Finite Group Databasebeta

← #7672362

Subgroups — #7672362

Order 512.

4684 conjugacy classes of subgroups.

The subgroup lattice has 929 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#59876C214yesmaximal, complemented
2#59872C214yesmaximal, complemented
3#59849C218yesmaximal, complemented
4#39762C211yesmaximal, characteristic, complemented
5#39635C211yesmaximal, characteristic, complemented
6#39579C218yesmaximal, complemented
7#39506C211yesmaximal, characteristic, complemented
8#39379C211yesmaximal, characteristic, complemented
9#37883C212yesmaximal, complemented
10#37695C212yesmaximal, complemented
11#36640C211yesmaximal, characteristic, complemented
12#36477C212yesmaximal, complemented
13#36304C214yesmaximal, complemented
14#36285C212yesmaximal, complemented
15#36200C214yesmaximal
16#36199C214yesmaximal, complemented
17#35650C214yesmaximal, complemented
18#35321C212yesmaximal, complemented
19#35247C212yesmaximal
20#34281C212yesmaximal, complemented
21#34196C212yesmaximal, complemented
22C2×C4×C4⋊Q8C211yesmaximal, characteristic, complemented
23C4×#529C211yesmaximal, characteristic
24C2×#541C2212yes—
25C22×C4⋊Q8C2211yescharacteristic
26C2×#529C2211yescharacteristic
27C22×C4×Q8C2212yes—
28#2864C2214yes—
29#2863C2214yes—
30#2859C2211yescharacteristic
31#2859C2211yescharacteristic
32#2859C2212yes—
33#2855C2214yes—
34#2855C2214yes—
35#2854C2214yes—
36#2851C2212yes—
37#2851C2214yes—
38#2851C2212yes—
39#2802C2218yes—
40#2793C2218yes—
41#2791C2218yes—
42#2783C2218yes—
43#2776C2218yes—
44#2725C2218yes—
45#2716C2218yes—
46#2713C2218yes—
47#2647C2212yes—
48#2642C2212yes—
49#2637C2218yes—
50#2629C2212yes—
51#2621C2212yes—
52#2608C2218yes—
53#2606C2218yes—
54#2594C2218yes—
55#2592C2214yes—
56#2590C2218yes—
57#2588C2218yes—
58#2587C2218yes—
59#2585C2218yes—
60#2585C2218yes—
61#2584C2214yes—
62#2582C2212yes—
63#2582C2212yes—
64#2573C2218yes—
65#2570C2214yes—
66#2570C2214yes—
67#2566C2214yes—
68#2565C2214yes—
69#2538C2212yes—
70#2538C2212yes—
71#2529C2218yes—
72#2528C2218yes—
73#2527C2218yes—
74#2525C2218yes—
75#2525C2218yes—
76#2524C2218yes—
77#2524C2218yes—
78#2523C2218yes—
79#2520C2218yes—
80#2515C2218yes—
81#2514C2214yes—
82#2514C2214yes—
83#2513C2214yes—
84#2512C2214yes—
85#2511C2214yes—
86#2509C2218yes—
87#2509C2214yes—
88#2508C2214yes—
89#2507C2214yes—
90#2507C2214yes—
91#2506C2214yes—
92#2497C2214yes—
93#2493C2218yes—
94#2489C2214yes—
95#2486C2214yes—
96#2484C2218yes—
97#2481C2218yes—
98#2473C2218yes—
99#2453C2214yes—
100#2446C2214yes—
101#2429C2214yes—
102#2421C2214yes—
103#2419C2218yes—
104#2413C2218yes—
105#2413C2218yes—
106#2409C2214yes—
107#2373C2218yes—
108#2373C2218yes—
