Finite Group Databasebeta

← #7642644

Subgroups — #7642644

Order 512.

4368 conjugacy classes of subgroups.

The subgroup lattice has 879 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#39679C214yesmaximal, complemented
2#39543C214yesmaximal
3#39293C214yesmaximal, complemented
4#39283C214yesmaximal, complemented
5#38287C214yesmaximal, complemented
6#38273C214yesmaximal, complemented
7#37958C214yesmaximal
8#37935C214yesmaximal, complemented
9#37028C214yesmaximal, complemented
10#37023C214yesmaximal, complemented
11#36635C212yesmaximal, complemented
12#35511C214yesmaximal, complemented
13#35494C214yesmaximal, complemented
14#35325C212yesmaximal
15#35315C212yesmaximal, complemented
16#35173C211yesmaximal, characteristic, complemented
17#35104C211yesmaximal, characteristic, complemented
18#35086C212yesmaximal
19#35014C212yesmaximal
20#34235C212yesmaximal, complemented
21C2×#2298C211yesmaximal, characteristic
22C2×#533C2212yes—
23C22×#117C2211yescharacteristic
24#2864C2214yescomplemented
25#2863C2214yescomplemented
26#2863C2214yescomplemented
27#2862C2212yescomplemented
28#2859C2212yescomplemented
29#2857C2212yes—
30#2857C2212yes—
31#2857C2212yes—
32#2855C2214yes—
33#2855C2214yes—
34#2851C2212yes—
35#2851C2214yes—
36#2848C2214yes—
37#2809C2218yescomplemented
38#2805C2218yescomplemented
39#2802C2218yescomplemented
40#2783C2218yes—
41#2777C2218yes—
42#2777C2218yes—
43#2775C2218yes—
44#2775C2218yes—
45#2774C2218yescomplemented
46#2773C2218yes—
47#2772C2218yes—
48#2769C2218yescomplemented
49#2767C2218yescomplemented
50#2766C2218yescomplemented
51#2759C2218yes—
52#2758C2218yescomplemented
53#2659C2214yes—
54#2652C2218yes—
55#2647C2212yescomplemented
56#2646C2214yes—
57#2645C2214yescomplemented
58#2642C2212yescomplemented
59#2628C2212yes—
60#2628C2212yes—
61#2627C2214yes—
62#2626C2214yes—
63#2621C2212yes—
64#2621C2212yes—
65#2612C2218yescomplemented
66#2611C2214yes—
67#2611C2214yes—
68#2606C2214yescomplemented
69#2605C2214yescomplemented
70#2604C2218yes—
71#2604C2218yes—
72#2599C2214yes—
73#2599C2214yes—
74#2596C2218yes—
75#2594C2218yes—
76#2590C2218yescomplemented
77#2589C2218yes—
78#2587C2218yes—
79#2585C2218yescomplemented
80#2584C2214yescomplemented
81#2584C2214yescomplemented
82#2583C2214yes—
83#2581C2218yescomplemented
84#2570C2214yescomplemented
85#2567C2214yescomplemented
86#2561C2214yes—
87#2550C2214yescomplemented
88#2546C2214yescomplemented
89#2533C2218yescomplemented
90#2533C2218yescomplemented
91#2532C2218yes—
92#2529C2218yes—
93#2528C2218yescomplemented
94#2528C2218yescomplemented
95#2519C2218yes—
96#2508C2218yescomplemented
97#2505C2218yes—
98#2505C2218yes—
99#2497C2214yes—
100#2496C2214yes—
