Finite Group Databasebeta

← #7658915

Subgroups — #7658915

Order 512.

4448 conjugacy classes of subgroups.

The subgroup lattice has 877 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#42983C212yesmaximal
2#42941C212yesmaximal, complemented
3#42702C214yesmaximal, complemented
4#42700C214yesmaximal, complemented
5#42337C214yesmaximal, complemented
6#42211C214yesmaximal, complemented
7#41624C218yesmaximal, complemented
8#41612C218yesmaximal, complemented
9#37641C211yesmaximal, characteristic, complemented
10#37612C212yesmaximal, complemented
11#37600C214yesmaximal, complemented
12#37537C212yesmaximal
13#36698C212yesmaximal, complemented
14#36691C211yesmaximal, characteristic, complemented
15#36033C212yesmaximal
16#35974C214yesmaximal, complemented
17#35938C214yesmaximal, complemented
18#35749C212yesmaximal, complemented
19#34231C212yesmaximal, complemented
20#34211C211yesmaximal, characteristic
21C2×#557C2212yescomplemented
22C2×#556C2212yes—
23C2×#533C2212yes—
24C22×#124C2211yescharacteristic
25C2×#519C2211yescharacteristic
26C2×#518C2211yescharacteristic
27#2845C2212yescomplemented
28#2844C2211yescharacteristic, complemented
29#2844C2211yescharacteristic, complemented
30#2843C2212yescomplemented
31#2843C2212yescomplemented
32#2841C2214yes—
33#2841C2214yes—
34#2838C2218yescomplemented
35#2836C2218yescomplemented
36#2833C2214yescomplemented
37#2830C2214yes—
38#2822C2212yescomplemented
39#2822C2212yescomplemented
40#2820C2214yes—
41#2820C2214yes—
42#2777C2218yescomplemented
43#2773C2218yescomplemented
44#2771C2214yes—
45#2768C2218yescomplemented
46#2765C2218yes—
47#2764C2214yes—
48#2764C2218yescomplemented
49#2763C2218yescomplemented
50#2759C2218yescomplemented
51#2754C2218yescomplemented
52#2738C2218yescomplemented
53#2736C2214yes—
54#2735C2214yes—
55#2735C2218yes—
56#2667C2218yescomplemented
57#2666C2218yescomplemented
58#2664C2218yescomplemented
59#2658C2214yes—
60#2654C2218yescomplemented
61#2654C2218yescomplemented
62#2652C2218yescomplemented
63#2651C2218yes—
64#2650C2218yescomplemented
65#2640C2214yes—
66#2638C2214yes—
67#2634C2214yescomplemented
68#2632C2218yes—
69#2626C2214yes—
70#2626C2214yes—
71#2625C2218yes—
72#2621C2212yes—
73#2621C2212yes—
74#2611C2214yes—
75#2611C2218yescomplemented
76#2604C2218yescomplemented
77#2599C2214yes—
78#2593C2214yes—
79#2592C2214yes—
80#2589C2218yescomplemented
81#2586C2214yescomplemented
82#2582C2212yescomplemented
83#2582C2212yescomplemented
84#2581C2212yescomplemented
85#2580C2212yes—
86#2573C2218yescomplemented
87#2568C2214yescomplemented
88#2568C2214yescomplemented
89#2561C2214yes—
90#2556C2218yescomplemented
91#2556C2218yescomplemented
92#2547C2212yes—
93#2546C2214yescomplemented
94#2546C2214yescomplemented
95#2546C2212yescomplemented
