Finite Group Databasebeta

← #7642470

Subgroups — #7642470

Order 512.

4766 conjugacy classes of subgroups.

The subgroup lattice has 935 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#39819C214yesmaximal, complemented
2#39691C214yesmaximal, complemented
3#39677C214yesmaximal, complemented
4#39541C214yesmaximal, complemented
5#37981C214yesmaximal, complemented
6#37956C214yesmaximal
7#37933C214yesmaximal
8#37793C214yesmaximal, complemented
9#36834C214yesmaximal, complemented
10#36829C214yesmaximal, complemented
11#36625C212yesmaximal
12#35444C214yesmaximal, complemented
13#35434C214yesmaximal, complemented
14#35325C212yesmaximal
15#35310C212yesmaximal
16#35173C211yesmaximal, characteristic, complemented
17#35104C211yesmaximal, characteristic, complemented
18#35087C212yesmaximal, complemented
19#35015C212yesmaximal, complemented
20#34235C212yesmaximal, complemented
21C2×#2296C211yesmaximal, characteristic
22C2×#541C2212yes—
23C2×#533C2212yes—
24C2×#533C2212yes—
25C22×#117C2211yescharacteristic
26C22×#117C2211yescharacteristic
27C23×C42C2211yescharacteristic
28#2857C2212yes—
29#2857C2212yes—
30#2857C2212yes—
31#2857C2212yes—
32#2857C2212yes—
33#2855C2214yes—
34#2855C2214yes—
35#2855C2214yes—
36#2851C2212yes—
37#2851C2214yes—
38#2851C2214yes—
39#2848C2214yes—
40#2848C2214yes—
41#2806C2218yescomplemented
42#2802C2218yescomplemented
43#2788C2218yes—
44#2787C2218yes—
45#2776C2218yescomplemented
46#2774C2218yescomplemented
47#2774C2218yescomplemented
48#2770C2218yes—
49#2768C2218yes—
50#2766C2218yescomplemented
51#2745C2218yes—
52#2738C2218yes—
53#2726C2218yescomplemented
54#2719C2218yescomplemented
55#2698C2218yes—
56#2689C2218yes—
57#2659C2214yes—
58#2655C2218yescomplemented
59#2646C2214yes—
60#2629C2212yes—
61#2628C2212yes—
62#2628C2212yes—
63#2627C2214yes—
64#2627C2214yes—
65#2625C2214yes—
66#2621C2212yes—
67#2621C2212yes—
68#2621C2212yes—
69#2611C2218yes—
70#2611C2214yes—
71#2611C2214yes—
72#2606C2214yescomplemented
73#2606C2218yescomplemented
74#2605C2214yescomplemented
75#2599C2218yes—
76#2599C2214yes—
77#2599C2214yes—
78#2590C2218yescomplemented
79#2590C2218yescomplemented
80#2590C2218yescomplemented
81#2588C2218yescomplemented
82#2584C2218yescomplemented
83#2584C2214yescomplemented
84#2584C2214yescomplemented
85#2583C2214yes—
86#2577C2218yes—
87#2570C2214yescomplemented
88#2567C2214yescomplemented
89#2561C2214yes—
90#2556C2218yes—
91#2550C2214yescomplemented
92#2546C2214yescomplemented
93#2533C2218yescomplemented
94#2530C2218yes—
95#2514C2214yescomplemented
96#2511C2214yescomplemented
97#2507C2214yescomplemented
98#2506C2214yescomplemented
99#2493C2218yes—
100#2484C2214yes—
101#2482C2214yes—
102#2480C2218yes—
103#2478C2218yes—
104#2478C2218yes—
105#2478C2218yes—
106#2475C2218yes—
