Finite Group Databasebeta

← #7654913

Subgroups — #7654913

Order 512.

4264 conjugacy classes of subgroups.

The subgroup lattice has 1050 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#42938C214yesmaximal
2#42231C218yesmaximal, complemented
3#39769C212yesmaximal, complemented
4#39643C212yesmaximal, complemented
5#39081C214yesmaximal
6#39067C214yesmaximal
7#38986C212yesmaximal, complemented
8#38984C212yesmaximal, complemented
9#38265C214yesmaximal
10#38251C214yesmaximal
11#37641C211yesmaximal, characteristic
12#37630C212yesmaximal, complemented
13#36598C212yesmaximal, complemented
14#36556C212yesmaximal, complemented
15#36313C212yesmaximal, complemented
16#36286C212yesmaximal, complemented
17#35818C214yesmaximal
18#35320C211yesmaximal, characteristic
19#35281C211yesmaximal, characteristic
20#35199C212yesmaximal, complemented
21#35187C212yesmaximal, complemented
22#34978C211yesmaximal, characteristic
23#34951C212yesmaximal, complemented
24#34216C211yesmaximal, characteristic
25#34154C211yesmaximal, characteristic
26#34154C211yesmaximal, characteristic
27C2×#533C2211yescharacteristic
28C2×#533C2211yescharacteristic
29C22×C4⋊Q8C2211yescharacteristic
30#2868C2212yes—
31#2864C2214yes—
32#2863C2214yes—
33#2863C2214yes—
34#2862C2212yes—
35#2862C2212yes—
36#2862C2214yes—
37#2862C2212yes—
38#2839C2218yes—
39#2822C2214yes—
40#2799C2218yes—
41#2794C2218yes—
42#2794C2218yes—
43#2789C2218yes—
44#2767C2218yes—
45#2762C2218yes—
46#2758C2218yes—
47#2755C2218yes—
48#2745C2218yes—
49#2744C2218yes—
50#2739C2218yes—
51#2738C2218yes—
52#2666C2218yes—
53#2660C2214yes—
54#2655C2218yes—
55#2655C2218yes—
56#2647C2214yes—
57#2645C2214yes—
58#2645C2214yes—
59#2642C2214yes—
60#2642C2214yes—
61#2625C2214yes—
62#2625C2214yes—
63#2621C2214yes—
64#2612C2214yes—
65#2605C2218yes—
66#2588C2218yes—
67#2588C2218yes—
68#2585C2218yes—
69#2582C2212yes—
70#2582C2212yes—
71#2582C2214yes—
72#2581C2214yes—
73#2575C2218yes—
74#2573C2218yes—
75#2571C2214yes—
76#2571C2211yescharacteristic
77#2570C2214yes—
78#2570C2214yes—
79#2570C2218yes—
80#2568C2212yes—
81#2568C2212yes—
82#2568C2214yes—
83#2568C2212yes—
84#2568C2212yes—
85#2568C2212yes—
86#2568C2212yes—
87#2567C2212yes—
88#2567C2212yes—
89#2552C2211yescharacteristic
90#2552C2211yescharacteristic
91#2551C2211yescharacteristic
92#2546C2212yes—
93#2546C2212yes—
94#2546C2212yes—
95#2546C2212yes—
96#2528C2218yes—
97#2527C2218yes—
98#2524C2218yes—
99#2524C2218yes—
100#2520C2218yes—
101#2520C2218yes—
102#2515C2218yes—
103#2514C2214yes—
104#2514C2214yes—
105#2514C2214yes—
106#2514C2214yes—
107#2511C2214yes—
