Finite Group Databasebeta

← C9×#4760 #13141722

Subgroups — C9×#4760 #13141722

Order 1728.

404 conjugacy classes of subgroups.

The subgroup lattice has 368 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C9×#940C211yesmaximal, characteristic
2C9×#888C211yesmaximal, characteristic, complemented
3C3×C9×#102C211yesmaximal, characteristic, complemented
4C9×#832C211yesmaximal, characteristic, complemented
5C9×#821C211yesmaximal, characteristic, complemented
6C8×C9×Dic3C211yesmaximal, characteristic, complemented
7C9×#809C211yesmaximal, characteristic, complemented
8C3×#4760C311yesmaximal, characteristic
9C9×#486—31nomaximal
10C2×C3×D4×C9C2211yescharacteristic
11C2×C9×#67—21no—
12C2×C9×#67—21no—
13C2×C9×D12C2211yescharacteristic
14C2×C9×Dic6—21no—
15C2×C3×C8×C9C2211yescharacteristic
16C3×C9×C4⋊C4C2211yescharacteristic
17C9×C4⋊Dic3C2211yescharacteristic
18C9×Dic3⋊C4—21no—
19C4×C9×Dic3C2211yescharacteristic
20C2×C9×C3⋊C8C2211yescharacteristic
21C3×#940C2×C311yescharacteristic
22C3×#888C2×C311yescharacteristic
23C32×#102C2×C311yescharacteristic
24C3×#832C2×C311yescharacteristic
25C3×#821C2×C311yescharacteristic
26C3×C8×Dic3C2×C311yescharacteristic
27C3×#809C2×C311yescharacteristic
28C9×C4⋊Q8—31no—
29C9×#127—31no—
30C9×#102—21no—
31C9×#102—31no—
32C9×#102—31no—
33C9×#102—31no—
34C9×#102D311yescharacteristic, complemented
35C4×C8×C9—31no—
36C23×C3×C9—21no—
37C22×D3×C9—21no—
38C3×D4×C9—21no—
39C3×D4×C9—21no—
40C2×C3×C4×C9—21no—
41C2×C3×C4×C9C2311yescharacteristic
42C9×#67—42no—
43C9×#67—42no—
44C2×C9×Dic3—21no—
45C2×C9×Dic3D411yescharacteristic
46C2×C9×Dic3D411yescharacteristic
47C9×D12—21no—
48C9×D12—21no—
49C9×Dic6—42no—
50C3×C8×C9—21no—
51C9×C3⋊C8—21no—
52C3×#486—31no—
53#4760C911yescharacteristic, direct product factor
54C2×C32×D4C22×C311yescharacteristic
55C2×C3×#67—21no—
56C2×C3×#67—21no—
57C2×C3×D12C22×C311yescharacteristic
58C2×C3×Dic6—21no—
59C2×C32×C8C22×C311yescharacteristic
60C32×C4⋊C4C22×C311yescharacteristic
61C3×C4⋊Dic3C22×C311yescharacteristic
62C3×Dic3⋊C4—21no—
63C3×C4×Dic3C22×C311yescharacteristic
64C2×C3×C3⋊C8C22×C311yescharacteristic
65C2×Q8×C9—61no—
66C2×D4×C9—21no—
67C2×D4×C9—31no—
68C2×D4×C9—61no—
69C2×D4×C9—61no—
70C2×D4×C9C2×D311yescharacteristic
71C2×C8×C9—21no—
72C2×C8×C9—31no—
73C2×C8×C9C2×D311yescharacteristic
74C9×C4⋊C4—21no—
75C9×C4⋊C4—31no—
76C9×C4⋊C4—61no—
77C9×C4⋊C4C2×D311yescharacteristic
78C42×C9—31no—
79C22×C3×C9—41no—
80C22×C3×C9—41no—
81C22×C3×C9—41no—
82C22×C3×C9C2×D411yescharacteristic
83C2×D3×C9—41no—
84C2×D3×C9—41no—
85C2×D3×C9—41no—
86C3×C4×C9—41no—
87C3×C4×C9#4111yescharacteristic
88C3×C4×C9#4111yescharacteristic
89C9×Dic3—41no—
90C9×Dic3D812yes—
91C9×Dic3SD1612yes—
92C3×C4⋊Q8—31no—
93C3×#127—31no—
94#940C2×C911yescharacteristic
95#888C2×C911yescharacteristic, complemented
96C3×#102—21no—
97C3×#102—31no—
98C3×#102—31no—
99C3×#102—31no—
100C3×#102C2×C911yescharacteristic, complemented
101C3×#102C3×D311yescharacteristic
102C3×C4×C8—31no—
103#832C2×C911yescharacteristic, complemented
104#821C2×C911yescharacteristic, complemented
105C8×Dic3C2×C911yescharacteristic, complemented
106#809C2×C911yescharacteristic, complemented
107C23×C32—21no—
108C22×C3×D3—21no—
