Finite Group Databasebeta

← #7655848

Subgroups — #7655848

Order 512.

4744 conjugacy classes of subgroups.

The subgroup lattice has 936 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#42499C214yesmaximal, complemented
2#42496C214yesmaximal, complemented
3#40636C218yesmaximal, complemented
4#40633C218yesmaximal, complemented
5#39495C212yesmaximal
6#39492C214yesmaximal, complemented
7#39367C212yesmaximal
8#39364C214yesmaximal, complemented
9#37561C212yesmaximal, complemented
10#37478C214yesmaximal, complemented
11#36599C212yesmaximal, complemented
12#36564C212yesmaximal, complemented
13#35934C214yesmaximal, complemented
14#35871C214yesmaximal, complemented
15#35167C211yesmaximal, characteristic, complemented
16#35002C212yesmaximal, complemented
17#34595C211yesmaximal, characteristic, complemented
18#34578C212yesmaximal, complemented
19#34194C212yesmaximal
20C2×#2357C211yesmaximal, characteristic
21C2×#544C2212yes—
22C2×#543C2214yes—
23C22×C4×D4C2211yescharacteristic
24#2857C2214yes—
25#2857C2212yes—
26#2857C2212yes—
27#2857C2214yes—
28#2845C2214yescomplemented
29#2844C2214yescomplemented
30#2841C2218yescomplemented
31#2841C2218yescomplemented
32#2807C2218yescomplemented
33#2804C2214yes—
34#2790C2218yescomplemented
35#2788C2218yescomplemented
36#2780C2218yes—
37#2732C2214yes—
38#2732C2214yes—
39#2729C2218yescomplemented
40#2729C2218yescomplemented
41#2720C2218yescomplemented
42#2704C2218yescomplemented
43#2692C2218yes—
44#2683C2214yes—
45#2677C2218yescomplemented
46#2667C2218yescomplemented
47#2667C2218yescomplemented
48#2666C2214yescomplemented
49#2666C2214yescomplemented
50#2666C2218yescomplemented
51#2665C2218yescomplemented
52#2665C2218yescomplemented
53#2660C2214yescomplemented
54#2659C2211yescharacteristic
55#2659C2212yes—
56#2659C2211yescharacteristic
57#2659C2212yes—
58#2659C2214yes—
59#2647C2214yescomplemented
60#2646C2214yes—
61#2646C2212yes—
62#2627C2212yes—
63#2627C2212yes—
64#2627C2218yescomplemented
65#2627C2218yescomplemented
66#2626C2214yes—
67#2626C2214yes—
68#2589C2218yescomplemented
69#2587C2218yescomplemented
70#2586C2218yescomplemented
71#2585C2218yescomplemented
72#2580C2214yes—
73#2570C2214yescomplemented
74#2569C2218yes—
75#2567C2212yescomplemented
76#2566C2214yes—
77#2556C2218yescomplemented
78#2556C2218yescomplemented
79#2552C2212yescomplemented
80#2552C2214yescomplemented
81#2551C2214yescomplemented
82#2551C2212yescomplemented
83#2550C2214yescomplemented
84#2550C2218yescomplemented
85#2549C2218yes—
86#2549C2218yescomplemented
87#2549C2218yescomplemented
