Finite Group Databasebeta

← #7643482

Subgroups — #7643482

Order 512.

4732 conjugacy classes of subgroups.

The subgroup lattice has 946 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#39987C214yesmaximal, complemented
2#39986C214yesmaximal, complemented
3#39178C214yesmaximal, complemented
4#38963C214yesmaximal, complemented
5#38449C218yesmaximal, complemented
6#38097C218yesmaximal
7#37428C212yesmaximal, complemented
8#37427C212yesmaximal, complemented
9#37311C214yesmaximal, complemented
10#36625C211yesmaximal, characteristic
11C2×#2851C211yesmaximal, characteristic
12#35640C212yesmaximal, complemented
13#35627C212yesmaximal, complemented
14#35566C212yesmaximal, complemented
15#35543C212yesmaximal, complemented
16#35253C212yesmaximal
17#35239C214yesmaximal, complemented
18#35181C212yesmaximal, complemented
19#35104C212yesmaximal, complemented
20#34180C212yesmaximal
21C2×#2296C211yesmaximal, characteristic
22C2×#544C2212yes—
23C2×#533C2211yescharacteristic
24C22×#125C2211yescharacteristic
25C22×#117C2211yescharacteristic
26C22×#117C2211yescharacteristic
27C23×C42C2211yescharacteristic
28#2857C2212yes—
29#2857C2212yes—
30#2857C2214yes—
31#2855C2214yes—
32#2851C2214yes—
33#2851C2212yes—
34#2851C2214yes—
35#2851C2212yes—
36#2851C2212yes—
37#2851C2212yes—
38#2851C2211yescharacteristic
39#2851C2211yescharacteristic
40#2851C2211yescharacteristic
41#2851C2211yescharacteristic
42#2851C2214yes—
43#2848C2214yes—
44#2807C2218yes—
45#2802C2218yescomplemented
46#2792C2218yescomplemented
47#2791C2218yescomplemented
48#2791C2218yescomplemented
49#2790C2218yes—
50#2790C2218yes—
51#2788C2218yes—
52#2774C2218yescomplemented
53#2774C2218yescomplemented
54#2768C2218yes—
55#2763C2218yes—
56#2755C2218yescomplemented
57#2729C2218yes—
58#2720C2218yes—
59#2713C2218yescomplemented
60#2666C2218yescomplemented
61#2666C2218yescomplemented
62#2646C2218yes—
63#2629C2214yes—
64#2628C2214yes—
65#2627C2218yes—
66#2606C2218yescomplemented
67#2605C2218yescomplemented
68#2584C2214yescomplemented
69#2584C2214yescomplemented
70#2583C2218yes—
71#2571C2214yescomplemented
72#2571C2214yescomplemented
73#2571C2214yescomplemented
74#2570C2214yescomplemented
75#2570C2214yescomplemented
76#2570C2214yescomplemented
77#2570C2218yescomplemented
78#2570C2218yescomplemented
79#2570C2214yescomplemented
80#2567C2214yescomplemented
81#2552C2214yescomplemented
82#2552C2214yescomplemented
83#2552C2214yescomplemented
84#2552C2214yescomplemented
85#2552C2214yescomplemented
86#2552C2214yescomplemented