96#2545C2214yes—
97#2545C2214yes—
98#2545C2214yes—
99#2532C2218yescomplemented
100#2532C2218yescomplemented
101#2527C2218yescomplemented
102#2525C2218yescomplemented
103#2522C2218yescomplemented
104#2519C2218yescomplemented
105#2519C2218yescomplemented
106#2515C2218yescomplemented
107#2514C2214yescomplemented
108#2513C2214yes—
109#2482C2218yes—
110#2482C2214yes—
111#2480C2218yes—
112#2475C2218yes—
113#2468C2218yes—
114#2462C2218yescomplemented
115#2448C2214yes—
116#2447C2214yes—
117#2446C2214yescomplemented
118#2446C2214yescomplemented
119#2435C2214yes—
120#2434C2214yes—
121#2402C2214yescomplemented
122#2401C2218yescomplemented
123#2399C2214yescomplemented
124#2399C2214yescomplemented
125#2396C2212yes—
126#2396C2212yes—
127#2396C2218yescomplemented
128#2395C2214yes—
129#2369C2212yescomplemented
130#2369C2212yescomplemented
131#2367C2214yes—
132#2367C2214yes—
133#2367C2214yes—
134#2365C2212yescomplemented
135#2365C2214yescomplemented
136#2365C2212yescomplemented
137#2362C2214yes—
138#2362C2214yes—
139#2357C2212yes—
140#2356C2218yescomplemented
141#2356C2212yescomplemented
142#2347C2214yes—
143#2346C2214yes—
144#2342C2218yes—
145#2332C2218yes—
146#2326C2212yes—
147#2326C2212yes—
148#2320C2214yescomplemented
149#2310C2211yescharacteristic
150#2309C2211yescharacteristic
151C4×#125C2214yescomplemented
152C4×#125C2214yescomplemented
153C4×#124C2212yes—
154C4×#124C2212yes—
155#2285C2211yescharacteristic
156#2283C2212yes—
157#2276C2214yescomplemented
158C4×#117C2211yescharacteristic
159C23×Q8C2311yescharacteristic
160C23×D4C2311yescharacteristic
161#557—48no—
162#556—48no—
163#533—216no—
164C2×C4⋊Q8C2312yes—
165C2×C4⋊Q8C2312yes—
166C2×C4⋊Q8C2314yes—
167C2×C4⋊Q8C2314yes—
168C2×C4⋊Q8C2312yes—
169C2×C4⋊Q8C2312yes—
170C2×#126C2318yes—
171C2×#125C2314yes—
172C2×#125C2314yes—
173C2×#125C2318yes—
174C2×#124—28no—
175C2×#124C2312yes—
176C2×#124C2312yes—
177C2×#124C2314yes—
178C2×#124C2314yes—
179C2×#124C2314yes—
180C2×C22⋊Q8C2314yes—
181C2×C22⋊Q8C2314yes—
182C2×C22⋊Q8C2314yes—
183#519—44no—
184#518—44no—
185C2×C4×Q8C2314yes—
186C2×C4×Q8C2314yes—
187C2×C4×Q8C2312yes—
188C2×C4×Q8C2314yes—
189C2×C4×Q8C2312yes—
190C2×C4×Q8C2312yes—
191C2×C4×Q8C2312yes—
192C2×C4×Q8C2312yes—
193C2×C4×Q8C2312yes—
194C2×C4×Q8C2314yes—
195C2×C4×Q8C2314yes—
196C2×C4×D4C2312yes—
197C2×C4×D4C2312yes—
198C2×C4×D4C2312yes—
199C2×C4×D4C2312yes—
200C2×#117C2314yes—
201C2×#117C2311yescharacteristic
202C2×#117C2311yescharacteristic
203C2×#117C2311yescharacteristic
204C2×#117C2311yescharacteristic
205C2×#117C2314yes—
206C2×#117C2314yes—
207C22×C22⋊C4C2314yes—
208C22×C22⋊C4C2314yes—
209C22×C42C2311yescharacteristic
210#401C2318yes—
211#400C2318yes—
212#400C2318yes—
213#400C2318yes—
214#400C2318yes—
215#400C2314yes—
216#400C2312yes—
217#400C2318yes—
