Finite Group Databasebeta

← #7681156

Subgroups — #7681156

Order 512.

4488 conjugacy classes of subgroups.

The subgroup lattice has 896 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#59934C214yesmaximal, complemented
2#59712C214yesmaximal
3#59668C214yesmaximal, complemented
4#59499C214yesmaximal
5#44419C218yesmaximal, complemented
6#44317C218yesmaximal
7#39691C214yesmaximal
8#39642C211yesmaximal, characteristic, complemented
9#39641C212yesmaximal, complemented
10#39635C211yesmaximal, characteristic, complemented
11#39629C212yesmaximal, complemented
12#39597C212yesmaximal
13#36565C211yesmaximal, characteristic, complemented
14#36564C212yesmaximal
15Q8×C4⋊Q8C211yesmaximal, characteristic, complemented
16#35583C214yesmaximal, complemented
17#35284C211yesmaximal, characteristic
18#35283C212yesmaximal
19#34950C212yesmaximal, complemented
20#34335C212yesmaximal, complemented
21#34281C212yesmaximal
22#34145C211yesmaximal, characteristic
23C4×#541C211yesmaximal, characteristic
24C2×Q82C2212yes—
25C2×#541C2211yescharacteristic
26C2×#533C2211yescharacteristic
27#2868C2212yes—
28#2868C2211yescharacteristic
29#2862C2212yes—
30#2859C2211yescharacteristic
31#2857C2214yes—
32#2857C2212yes—
33#2806C2218yes—
34#2806C2218yes—
35#2805C2218yes—
36#2802C2218yes—
37#2791C2218yes—
38#2791C2218yes—
39#2788C2218yes—
40#2774C2218yes—
41#2768C2218yes—
42#2713C2218yes—
43#2713C2218yes—
44#2677C2218yes—
45#2647C2212yes—
46#2647C2212yes—
47#2647C2212yes—
48#2629C2212yes—
49#2628C2214yes—
50#2612C2218yes—
51#2606C2218yes—
52#2605C2218yes—
53#2590C2218yes—
54#2588C2218yes—
55#2586C2218yes—
56#2586C2218yes—
57#2586C2218yes—
58#2585C2218yes—
59#2584C2218yes—
60#2582C2212yes—
61#2581C2214yes—
62#2567C2214yes—
63#2567C2212yes—
64#2567C2212yes—
65#2556C2218yes—
66#2552C2214yes—
67#2551C2214yes—
68#2551C2214yes—
69#2551C2218yes—
70#2551C2212yes—
71#2550C2214yes—
72#2550C2218yes—
73#2549C2218yes—
74#2546C2218yes—
75#2546C2214yes—
76#2520C2218yes—
77#2520C2218yes—
78#2511C2214yes—
79#2511C2214yes—
80#2511C2218yes—
81#2507C2214yes—
82#2507C2214yes—
83#2507C2214yes—
84#2507C2214yes—
85#2507C2214yes—
86#2507C2214yes—
87#2506C2214yes—
88#2497C2214yes—
89#2492C2218yes—
90#2492C2214yes—
91#2465C2218yes—
92#2462C2218yes—
93#2453C2214yes—
94#2451C2214yes—
95#2451C2218yes—
96#2451C2218yes—
97#2451C2214yes—
98#2451C2214yes—
99#2451C2214yes—
100#2446C2214yes—
101#2446C2218yes—
102#2446C2214yes—
103#2440C2214yes—
