Group #19136722 — subgroups

Subgroups — #19136722

Order 5504.

144 conjugacy classes of subgroups; only the 45 normal subgroups are shown.

normal subgroups only

This group has 144 conjugacy classes of subgroups — too many to draw. Only its 45 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	#14583315	C₂	1	1	yes	maximal, characteristic, complemented
2	#14583171	C₂	1	1	yes	maximal, characteristic, complemented
3	#14583166	C₂	1	1	yes	maximal, characteristic
4	#14582729	C₂	1	1	yes	maximal, characteristic, complemented
5	#14582715	C₂	1	1	yes	maximal, characteristic, complemented
6	#14582712	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂×SD₃₂×C₄₃	C₂	1	1	yes	maximal, characteristic, complemented
8	#13063356	—	2	1	no	—
9	#13063351	—	2	1	no	—
10	#13063331	C₂²	1	1	yes	characteristic
11	#13063265	C₂²	1	1	yes	characteristic
12	#13063264	—	2	1	no	—
13	C₁₆×D₄₃	—	2	1	no	—
14	#13063261	C₂²	1	1	yes	characteristic
15	#13063261	C₂²	1	1	yes	characteristic
16	#13063244	—	2	1	no	—
17	#13063242	—	2	1	no	—
18	C₂×Q₁₆×C₄₃	C₂²	1	1	yes	characteristic
19	C₂×D₈×C₄₃	C₂²	1	1	yes	characteristic
20	SD₃₂×C₄₃	—	2	1	no	—
21	SD₃₂×C₄₃	—	2	1	no	—
22	C₂×C₁₆×C₄₃	C₂²	1	1	yes	characteristic
23	C₂×Q₈×C₄₃	—	2	1	no	—
24	C₂×D₄×C₄₃	—	2	1	no	—
25	#10621898	D₄	1	1	yes	characteristic
26	Q₁₆×C₄₃	—	2	1	no	—
27	Q₁₆×C₄₃	—	2	1	no	—
28	D₈×C₄₃	—	2	1	no	—
29	D₈×C₄₃	—	2	1	no	—
30	C₂×C₈×C₄₃	C₂³	1	1	yes	characteristic
31	#10621885	—	4	1	no	—
32	#10621884	—	4	1	no	—
33	#10621883	—	4	1	no	—
34	#10621882	—	4	1	no	—
35	#10621877	—	2	1	no	—
36	#10621877	—	2	1	no	—
37	#10621877	D₄	1	1	yes	characteristic
38	#10621872	—	2	1	no	—
39	C₈×D₄₃	—	2	1	no	—
40	C₁₆×C₄₃	D₄	1	1	yes	characteristic
41	C₁₆×C₄₃	D₄	1	1	yes	characteristic
42	C₄₃⋊C₁₆	—	2	1	no	—
43	C₂³×C₄₃	—	4	1	no	—
44	Q₈×C₄₃	—	4	1	no	—
45	Q₈×C₄₃	—	4	1	no	—
46	D₄×C₄₃	—	4	1	no	—
47	D₄×C₄₃	—	4	1	no	—
48	C₂×C₄×C₄₃	—	4	1	no	—
49	C₂×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
50	C₂²⋊D₄₃	—	2	1	no	—
51	D₁₇₂	D₈	1	1	yes	characteristic
52	C₄×D₄₃	—	2	1	no	—
53	Dic₈₆	D₈	1	1	yes	characteristic
