Finite Group Databasebeta

← #7674547

Subgroups — #7674547

Order 512.

4660 conjugacy classes of subgroups.

The subgroup lattice has 978 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#43939C218yesmaximal, complemented
2#43057C218yesmaximal, complemented
3#39547C214yesmaximal, complemented
4#39546C214yesmaximal, complemented
5#38279C214yesmaximal, complemented
6#38278C214yesmaximal, complemented
7#38275C214yesmaximal, complemented
8#38274C214yesmaximal, complemented
9#37889C212yesmaximal, complemented
10#37888C212yesmaximal, complemented
11#37883C212yesmaximal, complemented
12#37882C212yesmaximal, complemented
13#35544C212yesmaximal, complemented
14#35516C212yesmaximal
15#35333C211yesmaximal, characteristic, complemented
16#35286C211yesmaximal, characteristic, complemented
17#35265C212yesmaximal, complemented
18C2×#2629C211yesmaximal, characteristic, complemented
19#34253C212yesmaximal, complemented
20#34217C211yesmaximal, characteristic, complemented
21#34183C211yesmaximal, characteristic, complemented
22#34065C211yesmaximal, characteristic
23#34048C211yesmaximal, characteristic, complemented
24C22×#125C2211yescharacteristic
25C2×#525C2211yescharacteristic
26C2×#520C2212yes—
27C2×C4×#41C2211yescharacteristic
28C22×#117C2211yescharacteristic
29#2864C2214yescomplemented
30#2859C2214yescomplemented
31#2859C2214yescomplemented
32#2851C2212yescomplemented
33#2851C2212yescomplemented
34#2794C2218yescomplemented
35#2793C2218yes—
36#2791C2218yescomplemented
37#2787C2218yescomplemented
38#2781C2218yes—
39#2779C2218yes—
40#2777C2218yes—
41#2772C2218yes—
42#2770C2218yescomplemented
43#2766C2218yescomplemented
44#2765C2218yescomplemented
45#2761C2218yes—
46#2739C2218yescomplemented
47#2721C2218yes—
48#2719C2218yescomplemented
49#2707C2218yes—
50#2647C2212yescomplemented
51#2647C2212yescomplemented
52#2647C2214yescomplemented
53#2647C2214yescomplemented
54#2629C2212yes—
55#2629C2212yes—
56#2629C2212yes—
57#2629C2212yes—
58#2629C2214yes—
59#2629C2214yes—
60#2629C2214yescomplemented
61#2606C2218yescomplemented
62#2601C2218yes—
63#2590C2218yescomplemented
64#2579C2218yes—
65#2571C2214yescomplemented
66#2566C2214yescomplemented
67#2565C2214yescomplemented
68#2558C2218yes—
69#2552C2214yescomplemented
70#2529C2218yes—
71#2529C2218yes—
72#2528C2218yescomplemented
73#2525C2218yes—
74#2524C2218yescomplemented
75#2519C2218yes—
76#2515C2218yescomplemented
77#2509C2214yescomplemented
78#2508C2214yescomplemented
79#2507C2214yescomplemented
80#2506C2214yescomplemented
81#2505C2218yes—
82#2497C2214yes—
83#2497C2214yes—
84#2496C2214yes—
85#2496C2214yes—
86#2495C2214yes—
87#2495C2214yes—
