Group #19134265 — subgroups

Subgroups — #19134265

Order 5504.

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

normal subgroups only

This group has 198 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	#14583302	C₂	1	1	yes	maximal, characteristic, complemented
2	#14583278	C₂	1	1	yes	maximal, characteristic, complemented
3	#14583273	C₂	1	1	yes	maximal, characteristic
4	#14583247	C₂	1	1	yes	maximal, characteristic
5	#14583246	C₂	1	1	yes	maximal, characteristic
6	#14582621	C₂	1	1	yes	maximal, characteristic, complemented
7	C₄₃×#500	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×#10621885	—	2	2	no	—
9	C₂×#10621884	—	2	2	no	—
10	#13063325	C₂²	1	1	yes	characteristic
11	#13063322	C₂²	1	1	yes	characteristic
12	#13063258	—	2	2	no	—
13	#13063247	—	2	2	no	—
14	#13063245	—	2	2	no	—
15	C₄×C₄₃⋊C₈	C₂²	1	1	yes	characteristic
16	C₄×C₄₃⋊C₈	C₂²	1	1	yes	characteristic
17	C₄⋊Q₈×C₄₃	C₂²	1	1	yes	characteristic
18	C₄⋊Q₈×C₄₃	C₂²	1	1	yes	characteristic
19	#107×C₄₃	—	2	2	no	—
20	C₄×C₈×C₄₃	C₂²	1	1	yes	characteristic
21	C₂×Q₈×C₄₃	—	2	1	no	—
22	C₂×Q₈×C₄₃	—	2	1	no	—
23	C₂×D₁₇₂	—	2	1	no	—
24	C₂×D₁₇₂	—	2	1	no	—
25	C₂×D₁₇₂	—	2	1	no	—
26	C₂×Dic₈₆	—	2	1	no	—
27	C₂×C₈×C₄₃	D₄	1	2	yes	—
28	C₄⋊C₄×C₄₃	—	2	1	no	—
29	C₄⋊C₄×C₄₃	—	2	1	no	—
30	C₄⋊C₄×C₄₃	—	2	1	no	—
31	C₄⋊C₄×C₄₃	—	2	1	no	—
32	C₄²×C₄₃	C₂³	1	1	yes	characteristic
33	#10621885	—	4	4	no	—
34	#10621884	—	4	4	no	—
35	C₄⋊Dic₄₃	—	2	1	no	—
36	C₄⋊Dic₄₃	—	2	1	no	—
37	C₂×C₄₃⋊C₈	D₄	1	2	yes	—
38	C₂×C₄₃⋊C₈	D₄	1	2	yes	—
39	C₂²×D₄₃	—	4	1	no	—
40	Q₈×C₄₃	—	4	2	no	—
41	Q₈×C₄₃	—	4	2	no	—
42	C₂×C₄×C₄₃	—	4	1	no	—
43	C₂×C₄×C₄₃	—	4	1	no	—
44	C₂×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
45	C₂×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
46	C₂×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
47	C₂×Dic₄₃	—	4	1	no	—
48	D₁₇₂	—	4	2	no	—
49	D₁₇₂	—	4	2	no	—
50	D₁₇₂	—	4	2	no	—
51	Dic₈₆	—	4	2	no	—
52	C₈×C₄₃	—	2	2	no	—
53	C₄₃⋊C₈	—	2	2	no	—
54	C₄₃⋊C₈	D₈	1	4	yes	—
55	C₂²×C₄₃	#127	1	1	yes	characteristic
56	C₂×D₄₃	—	8	1	no	—
57	C₂×D₄₃	—	8	1	no	—
58	C₂×D₄₃	—	8	1	no	—
59	C₄×C₄₃	—	8	1	no	—
