Group #14563248 — subgroups

Subgroups — #14563248

Order 2432.

178 conjugacy classes of subgroups; only the 57 normal subgroups are shown.

normal subgroups only

This group has 178 conjugacy classes of subgroups — too many to draw. Only its 57 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	#11926896	C₂	1	1	yes	maximal, characteristic, complemented
2	#11926894	C₂	1	1	yes	maximal, characteristic, complemented
3	#11926892	C₂	1	1	yes	maximal, characteristic
4	#11926892	C₂	1	1	yes	maximal, characteristic
5	#11926891	C₂	1	1	yes	maximal, characteristic
6	C₈×C₁₉⋊C₈	C₂	1	1	yes	maximal, characteristic, complemented
7	C₁₉×#487	C₂	1	1	yes	maximal, characteristic, complemented
8	C₁₉×C₄⋊Q₈	C₂²	1	1	yes	characteristic
9	C₁₉×C₄⋊Q₈	C₂²	1	1	yes	characteristic
10	#10597320	C₂²	1	1	yes	characteristic
11	#10597315	C₂²	1	1	yes	characteristic
12	C₁₉×#103	—	2	2	no	—
13	C₄×C₈×C₁₉	C₂²	1	1	yes	characteristic
14	#10597292	—	2	2	no	—
15	#10597278	—	2	2	no	—
16	#10597267	—	2	2	no	—
17	#10597266	—	2	2	no	—
18	#10597266	—	2	2	no	—
19	C₄×C₁₉⋊C₈	C₂²	1	1	yes	characteristic
20	C₄×C₁₉⋊C₈	C₂²	1	1	yes	characteristic
21	C₂×Q₈×C₁₉	—	2	1	no	—
22	C₂×Q₈×C₁₉	—	2	1	no	—
23	C₂×D₇₆	—	2	1	no	—
24	C₂×D₇₆	—	2	1	no	—
25	C₂×D₇₆	—	2	1	no	—
26	C₂×Dic₃₈	—	2	1	no	—
27	C₂×C₈×C₁₉	D₄	1	2	yes	—
28	C₄⋊C₄×C₁₉	—	2	1	no	—
29	C₄⋊C₄×C₁₉	—	2	1	no	—
30	C₄⋊C₄×C₁₉	—	2	1	no	—
31	C₄⋊C₄×C₁₉	—	2	1	no	—
32	C₄²×C₁₉	C₂³	1	1	yes	characteristic
33	C₄⋊Dic₁₉	—	2	1	no	—
34	C₄⋊Dic₁₉	—	2	1	no	—
35	C₂×C₁₉⋊C₈	D₄	1	2	yes	—
36	C₂×C₁₉⋊C₈	D₄	1	2	yes	—
37	C₂²×D₁₉	—	4	1	no	—
38	Q₈×C₁₉	—	4	2	no	—
39	Q₈×C₁₉	—	4	2	no	—
40	C₂×C₄×C₁₉	—	4	1	no	—
41	C₂×C₄×C₁₉	—	4	1	no	—
42	C₂×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
43	C₂×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
44	C₂×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
45	C₂×Dic₁₉	—	4	1	no	—
46	D₇₆	—	4	2	no	—
47	D₇₆	—	4	2	no	—
48	D₇₆	—	4	2	no	—
49	Dic₃₈	—	4	2	no	—
50	C₈×C₁₉	—	2	2	no	—
51	C₁₉⋊C₈	—	2	2	no	—
52	C₁₉⋊C₈	—	2	2	no	—
53	#1711	—	19	1	no	maximal, Sylow
54	C₂²×C₁₉	#127	1	1	yes	characteristic
