Finite Group Databasebeta

← #7688295

Subgroups — #7688295

Order 512.

5241 conjugacy classes of subgroups.

The subgroup lattice has 1134 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#59871C211yesmaximal, characteristic, complemented
2#59668C212yesmaximal, complemented
3#59569C214yesmaximal, complemented
4#59413C214yesmaximal, complemented
5#59127C212yesmaximal, complemented
6#59036C212yesmaximal, complemented
7#44943C214yesmaximal, complemented
8#44435C218yesmaximal, complemented
9#39982C214yesmaximal, complemented
10#39654C214yesmaximal, complemented
11#39606C212yesmaximal, complemented
12#38965C212yesmaximal, complemented
13#36560C211yesmaximal, characteristic, complemented
14Q8×#121C212yesmaximal, complemented
15#36481C212yesmaximal, complemented
16#36481C212yesmaximal, complemented
17#36407C212yesmaximal, complemented
18#36134C211yesmaximal, characteristic, complemented
19D4×C4⋊Q8C211yesmaximal, characteristic, complemented
20#35747C214yesmaximal, complemented
21#34953C212yesmaximal, complemented
22#34941C211yesmaximal, characteristic, complemented
23#34321C212yesmaximal
24#34216C212yesmaximal, complemented
25C4×#555C211yesmaximal, characteristic
26C4×D4×Q8C211yesmaximal, characteristic, complemented
27C2×#557C2212yes—
28C2×#555C2211yescharacteristic
29C2×D4×Q8C2211yescharacteristic
30C2×D4×Q8C2214yes—
31C2×D4×Q8C2212yes—
32C2×#533C2212yes—
33C22×C4⋊Q8C2212yes—
34C22×C4×Q8C2212yes—
35#2868C2211yescharacteristic
36#2863C2214yes—
37#2859C2212yes—
38#2857C2212yes—
39#2857C2212yes—
40#2857C2214yes—
41#2806C2218yes—
42#2806C2214yes—
43#2788C2218yes—
44#2780C2218yes—
45#2768C2218yes—
46#2768C2218yes—
47#2748C2218yes—
48#2704C2218yes—
49#2704C2218yes—
50#2692C2218yes—
51#2677C2218yes—
52#2666C2218yes—
53#2629C2214yes—
54#2606C2218yes—
55#2606C2218yes—
56#2587C2218yes—
57#2584C2214yes—
58#2584C2214yes—
59#2584C2214yes—
60#2583C2218yes—
61#2582C2214yes—
62#2574C2218yes—
63#2574C2214yes—
64#2568C2212yes—
65#2567C2211yescharacteristic
66#2567C2212yes—
67#2565C2214yes—
68#2563C2211yescharacteristic
69#2556C2218yes—
70#2556C2218yes—
71#2552C2212yes—
72#2552C2212yes—
73#2552C2211yescharacteristic
74#2552C2212yes—
75#2551C2212yes—
76#2551C2214yes—
77#2551C2212yes—
78#2550C2214yes—
79#2550C2218yes—
80#2546C2214yes—
81#2546C2212yes—
82#2546C2212yes—
83#2546C2212yes—
84#2542C2212yes—
85#2538C2214yes—
86#2538C2212yes—
87#2538C2214yes—
88#2538C2211yescharacteristic
89#2522C2218yes—
90#2522C2218yes—
91#2508C2212yes—
92#2507C2214yes—
93#2507C2214yes—
94#2507C2214yes—
95#2507C2214yes—
96#2506C2214yes—
97#2506C2214yes—
98#2502C2214yes—
99#2497C2212yes—
100#2465C2218yes—
101#2454C2218yes—
102#2454C2214yes—
103#2454C2214yes—
104#2454C2212yes—
105#2452C2214yes—
106#2451C2218yes—
107#2449C2218yes—
108#2441C2214yes—
109#2441C2214yes—
110#2441C2214yes—
111#2440C2214yes—
112#2440C2214yes—
113#2440C2214yes—
114#2439C2214yes—
115#2434C2214yes—
116#2434C2214yes—
