Group #14569749 — subgroups

Subgroups — #14569749

Order 2432.

524 conjugacy classes of subgroups; only the 181 normal subgroups are shown.

normal subgroups only

This group has 524 conjugacy classes of subgroups — too many to draw. Only its 181 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×#10597370	C₂	1	2	yes	maximal
2	#11926476	C₂	1	4	yes	maximal, complemented
3	#11926465	C₂	1	4	yes	maximal, complemented
4	#11926404	C₂	1	4	yes	maximal
5	C₂×C₁₉×#95	C₂	1	1	yes	maximal, characteristic
6	C₂³×C₄×C₁₉	C₂²	1	1	yes	characteristic
7	C₂³×C₄×C₁₉	C₂²	1	2	yes	—
8	C₂²×Dic₃₈	C₂²	1	2	yes	—
9	C₂×C₂²⋊Dic₁₉	C₂²	1	4	yes	—
10	C₂×C₄⋊Dic₁₉	C₂²	1	2	yes	—
11	C₂×C₄⋊Dic₁₉	C₂²	1	4	yes	—
12	C₂×C₄⋊Dic₁₉	C₂²	1	4	yes	—
13	#10597370	—	2	8	no	—
14	C₂×Dic₁₉⋊C₄	C₂²	1	4	yes	—
15	C₁₉×#95	C₂²	1	4	yes	—
16	C₁₉⋊#95	C₂²	1	8	yes	—
17	C₂⁴×C₁₉	C₂³	1	1	yes	characteristic
18	C₂²×C₄×C₁₉	—	4	2	no	—
19	C₂²×C₄×C₁₉	—	4	2	no	—
20	C₂²×C₄×C₁₉	—	4	2	no	—
21	C₂²×C₄×C₁₉	D₄	1	4	yes	—
22	C₂²×C₄×C₁₉	Q₈	1	8	yes	complemented
23	C₂²×C₄×C₁₉	C₂³	1	2	yes	—
24	C₂²×C₄×C₁₉	C₂³	1	4	yes	—
25	C₂²×Dic₁₉	C₂³	1	4	yes	—
26	C₂²×Dic₁₉	C₂³	1	4	yes	—
27	C₂×Dic₃₈	—	2	4	no	—
28	C₂×Dic₃₈	—	4	4	no	—
29	C₂²⋊Dic₁₉	—	2	8	no	—
30	C₄⋊Dic₁₉	—	2	4	no	—
31	C₄⋊Dic₁₉	—	4	4	no	—
32	C₄⋊Dic₁₉	—	4	4	no	—
33	Dic₁₉⋊C₄	—	2	8	no	—
34	C₂³×C₁₉	—	2	2	no	—
35	C₂³×C₁₉	—	2	1	no	—
36	C₂³×C₁₉	—	2	1	no	—
37	C₂³×C₁₉	C₂×D₄	1	2	yes	—
38	C₂³×C₁₉	C₂×Q₈	1	4	yes	—
39	C₂³×C₁₉	C₂⁴	1	1	yes	characteristic
40	C₂×C₄×C₁₉	—	2	4	no	—
41	C₂×C₄×C₁₉	—	2	4	no	—
42	C₂×C₄×C₁₉	—	2	4	no	—
43	C₂×C₄×C₁₉	—	4	4	no	—
44	C₂×C₄×C₁₉	—	4	8	no	—
45	C₂×C₄×C₁₉	C₂×D₄	1	4	yes	—
46	C₂×C₄×C₁₉	C₂×Q₈	1	8	yes	—
47	C₂×Dic₁₉	—	2	4	no	—
48	C₂×Dic₁₉	—	2	4	no	—
49	C₂×Dic₁₉	—	2	4	no	—
50	C₂×Dic₁₉	—	2	8	no	—
51	C₂×Dic₁₉	—	2	4	no	—
52	Dic₃₈	—	4	8	no	—
53	#2659	—	19	1	no	maximal, Sylow
54	C₂²×C₁₉	—	2	2	no	—
55	C₂²×C₁₉	—	2	2	no	—
56	C₂²×C₁₉	—	2	4	no	—
57	C₂²×C₁₉	—	2	4	no	—
58	C₂²×C₁₉	C₄⋊Q₈	1	4	yes	—
59	C₂²×C₁₉	C₂²×D₄	1	1	yes	characteristic
60	C₂²×C₁₉	C₂²×Q₈	1	2	yes	—
61	C₂²×C₁₉	H(5,𝔽₂)	1	2	yes	—
62	C₂²×C₁₉	H(5,𝔽₂)	1	1	yes	characteristic
63	C₂²×C₁₉	2₋¹⁺⁴	1	1	yes	characteristic
64	C₄×C₁₉	—	2	4	no	—
65	C₄×C₁₉	—	2	8	no	—
66	Dic₁₉	—	4	4	no	—
