Group #14566360 — subgroups

Subgroups — #14566360

Order 2432.

740 conjugacy classes of subgroups; only the 205 normal subgroups are shown.

normal subgroups only

This group has 740 conjugacy classes of subgroups — too many to draw. Only its 205 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×#10597320	C₂	1	1	yes	maximal, characteristic
2	C₂×C₄×D₇₆	C₂	1	2	yes	maximal, complemented
3	#11926446	C₂	1	2	yes	maximal, complemented
4	#11926422	C₂	1	8	yes	maximal, complemented
5	#11926410	C₂	1	1	yes	maximal, characteristic, complemented
6	C₁₉×#376	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂²×D₇₆	C₂²	1	2	yes	—
8	C₂²×D₇₆	C₂²	1	4	yes	—
9	C₂²×C₄×D₁₉	C₂²	1	4	yes	—
10	C₂×C₄²×C₁₉	C₂²	1	1	yes	characteristic
11	C₂×C₄²×C₁₉	C₂²	1	1	yes	characteristic
12	C₂×C₄²×C₁₉	C₂²	1	1	yes	characteristic
13	C₂×(C₂×D₁₉)⋊C₄	C₂²	1	4	yes	—
14	C₂×(C₂×D₁₉)⋊C₄	C₂²	1	8	yes	—
15	C₂×C₄⋊Dic₁₉	C₂²	1	2	yes	—
16	#10597320	C₄	1	8	yes	complemented
17	C₄×D₇₆	—	2	8	no	—
18	C₁₉×#95	C₂²	1	4	yes	—
19	C₁₉⋊#95	C₂²	1	4	yes	—
20	C₂³×D₁₉	C₂³	1	4	yes	—
21	C₂²×C₄×C₁₉	C₂³	1	2	yes	—
22	C₂²×C₄×C₁₉	C₂³	1	2	yes	—
23	C₂²×C₄×C₁₉	C₂³	1	2	yes	—
24	C₂²×C₄×C₁₉	C₂³	1	1	yes	characteristic
25	C₂²×Dic₁₉	C₂³	1	4	yes	—
26	C₂×D₇₆	—	2	4	no	—
27	C₂×D₇₆	—	2	4	no	—
28	C₂×D₇₆	—	4	8	no	—
29	C₂×D₇₆	C₂×C₄	1	8	yes	complemented
30	C₂×D₇₆	C₂×C₄	1	16	yes	complemented
31	C₂×C₄×D₁₉	—	2	8	no	—
32	C₂×C₄×D₁₉	—	4	8	no	—
33	C₄²×C₁₉	—	2	2	no	—
34	C₄²×C₁₉	C₂×C₄	1	4	yes	complemented
35	C₄²×C₁₉	D₄	1	4	yes	complemented
36	(C₂×D₁₉)⋊C₄	—	2	8	no	—
37	(C₂×D₁₉)⋊C₄	—	4	8	no	—
38	C₄⋊Dic₁₉	—	2	4	no	—
39	C₂³×C₁₉	C₂⁴	1	1	yes	characteristic
40	C₂²×D₁₉	—	2	4	no	—
41	C₂²×D₁₉	—	2	4	no	—
42	C₂²×D₁₉	—	2	8	no	—
43	C₂²×D₁₉	—	2	8	no	—
44	C₂²×D₁₉	C₂²×C₄	1	8	yes	—
45	C₂×C₄×C₁₉	—	2	4	no	—
46	C₂×C₄×C₁₉	—	2	4	no	—
47	C₂×C₄×C₁₉	—	2	2	no	—
48	C₂×C₄×C₁₉	—	2	4	no	—
49	C₂×C₄×C₁₉	C₂²×C₄	1	4	yes	—
50	C₂×C₄×C₁₉	C₂²×C₄	1	2	yes	—
51	C₂×C₄×C₁₉	C₂×D₄	1	4	yes	—
52	C₂×C₄×C₁₉	C₂×D₄	1	2	yes	—
53	C₂×C₄×C₁₉	#41	1	2	yes	—
54	C₂×Dic₁₉	—	2	4	no	—
55	C₂×Dic₁₉	—	2	8	no	—
56	D₇₆	—	2	16	no	—
57	D₇₆	—	4	16	no	—
58	C₄×D₁₉	—	4	16	no	—
59	#2328	—	19	1	no	maximal, Sylow
60	C₂²×C₁₉	C₂³×C₄	1	1	yes	characteristic
61	C₂²×C₁₉	C₂²×D₄	1	1	yes	characteristic
62	C₂²×C₁₉	C₂×#41	1	1	yes	characteristic
63	C₂²×C₁₉	H(5,𝔽₂)	1	4	yes	—
64	C₂×D₁₉	—	2	8	no	—
65	C₂×D₁₉	—	2	16	no	—
66	C₂×D₁₉	—	4	4	no	—
67	C₂×D₁₉	—	4	4	no	—
