380#389C2312yes—
381#389C2314yes—
382#389C2312yes—
383#389C2314yes—
384#389C2318yes—
385#389C2312yes—
386#389C2312yes—
387#389C2312yes—
388#389C2312yes—
389#389C2312yes—
390#389C2312yes—
391#389C2312yes—
392#389C2312yes—
393#389C2312yes—
394#389C2312yes—
395#389C2318yes—
396#388C2318yes—
397#388C2318yes—
398#388C2318yes—
399#388C2318yes—
400#388C2318yes—
401#388C2318yes—
402#388C2314yes—
403#388C2314yes—
404#388C2314yes—
405#388C2314yes—
406#388C2318yes—
407#388C2318yes—
408#388C2314yes—
409#388C2314yes—
410#388C2318yes—
411#388C2314yes—
412#388C2314yes—
413#388C2318yes—
414#388C2318yes—
415#387C2314yes—
416#387C2314yes—
417#387C2318yes—
418#387C2318yes—
419#387C2318yes—
420#387C2318yes—
421#387C2318yes—
422#387C2318yes—
423#387C2318yes—
424#387C2314yes—
425#387C2314yes—
426#387C2314yes—
427#387C2318yes—
428#387C2318yes—
429#387C2314yes—
430#387C2314yes—
431#387C2314yes—
432#387C2318yes—
433#387C2318yes—
434#387C2318yes—
435#387C2318yes—
436#386C2314yes—
437#386C2318yes—
438#386C2314yes—
439#386C2318yes—
440#385C2318yes—
441#385C2318yes—
442#385C2314yes—
443#385C2318yes—
444#385C2318yes—
445#385C2318yes—
446#385C2318yes—
447#385C2318yes—
448#385C2318yes—
449#385C2314yes—
450#384C2311yescharacteristic
451#384C2312yes—
452#384C2312yes—
453#384C2311yescharacteristic
454#384C2311yescharacteristic
455#384C2312yes—
456#384C2311yescharacteristic
457#384C2311yescharacteristic
458#384C2311yescharacteristic
459#384C2314yes—
460#384C2314yes—
461#384C2314yes—
462#383C2314yes—
463#383C2318yes—
464#383C2318yes—
465#382C2312yes—
466#382C2314yes—
467#382C2314yes—
468#382C2314yes—
469#382C2314yes—
470#382C2312yes—
471#382C2312yes—
472#382C2314yes—
473#382C2318yes—
474#382C2312yes—
475#381C2314yes—
476#381C2318yes—
477#381C2318yes—
478#381C2318yes—
479#380C2314yes—
480#380C2314yes—
481#380C2314yes—
482#380C2314yes—
483#380C2314yes—
484#380C2314yes—
485#380C2312yes—
486#380C2312yes—
487#380C2312yes—
488#380C2312yes—
489#380C2312yes—
490#380C2312yes—
491#380C2318yes—
492C4×C4⋊C4C2312yes—
493C4×C4⋊C4C2312yes—
494C4×C4⋊C4C2314yes—
495C4×C4⋊C4C2314yes—
496C4×C4⋊C4C2312yes—
497C4×C4⋊C4C2312yes—
498C4×C4⋊C4C2312yes—
499C4×C4⋊C4C2312yes—
500C4×C4⋊C4C2312yes—
501C4×C4⋊C4C2312yes—
502C4×C4⋊C4C2312yes—
503C4×C4⋊C4C2312yes—
504C4×C4⋊C4C2314yes—
505C4×C4⋊C4C2314yes—
506C4×C4⋊C4C2314yes—
507C4×C4⋊C4C2314yes—
508C4×C4⋊C4C2312yes—
509C4×C4⋊C4C2312yes—
510C4×C4⋊C4C2312yes—
511C4×C4⋊C4C2312yes—
512C4×C4⋊C4C2314yes—
513C4×C4⋊C4C2314yes—
514C4×C4⋊C4C2314yes—
515C4×C4⋊C4C2314yes—
516C4×C4⋊C4C2314yes—
