Finite Group Databasebeta

← C3×#10588478 #13141846

Subgroups — C3×#10588478 #13141846

Order 1728.

378 conjugacy classes of subgroups.

The subgroup lattice has 350 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#63509C211yesmaximal, characteristic
2C2×C3×#3674C211yesmaximal, characteristic, complemented
3C2×C3×#3664C211yesmaximal, characteristic
4C3×#63449C211yesmaximal, characteristic, complemented
5C3×C9×#103C211yesmaximal, characteristic, complemented
6C3×Dic9⋊C8C211yesmaximal, characteristic, complemented
7C3×#63369C211yesmaximal, characteristic
8C3×#4798—31nomaximal
9#10588478C311yesmaximal, characteristic, direct product factor
10C2×C3×Q8×C9C2211yescharacteristic
11C2×C3×D36C2211yescharacteristic
12C2×C3×Dic18C2211yescharacteristic
13C2×C3×C8×C9C2211yescharacteristic
14C3×C9×C4⋊C4C2211yescharacteristic
15C3×#3674—22no—
16C3×(C2×D9)⋊C4—21no—
17C3×(C2×D9)⋊C4—21no—
18C3×Dic9⋊C4—21no—
19C3×C4×Dic9—21no—
20C3×C4×Dic9C2211yescharacteristic
21C2×C3×C9⋊C8C2211yescharacteristic
22C3×#3664—22no—
23C3×#947—31no—
24C2×C3×#216—31no—
25C2×C3×#204—31no—
26C3×#887—31no—
27C32×#103D311yescharacteristic
28C3×Dic3⋊C8—31no—
29C3×#809—31no—
30#63509C2×C311yescharacteristic
31C2×#3674C2×C311yescharacteristic, complemented
32C2×#3664C2×C311yescharacteristic
33#63449C2×C311yescharacteristic, complemented
34C9×#103—21no—
35C9×#103C2×C311yescharacteristic, complemented
36Dic9⋊C8C2×C311yescharacteristic, complemented
37#63369C2×C311yescharacteristic
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×D36—21no—
49C3×Dic18—21no—
50C3×Dic18D412yes—
51C3×C8×C9—21no—
52C3×C9⋊C8—21no—
53C3×#464—91no—
54#4798—31no—
55C2×C32×Q8C2×D311yescharacteristic
56C2×C3×D12—31no—
57C2×C3×Dic6—31no—
58C2×C32×C8C2×D311yescharacteristic
59C32×C4⋊C4C2×D311yescharacteristic
60C3×#216—62no—
61C3×(C2×D3)⋊C4—61no—
62C3×(C2×D3)⋊C4—61no—
63C3×Dic3⋊C4—61no—
64C3×C4×Dic3—31no—
65C3×C4×Dic3—61no—
66C2×C3×C3⋊C8—31no—
67C3×#204—62no—
68C2×Q8×C9—21no—
69C2×Q8×C9C22×C311yescharacteristic
70C2×D36C22×C311yescharacteristic
71C2×Dic18C22×C311yescharacteristic
72C2×C8×C9—21no—
73C2×C8×C9C22×C311yescharacteristic
74C9×C4⋊C4—21no—
75C9×C4⋊C4C22×C311yescharacteristic
76#3674—22no—
77(C2×D9)⋊C4—21no—
78(C2×D9)⋊C4—21no—
79Dic9⋊C4—21no—
80C4×Dic9—21no—
81C4×Dic9C22×C311yescharacteristic
82C2×C9⋊C8C22×C311yescharacteristic
83#3664—22no—
84C22×C3×C9C2×D411yescharacteristic
85C2×C3×D9—41no—
86C2×C3×D9—41no—
87C2×C3×D9—41no—
88C3×C4×C9—41no—
89C3×C4×C9—41no—
90C3×C4×C9C2×D411yescharacteristic
91C3×C4×C9#4111yescharacteristic
92C3×Dic9—22no—
93C3×Dic9—21no—
94C3×Dic9—21no—
95C2×C3×Q16—91no—
96C2×C3×SD16—91no—
97C3×#124—91no—
98C3×C4×Q8—91no—
99#947—31no—
100C2×#216—31no—
101C2×#204—31no—
102#887—31no—
