Group #14574374 — subgroups

Subgroups — #14574374

Order 2432.

446 conjugacy classes of subgroups; only the 125 normal subgroups are shown.

normal subgroups only

This group has 446 conjugacy classes of subgroups — too many to draw. Only its 125 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	#11927095	C₂	1	2	yes	maximal, complemented
2	#11926921	C₂	1	1	yes	maximal, characteristic, complemented
3	#11926892	C₂	1	2	yes	maximal, complemented
4	#11926798	C₂	1	4	yes	maximal, complemented
5	#11926655	C₂	1	4	yes	maximal, complemented
6	C₄×#64515	C₂	1	1	yes	maximal, characteristic, complemented
7	C₁₉×#498	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×#64545	—	2	2	no	—
9	C₁₉×C₄⋊Q₈	C₂²	1	2	yes	—
10	#10597393	—	2	2	no	—
11	C₂×D₁₅₂	C₂²	1	4	yes	—
12	C₂×#64515	C₂²	1	2	yes	—
13	#10597341	—	2	2	no	—
14	#10597341	C₂²	1	4	yes	—
15	#10597339	—	2	2	no	—
16	#10597339	C₂²	1	4	yes	—
17	#10597320	C₂²	1	2	yes	—
18	C₄²×D₁₉	C₂²	1	1	yes	characteristic
19	C₁₉×#106	C₂²	1	4	yes	—
20	C₄×C₈×C₁₉	C₂²	1	1	yes	characteristic
21	#10597272	C₂²	1	2	yes	—
22	#10597266	C₂²	1	8	yes	—
23	C₄×C₁₉⋊C₈	C₂²	1	1	yes	characteristic
24	C₂×Q₈×C₁₉	—	2	2	no	—
25	#64545	—	4	8	no	—
26	C₂×D₇₆	—	2	4	no	—
27	C₂×D₇₆	—	2	2	no	—
28	C₂×D₇₆	—	2	2	no	—
29	C₂×D₇₆	C₂³	1	4	yes	—
30	C₂×C₄×D₁₉	—	2	4	no	—
31	C₂×C₄×D₁₉	D₄	1	2	yes	—
32	C₂×C₄×D₁₉	C₂³	1	1	yes	characteristic
33	C₂×C₈×C₁₉	C₂³	1	2	yes	—
34	C₄⋊C₄×C₁₉	—	2	2	no	—
35	C₄⋊C₄×C₁₉	C₂³	1	4	yes	—
36	C₄²×C₁₉	C₂³	1	1	yes	characteristic
37	(C₂×D₁₉)⋊C₄	—	2	4	no	—
38	(C₂×D₁₉)⋊C₄	—	2	4	no	—
39	C₄×Dic₁₉	D₄	1	2	yes	—
40	C₄×Dic₁₉	C₂³	1	1	yes	characteristic
41	C₂×C₁₉⋊C₈	C₂³	1	2	yes	—
42	D₁₅₂	—	2	8	no	—
43	#64515	—	2	4	no	—
44	C₂²×D₁₉	—	2	4	no	—
45	C₂²×D₁₉	C₂×D₄	1	1	yes	characteristic
46	Q₈×C₁₉	—	4	4	no	—
47	C₂×C₄×C₁₉	—	2	4	no	—
48	C₂×C₄×C₁₉	C₂×D₄	1	2	yes	—
49	C₂×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
50	C₂×Dic₁₉	C₂×D₄	1	1	yes	characteristic
51	C₂×Dic₁₉	C₂×D₄	1	2	yes	—
52	D₇₆	—	2	8	no	—
53	D₇₆	—	4	8	no	—
54	D₇₆	—	4	4	no	—
55	D₇₆	—	4	4	no	—
56	C₄×D₁₉	—	2	4	no	—
57	C₄×D₁₉	—	2	2	no	—
58	C₄×D₁₉	—	4	8	no	—
59	C₈×C₁₉	#41	1	4	yes	complemented
60	C₁₉⋊C₈	—	2	2	no	—
61	#3184	—	19	1	no	maximal, Sylow
62	C₂²×C₁₉	C₂²×D₄	1	1	yes	characteristic
