Finite Group Databasebeta

← #7985245

Subgroups — #7985245

Order 512.

5079 conjugacy classes of subgroups.

The subgroup lattice has 1129 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#59821C211yesmaximal, characteristic, complemented
2#59642C212yesmaximal, complemented
3#59421C212yesmaximal, complemented
4#59084C212yesmaximal, complemented
5#48228C218yesmaximal, complemented
6#45633C214yesmaximal, complemented
7#45292C214yesmaximal, complemented
8#44875C214yesmaximal, complemented
9#42841C214yesmaximal, complemented
10#42549C214yesmaximal, complemented
11#39633C212yesmaximal, complemented
12#39377C212yesmaximal, complemented
13#39245C214yesmaximal, complemented
14#38964C212yesmaximal, complemented
15#38931C212yesmaximal, complemented
16#36563C211yesmaximal, characteristic, complemented
17Q8×C4⋊Q8C211yesmaximal, characteristic, complemented
18Q8×C22⋊Q8C212yesmaximal, complemented
19#36464C212yesmaximal, complemented
20#36127C211yesmaximal, characteristic
21#35249C212yesmaximal, complemented
22#35170C212yesmaximal, complemented
23#34954C211yesmaximal, characteristic, complemented
24#34945C211yesmaximal, characteristic, complemented
25#34481C212yesmaximal, complemented
26C4×D4×Q8C211yesmaximal, characteristic, complemented
27C2×Q82C2212yes—
28C2×#556C2212yes—
29C2×D4×Q8C2211yescharacteristic
30C2×#547C2212yes—
31C2×#542C2214yes—
32C2×#532C2212yes—
33C22×C4×Q8C2212yes—
34#2868C2211yescharacteristic
35#2868C2212yes—
36#2859C2212yes—
37#2857C2212yes—
38#2857C2214yes—
39#2854C2214yes—
40#2854C2214yes—
41#2838C2218yes—
42#2807C2218yes—
43#2798C2218yes—
44#2790C2218yes—
45#2763C2218yes—
46#2759C2218yes—
47#2758C2218yes—
48#2731C2218yes—
49#2729C2218yes—
50#2727C2214yes—
51#2724C2218yes—
52#2720C2218yes—
53#2718C2218yes—
54#2717C2218yes—
55#2702C2218yes—
56#2698C2218yes—
57#2680C2218yes—
58#2674C2218yes—
59#2663C2218yes—
60#2654C2218yes—
61#2647C2214yes—
62#2632C2218yes—
63#2628C2214yes—
64#2593C2214yes—
65#2589C2218yes—
66#2582C2212yes—
67#2582C2214yes—
68#2582C2211yescharacteristic
69#2580C2214yes—
70#2580C2214yes—
71#2573C2214yes—
72#2571C2211yescharacteristic
73#2571C2211yescharacteristic
74#2570C2214yes—
75#2568C2211yescharacteristic
76#2567C2212yes—
77#2567C2214yes—
78#2567C2214yes—
79#2567C2212yes—
80#2560C2218yes—
81#2558C2218yes—
82#2553C2218yes—
83#2552C2212yes—
84#2551C2212yes—
85#2551C2214yes—
86#2551C2212yes—
87#2551C2214yes—
88#2550C2214yes—
89#2548C2211yescharacteristic
90#2548C2211yescharacteristic
91#2548C2212yes—
92#2547C2212yes—
93#2547C2211yescharacteristic
94#2542C2212yes—
95#2538C2211yescharacteristic
96#2538C2212yes—
97#2537C2212yes—
98#2537C2212yes—
99#2521C2218yes—
100#2518C2218yes—
101#2514C2212yes—
102#2513C2212yes—
103#2513C2212yes—
104#2512C2214yes—
105#2508C2214yes—
106#2507C2214yes—
107#2502C2214yes—
108#2501C2214yes—
109#2497C2214yes—
110#2496C2214yes—
