Finite Group Databasebeta

← C2×C3×((C3⋊D3)⋊C9)⋊C2 #14518281

Subgroups — C2×C3×((C3⋊D3)⋊C9)⋊C2 #14518281

Order 1944.

553 conjugacy classes of subgroups; only the 78 normal subgroups are shown.

normal subgroups only

This group has 553 conjugacy classes of subgroups — too many to draw. Only its 78 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×#4181C211yesmaximal, characteristic, complemented
2C2×C3×#4169C211yesmaximal, characteristic, complemented
3C2×C3×(C3⋊D3)⋊C9C211yesmaximal, characteristic, complemented
4C3×((C3⋊D3)⋊C9)⋊C2C214yesmaximal, direct product factor
5C2×C3×#1113—31nomaximal
6C2×C3×D3×D9—31nomaximal
7C2×((C3⋊D3)⋊C9)⋊C2C311yesmaximal, characteristic, direct product factor
8C2×C3×C32⋊C9C2211yescharacteristic, complemented
9C3×#4181C2212yescomplemented
10C3×#4169C2212yescomplemented
11C3×(C3⋊D3)⋊C9C2212yescomplemented
12C2×C32×C3⋊D3—31no—
13C2×C32×C3⋊D3—31no—
14C2×C32×C3⋊D3D311yescharacteristic
15C3×#1113—34no—
16C2×C3×C3⋊D9D311yescharacteristic, complemented
17C2×C3×D3×C9—31no—
18C2×C32×D9—31no—
19C2×C32×D9—61no—
20C3×D3×D9—34no—
21C2×#4181C2×C311yescharacteristic, complemented
22C2×#4169—21no—
23C2×#4169C2×C311yescharacteristic, complemented
24C2×(C3⋊D3)⋊C9—21no—
25C2×(C3⋊D3)⋊C9C2×C311yescharacteristic, complemented
26((C3⋊D3)⋊C9)⋊C2C2×C314yesdirect product factor
27C3×C32⋊C9C2311yescharacteristic, complemented, Sylow
28C2×#1113—31no—
29C2×C3×D32—91no—
30C2×C3×D32—91no—
31C2×C3×D32—91no—
32C22×C3×D9—91no—
33C2×D3×D9—31no—
34C2×C34C2×D311yescharacteristic
35C32×C3⋊D3—32no—
36C32×C3⋊D3—32no—
37C32×C3⋊D3C2×D312yes—
38C2×C32×C9—21no—
39C2×C32×C9C2×D311yescharacteristic, complemented
40C3×C3⋊D9C2×D312yescomplemented
41C3×D3×C9—32no—
42C32×D9—32no—
43C32×D9—62no—
44C2×C32⋊C9—21no—
45C2×C32⋊C9—21no—
46C2×C32⋊C9—41no—
47C2×C32⋊C9C22×C311yescharacteristic, complemented
48#4181C22×C312yescomplemented
49#4169—22no—
50#4169C22×C312yescomplemented
51(C3⋊D3)⋊C9—22no—
52(C3⋊D3)⋊C9C22×C312yescomplemented
53C2×C3×C3⋊D3—21no—
54C2×C3×C3⋊D3—31no—
55C2×C3×C3⋊D3—31no—
56C2×C3×C3⋊D3—31no—
57C2×C3×C3⋊D3—31no—
58C2×C3×C3⋊D3—61no—
59C2×C3×C3⋊D3—61no—
60C2×C3×C3⋊D3D911yescharacteristic, complemented
61C2×C3×C3⋊D3C3×D311yescharacteristic
62C2×C32×D3—31no—
63C2×C32×D3—91no—
64C2×C32×D3—91no—
65C2×C32×D3—91no—
66C2×C32×D3—91no—
67C2×C32×D3—91no—
68C2×C32×D3—181no—
69C2×C32×D3—181no—
70#1113—34no—
71C3×D32—94no—
72C3×D32—94no—
73C3×D32—94no—
74C22×C3×C9—91no—
75C2×C3⋊D9C3×D311yescharacteristic, complemented
76C2×D3×C9—31no—
77C2×D3×C9—61no—
78C2×C3×D9—31no—
79C2×C3×D9—31no—
80C2×C3×D9—61no—
81C2×C3×D9—61no—
82C2×C3×D9—61no—
83C2×C3×D9—62no—
84C2×C3×D9—94no—
85C2×C3×D9—91no—
86D3×D9—34no—
87C34C22×D311yescharacteristic
88C32×C9—21no—
