Subgroups — C₃₁×#2091 #16842024

Order 3968.

222 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃₁×#430	C₂	1	3	yes	maximal, complemented
2	C₃₁×#407	C₂	1	3	yes	maximal
3	C₃₁×#338	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂³×C₄×C₃₁	C₂²	1	1	yes	characteristic
5	C₂×M₁₆×C₃₁	C₂²	1	3	yes	—
6	C₂×M₁₆×C₃₁	C₂²	1	3	yes	—
7	C₃₁×#108	—	2	6	no	—
8	C₃₁×C₂²⋊C₈	—	2	6	no	—
9	C₂⁴×C₃₁	Q₈	1	1	yes	characteristic
10	C₂²×C₄×C₃₁	—	2	3	no	—
11	C₂²×C₄×C₃₁	—	2	3	no	—
12	C₂²×C₄×C₃₁	Q₈	1	1	yes	characteristic
13	C₂²×C₄×C₃₁	C₂³	1	1	yes	characteristic
14	M₁₆×C₃₁	—	2	6	no	—
15	M₁₆×C₃₁	—	2	6	no	—
16	C₂×C₈×C₃₁	—	2	3	no	—
17	C₂×C₈×C₃₁	D₄	1	6	yes	—
18	C₂³×C₃₁	—	2	3	no	—
19	C₂³×C₃₁	—	4	2	no	—
20	C₂³×C₃₁	C₂×Q₈	1	1	yes	characteristic
21	C₂×C₄×C₃₁	—	2	3	no	—
22	C₂×C₄×C₃₁	—	4	3	no	—
23	C₂×C₄×C₃₁	—	4	1	no	—
24	C₂×C₄×C₃₁	C₂×D₄	1	3	yes	—
25	C₂×C₄×C₃₁	#41	1	3	yes	—
26	C₈×C₃₁	—	2	6	no	—
27	C₈×C₃₁	—	4	3	no	—
28	#2091	C₃₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
29	C₂²×C₃₁	—	2	6	no	—
30	C₂²×C₃₁	—	4	1	no	—
31	C₂²×C₃₁	—	4	3	no	—
32	C₂²×C₃₁	—	4	1	no	—
33	C₂²×C₃₁	C₂²⋊Q₈	1	3	yes	—
34	C₄×C₃₁	—	4	1	no	—
35	C₄×C₃₁	#123	1	3	yes	—
36	C₄×C₃₁	#127	1	1	yes	characteristic
37	#430	C₂×C₃₁	1	3	yes	complemented
38	#407	C₂×C₃₁	1	3	yes	—
39	#338	C₂×C₃₁	1	1	yes	characteristic, complemented
40	C₂×C₃₁	—	2	3	no	—
41	C₂×C₃₁	—	4	2	no	—
42	C₂×C₃₁	#399	1	1	yes	characteristic
43	C₂³×C₄	C₂²×C₃₁	1	1	yes	characteristic
44	C₂×M₁₆	C₂²×C₃₁	1	3	yes	—
45	C₂×M₁₆	C₂²×C₃₁	1	3	yes	—
46	#108	—	2	6	no	—
47	C₂²⋊C₈	—	2	6	no	—
48	C₃₁	#2091	1	1	yes	characteristic, direct product factor, Sylow
49	C₂⁴	Q₈×C₃₁	1	1	yes	characteristic
50	C₂²×C₄	—	2	3	no	—
51	C₂²×C₄	—	2	3	no	—
52	C₂²×C₄	Q₈×C₃₁	1	1	yes	characteristic
53	C₂²×C₄	C₂³×C₃₁	1	1	yes	characteristic
54	M₁₆	—	2	6	no	—
55	M₁₆	—	2	6	no	—
56	C₂×C₈	—	2	3	no	—
57	C₂×C₈	D₄×C₃₁	1	6	yes	—
58	C₂³	—	2	3	no	—
59	C₂³	—	4	2	no	—
60	C₂³	C₂×Q₈×C₃₁	1	1	yes	characteristic
61	C₂×C₄	—	2	3	no	—
62	C₂×C₄	—	4	3	no	—
63	C₂×C₄	—	4	1	no	—
64	C₂×C₄	C₂×D₄×C₃₁	1	3	yes	—
65	C₂×C₄	#41×C₃₁	1	3	yes	—
66	C₈	—	2	6	no	—
67	C₈	—	4	3	no	—
68	C₂²	—	2	6	no	—
69	C₂²	—	4	1	no	—
70	C₂²	—	4	3	no	—
71	C₂²	—	4	1	no	—
72	C₂²	C₃₁×C₂²⋊Q₈	1	3	yes	—
73	C₄	—	4	1	no	—
74	C₄	C₃₁×#123	1	3	yes	—
75	C₄	C₃₁×#127	1	1	yes	characteristic
76	C₂	—	2	3	no	—
77	C₂	—	4	2	no	—
78	C₂	C₃₁×#399	1	1	yes	characteristic

	subgroup	G/H
center	C₄×C₃₁	#127
commutator, Frattini, cosocle	C₂²×C₄	C₂³×C₃₁
socle	C₂×C₃₁	#399
prime radical	C₂⁴×C₃₁	Q₈
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₄×C₃₁ ◁ C₂²×C₄×C₃₁ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₃₁×#430	C₂	semidirect
3. C₃₁×#338	C₂	semidirect
28. #2091	C₃₁	direct (N × H)
37. #430	C₂×C₃₁	semidirect
39. #338	C₂×C₃₁	semidirect
48. C₃₁	#2091	direct (N × H)

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
C₃₁×#430	2
C₃₁×#407	2
C₃₁×#338	2
#2091	31

Subgroups — C31×#2091 #16842024

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃₁×#2091 #16842024