Finite Group Databasebeta

← #7688293

Subgroups — #7688293

Order 512.

5459 conjugacy classes of subgroups.

The subgroup lattice has 1147 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#59870C211yesmaximal, characteristic, complemented
2#59459C212yesmaximal, complemented
3#59454C214yesmaximal, complemented
4#59322C212yesmaximal, complemented
5#59274C214yesmaximal, complemented
6#59136C212yesmaximal, complemented
7#44997C214yesmaximal, complemented
8#43981C218yesmaximal, complemented
9#39609C212yesmaximal, complemented
10#39604C214yesmaximal, complemented
11#38964C212yesmaximal, complemented
12#38963C214yesmaximal, complemented
13#36563C211yesmaximal, characteristic, complemented
14#36544C212yesmaximal, complemented
15#36290C212yesmaximal, complemented
16#36274C212yesmaximal, complemented
17#36193C212yesmaximal, complemented
18#36180C211yesmaximal, characteristic, complemented
19D4×C4⋊Q8C211yesmaximal, characteristic, complemented
20#35739C214yesmaximal, complemented
21#34941C211yesmaximal, characteristic, complemented
22C2×#2567C212yesmaximal, complemented
23#34308C212yesmaximal
24#34183C212yesmaximal, complemented
25C4×D4×Q8C211yesmaximal, characteristic, complemented
26C4×#547C211yesmaximal, characteristic
27C2×#554C2212yes—
28C2×D4×Q8C2211yescharacteristic
29C2×D4×Q8C2212yes—
30C2×#547C2211yescharacteristic
31C22×C4⋊Q8C2212yes—
32C2×#520C2214yes—
33C2×C4×#41C2212yes—
34C22×C4×Q8C2212yes—
35#2868C2211yescharacteristic
36#2859C2212yes—
37#2857C2212yes—
38#2857C2212yes—
39#2855C2214yes—
40#2851C2214yes—
41#2805C2214yes—
42#2792C2218yes—
43#2792C2218yes—
44#2791C2218yes—
45#2790C2218yes—
46#2774C2218yes—
47#2763C2218yes—
48#2755C2218yes—
49#2742C2218yes—
50#2729C2218yes—
51#2720C2218yes—
52#2628C2214yes—
53#2627C2218yes—
54#2589C2218yes—
55#2586C2218yes—
56#2584C2214yes—
57#2583C2218yes—
58#2582C2212yes—
59#2581C2214yes—
60#2580C2214yes—
61#2574C2214yes—
62#2571C2212yes—
63#2568C2212yes—
64#2567C2212yes—
65#2567C2214yes—
66#2567C2214yes—
67#2567C2214yes—
68#2567C2212yes—
69#2567C2211yescharacteristic
70#2567C2214yes—
71#2567C2214yes—
72#2567C2212yes—
73#2567C2218yes—
74#2564C2218yes—
75#2563C2211yescharacteristic
76#2552C2212yes—
77#2552C2212yes—
78#2552C2211yescharacteristic
79#2552C2212yes—
80#2551C2212yes—
81#2551C2212yes—
82#2550C2214yes—
83#2550C2214yes—
84#2546C2212yes—
85#2538C2211yescharacteristic
86#2520C2218yes—
87#2511C2214yes—
88#2511C2214yes—
89#2509C2214yes—
90#2509C2214yes—
91#2508C2212yes—
92#2508C2214yes—
93#2507C2214yes—
94#2507C2214yes—
95#2507C2214yes—
96#2505C2218yes—
97#2502C2214yes—
98#2497C2212yes—
99#2492C2214yes—
100#2473C2218yes—
101#2465C2218yes—
102#2454C2212yes—
103#2452C2214yes—
104#2451C2214yes—
105#2451C2214yes—
106#2451C2214yes—
107#2450C2218yes—
108#2449C2218yes—
109#2449C2218yes—
110#2442C2214yes—
111#2442C2214yes—
112#2440C2214yes—
113#2440C2214yes—
114#2440C2214yes—
115#2440C2214yes—
116#2440C2214yes—
117#2440C2214yes—
118#2439C2214yes—
