Finite Group Databasebeta

← #7688521

Subgroups — #7688521

Order 512.

7235 conjugacy classes of subgroups.

The subgroup lattice has 1196 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#3503C212yesmaximal, complemented
2#59832C211yesmaximal, characteristic, complemented
3#59667C212yesmaximal, complemented
4#59314C212yesmaximal, complemented
5#59151C212yesmaximal, complemented
6#59127C214yesmaximal, complemented
7#59113C214yesmaximal, complemented
8#45272C214yesmaximal, complemented
9#43891C218yesmaximal, complemented
10#39597C212yesmaximal, complemented
11#39592C214yesmaximal, complemented
12#39369C212yesmaximal, complemented
13#39368C214yesmaximal, complemented
14#36561C212yesmaximal, complemented
15Q8×C4⋊Q8C211yesmaximal, characteristic, complemented
16#36275C212yesmaximal, complemented
17#36180C211yesmaximal, characteristic, complemented
18#36133C212yesmaximal, complemented
19D4×C4⋊Q8C212yesmaximal, complemented
20D4×C4⋊Q8C211yesmaximal, characteristic, complemented
21#35739C214yesmaximal, complemented
22#34929C211yesmaximal, characteristic, complemented
23C2×#2551C212yesmaximal, complemented
24#34308C212yesmaximal
25C4×#554C211yesmaximal, characteristic, complemented
26C4×#547C211yesmaximal, characteristic
27#3503—232no—
28C2×Q82C2212yes—
29C2×Q82C2212yes—
30C2×#557C2214yes—
31C2×#554C2212yes—
32C2×#554C2214yes—
33C2×#554C2214yes—
34C2×#554C2211yescharacteristic
35C2×D4×Q8C2214yes—
36C2×D4×Q8C2218yes—
37C2×D4×Q8C2212yes—
38C2×#547C2211yescharacteristic
39C2×#544C2218yes—
40C2×#544C2214yes—
41C2×#533C2214yes—
42C2×#533C2212yes—
43C22×C4⋊Q8C2212yes—
44C22×C4⋊Q8C2214yes—
45C22×C4⋊Q8C2214yes—
46C2×#520C2214yes—
47C2×C4×#41C2212yes—
48#2868C2211yescharacteristic
49#2868C2212yes—
50#2857C2212yes—
51#2857C2214yes—
52#2857C2212yes—
53#2855C2214yes—
54#2734C2218yes—
55#2734C2214yes—
56#2726C2218yes—
57#2720C2218yes—
58#2720C2218yes—
59#2713C2218yes—
60#2713C2218yes—
61#2713C2218yes—
62#2677C2218yes—
63#2677C2218yes—
64#2677C2218yes—
65#2628C2214yes—
66#2627C2218yes—
67#2582C2212yes—
68#2581C2214yes—
69#2567C2212yes—
70#2567C2212yes—
71#2567C2214yes—
72#2564C2218yes—
73#2556C2214yes—
74#2556C2218yes—
75#2552C2212yes—
76#2552C2212yes—
77#2551C2214yes—
78#2551C2214yes—
79#2551C2212yes—
80#2551C2214yes—
81#2551C2212yes—
82#2551C2212yes—
83#2551C2211yescharacteristic
84#2551C2218yes—
85#2551C2214yes—
86#2551C2212yes—
87#2551C2214yes—
88#2551C2212yes—
89#2551C2214yes—
90#2551C2212yes—
91#2551C2214yes—
92#2546C2214yes—
93#2546C2212yes—
94#2546C2211yescharacteristic
95#2546C2214yes—
96#2542C2211yescharacteristic
97#2542C2214yes—
98#2538C2211yescharacteristic
99#2506C2214yes—
100#2506C2214yes—
101#2506C2214yes—
102#2506C2212yes—
103#2502C2214yes—
104#2492C2212yes—
105#2492C2214yes—
106#2487C2214yes—
107#2462C2218yes—
108#2462C2218yes—
109#2453C2214yes—
110#2452C2212yes—
111#2452C2214yes—
112#2451C2214yes—
113#2451C2214yes—
114#2451C2214yes—
115#2451C2214yes—
116#2449C2218yes—
117#2449C2218yes—
118#2449C2218yes—
119#2446C2214yes—
120#2441C2214yes—
121#2440C2214yes—
122#2440C2214yes—
123#2440C2214yes—
124#2440C2218yes—
125#2440C2214yes—