87#2551C2214yescomplemented
88#2550C2214yescomplemented
89#2550C2214yescomplemented
90#2550C2214yescomplemented
91#2550C2214yescomplemented
92#2550C2214yescomplemented
93#2550C2214yescomplemented
94#2549C2218yes—
95#2546C2214yescomplemented
96#2509C2214yescomplemented
97#2509C2214yescomplemented
98#2509C2214yescomplemented
99#2508C2214yescomplemented
100#2508C2214yescomplemented
101#2508C2214yescomplemented
102#2507C2214yescomplemented
103#2506C2214yescomplemented
104#2505C2218yes—
105#2505C2218yes—
106#2505C2218yes—
107#2502C2218yes—
108#2473C2218yes—
109#2442C2214yes—
110#2442C2218yes—
111#2441C2214yes—
112#2440C2214yes—
113#2440C2218yes—
114#2440C2218yes—
115#2439C2214yes—
116#2438C2218yes—
117#2438C2218yes—
118#2438C2218yes—
119#2437C2218yes—
120#2347C2214yes—
121#2346C2214yes—
122#2345C2214yes—
123#2344C2214yes—
124#2343C2218yes—
125#2342C2218yes—
126#2331C2218yescomplemented
127#2330C2218yescomplemented
128#2329C2218yes—
129#2317C2212yes—
130#2317C2212yes—
131#2317C2218yes—
132#2317C2212yes—
133#2317C2212yes—
134#2316C2212yes—
135#2314C2214yes—
136#2314C2214yes—
137C4×C22⋊Q8C2214yes—
138C4×C22⋊Q8C2214yes—
139#2296C2212yes—
140#2296C2212yes—
141#2296C2214yes—
142#2296C2212yes—
143#2296C2212yes—
144#2296C2212yes—
145#2296C2212yes—
146#2296C2212yes—
147C2×#389C2212yes—
148C2×#389C2212yes—
149C2×#389C2212yes—
150C2×#387C2214yes—
151C2×#385C2214yes—
152C2×#385C2214yes—
153#2285C2211yescharacteristic
154#2285C2214yes—
155#2283C2214yes—
156C2×#382C2211yescharacteristic
157#2280C2212yes—
158C2×#380C2212yes—
159#2274C2212yes—
160#2274C2212yes—
161C2×C4×C4⋊C4C2212yes—
162C2×C4×C4⋊C4C2212yes—
163C24×C4C2311yescharacteristic
164C24×C4C2312yes—
165#544—48no—
166#533—44no—
167C2×C4⋊Q8C2314yes—
168C2×C4⋊Q8C2318yes—
169C2×C4⋊Q8C2312yes—
170C2×C4⋊Q8C2314yes—
171C2×#125—44no—
172C2×#125C2314yes—
173C2×#125C2318yes—
174C2×#125C2314yes—
175C2×#125C2312yes—
176C2×#125C2312yes—
177C2×#125C2311yescharacteristic
178C2×#125C2311yescharacteristic
179C2×#125C2314yes—
180C2×C22⋊Q8C2318yes—
181C2×C22⋊Q8C2318yes—
182C2×C22⋊Q8C2314yes—
183C2×C22⋊Q8C2314yes—
184C2×C22⋊Q8C2314yes—
185C2×C4×Q8C2314yes—
186C2×#117—44no—
187C2×#117Q8116yescomplemented
188C2×#117C2312yes—
189C2×#117C2312yes—
190C2×#117C2312yes—
191C2×#117C2318yes—
192C2×#117C2312yes—
193C2×#117C2312yes—
194C2×#117C2311yescharacteristic
195C2×#117C2311yescharacteristic
196C2×#117C2312yes—
197C2×#117C2312yes—
198C2×#117C2312yes—
199C2×#117C2312yes—
200C22×C4⋊C4C2312yes—
201C22×C4⋊C4C2312yes—