103C3×C4⋊C8—91no—
104C3×#103—21no—
105C3×#103D911yescharacteristic, complemented
106C3×#103C3×D311yescharacteristic
107C3×#102—91no—
108Dic3⋊C8—31no—
109#809—31no—
110C22×C3×D3—61no—
111C32×Q8—21no—
112C32×Q8—21no—
113C2×C32×C4—21no—
114C2×C32×C4—21no—
115C2×C32×C4C22×D311yescharacteristic
116C2×C3×Dic3—31no—
117C2×C3×Dic3—31no—
118C2×C3×Dic3—61no—
119C3×D12—61no—
120C3×D12—61no—
121C3×Dic6—32no—
122C3×Dic6—61no—
123C22×D9—21no—
124C32×C8—21no—
125C3×C3⋊C8—61no—
126Q8×C9—22no—
127Q8×C9—21no—
128Q8×C9—21no—
129Q8×C9—41no—
130C2×C4×C9—21no—
131C2×C4×C9—21no—
132C2×C4×C9—21no—
133C2×C4×C9—41no—
134C2×C4×C9—41no—
135C2×C4×C9C23×C311yescharacteristic
136C2×Dic9—21no—
137C2×Dic9C3×D411yescharacteristic
138C2×Dic9C3×D411yescharacteristic
139D36—21no—
140D36—21no—
141Dic18—21no—
142Dic18C3×D412yes—
143C8×C9—21no—
144C8×C9—41no—
145C9⋊C8—21no—
146#464—91noSylow
147C2×C3×C9#12111yescharacteristic
148C2×C3×C9#13511yescharacteristic
149C2×C3×C9#13711yescharacteristic
150C3×D9—81no—
151C2×C3×Q8—21no—
152C2×C3×Q8—91no—
153C2×C3×Q8C2×D911yescharacteristic
154C2×C3×Q8C2×C3×D311yescharacteristic
155C2×C3×D4—91no—
156C2×D12—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#216—62no—
173(C2×D3)⋊C4—61no—
174(C2×D3)⋊C4—61no—
175Dic3⋊C4—61no—
176C4×Dic3—31no—
177C4×Dic3—61no—
178C2×C3⋊C8—31no—
179#204—62no—
180C22×C32D3×D411yescharacteristic
181C2×C3×D3—121no—
182C2×C3×D3—121no—
183C2×C3×D3—121no—
184C32×C4—41no—
185C32×C4—41no—
186C32×C4#23511yescharacteristic
187C32×C4D3×D411yescharacteristic
188C3×Dic3—62no—
189C3×Dic3—61no—
190C3×Dic3—61no—
191C22×C9—21no—
192C22×C9C2×C3×D411yescharacteristic
193C2×D9—41no—
194C2×D9—41no—
195C2×D9—41no—
196C4×C9—21no—
197C4×C9—21no—
198C4×C9—42no—
199C4×C9—41no—
200C4×C9—41no—
201C4×C9—81no—
202C4×C9C2×C3×D411yescharacteristic
203C4×C9C3×#4111yescharacteristic
204Dic9—22no—
205Dic9—21no—
206Dic9—21no—
207C2×Q16—91no—
208C2×SD16—91no—
209#124—91no—
210C4×Q8—91no—
211C4⋊C8—91no—
212#103C3×D911yescharacteristic, complemented
213#102—91no—
214C3×C9#46411yescharacteristic, complemented, Sylow
215C23×C3—181no—
216C22×D3—61no—
217C3×Q8—22no—
218C3×Q8—21no—
219C3×Q8—21no—
220C3×Q8—21no—
221C3×Q8—21no—
222C3×Q8—41no—
223C3×Q8—92no—
224C3×Q8—181no—
225C3×D4—181no—
226C3×D4—181no—
227C2×C3×C4—21no—
228C2×C3×C4—21no—
229C2×C3×C4—21no—
230C2×C3×C4—21no—
231C2×C3×C4—21no—
232C2×C3×C4—41no—
233C2×C3×C4—41no—
234C2×C3×C4—91no—
235C2×C3×C4—91no—
236C2×C3×C4—181no—
237C2×C3×C4C22×D911yescharacteristic
238C2×C3×C4C22×C3×D311yescharacteristic
239C2×Dic3—31no—
240C2×Dic3—31no—
241C2×Dic3—61no—
242D12—61no—
243D12—61no—
244Dic6—32no—
245Dic6—61no—
246C3×C8—21no—
247C3×C8—21no—
248C3×C8—41no—
249C3×C8—181no—
250C3⋊C8—61no—
251C2×C32#88411yescharacteristic
