Finite Group Databasebeta

← #7664893

Subgroups — #7664893

Order 512.

5498 conjugacy classes of subgroups.

The subgroup lattice has 1174 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#39498C212yesmaximal, complemented
2#39497C212yesmaximal, complemented
3#38966C212yesmaximal, complemented
4#38964C212yesmaximal, complemented
5#38963C214yesmaximal, complemented
6#38100C214yesmaximal, complemented
7#38098C214yesmaximal, complemented
8#38097C218yesmaximal, complemented
9#37875C214yesmaximal, complemented
10#37874C214yesmaximal, complemented
11#36290C212yesmaximal, complemented
12#36261C212yesmaximal, complemented
13#36215C214yesmaximal
14#36180C212yesmaximal, complemented
15#36165C212yesmaximal, complemented
16#35286C211yesmaximal, characteristic, complemented
17#35275C211yesmaximal, characteristic, complemented
18#35253C212yesmaximal, complemented
19#35253C212yesmaximal, complemented
20#35224C212yesmaximal, complemented
21#35181C211yesmaximal, characteristic, complemented
22D4×#117C211yesmaximal, characteristic
23D4×#117C211yesmaximal, characteristic
24C2×D4×C4⋊C4C211yesmaximal, characteristic
25C4×#544C211yesmaximal, characteristic, complemented
26C2×#2317C212yesmaximal, complemented
27C2×#554C2214yes—
28C2×#544C2211yescharacteristic
29C2×#544C2212yes—
30C22×C4×D4C2212yes—
31C22×C4×D4C2211yescharacteristic
32C22×#117C2212yes—
33C22×#117C2212yes—
34C23×C4⋊C4C2212yes—
35#2868C2212yescomplemented
36#2859C2212yescomplemented
37#2859C2212yescomplemented
38#2859C2212yescomplemented
39#2857C2214yescomplemented
40#2857C2214yescomplemented
41#2851C2214yes—
42#2851C2214yescomplemented
43#2851C2214yescomplemented
44#2848C2218yes—
45#2807C2218yescomplemented
46#2792C2218yescomplemented
47#2791C2218yescomplemented
48#2790C2218yescomplemented
49#2790C2218yescomplemented
50#2788C2218yescomplemented
51#2774C2218yescomplemented
52#2768C2218yescomplemented
53#2763C2218yescomplemented
54#2755C2218yescomplemented
55#2729C2218yescomplemented
56#2720C2218yescomplemented
57#2660C2214yescomplemented
58#2647C2214yescomplemented
59#2646C2214yes—
60#2629C2214yescomplemented
61#2629C2214yescomplemented
62#2628C2214yescomplemented
63#2628C2214yescomplemented
64#2627C2218yes—
65#2584C2214yescomplemented
66#2583C2218yescomplemented
67#2580C2214yes—
68#2579C2218yes—
69#2571C2212yescomplemented
70#2571C2212yescomplemented
71#2571C2212yescomplemented
72#2571C2212yescomplemented
73#2570C2214yescomplemented
74#2570C2214yescomplemented
75#2567C2214yescomplemented
76#2566C2214yes—
77#2564C2218yes—
78#2552C2214yescomplemented
79#2552C2212yescomplemented
80#2552C2212yescomplemented
81#2552C2212yescomplemented
82#2552C2212yescomplemented
83#2552C2212yescomplemented
84#2552C2212yescomplemented
85#2551C2212yescomplemented
86#2551C2212yescomplemented
87#2550C2214yescomplemented
88#2549C2218yescomplemented
89#2509C2214yescomplemented
90#2508C2214yescomplemented
91#2508C2214yescomplemented
92#2507C2214yescomplemented
93#2505C2218yescomplemented
94#2505C2218yescomplemented
95#2505C2218yescomplemented
96#2502C2218yescomplemented
97#2473C2218yescomplemented
98#2454C2214yes—
99#2452C2214yes—
100#2450C2218yes—
101#2449C2218yes—
102#2442C2214yes—
103#2442C2214yes—
104#2442C2214yescomplemented
105#2442C2214yescomplemented
106#2442C2214yescomplemented
107#2442C2214yescomplemented
108#2442C2214yescomplemented
109#2442C2214yescomplemented
