Finite Group Databasebeta

← C3×#10588447 #13141718

Subgroups — C3×#10588447 #13141718

Order 1728.

386 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×#63498C211yesmaximal, characteristic
2C2×C3×#3672C211yesmaximal, characteristic
3C2×C3×Dic36C211yesmaximal, characteristic, complemented
4C3×#63449C211yesmaximal, characteristic, complemented
5C3×C9×#102C211yesmaximal, characteristic
6C3×Dic9⋊C8C211yesmaximal, characteristic, complemented
7C3×#63368C211yesmaximal, characteristic, complemented
8C3×#4767—31nomaximal
9#10588447C311yesmaximal, characteristic, direct product factor
10C2×C3×D4×C9C2211yescharacteristic
11C2×C3×Dic18C2211yescharacteristic
12C2×C3×Dic18C2211yescharacteristic
13C2×C3×C8×C9C2211yescharacteristic
14C3×C9×C4⋊C4C2211yescharacteristic
15C3×#3676—21no—
16C3×#3676—21no—
17C3×#3672—22no—
18C3×Dic9⋊C4—21no—
19C3×C4×Dic9—21no—
20C3×C4×Dic9C2211yescharacteristic
21C2×C3×C9⋊C8C2211yescharacteristic
22C3×Dic36—22no—
23C3×#936—31no—
24C2×C3×#214—31no—
25C2×C3×Dic12—31no—
26C3×#887—31no—
27C32×#102D311yescharacteristic
28C3×Dic3⋊C8—31no—
29C3×#810—31no—
30#63498C2×C311yescharacteristic
31C2×#3672C2×C311yescharacteristic
32C2×Dic36C2×C311yescharacteristic, complemented
33#63449C2×C311yescharacteristic, complemented
34C9×#102—21no—
35C9×#102C2×C311yescharacteristic
36Dic9⋊C8C2×C311yescharacteristic, complemented
37#63368C2×C311yescharacteristic, complemented
38C23×C3×C9—21no—
39C3×D4×C9—21no—
40C3×D4×C9—21no—
41C2×C3×C4×C9—21no—
42C2×C3×C4×C9C2311yescharacteristic
43C2×C3×Dic9—21no—
44C2×C3×Dic9—21no—
45C2×C3×Dic9D411yescharacteristic
46C2×C3×Dic9D411yescharacteristic
47C3×Dic18—21no—
48C3×Dic18—21no—
49C3×Dic18—21no—
50C3×Dic18D412yes—
51C3×C8×C9—21no—
52C3×C9⋊C8—21no—
53C3×#464—91no—
54#4767—31no—
55C2×C32×D4C2×D311yescharacteristic
56C2×C3×Dic6—31no—
57C2×C3×Dic6—31no—
58C2×C32×C8C2×D311yescharacteristic
59C32×C4⋊C4C2×D311yescharacteristic
60C3×#217—61no—
61C3×#217—61no—
62C3×#214—62no—
63C3×Dic3⋊C4—61no—
64C3×C4×Dic3—31no—
65C3×C4×Dic3—61no—
66C2×C3×C3⋊C8—31no—
67C3×Dic12—62no—
68C2×D4×C9—21no—
69C2×D4×C9C22×C311yescharacteristic
70C2×Dic18C22×C311yescharacteristic
71C2×Dic18C22×C311yescharacteristic
72C2×C8×C9—21no—
73C2×C8×C9C22×C311yescharacteristic
74C9×C4⋊C4—21no—
75C9×C4⋊C4C22×C311yescharacteristic
76#3676—21no—
77#3676—21no—
78#3672—22no—
79Dic9⋊C4—21no—
80C4×Dic9—21no—
81C4×Dic9C22×C311yescharacteristic
82C2×C9⋊C8C22×C311yescharacteristic
83Dic36—22no—
84C22×C3×C9—41no—
85C22×C3×C9—41no—
86C22×C3×C9—41no—
87C22×C3×C9C2×D411yescharacteristic
88C3×C4×C9—41no—
89C3×C4×C9C2×D411yescharacteristic
90C3×C4×C9#4111yescharacteristic
91C3×Dic9—22no—
92C3×Dic9—21no—
93C3×Dic9—21no—
94C3×Dic9—41no—
95C2×C3×Q16—91no—
96C2×C3×SD16—91no—
97C3×#124—91no—
98C3×C4×Q8—91no—
99#936—31no—
100C2×#214—31no—
101C2×Dic12—31no—
102#887—31no—
103C3×C4⋊C8—91no—
104C3×#103—91no—
105C3×#102—21no—
106C3×#102D911yescharacteristic
