Finite Group Databasebeta

← C3×#10588442 #13141712

Subgroups — C3×#10588442 #13141712

Order 1728.

434 conjugacy classes of subgroups.

The subgroup lattice has 386 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#63502C211yesmaximal, characteristic
2C2×C3×#3672C211yesmaximal, characteristic, complemented
3C2×C3×#3664C211yesmaximal, characteristic, complemented
4C3×#63449C211yesmaximal, characteristic, complemented
5C3×C9×#102C211yesmaximal, characteristic, complemented
6C3×Dic9⋊C8C211yesmaximal, characteristic, complemented
7C3×#63369C211yesmaximal, characteristic, complemented
8C3×#4762—31nomaximal
9#10588442C311yesmaximal, characteristic, direct product factor
10C2×C3×D4×C9C2211yescharacteristic
11C2×C3×#611—21no—
12C2×C3×#611—21no—
13C2×C3×D36C2211yescharacteristic
14C2×C3×Dic18C2211yescharacteristic
15C2×C3×C8×C9C2211yescharacteristic
16C3×C9×C4⋊C4C2211yescharacteristic
17C3×#3672—22no—
18C3×Dic9⋊C4—21no—
19C3×C4×Dic9—21no—
20C3×C4×Dic9C2211yescharacteristic
21C2×C3×C9⋊C8C2211yescharacteristic
22C3×#3664—22no—
23C3×#940—31no—
24C2×C3×#214—31no—
25C2×C3×#204—31no—
26C3×#887—31no—
27C32×#102D311yescharacteristic
28C3×Dic3⋊C8—31no—
29C3×#809—31no—
30#63502C2×C311yescharacteristic
31C2×#3672C2×C311yescharacteristic, complemented
32C2×#3664C2×C311yescharacteristic, complemented
33#63449C2×C311yescharacteristic, complemented
34C9×#102—21no—
35C9×#102C2×C311yescharacteristic, complemented
36Dic9⋊C8C2×C311yescharacteristic, complemented
37#63369C2×C311yescharacteristic, complemented
38C23×C3×C9—21no—
39C22×C3×D9—21no—
40C3×D4×C9—21no—
41C3×D4×C9—21no—
42C2×C3×C4×C9—21no—
43C2×C3×C4×C9C2311yescharacteristic
44C3×#611—42no—
45C3×#611—42no—
46C2×C3×Dic9—21no—
47C2×C3×Dic9D411yescharacteristic
48C2×C3×Dic9D411yescharacteristic
49C3×D36—21no—
50C3×D36—21no—
51C3×Dic18—21no—
52C3×Dic18D412yescomplemented
53C3×C8×C9—21no—
54C3×C9⋊C8—21no—
55C3×#460—91no—
56#4762—31no—
57C2×C32×D4C2×D311yescharacteristic
58C2×C3×#67—61no—
59C2×C3×#67—61no—
60C2×C3×D12—31no—
61C2×C3×Dic6—31no—
62C2×C32×C8C2×D311yescharacteristic
63C32×C4⋊C4C2×D311yescharacteristic
64C3×#214—62no—
65C3×Dic3⋊C4—61no—
66C3×C4×Dic3—31no—
67C3×C4×Dic3—61no—
68C2×C3×C3⋊C8—31no—
69C3×#204—62no—
70C2×D4×C9—21no—
71C2×D4×C9C22×C311yescharacteristic
72C2×#611—21no—
73C2×#611—21no—
74C2×D36C22×C311yescharacteristic
75C2×Dic18C22×C311yescharacteristic
76C2×C8×C9—21no—
77C2×C8×C9C22×C311yescharacteristic
78C9×C4⋊C4—21no—
