Finite Group Databasebeta

← #7712416

Subgroups — #7712416

Order 512.

4568 conjugacy classes of subgroups.

The subgroup lattice has 921 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#59670C214yesmaximal, complemented
2#59460C214yesmaximal, complemented
3#45798C218yesmaximal, complemented
4#39707C218yesmaximal, complemented
5#39691C214yesmaximal, complemented
6#39688C214yesmaximal
7#39625C212yesmaximal, complemented
8#39497C212yesmaximal, complemented
9#37879C214yesmaximal, complemented
10#37624C212yesmaximal, complemented
11#37314C214yesmaximal, complemented
12#36645C211yesmaximal, characteristic, complemented
13#36640C211yesmaximal, characteristic, complemented
14#36600C211yesmaximal, characteristic, complemented
15#36584C211yesmaximal, characteristic, complemented
16#36132C212yesmaximal, complemented
17#36132C211yesmaximal, characteristic, complemented
18#36131C212yesmaximal, complemented
19D4×#125C211yesmaximal, characteristic, complemented
20#35336C212yesmaximal, complemented
21#35335C212yesmaximal, complemented
22#34383C212yesmaximal
23C4×#529C211yesmaximal, characteristic
24C2×#533C2212yes—
25C2×#533C2212yes—
26C2×#529C2211yescharacteristic
27C22×#125C2212yes—
28#2868C2212yes—
29#2864C2214yes—
30#2862C2212yes—
31#2859C2211yescharacteristic
32#2859C2212yes—
33#2859C2212yes—
34#2859C2212yes—
35#2859C2211yescharacteristic
36#2859C2211yescharacteristic
37#2859C2212yes—
38#2859C2211yescharacteristic
39#2857C2214yes—
40#2857C2214yes—
41#2851C2212yes—
42#2851C2212yes—
43#2851C2211yescharacteristic
44#2851C2211yescharacteristic
45#2851C2214yes—
46#2851C2212yes—
47#2841C2218yes—
48#2806C2218yes—
49#2792C2218yes—
50#2790C2218yes—
51#2788C2218yes—
52#2788C2218yes—
53#2784C2218yes—
54#2780C2218yes—
55#2774C2218yes—
56#2768C2218yes—
57#2763C2218yes—
58#2755C2218yes—
59#2734C2218yes—
60#2729C2218yes—
61#2729C2218yes—
62#2713C2218yes—
63#2704C2218yes—
64#2666C2218yes—
65#2660C2214yes—
66#2660C2214yes—
67#2647C2214yes—
68#2629C2214yes—
69#2629C2214yes—
70#2628C2214yes—
71#2590C2218yes—
72#2590C2218yes—
73#2588C2218yes—
74#2587C2218yes—
75#2587C2218yes—
76#2587C2218yes—
77#2585C2218yes—
78#2585C2218yes—
79#2584C2218yes—
80#2584C2218yes—
81#2583C2218yes—
82#2583C2218yes—
83#2574C2218yes—
84#2571C2212yes—
85#2571C2214yes—
86#2570C2214yes—
87#2570C2214yes—
88#2567C2214yes—
89#2566C2214yes—
90#2556C2218yes—
91#2552C2212yes—
92#2552C2212yes—
93#2551C2214yes—
94#2551C2214yes—
95#2551C2212yes—
96#2550C2214yes—
97#2550C2214yes—
98#2550C2214yes—
99#2509C2214yes—
100#2509C2218yes—
101#2507C2214yes—
102#2507C2214yes—
103#2506C2214yes—
104#2473C2218yes—
105#2465C2218yes—
106#2465C2218yes—
107#2465C2218yes—