252C2×C32#91611yescharacteristic
253C2×C32#91811yescharacteristic
254C3×D3—241no—
255C2×C9—21no—
256C2×C9—21no—
257C2×C9—21no—
258C2×C9C3×#12111yescharacteristic
259C2×C9C3×#13511yescharacteristic
260C2×C9C3×#13711yescharacteristic
261D9—81no—
262C2×Q8—91no—
263C2×Q8C2×C3×D911yescharacteristic
264C2×D4—91no—
265Q16—182no—
266SD16—182no—
267C2×C8—91no—
268C2×C8C2×C3×D911yescharacteristic
269C4⋊C4—181no—
270C4⋊C4C2×C3×D911yescharacteristic
271C22⋊C4—181no—
272C22⋊C4—181no—
273C42—91no—
274C42—181no—
275C22×C3—21no—
276C22×C3—361no—
277C22×C3—361no—
278C22×C3—361no—
279C22×C3D4×D911yescharacteristic
280C22×C3C3×D3×D411yescharacteristic
281C2×D3—121no—
282C2×D3—121no—
283C2×D3—121no—
284C3×C4—21no—
285C3×C4—21no—
286C3×C4—42no—
287C3×C4—41no—
288C3×C4—41no—
289C3×C4—41no—
290C3×C4—41no—
291C3×C4—81no—
292C3×C4—182no—
293C3×C4—181no—
294C3×C4—181no—
295C3×C4#369711yescharacteristic
296C3×C4D4×D911yescharacteristic
297C3×C4C3×#23511yescharacteristic
298C3×C4C3×D3×D411yescharacteristic
299Dic3—62no—
300Dic3—61no—
301Dic3—61no—
302C32#479811yescharacteristic
303C9—21no—
304C9C3×#46411yescharacteristic, complemented
305C23—181no—
306Q8—21no—
307Q8—21no—
308Q8—92no—
309Q8—181no—
310D4—181no—
311D4—181no—
312C2×C4—21no—
313C2×C4—21no—
314C2×C4—91no—
315C2×C4—91no—
316C2×C4—181no—
317C2×C4C22×C3×D911yescharacteristic
318C8—21no—
319C8—181no—
320C2×C3—21no—
321C2×C3—21no—
322C2×C3—21no—
323C2×C3—721no—
324C2×C3#6344611yescharacteristic
325C2×C3#6347811yescharacteristic
326C2×C3#6348011yescharacteristic
327C2×C3C3×#88411yescharacteristic
328C2×C3C3×#91611yescharacteristic
329C2×C3C3×#91811yescharacteristic
330D3—241no—
331C22—361no—
332C22—361no—
333C22—361no—
334C22C3×D4×D911yescharacteristic
335C4—41no—
336C4—41no—
337C4—181no—
338C4—181no—
339C4—182no—
340C4C3×#369711yescharacteristic
341C4C3×D4×D911yescharacteristic
342C3—21no—
343C3#1058847811yescharacteristic, direct product factor
344C3C3×#479811yescharacteristic
345C2—721no—
346C2C3×#6344611yescharacteristic
347C2C3×#6347811yescharacteristic
348C2C3×#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×#464
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
2. C2×C3×#3674C2semidirect
4. C3×#63449C2semidirect
5. C3×C9×#103C2semidirect
6. C3×Dic9⋊C8C2semidirect
9. #10588478C3direct (N × H)
31. C2×#3674C2×C3semidirect
33. #63449C2×C3semidirect
35. C9×#103C2×C3semidirect
36. Dic9⋊C8C2×C3semidirect
105. C3×#103D9semidirect
212. #103C3×D9semidirect
214. C3×C9#464semidirect
304. C9C3×#464semidirect
343. C3#10588478direct (N × H)

Maximal subgroups

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

subgroupindex
C3×#635092
C2×C3×#36742
C2×C3×#36642
C3×#634492
C3×C9×#1032
C3×Dic9⋊C82
C3×#633692
C3×#47983
#105884783