Finite Group Databasebeta

← D9×#395 #11808174

Subgroups — D9×#395 #11808174

Order 1152.

1362 conjugacy classes of subgroups; only the 266 normal subgroups are shown.

normal subgroups only

This group has 1362 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×Q8×D9C211yesmaximal, characteristic
2C2×C4⋊C4×D9C213yesmaximal
3C9×#395C211yesmaximal, characteristic, complemented
4#10588910C211yesmaximal, characteristic, complemented
5#10588659C213yesmaximal, complemented
6D9×#95C213yesmaximal
7#10588336C213yesmaximal, complemented
8D3×#395—31nomaximal
9C22×Q8×C9C2211yescharacteristic
10C2×Q8×D9—212no—
11C22×C4×D9C2211yescharacteristic
12C22×C4×D9C2213yes—
13C22×C4×D9C2213yes—
14C22×Dic18C2213yes—
15C2×C9×C4⋊C4C2213yes—
16C2×C4⋊Dic9C2213yes—
17C2×Dic9⋊C4C2213yes—
18C2×Dic9⋊C4C2213yes—
19C4⋊C4×D9—212no—
20C9×#95C2213yes—
21C9⋊#95C2216yes—
22C9⋊#95C2213yes—
23C22×D3×Q8—31no—
24C2×D3×C4⋊C4—33no—
25C3×#395D311yescharacteristic
26#5230—31no—
27#4979—33no—
28D3×#95—33no—
29#4656—33no—
30C23×D9C2311yescharacteristic
31C2×Q8×C9—26no—
32C22×C4×C9C2311yescharacteristic
33C22×C4×C9C2313yes—
34C22×C4×C9C2313yes—
35C22×Dic9C2311yescharacteristic
36C22×Dic9C2313yes—
37C22×Dic9C2313yes—
38Q8×D9—232no—
39C2×C4×D9—26no—
40C2×C4×D9—212no—
41C2×C4×D9—26no—
42C2×C4×D9—26no—
43C2×C4×D9D4112yes—
44C2×C4×D9Q8112yescomplemented
45C2×Dic18—26no—
46C2×Dic18—212no—
47C9×C4⋊C4—26no—
48C4⋊Dic9—26no—
49Dic9⋊C4—26no—
50Dic9⋊C4—26no—
51C2×#395—91noSylow
52C22×C3×Q8C2×D311yescharacteristic
53C2×D3×Q8—612no—
54C22×C4×D3—33no—
55C22×C4×D3—33no—
56C22×C4×D3—31no—
57C22×Dic6—33no—
58C2×C3×C4⋊C4C2×D313yes—
59C2×C4⋊Dic3—33no—
60C2×Dic3⋊C4—33no—
61C2×Dic3⋊C4—33no—
62D3×C4⋊C4—612no—
63C3×#95C2×D313yes—
64C3⋊#95—36no—
65C3⋊#95—33no—
66C23×C9C2411yescharacteristic
67C22×D9C2×D416yes—
68C22×D9C2×Q816yes—
69C22×D9#4112yes—
70Q8×C9—28no—
71C2×C4×C9—23no—
72C2×C4×C9—26no—
73C2×C4×C9—23no—
74C2×C4×C9—23no—
75C2×C4×C9C2×D416yes—
76C2×C4×C9C2×Q816yescomplemented
77C2×Dic9—23no—
78C2×Dic9—26no—
79C2×Dic9—23no—
80C2×Dic9—23no—
81C2×Dic9C2×D416yes—
82C2×Dic9C2×Q816yescomplemented
83C4×D9—224no—
84C4×D9—224no—
85C4×D9—44no—
86Dic18—224no—
87C23×Q8—91no—
88C22×C4⋊C4—93no—
89#395—91no—
90#395—93no—
91#395—93no—
92#395D911yescharacteristic, direct product factor
93C2×#95—93no—
94C23×D3—31no—
95C2×C3×Q8—26no—
96C22×C3×C4C22×D311yescharacteristic
97C22×C3×C4C22×D313yes—
98C22×C3×C4C22×D313yes—
99C22×Dic3—33no—
100C22×Dic3—33no—
101C22×Dic3—31no—
102D3×Q8—632no—
103C2×C4×D3—312no—
104C2×C4×D3—312no—
105C2×C4×D3—66no—
106C2×C4×D3—66no—
107C2×C4×D3—612no—
108C2×C4×D3—66no—
109C2×Dic6—612no—
110C2×Dic6—66no—
111C3×C4⋊C4—26no—
112C4⋊Dic3—66no—
113Dic3⋊C4—66no—
114Dic3⋊C4—66no—
115C22×C9C22×D413yes—
116C22×C9C22×Q813yes—
117C22×C9C2×#4111yescharacteristic
118C2×D9#12014yes—
119C2×D9C22⋊Q8112yes—
120C2×D9C4⋊Q8112yes—
121C4×C9—26no—
122C4×C9—26no—
123C4×C9—41no—
124Dic9—26no—
