Finite Group Databasebeta

← D9×#393 #11808104

Subgroups — D9×#393 #11808104

Order 1152.

1554 conjugacy classes of subgroups; only the 242 normal subgroups are shown.

normal subgroups only

This group has 1554 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
1C22×Q8×D9C211yesmaximal, characteristic, complemented
2C2×C22⋊C4×D9C213yesmaximal
3C9×#393C211yesmaximal, characteristic, complemented
4#10588911C211yesmaximal, characteristic, complemented
5#10588627C213yesmaximal, complemented
6#10588353C213yesmaximal, complemented
7D9×#95C213yesmaximal, complemented
8D3×#393—31nomaximal
9C24×D9C2211yescharacteristic
10C22×Q8×C9C2211yescharacteristic, complemented
11C2×Q8×D9—212no—
12C22×C4×D9C2213yes—
13C22×C4×D9C2213yes—
14C22×Dic18C2213yescomplemented
15C2×C9×C22⋊C4C2213yes—
16C2×#3676C2213yes—
17C2×(C2×D9)⋊C4C2213yes—
18C2×(C2×D9)⋊C4C2213yes—
19C22⋊C4×D9—212no—
20C9×#95C2213yescomplemented
21C9⋊#95C2216yescomplemented
22C9⋊#95C2213yescomplemented
23C22×D3×Q8—31no—
24C2×D3×C22⋊C4—33no—
25C3×#393D311yescharacteristic
26#5231—31no—
27#4947—33no—
28#4673—33no—
29D3×#95—33no—
30C24×C9C2311yescharacteristic
31C23×D9—26no—
32C23×D9—26no—
33C23×D9Q814yescomplemented
34C23×D9C2311yescharacteristic
35C23×D9C2311yescharacteristic
36C2×Q8×C9—26no—
37C22×C4×C9C2313yes—
38C22×C4×C9C2313yes—
39C22×Dic9C2313yes—
40C22×Dic9C2313yes—
41Q8×D9—232no—
42C2×C4×D9—212no—
43C2×C4×D9—26no—
44C2×C4×D9—212no—
45C2×C4×D9D4112yes—
46C2×Dic18—26no—
47C2×Dic18—212no—
48C9×C22⋊C4—26no—
49#3676—26no—
50(C2×D9)⋊C4—26no—
51(C2×D9)⋊C4—26no—
52C2×#393—91noSylow
53C24×D3—31no—
54C22×C3×Q8C2×D311yescharacteristic
55C2×D3×Q8—612no—
56C22×C4×D3—33no—
57C22×C4×D3—33no—
58C22×Dic6—33no—
59C2×C3×C22⋊C4C2×D313yes—
60C2×#217—33no—
61C2×(C2×D3)⋊C4—33no—
62C2×(C2×D3)⋊C4—33no—
63D3×C22⋊C4—612no—
64C3×#95C2×D313yes—
65C3⋊#95—36no—
66C3⋊#95—33no—
67C23×C9—23no—
68C23×C9—23no—
69C23×C9C2×Q812yescomplemented
70C23×C9C2411yescharacteristic
71C22×D9—23no—
72C22×D9—23no—
73C22×D9—224no—
74C22×D9—44no—
75C22×D9—412no—
76C22×D9C2×D416yes—
77C22×D9C2×Q812yes—
78C22×D9C2×Q812yescomplemented
79C22×D9#4116yes—
80Q8×C9—28no—
81C2×C4×C9—26no—
82C2×C4×C9—23no—
83C2×C4×C9—26no—
84C2×C4×C9C2×D416yes—
85C2×Dic9—26no—
86C2×Dic9—23no—
87C2×Dic9—26no—
88C2×Dic9C2×D416yes—
89C4×D9—224no—
90C4×D9—412no—
91Dic18—224no—
92C23×Q8—91no—
93C22×C22⋊C4—93no—
94#393—91no—
95#393—93no—
96#393—93no—
97#393D911yescharacteristic, direct product factor
98C2×#95—93no—
99C24×C3C22×D311yescharacteristic
100C23×D3—31no—
101C23×D3—34no—
102C23×D3—31no—
103C23×D3—66no—
104C23×D3—66no—
105C2×C3×Q8—26no—
106C22×C3×C4C22×D313yes—
107C22×C3×C4C22×D313yes—
108C22×Dic3—33no—
109C22×Dic3—33no—
110D3×Q8—632no—
111C2×C4×D3—312no—
112C2×C4×D3—612no—
113C2×C4×D3—66no—
114C2×C4×D3—612no—
115C2×Dic6—612no—
116C2×Dic6—66no—
117C3×C22⋊C4—26no—
118#217—66no—
119(C2×D3)⋊C4—66no—
120(C2×D3)⋊C4—66no—
121C22×C9—26no—
122C22×C9—41no—
123C22×C9—43no—
124C22×C9C22×D413yes—
125C22×C9C22×Q811yescharacteristic
126C22×C9C2×#4113yes—
127C2×D9—26no—
128C2×D9—41no—
129C2×D9—43no—
130C2×D9—416no—
131C2×D9#12014yes—
132C2×D9C22⋊Q8112yes—
133C2×D9#124112yes—
134C4×C9—26no—
135C4×C9—43no—
136Dic9—26no—
137Dic9—43no—
138C25—91no—
139C22×Q8—93no—
140C22×Q8—1812no—
141C22×Q8C2×D911yescharacteristic, complemented
142C23×C4—93no—
143C23×C4—93no—
144C2×C22⋊C4—93no—
145C2×C22⋊C4—93no—