126#2440C2214yes—
127#2440C2214yes—
128#2440C2214yes—
129#2440C2214yes—
130#2438C2218yes—
131#2438C2218yes—
132#2438C2218yes—
133#2434C2218yes—
134#2434C2214yes—
135#2434C2218yes—
136#2429C2212yes—
137#2429C2218yes—
138#2423C2214yes—
139#2417C2214yes—
140#2409C2218yes—
141#2396C2214yes—
142C2×#395C2218yes—
143#2370C2212yes—
144#2369C2211yescharacteristic
145#2368C2214yes—
146#2365C2212yes—
147#2365C2211yescharacteristic
148#2365C2214yes—
149#2365C2212yes—
150#2362C2212yes—
151#2361C2214yes—
152#2361C2212yes—
153#2360C2214yes—
154#2360C2214yes—
155#2360C2212yes—
156#2359C2218yes—
157#2359C2214yes—
158#2355C2211yescharacteristic
159#2354C2211yescharacteristic
160Q8×C4⋊C4C2212yes—
161Q8×C4⋊C4C2212yes—
162#2349C2212yes—
163D4×C4⋊C4C2212yes—
164D4×C4⋊C4C2212yes—
165D4×C4⋊C4C2211yescharacteristic
166D4×C4⋊C4C2214yes—
167D4×C4⋊C4C2212yes—
168D4×C4⋊C4C2212yes—
169D4×C4⋊C4C2211yescharacteristic
170#2345C2212yes—
171#2344C2214yes—
172#2344C2212yes—
173#2339C2214yes—
174#2339C2212yes—
175#2323C2214yes—
176#2322C2218yes—
177C4×C4⋊Q8C2212yes—
178C4×C4⋊Q8C2212yes—
179C4×C4⋊Q8C2211yescharacteristic
180C4×C4⋊Q8C2211yescharacteristic
181C4×C4⋊Q8C2211yescharacteristic
182C4×#125C2212yes—
183C4×C22⋊Q8C2212yes—
184C4×C22⋊Q8C2212yes—
185C4×C22⋊Q8C2212yes—
186C4×C22⋊Q8C2214yes—
187C4×#123C2214yes—
188C4×#121C2214yes—
189C4×#121C2212yes—
190#2293C2212yes—
191C2×#389C2214yes—
192C2×#389C2214yes—
193C2×#384C2212yes—
194C42×Q8C2211yescharacteristic
195C42×D4C2212yes—
196C42×D4C2211yescharacteristic
197C42×D4C2211yescharacteristic
198C2×C4×C4⋊C4C2212yes—
199C2×C4×C4⋊C4C2212yes—
200C22×#41C2312yes—
201C23×Q8C2318yes—
202C23×Q8C2314yes—
203Q82—216no—
204Q82—216no—
205#557—232no—
206#554—232no—
207#554—216no—
208#554—232no—
209#554D4116yescomplemented
210D4×Q8—264no—
211D4×Q8—232no—
212D4×Q8—48no—
213#547Q8116yescomplemented
214#544—232no—
215#544—264no—
216#533—232no—
217#533—216no—
218C2×C4⋊Q8—216no—
219C2×C4⋊Q8—232no—
220C2×C4⋊Q8—416no—
221C2×C4⋊Q8C2311yescharacteristic
222C2×C4⋊Q8C2312yes—
223C2×C4⋊Q8C2312yes—
224C2×C4⋊Q8C2314yes—
225C2×C4⋊Q8C2314yes—
226C2×C4⋊Q8C2314yes—
227C2×C4⋊Q8C2312yes—
228C2×C4⋊Q8C2318yes—
229C2×C4⋊Q8C2318yes—
230C2×C4⋊Q8C2314yes—
231C2×C4⋊Q8C2314yes—
232C2×C4⋊Q8C2314yes—
233C2×C4⋊Q8C2314yes—
234C2×C4⋊Q8C2312yes—
235C2×C4⋊Q8C2318yes—
236C2×C4⋊Q8C2318yes—
237C2×C4⋊Q8C2314yes—
238C2×C4⋊Q8C2314yes—
239C2×C4⋊Q8C2312yes—
240C2×C4⋊Q8C2318yes—
241C2×C4⋊Q8C2318yes—
242C2×C4⋊Q8C2314yes—
243C2×C4⋊Q8C2314yes—
244C2×C4⋊Q8C2312yes—
245C2×C4⋊Q8C2311yescharacteristic
246C2×C4⋊Q8C2311yescharacteristic
247C2×#125C2314yes—
248C2×#125C2318yes—
249C2×#125C2314yes—
250C2×#125C2318yes—
251C2×#125C2318yes—
252C2×#125C2312yes—
253C2×#123C2314yes—
254C2×C22⋊Q8C2318yes—
255C2×C22⋊Q8C2314yes—
256C2×C22⋊Q8C2312yes—
257C2×C22⋊Q8C2314yes—
258C2×C22⋊Q8C2312yes—
259C2×C22⋊Q8C2318yes—
260C2×C22⋊Q8C2312yes—
261C2×C22⋊Q8C2318yes—
262C2×C22⋊Q8C2318yes—
263C2×C22⋊Q8C2318yes—
264C2×C22⋊Q8C2318yes—
265C2×C22⋊Q8C2314yes—
266C2×C22⋊Q8C2318yes—
267C2×C22⋊Q8C2318yes—
268C2×C22⋊Q8C2312yes—
269C2×C22⋊Q8C2314yes—
270C2×C22⋊Q8C2312yes—
271C2×#121C2312yes—
272#520—232no—
