Group #19136953 — subgroups

Subgroups — #19136953

Order 5504.

780 conjugacy classes of subgroups; only the 325 normal subgroups are shown.

normal subgroups only

This group has 780 conjugacy classes of subgroups — too many to draw. Only its 325 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×C₄×C₂²⋊D₄₃	C₂	1	3	yes	maximal
2	#14582750	C₂	1	3	yes	maximal, complemented
3	C₄×C₂²⋊Dic₄₃	C₂	1	3	yes	maximal, complemented
4	#14582746	C₂	1	3	yes	maximal, complemented
5	#14582744	C₂	1	1	yes	maximal, characteristic, complemented
6	#95×D₄₃	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂×#95×C₄₃	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂²×C₂²⋊D₄₃	C₂²	1	1	yes	characteristic
9	C₂²×C₄×D₄₃	C₂²	1	3	yes	—
10	C₄×C₂²⋊D₄₃	C₄	1	24	yes	complemented
11	C₂×Dic₄₃⋊C₄	C₂²	1	3	yes	—
12	C₂×C₂²⋊Dic₄₃	C₂²	1	3	yes	—
13	C₂×(C₂×D₄₃)⋊C₄	C₂²	1	3	yes	—
14	C₂×C₄×Dic₄₃	C₂²	1	6	yes	—
15	C₂×C₄×Dic₄₃	C₂²	1	3	yes	—
16	C₄₃⋊#95	C₂²	1	3	yes	—
17	C₄₃⋊#95	C₂²	1	3	yes	—
18	C₂³×C₄×C₄₃	C₂²	1	3	yes	—
19	#95×C₄₃	C₂²	1	1	yes	characteristic
20	#95×C₄₃	C₂²	1	3	yes	—
21	C₂⁴×C₄₃	C₂³	1	1	yes	characteristic
22	C₂³×D₄₃	C₂³	1	1	yes	characteristic
23	C₂²×C₄×C₄₃	—	4	6	no	—
24	C₂²×C₄×C₄₃	C₂×C₄	1	12	yes	complemented
25	C₂²×C₄×C₄₃	C₂³	1	3	yes	—
26	C₂²×C₄×C₄₃	C₂³	1	3	yes	—
27	C₂×C₂²⋊D₄₃	C₂×C₄	1	12	yes	—
28	C₂²×Dic₄₃	C₂³	1	3	yes	—
29	C₂²×Dic₄₃	C₂³	1	3	yes	—
30	C₂²×Dic₄₃	C₂³	1	1	yes	characteristic
31	C₂×C₄×D₄₃	—	4	6	no	—
32	C₂×C₄×D₄₃	C₂×C₄	1	12	yes	complemented
33	C₂²⋊Dic₄₃	C₂×C₄	1	12	yes	complemented
34	(C₂×D₄₃)⋊C₄	C₂×C₄	1	12	yes	complemented
35	Dic₄₃⋊C₄	C₂×C₄	1	12	yes	complemented
36	C₄×Dic₄₃	—	4	6	no	—
37	C₄×Dic₄₃	C₂×C₄	1	12	yes	complemented
38	C₂³×C₄₃	—	2	3	no	—
39	C₂³×C₄₃	—	2	1	no	—
40	C₂³×C₄₃	C₂²×C₄	1	6	yes	—
41	C₂³×C₄₃	C₂⁴	1	1	yes	characteristic
42	C₂²×D₄₃	—	2	3	no	—
43	C₂²×D₄₃	—	2	1	no	—
44	C₂²×D₄₃	C₂²×C₄	1	6	yes	—
45	C₂×C₄×C₄₃	—	2	6	no	—
46	C₂×C₄×C₄₃	—	2	6	no	—
47	C₂×C₄×C₄₃	—	4	12	no	—
48	C₂×C₄×C₄₃	C₂²×C₄	1	6	yes	—
49	C₂×C₄×C₄₃	C₂²×C₄	1	6	yes	—
50	C₂²⋊D₄₃	C₄²	1	16	yes	complemented
51	C₂×Dic₄₃	—	2	3	no	—
52	C₂×Dic₄₃	—	2	6	no	—
53	C₂×Dic₄₃	—	2	3	no	—
54	C₂×Dic₄₃	C₂²×C₄	1	6	yes	—
55	C₂×Dic₄₃	C₂²×C₄	1	6	yes	—
56	C₂×Dic₄₃	C₂²×C₄	1	6	yes	—
57	C₄×D₄₃	—	4	12	no	—
58	C₂²×C₄₃	—	2	6	no	—
59	C₂²×C₄₃	—	2	6	no	—
60	C₂²×C₄₃	C₂×C₄²	1	4	yes	—
61	C₂²×C₄₃	C₂³×C₄	1	3	yes	—
62	C₂²×C₄₃	H(5,𝔽₂)	1	3	yes	—
63	C₂²×C₄₃	2₋¹⁺⁴	1	1	yes	characteristic
