Finite Group Databasebeta

← #7986731

Subgroups — #7986731

Order 512.

4523 conjugacy classes of subgroups.

The subgroup lattice has 1076 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#59869C211yesmaximal, characteristic, complemented
2#59681C212yesmaximal, complemented
3#59668C212yesmaximal, complemented
4#59081C212yesmaximal, complemented
5#51598C218yesmaximal, complemented
6#45500C214yesmaximal, complemented
7#45405C214yesmaximal, complemented
8#45073C214yesmaximal, complemented
9#42497C214yesmaximal
10#42488C214yesmaximal, complemented
11#39754C212yesmaximal, complemented
12#39625C212yesmaximal, complemented
13#39609C214yesmaximal, complemented
14#39597C212yesmaximal, complemented
15#38967C212yesmaximal
16#36563C211yesmaximal, characteristic, complemented
17Q8×C4⋊Q8C211yesmaximal, characteristic, complemented
18#36194C212yesmaximal
19#36193C212yesmaximal, complemented
20#36134C211yesmaximal, characteristic
21#35176C212yesmaximal
22#35173C212yesmaximal, complemented
23#34951C211yesmaximal, characteristic, complemented
24#34929C211yesmaximal, characteristic
25#34484C212yesmaximal
26C4×#554C211yesmaximal, characteristic
27C2×Q82C2212yes—
28C2×#554C2211yescharacteristic
29C2×#533C2212yes—
30C2×#533C2212yes—
31#2868C2211yescharacteristic
32#2868C2212yes—
33#2859C2212yes—
34#2857C2212yes—
35#2857C2214yes—
36#2857C2214yes—
37#2855C2214yes—
38#2841C2218yes—
39#2809C2214yes—
40#2806C2218yes—
41#2802C2218yes—
42#2802C2218yes—
43#2802C2218yes—
44#2792C2218yes—
45#2788C2218yes—
46#2774C2218yes—
47#2774C2218yes—
48#2768C2218yes—
49#2755C2218yes—
50#2742C2218yes—
51#2742C2218yes—
52#2734C2218yes—
53#2729C2218yes—
54#2713C2218yes—
55#2677C2218yes—
56#2667C2218yes—
57#2660C2214yes—
58#2659C2218yes—
59#2628C2218yes—
60#2628C2214yes—
61#2590C2218yes—
62#2585C2214yes—
63#2584C2218yes—
64#2584C2214yes—
65#2584C2214yes—
66#2582C2211yescharacteristic
67#2582C2212yes—
68#2581C2214yes—
69#2571C2214yes—
70#2571C2212yes—
71#2570C2214yes—
72#2568C2211yescharacteristic
73#2568C2214yes—
74#2567C2212yes—
75#2567C2212yes—
76#2567C2214yes—
77#2567C2214yes—
78#2563C2214yes—
79#2556C2214yes—
80#2552C2212yes—
81#2552C2211yescharacteristic
82#2552C2212yes—
83#2551C2214yes—
84#2551C2214yes—
85#2551C2212yes—
86#2551C2211yescharacteristic
87#2551C2214yes—
88#2551C2214yes—
89#2551C2212yes—
90#2550C2214yes—
91#2550C2214yes—
92#2550C2214yes—
93#2546C2214yes—
94#2546C2211yescharacteristic
95#2546C2214yes—
96#2546C2212yes—
97#2546C2211yescharacteristic
98#2546C2212yes—
99#2542C2212yes—
100#2542C2211yescharacteristic
101#2538C2212yes—
102#2538C2211yescharacteristic
103#2522C2218yes—
104#2520C2218yes—
105#2511C2214yes—
106#2511C2212yes—
107#2509C2214yes—
108#2509C2218yes—
109#2509C2212yes—
