Group #14572423 — subgroups

Subgroups — C₂×#11926652 #14572423

Order 2432.

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

normal subgroups only

This group has 480 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	C₂²×Dic₇₆	C₂	1	1	yes	maximal, characteristic
2	C₂×C₄×Dic₃₈	C₂	1	2	yes	maximal
3	#11926652	C₂	1	8	yes	maximal, direct product factor
4	C₂×#10597274	C₂	1	1	yes	maximal, characteristic
5	C₂×#10597273	C₂	1	2	yes	maximal
6	C₂×C₁₉×#97	C₂	1	1	yes	maximal, characteristic
7	C₂²×Dic₃₈	C₂²	1	2	yes	—
8	C₂²×C₈×C₁₉	C₂²	1	1	yes	characteristic
9	C₂²×C₈×C₁₉	C₂²	1	1	yes	characteristic
10	C₂×C₄²×C₁₉	C₂²	1	1	yes	characteristic
11	C₂×C₄⋊Dic₁₉	C₂²	1	2	yes	—
12	C₂×Dic₁₉⋊C₄	—	2	2	no	—
13	C₂×C₄×Dic₁₉	—	2	2	no	—
14	C₂×Dic₇₆	C₄	1	8	yes	complemented
15	C₂×Dic₇₆	C₂²	1	4	yes	—
16	C₄×Dic₃₈	—	2	4	no	—
17	C₄×Dic₃₈	C₂²	1	8	yes	—
18	C₁₉×#97	C₂²	1	4	yes	—
19	#10597274	C₂²	1	4	yes	—
20	#10597273	C₂²	1	8	yes	—
21	C₂²×C₄×C₁₉	D₄	1	2	yes	—
22	C₂²×C₄×C₁₉	C₂³	1	1	yes	characteristic
23	C₂²×Dic₁₉	—	2	2	no	—
24	C₂²×Dic₁₉	—	2	2	no	—
25	C₂×Dic₃₈	—	2	2	no	—
26	C₂×Dic₃₈	—	2	4	no	—
27	C₂×Dic₃₈	C₂×C₄	1	8	yes	—
28	C₂×Dic₃₈	C₂³	1	4	yes	—
29	C₂×C₈×C₁₉	—	2	2	no	—
30	C₂×C₈×C₁₉	C₂×C₄	1	4	yes	—
31	C₂×C₈×C₁₉	C₂³	1	2	yes	—
32	C₂×C₈×C₁₉	C₂³	1	2	yes	—
33	C₄²×C₁₉	D₄	1	2	yes	—
34	C₄²×C₁₉	C₂³	1	2	yes	—
35	C₄⋊Dic₁₉	—	2	2	no	—
36	C₄⋊Dic₁₉	C₂³	1	4	yes	—
37	Dic₁₉⋊C₄	—	2	8	no	—
38	C₄×Dic₁₉	—	2	8	no	—
39	Dic₇₆	C₂×C₄	1	16	yes	complemented
40	C₂³×C₁₉	C₂×D₄	1	1	yes	characteristic
41	C₂×C₄×C₁₉	—	2	4	no	—
42	C₂×C₄×C₁₉	C₂²×C₄	1	2	yes	—
43	C₂×C₄×C₁₉	C₂×D₄	1	4	yes	—
44	C₂×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
45	C₂×C₄×C₁₉	#41	1	2	yes	—
46	C₂×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
47	C₂×Dic₁₉	—	2	8	no	—
48	C₂×Dic₁₉	—	2	4	no	—
49	C₂×Dic₁₉	—	2	4	no	—
50	C₂×Dic₁₉	—	4	4	no	—
51	Dic₃₈	—	2	8	no	—
52	Dic₃₈	—	2	4	no	—
53	Dic₃₈	C₂²×C₄	1	8	yes	—
54	C₈×C₁₉	—	2	2	no	—
55	C₈×C₁₉	C₂²×C₄	1	4	yes	—
56	C₂×#441	—	19	1	no	maximal, Sylow
57	C₂²×C₁₉	C₄×D₄	1	2	yes	—
58	C₂²×C₁₉	#137	1	4	yes	—
59	C₂²×C₁₉	C₂²×D₄	1	1	yes	characteristic
60	C₄×C₁₉	—	2	4	no	—
61	C₄×C₁₉	C₄×D₄	1	2	yes	—