109#2371C2218yes—
110#2370C2214yes—
111#2370C2214yes—
112#2370C2218yes—
113#2359C2218yes—
114#2357C2214yes—
115#2356C2214yes—
116#2355C2212yes—
117#2355C2212yes—
118#2355C2214yes—
119#2355C2214yes—
120Q8×C4⋊C4C2212yes—
121Q8×C4⋊C4C2212yes—
122#2344C2218yes—
123#2344C2214yes—
124#2343C2218yes—
125Q8×C22⋊C4C2214yes—
126#2330C2212yes—
127#2327C2212yes—
128#2323C2214yes—
129#2323C2214yes—
130#2320C2214yes—
131#2320C2218yes—
132#2314C2212yes—
133C4×C4⋊Q8C2212yes—
134C4×C4⋊Q8C2211yescharacteristic
135C4×C4⋊Q8C2212yes—
136C4×C4⋊Q8C2214yes—
137C4×C4⋊Q8C2211yescharacteristic
138C4×C4⋊Q8C2214yes—
139C4×C4⋊Q8C2211yescharacteristic
140C4×C4⋊Q8C2211yescharacteristic
141C4×#125C2212yes—
142C4×#125C2214yes—
143C4×#125C2212yes—
144C4×#125C2212yes—
145C4×#126C2214yes—
146C4×#124C2212yes—
147C4×C22⋊Q8C2212yes—
148C4×C22⋊Q8C2214yes—
149C4×#123C2214yes—
150C4×#121C2212yes—
151#2298C2212yes—
152#2296C2214yes—
153#2295C2211yescharacteristic
154#2295C2214yes—
155C2×#391C2212yes—
156#2293C2211yescharacteristic
157C2×#389C2214yes—
158#2290C2212yes—
159#2285C2212yes—
160#2285C2214yes—
161C2×#384C2211yescharacteristic
162#2283C2214yes—
163#2283C2211yescharacteristic
164#2276C2214yes—
165C42×Q8C2211yescharacteristic
166C42×D4C2211yescharacteristic
167C42×D4C2212yes—
168C4×#117C2212yes—
169C2×C4×C4⋊C4C2214yes—
170C2×C43C2211yescharacteristic
171C23×Q8C2312yes—
172#541—216no—
173C2×C4⋊Q8—28no—
174C2×C4⋊Q8C2311yescharacteristic
175C2×C4⋊Q8C2312yes—
176C2×C4⋊Q8C2314yes—
177C2×C4⋊Q8C2311yescharacteristic
178#529—28no—
179C2×#126C2312yes—
180C2×#126C2318yes—
181C2×#125C2311yescharacteristic
182C2×#125C2314yes—
183C2×#125C2312yes—
184C2×#125C2318yes—
185C2×#125C2312yes—
186C2×#124C2311yescharacteristic
187C2×#123C2312yes—
188C2×#123C2318yes—
189C2×C22⋊Q8C2314yes—
190C2×C22⋊Q8C2311yescharacteristic
191C2×C22⋊Q8C2314yes—
192C2×#121C2311yescharacteristic
193C2×C4×Q8—216no—
194C2×C4×Q8C2312yes—
195C2×C4×Q8C2314yes—
196C2×C4×Q8C2312yes—
197C2×C4×Q8C2312yes—
198C2×C4×Q8C2312yes—
199C2×C4×Q8C2314yes—
200C2×C4×Q8C2312yes—
201C2×C4×Q8C2311yescharacteristic
202C2×C4×Q8C2314yes—
203C2×C4×Q8C2314yes—
204C2×C4×D4C2312yes—
205C2×C4×D4C2312yes—
206C2×C4×D4C2311yescharacteristic
207C2×C4×D4C2314yes—
208C2×#117C2312yes—
209C2×#117C2312yes—
210C2×#117C2318yes—
211C2×#117C2314yes—
212C22×C4⋊C4C2314yes—
213C22×C4⋊C4C2312yes—
214C22×C4⋊C4C2314yes—
215C22×C4⋊C4C2314yes—
216C22×C42C2311yescharacteristic
217C22×C42C2312yes—
218C22×C42C2314yes—
219C22×C42C2311yescharacteristic
220C22×C42C2312yes—
221C22×C42C2312yes—
222C22×C42C2311yescharacteristic
223#401C2318yes—
224#400C2318yes—
225#400C2318yes—
226#400C2318yes—
227#400C2318yes—
