Group #19134704 — subgroups

Subgroups — #19134704

Order 5504.

272 conjugacy classes of subgroups; only the 81 normal subgroups are shown.

normal subgroups only

This group has 272 conjugacy classes of subgroups — too many to draw. Only its 81 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	#14583374	C₂	1	1	yes	maximal, characteristic
2	C₂×#13063242	C₂	1	1	yes	maximal, characteristic
3	#14582671	C₂	1	2	yes	maximal, complemented
4	#14582670	C₂	1	2	yes	maximal, complemented
5	C₂×#100×C₄₃	C₂	1	1	yes	maximal, characteristic
6	C₂×#10621877	C₂²	1	2	yes	—
7	D₄×Dic₄₃	—	2	2	no	—
8	D₄×Dic₄₃	—	2	2	no	—
9	#13063284	C₂²	1	1	yes	characteristic
10	#13063284	C₂²	1	1	yes	characteristic
11	C₂×C₂²⋊Dic₄₃	C₄	1	4	yes	—
12	#13063242	—	2	2	no	—
13	C₂²×D₄×C₄₃	C₂²	1	1	yes	characteristic
14	C₂×M₁₆×C₄₃	C₂²	1	2	yes	—
15	#100×C₄₃	—	2	2	no	—
16	C₂⁴×C₄₃	C₂×C₄	1	2	yes	—
17	C₂×D₄×C₄₃	—	2	2	no	—
18	C₂×D₄×C₄₃	—	2	2	no	—
19	C₂×D₄×C₄₃	D₄	1	2	yes	—
20	C₂×D₄×C₄₃	D₄	1	2	yes	—
21	C₂²×C₄×C₄₃	C₂³	1	1	yes	characteristic
22	C₂²×Dic₄₃	—	2	4	no	—
23	M₁₆×C₄₃	—	2	2	no	—
24	M₁₆×C₄₃	—	2	2	no	—
25	C₂×C₈×C₄₃	—	2	2	no	—
26	C₂²⋊Dic₄₃	—	2	4	no	—
27	C₂²⋊Dic₄₃	C₂×C₄	1	2	yes	—
28	C₂²⋊Dic₄₃	C₂×C₄	1	2	yes	—
29	C₄⋊Dic₄₃	—	2	1	no	—
30	C₄⋊Dic₄₃	—	2	1	no	—
31	C₄×Dic₄₃	—	2	1	no	—
32	C₄×Dic₄₃	—	2	1	no	—
33	#10621877	—	2	2	no	—
34	#10621877	—	2	2	no	—
35	C₂×C₄₃⋊C₈	—	2	2	no	—
36	C₂³×C₄₃	—	2	2	no	—
37	C₂³×C₄₃	—	2	2	no	—
38	C₂³×C₄₃	—	8	2	no	—
39	C₂³×C₄₃	C₂²⋊C₄	1	4	yes	—
40	C₂³×C₄₃	C₂²×C₄	1	1	yes	characteristic
41	D₄×C₄₃	—	2	4	no	—
42	D₄×C₄₃	—	2	4	no	—
43	C₂×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
44	C₂×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
45	C₂×C₄×C₄₃	#41	1	2	yes	—
46	C₂×C₄×C₄₃	#41	1	2	yes	—
47	C₂×Dic₄₃	—	2	2	no	—
48	C₂×Dic₄₃	—	2	2	no	—
49	C₂×Dic₄₃	—	8	4	no	—
50	C₈×C₄₃	—	4	2	no	—
51	C₄₃⋊C₈	—	4	2	no	—
52	C₂²×C₄₃	—	2	4	no	—
53	C₂²×C₄₃	—	4	1	no	—
54	C₂²×C₄₃	—	4	4	no	—
55	C₂²×C₄₃	—	8	2	no	—
56	C₂²×C₄₃	—	8	2	no	—
57	C₂²×C₄₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
58	C₂²×C₄₃	#117	1	1	yes	characteristic
