Group #14564797 — subgroups

Subgroups — #14564797

Order 2432.

246 conjugacy classes of subgroups; only the 67 normal subgroups are shown.

normal subgroups only

This group has 246 conjugacy classes of subgroups — too many to draw. Only its 67 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	#11927175	C₂	1	1	yes	maximal, characteristic
2	#11926554	C₂	1	2	yes	maximal
3	#11926449	C₂	1	1	yes	maximal, characteristic
4	#11926305	C₂	1	2	yes	maximal
5	C₁₉×#343	C₂	1	1	yes	maximal, characteristic
6	C₂²×Dic₃₈	C₂²	1	1	yes	characteristic
7	C₂×M₁₆×C₁₉	C₂²	1	2	yes	—
8	C₂×C₄⋊C₄×C₁₉	C₂²	1	1	yes	characteristic
9	#10597372	C₂²	1	2	yes	—
10	#10597370	—	2	2	no	—
11	C₂×C₄×Dic₁₉	C₂²	1	1	yes	characteristic
12	#10597336	—	2	2	no	—
13	#10597334	—	2	2	no	—
14	C₁₉⋊#95	—	2	2	no	—
15	#10597273	—	2	2	no	—
16	#10597273	—	2	2	no	—
17	C₂²×C₄×C₁₉	D₄	1	2	yes	—
18	C₂²×C₄×C₁₉	C₂³	1	1	yes	characteristic
19	C₂²×Dic₁₉	—	2	1	no	—
20	C₂²×Dic₁₉	—	2	1	no	—
21	C₂×Dic₃₈	—	2	2	no	—
22	C₂×Dic₃₈	—	2	2	no	—
23	C₂×Dic₃₈	—	2	1	no	—
24	C₂×Dic₃₈	—	2	2	no	—
25	C₂×Dic₃₈	Q₈	1	2	yes	complemented
26	M₁₆×C₁₉	—	2	2	no	—
27	M₁₆×C₁₉	—	2	2	no	—
28	C₂×C₈×C₁₉	—	2	2	no	—
29	C₄⋊C₄×C₁₉	—	2	2	no	—
30	C₂²⋊Dic₁₉	—	2	2	no	—
31	C₄⋊Dic₁₉	—	2	2	no	—
32	C₄⋊Dic₁₉	D₄	1	2	yes	—
33	C₄⋊Dic₁₉	D₄	1	2	yes	—
34	Dic₁₉⋊C₄	—	2	4	no	—
35	C₄×Dic₁₉	—	2	2	no	—
36	C₄×Dic₁₉	—	2	2	no	—
37	C₂³×C₁₉	C₂×D₄	1	1	yes	characteristic
38	C₂×C₄×C₁₉	—	2	2	no	—
39	C₂×C₄×C₁₉	—	4	2	no	—
40	C₂×C₄×C₁₉	C₂×D₄	1	2	yes	—
41	C₂×C₄×C₁₉	C₂×Q₈	1	1	yes	characteristic
42	C₂×C₄×C₁₉	#41	1	2	yes	—
43	C₂×C₄×C₁₉	#41	1	1	yes	characteristic
44	C₂×Dic₁₉	—	2	2	no	—
45	C₂×Dic₁₉	—	2	2	no	—
46	C₂×Dic₁₉	—	2	2	no	—
47	C₂×Dic₁₉	—	2	2	no	—
48	C₂×Dic₁₉	—	4	1	no	—
49	C₂×Dic₁₉	—	4	1	no	—
50	C₂×Dic₁₉	—	4	1	no	—
51	C₂×Dic₁₉	—	4	1	no	—
52	Dic₃₈	—	2	4	no	—
53	Dic₃₈	—	4	2	no	—
54	Dic₃₈	—	8	2	no	—
55	C₈×C₁₉	—	4	2	no	—
56	#2028	—	19	1	no	maximal, Sylow
57	C₂²×C₁₉	—	2	1	no	—
58	C₂²×C₁₉	—	2	1	no	—
59	C₂²×C₁₉	#120	1	1	yes	characteristic
60	C₂²×C₁₉	C₂²⋊Q₈	1	1	yes	characteristic
61	C₂²×C₁₉	#124	1	1	yes	characteristic
62	C₄×C₁₉	—	4	2	no	—
63	C₄×C₁₉	C₂²⋊Q₈	1	2	yes	—
64	C₄×C₁₉	#124	1	2	yes	—