55	C₂×D₁₉	—	8	1	no	—
56	C₂×D₁₉	—	8	1	no	—
57	C₂×D₁₉	—	8	1	no	—
58	C₄×C₁₉	—	8	1	no	—
59	C₄×C₁₉	—	8	1	no	—
60	C₄×C₁₉	#135	1	2	yes	—
61	C₄×C₁₉	#135	1	2	yes	—
62	C₄×C₁₉	#135	1	2	yes	—
63	Dic₁₉	—	8	1	no	—
64	#487	—	19	1	no	—
65	#487	—	19	1	no	—
66	#487	D₁₉	1	1	yes	characteristic, complemented
67	#486	—	19	1	no	—
68	#486	—	19	1	no	—
69	#486	—	19	1	no	—
70	C₈²	—	19	1	no	—
71	C₂×C₁₉	#495	1	1	yes	characteristic
72	C₂×C₁₉	#495	1	1	yes	characteristic
73	C₂×C₁₉	#495	1	1	yes	characteristic
74	D₁₉	—	16	1	no	—
75	C₄⋊Q₈	—	19	1	no	—
76	C₄⋊Q₈	C₂×D₁₉	1	1	yes	characteristic
77	C₄⋊Q₈	C₂×D₁₉	1	1	yes	characteristic
78	#127	—	19	1	no	—
79	#103	—	2	2	no	—
80	#103	—	38	2	no	—
81	#103	—	38	2	no	—
82	#102	—	38	2	no	—
83	#102	—	38	2	no	—
84	#102	—	38	2	no	—
85	C₄×C₈	—	19	1	no	—
86	C₄×C₈	—	19	1	no	—
87	C₄×C₈	C₂×D₁₉	1	1	yes	characteristic
88	C₁₉	#1711	1	1	yes	characteristic, complemented, Sylow
89	C₂×Q₈	—	2	1	no	—
90	C₂×Q₈	—	2	1	no	—
91	C₂×Q₈	—	38	1	no	—
92	C₂×D₄	—	38	1	no	—
93	C₂×D₄	—	38	1	no	—
94	C₂×D₄	—	38	1	no	—
95	C₂×C₈	—	19	2	no	—
96	C₂×C₈	—	19	2	no	—
97	C₂×C₈	C₂²⋊D₁₉	1	2	yes	—
98	C₄⋊C₄	—	2	1	no	—
99	C₄⋊C₄	—	2	1	no	—
100	C₄⋊C₄	—	2	1	no	—
101	C₄⋊C₄	—	2	1	no	—
102	C₄⋊C₄	—	38	1	no	—
103	C₄⋊C₄	—	38	1	no	—
104	C₄²	C₂²×D₁₉	1	1	yes	characteristic
105	C₂³	—	76	1	no	—
106	Q₈	—	4	2	no	—
107	Q₈	—	4	2	no	—
108	Q₈	—	76	2	no	—
109	D₄	—	76	2	no	—
110	D₄	—	76	2	no	—
111	D₄	—	76	2	no	—
112	C₂×C₄	—	4	1	no	—
113	C₂×C₄	—	4	1	no	—
114	C₂×C₄	—	76	1	no	—
115	C₂×C₄	D₄×D₁₉	1	1	yes	characteristic
116	C₂×C₄	D₄×D₁₉	1	1	yes	characteristic
117	C₂×C₄	C₂×C₂²⋊D₁₉	1	1	yes	characteristic
118	C₈	—	2	2	no	—
119	C₈	—	38	2	no	—
120	C₈	—	38	2	no	—
121	C₂²	—	152	1	no	—
122	C₂²	—	152	1	no	—
123	C₂²	—	152	1	no	—
124	C₂²	#10597386	1	1	yes	characteristic
125	C₄	—	8	1	no	—
126	C₄	—	8	1	no	—
127	C₄	—	152	1	no	—
128	C₄	#10597362	1	2	yes	—
129	C₄	#10597365	1	2	yes	—
130	C₄	#10597396	1	2	yes	—
131	C₂	—	304	1	no	—
132	C₂	#11926925	1	1	yes	characteristic
133	C₂	#11926926	1	1	yes	characteristic
134	C₂	#11926929	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#11926896

