Subgroups — #392

Order 64.

161 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×D₄	C₂	1	3	yes	maximal, complemented
2	C₂×C₂²⋊C₄	C₂	1	3	yes	maximal, complemented
3	#95	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂⁴	C₂²	1	3	yes	—
5	C₂×D₄	—	2	12	no	—
6	C₂×D₄	—	2	6	no	—
7	C₂²×C₄	C₂²	1	1	yes	characteristic
8	C₂²×C₄	C₂²	1	3	yes	—
9	C₂²⋊C₄	—	2	6	no	—
10	C₂³	—	2	3	no	—
11	C₂³	—	2	6	no	—
12	C₂³	—	2	6	no	—
13	C₂³	—	2	3	no	—
14	C₂³	D₄	1	6	yes	complemented
15	C₂³	C₂³	1	1	yes	characteristic
16	D₄	—	2	24	no	—
17	C₂×C₄	—	2	6	no	—
18	C₂×C₄	—	2	3	no	—
19	C₂×C₄	D₄	1	6	yes	complemented
20	C₂²	—	2	12	no	—
21	C₂²	—	2	6	no	—
22	C₂²	—	4	3	no	—
23	C₂²	—	4	6	no	—
24	C₂²	—	4	3	no	—
25	C₂²	C₂×D₄	1	3	yes	—
26	C₂²	C₂×D₄	1	3	yes	—
27	C₂²	#41	1	1	yes	characteristic
28	C₄	—	2	6	no	—
29	C₄	—	4	1	no	—
30	C₂	—	4	6	no	—
31	C₂	#120	1	3	yes	—
32	C₂	#121	1	3	yes	—
33	C₂	#127	1	1	yes	characteristic

	subgroup	G/H
center, commutator, Frattini, socle, cosocle	C₂³	C₂³
LCS	G ▷ C₂³ ▷ C₁
UCS	C₁ ◁ C₂³ ◁ G
LECS	G ▷ C₂³ ▷ 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.