Finite Group Databasebeta

← C9×#3480 #11768201

Subgroups — C9×#3480 #11768201

Order 1152.

1668 conjugacy classes of subgroups.

The subgroup lattice has 387 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C9×#559C213yesmaximal, complemented
2C9×#557C211yesmaximal, characteristic, complemented
3C9×#556C213yesmaximal, complemented
4C9×#553C216yesmaximal, complemented
5C9×#550C211yesmaximal, characteristic, complemented
6C9×#548C212yesmaximal, complemented
7C9×#532C213yesmaximal, complemented
8C9×#529C216yesmaximal, complemented
9C4×C9×#41C212yesmaximal, complemented
10C4×C9×#41C213yesmaximal, complemented
11C2×C4×Q8×C9C211yesmaximal, characteristic, complemented
12C3×#3480C311yesmaximal, characteristic
13C2×C9×#41C2213yes—
14C2×C9×#41C2212yes—
15C22×Q8×C9C2211yescharacteristic
16C9×C4⋊Q8C2213yes—
17C9×#127C2213yes—
18C9×#126C22112yes—
19C9×#125C2216yes—
20C9×#124C2216yes—
21C9×#124C2216yes—
22C9×#123C22112yes—
23C9×C22⋊Q8C2216yes—
24C9×#121C2216yes—
25C9×#121C2216yes—
26C9×#121C2216yes—
27C4×Q8×C9C2213yes—
28C4×Q8×C9C2212yes—
29C4×Q8×C9C2211yescharacteristic
30C4×Q8×C9C2213yes—
31C4×Q8×C9C2213yes—
32C4×Q8×C9C2213yes—
33C4×Q8×C9C2211yescharacteristic
34C4×D4×C9C2216yes—
35C4×D4×C9C2216yes—
36C4×D4×C9C2216yes—
37C4×D4×C9C2213yes—
38C4×D4×C9C2216yes—
39C4×D4×C9C2216yes—
40C4×D4×C9C2213yes—
41C9×#117C2216yes—
42C9×#117C2216yes—
43C9×#117C2211yescharacteristic
44C2×C9×C4⋊C4C2213yes—
45C2×C42×C9C2216yes—
46C2×C42×C9C2213yes—
47C3×#559C2×C313yes—
48C3×#557C2×C311yescharacteristic
49C3×#556C2×C313yes—
50C3×#553C2×C316yes—
51C3×#550C2×C311yescharacteristic
52C3×#548C2×C312yes—
53C3×#532C2×C313yes—
54C3×#529C2×C316yes—
55C3×C4×#41C2×C313yes—
56C3×C4×#41C2×C312yes—
57C2×C3×C4×Q8C2×C311yescharacteristic
58C9×#41—28no—
59C9×#41—212no—
60C2×Q8×C9—24no—
61C2×Q8×C9C2313yes—
62C2×Q8×C9C2313yes—
63C2×Q8×C9C2311yescharacteristic
64C2×D4×C9C2316yes—
65C2×D4×C9C2316yes—
66C2×D4×C9C2313yes—
67C2×D4×C9C2316yes—
68C22×C4×C9C2313yes—
69C22×C4×C9C2316yes—
70C22×C4×C9C2316yes—
71C22×C4×C9C2313yes—
72C22×C4×C9C2316yes—
73C22×C4×C9C2311yescharacteristic
74C9×C4⋊C4C2313yes—
75C9×C4⋊C4C2313yes—
76C9×C4⋊C4C2316yes—
77C9×C4⋊C4C2311yescharacteristic
78C9×C4⋊C4C2311yescharacteristic
79C9×C4⋊C4C2316yes—
80C9×C4⋊C4C2316yes—
81C9×C4⋊C4C2316yes—
82C9×C4⋊C4C2316yes—
83C9×C22⋊C4C2312yes—
84C9×C22⋊C4C2316yes—
85C9×C22⋊C4C23112yes—
86C9×C22⋊C4C2316yes—
87C9×C22⋊C4C23112yes—
88C42×C9C2316yes—
89C42×C9C2316yes—
90C42×C9C2313yes—
91C42×C9C2313yes—
92C42×C9C2312yes—
93C42×C9C2313yes—
94C42×C9C2313yes—
95#3480C911yescharacteristic, direct product factor, Sylow
96C2×C3×#41C22×C313yes—
97C2×C3×#41C22×C312yes—
98C22×C3×Q8C22×C311yescharacteristic
99C3×C4⋊Q8C22×C313yes—
100C3×#127C22×C313yes—
101C3×#126C22×C3112yes—
102C3×#125C22×C316yes—
103C3×#124C22×C316yes—
104C3×#124C22×C316yes—
105C3×#123C22×C3112yes—
106C3×C22⋊Q8C22×C316yes—
107C3×#121C22×C316yes—
108C3×#121C22×C316yes—
109C3×#121C22×C316yes—
110C3×C4×Q8C22×C313yes—
111C3×C4×Q8C22×C313yes—
112C3×C4×Q8C22×C311yescharacteristic
113C3×C4×Q8C22×C313yes—
114C3×C4×Q8C22×C311yescharacteristic
115C3×C4×Q8C22×C312yes—
116C3×C4×Q8C22×C313yes—
