Finite Group Databasebeta

← C3×#63880 #11723205

Subgroups — C3×#63880 #11723205

Order 864.

490 conjugacy classes of subgroups.

The subgroup lattice has 386 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#626C211yesmaximal, characteristic
2C2×C3×#624C211yesmaximal, characteristic, complemented
3C2×C3×D3×Dic3C211yesmaximal, characteristic, complemented
4C3×#3752C211yesmaximal, characteristic, complemented
5C32×(C2×D3)⋊C4C211yesmaximal, characteristic, complemented
6C32×C4×Dic3C211yesmaximal, characteristic, complemented
7C3×Dic3⋊Dic3C211yesmaximal, characteristic, complemented
8C3×#67⋊C4—31nomaximal
9C3×C4×D12—31nomaximal
10#63880C311yesmaximal, characteristic, direct product factor
11C22×C3×C3⋊D3C2211yescharacteristic
12C22×C32×D3C2211yescharacteristic
13C2×C33×C4C2211yescharacteristic
14C2×C3×C3⋊Dic3C2211yescharacteristic
15C2×C32×Dic3C2211yescharacteristic
16C2×C32×Dic3C2211yescharacteristic
17C2×C32×Dic3C2211yescharacteristic
18C3×#626C414yescomplemented
19C3×#624—22no—
20C3×D3×Dic3—22no—
21C2×C3×#67—31no—
22C22×C3×Dic3—31no—
23C2×C3×D12—31no—
24C2×C3×C4×D3—31no—
25C2×C3×C4×D3—31no—
26C2×C3×C4×D3—31no—
27C2×#626C2×C311yescharacteristic
28C2×#624C2×C311yescharacteristic, complemented
29C2×D3×Dic3C2×C311yescharacteristic, complemented
30C32×C22⋊C4—31no—
31C32×C42—31no—
32#3752C2×C311yescharacteristic, complemented
33C3×(C2×D3)⋊C4—21no—
34C3×(C2×D3)⋊C4—31no—
35C3×(C2×D3)⋊C4—31no—
36C3×(C2×D3)⋊C4—61no—
37C3×(C2×D3)⋊C4D311yescharacteristic, complemented
38C3×(C2×D3)⋊C4C2×C311yescharacteristic, complemented
39C3×C4⋊Dic3—31no—
40C3×Dic3⋊C4—31no—
41C3×C4×Dic3—21no—
42C3×C4×Dic3D311yescharacteristic, complemented
43C3×C4×Dic3C2×C311yescharacteristic, complemented
44Dic3⋊Dic3C2×C311yescharacteristic, complemented
45C22×C33C2311yescharacteristic
46C2×C3×C3⋊D3—21no—
47C2×C3×C3⋊D3—21no—
48C2×C3×C3⋊D3C2×C412yescomplemented
49C2×C32×D3—21no—
50C2×C32×D3—21no—
51C2×C32×D3C2×C412yescomplemented
52C33×C4—21no—
53C3×C3⋊Dic3—21no—
54C32×Dic3—21no—
55C32×Dic3C2×C412yescomplemented
56C32×Dic3D412yescomplemented
57C3×C4×D4—91no—
58#67⋊C4—31no—
59C4×D12—31no—
60C23×C32—31no—
61C22×C3⋊D3C22×C311yescharacteristic
62C22×C3×D3—21no—
63C22×C3×D3—31no—
64C22×C3×D3—31no—
65C22×C3×D3—61no—
66C22×C3×D3C2×D311yescharacteristic
67C22×C3×D3C22×C311yescharacteristic
68C2×C32×C4—21no—
69C2×C32×C4—21no—
70C2×C32×C4—21no—
71C2×C32×C4—31no—
72C2×C32×C4—31no—
73C2×C32×C4—31no—
74C2×C32×C4—41no—
75C2×C32×C4C2×D311yescharacteristic
76C2×C32×C4C2×D311yescharacteristic
