Group #14577445 — subgroups

Subgroups — #14577445

Order 2432.

964 conjugacy classes of subgroups; only the 553 normal subgroups are shown.

normal subgroups only

This group has 964 conjugacy classes of subgroups — too many to draw. Only its 553 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	Q₈×Dic₃₈	C₂	1	4	yes	maximal, complemented
2	#11927273	C₂	1	4	yes	maximal, complemented
3	#11927270	C₂	1	8	yes	maximal, complemented
4	#11927175	C₂	1	6	yes	maximal
5	#11927101	C₂	1	6	yes	maximal
6	#11927022	C₂	1	2	yes	maximal
7	C₂×C₄×Q₈×C₁₉	C₂	1	1	yes	maximal, characteristic
8	C₂²×Q₈×C₁₉	C₂²	1	1	yes	characteristic
9	C₄×Q₈×C₁₉	C₂²	1	4	yes	—
10	C₄×Q₈×C₁₉	C₂²	1	4	yes	—
11	C₂×C₄⋊C₄×C₁₉	C₂²	1	3	yes	—
12	C₂×C₄²×C₁₉	C₂²	1	3	yes	—
13	Q₈×Dic₁₉	C₂²	1	8	yes	—
14	Q₈×Dic₁₉	C₂²	1	8	yes	—
15	#10597372	C₂²	1	12	yes	—
16	#10597370	C₂²	1	4	yes	—
17	#10597370	C₂²	1	12	yes	—
18	#10597336	C₂²	1	24	yes	—
19	#10597334	C₂²	1	24	yes	—
20	#10597316	C₂²	1	12	yes	—
21	#10597315	C₂²	1	6	yes	—
22	#10597315	C₂²	1	6	yes	—
23	C₄×Dic₃₈	C₂²	1	12	yes	—
24	C₄×Dic₃₈	C₂²	1	12	yes	—
25	C₂×Q₈×C₁₉	Q₈	1	8	yes	complemented
26	C₂×Q₈×C₁₉	C₂³	1	4	yes	—
27	C₂²×C₄×C₁₉	C₂³	1	1	yes	characteristic
28	C₂²×C₄×C₁₉	C₂³	1	3	yes	—
29	C₂²×C₄×C₁₉	C₂³	1	3	yes	—
30	C₂×Dic₃₈	C₂³	1	4	yes	—
31	C₂×Dic₃₈	C₂³	1	12	yes	—
32	C₄⋊C₄×C₁₉	C₂³	1	12	yes	—
33	C₄²×C₁₉	C₂³	1	6	yes	—
34	C₄²×C₁₉	C₂³	1	6	yes	—
35	C₂²⋊Dic₁₉	C₂³	1	8	yes	—
36	C₄⋊Dic₁₉	C₂³	1	12	yes	—
37	C₄⋊Dic₁₉	C₂³	1	12	yes	—
38	C₄⋊Dic₁₉	C₂³	1	4	yes	—
39	C₄⋊Dic₁₉	C₂³	1	12	yes	—
40	Dic₁₉⋊C₄	C₂³	1	8	yes	—
41	Dic₁₉⋊C₄	C₂³	1	24	yes	—
42	C₄×Dic₁₉	C₂³	1	24	yes	—
43	C₂³×C₁₉	C₂⁴	1	1	yes	characteristic
44	Q₈×C₁₉	C₂×Q₈	1	16	yes	—
45	C₂×C₄×C₁₉	—	2	2	no	—
46	C₂×C₄×C₁₉	—	4	3	no	—
47	C₂×C₄×C₁₉	C₂×Q₈	1	12	yes	—
48	C₂×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
49	C₂×C₄×C₁₉	C₂⁴	1	6	yes	—
50	C₂×C₄×C₁₉	C₂⁴	1	6	yes	—
51	C₂×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
52	C₂×Dic₁₉	C₂⁴	1	8	yes	—
53	C₂×Dic₁₉	C₂⁴	1	8	yes	—
54	Dic₃₈	—	2	8	no	—
55	Dic₃₈	—	4	12	no	—
56	#3502	—	19	1	no	maximal, Sylow
57	C₂²×C₁₉	—	2	1	no	—
58	C₂²×C₁₉	—	2	1	no	—
59	C₂²×C₁₉	C₂²×Q₈	1	2	yes	—
60	C₂²×C₁₉	C₂⁵	1	1	yes	characteristic