67	Dic₁₉	—	4	4	no	—
68	C₂×C₂²⋊Q₈	—	19	2	no	—
69	#398	—	19	4	no	—
70	#395	—	19	4	no	—
71	#380	—	19	4	no	—
72	C₂×#95	D₁₉	1	1	yes	characteristic
73	C₂×C₁₉	—	2	4	no	—
74	C₂×C₁₉	C₂×C₄⋊Q₈	1	1	yes	characteristic
75	C₂×C₁₉	#534	1	1	yes	characteristic
76	C₂×C₁₉	#537	1	1	yes	characteristic
77	C₂×C₁₉	#543	1	2	yes	—
78	C₂×C₁₉	#544	1	2	yes	—
79	C₂²×Q₈	—	19	2	no	—
80	C₂³×C₄	C₂×D₁₉	1	2	yes	—
81	C₂³×C₄	C₂×D₁₉	1	1	yes	characteristic
82	C₂²⋊Q₈	—	38	8	no	—
83	C₂×C₄⋊C₄	—	19	4	no	—
84	C₂×C₄⋊C₄	—	19	2	no	—
85	C₂×C₄⋊C₄	—	19	4	no	—
86	C₂×C₄⋊C₄	—	19	4	no	—
87	C₂×C₂²⋊C₄	—	19	4	no	—
88	#95	—	19	8	no	—
89	#95	C₂×D₁₉	1	4	yes	—
90	C₁₉	#2659	1	1	yes	characteristic, complemented, Sylow
91	C₂⁴	C₂²×D₁₉	1	1	yes	characteristic
92	C₂×Q₈	—	38	4	no	—
93	C₂×Q₈	—	76	4	no	—
94	C₂²×C₄	—	4	2	no	—
95	C₂²×C₄	—	4	2	no	—
96	C₂²×C₄	—	4	2	no	—
97	C₂²×C₄	—	19	4	no	—
98	C₂²×C₄	—	19	4	no	—
99	C₂²×C₄	Dic₃₈	1	8	yes	complemented
100	C₂²×C₄	D₇₆	1	4	yes	—
101	C₂²×C₄	C₂²×D₁₉	1	4	yes	—
102	C₂²×C₄	C₂²×D₁₉	1	2	yes	—
103	C₄⋊C₄	—	38	8	no	—
104	C₄⋊C₄	—	38	4	no	—
105	C₄⋊C₄	—	76	4	no	—
106	C₄⋊C₄	—	76	4	no	—
107	C₂²⋊C₄	—	38	8	no	—
108	C₂³	—	2	2	no	—
109	C₂³	—	2	1	no	—
110	C₂³	—	2	1	no	—
111	C₂³	C₂×Dic₃₈	1	4	yes	—
112	C₂³	C₂×D₇₆	1	2	yes	—
113	C₂³	C₂³×D₁₉	1	1	yes	characteristic
114	Q₈	—	76	8	no	—
115	C₂×C₄	—	2	4	no	—
116	C₂×C₄	—	2	4	no	—
117	C₂×C₄	—	2	4	no	—
118	C₂×C₄	—	4	8	no	—
119	C₂×C₄	—	4	4	no	—
120	C₂×C₄	—	38	4	no	—
121	C₂×C₄	—	38	4	no	—
122	C₂×C₄	—	38	4	no	—
123	C₂×C₄	—	38	8	no	—
124	C₂×C₄	—	38	4	no	—
125	C₂×C₄	C₂×Dic₃₈	1	8	yes	—
126	C₂×C₄	C₂×D₇₆	1	4	yes	—
127	C₂²	—	2	2	no	—
128	C₂²	—	2	2	no	—
129	C₂²	—	2	4	no	—
130	C₂²	—	2	4	no	—
131	C₂²	#10597315	1	4	yes	—
132	C₂²	C₂²×Dic₃₈	1	2	yes	—
133	C₂²	C₂²×D₇₆	1	1	yes	characteristic
134	C₂²	#10597430	1	2	yes	—
135	C₂²	#10597430	1	1	yes	characteristic
136	C₂²	#10597433	1	1	yes	characteristic
137	C₄	—	2	4	no	—
138	C₄	—	2	8	no	—
139	C₄	—	76	4	no	—
140	C₄	—	76	4	no	—
141	C₂	—	2	4	no	—
142	C₂	C₂×#10597315	1	1	yes	characteristic
143	C₂	#11927106	1	1	yes	characteristic
144	C₂	#11927125	1	1	yes	characteristic
145	C₂	#11927170	1	2	yes	—
146	C₂	#11927175	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×#10597370

