Finite Group Databasebeta

← #7656777

Subgroups — #7656777

Order 512.

4616 conjugacy classes of subgroups.

The subgroup lattice has 934 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#42941C214yesmaximal, complemented
2#42938C214yesmaximal, complemented
3#42353C218yesmaximal, complemented
4#42245C218yesmaximal, complemented
5#39640C212yesmaximal, complemented
6#39542C214yesmaximal
7#39512C212yesmaximal, complemented
8#37934C214yesmaximal
9#37466C214yesmaximal, complemented
10#37453C212yesmaximal
11#36545C212yesmaximal, complemented
12#36177C212yesmaximal, complemented
13#35818C214yesmaximal, complemented
14#35749C214yesmaximal, complemented
15#35013C212yesmaximal, complemented
16#35011C211yesmaximal, characteristic
17#34595C212yesmaximal, complemented
18#34578C211yesmaximal, characteristic
19#34203C212yesmaximal
20C2×#2362C211yesmaximal, characteristic
21C2×#557C2212yescomplemented
22C22×C22⋊Q8C2211yescharacteristic
23C22×C22⋊Q8C2212yes—
24C2×#519C2212yes—
25C22×C4×Q8C2211yescharacteristic
26C22×#117C2211yescharacteristic
27#2857C2212yes—
28#2857C2212yes—
29#2855C2214yes—
30#2851C2214yes—
31#2839C2218yescomplemented
32#2833C2218yescomplemented
33#2817C2218yes—
34#2810C2214yescomplemented
35#2806C2214yescomplemented
36#2805C2214yescomplemented
37#2805C2214yescomplemented
38#2776C2218yescomplemented
39#2774C2218yescomplemented
40#2771C2218yes—
41#2765C2218yes—
42#2765C2218yes—
43#2764C2218yes—
44#2745C2218yes—
45#2744C2218yes—
46#2739C2218yes—
47#2738C2218yes—
48#2667C2214yes—
49#2666C2218yescomplemented
50#2666C2218yescomplemented
51#2666C2218yescomplemented
52#2665C2214yes—
53#2659C2211yescharacteristic
54#2659C2211yescharacteristic
55#2659C2212yes—
56#2659C2212yes—
57#2655C2218yescomplemented
58#2655C2218yescomplemented
59#2646C2212yes—
60#2646C2214yes—
61#2634C2218yescomplemented
62#2627C2214yes—
63#2627C2214yes—
64#2627C2214yes—
65#2627C2214yes—
66#2627C2214yes—
67#2626C2212yes—
68#2626C2212yes—
69#2621C2214yes—
70#2621C2214yes—
71#2611C2218yes—
72#2599C2218yes—
73#2586C2218yescomplemented
74#2585C2218yescomplemented
75#2584C2214yescomplemented
76#2583C2218yes—
77#2582C2212yescomplemented
78#2581C2214yescomplemented
79#2581C2214yescomplemented
80#2575C2218yes—
81#2573C2218yes—
82#2571C2212yescomplemented
83#2570C2214yescomplemented
84#2568C2212yescomplemented
85#2568C2214yescomplemented
86#2546C2214yescomplemented
87#2546C2212yescomplemented
