Finite Group Databasebeta

← #7688620

Subgroups — #7688620

Order 512.

4765 conjugacy classes of subgroups.

The subgroup lattice has 1074 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#59832C211yesmaximal, characteristic, complemented
2#59712C214yesmaximal, complemented
3#59655C212yesmaximal
4#59464C212yesmaximal, complemented
5#59245C212yesmaximal, complemented
6#59081C214yesmaximal, complemented
7#45213C214yesmaximal
8#44167C218yesmaximal, complemented
9#39987C214yesmaximal, complemented
10#39660C214yesmaximal, complemented
11#39633C212yesmaximal
12#39182C212yesmaximal, complemented
13#36598C212yesmaximal, complemented
14#36563C211yesmaximal, characteristic, complemented
15Q8×C4⋊Q8C211yesmaximal, characteristic, complemented
16#36552C212yesmaximal, complemented
17#36288C212yesmaximal, complemented
18#36194C211yesmaximal, characteristic
19#36132C212yesmaximal
20#35867C214yesmaximal, complemented
21#34951C211yesmaximal, characteristic, complemented
22#34938C212yesmaximal, complemented
23#34335C212yesmaximal, complemented
24#34324C212yesmaximal
25C4×#554C211yesmaximal, characteristic
26C4×#556C211yesmaximal, characteristic
27C2×Q82C2212yes—
28C2×Q82C2212yes—
29C2×#556C2211yescharacteristic
30C2×#554C2211yescharacteristic
31C2×#533C2214yes—
32#2868C2211yescharacteristic
33#2868C2212yes—
34#2862C2214yes—
35#2859C2212yes—
36#2857C2212yes—
37#2851C2214yes—
38#2805C2218yes—
39#2790C2218yes—
40#2788C2218yes—
41#2788C2218yes—
42#2774C2218yes—
43#2763C2218yes—
44#2755C2218yes—
45#2734C2214yes—
46#2729C2218yes—
47#2729C2218yes—
48#2729C2218yes—
49#2666C2218yes—
50#2647C2214yes—
51#2612C2218yes—
52#2605C2218yes—
53#2590C2218yes—
54#2588C2218yes—
55#2588C2218yes—
56#2585C2214yes—
57#2582C2212yes—
58#2582C2211yescharacteristic
59#2582C2212yes—
60#2574C2218yes—
61#2571C2212yes—
62#2571C2214yes—
63#2570C2218yes—
64#2568C2214yes—
65#2568C2214yes—
66#2568C2211yescharacteristic
67#2567C2212yes—
68#2567C2214yes—
69#2567C2212yes—
70#2563C2212yes—
71#2552C2211yescharacteristic
72#2552C2212yes—
73#2551C2212yes—
74#2551C2214yes—
75#2551C2212yes—
76#2551C2214yes—
77#2551C2212yes—
78#2551C2212yes—
79#2550C2214yes—
80#2550C2214yes—
81#2550C2214yes—
82#2550C2214yes—
83#2549C2218yes—
84#2546C2214yes—
85#2546C2211yescharacteristic
86#2538C2212yes—
87#2511C2212yes—
88#2511C2214yes—
89#2511C2214yes—
90#2509C2212yes—
91#2509C2214yes—
92#2508C2214yes—
93#2508C2214yes—
94#2507C2214yes—
95#2505C2218yes—
96#2502C2214yes—
97#2497C2214yes—
98#2497C2214yes—
99#2492C2214yes—
100#2492C2214yes—
101#2492C2218yes—
102#2492C2214yes—
103#2465C2218yes—
104#2465C2218yes—
105#2453C2214yes—
106#2453C2214yes—
107#2453C2212yes—
108#2452C2214yes—
109#2452C2214yes—
