Group #14571681 — subgroups

Subgroups — #14571681

Order 2432.

580 conjugacy classes of subgroups; only the 133 normal subgroups are shown.

normal subgroups only

This group has 580 conjugacy classes of subgroups — too many to draw. Only its 133 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×#10597321	C₂	1	2	yes	maximal, complemented
2	#11926461	C₂	1	4	yes	maximal, complemented
3	#11926457	C₂	1	4	yes	maximal, complemented
4	#11926454	C₂	1	4	yes	maximal, complemented
5	C₁₉×#382	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂²×D₇₆	C₂²	1	2	yes	—
7	C₂²×D₇₆	C₂²	1	4	yes	—
8	C₂²×Dic₃₈	C₂²	1	2	yes	—
9	C₂×C₄⋊C₄×C₁₉	C₂²	1	2	yes	—
10	C₂×C₄²×C₁₉	C₂²	1	1	yes	characteristic
11	C₂×(C₂×D₁₉)⋊C₄	C₂²	1	4	yes	—
12	C₂×(C₂×D₁₉)⋊C₄	C₂²	1	4	yes	—
13	C₂×(C₂×D₁₉)⋊C₄	C₂²	1	8	yes	—
14	#10597321	—	2	8	no	—
15	C₁₉×#95	C₂²	1	4	yes	—
16	C₁₉⋊#95	C₂²	1	4	yes	—
17	C₂³×D₁₉	C₂³	1	4	yes	—
18	C₂²×C₄×C₁₉	C₂³	1	4	yes	—
19	C₂²×C₄×C₁₉	C₂³	1	1	yes	characteristic
20	C₂²×C₄×C₁₉	C₂³	1	2	yes	—
21	C₂²×Dic₁₉	C₂³	1	4	yes	—
22	C₂×D₇₆	—	2	4	no	—
23	C₂×D₇₆	—	4	4	no	—
24	C₂×D₇₆	—	4	8	no	—
25	C₂×D₇₆	—	4	4	no	—
26	C₂×Dic₃₈	—	2	4	no	—
27	C₂×Dic₃₈	—	4	4	no	—
28	C₄⋊C₄×C₁₉	—	4	2	no	—
29	C₄²×C₁₉	D₄	1	4	yes	complemented
30	(C₂×D₁₉)⋊C₄	—	2	8	no	—
31	(C₂×D₁₉)⋊C₄	—	2	8	no	—
32	(C₂×D₁₉)⋊C₄	—	4	8	no	—
33	C₂³×C₁₉	C₂⁴	1	1	yes	characteristic
34	C₂²×D₁₉	—	2	4	no	—
35	C₂²×D₁₉	—	2	8	no	—
36	C₂²×D₁₉	—	2	4	no	—
37	C₂²×D₁₉	—	2	8	no	—
38	C₂²×D₁₉	—	2	4	no	—
39	C₂×C₄×C₁₉	—	2	1	no	—
40	C₂×C₄×C₁₉	—	2	4	no	—
41	C₂×C₄×C₁₉	—	2	1	no	—
42	C₂×C₄×C₁₉	—	2	8	no	—
43	C₂×C₄×C₁₉	—	2	4	no	—
44	C₂×C₄×C₁₉	C₂×D₄	1	2	yes	—
45	C₂×C₄×C₁₉	C₂×D₄	1	4	yes	—
46	C₂×Dic₁₉	—	2	4	no	—
47	C₂×Dic₁₉	—	2	8	no	—
48	D₇₆	—	4	8	no	—
49	D₇₆	—	4	16	no	—
50	Dic₃₈	—	4	8	no	—
51	#2819	—	19	1	no	maximal, Sylow
52	C₂²×C₁₉	C₂²×D₄	1	1	yes	characteristic
53	C₂²×C₁₉	H(5,𝔽₂)	1	1	yes	characteristic
54	C₂²×C₁₉	H(5,𝔽₂)	1	4	yes	—
55	C₂²×C₁₉	2₋¹⁺⁴	1	1	yes	characteristic
56	C₂×D₁₉	—	4	4	no	—
57	C₂×D₁₉	—	4	4	no	—
58	C₂×D₁₉	—	4	4	no	—
59	C₂×D₁₉	—	4	8	no	—
60	C₂×D₁₉	—	4	8	no	—
