Group #19136828 — subgroups

Subgroups — #19136828

Order 5504.

138 conjugacy classes of subgroups; only the 47 normal subgroups are shown.

normal subgroups only

This group has 138 conjugacy classes of subgroups — too many to draw. Only its 47 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	#14583300	C₂	1	1	yes	maximal, characteristic, complemented
2	#14583284	C₂	1	1	yes	maximal, characteristic
3	#14582703	C₂	1	1	yes	maximal, characteristic, complemented
4	#14582701	C₂	1	1	yes	maximal, characteristic
5	#14582699	C₂	1	1	yes	maximal, characteristic
6	C₁₆×Dic₄₃	C₂	1	1	yes	maximal, characteristic, complemented
7	C₄₃×#358	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×#10621884	—	2	1	no	—
9	C₂×D₃₄₄	C₂²	1	1	yes	characteristic
10	#13063316	—	2	1	no	—
11	#13063314	—	2	1	no	—
12	C₂×C₄₃⋊C₁₆	C₂²	1	1	yes	characteristic
13	#13063259	C₂²	1	1	yes	characteristic
14	#13063256	—	2	1	no	—
15	C₈×Dic₄₃	C₂²	1	1	yes	characteristic
16	C₂×Q₁₆×C₄₃	C₂²	1	1	yes	characteristic
17	C₂×C₁₆×C₄₃	C₂²	1	1	yes	characteristic
18	#107×C₄₃	C₂²	1	1	yes	characteristic
19	C₂×Q₈×C₄₃	—	2	1	no	—
20	C₂×D₁₇₂	—	2	1	no	—
21	Q₁₆×C₄₃	—	2	1	no	—
22	Q₁₆×C₄₃	—	2	1	no	—
23	C₂×C₈×C₄₃	C₂³	1	1	yes	characteristic
24	C₄⋊C₄×C₄₃	—	2	1	no	—
25	#10621884	—	4	2	no	—
26	(C₂×D₄₃)⋊C₄	—	4	1	no	—
27	(C₂×D₄₃)⋊C₄	—	4	1	no	—
28	C₄⋊Dic₄₃	—	2	1	no	—
29	C₄⋊Dic₄₃	—	4	1	no	—
30	Dic₄₃⋊C₄	—	4	1	no	—
31	C₄×Dic₄₃	D₄	1	1	yes	characteristic
32	C₂×C₄₃⋊C₈	D₄	1	1	yes	characteristic
33	D₃₄₄	—	2	1	no	—
34	D₃₄₄	—	2	1	no	—
35	C₁₆×C₄₃	—	2	1	no	—
36	C₄₃⋊C₁₆	—	2	1	no	—
37	C₂²×D₄₃	—	4	1	no	—
38	Q₈×C₄₃	—	4	1	no	—
39	Q₈×C₄₃	—	4	1	no	—
40	C₂×C₄×C₄₃	—	4	1	no	—
41	C₂×C₄×C₄₃	—	4	1	no	—
42	C₂×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
43	C₂×Dic₄₃	—	4	1	no	—
44	C₂×Dic₄₃	D₈	1	1	yes	characteristic
45	C₂×Dic₄₃	D₈	1	1	yes	characteristic
46	D₁₇₂	—	4	1	no	—
47	D₁₇₂	—	4	1	no	—
48	C₈×C₄₃	#41	1	1	yes	characteristic
49	C₈×C₄₃	#41	1	1	yes	characteristic
50	C₄₃⋊C₈	SD₁₆	1	2	yes	—
51	C₂²×C₄₃	C₂×D₈	1	1	yes	characteristic
52	C₂×D₄₃	—	8	1	no	—
53	C₂×D₄₃	—	8	1	no	—
54	C₂×D₄₃	—	8	1	no	—
