Group #24999609 — subgroups

Subgroups — #24999609

Order 11008.

504 conjugacy classes of subgroups; only the 141 normal subgroups are shown.

normal subgroups only

This group has 504 conjugacy classes of subgroups — too many to draw. Only its 141 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	#19135543	C₂	1	2	yes	maximal
2	#19135396	C₂	1	1	yes	maximal, characteristic
3	#19132478	C₂	1	1	yes	maximal, characteristic
4	#19132436	C₂	1	2	yes	maximal
5	C₄₃×#2551	C₂	1	1	yes	maximal, characteristic
6	C₂×#13063325	C₂²	1	1	yes	characteristic
7	C₂×C₄⋊(C₄₃⋊C₈)	C₂²	1	2	yes	—
8	C₂×#13063248	—	2	2	no	—
9	C₂×C₄×C₄₃⋊C₈	C₂²	1	1	yes	characteristic
10	#14582661	—	2	2	no	—
11	#14582661	—	2	2	no	—
12	C₂×C₄⋊Q₈×C₄₃	—	2	2	no	—
13	C₄₃×#395	—	2	2	no	—
14	C₄₃×#389	—	2	2	no	—
15	C₄₃×#384	C₂²	1	1	yes	characteristic
16	C₄×C₄⋊C₄×C₄₃	C₂²	1	2	yes	—
17	C₂²×Dic₈₆	—	2	1	no	—
18	C₂²×C₄₃⋊C₈	—	2	1	no	—
19	C₂²×C₄₃⋊C₈	—	2	2	no	—
20	#13063325	—	2	2	no	—
21	#13063325	—	2	1	no	—
22	#13063325	Q₈	1	2	yes	complemented
23	C₂×C₄⋊Dic₄₃	—	2	2	no	—
24	C₄⋊(C₄₃⋊C₈)	—	2	2	no	—
25	C₄⋊(C₄₃⋊C₈)	—	2	2	no	—
26	#13063248	—	4	4	no	—
27	C₄×C₄₃⋊C₈	—	2	2	no	—
28	C₂²×Q₈×C₄₃	—	2	2	no	—
29	C₄⋊Q₈×C₄₃	—	4	4	no	—
30	C₄⋊Q₈×C₄₃	—	4	4	no	—
31	C₂×C₄⋊C₄×C₄₃	—	2	4	no	—
32	C₂×C₄⋊C₄×C₄₃	—	2	2	no	—
33	C₂×C₄⋊C₄×C₄₃	D₄	1	2	yes	—
34	C₂×C₄⋊C₄×C₄₃	D₄	1	2	yes	—
35	C₂×C₄⋊C₄×C₄₃	D₄	1	2	yes	—
36	C₂×C₄²×C₄₃	—	2	2	no	—
37	C₂×C₄²×C₄₃	C₂³	1	1	yes	characteristic
38	#95×C₄₃	—	2	2	no	—
39	#95×C₄₃	—	2	2	no	—
40	C₂×Q₈×C₄₃	—	4	8	no	—
41	C₂×Q₈×C₄₃	—	8	2	no	—
42	C₂²×C₄×C₄₃	—	2	2	no	—
43	C₂²×C₄×C₄₃	—	2	2	no	—
44	C₂²×C₄×C₄₃	—	2	2	no	—
45	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
46	C₂²×C₄×C₄₃	C₂×D₄	1	2	yes	—
47	C₂²×Dic₄₃	—	4	1	no	—
48	C₂×Dic₈₆	—	2	2	no	—
49	C₂×Dic₈₆	—	4	2	no	—
50	C₂×Dic₈₆	—	4	2	no	—
51	C₂×Dic₈₆	—	4	1	no	—
52	C₄⋊C₄×C₄₃	—	2	2	no	—
53	C₄⋊C₄×C₄₃	—	2	2	no	—
54	C₄⋊C₄×C₄₃	—	4	2	no	—
55	C₄⋊C₄×C₄₃	—	4	8	no	—
56	C₄⋊C₄×C₄₃	—	4	2	no	—
57	C₄⋊C₄×C₄₃	—	4	2	no	—
58	C₄⋊C₄×C₄₃	SD₁₆	1	4	yes	—
59	C₄⋊C₄×C₄₃	Q₁₆	1	4	yes	—
60	C₄²×C₄₃	—	4	2	no	—
61	C₄²×C₄₃	—	4	2	no	—
62	C₄²×C₄₃	C₂×Q₈	1	1	yes	characteristic
63	C₄²×C₄₃	#41	1	2	yes	—
64	C₄²×C₄₃	#41	1	1	yes	characteristic
65	C₄⋊Dic₄₃	—	2	4	no	—
66	C₄⋊Dic₄₃	—	4	2	no	—
67	C₂×C₄₃⋊C₈	—	2	2	no	—
68	C₂×C₄₃⋊C₈	—	4	1	no	—
69	C₂×C₄₃⋊C₈	—	4	1	no	—
70	C₂×C₄₃⋊C₈	—	4	2	no	—
