Finite Group Databasebeta

← #7642466

Subgroups — #7642466

Order 512.

4918 conjugacy classes of subgroups.

The subgroup lattice has 972 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#39636C214yesmaximal, complemented
2#39508C214yesmaximal, complemented
3#38128C214yesmaximal, complemented
4#38111C214yesmaximal, complemented
5#37897C212yesmaximal, complemented
6#37883C212yesmaximal, complemented
7#37881C214yesmaximal
8#37880C214yesmaximal, complemented
9#37709C212yesmaximal, complemented
10#37695C212yesmaximal, complemented
11#36772C218yesmaximal, complemented
12#36625C211yesmaximal, characteristic, complemented
13C2×#2857C211yesmaximal, characteristic, complemented
14#35380C218yesmaximal, complemented
15#35315C212yesmaximal, complemented
16#35310C212yesmaximal, complemented
17#35084C212yesmaximal
18#35015C212yesmaximal, complemented
19#35014C212yesmaximal, complemented
20#34245C212yesmaximal, complemented
21C2×#2290C211yesmaximal, characteristic
22C2×#541C2212yescomplemented
23C2×#533C2211yescharacteristic, complemented
24C22×C4⋊Q8C2211yescharacteristic, complemented
25C22×C22⋊Q8C2212yes—
26C22×C4×D4C2211yescharacteristic
27C22×#117C2211yescharacteristic
28C23×C42C2211yescharacteristic
29#2857C2214yes—
30#2857C2212yes—
31#2857C2212yes—
32#2857C2212yes—
33#2857C2212yescomplemented
34#2857C2214yescomplemented
35#2857C2212yescomplemented
36#2857C2212yescomplemented
37#2855C2214yes—
38#2855C2214yescomplemented
39#2851C2212yes—
40#2851C2212yescomplemented
41#2848C2214yes—
42#2848C2214yes—
43#2799C2218yescomplemented
44#2798C2218yescomplemented
45#2793C2218yescomplemented
46#2791C2218yescomplemented
47#2787C2218yescomplemented
48#2781C2218yes—
49#2779C2218yes—
50#2770C2218yescomplemented
51#2759C2218yescomplemented
52#2755C2218yescomplemented
53#2747C2218yescomplemented
54#2741C2218yes—
55#2716C2218yescomplemented
56#2713C2218yescomplemented
57#2702C2218yes—
58#2690C2218yescomplemented
59#2647C2212yescomplemented
60#2646C2214yes—
61#2646C2214yes—
62#2645C2214yescomplemented
63#2642C2212yescomplemented
64#2638C2218yes—
65#2629C2212yescomplemented
66#2627C2214yes—
67#2626C2214yes—
68#2625C2214yescomplemented
69#2621C2212yescomplemented
70#2596C2218yescomplemented
71#2594C2218yescomplemented
72#2590C2218yescomplemented
73#2589C2218yescomplemented
74#2588C2218yescomplemented
75#2587C2218yescomplemented
76#2585C2218yescomplemented
77#2585C2218yescomplemented
78#2583C2214yes—
79#2561C2214yes—
80#2533C2218yescomplemented
81#2528C2218yescomplemented
82#2525C2218yescomplemented
83#2511C2214yescomplemented
84#2509C2218yescomplemented
85#2507C2214yescomplemented
86#2505C2218yes—