119#2438C2218yes—
120#2438C2218yes—
121#2438C2218yes—
122#2434C2214yes—
123#2423C2212yes—
124#2423C2214yes—
125#2417C2214yes—
126#2409C2218yes—
127#2409C2214yes—
128#2396C2214yes—
129C2×#395C2218yes—
130#2370C2214yes—
131#2369C2212yes—
132#2365C2212yes—
133#2365C2211yescharacteristic
134#2365C2211yescharacteristic
135#2365C2212yes—
136#2362C2212yes—
137#2361C2214yes—
138#2361C2212yes—
139#2360C2214yes—
140#2360C2212yes—
141#2360C2214yes—
142#2360C2214yes—
143#2359C2218yes—
144#2359C2214yes—
145#2355C2212yes—
146#2355C2212yes—
147#2354C2211yescharacteristic
148Q8×C4⋊C4C2214yes—
149Q8×C4⋊C4C2211yescharacteristic
150Q8×C4⋊C4C2212yes—
151Q8×C4⋊C4C2212yes—
152#2349C2214yes—
153D4×C4⋊C4C2214yes—
154D4×C4⋊C4C2212yes—
155D4×C4⋊C4C2212yes—
156D4×C4⋊C4C2212yes—
157D4×C4⋊C4C2212yes—
158D4×C4⋊C4C2218yes—
159D4×C4⋊C4C2211yescharacteristic
160D4×C4⋊C4C2211yescharacteristic
161D4×C4⋊C4C2212yes—
162D4×C4⋊C4C2214yes—
163D4×C4⋊C4C2214yes—
164#2344C2214yes—
165#2344C2212yes—
166Q8×C22⋊C4C2212yes—
167#2339C2214yes—
168#2339C2212yes—
169#2323C2214yes—
170#2322C2218yes—
171#2317C2218yes—
172#2317C2214yes—
173C4×C4⋊Q8C2212yes—
174C4×C4⋊Q8C2211yescharacteristic
175C4×C4⋊Q8C2212yes—
176C4×C4⋊Q8C2211yescharacteristic
177C4×C4⋊Q8C2211yescharacteristic
178C4×#125C2212yes—
179C4×C22⋊Q8C2212yes—
180C4×C22⋊Q8C2214yes—
181C4×C22⋊Q8C2212yes—
182C4×C22⋊Q8C2212yes—
183C4×#123C2214yes—
184C4×#121C2212yes—
185C4×#121C2214yes—
186C2×#391C2214yes—
187#2293C2212yes—
188C2×#389C2214yes—
189C2×#389C2214yes—
190#2285C2214yes—
191#2285C2212yes—
192C2×#384C2212yes—
193C2×#384C2214yes—
194C42×Q8C2211yescharacteristic
195C42×D4C2212yes—
196C42×D4C2211yescharacteristic
197C42×D4C2211yescharacteristic
198C2×C4×C4⋊C4C2212yes—
199C22×#41C2312yes—
200C23×Q8C2312yes—
201C23×Q8C2314yes—
202#554—48no—
203D4×Q8—28no—
204D4×Q8—48no—
205#547Q8116yescomplemented
206C2×C4⋊Q8—48no—
207C2×C4⋊Q8C2311yescharacteristic
208C2×C4⋊Q8C2311yescharacteristic
209C2×C4⋊Q8C2312yes—
210C2×C4⋊Q8C2312yes—
211C2×C4⋊Q8C2314yes—
212C2×C4⋊Q8C2314yes—
213C2×C4⋊Q8C2314yes—
214C2×C4⋊Q8C2314yes—
215C2×C4⋊Q8C2312yes—
216C2×C4⋊Q8C2312yes—
217C2×C4⋊Q8C2311yescharacteristic
218C2×#125C2312yes—
219C2×#125C2314yes—
220C2×#125C2314yes—
221C2×#123C2314yes—
222C2×C22⋊Q8C2312yes—
223C2×C22⋊Q8C2312yes—
224C2×C22⋊Q8C2314yes—
225C2×C22⋊Q8C2318yes—
226C2×C22⋊Q8C2314yes—
227C2×C22⋊Q8C2314yes—
228C2×C22⋊Q8C2318yes—
229C2×C22⋊Q8C2318yes—
230C2×C22⋊Q8C2312yes—
231C2×#121C2312yes—
232#520—416no—
233C4×#41—216no—
234C2×C4×Q8—48no—
235C2×C4×Q8C2312yes—
236C2×C4×Q8C2312yes—
237C2×C4×Q8C2311yescharacteristic
238C2×C4×Q8C2311yescharacteristic
239C2×C4×Q8C2311yescharacteristic
240C2×C4×Q8C2312yes—
241C2×C4×Q8C2314yes—
242C2×C4×Q8C2314yes—
243C2×C4×Q8C2312yes—
244C2×C4×Q8C2312yes—
245C2×C4×Q8C2312yes—
246C2×C4×Q8C2314yes—
247C2×C4×Q8C2314yes—
248C2×C4×D4C2311yescharacteristic
249C2×C4×D4C2311yescharacteristic
250C2×C4×D4C2312yes—
251C2×C4×D4C2312yes—
252C2×C4×D4C2314yes—
