Group #19137337 — subgroups

Subgroups — #19137337

Order 5504.

444 conjugacy classes of subgroups; only the 237 normal subgroups are shown.

normal subgroups only

This group has 444 conjugacy classes of subgroups — too many to draw. Only its 237 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	#14582798	C₂	1	4	yes	maximal
2	#14582798	C₂	1	2	yes	maximal
3	#14582785	C₂	1	4	yes	maximal
4	#14582769	C₂	1	1	yes	maximal, characteristic
5	C₄⋊C₄×Dic₄₃	C₂	1	2	yes	maximal
6	#14582745	C₂	1	1	yes	maximal, characteristic
7	C₂×#125×C₄₃	C₂	1	1	yes	maximal, characteristic
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×C₄×Dic₄₃	C₂²	1	1	yes	characteristic
12	C₂×C₄×Dic₄₃	C₂²	1	4	yes	—
13	C₂×C₄×Dic₄₃	C₂²	1	1	yes	characteristic
14	C₄₃⋊#95	C₂²	1	4	yes	—
15	C₄₃⋊#95	C₂²	1	2	yes	—
16	C₄₃⋊#95	C₂²	1	4	yes	—
17	C₄₃⋊#95	C₂²	1	2	yes	—
18	#125×C₄₃	C₄	1	8	yes	complemented
19	C₂×C₄⋊C₄×C₄₃	C₂²	1	4	yes	—
20	C₂×C₄⋊C₄×C₄₃	C₂²	1	2	yes	—
21	C₂×C₄²×C₄₃	C₂²	1	1	yes	characteristic
22	C₂²×C₄×C₄₃	C₂³	1	2	yes	—
23	C₂²×C₄×C₄₃	C₂³	1	4	yes	—
24	C₂²×C₄×C₄₃	C₂³	1	1	yes	characteristic
25	C₂²×Dic₄₃	C₂³	1	1	yes	characteristic
26	C₂²×Dic₄₃	C₂³	1	1	yes	characteristic
27	C₂²×Dic₄₃	C₂³	1	4	yes	—
28	C₂²×Dic₄₃	C₂³	1	2	yes	—
29	C₄⋊C₄×C₄₃	C₂×C₄	1	16	yes	—
30	C₄⋊C₄×C₄₃	C₂×C₄	1	8	yes	—
31	C₄²×C₄₃	C₂×C₄	1	4	yes	—
32	C₄⋊Dic₄₃	—	2	4	no	—
33	C₄⋊Dic₄₃	—	4	4	no	—
34	C₄⋊Dic₄₃	—	4	4	no	—
35	C₄×Dic₄₃	—	2	2	no	—
36	C₄×Dic₄₃	—	4	4	no	—
37	C₄×Dic₄₃	Q₈	1	4	yes	—
38	C₂³×C₄₃	C₂⁴	1	1	yes	characteristic
39	C₂×C₄×C₄₃	—	2	4	no	—
40	C₂×C₄×C₄₃	—	2	2	no	—
41	C₂×C₄×C₄₃	—	2	2	no	—
42	C₂×C₄×C₄₃	—	2	4	no	—
43	C₂×C₄×C₄₃	C₂²×C₄	1	4	yes	—
44	C₂×C₄×C₄₃	C₂²×C₄	1	8	yes	—
45	C₂×C₄×C₄₃	C₂²×C₄	1	2	yes	—
46	C₂×C₄×C₄₃	C₂×Q₈	1	2	yes	—
47	C₂×C₄×C₄₃	#41	1	2	yes	—
48	C₂×Dic₄₃	—	2	2	no	—
49	C₂×Dic₄₃	—	2	2	no	—
50	C₂×Dic₄₃	—	2	1	no	—
51	C₂×Dic₄₃	—	2	1	no	—
52	C₂×Dic₄₃	—	2	4	no	—
53	C₂×Dic₄₃	—	2	4	no	—
54	C₂×Dic₄₃	—	2	2	no	—
55	C₂×Dic₄₃	—	2	4	no	—
56	C₂×Dic₄₃	—	2	2	no	—
57	C₂×Dic₄₃	C₂×Q₈	1	4	yes	—
58	C₂²×C₄₃	C₂³×C₄	1	1	yes	characteristic
59	C₂²×C₄₃	C₂²×Q₈	1	1	yes	characteristic
60	C₂²×C₄₃	C₂×#41	1	1	yes	characteristic
61	C₂²×C₄₃	H(5,𝔽₂)	1	2	yes	—
62	C₂²×C₄₃	2₋¹⁺⁴	1	2	yes	—
63	C₄×C₄₃	—	2	8	no	—
64	C₄×C₄₃	—	2	4	no	—
65	C₄×C₄₃	C₄×Q₈	1	4	yes	—
66	Dic₄₃	—	2	4	no	—
67	Dic₄₃	—	4	1	no	—
