Group #14563618 — subgroups

Subgroups — #14563618

Order 2432.

312 conjugacy classes of subgroups; only the 101 normal subgroups are shown.

normal subgroups only

This group has 312 conjugacy classes of subgroups — too many to draw. Only its 101 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×#10597318	C₂	1	1	yes	maximal, characteristic
2	C₂×Dic₁₉⋊C₈	C₂	1	2	yes	maximal, complemented
3	C₂×(C₂×D₁₉)⋊C₈	C₂	1	2	yes	maximal
4	#11926299	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₉×#336	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂²×C₄×D₁₉	C₂²	1	1	yes	characteristic
7	C₂²×C₈×C₁₉	C₂²	1	2	yes	—
8	C₂×C₄²×C₁₉	C₂²	1	1	yes	characteristic
9	C₂×(C₂×D₁₉)⋊C₄	C₄	1	2	yes	—
10	C₂×Dic₁₉⋊C₄	C₄	1	2	yes	—
11	C₂×C₄×Dic₁₉	C₂²	1	1	yes	characteristic
12	C₂²×C₁₉⋊C₈	C₂²	1	2	yes	—
13	#10597318	—	2	4	no	—
14	(C₂×D₁₉)⋊C₈	—	2	4	no	—
15	Dic₁₉⋊C₈	—	2	4	no	—
16	C₂³×D₁₉	C₂×C₄	1	1	yes	characteristic
17	C₂²×C₄×C₁₉	C₂×C₄	1	2	yes	—
18	C₂²×C₄×C₁₉	C₂³	1	1	yes	characteristic
19	C₂²×Dic₁₉	C₂×C₄	1	2	yes	—
20	C₂²×Dic₁₉	C₂×C₄	1	1	yes	characteristic
21	C₂×C₄×D₁₉	—	2	2	no	—
22	C₂×C₄×D₁₉	—	2	2	no	—
23	C₂×C₄×D₁₉	D₄	1	2	yes	—
24	C₂×C₄×D₁₉	Q₈	1	2	yes	—
25	C₂×C₈×C₁₉	—	2	2	no	—
26	C₂×C₈×C₁₉	—	2	2	no	—
27	C₂×C₈×C₁₉	—	2	2	no	—
28	C₄²×C₁₉	—	2	2	no	—
29	(C₂×D₁₉)⋊C₄	—	2	4	no	—
30	Dic₁₉⋊C₄	—	2	4	no	—
31	C₄×Dic₁₉	D₄	1	4	yes	—
32	C₂×C₁₉⋊C₈	—	2	2	no	—
33	C₂×C₁₉⋊C₈	—	2	2	no	—
34	C₂×C₁₉⋊C₈	—	2	2	no	—
35	C₂³×C₁₉	C₂²×C₄	1	1	yes	characteristic
36	C₂²×D₁₉	—	2	1	no	—
37	C₂²×D₁₉	—	2	1	no	—
38	C₂²×D₁₉	—	2	2	no	—
39	C₂²×D₁₉	—	2	2	no	—
40	C₂²×D₁₉	C₄⋊C₄	1	2	yes	—
41	C₂×C₄×C₁₉	—	2	2	no	—
42	C₂×C₄×C₁₉	—	2	2	no	—
43	C₂×C₄×C₁₉	—	2	2	no	—
44	C₂×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
45	C₂×C₄×C₁₉	C₂×D₄	1	2	yes	—
46	C₂×C₄×C₁₉	C₂×Q₈	1	1	yes	characteristic
47	C₂×C₄×C₁₉	#41	1	2	yes	—
48	C₂×Dic₁₉	—	2	1	no	—
49	C₂×Dic₁₉	—	2	1	no	—
50	C₂×Dic₁₉	—	2	2	no	—
51	C₂×Dic₁₉	—	2	2	no	—
52	C₂×Dic₁₉	C₂²⋊C₄	1	4	yes	—
53	C₂×Dic₁₉	C₄⋊C₄	1	2	yes	—
54	C₄×D₁₉	—	2	4	no	—
55	C₄×D₁₉	—	2	4	no	—
56	C₈×C₁₉	—	4	2	no	—
57	C₁₉⋊C₈	—	4	2	no	—
58	#1798	—	19	1	no	maximal, Sylow
59	C₂²×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
60	C₂²×C₁₉	C₂×C₄⋊C₄	1	1	yes	characteristic
61	C₂²×C₁₉	#117	1	1	yes	characteristic
62	C₂²×C₁₉	#131	1	2	yes	—
63	C₂²×C₁₉	#131	1	2	yes	—
64	C₂×D₁₉	—	2	2	no	—
65	C₂×D₁₉	—	2	4	no	—
66	C₂×D₁₉	—	4	2	no	—
67	C₂×D₁₉	—	4	1	no	—
68	C₂×D₁₉	—	4	1	no	—
