Subgroups — #20265271

Order 6464.

110 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×Dic₄₀₄	C₂	1	1	yes	maximal, characteristic
2	#15692220	C₂	1	2	yes	maximal
3	#15692178	C₂	1	2	yes	maximal
4	C₈×Dic₁₀₁	C₂	1	1	yes	maximal, characteristic
5	#107×C₁₀₁	C₂	1	1	yes	maximal, characteristic
6	C₂×Dic₂₀₂	C₂²	1	2	yes	—
7	Dic₄₀₄	C₄	1	4	yes	complemented
8	C₂×#11717579	C₂²	1	1	yes	characteristic
9	#13108053	—	2	2	no	—
10	C₄×Dic₁₀₁	—	2	2	no	—
11	C₄×Dic₁₀₁	C₂²	1	1	yes	characteristic
12	C₂×C₈×C₁₀₁	C₂²	1	1	yes	characteristic
13	C₄⋊C₄×C₁₀₁	C₂²	1	2	yes	—
14	C₂×C₄×C₁₀₁	—	2	2	no	—
15	C₂×C₄×C₁₀₁	C₂³	1	1	yes	characteristic
16	C₂×Dic₁₀₁	—	2	2	no	—
17	C₂×Dic₁₀₁	D₄	1	1	yes	characteristic
18	C₂×Dic₁₀₁	D₄	1	1	yes	characteristic
19	Dic₂₀₂	—	2	2	no	—
20	Dic₂₀₂	C₂×C₄	1	4	yes	—
21	C₈×C₁₀₁	C₂×C₄	1	2	yes	—
22	#11717579	—	2	1	no	—
23	C₂²×C₁₀₁	C₂×D₄	1	1	yes	characteristic
24	C₄×C₁₀₁	—	4	2	no	—
25	C₄×C₁₀₁	C₂²×C₄	1	1	yes	characteristic
26	C₄×C₁₀₁	#41	1	1	yes	characteristic
27	Dic₁₀₁	—	2	4	no	—
28	Dic₁₀₁	—	2	1	no	—
29	Dic₁₀₁	Q₁₆	1	2	yes	complemented
30	C₂×C₁₀₁	C₄×D₄	1	1	yes	characteristic
31	C₂×C₁₀₁	C₂×Q₁₆	1	1	yes	characteristic
32	C₂×C₁₀₁	#135	1	1	yes	characteristic
33	C₁₀₁	C₄×Q₁₆	1	1	yes	characteristic, complemented, Sylow
34	C₄×Q₁₆	—	101	1	no	maximal, Sylow
35	C₂×Q₁₆	—	101	1	no	—
36	C₄×Q₈	—	101	2	no	—
37	#107	D₁₀₁	1	1	yes	characteristic
38	#103	—	101	2	no	—
39	C₄×C₈	—	101	1	no	—
40	C₂×Q₈	—	101	2	no	—
41	Q₁₆	—	101	4	no	—
42	C₂×C₈	—	101	1	no	—
43	C₂×C₈	C₂×D₁₀₁	1	1	yes	characteristic
44	C₄⋊C₄	—	202	2	no	—
45	C₄⋊C₄	C₂×D₁₀₁	1	2	yes	—
46	C₄²	—	101	1	no	—
47	C₄²	—	202	2	no	—
48	Q₈	—	101	4	no	—
49	Q₈	—	202	2	no	—
50	C₂×C₄	—	2	2	no	—
51	C₂×C₄	—	101	1	no	—
52	C₂×C₄	—	101	1	no	—
53	C₂×C₄	—	202	2	no	—
54	C₂×C₄	C₂²×D₁₀₁	1	1	yes	characteristic
55	C₈	—	202	1	no	—
56	C₈	C₄×D₁₀₁	1	2	yes	—
57	C₂²	D₄×D₁₀₁	1	1	yes	characteristic
58	C₄	—	4	2	no	—
59	C₄	—	101	2	no	—
60	C₄	—	202	4	no	—
61	C₄	—	202	1	no	—
62	C₄	C₂×C₄×D₁₀₁	1	1	yes	characteristic
63	C₄	#13108075	1	1	yes	characteristic
64	C₂	#15692217	1	1	yes	characteristic
65	C₂	Q₁₆×D₁₀₁	1	1	yes	characteristic
66	C₂	#15692274	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	D₄×D₁₀₁
commutator	C₄×C₁₀₁	C₂²×C₄
Frattini	C₂×C₄	C₂²×D₁₀₁
Fitting	#107×C₁₀₁	C₂
socle	C₂²×C₁₀₁	C₂×D₄
hypercenter	#107	D₁₀₁
hypocenter	C₁₀₁	C₄×Q₁₆
LCS	G ▷ C₄×C₁₀₁ ▷ C₂×C₁₀₁ ▷ C₁₀₁
UCS	C₁ ◁ C₂² ◁ C₂×C₄ ◁ #107

Complements

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

N	H ≅ G/N	type
7. Dic₄₀₄	C₄	semidirect
29. Dic₁₀₁	Q₁₆	semidirect
33. C₁₀₁	C₄×Q₁₆	semidirect