68	Dic₄₃	—	4	4	no	—
69	Dic₄₃	—	4	1	no	—
70	#2330	—	43	1	no	maximal, Sylow
71	C₂×C₄₃	C₂×C₄×Q₈	1	1	yes	characteristic
72	C₂×C₄₃	#520	1	2	yes	—
73	C₂×C₄₃	#540	1	1	yes	characteristic
74	C₂×C₄₃	#541	1	1	yes	characteristic
75	C₂×C₄₃	#544	1	2	yes	—
76	C₂×#125	D₄₃	1	1	yes	characteristic
77	#389	—	43	4	no	—
78	#389	—	43	2	no	—
79	#387	—	43	4	no	—
80	#384	—	43	1	no	—
81	C₄×C₄⋊C₄	—	43	2	no	—
82	#376	—	43	1	no	—
83	C₄₃	#2330	1	1	yes	characteristic, complemented, Sylow
84	#125	Dic₄₃	1	8	yes	complemented
85	C₂×C₄⋊C₄	—	43	2	no	—
86	C₂×C₄⋊C₄	—	43	4	no	—
87	C₂×C₄⋊C₄	—	43	4	no	—
88	C₂×C₄⋊C₄	C₂×D₄₃	1	2	yes	—
89	C₂×C₄⋊C₄	C₂×D₄₃	1	4	yes	—
90	C₂×C₄²	—	43	1	no	—
91	C₂×C₄²	—	43	1	no	—
92	C₂×C₄²	—	43	4	no	—
93	C₂×C₄²	C₂×D₄₃	1	1	yes	characteristic
94	#95	—	43	2	no	—
95	#95	—	43	2	no	—
96	#95	—	43	4	no	—
97	#95	—	43	4	no	—
98	C₂²×C₄	—	43	2	no	—
99	C₂²×C₄	—	43	1	no	—
100	C₂²×C₄	—	43	1	no	—
101	C₂²×C₄	—	43	4	no	—
102	C₂²×C₄	C₂²×D₄₃	1	4	yes	—
103	C₂²×C₄	C₂²×D₄₃	1	2	yes	—
104	C₂²×C₄	C₂²×D₄₃	1	1	yes	characteristic
105	C₄⋊C₄	—	86	4	no	—
106	C₄⋊C₄	—	172	4	no	—
107	C₄⋊C₄	—	172	4	no	—
108	C₄⋊C₄	C₂×Dic₄₃	1	16	yes	—
109	C₄⋊C₄	C₂×Dic₄₃	1	8	yes	—
110	C₄²	—	43	4	no	—
111	C₄²	—	86	2	no	—
112	C₄²	—	172	4	no	—
113	C₄²	C₂×Dic₄₃	1	4	yes	—
114	C₂³	C₂³×D₄₃	1	1	yes	characteristic
115	C₂×C₄	—	2	4	no	—
116	C₂×C₄	—	2	2	no	—
117	C₂×C₄	—	2	4	no	—
118	C₂×C₄	—	2	2	no	—
119	C₂×C₄	—	43	4	no	—
120	C₂×C₄	—	86	2	no	—
121	C₂×C₄	—	86	2	no	—
122	C₂×C₄	—	86	1	no	—
123	C₂×C₄	—	86	1	no	—
124	C₂×C₄	—	86	4	no	—
125	C₂×C₄	—	86	4	no	—
126	C₂×C₄	—	86	2	no	—
127	C₂×C₄	—	86	4	no	—
128	C₂×C₄	—	86	2	no	—
129	C₂×C₄	Q₈×D₄₃	1	2	yes	—
130	C₂×C₄	#10621902	1	2	yes	—
131	C₂×C₄	C₂²×Dic₄₃	1	4	yes	—
132	C₂×C₄	C₂²×Dic₄₃	1	8	yes	—
133	C₂×C₄	C₂²×Dic₄₃	1	2	yes	—
134	C₂²	C₂³×Dic₄₃	1	1	yes	characteristic
135	C₂²	C₂×Q₈×D₄₃	1	1	yes	characteristic
136	C₂²	C₂×#10621902	1	1	yes	characteristic
137	C₂²	#13063371	1	2	yes	—
138	C₂²	#13063372	1	2	yes	—
139	C₄	—	2	8	no	—
140	C₄	—	2	4	no	—
141	C₄	—	86	4	no	—
142	C₄	—	172	1	no	—
143	C₄	—	172	4	no	—
144	C₄	—	172	1	no	—
145	C₄	Q₈×Dic₄₃	1	4	yes	—
146	C₂	C₂×Q₈×Dic₄₃	1	1	yes	characteristic
147	C₂	#14583382	1	2	yes	—
148	C₂	#14583505	1	1	yes	characteristic
149	C₂	#14583512	1	1	yes	characteristic
150	C₂	#14583529	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

