Finite Group Databasebeta

← C9×#4779 #13141762

Subgroups — C9×#4779 #13141762

Order 1728.

368 conjugacy classes of subgroups.

The subgroup lattice has 356 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C9×#938C211yesmaximal, characteristic
2C9×#892C211yesmaximal, characteristic, complemented
3C3×C9×#102C211yesmaximal, characteristic, complemented
4C9×#832C211yesmaximal, characteristic, complemented
5C9×(C2×D3)⋊C8C211yesmaximal, characteristic, complemented
6C9×#817C211yesmaximal, characteristic, complemented
7C9×#807C211yesmaximal, characteristic, complemented
8C3×#4779C311yesmaximal, characteristic
9C9×#482—31nomaximal
10C2×C3×D4×C9C2211yescharacteristic
11C2×C9×#67—21no—
12C2×C4×D3×C9C2211yescharacteristic
13C2×C3×C8×C9C2211yescharacteristic
14C3×C9×C4⋊C4C2211yescharacteristic
15C9×#217—21no—
16C9×(C2×D3)⋊C4—21no—
17C9×C4⋊Dic3C2211yescharacteristic
18C9×C4⋊Dic3C2211yescharacteristic
19C4×C9×Dic3—21no—
20C2×C9×C3⋊C8C2211yescharacteristic
21C3×#938C2×C311yescharacteristic
22C3×#892C2×C311yescharacteristic
23C32×#102C2×C311yescharacteristic
24C3×#832C2×C311yescharacteristic
25C3×(C2×D3)⋊C8C2×C311yescharacteristic
26C3×#817C2×C311yescharacteristic
27C3×#807C2×C311yescharacteristic
28C9×#121—31no—
29C9×#117—31no—
30C9×#107—31no—
31C9×#106—31no—
32C9×#102—21no—
33C9×#102—31no—
34C9×#102D311yescharacteristic, complemented
35C9×C22⋊C8—31no—
36C23×C3×C9—21no—
37C22×D3×C9D411yescharacteristic
38C3×D4×C9—21no—
39C3×D4×C9—21no—
40C2×C3×C4×C9—21no—
41C2×C3×C4×C9C2311yescharacteristic
42C9×#67—42no—
43C2×C9×Dic3—21no—
44C2×C9×Dic3—21no—
45C2×C9×Dic3D411yescharacteristic
46C4×D3×C9—21no—
47C4×D3×C9—21no—
48C3×C8×C9—21no—
49C9×C3⋊C8—21no—
50C3×#482—31no—
51#4779C911yescharacteristic, direct product factor
52C2×C32×D4C22×C311yescharacteristic
53C2×C3×#67—21no—
54C2×C3×C4×D3C22×C311yescharacteristic
55C2×C32×C8C22×C311yescharacteristic
56C32×C4⋊C4C22×C311yescharacteristic
57C3×#217—21no—
58C3×(C2×D3)⋊C4—21no—
59C3×C4⋊Dic3C22×C311yescharacteristic
60C3×C4⋊Dic3C22×C311yescharacteristic
61C3×C4×Dic3—21no—
62C2×C3×C3⋊C8C22×C311yescharacteristic
63C2×D4×C9—21no—
64C2×D4×C9—61no—
65C2×D4×C9C2×D311yescharacteristic
66C22×C4×C9—31no—
67C2×C8×C9—21no—
68C2×C8×C9—31no—
69C2×C8×C9C2×D311yescharacteristic
70C9×C4⋊C4—21no—
71C9×C4⋊C4—31no—
72C9×C4⋊C4—31no—
73C9×C4⋊C4C2×D311yescharacteristic
74C9×C22⋊C4—61no—
75C9×C22⋊C4—61no—
76C42×C9—61no—
77C22×C3×C9—41no—
78C22×C3×C9—41no—
79C22×C3×C9—41no—
80C22×C3×C9C2×D411yescharacteristic
81C2×D3×C9—21no—
82C2×D3×C9—21no—
83C2×D3×C9—21no—
84C3×C4×C9—41no—
85C3×C4×C9#4111yescharacteristic
86C3×C4×C9#4111yescharacteristic
87C9×Dic3—21no—
88C9×Dic3—41no—
89C9×Dic3—41no—
90C3×#121—31no—
91C3×#117—31no—
92#938C2×C911yescharacteristic
93#892C2×C911yescharacteristic, complemented
94C3×#107—31no—
95C3×#106—31no—
96C3×#102—21no—
97C3×#102—31no—
98C3×#102C2×C911yescharacteristic, complemented
99C3×#102C3×D311yescharacteristic
100C3×C22⋊C8—31no—
101#832C2×C911yescharacteristic, complemented
102(C2×D3)⋊C8C2×C911yescharacteristic, complemented
103#817C2×C911yescharacteristic, complemented
