Finite Group Databasebeta

← #7849682

Subgroups — #7849682

Order 512.

4852 conjugacy classes of subgroups.

The subgroup lattice has 926 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#59928C212yesmaximal, complemented
2#59771C214yesmaximal, complemented
3#59326C214yesmaximal, complemented
4#52291C211yesmaximal, characteristic, complemented
5#51794C214yesmaximal, complemented
6#47958C218yesmaximal, complemented
7#47814C214yesmaximal, complemented
8#46004C212yesmaximal, complemented
9#45361C214yesmaximal, complemented
10#44879C214yesmaximal, complemented
11#43550C218yesmaximal, complemented
12#42981C212yesmaximal, complemented
13#39628C214yesmaximal, complemented
14#39495C212yesmaximal, complemented
15#37306C211yesmaximal, characteristic, complemented
16#36288C212yesmaximal, complemented
17#35702C212yesmaximal, complemented
18#35620C212yesmaximal, complemented
19#34415C212yesmaximal
20#34275C211yesmaximal, characteristic
21C2×D4×Q8C2212yes—
22C2×#544C2212yescomplemented
23C2×#535C2211yescharacteristic
24C2×#520C2211yescharacteristic
25C2×#518C2211yescharacteristic
26#2862C2214yescomplemented
27#2857C2212yes—
28#2844C2214yescomplemented
29#2811C2212yescomplemented
30#2811C2211yescharacteristic, complemented
31#2809C2211yescharacteristic, complemented
32#2809C2212yescomplemented
33#2809C2212yescomplemented
34#2807C2214yes—
35#2804C2214yes—
36#2804C2218yescomplemented
37#2804C2212yescomplemented
38#2790C2218yescomplemented
39#2788C2218yes—
40#2784C2214yes—
41#2784C2218yescomplemented
42#2784C2212yescomplemented
43#2780C2218yes—
44#2780C2218yescomplemented
45#2780C2218yescomplemented
46#2768C2218yescomplemented
47#2763C2218yescomplemented
48#2763C2218yescomplemented
49#2742C2214yes—
50#2732C2214yes—
51#2732C2214yes—
52#2732C2212yescomplemented
53#2732C2218yescomplemented
54#2729C2218yescomplemented
55#2704C2218yescomplemented
56#2692C2218yes—
57#2683C2218yescomplemented
58#2683C2212yescomplemented
59#2647C2218yescomplemented
60#2628C2212yes—
61#2626C2214yes—
62#2626C2214yes—
63#2612C2214yescomplemented
64#2612C2218yescomplemented
65#2589C2218yescomplemented
66#2587C2218yescomplemented
67#2584C2214yescomplemented
68#2580C2212yes—
69#2580C2214yes—
70#2580C2218yescomplemented
71#2574C2218yes—
72#2574C2218yescomplemented
73#2568C2214yescomplemented
74#2566C2214yes—
75#2566C2214yes—
76#2565C2214yescomplemented
77#2564C2214yes—
78#2564C2218yescomplemented
79#2563C2214yes—
80#2563C2212yes—
81#2556C2218yescomplemented
82#2551C2212yescomplemented
83#2550C2214yescomplemented
84#2546C2212yescomplemented
85#2509C2214yescomplemented