517C4×C4⋊C4C2314yes—
518C4×C22⋊C4C2318yes—
519C4×C22⋊C4C2314yes—
520C4×C22⋊C4C2314yes—
521C4×C22⋊C4C2314yes—
522#376C2314yes—
523#376C2318yes—
524C2×#95C2314yes—
525C2×#95C2314yes—
526C43C2311yescharacteristic
527C43C2311yescharacteristic
528C43C2311yescharacteristic
529C43C2311yescharacteristic
530C43C2311yescharacteristic
531C43C2311yescharacteristic
532C43C2311yescharacteristic
533C43C2311yescharacteristic
534C22×Q8—28no—
535C22×Q8—44no—
536C22×Q8—44no—
537C22×Q8C2412yes—
538C22×Q8C2412yes—
539C22×Q8C2412yes—
540C22×Q8C2414yes—
541C22×Q8C2412yes—
542C22×Q8C2412yes—
543C22×D4C2414yes—
544C22×D4C2412yes—
545C22×D4C2412yes—
546C22×D4C2412yes—
547C23×C4C2414yes—
548C23×C4C2414yes—
549C23×C4C2411yescharacteristic
550C23×C4C2411yescharacteristic
551C23×C4C2411yescharacteristic
552C23×C4C2411yescharacteristic
553C23×C4C2411yescharacteristic
554C23×C4C2411yescharacteristic
555C23×C4C2414yes—
556C23×C4C2411yescharacteristic
557C23×C4C2418yes—
558C4⋊Q8—28no—
559C4⋊Q8—24no—
560C4⋊Q8—24no—
561C4⋊Q8—28no—
562C4⋊Q8—28no—
563C4⋊Q8—24no—
564C4⋊Q8—24no—
565C4⋊Q8—24no—
566#127—24no—
567#126—216no—
568#126—416no—
569#125—28no—
570#125—44no—
571#125—48no—
572#124—28no—
573#124—44no—
574#124—48no—
575#123—216no—
576#123—416no—
577#123—416no—
578C22⋊Q8—28no—
579C22⋊Q8—28no—
580C22⋊Q8—44no—
581#121—28no—
582#121—28no—
583#121—44no—
584C4×Q8—28no—
585C4×Q8—28no—
586C4×Q8—44no—
587C4×Q8—48no—
588C4×Q8—44no—
589C4×Q8—48no—
590C4×Q8—44no—
591C4×Q8—44no—
592C4×Q8—44no—
593C4×Q8—48no—
594C4×Q8—48no—
595C4×D4—216no—
596C4×D4—28no—
597C4×D4—28no—
598C4×D4—48no—
599C4×D4—48no—
600C4×D4—44no—
601C4×D4—416no—
602#117—216no—
603#117—416no—
604#117—48no—
605C2×C4⋊C4—28no—
606C2×C4⋊C4—28no—
607C2×C4⋊C4—48no—
608C2×C4⋊C4—44no—
609C2×C4⋊C4—44no—
610C2×C4⋊C4—44no—
611C2×C4⋊C4—48no—
612C2×C4⋊C4C2412yes—
613C2×C4⋊C4C2412yes—
614C2×C4⋊C4C2412yes—
615C2×C4⋊C4C2412yes—
616C2×C4⋊C4C2412yes—
617C2×C4⋊C4C2412yes—
618C2×C4⋊C4C2412yes—
619C2×C4⋊C4C2412yes—
620C2×C4⋊C4C2412yes—
621C2×C4⋊C4C2414yes—
622C2×C4⋊C4C2414yes—
623C2×C4⋊C4C2414yes—
624C2×C4⋊C4C2412yes—
625C2×C4⋊C4C2414yes—
626C2×C4⋊C4C2414yes—
627C2×C4⋊C4C2412yes—
628C2×C4⋊C4C2412yes—
629C2×C4⋊C4C2414yes—
630C2×C4⋊C4C2412yes—
631C2×C4⋊C4C2412yes—
632C2×C4⋊C4C2412yes—
633C2×C4⋊C4C2414yes—
634C2×C4⋊C4C2412yes—
635C2×C4⋊C4C2414yes—
636C2×C4⋊C4C2412yes—
637C2×C4⋊C4C2412yes—
638C2×C4⋊C4C2412yes—
639C2×C4⋊C4C2412yes—
640C2×C4⋊C4C2412yes—
641C2×C4⋊C4C2412yes—
642C2×C4⋊C4C2412yes—
643C2×C4⋊C4C2414yes—
644C2×C4⋊C4C2412yes—
645C2×C4⋊C4C2414yes—