273C4×#41—216no—
274C2×C4×Q8C2314yes—
275C2×C4×Q8C2312yes—
276C2×C4×Q8C2312yes—
277C2×C4×Q8C2314yes—
278C2×C4×Q8C2311yescharacteristic
279C2×C4×Q8C2314yes—
280C2×C4×Q8C2311yescharacteristic
281C2×C4×Q8C2314yes—
282C2×C4×Q8C2314yes—
283C2×C4×Q8C2312yes—
284C2×C4×Q8C2318yes—
285C2×C4×Q8C2312yes—
286C2×C4×Q8C2311yescharacteristic
287C2×C4×D4C2318yes—
288C2×C4×D4C2312yes—
289C2×C4×D4C2311yescharacteristic
290C2×C4×D4C2312yes—
291C2×C4×D4C2314yes—
292C2×C4×D4C2311yescharacteristic
293C2×C4×D4C2314yes—
294C2×C4×D4C2318yes—
295C2×C4×D4C2311yescharacteristic
296C2×C4×D4C2314yes—
297C2×C4×D4C2314yes—
298C2×C4×D4C2311yescharacteristic
299C2×C4×D4C2312yes—
300C2×C4×D4C2311yescharacteristic
301C2×C4×D4C2311yescharacteristic
302C2×#117C2314yes—
303C2×#117C2314yes—
304C2×#117C2318yes—
305C2×#117C2312yes—
306C22×C4⋊C4C2318yes—
307C22×C4⋊C4C2314yes—
308C22×C4⋊C4C2312yes—
309C22×C4⋊C4C2314yes—
310C22×C4⋊C4C2312yes—
311C22×C4⋊C4C2314yes—
312C22×C4⋊C4C2314yes—
313C22×C4⋊C4C2318yes—
314C22×C4⋊C4C2314yes—
315C22×C4⋊C4C2312yes—
316C22×C4⋊C4C2312yes—
317C22×C42C2314yes—
318C22×C42C2312yes—
319C22×C42C2312yes—
320C22×C42C2314yes—
321#400C2318yes—
322#400C2314yes—
323#400C2318yes—
324#400C2318yes—
325#399C2314yes—
326#399C2318yes—
327#399C2318yes—
328#398C2318yes—
329#398C2318yes—
330#398C2318yes—
331#398C2318yes—
332#398C2318yes—
333#398C2314yes—
334#398C2314yes—
335#398C2318yes—
336#398C2318yes—
337#398C2318yes—
338#398C2318yes—
339#398C2318yes—
340#396C2314yes—
341#396C2314yes—
342#396C2318yes—
343#395C2318yes—
344#395C2318yes—
345#395C2318yes—
346#395C2318yes—
347#395C2318yes—
348#395C2318yes—
349#395C2314yes—
350#395C2318yes—
351#395C2318yes—
352#395C2318yes—
353#395C2318yes—
354#395C2318yes—
355#395C2318yes—
356#395C2318yes—
357#395C2318yes—
358#393C2318yes—
359#393C2314yes—
360#391C2314yes—
361#391C2312yes—
362#391C2312yes—
363#391C2312yes—
364#391C2314yes—
365#391C2314yes—
366#391C2314yes—
367#391C2312yes—
368#391C2314yes—
369#391C2312yes—
370#391C2314yes—
371#391C2318yes—
372#391C2312yes—
373#391C2318yes—
374#391C2314yes—
375#391C2318yes—
376#390C2312yes—
377#390C2312yes—
378#390C2312yes—
379#389C2312yes—
380#389C2312yes—
381#389C2314yes—
382#389C2312yes—
383#389C2312yes—
384#389C2312yes—
385#389C2312yes—
386#389C2312yes—
387#389C2314yes—
388#389C2312yes—
389#389C2312yes—
390#389C2312yes—
391#389C2314yes—
392#389C2314yes—
393#389C2314yes—
394#389C2314yes—
395#389C2314yes—
396#389C2318yes—
397#389C2318yes—
398#389C2318yes—
399#389C2314yes—
400#389C2314yes—
401#389C2314yes—
402#389C2314yes—
403#389C2312yes—
404#389C2314yes—
405#389C2312yes—
406#389C2312yes—
407#389C2314yes—
408#389C2318yes—
409#389C2314yes—
410#389C2314yes—
411#389C2314yes—
412#389C2312yes—
413#389C2318yes—
414#389C2314yes—
415#389C2314yes—
416#389C2318yes—
417#389C2312yes—
418#389C2318yes—
419#389C2312yes—
420#388C2314yes—
421#388C2318yes—
422#388C2318yes—
423#388C2314yes—
424#388C2314yes—
425#388C2314yes—
426#388C2314yes—
427#387C2314yes—
428#387C2314yes—
429#387C2318yes—
430#387C2318yes—
431#387C2318yes—
432#387C2318yes—
433#387C2318yes—
434#387C2318yes—
435#387C2318yes—
