Subgroups — D₄×Q₈ #549

Order 64.

140 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×Q₈	C₂	1	2	yes	maximal, complemented
2	C₄⋊Q₈	C₂	1	3	yes	maximal, complemented
3	C₂²⋊Q₈	C₂	1	6	yes	maximal, complemented
4	C₄×Q₈	C₂	1	1	yes	maximal, characteristic, complemented
5	C₄×D₄	C₂	1	3	yes	maximal
6	C₂×Q₈	—	2	8	no	—
7	C₂×Q₈	C₂²	1	6	yes	—
8	C₂×Q₈	C₂²	1	1	yes	characteristic
9	C₂×D₄	C₂²	1	1	yes	characteristic
10	C₂²×C₄	C₂²	1	6	yes	—
11	C₄⋊C₄	C₂²	1	3	yes	—
12	C₄⋊C₄	C₂²	1	3	yes	—
13	C₄⋊C₄	C₂²	1	6	yes	—
14	C₂²⋊C₄	C₂²	1	6	yes	—
15	C₄²	C₂²	1	3	yes	—
16	C₂³	C₂³	1	2	yes	—
17	Q₈	—	2	12	no	—
18	Q₈	D₄	1	4	yes	direct product factor
19	D₄	Q₈	1	4	yes	direct product factor
20	C₂×C₄	—	2	12	no	—
21	C₂×C₄	C₂³	1	3	yes	—
22	C₂×C₄	C₂³	1	6	yes	—
23	C₂×C₄	C₂³	1	3	yes	—
24	C₂×C₄	C₂³	1	1	yes	characteristic
25	C₂²	—	2	2	no	—
26	C₂²	—	2	2	no	—
27	C₂²	C₂×Q₈	1	4	yes	complemented
28	C₂²	C₂⁴	1	1	yes	characteristic
29	C₄	—	2	6	no	—
30	C₄	—	2	3	no	—
31	C₄	C₂×D₄	1	6	yes	—
32	C₄	C₂×Q₈	1	2	yes	complemented
33	C₂	—	2	4	no	—
34	C₂	C₂²×D₄	1	1	yes	characteristic
35	C₂	C₂²×Q₈	1	1	yes	characteristic
36	C₂	2₋¹⁺⁴	1	1	yes	characteristic

	subgroup	G/H
center, commutator, Frattini, socle, cosocle	C₂²	C₂⁴
prime radical	C₂×D₄	C₂²
LCS	G ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂² ◁ G
LECS	G ▷ C₂² ▷ C₁

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.