Group #14571922 — subgroups

Subgroups — #14571922

Order 2432.

1068 conjugacy classes of subgroups; only the 237 normal subgroups are shown.

normal subgroups only

This group has 1068 conjugacy classes of subgroups — too many to draw. Only its 237 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	3	yes	maximal, complemented
2	#11926417	C₂	1	6	yes	maximal, complemented
3	#11926404	C₂	1	3	yes	maximal, complemented
4	#11926400	C₂	1	2	yes	maximal
5	C₂⁴×C₄×C₁₉	C₂	1	1	yes	maximal, characteristic
6	C₂⁵×C₁₉	C₂²	1	1	yes	characteristic
7	C₂³×C₄×C₁₉	—	2	12	no	—
8	C₂³×C₄×C₁₉	C₂²	1	3	yes	—
9	C₂³×C₄×C₁₉	C₂²	1	3	yes	—
10	C₂²×Dic₃₈	C₂²	1	1	yes	characteristic, complemented
11	C₂×C₂²⋊Dic₁₉	C₂²	1	6	yes	—
12	C₂×C₂²⋊Dic₁₉	C₂²	1	6	yes	—
13	C₂×C₄⋊Dic₁₉	C₂²	1	3	yes	complemented
14	#10597370	—	2	12	no	—
15	C₂×Dic₁₉⋊C₄	C₂²	1	6	yes	complemented
16	C₁₉⋊#95	C₂²	1	6	yes	complemented
17	C₂⁴×C₁₉	—	2	6	no	—
18	C₂⁴×C₁₉	—	2	6	no	—
19	C₂⁴×C₁₉	Q₈	1	4	yes	complemented
20	C₂⁴×C₁₉	C₂³	1	3	yes	—
21	C₂²×C₄×C₁₉	—	2	32	no	—
22	C₂²×C₄×C₁₉	—	2	6	no	—
23	C₂²×C₄×C₁₉	—	2	12	no	—
24	C₂²×C₄×C₁₉	—	2	12	no	—
25	C₂²×C₄×C₁₉	D₄	1	12	yes	—
26	C₂²×C₄×C₁₉	C₂³	1	3	yes	—
27	C₂²×C₄×C₁₉	C₂³	1	1	yes	characteristic
28	C₂²×Dic₁₉	C₂³	1	2	yes	—
29	C₂²×Dic₁₉	C₂³	1	6	yes	—
30	C₂×Dic₃₈	—	2	6	no	—
31	C₂²⋊Dic₁₉	—	2	12	no	—
32	C₂²⋊Dic₁₉	—	2	12	no	—
33	C₄⋊Dic₁₉	—	2	6	no	—
34	Dic₁₉⋊C₄	—	2	12	no	—
35	C₂³×C₁₉	—	2	8	no	—
36	C₂³×C₁₉	—	2	24	no	—
37	C₂³×C₁₉	—	2	24	no	—
38	C₂³×C₁₉	—	2	6	no	—
39	C₂³×C₁₉	—	2	6	no	—
40	C₂³×C₁₉	C₂×D₄	1	6	yes	—
41	C₂³×C₁₉	C₂×Q₈	1	6	yes	—
42	C₂³×C₁₉	#41	1	6	yes	—
43	C₂³×C₁₉	C₂⁴	1	1	yes	characteristic
44	C₂×C₄×C₁₉	—	2	24	no	—
45	C₂×C₄×C₁₉	—	2	6	no	—
46	C₂×C₄×C₁₉	—	2	24	no	—
47	C₂×C₄×C₁₉	C₂×D₄	1	6	yes	—
48	C₂×C₄×C₁₉	C₂×D₄	1	6	yes	—
49	C₂×Dic₁₉	—	2	6	no	—
50	C₂×Dic₁₉	—	2	6	no	—
51	C₂×Dic₁₉	—	2	12	no	—
52	Dic₃₈	—	4	4	no	—
53	#2848	—	19	1	no	maximal, Sylow
54	C₂²×C₁₉	—	2	32	no	—
55	C₂²×C₁₉	—	2	6	no	—
56	C₂²×C₁₉	—	2	12	no	—
57	C₂²×C₁₉	—	2	6	no	—
58	C₂²×C₁₉	—	2	12	no	—
59	C₂²×C₁₉	C₂²⋊Q₈	1	12	yes	complemented
60	C₂²×C₁₉	C₂²×D₄	1	3	yes	—
61	C₂²×C₁₉	C₂²×Q₈	1	1	yes	characteristic
