Finite Group Databasebeta

← C9×#2037 #11766758

Subgroups — C9×#2037 #11766758

Order 1152.

489 conjugacy classes of subgroups.

The subgroup lattice has 393 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C9×#535C211yesmaximal, characteristic
2C9×#428C211yesmaximal, characteristic, complemented
3C2×C9×#104C211yesmaximal, characteristic, complemented
4C9×#417C211yesmaximal, characteristic, complemented
5C2×C9×#100C211yesmaximal, characteristic, complemented
6C9×#390C211yesmaximal, characteristic, complemented
7C9×#339C211yesmaximal, characteristic, complemented
8C3×#2037C311yesmaximal, characteristic
9C2×C9×#41C2211yescharacteristic
10C22×D4×C9C2211yescharacteristic
11C2×C9×M16C2211yescharacteristic
12C2×C9×M16C2211yescharacteristic
13C9×#127—21no—
14C9×#124—21no—
15C9×#121—21no—
16C9×#121—21no—
17C9×#120—22no—
18C9×#117C2211yescharacteristic
19C2×C9×C4⋊C4C2211yescharacteristic
20C2×C9×C22⋊C4—22no—
21C2×C42×C9C2211yescharacteristic
22C9×#107—21no—
23C9×#106—21no—
24C9×#104—22no—
25C9×#103—21no—
26C9×#102—21no—
27C9×#100—22no—
28C3×#535C2×C311yescharacteristic
29C3×#428C2×C311yescharacteristic
30C2×C3×#104C2×C311yescharacteristic
31C3×#417C2×C311yescharacteristic
32C2×C3×#100C2×C311yescharacteristic
33C3×#390C2×C311yescharacteristic
34C3×#339C2×C311yescharacteristic
35C24×C9D412yes—
36C9×#41—21no—
37C9×#41—21no—
38C9×#41—21no—
39C9×#41—21no—
40C2×Q8×C9D411yescharacteristic
41C2×D4×C9—21no—
42C2×D4×C9—22no—
43C2×D4×C9—22no—
44C2×D4×C9—21no—
45C2×D4×C9—21no—
46C2×D4×C9—21no—
47C2×D4×C9—21no—
48C2×D4×C9—21no—
49C2×D4×C9—21no—
50C2×D4×C9D411yescharacteristic
51C22×C4×C9—21no—
52C22×C4×C9—21no—
53C22×C4×C9—21no—
54C22×C4×C9C2311yescharacteristic
55C9×M16—21no—
56C9×M16—21no—
57C9×M16—21no—
58C9×M16D412yescomplemented
59C2×C8×C9—21no—
60C2×C8×C9—21no—
61C9×C4⋊C4—21no—
62C9×C4⋊C4—21no—
63C9×C4⋊C4D411yescharacteristic
64C9×C4⋊C4D411yescharacteristic
65C9×C22⋊C4—22no—
66C9×C22⋊C4—22no—
67C9×C22⋊C4—21no—
68C9×C22⋊C4—44no—
69C42×C9—21no—
70C42×C9—21no—
71C42×C9—21no—
72#2037C911yescharacteristic, direct product factor, Sylow
73C2×C3×#41C22×C311yescharacteristic
74C22×C3×D4C22×C311yescharacteristic
75C2×C3×M16C22×C311yescharacteristic
76C2×C3×M16C22×C311yescharacteristic
77C3×#127—21no—
78C3×#124—21no—
79C3×#121—21no—
80C3×#121—21no—
81C3×#120—22no—
82C3×#117C22×C311yescharacteristic
83C2×C3×C4⋊C4C22×C311yescharacteristic
84C2×C3×C22⋊C4—22no—
85C2×C3×C42C22×C311yescharacteristic
86C3×#107—21no—
87C3×#106—21no—
88C3×#104—22no—
89C3×#103—21no—
90C3×#102—21no—
91C3×#100—22no—
92C23×C9—22no—
93C23×C9—21no—
94C23×C9—22no—
95C23×C9—22no—
96C23×C9—42no—
97C23×C9—42no—
98C23×C9C2×D411yescharacteristic
99Q8×C9—21no—
100Q8×C9—21no—
101D4×C9—21no—
102D4×C9—21no—
103D4×C9—41no—
104D4×C9—41no—
105D4×C9—41no—
106D4×C9—41no—
107D4×C9—41no—
108D4×C9—41no—
109D4×C9—82no—
110D4×C9—82no—
111C2×C4×C9—22no—
112C2×C4×C9—21no—
113C2×C4×C9—21no—
114C2×C4×C9—21no—
115C2×C4×C9—41no—
116C2×C4×C9—41no—
117C2×C4×C9—41no—
118C2×C4×C9—41no—
119C2×C4×C9—42no—
120C2×C4×C9—41no—
121C2×C4×C9C2×D411yescharacteristic
122C2×C4×C9C2×D411yescharacteristic
123C2×C4×C9C2×D411yescharacteristic
124C2×C4×C9#4111yescharacteristic
125C2×C4×C9#4111yescharacteristic
