Subgroups — #359

Order 64.

28 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#135	C₂	1	1	yes	maximal, characteristic
2	C₂×C₁₆	C₂	1	1	yes	maximal, characteristic, complemented
3	#108	C₂	1	1	yes	maximal, characteristic, complemented
4	#41	—	2	1	no	—
5	Q₁₆	C₄	1	1	yes	characteristic
6	SD₁₆	—	2	1	no	—
7	D₈	C₄	1	1	yes	characteristic
8	M₁₆	—	2	1	no	—
9	C₂×C₈	C₂²	1	1	yes	characteristic
10	C₁₆	—	2	1	no	—
11	Q₈	—	2	1	no	—
12	D₄	—	2	1	no	—
13	D₄	—	4	1	no	—
14	C₂×C₄	—	4	1	no	—
15	C₂×C₄	D₄	1	1	yes	characteristic
16	C₈	—	4	1	no	—
17	C₈	C₂×C₄	1	1	yes	characteristic
18	C₈	D₄	1	1	yes	characteristic
19	C₂²	—	4	1	no	—
20	C₂²	SD₁₆	1	1	yes	characteristic
21	C₄	—	4	1	no	—
22	C₄	C₂²⋊C₄	1	1	yes	characteristic
23	C₄	D₈	1	1	yes	characteristic
24	C₂	—	2	1	no	—
25	C₂	—	8	1	no	—
26	C₂	#102	1	1	yes	characteristic

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

N	H ≅ G/N	type
2. C₂×C₁₆	C₂	semidirect
3. #108	C₂	semidirect

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