Finite Group Databasebeta

← #7712642

Subgroups — #7712642

Order 512.

5312 conjugacy classes of subgroups.

The subgroup lattice has 940 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#59848C218yesmaximal, complemented
2#46018C214yesmaximal, complemented
3#46017C214yesmaximal, complemented
4#39827C218yesmaximal, complemented
5#39766C212yesmaximal, complemented
6#39548C214yesmaximal, complemented
7#39540C214yesmaximal, complemented
8#39382C212yesmaximal, complemented
9#37695C212yesmaximal, complemented
10#37694C212yesmaximal, complemented
11#37546C212yesmaximal, complemented
12#37329C214yesmaximal, complemented
13#36640C211yesmaximal, characteristic, complemented
14C2×#2858C211yesmaximal, characteristic, complemented
15#36602C212yesmaximal, complemented
16#36136C212yesmaximal, complemented
17#36111C214yesmaximal, complemented
18#35343C212yesmaximal, complemented
19#35332C212yesmaximal, complemented
20#34377C212yesmaximal, complemented
21C4×#529C211yesmaximal, characteristic, complemented
22C2×#541C2212yescomplemented
23C2×#540C2212yes—
24C22×C4⋊Q8C2211yescharacteristic
25C22×#127C2211yescharacteristic
26C2×#529C2211yescharacteristic
27C2×#529C2214yescomplemented
28C22×#124C2212yes—
29C22×#124C2212yes—
30#2864C2214yescomplemented
31#2861C2214yescomplemented
32#2859C2211yescharacteristic, complemented
33#2859C2211yescharacteristic, complemented
34#2859C2212yescomplemented
35#2858C2212yes—
36#2858C2212yes—
37#2858C2212yes—
38#2858C2214yes—
39#2858C2214yes—
40#2858C2212yes—
41#2851C2212yes—
42#2851C2212yes—
43#2851C2214yes—
44#2850C2214yescomplemented
45#2820C2214yescomplemented
46#2819C2214yescomplemented
47#2803C2218yescomplemented
48#2800C2218yescomplemented
49#2796C2218yescomplemented
50#2780C2218yescomplemented
51#2761C2218yescomplemented
52#2753C2218yescomplemented
53#2751C2218yescomplemented
54#2716C2218yescomplemented
55#2714C2218yescomplemented
56#2713C2218yescomplemented
57#2711C2218yescomplemented
58#2709C2218yes—
59#2707C2218yescomplemented
60#2701C2218yescomplemented
61#2694C2218yescomplemented
62#2673C2218yes—
63#2662C2218yescomplemented
64#2642C2212yescomplemented
65#2641C2212yes—
66#2626C2214yes—
67#2621C2212yescomplemented
68#2620C2214yescomplemented
69#2620C2214yescomplemented
70#2619C2212yes—
71#2617C2214yes—
72#2602C2218yescomplemented
73#2602C2218yescomplemented
74#2601C2218yescomplemented
75#2601C2218yescomplemented
76#2597C2218yescomplemented
77#2595C2218yescomplemented
78#2593C2218yescomplemented
79#2592C2214yescomplemented
80#2559C2218yescomplemented
81#2559C2218yescomplemented
82#2558C2218yescomplemented
83#2558C2218yescomplemented
84#2557C2218yescomplemented
85#2554C2218yescomplemented