68	C₂×D₁₉	—	4	8	no	—
69	C₄×C₁₉	—	2	4	no	—
70	C₄×C₁₉	—	2	4	no	—
71	C₄×C₁₉	—	4	2	no	—
72	C₄×C₁₉	C₄×D₄	1	4	yes	—
73	Dic₁₉	—	4	4	no	—
74	C₂×#127	—	19	1	no	—
75	C₂×C₄×D₄	—	19	2	no	—
76	#390	—	19	2	no	—
77	#386	—	19	8	no	—
78	#382	—	19	1	no	—
79	#376	D₁₉	1	1	yes	characteristic, complemented
80	C₂×C₁₉	C₂×C₄×D₄	1	1	yes	characteristic
81	C₂×C₁₉	#518	1	2	yes	—
82	C₂×C₁₉	#535	1	2	yes	—
83	C₂×C₁₉	#540	1	2	yes	—
84	D₁₉	—	4	8	no	—
85	C₂²×D₄	—	19	2	no	—
86	C₂²×D₄	—	19	4	no	—
87	C₂³×C₄	—	19	4	no	—
88	#127	—	19	8	no	—
89	C₄×D₄	—	38	8	no	—
90	C₂×C₄⋊C₄	—	19	2	no	—
91	C₂×C₂²⋊C₄	—	19	4	no	—
92	C₂×C₂²⋊C₄	—	19	8	no	—
93	C₂×C₄²	C₂×D₁₉	1	1	yes	characteristic
94	C₂×C₄²	C₂×D₁₉	1	1	yes	characteristic
95	C₂×C₄²	C₂×D₁₉	1	1	yes	characteristic
96	#95	—	19	4	no	—
97	#95	C₂×D₁₉	1	4	yes	—
98	C₁₉	#2328	1	1	yes	characteristic, complemented, Sylow
99	C₂⁴	—	19	4	no	—
100	C₂×D₄	—	19	8	no	—
101	C₂×D₄	—	19	16	no	—
102	C₂×D₄	—	38	4	no	—
103	C₂×D₄	—	38	4	no	—
104	C₂×D₄	—	76	8	no	—
105	C₂²×C₄	—	19	4	no	—
106	C₂²×C₄	—	38	8	no	—
107	C₂²×C₄	—	76	8	no	—
108	C₂²×C₄	C₂²×D₁₉	1	2	yes	—
109	C₂²×C₄	C₂²×D₁₉	1	2	yes	—
110	C₂²×C₄	C₂²×D₁₉	1	2	yes	—
111	C₂²×C₄	C₂²×D₁₉	1	1	yes	characteristic
112	C₄⋊C₄	—	38	4	no	—
113	C₂²⋊C₄	—	38	8	no	—
114	C₂²⋊C₄	—	76	8	no	—
115	C₄²	—	2	2	no	—
116	C₄²	C₄×D₁₉	1	4	yes	complemented
117	C₄²	D₇₆	1	4	yes	complemented
118	C₂³	—	19	8	no	—
119	C₂³	—	38	4	no	—
120	C₂³	—	38	4	no	—
121	C₂³	—	38	8	no	—
122	C₂³	—	38	8	no	—
123	C₂³	C₂³×D₁₉	1	1	yes	characteristic
124	D₄	—	38	16	no	—
125	D₄	—	76	16	no	—
126	C₂×C₄	—	2	4	no	—
127	C₂×C₄	—	2	4	no	—
128	C₂×C₄	—	2	2	no	—
129	C₂×C₄	—	2	4	no	—
130	C₂×C₄	—	38	4	no	—
131	C₂×C₄	—	38	8	no	—
132	C₂×C₄	—	76	16	no	—
133	C₂×C₄	C₂×C₄×D₁₉	1	4	yes	—
134	C₂×C₄	C₂×C₄×D₁₉	1	2	yes	—
135	C₂×C₄	C₂×D₇₆	1	4	yes	—
136	C₂×C₄	C₂×D₇₆	1	2	yes	—
137	C₂×C₄	#64541	1	2	yes	—
138	C₂²	—	38	8	no	—
139	C₂²	—	38	16	no	—
140	C₂²	—	76	4	no	—
141	C₂²	—	76	4	no	—
142	C₂²	—	76	8	no	—
143	C₂²	C₂²×C₄×D₁₉	1	1	yes	characteristic
144	C₂²	C₂²×D₇₆	1	1	yes	characteristic
145	C₂²	C₂×#64541	1	1	yes	characteristic
146	C₂²	#10597435	1	4	yes	—
147	C₄	—	2	4	no	—
148	C₄	—	2	4	no	—
149	C₄	—	4	2	no	—
150	C₄	—	76	4	no	—
151	C₄	C₄×D₇₆	1	4	yes	—
152	C₂	—	76	8	no	—
153	C₂	C₂×C₄×D₇₆	1	1	yes	characteristic
154	C₂	#11927018	1	2	yes	—
155	C₂	#11927113	1	2	yes	—
156	C₂	#11927149	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×#10597320

