Group #19136037 — subgroups

Subgroups — #19136037

Order 5504.

198 conjugacy classes of subgroups; only the 63 normal subgroups are shown.

normal subgroups only

This group has 198 conjugacy classes of subgroups — too many to draw. Only its 63 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×#13063259	C₂	1	1	yes	maximal, characteristic, complemented
2	#14582901	C₂	1	2	yes	maximal
3	#14582865	C₂	1	1	yes	maximal, characteristic
4	#14582667	C₂	1	2	yes	maximal, complemented
5	C₄₃×#341	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×#10621898	C₂²	1	1	yes	characteristic
7	C₂×#10621877	C₂²	1	1	yes	characteristic
8	C₂×C₄⋊Dic₄₃	C₂²	1	2	yes	—
9	#13063259	—	2	2	no	—
10	#13063250	—	2	2	no	—
11	#13063247	—	2	2	no	—
12	(C₂×D₄₃)⋊C₈	—	2	2	no	—
13	C₂×M₁₆×C₄₃	C₂²	1	2	yes	—
14	C₂²×C₈×C₄₃	C₂²	1	1	yes	characteristic
15	C₂²×C₄×C₄₃	C₂³	1	1	yes	characteristic
16	C₂×C₂²⋊D₄₃	—	2	1	no	—
17	C₂²×Dic₄₃	—	2	2	no	—
18	#10621898	—	2	2	no	—
19	#10621898	—	2	2	no	—
20	C₂×D₁₇₂	D₄	1	1	yes	characteristic
21	C₂×C₄×D₄₃	—	2	1	no	—
22	C₂×Dic₈₆	D₄	1	1	yes	characteristic
23	M₁₆×C₄₃	—	2	2	no	—
24	M₁₆×C₄₃	—	2	2	no	—
25	C₂×C₈×C₄₃	—	2	2	no	—
26	C₂×C₈×C₄₃	—	2	2	no	—
27	C₂×C₈×C₄₃	D₄	1	2	yes	—
28	C₄⋊Dic₄₃	—	2	2	no	—
29	C₄⋊Dic₄₃	—	2	2	no	—
30	#10621877	—	2	2	no	—
31	C₂×C₄₃⋊C₈	—	2	1	no	—
32	C₂³×C₄₃	#41	1	1	yes	characteristic
33	C₂²×D₄₃	—	2	1	no	—
34	C₂×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
35	C₂×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
36	C₂×C₄×C₄₃	#41	1	2	yes	—
37	C₂×C₄×C₄₃	#41	1	2	yes	—
38	C₂²⋊D₄₃	—	4	2	no	—
39	C₂×Dic₄₃	—	2	1	no	—
40	C₂×Dic₄₃	—	4	2	no	—
41	C₂×Dic₄₃	—	8	2	no	—
42	D₁₇₂	—	2	2	no	—
43	C₄×D₄₃	—	4	1	no	—
44	C₄×D₄₃	—	4	1	no	—
45	Dic₈₆	—	2	2	no	—
46	C₈×C₄₃	—	2	2	no	—
47	C₈×C₄₃	—	4	2	no	—
48	C₄₃⋊C₈	—	4	1	no	—
49	C₂²×C₄₃	—	2	1	no	—
50	C₂²×C₄₃	—	2	1	no	—
51	C₂²×C₄₃	#121	1	1	yes	characteristic
52	C₂²×C₄₃	#126	1	2	yes	—
53	C₂×D₄₃	—	4	1	no	—
54	C₂×D₄₃	—	4	1	no	—
55	C₂×D₄₃	—	4	1	no	—
56	C₄×C₄₃	#123	1	2	yes	—
57	C₄×C₄₃	#123	1	1	yes	characteristic