86#2554C2218yescomplemented
87#2540C2214yescomplemented
88#2521C2218yescomplemented
89#2516C2218yescomplemented
90#2490C2218yescomplemented
91#2481C2218yes—
92#2480C2218yes—
93#2479C2218yescomplemented
94#2474C2218yescomplemented
95#2473C2218yes—
96#2459C2218yescomplemented
97#2458C2218yescomplemented
98#2456C2218yescomplemented
99#2448C2214yescomplemented
100#2447C2214yescomplemented
101#2446C2214yescomplemented
102#2445C2214yes—
103#2429C2214yescomplemented
104#2428C2214yes—
105#2427C2214yescomplemented
106#2426C2214yescomplemented
107#2418C2218yes—
108#2411C2218yes—
109#2410C2218yes—
110#2409C2214yes—
111#2408C2214yes—
112#2405C2218yes—
113#2379C2214yescomplemented
114#2379C2214yescomplemented
115#2374C2218yescomplemented
116#2367C2214yescomplemented
117#2367C2214yescomplemented
118#2363C2218yescomplemented
119#2358C2218yes—
120#2342C2218yes—
121#2342C2218yes—
122Q8×C22⋊C4C2214yes—
123D4×C22⋊C4C2214yes—
124#2337C2218yescomplemented
125#2328C2212yes—
126#2327C2212yescomplemented
127#2326C2214yescomplemented
128#2326C2214yescomplemented
129#2315C2214yes—
130#2312C2214yes—
131C4×#125C2212yescomplemented
132C4×#125C2212yescomplemented
133C4×#125C2214yescomplemented
134C4×#125C2212yescomplemented
135C4×#126C2214yescomplemented
136C4×#124C2214yescomplemented
137C4×#124C2212yescomplemented
138C4×C22⋊Q8C2212yes—
139C4×#123C2214yes—
140C4×#121C2212yes—
141#2298C2212yescomplemented
142#2296C2214yes—
143#2295C2211yescharacteristic, complemented
144#2293C2211yescharacteristic, complemented
145C2×#390C2214yes—
146C2×#390C2214yes—
147#2290C2212yes—
148#2285C2212yes—
149#2283C2211yescharacteristic
150C42×Q8C2211yescharacteristic, complemented
151C42×D4C2212yes—
152C42×D4C2211yescharacteristic, complemented
153C4×#117C2212yescomplemented
154C2×C43C2211yescharacteristic
155C23×Q8C2312yes—
156C23×D4C2312yes—
157C23×D4C2314yes—
158#541—48no—
159#540—48no—
160C2×C4⋊Q8—44no—
161C2×C4⋊Q8C2312yes—
162C2×C4⋊Q8C2312yes—
163C2×C4⋊Q8C2314yes—
164C2×#127—44no—
165C2×#127C2312yes—
166C2×#127C2314yes—
167C2×#127C2312yes—
168#529—28no—
169#529—416no—
170C2×#126C2312yes—
171C2×#126C2318yes—
172C2×#126C2318yes—
173C2×#125C2311yescharacteristic
174C2×#125C2312yes—
175C2×#125C2312yes—
176C2×#125C2314yes—
177C2×#125C2318yes—
178C2×#124—216no—
179C2×#124—48no—
180C2×#124C2311yescharacteristic
181C2×#124C2314yes—
182C2×#124C2314yes—
183C2×#124C2314yes—
184C2×#124C2314yes—
185C2×#124C2314yes—
186C2×#124C2314yes—
187C2×#124C2314yes—
188C2×#124C2314yes—
189C2×#123C2312yes—
190C2×#123C2318yes—
191C2×#123C2318yes—
192C2×#123C2318yes—
193C2×C22⋊Q8C2311yescharacteristic
194C2×C22⋊Q8C2314yes—
195C2×C22⋊Q8C2314yes—
196C2×#121C2311yescharacteristic