202C22×C4⋊C4C2314yes—
203C22×C4⋊C4C2314yes—
204C22×C4⋊C4C2312yes—
205C22×C4⋊C4C2314yes—
206C22×C4⋊C4C2314yes—
207C22×C4⋊C4C2311yescharacteristic
208C22×C4⋊C4C2311yescharacteristic
209C22×C22⋊C4C2314yes—
210C22×C22⋊C4C2312yes—
211C22×C22⋊C4C2312yes—
212C22×C42—44no—
213C22×C42C2311yescharacteristic
214C22×C42C2311yescharacteristic
215C22×C42C2311yescharacteristic
216C22×C42C2311yescharacteristic
217C22×C42C2311yescharacteristic
218C22×C42C2311yescharacteristic
219C22×C42C2312yes—
220C22×C42C2312yes—
221C22×C42C2312yes—
222C22×C42C2312yes—
223C22×C42C2312yes—
224#400C2318yes—
225#400C2318yes—
226#400C2318yes—
227#400C2318yes—
228#400C2318yes—
229#400C2318yes—
230#400C2318yes—
231#400C2318yes—
232#400C2318yes—
233#400C2318yes—
234#400C2318yes—
235#399C2318yes—
236#398C2318yes—
237#398C2318yes—
238#398C2318yes—
239#398C2318yes—
240#398C2318yes—
241#398C2318yes—
242#398C2318yes—
243#398C2318yes—
244#398C2318yes—
245#398C2318yes—
246#398C2318yes—
247#398C2318yes—
248#398C2318yes—
249#398C2318yes—
250#398C2318yes—
251#398C2318yes—
252#398C2318yes—
253#398C2318yes—
254#396C2318yes—
255#396C2318yes—
256#395C2318yes—
257#395C2318yes—
258#395C2318yes—
259#395C2318yes—
260#395C2318yes—
261#395C2318yes—
262#395C2318yes—
263#393C2318yes—
264#391C2318yes—
265#391C2318yes—
266#391C2318yes—
267#391C2314yes—
268#391C2318yes—
269#391C2318yes—
270#391C2314yes—
271#389C2312yes—
272#389C2314yes—
273#389C2314yes—
274#389C2314yes—
275#389C2314yes—
276#389C2312yes—
277#389C2312yes—
278#389C2314yes—
279#389C2314yes—
280#389C2318yes—
281#389C2318yes—
282#389C2314yes—
283#389C2318yes—
284#389C2318yes—
285#389C2314yes—
286#389C2312yes—
287#389C2312yes—
288#389C2314yes—
289#389C2318yes—
290#389C2314yes—
291#389C2314yes—
292#389C2314yes—
293#389C2314yes—
294#389C2314yes—
295#389C2314yes—
296#389C2318yes—
297#389C2318yes—
298#389C2318yes—
299#389C2312yes—
300#389C2312yes—
301#389C2318yes—
302#389C2318yes—
303#389C2318yes—
304#389C2314yes—
305#389C2314yes—
306#389C2318yes—
307#389C2318yes—
308#389C2314yes—
309#389C2314yes—
310#389C2314yes—
311#389C2312yes—
312#389C2312yes—
313#389C2312yes—
314#389C2312yes—
315#389C2312yes—
316#389C2314yes—
317#389C2314yes—
318#388C2318yes—
319#388C2318yes—
320#388C2318yes—
321#388C2318yes—
322#387C2318yes—
323#387C2318yes—
324#387C2318yes—
325#387C2318yes—
326#387C2314yes—
327#387C2318yes—
328#387C2318yes—
329#387C2318yes—
330#387C2318yes—
331#387C2318yes—
332#387C2318yes—
333#387C2318yes—
334#387C2318yes—
335#387C2318yes—
336#387C2318yes—
