Finite Group Databasebeta

← #7987104

Subgroups — #7987104

Order 512.

4737 conjugacy classes of subgroups.

The subgroup lattice has 1077 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#59871C211yesmaximal, characteristic, complemented
2#59673C212yesmaximal, complemented
3#59445C212yesmaximal, complemented
4#59259C212yesmaximal, complemented
5#51595C218yesmaximal, complemented
6#45499C214yesmaximal, complemented
7#45044C214yesmaximal, complemented
8#44894C214yesmaximal, complemented
9#42497C214yesmaximal
10#42491C214yesmaximal, complemented
11#39753C212yesmaximal, complemented
12#39625C212yesmaximal, complemented
13#39609C212yesmaximal, complemented
14#39597C214yesmaximal, complemented
15#39369C212yesmaximal
16Q8×C4⋊Q8C211yesmaximal, characteristic, complemented
17Q8×C4⋊Q8C211yesmaximal, characteristic, complemented
18#36194C211yesmaximal, characteristic
19#36134C212yesmaximal
20#36133C212yesmaximal, complemented
21#35177C212yesmaximal
22#35167C212yesmaximal, complemented
23#34951C211yesmaximal, characteristic, complemented
24#34941C211yesmaximal, characteristic
25#34484C212yesmaximal
26C4×#554C211yesmaximal, characteristic
27C2×Q82C2212yes—
28C2×Q82C2212yes—
29C2×#554C2211yescharacteristic
30C2×#544C2214yes—
31C2×#533C2214yes—
32#2868C2212yes—
33#2868C2212yes—
34#2868C2211yescharacteristic
35#2857C2212yes—
36#2857C2214yes—
37#2857C2214yes—
38#2855C2214yes—
39#2841C2218yes—
40#2806C2214yes—
41#2805C2218yes—
42#2799C2218yes—
43#2792C2218yes—
44#2791C2218yes—
45#2774C2218yes—
46#2774C2218yes—
47#2768C2218yes—
48#2742C2218yes—
49#2734C2218yes—
50#2729C2218yes—
51#2720C2218yes—
52#2713C2218yes—
53#2713C2218yes—
54#2713C2218yes—
55#2677C2218yes—
56#2677C2218yes—
57#2665C2218yes—
58#2660C2214yes—
59#2659C2218yes—
60#2628C2218yes—
61#2628C2214yes—
62#2585C2218yes—
63#2585C2214yes—
64#2584C2214yes—
65#2582C2211yescharacteristic
66#2582C2214yes—
67#2581C2218yes—
68#2574C2214yes—
69#2571C2212yes—
70#2570C2214yes—
71#2568C2211yescharacteristic
72#2567C2211yescharacteristic
73#2567C2212yes—
74#2567C2214yes—
75#2567C2214yes—
76#2567C2214yes—
77#2567C2212yes—
78#2567C2212yes—
79#2565C2214yes—
80#2563C2212yes—
81#2563C2211yescharacteristic
82#2552C2214yes—
83#2552C2214yes—
84#2552C2212yes—
85#2552C2211yescharacteristic
86#2552C2212yes—
87#2552C2211yescharacteristic
88#2551C2214yes—
89#2551C2214yes—
90#2551C2212yes—
91#2551C2212yes—
92#2551C2214yes—
93#2551C2214yes—
94#2551C2212yes—
95#2551C2212yes—
96#2551C2214yes—
97#2551C2214yes—
98#2550C2214yes—
99#2550C2214yes—
100#2550C2214yes—
101#2550C2218yes—
102#2546C2211yescharacteristic
103#2546C2218yes—
104#2542C2214yes—
105#2538C2211yescharacteristic
