Finite Group Databasebeta

← #7746769

Subgroups — #7746769

Order 512.

5312 conjugacy classes of subgroups.

The subgroup lattice has 1061 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#45434C212yesmaximal, complemented
2#45086C214yesmaximal, complemented
3#44941C214yesmaximal, complemented
4#44940C214yesmaximal, complemented
5#44934C212yesmaximal, complemented
6#44908C214yesmaximal, complemented
7#44879C214yesmaximal, complemented
8#42931C214yesmaximal, complemented
9#42499C214yesmaximal, complemented
10#42497C214yesmaximal, complemented
11#36574C211yesmaximal, characteristic, complemented
12#36573C211yesmaximal, characteristic, complemented
13#36563C212yesmaximal, complemented
14#36559C212yesmaximal, complemented
15Q8×C4⋊Q8C211yesmaximal, characteristic, complemented
16Q8×#127C211yesmaximal, characteristic, complemented
17#35934C214yesmaximal, complemented
18#35928C214yesmaximal, complemented
19#35748C212yesmaximal, complemented
20#35739C212yesmaximal, complemented
21#35294C211yesmaximal, characteristic, complemented
22#35275C212yesmaximal, complemented
23#34552C211yesmaximal, characteristic, complemented
24#34226C212yesmaximal
25#34207C211yesmaximal, characteristic
26C2×Q82C2212yes—
27C2×#554C2214yes—
28C2×D4×Q8C2214yes—
29C2×D4×Q8C2212yes—
30C2×#544C2214yes—
31C2×#532C2211yescharacteristic
32C2×#520C2212yes—
33#2868C2212yes—
34#2868C2212yes—
35#2868C2211yescharacteristic
36#2859C2212yes—
37#2859C2212yes—
38#2859C2212yes—
39#2859C2211yescharacteristic
40#2841C2218yes—
41#2807C2218yes—
42#2780C2218yes—
43#2768C2218yes—
44#2742C2218yes—
45#2732C2218yes—
46#2729C2218yes—
47#2729C2218yes—
48#2720C2218yes—
49#2704C2218yes—
50#2692C2218yes—
51#2683C2218yes—
52#2677C2218yes—
53#2667C2218yes—
54#2660C2214yes—
55#2660C2214yes—
56#2659C2218yes—
57#2629C2212yes—
58#2628C2214yes—
59#2628C2212yes—
60#2627C2214yes—
61#2584C2214yes—
62#2583C2218yes—
63#2582C2214yes—
64#2581C2212yes—
65#2580C2214yes—
66#2580C2214yes—
67#2580C2212yes—
68#2570C2214yes—
69#2567C2214yes—
70#2567C2214yes—
71#2567C2212yes—
72#2566C2214yes—
73#2566C2214yes—
74#2564C2214yes—
75#2563C2214yes—
76#2556C2218yes—
77#2556C2218yes—
78#2552C2214yes—
79#2552C2214yes—
80#2552C2214yes—
81#2551C2214yes—
82#2551C2214yes—
83#2551C2214yes—
84#2551C2214yes—
85#2551C2214yes—
86#2550C2214yes—
87#2550C2214yes—
88#2550C2214yes—
89#2549C2218yes—
90#2549C2218yes—
91#2542C2214yes—
92#2542C2214yes—
93#2542C2214yes—
94#2542C2214yes—
95#2542C2212yes—
96#2542C2214yes—
97#2538C2214yes—
98#2538C2214yes—
99#2522C2218yes—
100#2509C2214yes—
101#2508C2214yes—
102#2507C2214yes—
103#2507C2214yes—
104#2465C2218yes—
105#2454C2214yes—
106#2454C2214yes—
107#2454C2214yes—
108#2453C2214yes—
109#2452C2214yes—