104#2429C2214yes—
105#2423C2218yes—
106#2423C2214yes—
107#2399C2218yes—
108#2373C2218yes—
109#2373C2218yes—
110#2371C2218yes—
111#2370C2218yes—
112#2370C2214yes—
113#2369C2212yes—
114#2369C2214yes—
115#2369C2214yes—
116#2369C2214yes—
117#2369C2212yes—
118#2368C2214yes—
119#2365C2214yes—
120#2365C2218yes—
121#2365C2212yes—
122#2360C2212yes—
123#2360C2212yes—
124#2355C2214yes—
125#2355C2212yes—
126#2351C2214yes—
127Q8×C4⋊C4C2214yes—
128Q8×C4⋊C4C2212yes—
129#2345C2214yes—
130#2336C2214yes—
131#2334C2214yes—
132#2331C2218yes—
133#2331C2214yes—
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⋊Q8C2214yes—
146C4×C4⋊Q8C2212yes—
147C4×C4⋊Q8C2211yescharacteristic
148C4×C4⋊Q8C2214yes—
149C4×C4⋊Q8C2212yes—
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#2295C2211yescharacteristic
162#2295C2212yes—
163#2295C2214yes—
164#2276C2214yes—
165C42×Q8C2212yes—
166C42×Q8C2211yescharacteristic
167C42×Q8C2211yescharacteristic
168C4×#117C2211yescharacteristic
169C4×#117C2212yes—
170C2×C4×C4⋊C4C2211yescharacteristic
171Q82—216no—
172#541Q8116yescomplemented
173#533—28no—
174C2×C4⋊Q8C2312yes—
175C2×C4⋊Q8C2314yes—
176C2×C4⋊Q8C2314yes—
177C2×C4⋊Q8C2314yes—
178C2×C4⋊Q8C2318yes—
179C2×C4⋊Q8C2311yescharacteristic
180C2×C4⋊Q8C2311yescharacteristic
181C2×C4⋊Q8C2314yes—
182C2×C4⋊Q8C2314yes—
183C2×C4⋊Q8C2318yes—
184C2×C4⋊Q8C2318yes—
185C2×C4⋊Q8C2311yescharacteristic
186C2×#126C2314yes—
187C2×#125C2312yes—
188C2×#125C2312yes—
189C2×#125C2318yes—
190C2×#125C2311yescharacteristic
191C2×#125C2314yes—
192C2×C22⋊Q8C2311yescharacteristic
193C2×C22⋊Q8C2311yescharacteristic
194C2×C22⋊Q8C2312yes—
195C2×C22⋊Q8C2314yes—
196C2×C22⋊Q8C2318yes—
197C2×C22⋊Q8C2312yes—
198C2×C4×Q8C2314yes—
199C2×C4×Q8C2312yes—
200C2×C4×Q8C2311yescharacteristic
201C2×C4×Q8C2312yes—
202C2×C4×Q8C2314yes—
203C2×C4×Q8C2312yes—
204C2×C4×Q8C2312yes—
205C2×C4×Q8C2312yes—
206C2×C4×Q8C2314yes—
207C2×C4×Q8C2318yes—
208C2×C4×Q8C2318yes—
209C2×C4×Q8C2314yes—
210C2×C4×Q8C2312yes—
211C2×C4×Q8C2311yescharacteristic
212C2×#117C2312yes—
213C2×#117C2311yescharacteristic
214C2×#117C2311yescharacteristic
215C22×C4⋊C4C2312yes—
216C22×C42C2311yescharacteristic
217C22×C42C2312yes—
218#400C2318yes—
219#400C2318yes—
220#400C2318yes—
221#400C2318yes—
222#400C2318yes—
223#400C2318yes—
224#400C2318yes—
225#399C2318yes—
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#396C2318yes—
243#395C2318yes—
244#395C2318yes—
245#395C2318yes—
246#395C2318yes—
247#395C2318yes—
