Finite Group Databasebeta

← C3×#10588718 #13142819

Subgroups — C3×#10588718 #13142819

Order 1728.

454 conjugacy classes of subgroups.

The subgroup lattice has 402 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×C9×#121C211yesmaximal, characteristic
2C2×C3×#3672C211yesmaximal, characteristic, complemented
3C3×#63486C211yesmaximal, characteristic, complemented
4C2×C3×#3667C211yesmaximal, characteristic, complemented
5C3×#63392C211yesmaximal, characteristic, complemented
6C3×#63368C211yesmaximal, characteristic, complemented
7C3×#63366C211yesmaximal, characteristic, complemented
8C3×#5042—31nomaximal
9#10588718C311yesmaximal, characteristic, direct product factor
10C2×C3×D4×C9—21no—
11C2×C3×D4×C9C2211yescharacteristic
12C22×C3×C4×C9C2211yescharacteristic
13C2×C3×Dic18C2211yescharacteristic
14C3×C9×C4⋊C4C2211yescharacteristic
15C3×C9×C22⋊C4—21no—
16C3×#3676—21no—
17C3×#3672—22no—
18C3×C4⋊Dic9C2211yescharacteristic
19C3×Dic9⋊C4—21no—
20C3×#3667—22no—
21C2×C3×C9⋊C8C2211yescharacteristic
22C2×C3×C9⋊C8C2211yescharacteristic
23C32×#121D311yescharacteristic
24C2×C3×#214—31no—
25C3×#924—31no—
26C2×C3×#208—31no—
27C3×#832—31no—
28C3×#810—31no—
29C3×#807—31no—
30C9×#121—21no—
31C9×#121C2×C311yescharacteristic
32C2×#3672C2×C311yescharacteristic, complemented
33#63486C2×C311yescharacteristic, complemented
34C2×#3667C2×C311yescharacteristic, complemented
35#63392C2×C311yescharacteristic, complemented
36#63368C2×C311yescharacteristic, complemented
37#63366C2×C311yescharacteristic, complemented
38C23×C3×C9—21no—
39C23×C3×C9D411yescharacteristic
40C3×D4×C9—21no—
41C3×D4×C9—21no—
42C3×D4×C9—42no—
43C2×C3×C4×C9—21no—
44C2×C3×C4×C9—21no—
45C2×C3×C4×C9—21no—
46C2×C3×C4×C9D411yescharacteristic
47C2×C3×C4×C9C2311yescharacteristic
48C2×C3×Dic9—21no—
49C2×C3×Dic9—21no—
50C3×Dic18—21no—
51C3×Dic18—21no—
52C3×C9⋊C8—21no—
53C3×C9⋊C8D412yescomplemented
54C3×#468—91no—
55#5042—31no—
56C2×C32×D4—21no—
57C2×C32×D4C2×D311yescharacteristic
58C22×C32×C4C2×D311yescharacteristic
59C2×C3×Dic6—31no—
60C32×C4⋊C4C2×D311yescharacteristic
61C32×C22⋊C4—21no—
62C3×#217—61no—
63C3×#214—62no—
64C3×C4⋊Dic3—31no—
65C3×Dic3⋊C4—61no—
66C3×#208—62no—
67C2×C3×C3⋊C8—31no—
68C2×C3×C3⋊C8—31no—
69C2×D4×C9—22no—
70C2×D4×C9—21no—
71C2×D4×C9—21no—
72C2×D4×C9C22×C311yescharacteristic
73C22×C4×C9—21no—
74C22×C4×C9C22×C311yescharacteristic
75C2×Dic18C22×C311yescharacteristic
76C9×C4⋊C4—21no—
77C9×C4⋊C4C22×C311yescharacteristic
78C9×C22⋊C4—22no—
79C9×C22⋊C4—21no—
80#3676—21no—
81#3672—22no—
82C4⋊Dic9C22×C311yescharacteristic
