Finite Group Databasebeta

← C9×#3482 #11768203

Subgroups — C9×#3482 #11768203

Order 1152.

1641 conjugacy classes of subgroups.

The subgroup lattice has 384 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C9×#557C211yesmaximal, characteristic, complemented
2C9×#556C213yesmaximal, complemented
3C9×#552C216yesmaximal, complemented
4D4×Q8×C9C211yesmaximal, characteristic, complemented
5C9×#548C212yesmaximal, complemented
6C9×#547C213yesmaximal, complemented
7C9×#533C213yesmaximal, complemented
8C9×#529C216yesmaximal, complemented
9C4×C9×#41C213yesmaximal, complemented
10C4×C9×#41C211yesmaximal, characteristic, complemented
11C2×C4×Q8×C9C212yesmaximal, complemented
12C3×#3482C311yesmaximal, characteristic
13C2×C9×#41C2213yes—
14C2×C9×#41C2211yescharacteristic
15C22×Q8×C9C2212yes—
16C9×C4⋊Q8C2213yes—
17C9×C4⋊Q8C2213yes—
18C9×#126C22112yes—
19C9×#125C2216yes—
20C9×#125C2216yes—
21C9×#124C2216yes—
22C9×#123C22112yes—
23C9×C22⋊Q8C2216yes—
24C9×C22⋊Q8C2216yes—
25C9×C22⋊Q8C2216yes—
26C9×#121C2216yes—
27C4×Q8×C9C2216yes—
28C4×Q8×C9C2213yes—
29C4×Q8×C9C2212yes—
30C4×Q8×C9C2211yescharacteristic
31C4×Q8×C9C2216yes—
32C4×Q8×C9C2213yes—
33C4×Q8×C9C2211yescharacteristic
34C4×D4×C9C2213yes—
35C4×D4×C9C2216yes—
36C4×D4×C9C2213yes—
37C4×D4×C9C2213yes—
38C4×D4×C9C2216yes—
39C4×D4×C9C2211yescharacteristic
40C9×#117C2216yes—
41C9×#117C2213yes—
42C9×#117C2216yes—
43C9×#117C2213yes—
44C2×C9×C4⋊C4C2216yes—
45C2×C42×C9C2216yes—
46C2×C42×C9C2213yes—
47C3×#557C2×C311yescharacteristic
48C3×#556C2×C313yes—
49C3×#552C2×C316yes—
50C3×D4×Q8C2×C311yescharacteristic
51C3×#548C2×C312yes—
52C3×#547C2×C313yes—
53C3×#533C2×C313yes—
54C3×#529C2×C316yes—
55C3×C4×#41C2×C313yes—
56C3×C4×#41C2×C311yescharacteristic
57C2×C3×C4×Q8C2×C312yes—
58C9×#41—24no—
59C9×#41—212no—
60C2×Q8×C9—28no—
61C2×Q8×C9C2316yes—
62C2×Q8×C9C2313yes—
63C2×Q8×C9C2311yescharacteristic
64C2×D4×C9C2316yes—
65C2×D4×C9C2313yes—
66C2×D4×C9C2311yescharacteristic
67C22×C4×C9C2316yes—
68C22×C4×C9C2316yes—
69C22×C4×C9C2313yes—
70C22×C4×C9C2313yes—
71C22×C4×C9C2312yes—
72C22×C4×C9C2313yes—
73C9×C4⋊C4C2313yes—
74C9×C4⋊C4C2316yes—
75C9×C4⋊C4C23112yes—
76C9×C4⋊C4C2311yescharacteristic
77C9×C4⋊C4C2316yes—
78C9×C4⋊C4C2313yes—
79C9×C4⋊C4C2313yes—
80C9×C4⋊C4C2316yes—
81C9×C4⋊C4C2316yes—
82C9×C4⋊C4C2316yes—
83C9×C22⋊C4C2312yes—
84C9×C22⋊C4C2316yes—
85C9×C22⋊C4C2316yes—
86C9×C22⋊C4C2316yes—
87C9×C22⋊C4C23112yes—
88C42×C9C2313yes—
89C42×C9C2316yes—
90C42×C9C2313yes—
91C42×C9C2316yes—
92C42×C9C2313yes—
93C42×C9C2311yescharacteristic
94C42×C9C2316yes—
95#3482C911yescharacteristic, direct product factor, Sylow
96C2×C3×#41C22×C313yes—
97C2×C3×#41C22×C311yescharacteristic
98C22×C3×Q8C22×C312yes—
99C3×C4⋊Q8C22×C313yes—
100C3×C4⋊Q8C22×C313yes—
101C3×#126C22×C3112yes—
102C3×#125C22×C316yes—
103C3×#125C22×C316yes—
104C3×#124C22×C316yes—
105C3×#123C22×C3112yes—
106C3×C22⋊Q8C22×C316yes—
107C3×C22⋊Q8C22×C316yes—
108C3×C22⋊Q8C22×C316yes—
109C3×#121C22×C316yes—
110C3×C4×Q8C22×C311yescharacteristic
111C3×C4×Q8C22×C316yes—
112C3×C4×Q8C22×C312yes—
113C3×C4×Q8C22×C316yes—
114C3×C4×Q8C22×C313yes—
115C3×C4×Q8C22×C311yescharacteristic
