Finite Group Databasebeta

← D9×#490 #11873560

Subgroups — D9×#490 #11873560

Order 1152.

732 conjugacy classes of subgroups; only the 150 normal subgroups are shown.

normal subgroups only

This group has 732 conjugacy classes of subgroups — too many to draw. Only its 150 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
1D9×#127C211yesmaximal, characteristic
2D9×#125C211yesmaximal, characteristic, complemented
3C9×#490C211yesmaximal, characteristic, complemented
4#10588751C211yesmaximal, characteristic, complemented
5#10588748C211yesmaximal, characteristic, complemented
6D9×#102C214yesmaximal, complemented
7#10588444C214yesmaximal, complemented
8#10588394C211yesmaximal, characteristic, complemented
9D9×#97C211yesmaximal, characteristic, complemented
10D3×#490—31nomaximal
11C2×D4×D9—22no—
12C2×D4×D9C2212yes—
13C9×#127C2211yescharacteristic
14C9×#125C2211yescharacteristic, complemented
15#63502—22no—
16#63502C2212yes—
17C2×C8×D9C2212yes—
18C4⋊C4×D9—22no—
19C4⋊C4×D9C2212yes—
20#63452C2212yescomplemented
21#63451—22no—
22#63436C2211yescharacteristic
23C42×D9C2211yescharacteristic
24#63432C2211yescharacteristic, complemented
25C9×#102C2214yescomplemented
26C9×#97C2211yescharacteristic, complemented
27#63392C2214yescomplemented
28#63380C2214yescomplemented
29#63375C2212yescomplemented
30#63369C2214yescomplemented
31#63362C2211yescharacteristic, complemented
32D3×#127—31no—
33D3×#125—31no—
34C3×#490D311yescharacteristic
35#5071—31no—
36#5067—31no—
37D3×#102—34no—
38#4764—34no—
39#4713—31no—
40D3×#97—31no—
41C23×D9—22no—
42C2×D4×C9—22no—
43C2×D4×C9C2312yes—
44C2×#611—22no—
45C2×#611—24no—
46D4×D9—28no—
47D4×D9—48no—
48C2×D36—22no—
49C2×D36C2312yes—
50C2×C4×D9—22no—
51C2×C4×D9D412yes—
52C2×C4×D9C2311yescharacteristic
53C2×C8×C9C2312yes—
54C9×C4⋊C4—22no—
55C9×C4⋊C4C2312yes—
56C42×C9C2311yescharacteristic
57C4⋊Dic9—22no—
58C4⋊Dic9C2312yes—
59Dic9⋊C4—22no—
60Dic9⋊C4—22no—
61Dic9⋊C4—22no—
62C4×Dic9D412yes—
63C4×Dic9C2311yescharacteristic
64C2×C9⋊C8C2312yes—
65C8×D9—24no—
66C2×#490—91noSylow
67C2×D3×D4—32no—
68C2×D3×D4—62no—
69C3×#127C2×D311yescharacteristic
70C3×#125C2×D311yescharacteristic
71#940—32no—
72#940—62no—
73C2×D3×C8—32no—
74D3×C4⋊C4—32no—
75D3×C4⋊C4—62no—
76#890—32no—
77#889—62no—
78#874—31no—
79C42×D3—31no—
80#870—31no—
81C3×#102C2×D314yes—
82C3×#97C2×D311yescharacteristic
83#832—34no—
84#821—34no—
85#815—32no—
86#809—34no—
87#803—31no—
88C23×C9—22no—
89C22×D9—22no—
90C22×D9—44no—
91C22×D9—48no—
92C22×D9C2×D411yescharacteristic
93D4×C9—24no—
94D4×C9—44no—
95C2×C4×C9—22no—
96C2×C4×C9C2×D412yes—
97C2×C4×C9C2411yescharacteristic
98#611—48no—
99#611—44no—
100C2×Dic9—22no—
101C2×Dic9C2×D412yes—
102C2×Dic9C2×D411yescharacteristic
103D36—24no—
104D36—44no—
105C4×D9—24no—
106C4×D9—44no—
107C4×D9#4114yes—
108C8×C9—22no—
109C9⋊C8—22no—
110C2×#127—91no—
111C2×#125—91no—
112#490—91no—
113#490—91no—
114#490—94no—
115#490—91no—
116#490D911yescharacteristic, direct product factor
117C2×#102—94no—
118C2×#97—91no—
119C23×D3—62no—
120C2×C3×D4—22no—
121C2×C3×D4C22×D312yes—
122C2×#67—64no—
123C2×#67—62no—
124D3×D4—68no—
125D3×D4—128no—
126C2×D12—32no—
127C2×D12—62no—
128C2×C4×D3—31no—
129C2×C4×D3—32no—
130C2×C4×D3—62no—
131C2×C3×C8C22×D312yes—
132C3×C4⋊C4—22no—
133C3×C4⋊C4C22×D312yes—
134C3×C42C22×D311yescharacteristic
135C4⋊Dic3—32no—
136C4⋊Dic3—62no—
137Dic3⋊C4—62no—
138Dic3⋊C4—62no—
139Dic3⋊C4—62no—
140C4×Dic3—32no—
141C4×Dic3—31no—
142C2×C3⋊C8—32no—
143D3×C8—64no—
144C22×C9—42no—
145C22×C9—44no—
146C22×C9C22×D411yescharacteristic
147C2×D9—42no—
148C2×D9—44no—
149C2×D9—88no—
150C2×D9#12412yes—
151C2×D9AGL(1,ℤ/8)14yes—