337#387C2318yes—
338#387C2318yes—
339#387C2318yes—
340#387C2318yes—
341#387C2314yes—
342#387C2314yes—
343#387C2314yes—
344#385C2314yes—
345#385C2318yes—
346#385C2318yes—
347#385C2318yes—
348#385C2318yes—
349#385C2318yes—
350#385C2318yes—
351#385C2318yes—
352#385C2314yes—
353#385C2314yes—
354#385C2314yes—
355#385C2314yes—
356#385C2314yes—
357#385C2314yes—
358#385C2318yes—
359#385C2318yes—
360#385C2318yes—
361#385C2314yes—
362#385C2314yes—
363#385C2314yes—
364#385C2314yes—
365#385C2314yes—
366#385C2314yes—
367#385C2314yes—
368#384C2318yes—
369#384C2314yes—
370#384C2314yes—
371#384C2314yes—
372#384C2312yes—
373#384C2318yes—
374#384C2314yes—
375#384C2318yes—
376#383C2318yes—
377#382C2314yes—
378#382C2314yes—
379#382C2311yescharacteristic
380#382C2312yes—
381#382C2312yes—
382#382C2318yes—
383#382C2314yes—
384#382C2318yes—
385#382C2318yes—
386#382C2311yescharacteristic
387#382C2318yes—
388#382C2314yes—
389#382C2314yes—
390#381C2318yes—
391#381C2314yes—
392#380C2314yes—
393#380C2312yes—
394#380C2312yes—
395#380C2318yes—
396#380C2318yes—
397#380C2314yes—
398#380C2314yes—
399#380C2314yes—
400#380C2314yes—
401#380C2312yes—
402#380C2314yes—
403#380C2314yes—
404#380C2312yes—
405#380C2318yes—
406#379C2314yes—
407C4×C4⋊C4C2314yes—
408C4×C4⋊C4C2314yes—
409C4×C4⋊C4C2314yes—
410C4×C4⋊C4C2314yes—
411C4×C4⋊C4C2314yes—
412C4×C4⋊C4C2318yes—
413C4×C4⋊C4C2314yes—
414C4×C4⋊C4C2314yes—
415C4×C4⋊C4C2314yes—
416C4×C4⋊C4C2314yes—
417C4×C4⋊C4C2314yes—
418C4×C4⋊C4C2314yes—
419C4×C4⋊C4C2314yes—
420C4×C4⋊C4C2314yes—
421C4×C4⋊C4C2314yes—
422C4×C4⋊C4C2314yes—
423C4×C4⋊C4C2314yes—
424C4×C4⋊C4C2314yes—
425C4×C4⋊C4C2314yes—
426C4×C4⋊C4C2314yes—
427C4×C22⋊C4C2318yes—
428C4×C22⋊C4C2318yes—
429C4×C22⋊C4C2318yes—
430C4×C22⋊C4C2314yes—
431C4×C22⋊C4C2314yes—
432#376C2318yes—
433C2×#95C2314yes—
434C2×#95C2314yes—
435C2×#95C2314yes—
436C2×#95C2314yes—
437C2×#95C2314yes—
438C25C2411yescharacteristic
439C22×Q8C2414yes—
440C22×Q8C2418yes—
441C23×C4—24no—
442C23×C4—24no—
443C23×C4—44no—
444C23×C4—44no—
445C23×C4—44no—
446C23×C4C2×Q818yes—
447C23×C4C2412yes—
448C23×C4C2412yes—
449C23×C4C2412yes—
450C23×C4C2411yescharacteristic
451C23×C4C2411yescharacteristic
452C23×C4C2411yescharacteristic
453C23×C4C2411yescharacteristic
454C23×C4C2411yescharacteristic
455C23×C4C2414yes—
456C23×C4C2414yes—
457C23×C4C2414yes—
458C23×C4C2412yes—
459C23×C4C2412yes—
460C23×C4C2412yes—
461C23×C4C2412yes—
462C23×C4C2412yes—
463C23×C4C2411yescharacteristic
464C4⋊Q8—44no—
465C4⋊Q8—48no—
466C4⋊Q8—48no—
467C4⋊Q8—416no—