61	C₄×C₁₉	—	2	1	no	—
62	C₄×C₁₉	—	2	6	no	—
63	C₄×C₁₉	C₂²×Q₈	1	12	yes	—
64	C₄×C₁₉	2₋¹⁺⁴	1	2	yes	—
65	Dic₁₉	—	2	8	no	—
66	Dic₁₉	—	2	8	no	—
67	Q₈²	—	19	4	no	—
68	#557	—	19	8	no	—
69	#557	—	19	4	no	—
70	#544	—	19	6	no	—
71	#533	—	19	6	no	—
72	#519	—	19	2	no	—
73	C₂×C₄×Q₈	D₁₉	1	1	yes	characteristic
74	C₂×C₁₉	—	2	2	no	—
75	C₂×C₁₉	C₂³×Q₈	1	1	yes	characteristic
76	C₂×C₁₉	C₂×2₋¹⁺⁴	1	1	yes	characteristic
77	C₂×C₁₉	#585	1	1	yes	characteristic
78	C₂²×Q₈	C₂×D₁₉	1	1	yes	characteristic
79	C₄⋊Q₈	—	19	24	no	—
80	C₄⋊Q₈	—	19	6	no	—
81	C₄⋊Q₈	—	19	6	no	—
82	#125	—	19	24	no	—
83	#125	—	19	12	no	—
84	C₂²⋊Q₈	—	19	4	no	—
85	C₂²⋊Q₈	—	19	12	no	—
86	C₄×Q₈	—	19	8	no	—
87	C₄×Q₈	—	19	8	no	—
88	C₄×Q₈	—	19	12	no	—
89	C₄×Q₈	—	19	12	no	—
90	C₄×Q₈	C₂×D₁₉	1	4	yes	—
91	C₄×Q₈	C₂×D₁₉	1	4	yes	—
92	#117	—	19	12	no	—
93	C₂×C₄⋊C₄	C₂×D₁₉	1	3	yes	—
94	C₂×C₄²	C₂×D₁₉	1	3	yes	—
95	C₁₉	#3502	1	1	yes	characteristic, complemented, Sylow
96	C₂×Q₈	—	19	4	no	—
97	C₂×Q₈	—	19	12	no	—
98	C₂×Q₈	Dic₃₈	1	8	yes	complemented
99	C₂×Q₈	C₂²×D₁₉	1	4	yes	—
100	C₂²×C₄	C₂²×D₁₉	1	1	yes	characteristic
101	C₂²×C₄	C₂²×D₁₉	1	3	yes	—
102	C₂²×C₄	C₂²×D₁₉	1	3	yes	—
103	C₄⋊C₄	—	19	8	no	—
104	C₄⋊C₄	—	19	24	no	—
105	C₄⋊C₄	—	19	12	no	—
106	C₄⋊C₄	—	19	12	no	—
107	C₄⋊C₄	—	19	4	no	—
108	C₄⋊C₄	—	19	12	no	—
109	C₄⋊C₄	C₂²×D₁₉	1	12	yes	—
110	C₂²⋊C₄	—	19	8	no	—
111	C₄²	—	19	24	no	—
112	C₄²	C₂²×D₁₉	1	6	yes	—
113	C₄²	C₂²×D₁₉	1	6	yes	—
114	C₂³	C₂³×D₁₉	1	1	yes	characteristic
115	Q₈	—	38	8	no	—
116	Q₈	—	76	12	no	—
117	Q₈	C₂×Dic₃₈	1	16	yes	—
118	C₂×C₄	—	2	2	no	—
119	C₂×C₄	—	4	3	no	—
120	C₂×C₄	—	19	8	no	—
121	C₂×C₄	—	19	8	no	—
122	C₂×C₄	C₂×Dic₃₈	1	12	yes	—
123	C₂×C₄	C₂³×D₁₉	1	1	yes	characteristic
124	C₂×C₄	C₂³×D₁₉	1	6	yes	—
125	C₂×C₄	C₂³×D₁₉	1	6	yes	—
126	C₂×C₄	C₂³×D₁₉	1	1	yes	characteristic
127	C₂²	—	2	1	no	—
128	C₂²	—	2	1	no	—
129	C₂²	C₂²×Dic₃₈	1	2	yes	—
130	C₂²	C₂⁴×D₁₉	1	1	yes	characteristic
131	C₄	—	2	1	no	—
132	C₄	—	2	6	no	—
133	C₄	—	38	8	no	—
134	C₄	—	38	8	no	—
135	C₄	C₂²×Dic₃₈	1	12	yes	—
136	C₄	#10597433	1	2	yes	—
137	C₂	—	2	2	no	—
138	C₂	C₂³×Dic₃₈	1	1	yes	characteristic
139	C₂	C₂×#10597433	1	1	yes	characteristic
140	C₂	#11927380	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

