Group #19142967 — subgroups

Subgroups — #19142967

Order 5504.

524 conjugacy classes of subgroups; only the 165 normal subgroups are shown.

normal subgroups only

This group has 524 conjugacy classes of subgroups — too many to draw. Only its 165 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×#13063317	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×#13063313	C₂	1	1	yes	maximal, characteristic
3	#14582805	C₂	1	2	yes	maximal, complemented
4	#14582801	C₂	1	2	yes	maximal
5	#14582790	C₂	1	8	yes	maximal, complemented
6	C₄³×C₄₃	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂²×Dic₈₆	C₂²	1	1	yes	characteristic
8	C₂²×D₁₇₂	C₂²	1	1	yes	characteristic
9	#13063317	—	2	4	no	—
10	#13063313	—	2	4	no	—
11	C₂×C₄⋊Dic₄₃	C₂²	1	2	yes	—
12	C₂×Dic₄₃⋊C₄	C₂²	1	4	yes	—
13	C₂×(C₂×D₄₃)⋊C₄	C₂²	1	8	yes	—
14	C₂×(C₂×D₄₃)⋊C₄	C₂²	1	4	yes	—
15	C₄₃⋊#95	C₂²	1	8	yes	—
16	C₂×C₄²×C₄₃	C₂²	1	4	yes	—
17	C₂×C₄²×C₄₃	C₂²	1	2	yes	—
18	C₂×C₄²×C₄₃	C₂²	1	1	yes	characteristic
19	C₂³×D₄₃	C₂³	1	2	yes	—
20	C₂²×C₄×C₄₃	C₂³	1	2	yes	—
21	C₂²×C₄×C₄₃	C₂³	1	4	yes	—
22	C₂²×C₄×C₄₃	C₂³	1	1	yes	characteristic
23	C₂²×Dic₄₃	C₂³	1	2	yes	—
24	C₂²×Dic₄₃	C₂³	1	4	yes	—
25	C₂×D₁₇₂	—	2	2	no	—
26	C₂×D₁₇₂	—	2	4	no	—
27	C₂×Dic₈₆	—	2	2	no	—
28	C₂×Dic₈₆	—	2	4	no	—
29	C₄²×C₄₃	—	2	8	no	—
30	C₄²×C₄₃	—	2	4	no	—
31	C₄²×C₄₃	D₄	1	4	yes	—
32	(C₂×D₄₃)⋊C₄	—	2	8	no	—
33	(C₂×D₄₃)⋊C₄	—	2	16	no	—
34	C₄⋊Dic₄₃	—	2	4	no	—
35	Dic₄₃⋊C₄	—	2	8	no	—
36	C₂³×C₄₃	C₂⁴	1	1	yes	characteristic
37	C₂²×D₄₃	—	2	2	no	—
38	C₂²×D₄₃	—	2	8	no	—
39	C₂²×D₄₃	—	2	4	no	—
40	C₂×C₄×C₄₃	—	2	4	no	—
41	C₂×C₄×C₄₃	—	2	4	no	—
42	C₂×C₄×C₄₃	—	2	4	no	—
43	C₂×C₄×C₄₃	C₂×D₄	1	4	yes	—
44	C₂×C₄×C₄₃	C₂×D₄	1	2	yes	—
45	C₂×C₄×C₄₃	#41	1	8	yes	—
46	C₂×C₄×C₄₃	#41	1	4	yes	—
47	C₂×Dic₄₃	—	2	4	no	—
48	C₂×Dic₄₃	—	2	2	no	—
49	C₂×Dic₄₃	—	2	8	no	—
50	C₂×Dic₄₃	—	2	4	no	—
51	D₁₇₂	—	4	4	no	—
52	Dic₈₆	—	4	4	no	—
53	C₂²×C₄₃	C₂²×D₄	1	1	yes	characteristic
54	C₂²×C₄₃	C₂×#41	1	2	yes	—
55	C₂²×C₄₃	C₂×#41	1	4	yes	—
56	C₂×D₄₃	—	4	2	no	—
57	C₂×D₄₃	—	4	8	no	—
58	C₂×D₄₃	—	4	4	no	—
59	C₄×C₄₃	—	2	8	no	—
