Finite Group Databasebeta

← #7746762

Subgroups — #7746762

Order 512.

4650 conjugacy classes of subgroups.

The subgroup lattice has 1030 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#45338C212yesmaximal, complemented
2#45329C214yesmaximal, complemented
3#45306C212yesmaximal, complemented
4#45295C214yesmaximal, complemented
5#45290C214yesmaximal, complemented
6#45078C214yesmaximal
7#45001C214yesmaximal, complemented
8#42901C214yesmaximal, complemented
9#42640C214yesmaximal, complemented
10#42549C214yesmaximal, complemented
11#36608C211yesmaximal, characteristic, complemented
12Q8×C4⋊Q8C211yesmaximal, characteristic, complemented
13#36194C212yesmaximal, complemented
14#36188C211yesmaximal, characteristic, complemented
15#36151C211yesmaximal, characteristic, complemented
16#36129C212yesmaximal, complemented
17#36030C212yesmaximal
18#35945C214yesmaximal, complemented
19#35867C214yesmaximal, complemented
20#35711C212yesmaximal, complemented
21#35283C212yesmaximal, complemented
22#35283C211yesmaximal, characteristic, complemented
23#34551C211yesmaximal, characteristic
24#34225C212yesmaximal, complemented
25#34209C211yesmaximal, characteristic, complemented
26C2×Q82C2212yes—
27C2×#556C2212yes—
28C2×#533C2212yes—
29C22×C4⋊Q8C2211yescharacteristic
30C2×#519C2212yes—
31#2868C2211yescharacteristic
32#2868C2212yes—
33#2862C2212yes—
34#2862C2211yescharacteristic
35#2857C2212yes—
36#2857C2212yes—
37#2857C2212yes—
38#2838C2218yes—
39#2810C2218yes—
40#2798C2218yes—
41#2789C2218yes—
42#2783C2218yes—
43#2775C2218yes—
44#2767C2218yes—
45#2759C2218yes—
46#2758C2218yes—
47#2745C2218yes—
48#2737C2218yes—
49#2731C2218yes—
50#2716C2218yes—
51#2666C2218yes—
52#2654C2218yes—
53#2647C2214yes—
54#2647C2212yes—
55#2632C2214yes—
56#2628C2214yes—
57#2628C2214yes—
58#2628C2212yes—
59#2612C2218yes—
60#2610C2214yes—
61#2605C2218yes—
62#2599C2214yes—
63#2590C2218yes—
64#2588C2218yes—
65#2581C2214yes—
66#2581C2212yes—
67#2581C2214yes—
68#2573C2218yes—
69#2571C2214yes—
70#2568C2212yes—
71#2568C2214yes—
72#2567C2214yes—
73#2567C2212yes—
74#2563C2214yes—
75#2551C2214yes—
76#2551C2214yes—
77#2551C2214yes—
78#2550C2214yes—
79#2547C2214yes—
80#2538C2214yes—
81#2536C2212yes—
82#2533C2218yes—
83#2526C2218yes—
84#2514C2214yes—
85#2514C2214yes—
86#2514C2214yes—
87#2511C2214yes—
88#2511C2214yes—
89#2511C2214yes—
90#2499C2214yes—
91#2497C2214yes—
92#2497C2214yes—
93#2496C2214yes—
94#2496C2214yes—
95#2492C2214yes—
96#2492C2214yes—
97#2492C2214yes—
98#2492C2214yes—
99#2492C2214yes—
100#2492C2214yes—
101#2489C2214yes—
102#2479C2218yes—
103#2469C2218yes—
