Finite Group Databasebeta

← #7985112

Subgroups — #7985112

Order 512.

4627 conjugacy classes of subgroups.

The subgroup lattice has 1104 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#59870C211yesmaximal, characteristic, complemented
2#59666C212yesmaximal, complemented
3#59259C212yesmaximal, complemented
4#59065C212yesmaximal, complemented
5#48521C218yesmaximal, complemented
6#45662C214yesmaximal, complemented
7#45329C214yesmaximal, complemented
8#45327C214yesmaximal, complemented
9#42656C214yesmaximal, complemented
10#42631C214yesmaximal, complemented
11#40220C214yesmaximal, complemented
12#39478C212yesmaximal, complemented
13#39478C212yesmaximal, complemented
14#39200C212yesmaximal, complemented
15#38911C212yesmaximal, complemented
16#36598C211yesmaximal, characteristic, complemented
17#36579C212yesmaximal, complemented
18#36454C212yesmaximal, complemented
19#36188C211yesmaximal, characteristic, complemented
20#36134C211yesmaximal, characteristic, complemented
21#35196C212yesmaximal
22#35179C212yesmaximal, complemented
23#34941C211yesmaximal, characteristic, complemented
24#34932C211yesmaximal, characteristic
25#34383C212yesmaximal, complemented
26C4×D4×Q8C211yesmaximal, characteristic, complemented
27C2×#556C2212yes—
28C2×D4×Q8C2211yescharacteristic
29C2×#533C2212yes—
30C2×#529C2212yes—
31C22×C4×Q8C2212yes—
32#2868C2211yescharacteristic
33#2862C2212yes—
34#2857C2212yes—
35#2857C2212yes—
36#2855C2214yes—
37#2855C2214yes—
38#2850C2214yes—
39#2827C2218yes—
40#2810C2218yes—
41#2805C2214yes—
42#2802C2218yes—
43#2798C2218yes—
44#2783C2218yes—
45#2773C2218yes—
46#2768C2218yes—
47#2767C2218yes—
48#2767C2218yes—
49#2754C2218yes—
50#2747C2218yes—
51#2747C2218yes—
52#2744C2218yes—
53#2740C2218yes—
54#2723C2218yes—
55#2689C2218yes—
56#2687C2218yes—
57#2652C2218yes—
58#2649C2218yes—
59#2627C2218yes—
60#2625C2214yes—
61#2625C2214yes—
62#2592C2214yes—
63#2588C2218yes—
64#2585C2218yes—
65#2582C2214yes—
66#2582C2214yes—
67#2582C2212yes—
68#2581C2218yes—
69#2581C2214yes—
70#2581C2214yes—
71#2575C2218yes—
72#2574C2214yes—
73#2571C2212yes—
74#2571C2212yes—
75#2570C2214yes—
76#2568C2212yes—
77#2568C2212yes—
78#2568C2212yes—
79#2567C2211yescharacteristic
80#2567C2212yes—
81#2565C2214yes—
82#2565C2214yes—
83#2565C2214yes—
84#2563C2211yescharacteristic
85#2553C2214yes—
86#2552C2211yescharacteristic
87#2552C2212yes—
88#2552C2211yescharacteristic
89#2550C2214yes—
90#2547C2212yes—
91#2547C2212yes—
92#2547C2211yescharacteristic
93#2542C2211yescharacteristic
94#2542C2212yes—
95#2538C2212yes—
96#2538C2211yescharacteristic
97#2537C2211yescharacteristic
98#2520C2218yes—
99#2517C2218yes—
100#2516C2218yes—
101#2511C2214yes—
102#2511C2214yes—
103#2511C2214yes—
104#2511C2214yes—
105#2511C2214yes—
106#2509C2214yes—
107#2508C2214yes—
