Finite Group Databasebeta

← #7712727

Subgroups — #7712727

Order 512.

4188 conjugacy classes of subgroups.

The subgroup lattice has 883 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#59922C214yesmaximal
2#59920C214yesmaximal
3#45797C218yesmaximal
4#39715C218yesmaximal, complemented
5#39680C214yesmaximal, complemented
6#39673C214yesmaximal, complemented
7#39181C212yesmaximal, complemented
8#39180C212yesmaximal, complemented
9#39177C214yesmaximal, complemented
10#37624C212yesmaximal
11#37311C214yesmaximal
12#36640C211yesmaximal, characteristic
13#36635C211yesmaximal, characteristic
14#36600C212yesmaximal, complemented
15#36600C211yesmaximal, characteristic, complemented
16#36584C211yesmaximal, characteristic, complemented
17#36565C212yesmaximal, complemented
18#36565C211yesmaximal, characteristic, complemented
19Q8×#125C211yesmaximal, characteristic, complemented
20#35337C212yesmaximal
21#35336C212yesmaximal
22#34373C212yesmaximal
23C4×#533C211yesmaximal, characteristic
24C2×#533C2211yescharacteristic
25#2864C2214yes—
26#2864C2212yes—
27#2863C2214yes—
28#2862C2212yes—
29#2862C2211yescharacteristic
30#2859C2212yes—
31#2859C2212yes—
32#2859C2212yes—
33#2859C2212yes—
34#2859C2211yescharacteristic
35#2859C2211yescharacteristic
36#2859C2211yescharacteristic
37#2857C2212yes—
38#2855C2214yes—
39#2851C2211yescharacteristic
40#2851C2212yes—
41#2851C2211yescharacteristic
42#2851C2212yes—
43#2851C2214yes—
44#2841C2218yes—
45#2809C2218yes—
46#2802C2218yes—
47#2799C2218yes—
48#2792C2218yes—
49#2791C2218yes—
50#2788C2218yes—
51#2774C2218yes—
52#2774C2218yes—
53#2768C2218yes—
54#2755C2218yes—
55#2755C2218yes—
56#2729C2218yes—
57#2726C2218yes—
58#2720C2218yes—
59#2713C2218yes—
60#2713C2218yes—
61#2666C2218yes—
62#2660C2214yes—
63#2647C2214yes—
64#2647C2214yes—
65#2647C2214yes—
66#2629C2214yes—
67#2628C2214yes—
68#2590C2218yes—
69#2590C2218yes—
70#2590C2218yes—
71#2589C2218yes—
72#2589C2218yes—
73#2588C2218yes—
74#2588C2218yes—
75#2587C2218yes—
76#2587C2218yes—
77#2586C2218yes—
78#2586C2218yes—
79#2586C2218yes—
80#2585C2218yes—
81#2585C2218yes—
82#2585C2218yes—
83#2585C2218yes—
84#2584C2214yes—
85#2582C2214yes—
86#2581C2214yes—
87#2571C2214yes—
88#2571C2212yes—
89#2570C2214yes—
90#2570C2214yes—
91#2570C2214yes—
92#2552C2214yes—
93#2552C2214yes—
94#2552C2212yes—
95#2552C2212yes—
96#2551C2214yes—
97#2551C2212yes—
98#2550C2214yes—
99#2550C2214yes—
100#2550C2214yes—
101#2546C2214yes—
102#2520C2218yes—
103#2511C2218yes—
104#2509C2214yes—
105#2509C2214yes—