110#2452C2214yes—
111#2452C2214yes—
112#2452C2218yes—
113#2452C2214yes—
114#2451C2214yes—
115#2451C2214yes—
116#2449C2218yes—
117#2441C2214yes—
118#2440C2218yes—
119#2440C2218yes—
120#2440C2214yes—
121#2440C2214yes—
122#2440C2214yes—
123#2440C2214yes—
124#2439C2214yes—
125#2438C2218yes—
126#2434C2218yes—
127#2409C2214yes—
128#2402C2212yes—
129#2402C2212yes—
130#2402C2212yes—
131#2399C2212yes—
132#2399C2212yes—
133#2399C2211yescharacteristic
134#2399C2211yescharacteristic
135#2396C2212yes—
136#2396C2214yes—
137#2396C2212yes—
138#2396C2212yes—
139#2396C2212yes—
140#2396C2211yescharacteristic
141#2396C2211yescharacteristic
142#2396C2212yes—
143C2×#395C2214yes—
144#2370C2214yes—
145#2369C2214yes—
146#2367C2214yes—
147#2367C2214yes—
148#2363C2214yes—
149#2363C2214yes—
150#2361C2214yes—
151#2361C2214yes—
152#2357C2214yes—
153#2355C2214yes—
154#2354C2214yes—
155#2351C2212yes—
156Q8×C4⋊C4C2214yes—
157Q8×C4⋊C4C2214yes—
158#2349C2214yes—
159#2349C2214yes—
160#2349C2212yes—
161D4×C4⋊C4C2214yes—
162D4×C4⋊C4C2214yes—
163D4×C4⋊C4C2214yes—
164#2341C2214yes—
165#2339C2214yes—
166#2331C2212yes—
167#2330C2212yes—
168#2326C2212yes—
169#2326C2212yes—
170#2324C2214yes—
171#2324C2214yes—
172#2319C2214yes—
173#2317C2214yes—
174#2311C2212yes—
175C4×C4⋊Q8C2211yescharacteristic
176C4×C4⋊Q8C2211yescharacteristic
177C4×C4⋊Q8C2212yes—
178C4×C4⋊Q8C2212yes—
179C4×#127C2211yescharacteristic
180C4×#127C2211yescharacteristic
181C4×#127C2212yes—
182C4×#127C2212yes—
183#2285C2212yes—
184C2×#384C2211yescharacteristic
185#2275C2214yes—
186C42×Q8C2211yescharacteristic
187C42×Q8C2211yescharacteristic
188C42×Q8C2212yes—
189C4×#117C2211yescharacteristic
190C4×#117C2212yes—
191C22×#41C2312yes—
192C23×Q8C2314yes—
193Q82—48no—
194#554—416no—
195D4×Q8—48no—
196D4×Q8—416no—
197#544—416no—
198#532Q8116yescomplemented
199C2×C4⋊Q8C2312yes—
200C2×C4⋊Q8C2314yes—
201C2×C4⋊Q8C2314yes—
202C2×C4⋊Q8C2314yes—
203C2×C4⋊Q8C2314yes—
204C2×C4⋊Q8C2314yes—
205C2×C4⋊Q8C2314yes—
206C2×C4⋊Q8C2314yes—
207C2×C4⋊Q8C2314yes—
208C2×C4⋊Q8C2318yes—
209C2×C4⋊Q8C2318yes—
210C2×C4⋊Q8C2311yescharacteristic
211C2×#127C2311yescharacteristic
212C2×#125C2314yes—
213C2×#125C2314yes—
214C2×#125C2312yes—
215C2×#125C2314yes—
216C2×#125C2318yes—
217C2×#124C2312yes—
218C2×C22⋊Q8C2314yes—
219C2×C22⋊Q8C2318yes—
220C2×C22⋊Q8C2318yes—
221C2×C22⋊Q8C2318yes—
222C2×C22⋊Q8C2318yes—
223C2×C22⋊Q8C2318yes—
224C2×C22⋊Q8C2318yes—
225C2×C22⋊Q8C2318yes—
226C2×C22⋊Q8C2318yes—
227C2×C22⋊Q8C2318yes—
228C2×#121C2314yes—
229#520—48no—
230C2×C4×Q8C2312yes—
231C2×C4×Q8C2312yes—
232C2×C4×Q8C2312yes—
233C2×C4×Q8C2311yescharacteristic
234C2×C4×Q8C2311yescharacteristic
235C2×C4×Q8C2312yes—
236C2×C4×Q8C2312yes—
237C2×C4×Q8C2314yes—
238C2×C4×Q8C2312yes—