64	C₂×D₄₃	—	2	6	no	—
65	C₂×D₄₃	—	2	6	no	—
66	C₂×D₄₃	C₂×C₄²	1	4	yes	—
67	C₄×C₄₃	—	2	6	no	—
68	C₄×C₄₃	—	2	6	no	—
69	Dic₄₃	—	2	6	no	—
70	Dic₄₃	—	2	6	no	—
71	Dic₄₃	C₂×C₄²	1	4	yes	—
72	#2275	—	43	1	no	maximal, Sylow
73	C₂×C₄₃	—	2	4	no	—
74	C₂×C₄₃	C₂²×C₄²	1	1	yes	characteristic
75	C₂×C₄₃	#518	1	3	yes	—
76	C₂×C₄₃	#520	1	3	yes	—
77	D₄₃	—	2	4	no	—
78	C₂×C₄×D₄	—	43	3	no	—
79	C₄×C₄⋊C₄	—	43	3	no	—
80	C₄×C₂²⋊C₄	—	43	3	no	—
81	C₄×C₂²⋊C₄	—	43	3	no	—
82	#376	—	43	1	no	—
83	C₂×#95	—	43	1	no	—
84	C₂×#95	D₄₃	1	1	yes	characteristic, complemented
85	C₄₃	#2275	1	1	yes	characteristic, complemented, Sylow
86	C₂²×D₄	—	43	1	no	—
87	C₂³×C₄	—	43	3	no	—
88	C₂³×C₄	C₂×D₄₃	1	3	yes	—
89	C₄×D₄	—	43	24	no	—
90	C₂×C₄⋊C₄	—	43	3	no	—
91	C₂×C₂²⋊C₄	—	43	3	no	—
92	C₂×C₂²⋊C₄	—	43	3	no	—
93	C₂×C₄²	—	43	3	no	—
94	C₂×C₄²	—	43	6	no	—
95	#95	—	43	3	no	—
96	#95	—	43	3	no	—
97	#95	C₂×D₄₃	1	1	yes	characteristic
98	#95	C₂×D₄₃	1	3	yes	—
99	C₂⁴	—	43	1	no	—
100	C₂⁴	C₂²×D₄₃	1	1	yes	characteristic
101	C₂×D₄	—	43	12	no	—
102	C₂²×C₄	—	4	6	no	—
103	C₂²×C₄	—	43	1	no	—
104	C₂²×C₄	—	43	3	no	—
105	C₂²×C₄	—	43	3	no	—
106	C₂²×C₄	—	43	12	no	—
107	C₂²×C₄	—	172	6	no	—
108	C₂²×C₄	C₄×D₄₃	1	12	yes	complemented
109	C₂²×C₄	C₂²×D₄₃	1	3	yes	—
110	C₂²×C₄	C₂²×D₄₃	1	3	yes	—
111	C₄⋊C₄	—	43	12	no	—
112	C₂²⋊C₄	—	43	12	no	—
113	C₂²⋊C₄	—	43	12	no	—
114	C₄²	—	43	12	no	—
115	C₄²	—	172	6	no	—
116	C₂³	—	2	3	no	—
117	C₂³	—	2	1	no	—
118	C₂³	—	43	6	no	—
119	C₂³	—	86	3	no	—
120	C₂³	—	86	1	no	—
121	C₂³	C₂×C₄×D₄₃	1	6	yes	—
122	C₂³	C₂³×D₄₃	1	1	yes	characteristic
123	D₄	—	43	16	no	—
124	C₂×C₄	—	2	6	no	—
125	C₂×C₄	—	2	6	no	—
126	C₂×C₄	—	4	12	no	—
127	C₂×C₄	—	43	6	no	—
128	C₂×C₄	—	43	6	no	—
129	C₂×C₄	—	43	6	no	—
130	C₂×C₄	—	86	3	no	—
131	C₂×C₄	—	86	6	no	—
132	C₂×C₄	—	86	3	no	—
133	C₂×C₄	—	172	12	no	—
134	C₂×C₄	C₂×C₄×D₄₃	1	6	yes	—
135	C₂×C₄	C₂×C₄×D₄₃	1	6	yes	—
136	C₂²	—	2	6	no	—
137	C₂²	—	2	6	no	—
138	C₂²	—	43	4	no	—
139	C₂²	—	86	6	no	—
140	C₂²	—	86	6	no	—
141	C₂²	C₄²×D₄₃	1	4	yes	—
142	C₂²	C₂²×C₄×D₄₃	1	3	yes	—
143	C₂²	#13063370	1	3	yes	—
144	C₂²	#13063373	1	1	yes	characteristic
145	C₄	—	2	6	no	—
146	C₄	—	2	6	no	—
147	C₄	—	43	4	no	—
148	C₄	—	86	6	no	—
149	C₄	—	86	6	no	—
150	C₂	—	2	4	no	—
151	C₂	—	86	4	no	—
152	C₂	C₂×C₄²×D₄₃	1	1	yes	characteristic
153	C₂	#14583372	1	3	yes	—
154	C₂	#14583380	1	3	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×C₄×C₂²⋊D₄₃