88#2494C2214yes—
89#2494C2214yes—
90#2493C2218yes—
91#2487C2214yes—
92#2486C2214yes—
93#2485C2214yes—
94#2485C2214yes—
95#2484C2218yescomplemented
96#2481C2218yes—
97#2480C2218yes—
98#2475C2218yescomplemented
99#2473C2218yes—
100#2473C2218yescomplemented
101#2442C2218yes—
102#2423C2214yes—
103#2422C2214yes—
104#2421C2214yes—
105#2420C2214yes—
106#2419C2218yes—
107#2418C2218yes—
108#2413C2218yes—
109C2×#398C2214yes—
110C2×#396C2214yes—
111#2370C2214yescomplemented
112#2370C2214yescomplemented
113#2353C2218yes—
114#2352C2218yes—
115Q8×C4⋊C4C2214yescomplemented
116D4×C4⋊C4C2218yes—
117D4×C4⋊C4C2214yescomplemented
118#2347C2214yescomplemented
119#2346C2214yescomplemented
120#2345C2218yes—
121#2345C2214yescomplemented
122#2344C2214yescomplemented
123#2330C2212yescomplemented
124#2330C2212yescomplemented
125#2324C2212yes—
126#2324C2212yes—
127#2323C2212yes—
128#2323C2212yes—
129#2322C2214yes—
130#2321C2214yes—
131#2320C2214yescomplemented
132#2319C2214yescomplemented
133#2317C2212yes—
134#2317C2212yes—
135#2317C2212yes—
136#2317C2214yescomplemented
137#2316C2212yes—
138#2316C2212yes—
139#2314C2211yescharacteristic
140#2314C2211yescharacteristic
141#2314C2212yes—
142#2314C2212yes—
143#2314C2211yescharacteristic
144#2314C2211yescharacteristic
145#2313C2214yes—
146#2312C2214yes—
147#2311C2212yes—
148C4×#125C2214yescomplemented
149#2298C2214yes—
150#2298C2214yes—
151#2297C2211yescharacteristic
152#2296C2211yescharacteristic
153#2295C2214yescomplemented
154#2293C2212yes—
155#2293C2212yes—
156#2293C2214yescomplemented
157C2×#389C2212yes—
158#2290C2212yes—
159#2290C2212yes—
160#2285C2211yescharacteristic
161#2285C2211yescharacteristic
162#2285C2212yescomplemented
163C2×#384C2211yescharacteristic
164C2×#384C2212yescomplemented
165#2280C2212yes—
166#2280C2211yescharacteristic
167C2×#380C2212yes—
168#2274C2212yes—
169C4×#117C2212yes—
170C4×#117C2211yescharacteristic
171C22×#41C2311yescharacteristic
172C24×C4C2311yescharacteristic
173C2×#126C2318yes—
174C2×#125—28no—
175C2×#125C2312yes—
176C2×#125C2314yes—
177C2×#125C2312yes—
178C2×#125C2318yes—
179C2×#125C2318yes—
180#525—28no—
181C2×#123C2312yes—
182C2×#123C2318yes—
183C2×C22⋊Q8C2311yescharacteristic
184C2×C22⋊Q8C2311yescharacteristic
185C2×#121C2311yescharacteristic
186C2×#121C2311yescharacteristic
187C2×#120C2312yes—
188#520—216no—
189C4×#41—28no—
190C2×C4×Q8C2312yes—
191C2×C4×Q8C2314yes—
192C2×C4×D4C2312yes—
193C2×C4×D4C2314yes—
194C2×C4×D4C2314yes—
195C2×C4×D4C2318yes—
196C2×C4×D4C2312yes—
197C2×C4×D4C2312yes—
198C2×#117—28no—
199C2×#117C2312yes—
200C2×#117C2311yescharacteristic
201C2×#117C2311yescharacteristic
202C2×#117C2311yescharacteristic