111#2496C2214yes—
112#2495C2214yes—
113#2494C2212yes—
114#2492C2214yes—
115#2492C2214yes—
116#2491C2214yes—
117#2491C2214yes—
118#2452C2214yes—
119#2452C2214yes—
120#2451C2214yes—
121#2451C2218yes—
122#2451C2214yes—
123#2448C2212yes—
124#2448C2214yes—
125#2448C2212yes—
126#2447C2212yes—
127#2440C2214yes—
128#2440C2218yes—
129#2440C2214yes—
130#2439C2214yes—
131#2436C2214yes—
132#2432C2214yes—
133#2432C2218yes—
134#2427C2214yes—
135#2426C2214yes—
136#2426C2214yes—
137#2423C2214yes—
138#2422C2214yes—
139#2422C2214yes—
140#2422C2214yes—
141#2421C2214yes—
142#2421C2212yes—
143#2415C2214yes—
144#2406C2218yes—
145#2401C2214yes—
146#2395C2214yes—
147#2383C2218yes—
148#2369C2212yes—
149#2367C2214yes—
150#2367C2214yes—
151#2365C2212yes—
152#2365C2211yescharacteristic
153#2363C2214yes—
154#2360C2214yes—
155#2360C2212yes—
156#2360C2214yes—
157#2355C2212yes—
158#2354C2212yes—
159Q8×C4⋊C4C2212yes—
160Q8×C4⋊C4C2212yes—
161Q8×C4⋊C4C2214yes—
162Q8×C4⋊C4C2212yes—
163Q8×C4⋊C4C2211yescharacteristic
164Q8×C4⋊C4C2212yes—
165D4×C4⋊C4C2212yes—
166D4×C4⋊C4C2212yes—
167D4×C4⋊C4C2212yes—
168D4×C4⋊C4C2211yescharacteristic
169#2347C2214yes—
170Q8×C22⋊C4C2214yes—
171Q8×C22⋊C4C2212yes—
172#2334C2218yes—
173#2326C2214yes—
174#2326C2214yes—
175#2323C2214yes—
176#2320C2214yes—
177#2317C2214yes—
178C4×C4⋊Q8C2212yes—
179C4×C4⋊Q8C2212yes—
180C4×C4⋊Q8C2212yes—
181C4×C4⋊Q8C2211yescharacteristic
182C4×C4⋊Q8C2211yescharacteristic
183C4×#127C2211yescharacteristic
184C4×#124C2212yes—
185C4×#124C2212yes—
186C4×#124C2212yes—
187C4×C22⋊Q8C2212yes—
188C4×C22⋊Q8C2214yes—
189C4×C22⋊Q8C2214yes—
190C4×C22⋊Q8C2212yes—
191#2295C2212yes—
192#2293C2212yes—
193#2293C2212yes—
194#2283C2212yes—
195C42×Q8C2211yescharacteristic
196C42×Q8C2211yescharacteristic
197C42×D4C2211yescharacteristic
198C42×D4C2212yes—
199C22×#41C2314yes—
200C23×Q8C2312yes—
201Q82—48no—
202#556—216no—
203D4×Q8—28no—
204#547—48no—
205#542—416no—
206#532—48no—
207C2×C4⋊Q8C2311yescharacteristic
208C2×C4⋊Q8C2312yes—
209C2×C4⋊Q8C2312yes—
210C2×C4⋊Q8C2314yes—
211C2×C4⋊Q8C2314yes—
212C2×C4⋊Q8C2314yes—
213C2×C4⋊Q8C2312yes—
214C2×C4⋊Q8C2318yes—
215C2×C4⋊Q8C2314yes—
216C2×C4⋊Q8C2312yes—
217C2×C4⋊Q8C2311yescharacteristic
218C2×#127C2311yescharacteristic
219C2×#126C2318yes—
220C2×#126C2318yes—
221C2×#125C2314yes—
222C2×#124C2312yes—
223C2×#124C2314yes—
224C2×#124C2312yes—
225C2×#124C2312yes—
226C2×#124C2314yes—
227C2×#124C2318yes—
228C2×#123C2318yes—
229C2×#123C2318yes—
230C2×#123C2318yes—
231C2×C22⋊Q8C2314yes—
232C2×C22⋊Q8C2314yes—
233C2×C22⋊Q8C2312yes—
234C2×C22⋊Q8C2312yes—
235C2×C22⋊Q8C2318yes—
236C2×C22⋊Q8C2314yes—
237C2×C22⋊Q8C2314yes—
238C2×C22⋊Q8C2318yes—
239C2×#121C2314yes—
240C2×#121C2314yes—
241C2×#121C2314yes—
242C2×C4×Q8—48no—
243C2×C4×Q8C2312yes—
244C2×C4×Q8C2312yes—
245C2×C4×Q8C2311yescharacteristic
246C2×C4×Q8C2311yescharacteristic
247C2×C4×Q8C2314yes—
248C2×C4×Q8C2311yescharacteristic