83Dic9⋊C4—21no—
84#3667—22no—
85C2×C9⋊C8C22×C311yescharacteristic
86C2×C9⋊C8C22×C311yescharacteristic
87C22×C3×C9—21no—
88C22×C3×C9—21no—
89C22×C3×C9—21no—
90C22×C3×C9—41no—
91C22×C3×C9—41no—
92C22×C3×C9—41no—
93C22×C3×C9C2×D411yescharacteristic
94C3×C4×C9—21no—
95C3×C4×C9—41no—
96C3×C4×C9C2×D411yescharacteristic
97C3×C4×C9#4111yescharacteristic
98C3×Dic9—41no—
99C3×Dic9—41no—
100C2×C3×SD16—91no—
101C2×C3×M16—91no—
102C3×C22⋊Q8—91no—
103C3×#121—21no—
104C3×#121D911yescharacteristic
105C3×#121C3×D311yescharacteristic
106C2×#214—31no—
107#924—31no—
108C2×#208—31no—
109C3×#107—91no—
110C3×#103—91no—
111C3×#102—91no—
112#832—31no—
113#810—31no—
114#807—31no—
115C23×C32—21no—
116C23×C32#6711yescharacteristic
117C32×D4—21no—
118C32×D4—21no—
119C32×D4—42no—
120C2×C32×C4—21no—
121C2×C32×C4—21no—
122C2×C32×C4—21no—
123C2×C32×C4#6711yescharacteristic
124C2×C32×C4C22×D311yescharacteristic
125C2×C3×Dic3—61no—
126C2×C3×Dic3—61no—
127C3×Dic6—61no—
128C3×Dic6—61no—
129C23×C9—22no—
130C23×C9—21no—
131C23×C9—21no—
132C23×C9C3×D411yescharacteristic
133C3×C3⋊C8—32no—
134C3×C3⋊C8—61no—
135D4×C9—21no—
136D4×C9—21no—
137D4×C9—41no—
138D4×C9—41no—
139D4×C9—44no—
140D4×C9—42no—
141C2×C4×C9—21no—
142C2×C4×C9—21no—
143C2×C4×C9—22no—
144C2×C4×C9—21no—
145C2×C4×C9—21no—
146C2×C4×C9—21no—
147C2×C4×C9—41no—
148C2×C4×C9—41no—
149C2×C4×C9C3×D411yescharacteristic
150C2×C4×C9C23×C311yescharacteristic
151C2×Dic9—21no—
152C2×Dic9—21no—
153Dic18—21no—
154Dic18—21no—
155C9⋊C8—21no—
156C9⋊C8C3×D412yescomplemented
157#468—91noSylow
158C2×C3×C9—41no—
159C2×C3×C9—81no—
160C2×C3×C9#12111yescharacteristic
161C2×C3×C9AGL(1,ℤ/8)11yescharacteristic
162C2×C3×C9#13711yescharacteristic
163C2×C3×Q8—91no—
164C2×C3×D4—22no—
165C2×C3×D4—21no—
166C2×C3×D4—21no—
167C2×C3×D4—21no—
168C2×C3×D4C2×D911yescharacteristic
169C2×C3×D4C2×C3×D311yescharacteristic
170C22×C3×C4—21no—
171C22×C3×C4C2×D911yescharacteristic
172C22×C3×C4C2×C3×D311yescharacteristic
173C2×Dic6—31no—
174C3×SD16—182no—
175C3×M16—182no—
176C2×C3×C8—91no—
177C2×C3×C8—91no—
178C3×C4⋊C4—21no—
179C3×C4⋊C4—91no—
180C3×C4⋊C4—181no—
181C3×C4⋊C4C2×D911yescharacteristic
182C3×C4⋊C4C2×C3×D311yescharacteristic
183C3×C22⋊C4—22no—
184C3×C22⋊C4—21no—
185C3×C22⋊C4—21no—
186C3×C22⋊C4—181no—
187#217—61no—
188#214—62no—
189C4⋊Dic3—31no—
190Dic3⋊C4—61no—
191#208—62no—
192C2×C3⋊C8—31no—
193C2×C3⋊C8—31no—
194C22×C32—21no—
195C22×C32—21no—
196C22×C32—21no—
197C22×C32—41no—
198C22×C32—41no—
199C22×C32—41no—
200C22×C32C2×#6711yescharacteristic
201C32×C4—21no—
202C32×C4—41no—