86#2509C2214yescomplemented
87#2508C2214yescomplemented
88#2505C2218yescomplemented
89#2505C2218yescomplemented
90#2492C2214yes—
91#2492C2218yescomplemented
92#2454C2214yes—
93#2452C2214yes—
94#2452C2214yes—
95#2452C2218yescomplemented
96#2452C2218yescomplemented
97#2450C2218yes—
98#2450C2218yes—
99#2450C2218yescomplemented
100#2450C2218yescomplemented
101#2450C2218yescomplemented
102#2450C2218yescomplemented
103#2450C2218yescomplemented
104#2442C2214yes—
105#2442C2214yescomplemented
106#2440C2214yescomplemented
107#2439C2214yes—
108#2439C2214yescomplemented
109#2439C2214yescomplemented
110#2437C2218yes—
111#2437C2218yes—
112#2434C2218yescomplemented
113#2429C2214yes—
114#2423C2218yescomplemented
115#2409C2214yes—
116#2409C2218yescomplemented
117#2396C2212yes—
118#2396C2214yescomplemented
119C2×#393C2214yes—
120#2379C2214yes—
121#2375C2214yes—
122#2372C2214yes—
123#2369C2214yescomplemented
124#2368C2218yescomplemented
125#2365C2212yescomplemented
126#2363C2214yes—
127#2363C2214yes—
128#2361C2214yes—
129#2361C2214yes—
130#2358C2214yes—
131#2358C2218yes—
132#2355C2212yescomplemented
133#2349C2214yes—
134#2349C2212yes—
135#2349C2218yescomplemented
136#2346C2214yes—
137D4×C22⋊C4C2214yes—
138#2328C2218yes—
139#2328C2212yes—
140#2326C2212yes—
141#2324C2214yes—
142#2321C2218yes—
143#2317C2211yescharacteristic
144#2317C2212yescomplemented
145#2315C2214yes—
146#2311C2212yes—
147C4×#127C2212yes—
148C4×#124C2212yes—
149C4×C22⋊Q8C2212yes—
150C4×C22⋊Q8C2214yescomplemented
151C4×#121C2214yes—
152#2297C2212yes—
153#2297C2211yescharacteristic
154#2296C2212yescomplemented
155#2295C2214yescomplemented
156C2×#390C2211yescharacteristic
157C2×#382C2212yescomplemented
158C4×#117C2211yescharacteristic
159C22×#41C2311yescharacteristic
160C23×Q8C2314yes—
161C23×D4C2311yescharacteristic
162D4×Q8—48no—
163#544—48no—
164#535Q8116yescomplemented
165C2×C4⋊Q8C2314yes—
166C2×C4⋊Q8C2314yes—
167C2×C4⋊Q8C2312yes—
168C2×C4⋊Q8C2312yes—
169C2×C4⋊Q8C2314yes—
170C2×C4⋊Q8C2314yes—
171C2×#127C2312yes—
172C2×#125C2314yes—
173C2×#125C2314yes—
174C2×#124C2312yes—
175C2×C22⋊Q8C2314yes—
176C2×C22⋊Q8C2318yes—
177C2×C22⋊Q8C2312yes—
178C2×C22⋊Q8C2318yes—
179C2×C22⋊Q8C2318yes—
180C2×C22⋊Q8C2314yes—
181C2×C22⋊Q8C2318yes—
182C2×C22⋊Q8C2314yes—
183C2×C22⋊Q8C2318yes—
184C2×#121C2314yes—
185C2×#120C2314yes—
186#520—44no—
187#518—44no—
188C2×C4×Q8C2312yes—
189C2×C4×Q8C2312yes—
190C2×C4×Q8C2312yes—
191C2×C4×Q8C2314yes—
192C2×C4×D4C2312yes—
193C2×C4×D4C2318yes—
194C2×C4×D4C2312yes—
195C2×C4×D4C2312yes—
196C2×C4×D4C2314yes—
197C2×C4×D4C2312yes—
198C2×C4×D4C2312yes—
199C2×C4×D4C2314yes—