108#2462C2218yes—
109#2453C2214yes—
110#2452C2214yes—
111#2452C2218yes—
112#2452C2214yes—
113#2451C2214yes—
114#2449C2218yes—
115#2442C2214yes—
116#2441C2214yes—
117#2440C2214yes—
118#2439C2214yes—
119#2439C2214yes—
120#2439C2214yes—
121#2376C2218yes—
122#2370C2214yes—
123#2370C2214yes—
124#2367C2214yes—
125#2365C2214yes—
126#2365C2218yes—
127#2360C2218yes—
128#2355C2212yes—
129#2354C2212yes—
130#2354C2214yes—
131#2352C2214yes—
132#2351C2214yes—
133Q8×C4⋊C4C2212yes—
134D4×C4⋊C4C2214yes—
135D4×C4⋊C4C2212yes—
136#2334C2218yes—
137#2330C2214yes—
138#2324C2214yes—
139#2323C2214yes—
140#2317C2214yes—
141#2317C2214yes—
142#2314C2214yes—
143C4×C4⋊Q8C2214yes—
144C4×C4⋊Q8C2214yes—
145C4×#125C2212yes—
146C4×#125C2212yes—
147C4×#125C2211yescharacteristic
148C4×#125C2212yes—
149C4×#125C2214yes—
150C4×#125C2211yescharacteristic
151C4×#125C2212yes—
152C4×#126C2214yes—
153C4×#124C2212yes—
154C4×C22⋊Q8C2212yes—
155C4×#123C2214yes—
156C4×#121C2212yes—
157#2298C2212yes—
158#2296C2214yes—
159#2295C2211yescharacteristic
160#2293C2211yescharacteristic
161#2290C2212yes—
162#2285C2212yes—
163#2285C2212yes—
164#2285C2212yes—
165#2283C2211yescharacteristic
166C42×Q8C2211yescharacteristic
167C42×D4C2211yescharacteristic
168C42×D4C2212yes—
169C4×#117C2212yes—
170C2×C43C2211yescharacteristic
171#533—48no—
172#533—48no—
173C2×C4⋊Q8C2314yes—
174C2×C4⋊Q8C2314yes—
175C2×C4⋊Q8C2314yes—
176C2×C4⋊Q8C2314yes—
177C2×C4⋊Q8C2318yes—
178C2×C4⋊Q8C2314yes—
179#529Q8116yescomplemented
180C2×#126C2312yes—
181C2×#125—48no—
182C2×#125C2312yes—
183C2×#125C2311yescharacteristic
184C2×#125C2312yes—
185C2×#125C2312yes—
186C2×#125C2311yescharacteristic
187C2×#125C2314yes—
188C2×#125C2314yes—
189C2×#125C2318yes—
190C2×#125C2314yes—
191C2×#125C2311yescharacteristic
192C2×#124C2311yescharacteristic
193C2×#123C2312yes—
194C2×C22⋊Q8C2318yes—
195C2×C22⋊Q8C2318yes—
196C2×C22⋊Q8C2318yes—
197C2×C22⋊Q8C2311yescharacteristic
198C2×#121C2311yescharacteristic
199C2×C4×Q8C2318yes—
200C2×C4×Q8C2314yes—
201C2×C4×Q8C2318yes—
202C2×C4×Q8C2312yes—
203C2×C4×Q8C2311yescharacteristic
204C2×C4×D4C2314yes—
205C2×C4×D4C2312yes—
206C2×C4×D4C2314yes—
207C2×C4×D4C2311yescharacteristic
208C2×C4×D4C2312yes—
209C2×#117C2312yes—
210C2×#117C2314yes—
211C2×#117C2314yes—
212C2×#117C2314yes—
213C2×#117C2312yes—
214C22×C4⋊C4C2314yes—
215C22×C4⋊C4C2318yes—
216C22×C42C2312yes—
217C22×C42C2311yescharacteristic
218C22×C42C2311yescharacteristic
219C22×C42C2312yes—
220C22×C42C2312yes—
221C22×C42C2311yescharacteristic
222#400C2318yes—
223#400C2318yes—
224#400C2318yes—
225#400C2318yes—
226#400C2318yes—
227#400C2318yes—
228#400C2318yes—
229#399C2318yes—
230#398C2318yes—
