Finite Group Databasebeta

← #7680328

Subgroups — #7680328

Order 512.

4348 conjugacy classes of subgroups.

The subgroup lattice has 886 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#59934C214yesmaximal, complemented
2#59694C214yesmaximal
3#59694C214yesmaximal
4#59681C214yesmaximal, complemented
5#44737C218yesmaximal, complemented
6#44721C218yesmaximal
7#39693C214yesmaximal
8#39641C211yesmaximal, characteristic, complemented
9#39638C212yesmaximal, complemented
10#39635C211yesmaximal, characteristic, complemented
11#39635C212yesmaximal, complemented
12#39599C212yesmaximal
13#36560C211yesmaximal, characteristic, complemented
14#36552C212yesmaximal
15Q8×#125C211yesmaximal, characteristic, complemented
16#35642C214yesmaximal, complemented
17#35336C212yesmaximal
18#35284C211yesmaximal, characteristic
19#34951C212yesmaximal, complemented
20#34337C212yesmaximal, complemented
21#34281C212yesmaximal
22#34145C211yesmaximal, characteristic
23C4×#541C211yesmaximal, characteristic
24C2×#557C2212yes—
25C2×#541C2211yescharacteristic
26C2×#533C2211yescharacteristic
27#2868C2211yescharacteristic
28#2859C2212yes—
29#2859C2212yes—
30#2859C2211yescharacteristic
31#2857C2212yes—
32#2851C2214yes—
33#2802C2218yes—
34#2802C2218yes—
35#2802C2218yes—
36#2802C2218yes—
37#2802C2218yes—
38#2791C2218yes—
39#2791C2218yes—
40#2790C2218yes—
41#2790C2218yes—
42#2774C2218yes—
43#2726C2218yes—
44#2704C2218yes—
45#2647C2212yes—
46#2647C2212yes—
47#2647C2212yes—
48#2629C2214yes—
49#2629C2212yes—
50#2612C2218yes—
51#2606C2218yes—
52#2606C2218yes—
53#2590C2218yes—
54#2590C2218yes—
55#2590C2218yes—
56#2590C2218yes—
57#2587C2218yes—
58#2587C2218yes—
59#2587C2218yes—
60#2587C2218yes—
61#2585C2218yes—
62#2585C2218yes—
63#2585C2218yes—
64#2585C2218yes—
65#2584C2214yes—
66#2582C2214yes—
67#2582C2212yes—
68#2570C2218yes—
69#2568C2212yes—
70#2565C2214yes—
71#2552C2214yes—
72#2552C2212yes—
73#2546C2214yes—
74#2546C2214yes—
75#2546C2214yes—
76#2546C2212yes—
77#2520C2218yes—
78#2511C2214yes—
79#2511C2214yes—
80#2511C2218yes—
81#2511C2214yes—
82#2509C2214yes—
83#2509C2218yes—
84#2508C2214yes—
85#2507C2218yes—
86#2507C2214yes—
87#2507C2214yes—
88#2507C2214yes—
89#2507C2218yes—
90#2507C2218yes—
91#2507C2218yes—
92#2507C2214yes—
93#2506C2218yes—
94#2505C2218yes—
95#2502C2214yes—
96#2497C2214yes—
97#2453C2214yes—
98#2453C2214yes—
99#2453C2214yes—
100#2451C2214yes—
101#2446C2214yes—
102#2446C2214yes—
103#2446C2214yes—
104#2429C2214yes—
105#2429C2214yes—
106#2429C2214yes—