203C32×C4D3×D411yescharacteristic
204C32×C4#23711yescharacteristic
205C3×Dic3—121no—
206C3×Dic3—121no—
207C22×C9—22no—
208C22×C9—21no—
209C22×C9—21no—
210C22×C9—21no—
211C22×C9—21no—
212C22×C9—41no—
213C22×C9—41no—
214C22×C9—42no—
215C22×C9—42no—
216C22×C9—42no—
217C22×C9—41no—
218C22×C9—41no—
219C22×C9—41no—
220C22×C9C2×C3×D411yescharacteristic
221C4×C9—21no—
222C4×C9—21no—
223C4×C9—21no—
224C4×C9—41no—
225C4×C9—42no—
226C4×C9—41no—
227C4×C9C2×C3×D411yescharacteristic
228C4×C9C3×#4111yescharacteristic
229Dic9—41no—
230Dic9—41no—
231C2×SD16—91no—
232C2×M16—91no—
233C22⋊Q8—91no—
234#121C3×D911yescharacteristic
235#107—91no—
236#103—91no—
237#102—91no—
238C3×C9#46811yescharacteristic, complemented, Sylow
239C23×C3—22no—
240C23×C3—21no—
241C23×C3—21no—
242C23×C3—21no—
243C23×C3#61111yescharacteristic
244C23×C3C3×#6711yescharacteristic
245C3×Q8—181no—
246C3×Q8—181no—
247C3×D4—21no—
248C3×D4—21no—
249C3×D4—21no—
250C3×D4—21no—
251C3×D4—41no—
252C3×D4—41no—
253C3×D4—42no—
254C3×D4—44no—
255C3×D4—42no—
256C2×C3×C4—21no—
257C2×C3×C4—21no—
258C2×C3×C4—21no—
259C2×C3×C4—21no—
260C2×C3×C4—22no—
261C2×C3×C4—21no—
262C2×C3×C4—21no—
263C2×C3×C4—21no—
264C2×C3×C4—21no—
265C2×C3×C4—41no—
266C2×C3×C4—41no—
267C2×C3×C4—181no—
268C2×C3×C4—181no—
269C2×C3×C4#61111yescharacteristic
270C2×C3×C4C22×D911yescharacteristic
271C2×C3×C4C3×#6711yescharacteristic
272C2×C3×C4C22×C3×D311yescharacteristic
273C2×Dic3—61no—
274C2×Dic3—61no—
275Dic6—61no—
276Dic6—61no—
277C3×C8—92no—
278C3×C8—181no—
279C3⋊C8—32no—
280C3⋊C8—61no—
281C2×C32—41no—
282C2×C32—81no—
283C2×C32#93211yescharacteristic
284C2×C32#93911yescharacteristic
285C2×C32#95111yescharacteristic
286C2×C9—21no—
287C2×C9—21no—
288C2×C9—21no—
289C2×C9—42no—
290C2×C9—41no—
291C2×C9—82no—
292C2×C9—81no—
293C2×C9C3×#12111yescharacteristic
294C2×C9C3×AGL(1,ℤ/8)11yescharacteristic
295C2×C9C3×#13711yescharacteristic
296C2×Q8—91no—
297C2×D4—21no—
298C2×D4C2×C3×D911yescharacteristic
299C22×C4C2×C3×D911yescharacteristic
300SD16—182no—
301M16—182no—
302C2×C8—91no—
303C2×C8—91no—
304C4⋊C4—91no—
305C4⋊C4—181no—
306C4⋊C4C2×C3×D911yescharacteristic
307C22⋊C4—21no—
308C22⋊C4—181no—
309C22×C3—22no—
310C22×C3—21no—
311C22×C3—21no—
312C22×C3—21no—
313C22×C3—21no—
314C22×C3—21no—
315C22×C3—21no—
316C22×C3—21no—
317C22×C3—41no—
318C22×C3—41no—
319C22×C3—42no—
320C22×C3—42no—
321C22×C3—42no—
322C22×C3—41no—
323C22×C3—41no—
324C22×C3—41no—
325C22×C3—41no—
326C22×C3—41no—
327C22×C3—41no—
328C22×C3C2×#61111yescharacteristic
329C22×C3C2×C3×#6711yescharacteristic