104#2469C2218yes—
105#2453C2214yes—
106#2451C2214yes—
107#2451C2218yes—
108#2451C2214yes—
109#2451C2214yes—
110#2451C2214yes—
111#2446C2218yes—
112#2446C2214yes—
113#2442C2214yes—
114#2439C2218yes—
115#2439C2214yes—
116#2439C2214yes—
117#2439C2214yes—
118#2429C2214yes—
119#2423C2214yes—
120#2423C2214yes—
121#2423C2214yes—
122#2421C2214yes—
123#2417C2214yes—
124#2415C2214yes—
125#2409C2214yes—
126#2402C2212yes—
127#2402C2211yescharacteristic
128#2401C2212yes—
129#2401C2212yes—
130#2401C2212yes—
131#2399C2214yes—
132#2398C2211yescharacteristic
133#2398C2212yes—
134#2396C2212yes—
135#2396C2214yes—
136#2396C2211yescharacteristic
137#2395C2212yes—
138#2395C2212yes—
139#2395C2212yes—
140#2392C2212yes—
141#2392C2211yescharacteristic
142#2370C2214yes—
143#2370C2214yes—
144#2369C2214yes—
145#2365C2214yes—
146#2365C2214yes—
147#2365C2214yes—
148#2362C2214yes—
149#2362C2214yes—
150#2362C2214yes—
151#2360C2214yes—
152#2356C2214yes—
153#2356C2212yes—
154#2356C2214yes—
155#2355C2214yes—
156#2354C2214yes—
157#2352C2214yes—
158#2351C2212yes—
159#2351C2214yes—
160Q8×C4⋊C4C2214yes—
161#2347C2214yes—
162#2346C2214yes—
163#2344C2214yes—
164#2344C2214yes—
165Q8×C22⋊C4C2214yes—
166#2331C2212yes—
167#2331C2214yes—
168#2327C2212yes—
169#2327C2212yes—
170#2323C2214yes—
171#2323C2214yes—
172#2320C2214yes—
173#2314C2214yes—
174#2314C2212yes—
175#2310C2212yes—
176C4×C4⋊Q8C2211yescharacteristic
177C4×C4⋊Q8C2212yes—
178C4×C4⋊Q8C2212yes—
179C4×C4⋊Q8C2211yescharacteristic
180C4×C4⋊Q8C2211yescharacteristic
181C4×C4⋊Q8C2211yescharacteristic
182C4×C4⋊Q8C2212yes—
183#2285C2212yes—
184#2285C2211yescharacteristic
185#2276C2214yes—
186C42×Q8C2211yescharacteristic
187C42×D4C2212yes—
188C42×D4C2211yescharacteristic
189C4×#117C2211yescharacteristic
190C4×#117C2212yes—
191C23×Q8C2312yes—
192Q82—48no—
193#556—48no—
194#533—216no—
195C2×C4⋊Q8—28no—
196C2×C4⋊Q8C2311yescharacteristic
197C2×C4⋊Q8C2312yes—
198C2×C4⋊Q8C2312yes—
199C2×C4⋊Q8C2312yes—
200C2×C4⋊Q8C2314yes—
201C2×C4⋊Q8C2314yes—
202C2×C4⋊Q8C2314yes—
203C2×C4⋊Q8C2314yes—
204C2×C4⋊Q8C2314yes—
205C2×C4⋊Q8C2314yes—
206C2×C4⋊Q8C2318yes—
207C2×C4⋊Q8C2311yescharacteristic
208C2×#126C2318yes—
209C2×#125C2314yes—
210C2×#124C2314yes—
211C2×C22⋊Q8C2314yes—
212C2×C22⋊Q8C2314yes—
213C2×C22⋊Q8C2314yes—
214C2×C22⋊Q8C2314yes—
215C2×C22⋊Q8C2314yes—
216#519—48no—
217C2×C4×Q8C2312yes—
218C2×C4×Q8C2312yes—
219C2×C4×Q8C2314yes—
220C2×C4×Q8C2314yes—
221C2×C4×Q8C2312yes—
222C2×C4×Q8C2311yescharacteristic
223C2×C4×Q8C2314yes—
224C2×C4×Q8C2314yes—
225C2×C4×Q8C2314yes—
226C2×C4×Q8C2312yes—
227C2×C4×Q8C2312yes—
228C2×C4×Q8C2314yes—