71	C₂×C₄₃⋊C₈	—	4	2	no	—
72	C₂×C₄₃⋊C₈	—	4	2	no	—
73	C₂³×C₄₃	#120	1	1	yes	characteristic
74	Q₈×C₄₃	—	8	8	no	—
75	C₂×C₄×C₄₃	—	2	1	no	—
76	C₂×C₄×C₄₃	—	2	1	no	—
77	C₂×C₄×C₄₃	—	2	4	no	—
78	C₂×C₄×C₄₃	—	2	4	no	—
79	C₂×C₄×C₄₃	—	4	2	no	—
80	C₂×C₄×C₄₃	—	4	2	no	—
81	C₂×C₄×C₄₃	—	4	2	no	—
82	C₂×C₄×C₄₃	—	4	2	no	—
83	C₂×C₄×C₄₃	—	4	4	no	—
84	C₂×C₄×C₄₃	—	4	2	no	—
85	C₂×C₄×C₄₃	C₂²⋊Q₈	1	1	yes	characteristic
86	C₂×C₄×C₄₃	C₂²⋊Q₈	1	2	yes	—
87	C₂×C₄×C₄₃	#124	1	1	yes	characteristic
88	C₂×C₄×C₄₃	#124	1	2	yes	—
89	C₂×C₄×C₄₃	C₂×SD₁₆	1	2	yes	—
90	C₂×C₄×C₄₃	C₂×Q₁₆	1	2	yes	—
91	C₂×C₄×C₄₃	AGL(1,ℤ/8)	1	2	yes	—
92	C₂×C₄×C₄₃	#137	1	2	yes	—
93	C₂×Dic₄₃	—	4	2	no	—
94	C₂×Dic₄₃	—	8	1	no	—
95	C₂×Dic₄₃	—	8	1	no	—
96	Dic₈₆	—	4	4	no	—
97	Dic₈₆	—	8	2	no	—
98	C₄₃⋊C₈	—	4	2	no	—
99	C₄₃⋊C₈	—	8	2	no	—
100	#10349	—	43	1	no	maximal, Sylow
101	C₂²×C₄₃	#393	1	1	yes	characteristic
102	C₂²×C₄₃	#450	1	2	yes	—
103	C₂²×C₄₃	#451	1	2	yes	—
104	C₂²×C₄₃	#453	1	1	yes	characteristic
105	C₂²×C₄₃	#454	1	1	yes	characteristic
106	C₄×C₄₃	—	2	1	no	—
107	C₄×C₄₃	—	2	1	no	—
108	C₄×C₄₃	—	4	4	no	—
109	C₄×C₄₃	—	4	4	no	—
110	C₄×C₄₃	—	8	2	no	—
111	C₄×C₄₃	#475	1	2	yes	—
112	C₄×C₄₃	#477	1	2	yes	—
113	C₄×C₄₃	#487	1	2	yes	—
114	C₄×C₄₃	#489	1	2	yes	—
115	Dic₄₃	—	8	2	no	—
116	#2551	D₄₃	1	1	yes	characteristic
117	#1987	—	43	2	no	—
118	#1956	—	43	1	no	—
119	#1296	—	43	1	no	—
120	#1279	—	43	2	no	—
121	C₂×C₄₃	#1629	1	1	yes	characteristic
122	C₂×C₄₃	#1633	1	1	yes	characteristic
123	C₂×C₄₃	#1637	1	2	yes	—
124	C₂×C₄₃	#2024	1	2	yes	—
125	C₂×C₄₃	#2027	1	1	yes	characteristic
126	C₂×C₄⋊Q₈	—	2	2	no	—
127	C₂×C₄⋊Q₈	—	43	1	no	—
128	C₂×C₄⋊C₈	—	43	2	no	—
129	C₂×#103	—	86	2	no	—
130	C₂×C₄×C₈	—	43	1	no	—
131	#395	—	2	2	no	—
132	#389	—	2	2	no	—
133	#384	C₂×D₄₃	1	1	yes	characteristic
134	C₄×C₄⋊C₄	C₂×D₄₃	1	2	yes	—
135	#340	—	86	2	no	—
136	#340	—	86	2	no	—
137	C₄₃	#10349	1	1	yes	characteristic, complemented, Sylow
138	C₂²×Q₈	—	2	2	no	—
139	C₂²×Q₈	—	86	1	no	—
140	C₂²×C₈	—	86	1	no	—
141	C₂²×C₈	—	86	2	no	—
142	C₄⋊Q₈	—	4	4	no	—
143	C₄⋊Q₈	—	4	4	no	—
144	C₄⋊Q₈	—	43	2	no	—
145	C₄⋊Q₈	—	86	2	no	—
146	C₄⋊Q₈	—	86	1	no	—
147	C₂×C₄⋊C₄	—	2	4	no	—
148	C₂×C₄⋊C₄	—	2	2	no	—
149	C₂×C₄⋊C₄	—	86	2	no	—
150	C₂×C₄⋊C₄	C₂²⋊D₄₃	1	2	yes	—
151	C₂×C₄⋊C₄	C₂²⋊D₄₃	1	2	yes	—
152	C₂×C₄⋊C₄	C₂²⋊D₄₃	1	2	yes	—
153	C₂×C₄²	—	2	2	no	—
154	C₂×C₄²	C₂²×D₄₃	1	1	yes	characteristic
