Finite Group Databasebeta

← #7642642

Subgroups — #7642642

Order 512.

4414 conjugacy classes of subgroups.

The subgroup lattice has 888 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#39678C214yesmaximal, complemented
2#39542C214yesmaximal
3#39077C214yesmaximal, complemented
4#39067C214yesmaximal, complemented
5#38261C214yesmaximal, complemented
6#38251C214yesmaximal, complemented
7#37959C214yesmaximal, complemented
8#37934C214yesmaximal
9#37017C214yesmaximal, complemented
10#37011C214yesmaximal, complemented
11#36635C212yesmaximal, complemented
12#35507C214yesmaximal, complemented
13#35496C214yesmaximal, complemented
14#35315C212yesmaximal, complemented
15#35311C212yesmaximal
16#35087C212yesmaximal, complemented
17#35033C211yesmaximal, characteristic
18#35015C212yesmaximal, complemented
19#35011C211yesmaximal, characteristic
20#34245C212yesmaximal
21C2×#2298C211yesmaximal, characteristic
22C22×C22⋊Q8C2212yes—
23C22×#117C2211yescharacteristic
24#2864C2214yescomplemented
25#2863C2214yescomplemented
26#2863C2214yescomplemented
27#2862C2212yescomplemented
28#2859C2212yescomplemented
29#2857C2212yes—
30#2857C2212yes—
31#2857C2212yes—
32#2855C2214yes—
33#2855C2214yes—
34#2855C2214yes—
35#2851C2212yes—
36#2851C2214yes—
37#2799C2218yescomplemented
38#2791C2218yescomplemented
39#2791C2218yescomplemented
40#2789C2218yescomplemented
41#2771C2218yes—
42#2767C2218yescomplemented
43#2765C2218yes—
44#2765C2218yes—
45#2764C2218yes—
46#2762C2218yescomplemented
47#2758C2218yescomplemented
48#2755C2218yescomplemented
49#2745C2218yes—
50#2744C2218yes—
51#2739C2218yes—
52#2738C2218yes—
53#2659C2214yes—
54#2655C2218yescomplemented
55#2647C2212yescomplemented
56#2646C2214yes—
57#2645C2214yescomplemented
58#2642C2212yescomplemented
59#2627C2214yes—
60#2626C2214yes—
61#2625C2214yes—
62#2625C2214yes—
63#2611C2218yes—
64#2608C2214yes—
65#2607C2214yes—
66#2605C2218yescomplemented
67#2599C2218yes—
68#2590C2218yescomplemented
69#2588C2218yescomplemented
70#2588C2218yescomplemented
71#2588C2218yescomplemented
72#2583C2214yes—
73#2583C2214yes—
74#2575C2218yes—
75#2573C2218yes—
76#2565C2218yescomplemented
77#2533C2218yescomplemented
78#2528C2218yescomplemented
79#2528C2218yescomplemented
80#2527C2218yes—
81#2524C2218yescomplemented
82#2520C2218yescomplemented
83#2515C2218yes—
84#2514C2214yescomplemented
85#2511C2214yescomplemented
86#2507C2214yescomplemented
87#2506C2214yescomplemented
88#2506C2218yescomplemented
89#2505C2218yes—
90#2503C2214yes—
91#2502C2214yes—
92#2502C2214yes—
93#2499C2214yes—
94#2499C2214yes—
95#2493C2218yes—
96#2493C2218yes—
97#2484C2214yes—
98#2484C2214yes—