Q₈×Dic₃₈

C₂

yes

maximal, complemented

#11927273

C₂

yes

maximal, complemented

#11927270

C₂

yes

maximal, complemented

#11927175

C₂

yes

maximal

#11927101

C₂

yes

maximal

#11927022

C₂

yes

maximal

C₂×C₄×Q₈×C₁₉

C₂

yes

maximal, characteristic

C₂²×Q₈×C₁₉

C₂²

yes

characteristic

C₄×Q₈×C₁₉

C₂²

yes

—

C₄×Q₈×C₁₉

C₂²

yes

—

C₂×C₄⋊C₄×C₁₉

C₂²

yes

—

C₂×C₄²×C₁₉

C₂²

yes

—

Q₈×Dic₁₉

C₂²

yes

—

Q₈×Dic₁₉

C₂²

yes

—

#10597372

C₂²

yes

—

#10597370

C₂²

yes

—

#10597370

C₂²

yes

—

#10597336

C₂²

yes

—

#10597334

C₂²

yes

—

#10597316

C₂²

yes

—

#10597315

C₂²

yes

—

#10597315

C₂²

yes

—

C₄×Dic₃₈

C₂²

yes

—

C₄×Dic₃₈

C₂²

yes

—

C₂×Q₈×C₁₉

Q₈

yes

complemented

C₂×Q₈×C₁₉

C₂³

yes

—

C₂²×C₄×C₁₉

C₂³

yes

characteristic

C₂²×C₄×C₁₉

C₂³

yes

—

C₂²×C₄×C₁₉

C₂³

yes

—

C₂×Dic₃₈

C₂³

yes

—

C₂×Dic₃₈

C₂³

yes

—

C₄⋊C₄×C₁₉

C₂³

yes

—

C₄²×C₁₉

C₂³

yes

—

C₄²×C₁₉

C₂³

yes

—

C₂²⋊Dic₁₉

C₂³

yes

—

C₄⋊Dic₁₉

C₂³

yes

—

C₄⋊Dic₁₉

C₂³

yes

—

C₄⋊Dic₁₉

C₂³

yes

—

C₄⋊Dic₁₉

C₂³

yes

—

Dic₁₉⋊C₄

C₂³

yes

—

Dic₁₉⋊C₄

C₂³

yes

—

C₄×Dic₁₉

C₂³

yes

—

C₂³×C₁₉

C₂⁴

yes

characteristic

Q₈×C₁₉

C₂×Q₈

yes

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

C₂×Q₈

yes

—

C₂×C₄×C₁₉

C₂⁴

yes

characteristic

C₂×C₄×C₁₉

C₂⁴

yes

—

C₂×C₄×C₁₉

C₂⁴

yes

—

C₂×C₄×C₁₉

C₂⁴

yes

characteristic

C₂×Dic₁₉

C₂⁴

yes

—

C₂×Dic₁₉

C₂⁴

yes

—

Dic₃₈

—

Dic₃₈

—

#3502

—

maximal, Sylow

C₂²×C₁₉

—

C₂²×C₁₉

—

C₂²×C₁₉

C₂²×Q₈

yes

—

C₂²×C₁₉

C₂⁵

yes

characteristic

C₄×C₁₉

—

C₄×C₁₉

—

C₄×C₁₉

C₂²×Q₈

yes

—

C₄×C₁₉

2₋¹⁺⁴

yes

—

Dic₁₉

—

Dic₁₉

—

Q₈²

—

—

—

—

—

—

C₂×C₄×Q₈

D₁₉

yes

characteristic

C₂×C₁₉

—

C₂×C₁₉

C₂³×Q₈

yes

characteristic

C₂×C₁₉

C₂×2₋¹⁺⁴

yes

characteristic

C₂×C₁₉

#585

yes

characteristic

C₂²×Q₈

C₂×D₁₉

yes

characteristic

C₄⋊Q₈

—

C₄⋊Q₈

—

C₄⋊Q₈

—

#125

—

#125

—

C₂²⋊Q₈

—

C₂²⋊Q₈

—

C₄×Q₈

—

C₄×Q₈

—

C₄×Q₈

—

C₄×Q₈

—

C₄×Q₈

C₂×D₁₉

yes

—

C₄×Q₈

C₂×D₁₉

yes

—

#117

—

C₂×C₄⋊C₄

C₂×D₁₉

yes

—

C₂×C₄²

C₂×D₁₉

yes

—

C₁₉

#3502

yes

characteristic, complemented, Sylow

C₂×Q₈

—

C₂×Q₈

—

C₂×Q₈