65	Dic₁₉	—	4	2	no	—
66	Dic₁₉	—	4	2	no	—
67	Dic₁₉	—	4	2	no	—
68	Dic₁₉	—	4	2	no	—
69	#544	—	19	1	no	—
70	#419	—	19	2	no	—
71	#391	—	19	1	no	—
72	#343	D₁₉	1	1	yes	characteristic
73	#339	—	19	2	no	—
74	C₂×C₁₉	—	2	1	no	—
75	C₂×C₁₉	—	2	1	no	—
76	C₂×C₁₉	#393	1	1	yes	characteristic
77	C₂×C₁₉	#455	1	1	yes	characteristic
78	C₂×C₁₉	#456	1	1	yes	characteristic
79	C₂²×Q₈	—	19	1	no	—
80	C₂×M₁₆	C₂×D₁₉	1	2	yes	—
81	C₄⋊Q₈	—	38	2	no	—
82	#125	—	38	2	no	—
83	C₂²⋊Q₈	—	38	2	no	—
84	#117	—	19	2	no	—
85	C₂×C₄⋊C₄	C₂×D₁₉	1	1	yes	characteristic
86	C₂×C₄²	—	19	1	no	—
87	#103	—	38	2	no	—
88	#103	—	38	2	no	—
89	#95	—	38	2	no	—
90	C₁₉	#2028	1	1	yes	characteristic, complemented, Sylow
91	C₂×Q₈	—	19	2	no	—
92	C₂×Q₈	—	38	2	no	—
93	C₂×Q₈	—	38	1	no	—
94	C₂×Q₈	—	38	2	no	—
95	C₂×Q₈	—	38	2	no	—
96	C₂²×C₄	—	38	1	no	—
97	C₂²×C₄	—	38	1	no	—
98	C₂²×C₄	D₇₆	1	2	yes	—
99	C₂²×C₄	C₂²×D₁₉	1	1	yes	characteristic
100	M₁₆	—	2	2	no	—
101	M₁₆	—	2	2	no	—
102	C₂×C₈	—	2	2	no	—
103	C₄⋊C₄	—	2	2	no	—
104	C₄⋊C₄	—	19	2	no	—
105	C₄⋊C₄	—	19	2	no	—
106	C₄⋊C₄	—	38	4	no	—
107	C₄⋊C₄	—	38	2	no	—
108	C₂²⋊C₄	—	38	2	no	—
109	C₄²	—	38	2	no	—
110	C₄²	—	38	2	no	—
111	C₂³	C₂×D₇₆	1	1	yes	characteristic
112	Q₈	—	38	4	no	—
113	Q₈	—	76	2	no	—
114	Q₈	—	152	2	no	—
115	C₂×C₄	—	2	2	no	—
116	C₂×C₄	—	4	2	no	—
117	C₂×C₄	—	38	2	no	—
118	C₂×C₄	—	38	2	no	—
119	C₂×C₄	—	38	2	no	—
120	C₂×C₄	—	38	2	no	—
121	C₂×C₄	—	76	1	no	—
122	C₂×C₄	—	76	1	no	—
123	C₂×C₄	—	76	1	no	—
124	C₂×C₄	—	76	1	no	—
125	C₂×C₄	#64541	1	2	yes	—
126	C₂×C₄	D₄×D₁₉	1	2	yes	—
127	C₂×C₄	#64543	1	1	yes	characteristic
128	C₂×C₄	Q₈×D₁₉	1	1	yes	characteristic
129	C₈	—	4	2	no	—
130	C₂²	—	2	1	no	—
131	C₂²	—	2	1	no	—
132	C₂²	#10597321	1	1	yes	characteristic
133	C₂²	#10597328	1	1	yes	characteristic
134	C₂²	#10597343	1	1	yes	characteristic
135	C₄	—	4	2	no	—
136	C₄	—	76	2	no	—
137	C₄	—	76	2	no	—
138	C₄	—	76	2	no	—
139	C₄	—	76	2	no	—
140	C₄	#10597331	1	2	yes	—
141	C₄	#10597342	1	2	yes	—
142	C₂	—	2	1	no	—
143	C₂	—	2	1	no	—
144	C₂	#11926457	1	1	yes	characteristic
145	C₂	#11926724	1	1	yes	characteristic
146	C₂	#11926729	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#11927175

