Subgroups — C₂²⋊#13108049 #20264957

Order 6464.

66 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#13108049	C₂	1	2	yes	maximal, complemented
2	C₂²×C₈×C₁₀₁	C₂	1	1	yes	maximal, characteristic
3	#13108049	—	2	2	no	—
4	C₂²×C₄×C₁₀₁	C₄	1	1	yes	characteristic
5	C₂×C₈×C₁₀₁	—	2	2	no	—
6	C₂×C₈×C₁₀₁	C₄	1	1	yes	characteristic
7	C₂×C₈×C₁₀₁	C₂²	1	1	yes	characteristic
8	C₂³×C₁₀₁	C₈	1	1	yes	characteristic
9	C₂×C₄×C₁₀₁	—	2	1	no	—
10	C₂×C₄×C₁₀₁	—	2	1	no	—
11	C₂×C₄×C₁₀₁	C₈	1	1	yes	characteristic
12	C₂×C₄×C₁₀₁	C₂×C₄	1	1	yes	characteristic
13	C₈×C₁₀₁	—	2	1	no	—
14	C₈×C₁₀₁	D₄	1	2	yes	—
15	C₂²×C₁₀₁	—	2	1	no	—
16	C₂²×C₁₀₁	—	2	1	no	—
17	C₂²×C₁₀₁	C₁₆	1	2	yes	complemented
18	C₂²×C₁₀₁	C₂×C₈	1	1	yes	characteristic
19	C₄×C₁₀₁	—	2	1	no	—
20	C₄×C₁₀₁	C₂²⋊C₄	1	1	yes	characteristic
21	C₄×C₁₀₁	M₁₆	1	1	yes	characteristic
22	C₂×C₁₀₁	—	2	2	no	—
23	C₂×C₁₀₁	C₂²⋊C₈	1	1	yes	characteristic
24	C₂×C₁₀₁	C₂×C₁₆	1	1	yes	characteristic
25	C₂×C₁₀₁	M₃₂	1	1	yes	characteristic
26	C₁₀₁	C₂²⋊C₁₆	1	1	yes	characteristic, complemented, Sylow
27	C₂²⋊C₁₆	—	101	1	no	maximal, Sylow
28	C₂²×C₈	D₁₀₁	1	1	yes	characteristic
29	C₂×C₁₆	—	101	2	no	—
30	C₂²×C₄	Dic₁₀₁	1	1	yes	characteristic
31	C₂×C₈	—	2	2	no	—
32	C₂×C₈	Dic₁₀₁	1	1	yes	characteristic
33	C₂×C₈	C₂×D₁₀₁	1	1	yes	characteristic
34	C₁₆	—	202	2	no	—
35	C₂³	#11717579	1	1	yes	characteristic
36	C₂×C₄	—	2	1	no	—
37	C₂×C₄	—	2	1	no	—
38	C₂×C₄	#11717579	1	1	yes	characteristic
39	C₂×C₄	C₂×Dic₁₀₁	1	1	yes	characteristic
40	C₈	—	2	1	no	—
41	C₈	C₂²⋊D₁₀₁	1	2	yes	—
42	C₂²	—	2	1	no	—
43	C₂²	—	2	1	no	—
44	C₂²	#13108049	1	2	yes	complemented
45	C₂²	C₂×#11717579	1	1	yes	characteristic
46	C₄	—	2	1	no	—
47	C₄	C₂²⋊Dic₁₀₁	1	1	yes	characteristic
48	C₄	#13108058	1	1	yes	characteristic
49	C₂	—	2	2	no	—
50	C₂	C₂²⋊#11717579	1	1	yes	characteristic
51	C₂	C₂×#13108049	1	1	yes	characteristic
52	C₂	#15692195	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂×C₈	C₂×D₁₀₁
commutator	C₂×C₁₀₁	C₂×C₁₆
Fitting	C₂²×C₈×C₁₀₁	C₂
socle	C₂²×C₁₀₁	C₂×C₈
hypercenter	C₂²×C₈	D₁₀₁
hypocenter	C₁₀₁	C₂²⋊C₁₆
LCS	G ▷ C₂×C₁₀₁ ▷ C₁₀₁
UCS	C₁ ◁ C₂×C₈ ◁ C₂²×C₈

Complements

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

N	H ≅ G/N	type
1. C₂×#13108049	C₂	semidirect
17. C₂²×C₁₀₁	C₁₆	semidirect
26. C₁₀₁	C₂²⋊C₁₆	semidirect
44. C₂²	#13108049	semidirect

Subgroups — C22⋊#13108049 #20264957

Conjugacy classes of subgroups

Complements

Subgroups — C₂²⋊#13108049 #20264957