108#2511C2214yes—
109#2511C2214yes—
110#2511C2218yes—
111#2511C2214yes—
112#2509C2214yes—
113#2509C2214yes—
114#2508C2214yes—
115#2508C2214yes—
116#2503C2214yes—
117#2503C2214yes—
118#2502C2214yes—
119#2453C2214yes—
120#2453C2214yes—
121#2451C2214yes—
122#2451C2214yes—
123#2446C2214yes—
124#2446C2214yes—
125#2446C2214yes—
126#2446C2214yes—
127#2446C2214yes—
128#2446C2214yes—
129#2441C2212yes—
130#2441C2212yes—
131#2439C2212yes—
132#2439C2212yes—
133#2434C2214yes—
134#2402C2218yes—
135#2396C2214yes—
136#2371C2214yes—
137#2371C2214yes—
138#2369C2212yes—
139#2369C2212yes—
140#2365C2211yescharacteristic
141#2365C2212yes—
142#2365C2211yescharacteristic
143#2365C2211yescharacteristic
144#2365C2211yescharacteristic
145#2365C2211yescharacteristic
146#2365C2211yescharacteristic
147#2365C2211yescharacteristic
148#2365C2211yescharacteristic
149#2365C2212yes—
150#2365C2214yes—
151#2362C2212yes—
152#2362C2212yes—
153#2362C2212yes—
154#2362C2212yes—
155#2362C2212yes—
156#2362C2212yes—
157#2362C2212yes—
158#2362C2212yes—
159#2356C2214yes—
160#2355C2214yes—
161#2355C2214yes—
162#2345C2214yes—
163Q8×C22⋊C4C2214yes—
164#2331C2214yes—
165#2331C2214yes—
166#2327C2214yes—
167#2320C2214yes—
168#2320C2214yes—
169#2317C2212yes—
170#2317C2212yes—
171#2316C2212yes—
172#2310C2212yes—
173#2310C2212yes—
174C4×C4⋊Q8C2212yes—
175C4×C4⋊Q8C2212yes—
176C4×C4⋊Q8C2214yes—
177C4×C4⋊Q8C2212yes—
178C4×C4⋊Q8C2212yes—
179C4×#125C2212yes—
180C4×#125C2212yes—
181C4×#125C2214yes—
182#2298C2214yes—
183#2298C2214yes—
184#2295C2212yes—
185#2295C2212yes—
186#2295C2212yes—
187#2295C2212yes—
188#2295C2214yes—
189#2295C2214yes—
190#2285C2211yescharacteristic
191#2274C2212yes—
192C42×Q8C2212yes—
193C42×Q8C2212yes—
194C42×Q8C2212yes—
195C42×Q8C2212yes—
196C4×#117C2211yescharacteristic
197C4×#117C2211yescharacteristic
198C4×#117C2211yescharacteristic
199C23×Q8C2312yes—
200#533—28no—
201#533—28no—
202C2×C4⋊Q8—28no—
203C2×C4⋊Q8C2312yes—
204C2×C4⋊Q8C2312yes—
205C2×C4⋊Q8C2312yes—
206C2×C4⋊Q8C2311yescharacteristic
207C2×C4⋊Q8C2312yes—
208C2×C4⋊Q8C2311yescharacteristic
209C2×C4⋊Q8C2312yes—
210C2×C4⋊Q8C2311yescharacteristic
211C2×C4⋊Q8C2311yescharacteristic
212C2×C4⋊Q8C2312yes—
213C2×C4⋊Q8C2314yes—
214C2×C4⋊Q8C2314yes—
215C2×C4⋊Q8C2314yes—
216C2×#125C2312yes—
217C2×#125C2312yes—
218C2×#125C2312yes—
219C2×#125C2312yes—
220C2×C22⋊Q8C2312yes—
221C2×C22⋊Q8C2312yes—
222C2×C22⋊Q8C2312yes—
223C2×C22⋊Q8C2312yes—
224C2×C4×Q8C2312yes—
225C2×C4×Q8C2312yes—
226C2×C4×Q8C2312yes—
227C2×C4×Q8C2312yes—
228C2×C4×Q8C2312yes—
229C2×C4×Q8C2312yes—
230C2×C4×Q8C2312yes—
231C2×C4×Q8C2312yes—
232C2×C4×Q8C2314yes—
