Finite Group Databasebeta

← C9×#4808 #13141896

Subgroups — C9×#4808 #13141896

Order 1728.

498 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
1C2×C9×#239C211yesmaximal, characteristic
2C2×C9×#216C211yesmaximal, characteristic, complemented
3C2×C9×#204C211yesmaximal, characteristic, complemented
4C9×#897C211yesmaximal, characteristic, complemented
5C3×C9×#103C211yesmaximal, characteristic, complemented
6C9×(C2×D3)⋊C8C211yesmaximal, characteristic, complemented
7C9×#809C211yesmaximal, characteristic, complemented
8C3×#4808C311yesmaximal, characteristic
9C9×#452—31nomaximal
10C2×C3×Q8×C9C2211yescharacteristic
11C9×#239—22no—
12C9×#239—22no—
13C2×C9×D12—21no—
14C2×C9×D12C2211yescharacteristic
15C2×C4×D3×C9—21no—
16C2×C4×D3×C9C2211yescharacteristic
17C2×C9×Dic6C2211yescharacteristic
18C2×C3×C8×C9C2211yescharacteristic
19C3×C9×C4⋊C4C2211yescharacteristic
20C9×#216—22no—
21C9×(C2×D3)⋊C4—21no—
22C9×C4⋊Dic3—21no—
23C2×C9×C3⋊C8C2211yescharacteristic
24C9×#204—22no—
25C2×C3×#239C2×C311yescharacteristic
26C2×C3×#216C2×C311yescharacteristic
27C2×C3×#204C2×C311yescharacteristic
28C3×#897C2×C311yescharacteristic
29C2×C9×#41—31no—
30C32×#103C2×C311yescharacteristic
31C3×(C2×D3)⋊C8C2×C311yescharacteristic
32C3×#809C2×C311yescharacteristic
33C2×C9×Q16—31no—
34C2×C9×SD16—31no—
35C9×C22⋊Q8—31no—
36C9×#103—21no—
37C9×#103D311yescharacteristic, complemented
38C9×#102—31no—
39C9×C22⋊C8—31no—
40C22×D3×C9—21no—
41C22×D3×C9D411yescharacteristic
42C3×Q8×C9—21no—
43C3×Q8×C9D412yes—
44C2×C3×C4×C9—21no—
45C2×C3×C4×C9—21no—
46C2×C3×C4×C9C2311yescharacteristic
47C2×C9×Dic3—21no—
48C2×C9×Dic3D411yescharacteristic
49C9×D12—24no—
50C9×D12—21no—
51C9×D12D412yes—
52C4×D3×C9—24no—
53C4×D3×C9—21no—
54C4×D3×C9—21no—
55C9×Dic6—21no—
56C9×Dic6—21no—
57C3×C8×C9—21no—
58C9×C3⋊C8—21no—
59C3×#452—31no—
60#4808C911yescharacteristic, direct product factor
61C2×C32×Q8C22×C311yescharacteristic
62C3×#239—22no—
63C3×#239—22no—
64C2×C3×D12—21no—
65C2×C3×D12C22×C311yescharacteristic
66C2×C3×C4×D3—21no—
67C2×C3×C4×D3C22×C311yescharacteristic
68C2×C3×Dic6C22×C311yescharacteristic
69C2×C32×C8C22×C311yescharacteristic
70C32×C4⋊C4C22×C311yescharacteristic
71C3×#216—22no—
72C3×(C2×D3)⋊C4—21no—
73C3×C4⋊Dic3—21no—
74C2×C3×C3⋊C8C22×C311yescharacteristic
75C3×#204—22no—
76C9×#41—62no—
77C9×#41—62no—
78C2×Q8×C9—21no—
79C2×Q8×C9—31no—
80C2×Q8×C9C2×D311yescharacteristic
81C2×D4×C9—31no—
82C2×D4×C9—61no—
83C22×C4×C9—31no—
84C22×C4×C9—61no—
85C9×Q16—62no—
86C9×SD16—62no—
87C2×C8×C9—21no—
88C2×C8×C9—31no—
89C2×C8×C9C2×D311yescharacteristic