63	C₂×D₁₉	—	2	1	no	—
64	C₂×D₁₉	—	2	2	no	—
65	C₂×D₁₉	—	4	4	no	—
66	C₂×D₁₉	—	4	4	no	—
67	C₂×D₁₉	—	4	4	no	—
68	C₄×C₁₉	—	4	4	no	—
69	C₄×C₁₉	AGL(1,ℤ/8)	1	4	yes	—
70	C₄×C₁₉	C₂×#41	1	2	yes	—
71	Dic₁₉	—	2	1	no	—
72	Dic₁₉	—	2	2	no	—
73	#532	—	19	2	no	—
74	#498	D₁₉	1	1	yes	characteristic, complemented
75	#493	—	19	1	no	—
76	#486	—	19	2	no	—
77	#469	—	19	4	no	—
78	#442	—	19	4	no	—
79	C₄×M₁₆	—	19	1	no	—
80	C₂×C₁₉	#532	1	1	yes	characteristic
81	C₂×C₁₉	C₂×AGL(1,ℤ/8)	1	2	yes	—
82	D₁₉	—	4	1	no	—
83	D₁₉	—	8	4	no	—
84	C₂×#41	—	38	2	no	—
85	C₂×D₈	—	19	4	no	—
86	C₂×M₁₆	—	19	2	no	—
87	C₄⋊Q₈	C₂×D₁₉	1	2	yes	—
88	#127	—	19	2	no	—
89	#124	—	38	2	no	—
90	#121	—	19	4	no	—
91	#121	—	38	2	no	—
92	C₄×D₄	—	19	4	no	—
93	C₄×D₄	—	38	2	no	—
94	C₂×C₄²	—	19	1	no	—
95	#106	C₂×D₁₉	1	4	yes	—
96	#102	—	19	8	no	—
97	#97	—	19	2	no	—
98	C₄×C₈	—	19	1	no	—
99	C₄×C₈	C₂×D₁₉	1	1	yes	characteristic
100	C₁₉	#3184	1	1	yes	characteristic, complemented, Sylow
101	#41	—	76	8	no	—
102	C₂×Q₈	—	2	2	no	—
103	C₂×D₄	—	19	4	no	—
104	C₂×D₄	—	38	4	no	—
105	C₂×D₄	—	38	2	no	—
106	C₂×D₄	—	38	2	no	—
107	C₂²×C₄	—	19	2	no	—
108	C₂²×C₄	—	19	1	no	—
109	C₂²×C₄	—	38	4	no	—
110	D₈	—	38	8	no	—
111	M₁₆	—	38	4	no	—
112	C₂×C₈	—	19	2	no	—
113	C₂×C₈	C₂²×D₁₉	1	2	yes	—
114	C₄⋊C₄	—	2	2	no	—
115	C₄⋊C₄	C₂²×D₁₉	1	4	yes	—
116	C₂²⋊C₄	—	38	4	no	—
117	C₂²⋊C₄	—	38	4	no	—
118	C₄²	—	19	2	no	—
119	C₄²	—	19	1	no	—
120	C₄²	C₂²×D₁₉	1	1	yes	characteristic
121	C₂³	—	19	1	no	—
122	C₂³	—	38	4	no	—
123	Q₈	—	4	4	no	—
124	D₄	—	38	8	no	—
125	D₄	—	76	8	no	—
126	D₄	—	76	4	no	—
127	D₄	—	76	4	no	—
128	C₂×C₄	—	2	4	no	—
129	C₂×C₄	—	19	1	no	—
130	C₂×C₄	—	19	2	no	—
131	C₂×C₄	—	38	2	no	—
132	C₂×C₄	—	38	4	no	—
133	C₂×C₄	—	76	8	no	—
134	C₂×C₄	D₄×D₁₉	1	2	yes	—
135	C₂×C₄	C₂³×D₁₉	1	1	yes	characteristic
136	C₈	—	38	2	no	—
137	C₈	#64545	1	4	yes	complemented
138	C₂²	—	38	2	no	—
139	C₂²	—	38	1	no	—
140	C₂²	—	76	4	no	—
141	C₂²	—	76	4	no	—
142	C₂²	—	76	4	no	—
143	C₂²	C₂×D₄×D₁₉	1	1	yes	characteristic
144	C₄	—	4	4	no	—
145	C₄	—	38	2	no	—
146	C₄	—	38	1	no	—
147	C₄	#10597360	1	4	yes	—
148	C₄	C₂×#64545	1	2	yes	—
149	C₂	—	76	1	no	—
150	C₂	—	152	4	no	—
151	C₂	#11927095	1	1	yes	characteristic
152	C₂	C₂×#10597360	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