200C2×C4×D4C2314yes—
201C2×C4×D4C2318yes—
202C2×C4×D4C2318yes—
203C2×#117C2312yes—
204C2×#117C2311yescharacteristic
205C2×#117C2312yes—
206C2×#117C2311yescharacteristic
207C2×#117C2312yes—
208C2×#117C2311yescharacteristic
209C22×C4⋊C4C2312yes—
210C22×C4⋊C4C2311yescharacteristic
211C22×C4⋊C4C2312yes—
212C22×C22⋊C4C2314yes—
213C22×C22⋊C4C2314yes—
214C22×C22⋊C4C2318yes—
215C22×C42C2311yescharacteristic
216C22×C42C2312yes—
217#400C2312yes—
218#400C2318yes—
219#400C2318yes—
220#400C2318yes—
221#400C2318yes—
222#400C2318yes—
223#400C2318yes—
224#400C2318yes—
225#400C2314yes—
226#400C2314yes—
227#399C2314yes—
228#399C2318yes—
229#399C2314yes—
230#399C2318yes—
231#399C2312yes—
232#399C2314yes—
233#398C2318yes—
234#398C2318yes—
235#398C2318yes—
236#398C2318yes—
237#398C2318yes—
238#398C2314yes—
239#398C2318yes—
240#398C2314yes—
241#398C2314yes—
242#398C2318yes—
243#396C2318yes—
244#396C2318yes—
245#396C2318yes—
246#396C2318yes—
247#396C2318yes—
248#396C2318yes—
249#396C2314yes—
250#396C2314yes—
251#396C2314yes—
252#396C2318yes—
253#396C2318yes—
254#395C2314yes—
255#395C2318yes—
256#395C2318yes—
257#395C2318yes—
258#395C2318yes—
259#395C2312yes—
260#395C2314yes—
261#393C2314yes—
262#393C2318yes—
263#393C2314yes—
264#393C2318yes—
265#393C2318yes—
266#393C2314yes—
267#393C2318yes—
268#393C2318yes—
269#393C2318yes—
270#393C2314yes—
271#393C2312yes—
272#393C2314yes—
273#391C2312yes—
274#391C2314yes—
275#391C2312yes—
276#391C2318yes—
277#391C2318yes—
278#391C2318yes—
279#391C2318yes—
280#391C2311yescharacteristic
281#391C2318yes—
282#391C2314yes—
283#391C2312yes—
284#391C2314yes—
285#391C2314yes—
286#391C2314yes—
287#391C2318yes—
288#391C2314yes—
289#391C2311yescharacteristic
290#390C2311yescharacteristic
291#390C2318yes—
292#390C2312yes—
293#390C2312yes—
294#390C2314yes—
295#390C2314yes—
296#390C2312yes—
297#390C2314yes—
298#390C2318yes—
299#390C2314yes—
300#390C2318yes—
301#390C2312yes—
302#390C2311yescharacteristic
303#389C2314yes—
304#389C2314yes—
305#389C2314yes—
306#389C2314yes—
307#389C2314yes—
308#389C2314yes—
309#389C2318yes—
310#389C2318yes—
311#389C2314yes—
312#389C2318yes—
313#389C2314yes—
314#389C2318yes—
315#389C2318yes—
316#389C2314yes—
317#389C2314yes—
318#389C2314yes—
319#389C2318yes—
320#389C2314yes—
321#389C2312yes—
322#388C2318yes—
323#388C2318yes—
324#388C2318yes—
325#388C2318yes—
326#388C2318yes—
327#388C2318yes—
328#388C2318yes—
329#388C2318yes—
330#387C2318yes—
331#387C2318yes—
332#387C2318yes—
333#387C2318yes—
334#387C2318yes—
335#387C2318yes—
336#387C2314yes—
337#387C2318yes—
338#387C2314yes—
339#387C2314yes—
