Group #19136675 — subgroups

Subgroups — #19136675

Order 5504.

150 conjugacy classes of subgroups; only the 43 normal subgroups are shown.

normal subgroups only

This group has 150 conjugacy classes of subgroups — too many to draw. Only its 43 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	#14583342	C₂	1	1	yes	maximal, characteristic
2	#14583340	C₂	1	1	yes	maximal, characteristic
3	#14583277	C₂	1	1	yes	maximal, characteristic, complemented
4	#14583015	C₂	1	1	yes	maximal, characteristic
5	#14582719	C₂	1	1	yes	maximal, characteristic, complemented
6	#14582714	C₂	1	1	yes	maximal, characteristic, complemented
7	C₄₃×#362	C₂	1	1	yes	maximal, characteristic, complemented
8	#13063347	C₂²	1	1	yes	characteristic
9	C₂×Dic₁₇₂	C₂²	1	1	yes	characteristic
10	C₂×#10621885	—	2	1	no	—
11	#13063333	—	2	1	no	—
12	#13063323	—	2	1	no	—
13	Dic₃₄₄	—	2	1	no	—
14	#13063271	—	2	1	no	—
15	#13063270	—	2	1	no	—
16	#13063268	—	2	1	no	—
17	#13063265	C₂²	1	1	yes	characteristic
18	#13063251	—	2	1	no	—
19	C₈×Dic₄₃	C₂²	1	1	yes	characteristic
20	C₂×Q₁₆×C₄₃	C₂²	1	1	yes	characteristic
21	M₃₂×C₄₃	C₂²	1	1	yes	characteristic
22	#108×C₄₃	C₂²	1	1	yes	characteristic
23	C₂×Q₈×C₄₃	—	2	1	no	—
24	#10621898	—	2	1	no	—
25	C₂×Dic₈₆	—	2	1	no	—
26	Q₁₆×C₄₃	—	2	1	no	—
27	Q₁₆×C₄₃	—	2	1	no	—
28	M₁₆×C₄₃	—	2	1	no	—
29	C₂×C₈×C₄₃	C₂³	1	1	yes	characteristic
30	#10621885	—	4	1	no	—
31	#10621885	—	4	1	no	—
32	Dic₄₃⋊C₄	—	4	2	no	—
33	C₄×Dic₄₃	D₄	1	1	yes	characteristic
34	C₂×C₄₃⋊C₈	D₄	1	1	yes	characteristic
35	Dic₁₇₂	—	2	1	no	—
36	Dic₁₇₂	—	2	1	no	—
37	Dic₁₇₂	D₄	1	1	yes	characteristic
38	D₃₄₄	D₄	1	1	yes	characteristic
39	#10621873	—	2	1	no	—
40	#10621872	—	4	1	no	—
41	C₈×D₄₃	—	4	1	no	—
42	C₁₆×C₄₃	—	2	1	no	—
43	C₄₃⋊C₁₆	—	2	1	no	—
44	Q₈×C₄₃	—	4	1	no	—
45	Q₈×C₄₃	—	4	1	no	—
46	C₂×C₄×C₄₃	—	4	1	no	—
47	C₂×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
48	C₂²⋊D₄₃	—	4	1	no	—
49	C₂×Dic₄₃	—	2	1	no	—
50	C₂×Dic₄₃	—	4	1	no	—
51	D₁₇₂	—	2	1	no	—
52	C₄×D₄₃	—	4	1	no	—
53	Dic₈₆	—	2	1	no	—
54	Dic₈₆	—	4	1	no	—
55	Dic₈₆	—	4	1	no	—
56	C₈×C₄₃	—	4	1	no	—
57	C₈×C₄₃	C₂×D₄	1	1	yes	characteristic
58	C₈×C₄₃	#41	1	1	yes	characteristic
59	C₄₃⋊C₈	D₈	1	1	yes	characteristic
60	C₄₃⋊C₈	D₈	1	1	yes	characteristic
61	C₂²×C₄₃	AGL(1,ℤ/8)	1	1	yes	characteristic
62	C₂×D₄₃	—	4	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	2	no	—
67	Dic₄₃	—	4	1	no	—
68	Dic₄₃	—	8	1	no	—
69	#2214	—	43	1	no	maximal, Sylow
70	C₂×C₄₃	—	2	1	no	—
71	C₂×C₄₃	#459	1	1	yes	characteristic
72	D₄₃	—	8	1	no	—
73	#510	—	43	1	no	—
74	#510	—	43	1	no	—
75	#494	—	43	1	no	—
76	#443	—	43	1	no	—
77	#364	—	43	1	no	—
78	#362	—	43	1	no	—
79	#362	D₄₃	1	1	yes	characteristic, complemented
80	C₄₃	#2214	1	1	yes	characteristic, complemented, Sylow
81	#135	—	43	1	no	—
82	C₂×Q₁₆	—	43	1	no	—
83	C₂×Q₁₆	—	86	1	no	—
84	C₂×Q₁₆	C₂×D₄₃	1	1	yes	characteristic
85	#131	—	86	1	no	—
86	C₄⋊Q₈	—	86	1	no	—
87	Q₃₂	—	86	1	no	—
88	Q₃₂	—	86	1	no	—
89	SD₃₂	—	86	1	no	—
90	SD₃₂	—	86	1	no	—
91	M₃₂	—	43	1	no	—
92	M₃₂	C₂×D₄₃	1	1	yes	characteristic
93	#108	C₂×D₄₃	1	1	yes	characteristic
94	#104	—	86	1	no	—
95	C₄×C₈	—	43	1	no	—
96	#41	—	86	1	no	—
97	C₂×Q₈	—	2	1	no	—
98	C₂×Q₈	—	86	1	no	—
99	Q₁₆	—	2	1	no	—
100	Q₁₆	—	2	1	no	—
101	Q₁₆	—	43	1	no	—
102	Q₁₆	—	86	1	no	—
103	Q₁₆	—	86	1	no	—
104	Q₁₆	—	172	1	no	—
105	Q₁₆	—	172	1	no	—
106	SD₁₆	—	86	1	no	—
107	D₈	—	43	1	no	—
108	M₁₆	—	2	1	no	—
109	M₁₆	—	172	1	no	—
110	C₂×C₈	—	43	1	no	—
111	C₂×C₈	—	172	1	no	—
112	C₂×C₈	C₂²×D₄₃	1	1	yes	characteristic
113	C₄⋊C₄	—	172	2	no	—
114	C₄²	—	43	1	no	—
115	C₁₆	—	2	1	no	—
116	C₁₆	—	86	1	no	—
117	Q₈	—	4	1	no	—
118	Q₈	—	4	1	no	—
119	Q₈	—	86	1	no	—
120	Q₈	—	172	1	no	—
121	Q₈	—	172	1	no	—
122	D₄	—	86	1	no	—
123	D₄	—	172	1	no	—
124	C₂×C₄	—	4	1	no	—
125	C₂×C₄	—	86	1	no	—
126	C₂×C₄	—	172	1	no	—
127	C₂×C₄	—	172	1	no	—
128	C₂×C₄	D₄×D₄₃	1	1	yes	characteristic
129	C₈	—	4	1	no	—
130	C₈	—	43	1	no	—
131	C₈	—	43	1	no	—
132	C₈	#10621898	1	1	yes	characteristic
133	C₈	D₄×D₄₃	1	1	yes	characteristic
134	C₂²	—	172	1	no	—
135	C₂²	#13063352	1	1	yes	characteristic
136	C₄	—	8	1	no	—
137	C₄	—	86	2	no	—
138	C₄	—	344	1	no	—
139	C₄	—	172	1	no	—
140	C₄	#13063298	1	1	yes	characteristic
141	C₄	D₈×D₄₃	1	1	yes	characteristic
142	C₂	—	2	1	no	—
143	C₂	—	344	1	no	—
144	C₂	#14583093	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#14583342