110#2451C2214yes—
111#2451C2214yes—
112#2451C2214yes—
113#2451C2218yes—
114#2451C2214yes—
115#2446C2218yes—
116#2446C2212yes—
117#2446C2218yes—
118#2440C2214yes—
119#2440C2214yes—
120#2439C2214yes—
121#2439C2214yes—
122#2439C2214yes—
123#2429C2218yes—
124#2429C2214yes—
125#2402C2214yes—
126#2399C2218yes—
127#2373C2218yes—
128#2373C2214yes—
129#2370C2212yes—
130#2369C2212yes—
131#2369C2211yescharacteristic
132#2369C2214yes—
133#2369C2212yes—
134#2369C2214yes—
135#2368C2214yes—
136#2367C2214yes—
137#2367C2212yes—
138#2365C2212yes—
139#2365C2214yes—
140#2365C2214yes—
141#2365C2218yes—
142#2365C2211yescharacteristic
143#2365C2212yes—
144#2362C2214yes—
145#2362C2212yes—
146#2360C2214yes—
147#2360C2212yes—
148#2356C2212yes—
149#2355C2211yescharacteristic
150#2355C2214yes—
151#2355C2212yes—
152#2355C2214yes—
153#2355C2212yes—
154#2355C2211yescharacteristic
155#2354C2212yes—
156#2354C2211yescharacteristic
157#2351C2214yes—
158Q8×C4⋊C4C2212yes—
159Q8×C4⋊C4C2212yes—
160Q8×C4⋊C4C2212yes—
161#2349C2212yes—
162D4×C4⋊C4C2211yescharacteristic
163#2347C2212yes—
164#2346C2214yes—
165#2345C2212yes—
166#2334C2218yes—
167#2331C2214yes—
168#2331C2218yes—
169#2326C2214yes—
170C4×C4⋊Q8C2212yes—
171C4×C4⋊Q8C2212yes—
172C4×C4⋊Q8C2212yes—
173C4×C4⋊Q8C2214yes—
174C4×C4⋊Q8C2214yes—
175C4×C4⋊Q8C2211yescharacteristic
176C4×C4⋊Q8C2211yescharacteristic
177C4×C4⋊Q8C2211yescharacteristic
178C4×#125C2212yes—
179C4×#125C2212yes—
180C4×#126C2214yes—
181C4×#124C2212yes—
182C4×C22⋊Q8C2214yes—
183C4×C22⋊Q8C2214yes—
184C4×C22⋊Q8C2212yes—
185C4×C22⋊Q8C2212yes—
186#2296C2214yes—
187#2295C2212yes—
188#2295C2214yes—
189#2295C2212yes—
190#2285C2212yes—
191#2276C2214yes—
192C42×Q8C2212yes—
193C42×Q8C2211yescharacteristic
194C42×Q8C2211yescharacteristic
195C42×D4C2212yes—
196C42×D4C2211yescharacteristic
197C4×#117C2212yes—
198C2×C4×C4⋊C4C2212yes—
199Q82—216no—
200Q82—48no—
201#556Q8116yescomplemented
202#554—28no—
203#533—416no—
204C2×C4⋊Q8C2311yescharacteristic
205C2×C4⋊Q8C2314yes—
206C2×C4⋊Q8C2318yes—
207C2×C4⋊Q8C2314yes—
208C2×C4⋊Q8C2314yes—
209C2×C4⋊Q8C2312yes—
210C2×C4⋊Q8C2314yes—
211C2×C4⋊Q8C2312yes—
212C2×C4⋊Q8C2312yes—
213C2×C4⋊Q8C2312yes—
214C2×C4⋊Q8C2314yes—
215C2×C4⋊Q8C2314yes—
216C2×C4⋊Q8C2314yes—
217C2×C4⋊Q8C2318yes—
218C2×C4⋊Q8C2311yescharacteristic
219C2×C4⋊Q8C2311yescharacteristic
220C2×#126C2314yes—
221C2×#125C2312yes—
222C2×#125C2312yes—
223C2×#125C2314yes—
224C2×#124C2312yes—
225C2×C22⋊Q8C2312yes—
226C2×C22⋊Q8C2314yes—
227C2×C22⋊Q8C2314yes—
228C2×C22⋊Q8C2318yes—
229C2×C22⋊Q8C2318yes—
230C2×C22⋊Q8C2312yes—
231C2×C4×Q8C2311yescharacteristic
232C2×C4×Q8C2312yes—
233C2×C4×Q8C2312yes—
234C2×C4×Q8C2311yescharacteristic
235C2×C4×Q8C2311yescharacteristic
236C2×C4×Q8C2314yes—
