Subgroups — #20265538

Order 6464.

100 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#15692254	C₂	1	1	yes	maximal, characteristic, complemented
2	#15692244	C₂	1	1	yes	maximal, characteristic
3	#15692179	C₂	1	1	yes	maximal, characteristic, complemented
4	#15692177	C₂	1	1	yes	maximal, characteristic
5	#15692175	C₂	1	1	yes	maximal, characteristic
6	#15692165	C₂	1	1	yes	maximal, characteristic, complemented
7	#103×C₁₀₁	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×Dic₂₀₂	—	2	1	no	—
9	C₂×D₄₀₄	C₂²	1	1	yes	characteristic
10	C₂×#11717579	C₂²	1	1	yes	characteristic
11	C₄⋊Dic₁₀₁	C₂²	1	1	yes	characteristic
12	#13108053	—	2	1	no	—
13	#13108051	—	2	1	no	—
14	#13108051	—	2	1	no	—
15	C₄×Dic₁₀₁	C₂²	1	1	yes	characteristic
16	C₂×Q₈×C₁₀₁	C₂²	1	1	yes	characteristic
17	C₂×C₈×C₁₀₁	C₂²	1	1	yes	characteristic
18	C₄⋊C₄×C₁₀₁	C₂²	1	1	yes	characteristic
19	C₂²×D₁₀₁	—	2	1	no	—
20	Q₈×C₁₀₁	—	2	1	no	—
21	Q₈×C₁₀₁	—	2	1	no	—
22	C₂×C₄×C₁₀₁	—	2	1	no	—
23	C₂×C₄×C₁₀₁	—	2	1	no	—
24	C₂×C₄×C₁₀₁	C₂³	1	1	yes	characteristic
25	C₂×Dic₁₀₁	—	2	1	no	—
26	C₂×Dic₁₀₁	D₄	1	1	yes	characteristic
27	C₂×Dic₁₀₁	D₄	1	1	yes	characteristic
28	D₄₀₄	—	2	1	no	—
29	D₄₀₄	—	2	1	no	—
30	Dic₂₀₂	—	4	2	no	—
31	C₈×C₁₀₁	—	2	1	no	—
32	#11717579	—	2	1	no	—
33	C₂²×C₁₀₁	C₂×D₄	1	1	yes	characteristic
34	C₂×D₁₀₁	—	4	1	no	—
35	C₂×D₁₀₁	—	4	1	no	—
36	C₂×D₁₀₁	—	4	1	no	—
37	C₄×C₁₀₁	—	4	1	no	—
38	C₄×C₁₀₁	—	4	1	no	—
39	C₄×C₁₀₁	#41	1	1	yes	characteristic
40	C₄×C₁₀₁	#41	1	1	yes	characteristic
41	Dic₁₀₁	—	2	1	no	—
42	Dic₁₀₁	—	2	1	no	—
43	Dic₁₀₁	—	4	1	no	—
44	C₂×C₁₀₁	#124	1	1	yes	characteristic
45	C₂×C₁₀₁	AGL(1,ℤ/8)	1	1	yes	characteristic
46	C₂×C₁₀₁	#137	1	1	yes	characteristic
47	D₁₀₁	—	8	1	no	—
48	C₁₀₁	#489	1	1	yes	characteristic, complemented, Sylow
49	#489	—	101	1	no	maximal, Sylow
50	C₄⋊Q₈	—	101	1	no	—
51	#124	—	101	1	no	—
52	#103	—	101	1	no	—
53	#103	D₁₀₁	1	1	yes	characteristic, complemented
54	#102	—	101	1	no	—
55	#102	—	101	1	no	—
56	#97	—	101	1	no	—
57	C₂×Q₈	—	202	1	no	—
58	C₂×Q₈	C₂×D₁₀₁	1	1	yes	characteristic
59	C₂×D₄	—	101	1	no	—
60	C₂×C₈	—	101	1	no	—
61	C₂×C₈	C₂×D₁₀₁	1	1	yes	characteristic
62	C₄⋊C₄	—	101	1	no	—
63	C₄⋊C₄	—	202	1	no	—
64	C₄⋊C₄	C₂×D₁₀₁	1	1	yes	characteristic
65	C₂²⋊C₄	—	202	1	no	—
66	C₂²⋊C₄	—	202	1	no	—
67	C₄²	—	101	1	no	—
68	C₂³	—	202	1	no	—
69	Q₈	—	2	1	no	—
70	Q₈	—	2	1	no	—
71	Q₈	—	404	2	no	—
72	D₄	—	202	1	no	—
73	D₄	—	202	1	no	—
74	C₂×C₄	—	2	1	no	—
75	C₂×C₄	—	2	1	no	—
76	C₂×C₄	—	101	1	no	—
77	C₂×C₄	—	101	1	no	—
78	C₂×C₄	—	202	1	no	—
79	C₂×C₄	C₂²×D₁₀₁	1	1	yes	characteristic
80	C₈	—	2	1	no	—
81	C₈	—	202	1	no	—
82	C₂²	—	404	1	no	—
83	C₂²	—	404	1	no	—
84	C₂²	—	404	1	no	—
85	C₂²	D₄×D₁₀₁	1	1	yes	characteristic
86	C₄	—	4	1	no	—
87	C₄	—	4	1	no	—
88	C₄	—	404	1	no	—
89	C₄	—	202	1	no	—
90	C₄	—	202	1	no	—
91	C₄	#13108073	1	1	yes	characteristic
92	C₄	#13108074	1	1	yes	characteristic
93	C₂	—	808	1	no	—
94	C₂	#15692241	1	1	yes	characteristic
95	C₂	#15692282	1	1	yes	characteristic
96	C₂	#15692287	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	D₄×D₁₀₁
commutator	C₂×C₄×C₁₀₁	C₂³
Frattini	C₂×C₄	C₂²×D₁₀₁
Fitting	#103×C₁₀₁	C₂
socle	C₂²×C₁₀₁	C₂×D₄
hypercenter	#103	D₁₀₁
hypocenter	C₁₀₁	#489
LCS	G ▷ C₂×C₄×C₁₀₁ ▷ C₂×C₁₀₁ ▷ C₁₀₁
UCS	C₁ ◁ C₂² ◁ C₂×C₄ ◁ #103

Complements

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

N	H ≅ G/N	type
1. #15692254	C₂	semidirect
3. #15692179	C₂	semidirect
6. #15692165	C₂	semidirect
7. #103×C₁₀₁	C₂	semidirect
48. C₁₀₁	#489	semidirect
53. #103	D₁₀₁	semidirect