155	C₄⋊C₈	—	86	2	no	—
156	C₄⋊C₈	—	86	2	no	—
157	#103	—	172	4	no	—
158	C₄×C₈	—	86	2	no	—
159	#95	—	2	2	no	—
160	#95	—	2	2	no	—
161	C₂×Q₈	—	4	8	no	—
162	C₂×Q₈	—	8	2	no	—
163	C₂×Q₈	—	86	2	no	—
164	C₂×Q₈	—	172	2	no	—
165	C₂×Q₈	—	172	2	no	—
166	C₂×Q₈	—	172	1	no	—
167	C₂²×C₄	—	2	2	no	—
168	C₂²×C₄	—	2	2	no	—
169	C₂²×C₄	—	2	2	no	—
170	C₂²×C₄	—	172	1	no	—
171	C₂²×C₄	C₂×C₂²⋊D₄₃	1	1	yes	characteristic
172	C₂²×C₄	C₂×C₂²⋊D₄₃	1	2	yes	—
173	C₂×C₈	—	86	2	no	—
174	C₂×C₈	—	172	2	no	—
175	C₂×C₈	—	172	2	no	—
176	C₂×C₈	—	172	2	no	—
177	C₂×C₈	—	172	1	no	—
178	C₂×C₈	—	172	1	no	—
179	C₄⋊C₄	—	2	2	no	—
180	C₄⋊C₄	—	2	2	no	—
181	C₄⋊C₄	—	4	2	no	—
182	C₄⋊C₄	—	4	8	no	—
183	C₄⋊C₄	—	4	2	no	—
184	C₄⋊C₄	—	4	2	no	—
185	C₄⋊C₄	—	86	4	no	—
186	C₄⋊C₄	—	172	2	no	—
187	C₄⋊C₄	#10621883	1	4	yes	—
188	C₄⋊C₄	#10621885	1	4	yes	—
189	C₄²	—	4	2	no	—
190	C₄²	—	4	2	no	—
191	C₄²	Q₈×D₄₃	1	1	yes	characteristic
192	C₄²	#10621902	1	2	yes	—
193	C₄²	#10621902	1	1	yes	characteristic
194	C₂³	#13063294	1	1	yes	characteristic
195	Q₈	—	8	8	no	—
196	Q₈	—	344	2	no	—
197	Q₈	—	172	4	no	—
198	C₂×C₄	—	2	1	no	—
199	C₂×C₄	—	2	1	no	—
200	C₂×C₄	—	2	4	no	—
201	C₂×C₄	—	2	4	no	—
202	C₂×C₄	—	4	2	no	—
203	C₂×C₄	—	4	2	no	—
204	C₂×C₄	—	4	2	no	—
205	C₂×C₄	—	4	2	no	—
206	C₂×C₄	—	4	4	no	—
207	C₂×C₄	—	4	2	no	—
208	C₂×C₄	—	344	1	no	—
209	C₂×C₄	—	344	1	no	—
210	C₂×C₄	—	172	2	no	—
211	C₂×C₄	#13063301	1	1	yes	characteristic
212	C₂×C₄	#13063301	1	2	yes	—
213	C₂×C₄	#13063314	1	1	yes	characteristic
214	C₂×C₄	#13063314	1	2	yes	—
215	C₂×C₄	C₂×#10621883	1	2	yes	—
216	C₂×C₄	C₂×#10621885	1	2	yes	—
217	C₂×C₄	#13063351	1	2	yes	—
218	C₂×C₄	#13063356	1	2	yes	—
219	C₈	—	344	2	no	—
220	C₈	—	172	2	no	—
221	C₂²	#14582810	1	1	yes	characteristic
222	C₂²	#14583050	1	2	yes	—
223	C₂²	#14583055	1	2	yes	—
224	C₂²	#14583067	1	1	yes	characteristic
225	C₂²	#14583072	1	1	yes	characteristic
226	C₄	—	2	1	no	—
227	C₄	—	2	1	no	—
228	C₄	—	4	4	no	—
229	C₄	—	4	4	no	—
230	C₄	—	8	2	no	—
231	C₄	—	344	2	no	—
232	C₄	#14583181	1	2	yes	—
233	C₄	#14583191	1	2	yes	—
234	C₄	#14583251	1	2	yes	—
235	C₄	#14583261	1	2	yes	—
236	C₂	#19133711	1	1	yes	characteristic
237	C₂	#19133735	1	1	yes	characteristic
238	C₂	#19133760	1	2	yes	—
239	C₂	#19135733	1	2	yes	—
240	C₂	#19135748	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#19135543

