Subgroups — C₃²×M₃₂ #63680

Order 288.

78 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃²×C₈	C₂	1	1	yes	maximal, characteristic
2	C₃²×C₁₆	C₂	1	2	yes	maximal, complemented
3	C₃×M₃₂	C₃	1	4	yes	maximal, direct product factor
4	C₂×C₃²×C₄	C₄	1	1	yes	characteristic
5	C₃²×C₈	C₄	1	1	yes	characteristic
6	C₃²×C₈	C₂²	1	1	yes	characteristic
7	C₂×C₃×C₈	C₂×C₃	1	4	yes	—
8	C₃×C₁₆	C₂×C₃	1	8	yes	complemented
9	C₂²×C₃²	C₈	1	1	yes	characteristic
10	C₃²×C₄	C₈	1	1	yes	characteristic
11	C₃²×C₄	C₂×C₄	1	1	yes	characteristic
12	M₃₂	C₃²	1	1	yes	characteristic, direct product factor, Sylow
13	C₂×C₃×C₄	C₃×C₄	1	4	yes	—
14	C₃×C₈	C₃×C₄	1	4	yes	—
15	C₃×C₈	C₂²×C₃	1	4	yes	—
16	C₂×C₃²	—	2	1	no	—
17	C₂×C₃²	C₂×C₈	1	1	yes	characteristic
18	C₂×C₈	C₂×C₃²	1	1	yes	characteristic
19	C₁₆	C₂×C₃²	1	2	yes	complemented
20	C₂²×C₃	C₃×C₈	1	4	yes	—
21	C₃×C₄	C₃×C₈	1	4	yes	—
22	C₃×C₄	C₂×C₃×C₄	1	4	yes	—
23	C₃²	M₃₂	1	1	yes	characteristic, direct product factor, Sylow
24	C₂×C₄	C₃²×C₄	1	1	yes	characteristic
25	C₈	C₃²×C₄	1	1	yes	characteristic
26	C₈	C₂²×C₃²	1	1	yes	characteristic
27	C₂×C₃	—	2	4	no	—
28	C₂×C₃	C₂×C₃×C₈	1	4	yes	—
29	C₂²	C₃²×C₈	1	1	yes	characteristic
30	C₄	C₃²×C₈	1	1	yes	characteristic
31	C₄	C₂×C₃²×C₄	1	1	yes	characteristic
32	C₃	C₃×M₃₂	1	4	yes	direct product factor
33	C₂	—	2	1	no	—
34	C₂	C₂×C₃²×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.