646C2×C4⋊C4C2414yes—
647C2×C4⋊C4C2414yes—
648C2×C4⋊C4C2414yes—
649C2×C4⋊C4C2414yes—
650C2×C4⋊C4C2414yes—
651C2×C4⋊C4C2418yes—
652C2×C4⋊C4C2418yes—
653C2×C4⋊C4C2418yes—
654C2×C4⋊C4C2412yes—
655C2×C4⋊C4C2418yes—
656C2×C4⋊C4C2412yes—
657C2×C4⋊C4C2418yes—
658C2×C4⋊C4C2414yes—
659C2×C4⋊C4C2412yes—
660C2×C4⋊C4C2414yes—
661C2×C4⋊C4C2412yes—
662C2×C4⋊C4C2418yes—
663C2×C4⋊C4C2418yes—
664C2×C4⋊C4C2414yes—
665C2×C4⋊C4C2414yes—
666C2×C22⋊C4C2414yes—
667C2×C22⋊C4C2414yes—
668C2×C22⋊C4C2414yes—
669C2×C22⋊C4C2414yes—
670C2×C22⋊C4C2414yes—
671C2×C22⋊C4C2414yes—
672C2×C22⋊C4C2414yes—
673C2×C22⋊C4C2414yes—
674C2×C22⋊C4C2414yes—
675C2×C22⋊C4C2418yes—
676C2×C22⋊C4C2418yes—
677C2×C22⋊C4C2418yes—
678C2×C22⋊C4C2418yes—
679C2×C22⋊C4C2418yes—
680C2×C22⋊C4C2414yes—
681C2×C22⋊C4C2414yes—
682C2×C22⋊C4C2418yes—
683C2×C22⋊C4C2418yes—
684C2×C22⋊C4C2414yes—
685C2×C22⋊C4C2414yes—
686C2×C42—24no—
687C2×C42—216no—
688C2×C42—24no—
689C2×C42—24no—
690C2×C42—42no—
691C2×C42—42no—
692C2×C42—42no—
693C2×C42#4118yes—
694C2×C42C2414yes—
695C2×C42C2414yes—
696C2×C42C2411yescharacteristic
697C2×C42C2414yes—
698C2×C42C2414yes—
699C2×C42C2411yescharacteristic
700C2×C42C2411yescharacteristic
701C2×C42C2411yescharacteristic
702C2×C42C2411yescharacteristic
703C2×C42C2414yes—
704C2×C42C2414yes—
705C2×C42C2411yescharacteristic
706C2×C42C2414yes—
707C2×C42C2411yescharacteristic
708C2×C42C2411yescharacteristic
709C2×C42C2411yescharacteristic
710C2×C42C2411yescharacteristic
711C2×C42C2411yescharacteristic
712C2×C42C2411yescharacteristic
713C2×C42C2411yescharacteristic
714C2×C42C2411yescharacteristic
715C2×C42C2418yes—
716C2×C42C2418yes—
717C2×C42C2418yes—
718C2×C42C2411yescharacteristic
719C2×C42C2411yescharacteristic
720C2×C42C2411yescharacteristic
721C2×C42C2411yescharacteristic
722C2×C42C2411yescharacteristic
723C2×C42C2411yescharacteristic
724C2×C42C2411yescharacteristic
725C2×C42C2411yescharacteristic
726C2×C42C2411yescharacteristic
727C2×C42C2411yescharacteristic
728C2×C42C2411yescharacteristic
729C2×C42C2411yescharacteristic
730C2×C42C2411yescharacteristic
731C2×C42C2411yescharacteristic
732#95C2414yes—
733#95C2414yes—
734#95C2414yes—
735#95C2414yes—
736#95C2414yes—
737#95C2414yes—
738#95C2414yes—
739#95C2414yes—
740#95C2414yes—
741#95C2414yes—
742#95C2418yes—
743#95C2414yes—
744#95C2414yes—
745#95C2414yes—
746#95C2414yes—
747#95C2418yes—
748#95C2418yes—
749#95C2414yes—
750#95C2414yes—
751#95C2418yes—
752#95C2414yes—
753#95C2414yes—
754#95C2414yes—
755#95C2414yes—
756#95C2418yes—
757#95C2418yes—
758#95C2418yes—