88#2533C2218yescomplemented
89#2527C2218yes—
90#2524C2218yescomplemented
91#2520C2218yescomplemented
92#2515C2218yes—
93#2514C2214yescomplemented
94#2514C2214yescomplemented
95#2514C2214yescomplemented
96#2511C2214yescomplemented
97#2509C2214yescomplemented
98#2505C2218yes—
99#2503C2214yes—
100#2503C2214yes—
101#2502C2214yes—
102#2493C2218yes—
103#2493C2218yes—
104#2483C2218yes—
105#2475C2218yes—
106#2475C2218yes—
107#2473C2218yes—
108#2462C2218yescomplemented
109#2462C2218yescomplemented
110#2462C2218yescomplemented
111#2446C2214yescomplemented
112#2446C2214yescomplemented
113#2446C2214yescomplemented
114#2434C2214yes—
115#2434C2214yes—
116#2434C2214yes—
117#2402C2218yescomplemented
118#2399C2218yescomplemented
119#2396C2214yes—
120#2396C2214yes—
121#2365C2212yescomplemented
122#2365C2214yescomplemented
123#2362C2218yes—
124#2362C2214yes—
125#2362C2214yes—
126#2362C2214yes—
127#2362C2214yes—
128#2360C2214yes—
129#2360C2214yes—
130#2356C2214yescomplemented
131#2355C2212yescomplemented
132#2355C2212yescomplemented
133#2344C2218yes—
134#2342C2218yes—
135#2329C2214yes—
136#2323C2214yes—
137#2323C2214yes—
138#2316C2212yes—
139#2315C2212yes—
140#2315C2212yes—
141#2313C2214yes—
142#2310C2212yes—
143C4×C22⋊Q8C2212yes—
144C4×C22⋊Q8C2212yes—
145C4×C22⋊Q8C2214yes—
146C4×C22⋊Q8C2214yes—
147C4×C22⋊Q8C2214yes—
148C2×#391C2211yescharacteristic
149C2×#389C2211yescharacteristic
150C2×#388C2212yes—
151C2×#388C2212yes—
152C2×#387C2212yes—
153#2283C2214yes—
154#2280C2212yes—
155#2274C2212yes—
156C2×C4×C4⋊C4C2212yes—
157C2×C4×C4⋊C4C2211yescharacteristic
158C2×C4×C22⋊C4C2211yescharacteristic
159C23×Q8C2312yes—
160C23×Q8C2311yescharacteristic
161C24×C4C2311yescharacteristic
162#557—48no—
163C2×C4⋊Q8C2312yes—
164C2×C4⋊Q8C2314yes—
165C2×C4⋊Q8C2312yes—
166C2×C4⋊Q8C2314yes—
167C2×#125C2314yes—
168C2×#125C2318yes—
169C2×C22⋊Q8—28no—
170C2×C22⋊Q8—216no—
171C2×C22⋊Q8C2314yes—
172C2×C22⋊Q8C2314yes—
173C2×C22⋊Q8C2312yes—
174C2×C22⋊Q8C2314yes—
175C2×C22⋊Q8C2314yes—
176C2×C22⋊Q8C2314yes—
177C2×C22⋊Q8C2312yes—
178C2×C22⋊Q8C2314yes—
179#519—48no—
180C2×C4×Q8—44no—
181C2×C4×Q8C2312yes—
182C2×C4×Q8C2314yes—
183C2×C4×Q8C2312yes—
184C2×C4×Q8C2314yes—
185C2×C4×Q8C2314yes—
186C2×C4×Q8C2312yes—
187C2×C4×Q8C2314yes—
188C2×C4×Q8C2314yes—
189C2×C4×Q8C2314yes—
190C2×C4×Q8C2312yes—
191C2×#117—44no—
192C2×#117C2312yes—
193C2×#117C2312yes—
194C2×#117C2312yes—
195C2×#117C2312yes—
