Finite Group Databasebeta

← D9×#392 #11808078

Subgroups — D9×#392 #11808078

Order 1152.

2718 conjugacy classes of subgroups; only the 266 normal subgroups are shown.

normal subgroups only

This group has 2718 conjugacy classes of subgroups — too many to draw. Only its 266 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
1C22×D4×D9C213yesmaximal, complemented
2C2×C22⋊C4×D9C213yesmaximal, complemented
3C9×#392C211yesmaximal, characteristic, complemented
4#10588903C213yesmaximal, complemented
5#10588640C213yesmaximal, complemented
6#10588351C211yesmaximal, characteristic, complemented
7D9×#95C211yesmaximal, characteristic, complemented
8D3×#392—31nomaximal
9C24×D9C2213yes—
10C22×D4×C9C2213yescomplemented
11C22×#611C2216yescomplemented
12C2×D4×D9—224no—
13C2×D4×D9—212no—
14C22×D36C2213yescomplemented
15C22×C4×D9C2211yescharacteristic
16C22×C4×D9C2213yes—
17C2×C9×C22⋊C4C2213yescomplemented
18C2×#3676C2213yescomplemented
19C2×(C2×D9)⋊C4C2213yescomplemented
20C2×(C2×D9)⋊C4C2213yescomplemented
21C22⋊C4×D9—212no—
22C9×#95C2211yescharacteristic, complemented
23C9⋊#95C2213yescomplemented
24C22×D3×D4—33no—
25C2×D3×C22⋊C4—33no—
26C3×#392D311yescharacteristic
27#5223—33no—
28#4960—33no—
29#4671—31no—
30D3×#95—31no—
31C24×C9C2313yes—
32C23×D9—26no—
33C23×D9—212no—
34C23×D9—212no—
35C23×D9—26no—
36C23×D9D4112yescomplemented
37C23×D9C2313yes—
38C23×D9C2311yescharacteristic
39C2×D4×C9—212no—
40C2×D4×C9—26no—
41C22×C4×C9C2311yescharacteristic
42C22×C4×C9C2313yes—
43C2×#611—212no—
44C2×#611—212no—
45C2×#611—212no—
46C22×Dic9C2311yescharacteristic
47C22×Dic9C2313yes—
48D4×D9—296no—
49C2×D36—212no—
50C2×D36—26no—
51C2×C4×D9—212no—
52C2×C4×D9—26no—
53C2×C4×D9D4112yescomplemented
54C9×C22⋊C4—26no—
55#3676—26no—
56(C2×D9)⋊C4—26no—
57(C2×D9)⋊C4—26no—
58C2×#392—91noSylow
59C24×D3—33no—
60C22×C3×D4C2×D313yes—
61C22×#67—36no—
62C2×D3×D4—612no—
63C2×D3×D4—624no—
64C22×D12—33no—
65C22×C4×D3—33no—
66C22×C4×D3—31no—
67C2×C3×C22⋊C4C2×D313yes—
68C2×#217—33no—
69C2×(C2×D3)⋊C4—33no—
70C2×(C2×D3)⋊C4—33no—
71D3×C22⋊C4—612no—
72C3×#95C2×D311yescharacteristic
73C3⋊#95—33no—
74C23×C9—23no—
75C23×C9—26no—
76C23×C9—26no—
77C23×C9—23no—
78C23×C9C2×D416yescomplemented
79C23×C9C2411yescharacteristic
80C22×D9—23no—
81C22×D9—26no—
82C22×D9—26no—
83C22×D9—23no—
84C22×D9—248no—
85C22×D9—224no—
86C22×D9—412no—
87C22×D9—424no—
88C22×D9—412no—
89C22×D9C2×D416yes—
90C22×D9C2×D416yes—
91C22×D9C2×D416yescomplemented
92C22×D9#4112yes—
93D4×C9—224no—
94C2×C4×C9—26no—
95C2×C4×C9—23no—
96C2×C4×C9C2×D416yescomplemented
97#611—248no—
98C2×Dic9—26no—
99C2×Dic9—23no—
100C2×Dic9C2×D416yescomplemented
101D36—224no—
102C4×D9—224no—
103C4×D9—44no—
104C23×D4—93no—
105C22×C22⋊C4—93no—
106#392—93no—
107#392—93no—
108#392—91no—
109#392D911yescharacteristic, direct product factor
110C2×#95—91no—
111C24×C3C22×D313yes—
112C23×D3—31no—
113C23×D3—312no—
114C23×D3—33no—
115C23×D3—66no—
116C23×D3—612no—
117C23×D3—612no—
118C23×D3—66no—
119C2×C3×D4—212no—
120C2×C3×D4—26no—
121C22×C3×C4C22×D311yescharacteristic
122C22×C3×C4C22×D313yes—
123C2×#67—612no—
124C2×#67—612no—
125C2×#67—612no—
126C22×Dic3—33no—
127C22×Dic3—31no—
128D3×D4—696no—
129C2×D12—612no—
130C2×D12—66no—
131C2×C4×D3—312no—
132C2×C4×D3—612no—
133C2×C4×D3—66no—
134C3×C22⋊C4—26no—
135#217—66no—
136(C2×D3)⋊C4—66no—
137(C2×D3)⋊C4—66no—
138C22×C9—212no—
139C22×C9—26no—
140C22×C9—43no—
141C22×C9—46no—
142C22×C9—43no—
