Subgroups — #1358

Order 128.

46 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#494	C₂	1	1	yes	maximal, characteristic
2	#364	C₂	1	2	yes	maximal
3	C₂×Q₁₆	—	2	2	no	—
4	C₄⋊Q₈	C₄	1	2	yes	—
5	M₃₂	—	2	2	no	—
6	C₄×C₈	C₂²	1	1	yes	characteristic
7	C₂×Q₈	—	2	2	no	—
8	Q₁₆	—	4	2	no	—
9	Q₁₆	—	4	2	no	—
10	C₂×C₈	D₄	1	2	yes	—
11	C₄⋊C₄	—	4	2	no	—
12	C₄²	C₂×C₄	1	1	yes	characteristic
13	C₁₆	—	4	2	no	—
14	Q₈	—	4	4	no	—
15	C₂×C₄	—	2	1	no	—
16	C₂×C₄	—	4	2	no	—
17	C₂×C₄	C₂²⋊C₄	1	1	yes	characteristic
18	C₈	D₈	1	2	yes	—
19	C₈	SD₁₆	1	2	yes	—
20	C₂²	#100	1	1	yes	characteristic
21	C₄	—	2	2	no	—
22	C₄	—	8	2	no	—
23	C₄	#102	1	2	yes	—
24	C₂	—	2	1	no	—
25	C₂	#331	1	1	yes	characteristic

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

subgroup	index
#494	2
#364	2