Finite Group Databasebeta

← D9×#829 #13139269

Subgroups — D9×#829 #13139269

Order 1728.

270 conjugacy classes of subgroups; only the 65 normal subgroups are shown.

normal subgroups only

This group has 270 conjugacy classes of subgroups — too many to draw. Only its 65 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
1C3×Q16×D9C211yesmaximal, characteristic
2D9×Dic12C211yesmaximal, characteristic
3#11720568C211yesmaximal, characteristic, complemented
4C9×#829C211yesmaximal, characteristic, complemented
5#11720244C211yesmaximal, characteristic, complemented
6#11720235C211yesmaximal, characteristic, complemented
7D9×C3⋊C16C211yesmaximal, characteristic
8D3×#829—31nomaximal
9D9×Q32—31nomaximal
10C3×Q8×D9—21no—
11D9×Dic6—21no—
12C3×C9×Q16C2211yescharacteristic
13#88521C2211yescharacteristic
14C3×#3674—21no—
15C9×Dic12C2211yescharacteristic
16C3×C8×D9C2211yescharacteristic
17C3×Dic36C2211yescharacteristic
18#88428—21no—
19C3⋊(C9⋊C16)C2211yescharacteristic
20C9×C3⋊C16C2211yescharacteristic
21C3×D3×Q16—31no—
22D3×Dic12—31no—
23#63656—31no—
24C3×#829D311yescharacteristic
25#63551—31no—
26#63550—31no—
27D3×C3⋊C16—31no—
28Q16×D9—31no—
29Q16×D9D311yescharacteristic
30C9×Q32—31no—
31#63388—31no—
32#63388—31no—
33#63388—61no—
34Dic72—31no—
35C16×D9—31no—
36C3×Q8×C9—21no—
37#6226—21no—
38C3×C4×D9—41no—
39C3×C4×D9D411yescharacteristic
40C9×Dic6—21no—
41C3×Dic18—21no—
42C3×Dic18—41no—
43Dic3×D9—41no—
44#6189—41no—
45C3×C8×C9C2311yescharacteristic
46C3×C9⋊C8D411yescharacteristic
47C2×#829—91no—
48D3×Q32—91no—
49C3×D3×Q8—61no—
50D3×Dic6—61no—
51C32×Q16C2×D311yescharacteristic
52#3746—31no—
53C3×#216—61no—
54C3×Dic12—31no—
55C3×Dic12C2×D311yescharacteristic
56C3×D3×C8—31no—
57#3719—61no—
58Q8×D9—21no—
59Q8×D9—61no—
60C3⋊(C3⋊C16)—31no—
61C3×C3⋊C16C2×D311yescharacteristic
62C9×Q16—21no—
63C9×Q16—31no—
64C9×Q16C2×D311yescharacteristic
65#3674—21no—
66#3674—61no—
67C8×D9C2×D311yescharacteristic
68Dic36—31no—
69Dic36—61no—
70Dic36C2×D311yescharacteristic
71C9×C16—31no—
72C9⋊C16—31no—
73C9⋊C16—61no—
74C2×C3×D9D811yescharacteristic
75C3×C4×C9—41no—
76C3×C4×C9C2×D411yescharacteristic
77C3⋊Dic9—41no—
78C9×Dic3—41no—
79C3×Dic9—41no—
80C3×Dic9D811yescharacteristic
81C2×C3×Q16—91no—
82D3×Q16—31no—
83D3×Q16—91no—
84C2×Dic12—91no—
85C3×Q32—31no—
86#829—91no—
87#829—91no—
88#829—91no—
89#829—91no—
90#829—91no—
91#829—181no—
92#829D911yescharacteristic, direct product factor
93C2×C3⋊C16—91no—
94Dic24—91no—
95D3×C16—91no—
96C32×Q8—21no—
97#634—61no—
98C3×C4×D3—31no—
99C3×C4×D3—121no—
100C3×Dic6—21no—
101C3×Dic6—61no—
102C3×Dic6—121no—
103#627—121no—
104D3×Dic3—121no—
105C32×C8C22×D311yescharacteristic
106C3×C3⋊C8—31no—
107Q8×C9—21no—
108Q8×C9—41no—
109Q8×C9—61no—
110C4×D9—41no—
111C4×D9—121no—
112C4×D9#6711yescharacteristic
113Dic18—21no—
114Dic18—41no—
115Dic18—61no—
116Dic18—121no—
117Dic18—121no—
118C8×C9—21no—
119C8×C9C22×D311yescharacteristic
120C9⋊C8#6711yescharacteristic
121C2×Q32—271noSylow
122C2×C3×C9C2×D811yescharacteristic
123C3×D9Q3212yescomplemented
124C2×C3×Q8—181no—
125D3×Q8—61no—
126D3×Q8—181no—
127C2×Dic6—181no—
128C3×Q16—21no—
129C3×Q16—31no—
130C3×Q16—91no—
131C3×Q16—181no—
132C3×Q16C2×D911yescharacteristic
133C3×Q16D3211yescharacteristic
