Finite Group Databasebeta

← #7632544

Subgroups — #7632544

Order 512.

4902 conjugacy classes of subgroups.

The subgroup lattice has 898 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#36481C214yesmaximal, complemented
2#36480C214yesmaximal, complemented
3#36478C214yesmaximal, complemented
4#36478C214yesmaximal, complemented
5#36039C214yesmaximal, complemented
6#35819C214yesmaximal, complemented
7#35815C214yesmaximal, complemented
8#35747C214yesmaximal, complemented
9#35585C212yesmaximal, complemented
10#35566C212yesmaximal, complemented
11#35402C218yesmaximal
12#35253C212yesmaximal
13#35146C214yesmaximal, complemented
14#34966C214yesmaximal, complemented
15#34739C212yesmaximal
16#34271C212yesmaximal, complemented
17#34213C212yesmaximal, complemented
18#34179C211yesmaximal, characteristic
19C2×#2347C211yesmaximal, characteristic
20#33996C211yesmaximal, characteristic
21C2×#544C2212yes—
22C2×#533C2212yes—
23C22×#117C2212yes—
24C22×#117C2211yescharacteristic
25#2863C2218yescomplemented
26#2863C2218yescomplemented
27#2857C2214yes—
28#2851C2214yes—
29#2666C2218yescomplemented
30#2666C2218yescomplemented
31#2629C2214yes—
32#2628C2214yes—
33#2606C2214yescomplemented
34#2606C2214yescomplemented
35#2606C2218yescomplemented
36#2606C2218yescomplemented
37#2605C2214yescomplemented
38#2605C2214yescomplemented
39#2605C2218yescomplemented
40#2605C2218yescomplemented
41#2589C2218yes—
42#2589C2218yes—
43#2587C2218yes—
44#2587C2218yes—
45#2584C2214yescomplemented
46#2584C2214yescomplemented
47#2574C2218yes—
48#2574C2218yes—
49#2570C2218yescomplemented
50#2569C2218yes—
51#2567C2214yescomplemented
52#2556C2218yes—
53#2556C2218yes—
54#2552C2214yescomplemented
55#2551C2214yescomplemented
56#2550C2214yescomplemented
57#2550C2214yescomplemented
58#2550C2218yescomplemented
59#2549C2218yes—
60#2546C2214yescomplemented
61#2522C2218yes—
62#2522C2218yes—
63#2509C2214yescomplemented
64#2509C2214yescomplemented
65#2508C2214yescomplemented
66#2508C2214yescomplemented
67#2507C2214yescomplemented
68#2507C2214yescomplemented
69#2506C2214yescomplemented
70#2506C2214yescomplemented
71#2497C2218yes—
72#2492C2218yes—
73#2465C2218yes—
74#2465C2218yes—
75#2442C2218yes—
76#2442C2212yes—
77#2442C2212yes—
78#2442C2214yes—
79#2441C2212yes—
80#2441C2214yes—
81#2441C2212yes—
82#2440C2218yes—
83#2440C2212yes—
84#2440C2214yes—
85#2440C2212yes—
86#2439C2212yes—
87#2439C2214yes—
88#2439C2212yes—
89#2438C2214yes—
90#2438C2218yes—
91#2438C2214yes—
92#2437C2214yes—
93#2437C2214yes—
94#2437C2218yes—
95#2429C2218yes—
96#2423C2218yes—
97#2402C2214yescomplemented
98#2402C2214yescomplemented
99#2399C2214yescomplemented
100#2399C2214yescomplemented
101#2396C2214yes—
102#2396C2214yes—