248#395C2318yes—
249#395C2318yes—
250#395C2318yes—
251#395C2318yes—
252#395C2318yes—
253#393C2318yes—
254#391C2312yes—
255#391C2314yes—
256#391C2314yes—
257#391C2318yes—
258#391C2318yes—
259#391C2318yes—
260#391C2314yes—
261#391C2312yes—
262#391C2314yes—
263#391C2314yes—
264#391C2314yes—
265#391C2318yes—
266#391C2318yes—
267#391C2318yes—
268#391C2318yes—
269#391C2318yes—
270#391C2318yes—
271#391C2318yes—
272#391C2318yes—
273#391C2312yes—
274#391C2314yes—
275#391C2318yes—
276#391C2312yes—
277#391C2314yes—
278#391C2314yes—
279#389C2312yes—
280#389C2314yes—
281#389C2314yes—
282#389C2314yes—
283#389C2312yes—
284#389C2314yes—
285#389C2314yes—
286#389C2314yes—
287#389C2314yes—
288#389C2314yes—
289#389C2318yes—
290#389C2318yes—
291#389C2314yes—
292#389C2314yes—
293#389C2318yes—
294#389C2318yes—
295#389C2314yes—
296#389C2318yes—
297#389C2318yes—
298#389C2314yes—
299#389C2312yes—
300#389C2318yes—
301#389C2314yes—
302#389C2314yes—
303#389C2318yes—
304#389C2318yes—
305#389C2318yes—
306#389C2318yes—
307#389C2318yes—
308#389C2318yes—
309#389C2318yes—
310#389C2314yes—
311#389C2318yes—
312#389C2314yes—
313#389C2314yes—
314#389C2314yes—
315#389C2314yes—
316#389C2314yes—
317#389C2314yes—
318#389C2314yes—
319#389C2312yes—
320#389C2314yes—
321#389C2314yes—
322#388C2314yes—
323#388C2314yes—
324#388C2314yes—
325#388C2318yes—
326#388C2318yes—
327#388C2318yes—
328#387C2314yes—
329#387C2314yes—
330#387C2314yes—
331#387C2314yes—
332#387C2314yes—
333#387C2314yes—
334#387C2314yes—
335#387C2314yes—
336#387C2318yes—
337#387C2318yes—
338#387C2318yes—
339#387C2318yes—
340#387C2318yes—
341#387C2318yes—
342#387C2318yes—
343#387C2314yes—
344#387C2318yes—
345#387C2318yes—
346#387C2318yes—
347#387C2318yes—
348#387C2318yes—
349#387C2318yes—
350#387C2314yes—
351#387C2318yes—
352#387C2318yes—
353#387C2318yes—
354#387C2318yes—
355#387C2318yes—
356#387C2318yes—
357#387C2314yes—
358#387C2318yes—
359#387C2318yes—
360#387C2314yes—
361#387C2318yes—
362#387C2314yes—
363#387C2318yes—
364#387C2314yes—
365#387C2314yes—
366#385C2314yes—
367#385C2314yes—
368#385C2314yes—
369#385C2318yes—
370#384C2314yes—
371#384C2314yes—
372#384C2311yescharacteristic
373#384C2312yes—
374#384C2312yes—
375#384C2314yes—
376#384C2312yes—
377#384C2318yes—
378#384C2314yes—
379#383C2314yes—
380#382C2312yes—
381#382C2311yescharacteristic
382#382C2314yes—
383#382C2314yes—
384#382C2318yes—
385#380C2312yes—
386#380C2314yes—
387#380C2314yes—
388#380C2318yes—