239C2×C4×Q8C2314yes—
240C2×C4×Q8C2314yes—
241C2×C4×Q8C2312yes—
242C2×C4×D4C2314yes—
243C2×C4×D4C2314yes—
244C2×C4×D4C2312yes—
245C2×C4×D4C2314yes—
246C2×C4×D4C2314yes—
247C2×C4×D4C2312yes—
248C2×C4×D4C2314yes—
249C2×C4×D4C2314yes—
250C2×C4×D4C2314yes—
251C2×C4×D4C2314yes—
252C2×C4×D4C2314yes—
253C2×C4×D4C2314yes—
254C2×C4×D4C2314yes—
255C2×#117C2312yes—
256C2×#117C2312yes—
257C2×#117C2311yescharacteristic
258C2×#117C2311yescharacteristic
259C2×#117C2314yes—
260C2×#117C2314yes—
261C22×C4⋊C4C2312yes—
262C22×C4⋊C4C2314yes—
263C22×C4⋊C4C2318yes—
264C22×C4⋊C4C2314yes—
265C22×C42C2311yescharacteristic
266#400C2314yes—
267#400C2314yes—
268#400C2312yes—
269#400C2318yes—
270#400C2311yescharacteristic
271#400C2311yescharacteristic
272#400C2312yes—
273#400C2312yes—
274#400C2312yes—
275#400C2312yes—
276#399C2311yescharacteristic
277#399C2314yes—
278#399C2314yes—
279#399C2314yes—
280#399C2318yes—
281#399C2318yes—
282#399C2312yes—
283#399C2311yescharacteristic
284#399C2314yes—
285#399C2318yes—
286#398C2318yes—
287#398C2318yes—
288#398C2318yes—
289#398C2312yes—
290#398C2318yes—
291#398C2318yes—
292#398C2318yes—
293#398C2318yes—
294#398C2312yes—
295#398C2312yes—
296#398C2312yes—
297#398C2312yes—
298#398C2312yes—
299#398C2312yes—
300#398C2312yes—
301#398C2312yes—
302#398C2312yes—
303#398C2312yes—
304#398C2312yes—
305#398C2318yes—
306#398C2318yes—
307#398C2318yes—
308#396C2318yes—
309#396C2318yes—
310#396C2318yes—
311#396C2318yes—
312#396C2318yes—
313#396C2318yes—
314#396C2312yes—
315#396C2312yes—
316#396C2312yes—
317#396C2312yes—
318#395C2314yes—
319#395C2318yes—
320#395C2318yes—
321#395C2314yes—
322#395C2318yes—
323#395C2318yes—
324#395C2314yes—
325#395C2318yes—
326#395C2318yes—
327#395C2314yes—
328#395C2311yescharacteristic
329#395C2318yes—
330#395C2311yescharacteristic
331#395C2312yes—
332#395C2312yes—
333#395C2312yes—
334#395C2312yes—
335#395C2312yes—
336#395C2318yes—
337#393C2318yes—
338#393C2318yes—
339#393C2314yes—
340#393C2311yescharacteristic
341#393C2314yes—
342#393C2311yescharacteristic
343#393C2312yes—
344#391C2312yes—
345#391C2312yes—
346#391C2314yes—
347#391C2314yes—
348#391C2318yes—
349#391C2318yes—
350#391C2318yes—
351#391C2318yes—
352#390C2314yes—
353#390C2314yes—
354#390C2314yes—
355#390C2312yes—
356#390C2312yes—
357#390C2314yes—
358#390C2314yes—
359#390C2314yes—
360#390C2314yes—
361#390C2314yes—
362#390C2318yes—
363#390C2318yes—
364#389C2314yes—
365#389C2314yes—
366#389C2314yes—
367#389C2314yes—
368#389C2314yes—
369#389C2314yes—
370#389C2318yes—
371#389C2314yes—
372#389C2314yes—
373#389C2318yes—
374#389C2318yes—
375#389C2314yes—
376#389C2314yes—
377#389C2318yes—
378#389C2318yes—
379#389C2318yes—
380#389C2314yes—
381#389C2314yes—
382#389C2314yes—