107#2473C2218yes—
108#2473C2218yes—
109#2465C2218yes—
110#2462C2218yescomplemented
111#2462C2218yescomplemented
112#2453C2214yescomplemented
113#2453C2218yescomplemented
114#2451C2214yescomplemented
115#2446C2214yescomplemented
116#2446C2214yescomplemented
117#2365C2214yescomplemented
118#2365C2214yescomplemented
119#2360C2218yes—
120#2356C2214yescomplemented
121#2351C2214yescomplemented
122#2343C2218yes—
123#2336C2218yescomplemented
124#2336C2214yescomplemented
125#2336C2214yescomplemented
126#2329C2214yes—
127#2329C2214yes—
128#2323C2214yes—
129#2323C2214yes—
130#2323C2214yes—
131#2320C2214yescomplemented
132#2316C2214yes—
133#2314C2212yes—
134#2313C2214yes—
135C4×C22⋊Q8C2214yes—
136C4×C22⋊Q8C2214yes—
137C4×C22⋊Q8C2214yes—
138C4×C22⋊Q8C2214yes—
139C4×C22⋊Q8C2214yes—
140#2296C2214yes—
141#2296C2214yes—
142#2296C2214yes—
143#2296C2212yes—
144#2296C2212yes—
145#2296C2212yes—
146#2296C2212yes—
147C2×#389C2212yes—
148C2×#389C2212yes—
149C2×#385C2212yes—
150C2×#385C2212yes—
151#2285C2212yes—
152#2283C2212yes—
153#2280C2214yes—
154#2276C2214yescomplemented
155C2×C4×C4⋊C4C2211yescharacteristic
156C2×C4×C4⋊C4C2211yescharacteristic
157C2×C4×C4⋊C4C2211yescharacteristic
158C2×C4×C4⋊C4C2211yescharacteristic
159C24×C4C2311yescharacteristic
160C24×C4C2312yes—
161#541—48no—
162#533—216no—
163#533—48no—
164C2×C4⋊Q8C2312yes—
165C2×C4⋊Q8C2312yes—
166C2×C4⋊Q8C2312yes—
167C2×C4⋊Q8C2312yes—
168C2×C4⋊Q8C2312yes—
169C2×#126C2318yes—
170C2×#125C2314yes—
171C2×#125C2318yes—
172C2×#125C2314yes—
173C2×#125C2312yes—
174C2×#125C2318yes—
175C2×C22⋊Q8C2314yes—
176C2×C22⋊Q8C2314yes—
177C2×C22⋊Q8C2314yes—
178C2×C22⋊Q8C2314yes—
179C2×C22⋊Q8C2314yes—
180C2×C22⋊Q8C2314yes—
181C2×C22⋊Q8C2314yes—
182C2×C4×Q8C2314yes—
183C2×C4×Q8C2314yes—
184C2×C4×Q8C2314yes—
185C2×C4×Q8C2318yes—
186C2×C4×Q8C2314yes—
187C2×C4×Q8C2314yes—
188C2×#117—28no—
189C2×#117—44no—
190C2×#117C2312yes—
191C2×#117C2314yes—
192C2×#117C2312yes—
193C2×#117C2312yes—
194C2×#117C2312yes—
195C2×#117C2312yes—
196C2×#117C2312yes—
197C2×#117C2314yes—
198C2×#117C2312yes—
199C2×#117C2312yes—
200C2×#117C2314yes—
201C22×C4⋊C4C2312yes—
202C22×C4⋊C4C2312yes—
203C22×C4⋊C4C2311yescharacteristic
204C22×C4⋊C4C2311yescharacteristic
205C22×C4⋊C4C2312yes—
206C22×C4⋊C4C2312yes—
207C22×C4⋊C4C2312yes—
208C22×C22⋊C4C2311yescharacteristic
209C22×C22⋊C4C2311yescharacteristic
210C22×C22⋊C4C2312yes—
211C22×C42—44no—
212C22×C42C2311yescharacteristic
213C22×C42C2312yes—
214C22×C42C2311yescharacteristic
215C22×C42C2311yescharacteristic
216C22×C42C2312yes—
217C22×C42C2311yescharacteristic
218C22×C42C2311yescharacteristic
219C22×C42C2312yes—
220C22×C42C2311yescharacteristic
221C22×C42C2311yescharacteristic
222C22×C42C2311yescharacteristic
223C22×C42C2311yescharacteristic
224C22×C42C2311yescharacteristic