249C2×C4×Q8C2311yescharacteristic
250C2×C4×Q8C2311yescharacteristic
251C2×C4×Q8C2311yescharacteristic
252C2×C4×Q8C2314yes—
253C2×C4×Q8C2314yes—
254C2×C4×Q8C2314yes—
255C2×C4×Q8C2312yes—
256C2×C4×Q8C2312yes—
257C2×C4×Q8C2314yes—
258C2×C4×Q8C2314yes—
259C2×C4×D4C2312yes—
260C2×C4×D4C2312yes—
261C2×C4×D4C2312yes—
262C2×C4×D4C2311yescharacteristic
263C2×C4×D4C2312yes—
264C2×C4×D4C2311yescharacteristic
265C2×C4×D4C2311yescharacteristic
266C2×C4×D4C2312yes—
267C2×C4×D4C2314yes—
268C2×C4×D4C2314yes—
269C2×#117C2314yes—
270C2×#117C2314yes—
271C22×C4⋊C4C2314yes—
272C22×C4⋊C4C2314yes—
273C22×C4⋊C4C2312yes—
274C22×C42C2312yes—
275C22×C42C2314yes—
276#401C2314yes—
277#400C2314yes—
278#400C2318yes—
279#400C2314yes—
280#400C2314yes—
281#400C2318yes—
282#400C2318yes—
283#400C2318yes—
284#400C2314yes—
285#399C2318yes—
286#399C2318yes—
287#399C2318yes—
288#399C2314yes—
289#398C2318yes—
290#398C2318yes—
291#398C2318yes—
292#398C2314yes—
293#398C2318yes—
294#398C2318yes—
295#398C2318yes—
296#397C2318yes—
297#397C2314yes—
298#397C2314yes—
299#397C2318yes—
300#397C2318yes—
301#397C2314yes—
302#397C2314yes—
303#397C2314yes—
304#397C2314yes—
305#397C2318yes—
306#396C2314yes—
307#396C2318yes—
308#396C2318yes—
309#396C2318yes—
310#395C2318yes—
311#395C2318yes—
312#395C2318yes—
313#395C2318yes—
314#395C2318yes—
315#395C2318yes—
316#394C2318yes—
317#394C2314yes—
318#394C2314yes—
319#394C2318yes—
320#394C2318yes—
321#394C2318yes—
322#394C2318yes—
323#393C2318yes—
324#393C2318yes—
325#393C2318yes—
326#393C2318yes—
327#391C2318yes—
328#391C2314yes—
329#391C2312yes—
330#391C2314yes—
331#391C2314yes—
332#391C2312yes—
333#391C2314yes—
334#391C2318yes—
335#391C2312yes—
336#391C2312yes—
337#391C2312yes—
338#391C2312yes—
339#391C2312yes—
340#391C2312yes—
341#391C2312yes—
342#391C2314yes—
343#391C2314yes—
344#391C2318yes—
345#391C2318yes—
346#390C2318yes—
347#390C2312yes—
348#390C2312yes—
349#390C2312yes—
350#390C2312yes—
351#390C2312yes—
352#390C2314yes—
353#390C2314yes—
354#390C2312yes—
355#390C2314yes—
356#390C2312yes—
357#390C2312yes—
358#390C2312yes—
359#390C2312yes—
360#389C2314yes—
361#389C2312yes—
362#389C2314yes—
363#389C2312yes—
364#389C2312yes—
365#389C2312yes—
366#389C2314yes—
367#389C2312yes—
368#389C2314yes—
369#389C2314yes—
370#389C2312yes—
371#389C2312yes—
372#389C2314yes—
373#389C2312yes—
374#389C2314yes—
375#389C2314yes—
376#389C2314yes—
377#389C2318yes—
378#389C2318yes—
379#389C2312yes—
380#389C2312yes—
381#389C2312yes—
382#389C2314yes—
383#389C2314yes—
384#389C2318yes—
385#389C2318yes—
386#389C2314yes—
387#389C2312yes—
388#389C2314yes—
389#389C2318yes—
390#389C2312yes—
391#389C2314yes—
392#389C2312yes—
393#389C2314yes—
394#389C2314yes—
395#389C2318yes—
396#388C2314yes—
397#388C2314yes—
398#388C2318yes—
399#388C2314yes—
400#388C2318yes—
401#388C2318yes—
402#388C2318yes—
403#388C2318yes—
404#388C2318yes—