89C32×C9C22×D311yescharacteristic, complemented
90C32⋊C9—21no—
91C32⋊C9—21no—
92C32⋊C9—41no—
93C32⋊C9C23×C311yescharacteristic, complemented
94C22×C3×D3—271no—
95C22×C3×D3—271no—
96C22×C3×D3—271no—
97C2×D32—91no—
98C2×D32—91no—
99C2×D32—91no—
100C22×D9—91no—
101C2×C33—21no—
102C2×C33—21no—
103C2×C33—21no—
104C2×C33—31no—
105C2×C33—41no—
106C2×C33—61no—
107C2×C33—61no—
108C2×C33—121no—
109C2×C33C2×D911yescharacteristic, complemented
110C2×C33D3211yescharacteristic
111C2×C33C2×C3×D311yescharacteristic
112C3×C3⋊D3—22no—
113C3×C3⋊D3—32no—
114C3×C3⋊D3—32no—
115C3×C3⋊D3—32no—
116C3×C3⋊D3—32no—
117C3×C3⋊D3—62no—
118C3×C3⋊D3—62no—
119C3×C3⋊D3C2×D912yescomplemented
120C3×C3⋊D3C2×C3×D312yes—
121C32×D3—32no—
122C32×D3—92no—
123C32×D3—92no—
124C32×D3—92no—
125C32×D3—92no—
126C32×D3—92no—
127C32×D3—182no—
128C32×D3—182no—
129C2×C3×C9—21no—
130C2×C3×C9—21no—
131C2×C3×C9—31no—
132C2×C3×C9—41no—
133C2×C3×C9—61no—
134C2×C3×C9—62no—
135C2×C3×C9—61no—
136C2×C3×C9—92no—
137C2×C3×C9C2×C3×D311yescharacteristic, complemented
138C3⋊D9C2×C3×D312yescomplemented
139D3×C9—32no—
140D3×C9—62no—
141C3×D9—32no—
142C3×D9—32no—
143C3×D9—62no—
144C3×D9—62no—
145C3×D9—62no—
146C3×D9—64no—
147C3×D9—92no—
148C22×C32—91no—
149C22×C32—271no—
150C22×C32—271no—
151C2×C3⋊D3—31no—
152C2×C3⋊D3—31no—
153C2×C3⋊D3C3×D911yescharacteristic, complemented
154C2×C3×D3—31no—
155C2×C3×D3—31no—
156C2×C3×D3—61no—
157C2×C3×D3—91no—
158C2×C3×D3—91no—
159C2×C3×D3—91no—
160C2×C3×D3—91no—
161C2×C3×D3—91no—
162C2×C3×D3—91no—
163C2×C3×D3—91no—
164C2×C3×D3—91no—
165C2×C3×D3—91no—
166C2×C3×D3—91no—
167C2×C3×D3—181no—
168C2×C3×D3—181no—
169C2×C3×D3—181no—
170C2×C3×D3—181no—
171C2×C3×D3—181no—
172C2×C3×D3—181no—
173C2×C3×D3—181no—
174C2×C3×D3—181no—
175C2×C3×D3—181no—
176C2×C3×D3—182no—
177C2×C3×D3—182no—
178C2×C3×D3—274no—
179C2×C3×D3—274no—
180C2×C3×D3—274no—
181D32—94no—
182D32—94no—
183D32—94no—
184C22×C9—91no—
185C22×C9—181no—
186C2×D9—31no—
187C2×D9—61no—
188C2×D9—91no—
189C2×D9—94no—
190C33—21no—
191C33—21no—
192C33—21no—
193C33—31no—
194C33—41no—
195C33—61no—
196C33—61no—
197C33—121no—
198C33C22×D911yescharacteristic, complemented
199C33C2×D3211yescharacteristic
200C33C22×C3×D311yescharacteristic
201C3×C9—21no—
202C3×C9—21no—
203C3×C9—31no—
204C3×C9—41no—
205C3×C9—61no—
206C3×C9—62no—
207C3×C9—61no—
208C3×C9C22×C3×D311yescharacteristic, complemented
209C23×C3—811no—
210C22×D3—271no—
211C22×D3—271no—
212C22×D3—271no—
213C2×C32—21no—
214C2×C32—21no—
215C2×C32—21no—
216C2×C32—21no—
217C2×C32—21no—
218C2×C32—31no—
219C2×C32—31no—
220C2×C32—41no—
221C2×C32—41no—
222C2×C32—61no—
223C2×C32—61no—
224C2×C32—61no—
225C2×C32—62no—
226C2×C32—62no—
227C2×C32—61no—
228C2×C32—61no—
229C2×C32—92no—
230C2×C32—121no—
231C2×C32—121no—