77C2×C32×C4C22×C311yescharacteristic
78C2×C3⋊Dic3C22×C311yescharacteristic
79C3×#67—34no—
80C2×C3×Dic3—21no—
81C2×C3×Dic3—21no—
82C2×C3×Dic3—21no—
83C2×C3×Dic3—31no—
84C2×C3×Dic3—31no—
85C2×C3×Dic3—61no—
86C2×C3×Dic3—62no—
87C2×C3×Dic3C2×D311yescharacteristic
88C2×C3×Dic3C2×D311yescharacteristic
89C2×C3×Dic3C2×D311yescharacteristic
90C2×C3×Dic3C22×C311yescharacteristic
91C2×C3×Dic3C22×C311yescharacteristic
92C2×C3×Dic3C22×C311yescharacteristic
93C3×D12—34no—
94C3×C4×D3—62no—
95C3×C4×D3—62no—
96C3×C4×D3—62no—
97#626C3×C414yescomplemented
98#624—22no—
99D3×Dic3—22no—
100C2×C33C22×C411yescharacteristic
101C2×C33C2×D411yescharacteristic
102C2×C33#4111yescharacteristic
103C3×C3⋊D3—22no—
104C32×D3—22no—
105C2×C3×D4—91no—
106C22×C3×C4—91no—
107C22×C3×C4—91no—
108C2×#67—31no—
109C22×Dic3—31no—
110C2×D12—31no—
111C2×C4×D3—31no—
112C2×C4×D3—31no—
113C2×C4×D3—31no—
114C3×C4⋊C4—91no—
115C3×C22⋊C4—31no—
116C3×C22⋊C4—31no—
117C3×C22⋊C4—61no—
118C3×C22⋊C4—91no—
119C3×C42—31no—
120C3×C42—31no—
121C3×C42—61no—
122(C2×D3)⋊C4—31no—
123(C2×D3)⋊C4—31no—
124(C2×D3)⋊C4—61no—
125(C2×D3)⋊C4C3×D311yescharacteristic, complemented
126C4⋊Dic3—31no—
127Dic3⋊C4—31no—
128C4×Dic3C3×D311yescharacteristic, complemented
129C22×C32—21no—
130C22×C32—21no—
131C22×C32—21no—
132C22×C32—32no—
133C22×C32—41no—
134C22×C32—61no—
135C22×C32—61no—
136C22×C32C22×D311yescharacteristic
137C22×C32C22×D311yescharacteristic
138C22×C32C23×C311yescharacteristic
139C2×C3⋊D3—21no—
140C2×C3⋊D3—21no—
141C2×C3⋊D3C2×C3×C412yescomplemented
142C2×C3×D3—21no—
143C2×C3×D3—21no—
144C2×C3×D3—21no—
145C2×C3×D3—21no—
146C2×C3×D3—22no—
147C2×C3×D3—32no—
148C2×C3×D3—32no—
149C2×C3×D3—41no—
150C2×C3×D3—41no—
151C2×C3×D3—62no—
152C2×C3×D3—61no—
153C2×C3×D3—61no—
154C2×C3×D3—61no—
155C2×C3×D3—61no—
156C2×C3×D3—121no—
157C2×C3×D3—121no—
158C2×C3×D3C4×D312yescomplemented
159C2×C3×D3C2×C3×C412yescomplemented
160C32×C4—21no—
161C32×C4—22no—
162C32×C4—21no—
163C32×C4—21no—
164C32×C4—32no—
165C32×C4—32no—
166C32×C4—41no—
167C32×C4—41no—
168C32×C4—42no—
169C32×C4—61no—
170C3⋊Dic3—21no—
171C3×Dic3—21no—
172C3×Dic3—21no—
173C3×Dic3—22no—
174C3×Dic3—22no—
175C3×Dic3—41no—
176C3×Dic3—61no—
177C3×Dic3—61no—
178C3×Dic3—121no—
179C3×Dic3C4×D312yescomplemented
180C3×Dic3D1212yescomplemented
181C3×Dic3C2×C3×C412yescomplemented
182C3×Dic3C3×D412yescomplemented
183C4×D4—91noSylow
184C33C4×D411yescharacteristic, complemented, Sylow
185C23×C3—31no—
186C23×C3—31no—
187C23×C3—61no—
188C23×C3—91no—
