Finite Group Databasebeta

← C3×#10588492 #13141871

Subgroups — C3×#10588492 #13141871

Order 1728.

402 conjugacy classes of subgroups.

The subgroup lattice has 374 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#63508C211yesmaximal, characteristic, complemented
2C2×C3×#3675C211yesmaximal, characteristic, complemented
3C2×C3×#3663C211yesmaximal, characteristic, complemented
4C3×#63457C211yesmaximal, characteristic
5C3×C9×#103C211yesmaximal, characteristic, complemented
6C3×#63380C211yesmaximal, characteristic, complemented
7C3×#63366C211yesmaximal, characteristic, complemented
8C3×#4812—31nomaximal
9#10588492C311yesmaximal, characteristic, direct product factor
10C2×C3×Q8×C9C2211yescharacteristic
11C2×C3×D36—21no—
12C2×C3×D36C2211yescharacteristic
13C2×C3×C4×D9C2211yescharacteristic
14C2×C3×C8×C9C2211yescharacteristic
15C3×C9×C4⋊C4C2211yescharacteristic
16C3×#3675—22no—
17C3×(C2×D9)⋊C4—21no—
18C3×(C2×D9)⋊C4—21no—
19C3×C4⋊Dic9C2211yescharacteristic
20C3×Dic9⋊C4—21no—
21C2×C3×C9⋊C8C2211yescharacteristic
22C3×#3663—22no—
23C3×#946—31no—
24C2×C3×#215—31no—
25C2×C3×ΓL(1,𝔽25)—31no—
26C3×#895—31no—
27C32×#103D311yescharacteristic
28C3×#821—31no—
29C3×#807—31no—
30#63508C2×C311yescharacteristic, complemented
31C2×#3675C2×C311yescharacteristic, complemented
32C2×#3663C2×C311yescharacteristic, complemented
33#63457C2×C311yescharacteristic
34C9×#103—21no—
35C9×#103C2×C311yescharacteristic, complemented
36#63380C2×C311yescharacteristic, complemented
37#63366C2×C311yescharacteristic, complemented
38C22×C3×D9—21no—
39C22×C3×D9D411yescharacteristic
40C3×Q8×C9—21no—
41C3×Q8×C9—21no—
42C2×C3×C4×C9—21no—
43C2×C3×C4×C9—21no—
44C2×C3×C4×C9C2311yescharacteristic
45C2×C3×Dic9—21no—
46C2×C3×Dic9D411yescharacteristic
47C3×D36—21no—
48C3×D36—21no—
49C3×D36—42no—
50C3×C4×D9—21no—
51C3×C4×D9—21no—
52C3×C8×C9—21no—
53C3×C9⋊C8D412yescomplemented
54C3×#468—91no—
55#4812—31no—
56C2×C32×Q8C2×D311yescharacteristic
57C2×C3×D12—31no—
58C2×C3×D12—61no—
59C2×C3×C4×D3—31no—
60C2×C32×C8C2×D311yescharacteristic
61C32×C4⋊C4C2×D311yescharacteristic
62C3×#215—62no—
63C3×(C2×D3)⋊C4—61no—
64C3×(C2×D3)⋊C4—61no—
65C3×C4⋊Dic3—31no—
66C3×Dic3⋊C4—61no—
67C2×C3×C3⋊C8—31no—
68C3×ΓL(1,𝔽25)—62no—
69C2×Q8×C9—21no—
70C2×Q8×C9C22×C311yescharacteristic
71C2×D36—21no—
72C2×D36C22×C311yescharacteristic
73C2×C4×D9C22×C311yescharacteristic
74C2×C8×C9—21no—
75C2×C8×C9C22×C311yescharacteristic
76C9×C4⋊C4—21no—
77C9×C4⋊C4C22×C311yescharacteristic
78#3675—22no—
79(C2×D9)⋊C4—21no—
80(C2×D9)⋊C4—21no—
81C4⋊Dic9C22×C311yescharacteristic
82Dic9⋊C4—21no—
83C2×C9⋊C8C22×C311yescharacteristic
84#3663—22no—
85C22×C3×C9C2×D411yescharacteristic
86C2×C3×D9—21no—
87C2×C3×D9—21no—
88C2×C3×D9—21no—
89C2×C3×D9—41no—
90C2×C3×D9—41no—
91C2×C3×D9—41no—
92C3×C4×C9—41no—
93C3×C4×C9—41no—
94C3×C4×C9C2×D411yescharacteristic
95C3×C4×C9#4111yescharacteristic
96C3×Dic9—21no—
97C3×Dic9—41no—
98C2×C3×SD16—91no—
99C2×C3×M16—91no—
100C3×C22⋊Q8—91no—
101C3×#121—91no—
102#946—31no—
103C2×#215—31no—
104C2×ΓL(1,𝔽25)—31no—
105#895—31no—
106C3×#107—91no—
107C3×#103—21no—
108C3×#103D911yescharacteristic, complemented
109C3×#103C3×D311yescharacteristic
110C3×#102—91no—