231#398C2318yes—
232#398C2318yes—
233#398C2318yes—
234#398C2318yes—
235#398C2318yes—
236#398C2318yes—
237#398C2318yes—
238#398C2318yes—
239#398C2318yes—
240#398C2318yes—
241#398C2318yes—
242#398C2318yes—
243#398C2318yes—
244#396C2318yes—
245#396C2318yes—
246#396C2318yes—
247#396C2318yes—
248#396C2318yes—
249#396C2318yes—
250#395C2318yes—
251#395C2318yes—
252#395C2318yes—
253#395C2318yes—
254#395C2318yes—
255#395C2318yes—
256#395C2318yes—
257#395C2318yes—
258#395C2318yes—
259#393C2318yes—
260#393C2318yes—
261#393C2318yes—
262#391C2318yes—
263#391C2318yes—
264#391C2312yes—
265#391C2314yes—
266#391C2318yes—
267#391C2318yes—
268#391C2318yes—
269#391C2318yes—
270#390C2312yes—
271#390C2314yes—
272#390C2318yes—
273#389C2312yes—
274#389C2314yes—
275#389C2312yes—
276#389C2314yes—
277#389C2314yes—
278#389C2314yes—
279#389C2312yes—
280#389C2312yes—
281#389C2312yes—
282#389C2312yes—
283#389C2318yes—
284#389C2318yes—
285#389C2314yes—
286#389C2314yes—
287#389C2314yes—
288#389C2314yes—
289#389C2318yes—
290#389C2318yes—
291#389C2314yes—
292#389C2314yes—
293#389C2318yes—
294#389C2314yes—
295#389C2318yes—
296#389C2318yes—
297#389C2318yes—
298#389C2318yes—
299#389C2314yes—
300#389C2314yes—
301#389C2314yes—
302#389C2318yes—
303#389C2318yes—
304#389C2318yes—
305#389C2318yes—
306#389C2318yes—
307#389C2318yes—
308#389C2314yes—
309#389C2314yes—
310#389C2314yes—
311#389C2318yes—
312#389C2314yes—
313#389C2314yes—
314#389C2314yes—
315#389C2318yes—
316#388C2314yes—
317#388C2314yes—
318#388C2314yes—
319#388C2318yes—
320#388C2318yes—
321#388C2318yes—
322#388C2318yes—
323#388C2318yes—
324#388C2318yes—
325#388C2314yes—
326#387C2314yes—
327#387C2314yes—
328#387C2314yes—
329#387C2314yes—
330#387C2314yes—
331#387C2318yes—
332#387C2314yes—
333#387C2318yes—
334#387C2314yes—
335#387C2314yes—
336#387C2314yes—
337#387C2314yes—
338#387C2314yes—
339#387C2314yes—
340#387C2318yes—
341#387C2318yes—
342#387C2318yes—
343#387C2318yes—
344#387C2318yes—
345#387C2318yes—
346#387C2318yes—
347#387C2318yes—
348#387C2318yes—
349#387C2318yes—
350#387C2318yes—
351#387C2318yes—
352#387C2318yes—
353#387C2318yes—
354#386C2318yes—
355#386C2314yes—
356#385C2318yes—
357#385C2318yes—
358#385C2318yes—
359#385C2318yes—
360#385C2318yes—
361#385C2318yes—
362#385C2318yes—
363#385C2318yes—
364#385C2318yes—
365#385C2314yes—
366#385C2314yes—
367#385C2314yes—
368#385C2314yes—
369#385C2314yes—
370#384C2314yes—
371#384C2314yes—
372#384C2314yes—
373#384C2312yes—
374#384C2314yes—
375#384C2314yes—
376#384C2312yes—
377#384C2312yes—
378#384C2314yes—
379#384C2312yes—
380#383C2312yes—
381#382C2311yescharacteristic
382#382C2311yescharacteristic
383#382C2312yes—
384#382C2312yes—