225#401C2318yes—
226#400C2318yes—
227#400C2318yes—
228#400C2318yes—
229#400C2314yes—
230#400C2318yes—
231#400C2314yes—
232#400C2318yes—
233#400C2318yes—
234#400C2318yes—
235#400C2318yes—
236#400C2318yes—
237#399C2314yes—
238#399C2314yes—
239#398C2318yes—
240#398C2318yes—
241#398C2314yes—
242#398C2314yes—
243#398C2318yes—
244#398C2318yes—
245#398C2318yes—
246#398C2318yes—
247#398C2318yes—
248#398C2318yes—
249#398C2318yes—
250#398C2318yes—
251#398C2314yes—
252#398C2314yes—
253#398C2318yes—
254#398C2318yes—
255#398C2318yes—
256#398C2318yes—
257#397C2314yes—
258#397C2314yes—
259#397C2318yes—
260#397C2318yes—
261#397C2314yes—
262#397C2314yes—
263#397C2318yes—
264#396C2318yes—
265#395C2318yes—
266#395C2318yes—
267#395C2314yes—
268#395C2314yes—
269#395C2318yes—
270#395C2318yes—
271#393C2314yes—
272#393C2314yes—
273#391C2314yes—
274#391C2314yes—
275#391C2318yes—
276#391C2314yes—
277#391C2314yes—
278#391C2318yes—
279#391C2318yes—
280#391C2314yes—
281#391C2314yes—
282#391C2314yes—
283#391C2314yes—
284#389C2318yes—
285#389C2318yes—
286#389C2314yes—
287#389C2314yes—
288#389C2318yes—
289#389C2318yes—
290#389C2318yes—
291#389C2318yes—
292#389C2318yes—
293#389C2318yes—
294#389C2314yes—
295#389C2314yes—
296#389C2314yes—
297#389C2314yes—
298#389C2314yes—
299#389C2314yes—
300#389C2318yes—
301#389C2318yes—
302#389C2318yes—
303#389C2318yes—
304#389C2318yes—
305#389C2314yes—
306#389C2314yes—
307#389C2314yes—
308#389C2318yes—
309#389C2314yes—
310#389C2314yes—
311#389C2314yes—
312#389C2314yes—
313#389C2314yes—
314#389C2314yes—
315#389C2314yes—
316#389C2314yes—
317#389C2314yes—
318#388C2318yes—
319#388C2318yes—
320#388C2318yes—
321#388C2318yes—
322#388C2318yes—
323#388C2318yes—
324#388C2318yes—
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#387C2318yes—
356#385C2314yes—
357#385C2318yes—
358#385C2318yes—
359#385C2318yes—
360#385C2318yes—
361#385C2318yes—
362#385C2318yes—
363#385C2318yes—
364#385C2318yes—
365#385C2318yes—
366#385C2314yes—
367#385C2314yes—
368#385C2314yes—
369#385C2314yes—
370#385C2314yes—
371#385C2314yes—
372#385C2314yes—
373#384C2312yes—
374#384C2312yes—
375#384C2312yes—
376#383C2318yes—
377#383C2318yes—
378#383C2314yes—
379#382C2312yes—
380#382C2312yes—
381#382C2318yes—
382#382C2314yes—
383#382C2312yes—
384#381C2318yes—
385#381C2314yes—
386#381C2318yes—
387#380C2314yes—
388#380C2314yes—
389#380C2314yes—
390#380C2314yes—
391#380C2318yes—
392#380C2314yes—
393#380C2314yes—
394#380C2314yes—
395#380C2314yes—
396#380C2314yes—
397#380C2314yes—
398#379C2318yes—
399C4×C4⋊C4C2314yes—
400C4×C4⋊C4C2314yes—
401C4×C4⋊C4C2314yes—
402C4×C4⋊C4C2312yes—
403C4×C4⋊C4C2318yes—
404C4×C4⋊C4C2312yes—
405C4×C4⋊C4C2312yes—
406C4×C4⋊C4C2318yes—
407C4×C4⋊C4C2312yes—
408C4×C4⋊C4C2318yes—
409C4×C4⋊C4C2312yes—