197C2×#121C2314yes—
198C2×#121C2318yes—
199C2×#121C2314yes—
200C2×#121C2318yes—
201C2×#120C2318yes—
202C2×C4×Q8C2311yescharacteristic
203C2×C4×Q8C2314yes—
204C2×C4×Q8C2314yes—
205C2×C4×Q8C2312yes—
206C2×C4×D4C2312yes—
207C2×C4×D4C2311yescharacteristic
208C2×C4×D4C2314yes—
209C2×C4×D4C2314yes—
210C2×C4×D4C2318yes—
211C2×C4×D4C2314yes—
212C2×C4×D4C2312yes—
213C2×#117C2312yes—
214C2×#117C2312yes—
215C2×#117C2314yes—
216C2×#117C2318yes—
217C22×C4⋊C4C2314yes—
218C22×C22⋊C4C2314yes—
219C22×C22⋊C4C2314yes—
220C22×C22⋊C4C2318yes—
221C22×C22⋊C4C2314yes—
222C22×C22⋊C4C2314yes—
223C22×C42C2312yes—
224C22×C42C2311yescharacteristic
225C22×C42C2311yescharacteristic
226C22×C42C2312yes—
227C22×C42C2312yes—
228C22×C42C2311yescharacteristic
229#400C2318yes—
230#400C2318yes—
231#400C2318yes—
232#399C2318yes—
233#399C2318yes—
234#398C2318yes—
235#398C2318yes—
236#398C2318yes—
237#397C2318yes—
238#397C2318yes—
239#397C2318yes—
240#397C2318yes—
241#397C2318yes—
242#397C2318yes—
243#396C2318yes—
244#396C2318yes—
245#396C2318yes—
246#396C2318yes—
247#396C2318yes—
248#396C2318yes—
249#395C2318yes—
250#394C2318yes—
251#394C2318yes—
252#394C2318yes—
253#394C2318yes—
254#394C2318yes—
255#394C2318yes—
256#394C2318yes—
257#394C2318yes—
258#394C2318yes—
259#394C2318yes—
260#394C2318yes—
261#394C2318yes—
262#394C2318yes—
263#393C2318yes—
264#393C2318yes—
265#392C2318yes—
266#392C2318yes—
267#392C2318yes—
268#392C2318yes—
269#391C2314yes—
270#391C2314yes—
271#391C2314yes—
272#391C2314yes—
273#391C2318yes—
274#391C2318yes—
275#391C2312yes—
276#390C2314yes—
277#390C2314yes—
278#390C2314yes—
279#390C2314yes—
280#390C2318yes—
281#390C2318yes—
282#390C2318yes—
283#390C2318yes—
284#390C2318yes—
285#390C2318yes—
286#390C2318yes—
287#390C2318yes—
288#390C2318yes—
289#390C2318yes—
290#390C2318yes—
291#390C2312yes—
292#389C2314yes—
293#389C2314yes—
294#389C2314yes—
295#389C2314yes—
296#389C2312yes—
297#389C2312yes—
298#389C2314yes—
299#389C2314yes—
300#389C2314yes—
301#389C2314yes—
302#389C2318yes—
303#388C2314yes—
304#388C2314yes—
305#388C2314yes—
306#388C2318yes—
307#388C2318yes—
308#388C2318yes—
309#388C2318yes—
310#388C2318yes—
311#388C2318yes—
312#388C2318yes—
313#388C2318yes—
314#388C2318yes—
315#388C2318yes—
316#388C2318yes—
317#388C2318yes—
318#388C2318yes—
319#388C2318yes—
320#388C2318yes—
321#388C2318yes—
322#388C2318yes—
323#388C2318yes—
324#388C2318yes—
325#388C2318yes—
326#388C2318yes—
327#388C2318yes—
328#388C2314yes—
329#387C2314yes—
330#387C2314yes—
331#387C2314yes—
332#387C2318yes—
333#387C2318yes—
334#387C2318yes—
335#387C2318yes—
336#387C2314yes—
337#387C2318yes—
338#387C2318yes—
339#387C2318yes—
340#387C2318yes—
341#386C2318yes—