101#2493C2218yes—
102#2492C2214yes—
103#2489C2214yes—
104#2484C2214yes—
105#2482C2214yes—
106#2480C2218yes—
107#2469C2218yes—
108#2462C2218yescomplemented
109#2429C2214yes—
110#2429C2214yes—
111#2423C2214yes—
112#2421C2214yes—
113#2365C2214yescomplemented
114#2365C2214yescomplemented
115#2360C2218yes—
116#2356C2214yescomplemented
117#2351C2214yescomplemented
118#2343C2218yes—
119#2336C2214yescomplemented
120#2336C2214yescomplemented
121#2334C2218yes—
122#2330C2212yescomplemented
123#2329C2214yes—
124#2329C2214yes—
125#2327C2212yescomplemented
126#2323C2214yes—
127#2323C2214yes—
128#2320C2214yescomplemented
129#2320C2214yescomplemented
130#2316C2214yes—
131#2312C2214yes—
132C4×C4⋊Q8C2212yescomplemented
133C4×C4⋊Q8C2212yescomplemented
134C4×#125C2214yescomplemented
135C4×C22⋊Q8C2214yes—
136C4×C22⋊Q8C2214yes—
137C4×C22⋊Q8C2214yes—
138#2298C2214yes—
139#2298C2214yes—
140#2298C2212yes—
141#2298C2212yes—
142#2298C2212yes—
143#2298C2212yes—
144#2295C2214yescomplemented
145#2295C2214yescomplemented
146C2×#388C2212yes—
147C2×#388C2212yes—
148C2×#387C2212yes—
149C2×#387C2212yes—
150#2283C2214yes—
151#2283C2212yes—
152#2276C2214yescomplemented
153C2×C4×C4⋊C4C2211yescharacteristic
154C2×C4×C4⋊C4C2211yescharacteristic
155C2×C4×C22⋊C4C2211yescharacteristic
156C2×C4×C22⋊C4C2211yescharacteristic
157C2×#376C2211yescharacteristic
158C2×C43C2211yescharacteristic
159C24×C4C2311yescharacteristic
160#533—216no—
161C2×C4⋊Q8C2312yes—
162C2×C4⋊Q8C2312yes—
163C2×C4⋊Q8C2312yes—
164C2×C4⋊Q8C2312yes—
165C2×C4⋊Q8C2312yes—
166C2×#126C2318yes—
167C2×#125C2314yes—
168C2×#125C2314yes—
169C2×#125C2312yes—
170C2×C22⋊Q8C2314yes—
171C2×C22⋊Q8C2314yes—
172C2×C22⋊Q8C2314yes—
173C2×C22⋊Q8C2314yes—
174C2×C22⋊Q8C2314yes—
175C2×C4×Q8C2314yes—
176C2×C4×Q8C2314yes—
177C2×C4×Q8C2314yes—
178C2×C4×Q8C2314yes—
179C2×C4×Q8C2314yes—
180C2×C4×Q8C2318yes—
181C2×#117—28no—
182C2×#117C2314yes—
183C2×#117C2312yes—
184C2×#117C2312yes—
185C2×#117C2312yes—
186C2×#117C2312yes—
187C22×C4⋊C4C2312yes—
188C22×C4⋊C4C2311yescharacteristic
189C22×C4⋊C4C2311yescharacteristic
190C22×C4⋊C4C2312yes—
191C22×C22⋊C4C2311yescharacteristic
192C22×C22⋊C4C2312yes—
193C22×C22⋊C4C2311yescharacteristic
194C22×C22⋊C4C2312yes—
195C22×C42C2311yescharacteristic
196C22×C42C2312yes—
197C22×C42C2311yescharacteristic
198C22×C42C2312yes—
199C22×C42C2311yescharacteristic
200C22×C42C2311yescharacteristic
201C22×C42C2311yescharacteristic
202C22×C42C2311yescharacteristic
203#401C2318yes—
204#400C2318yes—
205#400C2318yes—
206#400C2318yes—
207#400C2318yes—
208#400C2318yes—
209#400C2318yes—
210#400C2318yes—
211#400C2314yes—
212#400C2314yes—
213#400C2318yes—
214#400C2318yes—
215#400C2318yes—
