Group #14564378 — subgroups

Subgroups — #14564378

Order 2432.

240 conjugacy classes of subgroups; only the 109 normal subgroups are shown.

normal subgroups only

This group has 240 conjugacy classes of subgroups — too many to draw. Only its 109 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×#10597275	C₂	1	1	yes	maximal, characteristic
2	C₂×#10597274	C₂	1	1	yes	maximal, characteristic
3	#11926442	C₂	1	2	yes	maximal
4	#11926307	C₂	1	2	yes	maximal
5	C₂×C₁₉×#97	C₂	1	1	yes	maximal, characteristic
6	C₂²×C₈×C₁₉	C₂²	1	1	yes	characteristic
7	C₂²×C₈×C₁₉	C₂²	1	1	yes	characteristic
8	C₂×C₄²×C₁₉	C₂²	1	1	yes	characteristic
9	C₂×C₄⋊Dic₁₉	C₂²	1	2	yes	—
10	C₂×C₄⋊Dic₁₉	C₂²	1	2	yes	—
11	C₂×Dic₁₉⋊C₄	—	2	2	no	—
12	C₁₉×#97	—	2	2	no	—
13	C₁₉⋊#95	—	2	2	no	—
14	#10597275	—	2	2	no	—
15	#10597274	C₄	1	4	yes	complemented
16	C₂²×C₄×C₁₉	D₄	1	1	yes	characteristic
17	C₂²×C₄×C₁₉	D₄	1	1	yes	characteristic
18	C₂²×C₄×C₁₉	C₂³	1	1	yes	characteristic
19	C₂²×Dic₁₉	—	2	2	no	—
20	C₂²×Dic₁₉	—	2	2	no	—
21	C₂×C₈×C₁₉	—	2	1	no	—
22	C₂×C₈×C₁₉	—	2	1	no	—
23	C₂×C₈×C₁₉	C₂×C₄	1	2	yes	—
24	C₂×C₈×C₁₉	D₄	1	2	yes	—
25	C₂×C₈×C₁₉	Q₈	1	2	yes	—
26	C₂×C₈×C₁₉	Q₈	1	2	yes	—
27	C₄²×C₁₉	—	2	1	no	—
28	C₄²×C₁₉	—	2	1	no	—
29	C₄⋊Dic₁₉	—	2	2	no	—
30	C₄⋊Dic₁₉	—	2	2	no	—
31	C₄⋊Dic₁₉	—	2	2	no	—
32	C₄⋊Dic₁₉	C₂×C₄	1	4	yes	—
33	Dic₁₉⋊C₄	—	4	4	no	—
34	C₂³×C₁₉	C₂×D₄	1	1	yes	characteristic
35	C₂×C₄×C₁₉	—	2	1	no	—
36	C₂×C₄×C₁₉	—	2	1	no	—
37	C₂×C₄×C₁₉	—	2	2	no	—
38	C₂×C₄×C₁₉	—	2	2	no	—
39	C₂×C₄×C₁₉	C₂²×C₄	1	1	yes	characteristic
40	C₂×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
41	C₂×C₄×C₁₉	C₂×Q₈	1	1	yes	characteristic
42	C₂×C₄×C₁₉	C₂×Q₈	1	1	yes	characteristic
43	C₂×C₄×C₁₉	#41	1	1	yes	characteristic
44	C₂×C₄×C₁₉	#41	1	1	yes	characteristic
45	C₂×Dic₁₉	—	2	4	no	—
46	C₂×Dic₁₉	—	4	2	no	—
47	C₂×Dic₁₉	—	4	2	no	—
48	C₂×Dic₁₉	—	4	2	no	—
49	C₂×Dic₁₉	—	4	2	no	—
50	C₂×Dic₁₉	—	4	2	no	—
51	C₈×C₁₉	—	2	2	no	—
52	C₈×C₁₉	C₄⋊C₄	1	4	yes	complemented
53	#1944	—	19	1	no	maximal, Sylow
54	C₂²×C₁₉	C₄×D₄	1	1	yes	characteristic
55	C₂²×C₁₉	#121	1	1	yes	characteristic
56	C₂²×C₁₉	C₄⋊Q₈	1	1	yes	characteristic
57	C₂²×C₁₉	AGL(1,ℤ/8)	1	2	yes	—
58	C₂²×C₁₉	#137	1	2	yes	—
59	C₄×C₁₉	—	4	1	no	—
60	C₄×C₁₉	—	4	1	no	—
61	C₄×C₁₉	C₂×C₄⋊C₄	1	1	yes	characteristic
62	C₄×C₁₉	C₄×Q₈	1	1	yes	characteristic
63	C₄×C₁₉	C₂²⋊Q₈	1	1	yes	characteristic
64	C₄×C₁₉	#125	1	1	yes	characteristic
