Subgroups — #41×Dic₃₁ #14521520

Order 1984.

310 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#41×C₃₁	C₂	1	1	yes	maximal, characteristic
2	Q₈×Dic₃₁	C₂	1	2	yes	maximal, complemented
3	D₄×Dic₃₁	C₂	1	6	yes	maximal, complemented
4	#11758503	C₂	1	3	yes	maximal, complemented
5	C₂×C₄×Dic₃₁	C₂	1	3	yes	maximal, complemented
6	#41×C₃₁	C₄	1	8	yes	complemented
7	C₂×Q₈×C₃₁	C₂²	1	1	yes	characteristic
8	C₂×D₄×C₃₁	C₂²	1	3	yes	—
9	C₂²×C₄×C₃₁	C₂²	1	3	yes	—
10	C₂²×Dic₃₁	C₂²	1	6	yes	—
11	C₂²⋊Dic₃₁	C₂²	1	6	yes	—
12	C₄⋊Dic₃₁	C₂²	1	6	yes	—
13	C₄×Dic₃₁	C₂²	1	1	yes	characteristic
14	C₄×Dic₃₁	C₂²	1	3	yes	—
15	C₄×Dic₃₁	C₂²	1	6	yes	—
16	C₂³×C₃₁	C₂³	1	3	yes	—
17	Q₈×C₃₁	C₂×C₄	1	4	yes	complemented
18	D₄×C₃₁	C₂×C₄	1	12	yes	complemented
19	C₂×C₄×C₃₁	C₂×C₄	1	12	yes	complemented
20	C₂×C₄×C₃₁	C₂³	1	3	yes	—
21	C₂×C₄×C₃₁	C₂³	1	1	yes	characteristic
22	C₂×Dic₃₁	—	2	12	no	—
23	C₂×Dic₃₁	C₂³	1	6	yes	—
24	C₂×Dic₃₁	C₂³	1	2	yes	—
25	C₂²×C₃₁	—	2	6	no	—
26	C₂²×C₃₁	C₂²×C₄	1	6	yes	—
27	C₂²×C₃₁	C₂⁴	1	1	yes	characteristic
28	C₄×C₃₁	C₂²×C₄	1	2	yes	—
29	C₄×C₃₁	C₂²×C₄	1	6	yes	—
30	Dic₃₁	—	2	6	no	—
31	Dic₃₁	#41	1	4	yes	direct product factor
32	C₄×#41	—	31	1	no	maximal, Sylow
33	C₂×C₃₁	—	2	6	no	—
34	C₂×C₃₁	C₂³×C₄	1	1	yes	characteristic
35	C₂×C₃₁	C₂×#41	1	2	yes	—
36	C₂×#41	D₃₁	1	1	yes	characteristic
37	C₄×Q₈	—	31	2	no	—
38	C₄×D₄	—	31	6	no	—
39	#117	—	31	3	no	—
40	C₂×C₄²	—	31	3	no	—
41	C₃₁	C₄×#41	1	1	yes	characteristic, complemented, Sylow
42	#41	Dic₃₁	1	8	yes	direct product factor
43	C₂×Q₈	C₂×D₃₁	1	1	yes	characteristic
44	C₂×D₄	C₂×D₃₁	1	3	yes	—
45	C₂²×C₄	—	31	6	no	—
46	C₂²×C₄	C₂×D₃₁	1	3	yes	—
47	C₄⋊C₄	—	31	6	no	—
48	C₂²⋊C₄	—	31	6	no	—
49	C₄²	—	31	6	no	—
50	C₄²	—	31	1	no	—
51	C₄²	—	31	3	no	—
52	C₂³	C₂²×D₃₁	1	3	yes	—
53	Q₈	C₂×Dic₃₁	1	4	yes	complemented
54	D₄	C₂×Dic₃₁	1	12	yes	complemented
55	C₂×C₄	—	31	2	no	—
56	C₂×C₄	—	31	6	no	—
57	C₂×C₄	—	62	12	no	—
58	C₂×C₄	C₂×Dic₃₁	1	12	yes	complemented
59	C₂×C₄	C₂²×D₃₁	1	3	yes	—
60	C₂×C₄	C₂²×D₃₁	1	1	yes	characteristic
61	C₂²	—	2	6	no	—
62	C₂²	C₂²×Dic₃₁	1	6	yes	—
63	C₂²	C₂³×D₃₁	1	1	yes	characteristic
64	C₄	—	31	4	no	—
65	C₄	—	62	6	no	—
66	C₄	C₂²×Dic₃₁	1	2	yes	—
67	C₄	C₂²×Dic₃₁	1	6	yes	—
68	C₂	—	2	6	no	—
69	C₂	#41×D₃₁	1	2	yes	—
70	C₂	C₂³×Dic₃₁	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	C₂²×D₃₁
commutator	C₂×C₃₁	C₂³×C₄
Frattini	C₂²	C₂³×D₃₁
Fitting, prime radical	C₂×#41×C₃₁	C₂
socle, cosocle	C₂²×C₃₁	C₂⁴
hypercenter	C₂×#41	D₃₁
hypocenter	C₃₁	C₄×#41
LCS	G ▷ C₂×C₃₁ ▷ C₃₁
UCS	C₁ ◁ C₂×C₄ ◁ C₂×#41

Complements

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

N	H ≅ G/N	type
2. Q₈×Dic₃₁	C₂	semidirect
3. D₄×Dic₃₁	C₂	semidirect
4. #11758503	C₂	semidirect
5. C₂×C₄×Dic₃₁	C₂	semidirect
6. #41×C₃₁	C₄	semidirect
17. Q₈×C₃₁	C₂×C₄	semidirect
18. D₄×C₃₁	C₂×C₄	semidirect
19. C₂×C₄×C₃₁	C₂×C₄	semidirect
31. Dic₃₁	#41	direct (N × H)
41. C₃₁	C₄×#41	semidirect
42. #41	Dic₃₁	direct (N × H)
53. Q₈	C₂×Dic₃₁	semidirect
54. D₄	C₂×Dic₃₁	semidirect
58. C₂×C₄	C₂×Dic₃₁	semidirect

Maximal subgroups

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

subgroup	index
C₂×#41×C₃₁	2
Q₈×Dic₃₁	2
D₄×Dic₃₁	2
#11758503	2
C₂×C₄×Dic₃₁	2
C₄×#41	31

Subgroups — #41×Dic31 #14521520

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — #41×Dic₃₁ #14521520