116C3×C4×Q8C22×C313yes—
117C3×C4×D4C22×C311yescharacteristic
118C3×C4×D4C22×C313yes—
119C3×C4×D4C22×C316yes—
120C3×C4×D4C22×C313yes—
121C3×C4×D4C22×C313yes—
122C3×C4×D4C22×C316yes—
123C3×#117C22×C313yes—
124C3×#117C22×C316yes—
125C3×#117C22×C313yes—
126C3×#117C22×C316yes—
127C2×C3×C4⋊C4C22×C316yes—
128C2×C3×C42C22×C316yes—
129C2×C3×C42C22×C313yes—
130C23×C9C2413yes—
131C23×C9C2412yes—
132Q8×C9—212no—
133Q8×C9—26no—
134Q8×C9#4114yescomplemented
135D4×C9—212no—
136D4×C9—26no—
137D4×C9#4114yescomplemented
138C2×C4×C9—212no—
139C2×C4×C9—212no—
140C2×C4×C9—26no—
141C2×C4×C9—26no—
142C2×C4×C9—24no—
143C2×C4×C9—26no—
144C2×C4×C9C2412yes—
145C2×C4×C9C2411yescharacteristic
146C2×C4×C9C2413yes—
147C2×C4×C9C2413yes—
148C2×C4×C9C2416yes—
149C2×C4×C9C2416yes—
150C2×C4×C9C2413yes—
151C2×C4×C9C2411yescharacteristic
152C2×C4×C9C2411yescharacteristic
153#557C2×C911yescharacteristic, complemented
154#556C2×C913yescomplemented
155#552C2×C916yescomplemented
156D4×Q8C2×C911yescharacteristic, complemented
157#548C2×C912yescomplemented
158#547C2×C913yescomplemented
159#533C2×C913yescomplemented
160#529C2×C916yescomplemented
161C4×#41C2×C913yescomplemented
162C4×#41C2×C911yescharacteristic, complemented
163C2×C4×Q8C2×C912yescomplemented
164C3×#41—24no—
165C3×#41—212no—
166C2×C3×Q8—28no—
167C2×C3×Q8C23×C316yes—
168C2×C3×Q8C23×C313yes—
169C2×C3×Q8C23×C311yescharacteristic
170C2×C3×D4C23×C316yes—
171C2×C3×D4C23×C313yes—
172C2×C3×D4C23×C311yescharacteristic
173C22×C3×C4C23×C312yes—
174C22×C3×C4C23×C316yes—
175C22×C3×C4C23×C316yes—
176C22×C3×C4C23×C313yes—
177C22×C3×C4C23×C313yes—
178C22×C3×C4C23×C313yes—
179C3×C4⋊C4C23×C313yes—
180C3×C4⋊C4C23×C316yes—
181C3×C4⋊C4C23×C3112yes—
182C3×C4⋊C4C23×C311yescharacteristic
183C3×C4⋊C4C23×C316yes—
184C3×C4⋊C4C23×C313yes—
185C3×C4⋊C4C23×C313yes—
186C3×C4⋊C4C23×C316yes—
187C3×C4⋊C4C23×C316yes—
188C3×C4⋊C4C23×C316yes—
189C3×C22⋊C4C23×C312yes—
190C3×C22⋊C4C23×C316yes—
191C3×C22⋊C4C23×C316yes—
192C3×C22⋊C4C23×C316yes—
193C3×C22⋊C4C23×C3112yes—
194C3×C42C23×C313yes—
195C3×C42C23×C311yescharacteristic
196C3×C42C23×C313yes—
197C3×C42C23×C316yes—
198C3×C42C23×C316yes—
199C3×C42C23×C313yes—
200C3×C42C23×C316yes—
201C22×C9—22no—
202C22×C9—22no—
203C22×C9—23no—
204C22×C9—23no—
205C22×C9—23no—
206C22×C9C2×#4114yes—
207C22×C9C2511yescharacteristic
208C4×C9—23no—
209C4×C9—21no—
210C4×C9—26no—
211C4×C9—26no—
212C4×C9—22no—
213C4×C9—23no—
214C4×C9C2×#4116yes—
215C4×C9C2×#4112yes—
216C4×C92−1+412yes—
217C2×#41C22×C913yes—
218C2×#41C22×C911yescharacteristic
219C22×Q8C22×C912yes—
220C4⋊Q8C22×C913yes—
221C4⋊Q8C22×C913yes—
222#126C22×C9112yes—
223#125C22×C916yes—
224#125C22×C916yes—
225#124C22×C916yes—
226#123C22×C9112yes—
227C22⋊Q8C22×C916yes—
228C22⋊Q8C22×C916yes—
229C22⋊Q8C22×C916yes—
230#121C22×C916yes—
231C4×Q8C22×C911yescharacteristic
232C4×Q8C22×C916yes—
233C4×Q8C22×C912yes—
234C4×Q8C22×C916yes—
235C4×Q8C22×C913yes—
236C4×Q8C22×C911yescharacteristic
237C4×Q8C22×C913yes—
238C4×D4C22×C911yescharacteristic
239C4×D4C22×C913yes—
240C4×D4C22×C916yes—
241C4×D4C22×C913yes—
242C4×D4C22×C913yes—
243C4×D4C22×C916yes—
244#117C22×C913yes—
245#117C22×C916yes—