233C2×C4×Q8C2314yes—
234C2×C4×Q8C2312yes—
235C2×C4×Q8C2314yes—
236C2×C4×Q8C2312yes—
237C2×C4×Q8C2312yes—
238C2×C4×Q8C2312yes—
239C2×#117C2312yes—
240C2×#117C2311yescharacteristic
241C2×#117C2311yescharacteristic
242C2×#117C2312yes—
243C2×#117C2311yescharacteristic
244C2×#117C2311yescharacteristic
245C2×#117C2311yescharacteristic
246C2×#117C2311yescharacteristic
247C2×#117C2312yes—
248C22×C4⋊C4C2312yes—
249C22×C4⋊C4C2312yes—
250C22×C42C2311yescharacteristic
251#401C2318yes—
252#401C2318yes—
253#400C2318yes—
254#400C2318yes—
255#400C2318yes—
256#400C2318yes—
257#400C2318yes—
258#400C2318yes—
259#400C2318yes—
260#400C2318yes—
261#400C2318yes—
262#400C2318yes—
263#400C2318yes—
264#400C2314yes—
265#400C2318yes—
266#400C2318yes—
267#400C2318yes—
268#400C2318yes—
269#400C2318yes—
270#400C2318yes—
271#400C2318yes—
272#400C2318yes—
273#400C2318yes—
274#400C2318yes—
275#399C2314yes—
276#398C2318yes—
277#398C2318yes—
278#398C2318yes—
279#398C2318yes—
280#398C2318yes—
281#398C2318yes—
282#398C2318yes—
283#398C2318yes—
284#398C2314yes—
285#398C2318yes—
286#398C2318yes—
287#398C2314yes—
288#398C2318yes—
289#398C2318yes—
290#397C2318yes—
291#397C2318yes—
292#396C2314yes—
293#396C2314yes—
294#395C2318yes—
295#395C2318yes—
296#395C2318yes—
297#395C2314yes—
298#393C2314yes—
299#391C2314yes—
300#391C2314yes—
301#391C2314yes—
302#391C2314yes—
303#391C2314yes—
304#391C2314yes—
305#391C2314yes—
306#391C2314yes—
307#391C2314yes—
308#391C2314yes—
309#391C2314yes—
310#391C2314yes—
311#391C2314yes—
312#391C2314yes—
313#391C2314yes—
314#391C2314yes—
315#391C2312yes—
316#391C2312yes—
317#391C2314yes—
318#391C2314yes—
319#391C2314yes—
320#391C2314yes—
321#391C2314yes—
322#391C2314yes—
323#391C2318yes—
324#391C2314yes—
325#391C2314yes—
326#391C2314yes—
327#391C2318yes—
328#391C2318yes—
329#391C2318yes—
330#391C2318yes—
331#391C2312yes—
332#391C2314yes—
333#391C2312yes—
334#391C2312yes—
335#391C2312yes—
336#391C2312yes—
337#391C2312yes—
338#389C2314yes—
339#389C2312yes—
340#389C2314yes—
341#389C2312yes—
342#389C2312yes—
343#389C2312yes—
344#389C2314yes—
345#389C2318yes—
346#389C2312yes—
347#389C2312yes—
348#389C2314yes—
349#389C2314yes—
350#389C2318yes—
351#389C2314yes—
352#389C2314yes—
353#389C2314yes—
354#389C2312yes—
355#389C2312yes—
356#389C2314yes—
357#389C2314yes—
358#389C2314yes—
359#389C2312yes—
360#389C2312yes—
361#389C2312yes—
362#389C2314yes—
363#389C2312yes—
364#389C2314yes—
365#389C2318yes—
366#389C2314yes—
367#389C2314yes—
368#389C2314yes—
369#389C2312yes—
370#389C2312yes—
371#389C2312yes—
372#389C2312yes—
373#388C2314yes—
