Subgroups — #46780801

Order 33664.

86 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#30682343	C₂	1	1	yes	maximal, characteristic
2	#30681691	C₂	1	1	yes	maximal, characteristic
3	C₄⋊C₁₆×C₂₆₃	C₂	1	1	yes	maximal, characteristic
4	#22554470	—	2	1	no	—
5	#22554404	—	2	1	no	—
6	#22554404	C₄	1	2	yes	—
7	C₄⋊(C₂₆₃⋊C₈)	—	2	1	no	—
8	C₂×C₁₆×C₂₆₃	—	2	1	no	—
9	C₄×C₈×C₂₆₃	C₂²	1	1	yes	characteristic
10	C₂×Dic₅₂₆	—	4	1	no	—
11	C₂×C₂₆₃⋊C₈	—	4	1	no	—
12	C₄⋊Dic₂₆₃	—	2	2	no	—
13	C₄⋊Dic₂₆₃	—	4	1	no	—
14	C₂×C₈×C₂₆₃	C₂×C₄	1	1	yes	characteristic
15	C₂×C₈×C₂₆₃	D₄	1	1	yes	characteristic
16	C₄²×C₂₆₃	D₄	1	1	yes	characteristic
17	C₁₆×C₂₆₃	—	4	1	no	—
18	Dic₅₂₆	—	8	1	no	—
19	Dic₅₂₆	—	8	1	no	—
20	C₂×Dic₂₆₃	—	4	2	no	—
21	C₂₆₃⋊C₈	—	8	1	no	—
22	C₂×C₄×C₂₆₃	C₂²⋊C₄	1	1	yes	characteristic
23	C₂×C₄×C₂₆₃	D₈	1	1	yes	characteristic
24	C₂×C₄×C₂₆₃	SD₁₆	1	1	yes	characteristic
25	C₈×C₂₆₃	—	2	1	no	—
26	C₈×C₂₆₃	SD₁₆	1	1	yes	characteristic
27	C₈×C₂₆₃	Q₁₆	1	1	yes	characteristic
28	C₂²×C₂₆₃	#102	1	1	yes	characteristic
29	C₄×C₂₆₃	—	2	1	no	—
30	C₄×C₂₆₃	#101	1	1	yes	characteristic
31	C₄×C₂₆₃	#103	1	1	yes	characteristic
32	C₄×C₂₆₃	D₁₆	1	1	yes	characteristic
33	C₄×C₂₆₃	SD₃₂	1	1	yes	characteristic
34	Dic₂₆₃	—	8	2	no	—
35	C₂×C₂₆₃	#332	1	1	yes	characteristic
36	C₂×C₂₆₃	#357	1	1	yes	characteristic
37	C₂×C₂₆₃	#362	1	1	yes	characteristic
38	C₂₆₃	#1364	1	1	yes	characteristic, complemented, Sylow
39	#1364	—	263	1	no	maximal, Sylow
40	#500	—	263	1	no	—
41	C₄⋊C₁₆	D₂₆₃	1	1	yes	characteristic
42	#335	—	263	1	no	—
43	C₄⋊Q₈	—	526	1	no	—
44	C₂×C₁₆	—	2	1	no	—
45	#107	—	263	2	no	—
46	#107	—	526	1	no	—
47	C₄⋊C₈	—	526	1	no	—
48	C₄×C₈	C₂×D₂₆₃	1	1	yes	characteristic
49	C₂×Q₈	—	1052	1	no	—
50	C₂×C₈	—	1052	1	no	—
51	C₂×C₈	C₄×D₂₆₃	1	1	yes	characteristic
52	C₂×C₈	C₂²⋊D₂₆₃	1	1	yes	characteristic
53	C₄⋊C₄	—	526	2	no	—
54	C₄⋊C₄	—	1052	1	no	—
55	C₄²	D₁₀₅₂	1	1	yes	characteristic
56	C₁₆	—	4	1	no	—
57	Q₈	—	2104	1	no	—
58	Q₈	—	2104	1	no	—
59	C₂×C₄	—	1052	2	no	—
60	C₂×C₄	(C₂×D₂₆₃)⋊C₄	1	1	yes	characteristic
61	C₂×C₄	D₂₁₀₄	1	1	yes	characteristic
62	C₂×C₄	#16862365	1	1	yes	characteristic
63	C₈	—	2	1	no	—
64	C₈	—	2104	1	no	—
65	C₈	#16862364	1	1	yes	characteristic
66	C₈	#16862366	1	1	yes	characteristic
67	C₂²	#22554392	1	1	yes	characteristic
68	C₄	—	2	1	no	—
69	C₄	—	2104	2	no	—
70	C₄	#22554388	1	1	yes	characteristic
71	C₄	#22554393	1	1	yes	characteristic
72	C₄	D₄₂₀₈	1	1	yes	characteristic
73	C₄	#22554415	1	1	yes	characteristic
74	C₂	#30681683	1	1	yes	characteristic
75	C₂	#30681740	1	1	yes	characteristic
76	C₂	#30681755	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	#22554392
commutator	C₂×C₈×C₂₆₃	C₂×C₄
Frattini	C₄×C₈	C₂×D₂₆₃
Fitting	C₄⋊C₁₆×C₂₆₃	C₂
socle, prime radical	C₂²×C₂₆₃	#102
cosocle	C₄×C₈×C₂₆₃	C₂²
hypercenter	C₄⋊C₁₆	D₂₆₃
hypocenter	C₂₆₃	#1364
LCS	G ▷ C₂×C₈×C₂₆₃ ▷ C₂×C₄×C₂₆₃ ▷ C₂×C₂₆₃ ▷ C₂₆₃
UCS	C₁ ◁ C₂² ◁ C₄² ◁ C₄×C₈ ◁ C₄⋊C₁₆

Complements

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

N	H ≅ G/N	type
38. C₂₆₃	#1364	semidirect

Maximal subgroups

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

subgroup	index
#30682343	2
#30681691	2
C₄⋊C₁₆×C₂₆₃	2
#1364	263