110#2441C2214yescomplemented
111#2441C2214yescomplemented
112#2440C2214yes—
113#2440C2214yes—
114#2440C2214yescomplemented
115#2440C2214yescomplemented
116#2440C2214yescomplemented
117#2440C2214yescomplemented
118#2440C2218yescomplemented
119#2440C2214yescomplemented
120#2440C2214yescomplemented
121#2439C2214yescomplemented
122#2439C2214yescomplemented
123#2438C2218yes—
124#2438C2218yes—
125#2437C2218yes—
126#2437C2218yes—
127#2354C2211yescharacteristic
128#2354C2211yescharacteristic
129#2354C2211yescharacteristic
130#2354C2211yescharacteristic
131#2352C2212yes—
132#2352C2212yes—
133#2352C2212yes—
134#2352C2212yes—
135#2349C2214yes—
136#2349C2214yes—
137D4×C4⋊C4C2212yes—
138D4×C4⋊C4C2212yes—
139D4×C4⋊C4C2212yes—
140D4×C4⋊C4C2212yes—
141D4×C4⋊C4C2214yes—
142D4×C4⋊C4C2214yes—
143D4×C4⋊C4C2211yescharacteristic
144D4×C4⋊C4C2211yescharacteristic
145D4×C4⋊C4C2211yescharacteristic
146D4×C4⋊C4C2211yescharacteristic
147D4×C4⋊C4C2214yes—
148#2344C2212yes—
149#2344C2212yes—
150#2342C2214yes—
151#2342C2214yes—
152D4×C22⋊C4C2212yes—
153D4×C22⋊C4C2212yes—
154#2331C2212yescomplemented
155#2331C2212yescomplemented
156#2330C2212yescomplemented
157#2330C2212yescomplemented
158#2329C2214yes—
159#2317C2211yescharacteristic
160#2317C2218yes—
161#2317C2212yes—
162#2317C2212yes—
163#2317C2212yes—
164#2317C2211yescharacteristic
165#2317C2212yes—
166#2317C2214yescomplemented
167#2317C2214yescomplemented
168#2317C2214yescomplemented
169#2317C2214yescomplemented
170#2316C2211yescharacteristic
171#2316C2212yes—
172C4×C4⋊Q8C2212yescomplemented
173C4×C4⋊Q8C2212yescomplemented
174C4×#125C2212yescomplemented
175C4×#125C2212yescomplemented
176C4×C22⋊Q8C2214yes—
177#2293C2212yes—
178#2293C2212yes—
179C2×#389C2212yes—
180C2×#389C2214yescomplemented
181C2×#389C2214yescomplemented
182#2290C2214yes—
183#2290C2214yes—
184C2×#385C2218yes—
185C2×#385C2214yes—
186#2285C2211yescharacteristic
187#2285C2211yescharacteristic
188C2×#384C2211yescharacteristic
189C2×#384C2214yescomplemented
190C2×#382C2214yescomplemented
191#2280C2212yes—
192#2280C2212yes—
193C2×#380C2212yes—
194C42×D4C2212yes—
195C42×D4C2212yes—
196C4×#117C2211yescharacteristic
197C4×#117C2211yescharacteristic
198C2×C4×C4⋊C4C2211yescharacteristic
199C23×D4C2311yescharacteristic
200C24×C4C2312yes—
201C24×C4C2314yes—
202#554—416no—
203#544—28no—
204#544—48no—
205C2×C4⋊Q8C2312yes—
206C2×C4⋊Q8C2312yes—
207C2×C4⋊Q8C2314yes—
208C2×C4⋊Q8C2314yes—
209C2×C4⋊Q8C2314yes—
210C2×C4⋊Q8C2314yes—
211C2×#125C2312yes—
212C2×#125C2312yes—
213C2×#125C2314yes—
214C2×#125C2314yes—
215C2×#125C2314yes—
216C2×#125C2314yes—
217C2×#125C2314yes—
218C2×C22⋊Q8C2314yes—
219C2×C22⋊Q8C2318yes—
220C2×C22⋊Q8C2318yes—
221C2×C22⋊Q8C2318yes—
222C2×C22⋊Q8C2318yes—
223C2×C22⋊Q8C2318yes—
224C2×C4×Q8C2314yes—
225C2×C4×D4—48no—
226C2×C4×D4Q8116yescomplemented
227C2×C4×D4C2312yes—
228C2×C4×D4C2312yes—
229C2×C4×D4C2312yes—
230C2×C4×D4C2312yes—
231C2×C4×D4C2314yes—
232C2×C4×D4C2318yes—
233C2×C4×D4C2314yes—
234C2×C4×D4C2311yescharacteristic
235C2×C4×D4C2311yescharacteristic
236C2×C4×D4C2312yes—
237C2×C4×D4C2312yes—
238C2×C4×D4C2311yescharacteristic
239C2×C4×D4C2311yescharacteristic
240C2×#117—216no—
241C2×#117—48no—
242C2×#117C2311yescharacteristic
243C2×#117C2311yescharacteristic
244C2×#117C2312yes—
245C2×#117C2311yescharacteristic
246C2×#117C2312yes—
247C2×#117C2314yes—
248C2×#117C2312yes—
249C2×#117C2312yes—
