Finite Group Databasebeta

← #7715682

Subgroups — #7715682

Order 512.

4404 conjugacy classes of subgroups.

The subgroup lattice has 883 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#50184C214yesmaximal, complemented
2#50183C214yesmaximal, complemented
3#48797C214yesmaximal
4#48794C214yesmaximal
5#47821C214yesmaximal, complemented
6#47820C214yesmaximal, complemented
7#47791C214yesmaximal, complemented
8#47789C214yesmaximal, complemented
9#39819C214yesmaximal, complemented
10#39695C214yesmaximal, complemented
11#37985C214yesmaximal, complemented
12#37793C214yesmaximal, complemented
13#37641C211yesmaximal, characteristic, complemented
14#37565C211yesmaximal, characteristic, complemented
15#37383C212yesmaximal, complemented
16#37382C212yesmaximal, complemented
17#35325C212yesmaximal
18#35325C212yesmaximal
19#35310C212yesmaximal
20#34394C212yesmaximal, complemented
21#34052C211yesmaximal, characteristic
22C2×#541C2212yes—
23C2×#533C2212yes—
24C2×#533C2212yes—
25C22×#117C2211yescharacteristic
26C22×#117C2211yescharacteristic
27C22×#117C2211yescharacteristic
28#2857C2212yes—
29#2855C2214yes—
30#2855C2214yes—
31#2851C2212yes—
32#2848C2214yes—
33#2843C2214yescomplemented
34#2822C2214yescomplemented
35#2807C2218yes—
36#2805C2218yescomplemented
37#2802C2218yescomplemented
38#2794C2214yescomplemented
39#2792C2214yescomplemented
40#2791C2218yescomplemented
41#2789C2214yescomplemented
42#2787C2218yes—
43#2776C2218yescomplemented
44#2776C2218yescomplemented
45#2771C2218yes—
46#2770C2218yes—
47#2769C2214yescomplemented
48#2767C2218yescomplemented
49#2764C2218yes—
50#2763C2218yes—
51#2758C2218yescomplemented
52#2755C2218yescomplemented
53#2745C2218yes—
54#2744C2218yes—
55#2739C2218yes—
56#2738C2218yes—
57#2726C2218yescomplemented
58#2719C2218yescomplemented
59#2698C2218yes—
60#2689C2218yes—
61#2667C2214yes—
62#2665C2214yes—
63#2629C2212yes—
64#2628C2212yes—
65#2628C2212yes—
66#2628C2212yes—
67#2628C2212yes—
68#2625C2214yes—
69#2625C2214yes—
70#2625C2214yes—
71#2621C2212yes—
72#2621C2212yes—
73#2621C2212yes—
74#2621C2212yes—
75#2621C2212yes—
76#2612C2218yescomplemented
77#2612C2214yescomplemented
78#2611C2214yes—
79#2611C2214yes—
80#2611C2214yes—
81#2611C2214yes—
82#2606C2218yescomplemented
83#2599C2214yes—
84#2599C2214yes—
85#2599C2214yes—
86#2599C2214yes—
87#2590C2218yescomplemented
88#2589C2218yes—
89#2589C2218yes—
90#2586C2218yescomplemented
91#2583C2214yes—
92#2583C2214yes—
93#2582C2214yescomplemented
94#2577C2218yes—
95#2575C2218yes—
96#2570C2214yescomplemented
97#2568C2214yescomplemented
98#2561C2214yes—
99#2561C2214yes—
