Finite Group Databasebeta

← C9×#4782 #13141765

Subgroups — C9×#4782 #13141765

Order 1728.

440 conjugacy classes of subgroups.

The subgroup lattice has 404 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C9×#938C211yesmaximal, characteristic, complemented
2C2×C9×#213C211yesmaximal, characteristic, complemented
3C2×C9×ΓL(1,𝔽25)C211yesmaximal, characteristic, complemented
4C9×#895C211yesmaximal, characteristic, complemented
5C3×C9×#102C211yesmaximal, characteristic, complemented
6C9×#821C211yesmaximal, characteristic, complemented
7C9×#808C211yesmaximal, characteristic, complemented
8C3×#4782C311yesmaximal, characteristic
9C9×#469—31nomaximal
10C2×C3×D4×C9C2211yescharacteristic
11C2×C9×#67—21no—
12C2×C9×D12—21no—
13C2×C9×D12C2211yescharacteristic
14C2×C4×D3×C9C2211yescharacteristic
15C2×C3×C8×C9C2211yescharacteristic
16C3×C9×C4⋊C4C2211yescharacteristic
17C9×#217—21no—
18C9×#213—22no—
19C9×(C2×D3)⋊C4—21no—
20C9×C4⋊Dic3C2211yescharacteristic
21C2×C9×C3⋊C8C2211yescharacteristic
22C9×ΓL(1,𝔽25)—22no—
23C3×#938C2×C311yescharacteristic
24C2×C3×#213C2×C311yescharacteristic
25C2×C3×ΓL(1,𝔽25)C2×C311yescharacteristic
26C3×#895C2×C311yescharacteristic
27C32×#102C2×C311yescharacteristic
28C3×#821C2×C311yescharacteristic
29C3×#808C2×C311yescharacteristic
30C2×C9×D8—31no—
31C2×C9×M16—31no—
32C9×#121—31no—
33C9×#121—31no—
34C9×#106—31no—
35C9×#102—21no—
36C9×#102—31no—
37C9×#102D311yescharacteristic, complemented
38C23×C3×C9—21no—
39C22×D3×C9—21no—
40C22×D3×C9D411yescharacteristic
41C3×D4×C9—21no—
42C3×D4×C9—21no—
43C2×C3×C4×C9—21no—
44C2×C3×C4×C9C2311yescharacteristic
45C9×#67—42no—
46C2×C9×Dic3—21no—
47C2×C9×Dic3D411yescharacteristic
48C9×D12—21no—
49C9×D12—21no—
50C9×D12—42no—
51C4×D3×C9—21no—
52C4×D3×C9—21no—
53C3×C8×C9—21no—
54C9×C3⋊C8D412yescomplemented
55C3×#469—31no—
56#4782C911yescharacteristic, direct product factor
57C2×C32×D4C22×C311yescharacteristic
58C2×C3×#67—21no—
59C2×C3×D12—21no—
60C2×C3×D12C22×C311yescharacteristic
61C2×C3×C4×D3C22×C311yescharacteristic
62C2×C32×C8C22×C311yescharacteristic
63C32×C4⋊C4C22×C311yescharacteristic
64C3×#217—21no—
65C3×#213—22no—
66C3×(C2×D3)⋊C4—21no—
67C3×C4⋊Dic3C22×C311yescharacteristic
68C2×C3×C3⋊C8C22×C311yescharacteristic
69C3×ΓL(1,𝔽25)—22no—
70C2×D4×C9—21no—
71C2×D4×C9—31no—
72C2×D4×C9—61no—
73C2×D4×C9—61no—
74C2×D4×C9C2×D311yescharacteristic
75C22×C4×C9—31no—
76C9×D8—62no—
77C9×M16—62no—
78C2×C8×C9—21no—
79C2×C8×C9—31no—
80C2×C8×C9C2×D311yescharacteristic
81C9×C4⋊C4—21no—
82C9×C4⋊C4—31no—
83C9×C4⋊C4C2×D311yescharacteristic
84C9×C22⋊C4—61no—
85C9×C22⋊C4—61no—
