Group #14576302 — subgroups

Subgroups — #14576302

Order 2432.

392 conjugacy classes of subgroups; only the 139 normal subgroups are shown.

normal subgroups only

This group has 392 conjugacy classes of subgroups — too many to draw. Only its 139 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	Q₈×Dic₃₈	C₂	1	1	yes	maximal, characteristic, complemented
2	#11926890	C₂	1	3	yes	maximal, complemented
3	#11926834	C₂	1	3	yes	maximal, complemented
4	#11926741	C₂	1	3	yes	maximal, complemented
5	Q₈×C₁₉⋊C₈	C₂	1	1	yes	maximal, characteristic, complemented
6	C₄×#64526	C₂	1	3	yes	maximal, complemented
7	C₁₉×#550	C₂	1	1	yes	maximal, characteristic
8	C₂×#41×C₁₉	—	2	1	no	—
9	C₁₉×#127	C₂²	1	3	yes	—
10	C₁₉×#121	—	2	3	no	—
11	C₄×Q₈×C₁₉	C₂²	1	1	yes	characteristic
12	C₄×D₄×C₁₉	C₂²	1	3	yes	—
13	Q₈×Dic₁₉	—	2	1	no	—
14	C₂×#64526	C₂²	1	3	yes	—
15	#10597334	—	2	3	no	—
16	#10597315	C₂²	1	3	yes	—
17	C₄×Dic₃₈	C₂²	1	3	yes	—
18	#10597289	C₂²	1	6	yes	—
19	#10597289	C₂²	1	3	yes	—
20	#10597267	C₂²	1	1	yes	characteristic
21	#10597265	C₂²	1	3	yes	—
22	C₄⋊(C₁₉⋊C₈)	C₂²	1	3	yes	—
23	C₄×C₁₉⋊C₈	C₂²	1	3	yes	—
24	#41×C₁₉	—	4	4	no	—
25	C₂×Q₈×C₁₉	D₄	1	1	yes	characteristic
26	C₂×D₄×C₁₉	—	2	3	no	—
27	C₂×D₄×C₁₉	—	2	3	no	—
28	C₂×D₄×C₁₉	C₂³	1	3	yes	—
29	C₂²×C₄×C₁₉	—	2	3	no	—
30	C₂×Dic₃₈	—	2	3	no	—
31	C₂×Dic₃₈	C₂³	1	1	yes	characteristic
32	C₄⋊C₄×C₁₉	D₄	1	3	yes	—
33	C₄⋊C₄×C₁₉	C₂³	1	1	yes	characteristic
34	C₂²⋊C₄×C₁₉	—	2	3	no	—
35	C₄²×C₁₉	C₂³	1	3	yes	—
36	#64526	—	2	6	no	—
37	C₄⋊Dic₁₉	—	2	3	no	—
38	C₄⋊Dic₁₉	C₂³	1	3	yes	—
39	Dic₁₉⋊C₄	—	2	3	no	—
40	C₄×Dic₁₉	—	2	3	no	—
41	C₂×C₁₉⋊C₈	C₂³	1	3	yes	—
42	C₂×C₁₉⋊C₈	C₂³	1	1	yes	characteristic
43	C₂³×C₁₉	—	2	3	no	—
44	Q₈×C₁₉	SD₁₆	1	4	yes	complemented
45	D₄×C₁₉	—	2	3	no	—
46	D₄×C₁₉	—	2	3	no	—
47	D₄×C₁₉	—	4	6	no	—
48	D₄×C₁₉	—	8	3	no	—
49	C₂×C₄×C₁₉	—	2	1	no	—
50	C₂×C₄×C₁₉	—	4	6	no	—
51	C₂×C₄×C₁₉	C₂×D₄	1	3	yes	—
52	C₂×C₄×C₁₉	C₂×D₄	1	3	yes	—
53	C₂×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
54	C₂×Dic₁₉	—	2	1	no	—
55	C₂×Dic₁₉	—	2	3	no	—
56	Dic₃₈	—	2	1	no	—
57	Dic₃₈	—	8	3	no	—
58	Dic₃₈	#41	1	2	yes	complemented
59	C₁₉⋊C₈	—	2	3	no	—
60	C₁₉⋊C₈	—	2	1	no	—
61	#3362	—	19	1	no	maximal, Sylow
62	C₂²×C₁₉	—	4	3	no	—
63	C₂²×C₁₉	—	4	3	no	—
64	C₂²×C₁₉	—	4	3	no	—
65	C₂²×C₁₉	C₂²×D₄	1	1	yes	characteristic