117#2429C2214yes—
118#2429C2214yes—
119#2429C2214yes—
120#2429C2218yes—
121#2423C2212yes—
122#2423C2214yes—
123#2423C2214yes—
124#2423C2214yes—
125#2417C2218yes—
126#2417C2214yes—
127#2409C2214yes—
128#2399C2218yes—
129#2396C2214yes—
130#2372C2214yes—
131#2370C2214yes—
132#2370C2214yes—
133#2369C2212yes—
134#2369C2211yescharacteristic
135#2369C2214yes—
136#2369C2214yes—
137#2367C2218yes—
138#2365C2212yes—
139#2365C2212yes—
140#2365C2211yescharacteristic
141#2365C2212yes—
142#2365C2212yes—
143#2365C2212yes—
144#2363C2214yes—
145#2363C2212yes—
146#2363C2212yes—
147#2361C2214yes—
148#2360C2214yes—
149#2360C2212yes—
150#2354C2212yes—
151#2354C2211yescharacteristic
152#2354C2211yescharacteristic
153Q8×C4⋊C4C2212yes—
154Q8×C4⋊C4C2211yescharacteristic
155Q8×C4⋊C4C2212yes—
156D4×C4⋊C4C2212yes—
157D4×C4⋊C4C2212yes—
158D4×C4⋊C4C2212yes—
159D4×C4⋊C4C2211yescharacteristic
160#2347C2214yes—
161#2347C2214yes—
162#2346C2212yes—
163#2346C2212yes—
164#2345C2218yes—
165Q8×C22⋊C4C2212yes—
166Q8×C22⋊C4C2214yes—
167Q8×C22⋊C4C2214yes—
168#2337C2218yes—
169#2331C2218yes—
170#2324C2214yes—
171#2316C2214yes—
172C4×C4⋊Q8C2212yes—
173C4×C4⋊Q8C2212yes—
174C4×C4⋊Q8C2214yes—
175C4×C4⋊Q8C2214yes—
176C4×C4⋊Q8C2211yescharacteristic
177C4×C4⋊Q8C2211yescharacteristic
178C4×C4⋊Q8C2211yescharacteristic
179C4×C4⋊Q8C2214yes—
180C4×#125C2212yes—
181C4×#124C2214yes—
182C4×C22⋊Q8C2214yes—
183C4×C22⋊Q8C2212yes—
184C4×C22⋊Q8C2212yes—
185C4×#121C2214yes—
186C4×#121C2212yes—
187C4×#121C2212yes—
188#2296C2214yes—
189#2296C2214yes—
190#2293C2212yes—
191#2285C2212yes—
192#2274C2214yes—
193C42×Q8C2211yescharacteristic
194C42×D4C2212yes—
195C42×D4C2211yescharacteristic
196C42×D4C2211yescharacteristic
197C4×#117C2212yes—
198C4×#117C2212yes—
199C23×Q8C2312yes—
200C23×Q8C2314yes—
201#557—48no—
202#555Q8116yescomplemented
203D4×Q8—28no—
204D4×Q8—48no—
205D4×Q8—416no—
206#533—48no—
207C2×C4⋊Q8—216no—
208C2×C4⋊Q8C2314yes—
209C2×C4⋊Q8C2311yescharacteristic
210C2×C4⋊Q8C2312yes—
211C2×C4⋊Q8C2314yes—
212C2×C4⋊Q8C2314yes—
213C2×C4⋊Q8C2312yes—
214C2×C4⋊Q8C2312yes—
215C2×C4⋊Q8C2314yes—
216C2×C4⋊Q8C2312yes—
217C2×C4⋊Q8C2314yes—
218C2×C4⋊Q8C2318yes—
219C2×C4⋊Q8C2311yescharacteristic
220C2×C4⋊Q8C2311yescharacteristic
221C2×#125C2312yes—
222C2×#125C2314yes—
223C2×#125C2314yes—
224C2×#125C2314yes—
225C2×#125C2318yes—
226C2×#124C2314yes—
227C2×C22⋊Q8C2312yes—
228C2×C22⋊Q8C2314yes—
229C2×C22⋊Q8C2312yes—
230C2×C22⋊Q8C2314yes—
231C2×C22⋊Q8C2318yes—
232C2×C22⋊Q8C2314yes—
233C2×C22⋊Q8C2314yes—
234C2×C22⋊Q8C2314yes—
235C2×C22⋊Q8C2318yes—
236C2×C22⋊Q8C2318yes—
237C2×#121C2312yes—
238C2×#121C2312yes—
239C2×C4×Q8—48no—
240C2×C4×Q8C2312yes—
241C2×C4×Q8C2311yescharacteristic
242C2×C4×Q8C2311yescharacteristic
243C2×C4×Q8C2311yescharacteristic
244C2×C4×Q8C2312yes—
245C2×C4×Q8C2312yes—
246C2×C4×Q8C2314yes—
247C2×C4×Q8C2314yes—
248C2×C4×Q8C2312yes—
249C2×C4×Q8C2314yes—
250C2×C4×Q8C2312yes—
251C2×C4×Q8C2314yes—