110#2508C2214yes—
111#2508C2214yes—
112#2508C2214yes—
113#2507C2214yes—
114#2507C2214yes—
115#2507C2214yes—
116#2507C2214yes—
117#2506C2212yes—
118#2497C2218yes—
119#2492C2214yes—
120#2492C2214yes—
121#2492C2212yes—
122#2454C2214yes—
123#2453C2214yes—
124#2453C2212yes—
125#2452C2212yes—
126#2451C2218yes—
127#2451C2214yes—
128#2451C2214yes—
129#2446C2218yes—
130#2446C2214yes—
131#2446C2212yes—
132#2442C2214yes—
133#2441C2214yes—
134#2439C2214yes—
135#2439C2218yes—
136#2438C2218yes—
137#2429C2214yes—
138#2429C2214yes—
139#2429C2212yes—
140#2423C2214yes—
141#2423C2214yes—
142#2402C2214yes—
143#2396C2214yes—
144#2378C2218yes—
145#2370C2212yes—
146#2370C2214yes—
147#2370C2214yes—
148#2369C2214yes—
149#2369C2211yescharacteristic
150#2369C2212yes—
151#2369C2212yes—
152#2368C2214yes—
153#2365C2212yes—
154#2365C2214yes—
155#2362C2214yes—
156#2360C2212yes—
157#2355C2212yes—
158#2355C2211yescharacteristic
159#2355C2212yes—
160#2355C2212yes—
161#2354C2214yes—
162#2354C2212yes—
163Q8×C4⋊C4C2212yes—
164Q8×C4⋊C4C2212yes—
165Q8×C4⋊C4C2212yes—
166Q8×C4⋊C4C2212yes—
167#2349C2212yes—
168D4×C4⋊C4C2211yescharacteristic
169#2345C2212yes—
170#2344C2214yes—
171#2330C2214yes—
172#2330C2214yes—
173#2323C2214yes—
174#2323C2218yes—
175#2319C2214yes—
176#2316C2214yes—
177#2316C2214yes—
178C4×C4⋊Q8C2212yes—
179C4×C4⋊Q8C2212yes—
180C4×C4⋊Q8C2212yes—
181C4×C4⋊Q8C2212yes—
182C4×C4⋊Q8C2211yescharacteristic
183C4×C4⋊Q8C2211yescharacteristic
184C4×C4⋊Q8C2211yescharacteristic
185C4×#125C2212yes—
186C4×#125C2212yes—
187C4×C22⋊Q8C2212yes—
188C4×C22⋊Q8C2212yes—
189C4×C22⋊Q8C2214yes—
190#2295C2212yes—
191#2295C2212yes—
192#2293C2212yes—
193#2285C2214yes—
194C42×Q8C2211yescharacteristic
195C42×Q8C2211yescharacteristic
196C42×D4C2211yescharacteristic
197C42×D4C2212yes—
198C2×C4×C4⋊C4C2212yes—
199Q82—48no—
200#554Q8116yescomplemented
201#533—48no—
202#533—48no—
203C2×C4⋊Q8C2311yescharacteristic
204C2×C4⋊Q8C2311yescharacteristic
205C2×C4⋊Q8C2312yes—
206C2×C4⋊Q8C2312yes—
207C2×C4⋊Q8C2312yes—
208C2×C4⋊Q8C2314yes—
209C2×C4⋊Q8C2312yes—
210C2×C4⋊Q8C2314yes—
211C2×C4⋊Q8C2314yes—
212C2×C4⋊Q8C2312yes—
213C2×C4⋊Q8C2314yes—
214C2×C4⋊Q8C2312yes—
215C2×C4⋊Q8C2318yes—
216C2×C4⋊Q8C2312yes—
217C2×C4⋊Q8C2314yes—
218C2×C4⋊Q8C2318yes—
219C2×C4⋊Q8C2311yescharacteristic
220C2×#125C2312yes—
221C2×#125C2314yes—
222C2×#125C2314yes—
223C2×#125C2314yes—
224C2×#125C2312yes—
225C2×C22⋊Q8C2312yes—
226C2×C22⋊Q8C2312yes—
227C2×C22⋊Q8C2314yes—
228C2×C22⋊Q8C2312yes—
229C2×C22⋊Q8C2314yes—
230C2×C22⋊Q8C2314yes—
231C2×C22⋊Q8C2314yes—
232C2×C22⋊Q8C2312yes—
233C2×C22⋊Q8C2314yes—
234C2×C4×Q8C2312yes—
235C2×C4×Q8C2311yescharacteristic
236C2×C4×Q8C2312yes—
237C2×C4×Q8C2311yescharacteristic
238C2×C4×Q8C2311yescharacteristic