107#2402C2218yes—
108#2373C2218yes—
109#2373C2218yes—
110#2371C2218yes—
111#2370C2214yes—
112#2370C2218yes—
113#2370C2218yes—
114#2370C2214yes—
115#2369C2212yes—
116#2368C2214yes—
117#2365C2214yes—
118#2365C2214yes—
119#2365C2212yes—
120#2365C2212yes—
121#2360C2212yes—
122#2360C2212yes—
123#2360C2214yes—
124#2355C2214yes—
125Q8×C4⋊C4C2214yes—
126Q8×C4⋊C4C2214yes—
127Q8×C4⋊C4C2212yes—
128Q8×C4⋊C4C2212yes—
129Q8×C4⋊C4C2214yes—
130#2336C2214yes—
131#2334C2214yes—
132#2330C2214yes—
133#2330C2218yes—
134#2330C2211yescharacteristic
135#2330C2212yes—
136#2330C2212yes—
137#2327C2211yescharacteristic
138#2327C2212yes—
139#2323C2212yes—
140#2323C2214yes—
141#2320C2212yes—
142#2314C2211yescharacteristic
143#2314C2212yes—
144C4×C4⋊Q8C2214yes—
145C4×C4⋊Q8C2212yes—
146C4×C4⋊Q8C2214yes—
147C4×C4⋊Q8C2211yescharacteristic
148C4×C4⋊Q8C2212yes—
149C4×#125C2214yes—
150C4×#125C2214yes—
151C4×#125C2211yescharacteristic
152C4×#125C2212yes—
153C4×#126C2214yes—
154C4×C22⋊Q8C2214yes—
155C4×C22⋊Q8C2212yes—
156#2296C2212yes—
157#2295C2214yes—
158#2295C2214yes—
159#2295C2211yescharacteristic
160#2295C2212yes—
161#2295C2214yes—
162#2295C2212yes—
163#2295C2211yescharacteristic
164#2276C2214yes—
165C42×Q8C2212yes—
166C42×Q8C2211yescharacteristic
167C42×Q8C2211yescharacteristic
168C4×#117C2212yes—
169C4×#117C2211yescharacteristic
170C2×C4×C4⋊C4C2211yescharacteristic
171#557—216no—
172#541Q8116yescomplemented
173#533—28no—
174C2×C4⋊Q8C2312yes—
175C2×C4⋊Q8C2314yes—
176C2×C4⋊Q8C2311yescharacteristic
177C2×C4⋊Q8C2311yescharacteristic
178C2×C4⋊Q8C2314yes—
179C2×C4⋊Q8C2314yes—
180C2×C4⋊Q8C2311yescharacteristic
181C2×#126C2314yes—
182C2×#125C2314yes—
183C2×#125C2318yes—
184C2×#125C2312yes—
185C2×#125C2314yes—
186C2×#125C2312yes—
187C2×#125C2311yescharacteristic
188C2×#125C2314yes—
189C2×C22⋊Q8C2311yescharacteristic
190C2×C22⋊Q8C2311yescharacteristic
191C2×C22⋊Q8C2312yes—
192C2×C22⋊Q8C2314yes—
193C2×C22⋊Q8C2312yes—
194C2×C4×Q8C2314yes—
195C2×C4×Q8C2312yes—
196C2×C4×Q8C2312yes—
197C2×C4×Q8C2311yescharacteristic
198C2×C4×Q8C2314yes—
199C2×C4×Q8C2314yes—
200C2×C4×Q8C2312yes—
201C2×C4×Q8C2314yes—
202C2×C4×Q8C2314yes—
203C2×C4×Q8C2312yes—
204C2×C4×Q8C2314yes—
205C2×C4×Q8C2312yes—
206C2×C4×Q8C2312yes—
207C2×C4×Q8C2311yescharacteristic
208C2×#117C2312yes—
209C2×#117C2311yescharacteristic
210C2×#117C2311yescharacteristic
211C22×C4⋊C4C2312yes—
212C22×C42C2311yescharacteristic
213C22×C42C2312yes—
214#400C2318yes—
215#400C2318yes—
216#400C2318yes—
217#400C2318yes—
218#400C2318yes—
