Subgroups — C₂×#11758453 #14521574

Order 1984.

246 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₄²×C₃₁	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×(C₂×D₃₁)⋊C₄	C₂	1	3	yes	maximal
3	C₂×Dic₃₁⋊C₄	C₂	1	3	yes	maximal, complemented
4	#11758453	C₂	1	8	yes	maximal, direct product factor
5	C₂³×D₃₁	C₂²	1	1	yes	characteristic
6	C₂²×C₄×C₃₁	C₂²	1	3	yes	—
7	C₂²×Dic₃₁	C₂²	1	3	yes	—
8	C₄²×C₃₁	C₂²	1	4	yes	complemented
9	(C₂×D₃₁)⋊C₄	C₂²	1	12	yes	—
10	Dic₃₁⋊C₄	C₂²	1	12	yes	complemented
11	C₂³×C₃₁	C₂³	1	1	yes	characteristic
12	C₂²×D₃₁	—	2	6	no	—
13	C₂²×D₃₁	C₂³	1	2	yes	—
14	C₂×C₄×C₃₁	—	2	6	no	—
15	C₂×C₄×C₃₁	C₂³	1	6	yes	—
16	C₂×Dic₃₁	—	2	6	no	—
17	C₂×Dic₃₁	C₂³	1	6	yes	—
18	C₂²×C₃₁	#41	1	6	yes	—
19	C₂²×C₃₁	C₂⁴	1	1	yes	characteristic
20	C₂×D₃₁	—	2	6	no	—
21	C₂×D₃₁	—	4	4	no	—
22	C₄×C₃₁	—	2	6	no	—
23	Dic₃₁	—	2	6	no	—
24	C₂×#126	—	31	1	no	maximal, Sylow
25	C₂×C₃₁	#126	1	4	yes	complemented
26	C₂×C₃₁	C₂×#41	1	3	yes	—
27	D₃₁	—	4	2	no	—
28	#126	—	31	8	no	—
29	C₂×C₄⋊C₄	—	31	3	no	—
30	C₂×C₂²⋊C₄	—	31	3	no	—
31	C₂×C₄²	D₃₁	1	1	yes	characteristic, complemented
32	C₃₁	C₂×#126	1	1	yes	characteristic, complemented, Sylow
33	C₂⁴	—	31	1	no	—
34	C₂²×C₄	—	31	3	no	—
35	C₂²×C₄	C₂×D₃₁	1	3	yes	—
36	C₄⋊C₄	—	31	12	no	—
37	C₂²⋊C₄	—	31	12	no	—
38	C₄²	C₂×D₃₁	1	4	yes	complemented
39	C₂³	—	31	2	no	—
40	C₂³	—	62	6	no	—
41	C₂³	C₂²×D₃₁	1	1	yes	characteristic
42	C₂×C₄	—	2	6	no	—
43	C₂×C₄	—	31	6	no	—
44	C₂×C₄	—	62	6	no	—
45	C₂×C₄	C₂²×D₃₁	1	6	yes	—
46	C₂²	—	62	6	no	—
47	C₂²	—	124	4	no	—
48	C₂²	#92495	1	6	yes	—
49	C₂²	C₂³×D₃₁	1	1	yes	characteristic
50	C₄	—	2	6	no	—
51	C₄	—	62	6	no	—
52	C₂	—	124	2	no	—
53	C₂	#11758453	1	4	yes	direct product factor
54	C₂	C₂×#92495	1	3	yes	—

	subgroup	G/H
center	C₂³	C₂²×D₃₁
commutator, cosocle	C₂²×C₃₁	C₂⁴
Frattini	C₂²	C₂³×D₃₁
Fitting	C₂×C₄²×C₃₁	C₂
socle	C₂³×C₃₁	C₂³
prime radical	C₂³×D₃₁	C₂²
hypercenter	C₂×C₄²	D₃₁
hypocenter	C₃₁	C₂×#126
LCS	G ▷ C₂²×C₃₁ ▷ C₃₁
UCS	C₁ ◁ C₂³ ◁ C₂×C₄²

Complements

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

N	H ≅ G/N	type
1. C₂×C₄²×C₃₁	C₂	semidirect
3. C₂×Dic₃₁⋊C₄	C₂	semidirect
4. #11758453	C₂	direct (N × H)
8. C₄²×C₃₁	C₂²	semidirect
10. Dic₃₁⋊C₄	C₂²	semidirect
25. C₂×C₃₁	#126	semidirect
31. C₂×C₄²	D₃₁	semidirect
32. C₃₁	C₂×#126	semidirect
38. C₄²	C₂×D₃₁	semidirect
53. C₂	#11758453	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂×C₄²×C₃₁	2
C₂×(C₂×D₃₁)⋊C₄	2
C₂×Dic₃₁⋊C₄	2
#11758453	2
C₂×#126	31

Subgroups — C2×#11758453 #14521574

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#11758453 #14521574