Group #19140709 — subgroups

Subgroups — #19140709

Order 5504.

524 conjugacy classes of subgroups; only the 181 normal subgroups are shown.

normal subgroups only

This group has 524 conjugacy classes of subgroups — too many to draw. Only its 181 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×#13063304	C₂	1	2	yes	maximal
2	#14582831	C₂	1	4	yes	maximal, complemented
3	#14582820	C₂	1	4	yes	maximal, complemented
4	#14582759	C₂	1	4	yes	maximal
5	C₂×#95×C₄₃	C₂	1	1	yes	maximal, characteristic
6	C₂²×Dic₈₆	C₂²	1	2	yes	—
7	#13063304	—	2	8	no	—
8	C₂×C₄⋊Dic₄₃	C₂²	1	2	yes	—
9	C₂×C₄⋊Dic₄₃	C₂²	1	4	yes	—
10	C₂×C₄⋊Dic₄₃	C₂²	1	4	yes	—
11	C₂×Dic₄₃⋊C₄	C₂²	1	4	yes	—
12	C₂×C₂²⋊Dic₄₃	C₂²	1	4	yes	—
13	C₄₃⋊#95	C₂²	1	8	yes	—
14	C₂³×C₄×C₄₃	C₂²	1	1	yes	characteristic
15	C₂³×C₄×C₄₃	C₂²	1	2	yes	—
16	#95×C₄₃	C₂²	1	4	yes	—
17	C₂⁴×C₄₃	C₂³	1	1	yes	characteristic
18	C₂²×C₄×C₄₃	—	4	2	no	—
19	C₂²×C₄×C₄₃	—	4	2	no	—
20	C₂²×C₄×C₄₃	—	4	2	no	—
21	C₂²×C₄×C₄₃	D₄	1	4	yes	—
22	C₂²×C₄×C₄₃	Q₈	1	8	yes	complemented
23	C₂²×C₄×C₄₃	C₂³	1	2	yes	—
24	C₂²×C₄×C₄₃	C₂³	1	4	yes	—
25	C₂²×Dic₄₃	C₂³	1	4	yes	—
26	C₂²×Dic₄₃	C₂³	1	4	yes	—
27	C₂×Dic₈₆	—	2	4	no	—
28	C₂×Dic₈₆	—	4	4	no	—
29	C₂²⋊Dic₄₃	—	2	8	no	—
30	C₄⋊Dic₄₃	—	2	4	no	—
31	C₄⋊Dic₄₃	—	4	4	no	—
32	C₄⋊Dic₄₃	—	4	4	no	—
33	Dic₄₃⋊C₄	—	2	8	no	—
34	C₂³×C₄₃	—	2	2	no	—
35	C₂³×C₄₃	—	2	1	no	—
36	C₂³×C₄₃	—	2	1	no	—
37	C₂³×C₄₃	C₂×D₄	1	2	yes	—
38	C₂³×C₄₃	C₂×Q₈	1	4	yes	—
39	C₂³×C₄₃	C₂⁴	1	1	yes	characteristic
40	C₂×C₄×C₄₃	—	2	4	no	—
41	C₂×C₄×C₄₃	—	2	4	no	—
42	C₂×C₄×C₄₃	—	2	4	no	—
43	C₂×C₄×C₄₃	—	4	4	no	—
44	C₂×C₄×C₄₃	—	4	8	no	—
45	C₂×C₄×C₄₃	C₂×D₄	1	4	yes	—
46	C₂×C₄×C₄₃	C₂×Q₈	1	8	yes	—
47	C₂×Dic₄₃	—	2	4	no	—
48	C₂×Dic₄₃	—	2	4	no	—
49	C₂×Dic₄₃	—	2	4	no	—
50	C₂×Dic₄₃	—	2	8	no	—
51	C₂×Dic₄₃	—	2	4	no	—
52	Dic₈₆	—	4	8	no	—
53	C₂²×C₄₃	—	2	2	no	—
54	C₂²×C₄₃	—	2	2	no	—
55	C₂²×C₄₃	—	2	4	no	—
56	C₂²×C₄₃	—	2	4	no	—
57	C₂²×C₄₃	C₄⋊Q₈	1	4	yes	—
58	C₂²×C₄₃	C₂²×D₄	1	1	yes	characteristic
59	C₂²×C₄₃	C₂²×Q₈	1	2	yes	—
60	C₂²×C₄₃	H(5,𝔽₂)	1	2	yes	—
61	C₂²×C₄₃	H(5,𝔽₂)	1	1	yes	characteristic
62	C₂²×C₄₃	2₋¹⁺⁴	1	1	yes	characteristic
63	C₄×C₄₃	—	2	4	no	—
64	C₄×C₄₃	—	2	8	no	—
65	Dic₄₃	—	4	4	no	—
66	Dic₄₃	—	4	4	no	—
67	#2659	—	43	1	no	maximal, Sylow
