Finite Group Databasebeta

← #7687863

Subgroups — #7687863

Order 512.

5411 conjugacy classes of subgroups.

The subgroup lattice has 983 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#59659C211yesmaximal, characteristic, complemented
2#59390C214yesmaximal, complemented
3#59216C214yesmaximal, complemented
4#59211C212yesmaximal, complemented
5#59201C214yesmaximal, complemented
6#43791C214yesmaximal, complemented
7#43066C218yesmaximal, complemented
8#40173C214yesmaximal, complemented
9#39885C214yesmaximal, complemented
10#39529C214yesmaximal, complemented
11#36464C212yesmaximal, complemented
12#36456C212yesmaximal, complemented
13#36209C211yesmaximal, characteristic, complemented
14#36203C214yesmaximal, complemented
15#36160C212yesmaximal, complemented
16#35754C214yesmaximal, complemented
17#34943C211yesmaximal, characteristic, complemented
18#34935C212yesmaximal, complemented
19#34223C214yesmaximal, complemented
20C4×#546C212yesmaximal, complemented
21C2×Q82C2211yescharacteristic, complemented
22C2×#555C2211yescharacteristic
23C2×#546C2212yes—
24C2×#525C2214yes—
25C2×C4×#41C2212yes—
26C22×C4×D4C2212yescomplemented
27#2859C2211yescharacteristic, complemented
28#2857C2212yescomplemented
29#2857C2214yescomplemented
30#2854C2214yescomplemented
31#2847C2214yes—
32#2779C2218yescomplemented
33#2757C2218yescomplemented
34#2753C2218yescomplemented
35#2739C2218yescomplemented
36#2736C2218yescomplemented
37#2731C2214yescomplemented
38#2728C2214yescomplemented
39#2701C2218yes—
40#2697C2218yes—
41#2696C2218yescomplemented
42#2679C2214yes—
43#2678C2218yes—
44#2631C2214yes—
45#2630C2218yescomplemented
46#2606C2214yescomplemented
47#2602C2218yescomplemented
48#2593C2214yescomplemented
49#2572C2214yes—
50#2572C2214yescomplemented
51#2572C2218yescomplemented
52#2571C2211yescharacteristic, complemented
53#2570C2214yescomplemented
54#2563C2212yescomplemented
55#2563C2214yescomplemented
56#2558C2218yescomplemented
57#2545C2214yescomplemented
58#2538C2212yescomplemented
59#2538C2214yescomplemented
60#2538C2212yescomplemented
61#2537C2212yes—
62#2537C2211yescharacteristic
63#2536C2212yes—
64#2536C2214yescomplemented
65#2536C2214yescomplemented
66#2535C2214yes—
67#2534C2218yescomplemented
68#2534C2218yescomplemented
69#2526C2218yescomplemented
70#2525C2218yescomplemented
71#2525C2218yescomplemented
72#2523C2218yescomplemented
73#2518C2218yescomplemented
74#2518C2218yescomplemented
75#2518C2218yescomplemented
76#2515C2218yescomplemented
77#2515C2218yescomplemented
78#2513C2214yescomplemented
79#2508C2214yescomplemented
80#2500C2214yes—
81#2497C2214yescomplemented
82#2495C2214yescomplemented
83#2495C2214yescomplemented
84#2495C2214yescomplemented
85#2495C2214yescomplemented
86#2491C2214yescomplemented
87#2489C2214yescomplemented
88#2488C2218yescomplemented
89#2486C2214yescomplemented