106#2509C2218yes—
107#2507C2214yes—
108#2507C2218yes—
109#2506C2214yes—
110#2453C2218yes—
111#2453C2214yes—
112#2453C2214yes—
113#2451C2218yes—
114#2451C2214yes—
115#2451C2214yes—
116#2441C2214yes—
117#2439C2214yes—
118#2378C2218yes—
119#2370C2214yes—
120#2370C2218yes—
121#2369C2214yes—
122#2369C2218yes—
123#2362C2214yes—
124#2362C2214yes—
125#2355C2214yes—
126#2355C2214yes—
127#2355C2212yes—
128#2355C2212yes—
129#2351C2214yes—
130Q8×C4⋊C4C2212yes—
131Q8×C4⋊C4C2212yes—
132Q8×C4⋊C4C2214yes—
133#2336C2218yes—
134#2331C2214yes—
135#2331C2214yes—
136#2330C2214yes—
137#2327C2214yes—
138#2314C2214yes—
139#2314C2214yes—
140C4×C4⋊Q8C2212yes—
141C4×C4⋊Q8C2212yes—
142C4×C4⋊Q8C2212yes—
143C4×#125C2212yes—
144C4×#125C2212yes—
145C4×#125C2212yes—
146C4×#125C2212yes—
147C4×#125C2212yes—
148C4×#125C2211yescharacteristic
149C4×#125C2211yescharacteristic
150C4×#125C2214yes—
151C4×#125C2212yes—
152C4×#125C2214yes—
153C4×C22⋊Q8C2212yes—
154C4×C22⋊Q8C2214yes—
155C4×C22⋊Q8C2212yes—
156C4×C22⋊Q8C2214yes—
157#2296C2214yes—
158#2296C2212yes—
159#2295C2214yes—
160#2295C2212yes—
161#2295C2211yescharacteristic
162#2295C2211yescharacteristic
163#2285C2212yes—
164#2285C2211yescharacteristic
165#2283C2212yes—
166C42×Q8C2211yescharacteristic
167C42×Q8C2211yescharacteristic
168C42×Q8C2212yes—
169C4×#117C2212yes—
170C2×C43C2211yescharacteristic
171#533Q8116yescomplemented
172C2×C4⋊Q8C2312yes—
173C2×C4⋊Q8C2314yes—
174C2×C4⋊Q8C2314yes—
175C2×C4⋊Q8C2318yes—
176C2×C4⋊Q8C2311yescharacteristic
177C2×C4⋊Q8C2311yescharacteristic
178C2×#125C2312yes—
179C2×#125C2311yescharacteristic
180C2×#125C2311yescharacteristic
181C2×#125C2314yes—
182C2×#125C2312yes—
183C2×#125C2314yes—
184C2×#125C2314yes—
185C2×#125C2318yes—
186C2×#125C2312yes—
187C2×C22⋊Q8C2314yes—
188C2×C22⋊Q8C2311yescharacteristic
189C2×C22⋊Q8C2311yescharacteristic
190C2×C22⋊Q8C2312yes—
191C2×C4×Q8C2314yes—
192C2×C4×Q8C2312yes—
193C2×C4×Q8C2312yes—
194C2×C4×Q8C2314yes—
195C2×C4×Q8C2314yes—
196C2×C4×Q8C2314yes—
197C2×C4×Q8C2311yescharacteristic
198C2×C4×Q8C2311yescharacteristic
199C2×C4×Q8C2312yes—
200C2×#117C2314yes—
201C2×#117C2312yes—
202C2×#117C2312yes—
203C22×C42C2311yescharacteristic
204C22×C42C2312yes—
205C22×C42C2311yescharacteristic
206C22×C42C2312yes—
207C22×C42C2311yescharacteristic
208#400C2318yes—
209#400C2318yes—
210#400C2318yes—
211#400C2318yes—
212#400C2318yes—
213#400C2318yes—
214#400C2318yes—
215#400C2318yes—
216#400C2318yes—
217#400C2318yes—
218#400C2318yes—
219#399C2318yes—
220#398C2318yes—
221#398C2318yes—
