Finite Group Databasebeta

← C3×#10619874 #14518651

Subgroups — C3×#10619874 #14518651

Order 1944.

718 conjugacy classes of subgroups; only the 108 normal subgroups are shown.

normal subgroups only

This group has 718 conjugacy classes of subgroups — too many to draw. Only its 108 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×C3⋊(C3⋊D9)C211yesmaximal, characteristic, complemented
2C2×C32×C3⋊D9C211yesmaximal, characteristic, complemented
3C32×C9×Dic3C211yesmaximal, characteristic, complemented
4C3×#6292—31nomaximal
5C3×C4⋊(C3⋊D9)—31nomaximal
6#10619874C311yesmaximal, characteristic, direct product factor
7C3×#6192—33nomaximal
8C2×C33×C9C2211yescharacteristic
9C3×C3⋊(C3⋊D9)—21no—
10C32×C3⋊D9—21no—
11C2×C3×C3⋊(C3⋊D3)—31no—
12C2×C32×C3⋊D3—31no—
13C33×Dic3D311yescharacteristic
14C2×C3⋊(C3⋊D9)C2×C311yescharacteristic, complemented
15C2×C3×C3⋊D9—21no—
16C2×C3×C3⋊D9—31no—
17C2×C3×C3⋊D9—33no—
18C2×C3×C3⋊D9—63no—
19C2×C3×C3⋊D9—61no—
20C2×C3×C3⋊D9D311yescharacteristic, complemented
21C2×C3×C3⋊D9C2×C311yescharacteristic, complemented
22C2×C32×D9—33no—
23C32×C4×C9—31no—
24C3×C9×Dic3—21no—
25C3×C9×Dic3—23no—
26C3×C9×Dic3D313yescomplemented
27C3×C9×Dic3C2×C311yescharacteristic, complemented
28C33×C9D411yescharacteristic, complemented, Sylow
29C3×C4⋊(C3⋊D3)—91no—
30#6292—31no—
31C3×#626—93no—
32C3×#626—91no—
33C4⋊(C3⋊D9)—31no—
34C3×D36—93no—
35#6192—33no—
36C2×C34C2×D311yescharacteristic
37C3×C3⋊(C3⋊D3)—61no—
38C32×C3⋊D3—61no—
39C2×C32×C9—21no—
40C2×C32×C9—21no—
41C2×C32×C9—23no—
42C2×C32×C9—23no—
43C2×C32×C9—21no—
44C2×C32×C9—43no—
45C2×C32×C9—41no—
46C2×C32×C9C2×D311yescharacteristic
47C2×C32×C9C2×D313yes—
48C2×C32×C9C22×C311yescharacteristic
49C3⋊(C3⋊D9)—21no—
50C3×C3⋊D9—22no—
51C3×C3⋊D9—21no—
52C3×C3⋊D9—21no—
53C3×C3⋊D9—62no—
54C3×C3⋊D9—66no—
55C3×C3⋊D9—63no—
56C3×C3⋊D9—61no—
57C32×D9—63no—
58C2×C3⋊(C3⋊D3)—31no—
59C2×C3×C3⋊D3—31no—
60C2×C3×C3⋊D3—31no—
61C2×C3×C3⋊D3—61no—
62C2×C3×C3⋊D3—93no—
63C2×C3×C3⋊D3—91no—
64C2×C3×C3⋊D3—91no—
65C2×C3×C3⋊D3—181no—
66C2×C3×C3⋊D3—183no—
67C2×C32×D3—93no—
68C2×C32×D3—91no—
69C33×C4—31no—
70C32×Dic3—23no—
71C32×Dic3—21no—
72C32×Dic3D913yescomplemented
73C32×Dic3C3×D311yescharacteristic
74C32×Dic3C3⋊D311yescharacteristic
75C2×C3⋊D9—31no—
76C2×C3⋊D9—33no—
77C2×C3⋊D9—63no—
78C2×C3⋊D9—61no—
79C2×C3⋊D9C3×D311yescharacteristic, complemented
80C2×C3×D9—33no—
81C2×C3×D9—33no—
82C2×C3×D9—63no—
83C2×C3×D9—93no—
84C2×C3×D9—183no—
85C3×C4×C9—33no—
86C3×C4×C9—31no—
87C3×C4×C9—63no—
88C3×C4×C9—61no—
89C9×Dic3—23no—
90C9×Dic3C3×D313yescomplemented
91C34D1211yescharacteristic
92C32×C9—21no—
93C32×C9—21no—
94C32×C9—23no—
95C32×C9—23no—
96C32×C9—21no—
97C32×C9—43no—
98C32×C9—41no—
99C32×C9D1213yescomplemented
100C32×C9#6711yescharacteristic, complemented
101C32×C9C3×D411yescharacteristic, complemented
102C4⋊(C3⋊D3)—91no—
103C3×#67—271no—
104C3×D12—271no—
105C3×D12—273no—
106#626—93no—
107#626—91no—
108D36—93no—
109C2×C33—23no—
110C2×C33—23no—
111C2×C33—21no—
112C2×C33—21no—
113C2×C33—21no—
114C2×C33—41no—
115C2×C33—43no—
116C2×C33C2×D913yes—
117C2×C33D3211yescharacteristic
118C2×C33C2×C3×D311yescharacteristic
119C2×C33C2×C3⋊D311yescharacteristic
120C3⋊(C3⋊D3)—61no—
121C3×C3⋊D3—62no—
122C3×C3⋊D3—61no—
123C3×C3⋊D3—61no—
124C3×C3⋊D3—182no—
125C3×C3⋊D3—186no—
126C3×C3⋊D3—183no—
127C3×C3⋊D3—181no—
128C3×C3⋊D3—181no—
129C32×D3—183no—
130C32×D3—181no—
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×C9D3213yes—
145C2×C3×C9C2×C3×D313yes—
146C2×C3×C9C2×C3×D311yescharacteristic
147C3⋊D9—21no—
148C3⋊D9—62no—
149C3⋊D9—66no—
150C3⋊D9—63no—
151C3⋊D9—61no—
152C3×D9—66no—
153C3×D9—63no—
154C3×D9—63no—
155C3×D9—186no—
156C3×D9—183no—