239C2×C4×Q8C2311yescharacteristic
240C2×C4×Q8C2314yes—
241C2×C4×Q8C2312yes—
242C2×C4×Q8C2314yes—
243C2×C4×Q8C2314yes—
244C2×C4×Q8C2314yes—
245C2×C4×Q8C2311yescharacteristic
246C2×C4×Q8C2314yes—
247C2×C4×Q8C2314yes—
248C2×C4×Q8C2311yescharacteristic
249C2×C4×D4C2311yescharacteristic
250C2×C4×D4C2312yes—
251C2×C4×D4C2311yescharacteristic
252C2×C4×D4C2312yes—
253C2×C4×D4C2311yescharacteristic
254C2×#117C2314yes—
255C2×#117C2314yes—
256C2×#117C2318yes—
257C22×C4⋊C4C2312yes—
258C22×C4⋊C4C2312yes—
259C22×C42C2312yes—
260C22×C42C2314yes—
261#400C2318yes—
262#400C2314yes—
263#400C2318yes—
264#400C2318yes—
265#400C2318yes—
266#400C2318yes—
267#400C2314yes—
268#400C2318yes—
269#400C2314yes—
270#400C2318yes—
271#400C2314yes—
272#400C2314yes—
273#399C2318yes—
274#399C2318yes—
275#399C2314yes—
276#398C2318yes—
277#398C2314yes—
278#398C2318yes—
279#398C2314yes—
280#398C2318yes—
281#398C2318yes—
282#398C2314yes—
283#398C2318yes—
284#398C2318yes—
285#398C2314yes—
286#398C2318yes—
287#398C2314yes—
288#398C2314yes—
289#398C2318yes—
290#398C2318yes—
291#398C2318yes—
292#398C2318yes—
293#398C2318yes—
294#398C2318yes—
295#396C2314yes—
296#396C2318yes—
297#396C2314yes—
298#396C2318yes—
299#395C2318yes—
300#395C2318yes—
301#395C2318yes—
302#395C2318yes—
303#395C2318yes—
304#395C2318yes—
305#395C2318yes—
306#395C2318yes—
307#395C2318yes—
308#395C2314yes—
309#393C2318yes—
310#393C2318yes—
311#393C2314yes—
312#391C2312yes—
313#391C2314yes—
314#391C2312yes—
315#391C2312yes—
316#391C2314yes—
317#391C2312yes—
318#391C2312yes—
319#391C2314yes—
320#391C2312yes—
321#391C2314yes—
322#391C2314yes—
323#391C2318yes—
324#391C2314yes—
325#391C2312yes—
326#391C2312yes—
327#391C2312yes—
328#391C2312yes—
329#391C2314yes—
330#391C2312yes—
331#391C2314yes—
332#391C2318yes—
333#391C2318yes—
334#391C2318yes—
335#391C2318yes—
336#390C2312yes—
337#390C2314yes—
338#390C2312yes—
339#389C2312yes—
340#389C2312yes—
341#389C2312yes—
342#389C2312yes—
343#389C2314yes—
344#389C2312yes—
345#389C2312yes—
346#389C2314yes—
347#389C2312yes—
348#389C2314yes—
349#389C2314yes—
350#389C2312yes—
351#389C2312yes—
352#389C2314yes—
353#389C2314yes—
354#389C2312yes—
355#389C2312yes—
356#389C2314yes—
357#389C2312yes—
358#389C2318yes—
359#389C2314yes—
360#389C2314yes—
361#389C2314yes—
362#389C2318yes—
363#389C2318yes—
364#389C2318yes—
365#389C2314yes—
366#389C2314yes—
367#389C2318yes—
368#389C2314yes—
369#389C2312yes—
370#389C2318yes—
371#389C2314yes—
372#389C2318yes—
373#389C2314yes—
374#389C2318yes—
375#389C2314yes—
376#389C2314yes—
377#389C2314yes—
378#389C2312yes—
379#389C2318yes—
380#389C2318yes—
381#389C2318yes—
382#389C2312yes—
383#389C2318yes—
384#389C2318yes—
385#389C2312yes—
386#389C2312yes—
387#389C2312yes—
388#389C2314yes—