59	C₂²×C₄₃	#117	1	1	yes	characteristic
60	C₄×C₄₃	#123	1	2	yes	—
61	C₄×C₄₃	#123	1	2	yes	—
62	Dic₄₃	—	4	2	no	—
63	Dic₄₃	—	4	2	no	—
64	#1829	—	43	1	no	maximal, Sylow
65	C₂×C₄₃	—	2	1	no	—
66	C₂×C₄₃	—	2	1	no	—
67	C₂×C₄₃	—	2	1	no	—
68	C₂×C₄₃	—	4	4	no	—
69	C₂×C₄₃	#381	1	1	yes	characteristic
70	#518	—	43	1	no	—
71	C₂×#100	—	43	1	no	—
72	C₂×#100	D₄₃	1	1	yes	characteristic
73	#344	—	43	2	no	—
74	#344	—	43	2	no	—
75	C₄₃	#1829	1	1	yes	characteristic, complemented, Sylow
76	C₂²×D₄	C₂×D₄₃	1	1	yes	characteristic
77	C₂×M₁₆	—	43	2	no	—
78	C₂×M₁₆	C₂×D₄₃	1	2	yes	—
79	C₄×D₄	—	86	2	no	—
80	C₄×D₄	—	86	2	no	—
81	#117	—	43	1	no	—
82	#117	—	43	1	no	—
83	C₂×C₂²⋊C₄	—	43	4	no	—
84	#100	—	2	2	no	—
85	#100	—	86	2	no	—
86	C₂⁴	C₄×D₄₃	1	2	yes	—
87	C₂×D₄	—	2	2	no	—
88	C₂×D₄	—	2	2	no	—
89	C₂×D₄	D₁₇₂	1	2	yes	—
90	C₂×D₄	C₂²⋊D₄₃	1	2	yes	—
91	C₂²×C₄	—	86	4	no	—
92	C₂²×C₄	C₂²×D₄₃	1	1	yes	characteristic
93	M₁₆	—	2	2	no	—
94	M₁₆	—	2	2	no	—
95	M₁₆	—	86	2	no	—
96	M₁₆	—	86	2	no	—
97	C₂×C₈	—	2	2	no	—
98	C₂×C₈	—	86	2	no	—
99	C₄⋊C₄	—	86	1	no	—
100	C₄⋊C₄	—	86	1	no	—
101	C₂²⋊C₄	—	43	2	no	—
102	C₂²⋊C₄	—	43	2	no	—
103	C₂²⋊C₄	—	86	4	no	—
104	C₄²	—	86	1	no	—
105	C₄²	—	86	1	no	—
106	C₂³	—	2	2	no	—
107	C₂³	—	2	2	no	—
108	C₂³	—	8	2	no	—
109	C₂³	(C₂×D₄₃)⋊C₄	1	4	yes	—
110	C₂³	C₂×C₄×D₄₃	1	1	yes	characteristic
111	D₄	—	2	4	no	—
112	D₄	—	2	4	no	—
113	C₂×C₄	—	86	2	no	—
114	C₂×C₄	—	86	2	no	—
115	C₂×C₄	—	344	4	no	—
116	C₂×C₄	C₂×D₁₇₂	1	1	yes	characteristic
117	C₂×C₄	#10621900	1	2	yes	—
118	C₂×C₄	#10621900	1	2	yes	—
119	C₂×C₄	C₂×C₂²⋊D₄₃	1	1	yes	characteristic
120	C₈	—	4	2	no	—
121	C₈	—	172	2	no	—
122	C₂²	—	2	4	no	—
123	C₂²	—	4	1	no	—
124	C₂²	—	4	4	no	—
125	C₂²	—	8	2	no	—
126	C₂²	—	8	2	no	—
127	C₂²	C₂×(C₂×D₄₃)⋊C₄	1	1	yes	characteristic
128	C₂²	#13063281	1	1	yes	characteristic
129	C₂²	#13063281	1	1	yes	characteristic
130	C₄	—	172	2	no	—
131	C₄	—	172	2	no	—
132	C₄	#13063306	1	2	yes	—
133	C₄	#13063309	1	2	yes	—
134	C₂	—	2	1	no	—
135	C₂	—	2	1	no	—
136	C₂	—	2	1	no	—
137	C₂	—	4	4	no	—
138	C₂	#14582760	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#14583374

