Subgroups — #533

Order 64.

111 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄⋊Q₈	C₂	1	2	yes	maximal, complemented
2	#125	C₂	1	2	yes	maximal, complemented
3	C₂²⋊Q₈	C₂	1	4	yes	maximal
4	C₄×Q₈	C₂	1	4	yes	maximal, complemented
5	#117	C₂	1	2	yes	maximal
6	C₂×C₄²	C₂	1	1	yes	maximal, characteristic
7	C₂×Q₈	C₂²	1	4	yes	—
8	C₂²×C₄	C₂²	1	2	yes	—
9	C₂²×C₄	C₂²	1	1	yes	characteristic
10	C₄⋊C₄	C₂²	1	4	yes	—
11	C₄⋊C₄	C₂²	1	8	yes	—
12	C₄⋊C₄	C₂²	1	4	yes	—
13	C₂²⋊C₄	C₂²	1	4	yes	—
14	C₄²	C₂²	1	1	yes	characteristic
15	C₄²	C₂²	1	1	yes	characteristic
16	C₄²	C₂²	1	2	yes	—
17	C₄²	C₂²	1	4	yes	—
18	C₂³	C₂³	1	1	yes	characteristic
19	Q₈	—	2	8	no	—
20	C₂×C₄	—	2	4	no	—
21	C₂×C₄	Q₈	1	4	yes	complemented
22	C₂×C₄	C₂³	1	2	yes	—
23	C₂×C₄	C₂³	1	8	yes	—
24	C₂×C₄	C₂³	1	1	yes	characteristic
25	C₂×C₄	C₂³	1	2	yes	—
26	C₂×C₄	C₂³	1	1	yes	characteristic
27	C₂²	—	2	2	no	—
28	C₂²	C₂×Q₈	1	2	yes	—
29	C₂²	C₂⁴	1	1	yes	characteristic
30	C₄	—	2	2	no	—
31	C₄	—	2	8	no	—
32	C₄	C₂×Q₈	1	2	yes	—
33	C₄	C₂×Q₈	1	2	yes	—
34	C₄	#41	1	4	yes	—
35	C₂	—	2	2	no	—
36	C₂	C₂²×Q₈	1	1	yes	characteristic
37	C₂	C₂×#41	1	2	yes	—

	subgroup	G/H
center	C₂×C₄	C₂³
commutator, Frattini, socle, cosocle	C₂²	C₂⁴
prime radical	C₂³	C₂³
LCS	G ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂×C₄ ◁ 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.