Subgroups — C₂³×C₄×C₃₁₁ #23755607

Order 9952.

236 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂⁴×C₃₁₁	C₂	1	1	yes	maximal, characteristic
2	C₂²×C₄×C₃₁₁	C₂	1	14	yes	maximal, direct product factor
3	C₂³×C₃₁₁	C₄	1	8	yes	direct product factor
4	C₂³×C₃₁₁	C₂²	1	7	yes	—
5	C₂×C₄×C₃₁₁	C₂²	1	28	yes	direct product factor
6	C₂²×C₃₁₁	C₂×C₄	1	28	yes	direct product factor
7	C₂²×C₃₁₁	C₂³	1	7	yes	—
8	C₄×C₃₁₁	C₂³	1	8	yes	direct product factor
9	C₂×C₃₁₁	C₂²×C₄	1	14	yes	direct product factor
10	C₂×C₃₁₁	C₂⁴	1	1	yes	characteristic
11	C₃₁₁	C₂³×C₄	1	1	yes	characteristic, direct product factor, Sylow
12	C₂³×C₄	C₃₁₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
13	C₂⁴	C₂×C₃₁₁	1	1	yes	characteristic
14	C₂²×C₄	C₂×C₃₁₁	1	14	yes	direct product factor
15	C₂³	C₄×C₃₁₁	1	8	yes	direct product factor
16	C₂³	C₂²×C₃₁₁	1	7	yes	—
17	C₂×C₄	C₂²×C₃₁₁	1	28	yes	direct product factor
18	C₂²	C₂×C₄×C₃₁₁	1	28	yes	direct product factor
19	C₂²	C₂³×C₃₁₁	1	7	yes	—
20	C₄	C₂³×C₃₁₁	1	8	yes	direct product factor
21	C₂	C₂²×C₄×C₃₁₁	1	14	yes	direct product factor
22	C₂	C₂⁴×C₃₁₁	1	1	yes	characteristic

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