Subgroups — #46780915

Order 33664.

94 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#30682317	C₂	1	1	yes	maximal, characteristic
2	#30681737	C₂	1	1	yes	maximal, characteristic
3	#356×C₂₆₃	C₂	1	1	yes	maximal, characteristic
4	C₂×#16862366	—	2	1	no	—
5	C₂×#16862366	—	2	1	no	—
6	#22554470	C₄	1	1	yes	characteristic
7	#22554389	—	2	1	no	—
8	C₄×C₂₆₃⋊C₈	C₄	1	1	yes	characteristic
9	C₄⋊Q₈×C₂₆₃	C₂²	1	1	yes	characteristic
10	#101×C₂₆₃	—	2	1	no	—
11	C₂×Dic₅₂₆	—	2	1	no	—
12	#16862366	—	4	2	no	—
13	#16862366	—	4	2	no	—
14	#16862360	—	4	1	no	—
15	C₂×C₂₆₃⋊C₈	—	2	1	no	—
16	C₄⋊Dic₂₆₃	—	4	1	no	—
17	C₂×Q₈×C₂₆₃	D₄	1	1	yes	characteristic
18	C₂×Q₈×C₂₆₃	D₄	1	1	yes	characteristic
19	M₁₆×C₂₆₃	—	4	1	no	—
20	C₄⋊C₄×C₂₆₃	—	4	1	no	—
21	C₄²×C₂₆₃	C₂×C₄	1	1	yes	characteristic
22	Dic₅₂₆	—	4	1	no	—
23	Dic₅₂₆	—	4	1	no	—
24	C₂×Dic₂₆₃	—	4	1	no	—
25	C₂₆₃⋊C₈	—	2	2	no	—
26	C₂₆₃⋊C₈	—	8	1	no	—
27	Q₈×C₂₆₃	—	4	1	no	—
28	Q₈×C₂₆₃	—	4	1	no	—
29	C₂×C₄×C₂₆₃	—	2	1	no	—
30	C₂×C₄×C₂₆₃	—	2	1	no	—
31	C₂×C₄×C₂₆₃	—	2	1	no	—
32	C₂×C₄×C₂₆₃	C₂²⋊C₄	1	1	yes	characteristic
33	C₈×C₂₆₃	—	8	1	no	—
34	C₂²×C₂₆₃	#99	1	1	yes	characteristic
35	C₄×C₂₆₃	—	2	2	no	—
36	C₄×C₂₆₃	—	2	1	no	—
37	C₄×C₂₆₃	—	4	1	no	—
38	C₄×C₂₆₃	—	4	1	no	—
39	Dic₂₆₃	—	8	1	no	—
40	C₂×C₂₆₃	—	2	1	no	—
41	C₂×C₂₆₃	#353	1	1	yes	characteristic
42	C₂₆₃	#1411	1	1	yes	characteristic, complemented, Sylow
43	#1411	—	263	1	no	maximal, Sylow
44	#494	—	263	1	no	—
45	#356	—	263	1	no	—
46	#356	D₂₆₃	1	1	yes	characteristic
47	C₂×Q₁₆	—	526	1	no	—
48	C₂×Q₁₆	—	526	1	no	—
49	C₄⋊Q₈	—	263	1	no	—
50	C₄⋊Q₈	C₂×D₂₆₃	1	1	yes	characteristic
51	#101	—	2	1	no	—
52	#101	—	526	1	no	—
53	C₄×C₈	—	263	1	no	—
54	C₂×Q₈	—	526	1	no	—
55	C₂×Q₈	C₂²⋊D₂₆₃	1	1	yes	characteristic
56	C₂×Q₈	D₁₀₅₂	1	1	yes	characteristic
57	Q₁₆	—	1052	2	no	—
58	Q₁₆	—	1052	2	no	—
59	M₁₆	—	4	1	no	—
60	M₁₆	—	1052	1	no	—
61	C₂×C₈	—	526	1	no	—
62	C₄⋊C₄	—	4	1	no	—
63	C₄⋊C₄	—	1052	1	no	—
64	C₄²	C₄×D₂₆₃	1	1	yes	characteristic
65	Q₈	—	4	1	no	—
66	Q₈	—	4	1	no	—
67	Q₈	—	1052	1	no	—
68	Q₈	—	1052	1	no	—
69	C₂×C₄	—	2	1	no	—
70	C₂×C₄	—	2	1	no	—
71	C₂×C₄	—	2	1	no	—
72	C₂×C₄	—	1052	1	no	—
73	C₂×C₄	(C₂×D₂₆₃)⋊C₄	1	1	yes	characteristic
74	C₈	—	8	1	no	—
75	C₈	—	526	2	no	—
76	C₈	—	2104	1	no	—
77	C₂²	#22554384	1	1	yes	characteristic
78	C₄	—	2	2	no	—
79	C₄	—	2	1	no	—
80	C₄	—	4	1	no	—
81	C₄	—	4	1	no	—
82	C₄	—	2104	1	no	—
83	C₂	—	2	1	no	—
84	C₂	#30681730	1	1	yes	characteristic

	subgroup	G/H
center	C₂	#30681730
commutator	C₄²×C₂₆₃	C₂×C₄
Frattini	C₄⋊Q₈	C₂×D₂₆₃
Fitting	#356×C₂₆₃	C₂
socle	C₂×C₂₆₃	#353
prime radical	C₂²×C₂₆₃	#99
cosocle	C₄⋊Q₈×C₂₆₃	C₂²
hypercenter	#356	D₂₆₃
hypocenter	C₂₆₃	#1411
LCS	G ▷ C₄²×C₂₆₃ ▷ C₂×C₄×C₂₆₃ ▷ C₂²×C₂₆₃ ▷ C₂×C₂₆₃ ▷ C₂₆₃
UCS	C₁ ◁ C₂ ◁ C₂² ◁ C₂×C₄ ◁ C₄⋊Q₈ ◁ #356

Complements

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

N	H ≅ G/N	type
42. C₂₆₃	#1411	semidirect

Maximal subgroups

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

subgroup	index
#30682317	2
#30681737	2
#356×C₂₆₃	2
#1411	263