108#2508C2212yes—
109#2508C2214yes—
110#2507C2214yes—
111#2499C2214yes—
112#2497C2214yes—
113#2497C2212yes—
114#2496C2214yes—
115#2496C2212yes—
116#2496C2214yes—
117#2492C2214yes—
118#2489C2214yes—
119#2489C2212yes—
120#2489C2214yes—
121#2481C2218yes—
122#2469C2218yes—
123#2469C2218yes—
124#2454C2212yes—
125#2448C2214yes—
126#2447C2214yes—
127#2446C2214yes—
128#2441C2214yes—
129#2441C2214yes—
130#2429C2214yes—
131#2427C2212yes—
132#2426C2214yes—
133#2423C2212yes—
134#2423C2214yes—
135#2423C2214yes—
136#2422C2212yes—
137#2421C2214yes—
138#2421C2214yes—
139#2421C2214yes—
140#2420C2214yes—
141#2415C2214yes—
142#2409C2214yes—
143#2396C2214yes—
144#2395C2214yes—
145#2376C2218yes—
146#2370C2214yes—
147#2367C2214yes—
148#2365C2212yes—
149#2365C2212yes—
150#2365C2212yes—
151#2365C2212yes—
152#2365C2212yes—
153#2365C2211yescharacteristic
154#2365C2212yes—
155#2362C2214yes—
156#2360C2214yes—
157#2360C2212yes—
158#2355C2212yes—
159#2355C2214yes—
160#2355C2212yes—
161#2355C2212yes—
162#2354C2214yes—
163#2354C2212yes—
164#2352C2214yes—
165#2351C2214yes—
166Q8×C4⋊C4C2212yes—
167Q8×C4⋊C4C2212yes—
168Q8×C4⋊C4C2211yescharacteristic
169D4×C4⋊C4C2211yescharacteristic
170D4×C4⋊C4C2212yes—
171Q8×C22⋊C4C2212yes—
172#2334C2218yes—
173#2324C2214yes—
174#2323C2214yes—
175#2317C2214yes—
176#2314C2214yes—
177#2314C2214yes—
178#2310C2214yes—
179C4×C4⋊Q8C2212yes—
180C4×C4⋊Q8C2212yes—
181C4×C4⋊Q8C2211yescharacteristic
182C4×C4⋊Q8C2211yescharacteristic
183C4×C4⋊Q8C2211yescharacteristic
184C4×#125C2212yes—
185C4×C22⋊Q8C2214yes—
186C4×C22⋊Q8C2214yes—
187C4×C22⋊Q8C2212yes—
188C4×C22⋊Q8C2212yes—
189C4×C22⋊Q8C2212yes—
190C4×#121C2212yes—
191#2293C2212yes—
192#2285C2212yes—
193#2285C2212yes—
194#2285C2212yes—
195C42×Q8C2211yescharacteristic
196C42×D4C2211yescharacteristic
197C42×D4C2211yescharacteristic
198C42×D4C2212yes—
199C23×Q8C2312yes—
200#556—48no—
201D4×Q8—28no—
202#533—48no—
203C2×C4⋊Q8C2311yescharacteristic
204C2×C4⋊Q8C2311yescharacteristic
205C2×C4⋊Q8C2311yescharacteristic
206C2×C4⋊Q8C2312yes—
207C2×C4⋊Q8C2312yes—
208C2×C4⋊Q8C2312yes—
209C2×C4⋊Q8C2312yes—
210#529—216no—
211C2×#126C2314yes—
212C2×#126C2318yes—
213C2×#125C2312yes—
214C2×#125C2312yes—
215C2×#125C2314yes—
216C2×#124C2312yes—
217C2×#124C2314yes—
218C2×#123C2314yes—
219C2×C22⋊Q8C2312yes—
220C2×C22⋊Q8C2312yes—
221C2×C22⋊Q8C2314yes—
222C2×C22⋊Q8C2312yes—
223C2×C22⋊Q8C2314yes—
224C2×C22⋊Q8C2314yes—
225C2×C22⋊Q8C2314yes—
226C2×C22⋊Q8C2312yes—
227C2×C22⋊Q8C2314yes—
228C2×#121C2312yes—
229C2×#121C2312yes—
230C2×C4×Q8—48no—
231C2×C4×Q8C2312yes—
232C2×C4×Q8C2312yes—
233C2×C4×Q8C2311yescharacteristic
234C2×C4×Q8C2311yescharacteristic
235C2×C4×Q8C2311yescharacteristic
236C2×C4×Q8C2314yes—
237C2×C4×Q8C2312yes—
238C2×C4×Q8C2314yes—
239C2×C4×Q8C2312yes—
240C2×C4×Q8C2312yes—
