Group #14572012 — subgroups

Subgroups — #14572012

Order 2432.

504 conjugacy classes of subgroups; only the 197 normal subgroups are shown.

normal subgroups only

This group has 504 conjugacy classes of subgroups — too many to draw. Only its 197 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×#10597315	C₂	1	1	yes	maximal, characteristic
2	#11926451	C₂	1	4	yes	maximal
3	#11926449	C₂	1	4	yes	maximal
4	#11926409	C₂	1	4	yes	maximal
5	C₄²×Dic₁₉	C₂	1	1	yes	maximal, characteristic
6	C₂×C₁₉×C₄⋊Q₈	C₂	1	1	yes	maximal, characteristic
7	C₂²×Q₈×C₁₉	C₂²	1	2	yes	—
8	C₂²×Dic₃₈	C₂²	1	2	yes	—
9	C₁₉×C₄⋊Q₈	—	2	4	no	—
10	C₂×C₄⋊C₄×C₁₉	C₂²	1	2	yes	—
11	C₂×C₄⋊C₄×C₁₉	C₂²	1	2	yes	—
12	C₂×C₄²×C₁₉	C₂²	1	1	yes	characteristic
13	C₂×C₄⋊Dic₁₉	C₂²	1	2	yes	—
14	C₂×C₄⋊Dic₁₉	C₂²	1	2	yes	—
15	C₂×C₄×Dic₁₉	C₂²	1	2	yes	—
16	C₂×C₄×Dic₁₉	C₂²	1	2	yes	—
17	C₂×C₄×Dic₁₉	C₂²	1	2	yes	—
18	#10597315	—	2	4	no	—
19	C₁₉⋊#95	C₂²	1	16	yes	—
20	C₂×Q₈×C₁₉	—	2	4	no	—
21	C₂×Q₈×C₁₉	—	2	8	no	—
22	C₂²×C₄×C₁₉	C₂³	1	4	yes	—
23	C₂²×C₄×C₁₉	C₂³	1	1	yes	characteristic
24	C₂²×C₄×C₁₉	C₂³	1	1	yes	characteristic
25	C₂²×C₄×C₁₉	C₂³	1	1	yes	characteristic
26	C₂²×Dic₁₉	C₂³	1	4	yes	—
27	C₂²×Dic₁₉	C₂³	1	4	yes	—
28	C₂×Dic₃₈	—	2	4	no	—
29	C₂×Dic₃₈	—	2	8	no	—
30	C₄⋊C₄×C₁₉	—	2	4	no	—
31	C₄⋊C₄×C₁₉	—	2	4	no	—
32	C₄²×C₁₉	D₄	1	4	yes	—
33	C₄⋊Dic₁₉	—	2	4	no	—
34	C₄⋊Dic₁₉	—	2	4	no	—
35	C₄×Dic₁₉	—	2	4	no	—
36	C₄×Dic₁₉	—	2	4	no	—
37	C₄×Dic₁₉	Q₈	1	8	yes	complemented
38	C₂³×C₁₉	C₂⁴	1	1	yes	characteristic
39	Q₈×C₁₉	—	4	8	no	—
40	C₂×C₄×C₁₉	—	2	4	no	—
41	C₂×C₄×C₁₉	—	2	8	no	—
42	C₂×C₄×C₁₉	C₂×D₄	1	2	yes	—
43	C₂×C₄×C₁₉	C₂×D₄	1	2	yes	—
44	C₂×C₄×C₁₉	C₂×D₄	1	2	yes	—
45	C₂×C₄×C₁₉	C₂×Q₈	1	4	yes	—
46	C₂×C₄×C₁₉	#41	1	4	yes	—
47	C₂×C₄×C₁₉	#41	1	4	yes	—
48	C₂×Dic₁₉	—	2	4	no	—
49	C₂×Dic₁₉	—	2	4	no	—
50	C₂×Dic₁₉	—	2	4	no	—
51	C₂×Dic₁₉	—	2	8	no	—
52	C₂×Dic₁₉	C₂×Q₈	1	8	yes	—
53	Dic₃₈	—	4	8	no	—
54	#2862	—	19	1	no	maximal, Sylow
55	C₂²×C₁₉	C₂²×D₄	1	1	yes	characteristic
56	C₂²×C₁₉	C₂²×Q₈	1	2	yes	—
57	C₂²×C₁₉	C₂×#41	1	2	yes	—
58	C₂²×C₁₉	C₂×#41	1	2	yes	—
59	C₄×C₁₉	—	4	4	no	—
60	C₄×C₁₉	#124	1	4	yes	—
61	C₄×C₁₉	#124	1	4	yes	—
