Subgroups — #14521385

Order 1984.

104 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₄⋊Dic₃₁	C₂	1	1	yes	maximal, characteristic
2	#11758501	C₂	1	1	yes	maximal, characteristic
3	C₃₁×C₂²⋊C₈	C₂	1	1	yes	maximal, characteristic
4	#11758406	C₂	1	2	yes	maximal, complemented
5	#11758404	C₂	1	2	yes	maximal, complemented
6	C₂²×C₄×C₃₁	C₂²	1	1	yes	characteristic
7	C₂²×Dic₃₁	—	2	1	no	—
8	C₂×Dic₆₂	C₂²	1	1	yes	characteristic
9	C₂×C₈×C₃₁	C₂²	1	2	yes	—
10	C₂²⋊Dic₃₁	—	2	1	no	—
11	C₄⋊Dic₃₁	—	2	1	no	—
12	C₄⋊Dic₃₁	C₂²	1	2	yes	—
13	C₄⋊Dic₃₁	C₂²	1	1	yes	characteristic
14	Dic₃₁⋊C₄	—	2	1	no	—
15	C₂³×C₃₁	D₄	1	1	yes	characteristic
16	C₂×C₄×C₃₁	—	2	2	no	—
17	C₂×C₄×C₃₁	D₄	1	1	yes	characteristic
18	C₂×C₄×C₃₁	C₂³	1	1	yes	characteristic
19	C₂×Dic₃₁	—	2	1	no	—
20	C₂×Dic₃₁	—	2	1	no	—
21	C₂×Dic₃₁	—	2	2	no	—
22	C₂×Dic₃₁	—	4	2	no	—
23	Dic₆₂	—	2	2	no	—
24	C₈×C₃₁	—	2	2	no	—
25	C₂²×C₃₁	—	2	1	no	—
26	C₂²×C₃₁	—	2	1	no	—
27	C₂²×C₃₁	Q₁₆	1	2	yes	—
28	C₂²×C₃₁	C₂×D₄	1	1	yes	characteristic
29	C₄×C₃₁	—	2	1	no	—
30	C₄×C₃₁	#41	1	2	yes	—
31	Dic₃₁	—	4	1	no	—
32	Dic₃₁	—	4	1	no	—
33	Dic₃₁	—	4	2	no	—
34	#484	—	31	1	no	maximal, Sylow
35	C₂×C₃₁	—	2	2	no	—
36	C₂×C₃₁	#123	1	1	yes	characteristic
37	C₂×C₃₁	C₂×Q₁₆	1	1	yes	characteristic
38	C₂×C₃₁	AGL(1,ℤ/8)	1	1	yes	characteristic
39	C₂²⋊Q₈	—	31	1	no	—
40	C₂×C₄⋊C₄	—	31	1	no	—
41	#107	—	31	2	no	—
42	#103	—	31	2	no	—
43	C₂²⋊C₈	D₃₁	1	1	yes	characteristic
44	C₃₁	#484	1	1	yes	characteristic, complemented, Sylow
45	C₂×Q₈	—	31	1	no	—
46	C₂²×C₄	—	62	1	no	—
47	C₂²×C₄	C₂×D₃₁	1	1	yes	characteristic
48	C₂×C₈	C₂×D₃₁	1	2	yes	—
49	C₄⋊C₄	—	31	2	no	—
50	C₄⋊C₄	—	31	1	no	—
51	C₄⋊C₄	—	62	1	no	—
52	C₄⋊C₄	—	62	1	no	—
53	C₂²⋊C₄	—	62	1	no	—
54	C₂³	D₁₂₄	1	1	yes	characteristic
55	Q₈	—	62	2	no	—
56	C₂×C₄	—	2	2	no	—
57	C₂×C₄	—	62	1	no	—
58	C₂×C₄	—	62	1	no	—
59	C₂×C₄	—	62	2	no	—
60	C₂×C₄	—	124	2	no	—
61	C₂×C₄	D₁₂₄	1	1	yes	characteristic
62	C₂×C₄	C₂²×D₃₁	1	1	yes	characteristic
63	C₈	—	2	2	no	—
64	C₂²	—	2	1	no	—
65	C₂²	—	2	1	no	—
66	C₂²	Dic₁₂₄	1	2	yes	—
67	C₂²	C₂×D₁₂₄	1	1	yes	characteristic
68	C₄	—	2	1	no	—
69	C₄	—	124	1	no	—
70	C₄	—	124	2	no	—
71	C₄	—	124	1	no	—
72	C₄	#92497	1	2	yes	—
73	C₂	—	2	2	no	—
74	C₂	#11758463	1	1	yes	characteristic
75	C₂	C₂×Dic₁₂₄	1	1	yes	characteristic
76	C₂	#11758485	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	C₂×D₁₂₄
commutator, cosocle	C₂×C₄×C₃₁	C₂³
Frattini	C₂×C₄	C₂²×D₃₁
Fitting	C₃₁×C₂²⋊C₈	C₂
socle	C₂²×C₃₁	C₂×D₄
prime radical	C₂³×C₃₁	D₄
hypercenter	C₂²⋊C₈	D₃₁
hypocenter	C₃₁	#484
LCS	G ▷ C₂×C₄×C₃₁ ▷ C₂×C₃₁ ▷ C₃₁
UCS	C₁ ◁ C₂² ◁ C₂²×C₄ ◁ C₂²⋊C₈

Complements

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

N	H ≅ G/N	type
4. #11758406	C₂	semidirect
5. #11758404	C₂	semidirect
44. C₃₁	#484	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₄⋊Dic₃₁	2
#11758501	2
C₃₁×C₂²⋊C₈	2
#11758406	2
#11758404	2
#484	31