62	C₄×C₁₉	C₂³×C₄	1	1	yes	characteristic
63	C₄×C₁₉	C₂×#41	1	1	yes	characteristic
64	Dic₁₉	—	2	8	no	—
65	Dic₁₉	—	4	4	no	—
66	C₂²×Q₁₆	—	19	1	no	—
67	C₂×C₄×Q₈	—	19	2	no	—
68	#441	—	19	8	no	—
69	C₂×#106	—	19	1	no	—
70	C₂×#103	—	19	2	no	—
71	C₂×#97	D₁₉	1	1	yes	characteristic
72	C₂×C₁₉	#441	1	4	yes	complemented
73	C₂×C₁₉	C₂×C₄×D₄	1	1	yes	characteristic
74	C₂×C₁₉	C₂×#137	1	2	yes	—
75	C₂²×Q₈	—	19	2	no	—
76	C₂×Q₁₆	—	19	8	no	—
77	C₂×Q₁₆	—	19	4	no	—
78	C₂²×C₈	C₂×D₁₉	1	1	yes	characteristic
79	C₂²×C₈	C₂×D₁₉	1	1	yes	characteristic
80	C₄×Q₈	—	19	8	no	—
81	C₄×Q₈	—	38	4	no	—
82	C₂×C₄⋊C₄	—	19	2	no	—
83	C₂×C₄⋊C₄	—	38	2	no	—
84	C₂×C₄²	—	38	2	no	—
85	C₂×C₄²	C₂×D₁₉	1	1	yes	characteristic
86	#106	—	19	4	no	—
87	#103	—	19	8	no	—
88	#97	C₂×D₁₉	1	4	yes	—
89	C₁₉	C₂×#441	1	1	yes	characteristic, complemented, Sylow
90	C₂×Q₈	—	19	8	no	—
91	C₂×Q₈	—	19	4	no	—
92	C₂×Q₈	—	38	2	no	—
93	C₂×Q₈	—	38	4	no	—
94	C₂²×C₄	—	38	2	no	—
95	C₂²×C₄	—	38	2	no	—
96	C₂²×C₄	D₇₆	1	2	yes	—
97	C₂²×C₄	C₂²×D₁₉	1	1	yes	characteristic
98	Q₁₆	—	19	16	no	—
99	C₂×C₈	—	2	2	no	—
100	C₂×C₈	C₄×D₁₉	1	4	yes	—
101	C₂×C₈	C₂²×D₁₉	1	2	yes	—
102	C₂×C₈	C₂²×D₁₉	1	2	yes	—
103	C₄⋊C₄	—	19	4	no	—
104	C₄⋊C₄	—	38	8	no	—
105	C₄⋊C₄	—	38	2	no	—
106	C₄²	—	38	8	no	—
107	C₄²	D₇₆	1	2	yes	—
108	C₄²	C₂²×D₁₉	1	2	yes	—
109	C₂³	C₂×D₇₆	1	1	yes	characteristic
110	Q₈	—	19	8	no	—
111	Q₈	—	38	4	no	—
112	Q₈	—	38	8	no	—
113	C₂×C₄	—	2	4	no	—
114	C₂×C₄	—	38	4	no	—
115	C₂×C₄	—	38	8	no	—
116	C₂×C₄	—	38	4	no	—
117	C₂×C₄	—	76	4	no	—
118	C₂×C₄	C₂×C₄×D₁₉	1	2	yes	—
119	C₂×C₄	C₂×D₇₆	1	4	yes	—
120	C₂×C₄	C₂×D₇₆	1	1	yes	characteristic
121	C₂×C₄	#64541	1	2	yes	—
122	C₂×C₄	C₂³×D₁₉	1	1	yes	characteristic
123	C₈	—	2	2	no	—
124	C₈	C₂×C₄×D₁₉	1	4	yes	—
125	C₂²	C₄×D₇₆	1	2	yes	—
126	C₂²	#10597355	1	4	yes	—
127	C₂²	C₂²×D₇₆	1	1	yes	characteristic
128	C₄	—	2	4	no	—
129	C₄	—	38	8	no	—
130	C₄	—	76	4	no	—
131	C₄	C₄×D₇₆	1	2	yes	—
132	C₄	C₂²×C₄×D₁₉	1	1	yes	characteristic
133	C₄	C₂×#64541	1	1	yes	characteristic
134	C₂	#11926652	1	4	yes	direct product factor
135	C₂	C₂×C₄×D₇₆	1	1	yes	characteristic
136	C₂	C₂×#10597355	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