252C2×C4×Q8C2314yes—
253C2×C4×Q8C2314yes—
254C2×C4×Q8C2314yes—
255C2×C4×D4C2311yescharacteristic
256C2×C4×D4C2311yescharacteristic
257C2×C4×D4C2312yes—
258C2×C4×D4C2311yescharacteristic
259C2×C4×D4C2312yes—
260C2×C4×D4C2311yescharacteristic
261C2×C4×D4C2314yes—
262C2×C4×D4C2318yes—
263C2×C4×D4C2314yes—
264C2×C4×D4C2311yescharacteristic
265C2×C4×D4C2311yescharacteristic
266C2×#117C2312yes—
267C2×#117C2312yes—
268C2×#117C2314yes—
269C2×#117C2314yes—
270C2×#117C2312yes—
271C2×#117C2312yes—
272C22×C4⋊C4C2314yes—
273C22×C4⋊C4C2314yes—
274C22×C4⋊C4C2314yes—
275C22×C4⋊C4C2312yes—
276C22×C42C2312yes—
277C22×C42C2312yes—
278C22×C42C2314yes—
279#400C2318yes—
280#400C2314yes—
281#399C2314yes—
282#399C2318yes—
283#399C2318yes—
284#399C2318yes—
285#398C2318yes—
286#398C2318yes—
287#398C2318yes—
288#398C2314yes—
289#398C2318yes—
290#398C2318yes—
291#398C2318yes—
292#398C2318yes—
293#398C2318yes—
294#398C2318yes—
295#398C2318yes—
296#398C2318yes—
297#398C2318yes—
298#398C2314yes—
299#398C2318yes—
300#398C2318yes—
301#396C2314yes—
302#396C2318yes—
303#396C2314yes—
304#396C2318yes—
305#396C2318yes—
306#396C2318yes—
307#396C2318yes—
308#396C2318yes—
309#395C2314yes—
310#395C2318yes—
311#395C2318yes—
312#395C2318yes—
313#395C2318yes—
314#395C2318yes—
315#395C2318yes—
316#393C2314yes—
317#393C2318yes—
318#391C2312yes—
319#391C2312yes—
320#391C2312yes—
321#391C2314yes—
322#391C2314yes—
323#391C2314yes—
324#391C2312yes—
325#391C2312yes—
326#391C2314yes—
327#391C2314yes—
328#391C2314yes—
329#391C2314yes—
330#391C2318yes—
331#391C2318yes—
332#391C2318yes—
333#391C2318yes—
334#391C2318yes—
335#391C2314yes—
336#391C2314yes—
337#390C2312yes—
338#390C2314yes—
339#390C2318yes—
340#390C2312yes—
341#390C2312yes—
342#390C2314yes—
343#390C2312yes—
344#389C2312yes—
345#389C2312yes—
346#389C2312yes—
347#389C2318yes—
348#389C2318yes—
349#389C2312yes—
350#389C2318yes—
351#389C2318yes—
352#389C2318yes—
353#389C2312yes—
354#389C2312yes—
355#389C2314yes—
356#389C2318yes—
357#389C2312yes—
358#389C2314yes—
359#389C2312yes—
360#389C2312yes—
361#389C2314yes—
362#389C2312yes—
363#389C2312yes—
364#389C2314yes—
365#389C2314yes—
366#389C2314yes—
367#389C2314yes—
368#389C2314yes—
369#389C2314yes—
370#389C2318yes—
371#389C2314yes—
372#389C2314yes—
373#389C2314yes—
374#389C2314yes—
375#389C2318yes—
376#389C2318yes—
377#389C2318yes—
378#389C2314yes—
379#389C2314yes—
380#389C2318yes—
381#389C2314yes—
382#389C2314yes—
383#389C2312yes—
384#389C2312yes—
385#389C2312yes—
386#389C2314yes—
387#389C2314yes—
388#389C2314yes—
389#389C2312yes—
390#389C2312yes—
391#389C2318yes—
392#388C2314yes—
393#388C2314yes—
394#388C2318yes—
395#388C2314yes—
396#388C2318yes—
397#388C2314yes—
398#388C2318yes—
399#388C2318yes—
400#388C2314yes—
401#388C2314yes—
402#388C2314yes—
403#388C2318yes—
404#388C2314yes—
405#387C2314yes—
406#387C2314yes—
407#387C2318yes—
408#387C2318yes—
409#387C2318yes—
410#387C2314yes—
411#387C2318yes—