143C22×C9C22×D413yes—
144C22×C9C22×D413yes—
145C22×C9C2×#4111yescharacteristic
146C2×D9—212no—
147C2×D9—26no—
148C2×D9—43no—
149C2×D9—46no—
150C2×D9—43no—
151C2×D9—448no—
152C2×D9#120112yes—
153C2×D9#121112yes—
154C2×D9#12714yes—
155C4×C9—26no—
156C4×C9—41no—
157Dic9—26no—
158Dic9—41no—
159C25—93no—
160C22×D4—96no—
161C22×D4—93no—
162C22×D4—1812no—
163C22×D4—1824no—
164C22×D4C2×D913yescomplemented
165C23×C4—93no—
166C23×C4—91no—
167C2×C22⋊C4—93no—
168C2×C22⋊C4—93no—
169C2×C22⋊C4—93no—
170C2×C22⋊C4—1812no—
171C2×C22⋊C4C2×D913yescomplemented
172#95—93no—
173#95C2×D911yescharacteristic, complemented
174C23×C3—23no—
175C23×C3—26no—
176C23×C3—26no—
177C23×C3—23no—
178C23×C3D3×D416yes—
179C23×C3C23×D311yescharacteristic
180C22×D3—36no—
181C22×D3—36no—
182C22×D3—32no—
183C22×D3—36no—
184C22×D3—648no—
185C22×D3—624no—
186C22×D3—63no—
187C22×D3—66no—
188C22×D3—66no—
189C22×D3—63no—
190C22×D3—1212no—
191C22×D3—1212no—
192C22×D3—1224no—
193C3×D4—224no—
194C2×C3×C4—26no—
195C2×C3×C4—23no—
196C2×C3×C4D3×D416yes—
197#67—648no—
198C2×Dic3—36no—
199C2×Dic3—66no—
200C2×Dic3—63no—
201D12—624no—
202C4×D3—624no—
203C4×D3—124no—
204C2×C9—46no—
205C2×C9C2×#12013yes—
206C2×C9C2×#12113yes—
207C2×C9C2×#12711yescharacteristic
208D9—46no—
209D9#39218yesdirect product factor
210C24—91no—
211C24—912no—
212C24—93no—
213C24—186no—
214C24—1812no—
215C24—1812no—
216C24—186no—
217C24C22×D913yes—
218C2×D4—212no—
219C2×D4—26no—
220C2×D4—1812no—
221C2×D4—1812no—
222C2×D4—1896no—
223C2×D4—1812no—
224C2×D4—1812no—
225C2×D4—186no—
226C22×C4—93no—
227C22×C4—912no—
228C22×C4—91no—
229C22×C4—1812no—
230C22×C4—186no—
231C22×C4C22×D911yescharacteristic
232C22×C4C22×D913yes—
233C22⋊C4—26no—
234C22⋊C4—186no—
235C22⋊C4—186no—
236C22⋊C4—186no—
237C22×C3—212no—
238C22×C3—26no—
239C22×C3—43no—
240C22×C3—43no—
241C22×C3—46no—
242C22×C3C2×D3×D413yes—
243C22×C3C2×D3×D413yes—
244C22×C3D3×#4111yescharacteristic
245C2×D3—34no—
246C2×D3—312no—
247C2×D3—312no—
248C2×D3—612no—
249C2×D3—66no—
250C2×D3—1248no—
251C2×D3—123no—
252C2×D3—123no—
253C2×D3—126no—
254C3×C4—26no—
255C3×C4—41no—
256Dic3—66no—
257Dic3—121no—
258C9C2×#39211yescharacteristic, complemented, Sylow
259C23—23no—
260C23—26no—
261C23—26no—
262C23—23no—
263C23—96no—
264C23—96no—
265C23—92no—
266C23—96no—
267C23—1848no—
268C23—1824no—
269C23—183no—
270C23—186no—
271C23—186no—
272C23—183no—
273C23—3624no—
274C23—3612no—
275C23—3612no—
276C23D4×D916yescomplemented
277C23C23×D911yescharacteristic
278D4—224no—
279D4—1824no—
280D4—1848no—
281C2×C4—26no—
282C2×C4—23no—
283C2×C4—96no—
284C2×C4—1824no—
285C2×C4—186no—
286C2×C4—183no—
287C2×C4—364no—
288C2×C4D4×D916yescomplemented
289C2×C3—46no—
290C2×C3D3×#12013yes—
291C2×C3D3×#12113yes—
292C2×C3D3×#12711yescharacteristic
293D3—38no—
294D3—126no—
295C22—26no—
296C22—212no—
297C22—46no—
298C22—43no—
299C22—43no—
300C22—912no—
301C22—94no—
302C22—912no—
303C22—186no—
304C22—1812no—
305C22—3648no—
306C22—366no—
307C22—363no—
308C22—363no—
309C22C2×D4×D913yes—
310C22C2×D4×D913yes—
311C22#41×D911yescharacteristic
312C4—26no—
313C4—41no—
314C4—186no—
315C4—361no—
316C3D3×#39211yescharacteristic
317C2—46no—
318C2—98no—
319C2—366no—
320C2D9×#12013yes—
321C2D9×#12113yes—
322C2D9×#12711yescharacteristic
subgroupG/H
centerC23C23×D9
commutator, cosocleC23×C9C24
Frattini, socleC23×C3C23×D3
FittingC9×#392C2
hypercenter#392D9
hypocenterC9C2×#392
LCSG ▷ C23×C9 ▷ C9
UCSC1 ◁ C23 ◁ #392

