Group #19137146 — subgroups

Subgroups — C₄×#13063319 #19137146

Order 5504.

516 conjugacy classes of subgroups; only the 205 normal subgroups are shown.

normal subgroups only

This group has 516 conjugacy classes of subgroups — too many to draw. Only its 205 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×#13063319	C₂	1	1	yes	maximal, characteristic
2	#14582790	C₂	1	3	yes	maximal
3	#14582783	C₂	1	3	yes	maximal, complemented
4	#14582767	C₂	1	1	yes	maximal, characteristic, complemented
5	C₄×Dic₄₃⋊C₄	C₂	1	3	yes	maximal, complemented
6	C₄×(C₂×D₄₃)⋊C₄	C₂	1	3	yes	maximal
7	C₄³×C₄₃	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂²×C₄×D₄₃	C₂²	1	1	yes	characteristic
9	#13063319	C₄	1	8	yes	direct product factor
10	C₂×Dic₄₃⋊C₄	C₂²	1	3	yes	—
11	C₂×Dic₄₃⋊C₄	C₂²	1	3	yes	—
12	C₂×(C₂×D₄₃)⋊C₄	C₂²	1	3	yes	—
13	C₂×(C₂×D₄₃)⋊C₄	C₂²	1	3	yes	—
14	C₂×C₄×Dic₄₃	C₂²	1	3	yes	—
15	C₄₃⋊#95	C₂²	1	3	yes	—
16	C₄₃⋊#95	C₂²	1	3	yes	—
17	C₄₃⋊#95	C₂²	1	3	yes	—
18	C₄₃⋊#95	C₂²	1	3	yes	—
19	C₂×C₄²×C₄₃	C₂²	1	3	yes	—
20	C₂×C₄²×C₄₃	C₂²	1	3	yes	—
21	C₂×C₄²×C₄₃	C₂²	1	1	yes	characteristic
22	C₂³×D₄₃	C₂³	1	1	yes	characteristic
23	C₂²×C₄×C₄₃	C₂³	1	3	yes	—
24	C₂²×C₄×C₄₃	C₂³	1	3	yes	—
25	C₂²×C₄×C₄₃	C₂³	1	1	yes	characteristic
26	C₂²×Dic₄₃	C₂³	1	1	yes	characteristic
27	C₂²×Dic₄₃	C₂³	1	3	yes	—
28	C₂²×Dic₄₃	C₂³	1	3	yes	—
29	C₂×C₄×D₄₃	—	2	6	no	—
30	C₄²×C₄₃	—	2	6	no	—
31	C₄²×C₄₃	—	2	6	no	—
32	C₄²×C₄₃	C₂×C₄	1	4	yes	complemented
33	(C₂×D₄₃)⋊C₄	—	2	6	no	—
34	(C₂×D₄₃)⋊C₄	C₂×C₄	1	12	yes	—
35	Dic₄₃⋊C₄	—	2	6	no	—
36	Dic₄₃⋊C₄	C₂×C₄	1	12	yes	complemented
37	C₄×Dic₄₃	—	2	6	no	—
38	C₂³×C₄₃	C₂⁴	1	1	yes	characteristic
39	C₂²×D₄₃	—	2	3	no	—
40	C₂²×D₄₃	—	2	3	no	—
41	C₂²×D₄₃	C₂²×C₄	1	2	yes	—
42	C₂×C₄×C₄₃	—	2	3	no	—
43	C₂×C₄×C₄₃	—	2	3	no	—
44	C₂×C₄×C₄₃	—	2	3	no	—
45	C₂×C₄×C₄₃	—	2	3	no	—
46	C₂×C₄×C₄₃	C₂²×C₄	1	6	yes	—
47	C₂×C₄×C₄₃	#41	1	6	yes	—
48	C₂×C₄×C₄₃	#41	1	6	yes	—
49	C₂×Dic₄₃	—	2	3	no	—
50	C₂×Dic₄₃	—	2	3	no	—
51	C₂×Dic₄₃	—	2	3	no	—
52	C₂×Dic₄₃	—	2	3	no	—
53	C₂×Dic₄₃	—	2	3	no	—
54	C₂×Dic₄₃	—	2	3	no	—
55	C₂×Dic₄₃	C₂²×C₄	1	6	yes	—
56	C₄×D₄₃	—	4	4	no	—
57	C₂²×C₄₃	C₂³×C₄	1	1	yes	characteristic
58	C₂²×C₄₃	C₂×#41	1	3	yes	—
59	C₂²×C₄₃	C₂×#41	1	3	yes	—
60	C₂×D₄₃	—	2	6	no	—
61	C₂×D₄₃	—	4	1	no	—
62	C₂×D₄₃	—	4	3	no	—