C₂

yes

maximal

#19135396

C₂

yes

maximal, characteristic

#19132478

C₂

yes

maximal, characteristic

#19132436

C₂

yes

maximal

C₄₃×#2551

C₂

yes

maximal, characteristic

C₂×#13063325

C₂²

yes

characteristic

C₂×C₄⋊(C₄₃⋊C₈)

C₂²

yes

—

C₂×#13063248

—

C₂×C₄×C₄₃⋊C₈

C₂²

yes

characteristic

#14582661

—

#14582661

—

C₂×C₄⋊Q₈×C₄₃

—

C₄₃×#395

—

C₄₃×#389

—

C₄₃×#384

C₂²

yes

characteristic

C₄×C₄⋊C₄×C₄₃

C₂²

yes

—

C₂²×Dic₈₆

—

C₂²×C₄₃⋊C₈

—

C₂²×C₄₃⋊C₈

—

#13063325

—

#13063325

—

#13063325

Q₈

yes

complemented

C₂×C₄⋊Dic₄₃

—

C₄⋊(C₄₃⋊C₈)

—

C₄⋊(C₄₃⋊C₈)

—

#13063248

—

C₄×C₄₃⋊C₈

—

C₂²×Q₈×C₄₃

—

C₄⋊Q₈×C₄₃

—

C₄⋊Q₈×C₄₃

—

C₂×C₄⋊C₄×C₄₃

—

C₂×C₄⋊C₄×C₄₃

—

C₂×C₄⋊C₄×C₄₃

D₄

yes

—

C₂×C₄⋊C₄×C₄₃

D₄

yes

—

C₂×C₄⋊C₄×C₄₃

D₄

yes

—

C₂×C₄²×C₄₃

—

C₂×C₄²×C₄₃

C₂³

yes

characteristic

#95×C₄₃

—

#95×C₄₃

—

C₂×Q₈×C₄₃

—

C₂×Q₈×C₄₃

—

C₂²×C₄×C₄₃

—

C₂²×C₄×C₄₃

—

C₂²×C₄×C₄₃

—

C₂²×C₄×C₄₃

C₂×D₄

yes

characteristic

C₂²×C₄×C₄₃

C₂×D₄

yes

—

C₂²×Dic₄₃

—

C₂×Dic₈₆

—

C₂×Dic₈₆

—

C₂×Dic₈₆

—

C₂×Dic₈₆

—

C₄⋊C₄×C₄₃

—

C₄⋊C₄×C₄₃

—

C₄⋊C₄×C₄₃

—

C₄⋊C₄×C₄₃

—

C₄⋊C₄×C₄₃

—

C₄⋊C₄×C₄₃

—

C₄⋊C₄×C₄₃

SD₁₆

yes

—

C₄⋊C₄×C₄₃

Q₁₆

yes

—

C₄²×C₄₃

—

C₄²×C₄₃

—

C₄²×C₄₃

C₂×Q₈

yes

characteristic

C₄²×C₄₃

#41

yes

—

C₄²×C₄₃

#41

yes

characteristic

C₄⋊Dic₄₃

—

C₄⋊Dic₄₃

—

C₂×C₄₃⋊C₈

—

C₂×C₄₃⋊C₈

—

C₂×C₄₃⋊C₈

—

C₂×C₄₃⋊C₈

—

C₂×C₄₃⋊C₈

—

C₂×C₄₃⋊C₈

—

C₂³×C₄₃

#120

yes

characteristic

Q₈×C₄₃

—

C₂×C₄×C₄₃

—

C₂×C₄×C₄₃

—

C₂×C₄×C₄₃

—

C₂×C₄×C₄₃

—

C₂×C₄×C₄₃

—

C₂×C₄×C₄₃

—

C₂×C₄×C₄₃

—

C₂×C₄×C₄₃

—

C₂×C₄×C₄₃

—

C₂×C₄×C₄₃

—

C₂×C₄×C₄₃

C₂²⋊Q₈

yes

characteristic

C₂×C₄×C₄₃

C₂²⋊Q₈

yes

—

C₂×C₄×C₄₃

#124

yes

characteristic

C₂×C₄×C₄₃

#124

yes

—

C₂×C₄×C₄₃

C₂×SD₁₆

yes

—

C₂×C₄×C₄₃

C₂×Q₁₆

yes

—

C₂×C₄×C₄₃

AGL(1,ℤ/8)