90#2485C2214yes—
91#2485C2214yescomplemented
92#2485C2214yescomplemented
93#2472C2218yescomplemented
94#2472C2218yescomplemented
95#2459C2218yescomplemented
96#2452C2218yescomplemented
97#2452C2214yescomplemented
98#2439C2214yescomplemented
99#2439C2218yescomplemented
100#2439C2214yescomplemented
101#2426C2214yescomplemented
102#2426C2214yescomplemented
103#2422C2214yescomplemented
104#2420C2214yescomplemented
105#2420C2214yescomplemented
106#2414C2214yes—
107#2408C2214yescomplemented
108#2408C2214yescomplemented
109#2398C2214yescomplemented
110#2392C2218yescomplemented
111#2374C2218yescomplemented
112#2374C2218yescomplemented
113#2372C2214yescomplemented
114#2367C2212yescomplemented
115#2364C2214yes—
116#2363C2212yes—
117#2363C2214yescomplemented
118#2363C2214yescomplemented
119#2362C2214yescomplemented
120#2362C2214yescomplemented
121#2360C2212yescomplemented
122#2359C2214yescomplemented
123#2358C2214yes—
124#2357C2218yescomplemented
125#2356C2212yescomplemented
126#2354C2212yescomplemented
127#2353C2218yescomplemented
128#2352C2212yes—
129#2352C2214yescomplemented
130#2351C2214yescomplemented
131Q8×C4⋊C4C2212yescomplemented
132#2349C2212yescomplemented
133#2347C2214yescomplemented
134#2347C2214yescomplemented
135#2346C2214yescomplemented
136#2342C2214yescomplemented
137#2341C2214yes—
138#2339C2212yes—
139D4×C22⋊C4C2212yescomplemented
140#2321C2218yescomplemented
141#2321C2218yescomplemented
142#2318C2218yescomplemented
143C4×C4⋊Q8C2211yescharacteristic, complemented
144C4×#124C2212yescomplemented
145C4×C22⋊Q8C2212yescomplemented
146C4×C22⋊Q8C2214yescomplemented
147C4×C22⋊Q8C2214yescomplemented
148C4×#123C2214yescomplemented
149C4×#121C2212yes—
150C4×#121C2214yes—
151C4×#121C2214yescomplemented
152C4×#121C2214yescomplemented
153C4×#121C2214yescomplemented
154C4×#120C2214yes—
155#2285C2212yescomplemented
156#2283C2214yescomplemented
157#2280C2214yescomplemented
158#2280C2214yescomplemented
159#2275C2214yescomplemented
160C42×D4C2211yescharacteristic
161C42×D4C2212yescomplemented
162C2×C4×C22⋊C4C2214yescomplemented
163C22×#41C2312yes—
164C23×D4C2312yes—
165C24×C4C2314yes—
166Q82—44no—
167#555—44no—
168#546—216no—
169C2×C4⋊Q8C2311yescharacteristic
170C2×C4⋊Q8C2314yes—
171C2×C4⋊Q8C2314yes—
172C2×#125C2312yes—
173C2×#124C2312yes—
174C2×#124C2314yes—
175C2×#124C2314yes—
176#525—232no—
177C2×#123C2314yes—
178C2×#123C2318yes—
179C2×#123C2318yes—
180C2×C22⋊Q8C2312yes—
181C2×C22⋊Q8C2314yes—
182C2×C22⋊Q8C2314yes—
183C2×C22⋊Q8C2318yes—
184C2×C22⋊Q8C2314yes—
185C2×#121C2312yes—
186C2×#121C2314yes—
187C2×#121C2314yes—
188C2×#121C2314yes—
189C2×#121C2314yes—
190C2×#121C2314yes—
191C2×#120C2318yes—
192C2×#120C2314yes—
193C2×#120C2318yes—
194C4×#41—48no—
195C2×C4×Q8C2312yes—
196C2×C4×Q8C2312yes—
197C2×C4×Q8C2314yes—
198C2×C4×Q8C2314yes—
199C2×C4×Q8C2312yes—
200C2×C4×D4—48no—
201C2×C4×D4C2312yes—