117C3×C4×D4C22×C313yes—
118C3×C4×D4C22×C316yes—
119C3×C4×D4C22×C316yes—
120C3×C4×D4C22×C316yes—
121C3×C4×D4C22×C313yes—
122C3×C4×D4C22×C316yes—
123C3×C4×D4C22×C316yes—
124C3×#117C22×C311yescharacteristic
125C3×#117C22×C316yes—
126C3×#117C22×C316yes—
127C2×C3×C4⋊C4C22×C313yes—
128C2×C3×C42C22×C313yes—
129C2×C3×C42C22×C316yes—
130C23×C9C2416yes—
131C23×C9C2411yescharacteristic
132Q8×C9—26no—
133Q8×C9—26no—
134Q8×C9#4114yescomplemented
135D4×C9—212no—
136D4×C9—212no—
137D4×C9—26no—
138D4×C9—46no—
139C2×C4×C9—26no—
140C2×C4×C9—212no—
141C2×C4×C9—212no—
142C2×C4×C9—46no—
143C2×C4×C9—43no—
144C2×C4×C9#4114yescomplemented
145C2×C4×C9C2412yes—
146C2×C4×C9C2413yes—
147C2×C4×C9C2412yes—
148C2×C4×C9C2413yes—
149C2×C4×C9C2416yes—
150C2×C4×C9C2413yes—
151C2×C4×C9C2411yescharacteristic
152C2×C4×C9C2413yes—
153C2×C4×C9C2411yescharacteristic
154#559C2×C913yescomplemented
155#557C2×C911yescharacteristic, complemented
156#556C2×C913yescomplemented
157#553C2×C916yescomplemented
158#550C2×C911yescharacteristic, complemented
159#548C2×C912yescomplemented
160#532C2×C913yescomplemented
161#529C2×C916yescomplemented
162C4×#41C2×C913yescomplemented
163C4×#41C2×C912yescomplemented
164C2×C4×Q8C2×C911yescharacteristic, complemented
165C3×#41—28no—
166C3×#41—212no—
167C2×C3×Q8—24no—
168C2×C3×Q8C23×C313yes—
169C2×C3×Q8C23×C313yes—
170C2×C3×Q8C23×C311yescharacteristic
171C2×C3×D4C23×C316yes—
172C2×C3×D4C23×C316yes—
173C2×C3×D4C23×C313yes—
174C2×C3×D4C23×C316yes—
175C22×C3×C4C23×C313yes—
176C22×C3×C4C23×C316yes—
177C22×C3×C4C23×C316yes—
178C22×C3×C4C23×C313yes—
179C22×C3×C4C23×C316yes—
180C22×C3×C4C23×C311yescharacteristic
181C3×C4⋊C4C23×C313yes—
182C3×C4⋊C4C23×C313yes—
183C3×C4⋊C4C23×C316yes—
184C3×C4⋊C4C23×C311yescharacteristic
185C3×C4⋊C4C23×C311yescharacteristic
186C3×C4⋊C4C23×C316yes—
187C3×C4⋊C4C23×C316yes—
188C3×C4⋊C4C23×C316yes—
189C3×C4⋊C4C23×C316yes—
190C3×C22⋊C4C23×C312yes—
191C3×C22⋊C4C23×C316yes—
192C3×C22⋊C4C23×C3112yes—
193C3×C22⋊C4C23×C316yes—
194C3×C22⋊C4C23×C3112yes—
195C3×C42C23×C312yes—
196C3×C42C23×C313yes—
197C3×C42C23×C313yes—
198C3×C42C23×C316yes—
199C3×C42C23×C316yes—
200C3×C42C23×C313yes—
201C3×C42C23×C313yes—
202C22×C9—21no—
203C22×C9—21no—
204C22×C9—26no—
205C22×C9—26no—
206C22×C9—26no—
207C22×C9C2×#4112yes—
208C22×C9C2511yescharacteristic
209C4×C9—22no—
210C4×C9—26no—
211C4×C9—23no—
212C4×C9—22no—
213C4×C9—23no—
214C4×C9—23no—
215C4×C9C2×#4112yes—
216C4×C9C2×#4116yes—
217C4×C9C2×#4112yes—
218C2×#41C22×C913yes—
219C2×#41C22×C912yes—
220C22×Q8C22×C911yescharacteristic
221C4⋊Q8C22×C913yes—
222#127C22×C913yes—
223#126C22×C9112yes—
224#125C22×C916yes—
225#124C22×C916yes—
226#124C22×C916yes—
227#123C22×C9112yes—
228C22⋊Q8C22×C916yes—
229#121C22×C916yes—
230#121C22×C916yes—
231#121C22×C916yes—
232C4×Q8C22×C911yescharacteristic
233C4×Q8C22×C913yes—
234C4×Q8C22×C911yescharacteristic
235C4×Q8C22×C913yes—
236C4×Q8C22×C912yes—
237C4×Q8C22×C913yes—
238C4×Q8C22×C913yes—
239C4×D4C22×C916yes—
240C4×D4C22×C916yes—
241C4×D4C22×C913yes—
242C4×D4C22×C916yes—
243C4×D4C22×C916yes—
244C4×D4C22×C913yes—
245C4×D4C22×C916yes—
246#117C22×C911yescharacteristic
247#117C22×C916yes—