106#2538C2212yes—
107#2511C2214yes—
108#2511C2212yes—
109#2509C2214yes—
110#2509C2214yes—
111#2509C2212yes—
112#2508C2214yes—
113#2508C2214yes—
114#2508C2212yes—
115#2507C2214yes—
116#2507C2214yes—
117#2506C2214yes—
118#2506C2214yes—
119#2497C2214yes—
120#2497C2214yes—
121#2497C2212yes—
122#2492C2214yes—
123#2492C2214yes—
124#2465C2218yes—
125#2462C2218yes—
126#2462C2218yes—
127#2454C2212yes—
128#2453C2212yes—
129#2452C2214yes—
130#2451C2214yes—
131#2451C2214yes—
132#2446C2214yes—
133#2446C2212yes—
134#2441C2218yes—
135#2441C2214yes—
136#2440C2214yes—
137#2439C2214yes—
138#2438C2218yes—
139#2429C2218yes—
140#2423C2214yes—
141#2423C2214yes—
142#2423C2212yes—
143#2402C2214yes—
144#2396C2214yes—
145#2378C2218yes—
146#2370C2214yes—
147#2370C2212yes—
148#2369C2211yescharacteristic
149#2369C2212yes—
150#2369C2212yes—
151#2368C2214yes—
152#2365C2214yes—
153#2365C2214yes—
154#2365C2212yes—
155#2362C2214yes—
156#2360C2212yes—
157#2355C2212yes—
158#2355C2214yes—
159#2355C2211yescharacteristic
160#2354C2214yes—
161#2354C2212yes—
162Q8×C4⋊C4C2212yes—
163Q8×C4⋊C4C2212yes—
164Q8×C4⋊C4C2212yes—
165Q8×C4⋊C4C2212yes—
166Q8×C4⋊C4C2212yes—
167#2349C2212yes—
168D4×C4⋊C4C2211yescharacteristic
169#2345C2212yes—
170#2344C2214yes—
171#2331C2214yes—
172#2330C2214yes—
173#2323C2214yes—
174#2323C2218yes—
175#2319C2214yes—
176#2316C2214yes—
177C4×C4⋊Q8C2212yes—
178C4×C4⋊Q8C2212yes—
179C4×C4⋊Q8C2212yes—
180C4×C4⋊Q8C2211yescharacteristic
181C4×C4⋊Q8C2211yescharacteristic
182C4×C4⋊Q8C2211yescharacteristic
183C4×#125C2212yes—
184C4×#125C2212yes—
185C4×#125C2212yes—
186C4×C22⋊Q8C2212yes—
187C4×C22⋊Q8C2212yes—
188C4×C22⋊Q8C2214yes—
189#2295C2212yes—
190#2295C2212yes—
191#2293C2212yes—
192#2285C2212yes—
193#2285C2212yes—
194C42×Q8C2211yescharacteristic
195C42×Q8C2211yescharacteristic
196C42×D4C2212yes—
197C42×D4C2211yescharacteristic
198C2×C4×C4⋊C4C2212yes—
199Q82—48no—
200Q82—48no—
201#554Q8116yescomplemented
202#544—416no—
203#533—416no—
204C2×C4⋊Q8C2311yescharacteristic
205C2×C4⋊Q8C2311yescharacteristic
206C2×C4⋊Q8C2312yes—
207C2×C4⋊Q8C2314yes—
208C2×C4⋊Q8C2312yes—
209C2×C4⋊Q8C2314yes—
210C2×C4⋊Q8C2314yes—
211C2×C4⋊Q8C2314yes—
212C2×C4⋊Q8C2312yes—
213C2×C4⋊Q8C2312yes—
214C2×C4⋊Q8C2314yes—
215C2×C4⋊Q8C2314yes—
216C2×C4⋊Q8C2314yes—
217C2×C4⋊Q8C2314yes—
218C2×C4⋊Q8C2318yes—
219C2×C4⋊Q8C2318yes—
220C2×C4⋊Q8C2318yes—
221C2×C4⋊Q8C2311yescharacteristic
222C2×#125C2312yes—
223C2×#125C2312yes—
224C2×#125C2314yes—
225C2×#125C2318yes—
226C2×#125C2318yes—
227C2×#125C2312yes—
228C2×C22⋊Q8C2312yes—
229C2×C22⋊Q8C2314yes—
230C2×C22⋊Q8C2318yes—
231C2×C22⋊Q8C2318yes—
232C2×C22⋊Q8C2318yes—
233C2×C22⋊Q8C2312yes—
234C2×C22⋊Q8C2314yes—
235C2×C4×Q8C2311yescharacteristic