241C2×C4×Q8C2314yes—
242C2×C4×Q8C2314yes—
243C2×C4×Q8C2314yes—
244C2×C4×Q8C2314yes—
245C2×C4×Q8C2314yes—
246C2×C4×D4C2311yescharacteristic
247C2×C4×D4C2312yes—
248C2×C4×D4C2314yes—
249C2×C4×D4C2311yescharacteristic
250C2×C4×D4C2311yescharacteristic
251C2×C4×D4C2312yes—
252C2×C4×D4C2311yescharacteristic
253C2×C4×D4C2311yescharacteristic
254C2×C4×D4C2311yescharacteristic
255C2×#117C2314yes—
256C2×#117C2314yes—
257C2×#117C2314yes—
258C2×#117C2314yes—
259C22×C4⋊C4C2312yes—
260C22×C4⋊C4C2314yes—
261C22×C42C2312yes—
262C22×C42C2312yes—
263C22×C42C2314yes—
264#400C2318yes—
265#400C2318yes—
266#400C2318yes—
267#400C2318yes—
268#400C2318yes—
269#400C2318yes—
270#400C2318yes—
271#400C2318yes—
272#400C2318yes—
273#400C2318yes—
274#400C2314yes—
275#400C2318yes—
276#400C2318yes—
277#400C2314yes—
278#399C2318yes—
279#399C2318yes—
280#399C2314yes—
281#399C2314yes—
282#398C2318yes—
283#398C2318yes—
284#398C2318yes—
285#398C2318yes—
286#398C2318yes—
287#398C2318yes—
288#398C2318yes—
289#398C2314yes—
290#398C2318yes—
291#398C2314yes—
292#398C2314yes—
293#397C2318yes—
294#397C2318yes—
295#397C2318yes—
296#397C2314yes—
297#397C2318yes—
298#397C2318yes—
299#397C2318yes—
300#397C2314yes—
301#397C2314yes—
302#397C2318yes—
303#396C2314yes—
304#396C2318yes—
305#396C2314yes—
306#396C2318yes—
307#395C2314yes—
308#395C2318yes—
309#395C2318yes—
310#394C2314yes—
311#394C2318yes—
312#394C2314yes—
313#393C2314yes—
314#393C2318yes—
315#391C2314yes—
316#391C2312yes—
317#391C2312yes—
318#391C2314yes—
319#391C2312yes—
320#391C2312yes—
321#391C2314yes—
322#391C2314yes—
323#391C2314yes—
324#391C2314yes—
325#391C2314yes—
326#391C2318yes—
327#391C2318yes—
328#391C2314yes—
329#391C2314yes—
330#391C2314yes—
331#391C2314yes—
332#391C2314yes—
333#391C2314yes—
334#391C2314yes—
335#391C2312yes—
336#391C2314yes—
337#391C2312yes—
338#390C2312yes—
339#390C2314yes—
340#390C2318yes—
341#390C2312yes—
342#390C2312yes—
343#389C2312yes—
344#389C2312yes—
345#389C2312yes—
346#389C2314yes—
347#389C2312yes—
348#389C2312yes—
349#389C2314yes—
350#389C2312yes—
351#389C2312yes—
352#389C2314yes—
353#389C2312yes—
354#389C2312yes—
355#389C2312yes—
356#389C2314yes—
357#389C2312yes—
358#389C2314yes—
359#389C2314yes—
360#389C2314yes—
361#389C2318yes—
362#389C2318yes—
363#389C2312yes—
364#389C2314yes—
365#389C2318yes—
366#389C2318yes—
367#389C2318yes—
368#389C2314yes—
369#389C2314yes—
370#389C2314yes—
371#389C2314yes—
372#389C2312yes—
373#389C2318yes—
374#389C2314yes—
375#389C2312yes—
376#389C2312yes—
377#389C2312yes—
378#388C2318yes—
379#388C2318yes—
380#388C2318yes—
381#388C2318yes—
382#388C2314yes—
383#388C2314yes—
384#388C2318yes—
385#388C2318yes—
386#388C2318yes—
387#388C2318yes—
388#388C2318yes—
389#388C2318yes—
390#388C2318yes—
391#388C2314yes—
392#387C2314yes—
393#387C2314yes—
