Finite Group Databasebeta

← C9×#2486 #11767207

Subgroups — C9×#2486 #11767207

Order 1152.

936 conjugacy classes of subgroups.

The subgroup lattice has 363 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C9×#123C212yesmaximal
2C2×C4×D4×C9C211yesmaximal, characteristic
3C22×C9×C4⋊C4C211yesmaximal, characteristic, complemented
4C9×#398C212yesmaximal, complemented
5C9×#397C212yesmaximal, complemented
6C9×#389C212yesmaximal, complemented
7C9×#381C212yesmaximal, complemented
8C9×#380C211yesmaximal, characteristic, complemented
9C9×#380C212yesmaximal, complemented
10C3×#2486C311yesmaximal, characteristic
11C22×D4×C9C2211yescharacteristic
12C23×C4×C9C2212yes—
13C23×C4×C9C2211yescharacteristic
14C23×C4×C9C2211yescharacteristic
15C9×#123—28no—
16C4×D4×C9—24no—
17C2×C9×C4⋊C4—24no—
18C2×C9×C4⋊C4C2214yes—
19C2×C9×C4⋊C4C2212yes—
20C2×C9×C4⋊C4C2212yes—
21C2×C9×C4⋊C4C2212yes—
22C2×C9×C4⋊C4C2211yescharacteristic
23C2×C9×C22⋊C4C2212yes—
24C2×C9×C22⋊C4C2214yes—
25C2×C9×C22⋊C4C2211yescharacteristic
26C2×C9×C22⋊C4C2211yescharacteristic
27C2×C42×C9C2211yescharacteristic
28C9×#95C2214yes—
29C9×#95C2212yes—
30C9×#95C2214yes—
31C2×C3×#123C2×C312yes—
32C2×C3×C4×D4C2×C311yescharacteristic
33C22×C3×C4⋊C4C2×C311yescharacteristic
34C3×#398C2×C312yes—
35C3×#397C2×C312yes—
36C3×#389C2×C312yes—
37C3×#381C2×C312yes—
38C3×#380C2×C312yes—
39C3×#380C2×C311yescharacteristic
40C24×C9C2311yescharacteristic
41C24×C9C2311yescharacteristic
42C2×D4×C9—22no—
43C2×D4×C9—22no—
44C2×D4×C9D414yes—
45C22×C4×C9—24no—
46C22×C4×C9—24no—
47C22×C4×C9—24no—
48C22×C4×C9—24no—
49C22×C4×C9—22no—
50C22×C4×C9—24no—
51C22×C4×C9D414yes—
52C22×C4×C9C2311yescharacteristic
53C22×C4×C9C2314yes—
54C22×C4×C9C2314yes—
55C22×C4×C9C2311yescharacteristic
56C22×C4×C9C2311yescharacteristic
57C22×C4×C9C2311yescharacteristic
58C22×C4×C9C2311yescharacteristic
59C9×C4⋊C4—24no—
60C9×C4⋊C4—24no—
61C9×C4⋊C4—22no—
62C9×C4⋊C4—28no—
63C9×C4⋊C4—24no—
64C9×C22⋊C4—22no—
65C9×C22⋊C4—24no—
66C9×C22⋊C4—28no—
67C9×C22⋊C4—22no—
68C42×C9—22no—
69#2486C911yescharacteristic, direct product factor, Sylow
70C22×C3×D4C22×C311yescharacteristic
71C23×C3×C4C22×C311yescharacteristic
72C23×C3×C4C22×C312yes—
73C23×C3×C4C22×C311yescharacteristic
74C3×#123—28no—
75C3×C4×D4—24no—
76C2×C3×C4⋊C4—24no—
77C2×C3×C4⋊C4C22×C312yes—
78C2×C3×C4⋊C4C22×C312yes—
79C2×C3×C4⋊C4C22×C314yes—
80C2×C3×C4⋊C4C22×C312yes—
81C2×C3×C4⋊C4C22×C311yescharacteristic
82C2×C3×C22⋊C4C22×C312yes—
83C2×C3×C22⋊C4C22×C314yes—
84C2×C3×C22⋊C4C22×C311yescharacteristic
85C2×C3×C22⋊C4C22×C311yescharacteristic
86C2×C3×C42C22×C311yescharacteristic
87C3×#95C22×C314yes—
88C3×#95C22×C312yes—
89C3×#95C22×C314yes—
90C23×C9—22no—
91C23×C9—22no—
92C23×C9—21no—
93C23×C9—22no—
94C23×C9—21no—
95C23×C9—22no—
96C23×C9C2×D412yes—
97C23×C9C2×D412yes—
98C23×C9C2×D412yes—
99C23×C9#4112yes—
100C23×C9C2411yescharacteristic
101D4×C9—28no—
102C2×C4×C9—21no—
103C2×C4×C9—22no—
104C2×C4×C9—21no—
105C2×C4×C9—28no—
106C2×C4×C9—21no—
107C2×C4×C9—24no—
108C2×C4×C9—24no—
109C2×C4×C9—21no—
110C2×C4×C9—24no—
111C2×C4×C9—24no—
112C2×C4×C9—24no—
113C2×C4×C9—22no—
114C2×C4×C9—22no—
115C2×C4×C9—24no—