C₂

yes

maximal

#14582750

C₂

yes

maximal, complemented

C₄×C₂²⋊Dic₄₃

C₂

yes

maximal, complemented

#14582746

C₂

yes

maximal, complemented

#14582744

C₂

yes

maximal, characteristic, complemented

#95×D₄₃

C₂

yes

maximal, characteristic, complemented

C₂×#95×C₄₃

C₂

yes

maximal, characteristic, complemented

C₂²×C₂²⋊D₄₃

C₂²

yes

characteristic

C₂²×C₄×D₄₃

C₂²

yes

—

C₄×C₂²⋊D₄₃

C₄

yes

complemented

C₂×Dic₄₃⋊C₄

C₂²

yes

—

C₂×C₂²⋊Dic₄₃

C₂²

yes

—

C₂×(C₂×D₄₃)⋊C₄

C₂²

yes

—

C₂×C₄×Dic₄₃

C₂²

yes

—

C₂×C₄×Dic₄₃

C₂²

yes

—

C₄₃⋊#95

C₂²

yes

—

C₄₃⋊#95

C₂²

yes

—

C₂³×C₄×C₄₃

C₂²

yes

—

#95×C₄₃

C₂²

yes

characteristic

#95×C₄₃

C₂²

yes

—

C₂⁴×C₄₃

C₂³

yes

characteristic

C₂³×D₄₃

C₂³

yes

characteristic

C₂²×C₄×C₄₃

—

C₂²×C₄×C₄₃

C₂×C₄

yes

complemented

C₂²×C₄×C₄₃

C₂³

yes

—

C₂²×C₄×C₄₃

C₂³

yes

—

C₂×C₂²⋊D₄₃

C₂×C₄

yes

—

C₂²×Dic₄₃

C₂³

yes

—

C₂²×Dic₄₃

C₂³

yes

—

C₂²×Dic₄₃

C₂³

yes

characteristic

C₂×C₄×D₄₃

—

C₂×C₄×D₄₃

C₂×C₄

yes

complemented

C₂²⋊Dic₄₃

C₂×C₄

yes

complemented

(C₂×D₄₃)⋊C₄

C₂×C₄

yes

complemented

Dic₄₃⋊C₄

C₂×C₄

yes

complemented

C₄×Dic₄₃

—

C₄×Dic₄₃

C₂×C₄

yes

complemented

C₂³×C₄₃

—

C₂³×C₄₃

—

C₂³×C₄₃

C₂²×C₄

yes

—

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

C₂²×C₄

yes

—

C₂×C₄×C₄₃

C₂²×C₄

yes

—

C₂²⋊D₄₃

C₄²

yes

complemented

C₂×Dic₄₃

—

C₂×Dic₄₃

—

C₂×Dic₄₃

—

C₂×Dic₄₃

C₂²×C₄

yes

—

C₂×Dic₄₃

C₂²×C₄

yes

—

C₂×Dic₄₃

C₂²×C₄

yes

—

C₄×D₄₃

—

C₂²×C₄₃

—

C₂²×C₄₃

—

C₂²×C₄₃

C₂×C₄²

yes

—

C₂²×C₄₃

C₂³×C₄

yes

—

C₂²×C₄₃

H(5,𝔽₂)