218#400C2314yes—
219#400C2314yes—
220#400C2314yes—
221#400C2314yes—
222#400C2312yes—
223#400C2318yes—
224#400C2318yes—
225#399C2318yes—
226#399C2318yes—
227#399C2314yes—
228#399C2312yes—
229#399C2312yes—
230#399C2318yes—
231#399C2318yes—
232#399C2318yes—
233#398C2314yes—
234#398C2314yes—
235#398C2318yes—
236#398C2314yes—
237#398C2314yes—
238#398C2318yes—
239#398C2318yes—
240#398C2314yes—
241#398C2318yes—
242#398C2314yes—
243#398C2314yes—
244#398C2314yes—
245#398C2314yes—
246#398C2314yes—
247#398C2314yes—
248#398C2314yes—
249#398C2314yes—
250#398C2314yes—
251#398C2314yes—
252#398C2314yes—
253#398C2318yes—
254#398C2318yes—
255#397C2314yes—
256#397C2314yes—
257#397C2318yes—
258#397C2318yes—
259#397C2318yes—
260#397C2318yes—
261#397C2318yes—
262#397C2318yes—
263#397C2314yes—
264#397C2314yes—
265#397C2314yes—
266#397C2318yes—
267#397C2314yes—
268#397C2318yes—
269#396C2318yes—
270#396C2318yes—
271#396C2318yes—
272#396C2318yes—
273#396C2318yes—
274#396C2314yes—
275#396C2314yes—
276#396C2318yes—
277#395C2318yes—
278#395C2318yes—
279#395C2312yes—
280#395C2314yes—
281#395C2314yes—
282#395C2314yes—
283#395C2314yes—
284#395C2314yes—
285#395C2312yes—
286#394C2318yes—
287#394C2318yes—
288#393C2312yes—
289#393C2314yes—
290#393C2318yes—
291#393C2312yes—
292#393C2318yes—
293#393C2318yes—
294#391C2314yes—
295#391C2312yes—
296#391C2312yes—
297#391C2314yes—
298#391C2314yes—
299#391C2314yes—
300#391C2318yes—
301#391C2318yes—
302#391C2318yes—
303#391C2314yes—
304#391C2314yes—
305#391C2318yes—
306#391C2318yes—
307#391C2314yes—
308#390C2312yes—
309#390C2312yes—
310#390C2314yes—
311#390C2314yes—
312#390C2314yes—
313#389C2314yes—
314#389C2314yes—
315#389C2314yes—
316#389C2314yes—
317#389C2314yes—
318#389C2314yes—
319#389C2318yes—
320#389C2318yes—
321#389C2318yes—
322#389C2318yes—
323#389C2318yes—
324#389C2318yes—
325#388C2318yes—
326#388C2318yes—
327#388C2318yes—
328#388C2318yes—
329#388C2318yes—
330#388C2318yes—
331#388C2318yes—
332#388C2318yes—
333#388C2318yes—
334#388C2318yes—
335#388C2318yes—
336#388C2318yes—
337#388C2318yes—
338#388C2318yes—
339#388C2318yes—
340#388C2318yes—
341#388C2318yes—
342#388C2318yes—
343#388C2318yes—
344#388C2318yes—
345#388C2318yes—
346#388C2318yes—
347#388C2318yes—
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#387C2318yes—
362#387C2318yes—
363#385C2318yes—
364#385C2318yes—
365#385C2318yes—
366#385C2318yes—
367#385C2318yes—
368#385C2318yes—
369#385C2318yes—
370#384C2311yescharacteristic
371#384C2311yescharacteristic
372#383C2314yes—
373#383C2318yes—
374#383C2314yes—
375#383C2318yes—
376#382C2312yes—
377#382C2312yes—
378#382C2311yescharacteristic
379#382C2311yescharacteristic
380#382C2312yes—
381#382C2312yes—
382#382C2318yes—
383#382C2318yes—
384#381C2318yes—
385#381C2314yes—
