Finite Group Databasebeta

← C3×#10588483 #13141864

Subgroups — C3×#10588483 #13141864

Order 1728.

528 conjugacy classes of subgroups.

The subgroup lattice has 392 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#3701C211yesmaximal, characteristic
2C2×C3×#3663C211yesmaximal, characteristic, complemented
3C3×C4⋊C4×D9C211yesmaximal, characteristic, complemented
4C3×C9×#103C211yesmaximal, characteristic, complemented
5C3×#63395C211yesmaximal, characteristic, complemented
6C3×#63380C211yesmaximal, characteristic, complemented
7C3×#63369C211yesmaximal, characteristic, complemented
8C3×#4803—31nomaximal
9#10588483C311yesmaximal, characteristic, direct product factor
10C2×C3×Q8×C9C2211yescharacteristic
11C3×#3701—22no—
12C3×#3701C414yescomplemented
13C2×C3×D36—21no—
14C2×C3×D36C2211yescharacteristic
15C2×C3×C4×D9—21no—
16C2×C3×C4×D9—21no—
17C2×C3×C4×D9C2211yescharacteristic
18C2×C3×C8×C9C2211yescharacteristic
19C3×C9×C4⋊C4C2211yescharacteristic
20C3×C4⋊Dic9C2211yescharacteristic
21C3×Dic9⋊C4—21no—
22C2×C3×C9⋊C8C2211yescharacteristic
23C3×#3663—22no—
24C2×C3×#239—31no—
25C2×C3×ΓL(1,𝔽25)—31no—
26C3×D3×C4⋊C4—31no—
27C2×#3701C2×C311yescharacteristic
28C32×#103D311yescharacteristic
29C3×#835—31no—
30C3×#821—31no—
31C3×#809—31no—
32C2×#3663C2×C311yescharacteristic, complemented
33C4⋊C4×D9C2×C311yescharacteristic, complemented
34C9×#103—21no—
35C9×#103C2×C311yescharacteristic, complemented
36#63395C2×C311yescharacteristic, complemented
37#63380C2×C311yescharacteristic, complemented
38#63369C2×C311yescharacteristic, complemented
39C22×C3×D9—21no—
40C22×C3×D9D411yescharacteristic
41C3×Q8×C9—21no—
42C3×Q8×C9C2×C412yescomplemented
43C2×C3×C4×C9—21no—
44C2×C3×C4×C9—21no—
45C2×C3×C4×C9C2311yescharacteristic
46C2×C3×Dic9—21no—
47C2×C3×Dic9D411yescharacteristic
48C3×D36—24no—
49C3×D36—21no—
50C3×D36C2×C412yescomplemented
51C3×C4×D9—24no—
52C3×C4×D9—42no—
53C3×C4×D9C2×C412yes—
54C3×C4×D9D412yes—
55C3×C8×C9—21no—
56C3×C9⋊C8—21no—
57C3×#417—91no—
58#4803—31no—
59C2×C32×Q8C2×D311yescharacteristic
60C3×#239—34no—
61C3×#239—62no—
62C2×C3×D12—31no—
63C2×C3×D12—61no—
64C2×C3×C4×D3—31no—
65C2×C3×C4×D3—61no—
66C2×C3×C4×D3—61no—
67C2×C32×C8C2×D311yescharacteristic
68C32×C4⋊C4C2×D311yescharacteristic
69C3×C4⋊Dic3—31no—
70C3×Dic3⋊C4—61no—
71C2×C3×C3⋊C8—31no—
72C3×ΓL(1,𝔽25)—62no—
73C2×Q8×C9—21no—
74C2×Q8×C9C22×C311yescharacteristic
75#3701—22no—
76#3701C3×C414yescomplemented
77C2×D36—21no—
78C2×D36C22×C311yescharacteristic
79C2×C4×D9—21no—
80C2×C4×D9—21no—
81C2×C4×D9C22×C311yescharacteristic