103#2370C2214yescomplemented
104#2370C2214yescomplemented
105#2370C2214yescomplemented
106#2370C2214yescomplemented
107#2370C2214yescomplemented
108#2370C2214yescomplemented
109#2369C2214yescomplemented
110#2369C2214yescomplemented
111#2369C2214yescomplemented
112#2365C2214yescomplemented
113#2365C2214yescomplemented
114#2365C2214yescomplemented
115#2355C2214yescomplemented
116#2355C2214yescomplemented
117#2355C2214yescomplemented
118Q8×C4⋊C4C2214yescomplemented
119#2347C2214yes—
120#2347C2214yes—
121#2347C2214yes—
122#2347C2214yes—
123#2347C2214yes—
124#2347C2214yes—
125#2346C2214yes—
126#2346C2214yes—
127#2329C2218yes—
128#2329C2218yes—
129#2317C2212yes—
130#2317C2212yes—
131#2316C2212yes—
132#2316C2212yes—
133#2312C2214yes—
134C4×C4⋊Q8C2218yescomplemented
135C4×#125C2218yescomplemented
136C4×C22⋊Q8C2218yes—
137C4×C22⋊Q8C2218yes—
138C4×C22⋊Q8C2214yes—
139C4×C22⋊Q8C2214yes—
140#2296C2212yes—
141#2296C2212yes—
142C2×#389C2212yes—
143C2×#388C2214yes—
144#2285C2212yes—
145#2283C2214yes—
146C2×#383C2212yes—
147#2280C2212yes—
148C2×#380C2211yescharacteristic
149#2274C2211yescharacteristic
150#2274C2211yescharacteristic
151#2274C2211yescharacteristic
152#2274C2214yes—
153#2274C2212yes—
154#2274C2214yes—
155#2274C2211yescharacteristic
156#2273C2214yes—
157C4×#117C2214yes—
158C4×#117C2214yes—
159C4×#117C2214yes—
160C2×C4×C4⋊C4C2212yes—
161C2×C4×C4⋊C4C2212yes—
162C2×C4×C22⋊C4C2211yescharacteristic
163C24×C4C2311yescharacteristic
164#544—216no—
165#533—216no—
166C2×C4⋊Q8C2314yes—
167C2×C4⋊Q8C2312yes—
168C2×C4⋊Q8C2314yes—
169C2×C4⋊Q8C2312yes—
170C2×C4⋊Q8C2318yes—
171C2×#125C2314yes—
172C2×#125C2312yes—
173C2×#125C2312yes—
174C2×#125C2314yes—
175C2×#125C2318yes—
176C2×C22⋊Q8C2314yes—
177C2×C22⋊Q8C2318yes—
178C2×C22⋊Q8C2314yes—
179C2×C22⋊Q8C2314yes—
180C2×C22⋊Q8C2314yes—
181C2×C22⋊Q8C2318yes—
182C2×C4×Q8C2314yes—
183C2×C4×Q8C2314yes—
184C2×C4×Q8C2318yes—
185C2×C4×Q8C2318yes—
186C2×#117—216no—
187C2×#117Q8116yescomplemented
188C2×#117C2312yes—
189C2×#117C2312yes—
190C2×#117C2312yes—
191C2×#117C2314yes—
192C2×#117C2314yes—
193C2×#117C2312yes—
194C2×#117C2312yes—
195C2×#117C2314yes—
196C2×#117C2314yes—
197C2×#117C2312yes—
198C22×C4⋊C4C2312yes—
199C22×C4⋊C4C2312yes—
200C22×C4⋊C4C2312yes—
201C22×C4⋊C4C2314yes—
202C22×C4⋊C4C2311yescharacteristic
203C22×C4⋊C4C2311yescharacteristic
204C22×C22⋊C4C2314yes—
205C22×C22⋊C4C2312yes—
206C22×C22⋊C4C2312yes—
207C22×C22⋊C4C2312yes—
208C22×C42C2314yes—
209C22×C42C2312yes—
210C22×C42C2314yes—
211C22×C42C2312yes—
212#400C2318yes—
213#400C2318yes—
214#400C2314yes—
215#400C2318yes—
216#400C2318yes—
217#400C2318yes—
218#400C2314yes—
219#399C2314yes—
220#399C2318yes—
221#399C2314yes—
222#398C2318yes—
223#398C2318yes—
224#398C2314yes—
225#398C2318yes—
