Subgroups — #16854106

Order 3968.

1272 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#11758451	C₂	1	14	yes	maximal, complemented
2	C₄³×C₃₁	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂²×D₁₂₄	C₂²	1	28	yes	—
4	C₂×C₄²×C₃₁	C₂²	1	7	yes	—
5	#11758451	—	2	56	no	—
6	C₂³×D₃₁	C₂³	1	8	yes	—
7	C₂²×C₄×C₃₁	C₂³	1	7	yes	—
8	C₂×D₁₂₄	—	2	168	no	—
9	C₄²×C₃₁	D₄	1	28	yes	complemented
10	C₂³×C₃₁	C₂⁴	1	1	yes	characteristic
11	C₂²×D₃₁	—	2	56	no	—
12	C₂×C₄×C₃₁	C₂×D₄	1	42	yes	—
13	D₁₂₄	—	4	112	no	—
14	#2867	—	31	1	no	maximal, Sylow
15	C₂²×C₃₁	C₂²×D₄	1	7	yes	—
16	C₂×D₃₁	—	4	56	no	—
17	C₄×C₃₁	#127	1	28	yes	complemented
18	C₂×#127	—	31	14	no	—
19	C₄³	D₃₁	1	1	yes	characteristic, complemented
20	C₂×C₃₁	C₂×#127	1	7	yes	—
21	D₃₁	—	8	8	no	—
22	C₂²×D₄	—	31	28	no	—
23	#127	—	62	56	no	—
24	C₂×C₄²	C₂×D₃₁	1	7	yes	—
25	C₃₁	#2867	1	1	yes	characteristic, complemented, Sylow
26	C₂⁴	—	31	8	no	—
27	C₂×D₄	—	62	168	no	—
28	C₂²×C₄	C₂²×D₃₁	1	7	yes	—
29	C₄²	D₁₂₄	1	28	yes	complemented
30	C₂³	—	62	56	no	—
31	C₂³	C₂³×D₃₁	1	1	yes	characteristic
32	D₄	—	124	112	no	—
33	C₂×C₄	C₂×D₁₂₄	1	42	yes	—
34	C₂²	—	124	56	no	—
35	C₂²	C₂²×D₁₂₄	1	7	yes	—
36	C₄	#11758451	1	28	yes	complemented
37	C₂	—	248	8	no	—
38	C₂	C₂×#11758451	1	7	yes	—

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.