Finite Group Databasebeta

← D9×#399 #11808467

Subgroups — D9×#399 #11808467

Order 1152.

1362 conjugacy classes of subgroups; only the 242 normal subgroups are shown.

normal subgroups only

This group has 1362 conjugacy classes of subgroups — too many to draw. Only its 242 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
1C2×C4⋊C4×D9C213yesmaximal, complemented
2C2×C22⋊C4×D9C213yesmaximal
3C9×#399C211yesmaximal, characteristic, complemented
4#10588673C213yesmaximal, complemented
5#10588629C213yesmaximal, complemented
6#10588357C211yesmaximal, characteristic, complemented
7D9×#95C211yesmaximal, characteristic, complemented
8D3×#399—31nomaximal
9C24×D9C2211yescharacteristic
10C22×C4×D9C2213yes—
11C22×C4×D9C2213yes—
12C2×C9×C4⋊C4C2213yescomplemented
13C2×C9×C22⋊C4C2213yes—
14C2×#3676C2213yes—
15C2×(C2×D9)⋊C4C2213yes—
16C2×(C2×D9)⋊C4C2213yes—
17C2×C4⋊Dic9C2213yescomplemented
18C2×Dic9⋊C4C2216yescomplemented
19C4⋊C4×D9—212no—
20C22⋊C4×D9—212no—
21C9×#95C2211yescharacteristic, complemented
22C9⋊#95C2213yescomplemented
23C2×D3×C4⋊C4—33no—
24C2×D3×C22⋊C4—33no—
25C3×#399D311yescharacteristic
26#4993—33no—
27#4949—33no—
28#4677—31no—
29D3×#95—31no—
30C24×C9C2311yescharacteristic
31C23×D9—26no—
32C23×D9—26no—
33C23×D9Q814yes—
34C23×D9C2311yescharacteristic
35C23×D9C2311yescharacteristic
36C22×C4×C9C2313yes—
37C22×C4×C9C2313yes—
38C22×Dic9C2313yes—
39C22×Dic9C2313yes—
40C2×C4×D9—212no—
41C2×C4×D9—26no—
42C2×C4×D9—212no—
43C2×C4×D9D4112yes—
44C9×C4⋊C4—26no—
45C9×C22⋊C4—26no—
46#3676—26no—
47(C2×D9)⋊C4—26no—
48(C2×D9)⋊C4—26no—
49C4⋊Dic9—26no—
50Dic9⋊C4—212no—
51C2×#399—91noSylow
52C24×D3—31no—
53C22×C4×D3—33no—
54C22×C4×D3—33no—
55C2×C3×C4⋊C4C2×D313yes—
56C2×C3×C22⋊C4C2×D313yes—
57C2×#217—33no—
58C2×(C2×D3)⋊C4—33no—
59C2×(C2×D3)⋊C4—33no—
60C2×C4⋊Dic3—33no—
61C2×Dic3⋊C4—36no—
62D3×C4⋊C4—612no—
63D3×C22⋊C4—612no—
64C3×#95C2×D311yescharacteristic
65C3⋊#95—33no—
66C23×C9—23no—
67C23×C9—23no—
68C23×C9C2×Q812yes—
69C23×C9C2411yescharacteristic
70C22×D9—23no—
71C22×D9—23no—
72C22×D9—224no—
73C22×D9—412no—
74C22×D9—44no—
75C22×D9C2×D416yes—
76C22×D9C2×Q812yes—
77C22×D9C2×Q812yes—
78C22×D9#4116yes—
79C2×C4×C9—26no—
80C2×C4×C9—26no—
81C2×C4×C9—23no—
82C2×C4×C9C2×D416yes—
83C2×Dic9—26no—
84C2×Dic9—26no—
85C2×Dic9—23no—
86C2×Dic9C2×D416yes—
87C4×D9—224no—
88C4×D9—412no—
89C22×C4⋊C4—93no—
90C22×C22⋊C4—93no—
91#399—93no—
92#399—93no—
93#399—91no—
94#399D911yescharacteristic, direct product factor
95C2×#95—91no—
96C24×C3C22×D311yescharacteristic
97C23×D3—31no—
98C23×D3—34no—
99C23×D3—31no—
100C23×D3—66no—
101C23×D3—66no—
102C22×C3×C4C22×D313yes—
103C22×C3×C4C22×D313yes—
104C22×Dic3—33no—
105C22×Dic3—33no—
106C2×C4×D3—312no—
107C2×C4×D3—612no—
108C2×C4×D3—66no—
109C2×C4×D3—612no—
110C3×C4⋊C4—26no—
111C3×C22⋊C4—26no—
112#217—66no—
113(C2×D3)⋊C4—66no—
114(C2×D3)⋊C4—66no—
115C4⋊Dic3—66no—
116Dic3⋊C4—612no—
117C22×C9—26no—
118C22×C9—43no—
119C22×C9—41no—
120C22×C9C22×D413yes—
121C22×C9C22×Q811yescharacteristic
122C22×C9C2×#4113yes—
123C2×D9—26no—
124C2×D9—43no—
125C2×D9—41no—
126C2×D9—416no—
127C2×D9C22⋊Q8112yes—
128C2×D9#123112yes—
129C2×D9#12714yes—
130C4×C9—26no—
131C4×C9—43no—
132Dic9—26no—
133Dic9—43no—
134C25—91no—
135C23×C4—93no—
136C23×C4—93no—
137C2×C4⋊C4—96no—
138C2×C4⋊C4—93no—