228#400C2318yes—
229#400C2318yes—
230#400C2318yes—
231#400C2318yes—
232#400C2318yes—
233#398C2318yes—
234#398C2318yes—
235#398C2318yes—
236#398C2318yes—
237#398C2318yes—
238#398C2318yes—
239#398C2318yes—
240#398C2318yes—
241#398C2318yes—
242#398C2318yes—
243#398C2318yes—
244#397C2318yes—
245#397C2318yes—
246#397C2318yes—
247#397C2318yes—
248#396C2318yes—
249#396C2318yes—
250#396C2318yes—
251#396C2318yes—
252#396C2318yes—
253#395C2318yes—
254#393C2318yes—
255#391C2314yes—
256#391C2312yes—
257#391C2312yes—
258#391C2312yes—
259#391C2314yes—
260#391C2312yes—
261#391C2314yes—
262#391C2314yes—
263#391C2318yes—
264#391C2314yes—
265#391C2314yes—
266#391C2318yes—
267#391C2314yes—
268#391C2314yes—
269#391C2312yes—
270#390C2314yes—
271#390C2314yes—
272#390C2312yes—
273#389C2314yes—
274#389C2314yes—
275#389C2314yes—
276#389C2314yes—
277#389C2312yes—
278#389C2312yes—
279#389C2314yes—
280#389C2314yes—
281#389C2314yes—
282#389C2314yes—
283#389C2314yes—
284#389C2314yes—
285#389C2314yes—
286#389C2314yes—
287#389C2314yes—
288#389C2314yes—
289#389C2314yes—
290#389C2314yes—
291#389C2318yes—
292#389C2318yes—
293#389C2314yes—
294#389C2314yes—
295#389C2314yes—
296#389C2314yes—
297#389C2318yes—
298#389C2318yes—
299#389C2318yes—
300#389C2314yes—
301#389C2318yes—
302#389C2314yes—
303#389C2314yes—
304#389C2314yes—
305#389C2318yes—
306#389C2318yes—
307#388C2314yes—
308#388C2314yes—
309#388C2314yes—
310#388C2318yes—
311#388C2318yes—
312#388C2318yes—
313#388C2318yes—
314#388C2318yes—
315#388C2318yes—
316#388C2318yes—
317#388C2314yes—
318#388C2318yes—
319#388C2318yes—
320#387C2314yes—
321#387C2314yes—
322#387C2314yes—
323#387C2314yes—
324#387C2318yes—
325#387C2318yes—
326#387C2318yes—
327#387C2318yes—
328#387C2318yes—
329#387C2318yes—
330#387C2318yes—
331#387C2318yes—
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#387C2318yes—
348#387C2318yes—
349#387C2318yes—
350#387C2318yes—
351#387C2318yes—
352#387C2318yes—
353#387C2318yes—
354#387C2318yes—
355#386C2318yes—
356#386C2314yes—
357#385C2318yes—
358#385C2318yes—
359#385C2318yes—
360#385C2318yes—
361#385C2318yes—
362#385C2314yes—
363#384C2311yescharacteristic
364#384C2311yescharacteristic
365#384C2312yes—
366#384C2314yes—
367#384C2314yes—
368#384C2314yes—
369#384C2312yes—
370#384C2312yes—
371#383C2312yes—
372#383C2318yes—
373#383C2318yes—
374#383C2318yes—
375#382C2312yes—
376#382C2314yes—
377#382C2312yes—
378#382C2312yes—
379#382C2314yes—
380#382C2314yes—
381#382C2314yes—
382#382C2318yes—
383#382C2318yes—
384#381C2318yes—
385#381C2318yes—
386#381C2312yes—
387#381C2318yes—
388#380C2314yes—
389#380C2314yes—
390#380C2314yes—
391#380C2314yes—
392#380C2318yes—
