Group #14574184 — subgroups

Subgroups — #14574184

Order 2432.

348 conjugacy classes of subgroups; only the 149 normal subgroups are shown.

normal subgroups only

This group has 348 conjugacy classes of subgroups — too many to draw. Only its 149 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	#11927101	C₂	1	1	yes	maximal, characteristic
2	#11926954	C₂	1	4	yes	maximal, complemented
3	#11926943	C₂	1	4	yes	maximal, complemented
4	#11926584	C₂	1	4	yes	maximal
5	C₄×#64520	C₂	1	1	yes	maximal, characteristic
6	C₂×C₁₉×#125	C₂	1	1	yes	maximal, characteristic
7	C₁₉×#125	—	2	2	no	—
8	C₁₉×#125	C₂²	1	2	yes	—
9	C₁₉×#125	C₂²	1	2	yes	—
10	C₂×C₄⋊C₄×C₁₉	—	2	2	no	—
11	C₂×C₄⋊C₄×C₁₉	C₂²	1	2	yes	—
12	C₂×C₄²×C₁₉	C₂²	1	1	yes	characteristic
13	#10597372	C₂²	1	2	yes	—
14	#10597370	—	2	2	no	—
15	C₂×#64520	C₂²	1	2	yes	—
16	#10597316	C₂²	1	2	yes	—
17	#10597315	C₂²	1	2	yes	—
18	C₄×Dic₃₈	—	2	2	no	—
19	#10597265	C₂²	1	8	yes	—
20	#10597264	C₂²	1	8	yes	—
21	#10597260	C₂²	1	2	yes	—
22	C₄×C₁₉⋊C₈	C₂²	1	2	yes	—
23	C₂²×C₄×C₁₉	—	2	2	no	—
24	C₂²×C₄×C₁₉	D₄	1	2	yes	—
25	C₂²×C₄×C₁₉	C₂³	1	1	yes	characteristic
26	C₂×Dic₃₈	—	2	2	no	—
27	C₄⋊C₄×C₁₉	—	2	4	no	—
28	C₄⋊C₄×C₁₉	—	2	4	no	—
29	C₄⋊C₄×C₁₉	—	2	2	no	—
30	C₄⋊C₄×C₁₉	C₂³	1	4	yes	—
31	C₄²×C₁₉	D₄	1	2	yes	—
32	C₄²×C₁₉	C₂³	1	1	yes	characteristic
33	C₄²×C₁₉	C₂³	1	1	yes	characteristic
34	C₂²⋊Dic₁₉	—	2	2	no	—
35	C₄⋊Dic₁₉	—	2	2	no	—
36	C₄⋊Dic₁₉	C₂³	1	4	yes	—
37	Dic₁₉⋊C₄	—	2	4	no	—
38	C₄×Dic₁₉	—	2	2	no	—
39	#64520	Q₈	1	8	yes	complemented
40	C₂×C₁₉⋊C₈	C₂³	1	4	yes	—
41	C₂³×C₁₉	C₂×D₄	1	1	yes	characteristic
42	C₂×C₄×C₁₉	—	2	4	no	—
43	C₂×C₄×C₁₉	—	4	2	no	—
44	C₂×C₄×C₁₉	—	4	4	no	—
45	C₂×C₄×C₁₉	C₂×D₄	1	2	yes	—
46	C₂×C₄×C₁₉	C₂×D₄	1	2	yes	—
47	C₂×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
48	C₂×C₄×C₁₉	C₂×Q₈	1	4	yes	—
49	C₂×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
50	C₂×Dic₁₉	—	2	4	no	—
51	Dic₃₈	—	4	4	no	—
52	C₁₉⋊C₈	C₂×Q₈	1	8	yes	—
53	#3166	—	19	1	no	maximal, Sylow
54	C₂²×C₁₉	—	2	2	no	—
55	C₂²×C₁₉	C₄⋊Q₈	1	2	yes	—