111#821—31no—
112#807—31no—
113C22×C3×D3—31no—
114C22×C3×D3—61no—
115C32×Q8—21no—
116C32×Q8—21no—
117C2×C32×C4—21no—
118C2×C32×C4—21no—
119C2×C32×C4C22×D311yescharacteristic
120C2×C3×Dic3—31no—
121C2×C3×Dic3—61no—
122C3×D12—61no—
123C3×D12—61no—
124C3×D12—122no—
125C3×C4×D3—61no—
126C3×C4×D3—61no—
127C22×D9—21no—
128C22×D9C3×D411yescharacteristic
129C32×C8—21no—
130C3×C3⋊C8—32no—
131Q8×C9—22no—
132Q8×C9—21no—
133Q8×C9—21no—
134Q8×C9—41no—
135C2×C4×C9—21no—
136C2×C4×C9—21no—
137C2×C4×C9—21no—
138C2×C4×C9—41no—
139C2×C4×C9—41no—
140C2×C4×C9C23×C311yescharacteristic
141C2×Dic9—21no—
142C2×Dic9C3×D411yescharacteristic
143D36—21no—
144D36—21no—
145D36—42no—
146C4×D9—21no—
147C4×D9—21no—
148C8×C9—21no—
149C8×C9—41no—
150C9⋊C8C3×D412yescomplemented
151#468—91noSylow
152C2×C3×C9#12111yescharacteristic
153C2×C3×C9AGL(1,ℤ/8)11yescharacteristic
154C2×C3×C9#13711yescharacteristic
155C3×D9—41no—
156C3×D9—81no—
157C2×C3×Q8—21no—
158C2×C3×Q8C2×D911yescharacteristic
159C2×C3×Q8C2×C3×D311yescharacteristic
160C2×C3×D4—91no—
161C2×C3×D4—181no—
162C22×C3×C4—91no—
163C2×D12—31no—
164C2×D12—61no—
165C2×C4×D3—31no—
166C3×SD16—182no—
167C3×M16—182no—
168C2×C3×C8—21no—
169C2×C3×C8—91no—
170C2×C3×C8C2×D911yescharacteristic
171C2×C3×C8C2×C3×D311yescharacteristic
172C3×C4⋊C4—21no—
173C3×C4⋊C4—91no—
174C3×C4⋊C4—181no—
175C3×C4⋊C4C2×D911yescharacteristic
176C3×C4⋊C4C2×C3×D311yescharacteristic
177C3×C22⋊C4—181no—
178C3×C22⋊C4—181no—
179#215—62no—
180(C2×D3)⋊C4—61no—
181(C2×D3)⋊C4—61no—
182C4⋊Dic3—31no—
183Dic3⋊C4—61no—
184C2×C3⋊C8—31no—
185ΓL(1,𝔽25)—62no—
186C22×C32D3×D411yescharacteristic
187C2×C3×D3—61no—
188C2×C3×D3—61no—
189C2×C3×D3—61no—
190C2×C3×D3—121no—
191C2×C3×D3—121no—
192C2×C3×D3—121no—
193C32×C4—41no—
194C32×C4—41no—
195C32×C4#23511yescharacteristic
196C32×C4D3×D411yescharacteristic
197C3×Dic3—61no—
198C3×Dic3—121no—
199C22×C9—21no—
200C22×C9C2×C3×D411yescharacteristic
201C2×D9—21no—
202C2×D9—21no—
203C2×D9—21no—
204C2×D9—41no—
205C2×D9—41no—
206C2×D9—41no—
207C4×C9—21no—
208C4×C9—21no—
209C4×C9—42no—
210C4×C9—41no—
211C4×C9—41no—
212C4×C9—81no—
213C4×C9C2×C3×D411yescharacteristic
214C4×C9C3×#4111yescharacteristic
215Dic9—21no—
216Dic9—41no—
217C2×SD16—91no—
218C2×M16—91no—
219C22⋊Q8—91no—
220#121—91no—
221#107—91no—
222#103C3×D911yescharacteristic, complemented
223#102—91no—
224C3×C9#46811yescharacteristic, complemented, Sylow
225C23×C3—91no—
226C23×C3—181no—
227C22×D3—31no—
228C22×D3—61no—
229C3×Q8—22no—
230C3×Q8—21no—
231C3×Q8—21no—
232C3×Q8—21no—
233C3×Q8—21no—
234C3×Q8—41no—
235C3×D4—181no—
236C3×D4—181no—
237C3×D4—362no—
238C2×C3×C4—21no—
239C2×C3×C4—21no—
240C2×C3×C4—21no—
241C2×C3×C4—21no—
242C2×C3×C4—21no—
243C2×C3×C4—41no—
244C2×C3×C4—41no—
245C2×C3×C4—91no—
246C2×C3×C4—181no—
247C2×C3×C4—181no—
248C2×C3×C4—181no—
249C2×C3×C4C22×D911yescharacteristic
250C2×C3×C4C22×C3×D311yescharacteristic
251C2×Dic3—31no—
252C2×Dic3—61no—
253D12—61no—
254D12—61no—
255D12—122no—
256C4×D3—61no—
257C4×D3—61no—
258C3×C8—21no—
259C3×C8—21no—
260C3×C8—41no—
261C3×C8—92no—
262C3⋊C8—32no—
263C2×C32#88411yescharacteristic
264C2×C32#91411yescharacteristic
265C2×C32#91811yescharacteristic
266C3×D3—121no—