374#388C2314yes—
375#388C2314yes—
376#388C2314yes—
377#388C2314yes—
378#388C2314yes—
379#388C2314yes—
380#388C2314yes—
381#387C2318yes—
382#387C2318yes—
383#387C2314yes—
384#387C2314yes—
385#387C2314yes—
386#387C2314yes—
387#387C2314yes—
388#387C2318yes—
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#387C2314yes—
407#387C2314yes—
408#387C2318yes—
409#387C2318yes—
410#387C2318yes—
411#387C2318yes—
412#387C2314yes—
413#387C2314yes—
414#387C2318yes—
415#387C2318yes—
416#387C2314yes—
417#387C2314yes—
418#387C2314yes—
419#387C2314yes—
420#387C2314yes—
421#387C2314yes—
422#387C2314yes—
423#387C2314yes—
424#387C2314yes—
425#387C2314yes—
426#387C2314yes—
427#385C2318yes—
428#385C2318yes—
429#384C2312yes—
430#384C2311yescharacteristic
431#384C2311yescharacteristic
432#384C2312yes—
433#384C2314yes—
434#384C2314yes—
435#384C2314yes—
436#384C2314yes—
437#383C2318yes—
438#383C2318yes—
439#383C2318yes—
440#382C2314yes—
441#382C2312yes—
442#382C2312yes—
443#382C2312yes—
444#382C2314yes—
445#382C2314yes—
446#382C2314yes—
447#382C2318yes—
448#382C2314yes—
449#382C2318yes—
450#382C2318yes—
451#382C2314yes—
452#382C2314yes—
453#381C2318yes—
454#381C2318yes—
455#380C2318yes—
456#380C2312yes—
457#380C2312yes—
458C4×C4⋊C4C2311yescharacteristic
459C4×C4⋊C4C2311yescharacteristic
460C4×C4⋊C4C2314yes—
461C4×C4⋊C4C2312yes—
462C4×C4⋊C4C2312yes—
463C4×C4⋊C4C2312yes—
464C4×C4⋊C4C2318yes—
465C4×C4⋊C4C2314yes—
466C4×C4⋊C4C2314yes—
467C4×C4⋊C4C2314yes—
468C4×C4⋊C4C2318yes—
469C4×C4⋊C4C2311yescharacteristic
470C4×C4⋊C4C2311yescharacteristic
471C4×C4⋊C4C2318yes—
472C4×C4⋊C4C2314yes—
473C4×C4⋊C4C2314yes—
474C4×C4⋊C4C2314yes—
475C4×C4⋊C4C2311yescharacteristic
476C4×C4⋊C4C2311yescharacteristic
477C4×C4⋊C4C2314yes—
478C4×C4⋊C4C2312yes—
479C4×C4⋊C4C2314yes—
480C4×C4⋊C4C2312yes—
481C4×C4⋊C4C2311yescharacteristic
482C4×C4⋊C4C2312yes—
483C4×C4⋊C4C2314yes—
484C4×C4⋊C4C2314yes—
485C4×C4⋊C4C2312yes—
486C4×C4⋊C4C2314yes—
487C4×C4⋊C4C2314yes—
488C4×C4⋊C4C2312yes—
489C4×C4⋊C4C2312yes—
490C4×C4⋊C4C2314yes—
491C4×C4⋊C4C2312yes—
492C4×C4⋊C4C2314yes—
493C4×C4⋊C4C2314yes—
494C4×C4⋊C4C2314yes—
495C4×C4⋊C4C2311yescharacteristic
496C4×C4⋊C4C2311yescharacteristic
497C4×C4⋊C4C2311yescharacteristic
498C4×C4⋊C4C2311yescharacteristic
499C4×C4⋊C4C2314yes—
500C4×C4⋊C4C2314yes—
501C4×C4⋊C4C2314yes—
502C4×C4⋊C4C2314yes—
503C4×C4⋊C4C2311yescharacteristic
504C4×C22⋊C4C2318yes—
505C4×C22⋊C4C2312yes—
506C4×C22⋊C4C2312yes—
507C4×C22⋊C4C2312yes—
508C4×C22⋊C4C2312yes—
509C4×C22⋊C4C2312yes—
510C4×C22⋊C4C2312yes—
511#376C2314yes—
512#376C2314yes—
513#376C2312yes—
514#376C2318yes—
515#376C2312yes—