86C22×C3×C9—41no—
87C22×C3×C9—41no—
88C22×C3×C9—41no—
89C22×C3×C9C2×D411yescharacteristic
90C2×D3×C9—21no—
91C2×D3×C9—21no—
92C2×D3×C9—21no—
93C2×D3×C9—41no—
94C2×D3×C9—41no—
95C2×D3×C9—41no—
96C3×C4×C9—41no—
97C3×C4×C9C2×D411yescharacteristic
98C3×C4×C9#4111yescharacteristic
99C9×Dic3—21no—
100C9×Dic3—41no—
101C2×C3×D8—31no—
102C2×C3×M16—31no—
103C3×#121—31no—
104C3×#121—31no—
105#938C2×C911yescharacteristic, complemented
106C2×#213C2×C911yescharacteristic, complemented
107C2×ΓL(1,𝔽25)C2×C911yescharacteristic, complemented
108#895C2×C911yescharacteristic, complemented
109C3×#106—31no—
110C3×#102—21no—
111C3×#102—31no—
112C3×#102C2×C911yescharacteristic, complemented
113C3×#102C3×D311yescharacteristic
114#821C2×C911yescharacteristic, complemented
115#808C2×C911yescharacteristic, complemented
116C23×C32—21no—
117C22×C3×D3—21no—
118C22×C3×D3C3×D411yescharacteristic
119C32×D4—21no—
120C32×D4—21no—
121C2×C32×C4—21no—
122C2×C32×C4C23×C311yescharacteristic
123C3×#67—42no—
124C2×C3×Dic3—21no—
125C2×C3×Dic3C3×D411yescharacteristic
126C3×D12—21no—
127C3×D12—21no—
128C3×D12—42no—
129C3×C4×D3—21no—
130C3×C4×D3—21no—
131C23×C9—21no—
132C23×C9—31no—
133C23×C9—41no—
134C23×C9—61no—
135C32×C8—21no—
136C3×C3⋊C8C3×D412yes—
137D4×C9—22no—
138D4×C9—21no—
139D4×C9—21no—
140D4×C9—41no—
141D4×C9—61no—
142D4×C9—61no—
143D4×C9—122no—
144D4×C9—122no—
145C2×C4×C9—21no—
146C2×C4×C9—21no—
147C2×C4×C9—31no—
148C2×C4×C9—41no—
149C2×C4×C9—61no—
150C2×C4×C9—61no—
151C2×C4×C9—61no—
152C2×C4×C9C22×D311yescharacteristic
153C8×C9—21no—
154C8×C9—32no—
155C8×C9—41no—
156#469—31noSylow
157C2×C3×C9—81no—
158C2×C3×C9#12111yescharacteristic
159C2×C3×C9AGL(1,ℤ/8)11yescharacteristic
160C2×C3×C9AGL(1,ℤ/8)11yescharacteristic
161D3×C9—41no—
162D3×C9—81no—
163C2×C3×D4—21no—
164C2×C3×D4—31no—
165C2×C3×D4—61no—
166C2×C3×D4—61no—
167C2×C3×D4C22×C911yescharacteristic
168C2×C3×D4C2×C3×D311yescharacteristic
169C22×C3×C4—31no—
170C2×#67—21no—
171C2×D12—21no—
172C2×D12C22×C911yescharacteristic
173C2×C4×D3C22×C911yescharacteristic
174C3×D8—62no—
175C3×M16—62no—
176C2×C3×C8—21no—
177C2×C3×C8—31no—
178C2×C3×C8C22×C911yescharacteristic
179C2×C3×C8C2×C3×D311yescharacteristic
180C3×C4⋊C4—21no—
181C3×C4⋊C4—31no—
182C3×C4⋊C4C22×C911yescharacteristic
183C3×C4⋊C4C2×C3×D311yescharacteristic
184C3×C22⋊C4—61no—
185C3×C22⋊C4—61no—
186#217—21no—
187#213—22no—
188(C2×D3)⋊C4—21no—
189C4⋊Dic3C22×C911yescharacteristic
190C2×C3⋊C8C22×C911yescharacteristic
191ΓL(1,𝔽25)—22no—
192C22×C32—41no—
193C22×C32—41no—
194C22×C32—41no—
195C22×C32C2×C3×D411yescharacteristic
