Subgroups — #361

Order 64.

31 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	M₃₂	C₂	1	1	yes	maximal, characteristic, complemented
3	#108	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×D₄	—	2	1	no	—
5	D₈	—	2	1	no	—
6	D₈	C₄	1	2	yes	—
7	M₁₆	—	2	1	no	—
8	C₂×C₈	C₂²	1	1	yes	characteristic
9	C₁₆	—	2	1	no	—
10	C₂³	—	4	1	no	—
11	D₄	—	2	2	no	—
12	D₄	—	4	1	no	—
13	C₂×C₄	D₄	1	1	yes	characteristic
14	C₈	—	4	1	no	—
15	C₈	C₂×C₄	1	1	yes	characteristic
16	C₈	D₄	1	1	yes	characteristic
17	C₂²	—	4	2	no	—
18	C₂²	—	8	2	no	—
19	C₂²	SD₁₆	1	1	yes	characteristic
20	C₄	C₂²⋊C₄	1	1	yes	characteristic
21	C₄	D₈	1	1	yes	characteristic
22	C₂	—	2	1	no	—
23	C₂	—	8	2	no	—
24	C₂	#102	1	1	yes	characteristic

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

N	H ≅ G/N	type
2. M₃₂	C₂	semidirect
3. #108	C₂	semidirect

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