56	C₂²×C₁₉	C₂²×D₄	1	1	yes	characteristic
57	C₄×C₁₉	—	2	2	no	—
58	C₄×C₁₉	—	2	2	no	—
59	C₄×C₁₉	—	4	4	no	—
60	C₄×C₁₉	C₄⋊Q₈	1	2	yes	—
61	C₄×C₁₉	C₂²×Q₈	1	2	yes	—
62	Dic₁₉	—	4	4	no	—
63	#533	—	19	1	no	—
64	C₂×#125	D₁₉	1	1	yes	characteristic
65	#501	—	19	4	no	—
66	#499	—	19	4	no	—
67	#428	—	19	4	no	—
68	C₄×M₁₆	—	19	1	no	—
69	C₂×C₁₉	—	2	2	no	—
70	C₂×C₁₉	C₂×C₄⋊Q₈	1	1	yes	characteristic
71	C₂×C₁₉	#575	1	2	yes	—
72	C₂×M₁₆	—	19	2	no	—
73	C₄⋊Q₈	—	19	2	no	—
74	#125	—	2	2	no	—
75	#125	—	19	2	no	—
76	#125	C₂×D₁₉	1	2	yes	—
77	#125	C₂×D₁₉	1	2	yes	—
78	C₂²⋊Q₈	—	38	2	no	—
79	C₄×Q₈	—	38	2	no	—
80	#117	—	19	2	no	—
81	C₂×C₄⋊C₄	—	2	2	no	—
82	C₂×C₄⋊C₄	C₂×D₁₉	1	2	yes	—
83	C₂×C₄²	C₂×D₁₉	1	1	yes	characteristic
84	#107	—	19	8	no	—
85	#106	—	19	8	no	—
86	#97	—	19	2	no	—
87	C₄×C₈	—	19	2	no	—
88	C₁₉	#3166	1	1	yes	characteristic, complemented, Sylow
89	C₂×Q₈	—	38	2	no	—
90	C₂²×C₄	—	2	2	no	—
91	C₂²×C₄	C₂²⋊D₁₉	1	2	yes	—
92	C₂²×C₄	C₂²×D₁₉	1	1	yes	characteristic
93	M₁₆	—	19	8	no	—
94	C₂×C₈	—	19	4	no	—
95	C₄⋊C₄	—	2	4	no	—
96	C₄⋊C₄	—	2	4	no	—
97	C₄⋊C₄	—	2	2	no	—
98	C₄⋊C₄	—	19	4	no	—
99	C₄⋊C₄	—	38	4	no	—
100	C₄⋊C₄	—	38	2	no	—
101	C₄⋊C₄	C₂²×D₁₉	1	4	yes	—
102	C₂²⋊C₄	—	38	2	no	—
103	C₄²	—	38	2	no	—
104	C₄²	C₂²⋊D₁₉	1	2	yes	—
105	C₄²	C₂²×D₁₉	1	1	yes	characteristic
106	C₄²	C₂²×D₁₉	1	1	yes	characteristic
107	C₂³	C₂×C₂²⋊D₁₉	1	1	yes	characteristic
108	Q₈	—	76	4	no	—
109	C₂×C₄	—	2	4	no	—
110	C₂×C₄	—	4	2	no	—
111	C₂×C₄	—	4	4	no	—
112	C₂×C₄	—	38	4	no	—
113	C₂×C₄	Q₈×D₁₉	1	4	yes	—
114	C₂×C₄	C₂×C₂²⋊D₁₉	1	2	yes	—
115	C₂×C₄	C₂×C₂²⋊D₁₉	1	2	yes	—
116	C₂×C₄	C₂×C₂²⋊D₁₉	1	1	yes	characteristic
117	C₂×C₄	C₂³×D₁₉	1	1	yes	characteristic
118	C₈	—	19	8	no	—
119	C₂²	—	2	2	no	—
120	C₂²	#10597390	1	2	yes	—
121	C₂²	C₂²×C₂²⋊D₁₉	1	1	yes	characteristic
122	C₄	—	2	2	no	—
123	C₄	—	2	2	no	—
124	C₄	—	4	4	no	—
125	C₄	—	76	4	no	—
126	C₄	#10597390	1	2	yes	—
127	C₄	C₂×Q₈×D₁₉	1	2	yes	—
128	C₂	—	2	2	no	—
129	C₂	C₂×#10597390	1	1	yes	characteristic
130	C₂	#11927342	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