222#398C2318yes—
223#398C2318yes—
224#398C2318yes—
225#398C2318yes—
226#398C2318yes—
227#398C2318yes—
228#398C2318yes—
229#398C2318yes—
230#398C2318yes—
231#398C2318yes—
232#398C2318yes—
233#398C2318yes—
234#398C2318yes—
235#398C2318yes—
236#398C2318yes—
237#398C2318yes—
238#396C2318yes—
239#396C2318yes—
240#395C2318yes—
241#395C2318yes—
242#395C2318yes—
243#395C2318yes—
244#395C2318yes—
245#395C2318yes—
246#395C2318yes—
247#393C2318yes—
248#391C2312yes—
249#391C2312yes—
250#391C2314yes—
251#391C2314yes—
252#391C2314yes—
253#391C2314yes—
254#391C2318yes—
255#391C2318yes—
256#391C2318yes—
257#391C2314yes—
258#391C2314yes—
259#391C2318yes—
260#391C2318yes—
261#391C2318yes—
262#391C2318yes—
263#391C2318yes—
264#391C2318yes—
265#391C2314yes—
266#389C2314yes—
267#389C2314yes—
268#389C2312yes—
269#389C2314yes—
270#389C2314yes—
271#389C2314yes—
272#389C2314yes—
273#389C2312yes—
274#389C2314yes—
275#389C2314yes—
276#389C2314yes—
277#389C2314yes—
278#389C2312yes—
279#389C2312yes—
280#389C2312yes—
281#389C2314yes—
282#389C2312yes—
283#389C2314yes—
284#389C2318yes—
285#389C2314yes—
286#389C2314yes—
287#389C2314yes—
288#389C2314yes—
289#389C2318yes—
290#389C2314yes—
291#389C2318yes—
292#389C2314yes—
293#389C2314yes—
294#389C2318yes—
295#389C2318yes—
296#389C2318yes—
297#389C2318yes—
298#389C2314yes—
299#389C2314yes—
300#389C2318yes—
301#389C2318yes—
302#389C2318yes—
303#389C2318yes—
304#389C2318yes—
305#389C2314yes—
306#389C2318yes—
307#389C2318yes—
308#389C2318yes—
309#389C2318yes—
310#389C2314yes—
311#389C2314yes—
312#389C2314yes—
313#389C2318yes—
314#388C2318yes—
315#388C2318yes—
316#388C2318yes—
317#388C2318yes—
318#387C2314yes—
319#387C2318yes—
320#387C2314yes—
321#387C2318yes—
322#387C2318yes—
323#387C2318yes—
324#387C2318yes—
325#387C2318yes—
326#387C2314yes—
327#387C2318yes—
328#387C2318yes—
329#387C2314yes—
330#387C2314yes—
331#387C2314yes—
332#387C2318yes—
333#387C2318yes—
334#387C2318yes—
335#387C2318yes—
336#387C2318yes—
337#387C2318yes—
338#387C2318yes—
339#387C2318yes—
340#387C2318yes—
341#387C2318yes—
342#387C2318yes—
343#387C2318yes—
344#387C2318yes—
345#387C2318yes—
346#387C2318yes—
347#387C2314yes—
348#387C2318yes—
349#387C2318yes—
350#387C2318yes—
351#387C2318yes—
352#387C2318yes—
353#387C2314yes—
354#387C2314yes—
355#387C2314yes—
356#387C2314yes—
357#387C2314yes—
358#385C2314yes—
359#385C2318yes—
360#385C2314yes—
361#385C2318yes—
362#385C2314yes—
363#385C2314yes—
364#384C2312yes—
365#384C2312yes—
366#384C2314yes—
367#384C2314yes—
368#384C2314yes—