342#386C2318yes—
343#386C2318yes—
344#386C2318yes—
345#386C2318yes—
346#386C2318yes—
347#386C2318yes—
348#386C2318yes—
349#386C2318yes—
350#386C2318yes—
351#386C2314yes—
352#385C2318yes—
353#385C2318yes—
354#385C2318yes—
355#385C2318yes—
356#385C2318yes—
357#385C2318yes—
358#385C2318yes—
359#385C2318yes—
360#385C2318yes—
361#385C2318yes—
362#385C2314yes—
363#384C2312yes—
364#384C2312yes—
365#383C2312yes—
366#382C2312yes—
367#382C2312yes—
368#382C2314yes—
369#382C2312yes—
370#382C2314yes—
371#381C2312yes—
372#381C2318yes—
373#380C2312yes—
374#380C2314yes—
375#380C2318yes—
376#380C2314yes—
377#380C2318yes—
378#379C2318yes—
379#379C2318yes—
380C4×C4⋊C4C2314yes—
381C4×C4⋊C4C2314yes—
382C4×C4⋊C4C2314yes—
383C4×C4⋊C4C2314yes—
384C4×C4⋊C4C2314yes—
385C4×C4⋊C4C2318yes—
386C4×C4⋊C4C2318yes—
387C4×C4⋊C4C2312yes—
388C4×C4⋊C4C2314yes—
389C4×C4⋊C4C2312yes—
390C4×C4⋊C4C2311yescharacteristic
391C4×C4⋊C4C2311yescharacteristic
392C4×C4⋊C4C2312yes—
393C4×C4⋊C4C2312yes—
394C4×C22⋊C4C2314yes—
395C4×C22⋊C4C2314yes—
396C4×C22⋊C4C2314yes—
397C4×C22⋊C4C2318yes—
398C4×C22⋊C4C2318yes—
399C4×C22⋊C4C2318yes—
400C4×C22⋊C4C2312yes—
401C4×C22⋊C4C2318yes—
402C4×C22⋊C4C2314yes—
403C4×C22⋊C4C2318yes—
404C4×C22⋊C4C2314yes—
405C4×C22⋊C4C2312yes—
406C4×C22⋊C4C2312yes—
407#376C2312yes—
408#376C2312yes—
409C43C2312yes—
410C43C2311yescharacteristic
411C43C2311yescharacteristic
412C43C2312yes—
413C43C2311yescharacteristic
414C43C2311yescharacteristic
415C43C2312yes—
416C25C2414yes—
417C22×Q8—28no—
418C22×Q8—44no—
419C22×Q8—44no—
420C22×Q8C2414yes—
421C22×Q8C2411yescharacteristic
422C22×Q8C2414yes—
423C22×D4—28no—
424C22×D4—44no—
425C22×D4—48no—
426C22×D4—44no—
427C22×D4—48no—
428C22×D4—48no—
429C22×D4C2412yes—
430C22×D4C2414yes—
431C22×D4C2411yescharacteristic
432C22×D4C2418yes—
433C22×D4C2418yes—
434C22×D4C2414yes—
435C22×D4C2418yes—
436C22×D4C2418yes—
437C23×C4C2412yes—
438C23×C4C2412yes—
439C23×C4C2412yes—
440C23×C4C2411yescharacteristic
441C23×C4C2411yescharacteristic
442C23×C4C2414yes—
443C23×C4C2414yes—
444C23×C4C2418yes—
445C23×C4C2418yes—
446C23×C4C2411yescharacteristic
447C4⋊Q8—28no—
448C4⋊Q8—48no—
449C4⋊Q8—44no—
450#127—28no—
451#127—44no—
452#127—48no—
453#126—28no—
454#126—416no—
455#126—416no—
456#125—24no—
457#125—28no—
458#125—28no—
459#125—48no—
460#125—416no—
461#124—216no—
462#124—216no—
463#124—216no—
464#124—216no—
465#124—24no—
466#124—216no—
467#124—48no—
468#124—48no—
469#124—48no—
470#123—28no—
471#123—416no—
472#123—416no—
473#123—416no—
474C22⋊Q8—24no—
475C22⋊Q8—48no—
476C22⋊Q8—48no—
477#121—24no—
478#121—416no—
479#121—416no—
480#121—48no—
481#121—48no—
482#120—416no—
483C4×Q8—24no—
484C4×Q8—44no—
485C4×Q8—48no—
486C4×Q8—48no—