196C2×#117C2314yes—
197C2×#117C2318yes—
198C22×C4⋊C4C2312yes—
199C22×C4⋊C4C2312yes—
200C22×C4⋊C4C2314yes—
201C22×C4⋊C4C2311yescharacteristic
202C22×C4⋊C4C2312yes—
203C22×C4⋊C4C2311yescharacteristic
204C22×C4⋊C4C2311yescharacteristic
205C22×C4⋊C4C2312yes—
206C22×C22⋊C4C2314yes—
207C22×C22⋊C4C2311yescharacteristic
208C22×C22⋊C4C2311yescharacteristic
209C22×C22⋊C4C2312yes—
210C22×C22⋊C4C2312yes—
211C22×C42C2312yes—
212C22×C42C2312yes—
213C22×C42C2311yescharacteristic
214C22×C42C2311yescharacteristic
215C22×C42C2312yes—
216#401C2318yes—
217#401C2318yes—
218#400C2318yes—
219#400C2318yes—
220#400C2318yes—
221#400C2318yes—
222#400C2318yes—
223#400C2318yes—
224#400C2318yes—
225#400C2318yes—
226#400C2318yes—
227#400C2318yes—
228#400C2318yes—
229#400C2314yes—
230#400C2318yes—
231#400C2318yes—
232#400C2318yes—
233#400C2318yes—
234#400C2318yes—
235#400C2314yes—
236#400C2318yes—
237#399C2314yes—
238#399C2314yes—
239#398C2318yes—
240#398C2318yes—
241#398C2318yes—
242#398C2318yes—
243#398C2318yes—
244#398C2318yes—
245#398C2318yes—
246#398C2314yes—
247#398C2318yes—
248#398C2318yes—
249#398C2314yes—
250#398C2318yes—
251#398C2318yes—
252#398C2318yes—
253#398C2318yes—
254#398C2314yes—
255#398C2318yes—
256#398C2314yes—
257#397C2318yes—
258#397C2318yes—
259#397C2318yes—
260#397C2318yes—
261#396C2314yes—
262#396C2314yes—
263#396C2314yes—
264#396C2314yes—
265#395C2318yes—
266#395C2318yes—
267#395C2318yes—
268#395C2318yes—
269#395C2318yes—
270#395C2318yes—
271#395C2318yes—
272#395C2314yes—
273#395C2314yes—
274#393C2314yes—
275#393C2314yes—
276#391C2314yes—
277#391C2314yes—
278#391C2314yes—
279#391C2314yes—
280#391C2318yes—
281#391C2314yes—
282#391C2314yes—
283#391C2314yes—
284#391C2314yes—
285#391C2314yes—
286#391C2312yes—
287#391C2314yes—
288#391C2314yes—
289#391C2314yes—
290#391C2314yes—
291#391C2314yes—
292#391C2314yes—
293#391C2312yes—
294#389C2314yes—
295#389C2314yes—
296#389C2314yes—
297#389C2314yes—
298#389C2314yes—
299#389C2314yes—
300#389C2318yes—
301#389C2318yes—
302#389C2318yes—
303#389C2314yes—
304#389C2314yes—
305#389C2314yes—
306#389C2314yes—
307#389C2314yes—
308#389C2314yes—
309#389C2312yes—
310#389C2314yes—
311#389C2318yes—
312#389C2314yes—
313#389C2314yes—
314#389C2318yes—
315#389C2312yes—
316#388C2318yes—
317#388C2318yes—
318#388C2318yes—
319#388C2318yes—
320#388C2318yes—
321#388C2318yes—
322#388C2318yes—
323#388C2318yes—
324#387C2318yes—
