Subgroups — #14521287

Order 1984.

114 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×Q₁₆×C₃₁	C₂	1	1	yes	maximal, characteristic, complemented
2	#11758523	C₂	1	2	yes	maximal
3	C₂×C₈×D₃₁	C₂	1	1	yes	maximal, characteristic
4	#11758423	C₂	1	2	yes	maximal, complemented
5	#11758406	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×Q₈×C₃₁	C₂²	1	2	yes	—
7	C₂×C₄×D₃₁	C₂²	1	1	yes	characteristic
8	Q₁₆×C₃₁	—	2	2	no	—
9	C₂×C₈×C₃₁	C₂²	1	1	yes	characteristic
10	(C₂×D₃₁)⋊C₄	—	2	2	no	—
11	C₄⋊Dic₃₁	C₂²	1	2	yes	—
12	Dic₃₁⋊C₄	—	2	2	no	—
13	C₂×C₃₁⋊C₈	C₂²	1	1	yes	characteristic
14	C₈×D₃₁	—	2	2	no	—
15	C₂²×D₃₁	D₄	1	1	yes	characteristic
16	Q₈×C₃₁	—	2	2	no	—
17	Q₈×C₃₁	—	2	2	no	—
18	C₂×C₄×C₃₁	—	2	2	no	—
19	C₂×C₄×C₃₁	C₂³	1	1	yes	characteristic
20	C₂×Dic₃₁	—	2	2	no	—
21	C₂×Dic₃₁	D₄	1	1	yes	characteristic
22	C₄×D₃₁	—	2	1	no	—
23	C₄×D₃₁	—	2	1	no	—
24	C₈×C₃₁	D₄	1	2	yes	—
25	C₃₁⋊C₈	—	2	1	no	—
26	C₂²×C₃₁	C₂×D₄	1	1	yes	characteristic
27	C₂×D₃₁	—	2	1	no	—
28	C₂×D₃₁	—	2	1	no	—
29	C₂×D₃₁	Q₁₆	1	2	yes	complemented
30	C₄×C₃₁	—	4	2	no	—
31	C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
32	C₄×C₃₁	#41	1	1	yes	characteristic
33	Dic₃₁	—	2	1	no	—
34	Dic₃₁	—	4	2	no	—
35	#467	—	31	1	no	maximal, Sylow
36	C₂×C₃₁	#121	1	1	yes	characteristic
37	C₂×C₃₁	C₂×Q₁₆	1	1	yes	characteristic
38	C₂×C₃₁	#135	1	1	yes	characteristic
39	D₃₁	—	2	2	no	—
40	C₂×Q₁₆	D₃₁	1	1	yes	characteristic, complemented
41	C₂²×C₈	—	31	1	no	—
42	C₂²⋊Q₈	—	31	2	no	—
43	#107	—	31	1	no	—
44	#103	—	31	2	no	—
45	C₃₁	#467	1	1	yes	characteristic, complemented, Sylow
46	C₂×Q₈	C₂×D₃₁	1	2	yes	—
47	C₂²×C₄	—	31	1	no	—
48	Q₁₆	—	2	2	no	—
49	C₂×C₈	—	31	1	no	—
50	C₂×C₈	—	62	2	no	—
51	C₂×C₈	C₂×D₃₁	1	1	yes	characteristic
52	C₄⋊C₄	—	31	2	no	—
53	C₄⋊C₄	—	62	2	no	—
54	C₂²⋊C₄	—	62	2	no	—
55	C₂³	—	31	1	no	—
56	Q₈	—	2	2	no	—
57	Q₈	—	2	2	no	—
58	C₂×C₄	—	2	2	no	—
59	C₂×C₄	—	31	1	no	—
60	C₂×C₄	—	62	1	no	—
61	C₂×C₄	—	62	1	no	—
62	C₂×C₄	—	62	2	no	—
63	C₂×C₄	C₂²×D₃₁	1	1	yes	characteristic
64	C₈	—	62	1	no	—
65	C₈	C₂²⋊D₃₁	1	2	yes	—
66	C₂²	—	31	2	no	—
67	C₂²	—	62	1	no	—
68	C₂²	—	62	1	no	—
69	C₂²	D₄×D₃₁	1	1	yes	characteristic
70	C₄	—	4	2	no	—
71	C₄	—	62	1	no	—
72	C₄	—	124	2	no	—
73	C₄	#92497	1	1	yes	characteristic
74	C₄	C₂×C₂²⋊D₃₁	1	1	yes	characteristic
75	C₂	—	62	2	no	—
76	C₂	Q₁₆×D₃₁	1	1	yes	characteristic
77	C₂	#11758496	1	1	yes	characteristic
78	C₂	#11758515	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	D₄×D₃₁
commutator, cosocle	C₂×C₄×C₃₁	C₂³
Frattini	C₂×C₄	C₂²×D₃₁
Fitting	C₂×Q₁₆×C₃₁	C₂
socle	C₂²×C₃₁	C₂×D₄
prime radical	C₂²×D₃₁	D₄
hypercenter	C₂×Q₁₆	D₃₁
hypocenter	C₃₁	#467
LCS	G ▷ C₂×C₄×C₃₁ ▷ C₂×C₃₁ ▷ C₃₁
UCS	C₁ ◁ C₂² ◁ C₂×C₄ ◁ C₂×Q₁₆

Complements

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

N	H ≅ G/N	type
1. C₂×Q₁₆×C₃₁	C₂	semidirect
4. #11758423	C₂	semidirect
5. #11758406	C₂	semidirect
29. C₂×D₃₁	Q₁₆	semidirect
40. C₂×Q₁₆	D₃₁	semidirect
45. C₃₁	#467	semidirect

Maximal subgroups

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

subgroup	index
C₂×Q₁₆×C₃₁	2
#11758523	2
C₂×C₈×D₃₁	2
#11758423	2
#11758406	2
#467	31