Finite Group Databasebeta

← C3×#10619880 #14518656

Subgroups — C3×#10619880 #14518656

Order 1944.

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

normal subgroups only

This group has 758 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×D3×C9C211yesmaximal, characteristic, complemented
3C32×C3⋊Dic9C211yesmaximal, characteristic, complemented
4C3×#6291—31nomaximal
5C3×#6233—31nomaximal
6#10619880C311yesmaximal, characteristic, direct product factor
7C3×#6195—33nomaximal
8C2×C33×C9C2211yescharacteristic
9C3×C3⋊(C3⋊D9)—21no—
10C32×D3×C9—21no—
11C2×C3×C3⋊(C3⋊D3)—31no—
12C2×C33×D3D311yescharacteristic
13C32×C3⋊Dic3—31no—
14C22×C32×C9—31no—
15C2×C3⋊(C3⋊D9)C2×C311yescharacteristic, complemented
16C2×C3×C3⋊D9—31no—
17C2×C3×C3⋊D9—33no—
18C2×C3×C3⋊D9—63no—
19C2×C3×C3⋊D9—61no—
20C2×C3×D3×C9—21no—
21C2×C3×D3×C9—23no—
22C2×C3×D3×C9D313yescomplemented
23C2×C3×D3×C9C2×C311yescharacteristic, complemented
24C3×C3⋊Dic9—21no—
25C3×C3⋊Dic9D311yescharacteristic, complemented
26C3×C3⋊Dic9C2×C311yescharacteristic, complemented
27C32×Dic9—33no—
28C33×C9D411yescharacteristic, complemented, Sylow
29C3×#638—91no—
30#6291—31no—
31C3×#626—93no—
32C3×#626—91no—
33#6233—31no—
34C3×#611—93no—
35#6195—33no—
36C2×C34C2×D311yescharacteristic
37C3×C3⋊(C3⋊D3)—61no—
38C33×D3—21no—
39C2×C32×C9—21no—
40C2×C32×C9—21no—
41C2×C32×C9—23no—
42C2×C32×C9—21no—
43C2×C32×C9—23no—
44C2×C32×C9—43no—
45C2×C32×C9—41no—
46C2×C32×C9—61no—
47C2×C32×C9C2×D311yescharacteristic
48C2×C32×C9C2×D313yes—
49C2×C32×C9C22×C311yescharacteristic
50C3⋊(C3⋊D9)—21no—
51C3×C3⋊D9—62no—
52C3×C3⋊D9—66no—
53C3×C3⋊D9—61no—
54C3×C3⋊D9—63no—
55C3×D3×C9—22no—
56C3×D3×C9—26no—
57C3×D3×C9—23no—
58C3×D3×C9—21no—
59C22×C33—31no—
60C2×C3⋊(C3⋊D3)—31no—
61C2×C3×C3⋊D3—93no—
62C2×C3×C3⋊D3—91no—
63C2×C3×C3⋊D3—91no—
64C2×C3×C3⋊D3—181no—
65C2×C3×C3⋊D3—183no—
66C2×C32×D3—23no—
67C2×C32×D3—21no—
68C2×C32×D3D913yescomplemented
69C2×C32×D3C3×D311yescharacteristic
70C2×C32×D3C3⋊D311yescharacteristic
71C3×C3⋊Dic3—31no—
72C3×C3⋊Dic3—31no—
73C3×C3⋊Dic3—61no—
74C32×Dic3—93no—
75C32×Dic3—91no—
76C22×C3×C9—33no—
77C22×C3×C9—31no—
78C22×C3×C9—63no—
79C22×C3×C9—61no—
80C2×C3⋊D9—31no—
81C2×C3⋊D9—33no—
82C2×C3⋊D9—63no—
83C2×C3⋊D9—61no—
84C2×D3×C9—23no—
85C2×D3×C9C3×D313yescomplemented
86C2×C3×D9—93no—
87C2×C3×D9—183no—
88C3⋊Dic9C3×D311yescharacteristic, complemented
89C3×Dic9—33no—
90C3×Dic9—33no—
91C3×Dic9—63no—
92C34#6711yescharacteristic
93C32×C9—21no—
94C32×C9—21no—
95C32×C9—23no—
96C32×C9—21no—
97C32×C9—23no—
98C32×C9—43no—
99C32×C9—41no—
100C32×C9D1211yescharacteristic, complemented
101C32×C9#6713yescomplemented
102C32×C9C3×D411yescharacteristic, complemented
103#638—91no—
104C3×#67—271no—
105C3×#67—273no—
106C3×D12—271no—
107#626—93no—
108#626—91no—
109#611—93no—
110C2×C33—23no—
111C2×C33—23no—
