Group #14572427 — subgroups

Subgroups — C₂×#11926655 #14572427

Order 2432.

608 conjugacy classes of subgroups; only the 197 normal subgroups are shown.

normal subgroups only

This group has 608 conjugacy classes of subgroups — too many to draw. Only its 197 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	C₂²×D₁₅₂	C₂	1	1	yes	maximal, characteristic
2	C₂×#10597339	C₂	1	2	yes	maximal, complemented
3	#11926655	C₂	1	8	yes	maximal, direct product factor
4	C₂×#10597266	C₂	1	2	yes	maximal, complemented
5	C₂×#10597272	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×C₁₉×#106	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂²×D₇₆	C₂²	1	2	yes	—
8	C₂²×C₄×D₁₉	—	2	2	no	—
9	C₂²×C₈×C₁₉	C₂²	1	1	yes	characteristic
10	C₂×C₄⋊C₄×C₁₉	C₂²	1	2	yes	—
11	C₂×(C₂×D₁₉)⋊C₄	—	2	2	no	—
12	C₂×C₄×Dic₁₉	C₂²	1	1	yes	characteristic
13	C₂²×C₁₉⋊C₈	C₂²	1	1	yes	characteristic
14	C₂×D₁₅₂	C₄	1	8	yes	complemented
15	C₂×D₁₅₂	C₂²	1	4	yes	—
16	#10597339	—	2	4	no	—
17	#10597339	C₂²	1	8	yes	complemented
18	C₁₉×#106	C₂²	1	4	yes	complemented
19	#10597272	C₂²	1	4	yes	complemented
20	#10597266	C₂²	1	8	yes	complemented
21	C₂³×D₁₉	—	2	2	no	—
22	C₂²×C₄×C₁₉	—	2	2	no	—
23	C₂²×C₄×C₁₉	C₂³	1	1	yes	characteristic
24	C₂²×Dic₁₉	D₄	1	2	yes	—
25	C₂×D₇₆	—	2	2	no	—
26	C₂×D₇₆	—	2	4	no	—
27	C₂×D₇₆	C₂×C₄	1	8	yes	complemented
28	C₂×D₇₆	C₂³	1	4	yes	—
29	C₂×C₄×D₁₉	—	2	8	no	—
30	C₂×C₄×D₁₉	—	4	8	no	—
31	C₂×C₈×C₁₉	C₂×C₄	1	4	yes	complemented
32	C₂×C₈×C₁₉	C₂³	1	2	yes	—
33	C₄⋊C₄×C₁₉	—	2	2	no	—
34	C₄⋊C₄×C₁₉	C₂³	1	4	yes	—
35	(C₂×D₁₉)⋊C₄	—	2	8	no	—
36	C₄×Dic₁₉	D₄	1	2	yes	—
37	C₄×Dic₁₉	C₂³	1	2	yes	—
38	C₂×C₁₉⋊C₈	—	2	2	no	—
39	C₂×C₁₉⋊C₈	C₂³	1	2	yes	—
40	D₁₅₂	C₂×C₄	1	16	yes	complemented
41	C₂³×C₁₉	C₂×D₄	1	1	yes	characteristic
42	C₂²×D₁₉	—	2	8	no	—
43	C₂²×D₁₉	—	2	4	no	—
44	C₂²×D₁₉	—	4	4	no	—
45	C₂²×D₁₉	—	4	4	no	—
46	C₂×C₄×C₁₉	—	2	4	no	—
47	C₂×C₄×C₁₉	—	4	4	no	—
48	C₂×C₄×C₁₉	C₂²×C₄	1	2	yes	—
49	C₂×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
50	C₂×C₄×C₁₉	#41	1	2	yes	—
51	C₂×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
52	C₂×Dic₁₉	—	2	4	no	—
53	C₂×Dic₁₉	C₂×D₄	1	4	yes	—
54	D₇₆	—	2	8	no	—
55	D₇₆	—	2	4	no	—
56	D₇₆	C₂²×C₄	1	8	yes	complemented
57	C₄×D₁₉	—	4	16	no	—
58	C₈×C₁₉	C₂²×C₄	1	4	yes	complemented
59	C₁₉⋊C₈	—	2	2	no	—
60	C₂×#442	—	19	1	no	maximal, Sylow
61	C₂²×C₁₉	C₄×D₄	1	2	yes	—
62	C₂²×C₁₉	AGL(1,ℤ/8)	1	4	yes	—
63	C₂²×C₁₉	C₂²×D₄	1	1	yes	characteristic
64	C₂×D₁₉	—	2	8	no	—