226#398C2318yes—
227#398C2318yes—
228#398C2318yes—
229#398C2318yes—
230#398C2314yes—
231#398C2314yes—
232#398C2318yes—
233#398C2318yes—
234#398C2318yes—
235#398C2314yes—
236#396C2314yes—
237#396C2318yes—
238#396C2314yes—
239#396C2318yes—
240#396C2314yes—
241#396C2314yes—
242#395C2318yes—
243#395C2318yes—
244#395C2318yes—
245#395C2318yes—
246#395C2314yes—
247#395C2318yes—
248#395C2314yes—
249#393C2314yes—
250#393C2318yes—
251#393C2314yes—
252#391C2314yes—
253#391C2318yes—
254#391C2318yes—
255#391C2318yes—
256#391C2318yes—
257#391C2318yes—
258#391C2318yes—
259#391C2318yes—
260#391C2318yes—
261#391C2314yes—
262#391C2318yes—
263#389C2318yes—
264#389C2318yes—
265#389C2314yes—
266#389C2318yes—
267#389C2318yes—
268#389C2318yes—
269#389C2312yes—
270#389C2314yes—
271#389C2314yes—
272#389C2314yes—
273#389C2314yes—
274#389C2314yes—
275#389C2314yes—
276#389C2314yes—
277#389C2314yes—
278#389C2314yes—
279#389C2314yes—
280#389C2314yes—
281#389C2314yes—
282#389C2314yes—
283#389C2312yes—
284#389C2312yes—
285#389C2318yes—
286#389C2318yes—
287#389C2314yes—
288#389C2318yes—
289#389C2318yes—
290#389C2318yes—
291#389C2318yes—
292#389C2318yes—
293#389C2314yes—
294#389C2314yes—
295#389C2314yes—
296#389C2318yes—
297#389C2312yes—
298#389C2312yes—
299#389C2312yes—
300#389C2312yes—
301#389C2312yes—
302#388C2318yes—
303#388C2318yes—
304#388C2318yes—
305#388C2318yes—
306#388C2318yes—
307#388C2318yes—
308#388C2318yes—
309#388C2318yes—
310#387C2314yes—
311#387C2314yes—
312#387C2318yes—
313#387C2318yes—
314#387C2318yes—
315#387C2318yes—
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#387C2314yes—
331#387C2314yes—
332#385C2314yes—
333#385C2318yes—
334#385C2318yes—
335#385C2318yes—
336#385C2318yes—
337#385C2314yes—
338#385C2314yes—
339#385C2314yes—
340#385C2314yes—
341#385C2314yes—
342#385C2314yes—
343#385C2314yes—
344#384C2318yes—
345#384C2314yes—
346#384C2314yes—
347#384C2312yes—
348#384C2312yes—
349#383C2314yes—
350#383C2318yes—
351#383C2318yes—
352#383C2314yes—
353#382C2318yes—
354#382C2318yes—
355#382C2314yes—
356#382C2314yes—
357#382C2312yes—
358#382C2312yes—
359#381C2314yes—
360#380C2318yes—
361#380C2314yes—
362#380C2318yes—
363#380C2314yes—
364#380C2314yes—
365#380C2312yes—
366#380C2314yes—
367#380C2312yes—
368#380C2318yes—
369#380C2312yes—
370#380C2312yes—
371#380C2314yes—
372#380C2314yes—
373#379C2314yes—
374C4×C4⋊C4C2314yes—
375C4×C4⋊C4C2318yes—
376C4×C4⋊C4C2318yes—
377C4×C4⋊C4C2318yes—
378C4×C4⋊C4C2318yes—
379C4×C4⋊C4C2318yes—
380C4×C4⋊C4C2314yes—
381C4×C4⋊C4C2318yes—
382C4×C4⋊C4C2318yes—
383C4×C4⋊C4C2314yes—
384C4×C4⋊C4C2314yes—
385C4×C4⋊C4C2318yes—
386C4×C4⋊C4C2314yes—
387C4×C4⋊C4C2314yes—
388C4×C4⋊C4C2314yes—
389C4×C4⋊C4C2314yes—
390C4×C4⋊C4C2314yes—