405#388C2314yes—
406#388C2318yes—
407#388C2314yes—
408#388C2318yes—
409#388C2314yes—
410#388C2314yes—
411#388C2314yes—
412#388C2314yes—
413#388C2314yes—
414#388C2318yes—
415#388C2318yes—
416#388C2318yes—
417#387C2318yes—
418#387C2318yes—
419#387C2318yes—
420#387C2314yes—
421#387C2314yes—
422#387C2314yes—
423#387C2318yes—
424#387C2314yes—
425#387C2314yes—
426#387C2318yes—
427#387C2314yes—
428#387C2318yes—
429#386C2318yes—
430#386C2318yes—
431#385C2318yes—
432#385C2318yes—
433#385C2314yes—
434#385C2318yes—
435#385C2318yes—
436#385C2318yes—
437#385C2318yes—
438#385C2318yes—
439#385C2314yes—
440#385C2314yes—
441#385C2314yes—
442#385C2318yes—
443#385C2318yes—
444#384C2311yescharacteristic
445#384C2311yescharacteristic
446#384C2312yes—
447#384C2312yes—
448#384C2311yescharacteristic
449#384C2312yes—
450#384C2314yes—
451#384C2312yes—
452#384C2318yes—
453#384C2314yes—
454#384C2314yes—
455#384C2312yes—
456#384C2314yes—
457#384C2314yes—
458#383C2314yes—
459#383C2318yes—
460#382C2312yes—
461#382C2312yes—
462#382C2312yes—
463#382C2312yes—
464#382C2312yes—
465#382C2318yes—
466#382C2314yes—
467#381C2314yes—
468#380C2314yes—
469#380C2314yes—
470#380C2318yes—
471#380C2314yes—
472#380C2312yes—
473#380C2312yes—
474#380C2312yes—
475#380C2314yes—
476#380C2312yes—
477#380C2314yes—
478#380C2314yes—
479C4×C4⋊C4C2314yes—
480C4×C4⋊C4C2311yescharacteristic
481C4×C4⋊C4C2312yes—
482C4×C4⋊C4C2312yes—
483C4×C4⋊C4C2314yes—
484C4×C4⋊C4C2314yes—
485C4×C4⋊C4C2314yes—
486C4×C4⋊C4C2314yes—
487C4×C4⋊C4C2312yes—
488C4×C4⋊C4C2312yes—
489C4×C4⋊C4C2311yescharacteristic
490C4×C4⋊C4C2312yes—
491C4×C4⋊C4C2314yes—
492C4×C4⋊C4C2311yescharacteristic
493C4×C4⋊C4C2311yescharacteristic
494C4×C4⋊C4C2312yes—
495C4×C4⋊C4C2314yes—
496C4×C4⋊C4C2312yes—
497C4×C4⋊C4C2318yes—
498C4×C4⋊C4C2312yes—
499C4×C4⋊C4C2311yescharacteristic
500C4×C4⋊C4C2311yescharacteristic
501C4×C4⋊C4C2312yes—
502C4×C4⋊C4C2312yes—
503C4×C4⋊C4C2314yes—
504C4×C4⋊C4C2311yescharacteristic
505C4×C4⋊C4C2311yescharacteristic
506C4×C4⋊C4C2312yes—
507C4×C4⋊C4C2312yes—
508C4×C4⋊C4C2311yescharacteristic
509C4×C22⋊C4C2318yes—
510C4×C22⋊C4C2312yes—
511C4×C22⋊C4C2318yes—
512C4×C22⋊C4C2312yes—
513C4×C22⋊C4C2314yes—
514C4×C22⋊C4C2314yes—
515C4×C22⋊C4C2314yes—
516C4×C22⋊C4C2314yes—
517C4×C22⋊C4C2314yes—
518C4×C22⋊C4C2314yes—
519C4×C22⋊C4C2314yes—
520C4×C22⋊C4C2312yes—
521C4×C22⋊C4C2314yes—
522#376C2314yes—
523C43C2311yescharacteristic
524C43C2312yes—
525C43C2312yes—
526C2×#41—48no—
527C2×#41—48no—
528C2×#41—84no—
529C22×Q8—28no—
530C22×Q8—28no—
531C22×Q8—44no—
532C22×Q8C2412yes—
533C22×Q8C2414yes—
534C22×Q8C2412yes—
535C22×Q8C2411yescharacteristic
536C22×Q8C2411yescharacteristic
537C22×Q8C2414yes—
538C22×Q8C2418yes—
539C22×D4C2412yes—
540C22×D4C2412yes—
541C22×D4C2411yescharacteristic
542C22×D4C2412yes—
543C22×D4C2418yes—
544C23×C4C2414yes—
545C23×C4C2412yes—
546C23×C4C2412yes—