393#380C2312yes—
394C4×C4⋊C4C2314yes—
395C4×C4⋊C4C2314yes—
396C4×C4⋊C4C2314yes—
397C4×C4⋊C4C2318yes—
398C4×C4⋊C4C2314yes—
399C4×C4⋊C4C2314yes—
400C4×C4⋊C4C2318yes—
401C4×C4⋊C4C2312yes—
402C4×C4⋊C4C2312yes—
403C4×C4⋊C4C2314yes—
404C4×C4⋊C4C2314yes—
405C4×C4⋊C4C2314yes—
406C4×C4⋊C4C2314yes—
407C4×C4⋊C4C2314yes—
408C4×C4⋊C4C2314yes—
409C4×C4⋊C4C2314yes—
410C4×C4⋊C4C2314yes—
411C4×C4⋊C4C2314yes—
412C4×C4⋊C4C2314yes—
413C4×C4⋊C4C2318yes—
414C4×C4⋊C4C2318yes—
415C4×C4⋊C4C2314yes—
416C4×C4⋊C4C2318yes—
417C4×C4⋊C4C2318yes—
418C4×C4⋊C4C2318yes—
419C4×C4⋊C4C2311yescharacteristic
420C4×C4⋊C4C2311yescharacteristic
421C4×C4⋊C4C2314yes—
422C4×C4⋊C4C2314yes—
423C4×C4⋊C4C2314yes—
424C4×C4⋊C4C2314yes—
425C4×C4⋊C4C2312yes—
426C4×C4⋊C4C2312yes—
427C4×C22⋊C4C2314yes—
428C4×C22⋊C4C2314yes—
429C4×C22⋊C4C2314yes—
430C4×C22⋊C4C2314yes—
431C4×C22⋊C4C2312yes—
432C4×C22⋊C4C2318yes—
433C4×C22⋊C4C2314yes—
434C4×C22⋊C4C2318yes—
435C4×C22⋊C4C2312yes—
436C4×C22⋊C4C2312yes—
437#376C2312yes—
438#376C2318yes—
439#376C2312yes—
440#376C2318yes—
441C2×#95C2314yes—
442C2×#95C2314yes—
443C43C2312yes—
444C43C2312yes—
445C43C2311yescharacteristic
446C43C2311yescharacteristic
447C43C2311yescharacteristic
448C43C2311yescharacteristic
449C43C2312yes—
450C22×Q8—28no—
451C22×Q8—28no—
452C22×Q8—44no—
453C22×Q8C2411yescharacteristic
454C22×Q8C2412yes—
455C22×Q8C2414yes—
456C22×Q8C2412yes—
457C22×D4C2412yes—
458C22×D4C2411yescharacteristic
459C23×C4C2414yes—
460C23×C4C2412yes—
461C23×C4C2412yes—
462C23×C4C2414yes—
463C23×C4C2412yes—
464C23×C4C2411yescharacteristic
465C23×C4C2411yescharacteristic
466C23×C4C2411yescharacteristic
467C23×C4C2414yes—
468C4⋊Q8—28no—
469C4⋊Q8—216no—
470C4⋊Q8—24no—
471C4⋊Q8#4118yes—
472#126—232no—
473#126—28no—
474#125—232no—
475#125—24no—
476#125—28no—
477#125—216no—
478#125—44no—
479#124—24no—
480#123—28no—
481#123—416no—
482C22⋊Q8—216no—
483C22⋊Q8—24no—
484C22⋊Q8—48no—
485#121—24no—
486C4×Q8—216no—
487C4×Q8—28no—
488C4×Q8—28no—
489C4×Q8—28no—
490C4×Q8—28no—
491C4×Q8—216no—
492C4×Q8—216no—
493C4×Q8—24no—
494C4×Q8—28no—
495C4×Q8—48no—
496C4×D4—28no—
497C4×D4—24no—
498C4×D4—28no—
499C4×D4—48no—
500#117—28no—
501#117—28no—
502#117—416no—
503#117—48no—
504C2×C4⋊C4—28no—
505C2×C4⋊C4—216no—
506C2×C4⋊C4—216no—
507C2×C4⋊C4—48no—
508C2×C4⋊C4C2412yes—
509C2×C4⋊C4C2414yes—
510C2×C4⋊C4C2412yes—
511C2×C4⋊C4C2414yes—
512C2×C4⋊C4C2414yes—
513C2×C4⋊C4C2414yes—
514C2×C4⋊C4C2414yes—
515C2×C4⋊C4C2414yes—
516C2×C4⋊C4C2414yes—
517C2×C4⋊C4C2414yes—
518C2×C4⋊C4C2412yes—
519C2×C4⋊C4C2412yes—
520C2×C4⋊C4C2414yes—
521C2×C4⋊C4C2411yescharacteristic
522C2×C4⋊C4C2412yes—
523C2×C4⋊C4C2412yes—
524C2×C4⋊C4C2411yescharacteristic
525C2×C4⋊C4C2414yes—