232C2×C32—122no—
233C2×C32—272no—
234C2×C32—272no—
235C2×C32D3×D911yescharacteristic
236C2×C32((C3⋊D3)⋊C3)⋊C211yescharacteristic
237C2×C32C2×C3×D911yescharacteristic, complemented
238C2×C32C3×D3211yescharacteristic
239C3⋊D3—32no—
240C3⋊D3—32no—
241C3⋊D3C2×C3×D912yescomplemented
242C3×D3—32no—
243C3×D3—32no—
244C3×D3—62no—
245C3×D3—92no—
246C3×D3—92no—
247C3×D3—92no—
248C3×D3—92no—
249C3×D3—92no—
250C3×D3—92no—
251C3×D3—92no—
252C3×D3—92no—
253C3×D3—92no—
254C3×D3—92no—
255C3×D3—182no—
256C3×D3—182no—
257C3×D3—182no—
258C3×D3—182no—
259C3×D3—182no—
260C3×D3—182no—
261C3×D3—182no—
262C3×D3—182no—
263C3×D3—182no—
264C3×D3—184no—
265C3×D3—184no—
266C2×C9—31no—
267C2×C9—61no—
268C2×C9—61no—
269C2×C9—92no—
270C2×C9—121no—
271C2×C9—182no—
272D9—32no—
273D9—62no—
274D9—92no—
275C22×C3—91no—
276C22×C3—91no—
277C22×C3—181no—
278C22×C3—271no—
279C22×C3—271no—
280C22×C3—271no—
281C22×C3—271no—
282C22×C3—541no—
283C22×C3—541no—
284C22×C3—814no—
285C2×D3—31no—
286C2×D3—91no—
287C2×D3—91no—
288C2×D3—91no—
289C2×D3—91no—
290C2×D3—91no—
291C2×D3—181no—
292C2×D3—181no—
293C2×D3—274no—
294C2×D3—274no—
295C2×D3—274no—
296C32—21no—
297C32—21no—
298C32—21no—
299C32—21no—
300C32—21no—
301C32—31no—
302C32—31no—
303C32—41no—
304C32—41no—
305C32—61no—
306C32—61no—
307C32—61no—
308C32—62no—
309C32—62no—
310C32—61no—
311C32—61no—
312C32—121no—
313C32—121no—
314C32—122no—
315C32C2×D3×D911yescharacteristic
316C32C2×((C3⋊D3)⋊C3)⋊C211yescharacteristic
317C32C22×C3×D911yescharacteristic, complemented
318C32C2×C3×D3211yescharacteristic
319C9—31no—
320C9—61no—
321C9—61no—
322C9—121no—
323C23—811noSylow
324C2×C3—21no—
325C2×C3—21no—
326C2×C3—21no—
327C2×C3—31no—
328C2×C3—41no—
329C2×C3—61no—
330C2×C3—61no—
331C2×C3—92no—
332C2×C3—92no—
333C2×C3—121no—
334C2×C3—182no—
335C2×C3—272no—
336C2×C3—272no—
337C2×C3—272no—
338C2×C3—272no—
339C2×C3—542no—
340C2×C3—542no—
341C2×C3((C3⋊D3)⋊C9)⋊C211yescharacteristic, direct product factor
342C2×C3C3×D3×D911yescharacteristic
343C2×C3C3×((C3⋊D3)⋊C3)⋊C211yescharacteristic
344D3—32no—
345D3—92no—
346D3—92no—
347D3—92no—
348D3—92no—
349D3—92no—
350D3—182no—
351D3—182no—
352C22—91no—
353C22—271no—
354C22—271no—
355C22—814no—
356C3—21no—
357C3—21no—
358C3—21no—
359C3—31no—
360C3—41no—
361C3—61no—
362C3—61no—
363C3—121no—
364C3C2×((C3⋊D3)⋊C9)⋊C211yescharacteristic, direct product factor
365C3C2×C3×D3×D911yescharacteristic
366C3C2×C3×((C3⋊D3)⋊C3)⋊C211yescharacteristic
367C2—92no—
368C2—272no—
369C2—272no—
370C2C3×((C3⋊D3)⋊C9)⋊C211yescharacteristic, direct product factor
subgroupG/H
center, hypercenterC2×C3((C3⋊D3)⋊C9)⋊C2
commutator, cosocle, hypocenterC32⋊C9C23×C3
FrattiniC32C2×C3×D32
FittingC2×C3×C32⋊C9C22
socleC2×C33D32
LCSG ▷ C32⋊C9
UCSC1 ◁ C2×C3