202C2×C4×D4C2318yes—
203C2×C4×D4C2318yes—
204C2×C4×D4C2312yes—
205C2×C4×D4C2312yes—
206C2×C4×D4C2312yes—
207C2×C4×D4C2314yes—
208C2×C4×D4C2314yes—
209C2×C4×D4C2312yes—
210C2×C4×D4C2312yes—
211C2×C4×D4C2312yes—
212C2×C4×D4C2314yes—
213C2×C4×D4C2311yescharacteristic
214C2×C4×D4C2314yes—
215C2×C4×D4C2314yes—
216C2×C4×D4C2312yes—
217C2×C4×D4C2314yes—
218C2×#117C2314yes—
219C2×#117C2314yes—
220C2×#117C2314yes—
221C2×#117C2312yes—
222C2×#117C2314yes—
223C22×C4⋊C4C2312yes—
224C22×C22⋊C4C2314yes—
225C22×C22⋊C4C2314yes—
226C22×C22⋊C4C2314yes—
227C22×C42C2312yes—
228C22×C42C2314yes—
229C22×C42C2314yes—
230#400C2318yes—
231#400C2314yes—
232#400C2314yes—
233#400C2318yes—
234#400C2318yes—
235#398C2318yes—
236#398C2314yes—
237#398C2318yes—
238#397C2318yes—
239#397C2318yes—
240#397C2318yes—
241#397C2318yes—
242#397C2318yes—
243#397C2318yes—
244#397C2318yes—
245#396C2318yes—
246#396C2318yes—
247#396C2318yes—
248#396C2318yes—
249#396C2318yes—
250#396C2318yes—
251#394C2314yes—
252#394C2314yes—
253#394C2318yes—
254#394C2318yes—
255#394C2318yes—
256#394C2318yes—
257#394C2314yes—
258#394C2318yes—
259#394C2318yes—
260#394C2318yes—
261#394C2318yes—
262#393C2318yes—
263#393C2318yes—
264#393C2318yes—
265#393C2318yes—
266#392C2318yes—
267#392C2318yes—
268#391C2312yes—
269#391C2314yes—
270#391C2318yes—
271#391C2312yes—
272#391C2312yes—
273#391C2314yes—
274#390C2318yes—
275#390C2314yes—
276#390C2318yes—
277#390C2318yes—
278#390C2318yes—
279#390C2314yes—
280#390C2312yes—
281#390C2312yes—
282#390C2314yes—
283#390C2314yes—
284#390C2314yes—
285#390C2314yes—
286#389C2314yes—
287#389C2312yes—
288#389C2314yes—
289#389C2314yes—
290#389C2314yes—
291#389C2314yes—
292#389C2314yes—
293#389C2312yes—
294#389C2314yes—
295#389C2318yes—
296#389C2318yes—
297#389C2314yes—
298#389C2314yes—
299#389C2318yes—
300#389C2314yes—
301#388C2318yes—
302#388C2318yes—
303#388C2318yes—
304#388C2318yes—
305#388C2318yes—
306#388C2318yes—
307#388C2318yes—
308#388C2318yes—
309#388C2318yes—
310#388C2318yes—
311#388C2318yes—
312#388C2318yes—
313#388C2314yes—
314#388C2318yes—
315#388C2318yes—
316#388C2314yes—
317#388C2314yes—
318#388C2314yes—
319#388C2314yes—
320#388C2318yes—
321#388C2318yes—
322#388C2314yes—
323#388C2318yes—
324#388C2318yes—
325#388C2318yes—
326#388C2314yes—
327#388C2318yes—
328#387C2318yes—
329#387C2318yes—
330#387C2318yes—
331#387C2318yes—
332#387C2318yes—
333#387C2318yes—
334#387C2314yes—
335#387C2318yes—
336#387C2314yes—
337#387C2314yes—
338#386C2314yes—
339#386C2314yes—
340#386C2318yes—
341#386C2318yes—
342#386C2318yes—
343#386C2314yes—
344#386C2314yes—
345#386C2318yes—
346#386C2318yes—
347#386C2318yes—
348#386C2314yes—
349#386C2314yes—
350#386C2314yes—
351#386C2318yes—
352#385C2318yes—
353#385C2318yes—
354#385C2314yes—
355#385C2314yes—
356#385C2314yes—
357#385C2314yes—
358#385C2314yes—
359#384C2311yescharacteristic
