Subgroups — #532

Order 64.

155 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#41	C₂	1	2	yes	maximal, complemented
2	C₄⋊Q₈	C₂	1	1	yes	maximal, characteristic, complemented
3	#127	C₂	1	1	yes	maximal, characteristic, complemented
4	#124	C₂	1	2	yes	maximal, complemented
5	#121	C₂	1	4	yes	maximal, complemented
6	C₄×D₄	C₂	1	4	yes	maximal, complemented
7	C₂×C₄²	C₂	1	1	yes	maximal, characteristic, complemented
8	#41	—	2	8	no	—
9	C₂×Q₈	C₂²	1	2	yes	—
10	C₂×D₄	C₂²	1	4	yes	—
11	C₂×D₄	C₂²	1	4	yes	—
12	C₂×D₄	C₂²	1	2	yes	—
13	C₂²×C₄	C₂²	1	2	yes	—
14	C₂²×C₄	C₂²	1	4	yes	—
15	C₂²×C₄	C₂²	1	1	yes	characteristic
16	C₄⋊C₄	C₂²	1	4	yes	—
17	C₂²⋊C₄	C₂²	1	8	yes	—
18	C₄²	C₂²	1	1	yes	characteristic
19	C₄²	C₂²	1	1	yes	characteristic
20	C₄²	C₂²	1	2	yes	—
21	C₂³	C₂³	1	4	yes	—
22	C₂³	C₂³	1	1	yes	characteristic
23	Q₈	—	2	4	no	—
24	D₄	—	2	8	no	—
25	D₄	—	2	4	no	—
26	D₄	—	2	8	no	—
27	C₂×C₄	—	2	8	no	—
28	C₂×C₄	—	2	4	no	—
29	C₂×C₄	D₄	1	4	yes	complemented
30	C₂×C₄	C₂³	1	2	yes	—
31	C₂×C₄	C₂³	1	4	yes	—
32	C₂×C₄	C₂³	1	1	yes	characteristic
33	C₂×C₄	C₂³	1	2	yes	—
34	C₂×C₄	C₂³	1	1	yes	characteristic
35	C₂²	—	2	2	no	—
36	C₂²	—	2	4	no	—
37	C₂²	—	2	8	no	—
38	C₂²	C₂×D₄	1	2	yes	—
39	C₂²	C₂⁴	1	1	yes	characteristic
40	C₄	—	2	4	no	—
41	C₄	—	2	2	no	—
42	C₄	C₂×D₄	1	2	yes	—
43	C₄	C₂×D₄	1	2	yes	—
44	C₄	#41	1	4	yes	complemented
45	C₂	—	2	2	no	—
46	C₂	—	4	4	no	—
47	C₂	C₂²×D₄	1	1	yes	characteristic
48	C₂	C₂×#41	1	2	yes	—

	subgroup	G/H
center	C₂×C₄	C₂³
commutator, Frattini, socle, cosocle	C₂²	C₂⁴
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.