99#2483C2214yes—
100#2483C2214yes—
101#2475C2218yes—
102#2475C2218yes—
103#2473C2218yes—
104#2453C2214yescomplemented
105#2451C2214yescomplemented
106#2446C2214yescomplemented
107#2446C2214yescomplemented
108#2441C2214yes—
109#2439C2214yes—
110#2434C2214yes—
111#2368C2218yes—
112#2362C2214yes—
113#2362C2214yes—
114#2344C2214yes—
115#2342C2218yes—
116Q8×C22⋊C4C2214yes—
117#2336C2218yescomplemented
118#2332C2214yes—
119#2332C2214yes—
120#2330C2212yescomplemented
121#2329C2214yes—
122#2329C2214yes—
123#2327C2212yescomplemented
124#2320C2214yescomplemented
125#2317C2212yes—
126#2317C2212yes—
127#2315C2214yes—
128#2313C2214yes—
129#2313C2214yes—
130#2310C2212yes—
131#2310C2212yes—
132C4×C4⋊Q8C2212yescomplemented
133C4×C4⋊Q8C2212yescomplemented
134C4×#125C2214yescomplemented
135C4×C22⋊Q8C2214yes—
136C4×C22⋊Q8C2214yes—
137C4×C22⋊Q8C2214yes—
138#2298C2214yes—
139#2298C2212yes—
140#2298C2212yes—
141#2298C2214yes—
142#2298C2212yes—
143#2298C2212yes—
144#2295C2214yescomplemented
145#2295C2214yescomplemented
146C2×#388C2212yes—
147C2×#388C2212yes—
148C2×#387C2212yes—
149C2×#387C2212yes—
150#2283C2214yes—
151#2280C2212yes—
152#2274C2214yes—
153C2×C4×C4⋊C4C2211yescharacteristic
154C2×C4×C4⋊C4C2211yescharacteristic
155C2×C4×C22⋊C4C2211yescharacteristic
156C2×C4×C22⋊C4C2211yescharacteristic
157C2×#376C2211yescharacteristic
158C2×C43C2211yescharacteristic
159C23×Q8C2312yes—
160C24×C4C2311yescharacteristic
161C2×C4⋊Q8C2312yes—
162C2×C4⋊Q8C2312yes—
163C2×C4⋊Q8C2312yes—
164C2×#125C2314yes—
165C2×#125C2318yes—
166C2×#125C2312yes—
167C2×C22⋊Q8—216no—
168C2×C22⋊Q8C2314yes—
169C2×C22⋊Q8C2314yes—
170C2×C22⋊Q8C2314yes—
171C2×C22⋊Q8C2314yes—
172C2×C22⋊Q8C2314yes—
173C2×C4×Q8C2314yes—
174C2×C4×Q8C2314yes—
175C2×C4×Q8C2314yes—
176C2×#117—28no—
177C2×#117C2312yes—
178C2×#117C2312yes—
179C2×#117C2312yes—
180C2×#117C2312yes—
181C2×#117C2312yes—
182C2×#117C2312yes—
183C2×#117C2318yes—
184C22×C4⋊C4C2312yes—
185C22×C4⋊C4C2314yes—
186C22×C4⋊C4C2312yes—
187C22×C4⋊C4C2311yescharacteristic
188C22×C4⋊C4C2311yescharacteristic
189C22×C4⋊C4C2312yes—
190C22×C22⋊C4C2314yes—
191C22×C22⋊C4C2312yes—
192C22×C22⋊C4C2311yescharacteristic
193C22×C22⋊C4C2311yescharacteristic
194C22×C22⋊C4C2312yes—
195C22×C42C2311yescharacteristic
196C22×C42C2311yescharacteristic
197C22×C42C2312yes—
198C22×C42C2311yescharacteristic
199C22×C42C2312yes—
200C22×C42C2311yescharacteristic
201C22×C42C2311yescharacteristic
202C22×C42C2311yescharacteristic
203#401C2318yes—
204#401C2318yes—
205#400C2318yes—
206#400C2318yes—
207#400C2318yes—
208#400C2318yes—
209#400C2318yes—
210#400C2318yes—
211#400C2318yes—
212#400C2318yes—