C₂

yes

maximal, characteristic

C₂×C₄×D₇₆

C₂

yes

maximal, complemented

#11926446

C₂

yes

maximal, complemented

#11926422

C₂

yes

maximal, complemented

#11926410

C₂

yes

maximal, characteristic, complemented

C₁₉×#376

C₂

yes

maximal, characteristic, complemented

C₂²×D₇₆

C₂²

yes

—

C₂²×D₇₆

C₂²

yes

—

C₂²×C₄×D₁₉

C₂²

yes

—

C₂×C₄²×C₁₉

C₂²

yes

characteristic

C₂×C₄²×C₁₉

C₂²

yes

characteristic

C₂×C₄²×C₁₉

C₂²

yes

characteristic

C₂×(C₂×D₁₉)⋊C₄

C₂²

yes

—

C₂×(C₂×D₁₉)⋊C₄

C₂²

yes

—

C₂×C₄⋊Dic₁₉

C₂²

yes

—

#10597320

C₄

yes

complemented

C₄×D₇₆

—

C₁₉×#95

C₂²

yes

—

C₁₉⋊#95

C₂²

yes

—

C₂³×D₁₉

C₂³

yes

—

C₂²×C₄×C₁₉

C₂³

yes

—

C₂²×C₄×C₁₉

C₂³

yes

—

C₂²×C₄×C₁₉

C₂³

yes

—

C₂²×C₄×C₁₉

C₂³

yes

characteristic

C₂²×Dic₁₉

C₂³

yes

—

C₂×D₇₆

—

C₂×D₇₆

—

C₂×D₇₆

—

C₂×D₇₆

C₂×C₄

yes

complemented

C₂×D₇₆

C₂×C₄

yes

complemented

C₂×C₄×D₁₉

—

C₂×C₄×D₁₉

—

C₄²×C₁₉

—

C₄²×C₁₉

C₂×C₄

yes

complemented

C₄²×C₁₉

D₄

yes

complemented

(C₂×D₁₉)⋊C₄

—

(C₂×D₁₉)⋊C₄

—

C₄⋊Dic₁₉

—

C₂³×C₁₉

C₂⁴

yes

characteristic

C₂²×D₁₉

—

C₂²×D₁₉

—

C₂²×D₁₉

—

C₂²×D₁₉

—

C₂²×D₁₉

C₂²×C₄

yes

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

C₂²×C₄

yes

—

C₂×C₄×C₁₉

C₂²×C₄

yes

—

C₂×C₄×C₁₉

C₂×D₄

yes

—

C₂×C₄×C₁₉

C₂×D₄

yes

—

C₂×C₄×C₁₉

#41

yes

—

C₂×Dic₁₉

—

C₂×Dic₁₉

—

D₇₆

—

D₇₆

—

C₄×D₁₉

—

#2328

—

maximal, Sylow

C₂²×C₁₉

C₂³×C₄

yes

characteristic

C₂²×C₁₉

C₂²×D₄

yes

characteristic

C₂²×C₁₉

C₂×#41

yes

characteristic

C₂²×C₁₉

H(5,𝔽₂)