Complements

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

NH ≅ G/Ntype
1. C2×C3×#4181C2semidirect
2. C2×C3×#4169C2semidirect
3. C2×C3×(C3⋊D3)⋊C9C2semidirect
4. C3×((C3⋊D3)⋊C9)⋊C2C2direct (N × H)
7. C2×((C3⋊D3)⋊C9)⋊C2C3direct (N × H)
8. C2×C3×C32⋊C9C22semidirect
9. C3×#4181C22semidirect
10. C3×#4169C22semidirect
11. C3×(C3⋊D3)⋊C9C22semidirect
16. C2×C3×C3⋊D9D3semidirect
21. C2×#4181C2×C3semidirect
23. C2×#4169C2×C3semidirect
25. C2×(C3⋊D3)⋊C9C2×C3semidirect
26. ((C3⋊D3)⋊C9)⋊C2C2×C3direct (N × H)
27. C3×C32⋊C9C23semidirect
39. C2×C32×C9C2×D3semidirect
40. C3×C3⋊D9C2×D3semidirect
47. C2×C32⋊C9C22×C3semidirect
48. #4181C22×C3semidirect
50. #4169C22×C3semidirect
52. (C3⋊D3)⋊C9C22×C3semidirect
60. C2×C3×C3⋊D3D9semidirect
75. C2×C3⋊D9C3×D3semidirect
89. C32×C9C22×D3semidirect
93. C32⋊C9C23×C3semidirect
109. C2×C33C2×D9semidirect
119. C3×C3⋊D3C2×D9semidirect
137. C2×C3×C9C2×C3×D3semidirect
138. C3⋊D9C2×C3×D3semidirect
153. C2×C3⋊D3C3×D9semidirect
198. C33C22×D9semidirect
208. C3×C9C22×C3×D3semidirect
237. C2×C32C2×C3×D9semidirect
241. C3⋊D3C2×C3×D9semidirect
317. C32C22×C3×D9semidirect
341. C2×C3((C3⋊D3)⋊C9)⋊C2direct (N × H)
364. C3C2×((C3⋊D3)⋊C9)⋊C2direct (N × H)
370. C2C3×((C3⋊D3)⋊C9)⋊C2direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C3×#41812
C2×C3×#41692
C2×C3×(C3⋊D3)⋊C92
C3×((C3⋊D3)⋊C9)⋊C22
C2×C3×#11133
C2×C3×D3×D93
C2×((C3⋊D3)⋊C9)⋊C23