487C4×D4—28no—
488C4×D4—24no—
489C4×D4—44no—
490C4×D4—48no—
491C4×D4—48no—
492C4×D4—416no—
493C4×D4—48no—
494#117—28no—
495#117—28no—
496#117—416no—
497#117—48no—
498C2×C4⋊C4—48no—
499C2×C4⋊C4C2418yes—
500C2×C4⋊C4C2418yes—
501C2×C4⋊C4C2412yes—
502C2×C4⋊C4C2414yes—
503C2×C4⋊C4C2412yes—
504C2×C4⋊C4C2414yes—
505C2×C4⋊C4C2414yes—
506C2×C4⋊C4C2411yescharacteristic
507C2×C4⋊C4C2412yes—
508C2×C4⋊C4C2411yescharacteristic
509C2×C4⋊C4C2414yes—
510C2×C4⋊C4C2412yes—
511C2×C4⋊C4C2418yes—
512C2×C4⋊C4C2418yes—
513C2×C4⋊C4C2418yes—
514C2×C4⋊C4C2418yes—
515C2×C4⋊C4C2414yes—
516C2×C4⋊C4C2414yes—
517C2×C4⋊C4C2412yes—
518C2×C4⋊C4C2414yes—
519C2×C4⋊C4C2418yes—
520C2×C4⋊C4C2418yes—
521C2×C4⋊C4C2412yes—
522C2×C4⋊C4C2418yes—
523C2×C4⋊C4C2414yes—
524C2×C4⋊C4C2414yes—
525C2×C4⋊C4C2418yes—
526C2×C22⋊C4—216no—
527C2×C22⋊C4—216no—
528C2×C22⋊C4—48no—
529C2×C22⋊C4—48no—
530C2×C22⋊C4—416no—
531C2×C22⋊C4C2414yes—
532C2×C22⋊C4C2418yes—
533C2×C22⋊C4C2418yes—
534C2×C22⋊C4C2418yes—
535C2×C22⋊C4C2418yes—
536C2×C22⋊C4C2418yes—
537C2×C22⋊C4C2418yes—
538C2×C22⋊C4C2418yes—
539C2×C22⋊C4C2414yes—
540C2×C22⋊C4C2412yes—
541C2×C22⋊C4C2412yes—
542C2×C22⋊C4C2414yes—
543C2×C22⋊C4C2412yes—
544C2×C22⋊C4C2412yes—
545C2×C22⋊C4C2412yes—
546C2×C22⋊C4C2418yes—
547C2×C22⋊C4C2418yes—
548C2×C22⋊C4C2418yes—
549C2×C22⋊C4C2418yes—
550C2×C22⋊C4C2418yes—
551C2×C22⋊C4C2418yes—
552C2×C22⋊C4C2418yes—
553C2×C22⋊C4C2418yes—
554C2×C22⋊C4C2414yes—
555C2×C22⋊C4C2418yes—
556C2×C22⋊C4C2418yes—
557C2×C22⋊C4C2418yes—
558C2×C22⋊C4C2418yes—
559C2×C22⋊C4C2418yes—
560C2×C22⋊C4C2418yes—
561C2×C22⋊C4C2418yes—
562C2×C22⋊C4C2418yes—
563C2×C42—24no—
564C2×C42—28no—
565C2×C42—24no—
566C2×C42—44no—
567C2×C42—44no—
568C2×C42#4118yes—
569C2×C42C2414yes—
570C2×C42C2412yes—
571C2×C42C2412yes—
572C2×C42C2412yes—
573C2×C42C2412yes—
574C2×C42C2412yes—
575C2×C42C2411yescharacteristic
576C2×C42C2412yes—
577C2×C42C2411yescharacteristic
578C2×C42C2412yes—
579C2×C42C2418yes—
580C2×C42C2418yes—
581C2×C42C2414yes—
582C2×C42C2418yes—
583C2×C42C2414yes—
584C2×C42C2412yes—
585C2×C42C2412yes—
586C2×C42C2412yes—
587C2×C42C2412yes—
588C2×C42C2412yes—
589C2×C42C2412yes—
590C2×C42C2411yescharacteristic
591C2×C42C2411yescharacteristic
592C2×C42C2411yescharacteristic
593C2×C42C2411yescharacteristic
594C2×C42C2411yescharacteristic
595C2×C42C2411yescharacteristic
596#95C2414yes—
597#95C2414yes—
598#95C2414yes—
599#95C2414yes—
600#95C2412yes—
601#95C2412yes—
602#95C2414yes—
603#95C2414yes—
604#95C2414yes—
605#95C2418yes—
606#95C2414yes—
607#95C2418yes—
608#95C2418yes—
609#95C2418yes—
610#95C2418yes—
611#95C2418yes—
612#95C2418yes—
613#95C2414yes—
614#95C2418yes—
615#95C2418yes—
616#95C2418yes—
617#95C2418yes—
618#95C2418yes—
