Subgroups — #20265523

Order 6464.

118 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#15692255	C₂	1	1	yes	maximal, characteristic, complemented
2	#15692176	C₂	1	4	yes	maximal, complemented
3	C₄×#11717579	C₂	1	1	yes	maximal, characteristic, complemented
4	#127×C₁₀₁	C₂	1	1	yes	maximal, characteristic
5	C₂×Dic₂₀₂	—	2	1	no	—
6	C₂×#11717579	C₂²	1	2	yes	—
7	C₄⋊Dic₁₀₁	—	2	1	no	—
8	C₄⋊Dic₁₀₁	C₂²	1	2	yes	—
9	C₂×D₄×C₁₀₁	—	2	1	no	—
10	C₂×D₄×C₁₀₁	—	2	1	no	—
11	C₂×D₄×C₁₀₁	C₂²	1	2	yes	—
12	C₄²×C₁₀₁	C₂²	1	1	yes	characteristic
13	C₂³×C₁₀₁	—	2	2	no	—
14	D₄×C₁₀₁	—	2	4	no	—
15	D₄×C₁₀₁	—	4	2	no	—
16	D₄×C₁₀₁	—	4	2	no	—
17	C₂×C₄×C₁₀₁	D₄	1	1	yes	characteristic
18	C₂×C₄×C₁₀₁	D₄	1	1	yes	characteristic
19	C₂×C₄×C₁₀₁	C₂³	1	1	yes	characteristic
20	C₂×Dic₁₀₁	—	2	2	no	—
21	Dic₂₀₂	—	4	2	no	—
22	#11717579	—	2	2	no	—
23	C₂²×C₁₀₁	—	4	2	no	—
24	C₂²×C₁₀₁	—	4	2	no	—
25	C₂²×C₁₀₁	—	4	2	no	—
26	C₂²×C₁₀₁	C₂×D₄	1	1	yes	characteristic
27	C₄×C₁₀₁	D₈	1	2	yes	—
28	C₄×C₁₀₁	SD₁₆	1	2	yes	—
29	C₄×C₁₀₁	#41	1	2	yes	—
30	Dic₁₀₁	—	4	2	no	—
31	C₂×C₁₀₁	—	8	2	no	—
32	C₂×C₁₀₁	#124	1	1	yes	characteristic
33	C₂×C₁₀₁	C₂×D₈	1	1	yes	characteristic
34	C₂×C₁₀₁	C₂×SD₁₆	1	1	yes	characteristic
35	C₁₀₁	#486	1	1	yes	characteristic, complemented, Sylow
36	#486	—	101	1	no	maximal, Sylow
37	C₄⋊Q₈	—	101	1	no	—
38	#127	D₁₀₁	1	1	yes	characteristic
39	#102	—	101	4	no	—
40	C₄×C₈	—	101	1	no	—
41	C₂×Q₈	—	202	1	no	—
42	C₂×D₄	—	2	1	no	—
43	C₂×D₄	—	2	1	no	—
44	C₂×D₄	C₂×D₁₀₁	1	2	yes	—
45	C₂×C₈	—	101	2	no	—
46	C₄⋊C₄	—	101	2	no	—
47	C₄⋊C₄	—	202	1	no	—
48	C₄²	C₂×D₁₀₁	1	1	yes	characteristic
49	C₂³	—	2	2	no	—
50	Q₈	—	404	2	no	—
51	D₄	—	2	4	no	—
52	D₄	—	4	2	no	—
53	D₄	—	4	2	no	—
54	C₂×C₄	—	202	2	no	—
55	C₂×C₄	C₂²⋊D₁₀₁	1	1	yes	characteristic
56	C₂×C₄	C₂²⋊D₁₀₁	1	1	yes	characteristic
57	C₂×C₄	C₂²×D₁₀₁	1	1	yes	characteristic
58	C₈	—	202	2	no	—
59	C₂²	—	4	2	no	—
60	C₂²	—	4	2	no	—
61	C₂²	—	4	2	no	—
62	C₂²	C₂×C₂²⋊D₁₀₁	1	1	yes	characteristic
63	C₄	—	404	2	no	—
64	C₄	#13108059	1	2	yes	—
65	C₄	#13108062	1	2	yes	—
66	C₄	#13108073	1	2	yes	—
67	C₂	—	8	2	no	—
68	C₂	#15692242	1	1	yes	characteristic
69	C₂	C₂×#13108059	1	1	yes	characteristic
70	C₂	C₂×#13108062	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	C₂×C₂²⋊D₁₀₁
commutator	C₂×C₄×C₁₀₁	C₂³
Frattini	C₂×C₄	C₂²×D₁₀₁
Fitting	#127×C₁₀₁	C₂
socle	C₂²×C₁₀₁	C₂×D₄
hypercenter	#127	D₁₀₁
hypocenter	C₁₀₁	#486
LCS	G ▷ C₂×C₄×C₁₀₁ ▷ C₂×C₁₀₁ ▷ C₁₀₁
UCS	C₁ ◁ C₂² ◁ C₄² ◁ #127

Complements

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

N	H ≅ G/N	type
1. #15692255	C₂	semidirect
2. #15692176	C₂	semidirect
3. C₄×#11717579	C₂	semidirect
35. C₁₀₁	#486	semidirect