436#387C2318yes—
437#387C2318yes—
438#387C2314yes—
439#387C2314yes—
440#387C2314yes—
441#387C2314yes—
442#387C2314yes—
443#387C2314yes—
444#387C2314yes—
445#386C2314yes—
446#386C2318yes—
447#386C2318yes—
448#386C2314yes—
449#385C2318yes—
450#385C2318yes—
451#385C2318yes—
452#385C2318yes—
453#385C2318yes—
454#385C2318yes—
455#385C2314yes—
456#385C2314yes—
457#385C2318yes—
458#385C2318yes—
459#385C2314yes—
460#385C2314yes—
461#385C2314yes—
462#385C2314yes—
463#384C2311yescharacteristic
464#384C2312yes—
465#384C2312yes—
466#384C2311yescharacteristic
467#384C2311yescharacteristic
468#384C2312yes—
469#384C2314yes—
470#384C2314yes—
471#384C2312yes—
472#384C2314yes—
473#384C2312yes—
474#384C2314yes—
475#384C2314yes—
476#384C2314yes—
477#382C2312yes—
478#381C2318yes—
479#381C2314yes—
480#380C2314yes—
481#380C2318yes—
482#380C2314yes—
483#380C2312yes—
484#380C2312yes—
485#380C2314yes—
486#380C2312yes—
487#380C2314yes—
488#380C2314yes—
489#380C2312yes—
490C4×C4⋊C4C2311yescharacteristic
491C4×C4⋊C4C2312yes—
492C4×C4⋊C4C2314yes—
493C4×C4⋊C4C2314yes—
494C4×C4⋊C4C2311yescharacteristic
495C4×C4⋊C4C2312yes—
496C4×C4⋊C4C2314yes—
497C4×C4⋊C4C2312yes—
498C4×C4⋊C4C2312yes—
499C4×C4⋊C4C2314yes—
500C4×C4⋊C4C2314yes—
501C4×C4⋊C4C2312yes—
502C4×C4⋊C4C2312yes—
503C4×C4⋊C4C2311yescharacteristic
504C4×C4⋊C4C2312yes—
505C4×C4⋊C4C2311yescharacteristic
506C4×C4⋊C4C2312yes—
507C4×C4⋊C4C2311yescharacteristic
508C4×C4⋊C4C2312yes—
509C4×C4⋊C4C2314yes—
510C4×C4⋊C4C2311yescharacteristic
511C4×C4⋊C4C2312yes—
512C4×C4⋊C4C2314yes—
513C4×C4⋊C4C2312yes—
514C4×C4⋊C4C2312yes—
515C4×C4⋊C4C2312yes—
516C4×C4⋊C4C2311yescharacteristic
517C4×C4⋊C4C2312yes—
518C4×C4⋊C4C2314yes—
519C4×C4⋊C4C2314yes—
520C4×C4⋊C4C2312yes—
521C4×C4⋊C4C2311yescharacteristic
522C4×C4⋊C4C2311yescharacteristic
523C4×C22⋊C4C2314yes—
524C4×C22⋊C4C2314yes—
525C4×C22⋊C4C2312yes—
526C4×C22⋊C4C2314yes—
527C4×C22⋊C4C2312yes—
528C4×C22⋊C4C2312yes—
529C4×C22⋊C4C2314yes—
530C4×C22⋊C4C2312yes—
531C4×C22⋊C4C2312yes—
532C4×C22⋊C4C2318yes—
533C4×C22⋊C4C2314yes—
534C4×C22⋊C4C2312yes—
535C2×#95C2314yes—
536C2×#95C2314yes—
537C2×#95C2318yes—
538C43C2312yes—
539C43C2311yescharacteristic
540C2×#41—28no—
541C2×#41—28no—
542C2×#41C2×Q8116yescomplemented
543C22×Q8—216no—
544C22×Q8—232no—
545C22×Q8—416no—
546C22×Q8—48no—
547C22×Q8—88no—
548C22×Q8—84no—
549C22×Q8C2412yes—
550C22×Q8C2418yes—
551C22×Q8C2414yes—
552C22×Q8C2411yescharacteristic
553C22×Q8C2412yes—
554C22×Q8C2418yes—
555C22×Q8C2414yes—
556C22×Q8C2418yes—
557C22×Q8C2412yes—
558C22×D4C2411yescharacteristic
559C22×D4C2414yes—
560C22×D4C2411yescharacteristic
561C23×C4C2412yes—
562C23×C4C2414yes—
563C23×C4C2414yes—
564C23×C4C2412yes—
565C23×C4C2412yes—
566C23×C4C2412yes—
567C23×C4C2412yes—
568C23×C4C2414yes—
569C23×C4C2412yes—
570C23×C4C2418yes—
571C23×C4C2418yes—
572C23×C4C2414yes—
573C4⋊Q8—216no—
574C4⋊Q8—28no—
575C4⋊Q8—232no—
576C4⋊Q8—216no—
577C4⋊Q8—28no—
578C4⋊Q8—232no—
579C4⋊Q8—232no—
580C4⋊Q8—216no—
581C4⋊Q8—216no—
582C4⋊Q8—216no—
583C4⋊Q8—232no—
584C4⋊Q8—216no—
585C4⋊Q8—28no—
586C4⋊Q8—216no—
587C4⋊Q8—28no—
588C4⋊Q8—216no—
589C4⋊Q8—24no—
590C4⋊Q8—48no—
591C4⋊Q8—48no—