216#400C2318yes—
217#400C2318yes—
218#399C2318yes—
219#399C2314yes—
220#399C2314yes—
221#398C2318yes—
222#398C2314yes—
223#398C2314yes—
224#398C2318yes—
225#398C2318yes—
226#398C2314yes—
227#398C2318yes—
228#398C2318yes—
229#398C2318yes—
230#398C2314yes—
231#398C2318yes—
232#398C2318yes—
233#397C2314yes—
234#397C2314yes—
235#397C2314yes—
236#397C2314yes—
237#397C2318yes—
238#397C2318yes—
239#397C2318yes—
240#396C2318yes—
241#396C2318yes—
242#396C2318yes—
243#395C2318yes—
244#395C2318yes—
245#395C2314yes—
246#395C2314yes—
247#395C2318yes—
248#393C2314yes—
249#393C2314yes—
250#393C2318yes—
251#391C2314yes—
252#391C2314yes—
253#391C2314yes—
254#391C2314yes—
255#391C2314yes—
256#391C2318yes—
257#391C2318yes—
258#391C2318yes—
259#391C2314yes—
260#391C2314yes—
261#391C2314yes—
262#391C2314yes—
263#391C2314yes—
264#389C2314yes—
265#389C2314yes—
266#389C2314yes—
267#389C2314yes—
268#389C2314yes—
269#389C2314yes—
270#389C2318yes—
271#389C2318yes—
272#389C2314yes—
273#389C2314yes—
274#389C2318yes—
275#389C2318yes—
276#389C2314yes—
277#389C2318yes—
278#389C2318yes—
279#389C2318yes—
280#389C2318yes—
281#389C2314yes—
282#389C2318yes—
283#389C2318yes—
284#389C2318yes—
285#389C2318yes—
286#389C2318yes—
287#389C2318yes—
288#389C2314yes—
289#389C2314yes—
290#389C2314yes—
291#389C2314yes—
292#388C2318yes—
293#388C2318yes—
294#388C2318yes—
295#388C2318yes—
296#388C2318yes—
297#388C2318yes—
298#388C2318yes—
299#388C2318yes—
300#388C2318yes—
301#388C2318yes—
302#388C2318yes—
303#388C2314yes—
304#388C2314yes—
305#388C2314yes—
306#388C2314yes—
307#388C2314yes—
308#388C2314yes—
309#388C2314yes—
310#388C2314yes—
311#387C2318yes—
312#387C2318yes—
313#387C2318yes—
314#387C2318yes—
315#387C2318yes—
316#387C2318yes—
317#387C2318yes—
318#387C2318yes—
319#387C2318yes—
320#387C2318yes—
321#387C2314yes—
322#387C2318yes—
323#387C2318yes—
324#387C2318yes—
325#387C2318yes—
326#387C2318yes—
327#387C2318yes—
328#387C2318yes—
329#387C2314yes—
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#387C2314yes—
343#387C2314yes—
344#387C2314yes—
345#387C2314yes—
346#387C2314yes—
347#387C2314yes—
348#385C2318yes—
349#385C2318yes—
350#385C2318yes—
351#385C2318yes—
352#385C2318yes—
353#385C2318yes—
354#385C2318yes—
355#384C2312yes—
356#384C2312yes—
357#384C2312yes—
358#383C2318yes—
359#383C2318yes—
360#383C2314yes—
361#383C2318yes—
362#382C2314yes—
363#382C2312yes—
364#382C2312yes—
365#382C2318yes—
366#382C2318yes—
367#382C2318yes—
368#382C2314yes—
369#382C2314yes—
370#382C2312yes—
371#381C2318yes—
372#381C2314yes—
373#380C2314yes—
374#380C2314yes—
375#380C2314yes—
376#380C2318yes—
377#380C2314yes—
378#380C2314yes—
379#380C2314yes—
380#379C2318yes—