213#400C2318yes—
214#400C2318yes—
215#400C2318yes—
216#400C2318yes—
217#400C2318yes—
218#400C2318yes—
219#400C2318yes—
220#399C2318yes—
221#398C2318yes—
222#398C2318yes—
223#398C2318yes—
224#398C2318yes—
225#398C2318yes—
226#398C2318yes—
227#398C2318yes—
228#398C2318yes—
229#398C2318yes—
230#398C2318yes—
231#398C2318yes—
232#398C2318yes—
233#397C2318yes—
234#397C2318yes—
235#397C2318yes—
236#397C2318yes—
237#396C2318yes—
238#396C2318yes—
239#395C2318yes—
240#395C2318yes—
241#395C2318yes—
242#393C2318yes—
243#391C2314yes—
244#391C2314yes—
245#391C2318yes—
246#391C2318yes—
247#391C2314yes—
248#391C2314yes—
249#391C2314yes—
250#391C2314yes—
251#391C2314yes—
252#391C2314yes—
253#391C2314yes—
254#391C2314yes—
255#391C2318yes—
256#391C2318yes—
257#391C2314yes—
258#391C2314yes—
259#391C2314yes—
260#391C2314yes—
261#391C2314yes—
262#391C2314yes—
263#389C2314yes—
264#389C2314yes—
265#389C2314yes—
266#389C2314yes—
267#389C2314yes—
268#389C2314yes—
269#389C2314yes—
270#389C2314yes—
271#389C2314yes—
272#389C2318yes—
273#389C2314yes—
274#389C2314yes—
275#389C2318yes—
276#389C2318yes—
277#389C2318yes—
278#389C2318yes—
279#389C2314yes—
280#389C2314yes—
281#389C2314yes—
282#389C2314yes—
283#389C2314yes—
284#388C2314yes—
285#388C2318yes—
286#388C2314yes—
287#388C2318yes—
288#388C2318yes—
289#388C2318yes—
290#388C2314yes—
291#388C2314yes—
292#388C2314yes—
293#388C2314yes—
294#388C2314yes—
295#388C2314yes—
296#387C2318yes—
297#387C2318yes—
298#387C2314yes—
299#387C2318yes—
300#387C2318yes—
301#387C2318yes—
302#387C2318yes—
303#387C2318yes—
304#387C2318yes—
305#387C2318yes—
306#387C2318yes—
307#387C2318yes—
308#387C2318yes—
309#387C2318yes—
310#387C2318yes—
311#387C2318yes—
312#387C2318yes—
313#387C2318yes—
314#387C2318yes—
315#387C2318yes—
316#387C2318yes—
317#387C2318yes—
318#387C2318yes—
319#387C2318yes—
320#387C2318yes—
321#387C2318yes—
322#387C2318yes—
323#387C2314yes—
324#387C2318yes—
325#387C2318yes—
326#387C2318yes—
327#387C2318yes—
328#387C2318yes—
329#387C2318yes—
330#387C2318yes—
331#387C2314yes—
332#387C2318yes—
333#387C2314yes—
334#387C2314yes—
335#387C2314yes—
336#387C2314yes—
337#387C2314yes—
338#385C2318yes—
339#385C2318yes—
340#385C2318yes—
341#385C2318yes—
342#385C2314yes—
343#385C2314yes—
344#385C2314yes—
345#385C2314yes—
346#385C2318yes—
347#385C2318yes—
348#385C2318yes—
349#385C2318yes—
350#385C2318yes—
351#384C2312yes—
352#384C2312yes—
353#384C2314yes—
354#384C2314yes—
355#384C2312yes—
356#383C2318yes—
357#383C2318yes—
358#383C2318yes—
359#382C2314yes—
360#382C2318yes—
361#382C2314yes—
362#382C2314yes—
363#382C2312yes—
364#382C2314yes—
365#382C2314yes—