250C2×#117C2314yes—
251C2×#117C2314yes—
252C2×#117C2312yes—
253C2×#117C2312yes—
254C2×#117C2314yes—
255C2×#117C2311yescharacteristic
256C22×C4⋊C4—48no—
257C22×C4⋊C4C2312yes—
258C22×C4⋊C4C2311yescharacteristic
259C22×C4⋊C4C2311yescharacteristic
260C22×C4⋊C4C2312yes—
261C22×C4⋊C4C2312yes—
262C22×C4⋊C4C2314yes—
263C22×C4⋊C4C2314yes—
264C22×C4⋊C4C2314yes—
265C22×C4⋊C4C2318yes—
266C22×C4⋊C4C2314yes—
267C22×C4⋊C4C2314yes—
268C22×C4⋊C4C2312yes—
269C22×C4⋊C4C2312yes—
270C22×C4⋊C4C2312yes—
271C22×C4⋊C4C2318yes—
272C22×C4⋊C4C2312yes—
273C22×C4⋊C4C2311yescharacteristic
274C22×C22⋊C4C2314yes—
275C22×C22⋊C4C2314yes—
276C22×C22⋊C4C2314yes—
277C22×C22⋊C4C2312yes—
278C22×C42C2314yes—
279C22×C42C2312yes—
280C22×C42C2314yes—
281C22×C42C2311yescharacteristic
282#400C2318yes—
283#400C2318yes—
284#400C2318yes—
285#400C2318yes—
286#400C2318yes—
287#400C2318yes—
288#400C2318yes—
289#400C2318yes—
290#399C2318yes—
291#399C2318yes—
292#398C2318yes—
293#398C2318yes—
294#398C2318yes—
295#398C2318yes—
296#398C2318yes—
297#398C2318yes—
298#398C2318yes—
299#398C2318yes—
300#398C2318yes—
301#398C2318yes—
302#398C2318yes—
303#398C2318yes—
304#398C2318yes—
305#398C2318yes—
306#396C2318yes—
307#396C2318yes—
308#396C2318yes—
309#396C2318yes—
310#395C2318yes—
311#395C2318yes—
312#395C2318yes—
313#395C2318yes—
314#395C2318yes—
315#395C2318yes—
316#393C2318yes—
317#393C2318yes—
318#391C2314yes—
319#391C2314yes—
320#391C2318yes—
321#391C2314yes—
322#391C2318yes—
323#390C2312yes—
324#390C2312yes—
325#390C2312yes—
326#390C2312yes—
327#389C2312yes—
328#389C2312yes—
329#389C2312yes—
330#389C2312yes—
331#389C2312yes—
332#389C2312yes—
333#389C2312yes—
334#389C2312yes—
335#389C2314yes—
336#389C2314yes—
337#389C2312yes—
338#389C2314yes—
339#389C2314yes—
340#389C2314yes—
341#389C2314yes—
342#389C2314yes—
343#389C2314yes—
344#389C2314yes—
345#389C2314yes—
346#389C2314yes—
347#389C2314yes—
348#389C2314yes—
349#389C2314yes—
350#389C2314yes—
351#389C2314yes—
352#389C2318yes—
353#389C2314yes—
354#389C2314yes—
355#389C2314yes—
356#389C2314yes—
357#389C2318yes—
358#389C2318yes—
359#389C2318yes—
360#389C2314yes—
361#389C2314yes—
362#389C2318yes—
363#389C2312yes—
364#389C2314yes—
365#389C2314yes—
366#389C2312yes—
367#389C2312yes—
368#389C2318yes—
369#389C2314yes—
370#389C2314yes—
371#389C2314yes—
372#389C2318yes—
373#388C2314yes—
374#388C2314yes—
375#388C2314yes—
376#388C2314yes—
377#388C2314yes—
378#388C2314yes—
379#388C2314yes—
380#388C2314yes—
381#387C2314yes—
382#387C2314yes—
383#387C2314yes—
384#387C2314yes—
385#387C2314yes—
386#387C2318yes—
387#387C2318yes—
388#387C2314yes—
389#387C2318yes—
390#387C2318yes—
391#387C2318yes—
392#387C2318yes—
393#387C2314yes—
394#387C2314yes—
395#387C2314yes—
396#387C2314yes—
397#386C2314yes—
398#386C2314yes—
399#386C2314yes—
400#386C2314yes—
401#385C2318yes—
402#385C2318yes—
403#385C2318yes—
404#385C2314yes—
405#385C2318yes—
406#385C2318yes—
407#385C2318yes—
408#385C2314yes—
409#385C2318yes—
410#385C2318yes—
411#385C2318yes—
412#385C2318yes—
413#385C2318yes—
414#385C2318yes—
415#385C2314yes—
416#385C2318yes—
417#385C2318yes—
418#385C2318yes—
419#385C2318yes—
420#385C2318yes—
421#385C2314yes—
422#385C2314yes—
423#385C2314yes—
424#385C2318yes—
425#385C2318yes—
426#385C2318yes—
427#384C2312yes—
428#384C2312yes—
429#384C2314yes—
430#384C2318yes—
431#384C2314yes—
432#384C2314yes—
433#384C2311yescharacteristic
