Subgroups — #1359

Order 128.

51 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#492	C₂	1	1	yes	maximal, characteristic
2	#364	C₂	1	2	yes	maximal, complemented
3	C₂×SD₁₆	—	2	2	no	—
4	C₄⋊Q₈	C₄	1	1	yes	characteristic
5	#127	C₄	1	1	yes	characteristic
6	M₃₂	—	2	2	no	—
7	C₄×C₈	C₂²	1	1	yes	characteristic
8	C₂×Q₈	—	2	1	no	—
9	C₂×D₄	—	2	1	no	—
10	C₂×D₄	—	4	1	no	—
11	SD₁₆	—	4	2	no	—
12	SD₁₆	—	4	2	no	—
13	C₂×C₈	D₄	1	2	yes	—
14	C₄⋊C₄	—	4	1	no	—
15	C₄²	C₂×C₄	1	1	yes	characteristic
16	C₁₆	—	4	2	no	—
17	C₂³	—	4	1	no	—
18	Q₈	—	4	2	no	—
19	D₄	—	4	2	no	—
20	D₄	—	8	2	no	—
21	C₂×C₄	—	2	1	no	—
22	C₂×C₄	—	4	1	no	—
23	C₂×C₄	C₂²⋊C₄	1	1	yes	characteristic
24	C₈	D₈	1	2	yes	—
25	C₈	SD₁₆	1	2	yes	—
26	C₂²	—	8	2	no	—
27	C₂²	—	8	1	no	—
28	C₂²	#100	1	1	yes	characteristic
29	C₄	—	2	2	no	—
30	C₄	—	8	1	no	—
31	C₄	#102	1	2	yes	—
32	C₂	—	2	1	no	—
33	C₂	—	16	1	no	—
34	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
#492	2
#364	2