410C4×C4⋊C4C2318yes—
411C4×C4⋊C4C2312yes—
412C4×C4⋊C4C2318yes—
413C4×C4⋊C4C2312yes—
414C4×C4⋊C4C2314yes—
415C4×C4⋊C4C2314yes—
416C4×C4⋊C4C2312yes—
417C4×C4⋊C4C2314yes—
418C4×C4⋊C4C2314yes—
419C4×C4⋊C4C2314yes—
420C4×C22⋊C4C2314yes—
421C4×C22⋊C4C2318yes—
422C4×C22⋊C4C2318yes—
423C4×C22⋊C4C2318yes—
424#376C2314yes—
425#376C2318yes—
426C2×#95C2312yes—
427C2×#95C2312yes—
428C2×#95C2312yes—
429C2×#95C2312yes—
430C25C2411yescharacteristic
431C22×Q8C2414yes—
432C22×Q8C2414yes—
433C22×Q8C2414yes—
434C23×C4—24no—
435C23×C4—24no—
436C23×C4—24no—
437C23×C4—28no—
438C23×C4—44no—
439C23×C4—44no—
440C23×C4C2411yescharacteristic
441C23×C4C2411yescharacteristic
442C23×C4C2412yes—
443C23×C4C2411yescharacteristic
444C23×C4C2411yescharacteristic
445C23×C4C2412yes—
446C23×C4C2412yes—
447C23×C4C2412yes—
448C23×C4C2411yescharacteristic
449C23×C4C2411yescharacteristic
450C23×C4C2411yescharacteristic
451C23×C4C2411yescharacteristic
452C23×C4C2412yes—
453C23×C4C2412yes—
454C23×C4C2411yescharacteristic
455C23×C4C2412yes—
456C23×C4C2411yescharacteristic
457C23×C4C2412yes—
458C4⋊Q8—28no—
459C4⋊Q8—28no—
460C4⋊Q8—44no—
461C4⋊Q8—44no—
462C4⋊Q8—44no—
463#126—416no—
464#125—216no—
465#125—416no—
466#125—48no—
467#125—44no—
468#125—416no—
469C22⋊Q8—216no—
470C22⋊Q8—216no—
471C22⋊Q8—216no—
472C22⋊Q8—216no—
473C22⋊Q8—216no—
474C22⋊Q8—48no—
475C22⋊Q8—48no—
476C4×Q8—216no—
477C4×Q8—216no—
478C4×Q8—416no—
479C4×Q8—48no—
480C4×Q8—48no—
481C4×Q8—48no—
482#117—216no—
483#117—28no—
484#117—28no—
485#117—28no—
486#117—28no—
487#117—28no—
488#117—44no—
489#117—48no—
490#117—44no—
491#117—48no—
492#117—44no—
493C2×C4⋊C4—24no—
494C2×C4⋊C4—24no—
495C2×C4⋊C4—28no—
496C2×C4⋊C4—28no—
497C2×C4⋊C4—44no—
498C2×C4⋊C4—44no—
499C2×C4⋊C4—44no—
500C2×C4⋊C4C2414yes—
501C2×C4⋊C4C2412yes—
502C2×C4⋊C4C2412yes—
503C2×C4⋊C4C2412yes—
504C2×C4⋊C4C2412yes—
505C2×C4⋊C4C2414yes—
506C2×C4⋊C4C2414yes—
507C2×C4⋊C4C2414yes—
508C2×C4⋊C4C2414yes—
509C2×C4⋊C4C2414yes—
510C2×C4⋊C4C2414yes—
511C2×C4⋊C4C2414yes—
512C2×C4⋊C4C2414yes—
513C2×C4⋊C4C2414yes—
514C2×C4⋊C4C2418yes—
515C2×C4⋊C4C2418yes—
516C2×C4⋊C4C2418yes—
517C2×C4⋊C4C2418yes—
518C2×C4⋊C4C2414yes—
519C2×C4⋊C4C2414yes—
520C2×C4⋊C4C2414yes—
521C2×C4⋊C4C2414yes—
522C2×C4⋊C4C2418yes—
523C2×C4⋊C4C2418yes—
524C2×C4⋊C4C2414yes—
525C2×C4⋊C4C2414yes—
526C2×C4⋊C4C2414yes—
527C2×C4⋊C4C2414yes—
528C2×C4⋊C4C2414yes—
529C2×C4⋊C4C2414yes—
530C2×C4⋊C4C2414yes—
531C2×C4⋊C4C2418yes—
532C2×C4⋊C4C2414yes—
533C2×C4⋊C4C2418yes—
534C2×C4⋊C4C2418yes—
535C2×C4⋊C4C2414yes—
536C2×C4⋊C4C2418yes—
537C2×C4⋊C4C2418yes—
538C2×C4⋊C4C2418yes—
539C2×C4⋊C4C2418yes—
540C2×C4⋊C4C2418yes—
541C2×C4⋊C4C2418yes—
542C2×C22⋊C4—24no—
543C2×C22⋊C4—24no—
544C2×C22⋊C4—44no—
545C2×C22⋊C4C2414yes—
546C2×C22⋊C4C2412yes—
547C2×C22⋊C4C2412yes—
548C2×C22⋊C4C2412yes—