592C4⋊Q8—44no—
593C4⋊Q8—416no—
594C4⋊Q8—416no—
595C4⋊Q8—82no—
596C4⋊Q8—84no—
597C4⋊Q8C2×D418yes—
598C4⋊Q8C2×Q818yescomplemented
599#125—216no—
600#125—232no—
601#125—232no—
602#125—216no—
603#125—232no—
604#125C2×D4116yes—
605#123C2×Q8132yescomplemented
606C22⋊Q8—28no—
607C22⋊Q8—216no—
608C22⋊Q8—232no—
609C22⋊Q8—216no—
610C22⋊Q8—28no—
611C22⋊Q8—232no—
612C22⋊Q8—232no—
613C22⋊Q8—28no—
614C22⋊Q8—232no—
615C22⋊Q8—232no—
616C22⋊Q8—232no—
617C22⋊Q8—416no—
618C22⋊Q8—48no—
619C22⋊Q8—88no—
620C22⋊Q8C2×D4116yes—
621C22⋊Q8C2×D4132yes—
622C22⋊Q8C2×Q8116yescomplemented
623#121C2×Q8116yescomplemented
624C4×Q8—216no—
625C4×Q8—28no—
626C4×Q8—216no—
627C4×Q8—232no—
628C4×Q8—216no—
629C4×Q8—24no—
630C4×Q8—28no—
631C4×Q8—216no—
632C4×Q8—216no—
633C4×Q8—28no—
634C4×Q8—24no—
635C4×Q8—44no—
636C4×Q8C2×D418yes—
637C4×D4—28no—
638C4×D4—216no—
639C4×D4—28no—
640C4×D4—24no—
641C4×D4—216no—
642C4×D4—232no—
643C4×D4—24no—
644C4×D4—216no—
645C4×D4—232no—
646C4×D4—24no—
647C4×D4—48no—
648C4×D4C2×D418yes—
649C4×D4C2×D4116yes—
650C4×D4C2×Q818yescomplemented
651C4×D4C2×Q818yescomplemented
652#117—28no—
653#117—216no—
654#117—232no—
655#117—216no—
656C2×C4⋊C4—232no—
657C2×C4⋊C4—216no—
658C2×C4⋊C4—216no—
659C2×C4⋊C4—216no—
660C2×C4⋊C4—28no—
661C2×C4⋊C4—28no—
662C2×C4⋊C4—48no—
663C2×C4⋊C4—416no—
664C2×C4⋊C4—84no—
665C2×C4⋊C4C2×D4116yes—
666C2×C4⋊C4C2×Q8116yescomplemented
667C2×C4⋊C4C2418yes—
668C2×C4⋊C4C2414yes—
669C2×C4⋊C4C2414yes—
670C2×C4⋊C4C2412yes—
671C2×C4⋊C4C2412yes—
672C2×C4⋊C4C2414yes—
673C2×C4⋊C4C2414yes—
674C2×C4⋊C4C2418yes—
675C2×C4⋊C4C2418yes—
676C2×C4⋊C4C2414yes—
677C2×C4⋊C4C2418yes—
678C2×C4⋊C4C2418yes—
679C2×C4⋊C4C2418yes—
680C2×C4⋊C4C2412yes—
681C2×C4⋊C4C2414yes—
682C2×C4⋊C4C2412yes—
683C2×C4⋊C4C2414yes—
684C2×C4⋊C4C2414yes—
685C2×C4⋊C4C2414yes—
686C2×C4⋊C4C2412yes—
687C2×C4⋊C4C2414yes—
688C2×C4⋊C4C2411yescharacteristic
689C2×C4⋊C4C2412yes—
690C2×C4⋊C4C2411yescharacteristic
691C2×C4⋊C4C2414yes—
692C2×C4⋊C4C2414yes—
693C2×C4⋊C4C2418yes—
694C2×C4⋊C4C2414yes—
695C2×C4⋊C4C2418yes—
696C2×C4⋊C4C2418yes—
697C2×C4⋊C4C2414yes—
698C2×C4⋊C4C2411yescharacteristic
699C2×C4⋊C4C2412yes—
700C2×C4⋊C4C2412yes—
701C2×C4⋊C4C2414yes—
702C2×C4⋊C4C2412yes—
703C2×C4⋊C4C2412yes—
704C2×C4⋊C4C2412yes—
705C2×C4⋊C4C2418yes—
706C2×C4⋊C4C2418yes—
707C2×C4⋊C4C2418yes—
708C2×C4⋊C4C2418yes—
709C2×C4⋊C4C2414yes—
710C2×C4⋊C4C2414yes—
711C2×C4⋊C4C2412yes—
712C2×C4⋊C4C2414yes—
713C2×C4⋊C4C2414yes—
714C2×C4⋊C4C2418yes—
715C2×C4⋊C4C2414yes—
716C2×C4⋊C4C2412yes—
717C2×C4⋊C4C2412yes—
718C2×C4⋊C4C2412yes—
719C2×C4⋊C4C2411yescharacteristic
720C2×C4⋊C4C2414yes—
721C2×C4⋊C4C2411yescharacteristic
722C2×C4⋊C4C2414yes—
723C2×C4⋊C4C2412yes—
724C2×C4⋊C4C2411yescharacteristic
725C2×C4⋊C4C2412yes—
726C2×C4⋊C4C2414yes—
727C2×C4⋊C4C2411yescharacteristic
728C2×C4⋊C4C2412yes—
729C2×C4⋊C4C2411yescharacteristic
730C2×C4⋊C4C2411yescharacteristic
731C2×C22⋊C4C2418yes—
732C2×C22⋊C4C2414yes—
733C2×C22⋊C4C2414yes—
734C2×C22⋊C4C2414yes—
735C2×C22⋊C4C2414yes—
736C2×C22⋊C4C2412yes—
737C2×C22⋊C4C2412yes—
738C2×C22⋊C4C2414yes—
739C2×C22⋊C4C2412yes—
740C2×C22⋊C4C2414yes—
741C2×C22⋊C4C2418yes—
742C2×C22⋊C4C2414yes—