79C9×C4⋊C4C22×C311yescharacteristic
80#3672—22no—
81Dic9⋊C4—21no—
82C4×Dic9—21no—
83C4×Dic9C22×C311yescharacteristic
84C2×C9⋊C8C22×C311yescharacteristic
85#3664—22no—
86C22×C3×C9—41no—
87C22×C3×C9—41no—
88C22×C3×C9—41no—
89C22×C3×C9C2×D411yescharacteristic
90C2×C3×D9—41no—
91C2×C3×D9—41no—
92C2×C3×D9—41no—
93C3×C4×C9—41no—
94C3×C4×C9C2×D411yescharacteristic
95C3×C4×C9#4111yescharacteristic
96C3×Dic9—22no—
97C3×Dic9—21no—
98C3×Dic9SD1612yescomplemented
99C2×C3×SD16—91no—
100C2×C3×SD16—91no—
101C3×#127—91no—
102C3×C4×Q8—91no—
103#940—31no—
104C2×#214—31no—
105C2×#204—31no—
106#887—31no—
107C3×C4⋊C8—91no—
108C3×#102—21no—
109C3×#102—91no—
110C3×#102D911yescharacteristic, complemented
111C3×#102C3×D311yescharacteristic
112Dic3⋊C8—31no—
113#809—31no—
114C23×C32—21no—
115C22×C3×D3—61no—
116C32×D4—21no—
117C32×D4—21no—
118C2×C32×C4—21no—
119C2×C32×C4C22×D311yescharacteristic
120C3×#67—122no—
121C3×#67—122no—
122C2×C3×Dic3—31no—
123C2×C3×Dic3—31no—
124C2×C3×Dic3—61no—
125C3×D12—61no—
126C3×D12—61no—
127C3×Dic6—32no—
128C3×Dic6—61no—
129C23×C9—21no—
130C23×C9—41no—
131C22×D9—21no—
132C32×C8—21no—
133C3×C3⋊C8—61no—
134D4×C9—22no—
135D4×C9—21no—
136D4×C9—21no—
137D4×C9—41no—
138C2×C4×C9—21no—
139C2×C4×C9—21no—
140C2×C4×C9—41no—
141C2×C4×C9C23×C311yescharacteristic
142#611—42no—
143#611—42no—
144C2×Dic9—21no—
145C2×Dic9C3×D411yescharacteristic
146C2×Dic9C3×D411yescharacteristic
147D36—21no—
148D36—21no—
149Dic18—21no—
150Dic18C3×D412yescomplemented
151C8×C9—21no—
152C8×C9—41no—
153C9⋊C8—21no—
154#460—91noSylow
155C2×C3×C9—81no—
156C2×C3×C9#12111yescharacteristic
157C2×C3×C9C2×SD1611yescharacteristic
158C2×C3×C9AGL(1,ℤ/8)11yescharacteristic
159C3×D9—81no—
160C2×C3×Q8—91no—
161C2×C3×D4—21no—
162C2×C3×D4—91no—
163C2×C3×D4—181no—
164C2×C3×D4—181no—
165C2×C3×D4C2×D911yescharacteristic
166C2×C3×D4C2×C3×D311yescharacteristic
167C2×#67—61no—
168C2×#67—61no—
169C2×D12—31no—
170C2×Dic6—31no—
171C3×SD16—182no—
172C3×SD16—182no—
173C2×C3×C8—21no—
174C2×C3×C8—91no—
175C2×C3×C8C2×D911yescharacteristic
176C2×C3×C8C2×C3×D311yescharacteristic
177C3×C4⋊C4—21no—
178C3×C4⋊C4—181no—
179C3×C4⋊C4C2×D911yescharacteristic
180C3×C4⋊C4C2×C3×D311yescharacteristic
181C3×C42—91no—
182C3×C42—181no—
183#214—62no—
184Dic3⋊C4—61no—
185C4×Dic3—31no—
186C4×Dic3—61no—
187C2×C3⋊C8—31no—
188#204—62no—
189C22×C32—41no—
190C22×C32—41no—
191C22×C32—41no—
192C22×C32D3×D411yescharacteristic
193C2×C3×D3—121no—
194C2×C3×D3—121no—
195C2×C3×D3—121no—
