Subgroups — #131×C₂₅₁ #22548607

Order 8032.

62 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#41×C₂₅₁	C₂	1	1	yes	maximal, characteristic
2	M₁₆×C₂₅₁	C₂	1	3	yes	maximal, complemented
3	C₂×C₈×C₂₅₁	C₂	1	3	yes	maximal, complemented
4	Q₈×C₂₅₁	C₄	1	1	yes	characteristic
5	D₄×C₂₅₁	C₄	1	3	yes	—
6	C₂×C₄×C₂₅₁	C₂²	1	3	yes	—
7	C₈×C₂₅₁	C₂²	1	3	yes	—
8	C₈×C₂₅₁	C₂²	1	1	yes	characteristic
9	C₂²×C₂₅₁	C₂×C₄	1	3	yes	—
10	C₄×C₂₅₁	C₂×C₄	1	3	yes	—
11	C₄×C₂₅₁	C₂³	1	1	yes	characteristic
12	C₂×C₂₅₁	—	2	3	no	—
13	C₂×C₂₅₁	C₂²×C₄	1	1	yes	characteristic
14	C₂₅₁	#131	1	1	yes	characteristic, direct product factor, Sylow
15	#131	C₂₅₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
16	#41	C₂×C₂₅₁	1	1	yes	characteristic
17	M₁₆	C₂×C₂₅₁	1	3	yes	complemented
18	C₂×C₈	C₂×C₂₅₁	1	3	yes	complemented
19	Q₈	C₄×C₂₅₁	1	1	yes	characteristic
20	D₄	C₄×C₂₅₁	1	3	yes	—
21	C₂×C₄	C₂²×C₂₅₁	1	3	yes	—
22	C₈	C₂²×C₂₅₁	1	1	yes	characteristic
23	C₈	C₂²×C₂₅₁	1	3	yes	—
24	C₂²	C₂×C₄×C₂₅₁	1	3	yes	—
25	C₄	C₂×C₄×C₂₅₁	1	3	yes	—
26	C₄	C₂³×C₂₅₁	1	1	yes	characteristic
27	C₂	—	2	3	no	—
28	C₂	C₂²×C₄×C₂₅₁	1	1	yes	characteristic

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

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