Group #19136725 — subgroups

Subgroups — #19136725

Order 5504.

144 conjugacy classes of subgroups; only the 49 normal subgroups are shown.

normal subgroups only

This group has 144 conjugacy classes of subgroups — too many to draw. Only its 49 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×#13063270	C₂	1	1	yes	maximal, characteristic, complemented
2	#14583174	C₂	1	1	yes	maximal, characteristic, complemented
3	#14583169	C₂	1	1	yes	maximal, characteristic
4	#14582729	C₂	1	1	yes	maximal, characteristic, complemented
5	#14582716	C₂	1	1	yes	maximal, characteristic, complemented
6	#14582713	C₂	1	1	yes	maximal, characteristic, complemented
7	C₄₃×#504	C₂	1	1	yes	maximal, characteristic, complemented
8	#13063355	—	2	1	no	—
9	#13063350	—	2	1	no	—
10	C₂×Dic₁₇₂	C₂²	1	1	yes	characteristic
11	C₂×D₃₄₄	C₂²	1	1	yes	characteristic
12	#13063270	—	2	1	no	—
13	#13063270	—	2	1	no	—
14	#13063261	C₂²	1	1	yes	characteristic
15	#13063261	C₂²	1	1	yes	characteristic
16	#13063243	—	2	1	no	—
17	#13063241	—	2	1	no	—
18	#131×C₄₃	C₂²	1	1	yes	characteristic
19	M₃₂×C₄₃	—	2	1	no	—
20	M₃₂×C₄₃	C₂²	1	1	yes	characteristic
21	C₂×C₁₆×C₄₃	—	2	1	no	—
22	C₂×C₁₆×C₄₃	C₂²	1	1	yes	characteristic
23	#41×C₄₃	D₄	1	1	yes	characteristic
24	C₂×D₁₇₂	—	2	1	no	—
25	C₂×Dic₈₆	—	2	1	no	—
26	M₁₆×C₄₃	—	2	1	no	—
27	M₁₆×C₄₃	D₄	1	1	yes	characteristic
28	C₂×C₈×C₄₃	—	2	1	no	—
29	C₂×C₈×C₄₃	C₂³	1	1	yes	characteristic
30	#10621885	—	4	1	no	—
31	#10621884	—	4	1	no	—
32	#10621883	—	4	1	no	—
33	#10621882	—	4	1	no	—
34	#10621877	—	2	1	no	—
35	#10621877	—	2	1	no	—
36	Dic₁₇₂	—	2	1	no	—
37	Dic₁₇₂	—	2	1	no	—
38	D₃₄₄	—	2	1	no	—
39	D₃₄₄	—	2	1	no	—
40	C₁₆×C₄₃	—	2	1	no	—
41	C₁₆×C₄₃	D₄	1	1	yes	characteristic
42	C₁₆×C₄₃	D₄	1	1	yes	characteristic
43	C₂²×D₄₃	—	4	1	no	—
44	Q₈×C₄₃	D₈	1	1	yes	characteristic
45	D₄×C₄₃	—	2	1	no	—
46	D₄×C₄₃	D₈	1	1	yes	characteristic
47	C₂×C₄×C₄₃	—	2	1	no	—
48	C₂×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
49	C₂×Dic₄₃	—	4	1	no	—
50	D₁₇₂	—	4	1	no	—
51	D₁₇₂	—	4	1	no	—
52	Dic₈₆	—	4	1	no	—
53	Dic₈₆	—	4	1	no	—
54	C₈×C₄₃	—	2	1	no	—
55	C₈×C₄₃	C₂×D₄	1	1	yes	characteristic
56	C₈×C₄₃	#41	1	1	yes	characteristic
57	C₄₃⋊C₈	—	4	1	no	—
58	C₄₃⋊C₈	—	4	1	no	—
59	C₂²×C₄₃	—	2	1	no	—
