Finite Group Databasebeta

← #8110572

Subgroups — #8110572

Order 512.

4204 conjugacy classes of subgroups.

The subgroup lattice has 1081 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#59871C211yesmaximal, characteristic, complemented
2#59871C211yesmaximal, characteristic, complemented
3#59870C211yesmaximal, characteristic, complemented
4#59869C211yesmaximal, characteristic, complemented
5#53358C214yesmaximal, complemented
6#53196C214yesmaximal
7#46344C214yesmaximal, complemented
8#46181C214yesmaximal, complemented
9#45674C214yesmaximal
10#39754C212yesmaximal, complemented
11#39753C212yesmaximal, complemented
12#39643C212yesmaximal, complemented
13#39642C212yesmaximal, complemented
14#39480C212yesmaximal
15#39478C212yesmaximal
16#39353C212yesmaximal
17#39353C212yesmaximal
18#39180C212yesmaximal, complemented
19#39157C212yesmaximal
20#38984C212yesmaximal, complemented
21#38931C212yesmaximal
22#37377C214yesmaximal
23#37344C214yesmaximal, complemented
24#37295C214yesmaximal
25#36645C211yesmaximal, characteristic
26#36635C211yesmaximal, characteristic
27#36635C211yesmaximal, characteristic
28C2×#541C2214yes—
29C2×#533C2212yes—
30#2868C2211yescharacteristic
31#2868C2211yescharacteristic
32#2864C2212yes—
33#2864C2212yes—
34#2863C2212yes—
35#2863C2212yes—
36#2863C2212yes—
37#2863C2212yes—
38#2862C2211yescharacteristic
39#2862C2211yescharacteristic
40#2862C2212yes—
41#2859C2211yescharacteristic
42#2859C2211yescharacteristic
43#2859C2212yes—
44#2859C2212yes—
45#2857C2211yescharacteristic
46#2857C2211yescharacteristic
47#2857C2211yescharacteristic
48#2857C2211yescharacteristic
49#2857C2211yescharacteristic
50#2857C2212yes—
51#2857C2212yes—
52#2857C2212yes—
53#2857C2211yescharacteristic
54#2855C2212yes—
55#2855C2212yes—
56#2855C2212yes—
57#2855C2212yes—
58#2851C2212yes—
59#2851C2212yes—
60#2839C2218yes—
61#2809C2214yes—
62#2806C2214yes—
63#2806C2214yes—
64#2805C2214yes—
65#2802C2218yes—
66#2799C2218yes—
67#2791C2218yes—
68#2776C2218yes—
69#2774C2218yes—
70#2769C2218yes—
71#2767C2218yes—
72#2767C2218yes—
73#2762C2218yes—
74#2762C2218yes—
75#2762C2218yes—
76#2758C2218yes—
77#2755C2218yes—
78#2755C2218yes—
79#2747C2218yes—
80#2726C2218yes—
81#2722C2218yes—
82#2722C2218yes—
83#2719C2218yes—
84#2719C2218yes—
85#2719C2218yes—
86#2719C2218yes—
87#2713C2218yes—
88#2713C2218yes—
89#2713C2218yes—
90#2698C2218yes—
91#2698C2218yes—
92#2690C2218yes—
93#2689C2218yes—
94#2689C2218yes—
95#2660C2214yes—
96#2647C2214yes—
97#2647C2214yes—
98#2645C2214yes—
99#2625C2214yes—
100#2625C2214yes—
101#2584C2214yes—
102#2584C2214yes—
103#2584C2214yes—
104#2582C2214yes—
105#2582C2214yes—
106#2582C2214yes—
107#2581C2214yes—
108#2581C2214yes—