340#387C2318yes—
341#386C2318yes—
342#386C2318yes—
343#386C2318yes—
344#386C2314yes—
345#386C2314yes—
346#386C2314yes—
347#386C2318yes—
348#386C2314yes—
349#386C2318yes—
350#386C2318yes—
351#386C2318yes—
352#386C2318yes—
353#386C2314yes—
354#385C2318yes—
355#385C2318yes—
356#385C2318yes—
357#385C2318yes—
358#385C2318yes—
359#385C2318yes—
360#385C2318yes—
361#385C2318yes—
362#385C2318yes—
363#385C2314yes—
364#385C2318yes—
365#385C2314yes—
366#385C2318yes—
367#385C2318yes—
368#385C2318yes—
369#385C2318yes—
370#385C2318yes—
371#385C2318yes—
372#385C2318yes—
373#385C2314yes—
374#385C2318yes—
375#385C2318yes—
376#385C2314yes—
377#384C2312yes—
378#384C2314yes—
379#384C2312yes—
380#382C2314yes—
381#382C2314yes—
382#382C2314yes—
383#382C2314yes—
384#382C2314yes—
385#382C2312yes—
386#382C2318yes—
387#382C2312yes—
388#382C2318yes—
389#380C2318yes—
390#380C2318yes—
391#380C2318yes—
392#380C2318yes—
393#380C2314yes—
394#380C2314yes—
395#380C2314yes—
396#380C2312yes—
397#380C2314yes—
398#380C2314yes—
399#380C2318yes—
400#379C2318yes—
401C4×C4⋊C4C2314yes—
402C4×C4⋊C4C2312yes—
403C4×C4⋊C4C2314yes—
404C4×C4⋊C4C2314yes—
405C4×C4⋊C4C2318yes—
406C4×C4⋊C4C2314yes—
407C4×C4⋊C4C2314yes—
408C4×C4⋊C4C2314yes—
409C4×C4⋊C4C2314yes—
410C4×C4⋊C4C2312yes—
411C4×C4⋊C4C2312yes—
412C4×C4⋊C4C2312yes—
413C4×C22⋊C4C2314yes—
414C4×C22⋊C4C2318yes—
415C4×C22⋊C4C2318yes—
416C4×C22⋊C4C2314yes—
417C4×C22⋊C4C2318yes—
418C4×C22⋊C4C2314yes—
419C4×C22⋊C4C2314yes—
420#376C2312yes—
421#376C2318yes—
422C2×#95C2314yes—
423C2×#95C2318yes—
424C2×#95C2318yes—
425C43C2312yes—
426C25C2412yes—
427C2×#41—42no—
428C2×#41—42no—
429C2×#41C2×Q818yescomplemented
430C22×Q8—48no—
431C22×Q8—88no—
432C22×Q8C2414yes—
433C22×Q8C2412yes—
434C22×Q8C2418yes—
435C22×Q8C2412yes—
436C22×Q8C2414yes—
437C22×Q8C2411yescharacteristic
438C22×D4—42no—
439C22×D4—42no—
440C22×D4C2×Q818yes—
441C22×D4C2412yes—
442C22×D4C2418yes—
443C22×D4C2412yes—
444C22×D4C2412yes—
445C22×D4C2411yescharacteristic
446C23×C4C2412yes—
447C23×C4C2411yescharacteristic
448C23×C4C2412yes—
449C23×C4C2414yes—
450C23×C4C2412yes—
451C23×C4C2414yes—
452C23×C4C2418yes—
453C23×C4C2418yes—
454C23×C4C2414yes—
455C23×C4C2414yes—
456C23×C4C2414yes—
457C4⋊Q8—216no—
458C4⋊Q8—44no—
459C4⋊Q8—44no—
460C4⋊Q8—48no—
461C4⋊Q8—84no—
462C4⋊Q8—84no—
463#127C2×Q8116yescomplemented
464#125—48no—
465#125—48no—
466#124C2×Q8116yescomplemented
467C22⋊Q8—416no—
468C22⋊Q8—48no—
469C22⋊Q8—416no—
470C22⋊Q8—416no—
471C22⋊Q8—48no—
472C22⋊Q8—44no—
473C22⋊Q8—84no—
474C22⋊Q8—88no—
475C22⋊Q8—88no—
476#121C2×Q8132yescomplemented
477#120C2×Q8132yescomplemented