62	C₂²×C₁₉	C₂×#41	1	3	yes	—
63	C₄×C₁₉	—	2	6	no	—
64	C₄×C₁₉	#120	1	4	yes	—
65	Dic₁₉	—	4	2	no	—
66	Dic₁₉	—	4	6	no	—
67	C₂⁴×C₄	D₁₉	1	1	yes	characteristic
68	C₂×C₂²⋊Q₈	—	19	3	no	—
69	#385	—	19	6	no	—
70	#380	—	19	3	no	—
71	#379	—	19	2	no	—
72	C₂×C₁₉	—	2	12	no	—
73	C₂×C₁₉	C₂×#120	1	1	yes	characteristic
74	C₂×C₁₉	C₂×C₂²⋊Q₈	1	3	yes	—
75	C₂×C₁₉	#525	1	3	yes	—
76	C₂⁵	C₂×D₁₉	1	1	yes	characteristic
77	C₂²×Q₈	—	19	1	no	—
78	C₂³×C₄	—	2	12	no	—
79	C₂³×C₄	C₂×D₁₉	1	3	yes	—
80	C₂³×C₄	C₂×D₁₉	1	3	yes	—
81	C₂²⋊Q₈	—	38	12	no	—
82	C₂×C₄⋊C₄	—	19	3	no	—
83	C₂×C₄⋊C₄	—	19	6	no	—
84	C₂×C₂²⋊C₄	—	19	6	no	—
85	C₂×C₂²⋊C₄	—	19	6	no	—
86	#95	—	19	6	no	—
87	C₁₉	#2848	1	1	yes	characteristic, complemented, Sylow
88	C₂⁴	—	2	6	no	—
89	C₂⁴	—	2	6	no	—
90	C₂⁴	Dic₃₈	1	4	yes	complemented
91	C₂⁴	C₂²×D₁₉	1	3	yes	—
92	C₂×Q₈	—	38	6	no	—
93	C₂²×C₄	—	2	32	no	—
94	C₂²×C₄	—	2	6	no	—
95	C₂²×C₄	—	2	12	no	—
96	C₂²×C₄	—	2	12	no	—
97	C₂²×C₄	—	19	6	no	—
98	C₂²×C₄	—	19	2	no	—
99	C₂²×C₄	C₂²⋊D₁₉	1	12	yes	—
100	C₂²×C₄	C₂²×D₁₉	1	3	yes	—
101	C₂²×C₄	C₂²×D₁₉	1	1	yes	characteristic
102	C₄⋊C₄	—	38	12	no	—
103	C₄⋊C₄	—	38	6	no	—
104	C₂²⋊C₄	—	38	12	no	—
105	C₂²⋊C₄	—	38	12	no	—
106	C₂³	—	2	8	no	—
107	C₂³	—	2	24	no	—
108	C₂³	—	2	6	no	—
109	C₂³	—	2	6	no	—
110	C₂³	—	2	24	no	—
111	C₂³	C₂×Dic₃₈	1	6	yes	—
112	C₂³	#64541	1	6	yes	—
113	C₂³	C₂×C₂²⋊D₁₉	1	6	yes	—
114	C₂³	C₂³×D₁₉	1	1	yes	characteristic
115	Q₈	—	76	4	no	—
116	C₂×C₄	—	2	24	no	—
117	C₂×C₄	—	2	6	no	—
118	C₂×C₄	—	2	24	no	—
119	C₂×C₄	—	38	12	no	—
120	C₂×C₄	—	38	6	no	—
121	C₂×C₄	—	38	6	no	—
122	C₂×C₄	C₂×C₂²⋊D₁₉	1	6	yes	—
123	C₂×C₄	C₂×C₂²⋊D₁₉	1	6	yes	—
124	C₂²	—	2	32	no	—
125	C₂²	—	2	12	no	—
126	C₂²	—	2	12	no	—
127	C₂²	—	2	6	no	—
128	C₂²	—	2	6	no	—
129	C₂²	#10597370	1	12	yes	complemented
130	C₂²	C₂²×Dic₃₈	1	1	yes	characteristic
131	C₂²	C₂×#64541	1	3	yes	—
132	C₂²	C₂²×C₂²⋊D₁₉	1	3	yes	—
133	C₄	—	2	6	no	—
134	C₄	—	76	6	no	—
135	C₄	—	76	2	no	—
136	C₄	#10597399	1	4	yes	—
137	C₂	—	2	12	no	—
138	C₂	C₂×#10597399	1	1	yes	characteristic
139	C₂	C₂×#10597370	1	3	yes	—
140	C₂	#11927055	1	3	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×#10597370