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#387C2314yes—
351#387C2314yes—
352#387C2318yes—
353#385C2318yes—
354#385C2318yes—
355#385C2318yes—
356#385C2318yes—
357#385C2318yes—
358#385C2318yes—
359#385C2318yes—
360#385C2318yes—
361#385C2318yes—
362#385C2314yes—
363#385C2314yes—
364#385C2318yes—
365#384C2312yes—
366#384C2312yes—
367#383C2318yes—
368#383C2318yes—
369#383C2318yes—
370#382C2318yes—
371#382C2314yes—
372#382C2314yes—
373#382C2314yes—
374#382C2314yes—
375#382C2314yes—
376#381C2314yes—
377#381C2318yes—
378#381C2318yes—
379#381C2318yes—
380#381C2318yes—
381#381C2318yes—
382#380C2312yes—
383#380C2314yes—
384#380C2314yes—
385#380C2314yes—
386#380C2314yes—
387#380C2318yes—
388#380C2312yes—
389#380C2312yes—
390#380C2312yes—
391#380C2312yes—
392#380C2312yes—
393#379C2314yes—
394C4×C4⋊C4C2314yes—
395C4×C4⋊C4C2312yes—
396C4×C4⋊C4C2314yes—
397C4×C4⋊C4C2312yes—
398C4×C4⋊C4C2314yes—
399C4×C4⋊C4C2314yes—
400C4×C4⋊C4C2314yes—
401C4×C4⋊C4C2314yes—
402C4×C4⋊C4C2318yes—
403C4×C4⋊C4C2318yes—
404C4×C4⋊C4C2318yes—
405C4×C4⋊C4C2314yes—
406C4×C4⋊C4C2312yes—
407C4×C4⋊C4C2312yes—
408C4×C4⋊C4C2314yes—
409C4×C4⋊C4C2318yes—
410C4×C4⋊C4C2314yes—
411C4×C4⋊C4C2314yes—
412C4×C4⋊C4C2318yes—
413C4×C22⋊C4C2318yes—
414C4×C22⋊C4C2318yes—
415C4×C22⋊C4C2314yes—
416C4×C22⋊C4C2318yes—
417C4×C22⋊C4C2314yes—
418C4×C22⋊C4C2314yes—
419C4×C22⋊C4C2314yes—
420#376C2318yes—
421C2×#95C2312yes—
422C2×#95C2311yescharacteristic
423C2×#95C2311yescharacteristic
424C2×#95C2312yes—
425C2×#95C2312yes—
426C2×#95C2312yes—
427C25C2411yescharacteristic
428C22×Q8—28no—
429C22×Q8—24no—
430C22×Q8—42no—
431C22×Q8—44no—
432C22×Q8—42no—
433C22×Q8—44no—
434C22×Q8C2412yes—
435C22×Q8C2414yes—
436C22×Q8C2412yes—
437C22×Q8C2414yes—
438C22×Q8C2412yes—
439C22×Q8C2412yes—
440C23×C4—42no—
441C23×C4—42no—
442C23×C4#4118yes—
443C23×C4C2412yes—
444C23×C4C2412yes—
445C23×C4C2411yescharacteristic
446C23×C4C2412yes—
447C23×C4C2412yes—
448C23×C4C2412yes—
449C23×C4C2411yescharacteristic
450C23×C4C2414yes—
451C23×C4C2414yes—
452C23×C4C2411yescharacteristic
453C23×C4C2412yes—
454C23×C4C2411yescharacteristic
455C23×C4C2411yescharacteristic
456C23×C4C2411yescharacteristic
457C4⋊Q8—44no—
458C4⋊Q8—48no—
459C4⋊Q8—44no—
460C4⋊Q8—48no—
461#125—48no—
462#125—416no—
463C22⋊Q8—216no—
464C22⋊Q8—216no—
465C22⋊Q8—216no—
466C22⋊Q8—216no—
467C22⋊Q8—216no—
468C22⋊Q8—216no—
469C22⋊Q8—28no—
470C22⋊Q8—28no—
471C4×Q8—28no—
472C4×Q8—216no—
473C4×Q8—44no—