253C2×C4×D4C2312yes—
254C2×C4×D4C2314yes—
255C2×C4×D4C2311yescharacteristic
256C2×C4×D4C2314yes—
257C2×C4×D4C2318yes—
258C2×C4×D4C2318yes—
259C2×C4×D4C2314yes—
260C2×C4×D4C2311yescharacteristic
261C2×C4×D4C2311yescharacteristic
262C2×C4×D4C2311yescharacteristic
263C2×#117C2314yes—
264C2×#117C2312yes—
265C2×#117C2314yes—
266C2×#117C2318yes—
267C22×C4⋊C4C2312yes—
268C22×C4⋊C4C2318yes—
269C22×C4⋊C4C2314yes—
270C22×C4⋊C4C2312yes—
271C22×C4⋊C4C2314yes—
272C22×C4⋊C4C2314yes—
273C22×C4⋊C4C2314yes—
274C22×C4⋊C4C2314yes—
275C22×C4⋊C4C2314yes—
276C22×C4⋊C4C2318yes—
277C22×C4⋊C4C2312yes—
278C22×C42C2314yes—
279C22×C42C2312yes—
280C22×C42C2312yes—
281C22×C42C2314yes—
282#400C2318yes—
283#400C2318yes—
284#400C2318yes—
285#400C2318yes—
286#400C2314yes—
287#400C2318yes—
288#400C2318yes—
289#399C2314yes—
290#399C2318yes—
291#398C2314yes—
292#398C2318yes—
293#398C2318yes—
294#398C2318yes—
295#398C2318yes—
296#398C2318yes—
297#398C2318yes—
298#398C2318yes—
299#398C2318yes—
300#398C2314yes—
301#398C2318yes—
302#398C2318yes—
303#396C2314yes—
304#396C2314yes—
305#396C2318yes—
306#395C2318yes—
307#395C2314yes—
308#395C2318yes—
309#395C2318yes—
310#395C2318yes—
311#395C2318yes—
312#395C2318yes—
313#395C2318yes—
314#395C2318yes—
315#395C2318yes—
316#395C2318yes—
317#395C2318yes—
318#393C2314yes—
319#393C2318yes—
320#393C2318yes—
321#391C2314yes—
322#391C2312yes—
323#391C2312yes—
324#391C2314yes—
325#391C2312yes—
326#391C2312yes—
327#391C2314yes—
328#391C2314yes—
329#391C2318yes—
330#391C2312yes—
331#391C2314yes—
332#391C2318yes—
333#391C2314yes—
334#391C2314yes—
335#391C2318yes—
336#391C2314yes—
337#391C2312yes—
338#391C2314yes—
339#391C2318yes—
340#390C2312yes—
341#390C2312yes—
342#390C2312yes—
343#389C2312yes—
344#389C2312yes—
345#389C2314yes—
346#389C2312yes—
347#389C2314yes—
348#389C2312yes—
349#389C2312yes—
350#389C2312yes—
351#389C2312yes—
352#389C2312yes—
353#389C2314yes—
354#389C2312yes—
355#389C2312yes—
356#389C2312yes—
357#389C2314yes—
358#389C2318yes—
359#389C2314yes—
360#389C2318yes—
361#389C2314yes—
362#389C2314yes—
363#389C2318yes—
364#389C2314yes—
365#389C2318yes—
366#389C2318yes—
367#389C2318yes—
368#389C2314yes—
369#389C2318yes—
370#389C2318yes—
371#389C2318yes—
372#389C2314yes—
373#389C2314yes—
374#389C2318yes—
375#389C2314yes—
376#389C2314yes—
377#389C2314yes—
378#389C2314yes—
379#389C2314yes—
380#389C2312yes—
381#389C2312yes—
382#389C2312yes—
383#389C2314yes—
384#389C2314yes—
385#389C2314yes—
386#389C2314yes—
387#389C2312yes—
388#389C2312yes—
389#388C2314yes—
390#388C2314yes—
391#388C2318yes—
392#388C2318yes—
393#388C2314yes—
394#388C2314yes—
395#388C2314yes—
396#387C2314yes—
397#387C2314yes—
398#387C2318yes—
399#387C2318yes—
400#387C2314yes—
401#387C2318yes—
402#387C2318yes—
403#387C2318yes—
404#387C2318yes—
405#387C2318yes—
406#387C2314yes—
407#387C2318yes—
408#387C2318yes—
409#387C2318yes—
410#387C2318yes—
411#387C2314yes—
412#387C2314yes—
413#387C2314yes—
414#387C2314yes—
