Group #19134703 — subgroups

Subgroups — #19134703

Order 5504.

296 conjugacy classes of subgroups; only the 89 normal subgroups are shown.

normal subgroups only

This group has 296 conjugacy classes of subgroups — too many to draw. Only its 89 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#13063240	C₂	1	2	yes	maximal
2	#14582665	C₂	1	4	yes	maximal, complemented
3	C₄₃×#518	C₂	1	1	yes	maximal, characteristic
4	C₂×C₂²⋊Dic₄₃	C₂²	1	4	yes	—
5	#13063240	—	2	4	no	—
6	C₂²×D₄×C₄₃	C₂²	1	1	yes	characteristic
7	C₄×D₄×C₄₃	—	2	4	no	—
8	#117×C₄₃	C₄	1	2	yes	complemented
9	C₂×C₂²⋊C₄×C₄₃	C₄	1	2	yes	complemented
10	C₂×C₂²⋊C₄×C₄₃	C₂²	1	2	yes	—
11	C₂⁴×C₄₃	C₂×C₄	1	1	yes	characteristic
12	C₂⁴×C₄₃	C₂³	1	1	yes	characteristic
13	C₂×D₄×C₄₃	—	2	4	no	—
14	C₂×D₄×C₄₃	D₄	1	4	yes	—
15	C₂²×C₄×C₄₃	—	2	2	no	—
16	C₂²×C₄×C₄₃	—	2	2	no	—
17	C₂²×C₄×C₄₃	C₂×C₄	1	1	yes	characteristic
18	C₂²×Dic₄₃	—	2	4	no	—
19	C₄⋊C₄×C₄₃	—	2	2	no	—
20	C₂²⋊C₄×C₄₃	—	2	2	no	—
21	C₂²⋊C₄×C₄₃	—	2	2	no	—
22	C₂²⋊C₄×C₄₃	C₂×C₄	1	4	yes	—
23	C₄²×C₄₃	—	2	2	no	—
24	C₂²⋊Dic₄₃	—	2	4	no	—
25	C₂²⋊Dic₄₃	—	2	4	no	—
26	C₂³×C₄₃	—	2	2	no	—
27	C₂³×C₄₃	—	8	1	no	—
28	C₂³×C₄₃	—	8	1	no	—
29	C₂³×C₄₃	C₂²⋊C₄	1	2	yes	—
30	C₂³×C₄₃	C₂²×C₄	1	1	yes	characteristic
31	C₂³×C₄₃	C₂×D₄	1	2	yes	—
32	C₂³×C₄₃	#41	1	4	yes	—
33	D₄×C₄₃	—	2	8	no	—
34	C₂×C₄×C₄₃	—	2	2	no	—
35	C₂×C₄×C₄₃	—	2	4	no	—
36	C₂×C₄×C₄₃	—	8	2	no	—
37	C₂×C₄×C₄₃	—	8	2	no	—
38	C₂×C₄×C₄₃	C₂²⋊C₄	1	2	yes	—
39	C₂×Dic₄₃	—	4	4	no	—
40	C₂×Dic₄₃	—	8	4	no	—
41	C₂²×C₄₃	—	2	2	no	—
42	C₂²×C₄₃	—	4	1	no	—
43	C₂²×C₄₃	—	4	2	no	—
44	C₂²×C₄₃	—	4	4	no	—
45	C₂²×C₄₃	—	4	2	no	—
46	C₂²×C₄₃	—	8	2	no	—
47	C₂²×C₄₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
48	C₂²×C₄₃	#117	1	2	yes	—
49	C₂²×C₄₃	#123	1	4	yes	—
50	C₄×C₄₃	—	2	2	no	—
