Finite Group Databasebeta

← #7687922

Subgroups — #7687922

Order 512.

5027 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#59832C211yesmaximal, characteristic, complemented
2#59666C212yesmaximal, complemented
3#59551C214yesmaximal, complemented
4#59376C214yesmaximal, complemented
5#59259C212yesmaximal, complemented
6#59036C212yesmaximal, complemented
7#45359C214yesmaximal, complemented
8#43132C218yesmaximal, complemented
9#39980C214yesmaximal, complemented
10#39658C214yesmaximal, complemented
11#39608C212yesmaximal, complemented
12#38964C212yesmaximal, complemented
13#36564C212yesmaximal, complemented
14#36563C211yesmaximal, characteristic, complemented
15Q8×C22⋊Q8C212yesmaximal, complemented
16#36456C212yesmaximal, complemented
17#36407C212yesmaximal, complemented
18#36194C211yesmaximal, characteristic, complemented
19#36134C211yesmaximal, characteristic, complemented
20#35788C214yesmaximal, complemented
21#34952C212yesmaximal, complemented
22#34941C211yesmaximal, characteristic, complemented
23#34316C212yesmaximal
24#34213C212yesmaximal, complemented
25C4×D4×Q8C211yesmaximal, characteristic, complemented
26C4×#547C211yesmaximal, characteristic
27C2×Q82C2212yes—
28C2×D4×Q8C2211yescharacteristic
29C2×#547C2211yescharacteristic
30C2×#533C2212yes—
31C2×C4×#41C2212yes—
32C22×C4×Q8C2212yes—
33#2868C2211yescharacteristic
34#2859C2212yes—
35#2857C2212yes—
36#2857C2214yes—
37#2857C2212yes—
38#2857C2214yes—
39#2802C2218yes—
40#2790C2218yes—
41#2768C2218yes—
42#2763C2218yes—
43#2763C2218yes—
44#2748C2218yes—
45#2734C2214yes—
46#2732C2218yes—
47#2720C2218yes—
48#2692C2218yes—
49#2692C2218yes—
50#2667C2218yes—
51#2628C2214yes—
52#2607C2218yes—
53#2588C2218yes—
54#2586C2218yes—
55#2585C2218yes—
56#2582C2214yes—
57#2582C2212yes—
58#2582C2212yes—
59#2581C2214yes—
60#2580C2214yes—
61#2579C2218yes—
62#2574C2218yes—
63#2574C2218yes—
64#2574C2214yes—
65#2571C2212yes—
66#2567C2214yes—
67#2567C2211yescharacteristic
68#2567C2212yes—
69#2565C2214yes—
70#2563C2212yes—
71#2563C2211yescharacteristic
72#2563C2214yes—
73#2556C2218yes—
74#2552C2212yes—
75#2552C2211yescharacteristic
76#2552C2212yes—
77#2551C2212yes—
78#2551C2212yes—
79#2550C2214yes—
80#2550C2214yes—
81#2549C2218yes—
82#2546C2214yes—
83#2542C2212yes—
84#2538C2212yes—
85#2538C2212yes—
86#2538C2214yes—
87#2538C2211yescharacteristic
88#2520C2218yes—
89#2520C2218yes—
90#2508C2214yes—
91#2508C2214yes—
92#2508C2212yes—
93#2507C2214yes—
94#2507C2214yes—
95#2507C2214yes—
96#2497C2214yes—
97#2497C2214yes—
98#2497C2212yes—
99#2492C2214yes—
100#2487C2214yes—
101#2465C2218yes—
102#2454C2212yes—
103#2454C2214yes—
104#2452C2214yes—
105#2452C2214yes—
106#2452C2218yes—
107#2451C2214yes—
108#2451C2214yes—
109#2451C2218yes—
110#2451C2214yes—
111#2451C2214yes—
112#2441C2214yes—
113#2441C2214yes—
114#2440C2214yes—
115#2440C2218yes—
116#2440C2214yes—
117#2439C2214yes—
118#2439C2214yes—
