Subgroups — #1450

Order 128.

106 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#431	C₂	1	2	yes	maximal
2	C₂×C₄×C₈	C₂	1	1	yes	maximal, characteristic
3	#322	C₂	1	2	yes	maximal, complemented
4	C₈²	C₂	1	2	yes	maximal, complemented
5	C₂²×C₈	C₄	1	2	yes	—
6	C₂×C₄²	C₂²	1	1	yes	characteristic
7	C₄⋊C₈	C₄	1	4	yes	—
8	C₂²⋊C₈	C₄	1	4	yes	—
9	C₄×C₈	C₄	1	2	yes	—
10	C₄×C₈	C₂²	1	4	yes	—
11	C₄×C₈	C₂²	1	1	yes	characteristic
12	C₄×C₈	C₂²	1	1	yes	characteristic
13	C₂²×C₄	C₂×C₄	1	2	yes	—
14	C₂²×C₄	C₂×C₄	1	1	yes	characteristic
15	C₂×C₈	C₈	1	8	yes	complemented
16	C₂×C₈	C₂×C₄	1	8	yes	—
17	C₂×C₈	C₂×C₄	1	2	yes	—
18	C₂×C₈	C₂×C₄	1	2	yes	—
19	C₄²	C₂×C₄	1	1	yes	characteristic
20	C₄²	C₂×C₄	1	2	yes	—
21	C₄²	C₂³	1	1	yes	characteristic
22	C₂³	C₄²	1	1	yes	characteristic
23	C₂×C₄	—	2	4	no	—
24	C₂×C₄	C₄²	1	2	yes	—
25	C₂×C₄	C₄²	1	1	yes	characteristic
26	C₂×C₄	C₂×C₈	1	4	yes	—
27	C₂×C₄	C₂²×C₄	1	1	yes	characteristic
28	C₂×C₄	C₂²×C₄	1	2	yes	—
29	C₈	—	2	8	no	—
30	C₈	C₂×C₈	1	4	yes	—
31	C₈	C₂×C₈	1	4	yes	—
32	C₂²	—	2	2	no	—
33	C₂²	C₄×C₈	1	2	yes	—
34	C₂²	C₂×C₄²	1	1	yes	characteristic
35	C₄	—	2	2	no	—
36	C₄	C₄×C₈	1	2	yes	—
37	C₄	C₂²×C₈	1	2	yes	—
38	C₄	#131	1	4	yes	—
39	C₂	—	2	2	no	—
40	C₂	C₂×C₄×C₈	1	1	yes	characteristic
41	C₂	#405	1	2	yes	—

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.