87#2498C2218yes—
88#2497C2214yescomplemented
89#2493C2218yes—
90#2493C2218yescomplemented
91#2492C2214yescomplemented
92#2488C2218yes—
93#2486C2214yes—
94#2484C2218yescomplemented
95#2483C2214yes—
96#2481C2218yes—
97#2480C2218yes—
98#2478C2218yescomplemented
99#2475C2218yescomplemented
100#2473C2218yes—
101#2473C2218yescomplemented
102#2469C2218yescomplemented
103#2453C2218yescomplemented
104#2451C2214yescomplemented
105#2446C2214yescomplemented
106#2438C2218yescomplemented
107#2429C2214yescomplemented
108#2423C2214yescomplemented
109#2415C2214yes—
110#2415C2214yes—
111#2413C2218yes—
112#2409C2214yes—
113#2405C2214yes—
114#2368C2218yes—
115#2362C2214yescomplemented
116#2362C2214yescomplemented
117#2344C2214yescomplemented
118#2342C2218yes—
119Q8×C22⋊C4C2214yescomplemented
120#2332C2214yescomplemented
121#2332C2214yescomplemented
122#2330C2212yescomplemented
123#2329C2214yes—
124#2329C2214yes—
125#2327C2212yescomplemented
126#2323C2214yescomplemented
127#2322C2218yes—
128#2320C2214yescomplemented
129#2314C2212yescomplemented
130#2313C2214yes—
131#2313C2214yescomplemented
132#2312C2214yes—
133C4×C22⋊Q8C2214yes—
134C4×C22⋊Q8C2214yes—
135C4×C22⋊Q8C2214yes—
136C4×C22⋊Q8C2214yescomplemented
137#2296C2212yescomplemented
138C2×#391C2212yescomplemented
139C2×#389C2214yescomplemented
140#2290C2212yes—
141#2290C2214yes—
142#2290C2212yes—
143#2290C2214yes—
144#2290C2212yes—
145#2290C2212yes—
146C2×#388C2212yes—
147C2×#387C2212yes—
148C2×#386C2212yes—
149C2×#385C2212yes—
150#2285C2211yescharacteristic, complemented
151C2×#384C2211yescharacteristic, complemented
152#2280C2212yes—
153C2×#380C2214yes—
154#2274C2214yescomplemented
155C2×C4×C4⋊C4C2211yescharacteristic
156C2×C4×C22⋊C4C2211yescharacteristic
157C2×C4×C22⋊C4C2211yescharacteristic
158C2×#376C2211yescharacteristic
159C23×Q8C2312yes—
160C23×D4C2311yescharacteristic
161C24×C4C2311yescharacteristic
162C24×C4C2312yes—
163C24×C4C2311yescharacteristic
164#541—48no—
165#533—44no—
166C2×C4⋊Q8—44no—
167C2×C4⋊Q8C2312yes—
168C2×C4⋊Q8C2312yes—
169C2×C4⋊Q8C2314yes—
170C2×C4⋊Q8C2312yes—
171C2×#126C2318yes—
172C2×#125C2312yes—
173C2×#125C2318yes—
174C2×#123C2318yes—
175C2×C22⋊Q8—216no—
176C2×C22⋊Q8C2314yes—
177C2×C22⋊Q8C2314yes—
178C2×C22⋊Q8C2314yes—
179C2×C22⋊Q8C2314yes—
180C2×C22⋊Q8C2314yes—
181C2×C22⋊Q8C2314yes—
182C2×C22⋊Q8C2314yes—
183C2×C22⋊Q8C2314yes—
184C2×C22⋊Q8C2314yes—
185C2×C4×Q8C2314yes—
186C2×C4×Q8C2314yes—
187C2×C4×Q8C2314yes—
188C2×C4×D4—28no—
189C2×C4×D4C2312yes—
190C2×C4×D4C2312yes—
191C2×C4×D4C2312yes—
192C2×C4×D4C2312yes—
193C2×#117—44no—
194C2×#117C2312yes—
195C2×#117C2312yes—
196C2×#117C2318yes—
197C2×#117C2312yes—