65	C₂×D₁₉	—	4	4	no	—
66	C₂×D₁₉	—	4	4	no	—
67	C₂×D₁₉	—	4	16	no	—
68	C₄×C₁₉	—	4	4	no	—
69	C₄×C₁₉	C₄×D₄	1	2	yes	—
70	C₄×C₁₉	C₂³×C₄	1	1	yes	characteristic
71	C₄×C₁₉	C₂×#41	1	1	yes	characteristic
72	Dic₁₉	—	2	4	no	—
73	C₂²×D₈	—	19	1	no	—
74	C₂×C₄×D₄	—	19	2	no	—
75	#442	—	19	8	no	—
76	C₂×#106	D₁₉	1	1	yes	characteristic, complemented
77	C₂×#102	—	19	2	no	—
78	C₂×#97	—	19	1	no	—
79	C₂×C₁₉	#442	1	4	yes	complemented
80	C₂×C₁₉	C₂×C₄×D₄	1	1	yes	characteristic
81	C₂×C₁₉	C₂×AGL(1,ℤ/8)	1	2	yes	—
82	D₁₉	—	4	8	no	—
83	C₂²×D₄	—	19	2	no	—
84	C₂³×C₄	—	38	2	no	—
85	C₂×D₈	—	19	8	no	—
86	C₂×D₈	—	19	4	no	—
87	C₂²×C₈	—	19	1	no	—
88	C₂²×C₈	C₂×D₁₉	1	1	yes	characteristic
89	C₄×D₄	—	19	8	no	—
90	C₄×D₄	—	38	4	no	—
91	C₂×C₄⋊C₄	C₂×D₁₉	1	2	yes	—
92	C₂×C₂²⋊C₄	—	38	2	no	—
93	C₂×C₄²	—	19	1	no	—
94	#106	C₂×D₁₉	1	4	yes	complemented
95	#102	—	19	8	no	—
96	#97	—	19	4	no	—
97	C₁₉	C₂×#442	1	1	yes	characteristic, complemented, Sylow
98	C₂⁴	—	38	2	no	—
99	C₂×D₄	—	19	8	no	—
100	C₂×D₄	—	19	4	no	—
101	C₂×D₄	—	38	2	no	—
102	C₂×D₄	—	38	4	no	—
103	C₂²×C₄	—	2	2	no	—
104	C₂²×C₄	—	19	2	no	—
105	C₂²×C₄	—	38	8	no	—
106	C₂²×C₄	—	76	8	no	—
107	C₂²×C₄	C₂²×D₁₉	1	1	yes	characteristic
108	D₈	—	19	16	no	—
109	C₂×C₈	—	19	2	no	—
110	C₂×C₈	—	38	2	no	—
111	C₂×C₈	C₄×D₁₉	1	4	yes	complemented
112	C₂×C₈	C₂²×D₁₉	1	2	yes	—
113	C₄⋊C₄	—	2	2	no	—
114	C₄⋊C₄	C₂²×D₁₉	1	4	yes	—
115	C₂²⋊C₄	—	38	8	no	—
116	C₄²	—	19	2	no	—
117	C₄²	—	19	2	no	—
118	C₂³	—	38	4	no	—
119	C₂³	—	38	8	no	—
120	C₂³	—	76	4	no	—
121	C₂³	—	76	4	no	—
122	C₂³	D₄×D₁₉	1	1	yes	characteristic
123	D₄	—	19	8	no	—
124	D₄	—	38	4	no	—
125	D₄	—	38	8	no	—
126	C₂×C₄	—	2	4	no	—
127	C₂×C₄	—	4	4	no	—
128	C₂×C₄	—	19	4	no	—
129	C₂×C₄	—	38	4	no	—
130	C₂×C₄	—	76	16	no	—
131	C₂×C₄	C₂×C₄×D₁₉	1	2	yes	—
132	C₂×C₄	D₄×D₁₉	1	1	yes	characteristic
133	C₂×C₄	#64545	1	2	yes	—
134	C₂×C₄	C₂³×D₁₉	1	1	yes	characteristic
135	C₈	—	38	2	no	—
136	C₈	C₂×C₄×D₁₉	1	4	yes	complemented
137	C₂²	—	38	8	no	—
138	C₂²	—	76	4	no	—
139	C₂²	—	76	4	no	—
140	C₂²	—	76	16	no	—
141	C₂²	#10597339	1	2	yes	—
142	C₂²	#10597360	1	4	yes	—
143	C₂²	C₂×D₄×D₁₉	1	1	yes	characteristic
144	C₄	—	4	4	no	—
145	C₄	—	38	4	no	—
146	C₄	#10597339	1	2	yes	—
147	C₄	C₂²×C₄×D₁₉	1	1	yes	characteristic
148	C₄	C₂×#64545	1	1	yes	characteristic
149	C₂	—	76	8	no	—
150	C₂	#11926655	1	4	yes	direct product factor
151	C₂	C₂×#10597339	1	1	yes	characteristic
152	C₂	C₂×#10597360	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