389#389C2314yes—
390#389C2314yes—
391#389C2318yes—
392#389C2314yes—
393#389C2318yes—
394#389C2312yes—
395#389C2318yes—
396#389C2312yes—
397#388C2318yes—
398#388C2318yes—
399#388C2314yes—
400#388C2318yes—
401#388C2318yes—
402#388C2318yes—
403#388C2314yes—
404#387C2314yes—
405#387C2314yes—
406#387C2314yes—
407#387C2314yes—
408#387C2318yes—
409#387C2318yes—
410#387C2314yes—
411#387C2318yes—
412#387C2318yes—
413#387C2318yes—
414#387C2314yes—
415#387C2314yes—
416#387C2314yes—
417#387C2318yes—
418#387C2318yes—
419#387C2318yes—
420#387C2318yes—
421#387C2318yes—
422#387C2318yes—
423#387C2314yes—
424#387C2314yes—
425#387C2318yes—
426#387C2318yes—
427#387C2318yes—
428#387C2318yes—
429#387C2314yes—
430#387C2314yes—
431#385C2318yes—
432#385C2314yes—
433#385C2314yes—
434#385C2314yes—
435#385C2314yes—
436#384C2311yescharacteristic
437#384C2311yescharacteristic
438#384C2312yes—
439#384C2312yes—
440#384C2312yes—
441#384C2311yescharacteristic
442#384C2312yes—
443#384C2314yes—
444#384C2312yes—
445#384C2314yes—
446#384C2314yes—
447#384C2314yes—
448#384C2312yes—
449#384C2314yes—
450#382C2312yes—
451#382C2312yes—
452#382C2314yes—
453#382C2314yes—
454#382C2318yes—
455#382C2314yes—
456#382C2318yes—
457#381C2318yes—
458#380C2318yes—
459#380C2318yes—
460#380C2318yes—
461#380C2318yes—
462#380C2318yes—
463#380C2314yes—
464#380C2314yes—
465#380C2314yes—
466#380C2312yes—
467#380C2312yes—
468C4×C4⋊C4C2311yescharacteristic
469C4×C4⋊C4C2311yescharacteristic
470C4×C4⋊C4C2314yes—
471C4×C4⋊C4C2312yes—
472C4×C4⋊C4C2312yes—
473C4×C4⋊C4C2314yes—
474C4×C4⋊C4C2314yes—
475C4×C4⋊C4C2314yes—
476C4×C4⋊C4C2312yes—
477C4×C4⋊C4C2311yescharacteristic
478C4×C4⋊C4C2312yes—
479C4×C4⋊C4C2314yes—
480C4×C4⋊C4C2314yes—
481C4×C4⋊C4C2314yes—
482C4×C4⋊C4C2314yes—
483C4×C4⋊C4C2312yes—
484C4×C4⋊C4C2314yes—
485C4×C4⋊C4C2312yes—
486C4×C4⋊C4C2314yes—
487C4×C4⋊C4C2312yes—
488C4×C4⋊C4C2311yescharacteristic
489C4×C4⋊C4C2314yes—
490C4×C4⋊C4C2311yescharacteristic
491C4×C4⋊C4C2312yes—
492C4×C4⋊C4C2318yes—
493C4×C4⋊C4C2314yes—
494C4×C4⋊C4C2312yes—
495C4×C4⋊C4C2312yes—
496C4×C4⋊C4C2314yes—
497C4×C4⋊C4C2312yes—
498C4×C4⋊C4C2312yes—
499C4×C4⋊C4C2314yes—
500C4×C4⋊C4C2314yes—
501C4×C4⋊C4C2311yescharacteristic
502C4×C4⋊C4C2312yes—
503C4×C4⋊C4C2311yescharacteristic
504C4×C4⋊C4C2314yes—
505C4×C4⋊C4C2311yescharacteristic
506C4×C4⋊C4C2312yes—
507C4×C4⋊C4C2318yes—
508C4×C4⋊C4C2312yes—
509C4×C4⋊C4C2312yes—
510C4×C4⋊C4C2311yescharacteristic
511C4×C22⋊C4C2314yes—
512C4×C22⋊C4C2312yes—
513C4×C22⋊C4C2314yes—
514C4×C22⋊C4C2314yes—
515C4×C22⋊C4C2312yes—
516C4×C22⋊C4C2312yes—
517C4×C22⋊C4C2314yes—
518#376C2314yes—
519C2×#95C2314yes—
520C43C2312yes—
521C43C2312yes—
522C43C2311yescharacteristic
523C22×Q8C2412yes—
524C22×Q8C2411yescharacteristic
