Subgroups — C₃₁×#2166 #16842099

Order 3968.

122 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃₁×#405	C₂	1	1	yes	maximal, characteristic
2	C₃₁×#364	C₂	1	2	yes	maximal, complemented
3	C₃₁×#349	C₂	1	2	yes	maximal
4	C₃₁×#347	C₂	1	2	yes	maximal, complemented
5	C₂×M₁₆×C₃₁	C₂²	1	1	yes	characteristic
6	C₂²×C₈×C₃₁	C₄	1	1	yes	characteristic
7	C₃₁×#117	C₄	1	1	yes	characteristic
8	C₃₁×M₃₂	C₂²	1	4	yes	—
9	C₃₁×#97	C₄	1	1	yes	characteristic
10	C₃₁×#97	C₂²	1	1	yes	characteristic
11	C₄×C₈×C₃₁	C₄	1	1	yes	characteristic
12	C₄×C₈×C₃₁	C₂²	1	1	yes	characteristic
13	C₂²×C₄×C₃₁	C₂×C₄	1	1	yes	characteristic
14	M₁₆×C₃₁	—	2	2	no	—
15	C₂×C₈×C₃₁	—	2	2	no	—
16	C₂×C₈×C₃₁	C₂×C₄	1	1	yes	characteristic
17	C₂×C₈×C₃₁	C₂×C₄	1	1	yes	characteristic
18	C₂×C₈×C₃₁	C₂×C₄	1	1	yes	characteristic
19	C₂×C₈×C₃₁	C₂³	1	1	yes	characteristic
20	C₄⋊C₄×C₃₁	—	2	1	no	—
21	C₂²⋊C₄×C₃₁	—	2	1	no	—
22	C₄²×C₃₁	C₂×C₄	1	1	yes	characteristic
23	C₄²×C₃₁	C₂×C₄	1	1	yes	characteristic
24	C₁₆×C₃₁	—	2	4	no	—
25	C₂³×C₃₁	M₁₆	1	1	yes	characteristic
26	C₂×C₄×C₃₁	—	2	1	no	—
27	C₂×C₄×C₃₁	—	2	1	no	—
28	C₂×C₄×C₃₁	—	2	1	no	—
29	C₂×C₄×C₃₁	—	2	1	no	—
30	C₂×C₄×C₃₁	M₁₆	1	1	yes	characteristic
31	C₂×C₄×C₃₁	C₂²×C₄	1	1	yes	characteristic
32	C₈×C₃₁	—	2	1	no	—
33	C₈×C₃₁	—	2	1	no	—
34	C₈×C₃₁	M₁₆	1	2	yes	—
35	C₈×C₃₁	#41	1	2	yes	—
36	#2166	C₃₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
37	C₂²×C₃₁	—	2	1	no	—
38	C₂²×C₃₁	—	4	1	no	—
39	C₂²×C₃₁	C₂×M₁₆	1	1	yes	characteristic
40	C₄×C₃₁	—	2	1	no	—
41	C₄×C₃₁	—	4	1	no	—
42	C₄×C₃₁	—	4	1	no	—
43	C₄×C₃₁	#117	1	1	yes	characteristic
44	C₄×C₃₁	C₂×M₁₆	1	1	yes	characteristic
45	#405	C₂×C₃₁	1	1	yes	characteristic
46	#364	C₂×C₃₁	1	2	yes	complemented
47	#349	C₂×C₃₁	1	2	yes	—
48	#347	C₂×C₃₁	1	2	yes	complemented
49	C₂×C₃₁	—	2	1	no	—
50	C₂×C₃₁	—	4	1	no	—
51	C₂×C₃₁	#432	1	1	yes	characteristic
52	C₂×M₁₆	C₂²×C₃₁	1	1	yes	characteristic
53	C₂²×C₈	C₄×C₃₁	1	1	yes	characteristic
54	#117	C₄×C₃₁	1	1	yes	characteristic
55	M₃₂	C₂²×C₃₁	1	4	yes	—
56	#97	C₄×C₃₁	1	1	yes	characteristic
57	#97	C₂²×C₃₁	1	1	yes	characteristic
58	C₄×C₈	C₄×C₃₁	1	1	yes	characteristic
59	C₄×C₈	C₂²×C₃₁	1	1	yes	characteristic
60	C₃₁	#2166	1	1	yes	characteristic, direct product factor, Sylow
61	C₂²×C₄	C₂×C₄×C₃₁	1	1	yes	characteristic
62	M₁₆	—	2	2	no	—
63	C₂×C₈	—	2	2	no	—
64	C₂×C₈	C₂×C₄×C₃₁	1	1	yes	characteristic
65	C₂×C₈	C₂×C₄×C₃₁	1	1	yes	characteristic
66	C₂×C₈	C₂×C₄×C₃₁	1	1	yes	characteristic
67	C₂×C₈	C₂³×C₃₁	1	1	yes	characteristic
68	C₄⋊C₄	—	2	1	no	—
69	C₂²⋊C₄	—	2	1	no	—
70	C₄²	C₂×C₄×C₃₁	1	1	yes	characteristic
71	C₄²	C₂×C₄×C₃₁	1	1	yes	characteristic
72	C₁₆	—	2	4	no	—
73	C₂³	M₁₆×C₃₁	1	1	yes	characteristic
74	C₂×C₄	—	2	1	no	—
75	C₂×C₄	—	2	1	no	—
76	C₂×C₄	—	2	1	no	—
77	C₂×C₄	—	2	1	no	—
78	C₂×C₄	M₁₆×C₃₁	1	1	yes	characteristic
79	C₂×C₄	C₂²×C₄×C₃₁	1	1	yes	characteristic
80	C₈	—	2	1	no	—
81	C₈	—	2	1	no	—
82	C₈	M₁₆×C₃₁	1	2	yes	—
83	C₈	#41×C₃₁	1	2	yes	—
84	C₂²	—	2	1	no	—
85	C₂²	—	4	1	no	—
86	C₂²	C₂×M₁₆×C₃₁	1	1	yes	characteristic
87	C₄	—	2	1	no	—
88	C₄	—	4	1	no	—
89	C₄	—	4	1	no	—
90	C₄	C₃₁×#117	1	1	yes	characteristic
91	C₄	C₂×M₁₆×C₃₁	1	1	yes	characteristic
92	C₂	—	2	1	no	—
93	C₂	—	4	1	no	—
94	C₂	C₃₁×#432	1	1	yes	characteristic

	subgroup	G/H
center	C₄×C₃₁	#117
commutator	C₂×C₄	C₂²×C₄×C₃₁
Frattini, cosocle	C₂×C₈	C₂³×C₃₁
socle	C₂×C₃₁	#432
prime radical	C₂³×C₃₁	M₁₆
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₄×C₃₁ ◁ C₃₁×#97 ◁ G

Complements

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

N	H ≅ G/N	type
2. C₃₁×#364	C₂	semidirect
4. C₃₁×#347	C₂	semidirect
36. #2166	C₃₁	direct (N × H)
46. #364	C₂×C₃₁	semidirect
48. #347	C₂×C₃₁	semidirect
60. C₃₁	#2166	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×#405	2
C₃₁×#364	2
C₃₁×#349	2
C₃₁×#347	2
#2166	31

Subgroups — C31×#2166 #16842099

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃₁×#2166 #16842099