Group #19137155 — subgroups

Subgroups — C₄×#13063317 #19137155

Order 5504.

484 conjugacy classes of subgroups; only the 229 normal subgroups are shown.

normal subgroups only

This group has 484 conjugacy classes of subgroups — too many to draw. Only its 229 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
2	#14582797	C₂	1	2	yes	maximal
3	#14582783	C₂	1	4	yes	maximal
4	#14582765	C₂	1	1	yes	maximal, characteristic
5	C₄×Dic₄₃⋊C₄	C₂	1	4	yes	maximal
6	C₄×C₄⋊Dic₄₃	C₂	1	2	yes	maximal
7	C₄³×C₄₃	C₂	1	1	yes	maximal, characteristic
8	#13063317	C₄	1	8	yes	direct product factor
9	C₂×C₄⋊Dic₄₃	C₂²	1	2	yes	—
10	C₂×C₄⋊Dic₄₃	C₂²	1	2	yes	—
11	C₂×Dic₄₃⋊C₄	C₂²	1	4	yes	—
12	C₂×Dic₄₃⋊C₄	C₂²	1	4	yes	—
13	C₂×C₄×Dic₄₃	C₂²	1	4	yes	—
14	C₄₃⋊#95	C₂²	1	4	yes	—
15	C₄₃⋊#95	C₂²	1	4	yes	—
16	C₄₃⋊#95	C₂²	1	4	yes	—
17	C₂×C₄²×C₄₃	C₂²	1	1	yes	characteristic
18	C₂×C₄²×C₄₃	C₂²	1	2	yes	—
19	C₂×C₄²×C₄₃	C₂²	1	2	yes	—
20	C₂×C₄²×C₄₃	C₂²	1	1	yes	characteristic
21	C₂×C₄²×C₄₃	C₂²	1	1	yes	characteristic
22	C₂²×C₄×C₄₃	C₂³	1	2	yes	—
23	C₂²×C₄×C₄₃	C₂³	1	1	yes	characteristic
24	C₂²×C₄×C₄₃	C₂³	1	2	yes	—
25	C₂²×C₄×C₄₃	C₂³	1	1	yes	characteristic
26	C₂²×C₄×C₄₃	C₂³	1	1	yes	characteristic
27	C₂²×Dic₄₃	C₂³	1	4	yes	—
28	C₂²×Dic₄₃	C₂³	1	4	yes	—
29	C₄²×C₄₃	—	2	4	no	—
30	C₄²×C₄₃	—	2	2	no	—
31	C₄²×C₄₃	—	2	4	no	—
32	C₄²×C₄₃	C₂×C₄	1	4	yes	—
33	C₄²×C₄₃	Q₈	1	4	yes	—
34	C₄⋊Dic₄₃	—	2	4	no	—
35	C₄⋊Dic₄₃	C₂×C₄	1	8	yes	—
36	Dic₄₃⋊C₄	—	2	8	no	—
37	Dic₄₃⋊C₄	C₂×C₄	1	16	yes	—
38	C₄×Dic₄₃	—	2	8	no	—
39	C₂³×C₄₃	C₂⁴	1	1	yes	characteristic
40	C₂×C₄×C₄₃	—	2	2	no	—
41	C₂×C₄×C₄₃	—	2	2	no	—
42	C₂×C₄×C₄₃	—	2	2	no	—
43	C₂×C₄×C₄₃	—	2	2	no	—
44	C₂×C₄×C₄₃	—	2	2	no	—
45	C₂×C₄×C₄₃	C₂²×C₄	1	4	yes	—
46	C₂×C₄×C₄₃	C₂²×C₄	1	2	yes	—
47	C₂×C₄×C₄₃	C₂×Q₈	1	2	yes	—
48	C₂×C₄×C₄₃	C₂×Q₈	1	2	yes	—
49	C₂×C₄×C₄₃	C₂×Q₈	1	2	yes	—
50	C₂×C₄×C₄₃	#41	1	4	yes	—
51	C₂×C₄×C₄₃	#41	1	2	yes	—
52	C₂×C₄×C₄₃	#41	1	4	yes	—
53	C₂×Dic₄₃	—	2	4	no	—
54	C₂×Dic₄₃	—	2	4	no	—
55	C₂×Dic₄₃	—	2	4	no	—
56	C₂×Dic₄₃	—	2	4	no	—
57	C₂×Dic₄₃	—	2	4	no	—
58	C₂×Dic₄₃	C₂²×C₄	1	8	yes	—
59	C₂²×C₄₃	C₂³×C₄	1	1	yes	characteristic
60	C₂²×C₄₃	C₂²×Q₈	1	1	yes	characteristic
61	C₂²×C₄₃	C₂×#41	1	1	yes	characteristic
62	C₂²×C₄₃	C₂×#41	1	2	yes	—
63	C₂²×C₄₃	C₂×#41	1	2	yes	—
64	C₄×C₄₃	—	2	4	no	—
65	C₄×C₄₃	—	2	4	no	—
66	C₄×C₄₃	—	2	2	no	—
67	C₄×C₄₃	C₄×Q₈	1	4	yes	—
68	C₄×C₄₃	#125	1	4	yes	complemented
69	Dic₄₃	—	2	8	no	—
70	Dic₄₃	—	4	4	no	—