415#387C2314yes—
416#386C2314yes—
417#386C2318yes—
418#386C2318yes—
419#386C2314yes—
420#385C2318yes—
421#385C2318yes—
422#385C2314yes—
423#385C2318yes—
424#385C2318yes—
425#385C2318yes—
426#385C2318yes—
427#385C2318yes—
428#385C2314yes—
429#385C2318yes—
430#385C2318yes—
431#385C2318yes—
432#385C2314yes—
433#385C2318yes—
434#385C2318yes—
435#385C2314yes—
436#385C2314yes—
437#385C2314yes—
438#384C2312yes—
439#384C2311yescharacteristic
440#384C2311yescharacteristic
441#384C2312yes—
442#384C2311yescharacteristic
443#384C2312yes—
444#384C2318yes—
445#384C2314yes—
446#384C2314yes—
447#384C2318yes—
448#384C2314yes—
449#384C2314yes—
450#384C2314yes—
451#384C2312yes—
452#384C2312yes—
453#384C2312yes—
454#384C2312yes—
455#382C2312yes—
456#382C2314yes—
457#382C2314yes—
458#382C2314yes—
459#382C2318yes—
460#382C2314yes—
461#381C2318yes—
462#381C2314yes—
463#380C2312yes—
464#380C2312yes—
465#380C2314yes—
466#380C2318yes—
467#380C2314yes—
468#380C2314yes—
469#380C2312yes—
470#380C2312yes—
471#380C2314yes—
472#380C2312yes—
473#380C2314yes—
474#380C2314yes—
475#380C2312yes—
476#380C2318yes—
477C4×C4⋊C4C2311yescharacteristic
478C4×C4⋊C4C2312yes—
479C4×C4⋊C4C2314yes—
480C4×C4⋊C4C2314yes—
481C4×C4⋊C4C2312yes—
482C4×C4⋊C4C2311yescharacteristic
483C4×C4⋊C4C2312yes—
484C4×C4⋊C4C2312yes—
485C4×C4⋊C4C2314yes—
486C4×C4⋊C4C2314yes—
487C4×C4⋊C4C2312yes—
488C4×C4⋊C4C2312yes—
489C4×C4⋊C4C2314yes—
490C4×C4⋊C4C2311yescharacteristic
491C4×C4⋊C4C2311yescharacteristic
492C4×C4⋊C4C2312yes—
493C4×C4⋊C4C2314yes—
494C4×C4⋊C4C2312yes—
495C4×C4⋊C4C2314yes—
496C4×C4⋊C4C2312yes—
497C4×C4⋊C4C2312yes—
498C4×C4⋊C4C2314yes—
499C4×C4⋊C4C2318yes—
500C4×C4⋊C4C2311yescharacteristic
501C4×C4⋊C4C2311yescharacteristic
502C4×C4⋊C4C2314yes—
503C4×C4⋊C4C2314yes—
504C4×C4⋊C4C2312yes—
505C4×C4⋊C4C2312yes—
506C4×C4⋊C4C2311yescharacteristic
507C4×C4⋊C4C2311yescharacteristic
508C4×C4⋊C4C2311yescharacteristic
509C4×C4⋊C4C2312yes—
510C4×C22⋊C4C2312yes—
511C4×C22⋊C4C2314yes—
512C4×C22⋊C4C2318yes—
513C4×C22⋊C4C2314yes—
514C4×C22⋊C4C2312yes—
515C4×C22⋊C4C2314yes—
516C4×C22⋊C4C2312yes—
517C4×C22⋊C4C2312yes—
518C4×C22⋊C4C2314yes—
519C4×C22⋊C4C2312yes—
520C4×C22⋊C4C2314yes—
521C4×C22⋊C4C2312yes—
522C2×#95C2318yes—
523C2×#95C2314yes—
524C2×#95C2318yes—
525C43C2312yes—
526C43C2311yescharacteristic
527C2×#41—28no—
528C2×#41—28no—
529C2×#41C2×Q8116yes—
530C22×Q8—28no—
531C22×Q8—28no—
532C22×Q8—48no—
533C22×Q8—44no—
534C22×Q8—48no—
535C22×Q8—84no—
536C22×Q8C2412yes—
537C22×Q8C2414yes—
538C22×Q8C2412yes—
539C22×Q8C2411yescharacteristic
540C22×Q8C2412yes—
541C22×Q8C2414yes—
542C22×Q8C2418yes—
543C22×D4C2411yescharacteristic
544C22×D4C2414yes—
545C22×D4C2411yescharacteristic
546C23×C4C2412yes—
547C23×C4C2414yes—
548C23×C4C2412yes—
549C23×C4C2412yes—
550C23×C4C2414yes—
551C23×C4C2412yes—
552C23×C4C2414yes—
553C23×C4C2412yes—
554C23×C4C2412yes—
555C23×C4C2414yes—
556C23×C4C2418yes—
557C23×C4C2418yes—
558C4⋊Q8—28no—
559C4⋊Q8—24no—
560C4⋊Q8—24no—
561C4⋊Q8—28no—