369#384C2312yes—
370#384C2314yes—
371#384C2312yes—
372#384C2318yes—
373#383C2314yes—
374#382C2311yescharacteristic
375#382C2312yes—
376#382C2311yescharacteristic
377#382C2312yes—
378#382C2312yes—
379#382C2314yes—
380#382C2314yes—
381#382C2314yes—
382#382C2314yes—
383#382C2312yes—
384#382C2314yes—
385#382C2318yes—
386#382C2314yes—
387#382C2312yes—
388#381C2314yes—
389#380C2314yes—
390#380C2312yes—
391#380C2312yes—
392#380C2312yes—
393#380C2314yes—
394#380C2314yes—
395#380C2312yes—
396C4×C4⋊C4C2314yes—
397C4×C4⋊C4C2318yes—
398C4×C4⋊C4C2318yes—
399C4×C4⋊C4C2314yes—
400C4×C4⋊C4C2312yes—
401C4×C4⋊C4C2314yes—
402C4×C4⋊C4C2314yes—
403C4×C4⋊C4C2312yes—
404C4×C4⋊C4C2314yes—
405C4×C4⋊C4C2314yes—
406C4×C4⋊C4C2314yes—
407C4×C4⋊C4C2314yes—
408C4×C4⋊C4C2314yes—
409C4×C4⋊C4C2314yes—
410C4×C4⋊C4C2318yes—
411C4×C4⋊C4C2318yes—
412C4×C4⋊C4C2314yes—
413C4×C4⋊C4C2314yes—
414C4×C4⋊C4C2318yes—
415C4×C4⋊C4C2318yes—
416C4×C4⋊C4C2314yes—
417C4×C4⋊C4C2314yes—
418C4×C4⋊C4C2314yes—
419C4×C4⋊C4C2312yes—
420C4×C4⋊C4C2312yes—
421C4×C4⋊C4C2314yes—
422C4×C4⋊C4C2312yes—
423C4×C4⋊C4C2312yes—
424C4×C4⋊C4C2312yes—
425C4×C4⋊C4C2311yescharacteristic
426C4×C4⋊C4C2312yes—
427C4×C4⋊C4C2314yes—
428C4×C4⋊C4C2318yes—
429C4×C4⋊C4C2314yes—
430C4×C4⋊C4C2318yes—
431C4×C4⋊C4C2311yescharacteristic
432C4×C4⋊C4C2312yes—
433C4×C22⋊C4C2314yes—
434C4×C22⋊C4C2314yes—
435C4×C22⋊C4C2314yes—
436#376C2314yes—
437#376C2312yes—
438#376C2312yes—
439C43C2312yes—
440C43C2311yescharacteristic
441C43C2312yes—
442C43C2311yescharacteristic
443C43C2312yes—
444C43C2311yescharacteristic
445C43C2311yescharacteristic
446C43C2312yes—
447C22×Q8C2411yescharacteristic
448C22×Q8C2411yescharacteristic
449C22×Q8C2414yes—
450C22×Q8C2418yes—
451C22×Q8C2412yes—
452C23×C4C2411yescharacteristic
453C23×C4C2411yescharacteristic
454C23×C4C2412yes—
455C23×C4C2412yes—
456C23×C4C2411yescharacteristic
457C4⋊Q8—44no—
458C4⋊Q8—48no—
459C4⋊Q8—48no—
460C4⋊Q8—416no—
461C4⋊Q8C2×Q818yes—
462C4⋊Q8C2×Q818yes—
463#125—28no—
464#125—24no—
465#125—24no—
466#125—48no—
467#125—44no—
468#125—48no—
469#125—48no—
470#125—416no—
471#125C2×Q8116yes—
472C22⋊Q8—48no—
473C22⋊Q8C2×Q818yes—
474C22⋊Q8C2×Q818yes—
475C22⋊Q8C2×Q8116yes—
476C4×Q8—48no—
477C4×Q8—48no—
478C4×Q8—44no—
479C4×Q8—44no—
480C4×Q8—48no—
481C4×Q8—48no—
482C4×Q8C2×Q818yes—
483C4×Q8C2×Q818yes—
484C4×Q8C2×Q8116yes—
485#117—44no—
486#117—48no—
487#117C2×Q8116yes—
488C2×C4⋊C4C2414yes—
489C2×C4⋊C4C2414yes—
490C2×C4⋊C4C2412yes—
491C2×C4⋊C4C2414yes—
492C2×C4⋊C4C2412yes—
493C2×C4⋊C4C2414yes—
494C2×C4⋊C4C2414yes—