107C3×#102C3×D311yescharacteristic
108Dic3⋊C8—31no—
109#810—31no—
110C23×C32—21no—
111C32×D4—21no—
112C32×D4—21no—
113C2×C32×C4—21no—
114C2×C32×C4C22×D311yescharacteristic
115C2×C3×Dic3—31no—
116C2×C3×Dic3—31no—
117C2×C3×Dic3—61no—
118C2×C3×Dic3—61no—
119C3×Dic6—32no—
120C3×Dic6—61no—
121C3×Dic6—61no—
122C3×Dic6—61no—
123C23×C9—21no—
124C23×C9—41no—
125C32×C8—21no—
126C3×C3⋊C8—61no—
127D4×C9—22no—
128D4×C9—21no—
129D4×C9—21no—
130D4×C9—41no—
131C2×C4×C9—21no—
132C2×C4×C9—21no—
133C2×C4×C9—41no—
134C2×C4×C9C23×C311yescharacteristic
135C2×Dic9—21no—
136C2×Dic9—21no—
137C2×Dic9C3×D411yescharacteristic
138C2×Dic9C3×D411yescharacteristic
139Dic18—21no—
140Dic18—21no—
141Dic18—21no—
142Dic18C3×D412yes—
143C8×C9—21no—
144C8×C9—41no—
145C9⋊C8—21no—
146#464—91noSylow
147C2×C3×C9—81no—
148C2×C3×C9#12111yescharacteristic
149C2×C3×C9#13511yescharacteristic
150C2×C3×C9#13711yescharacteristic
151C2×C3×Q8—91no—
152C2×C3×Q8—91no—
153C2×C3×D4—21no—
154C2×C3×D4C2×D911yescharacteristic
155C2×C3×D4C2×C3×D311yescharacteristic
156C2×Dic6—31no—
157C2×Dic6—31no—
158C3×Q16—182no—
159C3×SD16—182no—
160C2×C3×C8—21no—
161C2×C3×C8—91no—
162C2×C3×C8C2×D911yescharacteristic
163C2×C3×C8C2×C3×D311yescharacteristic
164C3×C4⋊C4—21no—
165C3×C4⋊C4—181no—
166C3×C4⋊C4C2×D911yescharacteristic
167C3×C4⋊C4C2×C3×D311yescharacteristic
168C3×C22⋊C4—181no—
169C3×C22⋊C4—181no—
170C3×C42—91no—
171C3×C42—181no—
172#217—61no—
173#217—61no—
174#214—62no—
175Dic3⋊C4—61no—
176C4×Dic3—31no—
177C4×Dic3—61no—
178C2×C3⋊C8—31no—
179Dic12—62no—
180C22×C32—41no—
181C22×C32—41no—
182C22×C32—41no—
183C22×C32D3×D411yescharacteristic
184C32×C4—41no—
185C32×C4#23511yescharacteristic
186C32×C4D3×D411yescharacteristic
187C3×Dic3—62no—
188C3×Dic3—61no—
189C3×Dic3—61no—
190C3×Dic3—121no—
191C22×C9—21no—
192C22×C9—42no—
193C22×C9—41no—
194C22×C9—41no—
195C22×C9—41no—
196C22×C9—81no—
197C22×C9—81no—
198C22×C9C2×C3×D411yescharacteristic
199C4×C9—21no—
200C4×C9—21no—
201C4×C9—41no—
202C4×C9—81no—
203C4×C9C2×C3×D411yescharacteristic
204C4×C9C3×#4111yescharacteristic
205Dic9—22no—
206Dic9—21no—
207Dic9—21no—
208Dic9—41no—
209C2×Q16—91no—
210C2×SD16—91no—
211#124—91no—
212C4×Q8—91no—
213C4⋊C8—91no—
214#103—91no—
215#102C3×D911yescharacteristic
216C3×C9#46411yescharacteristic, complemented, Sylow
217C23×C3—21no—
218C23×C3—21no—
219C23×C3—41no—
220C3×Q8—92no—
221C3×Q8—181no—
222C3×Q8—181no—
223C3×Q8—181no—
224C3×D4—22no—
225C3×D4—21no—
226C3×D4—21no—
227C3×D4—21no—
228C3×D4—21no—
229C3×D4—41no—
230C2×C3×C4—21no—
231C2×C3×C4—21no—
232C2×C3×C4—21no—
233C2×C3×C4—41no—
234C2×C3×C4—91no—
235C2×C3×C4—91no—
236C2×C3×C4—181no—
237C2×C3×C4—181no—
238C2×C3×C4C22×D911yescharacteristic
239C2×C3×C4C22×C3×D311yescharacteristic
240C2×Dic3—31no—
241C2×Dic3—31no—
242C2×Dic3—61no—
243C2×Dic3—61no—
244Dic6—32no—
245Dic6—61no—
246Dic6—61no—
247Dic6—61no—
248C3×C8—21no—
249C3×C8—21no—
250C3×C8—41no—
251C3×C8—181no—
252C3⋊C8—61no—
253C2×C32—81no—
