Subgroups — D₄⋊C₈ #325

Order 64.

41 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄×D₄	C₂	1	1	yes	maximal, characteristic
2	C₄⋊C₈	C₂	1	1	yes	maximal, characteristic, complemented
3	C₄×C₈	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×D₄	C₄	1	1	yes	characteristic
5	C₂²×C₄	—	2	1	no	—
6	C₂×C₈	—	2	1	no	—
7	C₂×C₈	—	2	1	no	—
8	C₄⋊C₄	C₄	1	1	yes	characteristic
9	C₂²⋊C₄	—	2	1	no	—
10	C₄²	C₂²	1	1	yes	characteristic
11	C₂³	—	2	1	no	—
12	D₄	—	2	1	no	—
13	D₄	C₈	1	2	yes	complemented
14	C₂×C₄	—	2	1	no	—
15	C₂×C₄	—	4	1	no	—
16	C₂×C₄	—	4	1	no	—
17	C₂×C₄	C₂×C₄	1	1	yes	characteristic
18	C₂×C₄	D₄	1	1	yes	characteristic
19	C₂×C₄	D₄	1	1	yes	characteristic
20	C₈	—	2	2	no	—
21	C₈	—	4	1	no	—
22	C₂²	—	2	2	no	—
23	C₂²	—	4	1	no	—
24	C₂²	—	4	1	no	—
25	C₂²	C₂²⋊C₄	1	1	yes	characteristic
26	C₄	—	2	1	no	—
27	C₄	—	4	1	no	—
28	C₄	C₂×C₈	1	1	yes	characteristic
29	C₄	M₁₆	1	1	yes	characteristic
30	C₄	D₈	1	1	yes	characteristic
31	C₄	SD₁₆	1	1	yes	characteristic
32	C₂	—	4	2	no	—
33	C₂	C₂²⋊C₈	1	1	yes	characteristic
34	C₂	#102	1	1	yes	characteristic
35	C₂	#104	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.