Group #14568843 — subgroups

Subgroups — #14568843

Order 2432.

500 conjugacy classes of subgroups; only the 205 normal subgroups are shown.

normal subgroups only

This group has 500 conjugacy classes of subgroups — too many to draw. Only its 205 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×#10597315	C₂	1	1	yes	maximal, characteristic
2	C₂×C₄×Dic₃₈	C₂	1	1	yes	maximal, characteristic
3	#11926465	C₂	1	4	yes	maximal
4	#11926450	C₂	1	2	yes	maximal
5	#11926443	C₂	1	4	yes	maximal
6	#11926414	C₂	1	2	yes	maximal
7	C₄×C₄⋊C₄×C₁₉	C₂	1	1	yes	maximal, characteristic
8	C₂²×Dic₃₈	C₂²	1	1	yes	characteristic
9	C₂²×Dic₃₈	C₂²	1	2	yes	—
10	C₂×C₄⋊C₄×C₁₉	C₂²	1	2	yes	—
11	C₂×C₄²×C₁₉	C₂²	1	2	yes	—
12	C₂×C₄²×C₁₉	C₂²	1	1	yes	characteristic
13	C₂×C₄⋊Dic₁₉	C₂²	1	2	yes	—
14	C₂×C₄⋊Dic₁₉	C₂²	1	2	yes	—
15	C₂×C₄⋊Dic₁₉	C₂²	1	1	yes	characteristic
16	C₂×C₄⋊Dic₁₉	C₂²	1	8	yes	—
17	C₂×Dic₁₉⋊C₄	C₂²	1	2	yes	—
18	C₂×C₄×Dic₁₉	C₂²	1	2	yes	—
19	#10597315	—	2	4	no	—
20	C₄×Dic₃₈	—	2	4	no	—
21	C₁₉×#95	C₂²	1	2	yes	—
22	C₁₉⋊#95	C₂²	1	8	yes	—
23	C₂²×C₄×C₁₉	C₂³	1	1	yes	characteristic
24	C₂²×C₄×C₁₉	C₂³	1	4	yes	—
25	C₂²×C₄×C₁₉	C₂³	1	1	yes	characteristic
26	C₂²×C₄×C₁₉	C₂³	1	1	yes	characteristic
27	C₂²×Dic₁₉	C₂³	1	4	yes	—
28	C₂²×Dic₁₉	C₂³	1	2	yes	—
29	C₂²×Dic₁₉	C₂³	1	2	yes	—
30	C₂×Dic₃₈	—	2	2	no	—
31	C₂×Dic₃₈	—	2	2	no	—
32	C₂×Dic₃₈	—	2	4	no	—
33	C₂×Dic₃₈	—	4	4	no	—
34	C₂×Dic₃₈	Q₈	1	4	yes	complemented
35	C₄⋊C₄×C₁₉	Q₈	1	8	yes	complemented
36	C₄²×C₁₉	—	2	4	no	—
37	C₄²×C₁₉	D₄	1	4	yes	—
38	C₄⋊Dic₁₉	—	2	2	no	—
39	C₄⋊Dic₁₉	—	2	4	no	—
40	C₄⋊Dic₁₉	—	2	4	no	—
41	C₄⋊Dic₁₉	—	4	8	no	—
42	Dic₁₉⋊C₄	—	2	4	no	—
43	C₄×Dic₁₉	—	2	4	no	—