434#384C2311yescharacteristic
435#384C2312yes—
436#384C2312yes—
437#384C2314yes—
438#384C2314yes—
439#384C2318yes—
440#384C2312yes—
441#384C2311yescharacteristic
442#384C2312yes—
443#384C2311yescharacteristic
444#384C2314yes—
445#382C2312yes—
446#382C2312yes—
447#382C2314yes—
448#382C2312yes—
449#382C2312yes—
450#382C2314yes—
451#382C2314yes—
452#382C2314yes—
453#382C2314yes—
454#382C2314yes—
455#382C2314yes—
456#382C2318yes—
457#382C2318yes—
458#381C2314yes—
459#381C2314yes—
460#380C2318yes—
461#380C2318yes—
462#380C2314yes—
463#380C2318yes—
464#380C2318yes—
465#380C2318yes—
466#380C2312yes—
467#380C2312yes—
468#380C2312yes—
469#380C2312yes—
470#380C2314yes—
471#380C2314yes—
472#380C2312yes—
473#380C2312yes—
474#380C2312yes—
475#380C2312yes—
476#380C2314yes—
477#380C2314yes—
478#380C2312yes—
479#380C2312yes—
480#380C2312yes—
481#380C2312yes—
482#379C2314yes—
483#379C2314yes—
484C4×C4⋊C4C2314yes—
485C4×C4⋊C4C2311yescharacteristic
486C4×C4⋊C4C2311yescharacteristic
487C4×C4⋊C4C2312yes—
488C4×C4⋊C4C2312yes—
489C4×C4⋊C4C2314yes—
490C4×C4⋊C4C2314yes—
491C4×C4⋊C4C2311yescharacteristic
492C4×C4⋊C4C2311yescharacteristic
493C4×C4⋊C4C2312yes—
494C4×C4⋊C4C2312yes—
495C4×C4⋊C4C2312yes—
496C4×C4⋊C4C2312yes—
497C4×C4⋊C4C2312yes—
498C4×C4⋊C4C2311yescharacteristic
499C4×C4⋊C4C2312yes—
500C4×C4⋊C4C2312yes—
501C4×C4⋊C4C2312yes—
502C4×C4⋊C4C2311yescharacteristic
503C4×C4⋊C4C2311yescharacteristic
504C4×C4⋊C4C2311yescharacteristic
505C4×C4⋊C4C2312yes—
506C4×C4⋊C4C2312yes—
507C4×C22⋊C4C2314yes—
508C4×C22⋊C4C2312yes—
509C4×C22⋊C4C2312yes—
510C4×C22⋊C4C2312yes—
511C4×C22⋊C4C2312yes—
512C4×C22⋊C4C2314yes—
513C4×C22⋊C4C2314yes—
514C4×C22⋊C4C2314yes—
515C4×C22⋊C4C2314yes—
516C4×C22⋊C4C2314yes—
517C4×C22⋊C4C2314yes—
518C4×C22⋊C4C2314yes—
519#376C2312yes—
520#376C2312yes—
521C2×#95C2318yes—
522C2×#95C2312yes—
523C2×#95C2318yes—
524C2×#95C2314yes—
525C43C2312yes—
526C43C2312yes—
527C25C2412yes—
528C22×Q8C2414yes—
529C22×Q8C2418yes—
530C22×D4—24no—
531C22×D4—24no—
532C22×D4C2×Q818yes—
533C22×D4C2412yes—
534C22×D4C2411yescharacteristic
535C22×D4C2411yescharacteristic
536C23×C4—28no—
537C23×C4—28no—
538C23×C4—48no—
539C23×C4—48no—
540C23×C4—84no—
541C23×C4C2×Q8116yes—
542C23×C4C2414yes—
543C23×C4C2414yes—
544C23×C4C2412yes—
545C23×C4C2412yes—
546C23×C4C2412yes—
547C23×C4C2411yescharacteristic
548C23×C4C2412yes—
549C23×C4C2412yes—
550C23×C4C2412yes—
551C23×C4C2414yes—
552C23×C4C2414yes—
553C23×C4C2414yes—
554C23×C4C2418yes—
555C23×C4C2412yes—
556C23×C4C2418yes—
557C23×C4C2411yescharacteristic
558C23×C4C2411yescharacteristic
559C4⋊Q8—28no—
560C4⋊Q8—28no—
561C4⋊Q8—48no—
562C4⋊Q8—48no—
563C4⋊Q8—48no—
564C4⋊Q8—84no—
565#125—28no—
566#125—28no—
567#125—48no—
568#125—48no—
569#125—48no—
570#125—48no—
571#125—84no—
572C22⋊Q8—216no—
573C22⋊Q8—416no—
574C22⋊Q8—416no—
575C22⋊Q8—416no—
576C22⋊Q8—416no—
577C22⋊Q8—88no—
578C4×Q8—48no—
579C4×D4—216no—
580C4×D4—28no—
581C4×D4—28no—
582C4×D4—28no—
583C4×D4—28no—
584C4×D4—48no—
585C4×D4—416no—
586C4×D4C2×Q8116yes—
587C4×D4C2×Q8116yes—
588C4×D4C2×Q818yes—
589C4×D4C2×Q818yes—
590C4×D4C2×Q818yes—
591C4×D4C2×Q818yes—
592#117—28no—
593#117—24no—
594#117—24no—
595#117—28no—
596#117—24no—
597#117—28no—
598#117—28no—
599#117—216no—
600#117—216no—
601#117—48no—
602#117—48no—
603#117—44no—
604#117—44no—
605#117#4118yes—
606C2×C4⋊C4—24no—
607C2×C4⋊C4—24no—
608C2×C4⋊C4—28no—
609C2×C4⋊C4—28no—
610C2×C4⋊C4—28no—