229C2×C4×Q8C2314yes—
230C2×C4×Q8C2314yes—
231C2×C4×Q8C2314yes—
232C2×C4×D4C2312yes—
233C2×C4×D4C2312yes—
234C2×C4×D4C2311yescharacteristic
235C2×C4×D4C2312yes—
236C2×C4×D4C2312yes—
237C2×#117C2311yescharacteristic
238C2×#117C2312yes—
239C2×#117C2314yes—
240C2×#117C2311yescharacteristic
241C2×#117C2312yes—
242C2×#117C2312yes—
243C2×#117C2314yes—
244C2×#117C2314yes—
245C2×#117C2314yes—
246C22×C4⋊C4C2314yes—
247C22×C42C2311yescharacteristic
248C22×C42C2312yes—
249#401C2318yes—
250#401C2312yes—
251#400C2311yescharacteristic
252#400C2314yes—
253#400C2314yes—
254#400C2314yes—
255#400C2314yes—
256#400C2318yes—
257#400C2318yes—
258#400C2318yes—
259#400C2318yes—
260#400C2318yes—
261#400C2318yes—
262#400C2312yes—
263#400C2312yes—
264#400C2318yes—
265#400C2318yes—
266#400C2318yes—
267#400C2312yes—
268#400C2312yes—
269#400C2312yes—
270#400C2312yes—
271#400C2312yes—
272#399C2318yes—
273#399C2311yescharacteristic
274#399C2314yes—
275#399C2312yes—
276#398C2318yes—
277#398C2312yes—
278#398C2318yes—
279#398C2318yes—
280#398C2314yes—
281#398C2312yes—
282#398C2318yes—
283#398C2311yescharacteristic
284#398C2312yes—
285#398C2312yes—
286#398C2318yes—
287#397C2312yes—
288#397C2312yes—
289#397C2318yes—
290#397C2318yes—
291#397C2311yescharacteristic
292#397C2312yes—
293#397C2312yes—
294#397C2312yes—
295#397C2312yes—
296#397C2312yes—
297#397C2318yes—
298#396C2318yes—
299#396C2318yes—
300#396C2312yes—
301#396C2312yes—
302#396C2312yes—
303#396C2318yes—
304#395C2318yes—
305#395C2314yes—
306#395C2318yes—
307#395C2314yes—
308#395C2311yescharacteristic
309#395C2314yes—
310#395C2318yes—
311#395C2318yes—
312#395C2314yes—
313#394C2314yes—
314#394C2311yescharacteristic
315#394C2312yes—
316#394C2312yes—
317#394C2312yes—
318#394C2312yes—
319#393C2318yes—
320#393C2318yes—
321#393C2314yes—
322#393C2318yes—
323#393C2318yes—
324#393C2311yescharacteristic
325#393C2312yes—
326#392C2311yescharacteristic
327#391C2312yes—
328#391C2312yes—
329#391C2312yes—
330#391C2312yes—
331#391C2314yes—
332#391C2314yes—
333#391C2314yes—
334#391C2318yes—
335#391C2318yes—
336#391C2314yes—
337#391C2318yes—
338#391C2318yes—
339#391C2318yes—
340#391C2318yes—
341#391C2314yes—
342#391C2314yes—
343#391C2314yes—
344#391C2318yes—
345#391C2318yes—
346#391C2314yes—
347#391C2314yes—
348#391C2314yes—
349#391C2314yes—
350#391C2314yes—
351#391C2318yes—
352#390C2318yes—
353#389C2314yes—
354#389C2314yes—
355#389C2314yes—
356#389C2314yes—
357#389C2314yes—
358#389C2314yes—
359#389C2314yes—
360#389C2314yes—
361#389C2314yes—
362#389C2314yes—
363#389C2318yes—
364#389C2318yes—
365#389C2318yes—
