Subgroups — #2150

Order 128.

86 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×M₃₂	C₂	1	2	yes	maximal
2	C₂×C₄×C₈	C₂	1	1	yes	maximal, characteristic
3	C₄⋊C₁₆	C₂	1	4	yes	maximal, complemented
4	C₂²×C₈	C₄	1	1	yes	characteristic
5	C₂²×C₈	C₂²	1	1	yes	characteristic
6	C₂×C₄²	C₄	1	1	yes	characteristic
7	M₃₂	—	2	4	no	—
8	C₂×C₁₆	C₂²	1	4	yes	—
9	C₄×C₈	C₄	1	2	yes	—
10	C₄×C₈	C₂²	1	2	yes	—
11	C₂²×C₄	C₈	1	2	yes	—
12	C₂²×C₄	C₂×C₄	1	1	yes	characteristic
13	C₂×C₈	—	2	2	no	—
14	C₂×C₈	C₂×C₄	1	2	yes	—
15	C₂×C₈	C₂×C₄	1	1	yes	characteristic
16	C₂×C₈	D₄	1	2	yes	—
17	C₂×C₈	Q₈	1	2	yes	—
18	C₂×C₈	C₂³	1	1	yes	characteristic
19	C₄²	C₈	1	1	yes	characteristic
20	C₄²	C₈	1	1	yes	characteristic
21	C₄²	C₂×C₄	1	2	yes	—
22	C₁₆	—	2	4	no	—
23	C₂³	C₂×C₈	1	1	yes	characteristic
24	C₂×C₄	—	2	4	no	—
25	C₂×C₄	C₄⋊C₄	1	2	yes	—
26	C₂×C₄	C₂×C₈	1	2	yes	—
27	C₂×C₄	C₂×C₈	1	1	yes	characteristic
28	C₂×C₄	C₂×C₈	1	2	yes	—
29	C₂×C₄	M₁₆	1	2	yes	—
30	C₂×C₄	C₂²×C₄	1	1	yes	characteristic
31	C₈	—	2	2	no	—
32	C₈	C₄⋊C₄	1	2	yes	—
33	C₈	C₂×D₄	1	1	yes	characteristic
34	C₈	C₂×Q₈	1	1	yes	characteristic
35	C₂²	—	2	2	no	—
36	C₂²	C₄⋊C₈	1	2	yes	—
37	C₂²	C₂²×C₈	1	1	yes	characteristic
38	C₄	—	2	2	no	—
39	C₄	C₄⋊C₈	1	2	yes	—
40	C₄	M₃₂	1	4	yes	complemented
41	C₄	C₂×C₄⋊C₄	1	1	yes	characteristic
42	C₄	C₂×M₁₆	1	1	yes	characteristic
43	C₂	—	2	2	no	—
44	C₂	C₂×C₄⋊C₈	1	1	yes	characteristic
45	C₂	C₂×M₃₂	1	2	yes	—

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

N	H ≅ G/N	type
3. C₄⋊C₁₆	C₂	semidirect
40. C₄	M₃₂	semidirect

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