386#381C2314yes—
387#381C2314yes—
388#380C2314yes—
389#380C2312yes—
390#380C2312yes—
391#380C2318yes—
392#379C2318yes—
393#379C2314yes—
394#379C2318yes—
395C4×C4⋊C4C2318yes—
396C4×C4⋊C4C2318yes—
397C4×C4⋊C4C2318yes—
398C4×C4⋊C4C2314yes—
399C4×C4⋊C4C2314yes—
400C4×C4⋊C4C2314yes—
401C4×C4⋊C4C2314yes—
402C4×C4⋊C4C2318yes—
403C4×C4⋊C4C2314yes—
404C4×C4⋊C4C2314yes—
405C4×C4⋊C4C2312yes—
406C4×C4⋊C4C2318yes—
407C4×C4⋊C4C2314yes—
408C4×C4⋊C4C2312yes—
409C4×C4⋊C4C2312yes—
410C4×C4⋊C4C2312yes—
411C4×C4⋊C4C2312yes—
412C4×C4⋊C4C2312yes—
413C4×C4⋊C4C2314yes—
414C4×C4⋊C4C2318yes—
415C4×C4⋊C4C2314yes—
416C4×C22⋊C4C2314yes—
417C4×C22⋊C4C2318yes—
418C4×C22⋊C4C2314yes—
419C4×C22⋊C4C2318yes—
420C4×C22⋊C4C2314yes—
421C4×C22⋊C4C2318yes—
422#376C2314yes—
423#376C2312yes—
424#376C2318yes—
425#376C2314yes—
426C43C2312yes—
427C25C2412yes—
428C22×Q8—24no—
429C22×Q8—42no—
430C22×Q8—42no—
431C22×Q8C2414yes—
432C22×Q8C2412yes—
433C22×Q8C2412yes—
434C22×Q8C2414yes—
435C22×Q8C2412yes—
436C22×Q8C2412yes—
437C22×D4—24no—
438C22×D4—42no—
439C22×D4—42no—
440C22×D4C2412yes—
441C22×D4C2412yes—
442C23×C4C2411yescharacteristic
443C23×C4C2412yes—
444C23×C4C2414yes—
445C23×C4C2414yes—
446C23×C4C2412yes—
447C4⋊Q8—28no—
448C4⋊Q8—28no—
449C4⋊Q8—48no—
450C4⋊Q8—44no—
451C4⋊Q8—44no—
452C4⋊Q8—48no—
453#126—416no—
454#125—216no—
455#125—48no—
456#125—416no—
457#124—28no—
458#124—216no—
459#124—28no—
460#124—48no—
461#124—48no—
462C22⋊Q8—216no—
463C22⋊Q8—216no—
464C22⋊Q8—48no—
465C4×Q8—28no—
466C4×Q8—216no—
467C4×Q8—216no—
468C4×Q8—216no—
469C4×Q8—44no—
470C4×Q8—44no—
471C4×Q8—48no—
472C4×Q8—44no—
473C4×Q8—44no—
474C4×Q8—48no—
475C4×Q8—44no—
476C4×D4—28no—
477C4×D4—44no—
478C4×D4—44no—
479C4×D4—44no—
480#117—216no—
481#117—24no—
482#117—42no—
483#117—42no—
484#117—48no—
485#117—48no—
486#117—42no—
487C2×C4⋊C4C2411yescharacteristic
488C2×C4⋊C4C2414yes—
489C2×C4⋊C4C2412yes—
490C2×C4⋊C4C2414yes—
491C2×C4⋊C4C2414yes—
492C2×C4⋊C4C2418yes—
493C2×C4⋊C4C2418yes—
494C2×C4⋊C4C2418yes—
495C2×C4⋊C4C2414yes—
496C2×C4⋊C4C2414yes—
497C2×C4⋊C4C2412yes—
498C2×C4⋊C4C2411yescharacteristic
499C2×C4⋊C4C2411yescharacteristic
500C2×C4⋊C4C2411yescharacteristic
501C2×C4⋊C4C2411yescharacteristic
502C2×C4⋊C4C2414yes—
503C2×C4⋊C4C2414yes—
504C2×C4⋊C4C2414yes—
505C2×C4⋊C4C2412yes—
506C2×C4⋊C4C2418yes—
507C2×C4⋊C4C2414yes—
508C2×C4⋊C4C2414yes—
509C2×C4⋊C4C2418yes—
510C2×C4⋊C4C2418yes—
511C2×C4⋊C4C2414yes—
512C2×C4⋊C4C2414yes—
513C2×C4⋊C4C2418yes—
514C2×C4⋊C4C2418yes—
515C2×C4⋊C4C2412yes—
516C2×C4⋊C4C2412yes—
517C2×C4⋊C4C2412yes—
518C2×C4⋊C4C2412yes—
519C2×C4⋊C4C2414yes—
520C2×C4⋊C4C2414yes—
521C2×C4⋊C4C2414yes—
522C2×C4⋊C4C2414yes—
523C2×C4⋊C4C2418yes—
524C2×C4⋊C4C2418yes—
525C2×C4⋊C4C2414yes—
526C2×C4⋊C4C2414yes—
527C2×C4⋊C4C2414yes—
528C2×C4⋊C4C2414yes—