385#382C2314yes—
386#382C2314yes—
387#382C2314yes—
388#382C2312yes—
389#382C2314yes—
390#382C2314yes—
391#382C2312yes—
392#382C2318yes—
393#382C2314yes—
394#381C2312yes—
395#380C2314yes—
396#380C2314yes—
397#380C2318yes—
398#380C2314yes—
399#380C2314yes—
400#380C2314yes—
401#380C2312yes—
402#380C2312yes—
403#380C2318yes—
404#380C2312yes—
405C4×C4⋊C4C2314yes—
406C4×C4⋊C4C2314yes—
407C4×C4⋊C4C2314yes—
408C4×C4⋊C4C2314yes—
409C4×C4⋊C4C2314yes—
410C4×C4⋊C4C2314yes—
411C4×C4⋊C4C2312yes—
412C4×C4⋊C4C2312yes—
413C4×C4⋊C4C2314yes—
414C4×C4⋊C4C2314yes—
415C4×C4⋊C4C2314yes—
416C4×C4⋊C4C2314yes—
417C4×C4⋊C4C2314yes—
418C4×C4⋊C4C2318yes—
419C4×C4⋊C4C2318yes—
420C4×C4⋊C4C2312yes—
421C4×C4⋊C4C2312yes—
422C4×C4⋊C4C2314yes—
423C4×C4⋊C4C2318yes—
424C4×C4⋊C4C2314yes—
425C4×C4⋊C4C2312yes—
426C4×C4⋊C4C2311yescharacteristic
427C4×C4⋊C4C2314yes—
428C4×C4⋊C4C2314yes—
429C4×C4⋊C4C2318yes—
430C4×C4⋊C4C2311yescharacteristic
431C4×C4⋊C4C2312yes—
432C4×C22⋊C4C2314yes—
433C4×C22⋊C4C2314yes—
434C4×C22⋊C4C2314yes—
435C4×C22⋊C4C2318yes—
436C4×C22⋊C4C2314yes—
437C4×C22⋊C4C2312yes—
438C4×C22⋊C4C2312yes—
439C4×C22⋊C4C2312yes—
440C4×C22⋊C4C2314yes—
441#376C2312yes—
442#376C2312yes—
443C43C2312yes—
444C43C2312yes—
445C43C2311yescharacteristic
446C43C2312yes—
447C43C2311yescharacteristic
448C43C2311yescharacteristic
449C43C2311yescharacteristic
450C22×Q8C2411yescharacteristic
451C22×Q8C2418yes—
452C22×Q8C2418yes—
453C22×D4C2411yescharacteristic
454C22×D4C2412yes—
455C23×C4C2412yes—
456C23×C4C2412yes—
457C23×C4C2411yescharacteristic
458C23×C4C2411yescharacteristic
459C23×C4C2414yes—
460C23×C4C2412yes—
461C23×C4C2418yes—
462C23×C4C2411yescharacteristic
463C4⋊Q8—48no—
464C4⋊Q8—48no—
465C4⋊Q8—48no—
466C4⋊Q8—48no—
467C4⋊Q8—48no—
468C4⋊Q8—416no—
469#126C2×Q8116yes—
470#125—24no—
471#125—28no—
472#125—28no—
473#125—24no—
474#125—28no—
475#125—416no—
476#125—48no—
477#125—48no—
478#125—48no—
479#125C2×Q818yes—
480#124C2×Q818yes—
481#123C2×Q8116yes—
482C22⋊Q8—416no—
483C22⋊Q8—416no—
484C22⋊Q8—416no—
485C22⋊Q8C2×Q818yes—
486#121C2×Q818yes—
487C4×Q8—416no—
488C4×Q8—416no—
489C4×Q8—44no—
490C4×Q8—48no—
491C4×Q8C2×Q818yes—
492C4×D4—44no—
493C4×D4—48no—
494C4×D4—48no—
495C4×D4C2×Q818yes—
496C4×D4C2×Q8116yes—
497#117—28no—
498#117—48no—
499#117—48no—
500#117—48no—
501#117C2×Q8116yes—
502C2×C4⋊C4—48no—
503C2×C4⋊C4—416no—
504C2×C4⋊C4C2412yes—
505C2×C4⋊C4C2414yes—
506C2×C4⋊C4C2414yes—
507C2×C4⋊C4C2418yes—
508C2×C4⋊C4C2412yes—
509C2×C4⋊C4C2414yes—
510C2×C4⋊C4C2414yes—
511C2×C4⋊C4C2414yes—
512C2×C4⋊C4C2412yes—
513C2×C4⋊C4C2414yes—
514C2×C4⋊C4C2418yes—
515C2×C4⋊C4C2414yes—
516C2×C4⋊C4C2412yes—
517C2×C4⋊C4C2414yes—
518C2×C4⋊C4C2414yes—