109#2571C2212yes—
110#2571C2212yes—
111#2571C2214yes—
112#2570C2214yes—
113#2570C2214yes—
114#2568C2214yes—
115#2568C2214yes—
116#2568C2212yes—
117#2567C2212yes—
118#2567C2212yes—
119#2567C2212yes—
120#2565C2214yes—
121#2552C2212yes—
122#2552C2214yes—
123#2552C2212yes—
124#2552C2214yes—
125#2552C2212yes—
126#2552C2212yes—
127#2552C2214yes—
128#2550C2214yes—
129#2546C2212yes—
130#2546C2212yes—
131#2514C2214yes—
132#2511C2214yes—
133#2511C2214yes—
134#2511C2214yes—
135#2511C2214yes—
136#2509C2214yes—
137#2509C2214yes—
138#2508C2214yes—
139#2508C2214yes—
140#2508C2214yes—
141#2508C2214yes—
142#2507C2214yes—
143#2507C2214yes—
144#2506C2214yes—
145#2506C2214yes—
146#2506C2214yes—
147#2506C2214yes—
148#2496C2214yes—
149#2496C2214yes—
150#2496C2214yes—
151#2496C2214yes—
152#2495C2214yes—
153#2494C2214yes—
154#2489C2214yes—
155#2453C2214yes—
156#2453C2214yes—
157#2451C2214yes—
158#2446C2214yes—
159#2446C2214yes—
160#2421C2214yes—
161#2382C2218yes—
162#2369C2212yes—
163#2369C2212yes—
164#2369C2212yes—
165#2365C2212yes—
166#2365C2212yes—
167#2365C2212yes—
168#2355C2212yes—
169#2355C2212yes—
170#2355C2212yes—
171Q8×C4⋊C4C2212yes—
172Q8×C4⋊C4C2212yes—
173Q8×C4⋊C4C2212yes—
174#2331C2214yes—
175#2330C2214yes—
176#2330C2214yes—
177#2320C2214yes—
178#2314C2214yes—
179C4×C4⋊Q8C2212yes—
180C4×C4⋊Q8C2212yes—
181C4×C4⋊Q8C2211yescharacteristic
182C4×C4⋊Q8C2211yescharacteristic
183C4×C4⋊Q8C2211yescharacteristic
184C4×C4⋊Q8C2211yescharacteristic
185C4×C4⋊Q8C2212yes—
186C4×C4⋊Q8C2211yescharacteristic
187C4×C4⋊Q8C2211yescharacteristic
188C4×#125C2212yes—
189C4×#125C2212yes—
190C4×C22⋊Q8C2212yes—
191C4×C22⋊Q8C2212yes—
192C4×C22⋊Q8C2212yes—
193C4×C22⋊Q8C2212yes—
194#2295C2212yes—
195#2295C2212yes—
196#2295C2212yes—
197#2295C2212yes—
198#2285C2212yes—
199#2285C2212yes—
200#2283C2212yes—
201#2283C2212yes—
202C2×C43C2211yescharacteristic
203#541—416no—
204#533—48no—
205C2×C4⋊Q8C2311yescharacteristic
206C2×C4⋊Q8C2311yescharacteristic
207C2×C4⋊Q8C2311yescharacteristic
208C2×C4⋊Q8C2311yescharacteristic
209C2×C4⋊Q8C2312yes—
210C2×C4⋊Q8C2311yescharacteristic
211C2×C4⋊Q8C2311yescharacteristic
212C2×C4⋊Q8C2312yes—
213C2×C4⋊Q8C2312yes—
214C2×C4⋊Q8C2314yes—
215C2×C4⋊Q8C2312yes—
216C2×C4⋊Q8C2312yes—
217C2×#126C2318yes—
218C2×#126C2318yes—
219C2×#125C2312yes—
220C2×#125C2312yes—
221C2×#125C2314yes—
222C2×#125C2314yes—
223C2×#125C2314yes—
224C2×#125C2318yes—
225C2×#125C2318yes—
226C2×#125C2318yes—
227C2×C22⋊Q8C2312yes—
228C2×C22⋊Q8C2312yes—
229C2×C22⋊Q8C2312yes—
230C2×C22⋊Q8C2312yes—
231C2×C22⋊Q8C2312yes—
232C2×C22⋊Q8C2314yes—
233C2×C22⋊Q8C2312yes—
234C2×C4×Q8C2312yes—
235C2×C4×Q8C2312yes—
236C2×C4×Q8C2312yes—
237C2×C4×Q8C2312yes—
238C2×C4×Q8C2314yes—