529C2×C4⋊C4C2411yescharacteristic
530C2×C22⋊C4—216no—
531C2×C22⋊C4—48no—
532C2×C22⋊C4C2412yes—
533C2×C22⋊C4C2414yes—
534C2×C22⋊C4C2418yes—
535C2×C22⋊C4C2418yes—
536C2×C22⋊C4C2418yes—
537C2×C22⋊C4C2412yes—
538C2×C22⋊C4C2414yes—
539C2×C22⋊C4C2412yes—
540C2×C22⋊C4C2418yes—
541C2×C22⋊C4C2412yes—
542C2×C22⋊C4C2418yes—
543C2×C22⋊C4C2418yes—
544C2×C22⋊C4C2418yes—
545C2×C22⋊C4C2414yes—
546C2×C22⋊C4C2414yes—
547C2×C22⋊C4C2418yes—
548C2×C22⋊C4C2418yes—
549C2×C22⋊C4C2418yes—
550C2×C22⋊C4C2418yes—
551C2×C22⋊C4C2418yes—
552C2×C22⋊C4C2418yes—
553C2×C42#4118yes—
554C2×C42C2412yes—
555C2×C42C2412yes—
556C2×C42C2414yes—
557C2×C42C2412yes—
558C2×C42C2418yes—
559C2×C42C2418yes—
560C2×C42C2414yes—
561C2×C42C2414yes—
562C2×C42C2414yes—
563C2×C42C2412yes—
564C2×C42C2418yes—
565C2×C42C2414yes—
566C2×C42C2414yes—
567C2×C42C2418yes—
568C2×C42C2418yes—
569C2×C42C2411yescharacteristic
570C2×C42C2412yes—
571C2×C42C2411yescharacteristic
572#95C2414yes—
573#95C2414yes—
574#95C2412yes—
575#95C2414yes—
576#95C2414yes—
577#95C2414yes—
578#95C2414yes—
579#95C2418yes—
580#95C2418yes—
581#95C2414yes—
582#95C2418yes—
583#95C2414yes—
584#95C2414yes—
585#95C2412yes—
586#95C2414yes—
587#95C2414yes—
588#95C2414yes—
589#95C2418yes—
590#95C2414yes—
591#95C2418yes—
592#95C2418yes—
593#95C2418yes—
594#95C2418yes—
595#95C2414yes—
596#95C2412yes—
597#95C2418yes—
598#95C2414yes—
599#95C2414yes—
600#95C2418yes—
601#95C2418yes—
602#95C2418yes—
603#95C2412yes—
604#95C2418yes—
605#95C2414yes—
606#95C2414yes—
607#95C2418yes—
608#95C2418yes—
609#95C2414yes—
610#95C2414yes—
611#95C2418yes—
612#95C2418yes—
613#95C2418yes—
614C24—24no—
615C24—42no—
616C24—42no—
617C24—44no—
618C24—44no—
619C24C2514yes—
620C24C2511yescharacteristic
621C2×Q8—28no—
622C2×Q8—24no—
623C2×Q8—24no—
624C2×Q8—28no—
625C2×Q8—24no—
626C2×Q8—28no—
627C2×Q8—28no—
628C2×Q8—24no—
629C2×Q8—42no—
630C2×Q8—42no—
631C2×Q8—42no—
632C2×Q8—44no—
633C2×Q8—42no—
634C2×Q8—44no—
635C2×Q8—44no—
636C2×Q8—44no—
637C2×Q8—416no—
638C2×D4—24no—
639C2×D4—24no—
640C2×D4—24no—
641C2×D4—24no—
642C2×D4—42no—
643C2×D4—42no—
644C2×D4—416no—
645C22×C4—22no—
646C22×C4—22no—
647C22×C4—24no—
648C22×C4—28no—
649C22×C4—42no—
650C22×C4—42no—
651C22×C4—42no—
652C22×C4—42no—
653C22×C4—48no—
654C22×C4—44no—
655C22×C4—48no—
656C22×C4C2×#4114yes—
657C22×C4C2×#4118yes—
658C22×C4C2518yes—
659C22×C4C2512yes—
660C22×C4C2514yes—
661C22×C4C2512yes—
662C22×C4C2514yes—
663C22×C4C2514yes—
664C22×C4C2512yes—
665C22×C4C2514yes—
666C22×C4C2512yes—
667C22×C4C2514yes—
668C22×C4C2514yes—
669C22×C4C2512yes—
670C22×C4C2518yes—
671C22×C4C2512yes—
672C22×C4C2512yes—
673C22×C4C2511yescharacteristic
674C22×C4C2512yes—
675C22×C4C2511yescharacteristic
676C4⋊C4—28no—
677C4⋊C4—28no—
678C4⋊C4—216no—
679C4⋊C4—216no—
680C4⋊C4—28no—
681C4⋊C4—28no—
682C4⋊C4—22no—