468#125—48no—
469#125—44no—
470#125—44no—
471#125—42no—
472#125—42no—
473#125—48no—
474#125—48no—
475#125—416no—
476C22⋊Q8—416no—
477C22⋊Q8—48no—
478C22⋊Q8—48no—
479C22⋊Q8—416no—
480C22⋊Q8—48no—
481C4×Q8—48no—
482#117—28no—
483#117—28no—
484#117—28no—
485#117—44no—
486#117—44no—
487#117—416no—
488#117—42no—
489#117—42no—
490#117C2×Q8116yes—
491#117C2×Q8116yes—
492#117C2×Q8116yes—
493#117C2×Q8116yes—
494C2×C4⋊C4—28no—
495C2×C4⋊C4—28no—
496C2×C4⋊C4—48no—
497C2×C4⋊C4—48no—
498C2×C4⋊C4—44no—
499C2×C4⋊C4—48no—
500C2×C4⋊C4—48no—
501C2×C4⋊C4C2×Q818yes—
502C2×C4⋊C4C2×Q818yes—
503C2×C4⋊C4C2412yes—
504C2×C4⋊C4C2412yes—
505C2×C4⋊C4C2414yes—
506C2×C4⋊C4C2414yes—
507C2×C4⋊C4C2414yes—
508C2×C4⋊C4C2418yes—
509C2×C4⋊C4C2414yes—
510C2×C4⋊C4C2414yes—
511C2×C4⋊C4C2414yes—
512C2×C4⋊C4C2412yes—
513C2×C4⋊C4C2412yes—
514C2×C4⋊C4C2412yes—
515C2×C4⋊C4C2412yes—
516C2×C4⋊C4C2414yes—
517C2×C4⋊C4C2414yes—
518C2×C4⋊C4C2418yes—
519C2×C4⋊C4C2418yes—
520C2×C4⋊C4C2414yes—
521C2×C4⋊C4C2414yes—
522C2×C4⋊C4C2414yes—
523C2×C4⋊C4C2414yes—
524C2×C4⋊C4C2414yes—
525C2×C4⋊C4C2414yes—
526C2×C4⋊C4C2418yes—
527C2×C4⋊C4C2418yes—
528C2×C4⋊C4C2418yes—
529C2×C4⋊C4C2414yes—
530C2×C4⋊C4C2414yes—
531C2×C4⋊C4C2414yes—
532C2×C4⋊C4C2418yes—
533C2×C4⋊C4C2418yes—
534C2×C4⋊C4C2418yes—
535C2×C4⋊C4C2414yes—
536C2×C4⋊C4C2414yes—
537C2×C4⋊C4C2414yes—
538C2×C4⋊C4C2414yes—
539C2×C4⋊C4C2414yes—
540C2×C4⋊C4C2418yes—
541C2×C4⋊C4C2418yes—
542C2×C4⋊C4C2418yes—
543C2×C4⋊C4C2418yes—
544C2×C4⋊C4C2418yes—
545C2×C4⋊C4C2418yes—
546C2×C4⋊C4C2418yes—
547C2×C4⋊C4C2418yes—
548C2×C4⋊C4C2412yes—
549C2×C4⋊C4C2412yes—
550C2×C4⋊C4C2412yes—
551C2×C4⋊C4C2412yes—
552C2×C22⋊C4—48no—
553C2×C22⋊C4—44no—
554C2×C22⋊C4C2×Q8116yes—
555C2×C22⋊C4C2414yes—
556C2×C22⋊C4C2418yes—
557C2×C22⋊C4C2414yes—
558C2×C22⋊C4C2414yes—
559C2×C22⋊C4C2414yes—
560C2×C22⋊C4C2414yes—
561C2×C22⋊C4C2412yes—
562C2×C22⋊C4C2412yes—
563C2×C22⋊C4C2418yes—
564C2×C22⋊C4C2414yes—
565C2×C22⋊C4C2414yes—
566C2×C22⋊C4C2414yes—
567C2×C22⋊C4C2414yes—
568C2×C42—24no—
569C2×C42—24no—
570C2×C42—44no—
571C2×C42—44no—
572C2×C42—44no—
573C2×C42—42no—
574C2×C42—42no—
575C2×C42—42no—
576C2×C42—42no—
577C2×C42—44no—
578C2×C42C2×Q8116yes—
579C2×C42C2414yes—
580C2×C42C2414yes—
581C2×C42C2414yes—
582C2×C42C2412yes—
583C2×C42C2411yescharacteristic
584C2×C42C2411yescharacteristic
585C2×C42C2412yes—
586C2×C42C2411yescharacteristic
587C2×C42C2411yescharacteristic
588C2×C42C2412yes—
589C2×C42C2412yes—
590C2×C42C2418yes—
591C2×C42C2418yes—
592C2×C42C2418yes—
593C2×C42C2418yes—
594C2×C42C2412yes—
