Subgroups — #46782363

Order 33664.

192 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#30682341	C₂	1	4	yes	maximal
2	#30682318	C₂	1	1	yes	maximal, characteristic
3	C₈×C₂₆₃⋊C₈	C₂	1	1	yes	maximal, characteristic
4	#494×C₂₆₃	C₂	1	1	yes	maximal, characteristic
5	C₂×Dic₁₀₅₂	—	2	2	no	—
6	#22554470	C₂²	1	2	yes	—
7	#22554403	—	2	8	no	—
8	C₄×C₂₆₃⋊C₈	C₂²	1	2	yes	—
9	C₂×Q₁₆×C₂₆₃	—	2	2	no	—
10	C₄⋊Q₈×C₂₆₃	C₂²	1	2	yes	—
11	C₄×C₈×C₂₆₃	C₂²	1	1	yes	characteristic
12	C₂×Dic₅₂₆	—	2	2	no	—
13	Dic₁₀₅₂	—	4	4	no	—
14	C₂×C₂₆₃⋊C₈	D₄	1	4	yes	—
15	C₄⋊Dic₂₆₃	—	2	4	no	—
16	C₂×Q₈×C₂₆₃	—	2	2	no	—
17	Q₁₆×C₂₆₃	—	4	4	no	—
18	C₂×C₈×C₂₆₃	D₄	1	2	yes	—
19	C₄⋊C₄×C₂₆₃	—	2	4	no	—
20	C₄²×C₂₆₃	C₂³	1	1	yes	characteristic
21	Dic₅₂₆	—	4	4	no	—
22	C₂×Dic₂₆₃	—	4	2	no	—
23	C₂₆₃⋊C₈	Q₁₆	1	8	yes	complemented
24	Q₈×C₂₆₃	—	4	4	no	—
25	C₂×C₄×C₂₆₃	—	4	2	no	—
26	C₂×C₄×C₂₆₃	C₂×D₄	1	2	yes	—
27	C₂×C₄×C₂₆₃	C₂×D₄	1	1	yes	characteristic
28	C₈×C₂₆₃	D₈	1	4	yes	—
29	C₂²×C₂₆₃	#127	1	1	yes	characteristic
30	C₄×C₂₆₃	—	8	2	no	—
31	C₄×C₂₆₃	C₂×D₈	1	2	yes	—
32	C₄×C₂₆₃	C₂×Q₁₆	1	4	yes	—
33	Dic₂₆₃	—	8	2	no	—
34	C₂×C₂₆₃	#493	1	1	yes	characteristic
35	C₂×C₂₆₃	#494	1	2	yes	—
36	C₂₆₃	#1713	1	1	yes	characteristic, complemented, Sylow
37	#1713	—	263	1	no	maximal, Sylow
38	#500	—	263	4	no	—
39	#494	—	263	1	no	—
40	#494	D₂₆₃	1	1	yes	characteristic
41	C₈²	—	263	1	no	—
42	C₂×Q₁₆	—	2	2	no	—
43	C₂×Q₁₆	—	526	2	no	—
44	C₄⋊Q₈	—	263	2	no	—
45	C₄⋊Q₈	C₂×D₂₆₃	1	2	yes	—
46	#107	—	526	8	no	—
47	C₄×C₈	—	263	2	no	—
48	C₄×C₈	C₂×D₂₆₃	1	1	yes	characteristic
49	C₂×Q₈	—	2	2	no	—
50	C₂×Q₈	—	526	2	no	—
51	Q₁₆	—	4	4	no	—
52	Q₁₆	—	1052	4	no	—
53	C₂×C₈	—	263	4	no	—
54	C₂×C₈	C₂²⋊D₂₆₃	1	2	yes	—
55	C₄⋊C₄	—	2	4	no	—
56	C₄⋊C₄	—	526	4	no	—
57	C₄²	C₂²×D₂₆₃	1	1	yes	characteristic
58	Q₈	—	4	4	no	—
59	Q₈	—	1052	4	no	—
60	C₂×C₄	—	4	2	no	—
61	C₂×C₄	—	1052	2	no	—
62	C₂×C₄	D₄×D₂₆₃	1	2	yes	—
63	C₂×C₄	C₂×C₂²⋊D₂₆₃	1	1	yes	characteristic
64	C₈	—	263	8	no	—
65	C₈	#16862361	1	4	yes	—
66	C₂²	#22554466	1	1	yes	characteristic
67	C₄	—	8	2	no	—
68	C₄	—	2104	2	no	—
69	C₄	C₂×#16862361	1	2	yes	—
70	C₄	Q₁₆×D₂₆₃	1	4	yes	—
71	C₂	#30682314	1	1	yes	characteristic
72	C₂	#30682316	1	2	yes	—

	subgroup	G/H
center	C₂²	#22554466
commutator, cosocle	C₄²×C₂₆₃	C₂³
Frattini	C₄²	C₂²×D₂₆₃
Fitting	#494×C₂₆₃	C₂
socle, prime radical	C₂²×C₂₆₃	#127
hypercenter	#494	D₂₆₃
hypocenter	C₂₆₃	#1713
LCS	G ▷ C₄²×C₂₆₃ ▷ C₂²×C₂₆₃ ▷ C₂₆₃
UCS	C₁ ◁ C₂² ◁ C₄² ◁ #494

Complements

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

N	H ≅ G/N	type
23. C₂₆₃⋊C₈	Q₁₆	semidirect
36. C₂₆₃	#1713	semidirect

Maximal subgroups

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

subgroup	index
#30682341	2
#30682318	2
C₈×C₂₆₃⋊C₈	2
#494×C₂₆₃	2
#1713	263