516#376C2312yes—
517C43C2312yes—
518C43C2312yes—
519C43C2314yes—
520C43C2312yes—
521C43C2314yes—
522C22×Q8—28no—
523C22×Q8—44no—
524C22×Q8—44no—
525C22×Q8C2412yes—
526C22×Q8C2412yes—
527C22×Q8C2412yes—
528C22×Q8C2412yes—
529C22×Q8C2414yes—
530C22×Q8C2414yes—
531C22×Q8C2414yes—
532C23×C4C2411yescharacteristic
533C23×C4C2411yescharacteristic
534C23×C4C2411yescharacteristic
535C23×C4C2414yes—
536C4⋊Q8—28no—
537C4⋊Q8—28no—
538C4⋊Q8—28no—
539C4⋊Q8—28no—
540C4⋊Q8—28no—
541C4⋊Q8—24no—
542C4⋊Q8—24no—
543C4⋊Q8—24no—
544C4⋊Q8—24no—
545C4⋊Q8—44no—
546C4⋊Q8—48no—
547C4⋊Q8—48no—
548C4⋊Q8—48no—
549#125—28no—
550#125—28no—
551#125—28no—
552#125—44no—
553C22⋊Q8—28no—
554C22⋊Q8—28no—
555C22⋊Q8—28no—
556C22⋊Q8—28no—
557C4×Q8—28no—
558C4×Q8—28no—
559C4×Q8—28no—
560C4×Q8—28no—
561C4×Q8—28no—
562C4×Q8—28no—
563C4×Q8—28no—
564C4×Q8—28no—
565C4×Q8—48no—
566C4×Q8—44no—
567C4×Q8—44no—
568C4×Q8—44no—
569C4×Q8—44no—
570C4×Q8—48no—
571C4×Q8—48no—
572#117—28no—
573#117—28no—
574#117—24no—
575#117—24no—
576#117—24no—
577#117—44no—
578#117—42no—
579#117—42no—
580#117—42no—
581C2×C4⋊C4—28no—
582C2×C4⋊C4—28no—
583C2×C4⋊C4C2414yes—
584C2×C4⋊C4C2414yes—
585C2×C4⋊C4C2414yes—
586C2×C4⋊C4C2414yes—
587C2×C4⋊C4C2411yescharacteristic
588C2×C4⋊C4C2411yescharacteristic
589C2×C4⋊C4C2411yescharacteristic
590C2×C4⋊C4C2411yescharacteristic
591C2×C4⋊C4C2411yescharacteristic
592C2×C4⋊C4C2412yes—
593C2×C4⋊C4C2412yes—
594C2×C4⋊C4C2412yes—
595C2×C4⋊C4C2412yes—
596C2×C4⋊C4C2411yescharacteristic
597C2×C4⋊C4C2411yescharacteristic
598C2×C4⋊C4C2411yescharacteristic
599C2×C4⋊C4C2411yescharacteristic
600C2×C4⋊C4C2412yes—
601C2×C4⋊C4C2412yes—
602C2×C4⋊C4C2414yes—
603C2×C4⋊C4C2414yes—
604C2×C4⋊C4C2414yes—
605C2×C4⋊C4C2414yes—
606C2×C4⋊C4C2412yes—
607C2×C4⋊C4C2412yes—
608C2×C4⋊C4C2412yes—
609C2×C4⋊C4C2412yes—
610C2×C4⋊C4C2414yes—
611C2×C4⋊C4C2414yes—
612C2×C4⋊C4C2414yes—
613C2×C4⋊C4C2414yes—
614C2×C4⋊C4C2412yes—
615C2×C4⋊C4C2414yes—
616C2×C4⋊C4C2414yes—
617C2×C4⋊C4C2412yes—
618C2×C4⋊C4C2414yes—
619C2×C4⋊C4C2412yes—
620C2×C4⋊C4C2412yes—
621C2×C4⋊C4C2414yes—
622C2×C4⋊C4C2414yes—
623C2×C4⋊C4C2414yes—
624C2×C4⋊C4C2414yes—
625C2×C4⋊C4C2414yes—
626C2×C4⋊C4C2418yes—
627C2×C4⋊C4C2418yes—
628C2×C4⋊C4C2414yes—
629C2×C4⋊C4C2414yes—
630C2×C4⋊C4C2414yes—
631C2×C4⋊C4C2414yes—
632C2×C4⋊C4C2414yes—
633C2×C4⋊C4C2418yes—
634C2×C4⋊C4C2418yes—
635C2×C4⋊C4C2418yes—
636C2×C4⋊C4C2418yes—
637C2×C4⋊C4C2418yes—
638C2×C4⋊C4C2418yes—
639C2×C4⋊C4C2411yescharacteristic
640C2×C4⋊C4C2411yescharacteristic
641C2×C4⋊C4C2411yescharacteristic
642C2×C22⋊C4C2414yes—
643C2×C22⋊C4C2414yes—
644C2×C22⋊C4C2412yes—
