Subgroups — C₂×#15692255 #20265721

Order 6464.

290 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×Dic₂₀₂	C₂	1	2	yes	maximal
2	#15692255	C₂	1	8	yes	maximal, direct product factor
3	C₂×C₄⋊Dic₁₀₁	C₂	1	4	yes	maximal
4	C₂×C₄²×C₁₀₁	C₂	1	1	yes	maximal, characteristic
5	C₂×Dic₂₀₂	—	2	8	no	—
6	C₂×Dic₂₀₂	C₂²	1	8	yes	—
7	C₂²×Dic₁₀₁	C₂²	1	4	yes	—
8	C₄⋊Dic₁₀₁	C₂²	1	16	yes	—
9	C₂²×C₄×C₁₀₁	C₂²	1	1	yes	characteristic
10	C₂²×C₄×C₁₀₁	C₂²	1	2	yes	—
11	C₄²×C₁₀₁	C₂²	1	4	yes	—
12	C₂³×C₁₀₁	C₂³	1	1	yes	characteristic
13	C₂×C₄×C₁₀₁	D₄	1	4	yes	—
14	C₂×C₄×C₁₀₁	Q₈	1	8	yes	complemented
15	C₂×C₄×C₁₀₁	C₂³	1	2	yes	—
16	C₂×C₄×C₁₀₁	C₂³	1	4	yes	—
17	C₂×Dic₁₀₁	—	2	8	no	—
18	C₂×Dic₁₀₁	C₂³	1	8	yes	—
19	Dic₂₀₂	—	2	16	no	—
20	C₂²×C₁₀₁	C₂×D₄	1	2	yes	—
21	C₂²×C₁₀₁	C₂×Q₈	1	4	yes	—
22	C₂²×C₁₀₁	C₂⁴	1	1	yes	characteristic
23	C₄×C₁₀₁	C₂×D₄	1	4	yes	—
24	C₄×C₁₀₁	C₂×Q₈	1	8	yes	complemented
25	Dic₁₀₁	—	2	8	no	—
26	C₂×C₁₀₁	C₄⋊Q₈	1	4	yes	complemented
27	C₂×C₁₀₁	C₂²×D₄	1	1	yes	characteristic
28	C₂×C₁₀₁	C₂²×Q₈	1	2	yes	—
29	C₁₀₁	C₂×C₄⋊Q₈	1	1	yes	characteristic, complemented, Sylow
30	C₂×C₄⋊Q₈	—	101	1	no	maximal, Sylow
31	C₂²×Q₈	—	101	2	no	—
32	C₄⋊Q₈	—	101	8	no	—
33	C₂×C₄⋊C₄	—	101	4	no	—
34	C₂×C₄²	D₁₀₁	1	1	yes	characteristic
35	C₂×Q₈	—	101	8	no	—
36	C₂×Q₈	—	202	8	no	—
37	C₂²×C₄	—	101	4	no	—
38	C₂²×C₄	C₂×D₁₀₁	1	2	yes	—
39	C₂²×C₄	C₂×D₁₀₁	1	1	yes	characteristic
40	C₄⋊C₄	—	101	16	no	—
41	C₄²	C₂×D₁₀₁	1	4	yes	—
42	C₂³	C₂²×D₁₀₁	1	1	yes	characteristic
43	Q₈	—	202	16	no	—
44	C₂×C₄	—	101	8	no	—
45	C₂×C₄	—	202	8	no	—
46	C₂×C₄	Dic₂₀₂	1	8	yes	complemented
47	C₂×C₄	D₄₀₄	1	4	yes	—
48	C₂×C₄	C₂²×D₁₀₁	1	2	yes	—
49	C₂×C₄	C₂²×D₁₀₁	1	4	yes	—
50	C₂²	C₂×D₄₀₄	1	2	yes	—
51	C₂²	C₂×Dic₂₀₂	1	4	yes	—
52	C₂²	C₂³×D₁₀₁	1	1	yes	characteristic
53	C₄	—	202	8	no	—
54	C₄	C₂×D₄₀₄	1	4	yes	—
55	C₄	C₂×Dic₂₀₂	1	8	yes	complemented
56	C₂	#15692255	1	4	yes	direct product factor
57	C₂	C₂²×D₄₀₄	1	1	yes	characteristic
58	C₂	C₂²×Dic₂₀₂	1	2	yes	—

	subgroup	G/H
center	C₂³	C₂²×D₁₀₁
commutator	C₂²×C₁₀₁	C₂⁴
Frattini	C₂²	C₂³×D₁₀₁
Fitting	C₂×C₄²×C₁₀₁	C₂
socle	C₂³×C₁₀₁	C₂³
hypercenter	C₂×C₄²	D₁₀₁
hypocenter	C₁₀₁	C₂×C₄⋊Q₈
LCS	G ▷ C₂²×C₁₀₁ ▷ C₁₀₁
UCS	C₁ ◁ C₂³ ◁ C₂×C₄²

Complements

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

N	H ≅ G/N	type
2. #15692255	C₂	direct (N × H)
14. C₂×C₄×C₁₀₁	Q₈	semidirect
24. C₄×C₁₀₁	C₂×Q₈	semidirect
26. C₂×C₁₀₁	C₄⋊Q₈	semidirect
29. C₁₀₁	C₂×C₄⋊Q₈	semidirect
46. C₂×C₄	Dic₂₀₂	semidirect
55. C₄	C₂×Dic₂₀₂	semidirect
56. C₂	#15692255	direct (N × H)

Subgroups — C2×#15692255 #20265721

Conjugacy classes of subgroups

Complements

Subgroups — C₂×#15692255 #20265721