Group #14572008 — subgroups

Subgroups — #14572008

Order 2432.

524 conjugacy classes of subgroups; only the 157 normal subgroups are shown.

normal subgroups only

This group has 524 conjugacy classes of subgroups — too many to draw. Only its 157 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×#10597321	C₂	1	1	yes	maximal, characteristic
2	#11926449	C₂	1	2	yes	maximal, complemented
3	#11926445	C₂	1	2	yes	maximal
4	#11926434	C₂	1	8	yes	maximal, complemented
5	C₄²×Dic₁₉	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×C₁₉×#125	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂²×D₇₆	C₂²	1	1	yes	characteristic
8	C₂²×Dic₃₈	C₂²	1	1	yes	characteristic
9	C₁₉×#125	—	2	4	no	—
10	C₂×C₄⋊C₄×C₁₉	C₂²	1	4	yes	—
11	C₂×C₄⋊C₄×C₁₉	C₂²	1	2	yes	—
12	C₂×C₄²×C₁₉	C₂²	1	1	yes	characteristic
13	C₂×(C₂×D₁₉)⋊C₄	C₂²	1	4	yes	—
14	C₂×(C₂×D₁₉)⋊C₄	C₂²	1	8	yes	—
15	C₂×C₄×Dic₁₉	C₂²	1	4	yes	—
16	C₂×C₄×Dic₁₉	C₂²	1	2	yes	—
17	#10597321	—	2	4	no	—
18	C₁₉⋊#95	C₂²	1	8	yes	—
19	C₂³×D₁₉	C₂³	1	2	yes	—
20	C₂²×C₄×C₁₉	C₂³	1	4	yes	—
21	C₂²×C₄×C₁₉	C₂³	1	2	yes	—
22	C₂²×C₄×C₁₉	C₂³	1	1	yes	characteristic
23	C₂²×Dic₁₉	C₂³	1	2	yes	—
24	C₂²×Dic₁₉	C₂³	1	4	yes	—
25	C₂×D₇₆	—	2	2	no	—
26	C₂×D₇₆	—	2	4	no	—
27	C₂×Dic₃₈	—	2	2	no	—
28	C₂×Dic₃₈	—	2	4	no	—
29	C₄⋊C₄×C₁₉	—	2	8	no	—
30	C₄⋊C₄×C₁₉	—	2	4	no	—
31	C₄²×C₁₉	D₄	1	4	yes	—
32	(C₂×D₁₉)⋊C₄	—	2	8	no	—
33	(C₂×D₁₉)⋊C₄	—	2	16	no	—
34	C₄×Dic₁₉	—	2	4	no	—
35	C₄×Dic₁₉	—	2	8	no	—
36	C₂³×C₁₉	C₂⁴	1	1	yes	characteristic
37	C₂²×D₁₉	—	2	2	no	—
38	C₂²×D₁₉	—	2	8	no	—
39	C₂²×D₁₉	—	2	4	no	—
40	C₂×C₄×C₁₉	—	2	4	no	—
41	C₂×C₄×C₁₉	—	2	4	no	—
42	C₂×C₄×C₁₉	—	2	8	no	—
43	C₂×C₄×C₁₉	C₂×D₄	1	4	yes	—
44	C₂×C₄×C₁₉	C₂×D₄	1	2	yes	—
45	C₂×C₄×C₁₉	#41	1	4	yes	—
46	C₂×Dic₁₉	—	2	4	no	—
47	C₂×Dic₁₉	—	2	4	no	—
48	C₂×Dic₁₉	—	2	2	no	—
49	C₂×Dic₁₉	—	2	4	no	—
50	C₂×Dic₁₉	#41	1	8	yes	—
51	D₇₆	—	4	4	no	—
52	Dic₃₈	—	4	4	no	—
53	#2861	—	19	1	no	maximal, Sylow
54	C₂²×C₁₉	C₂²×D₄	1	1	yes	characteristic
55	C₂²×C₁₉	C₂×#41	1	2	yes	—
56	C₂²×C₁₉	C₂×#41	1	4	yes	—
57	C₂×D₁₉	—	4	2	no	—