562C4⋊Q8—48no—
563C4⋊Q8—48no—
564C4⋊Q8—48no—
565C4⋊Q8—44no—
566C4⋊Q8—48no—
567C4⋊Q8—82no—
568C4⋊Q8C2×Q818yescomplemented
569#125—28no—
570#125—48no—
571#125—84no—
572#123C2×Q8132yescomplemented
573C22⋊Q8—28no—
574C22⋊Q8—28no—
575C22⋊Q8—216no—
576C22⋊Q8—48no—
577C22⋊Q8—416no—
578C22⋊Q8—416no—
579C22⋊Q8—48no—
580C22⋊Q8—88no—
581C22⋊Q8C2×Q8116yescomplemented
582#121C2×Q8116yescomplemented
583C4×Q8—24no—
584C4×Q8—28no—
585C4×Q8—28no—
586C4×Q8—24no—
587C4×Q8—24no—
588C4×Q8—28no—
589C4×Q8—48no—
590C4×Q8—44no—
591C4×Q8—48no—
592C4×Q8—44no—
593C4×Q8—44no—
594C4×Q8—48no—
595C4×Q8—48no—
596C4×D4—28no—
597C4×D4—28no—
598C4×D4—28no—
599C4×D4—216no—
600C4×D4—24no—
601C4×D4—216no—
602C4×D4—24no—
603C4×D4—216no—
604C4×D4—24no—
605C4×D4—48no—
606C4×D4—416no—
607C4×D4—416no—
608C4×D4C2×Q818yes—
609C4×D4C2×Q818yescomplemented
610C4×D4#4118yes—
611#117—28no—
612#117—216no—
613#117—48no—
614#117—416no—
615C2×C4⋊C4—28no—
616C2×C4⋊C4—44no—
617C2×C4⋊C4—48no—
618C2×C4⋊C4—48no—
619C2×C4⋊C4—48no—
620C2×C4⋊C4—48no—
621C2×C4⋊C4—48no—
622C2×C4⋊C4—416no—
623C2×C4⋊C4—84no—
624C2×C4⋊C4—88no—
625C2×C4⋊C4C2×Q8116yescomplemented
626C2×C4⋊C4C2412yes—
627C2×C4⋊C4C2412yes—
628C2×C4⋊C4C2411yescharacteristic
629C2×C4⋊C4C2412yes—
630C2×C4⋊C4C2414yes—
631C2×C4⋊C4C2412yes—
632C2×C4⋊C4C2412yes—
633C2×C4⋊C4C2414yes—
634C2×C4⋊C4C2414yes—
635C2×C4⋊C4C2414yes—
636C2×C4⋊C4C2412yes—
637C2×C4⋊C4C2414yes—
638C2×C4⋊C4C2412yes—
639C2×C4⋊C4C2414yes—
640C2×C4⋊C4C2414yes—
641C2×C4⋊C4C2411yescharacteristic
642C2×C4⋊C4C2411yescharacteristic
643C2×C4⋊C4C2412yes—
644C2×C4⋊C4C2411yescharacteristic
645C2×C4⋊C4C2412yes—
646C2×C4⋊C4C2411yescharacteristic
647C2×C4⋊C4C2412yes—
648C2×C4⋊C4C2412yes—
649C2×C4⋊C4C2414yes—
650C2×C4⋊C4C2412yes—
651C2×C4⋊C4C2414yes—
652C2×C4⋊C4C2414yes—
653C2×C4⋊C4C2412yes—
654C2×C4⋊C4C2414yes—
655C2×C4⋊C4C2418yes—
656C2×C4⋊C4C2414yes—
657C2×C4⋊C4C2418yes—
658C2×C4⋊C4C2414yes—
659C2×C4⋊C4C2412yes—
660C2×C4⋊C4C2418yes—
661C2×C4⋊C4C2418yes—
662C2×C4⋊C4C2414yes—
663C2×C4⋊C4C2414yes—
664C2×C4⋊C4C2414yes—
665C2×C4⋊C4C2418yes—
666C2×C4⋊C4C2418yes—
667C2×C4⋊C4C2418yes—
668C2×C4⋊C4C2418yes—
669C2×C4⋊C4C2418yes—
670C2×C4⋊C4C2414yes—
671C2×C4⋊C4C2414yes—
672C2×C4⋊C4C2412yes—
673C2×C4⋊C4C2414yes—
674C2×C4⋊C4C2418yes—
675C2×C4⋊C4C2414yes—
676C2×C4⋊C4C2418yes—
677C2×C4⋊C4C2414yes—
678C2×C4⋊C4C2418yes—
679C2×C4⋊C4C2412yes—
680C2×C4⋊C4C2414yes—
681C2×C4⋊C4C2411yescharacteristic
682C2×C4⋊C4C2412yes—
683C2×C4⋊C4C2414yes—
684C2×C4⋊C4C2411yescharacteristic
685C2×C4⋊C4C2412yes—
686C2×C4⋊C4C2411yescharacteristic
687C2×C4⋊C4C2411yescharacteristic
688C2×C22⋊C4C2414yes—
689C2×C22⋊C4C2418yes—
690C2×C22⋊C4C2414yes—
691C2×C22⋊C4C2414yes—
692C2×C22⋊C4C2412yes—
693C2×C22⋊C4C2412yes—
694C2×C22⋊C4C2414yes—
695C2×C22⋊C4C2412yes—
696C2×C22⋊C4C2414yes—
697C2×C22⋊C4C2414yes—
698C2×C22⋊C4C2414yes—
699C2×C22⋊C4C2418yes—
700C2×C22⋊C4C2414yes—
701C2×C22⋊C4C2414yes—
702C2×C22⋊C4C2412yes—
703C2×C22⋊C4C2412yes—
704C2×C22⋊C4C2414yes—
705C2×C22⋊C4C2412yes—
