Finite Group Databasebeta

← #7672607

Subgroups — #7672607

Order 512.

4610 conjugacy classes of subgroups.

The subgroup lattice has 919 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#59916C218yesmaximal, complemented
2#59671C214yesmaximal, complemented
3#59462C214yesmaximal, complemented
4#39651C218yesmaximal, complemented
5#39183C212yesmaximal, complemented
6#38967C212yesmaximal, complemented
7#38101C214yesmaximal, complemented
8#36640C211yesmaximal, characteristic, complemented
9#36584C211yesmaximal, characteristic, complemented
10#36571C214yesmaximal, complemented
11#36565C211yesmaximal, characteristic, complemented
12#36551C214yesmaximal
13#36192C211yesmaximal, characteristic, complemented
14#36191C212yesmaximal, complemented
15D4×#125C212yesmaximal, complemented
16D4×#125C211yesmaximal, characteristic, complemented
17#35641C214yesmaximal, complemented
18#35337C212yesmaximal, complemented
19#35239C212yesmaximal, complemented
20#34243C212yesmaximal
21#34217C212yesmaximal, complemented
22C4×#529C211yesmaximal, characteristic
23C2×C4×#125C211yesmaximal, characteristic, complemented
24C2×#529C2211yescharacteristic
25C22×#125C2212yes—
26C22×#125C2211yescharacteristic
27#2864C2214yes—
28#2862C2212yes—
29#2859C2212yes—
30#2859C2211yescharacteristic
31#2859C2212yes—
32#2859C2211yescharacteristic
33#2857C2214yes—
34#2851C2212yes—
35#2851C2212yes—
36#2851C2212yes—
37#2851C2214yes—
38#2851C2212yes—
39#2851C2214yes—
40#2805C2218yes—
41#2802C2218yes—
42#2802C2218yes—
43#2791C2218yes—
44#2788C2218yes—
45#2768C2218yes—
46#2742C2218yes—
47#2742C2218yes—
48#2666C2218yes—
49#2647C2214yes—
50#2628C2214yes—
51#2590C2218yes—
52#2589C2218yes—
53#2589C2218yes—
54#2589C2218yes—
55#2588C2218yes—
56#2588C2218yes—
57#2586C2218yes—
58#2585C2218yes—
59#2583C2218yes—
60#2574C2218yes—
61#2574C2218yes—
62#2571C2212yes—
63#2571C2214yes—
64#2570C2214yes—
65#2570C2214yes—
66#2565C2214yes—
67#2563C2214yes—
68#2552C2214yes—
69#2552C2212yes—
70#2552C2214yes—
71#2552C2212yes—
72#2551C2212yes—
73#2550C2214yes—
74#2550C2214yes—
75#2550C2214yes—
76#2522C2218yes—
77#2522C2218yes—
78#2520C2218yes—
79#2520C2218yes—
80#2511C2218yes—
81#2509C2218yes—
82#2509C2214yes—
83#2509C2214yes—
84#2509C2214yes—
85#2506C2214yes—
86#2506C2218yes—
87#2505C2218yes—
88#2497C2218yes—
89#2487C2218yes—
90#2473C2218yes—
91#2473C2218yes—
92#2473C2218yes—
93#2454C2214yes—
94#2454C2214yes—
95#2453C2214yes—
96#2451C2214yes—
97#2450C2218yes—
98#2450C2218yes—
99#2442C2214yes—
100#2442C2214yes—
101#2442C2214yes—
102#2441C2214yes—
103#2440C2214yes—
104#2439C2214yes—
105#2438C2218yes—
106#2370C2218yes—