196C32×C4—41no—
197C32×C4#23511yescharacteristic
198C32×C4D3×D411yescharacteristic
199C3×Dic3—32no—
200C3×Dic3—62no—
201C3×Dic3—61no—
202C22×C9—21no—
203C22×C9—42no—
204C22×C9—41no—
205C22×C9—41no—
206C22×C9—41no—
207C22×C9—81no—
208C22×C9—81no—
209C22×C9C2×C3×D411yescharacteristic
210C2×D9—41no—
211C2×D9—41no—
212C2×D9—41no—
213C4×C9—21no—
214C4×C9—21no—
215C4×C9—41no—
216C4×C9—81no—
217C4×C9C2×C3×D411yescharacteristic
218C4×C9C3×#4111yescharacteristic
219Dic9—22no—
220Dic9—21no—
221Dic9C3×SD1612yescomplemented
222C2×SD16—91no—
223C2×SD16—91no—
224#127—91no—
225C4×Q8—91no—
226C4⋊C8—91no—
227#102—91no—
228#102C3×D911yescharacteristic, complemented
229C3×C9#46011yescharacteristic, complemented, Sylow
230C23×C3—21no—
231C23×C3—21no—
232C23×C3—41no—
233C23×C3—181no—
234C22×D3—61no—
235C3×Q8—92no—
236C3×Q8—181no—
237C3×D4—22no—
238C3×D4—21no—
239C3×D4—21no—
240C3×D4—21no—
241C3×D4—21no—
242C3×D4—41no—
243C3×D4—181no—
244C3×D4—181no—
245C3×D4—362no—
246C3×D4—362no—
247C2×C3×C4—21no—
248C2×C3×C4—21no—
249C2×C3×C4—21no—
250C2×C3×C4—41no—
251C2×C3×C4—91no—
252C2×C3×C4—91no—
253C2×C3×C4—181no—
254C2×C3×C4C22×D911yescharacteristic
255C2×C3×C4C22×C3×D311yescharacteristic
256#67—122no—
257#67—122no—
258C2×Dic3—31no—
259C2×Dic3—31no—
260C2×Dic3—61no—
261D12—61no—
262D12—61no—
263Dic6—32no—
264Dic6—61no—
265C3×C8—21no—
266C3×C8—21no—
267C3×C8—41no—
268C3×C8—181no—
269C3⋊C8—61no—
270C2×C32—81no—
271C2×C32#88411yescharacteristic
272C2×C32#91111yescharacteristic
273C2×C32D3×SD1611yescharacteristic
274C3×D3—241no—
275C2×C9—21no—
276C2×C9—21no—
277C2×C9—21no—
278C2×C9—82no—
279C2×C9—81no—
280C2×C9C3×#12111yescharacteristic
281C2×C9C2×C3×SD1611yescharacteristic
282C2×C9C3×AGL(1,ℤ/8)11yescharacteristic
283D9—81no—
284C2×Q8—91no—
285C2×D4—91no—
286C2×D4—181no—
287C2×D4—181no—
288C2×D4C2×C3×D911yescharacteristic
289SD16—182no—
290SD16—182no—
291C2×C8—91no—
292C2×C8C2×C3×D911yescharacteristic
293C4⋊C4—181no—
294C4⋊C4C2×C3×D911yescharacteristic
295C42—91no—
296C42—181no—
297C22×C3—21no—
298C22×C3—42no—
299C22×C3—41no—
300C22×C3—41no—
301C22×C3—41no—
302C22×C3—41no—
303C22×C3—41no—
304C22×C3—41no—
305C22×C3—81no—
306C22×C3—81no—
307C22×C3—361no—
308C22×C3—361no—
309C22×C3—361no—
310C22×C3D4×D911yescharacteristic
311C22×C3C3×D3×D411yescharacteristic
312C2×D3—121no—
313C2×D3—121no—
314C2×D3—121no—
315C3×C4—21no—
316C3×C4—21no—
317C3×C4—41no—
318C3×C4—41no—
319C3×C4—81no—
320C3×C4—92no—
321C3×C4—182no—
322C3×C4—181no—