219#400C2318yes—
220#400C2318yes—
221#400C2318yes—
222#400C2318yes—
223#400C2318yes—
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#398C2318yes—
239#398C2318yes—
240#398C2318yes—
241#398C2318yes—
242#398C2318yes—
243#398C2318yes—
244#398C2318yes—
245#398C2318yes—
246#396C2318yes—
247#396C2318yes—
248#396C2318yes—
249#395C2318yes—
250#391C2312yes—
251#391C2314yes—
252#391C2312yes—
253#391C2314yes—
254#391C2314yes—
255#391C2314yes—
256#391C2314yes—
257#391C2312yes—
258#391C2314yes—
259#391C2318yes—
260#391C2314yes—
261#391C2314yes—
262#391C2312yes—
263#391C2314yes—
264#391C2314yes—
265#391C2314yes—
266#389C2312yes—
267#389C2314yes—
268#389C2314yes—
269#389C2314yes—
270#389C2314yes—
271#389C2314yes—
272#389C2314yes—
273#389C2318yes—
274#389C2318yes—
275#389C2318yes—
276#389C2314yes—
277#389C2314yes—
278#389C2318yes—
279#389C2318yes—
280#389C2318yes—
281#389C2318yes—
282#389C2312yes—
283#389C2314yes—
284#389C2318yes—
285#389C2314yes—
286#389C2318yes—
287#389C2314yes—
288#389C2318yes—
289#389C2314yes—
290#389C2318yes—
291#389C2318yes—
292#389C2318yes—
293#389C2318yes—
294#389C2318yes—
295#389C2318yes—
296#389C2318yes—
297#389C2314yes—
298#389C2314yes—
299#389C2318yes—
300#389C2318yes—
301#389C2318yes—
302#389C2318yes—
303#389C2318yes—
304#389C2318yes—
305#389C2314yes—
306#389C2318yes—
307#389C2314yes—
308#389C2314yes—
309#389C2312yes—
310#389C2314yes—
311#389C2314yes—
312#389C2314yes—
313#389C2312yes—
314#389C2314yes—
315#389C2314yes—
316#388C2314yes—
317#388C2314yes—
318#388C2314yes—
319#388C2318yes—
320#388C2318yes—
321#388C2318yes—
322#387C2314yes—
323#387C2314yes—
324#387C2314yes—
325#387C2314yes—
326#387C2318yes—
327#387C2314yes—
328#387C2314yes—
329#387C2314yes—
330#387C2318yes—
331#387C2314yes—
332#387C2318yes—
333#387C2318yes—
334#387C2318yes—
335#387C2318yes—
336#387C2314yes—
337#387C2318yes—
338#387C2318yes—
339#387C2318yes—
340#387C2318yes—
341#387C2318yes—
342#387C2318yes—
343#387C2318yes—
344#387C2318yes—
345#387C2314yes—
346#387C2314yes—
347#387C2318yes—
348#387C2318yes—
349#387C2318yes—
350#387C2318yes—
351#387C2318yes—
352#387C2318yes—
353#387C2318yes—
354#387C2314yes—
355#387C2318yes—
356#387C2318yes—
357#387C2318yes—
358#387C2314yes—
359#387C2318yes—
360#387C2318yes—
361#387C2314yes—
362#387C2314yes—
363#387C2318yes—
364#385C2318yes—
365#385C2318yes—
366#385C2314yes—
367#385C2314yes—
368#385C2314yes—
369#385C2318yes—
370#384C2311yescharacteristic
371#384C2312yes—
372#384C2312yes—
373#384C2314yes—
374#384C2314yes—