yes

—

C₂×C₄×C₄₃

#137

yes

—

C₂×Dic₄₃

—

C₂×Dic₄₃

—

C₂×Dic₄₃

—

Dic₈₆

—

Dic₈₆

—

C₄₃⋊C₈

—

C₄₃⋊C₈

—

100

#10349

—

maximal, Sylow

101

C₂²×C₄₃

#393

yes

characteristic

102

C₂²×C₄₃

#450

yes

—

103

C₂²×C₄₃

#451

yes

—

104

C₂²×C₄₃

#453

yes

characteristic

105

C₂²×C₄₃

#454

yes

characteristic

106

C₄×C₄₃

—

107

C₄×C₄₃

—

108

C₄×C₄₃

—

109

C₄×C₄₃

—

110

C₄×C₄₃

—

111

C₄×C₄₃

#475

yes

—

112

C₄×C₄₃

#477

yes

—

113

C₄×C₄₃

#487

yes

—

114

C₄×C₄₃

#489

yes

—

115

Dic₄₃

—

116

#2551

D₄₃

yes

characteristic

117

#1987

—

118

#1956

—

119

#1296

—

120

#1279

—

121

C₂×C₄₃

#1629

yes

characteristic

122

C₂×C₄₃

#1633

yes

characteristic

123

C₂×C₄₃

#1637

yes

—

124

C₂×C₄₃

#2024

yes

—

125

C₂×C₄₃

#2027

yes

characteristic

126

C₂×C₄⋊Q₈

—

127

C₂×C₄⋊Q₈

—

128

C₂×C₄⋊C₈

—

129

C₂×#103

—

130

C₂×C₄×C₈

—

131

#395

—

132

#389

—

133

#384

C₂×D₄₃

yes

characteristic

134

C₄×C₄⋊C₄

C₂×D₄₃

yes

—

135

#340

—

136

#340

—

137

C₄₃

#10349

yes

characteristic, complemented, Sylow

138

C₂²×Q₈

—

139

C₂²×Q₈

—

140

C₂²×C₈

—

141

C₂²×C₈

—

142

C₄⋊Q₈

—

143

C₄⋊Q₈

—

144

C₄⋊Q₈

—

145

C₄⋊Q₈

—

146

C₄⋊Q₈

—

147

C₂×C₄⋊C₄

—

148

C₂×C₄⋊C₄

—

149

C₂×C₄⋊C₄

—

150

C₂×C₄⋊C₄

C₂²⋊D₄₃

yes

—

151

C₂×C₄⋊C₄

C₂²⋊D₄₃

yes

—

152

C₂×C₄⋊C₄

C₂²⋊D₄₃

yes

—

153

C₂×C₄²

—

154

C₂×C₄²

C₂²×D₄₃

yes

characteristic

155

C₄⋊C₈

—

156

C₄⋊C₈

—

157

#103

—

172

—

158

C₄×C₈

—

159

#95

—

160

#95

—

161

C₂×Q₈

—

162

C₂×Q₈

—

163

C₂×Q₈

—

164

C₂×Q₈

—

172

—

165

C₂×Q₈

—

172

—

166

C₂×Q₈

—

172

—

167

C₂²×C₄

—

168

C₂²×C₄

—

169

C₂²×C₄

—

170

C₂²×C₄

—

172

—

171

C₂²×C₄

C₂×C₂²⋊D₄₃

yes

characteristic

172

C₂²×C₄

C₂×C₂²⋊D₄₃

yes

—

173

C₂×C₈

—

174

C₂×C₈

—

172

—

175

C₂×C₈

—

172

—

176

C₂×C₈

—

172

—

177

C₂×C₈

—

172

—

178

C₂×C₈

—

172

—

179

C₄⋊C₄

—

180

C₄⋊C₄

—

181

C₄⋊C₄

—

182

C₄⋊C₄

—

183

C₄⋊C₄

—

184

C₄⋊C₄

—

185

C₄⋊C₄

—

186

C₄⋊C₄

—

172

—

187

C₄⋊C₄

#10621883

yes

—

188

C₄⋊C₄

#10621885

yes

—

189

C₄²

—

190

C₄²

—

191

C₄²

Q₈×D₄₃

yes