100#2550C2214yescomplemented
101#2546C2214yescomplemented
102#2533C2218yescomplemented
103#2530C2218yes—
104#2527C2218yes—
105#2514C2214yescomplemented
106#2511C2214yescomplemented
107#2509C2214yescomplemented
108#2509C2218yescomplemented
109#2508C2214yescomplemented
110#2484C2214yes—
111#2484C2214yes—
112#2482C2214yes—
113#2482C2214yes—
114#2480C2218yes—
115#2478C2218yes—
116#2478C2218yes—
117#2478C2218yes—
118#2475C2218yes—
119#2473C2218yes—
120#2462C2218yescomplemented
121#2453C2214yescomplemented
122#2453C2218yescomplemented
123#2451C2214yescomplemented
124#2446C2214yescomplemented
125#2446C2214yescomplemented
126#2378C2214yes—
127#2378C2214yes—
128#2369C2214yescomplemented
129#2365C2214yescomplemented
130#2356C2214yescomplemented
131#2351C2214yescomplemented
132#2347C2214yes—
133#2346C2214yes—
134#2330C2218yescomplemented
135#2323C2214yes—
136#2323C2214yes—
137#2323C2214yes—
138#2323C2214yes—
139#2323C2214yes—
140#2320C2218yescomplemented
141#2317C2212yes—
142#2317C2212yes—
143#2317C2212yes—
144#2317C2212yes—
145#2316C2212yes—
146#2316C2212yes—
147#2315C2212yes—
148#2315C2212yes—
149#2314C2212yes—
150C4×C22⋊Q8C2214yes—
151#2296C2214yes—
152#2296C2214yes—
153#2285C2211yescharacteristic
154#2285C2211yescharacteristic
155#2285C2211yescharacteristic
156#2285C2211yescharacteristic
157#2283C2212yes—
158#2283C2212yes—
159C24×C4C2311yescharacteristic
160#541—48no—
161#533—216no—
162#533—48no—
163C2×C4⋊Q8C2312yes—
164C2×C4⋊Q8C2312yes—
165C2×C4⋊Q8C2312yes—
166C2×C4⋊Q8C2312yes—
167C2×C4⋊Q8C2312yes—
168C2×#126C2318yes—
169C2×#125C2314yes—
170C2×#125C2312yes—
171C2×#125C2314yes—
172C2×#125C2318yes—
173C2×C22⋊Q8C2314yes—
174C2×C22⋊Q8C2314yes—
175C2×C22⋊Q8C2314yes—
176C2×C22⋊Q8C2314yes—
177C2×C22⋊Q8C2314yes—
178C2×C4×Q8C2314yes—
179C2×C4×Q8C2314yes—
180C2×C4×Q8C2314yes—
181C2×C4×Q8C2314yes—
182C2×C4×Q8C2314yes—
183C2×#117—28no—
184C2×#117—44no—
185C2×#117—44no—
186C2×#117C2312yes—
187C2×#117C2311yescharacteristic
188C2×#117C2311yescharacteristic
189C2×#117C2311yescharacteristic
190C2×#117C2311yescharacteristic
191C2×#117C2312yes—
192C2×#117C2312yes—
193C2×#117C2314yes—
194C2×#117C2311yescharacteristic
195C2×#117C2311yescharacteristic
196C2×#117C2312yes—
197C2×#117C2312yes—
198C2×#117C2312yes—
199C2×#117C2311yescharacteristic
200C2×#117C2311yescharacteristic
201C2×#117C2312yes—
202C2×#117C2311yescharacteristic
203C2×#117C2311yescharacteristic
204C2×#117C2314yes—
205C22×C4⋊C4C2312yes—
206C22×C4⋊C4C2312yes—
207C22×C4⋊C4C2312yes—
208C22×C22⋊C4C2312yes—
209C22×C22⋊C4C2311yescharacteristic
210C22×C22⋊C4C2312yes—
211C22×C22⋊C4C2311yescharacteristic