63	C₄×C₄₃	—	2	6	no	—
64	C₄×C₄₃	—	2	6	no	—
65	C₄×C₄₃	#126	1	4	yes	complemented
66	Dic₄₃	—	2	6	no	—
67	Dic₄₃	—	4	1	no	—
68	Dic₄₃	—	4	3	no	—
69	C₄×#126	—	43	1	no	maximal, Sylow
70	C₂×C₄₃	C₄×#41	1	3	yes	—
71	C₂×C₄₃	C₂×#126	1	1	yes	characteristic
72	C₂×C₄₃	#529	1	3	yes	—
73	D₄₃	—	4	2	no	—
74	C₂×#126	—	43	1	no	—
75	#388	—	43	3	no	—
76	#387	—	43	3	no	—
77	#383	—	43	1	no	—
78	C₄×C₄⋊C₄	—	43	3	no	—
79	C₄×C₂²⋊C₄	—	43	3	no	—
80	C₄³	D₄₃	1	1	yes	characteristic, complemented
81	C₄₃	C₄×#126	1	1	yes	characteristic, complemented, Sylow
82	C₂³×C₄	—	43	1	no	—
83	#126	—	43	8	no	—
84	C₂×C₄⋊C₄	—	43	3	no	—
85	C₂×C₄⋊C₄	—	43	3	no	—
86	C₂×C₂²⋊C₄	—	43	3	no	—
87	C₂×C₂²⋊C₄	—	43	3	no	—
88	C₂×C₄²	—	43	3	no	—
89	C₂×C₄²	C₂×D₄₃	1	3	yes	—
90	C₂×C₄²	C₂×D₄₃	1	3	yes	—
91	C₂×C₄²	C₂×D₄₃	1	1	yes	characteristic
92	#95	—	43	3	no	—
93	#95	—	43	3	no	—
94	#95	—	43	3	no	—
95	#95	—	43	3	no	—
96	C₂⁴	—	43	1	no	—
97	C₂²×C₄	—	43	3	no	—
98	C₂²×C₄	—	43	1	no	—
99	C₂²×C₄	—	43	3	no	—
100	C₂²×C₄	—	86	6	no	—
101	C₂²×C₄	C₂²×D₄₃	1	3	yes	—
102	C₂²×C₄	C₂²×D₄₃	1	3	yes	—
103	C₂²×C₄	C₂²×D₄₃	1	1	yes	characteristic
104	C₄⋊C₄	—	43	12	no	—
105	C₄⋊C₄	—	86	6	no	—
106	C₂²⋊C₄	—	43	12	no	—
107	C₂²⋊C₄	—	86	6	no	—
108	C₄²	—	2	6	no	—
109	C₄²	—	2	6	no	—
110	C₄²	—	86	6	no	—
111	C₄²	C₄×D₄₃	1	4	yes	complemented
112	C₂³	—	43	2	no	—
113	C₂³	—	86	3	no	—
114	C₂³	—	86	3	no	—
115	C₂³	C₂³×D₄₃	1	1	yes	characteristic
116	C₂×C₄	—	2	3	no	—
117	C₂×C₄	—	2	3	no	—
118	C₂×C₄	—	2	3	no	—
119	C₂×C₄	—	2	3	no	—
120	C₂×C₄	—	43	6	no	—
121	C₂×C₄	—	86	3	no	—
122	C₂×C₄	—	86	3	no	—
123	C₂×C₄	—	86	3	no	—
124	C₂×C₄	—	86	3	no	—
125	C₂×C₄	—	86	3	no	—
126	C₂×C₄	—	86	3	no	—
127	C₂×C₄	—	172	4	no	—
128	C₂×C₄	C₂×C₄×D₄₃	1	6	yes	—
129	C₂×C₄	#10621898	1	6	yes	—
130	C₂×C₄	#10621898	1	6	yes	—
131	C₂²	—	86	6	no	—
132	C₂²	—	172	1	no	—
133	C₂²	—	172	3	no	—
134	C₂²	C₂²×C₄×D₄₃	1	1	yes	characteristic
135	C₂²	C₂×#10621898	1	3	yes	—
136	C₂²	C₂×#10621898	1	3	yes	—
137	C₄	—	2	6	no	—
138	C₄	—	2	6	no	—
139	C₄	—	86	6	no	—
140	C₄	—	172	1	no	—
141	C₄	—	172	3	no	—
142	C₄	#13063319	1	4	yes	direct product factor
143	C₂	—	172	2	no	—
144	C₂	C₄×#10621898	1	3	yes	—
145	C₂	C₂×#13063319	1	1	yes	characteristic
146	C₂	#14583433	1	3	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×#13063319