375#384C2312yes—
376#384C2318yes—
377#384C2314yes—
378#384C2318yes—
379#384C2314yes—
380#383C2314yes—
381#382C2314yes—
382#382C2311yescharacteristic
383#382C2312yes—
384#382C2314yes—
385#382C2318yes—
386#380C2312yes—
387#380C2314yes—
388#380C2314yes—
389C4×C4⋊C4C2314yes—
390C4×C4⋊C4C2314yes—
391C4×C4⋊C4C2314yes—
392C4×C4⋊C4C2312yes—
393C4×C4⋊C4C2314yes—
394C4×C4⋊C4C2312yes—
395C4×C4⋊C4C2314yes—
396C4×C4⋊C4C2318yes—
397C4×C4⋊C4C2314yes—
398C4×C4⋊C4C2318yes—
399C4×C4⋊C4C2318yes—
400C4×C4⋊C4C2312yes—
401C4×C4⋊C4C2318yes—
402C4×C4⋊C4C2318yes—
403C4×C4⋊C4C2318yes—
404C4×C4⋊C4C2318yes—
405C4×C4⋊C4C2314yes—
406C4×C4⋊C4C2312yes—
407C4×C4⋊C4C2311yescharacteristic
408C4×C4⋊C4C2312yes—
409C4×C4⋊C4C2314yes—
410C4×C4⋊C4C2314yes—
411C4×C4⋊C4C2318yes—
412C4×C4⋊C4C2318yes—
413C4×C4⋊C4C2318yes—
414C4×C4⋊C4C2314yes—
415C4×C4⋊C4C2314yes—
416C4×C4⋊C4C2312yes—
417C4×C4⋊C4C2314yes—
418C4×C4⋊C4C2314yes—
419C4×C4⋊C4C2318yes—
420C4×C4⋊C4C2312yes—
421C4×C4⋊C4C2311yescharacteristic
422C4×C4⋊C4C2312yes—
423C4×C4⋊C4C2314yes—
424C4×C4⋊C4C2312yes—
425C4×C4⋊C4C2312yes—
426C4×C4⋊C4C2312yes—
427C4×C4⋊C4C2314yes—
428C4×C4⋊C4C2312yes—
429C4×C4⋊C4C2312yes—
430C4×C4⋊C4C2312yes—
431C4×C22⋊C4C2312yes—
432C4×C22⋊C4C2314yes—
433C4×C22⋊C4C2314yes—
434C4×C22⋊C4C2314yes—
435C4×C22⋊C4C2318yes—
436C4×C22⋊C4C2312yes—
437#376C2311yescharacteristic
438#376C2311yescharacteristic
439#376C2312yes—
440#376C2312yes—
441#376C2318yes—
442#376C2318yes—
443C2×#95C2312yes—
444C43C2314yes—
445C43C2312yes—
446C43C2312yes—
447C43C2311yescharacteristic
448C43C2311yescharacteristic
449C22×Q8C2411yescharacteristic
450C22×Q8C2414yes—
451C22×Q8C2412yes—
452C22×Q8C2411yescharacteristic
453C22×Q8C2412yes—
454C23×C4C2411yescharacteristic
455C23×C4C2411yescharacteristic
456C23×C4C2411yescharacteristic
457C23×C4C2414yes—
458C4⋊Q8—24no—
459C4⋊Q8—216no—
460C4⋊Q8—24no—
461C4⋊Q8—28no—
462C4⋊Q8—48no—
463C4⋊Q8—48no—
464C4⋊Q8C2×Q818yes—
465#126C2×Q8132yes—
466#125—28no—
467#125—232no—
468#125—216no—
469#125—48no—
470#125—44no—
471#125C2×Q818yes—
472#125C2×Q8132yes—
473C22⋊Q8—24no—
474C22⋊Q8—24no—
475C22⋊Q8—28no—
476C22⋊Q8—48no—
477C22⋊Q8C2×Q8116yes—
478C4×Q8—216no—
479C4×Q8—28no—
480C4×Q8—24no—
481C4×Q8—216no—
482C4×Q8—28no—
483C4×Q8—48no—
484C4×Q8—44no—
485C4×Q8—44no—
486C4×Q8—48no—
487C4×Q8—48no—
488C4×Q8—48no—
489C4×Q8—44no—
490C4×Q8C2×Q8116yes—
491C4×Q8#4118yes—
492#117—28no—
493#117—42no—
494#117C2×Q818yes—
495C2×C4⋊C4—44no—
496C2×C4⋊C4C2412yes—
497C2×C4⋊C4C2412yes—
498C2×C4⋊C4C2412yes—
499C2×C4⋊C4C2412yes—