Complements

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

NH ≅ G/Ntype
1. C22×D4×D9C2semidirect
2. C2×C22⋊C4×D9C2semidirect
3. C9×#392C2semidirect
4. #10588903C2semidirect
5. #10588640C2semidirect
6. #10588351C2semidirect
7. D9×#95C2semidirect
10. C22×D4×C9C22semidirect
11. C22×#611C22semidirect
14. C22×D36C22semidirect
17. C2×C9×C22⋊C4C22semidirect
18. C2×#3676C22semidirect
19. C2×(C2×D9)⋊C4C22semidirect
20. C2×(C2×D9)⋊C4C22semidirect
22. C9×#95C22semidirect
23. C9⋊#95C22semidirect
36. C23×D9D4semidirect
53. C2×C4×D9D4semidirect
78. C23×C9C2×D4semidirect
91. C22×D9C2×D4semidirect
96. C2×C4×C9C2×D4semidirect
100. C2×Dic9C2×D4semidirect
109. #392D9direct (N × H)
164. C22×D4C2×D9semidirect
171. C2×C22⋊C4C2×D9semidirect
173. #95C2×D9semidirect
209. D9#392direct (N × H)
258. C9C2×#392semidirect
276. C23D4×D9semidirect
288. C2×C4D4×D9semidirect

Maximal subgroups

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

subgroupindex
C22×D4×D92
C2×C22⋊C4×D92
C9×#3922
#105889032
#105886402
#105883512
D9×#952
D3×#3923