254C2×C32#88411yescharacteristic
255C2×C32#91211yescharacteristic
256C2×C32#91511yescharacteristic
257C2×C9—21no—
258C2×C9—21no—
259C2×C9—21no—
260C2×C9—82no—
261C2×C9—81no—
262C2×C9C3×#12111yescharacteristic
263C2×C9C3×#13511yescharacteristic
264C2×C9C3×#13711yescharacteristic
265C2×Q8—91no—
266C2×Q8—91no—
267C2×D4C2×C3×D911yescharacteristic
268Q16—182no—
269SD16—182no—
270C2×C8—91no—
271C2×C8C2×C3×D911yescharacteristic
272C4⋊C4—181no—
273C4⋊C4C2×C3×D911yescharacteristic
274C22⋊C4—181no—
275C22⋊C4—181no—
276C42—91no—
277C42—181no—
278C22×C3—21no—
279C22×C3—42no—
280C22×C3—41no—
281C22×C3—41no—
282C22×C3—41no—
283C22×C3—41no—
284C22×C3—41no—
285C22×C3—41no—
286C22×C3—81no—
287C22×C3—81no—
288C22×C3D4×D911yescharacteristic
289C22×C3C3×D3×D411yescharacteristic
290C3×C4—21no—
291C3×C4—21no—
292C3×C4—41no—
293C3×C4—41no—
294C3×C4—81no—
295C3×C4—182no—
296C3×C4—181no—
297C3×C4—181no—
298C3×C4—361no—
299C3×C4#369711yescharacteristic
300C3×C4D4×D911yescharacteristic
301C3×C4C3×#23511yescharacteristic
302C3×C4C3×D3×D411yescharacteristic
303Dic3—62no—
304Dic3—61no—
305Dic3—61no—
306Dic3—121no—
307C32#476711yescharacteristic
308C9—21no—
309C9C3×#46411yescharacteristic, complemented
310C23—21no—
311Q8—92no—
312Q8—181no—
313Q8—181no—
314Q8—181no—
315D4—21no—
316D4—21no—
317C2×C4—21no—
318C2×C4—91no—
319C2×C4—91no—
320C2×C4—181no—
321C2×C4—181no—
322C2×C4C22×C3×D911yescharacteristic
323C8—21no—
324C8—181no—
325C2×C3—21no—
326C2×C3—21no—
327C2×C3—21no—
328C2×C3—82no—
329C2×C3—81no—
330C2×C3—81no—
331C2×C3#6344611yescharacteristic
332C2×C3#6347411yescharacteristic
333C2×C3#6347711yescharacteristic
334C2×C3C3×#88411yescharacteristic
335C2×C3C3×#91211yescharacteristic
336C2×C3C3×#91511yescharacteristic
337C22—41no—
338C22—41no—
339C22—41no—
340C22C3×D4×D911yescharacteristic
341C4—41no—
342C4—181no—
343C4—181no—
344C4—182no—
345C4—361no—
346C4C3×#369711yescharacteristic
347C4C3×D4×D911yescharacteristic
348C3—21no—
349C3#1058844711yescharacteristic, direct product factor
350C3C3×#476711yescharacteristic
351C2—81no—
352C2C3×#6344611yescharacteristic
353C2C3×#6347411yescharacteristic
354C2C3×#6347711yescharacteristic
subgroupG/H
centerC22×C3D4×D9
commutator, cosocleC2×C4×C9C23×C3
FrattiniC2×C3×C4C22×C3×D3
FittingC3×C9×#102C2
socleC22×C32D3×D4
prime radicalC2×C32×D4C2×D3
hypercenterC3×#102D9
hypocenterC9C3×#464
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
3. C2×C3×Dic36C2semidirect
4. C3×#63449C2semidirect
6. C3×Dic9⋊C8C2semidirect
7. C3×#63368C2semidirect
9. #10588447C3direct (N × H)
32. C2×Dic36C2×C3semidirect
33. #63449C2×C3semidirect
36. Dic9⋊C8C2×C3semidirect
37. #63368C2×C3semidirect
216. C3×C9#464semidirect
309. C9C3×#464semidirect
349. C3#10588447direct (N × H)

Maximal subgroups

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

subgroupindex
C3×#634982
C2×C3×#36722
C2×C3×Dic362
C3×#634492
C3×C9×#1022
C3×Dic9⋊C82
C3×#633682
C3×#47673
#105884473