90C9×C4⋊C4—21no—
91C9×C4⋊C4—61no—
92C9×C4⋊C4C2×D311yescharacteristic
93C9×C22⋊C4—61no—
94C22×C3×C9C2×D411yescharacteristic
95C2×D3×C9—21no—
96C2×D3×C9—22no—
97C2×D3×C9—21no—
98C2×D3×C9—21no—
99C2×D3×C9—41no—
100C2×D3×C9—41no—
101C3×C4×C9—22no—
102C3×C4×C9—41no—
103C3×C4×C9C2×D411yescharacteristic
104C3×C4×C9C2×D411yescharacteristic
105C9×Dic3—21no—
106C9×Dic3—41no—
107C2×C3×#41—31no—
108C2×#239C2×C911yescharacteristic
109C2×C3×Q16—31no—
110C2×C3×SD16—31no—
111C3×C22⋊Q8—31no—
112C2×#216C2×C911yescharacteristic, complemented
113C2×#204C2×C911yescharacteristic, complemented
114#897C2×C911yescharacteristic, complemented
115C3×#103—21no—
116C3×#103C2×C911yescharacteristic, complemented
117C3×#103C3×D311yescharacteristic
118C3×#102—31no—
119C3×C22⋊C8—31no—
120(C2×D3)⋊C8C2×C911yescharacteristic, complemented
121#809C2×C911yescharacteristic, complemented
122C22×C3×D3—21no—
123C22×C3×D3C3×D411yescharacteristic
124C32×Q8—21no—
125C32×Q8C3×D412yes—
126C2×C32×C4—21no—
127C2×C32×C4—21no—
128C2×C32×C4C23×C311yescharacteristic
129C2×C3×Dic3—21no—
130C2×C3×Dic3C3×D411yescharacteristic
131C3×D12—24no—
132C3×D12—21no—
133C3×D12C3×D412yes—
134C3×C4×D3—24no—
135C3×C4×D3—21no—
136C3×C4×D3—21no—
137C3×Dic6—21no—
138C3×Dic6—21no—
139C23×C9—31no—
140C23×C9—61no—
141C32×C8—21no—
142C3×C3⋊C8—21no—
143Q8×C9—21no—
144Q8×C9—22no—
145Q8×C9—41no—
146Q8×C9—61no—
147Q8×C9—61no—
148Q8×C9D1212yes—
149D4×C9—32no—
150D4×C9—64no—
151D4×C9—61no—
152C2×C4×C9—21no—
153C2×C4×C9—21no—
154C2×C4×C9—21no—
155C2×C4×C9—31no—
156C2×C4×C9—41no—
157C2×C4×C9—41no—
158C2×C4×C9—64no—
159C2×C4×C9—61no—
160C2×C4×C9—61no—
161C2×C4×C9—61no—
162C2×C4×C9C22×D311yescharacteristic
163C8×C9—21no—
164C8×C9—41no—
165C8×C9—61no—
166#452—31noSylow
167C2×C3×C9#12011yescharacteristic
168C2×C3×C9#13511yescharacteristic
169C2×C3×C9#13711yescharacteristic
170D3×C9—41no—
171D3×C9—42no—
172C3×#41—62no—
173C3×#41—62no—
174C2×C3×Q8—21no—
175C2×C3×Q8—31no—
176C2×C3×Q8C22×C911yescharacteristic
177C2×C3×Q8C2×C3×D311yescharacteristic
178C2×C3×D4—31no—
179C2×C3×D4—61no—
180C22×C3×C4—31no—
181C22×C3×C4—61no—
182#239—22no—
183#239—22no—
184C2×D12—21no—
185C2×D12C22×C911yescharacteristic
186C2×C4×D3—21no—
187C2×C4×D3C22×C911yescharacteristic
188C2×Dic6C22×C911yescharacteristic
189C3×Q16—62no—
190C3×SD16—62no—
191C2×C3×C8—21no—
192C2×C3×C8—31no—
193C2×C3×C8C22×C911yescharacteristic
194C2×C3×C8C2×C3×D311yescharacteristic
195C3×C4⋊C4—21no—
196C3×C4⋊C4—61no—
197C3×C4⋊C4C22×C911yescharacteristic
198C3×C4⋊C4C2×C3×D311yescharacteristic
199C3×C22⋊C4—61no—
200#216—22no—
201(C2×D3)⋊C4—21no—
