Finite Group Databasebeta

← #7688573

Subgroups — #7688573

Order 512.

4987 conjugacy classes of subgroups.

The subgroup lattice has 1114 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#59924C211yesmaximal, characteristic, complemented
2#59673C212yesmaximal, complemented
3#59429C214yesmaximal, complemented
4#59230C212yesmaximal, complemented
5#59136C212yesmaximal, complemented
6#59036C214yesmaximal, complemented
7#45360C214yesmaximal, complemented
8#44233C218yesmaximal, complemented
9#39987C214yesmaximal, complemented
10#39652C214yesmaximal, complemented
11#39608C212yesmaximal, complemented
12#38967C212yesmaximal, complemented
13#36563C211yesmaximal, characteristic, complemented
14#36551C212yesmaximal, complemented
15#36480C212yesmaximal, complemented
16#36480C212yesmaximal, complemented
17#36194C211yesmaximal, characteristic, complemented
18#36132C212yesmaximal, complemented
19D4×C4⋊Q8C211yesmaximal, characteristic, complemented
20#35815C214yesmaximal, complemented
21#34941C211yesmaximal, characteristic, complemented
22#34938C212yesmaximal, complemented
23#34321C212yesmaximal
24#34216C212yesmaximal, complemented
25C4×#554C211yesmaximal, characteristic, complemented
26C4×#555C211yesmaximal, characteristic
27C2×#555C2211yescharacteristic
28C2×#554C2211yescharacteristic
29C2×D4×Q8C2212yes—
30C2×#533C2214yes—
31C22×C4⋊Q8C2212yes—
32#2868C2211yescharacteristic
33#2863C2214yes—
34#2859C2212yes—
35#2857C2212yes—
36#2857C2212yes—
37#2851C2214yes—
38#2811C2214yes—
39#2799C2218yes—
40#2790C2218yes—
41#2788C2218yes—
42#2788C2218yes—
43#2784C2218yes—
44#2763C2218yes—
45#2742C2218yes—
46#2729C2218yes—
47#2692C2218yes—
48#2692C2218yes—
49#2666C2218yes—
50#2628C2214yes—
51#2605C2218yes—
52#2605C2218yes—
53#2589C2218yes—
54#2582C2212yes—
55#2581C2218yes—
56#2574C2218yes—
57#2574C2214yes—
58#2571C2212yes—
59#2570C2218yes—
60#2567C2212yes—
61#2567C2214yes—
62#2567C2214yes—
63#2567C2214yes—
64#2567C2211yescharacteristic
65#2563C2212yes—
66#2563C2214yes—
67#2563C2214yes—
68#2563C2211yescharacteristic
69#2552C2211yescharacteristic
70#2552C2212yes—
71#2551C2212yes—
72#2551C2212yes—
73#2551C2212yes—
74#2551C2212yes—
75#2551C2212yes—
76#2550C2214yes—
77#2550C2214yes—
78#2550C2214yes—
79#2550C2214yes—
80#2549C2218yes—
81#2546C2212yes—
82#2538C2218yes—
83#2538C2212yes—
84#2538C2211yescharacteristic
85#2509C2214yes—
86#2509C2214yes—
87#2509C2214yes—
88#2508C2214yes—
89#2508C2214yes—
90#2508C2212yes—
91#2507C2214yes—
92#2497C2212yes—
93#2497C2214yes—
94#2497C2214yes—
95#2497C2214yes—
96#2492C2214yes—
97#2492C2214yes—
98#2492C2214yes—
99#2487C2214yes—
100#2465C2218yes—
101#2465C2218yes—
102#2465C2218yes—
103#2465C2218yes—
104#2465C2218yes—
105#2454C2214yes—
106#2454C2212yes—
107#2452C2214yes—
108#2452C2214yes—
109#2451C2214yes—
110#2450C2218yes—
111#2442C2214yes—
112#2440C2214yes—
113#2440C2214yes—