119#2439C2214yes—
120#2439C2218yes—
121#2429C2214yes—
122#2423C2214yes—
123#2423C2214yes—
124#2423C2212yes—
125#2409C2214yes—
126#2396C2214yes—
127#2396C2218yes—
128#2374C2218yes—
129#2370C2214yes—
130#2370C2214yes—
131#2369C2214yes—
132#2369C2212yes—
133#2369C2212yes—
134#2365C2212yes—
135#2365C2211yescharacteristic
136#2365C2212yes—
137#2365C2211yescharacteristic
138#2365C2212yes—
139#2365C2212yes—
140#2363C2214yes—
141#2362C2214yes—
142#2362C2212yes—
143#2361C2212yes—
144#2360C2214yes—
145#2360C2212yes—
146#2359C2214yes—
147#2355C2212yes—
148#2355C2214yes—
149#2355C2218yes—
150#2355C2212yes—
151#2354C2212yes—
152#2354C2212yes—
153#2354C2211yescharacteristic
154#2351C2214yes—
155Q8×C4⋊C4C2212yes—
156Q8×C4⋊C4C2212yes—
157Q8×C4⋊C4C2211yescharacteristic
158Q8×C4⋊C4C2214yes—
159D4×C4⋊C4C2212yes—
160D4×C4⋊C4C2211yescharacteristic
161D4×C4⋊C4C2211yescharacteristic
162#2345C2214yes—
163#2344C2212yes—
164#2341C2214yes—
165Q8×C22⋊C4C2212yes—
166Q8×C22⋊C4C2214yes—
167#2339C2212yes—
168#2335C2218yes—
169#2329C2218yes—
170#2324C2214yes—
171#2317C2214yes—
172C4×C4⋊Q8C2212yes—
173C4×C4⋊Q8C2212yes—
174C4×C4⋊Q8C2211yescharacteristic
175C4×C4⋊Q8C2211yescharacteristic
176C4×C4⋊Q8C2211yescharacteristic
177C4×#125C2212yes—
178C4×C22⋊Q8C2214yes—
179C4×C22⋊Q8C2214yes—
180C4×C22⋊Q8C2212yes—
181C4×C22⋊Q8C2214yes—
182C4×C22⋊Q8C2212yes—
183C4×C22⋊Q8C2212yes—
184C4×C22⋊Q8C2214yes—
185C4×C22⋊Q8C2214yes—
186C4×#123C2214yes—
187C4×#121C2212yes—
188#2297C2214yes—
189#2296C2214yes—
190#2293C2212yes—
191#2285C2212yes—
192#2285C2212yes—
193#2274C2214yes—
194C42×Q8C2211yescharacteristic
195C42×D4C2212yes—
196C42×D4C2211yescharacteristic
197C42×D4C2211yescharacteristic
198C2×C4×C4⋊C4C2212yes—
199C22×#41C2312yes—
200C23×Q8C2312yes—
201Q82—48no—
202D4×Q8—28no—
203#547Q8116yescomplemented
204#533—216no—
205C2×C4⋊Q8C2311yescharacteristic
206C2×C4⋊Q8C2312yes—
207C2×C4⋊Q8C2312yes—
208C2×C4⋊Q8C2314yes—
209C2×C4⋊Q8C2314yes—
210C2×C4⋊Q8C2312yes—
211C2×C4⋊Q8C2314yes—
212C2×C4⋊Q8C2318yes—
213C2×C4⋊Q8C2312yes—
214C2×C4⋊Q8C2311yescharacteristic
215C2×C4⋊Q8C2311yescharacteristic
216C2×#125C2314yes—
217C2×#125C2312yes—
218C2×#125C2314yes—
219C2×#123C2314yes—
220C2×C22⋊Q8C2314yes—
221C2×C22⋊Q8C2312yes—
222C2×C22⋊Q8C2314yes—
223C2×C22⋊Q8C2312yes—
224C2×C22⋊Q8C2314yes—
225C2×C22⋊Q8C2314yes—
226C2×C22⋊Q8C2318yes—
227C2×C22⋊Q8C2314yes—
228C2×C22⋊Q8C2318yes—
229C2×C22⋊Q8C2312yes—
230C2×#121C2312yes—
231C4×#41—48no—
232C2×C4×Q8—48no—
233C2×C4×Q8C2312yes—
234C2×C4×Q8C2312yes—
235C2×C4×Q8C2311yescharacteristic
236C2×C4×Q8C2311yescharacteristic
237C2×C4×Q8C2311yescharacteristic
238C2×C4×Q8C2314yes—
239C2×C4×Q8C2314yes—
240C2×C4×Q8C2314yes—
241C2×C4×Q8C2314yes—
242C2×C4×Q8C2312yes—
243C2×C4×Q8C2312yes—
244C2×C4×Q8C2314yes—
245C2×C4×Q8C2314yes—
246C2×C4×Q8C2312yes—
247C2×C4×Q8C2312yes—
248C2×C4×Q8C2314yes—
249C2×C4×D4C2311yescharacteristic
250C2×C4×D4C2311yescharacteristic
