Group #19135420 — subgroups

Subgroups — #19135420

Order 5504.

412 conjugacy classes of subgroups; only the 113 normal subgroups are shown.

normal subgroups only

This group has 412 conjugacy classes of subgroups — too many to draw. Only its 113 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×#13063246	C₂	1	4	yes	maximal, complemented
2	C₂×#13063236	C₂	1	1	yes	maximal, characteristic, complemented
3	#14582765	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×#127×C₄₃	C₂	1	1	yes	maximal, characteristic
5	C₂²×C₄₃⋊C₈	C₂²	1	2	yes	—
6	C₂×C₄⋊Dic₄₃	C₂²	1	2	yes	—
7	#13063246	—	2	8	no	—
8	#13063236	—	2	2	no	—
9	C₄₃⋊#95	—	2	2	no	—
10	C₂²×D₄×C₄₃	—	2	2	no	—
11	C₂²×D₄×C₄₃	C₂²	1	2	yes	—
12	#127×C₄₃	—	2	2	no	—
13	#127×C₄₃	C₄	1	4	yes	complemented
14	C₂×C₄²×C₄₃	C₂²	1	1	yes	characteristic
15	C₂⁴×C₄₃	—	2	2	no	—
16	C₂×D₄×C₄₃	—	2	8	no	—
17	C₂×D₄×C₄₃	—	2	2	no	—
18	C₂×D₄×C₄₃	—	2	4	no	—
19	C₂×D₄×C₄₃	—	2	4	no	—
20	C₂×D₄×C₄₃	—	4	8	no	—
21	C₂×D₄×C₄₃	C₂×C₄	1	4	yes	—
22	C₂²×C₄×C₄₃	D₄	1	2	yes	—
23	C₂²×C₄×C₄₃	C₂³	1	1	yes	characteristic
24	C₂²×Dic₄₃	—	2	2	no	—
25	C₄²×C₄₃	C₂×C₄	1	2	yes	—
26	C₄²×C₄₃	D₄	1	2	yes	—
27	C₄⋊Dic₄₃	—	2	4	no	—
28	C₂×C₄₃⋊C₈	—	2	2	no	—
29	C₂×C₄₃⋊C₈	—	2	2	no	—
30	C₂×C₄₃⋊C₈	D₄	1	4	yes	complemented
31	C₂³×C₄₃	—	2	4	no	—
32	C₂³×C₄₃	—	4	2	no	—
33	C₂³×C₄₃	—	4	2	no	—
34	C₂³×C₄₃	—	4	8	no	—
35	C₂³×C₄₃	C₂×D₄	1	1	yes	characteristic
36	D₄×C₄₃	—	2	8	no	—
37	D₄×C₄₃	—	4	16	no	—
38	D₄×C₄₃	—	4	4	no	—
39	C₂×C₄×C₄₃	—	2	4	no	—
40	C₂×C₄×C₄₃	C₂²⋊C₄	1	4	yes	—
41	C₂×C₄×C₄₃	C₂²×C₄	1	1	yes	characteristic
42	C₂×C₄×C₄₃	C₂×D₄	1	2	yes	—
43	C₂×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
44	C₂×C₄×C₄₃	#41	1	2	yes	—
45	C₂×Dic₄₃	—	4	2	no	—
46	C₂×Dic₄₃	—	4	4	no	—
47	C₄₃⋊C₈	—	2	4	no	—
48	C₂²×C₄₃	—	4	4	no	—
49	C₂²×C₄₃	—	4	8	no	—
50	C₂²×C₄₃	—	8	4	no	—
51	C₂²×C₄₃	—	8	4	no	—
52	C₂²×C₄₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
53	C₂²×C₄₃	#124	1	1	yes	characteristic
54	C₂²×C₄₃	#127	1	1	yes	characteristic
55	C₂²×C₄₃	AGL(1,ℤ/8)	1	4	yes	—
56	C₄×C₄₃	—	2	4	no	—