114#2440C2214yes—
115#2440C2214yes—
116#2439C2214yes—
117#2439C2214yes—
118#2439C2214yes—
119#2439C2214yes—
120#2434C2214yes—
121#2423C2212yes—
122#2423C2218yes—
123#2417C2214yes—
124#2409C2218yes—
125#2399C2218yes—
126#2396C2214yes—
127#2372C2214yes—
128#2370C2212yes—
129#2369C2212yes—
130#2369C2212yes—
131#2369C2212yes—
132#2369C2211yescharacteristic
133#2369C2212yes—
134#2369C2211yescharacteristic
135#2369C2212yes—
136#2368C2214yes—
137#2367C2218yes—
138#2365C2214yes—
139#2365C2214yes—
140#2365C2214yes—
141#2365C2214yes—
142#2363C2214yes—
143#2363C2212yes—
144#2363C2212yes—
145#2361C2214yes—
146#2360C2212yes—
147#2355C2212yes—
148#2355C2212yes—
149#2355C2211yescharacteristic
150#2354C2212yes—
151#2354C2211yescharacteristic
152#2354C2211yescharacteristic
153Q8×C4⋊C4C2212yes—
154#2349C2212yes—
155D4×C4⋊C4C2214yes—
156D4×C4⋊C4C2212yes—
157D4×C4⋊C4C2212yes—
158D4×C4⋊C4C2211yescharacteristic
159#2347C2214yes—
160#2347C2214yes—
161#2346C2212yes—
162#2346C2212yes—
163#2345C2212yes—
164#2345C2214yes—
165#2345C2214yes—
166Q8×C22⋊C4C2218yes—
167#2337C2218yes—
168#2331C2218yes—
169#2324C2214yes—
170#2316C2214yes—
171C4×C4⋊Q8C2212yes—
172C4×C4⋊Q8C2211yescharacteristic
173C4×C4⋊Q8C2211yescharacteristic
174C4×C4⋊Q8C2211yescharacteristic
175C4×C4⋊Q8C2214yes—
176C4×C4⋊Q8C2214yes—
177C4×C4⋊Q8C2214yes—
178C4×#125C2212yes—
179C4×#125C2212yes—
180C4×#124C2214yes—
181C4×C22⋊Q8C2212yes—
182C4×C22⋊Q8C2214yes—
183C4×C22⋊Q8C2212yes—
184C4×#121C2212yes—
185C4×#121C2214yes—
186C4×#121C2212yes—
187#2296C2214yes—
188#2293C2212yes—
189#2285C2212yes—
190#2285C2212yes—
191#2274C2214yes—
192C42×Q8C2211yescharacteristic
193C42×D4C2212yes—
194C42×D4C2211yescharacteristic
195C42×D4C2211yescharacteristic
196C4×#117C2212yes—
197C4×#117C2212yes—
198C2×C4×C4⋊C4C2212yes—
199C23×Q8C2314yes—
200#555Q8116yescomplemented
201#554—28no—
202D4×Q8—48no—
203#533—416no—
204C2×C4⋊Q8—216no—
205C2×C4⋊Q8C2314yes—
206C2×C4⋊Q8C2311yescharacteristic
207C2×C4⋊Q8C2312yes—
208C2×C4⋊Q8C2314yes—
209C2×C4⋊Q8C2314yes—
210C2×C4⋊Q8C2314yes—
211C2×C4⋊Q8C2314yes—
212C2×C4⋊Q8C2314yes—
213C2×C4⋊Q8C2314yes—
214C2×C4⋊Q8C2312yes—
215C2×C4⋊Q8C2312yes—
216C2×C4⋊Q8C2311yescharacteristic
217C2×C4⋊Q8C2311yescharacteristic
218C2×#125C2312yes—
219C2×#125C2312yes—
220C2×#125C2314yes—
221C2×#124C2314yes—
222C2×C22⋊Q8C2312yes—
223C2×C22⋊Q8C2314yes—
224C2×C22⋊Q8C2314yes—
225C2×C22⋊Q8C2318yes—
226C2×C22⋊Q8C2312yes—
227C2×C22⋊Q8C2318yes—
228C2×C22⋊Q8C2318yes—
229C2×C22⋊Q8C2314yes—
230C2×#121C2312yes—
231C2×#121C2312yes—
232C2×C4×Q8C2311yescharacteristic
233C2×C4×Q8C2311yescharacteristic
234C2×C4×Q8C2312yes—
235C2×C4×Q8C2312yes—
236C2×C4×Q8C2312yes—
237C2×C4×Q8C2318yes—
238C2×C4×Q8C2318yes—
239C2×C4×Q8C2311yescharacteristic
240C2×C4×Q8C2314yes—
241C2×C4×Q8C2318yes—
242C2×C4×D4C2311yescharacteristic
243C2×C4×D4C2311yescharacteristic
244C2×C4×D4C2312yes—