759#95C2414yes—
760#95C2414yes—
761#95C2418yes—
762#95C2418yes—
763#95C2414yes—
764#95C2414yes—
765#95C2418yes—
766#95C2414yes—
767#95C2414yes—
768#95C2414yes—
769#95C2414yes—
770#95C2418yes—
771#95C2418yes—
772#95C2418yes—
773#95C2418yes—
774C24C2514yes—
775C24C2511yescharacteristic
776C2×Q8—24no—
777C2×Q8—28no—
778C2×Q8—24no—
779C2×Q8—24no—
780C2×Q8—24no—
781C2×Q8—24no—
782C2×Q8—24no—
783C2×Q8—24no—
784C2×Q8—24no—
785C2×Q8—24no—
786C2×Q8—42no—
787C2×Q8—44no—
788C2×Q8—42no—
789C2×Q8—42no—
790C2×Q8—44no—
791C2×Q8—42no—
792C2×Q8—42no—
793C2×Q8—42no—
794C2×Q8—432no—
795C2×D4—28no—
796C2×D4—28no—
797C2×D4—28no—
798C2×D4—24no—
799C2×D4—24no—
800C2×D4—24no—
801C2×D4—24no—
802C2×D4—24no—
803C2×D4—24no—
804C2×D4—24no—
805C2×D4—42no—
806C2×D4—42no—
807C22×C4—22no—
808C22×C4—22no—
809C22×C4—22no—
810C22×C4—22no—
811C22×C4—22no—
812C22×C4—22no—
813C22×C4—22no—
814C22×C4—22no—
815C22×C4—28no—
816C22×C4—22no—
817C22×C4—28no—
818C22×C4—22no—
819C22×C4—22no—
820C22×C4—28no—
821C22×C4—28no—
822C22×C4—28no—
823C22×C4—22no—
824C22×C4—22no—
825C22×C4—28no—
826C22×C4—28no—
827C22×C4—41no—
828C22×C4—41no—
829C22×C4—41no—
830C22×C4—41no—
831C22×C4—44no—
832C22×C4—44no—
833C22×C4—48no—
834C22×C4—48no—
835C22×C4—48no—
836C22×C4C2×#4114yes—
837C22×C4C2×#4114yes—
838C22×C4C2×#4114yes—
839C22×C4H(5,𝔽2)14yes—
840C22×C4C2511yescharacteristic
841C22×C4C2511yescharacteristic
842C22×C4C2514yes—
843C22×C4C2514yes—
844C22×C4C2514yes—
845C22×C4C2514yes—
846C22×C4C2514yes—
847C22×C4C2514yes—
848C22×C4C2514yes—
849C22×C4C2514yes—
850C22×C4C2514yes—
851C22×C4C2514yes—
852C22×C4C2511yescharacteristic
853C22×C4C2511yescharacteristic
854C22×C4C2514yes—
855C22×C4C2511yescharacteristic
856C22×C4C2511yescharacteristic
857C22×C4C2511yescharacteristic
858C22×C4C2511yescharacteristic
859C22×C4C2511yescharacteristic
860C22×C4C2511yescharacteristic
861C22×C4C2511yescharacteristic
862C22×C4C2511yescharacteristic
863C22×C4C2511yescharacteristic
864C22×C4C2511yescharacteristic
865C4⋊C4—28no—
866C4⋊C4—28no—
867C4⋊C4—24no—
868C4⋊C4—24no—
869C4⋊C4—24no—
870C4⋊C4—24no—
871C4⋊C4—28no—
872C4⋊C4—28no—
873C4⋊C4—24no—
874C4⋊C4—28no—
875C4⋊C4—24no—
876C4⋊C4—28no—
877C4⋊C4—28no—
878C4⋊C4—24no—
879C4⋊C4—24no—
880C4⋊C4—24no—
881C4⋊C4—24no—
882C4⋊C4—28no—
883C4⋊C4—24no—
884C4⋊C4—24no—
885C4⋊C4—24no—
886C4⋊C4—24no—
887C4⋊C4—24no—
888C4⋊C4—24no—
889C4⋊C4—24no—
890C4⋊C4—24no—
891C4⋊C4—24no—
892C4⋊C4—24no—
893C4⋊C4—24no—
894C4⋊C4—24no—
895C4⋊C4—44no—
896C4⋊C4—44no—
897C4⋊C4—48no—
898C4⋊C4—42no—
899C4⋊C4—44no—
900C4⋊C4—42no—