526C2×C4⋊C4C2414yes—
527C2×C4⋊C4C2412yes—
528C2×C4⋊C4C2418yes—
529C2×C4⋊C4C2412yes—
530C2×C4⋊C4C2414yes—
531C2×C4⋊C4C2418yes—
532C2×C4⋊C4C2418yes—
533C2×C4⋊C4C2414yes—
534C2×C4⋊C4C2414yes—
535C2×C4⋊C4C2418yes—
536C2×C4⋊C4C2418yes—
537C2×C4⋊C4C2414yes—
538C2×C4⋊C4C2414yes—
539C2×C4⋊C4C2414yes—
540C2×C4⋊C4C2414yes—
541C2×C4⋊C4C2418yes—
542C2×C4⋊C4C2418yes—
543C2×C4⋊C4C2414yes—
544C2×C4⋊C4C2414yes—
545C2×C4⋊C4C2414yes—
546C2×C4⋊C4C2418yes—
547C2×C4⋊C4C2418yes—
548C2×C4⋊C4C2418yes—
549C2×C4⋊C4C2418yes—
550C2×C4⋊C4C2418yes—
551C2×C4⋊C4C2414yes—
552C2×C22⋊C4C2414yes—
553C2×C22⋊C4C2418yes—
554C2×C22⋊C4C2412yes—
555C2×C22⋊C4C2412yes—
556C2×C22⋊C4C2414yes—
557C2×C22⋊C4C2412yes—
558C2×C22⋊C4C2412yes—
559C2×C22⋊C4C2412yes—
560C2×C22⋊C4C2414yes—
561C2×C22⋊C4C2418yes—
562C2×C22⋊C4C2414yes—
563C2×C22⋊C4C2418yes—
564C2×C22⋊C4C2418yes—
565C2×C22⋊C4C2418yes—
566C2×C42—216no—
567C2×C42—24no—
568C2×C42—28no—
569C2×C42—44no—
570C2×C42—42no—
571C2×C42—44no—
572C2×C42#4118yes—
573C2×C42C2412yes—
574C2×C42C2412yes—
575C2×C42C2412yes—
576C2×C42C2414yes—
577C2×C42C2414yes—
578C2×C42C2414yes—
579C2×C42C2414yes—
580C2×C42C2418yes—
581C2×C42C2414yes—
582C2×C42C2411yescharacteristic
583C2×C42C2411yescharacteristic
584C2×C42C2412yes—
585C2×C42C2411yescharacteristic
586C2×C42C2412yes—
587C2×C42C2412yes—
588C2×C42C2412yes—
589C2×C42C2418yes—
590C2×C42C2418yes—
591C2×C42C2418yes—
592C2×C42C2414yes—
593C2×C42C2418yes—
594C2×C42C2412yes—
595C2×C42C2412yes—
596C2×C42C2412yes—
597C2×C42C2412yes—
598C2×C42C2412yes—
599C2×C42C2414yes—
600C2×C42C2411yescharacteristic
601C2×C42C2411yescharacteristic
602C2×C42C2411yescharacteristic
603C2×C42C2411yescharacteristic
604C2×C42C2411yescharacteristic
605C2×C42C2412yes—
606#95C2414yes—
607#95C2414yes—
608#95C2414yes—
609#95C2414yes—
610#95C2414yes—
611#95C2414yes—
612#95C2414yes—
613#95C2414yes—
614#95C2414yes—
615#95C2414yes—
616#95C2418yes—
617#95C2414yes—
618#95C2414yes—
619#95C2418yes—
620#95C2418yes—
621#95C2418yes—
622#95C2418yes—
623#95C2418yes—
624#95C2412yes—
625#95C2414yes—
626#95C2414yes—
627#95C2414yes—
628#95C2414yes—
629#95C2418yes—
630#95C2418yes—
631#95C2412yes—
632#95C2414yes—
633#95C2418yes—
634#95C2418yes—
635#95C2418yes—
636#95C2418yes—
637#95C2418yes—
638#95C2418yes—
639#95C2418yes—
640#95C2418yes—
641#95C2418yes—
642#95C2418yes—
643#95C2418yes—
644#95C2418yes—
645#95C2418yes—
646#95C2418yes—
647C24C2512yes—
648C24C2511yescharacteristic
649C2×Q8—24no—
650C2×Q8—28no—
651C2×Q8—24no—
652C2×Q8—22no—
653C2×Q8—28no—
654C2×Q8—24no—
655C2×Q8—24no—
656C2×Q8—24no—
657C2×Q8—24no—
658C2×Q8—44no—
659C2×Q8—432no—
660C2×Q8C2×#4118yes—
661C2×D4—24no—
662C2×D4—28no—
