Subgroups — #14521866

Order 1984.

248 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#11758567	C₂	1	2	yes	maximal, complemented
2	C₃₁×#131	C₂	1	1	yes	maximal, characteristic, complemented
3	#11758486	C₂	1	6	yes	maximal, complemented
4	C₂×Dic₁₂₄	C₂	1	3	yes	maximal, complemented
5	#11758481	C₂	1	3	yes	maximal, complemented
6	#41×C₃₁	C₂²	1	1	yes	characteristic
7	Q₈×D₃₁	—	2	2	no	—
8	#92497	—	2	6	no	—
9	#92495	C₂²	1	6	yes	—
10	C₂×Dic₆₂	C₂²	1	6	yes	—
11	M₁₆×C₃₁	C₂²	1	3	yes	—
12	C₂×C₈×C₃₁	C₂²	1	3	yes	—
13	Dic₁₂₄	C₂²	1	3	yes	—
14	Dic₁₂₄	C₂²	1	6	yes	—
15	D₂₄₈	C₂²	1	1	yes	characteristic
16	#92470	C₂²	1	6	yes	—
17	Q₈×C₃₁	D₄	1	1	yes	characteristic
18	D₄×C₃₁	D₄	1	3	yes	—
19	C₂×C₄×C₃₁	C₂³	1	3	yes	—
20	C₂²⋊D₃₁	—	2	6	no	—
21	C₂×Dic₃₁	—	2	6	no	—
22	D₁₂₄	C₂³	1	2	yes	—
23	C₄×D₃₁	—	2	6	no	—
24	Dic₆₂	—	2	6	no	—
25	Dic₆₂	C₂³	1	6	yes	—
26	C₈×C₃₁	C₂³	1	3	yes	—
27	C₈×C₃₁	C₂³	1	1	yes	characteristic
28	C₂²×C₃₁	C₂×D₄	1	3	yes	—
29	C₂×D₃₁	—	2	2	no	—
30	C₄×C₃₁	C₂×D₄	1	3	yes	—
31	C₄×C₃₁	C₂⁴	1	1	yes	characteristic
32	Dic₃₁	—	2	6	no	—
33	#578	—	31	1	no	maximal, Sylow
34	C₂×C₃₁	—	2	3	no	—
35	C₂×C₃₁	C₂²×D₄	1	1	yes	characteristic
36	D₃₁	—	4	2	no	—
37	2₋¹⁺⁴	—	31	2	no	—
38	#137	—	31	6	no	—
39	#135	—	31	3	no	—
40	C₂×Q₁₆	—	31	3	no	—
41	#131	D₃₁	1	1	yes	characteristic, complemented
42	C₃₁	#578	1	1	yes	characteristic, complemented, Sylow
43	#41	—	31	6	no	—
44	#41	—	62	6	no	—
45	#41	C₂×D₃₁	1	1	yes	characteristic
46	C₂×Q₈	—	31	6	no	—
47	C₂×Q₈	—	62	2	no	—
48	Q₁₆	—	31	3	no	—
49	Q₁₆	—	31	6	no	—
50	SD₁₆	—	31	6	no	—
51	D₈	—	31	1	no	—
52	M₁₆	C₂×D₃₁	1	3	yes	—
53	C₂×C₈	C₂×D₃₁	1	3	yes	—
54	Q₈	—	31	6	no	—
55	Q₈	—	62	6	no	—
56	Q₈	D₁₂₄	1	1	yes	characteristic
57	D₄	—	31	2	no	—
58	D₄	—	62	6	no	—
59	D₄	D₁₂₄	1	3	yes	—
60	C₂×C₄	—	62	6	no	—
61	C₂×C₄	—	62	6	no	—
62	C₂×C₄	C₂²×D₃₁	1	3	yes	—
63	C₈	C₂²×D₃₁	1	1	yes	characteristic
64	C₈	C₂²×D₃₁	1	3	yes	—
65	C₂²	—	62	2	no	—
66	C₂²	C₂×D₁₂₄	1	3	yes	—
67	C₄	—	62	6	no	—
68	C₄	C₂×D₁₂₄	1	3	yes	—
69	C₄	C₂³×D₃₁	1	1	yes	characteristic
70	C₂	—	2	3	no	—
71	C₂	—	124	2	no	—
72	C₂	C₂²×D₁₂₄	1	1	yes	characteristic

	subgroup	G/H
center	C₂	C₂²×D₁₂₄
commutator, cosocle	C₄×C₃₁	C₂⁴
Frattini	C₄	C₂³×D₃₁
Fitting	C₃₁×#131	C₂
socle	C₂×C₃₁	C₂²×D₄
hypercenter	#131	D₃₁
hypocenter	C₃₁	#578
LCS	G ▷ C₄×C₃₁ ▷ C₂×C₃₁ ▷ C₃₁
UCS	C₁ ◁ C₂ ◁ #41 ◁ #131

Complements

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

N	H ≅ G/N	type
1. #11758567	C₂	semidirect
2. C₃₁×#131	C₂	semidirect
3. #11758486	C₂	semidirect
4. C₂×Dic₁₂₄	C₂	semidirect
5. #11758481	C₂	semidirect
41. #131	D₃₁	semidirect
42. C₃₁	#578	semidirect

Maximal subgroups

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

subgroup	index
#11758567	2
C₃₁×#131	2
#11758486	2
C₂×Dic₁₂₄	2
#11758481	2
#578	31