901C4⋊C4—44no—
902C4⋊C4—44no—
903C4⋊C4—44no—
904C4⋊C4—44no—
905C4⋊C4—48no—
906C4⋊C4—42no—
907C4⋊C4—48no—
908C4⋊C4—42no—
909C4⋊C4—44no—
910C4⋊C4—48no—
911C4⋊C4—48no—
912C4⋊C4—42no—
913C4⋊C4—42no—
914C4⋊C4—44no—
915C4⋊C4—48no—
916C4⋊C4—48no—
917C4⋊C4—44no—
918C4⋊C4—44no—
919C22⋊C4—28no—
920C22⋊C4—28no—
921C22⋊C4—28no—
922C22⋊C4—28no—
923C22⋊C4—28no—
924C22⋊C4—28no—
925C22⋊C4—28no—
926C22⋊C4—28no—
927C22⋊C4—28no—
928C22⋊C4—48no—
929C22⋊C4—48no—
930C22⋊C4—48no—
931C22⋊C4—44no—
932C22⋊C4—48no—
933C22⋊C4—48no—
934C22⋊C4—44no—
935C22⋊C4—48no—
936C22⋊C4—48no—
937C22⋊C4—44no—
938C22⋊C4—44no—
939C42—28no—
940C42—28no—
941C42—28no—
942C42—22no—
943C42—22no—
944C42—22no—
945C42—22no—
946C42—28no—
947C42—28no—
948C42—22no—
949C42—22no—
950C42—22no—
951C42—22no—
952C42—22no—
953C42—22no—
954C42—28no—
955C42—22no—
956C42—22no—
957C42—22no—
958C42—22no—
959C42—28no—
960C42—41no—
961C42—41no—
962C42—41no—
963C42—41no—
964C42—41no—
965C42—41no—
966C42—41no—
967C42—41no—
968C42—48no—
969C42—48no—
970C42—48no—
971C42C2×#4114yes—
972C42C2×#4114yes—
973C42C2×#4114yes—
974C42C2×#4114yes—
975C422−1+414yes—
976C422−1+414yes—
977C23—21no—
978C23—21no—
979C23—21no—
980C23—21no—
981C23—24no—
982C23—24no—
983C23—24no—
984C23—24no—
985C23—24no—
986C23—24no—
987C23—24no—
988C23C22×#4112yes—
989C23C2×H(5,𝔽2)12yes—
990C23#58512yes—
991C23C2611yescharacteristic
992Q8—416no—
993Q8—48no—
994Q8—48no—
995Q8—48no—
996Q8—48no—
997Q8—84no—
998D4—416no—
999D4—48no—
1000D4—48no—
1001D4—84no—
1002C2×C4—21no—
1003C2×C4—21no—
1004C2×C4—21no—
1005C2×C4—21no—
1006C2×C4—21no—
1007C2×C4—21no—
1008C2×C4—21no—
1009C2×C4—21no—
1010C2×C4—21no—
1011C2×C4—21no—
1012C2×C4—21no—
1013C2×C4—21no—
1014C2×C4—21no—
1015C2×C4—21no—
1016C2×C4—28no—
1017C2×C4—28no—
1018C2×C4—28no—
1019C2×C4—28no—
1020C2×C4—24no—
1021C2×C4—24no—
1022C2×C4—24no—
1023C2×C4—24no—
1024C2×C4—24no—
1025C2×C4—24no—
1026C2×C4—24no—
1027C2×C4—24no—
1028C2×C4—24no—
1029C2×C4—21no—
1030C2×C4—21no—
1031C2×C4—24no—
1032C2×C4—24no—
1033C2×C4—24no—
1034C2×C4—21no—
1035C2×C4—21no—
1036C2×C4—24no—
1037C2×C4—24no—
1038C2×C4—24no—
1039C2×C4—24no—
1040C2×C4—24no—
1041C2×C4—24no—
1042C2×C4—24no—
1043C2×C4—21no—
1044C2×C4—21no—
1045C2×C4—21no—
1046C2×C4—21no—
1047C2×C4—21no—
1048C2×C4—21no—
1049C2×C4—24no—
1050C2×C4—21no—
1051C2×C4—24no—
1052C2×C4—24no—
1053C2×C4—24no—
1054C2×C4—24no—
1055C2×C4—24no—
1056C2×C4—21no—
1057C2×C4—24no—
1058C2×C4—24no—
1059C2×C4—24no—
1060C2×C4—24no—
1061C2×C4—24no—
1062C2×C4—24no—
1063C2×C4—24no—
1064C2×C4—24no—
1065C2×C4—44no—
1066C2×C4—44no—