198C2×#117C2312yes—
199C2×#117C2314yes—
200C22×C4⋊C4C2312yes—
201C22×C4⋊C4C2314yes—
202C22×C4⋊C4C2311yescharacteristic
203C22×C4⋊C4C2312yes—
204C22×C4⋊C4C2312yes—
205C22×C4⋊C4C2314yes—
206C22×C4⋊C4C2314yes—
207C22×C22⋊C4C2311yescharacteristic
208C22×C22⋊C4C2312yes—
209C22×C22⋊C4C2314yes—
210C22×C22⋊C4C2311yescharacteristic
211C22×C22⋊C4C2312yes—
212C22×C22⋊C4C2312yes—
213C22×C42—44no—
214C22×C42C2311yescharacteristic
215C22×C42C2311yescharacteristic
216C22×C42C2311yescharacteristic
217C22×C42C2311yescharacteristic
218C22×C42C2312yes—
219C22×C42C2311yescharacteristic
220C22×C42C2312yes—
221C22×C42C2311yescharacteristic
222C22×C42C2311yescharacteristic
223C22×C42C2312yes—
224C22×C42C2311yescharacteristic
225C22×C42C2311yescharacteristic
226#401C2318yes—
227#400C2318yes—
228#400C2318yes—
229#400C2318yes—
230#400C2318yes—
231#400C2318yes—
232#400C2318yes—
233#400C2318yes—
234#400C2318yes—
235#400C2318yes—
236#400C2318yes—
237#400C2318yes—
238#400C2318yes—
239#399C2318yes—
240#398C2318yes—
241#398C2318yes—
242#398C2318yes—
243#398C2318yes—
244#398C2318yes—
245#398C2318yes—
246#398C2318yes—
247#398C2318yes—
248#398C2318yes—
249#398C2318yes—
250#398C2318yes—
251#397C2318yes—
252#397C2318yes—
253#397C2318yes—
254#397C2318yes—
255#397C2318yes—
256#397C2318yes—
257#396C2318yes—
258#396C2318yes—
259#396C2318yes—
260#395C2318yes—
261#395C2318yes—
262#394C2318yes—
263#394C2318yes—
264#393C2318yes—
265#393C2318yes—
266#391C2314yes—
267#391C2314yes—
268#391C2314yes—
269#391C2318yes—
270#391C2318yes—
271#391C2318yes—
272#391C2318yes—
273#391C2314yes—
274#391C2314yes—
275#391C2314yes—
276#391C2314yes—
277#391C2314yes—
278#391C2318yes—
279#389C2314yes—
280#389C2314yes—
281#389C2318yes—
282#389C2318yes—
283#389C2318yes—
284#389C2318yes—
285#389C2318yes—
286#389C2314yes—
287#389C2318yes—
288#389C2314yes—
289#389C2318yes—
290#389C2314yes—
291#389C2314yes—
292#389C2314yes—
293#389C2314yes—
294#389C2314yes—
295#389C2314yes—
296#389C2314yes—
297#389C2314yes—
298#389C2318yes—
299#388C2318yes—
300#388C2318yes—
301#388C2318yes—
302#388C2318yes—
303#388C2318yes—
304#388C2318yes—
305#388C2318yes—
306#388C2318yes—
307#388C2318yes—
308#388C2318yes—
309#388C2318yes—
310#388C2318yes—
311#388C2318yes—
312#388C2314yes—
313#388C2314yes—
314#388C2314yes—
315#388C2314yes—
316#387C2318yes—
317#387C2318yes—
318#387C2318yes—
319#387C2318yes—
320#387C2318yes—
321#387C2318yes—
322#387C2318yes—
323#387C2318yes—
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#387C2314yes—
337#387C2314yes—
338#387C2318yes—
339#387C2318yes—
340#387C2318yes—
341#387C2318yes—
342#387C2318yes—
343#387C2314yes—
344#387C2314yes—
345#386C2318yes—
