Subgroups — #117

Order 32.

38 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₄	C₂	1	1	yes	maximal, characteristic
2	C₄⋊C₄	C₂	1	2	yes	maximal, complemented
3	C₂²⋊C₄	C₂	1	2	yes	maximal
4	C₄²	C₂	1	2	yes	maximal, complemented
5	C₂³	C₂²	1	1	yes	characteristic
6	C₂×C₄	C₄	1	4	yes	complemented
7	C₂×C₄	C₂²	1	4	yes	—
8	C₂×C₄	C₂²	1	1	yes	characteristic
9	C₂×C₄	C₂²	1	1	yes	characteristic
10	C₂²	—	2	2	no	—
11	C₂²	C₂×C₄	1	2	yes	—
12	C₂²	C₂³	1	1	yes	characteristic
13	C₄	—	2	4	no	—
14	C₄	C₂×C₄	1	2	yes	—
15	C₄	C₂×C₄	1	2	yes	—
16	C₂	—	2	2	no	—
17	C₂	C₂²×C₄	1	1	yes	characteristic
18	C₂	#41	1	2	yes	—

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.