394#387C2318yes—
395#387C2318yes—
396#387C2318yes—
397#387C2318yes—
398#387C2318yes—
399#387C2318yes—
400#387C2318yes—
401#387C2318yes—
402#387C2318yes—
403#387C2318yes—
404#387C2314yes—
405#387C2318yes—
406#387C2318yes—
407#387C2318yes—
408#387C2318yes—
409#387C2318yes—
410#387C2318yes—
411#387C2314yes—
412#387C2318yes—
413#387C2318yes—
414#387C2318yes—
415#387C2318yes—
416#387C2314yes—
417#387C2314yes—
418#387C2314yes—
419#387C2318yes—
420#387C2318yes—
421#386C2318yes—
422#386C2318yes—
423#386C2314yes—
424#385C2314yes—
425#385C2318yes—
426#385C2318yes—
427#385C2314yes—
428#385C2318yes—
429#385C2314yes—
430#385C2314yes—
431#385C2314yes—
432#384C2311yescharacteristic
433#384C2311yescharacteristic
434#384C2311yescharacteristic
435#384C2312yes—
436#384C2312yes—
437#384C2312yes—
438#384C2314yes—
439#384C2312yes—
440#384C2314yes—
441#384C2312yes—
442#384C2312yes—
443#384C2312yes—
444#384C2312yes—
445#384C2312yes—
446#382C2312yes—
447#382C2314yes—
448#382C2314yes—
449#382C2314yes—
450#382C2314yes—
451#382C2314yes—
452#382C2314yes—
453#382C2314yes—
454#382C2314yes—
455#382C2318yes—
456#382C2318yes—
457#381C2318yes—
458#381C2318yes—
459#380C2312yes—
460#380C2312yes—
461#380C2312yes—
462#380C2312yes—
463#380C2314yes—
464#380C2314yes—
465#380C2314yes—
466#380C2314yes—
467#380C2314yes—
468#380C2312yes—
469#380C2312yes—
470#380C2314yes—
471#380C2314yes—
472#380C2312yes—
473#380C2314yes—
474#380C2314yes—
475#380C2312yes—
476C4×C4⋊C4C2311yescharacteristic
477C4×C4⋊C4C2312yes—
478C4×C4⋊C4C2314yes—
479C4×C4⋊C4C2314yes—
480C4×C4⋊C4C2312yes—
481C4×C4⋊C4C2311yescharacteristic
482C4×C4⋊C4C2314yes—
483C4×C4⋊C4C2312yes—
484C4×C4⋊C4C2312yes—
485C4×C4⋊C4C2314yes—
486C4×C4⋊C4C2314yes—
487C4×C4⋊C4C2312yes—
488C4×C4⋊C4C2312yes—
489C4×C4⋊C4C2311yescharacteristic
490C4×C4⋊C4C2314yes—
491C4×C4⋊C4C2311yescharacteristic
492C4×C4⋊C4C2312yes—
493C4×C4⋊C4C2314yes—
494C4×C4⋊C4C2314yes—
495C4×C4⋊C4C2312yes—
496C4×C4⋊C4C2311yescharacteristic
497C4×C4⋊C4C2318yes—
498C4×C4⋊C4C2314yes—
499C4×C4⋊C4C2314yes—
500C4×C4⋊C4C2318yes—
501C4×C4⋊C4C2314yes—
502C4×C4⋊C4C2311yescharacteristic
503C4×C4⋊C4C2312yes—
504C4×C4⋊C4C2311yescharacteristic
505C4×C4⋊C4C2312yes—
506C4×C4⋊C4C2311yescharacteristic
507C4×C4⋊C4C2314yes—
508C4×C4⋊C4C2311yescharacteristic
509C4×C4⋊C4C2312yes—
510C4×C22⋊C4C2312yes—
511C4×C22⋊C4C2314yes—
512C4×C22⋊C4C2318yes—
513C4×C22⋊C4C2312yes—
514C4×C22⋊C4C2314yes—
515C4×C22⋊C4C2312yes—
516C4×C22⋊C4C2314yes—
517C4×C22⋊C4C2312yes—
518C4×C22⋊C4C2312yes—
519C4×C22⋊C4C2314yes—
520C4×C22⋊C4C2314yes—
521C4×C22⋊C4C2312yes—
522C43C2312yes—
523C43C2311yescharacteristic
524C22×Q8—28no—
525C22×Q8—28no—
526C22×Q8—44no—
527C22×Q8C2414yes—
528C22×Q8C2412yes—
529C22×Q8C2412yes—
530C22×Q8C2414yes—
531C22×Q8C2411yescharacteristic
532C22×Q8C2412yes—