381C4×C4⋊C4C2314yes—
382C4×C4⋊C4C2314yes—
383C4×C4⋊C4C2318yes—
384C4×C4⋊C4C2318yes—
385C4×C4⋊C4C2314yes—
386C4×C4⋊C4C2314yes—
387C4×C4⋊C4C2314yes—
388C4×C4⋊C4C2314yes—
389C4×C4⋊C4C2312yes—
390C4×C4⋊C4C2314yes—
391C4×C4⋊C4C2312yes—
392C4×C4⋊C4C2312yes—
393C4×C4⋊C4C2318yes—
394C4×C4⋊C4C2318yes—
395C4×C4⋊C4C2318yes—
396C4×C4⋊C4C2312yes—
397C4×C4⋊C4C2314yes—
398C4×C22⋊C4C2314yes—
399C4×C22⋊C4C2318yes—
400C4×C22⋊C4C2312yes—
401C4×C22⋊C4C2312yes—
402C4×C22⋊C4C2312yes—
403C4×C22⋊C4C2318yes—
404C4×C22⋊C4C2312yes—
405C4×C22⋊C4C2314yes—
406C4×C22⋊C4C2314yes—
407#376C2312yes—
408#376C2314yes—
409#376C2312yes—
410#376C2318yes—
411#376C2318yes—
412#376C2312yes—
413#376C2312yes—
414C2×#95C2312yes—
415C2×#95C2312yes—
416C2×#95C2312yes—
417C2×#95C2312yes—
418C2×#95C2312yes—
419C2×#95C2312yes—
420C43C2311yescharacteristic
421C43C2312yes—
422C43C2312yes—
423C43C2311yescharacteristic
424C43C2311yescharacteristic
425C43C2311yescharacteristic
426C25C2411yescharacteristic
427C22×Q8C2414yes—
428C22×Q8C2414yes—
429C22×Q8C2414yes—
430C23×C4—24no—
431C23×C4—42no—
432C23×C4—42no—
433C23×C4C2411yescharacteristic
434C23×C4C2412yes—
435C23×C4C2412yes—
436C23×C4C2411yescharacteristic
437C23×C4C2411yescharacteristic
438C23×C4C2412yes—
439C23×C4C2412yes—
440C23×C4C2411yescharacteristic
441C23×C4C2411yescharacteristic
442C23×C4C2412yes—
443C23×C4C2411yescharacteristic
444C23×C4C2412yes—
445C4⋊Q8—28no—
446C4⋊Q8—28no—
447C4⋊Q8—44no—
448C4⋊Q8—44no—
449C4⋊Q8—44no—
450#126—416no—
451#125—216no—
452#125—48no—
453#125—44no—
454C22⋊Q8—216no—
455C22⋊Q8—216no—
456C22⋊Q8—216no—
457C22⋊Q8—48no—
458C22⋊Q8—48no—
459C4×Q8—216no—
460C4×Q8—216no—
461C4×Q8—48no—
462C4×Q8—416no—
463C4×Q8—48no—
464C4×Q8—48no—
465#117—216no—
466#117—28no—
467#117—28no—
468#117—28no—
469#117—28no—
470C2×C4⋊C4—24no—
471C2×C4⋊C4—24no—
472C2×C4⋊C4—28no—
473C2×C4⋊C4—44no—
474C2×C4⋊C4C2412yes—
475C2×C4⋊C4C2412yes—
476C2×C4⋊C4C2412yes—
477C2×C4⋊C4C2412yes—
478C2×C4⋊C4C2414yes—
479C2×C4⋊C4C2414yes—
480C2×C4⋊C4C2414yes—
481C2×C4⋊C4C2414yes—
482C2×C4⋊C4C2414yes—
483C2×C4⋊C4C2414yes—
484C2×C4⋊C4C2418yes—
485C2×C4⋊C4C2418yes—
486C2×C4⋊C4C2414yes—
487C2×C4⋊C4C2414yes—
488C2×C4⋊C4C2418yes—
489C2×C4⋊C4C2414yes—
490C2×C4⋊C4C2414yes—
491C2×C4⋊C4C2418yes—
492C2×C4⋊C4C2414yes—
493C2×C4⋊C4C2418yes—
494C2×C4⋊C4C2414yes—
495C2×C4⋊C4C2418yes—
496C2×C4⋊C4C2418yes—
497C2×C4⋊C4C2418yes—
498C2×C4⋊C4C2418yes—
499C2×C4⋊C4C2418yes—
500C2×C4⋊C4C2414yes—
501C2×C4⋊C4C2414yes—
502C2×C4⋊C4C2418yes—
503C2×C4⋊C4C2418yes—
504C2×C4⋊C4C2418yes—
505C2×C4⋊C4C2418yes—
506C2×C4⋊C4C2414yes—
507C2×C4⋊C4C2414yes—
508C2×C4⋊C4C2414yes—
509C2×C4⋊C4C2418yes—
510C2×C22⋊C4—24no—
511C2×C22⋊C4—24no—
512C2×C22⋊C4—28no—
513C2×C22⋊C4—44no—