60	C₄×C₄₃	—	2	4	no	—
61	C₄×C₄₃	#124	1	4	yes	—
62	Dic₄₃	—	4	2	no	—
63	Dic₄₃	—	4	4	no	—
64	#2861	—	43	1	no	maximal, Sylow
65	C₂×C₄₃	C₂×#124	1	1	yes	characteristic
66	C₂×C₄₃	#529	1	4	yes	—
67	C₂×C₄₃	#532	1	2	yes	—
68	D₄₃	—	8	2	no	—
69	C₂×#125	—	43	1	no	—
70	C₂×#124	—	43	1	no	—
71	#391	—	43	2	no	—
72	#390	—	43	2	no	—
73	#388	—	43	8	no	—
74	C₄³	D₄₃	1	1	yes	characteristic, complemented
75	C₄₃	#2861	1	1	yes	characteristic, complemented, Sylow
76	C₂²×Q₈	—	43	1	no	—
77	C₂²×D₄	—	43	1	no	—
78	#125	—	86	4	no	—
79	#124	—	86	4	no	—
80	C₂×C₄⋊C₄	—	43	4	no	—
81	C₂×C₄⋊C₄	—	43	2	no	—
82	C₂×C₂²⋊C₄	—	43	4	no	—
83	C₂×C₂²⋊C₄	—	43	8	no	—
84	C₂×C₄²	C₂×D₄₃	1	4	yes	—
85	C₂×C₄²	C₂×D₄₃	1	2	yes	—
86	C₂×C₄²	C₂×D₄₃	1	1	yes	characteristic
87	#95	—	43	8	no	—
88	C₂⁴	—	43	2	no	—
89	C₂×Q₈	—	86	2	no	—
90	C₂×Q₈	—	86	4	no	—
91	C₂×D₄	—	86	2	no	—
92	C₂×D₄	—	86	4	no	—
93	C₂²×C₄	—	43	2	no	—
94	C₂²×C₄	—	43	4	no	—
95	C₂²×C₄	C₂²×D₄₃	1	2	yes	—
96	C₂²×C₄	C₂²×D₄₃	1	4	yes	—
97	C₂²×C₄	C₂²×D₄₃	1	1	yes	characteristic
98	C₄⋊C₄	—	86	8	no	—
99	C₄⋊C₄	—	86	4	no	—
100	C₂²⋊C₄	—	86	8	no	—
101	C₂²⋊C₄	—	86	16	no	—
102	C₄²	—	2	8	no	—
103	C₄²	—	2	4	no	—
104	C₄²	D₁₇₂	1	4	yes	—
105	C₂³	—	86	2	no	—
106	C₂³	—	86	8	no	—
107	C₂³	—	86	4	no	—
108	C₂³	C₂³×D₄₃	1	1	yes	characteristic
109	Q₈	—	172	4	no	—
110	D₄	—	172	4	no	—
111	C₂×C₄	—	2	4	no	—
112	C₂×C₄	—	2	4	no	—
113	C₂×C₄	—	2	4	no	—
114	C₂×C₄	—	86	2	no	—
115	C₂×C₄	—	86	4	no	—
116	C₂×C₄	—	86	8	no	—
117	C₂×C₄	—	86	4	no	—
118	C₂×C₄	C₂×D₁₇₂	1	4	yes	—
119	C₂×C₄	C₂×D₁₇₂	1	2	yes	—
120	C₂×C₄	#10621898	1	8	yes	—
121	C₂×C₄	#10621898	1	4	yes	—
122	C₂²	—	172	2	no	—
123	C₂²	—	172	8	no	—
124	C₂²	—	172	4	no	—
125	C₂²	C₂²×D₁₇₂	1	1	yes	characteristic
126	C₂²	C₂×#10621898	1	2	yes	—
127	C₂²	C₂×#10621898	1	4	yes	—
128	C₄	—	2	8	no	—
129	C₄	—	2	4	no	—
130	C₄	—	172	2	no	—
131	C₄	—	172	4	no	—
132	C₄	#13063313	1	4	yes	—
133	C₂	—	344	2	no	—
134	C₂	C₂×#13063313	1	1	yes	characteristic
135	C₂	#14583433	1	4	yes	—
136	C₂	#14583449	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×#13063317