88#2546C2212yescomplemented
89#2542C2214yes—
90#2538C2214yes—
91#2522C2218yescomplemented
92#2511C2214yescomplemented
93#2509C2214yescomplemented
94#2507C2214yescomplemented
95#2507C2214yescomplemented
96#2492C2218yescomplemented
97#2465C2218yescomplemented
98#2454C2214yes—
99#2452C2214yes—
100#2452C2214yes—
101#2452C2214yes—
102#2451C2214yescomplemented
103#2446C2214yescomplemented
104#2442C2214yes—
105#2440C2214yes—
106#2440C2218yescomplemented
107#2440C2218yescomplemented
108#2438C2218yes—
109#2438C2218yescomplemented
110#2438C2218yescomplemented
111#2437C2218yes—
112#2437C2218yes—
113#2429C2218yescomplemented
114#2402C2214yescomplemented
115#2399C2214yescomplemented
116#2396C2218yescomplemented
117#2396C2218yescomplemented
118#2370C2214yescomplemented
119#2369C2212yescomplemented
120#2369C2214yescomplemented
121#2365C2212yescomplemented
122#2357C2214yes—
123#2357C2214yes—
124#2357C2218yes—
125#2355C2212yescomplemented
126#2354C2212yes—
127#2354C2212yes—
128#2352C2214yes—
129#2352C2214yes—
130Q8×C4⋊C4C2212yescomplemented
131D4×C4⋊C4C2212yes—
132D4×C4⋊C4C2212yes—
133#2345C2214yes—
134#2342C2218yes—
135D4×C22⋊C4C2214yes—
136#2319C2214yes—
137#2318C2218yes—
138#2316C2212yes—
139#2315C2214yes—
140C4×C22⋊Q8C2214yes—
141C4×C22⋊Q8C2214yes—
142C4×C22⋊Q8C2212yes—
143C4×C22⋊Q8C2212yes—
144C2×#390C2211yescharacteristic
145C2×#390C2211yescharacteristic
146C2×#388C2212yes—
147C2×#388C2212yes—
148#2285C2212yes—
149#2283C2212yes—
150C2×#382C2211yescharacteristic
151#2280C2214yes—
152C2×#381C2212yes—
153C2×#380C2214yes—
154#2275C2214yes—
155C2×C4×C4⋊C4C2211yescharacteristic
156C2×C4×C4⋊C4C2211yescharacteristic
157C2×C4×C4⋊C4C2211yescharacteristic
158C2×C4×C22⋊C4C2212yes—
159C23×D4C2311yescharacteristic
160C24×C4C2312yes—
161#544—48no—
162#543—416no—
163C2×C4⋊Q8C2312yes—
164C2×C4⋊Q8C2312yes—
165C2×C4⋊Q8C2314yes—
166C2×C4⋊Q8C2318yes—
167C2×C4⋊Q8C2314yes—
168C2×C4⋊Q8C2314yes—
169C2×#125C2314yes—
170C2×#125C2318yes—
171C2×C22⋊Q8C2314yes—
172C2×C22⋊Q8C2312yes—
173C2×C22⋊Q8C2312yes—
174C2×C22⋊Q8C2318yes—
175C2×C22⋊Q8C2314yes—
176C2×C22⋊Q8C2318yes—
177C2×C22⋊Q8C2318yes—
178C2×C22⋊Q8C2318yes—
179C2×C22⋊Q8C2318yes—
180C2×C22⋊Q8C2318yes—
181C2×C22⋊Q8C2318yes—
182C2×C4×Q8C2312yes—
183C2×C4×Q8C2312yes—
184C2×C4×Q8C2314yes—
185C2×C4×Q8C2314yes—
186C2×C4×D4Q8116yescomplemented
187C2×C4×D4C2314yes—
188C2×C4×D4C2314yes—
189C2×C4×D4C2314yes—
190C2×C4×D4C2312yes—
191C2×C4×D4C2312yes—
192C2×#117C2314yes—
193C2×#117C2314yes—
194C2×#117C2314yes—
195C22×C4⋊C4C2311yescharacteristic
196C22×C4⋊C4C2311yescharacteristic
197C22×C4⋊C4C2311yescharacteristic