683C4⋊C4—28no—
684C4⋊C4—216no—
685C4⋊C4—24no—
686C4⋊C4—42no—
687C4⋊C4—42no—
688C4⋊C4—42no—
689C4⋊C4—42no—
690C4⋊C4—44no—
691C4⋊C4—44no—
692C4⋊C4—44no—
693C4⋊C4—44no—
694C4⋊C4—44no—
695C4⋊C4—48no—
696C4⋊C4—48no—
697C4⋊C4—44no—
698C4⋊C4—44no—
699C4⋊C4—44no—
700C4⋊C4—42no—
701C4⋊C4—41no—
702C4⋊C4—41no—
703C4⋊C4—41no—
704C4⋊C4—41no—
705C4⋊C4—44no—
706C4⋊C4—44no—
707C4⋊C4—48no—
708C4⋊C4—44no—
709C4⋊C4—42no—
710C4⋊C4—48no—
711C4⋊C4—44no—
712C4⋊C4—44no—
713C4⋊C4—44no—
714C4⋊C4—48no—
715C4⋊C4—44no—
716C4⋊C4—48no—
717C4⋊C4—48no—
718C4⋊C4H(5,𝔽2)14yes—
719C22⋊C4—216no—
720C22⋊C4—216no—
721C22⋊C4—216no—
722C22⋊C4—24no—
723C22⋊C4—28no—
724C22⋊C4—42no—
725C22⋊C4—44no—
726C22⋊C4—48no—
727C22⋊C4—48no—
728C22⋊C4—48no—
729C22⋊C4—44no—
730C22⋊C4—48no—
731C22⋊C4—48no—
732C22⋊C4—48no—
733C22⋊C4—44no—
734C22⋊C4—42no—
735C22⋊C4—42no—
736C22⋊C4—48no—
737C22⋊C4—48no—
738C22⋊C4—48no—
739C22⋊C4—48no—
740C42—216no—
741C42—24no—
742C42—24no—
743C42—28no—
744C42—24no—
745C42—216no—
746C42—28no—
747C42—28no—
748C42—44no—
749C42—48no—
750C42—44no—
751C42—48no—
752C42—42no—
753C42—44no—
754C42—48no—
755C42C2×#4114yes—
756C42C2×#4118yes—
757C42C2×#4114yes—
758C23—21no—
759C23—21no—
760C23—22no—
761C23—22no—
762C23—24no—
763C23—24no—
764C23—24no—
765C23—28no—
766C23—28no—
767C23—48no—
768C23—88no—
769C23—162no—
770C23—164no—
771C23—162no—
772C23C22×#4112yes—
773C23C2611yescharacteristic
774Q8—48no—
775Q8—48no—
776Q8—416no—
777Q8—48no—
778Q8—88no—
779Q8—84no—
780D4—48no—
781D4—48no—
782C2×C4—21no—
783C2×C4—21no—
784C2×C4—24no—
785C2×C4—22no—
786C2×C4—22no—
787C2×C4—22no—
788C2×C4—22no—
789C2×C4—28no—
790C2×C4—28no—
791C2×C4—28no—
792C2×C4—24no—
793C2×C4—24no—
794C2×C4—22no—
795C2×C4—22no—
796C2×C4—22no—
797C2×C4—24no—
798C2×C4—22no—
799C2×C4—22no—
800C2×C4—24no—
801C2×C4—28no—
802C2×C4—24no—
803C2×C4—24no—
804C2×C4—24no—
805C2×C4—28no—
806C2×C4—24no—
807C2×C4—24no—
808C2×C4—28no—
809C2×C4—24no—
810C2×C4—24no—
811C2×C4—24no—
812C2×C4—24no—
813C2×C4—24no—
814C2×C4—24no—
815C2×C4—24no—
816C2×C4—24no—
817C2×C4—24no—
818C2×C4—24no—
819C2×C4—28no—
820C2×C4—24no—
821C2×C4—24no—
822C2×C4—24no—
823C2×C4—24no—
824C2×C4—48no—
825C2×C4—48no—
826C2×C4—88no—
827C2×C4—164no—
828C2×C4C22×#4114yes—
829C2×C4C22×#4114yes—
830C2×C4C22×#4112yes—
831C2×C4C22×#4112yes—
832C2×C4C2×H(5,𝔽2)14yes—
833C2×C4C2×H(5,𝔽2)12yes—
834C2×C4#58512yes—
835C22—24no—
836C22—22no—
837C22—41no—
838C22—42no—
839C22—41no—
840C22—44no—
841C22—48no—
842C22—44no—
843C22—48no—
844C22—44no—
845C22—168no—
846C22C23×#4111yescharacteristic
847C22C22×H(5,𝔽2)11yescharacteristic
848C22C2×#58511yescharacteristic
849C222−1+612yes—
850C222−1+612yes—
851C4—24no—
852C4—24no—
853C4—24no—
854C4—22no—
855C4—42no—
856C4—42no—
857C4—44no—
858C4—42no—
859C4—44no—
860C4—44no—
861C4—44no—