C₂²×D₁₅₂

C₂

yes

maximal, characteristic

C₂×#10597339

C₂

yes

maximal, complemented

#11926655

C₂

yes

maximal, direct product factor

C₂×#10597266

C₂

yes

maximal, complemented

C₂×#10597272

C₂

yes

maximal, characteristic, complemented

C₂×C₁₉×#106

C₂

yes

maximal, characteristic, complemented

C₂²×D₇₆

C₂²

yes

—

C₂²×C₄×D₁₉

—

C₂²×C₈×C₁₉

C₂²

yes

characteristic

C₂×C₄⋊C₄×C₁₉

C₂²

yes

—

C₂×(C₂×D₁₉)⋊C₄

—

C₂×C₄×Dic₁₉

C₂²

yes

characteristic

C₂²×C₁₉⋊C₈

C₂²

yes

characteristic

C₂×D₁₅₂

C₄

yes

complemented

C₂×D₁₅₂

C₂²

yes

—

#10597339

—

#10597339

C₂²

yes

complemented

C₁₉×#106

C₂²

yes

complemented

#10597272

C₂²

yes

complemented

#10597266

C₂²

yes

complemented

C₂³×D₁₉

—

C₂²×C₄×C₁₉

—

C₂²×C₄×C₁₉

C₂³

yes

characteristic

C₂²×Dic₁₉

D₄

yes

—

C₂×D₇₆

—

C₂×D₇₆

—

C₂×D₇₆

C₂×C₄

yes

complemented

C₂×D₇₆

C₂³

yes

—

C₂×C₄×D₁₉

—

C₂×C₄×D₁₉

—

C₂×C₈×C₁₉

C₂×C₄

yes

complemented

C₂×C₈×C₁₉

C₂³

yes

—

C₄⋊C₄×C₁₉

—

C₄⋊C₄×C₁₉

C₂³

yes

—

(C₂×D₁₉)⋊C₄

—

C₄×Dic₁₉

D₄

yes

—

C₄×Dic₁₉

C₂³

yes

—

C₂×C₁₉⋊C₈

—

C₂×C₁₉⋊C₈

C₂³

yes

—

D₁₅₂

C₂×C₄

yes

complemented

C₂³×C₁₉

C₂×D₄

yes

characteristic

C₂²×D₁₉

—

C₂²×D₁₉

—

C₂²×D₁₉

—

C₂²×D₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

C₂²×C₄

yes

—

C₂×C₄×C₁₉

C₂×D₄

yes

characteristic

C₂×C₄×C₁₉

#41

yes

—

C₂×C₄×C₁₉

C₂⁴

yes

characteristic

C₂×Dic₁₉

—

C₂×Dic₁₉

C₂×D₄

yes

—

D₇₆

—

D₇₆

—

D₇₆

C₂²×C₄

yes

complemented

C₄×D₁₉

—

C₈×C₁₉

C₂²×C₄

yes

complemented

C₁₉⋊C₈

—

C₂×#442

—

maximal, Sylow

C₂²×C₁₉

C₄×D₄

yes

—

C₂²×C₁₉

AGL(1,ℤ/8)

