Subgroups — #338×C₁₅₁ #23751682

Order 9664.

86 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×M₁₆×C₁₅₁	C₂	1	3	yes	maximal
2	C₂²×C₄×C₁₅₁	C₂²	1	1	yes	characteristic
3	M₁₆×C₁₅₁	—	2	6	no	—
4	C₂×C₈×C₁₅₁	C₄	1	6	yes	—
5	C₂³×C₁₅₁	Q₈	1	1	yes	characteristic
6	C₂×C₄×C₁₅₁	C₂×C₄	1	3	yes	—
7	C₂×C₄×C₁₅₁	D₄	1	3	yes	—
8	C₈×C₁₅₁	—	2	6	no	—
9	C₂²×C₁₅₁	—	4	1	no	—
10	C₂²×C₁₅₁	C₄⋊C₄	1	3	yes	—
11	C₄×C₁₅₁	C₄²	1	1	yes	characteristic
12	C₄×C₁₅₁	C₂²⋊C₄	1	3	yes	—
13	C₂×C₁₅₁	—	2	3	no	—
14	C₂×C₁₅₁	#95	1	1	yes	characteristic
15	C₁₅₁	#338	1	1	yes	characteristic, direct product factor, Sylow
16	#338	C₁₅₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
17	C₂×M₁₆	C₂×C₁₅₁	1	3	yes	—
18	C₂²×C₄	C₂²×C₁₅₁	1	1	yes	characteristic
19	M₁₆	—	2	6	no	—
20	C₂×C₈	C₄×C₁₅₁	1	6	yes	—
21	C₂³	Q₈×C₁₅₁	1	1	yes	characteristic
22	C₂×C₄	C₂×C₄×C₁₅₁	1	3	yes	—
23	C₂×C₄	D₄×C₁₅₁	1	3	yes	—
24	C₈	—	2	6	no	—
25	C₂²	—	4	1	no	—
26	C₂²	C₄⋊C₄×C₁₅₁	1	3	yes	—
27	C₄	C₄²×C₁₅₁	1	1	yes	characteristic
28	C₄	C₂²⋊C₄×C₁₅₁	1	3	yes	—
29	C₂	—	2	3	no	—
30	C₂	#95×C₁₅₁	1	1	yes	characteristic

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

N	H ≅ G/N	type
15. C₁₅₁	#338	direct (N × H)
16. #338	C₁₅₁	direct (N × H)

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
C₂×M₁₆×C₁₅₁	2
#338	151