743C2×C22⋊C4C2414yes—
744C2×C22⋊C4C2414yes—
745C2×C22⋊C4C2412yes—
746C2×C22⋊C4C2412yes—
747C2×C22⋊C4C2412yes—
748C2×C22⋊C4C2414yes—
749C2×C42—216no—
750C2×C42—28no—
751C2×C42—28no—
752C2×C42—48no—
753C2×C42C2412yes—
754C2×C42C2414yes—
755C2×C42C2414yes—
756C2×C42C2418yes—
757C2×C42C2418yes—
758C2×C42C2412yes—
759C2×C42C2414yes—
760C2×C42C2414yes—
761C2×C42C2411yescharacteristic
762C2×C42C2414yes—
763C2×C42C2412yes—
764C2×C42C2411yescharacteristic
765C2×C42C2411yescharacteristic
766C2×C42C2412yes—
767C2×C42C2412yes—
768C2×C42C2412yes—
769C2×C42C2412yes—
770C2×C42C2412yes—
771C2×C42C2412yes—
772C2×C42C2412yes—
773C2×C42C2411yescharacteristic
774C2×C42C2412yes—
775C2×C42C2414yes—
776C2×C42C2414yes—
777C2×C42C2412yes—
778C2×C42C2411yescharacteristic
779C2×C42C2411yescharacteristic
780C2×C42C2411yescharacteristic
781#95C2412yes—
782#95C2414yes—
783#95C2412yes—
784#95C2418yes—
785#95C2414yes—
786#95C2414yes—
787#95C2414yes—
788#95C2414yes—
789#95C2414yes—
790#95C2414yes—
791#95C2418yes—
792#95C2418yes—
793#95C2412yes—
794#95C2414yes—
795#95C2414yes—
796#95C2412yes—
797#95C2412yes—
798#95C2412yes—
799#95C2412yes—
800#95C2414yes—
801#95C2418yes—
802#95C2414yes—
803#95C2414yes—
804#95C2414yes—
805#95C2412yes—
806#95C2412yes—
807#95C2414yes—
808#95C2414yes—
809#95C2418yes—
810#95C2418yes—
811#95C2414yes—
812#95C2414yes—
813#95C2414yes—
814#95C2414yes—
815#95C2414yes—
816#95C2418yes—
817#95C2418yes—
818#95C2418yes—
819C24C2512yes—
820C24C2512yes—
821#41—264no—
822C2×Q8—24no—
823C2×Q8—24no—
824C2×Q8—216no—
825C2×Q8—28no—
826C2×Q8—216no—
827C2×Q8—216no—
828C2×Q8—28no—
829C2×Q8—216no—
830C2×Q8—28no—
831C2×Q8—22no—
832C2×Q8—22no—
833C2×Q8—24no—
834C2×Q8—24no—
835C2×Q8—24no—
836C2×Q8—42no—
837C2×Q8—42no—
838C2×Q8—44no—
839C2×Q8—48no—
840C2×Q8—44no—
841C2×Q8—48no—
842C2×Q8—48no—
843C2×Q8—48no—
844C2×Q8—48no—
845C2×Q8—44no—
846C2×Q8—864no—
847C2×Q8—832no—
848C2×Q8C22×D414yes—
849C2×Q8C22×D418yes—
850C2×Q8C22×Q818yes—
851C2×D4—28no—
852C2×D4—28no—
853C2×D4—22no—
854C2×D4—22no—
855C2×D4C22×D414yes—
856C2×D4C22×Q814yes—
857C2×D4C22×Q8116yes—
858C2×D4C22×Q814yes—
859C2×D42−1+414yes—
860C22×C4—28no—
861C22×C4—28no—
862C22×C4—24no—
863C22×C4—24no—
864C22×C4—24no—
865C22×C4—24no—
866C22×C4—24no—
867C22×C4—24no—
868C22×C4—28no—
869C22×C4—28no—
870C22×C4—24no—
871C22×C4—216no—
872C22×C4—24no—
873C22×C4—24no—
874C22×C4—28no—
875C22×C4—24no—
876C22×C4—24no—
877C22×C4—28no—
878C22×C4—24no—
879C22×C4—24no—
880C22×C4—216no—
881C22×C4—44no—
882C22×C4—44no—
883C22×C4—42no—
884C22×C4—44no—
885C22×C4—42no—
886C22×C4—44no—
887C22×C4—48no—
888C22×C4—48no—
889C22×C4—48no—
890C22×C4—48no—
891C22×C4C22×D418yes—
892C22×C4C22×D4116yes—
893C22×C4C22×Q818yes—
894C22×C4C22×Q8116yes—
895C22×C4C22×Q818yes—
896C22×C4C2512yes—
897C22×C4C2512yes—
898C22×C4C2514yes—
899C22×C4C2511yescharacteristic
900C22×C4C2514yes—
901C22×C4C2512yes—
902C22×C4C2514yes—
903C22×C4C2518yes—
904C22×C4C2514yes—
905C22×C4C2512yes—
906C22×C4C2512yes—
907C22×C4C2512yes—
908C22×C4C2511yescharacteristic
909C22×C4C2514yes—
910C22×C4C2511yescharacteristic
911C22×C4C2512yes—
912C22×C4C2514yes—