60	C₄×C₄₃	—	8	1	no	—
61	C₄×C₄₃	C₂×D₈	1	2	yes	—
62	C₄×C₄₃	#137	1	2	yes	—
63	C₄×C₄₃	#137	1	2	yes	—
64	Dic₄₃	—	8	1	no	—
65	#1722	—	43	1	no	maximal, Sylow
66	C₂×C₄₃	#493	1	1	yes	characteristic
67	C₂×C₄₃	#497	1	1	yes	characteristic
68	C₂×C₄₃	#497	1	1	yes	characteristic
69	D₄₃	—	16	1	no	—
70	#500	—	43	1	no	—
71	#500	D₄₃	1	1	yes	characteristic, complemented
72	#494	—	43	1	no	—
73	#492	—	43	1	no	—
74	#486	—	43	1	no	—
75	#486	—	43	1	no	—
76	#322	—	43	1	no	—
77	C₄₃	#1722	1	1	yes	characteristic, complemented, Sylow
78	C₂×Q₁₆	—	86	2	no	—
79	C₂×SD₁₆	—	86	2	no	—
80	C₄⋊Q₈	—	43	1	no	—
81	C₄⋊Q₈	C₂×D₄₃	1	1	yes	characteristic
82	C₄⋊Q₈	C₂×D₄₃	1	1	yes	characteristic
83	#127	—	43	1	no	—
84	#107	—	2	2	no	—
85	#107	—	86	2	no	—
86	#102	—	86	2	no	—
87	#102	—	86	2	no	—
88	C₄×C₈	—	43	1	no	—
89	C₄×C₈	—	43	1	no	—
90	C₄×C₈	C₂×D₄₃	1	1	yes	characteristic
91	C₂×Q₈	—	2	1	no	—
92	C₂×Q₈	—	2	1	no	—
93	C₂×Q₈	—	86	1	no	—
94	C₂×D₄	—	86	1	no	—
95	C₂×D₄	—	86	1	no	—
96	C₂×D₄	—	86	1	no	—
97	Q₁₆	—	172	4	no	—
98	SD₁₆	—	172	4	no	—
99	C₂×C₈	—	43	2	no	—
100	C₂×C₈	—	43	2	no	—
101	C₂×C₈	C₂²⋊D₄₃	1	2	yes	—
102	C₄⋊C₄	—	2	1	no	—
103	C₄⋊C₄	—	2	1	no	—
104	C₄⋊C₄	—	2	1	no	—
105	C₄⋊C₄	—	2	1	no	—
106	C₄⋊C₄	—	86	1	no	—
107	C₄⋊C₄	—	86	1	no	—
108	C₄²	C₂²×D₄₃	1	1	yes	characteristic
109	C₂³	—	172	1	no	—
110	Q₈	—	4	2	no	—
111	Q₈	—	4	2	no	—
112	Q₈	—	172	2	no	—
113	D₄	—	172	2	no	—
114	D₄	—	172	2	no	—
115	D₄	—	172	2	no	—
116	C₂×C₄	—	4	1	no	—
117	C₂×C₄	—	4	1	no	—
118	C₂×C₄	—	172	1	no	—
119	C₂×C₄	D₄×D₄₃	1	1	yes	characteristic
120	C₂×C₄	D₄×D₄₃	1	1	yes	characteristic
121	C₂×C₄	C₂×C₂²⋊D₄₃	1	1	yes	characteristic
122	C₈	—	2	2	no	—
123	C₈	—	43	4	no	—
124	C₈	—	86	2	no	—
125	C₂²	—	344	1	no	—
126	C₂²	—	344	1	no	—
127	C₂²	—	344	1	no	—
128	C₂²	#13063321	1	1	yes	characteristic
129	C₄	—	8	1	no	—
130	C₄	—	8	1	no	—
131	C₄	—	344	1	no	—
132	C₄	D₈×D₄₃	1	2	yes	—
133	C₄	#13063356	1	2	yes	—
134	C₄	#13063357	1	2	yes	—
135	C₂	—	688	1	no	—
136	C₂	#14583274	1	1	yes	characteristic
137	C₂	#14583291	1	1	yes	characteristic
138	C₂	#14583292	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#14583302

