Subgroups — C₂²×M₃₂ #3405

Order 128.

200 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂³×C₈	C₂	1	1	yes	maximal, characteristic
2	C₂×M₃₂	C₂	1	12	yes	maximal, direct product factor
3	C₂²×C₁₆	C₂	1	2	yes	maximal, complemented
4	C₂³×C₄	C₄	1	1	yes	characteristic
5	C₂²×C₈	C₄	1	1	yes	characteristic
6	C₂²×C₈	C₄	1	6	yes	—
7	C₂²×C₈	C₂²	1	6	yes	—
8	C₂²×C₈	C₂²	1	1	yes	characteristic
9	M₃₂	C₂²	1	16	yes	direct product factor
10	C₂×C₁₆	C₂²	1	12	yes	complemented
11	C₂⁴	C₈	1	1	yes	characteristic
12	C₂²×C₄	C₈	1	6	yes	—
13	C₂²×C₄	C₈	1	1	yes	characteristic
14	C₂²×C₄	C₂×C₄	1	6	yes	—
15	C₂²×C₄	C₂×C₄	1	1	yes	characteristic
16	C₂×C₈	C₂×C₄	1	6	yes	—
17	C₂×C₈	C₂×C₄	1	12	yes	—
18	C₂×C₈	C₂×C₄	1	3	yes	—
19	C₂×C₈	C₂³	1	3	yes	—
20	C₂×C₈	C₂³	1	4	yes	—
21	C₁₆	C₂³	1	8	yes	complemented
22	C₂³	—	2	4	no	—
23	C₂³	C₂×C₈	1	6	yes	—
24	C₂³	C₂×C₈	1	1	yes	characteristic
25	C₂×C₄	C₂×C₈	1	12	yes	—
26	C₂×C₄	C₂×C₈	1	6	yes	—
27	C₂×C₄	C₂×C₈	1	3	yes	—
28	C₂×C₄	C₂²×C₄	1	4	yes	—
29	C₂×C₄	C₂²×C₄	1	3	yes	—
30	C₈	C₂²×C₄	1	4	yes	—
31	C₈	C₂²×C₄	1	3	yes	—
32	C₈	C₂⁴	1	1	yes	characteristic
33	C₂²	—	2	12	no	—
34	C₂²	M₃₂	1	4	yes	direct product factor
35	C₂²	C₂²×C₈	1	4	yes	—
36	C₂²	C₂²×C₈	1	3	yes	—
37	C₄	C₂²×C₈	1	3	yes	—
38	C₄	C₂²×C₈	1	4	yes	—
39	C₄	C₂³×C₄	1	1	yes	characteristic
40	C₂	—	2	4	no	—
41	C₂	C₂×M₃₂	1	6	yes	direct product factor
42	C₂	C₂³×C₈	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.