68	C₂×C₄₃	—	2	4	no	—
69	C₂×C₄₃	C₂×C₄⋊Q₈	1	1	yes	characteristic
70	C₂×C₄₃	#534	1	1	yes	characteristic
71	C₂×C₄₃	#537	1	1	yes	characteristic
72	C₂×C₄₃	#543	1	2	yes	—
73	C₂×C₄₃	#544	1	2	yes	—
74	C₂×C₂²⋊Q₈	—	43	2	no	—
75	#398	—	43	4	no	—
76	#395	—	43	4	no	—
77	#380	—	43	4	no	—
78	C₂×#95	D₄₃	1	1	yes	characteristic
79	C₄₃	#2659	1	1	yes	characteristic, complemented, Sylow
80	C₂²×Q₈	—	43	2	no	—
81	C₂³×C₄	C₂×D₄₃	1	2	yes	—
82	C₂³×C₄	C₂×D₄₃	1	1	yes	characteristic
83	C₂²⋊Q₈	—	86	8	no	—
84	C₂×C₄⋊C₄	—	43	4	no	—
85	C₂×C₄⋊C₄	—	43	2	no	—
86	C₂×C₄⋊C₄	—	43	4	no	—
87	C₂×C₄⋊C₄	—	43	4	no	—
88	C₂×C₂²⋊C₄	—	43	4	no	—
89	#95	—	43	8	no	—
90	#95	C₂×D₄₃	1	4	yes	—
91	C₂⁴	C₂²×D₄₃	1	1	yes	characteristic
92	C₂×Q₈	—	86	4	no	—
93	C₂×Q₈	—	172	4	no	—
94	C₂²×C₄	—	4	2	no	—
95	C₂²×C₄	—	4	2	no	—
96	C₂²×C₄	—	4	2	no	—
97	C₂²×C₄	—	43	4	no	—
98	C₂²×C₄	—	43	4	no	—
99	C₂²×C₄	Dic₈₆	1	8	yes	complemented
100	C₂²×C₄	D₁₇₂	1	4	yes	—
101	C₂²×C₄	C₂²×D₄₃	1	4	yes	—
102	C₂²×C₄	C₂²×D₄₃	1	2	yes	—
103	C₄⋊C₄	—	86	8	no	—
104	C₄⋊C₄	—	86	4	no	—
105	C₄⋊C₄	—	172	4	no	—
106	C₄⋊C₄	—	172	4	no	—
107	C₂²⋊C₄	—	86	8	no	—
108	C₂³	—	2	2	no	—
109	C₂³	—	2	1	no	—
110	C₂³	—	2	1	no	—
111	C₂³	C₂×Dic₈₆	1	4	yes	—
112	C₂³	C₂×D₁₇₂	1	2	yes	—
113	C₂³	C₂³×D₄₃	1	1	yes	characteristic
114	Q₈	—	172	8	no	—
115	C₂×C₄	—	2	4	no	—
116	C₂×C₄	—	2	4	no	—
117	C₂×C₄	—	2	4	no	—
118	C₂×C₄	—	4	8	no	—
119	C₂×C₄	—	4	4	no	—
120	C₂×C₄	—	86	4	no	—
121	C₂×C₄	—	86	4	no	—
122	C₂×C₄	—	86	4	no	—
123	C₂×C₄	—	86	8	no	—
124	C₂×C₄	—	86	4	no	—
125	C₂×C₄	C₂×Dic₈₆	1	8	yes	—
126	C₂×C₄	C₂×D₁₇₂	1	4	yes	—
127	C₂²	—	2	2	no	—
128	C₂²	—	2	2	no	—
129	C₂²	—	2	4	no	—
130	C₂²	—	2	4	no	—
131	C₂²	#13063325	1	4	yes	—
132	C₂²	C₂²×D₁₇₂	1	1	yes	characteristic
133	C₂²	C₂²×Dic₈₆	1	2	yes	—
134	C₂²	#13063370	1	2	yes	—
135	C₂²	#13063370	1	1	yes	characteristic
136	C₂²	#13063373	1	1	yes	characteristic
137	C₄	—	2	4	no	—
138	C₄	—	2	8	no	—
139	C₄	—	172	4	no	—
140	C₄	—	172	4	no	—
141	C₂	—	2	4	no	—
142	C₂	C₂×#13063325	1	1	yes	characteristic
143	C₂	#14583461	1	1	yes	characteristic
144	C₂	#14583480	1	1	yes	characteristic
145	C₂	#14583525	1	2	yes	—
146	C₂	#14583530	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×#13063304