198C22×C4⋊C4C2311yescharacteristic
199C22×C4⋊C4C2314yes—
200C22×C4⋊C4C2314yes—
201C22×C4⋊C4C2311yescharacteristic
202C22×C22⋊C4C2312yes—
203C22×C22⋊C4C2312yes—
204C22×C22⋊C4C2318yes—
205C22×C22⋊C4C2312yes—
206C22×C22⋊C4C2312yes—
207C22×C22⋊C4C2312yes—
208C22×C42C2311yescharacteristic
209C22×C42C2311yescharacteristic
210C22×C42C2312yes—
211C22×C42C2312yes—
212C22×C42C2311yescharacteristic
213#400C2318yes—
214#400C2318yes—
215#400C2318yes—
216#400C2318yes—
217#400C2314yes—
218#400C2318yes—
219#400C2314yes—
220#400C2314yes—
221#400C2314yes—
222#400C2318yes—
223#399C2318yes—
224#399C2318yes—
225#399C2318yes—
226#399C2318yes—
227#398C2318yes—
228#398C2318yes—
229#398C2318yes—
230#398C2318yes—
231#398C2314yes—
232#398C2318yes—
233#398C2318yes—
234#398C2318yes—
235#398C2318yes—
236#398C2318yes—
237#398C2318yes—
238#398C2314yes—
239#398C2318yes—
240#398C2318yes—
241#398C2314yes—
242#398C2314yes—
243#398C2314yes—
244#398C2314yes—
245#398C2318yes—
246#398C2314yes—
247#398C2318yes—
248#398C2314yes—
249#396C2318yes—
250#396C2318yes—
251#396C2318yes—
252#396C2318yes—
253#396C2318yes—
254#396C2318yes—
255#396C2318yes—
256#396C2318yes—
257#395C2318yes—
258#395C2318yes—
259#395C2318yes—
260#395C2318yes—
261#395C2318yes—
262#395C2318yes—
263#395C2318yes—
264#395C2314yes—
265#395C2314yes—
266#395C2314yes—
267#395C2318yes—
268#395C2314yes—
269#393C2318yes—
270#393C2318yes—
271#393C2318yes—
272#393C2318yes—
273#391C2314yes—
274#391C2314yes—
275#391C2318yes—
276#391C2318yes—
277#391C2318yes—
278#391C2314yes—
279#391C2314yes—
280#391C2314yes—
281#391C2318yes—
282#391C2314yes—
283#391C2312yes—
284#391C2312yes—
285#390C2314yes—
286#390C2314yes—
287#390C2314yes—
288#390C2314yes—
289#390C2314yes—
290#390C2314yes—
291#389C2314yes—
292#389C2314yes—
293#389C2314yes—
294#389C2318yes—
295#389C2318yes—
296#389C2314yes—
297#389C2314yes—
298#389C2314yes—
299#389C2318yes—
300#389C2318yes—
301#389C2318yes—
302#389C2318yes—
303#389C2314yes—
304#389C2318yes—
305#389C2314yes—
306#389C2314yes—
307#389C2314yes—
308#389C2314yes—
309#389C2314yes—
310#389C2318yes—
311#389C2312yes—
312#389C2312yes—
313#389C2314yes—
314#389C2314yes—
315#388C2318yes—
316#388C2318yes—
317#388C2318yes—
318#388C2318yes—
319#388C2318yes—
320#388C2318yes—
321#388C2318yes—
322#388C2318yes—
323#387C2318yes—
324#387C2318yes—
325#387C2318yes—
326#387C2318yes—
327#387C2318yes—
328#387C2318yes—
329#387C2318yes—
330#387C2318yes—
331#387C2314yes—
332#387C2318yes—
333#387C2314yes—
334#387C2318yes—
335#386C2318yes—
336#386C2318yes—
337#385C2318yes—
338#385C2318yes—
339#385C2314yes—