157C22×C32—271no—
158C2×C3⋊D3—31no—
159C2×C3⋊D3—91no—
160C2×C3⋊D3—93no—
161C2×C3⋊D3—91no—
162C2×C3⋊D3—181no—
163C2×C3⋊D3—183no—
164C2×C3×D3—93no—
165C2×C3×D3—93no—
166C2×C3×D3—91no—
167C2×C3×D3—91no—
168C2×C3×D3—181no—
169C2×C3×D3—183no—
170C2×C3×D3—273no—
171C2×C3×D3—271no—
172C2×C3×D3—271no—
173C2×C3×D3—543no—
174C2×C3×D3—541no—
175C32×C4—31no—
176C32×C4—33no—
177C32×C4—31no—
178C32×C4—61no—
179C32×C4—63no—
180C3×Dic3—23no—
181C3×Dic3—21no—
182C3×Dic3C3×D913yescomplemented
183C3×Dic3C3⋊D911yescharacteristic, complemented
184C3×Dic3C3×C3⋊D311yescharacteristic
185C2×D9—33no—
186C2×D9—93no—
187C2×D9—183no—
188C4×C9—33no—
189C4×C9—63no—
190C33—23no—
191C33—23no—
192C33—21no—
193C33—21no—
194C33—21no—
195C33—41no—
196C33—43no—
197C33D3613yescomplemented
198C33#62611yescharacteristic
199C33C3×D1211yescharacteristic
200C33C4⋊(C3⋊D3)11yescharacteristic
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#62613yescomplemented
215C3×C9C3×D1213yescomplemented
216C3×C9C3×#6711yescharacteristic, complemented
217C3×D4—811no—
218#67—271no—
219D12—271no—
220D12—273no—
221C2×C32—23no—
222C2×C32—23no—
223C2×C32—21no—
224C2×C32—21no—
225C2×C32—23no—
226C2×C32—23no—
227C2×C32—21no—
228C2×C32—23no—
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—541no—
239C2×C32D3×D913yes—
240C2×C32C2×C3×D913yes—
241C2×C32C2×C3⋊D911yescharacteristic
242C2×C32C3×D3211yescharacteristic
243C2×C32D3×C3⋊D311yescharacteristic
244C2×C32C2×C3×C3⋊D311yescharacteristic
245C3⋊D3—61no—
246C3⋊D3—182no—
247C3⋊D3—186no—
248C3⋊D3—183no—
249C3⋊D3—181no—
250C3⋊D3—181no—
251C3×D3—182no—
252C3×D3—186no—
253C3×D3—183no—
254C3×D3—183no—
255C3×D3—181no—
256C3×D3—181no—
257C3×D3—546no—
258C3×D3—542no—
259C3×D3—543no—
260C3×D3—541no—
261C3×D3—541no—
262C2×C9—23no—
263C2×C9—23no—
264C2×C9—43no—
265C2×C9C3×D3213yes—
266D9—63no—
267D9—186no—
268D9—183no—
269C22×C3—271no—
270C22×C3—271no—
271C22×C3—541no—
272C22×C3—811no—
273C2×D3—93no—
274C2×D3—91no—
275C2×D3—273no—
276C2×D3—271no—
277C2×D3—271no—
278C2×D3—543no—
279C2×D3—541no—
280C3×C4—33no—
281C3×C4—31no—
282C3×C4—31no—
283C3×C4—63no—
284C3×C4—61no—
285Dic3C3×C3⋊D911yescharacteristic, complemented
286C32—23no—
287C32—23no—
288C32—21no—
289C32—21no—
290C32—23no—
291C32—21no—
292C32—23no—
293C32—23no—
294C32—21no—
295C32—21no—
296C32—43no—
297C32—41no—
298C32—46no—
299C32—43no—
300C32—43no—
301C32—43no—
302C32—41no—
303C32#619213yescomplemented
304C32C3×D3613yescomplemented
305C32C4⋊(C3⋊D9)11yescharacteristic, complemented
306C32C3×#62611yescharacteristic
307C32#629211yescharacteristic
308C32C3×C4⋊(C3⋊D3)11yescharacteristic
309C9—23no—
310C9—23no—
311C9—43no—
312C9C3×#62613yescomplemented
313D4—811noSylow
314C2×C3—23no—
315C2×C3—21no—
316C2×C3—23no—
317C2×C3—21no—
318C2×C3—21no—
319C2×C3—43no—
320C2×C3—41no—
321C2×C3—542no—
322C2×C3—541no—
323C2×C3—541no—
324C2×C3—1621no—
325C2×C3C3×D3×D913yes—
326C2×C3D3×C3⋊D911yescharacteristic
327C2×C3C2×C3×C3⋊D911yescharacteristic
328C2×C3C3×D3×C3⋊D311yescharacteristic
329D3—183no—
330D3—181no—
331D3—546no—
332D3—542no—
333D3—541no—
334D3—543no—
335D3—541no—
336C22—271no—
337C22—811no—
338C4—31no—
339C3—23no—
340C3—21no—
341C3—21no—
342C3—23no—
343C3—21no—
344C3—43no—
345C3—41no—
346C3C3×#619213yescomplemented
347C3#1061987411yescharacteristic, direct product factor
348C3C3×C4⋊(C3⋊D9)11yescharacteristic, complemented
349C3C3×#629211yescharacteristic
350C2—541no—
351C2—1621no—
352C2C3×D3×C3⋊D911yescharacteristic
subgroupG/H
center, hypercenterC2×C3D3×C3⋊D9
commutator, cosocleC2×C32×C9C22×C3
FrattiniC2×C3C3×D3×C3⋊D3
FittingC2×C33×C9C22
socleC2×C34C2×D3
hypocenterC32×C9C3×D4
LCSG ▷ C2×C32×C9 ▷ C32×C9
UCSC1 ◁ C2×C3