#11927101

C₂

yes

maximal, characteristic

#11926954

C₂

yes

maximal, complemented

#11926943

C₂

yes

maximal, complemented

#11926584

C₂

yes

maximal

C₄×#64520

C₂

yes

maximal, characteristic

C₂×C₁₉×#125

C₂

yes

maximal, characteristic

C₁₉×#125

—

C₁₉×#125

C₂²

yes

—

C₁₉×#125

C₂²

yes

—

C₂×C₄⋊C₄×C₁₉

—

C₂×C₄⋊C₄×C₁₉

C₂²

yes

—

C₂×C₄²×C₁₉

C₂²

yes

characteristic

#10597372

C₂²

yes

—

#10597370

—

C₂×#64520

C₂²

yes

—

#10597316

C₂²

yes

—

#10597315

C₂²

yes

—

C₄×Dic₃₈

—

#10597265

C₂²

yes

—

#10597264

C₂²

yes

—

#10597260

C₂²

yes

—

C₄×C₁₉⋊C₈

C₂²

yes

—

C₂²×C₄×C₁₉

—

C₂²×C₄×C₁₉

D₄

yes

—

C₂²×C₄×C₁₉

C₂³

yes

characteristic

C₂×Dic₃₈

—

C₄⋊C₄×C₁₉

—

C₄⋊C₄×C₁₉

—

C₄⋊C₄×C₁₉

—

C₄⋊C₄×C₁₉

C₂³

yes

—

C₄²×C₁₉

D₄

yes

—

C₄²×C₁₉

C₂³

yes

characteristic

C₄²×C₁₉

C₂³

yes

characteristic

C₂²⋊Dic₁₉

—

C₄⋊Dic₁₉

—

C₄⋊Dic₁₉

C₂³

yes

—

Dic₁₉⋊C₄

—

C₄×Dic₁₉

—

#64520

Q₈

yes

complemented

C₂×C₁₉⋊C₈

C₂³

yes

—

C₂³×C₁₉

C₂×D₄

yes

characteristic

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

C₂×D₄

yes

—

C₂×C₄×C₁₉

C₂×D₄

yes

—

C₂×C₄×C₁₉

C₂×D₄

yes

characteristic

C₂×C₄×C₁₉

C₂×Q₈

yes

—

C₂×C₄×C₁₉

C₂⁴

yes

characteristic

C₂×Dic₁₉

—

Dic₃₈

—

C₁₉⋊C₈

C₂×Q₈

yes

—

#3166

—

maximal, Sylow

C₂²×C₁₉

—

C₂²×C₁₉

C₄⋊Q₈

yes

—

C₂²×C₁₉

C₂²×D₄

yes

characteristic

C₄×C₁₉

—

C₄×C₁₉

—

C₄×C₁₉

—

C₄×C₁₉

C₄⋊Q₈

yes

—

C₄×C₁₉

C₂²×Q₈

yes

—

Dic₁₉

—

#533

—

C₂×#125

D₁₉

yes

—

—

—

C₄×M₁₆

—

C₂×C₁₉

—

C₂×C₁₉

C₂×C₄⋊Q₈

yes

characteristic

C₂×C₁₉

#575

yes

—

C₂×M₁₆

—

C₄⋊Q₈

—

#125

—

#125

—

#125

C₂×D₁₉

yes

—

#125

C₂×D₁₉

yes

—

C₂²⋊Q₈

—

C₄×Q₈

—

#117

—

C₂×C₄⋊C₄

—

C₂×C₄⋊C₄

C₂×D₁₉

yes

—

C₂×C₄²

C₂×D₁₉

yes

—

—

—

C₄×C₈

—

C₁₉

#3166

yes

characteristic, complemented, Sylow

C₂×Q₈

—

C₂²×C₄

—

C₂²×C₄

C₂²⋊D₁₉

yes

—

C₂²×C₄

C₂²×D₁₉

yes

characteristic

M₁₆