391C4×C4⋊C4C2314yes—
392C4×C4⋊C4C2314yes—
393C4×C4⋊C4C2314yes—
394C4×C4⋊C4C2314yes—
395C4×C4⋊C4C2314yes—
396C4×C4⋊C4C2314yes—
397C4×C4⋊C4C2314yes—
398C4×C4⋊C4C2314yes—
399C4×C4⋊C4C2314yes—
400C4×C4⋊C4C2314yes—
401C4×C4⋊C4C2314yes—
402C4×C4⋊C4C2314yes—
403C4×C4⋊C4C2314yes—
404C4×C4⋊C4C2314yes—
405C4×C4⋊C4C2314yes—
406C4×C4⋊C4C2314yes—
407C4×C4⋊C4C2314yes—
408C4×C4⋊C4C2314yes—
409C4×C4⋊C4C2314yes—
410C4×C22⋊C4C2314yes—
411C4×C22⋊C4C2314yes—
412C4×C22⋊C4C2314yes—
413C4×C22⋊C4C2318yes—
414C4×C22⋊C4C2318yes—
415C4×C22⋊C4C2318yes—
416C4×C22⋊C4C2318yes—
417C4×C22⋊C4C2318yes—
418C4×C22⋊C4C2314yes—
419C4×C22⋊C4C2312yes—
420C4×C22⋊C4C2312yes—
421C4×C22⋊C4C2312yes—
422C4×C22⋊C4C2314yes—
423C4×C22⋊C4C2312yes—
424C4×C22⋊C4C2314yes—
425#376C2314yes—
426#376C2314yes—
427#376C2314yes—
428#376C2314yes—
429C2×#95C2314yes—
430C2×#95C2314yes—
431C2×#95C2311yescharacteristic
432C2×#95C2311yescharacteristic
433C2×#95C2312yes—
434C43C2318yes—
435C25C2411yescharacteristic
436C22×Q8C2414yes—
437C22×Q8C2418yes—
438C22×Q8C2414yes—
439C23×C4—28no—
440C23×C4C2×Q818yes—
441C23×C4C2412yes—
442C23×C4C2412yes—
443C23×C4C2411yescharacteristic
444C23×C4C2412yes—
445C23×C4C2414yes—
446C23×C4C2414yes—
447C23×C4C2414yes—
448C23×C4C2412yes—
449C23×C4C2412yes—
450C23×C4C2412yes—
451C23×C4C2411yescharacteristic
452C4⋊Q8—28no—
453C4⋊Q8—28no—
454C4⋊Q8—216no—
455C4⋊Q8—216no—
456C4⋊Q8—416no—
457#125—28no—
458#125—28no—
459#125—216no—
460#125—216no—
461#125—416no—
462C22⋊Q8—216no—
463C22⋊Q8—216no—
464C22⋊Q8—232no—
465C22⋊Q8—48no—
466C22⋊Q8—48no—
467C22⋊Q8—88no—
468C4×Q8—216no—
469C4×Q8—216no—
470C4×Q8—88no—
471C4×Q8—88no—
472#117—28no—
473#117—28no—
474#117—28no—
475#117—28no—
476#117—28no—
477#117—216no—
478#117—216no—
479#117C2×Q8132yes—
480#117C2×Q8132yes—
481#117#41116yes—
482C2×C4⋊C4—28no—
483C2×C4⋊C4—28no—
484C2×C4⋊C4—28no—
485C2×C4⋊C4—48no—
486C2×C4⋊C4C2×Q818yes—
487C2×C4⋊C4C2×Q818yes—
488C2×C4⋊C4C2412yes—
489C2×C4⋊C4C2412yes—
490C2×C4⋊C4C2414yes—
491C2×C4⋊C4C2414yes—
492C2×C4⋊C4C2414yes—
493C2×C4⋊C4C2414yes—
494C2×C4⋊C4C2418yes—
495C2×C4⋊C4C2412yes—
496C2×C4⋊C4C2412yes—
497C2×C4⋊C4C2412yes—
498C2×C4⋊C4C2412yes—
499C2×C4⋊C4C2414yes—
500C2×C4⋊C4C2414yes—
501C2×C4⋊C4C2414yes—
502C2×C4⋊C4C2414yes—
503C2×C4⋊C4C2414yes—
504C2×C4⋊C4C2414yes—
505C2×C4⋊C4C2414yes—
506C2×C4⋊C4C2414yes—
507C2×C4⋊C4C2418yes—
508C2×C4⋊C4C2418yes—
509C2×C4⋊C4C2418yes—
510C2×C4⋊C4C2414yes—
511C2×C4⋊C4C2418yes—
512C2×C4⋊C4C2414yes—
513C2×C4⋊C4C2414yes—
514C2×C4⋊C4C2414yes—
515C2×C4⋊C4C2418yes—
516C2×C4⋊C4C2418yes—
517C2×C4⋊C4C2418yes—
518C2×C4⋊C4C2414yes—
519C2×C4⋊C4C2414yes—
520C2×C4⋊C4C2414yes—
521C2×C4⋊C4C2418yes—
522C2×C4⋊C4C2418yes—
523C2×C4⋊C4C2418yes—
524C2×C4⋊C4C2418yes—
525C2×C4⋊C4C2418yes—
526C2×C4⋊C4C2414yes—