C₂

yes

maximal, characteristic

#14582790

C₂

yes

maximal

#14582783

C₂

yes

maximal, complemented

#14582767

C₂

yes

maximal, characteristic, complemented

C₄×Dic₄₃⋊C₄

C₂

yes

maximal, complemented

C₄×(C₂×D₄₃)⋊C₄

C₂

yes

maximal

C₄³×C₄₃

C₂

yes

maximal, characteristic, complemented

C₂²×C₄×D₄₃

C₂²

yes

characteristic

#13063319

C₄

yes

direct product factor

C₂×Dic₄₃⋊C₄

C₂²

yes

—

C₂×Dic₄₃⋊C₄

C₂²

yes

—

C₂×(C₂×D₄₃)⋊C₄

C₂²

yes

—

C₂×(C₂×D₄₃)⋊C₄

C₂²

yes

—

C₂×C₄×Dic₄₃

C₂²

yes

—

C₄₃⋊#95

C₂²

yes

—

C₄₃⋊#95

C₂²

yes

—

C₄₃⋊#95

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

characteristic

C₂²×C₄×C₄₃

C₂³

yes

—

C₂²×C₄×C₄₃

C₂³

yes

—

C₂²×C₄×C₄₃

C₂³

yes

characteristic

C₂²×Dic₄₃

C₂³

yes

characteristic

C₂²×Dic₄₃

C₂³

yes

—

C₂²×Dic₄₃

C₂³

yes

—

C₂×C₄×D₄₃

—

C₄²×C₄₃

—

C₄²×C₄₃

—

C₄²×C₄₃

C₂×C₄

yes

complemented

(C₂×D₄₃)⋊C₄

—

(C₂×D₄₃)⋊C₄

C₂×C₄

yes

—

Dic₄₃⋊C₄

—

Dic₄₃⋊C₄

C₂×C₄

yes

complemented

C₄×Dic₄₃

—

C₂³×C₄₃

C₂⁴

yes

characteristic

C₂²×D₄₃

—

C₂²×D₄₃

—

C₂²×D₄₃

C₂²×C₄

yes

—

C₂×C₄×C₄₃

—

C₂×C₄×C₄₃

—

C₂×C₄×C₄₃

—

C₂×C₄×C₄₃

—

C₂×C₄×C₄₃

C₂²×C₄

yes

—

C₂×C₄×C₄₃

#41

yes

—

C₂×C₄×C₄₃

#41

yes

—

C₂×Dic₄₃

—

C₂×Dic₄₃

—

C₂×Dic₄₃

—

C₂×Dic₄₃

—

C₂×Dic₄₃

—

C₂×Dic₄₃

—

C₂×Dic₄₃

C₂²×C₄

yes

—

C₄×D₄₃

—

C₂²×C₄₃

C₂³×C₄

yes

characteristic

C₂²×C₄₃

C₂×#41

yes

—

C₂²×C₄₃

C₂×#41

yes

—

C₂×D₄₃

—

C₂×D₄₃

—

C₂×D₄₃

—

C₄×C₄₃

—

C₄×C₄₃

—

C₄×C₄₃

#126

yes

complemented

Dic₄₃

—

Dic₄₃

—

Dic₄₃

—

C₄×#126

—

maximal, Sylow

C₂×C₄₃

C₄×#41

yes

—

C₂×C₄₃

C₂×#126

yes

characteristic

C₂×C₄₃

#529

yes

—

D₄₃

—

—

—

—

—

C₄×C₄⋊C₄

—

C₄×C₂²⋊C₄

—

C₄³

D₄₃

yes

characteristic, complemented

C₄₃

C₄×#126

yes

characteristic, complemented, Sylow

C₂³×C₄

—

#126

—

C₂×C₄⋊C₄

—

C₂×C₄⋊C₄

—

C₂×C₂²⋊C₄

—

C₂×C₂²⋊C₄

—

C₂×C₄²

—

C₂×C₄²

C₂×D₄₃

yes

—

C₂×C₄²

C₂×D₄₃

yes

—

C₂×C₄²

C₂×D₄₃

yes

—

—

—

—

C₂⁴

—

C₂²×C₄

—