346#386C2314yes—
347#386C2314yes—
348#386C2314yes—
349#386C2314yes—
350#385C2318yes—
351#385C2318yes—
352#385C2318yes—
353#385C2318yes—
354#385C2318yes—
355#385C2318yes—
356#385C2318yes—
357#385C2318yes—
358#385C2318yes—
359#385C2318yes—
360#385C2314yes—
361#385C2314yes—
362#385C2314yes—
363#385C2314yes—
364#384C2312yes—
365#384C2312yes—
366#384C2312yes—
367#384C2314yes—
368#383C2318yes—
369#382C2312yes—
370#382C2318yes—
371#381C2318yes—
372#381C2318yes—
373#381C2318yes—
374#381C2314yes—
375#380C2314yes—
376#380C2314yes—
377#380C2314yes—
378#380C2318yes—
379#380C2314yes—
380#380C2314yes—
381#380C2314yes—
382#380C2314yes—
383#380C2314yes—
384#380C2314yes—
385#380C2318yes—
386#380C2318yes—
387#380C2314yes—
388#380C2314yes—
389#379C2318yes—
390#379C2314yes—
391C4×C4⋊C4C2314yes—
392C4×C4⋊C4C2314yes—
393C4×C4⋊C4C2314yes—
394C4×C4⋊C4C2318yes—
395C4×C4⋊C4C2318yes—
396C4×C4⋊C4C2318yes—
397C4×C4⋊C4C2318yes—
398C4×C4⋊C4C2318yes—
399C4×C4⋊C4C2314yes—
400C4×C4⋊C4C2312yes—
401C4×C4⋊C4C2312yes—
402C4×C22⋊C4C2314yes—
403C4×C22⋊C4C2318yes—
404C4×C22⋊C4C2318yes—
405C4×C22⋊C4C2312yes—
406C4×C22⋊C4C2314yes—
407C4×C22⋊C4C2314yes—
408C4×C22⋊C4C2312yes—
409C4×C22⋊C4C2312yes—
410C4×C22⋊C4C2318yes—
411C4×C22⋊C4C2312yes—
412C4×C22⋊C4C2312yes—
413C4×C22⋊C4C2312yes—
414#376C2312yes—
415#376C2312yes—
416#376C2314yes—
417C2×#95C2312yes—
418C2×#95C2312yes—
419C2×#95C2312yes—
420C2×#95C2318yes—
421C2×#95C2312yes—
422C2×#95C2312yes—
423C25C2411yescharacteristic
424C25C2411yescharacteristic
425C22×Q8—28no—
426C22×Q8—44no—
427C22×Q8—44no—
428C22×Q8C2414yes—
429C22×Q8C2414yes—
430C22×Q8C2414yes—
431C22×D4—24no—
432C22×D4—44no—
433C22×D4C2412yes—
434C22×D4C2412yes—
435C23×C4—24no—
436C23×C4—28no—
437C23×C4—42no—
438C23×C4—42no—
439C23×C4—42no—
440C23×C4—42no—
441C23×C4—44no—
442C23×C4—44no—
443C23×C4#4118yes—
444C23×C4C2411yescharacteristic
445C23×C4C2414yes—
446C23×C4C2412yes—
447C23×C4C2412yes—
448C23×C4C2412yes—
449C23×C4C2412yes—
450C23×C4C2412yes—
451C23×C4C2411yescharacteristic
452C23×C4C2411yescharacteristic
453C23×C4C2411yescharacteristic
454C23×C4C2412yes—
455C23×C4C2412yes—
456C23×C4C2411yescharacteristic
457C23×C4C2414yes—
458C23×C4C2411yescharacteristic
459C23×C4C2412yes—
460C23×C4C2412yes—
461C23×C4C2411yescharacteristic
462C23×C4C2411yescharacteristic
463C23×C4C2411yescharacteristic
464C23×C4C2412yes—
465C4⋊Q8—28no—
466C4⋊Q8—48no—
467C4⋊Q8—44no—
468C4⋊Q8—44no—
469#126—416no—
470#125—28no—
471#125—416no—
472#123—416no—
473C22⋊Q8—216no—
474C22⋊Q8—216no—
475C22⋊Q8—216no—
476C22⋊Q8—216no—
477C22⋊Q8—216no—
478C22⋊Q8—48no—
479C22⋊Q8—48no—
480C22⋊Q8—48no—
481C22⋊Q8—48no—
482C4×Q8—48no—
483C4×Q8—48no—