yes

—

C₂×D₁₉

—

C₂×D₁₉

—

C₂×D₁₉

—

C₂×D₁₉

—

C₂×D₁₉

—

C₄×C₁₉

—

C₄×C₁₉

—

C₄×C₁₉

—

C₄×C₁₉

C₄×D₄

yes

—

Dic₁₉

—

C₂×#127

—

C₂×C₄×D₄

—

—

—

—

D₁₉

yes

characteristic, complemented

C₂×C₁₉

C₂×C₄×D₄

yes

characteristic

C₂×C₁₉

#518

yes

—

C₂×C₁₉

#535

yes

—

C₂×C₁₉

#540

yes

—

D₁₉

—

C₂²×D₄

—

C₂²×D₄

—

C₂³×C₄

—

#127

—

C₄×D₄

—

C₂×C₄⋊C₄

—

C₂×C₂²⋊C₄

—

C₂×C₂²⋊C₄

—

C₂×C₄²

C₂×D₁₉

yes

characteristic

C₂×C₄²

C₂×D₁₉

yes

characteristic

C₂×C₄²

C₂×D₁₉

yes

characteristic

#95

—

#95

C₂×D₁₉

yes

—

C₁₉

#2328

yes

characteristic, complemented, Sylow

C₂⁴

—

100

C₂×D₄

—

101

C₂×D₄

—

102

C₂×D₄

—

103

C₂×D₄

—

104

C₂×D₄

—

105

C₂²×C₄

—

106

C₂²×C₄

—

107

C₂²×C₄

—

108

C₂²×C₄

C₂²×D₁₉

yes

—

109

C₂²×C₄

C₂²×D₁₉

yes

—

110

C₂²×C₄

C₂²×D₁₉

yes

—

111

C₂²×C₄

C₂²×D₁₉

yes

characteristic

112

C₄⋊C₄

—

113

C₂²⋊C₄

—

114

C₂²⋊C₄

—

115

C₄²

—

116

C₄²

C₄×D₁₉

yes

complemented

117

C₄²

D₇₆

yes

complemented

118

C₂³

—

119

C₂³

—

120

C₂³

—

121

C₂³

—

122

C₂³

—

123

C₂³

C₂³×D₁₉

yes

characteristic

124

D₄

—

125

D₄

—

126

C₂×C₄

—

127

C₂×C₄

—

128

C₂×C₄

—

129

C₂×C₄

—

130

C₂×C₄

—

131

C₂×C₄

—

132

C₂×C₄

—

133

C₂×C₄

C₂×C₄×D₁₉

yes

—

134

C₂×C₄

C₂×C₄×D₁₉

yes

—

135

C₂×C₄

C₂×D₇₆

yes

—

136

C₂×C₄

C₂×D₇₆

yes

—

137

C₂×C₄

#64541

yes

—

138

C₂²

—

139

C₂²

—

140

C₂²

—

141

C₂²

—

142

C₂²

—

143

C₂²

C₂²×C₄×D₁₉

yes

characteristic

144

C₂²

C₂²×D₇₆

yes

characteristic

145

C₂²

C₂×#64541

yes

characteristic

146

C₂²

#10597435

yes

—

147

C₄

—

148

C₄

—

149

C₄

—

150

C₄

—

151

C₄

C₄×D₇₆

yes

—

152

C₂

—

153

C₂

C₂×C₄×D₇₆

yes

characteristic

154

C₂

#11927018

yes

—

155

C₂

#11927113

yes

—

156

C₂

#11927149

yes

—

	subgroup	G/H
center, Frattini	C₂³	C₂³×D₁₉
commutator	C₂²×C₁₉	C₂³×C₄
Fitting	C₁₉×#376	C₂
socle, cosocle	C₂³×C₁₉	C₂⁴
prime radical	C₂×#10597320	C₂
hypercenter	#376	D₁₉
hypocenter	C₁₉	#2328
LCS	G ▷ C₂²×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂³ ◁ #376

subgroup

G/H

center, Frattini

C₂³

C₂³×D₁₉

commutator

C₂²×C₁₉

C₂³×C₄

Fitting

C₁₉×#376

C₂

socle, cosocle

C₂³×C₁₉

C₂⁴

C₂

D₁₉

C₁₉

G ▷ C₂²×C₁₉ ▷ C₁₉

C₁ ◁ C₂³ ◁ #376

N	H ≅ G/N	type
2. C₂×C₄×D₇₆	C₂	semidirect
3. #11926446	C₂	semidirect
4. #11926422	C₂	semidirect
5. #11926410	C₂	semidirect
6. C₁₉×#376	C₂	semidirect
16. #10597320	C₄	semidirect
29. C₂×D₇₆	C₂×C₄	semidirect
30. C₂×D₇₆	C₂×C₄	semidirect
34. C₄²×C₁₉	C₂×C₄	semidirect
35. C₄²×C₁₉	D₄	semidirect
79. #376	D₁₉	semidirect
98. C₁₉	#2328	semidirect
116. C₄²	C₄×D₁₉	semidirect
117. C₄²	D₇₆	semidirect

H ≅ G/N

type

2. C₂×C₄×D₇₆

C₂

semidirect

3. #11926446

C₂

semidirect

4. #11926422

C₂

semidirect

5. #11926410

C₂

semidirect

6. C₁₉×#376

C₂

semidirect

16. #10597320

C₄

semidirect

29. C₂×D₇₆

C₂×C₄

semidirect

30. C₂×D₇₆

C₂×C₄

semidirect

34. C₄²×C₁₉

C₂×C₄

semidirect

35. C₄²×C₁₉

D₄

semidirect

79. #376

D₁₉

semidirect

98. C₁₉

#2328

semidirect

116. C₄²

C₄×D₁₉

semidirect

117. C₄²

D₇₆

semidirect

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
C₂×#10597320	2
C₂×C₄×D₇₆	2
#11926446	2
#11926422	2
#11926410	2
C₁₉×#376	2
#2328	19

subgroup

index

C₂×C₄×D₇₆

C₁₉×#376

Subgroups — #14566360

Conjugacy classes of subgroups

Complements

Maximal subgroups