547C23×C4C2412yes—
548C23×C4C2414yes—
549C23×C4C2414yes—
550C23×C4C2418yes—
551C4⋊Q8—28no—
552C4⋊Q8—28no—
553C4⋊Q8—24no—
554C4⋊Q8—48no—
555C4⋊Q8—44no—
556C4⋊Q8—48no—
557C4⋊Q8—48no—
558C4⋊Q8—416no—
559C4⋊Q8—84no—
560C4⋊Q8—82no—
561C4⋊Q8#4118yescomplemented
562#127—24no—
563#126—232no—
564#126—416no—
565#125—84no—
566#124—216no—
567#124—28no—
568#124—28no—
569#124—28no—
570#124—48no—
571#124—416no—
572#123—416no—
573#123—416no—
574#123—88no—
575C22⋊Q8—28no—
576C22⋊Q8—28no—
577C22⋊Q8—216no—
578C22⋊Q8—216no—
579C22⋊Q8—416no—
580C22⋊Q8—48no—
581C22⋊Q8—48no—
582C22⋊Q8—88no—
583#121—216no—
584#121—48no—
585#121—48no—
586C4×Q8—216no—
587C4×Q8—24no—
588C4×Q8—24no—
589C4×Q8—24no—
590C4×Q8—28no—
591C4×Q8—24no—
592C4×Q8—28no—
593C4×Q8—24no—
594C4×Q8—24no—
595C4×Q8—48no—
596C4×Q8—48no—
597C4×Q8—44no—
598C4×Q8—44no—
599C4×Q8—48no—
600C4×Q8—48no—
601C4×Q8—48no—
602C4×D4—28no—
603C4×D4—24no—
604C4×D4—28no—
605C4×D4—24no—
606C4×D4—28no—
607C4×D4—24no—
608C4×D4—28no—
609C4×D4—48no—
610C4×D4—48no—
611C4×D4—44no—
612#117—216no—
613#117—48no—
614C2×C4⋊C4—48no—
615C2×C4⋊C4—44no—
616C2×C4⋊C4—48no—
617C2×C4⋊C4C2411yescharacteristic
618C2×C4⋊C4C2411yescharacteristic
619C2×C4⋊C4C2412yes—
620C2×C4⋊C4C2412yes—
621C2×C4⋊C4C2414yes—
622C2×C4⋊C4C2414yes—
623C2×C4⋊C4C2412yes—
624C2×C4⋊C4C2412yes—
625C2×C4⋊C4C2414yes—
626C2×C4⋊C4C2414yes—
627C2×C4⋊C4C2412yes—
628C2×C4⋊C4C2411yescharacteristic
629C2×C4⋊C4C2411yescharacteristic
630C2×C4⋊C4C2412yes—
631C2×C4⋊C4C2411yescharacteristic
632C2×C4⋊C4C2412yes—
633C2×C4⋊C4C2418yes—
634C2×C4⋊C4C2414yes—
635C2×C4⋊C4C2411yescharacteristic
636C2×C4⋊C4C2412yes—
637C2×C4⋊C4C2411yescharacteristic
638C2×C4⋊C4C2411yescharacteristic
639C2×C4⋊C4C2411yescharacteristic
640C2×C4⋊C4C2412yes—
641C2×C4⋊C4C2412yes—
642C2×C4⋊C4C2412yes—
643C2×C4⋊C4C2414yes—
644C2×C4⋊C4C2412yes—
645C2×C4⋊C4C2414yes—
646C2×C4⋊C4C2412yes—
647C2×C4⋊C4C2412yes—
648C2×C4⋊C4C2414yes—
649C2×C4⋊C4C2414yes—
650C2×C4⋊C4C2414yes—
651C2×C4⋊C4C2418yes—
652C2×C4⋊C4C2414yes—
653C2×C4⋊C4C2414yes—
654C2×C4⋊C4C2412yes—
655C2×C4⋊C4C2418yes—
656C2×C4⋊C4C2418yes—
657C2×C4⋊C4C2418yes—
658C2×C4⋊C4C2418yes—
659C2×C4⋊C4C2414yes—
660C2×C4⋊C4C2414yes—
661C2×C4⋊C4C2418yes—
662C2×C4⋊C4C2414yes—
663C2×C4⋊C4C2418yes—
664C2×C4⋊C4C2418yes—
665C2×C4⋊C4C2418yes—
666C2×C4⋊C4C2412yes—
667C2×C4⋊C4C2414yes—
668C2×C4⋊C4C2414yes—
669C2×C4⋊C4C2412yes—
670C2×C4⋊C4C2412yes—
671C2×C4⋊C4C2412yes—
672C2×C22⋊C4C2418yes—
673C2×C22⋊C4C2412yes—
674C2×C22⋊C4C2414yes—
675C2×C22⋊C4C2412yes—
676C2×C22⋊C4C2414yes—
677C2×C22⋊C4C2414yes—
678C2×C22⋊C4C2412yes—
679C2×C22⋊C4C2414yes—
680C2×C22⋊C4C2418yes—
681C2×C22⋊C4C2414yes—
682C2×C22⋊C4C2418yes—
683C2×C22⋊C4C2414yes—
684C2×C22⋊C4C2414yes—
685C2×C22⋊C4C2414yes—
686C2×C22⋊C4C2414yes—
687C2×C22⋊C4C2414yes—
688C2×C22⋊C4C2414yes—
689C2×C22⋊C4C2414yes—
690C2×C22⋊C4C2414yes—
691C2×C22⋊C4C2418yes—
692C2×C22⋊C4C2418yes—
693C2×C22⋊C4C2414yes—