484C4×Q8—48no—
485C4×D4—28no—
486C4×D4—28no—
487C4×D4—28no—
488C4×D4—28no—
489#117—28no—
490#117—44no—
491#117—48no—
492#117—416no—
493#117—44no—
494#117—44no—
495C2×C4⋊C4—24no—
496C2×C4⋊C4—28no—
497C2×C4⋊C4—216no—
498C2×C4⋊C4—28no—
499C2×C4⋊C4—44no—
500C2×C4⋊C4—48no—
501C2×C4⋊C4—48no—
502C2×C4⋊C4C2414yes—
503C2×C4⋊C4C2412yes—
504C2×C4⋊C4C2412yes—
505C2×C4⋊C4C2414yes—
506C2×C4⋊C4C2418yes—
507C2×C4⋊C4C2418yes—
508C2×C4⋊C4C2414yes—
509C2×C4⋊C4C2418yes—
510C2×C4⋊C4C2414yes—
511C2×C4⋊C4C2414yes—
512C2×C4⋊C4C2414yes—
513C2×C4⋊C4C2414yes—
514C2×C4⋊C4C2418yes—
515C2×C4⋊C4C2414yes—
516C2×C4⋊C4C2418yes—
517C2×C4⋊C4C2414yes—
518C2×C4⋊C4C2414yes—
519C2×C4⋊C4C2414yes—
520C2×C4⋊C4C2414yes—
521C2×C4⋊C4C2418yes—
522C2×C4⋊C4C2414yes—
523C2×C4⋊C4C2418yes—
524C2×C4⋊C4C2418yes—
525C2×C4⋊C4C2414yes—
526C2×C4⋊C4C2418yes—
527C2×C4⋊C4C2418yes—
528C2×C4⋊C4C2418yes—
529C2×C4⋊C4C2414yes—
530C2×C4⋊C4C2418yes—
531C2×C4⋊C4C2418yes—
532C2×C4⋊C4C2418yes—
533C2×C4⋊C4C2418yes—
534C2×C22⋊C4—24no—
535C2×C22⋊C4—216no—
536C2×C22⋊C4—24no—
537C2×C22⋊C4—28no—
538C2×C22⋊C4—44no—
539C2×C22⋊C4—44no—
540C2×C22⋊C4C2414yes—
541C2×C22⋊C4C2414yes—
542C2×C22⋊C4C2412yes—
543C2×C22⋊C4C2412yes—
544C2×C22⋊C4C2412yes—
545C2×C22⋊C4C2412yes—
546C2×C22⋊C4C2418yes—
547C2×C22⋊C4C2418yes—
548C2×C22⋊C4C2414yes—
549C2×C22⋊C4C2414yes—
550C2×C22⋊C4C2418yes—
551C2×C22⋊C4C2418yes—
552C2×C22⋊C4C2414yes—
553C2×C22⋊C4C2414yes—
554C2×C22⋊C4C2414yes—
555C2×C22⋊C4C2414yes—
556C2×C22⋊C4C2418yes—
557C2×C22⋊C4C2418yes—
558C2×C22⋊C4C2418yes—
559C2×C22⋊C4C2418yes—
560C2×C42—24no—
561C2×C42—24no—
562C2×C42—24no—
563C2×C42—24no—
564C2×C42—42no—
565C2×C42—44no—
566C2×C42—42no—
567C2×C42—42no—
568C2×C42—44no—
569C2×C42—44no—
570C2×C42—42no—
571C2×C42—42no—
572C2×C42C2412yes—
573C2×C42C2412yes—
574C2×C42C2411yescharacteristic
575C2×C42C2412yes—
576C2×C42C2412yes—
577C2×C42C2412yes—
578C2×C42C2412yes—
579C2×C42C2411yescharacteristic
580C2×C42C2411yescharacteristic
581C2×C42C2412yes—
582C2×C42C2412yes—
583C2×C42C2414yes—
584C2×C42C2414yes—
585C2×C42C2418yes—
586C2×C42C2418yes—
587C2×C42C2418yes—
588C2×C42C2418yes—
589C2×C42C2412yes—
590C2×C42C2412yes—
591C2×C42C2412yes—
592C2×C42C2412yes—
593C2×C42C2411yescharacteristic
594#95C2414yes—
595#95C2414yes—
596#95C2414yes—
597#95C2414yes—
598#95C2414yes—
599#95C2414yes—
600#95C2414yes—
601#95C2414yes—
602#95C2414yes—
603#95C2414yes—
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—
620#95C2418yes—
621#95C2418yes—
622#95C2418yes—
623#95C2418yes—
624#95C2418yes—
625#95C2418yes—
626#95C2418yes—
627#95C2418yes—
628#95C2418yes—
629C24—24no—
630C24—24no—
631C24—22no—
632C24—24no—
633C24—41no—
634C24—41no—
