Subgroups — C₂×#11758405 #14521080

Order 1984.

130 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₈×C₃₁	C₂	1	1	yes	maximal, characteristic
2	C₂×C₄⋊Dic₃₁	C₂	1	2	yes	maximal
3	#11758405	C₂	1	4	yes	maximal, direct product factor
4	C₂²×C₄×C₃₁	C₂²	1	1	yes	characteristic
5	C₂²×Dic₃₁	—	2	2	no	—
6	C₂×C₈×C₃₁	C₄	1	4	yes	complemented
7	C₂×C₈×C₃₁	C₂²	1	2	yes	—
8	C₄⋊Dic₃₁	—	2	2	no	—
9	C₄⋊Dic₃₁	C₂²	1	4	yes	—
10	C₂³×C₃₁	D₄	1	1	yes	characteristic
11	C₂×C₄×C₃₁	C₂×C₄	1	2	yes	—
12	C₂×C₄×C₃₁	D₄	1	1	yes	characteristic
13	C₂×C₄×C₃₁	Q₈	1	2	yes	—
14	C₂×C₄×C₃₁	C₂³	1	1	yes	characteristic
15	C₂×Dic₃₁	—	2	4	no	—
16	C₂×Dic₃₁	—	4	4	no	—
17	C₈×C₃₁	C₂×C₄	1	4	yes	complemented
18	C₂²×C₃₁	C₄⋊C₄	1	2	yes	—
19	C₂²×C₃₁	SD₁₆	1	4	yes	—
20	C₂²×C₃₁	C₂×D₄	1	1	yes	characteristic
21	C₄×C₃₁	C₄⋊C₄	1	2	yes	—
22	C₄×C₃₁	C₂²×C₄	1	1	yes	characteristic
23	C₄×C₃₁	C₂×Q₈	1	1	yes	characteristic
24	Dic₃₁	—	4	4	no	—
25	C₂×#106	—	31	1	no	maximal, Sylow
26	C₂×C₃₁	#106	1	4	yes	complemented
27	C₂×C₃₁	C₂×C₄⋊C₄	1	1	yes	characteristic
28	C₂×C₃₁	C₂×SD₁₆	1	2	yes	—
29	C₂²×C₈	D₃₁	1	1	yes	characteristic
30	C₂×C₄⋊C₄	—	31	2	no	—
31	#106	—	31	4	no	—
32	C₃₁	C₂×#106	1	1	yes	characteristic, complemented, Sylow
33	C₂²×C₄	—	62	2	no	—
34	C₂²×C₄	C₂×D₃₁	1	1	yes	characteristic
35	C₂×C₈	Dic₃₁	1	4	yes	complemented
36	C₂×C₈	C₂×D₃₁	1	2	yes	—
37	C₄⋊C₄	—	31	4	no	—
38	C₄⋊C₄	—	62	2	no	—
39	C₂³	D₁₂₄	1	1	yes	characteristic
40	C₂×C₄	—	62	4	no	—
41	C₂×C₄	—	124	4	no	—
42	C₂×C₄	Dic₆₂	1	2	yes	—
43	C₂×C₄	D₁₂₄	1	1	yes	characteristic
44	C₂×C₄	C₂×Dic₃₁	1	2	yes	—
45	C₂×C₄	C₂²×D₃₁	1	1	yes	characteristic
46	C₈	C₂×Dic₃₁	1	4	yes	complemented
47	C₂²	#92470	1	4	yes	—
48	C₂²	C₄⋊Dic₃₁	1	2	yes	—
49	C₂²	C₂×D₁₂₄	1	1	yes	characteristic
50	C₄	—	124	4	no	—
51	C₄	C₄⋊Dic₃₁	1	2	yes	—
52	C₄	C₂×Dic₆₂	1	1	yes	characteristic
53	C₄	C₂²×Dic₃₁	1	1	yes	characteristic
54	C₂	#11758405	1	4	yes	direct product factor
55	C₂	C₂×#92470	1	2	yes	—
56	C₂	C₂×C₄⋊Dic₃₁	1	1	yes	characteristic

	subgroup	G/H
center	C₂³	D₁₂₄
commutator	C₄×C₃₁	C₂²×C₄
Frattini	C₂×C₄	C₂²×D₃₁
Fitting	C₂²×C₈×C₃₁	C₂
socle, prime radical	C₂³×C₃₁	D₄
cosocle	C₂×C₄×C₃₁	C₂³
hypercenter	C₂²×C₈	D₃₁
hypocenter	C₃₁	C₂×#106
LCS	G ▷ C₄×C₃₁ ▷ C₂×C₃₁ ▷ C₃₁
UCS	C₁ ◁ C₂³ ◁ C₂²×C₄ ◁ C₂²×C₈

Complements

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

N	H ≅ G/N	type
3. #11758405	C₂	direct (N × H)
6. C₂×C₈×C₃₁	C₄	semidirect
17. C₈×C₃₁	C₂×C₄	semidirect
26. C₂×C₃₁	#106	semidirect
32. C₃₁	C₂×#106	semidirect
35. C₂×C₈	Dic₃₁	semidirect
46. C₈	C₂×Dic₃₁	semidirect
54. C₂	#11758405	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂²×C₈×C₃₁	2
C₂×C₄⋊Dic₃₁	2
#11758405	2
C₂×#106	31

Subgroups — C2×#11758405 #14521080

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#11758405 #14521080