Subgroups — C₃₁×#7451 #21464210

Order 7936.

108 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃₁×#2252	C₂	1	1	yes	maximal, characteristic
2	C₃₁×C₄⋊C₃₂	C₂	1	1	yes	maximal, characteristic
3	C₃₁×#1371	C₂	1	1	yes	maximal, characteristic
4	C₃₁×#500	—	2	1	no	—
5	C₂×C₃₁×C₃₂	—	2	1	no	—
6	C₃₁×#366	—	2	1	no	—
7	C₃₁×#366	C₄	1	2	yes	—
8	C₄×C₁₆×C₃₁	C₂²	1	1	yes	characteristic
9	C₃₁×#335	—	2	1	no	—
10	C₃₁×C₄⋊Q₈	—	4	1	no	—
11	C₂×C₁₆×C₃₁	C₂×C₄	1	1	yes	characteristic
12	C₂×C₁₆×C₃₁	D₄	1	1	yes	characteristic
13	C₃₁×#107	—	2	2	no	—
14	C₃₁×#107	—	4	1	no	—
15	C₃₁×C₄⋊C₈	—	4	1	no	—
16	C₄×C₈×C₃₁	D₄	1	1	yes	characteristic
17	C₃₁×C₃₂	—	4	1	no	—
18	C₂×Q₈×C₃₁	—	8	1	no	—
19	C₂×C₈×C₃₁	—	8	1	no	—
20	C₂×C₈×C₃₁	C₂²⋊C₄	1	1	yes	characteristic
21	C₂×C₈×C₃₁	SD₁₆	1	1	yes	characteristic
22	C₄⋊C₄×C₃₁	—	4	2	no	—
23	C₄⋊C₄×C₃₁	—	8	1	no	—
24	C₄²×C₃₁	D₈	1	1	yes	characteristic
25	C₁₆×C₃₁	—	2	1	no	—
26	C₁₆×C₃₁	SD₁₆	1	1	yes	characteristic
27	C₁₆×C₃₁	Q₁₆	1	1	yes	characteristic
28	#7451	C₃₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
29	Q₈×C₃₁	—	16	2	no	—
30	C₂×C₄×C₃₁	—	8	2	no	—
31	C₂×C₄×C₃₁	#102	1	1	yes	characteristic
32	C₂×C₄×C₃₁	D₁₆	1	1	yes	characteristic
33	C₂×C₄×C₃₁	SD₃₂	1	1	yes	characteristic
34	C₈×C₃₁	—	2	1	no	—
35	C₈×C₃₁	—	16	1	no	—
36	C₈×C₃₁	#101	1	1	yes	characteristic
37	C₈×C₃₁	#103	1	1	yes	characteristic
38	#2252	C₂×C₃₁	1	1	yes	characteristic
39	C₄⋊C₃₂	C₂×C₃₁	1	1	yes	characteristic
40	#1371	C₂×C₃₁	1	1	yes	characteristic
41	C₂²×C₃₁	#357	1	1	yes	characteristic
42	C₄×C₃₁	—	2	1	no	—
43	C₄×C₃₁	—	16	2	no	—
44	C₄×C₃₁	#332	1	1	yes	characteristic
45	C₄×C₃₁	#362	1	1	yes	characteristic
46	C₄×C₃₁	SD₆₄	1	1	yes	characteristic
47	C₄×C₃₁	Q₆₄	1	1	yes	characteristic
48	#500	—	2	1	no	—
49	C₂×C₃₂	—	2	1	no	—
50	#366	—	2	1	no	—
51	#366	C₄×C₃₁	1	2	yes	—
52	C₄×C₁₆	C₂²×C₃₁	1	1	yes	characteristic
53	#335	—	2	1	no	—
54	C₂×C₃₁	#1364	1	1	yes	characteristic
55	C₂×C₃₁	#1416	1	1	yes	characteristic
56	C₂×C₃₁	#1419	1	1	yes	characteristic
57	C₄⋊Q₈	—	4	1	no	—
58	C₂×C₁₆	C₂×C₄×C₃₁	1	1	yes	characteristic
59	C₂×C₁₆	D₄×C₃₁	1	1	yes	characteristic
60	#107	—	2	2	no	—
61	#107	—	4	1	no	—
62	C₄⋊C₈	—	4	1	no	—
63	C₄×C₈	D₄×C₃₁	1	1	yes	characteristic
64	C₃₂	—	4	1	no	—
65	C₃₁	#7451	1	1	yes	characteristic, direct product factor, Sylow
66	C₂×Q₈	—	8	1	no	—
67	C₂×C₈	—	8	1	no	—
68	C₂×C₈	C₂²⋊C₄×C₃₁	1	1	yes	characteristic
69	C₂×C₈	SD₁₆×C₃₁	1	1	yes	characteristic
70	C₄⋊C₄	—	4	2	no	—
71	C₄⋊C₄	—	8	1	no	—
72	C₄²	D₈×C₃₁	1	1	yes	characteristic
73	C₁₆	—	2	1	no	—
74	C₁₆	SD₁₆×C₃₁	1	1	yes	characteristic
75	C₁₆	Q₁₆×C₃₁	1	1	yes	characteristic
76	Q₈	—	16	2	no	—
77	C₂×C₄	—	8	2	no	—
78	C₂×C₄	C₃₁×#102	1	1	yes	characteristic
79	C₂×C₄	C₃₁×D₁₆	1	1	yes	characteristic
80	C₂×C₄	C₃₁×SD₃₂	1	1	yes	characteristic
81	C₈	—	2	1	no	—
82	C₈	—	16	1	no	—
83	C₈	C₃₁×#101	1	1	yes	characteristic
84	C₈	C₃₁×#103	1	1	yes	characteristic
85	C₂²	C₃₁×#357	1	1	yes	characteristic
86	C₄	—	2	1	no	—
87	C₄	—	16	2	no	—
88	C₄	C₃₁×#332	1	1	yes	characteristic
89	C₄	C₃₁×#362	1	1	yes	characteristic
90	C₄	C₃₁×SD₆₄	1	1	yes	characteristic
91	C₄	C₃₁×Q₆₄	1	1	yes	characteristic
92	C₂	C₃₁×#1364	1	1	yes	characteristic
93	C₂	C₃₁×#1416	1	1	yes	characteristic
94	C₂	C₃₁×#1419	1	1	yes	characteristic

	subgroup	G/H
center, socle, prime radical	C₂²×C₃₁	#357
commutator	C₂×C₁₆	C₂×C₄×C₃₁
Frattini, cosocle	C₄×C₁₆	C₂²×C₃₁
LCS	G ▷ C₂×C₁₆ ▷ C₂×C₈ ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₃₁ ◁ C₄²×C₃₁ ◁ C₄×C₈×C₃₁ ◁ C₄×C₁₆×C₃₁ ◁ G

Complements

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

N	H ≅ G/N	type
28. #7451	C₃₁	direct (N × H)
65. C₃₁	#7451	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×#2252	2
C₃₁×C₄⋊C₃₂	2
C₃₁×#1371	2
#7451	31

Subgroups — C31×#7451 #21464210

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃₁×#7451 #21464210