340#385C2318yes—
341#385C2318yes—
342#385C2318yes—
343#385C2318yes—
344#385C2318yes—
345#385C2318yes—
346#385C2318yes—
347#385C2318yes—
348#385C2318yes—
349#385C2318yes—
350#385C2314yes—
351#384C2312yes—
352#384C2314yes—
353#384C2314yes—
354#384C2312yes—
355#384C2314yes—
356#384C2312yes—
357#384C2312yes—
358#383C2314yes—
359#382C2314yes—
360#382C2314yes—
361#382C2314yes—
362#382C2312yes—
363#382C2314yes—
364#382C2312yes—
365#381C2318yes—
366#381C2318yes—
367#381C2314yes—
368#381C2318yes—
369#380C2314yes—
370#380C2318yes—
371#380C2318yes—
372#380C2312yes—
373#380C2314yes—
374#380C2318yes—
375#380C2314yes—
376#380C2314yes—
377#380C2314yes—
378#380C2314yes—
379#380C2314yes—
380#380C2312yes—
381#380C2318yes—
382#380C2318yes—
383#380C2312yes—
384#380C2312yes—
385#380C2314yes—
386#379C2318yes—
387C4×C4⋊C4C2314yes—
388C4×C4⋊C4C2312yes—
389C4×C4⋊C4C2312yes—
390C4×C4⋊C4C2314yes—
391C4×C4⋊C4C2314yes—
392C4×C4⋊C4C2318yes—
393C4×C4⋊C4C2314yes—
394C4×C4⋊C4C2318yes—
395C4×C4⋊C4C2314yes—
396C4×C4⋊C4C2314yes—
397C4×C4⋊C4C2314yes—
398C4×C4⋊C4C2312yes—
399C4×C4⋊C4C2312yes—
400C4×C4⋊C4C2314yes—
401C4×C4⋊C4C2312yes—
402C4×C4⋊C4C2314yes—
403C4×C4⋊C4C2314yes—
404C4×C4⋊C4C2314yes—
405C4×C4⋊C4C2312yes—
406C4×C4⋊C4C2312yes—
407C4×C4⋊C4C2312yes—
408C4×C4⋊C4C2314yes—
409C4×C22⋊C4C2318yes—
410C4×C22⋊C4C2318yes—
411C4×C22⋊C4C2318yes—
412C4×C22⋊C4C2318yes—
413C4×C22⋊C4C2314yes—
414C4×C22⋊C4C2318yes—
415C4×C22⋊C4C2318yes—
416#376C2314yes—
417C2×#95C2312yes—
418C2×#95C2318yes—
419C2×#95C2312yes—
420C2×#95C2311yescharacteristic
421C2×#95C2311yescharacteristic
422C2×#95C2312yes—
423C2×#95C2312yes—
424C25C2412yes—
425C22×Q8C2412yes—
426C22×Q8C2412yes—
427C22×Q8C2414yes—
428C22×Q8C2418yes—
429C22×Q8C2414yes—
430C22×D4—42no—
431C22×D4—42no—
432C22×D4C2×Q818yes—
433C22×D4C2412yes—
434C22×D4C2412yes—
435C23×C4—82no—
436C23×C4—82no—
437C23×C4C2×Q8116yes—
438C23×C4C2411yescharacteristic
439C23×C4C2411yescharacteristic
440C23×C4C2412yes—
441C23×C4C2411yescharacteristic
442C23×C4C2412yes—
443C23×C4C2411yescharacteristic
444C23×C4C2418yes—
445C23×C4C2418yes—
446C23×C4C2412yes—
447C23×C4C2414yes—
448C23×C4C2414yes—
449C23×C4C2411yescharacteristic
450C23×C4C2411yescharacteristic
451C23×C4C2411yescharacteristic
452C4⋊Q8—44no—
453C4⋊Q8—44no—
454C4⋊Q8—48no—
455C4⋊Q8—416no—
456C4⋊Q8—84no—
457C4⋊Q8—84no—
458#125—48no—
459#125—416no—
460C22⋊Q8—28no—
461C22⋊Q8—216no—
462C22⋊Q8—28no—
463C22⋊Q8—416no—
464C22⋊Q8—48no—
465C22⋊Q8—416no—
466C22⋊Q8—416no—
467C22⋊Q8—416no—
468C22⋊Q8—416no—
469C22⋊Q8—88no—
470C22⋊Q8—88no—
471C4×Q8—44no—
472C4×Q8—44no—
