Subgroups — D₁₀₁⋊#131 #20266253

Order 6464.

266 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#15692343	C₂	1	2	yes	maximal, complemented
2	#15692342	C₂	1	6	yes	maximal, complemented
3	D₁₀₁⋊M₁₆	C₂	1	3	yes	maximal, complemented
4	C₂×D₁₀₁⋊C₈	C₂	1	3	yes	maximal, complemented
5	#41×D₁₀₁	C₂	1	1	yes	maximal, characteristic
6	#13108084	C₂²	1	6	yes	complemented
7	#13108083	C₂²	1	6	yes	complemented
8	D₁₀₁⋊C₈	C₂²	1	1	yes	characteristic
9	D₁₀₁⋊C₈	C₂²	1	3	yes	—
10	D₁₀₁⋊C₈	C₂²	1	6	yes	complemented
11	C₂×#11717581	C₂²	1	6	yes	complemented
12	#13108075	C₂²	1	1	yes	characteristic
13	#13108074	C₄	1	3	yes	—
14	#13108073	C₂²	1	3	yes	—
15	Q₈×D₁₀₁	C₄	1	1	yes	characteristic
16	D₄×D₁₀₁	C₄	1	3	yes	—
17	C₂×C₄×D₁₀₁	C₂²	1	3	yes	—
18	#41×C₁₀₁	C₄	1	1	yes	characteristic
19	C₂²×D₁₀₁	C₂×C₄	1	3	yes	—
20	Q₈×C₁₀₁	C₂×C₄	1	1	yes	characteristic
21	D₄×C₁₀₁	C₂×C₄	1	3	yes	—
22	C₂×C₄×C₁₀₁	C₂×C₄	1	3	yes	—
23	C₂²⋊D₁₀₁	C₂×C₄	1	6	yes	—
24	C₂×Dic₁₀₁	C₂³	1	3	yes	—
25	D₄₀₄	C₂×C₄	1	3	yes	—
26	C₄×D₁₀₁	C₂×C₄	1	3	yes	—
27	C₄×D₁₀₁	C₂×C₄	1	3	yes	—
28	C₄×D₁₀₁	C₂³	1	1	yes	characteristic
29	C₄×D₁₀₁	C₂³	1	3	yes	—
30	Dic₂₀₂	C₂×C₄	1	3	yes	—
31	#11717581	C₂³	1	2	yes	—
32	#11717581	C₂³	1	6	yes	—
33	C₂²×C₁₀₁	C₂²×C₄	1	3	yes	—
34	C₂×D₁₀₁	—	2	6	no	—
35	C₂×D₁₀₁	C₂²×C₄	1	3	yes	—
36	C₂×D₁₀₁	C₂²×C₄	1	1	yes	characteristic
37	C₄×C₁₀₁	C₂²×C₄	1	3	yes	—
38	C₄×C₁₀₁	C₂²×C₄	1	1	yes	characteristic
39	Dic₁₀₁	C₂²×C₄	1	3	yes	—
40	Dic₁₀₁	C₂⁴	1	1	yes	characteristic
41	C₂×C₁₀₁	—	2	3	no	—
42	C₂×C₁₀₁	C₂³×C₄	1	1	yes	characteristic
43	D₁₀₁	—	2	3	no	—
44	D₁₀₁	#131	1	2	yes	complemented
45	C₁₀₁	C₂×#131	1	1	yes	characteristic, complemented, Sylow
46	C₂×#131	—	101	1	no	maximal, Sylow
47	C₂×#41	—	101	1	no	—
48	#131	—	101	6	no	—
49	#131	—	101	2	no	—
50	C₂×M₁₆	—	101	3	no	—
51	C₂²×C₈	—	101	3	no	—
52	#41	—	101	1	no	—
53	#41	—	101	3	no	—
54	#41	—	101	3	no	—
55	#41	#87938	1	1	yes	characteristic
56	C₂×Q₈	—	101	1	no	—
57	C₂×D₄	—	101	3	no	—
58	C₂²×C₄	—	101	3	no	—
59	M₁₆	—	101	6	no	—
60	M₁₆	—	101	6	no	—
61	C₂×C₈	—	101	6	no	—
62	C₂×C₈	—	101	1	no	—
63	C₂×C₈	—	101	3	no	—
64	C₂×C₈	—	101	6	no	—
65	C₂³	—	101	3	no	—
66	Q₈	—	101	3	no	—
67	Q₈	C₂×#87938	1	1	yes	characteristic
68	D₄	—	101	6	no	—
69	D₄	—	101	3	no	—
70	D₄	C₂×#87938	1	3	yes	—
71	C₂×C₄	—	101	3	no	—
72	C₂×C₄	—	101	3	no	—
73	C₂×C₄	—	101	3	no	—
74	C₂×C₄	—	101	1	no	—
75	C₂×C₄	—	101	3	no	—
76	C₂×C₄	C₂×#87938	1	3	yes	—
77	C₈	—	101	2	no	—
78	C₈	—	101	6	no	—
79	C₂²	—	101	1	no	—
80	C₂²	—	101	3	no	—
81	C₂²	—	202	6	no	—
82	C₂²	C₂²×#87938	1	3	yes	—
83	C₄	—	101	1	no	—
84	C₄	—	101	3	no	—
85	C₄	C₂²×#87938	1	3	yes	—
86	C₄	C₂²×#87938	1	1	yes	characteristic
87	C₂	—	2	3	no	—
88	C₂	—	101	2	no	—
89	C₂	—	202	3	no	—
90	C₂	C₂³×#87938	1	1	yes	characteristic

	subgroup	G/H
center	C₄	C₂²×#87938
commutator, socle	C₂×C₁₀₁	C₂³×C₄
Frattini	C₂	C₂³×#87938
Fitting	#41×C₁₀₁	C₄
hypercenter	#41	#87938
hypocenter	C₁₀₁	C₂×#131
LCS	G ▷ C₂×C₁₀₁ ▷ C₁₀₁
UCS	C₁ ◁ C₄ ◁ #41

Complements

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

N	H ≅ G/N	type
1. #15692343	C₂	semidirect
2. #15692342	C₂	semidirect
3. D₁₀₁⋊M₁₆	C₂	semidirect
4. C₂×D₁₀₁⋊C₈	C₂	semidirect
6. #13108084	C₂²	semidirect
7. #13108083	C₂²	semidirect
10. D₁₀₁⋊C₈	C₂²	semidirect
11. C₂×#11717581	C₂²	semidirect
44. D₁₀₁	#131	semidirect
45. C₁₀₁	C₂×#131	semidirect

Subgroups — D101⋊#131 #20266253

Conjugacy classes of subgroups

Complements

Subgroups — D₁₀₁⋊#131 #20266253