44	C₂³×C₁₉	C₂⁴	1	1	yes	characteristic
45	C₂×C₄×C₁₉	—	2	4	no	—
46	C₂×C₄×C₁₉	—	2	4	no	—
47	C₂×C₄×C₁₉	—	2	2	no	—
48	C₂×C₄×C₁₉	C₂×D₄	1	2	yes	—
49	C₂×C₄×C₁₉	C₂×D₄	1	2	yes	—
50	C₂×C₄×C₁₉	C₂×D₄	1	2	yes	—
51	C₂×C₄×C₁₉	C₂×Q₈	1	8	yes	—
52	C₂×C₄×C₁₉	C₂×Q₈	1	4	yes	—
53	C₂×C₄×C₁₉	C₂×Q₈	1	2	yes	—
54	C₂×C₄×C₁₉	#41	1	2	yes	—
55	C₂×Dic₁₉	—	2	2	no	—
56	C₂×Dic₁₉	—	2	2	no	—
57	C₂×Dic₁₉	—	2	2	no	—
58	C₂×Dic₁₉	—	2	4	no	—
59	C₂×Dic₁₉	—	2	4	no	—
60	C₂×Dic₁₉	—	2	8	no	—
61	C₂×Dic₁₉	C₂×Q₈	1	4	yes	—
62	Dic₃₈	—	2	8	no	—
63	Dic₃₈	—	4	8	no	—
64	#2567	—	19	1	no	maximal, Sylow
65	C₂²×C₁₉	C₂²×D₄	1	1	yes	characteristic
66	C₂²×C₁₉	C₂²×Q₈	1	2	yes	—
67	C₂²×C₁₉	C₂²×Q₈	1	1	yes	characteristic
68	C₂²×C₁₉	C₂×#41	1	1	yes	characteristic
69	C₂²×C₁₉	H(5,𝔽₂)	1	2	yes	—
70	C₄×C₁₉	—	2	2	no	—
71	C₄×C₁₉	—	2	8	no	—
72	C₄×C₁₉	C₂²⋊Q₈	1	4	yes	—
73	C₄×C₁₉	C₄⋊Q₈	1	4	yes	—
74	Dic₁₉	—	2	4	no	—
75	Dic₁₉	—	4	4	no	—
76	Dic₁₉	—	4	2	no	—
77	C₂×C₄⋊Q₈	—	19	1	no	—
78	C₂×C₄×Q₈	—	19	1	no	—
79	#395	—	19	4	no	—
80	#391	—	19	2	no	—
81	#389	—	19	4	no	—
82	#384	—	19	2	no	—
83	C₄×C₄⋊C₄	D₁₉	1	1	yes	characteristic
84	C₂×C₁₉	C₂×C₂²⋊Q₈	1	1	yes	characteristic
85	C₂×C₁₉	C₂×C₄⋊Q₈	1	1	yes	characteristic
86	C₂×C₁₉	#535	1	1	yes	characteristic
87	C₂×C₁₉	#554	1	2	yes	—
88	C₂×C₁₉	Q₈²	1	2	yes	—
89	C₂²×Q₈	—	19	1	no	—
90	C₂²×Q₈	—	19	2	no	—
91	C₄⋊Q₈	—	38	4	no	—
92	C₄×Q₈	—	38	4	no	—
93	C₂×C₄⋊C₄	—	19	1	no	—
94	C₂×C₄⋊C₄	—	19	2	no	—
95	C₂×C₄⋊C₄	—	19	2	no	—
96	C₂×C₄⋊C₄	—	19	2	no	—
97	C₂×C₄⋊C₄	—	19	8	no	—
98	C₂×C₄⋊C₄	C₂×D₁₉	1	2	yes	—
99	C₂×C₄²	—	19	2	no	—
100	C₂×C₄²	C₂×D₁₉	1	2	yes	—
101	C₂×C₄²	C₂×D₁₉	1	1	yes	characteristic
102	#95	—	19	8	no	—
103	#95	C₂×D₁₉	1	2	yes	—
104	C₁₉	#2567	1	1	yes	characteristic, complemented, Sylow
