Group #19134255 — subgroups

Subgroups — #19134255

Order 5504.

186 conjugacy classes of subgroups; only the 61 normal subgroups are shown.

normal subgroups only

This group has 186 conjugacy classes of subgroups — too many to draw. Only its 61 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	#14583297	C₂	1	1	yes	maximal, characteristic, complemented
2	#14583279	C₂	1	1	yes	maximal, characteristic, complemented
3	#14583250	C₂	1	1	yes	maximal, characteristic, complemented
4	#14583246	C₂	1	1	yes	maximal, characteristic
5	#14583246	C₂	1	1	yes	maximal, characteristic
6	#14583246	C₂	1	1	yes	maximal, characteristic
7	C₄₃×#322	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×Dic₁₇₂	—	2	2	no	—
9	#13063325	C₂²	1	1	yes	characteristic
10	#13063325	C₂²	1	1	yes	characteristic
11	#13063325	C₂²	1	1	yes	characteristic
12	#13063322	C₂²	1	1	yes	characteristic
13	#13063257	—	2	2	no	—
14	#13063250	—	2	2	no	—
15	#13063247	—	2	2	no	—
16	#13063247	—	2	2	no	—
17	#13063247	—	2	2	no	—
18	C₄×C₈×C₄₃	C₂²	1	1	yes	characteristic
19	C₄×C₈×C₄₃	C₂²	1	1	yes	characteristic
20	C₄×C₈×C₄₃	C₂²	1	1	yes	characteristic
21	C₂×D₁₇₂	—	2	1	no	—
22	C₂×D₁₇₂	—	2	1	no	—
23	C₂×D₁₇₂	—	2	1	no	—
24	C₂×Dic₈₆	—	2	1	no	—
25	C₂×Dic₈₆	—	2	1	no	—
26	C₂×Dic₈₆	—	2	1	no	—
27	C₂×C₈×C₄₃	D₄	1	2	yes	—
28	C₂×C₈×C₄₃	D₄	1	2	yes	—
29	C₂×C₈×C₄₃	D₄	1	2	yes	—
30	C₄²×C₄₃	C₂³	1	1	yes	characteristic
31	C₄⋊Dic₄₃	—	2	1	no	—
32	C₄⋊Dic₄₃	—	2	1	no	—
33	C₄⋊Dic₄₃	—	2	1	no	—
34	C₄⋊Dic₄₃	—	2	1	no	—
35	C₄⋊Dic₄₃	—	2	1	no	—
36	C₄⋊Dic₄₃	—	2	1	no	—
37	Dic₁₇₂	—	4	4	no	—
38	C₂²×D₄₃	—	4	1	no	—
39	C₂×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
40	C₂×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
41	C₂×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
42	C₂×Dic₄₃	—	4	1	no	—
43	C₂×Dic₄₃	—	4	1	no	—
44	C₂×Dic₄₃	—	4	1	no	—
45	D₁₇₂	—	4	2	no	—
46	D₁₇₂	—	4	2	no	—
47	D₁₇₂	—	4	2	no	—
48	Dic₈₆	—	4	2	no	—
49	Dic₈₆	—	4	2	no	—
50	Dic₈₆	—	4	2	no	—
51	C₈×C₄₃	—	2	2	no	—
52	C₈×C₄₃	—	2	2	no	—
53	C₈×C₄₃	—	2	2	no	—
54	C₂²×C₄₃	#127	1	1	yes	characteristic
55	C₂×D₄₃	—	8	1	no	—
56	C₂×D₄₃	—	8	1	no	—
57	C₂×D₄₃	—	8	1	no	—
58	C₄×C₄₃	#135	1	2	yes	—
59	C₄×C₄₃	AGL(1,ℤ/8)	1	2	yes	—
60	C₄×C₄₃	#137	1	2	yes	—
61	Dic₄₃	—	8	1	no	—
62	Dic₄₃	—	8	1	no	—
63	Dic₄₃	—	8	1	no	—
64	#1720	—	43	1	no	maximal, Sylow
65	C₂×C₄₃	#495	1	1	yes	characteristic
66	C₂×C₄₃	#496	1	1	yes	characteristic
67	C₂×C₄₃	#497	1	1	yes	characteristic
68	D₄₃	—	16	1	no	—
69	#498	—	43	1	no	—
70	#494	—	43	1	no	—
71	#487	—	43	1	no	—
72	#486	—	43	1	no	—
73	#486	—	43	1	no	—
74	#486	—	43	1	no	—
75	#322	D₄₃	1	1	yes	characteristic, complemented
76	C₄₃	#1720	1	1	yes	characteristic, complemented, Sylow
77	C₂×Q₁₆	—	86	2	no	—
78	C₄⋊Q₈	—	43	1	no	—
79	C₄⋊Q₈	—	43	1	no	—
80	C₄⋊Q₈	—	43	1	no	—
81	#127	—	43	1	no	—
82	#106	—	86	2	no	—
83	#103	—	86	2	no	—
84	#102	—	86	2	no	—
85	#102	—	86	2	no	—
86	#102	—	86	2	no	—
87	C₄×C₈	C₂×D₄₃	1	1	yes	characteristic
88	C₄×C₈	C₂×D₄₃	1	1	yes	characteristic
89	C₄×C₈	C₂×D₄₃	1	1	yes	characteristic
90	C₂×Q₈	—	86	1	no	—
91	C₂×Q₈	—	86	1	no	—
92	C₂×Q₈	—	86	1	no	—
93	C₂×D₄	—	86	1	no	—
94	C₂×D₄	—	86	1	no	—
95	C₂×D₄	—	86	1	no	—
96	Q₁₆	—	172	4	no	—
97	C₂×C₈	D₁₇₂	1	2	yes	—
98	C₂×C₈	D₁₇₂	1	2	yes	—
99	C₂×C₈	D₁₇₂	1	2	yes	—
100	C₄⋊C₄	—	86	1	no	—
101	C₄⋊C₄	—	86	1	no	—
102	C₄⋊C₄	—	86	1	no	—
103	C₄⋊C₄	—	86	1	no	—
104	C₄⋊C₄	—	86	1	no	—
105	C₄⋊C₄	—	86	1	no	—
106	C₄²	C₂²×D₄₃	1	1	yes	characteristic
107	C₂³	—	172	1	no	—
108	Q₈	—	172	2	no	—
109	Q₈	—	172	2	no	—
110	Q₈	—	172	2	no	—
111	D₄	—	172	2	no	—
112	D₄	—	172	2	no	—
113	D₄	—	172	2	no	—
114	C₂×C₄	—	172	1	no	—
115	C₂×C₄	—	172	1	no	—
116	C₂×C₄	—	172	1	no	—
117	C₂×C₄	C₂×D₁₇₂	1	1	yes	characteristic
118	C₂×C₄	C₂×D₁₇₂	1	1	yes	characteristic
119	C₂×C₄	C₂×D₁₇₂	1	1	yes	characteristic
120	C₈	—	2	2	no	—
121	C₈	—	2	2	no	—
122	C₈	—	2	2	no	—
123	C₂²	—	344	1	no	—
124	C₂²	—	344	1	no	—
125	C₂²	—	344	1	no	—
126	C₂²	#13063322	1	1	yes	characteristic
127	C₄	—	344	1	no	—
128	C₄	—	344	1	no	—
129	C₄	—	344	1	no	—
130	C₄	#13063347	1	2	yes	—
131	C₄	#13063353	1	2	yes	—
132	C₄	#13063358	1	2	yes	—
133	C₂	—	688	1	no	—
134	C₂	#14583283	1	1	yes	characteristic
135	C₂	#14583288	1	1	yes	characteristic
136	C₂	#14583293	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#14583297

