Group #19134670 — subgroups

Subgroups — #19134670

Order 5504.

300 conjugacy classes of subgroups; only the 85 normal subgroups are shown.

normal subgroups only

This group has 300 conjugacy classes of subgroups — too many to draw. Only its 85 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×#13063284	C₂	1	1	yes	maximal, characteristic
2	#14582762	C₂	1	1	yes	maximal, characteristic
3	#14582665	C₂	1	4	yes	maximal
4	C₄₃×#381	C₂	1	1	yes	maximal, characteristic
5	#13063284	—	2	2	no	—
6	#13063284	—	2	2	no	—
7	C₂×C₄⋊Dic₄₃	C₄	1	2	yes	complemented
8	C₂×C₂²⋊Dic₄₃	C₂²	1	2	yes	—
9	C₂×C₂²⋊Dic₄₃	C₂²	1	2	yes	—
10	C₂×C₄×Dic₄₃	C₄	1	2	yes	complemented
11	C₄₃⋊#95	—	2	2	no	—
12	C₂³×C₄×C₄₃	C₂²	1	1	yes	characteristic
13	C₂×C₂²⋊C₄×C₄₃	C₂²	1	2	yes	—
14	#95×C₄₃	—	2	2	no	—
15	C₂⁴×C₄₃	C₂³	1	1	yes	characteristic
16	C₂²×C₄×C₄₃	—	2	2	no	—
17	C₂²×C₄×C₄₃	—	2	4	no	—
18	C₂²×C₄×C₄₃	C₂×C₄	1	1	yes	characteristic
19	C₂²×C₄×C₄₃	C₂×C₄	1	1	yes	characteristic
20	C₂²×C₄×C₄₃	D₄	1	2	yes	—
21	C₂²×C₄×C₄₃	D₄	1	2	yes	—
22	C₂²×Dic₄₃	—	2	2	no	—
23	C₂²×Dic₄₃	C₂×C₄	1	4	yes	—
24	C₂²⋊C₄×C₄₃	—	2	4	no	—
25	C₂²⋊Dic₄₃	—	2	2	no	—
26	C₂²⋊Dic₄₃	—	2	2	no	—
27	C₂²⋊Dic₄₃	—	2	4	no	—
28	C₄⋊Dic₄₃	—	2	4	no	—
29	C₄×Dic₄₃	—	2	4	no	—
30	C₂³×C₄₃	—	4	2	no	—
31	C₂³×C₄₃	C₂²×C₄	1	1	yes	characteristic
32	C₂³×C₄₃	C₂×D₄	1	1	yes	characteristic
33	C₂³×C₄₃	C₂×D₄	1	1	yes	characteristic
34	C₂³×C₄₃	#41	1	4	yes	—
35	C₂×C₄×C₄₃	—	2	2	no	—
36	C₂×C₄×C₄₃	—	2	2	no	—
37	C₂×C₄×C₄₃	—	2	4	no	—
38	C₂×C₄×C₄₃	—	2	4	no	—
39	C₂×C₄×C₄₃	—	4	4	no	—
40	C₂×C₄×C₄₃	—	4	2	no	—
41	C₂×C₄×C₄₃	C₂²⋊C₄	1	2	yes	—
42	C₂×C₄×C₄₃	C₂²⋊C₄	1	2	yes	—
43	C₂×Dic₄₃	—	2	4	no	—
44	C₂×Dic₄₃	—	4	4	no	—
45	C₂×Dic₄₃	—	4	4	no	—
46	C₂×Dic₄₃	—	4	2	no	—
47	C₂²×C₄₃	—	2	2	no	—
48	C₂²×C₄₃	—	2	2	no	—
49	C₂²×C₄₃	—	2	2	no	—
50	C₂²×C₄₃	—	4	4	no	—
51	C₂²×C₄₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
52	C₂²×C₄₃	#117	1	2	yes	—
53	C₂²×C₄₃	#123	1	2	yes	—
54	C₂²×C₄₃	#123	1	2	yes	—
55	C₄×C₄₃	—	2	2	no	—
56	C₄×C₄₃	—	2	2	no	—