yes

—

C₂²×C₄₃

2₋¹⁺⁴

yes

characteristic

C₂×D₄₃

—

C₂×D₄₃

—

C₂×D₄₃

C₂×C₄²

yes

—

C₄×C₄₃

—

C₄×C₄₃

—

Dic₄₃

—

Dic₄₃

—

Dic₄₃

C₂×C₄²

yes

—

#2275

—

maximal, Sylow

C₂×C₄₃

—

C₂×C₄₃

C₂²×C₄²

yes

characteristic

C₂×C₄₃

#518

yes

—

C₂×C₄₃

#520

yes

—

D₄₃

—

C₂×C₄×D₄

—

C₄×C₄⋊C₄

—

C₄×C₂²⋊C₄

—

C₄×C₂²⋊C₄

—

#376

—

C₂×#95

—

C₂×#95

D₄₃

yes

characteristic, complemented

C₄₃

#2275

yes

characteristic, complemented, Sylow

C₂²×D₄

—

C₂³×C₄

—

C₂³×C₄

C₂×D₄₃

yes

—

C₄×D₄

—

C₂×C₄⋊C₄

—

C₂×C₂²⋊C₄

—

C₂×C₂²⋊C₄

—

C₂×C₄²

—

C₂×C₄²

—

#95

—

#95

—

#95

C₂×D₄₃

yes

characteristic

#95

C₂×D₄₃

yes

—

C₂⁴

—

100

C₂⁴

C₂²×D₄₃

yes

characteristic

101

C₂×D₄

—

102

C₂²×C₄

—

103

C₂²×C₄

—

104

C₂²×C₄

—

105

C₂²×C₄

—

106

C₂²×C₄

—

107

C₂²×C₄

—

172

—

108

C₂²×C₄

C₄×D₄₃

yes

complemented

109

C₂²×C₄

C₂²×D₄₃

yes

—

110

C₂²×C₄

C₂²×D₄₃

yes

—

111

C₄⋊C₄

—

112

C₂²⋊C₄

—

113

C₂²⋊C₄

—

114

C₄²

—

115

C₄²

—

172

—

116

C₂³

—

117

C₂³

—

118

C₂³

—

119

C₂³

—

120

C₂³

—

121

C₂³

C₂×C₄×D₄₃

yes

—

122

C₂³

C₂³×D₄₃

yes

characteristic

123

D₄

—

124

C₂×C₄

—

125

C₂×C₄

—

126

C₂×C₄

—

127

C₂×C₄

—

128

C₂×C₄

—

129

C₂×C₄

—

130

C₂×C₄

—

131

C₂×C₄

—

132

C₂×C₄

—

133

C₂×C₄

—

172

—

134

C₂×C₄

C₂×C₄×D₄₃

yes

—

135

C₂×C₄

C₂×C₄×D₄₃

yes

—

136

C₂²

—

137

C₂²

—

138

C₂²

—

139

C₂²

—

140

C₂²

—

141

C₂²

C₄²×D₄₃

yes

—

142

C₂²

C₂²×C₄×D₄₃

yes

—

143

C₂²

#13063370

yes

—

144

C₂²

#13063373

yes

characteristic

145

C₄

—

146

C₄

—

147

C₄

—

148

C₄

—

149

C₄

—

150

C₂

—

151

C₂

—