239C2×C4×Q8C2312yes—
240C2×C4×Q8C2312yes—
241C2×C4×Q8C2314yes—
242C2×C4×Q8C2314yes—
243C2×C4×Q8C2314yes—
244C2×#117C2314yes—
245C22×C42C2311yescharacteristic
246C22×C42C2311yescharacteristic
247C22×C42C2311yescharacteristic
248C22×C42C2311yescharacteristic
249C22×C42C2311yescharacteristic
250C22×C42C2311yescharacteristic
251C22×C42C2311yescharacteristic
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#400C2318yes—
265#400C2318yes—
266#400C2318yes—
267#400C2318yes—
268#400C2318yes—
269#400C2318yes—
270#400C2318yes—
271#400C2318yes—
272#398C2318yes—
273#398C2318yes—
274#398C2318yes—
275#398C2318yes—
276#398C2318yes—
277#398C2318yes—
278#398C2318yes—
279#398C2318yes—
280#398C2318yes—
281#398C2318yes—
282#398C2318yes—
283#398C2318yes—
284#398C2318yes—
285#398C2318yes—
286#398C2318yes—
287#398C2318yes—
288#398C2318yes—
289#398C2318yes—
290#398C2318yes—
291#397C2318yes—
292#397C2318yes—
293#397C2318yes—
294#397C2318yes—
295#395C2318yes—
296#395C2318yes—
297#395C2318yes—
298#395C2318yes—
299#395C2318yes—
300#391C2312yes—
301#391C2312yes—
302#391C2312yes—
303#391C2312yes—
304#391C2314yes—
305#391C2312yes—
306#391C2312yes—
307#391C2314yes—
308#391C2312yes—
309#391C2312yes—
310#391C2312yes—
311#391C2314yes—
312#391C2314yes—
313#391C2314yes—
314#391C2314yes—
315#391C2312yes—
316#391C2314yes—
317#391C2312yes—
318#391C2314yes—
319#391C2314yes—
320#391C2318yes—
321#391C2318yes—
322#391C2312yes—
323#391C2318yes—
324#391C2318yes—
325#391C2318yes—
326#391C2312yes—
327#391C2312yes—
328#391C2312yes—
329#391C2312yes—
330#391C2312yes—
331#391C2312yes—
332#391C2312yes—
333#391C2312yes—
334#389C2312yes—
335#389C2312yes—
336#389C2312yes—
337#389C2312yes—
338#389C2312yes—
339#389C2312yes—
340#389C2312yes—
341#389C2312yes—
342#389C2312yes—
343#389C2312yes—
344#389C2314yes—
345#389C2312yes—
346#389C2312yes—
347#389C2312yes—
348#389C2312yes—
349#389C2312yes—
350#389C2312yes—
351#389C2312yes—
352#389C2312yes—
353#389C2314yes—
354#389C2314yes—
355#389C2312yes—
356#389C2312yes—
357#389C2314yes—
358#389C2314yes—
359#389C2314yes—
360#389C2314yes—
361#389C2314yes—
362#389C2314yes—
363#389C2314yes—
364#389C2314yes—
365#389C2314yes—
366#389C2318yes—
367#389C2314yes—
368#389C2312yes—
369#389C2314yes—
370#389C2312yes—
371#389C2314yes—
372#389C2314yes—
373#389C2318yes—
374#389C2318yes—
375#389C2318yes—
376#389C2314yes—
377#389C2318yes—
378#389C2318yes—
379#389C2318yes—
380#389C2314yes—
381#389C2314yes—
382#389C2312yes—
383#389C2318yes—
384#389C2312yes—
385#389C2312yes—
386#389C2312yes—
387#389C2312yes—
388#389C2312yes—
389#389C2312yes—
390#389C2312yes—
391#389C2312yes—
392#389C2312yes—
393#389C2318yes—
394#389C2314yes—
395#389C2314yes—