236C2×C4×Q8C2312yes—
237C2×C4×Q8C2311yescharacteristic
238C2×C4×Q8C2311yescharacteristic
239C2×C4×Q8C2314yes—
240C2×C4×Q8C2311yescharacteristic
241C2×C4×Q8C2311yescharacteristic
242C2×C4×Q8C2314yes—
243C2×C4×Q8C2312yes—
244C2×C4×Q8C2312yes—
245C2×C4×Q8C2314yes—
246C2×C4×Q8C2314yes—
247C2×C4×Q8C2314yes—
248C2×C4×Q8C2318yes—
249C2×C4×Q8C2311yescharacteristic
250C2×C4×D4C2311yescharacteristic
251C2×C4×D4C2311yescharacteristic
252C2×C4×D4C2312yes—
253C2×C4×D4C2312yes—
254C2×C4×D4C2311yescharacteristic
255C2×#117C2314yes—
256C2×#117C2314yes—
257C2×#117C2318yes—
258C22×C4⋊C4C2312yes—
259C22×C4⋊C4C2312yes—
260C22×C42C2312yes—
261C22×C42C2314yes—
262#400C2314yes—
263#400C2318yes—
264#400C2318yes—
265#400C2318yes—
266#400C2318yes—
267#400C2314yes—
268#400C2318yes—
269#400C2314yes—
270#400C2318yes—
271#400C2314yes—
272#400C2314yes—
273#399C2318yes—
274#399C2314yes—
275#399C2318yes—
276#398C2318yes—
277#398C2318yes—
278#398C2318yes—
279#398C2314yes—
280#398C2318yes—
281#398C2314yes—
282#398C2318yes—
283#398C2314yes—
284#398C2314yes—
285#398C2318yes—
286#398C2318yes—
287#398C2318yes—
288#398C2314yes—
289#398C2314yes—
290#398C2318yes—
291#398C2318yes—
292#398C2318yes—
293#396C2314yes—
294#396C2314yes—
295#396C2318yes—
296#396C2318yes—
297#395C2314yes—
298#395C2318yes—
299#395C2318yes—
300#395C2318yes—
301#395C2318yes—
302#395C2318yes—
303#395C2318yes—
304#395C2318yes—
305#395C2318yes—
306#395C2318yes—
307#395C2318yes—
308#395C2318yes—
309#395C2318yes—
310#393C2314yes—
311#393C2318yes—
312#393C2318yes—
313#391C2312yes—
314#391C2312yes—
315#391C2314yes—
316#391C2314yes—
317#391C2312yes—
318#391C2312yes—
319#391C2312yes—
320#391C2312yes—
321#391C2312yes—
322#391C2312yes—
323#391C2314yes—
324#391C2314yes—
325#391C2312yes—
326#391C2312yes—
327#391C2318yes—
328#391C2314yes—
329#391C2318yes—
330#391C2318yes—
331#391C2312yes—
332#391C2318yes—
333#391C2318yes—
334#391C2318yes—
335#390C2312yes—
336#390C2314yes—
337#390C2312yes—
338#389C2312yes—
339#389C2312yes—
340#389C2312yes—
341#389C2312yes—
342#389C2312yes—
343#389C2312yes—
344#389C2314yes—
345#389C2314yes—
346#389C2312yes—
347#389C2312yes—
348#389C2312yes—
349#389C2312yes—
350#389C2314yes—
351#389C2314yes—
352#389C2314yes—
353#389C2312yes—
354#389C2314yes—
355#389C2312yes—
356#389C2314yes—
357#389C2314yes—
358#389C2314yes—
359#389C2318yes—
360#389C2318yes—
361#389C2318yes—
362#389C2318yes—
363#389C2318yes—
364#389C2314yes—
365#389C2314yes—
366#389C2314yes—
367#389C2318yes—
368#389C2312yes—
369#389C2314yes—
370#389C2314yes—
371#389C2312yes—
372#389C2318yes—
373#389C2314yes—
374#389C2318yes—
375#389C2318yes—
376#389C2318yes—
377#389C2314yes—
378#389C2312yes—