196C2×C3×D3—21no—
197C2×C3×D3—21no—
198C2×C3×D3—21no—
199C2×C3×D3—41no—
200C2×C3×D3—41no—
201C2×C3×D3—41no—
202C32×C4—41no—
203C32×C4C2×C3×D411yescharacteristic
204C32×C4C3×#4111yescharacteristic
205C3×Dic3—21no—
206C3×Dic3—41no—
207C22×C9—21no—
208C22×C9—42no—
209C22×C9—41no—
210C22×C9—41no—
211C22×C9—41no—
212C22×C9—61no—
213C22×C9—61no—
214C22×C9—61no—
215C22×C9—81no—
216C22×C9—81no—
217C22×C9—121no—
218C22×C9—121no—
219C22×C9—121no—
220C22×C9D3×D411yescharacteristic
221C4×C9—21no—
222C4×C9—21no—
223C4×C9—41no—
224C4×C9—61no—
225C4×C9—81no—
226C4×C9—121no—
227C4×C9#23511yescharacteristic
228C4×C9D3×D411yescharacteristic
229C2×D8—31no—
230C2×M16—31no—
231#121—31no—
232#121—31no—
233#106—31no—
234#102—31no—
235#102D3×C911yescharacteristic, complemented
236C3×C9#46911yescharacteristic, complemented, Sylow
237C23×C3—21no—
238C23×C3—21no—
239C23×C3—31no—
240C23×C3—41no—
241C23×C3—61no—
242C22×D3—21no—
243C22×D3D4×C911yescharacteristic
244C3×D4—22no—
245C3×D4—21no—
246C3×D4—21no—
247C3×D4—21no—
248C3×D4—21no—
249C3×D4—41no—
250C3×D4—61no—
251C3×D4—61no—
252C3×D4—122no—
253C3×D4—122no—
254C2×C3×C4—21no—
255C2×C3×C4—21no—
256C2×C3×C4—21no—
257C2×C3×C4—31no—
258C2×C3×C4—41no—
259C2×C3×C4—61no—
260C2×C3×C4—61no—
261C2×C3×C4—61no—
262C2×C3×C4C23×C911yescharacteristic
263C2×C3×C4C22×C3×D311yescharacteristic
264#67—42no—
265C2×Dic3—21no—
266C2×Dic3D4×C911yescharacteristic
267D12—21no—
268D12—21no—
269D12—42no—
270C4×D3—21no—
271C4×D3—21no—
272C3×C8—21no—
273C3×C8—21no—
274C3×C8—32no—
275C3×C8—41no—
276C3⋊C8D4×C912yescomplemented
277C2×C32—81no—
278C2×C32C3×#12111yescharacteristic
279C2×C32C3×AGL(1,ℤ/8)11yescharacteristic
280C2×C32C3×AGL(1,ℤ/8)11yescharacteristic
281C3×D3—41no—
282C3×D3—81no—
283C2×C9—21no—
284C2×C9—21no—
285C2×C9—21no—
286C2×C9—82no—
287C2×C9—81no—
288C2×C9—121no—
289C2×C9—241no—
290C2×C9#88411yescharacteristic
291C2×C9#91111yescharacteristic
292C2×C9#91411yescharacteristic
293C2×D4—31no—
294C2×D4—61no—
295C2×D4—61no—
296C2×D4C2×D3×C911yescharacteristic
297C22×C4—31no—
298D8—62no—
299M16—62no—
300C2×C8—31no—
301C2×C8C2×D3×C911yescharacteristic
302C4⋊C4—31no—
303C4⋊C4C2×D3×C911yescharacteristic
304C22⋊C4—61no—
305C22⋊C4—61no—
306C22×C3—21no—
307C22×C3—42no—
308C22×C3—41no—
309C22×C3—41no—
310C22×C3—41no—
311C22×C3—41no—
312C22×C3—41no—
313C22×C3—41no—
314C22×C3—61no—
315C22×C3—61no—
316C22×C3—61no—
317C22×C3—81no—
318C22×C3—81no—
319C22×C3—121no—
320C22×C3—121no—
321C22×C3—121no—
322C22×C3C2×D4×C911yescharacteristic
323C22×C3C3×D3×D411yescharacteristic
324C2×D3—21no—
325C2×D3—21no—