57	C₄×C₄₃	—	8	2	no	—
58	Dic₄₃	—	4	4	no	—
59	Dic₄₃	—	8	2	no	—
60	#1820	—	43	1	no	maximal, Sylow
61	C₂×C₄₃	—	2	2	no	—
62	C₂×C₄₃	—	2	2	no	—
63	C₂×C₄₃	—	2	2	no	—
64	C₂×C₄₃	#381	1	1	yes	characteristic
65	C₂×C₄₃	#410	1	2	yes	—
66	C₂×#117	—	43	1	no	—
67	#381	—	43	1	no	—
68	#381	D₄₃	1	1	yes	characteristic
69	#342	—	43	4	no	—
70	C₄₃	#1820	1	1	yes	characteristic, complemented, Sylow
71	C₂³×C₄	C₂×D₄₃	1	1	yes	characteristic
72	#117	—	86	2	no	—
73	#117	—	86	2	no	—
74	C₂×C₄⋊C₄	—	43	2	no	—
75	C₂×C₂²⋊C₄	—	43	2	no	—
76	C₂×C₂²⋊C₄	—	43	2	no	—
77	C₂×C₂²⋊C₄	C₂×D₄₃	1	2	yes	—
78	C₂×C₄²	—	43	2	no	—
79	#95	—	2	2	no	—
80	#95	—	86	2	no	—
81	C₂⁴	C₂²×D₄₃	1	1	yes	characteristic
82	C₂²×C₄	—	2	4	no	—
83	C₂²×C₄	—	2	2	no	—
84	C₂²×C₄	—	43	4	no	—
85	C₂²×C₄	—	86	2	no	—
86	C₂²×C₄	C₄×D₄₃	1	1	yes	characteristic
87	C₂²×C₄	C₄×D₄₃	1	1	yes	characteristic
88	C₂²×C₄	D₁₇₂	1	2	yes	—
89	C₂²×C₄	C₂²⋊D₄₃	1	2	yes	—
90	C₄⋊C₄	—	86	4	no	—
91	C₂²⋊C₄	—	2	4	no	—
92	C₂²⋊C₄	—	86	2	no	—
93	C₂²⋊C₄	—	86	2	no	—
94	C₂²⋊C₄	—	86	4	no	—
95	C₄²	—	86	4	no	—
96	C₂³	—	4	2	no	—
97	C₂³	C₂×C₄×D₄₃	1	1	yes	characteristic
98	C₂³	C₂×D₁₇₂	1	1	yes	characteristic
99	C₂³	#10621900	1	4	yes	—
100	C₂³	C₂×C₂²⋊D₄₃	1	1	yes	characteristic
101	C₂×C₄	—	2	2	no	—
102	C₂×C₄	—	2	2	no	—
103	C₂×C₄	—	2	4	no	—
104	C₂×C₄	—	2	4	no	—
105	C₂×C₄	—	4	4	no	—
106	C₂×C₄	—	4	2	no	—
107	C₂×C₄	—	86	4	no	—
108	C₂×C₄	—	172	4	no	—
109	C₂×C₄	—	172	2	no	—
110	C₂×C₄	—	172	4	no	—
111	C₂×C₄	(C₂×D₄₃)⋊C₄	1	2	yes	—
112	C₂×C₄	(C₂×D₄₃)⋊C₄	1	2	yes	—
113	C₂²	—	2	2	no	—
114	C₂²	—	2	2	no	—
115	C₂²	—	2	2	no	—
116	C₂²	—	4	4	no	—
117	C₂²	C₂×(C₂×D₄₃)⋊C₄	1	1	yes	characteristic
118	C₂²	#13063281	1	2	yes	—
119	C₂²	#13063306	1	2	yes	—
120	C₂²	#13063309	1	2	yes	—
121	C₄	—	2	2	no	—
122	C₄	—	2	2	no	—
123	C₄	—	8	2	no	—
124	C₄	—	344	2	no	—
125	C₄	—	172	4	no	—
126	C₂	—	2	2	no	—
127	C₂	—	2	2	no	—
128	C₂	—	2	2	no	—
129	C₂	#14582760	1	1	yes	characteristic
130	C₂	#14582872	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×#13063284