105	C₂×Q₈	—	19	4	no	—
106	C₂×Q₈	—	38	2	no	—
107	C₂×Q₈	—	38	4	no	—
108	C₂×Q₈	—	38	2	no	—
109	C₂×Q₈	—	76	4	no	—
110	C₂²×C₄	—	19	2	no	—
111	C₂²×C₄	—	19	4	no	—
112	C₂²×C₄	—	19	2	no	—
113	C₂²×C₄	C₂²×D₁₉	1	4	yes	—
114	C₂²×C₄	C₂²×D₁₉	1	1	yes	characteristic
115	C₂²×C₄	C₂²×D₁₉	1	1	yes	characteristic
116	C₂²×C₄	C₂²×D₁₉	1	1	yes	characteristic
117	C₄⋊C₄	—	38	4	no	—
118	C₄⋊C₄	—	38	2	no	—
119	C₄⋊C₄	—	38	4	no	—
120	C₄⋊C₄	—	38	4	no	—
121	C₄⋊C₄	—	76	8	no	—
122	C₄⋊C₄	Dic₃₈	1	8	yes	complemented
123	C₄²	—	2	4	no	—
124	C₄²	—	38	4	no	—
125	C₄²	D₇₆	1	4	yes	—
126	C₂³	C₂³×D₁₉	1	1	yes	characteristic
127	Q₈	—	38	8	no	—
128	Q₈	—	76	8	no	—
129	C₂×C₄	—	2	4	no	—
130	C₂×C₄	—	2	4	no	—
131	C₂×C₄	—	2	2	no	—
132	C₂×C₄	—	19	4	no	—
133	C₂×C₄	—	38	2	no	—
134	C₂×C₄	—	38	2	no	—
135	C₂×C₄	—	38	2	no	—
136	C₂×C₄	—	38	4	no	—
137	C₂×C₄	—	38	4	no	—
138	C₂×C₄	—	38	8	no	—
139	C₂×C₄	C₂×Dic₃₈	1	8	yes	—
140	C₂×C₄	C₂×Dic₃₈	1	4	yes	—
141	C₂×C₄	C₂×D₇₆	1	2	yes	—
142	C₂×C₄	C₂×D₇₆	1	2	yes	—
143	C₂×C₄	C₂×D₇₆	1	2	yes	—
144	C₂×C₄	#64543	1	2	yes	—
145	C₂×C₄	Q₈×D₁₉	1	2	yes	—
146	C₂²	C₂²×Dic₃₈	1	2	yes	—
147	C₂²	C₂²×D₇₆	1	1	yes	characteristic
148	C₂²	C₂×#64543	1	1	yes	characteristic
149	C₂²	C₂×Q₈×D₁₉	1	1	yes	characteristic
150	C₂²	#10597435	1	2	yes	—
151	C₄	—	2	2	no	—
152	C₄	—	2	8	no	—
153	C₄	—	38	4	no	—
154	C₄	—	76	4	no	—
155	C₄	—	76	2	no	—
156	C₄	#10597315	1	4	yes	—
157	C₄	#10597343	1	4	yes	—
158	C₂	C₂×#10597343	1	1	yes	characteristic
159	C₂	C₂×#10597315	1	1	yes	characteristic
160	C₂	#11927113	1	1	yes	characteristic
161	C₂	#11927251	1	2	yes	—
162	C₂	Q₈×Dic₃₈	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×#10597315

