Group #14574373 — subgroups

Subgroups — #14574373

Order 2432.

446 conjugacy classes of subgroups; only the 133 normal subgroups are shown.

normal subgroups only

This group has 446 conjugacy classes of subgroups — too many to draw. Only its 133 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	#11927094	C₂	1	2	yes	maximal, complemented
2	#11926942	C₂	1	1	yes	maximal, characteristic, complemented
3	#11926921	C₂	1	1	yes	maximal, characteristic, complemented
4	#11926891	C₂	1	2	yes	maximal, complemented
5	#11926797	C₂	1	4	yes	maximal, complemented
6	#11926657	C₂	1	4	yes	maximal, complemented
7	C₄×M₁₆×C₁₉	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×#64541	—	2	2	no	—
9	C₂×M₁₆×C₁₉	C₂²	1	2	yes	—
10	C₂×C₄²×C₁₉	C₂²	1	1	yes	characteristic
11	#10597376	—	2	2	no	—
12	#10597376	C₂²	1	4	yes	—
13	C₂×D₁₅₂	C₂²	1	4	yes	—
14	#10597321	—	2	2	no	—
15	#10597320	C₂²	1	2	yes	—
16	C₄×D₇₆	—	2	2	no	—
17	C₄×D₇₆	C₂²	1	4	yes	—
18	#10597315	C₂²	1	2	yes	—
19	C₁₉×#97	C₂²	1	2	yes	—
20	C₄×C₈×C₁₉	C₂²	1	1	yes	characteristic
21	C₄×C₈×C₁₉	C₂²	1	1	yes	characteristic
22	#10597278	C₂²	1	8	yes	—
23	#10597274	C₂²	1	4	yes	—
24	C₂²×C₄×C₁₉	D₄	1	2	yes	—
25	C₂²×C₄×C₁₉	C₂³	1	1	yes	characteristic
26	C₂×C₂²⋊D₁₉	—	2	4	no	—
27	#64541	—	4	8	no	—
28	C₂×D₇₆	—	2	2	no	—
29	C₂×D₇₆	—	2	2	no	—
30	C₂×D₇₆	C₂³	1	4	yes	—
31	C₂×C₄×D₁₉	—	2	4	no	—
32	C₂×Dic₃₈	—	2	2	no	—
33	M₁₆×C₁₉	—	2	4	no	—
34	C₂×C₈×C₁₉	C₂³	1	2	yes	—
35	C₂×C₈×C₁₉	C₂³	1	2	yes	—
36	C₄²×C₁₉	D₄	1	2	yes	—
37	C₄²×C₁₉	C₂³	1	1	yes	characteristic
38	C₄²×C₁₉	C₂³	1	1	yes	characteristic
39	(C₂×D₁₉)⋊C₄	—	2	4	no	—
40	(C₂×D₁₉)⋊C₄	—	2	4	no	—
41	C₄⋊Dic₁₉	—	2	2	no	—
42	C₄⋊Dic₁₉	C₂³	1	4	yes	—
43	D₁₅₂	—	2	8	no	—
44	C₂³×C₁₉	C₂×D₄	1	1	yes	characteristic
45	C₂²×D₁₉	—	2	4	no	—
46	C₂×C₄×C₁₉	—	2	4	no	—
47	C₂×C₄×C₁₉	—	2	2	no	—
48	C₂×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
49	C₂×C₄×C₁₉	C₂×D₄	1	2	yes	—
50	C₂×C₄×C₁₉	C₂×D₄	1	2	yes	—
51	C₂×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
52	C₂²⋊D₁₉	—	4	8	no	—
53	C₂×Dic₁₉	—	2	4	no	—
54	D₇₆	—	2	8	no	—
55	D₇₆	—	4	4	no	—
56	D₇₆	—	4	4	no	—
57	C₄×D₁₉	—	4	8	no	—
58	Dic₃₈	—	4	4	no	—
59	C₈×C₁₉	—	2	2	no	—
60	C₈×C₁₉	#41	1	4	yes	complemented