248#117C22×C916yes—
249C2×C4⋊C4C22×C913yes—
250C2×C42C22×C913yes—
251C2×C42C22×C916yes—
252C23×C3C24×C316yes—
253C23×C3C24×C311yescharacteristic
254C3×Q8—26no—
255C3×Q8—26no—
256C3×Q8C3×#4114yes—
257C3×D4—212no—
258C3×D4—212no—
259C3×D4—26no—
260C3×D4—46no—
261C2×C3×C4—26no—
262C2×C3×C4—212no—
263C2×C3×C4—212no—
264C2×C3×C4—46no—
265C2×C3×C4—43no—
266C2×C3×C4C3×#4114yes—
267C2×C3×C4C24×C312yes—
268C2×C3×C4C24×C312yes—
269C2×C3×C4C24×C313yes—
270C2×C3×C4C24×C313yes—
271C2×C3×C4C24×C316yes—
272C2×C3×C4C24×C313yes—
273C2×C3×C4C24×C311yescharacteristic
274C2×C3×C4C24×C313yes—
275C2×C3×C4C24×C311yescharacteristic
276C2×C9—22no—
277C2×C9—46no—
278C2×C9C22×#4111yescharacteristic
279C2×C9C22×#4111yescharacteristic
280C2×C9#58511yescharacteristic
281#41—28no—
282#41—212no—
283C2×Q8—24no—
284C2×Q8C23×C913yes—
285C2×Q8C23×C913yes—
286C2×Q8C23×C911yescharacteristic
287C2×D4C23×C916yes—
288C2×D4C23×C916yes—
289C2×D4C23×C913yes—
290C2×D4C23×C916yes—
291C22×C4C23×C913yes—
292C22×C4C23×C916yes—
293C22×C4C23×C916yes—
294C22×C4C23×C913yes—
295C22×C4C23×C916yes—
296C22×C4C23×C911yescharacteristic
297C4⋊C4C23×C913yes—
298C4⋊C4C23×C913yes—
299C4⋊C4C23×C916yes—
300C4⋊C4C23×C911yescharacteristic
301C4⋊C4C23×C911yescharacteristic
302C4⋊C4C23×C916yes—
303C4⋊C4C23×C916yes—
304C4⋊C4C23×C916yes—
305C4⋊C4C23×C916yes—
306C22⋊C4C23×C912yes—
307C22⋊C4C23×C916yes—
308C22⋊C4C23×C9112yes—
309C22⋊C4C23×C916yes—
310C22⋊C4C23×C9112yes—
311C42C23×C912yes—
312C42C23×C913yes—
313C42C23×C913yes—
314C42C23×C916yes—
315C42C23×C916yes—
316C42C23×C913yes—
317C42C23×C913yes—
318C22×C3—21no—
319C22×C3—21no—
320C22×C3—26no—
321C22×C3—26no—
322C22×C3—26no—
323C22×C3C2×C3×#4112yes—
324C22×C3C25×C311yescharacteristic
325C3×C4—22no—
326C3×C4—26no—
327C3×C4—23no—
328C3×C4—22no—
329C3×C4—23no—
330C3×C4—23no—
331C3×C4C2×C3×#4112yes—
332C3×C4C2×C3×#4116yes—
333C3×C4C2×C3×#4112yes—
334C9#348011yescharacteristic, direct product factor, Sylow
335C23C24×C916yes—
336C23C24×C911yescharacteristic
337Q8—26no—
338Q8—26no—
339Q8C9×#4114yescomplemented
340D4—212no—
341D4—212no—
342D4—26no—
343D4—46no—
344C2×C4—26no—
345C2×C4—212no—
346C2×C4—212no—
347C2×C4—46no—
348C2×C4—43no—
349C2×C4C9×#4114yescomplemented
350C2×C4C24×C912yes—
351C2×C4C24×C912yes—
352C2×C4C24×C913yes—
353C2×C4C24×C913yes—
354C2×C4C24×C916yes—
355C2×C4C24×C913yes—
356C2×C4C24×C911yescharacteristic
357C2×C4C24×C911yescharacteristic
358C2×C4C24×C913yes—
359C2×C3—22no—
360C2×C3—46no—
361C2×C3C22×C3×#4111yescharacteristic
362C2×C3C22×C3×#4111yescharacteristic
363C2×C3C3×#58511yescharacteristic
364C22—21no—
365C22—21no—
366C22—26no—
367C22—26no—
368C22—26no—
369C22C2×C9×#4112yes—
370C22C25×C911yescharacteristic
371C4—22no—
372C4—26no—
373C4—23no—
374C4—22no—
375C4—23no—
376C4—23no—
377C4C2×C9×#4112yes—
378C4C2×C9×#4116yes—
379C4C2×C9×#4112yes—
380C3C3×#348011yescharacteristic
381C2—22no—
382C2—46no—
383C2C22×C9×#4111yescharacteristic
384C2C22×C9×#4111yescharacteristic
385C2C9×#58511yescharacteristic
subgroupG/H
centerC2×C4×C9C24
commutatorC22C25×C9
Frattini, socle, cosocleC22×C3C25×C3
prime radicalC3×#3480C3
LCSG ▷ C22 ▷ C1
UCSC1 ◁ C2×C4×C9 ◁ G