Complements

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

NH ≅ G/Ntype
1. C2×C3×C3⋊(C3⋊D9)C2semidirect
2. C2×C32×C3⋊D9C2semidirect
3. C32×C9×Dic3C2semidirect
6. #10619874C3direct (N × H)
14. C2×C3⋊(C3⋊D9)C2×C3semidirect
20. C2×C3×C3⋊D9D3semidirect
21. C2×C3×C3⋊D9C2×C3semidirect
26. C3×C9×Dic3D3semidirect
27. C3×C9×Dic3C2×C3semidirect
28. C33×C9D4semidirect
72. C32×Dic3D9semidirect
79. C2×C3⋊D9C3×D3semidirect
90. C9×Dic3C3×D3semidirect
99. C32×C9D12semidirect
100. C32×C9#67semidirect
101. C32×C9C3×D4semidirect
182. C3×Dic3C3×D9semidirect
183. C3×Dic3C3⋊D9semidirect
197. C33D36semidirect
214. C3×C9#626semidirect
215. C3×C9C3×D12semidirect
216. C3×C9C3×#67semidirect
285. Dic3C3×C3⋊D9semidirect
303. C32#6192semidirect
304. C32C3×D36semidirect
305. C32C4⋊(C3⋊D9)semidirect
312. C9C3×#626semidirect
346. C3C3×#6192semidirect
347. C3#10619874direct (N × H)
348. C3C3×C4⋊(C3⋊D9)semidirect

Maximal subgroups

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

subgroupindex
C2×C3×C3⋊(C3⋊D9)2
C2×C32×C3⋊D92
C32×C9×Dic32
C3×#62923
C3×C4⋊(C3⋊D9)3
#106198743
C3×#61923