Finite Group Databasebeta

← C9×#4885 #13142205

Subgroups — C9×#4885 #13142205

Order 1728.

354 conjugacy classes of subgroups.

The subgroup lattice has 346 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C9×#895C211yesmaximal, characteristic
2C9×#892C211yesmaximal, characteristic, complemented
3C3×C9×#107C211yesmaximal, characteristic, complemented
4C9×#821C211yesmaximal, characteristic, complemented
5C9×(C2×D3)⋊C8C211yesmaximal, characteristic, complemented
6C9×#809C211yesmaximal, characteristic, complemented
7C9×#808C211yesmaximal, characteristic, complemented
8C3×#4885C311yesmaximal, characteristic
9C9×#482—31nomaximal
10C2×C9×D12—21no—
11C2×C9×D12C2211yescharacteristic
12C2×C4×D3×C9C2211yescharacteristic
13C2×C3×C8×C9C2211yescharacteristic
14C3×C9×C4⋊C4C2211yescharacteristic
15C3×C9×C4⋊C4C2211yescharacteristic
16C9×(C2×D3)⋊C4—21no—
17C9×(C2×D3)⋊C4—21no—
18C9×C4⋊Dic3C2211yescharacteristic
19C4×C9×Dic3—21no—
20C2×C9×C3⋊C8C2211yescharacteristic
21C3×#895C2×C311yescharacteristic
22C3×#892C2×C311yescharacteristic
23C32×#107C2×C311yescharacteristic
24C3×#821C2×C311yescharacteristic
25C3×(C2×D3)⋊C8C2×C311yescharacteristic
26C3×#809C2×C311yescharacteristic
27C3×#808C2×C311yescharacteristic
28C9×#121—31no—
29C9×#117—31no—
30C9×#107—21no—
31C9×#107D311yescharacteristic, complemented
32C9×#106—31no—
33C9×#102—31no—
34C9×#102—31no—
35C9×C22⋊C8—31no—
36C22×D3×C9—21no—
37C22×D3×C9D411yescharacteristic
38C2×C3×C4×C9—21no—
39C2×C3×C4×C9—21no—
40C2×C3×C4×C9C2311yescharacteristic
41C2×C9×Dic3—21no—
42C2×C9×Dic3D411yescharacteristic
43C9×D12—21no—
44C9×D12—21no—
45C9×D12—42no—
46C4×D3×C9—21no—
47C4×D3×C9—21no—
48C3×C8×C9—21no—
49C9×C3⋊C8—21no—
50C3×#482—31no—
51#4885C911yescharacteristic, direct product factor
52C2×C3×D12—21no—
53C2×C3×D12C22×C311yescharacteristic
54C2×C3×C4×D3C22×C311yescharacteristic
55C2×C32×C8C22×C311yescharacteristic
56C32×C4⋊C4C22×C311yescharacteristic
57C32×C4⋊C4C22×C311yescharacteristic
58C3×(C2×D3)⋊C4—21no—
59C3×(C2×D3)⋊C4—21no—
60C3×C4⋊Dic3C22×C311yescharacteristic
61C3×C4×Dic3—21no—
62C2×C3×C3⋊C8C22×C311yescharacteristic
63C2×D4×C9—31no—
64C2×D4×C9—61no—
65C22×C4×C9—31no—
66C2×C8×C9—21no—
67C2×C8×C9—31no—
68C2×C8×C9C2×D311yescharacteristic
69C9×C4⋊C4—21no—
70C9×C4⋊C4—21no—
71C9×C4⋊C4—31no—
72C9×C4⋊C4C2×D311yescharacteristic
73C9×C4⋊C4C2×D311yescharacteristic
74C9×C22⋊C4—61no—
75C9×C22⋊C4—61no—
76C42×C9—61no—
77C22×C3×C9C2×D411yescharacteristic
78C2×D3×C9—21no—
79C2×D3×C9—21no—
80C2×D3×C9—21no—
81C2×D3×C9—41no—
82C2×D3×C9—41no—
83C2×D3×C9—41no—
84C3×C4×C9—41no—
85C3×C4×C9—41no—
86C3×C4×C9#4111yescharacteristic
87C3×C4×C9#4111yescharacteristic
88C9×Dic3—21no—
89C9×Dic3—41no—
90C3×#121—31no—
91C3×#117—31no—
92#895C2×C911yescharacteristic
93#892C2×C911yescharacteristic, complemented
94C3×#107—21no—
95C3×#107C2×C911yescharacteristic, complemented
96C3×#107C3×D311yescharacteristic
97C3×#106—31no—
98C3×#102—31no—
99C3×#102—31no—
100C3×C22⋊C8—31no—
101#821C2×C911yescharacteristic, complemented
102(C2×D3)⋊C8C2×C911yescharacteristic, complemented
103#809C2×C911yescharacteristic, complemented