645C2×C22⋊C4C2412yes—
646C2×C22⋊C4C2412yes—
647C2×C22⋊C4C2412yes—
648C2×C22⋊C4C2414yes—
649C2×C22⋊C4C2412yes—
650C2×C22⋊C4C2412yes—
651C2×C42#4118yes—
652C2×C42C2414yes—
653C2×C42C2414yes—
654C2×C42C2414yes—
655C2×C42C2412yes—
656C2×C42C2412yes—
657C2×C42C2412yes—
658C2×C42C2412yes—
659C2×C42C2412yes—
660C2×C42C2412yes—
661C2×C42C2412yes—
662C2×C42C2412yes—
663C2×C42C2412yes—
664C2×C42C2414yes—
665C2×C42C2414yes—
666C2×C42C2412yes—
667C2×C42C2412yes—
668C2×C42C2414yes—
669C2×C42C2414yes—
670C2×C42C2412yes—
671C2×C42C2412yes—
672C2×C42C2412yes—
673C2×C42C2412yes—
674C2×C42C2412yes—
675C2×C42C2412yes—
676C2×C42C2412yes—
677C2×C42C2414yes—
678C2×C42C2414yes—
679C2×C42C2414yes—
680C2×C42C2414yes—
681C2×C42C2418yes—
682C2×C42C2418yes—
683C2×C42C2411yescharacteristic
684C2×C42C2411yescharacteristic
685C2×C42C2411yescharacteristic
686C2×C42C2411yescharacteristic
687#95C2414yes—
688#95C2412yes—
689#95C2412yes—
690#95C2412yes—
691#95C2412yes—
692#95C2412yes—
693#95C2412yes—
694#95C2412yes—
695#95C2412yes—
696#95C2412yes—
697#95C2412yes—
698#95C2412yes—
699#95C2412yes—
700#95C2418yes—
701#95C2414yes—
702#95C2414yes—
703#95C2418yes—
704#95C2414yes—
705#95C2414yes—
706#95C2414yes—
707#95C2414yes—
708#95C2414yes—
709#95C2414yes—
710#95C2418yes—
711#95C2418yes—
712#95C2418yes—
713#95C2414yes—
714#95C2414yes—
715#95C2414yes—
716#95C2414yes—
717#95C2414yes—
718#95C2414yes—
719#95C2414yes—
720#95C2414yes—
721#95C2418yes—
722#95C2414yes—
723#95C2414yes—
724#95C2418yes—
725#95C2418yes—
726#95C2418yes—
727#95C2418yes—
728#95C2414yes—
729#95C2414yes—
730#95C2414yes—
731#95C2418yes—
732#95C2418yes—
733#95C2414yes—
734#95C2414yes—
735#95C2418yes—
736#95C2418yes—
737#95C2418yes—
738#95C2418yes—
739#95C2418yes—
740#95C2418yes—
741#95C2418yes—
742#95C2418yes—
743#95C2418yes—
744#95C2418yes—
745C24C2511yescharacteristic
746C2×Q8—24no—
747C2×Q8—24no—
748C2×Q8—24no—
749C2×Q8—24no—
750C2×Q8—28no—
751C2×Q8—28no—
752C2×Q8—24no—
753C2×Q8—24no—
754C2×Q8—24no—
755C2×Q8—24no—
756C2×Q8—28no—
757C2×Q8—24no—
758C2×Q8—24no—
759C2×Q8—24no—
760C2×Q8—24no—
761C2×Q8—28no—
762C2×Q8—28no—
763C2×Q8—44no—
764C2×Q8—44no—
765C2×Q8—44no—
766C2×Q8—44no—
767C2×Q8—816no—
768C22×C4—22no—
769C22×C4—22no—
770C22×C4—22no—
771C22×C4—22no—
772C22×C4—22no—
773C22×C4—22no—
774C22×C4—28no—
775C22×C4—44no—
776C22×C4—44no—
777C22×C4C2×#4114yes—
778C22×C4C2×#4114yes—
779C22×C4C2×#4114yes—
780C22×C4C2514yes—
781C22×C4C2512yes—
782C22×C4C2512yes—
783C22×C4C2512yes—
784C22×C4C2512yes—
785C22×C4C2512yes—
786C22×C4C2514yes—
787C22×C4C2514yes—
788C22×C4C2514yes—
789C22×C4C2518yes—
