Group #19136111 — subgroups

Subgroups — #19136111

Order 5504.

222 conjugacy classes of subgroups; only the 65 normal subgroups are shown.

normal subgroups only

This group has 222 conjugacy classes of subgroups — too many to draw. Only its 65 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	#14582948	C₂	1	1	yes	maximal, characteristic, complemented
2	#14582947	C₂	1	2	yes	maximal, complemented
3	#14582863	C₂	1	2	yes	maximal
4	C₄₃⋊#338	C₂	1	1	yes	maximal, characteristic, complemented
5	C₄₃×#407	C₂	1	1	yes	maximal, characteristic
6	C₂×#10621877	C₂²	1	2	yes	—
7	C₂×#10621877	C₂²	1	2	yes	—
8	#13063261	—	2	2	no	—
9	#13063260	—	2	4	no	—
10	C₂²⋊(C₄₃⋊C₈)	—	2	4	no	—
11	C₂³×C₄×C₄₃	C₂²	1	1	yes	characteristic
12	C₂×M₁₆×C₄₃	C₂²	1	1	yes	characteristic
13	C₂×M₁₆×C₄₃	C₂²	1	1	yes	characteristic
14	C₂²⋊C₈×C₄₃	—	2	2	no	—
15	C₂⁴×C₄₃	Q₈	1	1	yes	characteristic
16	C₂²×C₄×C₄₃	—	2	1	no	—
17	C₂²×C₄×C₄₃	—	2	2	no	—
18	C₂²×C₄×C₄₃	—	2	1	no	—
19	C₂²×C₄×C₄₃	—	2	2	no	—
20	C₂²×C₄×C₄₃	Q₈	1	1	yes	characteristic
21	C₂²×C₄×C₄₃	C₂³	1	1	yes	characteristic
22	M₁₆×C₄₃	—	2	2	no	—
23	M₁₆×C₄₃	—	2	2	no	—
24	C₂×C₈×C₄₃	—	2	1	no	—
25	C₂×C₈×C₄₃	D₄	1	2	yes	—
26	#10621877	—	2	2	no	—
27	#10621877	—	2	2	no	—
28	#10621877	—	2	2	no	—
29	#10621877	—	2	2	no	—
30	C₂×C₄₃⋊C₈	—	2	2	no	—
31	C₂×C₄₃⋊C₈	D₄	1	4	yes	—
32	C₂³×C₄₃	—	2	2	no	—
33	C₂³×C₄₃	—	2	1	no	—
34	C₂³×C₄₃	—	4	2	no	—
35	C₂³×C₄₃	C₂×Q₈	1	1	yes	characteristic
36	C₂×C₄×C₄₃	—	2	2	no	—
37	C₂×C₄×C₄₃	—	2	1	no	—
38	C₂×C₄×C₄₃	—	4	1	no	—
39	C₂×C₄×C₄₃	—	4	2	no	—
40	C₂×C₄×C₄₃	—	4	1	no	—
41	C₂×C₄×C₄₃	C₂×D₄	1	2	yes	—
42	C₂×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
43	C₂×C₄×C₄₃	#41	1	1	yes	characteristic
44	C₂×C₄×C₄₃	#41	1	2	yes	—
45	C₈×C₄₃	—	2	2	no	—
46	C₈×C₄₃	—	4	1	no	—
47	C₄₃⋊C₈	—	2	4	no	—
48	C₄₃⋊C₈	—	4	2	no	—
49	C₂²×C₄₃	—	2	4	no	—
50	C₂²×C₄₃	—	2	2	no	—
51	C₂²×C₄₃	—	4	1	no	—
52	C₂²×C₄₃	—	4	2	no	—
53	C₂²×C₄₃	—	4	1	no	—
54	C₂²×C₄₃	—	4	1	no	—
55	C₂²×C₄₃	C₂²⋊Q₈	1	2	yes	—
56	C₂²×C₄₃	C₂²⋊Q₈	1	1	yes	characteristic