212C22×C42C2311yescharacteristic
213C22×C42C2312yes—
214C22×C42C2312yes—
215C22×C42C2311yescharacteristic
216#401C2318yes—
217#400C2318yes—
218#400C2318yes—
219#400C2318yes—
220#400C2318yes—
221#400C2318yes—
222#400C2314yes—
223#400C2318yes—
224#400C2318yes—
225#400C2314yes—
226#400C2314yes—
227#400C2314yes—
228#400C2318yes—
229#400C2318yes—
230#400C2318yes—
231#400C2318yes—
232#400C2318yes—
233#400C2318yes—
234#399C2314yes—
235#399C2314yes—
236#399C2314yes—
237#399C2314yes—
238#398C2318yes—
239#398C2314yes—
240#398C2314yes—
241#398C2318yes—
242#398C2318yes—
243#398C2318yes—
244#398C2314yes—
245#398C2314yes—
246#398C2314yes—
247#398C2318yes—
248#398C2318yes—
249#398C2318yes—
250#398C2318yes—
251#398C2314yes—
252#398C2314yes—
253#398C2318yes—
254#398C2314yes—
255#398C2318yes—
256#398C2318yes—
257#398C2318yes—
258#397C2314yes—
259#397C2314yes—
260#397C2314yes—
261#397C2314yes—
262#397C2318yes—
263#397C2314yes—
264#397C2314yes—
265#397C2314yes—
266#397C2314yes—
267#397C2318yes—
268#397C2318yes—
269#396C2318yes—
270#395C2314yes—
271#395C2314yes—
272#395C2314yes—
273#395C2314yes—
274#395C2318yes—
275#395C2318yes—
276#393C2314yes—
277#393C2314yes—
278#393C2314yes—
279#393C2314yes—
280#391C2314yes—
281#391C2318yes—
282#391C2318yes—
283#391C2314yes—
284#391C2318yes—
285#391C2318yes—
286#391C2314yes—
287#391C2314yes—
288#391C2314yes—
289#391C2314yes—
290#391C2318yes—
291#391C2318yes—
292#389C2314yes—
293#389C2314yes—
294#389C2314yes—
295#389C2314yes—
296#389C2314yes—
297#389C2314yes—
298#389C2314yes—
299#389C2314yes—
300#389C2314yes—
301#389C2314yes—
302#389C2318yes—
303#389C2318yes—
304#389C2318yes—
305#389C2318yes—
306#389C2318yes—
307#389C2314yes—
308#389C2314yes—
309#389C2314yes—
310#389C2314yes—
311#389C2318yes—
312#389C2318yes—
313#389C2318yes—
314#389C2318yes—
315#389C2318yes—
316#389C2318yes—
317#389C2318yes—
318#389C2318yes—
319#389C2318yes—
320#389C2318yes—
321#388C2318yes—
322#388C2318yes—
323#388C2318yes—
324#388C2318yes—
325#388C2318yes—
326#388C2318yes—
327#388C2318yes—
328#388C2318yes—
329#388C2318yes—
330#388C2318yes—
331#388C2318yes—
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#387C2318yes—
357#387C2318yes—
358#387C2318yes—
359#387C2318yes—
360#387C2318yes—
361#385C2314yes—
362#385C2314yes—
363#385C2314yes—
364#385C2314yes—
365#385C2314yes—
366#385C2314yes—
367#385C2314yes—
368#385C2314yes—
369#385C2318yes—
370#385C2318yes—
371#385C2318yes—
372#385C2318yes—
373#385C2318yes—
374#385C2318yes—
375#385C2318yes—
376#384C2312yes—
377#384C2312yes—
378#384C2312yes—
379#384C2312yes—
380#384C2312yes—
381#383C2314yes—