383#389C2314yes—
384#389C2314yes—
385#389C2318yes—
386#389C2318yes—
387#389C2314yes—
388#389C2314yes—
389#389C2318yes—
390#389C2318yes—
391#389C2314yes—
392#389C2314yes—
393#389C2314yes—
394#389C2318yes—
395#388C2318yes—
396#388C2318yes—
397#388C2318yes—
398#388C2318yes—
399#388C2318yes—
400#388C2318yes—
401#387C2318yes—
402#387C2318yes—
403#387C2318yes—
404#387C2318yes—
405#387C2318yes—
406#387C2318yes—
407#386C2318yes—
408#386C2318yes—
409#386C2318yes—
410#385C2318yes—
411#385C2318yes—
412#385C2318yes—
413#385C2318yes—
414#385C2318yes—
415#385C2318yes—
416#385C2318yes—
417#385C2318yes—
418#385C2318yes—
419#385C2318yes—
420#385C2318yes—
421#385C2318yes—
422#385C2318yes—
423#384C2312yes—
424#384C2311yescharacteristic
425#384C2311yescharacteristic
426#384C2312yes—
427#384C2314yes—
428#384C2312yes—
429#384C2314yes—
430#384C2318yes—
431#384C2314yes—
432#384C2314yes—
433#384C2314yes—
434#384C2312yes—
435#384C2314yes—
436#384C2314yes—
437#384C2314yes—
438#382C2314yes—
439#382C2314yes—
440#382C2314yes—
441#382C2314yes—
442#382C2312yes—
443#382C2314yes—
444#381C2318yes—
445#380C2318yes—
446#380C2318yes—
447#380C2318yes—
448#380C2318yes—
449#380C2314yes—
450#380C2314yes—
451#380C2314yes—
452#380C2318yes—
453C4×C4⋊C4C2314yes—
454C4×C4⋊C4C2314yes—
455C4×C4⋊C4C2314yes—
456C4×C4⋊C4C2314yes—
457C4×C4⋊C4C2314yes—
458C4×C4⋊C4C2314yes—
459C4×C4⋊C4C2312yes—
460C4×C4⋊C4C2312yes—
461C4×C4⋊C4C2312yes—
462C4×C4⋊C4C2311yescharacteristic
463C4×C4⋊C4C2312yes—
464C4×C4⋊C4C2312yes—
465C4×C4⋊C4C2314yes—
466C4×C4⋊C4C2314yes—
467C4×C4⋊C4C2312yes—
468C4×C4⋊C4C2312yes—
469C4×C4⋊C4C2312yes—
470C4×C4⋊C4C2312yes—
471C4×C4⋊C4C2312yes—
472C4×C4⋊C4C2312yes—
473C4×C4⋊C4C2318yes—
474C4×C4⋊C4C2311yescharacteristic
475C4×C4⋊C4C2314yes—
476C4×C4⋊C4C2312yes—
477C4×C4⋊C4C2312yes—
478C4×C4⋊C4C2312yes—
479C4×C4⋊C4C2312yes—
480C4×C4⋊C4C2312yes—
481C4×C4⋊C4C2312yes—
482C4×C4⋊C4C2312yes—
483C4×C4⋊C4C2312yes—
484C4×C4⋊C4C2312yes—
485C4×C4⋊C4C2312yes—
486C4×C4⋊C4C2312yes—
487C4×C4⋊C4C2312yes—
488C4×C22⋊C4C2318yes—
489C4×C22⋊C4C2312yes—
490C4×C22⋊C4C2312yes—
491C4×C22⋊C4C2318yes—
492C4×C22⋊C4C2312yes—
493C4×C22⋊C4C2312yes—
494C4×C22⋊C4C2312yes—
495C4×C22⋊C4C2312yes—
496C4×C22⋊C4C2318yes—
497#376C2312yes—
498#376C2311yescharacteristic
499#376C2311yescharacteristic
500#376C2312yes—
501C2×#95C2314yes—
502C2×#95C2318yes—
503C43C2311yescharacteristic
504C43C2312yes—
505C43C2311yescharacteristic
506C43C2312yes—
507C2×#41—44no—
508C2×#41—44no—
509C2×#41C2×Q8116yescomplemented
510C22×Q8—48no—
511C22×Q8—416no—
512C22×Q8C2411yescharacteristic
513C22×Q8C2411yescharacteristic
514C22×Q8C2412yes—
515C22×Q8C2412yes—
516C22×Q8C2418yes—
517C22×Q8C2414yes—
518C22×Q8C2418yes—
519C22×D4C2414yes—
520C22×D4C2412yes—