245C2×C4×D4C2311yescharacteristic
246C2×C4×D4C2314yes—
247C2×C4×D4C2314yes—
248C2×C4×D4C2312yes—
249C2×C4×D4C2311yescharacteristic
250C2×C4×D4C2318yes—
251C2×C4×D4C2311yescharacteristic
252C2×C4×D4C2311yescharacteristic
253C2×#117C2312yes—
254C2×#117C2312yes—
255C2×#117C2314yes—
256C2×#117C2314yes—
257C2×#117C2312yes—
258C2×#117C2312yes—
259C22×C4⋊C4C2314yes—
260C22×C4⋊C4C2314yes—
261C22×C4⋊C4C2312yes—
262C22×C4⋊C4C2312yes—
263C22×C42C2312yes—
264C22×C42C2312yes—
265C22×C42C2314yes—
266#400C2314yes—
267#400C2318yes—
268#400C2318yes—
269#400C2318yes—
270#400C2318yes—
271#400C2318yes—
272#400C2318yes—
273#399C2318yes—
274#399C2314yes—
275#398C2318yes—
276#398C2318yes—
277#398C2314yes—
278#398C2318yes—
279#398C2318yes—
280#398C2318yes—
281#398C2314yes—
282#398C2318yes—
283#396C2314yes—
284#396C2314yes—
285#396C2318yes—
286#396C2318yes—
287#396C2318yes—
288#396C2318yes—
289#395C2318yes—
290#395C2314yes—
291#395C2318yes—
292#395C2318yes—
293#395C2318yes—
294#395C2318yes—
295#395C2318yes—
296#395C2318yes—
297#395C2318yes—
298#395C2318yes—
299#393C2318yes—
300#393C2314yes—
301#393C2318yes—
302#393C2318yes—
303#393C2318yes—
304#393C2318yes—
305#391C2312yes—
306#391C2314yes—
307#391C2318yes—
308#391C2318yes—
309#391C2318yes—
310#391C2312yes—
311#391C2312yes—
312#391C2318yes—
313#391C2314yes—
314#391C2318yes—
315#391C2318yes—
316#391C2312yes—
317#391C2318yes—
318#391C2314yes—
319#391C2314yes—
320#391C2318yes—
321#391C2318yes—
322#391C2314yes—
323#391C2314yes—
324#391C2318yes—
325#391C2312yes—
326#390C2312yes—
327#390C2312yes—
328#390C2314yes—
329#390C2318yes—
330#390C2312yes—
331#390C2312yes—
332#390C2314yes—
333#389C2312yes—
334#389C2312yes—
335#389C2312yes—
336#389C2312yes—
337#389C2312yes—
338#389C2312yes—
339#389C2312yes—
340#389C2312yes—
341#389C2312yes—
342#389C2312yes—
343#389C2312yes—
344#389C2312yes—
345#389C2314yes—
346#389C2314yes—
347#389C2318yes—
348#389C2318yes—
349#389C2318yes—
350#389C2314yes—
351#389C2314yes—
352#389C2314yes—
353#389C2314yes—
354#389C2314yes—
355#389C2314yes—
356#389C2314yes—
357#389C2312yes—
358#389C2314yes—
359#389C2314yes—
360#389C2314yes—
361#389C2318yes—
362#389C2318yes—
363#389C2314yes—
364#389C2314yes—
365#389C2314yes—
366#389C2314yes—
367#389C2314yes—
368#389C2314yes—
369#389C2312yes—
370#389C2312yes—
371#389C2314yes—
372#389C2314yes—
373#389C2314yes—
374#389C2312yes—
375#388C2314yes—
376#388C2314yes—
377#388C2318yes—
378#388C2314yes—
379#388C2318yes—
380#388C2318yes—
381#388C2318yes—
382#388C2318yes—
383#388C2314yes—
384#388C2314yes—
385#388C2314yes—
386#388C2314yes—
387#388C2314yes—
388#387C2314yes—
389#387C2314yes—
390#387C2314yes—
391#387C2314yes—
392#387C2314yes—
393#387C2318yes—
394#387C2318yes—
395#387C2318yes—
396#387C2314yes—
397#387C2314yes—
398#387C2318yes—
399#387C2318yes—
400#387C2318yes—
401#387C2318yes—
402#387C2318yes—
403#387C2314yes—