382#383C2318yes—
383#383C2318yes—
384#383C2314yes—
385#382C2312yes—
386#382C2312yes—
387#382C2312yes—
388#382C2312yes—
389#382C2312yes—
390#382C2312yes—
391#382C2312yes—
392#382C2312yes—
393#382C2318yes—
394#382C2318yes—
395#382C2312yes—
396#381C2318yes—
397#381C2318yes—
398#381C2314yes—
399#381C2314yes—
400#380C2314yes—
401#380C2312yes—
402#380C2312yes—
403#380C2312yes—
404#380C2312yes—
405#380C2312yes—
406#380C2312yes—
407#380C2312yes—
408#380C2312yes—
409#380C2318yes—
410#380C2314yes—
411#380C2314yes—
412#379C2318yes—
413C4×C4⋊C4C2314yes—
414C4×C4⋊C4C2314yes—
415C4×C4⋊C4C2314yes—
416C4×C4⋊C4C2318yes—
417C4×C4⋊C4C2318yes—
418C4×C4⋊C4C2318yes—
419C4×C4⋊C4C2314yes—
420C4×C4⋊C4C2318yes—
421C4×C4⋊C4C2314yes—
422C4×C4⋊C4C2314yes—
423C4×C4⋊C4C2314yes—
424C4×C22⋊C4C2314yes—
425C4×C22⋊C4C2314yes—
426C4×C22⋊C4C2318yes—
427#376C2318yes—
428#376C2314yes—
429#376C2314yes—
430C25C2411yescharacteristic
431C22×Q8C2414yes—
432C22×Q8C2414yes—
433C22×Q8C2414yes—
434C23×C4—24no—
435C23×C4—24no—
436C23×C4—24no—
437C23×C4C2411yescharacteristic
438C23×C4C2411yescharacteristic
439C23×C4C2411yescharacteristic
440C23×C4C2411yescharacteristic
441C23×C4C2411yescharacteristic
442C23×C4C2411yescharacteristic
443C23×C4C2412yes—
444C23×C4C2412yes—
445C23×C4C2412yes—
446C23×C4C2414yes—
447C23×C4C2412yes—
448C4⋊Q8—28no—
449C4⋊Q8—28no—
450C4⋊Q8—44no—
451C4⋊Q8—44no—
452C4⋊Q8—44no—
453#126—416no—
454#125—216no—
455#125—48no—
456#125—44no—
457#125—416no—
458C22⋊Q8—216no—
459C22⋊Q8—216no—
460C22⋊Q8—216no—
461C22⋊Q8—216no—
462C22⋊Q8—48no—
463C4×Q8—216no—
464C4×Q8—216no—
465C4×Q8—48no—
466C4×Q8—48no—
467C4×Q8—48no—
468#117—216no—
469#117—28no—
470#117—24no—
471#117—24no—
472#117—28no—
473#117—28no—
474#117—24no—
475#117—24no—
476#117—42no—
477#117—42no—
478#117—44no—
479#117—44no—
480#117—42no—
481#117—42no—
482#117—42no—
483#117—42no—
484#117—44no—
485#117—48no—
486#117—44no—
487C2×C4⋊C4—28no—
488C2×C4⋊C4—44no—
489C2×C4⋊C4—44no—
490C2×C4⋊C4C2414yes—
491C2×C4⋊C4C2412yes—
492C2×C4⋊C4C2412yes—
493C2×C4⋊C4C2412yes—
494C2×C4⋊C4C2412yes—
495C2×C4⋊C4C2414yes—
496C2×C4⋊C4C2414yes—
497C2×C4⋊C4C2414yes—
498C2×C4⋊C4C2418yes—
499C2×C4⋊C4C2418yes—
500C2×C4⋊C4C2418yes—
501C2×C4⋊C4C2414yes—
502C2×C4⋊C4C2414yes—
503C2×C4⋊C4C2414yes—
504C2×C4⋊C4C2418yes—
505C2×C4⋊C4C2412yes—
506C2×C4⋊C4C2412yes—
507C2×C4⋊C4C2412yes—
508C2×C4⋊C4C2412yes—
509C2×C4⋊C4C2412yes—
510C2×C4⋊C4C2412yes—
511C2×C4⋊C4C2414yes—
512C2×C4⋊C4C2414yes—
513C2×C4⋊C4C2418yes—
514C2×C4⋊C4C2414yes—
515C2×C4⋊C4C2418yes—
516C2×C4⋊C4C2418yes—
517C2×C4⋊C4C2418yes—
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⋊C4C2418yes—