366#381C2314yes—
367#381C2314yes—
368#381C2314yes—
369#381C2314yes—
370#381C2318yes—
371#381C2318yes—
372#381C2314yes—
373#381C2318yes—
374#380C2314yes—
375#380C2314yes—
376#380C2318yes—
377#380C2314yes—
378#380C2318yes—
379#380C2314yes—
380#380C2314yes—
381#379C2314yes—
382C4×C4⋊C4C2314yes—
383C4×C4⋊C4C2314yes—
384C4×C4⋊C4C2318yes—
385C4×C4⋊C4C2318yes—
386C4×C4⋊C4C2314yes—
387C4×C4⋊C4C2314yes—
388C4×C4⋊C4C2318yes—
389C4×C4⋊C4C2314yes—
390C4×C4⋊C4C2318yes—
391C4×C4⋊C4C2312yes—
392C4×C4⋊C4C2318yes—
393C4×C4⋊C4C2312yes—
394C4×C4⋊C4C2312yes—
395C4×C4⋊C4C2312yes—
396C4×C4⋊C4C2314yes—
397C4×C4⋊C4C2314yes—
398C4×C22⋊C4C2312yes—
399C4×C22⋊C4C2318yes—
400C4×C22⋊C4C2314yes—
401C4×C22⋊C4C2318yes—
402C4×C22⋊C4C2312yes—
403C4×C22⋊C4C2312yes—
404C4×C22⋊C4C2314yes—
405C4×C22⋊C4C2312yes—
406C4×C22⋊C4C2314yes—
407C4×C22⋊C4C2318yes—
408C4×C22⋊C4C2314yes—
409#376C2312yes—
410#376C2312yes—
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×Q8—28no—
428C22×Q8—44no—
429C22×Q8—44no—
430C22×Q8C2414yes—
431C22×Q8C2414yes—
432C22×Q8C2414yes—
433C23×C4—42no—
434C23×C4—42no—
435C23×C4#4118yes—
436C23×C4C2411yescharacteristic
437C23×C4C2411yescharacteristic
438C23×C4C2412yes—
439C23×C4C2412yes—
440C23×C4C2411yescharacteristic
441C23×C4C2411yescharacteristic
442C23×C4C2414yes—
443C23×C4C2414yes—
444C23×C4C2412yes—
445C23×C4C2412yes—
446C23×C4C2411yescharacteristic
447C23×C4C2412yes—
448C23×C4C2411yescharacteristic
449C23×C4C2412yes—
450C4⋊Q8—44no—
451C4⋊Q8—44no—
452C4⋊Q8—44no—
453#125—48no—
454#125—44no—
455#125—416no—
456C22⋊Q8—216no—
457C22⋊Q8—216no—
458C22⋊Q8—216no—
459C22⋊Q8—216no—
460C22⋊Q8—216no—
461C4×Q8—48no—
462C4×Q8—48no—
463C4×Q8—48no—
464#117—28no—
465#117—28no—
466#117—28no—
467#117—28no—
468#117—416no—
469#117—44no—
470#117—44no—
471C2×C4⋊C4—24no—
472C2×C4⋊C4—24no—
473C2×C4⋊C4—28no—
474C2×C4⋊C4—216no—
475C2×C4⋊C4—28no—
476C2×C4⋊C4—44no—
477C2×C4⋊C4C2412yes—
478C2×C4⋊C4C2412yes—
479C2×C4⋊C4C2412yes—
480C2×C4⋊C4C2412yes—
481C2×C4⋊C4C2414yes—
482C2×C4⋊C4C2418yes—
483C2×C4⋊C4C2418yes—
484C2×C4⋊C4C2414yes—
485C2×C4⋊C4C2414yes—
486C2×C4⋊C4C2414yes—
487C2×C4⋊C4C2414yes—
488C2×C4⋊C4C2414yes—
489C2×C4⋊C4C2414yes—
490C2×C4⋊C4C2418yes—
491C2×C4⋊C4C2414yes—
492C2×C4⋊C4C2418yes—
493C2×C4⋊C4C2414yes—
494C2×C4⋊C4C2418yes—
495C2×C4⋊C4C2414yes—
496C2×C4⋊C4C2418yes—
497C2×C4⋊C4C2418yes—
498C2×C4⋊C4C2418yes—
499C2×C4⋊C4C2414yes—
500C2×C4⋊C4C2414yes—
501C2×C4⋊C4C2418yes—
502C2×C4⋊C4C2418yes—
503C2×C4⋊C4C2418yes—
504C2×C4⋊C4C2418yes—
505C2×C4⋊C4C2418yes—
506C2×C4⋊C4C2418yes—
507C2×C4⋊C4C2414yes—
508C2×C4⋊C4C2414yes—
509C2×C4⋊C4C2414yes—
510C2×C4⋊C4C2418yes—
511C2×C22⋊C4—24no—