yes

—

C₂²×C₁₉

C₂²×D₄

yes

characteristic

C₂×D₁₉

—

C₂×D₁₉

—

C₂×D₁₉

—

C₂×D₁₉

—

C₄×C₁₉

—

C₄×C₁₉

C₄×D₄

yes

—

C₄×C₁₉

C₂³×C₄

yes

characteristic

C₄×C₁₉

C₂×#41

yes

characteristic

Dic₁₉

—

C₂²×D₈

—

C₂×C₄×D₄

—

#442

—

C₂×#106

D₁₉

yes

characteristic, complemented

C₂×#102

—

C₂×#97

—

C₂×C₁₉

#442

yes

complemented

C₂×C₁₉

C₂×C₄×D₄

yes

characteristic

C₂×C₁₉

C₂×AGL(1,ℤ/8)

yes

—

D₁₉

—

C₂²×D₄

—

C₂³×C₄

—

C₂×D₈

—

C₂×D₈

—

C₂²×C₈

—

C₂²×C₈

C₂×D₁₉

yes

characteristic

C₄×D₄

—

C₄×D₄

—

C₂×C₄⋊C₄

C₂×D₁₉

yes

—

C₂×C₂²⋊C₄

—

C₂×C₄²

—

#106

C₂×D₁₉

yes

complemented

#102

—

#97

—

C₁₉

C₂×#442

yes

characteristic, complemented, Sylow

C₂⁴

—

C₂×D₄

—

100

C₂×D₄

—

101

C₂×D₄

—

102

C₂×D₄

—

103

C₂²×C₄

—

104

C₂²×C₄

—

105

C₂²×C₄

—

106

C₂²×C₄

—

107

C₂²×C₄

C₂²×D₁₉

yes

characteristic

108

D₈

—

109

C₂×C₈

—

110

C₂×C₈

—

111

C₂×C₈

C₄×D₁₉

yes

complemented

112

C₂×C₈

C₂²×D₁₉

yes

—

113

C₄⋊C₄

—

114

C₄⋊C₄

C₂²×D₁₉

yes

—

115

C₂²⋊C₄

—

116

C₄²

—

117

C₄²

—

118

C₂³

—

119

C₂³

—

120

C₂³

—

121

C₂³

—

122

C₂³

D₄×D₁₉

yes

characteristic

123

D₄

—

124

D₄

—

125

D₄

—

126

C₂×C₄

—

127

C₂×C₄

—

128

C₂×C₄

—

129

C₂×C₄

—

130

C₂×C₄

—

131

C₂×C₄

C₂×C₄×D₁₉

yes

—

132

C₂×C₄

D₄×D₁₉

yes

characteristic

133

C₂×C₄

#64545

yes

—

134

C₂×C₄

C₂³×D₁₉

yes

characteristic

135

C₈

—

136

C₈

C₂×C₄×D₁₉

yes

complemented

137

C₂²

—

138

C₂²

—

139

C₂²

—

140

C₂²

—

141

C₂²

#10597339

yes

—

142

C₂²

#10597360

yes

—

143

C₂²

C₂×D₄×D₁₉

yes

characteristic

144

C₄

—

145

C₄

—

146

C₄

#10597339

yes

—

147

C₄

C₂²×C₄×D₁₉

yes

characteristic

148

C₄

C₂×#64545

yes

characteristic

149

C₂

—

150

C₂

#11926655

yes

direct product factor

151

C₂

C₂×#10597339

yes

characteristic

152

C₂

C₂×#10597360

yes

—

	subgroup	G/H
center	C₂³	D₄×D₁₉
commutator	C₄×C₁₉	C₂³×C₄
Frattini	C₂×C₄	C₂³×D₁₉
Fitting	C₂×C₁₉×#106	C₂
socle	C₂³×C₁₉	C₂×D₄
prime radical	C₂²×D₁₅₂	C₂
cosocle	C₂×C₄×C₁₉	C₂⁴
hypercenter	C₂×#106	D₁₉
hypocenter	C₁₉	C₂×#442
LCS	G ▷ C₄×C₁₉ ▷ C₂×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂³ ◁ C₂²×C₄ ◁ C₂×#106