862C4—42no—
863C4—42no—
864C4—44no—
865C4—48no—
866C4—44no—
867C4—48no—
868C4#346014yes—
869C2—42no—
870C2—84no—
871C2C2×#346011yescharacteristic
872C2#6286012yes—
873C2#6304811yescharacteristic
874C2#6306212yes—
875C2#6306311yescharacteristic
subgroupG/H
center, commutator, Frattini, socle, cosocleC23C26
prime radicalC23×D4C23
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23 ◁ G
LECSG ▷ C23 ▷ C1

Complements

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

NH ≅ G/Ntype
2. #42941C2semidirect
3. #42702C2semidirect
4. #42700C2semidirect
5. #42337C2semidirect
6. #42211C2semidirect
7. #41624C2semidirect
8. #41612C2semidirect
9. #37641C2semidirect
10. #37612C2semidirect
11. #37600C2semidirect
13. #36698C2semidirect
14. #36691C2semidirect
16. #35974C2semidirect
17. #35938C2semidirect
18. #35749C2semidirect
19. #34231C2semidirect
21. C2×#557C22semidirect
27. #2845C22semidirect
28. #2844C22semidirect
29. #2844C22semidirect
30. #2843C22semidirect
31. #2843C22semidirect
34. #2838C22semidirect
35. #2836C22semidirect
36. #2833C22semidirect
38. #2822C22semidirect
39. #2822C22semidirect
42. #2777C22semidirect
43. #2773C22semidirect
45. #2768C22semidirect
48. #2764C22semidirect
49. #2763C22semidirect
50. #2759C22semidirect
51. #2754C22semidirect
52. #2738C22semidirect
56. #2667C22semidirect
57. #2666C22semidirect
58. #2664C22semidirect
60. #2654C22semidirect
61. #2654C22semidirect
62. #2652C22semidirect
64. #2650C22semidirect
67. #2634C22semidirect
75. #2611C22semidirect
76. #2604C22semidirect
80. #2589C22semidirect
81. #2586C22semidirect
82. #2582C22semidirect
83. #2582C22semidirect
84. #2581C22semidirect
86. #2573C22semidirect
87. #2568C22semidirect
88. #2568C22semidirect
90. #2556C22semidirect
91. #2556C22semidirect
93. #2546C22semidirect
94. #2546C22semidirect
95. #2546C22semidirect
99. #2532C22semidirect
100. #2532C22semidirect
101. #2527C22semidirect
102. #2525C22semidirect
103. #2522C22semidirect
104. #2519C22semidirect
105. #2519C22semidirect
106. #2515C22semidirect
107. #2514C22semidirect
114. #2462C22semidirect
117. #2446C22semidirect
118. #2446C22semidirect
121. #2402C22semidirect
122. #2401C22semidirect
123. #2399C22semidirect
124. #2399C22semidirect
127. #2396C22semidirect
129. #2369C22semidirect
130. #2369C22semidirect
134. #2365C22semidirect
135. #2365C22semidirect
136. #2365C22semidirect
140. #2356C22semidirect
141. #2356C22semidirect
148. #2320C22semidirect
151. C4×#125C22semidirect
152. C4×#125C22semidirect
157. #2276C22semidirect

Maximal subgroups

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

subgroupindex
#429832
#429412
#427022
#427002
#423372
#422112
#416242
#416122
#376412
#376122
#376002
#375372
#366982
#366912
#360332
#359742
#359382
#357492
#342312
#342112