326C2×D3—21no—
327C2×D3—41no—
328C2×D3—41no—
329C2×D3—41no—
330C3×C4—21no—
331C3×C4—21no—
332C3×C4—41no—
333C3×C4—41no—
334C3×C4—61no—
335C3×C4—81no—
336C3×C4—121no—
337C3×C4C2×D4×C911yescharacteristic
338C3×C4C9×#4111yescharacteristic
339C3×C4C3×#23511yescharacteristic
340C3×C4C3×D3×D411yescharacteristic
341Dic3—21no—
342Dic3—41no—
343C32C3×#46911yescharacteristic
344C9—21no—
345C9#478211yescharacteristic, direct product factor
346C23—21no—
347C23—31no—
348C23—61no—
349D4—21no—
350D4—21no—
351D4—61no—
352D4—61no—
353D4—122no—
354D4—122no—
355C2×C4—21no—
356C2×C4—31no—
357C2×C4—61no—
358C2×C4—61no—
359C2×C4—61no—
360C2×C4C22×D3×C911yescharacteristic
361C8—21no—
362C8—32no—
363C2×C3—21no—
364C2×C3—21no—
365C2×C3—21no—
366C2×C3—82no—
367C2×C3—81no—
368C2×C3—81no—
369C2×C3—121no—
370C2×C3—241no—
371C2×C3C9×#12111yescharacteristic
372C2×C3C9×AGL(1,ℤ/8)11yescharacteristic
373C2×C3C9×AGL(1,ℤ/8)11yescharacteristic
374C2×C3C3×#88411yescharacteristic
375C2×C3C3×#91111yescharacteristic
376C2×C3C3×#91411yescharacteristic
377D3—41no—
378D3—81no—
379C22—41no—
380C22—41no—
381C22—41no—
382C22—61no—
383C22—61no—
384C22—61no—
385C22—121no—
386C22—121no—
387C22—121no—
388C22D3×D4×C911yescharacteristic
389C4—41no—
390C4—61no—
391C4—121no—
392C4C9×#23511yescharacteristic
393C4D3×D4×C911yescharacteristic
394C3—21no—
395C3C9×#46911yescharacteristic, complemented
396C3C3×#478211yescharacteristic
397C2—81no—
398C2—121no—
399C2—241no—
400C2C9×#88411yescharacteristic
401C2C9×#91111yescharacteristic
402C2C9×#91411yescharacteristic
subgroupG/H
centerC22×C9D3×D4
commutatorC2×C3×C4C23×C9
FrattiniC2×C3×C4C22×C3×D3
FittingC3×C9×#102C2
socleC22×C32C2×C3×D4
prime radicalC3×#4782C3
cosocleC2×C32×C4C23×C3
hypercenterC9×#102D3
hypocenterC3C9×#469
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
1. C9×#938C2semidirect
2. C2×C9×#213C2semidirect
3. C2×C9×ΓL(1,𝔽25)C2semidirect
4. C9×#895C2semidirect
5. C3×C9×#102C2semidirect
6. C9×#821C2semidirect
7. C9×#808C2semidirect
37. C9×#102D3semidirect
54. C9×C3⋊C8D4semidirect
56. #4782C9direct (N × H)
105. #938C2×C9semidirect
106. C2×#213C2×C9semidirect
107. C2×ΓL(1,𝔽25)C2×C9semidirect
108. #895C2×C9semidirect
112. C3×#102C2×C9semidirect
114. #821C2×C9semidirect
115. #808C2×C9semidirect
235. #102D3×C9semidirect
236. C3×C9#469semidirect
276. C3⋊C8D4×C9semidirect
345. C9#4782direct (N × H)
395. C3C9×#469semidirect

Maximal subgroups

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

subgroupindex
C9×#9382
C2×C9×#2132
C2×C9×ΓL(1,𝔽25)2
C9×#8952
C3×C9×#1022
C9×#8212
C9×#8082
C3×#47823
C9×#4693