Subgroups — #24923051

Order 10688.

58 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#19128772	C₂	1	2	yes	maximal, complemented
2	C₂×M₁₆×C₁₆₇	C₂	1	1	yes	maximal, characteristic
3	C₁₆₇⋊C₁₆	—	2	2	no	—
4	C₂²×C₄×C₁₆₇	C₄	1	1	yes	characteristic
5	M₁₆×C₁₆₇	—	2	2	no	—
6	C₂×C₈×C₁₆₇	C₄	1	1	yes	characteristic
7	C₂×C₈×C₁₆₇	C₂²	1	1	yes	characteristic
8	C₂³×C₁₆₇	C₈	1	1	yes	characteristic
9	C₂×C₄×C₁₆₇	—	2	1	no	—
10	C₂×C₄×C₁₆₇	—	2	1	no	—
11	C₂×C₄×C₁₆₇	C₈	1	1	yes	characteristic
12	C₂×C₄×C₁₆₇	C₂×C₄	1	1	yes	characteristic
13	C₈×C₁₆₇	—	2	1	no	—
14	C₈×C₁₆₇	D₄	1	2	yes	—
15	C₂²×C₁₆₇	—	2	1	no	—
16	C₂²×C₁₆₇	—	4	1	no	—
17	C₂²×C₁₆₇	C₂×C₈	1	1	yes	characteristic
18	C₄×C₁₆₇	—	2	1	no	—
19	C₄×C₁₆₇	C₂²⋊C₄	1	1	yes	characteristic
20	C₄×C₁₆₇	M₁₆	1	1	yes	characteristic
21	C₂×C₁₆₇	—	2	1	no	—
22	C₂×C₁₆₇	—	4	1	no	—
23	C₂×C₁₆₇	C₂²⋊C₈	1	1	yes	characteristic
24	C₁₆₇	#349	1	1	yes	characteristic, complemented, Sylow
25	#349	—	167	1	no	maximal, Sylow
26	C₂×M₁₆	D₁₆₇	1	1	yes	characteristic
27	M₃₂	—	167	2	no	—
28	C₂²×C₄	Dic₁₆₇	1	1	yes	characteristic
29	M₁₆	—	2	2	no	—
30	C₂×C₈	Dic₁₆₇	1	1	yes	characteristic
31	C₂×C₈	C₂×D₁₆₇	1	1	yes	characteristic
32	C₁₆	—	334	2	no	—
33	C₂³	C₁₆₇⋊C₈	1	1	yes	characteristic
34	C₂×C₄	—	2	1	no	—
35	C₂×C₄	—	2	1	no	—
36	C₂×C₄	C₁₆₇⋊C₈	1	1	yes	characteristic
37	C₂×C₄	C₂×Dic₁₆₇	1	1	yes	characteristic
38	C₈	—	2	1	no	—
39	C₈	C₂²⋊D₁₆₇	1	2	yes	—
40	C₂²	—	2	1	no	—
41	C₂²	—	4	1	no	—
42	C₂²	C₂×C₁₆₇⋊C₈	1	1	yes	characteristic
43	C₄	—	2	1	no	—
44	C₄	C₂²⋊Dic₁₆₇	1	1	yes	characteristic
45	C₄	#14581934	1	1	yes	characteristic
46	C₂	—	2	1	no	—
47	C₂	—	4	1	no	—
48	C₂	C₂²⋊(C₁₆₇⋊C₈)	1	1	yes	characteristic

	subgroup	G/H
center	C₄	C₂²⋊Dic₁₆₇
commutator	C₂²×C₁₆₇	C₂×C₈
Frattini	C₂×C₈	C₂×D₁₆₇
Fitting	C₂×M₁₆×C₁₆₇	C₂
socle	C₂×C₁₆₇	C₂²⋊C₈
prime radical	C₂³×C₁₆₇	C₈
cosocle	C₂×C₈×C₁₆₇	C₂²
hypercenter	C₂×M₁₆	D₁₆₇
hypocenter	C₁₆₇	#349
LCS	G ▷ C₂²×C₁₆₇ ▷ C₂×C₁₆₇ ▷ C₁₆₇
UCS	C₁ ◁ C₄ ◁ C₂×C₈ ◁ C₂×M₁₆

Complements

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

N	H ≅ G/N	type
1. #19128772	C₂	semidirect
24. C₁₆₇	#349	semidirect