330C3×C4—21no—
331C3×C4—21no—
332C3×C4—21no—
333C3×C4—21no—
334C3×C4—41no—
335C3×C4—42no—
336C3×C4—41no—
337C3×C4—41no—
338C3×C4—361no—
339C3×C4—361no—
340C3×C4D4×D911yescharacteristic
341C3×C4#369911yescharacteristic
342C3×C4C3×D3×D411yescharacteristic
343C3×C4C3×#23711yescharacteristic
344Dic3—121no—
345Dic3—121no—
346C32#504211yescharacteristic
347C9—21no—
348C9C3×#46811yescharacteristic, complemented
349C23—21no—
350C23C3×#61111yescharacteristic
351Q8—181no—
352Q8—181no—
353D4—21no—
354D4—21no—
355D4—42no—
356C2×C4—21no—
357C2×C4—21no—
358C2×C4—21no—
359C2×C4—181no—
360C2×C4—181no—
361C2×C4C3×#61111yescharacteristic
362C2×C4C22×C3×D911yescharacteristic
363C8—92no—
364C8—181no—
365C2×C3—21no—
366C2×C3—21no—
367C2×C3—21no—
368C2×C3—42no—
369C2×C3—41no—
370C2×C3—41no—
371C2×C3—82no—
372C2×C3—81no—
373C2×C3—81no—
374C2×C3#6349511yescharacteristic
375C2×C3#6350111yescharacteristic
376C2×C3#6351111yescharacteristic
377C2×C3C3×#93211yescharacteristic
378C2×C3C3×#93911yescharacteristic
379C2×C3C3×#95111yescharacteristic
380C22—21no—
381C22—21no—
382C22—21no—
383C22—41no—
384C22—41no—
385C22—41no—
386C22C2×C3×#61111yescharacteristic
387C4—21no—
388C4—41no—
389C4—361no—
390C4—361no—
391C4C3×D4×D911yescharacteristic
392C4C3×#369911yescharacteristic
393C3—21no—
394C3#1058871811yescharacteristic, direct product factor
395C3C3×#504211yescharacteristic
396C2—41no—
397C2—81no—
398C2C3×#6349511yescharacteristic
399C2C3×#6350111yescharacteristic
400C2C3×#6351111yescharacteristic
subgroupG/H
centerC22×C3C2×#611
commutator, cosocleC2×C4×C9C23×C3
FrattiniC2×C3×C4C22×C3×D3
FittingC3×C9×#121C2
socleC22×C32C2×#67
prime radicalC32×#121D3
hypercenterC3×#121D9
hypocenterC9C3×#468
LCSG ▷ C2×C4×C9 ▷ C2×C9 ▷ C9
UCSC1 ◁ C22×C3 ◁ C22×C3×C4 ◁ C3×#121

Complements

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

NH ≅ G/Ntype
2. C2×C3×#3672C2semidirect
3. C3×#63486C2semidirect
4. C2×C3×#3667C2semidirect
5. C3×#63392C2semidirect
6. C3×#63368C2semidirect
7. C3×#63366C2semidirect
9. #10588718C3direct (N × H)
32. C2×#3672C2×C3semidirect
33. #63486C2×C3semidirect
34. C2×#3667C2×C3semidirect
35. #63392C2×C3semidirect
36. #63368C2×C3semidirect
37. #63366C2×C3semidirect
53. C3×C9⋊C8D4semidirect
156. C9⋊C8C3×D4semidirect
238. C3×C9#468semidirect
348. C9C3×#468semidirect
394. C3#10588718direct (N × H)

Maximal subgroups

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

subgroupindex
C3×C9×#1212
C2×C3×#36722
C3×#634862
C2×C3×#36672
C3×#633922
C3×#633682
C3×#633662
C3×#50423
#105887183