202C4⋊Dic3—21no—
203C2×C3⋊C8C22×C911yescharacteristic
204#204—22no—
205C22×C32C2×C3×D411yescharacteristic
206C2×C3×D3—21no—
207C2×C3×D3—22no—
208C2×C3×D3—21no—
209C2×C3×D3—21no—
210C2×C3×D3—41no—
211C2×C3×D3—41no—
212C32×C4—22no—
213C32×C4—41no—
214C32×C4C2×C3×D411yescharacteristic
215C32×C4C2×C3×D411yescharacteristic
216C3×Dic3—21no—
217C3×Dic3—41no—
218C22×C9—21no—
219C22×C9—62no—
220C22×C9—61no—
221C22×C9—61no—
222C22×C9—61no—
223C22×C9—121no—
224C22×C9—121no—
225C22×C9D3×D411yescharacteristic
226C4×C9—22no—
227C4×C9—21no—
228C4×C9—21no—
229C4×C9—42no—
230C4×C9—41no—
231C4×C9—61no—
232C4×C9—81no—
233C4×C9—121no—
234C4×C9C2×D1211yescharacteristic
235C4×C9D3×D411yescharacteristic
236C2×#41—31no—
237C2×Q16—31no—
238C2×SD16—31no—
239C22⋊Q8—31no—
240#103D3×C911yescharacteristic, complemented
241#102—31no—
242C22⋊C8—31no—
243C3×C9#45211yescharacteristic, complemented, Sylow
244C23×C3—31no—
245C23×C3—61no—
246C22×D3—21no—
247C22×D3D4×C911yescharacteristic
248C3×Q8—21no—
249C3×Q8—21no—
250C3×Q8—22no—
251C3×Q8—41no—
252C3×Q8—61no—
253C3×Q8—61no—
254C3×Q8D4×C912yes—
255C3×Q8C3×D1212yes—
256C3×D4—32no—
257C3×D4—64no—
258C3×D4—61no—
259C2×C3×C4—21no—
260C2×C3×C4—21no—
261C2×C3×C4—21no—
262C2×C3×C4—21no—
263C2×C3×C4—21no—
264C2×C3×C4—31no—
265C2×C3×C4—41no—
266C2×C3×C4—41no—
267C2×C3×C4—64no—
268C2×C3×C4—61no—
269C2×C3×C4—61no—
270C2×C3×C4—61no—
271C2×C3×C4C23×C911yescharacteristic
272C2×C3×C4C22×C3×D311yescharacteristic
273C2×Dic3—21no—
274C2×Dic3D4×C911yescharacteristic
275D12—24no—
276D12—21no—
277D12D4×C912yes—
278C4×D3—24no—
279C4×D3—21no—
280C4×D3—21no—
281Dic6—21no—
282Dic6—21no—
283C3×C8—21no—
284C3×C8—21no—
285C3×C8—41no—
286C3×C8—61no—
287C3⋊C8—21no—
288C2×C32C3×#12011yescharacteristic
289C2×C32C3×#13511yescharacteristic
290C2×C32C3×#13711yescharacteristic
291C3×D3—41no—
292C3×D3—42no—
293C2×C9—21no—
294C2×C9—21no—
295C2×C9—21no—
296C2×C9—121no—
297C2×C9—122no—
298C2×C9#88211yescharacteristic
299C2×C9#91611yescharacteristic
300C2×C9#91811yescharacteristic
301#41—62no—
302#41—62no—
303C2×Q8—31no—
304C2×Q8C2×D3×C911yescharacteristic
305C2×D4—31no—
306C2×D4—61no—
307C22×C4—31no—
308C22×C4—61no—
309Q16—62no—
310SD16—62no—
311C2×C8—31no—
312C2×C8C2×D3×C911yescharacteristic
313C4⋊C4—61no—
314C4⋊C4C2×D3×C911yescharacteristic
315C22⋊C4—61no—
316C22×C3—21no—
317C22×C3—62no—
318C22×C3—61no—
319C22×C3—61no—
320C22×C3—61no—
321C22×C3—121no—
322C22×C3—121no—
323C22×C3C2×D4×C911yescharacteristic
324C22×C3C3×D3×D411yescharacteristic
325C2×D3—21no—
326C2×D3—22no—
327C2×D3—21no—
328C2×D3—21no—