495C2×C4⋊C4C2414yes—
496C2×C4⋊C4C2412yes—
497C2×C4⋊C4C2418yes—
498C2×C4⋊C4C2414yes—
499C2×C4⋊C4C2412yes—
500C2×C4⋊C4C2412yes—
501C2×C4⋊C4C2418yes—
502C2×C4⋊C4C2414yes—
503C2×C4⋊C4C2414yes—
504C2×C4⋊C4C2412yes—
505C2×C4⋊C4C2414yes—
506C2×C4⋊C4C2414yes—
507C2×C4⋊C4C2414yes—
508C2×C4⋊C4C2414yes—
509C2×C4⋊C4C2414yes—
510C2×C4⋊C4C2418yes—
511C2×C4⋊C4C2418yes—
512C2×C4⋊C4C2414yes—
513C2×C4⋊C4C2414yes—
514C2×C4⋊C4C2414yes—
515C2×C4⋊C4C2414yes—
516C2×C4⋊C4C2414yes—
517C2×C4⋊C4C2414yes—
518C2×C4⋊C4C2418yes—
519C2×C4⋊C4C2418yes—
520C2×C4⋊C4C2418yes—
521C2×C4⋊C4C2418yes—
522C2×C4⋊C4C2418yes—
523C2×C4⋊C4C2418yes—
524C2×C4⋊C4C2418yes—
525C2×C4⋊C4C2418yes—
526C2×C4⋊C4C2418yes—
527C2×C4⋊C4C2414yes—
528C2×C4⋊C4C2418yes—
529C2×C4⋊C4C2418yes—
530C2×C4⋊C4C2418yes—
531C2×C4⋊C4C2418yes—
532C2×C4⋊C4C2412yes—
533C2×C4⋊C4C2412yes—
534C2×C4⋊C4C2412yes—
535C2×C4⋊C4C2412yes—
536C2×C4⋊C4C2412yes—
537C2×C4⋊C4C2412yes—
538C2×C4⋊C4C2411yescharacteristic
539C2×C4⋊C4C2411yescharacteristic
540C2×C4⋊C4C2412yes—
541C2×C22⋊C4C2414yes—
542C2×C22⋊C4C2418yes—
543C2×C22⋊C4C2414yes—
544C2×C22⋊C4C2414yes—
545C2×C22⋊C4C2412yes—
546C2×C22⋊C4C2412yes—
547C2×C42—24no—
548C2×C42—44no—
549C2×C42—44no—
550C2×C42—42no—
551C2×C42C2×Q818yes—
552C2×C42C2412yes—
553C2×C42C2412yes—
554C2×C42C2414yes—
555C2×C42C2412yes—
556C2×C42C2412yes—
557C2×C42C2412yes—
558C2×C42C2414yes—
559C2×C42C2411yescharacteristic
560C2×C42C2412yes—
561C2×C42C2411yescharacteristic
562C2×C42C2411yescharacteristic
563C2×C42C2412yes—
564C2×C42C2418yes—
565C2×C42C2414yes—
566C2×C42C2414yes—
567C2×C42C2414yes—
568C2×C42C2414yes—
569C2×C42C2418yes—
570C2×C42C2418yes—
571C2×C42C2418yes—
572C2×C42C2418yes—
573C2×C42C2412yes—
574C2×C42C2412yes—
575C2×C42C2412yes—
576C2×C42C2412yes—
577C2×C42C2412yes—
578C2×C42C2412yes—
579C2×C42C2412yes—
580C2×C42C2411yescharacteristic
581C2×C42C2411yescharacteristic
582C2×C42C2411yescharacteristic
583C2×C42C2411yescharacteristic
584C2×C42C2411yescharacteristic
585#95C2414yes—
586#95C2414yes—
587#95C2414yes—
588#95C2414yes—
589#95C2414yes—
590#95C2414yes—
591#95C2414yes—
592#95C2414yes—
593#95C2414yes—
594#95C2414yes—
595#95C2414yes—
596#95C2412yes—
597#95C2412yes—
598#95C2418yes—
599#95C2414yes—
600#95C2414yes—
601#95C2414yes—
602#95C2414yes—
603#95C2414yes—
604#95C2414yes—
605#95C2414yes—
606#95C2418yes—
607#95C2418yes—
608#95C2414yes—
609#95C2414yes—
610#95C2414yes—
611#95C2418yes—
612#95C2418yes—
613#95C2418yes—
614#95C2418yes—
615#95C2418yes—
616#95C2418yes—
617#95C2418yes—
618#95C2418yes—