512C2×C22⋊C4—24no—
513C2×C22⋊C4—216no—
514C2×C22⋊C4—28no—
515C2×C22⋊C4—44no—
516C2×C22⋊C4C2414yes—
517C2×C22⋊C4C2412yes—
518C2×C22⋊C4C2412yes—
519C2×C22⋊C4C2412yes—
520C2×C22⋊C4C2412yes—
521C2×C22⋊C4C2418yes—
522C2×C22⋊C4C2418yes—
523C2×C22⋊C4C2414yes—
524C2×C22⋊C4C2414yes—
525C2×C22⋊C4C2418yes—
526C2×C22⋊C4C2414yes—
527C2×C22⋊C4C2418yes—
528C2×C22⋊C4C2414yes—
529C2×C22⋊C4C2414yes—
530C2×C42—24no—
531C2×C42—24no—
532C2×C42—28no—
533C2×C42—42no—
534C2×C42—42no—
535C2×C42—44no—
536C2×C42—42no—
537C2×C42—42no—
538C2×C42C2411yescharacteristic
539C2×C42C2411yescharacteristic
540C2×C42C2411yescharacteristic
541C2×C42C2411yescharacteristic
542C2×C42C2412yes—
543C2×C42C2412yes—
544C2×C42C2418yes—
545C2×C42C2412yes—
546C2×C42C2412yes—
547C2×C42C2412yes—
548C2×C42C2412yes—
549C2×C42C2412yes—
550C2×C42C2412yes—
551C2×C42C2412yes—
552C2×C42C2412yes—
553C2×C42C2412yes—
554C2×C42C2412yes—
555C2×C42C2414yes—
556C2×C42C2414yes—
557C2×C42C2418yes—
558C2×C42C2418yes—
559C2×C42C2418yes—
560C2×C42C2411yescharacteristic
561C2×C42C2411yescharacteristic
562C2×C42C2411yescharacteristic
563C2×C42C2411yescharacteristic
564C2×C42C2412yes—
565C2×C42C2412yes—
566C2×C42C2412yes—
567C2×C42C2412yes—
568#95C2414yes—
569#95C2414yes—
570#95C2414yes—
571#95C2414yes—
572#95C2414yes—
573#95C2414yes—
574#95C2414yes—
575#95C2414yes—
576#95C2414yes—
577#95C2414yes—
578#95C2414yes—
579#95C2414yes—
580#95C2418yes—
581#95C2418yes—
582#95C2418yes—
583#95C2418yes—
584#95C2418yes—
585#95C2418yes—
586#95C2418yes—
587#95C2418yes—
588#95C2418yes—
589#95C2418yes—
590#95C2418yes—
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—
607#95C2418yes—
608#95C2418yes—
609C24—24no—
610C24—42no—
611C24—41no—
612C24—41no—
613C24C2×#4114yes—
614C24C2512yes—
615C24C2511yescharacteristic
616C2×Q8—28no—
617C2×Q8—28no—
618C2×Q8—28no—
619C2×Q8—28no—
620C2×Q8—28no—
621C2×Q8—44no—
622C2×Q8—44no—
623C2×Q8—44no—
624C2×Q8—44no—
625C2×Q8—816no—
626C22×C4—22no—
627C22×C4—22no—
628C22×C4—24no—
629C22×C4—24no—
630C22×C4—22no—
631C22×C4—22no—
632C22×C4—22no—
633C22×C4—22no—
634C22×C4—28no—
635C22×C4—24no—
636C22×C4—24no—
637C22×C4—24no—
638C22×C4—28no—
639C22×C4—24no—
640C22×C4—24no—
641C22×C4—24no—
642C22×C4—416no—
643C22×C4—42no—
644C22×C4—42no—
645C22×C4—42no—
646C22×C4—42no—
647C22×C4—42no—
648C22×C4—48no—
649C22×C4—42no—
650C22×C4—42no—
651C22×C4—41no—
652C22×C4—41no—
653C22×C4—42no—
654C22×C4—42no—
655C22×C4—42no—
656C22×C4—42no—
657C22×C4—44no—
658C22×C4—44no—
659C22×C4C2×#4114yes—
660C22×C4C2×#4118yes—
661C22×C4C2×#4118yes—
662C22×C4C2×#4114yes—
663C22×C42−1+418yes—
664C22×C4C2511yescharacteristic
665C22×C4C2511yescharacteristic