69	C₄×C₁₉	—	4	2	no	—
70	C₄×C₁₉	#121	1	2	yes	—
71	C₄×C₁₉	C₂²⋊Q₈	1	2	yes	—
72	Dic₁₉	—	2	2	no	—
73	Dic₁₉	—	2	4	no	—
74	C₂×#117	—	19	1	no	—
75	C₂×C₄⋊C₈	—	19	2	no	—
76	C₂×C₂²⋊C₈	—	19	2	no	—
77	#336	—	19	1	no	—
78	#336	D₁₉	1	1	yes	characteristic, complemented
79	C₂×C₁₉	#380	1	1	yes	characteristic
80	C₂×C₁₉	#408	1	2	yes	—
81	C₂×C₁₉	#424	1	2	yes	—
82	C₂×C₁₉	#433	1	1	yes	characteristic
83	C₂×C₁₉	#433	1	1	yes	characteristic
84	D₁₉	—	4	2	no	—
85	C₂³×C₄	—	19	1	no	—
86	C₂²×C₈	—	19	2	no	—
87	C₂²×C₈	C₂×D₁₉	1	2	yes	—
88	#117	—	38	4	no	—
89	C₂×C₄⋊C₄	—	19	2	no	—
90	C₂×C₂²⋊C₄	—	19	2	no	—
91	C₂×C₄²	—	19	1	no	—
92	C₂×C₄²	C₂×D₁₉	1	1	yes	characteristic
93	C₄⋊C₈	—	38	4	no	—
94	C₂²⋊C₈	—	38	4	no	—
95	C₁₉	#1798	1	1	yes	characteristic, complemented, Sylow
96	C₂⁴	—	19	1	no	—
97	C₂²×C₄	—	19	2	no	—
98	C₂²×C₄	—	19	1	no	—
99	C₂²×C₄	—	19	2	no	—
100	C₂²×C₄	—	19	2	no	—
101	C₂²×C₄	—	38	2	no	—
102	C₂²×C₄	—	38	2	no	—
103	C₂²×C₄	C₄×D₁₉	1	2	yes	—
104	C₂²×C₄	C₂²×D₁₉	1	1	yes	characteristic
105	C₂×C₈	—	2	2	no	—
106	C₂×C₈	—	2	2	no	—
107	C₂×C₈	—	2	2	no	—
108	C₂×C₈	—	38	2	no	—
109	C₂×C₈	—	38	2	no	—
110	C₂×C₈	—	38	2	no	—
111	C₄⋊C₄	—	38	4	no	—
112	C₂²⋊C₄	—	38	4	no	—
113	C₄²	—	2	2	no	—
114	C₄²	—	19	4	no	—
115	C₂³	—	19	2	no	—
116	C₂³	—	38	1	no	—
117	C₂³	—	38	1	no	—
118	C₂³	—	38	2	no	—
119	C₂³	—	38	2	no	—
120	C₂³	C₂×C₄×D₁₉	1	1	yes	characteristic
121	C₂×C₄	—	2	2	no	—
122	C₂×C₄	—	2	2	no	—
123	C₂×C₄	—	2	2	no	—
124	C₂×C₄	—	19	4	no	—
125	C₂×C₄	—	19	2	no	—
126	C₂×C₄	—	38	1	no	—
127	C₂×C₄	—	38	1	no	—
128	C₂×C₄	—	38	2	no	—
129	C₂×C₄	—	38	2	no	—
130	C₂×C₄	—	38	4	no	—
131	C₂×C₄	—	38	4	no	—
132	C₂×C₄	#64541	1	2	yes	—
133	C₂×C₄	D₄×D₁₉	1	1	yes	characteristic
134	C₂×C₄	D₄×D₁₉	1	2	yes	—
135	C₂×C₄	Q₈×D₁₉	1	1	yes	characteristic
136	C₈	—	4	2	no	—
137	C₈	—	76	2	no	—
138	C₂²	—	38	4	no	—
139	C₂²	—	38	2	no	—
140	C₂²	—	76	1	no	—
141	C₂²	—	76	1	no	—
142	C₂²	—	76	2	no	—
143	C₂²	#10597318	1	1	yes	characteristic
144	C₂²	C₂²⋊C₄×D₁₉	1	1	yes	characteristic
145	C₂²	C₄⋊C₄×D₁₉	1	1	yes	characteristic
146	C₂²	#10597347	1	2	yes	—
147	C₂²	#10597353	1	2	yes	—
148	C₄	—	4	2	no	—
149	C₄	—	38	2	no	—
150	C₄	—	38	4	no	—
151	C₄	#10597330	1	2	yes	—
152	C₄	#10597342	1	2	yes	—
153	C₂	—	76	2	no	—
154	C₂	#11926403	1	1	yes	characteristic
155	C₂	#11926509	1	2	yes	—
156	C₂	#11926569	1	2	yes	—
157	C₂	#11926603	1	1	yes	characteristic
158	C₂	#11926606	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×#10597318