913C22×C4C2512yes—
914C22×C4C2512yes—
915C22×C4C2511yescharacteristic
916C22×C4C2512yes—
917C22×C4C2511yescharacteristic
918C22×C4C2511yescharacteristic
919C22×C4C2511yescharacteristic
920C4⋊C4—216no—
921C4⋊C4—28no—
922C4⋊C4—24no—
923C4⋊C4—28no—
924C4⋊C4—216no—
925C4⋊C4—216no—
926C4⋊C4—28no—
927C4⋊C4—216no—
928C4⋊C4—216no—
929C4⋊C4—28no—
930C4⋊C4—28no—
931C4⋊C4—28no—
932C4⋊C4—24no—
933C4⋊C4—28no—
934C4⋊C4—28no—
935C4⋊C4—216no—
936C4⋊C4—28no—
937C4⋊C4—216no—
938C4⋊C4—28no—
939C4⋊C4—216no—
940C4⋊C4—28no—
941C4⋊C4—24no—
942C4⋊C4—28no—
943C4⋊C4—24no—
944C4⋊C4—28no—
945C4⋊C4—216no—
946C4⋊C4—28no—
947C4⋊C4—24no—
948C4⋊C4—22no—
949C4⋊C4—24no—
950C4⋊C4—22no—
951C4⋊C4—24no—
952C4⋊C4—24no—
953C4⋊C4—22no—
954C4⋊C4—28no—
955C4⋊C4—24no—
956C4⋊C4—24no—
957C4⋊C4—48no—
958C4⋊C4—48no—
959C4⋊C4—48no—
960C4⋊C4—42no—
961C4⋊C4—48no—
962C4⋊C4—44no—
963C4⋊C4—44no—
964C4⋊C4—42no—
965C4⋊C4—44no—
966C4⋊C4—44no—
967C4⋊C4—48no—
968C4⋊C4—42no—
969C4⋊C4—44no—
970C4⋊C4C22×D418yes—
971C4⋊C4C22×D418yes—
972C4⋊C4C22×D414yes—
973C4⋊C4C22×D4116yes—
974C4⋊C4C22×D414yes—
975C4⋊C4C22×D4116yes—
976C4⋊C4C22×D418yes—
977C4⋊C4C22×Q814yes—
978C4⋊C4C22×Q818yes—
979C4⋊C4C22×Q8116yes—
980C4⋊C4C22×Q814yes—
981C4⋊C4C22×Q818yes—
982C4⋊C4H(5,𝔽2)14yes—
983C4⋊C42−1+414yes—
984C22⋊C4—216no—
985C22⋊C4—28no—
986C22⋊C4—24no—
987C22⋊C4—28no—
988C22⋊C4—28no—
989C22⋊C4—28no—
990C22⋊C4—28no—
991C22⋊C4—24no—
992C22⋊C4—24no—
993C22⋊C4—28no—
994C22⋊C4—48no—
995C22⋊C4—44no—
996C22⋊C4—44no—
997C22⋊C4C22×D4116yes—
998C22⋊C4C22×D418yes—
999C22⋊C4C22×Q818yes—
1000C22⋊C4C22×Q818yes—
1001C22⋊C4C22×Q8116yes—
1002C42—24no—
1003C42—24no—
1004C42—28no—
1005C42—28no—
1006C42—28no—
1007C42—24no—
1008C42—216no—
1009C42—216no—
1010C42—28no—
1011C42—24no—
1012C42—28no—
1013C42—22no—
1014C42—24no—
1015C42—24no—
1016C42—24no—
1017C42—24no—
1018C42—22no—
1019C42—24no—
1020C42—22no—
1021C42—24no—
1022C42—44no—
1023C42—44no—
1024C42—41no—
1025C42—42no—
1026C42C22×D414yes—
1027C42C22×D418yes—
1028C42C22×Q814yes—
1029C422−1+414yes—
1030C23—22no—
1031C23—22no—
1032C23—22no—
1033C23—22no—
1034C23—22no—
1035C23—22no—
1036C23—22no—
1037C23—22no—
1038C23—22no—
1039C23—22no—
1040C23C23×D414yes—
1041C23C23×Q814yes—
1042C23C23×Q814yes—
1043C23C2×2−1+414yes—
1044C23C2611yescharacteristic
1045Q8—216no—
1046Q8—28no—
1047Q8—48no—
1048Q8—416no—
1049Q8—432no—
1050Q8—48no—
1051Q8—816no—
1052Q8—88no—
1053Q8—816no—
1054D4—232no—
1055D4—28no—
1056D4D4×Q8116yescomplemented
1057C2×C4—24no—
1058C2×C4—22no—
1059C2×C4—22no—
1060C2×C4—22no—
1061C2×C4—22no—
1062C2×C4—24no—
1063C2×C4—21no—
1064C2×C4—22no—
1065C2×C4—21no—
1066C2×C4—22no—
1067C2×C4—22no—
1068C2×C4—22no—
1069C2×C4—22no—
1070C2×C4—22no—
1071C2×C4—21no—
1072C2×C4—22no—
1073C2×C4—22no—
1074C2×C4—24no—
1075C2×C4—21no—
1076C2×C4—21no—
1077C2×C4—22no—
1078C2×C4—21no—
1079C2×C4—24no—
1080C2×C4—22no—
1081C2×C4—232no—
1082C2×C4—216no—
1083C2×C4—216no—
1084C2×C4—216no—
1085C2×C4—24no—
1086C2×C4—22no—
1087C2×C4—24no—
1088C2×C4—28no—
1089C2×C4—24no—
1090C2×C4—24no—
1091C2×C4—21no—
1092C2×C4—28no—
1093C2×C4—24no—
1094C2×C4—24no—
1095C2×C4—22no—
1096C2×C4—21no—
1097C2×C4—22no—
1098C2×C4—21no—