112C2×C33—21no—
113C2×C33—21no—
114C2×C33—21no—
115C2×C33—41no—
116C2×C33—43no—
117C2×C33—61no—
118C2×C33C2×D913yes—
119C2×C33D3211yescharacteristic
120C2×C33C2×C3×D311yescharacteristic
121C2×C33C2×C3⋊D311yescharacteristic
122C3⋊(C3⋊D3)—61no—
123C3×C3⋊D3—182no—
124C3×C3⋊D3—186no—
125C3×C3⋊D3—183no—
126C3×C3⋊D3—181no—
127C3×C3⋊D3—181no—
128C32×D3—22no—
129C32×D3—26no—
130C32×D3—23no—
131C32×D3—21no—
132C32×D3—21no—
133C2×C3×C9—21no—
134C2×C3×C9—21no—
135C2×C3×C9—23no—
136C2×C3×C9—23no—
137C2×C3×C9—23no—
138C2×C3×C9—23no—
139C2×C3×C9—23no—
140C2×C3×C9—43no—
141C2×C3×C9—46no—
142C2×C3×C9—43no—
143C2×C3×C9—43no—
144C2×C3×C9—41no—
145C2×C3×C9—43no—
146C2×C3×C9—62no—
147C2×C3×C9—66no—
148C2×C3×C9—63no—
149C2×C3×C9—61no—
150C2×C3×C9D3213yes—
151C2×C3×C9C2×C3×D313yes—
152C2×C3×C9C2×C3×D311yescharacteristic
153C3⋊D9—62no—
154C3⋊D9—66no—
155C3⋊D9—61no—
156C3⋊D9—63no—
157D3×C9—26no—
158D3×C9—23no—
159C3×D9—186no—
160C3×D9—183no—
161C22×C32—31no—
162C22×C32—33no—
163C22×C32—31no—
164C22×C32—61no—
165C22×C32—63no—
166C2×C3⋊D3—91no—
167C2×C3⋊D3—93no—
168C2×C3⋊D3—91no—
169C2×C3⋊D3—181no—
170C2×C3⋊D3—183no—
171C2×C3×D3—23no—
172C2×C3×D3—21no—
173C2×C3×D3—273no—
174C2×C3×D3—271no—
175C2×C3×D3—271no—
176C2×C3×D3—543no—
177C2×C3×D3—541no—
178C2×C3×D3C3×D913yescomplemented
179C2×C3×D3C3⋊D911yescharacteristic, complemented
180C2×C3×D3C3×C3⋊D311yescharacteristic
181C32×C4—271no—
182C3⋊Dic3—31no—
183C3×Dic3—93no—
184C3×Dic3—93no—
185C3×Dic3—91no—
186C3×Dic3—91no—
187C3×Dic3—181no—
188C3×Dic3—183no—
189C22×C9—33no—
190C22×C9—63no—
191C2×D9—93no—
192C2×D9—183no—
193Dic9—33no—
194C33—23no—
195C33—23no—
196C33—21no—
197C33—21no—
198C33—21no—
199C33—41no—
200C33—43no—
201C33#61113yescomplemented
202C33#62611yescharacteristic
203C33C3×#6711yescharacteristic
204C33#63811yescharacteristic
205C3×C9—21no—
206C3×C9—21no—
207C3×C9—23no—
208C3×C9—23no—
209C3×C9—23no—
210C3×C9—23no—
211C3×C9—23no—
212C3×C9—43no—
213C3×C9—46no—
214C3×C9—43no—
215C3×C9—43no—
216C3×C9—41no—
217C3×C9—43no—
218C3×C9#62613yescomplemented
219C3×C9C3×D1211yescharacteristic, complemented
220C3×C9C3×#6713yescomplemented
221C3×D4—811no—
222#67—271no—
223#67—273no—
224D12—271no—
225C2×C32—23no—
226C2×C32—23no—
227C2×C32—21no—
228C2×C32—21no—
229C2×C32—23no—
230C2×C32—23no—
231C2×C32—21no—
232C2×C32—23no—
233C2×C32—21no—
234C2×C32—21no—
235C2×C32—43no—
236C2×C32—41no—
237C2×C32—46no—
238C2×C32—43no—
239C2×C32—43no—
240C2×C32—43no—
241C2×C32—41no—
242C2×C32—62no—
243C2×C32—66no—
244C2×C32—63no—
245C2×C32—61no—
246C2×C32—61no—
247C2×C32D3×D913yes—
248C2×C32C2×C3×D913yes—
249C2×C32C2×C3⋊D911yescharacteristic
250C2×C32C3×D3211yescharacteristic
251C2×C32D3×C3⋊D311yescharacteristic
252C2×C32C2×C3×C3⋊D311yescharacteristic
253C3⋊D3—182no—
254C3⋊D3—186no—
255C3⋊D3—183no—
256C3⋊D3—181no—
257C3⋊D3—181no—