251C2×C4×D4C2312yes—
252C2×C4×D4C2314yes—
253C2×C4×D4C2314yes—
254C2×C4×D4C2312yes—
255C2×C4×D4C2312yes—
256C2×C4×D4C2311yescharacteristic
257C2×C4×D4C2311yescharacteristic
258C2×C4×D4C2311yescharacteristic
259C2×C4×D4C2311yescharacteristic
260C2×#117C2314yes—
261C2×#117C2314yes—
262C2×#117C2314yes—
263C2×#117C2312yes—
264C2×#117C2314yes—
265C22×C4⋊C4C2312yes—
266C22×C4⋊C4C2314yes—
267C22×C4⋊C4C2312yes—
268C22×C4⋊C4C2312yes—
269C22×C42C2312yes—
270C22×C42C2312yes—
271C22×C42C2314yes—
272C22×C42C2314yes—
273#400C2318yes—
274#400C2318yes—
275#400C2318yes—
276#400C2314yes—
277#399C2318yes—
278#399C2314yes—
279#399C2318yes—
280#399C2318yes—
281#398C2318yes—
282#398C2318yes—
283#398C2314yes—
284#398C2314yes—
285#398C2318yes—
286#398C2318yes—
287#398C2318yes—
288#398C2318yes—
289#398C2318yes—
290#398C2318yes—
291#398C2318yes—
292#398C2318yes—
293#396C2314yes—
294#396C2318yes—
295#396C2318yes—
296#396C2318yes—
297#396C2314yes—
298#396C2318yes—
299#396C2318yes—
300#395C2318yes—
301#395C2314yes—
302#395C2318yes—
303#395C2318yes—
304#395C2318yes—
305#395C2318yes—
306#395C2318yes—
307#393C2318yes—
308#393C2314yes—
309#393C2318yes—
310#393C2318yes—
311#393C2318yes—
312#391C2312yes—
313#391C2314yes—
314#391C2312yes—
315#391C2312yes—
316#391C2314yes—
317#391C2312yes—
318#391C2314yes—
319#391C2314yes—
320#391C2312yes—
321#391C2318yes—
322#391C2318yes—
323#391C2318yes—
324#391C2318yes—
325#391C2314yes—
326#391C2318yes—
327#391C2318yes—
328#391C2314yes—
329#391C2318yes—
330#391C2314yes—
331#391C2312yes—
332#391C2314yes—
333#390C2318yes—
334#390C2314yes—
335#390C2312yes—
336#390C2312yes—
337#390C2314yes—
338#390C2318yes—
339#390C2312yes—
340#389C2312yes—
341#389C2312yes—
342#389C2314yes—
343#389C2312yes—
344#389C2314yes—
345#389C2312yes—
346#389C2312yes—
347#389C2312yes—
348#389C2312yes—
349#389C2312yes—
350#389C2314yes—
351#389C2312yes—
352#389C2312yes—
353#389C2312yes—
354#389C2312yes—
355#389C2314yes—
356#389C2314yes—
357#389C2314yes—
358#389C2314yes—
359#389C2314yes—
360#389C2314yes—
361#389C2314yes—
362#389C2314yes—
363#389C2314yes—
364#389C2318yes—
365#389C2314yes—
366#389C2314yes—
367#389C2318yes—
368#389C2318yes—
369#389C2318yes—
370#389C2318yes—
371#389C2314yes—
372#389C2318yes—
373#389C2318yes—
374#389C2312yes—
375#389C2312yes—
376#389C2314yes—
377#389C2314yes—
378#389C2314yes—
379#389C2314yes—
380#389C2312yes—
381#389C2312yes—
382#388C2314yes—
383#388C2314yes—
384#388C2318yes—
385#388C2314yes—
386#388C2318yes—
387#388C2314yes—
388#388C2318yes—
389#388C2318yes—
390#388C2314yes—
391#387C2314yes—
392#387C2314yes—
393#387C2318yes—
394#387C2318yes—
395#387C2318yes—
396#387C2318yes—
397#387C2314yes—
398#387C2318yes—
399#387C2318yes—
400#387C2318yes—
401#387C2318yes—
402#387C2314yes—
403#387C2318yes—
404#387C2314yes—
405#387C2314yes—
406#387C2318yes—
407#387C2318yes—
408#387C2318yes—
409#387C2314yes—
410#387C2314yes—
