Subgroups — #20266078

Order 6464.

94 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#15692315	C₂	1	1	yes	maximal, characteristic, complemented
2	#15692313	C₂	1	1	yes	maximal, characteristic, complemented
3	#15692225	C₂	1	1	yes	maximal, characteristic
4	#13108083	—	2	1	no	—
5	C₂²⋊#87938	—	2	1	no	—
6	C₂³×D₁₀₁	C₄	1	1	yes	characteristic, complemented
7	C₂×D₄₀₄	—	2	1	no	—
8	C₂×C₂²⋊D₁₀₁	C₂²	1	1	yes	characteristic
9	#13108051	—	2	1	no	—
10	C₂²⋊C₄×C₁₀₁	C₄	1	1	yes	characteristic, complemented
11	C₂³×C₁₀₁	C₂×C₄	1	1	yes	characteristic
12	C₂²×D₁₀₁	—	2	1	no	—
13	C₂²×D₁₀₁	—	4	2	no	—
14	C₂²×D₁₀₁	—	4	1	no	—
15	C₂²×D₁₀₁	D₄	1	1	yes	characteristic
16	C₂×#87938	—	4	1	no	—
17	C₂×C₄×C₁₀₁	—	2	1	no	—
18	C₂²⋊D₁₀₁	—	4	1	no	—
19	C₂×Dic₁₀₁	D₄	1	1	yes	characteristic
20	D₄₀₄	—	4	2	no	—
21	#11717581	—	4	1	no	—
22	C₂²×C₁₀₁	—	2	1	no	—
23	C₂²×C₁₀₁	—	4	1	no	—
24	C₂²×C₁₀₁	C₂²⋊C₄	1	1	yes	characteristic
25	C₂×D₁₀₁	—	2	2	no	—
26	C₂×D₁₀₁	—	2	1	no	—
27	C₂×D₁₀₁	—	4	1	no	—
28	C₂×D₁₀₁	—	4	2	no	—
29	C₂×D₁₀₁	—	4	1	no	—
30	C₂×D₁₀₁	—	4	1	no	—
31	C₂×D₁₀₁	—	4	2	no	—
32	#87938	—	8	1	no	—
33	C₄×C₁₀₁	—	4	1	no	—
34	Dic₁₀₁	—	2	1	no	—
35	C₂×C₁₀₁	—	2	1	no	—
36	C₂×C₁₀₁	—	4	1	no	—
37	C₂×C₁₀₁	#99	1	1	yes	characteristic
38	D₁₀₁	—	4	1	no	—
39	D₁₀₁	—	4	2	no	—
40	C₁₀₁	AΣL(1,𝔽₁₆)	1	1	yes	characteristic, complemented, Sylow
41	AΣL(1,𝔽₁₆)	—	101	1	no	maximal, Sylow
42	#120	—	101	1	no	—
43	#100	—	101	1	no	—
44	#99	—	101	1	no	—
45	C₂⁴	—	101	1	no	—
46	C₂×D₄	—	101	1	no	—
47	C₂×D₄	—	202	1	no	—
48	M₁₆	—	202	1	no	—
49	C₂²⋊C₄	—	202	1	no	—
50	C₂²⋊C₄	—	202	1	no	—
51	C₂²⋊C₄	#87938	1	1	yes	characteristic, complemented
52	C₂³	—	101	1	no	—
53	C₂³	—	404	1	no	—
54	C₂³	—	404	2	no	—
55	C₂³	—	202	1	no	—
56	C₂³	C₂×#87938	1	1	yes	characteristic
57	D₄	—	404	2	no	—
58	D₄	—	404	1	no	—
59	C₂×C₄	—	2	1	no	—
60	C₂×C₄	—	101	1	no	—
61	C₂×C₄	—	404	1	no	—
62	C₈	—	404	1	no	—
63	C₂²	—	2	1	no	—
64	C₂²	—	4	1	no	—
65	C₂²	—	404	1	no	—
66	C₂²	—	404	1	no	—
67	C₂²	—	404	2	no	—
68	C₂²	—	404	2	no	—
69	C₂²	—	404	1	no	—
70	C₂²	—	202	2	no	—
71	C₂²	—	202	1	no	—
72	C₂²	C₂²⋊#87938	1	1	yes	characteristic
73	C₄	—	4	1	no	—
74	C₄	—	808	1	no	—
75	C₄	—	202	1	no	—
76	C₂	—	2	1	no	—
77	C₂	—	4	1	no	—
78	C₂	—	404	1	no	—
79	C₂	—	404	2	no	—
80	C₂	#15692314	1	1	yes	characteristic

	subgroup	G/H
center	C₂	#15692314
commutator	C₂³×C₁₀₁	C₂×C₄
Frattini	C₂³	C₂×#87938
Fitting	C₂²⋊C₄×C₁₀₁	C₄
socle	C₂×C₁₀₁	#99
hypercenter	C₂²⋊C₄	#87938
hypocenter	C₁₀₁	AΣL(1,𝔽₁₆)
LCS	G ▷ C₂³×C₁₀₁ ▷ C₂²×C₁₀₁ ▷ C₂×C₁₀₁ ▷ C₁₀₁
UCS	C₁ ◁ C₂ ◁ C₂² ◁ C₂³ ◁ C₂²⋊C₄

Complements

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

N	H ≅ G/N	type
1. #15692315	C₂	semidirect
2. #15692313	C₂	semidirect
6. C₂³×D₁₀₁	C₄	semidirect
10. C₂²⋊C₄×C₁₀₁	C₄	semidirect
40. C₁₀₁	AΣL(1,𝔽₁₆)	semidirect
51. C₂²⋊C₄	#87938	semidirect