C₂

yes

maximal, characteristic, complemented

#14583279

C₂

yes

maximal, characteristic, complemented

#14583250

C₂

yes

maximal, characteristic, complemented

#14583246

C₂

yes

maximal, characteristic

#14583246

C₂

yes

maximal, characteristic

#14583246

C₂

yes

maximal, characteristic

C₄₃×#322

C₂

yes

maximal, characteristic, complemented

C₂×Dic₁₇₂

—

#13063325

C₂²

yes

characteristic

#13063325

C₂²

yes

characteristic

#13063325

C₂²

yes

characteristic

#13063322

C₂²

yes

—

—

—

—

—

C₄×C₈×C₄₃

C₂²

yes

characteristic

C₄×C₈×C₄₃

C₂²

yes

characteristic

C₄×C₈×C₄₃

C₂²

yes

characteristic

C₂×D₁₇₂

—

C₂×D₁₇₂

—

C₂×D₁₇₂

—

C₂×Dic₈₆

—

C₂×Dic₈₆

—

C₂×Dic₈₆

—

C₂×C₈×C₄₃

D₄

yes

—

C₂×C₈×C₄₃

D₄

yes

—

C₂×C₈×C₄₃

D₄

yes

—

C₄²×C₄₃

C₂³

yes

characteristic

C₄⋊Dic₄₃

—

C₄⋊Dic₄₃

—

C₄⋊Dic₄₃

—

C₄⋊Dic₄₃

—

C₄⋊Dic₄₃

—

C₄⋊Dic₄₃

—

Dic₁₇₂

—

C₂²×D₄₃

—

C₂×C₄×C₄₃

C₂×D₄

yes

characteristic

C₂×C₄×C₄₃

C₂×D₄

yes

characteristic

C₂×C₄×C₄₃

C₂×D₄

yes

characteristic

C₂×Dic₄₃

—

C₂×Dic₄₃

—

C₂×Dic₄₃

—

D₁₇₂

—

D₁₇₂

—

D₁₇₂

—

Dic₈₆

—

Dic₈₆

—

Dic₈₆

—

C₈×C₄₃

—

C₈×C₄₃

—

C₈×C₄₃

—

C₂²×C₄₃

#127

yes

characteristic

C₂×D₄₃

—

C₂×D₄₃

—

C₂×D₄₃

—

C₄×C₄₃

#135

yes

—

C₄×C₄₃

AGL(1,ℤ/8)