139C2×C4⋊C4—1812no—
140C2×C4⋊C4C2×D913yescomplemented
141C2×C22⋊C4—93no—
142C2×C22⋊C4—93no—
143C2×C22⋊C4—93no—
144C2×C22⋊C4—1812no—
145C2×C22⋊C4C2×D913yes—
146#95—93no—
147#95C2×D911yescharacteristic, complemented
148C23×C3—23no—
149C23×C3—23no—
150C23×C3D3×Q812yes—
151C23×C3C23×D311yescharacteristic
152C22×D3—36no—
153C22×D3—32no—
154C22×D3—36no—
155C22×D3—32no—
156C22×D3—624no—
157C22×D3—63no—
158C22×D3—63no—
159C22×D3—1212no—
160C22×D3—124no—
161C2×C3×C4—26no—
162C2×C3×C4—26no—
163C2×C3×C4—23no—
164C2×C3×C4D3×D416yes—
165C2×Dic3—36no—
166C2×Dic3—66no—
167C2×Dic3—66no—
168C2×Dic3—63no—
169C4×D3—624no—
170C4×D3—1212no—
171C2×C9—42no—
172C2×C9C2×C22⋊Q813yes—
173C2×C9C2×#12313yes—
174C2×C9C2×#12711yescharacteristic
175D9—42no—
176D9#39918yesdirect product factor
177C24—91no—
178C24—94no—
179C24—91no—
180C24—186no—
181C24—186no—
182C24C22×D911yescharacteristic
183C22×C4—93no—
184C22×C4—912no—
185C22×C4—93no—
186C22×C4—1812no—
187C22×C4—186no—
188C22×C4—1812no—
189C22×C4C22×D913yes—
190C22×C4C22×D913yes—
191C4⋊C4—26no—
192C4⋊C4—1812no—
193C4⋊C4—186no—
194C22⋊C4—26no—
195C22⋊C4—186no—
196C22⋊C4—186no—
197C22⋊C4—186no—
198C22×C3—26no—
199C22×C3—43no—
200C22×C3—41no—
201C22×C3C2×D3×D413yes—
202C22×C3C2×D3×Q811yescharacteristic
203C22×C3D3×#4113yes—
204C2×D3—312no—
205C2×D3—34no—
206C2×D3—312no—
207C2×D3—66no—
208C2×D3—1216no—
209C2×D3—123no—
210C2×D3—121no—
211C3×C4—26no—
212C3×C4—43no—
213Dic3—66no—
214Dic3—123no—
215C9C2×#39911yescharacteristic, complemented, Sylow
216C23—23no—
217C23—23no—
218C23—96no—
219C23—92no—
220C23—96no—
221C23—92no—
222C23—1824no—
223C23—183no—
224C23—183no—
225C23—3612no—
226C23—364no—
227C23Q8×D912yes—
228C23C23×D911yescharacteristic
229C2×C4—26no—
230C2×C4—23no—
231C2×C4—26no—
232C2×C4—96no—
233C2×C4—1824no—
234C2×C4—186no—
235C2×C4—183no—
236C2×C4—186no—
237C2×C4—3612no—
238C2×C4D4×D916yes—
239C2×C3—42no—
240C2×C3D3×C22⋊Q813yes—
241C2×C3D3×#12313yes—
242C2×C3D3×#12711yescharacteristic
243D3—38no—
244D3—122no—
245C22—26no—
246C22—43no—
247C22—41no—
248C22—912no—
249C22—912no—
250C22—94no—
251C22—186no—
252C22—3616no—
253C22—363no—
254C22—361no—
255C22C2×D4×D913yes—
256C22C2×Q8×D911yescharacteristic
257C22#41×D913yes—
258C4—26no—
259C4—43no—
260C4—186no—
261C4—363no—
262C3D3×#39911yescharacteristic
263C2—42no—
264C2—98no—
265C2—362no—
266C2D9×C22⋊Q813yes—
267C2D9×#12313yes—
268C2D9×#12711yescharacteristic
subgroupG/H
centerC23C23×D9
commutator, cosocleC23×C9C24
Frattini, socleC23×C3C23×D3
FittingC9×#399C2
prime radicalC24×D9C22
hypercenter#399D9
hypocenterC9C2×#399
LCSG ▷ C23×C9 ▷ C9
UCSC1 ◁ C23 ◁ #399

Complements

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

NH ≅ G/Ntype
1. C2×C4⋊C4×D9C2semidirect
3. C9×#399C2semidirect
4. #10588673C2semidirect
5. #10588629C2semidirect
6. #10588357C2semidirect
7. D9×#95C2semidirect
12. C2×C9×C4⋊C4C22semidirect
17. C2×C4⋊Dic9C22semidirect
18. C2×Dic9⋊C4C22semidirect
21. C9×#95C22semidirect
22. C9⋊#95C22semidirect
94. #399D9direct (N × H)
140. C2×C4⋊C4C2×D9semidirect
147. #95C2×D9semidirect
176. D9#399direct (N × H)
215. C9C2×#399semidirect

Maximal subgroups

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

subgroupindex
C2×C4⋊C4×D92
C2×C22⋊C4×D92
C9×#3992
#105886732
#105886292
#105883572
D9×#952
D3×#3993