237C2×C4×Q8C2314yes—
238C2×C4×Q8C2311yescharacteristic
239C2×C4×Q8C2314yes—
240C2×C4×Q8C2312yes—
241C2×C4×Q8C2314yes—
242C2×C4×Q8C2318yes—
243C2×C4×Q8C2318yes—
244C2×C4×Q8C2311yescharacteristic
245C2×C4×Q8C2312yes—
246C2×C4×Q8C2314yes—
247C2×C4×Q8C2311yescharacteristic
248C2×C4×Q8C2312yes—
249C2×C4×D4C2311yescharacteristic
250C2×C4×D4C2312yes—
251C2×C4×D4C2311yescharacteristic
252C2×C4×D4C2312yes—
253C2×C4×D4C2311yescharacteristic
254C2×#117C2312yes—
255C2×#117C2314yes—
256C2×#117C2312yes—
257C22×C4⋊C4C2312yes—
258C22×C4⋊C4C2312yes—
259C22×C42C2312yes—
260C22×C42C2314yes—
261#400C2318yes—
262#400C2318yes—
263#400C2318yes—
264#400C2314yes—
265#400C2318yes—
266#400C2318yes—
267#400C2318yes—
268#400C2318yes—
269#400C2314yes—
270#400C2318yes—
271#400C2314yes—
272#400C2314yes—
273#398C2318yes—
274#398C2318yes—
275#398C2314yes—
276#398C2314yes—
277#398C2314yes—
278#398C2318yes—
279#398C2318yes—
280#398C2318yes—
281#398C2318yes—
282#398C2318yes—
283#398C2318yes—
284#398C2314yes—
285#398C2318yes—
286#396C2318yes—
287#396C2318yes—
288#396C2318yes—
289#395C2318yes—
290#395C2318yes—
291#395C2318yes—
292#395C2318yes—
293#395C2318yes—
294#395C2318yes—
295#395C2318yes—
296#395C2318yes—
297#393C2318yes—
298#393C2318yes—
299#393C2318yes—
300#391C2314yes—
301#391C2312yes—
302#391C2314yes—
303#391C2318yes—
304#391C2312yes—
305#391C2312yes—
306#391C2318yes—
307#391C2312yes—
308#391C2312yes—
309#391C2314yes—
310#391C2312yes—
311#391C2312yes—
312#391C2318yes—
313#391C2314yes—
314#391C2318yes—
315#391C2318yes—
316#391C2312yes—
317#391C2312yes—
318#391C2314yes—
319#391C2314yes—
320#391C2318yes—
321#391C2318yes—
322#391C2314yes—
323#391C2318yes—
324#391C2318yes—
325#391C2318yes—
326#391C2312yes—
327#391C2318yes—
328#391C2312yes—
329#391C2312yes—
330#390C2314yes—
331#390C2312yes—
332#389C2312yes—
333#389C2312yes—
334#389C2312yes—
335#389C2312yes—
336#389C2314yes—
337#389C2312yes—
338#389C2314yes—
339#389C2314yes—
340#389C2318yes—
341#389C2314yes—
342#389C2314yes—
343#389C2312yes—
344#389C2314yes—
345#389C2312yes—
346#389C2312yes—
347#389C2312yes—
348#389C2314yes—
349#389C2318yes—
350#389C2312yes—
351#389C2312yes—
352#389C2314yes—
353#389C2318yes—
354#389C2318yes—
355#389C2314yes—
356#389C2314yes—
357#389C2314yes—
358#389C2314yes—
359#389C2314yes—
360#389C2314yes—
361#389C2314yes—
362#389C2312yes—
363#389C2318yes—
364#389C2314yes—
365#389C2318yes—
366#389C2314yes—
367#389C2318yes—
368#389C2314yes—
369#389C2312yes—
370#389C2312yes—
371#389C2312yes—
372#389C2314yes—
373#389C2318yes—
374#389C2314yes—
375#389C2314yes—
376#389C2312yes—
377#388C2314yes—
378#388C2314yes—
379#388C2314yes—
380#388C2318yes—
381#388C2318yes—
382#388C2318yes—
383#388C2318yes—