—

C₂×C₈

—

C₄⋊C₄

—

C₄⋊C₄

—

C₄⋊C₄

—

C₄⋊C₄

—

C₄⋊C₄

—

100

C₄⋊C₄

—

101

C₄⋊C₄

C₂²×D₁₉

yes

—

102

C₂²⋊C₄

—

103

C₄²

—

104

C₄²

C₂²⋊D₁₉

yes

—

105

C₄²

C₂²×D₁₉

yes

characteristic

106

C₄²

C₂²×D₁₉

yes

characteristic

107

C₂³

C₂×C₂²⋊D₁₉

yes

characteristic

108

Q₈

—

109

C₂×C₄

—

110

C₂×C₄

—

111

C₂×C₄

—

112

C₂×C₄

—

113

C₂×C₄

Q₈×D₁₉

yes

—

114

C₂×C₄

C₂×C₂²⋊D₁₉

yes

—

115

C₂×C₄

C₂×C₂²⋊D₁₉

yes

—

116

C₂×C₄

C₂×C₂²⋊D₁₉

yes

characteristic

117

C₂×C₄

C₂³×D₁₉

yes

characteristic

118

C₈

—

119

C₂²

—

120

C₂²

#10597390

yes

—

121

C₂²

C₂²×C₂²⋊D₁₉

yes

characteristic

122

C₄

—

123

C₄

—

124

C₄

—

125

C₄

—

126

C₄

#10597390

yes

—

127

C₄

C₂×Q₈×D₁₉

yes

—

128

C₂

—

129

C₂

C₂×#10597390

yes

characteristic

130

C₂

#11927342

yes

—

	subgroup	G/H
center	C₂²	C₂²×C₂²⋊D₁₉
commutator, cosocle	C₂×C₄×C₁₉	C₂⁴
Frattini	C₂×C₄	C₂³×D₁₉
Fitting	C₂×C₁₉×#125	C₂
socle	C₂²×C₁₉	C₂²×D₄
prime radical	C₂³×C₁₉	C₂×D₄
hypercenter	C₂×#125	D₁₉
hypocenter	C₁₉	#3166
LCS	G ▷ C₂×C₄×C₁₉ ▷ C₂×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂² ◁ C₂×C₄² ◁ C₂×#125

subgroup

G/H

center

C₂²

C₂²×C₂²⋊D₁₉

commutator, cosocle

C₂×C₄×C₁₉

C₂⁴

Frattini

C₂×C₄

C₂³×D₁₉

Fitting

C₂×C₁₉×#125

C₂

socle

C₂²×C₁₉

C₂²×D₄

prime radical

C₂³×C₁₉

C₂×D₄

D₁₉

C₁₉

G ▷ C₂×C₄×C₁₉ ▷ C₂×C₁₉ ▷ C₁₉

UCS

C₁ ◁ C₂² ◁ C₂×C₄² ◁ C₂×#125

N	H ≅ G/N	type
2. #11926954	C₂	semidirect
3. #11926943	C₂	semidirect
39. #64520	Q₈	semidirect
88. C₁₉	#3166	semidirect

H ≅ G/N

type

2. #11926954

C₂

semidirect

3. #11926943

C₂

semidirect

39. #64520

Q₈

semidirect

88. C₁₉

#3166

semidirect

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

subgroup	index
#11927101	2
#11926954	2
#11926943	2
#11926584	2
C₄×#64520	2
C₂×C₁₉×#125	2
#3166	19

subgroup

index

C₂×C₁₉×#125

Subgroups — #14574184

Conjugacy classes of subgroups

Complements

Maximal subgroups