619#95C2418yes—
620#95C2418yes—
621C24—28no—
622C24—28no—
623C24—28no—
624C24—44no—
625C24—44no—
626C24—44no—
627C24—44no—
628C24C2518yes—
629C24C2512yes—
630C24C2511yescharacteristic
631C2×Q8—22no—
632C2×Q8—28no—
633C2×Q8—28no—
634C2×Q8—28no—
635C2×Q8—28no—
636C2×Q8—42no—
637C2×Q8—44no—
638C2×Q8—44no—
639C2×Q8—816no—
640C2×D4—24no—
641C2×D4—28no—
642C2×D4—22no—
643C2×D4—28no—
644C2×D4—28no—
645C2×D4—28no—
646C2×D4—28no—
647C2×D4—216no—
648C2×D4—216no—
649C2×D4—42no—
650C2×D4—48no—
651C2×D4—48no—
652C2×D4—48no—
653C2×D4—44no—
654C2×D4—48no—
655C2×D4—44no—
656C2×D4—48no—
657C2×D4—48no—
658C2×D4—48no—
659C2×D4—48no—
660C2×D4—48no—
661C2×D4—48no—
662C2×D4—816no—
663C2×D4—832no—
664C22×C4—24no—
665C22×C4—24no—
666C22×C4—24no—
667C22×C4—22no—
668C22×C4—22no—
669C22×C4—24no—
670C22×C4—24no—
671C22×C4—28no—
672C22×C4—24no—
673C22×C4—24no—
674C22×C4—24no—
675C22×C4—24no—
676C22×C4—28no—
677C22×C4—42no—
678C22×C4—42no—
679C22×C4—44no—
680C22×C4—48no—
681C22×C4—44no—
682C22×C4—48no—
683C22×C4—44no—
684C22×C4—44no—
685C22×C4—48no—
686C22×C4—48no—
687C22×C4—48no—
688C22×C4—48no—
689C22×C4C2×#4114yes—
690C22×C4C2×#4114yes—
691C22×C4C2×#4114yes—
692C22×C4C2514yes—
693C22×C4C2512yes—
694C22×C4C2512yes—
695C22×C4C2514yes—
696C22×C4C2518yes—
697C22×C4C2518yes—
698C22×C4C2512yes—
699C22×C4C2518yes—
700C22×C4C2512yes—
701C22×C4C2511yescharacteristic
702C22×C4C2511yescharacteristic
703C22×C4C2511yescharacteristic
704C22×C4C2511yescharacteristic
705C22×C4C2511yescharacteristic
706C22×C4C2512yes—
707C22×C4C2512yes—
708C22×C4C2512yes—
709C22×C4C2511yescharacteristic
710C4⋊C4—24no—
711C4⋊C4—24no—
712C4⋊C4—22no—
713C4⋊C4—24no—
714C4⋊C4—22no—
715C4⋊C4—24no—
716C4⋊C4—216no—
717C4⋊C4—28no—
718C4⋊C4—216no—
719C4⋊C4—28no—
720C4⋊C4—28no—
721C4⋊C4—216no—
722C4⋊C4—28no—
723C4⋊C4—216no—
724C4⋊C4—48no—
725C4⋊C4—44no—
726C4⋊C4—44no—
727C4⋊C4—48no—
728C4⋊C4—42no—
729C4⋊C4—44no—
730C4⋊C4—42no—
731C4⋊C4—48no—
732C4⋊C4—48no—
733C4⋊C4—48no—
734C4⋊C4—44no—
735C4⋊C4—44no—
736C4⋊C4—48no—
737C22⋊C4—24no—
738C22⋊C4—28no—
739C22⋊C4—216no—
740C22⋊C4—216no—
741C22⋊C4—216no—
742C22⋊C4—216no—
743C22⋊C4—216no—
744C22⋊C4—24no—
745C22⋊C4—24no—
746C22⋊C4—24no—
747C22⋊C4—24no—
748C22⋊C4—216no—
749C22⋊C4—216no—
750C22⋊C4—28no—
751C22⋊C4—28no—
752C22⋊C4—48no—
753C22⋊C4—48no—
754C22⋊C4—48no—
755C22⋊C4—48no—
756C22⋊C4—48no—
757C22⋊C4—44no—
758C22⋊C4—48no—
759C22⋊C4—48no—
760C22⋊C4—48no—
761C22⋊C4—48no—
762C22⋊C4—48no—
763C22⋊C4—48no—
764C22⋊C4—48no—
765C22⋊C4—48no—
766C22⋊C4—48no—
767C22⋊C4—48no—
768C22⋊C4—48no—
769C42—24no—
770C42—28no—
771C42—24no—
772C42—24no—
773C42—22no—
774C42—22no—
775C42—24no—
776C42—24no—
777C42—24no—
778C42—24no—
779C42—42no—
780C42—42no—
781C42—42no—