61	#3184	—	19	1	no	maximal, Sylow
62	C₂²×C₁₉	—	2	1	no	—
63	C₂²×C₁₉	—	2	2	no	—
64	C₂²×C₁₉	C₂²×D₄	1	1	yes	characteristic
65	C₂×D₁₉	—	4	4	no	—
66	C₂×D₁₉	—	4	4	no	—
67	C₂×D₁₉	—	4	4	no	—
68	C₄×C₁₉	—	2	1	no	—
69	C₄×C₁₉	—	2	2	no	—
70	C₄×C₁₉	AGL(1,ℤ/8)	1	4	yes	—
71	C₄×C₁₉	C₂×#41	1	2	yes	—
72	Dic₁₉	—	4	4	no	—
73	#532	—	19	2	no	—
74	#498	—	19	1	no	—
75	#493	—	19	1	no	—
76	#486	—	19	2	no	—
77	#469	—	19	4	no	—
78	#442	—	19	4	no	—
79	C₄×M₁₆	D₁₉	1	1	yes	characteristic, complemented
80	C₂×C₁₉	—	4	1	no	—
81	C₂×C₁₉	#532	1	1	yes	characteristic
82	C₂×C₁₉	C₂×AGL(1,ℤ/8)	1	2	yes	—
83	D₁₉	—	8	4	no	—
84	C₂×#41	—	38	2	no	—
85	C₂×D₈	—	19	4	no	—
86	C₂×M₁₆	C₂×D₁₉	1	2	yes	—
87	C₄⋊Q₈	—	19	2	no	—
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	C₂×D₁₉	1	1	yes	characteristic
95	#106	—	19	4	no	—
96	#102	—	19	8	no	—
97	#97	C₂×D₁₉	1	2	yes	—
98	C₄×C₈	C₂×D₁₉	1	1	yes	characteristic
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	—	38	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	—	38	4	no	—
108	C₂²×C₄	D₇₆	1	2	yes	—
109	C₂²×C₄	C₂²×D₁₉	1	1	yes	characteristic
110	D₈	—	38	8	no	—
111	M₁₆	—	2	4	no	—
112	C₂×C₈	C₂²×D₁₉	1	2	yes	—
113	C₂×C₈	C₂²×D₁₉	1	2	yes	—
114	C₄⋊C₄	—	19	4	no	—
115	C₄⋊C₄	—	38	2	no	—
116	C₂²⋊C₄	—	38	4	no	—
117	C₂²⋊C₄	—	38	4	no	—
118	C₄²	D₇₆	1	2	yes	—
119	C₄²	C₂²×D₁₉	1	1	yes	characteristic
120	C₄²	C₂²×D₁₉	1	1	yes	characteristic
121	C₂³	—	38	4	no	—
122	C₂³	C₂×D₇₆	1	1	yes	characteristic
123	Q₈	—	76	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	2	no	—
129	C₂×C₄	—	2	4	no	—
130	C₂×C₄	—	38	4	no	—
131	C₂×C₄	—	76	8	no	—
132	C₂×C₄	C₂×D₇₆	1	1	yes	characteristic
133	C₂×C₄	C₂×D₇₆	1	2	yes	—
134	C₂×C₄	C₂×D₇₆	1	2	yes	—
135	C₂×C₄	C₂³×D₁₉	1	1	yes	characteristic
136	C₈	—	2	2	no	—
137	C₈	#64541	1	4	yes	complemented
138	C₂²	—	2	2	no	—
139	C₂²	—	2	1	no	—
140	C₂²	—	76	4	no	—
141	C₂²	—	76	4	no	—
142	C₂²	—	76	4	no	—
143	C₂²	C₂²×D₇₆	1	1	yes	characteristic
144	C₄	—	2	2	no	—
145	C₄	—	2	1	no	—
146	C₄	—	76	4	no	—
147	C₄	#10597354	1	4	yes	—
148	C₄	C₂×#64541	1	2	yes	—
149	C₂	—	4	1	no	—
150	C₂	—	152	4	no	—
151	C₂	#11927094	1	1	yes	characteristic
152	C₂	C₂×#10597354	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