521C22×D4C2414yes—
522C23×C4C2412yes—
523C23×C4C2411yescharacteristic
524C23×C4C2414yes—
525C23×C4C2418yes—
526C23×C4C2418yes—
527C23×C4C2414yes—
528C23×C4C2414yes—
529C23×C4C2414yes—
530C4⋊Q8—216no—
531C4⋊Q8—28no—
532C4⋊Q8—48no—
533C4⋊Q8—48no—
534C4⋊Q8—48no—
535C4⋊Q8—48no—
536C4⋊Q8—48no—
537C4⋊Q8—48no—
538C4⋊Q8—48no—
539C4⋊Q8—416no—
540C4⋊Q8—416no—
541C4⋊Q8C2×Q818yescomplemented
542#127C2×Q818yes—
543#125—216no—
544#125—44no—
545#125—48no—
546#125—48no—
547#125—416no—
548#124C2×Q8116yescomplemented
549C22⋊Q8—416no—
550C22⋊Q8—416no—
551C22⋊Q8—416no—
552C22⋊Q8—416no—
553C22⋊Q8—416no—
554C22⋊Q8—416no—
555C22⋊Q8—416no—
556C22⋊Q8—416no—
557C22⋊Q8—48no—
558C22⋊Q8—416no—
559#121C2×Q8132yescomplemented
560C4×Q8—28no—
561C4×Q8—24no—
562C4×Q8—28no—
563C4×Q8—28no—
564C4×Q8—24no—
565C4×Q8—28no—
566C4×Q8—28no—
567C4×Q8—44no—
568C4×Q8—48no—
569C4×Q8—44no—
570C4×Q8—48no—
571C4×Q8—48no—
572C4×D4—28no—
573C4×D4—216no—
574C4×D4—216no—
575C4×D4—48no—
576C4×D4—48no—
577C4×D4—44no—
578C4×D4—48no—
579C4×D4—48no—
580C4×D4—48no—
581C4×D4—48no—
582C4×D4—48no—
583C4×D4—48no—
584C4×D4C2×Q8132yescomplemented
585#117—24no—
586#117—28no—
587#117—28no—
588#117—42no—
589#117—48no—
590#117—48no—
591C2×C4⋊C4—48no—
592C2×C4⋊C4—44no—
593C2×C4⋊C4—48no—
594C2×C4⋊C4—416no—
595C2×C4⋊C4C2411yescharacteristic
596C2×C4⋊C4C2412yes—
597C2×C4⋊C4C2412yes—
598C2×C4⋊C4C2412yes—
599C2×C4⋊C4C2414yes—
600C2×C4⋊C4C2414yes—
601C2×C4⋊C4C2414yes—
602C2×C4⋊C4C2418yes—
603C2×C4⋊C4C2411yescharacteristic
604C2×C4⋊C4C2414yes—
605C2×C4⋊C4C2414yes—
606C2×C4⋊C4C2412yes—
607C2×C4⋊C4C2412yes—
608C2×C4⋊C4C2412yes—
609C2×C4⋊C4C2412yes—
610C2×C4⋊C4C2414yes—
611C2×C4⋊C4C2414yes—
612C2×C4⋊C4C2414yes—
613C2×C4⋊C4C2414yes—
614C2×C4⋊C4C2412yes—
615C2×C4⋊C4C2412yes—
616C2×C4⋊C4C2412yes—
617C2×C4⋊C4C2412yes—
618C2×C4⋊C4C2412yes—
619C2×C4⋊C4C2412yes—
620C2×C4⋊C4C2411yescharacteristic
621C2×C4⋊C4C2414yes—
622C2×C4⋊C4C2412yes—
623C2×C4⋊C4C2411yescharacteristic
624C2×C4⋊C4C2412yes—
625C2×C4⋊C4C2412yes—
626C2×C4⋊C4C2412yes—
627C2×C4⋊C4C2412yes—
628C2×C4⋊C4C2412yes—
629C2×C4⋊C4C2412yes—
630C2×C4⋊C4C2418yes—
631C2×C4⋊C4C2418yes—
632C2×C4⋊C4C2414yes—
633C2×C4⋊C4C2414yes—
634C2×C4⋊C4C2418yes—
635C2×C4⋊C4C2418yes—
636C2×C4⋊C4C2418yes—
637C2×C4⋊C4C2412yes—
638C2×C4⋊C4C2418yes—
639C2×C4⋊C4C2418yes—
640C2×C4⋊C4C2412yes—
641C2×C4⋊C4C2412yes—
642C2×C4⋊C4C2412yes—
643C2×C4⋊C4C2418yes—
644C2×C4⋊C4C2418yes—
645C2×C4⋊C4C2418yes—
646C2×C4⋊C4C2418yes—
647C2×C4⋊C4C2418yes—
648C2×C4⋊C4C2418yes—
649C2×C4⋊C4C2418yes—
650C2×C4⋊C4C2418yes—
651C2×C4⋊C4C2418yes—
652C2×C4⋊C4C2414yes—
653C2×C22⋊C4C2411yescharacteristic
654C2×C22⋊C4C2411yescharacteristic
655C2×C22⋊C4C2414yes—
656C2×C22⋊C4C2412yes—
657C2×C22⋊C4C2412yes—
658C2×C22⋊C4C2412yes—
659C2×C22⋊C4C2412yes—
