Subgroups — #20266052

Order 6464.

90 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	D₁₀₁⋊M₁₆	C₂	1	1	yes	maximal, characteristic
2	C₂×D₁₀₁⋊C₈	C₂	1	1	yes	maximal, characteristic
3	M₁₆×D₁₀₁	C₂	1	1	yes	maximal, characteristic
4	#13108084	C₄	1	2	yes	—
5	#13108083	—	2	1	no	—
6	D₁₀₁⋊C₈	—	2	1	no	—
7	D₁₀₁⋊C₈	—	2	1	no	—
8	D₁₀₁⋊C₈	C₄	1	2	yes	—
9	C₂×#11717581	—	2	1	no	—
10	C₂×C₄×D₁₀₁	C₂²	1	1	yes	characteristic
11	#13108058	C₄	1	1	yes	characteristic
12	#13108057	—	2	1	no	—
13	C₈×D₁₀₁	—	2	1	no	—
14	M₁₆×C₁₀₁	C₄	1	1	yes	characteristic
15	C₂²×D₁₀₁	Q₈	1	1	yes	characteristic
16	C₂×C₄×C₁₀₁	C₂×C₄	1	1	yes	characteristic
17	C₂×Dic₁₀₁	D₄	1	1	yes	characteristic
18	C₄×D₁₀₁	C₂×C₄	1	1	yes	characteristic
19	C₄×D₁₀₁	C₂×C₄	1	1	yes	characteristic
20	C₄×D₁₀₁	D₄	1	1	yes	characteristic
21	C₄×D₁₀₁	D₄	1	1	yes	characteristic
22	#11717581	—	2	2	no	—
23	#11717581	—	2	2	no	—
24	C₈×C₁₀₁	—	2	1	no	—
25	#11717579	—	2	1	no	—
26	C₂²×C₁₀₁	C₄⋊C₄	1	1	yes	characteristic
27	C₂×D₁₀₁	—	2	2	no	—
28	C₂×D₁₀₁	C₄⋊C₄	1	1	yes	characteristic
29	C₂×D₁₀₁	C₄⋊C₄	1	1	yes	characteristic
30	C₄×C₁₀₁	C₄²	1	1	yes	characteristic
31	C₄×C₁₀₁	C₂²⋊C₄	1	1	yes	characteristic
32	Dic₁₀₁	C₂²⋊C₄	1	1	yes	characteristic
33	Dic₁₀₁	C₂²⋊C₄	1	1	yes	characteristic
34	C₂×C₁₀₁	—	2	1	no	—
35	C₂×C₁₀₁	#95	1	1	yes	characteristic
36	D₁₀₁	—	2	1	no	—
37	D₁₀₁	#108	1	2	yes	—
38	C₁₀₁	#341	1	1	yes	characteristic, complemented, Sylow
39	#341	—	101	1	no	maximal, Sylow
40	C₂×M₁₆	—	101	1	no	—
41	C₂×M₁₆	—	101	1	no	—
42	C₂²×C₈	—	101	1	no	—
43	C₂²×C₄	—	101	1	no	—
44	M₁₆	—	101	2	no	—
45	M₁₆	—	101	1	no	—
46	M₁₆	—	202	1	no	—
47	M₁₆	—	202	1	no	—
48	M₁₆	#87938	1	1	yes	characteristic
49	C₂×C₈	—	101	2	no	—
50	C₂×C₈	—	202	1	no	—
51	C₂×C₈	—	202	1	no	—
52	C₂×C₈	—	202	1	no	—
53	C₂×C₈	—	202	1	no	—
54	C₂³	—	101	1	no	—
55	C₂×C₄	—	101	1	no	—
56	C₂×C₄	—	101	1	no	—
57	C₂×C₄	—	101	1	no	—
58	C₂×C₄	—	101	1	no	—
59	C₂×C₄	—	101	1	no	—
60	C₂×C₄	C₂×#87938	1	1	yes	characteristic
61	C₈	—	2	1	no	—
62	C₈	—	202	2	no	—
63	C₈	—	202	2	no	—
64	C₈	—	202	1	no	—
65	C₂²	—	101	1	no	—
66	C₂²	—	101	1	no	—
67	C₂²	—	202	2	no	—
68	C₂²	C₄⋊#87938	1	1	yes	characteristic
69	C₄	—	101	1	no	—
70	C₄	—	101	1	no	—
71	C₄	C₄×#87938	1	1	yes	characteristic
72	C₄	C₂²⋊#87938	1	1	yes	characteristic
73	C₂	—	2	1	no	—
74	C₂	—	101	2	no	—
75	C₂	—	202	1	no	—
76	C₂	(C₂×#87938)⋊C₄	1	1	yes	characteristic

	subgroup	G/H
center	C₄	C₂²⋊#87938
commutator	C₄×C₁₀₁	C₄²
Frattini	C₂×C₄	C₂×#87938
Fitting	M₁₆×C₁₀₁	C₄
socle	C₂×C₁₀₁	#95
hypercenter	M₁₆	#87938
hypocenter	C₁₀₁	#341
LCS	G ▷ C₄×C₁₀₁ ▷ C₂×C₁₀₁ ▷ C₁₀₁
UCS	C₁ ◁ C₄ ◁ C₂×C₄ ◁ M₁₆

Complements

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

N	H ≅ G/N	type
38. C₁₀₁	#341	semidirect