366#389C2314yes—
367#389C2318yes—
368#389C2314yes—
369#389C2318yes—
370#389C2318yes—
371#389C2314yes—
372#389C2314yes—
373#389C2318yes—
374#389C2314yes—
375#389C2314yes—
376#389C2318yes—
377#388C2318yes—
378#388C2318yes—
379#388C2318yes—
380#388C2318yes—
381#388C2318yes—
382#388C2318yes—
383#388C2318yes—
384#388C2318yes—
385#388C2318yes—
386#388C2318yes—
387#388C2318yes—
388#388C2318yes—
389#387C2318yes—
390#387C2318yes—
391#387C2318yes—
392#387C2318yes—
393#387C2318yes—
394#387C2318yes—
395#387C2318yes—
396#387C2318yes—
397#387C2318yes—
398#387C2318yes—
399#387C2318yes—
400#387C2318yes—
401#387C2318yes—
402#387C2318yes—
403#387C2318yes—
404#387C2318yes—
405#387C2318yes—
406#387C2318yes—
407#387C2318yes—
408#387C2318yes—
409#387C2318yes—
410#387C2318yes—
411#387C2318yes—
412#387C2318yes—
413#386C2318yes—
414#385C2318yes—
415#384C2311yescharacteristic
416#384C2311yescharacteristic
417#384C2312yes—
418#384C2312yes—
419#384C2314yes—
420#384C2314yes—
421#384C2314yes—
422#384C2314yes—
423#383C2318yes—
424#383C2314yes—
425#383C2318yes—
426#382C2318yes—
427#382C2314yes—
428#382C2318yes—
429#382C2314yes—
430#382C2312yes—
431#382C2312yes—
432#382C2312yes—
433#382C2314yes—
434#382C2314yes—
435#381C2318yes—
436#380C2314yes—
437#380C2314yes—
438#380C2314yes—
439#380C2314yes—
440#380C2314yes—
441#380C2314yes—
442#380C2318yes—
443#380C2314yes—
444#380C2314yes—
445#380C2314yes—
446C4×C4⋊C4C2314yes—
447C4×C4⋊C4C2314yes—
448C4×C4⋊C4C2314yes—
449C4×C4⋊C4C2314yes—
450C4×C4⋊C4C2314yes—
451C4×C4⋊C4C2314yes—
452C4×C4⋊C4C2314yes—
453C4×C4⋊C4C2314yes—
454C4×C4⋊C4C2314yes—
455C4×C4⋊C4C2314yes—
456C4×C4⋊C4C2311yescharacteristic
457C4×C4⋊C4C2312yes—
458C4×C4⋊C4C2311yescharacteristic
459C4×C4⋊C4C2314yes—
460C4×C4⋊C4C2312yes—
461C4×C4⋊C4C2318yes—
462C4×C4⋊C4C2314yes—
463C4×C4⋊C4C2318yes—
464C4×C4⋊C4C2318yes—
465C4×C4⋊C4C2318yes—
466C4×C4⋊C4C2312yes—
467C4×C4⋊C4C2312yes—
468C4×C4⋊C4C2314yes—
469C4×C4⋊C4C2314yes—
470C4×C4⋊C4C2312yes—
471C4×C4⋊C4C2312yes—
472C4×C4⋊C4C2312yes—
473C4×C4⋊C4C2312yes—
474C4×C4⋊C4C2312yes—
475C4×C4⋊C4C2312yes—
476C4×C4⋊C4C2312yes—
477C4×C4⋊C4C2312yes—
478C4×C4⋊C4C2312yes—
479C4×C4⋊C4C2312yes—
480C4×C22⋊C4C2318yes—
481C4×C22⋊C4C2312yes—
482C4×C22⋊C4C2312yes—
483C4×C22⋊C4C2312yes—
484C4×C22⋊C4C2312yes—
485C4×C22⋊C4C2312yes—
486C4×C22⋊C4C2312yes—
487C4×C22⋊C4C2312yes—
488C4×C22⋊C4C2312yes—
489C4×C22⋊C4C2312yes—
490C4×C22⋊C4C2312yes—
491C4×C22⋊C4C2312yes—
492C4×C22⋊C4C2312yes—
493C4×C22⋊C4C2312yes—
494C4×C22⋊C4C2312yes—
495C4×C22⋊C4C2312yes—
496#376C2312yes—
497#376C2311yescharacteristic
498#376C2311yescharacteristic