71	C₄×#125	—	43	1	no	maximal, Sylow
72	C₂×C₄₃	C₂×C₄×Q₈	1	1	yes	characteristic
73	C₂×C₄₃	C₄×#41	1	2	yes	—
74	C₂×C₄₃	C₂×#125	1	1	yes	characteristic
75	C₂×C₄₃	#529	1	2	yes	—
76	C₂×C₄₃	#533	1	1	yes	characteristic
77	C₂×#125	—	43	1	no	—
78	#389	—	43	2	no	—
79	#387	—	43	4	no	—
80	#382	—	43	1	no	—
81	C₄×C₄⋊C₄	—	43	2	no	—
82	C₄×C₄⋊C₄	—	43	4	no	—
83	C₄³	D₄₃	1	1	yes	characteristic
84	C₄₃	C₄×#125	1	1	yes	characteristic, complemented, Sylow
85	#125	—	43	8	no	—
86	C₂×C₄⋊C₄	—	43	4	no	—
87	C₂×C₄⋊C₄	—	43	2	no	—
88	C₂×C₄⋊C₄	—	43	4	no	—
89	C₂×C₄⋊C₄	—	43	2	no	—
90	C₂×C₄²	—	43	4	no	—
91	C₂×C₄²	C₂×D₄₃	1	2	yes	—
92	C₂×C₄²	C₂×D₄₃	1	1	yes	characteristic
93	C₂×C₄²	C₂×D₄₃	1	2	yes	—
94	C₂×C₄²	C₂×D₄₃	1	1	yes	characteristic
95	C₂×C₄²	C₂×D₄₃	1	1	yes	characteristic
96	#95	—	43	4	no	—
97	#95	—	43	4	no	—
98	#95	—	43	4	no	—
99	C₂²×C₄	—	43	4	no	—
100	C₂²×C₄	—	43	4	no	—
101	C₂²×C₄	C₂²×D₄₃	1	1	yes	characteristic
102	C₂²×C₄	C₂²×D₄₃	1	2	yes	—
103	C₂²×C₄	C₂²×D₄₃	1	2	yes	—
104	C₂²×C₄	C₂²×D₄₃	1	1	yes	characteristic
105	C₂²×C₄	C₂²×D₄₃	1	1	yes	characteristic
106	C₄⋊C₄	—	43	16	no	—
107	C₄⋊C₄	—	43	8	no	—
108	C₄⋊C₄	—	86	8	no	—
109	C₄⋊C₄	—	86	4	no	—
110	C₄²	—	2	4	no	—
111	C₄²	—	2	2	no	—
112	C₄²	—	2	4	no	—
113	C₄²	—	86	8	no	—
114	C₄²	Dic₈₆	1	4	yes	—
115	C₄²	C₄×D₄₃	1	4	yes	—
116	C₂³	C₂³×D₄₃	1	1	yes	characteristic
117	C₂×C₄	—	2	2	no	—
118	C₂×C₄	—	2	2	no	—
119	C₂×C₄	—	2	2	no	—
120	C₂×C₄	—	2	2	no	—
121	C₂×C₄	—	2	2	no	—
122	C₂×C₄	—	43	8	no	—
123	C₂×C₄	—	86	4	no	—
124	C₂×C₄	—	86	4	no	—
125	C₂×C₄	—	86	4	no	—
126	C₂×C₄	—	86	4	no	—
127	C₂×C₄	—	86	4	no	—
128	C₂×C₄	C₂×Dic₈₆	1	2	yes	—
129	C₂×C₄	C₂×Dic₈₆	1	2	yes	—
130	C₂×C₄	C₂×Dic₈₆	1	2	yes	—
131	C₂×C₄	C₂×C₄×D₄₃	1	4	yes	—
132	C₂×C₄	C₂×C₄×D₄₃	1	2	yes	—
133	C₂×C₄	#10621898	1	4	yes	—
134	C₂×C₄	#10621898	1	2	yes	—
135	C₂×C₄	#10621898	1	4	yes	—
136	C₂²	C₂²×C₄×D₄₃	1	1	yes	characteristic
137	C₂²	C₂²×Dic₈₆	1	1	yes	characteristic
138	C₂²	C₂×#10621898	1	1	yes	characteristic
139	C₂²	C₂×#10621898	1	2	yes	—
140	C₂²	C₂×#10621898	1	2	yes	—
141	C₄	—	2	4	no	—
142	C₄	—	2	4	no	—
143	C₄	—	2	2	no	—
144	C₄	—	86	8	no	—
145	C₄	—	172	4	no	—
146	C₄	C₄×Dic₈₆	1	4	yes	—
147	C₄	#13063317	1	4	yes	direct product factor
148	C₂	C₂×C₄×Dic₈₆	1	1	yes	characteristic
149	C₂	C₄×#10621898	1	2	yes	—
150	C₂	C₂×#13063317	1	1	yes	characteristic
151	C₂	#14583433	1	2	yes	—
152	C₂	#14583456	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×#13063317