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⋊C4C2312yes—
398C4×C4⋊C4C2314yes—
399C4×C4⋊C4C2314yes—
400C4×C4⋊C4C2312yes—
401C4×C4⋊C4C2318yes—
402C4×C4⋊C4C2318yes—
403C4×C4⋊C4C2314yes—
404C4×C4⋊C4C2318yes—
405C4×C4⋊C4C2318yes—
406C4×C4⋊C4C2314yes—
407C4×C4⋊C4C2311yescharacteristic
408C4×C4⋊C4C2312yes—
409C4×C4⋊C4C2312yes—
410C4×C4⋊C4C2318yes—
411C4×C4⋊C4C2318yes—
412C4×C4⋊C4C2314yes—
413C4×C4⋊C4C2312yes—
414C4×C4⋊C4C2314yes—
415C4×C4⋊C4C2314yes—
416C4×C4⋊C4C2314yes—
417C4×C4⋊C4C2314yes—
418C4×C4⋊C4C2318yes—
419C4×C4⋊C4C2318yes—
420C4×C4⋊C4C2312yes—
421C4×C4⋊C4C2314yes—
422C4×C4⋊C4C2311yescharacteristic
423C4×C4⋊C4C2312yes—
424C4×C4⋊C4C2312yes—
425C4×C4⋊C4C2312yes—
426C4×C4⋊C4C2314yes—
427C4×C4⋊C4C2314yes—
428C4×C4⋊C4C2312yes—
429C4×C4⋊C4C2312yes—
430C4×C4⋊C4C2312yes—
431C4×C22⋊C4C2314yes—
432C4×C22⋊C4C2312yes—
433C4×C22⋊C4C2312yes—
434C4×C22⋊C4C2318yes—
435C4×C22⋊C4C2314yes—
436C4×C22⋊C4C2314yes—
437#376C2311yescharacteristic
438#376C2311yescharacteristic
439#376C2312yes—
440#376C2312yes—
441#376C2318yes—
442#376C2318yes—
443C2×#95C2312yes—
444C43C2314yes—
445C43C2311yescharacteristic
446C43C2312yes—
447C43C2311yescharacteristic
448C43C2312yes—
449C22×Q8C2411yescharacteristic
450C22×Q8C2412yes—
451C22×Q8C2411yescharacteristic
452C22×Q8C2412yes—
453C22×Q8C2414yes—
454C22×Q8C2418yes—
455C22×Q8C2418yes—
456C23×C4C2411yescharacteristic
457C23×C4C2411yescharacteristic
458C23×C4C2414yes—
459C23×C4C2411yescharacteristic
460C4⋊Q8—24no—
461C4⋊Q8—24no—
462C4⋊Q8—232no—
463C4⋊Q8—216no—
464C4⋊Q8—216no—
465C4⋊Q8—28no—
466C4⋊Q8—216no—
467C4⋊Q8—48no—
468C4⋊Q8—88no—
469C4⋊Q8—88no—
470C4⋊Q8—84no—
471C4⋊Q8C2×Q818yes—
472#126C2×Q8132yes—
473#125—28no—
474#125—44no—
475#125—88no—
476#125C2×Q818yes—
477#125C2×Q8132yes—
478C22⋊Q8—24no—
479C22⋊Q8—24no—
480C22⋊Q8—28no—
481C22⋊Q8—88no—
482C22⋊Q8—84no—
483C22⋊Q8C2×Q8116yes—
484C4×Q8—216no—
485C4×Q8—28no—
486C4×Q8—28no—
487C4×Q8—28no—
488C4×Q8—24no—
489C4×Q8—28no—
490C4×Q8—216no—
491C4×Q8—48no—
492C4×Q8—44no—
493C4×Q8—84no—
494C4×Q8—88no—
495C4×Q8—88no—
496C4×Q8C2×Q8116yes—
497C4×Q8#4118yes—
498#117—28no—
499#117—42no—
500#117C2×Q818yes—
501C2×C4⋊C4—28no—
502C2×C4⋊C4C2412yes—
503C2×C4⋊C4C2414yes—
504C2×C4⋊C4C2412yes—
505C2×C4⋊C4C2412yes—
506C2×C4⋊C4C2412yes—
507C2×C4⋊C4C2412yes—
508C2×C4⋊C4C2412yes—
509C2×C4⋊C4C2411yescharacteristic
510C2×C4⋊C4C2412yes—
511C2×C4⋊C4C2414yes—
512C2×C4⋊C4C2412yes—
513C2×C4⋊C4C2414yes—
514C2×C4⋊C4C2412yes—
515C2×C4⋊C4C2414yes—