57	C₄×C₄₃	C₄×D₄	1	2	yes	—
58	C₄×C₄₃	#121	1	2	yes	—
59	Dic₄₃	—	8	2	no	—
60	#1961	—	43	1	no	maximal, Sylow
61	C₂×C₄₃	—	8	4	no	—
62	C₂×C₄₃	#390	1	1	yes	characteristic
63	C₂×C₄₃	#418	1	2	yes	—
64	C₂×C₄₃	#490	1	2	yes	—
65	C₂×C₄₃	#496	1	2	yes	—
66	C₂×#127	D₄₃	1	1	yes	characteristic
67	C₂×#102	—	43	4	no	—
68	C₂×#97	—	43	1	no	—
69	#382	—	43	1	no	—
70	C₄₃	#1961	1	1	yes	characteristic, complemented, Sylow
71	C₂²×D₄	—	2	2	no	—
72	C₂²×D₄	C₂×D₄₃	1	2	yes	—
73	C₂²×C₈	—	43	2	no	—
74	#127	—	2	2	no	—
75	#127	Dic₄₃	1	4	yes	complemented
76	C₂×C₄⋊C₄	—	43	2	no	—
77	C₂×C₄²	C₂×D₄₃	1	1	yes	characteristic
78	#102	—	86	8	no	—
79	#97	—	86	2	no	—
80	#95	—	86	2	no	—
81	C₂⁴	—	2	2	no	—
82	C₂×D₄	—	2	8	no	—
83	C₂×D₄	—	2	4	no	—
84	C₂×D₄	—	2	4	no	—
85	C₂×D₄	—	2	2	no	—
86	C₂×D₄	—	4	8	no	—
87	C₂×D₄	C₂×Dic₄₃	1	4	yes	—
88	C₂²×C₄	—	86	2	no	—
89	C₂²×C₄	C₂²⋊D₄₃	1	2	yes	—
90	C₂²×C₄	C₂²×D₄₃	1	1	yes	characteristic
91	C₂×C₈	—	43	4	no	—
92	C₂×C₈	—	86	2	no	—
93	C₂×C₈	—	86	2	no	—
94	C₄⋊C₄	—	86	4	no	—
95	C₄²	C₂×Dic₄₃	1	2	yes	—
96	C₄²	C₂²⋊D₄₃	1	2	yes	—
97	C₂³	—	2	4	no	—
98	C₂³	—	4	2	no	—
99	C₂³	—	4	2	no	—
100	C₂³	—	4	8	no	—
101	C₂³	C₂×C₂²⋊D₄₃	1	1	yes	characteristic
102	D₄	—	2	8	no	—
103	D₄	—	4	16	no	—
104	D₄	—	4	4	no	—
105	C₂×C₄	—	2	4	no	—
106	C₂×C₄	—	172	2	no	—
107	C₂×C₄	—	172	4	no	—
108	C₂×C₄	C₂²⋊Dic₄₃	1	4	yes	—
109	C₂×C₄	D₄×D₄₃	1	2	yes	—
110	C₂×C₄	#10621900	1	2	yes	—
111	C₂×C₄	C₂²×Dic₄₃	1	1	yes	characteristic
112	C₂×C₄	C₂×C₂²⋊D₄₃	1	1	yes	characteristic
113	C₈	—	86	4	no	—
114	C₂²	—	4	4	no	—
115	C₂²	—	4	8	no	—
116	C₂²	—	8	4	no	—
117	C₂²	—	8	4	no	—
118	C₂²	C₂×C₂²⋊Dic₄₃	1	1	yes	characteristic
119	C₂²	#13063312	1	1	yes	characteristic
120	C₂²	#13063321	1	1	yes	characteristic
121	C₂²	#13063351	1	4	yes	—
122	C₄	—	2	4	no	—
123	C₄	—	344	2	no	—
124	C₄	D₄×Dic₄₃	1	2	yes	—
125	C₄	#13063296	1	2	yes	—
126	C₂	—	8	4	no	—
127	C₂	#14582802	1	1	yes	characteristic
128	C₂	#14582904	1	2	yes	—
129	C₂	#14583263	1	2	yes	—
130	C₂	#14583286	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×#13063246