Complements

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

NH ≅ G/Ntype
1. C9×#559C2semidirect
2. C9×#557C2semidirect
3. C9×#556C2semidirect
4. C9×#553C2semidirect
5. C9×#550C2semidirect
6. C9×#548C2semidirect
7. C9×#532C2semidirect
8. C9×#529C2semidirect
9. C4×C9×#41C2semidirect
10. C4×C9×#41C2semidirect
11. C2×C4×Q8×C9C2semidirect
95. #3480C9direct (N × H)
134. Q8×C9#41semidirect
144. C2×C4×C9#41semidirect
154. #559C2×C9semidirect
155. #557C2×C9semidirect
156. #556C2×C9semidirect
157. #553C2×C9semidirect
158. #550C2×C9semidirect
159. #548C2×C9semidirect
160. #532C2×C9semidirect
161. #529C2×C9semidirect
162. C4×#41C2×C9semidirect
163. C4×#41C2×C9semidirect
164. C2×C4×Q8C2×C9semidirect
334. C9#3480direct (N × H)
339. Q8C9×#41semidirect
349. C2×C4C9×#41semidirect

Maximal subgroups

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

subgroupindex
C9×#5592
C9×#5572
C9×#5562
C9×#5532
C9×#5502
C9×#5482
C9×#5322
C9×#5292
C4×C9×#412
C2×C4×Q8×C92
C3×#34803