619#95C2414yes—
620#95C2414yes—
621#95C2418yes—
622#95C2418yes—
623#95C2418yes—
624#95C2418yes—
625#95C2418yes—
626#95C2418yes—
627#95C2418yes—
628#95C2418yes—
629#95C2418yes—
630C24C2511yescharacteristic
631C2×Q8—24no—
632C2×Q8—24no—
633C2×Q8—28no—
634C2×Q8—44no—
635C2×Q8—44no—
636C2×Q8—44no—
637C2×Q8—48no—
638C2×Q8—48no—
639C2×Q8—48no—
640C2×Q8C22×Q814yes—
641C2×Q8C22×Q814yes—
642C2×Q8C22×Q818yes—
643C22×C4—22no—
644C22×C4—24no—
645C22×C4—22no—
646C22×C4—24no—
647C22×C4—24no—
648C22×C4—42no—
649C22×C4—42no—
650C22×C4—42no—
651C22×C4—42no—
652C22×C4—42no—
653C22×C4C22×Q814yes—
654C22×C4C22×Q814yes—
655C22×C4C22×Q814yes—
656C22×C4C2512yes—
657C22×C4C2514yes—
658C22×C4C2514yes—
659C22×C4C2514yes—
660C22×C4C2518yes—
661C22×C4C2514yes—
662C22×C4C2512yes—
663C22×C4C2514yes—
664C22×C4C2518yes—
665C22×C4C2514yes—
666C22×C4C2511yescharacteristic
667C22×C4C2511yescharacteristic
668C22×C4C2511yescharacteristic
669C22×C4C2512yes—
670C22×C4C2512yes—
671C22×C4C2512yes—
672C22×C4C2512yes—
673C22×C4C2511yescharacteristic
674C22×C4C2512yes—
675C22×C4C2512yes—
676C22×C4C2511yescharacteristic
677C22×C4C2511yescharacteristic
678C4⋊C4—216no—
679C4⋊C4—28no—
680C4⋊C4—28no—
681C4⋊C4—28no—
682C4⋊C4—24no—
683C4⋊C4—24no—
684C4⋊C4—28no—
685C4⋊C4—28no—
686C4⋊C4—28no—
687C4⋊C4—24no—
688C4⋊C4—28no—
689C4⋊C4—24no—
690C4⋊C4—28no—
691C4⋊C4—216no—
692C4⋊C4—24no—
693C4⋊C4—28no—
694C4⋊C4—24no—
695C4⋊C4—44no—
696C4⋊C4—44no—
697C4⋊C4—44no—
698C4⋊C4—48no—
699C4⋊C4—48no—
700C4⋊C4—44no—
701C4⋊C4—44no—
702C4⋊C4—44no—
703C4⋊C4—44no—
704C4⋊C4—44no—
705C4⋊C4—44no—
706C4⋊C4—44no—
707C4⋊C4—44no—
708C4⋊C4—48no—
709C4⋊C4—48no—
710C4⋊C4—48no—
711C4⋊C4—48no—
712C4⋊C4—48no—
713C4⋊C4—48no—
714C4⋊C4—48no—
715C4⋊C4—48no—
716C4⋊C4—48no—
717C4⋊C4—44no—
718C4⋊C4—48no—
719C4⋊C4—48no—
720C4⋊C4—48no—
721C4⋊C4—48no—
722C4⋊C4C22×Q818yes—
723C4⋊C4C22×Q818yes—
724C4⋊C4C22×Q818yes—
725C4⋊C4C22×Q818yes—
726C4⋊C4C22×Q818yes—
727C4⋊C4C22×Q818yes—
728C4⋊C4C22×Q818yes—
729C4⋊C4C22×Q814yes—
730C4⋊C4C22×Q814yes—
731C22⋊C4—44no—
732C22⋊C4—48no—
733C22⋊C4—44no—
734C22⋊C4—44no—
735C22⋊C4C22×Q818yes—
736C22⋊C4C22×Q818yes—
737C42—24no—
738C42—22no—
739C42—24no—
740C42—24no—
741C42—24no—
742C42—24no—
743C42—22no—
744C42—22no—
745C42—24no—
746C42—24no—
747C42—28no—
748C42—28no—
749C42—42no—
750C42—42no—
751C42—42no—
752C42—42no—
753C42—42no—
754C42—48no—
755C42—44no—
756C42—44no—
757C42—44no—
758C42—44no—
759C42—48no—
760C42—48no—
761C42—48no—
762C42—48no—
763C42C22×Q814yes—
764C42C22×Q814yes—
765C42C22×Q814yes—