62	C₄×C₁₉	C₄⋊Q₈	1	4	yes	—
63	Dic₁₉	—	2	8	no	—
64	Dic₁₉	—	4	4	no	—
65	C₂×C₄⋊Q₈	—	19	1	no	—
66	C₂×C₄⋊Q₈	D₁₉	1	1	yes	characteristic
67	#391	—	19	4	no	—
68	#391	—	19	4	no	—
69	#382	—	19	4	no	—
70	C₄³	—	19	1	no	—
71	C₂×C₁₉	C₂×#124	1	1	yes	characteristic
72	C₂×C₁₉	C₂×#124	1	1	yes	characteristic
73	C₂×C₁₉	C₂×C₄⋊Q₈	1	1	yes	characteristic
74	C₂×C₁₉	#533	1	4	yes	—
75	C₂²×Q₈	—	19	2	no	—
76	C₂²×Q₈	C₂×D₁₉	1	2	yes	—
77	C₄⋊Q₈	—	2	4	no	—
78	C₄⋊Q₈	—	38	4	no	—
79	C₂×C₄⋊C₄	—	19	2	no	—
80	C₂×C₄⋊C₄	—	19	2	no	—
81	C₂×C₄⋊C₄	C₂×D₁₉	1	2	yes	—
82	C₂×C₄⋊C₄	C₂×D₁₉	1	2	yes	—
83	C₂×C₄²	—	19	2	no	—
84	C₂×C₄²	—	19	2	no	—
85	C₂×C₄²	—	19	2	no	—
86	C₂×C₄²	C₂×D₁₉	1	1	yes	characteristic
87	#95	—	19	16	no	—
88	C₁₉	#2862	1	1	yes	characteristic, complemented, Sylow
89	C₂×Q₈	—	2	8	no	—
90	C₂×Q₈	—	2	4	no	—
91	C₂×Q₈	—	38	8	no	—
92	C₂×Q₈	—	38	4	no	—
93	C₂²×C₄	—	19	4	no	—
94	C₂²×C₄	—	19	4	no	—
95	C₂²×C₄	C₂²×D₁₉	1	4	yes	—
96	C₂²×C₄	C₂²×D₁₉	1	1	yes	characteristic
97	C₂²×C₄	C₂²×D₁₉	1	1	yes	characteristic
98	C₂²×C₄	C₂²×D₁₉	1	1	yes	characteristic
99	C₄⋊C₄	—	2	4	no	—
100	C₄⋊C₄	—	2	4	no	—
101	C₄⋊C₄	—	38	4	no	—
102	C₄⋊C₄	—	38	4	no	—
103	C₄²	—	19	8	no	—
104	C₄²	—	38	4	no	—
105	C₄²	—	38	4	no	—
106	C₄²	C₂²⋊D₁₉	1	4	yes	—
107	C₂³	C₂³×D₁₉	1	1	yes	characteristic
108	Q₈	—	4	8	no	—
109	Q₈	—	76	8	no	—
110	C₂×C₄	—	2	8	no	—
111	C₂×C₄	—	2	4	no	—
112	C₂×C₄	—	19	8	no	—
113	C₂×C₄	—	38	4	no	—
114	C₂×C₄	—	38	4	no	—
115	C₂×C₄	—	38	8	no	—
116	C₂×C₄	—	38	4	no	—
117	C₂×C₄	#64543	1	4	yes	—
118	C₂×C₄	Q₈×D₁₉	1	4	yes	—
119	C₂×C₄	#64545	1	4	yes	—
120	C₂×C₄	C₂×C₂²⋊D₁₉	1	2	yes	—
121	C₂×C₄	C₂×C₂²⋊D₁₉	1	2	yes	—
122	C₂×C₄	C₂×C₂²⋊D₁₉	1	2	yes	—
123	C₂²	C₂×#64543	1	2	yes	—
124	C₂²	C₂×Q₈×D₁₉	1	2	yes	—
125	C₂²	C₂×#64545	1	2	yes	—
126	C₂²	C₂²×C₂²⋊D₁₉	1	1	yes	characteristic
127	C₄	—	4	4	no	—
128	C₄	—	38	8	no	—
129	C₄	—	76	4	no	—
130	C₄	#10597382	1	4	yes	—
131	C₄	#10597390	1	4	yes	—
132	C₄	#10597393	1	4	yes	—
133	C₂	C₂×#10597382	1	1	yes	characteristic
134	C₂	C₂×#10597393	1	1	yes	characteristic
135	C₂	C₂×#10597390	1	1	yes	characteristic
136	C₂	#11927099	1	4	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×#10597315