#11927095

C₂

yes

maximal, complemented

#11926921

C₂

yes

maximal, characteristic, complemented

#11926892

C₂

yes

maximal, complemented

#11926798

C₂

yes

maximal, complemented

#11926655

C₂

yes

maximal, complemented

C₄×#64515

C₂

yes

maximal, characteristic, complemented

C₁₉×#498

C₂

yes

maximal, characteristic, complemented

C₂×#64545

—

C₁₉×C₄⋊Q₈

C₂²

yes

—

#10597393

—

C₂×D₁₅₂

C₂²

yes

—

C₂×#64515

C₂²

yes

—

#10597341

—

#10597341

C₂²

yes

—

#10597339

—

#10597339

C₂²

yes

—

#10597320

C₂²

yes

—

C₄²×D₁₉

C₂²

yes

characteristic

C₁₉×#106

C₂²

yes

—

C₄×C₈×C₁₉

C₂²

yes

characteristic

#10597272

C₂²

yes

—

#10597266

C₂²

yes

—

C₄×C₁₉⋊C₈

C₂²

yes

characteristic

C₂×Q₈×C₁₉

—

#64545

—

C₂×D₇₆

—

C₂×D₇₆

—

C₂×D₇₆

—

C₂×D₇₆

C₂³

yes

—

C₂×C₄×D₁₉

—

C₂×C₄×D₁₉

D₄

yes

—

C₂×C₄×D₁₉

C₂³

yes

characteristic

C₂×C₈×C₁₉

C₂³

yes

—

C₄⋊C₄×C₁₉

—

C₄⋊C₄×C₁₉

C₂³

yes

—

C₄²×C₁₉

C₂³

yes

characteristic

(C₂×D₁₉)⋊C₄

—

(C₂×D₁₉)⋊C₄

—

C₄×Dic₁₉

D₄

yes

—

C₄×Dic₁₉

C₂³

yes

characteristic

C₂×C₁₉⋊C₈

C₂³

yes

—

D₁₅₂

—

#64515

—

C₂²×D₁₉

—

C₂²×D₁₉

C₂×D₄

yes

characteristic

Q₈×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

C₂×D₄

yes

—

C₂×C₄×C₁₉

C₂⁴

yes

characteristic

C₂×Dic₁₉

C₂×D₄

yes

characteristic

C₂×Dic₁₉

C₂×D₄

yes

—

D₇₆

—

D₇₆

—

D₇₆

—

D₇₆

—

C₄×D₁₉

—

C₄×D₁₉

—

C₄×D₁₉

—

C₈×C₁₉

#41

yes

complemented

C₁₉⋊C₈

—

#3184

—

maximal, Sylow

C₂²×C₁₉

C₂²×D₄

yes

characteristic

C₂×D₁₉

—

C₂×D₁₉

—

C₂×D₁₉

—

C₂×D₁₉

—

C₂×D₁₉

—

C₄×C₁₉

—

C₄×C₁₉

AGL(1,ℤ/8)

yes

—

C₄×C₁₉

C₂×#41

yes

—

Dic₁₉

—

Dic₁₉

—

#532

—

#498

D₁₉

yes

characteristic, complemented

—

—

—

—

C₄×M₁₆

—

C₂×C₁₉

#532

yes

characteristic

C₂×C₁₉

C₂×AGL(1,ℤ/8)