384#388C2318yes—
385#388C2314yes—
386#388C2314yes—
387#387C2314yes—
388#387C2314yes—
389#387C2314yes—
390#387C2314yes—
391#387C2314yes—
392#387C2314yes—
393#387C2314yes—
394#387C2314yes—
395#387C2318yes—
396#387C2318yes—
397#387C2318yes—
398#387C2318yes—
399#387C2318yes—
400#387C2318yes—
401#387C2314yes—
402#387C2314yes—
403#387C2314yes—
404#387C2314yes—
405#387C2318yes—
406#387C2318yes—
407#387C2314yes—
408#387C2318yes—
409#387C2314yes—
410#387C2318yes—
411#387C2318yes—
412#387C2318yes—
413#387C2318yes—
414#387C2314yes—
415#387C2318yes—
416#385C2314yes—
417#385C2318yes—
418#385C2318yes—
419#385C2318yes—
420#385C2318yes—
421#385C2314yes—
422#385C2314yes—
423#385C2318yes—
424#385C2314yes—
425#384C2312yes—
426#384C2314yes—
427#384C2312yes—
428#384C2311yescharacteristic
429#384C2312yes—
430#384C2311yescharacteristic
431#384C2311yescharacteristic
432#384C2314yes—
433#384C2312yes—
434#384C2314yes—
435#384C2312yes—
436#384C2314yes—
437#383C2314yes—
438#382C2312yes—
439#382C2312yes—
440#382C2314yes—
441#382C2314yes—
442#382C2314yes—
443#382C2318yes—
444#382C2318yes—
445#382C2318yes—
446#382C2312yes—
447#380C2314yes—
448#380C2314yes—
449#380C2312yes—
450#380C2314yes—
451#380C2312yes—
452#380C2314yes—
453#380C2314yes—
454C4×C4⋊C4C2312yes—
455C4×C4⋊C4C2312yes—
456C4×C4⋊C4C2314yes—
457C4×C4⋊C4C2311yescharacteristic
458C4×C4⋊C4C2311yescharacteristic
459C4×C4⋊C4C2314yes—
460C4×C4⋊C4C2312yes—
461C4×C4⋊C4C2312yes—
462C4×C4⋊C4C2314yes—
463C4×C4⋊C4C2314yes—
464C4×C4⋊C4C2314yes—
465C4×C4⋊C4C2312yes—
466C4×C4⋊C4C2312yes—
467C4×C4⋊C4C2314yes—
468C4×C4⋊C4C2312yes—
469C4×C4⋊C4C2318yes—
470C4×C4⋊C4C2314yes—
471C4×C4⋊C4C2318yes—
472C4×C4⋊C4C2314yes—
473C4×C4⋊C4C2314yes—
474C4×C4⋊C4C2314yes—
475C4×C4⋊C4C2314yes—
476C4×C4⋊C4C2312yes—
477C4×C4⋊C4C2312yes—
478C4×C4⋊C4C2312yes—
479C4×C4⋊C4C2311yescharacteristic
480C4×C4⋊C4C2311yescharacteristic
481C4×C4⋊C4C2314yes—
482C4×C4⋊C4C2312yes—
483C4×C4⋊C4C2318yes—
484C4×C4⋊C4C2312yes—
485C4×C4⋊C4C2314yes—
486C4×C4⋊C4C2318yes—
487C4×C4⋊C4C2318yes—
488C4×C4⋊C4C2314yes—
489C4×C4⋊C4C2311yescharacteristic
490C4×C4⋊C4C2314yes—
491C4×C4⋊C4C2312yes—
492C4×C4⋊C4C2311yescharacteristic
493C4×C4⋊C4C2312yes—
494C4×C4⋊C4C2314yes—
495C4×C4⋊C4C2314yes—
496C4×C4⋊C4C2312yes—
497C4×C4⋊C4C2312yes—
498C4×C4⋊C4C2311yescharacteristic
499C4×C4⋊C4C2311yescharacteristic
500C4×C4⋊C4C2312yes—
501C4×C4⋊C4C2314yes—
502C4×C4⋊C4C2312yes—
503C4×C4⋊C4C2312yes—
504C4×C4⋊C4C2312yes—
505C4×C4⋊C4C2311yescharacteristic
506C4×C22⋊C4C2312yes—
507C4×C22⋊C4C2314yes—
508C4×C22⋊C4C2314yes—
509C4×C22⋊C4C2314yes—
510C4×C22⋊C4C2314yes—
511C4×C22⋊C4C2314yes—
512C4×C22⋊C4C2314yes—
513C4×C22⋊C4C2312yes—
514C4×C22⋊C4C2318yes—
515C4×C22⋊C4C2312yes—
516#376C2314yes—