412#387C2314yes—
413#387C2318yes—
414#387C2318yes—
415#387C2314yes—
416#387C2314yes—
417#387C2318yes—
418#387C2318yes—
419#387C2318yes—
420#386C2318yes—
421#386C2318yes—
422#386C2314yes—
423#386C2314yes—
424#385C2318yes—
425#385C2314yes—
426#385C2318yes—
427#385C2318yes—
428#385C2318yes—
429#385C2318yes—
430#385C2318yes—
431#385C2318yes—
432#385C2314yes—
433#385C2314yes—
434#385C2314yes—
435#384C2312yes—
436#384C2312yes—
437#384C2314yes—
438#384C2311yescharacteristic
439#384C2311yescharacteristic
440#384C2311yescharacteristic
441#384C2312yes—
442#384C2312yes—
443#384C2312yes—
444#384C2314yes—
445#384C2312yes—
446#384C2312yes—
447#384C2314yes—
448#383C2318yes—
449#382C2312yes—
450#382C2314yes—
451#382C2314yes—
452#382C2314yes—
453#380C2312yes—
454#380C2312yes—
455#380C2318yes—
456#380C2318yes—
457#380C2314yes—
458#380C2318yes—
459#380C2314yes—
460#380C2312yes—
461#380C2312yes—
462#380C2314yes—
463#380C2312yes—
464#380C2314yes—
465#380C2314yes—
466#380C2314yes—
467#380C2312yes—
468C4×C4⋊C4C2311yescharacteristic
469C4×C4⋊C4C2312yes—
470C4×C4⋊C4C2314yes—
471C4×C4⋊C4C2314yes—
472C4×C4⋊C4C2312yes—
473C4×C4⋊C4C2311yescharacteristic
474C4×C4⋊C4C2312yes—
475C4×C4⋊C4C2318yes—
476C4×C4⋊C4C2314yes—
477C4×C4⋊C4C2318yes—
478C4×C4⋊C4C2318yes—
479C4×C4⋊C4C2318yes—
480C4×C4⋊C4C2318yes—
481C4×C4⋊C4C2314yes—
482C4×C4⋊C4C2312yes—
483C4×C4⋊C4C2312yes—
484C4×C4⋊C4C2312yes—
485C4×C4⋊C4C2318yes—
486C4×C4⋊C4C2314yes—
487C4×C4⋊C4C2311yescharacteristic
488C4×C4⋊C4C2312yes—
489C4×C4⋊C4C2311yescharacteristic
490C4×C4⋊C4C2311yescharacteristic
491C4×C4⋊C4C2312yes—
492C4×C4⋊C4C2312yes—
493C4×C4⋊C4C2314yes—
494C4×C4⋊C4C2311yescharacteristic
495C4×C4⋊C4C2311yescharacteristic
496C4×C4⋊C4C2312yes—
497C4×C4⋊C4C2312yes—
498C4×C4⋊C4C2314yes—
499C4×C4⋊C4C2314yes—
500C4×C4⋊C4C2311yescharacteristic
501C4×C4⋊C4C2312yes—
502C4×C4⋊C4C2311yescharacteristic
503C4×C4⋊C4C2312yes—
504C4×C4⋊C4C2312yes—
505C4×C4⋊C4C2312yes—
506C4×C22⋊C4C2314yes—
507C4×C22⋊C4C2312yes—
508C4×C22⋊C4C2314yes—
509C4×C22⋊C4C2318yes—
510C4×C22⋊C4C2314yes—
511C4×C22⋊C4C2318yes—
512C4×C22⋊C4C2314yes—
513C4×C22⋊C4C2312yes—
514C4×C22⋊C4C2314yes—
515C4×C22⋊C4C2312yes—
516C4×C22⋊C4C2312yes—
517C4×C22⋊C4C2314yes—
518C4×C22⋊C4C2314yes—
519C4×C22⋊C4C2312yes—
520C4×C22⋊C4C2314yes—
521C4×C22⋊C4C2312yes—
522#376C2314yes—
523#376C2314yes—
524C43C2312yes—
525C43C2314yes—
526C43C2311yescharacteristic
527C22×Q8—28no—
528C22×Q8—28no—
529C22×Q8—216no—
530C22×Q8—44no—
531C22×Q8—48no—
532C22×Q8—48no—
533C22×Q8C2414yes—
534C22×Q8C2414yes—
535C22×Q8C2412yes—
536C22×Q8C2411yescharacteristic
537C22×Q8C2412yes—
538C22×Q8C2418yes—
539C22×Q8C2412yes—
540C22×D4C2411yescharacteristic
541C22×D4C2411yescharacteristic
542C22×D4C2414yes—
543C23×C4C2412yes—
544C23×C4C2412yes—
545C23×C4C2412yes—
546C23×C4C2414yes—
547C23×C4C2412yes—
548C23×C4C2412yes—
549C23×C4C2418yes—
550C23×C4C2412yes—
551C23×C4C2414yes—
552C4⋊Q8—216no—
553C4⋊Q8—216no—