360#384C2314yes—
361#384C2312yes—
362#383C2318yes—
363#383C2318yes—
364#383C2318yes—
365#383C2314yes—
366#382C2314yes—
367#382C2318yes—
368#382C2314yes—
369#382C2314yes—
370#382C2318yes—
371#382C2312yes—
372#382C2312yes—
373#381C2318yes—
374#381C2318yes—
375#381C2318yes—
376#381C2314yes—
377#380C2312yes—
378#380C2314yes—
379#380C2314yes—
380#380C2314yes—
381#380C2314yes—
382#380C2318yes—
383#380C2314yes—
384#380C2314yes—
385#380C2312yes—
386#380C2314yes—
387#380C2314yes—
388#380C2314yes—
389#380C2314yes—
390#380C2314yes—
391#380C2314yes—
392#380C2314yes—
393#379C2318yes—
394#379C2314yes—
395#379C2318yes—
396C4×C4⋊C4C2314yes—
397C4×C4⋊C4C2312yes—
398C4×C4⋊C4C2314yes—
399C4×C4⋊C4C2314yes—
400C4×C4⋊C4C2314yes—
401C4×C4⋊C4C2318yes—
402C4×C4⋊C4C2314yes—
403C4×C4⋊C4C2312yes—
404C4×C4⋊C4C2318yes—
405C4×C4⋊C4C2318yes—
406C4×C4⋊C4C2312yes—
407C4×C4⋊C4C2314yes—
408C4×C4⋊C4C2311yescharacteristic
409C4×C4⋊C4C2314yes—
410C4×C4⋊C4C2312yes—
411C4×C22⋊C4C2318yes—
412C4×C22⋊C4C2314yes—
413C4×C22⋊C4C2314yes—
414C4×C22⋊C4C2318yes—
415C4×C22⋊C4C2318yes—
416C4×C22⋊C4C2318yes—
417C4×C22⋊C4C2318yes—
418C4×C22⋊C4C2312yes—
419C4×C22⋊C4C2312yes—
420C4×C22⋊C4C2314yes—
421C4×C22⋊C4C2312yes—
422C4×C22⋊C4C2314yes—
423C4×C22⋊C4C2314yes—
424C4×C22⋊C4C2318yes—
425C4×C22⋊C4C2318yes—
426C4×C22⋊C4C2314yes—
427C4×C22⋊C4C2314yes—
428C4×C22⋊C4C2314yes—
429C4×C22⋊C4C2314yes—
430C4×C22⋊C4C2314yes—
431C4×C22⋊C4C2314yes—
432#376C2314yes—
433#376C2314yes—
434C2×#95C2314yes—
435C2×#95C2314yes—
436C43C2311yescharacteristic
437C25C2414yes—
438C2×#41—44no—
439C2×#41—44no—
440C2×#41#41116yescomplemented
441C22×Q8C2412yes—
442C22×Q8C2412yes—
443C22×Q8C2414yes—
444C22×D4—28no—
445C22×D4—44no—
446C22×D4—44no—
447C22×D4C2412yes—
448C22×D4C2411yescharacteristic
449C22×D4C2414yes—
450C22×D4C2412yes—
451C22×D4C2414yes—
452C22×D4C2414yes—
453C22×D4C2418yes—
454C22×D4C2414yes—
455C22×D4C2414yes—
456C23×C4—216no—
457C23×C4—48no—
458C23×C4—48no—
459C23×C4C2412yes—
460C23×C4C2414yes—
461C23×C4C2414yes—
462C23×C4C2412yes—
463C23×C4C2412yes—
464C23×C4C2414yes—
465C23×C4C2414yes—
466C23×C4C2414yes—
467C23×C4C2414yes—
468C23×C4C2414yes—
469C23×C4C2414yes—
470C23×C4C2414yes—
471C4⋊Q8—24no—
472C4⋊Q8—48no—
473C4⋊Q8—48no—
474#125—82no—
475#124—28no—
476#124—48no—
477#124—48no—
478#123—232no—
479#123—216no—
480#123—88no—
481C22⋊Q8—216no—
482C22⋊Q8—216no—
483C22⋊Q8—28no—
484C22⋊Q8—84no—
485C22⋊Q8—88no—
486#121—216no—
487#121—216no—
488#121—216no—
489#121—28no—
490#121—48no—
491#121—48no—
492#120—232no—
493#120—216no—
494#120—88no—
495C4×Q8—28no—
496C4×Q8—44no—
497C4×Q8—48no—
498C4×Q8—44no—
499C4×Q8—48no—
500C4×D4—28no—
501C4×D4—232no—
502C4×D4—232no—
503C4×D4—28no—
504C4×D4—28no—
505C4×D4—28no—
506C4×D4—48no—
507C4×D4—42no—
508C4×D4—44no—
509C4×D4—44no—
510C4×D4—44no—
511C4×D4—44no—
512C4×D4—48no—
513C4×D4—48no—
514C4×D4—48no—
515C4×D4—48no—