706C2×C42—216no—
707C2×C42—28no—
708C2×C42—28no—
709C2×C42—48no—
710C2×C42C2412yes—
711C2×C42C2412yes—
712C2×C42C2414yes—
713C2×C42C2414yes—
714C2×C42C2414yes—
715C2×C42C2411yescharacteristic
716C2×C42C2412yes—
717C2×C42C2412yes—
718C2×C42C2414yes—
719C2×C42C2414yes—
720C2×C42C2411yescharacteristic
721C2×C42C2412yes—
722C2×C42C2412yes—
723C2×C42C2412yes—
724C2×C42C2412yes—
725C2×C42C2411yescharacteristic
726C2×C42C2412yes—
727C2×C42C2412yes—
728C2×C42C2412yes—
729C2×C42C2418yes—
730C2×C42C2418yes—
731C2×C42C2414yes—
732C2×C42C2414yes—
733C2×C42C2412yes—
734C2×C42C2411yescharacteristic
735C2×C42C2411yescharacteristic
736C2×C42C2411yescharacteristic
737C2×C42C2411yescharacteristic
738#95C2412yes—
739#95C2414yes—
740#95C2414yes—
741#95C2418yes—
742#95C2414yes—
743#95C2414yes—
744#95C2414yes—
745#95C2418yes—
746#95C2418yes—
747#95C2418yes—
748#95C2418yes—
749#95C2418yes—
750#95C2412yes—
751#95C2412yes—
752#95C2412yes—
753#95C2414yes—
754#95C2414yes—
755#95C2412yes—
756#95C2414yes—
757#95C2412yes—
758#95C2414yes—
759#95C2418yes—
760#95C2414yes—
761#95C2414yes—
762#95C2412yes—
763#95C2414yes—
764#95C2412yes—
765#95C2412yes—
766#95C2414yes—
767#95C2418yes—
768#95C2418yes—
769#95C2414yes—
770#95C2414yes—
771#95C2414yes—
772#95C2418yes—
773#95C2414yes—
774#95C2414yes—
775#95C2418yes—
776#95C2414yes—
777#95C2418yes—
778#95C2414yes—
779#95C2418yes—
780C24C2512yes—
781C24C2512yes—
782#41—264no—
783C2×Q8—24no—
784C2×Q8—22no—
785C2×Q8—28no—
786C2×Q8—24no—
787C2×Q8—22no—
788C2×Q8—24no—
789C2×Q8—24no—
790C2×Q8—24no—
791C2×Q8—28no—
792C2×Q8—28no—
793C2×Q8—24no—
794C2×Q8—44no—
795C2×Q8—42no—
796C2×Q8—42no—
797C2×Q8—44no—
798C2×Q8—48no—
799C2×Q8—48no—
800C2×Q8—48no—
801C2×Q8—44no—
802C2×Q8—432no—
803C2×Q8—832no—
804C2×Q8C22×Q818yes—
805C2×Q82−1+414yes—
806C2×D4—28no—
807C2×D4—28no—
808C2×D4—22no—
809C2×D4—22no—
810C2×D4C22×Q814yes—
811C2×D4C22×Q8116yes—
812C2×D4C22×Q814yes—
813C2×D4C2×#4114yes—
814C2×D4H(5,𝔽2)14yes—
815C22×C4—28no—
816C22×C4—28no—
817C22×C4—24no—
818C22×C4—24no—
819C22×C4—24no—
820C22×C4—24no—
821C22×C4—24no—
822C22×C4—24no—
823C22×C4—28no—
824C22×C4—28no—
825C22×C4—24no—
826C22×C4—28no—
827C22×C4—216no—
828C22×C4—24no—
829C22×C4—24no—
830C22×C4—24no—
831C22×C4—24no—
832C22×C4—28no—
833C22×C4—24no—
834C22×C4—24no—
835C22×C4—28no—
836C22×C4—44no—
837C22×C4—42no—
838C22×C4—44no—
839C22×C4—42no—
840C22×C4—44no—
841C22×C4—48no—
842C22×C4—44no—
843C22×C4—48no—
844C22×C4—48no—
845C22×C4—48no—
846C22×C4—48no—
847C22×C4C22×Q818yes—
848C22×C4C22×Q8116yes—
849C22×C4C22×Q818yes—
850C22×C4C2×#4118yes—
851C22×C4C2514yes—
852C22×C4C2512yes—
853C22×C4C2514yes—
854C22×C4C2511yescharacteristic
855C22×C4C2514yes—
856C22×C4C2512yes—
857C22×C4C2512yes—
858C22×C4C2512yes—
859C22×C4C2514yes—
860C22×C4C2518yes—
861C22×C4C2514yes—
862C22×C4C2512yes—
863C22×C4C2511yescharacteristic
864C22×C4C2512yes—
865C22×C4C2514yes—
866C22×C4C2512yes—
867C22×C4C2512yes—
868C22×C4C2511yescharacteristic