554C4⋊Q8—216no—
555C4⋊Q8—216no—
556C4⋊Q8—28no—
557C4⋊Q8—28no—
558C4⋊Q8—24no—
559C4⋊Q8—28no—
560C4⋊Q8—48no—
561C4⋊Q8—44no—
562C4⋊Q8—416no—
563C4⋊Q8C2×Q818yescomplemented
564C4⋊Q8#4118yes—
565#125—28no—
566#125—48no—
567#125—48no—
568#125—48no—
569#125—416no—
570#124C2×Q8132yescomplemented
571C22⋊Q8—28no—
572C22⋊Q8—28no—
573C22⋊Q8—216no—
574C22⋊Q8—416no—
575C22⋊Q8—416no—
576C22⋊Q8—416no—
577C22⋊Q8—48no—
578C22⋊Q8—48no—
579C22⋊Q8—48no—
580C22⋊Q8—48no—
581#121C2×Q8116yescomplemented
582#121C2×Q8116yescomplemented
583C4×Q8—24no—
584C4×Q8—24no—
585C4×Q8—24no—
586C4×Q8—28no—
587C4×Q8—48no—
588C4×Q8—44no—
589C4×Q8—44no—
590C4×Q8—48no—
591C4×Q8—48no—
592C4×Q8—44no—
593C4×Q8—44no—
594C4×Q8—48no—
595C4×Q8—48no—
596C4×Q8—48no—
597C4×Q8—48no—
598C4×D4—28no—
599C4×D4—24no—
600C4×D4—24no—
601C4×D4—24no—
602C4×D4—44no—
603C4×D4—42no—
604C4×D4—48no—
605C4×D4—48no—
606C4×D4—416no—
607C4×D4C2×Q818yescomplemented
608C4×D4C2×Q818yescomplemented
609#117—28no—
610#117—48no—
611#117—44no—
612#117—48no—
613#117C2×Q8116yescomplemented
614#117C2×Q8116yescomplemented
615C2×C4⋊C4—216no—
616C2×C4⋊C4—216no—
617C2×C4⋊C4—44no—
618C2×C4⋊C4—48no—
619C2×C4⋊C4C2411yescharacteristic
620C2×C4⋊C4C2412yes—
621C2×C4⋊C4C2412yes—
622C2×C4⋊C4C2414yes—
623C2×C4⋊C4C2414yes—
624C2×C4⋊C4C2418yes—
625C2×C4⋊C4C2418yes—
626C2×C4⋊C4C2414yes—
627C2×C4⋊C4C2411yescharacteristic
628C2×C4⋊C4C2412yes—
629C2×C4⋊C4C2414yes—
630C2×C4⋊C4C2412yes—
631C2×C4⋊C4C2412yes—
632C2×C4⋊C4C2418yes—
633C2×C4⋊C4C2412yes—
634C2×C4⋊C4C2411yescharacteristic
635C2×C4⋊C4C2411yescharacteristic
636C2×C4⋊C4C2411yescharacteristic
637C2×C4⋊C4C2412yes—
638C2×C4⋊C4C2412yes—
639C2×C4⋊C4C2414yes—
640C2×C4⋊C4C2411yescharacteristic
641C2×C4⋊C4C2412yes—
642C2×C4⋊C4C2412yes—
643C2×C4⋊C4C2414yes—
644C2×C4⋊C4C2418yes—
645C2×C4⋊C4C2414yes—
646C2×C4⋊C4C2412yes—
647C2×C4⋊C4C2414yes—
648C2×C4⋊C4C2414yes—
649C2×C4⋊C4C2414yes—
650C2×C4⋊C4C2414yes—
651C2×C4⋊C4C2414yes—
652C2×C4⋊C4C2414yes—
653C2×C4⋊C4C2414yes—
654C2×C4⋊C4C2414yes—
655C2×C4⋊C4C2418yes—
656C2×C4⋊C4C2418yes—
657C2×C4⋊C4C2418yes—
658C2×C4⋊C4C2418yes—
659C2×C4⋊C4C2412yes—
660C2×C4⋊C4C2414yes—
661C2×C4⋊C4C2414yes—
662C2×C4⋊C4C2412yes—
663C2×C4⋊C4C2414yes—
664C2×C4⋊C4C2418yes—
665C2×C4⋊C4C2418yes—
666C2×C4⋊C4C2414yes—
667C2×C4⋊C4C2418yes—
668C2×C4⋊C4C2418yes—
669C2×C4⋊C4C2414yes—
670C2×C4⋊C4C2412yes—
671C2×C4⋊C4C2414yes—
672C2×C4⋊C4C2418yes—
673C2×C4⋊C4C2411yescharacteristic
674C2×C4⋊C4C2411yescharacteristic
675C2×C4⋊C4C2412yes—
676C2×C4⋊C4C2412yes—
677C2×C4⋊C4C2412yes—
678C2×C4⋊C4C2412yes—
679C2×C4⋊C4C2411yescharacteristic
680C2×C22⋊C4C2414yes—
681C2×C22⋊C4C2414yes—
682C2×C22⋊C4C2412yes—
683C2×C22⋊C4C2414yes—
684C2×C22⋊C4C2412yes—
685C2×C22⋊C4C2412yes—
686C2×C22⋊C4C2418yes—
687C2×C22⋊C4C2414yes—
688C2×C22⋊C4C2414yes—
689C2×C22⋊C4C2414yes—
690C2×C22⋊C4C2414yes—
691C2×C22⋊C4C2418yes—
692C2×C22⋊C4C2418yes—
693C2×C22⋊C4C2414yes—
694C2×C22⋊C4C2412yes—
695C2×C22⋊C4C2414yes—
696C2×C22⋊C4C2414yes—