107#2370C2214yes—
108#2370C2214yes—
109#2370C2218yes—
110#2369C2214yes—
111#2368C2218yes—
112#2367C2214yes—
113#2359C2218yes—
114#2355C2212yes—
115#2354C2212yes—
116#2352C2214yes—
117#2351C2214yes—
118Q8×C4⋊C4C2212yes—
119D4×C4⋊C4C2218yes—
120D4×C4⋊C4C2212yes—
121D4×C4⋊C4C2214yes—
122D4×C4⋊C4C2214yes—
123#2345C2218yes—
124#2345C2218yes—
125#2334C2218yes—
126#2331C2214yes—
127#2330C2214yes—
128#2330C2214yes—
129#2316C2214yes—
130#2314C2214yes—
131C4×#125C2211yescharacteristic
132C4×#125C2212yes—
133C4×#125C2212yes—
134C4×#125C2211yescharacteristic
135C4×#125C2212yes—
136C4×#125C2212yes—
137C4×#125C2214yes—
138C4×#125C2214yes—
139C4×#125C2212yes—
140C4×#125C2212yes—
141C4×#125C2212yes—
142C4×#125C2211yescharacteristic
143C4×#125C2211yescharacteristic
144C4×#125C2214yes—
145C4×#126C2214yes—
146C4×#124C2212yes—
147C4×C22⋊Q8C2214yes—
148C4×C22⋊Q8C2212yes—
149C4×#123C2214yes—
150C4×#121C2214yes—
151C4×#121C2212yes—
152#2298C2212yes—
153#2296C2214yes—
154#2295C2211yescharacteristic
155#2293C2211yescharacteristic
156C2×#389C2212yes—
157#2290C2212yes—
158C2×#387C2214yes—
159#2285C2212yes—
160#2285C2212yes—
161#2283C2211yescharacteristic
162C2×#382C2211yescharacteristic
163#2274C2214yes—
164C42×Q8C2211yescharacteristic
165C42×D4C2212yes—
166C42×D4C2211yescharacteristic
167C4×#117C2212yes—
168C2×C4×C4⋊C4C2212yes—
169C2×C4×C4⋊C4C2214yes—
170C2×C43C2211yescharacteristic
171C2×C4⋊Q8C2314yes—
172C2×C4⋊Q8C2314yes—
173#529Q8116yescomplemented
174C2×#126C2312yes—
175C2×#125—216no—
176C2×#125—28no—
177C2×#125C2311yescharacteristic
178C2×#125C2312yes—
179C2×#125C2312yes—
180C2×#125C2314yes—
181C2×#125C2314yes—
182C2×#125C2318yes—
183C2×#125C2312yes—
184C2×#125C2314yes—
185C2×#125C2314yes—
186C2×#125C2311yescharacteristic
187C2×#125C2311yescharacteristic
188C2×#124C2311yescharacteristic
189C2×#123C2312yes—
190C2×C22⋊Q8C2318yes—
191C2×C22⋊Q8C2311yescharacteristic
192C2×#121C2311yescharacteristic
193C2×C4×Q8C2314yes—
194C2×C4×Q8C2312yes—
195C2×C4×Q8C2311yescharacteristic
196C2×C4×D4C2314yes—
197C2×C4×D4C2318yes—
198C2×C4×D4C2314yes—
199C2×C4×D4C2312yes—
200C2×C4×D4C2312yes—
201C2×C4×D4C2311yescharacteristic
202C2×#117C2312yes—
203C2×#117C2314yes—
204C2×#117C2314yes—
205C2×#117C2312yes—
206C22×C4⋊C4C2314yes—
207C22×C4⋊C4C2318yes—
208C22×C4⋊C4C2312yes—
209C22×C4⋊C4C2314yes—
210C22×C4⋊C4C2314yes—
211C22×C4⋊C4C2312yes—
212C22×C42C2311yescharacteristic
213C22×C42C2312yes—
214C22×C42C2312yes—
215C22×C42C2311yescharacteristic
216C22×C42C2314yes—
217C22×C42C2312yes—
218C22×C42C2311yescharacteristic
219#400C2318yes—
220#400C2318yes—
221#400C2318yes—
222#400C2318yes—
