Subgroups — #331

Order 64.

42 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#127	C₂	1	1	yes	maximal, characteristic
2	C₄⋊C₈	C₂	1	2	yes	maximal, complemented
3	C₂×D₄	—	2	2	no	—
4	C₂×D₄	C₄	1	2	yes	—
5	C₂×C₈	—	2	2	no	—
6	C₄²	C₂²	1	1	yes	characteristic
7	C₂³	—	2	2	no	—
8	D₄	—	4	2	no	—
9	D₄	—	4	2	no	—
10	D₄	—	4	2	no	—
11	C₂×C₄	C₂×C₄	1	1	yes	characteristic
12	C₂×C₄	D₄	1	2	yes	—
13	C₈	—	4	2	no	—
14	C₂²	—	4	2	no	—
15	C₂²	—	4	4	no	—
16	C₂²	C₂²⋊C₄	1	1	yes	characteristic
17	C₄	—	2	1	no	—
18	C₄	D₈	1	2	yes	—
19	C₄	SD₁₆	1	2	yes	—
20	C₂	—	8	2	no	—
21	C₂	#100	1	1	yes	characteristic
22	C₂	#102	1	2	yes	—

Splittings G = N ⋊ H with N normal; H ≅ G/N.

N	H ≅ G/N	type
2. C₄⋊C₈	C₂	semidirect

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
#127	2
C₄⋊C₈	2