404#387C2318yes—
405#387C2318yes—
406#387C2318yes—
407#386C2318yes—
408#386C2318yes—
409#386C2314yes—
410#386C2314yes—
411#385C2318yes—
412#385C2314yes—
413#385C2318yes—
414#385C2318yes—
415#385C2318yes—
416#385C2318yes—
417#385C2318yes—
418#385C2314yes—
419#385C2314yes—
420#385C2314yes—
421#385C2318yes—
422#384C2312yes—
423#384C2312yes—
424#384C2314yes—
425#384C2312yes—
426#384C2311yescharacteristic
427#384C2311yescharacteristic
428#384C2311yescharacteristic
429#384C2318yes—
430#384C2312yes—
431#384C2312yes—
432#384C2312yes—
433#383C2318yes—
434#382C2312yes—
435#382C2312yes—
436#382C2318yes—
437#382C2314yes—
438#382C2314yes—
439#382C2314yes—
440#382C2314yes—
441#382C2314yes—
442#380C2312yes—
443#380C2312yes—
444#380C2314yes—
445#380C2318yes—
446#380C2318yes—
447#380C2312yes—
448#380C2314yes—
449#380C2314yes—
450#380C2312yes—
451#380C2318yes—
452#380C2314yes—
453#380C2314yes—
454#380C2312yes—
455#380C2314yes—
456#380C2314yes—
457#380C2312yes—
458#380C2314yes—
459C4×C4⋊C4C2311yescharacteristic
460C4×C4⋊C4C2311yescharacteristic
461C4×C4⋊C4C2312yes—
462C4×C4⋊C4C2312yes—
463C4×C4⋊C4C2314yes—
464C4×C4⋊C4C2314yes—
465C4×C4⋊C4C2314yes—
466C4×C4⋊C4C2314yes—
467C4×C4⋊C4C2312yes—
468C4×C4⋊C4C2312yes—
469C4×C4⋊C4C2314yes—
470C4×C4⋊C4C2314yes—
471C4×C4⋊C4C2312yes—
472C4×C4⋊C4C2314yes—
473C4×C4⋊C4C2312yes—
474C4×C4⋊C4C2318yes—
475C4×C4⋊C4C2318yes—
476C4×C4⋊C4C2314yes—
477C4×C4⋊C4C2318yes—
478C4×C4⋊C4C2314yes—
479C4×C4⋊C4C2312yes—
480C4×C4⋊C4C2312yes—
481C4×C4⋊C4C2311yescharacteristic
482C4×C4⋊C4C2314yes—
483C4×C4⋊C4C2314yes—
484C4×C4⋊C4C2311yescharacteristic
485C4×C4⋊C4C2314yes—
486C4×C4⋊C4C2312yes—
487C4×C4⋊C4C2314yes—
488C4×C4⋊C4C2311yescharacteristic
489C4×C4⋊C4C2311yescharacteristic
490C4×C4⋊C4C2311yescharacteristic
491C4×C4⋊C4C2312yes—
492C4×C4⋊C4C2312yes—
493C4×C4⋊C4C2312yes—
494C4×C4⋊C4C2314yes—
495C4×C4⋊C4C2311yescharacteristic
496C4×C4⋊C4C2312yes—
497C4×C4⋊C4C2311yescharacteristic
498C4×C4⋊C4C2312yes—
499C4×C4⋊C4C2312yes—
500C4×C4⋊C4C2312yes—
501C4×C4⋊C4C2312yes—
502C4×C22⋊C4C2312yes—
503C4×C22⋊C4C2318yes—
504C4×C22⋊C4C2318yes—
505C4×C22⋊C4C2314yes—
506C4×C22⋊C4C2314yes—
507C4×C22⋊C4C2314yes—
508C4×C22⋊C4C2312yes—
509C4×C22⋊C4C2314yes—
510C4×C22⋊C4C2312yes—
511C4×C22⋊C4C2312yes—
512C4×C22⋊C4C2314yes—
513C4×C22⋊C4C2314yes—
514C4×C22⋊C4C2314yes—
515C4×C22⋊C4C2312yes—
516C4×C22⋊C4C2312yes—
517C4×C22⋊C4C2314yes—
518#376C2314yes—
519#376C2314yes—
520C2×#95C2314yes—
521C43C2312yes—
522C43C2314yes—
523C43C2311yescharacteristic
524C22×Q8—216no—
525C22×Q8—48no—
526C22×Q8—84no—
527C22×Q8C2411yescharacteristic
528C22×Q8C2418yes—
529C22×Q8C2412yes—
530C22×Q8C2414yes—
531C22×Q8C2418yes—
532C22×Q8C2412yes—
533C22×Q8C2412yes—
534C22×D4C2411yescharacteristic
535C22×D4C2411yescharacteristic
536C22×D4C2414yes—
537C23×C4C2412yes—
538C23×C4C2412yes—
539C23×C4C2412yes—
540C23×C4C2412yes—
541C23×C4C2412yes—