#14582798

C₂

yes

maximal

#14582798

C₂

yes

maximal

#14582785

C₂

yes

maximal

#14582769

C₂

yes

maximal, characteristic

C₄⋊C₄×Dic₄₃

C₂

yes

maximal

#14582745

C₂

yes

maximal, characteristic

C₂×#125×C₄₃

C₂

yes

maximal, characteristic

C₂×C₄⋊Dic₄₃

C₂²

yes

—

C₂×C₄⋊Dic₄₃

C₂²

yes

—

C₂×C₄⋊Dic₄₃

C₂²

yes

—

C₂×C₄×Dic₄₃

C₂²

yes

characteristic

C₂×C₄×Dic₄₃

C₂²

yes

—

C₂×C₄×Dic₄₃

C₂²

yes

characteristic

C₄₃⋊#95

C₂²

yes

—

C₄₃⋊#95

C₂²

yes

—

C₄₃⋊#95

C₂²

yes

—

C₄₃⋊#95

C₂²

yes

—

#125×C₄₃

C₄

yes

complemented

C₂×C₄⋊C₄×C₄₃

C₂²

yes

—

C₂×C₄⋊C₄×C₄₃

C₂²

yes

—

C₂×C₄²×C₄₃

C₂²

yes

characteristic

C₂²×C₄×C₄₃

C₂³

yes

—

C₂²×C₄×C₄₃

C₂³

yes

—

C₂²×C₄×C₄₃

C₂³

yes

characteristic

C₂²×Dic₄₃

C₂³

yes

characteristic

C₂²×Dic₄₃

C₂³

yes

characteristic

C₂²×Dic₄₃

C₂³

yes

—

C₂²×Dic₄₃

C₂³

yes

—

C₄⋊C₄×C₄₃

C₂×C₄

yes

—

C₄⋊C₄×C₄₃

C₂×C₄

yes

—

C₄²×C₄₃

C₂×C₄

yes

—

C₄⋊Dic₄₃

—

C₄⋊Dic₄₃

—

C₄⋊Dic₄₃

—

C₄×Dic₄₃

—

C₄×Dic₄₃

—

C₄×Dic₄₃

Q₈

yes

—

C₂³×C₄₃

C₂⁴

yes

characteristic

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×C₄×C₄₃

C₂²×C₄

yes

—

C₂×C₄×C₄₃

C₂×Q₈

yes

—

C₂×C₄×C₄₃

#41

yes

—

C₂×Dic₄₃

—

C₂×Dic₄₃

—

C₂×Dic₄₃

—

C₂×Dic₄₃

—

C₂×Dic₄₃

—

C₂×Dic₄₃

—

C₂×Dic₄₃

—

C₂×Dic₄₃

—

C₂×Dic₄₃

—

C₂×Dic₄₃

C₂×Q₈

yes

—

C₂²×C₄₃

C₂³×C₄

yes

characteristic

C₂²×C₄₃

C₂²×Q₈

yes

characteristic

C₂²×C₄₃

C₂×#41

yes

characteristic

C₂²×C₄₃

H(5,𝔽₂)