51	C₄×C₄₃	—	4	4	no	—
52	Dic₄₃	—	8	4	no	—
53	#1828	—	43	1	no	maximal, Sylow
54	C₂×C₄₃	—	2	4	no	—
55	C₂×C₄₃	—	2	1	no	—
56	C₂×C₄₃	—	2	2	no	—
57	C₂×C₄₃	—	4	2	no	—
58	C₂×C₄₃	#381	1	1	yes	characteristic
59	#518	D₄₃	1	1	yes	characteristic
60	C₂×#99	—	43	2	no	—
61	#342	—	43	4	no	—
62	C₄₃	#1828	1	1	yes	characteristic, complemented, Sylow
63	C₂²×D₄	C₂×D₄₃	1	1	yes	characteristic
64	C₄×D₄	—	2	4	no	—
65	#117	Dic₄₃	1	2	yes	complemented
66	C₂×C₂²⋊C₄	—	43	4	no	—
67	C₂×C₂²⋊C₄	Dic₄₃	1	2	yes	complemented
68	C₂×C₂²⋊C₄	C₂×D₄₃	1	2	yes	—
69	#99	—	86	4	no	—
70	C₂⁴	C₂×Dic₄₃	1	1	yes	characteristic
71	C₂⁴	C₂²×D₄₃	1	1	yes	characteristic
72	C₂×D₄	—	2	4	no	—
73	C₂×D₄	C₂²⋊D₄₃	1	4	yes	—
74	C₂²×C₄	—	2	2	no	—
75	C₂²×C₄	—	2	2	no	—
76	C₂²×C₄	—	86	4	no	—
77	C₂²×C₄	C₂×Dic₄₃	1	1	yes	characteristic
78	C₄⋊C₄	—	2	2	no	—
79	C₂²⋊C₄	—	2	2	no	—
80	C₂²⋊C₄	—	2	2	no	—
81	C₂²⋊C₄	—	86	4	no	—
82	C₂²⋊C₄	—	86	4	no	—
83	C₂²⋊C₄	C₂×Dic₄₃	1	4	yes	—
84	C₄²	—	2	2	no	—
85	C₂³	—	2	2	no	—
86	C₂³	—	8	1	no	—
87	C₂³	—	8	1	no	—
88	C₂³	C₂²⋊Dic₄₃	1	2	yes	—
89	C₂³	#10621898	1	4	yes	—
90	C₂³	C₂²×Dic₄₃	1	1	yes	characteristic
91	C₂³	C₂×C₂²⋊D₄₃	1	2	yes	—
92	D₄	—	2	8	no	—
93	C₂×C₄	—	2	2	no	—
94	C₂×C₄	—	2	4	no	—
95	C₂×C₄	—	8	2	no	—
96	C₂×C₄	—	8	2	no	—
97	C₂×C₄	—	344	4	no	—
98	C₂×C₄	—	172	4	no	—
99	C₂×C₄	C₂²⋊Dic₄₃	1	2	yes	—
100	C₂²	—	2	2	no	—
101	C₂²	—	4	2	no	—
102	C₂²	—	4	4	no	—
103	C₂²	—	4	1	no	—
104	C₂²	—	4	2	no	—
105	C₂²	—	8	2	no	—
106	C₂²	C₂×C₂²⋊Dic₄₃	1	1	yes	characteristic
107	C₂²	#13063284	1	2	yes	—
108	C₂²	#13063308	1	4	yes	—
109	C₄	—	2	2	no	—
110	C₄	—	4	4	no	—
111	C₄	—	344	4	no	—
112	C₂	—	2	1	no	—
113	C₂	—	2	4	no	—
114	C₂	—	2	2	no	—
115	C₂	—	4	2	no	—
116	C₂	#14582762	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×#13063240