527C2×C4⋊C4C2414yes—
528C2×C4⋊C4C2414yes—
529C2×C4⋊C4C2414yes—
530C2×C4⋊C4C2414yes—
531C2×C4⋊C4C2412yes—
532C2×C4⋊C4C2412yes—
533C2×C22⋊C4—216no—
534C2×C22⋊C4—44no—
535C2×C22⋊C4—82no—
536C2×C22⋊C4C2×Q8116yes—
537C2×C22⋊C4C2414yes—
538C2×C22⋊C4C2414yes—
539C2×C22⋊C4C2414yes—
540C2×C22⋊C4C2412yes—
541C2×C22⋊C4C2412yes—
542C2×C22⋊C4C2414yes—
543C2×C22⋊C4C2414yes—
544C2×C22⋊C4C2418yes—
545C2×C22⋊C4C2412yes—
546C2×C22⋊C4C2412yes—
547C2×C22⋊C4C2414yes—
548C2×C22⋊C4C2414yes—
549C2×C22⋊C4C2414yes—
550C2×C22⋊C4C2414yes—
551C2×C22⋊C4C2418yes—
552C2×C22⋊C4C2414yes—
553C2×C42—28no—
554C2×C42—216no—
555C2×C42—84no—
556C2×C42C2×Q8116yes—
557C2×C42C2414yes—
558C2×C42C2414yes—
559C2×C42C2414yes—
560C2×C42C2414yes—
561C2×C42C2414yes—
562C2×C42C2412yes—
563C2×C42C2412yes—
564C2×C42C2412yes—
565C2×C42C2412yes—
566C2×C42C2418yes—
567C2×C42C2414yes—
568C2×C42C2414yes—
569C2×C42C2418yes—
570C2×C42C2418yes—
571C2×C42C2418yes—
572C2×C42C2418yes—
573C2×C42C2418yes—
574C2×C42C2414yes—
575C2×C42C2414yes—
576C2×C42C2414yes—
577C2×C42C2414yes—
578C2×C42C2414yes—
579#95C2412yes—
580#95C2411yescharacteristic
581#95C2411yescharacteristic
582#95C2411yescharacteristic
583#95C2411yescharacteristic
584#95C2412yes—
585#95C2414yes—
586#95C2414yes—
587#95C2418yes—
588#95C2418yes—
589#95C2418yes—
590#95C2418yes—
591#95C2414yes—
592#95C2414yes—
593#95C2418yes—
594#95C2418yes—
595#95C2414yes—
596#95C2414yes—
597#95C2414yes—
598#95C2414yes—
599#95C2418yes—
600#95C2418yes—
601#95C2414yes—
602#95C2414yes—
603#95C2418yes—
604#95C2418yes—
605#95C2414yes—
606#95C2414yes—
607#95C2414yes—
608#95C2414yes—
609#95C2414yes—
610#95C2414yes—
611#95C2414yes—
612#95C2418yes—
613#95C2418yes—
614#95C2414yes—
615#95C2418yes—
616#95C2414yes—
617#95C2418yes—
618#95C2418yes—
619#95C2418yes—
620#95C2414yes—
621#95C2414yes—
622#95C2414yes—
623C24—24no—
624C24—42no—
625C24—41no—
626C24—41no—
627C24C22×Q814yes—
628C24C2512yes—
629C24C2511yescharacteristic
630C2×Q8—28no—
631C2×Q8—28no—
632C2×Q8—216no—
633C2×Q8—28no—
634C2×Q8—44no—
635C2×Q8—48no—
636C2×Q8—44no—
637C2×Q8—48no—
638C2×Q8—44no—
639C22×C4—24no—
640C22×C4—232no—
641C22×C4—24no—
642C22×C4—24no—
643C22×C4—24no—
644C22×C4—24no—
645C22×C4—24no—
646C22×C4—24no—
647C22×C4—28no—
648C22×C4—24no—
649C22×C4—28no—
650C22×C4—28no—
651C22×C4—42no—
652C22×C4—42no—
653C22×C4—44no—
654C22×C4—42no—
655C22×C4—44no—
656C22×C4—42no—
657C22×C4—44no—
658C22×C4—44no—
659C22×C4—44no—
660C22×C4—44no—
661C22×C4—44no—
662C22×C4—42no—
663C22×C4C22×Q814yes—
664C22×C4C22×Q818yes—
665C22×C4C22×Q818yes—
666C22×C4C22×Q818yes—
667C22×C4C22×Q818yes—
668C22×C4C22×Q814yes—
669C22×C4C2×#4118yes—
670C22×C4C2512yes—
671C22×C4C2514yes—
672C22×C4C2514yes—
673C22×C4C2512yes—
674C22×C4C2514yes—
675C22×C4C2514yes—