694C2×C22⋊C4C2414yes—
695C2×C22⋊C4C2418yes—
696C2×C22⋊C4C2418yes—
697C2×C22⋊C4C2414yes—
698C2×C22⋊C4C2414yes—
699C2×C42—28no—
700C2×C42—48no—
701C2×C42C2412yes—
702C2×C42C2412yes—
703C2×C42C2418yes—
704C2×C42C2411yescharacteristic
705C2×C42C2412yes—
706C2×C42C2412yes—
707C2×C42C2412yes—
708C2×C42C2412yes—
709C2×C42C2414yes—
710C2×C42C2412yes—
711C2×C42C2412yes—
712C2×C42C2414yes—
713C2×C42C2412yes—
714C2×C42C2411yescharacteristic
715C2×C42C2411yescharacteristic
716C2×C42C2412yes—
717C2×C42C2412yes—
718C2×C42C2412yes—
719C2×C42C2412yes—
720C2×C42C2418yes—
721C2×C42C2414yes—
722C2×C42C2414yes—
723C2×C42C2418yes—
724C2×C42C2412yes—
725C2×C42C2411yescharacteristic
726C2×C42C2412yes—
727C2×C42C2411yescharacteristic
728C2×C42C2411yescharacteristic
729C2×C42C2411yescharacteristic
730#95C2414yes—
731#95C2414yes—
732#95C2414yes—
733#95C2414yes—
734#95C2414yes—
735#95C2414yes—
736#95C2414yes—
737#95C2412yes—
738#95C2412yes—
739#95C2414yes—
740#95C2414yes—
741#95C2412yes—
742#95C2414yes—
743#95C2414yes—
744#95C2414yes—
745#95C2414yes—
746#95C2414yes—
747#95C2414yes—
748#95C2414yes—
749#95C2418yes—
750#95C2414yes—
751#95C2414yes—
752#95C2414yes—
753#95C2412yes—
754#95C2412yes—
755#95C2412yes—
756#95C2412yes—
757#95C2412yes—
758#95C2412yes—
759#95C2418yes—
760#95C2418yes—
761#95C2414yes—
762#95C2414yes—
763#95C2418yes—
764#95C2414yes—
765#95C2414yes—
766#95C2418yes—
767#95C2418yes—
768#95C2418yes—
769#95C2418yes—
770#95C2414yes—
771#95C2418yes—
772C24C2514yes—
773C24C2512yes—
774#41—832no—
775C2×Q8—22no—
776C2×Q8—24no—
777C2×Q8—28no—
778C2×Q8—22no—
779C2×Q8—24no—
780C2×Q8—22no—
781C2×Q8—24no—
782C2×Q8—28no—
783C2×Q8—22no—
784C2×Q8—24no—
785C2×Q8—24no—
786C2×Q8—28no—
787C2×Q8—44no—
788C2×Q8—44no—
789C2×Q8—44no—
790C2×Q8—48no—
791C2×Q8—48no—
792C2×Q8—48no—
793C2×Q8—432no—
794C2×Q8C2×#4118yes—
795C2×Q82−1+414yes—
796C2×Q82−1+414yes—
797C2×D4—216no—
798C2×D4—22no—
799C2×D4—24no—
800C2×D4—24no—
801C2×D4—24no—
802C2×D4—24no—
803C2×D4—22no—
804C2×D4—24no—
805C2×D4—24no—
806C2×D4—24no—
807C2×D4—42no—
808C2×D4—42no—
809C2×D4—48no—
810C2×D4—48no—
811C2×D4H(5,𝔽2)14yes—
812C22×C4—24no—
813C22×C4—28no—
814C22×C4—28no—
815C22×C4—28no—
816C22×C4—24no—
817C22×C4—24no—
818C22×C4—24no—
819C22×C4—24no—
820C22×C4—28no—
821C22×C4—28no—
822C22×C4—24no—
823C22×C4—24no—
824C22×C4—28no—
825C22×C4—24no—
826C22×C4—44no—
827C22×C4—42no—
828C22×C4—44no—
829C22×C4—48no—
830C22×C4—48no—
831C22×C4—48no—
832C22×C4—44no—
833C22×C4C2512yes—
834C22×C4C2512yes—
835C22×C4C2512yes—
836C22×C4C2512yes—
837C22×C4C2511yescharacteristic
838C22×C4C2512yes—
839C22×C4C2514yes—
840C22×C4C2512yes—
841C22×C4C2514yes—
842C22×C4C2514yes—
843C22×C4C2512yes—
844C22×C4C2512yes—
845C22×C4C2518yes—
846C22×C4C2514yes—
847C22×C4C2512yes—
848C22×C4C2514yes—
849C22×C4C2511yescharacteristic
850C22×C4C2511yescharacteristic
851C22×C4C2512yes—
852C22×C4C2511yescharacteristic
