Subgroups — C₂₆₃⋊#401 #30681881

Order 16832.

118 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂₆₃⋊#95	C₂	1	3	yes	maximal
2	C₂₆₃⋊#95	C₂	1	3	yes	maximal
3	#95×C₂₆₃	C₂	1	1	yes	maximal, characteristic
4	C₂²×Dic₂₆₃	C₂²	1	3	yes	—
5	C₂²×Dic₂₆₃	C₂²	1	1	yes	characteristic
6	C₂²×C₄×C₂₆₃	C₂²	1	3	yes	—
7	C₂×Dic₂₆₃	—	2	3	no	—
8	C₂×Dic₂₆₃	—	2	3	no	—
9	C₂×Dic₂₆₃	—	2	3	no	—
10	C₂×Dic₂₆₃	—	2	3	no	—
11	C₂³×C₂₆₃	C₂³	1	1	yes	characteristic
12	C₂×C₄×C₂₆₃	—	2	6	no	—
13	C₂×C₄×C₂₆₃	—	2	3	no	—
14	C₂²×C₂₆₃	#41	1	3	yes	—
15	C₂²×C₂₆₃	#41	1	3	yes	—
16	C₂²×C₂₆₃	#41	1	1	yes	characteristic
17	C₄×C₂₆₃	—	4	3	no	—
18	Dic₂₆₃	—	4	1	no	—
19	Dic₂₆₃	—	4	3	no	—
20	C₂×C₂₆₃	#126	1	3	yes	—
21	C₂×C₂₆₃	#126	1	1	yes	characteristic
22	C₂×C₂₆₃	#126	1	3	yes	—
23	C₂₆₃	#401	1	1	yes	characteristic, complemented, Sylow
24	#401	—	263	1	no	maximal, Sylow
25	#95	—	263	3	no	—
26	#95	—	263	3	no	—
27	#95	D₂₆₃	1	1	yes	characteristic
28	C₂²×C₄	—	263	3	no	—
29	C₂²×C₄	—	263	1	no	—
30	C₂²×C₄	C₂×D₂₆₃	1	3	yes	—
31	C₂³	C₂²×D₂₆₃	1	1	yes	characteristic
32	C₂×C₄	—	2	6	no	—
33	C₂×C₄	—	2	3	no	—
34	C₂×C₄	—	526	3	no	—
35	C₂×C₄	—	526	3	no	—
36	C₂×C₄	—	526	3	no	—
37	C₂×C₄	—	526	3	no	—
38	C₂²	#16862375	1	3	yes	—
39	C₂²	#16862376	1	3	yes	—
40	C₂²	#16862377	1	1	yes	characteristic
41	C₄	—	4	3	no	—
42	C₄	—	1052	1	no	—
43	C₄	—	1052	3	no	—
44	C₂	#22554463	1	3	yes	—
45	C₂	#22554464	1	1	yes	characteristic
46	C₂	#22554465	1	3	yes	—

	subgroup	G/H
center, Frattini	C₂³	C₂²×D₂₆₃
commutator, socle, prime radical, cosocle	C₂³×C₂₆₃	C₂³
Fitting	#95×C₂₆₃	C₂
hypercenter	#95	D₂₆₃
hypocenter	C₂₆₃	#401
LCS	G ▷ C₂³×C₂₆₃ ▷ C₂₆₃
UCS	C₁ ◁ C₂³ ◁ #95

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

N	H ≅ G/N	type
23. C₂₆₃	#401	semidirect

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