Finite Group Databasebeta

← #19144518

Subgroups — #19144518

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
2#14583234C212yesmaximal, complemented
3#14583229C212yesmaximal, complemented
4#14583217C212yesmaximal, complemented
5#14583212C212yesmaximal, complemented
6#14582939C212yesmaximal, complemented
7#14582898C212yesmaximal, complemented
8#14582863C211yesmaximal, characteristic, complemented
9C22×C4⋊C4×C43C211yesmaximal, characteristic, complemented
10C2×#10621898C2211yescharacteristic
11C2×#10621877C2212yes—
12#13063308—21no—
13#13063304C2211yescharacteristic
14#13063304C2211yescharacteristic
15#13063299C2211yescharacteristic
16#13063299C2211yescharacteristic
17#13063294—21no—
18C4×C22⋊D43—21no—
19C4×C22⋊D43—21no—
20#13063284C2211yescharacteristic
21#13063258C2214yescomplemented
22#13063256C2214yescomplemented
23#13063248C2214yescomplemented
24#13063245C2214yescomplemented
25C22⋊(C43⋊C8)C2212yes—
26C22⋊(C43⋊C8)C2212yes—
27C23×C4×C43—21no—
28C23×C4×C43C2211yescharacteristic
29C2×C4⋊C4×C43—21no—
30C2×C4⋊C4×C43—21no—
31C2×C4⋊C4×C43—21no—
32C2×C4⋊C4×C43C2212yes—
33C2×C4⋊C4×C43C2212yes—
34C2×C4⋊C4×C43C2212yes—
35C24×C43D411yescharacteristic
36C22×C4×C43—24no—
37C22×C4×C43—22no—
38C22×C4×C43—22no—
39C22×C4×C43—22no—
40C22×C4×C43—44no—
41C22×C4×C43D411yescharacteristic
42C22×C4×C43D411yescharacteristic
43C22×C4×C43D411yescharacteristic
44C22×C4×C43C2311yescharacteristic
45C22×C4×C43C2311yescharacteristic
46C22×C4×C43C2311yescharacteristic
47C2×C22⋊D43—21no—
48C2×C22⋊D43—21no—
49C2×C22⋊D43—21no—
50#10621898—24no—
51C2×D172C2311yescharacteristic
52C2×C4×D43—21no—
53C2×Dic86C2311yescharacteristic
54C4⋊C4×C43—22no—
55C4⋊C4×C43—22no—
56C4⋊C4×C43—22no—
57C4⋊C4×C43C2314yes—
58C22⋊Dic43—21no—
59C22⋊Dic43—21no—
60C22⋊Dic43—21no—
61(C2×D43)⋊C4—21no—
62(C2×D43)⋊C4—21no—
63C4⋊Dic43C2311yescharacteristic
64C4⋊Dic43C2311yescharacteristic
65Dic43⋊C4—21no—
66Dic43⋊C4—21no—
67C4×Dic43—21no—
68#10621877—24no—
69C2×C43⋊C8C2314yes—
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×C43—24no—
83C2×C4×C43—44no—
84C2×C4×C43—44no—
85C2×C4×C43—44no—
86C2×C4×C43C2×D411yescharacteristic
87C2×C4×C43C2×D411yescharacteristic
88C2×C4×C43C2×D411yescharacteristic
89C2×C4×C43#4114yes—
90C2×C4×C43C2411yescharacteristic
91C22⋊D43—42no—
92C22⋊D43—42no—
93C22⋊D43—42no—
94C2×Dic43—21no—
95C2×Dic43—21no—
96C2×Dic43—21no—
97D172—22no—
98C4×D43—42no—
99Dic86—22no—
100C43⋊C8—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—44no—
118C4×C43#12312yes—
119C4×C43C2×#4112yes—
120Dic43—41no—
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⋊C4D4311yescharacteristic, complemented
133#484—432no—
134#483—432no—
135#481—432no—
136#480—432no—
137#428—432no—
138#417—432no—
139#407—431no—