533C22×D4C2411yescharacteristic
534C22×D4C2411yescharacteristic
535C22×D4C2414yes—
536C23×C4C2412yes—
537C23×C4C2412yes—
538C23×C4C2412yes—
539C23×C4C2414yes—
540C23×C4C2412yes—
541C23×C4C2412yes—
542C23×C4C2412yes—
543C23×C4C2414yes—
544C4⋊Q8—28no—
545C4⋊Q8—24no—
546C4⋊Q8—24no—
547C4⋊Q8—28no—
548C4⋊Q8—24no—
549C4⋊Q8—28no—
550C4⋊Q8—44no—
551#126—216no—
552#126—416no—
553#125—28no—
554#125—44no—
555#125—48no—
556#124—28no—
557#124—48no—
558#123—216no—
559C22⋊Q8—28no—
560C22⋊Q8—28no—
561C22⋊Q8—28no—
562C22⋊Q8—216no—
563C22⋊Q8—44no—
564C22⋊Q8—48no—
565C22⋊Q8—48no—
566C22⋊Q8—48no—
567C22⋊Q8—48no—
568#121—28no—
569#121—44no—
570C4×Q8—24no—
571C4×Q8—28no—
572C4×Q8—24no—
573C4×Q8—24no—
574C4×Q8—28no—
575C4×Q8—48no—
576C4×Q8—44no—
577C4×Q8—48no—
578C4×Q8—44no—
579C4×Q8—44no—
580C4×Q8—48no—
581C4×Q8—48no—
582C4×Q8—48no—
583C4×Q8—48no—
584C4×Q8—48no—
585C4×D4—28no—
586C4×D4—216no—
587C4×D4—24no—
588C4×D4—24no—
589C4×D4—24no—
590C4×D4—44no—
591C4×D4—42no—
592C4×D4—42no—
593C4×D4#4118yes—
594#117—216no—
595#117—48no—
596#117—48no—
597#117—48no—
598C2×C4⋊C4—44no—
599C2×C4⋊C4—48no—
600C2×C4⋊C4C2411yescharacteristic
601C2×C4⋊C4C2412yes—
602C2×C4⋊C4C2412yes—
603C2×C4⋊C4C2414yes—
604C2×C4⋊C4C2414yes—
605C2×C4⋊C4C2412yes—
606C2×C4⋊C4C2414yes—
607C2×C4⋊C4C2414yes—
608C2×C4⋊C4C2411yescharacteristic
609C2×C4⋊C4C2412yes—
610C2×C4⋊C4C2411yescharacteristic
611C2×C4⋊C4C2411yescharacteristic
612C2×C4⋊C4C2414yes—
613C2×C4⋊C4C2412yes—
614C2×C4⋊C4C2411yescharacteristic
615C2×C4⋊C4C2411yescharacteristic
616C2×C4⋊C4C2412yes—
617C2×C4⋊C4C2412yes—
618C2×C4⋊C4C2412yes—
619C2×C4⋊C4C2411yescharacteristic
620C2×C4⋊C4C2412yes—
621C2×C4⋊C4C2414yes—
622C2×C4⋊C4C2414yes—
623C2×C4⋊C4C2411yescharacteristic
624C2×C4⋊C4C2412yes—
625C2×C4⋊C4C2412yes—
626C2×C4⋊C4C2412yes—
627C2×C4⋊C4C2414yes—
628C2×C4⋊C4C2412yes—
629C2×C4⋊C4C2414yes—
630C2×C4⋊C4C2414yes—
631C2×C4⋊C4C2412yes—
632C2×C4⋊C4C2412yes—
633C2×C4⋊C4C2414yes—
634C2×C4⋊C4C2414yes—
635C2×C4⋊C4C2414yes—
636C2×C4⋊C4C2414yes—
637C2×C4⋊C4C2414yes—
638C2×C4⋊C4C2414yes—
639C2×C4⋊C4C2418yes—
640C2×C4⋊C4C2418yes—
641C2×C4⋊C4C2418yes—
642C2×C4⋊C4C2412yes—
643C2×C4⋊C4C2418yes—
644C2×C4⋊C4C2414yes—
645C2×C4⋊C4C2418yes—
646C2×C4⋊C4C2414yes—
647C2×C4⋊C4C2418yes—
648C2×C4⋊C4C2414yes—
649C2×C4⋊C4C2414yes—
650C2×C4⋊C4C2414yes—
651C2×C4⋊C4C2414yes—
652C2×C4⋊C4C2412yes—
653C2×C4⋊C4C2412yes—
654C2×C4⋊C4C2414yes—
655C2×C4⋊C4C2414yes—
656C2×C4⋊C4C2414yes—
657C2×C4⋊C4C2418yes—
658C2×C4⋊C4C2411yescharacteristic
659C2×C22⋊C4C2414yes—
660C2×C22⋊C4C2414yes—
661C2×C22⋊C4C2414yes—
662C2×C22⋊C4C2414yes—
663C2×C22⋊C4C2414yes—
664C2×C22⋊C4C2412yes—
665C2×C22⋊C4C2412yes—
666C2×C22⋊C4C2412yes—
667C2×C22⋊C4C2414yes—
668C2×C22⋊C4C2418yes—
669C2×C22⋊C4C2418yes—
670C2×C22⋊C4C2414yes—
671C2×C22⋊C4C2414yes—
672C2×C22⋊C4C2414yes—