66	C₄×C₁₉	—	2	3	no	—
67	C₄×C₁₉	—	4	1	no	—
68	C₄×C₁₉	C₂×SD₁₆	1	6	yes	—
69	C₄×C₁₉	C₂×#41	1	1	yes	characteristic
70	C₄×C₁₉	2₋¹⁺⁴	1	1	yes	characteristic
71	Dic₁₉	—	2	2	no	—
72	Dic₁₉	—	4	3	no	—
73	Q₈²	—	19	1	no	—
74	#550	D₁₉	1	1	yes	characteristic
75	#486	—	19	3	no	—
76	#476	—	19	3	no	—
77	#460	—	19	3	no	—
78	C₈×Q₈	—	19	1	no	—
79	C₄×SD₁₆	—	19	3	no	—
80	C₂×C₁₉	—	8	3	no	—
81	C₂×C₁₉	#548	1	1	yes	characteristic
82	C₂×C₁₉	C₂²×SD₁₆	1	1	yes	characteristic
83	C₂×C₁₉	#576	1	1	yes	characteristic
84	C₂×#41	—	2	1	no	—
85	C₂×SD₁₆	—	19	3	no	—
86	C₄⋊Q₈	—	19	3	no	—
87	C₄⋊Q₈	—	38	3	no	—
88	#127	C₂×D₁₉	1	3	yes	—
89	#121	—	2	3	no	—
90	C₄×Q₈	—	19	3	no	—
91	C₄×Q₈	—	38	1	no	—
92	C₄×Q₈	C₂×D₁₉	1	1	yes	characteristic
93	C₄×D₄	C₂×D₁₉	1	3	yes	—
94	#106	—	19	3	no	—
95	C₄⋊C₈	—	19	3	no	—
96	#103	—	19	1	no	—
97	#102	—	19	3	no	—
98	#102	—	19	6	no	—
99	C₄×C₈	—	19	3	no	—
100	C₁₉	#3362	1	1	yes	characteristic, complemented, Sylow
101	#41	—	4	4	no	—
102	C₂×Q₈	—	19	1	no	—
103	C₂×Q₈	—	38	3	no	—
104	C₂×Q₈	C₂²⋊D₁₉	1	1	yes	characteristic
105	C₂×D₄	—	2	3	no	—
106	C₂×D₄	—	2	3	no	—
107	C₂×D₄	C₂²×D₁₉	1	3	yes	—
108	C₂²×C₄	—	2	3	no	—
109	SD₁₆	—	38	6	no	—
110	C₂×C₈	—	19	1	no	—
111	C₂×C₈	—	19	3	no	—
112	C₄⋊C₄	—	19	3	no	—
113	C₄⋊C₄	—	38	3	no	—
114	C₄⋊C₄	—	38	3	no	—
115	C₄⋊C₄	C₂²⋊D₁₉	1	3	yes	—
116	C₄⋊C₄	C₂²×D₁₉	1	1	yes	characteristic
117	C₂²⋊C₄	—	2	3	no	—
118	C₄²	—	38	3	no	—
119	C₄²	C₂²×D₁₉	1	3	yes	—
120	C₂³	—	2	3	no	—
121	Q₈	—	19	2	no	—
122	Q₈	—	38	1	no	—
123	Q₈	—	152	3	no	—
124	Q₈	#64526	1	4	yes	complemented
125	D₄	—	2	3	no	—
126	D₄	—	2	3	no	—
127	D₄	—	4	6	no	—
128	D₄	—	8	3	no	—
129	C₂×C₄	—	2	1	no	—
130	C₂×C₄	—	4	6	no	—
131	C₂×C₄	—	38	1	no	—
132	C₂×C₄	—	38	3	no	—
133	C₂×C₄	C₂×C₂²⋊D₁₉	1	3	yes	—
134	C₂×C₄	C₂×C₂²⋊D₁₉	1	3	yes	—
135	C₂×C₄	C₂³×D₁₉	1	1	yes	characteristic
136	C₈	—	38	3	no	—
137	C₈	—	38	1	no	—
138	C₂²	—	4	3	no	—
139	C₂²	—	4	3	no	—
140	C₂²	—	4	3	no	—
141	C₂²	C₂²×C₂²⋊D₁₉	1	1	yes	characteristic
142	C₄	—	2	3	no	—
143	C₄	—	4	1	no	—
144	C₄	—	38	2	no	—
145	C₄	—	76	3	no	—
146	C₄	C₂×#64526	1	6	yes	—
147	C₄	#41×D₁₉	1	1	yes	characteristic
148	C₄	#10597436	1	1	yes	characteristic
149	C₂	—	8	3	no	—
150	C₂	#11927201	1	1	yes	characteristic
151	C₂	C₂²×#64526	1	1	yes	characteristic
152	C₂	#11927347	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