126C2×C4×C9#4111yescharacteristic
127C8×C9—22no—
128C8×C9—41no—
129#535C2×C911yescharacteristic
130#428C2×C911yescharacteristic, complemented
131C2×#104C2×C911yescharacteristic, complemented
132#417C2×C911yescharacteristic, complemented
133C2×#100C2×C911yescharacteristic, complemented
134#390C2×C911yescharacteristic, complemented
135#339C2×C911yescharacteristic, complemented
136C24×C3C3×D412yes—
137C3×#41—21no—
138C3×#41—21no—
139C3×#41—21no—
140C3×#41—21no—
141C2×C3×Q8C3×D411yescharacteristic
142C2×C3×D4—21no—
143C2×C3×D4—22no—
144C2×C3×D4—22no—
145C2×C3×D4—21no—
146C2×C3×D4—21no—
147C2×C3×D4—21no—
148C2×C3×D4—21no—
149C2×C3×D4—21no—
150C2×C3×D4—21no—
151C2×C3×D4C3×D411yescharacteristic
152C22×C3×C4—21no—
153C22×C3×C4—21no—
154C22×C3×C4—21no—
155C22×C3×C4C23×C311yescharacteristic
156C3×M16—21no—
157C3×M16—21no—
158C3×M16—21no—
159C3×M16C3×D412yes—
160C2×C3×C8—21no—
161C2×C3×C8—21no—
162C3×C4⋊C4—21no—
163C3×C4⋊C4—21no—
164C3×C4⋊C4C3×D411yescharacteristic
165C3×C4⋊C4C3×D411yescharacteristic
166C3×C22⋊C4—22no—
167C3×C22⋊C4—22no—
168C3×C22⋊C4—21no—
169C3×C22⋊C4—44no—
170C3×C42—21no—
171C3×C42—21no—
172C3×C42—21no—
173C22×C9—21no—
174C22×C9—21no—
175C22×C9—44no—
176C22×C9—41no—
177C22×C9—42no—
178C22×C9—41no—
179C22×C9—42no—
180C22×C9—41no—
181C22×C9—42no—
182C22×C9—82no—
183C22×C9#12011yescharacteristic
184C22×C9#12111yescharacteristic
185C22×C9#12311yescharacteristic
186C4×C9—42no—
187C4×C9—41no—
188C4×C9—41no—
189C4×C9—41no—
190C4×C9—81no—
191C4×C9#12111yescharacteristic
192C4×C9#12111yescharacteristic
193C4×C9#12311yescharacteristic
194C4×C9#12411yescharacteristic
195C2×#41C22×C911yescharacteristic
196C22×D4C22×C911yescharacteristic
197C2×M16C22×C911yescharacteristic
198C2×M16C22×C911yescharacteristic
199#127—21no—
200#124—21no—
201#121—21no—
202#121—21no—
203#120—22no—
204#117C22×C911yescharacteristic
205C2×C4⋊C4C22×C911yescharacteristic
206C2×C22⋊C4—22no—
207C2×C42C22×C911yescharacteristic
208#107—21no—
209#106—21no—
210#104—22no—
211#103—21no—
212#102—21no—
213#100—22no—
214C23×C3—22no—
215C23×C3—21no—
216C23×C3—22no—
217C23×C3—22no—
218C23×C3—42no—
219C23×C3—42no—
220C23×C3C2×C3×D411yescharacteristic
221C3×Q8—21no—
222C3×Q8—21no—
223C3×D4—21no—
224C3×D4—21no—
225C3×D4—41no—
226C3×D4—41no—
227C3×D4—41no—
228C3×D4—41no—
229C3×D4—41no—
230C3×D4—41no—
231C3×D4—82no—
232C3×D4—82no—
233C2×C3×C4—22no—
234C2×C3×C4—21no—
235C2×C3×C4—21no—
236C2×C3×C4—21no—
237C2×C3×C4—41no—
238C2×C3×C4—41no—
239C2×C3×C4—41no—
240C2×C3×C4—41no—
241C2×C3×C4—42no—
242C2×C3×C4—41no—
243C2×C3×C4C2×C3×D411yescharacteristic
244C2×C3×C4C2×C3×D411yescharacteristic
245C2×C3×C4C2×C3×D411yescharacteristic
246C2×C3×C4C3×#4111yescharacteristic
247C2×C3×C4C3×#4111yescharacteristic
248C2×C3×C4C3×#4111yescharacteristic
249C3×C8—22no—
250C3×C8—41no—
251C2×C9—21no—
252C2×C9—21no—
253C2×C9—81no—
254C2×C9—82no—
255C2×C9#39411yescharacteristic
256C2×C9#45311yescharacteristic
257C2×C9#45511yescharacteristic
258C24D4×C912yes—
259#41—21no—
260#41—21no—
261#41—21no—
262#41—21no—
263C2×Q8D4×C911yescharacteristic
264C2×D4—21no—
265C2×D4—22no—
266C2×D4—22no—
267C2×D4—21no—
268C2×D4—21no—
269C2×D4—21no—
270C2×D4—21no—
271C2×D4—21no—
272C2×D4—21no—
273C2×D4D4×C911yescharacteristic