C₂

yes

maximal, characteristic

#11926554

C₂

yes

maximal

#11926449

C₂

yes

maximal, characteristic

#11926305

C₂

yes

maximal

C₁₉×#343

C₂

yes

maximal, characteristic

C₂²×Dic₃₈

C₂²

yes

characteristic

C₂×M₁₆×C₁₉

C₂²

yes

—

C₂×C₄⋊C₄×C₁₉

C₂²

yes

characteristic

#10597372

C₂²

yes

—

#10597370

—

C₂×C₄×Dic₁₉

C₂²

yes

characteristic

#10597336

—

#10597334

—

C₁₉⋊#95

—

#10597273

—

#10597273

—

C₂²×C₄×C₁₉

D₄

yes

—

C₂²×C₄×C₁₉

C₂³

yes

characteristic

C₂²×Dic₁₉

—

C₂²×Dic₁₉

—

C₂×Dic₃₈

—

C₂×Dic₃₈

—

C₂×Dic₃₈

—

C₂×Dic₃₈

—

C₂×Dic₃₈

Q₈

yes

complemented

M₁₆×C₁₉

—

M₁₆×C₁₉

—

C₂×C₈×C₁₉

—

C₄⋊C₄×C₁₉

—

C₂²⋊Dic₁₉

—

C₄⋊Dic₁₉

—

C₄⋊Dic₁₉

D₄

yes

—

C₄⋊Dic₁₉

D₄

yes

—

Dic₁₉⋊C₄

—

C₄×Dic₁₉

—

C₄×Dic₁₉

—

C₂³×C₁₉

C₂×D₄

yes

characteristic

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

C₂×D₄

yes

—

C₂×C₄×C₁₉

C₂×Q₈

yes

characteristic

C₂×C₄×C₁₉

#41

yes

—

C₂×C₄×C₁₉

#41

yes

characteristic

C₂×Dic₁₉

—

C₂×Dic₁₉

—

C₂×Dic₁₉

—

C₂×Dic₁₉

—

C₂×Dic₁₉

—

C₂×Dic₁₉

—

C₂×Dic₁₉

—

C₂×Dic₁₉

—

Dic₃₈

—

Dic₃₈

—

Dic₃₈

—

C₈×C₁₉

—

#2028

—

maximal, Sylow

C₂²×C₁₉

—

C₂²×C₁₉

—

C₂²×C₁₉

#120

yes

characteristic

C₂²×C₁₉

C₂²⋊Q₈

yes

characteristic

C₂²×C₁₉

#124

yes

characteristic

C₄×C₁₉

—

C₄×C₁₉

C₂²⋊Q₈

yes

—

C₄×C₁₉

#124

yes

—

Dic₁₉

—

Dic₁₉

—

Dic₁₉

—

Dic₁₉

—

—

—

—

D₁₉

yes

characteristic

#339

—

C₂×C₁₉

—

C₂×C₁₉

—

C₂×C₁₉

yes

C₂×C₁₉

yes

C₂×C₁₉

yes

C₂²×Q₈

—

C₂×M₁₆

C₂×D₁₉

yes

—

C₄⋊Q₈

—

#125

—

C₂²⋊Q₈

—

#117

—

C₂×C₄⋊C₄

C₂×D₁₉

yes

characteristic

C₂×C₄²

—

#103

—

#103

—

#95

—

C₁₉

#2028

yes

characteristic, complemented, Sylow

C₂×Q₈

—

C₂×Q₈

—

C₂×Q₈

—

C₂×Q₈

—

C₂×Q₈

—

C₂²×C₄

—

C₂²×C₄

—

C₂²×C₄

D₇₆

yes

—

C₂²×C₄

C₂²×D₁₉

yes

characteristic

100

M₁₆

—

101

M₁₆

—

102

C₂×C₈

—

103

C₄⋊C₄

—

104

C₄⋊C₄

—

105

C₄⋊C₄

—

106

C₄⋊C₄

—

107

C₄⋊C₄

—

108

C₂²⋊C₄

—

109

C₄²

—

110

C₄²

—

111

C₂³

C₂×D₇₆

yes

characteristic

112

Q₈

—

113

Q₈

—

114

Q₈

—

152

—

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

#64541

yes

—

126

C₂×C₄

D₄×D₁₉

yes

—

127

C₂×C₄

#64543

yes

characteristic

128

C₂×C₄

Q₈×D₁₉

yes

characteristic

129

C₈

—

130

C₂²

—

131

C₂²

—

132

C₂²

#10597321

yes

characteristic

133

C₂²

#10597328

yes

characteristic

134

C₂²

#10597343

yes

characteristic

135

C₄

—

136

C₄

—

137

C₄

—

138

C₄

—

139

C₄

—

140

C₄

#10597331

yes

—

141

C₄

#10597342

yes

—

142

C₂

—

143

C₂

—

144

C₂

#11926457

yes

characteristic

145

C₂

#11926724

yes

characteristic

146

C₂

#11926729

yes

characteristic

	subgroup	G/H
center	C₂²	#10597328
commutator, cosocle	C₂²×C₄×C₁₉	C₂³
Frattini	C₂²×C₄	C₂²×D₁₉
Fitting	C₁₉×#343	C₂
socle	C₂²×C₁₉	#120
prime radical	C₂³×C₁₉	C₂×D₄
hypercenter	#343	D₁₉
hypocenter	C₁₉	#2028
LCS	G ▷ C₂²×C₄×C₁₉ ▷ C₂×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂² ◁ C₂²×C₄ ◁ #343

subgroup

G/H

center

C₂²

#10597328

commutator, cosocle

C₂²×C₄×C₁₉

C₂³

Frattini

C₂²×C₄

C₂²×D₁₉

Fitting

C₁₉×#343

C₂

socle

C₂²×C₁₉

#120

prime radical

C₂³×C₁₉

C₂×D₄

D₁₉

C₁₉

G ▷ C₂²×C₄×C₁₉ ▷ C₂×C₁₉ ▷ C₁₉

UCS

C₁ ◁ C₂² ◁ C₂²×C₄ ◁ #343

N	H ≅ G/N	type
25. C₂×Dic₃₈	Q₈	semidirect
90. C₁₉	#2028	semidirect

H ≅ G/N

type

25. C₂×Dic₃₈

Q₈

semidirect

90. C₁₉

#2028

semidirect

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

subgroup	index
#11927175	2
#11926554	2
#11926449	2
#11926305	2
C₁₉×#343	2
#2028	19

subgroup

index

C₁₉×#343

Subgroups — #14564797

Conjugacy classes of subgroups

Complements

Maximal subgroups