C₂

yes

maximal, characteristic

#14582797

C₂

yes

maximal

#14582783

C₂

yes

maximal

#14582765

C₂

yes

maximal, characteristic

C₄×Dic₄₃⋊C₄

C₂

yes

maximal

C₄×C₄⋊Dic₄₃

C₂

yes

maximal

C₄³×C₄₃

C₂

yes

maximal, characteristic

#13063317

C₄

yes

direct product factor

C₂×C₄⋊Dic₄₃

C₂²

yes

—

C₂×C₄⋊Dic₄₃

C₂²

yes

—

C₂×Dic₄₃⋊C₄

C₂²

yes

—

C₂×Dic₄₃⋊C₄

C₂²

yes

—

C₂×C₄×Dic₄₃

C₂²

yes

—

C₄₃⋊#95

C₂²

yes

—

C₄₃⋊#95

C₂²

yes

—

C₄₃⋊#95

C₂²

yes

—

C₂×C₄²×C₄₃

C₂²

yes

characteristic

C₂×C₄²×C₄₃

C₂²

yes

—

C₂×C₄²×C₄₃

C₂²

yes

—

C₂×C₄²×C₄₃

C₂²

yes

characteristic

C₂×C₄²×C₄₃

C₂²

yes

characteristic

C₂²×C₄×C₄₃

C₂³

yes

—

C₂²×C₄×C₄₃

C₂³

yes

characteristic

C₂²×C₄×C₄₃

C₂³

yes

—

C₂²×C₄×C₄₃

C₂³

yes

characteristic

C₂²×C₄×C₄₃

C₂³

yes

characteristic

C₂²×Dic₄₃

C₂³

yes

—

C₂²×Dic₄₃

C₂³

yes

—

C₄²×C₄₃

—

C₄²×C₄₃

—

C₄²×C₄₃

—

C₄²×C₄₃

C₂×C₄

yes

—

C₄²×C₄₃

Q₈

yes

—

C₄⋊Dic₄₃

—

C₄⋊Dic₄₃

C₂×C₄

yes

—

Dic₄₃⋊C₄

—

Dic₄₃⋊C₄

C₂×C₄

yes

—

C₄×Dic₄₃

—

C₂³×C₄₃

C₂⁴

yes

characteristic

C₂×C₄×C₄₃

—

C₂×C₄×C₄₃

—

C₂×C₄×C₄₃

—

C₂×C₄×C₄₃

—

C₂×C₄×C₄₃

—

C₂×C₄×C₄₃

C₂²×C₄

yes

—

C₂×C₄×C₄₃

C₂²×C₄

yes

—

C₂×C₄×C₄₃

C₂×Q₈

yes

—

C₂×C₄×C₄₃

C₂×Q₈

yes

—

C₂×C₄×C₄₃

C₂×Q₈

yes

—

C₂×C₄×C₄₃

#41

yes

—

C₂×C₄×C₄₃

#41

yes

—

C₂×C₄×C₄₃

#41

yes

—

C₂×Dic₄₃

—

C₂×Dic₄₃

—

C₂×Dic₄₃

—

C₂×Dic₄₃

—

C₂×Dic₄₃

—

C₂×Dic₄₃

C₂²×C₄

yes

—

C₂²×C₄₃

C₂³×C₄

yes

characteristic

C₂²×C₄₃

C₂²×Q₈

yes

characteristic

C₂²×C₄₃

C₂×#41

yes

characteristic

C₂²×C₄₃

C₂×#41

yes

—

C₂²×C₄₃

C₂×#41

yes

—

C₄×C₄₃

—

C₄×C₄₃

—

C₄×C₄₃

—

C₄×C₄₃

C₄×Q₈

yes

—

C₄×C₄₃

#125

yes

complemented

Dic₄₃

—

Dic₄₃

—

C₄×#125

—

maximal, Sylow

C₂×C₄₃

C₂×C₄×Q₈

yes

characteristic

C₂×C₄₃

C₄×#41

yes

—

C₂×C₄₃

C₂×#125

yes

characteristic

C₂×C₄₃

#529

yes

—

C₂×C₄₃

yes

—

—

—

—

C₄×C₄⋊C₄

—

C₄×C₄⋊C₄

—

C₄³

D₄₃

yes

characteristic

C₄₃

C₄×#125

yes

characteristic, complemented, Sylow

#125

—

C₂×C₄⋊C₄

—

C₂×C₄⋊C₄

—

C₂×C₄⋊C₄

—

C₂×C₄⋊C₄

—

C₂×C₄²

—

C₂×C₄²

C₂×D₄₃

yes

—

C₂×C₄²

C₂×D₄₃

yes

characteristic

C₂×C₄²

C₂×D₄₃

yes

—

C₂×C₄²

C₂×D₄₃

yes

characteristic

C₂×C₄²

C₂×D₄₃

yes

—

—

—

C₂²×C₄

—

100

C₂²×C₄

—