61	C₄×C₁₉	—	2	4	no	—
62	C₄×C₁₉	—	2	2	no	—
63	C₄×C₁₉	—	4	4	no	—
64	Dic₁₉	—	4	4	no	—
65	C₂×#124	—	19	2	no	—
66	#394	—	19	4	no	—
67	#393	—	19	4	no	—
68	#392	—	19	4	no	—
69	#382	D₁₉	1	1	yes	characteristic, complemented
70	C₂×C₁₉	#535	1	2	yes	—
71	C₂×C₁₉	#537	1	1	yes	characteristic
72	C₂×C₁₉	H(3,𝔽₄)	1	2	yes	—
73	C₂×C₁₉	#562	1	2	yes	—
74	D₁₉	—	8	4	no	—
75	C₂²×Q₈	—	19	2	no	—
76	C₂²×D₄	—	19	2	no	—
77	C₂²×D₄	—	19	4	no	—
78	#124	—	38	8	no	—
79	C₂×C₄⋊C₄	C₂×D₁₉	1	2	yes	—
80	C₂×C₂²⋊C₄	—	19	4	no	—
81	C₂×C₂²⋊C₄	—	19	4	no	—
82	C₂×C₂²⋊C₄	—	19	8	no	—
83	C₂×C₄²	C₂×D₁₉	1	1	yes	characteristic
84	#95	—	19	4	no	—
85	#95	C₂×D₁₉	1	4	yes	—
86	C₁₉	#2819	1	1	yes	characteristic, complemented, Sylow
87	C₂⁴	—	19	4	no	—
88	C₂×Q₈	—	38	4	no	—
89	C₂×Q₈	—	76	4	no	—
90	C₂×D₄	—	38	4	no	—
91	C₂×D₄	—	76	4	no	—
92	C₂×D₄	—	76	4	no	—
93	C₂×D₄	—	76	8	no	—
94	C₂²×C₄	—	19	4	no	—
95	C₂²×C₄	C₂²×D₁₉	1	4	yes	—
96	C₂²×C₄	C₂²×D₁₉	1	2	yes	—
97	C₂²×C₄	C₂²×D₁₉	1	1	yes	characteristic
98	C₄⋊C₄	—	4	2	no	—
99	C₂²⋊C₄	—	38	8	no	—
100	C₂²⋊C₄	—	38	8	no	—
101	C₂²⋊C₄	—	76	8	no	—
102	C₄²	D₇₆	1	4	yes	complemented
103	C₂³	—	38	4	no	—
104	C₂³	—	38	4	no	—
105	C₂³	—	38	4	no	—
106	C₂³	—	38	8	no	—
107	C₂³	—	38	8	no	—
108	C₂³	C₂³×D₁₉	1	1	yes	characteristic
109	Q₈	—	76	8	no	—
110	D₄	—	76	8	no	—
111	D₄	—	76	16	no	—
112	C₂×C₄	—	2	1	no	—
113	C₂×C₄	—	2	1	no	—
114	C₂×C₄	—	2	4	no	—
115	C₂×C₄	—	2	4	no	—
116	C₂×C₄	—	2	8	no	—
117	C₂×C₄	—	38	4	no	—
118	C₂×C₄	—	38	8	no	—
119	C₂×C₄	C₂×D₇₆	1	2	yes	—
120	C₂×C₄	C₂×D₇₆	1	4	yes	—
121	C₂²	—	76	4	no	—
122	C₂²	—	76	4	no	—
123	C₂²	—	76	4	no	—
124	C₂²	—	76	8	no	—
125	C₂²	—	76	8	no	—
126	C₂²	C₂²×D₇₆	1	1	yes	characteristic
127	C₂²	#10597430	1	1	yes	characteristic
128	C₂²	#10597433	1	1	yes	characteristic
129	C₂²	#10597435	1	4	yes	—
130	C₄	—	2	4	no	—
131	C₄	—	2	2	no	—
132	C₄	—	4	4	no	—
133	C₄	—	76	4	no	—
134	C₂	—	152	4	no	—
135	C₂	#11927113	1	2	yes	—
136	C₂	#11927125	1	1	yes	characteristic
137	C₂	#11927286	1	2	yes	—
138	C₂	#11927292	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×#10597321