223#400C2318yes—
224#400C2318yes—
225#400C2318yes—
226#400C2318yes—
227#400C2318yes—
228#400C2318yes—
229#399C2318yes—
230#399C2318yes—
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#396C2318yes—
244#396C2318yes—
245#395C2318yes—
246#395C2318yes—
247#395C2318yes—
248#395C2318yes—
249#393C2318yes—
250#393C2318yes—
251#391C2312yes—
252#391C2314yes—
253#391C2318yes—
254#391C2318yes—
255#391C2318yes—
256#391C2318yes—
257#391C2318yes—
258#391C2318yes—
259#390C2312yes—
260#390C2314yes—
261#389C2312yes—
262#389C2312yes—
263#389C2312yes—
264#389C2312yes—
265#389C2314yes—
266#389C2314yes—
267#389C2314yes—
268#389C2314yes—
269#389C2314yes—
270#389C2314yes—
271#389C2314yes—
272#389C2314yes—
273#389C2312yes—
274#389C2312yes—
275#389C2314yes—
276#389C2314yes—
277#389C2314yes—
278#389C2318yes—
279#389C2314yes—
280#389C2318yes—
281#389C2318yes—
282#389C2318yes—
283#389C2318yes—
284#389C2318yes—
285#389C2318yes—
286#389C2318yes—
287#389C2314yes—
288#389C2318yes—
289#389C2314yes—
290#389C2318yes—
291#389C2318yes—
292#389C2318yes—
293#389C2318yes—
294#389C2318yes—
295#389C2314yes—
296#389C2314yes—
297#389C2314yes—
298#389C2314yes—
299#389C2314yes—
300#389C2314yes—
301#388C2314yes—
302#388C2314yes—
303#388C2314yes—
304#388C2318yes—
305#388C2318yes—
306#388C2318yes—
307#388C2314yes—
308#388C2318yes—
309#387C2314yes—
310#387C2314yes—
311#387C2314yes—
312#387C2314yes—
313#387C2314yes—
314#387C2314yes—
315#387C2314yes—
316#387C2314yes—
317#387C2314yes—
318#387C2314yes—
319#387C2314yes—
320#387C2318yes—
321#387C2318yes—
322#387C2318yes—
323#387C2318yes—
324#387C2314yes—
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#386C2318yes—
344#386C2314yes—
345#385C2318yes—
346#385C2318yes—
347#385C2314yes—
348#385C2318yes—
349#385C2318yes—
350#385C2318yes—
351#385C2318yes—
352#385C2318yes—
353#385C2318yes—
354#385C2318yes—
355#385C2318yes—
356#385C2318yes—
357#384C2314yes—
358#384C2314yes—
359#384C2314yes—
360#384C2312yes—
361#384C2312yes—
362#384C2318yes—
363#383C2312yes—
364#382C2311yescharacteristic
365#382C2312yes—
366#382C2314yes—
367#382C2312yes—
368#382C2311yescharacteristic
369#382C2314yes—
370#382C2312yes—
371#382C2312yes—
372#382C2314yes—
373#382C2314yes—
374#382C2314yes—
375#382C2318yes—
376#382C2314yes—
377#381C2312yes—
378#380C2318yes—
379#380C2318yes—
380#380C2314yes—
381#380C2314yes—
382#380C2318yes—
383#380C2318yes—
384#380C2318yes—
385#380C2314yes—
386#380C2312yes—
387#380C2314yes—
388#380C2318yes—
389C4×C4⋊C4C2314yes—
390C4×C4⋊C4C2314yes—
391C4×C4⋊C4C2314yes—
392C4×C4⋊C4C2314yes—
393C4×C4⋊C4C2314yes—
394C4×C4⋊C4C2312yes—