258C3×D3—26no—
259C3×D3—22no—
260C3×D3—23no—
261C3×D3—21no—
262C3×D3—21no—
263C3×D3—546no—
264C3×D3—542no—
265C3×D3—543no—
266C3×D3—541no—
267C3×D3—541no—
268C2×C9—23no—
269C2×C9—23no—
270C2×C9—43no—
271C2×C9—66no—
272C2×C9—63no—
273C2×C9C3×D3213yes—
274D9—186no—
275D9—183no—
276C22×C3—33no—
277C22×C3—31no—
278C22×C3—31no—
279C22×C3—63no—
280C22×C3—61no—
281C22×C3—811no—
282C2×D3—273no—
283C2×D3—271no—
284C2×D3—271no—
285C2×D3—543no—
286C2×D3—541no—
287C2×D3C3×C3⋊D911yescharacteristic, complemented
288C3×C4—271no—
289C3×C4—271no—
290C3×C4—541no—
291Dic3—93no—
292Dic3—91no—
293C32—23no—
294C32—23no—
295C32—21no—
296C32—21no—
297C32—23no—
298C32—21no—
299C32—23no—
300C32—23no—
301C32—21no—
302C32—21no—
303C32—43no—
304C32—41no—
305C32—46no—
306C32—43no—
307C32—43no—
308C32—43no—
309C32—41no—
310C32#619513yescomplemented
311C32C3×#61113yescomplemented
312C32#623311yescharacteristic, complemented
313C32C3×#62611yescharacteristic
314C32#629111yescharacteristic
315C32C3×#63811yescharacteristic
316C9—23no—
317C9—23no—
318C9—43no—
319C9C3×#62613yescomplemented
320D4—811noSylow
321C2×C3—21no—
322C2×C3—23no—
323C2×C3—21no—
324C2×C3—23no—
325C2×C3—21no—
326C2×C3—43no—
327C2×C3—41no—
328C2×C3—66no—
329C2×C3—62no—
330C2×C3—63no—
331C2×C3—61no—
332C2×C3—61no—
333C2×C3—1621no—
334C2×C3C3×D3×D913yes—
335C2×C3D3×C3⋊D911yescharacteristic
336C2×C3C2×C3×C3⋊D911yescharacteristic
337C2×C3C3×D3×C3⋊D311yescharacteristic
338D3—21no—
339D3—546no—
340D3—542no—
341D3—541no—
342D3—543no—
343D3—541no—
344C22—31no—
345C22—811no—
346C4—271no—
347C3—23no—
348C3—21no—
349C3—23no—
350C3—21no—
351C3—21no—
352C3—43no—
353C3—41no—
354C3C3×#619513yescomplemented
355C3#1061988011yescharacteristic, direct product factor
356C3C3×#623311yescharacteristic, complemented
357C3C3×#629111yescharacteristic
358C2—61no—
359C2—1621no—
360C2C3×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×D3×C9C2semidirect
3. C32×C3⋊Dic9C2semidirect
6. #10619880C3direct (N × H)
15. C2×C3⋊(C3⋊D9)C2×C3semidirect
22. C2×C3×D3×C9D3semidirect
23. C2×C3×D3×C9C2×C3semidirect
25. C3×C3⋊Dic9D3semidirect
26. C3×C3⋊Dic9C2×C3semidirect
28. C33×C9D4semidirect
68. C2×C32×D3D9semidirect
85. C2×D3×C9C3×D3semidirect
88. C3⋊Dic9C3×D3semidirect
100. C32×C9D12semidirect
101. C32×C9#67semidirect
102. C32×C9C3×D4semidirect
178. C2×C3×D3C3×D9semidirect
179. C2×C3×D3C3⋊D9semidirect
201. C33#611semidirect
218. C3×C9#626semidirect
219. C3×C9C3×D12semidirect
220. C3×C9C3×#67semidirect
287. C2×D3C3×C3⋊D9semidirect
310. C32#6195semidirect
311. C32C3×#611semidirect
312. C32#6233semidirect
319. C9C3×#626semidirect
354. C3C3×#6195semidirect
355. C3#10619880direct (N × H)
356. C3C3×#6233semidirect

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×D3×C92
C32×C3⋊Dic92
C3×#62913
C3×#62333
#106198803
C3×#61953