549C2×C22⋊C4C2412yes—
550C2×C22⋊C4C2418yes—
551C2×C22⋊C4C2418yes—
552C2×C22⋊C4C2418yes—
553C2×C22⋊C4C2418yes—
554C2×C22⋊C4C2414yes—
555C2×C22⋊C4C2418yes—
556C2×C22⋊C4C2418yes—
557C2×C42—24no—
558C2×C42—28no—
559C2×C42—42no—
560C2×C42—42no—
561C2×C42—42no—
562C2×C42—42no—
563C2×C42—44no—
564C2×C42—44no—
565C2×C42—42no—
566C2×C42—42no—
567C2×C42—42no—
568C2×C42—42no—
569C2×C42#4118yes—
570C2×C42C2412yes—
571C2×C42C2412yes—
572C2×C42C2412yes—
573C2×C42C2412yes—
574C2×C42C2418yes—
575C2×C42C2418yes—
576C2×C42C2412yes—
577C2×C42C2412yes—
578C2×C42C2412yes—
579C2×C42C2412yes—
580C2×C42C2412yes—
581C2×C42C2412yes—
582C2×C42C2418yes—
583C2×C42C2418yes—
584C2×C42C2418yes—
585C2×C42C2418yes—
586C2×C42C2411yescharacteristic
587C2×C42C2411yescharacteristic
588C2×C42C2411yescharacteristic
589C2×C42C2412yes—
590C2×C42C2411yescharacteristic
591C2×C42C2412yes—
592C2×C42C2412yes—
593C2×C42C2412yes—
594#95C2414yes—
595#95C2414yes—
596#95C2414yes—
597#95C2414yes—
598#95C2414yes—
599#95C2414yes—
600#95C2414yes—
601#95C2414yes—
602#95C2414yes—
603#95C2418yes—
604#95C2418yes—
605#95C2414yes—
606#95C2418yes—
607#95C2418yes—
608#95C2418yes—
609#95C2418yes—
610#95C2418yes—
611#95C2414yes—
612#95C2414yes—
613#95C2418yes—
614#95C2418yes—
615#95C2418yes—
616#95C2418yes—
617#95C2418yes—
618#95C2418yes—
619#95C2418yes—
620#95C2418yes—
621#95C2418yes—
622#95C2418yes—
623#95C2418yes—
624#95C2418yes—
625#95C2418yes—
626#95C2418yes—
627#95C2418yes—
628#95C2418yes—
629#95C2418yes—
630#95C2418yes—
631C24—22no—
632C24—22no—
633C24—22no—
634C24—24no—
635C24—42no—
636C24C2511yescharacteristic
637C24C2511yescharacteristic
638C24C2511yescharacteristic
639C2×Q8—28no—
640C2×Q8—28no—
641C2×Q8—28no—
642C2×Q8—28no—
643C2×Q8—28no—
644C2×Q8—48no—
645C2×Q8—44no—
646C2×Q8—44no—
647C22×C4—232no—
648C22×C4—22no—
649C22×C4—24no—
650C22×C4—22no—
651C22×C4—24no—
652C22×C4—22no—
653C22×C4—22no—
654C22×C4—22no—
655C22×C4—22no—
656C22×C4—22no—
657C22×C4—22no—
658C22×C4—22no—
659C22×C4—22no—
660C22×C4—22no—
661C22×C4—22no—
662C22×C4—22no—
663C22×C4—24no—
664C22×C4—22no—
665C22×C4—22no—
666C22×C4—24no—
667C22×C4—22no—
668C22×C4—22no—
669C22×C4—24no—
670C22×C4—24no—
671C22×C4—24no—
672C22×C4—24no—
673C22×C4—24no—
674C22×C4—24no—
675C22×C4—24no—
676C22×C4—24no—
677C22×C4—24no—
678C22×C4—24no—
679C22×C4—42no—
680C22×C4—42no—
681C22×C4—42no—
682C22×C4—42no—
683C22×C4—42no—
684C22×C4—42no—
685C22×C4—42no—
686C22×C4—42no—
687C22×C4—42no—
688C22×C4—42no—
689C22×C4—42no—
690C22×C4—42no—
691C22×C4—42no—
692C22×C4—432no—
693C22×C4C2×#4114yes—
694C22×C4C2×#4114yes—
695C22×C4C2×#4114yes—
696C22×C4H(5,𝔽2)14yes—
697C22×C42−1+414yes—
698C22×C42−1+418yes—
699C22×C4C2512yes—
700C22×C4C2518yes—
701C22×C4C2512yes—
702C22×C4C2514yes—
703C22×C4C2518yes—
704C22×C4C2518yes—
