Group #14577036 — subgroups

Subgroups — C₂×#11927175 #14577036

Order 2432.

1080 conjugacy classes of subgroups; only the 565 normal subgroups are shown.

normal subgroups only

This group has 1080 conjugacy classes of subgroups — too many to draw. Only its 565 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	#11927175	C₂	1	16	yes	maximal, direct product factor
2	C₂×#10597334	C₂	1	4	yes	maximal, complemented
3	C₂×#10597336	C₂	1	4	yes	maximal, complemented
4	C₂×#10597370	C₂	1	4	yes	maximal
5	C₂×#10597372	C₂	1	2	yes	maximal
6	C₂²×C₄⋊C₄×C₁₉	C₂	1	1	yes	maximal, characteristic
7	C₂³×C₄×C₁₉	C₂²	1	2	yes	—
8	C₂³×C₄×C₁₉	C₂²	1	1	yes	characteristic
9	C₂²×Dic₃₈	C₂²	1	4	yes	—
10	C₂×C₄⋊C₄×C₁₉	C₂²	1	4	yes	—
11	C₂×C₄⋊C₄×C₁₉	C₂²	1	8	yes	—
12	C₂×C₂²⋊Dic₁₉	C₂²	1	4	yes	—
13	#10597372	C₂²	1	16	yes	—
14	C₂×C₄⋊Dic₁₉	C₂²	1	4	yes	—
15	C₂×C₄⋊Dic₁₉	C₂²	1	2	yes	—
16	C₂×C₄⋊Dic₁₉	C₂²	1	2	yes	—
17	#10597370	C₂²	1	32	yes	—
18	C₂×Dic₁₉⋊C₄	C₂²	1	8	yes	—
19	C₂×C₄×Dic₁₉	C₂²	1	4	yes	—
20	#10597336	C₂²	1	32	yes	complemented
21	#10597334	C₂²	1	32	yes	complemented
22	C₂⁴×C₁₉	C₂³	1	1	yes	characteristic
23	C₂²×C₄×C₁₉	—	4	4	no	—
24	C₂²×C₄×C₁₉	Q₈	1	8	yes	complemented
25	C₂²×C₄×C₁₉	C₂³	1	4	yes	—
26	C₂²×C₄×C₁₉	C₂³	1	8	yes	—
27	C₂²×C₄×C₁₉	C₂³	1	2	yes	—
28	C₂²×C₄×C₁₉	C₂³	1	4	yes	—
29	C₂²×Dic₁₉	C₂³	1	4	yes	—
30	C₂²×Dic₁₉	C₂³	1	4	yes	—
31	C₂×Dic₃₈	—	4	8	no	—
32	C₂×Dic₃₈	C₂³	1	16	yes	—
33	C₄⋊C₄×C₁₉	C₂³	1	16	yes	—
34	C₂²⋊Dic₁₉	C₂³	1	16	yes	—
35	C₄⋊Dic₁₉	C₂³	1	8	yes	—
36	C₄⋊Dic₁₉	C₂³	1	16	yes	—
37	C₄⋊Dic₁₉	C₂³	1	8	yes	—
