Finite Group Databasebeta

← C3×#10588467 #13141714

Subgroups — C3×#10588467 #13141714

Order 1728.

422 conjugacy classes of subgroups.

The subgroup lattice has 380 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#63498C211yesmaximal, characteristic, complemented
2C2×C3×#3673C211yesmaximal, characteristic
3C2×C3×#3664C211yesmaximal, characteristic, complemented
4C3×#63455C211yesmaximal, characteristic, complemented
5C3×C9×#102C211yesmaximal, characteristic, complemented
6C3×Dic9⋊C8C211yesmaximal, characteristic, complemented
7C3×#63368C211yesmaximal, characteristic, complemented
8C3×#4787—31nomaximal
9#10588467C311yesmaximal, characteristic, direct product factor
10C2×C3×D4×C9C2211yescharacteristic
11C2×C3×D36C2211yescharacteristic
12C2×C3×C4×D9—21no—
13C2×C3×Dic18C2211yescharacteristic
14C2×C3×C8×C9C2211yescharacteristic
15C3×C9×C4⋊C4C2211yescharacteristic
16C3×#3676—21no—
17C3×#3676—21no—
18C3×#3673—22no—
19C3×(C2×D9)⋊C4—21no—
20C3×C4×Dic9C2211yescharacteristic
21C2×C3×C9⋊C8C2211yescharacteristic
22C3×#3664—22no—
23C3×#936—31no—
24C2×C3×#213—31no—
25C2×C3×#204—31no—
26C3×#893—31no—
27C32×#102D311yescharacteristic
28C3×Dic3⋊C8—31no—
29C3×#810—31no—
30#63498C2×C311yescharacteristic, complemented
31C2×#3673C2×C311yescharacteristic
32C2×#3664C2×C311yescharacteristic, complemented
33#63455C2×C311yescharacteristic, complemented
34C9×#102—21no—
35C9×#102C2×C311yescharacteristic, complemented
36Dic9⋊C8C2×C311yescharacteristic, complemented
37#63368C2×C311yescharacteristic, complemented
38C23×C3×C9—21no—
39C22×C3×D9—21no—
40C3×D4×C9—21no—
41C3×D4×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×D36D412yes—
49C3×C4×D9—42no—
50C3×Dic18—21no—
51C3×Dic18—21no—
52C3×C8×C9—21no—
53C3×C9⋊C8—21no—
54C3×#463—91no—
55#4787—31no—
56C2×C32×D4C2×D311yescharacteristic
57C2×C3×D12—31no—
58C2×C3×C4×D3—61no—
59C2×C3×Dic6—31no—
60C2×C32×C8C2×D311yescharacteristic
61C32×C4⋊C4C2×D311yescharacteristic
62C3×#217—61no—
63C3×#217—61no—
64C3×#213—62no—
65C3×(C2×D3)⋊C4—61no—
66C3×C4×Dic3—31no—
67C2×C3×C3⋊C8—31no—
68C3×#204—62no—
69C2×D4×C9—21no—
70C2×D4×C9C22×C311yescharacteristic
71C2×D36C22×C311yescharacteristic
72C2×C4×D9—21no—
73C2×Dic18C22×C311yescharacteristic
74C2×C8×C9—21no—
75C2×C8×C9C22×C311yescharacteristic
76C9×C4⋊C4—21no—
77C9×C4⋊C4C22×C311yescharacteristic
78#3676—21no—
79#3676—21no—
80#3673—22no—
81(C2×D9)⋊C4—21no—
82C4×Dic9C22×C311yescharacteristic
83C2×C9⋊C8C22×C311yescharacteristic
84#3664—22no—
85C22×C3×C9—41no—
86C22×C3×C9—41no—
87C22×C3×C9—41no—
88C22×C3×C9C2×D411yescharacteristic
89C2×C3×D9—22no—
90C2×C3×D9—41no—
91C2×C3×D9—41no—
92C3×C4×C9—41no—
93C3×C4×C9C2×D411yescharacteristic
94C3×C4×C9#4111yescharacteristic
95C3×Dic9—21no—
96C3×Dic9—21no—
97C3×Dic9—41no—
98C2×C3×SD16—91no—
99C2×C3×D8—91no—
100C3×#124—91no—
101C3×C4×D4—91no—
102#936—31no—
103C2×#213—31no—
104C2×#204—31no—
105#893—31no—
106C3×C4⋊C8—91no—
107C3×#103—91no—
108C3×#102—21no—
109C3×#102D911yescharacteristic, complemented
110C3×#102C3×D311yescharacteristic
111Dic3⋊C8—31no—
112#810—31no—
113C23×C32—21no—
114C22×C3×D3—61no—
115C32×D4—21no—