411#387C2318yes—
412#387C2318yes—
413#387C2314yes—
414#386C2318yes—
415#386C2318yes—
416#386C2314yes—
417#386C2314yes—
418#385C2318yes—
419#385C2318yes—
420#385C2318yes—
421#385C2314yes—
422#385C2318yes—
423#385C2318yes—
424#385C2318yes—
425#385C2314yes—
426#385C2314yes—
427#385C2314yes—
428#385C2314yes—
429#385C2314yes—
430#384C2312yes—
431#384C2311yescharacteristic
432#384C2311yescharacteristic
433#384C2311yescharacteristic
434#384C2312yes—
435#384C2314yes—
436#384C2318yes—
437#384C2314yes—
438#384C2312yes—
439#384C2312yes—
440#384C2312yes—
441#384C2312yes—
442#384C2312yes—
443#382C2312yes—
444#382C2314yes—
445#382C2318yes—
446#382C2314yes—
447#382C2318yes—
448#382C2314yes—
449#382C2314yes—
450#381C2314yes—
451#380C2312yes—
452#380C2314yes—
453#380C2312yes—
454#380C2314yes—
455#380C2312yes—
456#380C2314yes—
457#380C2314yes—
458#380C2314yes—
459#380C2318yes—
460#380C2314yes—
461#380C2314yes—
462#380C2318yes—
463#380C2312yes—
464#380C2314yes—
465#380C2312yes—
466#380C2312yes—
467C4×C4⋊C4C2311yescharacteristic
468C4×C4⋊C4C2312yes—
469C4×C4⋊C4C2314yes—
470C4×C4⋊C4C2314yes—
471C4×C4⋊C4C2311yescharacteristic
472C4×C4⋊C4C2312yes—
473C4×C4⋊C4C2312yes—
474C4×C4⋊C4C2314yes—
475C4×C4⋊C4C2312yes—
476C4×C4⋊C4C2314yes—
477C4×C4⋊C4C2314yes—
478C4×C4⋊C4C2312yes—
479C4×C4⋊C4C2312yes—
480C4×C4⋊C4C2311yescharacteristic
481C4×C4⋊C4C2314yes—
482C4×C4⋊C4C2311yescharacteristic
483C4×C4⋊C4C2314yes—
484C4×C4⋊C4C2312yes—
485C4×C4⋊C4C2318yes—
486C4×C4⋊C4C2318yes—
487C4×C4⋊C4C2314yes—
488C4×C4⋊C4C2318yes—
489C4×C4⋊C4C2314yes—
490C4×C4⋊C4C2318yes—
491C4×C4⋊C4C2318yes—
492C4×C4⋊C4C2311yescharacteristic
493C4×C4⋊C4C2312yes—
494C4×C4⋊C4C2312yes—
495C4×C4⋊C4C2314yes—
496C4×C4⋊C4C2311yescharacteristic
497C4×C4⋊C4C2312yes—
498C4×C4⋊C4C2314yes—
499C4×C4⋊C4C2311yescharacteristic
500C4×C4⋊C4C2314yes—
501C4×C4⋊C4C2311yescharacteristic
502C4×C4⋊C4C2312yes—
503C4×C4⋊C4C2311yescharacteristic
504C4×C4⋊C4C2314yes—
505C4×C4⋊C4C2312yes—
506C4×C4⋊C4C2312yes—
507C4×C22⋊C4C2314yes—
508C4×C22⋊C4C2312yes—
509C4×C22⋊C4C2318yes—
510C4×C22⋊C4C2318yes—
511C4×C22⋊C4C2318yes—
512C4×C22⋊C4C2314yes—
513C4×C22⋊C4C2312yes—
514C4×C22⋊C4C2312yes—
515C4×C22⋊C4C2314yes—
516C4×C22⋊C4C2314yes—
517C4×C22⋊C4C2312yes—
518C4×C22⋊C4C2318yes—
519C4×C22⋊C4C2314yes—
520C4×C22⋊C4C2312yes—
521C4×C22⋊C4C2312yes—
522C2×#95C2314yes—
523C43C2312yes—
524C43C2311yescharacteristic
525C2×#41—44no—
526C2×#41—44no—
527C2×#41C2×Q8116yescomplemented
528C22×Q8—28no—
529C22×Q8—28no—
530C22×Q8—44no—
531C22×Q8C2414yes—
532C22×Q8C2412yes—
533C22×Q8C2412yes—
534C22×Q8C2411yescharacteristic
535C22×Q8C2412yes—
536C22×Q8C2414yes—
537C22×Q8C2418yes—
538C22×D4C2411yescharacteristic
539C22×D4C2411yescharacteristic
540C22×D4C2414yes—
541C23×C4C2412yes—
542C23×C4C2412yes—
543C23×C4C2414yes—
544C23×C4C2412yes—
545C23×C4C2412yes—
546C23×C4C2412yes—
547C23×C4C2412yes—
548C23×C4C2414yes—
549C23×C4C2414yes—