500C2×C4⋊C4C2414yes—
501C2×C4⋊C4C2412yes—
502C2×C4⋊C4C2412yes—
503C2×C4⋊C4C2412yes—
504C2×C4⋊C4C2411yescharacteristic
505C2×C4⋊C4C2412yes—
506C2×C4⋊C4C2412yes—
507C2×C4⋊C4C2412yes—
508C2×C4⋊C4C2414yes—
509C2×C4⋊C4C2414yes—
510C2×C4⋊C4C2418yes—
511C2×C4⋊C4C2414yes—
512C2×C4⋊C4C2418yes—
513C2×C4⋊C4C2414yes—
514C2×C4⋊C4C2418yes—
515C2×C4⋊C4C2414yes—
516C2×C4⋊C4C2412yes—
517C2×C4⋊C4C2418yes—
518C2×C4⋊C4C2414yes—
519C2×C4⋊C4C2414yes—
520C2×C4⋊C4C2414yes—
521C2×C4⋊C4C2418yes—
522C2×C4⋊C4C2418yes—
523C2×C4⋊C4C2418yes—
524C2×C4⋊C4C2418yes—
525C2×C4⋊C4C2418yes—
526C2×C4⋊C4C2418yes—
527C2×C4⋊C4C2418yes—
528C2×C4⋊C4C2418yes—
529C2×C4⋊C4C2418yes—
530C2×C4⋊C4C2418yes—
531C2×C4⋊C4C2418yes—
532C2×C4⋊C4C2418yes—
533C2×C4⋊C4C2414yes—
534C2×C4⋊C4C2414yes—
535C2×C4⋊C4C2414yes—
536C2×C4⋊C4C2414yes—
537C2×C4⋊C4C2418yes—
538C2×C4⋊C4C2418yes—
539C2×C4⋊C4C2414yes—
540C2×C4⋊C4C2414yes—
541C2×C4⋊C4C2418yes—
542C2×C4⋊C4C2412yes—
543C2×C4⋊C4C2412yes—
544C2×C4⋊C4C2414yes—
545C2×C4⋊C4C2414yes—
546C2×C4⋊C4C2414yes—
547C2×C4⋊C4C2414yes—
548C2×C4⋊C4C2411yescharacteristic
549C2×C4⋊C4C2412yes—
550C2×C22⋊C4C2412yes—
551C2×C22⋊C4C2412yes—
552C2×C22⋊C4C2412yes—
553C2×C22⋊C4C2418yes—
554C2×C22⋊C4C2414yes—
555C2×C22⋊C4C2412yes—
556C2×C22⋊C4C2414yes—
557C2×C42—24no—
558C2×C42—44no—
559C2×C42C2411yescharacteristic
560C2×C42C2412yes—
561C2×C42C2411yescharacteristic
562C2×C42C2412yes—
563C2×C42C2418yes—
564C2×C42C2414yes—
565C2×C42C2414yes—
566C2×C42C2412yes—
567C2×C42C2411yescharacteristic
568C2×C42C2412yes—
569C2×C42C2412yes—
570C2×C42C2411yescharacteristic
571C2×C42C2411yescharacteristic
572C2×C42C2414yes—
573C2×C42C2414yes—
574C2×C42C2414yes—
575C2×C42C2418yes—
576C2×C42C2418yes—
577C2×C42C2418yes—
578C2×C42C2418yes—
579C2×C42C2414yes—
580C2×C42C2412yes—
581C2×C42C2414yes—
582C2×C42C2412yes—
583C2×C42C2414yes—
584C2×C42C2414yes—
585C2×C42C2414yes—
586C2×C42C2411yescharacteristic
587C2×C42C2411yescharacteristic
588C2×C42C2414yes—
589C2×C42C2412yes—
590C2×C42C2411yescharacteristic
591#95C2412yes—
592#95C2414yes—
593#95C2412yes—
594#95C2414yes—
595#95C2414yes—
596#95C2412yes—
597#95C2412yes—
598#95C2412yes—
599#95C2414yes—
600#95C2418yes—
601#95C2414yes—
602#95C2412yes—
603#95C2418yes—
604#95C2418yes—
605#95C2418yes—
606#95C2418yes—
607#95C2418yes—
608#95C2418yes—
609#95C2418yes—
610#95C2414yes—
611#95C2414yes—
612#95C2414yes—
613#95C2414yes—
614#95C2414yes—
615#95C2414yes—
616#95C2414yes—
617#95C2414yes—
618#95C2418yes—
619#95C2414yes—
620#95C2418yes—
621#95C2418yes—