C₂

yes

maximal, characteristic

C₂×C₄×Dic₃₈

C₂

yes

maximal, characteristic

#11926465

C₂

yes

maximal

#11926450

C₂

yes

maximal

#11926443

C₂

yes

maximal

#11926414

C₂

yes

maximal

C₄×C₄⋊C₄×C₁₉

C₂

yes

maximal, characteristic

C₂²×Dic₃₈

C₂²

yes

characteristic

C₂²×Dic₃₈

C₂²

yes

—

C₂×C₄⋊C₄×C₁₉

C₂²

yes

—

C₂×C₄²×C₁₉

C₂²

yes

—

C₂×C₄²×C₁₉

C₂²

yes

characteristic

C₂×C₄⋊Dic₁₉

C₂²

yes

—

C₂×C₄⋊Dic₁₉

C₂²

yes

—

C₂×C₄⋊Dic₁₉

C₂²

yes

characteristic

C₂×C₄⋊Dic₁₉

C₂²

yes

—

C₂×Dic₁₉⋊C₄

C₂²

yes

—

C₂×C₄×Dic₁₉

C₂²

yes

—

#10597315

—

C₄×Dic₃₈

—

C₁₉×#95

C₂²

yes

—

C₁₉⋊#95

C₂²

yes

—

C₂²×C₄×C₁₉

C₂³

yes

characteristic

C₂²×C₄×C₁₉

C₂³

yes

—

C₂²×C₄×C₁₉

C₂³

yes

characteristic

C₂²×C₄×C₁₉

C₂³

yes

characteristic

C₂²×Dic₁₉

C₂³

yes

—

C₂²×Dic₁₉

C₂³

yes

—

C₂²×Dic₁₉

C₂³

yes

—

C₂×Dic₃₈

—

C₂×Dic₃₈

—

C₂×Dic₃₈

—

C₂×Dic₃₈

—

C₂×Dic₃₈

Q₈

yes

complemented

C₄⋊C₄×C₁₉

Q₈

yes

complemented

C₄²×C₁₉

—

C₄²×C₁₉

D₄

yes

—

C₄⋊Dic₁₉

—

C₄⋊Dic₁₉

—

C₄⋊Dic₁₉

—

C₄⋊Dic₁₉

—

Dic₁₉⋊C₄

—

C₄×Dic₁₉

—

C₂³×C₁₉

C₂⁴

yes

characteristic

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

C₂×D₄

yes

—

C₂×C₄×C₁₉

C₂×D₄

yes

—

C₂×C₄×C₁₉

C₂×D₄

yes

—

C₂×C₄×C₁₉

C₂×Q₈

yes

—

C₂×C₄×C₁₉

C₂×Q₈

yes

—

C₂×C₄×C₁₉

C₂×Q₈

yes

—

C₂×C₄×C₁₉

#41

yes

—

C₂×Dic₁₉

—

C₂×Dic₁₉

—

C₂×Dic₁₉

—

C₂×Dic₁₉

—

C₂×Dic₁₉

—

C₂×Dic₁₉

—

C₂×Dic₁₉

C₂×Q₈

yes

—

Dic₃₈

—

Dic₃₈

—

#2567

—

maximal, Sylow

C₂²×C₁₉

C₂²×D₄

yes

characteristic

C₂²×C₁₉

C₂²×Q₈

yes

—

C₂²×C₁₉

C₂²×Q₈

yes

characteristic

C₂²×C₁₉

C₂×#41

yes

characteristic

C₂²×C₁₉

H(5,𝔽₂)

