Subgroups — #2177

Order 128.

86 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×D₁₆	C₂	1	1	yes	maximal, characteristic
2	C₄×D₈	C₂	1	2	yes	maximal, complemented
3	#367	C₂	1	1	yes	maximal, characteristic, complemented
4	#357	C₂	1	2	yes	maximal, complemented
5	#346	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×D₈	C₂²	1	2	yes	—
7	C₄×D₄	—	2	2	no	—
8	D₁₆	C₄	1	4	yes	complemented
9	C₂×C₁₆	C₂²	1	1	yes	characteristic
10	C₂×C₁₆	C₂²	1	1	yes	characteristic
11	#107	C₂²	1	2	yes	—
12	#102	—	2	2	no	—
13	C₄×C₈	C₂²	1	1	yes	characteristic
14	C₂×D₄	—	2	2	no	—
15	C₂²×C₄	—	4	2	no	—
16	D₈	—	2	2	no	—
17	D₈	C₂×C₄	1	4	yes	complemented
18	C₂×C₈	D₄	1	1	yes	characteristic
19	C₂×C₈	C₂³	1	1	yes	characteristic
20	C₄⋊C₄	—	2	2	no	—
21	C₂²⋊C₄	—	4	2	no	—
22	C₄²	D₄	1	1	yes	characteristic
23	C₁₆	—	2	1	no	—
24	C₁₆	C₂×C₄	1	2	yes	complemented
25	C₂³	—	4	2	no	—
26	D₄	—	2	4	no	—
27	D₄	—	4	2	no	—
28	C₂×C₄	—	4	2	no	—
29	C₂×C₄	—	8	4	no	—
30	C₂×C₄	D₈	1	2	yes	—
31	C₂×C₄	C₂×D₄	1	1	yes	characteristic
32	C₈	—	2	1	no	—
33	C₈	C₂²×C₄	1	1	yes	characteristic
34	C₈	#41	1	1	yes	characteristic
35	C₂²	—	4	4	no	—
36	C₂²	—	8	2	no	—
37	C₂²	—	8	2	no	—
38	C₂²	C₂×D₈	1	1	yes	characteristic
39	C₄	—	2	2	no	—
40	C₄	—	8	2	no	—
41	C₄	C₄×D₄	1	1	yes	characteristic
42	C₄	#135	1	1	yes	characteristic
43	C₂	—	8	4	no	—
44	C₂	C₄×D₈	1	1	yes	characteristic
45	C₂	#509	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.