517#376C2318yes—
518#376C2314yes—
519C2×#95C2314yes—
520C43C2314yes—
521C43C2312yes—
522C43C2311yescharacteristic
523C43C2312yes—
524C22×Q8C2412yes—
525C22×Q8C2411yescharacteristic
526C22×Q8C2411yescharacteristic
527C22×Q8C2412yes—
528C22×Q8C2418yes—
529C22×Q8C2418yes—
530C22×Q8C2414yes—
531C22×Q8C2412yes—
532C22×D4C2411yescharacteristic
533C23×C4C2412yes—
534C23×C4C2412yes—
535C23×C4C2414yes—
536C23×C4C2412yes—
537C23×C4C2414yes—
538C4⋊Q8—232no—
539C4⋊Q8—216no—
540C4⋊Q8—216no—
541C4⋊Q8—216no—
542C4⋊Q8—24no—
543C4⋊Q8—44no—
544C4⋊Q8—48no—
545C4⋊Q8—44no—
546C4⋊Q8—48no—
547C4⋊Q8—48no—
548C4⋊Q8—44no—
549C4⋊Q8—44no—
550C4⋊Q8—48no—
551C4⋊Q8—416no—
552C4⋊Q8C2×Q818yes—
553C4⋊Q8#4118yes—
554#126C2×Q8132yes—
555#125—28no—
556#125—28no—
557#125—48no—
558#124C2×Q8116yes—
559C22⋊Q8—216no—
560C22⋊Q8—28no—
561C22⋊Q8—416no—
562C22⋊Q8—416no—
563C22⋊Q8—48no—
564C22⋊Q8C2×Q8116yes—
565C4×Q8—216no—
566C4×Q8—216no—
567C4×Q8—24no—
568C4×Q8—24no—
569C4×Q8—28no—
570C4×Q8—28no—
571C4×Q8—24no—
572C4×Q8—24no—
573C4×Q8—44no—
574C4×Q8—416no—
575C4×Q8—48no—
576C4×Q8—48no—
577C4×Q8—42no—
578C4×Q8—44no—
579C4×Q8—416no—
580C4×Q8—48no—
581C4×Q8C2×Q8116yes—
582C4×Q8C2×Q818yes—
583C4×D4—28no—
584C4×D4—24no—
585C4×D4—44no—
586C4×D4—42no—
587C4×D4C2×Q818yes—
588#117—28no—
589#117—48no—
590#117C2×Q8116yes—
591C2×C4⋊C4—28no—
592C2×C4⋊C4—44no—
593C2×C4⋊C4C2411yescharacteristic
594C2×C4⋊C4C2411yescharacteristic
595C2×C4⋊C4C2414yes—
596C2×C4⋊C4C2412yes—
597C2×C4⋊C4C2412yes—
598C2×C4⋊C4C2414yes—
599C2×C4⋊C4C2412yes—
600C2×C4⋊C4C2411yescharacteristic
601C2×C4⋊C4C2411yescharacteristic
602C2×C4⋊C4C2412yes—
603C2×C4⋊C4C2414yes—
604C2×C4⋊C4C2414yes—
605C2×C4⋊C4C2418yes—
606C2×C4⋊C4C2412yes—
607C2×C4⋊C4C2412yes—
608C2×C4⋊C4C2412yes—
609C2×C4⋊C4C2414yes—
610C2×C4⋊C4C2412yes—
611C2×C4⋊C4C2418yes—
612C2×C4⋊C4C2414yes—
613C2×C4⋊C4C2418yes—
614C2×C4⋊C4C2414yes—
615C2×C4⋊C4C2411yescharacteristic
616C2×C4⋊C4C2411yescharacteristic
617C2×C4⋊C4C2412yes—
618C2×C4⋊C4C2412yes—
619C2×C4⋊C4C2414yes—
620C2×C4⋊C4C2414yes—
621C2×C4⋊C4C2412yes—
622C2×C4⋊C4C2412yes—
623C2×C4⋊C4C2414yes—
624C2×C4⋊C4C2418yes—
625C2×C4⋊C4C2418yes—
626C2×C4⋊C4C2418yes—
627C2×C4⋊C4C2414yes—
628C2×C4⋊C4C2412yes—
629C2×C4⋊C4C2414yes—
630C2×C4⋊C4C2418yes—
631C2×C4⋊C4C2414yes—
632C2×C4⋊C4C2418yes—
633C2×C4⋊C4C2412yes—
634C2×C4⋊C4C2418yes—
635C2×C4⋊C4C2414yes—
636C2×C4⋊C4C2414yes—
637C2×C4⋊C4C2418yes—
638C2×C4⋊C4C2414yes—
639C2×C4⋊C4C2414yes—
640C2×C4⋊C4C2418yes—
641C2×C4⋊C4C2412yes—
642C2×C4⋊C4C2414yes—
643C2×C4⋊C4C2414yes—
644C2×C4⋊C4C2412yes—
645C2×C4⋊C4C2414yes—
646C2×C4⋊C4C2411yescharacteristic
647C2×C4⋊C4C2412yes—
648C2×C4⋊C4C2411yescharacteristic
649C2×C4⋊C4C2414yes—
650C2×C4⋊C4C2412yes—
651C2×C4⋊C4C2412yes—
652C2×C4⋊C4C2412yes—