152C4×C9—22no—
153C4×C9—42no—
154C4×C9C2×#4112yes—
155Dic9—22no—
156Dic9—42no—
157Dic9#12412yes—
158C22×D4—92no—
159C22×D4—182no—
160C22×C8—92no—
161#127—92no—
162#127—91no—
163#127—182no—
164#127C2×D911yescharacteristic
165#125—92no—
166#125—91no—
167#125—182no—
168#125C2×D911yescharacteristic, complemented
169C2×C4⋊C4—92no—
170C2×C4⋊C4—182no—
171C2×C42—91no—
172#102—94no—
173#102—94no—
174#102—94no—
175#102C2×D914yescomplemented
176#97—92no—
177#97—91no—
178#97C2×D911yescharacteristic, complemented
179C23×C3—22no—
180C22×D3—31no—
181C22×D3—62no—
182C22×D3—124no—
183C22×D3—128no—
184C3×D4—24no—
185C3×D4—44no—
186C2×C3×C4—22no—
187C2×C3×C4D3×D412yes—
188C2×C3×C4C23×D311yescharacteristic
189#67—124no—
190#67—128no—
191C2×Dic3—31no—
192C2×Dic3—32no—
193C2×Dic3—62no—
194D12—64no—
195D12—124no—
196C4×D3—34no—
197C4×D3—64no—
198C4×D3—124no—
199C3×C8—22no—
200C3⋊C8—62no—
201C2×C9—82no—
202C2×C9C2×#12411yescharacteristic
203C2×C9C2×AGL(1,ℤ/8)12yes—
204D9—82no—
205D9#49014yesdirect product factor
206C24—182no—
207C2×D4—22no—
208C2×D4—92no—
209C2×D4—188no—
210C2×D4—184no—
211C2×D4—182no—
212C2×D4—182no—
213C2×D4—368no—
214C2×D4C22×D912yes—
215C22×C4—91no—
216C22×C4—92no—
217C22×C4—182no—
218C2×C8—92no—
219C2×C8—184no—
220C2×C8C22×D912yes—
221C4⋊C4—22no—
222C4⋊C4—92no—
223C4⋊C4—182no—
224C4⋊C4—182no—
225C4⋊C4—182no—
226C4⋊C4—182no—
227C4⋊C4C22×D912yes—
228C42—92no—
229C42—91no—
230C42C22×D911yescharacteristic
231C22×C3—42no—
232C22×C3—44no—
233C22×C3C2×D3×D411yescharacteristic
234C2×D3—32no—
235C2×D3—34no—
236C2×D3—122no—
237C2×D3—124no—
238C2×D3—248no—
239C3×C4—22no—
240C3×C4—42no—
241C3×C4D3×#4112yes—
242Dic3—32no—
243Dic3—62no—
244Dic3—122no—
245C9C2×#49011yescharacteristic, complemented, Sylow
246C23—22no—
247C23—91no—
248C23—182no—
249C23—364no—
250C23—368no—
251D4—24no—
252D4—44no—
253D4—184no—
254D4—364no—
255D4—364no—
256D4—368no—
257C2×C4—22no—
258C2×C4—91no—
259C2×C4—94no—
260C2×C4—92no—
261C2×C4—184no—
262C2×C4—182no—
263C2×C4—364no—
264C2×C4D4×D912yes—
265C2×C4C23×D911yescharacteristic
266C8—22no—
267C8—182no—
268C2×C3—82no—
269C2×C3D3×#12411yescharacteristic
270C2×C3D3×AGL(1,ℤ/8)12yes—
271D3—34no—
272D3—242no—
273C22—42no—
274C22—44no—
275C22—92no—
276C22—94no—
277C22—362no—
278C22—364no—
279C22—728no—
280C22C2×D4×D911yescharacteristic
281C4—22no—
282C4—42no—
283C4—92no—
284C4—182no—
285C4—362no—
286C4#41×D912yes—
287C3D3×#49011yescharacteristic
288C2—82no—
289C2—94no—
290C2—722no—
291C2D9×#12411yescharacteristic
292C2D9×AGL(1,ℤ/8)12yes—
subgroupG/H
centerC22C2×D4×D9
commutator, cosocleC2×C4×C9C24
FrattiniC2×C3×C4C23×D3
FittingC9×#490C2
socleC22×C3C2×D3×D4
prime radicalD9×#127C2
hypercenter#490D9
hypocenterC9C2×#490
LCSG ▷ C2×C4×C9 ▷ C2×C9 ▷ C9
UCSC1 ◁ C22 ◁ C42 ◁ #490

Complements

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

NH ≅ G/Ntype
2. D9×#125C2semidirect
3. C9×#490C2semidirect
4. #10588751C2semidirect
5. #10588748C2semidirect
6. D9×#102C2semidirect
7. #10588444C2semidirect
8. #10588394C2semidirect
9. D9×#97C2semidirect
14. C9×#125C22semidirect
20. #63452C22semidirect
24. #63432C22semidirect
25. C9×#102C22semidirect
26. C9×#97C22semidirect
27. #63392C22semidirect
28. #63380C22semidirect
29. #63375C22semidirect
30. #63369C22semidirect
31. #63362C22semidirect
116. #490D9direct (N × H)
168. #125C2×D9semidirect
175. #102C2×D9semidirect
178. #97C2×D9semidirect
205. D9#490direct (N × H)
245. C9C2×#490semidirect

Maximal subgroups

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

subgroupindex
D9×#1272
D9×#1252
C9×#4902
#105887512
#105887482
D9×#1022
#105884442
#105883942
D9×#972
D3×#4903