473C4×Q8—84no—
474C4×Q8—84no—
475C4×D4—48no—
476C4×D4—48no—
477C4×D4C2×Q8116yes—
478C4×D4C2×Q8116yes—
479C4×D4C2×Q8132yes—
480#117—48no—
481#117—84no—
482#117—84no—
483C2×C4⋊C4—24no—
484C2×C4⋊C4—24no—
485C2×C4⋊C4—42no—
486C2×C4⋊C4—42no—
487C2×C4⋊C4—84no—
488C2×C4⋊C4—84no—
489C2×C4⋊C4C2×Q818yes—
490C2×C4⋊C4C2414yes—
491C2×C4⋊C4C2412yes—
492C2×C4⋊C4C2412yes—
493C2×C4⋊C4C2414yes—
494C2×C4⋊C4C2414yes—
495C2×C4⋊C4C2414yes—
496C2×C4⋊C4C2412yes—
497C2×C4⋊C4C2414yes—
498C2×C4⋊C4C2414yes—
499C2×C4⋊C4C2418yes—
500C2×C4⋊C4C2414yes—
501C2×C4⋊C4C2412yes—
502C2×C4⋊C4C2412yes—
503C2×C4⋊C4C2412yes—
504C2×C4⋊C4C2414yes—
505C2×C4⋊C4C2414yes—
506C2×C4⋊C4C2418yes—
507C2×C4⋊C4C2418yes—
508C2×C4⋊C4C2412yes—
509C2×C4⋊C4C2412yes—
510C2×C4⋊C4C2412yes—
511C2×C4⋊C4C2412yes—
512C2×C4⋊C4C2414yes—
513C2×C4⋊C4C2414yes—
514C2×C4⋊C4C2412yes—
515C2×C4⋊C4C2418yes—
516C2×C4⋊C4C2418yes—
517C2×C4⋊C4C2414yes—
518C2×C4⋊C4C2412yes—
519C2×C4⋊C4C2414yes—
520C2×C4⋊C4C2412yes—
521C2×C4⋊C4C2414yes—
522C2×C4⋊C4C2418yes—
523C2×C4⋊C4C2418yes—
524C2×C4⋊C4C2418yes—
525C2×C4⋊C4C2414yes—
526C2×C4⋊C4C2414yes—
527C2×C4⋊C4C2414yes—
528C2×C4⋊C4C2414yes—
529C2×C4⋊C4C2418yes—
530C2×C4⋊C4C2418yes—
531C2×C4⋊C4C2418yes—
532C2×C4⋊C4C2418yes—
533C2×C4⋊C4C2412yes—
534C2×C4⋊C4C2414yes—
535C2×C4⋊C4C2418yes—
536C2×C4⋊C4C2414yes—
537C2×C4⋊C4C2411yescharacteristic
538C2×C4⋊C4C2412yes—
539C2×C4⋊C4C2411yescharacteristic
540C2×C22⋊C4—28no—
541C2×C22⋊C4—28no—
542C2×C22⋊C4—416no—
543C2×C22⋊C4—82no—
544C2×C22⋊C4—82no—
545C2×C22⋊C4C2×Q8116yes—
546C2×C22⋊C4C2414yes—
547C2×C22⋊C4C2418yes—
548C2×C22⋊C4C2418yes—
549C2×C22⋊C4C2418yes—
550C2×C22⋊C4C2414yes—
551C2×C22⋊C4C2418yes—
552C2×C22⋊C4C2418yes—
553C2×C22⋊C4C2418yes—
554C2×C22⋊C4C2418yes—
555C2×C22⋊C4C2418yes—
556C2×C22⋊C4C2418yes—
557C2×C22⋊C4C2418yes—
558C2×C22⋊C4C2418yes—
559C2×C22⋊C4C2414yes—
560C2×C22⋊C4C2414yes—
561C2×C42—42no—
562C2×C42—42no—
563C2×C42—82no—
564C2×C42—82no—
565C2×C42C2×Q818yes—
566C2×C42C2414yes—
567C2×C42C2414yes—
568C2×C42C2412yes—
569C2×C42C2412yes—
570C2×C42C2418yes—
571C2×C42C2418yes—
572C2×C42C2418yes—
573C2×C42C2414yes—
574C2×C42C2414yes—
575C2×C42C2414yes—
576C2×C42C2414yes—
577C2×C42C2412yes—
578C2×C42C2412yes—
579C2×C42C2412yes—
580C2×C42C2412yes—
581#95C2414yes—
582#95C2414yes—
583#95C2418yes—
584#95C2418yes—
585#95C2418yes—
586#95C2418yes—
587#95C2414yes—
588#95C2414yes—
589#95C2414yes—
590#95C2414yes—
591#95C2414yes—
592#95C2418yes—
593#95C2414yes—
594#95C2414yes—
595#95C2414yes—
596#95C2418yes—
597#95C2418yes—
598#95C2414yes—
599#95C2414yes—
600#95C2414yes—
601#95C2414yes—
602#95C2418yes—