1067C2×C4—44no—
1068C2×C4—416no—
1069C2×C4—416no—
1070C2×C4—88no—
1071C2×C4—816no—
1072C2×C4C22×#4112yes—
1073C2×C4C22×#4112yes—
1074C2×C4C22×#4112yes—
1075C2×C4C22×#4112yes—
1076C2×C4C22×#4112yes—
1077C2×C4C22×#4112yes—
1078C2×C4C2×H(5,𝔽2)12yes—
1079C2×C4C2×H(5,𝔽2)12yes—
1080C2×C4C2×2−1+412yes—
1081C2×C4C2×2−1+412yes—
1082C2×C4C2×2−1+412yes—
1083C2×C4C2×2−1+412yes—
1084C2×C4C2×2−1+412yes—
1085C2×C4C2×2−1+412yes—
1086C2×C4#58512yes—
1087C2×C4#58512yes—
1088C22—22no—
1089C22—22no—
1090C22—22no—
1091C22—22no—
1092C22—22no—
1093C22—22no—
1094C22—44no—
1095C22—44no—
1096C22—44no—
1097C22—44no—
1098C22—44no—
1099C22—44no—
1100C22—44no—
1101C22#350614yes—
1102C22C23×#4111yescharacteristic
1103C22C22×H(5,𝔽2)11yescharacteristic
1104C22C22×2−1+411yescharacteristic
1105C22C22×2−1+411yescharacteristic
1106C22C2×#58511yescharacteristic
1107C22C2×#58511yescharacteristic
1108C22C2×#58511yescharacteristic
1109C4—22no—
1110C4—22no—
1111C4—22no—
1112C4—22no—
1113C4—22no—
1114C4—22no—
1115C4—22no—
1116C4—44no—
1117C4—41no—
1118C4—41no—
1119C4—44no—
1120C4—44no—
1121C4—44no—
1122C4—44no—
1123C4—44no—
1124C4—44no—
1125C4—44no—
1126C4—44no—
1127C4—44no—
1128C4—41no—
1129C4—41no—
1130C4—44no—
1131C4#350714yes—
1132C4#350714yes—
1133C4#354414yes—
1134C2—24no—
1135C2—84no—
1136C2C2×#354411yescharacteristic
1137C2#6275911yescharacteristic
1138C2C2×#350611yescharacteristic
1139C2C2×#350711yescharacteristic
1140C2C2×#350711yescharacteristic
1141C2#6283111yescharacteristic
1142C2#6283111yescharacteristic
subgroupG/H
center, commutator, Frattini, socle, cosocleC23C26
prime radical#2856C22
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. #59870C2semidirect
3. #59864C2semidirect
4. #59863C2semidirect
5. #59436C2semidirect
6. #59435C2semidirect
7. #46332C2semidirect
8. #46285C2semidirect
9. #39801C2semidirect
10. #39771C2semidirect
11. #39754C2semidirect
12. #39545C2semidirect
13. #39515C2semidirect
14. #39498C2semidirect
15. #39199C2semidirect
16. #39190C2semidirect
17. #37632C2semidirect
18. #37140C2semidirect
19. #36635C2semidirect
21. #36177C2semidirect
22. #36176C2semidirect
24. #36116C2semidirect
25. #35111C2semidirect
26. #34384C2semidirect
27. C2×C4×C4⋊Q8C2semidirect

Maximal subgroups

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

subgroupindex
#598712
#598702
#598642
#598632
#594362
#594352
#463322
#462852
#398012
#397712
#397542
#395452
#395152
#394982
#391992
#391902
#376322
#371402
#366352
#366312
#361772
#361762
#361172
#361162
#351112
#343842
C2×C4×C4⋊Q82