519C2×C4⋊C4C2414yes—
520C2×C4⋊C4C2412yes—
521C2×C4⋊C4C2412yes—
522C2×C4⋊C4C2414yes—
523C2×C4⋊C4C2414yes—
524C2×C4⋊C4C2418yes—
525C2×C4⋊C4C2418yes—
526C2×C4⋊C4C2418yes—
527C2×C4⋊C4C2414yes—
528C2×C4⋊C4C2414yes—
529C2×C4⋊C4C2418yes—
530C2×C4⋊C4C2418yes—
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⋊C4C2418yes—
540C2×C4⋊C4C2418yes—
541C2×C4⋊C4C2414yes—
542C2×C4⋊C4C2418yes—
543C2×C4⋊C4C2418yes—
544C2×C4⋊C4C2414yes—
545C2×C4⋊C4C2418yes—
546C2×C4⋊C4C2418yes—
547C2×C4⋊C4C2418yes—
548C2×C4⋊C4C2412yes—
549C2×C4⋊C4C2412yes—
550C2×C4⋊C4C2411yescharacteristic
551C2×C4⋊C4C2412yes—
552C2×C4⋊C4C2411yescharacteristic
553C2×C4⋊C4C2412yes—
554C2×C22⋊C4C2414yes—
555C2×C22⋊C4C2414yes—
556C2×C22⋊C4C2418yes—
557C2×C22⋊C4C2418yes—
558C2×C22⋊C4C2414yes—
559C2×C22⋊C4C2414yes—
560C2×C22⋊C4C2414yes—
561C2×C22⋊C4C2414yes—
562C2×C22⋊C4C2418yes—
563C2×C22⋊C4C2418yes—
564C2×C22⋊C4C2412yes—
565C2×C22⋊C4C2412yes—
566C2×C22⋊C4C2412yes—
567C2×C22⋊C4C2412yes—
568C2×C22⋊C4C2412yes—
569C2×C42—28no—
570C2×C42—24no—
571C2×C42—24no—
572C2×C42—44no—
573C2×C42—44no—
574C2×C42C2×Q818yes—
575C2×C42C2414yes—
576C2×C42C2414yes—
577C2×C42C2412yes—
578C2×C42C2412yes—
579C2×C42C2412yes—
580C2×C42C2414yes—
581C2×C42C2412yes—
582C2×C42C2412yes—
583C2×C42C2411yescharacteristic
584C2×C42C2412yes—
585C2×C42C2412yes—
586C2×C42C2411yescharacteristic
587C2×C42C2412yes—
588C2×C42C2418yes—
589C2×C42C2418yes—
590C2×C42C2414yes—
591C2×C42C2414yes—
592C2×C42C2418yes—
593C2×C42C2418yes—
594C2×C42C2412yes—
595C2×C42C2412yes—
596C2×C42C2412yes—
597C2×C42C2412yes—
598C2×C42C2411yescharacteristic
599C2×C42C2412yes—
600C2×C42C2411yescharacteristic
601C2×C42C2411yescharacteristic
602C2×C42C2411yescharacteristic
603C2×C42C2411yescharacteristic
604C2×C42C2411yescharacteristic
605#95C2414yes—
606#95C2414yes—
607#95C2414yes—
608#95C2414yes—
609#95C2414yes—
610#95C2412yes—
611#95C2414yes—
612#95C2414yes—
613#95C2414yes—
614#95C2414yes—
615#95C2418yes—
616#95C2414yes—
617#95C2412yes—
618#95C2414yes—
619#95C2414yes—
620#95C2414yes—
621#95C2418yes—
622#95C2414yes—
623#95C2418yes—
624#95C2418yes—
625#95C2414yes—
626#95C2418yes—
627#95C2418yes—
628#95C2418yes—
629#95C2414yes—
630#95C2418yes—
631#95C2414yes—
632#95C2414yes—
633#95C2414yes—
634#95C2414yes—
635#95C2418yes—
636#95C2414yes—
637#95C2418yes—
638#95C2418yes—
639#95C2418yes—
640#95C2418yes—
641#95C2418yes—
642#95C2418yes—
643#95C2418yes—
644C24C2511yescharacteristic
645C24C2512yes—
646C2×Q8—24no—
647C2×Q8—216no—
648C2×Q8—48no—
649C2×Q8—48no—
650C2×Q8—48no—
651C2×Q8—48no—
652C2×Q8—48no—
653C2×Q8C22×Q814yes—
654C2×D4—24no—
655C2×D4—44no—
656C2×D4C22×Q814yes—
657C2×D4C22×Q818yes—
658C22×C4—24no—
659C22×C4—22no—