676C22×C4C2518yes—
677C22×C4C2514yes—
678C22×C4C2512yes—
679C22×C4C2514yes—
680C22×C4C2511yescharacteristic
681C22×C4C2511yescharacteristic
682C22×C4C2514yes—
683C22×C4C2514yes—
684C22×C4C2514yes—
685C22×C4C2514yes—
686C22×C4C2512yes—
687C22×C4C2512yes—
688C4⋊C4—28no—
689C4⋊C4—28no—
690C4⋊C4—24no—
691C4⋊C4—24no—
692C4⋊C4—28no—
693C4⋊C4—28no—
694C4⋊C4—24no—
695C4⋊C4—24no—
696C4⋊C4—24no—
697C4⋊C4—24no—
698C4⋊C4—28no—
699C4⋊C4—28no—
700C4⋊C4—28no—
701C4⋊C4—28no—
702C4⋊C4—28no—
703C4⋊C4—28no—
704C4⋊C4—216no—
705C4⋊C4—216no—
706C4⋊C4—216no—
707C4⋊C4—216no—
708C4⋊C4—28no—
709C4⋊C4—28no—
710C4⋊C4—28no—
711C4⋊C4—48no—
712C4⋊C4—44no—
713C4⋊C4—44no—
714C4⋊C4—44no—
715C4⋊C4—44no—
716C4⋊C4—44no—
717C4⋊C4—44no—
718C4⋊C4—48no—
719C4⋊C4—48no—
720C4⋊C4—48no—
721C4⋊C4—44no—
722C4⋊C4—44no—
723C4⋊C4—44no—
724C4⋊C4—48no—
725C4⋊C4—48no—
726C4⋊C4—48no—
727C4⋊C4—48no—
728C4⋊C4—48no—
729C4⋊C4C22×Q8116yes—
730C4⋊C4C22×Q8116yes—
731C4⋊C4C2×#4118yes—
732C4⋊C4C2×#4118yes—
733C22⋊C4—28no—
734C22⋊C4—28no—
735C22⋊C4—28no—
736C22⋊C4—28no—
737C22⋊C4—28no—
738C22⋊C4—24no—
739C22⋊C4—24no—
740C22⋊C4—42no—
741C22⋊C4—42no—
742C22⋊C4—48no—
743C22⋊C4—44no—
744C22⋊C4—44no—
745C22⋊C4—44no—
746C22⋊C4—44no—
747C22⋊C4C22×Q8132yes—
748C22⋊C4C2×#41116yes—
749C42—28no—
750C42—28no—
751C42—28no—
752C42—24no—
753C42—24no—
754C42—24no—
755C42—24no—
756C42—28no—
757C42—28no—
758C42—48no—
759C42—48no—
760C42—48no—
761C42—44no—
762C42—44no—
763C42—48no—
764C42—44no—
765C42—44no—
766C42—48no—
767C42—48no—
768C42C22×Q8116yes—
769C42C22×Q8116yes—
770C42C2×#41116yes—
771C23—22no—
772C23—21no—
773C23—21no—
774C23—22no—
775C23—22no—
776C23—22no—
777C23—22no—
778C23—22no—
779C23—22no—
780C23—28no—
781C23—44no—
782C23—44no—
783C23—84no—
784C23—84no—
785C23C23×Q814yes—
786C23C23×Q812yes—
787C23C22×#4114yes—
788C23C2611yescharacteristic
789Q8—416no—
790Q8—816no—
791Q8—88no—
792C2×C4—22no—
793C2×C4—22no—
794C2×C4—22no—
795C2×C4—28no—
796C2×C4—24no—
797C2×C4—24no—
798C2×C4—24no—
799C2×C4—22no—
800C2×C4—24no—
801C2×C4—24no—
802C2×C4—24no—
803C2×C4—28no—
804C2×C4—216no—
805C2×C4—216no—
806C2×C4—24no—
807C2×C4—24no—
808C2×C4—22no—
809C2×C4—22no—
810C2×C4—22no—
811C2×C4—24no—
812C2×C4—24no—
813C2×C4—24no—
814C2×C4—24no—
815C2×C4—28no—
816C2×C4—24no—
817C2×C4—24no—
818C2×C4—22no—
819C2×C4—22no—
820C2×C4—22no—
821C2×C4—24no—
822C2×C4—24no—
823C2×C4—24no—
824C2×C4—24no—
825C2×C4—28no—
826C2×C4—22no—
827C2×C4—28no—
828C2×C4—24no—
829C2×C4—24no—
830C2×C4—24no—
831C2×C4—24no—
832C2×C4—24no—
833C2×C4—24no—
834C2×C4—22no—
835C2×C4—22no—
836C2×C4—48no—
837C2×C4—48no—
838C2×C4—48no—
839C2×C4—88no—
840C2×C4—88no—
841C2×C4—88no—
842C2×C4—84no—
843C2×C4#533116yes—
844C2×C4C23×Q812yes—
845C2×C4C23×Q812yes—
846C2×C4C23×Q818yes—