516C2×C4⋊C4C2414yes—
517C2×C4⋊C4C2418yes—
518C2×C4⋊C4C2418yes—
519C2×C4⋊C4C2414yes—
520C2×C4⋊C4C2414yes—
521C2×C4⋊C4C2414yes—
522C2×C4⋊C4C2418yes—
523C2×C4⋊C4C2412yes—
524C2×C4⋊C4C2414yes—
525C2×C4⋊C4C2418yes—
526C2×C4⋊C4C2418yes—
527C2×C4⋊C4C2414yes—
528C2×C4⋊C4C2418yes—
529C2×C4⋊C4C2418yes—
530C2×C4⋊C4C2418yes—
531C2×C4⋊C4C2414yes—
532C2×C4⋊C4C2418yes—
533C2×C4⋊C4C2418yes—
534C2×C4⋊C4C2418yes—
535C2×C4⋊C4C2418yes—
536C2×C4⋊C4C2414yes—
537C2×C4⋊C4C2414yes—
538C2×C4⋊C4C2418yes—
539C2×C4⋊C4C2418yes—
540C2×C4⋊C4C2418yes—
541C2×C4⋊C4C2414yes—
542C2×C4⋊C4C2418yes—
543C2×C4⋊C4C2414yes—
544C2×C4⋊C4C2418yes—
545C2×C4⋊C4C2412yes—
546C2×C4⋊C4C2412yes—
547C2×C4⋊C4C2414yes—
548C2×C4⋊C4C2414yes—
549C2×C4⋊C4C2414yes—
550C2×C4⋊C4C2414yes—
551C2×C4⋊C4C2412yes—
552C2×C4⋊C4C2411yescharacteristic
553C2×C4⋊C4C2412yes—
554C2×C22⋊C4C2412yes—
555C2×C22⋊C4C2412yes—
556C2×C22⋊C4C2412yes—
557C2×C22⋊C4C2414yes—
558C2×C22⋊C4C2418yes—
559C2×C22⋊C4C2412yes—
560C2×C22⋊C4C2414yes—
561C2×C42—24no—
562C2×C42—44no—
563C2×C42C2411yescharacteristic
564C2×C42C2412yes—
565C2×C42C2411yescharacteristic
566C2×C42C2414yes—
567C2×C42C2418yes—
568C2×C42C2412yes—
569C2×C42C2411yescharacteristic
570C2×C42C2412yes—
571C2×C42C2414yes—
572C2×C42C2412yes—
573C2×C42C2414yes—
574C2×C42C2411yescharacteristic
575C2×C42C2412yes—
576C2×C42C2411yescharacteristic
577C2×C42C2414yes—
578C2×C42C2412yes—
579C2×C42C2414yes—
580C2×C42C2414yes—
581C2×C42C2414yes—
582C2×C42C2418yes—
583C2×C42C2418yes—
584C2×C42C2418yes—
585C2×C42C2414yes—
586C2×C42C2418yes—
587C2×C42C2414yes—
588C2×C42C2412yes—
589C2×C42C2414yes—
590C2×C42C2411yescharacteristic
591C2×C42C2411yescharacteristic
592C2×C42C2414yes—
593C2×C42C2412yes—
594C2×C42C2411yescharacteristic
595#95C2412yes—
596#95C2412yes—
597#95C2414yes—
598#95C2414yes—
599#95C2414yes—
600#95C2412yes—
601#95C2412yes—
602#95C2412yes—
603#95C2414yes—
604#95C2418yes—
605#95C2414yes—
606#95C2412yes—
607#95C2418yes—
608#95C2418yes—
609#95C2418yes—
610#95C2418yes—
611#95C2418yes—
612#95C2418yes—
613#95C2418yes—
614#95C2414yes—
615#95C2414yes—
616#95C2414yes—
617#95C2414yes—
618#95C2414yes—
619#95C2414yes—
620#95C2414yes—
621#95C2414yes—
622#95C2418yes—
623#95C2414yes—
624#95C2418yes—
625#95C2418yes—
626#95C2418yes—
627#95C2414yes—
628#95C2414yes—
629#95C2418yes—
630#95C2414yes—
631#95C2418yes—
632#95C2418yes—
633#95C2414yes—
634#95C2414yes—
635#95C2414yes—
636#95C2418yes—
637#95C2418yes—
638#95C2418yes—