474C4×Q8—48no—
475C4×Q8—48no—
476C4×Q8—44no—
477C4×Q8—48no—
478C4×Q8—48no—
479C4×Q8—44no—
480C4×Q8—48no—
481#117—28no—
482#117—44no—
483#117—44no—
484#117—48no—
485#117—416no—
486#117—44no—
487C2×C4⋊C4—24no—
488C2×C4⋊C4—28no—
489C2×C4⋊C4—216no—
490C2×C4⋊C4—28no—
491C2×C4⋊C4—28no—
492C2×C4⋊C4—24no—
493C2×C4⋊C4—42no—
494C2×C4⋊C4—44no—
495C2×C4⋊C4C2412yes—
496C2×C4⋊C4C2411yescharacteristic
497C2×C4⋊C4C2412yes—
498C2×C4⋊C4C2414yes—
499C2×C4⋊C4C2412yes—
500C2×C4⋊C4C2414yes—
501C2×C4⋊C4C2418yes—
502C2×C4⋊C4C2418yes—
503C2×C4⋊C4C2414yes—
504C2×C4⋊C4C2412yes—
505C2×C4⋊C4C2418yes—
506C2×C4⋊C4C2418yes—
507C2×C4⋊C4C2418yes—
508C2×C4⋊C4C2414yes—
509C2×C4⋊C4C2412yes—
510C2×C4⋊C4C2414yes—
511C2×C4⋊C4C2412yes—
512C2×C4⋊C4C2412yes—
513C2×C4⋊C4C2414yes—
514C2×C4⋊C4C2412yes—
515C2×C4⋊C4C2412yes—
516C2×C4⋊C4C2418yes—
517C2×C4⋊C4C2412yes—
518C2×C4⋊C4C2412yes—
519C2×C4⋊C4C2412yes—
520C2×C4⋊C4C2414yes—
521C2×C4⋊C4C2414yes—
522C2×C4⋊C4C2418yes—
523C2×C4⋊C4C2412yes—
524C2×C4⋊C4C2414yes—
525C2×C4⋊C4C2414yes—
526C2×C4⋊C4C2418yes—
527C2×C4⋊C4C2414yes—
528C2×C4⋊C4C2418yes—
529C2×C4⋊C4C2414yes—
530C2×C4⋊C4C2418yes—
531C2×C4⋊C4C2412yes—
532C2×C4⋊C4C2412yes—
533C2×C4⋊C4C2414yes—
534C2×C4⋊C4C2414yes—
535C2×C4⋊C4C2418yes—
536C2×C4⋊C4C2418yes—
537C2×C4⋊C4C2414yes—
538C2×C4⋊C4C2414yes—
539C2×C4⋊C4C2414yes—
540C2×C4⋊C4C2414yes—
541C2×C4⋊C4C2411yescharacteristic
542C2×C22⋊C4—28no—
543C2×C22⋊C4—216no—
544C2×C22⋊C4—24no—
545C2×C22⋊C4—24no—
546C2×C22⋊C4—44no—
547C2×C22⋊C4C2414yes—
548C2×C22⋊C4C2418yes—
549C2×C22⋊C4C2418yes—
550C2×C22⋊C4C2418yes—
551C2×C22⋊C4C2414yes—
552C2×C22⋊C4C2414yes—
553C2×C22⋊C4C2414yes—
554C2×C22⋊C4C2414yes—
555C2×C22⋊C4C2414yes—
556C2×C22⋊C4C2414yes—
557C2×C22⋊C4C2414yes—
558C2×C22⋊C4C2414yes—
559C2×C22⋊C4C2414yes—
560C2×C42—28no—
561C2×C42—44no—
562C2×C42—44no—
563C2×C42—42no—
564C2×C42—42no—
565C2×C42C2414yes—
566C2×C42C2418yes—
567C2×C42C2414yes—
568C2×C42C2414yes—
569C2×C42C2414yes—
570C2×C42C2412yes—
571C2×C42C2412yes—
572C2×C42C2414yes—
573C2×C42C2414yes—
574C2×C42C2414yes—
575C2×C42C2418yes—
576C2×C42C2412yes—
577C2×C42C2414yes—
578C2×C42C2418yes—
579C2×C42C2418yes—
580C2×C42C2412yes—
581#95C2414yes—
582#95C2414yes—
583#95C2414yes—
584#95C2418yes—
585#95C2414yes—
586#95C2418yes—
587#95C2418yes—
588#95C2414yes—
589#95C2418yes—
590#95C2418yes—
591#95C2418yes—
592#95C2414yes—
593#95C2414yes—
594#95C2418yes—
595#95C2418yes—
596#95C2414yes—
597#95C2414yes—