C₂

yes

maximal

#14582831

C₂

yes

maximal, complemented

#14582820

C₂

yes

maximal, complemented

#14582759

C₂

yes

maximal

C₂×#95×C₄₃

C₂

yes

maximal, characteristic

C₂²×Dic₈₆

C₂²

yes

—

#13063304

—

C₂×C₄⋊Dic₄₃

C₂²

yes

—

C₂×C₄⋊Dic₄₃

C₂²

yes

—

C₂×C₄⋊Dic₄₃

C₂²

yes

—

C₂×Dic₄₃⋊C₄

C₂²

yes

—

C₂×C₂²⋊Dic₄₃

C₂²

yes

—

C₄₃⋊#95

C₂²

yes

—

C₂³×C₄×C₄₃

C₂²

yes

characteristic

C₂³×C₄×C₄₃

C₂²

yes

—

#95×C₄₃

C₂²

yes

—

C₂⁴×C₄₃

C₂³

yes

characteristic

C₂²×C₄×C₄₃

—

C₂²×C₄×C₄₃

—

C₂²×C₄×C₄₃

—

C₂²×C₄×C₄₃

D₄

yes

—

C₂²×C₄×C₄₃

Q₈

yes

complemented

C₂²×C₄×C₄₃

C₂³

yes

—

C₂²×C₄×C₄₃

C₂³

yes

—

C₂²×Dic₄₃

C₂³

yes

—

C₂²×Dic₄₃

C₂³

yes

—

C₂×Dic₈₆

—

C₂×Dic₈₆

—

C₂²⋊Dic₄₃

—

C₄⋊Dic₄₃

—

C₄⋊Dic₄₃

—

C₄⋊Dic₄₃

—

Dic₄₃⋊C₄

—

C₂³×C₄₃

—

C₂³×C₄₃

—

C₂³×C₄₃

—

C₂³×C₄₃

C₂×D₄

yes

—

C₂³×C₄₃

C₂×Q₈

yes

—

C₂³×C₄₃

C₂⁴

yes

characteristic

C₂×C₄×C₄₃

—

C₂×C₄×C₄₃

—

C₂×C₄×C₄₃

—

C₂×C₄×C₄₃

—

C₂×C₄×C₄₃

—

C₂×C₄×C₄₃

C₂×D₄

yes

—

C₂×C₄×C₄₃

C₂×Q₈

yes

—

C₂×Dic₄₃

—

C₂×Dic₄₃

—

C₂×Dic₄₃

—

C₂×Dic₄₃

—

C₂×Dic₄₃

—

Dic₈₆

—

C₂²×C₄₃

—

C₂²×C₄₃

—

C₂²×C₄₃

—

C₂²×C₄₃

—

C₂²×C₄₃

C₄⋊Q₈

yes

—

C₂²×C₄₃

C₂²×D₄

yes

characteristic

C₂²×C₄₃

C₂²×Q₈

yes

—

C₂²×C₄₃

H(5,𝔽₂)

yes

—

C₂²×C₄₃

H(5,𝔽₂)