109C32×D4—21no—
110C32×D4—21no—
111C2×C32×C4—21no—
112C2×C32×C4C23×C311yescharacteristic
113C3×#67—42no—
114C3×#67—42no—
115C2×C3×Dic3—21no—
116C2×C3×Dic3C3×D411yescharacteristic
117C2×C3×Dic3C3×D411yescharacteristic
118C3×D12—21no—
119C3×D12—21no—
120C3×Dic6—42no—
121C23×C9—21no—
122C23×C9—41no—
123C23×C9—61no—
124C32×C8—21no—
125C3×C3⋊C8—21no—
126Q8×C9—122no—
127D4×C9—22no—
128D4×C9—21no—
129D4×C9—21no—
130D4×C9—41no—
131D4×C9—61no—
132D4×C9—61no—
133D4×C9—122no—
134D4×C9—122no—
135C2×C4×C9—21no—
136C2×C4×C9—21no—
137C2×C4×C9—31no—
138C2×C4×C9—31no—
139C2×C4×C9—41no—
140C2×C4×C9—61no—
141C2×C4×C9C22×D311yescharacteristic
142C8×C9—21no—
143C8×C9—41no—
144C8×C9—61no—
145#486—31noSylow
146C2×C3×C9—81no—
147C2×C3×C9#12411yescharacteristic
148C2×C3×C9C2×D811yescharacteristic
149C2×C3×C9C2×SD1611yescharacteristic
150D3×C9—81no—
151C2×C3×Q8—61no—
152C2×C3×D4—21no—
153C2×C3×D4—31no—
154C2×C3×D4—61no—
155C2×C3×D4—61no—
156C2×C3×D4C22×C911yescharacteristic
157C2×C3×D4C2×C3×D311yescharacteristic
158C2×#67—21no—
159C2×#67—21no—
160C2×D12C22×C911yescharacteristic
161C2×Dic6—21no—
162C2×C3×C8—21no—
163C2×C3×C8—31no—
164C2×C3×C8C22×C911yescharacteristic
165C2×C3×C8C2×C3×D311yescharacteristic
166C3×C4⋊C4—21no—
167C3×C4⋊C4—31no—
168C3×C4⋊C4—61no—
169C3×C4⋊C4C22×C911yescharacteristic
170C3×C4⋊C4C2×C3×D311yescharacteristic
171C3×C42—31no—
172C4⋊Dic3C22×C911yescharacteristic
173Dic3⋊C4—21no—
174C4×Dic3C22×C911yescharacteristic
175C2×C3⋊C8C22×C911yescharacteristic
176C22×C32—41no—
177C22×C32—41no—
178C22×C32—41no—
179C22×C32C2×C3×D411yescharacteristic
180C2×C3×D3—41no—
181C2×C3×D3—41no—
182C2×C3×D3—41no—
183C32×C4—41no—
184C32×C4C3×#4111yescharacteristic
185C32×C4C3×#4111yescharacteristic
186C3×Dic3—41no—
187C3×Dic3C3×D812yes—
188C3×Dic3C3×SD1612yes—
189C22×C9—21no—
190C22×C9—42no—
191C22×C9—41no—
192C22×C9—41no—
193C22×C9—41no—
194C22×C9—81no—
195C22×C9—81no—
196C22×C9—121no—
197C22×C9—121no—
198C22×C9—121no—
199C22×C9D3×D411yescharacteristic
200C4×C9—21no—
201C4×C9—21no—
202C4×C9—32no—
203C4×C9—32no—
204C4×C9—41no—
205C4×C9—81no—
206C4×C9—121no—
207C4×C9#23511yescharacteristic
208C4×C9#23711yescharacteristic
209C4⋊Q8—31no—
210#127—31no—
211#102—31no—
212#102—31no—
213#102—31no—
214#102D3×C911yescharacteristic, complemented
215C4×C8—31no—
216C3×C9#48611yescharacteristic, complemented, Sylow
217C23×C3—21no—
218C23×C3—21no—
219C23×C3—41no—
220C23×C3—61no—
221C22×D3—21no—
222C3×Q8—122no—
223C3×D4—22no—
224C3×D4—21no—
225C3×D4—21no—
226C3×D4—21no—
227C3×D4—21no—
228C3×D4—41no—
229C3×D4—61no—
230C3×D4—61no—
231C3×D4—122no—
232C3×D4—122no—
233C2×C3×C4—21no—
234C2×C3×C4—21no—
235C2×C3×C4—21no—
236C2×C3×C4—31no—
237C2×C3×C4—31no—
238C2×C3×C4—41no—
239C2×C3×C4—61no—
240C2×C3×C4C23×C911yescharacteristic
241C2×C3×C4C22×C3×D311yescharacteristic
242#67—42no—
243#67—42no—
244C2×Dic3—21no—
245C2×Dic3D4×C911yescharacteristic
246C2×Dic3D4×C911yescharacteristic
247D12—21no—
248D12—21no—
249Dic6—42no—
250C3×C8—21no—
251C3×C8—21no—
252C3×C8—41no—
253C3×C8—61no—
254C3⋊C8—21no—
255C2×C32—81no—
256C2×C32C3×#12411yescharacteristic
257C2×C32C2×C3×D811yescharacteristic
258C2×C32C2×C3×SD1611yescharacteristic
259C3×D3—81no—
260C2×C9—21no—
261C2×C9—21no—