#11927094

C₂

yes

maximal, complemented

#11926942

C₂

yes

maximal, characteristic, complemented

#11926921

C₂

yes

maximal, characteristic, complemented

#11926891

C₂

yes

maximal, complemented

#11926797

C₂

yes

maximal, complemented

#11926657

C₂

yes

maximal, complemented

C₄×M₁₆×C₁₉

C₂

yes

maximal, characteristic, complemented

C₂×#64541

—

C₂×M₁₆×C₁₉

C₂²

yes

—

C₂×C₄²×C₁₉

C₂²

yes

characteristic

#10597376

—

#10597376

C₂²

yes

—

C₂×D₁₅₂

C₂²

yes

—

#10597321

—

#10597320

C₂²

yes

—

C₄×D₇₆

—

C₄×D₇₆

C₂²

yes

—

#10597315

C₂²

yes

—

C₁₉×#97

C₂²

yes

—

C₄×C₈×C₁₉

C₂²

yes

characteristic

C₄×C₈×C₁₉

C₂²

yes

characteristic

#10597278

C₂²

yes

—

#10597274

C₂²

yes

—

C₂²×C₄×C₁₉

D₄

yes

—

C₂²×C₄×C₁₉

C₂³

yes

characteristic

C₂×C₂²⋊D₁₉

—

#64541

—

C₂×D₇₆

—

C₂×D₇₆

—

C₂×D₇₆

C₂³

yes

—

C₂×C₄×D₁₉

—

C₂×Dic₃₈

—

M₁₆×C₁₉

—

C₂×C₈×C₁₉

C₂³

yes

—

C₂×C₈×C₁₉

C₂³

yes

—

C₄²×C₁₉

D₄

yes

—

C₄²×C₁₉

C₂³

yes

characteristic

C₄²×C₁₉

C₂³

yes

characteristic

(C₂×D₁₉)⋊C₄

—

(C₂×D₁₉)⋊C₄

—

C₄⋊Dic₁₉

—

C₄⋊Dic₁₉

C₂³

yes

—

D₁₅₂

—

C₂³×C₁₉

C₂×D₄

yes

characteristic

C₂²×D₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

C₂×D₄

yes

characteristic

C₂×C₄×C₁₉

C₂×D₄

yes

—

C₂×C₄×C₁₉

C₂×D₄

yes

—

C₂×C₄×C₁₉

C₂⁴

yes

characteristic

C₂²⋊D₁₉

—

C₂×Dic₁₉

—

D₇₆

—

D₇₆

—

D₇₆

—

C₄×D₁₉

—

Dic₃₈

—

C₈×C₁₉

—

C₈×C₁₉

yes

—

C₂²×C₁₉

—

C₂²×C₁₉

—

C₂²×C₁₉

C₂²×D₄

yes

characteristic

C₂×D₁₉

—

C₂×D₁₉

—

C₂×D₁₉

—

C₄×C₁₉

—

C₄×C₁₉

—

C₄×C₁₉

AGL(1,ℤ/8)

yes

—

C₄×C₁₉

C₂×#41

yes

—

Dic₁₉

—

—

—

—

—

—

—

C₄×M₁₆

D₁₉

yes

characteristic, complemented

C₂×C₁₉

—

C₂×C₁₉

#532

yes

characteristic

C₂×C₁₉

C₂×AGL(1,ℤ/8)