379#389C2318yes—
380#389C2314yes—
381#389C2318yes—
382#389C2312yes—
383#389C2312yes—
384#389C2312yes—
385#389C2312yes—
386#389C2314yes—
387#389C2318yes—
388#389C2314yes—
389#389C2312yes—
390#388C2314yes—
391#388C2314yes—
392#388C2318yes—
393#388C2318yes—
394#388C2318yes—
395#388C2318yes—
396#388C2318yes—
397#387C2314yes—
398#387C2314yes—
399#387C2314yes—
400#387C2314yes—
401#387C2314yes—
402#387C2314yes—
403#387C2318yes—
404#387C2318yes—
405#387C2318yes—
406#387C2314yes—
407#387C2314yes—
408#387C2318yes—
409#387C2318yes—
410#387C2318yes—
411#387C2318yes—
412#387C2314yes—
413#387C2318yes—
414#387C2318yes—
415#387C2314yes—
416#387C2314yes—
417#387C2314yes—
418#387C2318yes—
419#387C2318yes—
420#387C2318yes—
421#387C2314yes—
422#387C2314yes—
423#387C2318yes—
424#387C2318yes—
425#387C2318yes—
426#385C2314yes—
427#385C2318yes—
428#385C2314yes—
429#385C2314yes—
430#385C2314yes—
431#384C2312yes—
432#384C2311yescharacteristic
433#384C2312yes—
434#384C2311yescharacteristic
435#384C2311yescharacteristic
436#384C2312yes—
437#384C2314yes—
438#384C2312yes—
439#384C2314yes—
440#384C2314yes—
441#384C2312yes—
442#384C2314yes—
443#384C2314yes—
444#384C2312yes—
445#384C2314yes—
446#384C2314yes—
447#384C2312yes—
448#384C2314yes—
449#382C2312yes—
450#382C2312yes—
451#382C2312yes—
452#382C2314yes—
453#382C2314yes—
454#382C2314yes—
455#382C2318yes—
456#381C2318yes—
457#380C2312yes—
458#380C2312yes—
459#380C2314yes—
460#380C2314yes—
461#380C2318yes—
462#380C2318yes—
463#380C2314yes—
464#380C2314yes—
465#380C2314yes—
466#380C2312yes—
467#380C2312yes—
468#380C2314yes—
469C4×C4⋊C4C2311yescharacteristic
470C4×C4⋊C4C2311yescharacteristic
471C4×C4⋊C4C2311yescharacteristic
472C4×C4⋊C4C2312yes—
473C4×C4⋊C4C2312yes—
474C4×C4⋊C4C2312yes—
475C4×C4⋊C4C2314yes—
476C4×C4⋊C4C2314yes—
477C4×C4⋊C4C2314yes—
478C4×C4⋊C4C2314yes—
479C4×C4⋊C4C2314yes—
480C4×C4⋊C4C2314yes—
481C4×C4⋊C4C2312yes—
482C4×C4⋊C4C2314yes—
483C4×C4⋊C4C2314yes—
484C4×C4⋊C4C2314yes—
485C4×C4⋊C4C2314yes—
486C4×C4⋊C4C2314yes—
487C4×C4⋊C4C2312yes—
488C4×C4⋊C4C2312yes—
489C4×C4⋊C4C2311yescharacteristic
490C4×C4⋊C4C2312yes—
491C4×C4⋊C4C2312yes—
492C4×C4⋊C4C2311yescharacteristic
493C4×C4⋊C4C2311yescharacteristic
494C4×C4⋊C4C2311yescharacteristic
495C4×C4⋊C4C2314yes—
496C4×C4⋊C4C2318yes—
497C4×C4⋊C4C2314yes—
498C4×C4⋊C4C2314yes—
499C4×C4⋊C4C2314yes—
500C4×C4⋊C4C2312yes—
501C4×C4⋊C4C2312yes—
502C4×C4⋊C4C2312yes—
503C4×C4⋊C4C2314yes—
504C4×C4⋊C4C2312yes—
505C4×C4⋊C4C2312yes—
506C4×C4⋊C4C2314yes—
507C4×C4⋊C4C2311yescharacteristic
508C4×C4⋊C4C2312yes—
509C4×C4⋊C4C2312yes—
510C4×C4⋊C4C2312yes—
511C4×C4⋊C4C2311yescharacteristic
512C4×C22⋊C4C2312yes—
513C4×C22⋊C4C2314yes—
514C4×C22⋊C4C2312yes—
