Subgroups — #20266047

Order 6464.

110 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
2	C₂×C₄×#87938	C₂	1	1	yes	maximal, characteristic
3	#15692213	C₂	1	1	yes	maximal, characteristic
4	C₂²×#87938	—	2	1	no	—
5	#13108084	—	2	1	no	—
6	#13108084	C₄	1	2	yes	complemented
7	C₂×#11717581	—	2	1	no	—
8	C₄×#87938	—	2	1	no	—
9	C₄×#87938	C₄	1	2	yes	complemented
10	C₂×C₄×D₁₀₁	C₂²	1	1	yes	characteristic
11	C₄⋊Dic₁₀₁	C₄	1	1	yes	characteristic, complemented
12	#13108051	—	2	1	no	—
13	C₄×Dic₁₀₁	—	2	1	no	—
14	C₄⋊C₄×C₁₀₁	C₄	1	1	yes	characteristic, complemented
15	C₂²×D₁₀₁	D₄	1	1	yes	characteristic
16	C₂×#87938	—	2	2	no	—
17	C₂×#87938	—	2	2	no	—
18	C₂×#87938	—	2	2	no	—
19	C₂×C₄×C₁₀₁	—	2	1	no	—
20	C₂×C₄×C₁₀₁	C₂×C₄	1	1	yes	characteristic
21	C₂×Dic₁₀₁	—	2	1	no	—
22	C₂×Dic₁₀₁	D₄	1	1	yes	characteristic
23	C₄×D₁₀₁	C₂×C₄	1	1	yes	characteristic
24	C₄×D₁₀₁	C₂×C₄	1	1	yes	characteristic
25	C₄×D₁₀₁	D₄	1	1	yes	characteristic
26	C₄×D₁₀₁	Q₈	1	1	yes	characteristic
27	#11717581	—	2	2	no	—
28	C₂²×C₁₀₁	C₂²⋊C₄	1	1	yes	characteristic
29	C₂×D₁₀₁	—	2	1	no	—
30	C₂×D₁₀₁	—	2	1	no	—
31	C₂×D₁₀₁	C₂²⋊C₄	1	1	yes	characteristic
32	C₂×D₁₀₁	C₄⋊C₄	1	1	yes	characteristic
33	#87938	—	2	4	no	—
34	C₄×C₁₀₁	—	4	1	no	—
35	C₄×C₁₀₁	C₄²	1	1	yes	characteristic
36	C₄×C₁₀₁	C₄⋊C₄	1	1	yes	characteristic
37	Dic₁₀₁	—	4	1	no	—
38	Dic₁₀₁	C₂²⋊C₄	1	1	yes	characteristic
39	Dic₁₀₁	C₄⋊C₄	1	1	yes	characteristic
40	C₂×C₁₀₁	#95	1	1	yes	characteristic
41	C₂×C₁₀₁	#104	1	1	yes	characteristic
42	C₂×C₁₀₁	#104	1	1	yes	characteristic
43	D₁₀₁	—	2	1	no	—
44	D₁₀₁	—	2	1	no	—
45	C₁₀₁	#339	1	1	yes	characteristic, complemented, Sylow
46	#339	—	101	1	no	maximal, Sylow
47	C₂×M₁₆	—	101	1	no	—
48	#117	—	101	1	no	—
49	C₂×C₄²	—	101	1	no	—
50	C₂²×C₄	—	101	1	no	—
51	C₂²×C₄	—	202	1	no	—
52	M₁₆	—	101	2	no	—
53	M₁₆	—	202	1	no	—
54	C₂×C₈	—	202	1	no	—
55	C₄⋊C₄	—	101	1	no	—
56	C₄⋊C₄	#87938	1	1	yes	characteristic, complemented
57	C₂²⋊C₄	—	202	1	no	—
58	C₄²	—	101	2	no	—
59	C₄²	—	202	1	no	—
60	C₄²	—	202	1	no	—
61	C₂³	—	101	1	no	—
62	C₂×C₄	—	2	1	no	—
63	C₂×C₄	—	101	1	no	—
64	C₂×C₄	—	101	1	no	—
65	C₂×C₄	—	101	1	no	—
66	C₂×C₄	—	101	1	no	—
67	C₂×C₄	—	101	1	no	—
68	C₂×C₄	—	202	1	no	—
69	C₂×C₄	—	202	2	no	—
70	C₂×C₄	—	202	2	no	—
71	C₂×C₄	—	202	2	no	—
72	C₂×C₄	C₂×#87938	1	1	yes	characteristic
73	C₈	—	202	2	no	—
74	C₂²	—	101	1	no	—
75	C₂²	—	101	1	no	—
76	C₂²	—	202	1	no	—
77	C₂²	—	202	1	no	—
78	C₂²	C₂²⋊#87938	1	1	yes	characteristic
79	C₄	—	4	1	no	—
80	C₄	—	101	1	no	—
81	C₄	—	101	1	no	—
82	C₄	—	404	1	no	—
83	C₄	—	202	4	no	—
84	C₄	C₄×#87938	1	1	yes	characteristic
85	C₄	C₄⋊#87938	1	1	yes	characteristic
86	C₂	—	202	1	no	—
87	C₂	—	202	1	no	—
88	C₂	(C₂×#87938)⋊C₄	1	1	yes	characteristic
89	C₂	#15692319	1	1	yes	characteristic
90	C₂	#15692320	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	C₂²⋊#87938
commutator	C₄×C₁₀₁	C₄²
Frattini	C₂×C₄	C₂×#87938
Fitting	C₄⋊C₄×C₁₀₁	C₄
socle	C₂²×C₁₀₁	C₂²⋊C₄
hypercenter	C₄⋊C₄	#87938
hypocenter	C₁₀₁	#339
LCS	G ▷ C₄×C₁₀₁ ▷ C₂×C₁₀₁ ▷ C₁₀₁
UCS	C₁ ◁ C₂² ◁ C₂×C₄ ◁ C₄⋊C₄

Complements

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

N	H ≅ G/N	type
6. #13108084	C₄	semidirect
9. C₄×#87938	C₄	semidirect
11. C₄⋊Dic₁₀₁	C₄	semidirect
14. C₄⋊C₄×C₁₀₁	C₄	semidirect
45. C₁₀₁	#339	semidirect
56. C₄⋊C₄	#87938	semidirect