203C2×#117C2311yescharacteristic
204C2×#117C2311yescharacteristic
205C2×#117C2311yescharacteristic
206C2×#117C2312yes—
207C2×#117C2311yescharacteristic
208C2×#117C2312yes—
209C2×#117C2314yes—
210C2×#117C2312yes—
211C2×#117C2312yes—
212C2×#117C2318yes—
213C22×C4⋊C4C2312yes—
214C22×C4⋊C4C2312yes—
215C22×C4⋊C4C2312yes—
216C22×C4⋊C4C2314yes—
217C22×C4⋊C4C2314yes—
218C22×C4⋊C4C2314yes—
219C22×C4⋊C4C2318yes—
220C22×C4⋊C4C2314yes—
221C22×C22⋊C4C2312yes—
222C22×C22⋊C4C2314yes—
223C22×C42C2312yes—
224C22×C42C2311yescharacteristic
225C22×C42C2311yescharacteristic
226#401C2318yes—
227#400C2318yes—
228#400C2318yes—
229#400C2318yes—
230#400C2318yes—
231#400C2318yes—
232#400C2318yes—
233#400C2318yes—
234#400C2318yes—
235#400C2318yes—
236#400C2318yes—
237#399C2318yes—
238#398C2318yes—
239#398C2318yes—
240#398C2318yes—
241#398C2318yes—
242#398C2318yes—
243#398C2318yes—
244#398C2318yes—
245#398C2318yes—
246#398C2318yes—
247#398C2318yes—
248#398C2318yes—
249#398C2318yes—
250#398C2318yes—
251#397C2318yes—
252#397C2318yes—
253#397C2318yes—
254#397C2318yes—
255#397C2318yes—
256#397C2318yes—
257#396C2318yes—
258#396C2318yes—
259#396C2318yes—
260#396C2318yes—
261#396C2318yes—
262#396C2318yes—
263#396C2318yes—
264#394C2318yes—
265#394C2318yes—
266#391C2314yes—
267#391C2312yes—
268#390C2314yes—
269#390C2312yes—
270#390C2314yes—
271#390C2314yes—
272#389C2314yes—
273#389C2314yes—
274#389C2314yes—
275#389C2314yes—
276#389C2318yes—
277#389C2314yes—
278#389C2314yes—
279#389C2314yes—
280#389C2314yes—
281#389C2314yes—
282#389C2314yes—
283#389C2314yes—
284#389C2314yes—
285#389C2314yes—
286#389C2314yes—
287#389C2318yes—
288#389C2318yes—
289#389C2314yes—
290#389C2314yes—
291#389C2314yes—
292#389C2312yes—
293#389C2312yes—
294#389C2318yes—
295#389C2318yes—
296#389C2314yes—
297#389C2314yes—
298#389C2318yes—
299#389C2318yes—
300#389C2318yes—
301#389C2314yes—
302#388C2314yes—
303#388C2314yes—
304#388C2314yes—
305#388C2314yes—
306#388C2314yes—
307#388C2314yes—
308#388C2314yes—
309#388C2314yes—
310#388C2318yes—
311#388C2318yes—
312#388C2314yes—
313#388C2314yes—
314#388C2314yes—
315#388C2314yes—
316#388C2314yes—
317#388C2314yes—
318#388C2318yes—
319#388C2318yes—
320#388C2318yes—
321#388C2318yes—
322#388C2318yes—
323#388C2318yes—
324#388C2318yes—
325#387C2318yes—
326#387C2318yes—
327#387C2318yes—
328#387C2318yes—
329#387C2314yes—
330#387C2314yes—
331#387C2314yes—
332#387C2314yes—
333#387C2314yes—
334#387C2314yes—
335#387C2314yes—
336#387C2314yes—
337#387C2318yes—
338#387C2318yes—
339#387C2314yes—
340#387C2314yes—
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#386C2318yes—
355#386C2314yes—