499#376C2318yes—
500#376C2314yes—
501#376C2312yes—
502C43C2311yescharacteristic
503C43C2312yes—
504C43C2311yescharacteristic
505C22×Q8—28no—
506C22×Q8—28no—
507C22×Q8—44no—
508C22×Q8C2411yescharacteristic
509C22×Q8C2414yes—
510C22×Q8C2412yes—
511C22×Q8C2414yes—
512C22×Q8C2412yes—
513C22×Q8C2414yes—
514C22×Q8C2418yes—
515C22×D4C2412yes—
516C22×D4C2411yescharacteristic
517C23×C4C2412yes—
518C23×C4C2412yes—
519C23×C4C2412yes—
520C23×C4C2412yes—
521C23×C4C2414yes—
522C23×C4C2411yescharacteristic
523C4⋊Q8—28no—
524C4⋊Q8—216no—
525C4⋊Q8—24no—
526C4⋊Q8—28no—
527C4⋊Q8—28no—
528C4⋊Q8—48no—
529C4⋊Q8—48no—
530C4⋊Q8—48no—
531C4⋊Q8—48no—
532C4⋊Q8—48no—
533C4⋊Q8—416no—
534C4⋊Q8#4118yes—
535#126—416no—
536#125—216no—
537#124—48no—
538C22⋊Q8—216no—
539C22⋊Q8—216no—
540C22⋊Q8—48no—
541C22⋊Q8—48no—
542C22⋊Q8—48no—
543C4×Q8—216no—
544C4×Q8—216no—
545C4×Q8—28no—
546C4×Q8—28no—
547C4×Q8—24no—
548C4×Q8—28no—
549C4×Q8—216no—
550C4×Q8—48no—
551C4×Q8—48no—
552C4×Q8—48no—
553C4×Q8—44no—
554C4×Q8—44no—
555C4×Q8—48no—
556C4×Q8—48no—
557C4×Q8—48no—
558C4×D4—28no—
559C4×D4—24no—
560C4×D4—28no—
561C4×D4—44no—
562C4×D4—44no—
563#117—24no—
564#117—216no—
565#117—24no—
566#117—28no—
567#117—44no—
568#117—48no—
569#117—48no—
570#117—44no—
571#117—48no—
572C2×C4⋊C4—216no—
573C2×C4⋊C4C2414yes—
574C2×C4⋊C4C2418yes—
575C2×C4⋊C4C2412yes—
576C2×C4⋊C4C2411yescharacteristic
577C2×C4⋊C4C2411yescharacteristic
578C2×C4⋊C4C2414yes—
579C2×C4⋊C4C2412yes—
580C2×C4⋊C4C2414yes—
581C2×C4⋊C4C2414yes—
582C2×C4⋊C4C2414yes—
583C2×C4⋊C4C2412yes—
584C2×C4⋊C4C2412yes—
585C2×C4⋊C4C2412yes—
586C2×C4⋊C4C2411yescharacteristic
587C2×C4⋊C4C2412yes—
588C2×C4⋊C4C2412yes—
589C2×C4⋊C4C2418yes—
590C2×C4⋊C4C2418yes—
591C2×C4⋊C4C2414yes—
592C2×C4⋊C4C2414yes—
593C2×C4⋊C4C2412yes—
594C2×C4⋊C4C2411yescharacteristic
595C2×C4⋊C4C2414yes—
596C2×C4⋊C4C2414yes—
597C2×C4⋊C4C2418yes—
598C2×C4⋊C4C2412yes—
599C2×C4⋊C4C2412yes—
600C2×C4⋊C4C2412yes—
601C2×C4⋊C4C2414yes—
602C2×C4⋊C4C2414yes—
603C2×C4⋊C4C2414yes—
604C2×C4⋊C4C2414yes—
605C2×C4⋊C4C2412yes—
606C2×C4⋊C4C2412yes—
607C2×C4⋊C4C2412yes—
608C2×C4⋊C4C2412yes—
609C2×C4⋊C4C2418yes—
610C2×C4⋊C4C2418yes—
611C2×C4⋊C4C2418yes—
612C2×C4⋊C4C2418yes—
613C2×C4⋊C4C2418yes—
614C2×C4⋊C4C2418yes—
615C2×C4⋊C4C2418yes—
616C2×C4⋊C4C2418yes—
617C2×C4⋊C4C2418yes—
618C2×C4⋊C4C2414yes—
619C2×C22⋊C4C2411yescharacteristic
620C2×C22⋊C4C2411yescharacteristic
621C2×C22⋊C4C2418yes—
622C2×C22⋊C4C2412yes—
623C2×C22⋊C4C2412yes—
624C2×C22⋊C4C2412yes—
625C2×C22⋊C4C2412yes—
626C2×C22⋊C4C2412yes—
627C2×C22⋊C4C2412yes—
628C2×C22⋊C4C2412yes—
629C2×C22⋊C4C2412yes—
630C2×C22⋊C4C2414yes—
