Subgroups — #1408

Order 128.

60 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	#353	C₂	1	2	yes	maximal, complemented
3	C₂×D₈	—	2	2	no	—
4	#127	C₄	1	1	yes	characteristic, complemented
5	#127	C₂²	1	1	yes	characteristic
6	#99	—	2	2	no	—
7	C₄×C₈	C₄	1	1	yes	characteristic, complemented
8	C₂×D₄	—	2	1	no	—
9	C₂×D₄	—	4	1	no	—
10	C₂×D₄	—	4	1	no	—
11	C₂×D₄	D₄	1	2	yes	—
12	D₈	—	4	4	no	—
13	C₂×C₈	—	2	1	no	—
14	C₂²⋊C₄	—	4	2	no	—
15	C₄²	C₂×C₄	1	1	yes	characteristic
16	C₂³	—	2	2	no	—
17	C₂³	—	4	1	no	—
18	D₄	—	4	2	no	—
19	D₄	—	4	2	no	—
20	D₄	—	8	2	no	—
21	D₄	—	8	2	no	—
22	C₂×C₄	—	2	1	no	—
23	C₂×C₄	—	8	2	no	—
24	C₂×C₄	C₂²⋊C₄	1	1	yes	characteristic
25	C₈	—	2	2	no	—
26	C₂²	—	4	2	no	—
27	C₂²	—	8	2	no	—
28	C₂²	—	8	2	no	—
29	C₂²	—	8	1	no	—
30	C₂²	#99	1	1	yes	characteristic
31	C₄	—	2	2	no	—
32	C₄	—	2	1	no	—
33	C₄	—	16	2	no	—
34	C₂	—	2	1	no	—
35	C₂	—	8	2	no	—
36	C₂	—	16	1	no	—
37	C₂	#353	1	1	yes	characteristic

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

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

subgroup	index
#493	2
#353	2