356#386C2314yes—
357#386C2314yes—
358#386C2318yes—
359#385C2318yes—
360#385C2318yes—
361#385C2318yes—
362#385C2318yes—
363#385C2318yes—
364#385C2318yes—
365#385C2318yes—
366#385C2314yes—
367#385C2314yes—
368#385C2314yes—
369#385C2318yes—
370#384C2314yes—
371#384C2311yescharacteristic
372#384C2311yescharacteristic
373#384C2312yes—
374#384C2314yes—
375#384C2314yes—
376#384C2314yes—
377#384C2312yes—
378#384C2318yes—
379#384C2312yes—
380#383C2318yes—
381#383C2318yes—
382#382C2312yes—
383#382C2314yes—
384#382C2311yescharacteristic
385#382C2311yescharacteristic
386#382C2314yes—
387#382C2318yes—
388#382C2314yes—
389#382C2318yes—
390#382C2318yes—
391#381C2314yes—
392#381C2318yes—
393#381C2312yes—
394#381C2318yes—
395#380C2314yes—
396#380C2314yes—
397#380C2314yes—
398#380C2314yes—
399#380C2312yes—
400#380C2312yes—
401#380C2312yes—
402#380C2312yes—
403#380C2318yes—
404#380C2318yes—
405#380C2318yes—
406#380C2312yes—
407#380C2312yes—
408#380C2318yes—
409#380C2314yes—
410#380C2314yes—
411#380C2314yes—
412#380C2314yes—
413#379C2314yes—
414#379C2312yes—
415C4×C4⋊C4C2314yes—
416C4×C4⋊C4C2314yes—
417C4×C4⋊C4C2318yes—
418C4×C4⋊C4C2318yes—
419C4×C4⋊C4C2314yes—
420C4×C4⋊C4C2312yes—
421C4×C4⋊C4C2312yes—
422C4×C4⋊C4C2312yes—
423C4×C4⋊C4C2312yes—
424C4×C4⋊C4C2312yes—
425C4×C4⋊C4C2314yes—
426C4×C4⋊C4C2314yes—
427C4×C4⋊C4C2312yes—
428C4×C4⋊C4C2318yes—
429C4×C4⋊C4C2318yes—
430C4×C4⋊C4C2314yes—
431C4×C4⋊C4C2312yes—
432C4×C4⋊C4C2312yes—
433C4×C22⋊C4C2314yes—
434C4×C22⋊C4C2314yes—
435C4×C22⋊C4C2314yes—
436C4×C22⋊C4C2312yes—
437C4×C22⋊C4C2318yes—
438C4×C22⋊C4C2312yes—
439C4×C22⋊C4C2318yes—
440C4×C22⋊C4C2314yes—
441C4×C22⋊C4C2314yes—
442C4×C22⋊C4C2312yes—
443C4×C22⋊C4C2312yes—
444#376C2314yes—
445#376C2312yes—
446#376C2318yes—
447C2×#95C2314yes—
448C2×#95C2314yes—
449C43C2312yes—
450C43C2314yes—
451C25C2411yescharacteristic
452C2×#41—24no—
453C2×#41—24no—
454C2×#41#4118yes—
455C22×Q8C2411yescharacteristic
456C22×D4C2412yes—
457C22×D4C2411yescharacteristic
458C22×D4C2412yes—
459C22×D4C2412yes—
460C23×C4—24no—
461C23×C4—24no—
462C23×C4—24no—
463C23×C4C2411yescharacteristic
464C23×C4C2411yescharacteristic
465C23×C4C2411yescharacteristic
466C23×C4C2411yescharacteristic
467C23×C4C2411yescharacteristic
468C23×C4C2412yes—
469C23×C4C2414yes—
470C23×C4C2414yes—
471C23×C4C2412yes—
472C23×C4C2418yes—
473C23×C4C2414yes—
474C23×C4C2412yes—
475C23×C4C2411yescharacteristic
476#126—88no—
477#125—28no—
478#125—28no—
479#125—216no—
480#125—88no—
481#125—88no—
482#123—28no—
483#123—88no—
484C22⋊Q8—24no—
485C22⋊Q8—24no—
486#121—24no—
487#121—24no—
488#120—28no—
489C4×Q8—216no—
490C4×Q8—28no—
491C4×D4—232no—
492C4×D4—216no—
