Subgroups — C₃₁×#2069 #16842002

Order 3968.

216 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	C₂×C₃₁×#100	C₂	1	3	yes	maximal
3	C₃₁×#338	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂²×D₄×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×#100	—	2	6	no	—
9	C₂⁴×C₃₁	Q₈	1	2	yes	—
10	C₂×D₄×C₃₁	—	2	3	no	—
11	C₂×D₄×C₃₁	—	2	3	no	—
12	C₂²×C₄×C₃₁	C₂³	1	1	yes	characteristic
13	M₁₆×C₃₁	—	2	3	no	—
14	M₁₆×C₃₁	—	2	3	no	—
15	M₁₆×C₃₁	—	2	3	no	—
16	M₁₆×C₃₁	D₄	1	6	yes	—
17	C₂×C₈×C₃₁	—	2	3	no	—
18	C₂×C₈×C₃₁	—	2	3	no	—
19	C₂³×C₃₁	—	2	6	no	—
20	C₂³×C₃₁	—	8	2	no	—
21	C₂³×C₃₁	C₂×Q₈	1	1	yes	characteristic
22	D₄×C₃₁	—	4	3	no	—
23	D₄×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	#2069	C₃₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
29	C₂²×C₃₁	—	4	1	no	—
30	C₂²×C₃₁	—	4	2	no	—
31	C₂²×C₃₁	—	8	6	no	—
32	C₂²×C₃₁	C₂²⋊Q₈	1	3	yes	—
33	C₄×C₃₁	#121	1	3	yes	—
34	C₄×C₃₁	#126	1	1	yes	characteristic
35	#430	C₂×C₃₁	1	3	yes	complemented
36	C₂×#100	C₂×C₃₁	1	3	yes	—
37	#338	C₂×C₃₁	1	1	yes	characteristic, complemented
38	C₂×C₃₁	—	2	3	no	—
39	C₂×C₃₁	—	8	2	no	—
40	C₂×C₃₁	#396	1	1	yes	characteristic
41	C₂²×D₄	C₂²×C₃₁	1	1	yes	characteristic
42	C₂×M₁₆	C₂²×C₃₁	1	3	yes	—
43	C₂×M₁₆	C₂²×C₃₁	1	3	yes	—
44	#108	—	2	6	no	—
45	#100	—	2	6	no	—
46	C₃₁	#2069	1	1	yes	characteristic, direct product factor, Sylow
47	C₂⁴	Q₈×C₃₁	1	2	yes	—
48	C₂×D₄	—	2	3	no	—
49	C₂×D₄	—	2	3	no	—
50	C₂²×C₄	C₂³×C₃₁	1	1	yes	characteristic
51	M₁₆	—	2	3	no	—
52	M₁₆	—	2	3	no	—
53	M₁₆	—	2	3	no	—
54	M₁₆	D₄×C₃₁	1	6	yes	—
55	C₂×C₈	—	2	3	no	—
56	C₂×C₈	—	2	3	no	—
57	C₂³	—	2	6	no	—
58	C₂³	—	8	2	no	—
59	C₂³	C₂×Q₈×C₃₁	1	1	yes	characteristic
60	D₄	—	4	3	no	—
61	D₄	—	4	1	no	—
62	C₂×C₄	C₂×D₄×C₃₁	1	3	yes	—
63	C₂×C₄	#41×C₃₁	1	3	yes	—
64	C₈	—	2	6	no	—
65	C₈	—	4	3	no	—
66	C₂²	—	4	1	no	—
67	C₂²	—	4	2	no	—
68	C₂²	—	8	6	no	—
69	C₂²	C₃₁×C₂²⋊Q₈	1	3	yes	—
70	C₄	C₃₁×#121	1	3	yes	—
71	C₄	C₃₁×#126	1	1	yes	characteristic
72	C₂	—	2	3	no	—
73	C₂	—	8	2	no	—
74	C₂	C₃₁×#396	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂×C₃₁	#396
commutator, Frattini, cosocle	C₂²×C₄	C₂³×C₃₁
prime radical	C₂²×D₄×C₃₁	C₂²
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×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. #2069	C₃₁	direct (N × H)
35. #430	C₂×C₃₁	semidirect
37. #338	C₂×C₃₁	semidirect
46. C₃₁	#2069	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
C₂×C₃₁×#100	2
C₃₁×#338	2
#2069	31

Subgroups — C31×#2069 #16842002

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃₁×#2069 #16842002