Subgroups — C₃₁×#1822 #16841755

Order 3968.

272 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃₁×#117	C₂	1	1	yes	maximal, characteristic
2	C₃₁×#407	C₂	1	2	yes	maximal
3	C₃₁×#343	C₂	1	4	yes	maximal, complemented
4	C₂³×C₄×C₃₁	C₂²	1	1	yes	characteristic
5	C₂×M₁₆×C₃₁	C₂²	1	4	yes	—
6	C₃₁×#117	—	2	4	no	—
7	C₂×C₄⋊C₄×C₃₁	C₂²	1	2	yes	—
8	C₂×C₂²⋊C₄×C₃₁	C₄	1	2	yes	—
9	C₂×C₄²×C₃₁	C₄	1	2	yes	—
10	C₃₁×C₂²⋊C₈	—	2	4	no	—
11	C₂⁴×C₃₁	C₂×C₄	1	1	yes	characteristic
12	C₂²×C₄×C₃₁	—	2	4	no	—
13	C₂²×C₄×C₃₁	C₂×C₄	1	1	yes	characteristic
14	C₂²×C₄×C₃₁	C₂×C₄	1	4	yes	—
15	C₂²×C₄×C₃₁	D₄	1	4	yes	—
16	C₂²×C₄×C₃₁	C₂³	1	1	yes	characteristic
17	M₁₆×C₃₁	—	2	8	no	—
18	C₂×C₈×C₃₁	—	2	4	no	—
19	C₄⋊C₄×C₃₁	—	2	4	no	—
20	C₂²⋊C₄×C₃₁	—	2	4	no	—
21	C₄²×C₃₁	—	2	4	no	—
22	C₂³×C₃₁	—	2	2	no	—
23	C₂³×C₃₁	—	4	2	no	—
24	C₂³×C₃₁	C₂²⋊C₄	1	2	yes	—
25	C₂³×C₃₁	C₂²×C₄	1	1	yes	characteristic
26	C₂×C₄×C₃₁	—	2	2	no	—
27	C₂×C₄×C₃₁	—	2	8	no	—
28	C₂×C₄×C₃₁	—	2	4	no	—
29	C₂×C₄×C₃₁	—	4	4	no	—
30	C₂×C₄×C₃₁	C₂²⋊C₄	1	2	yes	—
31	C₂×C₄×C₃₁	C₂×D₄	1	2	yes	—
32	C₂×C₄×C₃₁	#41	1	4	yes	—
33	C₈×C₃₁	—	4	4	no	—
34	#1822	C₃₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
35	C₂²×C₃₁	—	2	2	no	—
36	C₂²×C₃₁	—	2	2	no	—
37	C₂²×C₃₁	—	2	4	no	—
38	C₂²×C₃₁	—	4	4	no	—
39	C₂²×C₃₁	C₂×C₂²⋊C₄	1	1	yes	characteristic
40	C₂²×C₃₁	#117	1	2	yes	—
41	C₄×C₃₁	—	2	2	no	—
42	C₄×C₃₁	—	4	4	no	—
43	C₄×C₃₁	#123	1	4	yes	—
44	C₂×#117	C₂×C₃₁	1	1	yes	characteristic
45	#407	C₂×C₃₁	1	2	yes	—
46	#343	C₂×C₃₁	1	4	yes	complemented
47	C₂×C₃₁	—	2	2	no	—
48	C₂×C₃₁	—	4	2	no	—
49	C₂×C₃₁	#381	1	1	yes	characteristic
50	C₂×C₃₁	#413	1	2	yes	—
51	C₂³×C₄	C₂²×C₃₁	1	1	yes	characteristic
52	C₂×M₁₆	C₂²×C₃₁	1	4	yes	—
53	#117	—	2	4	no	—
54	C₂×C₄⋊C₄	C₂²×C₃₁	1	2	yes	—
55	C₂×C₂²⋊C₄	C₄×C₃₁	1	2	yes	—
56	C₂×C₄²	C₄×C₃₁	1	2	yes	—
57	C₂²⋊C₈	—	2	4	no	—
58	C₃₁	#1822	1	1	yes	characteristic, direct product factor, Sylow
59	C₂⁴	C₂×C₄×C₃₁	1	1	yes	characteristic
60	C₂²×C₄	—	2	4	no	—
61	C₂²×C₄	C₂×C₄×C₃₁	1	1	yes	characteristic
62	C₂²×C₄	C₂×C₄×C₃₁	1	4	yes	—
63	C₂²×C₄	D₄×C₃₁	1	4	yes	—
64	C₂²×C₄	C₂³×C₃₁	1	1	yes	characteristic
65	M₁₆	—	2	8	no	—
66	C₂×C₈	—	2	4	no	—
67	C₄⋊C₄	—	2	4	no	—
68	C₂²⋊C₄	—	2	4	no	—
69	C₄²	—	2	4	no	—
70	C₂³	—	2	2	no	—
71	C₂³	—	4	2	no	—
72	C₂³	C₂²⋊C₄×C₃₁	1	2	yes	—
73	C₂³	C₂²×C₄×C₃₁	1	1	yes	characteristic
74	C₂×C₄	—	2	2	no	—
75	C₂×C₄	—	2	8	no	—
76	C₂×C₄	—	2	4	no	—
77	C₂×C₄	—	4	4	no	—
78	C₂×C₄	C₂²⋊C₄×C₃₁	1	2	yes	—
79	C₂×C₄	C₂×D₄×C₃₁	1	2	yes	—
80	C₂×C₄	#41×C₃₁	1	4	yes	—
81	C₈	—	4	4	no	—
82	C₂²	—	2	2	no	—
83	C₂²	—	2	4	no	—
84	C₂²	—	2	2	no	—
85	C₂²	—	4	4	no	—
86	C₂²	C₂×C₂²⋊C₄×C₃₁	1	1	yes	characteristic
87	C₂²	C₃₁×#117	1	2	yes	—
88	C₄	—	2	2	no	—
89	C₄	—	4	4	no	—
90	C₄	C₃₁×#123	1	4	yes	—
91	C₂	—	2	2	no	—
92	C₂	—	4	2	no	—
93	C₂	C₃₁×#381	1	1	yes	characteristic
94	C₂	C₃₁×#413	1	2	yes	—

	subgroup	G/H
center, socle	C₂²×C₃₁	C₂×C₂²⋊C₄
commutator	C₂³	C₂²×C₄×C₃₁
Frattini, cosocle	C₂²×C₄	C₂³×C₃₁
prime radical	C₂⁴×C₃₁	C₂×C₄
LCS	G ▷ C₂³ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₃₁ ◁ C₂³×C₄×C₃₁ ◁ G

Complements

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

N	H ≅ G/N	type
3. C₃₁×#343	C₂	semidirect
34. #1822	C₃₁	direct (N × H)
46. #343	C₂×C₃₁	semidirect
58. C₃₁	#1822	direct (N × H)

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
C₂×C₃₁×#117	2
C₃₁×#407	2
C₃₁×#343	2
#1822	31

Subgroups — C31×#1822 #16841755

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃₁×#1822 #16841755