663C2×D4—22no—
664C2×D4—24no—
665C22×C4—24no—
666C22×C4—24no—
667C22×C4—24no—
668C22×C4—22no—
669C22×C4—24no—
670C22×C4—24no—
671C22×C4—22no—
672C22×C4—28no—
673C22×C4—28no—
674C22×C4—24no—
675C22×C4—28no—
676C22×C4—28no—
677C22×C4—28no—
678C22×C4—24no—
679C22×C4—24no—
680C22×C4—24no—
681C22×C4—24no—
682C22×C4—28no—
683C22×C4—42no—
684C22×C4—44no—
685C22×C4—44no—
686C22×C4—44no—
687C22×C4C2×#4114yes—
688C22×C4C2×#4114yes—
689C22×C4C2×#4114yes—
690C22×C4C2512yes—
691C22×C4C2512yes—
692C22×C4C2514yes—
693C22×C4C2514yes—
694C22×C4C2514yes—
695C22×C4C2518yes—
696C22×C4C2518yes—
697C22×C4C2514yes—
698C22×C4C2512yes—
699C22×C4C2514yes—
700C22×C4C2512yes—
701C22×C4C2511yescharacteristic
702C22×C4C2511yescharacteristic
703C22×C4C2512yes—
704C22×C4C2514yes—
705C22×C4C2511yescharacteristic
706C22×C4C2511yescharacteristic
707C22×C4C2512yes—
708C22×C4C2512yes—
709C22×C4C2511yescharacteristic
710C22×C4C2511yescharacteristic
711C4⋊C4—28no—
712C4⋊C4—28no—
713C4⋊C4—28no—
714C4⋊C4—24no—
715C4⋊C4—24no—
716C4⋊C4—28no—
717C4⋊C4—28no—
718C4⋊C4—28no—
719C4⋊C4—28no—
720C4⋊C4—28no—
721C4⋊C4—24no—
722C4⋊C4—24no—
723C4⋊C4—28no—
724C4⋊C4—22no—
725C4⋊C4—24no—
726C4⋊C4—22no—
727C4⋊C4—28no—
728C4⋊C4—24no—
729C4⋊C4—216no—
730C4⋊C4—216no—
731C4⋊C4—216no—
732C4⋊C4—24no—
733C4⋊C4—24no—
734C4⋊C4—28no—
735C4⋊C4—216no—
736C4⋊C4—216no—
737C4⋊C4—28no—
738C4⋊C4—28no—
739C4⋊C4—28no—
740C4⋊C4—44no—
741C4⋊C4—44no—
742C4⋊C4—44no—
743C4⋊C4—44no—
744C4⋊C4—44no—
745C4⋊C4—44no—
746C4⋊C4—48no—
747C4⋊C4—48no—
748C4⋊C4—44no—
749C4⋊C4—48no—
750C4⋊C4—48no—
751C4⋊C4—48no—
752C4⋊C4—48no—
753C4⋊C4—48no—
754C4⋊C4C2×#41116yes—
755C22⋊C4—24no—
756C22⋊C4—28no—
757C22⋊C4—216no—
758C22⋊C4—24no—
759C22⋊C4—24no—
760C22⋊C4—28no—
761C22⋊C4—24no—
762C22⋊C4—24no—
763C22⋊C4—216no—
764C22⋊C4—28no—
765C22⋊C4—44no—
766C22⋊C4—48no—
767C22⋊C4—48no—
768C22⋊C4—48no—
769C42—28no—
770C42—28no—
771C42—28no—
772C42—28no—
773C42—22no—
774C42—24no—
775C42—24no—
776C42—24no—
777C42—216no—
778C42—24no—
779C42—24no—
780C42—24no—
781C42—28no—
782C42—22no—
783C42—24no—
784C42—22no—
785C42—42no—
786C42—44no—
787C42—42no—
788C42—42no—
789C42—42no—
790C42—42no—
791C42—48no—
792C42—48no—
793C42—48no—
794C42—44no—
795C42—48no—
796C42C2×#4114yes—
797C42C2×#4114yes—
798C42C2×#4114yes—
799C42C2×#4114yes—
800C42C2×#4114yes—
801C422−1+418yes—
802C23—21no—
803C23—22no—
804C23—21no—
805C23—22no—
806C23—22no—
807C23—24no—
808C23—24no—
809C23—22no—
810C23C22×#4112yes—
811C23#58514yes—
812C23C2611yescharacteristic
813Q8—216no—
814Q8—416no—
815Q8—48no—
816Q8—44no—
817D4—48no—
818D4—44no—
819C2×C4—216no—
820C2×C4—22no—
821C2×C4—24no—
822C2×C4—21no—
823C2×C4—22no—
824C2×C4—22no—