542C23×C4C2418yes—
543C23×C4C2414yes—
544C23×C4C2412yes—
545C23×C4C2414yes—
546C4⋊Q8—216no—
547C4⋊Q8—216no—
548C4⋊Q8—216no—
549C4⋊Q8—216no—
550C4⋊Q8—28no—
551C4⋊Q8—24no—
552C4⋊Q8—48no—
553C4⋊Q8—48no—
554C4⋊Q8—48no—
555C4⋊Q8—44no—
556C4⋊Q8—82no—
557C4⋊Q8C2×Q818yescomplemented
558C4⋊Q8#4118yes—
559#125—28no—
560#125—28no—
561#125—48no—
562#124C2×Q8132yescomplemented
563C22⋊Q8—216no—
564C22⋊Q8—28no—
565C22⋊Q8—416no—
566C22⋊Q8—416no—
567C22⋊Q8—416no—
568C22⋊Q8—48no—
569C22⋊Q8—44no—
570C22⋊Q8—84no—
571#121C2×Q8116yes—
572#121C2×Q8116yescomplemented
573C4×Q8—24no—
574C4×Q8—24no—
575C4×Q8—44no—
576C4×Q8—44no—
577C4×Q8—44no—
578C4×Q8—416no—
579C4×Q8—42no—
580C4×Q8—416no—
581C4×Q8—88no—
582C4×Q8—84no—
583C4×D4—28no—
584C4×D4—24no—
585C4×D4—24no—
586C4×D4—24no—
587C4×D4—44no—
588C4×D4—42no—
589C4×D4—48no—
590C4×D4—48no—
591C4×D4—88no—
592C4×D4C2×Q818yes—
593C4×D4C2×Q818yescomplemented
594#117—28no—
595#117—48no—
596#117—44no—
597#117—48no—
598#117C2×Q8116yescomplemented
599#117C2×Q8116yescomplemented
600C2×C4⋊C4—216no—
601C2×C4⋊C4—216no—
602C2×C4⋊C4—28no—
603C2×C4⋊C4—44no—
604C2×C4⋊C4C2411yescharacteristic
605C2×C4⋊C4C2411yescharacteristic
606C2×C4⋊C4C2414yes—
607C2×C4⋊C4C2414yes—
608C2×C4⋊C4C2412yes—
609C2×C4⋊C4C2414yes—
610C2×C4⋊C4C2418yes—
611C2×C4⋊C4C2418yes—
612C2×C4⋊C4C2411yescharacteristic
613C2×C4⋊C4C2412yes—
614C2×C4⋊C4C2414yes—
615C2×C4⋊C4C2412yes—
616C2×C4⋊C4C2412yes—
617C2×C4⋊C4C2411yescharacteristic
618C2×C4⋊C4C2412yes—
619C2×C4⋊C4C2411yescharacteristic
620C2×C4⋊C4C2414yes—
621C2×C4⋊C4C2414yes—
622C2×C4⋊C4C2418yes—
623C2×C4⋊C4C2412yes—
624C2×C4⋊C4C2411yescharacteristic
625C2×C4⋊C4C2412yes—
626C2×C4⋊C4C2414yes—
627C2×C4⋊C4C2412yes—
628C2×C4⋊C4C2412yes—
629C2×C4⋊C4C2412yes—
630C2×C4⋊C4C2414yes—
631C2×C4⋊C4C2414yes—
632C2×C4⋊C4C2414yes—
633C2×C4⋊C4C2418yes—
634C2×C4⋊C4C2414yes—
635C2×C4⋊C4C2414yes—
636C2×C4⋊C4C2414yes—
637C2×C4⋊C4C2414yes—
638C2×C4⋊C4C2412yes—
639C2×C4⋊C4C2418yes—
640C2×C4⋊C4C2418yes—
641C2×C4⋊C4C2418yes—
642C2×C4⋊C4C2418yes—
643C2×C4⋊C4C2414yes—
644C2×C4⋊C4C2412yes—
645C2×C4⋊C4C2412yes—
646C2×C4⋊C4C2414yes—
647C2×C4⋊C4C2414yes—
648C2×C4⋊C4C2412yes—
649C2×C4⋊C4C2414yes—
650C2×C4⋊C4C2414yes—
651C2×C4⋊C4C2414yes—
652C2×C4⋊C4C2418yes—
653C2×C4⋊C4C2418yes—
654C2×C4⋊C4C2411yescharacteristic
655C2×C4⋊C4C2411yescharacteristic
656C2×C4⋊C4C2412yes—
657C2×C4⋊C4C2412yes—
658C2×C4⋊C4C2412yes—
659C2×C4⋊C4C2412yes—
660C2×C4⋊C4C2411yescharacteristic
661C2×C22⋊C4C2414yes—
662C2×C22⋊C4C2412yes—
663C2×C22⋊C4C2412yes—
664C2×C22⋊C4C2414yes—
665C2×C22⋊C4C2412yes—
666C2×C22⋊C4C2418yes—
667C2×C22⋊C4C2414yes—
668C2×C22⋊C4C2414yes—
669C2×C22⋊C4C2414yes—
670C2×C22⋊C4C2414yes—
671C2×C22⋊C4C2418yes—
672C2×C22⋊C4C2418yes—
673C2×C22⋊C4C2414yes—
674C2×C22⋊C4C2412yes—
675C2×C22⋊C4C2414yes—
676C2×C22⋊C4C2414yes—
677C2×C22⋊C4C2414yes—
678C2×C22⋊C4C2414yes—
679C2×C22⋊C4C2414yes—
680C2×C22⋊C4C2412yes—