527C2×C4⋊C4C2418yes—
528C2×C4⋊C4C2418yes—
529C2×C4⋊C4C2418yes—
530C2×C4⋊C4C2418yes—
531C2×C4⋊C4C2418yes—
532C2×C4⋊C4C2418yes—
533C2×C22⋊C4—28no—
534C2×C22⋊C4—44no—
535C2×C22⋊C4—42no—
536C2×C22⋊C4—42no—
537C2×C22⋊C4C2414yes—
538C2×C22⋊C4C2412yes—
539C2×C22⋊C4C2412yes—
540C2×C22⋊C4C2412yes—
541C2×C22⋊C4C2412yes—
542C2×C22⋊C4C2418yes—
543C2×C22⋊C4C2418yes—
544C2×C22⋊C4C2418yes—
545C2×C22⋊C4C2411yescharacteristic
546C2×C22⋊C4C2412yes—
547C2×C22⋊C4C2411yescharacteristic
548C2×C22⋊C4C2411yescharacteristic
549C2×C22⋊C4C2412yes—
550C2×C22⋊C4C2411yescharacteristic
551C2×C22⋊C4C2412yes—
552C2×C22⋊C4C2412yes—
553C2×C22⋊C4C2418yes—
554C2×C22⋊C4C2418yes—
555C2×C22⋊C4C2418yes—
556C2×C42—24no—
557C2×C42—28no—
558C2×C42—44no—
559C2×C42#4118yes—
560C2×C42C2412yes—
561C2×C42C2412yes—
562C2×C42C2412yes—
563C2×C42C2412yes—
564C2×C42C2412yes—
565C2×C42C2412yes—
566C2×C42C2412yes—
567C2×C42C2411yescharacteristic
568C2×C42C2411yescharacteristic
569C2×C42C2418yes—
570C2×C42C2414yes—
571C2×C42C2418yes—
572C2×C42C2418yes—
573C2×C42C2418yes—
574C2×C42C2418yes—
575C2×C42C2418yes—
576C2×C42C2411yescharacteristic
577C2×C42C2412yes—
578C2×C42C2411yescharacteristic
579#95C2414yes—
580#95C2414yes—
581#95C2418yes—
582#95C2418yes—
583#95C2418yes—
584#95C2414yes—
585#95C2414yes—
586#95C2414yes—
587#95C2414yes—
588#95C2418yes—
589#95C2414yes—
590#95C2414yes—
591#95C2414yes—
592#95C2418yes—
593#95C2418yes—
594#95C2414yes—
595#95C2414yes—
596#95C2414yes—
597#95C2414yes—
598#95C2414yes—
599#95C2414yes—
600#95C2414yes—
601#95C2418yes—
602#95C2418yes—
603#95C2418yes—
604#95C2418yes—
605#95C2418yes—
606#95C2418yes—
607#95C2418yes—
608#95C2418yes—
609#95C2418yes—
610#95C2418yes—
611#95C2418yes—
612#95C2418yes—
613#95C2418yes—
614#95C2418yes—
615#95C2418yes—
616#95C2418yes—
617#95C2418yes—
618#95C2418yes—
619#95C2418yes—
620C24—22no—
621C24—22no—
622C24—22no—
623C24—44no—
624C24C2511yescharacteristic
625C24C2511yescharacteristic
626C24C2511yescharacteristic
627C2×Q8—28no—
628C2×Q8—28no—
629C2×Q8—28no—
630C2×Q8—28no—
631C2×Q8—44no—
632C2×Q8—48no—
633C2×Q8—48no—
634C22×C4—232no—
635C22×C4—22no—
636C22×C4—22no—
637C22×C4—22no—
638C22×C4—22no—
639C22×C4—22no—
640C22×C4—22no—
641C22×C4—22no—
642C22×C4—22no—
643C22×C4—22no—
644C22×C4—22no—
645C22×C4—22no—
646C22×C4—22no—
647C22×C4—22no—
648C22×C4—22no—
649C22×C4—22no—
650C22×C4—24no—
651C22×C4—24no—
652C22×C4—24no—
653C22×C4—44no—
654C22×C4—44no—
655C22×C4—44no—
656C22×C4—44no—
657C22×C4—44no—
658C22×C4—44no—
659C22×C4—44no—
660C22×C4C2×#4114yes—
661C22×C4C2×#4118yes—
662C22×C4H(5,𝔽2)14yes—
663C22×C42−1+414yes—