101

C₂²×C₄

C₂²×D₄₃

yes

characteristic

102

C₂²×C₄

C₂²×D₄₃

yes

—

103

C₂²×C₄

C₂²×D₄₃

yes

—

104

C₂²×C₄

C₂²×D₄₃

yes

characteristic

105

C₂²×C₄

C₂²×D₄₃

yes

characteristic

106

C₄⋊C₄

—

107

C₄⋊C₄

—

108

C₄⋊C₄

—

109

C₄⋊C₄

—

110

C₄²

—

111

C₄²

—

112

C₄²

—

113

C₄²

—

114

C₄²

Dic₈₆

yes

—

115

C₄²

C₄×D₄₃

yes

—

116

C₂³

C₂³×D₄₃

yes

characteristic

117

C₂×C₄

—

118

C₂×C₄

—

119

C₂×C₄

—

120

C₂×C₄

—

121

C₂×C₄

—

122

C₂×C₄

—

123

C₂×C₄

—

124

C₂×C₄

—

125

C₂×C₄

—

126

C₂×C₄

—

127

C₂×C₄

—

128

C₂×C₄

C₂×Dic₈₆

yes

—

129

C₂×C₄

C₂×Dic₈₆

yes

—

130

C₂×C₄

C₂×Dic₈₆

yes

—

131

C₂×C₄

C₂×C₄×D₄₃

yes

—

132

C₂×C₄

C₂×C₄×D₄₃

yes

—

133

C₂×C₄

#10621898

yes

—

134

C₂×C₄

#10621898

yes

—

135

C₂×C₄

#10621898

yes

—

136

C₂²

C₂²×C₄×D₄₃

yes

characteristic

137

C₂²

C₂²×Dic₈₆

yes

characteristic

138

C₂²

C₂×#10621898

yes

characteristic

139

C₂²

C₂×#10621898

yes

—

140

C₂²

C₂×#10621898

yes

—

141

C₄

—

142

C₄

—

143

C₄

—

144

C₄

—

145

C₄

—

172

—

146

C₄

C₄×Dic₈₆

yes

—

147

C₄

#13063317

yes

direct product factor

148

C₂

C₂×C₄×Dic₈₆

yes

characteristic

149

C₂

C₄×#10621898

yes

—

150

C₂

C₂×#13063317

yes

characteristic

151

C₂

#14583433

yes

—

152

C₂

#14583456

yes

characteristic

	subgroup	G/H
center	C₂²×C₄	C₂²×D₄₃
commutator	C₂²×C₄₃	C₂³×C₄
Frattini	C₂³	C₂³×D₄₃
Fitting	C₄³×C₄₃	C₂
socle	C₂³×C₄₃	C₂⁴
hypercenter	C₄³	D₄₃
hypocenter	C₄₃	C₄×#125
LCS	G ▷ C₂²×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₂²×C₄ ◁ C₄³

subgroup

G/H

center

C₂²×C₄

C₂²×D₄₃

commutator

C₂²×C₄₃

C₂³×C₄

Frattini

C₂³

C₂³×D₄₃

Fitting

C₄³×C₄₃

C₂

socle

C₂³×C₄₃

C₂⁴

hypercenter

C₄³

D₄₃

C₄₃

G ▷ C₂²×C₄₃ ▷ C₄₃

C₁ ◁ C₂²×C₄ ◁ C₄³

N	H ≅ G/N	type
8. #13063317	C₄	direct (N × H)
68. C₄×C₄₃	#125	semidirect
84. C₄₃	C₄×#125	semidirect
147. C₄	#13063317	direct (N × H)

H ≅ G/N

type

8. #13063317

C₄

direct (N × H)

68. C₄×C₄₃

#125

semidirect

84. C₄₃

C₄×#125

semidirect

147. C₄

#13063317

direct (N × H)

Subgroups — C₄×#13063317 #19137155

Conjugacy classes of subgroups

Complements

Subgroups — C4×#13063317 #19137155

Conjugacy classes of subgroups

Complements

Subgroups — C₄×#13063317 #19137155