C₂

yes

maximal, characteristic

#14583340

C₂

yes

maximal, characteristic

#14583277

C₂

yes

maximal, characteristic, complemented

#14583015

C₂

yes

maximal, characteristic

#14582719

C₂

yes

maximal, characteristic, complemented

#14582714

C₂

yes

maximal, characteristic, complemented

C₄₃×#362

C₂

yes

maximal, characteristic, complemented

#13063347

C₂²

yes

characteristic

C₂×Dic₁₇₂

C₂²

yes

—

—

—

Dic₃₄₄

—

—

—

—

C₂²

yes

characteristic

#13063251

—

C₈×Dic₄₃

C₂²

yes

characteristic

C₂×Q₁₆×C₄₃

C₂²

yes

characteristic

M₃₂×C₄₃

C₂²

yes

characteristic

#108×C₄₃

C₂²

yes

characteristic

C₂×Q₈×C₄₃

—

#10621898

—

C₂×Dic₈₆

—

Q₁₆×C₄₃

—

Q₁₆×C₄₃

—

M₁₆×C₄₃

—

C₂×C₈×C₄₃

C₂³

yes

characteristic

#10621885

—

#10621885

—

Dic₄₃⋊C₄

—

C₄×Dic₄₃

D₄

yes

characteristic

C₂×C₄₃⋊C₈

D₄

yes

characteristic

Dic₁₇₂

—

Dic₁₇₂

—

Dic₁₇₂

D₄

yes

characteristic

D₃₄₄

D₄

yes

characteristic

#10621873

—

#10621872

—

C₈×D₄₃

—

C₁₆×C₄₃

—

C₄₃⋊C₁₆

—

Q₈×C₄₃

—

Q₈×C₄₃

—

C₂×C₄×C₄₃

—

C₂×C₄×C₄₃

C₂×D₄

yes

characteristic

C₂²⋊D₄₃

—

C₂×Dic₄₃

—

C₂×Dic₄₃

—

D₁₇₂

—

C₄×D₄₃

—

Dic₈₆

—

Dic₈₆

—

Dic₈₆

—

C₈×C₄₃

—

C₈×C₄₃

C₂×D₄

yes

characteristic

C₈×C₄₃

#41

yes

characteristic

C₄₃⋊C₈

D₈

yes

characteristic

C₄₃⋊C₈

D₈

yes

characteristic

C₂²×C₄₃

AGL(1,ℤ/8)