Dic₃₈

yes

complemented

C₂×Q₈

C₂²×D₁₉

yes

—

100

C₂²×C₄

C₂²×D₁₉

yes

characteristic

101

C₂²×C₄

C₂²×D₁₉

yes

—

102

C₂²×C₄

C₂²×D₁₉

yes

—

103

C₄⋊C₄

—

104

C₄⋊C₄

—

105

C₄⋊C₄

—

106

C₄⋊C₄

—

107

C₄⋊C₄

—

108

C₄⋊C₄

—

109

C₄⋊C₄

C₂²×D₁₉

yes

—

110

C₂²⋊C₄

—

111

C₄²

—

112

C₄²

C₂²×D₁₉

yes

—

113

C₄²

C₂²×D₁₉

yes

—

114

C₂³

C₂³×D₁₉

yes

characteristic

115

Q₈

—

116

Q₈

—

117

Q₈

C₂×Dic₃₈

yes

—

118

C₂×C₄

—

119

C₂×C₄

—

120

C₂×C₄

—

121

C₂×C₄

—

122

C₂×C₄

C₂×Dic₃₈

yes

—

123

C₂×C₄

C₂³×D₁₉

yes

characteristic

124

C₂×C₄

C₂³×D₁₉

yes

—

125

C₂×C₄

C₂³×D₁₉

yes

—

126

C₂×C₄

C₂³×D₁₉

yes

characteristic

127

C₂²

—

128

C₂²

—

129

C₂²

C₂²×Dic₃₈

yes

—

130

C₂²

C₂⁴×D₁₉

yes

characteristic

131

C₄

—

132

C₄

—

133

C₄

—

134

C₄

—

135

C₄

C₂²×Dic₃₈

yes

—

136

C₄

#10597433

yes

—

137

C₂

—

138

C₂

C₂³×Dic₃₈

yes

characteristic

139

C₂

C₂×#10597433

yes

characteristic

140

C₂

#11927380

yes

characteristic

	subgroup	G/H
center, Frattini	C₂²	C₂⁴×D₁₉
commutator, socle, cosocle	C₂²×C₁₉	C₂⁵
Fitting	C₂×C₄×Q₈×C₁₉	C₂
prime radical	C₂³×C₁₉	C₂⁴
hypercenter	C₂×C₄×Q₈	D₁₉
hypocenter	C₁₉	#3502
LCS	G ▷ C₂²×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂² ◁ C₂×C₄×Q₈

subgroup

G/H

center, Frattini

C₂²

C₂⁴×D₁₉

commutator, socle, cosocle

C₂²×C₁₉

C₂⁵

Fitting

C₂×C₄×Q₈×C₁₉

C₂

prime radical

C₂³×C₁₉

C₂⁴

hypercenter

C₂×C₄×Q₈

D₁₉

C₁₉

G ▷ C₂²×C₁₉ ▷ C₁₉

C₁ ◁ C₂² ◁ C₂×C₄×Q₈

N	H ≅ G/N	type
1. Q₈×Dic₃₈	C₂	semidirect
2. #11927273	C₂	semidirect
3. #11927270	C₂	semidirect
25. C₂×Q₈×C₁₉	Q₈	semidirect
95. C₁₉	#3502	semidirect
98. C₂×Q₈	Dic₃₈	semidirect

H ≅ G/N

type

1. Q₈×Dic₃₈

C₂

semidirect

2. #11927273

C₂

semidirect

3. #11927270

C₂

semidirect

25. C₂×Q₈×C₁₉

Q₈

semidirect

95. C₁₉

#3502

semidirect

98. C₂×Q₈

Dic₃₈

semidirect

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

subgroup	index
Q₈×Dic₃₈	2
#11927273	2
#11927270	2
#11927175	2
#11927101	2
#11927022	2
C₂×C₄×Q₈×C₁₉	2
#3502	19

subgroup

index

Q₈×Dic₃₈

C₂×C₄×Q₈×C₁₉

Subgroups — #14577445

Conjugacy classes of subgroups

Complements

Maximal subgroups