104#808C2×C911yescharacteristic, complemented
105C22×C3×D3—21no—
106C22×C3×D3C3×D411yescharacteristic
107C2×C32×C4—21no—
108C2×C32×C4—21no—
109C2×C32×C4C23×C311yescharacteristic
110C2×C3×Dic3—21no—
111C2×C3×Dic3C3×D411yescharacteristic
112C3×D12—21no—
113C3×D12—21no—
114C3×D12—42no—
115C3×C4×D3—21no—
116C3×C4×D3—21no—
117C23×C9—31no—
118C23×C9—61no—
119C32×C8—21no—
120C3×C3⋊C8—21no—
121D4×C9—61no—
122D4×C9—61no—
123D4×C9—122no—
124C2×C4×C9—21no—
125C2×C4×C9—21no—
126C2×C4×C9—21no—
127C2×C4×C9—31no—
128C2×C4×C9—41no—
129C2×C4×C9—41no—
130C2×C4×C9—61no—
131C2×C4×C9—61no—
132C2×C4×C9—61no—
133C2×C4×C9C22×D311yescharacteristic
134C8×C9—22no—
135C8×C9—21no—
136C8×C9—61no—
137#482—31noSylow
138C2×C3×C9#12311yescharacteristic
139C2×C3×C9#13511yescharacteristic
140C2×C3×C9AGL(1,ℤ/8)11yescharacteristic
141D3×C9—41no—
142D3×C9—81no—
143C2×C3×D4—31no—
144C2×C3×D4—61no—
145C22×C3×C4—31no—
146C2×D12—21no—
147C2×D12C22×C911yescharacteristic
148C2×C4×D3C22×C911yescharacteristic
149C2×C3×C8—21no—
150C2×C3×C8—31no—
151C2×C3×C8C22×C911yescharacteristic
152C2×C3×C8C2×C3×D311yescharacteristic
153C3×C4⋊C4—21no—
154C3×C4⋊C4—21no—
155C3×C4⋊C4—31no—
156C3×C4⋊C4C22×C911yescharacteristic
157C3×C4⋊C4C22×C911yescharacteristic
158C3×C4⋊C4C2×C3×D311yescharacteristic
159C3×C4⋊C4C2×C3×D311yescharacteristic
160C3×C22⋊C4—61no—
161C3×C22⋊C4—61no—
162C3×C42—61no—
163(C2×D3)⋊C4—21no—
164(C2×D3)⋊C4—21no—
165C4⋊Dic3C22×C911yescharacteristic
166C4×Dic3—21no—
167C2×C3⋊C8C22×C911yescharacteristic
168C22×C32C2×C3×D411yescharacteristic
169C2×C3×D3—21no—
170C2×C3×D3—21no—
171C2×C3×D3—21no—
172C2×C3×D3—41no—
173C2×C3×D3—41no—
174C2×C3×D3—41no—
175C32×C4—41no—
176C32×C4—41no—
177C32×C4C3×#4111yescharacteristic
178C32×C4C3×#4111yescharacteristic
179C3×Dic3—21no—
180C3×Dic3—41no—
181C22×C9—21no—
182C22×C9—61no—
183C22×C9—61no—
184C22×C9—61no—
185C22×C9—121no—
186C22×C9—121no—
187C22×C9—121no—
188C22×C9D3×D411yescharacteristic
189C4×C9—21no—
190C4×C9—21no—
191C4×C9—41no—
192C4×C9—41no—
193C4×C9—61no—
194C4×C9—81no—
195C4×C9—81no—
196C4×C9—121no—
197C4×C9#23511yescharacteristic
198C4×C9#23911yescharacteristic
199#121—31no—
200#117—31no—
201#107D3×C911yescharacteristic, complemented
202#106—31no—
203#102—31no—
204#102—31no—
205C22⋊C8—31no—
206C3×C9#48211yescharacteristic, complemented, Sylow
207C23×C3—31no—
208C23×C3—61no—
209C22×D3—21no—
210C22×D3D4×C911yescharacteristic
211C3×D4—61no—
212C3×D4—61no—
213C3×D4—122no—
214C2×C3×C4—21no—
215C2×C3×C4—21no—
216C2×C3×C4—21no—
217C2×C3×C4—21no—
218C2×C3×C4—21no—
219C2×C3×C4—31no—
220C2×C3×C4—41no—
221C2×C3×C4—41no—
222C2×C3×C4—61no—
223C2×C3×C4—61no—
224C2×C3×C4—61no—
225C2×C3×C4C23×C911yescharacteristic
226C2×C3×C4C22×C3×D311yescharacteristic
227C2×Dic3—21no—
228C2×Dic3D4×C911yescharacteristic
229D12—21no—
230D12—21no—
231D12—42no—
232C4×D3—21no—
233C4×D3—21no—
234C3×C8—22no—
235C3×C8—21no—
236C3×C8—21no—
237C3×C8—61no—
238C3⋊C8—21no—
239C2×C32C3×#12311yescharacteristic
240C2×C32C3×#13511yescharacteristic
241C2×C32C3×AGL(1,ℤ/8)11yescharacteristic
242C3×D3—41no—
243C3×D3—81no—
244C2×C9—21no—
245C2×C9—21no—
