Subgroups — #358

Order 64.

29 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×Q₁₆	C₂	1	1	yes	maximal, characteristic
2	C₂×C₁₆	C₂	1	1	yes	maximal, characteristic
3	#107	C₂	1	1	yes	maximal, characteristic
4	C₂×Q₈	—	2	1	no	—
5	Q₁₆	—	2	1	no	—
6	Q₁₆	C₄	1	2	yes	complemented
7	C₂×C₈	C₂²	1	1	yes	characteristic
8	C₄⋊C₄	—	2	1	no	—
9	C₁₆	—	2	1	no	—
10	Q₈	—	2	2	no	—
11	Q₈	—	4	1	no	—
12	C₂×C₄	—	4	1	no	—
13	C₂×C₄	—	4	1	no	—
14	C₂×C₄	D₄	1	1	yes	characteristic
15	C₈	C₂×C₄	1	1	yes	characteristic
16	C₈	D₄	1	1	yes	characteristic
17	C₂²	D₈	1	1	yes	characteristic
18	C₄	—	4	2	no	—
19	C₄	—	8	1	no	—
20	C₄	C₂²⋊C₄	1	1	yes	characteristic
21	C₄	SD₁₆	1	1	yes	characteristic
22	C₂	#102	1	1	yes	characteristic
23	C₂	SD₃₂	1	1	yes	characteristic
24	C₂	Q₃₂	1	1	yes	characteristic

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

N	H ≅ G/N	type
6. Q₁₆	C₄	semidirect

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