Subgroups — C₂×C₂²⋊C₄ #115

Order 32.

66 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂⁴	C₂	1	1	yes	maximal, characteristic
2	C₂²×C₄	C₂	1	2	yes	maximal, complemented
3	C₂²⋊C₄	C₂	1	4	yes	maximal, direct product factor
4	C₂³	—	2	4	no	—
5	C₂³	C₄	1	4	yes	complemented
6	C₂³	C₂²	1	2	yes	—
7	C₂³	C₂²	1	1	yes	characteristic
8	C₂×C₄	—	2	4	no	—
9	C₂×C₄	C₂²	1	4	yes	complemented
10	C₂²	—	2	8	no	—
11	C₂²	—	2	4	no	—
12	C₂²	C₂×C₄	1	2	yes	—
13	C₂²	C₂×C₄	1	4	yes	complemented
14	C₂²	D₄	1	4	yes	—
15	C₂²	C₂³	1	1	yes	characteristic
16	C₄	—	2	4	no	—
17	C₂	—	2	4	no	—
18	C₂	C₂²⋊C₄	1	4	yes	direct product factor
19	C₂	C₂²×C₄	1	1	yes	characteristic
20	C₂	C₂×D₄	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.