267C3×D3—241no—
268C2×C9—21no—
269C2×C9—21no—
270C2×C9—21no—
271C2×C9C3×#12111yescharacteristic
272C2×C9C3×AGL(1,ℤ/8)11yescharacteristic
273C2×C9C3×#13711yescharacteristic
274D9—41no—
275D9—81no—
276C2×Q8C2×C3×D911yescharacteristic
277C2×D4—91no—
278C2×D4—181no—
279C22×C4—91no—
280SD16—182no—
281M16—182no—
282C2×C8—91no—
283C2×C8C2×C3×D911yescharacteristic
284C4⋊C4—91no—
285C4⋊C4—181no—
286C4⋊C4C2×C3×D911yescharacteristic
287C22⋊C4—181no—
288C22⋊C4—181no—
289C22×C3—21no—
290C22×C3—181no—
291C22×C3—181no—
292C22×C3—181no—
293C22×C3—361no—
294C22×C3—361no—
295C22×C3—361no—
296C22×C3D4×D911yescharacteristic
297C22×C3C3×D3×D411yescharacteristic
298C2×D3—61no—
299C2×D3—61no—
300C2×D3—61no—
301C2×D3—121no—
302C2×D3—121no—
303C2×D3—121no—
304C3×C4—21no—
305C3×C4—21no—
306C3×C4—42no—
307C3×C4—41no—
308C3×C4—41no—
309C3×C4—41no—
310C3×C4—41no—
311C3×C4—81no—
312C3×C4—181no—
313C3×C4—361no—
314C3×C4#369711yescharacteristic
315C3×C4D4×D911yescharacteristic
316C3×C4C3×#23511yescharacteristic
317C3×C4C3×D3×D411yescharacteristic
318Dic3—61no—
319Dic3—121no—
320C32#481211yescharacteristic
321C9—21no—
322C9C3×#46811yescharacteristic, complemented
323C23—91no—
324C23—181no—
325Q8—21no—
326Q8—21no—
327D4—181no—
328D4—181no—
329D4—362no—
330C2×C4—21no—
331C2×C4—21no—
332C2×C4—91no—
333C2×C4—181no—
334C2×C4—181no—
335C2×C4—181no—
336C2×C4C22×C3×D911yescharacteristic
337C8—21no—
338C8—92no—
339C2×C3—21no—
340C2×C3—21no—
341C2×C3—21no—
342C2×C3—361no—
343C2×C3—721no—
344C2×C3#6344611yescharacteristic
345C2×C3#6347611yescharacteristic
346C2×C3#6348011yescharacteristic
347C2×C3C3×#88411yescharacteristic
348C2×C3C3×#91411yescharacteristic
349C2×C3C3×#91811yescharacteristic
350D3—121no—
351D3—241no—
352C22—181no—
353C22—181no—
354C22—181no—
355C22—361no—
356C22—361no—
357C22—361no—
358C22C3×D4×D911yescharacteristic
359C4—41no—
360C4—41no—
361C4—181no—
362C4—361no—
363C4C3×#369711yescharacteristic
364C4C3×D4×D911yescharacteristic
365C3—21no—
366C3#1058849211yescharacteristic, direct product factor
367C3C3×#481211yescharacteristic
368C2—361no—
369C2—721no—
370C2C3×#6344611yescharacteristic
371C2C3×#6347611yescharacteristic
372C2C3×#6348011yescharacteristic
subgroupG/H
centerC22×C3D4×D9
commutator, cosocleC2×C4×C9C23×C3
FrattiniC2×C3×C4C22×C3×D3
FittingC3×C9×#103C2
socleC22×C32D3×D4
prime radicalC3×#63457C2
hypercenterC3×#103D9
hypocenterC9C3×#468
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
1. C3×#63508C2semidirect
2. C2×C3×#3675C2semidirect
3. C2×C3×#3663C2semidirect
5. C3×C9×#103C2semidirect
6. C3×#63380C2semidirect
7. C3×#63366C2semidirect
9. #10588492C3direct (N × H)
30. #63508C2×C3semidirect
31. C2×#3675C2×C3semidirect
32. C2×#3663C2×C3semidirect
35. C9×#103C2×C3semidirect
36. #63380C2×C3semidirect
37. #63366C2×C3semidirect
53. C3×C9⋊C8D4semidirect
108. C3×#103D9semidirect
150. C9⋊C8C3×D4semidirect
222. #103C3×D9semidirect
224. C3×C9#468semidirect
322. C9C3×#468semidirect
366. C3#10588492direct (N × H)

Maximal subgroups

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

subgroupindex
C3×#635082
C2×C3×#36752
C2×C3×#36632
C3×#634572
C3×C9×#1032
C3×#633802
C3×#633662
C3×#48123
#105884923