516C4×D4—48no—
517#117—216no—
518#117—48no—
519#117—48no—
520#117—44no—
521#117—48no—
522C2×C4⋊C4—44no—
523C2×C4⋊C4C2412yes—
524C2×C4⋊C4C2412yes—
525C2×C4⋊C4C2412yes—
526C2×C4⋊C4C2412yes—
527C2×C4⋊C4C2414yes—
528C2×C4⋊C4C2414yes—
529C2×C4⋊C4C2414yes—
530C2×C4⋊C4C2414yes—
531C2×C4⋊C4C2414yes—
532C2×C4⋊C4C2412yes—
533C2×C4⋊C4C2418yes—
534C2×C4⋊C4C2418yes—
535C2×C4⋊C4C2412yes—
536C2×C4⋊C4C2414yes—
537C2×C4⋊C4C2414yes—
538C2×C4⋊C4C2414yes—
539C2×C4⋊C4C2411yescharacteristic
540C2×C4⋊C4C2414yes—
541C2×C4⋊C4C2414yes—
542C2×C4⋊C4C2418yes—
543C2×C4⋊C4C2412yes—
544C2×C4⋊C4C2418yes—
545C2×C4⋊C4C2414yes—
546C2×C4⋊C4C2414yes—
547C2×C4⋊C4C2418yes—
548C2×C4⋊C4C2418yes—
549C2×C4⋊C4C2414yes—
550C2×C4⋊C4C2418yes—
551C2×C22⋊C4—216no—
552C2×C22⋊C4—48no—
553C2×C22⋊C4—48no—
554C2×C22⋊C4C2412yes—
555C2×C22⋊C4C2412yes—
556C2×C22⋊C4C2414yes—
557C2×C22⋊C4C2414yes—
558C2×C22⋊C4C2414yes—
559C2×C22⋊C4C2414yes—
560C2×C22⋊C4C2414yes—
561C2×C22⋊C4C2414yes—
562C2×C22⋊C4C2418yes—
563C2×C22⋊C4C2418yes—
564C2×C22⋊C4C2418yes—
565C2×C22⋊C4C2414yes—
566C2×C22⋊C4C2412yes—
567C2×C22⋊C4C2418yes—
568C2×C22⋊C4C2418yes—
569C2×C22⋊C4C2414yes—
570C2×C22⋊C4C2414yes—
571C2×C22⋊C4C2414yes—
572C2×C22⋊C4C2414yes—
573C2×C22⋊C4C2414yes—
574C2×C22⋊C4C2414yes—
575C2×C22⋊C4C2414yes—
576C2×C22⋊C4C2418yes—
577C2×C22⋊C4C2418yes—
578C2×C22⋊C4C2414yes—
579C2×C22⋊C4C2418yes—
580C2×C22⋊C4C2414yes—
581C2×C22⋊C4C2414yes—
582C2×C22⋊C4C2418yes—
583C2×C22⋊C4C2418yes—
584C2×C22⋊C4C2418yes—
585C2×C22⋊C4C2418yes—
586C2×C22⋊C4C2418yes—
587C2×C22⋊C4C2414yes—
588C2×C22⋊C4C2418yes—
589C2×C42—28no—
590C2×C42—48no—
591C2×C42—48no—
592C2×C42C2412yes—
593C2×C42C2418yes—
594C2×C42C2412yes—
595C2×C42C2412yes—
596C2×C42C2412yes—
597C2×C42C2414yes—
598C2×C42C2411yescharacteristic
599C2×C42C2414yes—
600C2×C42C2414yes—
601C2×C42C2412yes—
602C2×C42C2414yes—
603C2×C42C2414yes—
604C2×C42C2418yes—
605C2×C42C2414yes—
606C2×C42C2414yes—
607C2×C42C2418yes—
608C2×C42C2411yescharacteristic
609C2×C42C2414yes—
610C2×C42C2414yes—
611C2×C42C2411yescharacteristic
612#95C2411yescharacteristic
613#95C2412yes—
614#95C2414yes—
615#95C2414yes—
616#95C2414yes—
617#95C2414yes—
618#95C2414yes—
619#95C2414yes—
620#95C2414yes—
621#95C2418yes—
622#95C2414yes—
623#95C2418yes—
624#95C2414yes—
625#95C2418yes—
626#95C2412yes—
627#95C2418yes—
628#95C2414yes—
629#95C2411yescharacteristic
630#95C2414yes—
631#95C2414yes—
632#95C2414yes—
633#95C2418yes—
634#95C2418yes—
635#95C2414yes—
636#95C2418yes—
637#95C2414yes—
638#95C2414yes—
639#95C2418yes—
640#95C2418yes—
641#95C2418yes—
642#95C2418yes—
643#95C2418yes—
644#95C2418yes—
645#95C2414yes—
646C24—28no—
647C24—28no—
648C24—44no—
649C24—44no—
650C24—44no—
651C24—44no—
652C24—44no—
653C24C2514yes—
654C24C2512yes—
655C24C2514yes—
656#41—432no—
657C2×Q8—24no—
658C2×Q8—24no—
659C2×Q8—24no—
660C2×Q8—42no—
661C2×Q8—42no—
662C2×Q8—44no—
663C2×Q8—44no—