C₂

yes

maximal, complemented

C₂×#13063236

C₂

yes

maximal, characteristic, complemented

#14582765

C₂

yes

maximal, characteristic, complemented

C₂×#127×C₄₃

C₂

yes

maximal, characteristic

C₂²×C₄₃⋊C₈

C₂²

yes

—

C₂×C₄⋊Dic₄₃

C₂²

yes

—

#13063246

—

#13063236

—

C₄₃⋊#95

—

C₂²×D₄×C₄₃

—

C₂²×D₄×C₄₃

C₂²

yes

—

#127×C₄₃

—

#127×C₄₃

C₄

yes

complemented

C₂×C₄²×C₄₃

C₂²

yes

characteristic

C₂⁴×C₄₃

—

C₂×D₄×C₄₃

—

C₂×D₄×C₄₃

—

C₂×D₄×C₄₃

—

C₂×D₄×C₄₃

—

C₂×D₄×C₄₃

—

C₂×D₄×C₄₃

C₂×C₄

yes

—

C₂²×C₄×C₄₃

D₄

yes

—

C₂²×C₄×C₄₃

C₂³

yes

characteristic

C₂²×Dic₄₃

—

C₄²×C₄₃

C₂×C₄

yes

—

C₄²×C₄₃

D₄

yes

—

C₄⋊Dic₄₃

—

C₂×C₄₃⋊C₈

—

C₂×C₄₃⋊C₈

—

C₂×C₄₃⋊C₈

D₄

yes

complemented

C₂³×C₄₃

—

C₂³×C₄₃

—

C₂³×C₄₃

—

C₂³×C₄₃

—

C₂³×C₄₃

C₂×D₄

yes

characteristic

D₄×C₄₃

—

D₄×C₄₃

—

D₄×C₄₃

—

C₂×C₄×C₄₃

—

C₂×C₄×C₄₃

C₂²⋊C₄

yes

—

C₂×C₄×C₄₃

C₂²×C₄

yes

characteristic

C₂×C₄×C₄₃

C₂×D₄

yes

—

C₂×C₄×C₄₃

C₂×D₄

yes

characteristic

C₂×C₄×C₄₃

#41

yes

—

C₂×Dic₄₃

—

C₂×Dic₄₃

—

C₄₃⋊C₈

—

C₂²×C₄₃

—

C₂²×C₄₃

—

C₂²×C₄₃

—

C₂²×C₄₃

—

C₂²×C₄₃

C₂×C₂²⋊C₄

yes

C₂²×C₄₃

yes

C₂²×C₄₃

yes

C₂²×C₄₃

yes

—

C₄×C₄₃

—

C₄×C₄₃

C₄×D₄

yes

—

C₄×C₄₃

#121

yes

—

Dic₄₃

—

#1961

—

maximal, Sylow

C₂×C₄₃

—

C₂×C₄₃

#390

yes

characteristic

C₂×C₄₃

#418

yes

—

C₂×C₄₃

#490

yes

—

C₂×C₄₃

#496

yes

—

C₂×#127

D₄₃

yes

characteristic

C₂×#102

—

C₂×#97

—

#382

—

C₄₃

#1961

yes

characteristic, complemented, Sylow

C₂²×D₄

—

C₂²×D₄

C₂×D₄₃

yes

—

C₂²×C₈

—

#127

—

#127

Dic₄₃

yes

complemented

C₂×C₄⋊C₄

—

C₂×C₄²

C₂×D₄₃

yes

—

—

—

C₂⁴

—

C₂×D₄

—

C₂×D₄

—

C₂×D₄

—

C₂×D₄

—

C₂×D₄

—

C₂×D₄

C₂×Dic₄₃

yes

—

C₂²×C₄

—

C₂²×C₄

C₂²⋊D₄₃

yes

—

C₂²×C₄

C₂²×D₄₃

yes

characteristic

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₄⋊C₄

—

C₄²

C₂×Dic₄₃

yes

—

C₄²

C₂²⋊D₄₃

yes

—

C₂³

—

C₂³

—

C₂³

—

100

C₂³

—

101

C₂³

C₂×C₂²⋊D₄₃

yes

characteristic

102

D₄

—

103

D₄

—

104

D₄

—

105

C₂×C₄

—

106

C₂×C₄

—

172

—

107

C₂×C₄

—

172

—

108

C₂×C₄

C₂²⋊Dic₄₃

yes

—

109

C₂×C₄

D₄×D₄₃

yes

—

110

C₂×C₄

#10621900

yes

—

111

C₂×C₄

C₂²×Dic₄₃

yes

characteristic

112

C₂×C₄

C₂×C₂²⋊D₄₃

yes

characteristic

113

C₈

—

114

C₂²

—

115

C₂²

—

116

C₂²

—

117

C₂²

—

118

C₂²

C₂×C₂²⋊Dic₄₃

yes

characteristic

119

C₂²

#13063312

yes

characteristic

120

C₂²

#13063321

yes

characteristic

121

C₂²

#13063351

yes

—

122

C₄

—

123

C₄

—

344

—

124

C₄

D₄×Dic₄₃

yes

—

125

C₄

#13063296

yes

—

126

C₂

—

127

C₂

#14582802

yes

characteristic

128

C₂

#14582904

yes

—

129

C₂

#14583263

yes

—

130

C₂

#14583286

yes

—

	subgroup	G/H
center	C₂³	C₂×C₂²⋊D₄₃
commutator	C₂×C₄×C₄₃	C₂²×C₄
Frattini	C₂²×C₄	C₂²×D₄₃
Fitting	C₂×#127×C₄₃	C₂
socle	C₂³×C₄₃	C₂×D₄
hypercenter	C₂×#127	D₄₃
hypocenter	C₄₃	#1961
LCS	G ▷ C₂×C₄×C₄₃ ▷ C₂×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₂³ ◁ C₂×C₄² ◁ C₂×#127

subgroup

G/H

center

C₂³

C₂×C₂²⋊D₄₃

commutator

C₂×C₄×C₄₃

C₂²×C₄

Frattini

C₂²×C₄

C₂²×D₄₃

Fitting

C₂×#127×C₄₃

C₂

socle

C₂³×C₄₃

C₂×D₄

D₄₃

C₄₃

G ▷ C₂×C₄×C₄₃ ▷ C₂×C₄₃ ▷ C₄₃

UCS

C₁ ◁ C₂³ ◁ C₂×C₄² ◁ C₂×#127

N	H ≅ G/N	type
1. C₂×#13063246	C₂	semidirect
2. C₂×#13063236	C₂	semidirect
3. #14582765	C₂	semidirect
13. #127×C₄₃	C₄	semidirect
30. C₂×C₄₃⋊C₈	D₄	semidirect
70. C₄₃	#1961	semidirect
75. #127	Dic₄₃	semidirect

H ≅ G/N

type

1. C₂×#13063246

C₂

semidirect

2. C₂×#13063236

C₂

semidirect

3. #14582765

C₂

semidirect

13. #127×C₄₃

C₄

semidirect

30. C₂×C₄₃⋊C₈

D₄

semidirect

70. C₄₃

#1961

semidirect

75. #127

Dic₄₃

semidirect

Subgroups — #19135420

Conjugacy classes of subgroups

Complements