666C22×C4C2512yes—
667C22×C4C2512yes—
668C22×C4C2514yes—
669C22×C4C2518yes—
670C22×C4C2514yes—
671C22×C4C2518yes—
672C22×C4C2518yes—
673C22×C4C2511yescharacteristic
674C22×C4C2511yescharacteristic
675C22×C4C2512yes—
676C22×C4C2518yes—
677C22×C4C2512yes—
678C22×C4C2511yescharacteristic
679C22×C4C2512yes—
680C22×C4C2512yes—
681C22×C4C2512yes—
682C22×C4C2511yescharacteristic
683C4⋊C4—24no—
684C4⋊C4—24no—
685C4⋊C4—24no—
686C4⋊C4—24no—
687C4⋊C4—28no—
688C4⋊C4—28no—
689C4⋊C4—216no—
690C4⋊C4—216no—
691C4⋊C4—28no—
692C4⋊C4—28no—
693C4⋊C4—28no—
694C4⋊C4—216no—
695C4⋊C4—28no—
696C4⋊C4—28no—
697C4⋊C4—28no—
698C4⋊C4—216no—
699C4⋊C4—44no—
700C4⋊C4—48no—
701C4⋊C4—44no—
702C4⋊C4—48no—
703C4⋊C4—48no—
704C4⋊C4—48no—
705C4⋊C4—44no—
706C4⋊C4—44no—
707C4⋊C4—48no—
708C4⋊C4—48no—
709C4⋊C4—48no—
710C4⋊C4—48no—
711C4⋊C4—48no—
712C4⋊C4—48no—
713C4⋊C4—44no—
714C4⋊C4—44no—
715C4⋊C4—44no—
716C4⋊C4—48no—
717C22⋊C4—24no—
718C22⋊C4—24no—
719C22⋊C4—24no—
720C22⋊C4—24no—
721C22⋊C4—216no—
722C22⋊C4—216no—
723C22⋊C4—216no—
724C22⋊C4—28no—
725C22⋊C4—28no—
726C22⋊C4—28no—
727C22⋊C4—44no—
728C22⋊C4—48no—
729C22⋊C4—44no—
730C22⋊C4—44no—
731C42—22no—
732C42—22no—
733C42—24no—
734C42—22no—
735C42—22no—
736C42—24no—
737C42—24no—
738C42—24no—
739C42—24no—
740C42—24no—
741C42—24no—
742C42—24no—
743C42—24no—
744C42—24no—
745C42—24no—
746C42—24no—
747C42—216no—
748C42—41no—
749C42—41no—
750C42—42no—
751C42—41no—
752C42—42no—
753C42—42no—
754C42—41no—
755C42—42no—
756C42—44no—
757C42—44no—
758C42—48no—
759C42—48no—
760C42—48no—
761C23—21no—
762C23—21no—
763C23—22no—
764C23—24no—
765C23—24no—
766C23—22no—
767C23—22no—
768C23—28no—
769C23—44no—
770C23—44no—
771C23—84no—
772C23—84no—
773C23C22×#4114yes—
774C23C22×#4112yes—
775C23C2×2−1+414yes—
776C23C2611yescharacteristic
777Q8—416no—
778Q8—88no—
779Q8—88no—
780C2×C4—22no—
781C2×C4—22no—
782C2×C4—22no—
783C2×C4—22no—
784C2×C4—22no—
785C2×C4—22no—
786C2×C4—21no—
787C2×C4—21no—
788C2×C4—22no—
789C2×C4—22no—
790C2×C4—28no—
791C2×C4—216no—
792C2×C4—21no—
793C2×C4—21no—
794C2×C4—22no—
795C2×C4—21no—
796C2×C4—21no—
797C2×C4—22no—
798C2×C4—28no—
799C2×C4—28no—
800C2×C4—22no—
801C2×C4—22no—
802C2×C4—22no—
803C2×C4—24no—
804C2×C4—28no—
805C2×C4—28no—
806C2×C4—24no—
807C2×C4—24no—
808C2×C4—24no—
809C2×C4—22no—
810C2×C4—24no—
811C2×C4—22no—
812C2×C4—22no—
813C2×C4—28no—
814C2×C4—28no—
815C2×C4—24no—
816C2×C4—22no—
817C2×C4—28no—
818C2×C4—28no—
819C2×C4—28no—
820C2×C4—28no—
821C2×C4—28no—
822C2×C4—24no—
823C2×C4—24no—
824C2×C4—28no—
825C2×C4—48no—
826C2×C4—44no—
827C2×C4—48no—
828C2×C4—48no—
829C2×C4—44no—
830C2×C4—44no—
831C2×C4—416no—
832C2×C4—44no—