C₂

yes

maximal, complemented

#11926461

C₂

yes

maximal, complemented

#11926457

C₂

yes

maximal, complemented

#11926454

C₂

yes

maximal, complemented

C₁₉×#382

C₂

yes

maximal, characteristic, complemented

C₂²×D₇₆

C₂²

yes

—

C₂²×D₇₆

C₂²

yes

—

C₂²×Dic₃₈

C₂²

yes

—

C₂×C₄⋊C₄×C₁₉

C₂²

yes

—

C₂×C₄²×C₁₉

C₂²

yes

characteristic

C₂×(C₂×D₁₉)⋊C₄

C₂²

yes

—

C₂×(C₂×D₁₉)⋊C₄

C₂²

yes

—

C₂×(C₂×D₁₉)⋊C₄

C₂²

yes

—

#10597321

—

C₁₉×#95

C₂²

yes

—

C₁₉⋊#95

C₂²

yes

—

C₂³×D₁₉

C₂³

yes

—

C₂²×C₄×C₁₉

C₂³

yes

—

C₂²×C₄×C₁₉

C₂³

yes

characteristic

C₂²×C₄×C₁₉

C₂³

yes

—

C₂²×Dic₁₉

C₂³

yes

—

C₂×D₇₆

—

C₂×D₇₆

—

C₂×D₇₆

—

C₂×D₇₆

—

C₂×Dic₃₈

—

C₂×Dic₃₈

—

C₄⋊C₄×C₁₉

—

C₄²×C₁₉

D₄

yes

complemented

(C₂×D₁₉)⋊C₄

—

(C₂×D₁₉)⋊C₄

—

(C₂×D₁₉)⋊C₄

—

C₂³×C₁₉

C₂⁴

yes

characteristic

C₂²×D₁₉

—

C₂²×D₁₉

—

C₂²×D₁₉

—

C₂²×D₁₉

—

C₂²×D₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

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

—

D₇₆

—

D₇₆

—

Dic₃₈

—

#2819

—

maximal, Sylow

C₂²×C₁₉

C₂²×D₄

yes

C₂²×C₁₉

yes

C₂²×C₁₉

yes

—

C₂²×C₁₉

2₋¹⁺⁴

yes

characteristic

C₂×D₁₉

—

C₂×D₁₉

—

C₂×D₁₉

—

C₂×D₁₉

—

C₂×D₁₉

—

C₄×C₁₉

—

C₄×C₁₉

—

C₄×C₁₉

—

Dic₁₉

—

—

—

—

—

D₁₉

yes

characteristic, complemented

C₂×C₁₉

#535

yes

—

C₂×C₁₉

#537

yes

characteristic

C₂×C₁₉

H(3,𝔽₄)

yes

—

C₂×C₁₉

#562

yes

—

D₁₉

—

C₂²×Q₈

—

C₂²×D₄

—

C₂²×D₄

—

#124

—

C₂×C₄⋊C₄

C₂×D₁₉

yes

—

C₂×C₂²⋊C₄

—

C₂×C₂²⋊C₄

—

C₂×C₂²⋊C₄

—

C₂×C₄²

C₂×D₁₉

yes

characteristic

#95

—

#95

C₂×D₁₉

yes

—

C₁₉

#2819

yes

characteristic, complemented, Sylow

C₂⁴

—

C₂×Q₈

—

C₂×Q₈

—

C₂×D₄

—

C₂×D₄

—

C₂×D₄

—

C₂×D₄

—

C₂²×C₄

—

C₂²×C₄

C₂²×D₁₉

yes

—

C₂²×C₄

C₂²×D₁₉

yes

—

C₂²×C₄

C₂²×D₁₉

yes

characteristic

C₄⋊C₄

—

C₂²⋊C₄

—

100

C₂²⋊C₄

—

101

C₂²⋊C₄

—

102

C₄²

D₇₆

yes

complemented

103

C₂³

—

104

C₂³

—

105

C₂³

—

106

C₂³

—

107

C₂³

—

108

C₂³

C₂³×D₁₉

yes

characteristic

109

Q₈

—

110

D₄

—

111

D₄

—

112

C₂×C₄

—

113

C₂×C₄

—

114

C₂×C₄

—

115

C₂×C₄

—

116

C₂×C₄

—

117

C₂×C₄

—

118

C₂×C₄

—

119

C₂×C₄

C₂×D₇₆

yes

—

120

C₂×C₄

C₂×D₇₆

yes

—

121

C₂²

—

122

C₂²

—

123

C₂²

—

124

C₂²

—

125

C₂²

—

126

C₂²

C₂²×D₇₆

yes

characteristic

127

C₂²

#10597430

yes

characteristic

128

C₂²

#10597433

yes

characteristic

129

C₂²

#10597435

yes

—

130

C₄

—

131

C₄

—

132

C₄

—

133

C₄

—

134

C₂

—

152

—

135

C₂

#11927113

yes

—

136

C₂

#11927125

yes

characteristic

137

C₂

#11927286

yes

—

138

C₂

#11927292

yes

—

	subgroup	G/H
center, Frattini	C₂³	C₂³×D₁₉
commutator, socle, cosocle	C₂³×C₁₉	C₂⁴
Fitting	C₁₉×#382	C₂
hypercenter	#382	D₁₉
hypocenter	C₁₉	#2819
LCS	G ▷ C₂³×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂³ ◁ #382

subgroup

G/H

center, Frattini

C₂³

C₂³×D₁₉

commutator, socle, cosocle

C₂³×C₁₉

C₂⁴

Fitting

C₁₉×#382

C₂

D₁₉

C₁₉

G ▷ C₂³×C₁₉ ▷ C₁₉

C₁ ◁ C₂³ ◁ #382

N	H ≅ G/N	type
1. C₂×#10597321	C₂	semidirect
2. #11926461	C₂	semidirect
3. #11926457	C₂	semidirect
4. #11926454	C₂	semidirect
5. C₁₉×#382	C₂	semidirect
29. C₄²×C₁₉	D₄	semidirect
69. #382	D₁₉	semidirect
86. C₁₉	#2819	semidirect
102. C₄²	D₇₆	semidirect

H ≅ G/N

type

1. C₂×#10597321

C₂

semidirect

2. #11926461

C₂

semidirect

3. #11926457

C₂

semidirect

4. #11926454

C₂

semidirect

5. C₁₉×#382

C₂

semidirect

29. C₄²×C₁₉

D₄

semidirect

69. #382

D₁₉

semidirect

86. C₁₉

#2819

semidirect

102. C₄²

D₇₆

semidirect

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

subgroup	index
C₂×#10597321	2
#11926461	2
#11926457	2
#11926454	2
C₁₉×#382	2
#2819	19

subgroup

index

C₁₉×#382

Subgroups — #14571681

Conjugacy classes of subgroups

Complements

Maximal subgroups