493C4×D4—216no—
494C4×D4—28no—
495C4×D4—28no—
496C4×D4—28no—
497#117—24no—
498#117—216no—
499#117—28no—
500#117—24no—
501#117—28no—
502#117—24no—
503#117—24no—
504#117—24no—
505#117—24no—
506#117—24no—
507#117—28no—
508#117—28no—
509#117—28no—
510#117—88no—
511C2×C4⋊C4—28no—
512C2×C4⋊C4—216no—
513C2×C4⋊C4—28no—
514C2×C4⋊C4—216no—
515C2×C4⋊C4—28no—
516C2×C4⋊C4—84no—
517C2×C4⋊C4—88no—
518C2×C4⋊C4—84no—
519C2×C4⋊C4C2412yes—
520C2×C4⋊C4C2414yes—
521C2×C4⋊C4C2412yes—
522C2×C4⋊C4C2412yes—
523C2×C4⋊C4C2412yes—
524C2×C4⋊C4C2412yes—
525C2×C4⋊C4C2414yes—
526C2×C4⋊C4C2418yes—
527C2×C4⋊C4C2414yes—
528C2×C4⋊C4C2414yes—
529C2×C4⋊C4C2418yes—
530C2×C4⋊C4C2418yes—
531C2×C4⋊C4C2412yes—
532C2×C4⋊C4C2412yes—
533C2×C4⋊C4C2414yes—
534C2×C4⋊C4C2411yescharacteristic
535C2×C4⋊C4C2411yescharacteristic
536C2×C4⋊C4C2412yes—
537C2×C4⋊C4C2412yes—
538C2×C4⋊C4C2412yes—
539C2×C4⋊C4C2412yes—
540C2×C4⋊C4C2412yes—
541C2×C4⋊C4C2414yes—
542C2×C4⋊C4C2418yes—
543C2×C4⋊C4C2418yes—
544C2×C4⋊C4C2418yes—
545C2×C4⋊C4C2418yes—
546C2×C4⋊C4C2418yes—
547C2×C4⋊C4C2418yes—
548C2×C4⋊C4C2418yes—
549C2×C4⋊C4C2418yes—
550C2×C4⋊C4C2418yes—
551C2×C4⋊C4C2414yes—
552C2×C4⋊C4C2414yes—
553C2×C4⋊C4C2418yes—
554C2×C4⋊C4C2418yes—
555C2×C4⋊C4C2418yes—
556C2×C4⋊C4C2414yes—
557C2×C4⋊C4C2414yes—
558C2×C4⋊C4C2418yes—
559C2×C4⋊C4C2414yes—
560C2×C4⋊C4C2418yes—
561C2×C22⋊C4—28no—
562C2×C22⋊C4—84no—
563C2×C22⋊C4C2412yes—
564C2×C22⋊C4C2412yes—
565C2×C22⋊C4C2412yes—
566C2×C22⋊C4C2412yes—
567C2×C22⋊C4C2414yes—
568C2×C22⋊C4C2412yes—
569C2×C22⋊C4C2418yes—
570C2×C22⋊C4C2414yes—
571C2×C22⋊C4C2412yes—
572C2×C22⋊C4C2412yes—
573C2×C22⋊C4C2414yes—
574C2×C22⋊C4C2412yes—
575C2×C22⋊C4C2412yes—
576C2×C22⋊C4C2412yes—
577C2×C22⋊C4C2412yes—
578C2×C22⋊C4C2418yes—
579C2×C22⋊C4C2418yes—
580C2×C22⋊C4C2414yes—
581C2×C22⋊C4C2418yes—
582C2×C22⋊C4C2414yes—
583C2×C22⋊C4C2414yes—
584C2×C22⋊C4C2414yes—
585C2×C22⋊C4C2414yes—
586C2×C22⋊C4C2414yes—
587C2×C22⋊C4C2414yes—
588C2×C22⋊C4C2414yes—
589C2×C22⋊C4C2418yes—
590C2×C42—24no—
591C2×C42—28no—
592C2×C42#4118yes—
593C2×C42C2412yes—
594C2×C42C2411yescharacteristic
595C2×C42C2411yescharacteristic
596C2×C42C2412yes—
597C2×C42C2412yes—
598C2×C42C2414yes—
599C2×C42C2418yes—
600C2×C42C2412yes—
601C2×C42C2414yes—
602C2×C42C2414yes—
603C2×C42C2414yes—
604C2×C42C2418yes—
605C2×C42C2414yes—
606C2×C42C2414yes—
607C2×C42C2414yes—
608C2×C42C2414yes—
609C2×C42C2414yes—
610C2×C42C2418yes—
611C2×C42C2411yescharacteristic
612C2×C42C2412yes—
613C2×C42C2411yescharacteristic
614#95C2418yes—
615#95C2418yes—
616#95C2418yes—
617#95C2418yes—
618#95C2414yes—
619#95C2414yes—
620#95C2414yes—
621#95C2414yes—
622#95C2414yes—
623#95C2414yes—