673C2×C22⋊C4C2412yes—
674C2×C22⋊C4C2412yes—
675C2×C22⋊C4C2414yes—
676C2×C22⋊C4C2418yes—
677C2×C22⋊C4C2418yes—
678C2×C22⋊C4C2414yes—
679C2×C22⋊C4C2414yes—
680C2×C22⋊C4C2412yes—
681C2×C42—28no—
682C2×C42—28no—
683C2×C42—48no—
684C2×C42C2412yes—
685C2×C42C2412yes—
686C2×C42C2414yes—
687C2×C42C2414yes—
688C2×C42C2411yescharacteristic
689C2×C42C2412yes—
690C2×C42C2411yescharacteristic
691C2×C42C2412yes—
692C2×C42C2412yes—
693C2×C42C2414yes—
694C2×C42C2412yes—
695C2×C42C2412yes—
696C2×C42C2412yes—
697C2×C42C2411yescharacteristic
698C2×C42C2412yes—
699C2×C42C2412yes—
700C2×C42C2412yes—
701C2×C42C2418yes—
702C2×C42C2418yes—
703C2×C42C2414yes—
704C2×C42C2414yes—
705C2×C42C2418yes—
706C2×C42C2418yes—
707C2×C42C2411yescharacteristic
708C2×C42C2412yes—
709C2×C42C2411yescharacteristic
710C2×C42C2411yescharacteristic
711C2×C42C2411yescharacteristic
712#95C2412yes—
713#95C2414yes—
714#95C2414yes—
715#95C2412yes—
716#95C2412yes—
717#95C2414yes—
718#95C2414yes—
719#95C2412yes—
720#95C2412yes—
721#95C2412yes—
722#95C2414yes—
723#95C2414yes—
724#95C2418yes—
725#95C2414yes—
726#95C2414yes—
727#95C2412yes—
728#95C2414yes—
729#95C2414yes—
730#95C2412yes—
731#95C2412yes—
732#95C2414yes—
733#95C2414yes—
734#95C2418yes—
735#95C2414yes—
736#95C2418yes—
737#95C2414yes—
738#95C2414yes—
739#95C2414yes—
740#95C2414yes—
741#95C2418yes—
742#95C2414yes—
743#95C2418yes—
744#95C2418yes—
745#95C2418yes—
746#95C2418yes—
747#95C2418yes—
748#95C2418yes—
749#95C2414yes—
750#95C2414yes—
751#95C2418yes—
752#95C2418yes—
753#95C2418yes—
754#95C2418yes—
755#95C2418yes—
756#95C2418yes—
757#95C2418yes—
758C24C2512yes—
759C24C2512yes—
760C2×Q8—22no—
761C2×Q8—24no—
762C2×Q8—28no—
763C2×Q8—24no—
764C2×Q8—22no—
765C2×Q8—24no—
766C2×Q8—24no—
767C2×Q8—28no—
768C2×Q8—24no—
769C2×Q8—28no—
770C2×Q8—28no—
771C2×Q8—24no—
772C2×Q8—24no—
773C2×Q8—28no—
774C2×Q8—44no—
775C2×Q8—42no—
776C2×Q8—42no—
777C2×Q8—432no—
778C2×Q82−1+414yes—
779C2×D4—28no—
780C2×D4—22no—
781C2×D4—22no—
782C2×D4—22no—
783C2×D4—22no—
784C2×D4—22no—
785C2×D4—44no—
786C2×D4—44no—
787C2×D4C2×#4114yes—
788C22×C4—24no—
789C22×C4—24no—
790C22×C4—28no—
791C22×C4—24no—
792C22×C4—24no—
793C22×C4—24no—
794C22×C4—24no—
795C22×C4—24no—
796C22×C4—24no—
797C22×C4—24no—
798C22×C4—28no—
799C22×C4—24no—
800C22×C4—24no—
801C22×C4—24no—
802C22×C4—24no—
803C22×C4—44no—
804C22×C4—44no—
805C22×C4—42no—
806C22×C4—42no—
807C22×C4—44no—
808C22×C4—42no—
809C22×C4—42no—
810C22×C4—44no—
811C22×C4C2×#4118yes—
812C22×C4C2514yes—
813C22×C4C2512yes—
814C22×C4C2514yes—
815C22×C4C2512yes—
816C22×C4C2511yescharacteristic
817C22×C4C2514yes—
818C22×C4C2514yes—
819C22×C4C2512yes—
820C22×C4C2512yes—
821C22×C4C2512yes—
822C22×C4C2512yes—
823C22×C4C2512yes—
824C22×C4C2518yes—
825C22×C4C2514yes—
826C22×C4C2514yes—
827C22×C4C2512yes—