134C2×C3×C8—91no—
135#216—61no—
136#216—181no—
137Dic12—31no—
138Dic12—91no—
139Dic12—91no—
140Dic12—181no—
141Dic12—181no—
142Dic12C2×D911yescharacteristic
143D3×C8—31no—
144C3×C16—31no—
145C3⋊C16—91no—
146C3⋊C16—91no—
147C3⋊C16—181no—
148C3⋊C16C2×D911yescharacteristic
149C2×C3×D3—31no—
150C32×C4—41no—
151C32×C4D3×D411yescharacteristic
152C3⋊Dic3—121no—
153C3×Dic3—31no—
154C3×Dic3—41no—
155C3×Dic3—121no—
156C2×D9#21311yescharacteristic
157C4×C9—21no—
158C4×C9—41no—
159C4×C9—81no—
160C4×C9—121no—
161C4×C9C2×#6711yescharacteristic
162Dic9—41no—
163Dic9—121no—
164Dic9—241no—
165Dic9#21311yescharacteristic
166C2×Q16—91no—
167C2×Q16—271no—
168Q32—31no—
169Q32—271no—
170Q32—271no—
171Q32—271no—
172C2×C16—271no—
173C3×C9C2×Q3211yescharacteristic, complemented, Sylow
174C3×Q8—21no—
175C3×Q8—21no—
176C3×Q8—41no—
177C3×Q8—61no—
178C3×Q8—181no—
179C3×Q8—361no—
180C2×C3×C4—91no—
181C2×C3×C4—361no—
182C2×Dic3—361no—
183C4×D3—31no—
184C4×D3—121no—
185C4×D3—361no—
186Dic6—21no—
187Dic6—61no—
188Dic6—121no—
189Dic6—181no—
190Dic6—181no—
191Dic6—361no—
192Dic6—361no—
193Dic6—361no—
194C3×C8—21no—
195C3×C8—91no—
196C3×C8C22×D911yescharacteristic
197C3×C8C2×D3211yescharacteristic
198C3⋊C8—31no—
199C2×C32D3×D811yescharacteristic
200C3×D3—32no—
201C2×C9—21no—
202C2×C9C2×#21311yescharacteristic
203D9#82912yesdirect product factor
204C2×Q8—181no—
205C2×Q8—541no—
206Q16—31no—
207Q16—91no—
208Q16—181no—
209Q16—271no—
210Q16—541no—
211Q16D3×D911yescharacteristic
212C2×C8—91no—
213C16—31no—
214C16—271no—
215C22×C3—91no—
216C2×D3—31no—
217C3×C4—21no—
218C3×C4—41no—
219C3×C4—41no—
220C3×C4—81no—
221C3×C4—91no—
222C3×C4—121no—
223C3×C4—361no—
224C3×C4D4×D911yescharacteristic
225C3×C4D3×#6711yescharacteristic
226Dic3—31no—
227Dic3—41no—
228Dic3—121no—
229Dic3—361no—
230Dic3—361no—
231Dic3—721no—
232C32D3×Q3211yescharacteristic
233C9—21no—
234C9C2×#82911yescharacteristic, complemented
235Q8—21no—
236Q8—61no—
237Q8—181no—
238Q8—361no—
239Q8—541no—
240Q8—1081no—
241C2×C4—91no—
242C2×C4—361no—
243C2×C4—1081no—
244C8—91no—
245C8C2×D3×D911yescharacteristic
246C2×C3—21no—
247C2×C3—92no—
248C2×C3D8×D911yescharacteristic
249C2×C3D3×#21311yescharacteristic
250D3—32no—
251C22—91no—
252C4—41no—
253C4—91no—
254C4—121no—
255C4—361no—
256C4—1081no—
257C4D9×#6711yescharacteristic
258C3—21no—
259C3D9×Q3211yescharacteristic, complemented
260C3D3×#82911yescharacteristic
261C2—92no—
262C2D9×#21311yescharacteristic
subgroupG/H
centerC2D9×#213
commutator, cosocleC3×C8×C9C23
FrattiniC3×C8C2×D32
FittingC3×C9×Q16C22
socleC2×C32D3×D8
prime radicalC2×C3×D9D8
hypercenterQ16D3×D9
hypocenterC3×C9C2×Q32
LCSG ▷ C3×C8×C9 ▷ C3×C4×C9 ▷ C2×C3×C9 ▷ C3×C9
UCSC1 ◁ C2 ◁ C4 ◁ C8 ◁ Q16

Complements

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

NH ≅ G/Ntype
3. #11720568C2semidirect
4. C9×#829C2semidirect
5. #11720244C2semidirect
6. #11720235C2semidirect
92. #829D9direct (N × H)
123. C3×D9Q32semidirect
173. C3×C9C2×Q32semidirect
203. D9#829direct (N × H)
234. C9C2×#829semidirect
259. C3D9×Q32semidirect

Maximal subgroups

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

subgroupindex
C3×Q16×D92
D9×Dic122
#117205682
C9×#8292
#117202442
#117202352
D9×C3⋊C162
D3×#8293
D9×Q323