C₂²×Dic₇₆

C₂

yes

maximal, characteristic

C₂×C₄×Dic₃₈

C₂

yes

maximal

#11926652

C₂

yes

maximal, direct product factor

C₂×#10597274

C₂

yes

maximal, characteristic

C₂×#10597273

C₂

yes

maximal

C₂×C₁₉×#97

C₂

yes

maximal, characteristic

C₂²×Dic₃₈

C₂²

yes

—

C₂²×C₈×C₁₉

C₂²

yes

characteristic

C₂²×C₈×C₁₉

C₂²

yes

characteristic

C₂×C₄²×C₁₉

C₂²

yes

characteristic

C₂×C₄⋊Dic₁₉

C₂²

yes

—

C₂×Dic₁₉⋊C₄

—

C₂×C₄×Dic₁₉

—

C₂×Dic₇₆

C₄

yes

complemented

C₂×Dic₇₆

C₂²

yes

—

C₄×Dic₃₈

—

C₄×Dic₃₈

C₂²

yes

—

C₁₉×#97

C₂²

yes

—

#10597274

C₂²

yes

—

#10597273

C₂²

yes

—

C₂²×C₄×C₁₉

D₄

yes

—

C₂²×C₄×C₁₉

C₂³

yes

characteristic

C₂²×Dic₁₉

—

C₂²×Dic₁₉

—

C₂×Dic₃₈

—

C₂×Dic₃₈

—

C₂×Dic₃₈

C₂×C₄

yes

—

C₂×Dic₃₈

C₂³

yes

—

C₂×C₈×C₁₉

—

C₂×C₈×C₁₉

C₂×C₄

yes

—

C₂×C₈×C₁₉

C₂³

yes

—

C₂×C₈×C₁₉

C₂³

yes

—

C₄²×C₁₉

D₄

yes

—

C₄²×C₁₉

C₂³

yes

—

C₄⋊Dic₁₉

—

C₄⋊Dic₁₉

C₂³

yes

—

Dic₁₉⋊C₄

—

C₄×Dic₁₉

—

Dic₇₆

C₂×C₄

yes

complemented

C₂³×C₁₉

C₂×D₄

yes

characteristic

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

C₂²×C₄

yes

—

C₂×C₄×C₁₉

C₂×D₄

yes

—

C₂×C₄×C₁₉

C₂×D₄

yes

characteristic

C₂×C₄×C₁₉

#41

yes

—

C₂×C₄×C₁₉

C₂⁴

yes

characteristic

C₂×Dic₁₉

—

C₂×Dic₁₉

—

C₂×Dic₁₉

—

C₂×Dic₁₉

—

Dic₃₈

—

Dic₃₈

—

Dic₃₈

C₂²×C₄

yes

—

C₈×C₁₉

—

C₈×C₁₉

C₂²×C₄

yes

—

C₂×#441

—

maximal, Sylow

C₂²×C₁₉

C₄×D₄

yes

—

C₂²×C₁₉

#137

yes

—

C₂²×C₁₉

C₂²×D₄

yes

characteristic

C₄×C₁₉

—

C₄×C₁₉

C₄×D₄

yes

—

C₄×C₁₉

C₂³×C₄

yes

characteristic

C₄×C₁₉

C₂×#41

yes

characteristic

Dic₁₉

—

Dic₁₉

—

C₂²×Q₁₆

—

C₂×C₄×Q₈

—

#441

—

C₂×#106

—

C₂×#103

—

C₂×#97

D₁₉

yes

characteristic

C₂×C₁₉

#441

yes

complemented

C₂×C₁₉

C₂×C₄×D₄

yes

characteristic

C₂×C₁₉

C₂×#137

yes

—

C₂²×Q₈

—

C₂×Q₁₆

—

C₂×Q₁₆

—

C₂²×C₈

C₂×D₁₉

yes

characteristic

C₂²×C₈

C₂×D₁₉

yes

characteristic

C₄×Q₈

—

C₄×Q₈

—

C₂×C₄⋊C₄

—

C₂×C₄⋊C₄

—

C₂×C₄²

—

C₂×C₄²

C₂×D₁₉

yes

—

—

C₂×D₁₉

yes

—

C₁₉

C₂×#441

yes

characteristic, complemented, Sylow

C₂×Q₈

—

C₂×Q₈

—

C₂×Q₈

—

C₂×Q₈

—

C₂²×C₄

—

C₂²×C₄

—

C₂²×C₄

D₇₆

yes

—

C₂²×C₄

C₂²×D₁₉

yes

characteristic

Q₁₆

—

C₂×C₈

—

100

C₂×C₈

C₄×D₁₉

yes

—

101

C₂×C₈

C₂²×D₁₉

yes