57	C₄×C₄₃	—	4	1	no	—
58	C₄×C₄₃	#123	1	1	yes	characteristic
59	C₄×C₄₃	#123	1	2	yes	—
60	C₄×C₄₃	#127	1	1	yes	characteristic
61	#2091	—	43	1	no	maximal, Sylow
62	C₂×C₄₃	—	2	2	no	—
63	C₂×C₄₃	—	2	1	no	—
64	C₂×C₄₃	—	4	2	no	—
65	C₂×C₄₃	#399	1	1	yes	characteristic
66	#430	—	43	2	no	—
67	#430	—	43	1	no	—
68	#407	—	43	2	no	—
69	#407	D₄₃	1	1	yes	characteristic
70	#338	—	43	1	no	—
71	C₄₃	#2091	1	1	yes	characteristic, complemented, Sylow
72	C₂³×C₄	C₂×D₄₃	1	1	yes	characteristic
73	C₂×M₁₆	—	43	2	no	—
74	C₂×M₁₆	—	43	2	no	—
75	C₂×M₁₆	C₂×D₄₃	1	1	yes	characteristic
76	C₂×M₁₆	C₂×D₄₃	1	1	yes	characteristic
77	#108	—	86	4	no	—
78	#108	—	86	2	no	—
79	C₂²⋊C₈	—	2	2	no	—
80	C₂²⋊C₈	—	86	4	no	—
81	C₂⁴	Dic₈₆	1	1	yes	characteristic
82	C₂²×C₄	—	2	1	no	—
83	C₂²×C₄	—	2	2	no	—
84	C₂²×C₄	—	2	2	no	—
85	C₂²×C₄	—	2	1	no	—
86	C₂²×C₄	Dic₈₆	1	1	yes	characteristic
87	C₂²×C₄	C₂²×D₄₃	1	1	yes	characteristic
88	M₁₆	—	2	2	no	—
89	M₁₆	—	2	2	no	—
90	M₁₆	—	86	2	no	—
91	M₁₆	—	86	2	no	—
92	M₁₆	—	86	2	no	—
93	M₁₆	—	86	2	no	—
94	C₂×C₈	—	2	1	no	—
95	C₂×C₈	—	43	4	no	—
96	C₂×C₈	—	86	2	no	—
97	C₂×C₈	C₂²⋊D₄₃	1	2	yes	—
98	C₂³	—	2	2	no	—
99	C₂³	—	2	1	no	—
100	C₂³	—	4	2	no	—
101	C₂³	C₂×Dic₈₆	1	1	yes	characteristic
102	C₂×C₄	—	2	2	no	—
103	C₂×C₄	—	2	1	no	—
104	C₂×C₄	—	4	1	no	—
105	C₂×C₄	—	4	2	no	—
106	C₂×C₄	—	4	1	no	—
107	C₂×C₄	#10621898	1	1	yes	characteristic
108	C₂×C₄	D₄×D₄₃	1	2	yes	—
109	C₂×C₄	#10621900	1	2	yes	—
110	C₂×C₄	C₂×C₂²⋊D₄₃	1	1	yes	characteristic
111	C₈	—	2	2	no	—
112	C₈	—	4	1	no	—
113	C₈	—	86	4	no	—
114	C₈	—	172	2	no	—
115	C₂²	—	2	4	no	—
116	C₂²	—	2	2	no	—
117	C₂²	—	4	1	no	—
118	C₂²	—	4	2	no	—
119	C₂²	—	4	1	no	—
120	C₂²	—	4	1	no	—
121	C₂²	#13063302	1	2	yes	—
122	C₂²	#13063304	1	1	yes	characteristic
123	C₄	—	4	1	no	—
124	C₄	#13063306	1	1	yes	characteristic
125	C₄	#13063307	1	2	yes	—
126	C₄	#13063321	1	1	yes	characteristic
127	C₂	—	2	2	no	—
128	C₂	—	2	1	no	—
129	C₂	—	4	2	no	—
130	C₂	#14582835	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#14582948