C₂

yes

maximal

#14582665

C₂

yes

maximal, complemented

C₄₃×#518

C₂

yes

maximal, characteristic

C₂×C₂²⋊Dic₄₃

C₂²

yes

—

#13063240

—

C₂²×D₄×C₄₃

C₂²

yes

characteristic

C₄×D₄×C₄₃

—

#117×C₄₃

C₄

yes

complemented

C₂×C₂²⋊C₄×C₄₃

C₄

yes

complemented

C₂×C₂²⋊C₄×C₄₃

C₂²

yes

—

C₂⁴×C₄₃

C₂×C₄

yes

characteristic

C₂⁴×C₄₃

C₂³

yes

characteristic

C₂×D₄×C₄₃

—

C₂×D₄×C₄₃

D₄

yes

—

C₂²×C₄×C₄₃

—

C₂²×C₄×C₄₃

—

C₂²×C₄×C₄₃

C₂×C₄

yes

characteristic

C₂²×Dic₄₃

—

C₄⋊C₄×C₄₃

—

C₂²⋊C₄×C₄₃

—

C₂²⋊C₄×C₄₃

—

C₂²⋊C₄×C₄₃

C₂×C₄

yes

—

C₄²×C₄₃

—

C₂²⋊Dic₄₃

—

C₂²⋊Dic₄₃

—

C₂³×C₄₃

—

C₂³×C₄₃

—

C₂³×C₄₃

—

C₂³×C₄₃

C₂²⋊C₄

yes

—

C₂³×C₄₃

C₂²×C₄

yes

characteristic

C₂³×C₄₃

C₂×D₄

yes

—

C₂³×C₄₃

#41

yes

—

D₄×C₄₃

—

C₂×C₄×C₄₃

—

C₂×C₄×C₄₃

—

C₂×C₄×C₄₃

—

C₂×C₄×C₄₃

—

C₂×C₄×C₄₃

C₂²⋊C₄

yes

—

C₂×Dic₄₃

—

C₂×Dic₄₃

—

C₂²×C₄₃

—

C₂²×C₄₃

—

C₂²×C₄₃

—

C₂²×C₄₃

—

C₂²×C₄₃

—

C₂²×C₄₃

—

C₂²×C₄₃

C₂×C₂²⋊C₄

yes

characteristic

C₂²×C₄₃

#117

yes

—

C₂²×C₄₃

#123

yes

—

C₄×C₄₃

—

C₄×C₄₃

—

Dic₄₃

—

#1828

—

maximal, Sylow

C₂×C₄₃

—

C₂×C₄₃

—

C₂×C₄₃

—

C₂×C₄₃

—

C₂×C₄₃

#381

yes

characteristic

#518

D₄₃

yes

characteristic

C₂×#99

—

#342

—

C₄₃

#1828

yes

characteristic, complemented, Sylow

C₂²×D₄

C₂×D₄₃

yes

characteristic

C₄×D₄

—

#117

Dic₄₃

yes

complemented

C₂×C₂²⋊C₄

—

C₂×C₂²⋊C₄

Dic₄₃

yes

complemented

C₂×C₂²⋊C₄

C₂×D₄₃

yes

—

#99

—

C₂⁴

C₂×Dic₄₃

yes

characteristic

C₂⁴

C₂²×D₄₃

yes

characteristic

C₂×D₄

—

C₂×D₄

C₂²⋊D₄₃

yes

—

C₂²×C₄

—

C₂²×C₄

—

C₂²×C₄

—

C₂²×C₄

C₂×Dic₄₃

yes

characteristic

C₄⋊C₄

—

C₂²⋊C₄

—

C₂²⋊C₄

—

C₂²⋊C₄

—

C₂²⋊C₄

—

C₂²⋊C₄

C₂×Dic₄₃

yes

—

C₄²

—

C₂³

—

C₂³

—

C₂³

—

C₂³

C₂²⋊Dic₄₃

yes

—

C₂³

#10621898

yes

—

C₂³

C₂²×Dic₄₃

yes

characteristic

C₂³

C₂×C₂²⋊D₄₃

yes

—

D₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

344

—

C₂×C₄

—

172

—

C₂×C₄

C₂²⋊Dic₄₃

yes

—

100

C₂²

—

101

C₂²

—

102

C₂²

—

103

C₂²

—

104

C₂²

—

105

C₂²

—

106

C₂²

C₂×C₂²⋊Dic₄₃

yes

characteristic

107

C₂²

#13063284

yes

—

108

C₂²

#13063308

yes

—

109

C₄

—

110

C₄

—

111

C₄

—

344

—

112

C₂

—

113

C₂

—

114

C₂

—

115

C₂

—

116

C₂

#14582762

yes

characteristic

	subgroup	G/H
center	C₂	#14582762
commutator	C₂³×C₄₃	C₂²×C₄
Frattini	C₂⁴	C₂²×D₄₃
Fitting	C₄₃×#518	C₂
socle	C₂×C₄₃	#381
hypercenter	#518	D₄₃
hypocenter	C₄₃	#1828
LCS	G ▷ C₂³×C₄₃ ▷ C₂×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₂ ◁ C₂⁴ ◁ #518

subgroup

G/H

center

C₂

#14582762

commutator

C₂³×C₄₃

C₂²×C₄

Frattini

C₂⁴

C₂²×D₄₃

Fitting

C₄₃×#518

C₂

C₂×C₄₃

D₄₃

C₄₃

G ▷ C₂³×C₄₃ ▷ C₂×C₄₃ ▷ C₄₃

UCS

C₁ ◁ C₂ ◁ C₂⁴ ◁ #518

N	H ≅ G/N	type
2. #14582665	C₂	semidirect
8. #117×C₄₃	C₄	semidirect
9. C₂×C₂²⋊C₄×C₄₃	C₄	semidirect
62. C₄₃	#1828	semidirect
65. #117	Dic₄₃	semidirect
67. C₂×C₂²⋊C₄	Dic₄₃	semidirect

H ≅ G/N

type

2. #14582665

C₂

semidirect

8. #117×C₄₃

C₄

semidirect

9. C₂×C₂²⋊C₄×C₄₃

C₄

semidirect

62. C₄₃

#1828

semidirect

65. #117

Dic₄₃

semidirect

67. C₂×C₂²⋊C₄

Dic₄₃

semidirect

Subgroups — #19134703

Conjugacy classes of subgroups

Complements