603#95C2414yes—
604#95C2418yes—
605#95C2418yes—
606#95C2414yes—
607#95C2414yes—
608#95C2418yes—
609#95C2414yes—
610#95C2414yes—
611#95C2414yes—
612#95C2418yes—
613#95C2418yes—
614#95C2418yes—
615#95C2418yes—
616#95C2418yes—
617C24—24no—
618C24—24no—
619C24—42no—
620C24—42no—
621C24—42no—
622C24—42no—
623C24C22×Q818yes—
624C24C2514yes—
625C24C2511yescharacteristic
626C2×Q8—24no—
627C2×Q8—28no—
628C2×Q8—24no—
629C2×Q8—42no—
630C2×Q8—42no—
631C2×Q8—42no—
632C2×Q8—44no—
633C2×Q8—44no—
634C2×Q8—42no—
635C2×Q8—48no—
636C2×Q8—44no—
637C2×Q8—44no—
638C2×Q8—48no—
639C2×Q8—44no—
640C2×Q8—48no—
641C2×D4—24no—
642C2×D4—24no—
643C2×D4—416no—
644C2×D4—42no—
645C2×D4—42no—
646C2×D4C22×Q818yes—
647C2×D4C22×Q818yes—
648C22×C4—22no—
649C22×C4—22no—
650C22×C4—22no—
651C22×C4—22no—
652C22×C4—24no—
653C22×C4—22no—
654C22×C4—24no—
655C22×C4—22no—
656C22×C4—41no—
657C22×C4—41no—
658C22×C4—41no—
659C22×C4—41no—
660C22×C4—42no—
661C22×C4—42no—
662C22×C4—44no—
663C22×C4—44no—
664C22×C4—44no—
665C22×C4—44no—
666C22×C4—41no—
667C22×C4—41no—
668C22×C4—41no—
669C22×C4—41no—
670C22×C4—42no—
671C22×C4—42no—
672C22×C4—41no—
673C22×C4—41no—
674C22×C4—42no—
675C22×C4—42no—
676C22×C4—48no—
677C22×C4—48no—
678C22×C4—48no—
679C22×C4—48no—
680C22×C4—48no—
681C22×C4—48no—
682C22×C4—816no—
683C22×C4C22×Q814yes—
684C22×C4C22×Q814yes—
685C22×C4C22×Q814yes—
686C22×C4C22×Q818yes—
687C22×C4C22×Q8116yes—
688C22×C4C22×Q8116yes—
689C22×C4H(5,𝔽2)14yes—
690C22×C42−1+414yes—
691C22×C4C2514yes—
692C22×C4C2514yes—
693C22×C4C2512yes—
694C22×C4C2514yes—
695C22×C4C2514yes—
696C22×C4C2518yes—
697C22×C4C2514yes—
698C22×C4C2512yes—
699C22×C4C2514yes—
700C22×C4C2518yes—
701C22×C4C2511yescharacteristic
702C22×C4C2512yes—
703C22×C4C2512yes—
704C22×C4C2512yes—
705C22×C4C2512yes—
706C22×C4C2512yes—
707C22×C4C2512yes—
708C22×C4C2511yescharacteristic
709C4⋊C4—28no—
710C4⋊C4—24no—
711C4⋊C4—28no—
712C4⋊C4—28no—
713C4⋊C4—216no—
714C4⋊C4—28no—
715C4⋊C4—24no—
716C4⋊C4—28no—
717C4⋊C4—24no—
718C4⋊C4—24no—
719C4⋊C4—28no—
720C4⋊C4—28no—
721C4⋊C4—42no—
722C4⋊C4—42no—
723C4⋊C4—42no—
724C4⋊C4—42no—
725C4⋊C4—44no—
726C4⋊C4—44no—
727C4⋊C4—48no—
728C4⋊C4—48no—
729C4⋊C4—44no—
730C4⋊C4—44no—
731C4⋊C4—42no—
732C4⋊C4—42no—
733C4⋊C4—42no—
734C4⋊C4—42no—
735C4⋊C4—44no—
736C4⋊C4—44no—
737C4⋊C4—42no—
738C4⋊C4—48no—
739C4⋊C4—48no—
740C4⋊C4—44no—
741C4⋊C4—48no—
742C4⋊C4—48no—
743C4⋊C4—48no—
744C4⋊C4—44no—
745C4⋊C4—48no—
746C4⋊C4—44no—
747C4⋊C4—44no—
748C4⋊C4—44no—
749C4⋊C4—48no—
750C4⋊C4—48no—
751C4⋊C4—48no—
752C4⋊C4—44no—
753C4⋊C4—44no—
754C4⋊C4—48no—
755C4⋊C4—42no—
756C4⋊C4C22×Q818yes—
