Subgroups — C₃₁×#7843 #21464602

Order 7936.

526 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃₁×#1744	C₂	1	2	yes	maximal
2	C₄²×C₈×C₃₁	C₂	1	1	yes	maximal, characteristic
3	C₂×C₃₁×#322	C₂	1	4	yes	maximal
4	C₂×C₄×C₈×C₃₁	C₄	1	4	yes	—
5	C₂×C₄×C₈×C₃₁	C₂²	1	2	yes	—
6	C₂×C₄×C₈×C₃₁	C₂²	1	4	yes	—
7	C₄³×C₃₁	C₂²	1	1	yes	characteristic
8	C₃₁×#336	C₄	1	8	yes	—
9	C₃₁×#322	C₄	1	16	yes	complemented
10	C₂²×C₈×C₃₁	C₂×C₄	1	4	yes	—
11	C₂²×C₈×C₃₁	C₂×C₄	1	8	yes	—
12	C₂×C₄²×C₃₁	C₂×C₄	1	4	yes	—
13	C₂×C₄²×C₃₁	C₂×C₄	1	2	yes	—
14	C₂×C₄²×C₃₁	C₂³	1	1	yes	characteristic
15	C₄×C₈×C₃₁	—	2	8	no	—
16	C₄×C₈×C₃₁	C₂×C₄	1	8	yes	—
17	C₄×C₈×C₃₁	C₂×C₄	1	16	yes	—
18	C₂²×C₄×C₃₁	C₄²	1	4	yes	—
19	C₂²×C₄×C₃₁	C₂²×C₄	1	1	yes	characteristic
20	C₂²×C₄×C₃₁	C₂²×C₄	1	2	yes	—
21	C₂×C₈×C₃₁	—	2	8	no	—
22	C₂×C₈×C₃₁	—	2	16	no	—
23	C₂×C₈×C₃₁	C₄²	1	8	yes	—
24	C₂×C₈×C₃₁	C₄²	1	16	yes	—
25	C₄²×C₃₁	—	2	8	no	—
26	C₄²×C₃₁	M₁₆	1	8	yes	—
27	C₄²×C₃₁	C₂²×C₄	1	4	yes	—
28	#7843	C₃₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
29	C₂³×C₃₁	C₂×C₄²	1	1	yes	characteristic
30	C₂×C₄×C₃₁	—	2	8	no	—
31	C₂×C₄×C₃₁	#97	1	8	yes	—
32	C₂×C₄×C₃₁	C₂×C₄²	1	2	yes	—
33	C₂×C₄×C₃₁	C₂×C₄²	1	4	yes	—
34	C₂×C₄×C₃₁	C₂×M₁₆	1	4	yes	—
35	C₂×C₄×C₃₁	#131	1	8	yes	—
36	C₈×C₃₁	—	2	8	no	—
37	C₈×C₃₁	—	2	16	no	—
38	#1744	C₂×C₃₁	1	2	yes	—
39	C₄²×C₈	C₂×C₃₁	1	1	yes	characteristic
40	C₂×#322	C₂×C₃₁	1	4	yes	—
41	C₂²×C₃₁	C₄³	1	1	yes	characteristic
42	C₂²×C₃₁	C₂×#97	1	2	yes	—
43	C₂²×C₃₁	#405	1	4	yes	—
44	C₄×C₃₁	—	2	8	no	—
45	C₄×C₃₁	C₄×M₁₆	1	4	yes	—
46	C₄×C₃₁	#405	1	8	yes	—
47	C₂×C₄×C₈	C₄×C₃₁	1	4	yes	—
48	C₂×C₄×C₈	C₂²×C₃₁	1	2	yes	—
49	C₂×C₄×C₈	C₂²×C₃₁	1	4	yes	—
50	C₄³	C₂²×C₃₁	1	1	yes	characteristic
51	#336	C₄×C₃₁	1	8	yes	—
52	#322	C₄×C₃₁	1	16	yes	complemented
53	C₂×C₃₁	#1452	1	4	yes	—
54	C₂×C₃₁	C₄×#97	1	1	yes	characteristic
55	C₂×C₃₁	#1726	1	2	yes	—
56	C₂²×C₈	C₂×C₄×C₃₁	1	8	yes	—
57	C₂²×C₈	C₂×C₄×C₃₁	1	4	yes	—
58	C₂×C₄²	C₂×C₄×C₃₁	1	4	yes	—
59	C₂×C₄²	C₂×C₄×C₃₁	1	2	yes	—
60	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
61	C₄×C₈	—	2	8	no	—
62	C₄×C₈	C₂×C₄×C₃₁	1	8	yes	—
63	C₄×C₈	C₂×C₄×C₃₁	1	16	yes	—
64	C₃₁	#7843	1	1	yes	characteristic, direct product factor, Sylow
65	C₂²×C₄	C₄²×C₃₁	1	4	yes	—
66	C₂²×C₄	C₂²×C₄×C₃₁	1	1	yes	characteristic
67	C₂²×C₄	C₂²×C₄×C₃₁	1	2	yes	—
68	C₂×C₈	—	2	8	no	—
69	C₂×C₈	—	2	16	no	—
70	C₂×C₈	C₄²×C₃₁	1	8	yes	—
71	C₂×C₈	C₄²×C₃₁	1	16	yes	—
72	C₄²	—	2	8	no	—
73	C₄²	M₁₆×C₃₁	1	8	yes	—
74	C₄²	C₂²×C₄×C₃₁	1	4	yes	—
75	C₂³	C₂×C₄²×C₃₁	1	1	yes	characteristic
76	C₂×C₄	—	2	8	no	—
77	C₂×C₄	C₃₁×#97	1	8	yes	—
78	C₂×C₄	C₂×C₄²×C₃₁	1	2	yes	—
79	C₂×C₄	C₂×C₄²×C₃₁	1	4	yes	—
80	C₂×C₄	C₂×M₁₆×C₃₁	1	4	yes	—
81	C₂×C₄	C₃₁×#131	1	8	yes	—
82	C₈	—	2	8	no	—
83	C₈	—	2	16	no	—
84	C₂²	C₄³×C₃₁	1	1	yes	characteristic
85	C₂²	C₂×C₃₁×#97	1	2	yes	—
86	C₂²	C₃₁×#405	1	4	yes	—
87	C₄	—	2	8	no	—
88	C₄	C₄×M₁₆×C₃₁	1	4	yes	—
89	C₄	C₃₁×#405	1	8	yes	—
90	C₂	C₃₁×#1452	1	4	yes	—
91	C₂	C₄×C₃₁×#97	1	1	yes	characteristic
92	C₂	C₃₁×#1726	1	2	yes	—

	subgroup	G/H
center	C₂×C₄²×C₃₁	C₂³
commutator	C₂²	C₄³×C₃₁
Frattini, cosocle	C₂×C₄²	C₂³×C₃₁
socle, prime radical	C₂³×C₃₁	C₂×C₄²
LCS	G ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂×C₄²×C₃₁ ◁ G

Complements

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

N	H ≅ G/N	type
9. C₃₁×#322	C₄	semidirect
28. #7843	C₃₁	direct (N × H)
52. #322	C₄×C₃₁	semidirect
64. C₃₁	#7843	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×#1744	2
C₄²×C₈×C₃₁	2
C₂×C₃₁×#322	2
#7843	31

Subgroups — C31×#7843 #21464602

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃₁×#7843 #21464602