Subgroups — #14521155

Order 1984.

108 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×Dic₁₂₄	C₂	1	1	yes	maximal, characteristic
2	#11758464	C₂	1	2	yes	maximal
3	C₃₁×#106	C₂	1	1	yes	maximal, characteristic
4	#11758403	C₂	1	1	yes	maximal, characteristic
5	#11758398	C₂	1	2	yes	maximal
6	C₂×Dic₆₂	C₂²	1	2	yes	—
7	C₂×C₈×C₃₁	C₂²	1	1	yes	characteristic
8	C₄⋊C₄×C₃₁	C₂²	1	2	yes	—
9	Dic₃₁⋊C₄	—	2	2	no	—
10	C₄×Dic₃₁	—	2	2	no	—
11	C₄×Dic₃₁	C₂²	1	1	yes	characteristic
12	C₂×C₃₁⋊C₈	C₂²	1	1	yes	characteristic
13	Dic₁₂₄	C₄	1	4	yes	complemented
14	C₂×C₄×C₃₁	—	2	2	no	—
15	C₂×C₄×C₃₁	C₂³	1	1	yes	characteristic
16	C₂×Dic₃₁	—	2	2	no	—
17	C₂×Dic₃₁	D₄	1	2	yes	—
18	Dic₆₂	—	2	2	no	—
19	Dic₆₂	C₂×C₄	1	4	yes	—
20	C₈×C₃₁	C₂×C₄	1	2	yes	—
21	C₃₁⋊C₈	—	2	1	no	—
22	C₂²×C₃₁	C₂×D₄	1	1	yes	characteristic
23	C₄×C₃₁	—	4	2	no	—
24	C₄×C₃₁	C₂²×C₄	1	1	yes	characteristic
25	C₄×C₃₁	#41	1	1	yes	characteristic
26	Dic₃₁	—	2	4	no	—
27	Dic₃₁	—	2	2	no	—
28	#441	—	31	1	no	maximal, Sylow
29	C₂×C₃₁	C₄×D₄	1	1	yes	characteristic
30	C₂×C₃₁	#137	1	2	yes	—
31	C₂×Q₁₆	—	31	1	no	—
32	C₄×Q₈	—	31	2	no	—
33	#106	D₃₁	1	1	yes	characteristic
34	#103	—	31	2	no	—
35	#97	—	31	1	no	—
36	C₃₁	#441	1	1	yes	characteristic, complemented, Sylow
37	C₂×Q₈	—	31	2	no	—
38	Q₁₆	—	31	4	no	—
39	C₂×C₈	—	31	1	no	—
40	C₂×C₈	C₂×D₃₁	1	1	yes	characteristic
41	C₄⋊C₄	—	62	2	no	—
42	C₄⋊C₄	C₂×D₃₁	1	2	yes	—
43	C₄²	—	31	1	no	—
44	C₄²	—	62	2	no	—
45	Q₈	—	31	4	no	—
46	Q₈	—	62	2	no	—
47	C₂×C₄	—	2	2	no	—
48	C₂×C₄	—	31	2	no	—
49	C₂×C₄	—	62	2	no	—
50	C₂×C₄	C₂²×D₃₁	1	1	yes	characteristic
51	C₈	—	62	1	no	—
52	C₈	C₄×D₃₁	1	2	yes	—
53	C₂²	D₄×D₃₁	1	1	yes	characteristic
54	C₄	—	4	2	no	—
55	C₄	—	62	4	no	—
56	C₄	—	62	2	no	—
57	C₄	C₂×C₄×D₃₁	1	1	yes	characteristic
58	C₄	#92499	1	1	yes	characteristic
59	C₂	#11758470	1	1	yes	characteristic
60	C₂	#11758492	1	2	yes	—

	subgroup	G/H
center	C₂²	D₄×D₃₁
commutator	C₄×C₃₁	C₂²×C₄
Frattini	C₂×C₄	C₂²×D₃₁
Fitting	C₃₁×#106	C₂
socle, prime radical	C₂²×C₃₁	C₂×D₄
cosocle	C₂×C₄×C₃₁	C₂³
hypercenter	#106	D₃₁
hypocenter	C₃₁	#441
LCS	G ▷ C₄×C₃₁ ▷ C₂×C₃₁ ▷ C₃₁
UCS	C₁ ◁ C₂² ◁ C₂×C₄ ◁ #106

Complements

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

N	H ≅ G/N	type
13. Dic₁₂₄	C₄	semidirect
36. C₃₁	#441	semidirect

Maximal subgroups

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

subgroup	index
C₂×Dic₁₂₄	2
#11758464	2
C₃₁×#106	2
#11758403	2
#11758398	2
#441	31