664C22×C4C2518yes—
665C22×C4C2518yes—
666C22×C4C2512yes—
667C22×C4C2512yes—
668C22×C4C2512yes—
669C22×C4C2512yes—
670C22×C4C2512yes—
671C22×C4C2514yes—
672C22×C4C2518yes—
673C22×C4C2518yes—
674C22×C4C2512yes—
675C22×C4C2514yes—
676C22×C4C2512yes—
677C22×C4C2512yes—
678C22×C4C2511yescharacteristic
679C22×C4C2511yescharacteristic
680C22×C4C2511yescharacteristic
681C22×C4C2511yescharacteristic
682C4⋊C4—24no—
683C4⋊C4—24no—
684C4⋊C4—24no—
685C4⋊C4—24no—
686C4⋊C4—28no—
687C4⋊C4—28no—
688C4⋊C4—216no—
689C4⋊C4—216no—
690C4⋊C4—28no—
691C4⋊C4—28no—
692C4⋊C4—28no—
693C4⋊C4—28no—
694C4⋊C4—216no—
695C4⋊C4—28no—
696C4⋊C4—216no—
697C4⋊C4—42no—
698C4⋊C4—42no—
699C4⋊C4—42no—
700C4⋊C4—42no—
701C4⋊C4—42no—
702C4⋊C4—42no—
703C4⋊C4—44no—
704C4⋊C4—44no—
705C4⋊C4—44no—
706C4⋊C4—44no—
707C4⋊C4—48no—
708C4⋊C4—48no—
709C4⋊C4—44no—
710C4⋊C4—44no—
711C4⋊C4—48no—
712C4⋊C4—48no—
713C4⋊C4—48no—
714C4⋊C4—48no—
715C4⋊C4—48no—
716C4⋊C4—44no—
717C4⋊C4—44no—
718C4⋊C4—44no—
719C4⋊C4—44no—
720C4⋊C4—48no—
721C4⋊C4—44no—
722C4⋊C4—48no—
723C4⋊C4—48no—
724C4⋊C4—48no—
725C22⋊C4—216no—
726C22⋊C4—28no—
727C22⋊C4—216no—
728C22⋊C4—216no—
729C22⋊C4—24no—
730C22⋊C4—24no—
731C22⋊C4—24no—
732C22⋊C4—24no—
733C22⋊C4—41no—
734C22⋊C4—42no—
735C22⋊C4—41no—
736C22⋊C4—41no—
737C22⋊C4—42no—
738C22⋊C4—41no—
739C22⋊C4—42no—
740C22⋊C4—42no—
741C22⋊C4—48no—
742C22⋊C4—48no—
743C22⋊C4—48no—
744C42—22no—
745C42—22no—
746C42—24no—
747C42—216no—
748C42—24no—
749C42—24no—
750C42—24no—
751C42—24no—
752C42—24no—
753C42—24no—
754C42—44no—
755C42—48no—
756C42—48no—
757C42—48no—
758C42—48no—
759C42—48no—
760C42C2×#4114yes—
761C42C2×#4118yes—
762C42C2×#4114yes—
763C23—28no—
764C23—21no—
765C23—21no—
766C23—21no—
767C23—21no—
768C23—21no—
769C23—21no—
770C23—24no—
771C23—24no—
772C23—24no—
773C23—84no—
774C23—84no—
775C23—84no—
776C23C22×#4112yes—
777C23C2×H(5,𝔽2)12yes—
778C23C2×2−1+412yes—
779C23C2611yescharacteristic
780Q8—416no—
781Q8—88no—
782Q8—88no—
783C2×C4—28no—
784C2×C4—28no—
785C2×C4—28no—
786C2×C4—21no—
787C2×C4—21no—
788C2×C4—21no—
789C2×C4—21no—
790C2×C4—21no—
791C2×C4—21no—
792C2×C4—24no—
793C2×C4—24no—
794C2×C4—28no—
795C2×C4—28no—
796C2×C4—28no—
797C2×C4—22no—
798C2×C4—22no—
799C2×C4—28no—
800C2×C4—28no—
801C2×C4—22no—
802C2×C4—22no—
803C2×C4—22no—
804C2×C4—22no—
805C2×C4—24no—
806C2×C4—24no—
807C2×C4—28no—
808C2×C4—28no—
809C2×C4—28no—
810C2×C4—28no—
811C2×C4—28no—
812C2×C4—24no—
813C2×C4—24no—
814C2×C4—28no—
815C2×C4—28no—
816C2×C4—28no—
817C2×C4—28no—
818C2×C4—28no—
819C2×C4—24no—
820C2×C4—24no—
821C2×C4—24no—
822C2×C4—24no—
823C2×C4—24no—
824C2×C4—24no—
825C2×C4—24no—
826C2×C4—24no—