869C22×C4C2511yescharacteristic
870C22×C4C2512yes—
871C22×C4C2512yes—
872C22×C4C2511yescharacteristic
873C22×C4C2511yescharacteristic
874C22×C4C2511yescharacteristic
875C4⋊C4—28no—
876C4⋊C4—28no—
877C4⋊C4—24no—
878C4⋊C4—24no—
879C4⋊C4—24no—
880C4⋊C4—22no—
881C4⋊C4—28no—
882C4⋊C4—24no—
883C4⋊C4—24no—
884C4⋊C4—24no—
885C4⋊C4—24no—
886C4⋊C4—22no—
887C4⋊C4—28no—
888C4⋊C4—24no—
889C4⋊C4—24no—
890C4⋊C4—28no—
891C4⋊C4—28no—
892C4⋊C4—28no—
893C4⋊C4—22no—
894C4⋊C4—22no—
895C4⋊C4—28no—
896C4⋊C4—24no—
897C4⋊C4—24no—
898C4⋊C4—22no—
899C4⋊C4—24no—
900C4⋊C4—28no—
901C4⋊C4—28no—
902C4⋊C4—28no—
903C4⋊C4—24no—
904C4⋊C4—44no—
905C4⋊C4—48no—
906C4⋊C4—48no—
907C4⋊C4—48no—
908C4⋊C4—44no—
909C4⋊C4—44no—
910C4⋊C4—44no—
911C4⋊C4—48no—
912C4⋊C4—48no—
913C4⋊C4—48no—
914C4⋊C4—42no—
915C4⋊C4—44no—
916C4⋊C4—48no—
917C4⋊C4—48no—
918C4⋊C4—48no—
919C4⋊C4—44no—
920C4⋊C4—44no—
921C4⋊C4—42no—
922C4⋊C4—44no—
923C4⋊C4—48no—
924C4⋊C4—48no—
925C4⋊C4—44no—
926C4⋊C4—44no—
927C4⋊C4—48no—
928C4⋊C4—42no—
929C4⋊C4—44no—
930C4⋊C4C22×Q814yes—
931C4⋊C4C22×Q818yes—
932C4⋊C4C22×Q8116yes—
933C4⋊C4C22×Q814yes—
934C4⋊C4C22×Q818yes—
935C4⋊C4C2×#4114yes—
936C4⋊C42−1+414yes—
937C22⋊C4—28no—
938C22⋊C4—28no—
939C22⋊C4—28no—
940C22⋊C4—216no—
941C22⋊C4—24no—
942C22⋊C4—28no—
943C22⋊C4—24no—
944C22⋊C4—24no—
945C22⋊C4—28no—
946C22⋊C4—44no—
947C22⋊C4—44no—
948C22⋊C4—48no—
949C22⋊C4—44no—
950C22⋊C4—44no—
951C22⋊C4C22×Q818yes—
952C22⋊C4C22×Q818yes—
953C22⋊C4C22×Q8116yes—
954C22⋊C4C2×#4118yes—
955C42—24no—
956C42—28no—
957C42—24no—
958C42—28no—
959C42—24no—
960C42—28no—
961C42—24no—
962C42—24no—
963C42—24no—
964C42—24no—
965C42—24no—
966C42—28no—
967C42—24no—
968C42—28no—
969C42—22no—
970C42—22no—
971C42—24no—
972C42—22no—
973C42—24no—
974C42—44no—
975C42—44no—
976C42—48no—
977C42—48no—
978C42—42no—
979C42—41no—
980C42C22×Q814yes—
981C42C2×#4114yes—
982C42H(5,𝔽2)14yes—
983C23—22no—
984C23—22no—
985C23—22no—
986C23—22no—
987C23—22no—
988C23—22no—
989C23—22no—
990C23—22no—
991C23—22no—
992C23—22no—
993C23C23×Q814yes—
994C23C23×Q814yes—
995C23C22×#4114yes—
996C23C2×H(5,𝔽2)14yes—
997C23C2611yescharacteristic
998Q8—216no—
999Q8—28no—
1000Q8—416no—
1001Q8—48no—
1002Q8—48no—
1003Q8—88no—
1004Q8—816no—
1005D4—232no—
1006D4—28no—
1007D4#554116yescomplemented
1008C2×C4—22no—
1009C2×C4—22no—
1010C2×C4—24no—
1011C2×C4—22no—
1012C2×C4—22no—
1013C2×C4—22no—
1014C2×C4—22no—
1015C2×C4—21no—
1016C2×C4—24no—
1017C2×C4—22no—
1018C2×C4—21no—
1019C2×C4—21no—
1020C2×C4—22no—
1021C2×C4—22no—
1022C2×C4—21no—
1023C2×C4—21no—
1024C2×C4—21no—
1025C2×C4—22no—
1026C2×C4—232no—
1027C2×C4—216no—
1028C2×C4—216no—
1029C2×C4—216no—
1030C2×C4—24no—
1031C2×C4—22no—
1032C2×C4—22no—
1033C2×C4—24no—
1034C2×C4—22no—
1035C2×C4—22no—
1036C2×C4—24no—
1037C2×C4—22no—
1038C2×C4—24no—
1039C2×C4—24no—
1040C2×C4—21no—
1041C2×C4—22no—
1042C2×C4—24no—
1043C2×C4—24no—
1044C2×C4—28no—
1045C2×C4—22no—
1046C2×C4—22no—
1047C2×C4—28no—
1048C2×C4—24no—
1049C2×C4—21no—
1050C2×C4—22no—
1051C2×C4—22no—
