Subgroups — D₁₀₁⋊#100 #20266160

Order 6464.

186 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	D₁₀₁⋊M₁₆	C₂	1	2	yes	maximal, complemented
2	#15692315	C₂	1	4	yes	maximal, complemented
3	C₂×D₄×D₁₀₁	C₂	1	1	yes	maximal, characteristic
4	#13108084	—	2	2	no	—
5	#13108083	C₂²	1	4	yes	complemented
6	D₁₀₁⋊C₈	—	2	2	no	—
7	C₂³×D₁₀₁	C₄	1	2	yes	—
8	C₂×D₄₀₄	C₄	1	1	yes	characteristic
9	C₂×C₂²⋊D₁₀₁	C₂²	1	2	yes	—
10	D₄×D₁₀₁	—	2	2	no	—
11	D₄×D₁₀₁	—	2	2	no	—
12	C₂×C₄×D₁₀₁	C₂²	1	1	yes	characteristic
13	C₂×D₄×C₁₀₁	C₄	1	1	yes	characteristic
14	C₂³×C₁₀₁	C₂×C₄	1	2	yes	—
15	C₂²×D₁₀₁	—	2	2	no	—
16	C₂²×D₁₀₁	—	2	2	no	—
17	C₂²×D₁₀₁	—	4	4	no	—
18	C₂²×D₁₀₁	C₂×C₄	1	1	yes	characteristic
19	C₂²×D₁₀₁	C₂×C₄	1	2	yes	—
20	D₄×C₁₀₁	—	2	2	no	—
21	C₂×C₄×C₁₀₁	C₂×C₄	1	1	yes	characteristic
22	C₂²⋊D₁₀₁	—	2	4	no	—
23	C₂×Dic₁₀₁	C₂³	1	1	yes	characteristic
24	D₄₀₄	—	2	2	no	—
25	C₄×D₁₀₁	D₄	1	2	yes	—
26	C₄×D₁₀₁	D₄	1	2	yes	—
27	#11717581	—	2	4	no	—
28	C₂²×C₁₀₁	—	2	2	no	—
29	C₂²×C₁₀₁	—	4	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	—	4	4	no	—
34	C₂×D₁₀₁	—	4	4	no	—
35	C₂×D₁₀₁	—	4	2	no	—
36	C₂×D₁₀₁	C₂²⋊C₄	1	1	yes	characteristic
37	C₂×D₁₀₁	C₂²⋊C₄	1	1	yes	characteristic
38	C₄×C₁₀₁	C₂²⋊C₄	1	2	yes	—
39	Dic₁₀₁	C₂×D₄	1	2	yes	—
40	C₂×C₁₀₁	—	2	1	no	—
41	C₂×C₁₀₁	—	4	2	no	—
42	C₂×C₁₀₁	C₂×C₂²⋊C₄	1	1	yes	characteristic
43	D₁₀₁	—	2	1	no	—
44	D₁₀₁	—	4	2	no	—
45	D₁₀₁	#100	1	2	yes	complemented
46	C₁₀₁	C₂×#100	1	1	yes	characteristic, complemented, Sylow
47	C₂×#100	—	101	1	no	maximal, Sylow
48	C₂²×D₄	—	101	1	no	—
49	C₂×M₁₆	—	101	2	no	—
50	#100	—	101	4	no	—
51	C₂⁴	—	101	2	no	—
52	C₂×D₄	—	101	2	no	—
53	C₂×D₄	—	101	1	no	—
54	C₂×D₄	—	202	2	no	—
55	C₂×D₄	—	202	2	no	—
56	C₂×D₄	#87938	1	1	yes	characteristic
57	C₂²×C₄	—	101	1	no	—
58	M₁₆	—	101	4	no	—
59	M₁₆	—	202	2	no	—
60	C₂×C₈	—	202	2	no	—
61	C₂³	—	101	1	no	—
62	C₂³	—	101	2	no	—
63	C₂³	—	404	4	no	—
64	C₂³	—	202	2	no	—
65	C₂³	—	202	2	no	—
66	C₂³	C₂×#87938	1	2	yes	—
67	D₄	—	2	2	no	—
68	D₄	—	202	4	no	—
69	D₄	—	202	2	no	—
70	C₂×C₄	—	101	1	no	—
71	C₂×C₄	—	101	2	no	—
72	C₂×C₄	—	101	2	no	—
73	C₂×C₄	C₂×#87938	1	1	yes	characteristic
74	C₈	—	202	4	no	—
75	C₂²	—	2	2	no	—
76	C₂²	—	4	2	no	—
77	C₂²	—	101	1	no	—
78	C₂²	—	101	1	no	—
79	C₂²	—	404	2	no	—
80	C₂²	—	404	4	no	—
81	C₂²	—	404	4	no	—
82	C₂²	—	202	2	no	—
83	C₂²	—	202	2	no	—
84	C₂²	C₂²×#87938	1	1	yes	characteristic
85	C₄	—	101	2	no	—
86	C₄	C₂²⋊#87938	1	2	yes	—
87	C₂	—	2	1	no	—
88	C₂	—	4	2	no	—
89	C₂	—	101	2	no	—
90	C₂	—	404	2	no	—
91	C₂	—	202	1	no	—
92	C₂	C₂×C₂²⋊#87938	1	1	yes	characteristic

	subgroup	G/H
center	C₂	C₂×C₂²⋊#87938
commutator	C₂²×C₁₀₁	C₂²×C₄
Frattini	C₂²	C₂²×#87938
Fitting	C₂×D₄×C₁₀₁	C₄
socle	C₂×C₁₀₁	C₂×C₂²⋊C₄
hypercenter	C₂×D₄	#87938
hypocenter	C₁₀₁	C₂×#100
LCS	G ▷ C₂²×C₁₀₁ ▷ C₂×C₁₀₁ ▷ C₁₀₁
UCS	C₁ ◁ C₂ ◁ C₂×C₄ ◁ C₂×D₄

Complements

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

N	H ≅ G/N	type
1. D₁₀₁⋊M₁₆	C₂	semidirect
2. #15692315	C₂	semidirect
5. #13108083	C₂²	semidirect
45. D₁₀₁	#100	semidirect
46. C₁₀₁	C₂×#100	semidirect

Subgroups — D101⋊#100 #20266160

Conjugacy classes of subgroups

Complements

Subgroups — D₁₀₁⋊#100 #20266160