55	C₄×C₄₃	—	8	1	no	—
56	C₄×C₄₃	—	8	1	no	—
57	C₄×C₄₃	#124	1	1	yes	characteristic
58	C₄×C₄₃	C₂×SD₁₆	1	1	yes	characteristic
59	Dic₄₃	—	2	1	no	—
60	Dic₄₃	—	2	1	no	—
61	Dic₄₃	—	8	1	no	—
62	#2242	—	43	1	no	maximal, Sylow
63	C₂×C₄₃	#486	1	1	yes	characteristic
64	C₂×C₄₃	#508	1	1	yes	characteristic
65	C₂×C₄₃	#508	1	1	yes	characteristic
66	D₄₃	—	16	1	no	—
67	#499	—	43	1	no	—
68	#495	—	43	1	no	—
69	#358	—	43	1	no	—
70	#358	D₄₃	1	1	yes	characteristic, complemented
71	#357	—	43	1	no	—
72	#357	—	43	1	no	—
73	C₄×C₁₆	—	43	1	no	—
74	C₄₃	#2242	1	1	yes	characteristic, complemented, Sylow
75	C₂×Q₁₆	C₂×D₄₃	1	1	yes	characteristic
76	C₂×SD₁₆	—	86	1	no	—
77	C₂×D₈	—	43	1	no	—
78	#125	—	86	1	no	—
79	#124	—	86	1	no	—
80	C₂×C₁₆	—	43	1	no	—
81	C₂×C₁₆	C₂×D₄₃	1	1	yes	characteristic
82	#107	—	43	1	no	—
83	#107	C₂×D₄₃	1	1	yes	characteristic
84	#106	—	86	1	no	—
85	C₄×C₈	—	43	1	no	—
86	C₂×Q₈	—	2	1	no	—
87	C₂×D₄	—	86	1	no	—
88	Q₁₆	—	2	1	no	—
89	Q₁₆	—	2	1	no	—
90	SD₁₆	—	172	2	no	—
91	D₈	—	86	1	no	—
92	D₈	—	86	1	no	—
93	C₂×C₈	—	43	1	no	—
94	C₂×C₈	C₂²×D₄₃	1	1	yes	characteristic
95	C₄⋊C₄	—	2	1	no	—
96	C₄⋊C₄	—	86	1	no	—
97	C₄⋊C₄	—	172	1	no	—
98	C₄⋊C₄	—	172	1	no	—
99	C₂²⋊C₄	—	172	1	no	—
100	C₂²⋊C₄	—	172	1	no	—
101	C₄²	—	43	1	no	—
102	C₁₆	—	2	1	no	—
103	C₁₆	—	86	1	no	—
104	C₂³	—	172	1	no	—
105	Q₈	—	4	1	no	—
106	Q₈	—	4	1	no	—
107	D₄	—	172	1	no	—
108	D₄	—	172	1	no	—
109	C₂×C₄	—	4	1	no	—
110	C₂×C₄	—	4	1	no	—
111	C₂×C₄	—	43	1	no	—
112	C₂×C₄	—	43	1	no	—
113	C₂×C₄	—	172	1	no	—
114	C₂×C₄	D₄×D₄₃	1	1	yes	characteristic
115	C₈	—	43	2	no	—
116	C₈	#10621898	1	1	yes	characteristic
117	C₈	#10621900	1	1	yes	characteristic
118	C₂²	—	344	1	no	—
119	C₂²	—	344	1	no	—
120	C₂²	—	344	1	no	—
121	C₂²	D₈×D₄₃	1	1	yes	characteristic
122	C₄	—	8	1	no	—
123	C₄	—	8	1	no	—
124	C₄	—	86	1	no	—
125	C₄	—	86	1	no	—
126	C₄	—	344	1	no	—
127	C₄	#13063311	1	1	yes	characteristic
128	C₄	SD₁₆×D₄₃	1	1	yes	characteristic
129	C₂	—	688	1	no	—
130	C₂	#14583244	1	1	yes	characteristic
131	C₂	#14583330	1	1	yes	characteristic
132	C₂	#14583332	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#14583300

