Subgroups — #482

Order 64.

53 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#121	C₂	1	1	yes	maximal, characteristic
2	#117	C₂	1	1	yes	maximal, characteristic, complemented
3	#107	C₂	1	1	yes	maximal, characteristic, complemented
4	#106	C₂	1	1	yes	maximal, characteristic, complemented
5	#102	C₂	1	1	yes	maximal, characteristic, complemented
6	#102	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂²⋊C₈	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×D₄	—	2	1	no	—
9	C₂×D₄	C₂²	1	1	yes	characteristic
10	C₂²×C₄	C₂²	1	1	yes	characteristic
11	C₂×C₈	C₂²	1	1	yes	characteristic
12	C₂×C₈	C₂²	1	1	yes	characteristic
13	C₄⋊C₄	C₂²	1	1	yes	characteristic
14	C₄⋊C₄	C₂²	1	1	yes	characteristic
15	C₄⋊C₄	C₂²	1	1	yes	characteristic
16	C₂²⋊C₄	—	2	1	no	—
17	C₂²⋊C₄	—	2	1	no	—
18	C₄²	—	2	1	no	—
19	C₂³	—	2	1	no	—
20	C₂³	D₄	1	1	yes	characteristic
21	D₄	—	2	1	no	—
22	D₄	—	2	1	no	—
23	D₄	—	4	2	no	—
24	C₂×C₄	—	2	1	no	—
25	C₂×C₄	—	2	1	no	—
26	C₂×C₄	—	2	1	no	—
27	C₂×C₄	—	2	1	no	—
28	C₂×C₄	—	2	1	no	—
29	C₂×C₄	D₄	1	1	yes	characteristic
30	C₂×C₄	C₂³	1	1	yes	characteristic
31	C₈	—	2	1	no	—
32	C₈	—	2	1	no	—
33	C₂²	—	2	1	no	—
34	C₂²	—	2	1	no	—
35	C₂²	—	2	1	no	—
36	C₂²	—	4	1	no	—
37	C₂²	—	4	1	no	—
38	C₂²	—	4	1	no	—
39	C₂²	C₂×D₄	1	1	yes	characteristic
40	C₄	—	2	1	no	—
41	C₄	—	4	1	no	—
42	C₄	—	4	1	no	—
43	C₄	—	4	1	no	—
44	C₄	#41	1	1	yes	characteristic
45	C₄	#41	1	1	yes	characteristic
46	C₂	—	4	1	no	—
47	C₂	—	8	1	no	—
48	C₂	#123	1	1	yes	characteristic
49	C₂	#135	1	1	yes	characteristic
50	C₂	AGL(1,ℤ/8)	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²	C₂×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂³
prime radical	#121	C₂
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂² ◁ C₂²×C₄ ◁ G
LECS	G ▷ C₂×C₄ ▷ C₂ ▷ 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.