Subgroups — #23752628

Order 9664.

84 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#18012745	C₂	1	1	yes	maximal, characteristic
2	#18012679	C₂	1	1	yes	maximal, characteristic, complemented
3	#18012678	C₂	1	2	yes	maximal, complemented
4	C₁₆×D₁₅₁	C₂	1	2	yes	maximal, complemented
5	C₂×C₁₆×C₁₅₁	C₂	1	1	yes	maximal, characteristic, complemented
6	#14559004	C₄	1	1	yes	characteristic
7	#14558988	C₄	1	1	yes	characteristic
8	#14558987	C₄	1	2	yes	—
9	C₈×D₁₅₁	C₂²	1	2	yes	—
10	C₁₅₁⋊C₁₆	C₂²	1	2	yes	—
11	C₂×C₈×C₁₅₁	C₂²	1	1	yes	characteristic
12	C₁₆×C₁₅₁	C₂²	1	1	yes	characteristic
13	C₁₆×C₁₅₁	C₂²	1	1	yes	characteristic
14	Dic₃₀₂	C₈	1	1	yes	characteristic
15	D₆₀₄	C₈	1	1	yes	characteristic
16	C₂²⋊D₁₅₁	C₈	1	2	yes	—
17	C₄×D₁₅₁	C₂×C₄	1	2	yes	—
18	C₁₅₁⋊C₈	C₂×C₄	1	2	yes	—
19	C₂×C₄×C₁₅₁	C₂×C₄	1	1	yes	characteristic
20	C₈×C₁₅₁	C₂×C₄	1	1	yes	characteristic
21	C₈×C₁₅₁	C₂³	1	1	yes	characteristic
22	C₂²×C₁₅₁	C₂×C₈	1	1	yes	characteristic
23	C₂×D₁₅₁	C₂×C₈	1	2	yes	—
24	C₄×C₁₅₁	C₂×C₈	1	1	yes	characteristic
25	C₄×C₁₅₁	C₂²×C₄	1	1	yes	characteristic
26	Dic₁₅₁	C₂×C₈	1	2	yes	—
27	C₂×C₁₅₁	—	2	1	no	—
28	C₂×C₁₅₁	C₂²×C₈	1	1	yes	characteristic
29	D₁₅₁	—	2	2	no	—
30	C₁₅₁	#504	1	1	yes	characteristic, complemented, Sylow
31	#504	—	151	1	no	maximal, Sylow
32	#131	—	151	1	no	—
33	M₃₂	—	151	1	no	—
34	M₃₂	—	151	2	no	—
35	C₂×C₁₆	—	151	2	no	—
36	C₂×C₁₆	D₁₅₁	1	1	yes	characteristic, complemented
37	#41	—	151	1	no	—
38	M₁₆	—	151	1	no	—
39	M₁₆	—	151	2	no	—
40	C₂×C₈	—	151	2	no	—
41	C₂×C₈	C₂×D₁₅₁	1	1	yes	characteristic
42	C₁₆	—	151	2	no	—
43	C₁₆	C₂×D₁₅₁	1	1	yes	characteristic
44	C₁₆	C₂×D₁₅₁	1	1	yes	characteristic
45	Q₈	—	151	1	no	—
46	D₄	—	151	2	no	—
47	D₄	—	151	1	no	—
48	C₂×C₄	—	151	2	no	—
49	C₂×C₄	C₄×D₁₅₁	1	1	yes	characteristic
50	C₈	—	151	2	no	—
51	C₈	C₄×D₁₅₁	1	1	yes	characteristic
52	C₈	C₂²×D₁₅₁	1	1	yes	characteristic
53	C₂²	—	151	2	no	—
54	C₂²	C₈×D₁₅₁	1	1	yes	characteristic
55	C₄	—	151	2	no	—
56	C₄	C₈×D₁₅₁	1	1	yes	characteristic
57	C₄	C₂×C₄×D₁₅₁	1	1	yes	characteristic
58	C₂	—	2	1	no	—
59	C₂	—	302	2	no	—
60	C₂	C₂×C₈×D₁₅₁	1	1	yes	characteristic

	subgroup	G/H
center	C₁₆	C₂×D₁₅₁
commutator, socle	C₂×C₁₅₁	C₂²×C₈
Frattini	C₈	C₂²×D₁₅₁
Fitting	C₂×C₁₆×C₁₅₁	C₂
prime radical	#14559004	C₄
cosocle	C₈×C₁₅₁	C₂³
hypercenter	C₂×C₁₆	D₁₅₁
hypocenter	C₁₅₁	#504
LCS	G ▷ C₂×C₁₅₁ ▷ C₁₅₁
UCS	C₁ ◁ C₁₆ ◁ C₂×C₁₆

Complements

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

N	H ≅ G/N	type
2. #18012679	C₂	semidirect
3. #18012678	C₂	semidirect
4. C₁₆×D₁₅₁	C₂	semidirect
5. C₂×C₁₆×C₁₅₁	C₂	semidirect
30. C₁₅₁	#504	semidirect
36. C₂×C₁₆	D₁₅₁	semidirect