514C2×C22⋊C4C2412yes—
515C2×C22⋊C4C2412yes—
516C2×C22⋊C4C2412yes—
517C2×C22⋊C4C2412yes—
518C2×C22⋊C4C2414yes—
519C2×C22⋊C4C2414yes—
520C2×C22⋊C4C2414yes—
521C2×C22⋊C4C2418yes—
522C2×C22⋊C4C2418yes—
523C2×C22⋊C4C2414yes—
524C2×C22⋊C4C2418yes—
525C2×C22⋊C4C2418yes—
526C2×C22⋊C4C2418yes—
527C2×C22⋊C4C2418yes—
528C2×C42—24no—
529C2×C42—28no—
530C2×C42—42no—
531C2×C42—42no—
532C2×C42—44no—
533C2×C42—42no—
534C2×C42—42no—
535C2×C42#4118yes—
536C2×C42C2411yescharacteristic
537C2×C42C2411yescharacteristic
538C2×C42C2411yescharacteristic
539C2×C42C2411yescharacteristic
540C2×C42C2418yes—
541C2×C42C2418yes—
542C2×C42C2412yes—
543C2×C42C2412yes—
544C2×C42C2412yes—
545C2×C42C2412yes—
546C2×C42C2412yes—
547C2×C42C2412yes—
548C2×C42C2412yes—
549C2×C42C2412yes—
550C2×C42C2412yes—
551C2×C42C2412yes—
552C2×C42C2418yes—
553C2×C42C2418yes—
554C2×C42C2418yes—
555C2×C42C2418yes—
556C2×C42C2411yescharacteristic
557C2×C42C2411yescharacteristic
558C2×C42C2411yescharacteristic
559C2×C42C2411yescharacteristic
560C2×C42C2412yes—
561C2×C42C2412yes—
562C2×C42C2412yes—
563C2×C42C2412yes—
564C2×C42C2412yes—
565C2×C42C2412yes—
566#95C2414yes—
567#95C2414yes—
568#95C2414yes—
569#95C2414yes—
570#95C2414yes—
571#95C2414yes—
572#95C2414yes—
573#95C2414yes—
574#95C2414yes—
575#95C2414yes—
576#95C2414yes—
577#95C2414yes—
578#95C2414yes—
579#95C2418yes—
580#95C2414yes—
581#95C2418yes—
582#95C2418yes—
583#95C2418yes—
584#95C2418yes—
585#95C2418yes—
586#95C2418yes—
587#95C2418yes—
588#95C2418yes—
589#95C2414yes—
590#95C2414yes—
591#95C2418yes—
592#95C2418yes—
593#95C2418yes—
594#95C2418yes—
595#95C2418yes—
596#95C2418yes—
597#95C2418yes—
598#95C2418yes—
599#95C2418yes—
600#95C2418yes—
601#95C2418yes—
602#95C2418yes—
603#95C2418yes—
604#95C2418yes—
605#95C2418yes—
606#95C2418yes—
607C24—22no—
608C24—24no—
609C24—42no—
610C24—41no—
611C24—41no—
612C24C2512yes—
613C24C2511yescharacteristic
614C2×Q8—28no—
615C2×Q8—28no—
616C2×Q8—28no—
617C2×Q8—28no—
618C2×Q8—28no—
619C2×Q8—48no—
620C2×Q8—44no—
621C2×Q8—44no—
622C22×C4—24no—
623C22×C4—22no—
624C22×C4—22no—
625C22×C4—22no—
626C22×C4—22no—
627C22×C4—22no—
628C22×C4—24no—
629C22×C4—24no—
630C22×C4—24no—
631C22×C4—24no—
632C22×C4—24no—
633C22×C4—24no—
634C22×C4—24no—
635C22×C4—24no—
636C22×C4—24no—
637C22×C4—42no—
638C22×C4—42no—
639C22×C4—42no—
640C22×C4—42no—
641C22×C4—42no—
642C22×C4—42no—
643C22×C4—42no—
644C22×C4—41no—
645C22×C4—41no—
646C22×C4—42no—
647C22×C4—42no—
648C22×C4—42no—
649C22×C4—42no—
650C22×C4—416no—
651C22×C4C2×#4114yes—
652C22×C4C2×#4114yes—
653C22×C4C2×#4114yes—
654C22×C42−1+418yes—
655C22×C4C2511yescharacteristic
656C22×C4C2511yescharacteristic
657C22×C4C2512yes—
658C22×C4C2514yes—