subgroup

G/H

center

C₂³

D₄×D₁₉

commutator

C₄×C₁₉

C₂³×C₄

Frattini

C₂×C₄

C₂³×D₁₉

Fitting

C₂×C₁₉×#106

C₂

socle

C₂³×C₁₉

C₂×D₄

prime radical

C₂²×D₁₅₂

C₂

cosocle

C₂×C₄×C₁₉

C₂⁴

D₁₉

C₁₉

G ▷ C₄×C₁₉ ▷ C₂×C₁₉ ▷ C₁₉

UCS

C₁ ◁ C₂³ ◁ C₂²×C₄ ◁ C₂×#106

N	H ≅ G/N	type
2. C₂×#10597339	C₂	semidirect
3. #11926655	C₂	direct (N × H)
4. C₂×#10597266	C₂	semidirect
5. C₂×#10597272	C₂	semidirect
6. C₂×C₁₉×#106	C₂	semidirect
14. C₂×D₁₅₂	C₄	semidirect
17. #10597339	C₂²	semidirect
18. C₁₉×#106	C₂²	semidirect
19. #10597272	C₂²	semidirect
20. #10597266	C₂²	semidirect
27. C₂×D₇₆	C₂×C₄	semidirect
31. C₂×C₈×C₁₉	C₂×C₄	semidirect
40. D₁₅₂	C₂×C₄	semidirect
56. D₇₆	C₂²×C₄	semidirect
58. C₈×C₁₉	C₂²×C₄	semidirect
76. C₂×#106	D₁₉	semidirect
79. C₂×C₁₉	#442	semidirect
94. #106	C₂×D₁₉	semidirect
97. C₁₉	C₂×#442	semidirect
111. C₂×C₈	C₄×D₁₉	semidirect
136. C₈	C₂×C₄×D₁₉	semidirect
150. C₂	#11926655	direct (N × H)

H ≅ G/N

type

2. C₂×#10597339

C₂

semidirect

3. #11926655

C₂

direct (N × H)

4. C₂×#10597266

C₂

semidirect

5. C₂×#10597272

C₂

semidirect

6. C₂×C₁₉×#106

C₂

semidirect

14. C₂×D₁₅₂

C₄

semidirect

17. #10597339

C₂²

semidirect

18. C₁₉×#106

C₂²

semidirect

19. #10597272

C₂²

semidirect

20. #10597266

C₂²

semidirect

27. C₂×D₇₆

C₂×C₄

semidirect

31. C₂×C₈×C₁₉

C₂×C₄

semidirect

40. D₁₅₂

C₂×C₄

semidirect

56. D₇₆

C₂²×C₄

semidirect

58. C₈×C₁₉

C₂²×C₄

semidirect

76. C₂×#106

D₁₉

semidirect

79. C₂×C₁₉

#442

semidirect

94. #106

C₂×D₁₉

semidirect

97. C₁₉

C₂×#442

semidirect

111. C₂×C₈

C₄×D₁₉

semidirect

136. C₈

C₂×C₄×D₁₉

semidirect

150. C₂

#11926655

direct (N × H)

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

subgroup	index
C₂²×D₁₅₂	2
C₂×#10597339	2
#11926655	2
C₂×#10597266	2
C₂×#10597272	2
C₂×C₁₉×#106	2
C₂×#442	19

subgroup

index

C₂²×D₁₅₂

C₂×C₁₉×#106

Subgroups — C₂×#11926655 #14572427

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C2×#11926655 #14572427

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#11926655 #14572427