C₂²×C₄

—

C₂²×C₄

—

100

C₂²×C₄

—

101

C₂²×C₄

C₂²×D₄₃

yes

—

102

C₂²×C₄

C₂²×D₄₃

yes

—

103

C₂²×C₄

C₂²×D₄₃

yes

characteristic

104

C₄⋊C₄

—

105

C₄⋊C₄

—

106

C₂²⋊C₄

—

107

C₂²⋊C₄

—

108

C₄²

—

109

C₄²

—

110

C₄²

—

111

C₄²

C₄×D₄₃

yes

complemented

112

C₂³

—

113

C₂³

—

114

C₂³

—

115

C₂³

C₂³×D₄₃

yes

characteristic

116

C₂×C₄

—

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

—

172

—

128

C₂×C₄

C₂×C₄×D₄₃

yes

—

129

C₂×C₄

#10621898

yes

—

130

C₂×C₄

#10621898

yes

—

131

C₂²

—

132

C₂²

—

172

—

133

C₂²

—

172

—

134

C₂²

C₂²×C₄×D₄₃

yes

characteristic

135

C₂²

C₂×#10621898

yes

—

136

C₂²

C₂×#10621898

yes

—

137

C₄

—

138

C₄

—

139

C₄

—

140

C₄

—

172

—

141

C₄

—

172

—

142

C₄

#13063319

yes

direct product factor

143

C₂

—

172

—

144

C₂

C₄×#10621898

yes

—

145

C₂

C₂×#13063319

yes

characteristic

146

C₂

#14583433

yes

—

	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×#126
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
3. #14582783	C₂	semidirect
4. #14582767	C₂	semidirect
5. C₄×Dic₄₃⋊C₄	C₂	semidirect
7. C₄³×C₄₃	C₂	semidirect
9. #13063319	C₄	direct (N × H)
32. C₄²×C₄₃	C₂×C₄	semidirect
36. Dic₄₃⋊C₄	C₂×C₄	semidirect
65. C₄×C₄₃	#126	semidirect
80. C₄³	D₄₃	semidirect
81. C₄₃	C₄×#126	semidirect
111. C₄²	C₄×D₄₃	semidirect
142. C₄	#13063319	direct (N × H)

H ≅ G/N

type

3. #14582783

C₂

semidirect

4. #14582767

C₂

semidirect

5. C₄×Dic₄₃⋊C₄

C₂

semidirect

7. C₄³×C₄₃

C₂

semidirect

9. #13063319

C₄

direct (N × H)

32. C₄²×C₄₃

C₂×C₄

semidirect

36. Dic₄₃⋊C₄

C₂×C₄

semidirect

65. C₄×C₄₃

#126

semidirect

80. C₄³

D₄₃

semidirect

81. C₄₃

C₄×#126

semidirect

111. C₄²

C₄×D₄₃

semidirect

142. C₄

#13063319

direct (N × H)

Subgroups — C₄×#13063319 #19137146

Conjugacy classes of subgroups

Complements

Subgroups — C4×#13063319 #19137146

Conjugacy classes of subgroups

Complements

Subgroups — C₄×#13063319 #19137146