396#389C2318yes—
397#388C2318yes—
398#388C2318yes—
399#387C2314yes—
400#387C2314yes—
401#387C2314yes—
402#387C2314yes—
403#387C2318yes—
404#387C2318yes—
405#387C2318yes—
406#387C2318yes—
407#387C2318yes—
408#387C2318yes—
409#387C2318yes—
410#387C2318yes—
411#387C2318yes—
412#387C2318yes—
413#387C2314yes—
414#387C2318yes—
415#387C2318yes—
416#387C2318yes—
417#387C2318yes—
418#387C2314yes—
419#387C2314yes—
420#387C2314yes—
421#387C2314yes—
422#387C2314yes—
423#387C2314yes—
424#387C2314yes—
425#387C2314yes—
426#387C2314yes—
427#387C2314yes—
428#387C2314yes—
429#387C2318yes—
430#387C2318yes—
431#387C2318yes—
432#387C2318yes—
433#387C2318yes—
434#387C2318yes—
435#387C2318yes—
436#387C2318yes—
437#385C2314yes—
438#385C2314yes—
439#385C2314yes—
440#385C2314yes—
441#384C2311yescharacteristic
442#384C2311yescharacteristic
443#384C2312yes—
444#384C2311yescharacteristic
445#384C2311yescharacteristic
446#384C2311yescharacteristic
447#384C2311yescharacteristic
448#384C2312yes—
449#384C2312yes—
450#384C2312yes—
451#384C2314yes—
452#384C2314yes—
453#384C2314yes—
454#384C2312yes—
455#384C2314yes—
456#384C2314yes—
457#384C2312yes—
458#384C2312yes—
459#383C2318yes—
460#383C2314yes—
461#383C2314yes—
462#382C2312yes—
463#382C2312yes—
464#382C2314yes—
465#382C2314yes—
466#382C2318yes—
467#382C2318yes—
468#382C2312yes—
469#382C2314yes—
470#382C2314yes—
471#382C2318yes—
472#382C2314yes—
473#382C2314yes—
474#382C2312yes—
475#382C2312yes—
476#382C2312yes—
477#381C2314yes—
478#381C2314yes—
479#380C2312yes—
480#380C2312yes—
481#380C2312yes—
482#380C2312yes—
483#380C2312yes—
484#380C2312yes—
485#380C2312yes—
486#380C2312yes—
487#380C2312yes—
488#380C2314yes—
489#380C2314yes—
490#380C2312yes—
491#380C2312yes—
492#380C2312yes—
493C4×C4⋊C4C2312yes—
494C4×C4⋊C4C2312yes—
495C4×C4⋊C4C2312yes—
496C4×C4⋊C4C2312yes—
497C4×C4⋊C4C2314yes—
498C4×C4⋊C4C2314yes—
499C4×C4⋊C4C2314yes—
500C4×C4⋊C4C2314yes—
501C4×C4⋊C4C2312yes—
502C4×C4⋊C4C2312yes—
503C4×C4⋊C4C2312yes—
504C4×C4⋊C4C2312yes—
505C4×C4⋊C4C2314yes—
506C4×C4⋊C4C2314yes—
507C4×C4⋊C4C2312yes—
508C4×C4⋊C4C2312yes—
509C4×C4⋊C4C2312yes—
510C4×C4⋊C4C2312yes—
511C4×C4⋊C4C2314yes—
512C4×C4⋊C4C2314yes—
513C4×C4⋊C4C2314yes—
514C4×C4⋊C4C2314yes—
515C4×C4⋊C4C2314yes—
516C4×C4⋊C4C2314yes—
517C4×C4⋊C4C2314yes—
518C4×C4⋊C4C2314yes—
519C4×C4⋊C4C2314yes—
520C4×C22⋊C4C2314yes—
521C4×C22⋊C4C2314yes—
522#376C2314yes—
523#376C2314yes—
524C43C2311yescharacteristic
525C43C2311yescharacteristic
526C43C2311yescharacteristic
527C43C2311yescharacteristic
528C43C2311yescharacteristic
529C43C2311yescharacteristic
530C43C2311yescharacteristic
531C43C2311yescharacteristic
532C22×Q8C2412yes—
533C22×Q8C2412yes—
534C22×Q8C2412yes—