395C4×C4⋊C4C2314yes—
396C4×C4⋊C4C2314yes—
397C4×C4⋊C4C2314yes—
398C4×C4⋊C4C2312yes—
399C4×C4⋊C4C2318yes—
400C4×C4⋊C4C2314yes—
401C4×C4⋊C4C2312yes—
402C4×C4⋊C4C2314yes—
403C4×C4⋊C4C2318yes—
404C4×C4⋊C4C2314yes—
405C4×C4⋊C4C2314yes—
406C4×C4⋊C4C2312yes—
407C4×C4⋊C4C2314yes—
408C4×C4⋊C4C2314yes—
409C4×C4⋊C4C2314yes—
410C4×C4⋊C4C2314yes—
411C4×C4⋊C4C2318yes—
412C4×C4⋊C4C2314yes—
413C4×C4⋊C4C2318yes—
414C4×C4⋊C4C2314yes—
415C4×C4⋊C4C2312yes—
416C4×C4⋊C4C2312yes—
417C4×C4⋊C4C2312yes—
418C4×C4⋊C4C2311yescharacteristic
419C4×C4⋊C4C2312yes—
420C4×C4⋊C4C2318yes—
421C4×C4⋊C4C2318yes—
422C4×C4⋊C4C2314yes—
423C4×C4⋊C4C2314yes—
424C4×C4⋊C4C2318yes—
425C4×C4⋊C4C2311yescharacteristic
426C4×C22⋊C4C2314yes—
427C4×C22⋊C4C2314yes—
428C4×C22⋊C4C2314yes—
429C4×C22⋊C4C2318yes—
430C4×C22⋊C4C2318yes—
431C4×C22⋊C4C2314yes—
432C4×C22⋊C4C2318yes—
433C4×C22⋊C4C2314yes—
434C4×C22⋊C4C2312yes—
435C4×C22⋊C4C2312yes—
436C4×C22⋊C4C2312yes—
437#376C2312yes—
438#376C2312yes—
439C2×#95C2314yes—
440C2×#95C2314yes—
441C2×#95C2314yes—
442C43C2312yes—
443C43C2312yes—
444C43C2311yescharacteristic
445C43C2311yescharacteristic
446C43C2311yescharacteristic
447C43C2311yescharacteristic
448C43C2312yes—
449C22×Q8C2411yescharacteristic
450C22×Q8C2418yes—
451C22×D4C2412yes—
452C22×D4C2411yescharacteristic
453C23×C4C2414yes—
454C23×C4C2412yes—
455C23×C4C2411yescharacteristic
456C23×C4C2412yes—
457C23×C4C2411yescharacteristic
458C23×C4C2411yescharacteristic
459C23×C4C2418yes—
460C23×C4C2414yes—
461C23×C4C2414yes—
462C23×C4C2412yes—
463C4⋊Q8—48no—
464C4⋊Q8—48no—
465#126C2×Q8116yes—
466#125—28no—
467#125—216no—
468#125—216no—
469#125—232no—
470#125—28no—
471#125—24no—
472#125—48no—
473#125—44no—
474#125—48no—
475#125C2×Q818yes—
476#125#4118yes—
477#124C2×Q818yes—
478#123C2×Q8116yes—
479C22⋊Q8—416no—
480C22⋊Q8C2×Q818yes—
481#121C2×Q818yes—
482C4×Q8—44no—
483C4×Q8—48no—
484C4×Q8C2×Q818yes—
485C4×D4—44no—
486C4×D4—48no—
487C4×D4—416no—
488C4×D4—48no—
489C4×D4C2×Q818yes—
490C4×D4C2×Q8116yes—
491#117—44no—
492#117—48no—
493#117—48no—
494#117C2×Q8116yes—
495C2×C4⋊C4—28no—
496C2×C4⋊C4—216no—
497C2×C4⋊C4—216no—
498C2×C4⋊C4—232no—
499C2×C4⋊C4—44no—
500C2×C4⋊C4—48no—
501C2×C4⋊C4C2412yes—
502C2×C4⋊C4C2414yes—
503C2×C4⋊C4C2412yes—
504C2×C4⋊C4C2414yes—
505C2×C4⋊C4C2418yes—
506C2×C4⋊C4C2414yes—
507C2×C4⋊C4C2414yes—
508C2×C4⋊C4C2418yes—
509C2×C4⋊C4C2414yes—
510C2×C4⋊C4C2418yes—
511C2×C4⋊C4C2418yes—
512C2×C4⋊C4C2412yes—
513C2×C4⋊C4C2414yes—
514C2×C4⋊C4C2414yes—
515C2×C4⋊C4C2412yes—
516C2×C4⋊C4C2412yes—
517C2×C4⋊C4C2414yes—
518C2×C4⋊C4C2414yes—
519C2×C4⋊C4C2414yes—
520C2×C4⋊C4C2414yes—
521C2×C4⋊C4C2414yes—