598#95C2418yes—
599#95C2418yes—
600#95C2418yes—
601#95C2418yes—
602#95C2418yes—
603#95C2414yes—
604#95C2418yes—
605#95C2418yes—
606#95C2418yes—
607#95C2418yes—
608#95C2418yes—
609#95C2418yes—
610#95C2414yes—
611#95C2414yes—
612#95C2414yes—
613#95C2414yes—
614#95C2418yes—
615#95C2418yes—
616#95C2418yes—
617#95C2418yes—
618#95C2418yes—
619#95C2418yes—
620#95C2418yes—
621#95C2418yes—
622C24—22no—
623C24—22no—
624C24—41no—
625C24—41no—
626C24—41no—
627C24—41no—
628C24C2×#4114yes—
629C24C2512yes—
630C24C2511yescharacteristic
631C2×Q8—28no—
632C2×Q8—24no—
633C2×Q8—28no—
634C2×Q8—24no—
635C2×Q8—24no—
636C2×Q8—28no—
637C2×Q8—24no—
638C2×Q8—24no—
639C2×Q8—28no—
640C2×Q8—24no—
641C2×Q8—42no—
642C2×Q8—44no—
643C2×Q8—42no—
644C2×Q8—42no—
645C2×Q8—44no—
646C2×Q8—42no—
647C2×Q8—42no—
648C2×Q8—42no—
649C2×Q8—416no—
650C2×Q8—432no—
651C22×C4—22no—
652C22×C4—24no—
653C22×C4—22no—
654C22×C4—24no—
655C22×C4—24no—
656C22×C4—28no—
657C22×C4—24no—
658C22×C4—24no—
659C22×C4—24no—
660C22×C4—24no—
661C22×C4—28no—
662C22×C4—22no—
663C22×C4—22no—
664C22×C4—24no—
665C22×C4—24no—
666C22×C4—416no—
667C22×C4—41no—
668C22×C4—41no—
669C22×C4—42no—
670C22×C4—41no—
671C22×C4—42no—
672C22×C4—44no—
673C22×C4—42no—
674C22×C4—41no—
675C22×C4—42no—
676C22×C4—41no—
677C22×C4—41no—
678C22×C4—42no—
679C22×C4—44no—
680C22×C4—42no—
681C22×C4—41no—
682C22×C4—41no—
683C22×C4—42no—
684C22×C4—44no—
685C22×C4—44no—
686C22×C4—41no—
687C22×C4—41no—
688C22×C4C2×#4118yes—
689C22×C4C2×#4114yes—
690C22×C4C2×#4118yes—
691C22×C4C2×#4114yes—
692C22×C42−1+414yes—
693C22×C42−1+414yes—
694C22×C4C2514yes—
695C22×C4C2514yes—
696C22×C4C2512yes—
697C22×C4C2514yes—
698C22×C4C2518yes—
699C22×C4C2514yes—
700C22×C4C2512yes—
701C22×C4C2514yes—
702C22×C4C2512yes—
703C22×C4C2514yes—
704C22×C4C2514yes—
705C22×C4C2518yes—
706C22×C4C2512yes—
707C22×C4C2511yescharacteristic
708C22×C4C2512yes—
709C22×C4C2512yes—
710C22×C4C2512yes—
711C22×C4C2511yescharacteristic
712C4⋊C4—28no—
713C4⋊C4—24no—
714C4⋊C4—24no—
715C4⋊C4—28no—
716C4⋊C4—216no—
717C4⋊C4—216no—
718C4⋊C4—216no—
719C4⋊C4—24no—
720C4⋊C4—22no—
721C4⋊C4—24no—
722C4⋊C4—28no—
723C4⋊C4—216no—
724C4⋊C4—216no—
725C4⋊C4—24no—
726C4⋊C4—24no—
727C4⋊C4—28no—
728C4⋊C4—28no—
729C4⋊C4—42no—
730C4⋊C4—44no—
731C4⋊C4—42no—
732C4⋊C4—44no—
733C4⋊C4—44no—
734C4⋊C4—42no—
735C4⋊C4—44no—
736C4⋊C4—44no—
737C4⋊C4—48no—
738C4⋊C4—44no—
739C4⋊C4—44no—
740C4⋊C4—48no—
741C4⋊C4—42no—
742C4⋊C4—42no—