C₂

yes

maximal, characteristic

C₂×Dic₁₉⋊C₈

C₂

yes

maximal, complemented

C₂×(C₂×D₁₉)⋊C₈

C₂

yes

maximal

#11926299

C₂

yes

maximal, characteristic, complemented

C₁₉×#336

C₂

yes

maximal, characteristic, complemented

C₂²×C₄×D₁₉

C₂²

yes

characteristic

C₂²×C₈×C₁₉

C₂²

yes

—

C₂×C₄²×C₁₉

C₂²

yes

characteristic

C₂×(C₂×D₁₉)⋊C₄

C₄

yes

—

C₂×Dic₁₉⋊C₄

C₄

yes

—

C₂×C₄×Dic₁₉

C₂²

yes

characteristic

C₂²×C₁₉⋊C₈

C₂²

yes

—

#10597318

—

(C₂×D₁₉)⋊C₈

—

Dic₁₉⋊C₈

—

C₂³×D₁₉

C₂×C₄

yes

characteristic

C₂²×C₄×C₁₉

C₂×C₄

yes

—

C₂²×C₄×C₁₉

C₂³

yes

characteristic

C₂²×Dic₁₉

C₂×C₄

yes

—

C₂²×Dic₁₉

C₂×C₄

yes

characteristic

C₂×C₄×D₁₉

—

C₂×C₄×D₁₉

—

C₂×C₄×D₁₉

D₄

yes

—

C₂×C₄×D₁₉

Q₈

yes

—

C₂×C₈×C₁₉

—

C₂×C₈×C₁₉

—

C₂×C₈×C₁₉

—

C₄²×C₁₉

—

(C₂×D₁₉)⋊C₄

—

Dic₁₉⋊C₄

—

C₄×Dic₁₉

D₄

yes

—

C₂×C₁₉⋊C₈

—

C₂×C₁₉⋊C₈

—

C₂×C₁₉⋊C₈

—

C₂³×C₁₉

C₂²×C₄

yes

characteristic

C₂²×D₁₉

—

C₂²×D₁₉

—

C₂²×D₁₉

—

C₂²×D₁₉

—

C₂²×D₁₉

C₄⋊C₄

yes

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

C₂×D₄

yes

characteristic

C₂×C₄×C₁₉

C₂×D₄

yes

—

C₂×C₄×C₁₉

C₂×Q₈

yes

characteristic

C₂×C₄×C₁₉

#41

yes

—

C₂×Dic₁₉

—

C₂×Dic₁₉

—

C₂×Dic₁₉

—

C₂×Dic₁₉

—

C₂×Dic₁₉

C₂²⋊C₄

yes

—

C₂×Dic₁₉

C₄⋊C₄

yes

—

C₄×D₁₉

—

C₄×D₁₉

—

C₈×C₁₉

—

C₁₉⋊C₈

—

#1798

—

maximal, Sylow

C₂²×C₁₉

C₂×C₂²⋊C₄

yes

characteristic

C₂²×C₁₉

C₂×C₄⋊C₄

yes

C₂²×C₁₉

yes

C₂²×C₁₉

yes

—

C₂²×C₁₉

#131

yes

—

C₂×D₁₉

—

C₂×D₁₉

—

C₂×D₁₉

—

C₂×D₁₉

—

C₂×D₁₉

—

C₄×C₁₉

—

C₄×C₁₉

#121

yes

—

C₄×C₁₉

C₂²⋊Q₈

yes

—

Dic₁₉

—

Dic₁₉

—

C₂×#117

—

C₂×C₄⋊C₈

—

C₂×C₂²⋊C₈

—

#336

—

#336

D₁₉

yes

characteristic, complemented

C₂×C₁₉

#380

yes

characteristic

C₂×C₁₉

#408

yes

—

C₂×C₁₉

#424

yes

—

C₂×C₁₉

yes

C₂×C₁₉

yes

D₁₉

—

C₂³×C₄

—

C₂²×C₈

—

C₂²×C₈

C₂×D₁₉

yes

—

#117

—

C₂×C₄⋊C₄

—

C₂×C₂²⋊C₄

—

C₂×C₄²

—

C₂×C₄²

C₂×D₁₉

yes

characteristic

C₄⋊C₈

—

C₂²⋊C₈

—

C₁₉

#1798

yes

characteristic, complemented, Sylow

C₂⁴

—

C₂²×C₄

—

C₂²×C₄

—

C₂²×C₄

—

100

C₂²×C₄

—

101

C₂²×C₄

—

102

C₂²×C₄

—

103

C₂²×C₄

C₄×D₁₉

yes

—

104

C₂²×C₄

C₂²×D₁₉

yes

characteristic