660C22×C4—22no—
661C22×C4—24no—
662C22×C4—24no—
663C22×C4—24no—
664C22×C4—24no—
665C22×C4—24no—
666C22×C4—28no—
667C22×C4—42no—
668C22×C4—42no—
669C22×C4—42no—
670C22×C4—42no—
671C22×C4—48no—
672C22×C4—44no—
673C22×C4—44no—
674C22×C4—48no—
675C22×C4—48no—
676C22×C4C22×Q814yes—
677C22×C4C22×Q814yes—
678C22×C4C22×Q818yes—
679C22×C4C22×Q814yes—
680C22×C4C2512yes—
681C22×C4C2514yes—
682C22×C4C2514yes—
683C22×C4C2514yes—
684C22×C4C2514yes—
685C22×C4C2514yes—
686C22×C4C2518yes—
687C22×C4C2518yes—
688C22×C4C2514yes—
689C22×C4C2511yescharacteristic
690C22×C4C2512yes—
691C22×C4C2512yes—
692C22×C4C2512yes—
693C22×C4C2511yescharacteristic
694C22×C4C2511yescharacteristic
695C22×C4C2511yescharacteristic
696C22×C4C2512yes—
697C22×C4C2512yes—
698C22×C4C2512yes—
699C22×C4C2511yescharacteristic
700C22×C4C2511yescharacteristic
701C4⋊C4—28no—
702C4⋊C4—24no—
703C4⋊C4—28no—
704C4⋊C4—216no—
705C4⋊C4—24no—
706C4⋊C4—28no—
707C4⋊C4—216no—
708C4⋊C4—28no—
709C4⋊C4—28no—
710C4⋊C4—28no—
711C4⋊C4—28no—
712C4⋊C4—24no—
713C4⋊C4—24no—
714C4⋊C4—28no—
715C4⋊C4—28no—
716C4⋊C4—24no—
717C4⋊C4—24no—
718C4⋊C4—28no—
719C4⋊C4—28no—
720C4⋊C4—28no—
721C4⋊C4—48no—
722C4⋊C4—48no—
723C4⋊C4—48no—
724C4⋊C4—44no—
725C4⋊C4—44no—
726C4⋊C4—44no—
727C4⋊C4—48no—
728C4⋊C4—48no—
729C4⋊C4—48no—
730C4⋊C4—48no—
731C4⋊C4—48no—
732C4⋊C4—44no—
733C4⋊C4—44no—
734C4⋊C4—44no—
735C4⋊C4—44no—
736C4⋊C4—48no—
737C4⋊C4—48no—
738C4⋊C4—48no—
739C4⋊C4—44no—
740C4⋊C4—48no—
741C4⋊C4—44no—
742C4⋊C4—48no—
743C4⋊C4—48no—
744C4⋊C4—48no—
745C4⋊C4C22×Q818yes—
746C4⋊C4C22×Q818yes—
747C4⋊C4C22×Q814yes—
748C4⋊C4C22×Q818yes—
749C4⋊C4C22×Q814yes—
750C4⋊C4C22×Q818yes—
751C22⋊C4—28no—
752C22⋊C4—28no—
753C22⋊C4—44no—
754C22⋊C4—44no—
755C22⋊C4—48no—
756C22⋊C4—48no—
757C22⋊C4—44no—
758C22⋊C4—48no—
759C22⋊C4—44no—
760C22⋊C4—48no—
761C22⋊C4C22×Q818yes—
762C22⋊C4C22×Q818yes—
763C22⋊C4C22×Q818yes—
764C22⋊C4C22×Q818yes—
765C22⋊C4C22×Q818yes—
766C42—24no—
767C42—28no—
768C42—24no—
769C42—22no—
770C42—24no—
771C42—22no—
772C42—24no—
773C42—24no—
774C42—24no—
775C42—24no—
776C42—24no—
777C42—28no—
778C42—28no—
779C42—42no—
780C42—42no—
781C42—42no—
782C42—42no—
783C42—48no—
784C42—48no—
785C42—44no—
786C42—44no—
787C42—48no—
788C42—48no—
789C42C22×Q814yes—
790C42C22×Q814yes—
791C42C22×Q814yes—
792C42C22×Q814yes—
793C42C22×Q818yes—
794C42H(5,𝔽2)14yes—
795C422−1+414yes—
796C23—21no—
797C23—22no—
798C23—22no—
799C23—21no—
800C23—24no—
801C23—22no—
802C23—24no—
803C23—22no—
804C23C23×Q814yes—
805C23C23×Q812yes—
806C23C2611yescharacteristic
807Q8—28no—
808Q8—816no—
809Q8—816no—
810D4—28no—
811D4—48no—
812C2×C4—21no—
813C2×C4—22no—
814C2×C4—22no—
815C2×C4—21no—
816C2×C4—22no—
817C2×C4—22no—