790C22×C4C2512yes—
791C22×C4C2512yes—
792C22×C4C2512yes—
793C22×C4C2512yes—
794C22×C4C2514yes—
795C22×C4C2514yes—
796C22×C4C2511yescharacteristic
797C22×C4C2511yescharacteristic
798C22×C4C2511yescharacteristic
799C22×C4C2512yes—
800C22×C4C2512yes—
801C22×C4C2512yes—
802C22×C4C2511yescharacteristic
803C22×C4C2511yescharacteristic
804C22×C4C2511yescharacteristic
805C4⋊C4—28no—
806C4⋊C4—28no—
807C4⋊C4—28no—
808C4⋊C4—28no—
809C4⋊C4—24no—
810C4⋊C4—24no—
811C4⋊C4—24no—
812C4⋊C4—24no—
813C4⋊C4—28no—
814C4⋊C4—28no—
815C4⋊C4—28no—
816C4⋊C4—28no—
817C4⋊C4—24no—
818C4⋊C4—24no—
819C4⋊C4—24no—
820C4⋊C4—24no—
821C4⋊C4—22no—
822C4⋊C4—22no—
823C4⋊C4—22no—
824C4⋊C4—28no—
825C4⋊C4—28no—
826C4⋊C4—28no—
827C4⋊C4—28no—
828C4⋊C4—28no—
829C4⋊C4—28no—
830C4⋊C4—24no—
831C4⋊C4—28no—
832C4⋊C4—24no—
833C4⋊C4—22no—
834C4⋊C4—22no—
835C4⋊C4—22no—
836C4⋊C4—22no—
837C4⋊C4—22no—
838C4⋊C4—22no—
839C4⋊C4—24no—
840C4⋊C4—24no—
841C4⋊C4—42no—
842C4⋊C4—42no—
843C4⋊C4—44no—
844C4⋊C4—44no—
845C4⋊C4—44no—
846C4⋊C4—48no—
847C4⋊C4—44no—
848C4⋊C4—44no—
849C4⋊C4—44no—
850C4⋊C4—48no—
851C4⋊C4—44no—
852C4⋊C4—44no—
853C4⋊C4—44no—
854C4⋊C4—44no—
855C4⋊C4—48no—
856C4⋊C4—48no—
857C4⋊C4—48no—
858C4⋊C4—48no—
859C4⋊C4—48no—
860C4⋊C4—48no—
861C4⋊C42−1+414yes—
862C4⋊C42−1+414yes—
863C4⋊C42−1+414yes—
864C22⋊C4—28no—
865C22⋊C4—28no—
866C22⋊C4—24no—
867C22⋊C4—24no—
868C22⋊C4—24no—
869C22⋊C4—44no—
870C22⋊C4—42no—
871C22⋊C4—42no—
872C22⋊C4—42no—
873C42—28no—
874C42—28no—
875C42—24no—
876C42—24no—
877C42—24no—
878C42—24no—
879C42—24no—
880C42—28no—
881C42—28no—
882C42—24no—
883C42—24no—
884C42—28no—
885C42—28no—
886C42—24no—
887C42—24no—
888C42—28no—
889C42—24no—
890C42—24no—
891C42—24no—
892C42—24no—
893C42—24no—
894C42—24no—
895C42—42no—
896C42—42no—
897C42—42no—
898C42—44no—
899C42—48no—
900C42—44no—
901C42—48no—
902C42—44no—
903C42—44no—
904C42C2×#4114yes—
905C42C2×#4114yes—
906C42C2×#4114yes—
907C42C2×#4114yes—
908C23—21no—
909C23—21no—
910C23—21no—
911C23—21no—
912C23—21no—
913C23—21no—
914C23C22×#4112yes—
915C23C2611yescharacteristic
916Q8—48no—
917Q8—48no—
918Q8—48no—
919Q8—48no—
920Q8—416no—
921Q8—88no—
922Q8—88no—
923C2×C4—22no—
924C2×C4—22no—
925C2×C4—21no—
926C2×C4—21no—
927C2×C4—21no—
928C2×C4—22no—
929C2×C4—22no—
930C2×C4—22no—
931C2×C4—22no—
932C2×C4—21no—
933C2×C4—21no—
934C2×C4—21no—
935C2×C4—28no—
936C2×C4—28no—
937C2×C4—28no—
938C2×C4—24no—
939C2×C4—24no—
940C2×C4—24no—
941C2×C4—24no—
942C2×C4—28no—
943C2×C4—22no—
944C2×C4—22no—
945C2×C4—22no—
946C2×C4—22no—
947C2×C4—22no—
948C2×C4—22no—
949C2×C4—22no—
950C2×C4—22no—
951C2×C4—22no—
952C2×C4—22no—
953C2×C4—22no—
954C2×C4—22no—