C₂

yes

maximal, characteristic, complemented

C₂×#13063313

C₂

yes

maximal, characteristic

#14582805

C₂

yes

maximal, complemented

#14582801

C₂

yes

maximal

#14582790

C₂

yes

maximal, complemented

C₄³×C₄₃

C₂

yes

maximal, characteristic, complemented

C₂²×Dic₈₆

C₂²

yes

characteristic

C₂²×D₁₇₂

C₂²

yes

characteristic

#13063317

—

#13063313

—

C₂×C₄⋊Dic₄₃

C₂²

yes

—

C₂×Dic₄₃⋊C₄

C₂²

yes

—

C₂×(C₂×D₄₃)⋊C₄

C₂²

yes

—

C₂×(C₂×D₄₃)⋊C₄

C₂²

yes

—

C₄₃⋊#95

C₂²

yes

—

C₂×C₄²×C₄₃

C₂²

yes

—

C₂×C₄²×C₄₃

C₂²

yes

—

C₂×C₄²×C₄₃

C₂²

yes

characteristic

C₂³×D₄₃

C₂³

yes

—

C₂²×C₄×C₄₃

C₂³

yes

—

C₂²×C₄×C₄₃

C₂³

yes

—

C₂²×C₄×C₄₃

C₂³

yes

characteristic

C₂²×Dic₄₃

C₂³

yes

—

C₂²×Dic₄₃

C₂³

yes

—

C₂×D₁₇₂

—

C₂×D₁₇₂

—

C₂×Dic₈₆

—

C₂×Dic₈₆

—

C₄²×C₄₃

—

C₄²×C₄₃

—

C₄²×C₄₃

D₄

yes

—

(C₂×D₄₃)⋊C₄

—

(C₂×D₄₃)⋊C₄

—

C₄⋊Dic₄₃

—

Dic₄₃⋊C₄

—

C₂³×C₄₃

C₂⁴

yes

characteristic

C₂²×D₄₃

—

C₂²×D₄₃

—

C₂²×D₄₃

—

C₂×C₄×C₄₃

—

C₂×C₄×C₄₃

—

C₂×C₄×C₄₃

—

C₂×C₄×C₄₃

C₂×D₄

yes

—

C₂×C₄×C₄₃

C₂×D₄

yes

—

C₂×C₄×C₄₃

#41

yes

—

C₂×C₄×C₄₃

#41

yes

—

C₂×Dic₄₃

—

C₂×Dic₄₃

—

C₂×Dic₄₃

—

C₂×Dic₄₃

—

D₁₇₂

—

Dic₈₆

—

C₂²×C₄₃

C₂²×D₄

yes

characteristic

C₂²×C₄₃

C₂×#41

yes

—

C₂²×C₄₃

C₂×#41

yes

—

C₂×D₄₃

—

C₂×D₄₃

—

C₂×D₄₃

—

C₄×C₄₃

—

C₄×C₄₃

—

C₄×C₄₃

#124

yes

—

Dic₄₃

—

Dic₄₃

—

—

C₂×C₄₃

yes

C₂×C₄₃

yes

—

C₂×C₄₃

#532

yes

—

D₄₃

—

—

—

—

—

—

C₄³

D₄₃

yes

characteristic, complemented

C₄₃

#2861

yes

characteristic, complemented, Sylow

C₂²×Q₈

—

C₂²×D₄

—

#125

—

#124

—

C₂×C₄⋊C₄

—

C₂×C₄⋊C₄

—

C₂×C₂²⋊C₄

—

C₂×C₂²⋊C₄

—

C₂×C₄²

C₂×D₄₃

yes

—

C₂×C₄²

C₂×D₄₃

yes

—

C₂×C₄²

C₂×D₄₃

yes

characteristic

#95

—

C₂⁴

—

C₂×Q₈

—

C₂×Q₈

—

C₂×D₄

—

C₂×D₄

—

C₂²×C₄

—

C₂²×C₄

—

C₂²×C₄

C₂²×D₄₃

yes

—

C₂²×C₄

C₂²×D₄₃

yes

—

C₂²×C₄

C₂²×D₄₃

yes

characteristic

C₄⋊C₄

—

C₄⋊C₄

—

100

C₂²⋊C₄

—

101

C₂²⋊C₄

—

102

C₄²

—

103

C₄²

—

104

C₄²

D₁₇₂

yes

—

105

C₂³

—

106

C₂³

—

107

C₂³

—

108

C₂³

C₂³×D₄₃

yes

characteristic

109

Q₈

—

172

—

110

D₄

—

172

—

111

C₂×C₄

—

112

C₂×C₄

—

113

C₂×C₄

—

114

C₂×C₄

—

115

C₂×C₄

—

116

C₂×C₄

—

117

C₂×C₄

—

118

C₂×C₄

C₂×D₁₇₂

yes

—

119

C₂×C₄

C₂×D₁₇₂

yes

—

120

C₂×C₄

#10621898

yes

—

121

C₂×C₄

#10621898

yes

—

122

C₂²

—

172

—

123

C₂²

—

172

—

124

C₂²

—

172

—

125

C₂²

C₂²×D₁₇₂

yes

characteristic

126

C₂²

C₂×#10621898

yes

—

127

C₂²

C₂×#10621898

yes

—

128

C₄

—

129

C₄

—

130

C₄

—

172

—

131

C₄

—

172

—

132

C₄

#13063313

yes

—

133

C₂

—

344

—

134

C₂

C₂×#13063313

yes

characteristic

135

C₂

#14583433

yes

—

136

C₂

#14583449

yes

—

	subgroup	G/H
center, Frattini	C₂³	C₂³×D₄₃
commutator, socle	C₂³×C₄₃	C₂⁴
Fitting	C₄³×C₄₃	C₂
hypercenter	C₄³	D₄₃
hypocenter	C₄₃	#2861
LCS	G ▷ C₂³×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₂³ ◁ C₄³

subgroup

G/H

center, Frattini

C₂³

C₂³×D₄₃

commutator, socle

C₂³×C₄₃

C₂⁴

Fitting

C₄³×C₄₃

C₂

hypercenter

C₄³

D₄₃

C₄₃

G ▷ C₂³×C₄₃ ▷ C₄₃

C₁ ◁ C₂³ ◁ C₄³

N	H ≅ G/N	type
1. C₂×#13063317	C₂	semidirect
3. #14582805	C₂	semidirect
5. #14582790	C₂	semidirect
6. C₄³×C₄₃	C₂	semidirect
74. C₄³	D₄₃	semidirect
75. C₄₃	#2861	semidirect

H ≅ G/N

type

1. C₂×#13063317

C₂

semidirect

3. #14582805

C₂

semidirect

5. #14582790

C₂

semidirect

6. C₄³×C₄₃

C₂

semidirect

74. C₄³

D₄₃

semidirect

75. C₄₃

#2861

semidirect

Subgroups — #19142967

Conjugacy classes of subgroups

Complements