535C22×Q8C2412yes—
536C22×Q8C2414yes—
537C22×Q8C2412yes—
538C22×Q8C2412yes—
539C23×C4C2411yescharacteristic
540C23×C4C2411yescharacteristic
541C23×C4C2411yescharacteristic
542C23×C4C2411yescharacteristic
543C23×C4C2411yescharacteristic
544C23×C4C2411yescharacteristic
545C23×C4C2411yescharacteristic
546C4⋊Q8—24no—
547C4⋊Q8—24no—
548C4⋊Q8—24no—
549C4⋊Q8—24no—
550C4⋊Q8—24no—
551C4⋊Q8—24no—
552C4⋊Q8—28no—
553C4⋊Q8—44no—
554C4⋊Q8—44no—
555C4⋊Q8—44no—
556C4⋊Q8—44no—
557C4⋊Q8—48no—
558#126—416no—
559#126—416no—
560#125—28no—
561#125—44no—
562#125—48no—
563#125—48no—
564#125—48no—
565#125—416no—
566#125—416no—
567#125—416no—
568C22⋊Q8—28no—
569C22⋊Q8—28no—
570C22⋊Q8—44no—
571C22⋊Q8—48no—
572C22⋊Q8—44no—
573C22⋊Q8—44no—
574C22⋊Q8—44no—
575C4×Q8—28no—
576C4×Q8—28no—
577C4×Q8—28no—
578C4×Q8—44no—
579C4×Q8—44no—
580C4×Q8—48no—
581C4×Q8—44no—
582C4×Q8—48no—
583C4×Q8—48no—
584C4×Q8—48no—
585#117—216no—
586C2×C4⋊C4C2414yes—
587C2×C4⋊C4C2414yes—
588C2×C4⋊C4C2412yes—
589C2×C4⋊C4C2412yes—
590C2×C4⋊C4C2412yes—
591C2×C4⋊C4C2412yes—
592C2×C4⋊C4C2412yes—
593C2×C4⋊C4C2412yes—
594C2×C4⋊C4C2414yes—
595C2×C4⋊C4C2414yes—
596C2×C4⋊C4C2414yes—
597C2×C4⋊C4C2414yes—
598C2×C4⋊C4C2414yes—
599C2×C4⋊C4C2412yes—
600C2×C4⋊C4C2414yes—
601C2×C4⋊C4C2414yes—
602C2×C4⋊C4C2412yes—
603C2×C4⋊C4C2414yes—
604C2×C4⋊C4C2412yes—
605C2×C4⋊C4C2412yes—
606C2×C4⋊C4C2414yes—
607C2×C4⋊C4C2414yes—
608C2×C4⋊C4C2412yes—
609C2×C4⋊C4C2412yes—
610C2×C4⋊C4C2412yes—
611C2×C4⋊C4C2412yes—
612C2×C4⋊C4C2412yes—
613C2×C4⋊C4C2412yes—
614C2×C4⋊C4C2412yes—
615C2×C4⋊C4C2412yes—
616C2×C4⋊C4C2412yes—
617C2×C4⋊C4C2412yes—
618C2×C4⋊C4C2412yes—
619C2×C4⋊C4C2412yes—
620C2×C4⋊C4C2412yes—
621C2×C4⋊C4C2414yes—
622C2×C4⋊C4C2412yes—
623C2×C4⋊C4C2414yes—
624C2×C4⋊C4C2414yes—
625C2×C4⋊C4C2414yes—
626C2×C4⋊C4C2414yes—
627C2×C4⋊C4C2412yes—
628C2×C4⋊C4C2414yes—
629C2×C4⋊C4C2412yes—
630C2×C4⋊C4C2418yes—
631C2×C4⋊C4C2418yes—
632C2×C4⋊C4C2412yes—
633C2×C4⋊C4C2418yes—
634C2×C4⋊C4C2414yes—
635C2×C4⋊C4C2414yes—
636C2×C4⋊C4C2412yes—
637C2×C4⋊C4C2418yes—
638C2×C4⋊C4C2418yes—
639C2×C4⋊C4C2418yes—
640C2×C4⋊C4C2418yes—
641C2×C4⋊C4C2412yes—
642C2×C4⋊C4C2412yes—
643C2×C4⋊C4C2414yes—
644C2×C4⋊C4C2418yes—
645C2×C4⋊C4C2418yes—
646C2×C4⋊C4C2418yes—
647C2×C4⋊C4C2418yes—
648C2×C4⋊C4C2418yes—
649C2×C4⋊C4C2414yes—
650C2×C4⋊C4C2414yes—
651C2×C22⋊C4C2414yes—
652C2×C22⋊C4C2414yes—
653C2×C22⋊C4C2414yes—
654C2×C22⋊C4C2414yes—
655C2×C22⋊C4C2414yes—
656C2×C22⋊C4C2414yes—
657C2×C42—24no—
658C2×C42—24no—
659C2×C42—24no—
660C2×C42—24no—
661C2×C42—24no—
662C2×C42—42no—
663C2×C42—42no—
664C2×C42C2414yes—
665C2×C42C2414yes—
666C2×C42C2411yescharacteristic
667C2×C42C2411yescharacteristic
668C2×C42C2414yes—
669C2×C42C2411yescharacteristic