664C2×Q8—44no—
665C2×Q8C2×#4118yes—
666C2×D4—24no—
667C2×D4—216no—
668C2×D4—28no—
669C2×D4—216no—
670C2×D4—28no—
671C2×D4—24no—
672C2×D4—24no—
673C2×D4—24no—
674C2×D4—24no—
675C2×D4—24no—
676C2×D4—44no—
677C2×D4—44no—
678C2×D4—44no—
679C2×D4—41no—
680C2×D4—44no—
681C2×D4—44no—
682C2×D4—44no—
683C2×D4—44no—
684C2×D4—48no—
685C2×D4—48no—
686C2×D4—44no—
687C2×D4—44no—
688C2×D4—44no—
689C2×D4—432no—
690C2×D4C2×#4118yes—
691C2×D4C2×#41116yes—
692C22×C4—24no—
693C22×C4—24no—
694C22×C4—28no—
695C22×C4—28no—
696C22×C4—24no—
697C22×C4—28no—
698C22×C4—28no—
699C22×C4—24no—
700C22×C4—28no—
701C22×C4—28no—
702C22×C4—28no—
703C22×C4—28no—
704C22×C4—24no—
705C22×C4—28no—
706C22×C4—28no—
707C22×C4—24no—
708C22×C4—28no—
709C22×C4—44no—
710C22×C4—44no—
711C22×C4—44no—
712C22×C4—44no—
713C22×C4—44no—
714C22×C4—44no—
715C22×C4—44no—
716C22×C4—44no—
717C22×C4—44no—
718C22×C4—44no—
719C22×C4—42no—
720C22×C4—42no—
721C22×C4—44no—
722C22×C4—44no—
723C22×C4—44no—
724C22×C4—44no—
725C22×C4—44no—
726C22×C4—832no—
727C22×C4C2×#4118yes—
728C22×C4C2×#41116yes—
729C22×C4C2514yes—
730C22×C4C2512yes—
731C22×C4C2514yes—
732C22×C4C2514yes—
733C22×C4C2511yescharacteristic
734C22×C4C2514yes—
735C22×C4C2514yes—
736C22×C4C2512yes—
737C22×C4C2512yes—
738C22×C4C2518yes—
739C22×C4C2514yes—
740C22×C4C2514yes—
741C22×C4C2512yes—
742C22×C4C2514yes—
743C22×C4C2511yescharacteristic
744C22×C4C2511yescharacteristic
745C22×C4C2512yes—
746C4⋊C4—28no—
747C4⋊C4—28no—
748C4⋊C4—24no—
749C4⋊C4—216no—
750C4⋊C4—216no—
751C4⋊C4—24no—
752C4⋊C4—28no—
753C4⋊C4—24no—
754C4⋊C4—24no—
755C4⋊C4—28no—
756C4⋊C4—24no—
757C4⋊C4—28no—
758C4⋊C4—24no—
759C4⋊C4—28no—
760C4⋊C4—44no—
761C4⋊C4—44no—
762C4⋊C4—44no—
763C4⋊C4—44no—
764C4⋊C4—41no—
765C4⋊C4—42no—
766C4⋊C4—48no—
767C4⋊C4—44no—
768C4⋊C4—48no—
769C4⋊C4—44no—
770C4⋊C4—48no—
771C4⋊C4—48no—
772C4⋊C4—44no—
773C4⋊C4—48no—
774C22⋊C4—216no—
775C22⋊C4—28no—
776C22⋊C4—24no—
777C22⋊C4—216no—
778C22⋊C4—216no—
779C22⋊C4—24no—
780C22⋊C4—28no—
781C22⋊C4—28no—
782C22⋊C4—28no—
783C22⋊C4—216no—
784C22⋊C4—216no—
785C22⋊C4—28no—
786C22⋊C4—28no—
787C22⋊C4—28no—
788C22⋊C4—24no—
789C22⋊C4—28no—
790C22⋊C4—44no—
791C22⋊C4—44no—
792C22⋊C4—44no—
793C22⋊C4—44no—
794C22⋊C4—48no—
795C22⋊C4—44no—
796C22⋊C4—44no—
797C22⋊C4—48no—
798C22⋊C4—44no—
799C22⋊C4—44no—
800C22⋊C4—44no—
801C22⋊C4—48no—
802C22⋊C4—48no—
803C22⋊C4—48no—
804C22⋊C4—48no—
805C22⋊C4—48no—
806C22⋊C4—48no—
807C22⋊C4—44no—
808C22⋊C4—48no—
809C42—216no—
810C42—24no—
811C42—24no—
812C42—24no—
813C42—24no—
814C42—28no—
815C42—24no—
816C42—28no—
817C42—22no—
818C42—28no—
819C42—44no—
820C42—44no—
821C42—44no—
822C42—44no—
823C42—48no—
824C42—44no—
825C42—48no—
826C42—44no—
827C42—41no—
828C42H(5,𝔽2)14yes—
829C23—22no—
830C23—24no—
831C23—24no—
832C23—22no—
833C23—22no—
834C23—24no—
835C23—22no—
836C23—24no—
837C23—24no—
838C23—22no—
839C23—24no—
840C23—22no—
841C23—24no—