54	C₈×C₄₃	C₂×D₄	1	1	yes	characteristic
55	C₈×C₄₃	#41	1	1	yes	characteristic
56	C₄₃⋊C₈	—	2	1	no	—
57	C₄₃⋊C₈	—	4	1	no	—
58	C₄₃⋊C₈	—	4	1	no	—
59	C₂²×C₄₃	—	8	1	no	—
60	C₂²×C₄₃	—	16	1	no	—
61	C₂²×C₄₃	#135	1	1	yes	characteristic
62	C₂×D₄₃	—	2	1	no	—
63	C₄×C₄₃	—	8	1	no	—
64	C₄×C₄₃	#121	1	1	yes	characteristic
65	C₄×C₄₃	C₂×D₈	1	1	yes	characteristic
66	Dic₄₃	—	2	1	no	—
67	#2223	—	43	1	no	maximal, Sylow
68	C₂×C₄₃	—	2	1	no	—
69	C₂×C₄₃	—	16	1	no	—
70	C₂×C₄₃	#466	1	1	yes	characteristic
71	D₄₃	—	4	1	no	—
72	C₂×SD₃₂	D₄₃	1	1	yes	characteristic, complemented
73	#504	—	43	1	no	—
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	C₂×D₄₃	1	1	yes	characteristic
83	C₂×D₈	C₂×D₄₃	1	1	yes	characteristic
84	#131	—	43	1	no	—
85	SD₃₂	—	2	1	no	—
86	SD₃₂	—	2	1	no	—
87	M₃₂	—	43	1	no	—
88	M₃₂	—	86	1	no	—
89	C₂×C₁₆	—	86	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	—	43	1	no	—
96	C₂×Q₈	—	2	1	no	—
97	C₂×D₄	—	2	1	no	—
98	Q₁₆	—	2	1	no	—
99	Q₁₆	—	2	1	no	—
100	Q₁₆	—	172	1	no	—
101	SD₁₆	—	172	1	no	—
102	SD₁₆	—	172	1	no	—
103	D₈	—	2	1	no	—
104	D₈	—	2	1	no	—
105	D₈	—	172	1	no	—
106	M₁₆	—	43	1	no	—
107	M₁₆	—	86	1	no	—
108	M₁₆	—	86	1	no	—
109	M₁₆	—	86	1	no	—
110	C₂×C₈	—	86	1	no	—
111	C₂×C₈	C₂²×D₄₃	1	1	yes	characteristic
112	C₁₆	—	86	1	no	—
113	C₁₆	C₂²⋊D₄₃	1	1	yes	characteristic
114	C₁₆	C₂²⋊D₄₃	1	1	yes	characteristic
115	C₂³	—	4	1	no	—
116	Q₈	—	4	1	no	—
117	Q₈	—	4	1	no	—
118	Q₈	—	43	1	no	—
119	D₄	—	4	1	no	—
120	D₄	—	4	1	no	—
121	D₄	—	43	1	no	—
122	D₄	—	86	1	no	—
123	C₂×C₄	—	4	1	no	—
124	C₂×C₄	—	86	1	no	—
125	C₂×C₄	D₄×D₄₃	1	1	yes	characteristic
126	C₈	—	86	1	no	—
127	C₈	—	172	1	no	—
128	C₈	—	172	1	no	—
129	C₈	#10621900	1	1	yes	characteristic
130	C₈	C₂×C₂²⋊D₄₃	1	1	yes	characteristic
131	C₂²	—	8	1	no	—
132	C₂²	—	16	1	no	—
133	C₂²	—	86	1	no	—
134	C₂²	#13063344	1	1	yes	characteristic
135	C₄	—	8	1	no	—
136	C₄	—	86	1	no	—
137	C₄	#13063296	1	1	yes	characteristic
138	C₄	D₈×D₄₃	1	1	yes	characteristic
139	C₂	—	2	1	no	—
140	C₂	—	16	1	no	—
141	C₂	—	172	1	no	—
142	C₂	#14583132	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#14583315