116C32×D4—21no—
117C2×C32×C4—21no—
118C2×C32×C4C22×D311yescharacteristic
119C2×C3×Dic3—31no—
120C2×C3×Dic3—31no—
121C2×C3×Dic3—61no—
122C3×D12—32no—
123C3×D12—61no—
124C3×C4×D3—122no—
125C3×Dic6—61no—
126C3×Dic6—61no—
127C23×C9—21no—
128C23×C9—41no—
129C22×D9—21no—
130C32×C8—21no—
131C3×C3⋊C8—61no—
132D4×C9—22no—
133D4×C9—21no—
134D4×C9—21no—
135D4×C9—41no—
136C2×C4×C9—21no—
137C2×C4×C9—21no—
138C2×C4×C9—41no—
139C2×C4×C9C23×C311yescharacteristic
140C2×Dic9—21no—
141C2×Dic9C3×D411yescharacteristic
142C2×Dic9C3×D411yescharacteristic
143D36—21no—
144D36C3×D412yes—
145C4×D9—42no—
146Dic18—21no—
147Dic18—21no—
148C8×C9—21no—
149C8×C9—41no—
150C9⋊C8—21no—
151#463—91noSylow
152C2×C3×C9—81no—
153C2×C3×C9#12111yescharacteristic
154C2×C3×C9#13511yescharacteristic
155C2×C3×C9AGL(1,ℤ/8)11yescharacteristic
156C3×D9—42no—
157C2×C3×Q8—91no—
158C2×C3×D4—21no—
159C2×C3×D4—91no—
160C2×C3×D4C2×D911yescharacteristic
161C2×C3×D4C2×C3×D311yescharacteristic
162C22×C3×C4—181no—
163C2×D12—31no—
164C2×C4×D3—61no—
165C2×Dic6—31no—
166C3×SD16—182no—
167C3×D8—182no—
168C2×C3×C8—21no—
169C2×C3×C8—91no—
170C2×C3×C8C2×D911yescharacteristic
171C2×C3×C8C2×C3×D311yescharacteristic
172C3×C4⋊C4—21no—
173C3×C4⋊C4C2×D911yescharacteristic
174C3×C4⋊C4C2×C3×D311yescharacteristic
175C3×C22⋊C4—181no—
176C3×C22⋊C4—181no—
177C3×C22⋊C4—181no—
178C3×C42—91no—
179#217—61no—
180#217—61no—
181#213—62no—
182(C2×D3)⋊C4—61no—
183C4×Dic3—31no—
184C2×C3⋊C8—31no—
185#204—62no—
186C22×C32—41no—
187C22×C32—41no—
188C22×C32—41no—
189C22×C32D3×D411yescharacteristic
190C2×C3×D3—62no—
191C2×C3×D3—121no—
192C2×C3×D3—121no—
193C32×C4—41no—
194C32×C4#23511yescharacteristic
195C32×C4D3×D411yescharacteristic
196C3×Dic3—61no—
197C3×Dic3—61no—
198C3×Dic3—121no—
199C22×C9—21no—
200C22×C9—42no—
201C22×C9—41no—
202C22×C9—41no—
203C22×C9—41no—
204C22×C9—81no—
205C22×C9—81no—
206C22×C9C2×C3×D411yescharacteristic
207C2×D9—22no—
208C2×D9—41no—
209C2×D9—41no—
210C4×C9—21no—
211C4×C9—21no—
212C4×C9—41no—
213C4×C9—81no—
214C4×C9C2×C3×D411yescharacteristic
215C4×C9C3×#4111yescharacteristic
216Dic9—21no—
217Dic9—21no—
218Dic9—41no—
219C2×SD16—91no—
220C2×D8—91no—
221#124—91no—
222C4×D4—91no—
223C4⋊C8—91no—
224#103—91no—
225#102C3×D911yescharacteristic, complemented
226C3×C9#46311yescharacteristic, complemented, Sylow
227C23×C3—21no—
228C23×C3—21no—
229C23×C3—41no—
230C23×C3—181no—
231C22×D3—61no—
232C3×Q8—181no—
233C3×Q8—181no—
234C3×D4—22no—
235C3×D4—21no—
236C3×D4—21no—
237C3×D4—21no—
238C3×D4—21no—
239C3×D4—41no—
240C3×D4—92no—
241C3×D4—181no—
242C2×C3×C4—21no—
243C2×C3×C4—21no—
244C2×C3×C4—21no—
245C2×C3×C4—41no—
246C2×C3×C4—91no—
247C2×C3×C4—91no—
248C2×C3×C4—181no—
249C2×C3×C4—362no—
250C2×C3×C4C22×D911yescharacteristic
251C2×C3×C4C22×C3×D311yescharacteristic
252C2×Dic3—31no—
253C2×Dic3—31no—
254C2×Dic3—61no—
255D12—32no—
256D12—61no—
257C4×D3—122no—
258Dic6—61no—
259Dic6—61no—
260C3×C8—21no—
261C3×C8—21no—
262C3×C8—41no—
263C3×C8—181no—
264C3⋊C8—61no—
265C2×C32—81no—
266C2×C32#88411yescharacteristic
267C2×C32#91111yescharacteristic
268C2×C32#91611yescharacteristic
269C3×D3—122no—
