Finite Group Databasebeta

← C3×#10588498 #13141836

Subgroups — C3×#10588498 #13141836

Order 1728.

402 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
1C3×#63506C211yesmaximal, characteristic, complemented
2C2×C3×#3675C211yesmaximal, characteristic
3C2×C3×#3664C211yesmaximal, characteristic
4C3×#63455C211yesmaximal, characteristic
5C3×C9×#103C211yesmaximal, characteristic, complemented
6C3×Dic9⋊C8C211yesmaximal, characteristic, complemented
7C3×#63368C211yesmaximal, characteristic, complemented
8C3×#4818—31nomaximal
9#10588498C311yesmaximal, characteristic, direct product factor
10C2×C3×Q8×C9C2211yescharacteristic
11C2×C3×D36C2211yescharacteristic
12C2×C3×C4×D9—21no—
13C2×C3×Dic18C2211yescharacteristic
14C2×C3×C8×C9C2211yescharacteristic
15C3×C9×C4⋊C4C2211yescharacteristic
16C3×#3675—22no—
17C3×(C2×D9)⋊C4—21no—
18C3×Dic9⋊C4—21no—
19C3×Dic9⋊C4—21no—
20C3×C4×Dic9C2211yescharacteristic
21C2×C3×C9⋊C8C2211yescharacteristic
22C3×#3664—22no—
23C3×#944—31no—
24C2×C3×#215—31no—
25C2×C3×#204—31no—
26C3×#893—31no—
27C32×#103D311yescharacteristic
28C3×Dic3⋊C8—31no—
29C3×#810—31no—
30#63506C2×C311yescharacteristic, complemented
31C2×#3675C2×C311yescharacteristic
32C2×#3664C2×C311yescharacteristic
33#63455C2×C311yescharacteristic
34C9×#103—21no—
35C9×#103C2×C311yescharacteristic, complemented
36Dic9⋊C8C2×C311yescharacteristic, complemented
37#63368C2×C311yescharacteristic, complemented
38C22×C3×D9—21no—
39C3×Q8×C9—21no—
40C3×Q8×C9—21no—
41C2×C3×C4×C9—21no—
42C2×C3×C4×C9—21no—
43C2×C3×C4×C9C2311yescharacteristic
44C2×C3×Dic9—21no—
45C2×C3×Dic9D411yescharacteristic
46C2×C3×Dic9D411yescharacteristic
47C3×D36—21no—
48C3×D36D412yes—
49C3×C4×D9—42no—
50C3×Dic18—21no—
51C3×Dic18—21no—
52C3×C8×C9—21no—
53C3×C9⋊C8—21no—
54C3×#461—91no—
55#4818—31no—
56C2×C32×Q8C2×D311yescharacteristic
57C2×C3×D12—31no—
58C2×C3×C4×D3—61no—
59C2×C3×Dic6—31no—
60C2×C32×C8C2×D311yescharacteristic
61C32×C4⋊C4C2×D311yescharacteristic
62C3×#215—62no—
63C3×(C2×D3)⋊C4—61no—
64C3×Dic3⋊C4—61no—
65C3×Dic3⋊C4—61no—
66C3×C4×Dic3—31no—
67C2×C3×C3⋊C8—31no—
68C3×#204—62no—
69C2×Q8×C9—21no—
70C2×Q8×C9C22×C311yescharacteristic
71C2×D36C22×C311yescharacteristic
72C2×C4×D9—21no—
73C2×Dic18C22×C311yescharacteristic
74C2×C8×C9—21no—
75C2×C8×C9C22×C311yescharacteristic
76C9×C4⋊C4—21no—
77C9×C4⋊C4C22×C311yescharacteristic
78#3675—22no—
79(C2×D9)⋊C4—21no—
80Dic9⋊C4—21no—
81Dic9⋊C4—21no—
82C4×Dic9C22×C311yescharacteristic
83C2×C9⋊C8C22×C311yescharacteristic
84#3664—22no—
85C22×C3×C9C2×D411yescharacteristic
86C2×C3×D9—22no—
87C2×C3×D9—41no—
88C2×C3×D9—41no—
89C3×C4×C9—41no—
90C3×C4×C9—41no—
91C3×C4×C9C2×D411yescharacteristic
92C3×C4×C9#4111yescharacteristic
93C3×Dic9—21no—
94C3×Dic9—41no—
95C3×Dic9SD1612yescomplemented
96C2×C3×SD16—91no—
97C2×C3×SD16—91no—
98C3×C4⋊Q8—91no—
99C3×C4×D4—91no—
100#944—31no—
101C2×#215—31no—
102C2×#204—31no—
103#893—31no—
104C3×C4⋊C8—91no—
105C3×#103—21no—
106C3×#103—91no—
107C3×#103D911yescharacteristic, complemented
108C3×#103C3×D311yescharacteristic
109Dic3⋊C8—31no—