525C22×Q8C2412yes—
526C22×Q8C2411yescharacteristic
527C22×Q8C2414yes—
528C22×Q8C2414yes—
529C22×Q8C2418yes—
530C22×Q8C2412yes—
531C22×D4C2411yescharacteristic
532C23×C4C2412yes—
533C23×C4C2412yes—
534C23×C4C2414yes—
535C23×C4C2412yes—
536C23×C4C2414yes—
537C4⋊Q8—24no—
538C4⋊Q8—28no—
539C4⋊Q8—24no—
540C4⋊Q8—44no—
541C4⋊Q8—48no—
542C4⋊Q8—44no—
543C4⋊Q8—44no—
544C4⋊Q8—48no—
545C4⋊Q8—48no—
546C4⋊Q8—44no—
547C4⋊Q8—48no—
548C4⋊Q8—44no—
549C4⋊Q8—416no—
550C4⋊Q8—88no—
551C4⋊Q8—84no—
552C4⋊Q8—82no—
553C4⋊Q8C2×Q818yes—
554#125—28no—
555#125—48no—
556#125—48no—
557#125—48no—
558#125C2×Q8116yes—
559C22⋊Q8—48no—
560C22⋊Q8—44no—
561C22⋊Q8—44no—
562C22⋊Q8—44no—
563C22⋊Q8—48no—
564C22⋊Q8—48no—
565C22⋊Q8—84no—
566C22⋊Q8C2×Q8132yes—
567C22⋊Q8C2×Q8116yes—
568C4×Q8—24no—
569C4×Q8—24no—
570C4×Q8—28no—
571C4×Q8—24no—
572C4×Q8—28no—
573C4×Q8—24no—
574C4×Q8—44no—
575C4×Q8—48no—
576C4×Q8—42no—
577C4×Q8—48no—
578C4×Q8—48no—
579C4×Q8—48no—
580C4×Q8—48no—
581C4×Q8—84no—
582C4×Q8C2×Q818yes—
583C4×D4—24no—
584C4×D4—44no—
585C4×D4—42no—
586C4×D4C2×Q8116yes—
587C4×D4C2×Q818yes—
588#117—48no—
589#117—48no—
590#117—88no—
591C2×C4⋊C4—28no—
592C2×C4⋊C4C2×Q8116yes—
593C2×C4⋊C4C2412yes—
594C2×C4⋊C4C2414yes—
595C2×C4⋊C4C2412yes—
596C2×C4⋊C4C2414yes—
597C2×C4⋊C4C2412yes—
598C2×C4⋊C4C2411yescharacteristic
599C2×C4⋊C4C2411yescharacteristic
600C2×C4⋊C4C2412yes—
601C2×C4⋊C4C2414yes—
602C2×C4⋊C4C2412yes—
603C2×C4⋊C4C2411yescharacteristic
604C2×C4⋊C4C2411yescharacteristic
605C2×C4⋊C4C2414yes—
606C2×C4⋊C4C2412yes—
607C2×C4⋊C4C2411yescharacteristic
608C2×C4⋊C4C2412yes—
609C2×C4⋊C4C2411yescharacteristic
610C2×C4⋊C4C2412yes—
611C2×C4⋊C4C2412yes—
612C2×C4⋊C4C2412yes—
613C2×C4⋊C4C2414yes—
614C2×C4⋊C4C2414yes—
615C2×C4⋊C4C2412yes—
616C2×C4⋊C4C2414yes—
617C2×C4⋊C4C2414yes—
618C2×C4⋊C4C2412yes—
619C2×C4⋊C4C2412yes—
620C2×C4⋊C4C2412yes—
621C2×C4⋊C4C2414yes—
622C2×C4⋊C4C2414yes—
623C2×C4⋊C4C2414yes—
624C2×C4⋊C4C2418yes—
625C2×C4⋊C4C2414yes—
626C2×C4⋊C4C2418yes—
627C2×C4⋊C4C2418yes—
628C2×C4⋊C4C2414yes—
629C2×C4⋊C4C2414yes—
630C2×C4⋊C4C2418yes—
631C2×C4⋊C4C2418yes—
632C2×C4⋊C4C2418yes—
633C2×C4⋊C4C2414yes—
634C2×C4⋊C4C2412yes—
635C2×C4⋊C4C2414yes—
636C2×C4⋊C4C2412yes—
637C2×C4⋊C4C2412yes—
638C2×C4⋊C4C2418yes—
639C2×C4⋊C4C2414yes—
640C2×C4⋊C4C2418yes—
641C2×C4⋊C4C2418yes—
642C2×C4⋊C4C2414yes—
643C2×C4⋊C4C2412yes—
644C2×C4⋊C4C2414yes—
645C2×C4⋊C4C2414yes—
646C2×C4⋊C4C2418yes—
647C2×C4⋊C4C2414yes—
648C2×C4⋊C4C2414yes—
649C2×C4⋊C4C2418yes—
650C2×C4⋊C4C2414yes—
651C2×C4⋊C4C2418yes—
652C2×C4⋊C4C2414yes—
653C2×C4⋊C4C2411yescharacteristic
654C2×C4⋊C4C2414yes—
655C2×C4⋊C4C2412yes—
656C2×C4⋊C4C2411yescharacteristic
657C2×C4⋊C4C2412yes—
658C2×C4⋊C4C2412yes—
659C2×C4⋊C4C2414yes—
660C2×C4⋊C4C2411yescharacteristic