478C4×Q8—44no—
479C4×Q8—44no—
480C4×Q8—44no—
481C4×Q8—48no—
482C4×D4—28no—
483C4×D4—416no—
484C4×D4—44no—
485C4×D4—44no—
486C4×D4—48no—
487C4×D4—48no—
488C4×D4—44no—
489C4×D4—48no—
490C4×D4—44no—
491C4×D4—88no—
492C4×D4—88no—
493#117—24no—
494#117—28no—
495#117—42no—
496#117—44no—
497#117—44no—
498#117C2×Q818yescomplemented
499C2×C4⋊C4—44no—
500C2×C4⋊C4—42no—
501C2×C4⋊C4—44no—
502C2×C4⋊C4C2411yescharacteristic
503C2×C4⋊C4C2412yes—
504C2×C4⋊C4C2414yes—
505C2×C4⋊C4C2414yes—
506C2×C4⋊C4C2412yes—
507C2×C4⋊C4C2418yes—
508C2×C4⋊C4C2414yes—
509C2×C4⋊C4C2414yes—
510C2×C4⋊C4C2412yes—
511C2×C4⋊C4C2414yes—
512C2×C4⋊C4C2411yescharacteristic
513C2×C4⋊C4C2411yescharacteristic
514C2×C4⋊C4C2412yes—
515C2×C4⋊C4C2412yes—
516C2×C4⋊C4C2418yes—
517C2×C4⋊C4C2418yes—
518C2×C4⋊C4C2418yes—
519C2×C4⋊C4C2414yes—
520C2×C4⋊C4C2412yes—
521C2×C4⋊C4C2412yes—
522C2×C4⋊C4C2418yes—
523C2×C4⋊C4C2414yes—
524C2×C4⋊C4C2414yes—
525C2×C4⋊C4C2414yes—
526C2×C4⋊C4C2414yes—
527C2×C4⋊C4C2418yes—
528C2×C4⋊C4C2418yes—
529C2×C4⋊C4C2418yes—
530C2×C4⋊C4C2418yes—
531C2×C4⋊C4C2418yes—
532C2×C4⋊C4C2414yes—
533C2×C4⋊C4C2418yes—
534C2×C4⋊C4C2414yes—
535C2×C4⋊C4C2414yes—
536C2×C4⋊C4C2414yes—
537C2×C4⋊C4C2418yes—
538C2×C4⋊C4C2412yes—
539C2×C4⋊C4C2414yes—
540C2×C4⋊C4C2412yes—
541C2×C4⋊C4C2411yescharacteristic
542C2×C22⋊C4—48no—
543C2×C22⋊C4—48no—
544C2×C22⋊C4—88no—
545C2×C22⋊C4C2412yes—
546C2×C22⋊C4C2414yes—
547C2×C22⋊C4C2418yes—
548C2×C22⋊C4C2414yes—
549C2×C22⋊C4C2414yes—
550C2×C22⋊C4C2412yes—
551C2×C22⋊C4C2414yes—
552C2×C22⋊C4C2414yes—
553C2×C22⋊C4C2418yes—
554C2×C22⋊C4C2418yes—
555C2×C22⋊C4C2418yes—
556C2×C22⋊C4C2418yes—
557C2×C22⋊C4C2414yes—
558C2×C22⋊C4C2414yes—
559C2×C22⋊C4C2414yes—
560C2×C22⋊C4C2418yes—
561C2×C22⋊C4C2418yes—
562C2×C22⋊C4C2418yes—
563C2×C22⋊C4C2418yes—
564C2×C22⋊C4C2414yes—
565C2×C22⋊C4C2414yes—
566C2×C22⋊C4C2418yes—
567C2×C22⋊C4C2414yes—
568C2×C22⋊C4C2412yes—
569C2×C22⋊C4C2418yes—
570C2×C42—44no—
571C2×C42—42no—
572C2×C42C2412yes—
573C2×C42C2412yes—
574C2×C42C2414yes—
575C2×C42C2414yes—
576C2×C42C2414yes—
577C2×C42C2414yes—
578C2×C42C2412yes—
579C2×C42C2414yes—
580C2×C42C2418yes—
581C2×C42C2418yes—
582C2×C42C2414yes—
583C2×C42C2411yescharacteristic
584C2×C42C2411yescharacteristic
585C2×C42C2412yes—
586C2×C42C2412yes—
587C2×C42C2412yes—
588#95C2418yes—
589#95C2412yes—
590#95C2414yes—
591#95C2418yes—
592#95C2418yes—
593#95C2418yes—
594#95C2418yes—
595#95C2414yes—
596#95C2418yes—
597#95C2418yes—
598#95C2414yes—
599#95C2418yes—
600#95C2414yes—
601#95C2414yes—
602#95C2418yes—
603#95C2418yes—
604#95C2414yes—
605#95C2414yes—
606#95C2418yes—
607#95C2414yes—
608#95C2418yes—