Q₈×Dic₃₈

C₂

yes

maximal, characteristic, complemented

#11926890

C₂

yes

maximal, complemented

#11926834

C₂

yes

maximal, complemented

#11926741

C₂

yes

maximal, complemented

Q₈×C₁₉⋊C₈

C₂

yes

maximal, characteristic, complemented

C₄×#64526

C₂

yes

maximal, complemented

C₁₉×#550

C₂

yes

maximal, characteristic

C₂×#41×C₁₉

—

C₁₉×#127

C₂²

yes

—

C₁₉×#121

—

C₄×Q₈×C₁₉

C₂²

yes

characteristic

C₄×D₄×C₁₉

C₂²

yes

—

Q₈×Dic₁₉

—

C₂×#64526

C₂²

yes

—

#10597334

—

#10597315

C₂²

yes

—

C₄×Dic₃₈

C₂²

yes

—

#10597289

C₂²

yes

—

#10597289

C₂²

yes

—

#10597267

C₂²

yes

characteristic

#10597265

C₂²

yes

—

C₄⋊(C₁₉⋊C₈)

C₂²

yes

—

C₄×C₁₉⋊C₈

C₂²

yes

—

#41×C₁₉

—

C₂×Q₈×C₁₉

D₄

yes

characteristic

C₂×D₄×C₁₉

—

C₂×D₄×C₁₉

—

C₂×D₄×C₁₉

C₂³

yes

—

C₂²×C₄×C₁₉

—

C₂×Dic₃₈

—

C₂×Dic₃₈

C₂³

yes

characteristic

C₄⋊C₄×C₁₉

D₄

yes

—

C₄⋊C₄×C₁₉

C₂³

yes

characteristic

C₂²⋊C₄×C₁₉

—

C₄²×C₁₉

C₂³

yes

—

#64526

—

C₄⋊Dic₁₉

—

C₄⋊Dic₁₉

C₂³

yes

—

Dic₁₉⋊C₄

—

C₄×Dic₁₉

—

C₂×C₁₉⋊C₈

C₂³

yes

—

C₂×C₁₉⋊C₈

C₂³

yes

characteristic

C₂³×C₁₉

—

Q₈×C₁₉

SD₁₆

yes

complemented

D₄×C₁₉

—

D₄×C₁₉

—

D₄×C₁₉

—

D₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

C₂×D₄

yes

—

C₂×C₄×C₁₉

C₂×D₄

yes

—

C₂×C₄×C₁₉

C₂⁴

yes

characteristic

C₂×Dic₁₉

—

C₂×Dic₁₉

—

Dic₃₈

—

Dic₃₈

—

Dic₃₈

#41

yes

complemented

C₁₉⋊C₈

—

C₁₉⋊C₈

—

#3362

—

maximal, Sylow

C₂²×C₁₉

—

C₂²×C₁₉

—

C₂²×C₁₉

—

C₂²×C₁₉

C₂²×D₄

yes

characteristic

C₄×C₁₉

—

C₄×C₁₉

—

C₄×C₁₉

C₂×SD₁₆

yes

—

C₄×C₁₉

C₂×#41

yes

characteristic

C₄×C₁₉

2₋¹⁺⁴

yes

characteristic

Dic₁₉

—

Dic₁₉

—

Q₈²

—

#550

D₁₉

yes

—

—

—

C₈×Q₈

—

C₄×SD₁₆

—

C₂×C₁₉

—

C₂×C₁₉

#548

yes

characteristic

C₂×C₁₉

C₂²×SD₁₆

yes

characteristic

C₂×C₁₉

#576

yes

characteristic

C₂×#41

—

C₂×SD₁₆

—

C₄⋊Q₈

—

C₄⋊Q₈

—

#127

C₂×D₁₉

yes

—

#121

—

C₄×Q₈

—

C₄×Q₈

—

C₄×Q₈

C₂×D₁₉

yes

characteristic

C₄×D₄

C₂×D₁₉

yes

—

#106

—

C₄⋊C₈

—

#103

—

#102

—

#102

—

C₄×C₈

—

100

C₁₉

#3362

yes

characteristic, complemented, Sylow

101

#41

—

102

C₂×Q₈

—

103

C₂×Q₈

—

104

C₂×Q₈

C₂²⋊D₁₉

yes

characteristic

105

C₂×D₄

—

106

C₂×D₄

—

107

C₂×D₄

C₂²×D₁₉

yes

—

108

C₂²×C₄

—

109

SD₁₆

—

110

C₂×C₈

—

111

C₂×C₈