639#95C2418yes—
640C24C2511yescharacteristic
641C2×Q8—24no—
642C2×Q8—22no—
643C2×Q8—24no—
644C2×Q8—28no—
645C2×Q8—216no—
646C2×Q8—24no—
647C2×Q8—24no—
648C2×Q8—216no—
649C2×Q8—24no—
650C2×Q8—48no—
651C2×Q8—48no—
652C2×Q8—44no—
653C2×Q8—44no—
654C2×Q8—48no—
655C2×Q8—44no—
656C2×Q8—48no—
657C2×Q8C22×Q818yes—
658C2×Q8C2×#4114yes—
659C22×C4—22no—
660C22×C4—22no—
661C22×C4—22no—
662C22×C4—24no—
663C22×C4—22no—
664C22×C4—28no—
665C22×C4—44no—
666C22×C4—44no—
667C22×C4—42no—
668C22×C4C22×Q814yes—
669C22×C4C2512yes—
670C22×C4C2511yescharacteristic
671C22×C4C2514yes—
672C22×C4C2514yes—
673C22×C4C2518yes—
674C22×C4C2512yes—
675C22×C4C2512yes—
676C22×C4C2511yescharacteristic
677C22×C4C2518yes—
678C22×C4C2514yes—
679C22×C4C2512yes—
680C22×C4C2512yes—
681C22×C4C2512yes—
682C22×C4C2514yes—
683C22×C4C2514yes—
684C22×C4C2511yescharacteristic
685C22×C4C2512yes—
686C22×C4C2512yes—
687C22×C4C2511yescharacteristic
688C22×C4C2514yes—
689C22×C4C2511yescharacteristic
690C22×C4C2511yescharacteristic
691C4⋊C4—24no—
692C4⋊C4—24no—
693C4⋊C4—24no—
694C4⋊C4—24no—
695C4⋊C4—24no—
696C4⋊C4—24no—
697C4⋊C4—22no—
698C4⋊C4—28no—
699C4⋊C4—216no—
700C4⋊C4—216no—
701C4⋊C4—28no—
702C4⋊C4—24no—
703C4⋊C4—28no—
704C4⋊C4—28no—
705C4⋊C4—24no—
706C4⋊C4—28no—
707C4⋊C4—28no—
708C4⋊C4—216no—
709C4⋊C4—28no—
710C4⋊C4—28no—
711C4⋊C4—24no—
712C4⋊C4—42no—
713C4⋊C4—48no—
714C4⋊C4—44no—
715C4⋊C4—44no—
716C4⋊C4—48no—
717C4⋊C4—44no—
718C4⋊C4—48no—
719C4⋊C4—48no—
720C4⋊C4—48no—
721C4⋊C4—48no—
722C4⋊C4—48no—
723C4⋊C4—48no—
724C4⋊C4—48no—
725C4⋊C4—48no—
726C4⋊C4—44no—
727C4⋊C4—44no—
728C4⋊C4—48no—
729C4⋊C4—48no—
730C4⋊C4—48no—
731C4⋊C4—44no—
732C4⋊C4—48no—
733C4⋊C4—44no—
734C4⋊C4C22×Q818yes—
735C4⋊C4C22×Q818yes—
736C4⋊C4C22×Q8116yes—
737C4⋊C4C22×Q8116yes—
738C4⋊C4C22×Q8116yes—
739C4⋊C4C22×Q8116yes—
740C4⋊C4C2×#4118yes—
741C4⋊C4C2×#4114yes—
742C4⋊C42−1+418yes—
743C22⋊C4—24no—
744C22⋊C4—24no—
745C22⋊C4—42no—
746C22⋊C4—48no—
747C22⋊C4—44no—
748C22⋊C4C22×Q818yes—
749C22⋊C4C22×Q8116yes—
750C42—22no—
751C42—22no—
752C42—22no—
753C42—24no—
754C42—216no—
755C42—28no—
756C42—28no—
757C42—24no—
758C42—24no—
759C42—28no—
760C42—28no—
761C42—24no—
762C42—24no—
763C42—22no—
764C42—22no—
765C42—44no—
766C42—48no—
767C42—44no—
768C42—44no—
769C42—42no—
770C42—48no—
771C42—44no—
772C42—44no—
773C42—48no—
774C42—48no—
775C42—44no—
776C42—42no—
777C42C22×Q814yes—
778C42C22×Q814yes—
779C42C22×Q8116yes—
780C42C2×#4114yes—
781C42C2×#4118yes—
782C23—21no—