653C2×C4⋊C4C2412yes—
654C2×C4⋊C4C2411yescharacteristic
655C2×C22⋊C4C2414yes—
656C2×C22⋊C4C2414yes—
657C2×C22⋊C4C2412yes—
658C2×C22⋊C4C2418yes—
659C2×C22⋊C4C2412yes—
660C2×C22⋊C4C2414yes—
661C2×C22⋊C4C2418yes—
662C2×C22⋊C4C2414yes—
663C2×C22⋊C4C2414yes—
664C2×C22⋊C4C2412yes—
665C2×C22⋊C4C2414yes—
666C2×C42—28no—
667C2×C42—48no—
668C2×C42C2414yes—
669C2×C42C2412yes—
670C2×C42C2412yes—
671C2×C42C2411yescharacteristic
672C2×C42C2411yescharacteristic
673C2×C42C2412yes—
674C2×C42C2414yes—
675C2×C42C2414yes—
676C2×C42C2418yes—
677C2×C42C2414yes—
678C2×C42C2411yescharacteristic
679C2×C42C2412yes—
680C2×C42C2412yes—
681C2×C42C2412yes—
682C2×C42C2412yes—
683C2×C42C2412yes—
684C2×C42C2412yes—
685C2×C42C2412yes—
686C2×C42C2412yes—
687C2×C42C2418yes—
688C2×C42C2418yes—
689C2×C42C2414yes—
690C2×C42C2414yes—
691C2×C42C2412yes—
692C2×C42C2414yes—
693C2×C42C2418yes—
694C2×C42C2411yescharacteristic
695C2×C42C2412yes—
696C2×C42C2414yes—
697C2×C42C2412yes—
698C2×C42C2414yes—
699C2×C42C2411yescharacteristic
700C2×C42C2412yes—
701C2×C42C2411yescharacteristic
702C2×C42C2411yescharacteristic
703#95C2412yes—
704#95C2414yes—
705#95C2414yes—
706#95C2414yes—
707#95C2414yes—
708#95C2414yes—
709#95C2412yes—
710#95C2414yes—
711#95C2414yes—
712#95C2414yes—
713#95C2418yes—
714#95C2414yes—
715#95C2414yes—
716#95C2418yes—
717#95C2414yes—
718#95C2412yes—
719#95C2414yes—
720#95C2412yes—
721#95C2412yes—
722#95C2414yes—
723#95C2414yes—
724#95C2418yes—
725#95C2414yes—
726#95C2414yes—
727#95C2412yes—
728#95C2414yes—
729#95C2412yes—
730#95C2412yes—
731#95C2414yes—
732#95C2412yes—
733#95C2414yes—
734#95C2418yes—
735#95C2418yes—
736#95C2418yes—
737#95C2414yes—
738#95C2414yes—
739#95C2414yes—
740#95C2414yes—
741#95C2418yes—
742#95C2418yes—
743#95C2418yes—
744#95C2418yes—
745#95C2414yes—
746#95C2418yes—
747#95C2414yes—
748#95C2414yes—
749#95C2414yes—
750#95C2414yes—
751#95C2418yes—
752#95C2418yes—
753C24C2512yes—
754C2×Q8—24no—
755C2×Q8—24no—
756C2×Q8—22no—
757C2×Q8—216no—
758C2×Q8—22no—
759C2×Q8—216no—
760C2×Q8—22no—
761C2×Q8—22no—
762C2×Q8—24no—
763C2×Q8—24no—
764C2×Q8—22no—
765C2×Q8—24no—
766C2×Q8—42no—
767C2×Q8—42no—
768C2×Q8—48no—
769C2×Q8—48no—
770C2×Q8—48no—
771C2×Q8—48no—
772C2×Q8—44no—
773C2×Q8—44no—
774C2×Q8—44no—
775C2×Q8C22×Q814yes—
776C2×Q8C22×Q818yes—
777C2×Q8C2×#4118yes—
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—28no—
787C22×C4—24no—
788C22×C4—44no—
789C22×C4—44no—
790C22×C4—44no—
791C22×C4—42no—
792C22×C4—44no—
793C22×C4—42no—
794C22×C4—44no—
795C22×C4C22×Q818yes—
796C22×C4C2512yes—
797C22×C4C2512yes—
798C22×C4C2512yes—
799C22×C4C2514yes—
800C22×C4C2512yes—
801C22×C4C2512yes—
802C22×C4C2511yescharacteristic
803C22×C4C2512yes—
804C22×C4C2514yes—
