Finite Group Databasebeta

← #19144520

Subgroups — #19144520

Order 5504.

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

normal subgroups only

This group has 458 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.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#14583410C211yesmaximal, characteristic
2C22×C4⋊Dic43C211yesmaximal, characteristic, complemented
3#14583235C212yesmaximal, complemented
4#14583230C212yesmaximal, complemented
5#14583218C212yesmaximal, complemented
6#14583213C212yesmaximal, complemented
7#14582941C212yesmaximal, complemented
8#14582901C212yesmaximal, complemented
9C43×#407C211yesmaximal, characteristic, complemented
10C2×#10621898C2211yescharacteristic
11C23×Dic43—21no—
12#13063308—21no—
13#13063304C2211yescharacteristic
14#13063304C2211yescharacteristic
15#13063299C2211yescharacteristic
16#13063299C2211yescharacteristic
17#13063294—21no—
18C4×C22⋊D43—21no—
19C4×C22⋊D43—21no—
20#13063284C2211yescharacteristic
21C2×C4⋊Dic43—21no—
22C2×C4⋊Dic43—21no—
23C2×C4⋊Dic43—21no—
24C2×C4⋊Dic43C2212yes—
25C2×C4⋊Dic43C2212yes—
26C2×C4⋊Dic43C2212yes—
27#13063259C2214yescomplemented
28#13063257C2214yescomplemented
29#13063250C2214yescomplemented
30#13063247C2214yescomplemented
31C23×C4×C43C2211yescharacteristic
32C2×M16×C43C2212yes—
33C22⋊C8×C43C2212yes—
34C22⋊C8×C43C2212yes—
35C24×C43D411yescharacteristic
36C22×C4×C43—24no—
37C22×C4×C43D411yescharacteristic
38C22×C4×C43D411yescharacteristic
39C22×C4×C43D411yescharacteristic
40C22×C4×C43C2311yescharacteristic
41C22×C4×C43C2311yescharacteristic
42C22×C4×C43C2311yescharacteristic
43C2×C22⋊D43—21no—
44C2×C22⋊D43—21no—
45C2×C22⋊D43—21no—
46C22×Dic43—22no—
47C22×Dic43—22no—
48C22×Dic43—22no—
49C22×Dic43—44no—
50#10621898—24no—
51C2×D172C2311yescharacteristic
52C2×C4×D43—21no—
53C2×Dic86C2311yescharacteristic
54M16×C43—24no—
55C2×C8×C43C2314yes—
56C22⋊Dic43—21no—
57C22⋊Dic43—21no—
58C22⋊Dic43—21no—
59(C2×D43)⋊C4—21no—
60(C2×D43)⋊C4—21no—
61C4⋊Dic43—22no—
62C4⋊Dic43—22no—
63C4⋊Dic43—22no—
64C4⋊Dic43C2314yes—
65C4⋊Dic43C2311yescharacteristic
66C4⋊Dic43C2311yescharacteristic
67Dic43⋊C4—21no—
68Dic43⋊C4—21no—
69C4×Dic43—21no—
70C23×C43—22no—
71C23×C43—22no—
72C23×C43—22no—
73C23×C43C2×D411yescharacteristic
74C23×C43C2×D411yescharacteristic
75C23×C43C2×D411yescharacteristic
76C22×D43—21no—
77C2×C4×C43—22no—
78C2×C4×C43—22no—
79C2×C4×C43—22no—
80C2×C4×C43—22no—
81C2×C4×C43—22no—
82C2×C4×C43C2×D411yescharacteristic
83C2×C4×C43C2×D411yescharacteristic
84C2×C4×C43C2×D411yescharacteristic
85C2×C4×C43#4114yes—
86C2×C4×C43C2411yescharacteristic
87C22⋊D43—42no—
88C22⋊D43—42no—
89C22⋊D43—42no—
90C2×Dic43—21no—
91C2×Dic43—21no—
92C2×Dic43—21no—
93C2×Dic43—24no—
94C2×Dic43—44no—
95C2×Dic43—44no—
96C2×Dic43—44no—
97D172—22no—
98C4×D43—42no—
99Dic86—22no—
100C8×C43—24no—
101C22×C43—28no—
102C22×C43—21no—
103C22×C43—21no—
104C22×C43—21no—
105C22×C43—21no—
106C22×C43—21no—
107C22×C43—21no—
108C22×C43#12312yes—
109C22×C43AGL(1,ℤ/8)12yes—
110C22×C43#13712yes—
111C22×C43C22×D411yescharacteristic
112C2×D43—41no—
113C2×D43—41no—
114C2×D43—41no—
115C4×C43—21no—
116C4×C43—21no—
117C4×C43#12312yes—
118C4×C43C2×#4112yes—
119Dic43—41no—
120Dic43—44no—
121Dic43—41no—
122Dic43—41no—
123#3092—431nomaximal, Sylow
124C2×C43—22no—
125C2×C43—22no—
126C2×C43—22no—