58	C₂×D₁₉	—	4	8	no	—
59	C₂×D₁₉	—	4	4	no	—
60	C₄×C₁₉	—	2	4	no	—
61	C₄×C₁₉	—	4	4	no	—
62	C₄×C₁₉	#124	1	4	yes	—
63	Dic₁₉	—	2	8	no	—
64	Dic₁₉	—	4	2	no	—
65	C₂×#125	D₁₉	1	1	yes	characteristic, complemented
66	C₂×#124	—	19	1	no	—
67	#391	—	19	2	no	—
68	#390	—	19	2	no	—
69	#388	—	19	8	no	—
70	C₄³	—	19	1	no	—
71	C₂×C₁₉	C₂×#124	1	1	yes	characteristic
72	C₂×C₁₉	#529	1	4	yes	—
73	C₂×C₁₉	#532	1	2	yes	—
74	D₁₉	—	8	2	no	—
75	C₂²×Q₈	—	19	1	no	—
76	C₂²×D₄	—	19	1	no	—
77	#125	—	2	4	no	—
78	#124	—	38	4	no	—
79	C₂×C₄⋊C₄	C₂×D₁₉	1	4	yes	—
80	C₂×C₄⋊C₄	C₂×D₁₉	1	2	yes	—
81	C₂×C₂²⋊C₄	—	19	4	no	—
82	C₂×C₂²⋊C₄	—	19	8	no	—
83	C₂×C₄²	—	19	4	no	—
84	C₂×C₄²	—	19	2	no	—
85	C₂×C₄²	C₂×D₁₉	1	1	yes	characteristic
86	#95	—	19	8	no	—
87	C₁₉	#2861	1	1	yes	characteristic, complemented, Sylow
88	C₂⁴	—	19	2	no	—
89	C₂×Q₈	—	38	4	no	—
90	C₂×Q₈	—	38	2	no	—
91	C₂×D₄	—	38	4	no	—
92	C₂×D₄	—	38	2	no	—
93	C₂²×C₄	—	19	4	no	—
94	C₂²×C₄	—	19	2	no	—
95	C₂²×C₄	C₂²×D₁₉	1	4	yes	—
96	C₂²×C₄	C₂²×D₁₉	1	2	yes	—
97	C₂²×C₄	C₂²×D₁₉	1	1	yes	characteristic
98	C₄⋊C₄	—	2	8	no	—
99	C₄⋊C₄	—	2	4	no	—
100	C₂²⋊C₄	—	38	16	no	—
101	C₂²⋊C₄	—	38	8	no	—
102	C₄²	—	38	8	no	—
103	C₄²	—	38	4	no	—
104	C₄²	C₂²⋊D₁₉	1	4	yes	—
105	C₂³	—	38	4	no	—
106	C₂³	—	38	8	no	—
107	C₂³	—	38	2	no	—
108	C₂³	C₂³×D₁₉	1	1	yes	characteristic
109	Q₈	—	76	4	no	—
110	D₄	—	76	4	no	—
111	C₂×C₄	—	2	4	no	—
112	C₂×C₄	—	2	8	no	—
113	C₂×C₄	—	2	4	no	—
114	C₂×C₄	—	19	8	no	—
115	C₂×C₄	—	38	4	no	—
116	C₂×C₄	—	38	4	no	—
117	C₂×C₄	—	38	4	no	—
118	C₂×C₄	—	38	2	no	—
119	C₂×C₄	#64545	1	4	yes	—
120	C₂×C₄	C₂×C₂²⋊D₁₉	1	4	yes	—
121	C₂×C₄	C₂×C₂²⋊D₁₉	1	2	yes	—
122	C₂²	—	76	2	no	—
123	C₂²	—	76	8	no	—
124	C₂²	—	76	4	no	—
125	C₂²	C₂×#64545	1	2	yes	—
126	C₂²	#41×D₁₉	1	4	yes	—
127	C₂²	C₂²×C₂²⋊D₁₉	1	1	yes	characteristic
128	C₄	—	2	4	no	—
129	C₄	—	4	4	no	—
130	C₄	—	38	8	no	—
131	C₄	—	76	2	no	—
132	C₄	#10597393	1	4	yes	—
133	C₂	—	152	2	no	—
134	C₂	C₂×#10597393	1	1	yes	characteristic
135	C₂	#11927079	1	4	yes	—
136	C₂	#11927090	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×#10597321