766C42C22×Q814yes—
767C42C22×Q818yes—
768C42C22×Q818yes—
769C422−1+414yes—
770C23—21no—
771C23—21no—
772C23—22no—
773C23—22no—
774C23C23×Q812yes—
775C23C2611yescharacteristic
776Q8—28no—
777Q8—28no—
778Q8—48no—
779Q8—88no—
780Q8—168no—
781C2×C4—21no—
782C2×C4—22no—
783C2×C4—22no—
784C2×C4—22no—
785C2×C4—22no—
786C2×C4—22no—
787C2×C4—22no—
788C2×C4—22no—
789C2×C4—24no—
790C2×C4—24no—
791C2×C4—24no—
792C2×C4—24no—
793C2×C4—21no—
794C2×C4—28no—
795C2×C4—28no—
796C2×C4—22no—
797C2×C4—24no—
798C2×C4—24no—
799C2×C4—28no—
800C2×C4—24no—
801C2×C4—24no—
802C2×C4—22no—
803C2×C4—22no—
804C2×C4—22no—
805C2×C4—22no—
806C2×C4—24no—
807C2×C4—24no—
808C2×C4—24no—
809C2×C4—24no—
810C2×C4—28no—
811C2×C4—24no—
812C2×C4—28no—
813C2×C4—24no—
814C2×C4—22no—
815C2×C4—28no—
816C2×C4—24no—
817C2×C4—24no—
818C2×C4—28no—
819C2×C4—24no—
820C2×C4—24no—
821C2×C4—24no—
822C2×C4—24no—
823C2×C4—24no—
824C2×C4—28no—
825C2×C4—24no—
826C2×C4—44no—
827C2×C4—48no—
828C2×C4—48no—
829C2×C4C23×Q812yes—
830C2×C4C23×Q812yes—
831C2×C4C23×Q812yes—
832C2×C4C23×Q812yes—
833C2×C4C23×Q814yes—
834C2×C4C23×Q814yes—
835C2×C4C23×Q814yes—
836C2×C4C23×Q814yes—
837C2×C4C23×Q812yes—
838C2×C4C23×Q812yes—
839C2×C4C2×2−1+414yes—
840C2×C4C2×2−1+412yes—
841C2×C4#58514yes—
842C2×C4#58512yes—
843C2×C4#58514yes—
844C22—22no—
845C22—22no—
846C22—22no—
847C22—42no—
848C22—42no—
849C22C24×Q811yescharacteristic
850C22C22×2−1+411yescharacteristic
851C22C2×#58512yes—
852C22C2×#58512yes—
853C22C2×#58511yescharacteristic
854C4—24no—
855C4—22no—
856C4—22no—
857C4—24no—
858C4—24no—
859C4—22no—
860C4—22no—
861C4—24no—
862C4—24no—
863C4—24no—
864C4—44no—
865C4—44no—
866C4—48no—
867C4—42no—
868C4—44no—
869C4—42no—
870C4—44no—
871C4—44no—
872C4—48no—
873C4—44no—
874C4#350214yes—
875C4#350414yes—
876C2—42no—
877C2#6276112yes—
878C2C2×#350211yescharacteristic
879C2C2×#350411yescharacteristic
880C2#6281311yescharacteristic
881C2#6282712yes—
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
4. #39715C2semidirect
5. #39680C2semidirect
6. #39673C2semidirect
7. #39181C2semidirect
8. #39180C2semidirect
9. #39177C2semidirect
14. #36600C2semidirect
15. #36600C2semidirect
16. #36584C2semidirect
17. #36565C2semidirect
18. #36565C2semidirect
19. Q8×#125C2semidirect
171. #533Q8semidirect

Maximal subgroups

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

subgroupindex
#599222
#599202
#457972
#397152
#396802
#396732
#391812
#391802
#391772
#376242
#373112
#366402
#366352
#366002
#365842
#365652
Q8×#1252
#353372
#353362
#343732
C4×#5332