yes

—

D₁₉

—

D₁₉

—

C₂×#41

—

C₂×D₈

—

C₂×M₁₆

—

C₄⋊Q₈

C₂×D₁₉

yes

—

—

—

—

—

C₄×D₄

—

C₄×D₄

—

C₂×C₄²

—

#106

C₂×D₁₉

yes

—

#102

—

#97

—

C₄×C₈

—

C₄×C₈

C₂×D₁₉

yes

characteristic

100

C₁₉

#3184

yes

characteristic, complemented, Sylow

101

#41

—

102

C₂×Q₈

—

103

C₂×D₄

—

104

C₂×D₄

—

105

C₂×D₄

—

106

C₂×D₄

—

107

C₂²×C₄

—

108

C₂²×C₄

—

109

C₂²×C₄

—

110

D₈

—

111

M₁₆

—

112

C₂×C₈

—

113

C₂×C₈

C₂²×D₁₉

yes

—

114

C₄⋊C₄

—

115

C₄⋊C₄

C₂²×D₁₉

yes

—

116

C₂²⋊C₄

—

117

C₂²⋊C₄

—

118

C₄²

—

119

C₄²

—

120

C₄²

C₂²×D₁₉

yes

characteristic

121

C₂³

—

122

C₂³

—

123

Q₈

—

124

D₄

—

125

D₄

—

126

D₄

—

127

D₄

—

128

C₂×C₄

—

129

C₂×C₄

—

130

C₂×C₄

—

131

C₂×C₄

—

132

C₂×C₄

—

133

C₂×C₄

—

134

C₂×C₄

D₄×D₁₉

yes

—

135

C₂×C₄

C₂³×D₁₉

yes

characteristic

136

C₈

—

137

C₈

#64545

yes

complemented

138

C₂²

—

139

C₂²

—

140

C₂²

—

141

C₂²

—

142

C₂²

—

143

C₂²

C₂×D₄×D₁₉

yes

characteristic

144

C₄

—

145

C₄

—

146

C₄

—

147

C₄

#10597360

yes

—

148

C₄

C₂×#64545

yes

—

149

C₂

—

150

C₂

—

152

—

151

C₂

#11927095

yes

characteristic

152

C₂

C₂×#10597360

yes

—

	subgroup	G/H
center	C₂²	C₂×D₄×D₁₉
commutator, cosocle	C₂×C₄×C₁₉	C₂⁴
Frattini	C₂×C₄	C₂³×D₁₉
Fitting	C₁₉×#498	C₂
socle	C₂²×C₁₉	C₂²×D₄
hypercenter	#498	D₁₉
hypocenter	C₁₉	#3184
LCS	G ▷ C₂×C₄×C₁₉ ▷ C₂×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂² ◁ C₄² ◁ #498

subgroup

G/H

center

C₂²

C₂×D₄×D₁₉

commutator, cosocle

C₂×C₄×C₁₉

C₂⁴

Frattini

C₂×C₄

C₂³×D₁₉

Fitting

C₁₉×#498

C₂

socle

C₂²×C₁₉

C₂²×D₄

D₁₉

C₁₉

G ▷ C₂×C₄×C₁₉ ▷ C₂×C₁₉ ▷ C₁₉

UCS

C₁ ◁ C₂² ◁ C₄² ◁ #498

N	H ≅ G/N	type
1. #11927095	C₂	semidirect
2. #11926921	C₂	semidirect
3. #11926892	C₂	semidirect
4. #11926798	C₂	semidirect
5. #11926655	C₂	semidirect
6. C₄×#64515	C₂	semidirect
7. C₁₉×#498	C₂	semidirect
59. C₈×C₁₉	#41	semidirect
74. #498	D₁₉	semidirect
100. C₁₉	#3184	semidirect
137. C₈	#64545	semidirect

H ≅ G/N

type

1. #11927095

C₂

semidirect

2. #11926921

C₂

semidirect

3. #11926892

C₂

semidirect

4. #11926798

C₂

semidirect

5. #11926655

C₂

semidirect

6. C₄×#64515

C₂

semidirect

7. C₁₉×#498

C₂

semidirect

59. C₈×C₁₉

#41

semidirect

74. #498

D₁₉

semidirect

100. C₁₉

#3184

semidirect

137. C₈

#64545

semidirect

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

subgroup	index
#11927095	2
#11926921	2
#11926892	2
#11926798	2
#11926655	2
C₄×#64515	2
C₁₉×#498	2
#3184	19

subgroup

index

C₁₉×#498

Subgroups — #14574374

Conjugacy classes of subgroups

Complements

Maximal subgroups