595C2×C42C2412yes—
596C2×C42C2412yes—
597C2×C42C2412yes—
598C2×C42C2414yes—
599C2×C42C2414yes—
600#95C2418yes—
601#95C2414yes—
602#95C2414yes—
603#95C2414yes—
604#95C2414yes—
605#95C2414yes—
606#95C2414yes—
607#95C2414yes—
608#95C2414yes—
609#95C2418yes—
610#95C2418yes—
611#95C2418yes—
612#95C2418yes—
613#95C2418yes—
614#95C2414yes—
615#95C2418yes—
616#95C2418yes—
617#95C2414yes—
618#95C2418yes—
619#95C2418yes—
620#95C2418yes—
621#95C2418yes—
622#95C2414yes—
623#95C2414yes—
624#95C2418yes—
625#95C2418yes—
626#95C2414yes—
627#95C2414yes—
628#95C2414yes—
629#95C2414yes—
630#95C2414yes—
631#95C2414yes—
632#95C2418yes—
633#95C2418yes—
634#95C2418yes—
635#95C2418yes—
636#95C2418yes—
637#95C2418yes—
638C24—22no—
639C24—22no—
640C24—24no—
641C24—42no—
642C24C22×Q814yes—
643C24C2511yescharacteristic
644C24C2511yescharacteristic
645C24C2511yescharacteristic
646C2×Q8—28no—
647C2×Q8—44no—
648C2×Q8—44no—
649C2×Q8—48no—
650C2×Q8—48no—
651C2×Q8—48no—
652C22×C4—22no—
653C22×C4—22no—
654C22×C4—28no—
655C22×C4—232no—
656C22×C4—22no—
657C22×C4—22no—
658C22×C4—22no—
659C22×C4—22no—
660C22×C4—22no—
661C22×C4—22no—
662C22×C4—22no—
663C22×C4—22no—
664C22×C4—24no—
665C22×C4—24no—
666C22×C4—24no—
667C22×C4—24no—
668C22×C4—28no—
669C22×C4—28no—
670C22×C4—28no—
671C22×C4—24no—
672C22×C4—24no—
673C22×C4—24no—
674C22×C4—42no—
675C22×C4—42no—
676C22×C4—42no—
677C22×C4—42no—
678C22×C4—44no—
679C22×C4—42no—
680C22×C4—42no—
681C22×C4—42no—
682C22×C4—42no—
683C22×C4—42no—
684C22×C4—42no—
685C22×C4—42no—
686C22×C4—44no—
687C22×C4—44no—
688C22×C4—44no—
689C22×C4—44no—
690C22×C4—44no—
691C22×C4—44no—
692C22×C4—432no—
693C22×C4C22×Q814yes—
694C22×C4C22×Q818yes—
695C22×C4C22×Q814yes—
696C22×C4C22×Q814yes—
697C22×C4C22×Q814yes—
698C22×C4C22×Q814yes—
699C22×C4C22×Q818yes—
700C22×C4C22×Q814yes—
701C22×C4H(5,𝔽2)14yes—
702C22×C42−1+414yes—
703C22×C4C2518yes—
704C22×C4C2514yes—
705C22×C4C2514yes—
706C22×C4C2512yes—
707C22×C4C2512yes—
708C22×C4C2512yes—
709C22×C4C2514yes—
710C22×C4C2514yes—
711C22×C4C2518yes—
712C22×C4C2514yes—
713C22×C4C2514yes—
714C22×C4C2511yescharacteristic
715C22×C4C2511yescharacteristic
716C22×C4C2514yes—
717C22×C4C2514yes—
718C22×C4C2512yes—
719C22×C4C2511yescharacteristic
720C22×C4C2511yescharacteristic
721C4⋊C4—28no—
722C4⋊C4—28no—
723C4⋊C4—24no—
724C4⋊C4—24no—
725C4⋊C4—24no—
726C4⋊C4—24no—
727C4⋊C4—28no—
728C4⋊C4—28no—
729C4⋊C4—24no—
730C4⋊C4—24no—
731C4⋊C4—28no—
732C4⋊C4—216no—
733C4⋊C4—28no—
734C4⋊C4—28no—
735C4⋊C4—44no—
736C4⋊C4—44no—
737C4⋊C4—44no—