635C24—41no—
636C24—41no—
637C24—42no—
638C24C2×#4114yes—
639C24C2512yes—
640C24C2511yescharacteristic
641C24C2511yescharacteristic
642C24C2511yescharacteristic
643C2×Q8—28no—
644C2×Q8—28no—
645C2×Q8—28no—
646C2×Q8—28no—
647C2×Q8—28no—
648C2×Q8—44no—
649C2×Q8—44no—
650C2×Q8—44no—
651C2×Q8—44no—
652C2×Q8—816no—
653C2×D4—24no—
654C2×D4—24no—
655C2×D4—28no—
656C2×D4—44no—
657C2×D4—416no—
658C22×C4—24no—
659C22×C4—22no—
660C22×C4—24no—
661C22×C4—22no—
662C22×C4—22no—
663C22×C4—24no—
664C22×C4—22no—
665C22×C4—22no—
666C22×C4—22no—
667C22×C4—22no—
668C22×C4—22no—
669C22×C4—28no—
670C22×C4—22no—
671C22×C4—24no—
672C22×C4—24no—
673C22×C4—216no—
674C22×C4—24no—
675C22×C4—28no—
676C22×C4—24no—
677C22×C4—24no—
678C22×C4—24no—
679C22×C4—24no—
680C22×C4—24no—
681C22×C4—24no—
682C22×C4—24no—
683C22×C4—24no—
684C22×C4—24no—
685C22×C4—24no—
686C22×C4—24no—
687C22×C4—416no—
688C22×C4—41no—
689C22×C4—41no—
690C22×C4—41no—
691C22×C4—42no—
692C22×C4—42no—
693C22×C4—42no—
694C22×C4—41no—
695C22×C4—42no—
696C22×C4—41no—
697C22×C4—41no—
698C22×C4—41no—
699C22×C4—42no—
700C22×C4—42no—
701C22×C4—42no—
702C22×C4—42no—
703C22×C4—42no—
704C22×C4—41no—
705C22×C4—42no—
706C22×C4—42no—
707C22×C4—42no—
708C22×C4—42no—
709C22×C4—42no—
710C22×C4—44no—
711C22×C4—44no—
712C22×C4—432no—
713C22×C4—416no—
714C22×C4C2×#4114yes—
715C22×C4C2×#4114yes—
716C22×C4C2×#4114yes—
717C22×C4C2×#4114yes—
718C22×C4C2×#4114yes—
719C22×C4C2×#4114yes—
720C22×C42−1+418yes—
721C22×C4C2512yes—
722C22×C4C2514yes—
723C22×C4C2512yes—
724C22×C4C2512yes—
725C22×C4C2518yes—
726C22×C4C2514yes—
727C22×C4C2518yes—
728C22×C4C2518yes—
729C22×C4C2518yes—
730C22×C4C2512yes—
731C22×C4C2511yescharacteristic
732C22×C4C2511yescharacteristic
733C22×C4C2511yescharacteristic
734C22×C4C2512yes—
735C22×C4C2512yes—
736C22×C4C2512yes—
737C22×C4C2511yescharacteristic
738C4⋊C4—24no—
739C4⋊C4—24no—
740C4⋊C4—28no—
741C4⋊C4—28no—
742C4⋊C4—216no—
743C4⋊C4—216no—
744C4⋊C4—28no—
745C4⋊C4—216no—
746C4⋊C4—28no—
747C4⋊C4—216no—
748C4⋊C4—28no—
749C4⋊C4—28no—
750C4⋊C4—28no—
751C4⋊C4—216no—
752C4⋊C4—28no—
753C4⋊C4—44no—
754C4⋊C4—48no—
755C4⋊C4—44no—
756C4⋊C4—44no—
757C4⋊C4—44no—
758C4⋊C4—44no—
759C4⋊C4—48no—
760C4⋊C4—48no—
761C4⋊C4—48no—
762C4⋊C4—44no—
763C4⋊C4—48no—
764C4⋊C4—44no—
765C4⋊C4—48no—
766C4⋊C4—48no—
767C4⋊C4—48no—
768C4⋊C4—48no—
769C4⋊C4—48no—
770C22⋊C4—24no—
771C22⋊C4—24no—
772C22⋊C4—216no—
773C22⋊C4—216no—
774C22⋊C4—216no—
775C22⋊C4—28no—
776C22⋊C4—216no—
777C22⋊C4—24no—
778C22⋊C4—24no—
779C22⋊C4—28no—
780C22⋊C4—28no—
781C22⋊C4—28no—
782C22⋊C4—44no—
783C22⋊C4—44no—
784C22⋊C4—44no—
785C22⋊C4—44no—
786C22⋊C4—48no—
787C22⋊C4—48no—
788C22⋊C4—48no—
789C22⋊C4—48no—