609#95C2414yes—
610#95C2414yes—
611#95C2414yes—
612#95C2414yes—
613#95C2412yes—
614#95C2414yes—
615#95C2418yes—
616#95C2414yes—
617#95C2418yes—
618#95C2418yes—
619#95C2418yes—
620#95C2418yes—
621#95C2414yes—
622C24—42no—
623C24—44no—
624C24—44no—
625C24—42no—
626C24C22×Q818yes—
627C24C2511yescharacteristic
628C24C2514yes—
629C24C2512yes—
630#41—416no—
631C2×Q8—216no—
632C2×Q8—28no—
633C2×Q8—24no—
634C2×Q8—41no—
635C2×Q8—42no—
636C2×Q8—44no—
637C2×Q8—41no—
638C2×Q8—42no—
639C2×Q8—44no—
640C2×Q8—44no—
641C2×Q8—48no—
642C2×Q8—48no—
643C2×Q8—44no—
644C2×Q8—42no—
645C2×Q8—48no—
646C2×Q8—832no—
647C2×Q8C22×Q814yes—
648C2×D4—24no—
649C2×D4—24no—
650C2×D4—416no—
651C2×D4—42no—
652C2×D4—42no—
653C2×D4—41no—
654C2×D4—48no—
655C2×D4—48no—
656C2×D4—42no—
657C2×D4—42no—
658C2×D4—41no—
659C2×D4C22×Q818yes—
660C2×D4C22×Q818yes—
661C2×D4C22×Q8132yes—
662C2×D4C22×Q818yes—
663C2×D4C22×Q814yes—
664C22×C4—24no—
665C22×C4—22no—
666C22×C4—24no—
667C22×C4—22no—
668C22×C4—28no—
669C22×C4—24no—
670C22×C4—42no—
671C22×C4—44no—
672C22×C4—48no—
673C22×C4—48no—
674C22×C4—44no—
675C22×C4—48no—
676C22×C4—44no—
677C22×C4—42no—
678C22×C4—48no—
679C22×C4—44no—
680C22×C4—44no—
681C22×C4—48no—
682C22×C4—44no—
683C22×C4—42no—
684C22×C4—44no—
685C22×C4—48no—
686C22×C4—48no—
687C22×C4—48no—
688C22×C4—48no—
689C22×C4—48no—
690C22×C4C22×Q814yes—
691C22×C4C22×Q818yes—
692C22×C4C2514yes—
693C22×C4C2512yes—
694C22×C4C2514yes—
695C22×C4C2518yes—
696C22×C4C2512yes—
697C22×C4C2514yes—
698C22×C4C2512yes—
699C22×C4C2512yes—
700C22×C4C2514yes—
701C22×C4C2518yes—
702C22×C4C2514yes—
703C22×C4C2511yescharacteristic
704C22×C4C2514yes—
705C22×C4C2512yes—
706C22×C4C2512yes—
707C22×C4C2512yes—
708C22×C4C2511yescharacteristic
709C4⋊C4—22no—
710C4⋊C4—24no—
711C4⋊C4—28no—
712C4⋊C4—216no—
713C4⋊C4—28no—
714C4⋊C4—24no—
715C4⋊C4—28no—
716C4⋊C4—44no—
717C4⋊C4—42no—
718C4⋊C4—44no—
719C4⋊C4—41no—
720C4⋊C4—41no—
721C4⋊C4—42no—
722C4⋊C4—42no—
723C4⋊C4—48no—
724C4⋊C4—48no—
725C4⋊C4—48no—
726C4⋊C4—42no—
727C4⋊C4—44no—
728C4⋊C4—48no—
729C4⋊C4—44no—
730C4⋊C4—42no—
731C4⋊C4—44no—
732C4⋊C4—48no—
733C4⋊C4—48no—
734C4⋊C4—44no—
735C4⋊C4—44no—
736C4⋊C4—44no—
737C4⋊C4—48no—
738C4⋊C4—48no—
739C4⋊C4—44no—
740C4⋊C4—48no—
741C4⋊C4—48no—
742C4⋊C4—44no—
743C4⋊C4—44no—
744C4⋊C4—48no—
745C4⋊C4—44no—
746C4⋊C4—42no—
747C4⋊C4C22×Q818yes—
748C4⋊C4H(5,𝔽2)14yes—
749C22⋊C4—24no—
750C22⋊C4—28no—
751C22⋊C4—28no—
752C22⋊C4—216no—
753C22⋊C4—28no—
754C22⋊C4—42no—
755C22⋊C4—48no—
756C22⋊C4—44no—
757C22⋊C4—44no—
758C22⋊C4—48no—
759C22⋊C4—48no—
760C22⋊C4—48no—
761C22⋊C4—44no—
762C22⋊C4—44no—
763C22⋊C4—48no—
764C22⋊C4—48no—