515C4×C22⋊C4C2314yes—
516C4×C22⋊C4C2314yes—
517C4×C22⋊C4C2314yes—
518C4×C22⋊C4C2312yes—
519#376C2314yes—
520C2×#95C2314yes—
521C43C2312yes—
522C43C2312yes—
523C43C2311yescharacteristic
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—28no—
539C4⋊Q8—216no—
540C4⋊Q8—24no—
541C4⋊Q8—24no—
542C4⋊Q8—48no—
543C4⋊Q8—44no—
544C4⋊Q8—48no—
545C4⋊Q8—48no—
546C4⋊Q8—48no—
547C4⋊Q8—48no—
548C4⋊Q8—416no—
549C4⋊Q8—44no—
550C4⋊Q8—48no—
551C4⋊Q8—44no—
552C4⋊Q8—48no—
553C4⋊Q8—416no—
554C4⋊Q8—416no—
555C4⋊Q8C2×Q818yes—
556#125—28no—
557#125—44no—
558#125—48no—
559#125—416no—
560#125—416no—
561#125C2×Q8116yes—
562C22⋊Q8—28no—
563C22⋊Q8—416no—
564C22⋊Q8—416no—
565C22⋊Q8—48no—
566C22⋊Q8—416no—
567C22⋊Q8C2×Q8132yes—
568C22⋊Q8C2×Q8116yes—
569C4×Q8—216no—
570C4×Q8—24no—
571C4×Q8—24no—
572C4×Q8—24no—
573C4×Q8—24no—
574C4×Q8—24no—
575C4×Q8—28no—
576C4×Q8—44no—
577C4×Q8—48no—
578C4×Q8—44no—
579C4×Q8—416no—
580C4×Q8—48no—
581C4×Q8—48no—
582C4×Q8—48no—
583C4×Q8C2×Q818yes—
584C4×D4—24no—
585C4×D4—42no—
586C4×D4—44no—
587C4×D4C2×Q8116yes—
588C4×D4C2×Q818yes—
589#117—48no—
590#117—416no—
591#117—48no—
592C2×C4⋊C4—28no—
593C2×C4⋊C4C2×Q8116yes—
594C2×C4⋊C4C2412yes—
595C2×C4⋊C4C2414yes—
596C2×C4⋊C4C2412yes—
597C2×C4⋊C4C2414yes—
598C2×C4⋊C4C2414yes—
599C2×C4⋊C4C2411yescharacteristic
600C2×C4⋊C4C2412yes—
601C2×C4⋊C4C2411yescharacteristic
602C2×C4⋊C4C2414yes—
603C2×C4⋊C4C2414yes—
604C2×C4⋊C4C2412yes—
605C2×C4⋊C4C2418yes—
606C2×C4⋊C4C2418yes—
607C2×C4⋊C4C2414yes—
608C2×C4⋊C4C2411yescharacteristic
609C2×C4⋊C4C2412yes—
610C2×C4⋊C4C2412yes—
611C2×C4⋊C4C2411yescharacteristic
612C2×C4⋊C4C2411yescharacteristic
613C2×C4⋊C4C2412yes—
614C2×C4⋊C4C2411yescharacteristic
615C2×C4⋊C4C2412yes—
616C2×C4⋊C4C2412yes—
617C2×C4⋊C4C2412yes—
618C2×C4⋊C4C2414yes—
619C2×C4⋊C4C2414yes—
620C2×C4⋊C4C2414yes—
621C2×C4⋊C4C2412yes—
622C2×C4⋊C4C2414yes—
623C2×C4⋊C4C2412yes—
624C2×C4⋊C4C2412yes—
625C2×C4⋊C4C2412yes—
626C2×C4⋊C4C2412yes—
627C2×C4⋊C4C2414yes—
628C2×C4⋊C4C2418yes—
629C2×C4⋊C4C2414yes—
630C2×C4⋊C4C2418yes—
631C2×C4⋊C4C2418yes—
632C2×C4⋊C4C2414yes—
633C2×C4⋊C4C2418yes—
634C2×C4⋊C4C2412yes—
635C2×C4⋊C4C2414yes—
636C2×C4⋊C4C2414yes—
637C2×C4⋊C4C2412yes—
638C2×C4⋊C4C2418yes—
639C2×C4⋊C4C2414yes—
640C2×C4⋊C4C2418yes—
641C2×C4⋊C4C2418yes—
642C2×C4⋊C4C2418yes—
643C2×C4⋊C4C2414yes—
644C2×C4⋊C4C2414yes—
645C2×C4⋊C4C2414yes—
646C2×C4⋊C4C2418yes—
647C2×C4⋊C4C2418yes—
648C2×C4⋊C4C2412yes—
649C2×C4⋊C4C2414yes—
650C2×C4⋊C4C2414yes—
651C2×C4⋊C4C2418yes—
652C2×C4⋊C4C2414yes—
653C2×C4⋊C4C2414yes—
654C2×C4⋊C4C2411yescharacteristic
655C2×C4⋊C4C2414yes—
656C2×C4⋊C4C2412yes—
657C2×C4⋊C4C2411yescharacteristic
658C2×C4⋊C4C2412yes—
659C2×C4⋊C4C2412yes—
660C2×C4⋊C4C2414yes—