805C22×C4C2514yes—
806C22×C4C2514yes—
807C22×C4C2512yes—
808C22×C4C2518yes—
809C22×C4C2512yes—
810C22×C4C2511yescharacteristic
811C22×C4C2512yes—
812C22×C4C2514yes—
813C22×C4C2512yes—
814C22×C4C2514yes—
815C22×C4C2511yescharacteristic
816C22×C4C2512yes—
817C22×C4C2511yescharacteristic
818C22×C4C2511yescharacteristic
819C22×C4C2511yescharacteristic
820C22×C4C2511yescharacteristic
821C4⋊C4—22no—
822C4⋊C4—28no—
823C4⋊C4—22no—
824C4⋊C4—24no—
825C4⋊C4—216no—
826C4⋊C4—28no—
827C4⋊C4—216no—
828C4⋊C4—28no—
829C4⋊C4—24no—
830C4⋊C4—24no—
831C4⋊C4—28no—
832C4⋊C4—24no—
833C4⋊C4—24no—
834C4⋊C4—28no—
835C4⋊C4—24no—
836C4⋊C4—28no—
837C4⋊C4—28no—
838C4⋊C4—216no—
839C4⋊C4—24no—
840C4⋊C4—22no—
841C4⋊C4—22no—
842C4⋊C4—24no—
843C4⋊C4—24no—
844C4⋊C4—24no—
845C4⋊C4—22no—
846C4⋊C4—24no—
847C4⋊C4—22no—
848C4⋊C4—24no—
849C4⋊C4—28no—
850C4⋊C4—28no—
851C4⋊C4—44no—
852C4⋊C4—42no—
853C4⋊C4—44no—
854C4⋊C4—42no—
855C4⋊C4—44no—
856C4⋊C4—44no—
857C4⋊C4—44no—
858C4⋊C4—48no—
859C4⋊C4—42no—
860C4⋊C4—48no—
861C4⋊C4—48no—
862C4⋊C4—48no—
863C4⋊C4—42no—
864C4⋊C4—44no—
865C4⋊C4—48no—
866C4⋊C4—44no—
867C4⋊C4—48no—
868C4⋊C4—44no—
869C4⋊C4—44no—
870C4⋊C4—48no—
871C4⋊C4—44no—
872C4⋊C4—44no—
873C4⋊C4—48no—
874C4⋊C4C22×Q814yes—
875C4⋊C4C22×Q818yes—
876C4⋊C4C22×Q814yes—
877C4⋊C4C22×Q8116yes—
878C4⋊C4C22×Q818yes—
879C4⋊C4C22×Q818yes—
880C4⋊C4C2×#4118yes—
881C4⋊C4C2×#4118yes—
882C4⋊C4H(5,𝔽2)14yes—
883C22⋊C4—28no—
884C22⋊C4—24no—
885C22⋊C4—28no—
886C22⋊C4—44no—
887C22⋊C4—48no—
888C22⋊C4—44no—
889C22⋊C4—42no—
890C22⋊C4—48no—
891C22⋊C4C22×Q8116yes—
892C22⋊C4C22×Q818yes—
893C22⋊C4C22×Q8116yes—
894C42—24no—
895C42—216no—
896C42—28no—
897C42—28no—
898C42—24no—
899C42—28no—
900C42—28no—
901C42—24no—
902C42—22no—
903C42—24no—
904C42—24no—
905C42—24no—
906C42—24no—
907C42—24no—
908C42—24no—
909C42—22no—
910C42—22no—
911C42—24no—
912C42—24no—
913C42—44no—
914C42—44no—
915C42—41no—
916C42—42no—
917C42—44no—
918C42—42no—
919C42—48no—
920C42—42no—
921C42—44no—
922C42—48no—
923C42—48no—
924C42C22×Q8116yes—
925C42C22×Q814yes—
926C42C22×Q818yes—
927C42C2×#4114yes—
928C422−1+414yes—
929C23—22no—
930C23—22no—
931C23—22no—
932C23—22no—
933C23—22no—
934C23—22no—
935C23C23×Q814yes—
936C23C2611yescharacteristic
937Q8—216no—
938Q8—28no—
939Q8—48no—
940Q8—48no—
941Q8—44no—
942Q8—816no—
943Q8—816no—
944Q8—164no—
945D4—28no—
946C2×C4—24no—
947C2×C4—21no—
948C2×C4—22no—
949C2×C4—22no—
950C2×C4—24no—
951C2×C4—22no—
952C2×C4—22no—
953C2×C4—21no—
954C2×C4—22no—
955C2×C4—22no—
956C2×C4—21no—
957C2×C4—22no—
958C2×C4—24no—
959C2×C4—21no—
960C2×C4—22no—
961C2×C4—21no—
962C2×C4—21no—
963C2×C4—24no—
964C2×C4—216no—
965C2×C4—24no—
966C2×C4—22no—
967C2×C4—22no—
968C2×C4—24no—
969C2×C4—24no—
970C2×C4—22no—