660C2×C22⋊C4C2418yes—
661C2×C22⋊C4C2418yes—
662C2×C22⋊C4C2414yes—
663C2×C22⋊C4C2418yes—
664C2×C22⋊C4C2412yes—
665C2×C22⋊C4C2418yes—
666C2×C22⋊C4C2418yes—
667C2×C22⋊C4C2418yes—
668C2×C22⋊C4C2418yes—
669C2×C22⋊C4C2418yes—
670C2×C22⋊C4C2418yes—
671C2×C22⋊C4C2418yes—
672C2×C42C2×Q818yescomplemented
673C2×C42C2411yescharacteristic
674C2×C42C2414yes—
675C2×C42C2411yescharacteristic
676C2×C42C2412yes—
677C2×C42C2411yescharacteristic
678C2×C42C2412yes—
679C2×C42C2412yes—
680C2×C42C2412yes—
681C2×C42C2412yes—
682C2×C42C2412yes—
683C2×C42C2412yes—
684C2×C42C2412yes—
685C2×C42C2412yes—
686C2×C42C2412yes—
687C2×C42C2412yes—
688C2×C42C2412yes—
689C2×C42C2412yes—
690C2×C42C2412yes—
691C2×C42C2414yes—
692C2×C42C2418yes—
693C2×C42C2418yes—
694C2×C42C2418yes—
695C2×C42C2412yes—
696C2×C42C2411yescharacteristic
697C2×C42C2411yescharacteristic
698C2×C42C2411yescharacteristic
699C2×C42C2412yes—
700C2×C42C2412yes—
701#95C2412yes—
702#95C2411yescharacteristic
703#95C2418yes—
704#95C2418yes—
705#95C2418yes—
706#95C2418yes—
707#95C2414yes—
708#95C2412yes—
709#95C2412yes—
710#95C2412yes—
711#95C2412yes—
712#95C2412yes—
713#95C2412yes—
714#95C2412yes—
715#95C2412yes—
716#95C2412yes—
717#95C2412yes—
718#95C2412yes—
719#95C2411yescharacteristic
720#95C2411yescharacteristic
721#95C2412yes—
722#95C2411yescharacteristic
723#95C2412yes—
724#95C2412yes—
725#95C2412yes—
726#95C2412yes—
727#95C2412yes—
728#95C2412yes—
729#95C2412yes—
730#95C2412yes—
731#95C2412yes—
732#95C2418yes—
733#95C2418yes—
734#95C2418yes—
735#95C2418yes—
736#95C2418yes—
737#95C2418yes—
738#95C2414yes—
739#95C2418yes—
740#95C2418yes—
741#95C2418yes—
742#95C2418yes—
743C24C2511yescharacteristic
744C24C2514yes—
745#41—432no—
746C2×Q8—22no—
747C2×Q8—24no—
748C2×Q8—22no—
749C2×Q8—24no—
750C2×Q8—24no—
751C2×Q8—216no—
752C2×Q8—28no—
753C2×Q8—24no—
754C2×Q8—24no—
755C2×Q8—24no—
756C2×Q8—42no—
757C2×Q8—48no—
758C2×Q8—48no—
759C2×Q8—48no—
760C2×Q8—48no—
761C2×Q8—48no—
762C2×Q8—48no—
763C2×Q8—832no—
764C2×Q8C22×Q818yes—
765C2×D4—28no—
766C2×D4—24no—
767C2×D4—28no—
768C2×D4—24no—
769C2×D4—44no—
770C2×D4—44no—
771C2×D4C22×Q8116yes—
772C2×D4C22×Q818yes—
773C2×D4C22×Q8116yes—
774C22×C4—24no—
775C22×C4—22no—
776C22×C4—24no—
777C22×C4—22no—
778C22×C4—28no—
779C22×C4—216no—
780C22×C4—216no—
781C22×C4—44no—
782C22×C4—44no—
783C22×C4—48no—
784C22×C4—48no—
785C22×C4—48no—
786C22×C4—48no—
787C22×C4—48no—
788C22×C4—44no—
789C22×C4—44no—
790C22×C4—48no—
791C22×C4—48no—
792C22×C4C22×Q818yes—
793C22×C4C22×Q814yes—
794C22×C4C22×Q8116yes—
795C22×C4C2511yescharacteristic
796C22×C4C2512yes—
797C22×C4C2512yes—
798C22×C4C2518yes—
799C22×C4C2512yes—
800C22×C4C2512yes—
801C22×C4C2512yes—
802C22×C4C2512yes—
803C22×C4C2511yescharacteristic