705C22×C4C2518yes—
706C22×C4C2512yes—
707C22×C4C2514yes—
708C22×C4C2512yes—
709C22×C4C2511yescharacteristic
710C22×C4C2512yes—
711C22×C4C2511yescharacteristic
712C22×C4C2512yes—
713C22×C4C2511yescharacteristic
714C22×C4C2512yes—
715C22×C4C2512yes—
716C22×C4C2511yescharacteristic
717C4⋊C4—24no—
718C4⋊C4—24no—
719C4⋊C4—24no—
720C4⋊C4—24no—
721C4⋊C4—28no—
722C4⋊C4—28no—
723C4⋊C4—216no—
724C4⋊C4—216no—
725C4⋊C4—28no—
726C4⋊C4—28no—
727C4⋊C4—28no—
728C4⋊C4—28no—
729C4⋊C4—216no—
730C4⋊C4—28no—
731C4⋊C4—28no—
732C4⋊C4—28no—
733C4⋊C4—28no—
734C4⋊C4—28no—
735C4⋊C4—28no—
736C4⋊C4—216no—
737C4⋊C4—216no—
738C4⋊C4—28no—
739C4⋊C4—28no—
740C4⋊C4—216no—
741C4⋊C4—44no—
742C4⋊C4—44no—
743C4⋊C4—44no—
744C4⋊C4—44no—
745C4⋊C4—44no—
746C4⋊C4—44no—
747C4⋊C4—44no—
748C4⋊C4—48no—
749C4⋊C4—48no—
750C4⋊C4—44no—
751C4⋊C4—48no—
752C4⋊C4—44no—
753C4⋊C4—48no—
754C4⋊C4—48no—
755C4⋊C4—48no—
756C4⋊C4—48no—
757C4⋊C4—48no—
758C4⋊C4—48no—
759C22⋊C4—216no—
760C22⋊C4—28no—
761C22⋊C4—216no—
762C22⋊C4—216no—
763C22⋊C4—216no—
764C22⋊C4—24no—
765C22⋊C4—24no—
766C22⋊C4—24no—
767C22⋊C4—24no—
768C22⋊C4—44no—
769C22⋊C4—48no—
770C22⋊C4—48no—
771C42—24no—
772C42—24no—
773C42—216no—
774C42—24no—
775C42—24no—
776C42—24no—
777C42—24no—
778C42—24no—
779C42—24no—
780C42—216no—
781C42—41no—
782C42—42no—
783C42—41no—
784C42—41no—
785C42—42no—
786C42—41no—
787C42—42no—
788C42—42no—
789C42—48no—
790C42—48no—
791C42—48no—
792C42—48no—
793C42C2×#4118yes—
794C42C2×#4118yes—
795C23—21no—
796C23—21no—
797C23—22no—
798C23—28no—
799C23—21no—
800C23—21no—
801C23—21no—
802C23—21no—
803C23—22no—
804C23—22no—
805C23—22no—
806C23—22no—
807C23—48no—
808C23—48no—
809C23—44no—
810C23—44no—
811C23C22×#4112yes—
812C23C2×H(5,𝔽2)12yes—
813C23C2×2−1+412yes—
814C23C2×2−1+414yes—
815C23C2611yescharacteristic
816Q8—416no—
817Q8—416no—
818Q8—88no—
819C2×C4—28no—
820C2×C4—28no—
821C2×C4—28no—
822C2×C4—216no—
823C2×C4—21no—
824C2×C4—21no—
825C2×C4—22no—
826C2×C4—22no—
827C2×C4—22no—
828C2×C4—21no—
829C2×C4—21no—
830C2×C4—24no—
831C2×C4—21no—
832C2×C4—21no—
833C2×C4—22no—
834C2×C4—24no—
835C2×C4—22no—
836C2×C4—22no—
837C2×C4—28no—
838C2×C4—28no—
839C2×C4—28no—
840C2×C4—28no—
841C2×C4—22no—
842C2×C4—22no—
843C2×C4—28no—
844C2×C4—28no—
845C2×C4—22no—
846C2×C4—24no—
847C2×C4—24no—
848C2×C4—28no—
849C2×C4—28no—
850C2×C4—28no—
851C2×C4—28no—
852C2×C4—28no—
853C2×C4—28no—
854C2×C4—24no—
855C2×C4—24no—
856C2×C4—24no—
857C2×C4—22no—
858C2×C4—28no—
859C2×C4—28no—
860C2×C4—24no—
861C2×C4—28no—
862C2×C4—28no—
863C2×C4—24no—
864C2×C4—24no—
865C2×C4—22no—
866C2×C4—48no—
867C2×C4—44no—
868C2×C4—48no—
869C2×C4—48no—
870C2×C4—48no—
871C2×C4—48no—
872C2×C4—44no—
873C2×C4—44no—
874C2×C4—84no—
875C2×C4—84no—
876C2×C4C22×#4114yes—
877C2×C4C22×#4112yes—
878C2×C4C22×#4114yes—
879C2×C4C22×#4112yes—