611C2×C4⋊C4—48no—
612C2×C4⋊C4—48no—
613C2×C4⋊C4—48no—
614C2×C4⋊C4—48no—
615C2×C4⋊C4—44no—
616C2×C4⋊C4—44no—
617C2×C4⋊C4—44no—
618C2×C4⋊C4—48no—
619C2×C4⋊C4—416no—
620C2×C4⋊C4—88no—
621C2×C4⋊C4—82no—
622C2×C4⋊C4C2×Q818yes—
623C2×C4⋊C4C2412yes—
624C2×C4⋊C4C2412yes—
625C2×C4⋊C4C2414yes—
626C2×C4⋊C4C2414yes—
627C2×C4⋊C4C2411yescharacteristic
628C2×C4⋊C4C2411yescharacteristic
629C2×C4⋊C4C2412yes—
630C2×C4⋊C4C2412yes—
631C2×C4⋊C4C2412yes—
632C2×C4⋊C4C2412yes—
633C2×C4⋊C4C2414yes—
634C2×C4⋊C4C2414yes—
635C2×C4⋊C4C2414yes—
636C2×C4⋊C4C2412yes—
637C2×C4⋊C4C2412yes—
638C2×C4⋊C4C2411yescharacteristic
639C2×C4⋊C4C2411yescharacteristic
640C2×C4⋊C4C2411yescharacteristic
641C2×C4⋊C4C2411yescharacteristic
642C2×C4⋊C4C2412yes—
643C2×C4⋊C4C2412yes—
644C2×C4⋊C4C2412yes—
645C2×C4⋊C4C2412yes—
646C2×C4⋊C4C2414yes—
647C2×C4⋊C4C2414yes—
648C2×C4⋊C4C2414yes—
649C2×C4⋊C4C2418yes—
650C2×C4⋊C4C2418yes—
651C2×C4⋊C4C2414yes—
652C2×C4⋊C4C2414yes—
653C2×C4⋊C4C2414yes—
654C2×C4⋊C4C2414yes—
655C2×C4⋊C4C2414yes—
656C2×C4⋊C4C2418yes—
657C2×C4⋊C4C2418yes—
658C2×C4⋊C4C2418yes—
659C2×C4⋊C4C2418yes—
660C2×C4⋊C4C2414yes—
661C2×C4⋊C4C2418yes—
662C2×C4⋊C4C2418yes—
663C2×C4⋊C4C2414yes—
664C2×C4⋊C4C2414yes—
665C2×C4⋊C4C2414yes—
666C2×C4⋊C4C2418yes—
667C2×C4⋊C4C2418yes—
668C2×C4⋊C4C2414yes—
669C2×C4⋊C4C2418yes—
670C2×C4⋊C4C2418yes—
671C2×C4⋊C4C2418yes—
672C2×C4⋊C4C2418yes—
673C2×C4⋊C4C2412yes—
674C2×C4⋊C4C2412yes—
675C2×C4⋊C4C2412yes—
676C2×C4⋊C4C2412yes—
677C2×C4⋊C4C2414yes—
678C2×C4⋊C4C2418yes—
679C2×C4⋊C4C2411yescharacteristic
680C2×C4⋊C4C2411yescharacteristic
681C2×C4⋊C4C2412yes—
682C2×C4⋊C4C2411yescharacteristic
683C2×C4⋊C4C2411yescharacteristic
684C2×C22⋊C4—216no—
685C2×C22⋊C4—48no—
686C2×C22⋊C4—48no—
687C2×C22⋊C4C2×Q8116yes—
688C2×C22⋊C4C2412yes—
689C2×C22⋊C4C2414yes—
690C2×C22⋊C4C2414yes—
691C2×C22⋊C4C2414yes—
692C2×C22⋊C4C2414yes—
693C2×C22⋊C4C2418yes—
694C2×C22⋊C4C2412yes—
695C2×C22⋊C4C2412yes—
696C2×C22⋊C4C2414yes—
697C2×C22⋊C4C2414yes—
698C2×C22⋊C4C2414yes—
699C2×C22⋊C4C2414yes—
700C2×C22⋊C4C2414yes—
701C2×C22⋊C4C2414yes—
702C2×C22⋊C4C2418yes—
703C2×C22⋊C4C2414yes—
704C2×C22⋊C4C2414yes—
705C2×C22⋊C4C2414yes—
706C2×C22⋊C4C2414yes—
707C2×C22⋊C4C2412yes—
708C2×C22⋊C4C2412yes—
709C2×C22⋊C4C2412yes—
710C2×C22⋊C4C2412yes—
711C2×C22⋊C4C2412yes—
712C2×C42—216no—
713C2×C42—48no—
714C2×C42—44no—
715C2×C42C2×Q818yes—
716C2×C42C2412yes—
717C2×C42C2414yes—
718C2×C42C2414yes—
719C2×C42C2414yes—
720C2×C42C2414yes—
721C2×C42C2412yes—
722C2×C42C2412yes—
723C2×C42C2414yes—
724C2×C42C2412yes—
725C2×C42C2412yes—
726C2×C42C2412yes—
727C2×C42C2412yes—
728C2×C42C2414yes—
729C2×C42C2414yes—
730C2×C42C2414yes—
731C2×C42C2412yes—
732C2×C42C2412yes—
733C2×C42C2412yes—
734C2×C42C2412yes—
735C2×C42C2411yescharacteristic
736C2×C42C2411yescharacteristic
737C2×C42C2411yescharacteristic
738C2×C42C2411yescharacteristic
739C2×C42C2412yes—
740#95C2414yes—
741#95C2414yes—
742#95C2414yes—
743#95C2414yes—
744#95C2418yes—
745#95C2418yes—
746#95C2418yes—
747#95C2418yes—
748#95C2418yes—
749#95C2418yes—
750#95C2418yes—
751#95C2418yes—
752#95C2412yes—
753#95C2412yes—
754#95C2412yes—
755#95C2412yes—
756#95C2412yes—
757#95C2412yes—
758#95C2412yes—
759#95C2412yes—
760#95C2414yes—
761#95C2414yes—
762#95C2414yes—
763#95C2414yes—
764#95C2414yes—
765#95C2414yes—
766#95C2414yes—
767#95C2414yes—
768#95C2414yes—
769#95C2414yes—
770#95C2414yes—
771#95C2414yes—
772#95C2414yes—