790C42—24no—
791C42—24no—
792C42—24no—
793C42—22no—
794C42—24no—
795C42—22no—
796C42—24no—
797C42—22no—
798C42—24no—
799C42—24no—
800C42—42no—
801C42—42no—
802C42—42no—
803C42—42no—
804C42—42no—
805C42—44no—
806C42—48no—
807C42—48no—
808C42—44no—
809C42—48no—
810C42—48no—
811C42H(5,𝔽2)14yes—
812C23—21no—
813C23—21no—
814C23—22no—
815C23—21no—
816C23—21no—
817C23—22no—
818C23—21no—
819C23—22no—
820C23—21no—
821C23—22no—
822C23—28no—
823C23—28no—
824C23—22no—
825C23—22no—
826C23—24no—
827C23—22no—
828C23—24no—
829C23—44no—
830C23—48no—
831C23—48no—
832C23—44no—
833C23—44no—
834C23—44no—
835C23—84no—
836C23—84no—
837C23C22×#4112yes—
838C23C22×#4112yes—
839C23C22×#4112yes—
840C23C2×2−1+414yes—
841C23#58514yes—
842C23C2611yescharacteristic
843Q8—416no—
844Q8—88no—
845Q8—88no—
846D4—48no—
847D4—48no—
848C2×C4—216no—
849C2×C4—21no—
850C2×C4—21no—
851C2×C4—22no—
852C2×C4—22no—
853C2×C4—21no—
854C2×C4—22no—
855C2×C4—21no—
856C2×C4—21no—
857C2×C4—22no—
858C2×C4—22no—
859C2×C4—22no—
860C2×C4—21no—
861C2×C4—28no—
862C2×C4—28no—
863C2×C4—28no—
864C2×C4—22no—
865C2×C4—22no—
866C2×C4—28no—
867C2×C4—22no—
868C2×C4—28no—
869C2×C4—22no—
870C2×C4—24no—
871C2×C4—28no—
872C2×C4—28no—
873C2×C4—22no—
874C2×C4—24no—
875C2×C4—28no—
876C2×C4—28no—
877C2×C4—24no—
878C2×C4—24no—
879C2×C4—22no—
880C2×C4—24no—
881C2×C4—24no—
882C2×C4—24no—
883C2×C4—28no—
884C2×C4—28no—
885C2×C4—28no—
886C2×C4—28no—
887C2×C4—28no—
888C2×C4—28no—
889C2×C4—22no—
890C2×C4—22no—
891C2×C4—24no—
892C2×C4—44no—
893C2×C4—44no—
894C2×C4—44no—
895C2×C4—48no—
896C2×C4—48no—
897C2×C4—48no—
898C2×C4—48no—
899C2×C4—48no—
900C2×C4—48no—
901C2×C4—44no—
902C2×C4—44no—
903C2×C4—416no—
904C2×C4—44no—
905C2×C4—48no—
906C2×C4—84no—
907C2×C4—84no—
908C2×C4—88no—
909C2×C4C22×#4112yes—
910C2×C4C22×#4112yes—
911C2×C4C22×#4112yes—
912C2×C4C22×#4112yes—
913C2×C4C2×H(5,𝔽2)14yes—
914C2×C4C2×H(5,𝔽2)12yes—
915C2×C4C2×2−1+414yes—
916C2×C4C2×2−1+414yes—
917C2×C4#58512yes—
918C22—22no—
919C22—22no—
920C22—22no—
921C22—24no—
922C22—24no—
923C22—24no—
924C22—24no—
925C22—22no—
926C22—22no—
927C22—22no—
928C22—22no—
929C22—416no—
930C22—42no—
931C22—42no—
932C22—42no—
933C22—42no—
934C22—44no—
935C22—44no—
936C22—42no—
937C22—88no—
938C22#345514yes—
939C22#350914yes—
940C22C23×#4111yescharacteristic
941C22C22×H(5,𝔽2)11yescharacteristic
942C22C22×2−1+412yes—
943C22C2×#58511yescharacteristic
944C22C2×#58512yes—
945C4—22no—
946C4—22no—
947C4—22no—
948C4—24no—
949C4—24no—
950C4—24no—
951C4—42no—
952C4—48no—
953C4—42no—
954C4—42no—
955C4—44no—
956C4—48no—
957C4—48no—
958C4—44no—
959C4—48no—
960C4—42no—
961C4#350514yes—
962C2—24no—
963C2—24no—
964C2—42no—