104#807C2×C911yescharacteristic, complemented
105C23×C32—21no—
106C22×C3×D3C3×D411yescharacteristic
107C32×D4—21no—
108C32×D4—21no—
109C2×C32×C4—21no—
110C2×C32×C4C23×C311yescharacteristic
111C3×#67—42no—
112C2×C3×Dic3—21no—
113C2×C3×Dic3—21no—
114C2×C3×Dic3C3×D411yescharacteristic
115C3×C4×D3—21no—
116C3×C4×D3—21no—
117C23×C9—21no—
118C23×C9—31no—
119C23×C9—41no—
120C32×C8—21no—
121C3×C3⋊C8—21no—
122D4×C9—22no—
123D4×C9—21no—
124D4×C9—21no—
125D4×C9—41no—
126D4×C9—122no—
127C2×C4×C9—21no—
128C2×C4×C9—21no—
129C2×C4×C9—31no—
130C2×C4×C9—41no—
131C2×C4×C9—61no—
132C2×C4×C9—61no—
133C2×C4×C9—61no—
134C2×C4×C9—61no—
135C2×C4×C9C22×D311yescharacteristic
136C8×C9—21no—
137C8×C9—41no—
138C8×C9—61no—
139#482—31noSylow
140C2×C3×C9—81no—
141C2×C3×C9#12311yescharacteristic
142C2×C3×C9#13511yescharacteristic
143C2×C3×C9AGL(1,ℤ/8)11yescharacteristic
144D3×C9—41no—
145C2×C3×D4—21no—
146C2×C3×D4—61no—
147C2×C3×D4C22×C911yescharacteristic
148C2×C3×D4C2×C3×D311yescharacteristic
149C22×C3×C4—31no—
150C2×#67—21no—
151C2×C4×D3C22×C911yescharacteristic
152C2×C3×C8—21no—
153C2×C3×C8—31no—
154C2×C3×C8C22×C911yescharacteristic
155C2×C3×C8C2×C3×D311yescharacteristic
156C3×C4⋊C4—21no—
157C3×C4⋊C4—31no—
158C3×C4⋊C4—31no—
159C3×C4⋊C4C22×C911yescharacteristic
160C3×C4⋊C4C2×C3×D311yescharacteristic
161C3×C22⋊C4—61no—
162C3×C22⋊C4—61no—
163C3×C42—61no—
164#217—21no—
165(C2×D3)⋊C4—21no—
166C4⋊Dic3C22×C911yescharacteristic
167C4⋊Dic3C22×C911yescharacteristic
168C4×Dic3—21no—
169C2×C3⋊C8C22×C911yescharacteristic
170C22×C32—41no—
171C22×C32—41no—
172C22×C32—41no—
173C22×C32C2×C3×D411yescharacteristic
174C2×C3×D3—21no—
175C2×C3×D3—21no—
176C2×C3×D3—21no—
177C32×C4—41no—
178C32×C4C3×#4111yescharacteristic
179C32×C4C3×#4111yescharacteristic
180C3×Dic3—21no—
181C3×Dic3—41no—
182C3×Dic3—41no—
183C22×C9—21no—
184C22×C9—42no—
185C22×C9—41no—
186C22×C9—41no—
187C22×C9—41no—
188C22×C9—61no—
189C22×C9—61no—
190C22×C9—61no—
191C22×C9—81no—
192C22×C9—81no—
193C22×C9D3×D411yescharacteristic
194C4×C9—21no—
195C4×C9—21no—
196C4×C9—41no—
197C4×C9—61no—
198C4×C9—81no—
199C4×C9—121no—
200C4×C9—121no—
201C4×C9#23511yescharacteristic
202C4×C9#23711yescharacteristic
203#121—31no—
204#117—31no—
205#107—31no—
206#106—31no—
207#102—31no—
208#102D3×C911yescharacteristic, complemented
209C22⋊C8—31no—
210C3×C9#48211yescharacteristic, complemented, Sylow
211C23×C3—21no—
212C23×C3—21no—
213C23×C3—31no—
214C23×C3—41no—
215C22×D3D4×C911yescharacteristic
216C3×D4—22no—
217C3×D4—21no—
218C3×D4—21no—
219C3×D4—21no—
220C3×D4—21no—
221C3×D4—41no—
222C3×D4—122no—
223C2×C3×C4—21no—
224C2×C3×C4—21no—
225C2×C3×C4—21no—
226C2×C3×C4—31no—
227C2×C3×C4—41no—
228C2×C3×C4—61no—
229C2×C3×C4—61no—
230C2×C3×C4—61no—
231C2×C3×C4—61no—
232C2×C3×C4C23×C911yescharacteristic
233C2×C3×C4C22×C3×D311yescharacteristic
234#67—42no—
235C2×Dic3—21no—
236C2×Dic3—21no—
237C2×Dic3D4×C911yescharacteristic
238C4×D3—21no—
239C4×D3—21no—
240C3×C8—21no—
241C3×C8—21no—
242C3×C8—41no—
243C3×C8—61no—
244C3⋊C8—21no—
245C2×C32—81no—
246C2×C32C3×#12311yescharacteristic
247C2×C32C3×#13511yescharacteristic
