Finite Group Databasebeta

← C3×#10588488 #13141878

Subgroups — C3×#10588488 #13141878

Order 1728.

498 conjugacy classes of subgroups.

The subgroup lattice has 404 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#3701C211yesmaximal, characteristic
2C2×C3×#3674C211yesmaximal, characteristic, complemented
3C2×C3×#3664C211yesmaximal, characteristic, complemented
4C3×#63459C211yesmaximal, characteristic, complemented
5C3×C9×#103C211yesmaximal, characteristic, complemented
6C3×(C2×D9)⋊C8C211yesmaximal, characteristic, complemented
7C3×#63369C211yesmaximal, characteristic, complemented
8C3×#4808—31nomaximal
9#10588488C311yesmaximal, characteristic, direct product factor
10C2×C3×Q8×C9C2211yescharacteristic
11C3×#3701—22no—
12C3×#3701—22no—
13C2×C3×D36—21no—
14C2×C3×D36C2211yescharacteristic
15C2×C3×C4×D9—21no—
16C2×C3×C4×D9C2211yescharacteristic
17C2×C3×Dic18C2211yescharacteristic
18C2×C3×C8×C9C2211yescharacteristic
19C3×C9×C4⋊C4C2211yescharacteristic
20C3×#3674—22no—
21C3×(C2×D9)⋊C4—21no—
22C3×C4⋊Dic9—21no—
23C2×C3×C9⋊C8C2211yescharacteristic
24C3×#3664—22no—
25C2×C3×#239—31no—
26C2×C3×#216—31no—
27C2×C3×#204—31no—
28C3×#897—31no—
29C2×#3701C2×C311yescharacteristic
30C32×#103D311yescharacteristic
31C3×(C2×D3)⋊C8—31no—
32C3×#809—31no—
33C2×#3674C2×C311yescharacteristic, complemented
34C2×#3664C2×C311yescharacteristic, complemented
35#63459C2×C311yescharacteristic, complemented
36C9×#103—21no—
37C9×#103C2×C311yescharacteristic, complemented
38(C2×D9)⋊C8C2×C311yescharacteristic, complemented
39#63369C2×C311yescharacteristic, complemented
40C22×C3×D9—21no—
41C22×C3×D9D411yescharacteristic
42C3×Q8×C9—21no—
43C3×Q8×C9D412yes—
44C2×C3×C4×C9—21no—
45C2×C3×C4×C9—21no—
46C2×C3×C4×C9C2311yescharacteristic
47C2×C3×Dic9—21no—
48C2×C3×Dic9D411yescharacteristic
49C3×D36—24no—
50C3×D36—21no—
51C3×D36D412yes—
52C3×C4×D9—24no—
53C3×C4×D9—21no—
54C3×C4×D9—21no—
55C3×Dic18—21no—
56C3×Dic18—21no—
57C3×C8×C9—21no—
58C3×C9⋊C8—21no—
59C3×#452—91no—
60#4808—31no—
61C2×C32×Q8C2×D311yescharacteristic
62C3×#239—62no—
63C3×#239—62no—
64C2×C3×D12—31no—
65C2×C3×D12—61no—
66C2×C3×C4×D3—31no—
67C2×C3×C4×D3—61no—
68C2×C3×Dic6—31no—
69C2×C32×C8C2×D311yescharacteristic
70C32×C4⋊C4C2×D311yescharacteristic
71C3×#216—62no—
72C3×(C2×D3)⋊C4—61no—
73C3×C4⋊Dic3—61no—
74C2×C3×C3⋊C8—31no—
75C3×#204—62no—
76C2×Q8×C9—21no—
77C2×Q8×C9C22×C311yescharacteristic
78#3701—22no—
79#3701—22no—
80C2×D36—21no—