60	C₂²×C₄₃	#135	1	1	yes	characteristic
61	C₂×D₄₃	—	8	1	no	—
62	C₂×D₄₃	—	16	1	no	—
63	C₄×C₄₃	—	2	1	no	—
64	C₄×C₄₃	#121	1	1	yes	characteristic
65	C₄×C₄₃	C₂×D₈	1	1	yes	characteristic
66	Dic₄₃	—	8	1	no	—
67	#2223	—	43	1	no	maximal, Sylow
68	C₂×C₄₃	—	2	1	no	—
69	C₂×C₄₃	—	4	1	no	—
70	C₂×C₄₃	#466	1	1	yes	characteristic
71	D₄₃	—	16	1	no	—
72	C₂×SD₃₂	—	43	1	no	—
73	#504	D₄₃	1	1	yes	characteristic, complemented
74	#473	—	43	1	no	—
75	#472	—	43	1	no	—
76	#368	—	43	1	no	—
77	#362	—	43	1	no	—
78	#361	—	43	1	no	—
79	C₄₃	#2223	1	1	yes	characteristic, complemented, Sylow
80	#137	—	86	1	no	—
81	AGL(1,ℤ/8)	—	86	1	no	—
82	C₂×Q₁₆	—	43	1	no	—
83	C₂×D₈	—	43	1	no	—
84	#131	C₂×D₄₃	1	1	yes	characteristic
85	SD₃₂	—	86	1	no	—
86	SD₃₂	—	86	1	no	—
87	M₃₂	—	2	1	no	—
88	M₃₂	C₂×D₄₃	1	1	yes	characteristic
89	C₂×C₁₆	—	2	1	no	—
90	C₂×C₁₆	C₂×D₄₃	1	1	yes	characteristic
91	#108	—	43	1	no	—
92	#108	—	43	1	no	—
93	#101	—	86	1	no	—
94	#100	—	86	1	no	—
95	#41	D₁₇₂	1	1	yes	characteristic
96	C₂×Q₈	—	86	1	no	—
97	C₂×D₄	—	86	1	no	—
98	Q₁₆	—	86	1	no	—
99	Q₁₆	—	86	1	no	—
100	Q₁₆	—	172	1	no	—
101	SD₁₆	—	172	1	no	—
102	SD₁₆	—	172	1	no	—
103	D₈	—	86	1	no	—
104	D₈	—	86	1	no	—
105	D₈	—	172	1	no	—
106	M₁₆	—	2	1	no	—
107	M₁₆	—	86	1	no	—
108	M₁₆	—	86	1	no	—
109	M₁₆	D₁₇₂	1	1	yes	characteristic
110	C₂×C₈	—	2	1	no	—
111	C₂×C₈	C₂²×D₄₃	1	1	yes	characteristic
112	C₁₆	—	2	1	no	—
113	C₁₆	C₂²⋊D₄₃	1	1	yes	characteristic
114	C₁₆	C₂²⋊D₄₃	1	1	yes	characteristic
115	C₂³	—	172	1	no	—
116	Q₈	—	172	1	no	—
117	Q₈	—	172	1	no	—
118	Q₈	D₃₄₄	1	1	yes	characteristic
119	D₄	—	2	1	no	—
120	D₄	—	172	1	no	—
121	D₄	—	172	1	no	—
122	D₄	D₃₄₄	1	1	yes	characteristic
123	C₂×C₄	—	2	1	no	—
124	C₂×C₄	—	172	1	no	—
125	C₂×C₄	C₂×D₁₇₂	1	1	yes	characteristic
126	C₈	—	2	1	no	—
127	C₈	—	172	1	no	—
128	C₈	—	172	1	no	—
129	C₈	#10621898	1	1	yes	characteristic
130	C₈	C₂×C₂²⋊D₄₃	1	1	yes	characteristic
131	C₂²	—	2	1	no	—
132	C₂²	—	344	1	no	—
133	C₂²	—	688	1	no	—
134	C₂²	#13063347	1	1	yes	characteristic
135	C₄	—	2	1	no	—
136	C₄	—	344	1	no	—
137	C₄	#13063299	1	1	yes	characteristic
138	C₄	C₂×D₃₄₄	1	1	yes	characteristic
139	C₂	—	2	1	no	—
140	C₂	—	4	1	no	—
141	C₂	—	688	1	no	—
142	C₂	#14583135	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×#13063270