105

C₂×C₈

—

106

C₂×C₈

—

107

C₂×C₈

—

108

C₂×C₈

—

109

C₂×C₈

—

110

C₂×C₈

—

111

C₄⋊C₄

—

112

C₂²⋊C₄

—

113

C₄²

—

114

C₄²

—

115

C₂³

—

116

C₂³

—

117

C₂³

—

118

C₂³

—

119

C₂³

—

120

C₂³

C₂×C₄×D₁₉

yes

characteristic

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

—

130

C₂×C₄

—

131

C₂×C₄

—

132

C₂×C₄

#64541

yes

—

133

C₂×C₄

D₄×D₁₉

yes

characteristic

134

C₂×C₄

D₄×D₁₉

yes

—

135

C₂×C₄

Q₈×D₁₉

yes

characteristic

136

C₈

—

137

C₈

—

138

C₂²

—

139

C₂²

—

140

C₂²

—

141

C₂²

—

142

C₂²

—

143

C₂²

#10597318

yes

characteristic

144

C₂²

C₂²⋊C₄×D₁₉

yes

characteristic

145

C₂²

C₄⋊C₄×D₁₉

yes

characteristic

146

C₂²

#10597347

yes

—

147

C₂²

#10597353

yes

—

148

C₄

—

149

C₄

—

150

C₄

—

151

C₄

#10597330

yes

—

152

C₄

#10597342

yes

—

153

C₂

—

154

C₂

#11926403

yes

characteristic

155

C₂

#11926509

yes

—

156

C₂

#11926569

yes

—

157

C₂

#11926603

yes

characteristic

158

C₂

#11926606

yes

characteristic

	subgroup	G/H
center, Frattini	C₂²×C₄	C₂²×D₁₉
commutator, socle	C₂³×C₁₉	C₂²×C₄
Fitting	C₁₉×#336	C₂
prime radical	C₂³×D₁₉	C₂×C₄
cosocle	C₂²×C₄×C₁₉	C₂³
hypercenter	#336	D₁₉
hypocenter	C₁₉	#1798
LCS	G ▷ C₂³×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂²×C₄ ◁ #336

subgroup

G/H

center, Frattini

C₂²×C₄

C₂²×D₁₉

commutator, socle

C₂³×C₁₉

C₂²×C₄

Fitting

C₁₉×#336

C₂

prime radical

C₂³×D₁₉

C₂×C₄

cosocle

C₂²×C₄×C₁₉

C₂³

D₁₉

C₁₉

G ▷ C₂³×C₁₉ ▷ C₁₉

C₁ ◁ C₂²×C₄ ◁ #336

N	H ≅ G/N	type
2. C₂×Dic₁₉⋊C₈	C₂	semidirect
4. #11926299	C₂	semidirect
5. C₁₉×#336	C₂	semidirect
78. #336	D₁₉	semidirect
95. C₁₉	#1798	semidirect

H ≅ G/N

type

2. C₂×Dic₁₉⋊C₈

C₂

semidirect

4. #11926299

C₂

semidirect

5. C₁₉×#336

C₂

semidirect

78. #336

D₁₉

semidirect

95. C₁₉

#1798

semidirect

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

subgroup	index
C₂×#10597318	2
C₂×Dic₁₉⋊C₈	2
C₂×(C₂×D₁₉)⋊C₈	2
#11926299	2
C₁₉×#336	2
#1798	19

subgroup

index

C₂×#10597318

C₂×Dic₁₉⋊C₈

C₂×(C₂×D₁₉)⋊C₈

#11926299

C₁₉×#336

#1798

Subgroups — #14563618

Conjugacy classes of subgroups

Complements

Maximal subgroups