82C2×C8×C9—21no—
83C2×C8×C9C22×C311yescharacteristic
84C9×C4⋊C4—21no—
85C9×C4⋊C4C22×C311yescharacteristic
86C4⋊Dic9C22×C311yescharacteristic
87Dic9⋊C4—21no—
88C2×C9⋊C8C22×C311yescharacteristic
89#3663—22no—
90C22×C3×C9C2×D411yescharacteristic
91C2×C3×D9—21no—
92C2×C3×D9—21no—
93C2×C3×D9—22no—
94C2×C3×D9—41no—
95C2×C3×D9—41no—
96C2×C3×D9C22⋊C412yes—
97C3×C4×C9—22no—
98C3×C4×C9—41no—
99C3×C4×C9C22×C411yescharacteristic
100C3×C4×C9C2×D411yescharacteristic
101C3×Dic9—41no—
102C3×Dic9C22⋊C412yes—
103C2×C3×#41—91no—
104C2×#239—31no—
105C2×C3×M16—91no—
106C2×C3×C4⋊C4—91no—
107C2×ΓL(1,𝔽25)—31no—
108D3×C4⋊C4—31no—
109C3×#103—21no—
110C3×#103—91no—
111C3×#103D911yescharacteristic, complemented
112C3×#103C3×D311yescharacteristic
113C3×#102—91no—
114C3×#102—91no—
115#835—31no—
116#821—31no—
117#809—31no—
118C22×C3×D3—31no—
119C22×C3×D3—61no—
120C32×Q8—21no—
121C32×Q8C4×D312yes—
122C2×C32×C4—21no—
123C2×C32×C4—21no—
124C2×C32×C4C22×D311yescharacteristic
125C2×C3×Dic3—31no—
126C2×C3×Dic3—61no—
127C3×D12—32no—
128C3×D12—64no—
129C3×D12—61no—
130C3×C4×D3—32no—
131C3×C4×D3—32no—
132C3×C4×D3—64no—
133C3×C4×D3—122no—
134C22×D9—21no—
135C22×D9C3×D411yescharacteristic
136C32×C8—21no—
137C3×C3⋊C8—61no—
138Q8×C9—21no—
139Q8×C9—22no—
140Q8×C9—41no—
141Q8×C9C2×C3×C412yescomplemented
142C2×C4×C9—21no—
143C2×C4×C9—21no—
144C2×C4×C9—21no—
145C2×C4×C9—41no—
146C2×C4×C9—41no—
147C2×C4×C9C23×C311yescharacteristic
148C2×Dic9—21no—
149C2×Dic9C3×D411yescharacteristic
150D36—24no—
151D36—21no—
152D36C2×C3×C412yescomplemented
153C4×D9—24no—
154C4×D9—42no—
155C4×D9C2×C3×C412yes—
156C4×D9C3×D412yes—
157C8×C9—21no—
158C8×C9—41no—
159C9⋊C8—21no—
160#417—91noSylow
161C2×C3×C9C2×C22⋊C411yescharacteristic
162C2×C3×C9AGL(1,ℤ/8)11yescharacteristic
163C2×C3×C9#13711yescharacteristic
164C3×D9—22no—
165C3×D9—42no—
166C3×#41—94no—
167C3×#41—182no—
168C2×C3×Q8—21no—
169C2×C3×Q8C2×D911yescharacteristic
170C2×C3×Q8C2×C3×D311yescharacteristic
171C2×C3×D4—91no—
172C2×C3×D4—181no—
173C22×C3×C4—91no—
174C22×C3×C4—181no—
175C22×C3×C4—181no—
176#239—34no—
177#239—62no—
178C2×D12—31no—
179C2×D12—61no—
180C2×C4×D3—31no—
181C2×C4×D3—61no—
182C2×C4×D3—61no—
183C3×M16—182no—
184C2×C3×C8—21no—
185C2×C3×C8—91no—
186C2×C3×C8C2×D911yescharacteristic
187C2×C3×C8C2×C3×D311yescharacteristic
188C3×C4⋊C4—21no—
189C3×C4⋊C4—91no—
190C3×C4⋊C4—181no—
191C3×C4⋊C4C2×D911yescharacteristic
192C3×C4⋊C4C2×C3×D311yescharacteristic
193C4⋊Dic3—31no—
194Dic3⋊C4—61no—
195C2×C3⋊C8—31no—
196ΓL(1,𝔽25)—62no—
197C22×C32D3×D411yescharacteristic
