Subgroups — #442

Order 64.

66 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×D₈	C₂	1	1	yes	maximal, characteristic
2	C₄×D₄	C₂	1	2	yes	maximal, complemented
3	#106	C₂	1	1	yes	maximal, characteristic, complemented
4	#102	C₂	1	2	yes	maximal, complemented
5	#97	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×D₄	C₂²	1	2	yes	—
7	C₂²×C₄	—	2	2	no	—
8	D₈	C₄	1	4	yes	complemented
9	C₂×C₈	C₂²	1	1	yes	characteristic
10	C₂×C₈	C₂²	1	1	yes	characteristic
11	C₄⋊C₄	C₂²	1	2	yes	—
12	C₂²⋊C₄	—	2	2	no	—
13	C₄²	C₂²	1	1	yes	characteristic
14	C₂³	—	2	2	no	—
15	D₄	—	2	2	no	—
16	D₄	C₂×C₄	1	4	yes	complemented
17	C₂×C₄	—	2	2	no	—
18	C₂×C₄	—	4	4	no	—
19	C₂×C₄	D₄	1	2	yes	—
20	C₂×C₄	C₂³	1	1	yes	characteristic
21	C₈	—	2	1	no	—
22	C₈	C₂×C₄	1	2	yes	complemented
23	C₂²	—	2	4	no	—
24	C₂²	—	4	2	no	—
25	C₂²	—	4	2	no	—
26	C₂²	C₂×D₄	1	1	yes	characteristic
27	C₄	—	2	2	no	—
28	C₄	—	4	2	no	—
29	C₄	C₂²×C₄	1	1	yes	characteristic
30	C₄	#41	1	1	yes	characteristic
31	C₂	—	4	4	no	—
32	C₂	C₄×D₄	1	1	yes	characteristic
33	C₂	AGL(1,ℤ/8)	1	2	yes	—

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.