81C2×D36C22×C311yescharacteristic
82C2×C4×D9—21no—
83C2×C4×D9C22×C311yescharacteristic
84C2×Dic18C22×C311yescharacteristic
85C2×C8×C9—21no—
86C2×C8×C9C22×C311yescharacteristic
87C9×C4⋊C4—21no—
88C9×C4⋊C4C22×C311yescharacteristic
89#3674—22no—
90(C2×D9)⋊C4—21no—
91C4⋊Dic9—21no—
92C2×C9⋊C8C22×C311yescharacteristic
93#3664—22no—
94C22×C3×C9C2×D411yescharacteristic
95C2×C3×D9—21no—
96C2×C3×D9—22no—
97C2×C3×D9—21no—
98C2×C3×D9—21no—
99C2×C3×D9—41no—
100C2×C3×D9—41no—
101C3×C4×C9—22no—
102C3×C4×C9—41no—
103C3×C4×C9C2×D411yescharacteristic
104C3×C4×C9C2×D411yescharacteristic
105C3×Dic9—21no—
106C3×Dic9—41no—
107C2×C3×#41—91no—
108C2×#239—31no—
109C2×C3×Q16—91no—
110C2×C3×SD16—91no—
111C3×C22⋊Q8—91no—
112C2×#216—31no—
113C2×#204—31no—
114#897—31no—
115C3×#103—21no—
116C3×#103D911yescharacteristic, complemented
117C3×#103C3×D311yescharacteristic
118C3×#102—91no—
119C3×C22⋊C8—91no—
120(C2×D3)⋊C8—31no—
121#809—31no—
122C22×C3×D3—31no—
123C22×C3×D3—61no—
124C32×Q8—21no—
125C32×Q8D1212yes—
126C2×C32×C4—21no—
127C2×C32×C4—21no—
128C2×C32×C4C22×D311yescharacteristic
129C2×C3×Dic3—31no—
130C2×C3×Dic3—61no—
131C3×D12—32no—
132C3×D12—64no—
133C3×D12—61no—
134C3×C4×D3—64no—
135C3×C4×D3—61no—
136C3×C4×D3—61no—
137C3×Dic6—61no—
138C3×Dic6—61no—
139C22×D9—21no—
140C22×D9C3×D411yescharacteristic
141C32×C8—21no—
142C3×C3⋊C8—61no—
143Q8×C9—21no—
144Q8×C9—22no—
145Q8×C9—41no—
146Q8×C9C3×D412yes—
147C2×C4×C9—21no—
148C2×C4×C9—21no—
149C2×C4×C9—21no—
150C2×C4×C9—41no—
151C2×C4×C9—41no—
152C2×C4×C9C23×C311yescharacteristic
153C2×Dic9—21no—
154C2×Dic9C3×D411yescharacteristic
155D36—24no—
156D36—21no—
157D36C3×D412yes—
158C4×D9—24no—
159C4×D9—21no—
160C4×D9—21no—
161Dic18—21no—
162Dic18—21no—
163C8×C9—21no—
164C8×C9—41no—
165C9⋊C8—21no—
166#452—91noSylow
167C2×C3×C9#12011yescharacteristic
168C2×C3×C9#13511yescharacteristic
169C2×C3×C9#13711yescharacteristic
170C3×D9—41no—
171C3×D9—42no—
172C3×#41—182no—
173C3×#41—182no—
174C2×C3×Q8—21no—
175C2×C3×Q8—91no—
176C2×C3×Q8C2×D911yescharacteristic
177C2×C3×Q8C2×C3×D311yescharacteristic
178C2×C3×D4—91no—
179C2×C3×D4—181no—
180C22×C3×C4—91no—
181C22×C3×C4—181no—
182#239—62no—
183#239—62no—
184C2×D12—31no—
185C2×D12—61no—
186C2×C4×D3—31no—
187C2×C4×D3—61no—
188C2×Dic6—31no—
189C3×Q16—182no—
190C3×SD16—182no—
191C2×C3×C8—21no—
192C2×C3×C8—91no—
193C2×C3×C8C2×D911yescharacteristic
194C2×C3×C8C2×C3×D311yescharacteristic
195C3×C4⋊C4—21no—
196C3×C4⋊C4—181no—
