Subgroups — #333

Order 64.

32 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄⋊Q₈	C₂	1	1	yes	maximal, characteristic
2	C₄⋊C₈	C₂	1	2	yes	maximal
3	C₂×Q₈	C₄	1	2	yes	—
4	C₂×C₈	—	2	2	no	—
5	C₄⋊C₄	—	2	2	no	—
6	C₄²	C₂²	1	1	yes	characteristic
7	Q₈	—	4	2	no	—
8	C₂×C₄	—	2	2	no	—
9	C₂×C₄	C₂×C₄	1	1	yes	characteristic
10	C₂×C₄	D₄	1	2	yes	—
11	C₈	—	4	2	no	—
12	C₂²	C₂²⋊C₄	1	1	yes	characteristic
13	C₄	—	2	1	no	—
14	C₄	—	4	2	no	—
15	C₄	SD₁₆	1	2	yes	—
16	C₄	Q₁₆	1	2	yes	—
17	C₂	#100	1	1	yes	characteristic
18	C₂	#103	1	2	yes	—

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

subgroup	index
C₄⋊Q₈	2
C₄⋊C₈	2