681C2×C22⋊C4C2412yes—
682C2×C42—28no—
683C2×C42—28no—
684C2×C42—48no—
685C2×C42C2412yes—
686C2×C42C2414yes—
687C2×C42C2414yes—
688C2×C42C2411yescharacteristic
689C2×C42C2411yescharacteristic
690C2×C42C2412yes—
691C2×C42C2414yes—
692C2×C42C2414yes—
693C2×C42C2411yescharacteristic
694C2×C42C2412yes—
695C2×C42C2412yes—
696C2×C42C2412yes—
697C2×C42C2412yes—
698C2×C42C2412yes—
699C2×C42C2412yes—
700C2×C42C2412yes—
701C2×C42C2412yes—
702C2×C42C2418yes—
703C2×C42C2414yes—
704C2×C42C2418yes—
705C2×C42C2412yes—
706C2×C42C2414yes—
707C2×C42C2414yes—
708C2×C42C2414yes—
709C2×C42C2418yes—
710C2×C42C2412yes—
711C2×C42C2411yescharacteristic
712C2×C42C2414yes—
713C2×C42C2411yescharacteristic
714C2×C42C2411yescharacteristic
715C2×C42C2411yescharacteristic
716#95C2412yes—
717#95C2414yes—
718#95C2414yes—
719#95C2414yes—
720#95C2412yes—
721#95C2412yes—
722#95C2414yes—
723#95C2414yes—
724#95C2414yes—
725#95C2414yes—
726#95C2414yes—
727#95C2414yes—
728#95C2414yes—
729#95C2412yes—
730#95C2412yes—
731#95C2414yes—
732#95C2414yes—
733#95C2412yes—
734#95C2412yes—
735#95C2418yes—
736#95C2414yes—
737#95C2418yes—
738#95C2418yes—
739#95C2414yes—
740#95C2412yes—
741#95C2412yes—
742#95C2418yes—
743#95C2418yes—
744#95C2414yes—
745#95C2414yes—
746#95C2414yes—
747#95C2414yes—
748#95C2414yes—
749#95C2418yes—
750#95C2418yes—
751#95C2418yes—
752#95C2414yes—
753#95C2418yes—
754#95C2418yes—
755#95C2414yes—
756#95C2414yes—
757#95C2418yes—
758#95C2418yes—
759#95C2418yes—
760C24C2512yes—
761C24C2512yes—
762C2×Q8—22no—
763C2×Q8—216no—
764C2×Q8—28no—
765C2×Q8—216no—
766C2×Q8—22no—
767C2×Q8—24no—
768C2×Q8—22no—
769C2×Q8—42no—
770C2×Q8—42no—
771C2×Q8—42no—
772C2×Q8—48no—
773C2×Q8—42no—
774C2×Q8—48no—
775C2×Q8—42no—
776C2×Q8—44no—
777C2×Q8—42no—
778C2×Q8—48no—
779C2×Q8—48no—
780C2×Q8—44no—
781C2×Q8—832no—
782C2×Q8C22×Q818yes—
783C2×Q8C2×#4118yes—
784C2×D4—22no—
785C2×D4—22no—
786C2×D4—22no—
787C2×D4—22no—
788C2×D4—44no—
789C2×D4—44no—
790C2×D4C22×Q814yes—
791C2×D4C22×Q814yes—
792C2×D4C22×Q8116yes—
793C22×C4—24no—
794C22×C4—24no—
795C22×C4—24no—
796C22×C4—24no—
797C22×C4—24no—
798C22×C4—24no—
799C22×C4—24no—
800C22×C4—24no—
801C22×C4—24no—
802C22×C4—24no—
803C22×C4—24no—
804C22×C4—24no—
805C22×C4—216no—
806C22×C4—28no—
807C22×C4—24no—
808C22×C4—42no—
809C22×C4—44no—
810C22×C4—44no—
811C22×C4—44no—
812C22×C4—48no—
813C22×C4—42no—
814C22×C4—44no—
815C22×C4—44no—
816C22×C4—48no—
817C22×C4—42no—
818C22×C4C22×Q818yes—
819C22×C4C22×Q818yes—
820C22×C4C2512yes—
821C22×C4C2512yes—
822C22×C4C2512yes—
823C22×C4C2512yes—
824C22×C4C2514yes—
825C22×C4C2512yes—
826C22×C4C2514yes—
827C22×C4C2512yes—
828C22×C4C2514yes—
829C22×C4C2514yes—
830C22×C4C2518yes—
831C22×C4C2512yes—
832C22×C4C2511yescharacteristic
833C22×C4C2512yes—
834C22×C4C2511yescharacteristic
835C22×C4C2514yes—
836C22×C4C2512yes—
837C22×C4C2511yescharacteristic
838C22×C4C2514yes—