246C2×C9—21no—
247C2×C9—121no—
248C2×C9—241no—
249C2×C9#89411yescharacteristic
250C2×C9#91111yescharacteristic
251C2×C9#91911yescharacteristic
252C2×D4—31no—
253C2×D4—61no—
254C22×C4—31no—
255C2×C8—31no—
256C2×C8C2×D3×C911yescharacteristic
257C4⋊C4—31no—
258C4⋊C4C2×D3×C911yescharacteristic
259C4⋊C4C2×D3×C911yescharacteristic
260C22⋊C4—61no—
261C22⋊C4—61no—
262C42—61no—
263C22×C3—21no—
264C22×C3—61no—
265C22×C3—61no—
266C22×C3—61no—
267C22×C3—121no—
268C22×C3—121no—
269C22×C3—121no—
270C22×C3C2×D4×C911yescharacteristic
271C22×C3C3×D3×D411yescharacteristic
272C2×D3—21no—
273C2×D3—21no—
274C2×D3—21no—
275C2×D3—41no—
276C2×D3—41no—
277C2×D3—41no—
278C3×C4—21no—
279C3×C4—21no—
280C3×C4—41no—
281C3×C4—41no—
282C3×C4—41no—
283C3×C4—41no—
284C3×C4—61no—
285C3×C4—81no—
286C3×C4—81no—
287C3×C4—121no—
288C3×C4C9×#4111yescharacteristic
289C3×C4C9×#4111yescharacteristic
290C3×C4C3×#23511yescharacteristic
291C3×C4C3×#23911yescharacteristic
292Dic3—21no—
293Dic3—41no—
294C32C3×#48211yescharacteristic
295C9—21no—
296C9#488511yescharacteristic, direct product factor
297C23—31no—
298C23—61no—
299D4—61no—
300D4—61no—
301D4—122no—
302C2×C4—21no—
303C2×C4—21no—
304C2×C4—31no—
305C2×C4—61no—
306C2×C4—61no—
307C2×C4—61no—
308C2×C4C22×D3×C911yescharacteristic
309C8—21no—
310C8—61no—
311C2×C3—21no—
312C2×C3—21no—
313C2×C3—21no—
314C2×C3—121no—
315C2×C3—241no—
316C2×C3C9×#12311yescharacteristic
317C2×C3C9×#13511yescharacteristic
318C2×C3C9×AGL(1,ℤ/8)11yescharacteristic
319C2×C3C3×#89411yescharacteristic
320C2×C3C3×#91111yescharacteristic
321C2×C3C3×#91911yescharacteristic
322D3—41no—
323D3—81no—
324C22—61no—
325C22—61no—
326C22—61no—
327C22—121no—
328C22—121no—
329C22—121no—
330C22D3×D4×C911yescharacteristic
331C4—41no—
332C4—41no—
333C4—61no—
334C4—121no—
335C4C9×#23511yescharacteristic
336C4C9×#23911yescharacteristic
337C3—21no—
338C3C9×#48211yescharacteristic, complemented
339C3C3×#488511yescharacteristic
340C2—121no—
341C2—241no—
342C2C9×#89411yescharacteristic
343C2C9×#91111yescharacteristic
344C2C9×#91911yescharacteristic
subgroupG/H
centerC22×C9D3×D4
commutatorC2×C3×C4C23×C9
FrattiniC2×C3×C4C22×C3×D3
FittingC3×C9×#107C2
socleC22×C32C2×C3×D4
prime radicalC3×#895C2×C3
cosocleC2×C32×C4C23×C3
hypercenterC9×#107D3
hypocenterC3C9×#482
LCSG ▷ C2×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C22×C9 ◁ C2×C4×C9 ◁ C9×#107

Complements

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

NH ≅ G/Ntype
2. C9×#892C2semidirect
3. C3×C9×#107C2semidirect
4. C9×#821C2semidirect
5. C9×(C2×D3)⋊C8C2semidirect
6. C9×#809C2semidirect
7. C9×#808C2semidirect
31. C9×#107D3semidirect
51. #4885C9direct (N × H)
93. #892C2×C9semidirect
95. C3×#107C2×C9semidirect
101. #821C2×C9semidirect
102. (C2×D3)⋊C8C2×C9semidirect
103. #809C2×C9semidirect
104. #808C2×C9semidirect
201. #107D3×C9semidirect
206. C3×C9#482semidirect
296. C9#4885direct (N × H)
338. C3C9×#482semidirect

Maximal subgroups

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

subgroupindex
C9×#8952
C9×#8922
C3×C9×#1072
C9×#8212
C9×(C2×D3)⋊C82
C9×#8092
C9×#8082
C3×#48853
C9×#4823