197C3×C4⋊C4C2×D911yescharacteristic
198C3×C4⋊C4C2×C3×D311yescharacteristic
199C3×C22⋊C4—181no—
200#216—62no—
201(C2×D3)⋊C4—61no—
202C4⋊Dic3—61no—
203C2×C3⋊C8—31no—
204#204—62no—
205C22×C32D3×D411yescharacteristic
206C2×C3×D3—62no—
207C2×C3×D3—61no—
208C2×C3×D3—61no—
209C2×C3×D3—61no—
210C2×C3×D3—121no—
211C2×C3×D3—121no—
212C32×C4—22no—
213C32×C4—41no—
214C32×C4C2×D1211yescharacteristic
215C32×C4D3×D411yescharacteristic
216C3×Dic3—61no—
217C3×Dic3—121no—
218C22×C9—21no—
219C22×C9C2×C3×D411yescharacteristic
220C2×D9—21no—
221C2×D9—22no—
222C2×D9—21no—
223C2×D9—21no—
224C2×D9—41no—
225C2×D9—41no—
226C4×C9—22no—
227C4×C9—21no—
228C4×C9—21no—
229C4×C9—42no—
230C4×C9—41no—
231C4×C9—81no—
232C4×C9C2×C3×D411yescharacteristic
233C4×C9C2×C3×D411yescharacteristic
234Dic9—21no—
235Dic9—41no—
236C2×#41—91no—
237C2×Q16—91no—
238C2×SD16—91no—
239C22⋊Q8—91no—
240#103C3×D911yescharacteristic, complemented
241#102—91no—
242C22⋊C8—91no—
243C3×C9#45211yescharacteristic, complemented, Sylow
244C23×C3—91no—
245C23×C3—181no—
246C22×D3—31no—
247C22×D3—61no—
248C3×Q8—21no—
249C3×Q8—21no—
250C3×Q8—22no—
251C3×Q8—41no—
252C3×Q8—181no—
253C3×Q8—181no—
254C3×Q8D3612yes—
255C3×Q8C3×D1212yes—
256C3×D4—92no—
257C3×D4—184no—
258C3×D4—181no—
259C2×C3×C4—21no—
260C2×C3×C4—21no—
261C2×C3×C4—21no—
262C2×C3×C4—21no—
263C2×C3×C4—21no—
264C2×C3×C4—41no—
265C2×C3×C4—41no—
266C2×C3×C4—91no—
267C2×C3×C4—184no—
268C2×C3×C4—181no—
269C2×C3×C4—181no—
270C2×C3×C4—181no—
271C2×C3×C4C22×D911yescharacteristic
272C2×C3×C4C22×C3×D311yescharacteristic
273C2×Dic3—31no—
274C2×Dic3—61no—
275D12—32no—
276D12—64no—
277D12—61no—
278C4×D3—64no—
279C4×D3—61no—
280C4×D3—61no—
281Dic6—61no—
282Dic6—61no—
283C3×C8—21no—
284C3×C8—21no—
285C3×C8—41no—
286C3×C8—181no—
287C3⋊C8—61no—
288C2×C32#88211yescharacteristic
289C2×C32#91611yescharacteristic
290C2×C32#91811yescharacteristic
291C3×D3—121no—
292C3×D3—122no—
293C2×C9—21no—
294C2×C9—21no—
295C2×C9—21no—
296C2×C9C3×#12011yescharacteristic
297C2×C9C3×#13511yescharacteristic
298C2×C9C3×#13711yescharacteristic
299D9—41no—
300D9—42no—
301#41—182no—
302#41—182no—
303C2×Q8—91no—
304C2×Q8C2×C3×D911yescharacteristic
305C2×D4—91no—
306C2×D4—181no—
307C22×C4—91no—
308C22×C4—181no—
309Q16—182no—
310SD16—182no—
311C2×C8—91no—
312C2×C8C2×C3×D911yescharacteristic
313C4⋊C4—181no—
314C4⋊C4C2×C3×D911yescharacteristic
315C22⋊C4—181no—
316C22×C3—21no—
317C22×C3—182no—
318C22×C3—181no—
319C22×C3—181no—