631C2×C22⋊C4C2418yes—
632C2×C22⋊C4C2412yes—
633C2×C22⋊C4C2412yes—
634C2×C22⋊C4C2412yes—
635C2×C22⋊C4C2412yes—
636C2×C22⋊C4C2412yes—
637C2×C22⋊C4C2412yes—
638C2×C22⋊C4C2418yes—
639C2×C22⋊C4C2418yes—
640C2×C22⋊C4C2418yes—
641C2×C42—24no—
642C2×C42—28no—
643C2×C42C2411yescharacteristic
644C2×C42C2414yes—
645C2×C42C2414yes—
646C2×C42C2412yes—
647C2×C42C2418yes—
648C2×C42C2412yes—
649C2×C42C2412yes—
650C2×C42C2411yescharacteristic
651C2×C42C2411yescharacteristic
652C2×C42C2412yes—
653C2×C42C2412yes—
654C2×C42C2412yes—
655C2×C42C2412yes—
656C2×C42C2412yes—
657C2×C42C2412yes—
658C2×C42C2412yes—
659C2×C42C2412yes—
660C2×C42C2418yes—
661C2×C42C2412yes—
662C2×C42C2411yescharacteristic
663C2×C42C2412yes—
664C2×C42C2414yes—
665C2×C42C2414yes—
666C2×C42C2414yes—
667C2×C42C2418yes—
668C2×C42C2418yes—
669C2×C42C2418yes—
670C2×C42C2411yescharacteristic
671C2×C42C2411yescharacteristic
672C2×C42C2412yes—
673#95C2412yes—
674#95C2411yescharacteristic
675#95C2412yes—
676#95C2412yes—
677#95C2412yes—
678#95C2412yes—
679#95C2412yes—
680#95C2412yes—
681#95C2412yes—
682#95C2412yes—
683#95C2412yes—
684#95C2412yes—
685#95C2412yes—
686#95C2418yes—
687#95C2418yes—
688#95C2418yes—
689#95C2418yes—
690#95C2414yes—
691#95C2411yescharacteristic
692#95C2411yescharacteristic
693#95C2412yes—
694#95C2412yes—
695#95C2412yes—
696#95C2412yes—
697#95C2412yes—
698#95C2412yes—
699#95C2412yes—
700#95C2412yes—
701#95C2418yes—
702#95C2418yes—
703#95C2411yescharacteristic
704#95C2412yes—
705#95C2412yes—
706#95C2418yes—
707#95C2418yes—
708#95C2418yes—
709#95C2418yes—
710#95C2418yes—
711#95C2418yes—
712#95C2418yes—
713#95C2414yes—
714#95C2418yes—
715#95C2418yes—
716#95C2418yes—
717#95C2418yes—
718#95C2418yes—
719#95C2418yes—
720#95C2418yes—
721#95C2418yes—
722#95C2418yes—
723#95C2418yes—
724#95C2418yes—
725C24C2512yes—
726C24C2511yescharacteristic
727C2×Q8—28no—
728C2×Q8—28no—
729C2×Q8—24no—
730C2×Q8—22no—
731C2×Q8—24no—
732C2×Q8—24no—
733C2×Q8—28no—
734C2×Q8—24no—
735C2×Q8—24no—
736C2×Q8—28no—
737C2×Q8—28no—
738C2×Q8—24no—
739C2×Q8—28no—
740C2×Q8—44no—
741C2×Q8—48no—
742C2×Q8—48no—
743C2×Q8—48no—
744C2×Q8—48no—
745C2×Q8—432no—
746C2×Q8C2×#4118yes—
747C2×D4—24no—
748C2×D4—22no—
749C2×D4—24no—
750C2×D4—42no—
751C2×D4—42no—
752C22×C4—22no—
753C22×C4—22no—
754C22×C4—28no—
755C22×C4—24no—
756C22×C4—24no—
757C22×C4—24no—
758C22×C4—24no—
759C22×C4—28no—
760C22×C4—24no—
761C22×C4—24no—
762C22×C4—24no—
763C22×C4—24no—
764C22×C4—24no—
765C22×C4—24no—
766C22×C4—24no—
767C22×C4—24no—
768C22×C4—44no—
769C22×C42−1+414yes—
770C22×C4C2512yes—
771C22×C4C2512yes—
772C22×C4C2512yes—