C₂

yes

maximal, characteristic, complemented

#14583284

C₂

yes

maximal, characteristic

#14582703

C₂

yes

maximal, characteristic, complemented

#14582701

C₂

yes

maximal, characteristic

#14582699

C₂

yes

maximal, characteristic

C₁₆×Dic₄₃

C₂

yes

maximal, characteristic, complemented

C₄₃×#358

C₂

yes

maximal, characteristic, complemented

C₂×#10621884

—

C₂×D₃₄₄

C₂²

yes

characteristic

#13063316

—

#13063314

—

C₂×C₄₃⋊C₁₆

C₂²

yes

characteristic

#13063259

C₂²

yes

characteristic

#13063256

—

C₈×Dic₄₃

C₂²

yes

characteristic

C₂×Q₁₆×C₄₃

C₂²

yes

characteristic

C₂×C₁₆×C₄₃

C₂²

yes

characteristic

#107×C₄₃

C₂²

yes

characteristic

C₂×Q₈×C₄₃

—

C₂×D₁₇₂

—

Q₁₆×C₄₃

—

Q₁₆×C₄₃

—

C₂×C₈×C₄₃

C₂³

yes

characteristic

C₄⋊C₄×C₄₃

—

#10621884

—

(C₂×D₄₃)⋊C₄

—

(C₂×D₄₃)⋊C₄

—

C₄⋊Dic₄₃

—

C₄⋊Dic₄₃

—

Dic₄₃⋊C₄

—

C₄×Dic₄₃

D₄

yes

characteristic

C₂×C₄₃⋊C₈

D₄

yes

characteristic

D₃₄₄

—

D₃₄₄

—

C₁₆×C₄₃

—

C₄₃⋊C₁₆

—

C₂²×D₄₃

—

Q₈×C₄₃

—

Q₈×C₄₃

—

C₂×C₄×C₄₃

—

C₂×C₄×C₄₃

—

C₂×C₄×C₄₃

C₂×D₄

yes

characteristic

C₂×Dic₄₃

—

C₂×Dic₄₃

D₈

yes

characteristic

C₂×Dic₄₃

D₈

yes

characteristic

D₁₇₂

—

D₁₇₂

—

C₈×C₄₃

yes

C₈×C₄₃

yes

C₄₃⋊C₈

SD₁₆

yes

—

C₂²×C₄₃

C₂×D₈

yes

characteristic

C₂×D₄₃

—

C₂×D₄₃

—

C₂×D₄₃

—

C₄×C₄₃

—

C₄×C₄₃

—

C₄×C₄₃

#124

yes

characteristic

C₄×C₄₃

C₂×SD₁₆

yes

characteristic

Dic₄₃

—

Dic₄₃

—

Dic₄₃

—

—

C₂×C₄₃

yes

C₂×C₄₃

yes

C₂×C₄₃

yes

D₄₃

—

—

—

—

D₄₃

yes

characteristic, complemented

#357

—

#357

—

C₄×C₁₆

—

C₄₃

#2242

yes

characteristic, complemented, Sylow

C₂×Q₁₆

C₂×D₄₃

yes

characteristic

C₂×SD₁₆

—

C₂×D₈

—

#125

—

#124

—

C₂×C₁₆

—

C₂×C₁₆

C₂×D₄₃

yes

characteristic

#107

—

#107

C₂×D₄₃

yes

characteristic

#106

—

C₄×C₈

—

C₂×Q₈

—

C₂×D₄

—

Q₁₆

—

Q₁₆

—

SD₁₆

—

172

—

D₈

—

D₈

—

C₂×C₈

—

C₂×C₈

C₂²×D₄₃

yes

characteristic

C₄⋊C₄

—

C₄⋊C₄

—

C₄⋊C₄

—

172

—

C₄⋊C₄

—

172

—

C₂²⋊C₄

—

172

—

100

C₂²⋊C₄

—

172

—

101

C₄²

—

102

C₁₆

—

103

C₁₆

—

104

C₂³

—

172

—

105

Q₈

—

106

Q₈

—

107

D₄

—

172

—

108

D₄

—

172

—

109

C₂×C₄

—

110

C₂×C₄

—

111

C₂×C₄

—

112

C₂×C₄

—

113

C₂×C₄

—

172

—

114

C₂×C₄

D₄×D₄₃

yes

characteristic

115

C₈

—

116

C₈

#10621898

yes

characteristic

117

C₈

#10621900

yes

characteristic

118

C₂²

—

344

—

119

C₂²

—

344

—

120

C₂²

—

344

—

121

C₂²

D₈×D₄₃

yes

characteristic

122

C₄

—

123

C₄

—

124

C₄

—

125

C₄

—

126

C₄

—

344

—

127

C₄

#13063311

yes

characteristic

128

C₄

SD₁₆×D₄₃

yes

characteristic

129

C₂

—

688

—

130

C₂

#14583244

yes

characteristic

131

C₂

#14583330

yes

characteristic

132

C₂

#14583332

yes

characteristic

	subgroup	G/H
center	C₂²	D₈×D₄₃
commutator	C₂×C₈×C₄₃	C₂³
Frattini	C₂×C₈	C₂²×D₄₃
Fitting	C₄₃×#358	C₂
socle	C₂²×C₄₃	C₂×D₈
hypercenter	#358	D₄₃
hypocenter	C₄₃	#2242
LCS	G ▷ C₂×C₈×C₄₃ ▷ C₄×C₄₃ ▷ C₂×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₂² ◁ C₂×C₄ ◁ C₂×C₈ ◁ #358

subgroup

G/H

center

C₂²

D₈×D₄₃

commutator

C₂×C₈×C₄₃

C₂³

Frattini

C₂×C₈

C₂²×D₄₃

Fitting

C₄₃×#358

C₂

socle

C₂²×C₄₃

C₂×D₈

D₄₃

C₄₃

G ▷ C₂×C₈×C₄₃ ▷ C₄×C₄₃ ▷ C₂×C₄₃ ▷ C₄₃

UCS

C₁ ◁ C₂² ◁ C₂×C₄ ◁ C₂×C₈ ◁ #358

N	H ≅ G/N	type
1. #14583300	C₂	semidirect
3. #14582703	C₂	semidirect
6. C₁₆×Dic₄₃	C₂	semidirect
7. C₄₃×#358	C₂	semidirect
70. #358	D₄₃	semidirect
74. C₄₃	#2242	semidirect

H ≅ G/N

type

1. #14583300

C₂

semidirect

3. #14582703

C₂

semidirect

6. C₁₆×Dic₄₃

C₂

semidirect

7. C₄₃×#358

C₂

semidirect

70. #358

D₄₃

semidirect

74. C₄₃

#2242

semidirect

Subgroups — #19136828

Conjugacy classes of subgroups

Complements