622#95C2418yes—
623#95C2414yes—
624#95C2418yes—
625#95C2414yes—
626#95C2418yes—
627#95C2414yes—
628#95C2414yes—
629#95C2414yes—
630#95C2418yes—
631#95C2414yes—
632#95C2418yes—
633#95C2418yes—
634#95C2418yes—
635#95C2418yes—
636C24C2511yescharacteristic
637C2×Q8—24no—
638C2×Q8—22no—
639C2×Q8—28no—
640C2×Q8—24no—
641C2×Q8—24no—
642C2×Q8—24no—
643C2×Q8—28no—
644C2×Q8—24no—
645C2×Q8—28no—
646C2×Q8—44no—
647C2×Q8C22×Q818yes—
648C2×Q8C2×#4114yes—
649C22×C4—22no—
650C22×C4—22no—
651C22×C4—22no—
652C22×C4—24no—
653C22×C4—22no—
654C22×C4—44no—
655C22×C4—44no—
656C22×C4—42no—
657C22×C4—44no—
658C22×C4C22×Q814yes—
659C22×C4C2511yescharacteristic
660C22×C4C2512yes—
661C22×C4C2514yes—
662C22×C4C2514yes—
663C22×C4C2514yes—
664C22×C4C2512yes—
665C22×C4C2512yes—
666C22×C4C2514yes—
667C22×C4C2518yes—
668C22×C4C2512yes—
669C22×C4C2518yes—
670C22×C4C2511yescharacteristic
671C22×C4C2512yes—
672C22×C4C2514yes—
673C22×C4C2512yes—
674C22×C4C2514yes—
675C22×C4C2511yescharacteristic
676C22×C4C2512yes—
677C22×C4C2511yescharacteristic
678C22×C4C2512yes—
679C22×C4C2511yescharacteristic
680C22×C4C2511yescharacteristic
681C4⋊C4—24no—
682C4⋊C4—24no—
683C4⋊C4—24no—
684C4⋊C4—24no—
685C4⋊C4—24no—
686C4⋊C4—24no—
687C4⋊C4—22no—
688C4⋊C4—28no—
689C4⋊C4—24no—
690C4⋊C4—216no—
691C4⋊C4—216no—
692C4⋊C4—28no—
693C4⋊C4—216no—
694C4⋊C4—28no—
695C4⋊C4—24no—
696C4⋊C4—24no—
697C4⋊C4—28no—
698C4⋊C4—24no—
699C4⋊C4—28no—
700C4⋊C4—44no—
701C4⋊C4—44no—
702C4⋊C4—44no—
703C4⋊C4—48no—
704C4⋊C4—44no—
705C4⋊C4—44no—
706C4⋊C4—44no—
707C4⋊C4—48no—
708C4⋊C4—48no—
709C4⋊C4—44no—
710C4⋊C4—48no—
711C4⋊C4—42no—
712C4⋊C4—48no—
713C4⋊C4—44no—
714C4⋊C4—48no—
715C4⋊C4—44no—
716C4⋊C4—48no—
717C4⋊C4—48no—
718C4⋊C4—44no—
719C4⋊C4—48no—
720C4⋊C4—48no—
721C4⋊C4—48no—
722C4⋊C4—48no—
723C4⋊C4—48no—
724C4⋊C4—48no—
725C4⋊C4—48no—
726C4⋊C4—48no—
727C4⋊C4C22×Q818yes—
728C4⋊C4C22×Q818yes—
729C4⋊C4C22×Q8116yes—
730C4⋊C4C22×Q8116yes—
731C4⋊C4C22×Q8116yes—
732C4⋊C4C22×Q8116yes—
733C4⋊C4C2×#4114yes—
734C4⋊C4C2×#4118yes—
735C22⋊C4—24no—
736C22⋊C4—24no—
737C22⋊C4—44no—
738C22⋊C4—42no—
739C22⋊C4—48no—
740C22⋊C4C22×Q818yes—
741C22⋊C4C22×Q8116yes—
742C42—22no—
743C42—22no—
744C42—22no—
745C42—24no—
746C42—216no—
747C42—28no—
748C42—24no—
749C42—24no—
750C42—22no—
751C42—22no—
752C42—24no—
753C42—28no—
754C42—24no—
755C42—44no—
756C42—42no—
757C42—44no—
758C42—44no—
759C42—42no—
760C42—44no—
761C42—44no—
762C42—48no—
763C42—44no—
764C42—48no—
765C42—48no—
766C42—44no—
767C42—48no—
768C42—44no—
769C42C22×Q814yes—