782C42—42no—
783C42—42no—
784C42—42no—
785C42—48no—
786C42—48no—
787C42—44no—
788C42—44no—
789C42—48no—
790C42C2×#4114yes—
791C42C2×#4114yes—
792C42C2×#4114yes—
793C42C2×#4114yes—
794C42H(5,𝔽2)14yes—
795C42H(5,𝔽2)14yes—
796C23—21no—
797C23—21no—
798C23—22no—
799C23—22no—
800C23—28no—
801C23—22no—
802C23—28no—
803C23—22no—
804C23—28no—
805C23—24no—
806C23—28no—
807C23—28no—
808C23—28no—
809C23—28no—
810C23—24no—
811C23—416no—
812C23—88no—
813C23—88no—
814C23—88no—
815C23—88no—
816C23—88no—
817C23—88no—
818C23C22×#4112yes—
819C23#58514yes—
820C23C2611yescharacteristic
821Q8—44no—
822Q8—416no—
823Q8—88no—
824D4—44no—
825D4—48no—
826D4—416no—
827D4—88no—
828D4—816no—
829D4—816no—
830D4—816no—
831D4—168no—
832C2×C4—216no—
833C2×C4—22no—
834C2×C4—21no—
835C2×C4—21no—
836C2×C4—22no—
837C2×C4—22no—
838C2×C4—22no—
839C2×C4—22no—
840C2×C4—22no—
841C2×C4—22no—
842C2×C4—22no—
843C2×C4—22no—
844C2×C4—22no—
845C2×C4—28no—
846C2×C4—28no—
847C2×C4—22no—
848C2×C4—22no—
849C2×C4—28no—
850C2×C4—22no—
851C2×C4—24no—
852C2×C4—22no—
853C2×C4—22no—
854C2×C4—24no—
855C2×C4—28no—
856C2×C4—28no—
857C2×C4—28no—
858C2×C4—28no—
859C2×C4—22no—
860C2×C4—22no—
861C2×C4—22no—
862C2×C4—24no—
863C2×C4—28no—
864C2×C4—28no—
865C2×C4—24no—
866C2×C4—24no—
867C2×C4—24no—
868C2×C4—24no—
869C2×C4—24no—
870C2×C4—28no—
871C2×C4—28no—
872C2×C4—44no—
873C2×C4—48no—
874C2×C4—48no—
875C2×C4—88no—
876C2×C4—88no—
877C2×C4—816no—
878C2×C4—168no—
879C2×C4C22×#4112yes—
880C2×C4C22×#4112yes—
881C2×C4C22×#4112yes—
882C2×C4C22×#4112yes—
883C2×C4C22×#4112yes—
884C2×C4C22×#4112yes—
885C2×C4C2×H(5,𝔽2)14yes—
886C2×C4C2×H(5,𝔽2)14yes—
887C2×C4C2×H(5,𝔽2)12yes—
888C2×C4C2×H(5,𝔽2)12yes—
889C2×C4#58514yes—
890C22—24no—
891C22—22no—
892C22—22no—
893C22—24no—
894C22—44no—
895C22—48no—
896C22—48no—
897C22—42no—
898C22—48no—
899C22—42no—
900C22—48no—
901C22—42no—
902C22—48no—
903C22—48no—
904C22—48no—
905C22—44no—
906C22—1616no—
907C22#351214yes—
908C22C23×#4111yescharacteristic
909C22C22×H(5,𝔽2)11yescharacteristic
910C22C22×H(5,𝔽2)11yescharacteristic
911C22C2×#58512yes—
912C22C2×#58512yes—
913C4—24no—
914C4—22no—
915C4—22no—
916C4—22no—
917C4—22no—
918C4—22no—
919C4—24no—
920C4—24no—
921C4—42no—
922C4—44no—
923C4—48no—
924C4—42no—
925C4—48no—
926C4—42no—
927C4—42no—
928C4—44no—
929C4—48no—
930C4#350814yes—
931C2—24no—
932C2—82no—
933C2—88no—
934C2#6274812yes—
935C2C2×#350811yescharacteristic
936C2C2×#351211yescharacteristic
937C2#6281511yescharacteristic
938C2#6282412yes—
subgroupG/H
center, commutator, Frattini, socle, cosocleC23C26
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23 ◁ G
LECSG ▷ C23 ▷ C1

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
1. #59848C2semidirect