246#117C22×C913yes—
247#117C22×C916yes—
248C2×C4⋊C4C22×C916yes—
249C2×C42C22×C916yes—
250C2×C42C22×C913yes—
251C23×C3C24×C313yes—
252C23×C3C24×C312yes—
253C3×Q8—212no—
254C3×Q8—26no—
255C3×Q8C3×#4114yes—
256C3×D4—212no—
257C3×D4—26no—
258C3×D4C3×#4114yes—
259C2×C3×C4—212no—
260C2×C3×C4—212no—
261C2×C3×C4—26no—
262C2×C3×C4—26no—
263C2×C3×C4—24no—
264C2×C3×C4—26no—
265C2×C3×C4C24×C312yes—
266C2×C3×C4C24×C311yescharacteristic
267C2×C3×C4C24×C313yes—
268C2×C3×C4C24×C313yes—
269C2×C3×C4C24×C316yes—
270C2×C3×C4C24×C316yes—
271C2×C3×C4C24×C313yes—
272C2×C3×C4C24×C311yescharacteristic
273C2×C3×C4C24×C311yescharacteristic
274C2×C9—24no—
275C2×C9—43no—
276C2×C9C22×#4111yescharacteristic
277C2×C9C22×#4111yescharacteristic
278C2×C9C2×2−1+411yescharacteristic
279#41—24no—
280#41—212no—
281C2×Q8—28no—
282C2×Q8C23×C916yes—
283C2×Q8C23×C913yes—
284C2×Q8C23×C911yescharacteristic
285C2×D4C23×C916yes—
286C2×D4C23×C913yes—
287C2×D4C23×C911yescharacteristic
288C22×C4C23×C912yes—
289C22×C4C23×C916yes—
290C22×C4C23×C916yes—
291C22×C4C23×C913yes—
292C22×C4C23×C913yes—
293C22×C4C23×C913yes—
294C4⋊C4C23×C913yes—
295C4⋊C4C23×C916yes—
296C4⋊C4C23×C9112yes—
297C4⋊C4C23×C911yescharacteristic
298C4⋊C4C23×C916yes—
299C4⋊C4C23×C913yes—
300C4⋊C4C23×C913yes—
301C4⋊C4C23×C916yes—
302C4⋊C4C23×C916yes—
303C4⋊C4C23×C916yes—
304C22⋊C4C23×C912yes—
305C22⋊C4C23×C916yes—
306C22⋊C4C23×C916yes—
307C22⋊C4C23×C916yes—
308C22⋊C4C23×C9112yes—
309C42C23×C913yes—
310C42C23×C911yescharacteristic
311C42C23×C913yes—
312C42C23×C916yes—
313C42C23×C916yes—
314C42C23×C913yes—
315C42C23×C916yes—
316C22×C3—22no—
317C22×C3—22no—
318C22×C3—23no—
319C22×C3—23no—
320C22×C3—23no—
321C22×C3C2×C3×#4114yes—
322C22×C3C25×C311yescharacteristic
323C3×C4—23no—
324C3×C4—21no—
325C3×C4—26no—
326C3×C4—26no—
327C3×C4—22no—
328C3×C4—23no—
329C3×C4C2×C3×#4116yes—
330C3×C4C2×C3×#4112yes—
331C3×C4C3×2−1+412yes—
332C9#348211yescharacteristic, direct product factor, Sylow
333C23C24×C913yes—
334C23C24×C912yes—
335Q8—212no—
336Q8—26no—
337Q8C9×#4114yescomplemented
338D4—212no—
339D4—26no—
340D4C9×#4114yescomplemented
341C2×C4—212no—
342C2×C4—212no—
343C2×C4—26no—
344C2×C4—26no—
345C2×C4—24no—
346C2×C4—26no—
347C2×C4C24×C912yes—
348C2×C4C24×C911yescharacteristic
349C2×C4C24×C913yes—
350C2×C4C24×C913yes—
351C2×C4C24×C916yes—
352C2×C4C24×C916yes—
353C2×C4C24×C913yes—
354C2×C4C24×C911yescharacteristic
355C2×C4C24×C911yescharacteristic
356C2×C3—24no—
357C2×C3—43no—
358C2×C3C22×C3×#4111yescharacteristic
359C2×C3C22×C3×#4111yescharacteristic
360C2×C3C2×C3×2−1+411yescharacteristic
361C22—22no—
362C22—22no—
363C22—23no—
364C22—23no—
365C22—23no—
366C22C2×C9×#4114yes—
367C22C25×C911yescharacteristic
368C4—23no—
369C4—21no—
370C4—26no—
371C4—26no—
372C4—22no—
373C4—23no—
374C4C2×C9×#4116yes—
375C4C2×C9×#4112yes—
376C4C9×2−1+412yes—
377C3C3×#348211yescharacteristic
378C2—24no—
379C2—43no—
380C2C22×C9×#4111yescharacteristic
381C2C22×C9×#4111yescharacteristic
382C2C2×C9×2−1+411yescharacteristic
subgroupG/H
centerC2×C4×C9C24
commutatorC22C25×C9
Frattini, socle, cosocleC22×C3C25×C3
prime radicalC3×#3482C3
LCSG ▷ C22 ▷ C1
UCSC1 ◁ C2×C4×C9 ◁ G