1052C2×C4—21no—
1053C2×C4—22no—
1054C2×C4—24no—
1055C2×C4—24no—
1056C2×C4—24no—
1057C2×C4—22no—
1058C2×C4—24no—
1059C2×C4—22no—
1060C2×C4—22no—
1061C2×C4—22no—
1062C2×C4—24no—
1063C2×C4—24no—
1064C2×C4—24no—
1065C2×C4—28no—
1066C2×C4—48no—
1067C2×C4—416no—
1068C2×C4—416no—
1069C2×C4—48no—
1070C2×C4—48no—
1071C2×C4—88no—
1072C2×C4—816no—
1073C2×C4—168no—
1074C2×C4C23×Q812yes—
1075C2×C4C23×Q814yes—
1076C2×C4C23×Q814yes—
1077C2×C4C23×Q818yes—
1078C2×C4C23×Q812yes—
1079C2×C4C23×Q812yes—
1080C2×C4C22×#4114yes—
1081C2×C4C22×#4112yes—
1082C2×C4C22×#4112yes—
1083C2×C4C22×#4112yes—
1084C2×C4C2×H(5,𝔽2)12yes—
1085C2×C4C2×H(5,𝔽2)12yes—
1086C2×C4C2×H(5,𝔽2)12yes—
1087C2×C4C2×H(5,𝔽2)12yes—
1088C2×C4C2×2−1+414yes—
1089C2×C4C2×2−1+414yes—
1090C2×C4C2×2−1+412yes—
1091C2×C4C2×2−1+412yes—
1092C22—24no—
1093C22—24no—
1094C22—24no—
1095C22—24no—
1096C22—24no—
1097C22—24no—
1098C22—24no—
1099C22—24no—
1100C22—24no—
1101C22—42no—
1102C22—42no—
1103C22—42no—
1104C22—42no—
1105C22C2×#55418yes—
1106C22C24×Q811yescharacteristic
1107C22C23×#4111yescharacteristic
1108C22C22×H(5,𝔽2)11yescharacteristic
1109C22C22×H(5,𝔽2)11yescharacteristic
1110C22C22×2−1+411yescharacteristic
1111C22C22×2−1+411yescharacteristic
1112C22H(7,𝔽2)11yescharacteristic
1113C4—22no—
1114C4—24no—
1115C4—22no—
1116C4—24no—
1117C4—24no—
1118C4—24no—
1119C4—22no—
1120C4—24no—
1121C4—28no—
1122C4—42no—
1123C4—44no—
1124C4—42no—
1125C4—44no—
1126C4—42no—
1127C4—44no—
1128C4—41no—
1129C4—42no—
1130C4—42no—
1131C4—44no—
1132C4—44no—
1133C4—48no—
1134C4C2×#55414yes—
1135C4#350314yes—
1136C4#352014yes—
1137C2—28no—
1138C2—44no—
1139C2C22×#55411yescharacteristic
1140C2C2×#352011yescharacteristic
1141C2C2×#350311yescharacteristic
1142C2#6291211yescharacteristic
1143C2Q8×2−1+411yescharacteristic
1144C2#6300011yescharacteristic
1145C2#6303711yescharacteristic
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. #59870C2semidirect
2. #59459C2semidirect
3. #59454C2semidirect
4. #59322C2semidirect
5. #59274C2semidirect
6. #59136C2semidirect
7. #44997C2semidirect
8. #43981C2semidirect
9. #39609C2semidirect
10. #39604C2semidirect
11. #38964C2semidirect
12. #38963C2semidirect
13. #36563C2semidirect
14. #36544C2semidirect
15. #36290C2semidirect
16. #36274C2semidirect
17. #36193C2semidirect
18. #36180C2semidirect
19. D4×C4⋊Q8C2semidirect
20. #35739C2semidirect
21. #34941C2semidirect
22. C2×#2567C2semidirect
24. #34183C2semidirect
25. C4×D4×Q8C2semidirect
205. #547Q8semidirect
568. C4⋊Q8C2×Q8semidirect
572. #123C2×Q8semidirect
581. C22⋊Q8C2×Q8semidirect
582. #121C2×Q8semidirect
609. C4×D4C2×Q8semidirect
625. C2×C4⋊C4C2×Q8semidirect
1007. D4#554semidirect

Maximal subgroups

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

subgroupindex
#598702
#594592
#594542
#593222
#592742
#591362
#449972
#439812
#396092
#396042
#389642
#389632
#365632
#365442
#362902
#362742
#361932
#361802
D4×C4⋊Q82
#357392
#349412
C2×#25672
#343082
#341832
C4×D4×Q82
C4×#5472