C₂

yes

maximal, characteristic, complemented

#14582947

C₂

yes

maximal, complemented

#14582863

C₂

yes

maximal

C₄₃⋊#338

C₂

yes

maximal, characteristic, complemented

C₄₃×#407

C₂

yes

maximal, characteristic

C₂×#10621877

C₂²

yes

—

C₂×#10621877

C₂²

yes

—

#13063261

—

#13063260

—

C₂²⋊(C₄₃⋊C₈)

—

C₂³×C₄×C₄₃

C₂²

yes

characteristic

C₂×M₁₆×C₄₃

C₂²

yes

characteristic

C₂×M₁₆×C₄₃

C₂²

yes

characteristic

C₂²⋊C₈×C₄₃

—

C₂⁴×C₄₃

Q₈

yes

characteristic

C₂²×C₄×C₄₃

—

C₂²×C₄×C₄₃

—

C₂²×C₄×C₄₃

—

C₂²×C₄×C₄₃

—

C₂²×C₄×C₄₃

Q₈

yes

characteristic

C₂²×C₄×C₄₃

C₂³

yes

characteristic

M₁₆×C₄₃

—

M₁₆×C₄₃

—

C₂×C₈×C₄₃

—

C₂×C₈×C₄₃

D₄

yes

—

—

—

—

—

C₂×C₄₃⋊C₈

—

C₂×C₄₃⋊C₈

D₄

yes

—

C₂³×C₄₃

—

C₂³×C₄₃

—

C₂³×C₄₃

—

C₂³×C₄₃

C₂×Q₈

yes

characteristic

C₂×C₄×C₄₃

—

C₂×C₄×C₄₃

—

C₂×C₄×C₄₃

—

C₂×C₄×C₄₃

—

C₂×C₄×C₄₃

—

C₂×C₄×C₄₃

C₂×D₄

yes

—

C₂×C₄×C₄₃

C₂×D₄

yes

C₂×C₄×C₄₃

yes

C₂×C₄×C₄₃

yes

—

C₈×C₄₃

—

C₈×C₄₃

—

C₄₃⋊C₈

—

C₄₃⋊C₈

—

C₂²×C₄₃

—

C₂²×C₄₃

—

C₂²×C₄₃

—

C₂²×C₄₃

—

C₂²×C₄₃

—

C₂²×C₄₃

—

C₂²×C₄₃

C₂²⋊Q₈

yes

—

C₂²×C₄₃

C₂²⋊Q₈

yes

characteristic

C₄×C₄₃

—

C₄×C₄₃

#123

yes

characteristic

C₄×C₄₃

#123

yes

—

C₄×C₄₃

yes

—

C₂×C₄₃

—

C₂×C₄₃

—

C₂×C₄₃

—

C₂×C₄₃

yes

—

—

—

D₄₃

yes

characteristic

#338

—

C₄₃

#2091

yes

characteristic, complemented, Sylow

C₂³×C₄

C₂×D₄₃

yes

characteristic

C₂×M₁₆

—

C₂×M₁₆

—

C₂×M₁₆

C₂×D₄₃

yes

characteristic

C₂×M₁₆

C₂×D₄₃

yes

characteristic

#108

—

#108

—

C₂²⋊C₈

—

C₂²⋊C₈

—

C₂⁴

Dic₈₆

yes

characteristic

C₂²×C₄

—

C₂²×C₄

—

C₂²×C₄

—

C₂²×C₄

—

C₂²×C₄

Dic₈₆

yes

characteristic

C₂²×C₄

C₂²×D₄₃

yes

characteristic

M₁₆

—

M₁₆

—

M₁₆

—

M₁₆

—

M₁₆

—

M₁₆

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

C₂²⋊D₄₃

yes

—

C₂³

—

C₂³

—

100

C₂³

—

101

C₂³

C₂×Dic₈₆

yes

characteristic

102

C₂×C₄

—

103

C₂×C₄

—

104

C₂×C₄

—

105

C₂×C₄

—

106

C₂×C₄

—

107

C₂×C₄

#10621898

yes

characteristic

108

C₂×C₄

D₄×D₄₃

yes

—

109

C₂×C₄

#10621900

yes

—

110

C₂×C₄

C₂×C₂²⋊D₄₃

yes

characteristic

111

C₈

—

112

C₈

—

113

C₈

—

114

C₈

—

172

—

115

C₂²

—

116

C₂²

—

117

C₂²

—

118

C₂²

—

119

C₂²

—

120

C₂²

—

121

C₂²

#13063302

yes

—

122

C₂²

#13063304

yes

characteristic

123

C₄

—

124

C₄

#13063306

yes

characteristic

125

C₄

#13063307

yes

—

126

C₄

#13063321

yes

characteristic

127

C₂

—

128

C₂

—

129

C₂

—

130

C₂

#14582835

yes

characteristic

	subgroup	G/H
center	C₄	#13063321
commutator	C₂²×C₄×C₄₃	C₂³
Frattini	C₂²×C₄	C₂²×D₄₃
Fitting	C₄₃×#407	C₂
socle	C₂×C₄₃	#399
hypercenter	#407	D₄₃
hypocenter	C₄₃	#2091
LCS	G ▷ C₂²×C₄×C₄₃ ▷ C₂×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₄ ◁ C₂²×C₄ ◁ #407

subgroup

G/H

center

C₄

#13063321

commutator

C₂²×C₄×C₄₃

C₂³

Frattini

C₂²×C₄

C₂²×D₄₃

Fitting

C₄₃×#407

C₂

C₂×C₄₃

D₄₃

C₄₃

G ▷ C₂²×C₄×C₄₃ ▷ C₂×C₄₃ ▷ C₄₃

UCS

C₁ ◁ C₄ ◁ C₂²×C₄ ◁ #407

N	H ≅ G/N	type
1. #14582948	C₂	semidirect
2. #14582947	C₂	semidirect
4. C₄₃⋊#338	C₂	semidirect
71. C₄₃	#2091	semidirect

H ≅ G/N

type

1. #14582948

C₂

semidirect

2. #14582947

C₂

semidirect

4. C₄₃⋊#338

C₂

semidirect

71. C₄₃

#2091

semidirect

Subgroups — #19136111

Conjugacy classes of subgroups

Complements