522C2×C4⋊C4C2414yes—
523C2×C4⋊C4C2414yes—
524C2×C4⋊C4C2414yes—
525C2×C4⋊C4C2414yes—
526C2×C4⋊C4C2414yes—
527C2×C4⋊C4C2418yes—
528C2×C4⋊C4C2414yes—
529C2×C4⋊C4C2418yes—
530C2×C4⋊C4C2418yes—
531C2×C4⋊C4C2418yes—
532C2×C4⋊C4C2418yes—
533C2×C4⋊C4C2418yes—
534C2×C4⋊C4C2418yes—
535C2×C4⋊C4C2418yes—
536C2×C4⋊C4C2418yes—
537C2×C4⋊C4C2418yes—
538C2×C4⋊C4C2418yes—
539C2×C4⋊C4C2418yes—
540C2×C4⋊C4C2412yes—
541C2×C4⋊C4C2412yes—
542C2×C4⋊C4C2411yescharacteristic
543C2×C4⋊C4C2412yes—
544C2×C4⋊C4C2411yescharacteristic
545C2×C4⋊C4C2412yes—
546C2×C4⋊C4C2414yes—
547C2×C4⋊C4C2412yes—
548C2×C22⋊C4C2418yes—
549C2×C22⋊C4C2414yes—
550C2×C22⋊C4C2414yes—
551C2×C22⋊C4C2418yes—
552C2×C22⋊C4C2414yes—
553C2×C22⋊C4C2414yes—
554C2×C22⋊C4C2418yes—
555C2×C22⋊C4C2418yes—
556C2×C22⋊C4C2412yes—
557C2×C22⋊C4C2412yes—
558C2×C22⋊C4C2412yes—
559C2×C22⋊C4C2412yes—
560C2×C22⋊C4C2412yes—
561C2×C42—24no—
562C2×C42—28no—
563C2×C42—42no—
564C2×C42—44no—
565C2×C42—48no—
566C2×C42—44no—
567C2×C42C2×Q818yes—
568C2×C42C2411yescharacteristic
569C2×C42C2412yes—
570C2×C42C2412yes—
571C2×C42C2414yes—
572C2×C42C2414yes—
573C2×C42C2412yes—
574C2×C42C2411yescharacteristic
575C2×C42C2411yescharacteristic
576C2×C42C2412yes—
577C2×C42C2412yes—
578C2×C42C2414yes—
579C2×C42C2418yes—
580C2×C42C2418yes—
581C2×C42C2414yes—
582C2×C42C2418yes—
583C2×C42C2414yes—
584C2×C42C2418yes—
585C2×C42C2412yes—
586C2×C42C2412yes—
587C2×C42C2412yes—
588C2×C42C2412yes—
589C2×C42C2412yes—
590C2×C42C2412yes—
591C2×C42C2412yes—
592C2×C42C2414yes—
593C2×C42C2414yes—
594C2×C42C2411yescharacteristic
595C2×C42C2412yes—
596C2×C42C2411yescharacteristic
597C2×C42C2411yescharacteristic
598C2×C42C2411yescharacteristic
599C2×C42C2411yescharacteristic
600#95C2414yes—
601#95C2414yes—
602#95C2414yes—
603#95C2414yes—
604#95C2414yes—
605#95C2414yes—
606#95C2414yes—
607#95C2414yes—
608#95C2414yes—
609#95C2414yes—
610#95C2414yes—
611#95C2414yes—
612#95C2414yes—
613#95C2414yes—
614#95C2414yes—
615#95C2414yes—
616#95C2412yes—
617#95C2414yes—
618#95C2414yes—
619#95C2414yes—
620#95C2414yes—
621#95C2418yes—
622#95C2418yes—
623#95C2418yes—
624#95C2418yes—
625#95C2418yes—
626#95C2418yes—
627#95C2412yes—
628#95C2414yes—
629#95C2418yes—
630#95C2418yes—
631#95C2418yes—
632#95C2418yes—
633#95C2418yes—
634#95C2418yes—
635#95C2418yes—
636#95C2418yes—
637#95C2418yes—
638#95C2418yes—
639#95C2418yes—
640#95C2418yes—
641C24C2512yes—
642C24C2511yescharacteristic
643C2×Q8—24no—
644C2×Q8—48no—
645C2×Q8—48no—
646C2×Q8—48no—
647C2×Q8C22×Q814yes—
648C2×D4—28no—
649C2×D4—24no—
650C2×D4C22×Q818yes—
651C2×D4C22×Q814yes—
652C22×C4—24no—
653C22×C4—22no—
654C22×C4—24no—