C₂

yes

maximal, complemented

#11926417

C₂

yes

maximal, complemented

#11926404

C₂

yes

maximal, complemented

#11926400

C₂

yes

maximal

C₂⁴×C₄×C₁₉

C₂

yes

maximal, characteristic

C₂⁵×C₁₉

C₂²

yes

characteristic

C₂³×C₄×C₁₉

—

C₂³×C₄×C₁₉

C₂²

yes

—

C₂³×C₄×C₁₉

C₂²

yes

—

C₂²×Dic₃₈

C₂²

yes

characteristic, complemented

C₂×C₂²⋊Dic₁₉

C₂²

yes

—

C₂×C₂²⋊Dic₁₉

C₂²

yes

—

C₂×C₄⋊Dic₁₉

C₂²

yes

complemented

#10597370

—

C₂×Dic₁₉⋊C₄

C₂²

yes

complemented

C₁₉⋊#95

C₂²

yes

complemented

C₂⁴×C₁₉

—

C₂⁴×C₁₉

—

C₂⁴×C₁₉

Q₈

yes

complemented

C₂⁴×C₁₉

C₂³

yes

—

C₂²×C₄×C₁₉

—

C₂²×C₄×C₁₉

—

C₂²×C₄×C₁₉

—

C₂²×C₄×C₁₉

—

C₂²×C₄×C₁₉

D₄

yes

—

C₂²×C₄×C₁₉

C₂³

yes

—

C₂²×C₄×C₁₉

C₂³

yes

characteristic

C₂²×Dic₁₉

C₂³

yes

—

C₂²×Dic₁₉

C₂³

yes

—

C₂×Dic₃₈

—

C₂²⋊Dic₁₉

—

C₂²⋊Dic₁₉

—

C₄⋊Dic₁₉

—

Dic₁₉⋊C₄

—

C₂³×C₁₉

—

C₂³×C₁₉

—

C₂³×C₁₉

—

C₂³×C₁₉

—

C₂³×C₁₉

—

C₂³×C₁₉

C₂×D₄

yes

—

C₂³×C₁₉

C₂×Q₈

yes

—

C₂³×C₁₉

#41

yes

—

C₂³×C₁₉

C₂⁴

yes

characteristic

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

C₂×D₄

yes

—

C₂×C₄×C₁₉

C₂×D₄

yes

—

C₂×Dic₁₉

—

C₂×Dic₁₉

—

C₂×Dic₁₉

—

Dic₃₈

—

#2848

—

maximal, Sylow

C₂²×C₁₉

—

C₂²×C₁₉

—

C₂²×C₁₉

—

C₂²×C₁₉

—

C₂²×C₁₉

—

C₂²×C₁₉

C₂²⋊Q₈

yes

complemented

C₂²×C₁₉

C₂²×D₄

yes

—

C₂²×C₁₉

C₂²×Q₈

yes

characteristic

C₂²×C₁₉

C₂×#41

yes

—

C₄×C₁₉

—

C₄×C₁₉

#120

yes

—

Dic₁₉

—

Dic₁₉

—

C₂⁴×C₄

D₁₉

yes

characteristic

C₂×C₂²⋊Q₈

—

#385

—

#380

—

#379

—

C₂×C₁₉

—

C₂×C₁₉

C₂×#120

yes

characteristic

C₂×C₁₉

C₂×C₂²⋊Q₈

yes

—

C₂×C₁₉

#525

yes

—

C₂⁵

C₂×D₁₉

yes

characteristic

C₂²×Q₈

—

C₂³×C₄

—

C₂³×C₄

C₂×D₁₉

yes

—

C₂³×C₄

C₂×D₁₉

yes

—

C₂²⋊Q₈

—

C₂×C₄⋊C₄

—

C₂×C₄⋊C₄

—

C₂×C₂²⋊C₄

—

C₂×C₂²⋊C₄

—

#95

—

C₁₉

#2848

yes

characteristic, complemented, Sylow

C₂⁴

—

C₂⁴

—

C₂⁴

Dic₃₈

yes

complemented

C₂⁴

C₂²×D₁₉

yes

—

C₂×Q₈

—

C₂²×C₄

—

C₂²×C₄

—

C₂²×C₄

—

C₂²×C₄

—

C₂²×C₄

—

C₂²×C₄

—

C₂²×C₄

C₂²⋊D₁₉

yes

—

100

C₂²×C₄

C₂²×D₁₉

yes

—

101

C₂²×C₄

C₂²×D₁₉

yes

characteristic

102

C₄⋊C₄

—

103

C₄⋊C₄

—

104

C₂²⋊C₄

—

105

C₂²⋊C₄

—

106

C₂³

—

107

C₂³

—

108