125Dic9—26no—
126Dic9—41no—
127C22×Q8—93no—
128C22×Q8—1812no—
129C22×Q8C2×D911yescharacteristic
130C23×C4—93no—
131C23×C4—93no—
132C23×C4—91no—
133C2×C4⋊C4—93no—
134C2×C4⋊C4—93no—
135C2×C4⋊C4—93no—
136C2×C4⋊C4—1812no—
137C2×C4⋊C4C2×D913yes—
138#95—93no—
139#95—96no—
140#95C2×D913yes—
141C23×C3C23×D311yescharacteristic
142C22×D3—36no—
143C22×D3—36no—
144C22×D3—32no—
145C3×Q8—28no—
146C2×C3×C4—23no—
147C2×C3×C4—26no—
148C2×C3×C4—23no—
149C2×C3×C4—23no—
150C2×C3×C4D3×D416yes—
151C2×C3×C4D3×Q816yes—
152C2×Dic3—36no—
153C2×Dic3—36no—
154C2×Dic3—63no—
155C2×Dic3—66no—
156C2×Dic3—63no—
157C2×Dic3—63no—
158C4×D3—624no—
159C4×D3—624no—
160C4×D3—124no—
161Dic6—624no—
162C2×C9C2×#12011yescharacteristic
163C2×C9C2×C22⋊Q813yes—
164C2×C9C2×C4⋊Q813yes—
165D9#39518yesdirect product factor
166C24—91no—
167C2×Q8—26no—
168C2×Q8—1812no—
169C2×Q8—1832no—
170C2×Q8—186no—
171C22×C4—93no—
172C22×C4—93no—
173C22×C4—912no—
174C22×C4—912no—
175C22×C4—91no—
176C22×C4—186no—
177C22×C4—1812no—
178C22×C4—186no—
179C22×C4—186no—
180C22×C4C22×D911yescharacteristic
181C22×C4C22×D913yes—
182C22×C4C22×D913yes—
183C4⋊C4—26no—
184C4⋊C4—186no—
185C4⋊C4—186no—
186C4⋊C4—186no—
187C22×C3C2×D3×D413yes—
188C22×C3C2×D3×Q813yes—
189C22×C3D3×#4111yescharacteristic
190C2×D3—312no—
191C2×D3—34no—
192C2×D3—312no—
193C3×C4—26no—
194C3×C4—26no—
195C3×C4—41no—
196Dic3—66no—
197Dic3—66no—
198Dic3—121no—
199C9C2×#39511yescharacteristic, complemented, Sylow
200C23—96no—
201C23—96no—
202C23—92no—
203C23C23×D911yescharacteristic
204Q8—28no—
205Q8—1824no—
206C2×C4—23no—
207C2×C4—26no—
208C2×C4—23no—
209C2×C4—23no—
210C2×C4—96no—
211C2×C4—96no—
212C2×C4—1824no—
213C2×C4—1824no—
214C2×C4—183no—
215C2×C4—186no—
216C2×C4—183no—
217C2×C4—183no—
218C2×C4—364no—
219C2×C4D4×D916yes—
220C2×C4Q8×D916yescomplemented
221C2×C3D3×#12011yescharacteristic
222C2×C3D3×C22⋊Q813yes—
223C2×C3D3×C4⋊Q813yes—
224D3—38no—
225C22—912no—
226C22—912no—
227C22—94no—
228C22C2×D4×D913yes—
229C22C2×Q8×D913yes—
230C22#41×D911yescharacteristic
231C4—26no—
232C4—26no—
233C4—41no—
234C4—186no—
235C4—186no—
236C4—361no—
237C3D3×#39511yescharacteristic
238C2—98no—
239C2D9×#12011yescharacteristic
240C2D9×C22⋊Q813yes—
241C2D9×C4⋊Q813yes—
subgroupG/H
centerC23C23×D9
commutator, cosocleC23×C9C24
Frattini, socleC23×C3C23×D3
FittingC9×#395C2
prime radicalC23×D9C23
hypercenter#395D9
hypocenterC9C2×#395
LCSG ▷ C23×C9 ▷ C9
UCSC1 ◁ C23 ◁ #395

Complements

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

NH ≅ G/Ntype
3. C9×#395C2semidirect
4. #10588910C2semidirect
5. #10588659C2semidirect
7. #10588336C2semidirect
44. C2×C4×D9Q8semidirect
76. C2×C4×C9C2×Q8semidirect
82. C2×Dic9C2×Q8semidirect
92. #395D9direct (N × H)
165. D9#395direct (N × H)
199. C9C2×#395semidirect
220. C2×C4Q8×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×C4⋊C4×D92
C9×#3952
#105889102
#105886592
D9×#952
#105883362
D3×#3953