Subgroups — #20266152

Order 6464.

158 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#13108084	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×D₁₀₁⋊C₈	C₂	1	1	yes	maximal, characteristic, complemented
3	#15692312	C₂	1	4	yes	maximal, complemented
4	C₂×#13108075	C₂	1	1	yes	maximal, characteristic
5	#13108084	—	2	2	no	—
6	D₁₀₁⋊C₈	—	2	2	no	—
7	C₂×#11717581	C₂²	1	2	yes	—
8	C₂×#11717581	C₂²	1	2	yes	—
9	#13108075	—	2	2	no	—
10	#13108075	—	2	2	no	—
11	C₂×D₄₀₄	C₄	1	2	yes	—
12	C₂×D₄₀₄	C₄	1	1	yes	characteristic
13	C₂×C₄×D₁₀₁	C₂²	1	2	yes	—
14	C₂×C₄×D₁₀₁	C₂²	1	1	yes	characteristic
15	C₂×Q₈×C₁₀₁	C₄	1	1	yes	characteristic
16	C₂²×D₁₀₁	C₂×C₄	1	2	yes	—
17	C₂²×D₁₀₁	C₂×C₄	1	1	yes	characteristic
18	Q₈×C₁₀₁	—	2	2	no	—
19	C₂×C₄×C₁₀₁	C₂×C₄	1	2	yes	—
20	C₂×C₄×C₁₀₁	C₂×C₄	1	1	yes	characteristic
21	C₂×Dic₁₀₁	C₂³	1	1	yes	characteristic
22	D₄₀₄	—	2	4	no	—
23	D₄₀₄	—	2	2	no	—
24	C₄×D₁₀₁	—	2	2	no	—
25	C₄×D₁₀₁	—	2	2	no	—
26	C₄×D₁₀₁	D₄	1	2	yes	—
27	C₄×D₁₀₁	D₄	1	2	yes	—
28	#11717581	—	2	2	no	—
29	#11717581	—	2	2	no	—
30	C₂²×C₁₀₁	C₂²×C₄	1	1	yes	characteristic
31	C₂×D₁₀₁	—	2	2	no	—
32	C₂×D₁₀₁	—	2	2	no	—
33	C₂×D₁₀₁	—	2	4	no	—
34	C₂×D₁₀₁	C₂²⋊C₄	1	2	yes	—
35	C₄×C₁₀₁	—	2	2	no	—
36	C₄×C₁₀₁	C₂²⋊C₄	1	2	yes	—
37	Dic₁₀₁	C₂×D₄	1	1	yes	characteristic
38	Dic₁₀₁	C₂×D₄	1	1	yes	characteristic
39	C₂×C₁₀₁	C₂×C₂²⋊C₄	1	1	yes	characteristic
40	C₂×C₁₀₁	#131	1	2	yes	—
41	D₁₀₁	—	2	2	no	—
42	D₁₀₁	—	4	2	no	—
43	C₁₀₁	#408	1	1	yes	characteristic, complemented, Sylow
44	#408	—	101	1	no	maximal, Sylow
45	C₂×#41	—	101	1	no	—
46	C₂×M₁₆	—	101	1	no	—
47	C₂²×C₈	—	101	1	no	—
48	C₂²⋊C₈	—	101	4	no	—
49	#41	—	202	2	no	—
50	#41	—	202	2	no	—
51	C₂×Q₈	#87938	1	1	yes	characteristic
52	C₂×D₄	—	101	2	no	—
53	C₂×D₄	—	101	1	no	—
54	C₂²×C₄	—	101	1	no	—
55	C₂²×C₄	—	101	2	no	—
56	M₁₆	—	202	2	no	—
57	C₂×C₈	—	101	2	no	—
58	C₂×C₈	—	101	2	no	—
59	C₂×C₈	—	202	2	no	—
60	C₂³	—	101	1	no	—
61	C₂³	—	101	2	no	—
62	Q₈	—	2	2	no	—
63	D₄	—	202	4	no	—
64	D₄	—	202	2	no	—
65	C₂×C₄	—	101	1	no	—
66	C₂×C₄	—	101	2	no	—
67	C₂×C₄	—	101	2	no	—
68	C₂×C₄	—	202	2	no	—
69	C₂×C₄	—	202	2	no	—
70	C₂×C₄	C₂×#87938	1	2	yes	—
71	C₂×C₄	C₂×#87938	1	1	yes	characteristic
72	C₈	—	202	2	no	—
73	C₈	—	202	2	no	—
74	C₂²	—	101	2	no	—
75	C₂²	—	202	2	no	—
76	C₂²	—	202	4	no	—
77	C₂²	—	202	2	no	—
78	C₂²	C₂²×#87938	1	1	yes	characteristic
79	C₄	—	2	2	no	—
80	C₄	—	101	1	no	—
81	C₄	—	101	1	no	—
82	C₄	C₂²⋊#87938	1	2	yes	—
83	C₂	—	404	2	no	—
84	C₂	—	202	2	no	—
85	C₂	C₂×C₂²⋊#87938	1	1	yes	characteristic
86	C₂	#15692343	1	2	yes	—

	subgroup	G/H
center, Frattini	C₂²	C₂²×#87938
commutator, socle	C₂²×C₁₀₁	C₂²×C₄
Fitting	C₂×Q₈×C₁₀₁	C₄
hypercenter	C₂×Q₈	#87938
hypocenter	C₁₀₁	#408
LCS	G ▷ C₂²×C₁₀₁ ▷ C₁₀₁
UCS	C₁ ◁ C₂² ◁ C₂×Q₈

Complements

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

N	H ≅ G/N	type
1. C₂×#13108084	C₂	semidirect
2. C₂×D₁₀₁⋊C₈	C₂	semidirect
3. #15692312	C₂	semidirect
43. C₁₀₁	#408	semidirect