C₂

yes

maximal, characteristic

#11926451

C₂

yes

maximal

#11926449

C₂

yes

maximal

#11926409

C₂

yes

maximal

C₄²×Dic₁₉

C₂

yes

maximal, characteristic

C₂×C₁₉×C₄⋊Q₈

C₂

yes

maximal, characteristic

C₂²×Q₈×C₁₉

C₂²

yes

—

C₂²×Dic₃₈

C₂²

yes

—

C₁₉×C₄⋊Q₈

—

C₂×C₄⋊C₄×C₁₉

C₂²

yes

—

C₂×C₄⋊C₄×C₁₉

C₂²

yes

—

C₂×C₄²×C₁₉

C₂²

yes

characteristic

C₂×C₄⋊Dic₁₉

C₂²

yes

—

C₂×C₄⋊Dic₁₉

C₂²

yes

—

C₂×C₄×Dic₁₉

C₂²

yes

—

C₂×C₄×Dic₁₉

C₂²

yes

—

C₂×C₄×Dic₁₉

C₂²

yes

—

#10597315

—

C₁₉⋊#95

C₂²

yes

—

C₂×Q₈×C₁₉

—

C₂×Q₈×C₁₉

—

C₂²×C₄×C₁₉

C₂³

yes

—

C₂²×C₄×C₁₉

C₂³

yes

characteristic

C₂²×C₄×C₁₉

C₂³

yes

characteristic

C₂²×C₄×C₁₉

C₂³

yes

characteristic

C₂²×Dic₁₉

C₂³

yes

—

C₂²×Dic₁₉

C₂³

yes

—

C₂×Dic₃₈

—

C₂×Dic₃₈

—

C₄⋊C₄×C₁₉

—

C₄⋊C₄×C₁₉

—

C₄²×C₁₉

D₄

yes

—

C₄⋊Dic₁₉

—

C₄⋊Dic₁₉

—

C₄×Dic₁₉

—

C₄×Dic₁₉

—

C₄×Dic₁₉

Q₈

yes

complemented

C₂³×C₁₉

C₂⁴

yes

characteristic

Q₈×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

—

C₂×C₄×C₁₉

C₂×Q₈

yes

—

C₂×C₄×C₁₉

#41

yes

—

C₂×C₄×C₁₉

#41

yes

—

C₂×Dic₁₉

—

C₂×Dic₁₉

—

C₂×Dic₁₉

—

C₂×Dic₁₉

—

C₂×Dic₁₉

C₂×Q₈

yes

—

Dic₃₈

—

#2862

—

maximal, Sylow

C₂²×C₁₉

C₂²×D₄

yes

characteristic

C₂²×C₁₉

C₂²×Q₈

yes

—

C₂²×C₁₉

C₂×#41

yes

—

C₂²×C₁₉

C₂×#41

yes

—

C₄×C₁₉

—

C₄×C₁₉

#124

yes

—

C₄×C₁₉

#124

yes

—

C₄×C₁₉

C₄⋊Q₈

yes

—

Dic₁₉

—

Dic₁₉

—

C₂×C₄⋊Q₈

—

C₂×C₄⋊Q₈

D₁₉

yes

—

—

—

C₄³

—

C₂×C₁₉

yes

C₂×C₁₉

yes

C₂×C₁₉

C₂×C₄⋊Q₈

yes

characteristic

C₂×C₁₉

#533

yes

—

C₂²×Q₈

—

C₂²×Q₈

C₂×D₁₉

yes

—

C₄⋊Q₈

—

C₄⋊Q₈

—

C₂×C₄⋊C₄

—

C₂×C₄⋊C₄

—

C₂×C₄⋊C₄

C₂×D₁₉

yes

—

C₂×C₄⋊C₄

C₂×D₁₉

yes

—

C₂×C₄²

—

C₂×C₄²

—

C₂×C₄²

—

C₂×C₄²

C₂×D₁₉

yes

characteristic

#95

—

C₁₉

#2862

yes

characteristic, complemented, Sylow

C₂×Q₈

—

C₂×Q₈

—

C₂×Q₈

—

C₂×Q₈

—

C₂²×C₄

—

C₂²×C₄

—

C₂²×C₄

C₂²×D₁₉