770C42C22×Q814yes—
771C42C22×Q8116yes—
772C42C2×#4114yes—
773C42C2×#4118yes—
774C23—21no—
775C23—22no—
776C23—21no—
777C23—22no—
778C23C23×Q812yes—
779C23C2611yescharacteristic
780Q8—216no—
781Q8—28no—
782Q8—44no—
783Q8—416no—
784Q8—84no—
785C2×C4—24no—
786C2×C4—21no—
787C2×C4—22no—
788C2×C4—24no—
789C2×C4—22no—
790C2×C4—21no—
791C2×C4—24no—
792C2×C4—24no—
793C2×C4—22no—
794C2×C4—22no—
795C2×C4—22no—
796C2×C4—24no—
797C2×C4—24no—
798C2×C4—28no—
799C2×C4—21no—
800C2×C4—21no—
801C2×C4—22no—
802C2×C4—22no—
803C2×C4—24no—
804C2×C4—28no—
805C2×C4—24no—
806C2×C4—22no—
807C2×C4—24no—
808C2×C4—22no—
809C2×C4—22no—
810C2×C4—24no—
811C2×C4—22no—
812C2×C4—28no—
813C2×C4—24no—
814C2×C4—24no—
815C2×C4—28no—
816C2×C4—24no—
817C2×C4—28no—
818C2×C4—24no—
819C2×C4—28no—
820C2×C4—22no—
821C2×C4—22no—
822C2×C4—24no—
823C2×C4—24no—
824C2×C4—24no—
825C2×C4—24no—
826C2×C4—22no—
827C2×C4—24no—
828C2×C4—28no—
829C2×C4—24no—
830C2×C4—22no—
831C2×C4—44no—
832C2×C4—82no—
833C2×C4—88no—
834C2×C4C23×Q814yes—
835C2×C4C23×Q814yes—
836C2×C4C23×Q818yes—
837C2×C4C23×Q818yes—
838C2×C4C23×Q812yes—
839C2×C4C23×Q812yes—
840C2×C4C22×#4114yes—
841C2×C4C22×#4112yes—
842C2×C4C22×#4114yes—
843C2×C4C22×#4112yes—
844C2×C4C22×#4112yes—
845C2×C4#58512yes—
846C2×C4#58514yes—
847C22—24no—
848C22—22no—
849C22—41no—
850C22—41no—
851C22—42no—
852C22C24×Q811yescharacteristic
853C22C23×#4111yescharacteristic
854C22C2×#58512yes—
855C22C2×#58511yescharacteristic
856C222−1+612yes—
857C4—24no—
858C4—28no—
859C4—24no—
860C4—24no—
861C4—22no—
862C4—24no—
863C4—22no—
864C4—28no—
865C4—41no—
866C4—42no—
867C4—48no—
868C4—44no—
869C4—41no—
870C4—42no—
871C4—42no—
872C4—42no—
873C4—44no—
874C4—48no—
875C4—44no—
876C4—44no—
877C4Q8×#4114yes—
878C4#351214yes—
879C2—42no—
880C2C2×Q8×#4111yescharacteristic
881C2C2×#351211yescharacteristic
882C2#6286111yescharacteristic
883C2#6296712yes—
884C2#6300412yes—
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. #59934C2semidirect
4. #59681C2semidirect
5. #44737C2semidirect
8. #39641C2semidirect
9. #39638C2semidirect
10. #39635C2semidirect
11. #39635C2semidirect
13. #36560C2semidirect
15. Q8×#125C2semidirect
16. #35642C2semidirect
19. #34951C2semidirect
20. #34337C2semidirect
172. #541Q8semidirect

Maximal subgroups

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

subgroupindex
#599342
#596942
#596812
#447372
#447212
#396932
#396412
#396382
#396352
#395992
#365602
#365522
Q8×#1252
#356422
#353362
#352842
#349512
#343372
#342812
#341452
C4×#5412