C₂

yes

maximal, characteristic, complemented

#11926894

C₂

yes

maximal, characteristic, complemented

#11926892

C₂

yes

maximal, characteristic

#11926892

C₂

yes

maximal, characteristic

#11926891

C₂

yes

maximal, characteristic

C₈×C₁₉⋊C₈

C₂

yes

maximal, characteristic, complemented

C₁₉×#487

C₂

yes

maximal, characteristic, complemented

C₁₉×C₄⋊Q₈

C₂²

yes

characteristic

C₁₉×C₄⋊Q₈

C₂²

yes

characteristic

#10597320

C₂²

yes

characteristic

#10597315

C₂²

yes

characteristic

C₁₉×#103

—

C₄×C₈×C₁₉

C₂²

yes

—

—

—

—

—

C₄×C₁₉⋊C₈

C₂²

yes

characteristic

C₄×C₁₉⋊C₈

C₂²

yes

characteristic

C₂×Q₈×C₁₉

—

C₂×Q₈×C₁₉

—

C₂×D₇₆

—

C₂×D₇₆

—

C₂×D₇₆

—

C₂×Dic₃₈

—

C₂×C₈×C₁₉

D₄

yes

—

C₄⋊C₄×C₁₉

—

C₄⋊C₄×C₁₉

—

C₄⋊C₄×C₁₉

—

C₄⋊C₄×C₁₉

—

C₄²×C₁₉

C₂³

yes

characteristic

C₄⋊Dic₁₉

—

C₄⋊Dic₁₉

—

C₂×C₁₉⋊C₈

D₄

yes

—

C₂×C₁₉⋊C₈

D₄

yes

—

C₂²×D₁₉

—

Q₈×C₁₉

—

Q₈×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

C₂×D₄

yes

characteristic

C₂×C₄×C₁₉

C₂×D₄

yes

characteristic

C₂×C₄×C₁₉

C₂×D₄

yes

characteristic

C₂×Dic₁₉

—

D₇₆

—

D₇₆

—

D₇₆

—

Dic₃₈

—

C₈×C₁₉

—

C₁₉⋊C₈

—

C₁₉⋊C₈

—

—

C₂²×C₁₉

yes

C₂×D₁₉

—

C₂×D₁₉

—

C₂×D₁₉

—

C₄×C₁₉

—

C₄×C₁₉

—

C₄×C₁₉

#135

yes

—

C₄×C₁₉

#135

yes

—

C₄×C₁₉

#135

yes

—

Dic₁₉

—

#487

—

#487

—

#487

D₁₉

yes

characteristic, complemented

#486

—

#486

—

#486

—

C₈²

—

C₂×C₁₉

yes

C₂×C₁₉

yes

C₂×C₁₉

yes

D₁₉

—

C₄⋊Q₈

—

C₄⋊Q₈

C₂×D₁₉

yes

characteristic

C₄⋊Q₈

C₂×D₁₉

yes

—

—

—

—

—

—

—

C₄×C₈

—

C₄×C₈

—

C₄×C₈

C₂×D₁₉

yes

characteristic

C₁₉

#1711

yes

characteristic, complemented, Sylow

C₂×Q₈

—

C₂×Q₈

—

C₂×Q₈

—

C₂×D₄

—

C₂×D₄

—

C₂×D₄

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

C₂²⋊D₁₉

yes

—

C₄⋊C₄

—

C₄⋊C₄

—

100

C₄⋊C₄

—

101

C₄⋊C₄

—

102

C₄⋊C₄

—

103

C₄⋊C₄

—

104

C₄²

C₂²×D₁₉

yes

characteristic

105

C₂³

—

106

Q₈

—

107

Q₈

—

108

Q₈

—

109

D₄

—

110

D₄

—

111

D₄

—

112

C₂×C₄

—

113

C₂×C₄

—

114

C₂×C₄

—

115

C₂×C₄

D₄×D₁₉

yes

characteristic

116

C₂×C₄

D₄×D₁₉

yes

characteristic

117

C₂×C₄

C₂×C₂²⋊D₁₉

yes

characteristic

118

C₈

—

119

C₈

—

120

C₈

—

121

C₂²

—

152

—

122

C₂²

—

152

—

123

C₂²

—

152

—

124

C₂²

#10597386

yes

characteristic

125

C₄

—

126

C₄

—

127

C₄

—

152

—

128

C₄

#10597362

yes

—

129

C₄

#10597365

yes

—

130

C₄

#10597396

yes

—

131

C₂

—

304

—

132

C₂

#11926925

yes

characteristic

133

C₂

#11926926

yes

characteristic

134

C₂

#11926929

yes

characteristic

	subgroup	G/H
center	C₂²	#10597386
commutator, cosocle	C₄²×C₁₉	C₂³
Frattini	C₄²	C₂²×D₁₉
Fitting	C₁₉×#487	C₂
socle	C₂²×C₁₉	#127
prime radical	#10597320	C₂²
hypercenter	#487	D₁₉
hypocenter	C₁₉	#1711
LCS	G ▷ C₄²×C₁₉ ▷ C₂²×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂² ◁ C₄² ◁ #487

subgroup

G/H

center

C₂²

#10597386

commutator, cosocle

C₄²×C₁₉

C₂³

Frattini

C₄²

C₂²×D₁₉

Fitting

C₁₉×#487

C₂

C₂²×C₁₉

C₂²

D₁₉

C₁₉

G ▷ C₄²×C₁₉ ▷ C₂²×C₁₉ ▷ C₁₉

UCS

C₁ ◁ C₂² ◁ C₄² ◁ #487

N	H ≅ G/N	type
1. #11926896	C₂	semidirect
2. #11926894	C₂	semidirect
6. C₈×C₁₉⋊C₈	C₂	semidirect
7. C₁₉×#487	C₂	semidirect
66. #487	D₁₉	semidirect
88. C₁₉	#1711	semidirect

H ≅ G/N

type

1. #11926896

C₂

semidirect

2. #11926894

C₂

semidirect

6. C₈×C₁₉⋊C₈

C₂

semidirect

7. C₁₉×#487

C₂

semidirect

66. #487

D₁₉

semidirect

88. C₁₉

#1711

semidirect

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

subgroup	index
#11926896	2
#11926894	2
#11926892	2
#11926891	2
C₈×C₁₉⋊C₈	2
C₁₉×#487	2
#1711	19

subgroup

index

C₈×C₁₉⋊C₈

C₁₉×#487

#1711

Subgroups — #14563248

Conjugacy classes of subgroups

Complements

Maximal subgroups