140C43#309211yescharacteristic, complemented, Sylow
141C2×#41—431no—
142C23×C4—21no—
143C23×C4C2×D4311yescharacteristic
144C2×M16—432no—
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—21no—
155C2×C4⋊C4—21no—
156C2×C4⋊C4—21no—
157C2×C4⋊C4C2×D4312yes—
158C2×C4⋊C4C2×D4312yes—
159C2×C4⋊C4C2×D4312yes—
160#107—434no—
161#106—434no—
162#103—434no—
163#102—434no—
164C22⋊C8—432no—
165C22⋊C8—432no—
166C24C22⋊D4311yescharacteristic
167#41—864no—
168C2×Q8—431no—
169C2×D4—431no—
170C2×D4—861no—
171C2×D4—861no—
172C2×D4—861no—
173C22×C4—24no—
174C22×C4—22no—
175C22×C4—22no—
176C22×C4—22no—
177C22×C4—44no—
178C22×C4—861no—
179C22×C4C22⋊D4311yescharacteristic
180C22×C4C22⋊D4311yescharacteristic
181C22×C4C22⋊D4311yescharacteristic
182C22×C4C22×D4311yescharacteristic
183C22×C4C22×D4311yescharacteristic
184C22×C4C22×D4311yescharacteristic
185M16—864no—
186C2×C8—434no—
187C4⋊C4—22no—
188C4⋊C4—22no—
189C4⋊C4—22no—
190C4⋊C4—431no—
191C4⋊C4—431no—
192C4⋊C4—861no—
193C4⋊C4—861no—
194C4⋊C4C22×D4314yes—
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×C22⋊D4311yescharacteristic
206C23C2×C22⋊D4311yescharacteristic
207C23C2×C22⋊D4311yescharacteristic
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—24no—
219C2×C4—44no—
220C2×C4—44no—
221C2×C4—44no—
222C2×C4—861no—
223C2×C4—861no—
224C2×C4—861no—
225C2×C4—1722no—
226C2×C4#1062189814yes—
227C2×C4C2×C22⋊D4311yescharacteristic
228C2×C4C2×C22⋊D4311yescharacteristic
229C2×C4C2×C22⋊D4311yescharacteristic
230C2×C4C23×D4311yescharacteristic
231C8—864no—
232C22—28no—
233C22—21no—
234C22—21no—
235C22—21no—
236C22—21no—
237C22—21no—
238C22—21no—
239C22—1721no—
240C22—1721no—
241C22—1721no—
242C22#1306330812yes—
243C22#1306335112yes—
244C22#1306335612yes—
245C22C22×C22⋊D4311yescharacteristic
246C4—21no—
247C4—21no—
248C4—44no—
249C4—1721no—
250C4—1721no—
251C4—1721no—
252C4#1306330812yes—
253C4C2×#1062189812yes—
254C2—22no—
255C2—22no—
256C2—22no—
257C2—3441no—
258C2C2×#1306330811yescharacteristic
259C2C2×#1306335111yescharacteristic
260C2C2×#1306335611yescharacteristic
subgroupG/H
centerC22C22×C22⋊D43
commutatorC2×C4×C43C24
FrattiniC2×C4C23×D43
FittingC22×C4⋊C4×C43C2
socleC22×C43C22×D4
hypercenterC22×C4⋊C4D43
hypocenterC43#3092
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C23×C4 ◁ C22×C4⋊C4

Complements

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

NH ≅ G/Ntype
2. #14583234C2semidirect
3. #14583229C2semidirect
4. #14583217C2semidirect
5. #14583212C2semidirect
6. #14582939C2semidirect
7. #14582898C2semidirect
8. #14582863C2semidirect
9. C22×C4⋊C4×C43C2semidirect
21. #13063258C22semidirect
22. #13063256C22semidirect
23. #13063248C22semidirect
24. #13063245C22semidirect
132. C22×C4⋊C4D43semidirect
140. C43#3092semidirect