743C4⋊C4—42no—
744C4⋊C4—42no—
745C4⋊C4—48no—
746C4⋊C4—42no—
747C4⋊C4—44no—
748C4⋊C4—42no—
749C4⋊C4—44no—
750C4⋊C4—44no—
751C4⋊C4—48no—
752C4⋊C4—48no—
753C4⋊C4—44no—
754C4⋊C4—44no—
755C4⋊C4—44no—
756C4⋊C4—48no—
757C4⋊C4—48no—
758C4⋊C4H(5,𝔽2)14yes—
759C22⋊C4—216no—
760C22⋊C4—216no—
761C22⋊C4—216no—
762C22⋊C4—28no—
763C22⋊C4—28no—
764C22⋊C4—28no—
765C22⋊C4—28no—
766C22⋊C4—28no—
767C22⋊C4—44no—
768C22⋊C4—44no—
769C22⋊C4—44no—
770C22⋊C4—44no—
771C22⋊C4—44no—
772C42—28no—
773C42—28no—
774C42—24no—
775C42—216no—
776C42—28no—
777C42—28no—
778C42—28no—
779C42—24no—
780C42—28no—
781C42—42no—
782C42—44no—
783C42—42no—
784C42—44no—
785C42—48no—
786C42—48no—
787C42—48no—
788C23—21no—
789C23—21no—
790C23—21no—
791C23—21no—
792C23—22no—
793C23—22no—
794C23—22no—
795C23—22no—
796C23—22no—
797C23—22no—
798C23—28no—
799C23—44no—
800C23—44no—
801C23—82no—
802C23—82no—
803C23—82no—
804C23—82no—
805C23C22×#4114yes—
806C23C22×#4112yes—
807C23C2×2−1+412yes—
808C23C2×2−1+412yes—
809C23C2611yescharacteristic
810Q8—48no—
811Q8—416no—
812Q8—48no—
813Q8—48no—
814Q8—416no—
815Q8—84no—
816C2×C4—22no—
817C2×C4—22no—
818C2×C4—21no—
819C2×C4—22no—
820C2×C4—22no—
821C2×C4—21no—
822C2×C4—22no—
823C2×C4—22no—
824C2×C4—22no—
825C2×C4—22no—
826C2×C4—28no—
827C2×C4—216no—
828C2×C4—24no—
829C2×C4—28no—
830C2×C4—24no—
831C2×C4—28no—
832C2×C4—24no—
833C2×C4—24no—
834C2×C4—24no—
835C2×C4—22no—
836C2×C4—24no—
837C2×C4—28no—
838C2×C4—22no—
839C2×C4—24no—
840C2×C4—22no—
841C2×C4—22no—
842C2×C4—22no—
843C2×C4—24no—
844C2×C4—24no—
845C2×C4—24no—
846C2×C4—24no—
847C2×C4—24no—
848C2×C4—24no—
849C2×C4—22no—
850C2×C4—24no—
851C2×C4—24no—
852C2×C4—28no—
853C2×C4—24no—
854C2×C4—24no—
855C2×C4—24no—
856C2×C4—24no—
857C2×C4—28no—
858C2×C4—28no—
859C2×C4—24no—
860C2×C4—24no—
861C2×C4—22no—
862C2×C4—22no—
863C2×C4—22no—
864C2×C4—44no—
865C2×C4—48no—
866C2×C4—44no—
867C2×C4—44no—
868C2×C4—48no—
869C2×C4—48no—
870C2×C4—416no—
871C2×C4—48no—
872C2×C4—88no—
873C2×C4—84no—
874C2×C4—82no—
875C2×C4—82no—
876C2×C4C22×#4114yes—
877C2×C4C22×#4112yes—
878C2×C4C22×#4112yes—
879C2×C4C2×H(5,𝔽2)14yes—
880C2×C4C2×H(5,𝔽2)12yes—
881C2×C4C2×2−1+414yes—
882C2×C4C2×2−1+414yes—
883C2×C4#58512yes—
884C22—22no—
885C22—22no—
886C22—22no—
887C22—22no—
888C22—22no—
889C22—22no—
890C22—24no—
891C22—24no—
892C22—24no—
893C22—42no—
894C22—42no—
895C22—42no—
896C22—42no—
897C22—88no—
898C22#350914yes—
899C22C23×#4111yescharacteristic