697C2×C22⋊C4C2414yes—
698C2×C22⋊C4C2414yes—
699C2×C22⋊C4C2412yes—
700C2×C22⋊C4C2412yes—
701C2×C42—28no—
702C2×C42—28no—
703C2×C42—48no—
704C2×C42C2412yes—
705C2×C42C2414yes—
706C2×C42C2414yes—
707C2×C42C2414yes—
708C2×C42C2414yes—
709C2×C42C2411yescharacteristic
710C2×C42C2412yes—
711C2×C42C2411yescharacteristic
712C2×C42C2412yes—
713C2×C42C2412yes—
714C2×C42C2412yes—
715C2×C42C2411yescharacteristic
716C2×C42C2412yes—
717C2×C42C2412yes—
718C2×C42C2412yes—
719C2×C42C2412yes—
720C2×C42C2412yes—
721C2×C42C2412yes—
722C2×C42C2418yes—
723C2×C42C2414yes—
724C2×C42C2418yes—
725C2×C42C2418yes—
726C2×C42C2414yes—
727C2×C42C2414yes—
728C2×C42C2411yescharacteristic
729C2×C42C2414yes—
730C2×C42C2412yes—
731C2×C42C2414yes—
732C2×C42C2411yescharacteristic
733C2×C42C2411yescharacteristic
734C2×C42C2411yescharacteristic
735#95C2412yes—
736#95C2412yes—
737#95C2414yes—
738#95C2414yes—
739#95C2414yes—
740#95C2414yes—
741#95C2414yes—
742#95C2414yes—
743#95C2414yes—
744#95C2412yes—
745#95C2412yes—
746#95C2414yes—
747#95C2414yes—
748#95C2412yes—
749#95C2412yes—
750#95C2418yes—
751#95C2414yes—
752#95C2418yes—
753#95C2418yes—
754#95C2414yes—
755#95C2414yes—
756#95C2412yes—
757#95C2414yes—
758#95C2412yes—
759#95C2412yes—
760#95C2414yes—
761#95C2418yes—
762#95C2418yes—
763#95C2414yes—
764#95C2414yes—
765#95C2414yes—
766#95C2418yes—
767#95C2414yes—
768#95C2418yes—
769#95C2418yes—
770#95C2414yes—
771#95C2418yes—
772#95C2418yes—
773#95C2414yes—
774#95C2418yes—
775C24C2512yes—
776C24C2512yes—
777C2×Q8—22no—
778C2×Q8—28no—
779C2×Q8—28no—
780C2×Q8—216no—
781C2×Q8—22no—
782C2×Q8—24no—
783C2×Q8—24no—
784C2×Q8—24no—
785C2×Q8—28no—
786C2×Q8—28no—
787C2×Q8—28no—
788C2×Q8—42no—
789C2×Q8—44no—
790C2×Q8—42no—
791C2×Q8—42no—
792C2×Q8—42no—
793C2×Q8—48no—
794C2×Q8—48no—
795C2×Q8—432no—
796C2×Q8—832no—
797C2×Q8C22×Q818yes—
798C2×Q8C2×#4118yes—
799C2×Q8H(5,𝔽2)14yes—
800C2×D4—22no—
801C2×D4—22no—
802C2×D4—22no—
803C2×D4—22no—
804C2×D4—44no—
805C2×D4—44no—
806C2×D4C22×Q814yes—
807C2×D4C22×Q814yes—
808C2×D4C22×Q8116yes—
809C22×C4—24no—
810C22×C4—24no—
811C22×C4—24no—
812C22×C4—24no—
813C22×C4—24no—
814C22×C4—24no—
815C22×C4—28no—
816C22×C4—24no—
817C22×C4—24no—
818C22×C4—24no—
819C22×C4—24no—
820C22×C4—28no—
821C22×C4—24no—
822C22×C4—24no—
823C22×C4—216no—
824C22×C4—24no—
825C22×C4—44no—
826C22×C4—42no—
827C22×C4—44no—
828C22×C4—48no—
829C22×C4—48no—
830C22×C4—42no—
831C22×C4—44no—
832C22×C4—42no—
833C22×C4—44no—
834C22×C4C22×Q818yes—
835C22×C4C22×Q818yes—
836C22×C4C2512yes—
837C22×C4C2512yes—
838C22×C4C2512yes—
839C22×C4C2512yes—
840C22×C4C2512yes—
841C22×C4C2514yes—
842C22×C4C2511yescharacteristic
843C22×C4C2514yes—
844C22×C4C2514yes—
845C22×C4C2514yes—
846C22×C4C2512yes—
847C22×C4C2518yes—
848C22×C4C2512yes—
849C22×C4C2511yescharacteristic
850C22×C4C2514yes—
851C22×C4C2512yes—
852C22×C4C2511yescharacteristic
853C22×C4C2514yes—
854C22×C4C2511yescharacteristic
855C22×C4C2512yes—