58	C₄×C₄₃	#124	1	1	yes	characteristic
59	Dic₄₃	—	4	1	no	—
60	Dic₄₃	—	8	2	no	—
61	#2078	—	43	1	no	maximal, Sylow
62	C₂×C₄₃	—	2	2	no	—
63	C₂×C₄₃	#397	1	1	yes	characteristic
64	C₂×C₄₃	#472	1	1	yes	characteristic
65	C₂×C₄₃	#473	1	1	yes	characteristic
66	D₄₃	—	8	1	no	—
67	C₂×#107	—	43	1	no	—
68	#417	—	43	2	no	—
69	#408	—	43	1	no	—
70	#343	—	43	2	no	—
71	#341	D₄₃	1	1	yes	characteristic, complemented
72	C₄₃	#2078	1	1	yes	characteristic, complemented, Sylow
73	C₂×#41	—	43	1	no	—
74	C₂×M₁₆	—	43	1	no	—
75	C₂×M₁₆	C₂×D₄₃	1	2	yes	—
76	C₂²×C₈	C₂×D₄₃	1	1	yes	characteristic
77	C₂×C₄⋊C₄	—	43	2	no	—
78	#107	—	86	2	no	—
79	#103	—	86	2	no	—
80	#102	—	86	2	no	—
81	C₂²⋊C₈	—	86	2	no	—
82	#41	—	86	2	no	—
83	#41	—	86	2	no	—
84	C₂×Q₈	—	43	1	no	—
85	C₂×D₄	—	43	1	no	—
86	C₂×D₄	—	86	1	no	—
87	C₂²×C₄	—	86	1	no	—
88	C₂²×C₄	—	86	2	no	—
89	C₂²×C₄	C₂²×D₄₃	1	1	yes	characteristic
90	M₁₆	—	2	2	no	—
91	M₁₆	—	2	2	no	—
92	M₁₆	—	86	2	no	—
93	C₂×C₈	—	2	2	no	—
94	C₂×C₈	—	2	2	no	—
95	C₂×C₈	—	86	1	no	—
96	C₂×C₈	D₁₇₂	1	2	yes	—
97	C₄⋊C₄	—	86	2	no	—
98	C₄⋊C₄	—	86	2	no	—
99	C₂³	—	86	1	no	—
100	C₂³	#10621902	1	1	yes	characteristic
101	Q₈	—	86	2	no	—
102	D₄	—	86	2	no	—
103	D₄	—	172	2	no	—
104	C₂×C₄	—	86	1	no	—
105	C₂×C₄	—	344	2	no	—
106	C₂×C₄	—	172	2	no	—
107	C₂×C₄	—	172	1	no	—
108	C₂×C₄	—	172	1	no	—
109	C₂×C₄	C₂×D₁₇₂	1	1	yes	characteristic
110	C₂×C₄	#10621898	1	2	yes	—
111	C₂×C₄	D₄×D₄₃	1	1	yes	characteristic
112	C₂×C₄	#10621900	1	2	yes	—
113	C₈	—	2	2	no	—
114	C₈	—	4	2	no	—
115	C₈	—	172	1	no	—
116	C₂²	—	2	1	no	—
117	C₂²	—	2	1	no	—
118	C₂²	—	172	1	no	—
119	C₂²	—	172	1	no	—
120	C₂²	—	172	1	no	—
121	C₂²	#13063300	1	1	yes	characteristic
122	C₂²	#13063320	1	2	yes	—
123	C₄	—	344	2	no	—
124	C₄	—	172	1	no	—
125	C₄	#13063307	1	2	yes	—
126	C₄	#13063309	1	1	yes	characteristic
127	C₄	#13063313	1	1	yes	characteristic
128	C₂	—	2	2	no	—
129	C₂	—	344	1	no	—
130	C₂	#14582826	1	1	yes	characteristic
131	C₂	#14583170	1	1	yes	characteristic
132	C₂	#14583175	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×#13063259