955C2×C4—24no—
956C2×C4—24no—
957C2×C4—24no—
958C2×C4—24no—
959C2×C4—22no—
960C2×C4—24no—
961C2×C4—24no—
962C2×C4—22no—
963C2×C4—22no—
964C2×C4—22no—
965C2×C4—24no—
966C2×C4—24no—
967C2×C4—22no—
968C2×C4—22no—
969C2×C4—22no—
970C2×C4—22no—
971C2×C4—22no—
972C2×C4—22no—
973C2×C4—22no—
974C2×C4—22no—
975C2×C4—22no—
976C2×C4—24no—
977C2×C4—24no—
978C2×C4—22no—
979C2×C4—22no—
980C2×C4—24no—
981C2×C4—24no—
982C2×C4—24no—
983C2×C4—24no—
984C2×C4—28no—
985C2×C4—28no—
986C2×C4—88no—
987C2×C4C22×#4112yes—
988C2×C4C22×#4112yes—
989C2×C4C22×#4112yes—
990C2×C4C22×#4112yes—
991C2×C4C22×#4112yes—
992C2×C4C22×#4112yes—
993C2×C4C2×2−1+414yes—
994C2×C4C2×2−1+414yes—
995C2×C4C2×2−1+414yes—
996C2×C4C2×2−1+412yes—
997C2×C4C2×2−1+412yes—
998C2×C4C2×2−1+412yes—
999C2×C4#58512yes—
1000C2×C4#58512yes—
1001C2×C4#58512yes—
1002C22—22no—
1003C22—22no—
1004C22—22no—
1005C22—41no—
1006C22—41no—
1007C22—41no—
1008C22—41no—
1009C22C23×#4111yescharacteristic
1010C22C22×2−1+411yescharacteristic
1011C22C22×2−1+411yescharacteristic
1012C22C22×2−1+411yescharacteristic
1013C22C2×#58511yescharacteristic
1014C22C2×#58511yescharacteristic
1015C22C2×#58511yescharacteristic
1016C4—24no—
1017C4—24no—
1018C4—24no—
1019C4—22no—
1020C4—22no—
1021C4—22no—
1022C4—42no—
1023C4—44no—
1024C4—42no—
1025C4—42no—
1026C4—42no—
1027C4—42no—
1028C4—42no—
1029C4—42no—
1030C4—42no—
1031C4—42no—
1032C4—44no—
1033C4—44no—
1034C4—48no—
1035C4—44no—
1036C4—44no—
1037C4—44no—
1038C4#346114yes—
1039C4#350914yes—
1040C4#351014yes—
1041C2—42no—
1042C2C2×#346111yescharacteristic
1043C2C2×#350911yescharacteristic
1044C2C2×#351011yescharacteristic
1045C2#6302511yescharacteristic
1046C2#6303211yescharacteristic
1047C2#6303211yescharacteristic
1048C2#6303411yescharacteristic
subgroupG/H
center, commutator, Frattini, socle, cosocleC23C26
prime radicalC24C25
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23 ◁ G
LECSG ▷ C23 ▷ C1

Complements

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

NH ≅ G/Ntype
2. #42231C2semidirect
3. #39769C2semidirect
4. #39643C2semidirect
7. #38986C2semidirect
8. #38984C2semidirect
12. #37630C2semidirect
13. #36598C2semidirect
14. #36556C2semidirect
15. #36313C2semidirect
16. #36286C2semidirect
20. #35199C2semidirect
21. #35187C2semidirect
23. #34951C2semidirect

Maximal subgroups

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

subgroupindex
#429382
#422312
#397692
#396432
#390812
#390672
#389862
#389842
#382652
#382512
#376412
#376302
#365982
#365562
#363132
#362862
#358182
#353202
#352812
#351992
#351872
#349782
#349512
#342162
#341542