624#95C2414yes—
625#95C2418yes—
626#95C2418yes—
627#95C2418yes—
628#95C2418yes—
629#95C2414yes—
630#95C2414yes—
631#95C2414yes—
632#95C2414yes—
633#95C2414yes—
634#95C2414yes—
635#95C2414yes—
636#95C2418yes—
637#95C2414yes—
638#95C2414yes—
639#95C2418yes—
640#95C2418yes—
641#95C2414yes—
642#95C2414yes—
643#95C2418yes—
644#95C2418yes—
645#95C2418yes—
646#95C2414yes—
647#95C2414yes—
648#95C2418yes—
649#95C2418yes—
650#95C2418yes—
651#95C2418yes—
652C24—22no—
653C24—22no—
654C24—22no—
655C24—42no—
656C24—42no—
657C24C2511yescharacteristic
658C24C2511yescharacteristic
659C24C2512yes—
660C24C2511yescharacteristic
661#41—232no—
662C2×Q8—22no—
663C2×Q8—22no—
664C2×Q8C2×#4114yes—
665C2×D4—24no—
666C2×D4—24no—
667C2×D4—24no—
668C2×D4—24no—
669C2×D4—22no—
670C2×D4—22no—
671C2×D4—44no—
672C2×D4—44no—
673C2×D4C2×#4118yes—
674C2×D4C2×#4114yes—
675C22×C4—24no—
676C22×C4—24no—
677C22×C4—22no—
678C22×C4—22no—
679C22×C4—22no—
680C22×C4—24no—
681C22×C4—28no—
682C22×C4—216no—
683C22×C4—28no—
684C22×C4—28no—
685C22×C4—22no—
686C22×C4—22no—
687C22×C4—22no—
688C22×C4—22no—
689C22×C4—22no—
690C22×C4—22no—
691C22×C4—22no—
692C22×C4—22no—
693C22×C4—22no—
694C22×C4—22no—
695C22×C4—22no—
696C22×C4—22no—
697C22×C4—42no—
698C22×C4—44no—
699C22×C4—42no—
700C22×C4—44no—
701C22×C4—44no—
702C22×C4—44no—
703C22×C4—42no—
704C22×C4—44no—
705C22×C4—48no—
706C22×C4—48no—
707C22×C4—42no—
708C22×C4—44no—
709C22×C4—416no—
710C22×C4C2×#4118yes—
711C22×C4C2×#4118yes—
712C22×C4C2×#4114yes—
713C22×C4C2×#4114yes—
714C22×C42−1+414yes—
715C22×C4C2511yescharacteristic
716C22×C4C2511yescharacteristic
717C22×C4C2512yes—
718C22×C4C2514yes—
719C22×C4C2514yes—
720C22×C4C2514yes—
721C22×C4C2514yes—
722C22×C4C2512yes—
723C22×C4C2512yes—
724C22×C4C2514yes—
725C22×C4C2518yes—
726C22×C4C2514yes—
727C22×C4C2518yes—
728C22×C4C2512yes—
729C22×C4C2512yes—
730C22×C4C2512yes—
731C22×C4C2512yes—
732C22×C4C2511yescharacteristic
733C22×C4C2511yescharacteristic
734C4⋊C4—24no—
735C4⋊C4—28no—
736C4⋊C4—24no—
737C4⋊C4—24no—
738C4⋊C4—24no—
739C4⋊C4—24no—
740C4⋊C4—216no—
741C4⋊C4—28no—
742C4⋊C4—216no—
743C4⋊C4—216no—
744C4⋊C4—28no—
745C4⋊C4—28no—
746C4⋊C4—24no—
747C4⋊C4—28no—
748C4⋊C4—24no—
749C4⋊C4—22no—
750C4⋊C4—22no—
751C4⋊C4—24no—
752C4⋊C4—24no—
753C4⋊C4—24no—
754C4⋊C4—24no—
755C4⋊C4—24no—
756C4⋊C4—44no—
757C4⋊C4—48no—
758C4⋊C4—48no—
759C4⋊C4—48no—
760C4⋊C4—48no—
761C4⋊C4—48no—
762C4⋊C4—48no—
763C4⋊C4—44no—
764C4⋊C4—44no—
765C4⋊C4—44no—
766C4⋊C4—48no—
767C4⋊C4—48no—
768C4⋊C4—48no—
769C4⋊C4—48no—
770C4⋊C4—48no—
771C4⋊C4—44no—
772C4⋊C4—44no—
773C4⋊C4—48no—
774C4⋊C4—48no—
775C4⋊C4—48no—
776C22⋊C4—216no—
777C22⋊C4—28no—
778C22⋊C4—24no—