274C22×C4—21no—
275C22×C4—21no—
276C22×C4—21no—
277C22×C4C23×C911yescharacteristic
278M16—21no—
279M16—21no—
280M16—21no—
281M16D4×C912yescomplemented
282C2×C8—21no—
283C2×C8—21no—
284C4⋊C4—21no—
285C4⋊C4—21no—
286C4⋊C4D4×C911yescharacteristic
287C4⋊C4D4×C911yescharacteristic
288C22⋊C4—22no—
289C22⋊C4—22no—
290C22⋊C4—21no—
291C22⋊C4—44no—
292C42—21no—
293C42—21no—
294C42—21no—
295C22×C3—21no—
296C22×C3—21no—
297C22×C3—44no—
298C22×C3—41no—
299C22×C3—42no—
300C22×C3—41no—
301C22×C3—42no—
302C22×C3—41no—
303C22×C3—42no—
304C22×C3—82no—
305C22×C3C3×#12011yescharacteristic
306C22×C3C3×#12111yescharacteristic
307C22×C3C3×#12311yescharacteristic
308C3×C4—42no—
309C3×C4—41no—
310C3×C4—41no—
311C3×C4—41no—
312C3×C4—81no—
313C3×C4C3×#12111yescharacteristic
314C3×C4C3×#12111yescharacteristic
315C3×C4C3×#12311yescharacteristic
316C3×C4C3×#12411yescharacteristic
317C9#203711yescharacteristic, direct product factor, Sylow
318C23—22no—
319C23—21no—
320C23—22no—
321C23—22no—
322C23—42no—
323C23—42no—
324C23C2×D4×C911yescharacteristic
325Q8—21no—
326Q8—21no—
327D4—21no—
328D4—21no—
329D4—41no—
330D4—41no—
331D4—41no—
332D4—41no—
333D4—41no—
334D4—41no—
335D4—82no—
336D4—82no—
337C2×C4—22no—
338C2×C4—21no—
339C2×C4—21no—
340C2×C4—21no—
341C2×C4—41no—
342C2×C4—41no—
343C2×C4—41no—
344C2×C4—41no—
345C2×C4—42no—
346C2×C4—41no—
347C2×C4C2×D4×C911yescharacteristic
348C2×C4C2×D4×C911yescharacteristic
349C2×C4C2×D4×C911yescharacteristic
350C2×C4C9×#4111yescharacteristic
351C2×C4C9×#4111yescharacteristic
352C2×C4C9×#4111yescharacteristic
353C8—22no—
354C8—41no—
355C2×C3—21no—
356C2×C3—21no—
357C2×C3—82no—
358C2×C3—81no—
359C2×C3C3×#39411yescharacteristic
360C2×C3C3×#45311yescharacteristic
361C2×C3C3×#45511yescharacteristic
362C22—21no—
363C22—21no—
364C22—44no—
365C22—41no—
366C22—42no—
367C22—41no—
368C22—42no—
369C22—41no—
370C22—42no—
371C22—82no—
372C22C9×#12011yescharacteristic
373C22C9×#12111yescharacteristic
374C22C9×#12311yescharacteristic
375C4—42no—
376C4—41no—
377C4—41no—
378C4—41no—
379C4—81no—
380C4C9×#12111yescharacteristic
381C4C9×#12111yescharacteristic
382C4C9×#12311yescharacteristic
383C4C9×#12411yescharacteristic
384C3C3×#203711yescharacteristic
385C2—21no—
386C2—21no—
387C2—82no—
388C2—81no—
389C2C9×#39411yescharacteristic
390C2C9×#45311yescharacteristic
391C2C9×#45511yescharacteristic
subgroupG/H
centerC22×C9#120
commutatorC22×C4C23×C9
Frattini, cosocleC22×C3×C4C23×C3
socleC22×C3C3×#120
prime radicalC3×#535C2×C3
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C9 ◁ C22×C4×C9 ◁ G

Complements

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

NH ≅ G/Ntype
2. C9×#428C2semidirect
3. C2×C9×#104C2semidirect
4. C9×#417C2semidirect
5. C2×C9×#100C2semidirect
6. C9×#390C2semidirect
7. C9×#339C2semidirect
58. C9×M16D4semidirect
72. #2037C9direct (N × H)
130. #428C2×C9semidirect
131. C2×#104C2×C9semidirect
132. #417C2×C9semidirect
133. C2×#100C2×C9semidirect
134. #390C2×C9semidirect
135. #339C2×C9semidirect
281. M16D4×C9semidirect
317. C9#2037direct (N × H)

Maximal subgroups

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

subgroupindex
C9×#5352
C9×#4282
C2×C9×#1042
C9×#4172
C2×C9×#1002
C9×#3902
C9×#3392
C3×#20373