825C2×C4—22no—
826C2×C4—22no—
827C2×C4—22no—
828C2×C4—22no—
829C2×C4—22no—
830C2×C4—22no—
831C2×C4—24no—
832C2×C4—21no—
833C2×C4—28no—
834C2×C4—28no—
835C2×C4—28no—
836C2×C4—24no—
837C2×C4—24no—
838C2×C4—24no—
839C2×C4—24no—
840C2×C4—22no—
841C2×C4—28no—
842C2×C4—22no—
843C2×C4—22no—
844C2×C4—22no—
845C2×C4—24no—
846C2×C4—22no—
847C2×C4—24no—
848C2×C4—24no—
849C2×C4—24no—
850C2×C4—28no—
851C2×C4—28no—
852C2×C4—24no—
853C2×C4—22no—
854C2×C4—24no—
855C2×C4—24no—
856C2×C4—28no—
857C2×C4—28no—
858C2×C4—24no—
859C2×C4—22no—
860C2×C4—22no—
861C2×C4—28no—
862C2×C4—24no—
863C2×C4—24no—
864C2×C4—24no—
865C2×C4—24no—
866C2×C4—24no—
867C2×C4—48no—
868C2×C4—416no—
869C2×C4—416no—
870C2×C4—48no—
871C2×C4—88no—
872C2×C4C22×#4112yes—
873C2×C4C22×#4118yes—
874C2×C4C22×#4114yes—
875C2×C4C22×#4112yes—
876C2×C4C22×#4112yes—
877C2×C4C22×#4112yes—
878C2×C4C22×#4112yes—
879C2×C4C22×#4112yes—
880C2×C4C22×#4112yes—
881C2×C4C2×2−1+414yes—
882C2×C4C2×2−1+414yes—
883C2×C4C2×2−1+414yes—
884C2×C4#58512yes—
885C22—24no—
886C22—22no—
887C22—24no—
888C22—22no—
889C22—44no—
890C22—42no—
891C22—42no—
892C22—44no—
893C22—42no—
894C22#351214yes—
895C22C23×#4111yescharacteristic
896C22C23×#4111yescharacteristic
897C22C22×2−1+412yes—
898C22C2×#58512yes—
899C22C2×#58511yescharacteristic
900C4—24no—
901C4—24no—
902C4—22no—
903C4—22no—
904C4—22no—
905C4—24no—
906C4—22no—
907C4—28no—
908C4—44no—
909C4—48no—
910C4—42no—
911C4—44no—
912C4—44no—
913C4—42no—
914C4—48no—
915C4—42no—
916C4—44no—
917C4—42no—
918C4—44no—
919C4#347514yes—
920C4#350914yes—
921C2—24no—
922C2—82no—
923C2C2×#347511yescharacteristic
924C2#6278812yes—
925C2C2×#350911yescharacteristic
926C2C2×#351211yescharacteristic
927C2#6283112yes—
subgroupG/H
center, commutator, Frattini, socle, cosocleC23C26
prime radicalC2×#121C23
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23 ◁ G
LECSG ▷ C23 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #59876C2semidirect
2. #59872C2semidirect
3. #59849C2semidirect
4. #39762C2semidirect
5. #39635C2semidirect
6. #39579C2semidirect
7. #39506C2semidirect
8. #39379C2semidirect
9. #37883C2semidirect
10. #37695C2semidirect
11. #36640C2semidirect
12. #36477C2semidirect
13. #36304C2semidirect
14. #36285C2semidirect
16. #36199C2semidirect
17. #35650C2semidirect
18. #35321C2semidirect
20. #34281C2semidirect
21. #34196C2semidirect
22. C2×C4×C4⋊Q8C2semidirect

Maximal subgroups

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

subgroupindex
#598762
#598722
#598492
#397622
#396352
#395792
#395062
#393792
#378832
#376952
#366402
#364772
#363042
#362852
#362002
#361992
#356502
#353212
#352472
#342812
#341962
C2×C4×C4⋊Q82
C4×#5292