Subgroups — #27165656

Order 12832.

38 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#20264350	C₂	1	2	yes	maximal
2	C₂×Q₈×C₄₀₁	C₂	1	1	yes	maximal, characteristic
3	#15691999	—	2	2	no	—
4	Q₈×C₄₀₁	—	2	2	no	—
5	C₂×C₄×C₄₀₁	C₄	1	2	yes	—
6	C₂×C₄×C₄₀₁	C₂²	1	1	yes	characteristic
7	C₂²×C₄₀₁	C₂×C₄	1	1	yes	characteristic
8	C₄×C₄₀₁	—	2	2	no	—
9	C₄×C₄₀₁	D₄	1	2	yes	—
10	C₂×C₄₀₁	—	2	1	no	—
11	C₂×C₄₀₁	C₂²⋊C₄	1	1	yes	characteristic
12	C₄₀₁	#101	1	1	yes	characteristic, complemented, Sylow
13	#101	—	401	1	no	maximal, Sylow
14	C₂×Q₈	D₄₀₁	1	1	yes	characteristic
15	M₁₆	—	401	2	no	—
16	Q₈	—	2	2	no	—
17	C₂×C₄	Dic₄₀₁	1	2	yes	—
18	C₂×C₄	C₂×D₄₀₁	1	1	yes	characteristic
19	C₈	—	802	2	no	—
20	C₂²	C₂×Dic₄₀₁	1	1	yes	characteristic
21	C₄	—	2	2	no	—
22	C₄	C₂²⋊D₄₀₁	1	2	yes	—
23	C₂	—	2	1	no	—
24	C₂	C₂²⋊Dic₄₀₁	1	1	yes	characteristic

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

N	H ≅ G/N	type
12. C₄₀₁	#101	semidirect

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