853C22×C4C2512yes—
854C22×C4C2511yescharacteristic
855C22×C4C2511yescharacteristic
856C22×C4C2511yescharacteristic
857C4⋊C4—24no—
858C4⋊C4—24no—
859C4⋊C4—22no—
860C4⋊C4—24no—
861C4⋊C4—22no—
862C4⋊C4—216no—
863C4⋊C4—28no—
864C4⋊C4—28no—
865C4⋊C4—22no—
866C4⋊C4—24no—
867C4⋊C4—22no—
868C4⋊C4—28no—
869C4⋊C4—24no—
870C4⋊C4—28no—
871C4⋊C4—24no—
872C4⋊C4—28no—
873C4⋊C4—28no—
874C4⋊C4—24no—
875C4⋊C4—22no—
876C4⋊C4—22no—
877C4⋊C4—24no—
878C4⋊C4—24no—
879C4⋊C4—24no—
880C4⋊C4—24no—
881C4⋊C4—22no—
882C4⋊C4—22no—
883C4⋊C4—22no—
884C4⋊C4—24no—
885C4⋊C4—28no—
886C4⋊C4—24no—
887C4⋊C4—24no—
888C4⋊C4—44no—
889C4⋊C4—44no—
890C4⋊C4—44no—
891C4⋊C4—48no—
892C4⋊C4—44no—
893C4⋊C4—44no—
894C4⋊C4—42no—
895C4⋊C4—48no—
896C4⋊C4—48no—
897C4⋊C4—48no—
898C4⋊C4—48no—
899C4⋊C4—44no—
900C4⋊C4—44no—
901C4⋊C4—48no—
902C4⋊C4—44no—
903C4⋊C4—48no—
904C4⋊C4—48no—
905C4⋊C4—48no—
906C4⋊C4—42no—
907C4⋊C4—44no—
908C4⋊C4—42no—
909C4⋊C4—44no—
910C4⋊C4C2×#4118yes—
911C4⋊C4C2×#4118yes—
912C22⋊C4—24no—
913C22⋊C4—28no—
914C22⋊C4—216no—
915C22⋊C4—28no—
916C22⋊C4—28no—
917C22⋊C4—216no—
918C22⋊C4—28no—
919C22⋊C4—24no—
920C22⋊C4—28no—
921C22⋊C4—216no—
922C22⋊C4—24no—
923C22⋊C4—28no—
924C22⋊C4—28no—
925C22⋊C4—28no—
926C22⋊C4—28no—
927C22⋊C4—28no—
928C22⋊C4—28no—
929C22⋊C4—44no—
930C22⋊C4—44no—
931C22⋊C4—48no—
932C22⋊C4—48no—
933C22⋊C4—44no—
934C22⋊C4—48no—
935C22⋊C4—44no—
936C22⋊C4—48no—
937C22⋊C4—44no—
938C22⋊C4—44no—
939C42—216no—
940C42—24no—
941C42—28no—
942C42—24no—
943C42—24no—
944C42—24no—
945C42—24no—
946C42—28no—
947C42—24no—
948C42—24no—
949C42—22no—
950C42—24no—
951C42—24no—
952C42—24no—
953C42—22no—
954C42—22no—
955C42—24no—
956C42—24no—
957C42—24no—
958C42—44no—
959C42—44no—
960C42—48no—
961C42—48no—
962C42—42no—
963C42—41no—
964C42—42no—
965C42C2×#4114yes—
966C42H(5,𝔽2)14yes—
967C422−1+414yes—
968C23—22no—
969C23—22no—
970C23—22no—
971C23—22no—
972C23—22no—
973C23—22no—
974C23—24no—
975C23—24no—
976C23—24no—
977C23—24no—
978C23—24no—
979C23—24no—
980C23—24no—
981C23C2×H(5,𝔽2)14yes—
982C23C2611yescharacteristic
983Q8—28no—
984Q8—216no—
985Q8—28no—
986Q8—416no—
987Q8—48no—
988Q8—88no—
989Q8—168no—
990D4—28no—
991D4—48no—
992D4—48no—
993D4—48no—
994D4—816no—
995C2×C4—22no—
996C2×C4—22no—
997C2×C4—24no—
998C2×C4—22no—
999C2×C4—21no—
1000C2×C4—21no—
1001C2×C4—21no—
1002C2×C4—22no—
1003C2×C4—24no—
1004C2×C4—21no—
1005C2×C4—21no—
1006C2×C4—21no—
1007C2×C4—24no—
1008C2×C4—24no—
1009C2×C4—22no—
1010C2×C4—24no—
1011C2×C4—22no—
1012C2×C4—22no—
1013C2×C4—22no—
1014C2×C4—22no—
1015C2×C4—22no—
1016C2×C4—22no—
1017C2×C4—24no—
1018C2×C4—21no—
1019C2×C4—22no—
1020C2×C4—22no—
1021C2×C4—22no—
1022C2×C4—22no—
1023C2×C4—24no—
1024C2×C4—28no—
1025C2×C4—28no—
1026C2×C4—24no—
1027C2×C4—24no—
1028C2×C4—22no—
1029C2×C4—22no—
1030C2×C4—22no—
1031C2×C4—22no—
1032C2×C4—22no—
1033C2×C4—21no—
1034C2×C4—22no—
1035C2×C4—22no—
1036C2×C4—21no—
1037C2×C4—22no—
