Subgroups — #14521526

Order 1984.

266 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×Dic₆₂	C₂	1	1	yes	maximal, characteristic
2	C₃₁×#117	C₂	1	1	yes	maximal, characteristic
3	#11758503	C₂	1	1	yes	maximal, characteristic
4	#11758464	C₂	1	4	yes	maximal, complemented
5	#11758454	C₂	1	4	yes	maximal
6	C₄×Dic₆₂	C₂	1	4	yes	maximal, complemented
7	C₂²×C₄×C₃₁	C₂²	1	1	yes	characteristic
8	C₂²×Dic₃₁	C₂²	1	2	yes	—
9	C₂×Dic₆₂	C₄	1	8	yes	complemented
10	C₂×Dic₆₂	C₂²	1	2	yes	—
11	C₂×Dic₆₂	C₂²	1	2	yes	—
12	C₄⋊C₄×C₃₁	C₂²	1	2	yes	—
13	C₂²⋊C₄×C₃₁	C₂²	1	2	yes	—
14	C₄²×C₃₁	C₂²	1	2	yes	—
15	C₂²⋊Dic₃₁	C₂²	1	2	yes	—
16	C₄⋊Dic₃₁	C₂²	1	2	yes	—
17	Dic₃₁⋊C₄	C₂²	1	8	yes	—
18	C₄×Dic₃₁	C₂²	1	8	yes	—
19	C₄×Dic₃₁	C₂²	1	2	yes	—
20	C₂³×C₃₁	C₂³	1	1	yes	characteristic
21	C₂×C₄×C₃₁	C₂×C₄	1	4	yes	—
22	C₂×C₄×C₃₁	C₂³	1	4	yes	—
23	C₂×C₄×C₃₁	C₂³	1	1	yes	characteristic
24	C₂×C₄×C₃₁	C₂³	1	1	yes	characteristic
25	C₂×Dic₃₁	C₂×C₄	1	8	yes	—
26	C₂×Dic₃₁	C₂³	1	4	yes	—
27	C₂×Dic₃₁	C₂³	1	4	yes	—
28	Dic₆₂	C₂×C₄	1	8	yes	—
29	Dic₆₂	C₂×C₄	1	8	yes	—
30	C₂²×C₃₁	—	2	2	no	—
31	C₂²×C₃₁	C₂²×C₄	1	2	yes	—
32	C₂²×C₃₁	C₂⁴	1	1	yes	characteristic
33	C₄×C₃₁	—	2	4	no	—
34	C₄×C₃₁	C₂²×C₄	1	2	yes	—
35	C₄×C₃₁	C₂²×C₄	1	2	yes	—
36	Dic₃₁	—	2	4	no	—
37	Dic₃₁	C₂²×C₄	1	8	yes	—
38	#519	—	31	1	no	maximal, Sylow
39	C₂×C₃₁	—	2	2	no	—
40	C₂×C₃₁	C₂³×C₄	1	1	yes	characteristic
41	C₂×C₃₁	2₋¹⁺⁴	1	2	yes	—
42	C₂²×Q₈	—	31	1	no	—
43	C₄×Q₈	—	31	4	no	—
44	C₄×Q₈	—	31	4	no	—
45	#117	—	31	1	no	—
46	#117	—	31	4	no	—
47	#117	D₃₁	1	1	yes	characteristic
48	C₃₁	#519	1	1	yes	characteristic, complemented, Sylow
49	C₂×Q₈	—	31	8	no	—
50	C₂×Q₈	—	31	2	no	—
51	C₂×Q₈	—	31	2	no	—
52	C₂²×C₄	—	31	2	no	—
53	C₂²×C₄	C₂×D₃₁	1	1	yes	characteristic
54	C₄⋊C₄	—	31	8	no	—
55	C₄⋊C₄	—	31	2	no	—
56	C₄⋊C₄	C₂×D₃₁	1	2	yes	—
57	C₂²⋊C₄	—	31	2	no	—
58	C₂²⋊C₄	C₂×D₃₁	1	2	yes	—
59	C₄²	—	31	8	no	—
60	C₄²	—	31	2	no	—
61	C₄²	C₂×D₃₁	1	2	yes	—
62	C₂³	C₂²×D₃₁	1	1	yes	characteristic
63	Q₈	—	31	8	no	—
64	Q₈	—	31	8	no	—
65	C₂×C₄	—	31	8	no	—
66	C₂×C₄	—	31	4	no	—
67	C₂×C₄	—	31	4	no	—
68	C₂×C₄	C₄×D₃₁	1	4	yes	—
69	C₂×C₄	C₂²×D₃₁	1	4	yes	—
70	C₂×C₄	C₂²×D₃₁	1	1	yes	characteristic
71	C₂×C₄	C₂²×D₃₁	1	1	yes	characteristic
72	C₂²	—	2	2	no	—
73	C₂²	C₂×C₄×D₃₁	1	2	yes	—
74	C₂²	C₂³×D₃₁	1	1	yes	characteristic
75	C₄	—	2	4	no	—
76	C₄	—	31	8	no	—
77	C₄	—	62	4	no	—
78	C₄	C₂×C₄×D₃₁	1	2	yes	—
79	C₄	C₂×C₄×D₃₁	1	2	yes	—
80	C₂	—	2	2	no	—
81	C₂	C₂²×C₄×D₃₁	1	1	yes	characteristic
82	C₂	#11758567	1	2	yes	—

	subgroup	G/H
center, Frattini	C₂²	C₂³×D₃₁
commutator	C₂×C₃₁	C₂³×C₄
Fitting	C₃₁×#117	C₂
socle, cosocle	C₂²×C₃₁	C₂⁴
prime radical	C₂³×C₃₁	C₂³
hypercenter	#117	D₃₁
hypocenter	C₃₁	#519
LCS	G ▷ C₂×C₃₁ ▷ C₃₁
UCS	C₁ ◁ C₂² ◁ #117

Complements

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

N	H ≅ G/N	type
4. #11758464	C₂	semidirect
6. C₄×Dic₆₂	C₂	semidirect
9. C₂×Dic₆₂	C₄	semidirect
48. C₃₁	#519	semidirect

Maximal subgroups

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

subgroup	index
C₂²×Dic₆₂	2
C₃₁×#117	2
#11758503	2
#11758464	2
#11758454	2
C₄×Dic₆₂	2
#519	31