661C2×C4⋊C4C2411yescharacteristic
662C2×C22⋊C4C2414yes—
663C2×C22⋊C4C2412yes—
664C2×C22⋊C4C2414yes—
665C2×C22⋊C4C2418yes—
666C2×C22⋊C4C2414yes—
667C2×C22⋊C4C2418yes—
668C2×C22⋊C4C2412yes—
669C2×C22⋊C4C2414yes—
670C2×C22⋊C4C2414yes—
671C2×C22⋊C4C2414yes—
672C2×C22⋊C4C2412yes—
673C2×C42—28no—
674C2×C42—48no—
675C2×C42C2412yes—
676C2×C42C2418yes—
677C2×C42C2414yes—
678C2×C42C2412yes—
679C2×C42C2411yescharacteristic
680C2×C42C2411yescharacteristic
681C2×C42C2411yescharacteristic
682C2×C42C2412yes—
683C2×C42C2412yes—
684C2×C42C2414yes—
685C2×C42C2412yes—
686C2×C42C2412yes—
687C2×C42C2412yes—
688C2×C42C2414yes—
689C2×C42C2412yes—
690C2×C42C2412yes—
691C2×C42C2412yes—
692C2×C42C2412yes—
693C2×C42C2412yes—
694C2×C42C2418yes—
695C2×C42C2418yes—
696C2×C42C2418yes—
697C2×C42C2414yes—
698C2×C42C2414yes—
699C2×C42C2411yescharacteristic
700C2×C42C2412yes—
701C2×C42C2412yes—
702C2×C42C2412yes—
703C2×C42C2411yescharacteristic
704C2×C42C2411yescharacteristic
705C2×C42C2411yescharacteristic
706#95C2412yes—
707#95C2414yes—
708#95C2414yes—
709#95C2414yes—
710#95C2414yes—
711#95C2414yes—
712#95C2414yes—
713#95C2414yes—
714#95C2412yes—
715#95C2414yes—
716#95C2412yes—
717#95C2414yes—
718#95C2414yes—
719#95C2412yes—
720#95C2414yes—
721#95C2414yes—
722#95C2412yes—
723#95C2412yes—
724#95C2412yes—
725#95C2412yes—
726#95C2414yes—
727#95C2412yes—
728#95C2418yes—
729#95C2418yes—
730#95C2414yes—
731#95C2414yes—
732#95C2414yes—
733#95C2414yes—
734#95C2418yes—
735#95C2414yes—
736#95C2418yes—
737#95C2418yes—
738#95C2418yes—
739#95C2418yes—
740#95C2418yes—
741#95C2414yes—
742#95C2414yes—
743#95C2414yes—
744#95C2414yes—
745#95C2414yes—
746#95C2418yes—
747#95C2414yes—
748#95C2414yes—
749#95C2414yes—
750#95C2414yes—
751#95C2414yes—
752#95C2418yes—
753#95C2418yes—
754C24C2512yes—
755C2×Q8—22no—
756C2×Q8—24no—
757C2×Q8—216no—
758C2×Q8—22no—
759C2×Q8—22no—
760C2×Q8—22no—
761C2×Q8—24no—
762C2×Q8—24no—
763C2×Q8—24no—
764C2×Q8—42no—
765C2×Q8—42no—
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×Q8—48no—
776C2×Q8C22×Q814yes—
777C2×Q8C22×Q818yes—
778C2×Q8H(5,𝔽2)14yes—
779C2×D4—22no—
780C2×D4—22no—
781C2×D4C22×Q814yes—
782C22×C4—24no—
783C22×C4—24no—
784C22×C4—24no—
785C22×C4—24no—
786C22×C4—24no—
787C22×C4—28no—
788C22×C4—24no—
789C22×C4—44no—
790C22×C4—44no—
791C22×C4—44no—
792C22×C4—42no—
793C22×C4—44no—
794C22×C4—42no—
795C22×C4C22×Q818yes—
796C22×C4C22×Q8116yes—
797C22×C4C2512yes—
798C22×C4C2512yes—
799C22×C4C2512yes—
800C22×C4C2512yes—
801C22×C4C2514yes—
802C22×C4C2514yes—
803C22×C4C2512yes—
804C22×C4C2514yes—
805C22×C4C2512yes—
806C22×C4C2511yescharacteristic
807C22×C4C2518yes—
808C22×C4C2514yes—
809C22×C4C2514yes—
810C22×C4C2512yes—