773#95C2414yes—
774#95C2414yes—
775#95C2414yes—
776#95C2418yes—
777#95C2418yes—
778#95C2418yes—
779#95C2418yes—
780C24—24no—
781C24—24no—
782C24—24no—
783C24—24no—
784C24—42no—
785C24—42no—
786C24C22×Q818yes—
787C24C2512yes—
788C24C2511yescharacteristic
789C24C2512yes—
790C2×Q8—28no—
791C2×Q8—44no—
792C2×Q8—44no—
793C2×Q8—48no—
794C2×Q8—48no—
795C2×Q8—48no—
796C2×D4—24no—
797C2×D4—24no—
798C2×D4—232no—
799C2×D4—22no—
800C2×D4—22no—
801C2×D4C22×Q818yes—
802C2×D4C22×Q814yes—
803C2×D4C22×Q814yes—
804C2×D4H(5,𝔽2)14yes—
805C2×D42−1+414yes—
806C22×C4—24no—
807C22×C4—24no—
808C22×C4—264no—
809C22×C4—24no—
810C22×C4—24no—
811C22×C4—24no—
812C22×C4—24no—
813C22×C4—24no—
814C22×C4—22no—
815C22×C4—24no—
816C22×C4—24no—
817C22×C4—24no—
818C22×C4—22no—
819C22×C4—24no—
820C22×C4—28no—
821C22×C4—28no—
822C22×C4—24no—
823C22×C4—28no—
824C22×C4—28no—
825C22×C4—216no—
826C22×C4—28no—
827C22×C4—28no—
828C22×C4—28no—
829C22×C4—42no—
830C22×C4—41no—
831C22×C4—44no—
832C22×C4—42no—
833C22×C4—41no—
834C22×C4—44no—
835C22×C4—42no—
836C22×C4—44no—
837C22×C4—44no—
838C22×C4—44no—
839C22×C4—48no—
840C22×C4—48no—
841C22×C4—44no—
842C22×C4—44no—
843C22×C4—48no—
844C22×C4—48no—
845C22×C4—48no—
846C22×C4—44no—
847C22×C4—42no—
848C22×C4—832no—
849C22×C4C22×Q814yes—
850C22×C4C22×Q818yes—
851C22×C4C22×Q818yes—
852C22×C4C22×Q818yes—
853C22×C4C22×Q818yes—
854C22×C4C22×Q818yes—
855C22×C4C22×Q814yes—
856C22×C4C22×Q814yes—
857C22×C4C2×#4114yes—
858C22×C4H(5,𝔽2)14yes—
859C22×C4C2512yes—
860C22×C4C2514yes—
861C22×C4C2514yes—
862C22×C4C2512yes—
863C22×C4C2512yes—
864C22×C4C2512yes—
865C22×C4C2514yes—
866C22×C4C2514yes—
867C22×C4C2514yes—
868C22×C4C2512yes—
869C22×C4C2518yes—
870C22×C4C2514yes—
871C22×C4C2512yes—
872C22×C4C2511yescharacteristic
873C22×C4C2511yescharacteristic
874C22×C4C2511yescharacteristic
875C22×C4C2512yes—
876C22×C4C2512yes—
877C22×C4C2512yes—
878C22×C4C2512yes—
879C22×C4C2511yescharacteristic
880C22×C4C2511yescharacteristic
881C22×C4C2511yescharacteristic
882C4⋊C4—28no—
883C4⋊C4—28no—
884C4⋊C4—24no—
885C4⋊C4—24no—
886C4⋊C4—24no—
887C4⋊C4—24no—
888C4⋊C4—22no—
889C4⋊C4—22no—
890C4⋊C4—28no—
891C4⋊C4—28no—
892C4⋊C4—28no—
893C4⋊C4—24no—
894C4⋊C4—24no—
895C4⋊C4—28no—
896C4⋊C4—28no—
897C4⋊C4—22no—
898C4⋊C4—22no—
899C4⋊C4—24no—
900C4⋊C4—24no—
901C4⋊C4—28no—
902C4⋊C4—22no—
903C4⋊C4—22no—
904C4⋊C4—24no—
905C4⋊C4—24no—
906C4⋊C4—24no—
907C4⋊C4—24no—
908C4⋊C4—48no—
909C4⋊C4—48no—
910C4⋊C4—44no—
911C4⋊C4—44no—
912C4⋊C4—44no—
913C4⋊C4—44no—
914C4⋊C4—48no—
915C4⋊C4—48no—
916C4⋊C4—48no—
917C4⋊C4—44no—
918C4⋊C4—48no—
919C4⋊C4—44no—
920C4⋊C4—48no—
921C4⋊C4—44no—
922C4⋊C4—48no—
923C4⋊C4—42no—
924C4⋊C4—42no—
925C4⋊C4—44no—
926C4⋊C4—48no—
927C4⋊C4—44no—
928C4⋊C4—44no—
929C4⋊C4—48no—
930C4⋊C4—48no—
931C4⋊C4—48no—
932C4⋊C4—48no—
933C4⋊C4—48no—
934C4⋊C4—44no—
935C4⋊C4—48no—
936C4⋊C4—42no—
937C4⋊C4—42no—
938C4⋊C4C22×Q818yes—
939C4⋊C4C22×Q814yes—
940C4⋊C4C22×Q814yes—
941C4⋊C4C2×#4114yes—
942C4⋊C4C2×#4114yes—
943C22⋊C4—28no—
944C22⋊C4—24no—
945C22⋊C4—24no—
946C22⋊C4—28no—
947C22⋊C4—216no—
948C22⋊C4—24no—
949C22⋊C4—28no—
950C22⋊C4—28no—
951C22⋊C4—28no—
952C22⋊C4—28no—
953C22⋊C4—28no—
954C22⋊C4—28no—
955C22⋊C4—44no—
956C22⋊C4—44no—
957C22⋊C4—48no—
958C22⋊C4—44no—
959C22⋊C4—44no—
960C22⋊C4—44no—
961C22⋊C4—44no—
962C22⋊C4C22×Q818yes—
963C22⋊C4C22×Q818yes—
964C22⋊C4C22×Q818yes—
965C22⋊C4C22×Q818yes—
966C22⋊C4C2×#4118yes—
967C42—28no—