738C4⋊C4—44no—
739C4⋊C4—44no—
740C4⋊C4—44no—
741C4⋊C4—48no—
742C4⋊C4—44no—
743C4⋊C4—48no—
744C4⋊C4—48no—
745C4⋊C4—48no—
746C4⋊C4—48no—
747C4⋊C4—44no—
748C4⋊C4—44no—
749C4⋊C4—44no—
750C4⋊C4—44no—
751C4⋊C4—44no—
752C4⋊C4—44no—
753C4⋊C4—44no—
754C4⋊C4—48no—
755C4⋊C4—48no—
756C4⋊C4—48no—
757C4⋊C4—44no—
758C4⋊C4—48no—
759C4⋊C4—48no—
760C4⋊C4—48no—
761C4⋊C4—48no—
762C4⋊C4—48no—
763C4⋊C4—48no—
764C4⋊C4—48no—
765C4⋊C4—48no—
766C4⋊C4C22×Q818yes—
767C4⋊C4C22×Q818yes—
768C4⋊C4C22×Q818yes—
769C4⋊C4C22×Q818yes—
770C22⋊C4—28no—
771C22⋊C4—28no—
772C22⋊C4—28no—
773C22⋊C4—216no—
774C22⋊C4—28no—
775C22⋊C4—28no—
776C22⋊C4—48no—
777C22⋊C4—42no—
778C22⋊C4—42no—
779C22⋊C4—44no—
780C22⋊C4—44no—
781C22⋊C4C22×Q8116yes—
782C22⋊C4C22×Q8116yes—
783C42—24no—
784C42—24no—
785C42—22no—
786C42—22no—
787C42—22no—
788C42—22no—
789C42—28no—
790C42—28no—
791C42—28no—
792C42—42no—
793C42—42no—
794C42—42no—
795C42—42no—
796C42—42no—
797C42—42no—
798C42—48no—
799C42—48no—
800C42—48no—
801C42—48no—
802C42C22×Q8116yes—
803C42C22×Q8116yes—
804C23—21no—
805C23—21no—
806C23—22no—
807C23—22no—
808C23—22no—
809C23—21no—
810C23—21no—
811C23—22no—
812C23—22no—
813C23—28no—
814C23—28no—
815C23—44no—
816C23—48no—
817C23—48no—
818C23C23×Q812yes—
819C23C23×Q812yes—
820C23C23×Q812yes—
821C23C2×H(5,𝔽2)12yes—
822C23C2×2−1+412yes—
823C23#58514yes—
824C23C2611yescharacteristic
825Q8—88no—
826Q8—168no—
827C2×C4—22no—
828C2×C4—21no—
829C2×C4—21no—
830C2×C4—21no—
831C2×C4—21no—
832C2×C4—24no—
833C2×C4—24no—
834C2×C4—24no—
835C2×C4—24no—
836C2×C4—22no—
837C2×C4—28no—
838C2×C4—216no—
839C2×C4—28no—
840C2×C4—28no—
841C2×C4—28no—
842C2×C4—28no—
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—24no—
852C2×C4—24no—
853C2×C4—28no—
854C2×C4—24no—
855C2×C4—24no—
856C2×C4—24no—
857C2×C4—24no—
858C2×C4—28no—
859C2×C4—28no—
860C2×C4—28no—
861C2×C4—28no—
862C2×C4—24no—
863C2×C4—24no—
864C2×C4—24no—
865C2×C4—24no—
866C2×C4—24no—
867C2×C4—24no—
868C2×C4—24no—
869C2×C4—22no—
870C2×C4—22no—
871C2×C4—22no—
872C2×C4—22no—
873C2×C4—22no—
874C2×C4—22no—
875C2×C4—24no—
876C2×C4—48no—
877C2×C4—48no—
878C2×C4—48no—
879C2×C4—48no—
880C2×C4—48no—
881C2×C4—48no—
882C2×C4—48no—
883C2×C4—88no—
884C2×C4—88no—
885C2×C4—88no—
886C2×C4#544116yes—
887C2×C4C23×Q812yes—
888C2×C4C23×Q818yes—
889C2×C4C23×Q818yes—
890C2×C4C23×Q812yes—
891C2×C4C23×Q812yes—
892C2×C4C23×Q812yes—
893C2×C4C2×H(5,𝔽2)12yes—
894C2×C4C2×H(5,𝔽2)12yes—
895C2×C4C2×2−1+412yes—
896C2×C4C2×2−1+412yes—
897C2×C4#58514yes—
898C22—22no—
899C22—22no—
900C22—22no—
901C22—24no—