—

102

C₂×C₈

C₂²×D₁₉

yes

—

103

C₄⋊C₄

—

104

C₄⋊C₄

—

105

C₄⋊C₄

—

106

C₄²

—

107

C₄²

D₇₆

yes

—

108

C₄²

C₂²×D₁₉

yes

—

109

C₂³

C₂×D₇₆

yes

characteristic

110

Q₈

—

111

Q₈

—

112

Q₈

—

113

C₂×C₄

—

114

C₂×C₄

—

115

C₂×C₄

—

116

C₂×C₄

—

117

C₂×C₄

—

118

C₂×C₄

C₂×C₄×D₁₉

yes

—

119

C₂×C₄

C₂×D₇₆

yes

—

120

C₂×C₄

C₂×D₇₆

yes

characteristic

121

C₂×C₄

#64541

yes

—

122

C₂×C₄

C₂³×D₁₉

yes

characteristic

123

C₈

—

124

C₈

C₂×C₄×D₁₉

yes

—

125

C₂²

C₄×D₇₆

yes

—

126

C₂²

#10597355

yes

—

127

C₂²

C₂²×D₇₆

yes

characteristic

128

C₄

—

129

C₄

—

130

C₄

—

131

C₄

C₄×D₇₆

yes

—

132

C₄

C₂²×C₄×D₁₉

yes

characteristic

133

C₄

C₂×#64541

yes

characteristic

134

C₂

#11926652

yes

direct product factor

135

C₂

C₂×C₄×D₇₆

yes

characteristic

136

C₂

C₂×#10597355

yes

—

	subgroup	G/H
center	C₂³	C₂×D₇₆
commutator	C₄×C₁₉	C₂³×C₄
Frattini	C₂×C₄	C₂³×D₁₉
Fitting	C₂×C₁₉×#97	C₂
socle, prime radical	C₂³×C₁₉	C₂×D₄
cosocle	C₂×C₄×C₁₉	C₂⁴
hypercenter	C₂×#97	D₁₉
hypocenter	C₁₉	C₂×#441
LCS	G ▷ C₄×C₁₉ ▷ C₂×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂³ ◁ C₂×C₄² ◁ C₂×#97

subgroup

G/H

center

C₂³

C₂×D₇₆

commutator

C₄×C₁₉

C₂³×C₄

Frattini

C₂×C₄

C₂³×D₁₉

Fitting

C₂×C₁₉×#97

C₂

socle, prime radical

C₂³×C₁₉

C₂×D₄

cosocle

C₂×C₄×C₁₉

C₂⁴

hypercenter

C₂×#97

D₁₉

hypocenter

C₁₉

C₂×#441

LCS

G ▷ C₄×C₁₉ ▷ C₂×C₁₉ ▷ C₁₉

UCS

C₁ ◁ C₂³ ◁ C₂×C₄² ◁ C₂×#97

N	H ≅ G/N	type
3. #11926652	C₂	direct (N × H)
14. C₂×Dic₇₆	C₄	semidirect
39. Dic₇₆	C₂×C₄	semidirect
72. C₂×C₁₉	#441	semidirect
89. C₁₉	C₂×#441	semidirect
134. C₂	#11926652	direct (N × H)

H ≅ G/N

type

3. #11926652

C₂

direct (N × H)

14. C₂×Dic₇₆

C₄

semidirect

39. Dic₇₆

C₂×C₄

semidirect

72. C₂×C₁₉

#441

semidirect

89. C₁₉

C₂×#441

semidirect

134. C₂

#11926652

direct (N × H)

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

subgroup	index
C₂²×Dic₇₆	2
C₂×C₄×Dic₃₈	2
#11926652	2
C₂×#10597274	2
C₂×#10597273	2
C₂×C₁₉×#97	2
C₂×#441	19

subgroup

index

C₂²×Dic₇₆

C₂×C₄×Dic₃₈

C₂×C₁₉×#97

Subgroups — C₂×#11926652 #14572423

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C2×#11926652 #14572423

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#11926652 #14572423