779C22⋊C4—24no—
780C22⋊C4—24no—
781C22⋊C4—24no—
782C22⋊C4—24no—
783C22⋊C4—28no—
784C22⋊C4—24no—
785C22⋊C4—24no—
786C22⋊C4—24no—
787C22⋊C4—24no—
788C22⋊C4—28no—
789C22⋊C4—24no—
790C22⋊C4—24no—
791C22⋊C4—48no—
792C22⋊C4—48no—
793C22⋊C4—44no—
794C22⋊C4—44no—
795C22⋊C4—44no—
796C22⋊C4—44no—
797C22⋊C4—48no—
798C22⋊C4—44no—
799C22⋊C4—48no—
800C22⋊C4—44no—
801C22⋊C4—44no—
802C22⋊C4—44no—
803C42—22no—
804C42—22no—
805C42—24no—
806C42—24no—
807C42—28no—
808C42—24no—
809C42—216no—
810C42—28no—
811C42—28no—
812C42—24no—
813C42—44no—
814C42—48no—
815C42—44no—
816C42—44no—
817C42—44no—
818C42—48no—
819C42—44no—
820C42—44no—
821C42C2×#4114yes—
822C42C2×#4114yes—
823C42C2×#4118yes—
824C23—22no—
825C23—22no—
826C23—22no—
827C23—22no—
828C23—24no—
829C23—24no—
830C23—21no—
831C23—21no—
832C23—21no—
833C23—21no—
834C23—21no—
835C23—21no—
836C23—22no—
837C23—22no—
838C23—22no—
839C23—22no—
840C23—48no—
841C23—44no—
842C23—84no—
843C23—82no—
844C23—82no—
845C23C22×#4114yes—
846C23C22×#4112yes—
847C23C22×#4112yes—
848C23C2×2−1+412yes—
849C23C2611yescharacteristic
850Q8—28no—
851D4—216no—
852D4—28no—
853D4—84no—
854D4—84no—
855C2×C4—22no—
856C2×C4—22no—
857C2×C4—22no—
858C2×C4—22no—
859C2×C4—22no—
860C2×C4—22no—
861C2×C4—216no—
862C2×C4—24no—
863C2×C4—24no—
864C2×C4—22no—
865C2×C4—22no—
866C2×C4—22no—
867C2×C4—22no—
868C2×C4—24no—
869C2×C4—28no—
870C2×C4—21no—
871C2×C4—21no—
872C2×C4—28no—
873C2×C4—21no—
874C2×C4—21no—
875C2×C4—24no—
876C2×C4—24no—
877C2×C4—24no—
878C2×C4—21no—
879C2×C4—21no—
880C2×C4—24no—
881C2×C4—24no—
882C2×C4—22no—
883C2×C4—22no—
884C2×C4—24no—
885C2×C4—28no—
886C2×C4—24no—
887C2×C4—24no—
888C2×C4—24no—
889C2×C4—28no—
890C2×C4—24no—
891C2×C4—28no—
892C2×C4—24no—
893C2×C4—24no—
894C2×C4—22no—
895C2×C4—22no—
896C2×C4—24no—
897C2×C4—24no—
898C2×C4—24no—
899C2×C4—28no—
900C2×C4—24no—
901C2×C4—24no—
902C2×C4—48no—
903C2×C4—416no—
904C2×C4—44no—
905C2×C4—44no—
906C2×C4—44no—
907C2×C4—44no—
908C2×C4—44no—
909C2×C4—84no—
910C2×C4—88no—
911C2×C4—88no—
912C2×C4—816no—
913C2×C4#552116yes—
914C2×C4C22×#4114yes—
915C2×C4C22×#4114yes—
916C2×C4C22×#4114yes—
917C2×C4C22×#4112yes—
918C2×C4C22×#4112yes—
919C2×C4C22×#4112yes—
920C2×C4C22×#4112yes—
921C2×C4C2×2−1+412yes—
922C2×C4C2×2−1+412yes—
923C22—24no—
924C22—22no—
925C22—22no—
926C22—24no—
927C22—24no—
928C22—24no—
929C22—24no—
930C22—44no—
931C22—44no—
932C22—42no—
933C22—42no—
934C22—41no—
935C22—41no—
936C22—41no—
937C22—41no—
938C22—42no—
939C22—42no—
940C22—41no—
941C22—41no—
942C22—88no—
943C22C2×#55214yes—
944C22C23×#4111yescharacteristic
945C22C23×#4111yescharacteristic
946C22C22×2−1+411yescharacteristic
947C22H(7,𝔽2)12yes—