152

C₂

C₂×C₄²×D₄₃

yes

characteristic

153

C₂

#14583372

yes

—

154

C₂

#14583380

yes

—

	subgroup	G/H
center, Frattini	C₂³	C₂³×D₄₃
commutator	C₂×C₄₃	C₂²×C₄²
Fitting	C₂×#95×C₄₃	C₂
socle	C₂³×C₄₃	C₂⁴
hypercenter	C₂×#95	D₄₃
hypocenter	C₄₃	#2275
LCS	G ▷ C₂×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₂³ ◁ C₂×#95

subgroup

G/H

center, Frattini

C₂³

C₂³×D₄₃

commutator

C₂×C₄₃

C₂²×C₄²

Fitting

C₂×#95×C₄₃

C₂

socle

C₂³×C₄₃

C₂⁴

hypercenter

C₂×#95

D₄₃

C₄₃

G ▷ C₂×C₄₃ ▷ C₄₃

C₁ ◁ C₂³ ◁ C₂×#95

N	H ≅ G/N	type
2. #14582750	C₂	semidirect
3. C₄×C₂²⋊Dic₄₃	C₂	semidirect
4. #14582746	C₂	semidirect
5. #14582744	C₂	semidirect
6. #95×D₄₃	C₂	semidirect
7. C₂×#95×C₄₃	C₂	semidirect
10. C₄×C₂²⋊D₄₃	C₄	semidirect
24. C₂²×C₄×C₄₃	C₂×C₄	semidirect
32. C₂×C₄×D₄₃	C₂×C₄	semidirect
33. C₂²⋊Dic₄₃	C₂×C₄	semidirect
34. (C₂×D₄₃)⋊C₄	C₂×C₄	semidirect
35. Dic₄₃⋊C₄	C₂×C₄	semidirect
37. C₄×Dic₄₃	C₂×C₄	semidirect
50. C₂²⋊D₄₃	C₄²	semidirect
84. C₂×#95	D₄₃	semidirect
85. C₄₃	#2275	semidirect
108. C₂²×C₄	C₄×D₄₃	semidirect

H ≅ G/N

type

2. #14582750

C₂

semidirect

3. C₄×C₂²⋊Dic₄₃

C₂

semidirect

4. #14582746

C₂

semidirect

5. #14582744

C₂

semidirect

6. #95×D₄₃

C₂

semidirect

7. C₂×#95×C₄₃

C₂

semidirect

10. C₄×C₂²⋊D₄₃

C₄

semidirect

24. C₂²×C₄×C₄₃

C₂×C₄

semidirect

32. C₂×C₄×D₄₃

C₂×C₄

semidirect

33. C₂²⋊Dic₄₃

C₂×C₄

semidirect

34. (C₂×D₄₃)⋊C₄

C₂×C₄

semidirect

35. Dic₄₃⋊C₄

C₂×C₄

semidirect

37. C₄×Dic₄₃

C₂×C₄

semidirect

50. C₂²⋊D₄₃

C₄²

semidirect

84. C₂×#95

D₄₃

semidirect

85. C₄₃

#2275

semidirect

108. C₂²×C₄

C₄×D₄₃

semidirect

Subgroups — #19136953

Conjugacy classes of subgroups

Complements