804C22×C4C2518yes—
805C22×C4C2514yes—
806C22×C4C2514yes—
807C22×C4C2511yescharacteristic
808C22×C4C2512yes—
809C22×C4C2514yes—
810C22×C4C2511yescharacteristic
811C22×C4C2512yes—
812C22×C4C2511yescharacteristic
813C22×C4C2512yes—
814C22×C4C2512yes—
815C22×C4C2512yes—
816C22×C4C2512yes—
817C22×C4C2511yescharacteristic
818C4⋊C4—22no—
819C4⋊C4—24no—
820C4⋊C4—24no—
821C4⋊C4—28no—
822C4⋊C4—24no—
823C4⋊C4—28no—
824C4⋊C4—28no—
825C4⋊C4—216no—
826C4⋊C4—22no—
827C4⋊C4—24no—
828C4⋊C4—24no—
829C4⋊C4—28no—
830C4⋊C4—28no—
831C4⋊C4—28no—
832C4⋊C4—28no—
833C4⋊C4—24no—
834C4⋊C4—24no—
835C4⋊C4—24no—
836C4⋊C4—24no—
837C4⋊C4—22no—
838C4⋊C4—24no—
839C4⋊C4—24no—
840C4⋊C4—24no—
841C4⋊C4—22no—
842C4⋊C4—28no—
843C4⋊C4—216no—
844C4⋊C4—216no—
845C4⋊C4—24no—
846C4⋊C4—24no—
847C4⋊C4—28no—
848C4⋊C4—24no—
849C4⋊C4—24no—
850C4⋊C4—24no—
851C4⋊C4—24no—
852C4⋊C4—24no—
853C4⋊C4—24no—
854C4⋊C4—28no—
855C4⋊C4—44no—
856C4⋊C4—44no—
857C4⋊C4—48no—
858C4⋊C4—48no—
859C4⋊C4—48no—
860C4⋊C4—42no—
861C4⋊C4—42no—
862C4⋊C4—42no—
863C4⋊C4—48no—
864C4⋊C4—42no—
865C4⋊C4—48no—
866C4⋊C4—48no—
867C4⋊C4—48no—
868C4⋊C4—48no—
869C4⋊C4—48no—
870C4⋊C4—48no—
871C4⋊C4—48no—
872C4⋊C4—48no—
873C4⋊C4—48no—
874C4⋊C4—48no—
875C4⋊C4C22×Q8116yes—
876C22⋊C4—22no—
877C22⋊C4—22no—
878C22⋊C4—24no—
879C22⋊C4—24no—
880C22⋊C4—28no—
881C22⋊C4—216no—
882C22⋊C4—24no—
883C22⋊C4—24no—
884C22⋊C4—216no—
885C22⋊C4—42no—
886C22⋊C4—44no—
887C22⋊C4—48no—
888C22⋊C4—48no—
889C22⋊C4—48no—
890C22⋊C4—48no—
891C22⋊C4—48no—
892C22⋊C4—48no—
893C22⋊C4—48no—
894C22⋊C4C22×Q8132yes—
895C42—22no—
896C42—24no—
897C42—28no—
898C42—24no—
899C42—24no—
900C42—24no—
901C42—24no—
902C42—24no—
903C42—24no—
904C42—24no—
905C42—24no—
906C42—24no—
907C42—24no—
908C42—24no—
909C42—22no—
910C42—22no—
911C42—24no—
912C42—24no—
913C42—44no—
914C42—48no—
915C42—48no—
916C42—48no—
917C42C22×Q818yes—
918C42C22×Q814yes—
919C42C22×Q814yes—
920C42H(5,𝔽2)14yes—
921C42H(5,𝔽2)18yes—
922C422−1+418yes—
923C23—22no—
924C23—21no—
925C23—28no—
926C23—24no—
927C23—22no—
928C23—28no—
929C23—21no—
930C23—24no—
931C23C23×Q818yes—
932C23C23×Q812yes—
933C23C2611yescharacteristic
934Q8—28no—
935Q8—28no—
936Q8—216no—
937Q8—48no—
938Q8—816no—
939Q8—88no—
940Q8—168no—
941D4—216no—
942D4—232no—
943D4—416no—
944C2×C4—22no—
945C2×C4—24no—
946C2×C4—22no—
947C2×C4—22no—
948C2×C4—22no—
949C2×C4—22no—
950C2×C4—22no—
951C2×C4—21no—
952C2×C4—22no—
953C2×C4—22no—
954C2×C4—22no—
955C2×C4—22no—
956C2×C4—22no—
957C2×C4—22no—
958C2×C4—24no—
959C2×C4—21no—
960C2×C4—28no—
961C2×C4—216no—
962C2×C4—21no—
963C2×C4—22no—
964C2×C4—21no—
965C2×C4—22no—
966C2×C4—22no—
967C2×C4—22no—
968C2×C4—22no—
969C2×C4—22no—
970C2×C4—22no—
971C2×C4—24no—
972C2×C4—22no—
973C2×C4—22no—
974C2×C4—24no—
975C2×C4—28no—
