Finite Group Databasebeta

← C9×#2487 #11767208

Subgroups — C9×#2487 #11767208

Order 1152.

876 conjugacy classes of subgroups.

The subgroup lattice has 357 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C4×D4×C9C211yesmaximal, characteristic
2C22×C9×C4⋊C4C211yesmaximal, characteristic, complemented
3C9×#400C212yesmaximal, complemented
4C9×#399C212yesmaximal, complemented
5C9×#389C212yesmaximal, complemented
6C9×#386C212yesmaximal
7C9×#385C212yesmaximal, complemented
8C9×#380C211yesmaximal, characteristic, complemented
9C9×#380C212yesmaximal, complemented
10C3×#2487C311yesmaximal, characteristic
11C22×D4×C9C2211yescharacteristic
12C23×C4×C9C2211yescharacteristic
13C23×C4×C9C2211yescharacteristic
14C23×C4×C9C2212yes—
15C4×D4×C9—24no—
16C2×C9×C4⋊C4—24no—
17C2×C9×C4⋊C4C2212yes—
18C2×C9×C4⋊C4C2212yes—
19C2×C9×C4⋊C4C2212yes—
20C2×C9×C4⋊C4C2211yescharacteristic
21C2×C9×C4⋊C4C2214yes—
22C2×C9×C22⋊C4C2212yes—
23C2×C9×C22⋊C4C2211yescharacteristic
24C2×C9×C22⋊C4C2211yescharacteristic
25C2×C9×C22⋊C4C2214yes—
26C2×C42×C9C2211yescharacteristic
27C9×#95C2214yes—
28C9×#95C2212yes—
29C9×#95C2214yes—
30C2×C3×C4×D4C2×C311yescharacteristic
31C22×C3×C4⋊C4C2×C311yescharacteristic
32C3×#400C2×C312yes—
33C3×#399C2×C312yes—
34C3×#389C2×C312yes—
35C3×#386C2×C312yes—
36C3×#385C2×C312yes—
37C3×#380C2×C312yes—
38C3×#380C2×C311yescharacteristic
39C24×C9C2311yescharacteristic
40C24×C9C2311yescharacteristic
41C2×D4×C9—22no—
42C2×D4×C9—22no—
43C2×D4×C9Q814yes—
44C22×C4×C9—24no—
45C22×C4×C9—24no—
46C22×C4×C9—22no—
47C22×C4×C9—24no—
48C22×C4×C9—44no—
49C22×C4×C9D414yes—
50C22×C4×C9C2311yescharacteristic
51C22×C4×C9C2314yes—
52C22×C4×C9C2314yes—
53C22×C4×C9C2311yescharacteristic
54C22×C4×C9C2311yescharacteristic
55C22×C4×C9C2311yescharacteristic
56C22×C4×C9C2311yescharacteristic
57C9×C4⋊C4—24no—
58C9×C4⋊C4—24no—
59C9×C4⋊C4—22no—
60C9×C4⋊C4—24no—
61C9×C4⋊C4—44no—
62C9×C22⋊C4—22no—
63C9×C22⋊C4—24no—
64C9×C22⋊C4—22no—
65C9×C22⋊C4—44no—
66C42×C9—22no—
67#2487C911yescharacteristic, direct product factor, Sylow
68C22×C3×D4C22×C311yescharacteristic
69C23×C3×C4C22×C311yescharacteristic
70C23×C3×C4C22×C311yescharacteristic
71C23×C3×C4C22×C312yes—
72C3×C4×D4—24no—
73C2×C3×C4⋊C4—24no—
74C2×C3×C4⋊C4C22×C312yes—
75C2×C3×C4⋊C4C22×C312yes—
76C2×C3×C4⋊C4C22×C312yes—
77C2×C3×C4⋊C4C22×C311yescharacteristic
78C2×C3×C4⋊C4C22×C314yes—
79C2×C3×C22⋊C4C22×C312yes—
80C2×C3×C22⋊C4C22×C311yescharacteristic
81C2×C3×C22⋊C4C22×C311yescharacteristic
82C2×C3×C22⋊C4C22×C314yes—
83C2×C3×C42C22×C311yescharacteristic
84C3×#95C22×C314yes—
85C3×#95C22×C312yes—
86C3×#95C22×C314yes—
87C23×C9—22no—
88C23×C9—22no—
89C23×C9—21no—
90C23×C9—22no—
91C23×C9—21no—
92C23×C9—22no—
93C23×C9C2×D412yes—
94C23×C9C2×Q812yes—
95C23×C9C2×Q812yes—
96C23×C9#4112yes—
97C23×C9C2411yescharacteristic
98D4×C9—28no—
99C2×C4×C9—21no—
100C2×C4×C9—22no—
101C2×C4×C9—21no—
102C2×C4×C9—28no—
103C2×C4×C9—21no—
104C2×C4×C9—21no—
105C2×C4×C9—24no—
106C2×C4×C9—24no—
107C2×C4×C9—24no—