—

112

C₄⋊C₄

—

113

C₄⋊C₄

—

114

C₄⋊C₄

—

115

C₄⋊C₄

C₂²⋊D₁₉

yes

—

116

C₄⋊C₄

C₂²×D₁₉

yes

characteristic

117

C₂²⋊C₄

—

118

C₄²

—

119

C₄²

C₂²×D₁₉

yes

—

120

C₂³

—

121

Q₈

—

122

Q₈

—

123

Q₈

—

152

—

124

Q₈

#64526

yes

complemented

125

D₄

—

126

D₄

—

127

D₄

—

128

D₄

—

129

C₂×C₄

—

130

C₂×C₄

—

131

C₂×C₄

—

132

C₂×C₄

—

133

C₂×C₄

C₂×C₂²⋊D₁₉

yes

—

134

C₂×C₄

C₂×C₂²⋊D₁₉

yes

—

135

C₂×C₄

C₂³×D₁₉

yes

characteristic

136

C₈

—

137

C₈

—

138

C₂²

—

139

C₂²

—

140

C₂²

—

141

C₂²

C₂²×C₂²⋊D₁₉

yes

characteristic

142

C₄

—

143

C₄

—

144

C₄

—

145

C₄

—

146

C₄

C₂×#64526

yes

—

147

C₄

#41×D₁₉

yes

characteristic

148

C₄

#10597436

yes

characteristic

149

C₂

—

150

C₂

#11927201

yes

characteristic

151

C₂

C₂²×#64526

yes

characteristic

152

C₂

#11927347

yes

characteristic

	subgroup	G/H
center	C₂²	C₂²×C₂²⋊D₁₉
commutator, cosocle	C₂×C₄×C₁₉	C₂⁴
Frattini	C₂×C₄	C₂³×D₁₉
Fitting, prime radical	C₁₉×#550	C₂
socle	C₂²×C₁₉	C₂²×D₄
hypercenter	#550	D₁₉
hypocenter	C₁₉	#3362
LCS	G ▷ C₂×C₄×C₁₉ ▷ C₂×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂² ◁ C₄×Q₈ ◁ #550

subgroup

G/H

center

C₂²

C₂²×C₂²⋊D₁₉

commutator, cosocle

C₂×C₄×C₁₉

C₂⁴

Frattini

C₂×C₄

C₂³×D₁₉

Fitting, prime radical

C₁₉×#550

C₂

socle

C₂²×C₁₉

C₂²×D₄

D₁₉

C₁₉

G ▷ C₂×C₄×C₁₉ ▷ C₂×C₁₉ ▷ C₁₉

UCS

C₁ ◁ C₂² ◁ C₄×Q₈ ◁ #550

N	H ≅ G/N	type
1. Q₈×Dic₃₈	C₂	semidirect
2. #11926890	C₂	semidirect
3. #11926834	C₂	semidirect
4. #11926741	C₂	semidirect
5. Q₈×C₁₉⋊C₈	C₂	semidirect
6. C₄×#64526	C₂	semidirect
44. Q₈×C₁₉	SD₁₆	semidirect
58. Dic₃₈	#41	semidirect
100. C₁₉	#3362	semidirect
124. Q₈	#64526	semidirect

H ≅ G/N

type

1. Q₈×Dic₃₈

C₂

semidirect

2. #11926890

C₂

semidirect

3. #11926834

C₂

semidirect

4. #11926741

C₂

semidirect

5. Q₈×C₁₉⋊C₈

C₂

semidirect

6. C₄×#64526

C₂

semidirect

44. Q₈×C₁₉

SD₁₆

semidirect

58. Dic₃₈

#41

semidirect

100. C₁₉

#3362

semidirect

124. Q₈

#64526

semidirect

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

subgroup	index
Q₈×Dic₃₈	2
#11926890	2
#11926834	2
#11926741	2
Q₈×C₁₉⋊C₈	2
C₄×#64526	2
C₁₉×#550	2
#3362	19

subgroup

index

Q₈×Dic₃₈

Q₈×C₁₉⋊C₈

C₁₉×#550

Subgroups — #14576302

Conjugacy classes of subgroups

Complements

Maximal subgroups