C₂³

—

109

C₂³

—

110

C₂³

—

111

C₂³

C₂×Dic₃₈

yes

—

112

C₂³

#64541

yes

—

113

C₂³

C₂×C₂²⋊D₁₉

yes

—

114

C₂³

C₂³×D₁₉

yes

characteristic

115

Q₈

—

116

C₂×C₄

—

117

C₂×C₄

—

118

C₂×C₄

—

119

C₂×C₄

—

120

C₂×C₄

—

121

C₂×C₄

—

122

C₂×C₄

C₂×C₂²⋊D₁₉

yes

—

123

C₂×C₄

C₂×C₂²⋊D₁₉

yes

—

124

C₂²

—

125

C₂²

—

126

C₂²

—

127

C₂²

—

128

C₂²

—

129

C₂²

#10597370

yes

complemented

130

C₂²

C₂²×Dic₃₈

yes

characteristic

131

C₂²

C₂×#64541

yes

—

132

C₂²

C₂²×C₂²⋊D₁₉

yes

—

133

C₄

—

134

C₄

—

135

C₄

—

136

C₄

#10597399

yes

—

137

C₂

—

138

C₂

C₂×#10597399

yes

characteristic

139

C₂

C₂×#10597370

yes

—

140

C₂

#11927055

yes

—

	subgroup	G/H
center, Frattini	C₂³	C₂³×D₁₉
commutator, socle, cosocle	C₂³×C₁₉	C₂⁴
Fitting	C₂⁴×C₄×C₁₉	C₂
prime radical	C₂⁵×C₁₉	C₂²
hypercenter	C₂⁴×C₄	D₁₉
hypocenter	C₁₉	#2848
LCS	G ▷ C₂³×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂³ ◁ C₂⁴×C₄

subgroup

G/H

center, Frattini

C₂³

C₂³×D₁₉

commutator, socle, cosocle

C₂³×C₁₉

C₂⁴

Fitting

C₂⁴×C₄×C₁₉

C₂

prime radical

C₂⁵×C₁₉

C₂²

hypercenter

C₂⁴×C₄

D₁₉

C₁₉

G ▷ C₂³×C₁₉ ▷ C₁₉

C₁ ◁ C₂³ ◁ C₂⁴×C₄

N	H ≅ G/N	type
1. C₂×#10597370	C₂	semidirect
2. #11926417	C₂	semidirect
3. #11926404	C₂	semidirect
10. C₂²×Dic₃₈	C₂²	semidirect
13. C₂×C₄⋊Dic₁₉	C₂²	semidirect
15. C₂×Dic₁₉⋊C₄	C₂²	semidirect
16. C₁₉⋊#95	C₂²	semidirect
19. C₂⁴×C₁₉	Q₈	semidirect
59. C₂²×C₁₉	C₂²⋊Q₈	semidirect
87. C₁₉	#2848	semidirect
90. C₂⁴	Dic₃₈	semidirect
129. C₂²	#10597370	semidirect

H ≅ G/N

type

1. C₂×#10597370

C₂

semidirect

2. #11926417

C₂

semidirect

3. #11926404

C₂

semidirect

10. C₂²×Dic₃₈

C₂²

semidirect

13. C₂×C₄⋊Dic₁₉

C₂²

semidirect

15. C₂×Dic₁₉⋊C₄

C₂²

semidirect

16. C₁₉⋊#95

C₂²

semidirect

19. C₂⁴×C₁₉

Q₈

semidirect

59. C₂²×C₁₉

C₂²⋊Q₈

semidirect

87. C₁₉

#2848

semidirect

90. C₂⁴

Dic₃₈

semidirect

129. C₂²

#10597370

semidirect

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

subgroup	index
C₂×#10597370	2
#11926417	2
#11926404	2
#11926400	2
C₂⁴×C₄×C₁₉	2
#2848	19

subgroup

index

C₂⁴×C₄×C₁₉

Subgroups — #14571922

Conjugacy classes of subgroups

Complements

Maximal subgroups