320C22×C3—181no—
321C22×C3—361no—
322C22×C3—361no—
323C22×C3D4×D911yescharacteristic
324C22×C3C3×D3×D411yescharacteristic
325C2×D3—62no—
326C2×D3—61no—
327C2×D3—61no—
328C2×D3—61no—
329C2×D3—121no—
330C2×D3—121no—
331C3×C4—22no—
332C3×C4—22no—
333C3×C4—21no—
334C3×C4—21no—
335C3×C4—42no—
336C3×C4—41no—
337C3×C4—41no—
338C3×C4—81no—
339C3×C4—181no—
340C3×C4—361no—
341C3×C4C2×D3611yescharacteristic
342C3×C4D4×D911yescharacteristic
343C3×C4C2×C3×D1211yescharacteristic
344C3×C4C3×D3×D411yescharacteristic
345Dic3—61no—
346Dic3—121no—
347C32#480811yescharacteristic
348C9—21no—
349C9C3×#45211yescharacteristic, complemented
350C23—91no—
351C23—181no—
352Q8—21no—
353Q8—181no—
354Q8—181no—
355Q8C3×D3612yes—
356D4—92no—
357D4—184no—
358D4—181no—
359C2×C4—21no—
360C2×C4—21no—
361C2×C4—91no—
362C2×C4—184no—
363C2×C4—181no—
364C2×C4—181no—
365C2×C4—181no—
366C2×C4C22×C3×D911yescharacteristic
367C8—21no—
368C8—181no—
369C2×C3—21no—
370C2×C3—21no—
371C2×C3—21no—
372C2×C3—361no—
373C2×C3—362no—
374C2×C3#6344411yescharacteristic
375C2×C3#6347811yescharacteristic
376C2×C3#6348011yescharacteristic
377C2×C3C3×#88211yescharacteristic
378C2×C3C3×#91611yescharacteristic
379C2×C3C3×#91811yescharacteristic
380D3—121no—
381D3—122no—
382C22—181no—
383C22—181no—
384C22—182no—
385C22—181no—
386C22—361no—
387C22—361no—
388C22C3×D4×D911yescharacteristic
389C4—22no—
390C4—41no—
391C4—181no—
392C4—361no—
393C4C2×C3×D3611yescharacteristic
394C4C3×D4×D911yescharacteristic
395C3—21no—
396C3#1058848811yescharacteristic, direct product factor
397C3C3×#480811yescharacteristic
398C2—361no—
399C2—362no—
400C2C3×#6344411yescharacteristic
401C2C3×#6347811yescharacteristic
402C2C3×#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×#3701C2
hypercenterC3×#103D9
hypocenterC9C3×#452
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
3. C2×C3×#3664C2semidirect
4. C3×#63459C2semidirect
5. C3×C9×#103C2semidirect
6. C3×(C2×D9)⋊C8C2semidirect
7. C3×#63369C2semidirect
9. #10588488C3direct (N × H)
33. C2×#3674C2×C3semidirect
34. C2×#3664C2×C3semidirect
35. #63459C2×C3semidirect
37. C9×#103C2×C3semidirect
38. (C2×D9)⋊C8C2×C3semidirect
39. #63369C2×C3semidirect
116. C3×#103D9semidirect
240. #103C3×D9semidirect
243. C3×C9#452semidirect
349. C9C3×#452semidirect
396. C3#10588488direct (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×#36742
C2×C3×#36642
C3×#634592
C3×C9×#1032
C3×(C2×D9)⋊C82
C3×#633692
C3×#48083
#105884883