108C2×C4×C9—22no—
109C2×C4×C9—24no—
110C2×C4×C9—24no—
111C2×C4×C9—22no—
112C2×C4×C9—24no—
113C2×C4×C9—48no—
114C2×C4×C9—44no—
115C2×C4×C9C2×D412yes—
116C2×C4×C9C2×D412yes—
117C2×C4×C9C2×Q812yes—
118C2×C4×C9#4114yes—
119C2×C4×D4C2×C911yescharacteristic
120C22×C4⋊C4C2×C911yescharacteristic, complemented
121#400C2×C912yescomplemented
122#399C2×C912yescomplemented
123#389C2×C912yescomplemented
124#386C2×C912yes—
125#385C2×C912yescomplemented
126#380C2×C912yescomplemented
127#380C2×C911yescharacteristic, complemented
128C24×C3C23×C311yescharacteristic
129C24×C3C23×C311yescharacteristic
130C2×C3×D4—22no—
131C2×C3×D4—22no—
132C2×C3×D4C3×Q814yes—
133C22×C3×C4—24no—
134C22×C3×C4—24no—
135C22×C3×C4—22no—
136C22×C3×C4—24no—
137C22×C3×C4—44no—
138C22×C3×C4C3×D414yes—
139C22×C3×C4C23×C311yescharacteristic
140C22×C3×C4C23×C314yes—
141C22×C3×C4C23×C314yes—
142C22×C3×C4C23×C311yescharacteristic
143C22×C3×C4C23×C311yescharacteristic
144C22×C3×C4C23×C311yescharacteristic
145C22×C3×C4C23×C311yescharacteristic
146C3×C4⋊C4—24no—
147C3×C4⋊C4—24no—
148C3×C4⋊C4—22no—
149C3×C4⋊C4—24no—
150C3×C4⋊C4—44no—
151C3×C22⋊C4—22no—
152C3×C22⋊C4—24no—
153C3×C22⋊C4—22no—
154C3×C22⋊C4—44no—
155C3×C42—22no—
156C22×C9—22no—
157C22×C9—22no—
158C22×C9—24no—
159C22×C9—24no—
160C22×C9—22no—
161C22×C9—24no—
162C22×C9—41no—
163C22×C9—41no—
164C22×C9—42no—
165C22×C9C22⋊Q814yes—
166C22×C9C22×D411yescharacteristic
167C22×C9C22×Q811yescharacteristic
168C22×C9C2×#4111yescharacteristic
169C22×C9C2×#4112yes—
170C22×C9H(5,𝔽2)12yes—
171C4×C9—22no—
172C4×C9—22no—
173C4×C9—41no—
174C4×C9—41no—
175C4×C9—44no—
176C4×C9—44no—
177C4×C9#12314yes—
178C22×D4C22×C911yescharacteristic
179C23×C4C22×C911yescharacteristic
180C23×C4C22×C911yescharacteristic
181C23×C4C22×C912yes—
182C4×D4—24no—
183C2×C4⋊C4—24no—
184C2×C4⋊C4C22×C912yes—
185C2×C4⋊C4C22×C912yes—
186C2×C4⋊C4C22×C911yescharacteristic
187C2×C4⋊C4C22×C912yes—
188C2×C4⋊C4C22×C914yes—
189C2×C22⋊C4C22×C911yescharacteristic
190C2×C22⋊C4C22×C911yescharacteristic
191C2×C22⋊C4C22×C912yes—
192C2×C22⋊C4C22×C914yes—
193C2×C42C22×C911yescharacteristic
194#95C22×C914yes—
195#95C22×C912yes—
196#95C22×C914yes—
197C23×C3—22no—
198C23×C3—22no—
199C23×C3—21no—
200C23×C3—22no—
201C23×C3—21no—
202C23×C3—22no—
203C23×C3C2×C3×D412yes—
204C23×C3C2×C3×Q812yes—
205C23×C3C2×C3×Q812yes—
206C23×C3C3×#4112yes—
207C23×C3C24×C311yescharacteristic
208C3×D4—28no—
209C2×C3×C4—21no—
210C2×C3×C4—22no—
211C2×C3×C4—21no—
212C2×C3×C4—28no—
213C2×C3×C4—21no—
214C2×C3×C4—21no—
215C2×C3×C4—24no—
216C2×C3×C4—24no—
217C2×C3×C4—24no—
218C2×C3×C4—22no—
219C2×C3×C4—24no—
220C2×C3×C4—24no—
221C2×C3×C4—22no—
222C2×C3×C4—24no—
223C2×C3×C4—48no—
224C2×C3×C4—44no—
225C2×C3×C4C2×C3×D412yes—
226C2×C3×C4C2×C3×D412yes—
227C2×C3×C4C2×C3×Q812yes—
228C2×C3×C4C3×#4114yes—
229C2×C9—24no—
230C2×C9—42no—
231C2×C9C2×C22⋊Q811yescharacteristic
232C2×C9C2×#12311yescharacteristic
233C2×C9#53511yescharacteristic
234C2×C9#55312yes—
235C2×C9#55412yes—
236C24C23×C911yescharacteristic