773C22×C4C2512yes—
774C22×C4C2518yes—
775C22×C4C2512yes—
776C22×C4C2512yes—
777C22×C4C2514yes—
778C22×C4C2511yescharacteristic
779C22×C4C2514yes—
780C22×C4C2512yes—
781C22×C4C2512yes—
782C22×C4C2514yes—
783C22×C4C2518yes—
784C22×C4C2511yescharacteristic
785C22×C4C2514yes—
786C22×C4C2511yescharacteristic
787C22×C4C2511yescharacteristic
788C22×C4C2512yes—
789C22×C4C2511yescharacteristic
790C22×C4C2512yes—
791C22×C4C2511yescharacteristic
792C22×C4C2512yes—
793C4⋊C4—216no—
794C4⋊C4—28no—
795C4⋊C4—28no—
796C4⋊C4—216no—
797C4⋊C4—216no—
798C4⋊C4—28no—
799C4⋊C4—22no—
800C4⋊C4—22no—
801C4⋊C4—24no—
802C4⋊C4—28no—
803C4⋊C4—28no—
804C4⋊C4—24no—
805C4⋊C4—28no—
806C4⋊C4—22no—
807C4⋊C4—24no—
808C4⋊C4—22no—
809C4⋊C4—28no—
810C4⋊C4—24no—
811C4⋊C4—24no—
812C4⋊C4—24no—
813C4⋊C4—24no—
814C4⋊C4—24no—
815C4⋊C4—24no—
816C4⋊C4—24no—
817C4⋊C4—24no—
818C4⋊C4—28no—
819C4⋊C4—216no—
820C4⋊C4—28no—
821C4⋊C4—28no—
822C4⋊C4—28no—
823C4⋊C4—42no—
824C4⋊C4—42no—
825C4⋊C4—44no—
826C4⋊C4—44no—
827C4⋊C4—42no—
828C4⋊C4—42no—
829C4⋊C4—48no—
830C4⋊C4—48no—
831C4⋊C4—48no—
832C4⋊C4—48no—
833C4⋊C4—48no—
834C4⋊C4—48no—
835C4⋊C4—48no—
836C4⋊C4—48no—
837C4⋊C4—48no—
838C4⋊C4C2×#41116yes—
839C22⋊C4—24no—
840C22⋊C4—24no—
841C22⋊C4—216no—
842C22⋊C4—22no—
843C22⋊C4—22no—
844C22⋊C4—24no—
845C22⋊C4—24no—
846C22⋊C4—24no—
847C22⋊C4—24no—
848C22⋊C4—24no—
849C22⋊C4—24no—
850C22⋊C4—42no—
851C22⋊C4—42no—
852C22⋊C4—44no—
853C22⋊C4—48no—
854C22⋊C4—42no—
855C22⋊C4—42no—
856C22⋊C4—42no—
857C22⋊C4—42no—
858C22⋊C4—48no—
859C22⋊C4—48no—
860C22⋊C4—48no—
861C42—24no—
862C42—24no—
863C42—24no—
864C42—24no—
865C42—22no—
866C42—216no—
867C42—22no—
868C42—28no—
869C42—28no—
870C42—24no—
871C42—24no—
872C42—22no—
873C42—22no—
874C42—24no—
875C42—24no—
876C42—24no—
877C42—216no—
878C42—24no—
879C42—24no—
880C42—24no—
881C42—24no—
882C42—44no—
883C42—44no—
884C42—44no—
885C42—48no—
886C42—48no—
887C42—48no—
888C42C2×#4114yes—
889C42H(5,𝔽2)14yes—
890C422−1+418yes—
891C23—21no—
892C23—21no—
893C23—22no—
894C23—22no—
895C23—22no—
896C23—22no—
897C23—22no—
898C23—22no—
899C23—22no—
900C23—22no—
901C23—22no—
902C23C2×2−1+412yes—
903C23C2611yescharacteristic
904Q8—28no—
905Q8—216no—
906Q8—416no—
907Q8—416no—
908Q8—48no—
909Q8—88no—
910Q8—168no—
911D4—48no—
912D4—44no—
913C2×C4—21no—
914C2×C4—22no—
915C2×C4—24no—
916C2×C4—21no—
917C2×C4—22no—
918C2×C4—22no—
919C2×C4—22no—
920C2×C4—24no—
921C2×C4—22no—
922C2×C4—22no—
923C2×C4—28no—
924C2×C4—22no—
925C2×C4—22no—
926C2×C4—22no—
927C2×C4—22no—
928C2×C4—28no—
929C2×C4—24no—
930C2×C4—21no—
931C2×C4—21no—
932C2×C4—24no—
933C2×C4—24no—
934C2×C4—24no—