C₂

yes

maximal

#11926476

C₂

yes

maximal, complemented

#11926465

C₂

yes

maximal, complemented

#11926404

C₂

yes

maximal

C₂×C₁₉×#95

C₂

yes

maximal, characteristic

C₂³×C₄×C₁₉

C₂²

yes

characteristic

C₂³×C₄×C₁₉

C₂²

yes

—

C₂²×Dic₃₈

C₂²

yes

—

C₂×C₂²⋊Dic₁₉

C₂²

yes

—

C₂×C₄⋊Dic₁₉

C₂²

yes

—

C₂×C₄⋊Dic₁₉

C₂²

yes

—

C₂×C₄⋊Dic₁₉

C₂²

yes

—

#10597370

—

C₂×Dic₁₉⋊C₄

C₂²

yes

—

C₁₉×#95

C₂²

yes

—

C₁₉⋊#95

C₂²

yes

—

C₂⁴×C₁₉

C₂³

yes

characteristic

C₂²×C₄×C₁₉

—

C₂²×C₄×C₁₉

—

C₂²×C₄×C₁₉

—

C₂²×C₄×C₁₉

D₄

yes

—

C₂²×C₄×C₁₉

Q₈

yes

complemented

C₂²×C₄×C₁₉

C₂³

yes

—

C₂²×C₄×C₁₉

C₂³

yes

—

C₂²×Dic₁₉

C₂³

yes

—

C₂²×Dic₁₉

C₂³

yes

—

C₂×Dic₃₈

—

C₂×Dic₃₈

—

C₂²⋊Dic₁₉

—

C₄⋊Dic₁₉

—

C₄⋊Dic₁₉

—

C₄⋊Dic₁₉

—

Dic₁₉⋊C₄

—

C₂³×C₁₉

—

C₂³×C₁₉

—

C₂³×C₁₉

—

C₂³×C₁₉

C₂×D₄

yes

—

C₂³×C₁₉

C₂×Q₈

yes

—

C₂³×C₁₉

C₂⁴

yes

characteristic

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

C₂×D₄

yes

—

C₂×C₄×C₁₉

C₂×Q₈

yes

—

C₂×Dic₁₉

—

C₂×Dic₁₉

—

C₂×Dic₁₉

—

C₂×Dic₁₉

—

C₂×Dic₁₉

—

Dic₃₈

—

#2659

—

maximal, Sylow

C₂²×C₁₉

—

C₂²×C₁₉

—

C₂²×C₁₉

—

C₂²×C₁₉

—

C₂²×C₁₉

C₄⋊Q₈

yes

—

C₂²×C₁₉

C₂²×D₄

yes

characteristic

C₂²×C₁₉

C₂²×Q₈

yes

—

C₂²×C₁₉

H(5,𝔽₂)

yes

—

C₂²×C₁₉

H(5,𝔽₂)