329C2×D3—41no—
330C2×D3—41no—
331C3×C4—22no—
332C3×C4—22no—
333C3×C4—21no—
334C3×C4—21no—
335C3×C4—42no—
336C3×C4—41no—
337C3×C4—41no—
338C3×C4—61no—
339C3×C4—81no—
340C3×C4—121no—
341C3×C4C2×D4×C911yescharacteristic
342C3×C4C2×D4×C911yescharacteristic
343C3×C4C2×C3×D1211yescharacteristic
344C3×C4C3×D3×D411yescharacteristic
345Dic3—21no—
346Dic3—41no—
347C32C3×#45211yescharacteristic
348C9—21no—
349C9#480811yescharacteristic, direct product factor
350C23—31no—
351C23—61no—
352Q8—21no—
353Q8—61no—
354Q8—61no—
355Q8C9×D1212yes—
356D4—32no—
357D4—64no—
358D4—61no—
359C2×C4—21no—
360C2×C4—21no—
361C2×C4—31no—
362C2×C4—64no—
363C2×C4—61no—
364C2×C4—61no—
365C2×C4—61no—
366C2×C4C22×D3×C911yescharacteristic
367C8—21no—
368C8—61no—
369C2×C3—21no—
370C2×C3—21no—
371C2×C3—21no—
372C2×C3—121no—
373C2×C3—122no—
374C2×C3C9×#12011yescharacteristic
375C2×C3C9×#13511yescharacteristic
376C2×C3C9×#13711yescharacteristic
377C2×C3C3×#88211yescharacteristic
378C2×C3C3×#91611yescharacteristic
379C2×C3C3×#91811yescharacteristic
380D3—41no—
381D3—42no—
382C22—61no—
383C22—61no—
384C22—62no—
385C22—61no—
386C22—121no—
387C22—121no—
388C22D3×D4×C911yescharacteristic
389C4—22no—
390C4—41no—
391C4—61no—
392C4—121no—
393C4C2×C9×D1211yescharacteristic
394C4D3×D4×C911yescharacteristic
395C3—21no—
396C3C9×#45211yescharacteristic, complemented
397C3C3×#480811yescharacteristic
398C2—121no—
399C2—122no—
400C2C9×#88211yescharacteristic
401C2C9×#91611yescharacteristic
402C2C9×#91811yescharacteristic
subgroupG/H
centerC22×C9D3×D4
commutatorC2×C3×C4C23×C9
FrattiniC2×C3×C4C22×C3×D3
FittingC3×C9×#103C2
socleC22×C32C2×C3×D4
prime radicalC2×C3×#239C2×C3
cosocleC2×C32×C4C23×C3
hypercenterC9×#103D3
hypocenterC3C9×#452
LCSG ▷ C2×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C22×C9 ◁ C2×C4×C9 ◁ C9×#103

Complements

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

NH ≅ G/Ntype
2. C2×C9×#216C2semidirect
3. C2×C9×#204C2semidirect
4. C9×#897C2semidirect
5. C3×C9×#103C2semidirect
6. C9×(C2×D3)⋊C8C2semidirect
7. C9×#809C2semidirect
37. C9×#103D3semidirect
60. #4808C9direct (N × H)
112. C2×#216C2×C9semidirect
113. C2×#204C2×C9semidirect
114. #897C2×C9semidirect
116. C3×#103C2×C9semidirect
120. (C2×D3)⋊C8C2×C9semidirect
121. #809C2×C9semidirect
240. #103D3×C9semidirect
243. C3×C9#452semidirect
349. C9#4808direct (N × H)
396. C3C9×#452semidirect

Maximal subgroups

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

subgroupindex
C2×C9×#2392
C2×C9×#2162
C2×C9×#2042
C9×#8972
C3×C9×#1032
C9×(C2×D3)⋊C82
C9×#8092
C3×#48083
C9×#4523