65	Dic₁₉	—	4	4	no	—
66	Dic₁₉	—	8	2	no	—
67	C₂×#107	—	19	1	no	—
68	C₂×#106	—	19	1	no	—
69	C₂×#97	D₁₉	1	1	yes	characteristic
70	#389	—	19	2	no	—
71	#340	—	19	2	no	—
72	C₂×C₁₉	#389	1	1	yes	characteristic
73	C₂×C₁₉	#440	1	2	yes	—
74	C₂×C₁₉	#469	1	1	yes	characteristic
75	C₂×C₁₉	#470	1	1	yes	characteristic
76	C₂×C₁₉	#501	1	2	yes	—
77	C₂²×C₈	C₂×D₁₉	1	1	yes	characteristic
78	C₂²×C₈	C₂×D₁₉	1	1	yes	characteristic
79	C₂×C₄⋊C₄	—	19	2	no	—
80	C₂×C₄⋊C₄	—	19	2	no	—
81	C₂×C₄⋊C₄	—	38	2	no	—
82	C₂×C₄²	C₂×D₁₉	1	1	yes	characteristic
83	#107	—	38	2	no	—
84	#106	—	19	4	no	—
85	#97	—	2	2	no	—
86	#95	—	38	2	no	—
87	C₁₉	#1944	1	1	yes	characteristic, complemented, Sylow
88	C₂²×C₄	—	38	2	no	—
89	C₂²×C₄	—	38	2	no	—
90	C₂²×C₄	D₇₆	1	1	yes	characteristic
91	C₂²×C₄	D₇₆	1	1	yes	characteristic
92	C₂²×C₄	C₂²×D₁₉	1	1	yes	characteristic
93	C₂×C₈	—	2	1	no	—
94	C₂×C₈	—	2	1	no	—
95	C₂×C₈	Dic₃₈	1	2	yes	—
96	C₂×C₈	Dic₃₈	1	2	yes	—
97	C₂×C₈	C₄×D₁₉	1	2	yes	—
98	C₂×C₈	C₂²⋊D₁₉	1	2	yes	—
99	C₄⋊C₄	—	19	4	no	—
100	C₄⋊C₄	—	38	2	no	—
101	C₄⋊C₄	—	38	2	no	—
102	C₄⋊C₄	—	38	2	no	—
103	C₄⋊C₄	—	76	4	no	—
104	C₄²	—	2	1	no	—
105	C₄²	—	2	1	no	—
106	C₂³	C₂×D₇₆	1	1	yes	characteristic
107	C₂×C₄	—	2	1	no	—
108	C₂×C₄	—	2	1	no	—
109	C₂×C₄	—	2	2	no	—
110	C₂×C₄	—	2	2	no	—
111	C₂×C₄	—	38	4	no	—
112	C₂×C₄	—	76	2	no	—
113	C₂×C₄	—	76	2	no	—
114	C₂×C₄	—	76	2	no	—
115	C₂×C₄	—	76	2	no	—
116	C₂×C₄	—	76	2	no	—
117	C₂×C₄	C₂×Dic₃₈	1	1	yes	characteristic
118	C₂×C₄	C₂×Dic₃₈	1	1	yes	characteristic
119	C₂×C₄	C₂×C₄×D₁₉	1	1	yes	characteristic
120	C₂×C₄	#64541	1	1	yes	characteristic
121	C₂×C₄	#64541	1	1	yes	characteristic
122	C₂×C₄	C₂×C₂²⋊D₁₉	1	1	yes	characteristic
123	C₈	—	2	2	no	—
124	C₈	Dic₁₉⋊C₄	1	4	yes	complemented
125	C₂²	#10597315	1	1	yes	characteristic
126	C₂²	C₄×D₇₆	1	1	yes	characteristic
127	C₂²	#10597354	1	2	yes	—
128	C₂²	#10597355	1	2	yes	—
129	C₂²	#10597376	1	1	yes	characteristic
130	C₄	—	4	1	no	—
131	C₄	—	4	1	no	—
132	C₄	—	76	4	no	—
133	C₄	—	152	2	no	—
134	C₄	C₄×Dic₃₈	1	1	yes	characteristic
135	C₄	#10597316	1	1	yes	characteristic
136	C₄	C₂×Dic₁₉⋊C₄	1	1	yes	characteristic
137	C₄	#10597370	1	1	yes	characteristic
138	C₂	#11926442	1	1	yes	characteristic
139	C₂	#11926646	1	2	yes	—
140	C₂	#11926797	1	1	yes	characteristic
141	C₂	#11926802	1	1	yes	characteristic
142	C₂	#11926953	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×#10597275