839C22×C4C2512yes—
840C22×C4C2511yescharacteristic
841C22×C4C2511yescharacteristic
842C22×C4C2511yescharacteristic
843C22×C4C2511yescharacteristic
844C4⋊C4—22no—
845C4⋊C4—28no—
846C4⋊C4—216no—
847C4⋊C4—216no—
848C4⋊C4—28no—
849C4⋊C4—28no—
850C4⋊C4—22no—
851C4⋊C4—24no—
852C4⋊C4—28no—
853C4⋊C4—24no—
854C4⋊C4—24no—
855C4⋊C4—28no—
856C4⋊C4—28no—
857C4⋊C4—28no—
858C4⋊C4—216no—
859C4⋊C4—22no—
860C4⋊C4—22no—
861C4⋊C4—24no—
862C4⋊C4—24no—
863C4⋊C4—24no—
864C4⋊C4—22no—
865C4⋊C4—24no—
866C4⋊C4—22no—
867C4⋊C4—24no—
868C4⋊C4—24no—
869C4⋊C4—24no—
870C4⋊C4—44no—
871C4⋊C4—44no—
872C4⋊C4—44no—
873C4⋊C4—44no—
874C4⋊C4—48no—
875C4⋊C4—42no—
876C4⋊C4—44no—
877C4⋊C4—42no—
878C4⋊C4—44no—
879C4⋊C4—42no—
880C4⋊C4—44no—
881C4⋊C4—42no—
882C4⋊C4—48no—
883C4⋊C4—48no—
884C4⋊C4—48no—
885C4⋊C4—44no—
886C4⋊C4—44no—
887C4⋊C4—48no—
888C4⋊C4—44no—
889C4⋊C4—44no—
890C4⋊C4—44no—
891C4⋊C4—44no—
892C4⋊C4—48no—
893C4⋊C4—48no—
894C4⋊C4C22×Q814yes—
895C4⋊C4C22×Q814yes—
896C4⋊C4C22×Q818yes—
897C4⋊C4C22×Q818yes—
898C4⋊C4C2×#4118yes—
899C4⋊C4C2×#4118yes—
900C4⋊C4H(5,𝔽2)14yes—
901C22⋊C4—28no—
902C22⋊C4—24no—
903C22⋊C4—28no—
904C22⋊C4—24no—
905C22⋊C4—24no—
906C22⋊C4—44no—
907C22⋊C4—44no—
908C22⋊C4—44no—
909C22⋊C4—48no—
910C22⋊C4—44no—
911C22⋊C4—42no—
912C22⋊C4—44no—
913C22⋊C4—44no—
914C22⋊C4—48no—
915C22⋊C4—44no—
916C22⋊C4—48no—
917C22⋊C4—44no—
918C22⋊C4C22×Q8116yes—
919C22⋊C4C22×Q8116yes—
920C22⋊C4C22×Q818yes—
921C22⋊C4C22×Q818yes—
922C42—24no—
923C42—24no—
924C42—24no—
925C42—24no—
926C42—24no—
927C42—28no—
928C42—28no—
929C42—22no—
930C42—24no—
931C42—24no—
932C42—24no—
933C42—24no—
934C42—24no—
935C42—28no—
936C42—22no—
937C42—28no—
938C42—22no—
939C42—44no—
940C42—44no—
941C42—44no—
942C42—48no—
943C42—48no—
944C42—42no—
945C42—44no—
946C42—48no—
947C42—42no—
948C42—41no—
949C42C22×Q8116yes—
950C42C22×Q814yes—
951C42C2×#4114yes—
952C422−1+414yes—
953C23—22no—
954C23—22no—
955C23—22no—
956C23—22no—
957C23—22no—
958C23—22no—
959C23—22no—
960C23—22no—
961C23—22no—
962C23—22no—
963C23—22no—
964C23—22no—
965C23C23×Q814yes—
966C23C23×Q814yes—
967C23C2611yescharacteristic
968Q8—48no—
969Q8—48no—
970Q8—432no—
971Q8—44no—
972Q8—84no—
973Q8—88no—
974Q8—816no—
975D4—28no—
976D4—28no—
977D4—416no—
978C2×C4—22no—
979C2×C4—22no—
980C2×C4—22no—
981C2×C4—24no—
982C2×C4—21no—
983C2×C4—22no—
984C2×C4—21no—
985C2×C4—24no—
986C2×C4—21no—
987C2×C4—22no—
988C2×C4—24no—
989C2×C4—21no—
990C2×C4—22no—
991C2×C4—24no—
992C2×C4—21no—
993C2×C4—21no—
994C2×C4—216no—
995C2×C4—216no—
996C2×C4—22no—
997C2×C4—22no—
998C2×C4—22no—
999C2×C4—22no—
1000C2×C4—28no—
1001C2×C4—22no—
1002C2×C4—22no—
1003C2×C4—24no—
1004C2×C4—21no—
1005C2×C4—24no—
1006C2×C4—24no—
1007C2×C4—28no—
1008C2×C4—22no—
1009C2×C4—22no—
1010C2×C4—22no—
1011C2×C4—22no—
1012C2×C4—22no—
1013C2×C4—24no—
1014C2×C4—22no—
1015C2×C4—21no—
1016C2×C4—22no—
1017C2×C4—24no—
1018C2×C4—24no—
1019C2×C4—24no—