659C22×C4C2518yes—
660C22×C4C2514yes—
661C22×C4C2512yes—
662C22×C4C2518yes—
663C22×C4C2511yescharacteristic
664C22×C4C2511yescharacteristic
665C22×C4C2518yes—
666C22×C4C2518yes—
667C22×C4C2512yes—
668C22×C4C2511yescharacteristic
669C22×C4C2512yes—
670C22×C4C2512yes—
671C22×C4C2512yes—
672C22×C4C2512yes—
673C22×C4C2511yescharacteristic
674C4⋊C4—24no—
675C4⋊C4—24no—
676C4⋊C4—24no—
677C4⋊C4—24no—
678C4⋊C4—28no—
679C4⋊C4—28no—
680C4⋊C4—216no—
681C4⋊C4—216no—
682C4⋊C4—28no—
683C4⋊C4—28no—
684C4⋊C4—28no—
685C4⋊C4—28no—
686C4⋊C4—28no—
687C4⋊C4—216no—
688C4⋊C4—28no—
689C4⋊C4—28no—
690C4⋊C4—216no—
691C4⋊C4—28no—
692C4⋊C4—44no—
693C4⋊C4—44no—
694C4⋊C4—48no—
695C4⋊C4—48no—
696C4⋊C4—48no—
697C4⋊C4—48no—
698C4⋊C4—48no—
699C4⋊C4—48no—
700C4⋊C4—44no—
701C4⋊C4—44no—
702C4⋊C4—48no—
703C4⋊C4—48no—
704C4⋊C4—48no—
705C4⋊C4—48no—
706C4⋊C4—44no—
707C4⋊C4—44no—
708C4⋊C4—44no—
709C4⋊C4—48no—
710C22⋊C4—216no—
711C22⋊C4—216no—
712C22⋊C4—24no—
713C22⋊C4—24no—
714C22⋊C4—24no—
715C22⋊C4—24no—
716C22⋊C4—28no—
717C22⋊C4—28no—
718C22⋊C4—28no—
719C22⋊C4—44no—
720C22⋊C4—48no—
721C22⋊C4—48no—
722C22⋊C4—48no—
723C22⋊C4—48no—
724C42—22no—
725C42—22no—
726C42—22no—
727C42—22no—
728C42—216no—
729C42—24no—
730C42—24no—
731C42—24no—
732C42—24no—
733C42—24no—
734C42—24no—
735C42—24no—
736C42—24no—
737C42—24no—
738C42—24no—
739C42—216no—
740C42—41no—
741C42—41no—
742C42—42no—
743C42—41no—
744C42—42no—
745C42—42no—
746C42—41no—
747C42—42no—
748C42—48no—
749C42—48no—
750C42—48no—
751C42—48no—
752C42C2×#4118yes—
753C42C2×#4118yes—
754C23—21no—
755C23—21no—
756C23—22no—
757C23—22no—
758C23—24no—
759C23—24no—
760C23—22no—
761C23—22no—
762C23—44no—
763C23—44no—
764C23—44no—
765C23—84no—
766C23—84no—
767C23C22×#4112yes—
768C23C2×2−1+414yes—
769C23C2611yescharacteristic
770Q8—416no—
771Q8—416no—
772Q8—88no—
773C2×C4—22no—
774C2×C4—24no—
775C2×C4—22no—
776C2×C4—22no—
777C2×C4—22no—
778C2×C4—22no—
779C2×C4—22no—
780C2×C4—21no—
781C2×C4—21no—
782C2×C4—24no—
783C2×C4—28no—
784C2×C4—28no—
785C2×C4—21no—
786C2×C4—21no—
787C2×C4—21no—
788C2×C4—21no—
789C2×C4—28no—
790C2×C4—28no—
791C2×C4—22no—
792C2×C4—22no—
793C2×C4—22no—
794C2×C4—22no—
795C2×C4—24no—
796C2×C4—28no—
797C2×C4—28no—
798C2×C4—24no—
799C2×C4—24no—
800C2×C4—28no—
801C2×C4—24no—
802C2×C4—22no—
803C2×C4—22no—
804C2×C4—22no—
805C2×C4—28no—
806C2×C4—22no—
807C2×C4—28no—
808C2×C4—28no—
809C2×C4—24no—
810C2×C4—28no—
811C2×C4—28no—
812C2×C4—24no—
813C2×C4—28no—
814C2×C4—28no—
815C2×C4—22no—
816C2×C4—22no—
817C2×C4—44no—
818C2×C4—48no—
819C2×C4—48no—
820C2×C4—48no—
821C2×C4—44no—
822C2×C4—44no—
823C2×C4—44no—
824C2×C4—48no—
825C2×C4—84no—
826C2×C4—84no—
827C2×C4C22×#4114yes—
828C2×C4C22×#4112yes—