757C4⋊C4C22×Q814yes—
758C4⋊C4C22×Q814yes—
759C22⋊C4—28no—
760C22⋊C4—216no—
761C22⋊C4—28no—
762C22⋊C4—216no—
763C22⋊C4—216no—
764C22⋊C4—48no—
765C22⋊C4—48no—
766C22⋊C4—48no—
767C22⋊C4—48no—
768C22⋊C4—48no—
769C22⋊C4—48no—
770C22⋊C4—48no—
771C22⋊C4—48no—
772C22⋊C4C22×Q8116yes—
773C22⋊C4C22×Q8116yes—
774C42—24no—
775C42—24no—
776C42—28no—
777C42—28no—
778C42—42no—
779C42—42no—
780C42—44no—
781C42—44no—
782C42—44no—
783C42—44no—
784C42—48no—
785C42—48no—
786C42—48no—
787C42C22×Q818yes—
788C42C22×Q818yes—
789C23—21no—
790C23—21no—
791C23—21no—
792C23—21no—
793C23—24no—
794C23—24no—
795C23—24no—
796C23—24no—
797C23—24no—
798C23—24no—
799C23—216no—
800C23—48no—
801C23—48no—
802C23—84no—
803C23—84no—
804C23—84no—
805C23—84no—
806C23C23×Q818yes—
807C23C23×Q812yes—
808C23C2×H(5,𝔽2)12yes—
809C23C2×2−1+412yes—
810C23C2611yescharacteristic
811Q8—48no—
812Q8—84no—
813Q8—88no—
814Q8—164no—
815Q8—168no—
816D4—216no—
817D4—48no—
818C2×C4—22no—
819C2×C4—22no—
820C2×C4—22no—
821C2×C4—22no—
822C2×C4—21no—
823C2×C4—21no—
824C2×C4—22no—
825C2×C4—22no—
826C2×C4—22no—
827C2×C4—22no—
828C2×C4—22no—
829C2×C4—22no—
830C2×C4—22no—
831C2×C4—22no—
832C2×C4—28no—
833C2×C4—28no—
834C2×C4—28no—
835C2×C4—28no—
836C2×C4—24no—
837C2×C4—24no—
838C2×C4—24no—
839C2×C4—22no—
840C2×C4—24no—
841C2×C4—24no—
842C2×C4—24no—
843C2×C4—22no—
844C2×C4—22no—
845C2×C4—22no—
846C2×C4—24no—
847C2×C4—24no—
848C2×C4—24no—
849C2×C4—24no—
850C2×C4—28no—
851C2×C4—28no—
852C2×C4—24no—
853C2×C4—24no—
854C2×C4—24no—
855C2×C4—24no—
856C2×C4—24no—
857C2×C4—24no—
858C2×C4—28no—
859C2×C4—28no—
860C2×C4—22no—
861C2×C4—22no—
862C2×C4—24no—
863C2×C4—24no—
864C2×C4—44no—
865C2×C4—416no—
866C2×C4—416no—
867C2×C4—48no—
868C2×C4—44no—
869C2×C4—44no—
870C2×C4—82no—
871C2×C4—82no—
872C2×C4—84no—
873C2×C4—84no—
874C2×C4—168no—
875C2×C4—168no—
876C2×C4C23×Q814yes—
877C2×C4C23×Q812yes—
878C2×C4C23×Q814yes—
879C2×C4C23×Q814yes—
880C2×C4C23×Q814yes—
881C2×C4C23×Q812yes—
882C2×C4C2×H(5,𝔽2)14yes—
883C2×C4C2×2−1+414yes—
884C2×C4#58512yes—
885C2×C4#58512yes—
886C22—22no—
887C22—22no—
888C22—22no—
889C22—22no—
890C22—22no—
891C22—22no—
892C22—28no—
893C22—28no—
894C22—28no—
895C22—44no—
896C22—44no—
897C22—44no—
898C22—44no—
899C22—816no—
900C22#350314yes—
901C22C24×Q811yescharacteristic
902C22C22×H(5,𝔽2)11yescharacteristic
903C22C22×2−1+411yescharacteristic
904C22C2×#58511yescharacteristic
905C22C2×#58511yescharacteristic
906C22H(7,𝔽2)11yescharacteristic
907C22H(7,𝔽2)11yescharacteristic
908C4—24no—
909C4—24no—
910C4—24no—
911C4—24no—
912C4—24no—
913C4—24no—
914C4—22no—
915C4—42no—
