Subgroups — #14521413

Order 1984.

110 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃₁×#127	C₂	1	1	yes	maximal, characteristic
2	#11758447	C₂	1	1	yes	maximal, characteristic, complemented
3	#11758420	C₂	1	4	yes	maximal, complemented
4	#11758391	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×D₄×C₃₁	—	2	2	no	—
6	C₂×D₄×C₃₁	C₂²	1	2	yes	—
7	C₄²×C₃₁	C₂²	1	1	yes	characteristic
8	C₄⋊Dic₃₁	C₂²	1	2	yes	—
9	Dic₃₁⋊C₄	—	2	2	no	—
10	C₂×C₃₁⋊C₈	C₂²	1	2	yes	—
11	C₂³×C₃₁	—	2	2	no	—
12	D₄×C₃₁	—	2	4	no	—
13	D₄×C₃₁	—	4	4	no	—
14	C₂×C₄×C₃₁	D₄	1	2	yes	—
15	C₂×C₄×C₃₁	C₂³	1	1	yes	characteristic
16	C₂×Dic₃₁	—	2	2	no	—
17	C₃₁⋊C₈	—	2	2	no	—
18	C₂²×C₃₁	—	4	2	no	—
19	C₂²×C₃₁	—	4	4	no	—
20	C₂²×C₃₁	C₂×D₄	1	1	yes	characteristic
21	C₄×C₃₁	—	2	2	no	—
22	C₄×C₃₁	#41	1	2	yes	—
23	Dic₃₁	—	4	2	no	—
24	#490	—	31	1	no	maximal, Sylow
25	C₂×C₃₁	—	8	2	no	—
26	C₂×C₃₁	#124	1	1	yes	characteristic
27	C₂×C₃₁	AGL(1,ℤ/8)	1	2	yes	—
28	#127	D₃₁	1	1	yes	characteristic
29	#125	—	31	1	no	—
30	#102	—	31	4	no	—
31	#97	—	31	1	no	—
32	C₃₁	#490	1	1	yes	characteristic, complemented, Sylow
33	C₂×D₄	—	2	2	no	—
34	C₂×D₄	C₂×D₃₁	1	2	yes	—
35	C₂×C₈	—	31	2	no	—
36	C₄⋊C₄	—	31	2	no	—
37	C₄⋊C₄	—	62	2	no	—
38	C₄²	C₂×D₃₁	1	1	yes	characteristic
39	C₂³	—	2	2	no	—
40	D₄	—	2	4	no	—
41	D₄	—	4	4	no	—
42	C₂×C₄	—	62	2	no	—
43	C₂×C₄	C₂²⋊D₃₁	1	2	yes	—
44	C₂×C₄	C₂²×D₃₁	1	1	yes	characteristic
45	C₈	—	62	2	no	—
46	C₂²	—	4	4	no	—
47	C₂²	—	4	2	no	—
48	C₂²	C₂×C₂²⋊D₃₁	1	1	yes	characteristic
49	C₄	—	2	2	no	—
50	C₄	—	124	2	no	—
51	C₄	#92497	1	2	yes	—
52	C₂	—	8	2	no	—
53	C₂	#11758509	1	2	yes	—
54	C₂	#11758513	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	C₂×C₂²⋊D₃₁
commutator, cosocle	C₂×C₄×C₃₁	C₂³
Frattini	C₂×C₄	C₂²×D₃₁
Fitting, prime radical	C₃₁×#127	C₂
socle	C₂²×C₃₁	C₂×D₄
hypercenter	#127	D₃₁
hypocenter	C₃₁	#490
LCS	G ▷ C₂×C₄×C₃₁ ▷ C₂×C₃₁ ▷ C₃₁
UCS	C₁ ◁ C₂² ◁ C₄² ◁ #127

Complements

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

N	H ≅ G/N	type
2. #11758447	C₂	semidirect
3. #11758420	C₂	semidirect
4. #11758391	C₂	semidirect
32. C₃₁	#490	semidirect

Maximal subgroups

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

subgroup	index
C₃₁×#127	2
#11758447	2
#11758420	2
#11758391	2
#490	31