856C22×C4C2512yes—
857C22×C4C2511yescharacteristic
858C22×C4C2511yescharacteristic
859C22×C4C2511yescharacteristic
860C4⋊C4—216no—
861C4⋊C4—216no—
862C4⋊C4—28no—
863C4⋊C4—28no—
864C4⋊C4—22no—
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—28no—
874C4⋊C4—22no—
875C4⋊C4—216no—
876C4⋊C4—22no—
877C4⋊C4—24no—
878C4⋊C4—24no—
879C4⋊C4—24no—
880C4⋊C4—28no—
881C4⋊C4—28no—
882C4⋊C4—216no—
883C4⋊C4—24no—
884C4⋊C4—28no—
885C4⋊C4—28no—
886C4⋊C4—24no—
887C4⋊C4—22no—
888C4⋊C4—24no—
889C4⋊C4—24no—
890C4⋊C4—44no—
891C4⋊C4—44no—
892C4⋊C4—44no—
893C4⋊C4—44no—
894C4⋊C4—42no—
895C4⋊C4—48no—
896C4⋊C4—44no—
897C4⋊C4—44no—
898C4⋊C4—44no—
899C4⋊C4—44no—
900C4⋊C4—42no—
901C4⋊C4—44no—
902C4⋊C4—48no—
903C4⋊C4—48no—
904C4⋊C4—48no—
905C4⋊C4—42no—
906C4⋊C4—44no—
907C4⋊C4—48no—
908C4⋊C4—44no—
909C4⋊C4—48no—
910C4⋊C4—48no—
911C4⋊C4—48no—
912C4⋊C4—48no—
913C4⋊C4—44no—
914C4⋊C4C22×Q814yes—
915C4⋊C4C22×Q814yes—
916C4⋊C4C22×Q818yes—
917C4⋊C4C22×Q818yes—
918C4⋊C4C2×#4118yes—
919C4⋊C4C2×#4118yes—
920C4⋊C42−1+414yes—
921C22⋊C4—28no—
922C22⋊C4—24no—
923C22⋊C4—24no—
924C22⋊C4—28no—
925C22⋊C4—28no—
926C22⋊C4—24no—
927C22⋊C4—44no—
928C22⋊C4—44no—
929C22⋊C4—44no—
930C22⋊C4—44no—
931C22⋊C4—48no—
932C22⋊C4—44no—
933C22⋊C4—42no—
934C22⋊C4—48no—
935C22⋊C4—44no—
936C22⋊C4—44no—
937C22⋊C4—48no—
938C22⋊C4C22×Q8116yes—
939C22⋊C4C22×Q8116yes—
940C22⋊C4C22×Q818yes—
941C22⋊C4C22×Q818yes—
942C42—24no—
943C42—24no—
944C42—24no—
945C42—24no—
946C42—24no—
947C42—24no—
948C42—24no—
949C42—24no—
950C42—28no—
951C42—28no—
952C42—24no—
953C42—22no—
954C42—28no—
955C42—22no—
956C42—24no—
957C42—24no—
958C42—28no—
959C42—22no—
960C42—44no—
961C42—44no—
962C42—41no—
963C42—42no—
964C42—44no—
965C42—44no—
966C42—48no—
967C42—48no—
968C42—48no—
969C42C22×Q8116yes—
970C42C22×Q814yes—
971C42C2×#4114yes—
972C42H(5,𝔽2)14yes—
973C23—22no—
974C23—22no—
975C23—22no—
976C23—22no—
977C23—22no—
978C23—22no—
979C23—22no—
980C23—22no—
981C23—22no—
982C23—22no—
983C23—22no—
984C23—22no—
985C23C23×Q814yes—
986C23C23×Q814yes—
987C23C2611yescharacteristic
988Q8—28no—
989Q8—216no—
990Q8—48no—
991Q8—416no—
992Q8—48no—
993Q8—416no—
994Q8—816no—
995D4—28no—
996D4—28no—
997D4—416no—
998C2×C4—22no—
999C2×C4—22no—
1000C2×C4—22no—
1001C2×C4—21no—
1002C2×C4—22no—
1003C2×C4—24no—
1004C2×C4—22no—
1005C2×C4—24no—
1006C2×C4—24no—
1007C2×C4—22no—
1008C2×C4—21no—
1009C2×C4—21no—
1010C2×C4—22no—
1011C2×C4—21no—
1012C2×C4—22no—
1013C2×C4—21no—
1014C2×C4—24no—
1015C2×C4—21no—
1016C2×C4—216no—
1017C2×C4—216no—
1018C2×C4—22no—
1019C2×C4—22no—
1020C2×C4—22no—
1021C2×C4—28no—
1022C2×C4—22no—
1023C2×C4—22no—
1024C2×C4—22no—
1025C2×C4—22no—
1026C2×C4—24no—
1027C2×C4—24no—
1028C2×C4—21no—
1029C2×C4—24no—
1030C2×C4—24no—
1031C2×C4—28no—
1032C2×C4—28no—
1033C2×C4—22no—
1034C2×C4—22no—
1035C2×C4—22no—
1036C2×C4—21no—
1037C2×C4—24no—
1038C2×C4—22no—
1039C2×C4—22no—
1040C2×C4—24no—
1041C2×C4—22no—
1042C2×C4—21no—
1043C2×C4—22no—
1044C2×C4—24no—
