Subgroups — C₃²×C₄×C₃₁² #46829338

Order 34596.

612 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃²×C₃₁²	C₂	1	1	yes	maximal, characteristic
2	C₃×C₄×C₃₁²	C₃	1	4	yes	maximal, direct product factor
3	C₃²×C₃₁²	C₄	1	1	yes	characteristic, direct product factor, Hall
4	C₂×C₃×C₃₁²	C₂×C₃	1	4	yes	—
5	C₄×C₃₁²	C₃²	1	1	yes	characteristic, direct product factor, Hall
6	C₃×C₃₁²	C₃×C₄	1	4	yes	direct product factor
7	C₂×C₃₁²	C₂×C₃²	1	1	yes	characteristic
8	C₃²×C₄×C₃₁	C₃₁	1	32	yes	maximal, direct product factor
9	C₃₁²	C₃²×C₄	1	1	yes	characteristic, direct product factor, Sylow
10	C₂×C₃²×C₃₁	C₂×C₃₁	1	32	yes	—
11	C₃×C₄×C₃₁	C₃×C₃₁	1	128	yes	direct product factor
12	C₃²×C₃₁	C₄×C₃₁	1	32	yes	direct product factor
13	C₂×C₃×C₃₁	C₂×C₃×C₃₁	1	128	yes	—
14	C₄×C₃₁	C₃²×C₃₁	1	32	yes	direct product factor
15	C₃×C₃₁	C₃×C₄×C₃₁	1	128	yes	direct product factor
16	C₂×C₃₁	C₂×C₃²×C₃₁	1	32	yes	—
17	C₃²×C₄	C₃₁²	1	1	yes	characteristic, direct product factor, Hall
18	C₃₁	C₃²×C₄×C₃₁	1	32	yes	direct product factor
19	C₂×C₃²	C₂×C₃₁²	1	1	yes	characteristic
20	C₃×C₄	C₃×C₃₁²	1	4	yes	direct product factor
21	C₃²	C₄×C₃₁²	1	1	yes	characteristic, direct product factor, Sylow
22	C₂×C₃	C₂×C₃×C₃₁²	1	4	yes	—
23	C₄	C₃²×C₃₁²	1	1	yes	characteristic, direct product factor, Sylow
24	C₃	C₃×C₄×C₃₁²	1	4	yes	direct product factor
25	C₂	C₂×C₃²×C₃₁²	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.