198C2×C3×D3—32no—
199C2×C3×D3—61no—
200C2×C3×D3—61no—
201C2×C3×D3—62no—
202C2×C3×D3—121no—
203C2×C3×D3—121no—
204C32×C4—22no—
205C32×C4—41no—
206C32×C4C2×C4×D311yescharacteristic
207C32×C4D3×D411yescharacteristic
208C3×Dic3—32no—
209C3×Dic3—121no—
210C22×C9—21no—
211C22×C9C2×C3×D411yescharacteristic
212C2×D9—21no—
213C2×D9—21no—
214C2×D9—22no—
215C2×D9—41no—
216C2×D9—41no—
217C2×D9C3×C22⋊C412yes—
218C4×C9—22no—
219C4×C9—21no—
220C4×C9—21no—
221C4×C9—42no—
222C4×C9—41no—
223C4×C9—81no—
224C4×C9C22×C3×C411yescharacteristic
225C4×C9C2×C3×D411yescharacteristic
226Dic9—41no—
227Dic9C3×C22⋊C412yes—
228C2×#41—91no—
229C2×M16—91no—
230C2×C4⋊C4—91no—
231#103—91no—
232#103C3×D911yescharacteristic, complemented
233#102—91no—
234#102—91no—
235C3×C9#41711yescharacteristic, complemented, Sylow
236C23×C3—91no—
237C23×C3—181no—
238C22×D3—31no—
239C22×D3—61no—
240C3×Q8—21no—
241C3×Q8—21no—
242C3×Q8—22no—
243C3×Q8—41no—
244C3×Q8C4×D912yescomplemented
245C3×Q8C3×C4×D312yes—
246C3×D4—92no—
247C3×D4—184no—
248C3×D4—181no—
249C2×C3×C4—21no—
250C2×C3×C4—21no—
251C2×C3×C4—21no—
252C2×C3×C4—21no—
253C2×C3×C4—21no—
254C2×C3×C4—41no—
255C2×C3×C4—41no—
256C2×C3×C4—91no—
257C2×C3×C4—92no—
258C2×C3×C4—92no—
259C2×C3×C4—184no—
260C2×C3×C4—181no—
261C2×C3×C4—362no—
262C2×C3×C4C22×D911yescharacteristic
263C2×C3×C4C22×C3×D311yescharacteristic
264C2×Dic3—31no—
265C2×Dic3—61no—
266D12—32no—
267D12—64no—
268D12—61no—
269C4×D3—32no—
270C4×D3—32no—
271C4×D3—64no—
272C4×D3—122no—
273C3×C8—21no—
274C3×C8—21no—
275C3×C8—41no—
276C3×C8—181no—
277C3⋊C8—61no—
278C2×C32D3×C22⋊C411yescharacteristic
279C2×C32#91411yescharacteristic
280C2×C32#91811yescharacteristic
281C3×D3—62no—
282C3×D3—122no—
283C2×C9—21no—
284C2×C9—21no—
285C2×C9—21no—
286C2×C9C2×C3×C22⋊C411yescharacteristic
287C2×C9C3×AGL(1,ℤ/8)11yescharacteristic
288C2×C9C3×#13711yescharacteristic
289D9—22no—
290D9—42no—
291#41—94no—
292#41—182no—
293C2×Q8C2×C3×D911yescharacteristic
294C2×D4—91no—
295C2×D4—181no—
296C22×C4—91no—
297C22×C4—181no—
298C22×C4—181no—
299M16—182no—
300C2×C8—91no—
301C2×C8C2×C3×D911yescharacteristic
302C4⋊C4—91no—
303C4⋊C4—181no—
304C4⋊C4C2×C3×D911yescharacteristic
305C22×C3—21no—
306C22×C3—92no—
307C22×C3—181no—
308C22×C3—181no—
309C22×C3—182no—
310C22×C3—361no—
311C22×C3—361no—
312C22×C3D4×D911yescharacteristic
313C22×C3C3×D3×D411yescharacteristic
314C2×D3—32no—
315C2×D3—61no—
316C2×D3—61no—
317C2×D3—62no—
318C2×D3—121no—
319C2×D3—121no—
320C3×C4—22no—
321C3×C4—22no—
322C3×C4—21no—
323C3×C4—21no—
324C3×C4—42no—