116C2×C4×C9—48no—
117C2×C4×C9—44no—
118C2×C4×C9C2×D412yes—
119C2×C4×C9C2×D412yes—
120C2×C4×C9C2×D412yes—
121C2×C4×C9#4114yes—
122C2×#123C2×C912yes—
123C2×C4×D4C2×C911yescharacteristic
124C22×C4⋊C4C2×C911yescharacteristic, complemented
125#398C2×C912yescomplemented
126#397C2×C912yescomplemented
127#389C2×C912yescomplemented
128#381C2×C912yescomplemented
129#380C2×C912yescomplemented
130#380C2×C911yescharacteristic, complemented
131C24×C3C23×C311yescharacteristic
132C24×C3C23×C311yescharacteristic
133C2×C3×D4—22no—
134C2×C3×D4—22no—
135C2×C3×D4C3×D414yes—
136C22×C3×C4—24no—
137C22×C3×C4—24no—
138C22×C3×C4—24no—
139C22×C3×C4—24no—
140C22×C3×C4—22no—
141C22×C3×C4—24no—
142C22×C3×C4C3×D414yes—
143C22×C3×C4C23×C311yescharacteristic
144C22×C3×C4C23×C311yescharacteristic
145C22×C3×C4C23×C314yes—
146C22×C3×C4C23×C314yes—
147C22×C3×C4C23×C311yescharacteristic
148C22×C3×C4C23×C311yescharacteristic
149C22×C3×C4C23×C311yescharacteristic
150C3×C4⋊C4—24no—
151C3×C4⋊C4—24no—
152C3×C4⋊C4—22no—
153C3×C4⋊C4—28no—
154C3×C4⋊C4—24no—
155C3×C22⋊C4—22no—
156C3×C22⋊C4—24no—
157C3×C22⋊C4—28no—
158C3×C22⋊C4—22no—
159C3×C42—22no—
160C22×C9—22no—
161C22×C9—22no—
162C22×C9—24no—
163C22×C9—24no—
164C22×C9—22no—
165C22×C9—24no—
166C22×C9—41no—
167C22×C9—41no—
168C22×C9—42no—
169C22×C9#12114yes—
170C22×C9C22×D411yescharacteristic
171C22×C9C22×D411yescharacteristic
172C22×C9C2×#4111yescharacteristic
173C22×C9C2×#4112yes—
174C22×C92−1+412yes—
175C4×C9—22no—
176C4×C9—22no—
177C4×C9—44no—
178C4×C9—41no—
179C4×C9—41no—
180C4×C9—44no—
181C4×C9#12314yescomplemented
182C22×D4C22×C911yescharacteristic
183C23×C4C22×C912yes—
184C23×C4C22×C911yescharacteristic
185C23×C4C22×C911yescharacteristic
186#123—28no—
187C4×D4—24no—
188C2×C4⋊C4—24no—
189C2×C4⋊C4C22×C912yes—
190C2×C4⋊C4C22×C912yes—
191C2×C4⋊C4C22×C911yescharacteristic
192C2×C4⋊C4C22×C914yes—
193C2×C4⋊C4C22×C912yes—
194C2×C22⋊C4C22×C911yescharacteristic
195C2×C22⋊C4C22×C911yescharacteristic
196C2×C22⋊C4C22×C912yes—
197C2×C22⋊C4C22×C914yes—
198C2×C42C22×C911yescharacteristic
199#95C22×C914yes—
200#95C22×C912yes—
201#95C22×C914yes—
202C23×C3—22no—
203C23×C3—22no—
204C23×C3—21no—
205C23×C3—22no—
206C23×C3—21no—
207C23×C3—22no—
208C23×C3C2×C3×D412yes—
209C23×C3C2×C3×D412yes—
210C23×C3C2×C3×D412yes—
211C23×C3C3×#4112yes—
212C23×C3C24×C311yescharacteristic
213C3×D4—28no—
214C2×C3×C4—21no—
215C2×C3×C4—22no—
216C2×C3×C4—21no—
217C2×C3×C4—28no—
218C2×C3×C4—21no—
219C2×C3×C4—24no—
220C2×C3×C4—24no—
221C2×C3×C4—21no—
222C2×C3×C4—24no—
223C2×C3×C4—24no—
224C2×C3×C4—24no—
225C2×C3×C4—22no—
226C2×C3×C4—22no—
227C2×C3×C4—24no—
228C2×C3×C4—48no—
229C2×C3×C4—44no—
230C2×C3×C4C2×C3×D412yes—
231C2×C3×C4C2×C3×D412yes—
232C2×C3×C4C2×C3×D412yes—
233C2×C3×C4C3×#4114yes—
234C2×C9—24no—
235C2×C9—42no—
236C2×C9C2×#12111yescharacteristic
237C2×C9C2×#12311yescharacteristic
238C2×C9#53611yescharacteristic
239C2×C9#54712yes—
240C2×C9#55212yes—
241C24C23×C911yescharacteristic
242C24C23×C911yescharacteristic
243C2×D4—22no—
244C2×D4—22no—
245C2×D4D4×C914yes—
246C22×C4—24no—
247C22×C4—24no—
248C22×C4—24no—
249C22×C4—24no—
250C22×C4—22no—
251C22×C4—24no—