C₂

yes

maximal, characteristic

#11926449

C₂

yes

maximal, complemented

#11926445

C₂

yes

maximal

#11926434

C₂

yes

maximal, complemented

C₄²×Dic₁₉

C₂

yes

maximal, characteristic, complemented

C₂×C₁₉×#125

C₂

yes

maximal, characteristic, complemented

C₂²×D₇₆

C₂²

yes

characteristic

C₂²×Dic₃₈

C₂²

yes

characteristic

C₁₉×#125

—

C₂×C₄⋊C₄×C₁₉

C₂²

yes

—

C₂×C₄⋊C₄×C₁₉

C₂²

yes

—

C₂×C₄²×C₁₉

C₂²

yes

characteristic

C₂×(C₂×D₁₉)⋊C₄

C₂²

yes

—

C₂×(C₂×D₁₉)⋊C₄

C₂²

yes

—

C₂×C₄×Dic₁₉

C₂²

yes

—

C₂×C₄×Dic₁₉

C₂²

yes

—

#10597321

—

C₁₉⋊#95

C₂²

yes

—

C₂³×D₁₉

C₂³

yes

—

C₂²×C₄×C₁₉

C₂³

yes

—

C₂²×C₄×C₁₉

C₂³

yes

—

C₂²×C₄×C₁₉

C₂³

yes

characteristic

C₂²×Dic₁₉

C₂³

yes

—

C₂²×Dic₁₉

C₂³

yes

—

C₂×D₇₆

—

C₂×D₇₆

—

C₂×Dic₃₈

—

C₂×Dic₃₈

—

C₄⋊C₄×C₁₉

—

C₄⋊C₄×C₁₉

—

C₄²×C₁₉

D₄

yes

—

(C₂×D₁₉)⋊C₄

—

(C₂×D₁₉)⋊C₄

—

C₄×Dic₁₉

—

C₄×Dic₁₉

—

C₂³×C₁₉

C₂⁴

yes

characteristic

C₂²×D₁₉

—

C₂²×D₁₉

—

C₂²×D₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

C₂×D₄

yes

—

C₂×C₄×C₁₉

C₂×D₄

yes

—

C₂×C₄×C₁₉

#41

yes

—

C₂×Dic₁₉

—

C₂×Dic₁₉

—

C₂×Dic₁₉

—

C₂×Dic₁₉

—

C₂×Dic₁₉

#41

yes

—

D₇₆

—

Dic₃₈

—

#2861

—

maximal, Sylow

C₂²×C₁₉

C₂²×D₄

yes

characteristic

C₂²×C₁₉

C₂×#41

yes

—

C₂²×C₁₉

C₂×#41

yes

—

C₂×D₁₉

—

C₂×D₁₉

—

C₂×D₁₉

—

C₄×C₁₉

—

C₄×C₁₉

—

C₄×C₁₉

#124

yes

—

Dic₁₉

—

Dic₁₉

—

C₂×#125

D₁₉

yes

characteristic, complemented

—

—

—

—

C₄³

—

C₂×C₁₉

C₂×#124

yes

characteristic

C₂×C₁₉

#529

yes

—

C₂×C₁₉

#532

yes

—

D₁₉

—

C₂²×Q₈

—

C₂²×D₄

—

#125

—

#124

—

C₂×C₄⋊C₄

C₂×D₁₉

yes

—

C₂×C₄⋊C₄

C₂×D₁₉

yes

—

C₂×C₂²⋊C₄

—

C₂×C₂²⋊C₄

—

C₂×C₄²

—

C₂×C₄²

—

C₂×C₄²

C₂×D₁₉

yes

characteristic

#95

—

C₁₉

#2861

yes

characteristic, complemented, Sylow

C₂⁴

—

C₂×Q₈

—

C₂×Q₈

—

C₂×D₄

—

C₂×D₄

—

C₂²×C₄

—

C₂²×C₄

—

C₂²×C₄

C₂²×D₁₉

yes

—

C₂²×C₄

C₂²×D₁₉

yes