828C22×C4C2512yes—
829C22×C4C2511yescharacteristic
830C22×C4C2511yescharacteristic
831C22×C4C2511yescharacteristic
832C22×C4C2512yes—
833C22×C4C2511yescharacteristic
834C22×C4C2511yescharacteristic
835C22×C4C2511yescharacteristic
836C4⋊C4—28no—
837C4⋊C4—28no—
838C4⋊C4—28no—
839C4⋊C4—24no—
840C4⋊C4—24no—
841C4⋊C4—24no—
842C4⋊C4—22no—
843C4⋊C4—28no—
844C4⋊C4—28no—
845C4⋊C4—24no—
846C4⋊C4—24no—
847C4⋊C4—22no—
848C4⋊C4—24no—
849C4⋊C4—28no—
850C4⋊C4—28no—
851C4⋊C4—24no—
852C4⋊C4—22no—
853C4⋊C4—24no—
854C4⋊C4—28no—
855C4⋊C4—22no—
856C4⋊C4—22no—
857C4⋊C4—24no—
858C4⋊C4—22no—
859C4⋊C4—24no—
860C4⋊C4—28no—
861C4⋊C4—24no—
862C4⋊C4—28no—
863C4⋊C4—28no—
864C4⋊C4—24no—
865C4⋊C4—24no—
866C4⋊C4—22no—
867C4⋊C4—22no—
868C4⋊C4—24no—
869C4⋊C4—24no—
870C4⋊C4—44no—
871C4⋊C4—44no—
872C4⋊C4—44no—
873C4⋊C4—42no—
874C4⋊C4—42no—
875C4⋊C4—44no—
876C4⋊C4—44no—
877C4⋊C4—48no—
878C4⋊C4—44no—
879C4⋊C4—44no—
880C4⋊C4—44no—
881C4⋊C4—42no—
882C4⋊C4—44no—
883C4⋊C4—48no—
884C4⋊C4—48no—
885C4⋊C4—48no—
886C4⋊C4—48no—
887C4⋊C4—48no—
888C4⋊C4—44no—
889C4⋊C4—48no—
890C4⋊C4—44no—
891C4⋊C4—44no—
892C4⋊C4—44no—
893C4⋊C4—44no—
894C4⋊C4C2×#4114yes—
895C22⋊C4—28no—
896C22⋊C4—28no—
897C22⋊C4—28no—
898C22⋊C4—28no—
899C22⋊C4—28no—
900C22⋊C4—24no—
901C22⋊C4—24no—
902C22⋊C4—24no—
903C22⋊C4—28no—
904C22⋊C4—44no—
905C22⋊C4—44no—
906C22⋊C4—44no—
907C22⋊C4—48no—
908C22⋊C4—48no—
909C22⋊C4—44no—
910C22⋊C4—42no—
911C22⋊C4—42no—
912C22⋊C4—44no—
913C22⋊C4—44no—
914C22⋊C4—48no—
915C22⋊C4—48no—
916C22⋊C4C2×#4118yes—
917C42—24no—
918C42—24no—
919C42—24no—
920C42—28no—
921C42—24no—
922C42—24no—
923C42—24no—
924C42—24no—
925C42—24no—
926C42—28no—
927C42—24no—
928C42—22no—
929C42—24no—
930C42—28no—
931C42—22no—
932C42—22no—
933C42—24no—
934C42—44no—
935C42—44no—
936C42—41no—
937C42—42no—
938C42—48no—
939C42—48no—
940C42—48no—
941C42—48no—
942C42C2×#4114yes—
943C42H(5,𝔽2)14yes—
944C422−1+414yes—
945C23—22no—
946C23—22no—
947C23—22no—
948C23—22no—
949C23—22no—
950C23—22no—
951C23—22no—
952C23—22no—
953C23—22no—
954C23—22no—
955C23—22no—
956C23—22no—
957C23—22no—
958C23C22×#4114yes—
959C23C2611yescharacteristic
960Q8—28no—
961Q8—416no—
962Q8—48no—
963Q8—48no—
964Q8—48no—
965Q8—416no—
966D4—28no—
967D4—44no—
968D4—88no—
969C2×C4—22no—
970C2×C4—22no—
971C2×C4—22no—
972C2×C4—21no—
973C2×C4—22no—
974C2×C4—21no—
975C2×C4—21no—
976C2×C4—21no—
977C2×C4—21no—
978C2×C4—21no—
979C2×C4—216no—
980C2×C4—22no—
981C2×C4—22no—
982C2×C4—22no—
983C2×C4—24no—
984C2×C4—22no—
985C2×C4—24no—
986C2×C4—24no—
987C2×C4—22no—
988C2×C4—22no—
989C2×C4—24no—
990C2×C4—22no—
991C2×C4—24no—
992C2×C4—22no—
993C2×C4—28no—
994C2×C4—24no—
995C2×C4—22no—
996C2×C4—21no—
997C2×C4—24no—
998C2×C4—22no—
999C2×C4—22no—
1000C2×C4—22no—
1001C2×C4—28no—
1002C2×C4—24no—
1003C2×C4—24no—
1004C2×C4—22no—
1005C2×C4—24no—
1006C2×C4—22no—