yes

characteristic

C₂²×C₄₃

2₋¹⁺⁴

yes

characteristic

C₄×C₄₃

—

C₄×C₄₃

—

Dic₄₃

—

Dic₄₃

—

#2659

—

maximal, Sylow

C₂×C₄₃

—

C₂×C₄₃

C₂×C₄⋊Q₈

yes

C₂×C₄₃

yes

C₂×C₄₃

yes

C₂×C₄₃

yes

—

C₂×C₄₃

#544

yes

—

C₂×C₂²⋊Q₈

—

#398

—

#395

—

#380

—

C₂×#95

D₄₃

yes

characteristic

C₄₃

#2659

yes

characteristic, complemented, Sylow

C₂²×Q₈

—

C₂³×C₄

C₂×D₄₃

yes

—

C₂³×C₄

C₂×D₄₃

yes

characteristic

C₂²⋊Q₈

—

C₂×C₄⋊C₄

—

C₂×C₄⋊C₄

—

C₂×C₄⋊C₄

—

C₂×C₄⋊C₄

—

C₂×C₂²⋊C₄

—

#95

—

#95

C₂×D₄₃

yes

—

C₂⁴

C₂²×D₄₃

yes

characteristic

C₂×Q₈

—

C₂×Q₈

—

172

—

C₂²×C₄

—

C₂²×C₄

—

C₂²×C₄

—

C₂²×C₄

—

C₂²×C₄

—

C₂²×C₄

Dic₈₆

yes

complemented

100

C₂²×C₄

D₁₇₂

yes

—

101

C₂²×C₄

C₂²×D₄₃

yes

—

102

C₂²×C₄

C₂²×D₄₃

yes

—

103

C₄⋊C₄

—

104

C₄⋊C₄

—

105

C₄⋊C₄

—

172

—

106

C₄⋊C₄

—

172

—

107

C₂²⋊C₄

—

108

C₂³

—

109

C₂³

—

110

C₂³

—

111

C₂³

C₂×Dic₈₆

yes

—

112

C₂³

C₂×D₁₇₂

yes

—

113

C₂³

C₂³×D₄₃

yes

characteristic

114

Q₈

—

172

—

115

C₂×C₄

—

116

C₂×C₄

—

117

C₂×C₄

—

118

C₂×C₄

—

119

C₂×C₄

—

120

C₂×C₄

—

121

C₂×C₄

—

122

C₂×C₄

—

123

C₂×C₄

—

124

C₂×C₄

—

125

C₂×C₄

C₂×Dic₈₆

yes

—

126

C₂×C₄

C₂×D₁₇₂

yes

—

127

C₂²

—

128

C₂²

—

129

C₂²

—

130

C₂²

—

131

C₂²

#13063325

yes

—

132

C₂²

C₂²×D₁₇₂

yes

characteristic

133

C₂²

C₂²×Dic₈₆

yes

—

134

C₂²

#13063370

yes

—

135

C₂²

#13063370

yes

characteristic

136

C₂²

#13063373

yes

characteristic

137

C₄

—

138

C₄

—

139

C₄

—

172

—

140

C₄

—

172

—

141

C₂

—

142

C₂

C₂×#13063325

yes

characteristic

143

C₂

#14583461

yes

characteristic

144

C₂

#14583480

yes

characteristic

145

C₂

#14583525

yes

—

146

C₂

#14583530

yes

—

	subgroup	G/H
center, Frattini	C₂³	C₂³×D₄₃
commutator, socle	C₂³×C₄₃	C₂⁴
Fitting	C₂×#95×C₄₃	C₂
hypercenter	C₂×#95	D₄₃
hypocenter	C₄₃	#2659
LCS	G ▷ C₂³×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₂³ ◁ C₂×#95

subgroup

G/H

center, Frattini

C₂³

C₂³×D₄₃

commutator, socle

C₂³×C₄₃

C₂⁴

Fitting

C₂×#95×C₄₃

C₂

hypercenter

C₂×#95

D₄₃

C₄₃

G ▷ C₂³×C₄₃ ▷ C₄₃

C₁ ◁ C₂³ ◁ C₂×#95

N	H ≅ G/N	type
2. #14582831	C₂	semidirect
3. #14582820	C₂	semidirect
22. C₂²×C₄×C₄₃	Q₈	semidirect
79. C₄₃	#2659	semidirect
99. C₂²×C₄	Dic₈₆	semidirect

H ≅ G/N

type

2. #14582831

C₂

semidirect

3. #14582820

C₂

semidirect

22. C₂²×C₄×C₄₃

Q₈

semidirect

79. C₄₃

#2659

semidirect

99. C₂²×C₄

Dic₈₆

semidirect

Subgroups — #19140709

Conjugacy classes of subgroups

Complements