2. #46018C2semidirect
3. #46017C2semidirect
4. #39827C2semidirect
5. #39766C2semidirect
6. #39548C2semidirect
7. #39540C2semidirect
8. #39382C2semidirect
9. #37695C2semidirect
10. #37694C2semidirect
11. #37546C2semidirect
12. #37329C2semidirect
13. #36640C2semidirect
14. C2×#2858C2semidirect
15. #36602C2semidirect
16. #36136C2semidirect
17. #36111C2semidirect
18. #35343C2semidirect
19. #35332C2semidirect
20. #34377C2semidirect
21. C4×#529C2semidirect
22. C2×#541C22semidirect
27. C2×#529C22semidirect
30. #2864C22semidirect
31. #2861C22semidirect
32. #2859C22semidirect
33. #2859C22semidirect
34. #2859C22semidirect
44. #2850C22semidirect
45. #2820C22semidirect
46. #2819C22semidirect
47. #2803C22semidirect
48. #2800C22semidirect
49. #2796C22semidirect
50. #2780C22semidirect
51. #2761C22semidirect
52. #2753C22semidirect
53. #2751C22semidirect
54. #2716C22semidirect
55. #2714C22semidirect
56. #2713C22semidirect
57. #2711C22semidirect
59. #2707C22semidirect
60. #2701C22semidirect
61. #2694C22semidirect
63. #2662C22semidirect
64. #2642C22semidirect
67. #2621C22semidirect
68. #2620C22semidirect
69. #2620C22semidirect
72. #2602C22semidirect
73. #2602C22semidirect
74. #2601C22semidirect
75. #2601C22semidirect
76. #2597C22semidirect
77. #2595C22semidirect
78. #2593C22semidirect
79. #2592C22semidirect
80. #2559C22semidirect
81. #2559C22semidirect
82. #2558C22semidirect
83. #2558C22semidirect
84. #2557C22semidirect
85. #2554C22semidirect
86. #2554C22semidirect
87. #2540C22semidirect
88. #2521C22semidirect
89. #2516C22semidirect
90. #2490C22semidirect
93. #2479C22semidirect
94. #2474C22semidirect
96. #2459C22semidirect
97. #2458C22semidirect
98. #2456C22semidirect
99. #2448C22semidirect
100. #2447C22semidirect
101. #2446C22semidirect
103. #2429C22semidirect
105. #2427C22semidirect
106. #2426C22semidirect
113. #2379C22semidirect
114. #2379C22semidirect
115. #2374C22semidirect
116. #2367C22semidirect
117. #2367C22semidirect
118. #2363C22semidirect
124. #2337C22semidirect
126. #2327C22semidirect
127. #2326C22semidirect
128. #2326C22semidirect
131. C4×#125C22semidirect
132. C4×#125C22semidirect
133. C4×#125C22semidirect
134. C4×#125C22semidirect
135. C4×#126C22semidirect
136. C4×#124C22semidirect
137. C4×#124C22semidirect
141. #2298C22semidirect
143. #2295C22semidirect
144. #2293C22semidirect
150. C42×Q8C22semidirect
152. C42×D4C22semidirect
153. C4×#117C22semidirect

Maximal subgroups

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

subgroupindex
#598482
#460182
#460172
#398272
#397662
#395482
#395402
#393822
#376952
#376942
#375462
#373292
#366402
C2×#28582
#366022
#361362
#361112
#353432
#353322
#343772
C4×#5292