yes

characteristic

C₂²×C₁₉

2₋¹⁺⁴

yes

characteristic

C₄×C₁₉

—

C₄×C₁₉

—

Dic₁₉

—

Dic₁₉

—

C₂×C₂²⋊Q₈

—

#398

—

#395

—

#380

—

C₂×#95

D₁₉

yes

characteristic

C₂×C₁₉

—

C₂×C₁₉

C₂×C₄⋊Q₈

yes

C₂×C₁₉

yes

C₂×C₁₉

yes

C₂×C₁₉

yes

—

C₂×C₁₉

#544

yes

—

C₂²×Q₈

—

C₂³×C₄

C₂×D₁₉

yes

—

C₂³×C₄

C₂×D₁₉

yes

characteristic

C₂²⋊Q₈

—

C₂×C₄⋊C₄

—

C₂×C₄⋊C₄

—

C₂×C₄⋊C₄

—

C₂×C₄⋊C₄

—

C₂×C₂²⋊C₄

—

#95

—

#95

C₂×D₁₉

yes

—

C₁₉

#2659

yes

characteristic, complemented, Sylow

C₂⁴

C₂²×D₁₉

yes

characteristic

C₂×Q₈

—

C₂×Q₈

—

C₂²×C₄

—

C₂²×C₄

—

C₂²×C₄

—

C₂²×C₄

—

C₂²×C₄

—

C₂²×C₄

Dic₃₈

yes

complemented

100

C₂²×C₄

D₇₆

yes

—

101

C₂²×C₄

C₂²×D₁₉

yes

—

102

C₂²×C₄

C₂²×D₁₉

yes

—

103

C₄⋊C₄

—

104

C₄⋊C₄

—

105

C₄⋊C₄

—

106

C₄⋊C₄

—

107

C₂²⋊C₄

—

108

C₂³

—

109

C₂³

—

110

C₂³

—

111

C₂³

C₂×Dic₃₈

yes

—

112

C₂³

C₂×D₇₆

yes

—

113

C₂³

C₂³×D₁₉

yes

characteristic

114

Q₈

—

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

C₂×Dic₃₈

yes

—

126

C₂×C₄

C₂×D₇₆

yes

—

127

C₂²

—

128

C₂²

—

129

C₂²

—

130

C₂²

—

131

C₂²

#10597315

yes

—

132

C₂²

C₂²×Dic₃₈

yes

—

133

C₂²

C₂²×D₇₆

yes

characteristic

134

C₂²

#10597430

yes

—

135

C₂²

#10597430

yes

characteristic

136

C₂²

#10597433

yes

characteristic

137

C₄

—

138

C₄

—

139

C₄

—

140

C₄

—

141

C₂

—

142

C₂

C₂×#10597315

yes

characteristic

143

C₂

#11927106

yes

characteristic

144

C₂

#11927125

yes

characteristic

145

C₂

#11927170

yes

—

146

C₂

#11927175

yes

—

	subgroup	G/H
center, Frattini	C₂³	C₂³×D₁₉
commutator, socle, cosocle	C₂³×C₁₉	C₂⁴
Fitting	C₂×C₁₉×#95	C₂
prime radical	C₂⁴×C₁₉	C₂³
hypercenter	C₂×#95	D₁₉
hypocenter	C₁₉	#2659
LCS	G ▷ C₂³×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂³ ◁ C₂×#95

subgroup

G/H

center, Frattini

C₂³

C₂³×D₁₉

commutator, socle, cosocle

C₂³×C₁₉

C₂⁴

Fitting

C₂×C₁₉×#95

C₂

prime radical

C₂⁴×C₁₉

C₂³

hypercenter

C₂×#95

D₁₉

C₁₉

G ▷ C₂³×C₁₉ ▷ C₁₉

C₁ ◁ C₂³ ◁ C₂×#95

N	H ≅ G/N	type
2. #11926476	C₂	semidirect
3. #11926465	C₂	semidirect
22. C₂²×C₄×C₁₉	Q₈	semidirect
90. C₁₉	#2659	semidirect
99. C₂²×C₄	Dic₃₈	semidirect

H ≅ G/N

type

2. #11926476

C₂

semidirect

3. #11926465

C₂

semidirect

22. C₂²×C₄×C₁₉

Q₈

semidirect

90. C₁₉

#2659

semidirect

99. C₂²×C₄

Dic₃₈

semidirect

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

subgroup	index
C₂×#10597370	2
#11926476	2
#11926465	2
#11926404	2
C₂×C₁₉×#95	2
#2659	19

subgroup

index

C₂×C₁₉×#95

Subgroups — #14569749

Conjugacy classes of subgroups

Complements

Maximal subgroups