C₂

yes

maximal, characteristic

C₂×#10597274

C₂

yes

maximal, characteristic

#11926442

C₂

yes

maximal

#11926307

C₂

yes

maximal

C₂×C₁₉×#97

C₂

yes

maximal, characteristic

C₂²×C₈×C₁₉

C₂²

yes

characteristic

C₂²×C₈×C₁₉

C₂²

yes

characteristic

C₂×C₄²×C₁₉

C₂²

yes

characteristic

C₂×C₄⋊Dic₁₉

C₂²

yes

—

C₂×C₄⋊Dic₁₉

C₂²

yes

—

C₂×Dic₁₉⋊C₄

—

C₁₉×#97

—

C₁₉⋊#95

—

#10597275

—

#10597274

C₄

yes

complemented

C₂²×C₄×C₁₉

D₄

yes

characteristic

C₂²×C₄×C₁₉

D₄

yes

characteristic

C₂²×C₄×C₁₉

C₂³

yes

characteristic

C₂²×Dic₁₉

—

C₂²×Dic₁₉

—

C₂×C₈×C₁₉

—

C₂×C₈×C₁₉

—

C₂×C₈×C₁₉

C₂×C₄

yes

—

C₂×C₈×C₁₉

D₄

yes

—

C₂×C₈×C₁₉

Q₈

yes

—

C₂×C₈×C₁₉

Q₈

yes

—

C₄²×C₁₉

—

C₄²×C₁₉

—

C₄⋊Dic₁₉

—

C₄⋊Dic₁₉

—

C₄⋊Dic₁₉

—

C₄⋊Dic₁₉

C₂×C₄

yes

—

Dic₁₉⋊C₄

—

C₂³×C₁₉

C₂×D₄

yes

characteristic

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

C₂²×C₄

yes

characteristic

C₂×C₄×C₁₉

C₂×D₄

yes

characteristic

C₂×C₄×C₁₉

C₂×Q₈

yes

characteristic

C₂×C₄×C₁₉

C₂×Q₈

yes

C₂×C₄×C₁₉

yes

C₂×C₄×C₁₉

yes

C₂×Dic₁₉

—

C₂×Dic₁₉

—

C₂×Dic₁₉

—

C₂×Dic₁₉

—

C₂×Dic₁₉

—

C₂×Dic₁₉

—

C₈×C₁₉

—

C₈×C₁₉

C₄⋊C₄

yes

complemented

#1944

—

maximal, Sylow

C₂²×C₁₉

C₄×D₄

yes

characteristic

C₂²×C₁₉

#121

yes

characteristic

C₂²×C₁₉

C₄⋊Q₈

yes

characteristic

C₂²×C₁₉

AGL(1,ℤ/8)