262C2×C9—21no—
263C2×C9—82no—
264C2×C9—81no—
265C2×C9—241no—
266C2×C9#88511yescharacteristic
267C2×C9D3×D811yescharacteristic
268C2×C9D3×SD1611yescharacteristic
269C2×Q8—61no—
270C2×D4—31no—
271C2×D4—61no—
272C2×D4—61no—
273C2×D4C2×D3×C911yescharacteristic
274C2×C8—31no—
275C2×C8C2×D3×C911yescharacteristic
276C4⋊C4—31no—
277C4⋊C4—61no—
278C4⋊C4C2×D3×C911yescharacteristic
279C42—31no—
280C22×C3—21no—
281C22×C3—42no—
282C22×C3—41no—
283C22×C3—41no—
284C22×C3—41no—
285C22×C3—41no—
286C22×C3—41no—
287C22×C3—41no—
288C22×C3—81no—
289C22×C3—81no—
290C22×C3—121no—
291C22×C3—121no—
292C22×C3—121no—
293C22×C3C2×D4×C911yescharacteristic
294C22×C3C3×D3×D411yescharacteristic
295C2×D3—41no—
296C2×D3—41no—
297C2×D3—41no—
298C3×C4—21no—
299C3×C4—21no—
300C3×C4—32no—
301C3×C4—32no—
302C3×C4—41no—
303C3×C4—41no—
304C3×C4—81no—
305C3×C4—121no—
306C3×C4C9×#4111yescharacteristic
307C3×C4C9×#4111yescharacteristic
308C3×C4C3×#23511yescharacteristic
309C3×C4C3×#23711yescharacteristic
310Dic3—41no—
311Dic3C9×D812yes—
312Dic3C9×SD1612yes—
313C32C3×#48611yescharacteristic
314C9—21no—
315C9#476011yescharacteristic, direct product factor
316C23—21no—
317C23—61no—
318Q8—122no—
319D4—21no—
320D4—21no—
321D4—61no—
322D4—61no—
323D4—122no—
324D4—122no—
325C2×C4—21no—
326C2×C4—31no—
327C2×C4—31no—
328C2×C4—61no—
329C2×C4C22×D3×C911yescharacteristic
330C8—21no—
331C8—61no—
332C2×C3—21no—
333C2×C3—21no—
334C2×C3—21no—
335C2×C3—82no—
336C2×C3—81no—
337C2×C3—81no—
338C2×C3—241no—
339C2×C3C9×#12411yescharacteristic
340C2×C3C2×C9×D811yescharacteristic
341C2×C3C2×C9×SD1611yescharacteristic
342C2×C3C3×#88511yescharacteristic
343C2×C3C3×D3×D811yescharacteristic
344C2×C3C3×D3×SD1611yescharacteristic
345D3—81no—
346C22—41no—
347C22—41no—
348C22—41no—
349C22—121no—
350C22—121no—
351C22—121no—
352C22D3×D4×C911yescharacteristic
353C4—32no—
354C4—32no—
355C4—41no—
356C4—121no—
357C4C9×#23511yescharacteristic
358C4C9×#23711yescharacteristic
359C3—21no—
360C3C9×#48611yescharacteristic, complemented
361C3C3×#476011yescharacteristic
362C2—81no—
363C2—241no—
364C2C9×#88511yescharacteristic
365C2D3×C9×D811yescharacteristic
366C2D3×C9×SD1611yescharacteristic
subgroupG/H
centerC22×C9D3×D4
commutatorC2×C3×C4C23×C9
FrattiniC2×C3×C4C22×C3×D3
FittingC3×C9×#102C2
socleC22×C32C2×C3×D4
prime radicalC3×#940C2×C3
cosocleC2×C32×C4C23×C3
hypercenterC9×#102D3
hypocenterC3C9×#486
LCSG ▷ C2×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C22×C9 ◁ C2×C4×C9 ◁ C9×#102

Complements

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

NH ≅ G/Ntype
2. C9×#888C2semidirect
3. C3×C9×#102C2semidirect
4. C9×#832C2semidirect
5. C9×#821C2semidirect
6. C8×C9×Dic3C2semidirect
7. C9×#809C2semidirect
34. C9×#102D3semidirect
53. #4760C9direct (N × H)
95. #888C2×C9semidirect
100. C3×#102C2×C9semidirect
103. #832C2×C9semidirect
104. #821C2×C9semidirect
105. C8×Dic3C2×C9semidirect
106. #809C2×C9semidirect
214. #102D3×C9semidirect
216. C3×C9#486semidirect
315. C9#4760direct (N × H)
360. C3C9×#486semidirect

Maximal subgroups

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

subgroupindex
C9×#9402
C9×#8882
C3×C9×#1022
C9×#8322
C9×#8212
C8×C9×Dic32
C9×#8092
C3×#47603
C9×#4863