661C2×C22⋊C4C2412yes—
662C2×C22⋊C4C2414yes—
663C2×C22⋊C4C2414yes—
664C2×C22⋊C4C2418yes—
665C2×C22⋊C4C2414yes—
666C2×C22⋊C4C2418yes—
667C2×C22⋊C4C2414yes—
668C2×C22⋊C4C2412yes—
669C2×C22⋊C4C2414yes—
670C2×C22⋊C4C2414yes—
671C2×C22⋊C4C2412yes—
672C2×C42—28no—
673C2×C42—48no—
674C2×C42C2412yes—
675C2×C42C2414yes—
676C2×C42C2411yescharacteristic
677C2×C42C2412yes—
678C2×C42C2412yes—
679C2×C42C2411yescharacteristic
680C2×C42C2412yes—
681C2×C42C2412yes—
682C2×C42C2412yes—
683C2×C42C2414yes—
684C2×C42C2411yescharacteristic
685C2×C42C2412yes—
686C2×C42C2412yes—
687C2×C42C2414yes—
688C2×C42C2412yes—
689C2×C42C2412yes—
690C2×C42C2412yes—
691C2×C42C2418yes—
692C2×C42C2418yes—
693C2×C42C2418yes—
694C2×C42C2418yes—
695C2×C42C2412yes—
696C2×C42C2412yes—
697C2×C42C2411yescharacteristic
698C2×C42C2412yes—
699C2×C42C2414yes—
700C2×C42C2414yes—
701C2×C42C2412yes—
702C2×C42C2411yescharacteristic
703C2×C42C2411yescharacteristic
704C2×C42C2411yescharacteristic
705#95C2412yes—
706#95C2414yes—
707#95C2414yes—
708#95C2414yes—
709#95C2414yes—
710#95C2414yes—
711#95C2414yes—
712#95C2414yes—
713#95C2412yes—
714#95C2414yes—
715#95C2412yes—
716#95C2414yes—
717#95C2412yes—
718#95C2414yes—
719#95C2414yes—
720#95C2414yes—
721#95C2412yes—
722#95C2414yes—
723#95C2412yes—
724#95C2412yes—
725#95C2412yes—
726#95C2414yes—
727#95C2412yes—
728#95C2414yes—
729#95C2418yes—
730#95C2418yes—
731#95C2418yes—
732#95C2418yes—
733#95C2414yes—
734#95C2418yes—
735#95C2418yes—
736#95C2418yes—
737#95C2418yes—
738#95C2418yes—
739#95C2418yes—
740#95C2414yes—
741#95C2414yes—
742#95C2414yes—
743#95C2414yes—
744#95C2414yes—
745#95C2414yes—
746#95C2414yes—
747#95C2414yes—
748#95C2414yes—
749#95C2414yes—
750#95C2418yes—
751#95C2418yes—
752#95C2418yes—
753C24C2512yes—
754C2×Q8—22no—
755C2×Q8—24no—
756C2×Q8—22no—
757C2×Q8—24no—
758C2×Q8—28no—
759C2×Q8—22no—
760C2×Q8—22no—
761C2×Q8—24no—
762C2×Q8—24no—
763C2×Q8—22no—
764C2×Q8—24no—
765C2×Q8—24no—
766C2×Q8—42no—
767C2×Q8—42no—
768C2×Q8—44no—
769C2×Q8—44no—
770C2×Q8—44no—
771C2×Q8—44no—
772C2×Q8—44no—
773C2×Q8—48no—
774C2×Q8—48no—
775C2×Q8—48no—
776C2×Q8C22×Q814yes—
777C2×Q8C22×Q818yes—
778C2×D4—22no—
779C2×D4—22no—
780C2×D4C22×Q814yes—
781C22×C4—24no—
782C22×C4—24no—
783C22×C4—24no—
784C22×C4—24no—
785C22×C4—24no—
786C22×C4—24no—
787C22×C4—28no—
788C22×C4—44no—
789C22×C4—44no—
790C22×C4—44no—
791C22×C4—44no—
792C22×C4—42no—
793C22×C4—42no—
794C22×C4C22×Q818yes—
795C22×C4C22×Q8116yes—
796C22×C4C2512yes—
797C22×C4C2514yes—
798C22×C4C2514yes—
799C22×C4C2511yescharacteristic
800C22×C4C2512yes—
801C22×C4C2512yes—
802C22×C4C2514yes—
803C22×C4C2512yes—
804C22×C4C2514yes—
805C22×C4C2512yes—
806C22×C4C2514yes—
807C22×C4C2512yes—
808C22×C4C2512yes—
809C22×C4C2518yes—
810C22×C4C2512yes—