847C2×C4C23×Q818yes—
848C2×C4C23×Q814yes—
849C2×C4C22×#4118yes—
850C2×C4C22×#4118yes—
851C2×C4C22×#4114yes—
852C2×C4C22×#4114yes—
853C2×C4#58514yes—
854C22—24no—
855C22—24no—
856C22—22no—
857C22—22no—
858C22—24no—
859C22—24no—
860C22—24no—
861C22—42no—
862C22—42no—
863C22—42no—
864C22—42no—
865C22—88no—
866C22C2×#53314yes—
867C22C24×Q811yescharacteristic
868C22C23×#4112yes—
869C22C2×#58512yes—
870C22H(7,𝔽2)11yescharacteristic
871C222−1+611yescharacteristic
872C4—24no—
873C4—28no—
874C4—28no—
875C4—28no—
876C4—28no—
877C4—22no—
878C4—22no—
879C4—42no—
880C4—44no—
881C4—48no—
882C4—44no—
883C4—44no—
884C4—44no—
885C4—44no—
886C4—42no—
887C4—42no—
888C4—44no—
889C4C2×#53318yes—
890C2—24no—
891C2—44no—
892C2C22×#53311yescharacteristic
893C2#6281311yescharacteristic
894C2#6285411yescharacteristic
895C2#6300812yes—
896C2#6300912yes—
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. #36481C2semidirect
2. #36480C2semidirect
3. #36478C2semidirect
4. #36478C2semidirect
5. #36039C2semidirect
6. #35819C2semidirect
7. #35815C2semidirect
8. #35747C2semidirect
9. #35585C2semidirect
10. #35566C2semidirect
13. #35146C2semidirect
14. #34966C2semidirect
16. #34271C2semidirect
17. #34213C2semidirect
25. #2863C22semidirect
26. #2863C22semidirect
29. #2666C22semidirect
30. #2666C22semidirect
33. #2606C22semidirect
34. #2606C22semidirect
35. #2606C22semidirect
36. #2606C22semidirect
37. #2605C22semidirect
38. #2605C22semidirect
39. #2605C22semidirect
40. #2605C22semidirect
45. #2584C22semidirect
46. #2584C22semidirect
49. #2570C22semidirect
51. #2567C22semidirect
54. #2552C22semidirect
55. #2551C22semidirect
56. #2550C22semidirect
57. #2550C22semidirect
58. #2550C22semidirect
60. #2546C22semidirect
63. #2509C22semidirect
64. #2509C22semidirect
65. #2508C22semidirect
66. #2508C22semidirect
67. #2507C22semidirect
68. #2507C22semidirect
69. #2506C22semidirect
70. #2506C22semidirect
97. #2402C22semidirect
98. #2402C22semidirect
99. #2399C22semidirect
100. #2399C22semidirect
103. #2370C22semidirect
104. #2370C22semidirect
105. #2370C22semidirect
106. #2370C22semidirect
107. #2370C22semidirect
108. #2370C22semidirect
109. #2369C22semidirect
110. #2369C22semidirect
111. #2369C22semidirect
112. #2365C22semidirect
113. #2365C22semidirect
114. #2365C22semidirect
115. #2355C22semidirect
116. #2355C22semidirect
117. #2355C22semidirect
118. Q8×C4⋊C4C22semidirect
134. C4×C4⋊Q8C22semidirect
135. C4×#125C22semidirect
187. C2×#117Q8semidirect

Maximal subgroups

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

subgroupindex
#364812
#364802
#364782
#360392
#358192
#358152
#357472
#355852
#355662
#354022
#352532
#351462
#349662
#347392
#342712
#342132
#341792
C2×#23472
#339962