655C22×C4—24no—
656C22×C4—22no—
657C22×C4—24no—
658C22×C4—24no—
659C22×C4—24no—
660C22×C4—28no—
661C22×C4—28no—
662C22×C4—24no—
663C22×C4—28no—
664C22×C4—28no—
665C22×C4—216no—
666C22×C4—42no—
667C22×C4—44no—
668C22×C4—42no—
669C22×C4—42no—
670C22×C4—44no—
671C22×C4—44no—
672C22×C4—44no—
673C22×C4—48no—
674C22×C4—44no—
675C22×C4—48no—
676C22×C4C22×Q814yes—
677C22×C4C22×Q814yes—
678C22×C4C22×Q814yes—
679C22×C4C22×Q818yes—
680C22×C4C2514yes—
681C22×C4C2514yes—
682C22×C4C2512yes—
683C22×C4C2514yes—
684C22×C4C2512yes—
685C22×C4C2512yes—
686C22×C4C2518yes—
687C22×C4C2514yes—
688C22×C4C2514yes—
689C22×C4C2518yes—
690C22×C4C2511yescharacteristic
691C22×C4C2511yescharacteristic
692C22×C4C2512yes—
693C22×C4C2512yes—
694C22×C4C2512yes—
695C22×C4C2511yescharacteristic
696C22×C4C2511yescharacteristic
697C22×C4C2512yes—
698C22×C4C2514yes—
699C22×C4C2511yescharacteristic
700C22×C4C2511yescharacteristic
701C4⋊C4—28no—
702C4⋊C4—216no—
703C4⋊C4—28no—
704C4⋊C4—28no—
705C4⋊C4—216no—
706C4⋊C4—216no—
707C4⋊C4—28no—
708C4⋊C4—216no—
709C4⋊C4—24no—
710C4⋊C4—28no—
711C4⋊C4—24no—
712C4⋊C4—24no—
713C4⋊C4—28no—
714C4⋊C4—28no—
715C4⋊C4—24no—
716C4⋊C4—24no—
717C4⋊C4—28no—
718C4⋊C4—44no—
719C4⋊C4—44no—
720C4⋊C4—44no—
721C4⋊C4—44no—
722C4⋊C4—44no—
723C4⋊C4—44no—
724C4⋊C4—44no—
725C4⋊C4—44no—
726C4⋊C4—44no—
727C4⋊C4—48no—
728C4⋊C4—44no—
729C4⋊C4—48no—
730C4⋊C4—48no—
731C4⋊C4—48no—
732C4⋊C4—48no—
733C4⋊C4—48no—
734C4⋊C4—48no—
735C4⋊C4—48no—
736C4⋊C4—48no—
737C4⋊C4—48no—
738C4⋊C4—48no—
739C4⋊C4—48no—
740C4⋊C4C22×Q818yes—
741C4⋊C4C22×Q818yes—
742C4⋊C4C22×Q814yes—
743C4⋊C4C22×Q818yes—
744C4⋊C4C22×Q814yes—
745C4⋊C4C22×Q818yes—
746C4⋊C4C2×#41116yes—
747C4⋊C4C2×#4118yes—
748C22⋊C4—216no—
749C22⋊C4—28no—
750C22⋊C4—44no—
751C22⋊C4—48no—
752C22⋊C4—44no—
753C22⋊C4—48no—
754C22⋊C4—48no—
755C22⋊C4—44no—
756C22⋊C4C22×Q818yes—
757C22⋊C4C22×Q818yes—
758C22⋊C4C22×Q818yes—
759C22⋊C4C22×Q818yes—
760C22⋊C4C22×Q818yes—
761C42—24no—
762C42—28no—
763C42—22no—
764C42—24no—
765C42—22no—
766C42—24no—
767C42—28no—
768C42—28no—
769C42—22no—
770C42—24no—
771C42—24no—
772C42—42no—
773C42—44no—
774C42—42no—
775C42—42no—
776C42—44no—
777C42—42no—
778C42—42no—
779C42—42no—
780C42—42no—
781C42—48no—
782C42—48no—
783C42—44no—
784C42—48no—
785C42—44no—
786C42—48no—
787C42C22×Q814yes—
788C42C22×Q814yes—
789C42C22×Q814yes—
790C42C22×Q814yes—
791C42C22×Q818yes—
792C42C2×#4114yes—
793C23—21no—
794C23—22no—
795C23—21no—
796C23—22no—
797C23—22no—
798C23—24no—
799C23—24no—
800C23C23×Q814yes—
801C23C23×Q812yes—
802C23#58514yes—
803C23C2611yescharacteristic
804Q8—28no—
805Q8—168no—
806D4—216no—
807D4—28no—