811C22×C4C2511yescharacteristic
812C22×C4C2512yes—
813C22×C4C2514yes—
814C22×C4C2512yes—
815C22×C4C2512yes—
816C22×C4C2512yes—
817C22×C4C2511yescharacteristic
818C22×C4C2511yescharacteristic
819C22×C4C2511yescharacteristic
820C22×C4C2511yescharacteristic
821C22×C4C2511yescharacteristic
822C4⋊C4—28no—
823C4⋊C4—24no—
824C4⋊C4—24no—
825C4⋊C4—28no—
826C4⋊C4—28no—
827C4⋊C4—216no—
828C4⋊C4—28no—
829C4⋊C4—24no—
830C4⋊C4—24no—
831C4⋊C4—22no—
832C4⋊C4—28no—
833C4⋊C4—24no—
834C4⋊C4—28no—
835C4⋊C4—216no—
836C4⋊C4—28no—
837C4⋊C4—28no—
838C4⋊C4—22no—
839C4⋊C4—24no—
840C4⋊C4—24no—
841C4⋊C4—24no—
842C4⋊C4—22no—
843C4⋊C4—22no—
844C4⋊C4—22no—
845C4⋊C4—24no—
846C4⋊C4—28no—
847C4⋊C4—24no—
848C4⋊C4—24no—
849C4⋊C4—24no—
850C4⋊C4—24no—
851C4⋊C4—22no—
852C4⋊C4—24no—
853C4⋊C4—24no—
854C4⋊C4—28no—
855C4⋊C4—44no—
856C4⋊C4—42no—
857C4⋊C4—44no—
858C4⋊C4—48no—
859C4⋊C4—44no—
860C4⋊C4—44no—
861C4⋊C4—44no—
862C4⋊C4—48no—
863C4⋊C4—44no—
864C4⋊C4—48no—
865C4⋊C4—48no—
866C4⋊C4—44no—
867C4⋊C4—48no—
868C4⋊C4—42no—
869C4⋊C4—44no—
870C4⋊C4—42no—
871C4⋊C4—44no—
872C4⋊C4—48no—
873C4⋊C4—44no—
874C4⋊C4—48no—
875C4⋊C4—48no—
876C4⋊C4—48no—
877C4⋊C4—44no—
878C4⋊C4—44no—
879C4⋊C4—44no—
880C4⋊C4—48no—
881C4⋊C4—48no—
882C4⋊C4C22×Q814yes—
883C4⋊C4C22×Q8116yes—
884C4⋊C4C22×Q818yes—
885C4⋊C4C22×Q814yes—
886C4⋊C4C22×Q818yes—
887C4⋊C4C22×Q818yes—
888C4⋊C4C22×Q8116yes—
889C4⋊C4H(5,𝔽2)14yes—
890C22⋊C4—28no—
891C22⋊C4—24no—
892C22⋊C4—44no—
893C22⋊C4—44no—
894C22⋊C4—44no—
895C22⋊C4—48no—
896C22⋊C4—48no—
897C22⋊C4—44no—
898C22⋊C4—42no—
899C22⋊C4C22×Q8116yes—
900C22⋊C4C22×Q818yes—
901C42—24no—
902C42—28no—
903C42—24no—
904C42—216no—
905C42—28no—
906C42—24no—
907C42—24no—
908C42—22no—
909C42—22no—
910C42—24no—
911C42—24no—
912C42—24no—
913C42—24no—
914C42—24no—
915C42—24no—
916C42—28no—
917C42—22no—
918C42—24no—
919C42—24no—
920C42—44no—
921C42—44no—
922C42—41no—
923C42—42no—
924C42—42no—
925C42—48no—
926C42—48no—
927C42—48no—
928C42C22×Q818yes—
929C42C22×Q814yes—
930C422−1+414yes—
931C422−1+414yes—
932C23—22no—
933C23—22no—
934C23—22no—
935C23—22no—
936C23—22no—
937C23—22no—
938C23C23×Q814yes—
939C23C2611yescharacteristic
940Q8—28no—
941Q8—28no—
942Q8—48no—
943Q8—48no—
944Q8—48no—
945Q8—816no—
946Q8—168no—
947Q8—164no—
948D4—28no—
949C2×C4—24no—
950C2×C4—21no—
951C2×C4—21no—
952C2×C4—22no—
953C2×C4—22no—
954C2×C4—22no—
955C2×C4—22no—
956C2×C4—22no—
957C2×C4—22no—
958C2×C4—22no—
959C2×C4—22no—
960C2×C4—21no—
961C2×C4—22no—
962C2×C4—21no—
963C2×C4—21no—
964C2×C4—22no—
965C2×C4—21no—
966C2×C4—24no—
967C2×C4—216no—
968C2×C4—24no—
969C2×C4—24no—
970C2×C4—22no—
971C2×C4—22no—
972C2×C4—28no—
973C2×C4—24no—
974C2×C4—22no—
975C2×C4—21no—
976C2×C4—21no—