971C2×C4—22no—
972C2×C4—22no—
973C2×C4—24no—
974C2×C4—24no—
975C2×C4—21no—
976C2×C4—24no—
977C2×C4—28no—
978C2×C4—22no—
979C2×C4—22no—
980C2×C4—22no—
981C2×C4—22no—
982C2×C4—22no—
983C2×C4—24no—
984C2×C4—22no—
985C2×C4—21no—
986C2×C4—22no—
987C2×C4—22no—
988C2×C4—21no—
989C2×C4—22no—
990C2×C4—22no—
991C2×C4—28no—
992C2×C4—22no—
993C2×C4—24no—
994C2×C4—28no—
995C2×C4—24no—
996C2×C4—24no—
997C2×C4—22no—
998C2×C4—22no—
999C2×C4—22no—
1000C2×C4—24no—
1001C2×C4—22no—
1002C2×C4—22no—
1003C2×C4—24no—
1004C2×C4—48no—
1005C2×C4—88no—
1006C2×C4—84no—
1007C2×C4—88no—
1008C2×C4C23×Q814yes—
1009C2×C4C23×Q814yes—
1010C2×C4C23×Q812yes—
1011C2×C4C23×Q814yes—
1012C2×C4C23×Q818yes—
1013C2×C4C23×Q812yes—
1014C2×C4C23×Q812yes—
1015C2×C4C22×#4118yes—
1016C2×C4C22×#4112yes—
1017C2×C4C22×#4112yes—
1018C2×C4C22×#4112yes—
1019C2×C4C2×H(5,𝔽2)14yes—
1020C2×C4C2×H(5,𝔽2)12yes—
1021C2×C4C2×2−1+412yes—
1022C2×C4C2×2−1+412yes—
1023C2×C4C2×2−1+412yes—
1024C2×C4#58512yes—
1025C2×C4#58512yes—
1026C22—24no—
1027C22—24no—
1028C22—24no—
1029C22—42no—
1030C22—42no—
1031C22—42no—
1032C22—42no—
1033C22C24×Q811yescharacteristic
1034C22C23×#4111yescharacteristic
1035C22C22×H(5,𝔽2)11yescharacteristic
1036C22C22×2−1+411yescharacteristic
1037C22C2×#58511yescharacteristic
1038C22C2×#58511yescharacteristic
1039C222−1+611yescharacteristic
1040C4—28no—
1041C4—22no—
1042C4—22no—
1043C4—24no—
1044C4—24no—
1045C4—24no—
1046C4—24no—
1047C4—22no—
1048C4—28no—
1049C4—42no—
1050C4—44no—
1051C4—44no—
1052C4—42no—
1053C4—44no—
1054C4—48no—
1055C4—41no—
1056C4—42no—
1057C4—44no—
1058C4—42no—
1059C4—42no—
1060C4—42no—
1061C4—42no—
1062C4Q8×#4114yes—
1063C4#350314yes—
1064C4#351814yes—
1065C2—44no—
1066C2C2×Q8×#4111yescharacteristic
1067C2C2×#351811yescharacteristic
1068C2C2×#350311yescharacteristic
1069C2#6295911yescharacteristic
1070C2#6298411yescharacteristic
1071C2#6300411yescharacteristic
1072C2#6302111yescharacteristic
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. #59832C2semidirect
2. #59712C2semidirect
4. #59464C2semidirect
5. #59245C2semidirect
6. #59081C2semidirect
8. #44167C2semidirect
9. #39987C2semidirect
10. #39660C2semidirect
12. #39182C2semidirect
13. #36598C2semidirect
14. #36563C2semidirect
15. Q8×C4⋊Q8C2semidirect
16. #36552C2semidirect
17. #36288C2semidirect
20. #35867C2semidirect
21. #34951C2semidirect
22. #34938C2semidirect
23. #34335C2semidirect
201. #556Q8semidirect

Maximal subgroups

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

subgroupindex
#598322
#597122
#596552
#594642
#592452
#590812
#452132
#441672
#399872
#396602
#396332
#391822
#365982
#365632
Q8×C4⋊Q82
#365522
#362882
#361942
#361322
#358672
#349512
#349382
#343352
#343242
C4×#5542
C4×#5562