550C23×C4C2414yes—
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—82no—
560C4⋊Q8C2×Q818yescomplemented
561C4⋊Q8#4118yescomplemented
562#125—216no—
563#125—44no—
564#125—84no—
565#123C2×Q8132yescomplemented
566C22⋊Q8—216no—
567C22⋊Q8—28no—
568C22⋊Q8—28no—
569C22⋊Q8—216no—
570C22⋊Q8—216no—
571C22⋊Q8—84no—
572C22⋊Q8—88no—
573C22⋊Q8—88no—
574C22⋊Q8—84no—
575C22⋊Q8C2×Q8116yescomplemented
576#121C2×Q8116yes—
577C4×Q8—216no—
578C4×Q8—24no—
579C4×Q8—216no—
580C4×Q8—24no—
581C4×Q8—24no—
582C4×Q8—28no—
583C4×Q8—28no—
584C4×Q8—48no—
585C4×Q8—44no—
586C4×Q8—48no—
587C4×Q8—44no—
588C4×Q8—44no—
589C4×Q8—48no—
590C4×Q8—44no—
591C4×Q8—48no—
592C4×Q8—48no—
593C4×D4—28no—
594C4×D4—24no—
595C4×D4—24no—
596C4×D4—44no—
597C4×D4—42no—
598C4×D4—42no—
599C4×D4—44no—
600C4×D4—48no—
601C4×D4—48no—
602C4×D4C2×Q818yes—
603C4×D4C2×Q818yescomplemented
604#117—216no—
605#117—48no—
606#117—48no—
607#117—48no—
608#117—44no—
609C2×C4⋊C4—44no—
610C2×C4⋊C4—44no—
611C2×C4⋊C4—48no—
612C2×C4⋊C4C2×Q8116yescomplemented
613C2×C4⋊C4C2411yescharacteristic
614C2×C4⋊C4C2411yescharacteristic
615C2×C4⋊C4C2412yes—
616C2×C4⋊C4C2412yes—
617C2×C4⋊C4C2414yes—
618C2×C4⋊C4C2412yes—
619C2×C4⋊C4C2411yescharacteristic
620C2×C4⋊C4C2412yes—
621C2×C4⋊C4C2412yes—
622C2×C4⋊C4C2414yes—
623C2×C4⋊C4C2414yes—
624C2×C4⋊C4C2414yes—
625C2×C4⋊C4C2411yescharacteristic
626C2×C4⋊C4C2411yescharacteristic
627C2×C4⋊C4C2412yes—
628C2×C4⋊C4C2412yes—
629C2×C4⋊C4C2412yes—
630C2×C4⋊C4C2411yescharacteristic
631C2×C4⋊C4C2412yes—
632C2×C4⋊C4C2418yes—
633C2×C4⋊C4C2418yes—
634C2×C4⋊C4C2414yes—
635C2×C4⋊C4C2411yescharacteristic
636C2×C4⋊C4C2412yes—
637C2×C4⋊C4C2414yes—
638C2×C4⋊C4C2412yes—
639C2×C4⋊C4C2414yes—
640C2×C4⋊C4C2414yes—
641C2×C4⋊C4C2414yes—
642C2×C4⋊C4C2414yes—
643C2×C4⋊C4C2414yes—
644C2×C4⋊C4C2414yes—
645C2×C4⋊C4C2414yes—
646C2×C4⋊C4C2414yes—
647C2×C4⋊C4C2418yes—
648C2×C4⋊C4C2418yes—
649C2×C4⋊C4C2412yes—
650C2×C4⋊C4C2418yes—
651C2×C4⋊C4C2414yes—
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⋊C4C2412yes—
661C2×C4⋊C4C2414yes—
662C2×C4⋊C4C2414yes—
663C2×C4⋊C4C2414yes—
664C2×C4⋊C4C2418yes—
665C2×C4⋊C4C2414yes—
666C2×C4⋊C4C2411yescharacteristic
667C2×C4⋊C4C2412yes—
668C2×C4⋊C4C2414yes—
669C2×C4⋊C4C2411yescharacteristic
670C2×C4⋊C4C2412yes—
671C2×C4⋊C4C2412yes—
672C2×C4⋊C4C2412yes—
673C2×C22⋊C4C2412yes—
674C2×C22⋊C4C2418yes—
675C2×C22⋊C4C2412yes—
676C2×C22⋊C4C2414yes—
677C2×C22⋊C4C2414yes—
678C2×C22⋊C4C2414yes—
679C2×C22⋊C4C2414yes—
680C2×C22⋊C4C2414yes—
681C2×C22⋊C4C2414yes—
682C2×C22⋊C4C2418yes—
683C2×C22⋊C4C2412yes—
684C2×C22⋊C4C2414yes—
685C2×C22⋊C4C2412yes—
686C2×C22⋊C4C2414yes—
687C2×C22⋊C4C2418yes—
688C2×C22⋊C4C2418yes—
689C2×C22⋊C4C2414yes—
690C2×C22⋊C4C2412yes—
691C2×C22⋊C4C2412yes—
692C2×C22⋊C4C2414yes—
693C2×C42—28no—
694C2×C42—28no—
695C2×C42—48no—
696C2×C42—48no—
697C2×C42C2412yes—
698C2×C42C2412yes—
699C2×C42C2418yes—
700C2×C42C2414yes—
701C2×C42C2412yes—
702C2×C42C2414yes—