670C2×C42C2414yes—
671C2×C42C2414yes—
672C2×C42C2414yes—
673C2×C42C2411yescharacteristic
674C2×C42C2411yescharacteristic
675C2×C42C2411yescharacteristic
676C2×C42C2411yescharacteristic
677C2×C42C2411yescharacteristic
678C2×C42C2411yescharacteristic
679C2×C42C2411yescharacteristic
680C2×C42C2411yescharacteristic
681C2×C42C2411yescharacteristic
682C2×C42C2411yescharacteristic
683C2×C42C2411yescharacteristic
684C2×C42C2411yescharacteristic
685C2×C42C2411yescharacteristic
686C2×C42C2411yescharacteristic
687C2×C42C2411yescharacteristic
688C2×C42C2411yescharacteristic
689C2×C42C2411yescharacteristic
690C2×C42C2418yes—
691C2×C42C2418yes—
692C2×C42C2418yes—
693C2×C42C2418yes—
694C2×C42C2411yescharacteristic
695C2×C42C2411yescharacteristic
696C2×C42C2411yescharacteristic
697C2×C42C2411yescharacteristic
698C2×C42C2411yescharacteristic
699C2×C42C2411yescharacteristic
700C2×C42C2411yescharacteristic
701C2×C42C2411yescharacteristic
702#95C2414yes—
703#95C2414yes—
704#95C2414yes—
705#95C2414yes—
706#95C2414yes—
707#95C2414yes—
708#95C2414yes—
709#95C2414yes—
710#95C2414yes—
711#95C2414yes—
712#95C2414yes—
713#95C2414yes—
714#95C2414yes—
715#95C2414yes—
716#95C2414yes—
717#95C2414yes—
718#95C2414yes—
719#95C2414yes—
720#95C2414yes—
721#95C2414yes—
722#95C2414yes—
723#95C2414yes—
724#95C2414yes—
725#95C2414yes—
726#95C2414yes—
727#95C2414yes—
728#95C2414yes—
729#95C2414yes—
730#95C2414yes—
731#95C2414yes—
732#95C2418yes—
733#95C2418yes—
734#95C2414yes—
735#95C2414yes—
736#95C2414yes—
737#95C2418yes—
738#95C2414yes—
739#95C2414yes—
740#95C2414yes—
741#95C2418yes—
742#95C2418yes—
743#95C2418yes—
744#95C2418yes—
745#95C2418yes—
746#95C2418yes—
747#95C2418yes—
748#95C2418yes—
749#95C2418yes—
750#95C2418yes—
751#95C2418yes—
752#95C2418yes—
753#95C2418yes—
754C24C2511yescharacteristic
755C2×Q8—24no—
756C2×Q8—24no—
757C2×Q8—24no—
758C2×Q8—24no—
759C2×Q8—24no—
760C2×Q8—24no—
761C2×Q8—24no—
762C2×Q8—24no—
763C2×Q8—24no—
764C2×Q8—24no—
765C2×Q8—24no—
766C2×Q8—28no—
767C2×Q8—24no—
768C2×Q8—42no—
769C2×Q8—44no—
770C2×Q8—42no—
771C2×Q8—42no—
772C2×Q8—42no—
773C2×Q8—42no—
774C2×Q8—44no—
775C2×Q8—42no—
776C22×C4—22no—
777C22×C4—22no—
778C22×C4—22no—
779C22×C4—22no—
780C22×C4—22no—
781C22×C4—22no—
782C22×C4—22no—
783C22×C4—22no—
784C22×C4—22no—
785C22×C4—22no—
786C22×C4—22no—
787C22×C4—22no—
788C22×C4—22no—
789C22×C4—22no—
790C22×C4—22no—
791C22×C4—22no—
792C22×C4—41no—
793C22×C4—41no—
794C22×C4—41no—
795C22×C4—41no—
796C22×C4H(5,𝔽2)14yes—
797C22×C4C2511yescharacteristic
798C22×C4C2511yescharacteristic
799C22×C4C2514yes—
800C22×C4C2514yes—
801C22×C4C2514yes—
802C22×C4C2514yes—
803C22×C4C2514yes—
804C22×C4C2514yes—