833C2×C4—44no—
834C2×C4—84no—
835C2×C4—84no—
836C2×C4—88no—
837C2×C4C22×#4112yes—
838C2×C4C22×#4114yes—
839C2×C4C22×#4112yes—
840C2×C4C2×2−1+414yes—
841C2×C4C2×2−1+414yes—
842C2×C4#58514yes—
843C2×C4#58512yes—
844C2×C4#58512yes—
845C22—22no—
846C22—24no—
847C22—24no—
848C22—22no—
849C22—24no—
850C22—24no—
851C22—24no—
852C22—44no—
853C22—44no—
854C22—88no—
855C22#350914yes—
856C22C23×#4111yescharacteristic
857C22C22×2−1+412yes—
858C22C2×#58511yescharacteristic
859C22C2×#58511yescharacteristic
860C22C2×#58512yes—
861C4—22no—
862C4—24no—
863C4—24no—
864C4—24no—
865C4—24no—
866C4—48no—
867C4—41no—
868C4—41no—
869C4—42no—
870C4—44no—
871C4—48no—
872C4—48no—
873C4—42no—
874C4—44no—
875C4—41no—
876C4—41no—
877C4—42no—
878C4—48no—
879C4#349114yes—
880C2—24no—
881C2—44no—
882C2#6268611yescharacteristic
883C2C2×#349111yescharacteristic
884C2C2×#350911yescharacteristic
885C2#6282312yes—
886C2#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. #39678C2semidirect
3. #39077C2semidirect
4. #39067C2semidirect
5. #38261C2semidirect
6. #38251C2semidirect
7. #37959C2semidirect
9. #37017C2semidirect
10. #37011C2semidirect
11. #36635C2semidirect
12. #35507C2semidirect
13. #35496C2semidirect
14. #35315C2semidirect
16. #35087C2semidirect
18. #35015C2semidirect
24. #2864C22semidirect
25. #2863C22semidirect
26. #2863C22semidirect
27. #2862C22semidirect
28. #2859C22semidirect
37. #2799C22semidirect
38. #2791C22semidirect
39. #2791C22semidirect
40. #2789C22semidirect
42. #2767C22semidirect
46. #2762C22semidirect
47. #2758C22semidirect
48. #2755C22semidirect
54. #2655C22semidirect
55. #2647C22semidirect
57. #2645C22semidirect
58. #2642C22semidirect
66. #2605C22semidirect
68. #2590C22semidirect
69. #2588C22semidirect
70. #2588C22semidirect
71. #2588C22semidirect
76. #2565C22semidirect
77. #2533C22semidirect
78. #2528C22semidirect
79. #2528C22semidirect
81. #2524C22semidirect
82. #2520C22semidirect
84. #2514C22semidirect
85. #2511C22semidirect
86. #2507C22semidirect
87. #2506C22semidirect
88. #2506C22semidirect
104. #2453C22semidirect
105. #2451C22semidirect
106. #2446C22semidirect
107. #2446C22semidirect
117. #2336C22semidirect
120. #2330C22semidirect
123. #2327C22semidirect
124. #2320C22semidirect
132. C4×C4⋊Q8C22semidirect
133. C4×C4⋊Q8C22semidirect
134. C4×#125C22semidirect
144. #2295C22semidirect
145. #2295C22semidirect

Maximal subgroups

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

subgroupindex
#396782
#395422
#390772
#390672
#382612
#382512
#379592
#379342
#370172
#370112
#366352
#355072
#354962
#353152
#353112
#350872
#350332
#350152
#350112
#342452
C2×#22982