C₂

yes

maximal, characteristic, complemented

#14583171

C₂

yes

maximal, characteristic, complemented

#14583166

C₂

yes

maximal, characteristic

#14582729

C₂

yes

maximal, characteristic, complemented

#14582715

C₂

yes

maximal, characteristic, complemented

#14582712

C₂

yes

maximal, characteristic, complemented

C₂×SD₃₂×C₄₃

C₂

yes

maximal, characteristic, complemented

#13063356

—

#13063351

—

#13063331

C₂²

yes

characteristic

#13063265

C₂²

yes

characteristic

#13063264

—

C₁₆×D₄₃

—

#13063261

C₂²

yes

characteristic

#13063261

C₂²

yes

characteristic

#13063244

—

#13063242

—

C₂×Q₁₆×C₄₃

C₂²

yes

characteristic

C₂×D₈×C₄₃

C₂²

yes

characteristic

SD₃₂×C₄₃

—

SD₃₂×C₄₃

—

C₂×C₁₆×C₄₃

C₂²

yes

characteristic

C₂×Q₈×C₄₃

—

C₂×D₄×C₄₃

—

#10621898

D₄

yes

characteristic

Q₁₆×C₄₃

—

Q₁₆×C₄₃

—

D₈×C₄₃

—

D₈×C₄₃

—

C₂×C₈×C₄₃

C₂³

yes

—

—

—

—

—

—

D₄

yes

characteristic

#10621872

—

C₈×D₄₃

—

C₁₆×C₄₃

D₄

yes

characteristic

C₁₆×C₄₃

D₄

yes

characteristic

C₄₃⋊C₁₆

—

C₂³×C₄₃

—

Q₈×C₄₃

—

Q₈×C₄₃

—

D₄×C₄₃

—

D₄×C₄₃

—

C₂×C₄×C₄₃

—

C₂×C₄×C₄₃

C₂×D₄

yes

characteristic

C₂²⋊D₄₃

—

D₁₇₂

D₈

yes

characteristic

C₄×D₄₃

—

Dic₈₆

D₈

yes

characteristic

C₈×C₄₃

C₂×D₄

yes

characteristic

C₈×C₄₃

#41

yes

characteristic

C₄₃⋊C₈

—

C₄₃⋊C₈

—

C₄₃⋊C₈

—

C₂²×C₄₃

—

C₂²×C₄₃

—

C₂²×C₄₃

#135

yes

characteristic

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

D₄₃

yes

characteristic, complemented

—

—

—

—

—

—

C₄₃

#2223

yes

characteristic, complemented, Sylow

#137

—

AGL(1,ℤ/8)

—

C₂×Q₁₆

C₂×D₄₃

yes

characteristic

C₂×D₈

C₂×D₄₃

yes

characteristic

#131

—

SD₃₂

—

SD₃₂

—

M₃₂

—

M₃₂

—

C₂×C₁₆

—

C₂×C₁₆

C₂×D₄₃

yes

—

—

—

—

—

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

—

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

—

116

Q₈

—

117

Q₈

—

118

Q₈

—

119

D₄

—

120

D₄

—

121

D₄

—

122

D₄

—

123

C₂×C₄

—

124

C₂×C₄

—

125

C₂×C₄

D₄×D₄₃

yes

characteristic

126

C₈

—

127

C₈

—

172

—

128

C₈

—

172

—

129

C₈

#10621900

yes

characteristic

130

C₈

C₂×C₂²⋊D₄₃

yes

characteristic

131

C₂²

—

132

C₂²

—

133

C₂²

—

134

C₂²

#13063344

yes

characteristic

135

C₄

—

136

C₄

—

137

C₄

#13063296

yes

characteristic

138

C₄

D₈×D₄₃

yes

characteristic

139

C₂

—

140

C₂

—

141

C₂

—

172

—

142

C₂

#14583132

yes

characteristic

	subgroup	G/H
center	C₂	#14583132
commutator	C₂×C₈×C₄₃	C₂³
Frattini	C₂×C₈	C₂²×D₄₃
Fitting	C₂×SD₃₂×C₄₃	C₂
socle	C₂×C₄₃	#466
hypercenter	C₂×SD₃₂	D₄₃
hypocenter	C₄₃	#2223
LCS	G ▷ C₂×C₈×C₄₃ ▷ C₄×C₄₃ ▷ C₂×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₂ ◁ C₂×C₄ ◁ C₂×C₈ ◁ C₂×SD₃₂

subgroup

G/H

center

C₂

#14583132

commutator

C₂×C₈×C₄₃

C₂³

Frattini

C₂×C₈

C₂²×D₄₃

Fitting

C₂×SD₃₂×C₄₃

C₂

socle

C₂×C₄₃

#466

hypercenter

C₂×SD₃₂

D₄₃

hypocenter

C₄₃

#2223

LCS

G ▷ C₂×C₈×C₄₃ ▷ C₄×C₄₃ ▷ C₂×C₄₃ ▷ C₄₃

UCS

C₁ ◁ C₂ ◁ C₂×C₄ ◁ C₂×C₈ ◁ C₂×SD₃₂

N	H ≅ G/N	type
1. #14583315	C₂	semidirect
2. #14583171	C₂	semidirect
4. #14582729	C₂	semidirect
5. #14582715	C₂	semidirect
6. #14582712	C₂	semidirect
7. C₂×SD₃₂×C₄₃	C₂	semidirect
72. C₂×SD₃₂	D₄₃	semidirect
79. C₄₃	#2223	semidirect

H ≅ G/N

type

1. #14583315

C₂

semidirect

2. #14583171

C₂

semidirect

4. #14582729

C₂

semidirect

5. #14582715

C₂

semidirect

6. #14582712

C₂

semidirect

7. C₂×SD₃₂×C₄₃

C₂

semidirect

72. C₂×SD₃₂

D₄₃

semidirect

79. C₄₃

#2223

semidirect

Subgroups — #19136722

Conjugacy classes of subgroups

Complements