1038C2×C4—24no—
1039C2×C4—22no—
1040C2×C4—24no—
1041C2×C4—22no—
1042C2×C4—24no—
1043C2×C4—22no—
1044C2×C4—22no—
1045C2×C4—22no—
1046C2×C4—22no—
1047C2×C4—22no—
1048C2×C4—24no—
1049C2×C4—24no—
1050C2×C4—28no—
1051C2×C4—22no—
1052C2×C4—416no—
1053C2×C4—48no—
1054C2×C4—48no—
1055C2×C4—416no—
1056C2×C4—48no—
1057C2×C4—88no—
1058C2×C4—816no—
1059C2×C4C22×#4118yes—
1060C2×C4C22×#4112yes—
1061C2×C4C22×#4112yes—
1062C2×C4C22×#4112yes—
1063C2×C4C2×H(5,𝔽2)12yes—
1064C2×C4C2×H(5,𝔽2)12yes—
1065C2×C4C2×H(5,𝔽2)12yes—
1066C2×C4C2×H(5,𝔽2)12yes—
1067C2×C4C2×2−1+414yes—
1068C2×C4C2×2−1+414yes—
1069C2×C4C2×2−1+412yes—
1070C2×C4C2×2−1+412yes—
1071C2×C4C2×2−1+412yes—
1072C2×C4C2×2−1+412yes—
1073C2×C4C2×2−1+412yes—
1074C22—24no—
1075C22—24no—
1076C22—24no—
1077C22—42no—
1078C22—42no—
1079C22—42no—
1080C22—42no—
1081C22—44no—
1082C22—44no—
1083C22—44no—
1084C22—44no—
1085C22—44no—
1086C22—44no—
1087C22—44no—
1088C22C23×#4111yescharacteristic
1089C22C22×H(5,𝔽2)11yescharacteristic
1090C22C22×H(5,𝔽2)11yescharacteristic
1091C22C22×2−1+411yescharacteristic
1092C22C22×2−1+411yescharacteristic
1093C22C22×2−1+411yescharacteristic
1094C22H(7,𝔽2)11yescharacteristic
1095C4—22no—
1096C4—24no—
1097C4—24no—
1098C4—28no—
1099C4—22no—
1100C4—22no—
1101C4—44no—
1102C4—42no—
1103C4—42no—
1104C4—42no—
1105C4—42no—
1106C4—41no—
1107C4—42no—
1108C4—44no—
1109C4—44no—
1110C4—42no—
1111C4—42no—
1112C4—48no—
1113C4—44no—
1114C4—42no—
1115C4—42no—
1116C4#352014yes—
1117C4#352214yes—
1118C4#355214yes—
1119C2—44no—
1120C2—84no—
1121C2C2×#355211yescharacteristic
1122C2C2×#352011yescharacteristic
1123C2C2×#352211yescharacteristic
1124C2#6291211yescharacteristic
1125C2#6294311yescharacteristic
1126C2#6299911yescharacteristic
1127C2#6303711yescharacteristic
subgroupG/H
center, commutator, Frattini, socle, cosocleC23C26
prime radical#36127C2
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23 ◁ G
LECSG ▷ C23 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #59821C2semidirect
2. #59642C2semidirect
3. #59421C2semidirect
4. #59084C2semidirect
5. #48228C2semidirect
6. #45633C2semidirect
7. #45292C2semidirect
8. #44875C2semidirect
9. #42841C2semidirect
10. #42549C2semidirect
11. #39633C2semidirect
12. #39377C2semidirect
13. #39245C2semidirect
14. #38964C2semidirect
15. #38931C2semidirect
16. #36563C2semidirect
17. Q8×C4⋊Q8C2semidirect
18. Q8×C22⋊Q8C2semidirect
19. #36464C2semidirect
21. #35249C2semidirect
22. #35170C2semidirect
23. #34954C2semidirect
24. #34945C2semidirect
25. #34481C2semidirect
26. C4×D4×Q8C2semidirect
561. C4⋊Q8#41semidirect

Maximal subgroups

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

subgroupindex
#598212
#596422
#594212
#590842
#482282
#456332
#452922
#448752
#428412
#425492
#396332
#393772
#392452
#389642
#389312
#365632
Q8×C4⋊Q82
Q8×C22⋊Q82
#364642
#361272
#352492
#351702
#349542
#349452
#344812
C4×D4×Q82