Complements

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

NH ≅ G/Ntype
1. C9×#557C2semidirect
2. C9×#556C2semidirect
3. C9×#552C2semidirect
4. D4×Q8×C9C2semidirect
5. C9×#548C2semidirect
6. C9×#547C2semidirect
7. C9×#533C2semidirect
8. C9×#529C2semidirect
9. C4×C9×#41C2semidirect
10. C4×C9×#41C2semidirect
11. C2×C4×Q8×C9C2semidirect
95. #3482C9direct (N × H)
134. Q8×C9#41semidirect
137. D4×C9#41semidirect
153. #557C2×C9semidirect
154. #556C2×C9semidirect
155. #552C2×C9semidirect
156. D4×Q8C2×C9semidirect
157. #548C2×C9semidirect
158. #547C2×C9semidirect
159. #533C2×C9semidirect
160. #529C2×C9semidirect
161. C4×#41C2×C9semidirect
162. C4×#41C2×C9semidirect
163. C2×C4×Q8C2×C9semidirect
332. C9#3482direct (N × H)
337. Q8C9×#41semidirect
340. D4C9×#41semidirect

Maximal subgroups

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

subgroupindex
C9×#5572
C9×#5562
C9×#5522
D4×Q8×C92
C9×#5482
C9×#5472
C9×#5332
C9×#5292
C4×C9×#412
C2×C4×Q8×C92
C3×#34823