yes

—

D₁₉

—

C₂×#41

—

C₂×D₈

—

C₂×M₁₆

C₂×D₁₉

yes

—

C₄⋊Q₈

—

—

—

—

—

C₄×D₄

—

C₄×D₄

—

C₂×C₄²

C₂×D₁₉

yes

—

—

C₂×D₁₉

yes

—

C₄×C₈

C₂×D₁₉

yes

characteristic

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

D₇₆

yes

—

109

C₂²×C₄

C₂²×D₁₉

yes

characteristic

110

D₈

—

111

M₁₆

—

112

C₂×C₈

C₂²×D₁₉

yes

—

113

C₂×C₈

C₂²×D₁₉

yes

—

114

C₄⋊C₄

—

115

C₄⋊C₄

—

116

C₂²⋊C₄

—

117

C₂²⋊C₄

—

118

C₄²

D₇₆

yes

—

119

C₄²

C₂²×D₁₉

yes

characteristic

120

C₄²

C₂²×D₁₉

yes

characteristic

121

C₂³

—

122

C₂³

C₂×D₇₆

yes

characteristic

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

C₂×D₇₆

yes

characteristic

133

C₂×C₄

C₂×D₇₆

yes

—

134

C₂×C₄

C₂×D₇₆

yes

—

135

C₂×C₄

C₂³×D₁₉

yes

characteristic

136

C₈

—

137

C₈

#64541

yes

complemented

138

C₂²

—

139

C₂²

—

140

C₂²

—

141

C₂²

—

142

C₂²

—

143

C₂²

C₂²×D₇₆

yes

characteristic

144

C₄

—

145

C₄

—

146

C₄

—

147

C₄

#10597354

yes

—

148

C₄

C₂×#64541

yes

—

149

C₂

—

150

C₂

—

152

—

151

C₂

#11927094

yes

characteristic

152

C₂

C₂×#10597354

yes

—

	subgroup	G/H
center	C₂²	C₂²×D₇₆
commutator, cosocle	C₂×C₄×C₁₉	C₂⁴
Frattini	C₂×C₄	C₂³×D₁₉
Fitting	C₄×M₁₆×C₁₉	C₂
socle	C₂²×C₁₉	C₂²×D₄
hypercenter	C₄×M₁₆	D₁₉
hypocenter	C₁₉	#3184
LCS	G ▷ C₂×C₄×C₁₉ ▷ C₂×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂² ◁ C₂×C₄² ◁ C₄×M₁₆

subgroup

G/H

center

C₂²

C₂²×D₇₆

commutator, cosocle

C₂×C₄×C₁₉

C₂⁴

Frattini

C₂×C₄

C₂³×D₁₉

Fitting

C₄×M₁₆×C₁₉

C₂

socle

C₂²×C₁₉

C₂²×D₄

hypercenter

C₄×M₁₆

D₁₉

hypocenter

C₁₉

#3184

LCS

G ▷ C₂×C₄×C₁₉ ▷ C₂×C₁₉ ▷ C₁₉

UCS

C₁ ◁ C₂² ◁ C₂×C₄² ◁ C₄×M₁₆

N	H ≅ G/N	type
1. #11927094	C₂	semidirect
2. #11926942	C₂	semidirect
3. #11926921	C₂	semidirect
4. #11926891	C₂	semidirect
5. #11926797	C₂	semidirect
6. #11926657	C₂	semidirect
7. C₄×M₁₆×C₁₉	C₂	semidirect
60. C₈×C₁₉	#41	semidirect
79. C₄×M₁₆	D₁₉	semidirect
100. C₁₉	#3184	semidirect
137. C₈	#64541	semidirect

H ≅ G/N

type

1. #11927094

C₂

semidirect

2. #11926942

C₂

semidirect

3. #11926921

C₂

semidirect

4. #11926891

C₂

semidirect

5. #11926797

C₂

semidirect

6. #11926657

C₂

semidirect

7. C₄×M₁₆×C₁₉

C₂

semidirect

60. C₈×C₁₉

#41

semidirect

79. C₄×M₁₆

D₁₉

semidirect

100. C₁₉

#3184

semidirect

137. C₈

#64541

semidirect

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

subgroup	index
#11927094	2
#11926942	2
#11926921	2
#11926891	2
#11926797	2
#11926657	2
C₄×M₁₆×C₁₉	2
#3184	19

subgroup

index

C₄×M₁₆×C₁₉

Subgroups — #14574373

Conjugacy classes of subgroups

Complements

Maximal subgroups