902C22—24no—
903C22—24no—
904C22—24no—
905C22—22no—
906C22—22no—
907C22—22no—
908C22—22no—
909C22—416no—
910C22—42no—
911C22—42no—
912C22C2×#54414yes—
913C22#350414yes—
914C22C24×Q811yescharacteristic
915C22C22×H(5,𝔽2)11yescharacteristic
916C22C22×2−1+411yescharacteristic
917C22C2×#58512yes—
918C22C2×#58512yes—
919C4—28no—
920C4—28no—
921C4—24no—
922C4—22no—
923C4—22no—
924C4—42no—
925C4—42no—
926C4—42no—
927C4—44no—
928C4—48no—
929C4—44no—
930C4—44no—
931C4—44no—
932C4—44no—
933C4—44no—
934C4—48no—
935C4C2×#54414yes—
936C4C2×#54414yes—
937C2—24no—
938C2—24no—
939C2—42no—
940C2C22×#54411yescharacteristic
941C2C2×#350411yescharacteristic
942C2#6281311yescharacteristic
943C2#6282112yes—
944C2#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. #39987C2semidirect
2. #39986C2semidirect
3. #39178C2semidirect
4. #38963C2semidirect
5. #38449C2semidirect
7. #37428C2semidirect
8. #37427C2semidirect
9. #37311C2semidirect
12. #35640C2semidirect
13. #35627C2semidirect
14. #35566C2semidirect
15. #35543C2semidirect
17. #35239C2semidirect
18. #35181C2semidirect
19. #35104C2semidirect
45. #2802C22semidirect
46. #2792C22semidirect
47. #2791C22semidirect
48. #2791C22semidirect
52. #2774C22semidirect
53. #2774C22semidirect
56. #2755C22semidirect
59. #2713C22semidirect
60. #2666C22semidirect
61. #2666C22semidirect
66. #2606C22semidirect
67. #2605C22semidirect
68. #2584C22semidirect
69. #2584C22semidirect
71. #2571C22semidirect
72. #2571C22semidirect
73. #2571C22semidirect
74. #2570C22semidirect
75. #2570C22semidirect
76. #2570C22semidirect
77. #2570C22semidirect
78. #2570C22semidirect
79. #2570C22semidirect
80. #2567C22semidirect
81. #2552C22semidirect
82. #2552C22semidirect
83. #2552C22semidirect
84. #2552C22semidirect
85. #2552C22semidirect
86. #2552C22semidirect
87. #2551C22semidirect
88. #2550C22semidirect
89. #2550C22semidirect
90. #2550C22semidirect
91. #2550C22semidirect
92. #2550C22semidirect
93. #2550C22semidirect
95. #2546C22semidirect
96. #2509C22semidirect
97. #2509C22semidirect
98. #2509C22semidirect
99. #2508C22semidirect
100. #2508C22semidirect
101. #2508C22semidirect
102. #2507C22semidirect
103. #2506C22semidirect
126. #2331C22semidirect
127. #2330C22semidirect
187. C2×#117Q8semidirect

Maximal subgroups

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

subgroupindex
#399872
#399862
#391782
#389632
#384492
#380972
#374282
#374272
#373112
#366252
C2×#28512
#356402
#356272
#355662
#355432
#352532
#352392
#351812
#351042
#341802
C2×#22962