C₂

yes

maximal, characteristic, complemented

#14583278

C₂

yes

maximal, characteristic, complemented

#14583273

C₂

yes

maximal, characteristic

#14583247

C₂

yes

maximal, characteristic

#14583246

C₂

yes

maximal, characteristic

#14582621

C₂

yes

maximal, characteristic, complemented

C₄₃×#500

C₂

yes

maximal, characteristic, complemented

C₂×#10621885

—

C₂×#10621884

—

#13063325

C₂²

yes

characteristic

#13063322

C₂²

yes

—

—

—

C₄×C₄₃⋊C₈

C₂²

yes

characteristic

C₄×C₄₃⋊C₈

C₂²

yes

characteristic

C₄⋊Q₈×C₄₃

C₂²

yes

characteristic

C₄⋊Q₈×C₄₃

C₂²

yes

characteristic

#107×C₄₃

—

C₄×C₈×C₄₃

C₂²

yes

characteristic

C₂×Q₈×C₄₃

—

C₂×Q₈×C₄₃

—

C₂×D₁₇₂

—

C₂×D₁₇₂

—

C₂×D₁₇₂

—

C₂×Dic₈₆

—

C₂×C₈×C₄₃

D₄

yes

—

C₄⋊C₄×C₄₃

—

C₄⋊C₄×C₄₃

—

C₄⋊C₄×C₄₃

—

C₄⋊C₄×C₄₃

—

C₄²×C₄₃

C₂³

yes

characteristic

#10621885

—

#10621884

—

C₄⋊Dic₄₃

—

C₄⋊Dic₄₃

—

C₂×C₄₃⋊C₈

D₄

yes

—

C₂×C₄₃⋊C₈

D₄

yes

—

C₂²×D₄₃

—

Q₈×C₄₃

—

Q₈×C₄₃

—

C₂×C₄×C₄₃

—

C₂×C₄×C₄₃

—

C₂×C₄×C₄₃

C₂×D₄

yes

characteristic

C₂×C₄×C₄₃

C₂×D₄

yes

characteristic

C₂×C₄×C₄₃

C₂×D₄

yes

characteristic

C₂×Dic₄₃

—

D₁₇₂

—

D₁₇₂

—

D₁₇₂

—

Dic₈₆

—

C₈×C₄₃

—

C₄₃⋊C₈

—

C₄₃⋊C₈

D₈

yes

—

C₂²×C₄₃

#127

yes

characteristic

C₂×D₄₃

—

C₂×D₄₃

—

C₂×D₄₃

—

C₄×C₄₃

—

C₄×C₄₃

—

C₄×C₄₃

C₂×D₈

yes

—

C₄×C₄₃

#137

yes

—

C₄×C₄₃

#137

yes

—

Dic₄₃

—

—

C₂×C₄₃

yes

C₂×C₄₃

yes

C₂×C₄₃

yes

D₄₃

—

#500

—

#500

D₄₃

yes

characteristic, complemented

—

—

—

—

—

C₄₃

#1722

yes

characteristic, complemented, Sylow

C₂×Q₁₆

—

C₂×SD₁₆

—

C₄⋊Q₈

—

C₄⋊Q₈

C₂×D₄₃

yes

characteristic

C₄⋊Q₈

C₂×D₄₃

yes

—

—

—

—

—

C₄×C₈

—

C₄×C₈

—

C₄×C₈

C₂×D₄₃

yes

characteristic

C₂×Q₈

—

C₂×Q₈

—

C₂×Q₈

—

C₂×D₄

—

C₂×D₄

—

C₂×D₄

—

Q₁₆

—

172

—

SD₁₆

—

172

—

C₂×C₈

—

100

C₂×C₈

—

101

C₂×C₈

C₂²⋊D₄₃

yes

—

102

C₄⋊C₄

—

103

C₄⋊C₄

—

104

C₄⋊C₄

—

105

C₄⋊C₄

—

106

C₄⋊C₄

—

107

C₄⋊C₄

—

108

C₄²

C₂²×D₄₃

yes

characteristic

109

C₂³

—

172

—

110

Q₈

—

111

Q₈

—

112

Q₈

—

172

—

113

D₄

—

172

—

114

D₄

—

172

—

115

D₄

—

172

—

116

C₂×C₄

—

117

C₂×C₄

—

118

C₂×C₄

—

172

—

119

C₂×C₄

D₄×D₄₃

yes

characteristic

120

C₂×C₄

D₄×D₄₃

yes

characteristic

121

C₂×C₄

C₂×C₂²⋊D₄₃

yes

characteristic

122

C₈

—

123

C₈

—

124

C₈

—

125

C₂²

—

344

—

126

C₂²

—

344

—

127

C₂²

—

344

—

128

C₂²

#13063321

yes

characteristic

129

C₄

—

130

C₄

—

131

C₄

—

344

—

132

C₄

D₈×D₄₃

yes

—

133

C₄

#13063356

yes

—

134

C₄

#13063357

yes

—

135

C₂

—

688

—

136

C₂

#14583274

yes

characteristic

137

C₂

#14583291

yes

characteristic

138

C₂

#14583292

yes

characteristic

	subgroup	G/H
center	C₂²	#13063321
commutator	C₄²×C₄₃	C₂³
Frattini	C₄²	C₂²×D₄₃
Fitting	C₄₃×#500	C₂
socle	C₂²×C₄₃	#127
hypercenter	#500	D₄₃
hypocenter	C₄₃	#1722
LCS	G ▷ C₄²×C₄₃ ▷ C₂²×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₂² ◁ C₄² ◁ #500

subgroup

G/H

center

C₂²

#13063321

commutator

C₄²×C₄₃

C₂³

Frattini

C₄²

C₂²×D₄₃

Fitting

C₄₃×#500

C₂

C₂²×C₄₃

D₄₃

C₄₃

G ▷ C₄²×C₄₃ ▷ C₂²×C₄₃ ▷ C₄₃

UCS

C₁ ◁ C₂² ◁ C₄² ◁ #500

N	H ≅ G/N	type
1. #14583302	C₂	semidirect
2. #14583278	C₂	semidirect
6. #14582621	C₂	semidirect
7. C₄₃×#500	C₂	semidirect
71. #500	D₄₃	semidirect
77. C₄₃	#1722	semidirect

H ≅ G/N

type

1. #14583302

C₂

semidirect

2. #14583278

C₂

semidirect

6. #14582621

C₂

semidirect

7. C₄₃×#500

C₂

semidirect

71. #500

D₄₃

semidirect

77. C₄₃

#1722

semidirect

Subgroups — #19134265

Conjugacy classes of subgroups

Complements