976C2×C4—28no—
977C2×C4—28no—
978C2×C4—28no—
979C2×C4—28no—
980C2×C4—28no—
981C2×C4—22no—
982C2×C4—22no—
983C2×C4—22no—
984C2×C4—22no—
985C2×C4—22no—
986C2×C4—22no—
987C2×C4—22no—
988C2×C4—28no—
989C2×C4—22no—
990C2×C4—22no—
991C2×C4—22no—
992C2×C4—22no—
993C2×C4—28no—
994C2×C4—416no—
995C2×C4—816no—
996C2×C4—88no—
997C2×C4—816no—
998C2×C4—164no—
999C2×C4—164no—
1000C2×C4C23×Q814yes—
1001C2×C4C23×Q812yes—
1002C2×C4C23×Q818yes—
1003C2×C4C23×Q812yes—
1004C2×C4C23×Q814yes—
1005C2×C4C2×H(5,𝔽2)12yes—
1006C2×C4C2×H(5,𝔽2)14yes—
1007C2×C4C2×H(5,𝔽2)12yes—
1008C2×C4C2×H(5,𝔽2)14yes—
1009C2×C4C2×H(5,𝔽2)12yes—
1010C2×C4C2×H(5,𝔽2)14yes—
1011C2×C4C2×2−1+414yes—
1012C2×C4C2×2−1+414yes—
1013C2×C4C2×2−1+414yes—
1014C2×C4#58512yes—
1015C22—22no—
1016C22—28no—
1017C22—24no—
1018C22—216no—
1019C22—44no—
1020C22—41no—
1021C22—41no—
1022C22—44no—
1023C22—48no—
1024C22—42no—
1025C22C24×Q811yescharacteristic
1026C22C22×H(5,𝔽2)11yescharacteristic
1027C22C22×H(5,𝔽2)12yes—
1028C22C22×2−1+412yes—
1029C22C2×#58511yescharacteristic
1030C4—22no—
1031C4—28no—
1032C4—24no—
1033C4—24no—
1034C4—22no—
1035C4—22no—
1036C4—24no—
1037C4—24no—
1038C4—24no—
1039C4—44no—
1040C4—48no—
1041C4—41no—
1042C4—44no—
1043C4—42no—
1044C4—41no—
1045C4—42no—
1046C4—42no—
1047C4—42no—
1048C4—42no—
1049C4—48no—
1050C4—42no—
1051C4#350114yes—
1052C4#350318yes—
1053C2—42no—
1054C2—48no—
1055C2C2×#350111yescharacteristic
1056C2C2×#350312yes—
1057C2#6283211yescharacteristic
1058C2#6283311yescharacteristic
1059C2#6283512yes—
subgroupG/H
center, commutator, Frattini, socle, cosocleC23C26
prime radicalC2×#532C22
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23 ◁ G
LECSG ▷ C23 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #45434C2semidirect
2. #45086C2semidirect
3. #44941C2semidirect
4. #44940C2semidirect
5. #44934C2semidirect
6. #44908C2semidirect
7. #44879C2semidirect
8. #42931C2semidirect
9. #42499C2semidirect
10. #42497C2semidirect
11. #36574C2semidirect
12. #36573C2semidirect
13. #36563C2semidirect
14. #36559C2semidirect
15. Q8×C4⋊Q8C2semidirect
16. Q8×#127C2semidirect
17. #35934C2semidirect
18. #35928C2semidirect
19. #35748C2semidirect
20. #35739C2semidirect
21. #35294C2semidirect
22. #35275C2semidirect
23. #34552C2semidirect
198. #532Q8semidirect
509. C2×#41C2×Q8semidirect
541. C4⋊Q8C2×Q8semidirect
548. #124C2×Q8semidirect
559. #121C2×Q8semidirect
584. C4×D4C2×Q8semidirect
672. C2×C42C2×Q8semidirect

Maximal subgroups

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

subgroupindex
#454342
#450862
#449412
#449402
#449342
#449082
#448792
#429312
#424992
#424972
#365742
#365732
#365632
#365592
Q8×C4⋊Q82
Q8×#1272
#359342
#359282
#357482
#357392
#352942
#352752
#345522
#342262
#342072