Finite Group Databasebeta

← C3×C9×#626 #14518613

Subgroups — C3×C9×#626 #14518613

Order 1944.

718 conjugacy classes of subgroups; only the 140 normal subgroups are shown.

normal subgroups only

This group has 718 conjugacy classes of subgroups — too many to draw. Only its 140 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×C9×C3⋊D3C211yesmaximal, characteristic, complemented
2C2×C32×D3×C9C211yesmaximal, characteristic, complemented
3C32×C9×Dic3C211yesmaximal, characteristic, complemented
4C32×#626C311yesmaximal, characteristic
5C3×C9×#67—31nomaximal
6C3×C9×D12—31nomaximal
7C9×#626C313yesmaximal, direct product factor
8C2×C33×C9C2211yescharacteristic
9C3×C9×C3⋊D3—21no—
10C32×D3×C9—21no—
11C2×C32×C3⋊D3C2×C311yescharacteristic
12C2×C33×D3C2×C311yescharacteristic
13C33×Dic3C2×C311yescharacteristic
14C22×C32×C9—31no—
15C2×C9×C3⋊D3C2×C313yescomplemented
16C2×C3×D3×C9—21no—
17C2×C3×D3×C9—23no—
18C2×C3×D3×C9—31no—
19C2×C3×D3×C9—31no—
20C2×C3×D3×C9—61no—
21C2×C3×D3×C9D311yescharacteristic, complemented
22C2×C3×D3×C9C2×C313yescomplemented
23C32×C4×C9—31no—
24C3×C9×Dic3—21no—
25C3×C9×Dic3—23no—
26C3×C9×Dic3D311yescharacteristic, complemented
27C3×C9×Dic3C2×C313yescomplemented
28C33×C9D411yescharacteristic, complemented, Sylow
29C32×#67—31no—
30C32×D12—31no—
31C3×#626C913yesdirect product factor
32C3×#626C3211yescharacteristic
33C3×D4×C9—91no—
34C9×#67—33no—
35C9×D12—33no—
36C2×C34C22×C311yescharacteristic
37C32×C3⋊D3—21no—
38C33×D3—21no—
39C2×C32×C9—21no—
40C2×C32×C9—21no—
41C2×C32×C9—21no—
42C2×C32×C9—23no—
43C2×C32×C9—23no—
44C2×C32×C9—43no—
45C2×C32×C9—41no—
46C2×C32×C9—61no—
47C2×C32×C9C2×D311yescharacteristic
48C2×C32×C9C2×D311yescharacteristic
49C2×C32×C9C22×C313yes—
50C9×C3⋊D3—23no—
51C3×D3×C9—22no—
52C3×D3×C9—26no—
53C3×D3×C9—21no—
54C3×D3×C9—23no—
55C3×D3×C9—62no—
56C3×D3×C9—61no—
57C3×D3×C9—61no—
58C22×C33—31no—
59C2×C3×C3⋊D3C2×C913yescomplemented
60C2×C3×C3⋊D3C2×C3211yescharacteristic
61C2×C32×D3—23no—
62C2×C32×D3—21no—
63C2×C32×D3—31no—
64C2×C32×D3—31no—
65C2×C32×D3—61no—
66C2×C32×D3C2×C913yescomplemented
67C2×C32×D3C3×D311yescharacteristic
68C2×C32×D3C2×C3211yescharacteristic
69C33×C4—31no—
70C32×Dic3—23no—
71C32×Dic3—21no—
72C32×Dic3C2×C913yescomplemented
73C32×Dic3C3×D311yescharacteristic
74C32×Dic3C2×C3211yescharacteristic
75C22×C3×C9—31no—
76C22×C3×C9—33no—
77C22×C3×C9—63no—
78C22×C3×C9—61no—
79C22×C3×C9—91no—
80C2×D3×C9—23no—
81C2×D3×C9—33no—
82C2×D3×C9—33no—
83C2×D3×C9—63no—
84C2×D3×C9C3×D313yescomplemented
85C3×C4×C9—31no—
86C3×C4×C9—33no—
87C3×C4×C9—63no—
88C3×C4×C9—61no—
89C9×Dic3—23no—
90C9×Dic3C3×D313yescomplemented
91C34C3×D411yescharacteristic
92C32×C9—21no—
93C32×C9—21no—
94C32×C9—21no—
95C32×C9—23no—
96C32×C9—23no—
97C32×C9—43no—
98C32×C9—41no—
99C32×C9D1211yescharacteristic, complemented
100C32×C9#6711yescharacteristic, complemented
101C32×C9C3×D413yescomplemented
102C32×D4—91no—
103C3×#67—33no—
104C3×#67—31no—
105C3×D12—33no—
106C3×D12—31no—
107#626C3×C911yescharacteristic, direct product factor
108D4×C9—93no—
109C2×C33—23no—
110C2×C33—23no—
111C2×C33—21no—
112C2×C33—21no—
113C2×C33—21no—
114C2×C33—41no—
115C2×C33—43no—
116C2×C33—61no—
117C2×C33C22×C913yes—
118C2×C33C2×C3×D311yescharacteristic
119C2×C33C2×C3×D311yescharacteristic
120C2×C33C22×C3211yescharacteristic
121C3×C3⋊D3—23no—
122C3×C3⋊D3—21no—
123C32×D3—22no—
124C32×D3—26no—
125C32×D3—23no—
126C32×D3—21no—
127C32×D3—21no—
128C32×D3—62no—
129C32×D3—61no—
130C32×D3—61no—
131C2×C3×C9—21no—
132C2×C3×C9—21no—
133C2×C3×C9—23no—
134C2×C3×C9—23no—
135C2×C3×C9—23no—
136C2×C3×C9—23no—
137C2×C3×C9—23no—
138C2×C3×C9—43no—
139C2×C3×C9—46no—
140C2×C3×C9—43no—
141C2×C3×C9—43no—
142C2×C3×C9—41no—
143C2×C3×C9—43no—
144C2×C3×C9—62no—
145C2×C3×C9—66no—
146C2×C3×C9—61no—
147C2×C3×C9—63no—
148C2×C3×C9—181no—
149C2×C3×C9D3211yescharacteristic
150C2×C3×C9C2×C3×D313yes—
151C2×C3×C9C2×C3×D313yes—
152D3×C9—26no—
153D3×C9—23no—
154D3×C9—66no—
155D3×C9—63no—
156D3×C9—63no—
157C22×C32—31no—
158C22×C32—33no—
159C22×C32—31no—