127C2×C43C2×#12311yescharacteristic
128C2×C43C2×AGL(1,ℤ/8)11yescharacteristic
129C2×C43C2×#13711yescharacteristic
130D43—81no—
131#525—431no—
132C22×C4⋊C4—431no—
133#484—432no—
134#483—432no—
135#481—432no—
136#480—432no—
137#428—432no—
138#417—432no—
139#407D4311yescharacteristic, complemented
140C43#309211yescharacteristic, complemented, Sylow
141C2×#41—431no—
142C23×C4—861no—
143C23×C4C2×D4311yescharacteristic
144C2×M16C2×D4312yes—
145#123—861no—
146C22⋊Q8—431no—
147C22⋊Q8—431no—
148#121—431no—
149#121—431no—
150#120—861no—
151C4×D4—861no—
152C4×D4—861no—
153#117—431no—
154C2×C4⋊C4—432no—
155C2×C4⋊C4—432no—
156C2×C4⋊C4—432no—
157C2×C4⋊C4—861no—
158C2×C4⋊C4—861no—
159C2×C4⋊C4—861no—
160#107—434no—
161#106—434no—
162#103—434no—
163#102—434no—
164C22⋊C8C2×D4312yes—
165C22⋊C8C2×D4312yes—
166C24D17211yescharacteristic
167#41—864no—
168C2×Q8—431no—
169C2×D4—431no—
170C2×D4—861no—
171C2×D4—861no—
172C2×D4—861no—
173C22×C4—24no—
174C22×C4—862no—
175C22×C4—862no—
176C22×C4—862no—
177C22×C4—861no—
178C22×C4—1724no—
179C22×C4D17211yescharacteristic
180C22×C4D17211yescharacteristic
181C22×C4D17211yescharacteristic
182C22×C4C22×D4311yescharacteristic
183C22×C4C22×D4311yescharacteristic
184C22×C4C22×D4311yescharacteristic
185M16—24no—
186C2×C8C22×D4314yes—
187C4⋊C4—434no—
188C4⋊C4—431no—
189C4⋊C4—431no—
190C4⋊C4—862no—
191C4⋊C4—862no—
192C4⋊C4—862no—
193C4⋊C4—861no—
194C4⋊C4—861no—
195C22⋊C4—861no—
196C22⋊C4—861no—
197C22⋊C4—861no—
198C22⋊C4—861no—
199C22⋊C4—861no—
200C42—861no—
201C23—22no—
202C23—22no—
203C23—22no—
204C23—861no—
205C23C2×D17211yescharacteristic
206C23C2×D17211yescharacteristic
207C23C2×D17211yescharacteristic
208Q8—862no—
209D4—862no—
210D4—1722no—
211D4—1722no—
212D4—1722no—
213C2×C4—22no—
214C2×C4—22no—
215C2×C4—22no—
216C2×C4—22no—
217C2×C4—22no—
218C2×C4—861no—
219C2×C4—861no—
220C2×C4—861no—
221C2×C4—864no—
222C2×C4—1724no—
223C2×C4—1724no—
224C2×C4—1724no—
225C2×C4—1722no—
226C2×C4C2×D17211yescharacteristic
227C2×C4C2×D17211yescharacteristic
228C2×C4C2×D17211yescharacteristic
229C2×C4#1062190014yes—
230C2×C4C23×D4311yescharacteristic
231C8—24no—
232C22—28no—
233C22—21no—
234C22—21no—
235C22—21no—
236C22—21no—
237C22—21no—
238C22—21no—
239C22—1721no—
240C22—1721no—
241C22—1721no—
242C22#1306330912yes—
243C22#1306335312yes—
244C22#1306335812yes—
245C22C22×D17211yescharacteristic
246C4—21no—
247C4—21no—
248C4—1721no—
249C4—1724no—
250C4—1721no—
251C4—1721no—
252C4#1306330912yes—
253C4C2×#1062190012yes—
254C2—22no—
255C2—22no—
256C2—22no—
257C2—3441no—
258C2C2×#1306330911yescharacteristic
259C2C2×#1306335311yescharacteristic
260C2C2×#1306335811yescharacteristic
subgroupG/H
centerC22C22×D172
commutatorC2×C4×C43C24
FrattiniC2×C4C23×D43
FittingC43×#407C2
socleC22×C43C22×D4
hypercenter#407D43
hypocenterC43#3092
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C23×C4 ◁ #407

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
2. C22×C4⋊Dic43C2semidirect
3. #14583235C2semidirect
4. #14583230C2semidirect
5. #14583218C2semidirect
6. #14583213C2semidirect
7. #14582941C2semidirect
8. #14582901C2semidirect
9. C43×#407C2semidirect
27. #13063259C22semidirect
28. #13063257C22semidirect
29. #13063250C22semidirect
30. #13063247C22semidirect
139. #407D43semidirect
140. C43#3092semidirect