Subgroups — D₃₁×#401 #16849006

Order 3968.

516 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃₁⋊#401	C₂	1	7	yes	maximal, complemented
2	#95×D₃₁	C₂	1	7	yes	maximal
3	C₃₁×#401	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂²×C₄×D₃₁	C₂²	1	7	yes	—
5	C₃₁×#95	C₂²	1	7	yes	—
6	C₃₁⋊#95	C₂²	1	21	yes	—
7	C₂³×D₃₁	C₂³	1	1	yes	characteristic
8	C₂²×C₄×C₃₁	C₂³	1	7	yes	—
9	C₂²×Dic₃₁	C₂³	1	7	yes	—
10	C₂×C₄×D₃₁	—	2	42	no	—
11	C₂³×C₃₁	C₂⁴	1	1	yes	characteristic
12	C₂²×D₃₁	#41	1	14	yes	—
13	C₂×C₄×C₃₁	—	2	21	no	—
14	C₂×Dic₃₁	—	2	21	no	—
15	C₄×D₃₁	—	4	28	no	—
16	C₂×#401	—	31	1	no	maximal, Sylow
17	C₂²×C₃₁	C₂×#41	1	7	yes	—
18	C₂×D₃₁	#126	1	28	yes	—
19	C₄×C₃₁	—	4	7	no	—
20	Dic₃₁	—	4	7	no	—
21	#401	—	31	7	no	—
22	#401	D₃₁	1	1	yes	characteristic, direct product factor
23	C₂×#95	—	31	7	no	—
24	C₂×C₃₁	C₂×#126	1	7	yes	—
25	D₃₁	#401	1	8	yes	direct product factor
26	C₂³×C₄	—	31	7	no	—
27	#95	—	31	21	no	—
28	#95	C₂×D₃₁	1	7	yes	—
29	C₃₁	C₂×#401	1	1	yes	characteristic, complemented, Sylow
30	C₂⁴	—	31	1	no	—
31	C₂²×C₄	—	31	7	no	—
32	C₂²×C₄	—	62	42	no	—
33	C₂²×C₄	C₂²×D₃₁	1	7	yes	—
34	C₂³	—	31	14	no	—
35	C₂³	C₂³×D₃₁	1	1	yes	characteristic
36	C₂×C₄	—	2	21	no	—
37	C₂×C₄	—	62	21	no	—
38	C₂×C₄	—	124	28	no	—
39	C₂²	—	31	28	no	—
40	C₂²	#41×D₃₁	1	7	yes	—
41	C₄	—	4	7	no	—
42	C₄	—	124	7	no	—
43	C₂	—	31	8	no	—
44	C₂	#126×D₃₁	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.