Subgroups — #1357

Order 128.

56 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#493	C₂	1	1	yes	maximal, characteristic
2	#364	C₂	1	2	yes	maximal, complemented
3	C₂×D₈	—	2	2	no	—
4	#127	C₄	1	2	yes	—
5	M₃₂	—	2	2	no	—
6	C₄×C₈	C₂²	1	1	yes	characteristic
7	C₂×D₄	—	2	2	no	—
8	C₂×D₄	—	4	2	no	—
9	D₈	—	4	2	no	—
10	D₈	—	4	2	no	—
11	C₂×C₈	D₄	1	2	yes	—
12	C₄²	C₂×C₄	1	1	yes	characteristic
13	C₁₆	—	4	2	no	—
14	C₂³	—	4	2	no	—
15	D₄	—	4	4	no	—
16	D₄	—	8	4	no	—
17	C₂×C₄	—	2	1	no	—
18	C₂×C₄	C₂²⋊C₄	1	1	yes	characteristic
19	C₈	D₈	1	2	yes	—
20	C₈	SD₁₆	1	2	yes	—
21	C₂²	—	8	4	no	—
22	C₂²	—	8	2	no	—
23	C₂²	#100	1	1	yes	characteristic
24	C₄	—	2	2	no	—
25	C₄	#102	1	2	yes	—
26	C₂	—	2	1	no	—
27	C₂	—	16	2	no	—
28	C₂	#331	1	1	yes	characteristic

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

N	H ≅ G/N	type
2. #364	C₂	semidirect

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

subgroup	index
#493	2
#364	2