110#810—31no—
111C22×C3×D3—61no—
112C32×Q8—21no—
113C32×Q8—21no—
114C2×C32×C4—21no—
115C2×C32×C4—21no—
116C2×C32×C4C22×D311yescharacteristic
117C2×C3×Dic3—31no—
118C2×C3×Dic3—31no—
119C2×C3×Dic3—61no—
120C3×D12—32no—
121C3×D12—61no—
122C3×C4×D3—122no—
123C3×Dic6—61no—
124C3×Dic6—61no—
125C22×D9—21no—
126C32×C8—21no—
127C3×C3⋊C8—61no—
128Q8×C9—22no—
129Q8×C9—21no—
130Q8×C9—21no—
131Q8×C9—41no—
132C2×C4×C9—21no—
133C2×C4×C9—21no—
134C2×C4×C9—21no—
135C2×C4×C9—41no—
136C2×C4×C9—41no—
137C2×C4×C9C23×C311yescharacteristic
138C2×Dic9—21no—
139C2×Dic9C3×D411yescharacteristic
140C2×Dic9C3×D411yescharacteristic
141D36—21no—
142D36C3×D412yes—
143C4×D9—42no—
144Dic18—21no—
145Dic18—21no—
146C8×C9—21no—
147C8×C9—41no—
148C9⋊C8—21no—
149#461—91noSylow
150C2×C3×C9#12111yescharacteristic
151C2×C3×C9C2×SD1611yescharacteristic
152C2×C3×C9#13711yescharacteristic
153C3×D9—42no—
154C2×C3×Q8—21no—
155C2×C3×Q8—91no—
156C2×C3×Q8C2×D911yescharacteristic
157C2×C3×Q8C2×C3×D311yescharacteristic
158C2×C3×D4—91no—
159C22×C3×C4—181no—
160C2×D12—31no—
161C2×C4×D3—61no—
162C2×Dic6—31no—
163C3×SD16—182no—
164C3×SD16—182no—
165C2×C3×C8—21no—
166C2×C3×C8—91no—
167C2×C3×C8C2×D911yescharacteristic
168C2×C3×C8C2×C3×D311yescharacteristic
169C3×C4⋊C4—21no—
170C3×C4⋊C4—181no—
171C3×C4⋊C4—181no—
172C3×C4⋊C4C2×D911yescharacteristic
173C3×C4⋊C4C2×C3×D311yescharacteristic
174C3×C22⋊C4—181no—
175C3×C42—91no—
176#215—62no—
177(C2×D3)⋊C4—61no—
178Dic3⋊C4—61no—
179Dic3⋊C4—61no—
180C4×Dic3—31no—
181C2×C3⋊C8—31no—
182#204—62no—
183C22×C32D3×D411yescharacteristic
184C2×C3×D3—62no—
185C2×C3×D3—121no—
186C2×C3×D3—121no—
187C32×C4—41no—
188C32×C4—41no—
189C32×C4#23511yescharacteristic
190C32×C4D3×D411yescharacteristic
191C3×Dic3—32no—
192C3×Dic3—61no—
193C3×Dic3—121no—
194C22×C9—21no—
195C22×C9C2×C3×D411yescharacteristic
196C2×D9—22no—
197C2×D9—41no—
198C2×D9—41no—
199C4×C9—21no—
200C4×C9—21no—
201C4×C9—42no—
202C4×C9—41no—
203C4×C9—41no—
204C4×C9—81no—
205C4×C9C2×C3×D411yescharacteristic
206C4×C9C3×#4111yescharacteristic
207Dic9—21no—
208Dic9—41no—
209Dic9C3×SD1612yescomplemented
210C2×SD16—91no—
211C2×SD16—91no—
212C4⋊Q8—91no—
213C4×D4—91no—
214C4⋊C8—91no—
215#103—91no—
216#103C3×D911yescharacteristic, complemented
217C3×C9#46111yescharacteristic, complemented, Sylow
218C23×C3—181no—
219C22×D3—61no—
220C3×Q8—22no—
221C3×Q8—21no—
222C3×Q8—21no—
223C3×Q8—21no—
224C3×Q8—21no—
225C3×Q8—41no—
226C3×Q8—181no—
227C3×Q8—181no—
228C3×D4—92no—
229C3×D4—181no—
230C2×C3×C4—21no—
231C2×C3×C4—21no—
232C2×C3×C4—21no—
233C2×C3×C4—21no—
234C2×C3×C4—21no—
235C2×C3×C4—41no—
236C2×C3×C4—41no—
237C2×C3×C4—91no—
238C2×C3×C4—91no—
239C2×C3×C4—181no—
240C2×C3×C4—362no—
241C2×C3×C4C22×D911yescharacteristic
242C2×C3×C4C22×C3×D311yescharacteristic
243C2×Dic3—31no—
244C2×Dic3—31no—
245C2×Dic3—61no—
246D12—32no—
247D12—61no—
248C4×D3—122no—
249Dic6—61no—
250Dic6—61no—
251C3×C8—21no—
252C3×C8—21no—
253C3×C8—41no—
254C3×C8—181no—
255C3⋊C8—61no—
256C2×C32#88411yescharacteristic
257C2×C32D3×SD1611yescharacteristic