160C22×C32—61no—
161C22×C32—63no—
162C22×C32—91no—
163C2×C3⋊D3C2×C3×C911yescharacteristic, complemented
164C2×C3×D3—23no—
165C2×C3×D3—21no—
166C2×C3×D3—33no—
167C2×C3×D3—33no—
168C2×C3×D3—31no—
169C2×C3×D3—31no—
170C2×C3×D3—61no—
171C2×C3×D3—63no—
172C2×C3×D3D3×C913yescomplemented
173C2×C3×D3C2×C3×C911yescharacteristic, complemented
174C2×C3×D3C32×D311yescharacteristic
175C32×C4—31no—
176C32×C4—33no—
177C32×C4—31no—
178C32×C4—61no—
179C32×C4—63no—
180C3×Dic3—23no—
181C3×Dic3—21no—
182C3×Dic3D3×C913yescomplemented
183C3×Dic3C2×C3×C911yescharacteristic, complemented
184C3×Dic3C32×D311yescharacteristic
185C22×C9—33no—
186C22×C9—63no—
187C22×C9—93no—
188C4×C9—33no—
189C4×C9—63no—
190C33—23no—
191C33—23no—
192C33—21no—
193C33—21no—
194C33—21no—
195C33—41no—
196C33—43no—
197C33D4×C913yescomplemented
198C33C3×D1211yescharacteristic
199C33C3×#6711yescharacteristic
200C33C32×D411yescharacteristic
201C3×C9—21no—
202C3×C9—21no—
203C3×C9—23no—
204C3×C9—23no—
205C3×C9—23no—
206C3×C9—23no—
207C3×C9—23no—
208C3×C9—43no—
209C3×C9—46no—
210C3×C9—43no—
211C3×C9—43no—
212C3×C9—41no—
213C3×C9—43no—
214C3×C9#62611yescharacteristic, direct product factor
215C3×C9C3×D1213yescomplemented
216C3×C9C3×#6713yescomplemented
217C3×D4—91no—
218C3×D4—93no—
219#67—31no—
220D12—31no—
221C2×C32—23no—
222C2×C32—23no—
223C2×C32—21no—
224C2×C32—21no—
225C2×C32—23no—
226C2×C32—23no—
227C2×C32—23no—
228C2×C32—21no—
229C2×C32—21no—
230C2×C32—21no—
231C2×C32—43no—
232C2×C32—41no—
233C2×C32—46no—
234C2×C32—43no—
235C2×C32—43no—
236C2×C32—43no—
237C2×C32—41no—
238C2×C32—62no—
239C2×C32—66no—
240C2×C32—63no—
241C2×C32—61no—
242C2×C32—61no—
243C2×C32—181no—
244C2×C32C2×D3×C913yes—
245C2×C32C2×D3×C913yes—
246C2×C32C22×C3×C911yescharacteristic
247C2×C32C3×D3211yescharacteristic
248C2×C32C2×C32×D311yescharacteristic
249C2×C32C2×C32×D311yescharacteristic
250C3⋊D3—21no—
251C3×D3—26no—
252C3×D3—22no—
253C3×D3—23no—
254C3×D3—21no—
255C3×D3—21no—
256C3×D3—62no—
257C3×D3—66no—
258C3×D3—63no—
259C3×D3—63no—
260C3×D3—61no—
261C3×D3—61no—
262C2×C9—23no—
263C2×C9—23no—
264C2×C9—43no—
265C2×C9—66no—
266C2×C9—63no—
267C2×C9—183no—
268C2×C9C3×D3213yes—
269C22×C3—33no—
270C22×C3—31no—
271C22×C3—31no—
272C22×C3—63no—
273C22×C3—61no—
274C22×C3—93no—
275C22×C3—91no—
276C2×D3—31no—
277C2×D3—31no—
278C2×D3—61no—
279C2×D3C3×D3×C911yescharacteristic, complemented
280C3×C4—33no—
281C3×C4—31no—
282C3×C4—31no—
283C3×C4—63no—
284C3×C4—61no—
285Dic3C3×D3×C911yescharacteristic, complemented
286C32—23no—
287C32—23no—
288C32—21no—
289C32—21no—
290C32—23no—
291C32—21no—
292C32—23no—
293C32—21no—
294C32—23no—
295C32—21no—
296C32—43no—
297C32—41no—
298C32—46no—
299C32—43no—
300C32—43no—
301C32—43no—
302C32—41no—
303C32C9×D1213yescomplemented
304C32C9×#6713yescomplemented
305C32C3×D4×C911yescharacteristic, complemented
306C32C3×#62611yescharacteristic
307C32C32×D1211yescharacteristic
308C32C32×#6711yescharacteristic
309C9—23no—
310C9—23no—
311C9—43no—
312C9C3×#62613yesdirect product factor
313D4—91noSylow
314C2×C3—23no—
315C2×C3—21no—
316C2×C3—21no—
317C2×C3—23no—
318C2×C3—21no—
319C2×C3—43no—
320C2×C3—41no—
321C2×C3—66no—
322C2×C3—62no—
323C2×C3—61no—
324C2×C3—63no—
325C2×C3—61no—
326C2×C3—183no—
327C2×C3—181no—
328C2×C3D32×C913yes—
329C2×C3C2×C3×D3×C911yescharacteristic
330C2×C3C2×C3×D3×C911yescharacteristic
331C2×C3C32×D3211yescharacteristic
332D3—21no—
333D3—62no—
334D3—61no—
335D3—61no—
336C22—31no—
337C22—91no—
338C4—31no—
339C3—21no—
340C3—23no—
341C3—21no—
342C3—23no—
343C3—21no—
344C3—43no—
345C3—41no—
346C3C9×#62613yesdirect product factor
347C3C3×C9×D1211yescharacteristic, complemented
348C3C3×C9×#6711yescharacteristic, complemented
349C3C32×#62611yescharacteristic
350C2—61no—
351C2—181no—
352C2C3×D32×C911yescharacteristic
subgroupG/H
center, hypercenterC2×C3×C9D32
commutatorC2×C32C22×C3×C9
FrattiniC2×C3C32×D32
FittingC2×C33×C9C22
socleC2×C34C22×C3
prime radicalC32×#626C3
cosocleC2×C33C22×C32
hypocenterC32C3×D4×C9
LCSG ▷ C2×C32 ▷ C32
UCSC1 ◁ C2×C3×C9