935C2×C4—22no—
936C2×C4—22no—
937C2×C4—28no—
938C2×C4—22no—
939C2×C4—22no—
940C2×C4—22no—
941C2×C4—22no—
942C2×C4—22no—
943C2×C4—28no—
944C2×C4—22no—
945C2×C4—22no—
946C2×C4—28no—
947C2×C4—22no—
948C2×C4—22no—
949C2×C4—22no—
950C2×C4—22no—
951C2×C4—24no—
952C2×C4—22no—
953C2×C4—22no—
954C2×C4—22no—
955C2×C4—22no—
956C2×C4—22no—
957C2×C4—22no—
958C2×C4—28no—
959C2×C4—28no—
960C2×C4—22no—
961C2×C4—28no—
962C2×C4—28no—
963C2×C4—22no—
964C2×C4—22no—
965C2×C4—416no—
966C2×C4—48no—
967C2×C4—48no—
968C2×C4—48no—
969C2×C4—48no—
970C2×C4C22×#4118yes—
971C2×C4C22×#4114yes—
972C2×C4C22×#4112yes—
973C2×C4C2×H(5,𝔽2)12yes—
974C2×C4C2×H(5,𝔽2)12yes—
975C2×C4C2×H(5,𝔽2)12yes—
976C2×C4C2×2−1+414yes—
977C2×C4C2×2−1+414yes—
978C2×C4C2×2−1+412yes—
979C2×C4C2×2−1+414yes—
980C2×C4C2×2−1+412yes—
981C2×C4#58514yes—
982C22—22no—
983C22—24no—
984C22—42no—
985C22—41no—
986C22—41no—
987C22—42no—
988C22—42no—
989C22—42no—
990C22—42no—
991C22—42no—
992C22—42no—
993C22—42no—
994C22C23×#4111yescharacteristic
995C22C22×H(5,𝔽2)11yescharacteristic
996C22C22×2−1+411yescharacteristic
997C22C22×2−1+412yes—
998C22C2×#58512yes—
999C4—22no—
1000C4—28no—
1001C4—22no—
1002C4—24no—
1003C4—22no—
1004C4—24no—
1005C4—42no—
1006C4—44no—
1007C4—42no—
1008C4—42no—
1009C4—42no—
1010C4—48no—
1011C4—41no—
1012C4—44no—
1013C4—41no—
1014C4—48no—
1015C4—44no—
1016C4—42no—
1017C4—42no—
1018C4—42no—
1019C4—42no—
1020C4#351818yes—
1021C4#352014yes—
1022C2—42no—
1023C2—82no—
1024C2C2×#352011yescharacteristic
1025C2C2×#351812yes—
1026C2#6283311yescharacteristic
1027C2#6283611yescharacteristic
1028C2#6283712yes—
subgroupG/H
center, commutator, Frattini, socle, cosocleC23C26
prime radical#392C23
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23 ◁ G
LECSG ▷ C23 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #45338C2semidirect
2. #45329C2semidirect
3. #45306C2semidirect
4. #45295C2semidirect
5. #45290C2semidirect
7. #45001C2semidirect
8. #42901C2semidirect
9. #42640C2semidirect
10. #42549C2semidirect
11. #36608C2semidirect
12. Q8×C4⋊Q8C2semidirect
13. #36194C2semidirect
14. #36188C2semidirect
15. #36151C2semidirect
16. #36129C2semidirect
18. #35945C2semidirect
19. #35867C2semidirect
20. #35711C2semidirect
21. #35283C2semidirect
22. #35283C2semidirect
24. #34225C2semidirect
25. #34209C2semidirect

Maximal subgroups

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

subgroupindex
#453382
#453292
#453062
#452952
#452902
#450782
#450012
#429012
#426402
#425492
#366082
Q8×C4⋊Q82
#361942
#361882
#361512
#361292
#360302
#359452
#358672
#357112
#352832
#345512
#342252
#342092