765C22⋊C4—44no—
766C22⋊C4—48no—
767C22⋊C4—48no—
768C22⋊C4—44no—
769C22⋊C4—48no—
770C22⋊C4—44no—
771C22⋊C4—44no—
772C22⋊C4C22×Q818yes—
773C22⋊C4C22×Q8132yes—
774C42—24no—
775C42—28no—
776C42—24no—
777C42—28no—
778C42—28no—
779C42—24no—
780C42—28no—
781C42—41no—
782C42—42no—
783C42—42no—
784C42—41no—
785C42—44no—
786C42—48no—
787C42—48no—
788C42—44no—
789C42C22×Q818yes—
790C23—22no—
791C23—21no—
792C23—24no—
793C23—28no—
794C23—24no—
795C23—22no—
796C23—22no—
797C23—24no—
798C23—21no—
799C23—22no—
800C23—24no—
801C23—28no—
802C23—48no—
803C23—416no—
804C23—162no—
805C23—162no—
806C23—164no—
807C23C23×Q812yes—
808C23C23×Q818yes—
809C23C23×Q814yes—
810C23C2611yescharacteristic
811Q8—44no—
812Q8—48no—
813Q8—84no—
814Q8—88no—
815Q8—816no—
816Q8—88no—
817D4—216no—
818D4—48no—
819D4—432no—
820D4—44no—
821D4—48no—
822C2×C4—22no—
823C2×C4—21no—
824C2×C4—24no—
825C2×C4—22no—
826C2×C4—22no—
827C2×C4—21no—
828C2×C4—24no—
829C2×C4—22no—
830C2×C4—24no—
831C2×C4—28no—
832C2×C4—216no—
833C2×C4—22no—
834C2×C4—22no—
835C2×C4—24no—
836C2×C4—24no—
837C2×C4—22no—
838C2×C4—24no—
839C2×C4—28no—
840C2×C4—24no—
841C2×C4—22no—
842C2×C4—24no—
843C2×C4—24no—
844C2×C4—24no—
845C2×C4—28no—
846C2×C4—28no—
847C2×C4—28no—
848C2×C4—24no—
849C2×C4—22no—
850C2×C4—24no—
851C2×C4—24no—
852C2×C4—24no—
853C2×C4—24no—
854C2×C4—28no—
855C2×C4—28no—
856C2×C4—24no—
857C2×C4—22no—
858C2×C4—24no—
859C2×C4—28no—
860C2×C4—24no—
861C2×C4—24no—
862C2×C4—84no—
863C2×C4—88no—
864C2×C4—88no—
865C2×C4—816no—
866C2×C4—162no—
867C2×C4—164no—
868C2×C4—164no—
869C2×C4—164no—
870C2×C4—168no—
871C2×C4C23×Q812yes—
872C2×C4C23×Q818yes—
873C2×C4C23×Q814yes—
874C2×C4C23×Q812yes—
875C2×C4C2×H(5,𝔽2)14yes—
876C2×C4C2×H(5,𝔽2)12yes—
877C2×C4#58514yes—
878C2×C4#58512yes—
879C22—28no—
880C22—216no—
881C22—24no—
882C22—22no—
883C22—24no—
884C22—28no—
885C22—42no—
886C22—41no—
887C22—44no—
888C22—44no—
889C22—42no—
890C22—41no—
891C22—44no—
892C22—42no—
893C22—48no—
894C22—168no—
895C22C24×Q811yescharacteristic
896C22C22×H(5,𝔽2)11yescharacteristic
897C22C2×#58512yes—
898C22C2×#58511yescharacteristic
899C22H(7,𝔽2)12yes—
900C4—28no—
901C4—22no—
902C4—24no—
903C4—24no—
904C4—24no—
905C4—44no—
906C4—42no—
907C4—44no—
908C4—42no—
909C4—42no—
910C4—44no—
911C4—48no—
912C4—42no—
913C4—44no—
914C4—44no—
915C4—48no—
916C4#350114yes—
917C2—44no—
918C2—48no—
919C2—42no—
920C2C2×#350111yescharacteristic
921C2#6291012yes—
922C2#6298912yes—
923C2#6303511yescharacteristic
924C2#6304511yescharacteristic
subgroupG/H
center, commutator, Frattini, socle, cosocleC23C26
prime radicalC2×#535C22