916C4—44no—
917C4—42no—
918C4—44no—
919C4—48no—
920C4—44no—
921C4—44no—
922C4—48no—
923C4—44no—
924C4—44no—
925C4#345814yes—
926C2—24no—
927C2—48no—
928C2C2×#345811yescharacteristic
929C2C2×#350311yescharacteristic
930C2#6284311yescharacteristic
931C2#6290211yescharacteristic
932C2#6290511yescharacteristic
933C2#6296111yescharacteristic
934C2#6296211yescharacteristic
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. #42499C2semidirect
2. #42496C2semidirect
3. #40636C2semidirect
4. #40633C2semidirect
6. #39492C2semidirect
8. #39364C2semidirect
9. #37561C2semidirect
10. #37478C2semidirect
11. #36599C2semidirect
12. #36564C2semidirect
13. #35934C2semidirect
14. #35871C2semidirect
15. #35167C2semidirect
16. #35002C2semidirect
17. #34595C2semidirect
18. #34578C2semidirect
28. #2845C22semidirect
29. #2844C22semidirect
30. #2841C22semidirect
31. #2841C22semidirect
32. #2807C22semidirect
34. #2790C22semidirect
35. #2788C22semidirect
39. #2729C22semidirect
40. #2729C22semidirect
41. #2720C22semidirect
42. #2704C22semidirect
45. #2677C22semidirect
46. #2667C22semidirect
47. #2667C22semidirect
48. #2666C22semidirect
49. #2666C22semidirect
50. #2666C22semidirect
51. #2665C22semidirect
52. #2665C22semidirect
53. #2660C22semidirect
59. #2647C22semidirect
64. #2627C22semidirect
65. #2627C22semidirect
68. #2589C22semidirect
69. #2587C22semidirect
70. #2586C22semidirect
71. #2585C22semidirect
73. #2570C22semidirect
75. #2567C22semidirect
77. #2556C22semidirect
78. #2556C22semidirect
79. #2552C22semidirect
80. #2552C22semidirect
81. #2551C22semidirect
82. #2551C22semidirect
83. #2550C22semidirect
84. #2550C22semidirect
86. #2549C22semidirect
87. #2549C22semidirect
88. #2546C22semidirect
91. #2522C22semidirect
92. #2511C22semidirect
93. #2509C22semidirect
94. #2507C22semidirect
95. #2507C22semidirect
96. #2492C22semidirect
97. #2465C22semidirect
102. #2451C22semidirect
103. #2446C22semidirect
106. #2440C22semidirect
107. #2440C22semidirect
109. #2438C22semidirect
110. #2438C22semidirect
113. #2429C22semidirect
114. #2402C22semidirect
115. #2399C22semidirect
116. #2396C22semidirect
117. #2396C22semidirect
118. #2370C22semidirect
119. #2369C22semidirect
120. #2369C22semidirect
121. #2365C22semidirect
125. #2355C22semidirect
130. Q8×C4⋊C4C22semidirect
186. C2×C4×D4Q8semidirect

Maximal subgroups

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

subgroupindex
#424992
#424962
#406362
#406332
#394952
#394922
#393672
#393642
#375612
#374782
#365992
#365642
#359342
#358712
#351672
#350022
#345952
#345782
#341942
C2×#23572