900C22C22×H(5,𝔽2)11yescharacteristic
901C22C22×2−1+411yescharacteristic
902C22C22×2−1+411yescharacteristic
903C22C2×#58511yescharacteristic
904C222−1+611yescharacteristic
905C222−1+611yescharacteristic
906C4—24no—
907C4—24no—
908C4—24no—
909C4—24no—
910C4—22no—
911C4—44no—
912C4—48no—
913C4—44no—
914C4—44no—
915C4—44no—
916C4—44no—
917C4—42no—
918C4—42no—
919C4—44no—
920C4—48no—
921C4—44no—
922C4—42no—
923C4#345914yes—
924C2—24no—
925C2—44no—
926C2C2×#345911yescharacteristic
927C2C2×#350911yescharacteristic
928C2#6286011yescharacteristic
929C2#6289311yescharacteristic
930C2#6290411yescharacteristic
931C2#6291511yescharacteristic
932C2#6293211yescharacteristic
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. #42941C2semidirect
2. #42938C2semidirect
3. #42353C2semidirect
4. #42245C2semidirect
5. #39640C2semidirect
7. #39512C2semidirect
9. #37466C2semidirect
11. #36545C2semidirect
12. #36177C2semidirect
13. #35818C2semidirect
14. #35749C2semidirect
15. #35013C2semidirect
17. #34595C2semidirect
21. C2×#557C22semidirect
31. #2839C22semidirect
32. #2833C22semidirect
34. #2810C22semidirect
35. #2806C22semidirect
36. #2805C22semidirect
37. #2805C22semidirect
38. #2776C22semidirect
39. #2774C22semidirect
49. #2666C22semidirect
50. #2666C22semidirect
51. #2666C22semidirect
57. #2655C22semidirect
58. #2655C22semidirect
61. #2634C22semidirect
73. #2586C22semidirect
74. #2585C22semidirect
75. #2584C22semidirect
77. #2582C22semidirect
78. #2581C22semidirect
79. #2581C22semidirect
82. #2571C22semidirect
83. #2570C22semidirect
84. #2568C22semidirect
85. #2568C22semidirect
86. #2546C22semidirect
87. #2546C22semidirect
88. #2533C22semidirect
90. #2524C22semidirect
91. #2520C22semidirect
93. #2514C22semidirect
94. #2514C22semidirect
95. #2514C22semidirect
96. #2511C22semidirect
97. #2509C22semidirect
108. #2462C22semidirect
109. #2462C22semidirect
110. #2462C22semidirect
111. #2446C22semidirect
112. #2446C22semidirect
113. #2446C22semidirect
117. #2402C22semidirect
118. #2399C22semidirect
121. #2365C22semidirect
122. #2365C22semidirect
130. #2356C22semidirect
131. #2355C22semidirect
132. #2355C22semidirect

Maximal subgroups

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

subgroupindex
#429412
#429382
#423532
#422452
#396402
#395422
#395122
#379342
#374662
#374532
#365452
#361772
#358182
#357492
#350132
#350112
#345952
#345782
#342032
C2×#23622