811C22×C4C2511yescharacteristic
812C22×C4C2512yes—
813C22×C4C2514yes—
814C22×C4C2512yes—
815C22×C4C2511yescharacteristic
816C22×C4C2512yes—
817C22×C4C2511yescharacteristic
818C22×C4C2511yescharacteristic
819C22×C4C2511yescharacteristic
820C22×C4C2511yescharacteristic
821C4⋊C4—24no—
822C4⋊C4—28no—
823C4⋊C4—24no—
824C4⋊C4—22no—
825C4⋊C4—28no—
826C4⋊C4—24no—
827C4⋊C4—24no—
828C4⋊C4—22no—
829C4⋊C4—24no—
830C4⋊C4—28no—
831C4⋊C4—28no—
832C4⋊C4—24no—
833C4⋊C4—22no—
834C4⋊C4—24no—
835C4⋊C4—22no—
836C4⋊C4—24no—
837C4⋊C4—24no—
838C4⋊C4—28no—
839C4⋊C4—28no—
840C4⋊C4—28no—
841C4⋊C4—24no—
842C4⋊C4—24no—
843C4⋊C4—24no—
844C4⋊C4—24no—
845C4⋊C4—22no—
846C4⋊C4—22no—
847C4⋊C4—28no—
848C4⋊C4—24no—
849C4⋊C4—44no—
850C4⋊C4—44no—
851C4⋊C4—44no—
852C4⋊C4—48no—
853C4⋊C4—42no—
854C4⋊C4—44no—
855C4⋊C4—42no—
856C4⋊C4—44no—
857C4⋊C4—44no—
858C4⋊C4—48no—
859C4⋊C4—48no—
860C4⋊C4—44no—
861C4⋊C4—48no—
862C4⋊C4—48no—
863C4⋊C4—48no—
864C4⋊C4—44no—
865C4⋊C4—44no—
866C4⋊C4—42no—
867C4⋊C4—48no—
868C4⋊C4—48no—
869C4⋊C4—48no—
870C4⋊C4—44no—
871C4⋊C4—44no—
872C4⋊C4—48no—
873C4⋊C4—48no—
874C4⋊C4—48no—
875C4⋊C4—44no—
876C4⋊C4—44no—
877C4⋊C4—44no—
878C4⋊C4—42no—
879C4⋊C4—44no—
880C4⋊C4—44no—
881C4⋊C4C22×Q814yes—
882C4⋊C4C22×Q8116yes—
883C4⋊C4C22×Q818yes—
884C4⋊C4C22×Q814yes—
885C4⋊C4C22×Q818yes—
886C4⋊C4C22×Q818yes—
887C4⋊C4C22×Q8116yes—
888C4⋊C42−1+414yes—
889C22⋊C4—24no—
890C22⋊C4—44no—
891C22⋊C4—44no—
892C22⋊C4—48no—
893C22⋊C4—44no—
894C22⋊C4—48no—
895C22⋊C4—42no—
896C22⋊C4—44no—
897C22⋊C4—44no—
898C22⋊C4C22×Q8116yes—
899C22⋊C4C22×Q818yes—
900C42—24no—
901C42—24no—
902C42—24no—
903C42—24no—
904C42—28no—
905C42—24no—
906C42—24no—
907C42—22no—
908C42—24no—
909C42—28no—
910C42—24no—
911C42—24no—
912C42—28no—
913C42—24no—
914C42—22no—
915C42—22no—
916C42—24no—
917C42—44no—
918C42—44no—
919C42—48no—
920C42—48no—
921C42—48no—
922C42—42no—
923C42—48no—
924C42—42no—
925C42—41no—
926C42—42no—
927C42C22×Q818yes—
928C42C22×Q814yes—
929C42H(5,𝔽2)14yes—
930C422−1+414yes—
931C23—22no—
932C23—22no—
933C23—22no—
934C23—22no—
935C23—22no—
936C23—22no—
937C23C23×Q814yes—
938C23C2611yescharacteristic
939Q8—28no—
940Q8—48no—
941Q8—48no—
942Q8—44no—
943Q8—48no—
944Q8—88no—
945Q8—88no—
946Q8—168no—
947D4—28no—
948C2×C4—22no—
949C2×C4—22no—
950C2×C4—21no—
951C2×C4—22no—
952C2×C4—22no—
953C2×C4—22no—
954C2×C4—22no—
955C2×C4—21no—
956C2×C4—24no—
957C2×C4—22no—
958C2×C4—21no—
959C2×C4—24no—
960C2×C4—21no—
961C2×C4—21no—
962C2×C4—22no—
963C2×C4—21no—
964C2×C4—216no—
965C2×C4—22no—
966C2×C4—22no—
967C2×C4—24no—
968C2×C4—22no—
969C2×C4—22no—
970C2×C4—24no—
971C2×C4—22no—
972C2×C4—24no—
973C2×C4—28no—
974C2×C4—21no—
975C2×C4—22no—
976C2×C4—22no—
977C2×C4—24no—
978C2×C4—22no—
979C2×C4—22no—
980C2×C4—24no—
981C2×C4—22no—
