Subgroups — C₃₁×#2103 #16842036

Order 3968.

148 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃₁×#430	C₂	1	1	yes	maximal, characteristic
2	C₃₁×#424	C₂	1	1	yes	maximal, characteristic
3	C₃₁×#344	C₂	1	2	yes	maximal
4	C₃₁×#341	C₂	1	2	yes	maximal
5	C₃₁×#338	C₂	1	1	yes	maximal, characteristic
6	C₂×M₁₆×C₃₁	C₂²	1	2	yes	—
7	C₂×M₁₆×C₃₁	C₂²	1	2	yes	—
8	C₂×M₁₆×C₃₁	C₂²	1	1	yes	characteristic
9	C₂²×C₈×C₃₁	C₂²	1	1	yes	characteristic
10	C₃₁×#117	C₂²	1	1	yes	characteristic
11	C₃₁×#108	—	2	2	no	—
12	C₃₁×C₄⋊C₈	—	2	2	no	—
13	C₂²×C₄×C₃₁	C₂³	1	1	yes	characteristic
14	M₁₆×C₃₁	—	2	2	no	—
15	M₁₆×C₃₁	—	2	2	no	—
16	M₁₆×C₃₁	—	2	2	no	—
17	M₁₆×C₃₁	—	2	2	no	—
18	M₁₆×C₃₁	—	2	2	no	—
19	C₂×C₈×C₃₁	—	2	1	no	—
20	C₂×C₈×C₃₁	—	2	2	no	—
21	C₂×C₈×C₃₁	—	2	2	no	—
22	C₂×C₈×C₃₁	—	2	2	no	—
23	C₂×C₈×C₃₁	D₄	1	2	yes	—
24	C₄⋊C₄×C₃₁	—	2	1	no	—
25	C₂²⋊C₄×C₃₁	Q₈	1	2	yes	—
26	C₄²×C₃₁	—	2	1	no	—
27	C₂³×C₃₁	C₂×Q₈	1	1	yes	characteristic
28	C₂×C₄×C₃₁	—	2	2	no	—
29	C₂×C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
30	C₂×C₄×C₃₁	#41	1	2	yes	—
31	C₂×C₄×C₃₁	#41	1	2	yes	—
32	C₂×C₄×C₃₁	#41	1	1	yes	characteristic
33	C₈×C₃₁	—	2	2	no	—
34	C₈×C₃₁	—	4	1	no	—
35	C₈×C₃₁	—	4	2	no	—
36	C₈×C₃₁	—	4	2	no	—
37	#2103	C₃₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
38	C₂²×C₃₁	—	4	1	no	—
39	C₂²×C₃₁	C₂²⋊Q₈	1	1	yes	characteristic
40	C₂²×C₃₁	#125	1	2	yes	—
41	C₄×C₃₁	—	4	2	no	—
42	C₄×C₃₁	#123	1	1	yes	characteristic
43	C₄×C₃₁	#124	1	1	yes	characteristic
44	C₄×C₃₁	#126	1	2	yes	—
45	#430	C₂×C₃₁	1	1	yes	characteristic
46	#424	C₂×C₃₁	1	1	yes	characteristic
47	#344	C₂×C₃₁	1	2	yes	—
48	#341	C₂×C₃₁	1	2	yes	—
49	#338	C₂×C₃₁	1	1	yes	characteristic
50	C₂×C₃₁	—	2	1	no	—
51	C₂×C₃₁	—	2	2	no	—
52	C₂×C₃₁	#400	1	1	yes	characteristic
53	C₂×M₁₆	C₂²×C₃₁	1	2	yes	—
54	C₂×M₁₆	C₂²×C₃₁	1	2	yes	—
55	C₂×M₁₆	C₂²×C₃₁	1	1	yes	characteristic
56	C₂²×C₈	C₂²×C₃₁	1	1	yes	characteristic
57	#117	C₂²×C₃₁	1	1	yes	characteristic
58	#108	—	2	2	no	—
59	C₄⋊C₈	—	2	2	no	—
60	C₃₁	#2103	1	1	yes	characteristic, direct product factor, Sylow
61	C₂²×C₄	C₂³×C₃₁	1	1	yes	characteristic
62	M₁₆	—	2	2	no	—
63	M₁₆	—	2	2	no	—
64	M₁₆	—	2	2	no	—
65	M₁₆	—	2	2	no	—
66	M₁₆	—	2	2	no	—
67	C₂×C₈	—	2	1	no	—
68	C₂×C₈	—	2	2	no	—
69	C₂×C₈	—	2	2	no	—
70	C₂×C₈	—	2	2	no	—
71	C₂×C₈	D₄×C₃₁	1	2	yes	—
72	C₄⋊C₄	—	2	1	no	—
73	C₂²⋊C₄	Q₈×C₃₁	1	2	yes	—
74	C₄²	—	2	1	no	—
75	C₂³	C₂×Q₈×C₃₁	1	1	yes	characteristic
76	C₂×C₄	—	2	2	no	—
77	C₂×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
78	C₂×C₄	#41×C₃₁	1	2	yes	—
79	C₂×C₄	#41×C₃₁	1	2	yes	—
80	C₂×C₄	#41×C₃₁	1	1	yes	characteristic
81	C₈	—	2	2	no	—
82	C₈	—	4	1	no	—
83	C₈	—	4	2	no	—
84	C₈	—	4	2	no	—
85	C₂²	—	4	1	no	—
86	C₂²	C₃₁×C₂²⋊Q₈	1	1	yes	characteristic
87	C₂²	C₃₁×#125	1	2	yes	—
88	C₄	—	4	2	no	—
89	C₄	C₃₁×#123	1	1	yes	characteristic
90	C₄	C₃₁×#124	1	1	yes	characteristic
91	C₄	C₃₁×#126	1	2	yes	—
92	C₂	—	2	1	no	—
93	C₂	—	2	2	no	—
94	C₂	C₃₁×#400	1	1	yes	characteristic

	subgroup	G/H
center	C₄×C₃₁	#124
commutator, Frattini, cosocle	C₂²×C₄	C₂³×C₃₁
socle	C₂×C₃₁	#400
prime radical	C₂³×C₃₁	C₂×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
37. #2103	C₃₁	direct (N × H)
60. C₃₁	#2103	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×#424	2
C₃₁×#344	2
C₃₁×#341	2
C₃₁×#338	2
#2103	31

Subgroups — C31×#2103 #16842036

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃₁×#2103 #16842036