977C2×C4—22no—
978C2×C4—24no—
979C2×C4—24no—
980C2×C4—24no—
981C2×C4—28no—
982C2×C4—24no—
983C2×C4—22no—
984C2×C4—22no—
985C2×C4—22no—
986C2×C4—24no—
987C2×C4—22no—
988C2×C4—22no—
989C2×C4—24no—
990C2×C4—22no—
991C2×C4—24no—
992C2×C4—24no—
993C2×C4—22no—
994C2×C4—21no—
995C2×C4—22no—
996C2×C4—22no—
997C2×C4—22no—
998C2×C4—24no—
999C2×C4—24no—
1000C2×C4—28no—
1001C2×C4—22no—
1002C2×C4—22no—
1003C2×C4—22no—
1004C2×C4—24no—
1005C2×C4—24no—
1006C2×C4—22no—
1007C2×C4—416no—
1008C2×C4—48no—
1009C2×C4—88no—
1010C2×C4—84no—
1011C2×C4C23×Q814yes—
1012C2×C4C23×Q812yes—
1013C2×C4C23×Q814yes—
1014C2×C4C23×Q814yes—
1015C2×C4C23×Q818yes—
1016C2×C4C23×Q812yes—
1017C2×C4C23×Q812yes—
1018C2×C4C2×H(5,𝔽2)14yes—
1019C2×C4C2×H(5,𝔽2)14yes—
1020C2×C4C2×H(5,𝔽2)12yes—
1021C2×C4C2×H(5,𝔽2)12yes—
1022C2×C4C2×2−1+412yes—
1023C2×C4C2×2−1+412yes—
1024C2×C4C2×2−1+412yes—
1025C2×C4C2×2−1+412yes—
1026C2×C4C2×2−1+412yes—
1027C2×C4C2×2−1+412yes—
1028C2×C4#58512yes—
1029C22—24no—
1030C22—24no—
1031C22—24no—
1032C22—42no—
1033C22—42no—
1034C22—42no—
1035C22—42no—
1036C22C24×Q811yescharacteristic
1037C22C22×H(5,𝔽2)11yescharacteristic
1038C22C22×H(5,𝔽2)11yescharacteristic
1039C22C22×2−1+411yescharacteristic
1040C22C22×2−1+411yescharacteristic
1041C22C2×#58511yescharacteristic
1042C222−1+611yescharacteristic
1043C4—24no—
1044C4—28no—
1045C4—22no—
1046C4—24no—
1047C4—24no—
1048C4—24no—
1049C4—24no—
1050C4—22no—
1051C4—22no—
1052C4—42no—
1053C4—44no—
1054C4—44no—
1055C4—44no—
1056C4—48no—
1057C4—42no—
1058C4—41no—
1059C4—42no—
1060C4—44no—
1061C4—44no—
1062C4—42no—
1063C4—42no—
1064C4—42no—
1065C4#350214yes—
1066C4#350314yes—
1067C4#354414yes—
1068C2—44no—
1069C2C2×#354411yescharacteristic
1070C2C2×#350211yescharacteristic
1071C2C2×#350311yescharacteristic
1072C2#6291311yescharacteristic
1073C2#6295911yescharacteristic
1074C2Q8×H(5,𝔽2)11yescharacteristic
1075C2#6301411yescharacteristic
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. #59871C2semidirect
2. #59673C2semidirect
3. #59445C2semidirect
4. #59259C2semidirect
5. #51595C2semidirect
6. #45499C2semidirect
7. #45044C2semidirect
8. #44894C2semidirect
10. #42491C2semidirect
11. #39753C2semidirect
12. #39625C2semidirect
13. #39609C2semidirect
14. #39597C2semidirect
16. Q8×C4⋊Q8C2semidirect
17. Q8×C4⋊Q8C2semidirect
20. #36133C2semidirect
22. #35167C2semidirect
23. #34951C2semidirect
201. #554Q8semidirect

Maximal subgroups

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

subgroupindex
#598712
#596732
#594452
#592592
#515952
#454992
#450442
#448942
#424972
#424912
#397532
#396252
#396092
#395972
#393692
Q8×C4⋊Q82
#361942
#361342
#361332
#351772
#351672
#349512
#349412
#344842
C4×#5542