805C22×C4C2511yescharacteristic
806C22×C4C2511yescharacteristic
807C22×C4C2514yes—
808C22×C4C2514yes—
809C22×C4C2514yes—
810C22×C4C2514yes—
811C22×C4C2514yes—
812C22×C4C2514yes—
813C22×C4C2511yescharacteristic
814C22×C4C2511yescharacteristic
815C22×C4C2511yescharacteristic
816C22×C4C2511yescharacteristic
817C22×C4C2511yescharacteristic
818C22×C4C2511yescharacteristic
819C22×C4C2511yescharacteristic
820C22×C4C2511yescharacteristic
821C22×C4C2511yescharacteristic
822C22×C4C2511yescharacteristic
823C4⋊C4—28no—
824C4⋊C4—28no—
825C4⋊C4—24no—
826C4⋊C4—24no—
827C4⋊C4—28no—
828C4⋊C4—28no—
829C4⋊C4—24no—
830C4⋊C4—24no—
831C4⋊C4—24no—
832C4⋊C4—28no—
833C4⋊C4—28no—
834C4⋊C4—28no—
835C4⋊C4—28no—
836C4⋊C4—28no—
837C4⋊C4—24no—
838C4⋊C4—24no—
839C4⋊C4—24no—
840C4⋊C4—24no—
841C4⋊C4—28no—
842C4⋊C4—24no—
843C4⋊C4—24no—
844C4⋊C4—24no—
845C4⋊C4—24no—
846C4⋊C4—24no—
847C4⋊C4—24no—
848C4⋊C4—24no—
849C4⋊C4—24no—
850C4⋊C4—24no—
851C4⋊C4—24no—
852C4⋊C4—24no—
853C4⋊C4—24no—
854C4⋊C4—24no—
855C4⋊C4—28no—
856C4⋊C4—24no—
857C4⋊C4—28no—
858C4⋊C4—28no—
859C4⋊C4—24no—
860C4⋊C4—42no—
861C4⋊C4—44no—
862C4⋊C4—48no—
863C4⋊C4—44no—
864C4⋊C4—44no—
865C4⋊C4—44no—
866C4⋊C4—44no—
867C4⋊C4—42no—
868C4⋊C4—44no—
869C4⋊C4—42no—
870C4⋊C4—48no—
871C4⋊C4—48no—
872C4⋊C4—42no—
873C4⋊C4—44no—
874C4⋊C4—42no—
875C4⋊C4—42no—
876C4⋊C4—48no—
877C4⋊C4—44no—
878C4⋊C4—48no—
879C4⋊C4—48no—
880C4⋊C4—48no—
881C4⋊C4—48no—
882C4⋊C4—48no—
883C4⋊C4—48no—
884C4⋊C4—48no—
885C4⋊C4—48no—
886C4⋊C4—44no—
887C4⋊C4—44no—
888C22⋊C4—28no—
889C22⋊C4—28no—
890C22⋊C4—28no—
891C22⋊C4—28no—
892C22⋊C4—44no—
893C22⋊C4—44no—
894C42—22no—
895C42—22no—
896C42—22no—
897C42—22no—
898C42—28no—
899C42—28no—
900C42—22no—
901C42—22no—
902C42—22no—
903C42—22no—
904C42—22no—
905C42—22no—
906C42—22no—
907C42—22no—
908C42—22no—
909C42—22no—
910C42—22no—
911C42—22no—
912C42—28no—
913C42—28no—
914C42—28no—
915C42—22no—
916C42—22no—
917C42—22no—
918C42—22no—
919C42—28no—
920C42—41no—
921C42—41no—
922C42—41no—
923C42—41no—
924C42—48no—
925C42—48no—
926C42—48no—
927C42—48no—
928C422−1+414yes—
929C422−1+414yes—
930C422−1+414yes—
931C422−1+414yes—
932C23—21no—
933C23—21no—
934C23—21no—
935C23—21no—
936C23—21no—
937C23—21no—
938C23C2×H(5,𝔽2)12yes—
939C23C2611yescharacteristic
940Q8—48no—
941Q8—48no—
942Q8—48no—
943Q8—84no—
944Q8—84no—
945Q8—88no—
946Q8—84no—
947C2×C4—21no—
948C2×C4—21no—
949C2×C4—21no—
950C2×C4—21no—
951C2×C4—21no—
952C2×C4—21no—
953C2×C4—21no—
954C2×C4—21no—
955C2×C4—21no—
956C2×C4—21no—
957C2×C4—21no—
958C2×C4—21no—
959C2×C4—21no—
960C2×C4—21no—
961C2×C4—28no—
962C2×C4—21no—
963C2×C4—21no—
964C2×C4—24no—
965C2×C4—24no—
966C2×C4—24no—
967C2×C4—24no—
968C2×C4—24no—
969C2×C4—24no—
970C2×C4—24no—
971C2×C4—24no—