yes

—

C₄×C₄₃

#137

yes

—

Dic₄₃

—

Dic₄₃

—

Dic₄₃

—

—

C₂×C₄₃

yes

C₂×C₄₃

yes

C₂×C₄₃

yes

D₄₃

—

—

—

—

—

—

—

D₄₃

yes

characteristic, complemented

C₄₃

#1720

yes

characteristic, complemented, Sylow

C₂×Q₁₆

—

C₄⋊Q₈

—

C₄⋊Q₈

—

C₄⋊Q₈

—

—

—

—

—

—

—

C₄×C₈

C₂×D₄₃

yes

characteristic

C₄×C₈

C₂×D₄₃

yes

characteristic

C₄×C₈

C₂×D₄₃

yes

characteristic

C₂×Q₈

—

C₂×Q₈

—

C₂×Q₈

—

C₂×D₄

—

C₂×D₄

—

C₂×D₄

—

Q₁₆

—

172

—

C₂×C₈

D₁₇₂

yes

—

C₂×C₈

D₁₇₂

yes

—

C₂×C₈

D₁₇₂

yes

—

100

C₄⋊C₄

—

101

C₄⋊C₄

—

102

C₄⋊C₄

—

103

C₄⋊C₄

—

104

C₄⋊C₄

—

105

C₄⋊C₄

—

106

C₄²

C₂²×D₄₃

yes

characteristic

107

C₂³

—

172

—

108

Q₈

—

172

—

109

Q₈

—

172

—

110

Q₈

—

172

—

111

D₄

—

172

—

112

D₄

—

172

—

113

D₄

—

172

—

114

C₂×C₄

—

172

—

115

C₂×C₄

—

172

—

116

C₂×C₄

—

172

—

117

C₂×C₄

C₂×D₁₇₂

yes

characteristic

118

C₂×C₄

C₂×D₁₇₂

yes

characteristic

119

C₂×C₄

C₂×D₁₇₂

yes

characteristic

120

C₈

—

121

C₈

—

122

C₈

—

123

C₂²

—

344

—

124

C₂²

—

344

—

125

C₂²

—

344

—

126

C₂²

#13063322

yes

characteristic

127

C₄

—

344

—

128

C₄

—

344

—

129

C₄

—

344

—

130

C₄

#13063347

yes

—

131

C₄

#13063353

yes

—

132

C₄

#13063358

yes

—

133

C₂

—

688

—

134

C₂

#14583283

yes

characteristic

135

C₂

#14583288

yes

characteristic

136

C₂

#14583293

yes

characteristic

	subgroup	G/H
center	C₂²	#13063322
commutator	C₄²×C₄₃	C₂³
Frattini	C₄²	C₂²×D₄₃
Fitting	C₄₃×#322	C₂
socle	C₂²×C₄₃	#127
hypercenter	#322	D₄₃
hypocenter	C₄₃	#1720
LCS	G ▷ C₄²×C₄₃ ▷ C₂²×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₂² ◁ C₄² ◁ #322

subgroup

G/H

center

C₂²

#13063322

commutator

C₄²×C₄₃

C₂³

Frattini

C₄²

C₂²×D₄₃

Fitting

C₄₃×#322

C₂

C₂²×C₄₃

D₄₃

C₄₃

G ▷ C₄²×C₄₃ ▷ C₂²×C₄₃ ▷ C₄₃

UCS

C₁ ◁ C₂² ◁ C₄² ◁ #322

N	H ≅ G/N	type
1. #14583297	C₂	semidirect
2. #14583279	C₂	semidirect
3. #14583250	C₂	semidirect
7. C₄₃×#322	C₂	semidirect
75. #322	D₄₃	semidirect
76. C₄₃	#1720	semidirect

H ≅ G/N

type

1. #14583297

C₂

semidirect

2. #14583279

C₂

semidirect

3. #14583250

C₂

semidirect

7. C₄₃×#322

C₂

semidirect

75. #322

D₄₃

semidirect

76. C₄₃

#1720

semidirect

Subgroups — #19134255

Conjugacy classes of subgroups

Complements