—

C₂²×C₄

C₂²×D₁₉

yes

characteristic

C₄⋊C₄

—

C₄⋊C₄

—

100

C₂²⋊C₄

—

101

C₂²⋊C₄

—

102

C₄²

—

103

C₄²

—

104

C₄²

C₂²⋊D₁₉

yes

—

105

C₂³

—

106

C₂³

—

107

C₂³

—

108

C₂³

C₂³×D₁₉

yes

characteristic

109

Q₈

—

110

D₄

—

111

C₂×C₄

—

112

C₂×C₄

—

113

C₂×C₄

—

114

C₂×C₄

—

115

C₂×C₄

—

116

C₂×C₄

—

117

C₂×C₄

—

118

C₂×C₄

—

119

C₂×C₄

#64545

yes

—

120

C₂×C₄

C₂×C₂²⋊D₁₉

yes

—

121

C₂×C₄

C₂×C₂²⋊D₁₉

yes

—

122

C₂²

—

123

C₂²

—

124

C₂²

—

125

C₂²

C₂×#64545

yes

—

126

C₂²

#41×D₁₉

yes

—

127

C₂²

C₂²×C₂²⋊D₁₉

yes

characteristic

128

C₄

—

129

C₄

—

130

C₄

—

131

C₄

—

132

C₄

#10597393

yes

—

133

C₂

—

152

—

134

C₂

C₂×#10597393

yes

characteristic

135

C₂

#11927079

yes

—

136

C₂

#11927090

yes

—

	subgroup	G/H
center, Frattini	C₂³	C₂³×D₁₉
commutator, socle, cosocle	C₂³×C₁₉	C₂⁴
Fitting	C₂×C₁₉×#125	C₂
prime radical	C₂²×D₇₆	C₂²
hypercenter	C₂×#125	D₁₉
hypocenter	C₁₉	#2861
LCS	G ▷ C₂³×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂³ ◁ C₂×#125

subgroup

G/H

center, Frattini

C₂³

C₂³×D₁₉

commutator, socle, cosocle

C₂³×C₁₉

C₂⁴

Fitting

C₂×C₁₉×#125

C₂

prime radical

C₂²×D₇₆

C₂²

D₁₉

C₁₉

G ▷ C₂³×C₁₉ ▷ C₁₉

C₁ ◁ C₂³ ◁ C₂×#125

N	H ≅ G/N	type
2. #11926449	C₂	semidirect
4. #11926434	C₂	semidirect
5. C₄²×Dic₁₉	C₂	semidirect
6. C₂×C₁₉×#125	C₂	semidirect
65. C₂×#125	D₁₉	semidirect
87. C₁₉	#2861	semidirect

H ≅ G/N

type

2. #11926449

C₂

semidirect

4. #11926434

C₂

semidirect

5. C₄²×Dic₁₉

C₂

semidirect

6. C₂×C₁₉×#125

C₂

semidirect

65. C₂×#125

D₁₉

semidirect

87. C₁₉

#2861

semidirect

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

subgroup	index
C₂×#10597321	2
#11926449	2
#11926445	2
#11926434	2
C₄²×Dic₁₉	2
C₂×C₁₉×#125	2
#2861	19

subgroup

index

C₄²×Dic₁₉

C₂×C₁₉×#125

#2861

Subgroups — #14572008

Conjugacy classes of subgroups

Complements

Maximal subgroups