703C2×C42C2411yescharacteristic
704C2×C42C2412yes—
705C2×C42C2411yescharacteristic
706C2×C42C2414yes—
707C2×C42C2412yes—
708C2×C42C2412yes—
709C2×C42C2412yes—
710C2×C42C2412yes—
711C2×C42C2412yes—
712C2×C42C2411yescharacteristic
713C2×C42C2412yes—
714C2×C42C2412yes—
715C2×C42C2414yes—
716C2×C42C2418yes—
717C2×C42C2414yes—
718C2×C42C2418yes—
719C2×C42C2414yes—
720C2×C42C2414yes—
721C2×C42C2418yes—
722C2×C42C2412yes—
723C2×C42C2411yescharacteristic
724C2×C42C2411yescharacteristic
725C2×C42C2411yescharacteristic
726C2×C42C2411yescharacteristic
727#95C2412yes—
728#95C2414yes—
729#95C2414yes—
730#95C2414yes—
731#95C2414yes—
732#95C2414yes—
733#95C2414yes—
734#95C2412yes—
735#95C2412yes—
736#95C2412yes—
737#95C2418yes—
738#95C2412yes—
739#95C2412yes—
740#95C2414yes—
741#95C2418yes—
742#95C2418yes—
743#95C2418yes—
744#95C2414yes—
745#95C2414yes—
746#95C2418yes—
747#95C2414yes—
748#95C2412yes—
749#95C2414yes—
750#95C2414yes—
751#95C2414yes—
752#95C2412yes—
753#95C2412yes—
754#95C2414yes—
755#95C2418yes—
756#95C2414yes—
757#95C2418yes—
758#95C2418yes—
759#95C2414yes—
760#95C2418yes—
761#95C2414yes—
762#95C2418yes—
763#95C2414yes—
764#95C2414yes—
765#95C2418yes—
766#95C2418yes—
767#95C2414yes—
768#95C2418yes—
769C24C2512yes—
770C24C2512yes—
771#41—432no—
772C2×Q8—22no—
773C2×Q8—28no—
774C2×Q8—28no—
775C2×Q8—24no—
776C2×Q8—24no—
777C2×Q8—22no—
778C2×Q8—24no—
779C2×Q8—24no—
780C2×Q8—28no—
781C2×Q8—24no—
782C2×Q8—44no—
783C2×Q8—42no—
784C2×Q8—42no—
785C2×Q8—44no—
786C2×Q8—44no—
787C2×Q8—48no—
788C2×Q8—48no—
789C2×Q8—48no—
790C2×Q8—432no—
791C2×Q8C22×Q818yes—
792C2×Q8C2×#4118yes—
793C2×Q82−1+414yes—
794C2×D4—22no—
795C2×D4—22no—
796C2×D4—22no—
797C2×D4—22no—
798C2×D4—44no—
799C2×D4—44no—
800C2×D4C22×Q814yes—
801C2×D4C22×Q814yes—
802C2×D4C22×Q8116yes—
803C22×C4—24no—
804C22×C4—24no—
805C22×C4—24no—
806C22×C4—24no—
807C22×C4—24no—
808C22×C4—28no—
809C22×C4—24no—
810C22×C4—24no—
811C22×C4—24no—
812C22×C4—24no—
813C22×C4—28no—
814C22×C4—24no—
815C22×C4—24no—
816C22×C4—24no—
817C22×C4—44no—
818C22×C4—44no—
819C22×C4—44no—
820C22×C4—44no—
821C22×C4—44no—
822C22×C4—44no—
823C22×C4—42no—
824C22×C4—42no—
825C22×C4—44no—
826C22×C4—42no—
827C22×C4—42no—
828C22×C4—44no—
829C22×C4—44no—
830C22×C4C22×Q818yes—
831C22×C4C22×Q818yes—
832C22×C4C22×Q8116yes—
833C22×C4C2512yes—
834C22×C4C2512yes—
835C22×C4C2511yescharacteristic
836C22×C4C2514yes—
837C22×C4C2512yes—
838C22×C4C2512yes—
839C22×C4C2518yes—
840C22×C4C2514yes—
841C22×C4C2512yes—
842C22×C4C2514yes—
843C22×C4C2514yes—
844C22×C4C2512yes—
845C22×C4C2512yes—
846C22×C4C2512yes—
847C22×C4C2511yescharacteristic
848C22×C4C2512yes—
849C22×C4C2514yes—
850C22×C4C2511yescharacteristic
851C22×C4C2514yes—
852C22×C4C2511yescharacteristic
853C22×C4C2512yes—
854C22×C4C2511yescharacteristic
855C22×C4C2511yescharacteristic
856C22×C4C2511yescharacteristic
857C4⋊C4—28no—
858C4⋊C4—22no—
859C4⋊C4—24no—