325C3×C4—41no—
326C3×C4—41no—
327C3×C4—81no—
328C3×C4—92no—
329C3×C4—361no—
330C3×C4C2×C4×D911yescharacteristic
331C3×C4D4×D911yescharacteristic
332C3×C4C2×C3×C4×D311yescharacteristic
333C3×C4C3×D3×D411yescharacteristic
334Dic3—32no—
335Dic3—121no—
336C32#480311yescharacteristic
337C9—21no—
338C9C3×#41711yescharacteristic, complemented
339C23—91no—
340C23—181no—
341Q8—21no—
342Q8C3×C4×D912yescomplemented
343D4—92no—
344D4—184no—
345D4—181no—
346C2×C4—21no—
347C2×C4—21no—
348C2×C4—91no—
349C2×C4—92no—
350C2×C4—92no—
351C2×C4—184no—
352C2×C4—181no—
353C2×C4—362no—
354C2×C4C22×C3×D911yescharacteristic
355C8—21no—
356C8—181no—
357C2×C3—21no—
358C2×C3—21no—
359C2×C3—21no—
360C2×C3—182no—
361C2×C3—362no—
362C2×C3C22⋊C4×D911yescharacteristic
363C2×C3#6347611yescharacteristic
364C2×C3#6348011yescharacteristic
365C2×C3C3×D3×C22⋊C411yescharacteristic
366C2×C3C3×#91411yescharacteristic
367C2×C3C3×#91811yescharacteristic
368D3—62no—
369D3—122no—
370C22—92no—
371C22—181no—
372C22—181no—
373C22—182no—
374C22—361no—
375C22—361no—
376C22C3×D4×D911yescharacteristic
377C4—22no—
378C4—41no—
379C4—92no—
380C4—361no—
381C4C2×C3×C4×D911yescharacteristic
382C4C3×D4×D911yescharacteristic
383C3—21no—
384C3#1058848311yescharacteristic, direct product factor
385C3C3×#480311yescharacteristic
386C2—182no—
387C2—362no—
388C2C3×C22⋊C4×D911yescharacteristic
389C2C3×#6347611yescharacteristic
390C2C3×#6348011yescharacteristic
subgroupG/H
centerC22×C3D4×D9
commutatorC4×C9C22×C3×C4
FrattiniC2×C3×C4C22×C3×D3
FittingC3×C9×#103C2
socleC22×C32D3×D4
prime radicalC2×C3×#3701C2
cosocleC2×C4×C9C23×C3
hypercenterC3×#103D9
hypocenterC9C3×#417
LCSG ▷ 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×#3663C2semidirect
3. C3×C4⋊C4×D9C2semidirect
4. C3×C9×#103C2semidirect
5. C3×#63395C2semidirect
6. C3×#63380C2semidirect
7. C3×#63369C2semidirect
9. #10588483C3direct (N × H)
12. C3×#3701C4semidirect
32. C2×#3663C2×C3semidirect
33. C4⋊C4×D9C2×C3semidirect
35. C9×#103C2×C3semidirect
36. #63395C2×C3semidirect
37. #63380C2×C3semidirect
38. #63369C2×C3semidirect
42. C3×Q8×C9C2×C4semidirect
50. C3×D36C2×C4semidirect
76. #3701C3×C4semidirect
111. C3×#103D9semidirect
141. Q8×C9C2×C3×C4semidirect
152. D36C2×C3×C4semidirect
232. #103C3×D9semidirect
235. C3×C9#417semidirect
244. C3×Q8C4×D9semidirect
338. C9C3×#417semidirect
342. Q8C3×C4×D9semidirect
384. C3#10588483direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C3×#37012
C2×C3×#36632
C3×C4⋊C4×D92
C3×C9×#1032
C3×#633952
C3×#633802
C3×#633692
C3×#48033
#105884833