270C2×C9—21no—
271C2×C9—21no—
272C2×C9—21no—
273C2×C9—82no—
274C2×C9—81no—
275C2×C9C3×#12111yescharacteristic
276C2×C9C3×#13511yescharacteristic
277C2×C9C3×AGL(1,ℤ/8)11yescharacteristic
278D9—42no—
279C2×Q8—91no—
280C2×D4—91no—
281C2×D4C2×C3×D911yescharacteristic
282C22×C4—181no—
283SD16—182no—
284D8—182no—
285C2×C8—91no—
286C2×C8C2×C3×D911yescharacteristic
287C4⋊C4C2×C3×D911yescharacteristic
288C22⋊C4—181no—
289C22⋊C4—181no—
290C22⋊C4—181no—
291C42—91no—
292C22×C3—21no—
293C22×C3—42no—
294C22×C3—41no—
295C22×C3—41no—
296C22×C3—41no—
297C22×C3—41no—
298C22×C3—41no—
299C22×C3—41no—
300C22×C3—81no—
301C22×C3—81no—
302C22×C3—182no—
303C22×C3—361no—
304C22×C3—361no—
305C22×C3D4×D911yescharacteristic
306C22×C3C3×D3×D411yescharacteristic
307C2×D3—62no—
308C2×D3—121no—
309C2×D3—121no—
310C3×C4—21no—
311C3×C4—21no—
312C3×C4—41no—
313C3×C4—41no—
314C3×C4—81no—
315C3×C4—181no—
316C3×C4—181no—
317C3×C4—361no—
318C3×C4#369711yescharacteristic
319C3×C4D4×D911yescharacteristic
320C3×C4C3×#23511yescharacteristic
321C3×C4C3×D3×D411yescharacteristic
322Dic3—61no—
323Dic3—61no—
324Dic3—121no—
325C32#478711yescharacteristic
326C9—21no—
327C9C3×#46311yescharacteristic, complemented
328C23—21no—
329C23—181no—
330Q8—181no—
331Q8—181no—
332D4—21no—
333D4—21no—
334D4—92no—
335D4—181no—
336C2×C4—21no—
337C2×C4—91no—
338C2×C4—91no—
339C2×C4—181no—
340C2×C4—362no—
341C2×C4C22×C3×D911yescharacteristic
342C8—21no—
343C8—181no—
344C2×C3—21no—
345C2×C3—21no—
346C2×C3—21no—
347C2×C3—82no—
348C2×C3—81no—
349C2×C3—81no—
350C2×C3—362no—
351C2×C3#6344611yescharacteristic
352C2×C3#6347311yescharacteristic
353C2×C3#6347811yescharacteristic
354C2×C3C3×#88411yescharacteristic
355C2×C3C3×#91111yescharacteristic
356C2×C3C3×#91611yescharacteristic
357D3—122no—
358C22—41no—
359C22—41no—
360C22—41no—
361C22—182no—
362C22—361no—
363C22—361no—
364C22C3×D4×D911yescharacteristic
365C4—41no—
366C4—181no—
367C4—181no—
368C4—361no—
369C4C3×#369711yescharacteristic
370C4C3×D4×D911yescharacteristic
371C3—21no—
372C3#1058846711yescharacteristic, direct product factor
373C3C3×#478711yescharacteristic
374C2—81no—
375C2—362no—
376C2C3×#6344611yescharacteristic
377C2C3×#6347311yescharacteristic
378C2C3×#6347811yescharacteristic
subgroupG/H
centerC22×C3D4×D9
commutator, cosocleC2×C4×C9C23×C3
FrattiniC2×C3×C4C22×C3×D3
FittingC3×C9×#102C2
socleC22×C32D3×D4
prime radicalC2×C3×#3673C2
hypercenterC3×#102D9
hypocenterC9C3×#463
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
1. C3×#63498C2semidirect
3. C2×C3×#3664C2semidirect
4. C3×#63455C2semidirect
5. C3×C9×#102C2semidirect
6. C3×Dic9⋊C8C2semidirect
7. C3×#63368C2semidirect
9. #10588467C3direct (N × H)
30. #63498C2×C3semidirect
32. C2×#3664C2×C3semidirect
33. #63455C2×C3semidirect
35. C9×#102C2×C3semidirect
36. Dic9⋊C8C2×C3semidirect
37. #63368C2×C3semidirect
109. C3×#102D9semidirect
225. #102C3×D9semidirect
226. C3×C9#463semidirect
327. C9C3×#463semidirect
372. C3#10588467direct (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×#36732
C2×C3×#36642
C3×#634552
C3×C9×#1022
C3×Dic9⋊C82
C3×#633682
C3×#47873
#105884673