827C2×C4—48no—
828C2×C4—48no—
829C2×C4—84no—
830C2×C4—84no—
831C2×C4—88no—
832C2×C4C22×#4114yes—
833C2×C4C22×#4112yes—
834C2×C4C22×#4114yes—
835C2×C4C22×#4112yes—
836C2×C4C2×H(5,𝔽2)12yes—
837C2×C4C2×H(5,𝔽2)12yes—
838C2×C4C2×2−1+412yes—
839C2×C4C2×2−1+412yes—
840C22—22no—
841C22—22no—
842C22—22no—
843C22—24no—
844C22—24no—
845C22—24no—
846C22—42no—
847C22—42no—
848C22—42no—
849C22—42no—
850C22—42no—
851C22—42no—
852C22—88no—
853C22C23×#4111yescharacteristic
854C22C22×H(5,𝔽2)11yescharacteristic
855C22C22×2−1+411yescharacteristic
856C222−1+614yes—
857C4—22no—
858C4—22no—
859C4—22no—
860C4—24no—
861C4—24no—
862C4—48no—
863C4—42no—
864C4—42no—
865C4—48no—
866C4—42no—
867C4—42no—
868C4—42no—
869C4—44no—
870C4—44no—
871C4—42no—
872C4—48no—
873C4—48no—
874C4#349214yes—
875C2—42no—
876C2—42no—
877C2—42no—
878C2C2×#349211yescharacteristic
879C2#6286012yes—
880C2#6288612yes—
881C2#6288912yes—
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. #50184C2semidirect
2. #50183C2semidirect
5. #47821C2semidirect
6. #47820C2semidirect
7. #47791C2semidirect
8. #47789C2semidirect
9. #39819C2semidirect
10. #39695C2semidirect
11. #37985C2semidirect
12. #37793C2semidirect
13. #37641C2semidirect
14. #37565C2semidirect
15. #37383C2semidirect
16. #37382C2semidirect
20. #34394C2semidirect
33. #2843C22semidirect
34. #2822C22semidirect
36. #2805C22semidirect
37. #2802C22semidirect
38. #2794C22semidirect
39. #2792C22semidirect
40. #2791C22semidirect
41. #2789C22semidirect
43. #2776C22semidirect
44. #2776C22semidirect
47. #2769C22semidirect
48. #2767C22semidirect
51. #2758C22semidirect
52. #2755C22semidirect
57. #2726C22semidirect
58. #2719C22semidirect
76. #2612C22semidirect
77. #2612C22semidirect
82. #2606C22semidirect
87. #2590C22semidirect
90. #2586C22semidirect
93. #2582C22semidirect
96. #2570C22semidirect
97. #2568C22semidirect
100. #2550C22semidirect
101. #2546C22semidirect
102. #2533C22semidirect
105. #2514C22semidirect
106. #2511C22semidirect
107. #2509C22semidirect
108. #2509C22semidirect
109. #2508C22semidirect
120. #2462C22semidirect
121. #2453C22semidirect
122. #2453C22semidirect
123. #2451C22semidirect
124. #2446C22semidirect
125. #2446C22semidirect
128. #2369C22semidirect
129. #2365C22semidirect
130. #2356C22semidirect
131. #2351C22semidirect
134. #2330C22semidirect
140. #2320C22semidirect

Maximal subgroups

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

subgroupindex
#501842
#501832
#487972
#487942
#478212
#478202
#477912
#477892
#398192
#396952
#379852
#377932
#376412
#375652
#373832
#373822
#353252
#353102
#343942
#340522