972C2×C4—21no—
973C2×C4—21no—
974C2×C4—21no—
975C2×C4—21no—
976C2×C4—21no—
977C2×C4—21no—
978C2×C4—21no—
979C2×C4—24no—
980C2×C4—24no—
981C2×C4—24no—
982C2×C4—24no—
983C2×C4—24no—
984C2×C4—24no—
985C2×C4—24no—
986C2×C4—24no—
987C2×C4—24no—
988C2×C4—24no—
989C2×C4—24no—
990C2×C4—24no—
991C2×C4—24no—
992C2×C4—24no—
993C2×C4—24no—
994C2×C4—24no—
995C2×C4—24no—
996C2×C4—21no—
997C2×C4—21no—
998C2×C4—24no—
999C2×C4—24no—
1000C2×C4—24no—
1001C2×C4—24no—
1002C2×C4—24no—
1003C2×C4—24no—
1004C2×C4—21no—
1005C2×C4—24no—
1006C2×C4—24no—
1007C2×C4—24no—
1008C2×C4—24no—
1009C2×C4—24no—
1010C2×C4—44no—
1011C2×C4—44no—
1012C2×C4—44no—
1013C2×C4—44no—
1014C2×C4—44no—
1015C2×C4—44no—
1016C2×C4C2×H(5,𝔽2)12yes—
1017C2×C4C2×H(5,𝔽2)12yes—
1018C2×C4C2×2−1+412yes—
1019C2×C4C2×2−1+412yes—
1020C2×C4C2×2−1+412yes—
1021C2×C4C2×2−1+412yes—
1022C2×C4C2×2−1+412yes—
1023C2×C4C2×2−1+412yes—
1024C2×C4C2×2−1+412yes—
1025C2×C4C2×2−1+412yes—
1026C2×C4C2×2−1+412yes—
1027C2×C4C2×2−1+412yes—
1028C2×C4C2×2−1+412yes—
1029C2×C4C2×2−1+412yes—
1030C2×C4#58512yes—
1031C2×C4#58512yes—
1032C22—22no—
1033C22—22no—
1034C22—22no—
1035C22—41no—
1036C22—41no—
1037C22—41no—
1038C22—41no—
1039C22C22×H(5,𝔽2)11yescharacteristic
1040C22C22×2−1+411yescharacteristic
1041C22C22×2−1+411yescharacteristic
1042C22C22×2−1+411yescharacteristic
1043C22C22×2−1+411yescharacteristic
1044C22C2×#58511yescharacteristic
1045C22C2×#58511yescharacteristic
1046C4—22no—
1047C4—22no—
1048C4—22no—
1049C4—22no—
1050C4—22no—
1051C4—22no—
1052C4—22no—
1053C4—44no—
1054C4—44no—
1055C4—41no—
1056C4—44no—
1057C4—41no—
1058C4—44no—
1059C4—44no—
1060C4—44no—
1061C4—44no—
1062C4—41no—
1063C4—41no—
1064C4—44no—
1065C4—44no—
1066C4—44no—
1067C4—44no—
1068C4—44no—
1069C4#354414yes—
1070C4#355514yes—
1071C4#355614yes—
1072C2—42no—
1073C2C2×#354411yescharacteristic
1074C2C2×#355511yescharacteristic
1075C2C2×#355611yescharacteristic
1076C2#6283111yescharacteristic
1077C2#6283511yescharacteristic
1078C2#6283511yescharacteristic
1079C2#6283711yescharacteristic
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
1. #59871C2semidirect
2. #59871C2semidirect
3. #59870C2semidirect
4. #59869C2semidirect
5. #53358C2semidirect
7. #46344C2semidirect
8. #46181C2semidirect
10. #39754C2semidirect
11. #39753C2semidirect
12. #39643C2semidirect
13. #39642C2semidirect
18. #39180C2semidirect
20. #38984C2semidirect
23. #37344C2semidirect

Maximal subgroups

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

subgroupindex
#598712
#598702
#598692
#533582
#531962
#463442
#461812
#456742
#397542
#397532
#396432
#396422
#394802
#394782
#393532
#391802
#391572
#389842
#389312
#373772
#373442
#372952
#366452
#366352