Subgroups — C₂×#11758451 #14521589

Order 1984.

498 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×D₁₂₄	C₂	1	6	yes	maximal, complemented
2	C₂×C₄²×C₃₁	C₂	1	1	yes	maximal, characteristic, complemented
3	#11758451	C₂	1	8	yes	maximal, direct product factor
4	C₂³×D₃₁	C₂²	1	4	yes	—
5	C₂²×C₄×C₃₁	C₂²	1	3	yes	—
6	C₂×D₁₂₄	—	2	24	no	—
7	C₂×D₁₂₄	C₂²	1	24	yes	complemented
8	C₄²×C₃₁	C₂²	1	4	yes	complemented
9	C₂³×C₃₁	C₂³	1	1	yes	characteristic
10	C₂²×D₃₁	—	2	24	no	—
11	C₂²×D₃₁	C₂³	1	8	yes	—
12	C₂×C₄×C₃₁	D₄	1	12	yes	complemented
13	C₂×C₄×C₃₁	C₂³	1	6	yes	—
14	D₁₂₄	—	2	48	no	—
15	C₂²×C₃₁	C₂×D₄	1	6	yes	—
16	C₂²×C₃₁	C₂⁴	1	1	yes	characteristic
17	C₂×D₃₁	—	2	24	no	—
18	C₂×D₃₁	—	4	16	no	—
19	C₄×C₃₁	C₂×D₄	1	12	yes	complemented
20	C₂×#127	—	31	1	no	maximal, Sylow
21	C₂×C₃₁	#127	1	4	yes	complemented
22	C₂×C₃₁	C₂²×D₄	1	3	yes	—
23	D₃₁	—	4	8	no	—
24	C₂²×D₄	—	31	6	no	—
25	#127	—	31	8	no	—
26	C₂×C₄²	D₃₁	1	1	yes	characteristic, complemented
27	C₃₁	C₂×#127	1	1	yes	characteristic, complemented, Sylow
28	C₂⁴	—	31	4	no	—
29	C₂×D₄	—	31	24	no	—
30	C₂×D₄	—	62	24	no	—
31	C₂²×C₄	C₂×D₃₁	1	3	yes	—
32	C₄²	C₂×D₃₁	1	4	yes	complemented
33	C₂³	—	31	8	no	—
34	C₂³	—	62	24	no	—
35	C₂³	C₂²×D₃₁	1	1	yes	characteristic
36	D₄	—	62	48	no	—
37	C₂×C₄	D₁₂₄	1	12	yes	complemented
38	C₂×C₄	C₂²×D₃₁	1	6	yes	—
39	C₂²	—	62	24	no	—
40	C₂²	—	124	16	no	—
41	C₂²	C₂×D₁₂₄	1	6	yes	—
42	C₂²	C₂³×D₃₁	1	1	yes	characteristic
43	C₄	C₂×D₁₂₄	1	12	yes	complemented
44	C₂	—	124	8	no	—
45	C₂	#11758451	1	4	yes	direct product factor
46	C₂	C₂²×D₁₂₄	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
hypercenter	C₂×C₄²	D₃₁
hypocenter	C₃₁	C₂×#127
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. C₂²×D₁₂₄	C₂	semidirect
2. C₂×C₄²×C₃₁	C₂	semidirect
3. #11758451	C₂	direct (N × H)
7. C₂×D₁₂₄	C₂²	semidirect
8. C₄²×C₃₁	C₂²	semidirect
12. C₂×C₄×C₃₁	D₄	semidirect
19. C₄×C₃₁	C₂×D₄	semidirect
21. C₂×C₃₁	#127	semidirect
26. C₂×C₄²	D₃₁	semidirect
27. C₃₁	C₂×#127	semidirect
32. C₄²	C₂×D₃₁	semidirect
37. C₂×C₄	D₁₂₄	semidirect
43. C₄	C₂×D₁₂₄	semidirect
45. C₂	#11758451	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×D₁₂₄	2
C₂×C₄²×C₃₁	2
#11758451	2
C₂×#127	31

Subgroups — C2×#11758451 #14521589

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#11758451 #14521589