yes

characteristic

C₂×D₄₃

—

C₄×C₄₃

—

C₄×C₄₃

#121

yes

characteristic

C₄×C₄₃

C₂×D₈

yes

characteristic

Dic₄₃

—

Dic₄₃

—

Dic₄₃

—

#2214

—

maximal, Sylow

C₂×C₄₃

—

C₂×C₄₃

#459

yes

characteristic

D₄₃

—

—

—

—

—

—

—

D₄₃

yes

characteristic, complemented

C₄₃

#2214

yes

characteristic, complemented, Sylow

#135

—

C₂×Q₁₆

—

C₂×Q₁₆

—

C₂×Q₁₆

C₂×D₄₃

yes

characteristic

#131

—

C₄⋊Q₈

—

Q₃₂

—

Q₃₂

—

SD₃₂

—

SD₃₂

—

M₃₂

—

M₃₂

C₂×D₄₃

yes

characteristic

#108

C₂×D₄₃

yes

characteristic

#104

—

C₄×C₈

—

#41

—

C₂×Q₈

—

C₂×Q₈

—

Q₁₆

—

100

Q₁₆

—

101

Q₁₆

—

102

Q₁₆

—

103

Q₁₆

—

104

Q₁₆

—

172

—

105

Q₁₆

—

172

—

106

SD₁₆

—

107

D₈

—

108

M₁₆

—

109

M₁₆

—

172

—

110

C₂×C₈

—

111

C₂×C₈

—

172

—

112

C₂×C₈

C₂²×D₄₃

yes

characteristic

113

C₄⋊C₄

—

172

—

114

C₄²

—

115

C₁₆

—

116

C₁₆

—

117

Q₈

—

118

Q₈

—

119

Q₈

—

120

Q₈

—

172

—

121

Q₈

—

172

—

122

D₄

—

123

D₄

—

172

—

124

C₂×C₄

—

125

C₂×C₄

—

126

C₂×C₄

—

172

—

127

C₂×C₄

—

172

—

128

C₂×C₄

D₄×D₄₃

yes

characteristic

129

C₈

—

130

C₈

—

131

C₈

—

132

C₈

#10621898

yes

characteristic

133

C₈

D₄×D₄₃

yes

characteristic

134

C₂²

—

172

—

135

C₂²

#13063352

yes

characteristic

136

C₄

—

137

C₄

—

138

C₄

—

344

—

139

C₄

—

172

—

140

C₄

#13063298

yes

characteristic

141

C₄

D₈×D₄₃

yes

characteristic

142

C₂

—

143

C₂

—

344

—

144

C₂

#14583093

yes

characteristic

	subgroup	G/H
center	C₂	#14583093
commutator	C₂×C₈×C₄₃	C₂³
Frattini	C₂×C₈	C₂²×D₄₃
Fitting	C₄₃×#362	C₂
socle	C₂×C₄₃	#459
hypercenter	#362	D₄₃
hypocenter	C₄₃	#2214
LCS	G ▷ C₂×C₈×C₄₃ ▷ C₄×C₄₃ ▷ C₂×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₂ ◁ C₂×C₄ ◁ C₂×C₈ ◁ #362

subgroup

G/H

center

C₂

#14583093

commutator

C₂×C₈×C₄₃

C₂³

Frattini

C₂×C₈

C₂²×D₄₃

Fitting

C₄₃×#362

C₂

C₂×C₄₃

D₄₃

C₄₃

G ▷ C₂×C₈×C₄₃ ▷ C₄×C₄₃ ▷ C₂×C₄₃ ▷ C₄₃

UCS

C₁ ◁ C₂ ◁ C₂×C₄ ◁ C₂×C₈ ◁ #362

N	H ≅ G/N	type
3. #14583277	C₂	semidirect
5. #14582719	C₂	semidirect
6. #14582714	C₂	semidirect
7. C₄₃×#362	C₂	semidirect
79. #362	D₄₃	semidirect
80. C₄₃	#2214	semidirect

H ≅ G/N

type

3. #14583277

C₂

semidirect

5. #14582719

C₂

semidirect

6. #14582714

C₂

semidirect

7. C₄₃×#362

C₂

semidirect

79. #362

D₄₃

semidirect

80. C₄₃

#2214

semidirect

Subgroups — #19136675

Conjugacy classes of subgroups

Complements