Subgroups — #485

Order 64.

48 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²⋊Q₈	C₂	1	1	yes	maximal, characteristic
2	#117	C₂	1	1	yes	maximal, characteristic
3	#107	C₂	1	1	yes	maximal, characteristic, complemented
4	#106	C₂	1	1	yes	maximal, characteristic, complemented
5	#103	C₂	1	1	yes	maximal, characteristic, complemented
6	#103	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂²⋊C₈	C₂	1	1	yes	maximal, characteristic
8	C₂×Q₈	C₂²	1	1	yes	characteristic
9	C₂²×C₄	C₂²	1	1	yes	characteristic
10	C₂×C₈	C₂²	1	1	yes	characteristic
11	C₂×C₈	C₂²	1	1	yes	characteristic
12	C₄⋊C₄	—	2	1	no	—
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	D₄	1	1	yes	characteristic
20	Q₈	—	2	1	no	—
21	Q₈	—	2	1	no	—
22	C₂×C₄	—	2	1	no	—
23	C₂×C₄	—	2	1	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	D₄	1	1	yes	characteristic
29	C₂×C₄	C₂³	1	1	yes	characteristic
30	C₈	—	2	1	no	—
31	C₈	—	2	1	no	—
32	C₂²	—	2	1	no	—
33	C₂²	—	2	1	no	—
34	C₂²	—	2	1	no	—
35	C₂²	C₂×D₄	1	1	yes	characteristic
36	C₄	—	2	1	no	—
37	C₄	—	4	1	no	—
38	C₄	—	4	1	no	—
39	C₄	—	4	1	no	—
40	C₄	—	4	1	no	—
41	C₄	#41	1	1	yes	characteristic
42	C₄	#41	1	1	yes	characteristic
43	C₂	—	4	1	no	—
44	C₂	#123	1	1	yes	characteristic
45	C₂	#135	1	1	yes	characteristic
46	C₂	#137	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²	C₂×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂³
prime radical	C₂³	D₄
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.