323C3×C4#369711yescharacteristic
324C3×C4D4×D911yescharacteristic
325C3×C4C3×#23511yescharacteristic
326C3×C4C3×D3×D411yescharacteristic
327Dic3—32no—
328Dic3—62no—
329Dic3—61no—
330C32#476211yescharacteristic
331C9—21no—
332C9C3×#46011yescharacteristic, complemented
333C23—21no—
334C23—181no—
335Q8—92no—
336Q8—181no—
337D4—21no—
338D4—21no—
339D4—181no—
340D4—181no—
341D4—362no—
342D4—362no—
343C2×C4—21no—
344C2×C4—91no—
345C2×C4—91no—
346C2×C4—181no—
347C2×C4C22×C3×D911yescharacteristic
348C8—21no—
349C8—181no—
350C2×C3—21no—
351C2×C3—21no—
352C2×C3—21no—
353C2×C3—82no—
354C2×C3—81no—
355C2×C3—81no—
356C2×C3—721no—
357C2×C3#6344611yescharacteristic
358C2×C3#6347311yescharacteristic
359C2×C3SD16×D911yescharacteristic
360C2×C3C3×#88411yescharacteristic
361C2×C3C3×#91111yescharacteristic
362C2×C3C3×D3×SD1611yescharacteristic
363D3—241no—
364C22—41no—
365C22—41no—
366C22—41no—
367C22—361no—
368C22—361no—
369C22—361no—
370C22C3×D4×D911yescharacteristic
371C4—41no—
372C4—92no—
373C4—181no—
374C4—182no—
375C4C3×#369711yescharacteristic
376C4C3×D4×D911yescharacteristic
377C3—21no—
378C3#1058844211yescharacteristic, direct product factor
379C3C3×#476211yescharacteristic
380C2—81no—
381C2—721no—
382C2C3×#6344611yescharacteristic
383C2C3×#6347311yescharacteristic
384C2C3×SD16×D911yescharacteristic
subgroupG/H
centerC22×C3D4×D9
commutator, cosocleC2×C4×C9C23×C3
FrattiniC2×C3×C4C22×C3×D3
FittingC3×C9×#102C2
socleC22×C32D3×D4
prime radicalC3×#63502C2
hypercenterC3×#102D9
hypocenterC9C3×#460
LCSG ▷ C2×C4×C9 ▷ C2×C9 ▷ C9
UCSC1 ◁ C22×C3 ◁ C2×C3×C4 ◁ C3×#102

Complements

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

NH ≅ G/Ntype
2. C2×C3×#3672C2semidirect
3. C2×C3×#3664C2semidirect
4. C3×#63449C2semidirect
5. C3×C9×#102C2semidirect
6. C3×Dic9⋊C8C2semidirect
7. C3×#63369C2semidirect
9. #10588442C3direct (N × H)
31. C2×#3672C2×C3semidirect
32. C2×#3664C2×C3semidirect
33. #63449C2×C3semidirect
35. C9×#102C2×C3semidirect
36. Dic9⋊C8C2×C3semidirect
37. #63369C2×C3semidirect
52. C3×Dic18D4semidirect
98. C3×Dic9SD16semidirect
110. C3×#102D9semidirect
150. Dic18C3×D4semidirect
221. Dic9C3×SD16semidirect
228. #102C3×D9semidirect
229. C3×C9#460semidirect
332. C9C3×#460semidirect
378. C3#10588442direct (N × H)

Maximal subgroups

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

subgroupindex
C3×#635022
C2×C3×#36722
C2×C3×#36642
C3×#634492
C3×C9×#1022
C3×Dic9⋊C82
C3×#633692
C3×#47623
#105884423