Subgroups — #10620296

Order 656.

22 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄×D₄₁	C₂	1	1	yes	maximal, characteristic
2	#66493	C₂	1	2	yes	maximal, complemented
3	C₂×D₄₁	C₄	1	1	yes	characteristic
4	C₄×C₄₁	C₄	1	1	yes	characteristic
5	Dic₄₁	C₂²	1	1	yes	characteristic
6	C₂×C₄₁	C₂×C₄	1	1	yes	characteristic
7	D₄₁	C₈	1	2	yes	complemented
8	C₄₁	C₂×C₈	1	1	yes	characteristic, complemented, Sylow
9	C₂×C₈	—	41	1	no	maximal, Sylow
10	C₂×C₄	—	41	1	no	—
11	C₈	—	41	2	no	—
12	C₂²	—	41	1	no	—
13	C₄	—	41	1	no	—
14	C₄	#4223	1	1	yes	characteristic
15	C₂	—	41	2	no	—
16	C₂	C₂×#4223	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.