Complements

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

NH ≅ G/Ntype
1. C2×C3×C9×C3⋊D3C2semidirect
2. C2×C32×D3×C9C2semidirect
3. C32×C9×Dic3C2semidirect
7. C9×#626C3direct (N × H)
15. C2×C9×C3⋊D3C2×C3semidirect
21. C2×C3×D3×C9D3semidirect
22. C2×C3×D3×C9C2×C3semidirect
26. C3×C9×Dic3D3semidirect
27. C3×C9×Dic3C2×C3semidirect
28. C33×C9D4semidirect
31. C3×#626C9direct (N × H)
59. C2×C3×C3⋊D3C2×C9semidirect
66. C2×C32×D3C2×C9semidirect
72. C32×Dic3C2×C9semidirect
84. C2×D3×C9C3×D3semidirect
90. C9×Dic3C3×D3semidirect
99. C32×C9D12semidirect
100. C32×C9#67semidirect
101. C32×C9C3×D4semidirect
107. #626C3×C9direct (N × H)
163. C2×C3⋊D3C2×C3×C9semidirect
172. C2×C3×D3D3×C9semidirect
173. C2×C3×D3C2×C3×C9semidirect
182. C3×Dic3D3×C9semidirect
183. C3×Dic3C2×C3×C9semidirect
197. C33D4×C9semidirect
214. C3×C9#626direct (N × H)
215. C3×C9C3×D12semidirect
216. C3×C9C3×#67semidirect
279. C2×D3C3×D3×C9semidirect
285. Dic3C3×D3×C9semidirect
303. C32C9×D12semidirect
304. C32C9×#67semidirect
305. C32C3×D4×C9semidirect
312. C9C3×#626direct (N × H)
346. C3C9×#626direct (N × H)
347. C3C3×C9×D12semidirect
348. C3C3×C9×#67semidirect

Maximal subgroups

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

subgroupindex
C2×C3×C9×C3⋊D32
C2×C32×D3×C92
C32×C9×Dic32
C32×#6263
C3×C9×#673
C3×C9×D123
C9×#6263