982C2×C4—24no—
983C2×C4—24no—
984C2×C4—24no—
985C2×C4—24no—
986C2×C4—21no—
987C2×C4—22no—
988C2×C4—21no—
989C2×C4—22no—
990C2×C4—22no—
991C2×C4—22no—
992C2×C4—22no—
993C2×C4—22no—
994C2×C4—24no—
995C2×C4—22no—
996C2×C4—24no—
997C2×C4—28no—
998C2×C4—24no—
999C2×C4—24no—
1000C2×C4—22no—
1001C2×C4—24no—
1002C2×C4—24no—
1003C2×C4—28no—
1004C2×C4—22no—
1005C2×C4—22no—
1006C2×C4—22no—
1007C2×C4—416no—
1008C2×C4—48no—
1009C2×C4—88no—
1010C2×C4—84no—
1011C2×C4C23×Q814yes—
1012C2×C4C23×Q812yes—
1013C2×C4C23×Q814yes—
1014C2×C4C23×Q814yes—
1015C2×C4C23×Q818yes—
1016C2×C4C23×Q812yes—
1017C2×C4C23×Q812yes—
1018C2×C4C2×H(5,𝔽2)12yes—
1019C2×C4C2×H(5,𝔽2)12yes—
1020C2×C4C2×H(5,𝔽2)12yes—
1021C2×C4C2×2−1+414yes—
1022C2×C4C2×2−1+412yes—
1023C2×C4C2×2−1+412yes—
1024C2×C4C2×2−1+412yes—
1025C2×C4C2×2−1+412yes—
1026C2×C4#58512yes—
1027C2×C4#58512yes—
1028C22—24no—
1029C22—24no—
1030C22—24no—
1031C22—42no—
1032C22—42no—
1033C22—42no—
1034C22—42no—
1035C22C24×Q811yescharacteristic
1036C22C22×H(5,𝔽2)11yescharacteristic
1037C22C22×2−1+411yescharacteristic
1038C22C22×2−1+411yescharacteristic
1039C22C2×#58511yescharacteristic
1040C22C2×#58511yescharacteristic
1041C22H(7,𝔽2)11yescharacteristic
1042C4—24no—
1043C4—28no—
1044C4—22no—
1045C4—24no—
1046C4—24no—
1047C4—24no—
1048C4—22no—
1049C4—22no—
1050C4—42no—
1051C4—44no—
1052C4—42no—
1053C4—44no—
1054C4—41no—
1055C4—42no—
1056C4—44no—
1057C4—42no—
1058C4—44no—
1059C4—42no—
1060C4—42no—
1061C4—48no—
1062C4—44no—
1063C4—42no—
1064C4#350214yes—
1065C4#350314yes—
1066C4#354714yes—
1067C2—44no—
1068C2C2×#354711yescharacteristic
1069C2C2×#350211yescharacteristic
1070C2C2×#350311yescharacteristic
1071C2#6294311yescharacteristic
1072C2#6295511yescharacteristic
1073C2#6298911yescharacteristic
1074C2#6302511yescharacteristic
subgroupG/H
center, commutator, Frattini, socle, cosocleC23C26
prime radicalC22×D4C24
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23 ◁ G
LECSG ▷ C23 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #59869C2semidirect
2. #59681C2semidirect
3. #59668C2semidirect
4. #59081C2semidirect
5. #51598C2semidirect
6. #45500C2semidirect
7. #45405C2semidirect
8. #45073C2semidirect
10. #42488C2semidirect
11. #39754C2semidirect
12. #39625C2semidirect
13. #39609C2semidirect
14. #39597C2semidirect
16. #36563C2semidirect
17. Q8×C4⋊Q8C2semidirect
19. #36193C2semidirect
22. #35173C2semidirect
23. #34951C2semidirect
200. #554Q8semidirect

Maximal subgroups

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

subgroupindex
#598692
#596812
#596682
#590812
#515982
#455002
#454052
#450732
#424972
#424882
#397542
#396252
#396092
#395972
#389672
#365632
Q8×C4⋊Q82
#361942
#361932
#361342
#351762
#351732
#349512
#349292
#344842
C4×#5542