38	Dic₁₉⋊C₄	C₂³	1	32	yes	—
39	C₄×Dic₁₉	C₂³	1	16	yes	—
40	C₂³×C₁₉	—	2	2	no	—
41	C₂³×C₁₉	—	2	2	no	—
42	C₂³×C₁₉	C₂×Q₈	1	4	yes	—
43	C₂³×C₁₉	C₂⁴	1	2	yes	—
44	C₂³×C₁₉	C₂⁴	1	1	yes	characteristic
45	C₂×C₄×C₁₉	—	2	8	no	—
46	C₂×C₄×C₁₉	—	4	8	no	—
47	C₂×C₄×C₁₉	C₂×Q₈	1	8	yes	—
48	C₂×C₄×C₁₉	C₂×Q₈	1	16	yes	complemented
49	C₂×C₄×C₁₉	C₂⁴	1	8	yes	—
50	C₂×C₄×C₁₉	C₂⁴	1	4	yes	—
51	C₂×Dic₁₉	—	2	8	no	—
52	C₂×Dic₁₉	—	2	8	no	—
53	C₂×Dic₁₉	C₂⁴	1	8	yes	—
54	C₂×Dic₁₉	C₂⁴	1	8	yes	—
55	Dic₃₈	—	4	16	no	—
56	C₂×#544	—	19	1	no	maximal, Sylow
57	C₂²×C₁₉	—	2	8	no	—
58	C₂²×C₁₉	—	2	2	no	—
59	C₂²×C₁₉	—	2	2	no	—
60	C₂²×C₁₉	C₂²×Q₈	1	4	yes	—
61	C₂²×C₁₉	C₂²×Q₈	1	2	yes	—
62	C₂²×C₁₉	H(5,𝔽₂)	1	2	yes	—
63	C₂²×C₁₉	2₋¹⁺⁴	1	2	yes	—
64	C₂²×C₁₉	C₂⁵	1	1	yes	characteristic
65	C₄×C₁₉	—	2	8	no	—
66	C₄×C₁₉	C₂²×Q₈	1	8	yes	—
67	Dic₁₉	—	2	8	no	—
68	Dic₁₉	—	2	8	no	—
69	#544	—	19	16	no	—
70	C₂×C₄⋊Q₈	—	19	4	no	—
71	C₂×#125	—	19	4	no	—
72	C₂×C₂²⋊Q₈	—	19	4	no	—
73	C₂×#117	—	19	2	no	—
74	C₂²×C₄⋊C₄	D₁₉	1	1	yes	characteristic
75	C₂×C₁₉	—	2	4	no	—
76	C₂×C₁₉	#544	1	4	yes	complemented
77	C₂×C₁₉	C₂³×Q₈	1	1	yes	characteristic
78	C₂×C₁₉	C₂×H(5,𝔽₂)	1	1	yes	characteristic
79	C₂×C₁₉	C₂×2₋¹⁺⁴	1	1	yes	characteristic
80	C₂²×Q₈	—	19	4	no	—
81	C₂³×C₄	C₂×D₁₉	1	2	yes	—
82	C₂³×C₄	C₂×D₁₉	1	1	yes	characteristic
83	C₄⋊Q₈	—	19	32	no	—
84	#125	—	19	32	no	—
85	C₂²⋊Q₈	—	19	32	no	—
86	#117	—	19	16	no	—
87	C₂×C₄⋊C₄	—	19	2	no	—
88	C₂×C₄⋊C₄	—	19	2	no	—
89	C₂×C₄⋊C₄	—	19	4	no	—
90	C₂×C₄⋊C₄	—	19	8	no	—
91	C₂×C₄⋊C₄	C₂×D₁₉	1	4	yes	—
92	C₂×C₄⋊C₄	C₂×D₁₉	1	8	yes	—
