Subgroups — #23752036

Order 9664.

42 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#18012679	C₂	1	1	yes	maximal, characteristic
2	#18012671	C₂	1	1	yes	maximal, characteristic
3	#108×C₁₅₁	C₂	1	1	yes	maximal, characteristic
4	C₄⋊Dic₁₅₁	—	2	1	no	—
5	C₁₅₁⋊C₁₆	C₄	1	2	yes	complemented
6	M₁₆×C₁₅₁	—	2	1	no	—
7	C₂×C₈×C₁₅₁	C₂²	1	1	yes	characteristic
8	C₂×Dic₁₅₁	—	4	1	no	—
9	C₂×C₄×C₁₅₁	D₄	1	1	yes	characteristic
10	C₈×C₁₅₁	—	4	1	no	—
11	C₈×C₁₅₁	C₂×C₄	1	1	yes	characteristic
12	C₈×C₁₅₁	Q₈	1	1	yes	characteristic
13	C₂²×C₁₅₁	SD₁₆	1	1	yes	characteristic
14	C₄×C₁₅₁	C₄⋊C₄	1	1	yes	characteristic
15	C₄×C₁₅₁	SD₁₆	1	1	yes	characteristic
16	Dic₁₅₁	—	8	1	no	—
17	C₂×C₁₅₁	—	2	1	no	—
18	C₂×C₁₅₁	#106	1	1	yes	characteristic
19	C₁₅₁	#365	1	1	yes	characteristic, complemented, Sylow
20	#365	—	151	1	no	maximal, Sylow
21	M₃₂	—	151	1	no	—
22	#108	D₁₅₁	1	1	yes	characteristic
23	#106	—	151	1	no	—
24	M₁₆	—	2	1	no	—
25	C₂×C₈	C₂×D₁₅₁	1	1	yes	characteristic
26	C₄⋊C₄	—	302	1	no	—
27	C₁₆	—	151	2	no	—
28	C₂×C₄	—	604	1	no	—
29	C₂×C₄	C₂²⋊D₁₅₁	1	1	yes	characteristic
30	C₈	—	4	1	no	—
31	C₈	C₄×D₁₅₁	1	1	yes	characteristic
32	C₈	Dic₃₀₂	1	1	yes	characteristic
33	C₂²	#14558991	1	1	yes	characteristic
34	C₄	—	1208	1	no	—
35	C₄	Dic₁₅₁⋊C₄	1	1	yes	characteristic
36	C₄	#14558992	1	1	yes	characteristic
37	C₂	—	2	1	no	—
38	C₂	#18012670	1	1	yes	characteristic

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

N	H ≅ G/N	type
5. C₁₅₁⋊C₁₆	C₄	semidirect
19. C₁₅₁	#365	semidirect