842C23—24no—
843C23—24no—
844C23—24no—
845C23—24no—
846C23—24no—
847C23—24no—
848C23—416no—
849C23—416no—
850C23—88no—
851C23—88no—
852C23—88no—
853C23—88no—
854C23—88no—
855C23C22×#4114yes—
856C23C22×#4118yes—
857C23C2611yescharacteristic
858Q8—216no—
859Q8—84no—
860Q8—164no—
861D4—216no—
862D4—416no—
863D4—416no—
864D4—44no—
865D4—416no—
866D4—48no—
867D4—88no—
868D4—816no—
869D4—164no—
870C2×C4—22no—
871C2×C4—24no—
872C2×C4—22no—
873C2×C4—21no—
874C2×C4—24no—
875C2×C4—22no—
876C2×C4—21no—
877C2×C4—216no—
878C2×C4—22no—
879C2×C4—22no—
880C2×C4—28no—
881C2×C4—28no—
882C2×C4—24no—
883C2×C4—24no—
884C2×C4—24no—
885C2×C4—22no—
886C2×C4—22no—
887C2×C4—22no—
888C2×C4—24no—
889C2×C4—24no—
890C2×C4—24no—
891C2×C4—24no—
892C2×C4—24no—
893C2×C4—22no—
894C2×C4—24no—
895C2×C4—24no—
896C2×C4—24no—
897C2×C4—21no—
898C2×C4—24no—
899C2×C4—28no—
900C2×C4—24no—
901C2×C4—24no—
902C2×C4—24no—
903C2×C4—22no—
904C2×C4—24no—
905C2×C4—22no—
906C2×C4—22no—
907C2×C4—24no—
908C2×C4—24no—
909C2×C4—28no—
910C2×C4—24no—
911C2×C4—22no—
912C2×C4—416no—
913C2×C4—416no—
914C2×C4—416no—
915C2×C4—48no—
916C2×C4—88no—
917C2×C4—84no—
918C2×C4—88no—
919C2×C4—88no—
920C2×C4—88no—
921C2×C4—88no—
922C2×C4—88no—
923C2×C4C22×#4114yes—
924C2×C4C22×#4118yes—
925C2×C4C22×#4114yes—
926C2×C4C2×H(5,𝔽2)12yes—
927C2×C4C2×H(5,𝔽2)14yes—
928C2×C4#58512yes—
929C2×C4#58514yes—
930C22—28no—
931C22—24no—
932C22—24no—
933C22—28no—
934C22—28no—
935C22—24no—
936C22—44no—
937C22—42no—
938C22—44no—
939C22—42no—
940C22—44no—
941C22—42no—
942C22—44no—
943C22—42no—
944C22—44no—
945C22—44no—
946C22—44no—
947C22—44no—
948C22—44no—
949C22—44no—
950C22—44no—
951C22—832no—
952C22C23×#4112yes—
953C22C22×H(5,𝔽2)11yescharacteristic
954C22C2×#58512yes—
955C22C2×#58511yescharacteristic
956C22H(7,𝔽2)11yescharacteristic
957C4—24no—
958C4—28no—
959C4—22no—
960C4—22no—
961C4—42no—
962C4—44no—
963C4—48no—
964C4—44no—
965C4—44no—
966C4—42no—
967C4—44no—
968C4—42no—
969C4—44no—
970C4—44no—
971C4—41no—
972C4—44no—
973C4#350518yes—
974C2—48no—
975C2—44no—
976C2—84no—
977C2#41211yescharacteristic
978C2C2×#350512yes—
979C2#6293011yescharacteristic
980C2#6299412yes—
981C2#6302811yescharacteristic
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. #59659C2semidirect
2. #59390C2semidirect
3. #59216C2semidirect
4. #59211C2semidirect
5. #59201C2semidirect
6. #43791C2semidirect
7. #43066C2semidirect
8. #40173C2semidirect
9. #39885C2semidirect
10. #39529C2semidirect
11. #36464C2semidirect
12. #36456C2semidirect
13. #36209C2semidirect
14. #36203C2semidirect
15. #36160C2semidirect
16. #35754C2semidirect
17. #34943C2semidirect
18. #34935C2semidirect
19. #34223C2semidirect
20. C4×#546C2semidirect
21. C2×Q82C22semidirect
26. C22×C4×D4C22semidirect
27. #2859C22semidirect
28. #2857C22semidirect
29. #2857C22semidirect
30. #2854C22semidirect
32. #2779C22semidirect