968C42—28no—
969C42—28no—
970C42—24no—
971C42—24no—
972C42—28no—
973C42—28no—
974C42—24no—
975C42—24no—
976C42—24no—
977C42—24no—
978C42—24no—
979C42—44no—
980C42—44no—
981C42—44no—
982C42—42no—
983C42—42no—
984C42—42no—
985C42—42no—
986C42C22×Q814yes—
987C42C22×Q814yes—
988C42C22×Q814yes—
989C42C22×Q814yes—
990C42C2×#4118yes—
991C23—22no—
992C23—22no—
993C23—21no—
994C23—21no—
995C23—22no—
996C23—21no—
997C23—22no—
998C23—21no—
999C23—22no—
1000C23—22no—
1001C23—22no—
1002C23—22no—
1003C23—22no—
1004C23—22no—
1005C23—216no—
1006C23—216no—
1007C23—48no—
1008C23—48no—
1009C23—48no—
1010C23—48no—
1011C23—48no—
1012C23C23×Q814yes—
1013C23C23×Q814yes—
1014C23C23×Q812yes—
1015C23C22×#4112yes—
1016C23C2×H(5,𝔽2)14yes—
1017C23C2×H(5,𝔽2)12yes—
1018C23C2×2−1+414yes—
1019C23C2611yescharacteristic
1020Q8—88no—
1021Q8—168no—
1022D4—216no—
1023D4—28no—
1024D4#544116yescomplemented
1025C2×C4—22no—
1026C2×C4—22no—
1027C2×C4—22no—
1028C2×C4—22no—
1029C2×C4—21no—
1030C2×C4—22no—
1031C2×C4—22no—
1032C2×C4—21no—
1033C2×C4—21no—
1034C2×C4—21no—
1035C2×C4—22no—
1036C2×C4—21no—
1037C2×C4—21no—
1038C2×C4—22no—
1039C2×C4—216no—
1040C2×C4—28no—
1041C2×C4—216no—
1042C2×C4—216no—
1043C2×C4—216no—
1044C2×C4—216no—
1045C2×C4—24no—
1046C2×C4—24no—
1047C2×C4—22no—
1048C2×C4—22no—
1049C2×C4—24no—
1050C2×C4—22no—
1051C2×C4—22no—
1052C2×C4—24no—
1053C2×C4—24no—
1054C2×C4—24no—
1055C2×C4—24no—
1056C2×C4—22no—
1057C2×C4—22no—
1058C2×C4—22no—
1059C2×C4—22no—
1060C2×C4—22no—
1061C2×C4—28no—
1062C2×C4—24no—
1063C2×C4—24no—
1064C2×C4—28no—
1065C2×C4—24no—
1066C2×C4—22no—
1067C2×C4—22no—
1068C2×C4—22no—
1069C2×C4—24no—
1070C2×C4—24no—
1071C2×C4—22no—
1072C2×C4—22no—
1073C2×C4—22no—
1074C2×C4—24no—
1075C2×C4—24no—
1076C2×C4—28no—
1077C2×C4—24no—
1078C2×C4—22no—
1079C2×C4—22no—
1080C2×C4—22no—
1081C2×C4—24no—
1082C2×C4—24no—
1083C2×C4—24no—
1084C2×C4—44no—
1085C2×C4—416no—
1086C2×C4—416no—
1087C2×C4—48no—
1088C2×C4—84no—
1089C2×C4—88no—
1090C2×C4—88no—
1091C2×C4—816no—
1092C2×C4—88no—
1093C2×C4—816no—
1094C2×C4#554116yescomplemented
1095C2×C4C23×Q812yes—
1096C2×C4C23×Q812yes—
1097C2×C4C23×Q812yes—
1098C2×C4C23×Q814yes—
1099C2×C4C23×Q814yes—
1100C2×C4C23×Q812yes—
1101C2×C4C23×Q812yes—
1102C2×C4C23×Q812yes—
1103C2×C4C22×#4114yes—
1104C2×C4C22×#4114yes—
1105C2×C4C22×#4112yes—
1106C2×C4C22×#4112yes—
1107C2×C4C2×H(5,𝔽2)12yes—
1108C2×C4C2×H(5,𝔽2)12yes—
1109C2×C4C2×H(5,𝔽2)12yes—
1110C2×C4C2×2−1+412yes—
1111C22—24no—
1112C22—22no—
1113C22—24no—
1114C22—22no—
1115C22—22no—
1116C22—24no—
1117C22—22no—
1118C22—24no—
1119C22—22no—
1120C22—24no—
1121C22—22no—
1122C22—24no—
1123C22—24no—
1124C22—24no—
1125C22—24no—
1126C22—432no—
1127C22—42no—
1128C22—42no—
1129C22—42no—
1130C22—42no—
1131C22C2×#54418yes—
1132C22C2×#55414yes—
1133C22C24×Q811yescharacteristic
1134C22C23×#4111yescharacteristic
1135C22C22×H(5,𝔽2)11yescharacteristic
1136C22C22×H(5,𝔽2)11yescharacteristic
1137C22C22×2−1+411yescharacteristic
1138C22H(7,𝔽2)11yescharacteristic
1139C222−1+611yescharacteristic
1140C4—24no—
1141C4—24no—
1142C4—22no—
1143C4—22no—
1144C4—22no—
1145C4—24no—
1146C4—24no—
1147C4—44no—
1148C4—44no—
1149C4—42no—
1150C4—42no—
1151C4—44no—
1152C4—44no—
1153C4—42no—
1154C4—48no—
1155C4—44no—
1156C4—42no—
1157C4—42no—
1158C4—44no—
1159C4—42no—
1160C4C2×#54414yes—
1161C4C2×#55414yes—
1162C4C2×#55414yes—
1163C2—24no—
1164C2—28no—
1165C2—44no—
1166C2C22×#54411yescharacteristic
