Subgroups — C₂×C₄⋊C₈ #422

Order 64.

69 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₈	C₂	1	2	yes	maximal
2	C₂×C₄²	C₂	1	1	yes	maximal, characteristic
3	C₄⋊C₈	C₂	1	4	yes	maximal, direct product factor
4	C₂²×C₄	C₄	1	1	yes	characteristic
5	C₂²×C₄	C₄	1	1	yes	characteristic
6	C₂²×C₄	C₂²	1	1	yes	characteristic
7	C₂×C₈	—	2	4	no	—
8	C₂×C₈	C₂²	1	4	yes	—
9	C₄²	C₄	1	2	yes	—
10	C₄²	C₂²	1	2	yes	—
11	C₂³	C₂×C₄	1	1	yes	characteristic
12	C₂×C₄	—	2	2	no	—
13	C₂×C₄	C₈	1	4	yes	complemented
14	C₂×C₄	C₂×C₄	1	2	yes	—
15	C₂×C₄	C₂×C₄	1	1	yes	characteristic
16	C₂×C₄	C₂×C₄	1	2	yes	—
17	C₂×C₄	D₄	1	2	yes	—
18	C₂×C₄	Q₈	1	2	yes	—
19	C₂×C₄	C₂³	1	1	yes	characteristic
20	C₈	—	2	4	no	—
21	C₂²	C₄⋊C₄	1	2	yes	—
22	C₂²	C₂×C₈	1	2	yes	—
23	C₂²	M₁₆	1	2	yes	—
24	C₂²	C₂²×C₄	1	1	yes	characteristic
25	C₄	—	2	2	no	—
26	C₄	C₄⋊C₄	1	2	yes	—
27	C₄	C₂×C₈	1	4	yes	complemented
28	C₄	C₂×D₄	1	1	yes	characteristic
29	C₄	C₂×Q₈	1	1	yes	characteristic
30	C₂	C₄⋊C₈	1	4	yes	direct product factor
31	C₂	C₂×C₄⋊C₄	1	1	yes	characteristic
32	C₂	C₂²×C₈	1	1	yes	characteristic
33	C₂	C₂×M₁₆	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.