yes

—

C₂²×C₄₃

2₋¹⁺⁴

yes

—

C₄×C₄₃

—

C₄×C₄₃

—

C₄×C₄₃

C₄×Q₈

yes

—

Dic₄₃

—

Dic₄₃

—

Dic₄₃

—

Dic₄₃

—

#2330

—

maximal, Sylow

C₂×C₄₃

C₂×C₄×Q₈

yes

characteristic

C₂×C₄₃

#520

yes

—

C₂×C₄₃

yes

C₂×C₄₃

yes

C₂×C₄₃

yes

—

C₂×#125

D₄₃

yes

—

—

—

—

C₄×C₄⋊C₄

—

#376

—

C₄₃

#2330

yes

characteristic, complemented, Sylow

#125

Dic₄₃

yes

complemented

C₂×C₄⋊C₄

—

C₂×C₄⋊C₄

—

C₂×C₄⋊C₄

—

C₂×C₄⋊C₄

C₂×D₄₃

yes

—

C₂×C₄⋊C₄

C₂×D₄₃

yes

—

C₂×C₄²

—

C₂×C₄²

—

C₂×C₄²

—

C₂×C₄²

C₂×D₄₃

yes

—

—

—

—

C₂²×C₄

—

C₂²×C₄

—

100

C₂²×C₄

—

101

C₂²×C₄

—

102

C₂²×C₄

C₂²×D₄₃

yes

—

103

C₂²×C₄

C₂²×D₄₃

yes

—

104

C₂²×C₄

C₂²×D₄₃

yes

characteristic

105

C₄⋊C₄

—

106

C₄⋊C₄

—

172

—

107

C₄⋊C₄

—

172

—

108

C₄⋊C₄

C₂×Dic₄₃

yes

—

109

C₄⋊C₄

C₂×Dic₄₃

yes

—

110

C₄²

—

111

C₄²

—

112

C₄²

—

172

—

113

C₄²

C₂×Dic₄₃

yes

—

114

C₂³

C₂³×D₄₃

yes

characteristic

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

—

126

C₂×C₄

—

127

C₂×C₄

—

128

C₂×C₄

—

129

C₂×C₄

Q₈×D₄₃

yes

—

130

C₂×C₄

#10621902

yes

—

131

C₂×C₄

C₂²×Dic₄₃

yes

—

132

C₂×C₄

C₂²×Dic₄₃

yes

—

133

C₂×C₄

C₂²×Dic₄₃

yes

—

134

C₂²

C₂³×Dic₄₃

yes

characteristic

135

C₂²

C₂×Q₈×D₄₃

yes

characteristic

136

C₂²

C₂×#10621902

yes

characteristic

137

C₂²

#13063371

yes

—

138

C₂²

#13063372

yes

—

139

C₄

—

140

C₄

—

141

C₄

—

142

C₄

—

172

—

143

C₄

—

172

—

144

C₄

—

172

—

145

C₄

Q₈×Dic₄₃

yes

—

146

C₂

C₂×Q₈×Dic₄₃

yes

characteristic

147

C₂

#14583382

yes

—

148

C₂

#14583505

yes

characteristic

149

C₂

#14583512

yes

characteristic

150

C₂

#14583529

yes

—

	subgroup	G/H
center, Frattini	C₂³	C₂³×D₄₃
commutator	C₂²×C₄₃	C₂³×C₄
Fitting	C₂×#125×C₄₃	C₂
socle	C₂³×C₄₃	C₂⁴
hypercenter	C₂×#125	D₄₃
hypocenter	C₄₃	#2330
LCS	G ▷ C₂²×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₂³ ◁ C₂×#125

subgroup

G/H

center, Frattini

C₂³

C₂³×D₄₃

commutator

C₂²×C₄₃

C₂³×C₄

Fitting

C₂×#125×C₄₃

C₂

socle

C₂³×C₄₃

C₂⁴

D₄₃

C₄₃

G ▷ C₂²×C₄₃ ▷ C₄₃

C₁ ◁ C₂³ ◁ C₂×#125

N	H ≅ G/N	type
18. #125×C₄₃	C₄	semidirect
83. C₄₃	#2330	semidirect
84. #125	Dic₄₃	semidirect

H ≅ G/N

type

18. #125×C₄₃

C₄

semidirect

83. C₄₃

#2330

semidirect

84. #125

Dic₄₃

semidirect

Subgroups — #19137337

Conjugacy classes of subgroups

Complements