C₂

yes

maximal, characteristic

#14582762

C₂

yes

maximal, characteristic

#14582665

C₂

yes

maximal

C₄₃×#381

C₂

yes

maximal, characteristic

#13063284

—

#13063284

—

C₂×C₄⋊Dic₄₃

C₄

yes

complemented

C₂×C₂²⋊Dic₄₃

C₂²

yes

—

C₂×C₂²⋊Dic₄₃

C₂²

yes

—

C₂×C₄×Dic₄₃

C₄

yes

complemented

C₄₃⋊#95

—

C₂³×C₄×C₄₃

C₂²

yes

characteristic

C₂×C₂²⋊C₄×C₄₃

C₂²

yes

—

#95×C₄₃

—

C₂⁴×C₄₃

C₂³

yes

characteristic

C₂²×C₄×C₄₃

—

C₂²×C₄×C₄₃

—

C₂²×C₄×C₄₃

C₂×C₄

yes

characteristic

C₂²×C₄×C₄₃

C₂×C₄

yes

characteristic

C₂²×C₄×C₄₃

D₄

yes

—

C₂²×C₄×C₄₃

D₄

yes

—

C₂²×Dic₄₃

—

C₂²×Dic₄₃

C₂×C₄

yes

—

C₂²⋊C₄×C₄₃

—

C₂²⋊Dic₄₃

—

C₂²⋊Dic₄₃

—

C₂²⋊Dic₄₃

—

C₄⋊Dic₄₃

—

C₄×Dic₄₃

—

C₂³×C₄₃

—

C₂³×C₄₃

C₂²×C₄

yes

characteristic

C₂³×C₄₃

C₂×D₄

yes

characteristic

C₂³×C₄₃

C₂×D₄

yes

characteristic

C₂³×C₄₃

#41

yes

—

C₂×C₄×C₄₃

—

C₂×C₄×C₄₃

—

C₂×C₄×C₄₃

—

C₂×C₄×C₄₃

—

C₂×C₄×C₄₃

—

C₂×C₄×C₄₃

—

C₂×C₄×C₄₃

C₂²⋊C₄

yes

—

C₂×C₄×C₄₃

C₂²⋊C₄

yes

—

C₂×Dic₄₃

—

C₂×Dic₄₃

—

C₂×Dic₄₃

—

C₂×Dic₄₃

—

C₂²×C₄₃

—

C₂²×C₄₃

—

C₂²×C₄₃

—

C₂²×C₄₃

—

C₂²×C₄₃

C₂×C₂²⋊C₄

yes

characteristic

C₂²×C₄₃

#117

yes

—

C₂²×C₄₃

#123

yes

—

C₂²×C₄₃

#123

yes

—

C₄×C₄₃

—

C₄×C₄₃

—

C₄×C₄₃

—

Dic₄₃

—

Dic₄₃

—

#1820

—

maximal, Sylow

C₂×C₄₃

—

C₂×C₄₃

—

C₂×C₄₃

—

C₂×C₄₃

#381

yes

characteristic

C₂×C₄₃

#410

yes

—

C₂×#117

—

#381

—

#381

D₄₃

yes

characteristic

#342

—

C₄₃

#1820

yes

characteristic, complemented, Sylow

C₂³×C₄

C₂×D₄₃

yes

characteristic

#117

—

#117

—

C₂×C₄⋊C₄

—

C₂×C₂²⋊C₄

—

C₂×C₂²⋊C₄

—

C₂×C₂²⋊C₄

C₂×D₄₃

yes

—

C₂×C₄²

—

#95

—

#95

—

C₂⁴

C₂²×D₄₃

yes

characteristic

C₂²×C₄

—

C₂²×C₄

—

C₂²×C₄

—

C₂²×C₄

—

C₂²×C₄

C₄×D₄₃

yes

characteristic

C₂²×C₄

C₄×D₄₃

yes

characteristic

C₂²×C₄

D₁₇₂

yes

—

C₂²×C₄

C₂²⋊D₄₃

yes

—

C₄⋊C₄

—

C₂²⋊C₄

—

C₂²⋊C₄

—

C₂²⋊C₄

—

C₂²⋊C₄

—

C₄²

—

C₂³

—

C₂³

C₂×C₄×D₄₃

yes

characteristic

C₂³

C₂×D₁₇₂

yes

characteristic

C₂³

#10621900

yes

—

100

C₂³

C₂×C₂²⋊D₄₃

yes

characteristic

101

C₂×C₄

—

102

C₂×C₄

—

103

C₂×C₄

—

104

C₂×C₄

—

105

C₂×C₄

—

106

C₂×C₄

—

107

C₂×C₄

—

108

C₂×C₄

—

172

—

109

C₂×C₄

—

172

—

110

C₂×C₄

—

172

—

111

C₂×C₄

(C₂×D₄₃)⋊C₄

yes

—

112

C₂×C₄

(C₂×D₄₃)⋊C₄

yes

—

113

C₂²

—

114

C₂²

—

115

C₂²

—

116

C₂²

—

117

C₂²

C₂×(C₂×D₄₃)⋊C₄

yes

characteristic

118

C₂²

#13063281

yes

—

119

C₂²

#13063306

yes

—

120

C₂²

#13063309

yes

—

121

C₄

—

122

C₄

—

123

C₄

—

124

C₄

—

344

—

125

C₄

—

172

—

126

C₂

—

127

C₂

—

128

C₂

—

129

C₂

#14582760

yes

characteristic

130

C₂

#14582872

yes

—

	subgroup	G/H
center	C₂²	C₂×(C₂×D₄₃)⋊C₄
commutator	C₂³×C₄₃	C₂²×C₄
Frattini	C₂⁴	C₂²×D₄₃
Fitting	C₄₃×#381	C₂
socle	C₂²×C₄₃	C₂×C₂²⋊C₄
hypercenter	#381	D₄₃
hypocenter	C₄₃	#1820
LCS	G ▷ C₂³×C₄₃ ▷ C₂×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₂² ◁ C₂³×C₄ ◁ #381

subgroup

G/H

center

C₂²

C₂×(C₂×D₄₃)⋊C₄

commutator

C₂³×C₄₃

C₂²×C₄

Frattini

C₂⁴

C₂²×D₄₃

Fitting

C₄₃×#381

C₂

socle

C₂²×C₄₃

C₂×C₂²⋊C₄

D₄₃

C₄₃

G ▷ C₂³×C₄₃ ▷ C₂×C₄₃ ▷ C₄₃

UCS

C₁ ◁ C₂² ◁ C₂³×C₄ ◁ #381

N	H ≅ G/N	type
7. C₂×C₄⋊Dic₄₃	C₄	semidirect
10. C₂×C₄×Dic₄₃	C₄	semidirect
70. C₄₃	#1820	semidirect

H ≅ G/N

type

7. C₂×C₄⋊Dic₄₃

C₄

semidirect

10. C₂×C₄×Dic₄₃

C₄

semidirect

70. C₄₃

#1820

semidirect

Subgroups — #19134670

Conjugacy classes of subgroups

Complements