860C4⋊C4—22no—
861C4⋊C4—216no—
862C4⋊C4—216no—
863C4⋊C4—28no—
864C4⋊C4—28no—
865C4⋊C4—24no—
866C4⋊C4—22no—
867C4⋊C4—28no—
868C4⋊C4—24no—
869C4⋊C4—22no—
870C4⋊C4—28no—
871C4⋊C4—24no—
872C4⋊C4—24no—
873C4⋊C4—24no—
874C4⋊C4—24no—
875C4⋊C4—22no—
876C4⋊C4—24no—
877C4⋊C4—28no—
878C4⋊C4—22no—
879C4⋊C4—24no—
880C4⋊C4—24no—
881C4⋊C4—28no—
882C4⋊C4—22no—
883C4⋊C4—24no—
884C4⋊C4—44no—
885C4⋊C4—44no—
886C4⋊C4—44no—
887C4⋊C4—44no—
888C4⋊C4—44no—
889C4⋊C4—44no—
890C4⋊C4—44no—
891C4⋊C4—42no—
892C4⋊C4—48no—
893C4⋊C4—44no—
894C4⋊C4—48no—
895C4⋊C4—48no—
896C4⋊C4—42no—
897C4⋊C4—44no—
898C4⋊C4—44no—
899C4⋊C4—48no—
900C4⋊C4—48no—
901C4⋊C4—48no—
902C4⋊C4—48no—
903C4⋊C4—44no—
904C4⋊C4—44no—
905C4⋊C4—44no—
906C4⋊C4—42no—
907C4⋊C4—44no—
908C4⋊C4—44no—
909C4⋊C4—48no—
910C4⋊C4C22×Q814yes—
911C4⋊C4C22×Q818yes—
912C4⋊C4C22×Q8116yes—
913C4⋊C4C22×Q814yes—
914C4⋊C4C22×Q818yes—
915C4⋊C4C2×#4118yes—
916C4⋊C4C2×#4118yes—
917C22⋊C4—216no—
918C22⋊C4—28no—
919C22⋊C4—24no—
920C22⋊C4—24no—
921C22⋊C4—28no—
922C22⋊C4—44no—
923C22⋊C4—44no—
924C22⋊C4—48no—
925C22⋊C4—44no—
926C22⋊C4—44no—
927C22⋊C4—44no—
928C22⋊C4—42no—
929C22⋊C4—42no—
930C22⋊C4—44no—
931C22⋊C4—48no—
932C22⋊C4—44no—
933C22⋊C4—48no—
934C22⋊C4C22×Q818yes—
935C22⋊C4C22×Q818yes—
936C22⋊C4C22×Q8116yes—
937C42—24no—
938C42—24no—
939C42—24no—
940C42—216no—
941C42—24no—
942C42—24no—
943C42—24no—
944C42—24no—
945C42—24no—
946C42—28no—
947C42—28no—
948C42—24no—
949C42—22no—
950C42—24no—
951C42—28no—
952C42—22no—
953C42—22no—
954C42—24no—
955C42—44no—
956C42—44no—
957C42—44no—
958C42—44no—
959C42—48no—
960C42—48no—
961C42—48no—
962C42—42no—
963C42—41no—
964C42C22×Q814yes—
965C42C2×#4114yes—
966C42H(5,𝔽2)14yes—
967C23—22no—
968C23—22no—
969C23—22no—
970C23—22no—
971C23—22no—
972C23—22no—
973C23—22no—
974C23—22no—
975C23—22no—
976C23—22no—
977C23—22no—
978C23—22no—
979C23C23×Q814yes—
980C23C23×Q814yes—
981C23C2611yescharacteristic
982Q8—216no—
983Q8—28no—
984Q8—216no—
985Q8—416no—
986Q8—88no—
987Q8—84no—
988Q8—168no—
989D4—28no—
990D4—28no—
991D4—416no—
992C2×C4—22no—
993C2×C4—22no—
994C2×C4—22no—
995C2×C4—24no—
996C2×C4—24no—
997C2×C4—22no—
998C2×C4—21no—
999C2×C4—24no—
1000C2×C4—21no—
1001C2×C4—21no—
1002C2×C4—22no—
1003C2×C4—24no—
1004C2×C4—22no—
1005C2×C4—21no—
1006C2×C4—21no—
1007C2×C4—21no—
1008C2×C4—216no—
1009C2×C4—216no—
1010C2×C4—22no—
1011C2×C4—22no—
1012C2×C4—22no—
1013C2×C4—28no—
1014C2×C4—22no—
1015C2×C4—22no—
1016C2×C4—22no—
1017C2×C4—22no—
1018C2×C4—24no—
1019C2×C4—24no—
1020C2×C4—22no—
1021C2×C4—24no—
1022C2×C4—22no—
1023C2×C4—21no—
1024C2×C4—24no—
1025C2×C4—22no—
1026C2×C4—22no—
1027C2×C4—22no—
1028C2×C4—22no—
1029C2×C4—21no—
1030C2×C4—21no—
1031C2×C4—22no—
1032C2×C4—24no—
1033C2×C4—24no—
1034C2×C4—22no—
1035C2×C4—24no—
1036C2×C4—28no—
1037C2×C4—22no—
1038C2×C4—22no—
1039C2×C4—24no—
1040C2×C4—24no—
1041C2×C4—22no—
1042C2×C4—22no—
1043C2×C4—24no—
1044C2×C4—22no—
1045C2×C4—28no—