yes

—

C₂²×C₁₉

#137

yes

—

C₄×C₁₉

—

C₄×C₁₉

—

C₄×C₁₉

C₂×C₄⋊C₄

yes

characteristic

C₄×C₁₉

C₄×Q₈

yes

characteristic

C₄×C₁₉

C₂²⋊Q₈

yes

characteristic

C₄×C₁₉

#125

yes

characteristic

Dic₁₉

—

Dic₁₉

—

C₂×#107

—

C₂×#106

—

C₂×#97

D₁₉

yes

characteristic

#389

—

#340

—

C₂×C₁₉

#389

yes

characteristic

C₂×C₁₉

#440

yes

—

C₂×C₁₉

yes

C₂×C₁₉

yes

C₂×C₁₉

yes

—

C₂²×C₈

C₂×D₁₉

yes

characteristic

C₂²×C₈

C₂×D₁₉

yes

characteristic

C₂×C₄⋊C₄

—

C₂×C₄⋊C₄

—

C₂×C₄⋊C₄

—

C₂×C₄²

C₂×D₁₉

yes

—

—

—

—

C₁₉

#1944

yes

characteristic, complemented, Sylow

C₂²×C₄

—

C₂²×C₄

—

C₂²×C₄

D₇₆

yes

characteristic

C₂²×C₄

D₇₆

yes

characteristic

C₂²×C₄

C₂²×D₁₉

yes

characteristic

C₂×C₈

—

C₂×C₈

—

C₂×C₈

Dic₃₈

yes

—

C₂×C₈

Dic₃₈

yes

—

C₂×C₈

C₄×D₁₉

yes

—

C₂×C₈

C₂²⋊D₁₉

yes

—

C₄⋊C₄

—

100

C₄⋊C₄

—

101

C₄⋊C₄

—

102

C₄⋊C₄

—

103

C₄⋊C₄

—

104

C₄²

—

105

C₄²

—

106

C₂³

C₂×D₇₆

yes

characteristic

107

C₂×C₄

—

108

C₂×C₄

—

109

C₂×C₄

—

110

C₂×C₄

—

111

C₂×C₄

—

112

C₂×C₄

—

113

C₂×C₄

—

114

C₂×C₄

—

115

C₂×C₄

—

116

C₂×C₄

—

117

C₂×C₄

C₂×Dic₃₈

yes

characteristic

118

C₂×C₄

C₂×Dic₃₈

yes

characteristic

119

C₂×C₄

C₂×C₄×D₁₉

yes

characteristic

120

C₂×C₄

#64541

yes

characteristic

121

C₂×C₄

#64541

yes

characteristic

122

C₂×C₄

C₂×C₂²⋊D₁₉

yes

characteristic

123

C₈

—

124

C₈

Dic₁₉⋊C₄

yes

complemented

125

C₂²

#10597315

yes

characteristic

126

C₂²

C₄×D₇₆

yes

characteristic

127

C₂²

#10597354

yes

—

128

C₂²

#10597355

yes

—

129

C₂²

#10597376

yes

characteristic

130

C₄

—

131

C₄

—

132

C₄

—

133

C₄

—

152

—

134

C₄

C₄×Dic₃₈

yes

characteristic

135

C₄

#10597316

yes

characteristic

136

C₄

C₂×Dic₁₉⋊C₄

yes

characteristic

137

C₄

#10597370

yes

characteristic

138

C₂

#11926442

yes

characteristic

139

C₂

#11926646

yes

—

140

C₂

#11926797

yes

characteristic

141

C₂

#11926802

yes

characteristic

142

C₂

#11926953

yes

—

	subgroup	G/H
center	C₂³	C₂×D₇₆
commutator	C₂×C₄×C₁₉	C₂²×C₄
Frattini	C₂²×C₄	C₂²×D₁₉
Fitting	C₂×C₁₉×#97	C₂
socle, prime radical	C₂³×C₁₉	C₂×D₄
cosocle	C₂²×C₄×C₁₉	C₂³
hypercenter	C₂×#97	D₁₉
hypocenter	C₁₉	#1944
LCS	G ▷ C₂×C₄×C₁₉ ▷ C₂×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂³ ◁ C₂×C₄² ◁ C₂×#97

subgroup

G/H

center

C₂³

C₂×D₇₆

commutator

C₂×C₄×C₁₉

C₂²×C₄

Frattini

C₂²×C₄

C₂²×D₁₉

Fitting

C₂×C₁₉×#97

C₂

socle, prime radical

C₂³×C₁₉

C₂×D₄

cosocle

C₂²×C₄×C₁₉

C₂³

hypercenter

C₂×#97

D₁₉

hypocenter

C₁₉

#1944

LCS

G ▷ C₂×C₄×C₁₉ ▷ C₂×C₁₉ ▷ C₁₉

UCS

C₁ ◁ C₂³ ◁ C₂×C₄² ◁ C₂×#97

N	H ≅ G/N	type
15. #10597274	C₄	semidirect
52. C₈×C₁₉	C₄⋊C₄	semidirect
87. C₁₉	#1944	semidirect
124. C₈	Dic₁₉⋊C₄	semidirect

H ≅ G/N

type

15. #10597274

C₄

semidirect

52. C₈×C₁₉

C₄⋊C₄

semidirect

87. C₁₉

#1944

semidirect

124. C₈

Dic₁₉⋊C₄

semidirect

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

subgroup	index
C₂×#10597275	2
C₂×#10597274	2
#11926442	2
#11926307	2
C₂×C₁₉×#97	2
#1944	19

subgroup

index

C₂×C₁₉×#97

Subgroups — #14564378

Conjugacy classes of subgroups

Complements

Maximal subgroups