818C2×C4—22no—
819C2×C4—22no—
820C2×C4—22no—
821C2×C4—22no—
822C2×C4—22no—
823C2×C4—22no—
824C2×C4—24no—
825C2×C4—24no—
826C2×C4—22no—
827C2×C4—216no—
828C2×C4—28no—
829C2×C4—28no—
830C2×C4—24no—
831C2×C4—24no—
832C2×C4—28no—
833C2×C4—28no—
834C2×C4—24no—
835C2×C4—22no—
836C2×C4—24no—
837C2×C4—24no—
838C2×C4—24no—
839C2×C4—24no—
840C2×C4—22no—
841C2×C4—22no—
842C2×C4—24no—
843C2×C4—24no—
844C2×C4—24no—
845C2×C4—24no—
846C2×C4—24no—
847C2×C4—28no—
848C2×C4—28no—
849C2×C4—24no—
850C2×C4—24no—
851C2×C4—24no—
852C2×C4—24no—
853C2×C4—24no—
854C2×C4—28no—
855C2×C4—24no—
856C2×C4—28no—
857C2×C4—44no—
858C2×C4—48no—
859C2×C4—48no—
860C2×C4—88no—
861C2×C4—816no—
862C2×C4C23×Q812yes—
863C2×C4C23×Q812yes—
864C2×C4C23×Q812yes—
865C2×C4C23×Q812yes—
866C2×C4C23×Q814yes—
867C2×C4C23×Q814yes—
868C2×C4C23×Q814yes—
869C2×C4C23×Q812yes—
870C2×C4C23×Q812yes—
871C2×C4C2×H(5,𝔽2)14yes—
872C2×C4C2×H(5,𝔽2)12yes—
873C2×C4C2×2−1+414yes—
874C2×C4C2×2−1+412yes—
875C2×C4#58514yes—
876C2×C4#58514yes—
877C22—22no—
878C22—24no—
879C22—22no—
880C22—24no—
881C22—22no—
882C22—24no—
883C22—42no—
884C22—44no—
885C22—42no—
886C22—44no—
887C22C24×Q811yescharacteristic
888C22C22×H(5,𝔽2)11yescharacteristic
889C22C22×2−1+411yescharacteristic
890C22C2×#58512yes—
891C22C2×#58512yes—
892C4—24no—
893C4—24no—
894C4—22no—
895C4—24no—
896C4—22no—
897C4—24no—
898C4—22no—
899C4—22no—
900C4—24no—
901C4—24no—
902C4—44no—
903C4—48no—
904C4—44no—
905C4—44no—
906C4—48no—
907C4—44no—
908C4—44no—
909C4—44no—
910C4—42no—
911C4#350314yes—
912C4#350414yes—
913C2—42no—
914C2—44no—
915C2#6274812yes—
916C2C2×#350311yescharacteristic
917C2C2×#350411yescharacteristic
918C2#6281311yescharacteristic
919C2#6283812yes—
subgroupG/H
center, commutator, Frattini, socle, cosocleC23C26
prime radicalC2×#121C23
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23 ◁ G
LECSG ▷ C23 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #59670C2semidirect
2. #59460C2semidirect
3. #45798C2semidirect
4. #39707C2semidirect
5. #39691C2semidirect
7. #39625C2semidirect
8. #39497C2semidirect
9. #37879C2semidirect
10. #37624C2semidirect
11. #37314C2semidirect
12. #36645C2semidirect
13. #36640C2semidirect
14. #36600C2semidirect
15. #36584C2semidirect
16. #36132C2semidirect
17. #36132C2semidirect
18. #36131C2semidirect
19. D4×#125C2semidirect
20. #35336C2semidirect
21. #35335C2semidirect
179. #529Q8semidirect

Maximal subgroups

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

subgroupindex
#596702
#594602
#457982
#397072
#396912
#396882
#396252
#394972
#378792
#376242
#373142
#366452
#366402
#366002
#365842
#361322
#361312
D4×#1252
#353362
#353352
#343832
C4×#5292