1167C2C22×#55411yescharacteristic
1168C2#6285411yescharacteristic
1169C2#6291211yescharacteristic
1170C2#6294211yescharacteristic
1171C2#6298511yescharacteristic
1172C2#6300011yescharacteristic
subgroupG/H
center, commutator, Frattini, socle, cosocleC23C26
prime radicalC23×D4C23
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23 ◁ G
LECSG ▷ C23 ▷ C1

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
1. #39498C2semidirect
2. #39497C2semidirect
3. #38966C2semidirect
4. #38964C2semidirect
5. #38963C2semidirect
6. #38100C2semidirect
7. #38098C2semidirect
8. #38097C2semidirect
9. #37875C2semidirect
10. #37874C2semidirect
11. #36290C2semidirect
12. #36261C2semidirect
14. #36180C2semidirect
15. #36165C2semidirect
16. #35286C2semidirect
17. #35275C2semidirect
18. #35253C2semidirect
19. #35253C2semidirect
20. #35224C2semidirect
21. #35181C2semidirect
25. C4×#544C2semidirect
26. C2×#2317C2semidirect
35. #2868C22semidirect
36. #2859C22semidirect
37. #2859C22semidirect
38. #2859C22semidirect
39. #2857C22semidirect
40. #2857C22semidirect
42. #2851C22semidirect
43. #2851C22semidirect
45. #2807C22semidirect
46. #2792C22semidirect
47. #2791C22semidirect
48. #2790C22semidirect
49. #2790C22semidirect
50. #2788C22semidirect
51. #2774C22semidirect
52. #2768C22semidirect
53. #2763C22semidirect
54. #2755C22semidirect
55. #2729C22semidirect
56. #2720C22semidirect
57. #2660C22semidirect
58. #2647C22semidirect
60. #2629C22semidirect
61. #2629C22semidirect
62. #2628C22semidirect
63. #2628C22semidirect
65. #2584C22semidirect
66. #2583C22semidirect
69. #2571C22semidirect
70. #2571C22semidirect
71. #2571C22semidirect
72. #2571C22semidirect
73. #2570C22semidirect
74. #2570C22semidirect
75. #2567C22semidirect
78. #2552C22semidirect
79. #2552C22semidirect
80. #2552C22semidirect
81. #2552C22semidirect
82. #2552C22semidirect
83. #2552C22semidirect
84. #2552C22semidirect
85. #2551C22semidirect
86. #2551C22semidirect
87. #2550C22semidirect
88. #2549C22semidirect
89. #2509C22semidirect
90. #2508C22semidirect
91. #2508C22semidirect
92. #2507C22semidirect
93. #2505C22semidirect
94. #2505C22semidirect
95. #2505C22semidirect
96. #2502C22semidirect
97. #2473C22semidirect
104. #2442C22semidirect
105. #2442C22semidirect
106. #2442C22semidirect
107. #2442C22semidirect
108. #2442C22semidirect
109. #2442C22semidirect
110. #2441C22semidirect
111. #2441C22semidirect
114. #2440C22semidirect
115. #2440C22semidirect
116. #2440C22semidirect
117. #2440C22semidirect
118. #2440C22semidirect
119. #2440C22semidirect
120. #2440C22semidirect
121. #2439C22semidirect
122. #2439C22semidirect
154. #2331C22semidirect
155. #2331C22semidirect
156. #2330C22semidirect
157. #2330C22semidirect
166. #2317C22semidirect
167. #2317C22semidirect
168. #2317C22semidirect
169. #2317C22semidirect
172. C4×C4⋊Q8C22semidirect
173. C4×C4⋊Q8C22semidirect
174. C4×#125C22semidirect
175. C4×#125C22semidirect
180. C2×#389C22semidirect
181. C2×#389C22semidirect
189. C2×#384C22semidirect
190. C2×#382C22semidirect
226. C2×C4×D4Q8semidirect
1024. D4#544semidirect
1094. C2×C4#554semidirect

Maximal subgroups

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

subgroupindex
#394982
#394972
#389662
#389642
#389632
#381002
#380982
#380972
#378752
#378742
#362902
#362612
#362152
#361802
#361652
#352862
#352752
#352532
#352242
#351812
D4×#1172
C2×D4×C4⋊C42
C4×#5442
C2×#23172