1020C2×C4—21no—
1021C2×C4—22no—
1022C2×C4—22no—
1023C2×C4—24no—
1024C2×C4—22no—
1025C2×C4—22no—
1026C2×C4—22no—
1027C2×C4—24no—
1028C2×C4—24no—
1029C2×C4—24no—
1030C2×C4—22no—
1031C2×C4—24no—
1032C2×C4—22no—
1033C2×C4—22no—
1034C2×C4—28no—
1035C2×C4—48no—
1036C2×C4—48no—
1037C2×C4—48no—
1038C2×C4—88no—
1039C2×C4—84no—
1040C2×C4—816no—
1041C2×C4—88no—
1042C2×C4C23×Q814yes—
1043C2×C4C23×Q814yes—
1044C2×C4C23×Q812yes—
1045C2×C4C23×Q818yes—
1046C2×C4C23×Q812yes—
1047C2×C4C23×Q812yes—
1048C2×C4C22×#4112yes—
1049C2×C4C22×#4118yes—
1050C2×C4C22×#4112yes—
1051C2×C4C22×#4112yes—
1052C2×C4C2×H(5,𝔽2)14yes—
1053C2×C4C2×H(5,𝔽2)12yes—
1054C2×C4C2×2−1+412yes—
1055C2×C4C2×2−1+412yes—
1056C2×C4C2×2−1+412yes—
1057C2×C4#58512yes—
1058C2×C4#58512yes—
1059C22—24no—
1060C22—24no—
1061C22—24no—
1062C22—24no—
1063C22—24no—
1064C22—24no—
1065C22—42no—
1066C22—42no—
1067C22—42no—
1068C22—42no—
1069C22—42no—
1070C22—42no—
1071C22—42no—
1072C22—42no—
1073C22C24×Q811yescharacteristic
1074C22C23×#4111yescharacteristic
1075C22C22×H(5,𝔽2)11yescharacteristic
1076C22C22×2−1+411yescharacteristic
1077C22C2×#58511yescharacteristic
1078C22C2×#58511yescharacteristic
1079C22H(7,𝔽2)11yescharacteristic
1080C4—22no—
1081C4—24no—
1082C4—28no—
1083C4—28no—
1084C4—22no—
1085C4—24no—
1086C4—22no—
1087C4—24no—
1088C4—42no—
1089C4—48no—
1090C4—41no—
1091C4—42no—
1092C4—44no—
1093C4—44no—
1094C4—44no—
1095C4—42no—
1096C4—42no—
1097C4—42no—
1098C4—42no—
1099C4—42no—
1100C4—44no—
1101C4Q8×#4114yes—
1102C4#350314yes—
1103C4#351814yes—
1104C2—44no—
1105C2—44no—
1106C2C2×Q8×#4111yescharacteristic
1107C2C2×#351811yescharacteristic
1108C2C2×#350311yescharacteristic
1109C2#6292911yescharacteristic
1110C2#6298311yescharacteristic
1111C2#6298911yescharacteristic
1112C2#6302211yescharacteristic
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. #59924C2semidirect
2. #59673C2semidirect
3. #59429C2semidirect
4. #59230C2semidirect
5. #59136C2semidirect
6. #59036C2semidirect
7. #45360C2semidirect
8. #44233C2semidirect
9. #39987C2semidirect
10. #39652C2semidirect
11. #39608C2semidirect
12. #38967C2semidirect
13. #36563C2semidirect
14. #36551C2semidirect
15. #36480C2semidirect
16. #36480C2semidirect
17. #36194C2semidirect
18. #36132C2semidirect
19. D4×C4⋊Q8C2semidirect
20. #35815C2semidirect
21. #34941C2semidirect
22. #34938C2semidirect
24. #34216C2semidirect
25. C4×#554C2semidirect
200. #555Q8semidirect
557. C4⋊Q8C2×Q8semidirect
562. #124C2×Q8semidirect
572. #121C2×Q8semidirect
593. C4×D4C2×Q8semidirect
598. #117C2×Q8semidirect
599. #117C2×Q8semidirect

Maximal subgroups

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

subgroupindex
#599242
#596732
#594292
#592302
#591362
#590362
#453602
#442332
#399872
#396522
#396082
#389672
#365632
#365512
#364802
#361942
#361322
D4×C4⋊Q82
#358152
#349412
#349382
#343212
#342162
C4×#5542
C4×#5552