808C2×C4—22no—
809C2×C4—21no—
810C2×C4—22no—
811C2×C4—24no—
812C2×C4—22no—
813C2×C4—22no—
814C2×C4—22no—
815C2×C4—22no—
816C2×C4—24no—
817C2×C4—24no—
818C2×C4—22no—
819C2×C4—21no—
820C2×C4—24no—
821C2×C4—28no—
822C2×C4—28no—
823C2×C4—216no—
824C2×C4—28no—
825C2×C4—22no—
826C2×C4—24no—
827C2×C4—24no—
828C2×C4—28no—
829C2×C4—24no—
830C2×C4—22no—
831C2×C4—22no—
832C2×C4—24no—
833C2×C4—24no—
834C2×C4—22no—
835C2×C4—22no—
836C2×C4—22no—
837C2×C4—24no—
838C2×C4—28no—
839C2×C4—24no—
840C2×C4—22no—
841C2×C4—22no—
842C2×C4—22no—
843C2×C4—24no—
844C2×C4—28no—
845C2×C4—28no—
846C2×C4—28no—
847C2×C4—24no—
848C2×C4—24no—
849C2×C4—24no—
850C2×C4—24no—
851C2×C4—28no—
852C2×C4—24no—
853C2×C4—24no—
854C2×C4—24no—
855C2×C4—48no—
856C2×C4—416no—
857C2×C4—48no—
858C2×C4—88no—
859C2×C4—816no—
860C2×C4—88no—
861C2×C4C23×Q812yes—
862C2×C4C23×Q812yes—
863C2×C4C23×Q812yes—
864C2×C4C23×Q812yes—
865C2×C4C23×Q814yes—
866C2×C4C23×Q814yes—
867C2×C4C23×Q814yes—
868C2×C4C23×Q812yes—
869C2×C4C23×Q812yes—
870C2×C4C22×#4114yes—
871C2×C4C22×#4118yes—
872C2×C4C22×#4112yes—
873C2×C4#58512yes—
874C2×C4#58514yes—
875C22—22no—
876C22—24no—
877C22—24no—
878C22—22no—
879C22—24no—
880C22—24no—
881C22—24no—
882C22—44no—
883C22—44no—
884C22#350414yes—
885C22C24×Q811yescharacteristic
886C22C23×#4111yescharacteristic
887C22C2×#58512yes—
888C22C2×#58512yes—
889C22C2×#58511yescharacteristic
890C4—22no—
891C4—22no—
892C4—22no—
893C4—24no—
894C4—24no—
895C4—24no—
896C4—28no—
897C4—24no—
898C4—22no—
899C4—42no—
900C4—44no—
901C4—44no—
902C4—48no—
903C4—42no—
904C4—42no—
905C4—44no—
906C4—44no—
907C4—48no—
908C4—44no—
909C4Q8×#4114yes—
910C4#350414yes—
911C2—24no—
912C2—44no—
913C2C2×Q8×#4111yescharacteristic
914C2C2×#350411yescharacteristic
915C2C2×#350411yescharacteristic
916C2#6281612yes—
917C2#6282712yes—
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. #59916C2semidirect
2. #59671C2semidirect
3. #59462C2semidirect
4. #39651C2semidirect
5. #39183C2semidirect
6. #38967C2semidirect
7. #38101C2semidirect
8. #36640C2semidirect
9. #36584C2semidirect
10. #36571C2semidirect
11. #36565C2semidirect
13. #36192C2semidirect
14. #36191C2semidirect
15. D4×#125C2semidirect
16. D4×#125C2semidirect
17. #35641C2semidirect
18. #35337C2semidirect
19. #35239C2semidirect
21. #34217C2semidirect
23. C2×C4×#125C2semidirect
173. #529Q8semidirect

Maximal subgroups

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

subgroupindex
#599162
#596712
#594622
#396512
#391832
#389672
#381012
#366402
#365842
#365712
#365652
#365512
#361922
#361912
D4×#1252
#356412
#353372
#352392
#342432
#342172
C4×#5292
C2×C4×#1252