C₂

yes

maximal, characteristic, complemented

#14582901

C₂

yes

maximal

#14582865

C₂

yes

maximal, characteristic

#14582667

C₂

yes

maximal, complemented

C₄₃×#341

C₂

yes

maximal, characteristic, complemented

C₂×#10621898

C₂²

yes

characteristic

C₂×#10621877

C₂²

yes

characteristic

C₂×C₄⋊Dic₄₃

C₂²

yes

—

#13063259

—

#13063250

—

#13063247

—

(C₂×D₄₃)⋊C₈

—

C₂×M₁₆×C₄₃

C₂²

yes

—

C₂²×C₈×C₄₃

C₂²

yes

characteristic

C₂²×C₄×C₄₃

C₂³

yes

characteristic

C₂×C₂²⋊D₄₃

—

C₂²×Dic₄₃

—

#10621898

—

#10621898

—

C₂×D₁₇₂

D₄

yes

characteristic

C₂×C₄×D₄₃

—

C₂×Dic₈₆

D₄

yes

characteristic

M₁₆×C₄₃

—

M₁₆×C₄₃

—

C₂×C₈×C₄₃

—

C₂×C₈×C₄₃

—

C₂×C₈×C₄₃

D₄

yes

—

C₄⋊Dic₄₃

—

C₄⋊Dic₄₃

—

#10621877

—

C₂×C₄₃⋊C₈

—

C₂³×C₄₃

#41

yes

characteristic

C₂²×D₄₃

—

C₂×C₄×C₄₃

C₂×D₄

yes

characteristic

C₂×C₄×C₄₃

C₂×D₄

yes

characteristic

C₂×C₄×C₄₃

#41

yes

—

C₂×C₄×C₄₃

#41

yes

—

C₂²⋊D₄₃

—

C₂×Dic₄₃

—

C₂×Dic₄₃

—

C₂×Dic₄₃

—

D₁₇₂

—

C₄×D₄₃

—

C₄×D₄₃

—

Dic₈₆

—

C₈×C₄₃

—

C₈×C₄₃

—

C₄₃⋊C₈

—

C₂²×C₄₃

—

C₂²×C₄₃

—

C₂²×C₄₃

#121

yes

characteristic

C₂²×C₄₃

#126

yes

—

C₂×D₄₃

—

C₂×D₄₃

—

C₂×D₄₃

—

C₄×C₄₃

#123

yes

—

C₄×C₄₃

yes

C₄×C₄₃

yes

Dic₄₃

—

Dic₄₃

—

#2078

—

maximal, Sylow

C₂×C₄₃

—

C₂×C₄₃

yes

C₂×C₄₃

yes

C₂×C₄₃

yes

D₄₃

—

—

—

—

—

D₄₃

yes

characteristic, complemented

C₄₃

#2078

yes

characteristic, complemented, Sylow

C₂×#41

—

C₂×M₁₆

—

C₂×M₁₆

C₂×D₄₃

yes

—

C₂²×C₈

C₂×D₄₃

yes

characteristic

C₂×C₄⋊C₄

—

#107

—

#103

—

#102

—

C₂²⋊C₈

—

#41

—

#41

—

C₂×Q₈

—

C₂×D₄

—

C₂×D₄

—

C₂²×C₄

—

C₂²×C₄

—

C₂²×C₄

C₂²×D₄₃

yes

characteristic

M₁₆

—

M₁₆

—

M₁₆

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

D₁₇₂

yes

—

C₄⋊C₄

—

C₄⋊C₄

—

C₂³

—

100

C₂³

#10621902

yes

characteristic

101

Q₈

—

102

D₄

—

103

D₄

—

172

—

104

C₂×C₄

—

105

C₂×C₄

—

344

—

106

C₂×C₄

—

172

—

107

C₂×C₄

—

172

—

108

C₂×C₄

—

172

—

109

C₂×C₄

C₂×D₁₇₂

yes

characteristic

110

C₂×C₄

#10621898

yes

—

111

C₂×C₄

D₄×D₄₃

yes

characteristic

112

C₂×C₄

#10621900

yes

—

113

C₈

—

114

C₈

—

115

C₈

—

172

—

116

C₂²

—

117

C₂²

—

118

C₂²

—

172

—

119

C₂²

—

172

—

120

C₂²

—

172

—

121

C₂²

#13063300

yes

characteristic

122

C₂²

#13063320

yes

—

123

C₄

—

344

—

124

C₄

—

172

—

125

C₄

#13063307

yes

—

126

C₄

#13063309

yes

characteristic

127

C₄

#13063313

yes

characteristic

128

C₂

—

129

C₂

—

344

—

130

C₂

#14582826

yes

characteristic

131

C₂

#14583170

yes

characteristic

132

C₂

#14583175

yes

characteristic

	subgroup	G/H
center	C₂²	#13063300
commutator	C₂²×C₄×C₄₃	C₂³
Frattini	C₂²×C₄	C₂²×D₄₃
Fitting	C₄₃×#341	C₂
socle	C₂²×C₄₃	#121
hypercenter	#341	D₄₃
hypocenter	C₄₃	#2078
LCS	G ▷ C₂²×C₄×C₄₃ ▷ C₂×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₂² ◁ C₂²×C₄ ◁ #341

subgroup

G/H

center

C₂²

#13063300

commutator

C₂²×C₄×C₄₃

C₂³

Frattini

C₂²×C₄

C₂²×D₄₃

Fitting

C₄₃×#341

C₂

C₂²×C₄₃

D₄₃

C₄₃

G ▷ C₂²×C₄×C₄₃ ▷ C₂×C₄₃ ▷ C₄₃

UCS

C₁ ◁ C₂² ◁ C₂²×C₄ ◁ #341

N	H ≅ G/N	type
1. C₂×#13063259	C₂	semidirect
4. #14582667	C₂	semidirect
5. C₄₃×#341	C₂	semidirect
71. #341	D₄₃	semidirect
72. C₄₃	#2078	semidirect

H ≅ G/N

type

1. C₂×#13063259

C₂

semidirect

4. #14582667

C₂

semidirect

5. C₄₃×#341

C₂

semidirect

71. #341

D₄₃

semidirect

72. C₄₃

#2078

semidirect

Subgroups — #19136037

Conjugacy classes of subgroups

Complements