880C2×C4C2×H(5,𝔽2)12yes—
881C2×C4C2×H(5,𝔽2)12yes—
882C2×C4C2×2−1+412yes—
883C2×C4C2×2−1+414yes—
884C2×C4C2×2−1+414yes—
885C2×C4C2×2−1+412yes—
886C2×C4#58514yes—
887C22—22no—
888C22—24no—
889C22—24no—
890C22—22no—
891C22—22no—
892C22—22no—
893C22—24no—
894C22—24no—
895C22—416no—
896C22—41no—
897C22—41no—
898C22—42no—
899C22—42no—
900C22—41no—
901C22—41no—
902C22#350914yes—
903C22C23×#4111yescharacteristic
904C22C22×H(5,𝔽2)11yescharacteristic
905C22C22×2−1+411yescharacteristic
906C22C22×2−1+412yes—
907C22C2×#58512yes—
908C4—22no—
909C4—22no—
910C4—22no—
911C4—24no—
912C4—24no—
913C4—24no—
914C4—24no—
915C4—24no—
916C4—48no—
917C4—42no—
918C4—42no—
919C4—44no—
920C4—44no—
921C4—48no—
922C4—48no—
923C4—42no—
924C4—48no—
925C4#349214yes—
926C2—24no—
927C2—42no—
928C2—42no—
929C2#6268611yescharacteristic
930C2C2×#349211yescharacteristic
931C2C2×#350911yescharacteristic
932C2#6281912yes—
933C2#6283712yes—
subgroupG/H
center, commutator, Frattini, socle, cosocleC23C26
prime radicalC25C24
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23 ◁ G
LECSG ▷ C23 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #39819C2semidirect
2. #39691C2semidirect
3. #39677C2semidirect
4. #39541C2semidirect
5. #37981C2semidirect
8. #37793C2semidirect
9. #36834C2semidirect
10. #36829C2semidirect
12. #35444C2semidirect
13. #35434C2semidirect
16. #35173C2semidirect
17. #35104C2semidirect
18. #35087C2semidirect
19. #35015C2semidirect
20. #34235C2semidirect
41. #2806C22semidirect
42. #2802C22semidirect
45. #2776C22semidirect
46. #2774C22semidirect
47. #2774C22semidirect
50. #2766C22semidirect
53. #2726C22semidirect
54. #2719C22semidirect
58. #2655C22semidirect
72. #2606C22semidirect
73. #2606C22semidirect
74. #2605C22semidirect
78. #2590C22semidirect
79. #2590C22semidirect
80. #2590C22semidirect
81. #2588C22semidirect
82. #2584C22semidirect
83. #2584C22semidirect
84. #2584C22semidirect
87. #2570C22semidirect
88. #2567C22semidirect
91. #2550C22semidirect
92. #2546C22semidirect
93. #2533C22semidirect
95. #2514C22semidirect
96. #2511C22semidirect
97. #2507C22semidirect
98. #2506C22semidirect
110. #2462C22semidirect
111. #2462C22semidirect
112. #2453C22semidirect
113. #2453C22semidirect
114. #2451C22semidirect
115. #2446C22semidirect
116. #2446C22semidirect
117. #2365C22semidirect
118. #2365C22semidirect
120. #2356C22semidirect
121. #2351C22semidirect
123. #2336C22semidirect
124. #2336C22semidirect
125. #2336C22semidirect
131. #2320C22semidirect
154. #2276C22semidirect

Maximal subgroups

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

subgroupindex
#398192
#396912
#396772
#395412
#379812
#379562
#379332
#377932
#368342
#368292
#366252
#354442
#354342
#353252
#353102
#351732
#351042
#350872
#350152
#342352
C2×#22962