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23 ◁ G
LECSG ▷ C23 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #59928C2semidirect
2. #59771C2semidirect
3. #59326C2semidirect
4. #52291C2semidirect
5. #51794C2semidirect
6. #47958C2semidirect
7. #47814C2semidirect
8. #46004C2semidirect
9. #45361C2semidirect
10. #44879C2semidirect
11. #43550C2semidirect
12. #42981C2semidirect
13. #39628C2semidirect
14. #39495C2semidirect
15. #37306C2semidirect
16. #36288C2semidirect
17. #35702C2semidirect
18. #35620C2semidirect
22. C2×#544C22semidirect
26. #2862C22semidirect
28. #2844C22semidirect
29. #2811C22semidirect
30. #2811C22semidirect
31. #2809C22semidirect
32. #2809C22semidirect
33. #2809C22semidirect
36. #2804C22semidirect
37. #2804C22semidirect
38. #2790C22semidirect
41. #2784C22semidirect
42. #2784C22semidirect
44. #2780C22semidirect
45. #2780C22semidirect
46. #2768C22semidirect
47. #2763C22semidirect
48. #2763C22semidirect
52. #2732C22semidirect
53. #2732C22semidirect
54. #2729C22semidirect
55. #2704C22semidirect
57. #2683C22semidirect
58. #2683C22semidirect
59. #2647C22semidirect
63. #2612C22semidirect
64. #2612C22semidirect
65. #2589C22semidirect
66. #2587C22semidirect
67. #2584C22semidirect
70. #2580C22semidirect
72. #2574C22semidirect
73. #2568C22semidirect
76. #2565C22semidirect
78. #2564C22semidirect
81. #2556C22semidirect
82. #2551C22semidirect
83. #2550C22semidirect
84. #2546C22semidirect
85. #2509C22semidirect
86. #2509C22semidirect
87. #2508C22semidirect
88. #2505C22semidirect
89. #2505C22semidirect
91. #2492C22semidirect
95. #2452C22semidirect
96. #2452C22semidirect
99. #2450C22semidirect
100. #2450C22semidirect
101. #2450C22semidirect
102. #2450C22semidirect
103. #2450C22semidirect
105. #2442C22semidirect
106. #2440C22semidirect
108. #2439C22semidirect
109. #2439C22semidirect
112. #2434C22semidirect
114. #2423C22semidirect
116. #2409C22semidirect
118. #2396C22semidirect
123. #2369C22semidirect
124. #2368C22semidirect
125. #2365C22semidirect
132. #2355C22semidirect
135. #2349C22semidirect
144. #2317C22semidirect
150. C4×C22⋊Q8C22semidirect
154. #2296C22semidirect
155. #2295C22semidirect
157. C2×#382C22semidirect
164. #535Q8semidirect
429. C2×#41C2×Q8semidirect
463. #127C2×Q8semidirect
466. #124C2×Q8semidirect
476. #121C2×Q8semidirect
477. #120C2×Q8semidirect
498. #117C2×Q8semidirect

Maximal subgroups

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

subgroupindex
#599282
#597712
#593262
#522912
#517942
#479582
#478142
#460042
#453612
#448792
#435502
#429812
#396282
#394952
#373062
#362882
#357022
#356202
#344152
#342752