characteristic

192

C₄²

#10621902

yes

—

193

C₄²

#10621902

yes

characteristic

194

C₂³

#13063294

yes

characteristic

195

Q₈

—

196

Q₈

—

344

—

197

Q₈

—

172

—

198

C₂×C₄

—

199

C₂×C₄

—

200

C₂×C₄

—

201

C₂×C₄

—

202

C₂×C₄

—

203

C₂×C₄

—

204

C₂×C₄

—

205

C₂×C₄

—

206

C₂×C₄

—

207

C₂×C₄

—

208

C₂×C₄

—

344

—

209

C₂×C₄

—

344

—

210

C₂×C₄

—

172

—

211

C₂×C₄

#13063301

yes

characteristic

212

C₂×C₄

#13063301

yes

—

213

C₂×C₄

#13063314

yes

characteristic

214

C₂×C₄

#13063314

yes

—

215

C₂×C₄

C₂×#10621883

yes

—

216

C₂×C₄

C₂×#10621885

yes

—

217

C₂×C₄

#13063351

yes

—

218

C₂×C₄

#13063356

yes

—

219

C₈

—

344

—

220

C₈

—

172

—

221

C₂²

#14582810

yes

characteristic

222

C₂²

#14583050

yes

—

223

C₂²

#14583055

yes

—

224

C₂²

#14583067

yes

characteristic

225

C₂²

#14583072

yes

characteristic

226

C₄

—

227

C₄

—

228

C₄

—

229

C₄

—

230

C₄

—

231

C₄

—

344

—

232

C₄

#14583181

yes

—

233

C₄

#14583191

yes

—

234

C₄

#14583251

yes

—

235

C₄

#14583261

yes

—

236

C₂

#19133711

yes

characteristic

237

C₂

#19133735

yes

characteristic

238

C₂

#19133760

yes

—

239

C₂

#19135733

yes

—

240

C₂

#19135748

yes

characteristic

	subgroup	G/H
center	C₂³	#13063294
commutator, cosocle	C₂×C₄²×C₄₃	C₂³
Frattini	C₂×C₄²	C₂²×D₄₃
Fitting	C₄₃×#2551	C₂
socle, prime radical	C₂³×C₄₃	#120
hypercenter	#2551	D₄₃
hypocenter	C₄₃	#10349
LCS	G ▷ C₂×C₄²×C₄₃ ▷ C₂²×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₂³ ◁ C₂×C₄² ◁ #2551

subgroup

G/H

center

C₂³

#13063294

commutator, cosocle

C₂×C₄²×C₄₃

C₂³

Frattini

C₂×C₄²

C₂²×D₄₃

Fitting

C₄₃×#2551

C₂

C₂³×C₄₃

D₄₃

C₄₃

G ▷ C₂×C₄²×C₄₃ ▷ C₂²×C₄₃ ▷ C₄₃

UCS

C₁ ◁ C₂³ ◁ C₂×C₄² ◁ #2551

N	H ≅ G/N	type
22. #13063325	Q₈	semidirect
137. C₄₃	#10349	semidirect

H ≅ G/N

type

22. #13063325

Q₈

semidirect

137. C₄₃

#10349

semidirect

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
#19135543	2
#19135396	2
#19132478	2
#19132436	2
C₄₃×#2551	2
#10349	43

subgroup

index

C₄₃×#2551

Subgroups — #24999609

Conjugacy classes of subgroups

Complements

Maximal subgroups