93	C₂×C₂²⋊C₄	—	19	4	no	—
94	C₂×C₄²	—	19	4	no	—
95	C₁₉	C₂×#544	1	1	yes	characteristic, complemented, Sylow
96	C₂⁴	C₂²×D₁₉	1	1	yes	characteristic
97	C₂×Q₈	—	19	16	no	—
98	C₂×Q₈	—	76	8	no	—
99	C₂²×C₄	—	4	4	no	—
100	C₂²×C₄	—	19	4	no	—
101	C₂²×C₄	—	19	4	no	—
102	C₂²×C₄	Dic₃₈	1	8	yes	complemented
103	C₂²×C₄	C₂²×D₁₉	1	4	yes	—
104	C₂²×C₄	C₂²×D₁₉	1	8	yes	—
105	C₂²×C₄	C₂²×D₁₉	1	2	yes	—
106	C₂²×C₄	C₂²×D₁₉	1	4	yes	—
107	C₄⋊C₄	—	19	32	no	—
108	C₄⋊C₄	—	19	8	no	—
109	C₄⋊C₄	—	19	8	no	—
110	C₄⋊C₄	—	19	16	no	—
111	C₄⋊C₄	C₂²×D₁₉	1	16	yes	—
112	C₂²⋊C₄	—	19	16	no	—
113	C₄²	—	19	16	no	—
114	C₂³	—	2	2	no	—
115	C₂³	—	2	2	no	—
116	C₂³	C₂×Dic₃₈	1	4	yes	—
117	C₂³	C₂³×D₁₉	1	2	yes	—
118	C₂³	C₂³×D₁₉	1	1	yes	characteristic
119	Q₈	—	76	16	no	—
120	C₂×C₄	—	2	8	no	—
121	C₂×C₄	—	4	8	no	—
122	C₂×C₄	—	19	8	no	—
123	C₂×C₄	—	19	8	no	—
124	C₂×C₄	—	38	8	no	—
125	C₂×C₄	—	38	8	no	—
126	C₂×C₄	C₂×Dic₃₈	1	8	yes	—
127	C₂×C₄	C₂×Dic₃₈	1	16	yes	complemented
128	C₂×C₄	C₂³×D₁₉	1	8	yes	—
129	C₂×C₄	C₂³×D₁₉	1	4	yes	—
130	C₂²	—	2	2	no	—
131	C₂²	—	2	2	no	—
132	C₂²	—	2	8	no	—
133	C₂²	C₂²×Dic₃₈	1	4	yes	—
134	C₂²	C₂²×Dic₃₈	1	2	yes	—
135	C₂²	#10597430	1	2	yes	—
136	C₂²	#10597433	1	2	yes	—
137	C₂²	C₂⁴×D₁₉	1	1	yes	characteristic
138	C₄	—	2	8	no	—
139	C₄	—	38	8	no	—
140	C₄	—	38	8	no	—
141	C₄	C₂²×Dic₃₈	1	8	yes	—
142	C₂	—	2	4	no	—
143	C₂	#11927175	1	4	yes	direct product factor
144	C₂	C₂³×Dic₃₈	1	1	yes	characteristic
145	C₂	C₂×#10597430	1	1	yes	characteristic
146	C₂	C₂×#10597433	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#11927175