1099C2×C4—22no—
1100C2×C4—24no—
1101C2×C4—22no—
1102C2×C4—22no—
1103C2×C4—24no—
1104C2×C4—24no—
1105C2×C4—22no—
1106C2×C4—24no—
1107C2×C4—22no—
1108C2×C4—22no—
1109C2×C4—24no—
1110C2×C4—24no—
1111C2×C4—28no—
1112C2×C4—416no—
1113C2×C4—48no—
1114C2×C4—416no—
1115C2×C4—48no—
1116C2×C4—416no—
1117C2×C4—48no—
1118C2×C4—816no—
1119C2×C4—816no—
1120C2×C4C23×D414yes—
1121C2×C4C23×D414yes—
1122C2×C4C23×D412yes—
1123C2×C4C23×D418yes—
1124C2×C4C23×D414yes—
1125C2×C4C23×D412yes—
1126C2×C4C23×D412yes—
1127C2×C4C23×Q812yes—
1128C2×C4C23×Q814yes—
1129C2×C4C23×Q814yes—
1130C2×C4C23×Q818yes—
1131C2×C4C23×Q812yes—
1132C2×C4C23×Q812yes—
1133C2×C4C2×H(5,𝔽2)14yes—
1134C2×C4C2×H(5,𝔽2)12yes—
1135C2×C4C2×2−1+412yes—
1136C2×C4C2×2−1+414yes—
1137C2×C4C2×2−1+412yes—
1138C2×C4C2×2−1+412yes—
1139C2×C4C2×2−1+412yes—
1140C2×C4C2×2−1+412yes—
1141C22—24no—
1142C22—24no—
1143C22—24no—
1144C22—24no—
1145C22—24no—
1146C22—24no—
1147C22—24no—
1148C22—24no—
1149C22—24no—
1150C22—42no—
1151C22—42no—
1152C22—42no—
1153C22—42no—
1154C22C2×D4×Q818yes—
1155C22C24×D411yescharacteristic
1156C22C24×Q811yescharacteristic
1157C22C22×H(5,𝔽2)11yescharacteristic
1158C22C22×2−1+411yescharacteristic
1159C22C22×2−1+411yescharacteristic
1160C22C22×2−1+411yescharacteristic
1161C22H(7,𝔽2)11yescharacteristic
1162C4—24no—
1163C4—24no—
1164C4—22no—
1165C4—28no—
1166C4—22no—
1167C4—24no—
1168C4—24no—
1169C4—24no—
1170C4—24no—
1171C4—22no—
1172C4—24no—
1173C4—28no—
1174C4—44no—
1175C4—48no—
1176C4—44no—
1177C4—41no—
1178C4—44no—
1179C4—42no—
1180C4—44no—
1181C4—42no—
1182C4—42no—
1183C4C2×D4×Q814yes—
1184C4#349914yes—
1185C4#350314yescomplemented
1186C2—28no—
1187C2—44no—
1188C2C22×D4×Q811yescharacteristic
1189C2C2×#350311yescharacteristic
1190C2C2×#349911yescharacteristic
1191C2#6294511yescharacteristic
1192C2D4×H(5,𝔽2)11yescharacteristic
1193C2Q8×2−1+411yescharacteristic
1194C2#6301611yescharacteristic
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. C2×#3503C2semidirect
2. #59832C2semidirect
3. #59667C2semidirect
4. #59314C2semidirect
5. #59151C2semidirect
6. #59127C2semidirect
7. #59113C2semidirect
8. #45272C2semidirect
9. #43891C2semidirect
10. #39597C2semidirect
11. #39592C2semidirect
12. #39369C2semidirect
13. #39368C2semidirect
14. #36561C2semidirect
15. Q8×C4⋊Q8C2semidirect
16. #36275C2semidirect
17. #36180C2semidirect
18. #36133C2semidirect
19. D4×C4⋊Q8C2semidirect
20. D4×C4⋊Q8C2semidirect
21. #35739C2semidirect
22. #34929C2semidirect
23. C2×#2551C2semidirect
25. C4×#554C2semidirect
209. #554D4semidirect
213. #547Q8semidirect
542. C2×#41C2×Q8semidirect
598. C4⋊Q8C2×Q8semidirect
605. #123C2×Q8semidirect
622. C22⋊Q8C2×Q8semidirect
623. #121C2×Q8semidirect
650. C4×D4C2×Q8semidirect
651. C4×D4C2×Q8semidirect
666. C2×C4⋊C4C2×Q8semidirect
1056. D4D4×Q8semidirect
1185. C4#3503semidirect

Maximal subgroups

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

subgroupindex
C2×#35032
#598322
#596672
#593142
#591512
#591272
#591132
#452722
#438912
#395972
#395922
#393692
#393682
#365612
Q8×C4⋊Q82
#362752
#361802
#361332
D4×C4⋊Q82
#357392
#349292
C2×#25512
#343082
C4×#5542
C4×#5472