Subgroups — #20266029

Order 6464.

90 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#15692312	C₂	1	1	yes	maximal, characteristic, complemented
2	(C₂×#87938)⋊C₄	C₂	1	1	yes	maximal, characteristic, complemented
3	#15692230	C₂	1	1	yes	maximal, characteristic
4	C₂²×#87938	—	2	1	no	—
5	C₂×#11717581	—	2	1	no	—
6	C₂×D₄₀₄	—	2	1	no	—
7	C₂×D₄₀₄	C₄	1	1	yes	characteristic, complemented
8	C₂×C₄×D₁₀₁	C₂²	1	1	yes	characteristic
9	#13108051	—	2	1	no	—
10	C₄⋊C₄×C₁₀₁	C₄	1	1	yes	characteristic, complemented
11	C₂²×D₁₀₁	—	2	1	no	—
12	C₂²×D₁₀₁	D₄	1	1	yes	characteristic
13	C₂×#87938	—	2	2	no	—
14	C₂×#87938	—	4	1	no	—
15	C₂×#87938	—	4	1	no	—
16	C₂×C₄×C₁₀₁	—	2	1	no	—
17	C₂×C₄×C₁₀₁	C₂×C₄	1	1	yes	characteristic
18	C₂×Dic₁₀₁	D₄	1	1	yes	characteristic
19	D₄₀₄	—	4	1	no	—
20	D₄₀₄	—	4	1	no	—
21	D₄₀₄	—	4	1	no	—
22	C₄×D₁₀₁	—	4	1	no	—
23	#11717581	—	4	1	no	—
24	C₂²×C₁₀₁	C₂²⋊C₄	1	1	yes	characteristic
25	C₂×D₁₀₁	—	2	1	no	—
26	C₂×D₁₀₁	—	2	1	no	—
27	C₂×D₁₀₁	—	4	1	no	—
28	C₂×D₁₀₁	—	4	1	no	—
29	C₂×D₁₀₁	—	4	1	no	—
30	C₂×D₁₀₁	D₈	1	1	yes	characteristic
31	C₂×D₁₀₁	SD₁₆	1	1	yes	characteristic
32	#87938	—	4	2	no	—
33	C₄×C₁₀₁	—	2	1	no	—
34	C₄×C₁₀₁	—	4	1	no	—
35	Dic₁₀₁	—	2	1	no	—
36	C₂×C₁₀₁	#99	1	1	yes	characteristic
37	C₂×C₁₀₁	#102	1	1	yes	characteristic
38	C₂×C₁₀₁	#104	1	1	yes	characteristic
39	D₁₀₁	—	2	1	no	—
40	D₁₀₁	—	2	1	no	—
41	D₁₀₁	—	8	1	no	—
42	C₁₀₁	#327	1	1	yes	characteristic, complemented, Sylow
43	#327	—	101	1	no	maximal, Sylow
44	#121	—	101	1	no	—
45	C₂²⋊C₈	—	101	1	no	—
46	#95	—	101	1	no	—
47	C₂×D₄	—	101	1	no	—
48	C₂×D₄	—	202	1	no	—
49	C₂²×C₄	—	101	1	no	—
50	C₂²×C₄	—	202	1	no	—
51	C₂×C₈	—	202	1	no	—
52	C₄⋊C₄	#87938	1	1	yes	characteristic, complemented
53	C₂²⋊C₄	—	202	1	no	—
54	C₂³	—	101	1	no	—
55	C₂³	—	202	1	no	—
56	D₄	—	404	1	no	—
57	D₄	—	404	1	no	—
58	D₄	—	404	1	no	—
59	C₂×C₄	—	2	1	no	—
60	C₂×C₄	—	101	1	no	—
61	C₂×C₄	—	404	1	no	—
62	C₂×C₄	—	404	1	no	—
63	C₂×C₄	—	404	1	no	—
64	C₂×C₄	—	202	2	no	—
65	C₂×C₄	C₂×#87938	1	1	yes	characteristic
66	C₈	—	404	1	no	—
67	C₂²	—	101	1	no	—
68	C₂²	—	101	1	no	—
69	C₂²	—	404	1	no	—
70	C₂²	—	404	1	no	—
71	C₂²	—	404	1	no	—
72	C₂²	—	202	1	no	—
73	C₂²	—	202	1	no	—
74	C₂²	C₂²⋊#87938	1	1	yes	characteristic
75	C₄	—	2	1	no	—
76	C₄	—	4	1	no	—
77	C₄	—	404	2	no	—
78	C₄	—	202	1	no	—
79	C₂	—	808	1	no	—
80	C₂	—	202	1	no	—
81	C₂	—	202	1	no	—
82	C₂	#15692314	1	1	yes	characteristic
83	C₂	#15692317	1	1	yes	characteristic
84	C₂	#15692320	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	C₂²⋊#87938
commutator	C₂×C₄×C₁₀₁	C₂×C₄
Frattini	C₂×C₄	C₂×#87938
Fitting	C₄⋊C₄×C₁₀₁	C₄
socle	C₂²×C₁₀₁	C₂²⋊C₄
hypercenter	C₄⋊C₄	#87938
hypocenter	C₁₀₁	#327
LCS	G ▷ C₂×C₄×C₁₀₁ ▷ C₂²×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
1. #15692312	C₂	semidirect
2. (C₂×#87938)⋊C₄	C₂	semidirect
7. C₂×D₄₀₄	C₄	semidirect
10. C₄⋊C₄×C₁₀₁	C₄	semidirect
42. C₁₀₁	#327	semidirect
52. C₄⋊C₄	#87938	semidirect