C₂

yes

maximal, direct product factor

C₂×#10597334

C₂

yes

maximal, complemented

C₂×#10597336

C₂

yes

maximal, complemented

C₂×#10597370

C₂

yes

maximal

C₂×#10597372

C₂

yes

maximal

C₂²×C₄⋊C₄×C₁₉

C₂

yes

maximal, characteristic

C₂³×C₄×C₁₉

C₂²

yes

—

C₂³×C₄×C₁₉

C₂²

yes

characteristic

C₂²×Dic₃₈

C₂²

yes

—

C₂×C₄⋊C₄×C₁₉

C₂²

yes

—

C₂×C₄⋊C₄×C₁₉

C₂²

yes

—

C₂×C₂²⋊Dic₁₉

C₂²

yes

—

#10597372

C₂²

yes

—

C₂×C₄⋊Dic₁₉

C₂²

yes

—

C₂×C₄⋊Dic₁₉

C₂²

yes

—

C₂×C₄⋊Dic₁₉

C₂²

yes

—

#10597370

C₂²

yes

—

C₂×Dic₁₉⋊C₄

C₂²

yes

—

C₂×C₄×Dic₁₉

C₂²

yes

—

#10597336

C₂²

yes

complemented

#10597334

C₂²

yes

complemented

C₂⁴×C₁₉

C₂³

yes

characteristic

C₂²×C₄×C₁₉

—

C₂²×C₄×C₁₉

Q₈

yes

complemented

C₂²×C₄×C₁₉

C₂³

yes

—

C₂²×C₄×C₁₉

C₂³

yes

—

C₂²×C₄×C₁₉

C₂³

yes

—

C₂²×C₄×C₁₉

C₂³

yes

—

C₂²×Dic₁₉

C₂³

yes

—

C₂²×Dic₁₉

C₂³

yes

—

C₂×Dic₃₈

—

C₂×Dic₃₈

C₂³

yes

—

C₄⋊C₄×C₁₉

C₂³

yes

—

C₂²⋊Dic₁₉

C₂³

yes

—

C₄⋊Dic₁₉

C₂³

yes

—

C₄⋊Dic₁₉

C₂³

yes

—

C₄⋊Dic₁₉

C₂³

yes

—

Dic₁₉⋊C₄

C₂³

yes

—

C₄×Dic₁₉

C₂³

yes

—

C₂³×C₁₉

—

C₂³×C₁₉

—

C₂³×C₁₉

C₂×Q₈

yes

—

C₂³×C₁₉

C₂⁴

yes

—

C₂³×C₁₉

C₂⁴

yes

characteristic

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

C₂×Q₈

yes

—

C₂×C₄×C₁₉

C₂×Q₈

yes

complemented

C₂×C₄×C₁₉

C₂⁴

yes

—

C₂×C₄×C₁₉

C₂⁴

yes

—

C₂×Dic₁₉

—

C₂×Dic₁₉

—

C₂×Dic₁₉

C₂⁴

yes

—

C₂×Dic₁₉

C₂⁴

yes

—

Dic₃₈

—

C₂×#544

—

maximal, Sylow

C₂²×C₁₉

—

C₂²×C₁₉

—

C₂²×C₁₉

—

C₂²×C₁₉

C₂²×Q₈

yes

—

C₂²×C₁₉

C₂²×Q₈

yes

—

C₂²×C₁₉

H(5,𝔽₂)

yes

—

C₂²×C₁₉

2₋¹⁺⁴

yes

—

C₂²×C₁₉

C₂⁵

yes

characteristic

C₄×C₁₉

—

C₄×C₁₉

C₂²×Q₈

yes

—

Dic₁₉

—

Dic₁₉

—

#544

—

C₂×C₄⋊Q₈

—

C₂×#125

—

C₂×C₂²⋊Q₈

—

C₂×#117

—

C₂²×C₄⋊C₄

D₁₉

yes

characteristic

C₂×C₁₉

—

C₂×C₁₉

#544

yes

complemented

C₂×C₁₉

C₂³×Q₈

yes

characteristic

C₂×C₁₉

C₂×H(5,𝔽₂)

