Subgroups — #14521410

Order 1984.

100 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#11758524	C₂	1	1	yes	maximal, characteristic
2	#11758465	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃₁×#103	C₂	1	1	yes	maximal, characteristic, complemented
4	#11758423	C₂	1	1	yes	maximal, characteristic, complemented
5	#11758409	C₂	1	1	yes	maximal, characteristic
6	#11758403	C₂	1	1	yes	maximal, characteristic, complemented
7	#11758397	C₂	1	1	yes	maximal, characteristic
8	C₂×Q₈×C₃₁	C₂²	1	1	yes	characteristic
9	C₂×D₁₂₄	C₂²	1	1	yes	characteristic
10	C₂×Dic₆₂	—	2	1	no	—
11	C₂×C₈×C₃₁	C₂²	1	1	yes	characteristic
12	C₄⋊C₄×C₃₁	C₂²	1	1	yes	characteristic
13	(C₂×D₃₁)⋊C₄	—	2	1	no	—
14	(C₂×D₃₁)⋊C₄	—	2	1	no	—
15	C₄⋊Dic₃₁	C₂²	1	1	yes	characteristic
16	Dic₃₁⋊C₄	—	2	1	no	—
17	C₄×Dic₃₁	C₂²	1	1	yes	characteristic
18	C₂×C₃₁⋊C₈	C₂²	1	1	yes	characteristic
19	C₂²×D₃₁	—	2	1	no	—
20	Q₈×C₃₁	—	2	1	no	—
21	Q₈×C₃₁	—	2	1	no	—
22	C₂×C₄×C₃₁	—	2	1	no	—
23	C₂×C₄×C₃₁	—	2	1	no	—
24	C₂×C₄×C₃₁	C₂³	1	1	yes	characteristic
25	C₂×Dic₃₁	—	2	1	no	—
26	C₂×Dic₃₁	D₄	1	1	yes	characteristic
27	C₂×Dic₃₁	D₄	1	1	yes	characteristic
28	D₁₂₄	—	2	1	no	—
29	D₁₂₄	—	2	1	no	—
30	Dic₆₂	—	4	2	no	—
31	C₈×C₃₁	—	2	1	no	—
32	C₃₁⋊C₈	—	2	1	no	—
33	C₂²×C₃₁	C₂×D₄	1	1	yes	characteristic
34	C₂×D₃₁	—	4	1	no	—
35	C₂×D₃₁	—	4	1	no	—
36	C₂×D₃₁	—	4	1	no	—
37	C₄×C₃₁	—	4	1	no	—
38	C₄×C₃₁	—	4	1	no	—
39	C₄×C₃₁	#41	1	1	yes	characteristic
40	C₄×C₃₁	#41	1	1	yes	characteristic
41	Dic₃₁	—	2	1	no	—
42	Dic₃₁	—	2	1	no	—
43	Dic₃₁	—	4	1	no	—
44	#489	—	31	1	no	maximal, Sylow
45	C₂×C₃₁	#124	1	1	yes	characteristic
46	C₂×C₃₁	AGL(1,ℤ/8)	1	1	yes	characteristic
47	C₂×C₃₁	#137	1	1	yes	characteristic
48	D₃₁	—	8	1	no	—
49	C₄⋊Q₈	—	31	1	no	—
50	#124	—	31	1	no	—
51	#103	—	31	1	no	—
52	#103	D₃₁	1	1	yes	characteristic, complemented
53	#102	—	31	1	no	—
54	#102	—	31	1	no	—
55	#97	—	31	1	no	—
56	C₃₁	#489	1	1	yes	characteristic, complemented, Sylow
57	C₂×Q₈	—	62	1	no	—
58	C₂×Q₈	C₂×D₃₁	1	1	yes	characteristic
59	C₂×D₄	—	31	1	no	—
60	C₂×C₈	—	31	1	no	—
61	C₂×C₈	C₂×D₃₁	1	1	yes	characteristic
62	C₄⋊C₄	—	31	1	no	—
63	C₄⋊C₄	—	62	1	no	—
64	C₄⋊C₄	C₂×D₃₁	1	1	yes	characteristic
65	C₂²⋊C₄	—	62	1	no	—
66	C₂²⋊C₄	—	62	1	no	—
67	C₄²	—	31	1	no	—
68	C₂³	—	62	1	no	—
69	Q₈	—	2	1	no	—
70	Q₈	—	2	1	no	—
71	Q₈	—	124	2	no	—
72	D₄	—	62	1	no	—
73	D₄	—	62	1	no	—
74	C₂×C₄	—	2	1	no	—
75	C₂×C₄	—	2	1	no	—
76	C₂×C₄	—	31	1	no	—
77	C₂×C₄	—	31	1	no	—
78	C₂×C₄	—	62	1	no	—
79	C₂×C₄	C₂²×D₃₁	1	1	yes	characteristic
80	C₈	—	2	1	no	—
81	C₈	—	62	1	no	—
82	C₂²	—	124	1	no	—
83	C₂²	—	124	1	no	—
84	C₂²	—	124	1	no	—
85	C₂²	D₄×D₃₁	1	1	yes	characteristic
86	C₄	—	4	1	no	—
87	C₄	—	4	1	no	—
88	C₄	—	62	1	no	—
89	C₄	—	62	1	no	—
90	C₄	—	124	1	no	—
91	C₄	#92495	1	1	yes	characteristic
92	C₄	#92497	1	1	yes	characteristic
93	C₂	—	248	1	no	—
94	C₂	#11758462	1	1	yes	characteristic
95	C₂	#11758491	1	1	yes	characteristic
96	C₂	#11758495	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	D₄×D₃₁
commutator, cosocle	C₂×C₄×C₃₁	C₂³
Frattini	C₂×C₄	C₂²×D₃₁
Fitting	C₃₁×#103	C₂
socle	C₂²×C₃₁	C₂×D₄
prime radical	C₂×D₁₂₄	C₂²
hypercenter	#103	D₃₁
hypocenter	C₃₁	#489
LCS	G ▷ C₂×C₄×C₃₁ ▷ C₂×C₃₁ ▷ C₃₁
UCS	C₁ ◁ C₂² ◁ C₂×C₄ ◁ #103

Complements

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

N	H ≅ G/N	type
2. #11758465	C₂	semidirect
3. C₃₁×#103	C₂	semidirect
4. #11758423	C₂	semidirect
6. #11758403	C₂	semidirect
52. #103	D₃₁	semidirect
56. C₃₁	#489	semidirect

Maximal subgroups

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

subgroup	index
#11758524	2
#11758465	2
C₃₁×#103	2
#11758423	2
#11758409	2
#11758403	2
#11758397	2
#489	31