965C2—82no—
966C2C2×#345511yescharacteristic
967C2C2×#350511yescharacteristic
968C2C2×#350911yescharacteristic
969C2#6281912yes—
970C2#6283112yes—
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
1. #39636C2semidirect
2. #39508C2semidirect
3. #38128C2semidirect
4. #38111C2semidirect
5. #37897C2semidirect
6. #37883C2semidirect
8. #37880C2semidirect
9. #37709C2semidirect
10. #37695C2semidirect
11. #36772C2semidirect
12. #36625C2semidirect
13. C2×#2857C2semidirect
14. #35380C2semidirect
15. #35315C2semidirect
16. #35310C2semidirect
18. #35015C2semidirect
19. #35014C2semidirect
20. #34245C2semidirect
22. C2×#541C22semidirect
23. C2×#533C22semidirect
24. C22×C4⋊Q8C22semidirect
33. #2857C22semidirect
34. #2857C22semidirect
35. #2857C22semidirect
36. #2857C22semidirect
38. #2855C22semidirect
40. #2851C22semidirect
43. #2799C22semidirect
44. #2798C22semidirect
45. #2793C22semidirect
46. #2791C22semidirect
47. #2787C22semidirect
50. #2770C22semidirect
51. #2759C22semidirect
52. #2755C22semidirect
53. #2747C22semidirect
55. #2716C22semidirect
56. #2713C22semidirect
58. #2690C22semidirect
59. #2647C22semidirect
62. #2645C22semidirect
63. #2642C22semidirect
65. #2629C22semidirect
68. #2625C22semidirect
69. #2621C22semidirect
70. #2596C22semidirect
71. #2594C22semidirect
72. #2590C22semidirect
73. #2589C22semidirect
74. #2588C22semidirect
75. #2587C22semidirect
76. #2585C22semidirect
77. #2585C22semidirect
80. #2533C22semidirect
81. #2528C22semidirect
82. #2525C22semidirect
83. #2511C22semidirect
84. #2509C22semidirect
85. #2507C22semidirect
88. #2497C22semidirect
90. #2493C22semidirect
91. #2492C22semidirect
94. #2484C22semidirect
98. #2478C22semidirect
99. #2475C22semidirect
101. #2473C22semidirect
102. #2469C22semidirect
103. #2453C22semidirect
104. #2451C22semidirect
105. #2446C22semidirect
106. #2438C22semidirect
107. #2429C22semidirect
108. #2423C22semidirect
115. #2362C22semidirect
116. #2362C22semidirect
117. #2344C22semidirect
119. Q8×C22⋊C4C22semidirect
120. #2332C22semidirect
121. #2332C22semidirect
122. #2330C22semidirect
125. #2327C22semidirect
126. #2323C22semidirect
128. #2320C22semidirect
129. #2314C22semidirect
131. #2313C22semidirect
136. C4×C22⋊Q8C22semidirect
137. #2296C22semidirect
138. C2×#391C22semidirect
139. C2×#389C22semidirect
150. #2285C22semidirect
151. C2×#384C22semidirect
154. #2274C22semidirect

Maximal subgroups

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

subgroupindex
#396362
#395082
#381282
#381112
#378972
#378832
#378812
#378802
#377092
#376952
#367722
#366252
C2×#28572
#353802
#353152
#353102
#350842
#350152
#350142
#342452
C2×#22902