1046C2×C4—24no—
1047C2×C4—24no—
1048C2×C4—22no—
1049C2×C4—416no—
1050C2×C4—416no—
1051C2×C4—48no—
1052C2×C4—48no—
1053C2×C4—84no—
1054C2×C4—84no—
1055C2×C4—88no—
1056C2×C4—88no—
1057C2×C4C23×Q812yes—
1058C2×C4C23×Q814yes—
1059C2×C4C23×Q814yes—
1060C2×C4C23×Q818yes—
1061C2×C4C23×Q812yes—
1062C2×C4C23×Q812yes—
1063C2×C4C22×#4112yes—
1064C2×C4C22×#4118yes—
1065C2×C4C22×#4112yes—
1066C2×C4C22×#4112yes—
1067C2×C4C2×H(5,𝔽2)12yes—
1068C2×C4C2×H(5,𝔽2)12yes—
1069C2×C4C2×H(5,𝔽2)12yes—
1070C2×C4C2×2−1+414yes—
1071C2×C4C2×2−1+412yes—
1072C2×C4#58512yes—
1073C2×C4#58512yes—
1074C22—24no—
1075C22—24no—
1076C22—24no—
1077C22—24no—
1078C22—24no—
1079C22—24no—
1080C22—42no—
1081C22—42no—
1082C22—42no—
1083C22—42no—
1084C22—42no—
1085C22—42no—
1086C22—42no—
1087C22—42no—
1088C22C24×Q811yescharacteristic
1089C22C23×#4111yescharacteristic
1090C22C22×H(5,𝔽2)11yescharacteristic
1091C22C22×2−1+411yescharacteristic
1092C22C2×#58511yescharacteristic
1093C22C2×#58511yescharacteristic
1094C22H(7,𝔽2)11yescharacteristic
1095C4—22no—
1096C4—22no—
1097C4—24no—
1098C4—28no—
1099C4—24no—
1100C4—28no—
1101C4—22no—
1102C4—24no—
1103C4—42no—
1104C4—42no—
1105C4—48no—
1106C4—42no—
1107C4—42no—
1108C4—42no—
1109C4—41no—
1110C4—44no—
1111C4—42no—
1112C4—42no—
1113C4—44no—
1114C4—44no—
1115C4—44no—
1116C4Q8×#4114yes—
1117C4#350114yes—
1118C4#352014yes—
1119C2—44no—
1120C2—44no—
1121C2C2×Q8×#4111yescharacteristic
1122C2C2×#350111yescharacteristic
1123C2C2×#352011yescharacteristic
1124C2#6293011yescharacteristic
1125C2Q8×2−1+411yescharacteristic
1126C2#6300611yescharacteristic
1127C2#6303411yescharacteristic
subgroupG/H
center, commutator, Frattini, socle, cosocleC23C26
prime radicalC2×#547C22
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23 ◁ G
LECSG ▷ C23 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #59832C2semidirect
2. #59666C2semidirect
3. #59551C2semidirect
4. #59376C2semidirect
5. #59259C2semidirect
6. #59036C2semidirect
7. #45359C2semidirect
8. #43132C2semidirect
9. #39980C2semidirect
10. #39658C2semidirect
11. #39608C2semidirect
12. #38964C2semidirect
13. #36564C2semidirect
14. #36563C2semidirect
15. Q8×C22⋊Q8C2semidirect
16. #36456C2semidirect
17. #36407C2semidirect
18. #36194C2semidirect
19. #36134C2semidirect
20. #35788C2semidirect
21. #34952C2semidirect
22. #34941C2semidirect
24. #34213C2semidirect
25. C4×D4×Q8C2semidirect
203. #547Q8semidirect
527. C2×#41C2×Q8semidirect
560. C4⋊Q8C2×Q8semidirect
561. C4⋊Q8#41semidirect
565. #123C2×Q8semidirect
575. C22⋊Q8C2×Q8semidirect
603. C4×D4C2×Q8semidirect
612. C2×C4⋊C4C2×Q8semidirect

Maximal subgroups

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

subgroupindex
#598322
#596662
#595512
#593762
#592592
#590362
#453592
#431322
#399802
#396582
#396082
#389642
#365642
#365632
Q8×C22⋊Q82
#364562
#364072
#361942
#361342
#357882
#349522
#349412
#343162
#342132
C4×D4×Q82
C4×#5472