258C2×C32#91811yescharacteristic
259C3×D3—122no—
260C2×C9—21no—
261C2×C9—21no—
262C2×C9—21no—
263C2×C9C3×#12111yescharacteristic
264C2×C9C2×C3×SD1611yescharacteristic
265C2×C9C3×#13711yescharacteristic
266D9—42no—
267C2×Q8—91no—
268C2×Q8C2×C3×D911yescharacteristic
269C2×D4—91no—
270C22×C4—181no—
271SD16—182no—
272SD16—182no—
273C2×C8—91no—
274C2×C8C2×C3×D911yescharacteristic
275C4⋊C4—181no—
276C4⋊C4—181no—
277C4⋊C4C2×C3×D911yescharacteristic
278C22⋊C4—181no—
279C42—91no—
280C22×C3—21no—
281C22×C3—182no—
282C22×C3—361no—
283C22×C3—361no—
284C22×C3D4×D911yescharacteristic
285C22×C3C3×D3×D411yescharacteristic
286C2×D3—62no—
287C2×D3—121no—
288C2×D3—121no—
289C3×C4—21no—
290C3×C4—21no—
291C3×C4—42no—
292C3×C4—41no—
293C3×C4—41no—
294C3×C4—41no—
295C3×C4—41no—
296C3×C4—81no—
297C3×C4—92no—
298C3×C4—181no—
299C3×C4—361no—
300C3×C4#369711yescharacteristic
301C3×C4D4×D911yescharacteristic
302C3×C4C3×#23511yescharacteristic
303C3×C4C3×D3×D411yescharacteristic
304Dic3—32no—
305Dic3—61no—
306Dic3—121no—
307C32#481811yescharacteristic
308C9—21no—
309C9C3×#46111yescharacteristic, complemented
310C23—181no—
311Q8—21no—
312Q8—21no—
313Q8—181no—
314Q8—181no—
315D4—92no—
316D4—181no—
317C2×C4—21no—
318C2×C4—21no—
319C2×C4—91no—
320C2×C4—91no—
321C2×C4—181no—
322C2×C4—362no—
323C2×C4C22×C3×D911yescharacteristic
324C8—21no—
325C8—181no—
326C2×C3—21no—
327C2×C3—21no—
328C2×C3—21no—
329C2×C3—362no—
330C2×C3#6344611yescharacteristic
331C2×C3SD16×D911yescharacteristic
332C2×C3#6348011yescharacteristic
333C2×C3C3×#88411yescharacteristic
334C2×C3C3×D3×SD1611yescharacteristic
335C2×C3C3×#91811yescharacteristic
336D3—122no—
337C22—182no—
338C22—361no—
339C22—361no—
340C22C3×D4×D911yescharacteristic
341C4—41no—
342C4—41no—
343C4—92no—
344C4—181no—
345C4—361no—
346C4C3×#369711yescharacteristic
347C4C3×D4×D911yescharacteristic
348C3—21no—
349C3#1058849811yescharacteristic, direct product factor
350C3C3×#481811yescharacteristic
351C2—362no—
352C2C3×#6344611yescharacteristic
353C2C3×SD16×D911yescharacteristic
354C2C3×#6348011yescharacteristic
subgroupG/H
centerC22×C3D4×D9
commutator, cosocleC2×C4×C9C23×C3
FrattiniC2×C3×C4C22×C3×D3
FittingC3×C9×#103C2
socleC22×C32D3×D4
prime radicalC2×C3×D36C22
hypercenterC3×#103D9
hypocenterC9C3×#461
LCSG ▷ C2×C4×C9 ▷ C2×C9 ▷ C9
UCSC1 ◁ C22×C3 ◁ C2×C3×C4 ◁ C3×#103

Complements

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

NH ≅ G/Ntype
1. C3×#63506C2semidirect
5. C3×C9×#103C2semidirect
6. C3×Dic9⋊C8C2semidirect
7. C3×#63368C2semidirect
9. #10588498C3direct (N × H)
30. #63506C2×C3semidirect
35. C9×#103C2×C3semidirect
36. Dic9⋊C8C2×C3semidirect
37. #63368C2×C3semidirect
95. C3×Dic9SD16semidirect
107. C3×#103D9semidirect
209. Dic9C3×SD16semidirect
216. #103C3×D9semidirect
217. C3×C9#461semidirect
309. C9C3×#461semidirect
349. C3#10588498direct (N × H)

Maximal subgroups

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

subgroupindex
C3×#635062
C2×C3×#36752
C2×C3×#36642
C3×#634552
C3×C9×#1032
C3×Dic9⋊C82
C3×#633682
C3×#48183
#105884983