Subgroups — #30682227

Order 16832.

108 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#22554469	C₂	1	1	yes	maximal, characteristic, complemented
2	#22554432	C₂	1	1	yes	maximal, characteristic
3	#22554401	C₂	1	1	yes	maximal, characteristic, complemented
4	Dic₂₆₃⋊C₈	C₂	1	1	yes	maximal, characteristic, complemented
5	#22554392	C₂	1	1	yes	maximal, characteristic
6	#22554390	C₂	1	1	yes	maximal, characteristic
7	#106×C₂₆₃	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×Dic₅₂₆	—	2	1	no	—
9	C₂×D₁₀₅₂	C₂²	1	1	yes	characteristic
10	C₂×C₄×D₂₆₃	—	2	1	no	—
11	C₂×C₂₆₃⋊C₈	C₂²	1	1	yes	characteristic
12	C₄⋊Dic₂₆₃	C₂²	1	1	yes	characteristic
13	Dic₂₆₃⋊C₄	—	2	1	no	—
14	(C₂×D₂₆₃)⋊C₄	—	2	1	no	—
15	C₄×Dic₂₆₃	C₂²	1	1	yes	characteristic
16	C₂×C₈×C₂₆₃	C₂²	1	1	yes	characteristic
17	C₄⋊C₄×C₂₆₃	C₂²	1	1	yes	characteristic
18	C₄⋊C₄×C₂₆₃	C₂²	1	1	yes	characteristic
19	C₂²×D₂₆₃	—	2	1	no	—
20	Dic₅₂₆	—	4	2	no	—
21	D₁₀₅₂	—	2	1	no	—
22	D₁₀₅₂	Q₈	1	2	yes	complemented
23	C₂×Dic₂₆₃	—	2	1	no	—
24	C₂×Dic₂₆₃	D₄	1	1	yes	characteristic
25	C₂×Dic₂₆₃	D₄	1	1	yes	characteristic
26	C₄×D₂₆₃	—	4	2	no	—
27	C₂₆₃⋊C₈	—	2	1	no	—
28	C₂×C₄×C₂₆₃	—	2	1	no	—
29	C₂×C₄×C₂₆₃	—	2	1	no	—
30	C₂×C₄×C₂₆₃	C₂³	1	1	yes	characteristic
31	C₈×C₂₆₃	—	2	1	no	—
32	C₂²×C₂₆₃	C₂×D₄	1	1	yes	characteristic
33	C₂×D₂₆₃	—	2	2	no	—
34	C₂×D₂₆₃	—	4	1	no	—
35	C₂×D₂₆₃	—	4	1	no	—
36	C₄×C₂₆₃	—	4	1	no	—
37	C₄×C₂₆₃	—	4	1	no	—
38	C₄×C₂₆₃	C₂×Q₈	1	1	yes	characteristic
39	C₄×C₂₆₃	#41	1	1	yes	characteristic
40	Dic₂₆₃	—	2	1	no	—
41	Dic₂₆₃	—	4	1	no	—
42	Dic₂₆₃	SD₁₆	1	2	yes	—
43	C₂×C₂₆₃	C₂²⋊Q₈	1	1	yes	characteristic
44	C₂×C₂₆₃	C₂×SD₁₆	1	1	yes	characteristic
45	C₂×C₂₆₃	AGL(1,ℤ/8)	1	1	yes	characteristic
46	D₂₆₃	—	4	2	no	—
47	C₂₆₃	#476	1	1	yes	characteristic, complemented, Sylow
48	#476	—	263	1	no	maximal, Sylow
49	C₄⋊Q₈	—	263	1	no	—
50	C₄×D₄	—	263	1	no	—
51	#106	—	263	1	no	—
52	#106	D₂₆₃	1	1	yes	characteristic, complemented
53	C₄⋊C₈	—	263	1	no	—
54	#102	—	263	1	no	—
55	#102	—	263	1	no	—
56	C₂×Q₈	—	526	1	no	—
57	C₂×D₄	—	263	1	no	—
58	C₂²×C₄	—	526	1	no	—
59	C₂×C₈	—	263	1	no	—
60	C₂×C₈	C₂×D₂₆₃	1	1	yes	characteristic
61	C₄⋊C₄	—	263	1	no	—
62	C₄⋊C₄	—	526	1	no	—
63	C₄⋊C₄	C₂×D₂₆₃	1	1	yes	characteristic
64	C₄⋊C₄	C₂×D₂₆₃	1	1	yes	characteristic
65	C₂²⋊C₄	—	526	1	no	—
66	C₄²	—	263	1	no	—
67	C₂³	—	526	1	no	—
68	Q₈	—	1052	2	no	—
69	D₄	—	263	2	no	—
70	D₄	—	526	1	no	—
71	C₂×C₄	—	2	1	no	—
72	C₂×C₄	—	2	1	no	—
73	C₂×C₄	—	263	1	no	—
74	C₂×C₄	—	263	1	no	—
75	C₂×C₄	—	526	1	no	—
76	C₂×C₄	—	1052	2	no	—
77	C₂×C₄	C₂²×D₂₆₃	1	1	yes	characteristic
78	C₈	—	2	1	no	—
79	C₈	—	526	1	no	—
80	C₂²	—	526	2	no	—
81	C₂²	—	1052	1	no	—
82	C₂²	—	1052	1	no	—
83	C₂²	D₄×D₂₆₃	1	1	yes	characteristic
84	C₄	—	4	1	no	—
85	C₄	—	4	1	no	—
86	C₄	—	263	2	no	—
87	C₄	—	526	1	no	—
88	C₄	—	1052	1	no	—
89	C₄	Q₈×D₂₆₃	1	1	yes	characteristic
90	C₄	#16862376	1	1	yes	characteristic
91	C₂	—	1052	2	no	—
92	C₂	#22554448	1	1	yes	characteristic
93	C₂	SD₁₆×D₂₆₃	1	1	yes	characteristic
94	C₂	#22554497	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	D₄×D₂₆₃
commutator, cosocle	C₂×C₄×C₂₆₃	C₂³
Frattini	C₂×C₄	C₂²×D₂₆₃
Fitting	#106×C₂₆₃	C₂
socle	C₂²×C₂₆₃	C₂×D₄
prime radical	C₂×D₁₀₅₂	C₂²
hypercenter	#106	D₂₆₃
hypocenter	C₂₆₃	#476
LCS	G ▷ C₂×C₄×C₂₆₃ ▷ C₂×C₂₆₃ ▷ C₂₆₃
UCS	C₁ ◁ C₂² ◁ C₂×C₄ ◁ #106

Complements

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

N	H ≅ G/N	type
1. #22554469	C₂	semidirect
3. #22554401	C₂	semidirect
4. Dic₂₆₃⋊C₈	C₂	semidirect
7. #106×C₂₆₃	C₂	semidirect
22. D₁₀₅₂	Q₈	semidirect
47. C₂₆₃	#476	semidirect
52. #106	D₂₆₃	semidirect

Maximal subgroups

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

subgroup	index
#22554469	2
#22554432	2
#22554401	2
Dic₂₆₃⋊C₈	2
#22554392	2
#22554390	2
#106×C₂₆₃	2
#476	263