Subgroups — #20265298

Order 6464.

104 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#15692277	C₂	1	1	yes	maximal, characteristic
2	#15692263	C₂	1	2	yes	maximal, complemented
3	#15692181	C₂	1	2	yes	maximal, complemented
4	#15692165	C₂	1	1	yes	maximal, characteristic, complemented
5	#108×C₁₀₁	C₂	1	1	yes	maximal, characteristic, complemented
6	#13108074	C₂²	1	2	yes	—
7	Dic₄₀₄	C₄	1	1	yes	characteristic, complemented
8	#13108063	C₄	1	2	yes	complemented
9	D₈₀₈	C₄	1	1	yes	characteristic, complemented
10	#13108057	—	2	2	no	—
11	C₂×#11717579	C₂²	1	1	yes	characteristic
12	C₈×D₁₀₁	—	2	2	no	—
13	C₄×Dic₁₀₁	C₂²	1	1	yes	characteristic
14	M₁₆×C₁₀₁	C₂²	1	2	yes	—
15	C₂×C₈×C₁₀₁	C₂²	1	1	yes	characteristic
16	C₂×C₄×C₁₀₁	C₂³	1	1	yes	characteristic
17	C₂²⋊D₁₀₁	—	2	2	no	—
18	C₂×Dic₁₀₁	—	2	1	no	—
19	D₄₀₄	C₂×C₄	1	2	yes	—
20	C₄×D₁₀₁	—	2	2	no	—
21	Dic₂₀₂	C₂×C₄	1	2	yes	—
22	C₈×C₁₀₁	—	2	2	no	—
23	C₈×C₁₀₁	C₂×C₄	1	1	yes	characteristic
24	C₈×C₁₀₁	C₂×C₄	1	1	yes	characteristic
25	#11717579	D₄	1	2	yes	—
26	C₂²×C₁₀₁	#41	1	1	yes	characteristic
27	C₂×D₁₀₁	—	2	2	no	—
28	C₄×C₁₀₁	C₂²×C₄	1	1	yes	characteristic
29	C₄×C₁₀₁	C₂×D₄	1	1	yes	characteristic
30	Dic₁₀₁	—	2	2	no	—
31	Dic₁₀₁	—	4	1	no	—
32	C₂×C₁₀₁	—	2	1	no	—
33	C₂×C₁₀₁	C₄×D₄	1	1	yes	characteristic
34	D₁₀₁	—	4	2	no	—
35	C₁₀₁	#444	1	1	yes	characteristic, complemented, Sylow
36	#444	—	101	1	no	maximal, Sylow
37	#135	—	101	1	no	—
38	#131	—	101	2	no	—
39	#108	D₁₀₁	1	1	yes	characteristic, complemented
40	#104	—	101	2	no	—
41	#97	—	101	1	no	—
42	#41	—	101	2	no	—
43	Q₁₆	—	101	1	no	—
44	SD₁₆	—	101	2	no	—
45	D₈	—	101	1	no	—
46	M₁₆	—	202	2	no	—
47	M₁₆	C₂×D₁₀₁	1	2	yes	—
48	C₂×C₈	—	101	1	no	—
49	C₂×C₈	—	202	2	no	—
50	C₂×C₈	C₂×D₁₀₁	1	1	yes	characteristic
51	C₄²	—	101	1	no	—
52	Q₈	—	101	2	no	—
53	D₄	—	101	2	no	—
54	D₄	—	202	2	no	—
55	C₂×C₄	—	202	1	no	—
56	C₂×C₄	—	202	2	no	—
57	C₂×C₄	C₂²×D₁₀₁	1	1	yes	characteristic
58	C₈	—	2	2	no	—
59	C₈	—	101	2	no	—
60	C₈	C₄×D₁₀₁	1	1	yes	characteristic
61	C₈	C₄×D₁₀₁	1	1	yes	characteristic
62	C₂²	—	202	2	no	—
63	C₂²	#13108075	1	1	yes	characteristic
64	C₄	—	404	1	no	—
65	C₄	—	202	2	no	—
66	C₄	C₂×C₄×D₁₀₁	1	1	yes	characteristic
67	C₄	D₄×D₁₀₁	1	1	yes	characteristic
68	C₂	—	2	1	no	—
69	C₂	—	404	2	no	—
70	C₂	#15692217	1	1	yes	characteristic

	subgroup	G/H
center	C₄	D₄×D₁₀₁
commutator	C₄×C₁₀₁	C₂²×C₄
Frattini	C₂×C₄	C₂²×D₁₀₁
Fitting	#108×C₁₀₁	C₂
socle	C₂×C₁₀₁	C₄×D₄
hypercenter	#108	D₁₀₁
hypocenter	C₁₀₁	#444
LCS	G ▷ C₄×C₁₀₁ ▷ C₂×C₁₀₁ ▷ C₁₀₁
UCS	C₁ ◁ C₄ ◁ C₂×C₄ ◁ #108

Complements

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

N	H ≅ G/N	type
2. #15692263	C₂	semidirect
3. #15692181	C₂	semidirect
4. #15692165	C₂	semidirect
5. #108×C₁₀₁	C₂	semidirect
7. Dic₄₀₄	C₄	semidirect
8. #13108063	C₄	semidirect
9. D₈₀₈	C₄	semidirect
35. C₁₀₁	#444	semidirect
39. #108	D₁₀₁	semidirect