146C2×C22⋊C4—93no—
147C2×C22⋊C4—1812no—
148C2×C22⋊C4C2×D913yes—
149#95—96no—
150#95—93no—
151#95C2×D913yescomplemented
152C23×C3—23no—
153C23×C3—23no—
154C23×C3D3×Q812yes—
155C23×C3C23×D311yescharacteristic
156C22×D3—36no—
157C22×D3—32no—
158C22×D3—36no—
159C22×D3—32no—
160C22×D3—624no—
161C22×D3—63no—
162C22×D3—63no—
163C22×D3—1212no—
164C22×D3—124no—
165C3×Q8—28no—
166C2×C3×C4—26no—
167C2×C3×C4—23no—
168C2×C3×C4—26no—
169C2×C3×C4D3×D416yes—
170C2×Dic3—36no—
171C2×Dic3—66no—
172C2×Dic3—63no—
173C2×Dic3—66no—
174C4×D3—624no—
175C4×D3—1212no—
176Dic6—624no—
177C2×C9—42no—
178C2×C9C2×#12011yescharacteristic
179C2×C9C2×C22⋊Q813yes—
180C2×C9C2×#12413yes—
181D9—42no—
182D9#39318yesdirect product factor
183C24—91no—
184C24—94no—
185C24—91no—
186C24—186no—
187C24—186no—
188C24C22×D911yescharacteristic
189C2×Q8—26no—
190C2×Q8—1812no—
191C2×Q8—1832no—
192C2×Q8—186no—
193C22×C4—93no—
194C22×C4—912no—
195C22×C4—93no—
196C22×C4—1812no—
197C22×C4—186no—
198C22×C4—1812no—
199C22×C4C22×D913yes—
200C22×C4C22×D913yes—
201C22⋊C4—26no—
202C22⋊C4—186no—
203C22⋊C4—186no—
204C22⋊C4—186no—
205C22×C3—26no—
206C22×C3—43no—
207C22×C3—41no—
208C22×C3C2×D3×D413yes—
209C22×C3C2×D3×Q811yescharacteristic
210C22×C3D3×#4113yes—
211C2×D3—312no—
212C2×D3—34no—
213C2×D3—312no—
214C2×D3—66no—
215C2×D3—1216no—
216C2×D3—123no—
217C2×D3—121no—
218C3×C4—26no—
219C3×C4—43no—
220Dic3—66no—
221Dic3—123no—
222C9C2×#39311yescharacteristic, complemented, Sylow
223C23—23no—
224C23—23no—
225C23—96no—
226C23—92no—
227C23—96no—
228C23—92no—
229C23—1824no—
230C23—183no—
231C23—183no—
232C23—3612no—
233C23—364no—
234C23Q8×D912yescomplemented
235C23C23×D911yescharacteristic
236Q8—28no—
237Q8—1824no—
238C2×C4—26no—
239C2×C4—23no—
240C2×C4—26no—
241C2×C4—96no—
242C2×C4—1824no—
243C2×C4—186no—
244C2×C4—183no—
245C2×C4—186no—
246C2×C4—3612no—
247C2×C4D4×D916yes—
248C2×C3—42no—
249C2×C3D3×#12011yescharacteristic
250C2×C3D3×C22⋊Q813yes—
251C2×C3D3×#12413yes—
252D3—38no—
253D3—122no—
254C22—26no—
255C22—43no—
256C22—41no—
257C22—912no—
258C22—912no—
259C22—94no—
260C22—186no—
261C22—3616no—
262C22—363no—
263C22—361no—
264C22C2×D4×D913yes—
265C22C2×Q8×D911yescharacteristic
266C22#41×D913yes—
267C4—26no—
268C4—43no—
269C4—186no—
270C4—363no—
271C3D3×#39311yescharacteristic
272C2—42no—
273C2—98no—
274C2—362no—
275C2D9×#12011yescharacteristic
276C2D9×C22⋊Q813yes—
277C2D9×#12413yes—
subgroupG/H
centerC23C23×D9
commutator, cosocleC23×C9C24
Frattini, socleC23×C3C23×D3
FittingC9×#393C2
prime radicalC24×D9C22
hypercenter#393D9
hypocenterC9C2×#393
LCSG ▷ C23×C9 ▷ C9
UCSC1 ◁ C23 ◁ #393

Complements

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

NH ≅ G/Ntype
1. C22×Q8×D9C2semidirect
3. C9×#393C2semidirect
4. #10588911C2semidirect
5. #10588627C2semidirect
6. #10588353C2semidirect
7. D9×#95C2semidirect
10. C22×Q8×C9C22semidirect
14. C22×Dic18C22semidirect
20. C9×#95C22semidirect
21. C9⋊#95C22semidirect
22. C9⋊#95C22semidirect
33. C23×D9Q8semidirect
69. C23×C9C2×Q8semidirect
78. C22×D9C2×Q8semidirect
97. #393D9direct (N × H)
141. C22×Q8C2×D9semidirect
151. #95C2×D9semidirect
182. D9#393direct (N × H)
222. C9C2×#393semidirect
234. C23Q8×D9semidirect

Maximal subgroups

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

subgroupindex
C22×Q8×D92
C2×C22⋊C4×D92
C9×#3932
#105889112
#105886272
#105883532
D9×#952
D3×#3933