248C2×C32C3×AGL(1,ℤ/8)11yescharacteristic
249C3×D3—41no—
250C2×C9—21no—
251C2×C9—21no—
252C2×C9—21no—
253C2×C9—82no—
254C2×C9—81no—
255C2×C9—121no—
256C2×C9#88311yescharacteristic
257C2×C9#91111yescharacteristic
258C2×C9#91611yescharacteristic
259C2×D4—61no—
260C2×D4C2×D3×C911yescharacteristic
261C22×C4—31no—
262C2×C8—31no—
263C2×C8C2×D3×C911yescharacteristic
264C4⋊C4—31no—
265C4⋊C4—31no—
266C4⋊C4C2×D3×C911yescharacteristic
267C22⋊C4—61no—
268C22⋊C4—61no—
269C42—61no—
270C22×C3—21no—
271C22×C3—42no—
272C22×C3—41no—
273C22×C3—41no—
274C22×C3—41no—
275C22×C3—41no—
276C22×C3—41no—
277C22×C3—41no—
278C22×C3—61no—
279C22×C3—61no—
280C22×C3—61no—
281C22×C3—81no—
282C22×C3—81no—
283C22×C3C2×D4×C911yescharacteristic
284C22×C3C3×D3×D411yescharacteristic
285C2×D3—21no—
286C2×D3—21no—
287C2×D3—21no—
288C3×C4—21no—
289C3×C4—21no—
290C3×C4—41no—
291C3×C4—41no—
292C3×C4—61no—
293C3×C4—81no—
294C3×C4—121no—
295C3×C4—121no—
296C3×C4C9×#4111yescharacteristic
297C3×C4C9×#4111yescharacteristic
298C3×C4C3×#23511yescharacteristic
299C3×C4C3×#23711yescharacteristic
300Dic3—21no—
301Dic3—41no—
302Dic3—41no—
303C32C3×#48211yescharacteristic
304C9—21no—
305C9#477911yescharacteristic, direct product factor
306C23—21no—
307C23—31no—
308D4—21no—
309D4—21no—
310D4—122no—
311C2×C4—21no—
312C2×C4—31no—
313C2×C4—61no—
314C2×C4—61no—
315C2×C4—61no—
316C2×C4—61no—
317C2×C4C22×D3×C911yescharacteristic
318C8—21no—
319C8—61no—
320C2×C3—21no—
321C2×C3—21no—
322C2×C3—21no—
323C2×C3—82no—
324C2×C3—81no—
325C2×C3—81no—
326C2×C3—121no—
327C2×C3C9×#12311yescharacteristic
328C2×C3C9×#13511yescharacteristic
329C2×C3C9×AGL(1,ℤ/8)11yescharacteristic
330C2×C3C3×#88311yescharacteristic
331C2×C3C3×#91111yescharacteristic
332C2×C3C3×#91611yescharacteristic
333D3—41no—
334C22—41no—
335C22—41no—
336C22—41no—
337C22—61no—
338C22—61no—
339C22—61no—
340C22D3×D4×C911yescharacteristic
341C4—41no—
342C4—61no—
343C4—121no—
344C4—121no—
345C4C9×#23511yescharacteristic
346C4C9×#23711yescharacteristic
347C3—21no—
348C3C9×#48211yescharacteristic, complemented
349C3C3×#477911yescharacteristic
350C2—81no—
351C2—121no—
352C2C9×#88311yescharacteristic
353C2C9×#91111yescharacteristic
354C2C9×#91611yescharacteristic
subgroupG/H
centerC22×C9D3×D4
commutatorC2×C3×C4C23×C9
FrattiniC2×C3×C4C22×C3×D3
FittingC3×C9×#102C2
socleC22×C32C2×C3×D4
prime radicalC3×#938C2×C3
cosocleC2×C32×C4C23×C3
hypercenterC9×#102D3
hypocenterC3C9×#482
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×#892C2semidirect
3. C3×C9×#102C2semidirect
4. C9×#832C2semidirect
5. C9×(C2×D3)⋊C8C2semidirect
6. C9×#817C2semidirect
7. C9×#807C2semidirect
34. C9×#102D3semidirect
51. #4779C9direct (N × H)
93. #892C2×C9semidirect
98. C3×#102C2×C9semidirect
101. #832C2×C9semidirect
102. (C2×D3)⋊C8C2×C9semidirect
103. #817C2×C9semidirect
104. #807C2×C9semidirect
208. #102D3×C9semidirect
210. C3×C9#482semidirect
305. C9#4779direct (N × H)
348. C3C9×#482semidirect

Maximal subgroups

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

subgroupindex
C9×#9382
C9×#8922
C3×C9×#1022
C9×#8322
C9×(C2×D3)⋊C82
C9×#8172
C9×#8072
C3×#47793
C9×#4823