C₂

yes

maximal, characteristic, complemented

#14583174

C₂

yes

maximal, characteristic, complemented

#14583169

C₂

yes

maximal, characteristic

#14582729

C₂

yes

maximal, characteristic, complemented

#14582716

C₂

yes

maximal, characteristic, complemented

#14582713

C₂

yes

maximal, characteristic, complemented

C₄₃×#504

C₂

yes

maximal, characteristic, complemented

#13063355

—

#13063350

—

C₂×Dic₁₇₂

C₂²

yes

characteristic

C₂×D₃₄₄

C₂²

yes

—

—

C₂²

yes

characteristic

#13063261

C₂²

yes

characteristic

#13063243

—

#13063241

—

#131×C₄₃

C₂²

yes

characteristic

M₃₂×C₄₃

—

M₃₂×C₄₃

C₂²

yes

characteristic

C₂×C₁₆×C₄₃

—

C₂×C₁₆×C₄₃

C₂²

yes

characteristic

#41×C₄₃

D₄

yes

characteristic

C₂×D₁₇₂

—

C₂×Dic₈₆

—

M₁₆×C₄₃

—

M₁₆×C₄₃

D₄

yes

characteristic

C₂×C₈×C₄₃

—

C₂×C₈×C₄₃

C₂³

yes

—

—

—

—

—

—

Dic₁₇₂

—

Dic₁₇₂

—

D₃₄₄

—

D₃₄₄

—

C₁₆×C₄₃

—

C₁₆×C₄₃

D₄

yes

characteristic

C₁₆×C₄₃

D₄

yes

characteristic

C₂²×D₄₃

—

Q₈×C₄₃

D₈

yes

characteristic

D₄×C₄₃

—

D₄×C₄₃

D₈

yes

characteristic

C₂×C₄×C₄₃

—

C₂×C₄×C₄₃

C₂×D₄

yes

characteristic

C₂×Dic₄₃

—

D₁₇₂

—

D₁₇₂

—

Dic₈₆

—

Dic₈₆

—

C₈×C₄₃

—

C₈×C₄₃

C₂×D₄

yes

characteristic

C₈×C₄₃

#41

yes

characteristic

C₄₃⋊C₈

—

C₄₃⋊C₈

—

C₂²×C₄₃

—

C₂²×C₄₃

#135

yes

characteristic

C₂×D₄₃

—

C₂×D₄₃

—

C₄×C₄₃

—

C₄×C₄₃

#121

yes

characteristic

C₄×C₄₃

C₂×D₈

yes

characteristic

Dic₄₃

—

#2223

—

maximal, Sylow

C₂×C₄₃

—

C₂×C₄₃

—

C₂×C₄₃

#466

yes

characteristic

D₄₃

—

C₂×SD₃₂

—

#504

D₄₃

yes

characteristic, complemented

—

—

—

—

—

C₄₃

#2223

yes

characteristic, complemented, Sylow

#137

—

AGL(1,ℤ/8)

—

C₂×Q₁₆

—

C₂×D₈

—

#131

C₂×D₄₃

yes

characteristic

SD₃₂

—

SD₃₂

—

M₃₂

—

M₃₂

C₂×D₄₃

yes

characteristic

C₂×C₁₆

—

C₂×C₁₆

C₂×D₄₃

yes

—

—

—

—

D₁₇₂

yes

characteristic

C₂×Q₈

—

C₂×D₄

—

Q₁₆

—

Q₁₆

—

100

Q₁₆

—

172

—

101

SD₁₆

—

172

—

102

SD₁₆

—

172

—

103

D₈

—

104

D₈

—

105

D₈

—

172

—

106

M₁₆

—

107

M₁₆

—

108

M₁₆

—

109

M₁₆

D₁₇₂

yes

characteristic

110

C₂×C₈

—

111

C₂×C₈

C₂²×D₄₃

yes

characteristic

112

C₁₆

—

113

C₁₆

C₂²⋊D₄₃

yes

characteristic

114

C₁₆

C₂²⋊D₄₃

yes

characteristic

115

C₂³

—

172

—

116

Q₈

—

172

—

117

Q₈

—

172

—

118

Q₈

D₃₄₄

yes

characteristic

119

D₄

—

120

D₄

—

172

—

121

D₄

—

172

—

122

D₄

D₃₄₄

yes

characteristic

123

C₂×C₄

—

124

C₂×C₄

—

172

—

125

C₂×C₄

C₂×D₁₇₂

yes

characteristic

126

C₈

—

127

C₈

—

172

—

128

C₈

—

172

—

129

C₈

#10621898

yes

characteristic

130

C₈

C₂×C₂²⋊D₄₃

yes

characteristic

131

C₂²

—

132

C₂²

—

344

—

133

C₂²

—

688

—

134

C₂²

#13063347

yes

characteristic

135

C₄

—

136

C₄

—

344

—

137

C₄

#13063299

yes

characteristic

138

C₄

C₂×D₃₄₄

yes

characteristic

139

C₂

—

140

C₂

—

141

C₂

—

688

—

142

C₂

#14583135

yes

characteristic

	subgroup	G/H
center	C₂	#14583135
commutator	C₂×C₈×C₄₃	C₂³
Frattini	C₂×C₈	C₂²×D₄₃
Fitting	C₄₃×#504	C₂
socle	C₂×C₄₃	#466
hypercenter	#504	D₄₃
hypocenter	C₄₃	#2223
LCS	G ▷ C₂×C₈×C₄₃ ▷ C₄×C₄₃ ▷ C₂×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₂ ◁ C₂×C₄ ◁ #131 ◁ #504

subgroup

G/H

center

C₂

#14583135

commutator

C₂×C₈×C₄₃

C₂³

Frattini

C₂×C₈

C₂²×D₄₃

Fitting

C₄₃×#504

C₂

C₂×C₄₃

D₄₃

C₄₃

G ▷ C₂×C₈×C₄₃ ▷ C₄×C₄₃ ▷ C₂×C₄₃ ▷ C₄₃

UCS

C₁ ◁ C₂ ◁ C₂×C₄ ◁ #131 ◁ #504

N	H ≅ G/N	type
1. C₂×#13063270	C₂	semidirect
2. #14583174	C₂	semidirect
4. #14582729	C₂	semidirect
5. #14582716	C₂	semidirect
6. #14582713	C₂	semidirect
7. C₄₃×#504	C₂	semidirect
73. #504	D₄₃	semidirect
79. C₄₃	#2223	semidirect

H ≅ G/N

type

1. C₂×#13063270

C₂

semidirect

2. #14583174

C₂

semidirect

4. #14582729

C₂

semidirect

5. #14582716

C₂

semidirect

6. #14582713

C₂

semidirect

7. C₄₃×#504

C₂

semidirect

73. #504

D₄₃

semidirect

79. C₄₃

#2223

semidirect

Subgroups — #19136725

Conjugacy classes of subgroups

Complements