yes

—

C₂²×C₄

C₂²×D₁₉

yes

characteristic

C₂²×C₄

C₂²×D₁₉

yes

characteristic

C₂²×C₄

C₂²×D₁₉

yes

characteristic

C₄⋊C₄

—

100

C₄⋊C₄

—

101

C₄⋊C₄

—

102

C₄⋊C₄

—

103

C₄²

—

104

C₄²

—

105

C₄²

—

106

C₄²

C₂²⋊D₁₉

yes

—

107

C₂³

C₂³×D₁₉

yes

characteristic

108

Q₈

—

109

Q₈

—

110

C₂×C₄

—

111

C₂×C₄

—

112

C₂×C₄

—

113

C₂×C₄

—

114

C₂×C₄

—

115

C₂×C₄

—

116

C₂×C₄

—

117

C₂×C₄

#64543

yes

—

118

C₂×C₄

Q₈×D₁₉

yes

—

119

C₂×C₄

#64545

yes

—

120

C₂×C₄

C₂×C₂²⋊D₁₉

yes

—

121

C₂×C₄

C₂×C₂²⋊D₁₉

yes

—

122

C₂×C₄

C₂×C₂²⋊D₁₉

yes

—

123

C₂²

C₂×#64543

yes

—

124

C₂²

C₂×Q₈×D₁₉

yes

—

125

C₂²

C₂×#64545

yes

—

126

C₂²

C₂²×C₂²⋊D₁₉

yes

characteristic

127

C₄

—

128

C₄

—

129

C₄

—

130

C₄

#10597382

yes

—

131

C₄

#10597390

yes

—

132

C₄

#10597393

yes

—

133

C₂

C₂×#10597382

yes

characteristic

134

C₂

C₂×#10597393

yes

characteristic

135

C₂

C₂×#10597390

yes

characteristic

136

C₂

#11927099

yes

—

	subgroup	G/H
center, Frattini	C₂³	C₂³×D₁₉
commutator, socle, prime radical, cosocle	C₂³×C₁₉	C₂⁴
Fitting	C₂×C₁₉×C₄⋊Q₈	C₂
hypercenter	C₂×C₄⋊Q₈	D₁₉
hypocenter	C₁₉	#2862
LCS	G ▷ C₂³×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂³ ◁ C₂×C₄⋊Q₈

subgroup

G/H

center, Frattini

C₂³

C₂³×D₁₉

commutator, socle, prime radical, cosocle

C₂³×C₁₉

C₂⁴

Fitting

C₂×C₁₉×C₄⋊Q₈

C₂

hypercenter

C₂×C₄⋊Q₈

D₁₉

C₁₉

G ▷ C₂³×C₁₉ ▷ C₁₉

C₁ ◁ C₂³ ◁ C₂×C₄⋊Q₈

N	H ≅ G/N	type
37. C₄×Dic₁₉	Q₈	semidirect
88. C₁₉	#2862	semidirect

H ≅ G/N

type

37. C₄×Dic₁₉

Q₈

semidirect

88. C₁₉

#2862

semidirect

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

subgroup	index
C₂×#10597315	2
#11926451	2
#11926449	2
#11926409	2
C₄²×Dic₁₉	2
C₂×C₁₉×C₄⋊Q₈	2
#2862	19

subgroup

index

C₄²×Dic₁₉

C₂×C₁₉×C₄⋊Q₈

#2862

Subgroups — #14572012

Conjugacy classes of subgroups

Complements

Maximal subgroups