yes

characteristic

C₂×C₁₉

C₂×2₋¹⁺⁴

yes

characteristic

C₂²×Q₈

—

C₂³×C₄

C₂×D₁₉

yes

—

C₂³×C₄

C₂×D₁₉

yes

characteristic

C₄⋊Q₈

—

#125

—

C₂²⋊Q₈

—

#117

—

C₂×C₄⋊C₄

—

C₂×C₄⋊C₄

—

C₂×C₄⋊C₄

—

C₂×C₄⋊C₄

—

C₂×C₄⋊C₄

C₂×D₁₉

yes

—

C₂×C₄⋊C₄

C₂×D₁₉

yes

—

C₂×C₂²⋊C₄

—

C₂×C₄²

—

C₁₉

C₂×#544

yes

characteristic, complemented, Sylow

C₂⁴

C₂²×D₁₉

yes

characteristic

C₂×Q₈

—

C₂×Q₈

—

C₂²×C₄

—

100

C₂²×C₄

—

101

C₂²×C₄

—

102

C₂²×C₄

Dic₃₈

yes

complemented

103

C₂²×C₄

C₂²×D₁₉

yes

—

104

C₂²×C₄

C₂²×D₁₉

yes

—

105

C₂²×C₄

C₂²×D₁₉

yes

—

106

C₂²×C₄

C₂²×D₁₉

yes

—

107

C₄⋊C₄

—

108

C₄⋊C₄

—

109

C₄⋊C₄

—

110

C₄⋊C₄

—

111

C₄⋊C₄

C₂²×D₁₉

yes

—

112

C₂²⋊C₄

—

113

C₄²

—

114

C₂³

—

115

C₂³

—

116

C₂³

C₂×Dic₃₈

yes

—

117

C₂³

C₂³×D₁₉

yes

—

118

C₂³

C₂³×D₁₉

yes

characteristic

119

Q₈

—

120

C₂×C₄

—

121

C₂×C₄

—

122

C₂×C₄

—

123

C₂×C₄

—

124

C₂×C₄

—

125

C₂×C₄

—

126

C₂×C₄

C₂×Dic₃₈

yes

—

127

C₂×C₄

C₂×Dic₃₈

yes

complemented

128

C₂×C₄

C₂³×D₁₉

yes

—

129

C₂×C₄

C₂³×D₁₉

yes

—

130

C₂²

—

131

C₂²

—

132

C₂²

—

133

C₂²

C₂²×Dic₃₈

yes

—

134

C₂²

C₂²×Dic₃₈

yes

—

135

C₂²

#10597430

yes

—

136

C₂²

#10597433

yes

—

137

C₂²

C₂⁴×D₁₉

yes

characteristic

138

C₄

—

139

C₄

—

140

C₄

—

141

C₄

C₂²×Dic₃₈

yes

—

142

C₂

—

143

C₂

#11927175

yes

direct product factor

144

C₂

C₂³×Dic₃₈

yes

characteristic

145

C₂

C₂×#10597430

yes

characteristic

146

C₂

C₂×#10597433

yes

characteristic

	subgroup	G/H
center	C₂³	C₂³×D₁₉
commutator, cosocle	C₂²×C₁₉	C₂⁵
Frattini	C₂²	C₂⁴×D₁₉
Fitting	C₂²×C₄⋊C₄×C₁₉	C₂
socle	C₂³×C₁₉	C₂⁴
prime radical	C₂⁴×C₁₉	C₂³
hypercenter	C₂²×C₄⋊C₄	D₁₉
hypocenter	C₁₉	C₂×#544
LCS	G ▷ C₂²×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂³ ◁ C₂²×C₄⋊C₄

subgroup

G/H

center

C₂³

C₂³×D₁₉

commutator, cosocle

C₂²×C₁₉

C₂⁵

Frattini

C₂²

C₂⁴×D₁₉

Fitting

C₂²×C₄⋊C₄×C₁₉

C₂

socle

C₂³×C₁₉

C₂⁴

prime radical

C₂⁴×C₁₉

C₂³

hypercenter

C₂²×C₄⋊C₄

D₁₉

C₁₉

G ▷ C₂²×C₁₉ ▷ C₁₉

C₁ ◁ C₂³ ◁ C₂²×C₄⋊C₄

N	H ≅ G/N	type
1. #11927175	C₂	direct (N × H)
2. C₂×#10597334	C₂	semidirect
3. C₂×#10597336	C₂	semidirect
20. #10597336	C₂²	semidirect
21. #10597334	C₂²	semidirect
24. C₂²×C₄×C₁₉	Q₈	semidirect
48. C₂×C₄×C₁₉	C₂×Q₈	semidirect
76. C₂×C₁₉	#544	semidirect
95. C₁₉	C₂×#544	semidirect
102. C₂²×C₄	Dic₃₈	semidirect
127. C₂×C₄	C₂×Dic₃₈	semidirect
143. C₂	#11927175	direct (N × H)

H ≅ G/N

type

1. #11927175

C₂

direct (N × H)

2. C₂×#10597334

C₂

semidirect

3. C₂×#10597336

C₂

semidirect

20. #10597336

C₂²

semidirect

21. #10597334

C₂²

semidirect

24. C₂²×C₄×C₁₉

Q₈

semidirect

48. C₂×C₄×C₁₉

C₂×Q₈

semidirect

76. C₂×C₁₉

#544

semidirect

95. C₁₉

C₂×#544

semidirect

102. C₂²×C₄

Dic₃₈

semidirect

127. C₂×C₄

C₂×Dic₃₈

semidirect

143. C₂

#11927175

direct (N × H)

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

subgroup	index
#11927175	2
C₂×#10597334	2
C₂×#10597336	2
C₂×#10597370	2
C₂×#10597372	2
C₂²×C₄⋊C₄×C₁₉	2
C₂×#544	19

subgroup

index

C₂²×C₄⋊C₄×C₁₉

Subgroups — C₂×#11927175 #14577036

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C2×#11927175 #14577036

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#11927175 #14577036