yes

—

C₄×C₁₉

—

C₄×C₁₉

—

C₄×C₁₉

C₂²⋊Q₈

yes

—

C₄×C₁₉

C₄⋊Q₈

yes

—

Dic₁₉

—

Dic₁₉

—

Dic₁₉

—

C₂×C₄⋊Q₈

—

C₂×C₄×Q₈

—

—

—

—

—

C₄×C₄⋊C₄

D₁₉

yes

characteristic

C₂×C₁₉

C₂×C₂²⋊Q₈

yes

characteristic

C₂×C₁₉

C₂×C₄⋊Q₈

yes

C₂×C₁₉

yes

C₂×C₁₉

yes

—

C₂×C₁₉

Q₈²

yes

—

C₂²×Q₈

—

C₂²×Q₈

—

C₄⋊Q₈

—

C₄×Q₈

—

C₂×C₄⋊C₄

—

C₂×C₄⋊C₄

—

C₂×C₄⋊C₄

—

C₂×C₄⋊C₄

—

C₂×C₄⋊C₄

—

C₂×C₄⋊C₄

C₂×D₁₉

yes

—

C₂×C₄²

—

100

C₂×C₄²

C₂×D₁₉

yes

—

101

C₂×C₄²

C₂×D₁₉

yes

characteristic

102

#95

—

103

#95

C₂×D₁₉

yes

—

104

C₁₉

#2567

yes

characteristic, complemented, Sylow

105

C₂×Q₈

—

106

C₂×Q₈

—

107

C₂×Q₈

—

108

C₂×Q₈

—

109

C₂×Q₈

—

110

C₂²×C₄

—

111

C₂²×C₄

—

112

C₂²×C₄

—

113

C₂²×C₄

C₂²×D₁₉

yes

—

114

C₂²×C₄

C₂²×D₁₉

yes

characteristic

115

C₂²×C₄

C₂²×D₁₉

yes

characteristic

116

C₂²×C₄

C₂²×D₁₉

yes

characteristic

117

C₄⋊C₄

—

118

C₄⋊C₄

—

119

C₄⋊C₄

—

120

C₄⋊C₄

—

121

C₄⋊C₄

—

122

C₄⋊C₄

Dic₃₈

yes

complemented

123

C₄²

—

124

C₄²

—

125

C₄²

D₇₆

yes

—

126

C₂³

C₂³×D₁₉

yes

characteristic

127

Q₈

—

128

Q₈

—

129

C₂×C₄

—

130

C₂×C₄

—

131

C₂×C₄

—

132

C₂×C₄

—

133

C₂×C₄

—

134

C₂×C₄

—

135

C₂×C₄

—

136

C₂×C₄

—

137

C₂×C₄

—

138

C₂×C₄

—

139

C₂×C₄

C₂×Dic₃₈

yes

—

140

C₂×C₄

C₂×Dic₃₈

yes

—

141

C₂×C₄

C₂×D₇₆

yes

—

142

C₂×C₄

C₂×D₇₆

yes

—

143

C₂×C₄

C₂×D₇₆

yes

—

144

C₂×C₄

#64543

yes

—

145

C₂×C₄

Q₈×D₁₉

yes

—

146

C₂²

C₂²×Dic₃₈

yes

—

147

C₂²

C₂²×D₇₆

yes

characteristic

148

C₂²

C₂×#64543

yes

characteristic

149

C₂²

C₂×Q₈×D₁₉

yes

characteristic

150

C₂²

#10597435

yes

—

151

C₄

—

152

C₄

—

153

C₄

—

154

C₄

—

155

C₄

—

156

C₄

#10597315

yes

—

157

C₄

#10597343

yes

—

158

C₂

C₂×#10597343

yes

characteristic

159

C₂

C₂×#10597315

yes

characteristic

160

C₂

#11927113

yes

characteristic

161

C₂

#11927251

yes

—

162

C₂

Q₈×Dic₃₈

yes

—

	subgroup	G/H
center, Frattini	C₂³	C₂³×D₁₉
commutator, socle, prime radical, cosocle	C₂³×C₁₉	C₂⁴
Fitting	C₄×C₄⋊C₄×C₁₉	C₂
hypercenter	C₄×C₄⋊C₄	D₁₉
hypocenter	C₁₉	#2567
LCS	G ▷ C₂³×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂³ ◁ C₄×C₄⋊C₄

subgroup

G/H

center, Frattini

C₂³

C₂³×D₁₉

commutator, socle, prime radical, cosocle

C₂³×C₁₉

C₂⁴

Fitting

C₄×C₄⋊C₄×C₁₉

C₂

hypercenter

C₄×C₄⋊C₄

D₁₉

C₁₉

G ▷ C₂³×C₁₉ ▷ C₁₉

C₁ ◁ C₂³ ◁ C₄×C₄⋊C₄

N	H ≅ G/N	type
34. C₂×Dic₃₈	Q₈	semidirect
35. C₄⋊C₄×C₁₉	Q₈	semidirect
104. C₁₉	#2567	semidirect
122. C₄⋊C₄	Dic₃₈	semidirect

H ≅ G/N

type

34. C₂×Dic₃₈

Q₈

semidirect

35. C₄⋊C₄×C₁₉

Q₈

semidirect

104. C₁₉

#2567

semidirect

122. C₄⋊C₄

Dic₃₈

semidirect

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

subgroup	index
C₂×#10597315	2
C₂×C₄×Dic₃₈	2
#11926465	2
#11926450	2
#11926443	2
#11926414	2
C₄×C₄⋊C₄×C₁₉	2
#2567	19

subgroup

index

C₂×C₄×Dic₃₈

C₄×C₄⋊C₄×C₁₉

Subgroups — #14568843

Conjugacy classes of subgroups

Complements

Maximal subgroups