1045C2×C4—24no—
1046C2×C4—22no—
1047C2×C4—24no—
1048C2×C4—24no—
1049C2×C4—22no—
1050C2×C4—22no—
1051C2×C4—22no—
1052C2×C4—24no—
1053C2×C4—24no—
1054C2×C4—48no—
1055C2×C4—416no—
1056C2×C4—48no—
1057C2×C4—48no—
1058C2×C4—84no—
1059C2×C4—816no—
1060C2×C4—88no—
1061C2×C4C23×Q814yes—
1062C2×C4C23×Q814yes—
1063C2×C4C23×Q812yes—
1064C2×C4C23×Q818yes—
1065C2×C4C23×Q812yes—
1066C2×C4C23×Q812yes—
1067C2×C4C22×#4112yes—
1068C2×C4C22×#4118yes—
1069C2×C4C22×#4112yes—
1070C2×C4C22×#4112yes—
1071C2×C4C2×H(5,𝔽2)12yes—
1072C2×C4C2×H(5,𝔽2)14yes—
1073C2×C4C2×H(5,𝔽2)12yes—
1074C2×C4C2×H(5,𝔽2)12yes—
1075C2×C4C2×H(5,𝔽2)12yes—
1076C2×C4C2×2−1+414yes—
1077C2×C4C2×2−1+412yes—
1078C2×C4#58512yes—
1079C22—24no—
1080C22—24no—
1081C22—24no—
1082C22—24no—
1083C22—24no—
1084C22—24no—
1085C22—42no—
1086C22—42no—
1087C22—42no—
1088C22—42no—
1089C22—42no—
1090C22—42no—
1091C22—42no—
1092C22—42no—
1093C22C24×Q811yescharacteristic
1094C22C23×#4111yescharacteristic
1095C22C22×H(5,𝔽2)11yescharacteristic
1096C22C22×H(5,𝔽2)11yescharacteristic
1097C22C22×2−1+411yescharacteristic
1098C22C2×#58511yescharacteristic
1099C222−1+611yescharacteristic
1100C4—28no—
1101C4—22no—
1102C4—22no—
1103C4—24no—
1104C4—24no—
1105C4—28no—
1106C4—24no—
1107C4—22no—
1108C4—24no—
1109C4—42no—
1110C4—42no—
1111C4—42no—
1112C4—48no—
1113C4—42no—
1114C4—44no—
1115C4—41no—
1116C4—44no—
1117C4—42no—
1118C4—44no—
1119C4—42no—
1120C4—44no—
1121C4Q8×#4114yes—
1122C4#350314yes—
1123C4#351914yes—
1124C2—44no—
1125C2—44no—
1126C2C2×Q8×#4111yescharacteristic
1127C2C2×#351911yescharacteristic
1128C2C2×#350311yescharacteristic
1129C2#6292511yescharacteristic
1130C2Q8×H(5,𝔽2)11yescharacteristic
1131C2#6299811yescharacteristic
1132C2#6303911yescharacteristic
subgroupG/H
center, commutator, Frattini, socle, cosocleC23C26
prime radicalC2×#555C22
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. #59668C2semidirect
3. #59569C2semidirect
4. #59413C2semidirect
5. #59127C2semidirect
6. #59036C2semidirect
7. #44943C2semidirect
8. #44435C2semidirect
9. #39982C2semidirect
10. #39654C2semidirect
11. #39606C2semidirect
12. #38965C2semidirect
13. #36560C2semidirect
14. Q8×#121C2semidirect
15. #36481C2semidirect
16. #36481C2semidirect
17. #36407C2semidirect
18. #36134C2semidirect
19. D4×C4⋊Q8C2semidirect
20. #35747C2semidirect
21. #34953C2semidirect
22. #34941C2semidirect
24. #34216C2semidirect
26. C4×D4×Q8C2semidirect
202. #555Q8semidirect
563. C4⋊Q8C2×Q8semidirect
570. #124C2×Q8semidirect
581. #121C2×Q8semidirect
582. #121C2×Q8semidirect
607. C4×D4C2×Q8semidirect
608. C4×D4C2×Q8semidirect
613. #117C2×Q8semidirect
614. #117C2×Q8semidirect

Maximal subgroups

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

subgroupindex
#598712
#596682
#595692
#594132
#591272
#590362
#449432
#444352
#399822
#396542
#396062
#389652
#365602
Q8×#1212
#364812
#364072
#361342
D4×C4⋊Q82
#357472
#349532
#349412
#343212
#342162
C4×#5552
C4×D4×Q82