C₂

yes

maximal, characteristic

C₂×#13063242

C₂

yes

maximal, characteristic

#14582671

C₂

yes

maximal, complemented

#14582670

C₂

yes

maximal, complemented

C₂×#100×C₄₃

C₂

yes

maximal, characteristic

C₂×#10621877

C₂²

yes

—

D₄×Dic₄₃

—

D₄×Dic₄₃

—

#13063284

C₂²

yes

characteristic

#13063284

C₂²

yes

characteristic

C₂×C₂²⋊Dic₄₃

C₄

yes

—

#13063242

—

C₂²×D₄×C₄₃

C₂²

yes

characteristic

C₂×M₁₆×C₄₃

C₂²

yes

—

#100×C₄₃

—

C₂⁴×C₄₃

C₂×C₄

yes

—

C₂×D₄×C₄₃

—

C₂×D₄×C₄₃

—

C₂×D₄×C₄₃

D₄

yes

—

C₂×D₄×C₄₃

D₄

yes

—

C₂²×C₄×C₄₃

C₂³

yes

characteristic

C₂²×Dic₄₃

—

M₁₆×C₄₃

—

M₁₆×C₄₃

—

C₂×C₈×C₄₃

—

C₂²⋊Dic₄₃

—

C₂²⋊Dic₄₃

C₂×C₄

yes

—

C₂²⋊Dic₄₃

C₂×C₄

yes

—

C₄⋊Dic₄₃

—

C₄⋊Dic₄₃

—

C₄×Dic₄₃

—

C₄×Dic₄₃

—

#10621877

—

#10621877

—

C₂×C₄₃⋊C₈

—

C₂³×C₄₃

—

C₂³×C₄₃

—

C₂³×C₄₃

—

C₂³×C₄₃

C₂²⋊C₄

yes

—

C₂³×C₄₃

C₂²×C₄

yes

characteristic

D₄×C₄₃

—

D₄×C₄₃

—

C₂×C₄×C₄₃

C₂×D₄

yes

characteristic

C₂×C₄×C₄₃

C₂×D₄

yes

characteristic

C₂×C₄×C₄₃

#41

yes

—

C₂×C₄×C₄₃

#41

yes

—

C₂×Dic₄₃

—

C₂×Dic₄₃

—

C₂×Dic₄₃

—

C₈×C₄₃

—

C₄₃⋊C₈

—

C₂²×C₄₃

—

C₂²×C₄₃

—

C₂²×C₄₃

—

C₂²×C₄₃

—

C₂²×C₄₃

—

C₂²×C₄₃

C₂×C₂²⋊C₄

yes

C₂²×C₄₃

yes

C₂²×C₄₃

yes

C₄×C₄₃

yes

—

C₄×C₄₃

#123

yes

—

Dic₄₃

—

Dic₄₃

—

#1829

—

maximal, Sylow

C₂×C₄₃

—

C₂×C₄₃

—

C₂×C₄₃

—

C₂×C₄₃

—

C₂×C₄₃

yes

—

—

D₄₃

yes

characteristic

#344

—

#344

—

C₄₃

#1829

yes

characteristic, complemented, Sylow

C₂²×D₄

C₂×D₄₃

yes

characteristic

C₂×M₁₆

—

C₂×M₁₆

C₂×D₄₃

yes

—

C₄×D₄

—

C₄×D₄

—

#117

—

#117

—

C₂×C₂²⋊C₄

—

#100

—

#100

—

C₂⁴

C₄×D₄₃

yes

—

C₂×D₄

—

C₂×D₄

—

C₂×D₄

D₁₇₂

yes

—

C₂×D₄

C₂²⋊D₄₃

yes

—

C₂²×C₄

—

C₂²×C₄

C₂²×D₄₃

yes

characteristic

M₁₆

—

M₁₆

—

M₁₆

—

M₁₆

—

C₂×C₈

—

C₂×C₈

—

C₄⋊C₄

—

100

C₄⋊C₄

—

101

C₂²⋊C₄

—

102

C₂²⋊C₄

—

103

C₂²⋊C₄

—

104

C₄²

—

105

C₄²

—

106

C₂³

—

107

C₂³

—

108

C₂³

—

109

C₂³

(C₂×D₄₃)⋊C₄

yes

—

110

C₂³

C₂×C₄×D₄₃

yes

characteristic

111

D₄

—

112

D₄

—

113

C₂×C₄

—

114

C₂×C₄

—

115

C₂×C₄

—

344

—

116

C₂×C₄

C₂×D₁₇₂

yes

characteristic

117

C₂×C₄

#10621900

yes

—

118

C₂×C₄

#10621900

yes

—

119

C₂×C₄

C₂×C₂²⋊D₄₃

yes

characteristic

120

C₈

—

121

C₈

—

172

—

122

C₂²

—

123

C₂²

—

124

C₂²

—

125

C₂²

—

126

C₂²

—

127

C₂²

C₂×(C₂×D₄₃)⋊C₄

yes

characteristic

128

C₂²

#13063281

yes

characteristic

129

C₂²

#13063281

yes

characteristic

130

C₄

—

172

—

131

C₄

—

172

—

132

C₄

#13063306

yes

—

133

C₄

#13063309

yes

—

134

C₂

—

135

C₂

—

136

C₂

—

137

C₂

—

138

C₂

#14582760

yes

characteristic

	subgroup	G/H
center	C₂	#14582760
commutator	C₂³×C₄₃	C₂²×C₄
Frattini	C₂²×C₄	C₂²×D₄₃
Fitting	C₂×#100×C₄₃	C₂
socle	C₂×C₄₃	#381
hypercenter	C₂×#100	D₄₃
hypocenter	C₄₃	#1829
LCS	G ▷ C₂³×C₄₃ ▷ C₂×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₂ ◁ C₂²×C₄ ◁ C₂×#100

subgroup

G/H

center

C₂

#14582760

commutator

C₂³×C₄₃

C₂²×C₄

Frattini

C₂²×C₄

C₂²×D₄₃

Fitting

C₂×#100×C₄₃

C₂

C₂×C₄₃

D₄₃

C₄₃

G ▷ C₂³×C₄₃ ▷ C₂×C₄₃ ▷ C₄₃

UCS

C₁ ◁ C₂ ◁ C₂²×C₄ ◁ C₂×#100

N	H ≅ G/N	type
3. #14582671	C₂	semidirect
4. #14582670	C₂	semidirect
75. C₄₃	#1829	semidirect

H ≅ G/N

type

3. #14582671

C₂

semidirect

4. #14582670

C₂

semidirect

75. C₄₃

#1829

semidirect

Subgroups — #19134704

Conjugacy classes of subgroups

Complements