783C23—22no—
784C23—21no—
785C23—22no—
786C23C23×Q812yes—
787C23C2611yescharacteristic
788Q8—216no—
789Q8—28no—
790Q8—44no—
791Q8—88no—
792Q8—84no—
793Q8—816no—
794Q8—816no—
795C2×C4—24no—
796C2×C4—21no—
797C2×C4—22no—
798C2×C4—22no—
799C2×C4—24no—
800C2×C4—24no—
801C2×C4—24no—
802C2×C4—21no—
803C2×C4—24no—
804C2×C4—22no—
805C2×C4—24no—
806C2×C4—22no—
807C2×C4—24no—
808C2×C4—24no—
809C2×C4—22no—
810C2×C4—28no—
811C2×C4—21no—
812C2×C4—21no—
813C2×C4—22no—
814C2×C4—22no—
815C2×C4—28no—
816C2×C4—24no—
817C2×C4—22no—
818C2×C4—22no—
819C2×C4—24no—
820C2×C4—24no—
821C2×C4—22no—
822C2×C4—24no—
823C2×C4—28no—
824C2×C4—24no—
825C2×C4—22no—
826C2×C4—22no—
827C2×C4—28no—
828C2×C4—24no—
829C2×C4—22no—
830C2×C4—28no—
831C2×C4—24no—
832C2×C4—28no—
833C2×C4—24no—
834C2×C4—24no—
835C2×C4—22no—
836C2×C4—24no—
837C2×C4—24no—
838C2×C4—28no—
839C2×C4—22no—
840C2×C4—44no—
841C2×C4—82no—
842C2×C4—88no—
843C2×C4C23×Q814yes—
844C2×C4C23×Q814yes—
845C2×C4C23×Q818yes—
846C2×C4C23×Q818yes—
847C2×C4C23×Q812yes—
848C2×C4C23×Q812yes—
849C2×C4C22×#4114yes—
850C2×C4C22×#4112yes—
851C2×C4C22×#4114yes—
852C2×C4C22×#4112yes—
853C2×C4C22×#4112yes—
854C2×C4C2×2−1+418yes—
855C2×C4C2×2−1+414yes—
856C2×C4#58512yes—
857C22—24no—
858C22—22no—
859C22—41no—
860C22—41no—
861C22—42no—
862C22C24×Q811yescharacteristic
863C22C23×#4111yescharacteristic
864C22C22×2−1+412yes—
865C22C2×#58511yescharacteristic
866C22H(7,𝔽2)12yes—
867C4—24no—
868C4—24no—
869C4—28no—
870C4—24no—
871C4—22no—
872C4—24no—
873C4—28no—
874C4—22no—
875C4—28no—
876C4—41no—
877C4—42no—
878C4—41no—
879C4—42no—
880C4—48no—
881C4—44no—
882C4—42no—
883C4—42no—
884C4—44no—
885C4—48no—
886C4—44no—
887C4Q8×#4114yes—
888C4#350914yes—
889C2—42no—
890C2C2×Q8×#4111yescharacteristic
891C2C2×#350911yescharacteristic
892C2#6285811yescharacteristic
893C2#6295112yes—
894C2Q8×2−1+412yes—
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
3. #59668C2semidirect
5. #44419C2semidirect
8. #39642C2semidirect
9. #39641C2semidirect
10. #39635C2semidirect
11. #39629C2semidirect
13. #36565C2semidirect
15. Q8×C4⋊Q8C2semidirect
16. #35583C2semidirect
19. #34950C2semidirect
20. #34335C2semidirect
172. #541Q8semidirect

Maximal subgroups

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

subgroupindex
#599342
#597122
#596682
#594992
#444192
#443172
#396912
#396422
#396412
#396352
#396292
#395972
#365652
#365642
Q8×C4⋊Q82
#355832
#352842
#352832
#349502
#343352
#342812
#341452
C4×#5412