Subgroups — C₂×#124 #526

Order 64.

165 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, complemented
2	C₂²×D₄	C₂	1	1	yes	maximal, characteristic
3	#124	C₂	1	8	yes	maximal, direct product factor
4	C₂×C₂²⋊C₄	C₂	1	4	yes	maximal, complemented
5	C₂×C₄²	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂⁴	C₂²	1	2	yes	—
7	C₂×Q₈	—	2	4	no	—
8	C₂×Q₈	C₂²	1	4	yes	complemented
9	C₂×D₄	—	2	4	no	—
10	C₂×D₄	C₂²	1	4	yes	—
11	C₂²×C₄	C₂²	1	2	yes	—
12	C₂²×C₄	C₂²	1	2	yes	—
13	C₂²×C₄	C₂²	1	1	yes	characteristic
14	C₂²⋊C₄	C₂²	1	16	yes	complemented
15	C₄²	C₂²	1	4	yes	complemented
16	C₂³	—	2	4	no	—
17	C₂³	—	2	8	no	—
18	C₂³	C₂³	1	4	yes	—
19	C₂³	C₂³	1	1	yes	characteristic
20	Q₈	—	2	8	no	—
21	D₄	—	2	8	no	—
22	C₂×C₄	—	2	4	no	—
23	C₂×C₄	—	2	4	no	—
24	C₂×C₄	D₄	1	4	yes	—
25	C₂×C₄	C₂³	1	4	yes	—
26	C₂×C₄	C₂³	1	4	yes	—
27	C₂×C₄	C₂³	1	2	yes	—
28	C₂²	—	2	4	no	—
29	C₂²	—	2	8	no	—
30	C₂²	—	4	8	no	—
31	C₂²	C₂×D₄	1	2	yes	—
32	C₂²	#41	1	4	yes	—
33	C₂²	C₂⁴	1	1	yes	characteristic
34	C₄	—	2	4	no	—
35	C₄	—	2	4	no	—
36	C₄	C₂×D₄	1	4	yes	—
37	C₂	—	4	4	no	—
38	C₂	#124	1	4	yes	direct product factor
39	C₂	C₂²×D₄	1	1	yes	characteristic
40	C₂	C₂×#41	1	2	yes	—

	subgroup	G/H
center, socle	C₂³	C₂³
commutator, Frattini, cosocle	C₂²	C₂⁴
prime radical	C₂²×D₄	C₂
LCS	G ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂³ ◁ 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.