252C22×C4D4×C914yes—
253C22×C4C23×C911yescharacteristic
254C22×C4C23×C911yescharacteristic
255C22×C4C23×C914yes—
256C22×C4C23×C914yes—
257C22×C4C23×C911yescharacteristic
258C22×C4C23×C911yescharacteristic
259C22×C4C23×C911yescharacteristic
260C4⋊C4—24no—
261C4⋊C4—24no—
262C4⋊C4—22no—
263C4⋊C4—28no—
264C4⋊C4—24no—
265C22⋊C4—22no—
266C22⋊C4—24no—
267C22⋊C4—28no—
268C22⋊C4—22no—
269C42—22no—
270C22×C3—22no—
271C22×C3—22no—
272C22×C3—24no—
273C22×C3—24no—
274C22×C3—22no—
275C22×C3—24no—
276C22×C3—41no—
277C22×C3—41no—
278C22×C3—42no—
279C22×C3C3×#12114yes—
280C22×C3C22×C3×D411yescharacteristic
281C22×C3C22×C3×D411yescharacteristic
282C22×C3C2×C3×#4111yescharacteristic
283C22×C3C2×C3×#4112yes—
284C22×C3C3×2−1+412yes—
285C3×C4—22no—
286C3×C4—22no—
287C3×C4—44no—
288C3×C4—41no—
289C3×C4—41no—
290C3×C4—44no—
291C3×C4C3×#12314yes—
292C9#248611yescharacteristic, direct product factor, Sylow
293C23—22no—
294C23—22no—
295C23—21no—
296C23—22no—
297C23—21no—
298C23—22no—
299C23C2×D4×C912yes—
300C23C2×D4×C912yes—
301C23C2×D4×C912yes—
302C23C9×#4112yes—
303C23C24×C911yescharacteristic
304D4—28no—
305C2×C4—21no—
306C2×C4—22no—
307C2×C4—21no—
308C2×C4—28no—
309C2×C4—21no—
310C2×C4—24no—
311C2×C4—24no—
312C2×C4—21no—
313C2×C4—24no—
314C2×C4—24no—
315C2×C4—24no—
316C2×C4—22no—
317C2×C4—22no—
318C2×C4—24no—
319C2×C4—48no—
320C2×C4—44no—
321C2×C4C2×D4×C912yes—
322C2×C4C2×D4×C912yes—
323C2×C4C2×D4×C912yes—
324C2×C4C9×#4114yes—
325C2×C3—24no—
326C2×C3—42no—
327C2×C3C2×C3×#12111yescharacteristic
328C2×C3C2×C3×#12311yescharacteristic
329C2×C3C3×#53611yescharacteristic
330C2×C3C3×#54712yes—
331C2×C3C3×#55212yes—
332C22—22no—
333C22—22no—
334C22—24no—
335C22—24no—
336C22—22no—
337C22—24no—
338C22—41no—
339C22—41no—
340C22—42no—
341C22C9×#12114yes—
342C22C22×D4×C911yescharacteristic
343C22C22×D4×C911yescharacteristic
344C22C2×C9×#4111yescharacteristic
345C22C2×C9×#4112yes—
346C22C9×2−1+412yes—
347C4—22no—
348C4—22no—
349C4—44no—
350C4—41no—
351C4—41no—
352C4—44no—
353C4C9×#12314yescomplemented
354C3C3×#248611yescharacteristic
355C2—24no—
356C2—42no—
357C2C2×C9×#12111yescharacteristic
358C2C2×C9×#12311yescharacteristic
359C2C9×#53611yescharacteristic
360C2C9×#54712yes—
361C2C9×#55212yes—
subgroupG/H
centerC23×C9C24
commutatorC23C24×C9
Frattini, socle, cosocleC23×C3C24×C3
prime radicalC22×C3×D4C22×C3
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23×C9 ◁ G

Complements

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

NH ≅ G/Ntype
3. C22×C9×C4⋊C4C2semidirect
4. C9×#398C2semidirect
5. C9×#397C2semidirect
6. C9×#389C2semidirect
7. C9×#381C2semidirect
8. C9×#380C2semidirect
9. C9×#380C2semidirect
69. #2486C9direct (N × H)
124. C22×C4⋊C4C2×C9semidirect
125. #398C2×C9semidirect
126. #397C2×C9semidirect
127. #389C2×C9semidirect
128. #381C2×C9semidirect
129. #380C2×C9semidirect
130. #380C2×C9semidirect
181. C4×C9#123semidirect
292. C9#2486direct (N × H)
353. C4C9×#123semidirect

Maximal subgroups

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

subgroupindex
C2×C9×#1232
C2×C4×D4×C92
C22×C9×C4⋊C42
C9×#3982
C9×#3972
C9×#3892
C9×#3812
C9×#3802
C3×#24863