948C222−1+612yes—
949C4—24no—
950C4—24no—
951C4—24no—
952C4—44no—
953C4—42no—
954C4—42no—
955C4—48no—
956C4—44no—
957C4—48no—
958C4—42no—
959C4—44no—
960C4—42no—
961C4—44no—
962C4—44no—
963C4—44no—
964C4—41no—
965C4—41no—
966C4C2×#55214yes—
967C4C2×#55214yes—
968C2—24no—
969C2—44no—
970C2—81no—
971C2—81no—
972C2C22×#55211yescharacteristic
973C2#6285612yes—
974C2#6285811yescharacteristic
975C2#6286111yescharacteristic
976C2#6287712yes—
subgroupG/H
center, commutator, Frattini, socle, cosocleC23C26
prime radicalC2×#525C22
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23 ◁ G
LECSG ▷ C23 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #43939C2semidirect
2. #43057C2semidirect
3. #39547C2semidirect
4. #39546C2semidirect
5. #38279C2semidirect
6. #38278C2semidirect
7. #38275C2semidirect
8. #38274C2semidirect
9. #37889C2semidirect
10. #37888C2semidirect
11. #37883C2semidirect
12. #37882C2semidirect
13. #35544C2semidirect
15. #35333C2semidirect
16. #35286C2semidirect
17. #35265C2semidirect
18. C2×#2629C2semidirect
19. #34253C2semidirect
20. #34217C2semidirect
21. #34183C2semidirect
23. #34048C2semidirect
29. #2864C22semidirect
30. #2859C22semidirect
31. #2859C22semidirect
32. #2851C22semidirect
33. #2851C22semidirect
34. #2794C22semidirect
36. #2791C22semidirect
37. #2787C22semidirect
42. #2770C22semidirect
43. #2766C22semidirect
44. #2765C22semidirect
46. #2739C22semidirect
48. #2719C22semidirect
50. #2647C22semidirect
51. #2647C22semidirect
52. #2647C22semidirect
53. #2647C22semidirect
60. #2629C22semidirect
61. #2606C22semidirect
63. #2590C22semidirect
65. #2571C22semidirect
66. #2566C22semidirect
67. #2565C22semidirect
69. #2552C22semidirect
72. #2528C22semidirect
74. #2524C22semidirect
76. #2515C22semidirect
77. #2509C22semidirect
78. #2508C22semidirect
79. #2507C22semidirect
80. #2506C22semidirect
95. #2484C22semidirect
98. #2475C22semidirect
100. #2473C22semidirect
111. #2370C22semidirect
112. #2370C22semidirect
115. Q8×C4⋊C4C22semidirect
117. D4×C4⋊C4C22semidirect
118. #2347C22semidirect
119. #2346C22semidirect
121. #2345C22semidirect
122. #2344C22semidirect
123. #2330C22semidirect
124. #2330C22semidirect
131. #2320C22semidirect
132. #2319C22semidirect
136. #2317C22semidirect
148. C4×#125C22semidirect
153. #2295C22semidirect
156. #2293C22semidirect
162. #2285C22semidirect
164. C2×#384C22semidirect

Maximal subgroups

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

subgroupindex
#439392
#430572
#395472
#395462
#382792
#382782
#382752
#382742
#378892
#378882
#378832
#378822
#355442
#355162
#353332
#352862
#352652
C2×#26292
#342532
#342172
#341832
#340652
#340482