237C24C23×C911yescharacteristic
238C2×D4—22no—
239C2×D4—22no—
240C2×D4Q8×C914yes—
241C22×C4—24no—
242C22×C4—24no—
243C22×C4—22no—
244C22×C4—24no—
245C22×C4—44no—
246C22×C4D4×C914yes—
247C22×C4C23×C911yescharacteristic
248C22×C4C23×C914yes—
249C22×C4C23×C914yes—
250C22×C4C23×C911yescharacteristic
251C22×C4C23×C911yescharacteristic
252C22×C4C23×C911yescharacteristic
253C22×C4C23×C911yescharacteristic
254C4⋊C4—24no—
255C4⋊C4—24no—
256C4⋊C4—22no—
257C4⋊C4—24no—
258C4⋊C4—44no—
259C22⋊C4—22no—
260C22⋊C4—24no—
261C22⋊C4—22no—
262C22⋊C4—44no—
263C42—22no—
264C22×C3—22no—
265C22×C3—22no—
266C22×C3—24no—
267C22×C3—24no—
268C22×C3—22no—
269C22×C3—24no—
270C22×C3—41no—
271C22×C3—41no—
272C22×C3—42no—
273C22×C3C3×C22⋊Q814yes—
274C22×C3C22×C3×D411yescharacteristic
275C22×C3C22×C3×Q811yescharacteristic
276C22×C3C2×C3×#4111yescharacteristic
277C22×C3C2×C3×#4112yes—
278C22×C3C3×H(5,𝔽2)12yes—
279C3×C4—22no—
280C3×C4—22no—
281C3×C4—41no—
282C3×C4—44no—
283C3×C4—41no—
284C3×C4—44no—
285C3×C4C3×#12314yes—
286C9#248711yescharacteristic, direct product factor, Sylow
287C23—22no—
288C23—22no—
289C23—21no—
290C23—22no—
291C23—21no—
292C23—22no—
293C23C2×D4×C912yes—
294C23C2×Q8×C912yes—
295C23C2×Q8×C912yes—
296C23C9×#4112yes—
297C23C24×C911yescharacteristic
298D4—28no—
299C2×C4—21no—
300C2×C4—22no—
301C2×C4—21no—
302C2×C4—28no—
303C2×C4—21no—
304C2×C4—21no—
305C2×C4—24no—
306C2×C4—24no—
307C2×C4—24no—
308C2×C4—22no—
309C2×C4—24no—
310C2×C4—24no—
311C2×C4—22no—
312C2×C4—24no—
313C2×C4—48no—
314C2×C4—44no—
315C2×C4C2×D4×C912yes—
316C2×C4C2×D4×C912yes—
317C2×C4C2×Q8×C912yes—
318C2×C4C9×#4114yes—
319C2×C3—24no—
320C2×C3—42no—
321C2×C3C2×C3×C22⋊Q811yescharacteristic
322C2×C3C2×C3×#12311yescharacteristic
323C2×C3C3×#53511yescharacteristic
324C2×C3C3×#55312yes—
325C2×C3C3×#55412yes—
326C22—22no—
327C22—22no—
328C22—24no—
329C22—24no—
330C22—22no—
331C22—24no—
332C22—41no—
333C22—41no—
334C22—42no—
335C22C9×C22⋊Q814yes—
336C22C22×D4×C911yescharacteristic
337C22C22×Q8×C911yescharacteristic
338C22C2×C9×#4111yescharacteristic
339C22C2×C9×#4112yes—
340C22C9×H(5,𝔽2)12yes—
341C4—22no—
342C4—22no—
343C4—41no—
344C4—44no—
345C4—41no—
346C4—44no—
347C4C9×#12314yes—
348C3C3×#248711yescharacteristic
349C2—24no—
350C2—42no—
351C2C2×C9×C22⋊Q811yescharacteristic
352C2C2×C9×#12311yescharacteristic
353C2C9×#53511yescharacteristic
354C2C9×#55312yes—
355C2C9×#55412yes—
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
2. C22×C9×C4⋊C4C2semidirect
3. C9×#400C2semidirect
4. C9×#399C2semidirect
5. C9×#389C2semidirect
7. C9×#385C2semidirect
8. C9×#380C2semidirect
9. C9×#380C2semidirect
67. #2487C9direct (N × H)
120. C22×C4⋊C4C2×C9semidirect
121. #400C2×C9semidirect
122. #399C2×C9semidirect
123. #389C2×C9semidirect
125. #385C2×C9semidirect
126. #380C2×C9semidirect
127. #380C2×C9semidirect
286. C9#2487direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C4×D4×C92
C22×C9×C4⋊C42
C9×#4002
C9×#3992
C9×#3892
C9×#3862
C9×#3852
C9×#3802
C3×#24873