1007C2×C4—21no—
1008C2×C4—21no—
1009C2×C4—22no—
1010C2×C4—24no—
1011C2×C4—22no—
1012C2×C4—24no—
1013C2×C4—24no—
1014C2×C4—24no—
1015C2×C4—28no—
1016C2×C4—22no—
1017C2×C4—24no—
1018C2×C4—22no—
1019C2×C4—22no—
1020C2×C4—22no—
1021C2×C4—22no—
1022C2×C4—22no—
1023C2×C4—24no—
1024C2×C4—22no—
1025C2×C4—24no—
1026C2×C4—22no—
1027C2×C4—24no—
1028C2×C4—416no—
1029C2×C4—48no—
1030C2×C4—48no—
1031C2×C4—48no—
1032C2×C4—84no—
1033C2×C4—84no—
1034C2×C4—88no—
1035C2×C4C22×#4112yes—
1036C2×C4C22×#4114yes—
1037C2×C4C22×#4112yes—
1038C2×C4C22×#4112yes—
1039C2×C4C2×H(5,𝔽2)12yes—
1040C2×C4C2×H(5,𝔽2)12yes—
1041C2×C4C2×H(5,𝔽2)12yes—
1042C2×C4C2×2−1+414yes—
1043C2×C4C2×2−1+412yes—
1044C2×C4C2×2−1+412yes—
1045C2×C4C2×2−1+412yes—
1046C2×C4C2×2−1+412yes—
1047C2×C4#58512yes—
1048C2×C4#58512yes—
1049C22—24no—
1050C22—24no—
1051C22—24no—
1052C22—42no—
1053C22—42no—
1054C22—42no—
1055C22—42no—
1056C22—42no—
1057C22—42no—
1058C22—42no—
1059C22—42no—
1060C22—42no—
1061C22—42no—
1062C22—42no—
1063C22C23×#4111yescharacteristic
1064C22C22×H(5,𝔽2)11yescharacteristic
1065C22C22×2−1+411yescharacteristic
1066C22C22×2−1+411yescharacteristic
1067C22C2×#58511yescharacteristic
1068C22C2×#58511yescharacteristic
1069C222−1+611yescharacteristic
1070C4—22no—
1071C4—24no—
1072C4—24no—
1073C4—22no—
1074C4—22no—
1075C4—42no—
1076C4—48no—
1077C4—42no—
1078C4—42no—
1079C4—44no—
1080C4—42no—
1081C4—44no—
1082C4—42no—
1083C4—44no—
1084C4—42no—
1085C4—41no—
1086C4—44no—
1087C4—42no—
1088C4—44no—
1089C4—42no—
1090C4—44no—
1091C4#350714yes—
1092C4#352014yes—
1093C4#355414yes—
1094C2—44no—
1095C2—82no—
1096C2C2×#355411yescharacteristic
1097C2C2×#352011yescharacteristic
1098C2C2×#350711yescharacteristic
1099C2#6292511yescharacteristic
1100C2#6294711yescharacteristic
1101C2#6300911yescharacteristic
1102C2#6303411yescharacteristic
subgroupG/H
center, commutator, Frattini, socle, cosocleC23C26
prime radical#2537C22
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. #59666C2semidirect
3. #59259C2semidirect
4. #59065C2semidirect
5. #48521C2semidirect
6. #45662C2semidirect
7. #45329C2semidirect
8. #45327C2semidirect
9. #42656C2semidirect
10. #42631C2semidirect
11. #40220C2semidirect
12. #39478C2semidirect
13. #39478C2semidirect
14. #39200C2semidirect
15. #38911C2semidirect
16. #36598C2semidirect
17. #36579C2semidirect
18. #36454C2semidirect
19. #36188C2semidirect
20. #36134C2semidirect
22. #35179C2semidirect
23. #34941C2semidirect
25. #34383C2semidirect
26. C4×D4×Q8C2semidirect

Maximal subgroups

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

subgroupindex
#598702
#596662
#592592
#590652
#485212
#456622
#453292
#453272
#426562
#426312
#402202
#394782
#392002
#389112
#365982
#365792
#364542
#361882
#361342
#351962
#351792
#349412
#349322
#343832
C4×D4×Q82