33. #2757C22semidirect
34. #2753C22semidirect
35. #2739C22semidirect
36. #2736C22semidirect
37. #2731C22semidirect
38. #2728C22semidirect
41. #2696C22semidirect
45. #2630C22semidirect
46. #2606C22semidirect
47. #2602C22semidirect
48. #2593C22semidirect
50. #2572C22semidirect
51. #2572C22semidirect
52. #2571C22semidirect
53. #2570C22semidirect
54. #2563C22semidirect
55. #2563C22semidirect
56. #2558C22semidirect
57. #2545C22semidirect
58. #2538C22semidirect
59. #2538C22semidirect
60. #2538C22semidirect
64. #2536C22semidirect
65. #2536C22semidirect
67. #2534C22semidirect
68. #2534C22semidirect
69. #2526C22semidirect
70. #2525C22semidirect
71. #2525C22semidirect
72. #2523C22semidirect
73. #2518C22semidirect
74. #2518C22semidirect
75. #2518C22semidirect
76. #2515C22semidirect
77. #2515C22semidirect
78. #2513C22semidirect
79. #2508C22semidirect
81. #2497C22semidirect
82. #2495C22semidirect
83. #2495C22semidirect
84. #2495C22semidirect
85. #2495C22semidirect
86. #2491C22semidirect
87. #2489C22semidirect
88. #2488C22semidirect
89. #2486C22semidirect
91. #2485C22semidirect
92. #2485C22semidirect
93. #2472C22semidirect
94. #2472C22semidirect
95. #2459C22semidirect
96. #2452C22semidirect
97. #2452C22semidirect
98. #2439C22semidirect
99. #2439C22semidirect
100. #2439C22semidirect
101. #2426C22semidirect
102. #2426C22semidirect
103. #2422C22semidirect
104. #2420C22semidirect
105. #2420C22semidirect
107. #2408C22semidirect
108. #2408C22semidirect
109. #2398C22semidirect
110. #2392C22semidirect
111. #2374C22semidirect
112. #2374C22semidirect
113. #2372C22semidirect
114. #2367C22semidirect
117. #2363C22semidirect
118. #2363C22semidirect
119. #2362C22semidirect
120. #2362C22semidirect
121. #2360C22semidirect
122. #2359C22semidirect
124. #2357C22semidirect
125. #2356C22semidirect
126. #2354C22semidirect
127. #2353C22semidirect
129. #2352C22semidirect
130. #2351C22semidirect
131. Q8×C4⋊C4C22semidirect
132. #2349C22semidirect
133. #2347C22semidirect
134. #2347C22semidirect
135. #2346C22semidirect
136. #2342C22semidirect
139. D4×C22⋊C4C22semidirect
140. #2321C22semidirect
141. #2321C22semidirect
142. #2318C22semidirect
143. C4×C4⋊Q8C22semidirect
144. C4×#124C22semidirect
145. C4×C22⋊Q8C22semidirect
146. C4×C22⋊Q8C22semidirect
147. C4×C22⋊Q8C22semidirect
148. C4×#123C22semidirect
151. C4×#121C22semidirect
152. C4×#121C22semidirect
153. C4×#121C22semidirect
155. #2285C22semidirect
156. #2283C22semidirect
157. #2280C22semidirect
158. #2280C22semidirect
159. #2275C22semidirect
161. C42×D4C22semidirect
162. C2×C4×C22⋊C4C22semidirect
440. C2×#41#41semidirect

Maximal subgroups

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

subgroupindex
#596592
#593902
#592162
#592112
#592012
#437912
#430662
#401732
#398852
#395292
#364642
#364562
#362092
#362032
#361602
#357542
#349432
#349352
#342232
C4×#5462