829C2×C4C22×#4114yes—
830C2×C4C22×#4112yes—
831C2×C4C2×2−1+414yes—
832C2×C4C2×2−1+414yes—
833C2×C4#58514yes—
834C2×C4#58512yes—
835C2×C4#58512yes—
836C22—22no—
837C22—24no—
838C22—24no—
839C22—22no—
840C22—42no—
841C22—42no—
842C22—44no—
843C22—44no—
844C22—42no—
845C22—88no—
846C22#350914yes—
847C22C23×#4111yescharacteristic
848C22C22×2−1+412yes—
849C22C2×#58511yescharacteristic
850C22C2×#58511yescharacteristic
851C22C2×#58512yes—
852C4—22no—
853C4—24no—
854C4—24no—
855C4—24no—
856C4—24no—
857C4—24no—
858C4—42no—
859C4—48no—
860C4—41no—
861C4—41no—
862C4—44no—
863C4—48no—
864C4—48no—
865C4—42no—
866C4—44no—
867C4—41no—
868C4—41no—
869C4—48no—
870C4#349314yes—
871C2—24no—
872C2—82no—
873C2#6268611yescharacteristic
874C2C2×#349311yescharacteristic
875C2C2×#350911yescharacteristic
876C2#6282312yes—
877C2#6283112yes—
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. #39679C2semidirect
3. #39293C2semidirect
4. #39283C2semidirect
5. #38287C2semidirect
6. #38273C2semidirect
8. #37935C2semidirect
9. #37028C2semidirect
10. #37023C2semidirect
11. #36635C2semidirect
12. #35511C2semidirect
13. #35494C2semidirect
15. #35315C2semidirect
16. #35173C2semidirect
17. #35104C2semidirect
20. #34235C2semidirect
24. #2864C22semidirect
25. #2863C22semidirect
26. #2863C22semidirect
27. #2862C22semidirect
28. #2859C22semidirect
37. #2809C22semidirect
38. #2805C22semidirect
39. #2802C22semidirect
45. #2774C22semidirect
48. #2769C22semidirect
49. #2767C22semidirect
50. #2766C22semidirect
52. #2758C22semidirect
55. #2647C22semidirect
57. #2645C22semidirect
58. #2642C22semidirect
65. #2612C22semidirect
68. #2606C22semidirect
69. #2605C22semidirect
76. #2590C22semidirect
79. #2585C22semidirect
80. #2584C22semidirect
81. #2584C22semidirect
83. #2581C22semidirect
84. #2570C22semidirect
85. #2567C22semidirect
87. #2550C22semidirect
88. #2546C22semidirect
89. #2533C22semidirect
90. #2533C22semidirect
93. #2528C22semidirect
94. #2528C22semidirect
96. #2508C22semidirect
108. #2462C22semidirect
113. #2365C22semidirect
114. #2365C22semidirect
116. #2356C22semidirect
117. #2351C22semidirect
119. #2336C22semidirect
120. #2336C22semidirect
122. #2330C22semidirect
125. #2327C22semidirect
128. #2320C22semidirect
129. #2320C22semidirect
132. C4×C4⋊Q8C22semidirect
133. C4×C4⋊Q8C22semidirect
134. C4×#125C22semidirect
144. #2295C22semidirect
145. #2295C22semidirect
152. #2276C22semidirect

Maximal subgroups

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

subgroupindex
#396792
#395432
#392932
#392832
#382872
#382732
#379582
#379352
#370282
#370232
#366352
#355112
#354942
#353252
#353152
#351732
#351042
#350862
#350142
#342352
C2×#22982