189C22×D3—31no—
190C22×D3—31no—
191C22×D3—61no—
192C22×D3C2×C3×D311yescharacteristic
193C3×D4—94no—
194C2×C3×C4—21no—
195C2×C3×C4—21no—
196C2×C3×C4—21no—
197C2×C3×C4—31no—
198C2×C3×C4—31no—
199C2×C3×C4—31no—
200C2×C3×C4—31no—
201C2×C3×C4—31no—
202C2×C3×C4—31no—
203C2×C3×C4—41no—
204C2×C3×C4—61no—
205C2×C3×C4—61no—
206C2×C3×C4—61no—
207C2×C3×C4—91no—
208C2×C3×C4—182no—
209C2×C3×C4—182no—
210C2×C3×C4D3211yescharacteristic
211C2×C3×C4C2×C3×D311yescharacteristic
212C2×C3×C4C2×C3×D311yescharacteristic
213#67—34no—
214C2×Dic3—31no—
215C2×Dic3—31no—
216C2×Dic3—61no—
217C2×Dic3—62no—
218C2×Dic3C2×C3×D311yescharacteristic
219C2×Dic3C2×C3×D311yescharacteristic
220C2×Dic3C2×C3×D311yescharacteristic
221D12—34no—
222C4×D3—62no—
223C4×D3—62no—
224C4×D3—62no—
225C2×C32—21no—
226C2×C32—21no—
227C2×C32—21no—
228C2×C32—21no—
229C2×C32—21no—
230C2×C32—21no—
231C2×C32—21no—
232C2×C32—21no—
233C2×C32—21no—
234C2×C32—41no—
235C2×C32—41no—
236C2×C32—41no—
237C2×C32—62no—
238C2×C32C2×C4×D311yescharacteristic
239C2×C32C2×C4×D311yescharacteristic
240C2×C32C2×D1211yescharacteristic
241C2×C32#23511yescharacteristic
242C2×C32D3×D411yescharacteristic
243C2×C32#23711yescharacteristic
244C2×C32C22×C3×C411yescharacteristic
245C2×C32C2×C3×D411yescharacteristic
246C2×C32C3×#4111yescharacteristic
247C3⋊D3—22no—
248C3×D3—22no—
249C3×D3—22no—
250C3×D3—42no—
251C3×D3—62no—
252C3×D3—62no—
253C3×D3—122no—
254C2×D4—91no—
255C22×C4—91no—
256C22×C4—91no—
257C4⋊C4—91no—
258C22⋊C4—31no—
259C22⋊C4—91no—
260C42—31no—
261C22×C3—21no—
262C22×C3—21no—
263C22×C3—21no—
264C22×C3—32no—
265C22×C3—32no—
266C22×C3—41no—
267C22×C3—62no—
268C22×C3—61no—
269C22×C3—61no—
270C22×C3—61no—
271C22×C3—61no—
272C22×C3—92no—
273C22×C3—121no—
274C22×C3—121no—
275C22×C3—181no—
276C22×C3—181no—
277C22×C3C2×D3211yescharacteristic
278C22×C3C22×C3×D311yescharacteristic
279C22×C3C22×C3×D311yescharacteristic
280C2×D3—21no—
281C2×D3—21no—
282C2×D3—32no—
283C2×D3—32no—
284C2×D3—62no—
285C2×D3—61no—
286C2×D3—61no—
287C2×D3—61no—
288C2×D3—61no—
289C2×D3—121no—
290C2×D3—121no—
291C2×D3C3×C4×D312yescomplemented
292C3×C4—22no—
293C3×C4—21no—
294C3×C4—21no—
295C3×C4—21no—
296C3×C4—32no—
297C3×C4—32no—
298C3×C4—32no—
299C3×C4—32no—
300C3×C4—41no—
301C3×C4—41no—
302C3×C4—42no—
303C3×C4—62no—
304C3×C4—62no—
305C3×C4—61no—
306C3×C4—61no—
307C3×C4—121no—
308C3×C4—181no—
309Dic3—21no—
310Dic3—61no—
311Dic3—61no—
312Dic3—121no—
313Dic3C3×C4×D312yescomplemented
314Dic3C3×D1212yescomplemented
315C32—21no—
316C32—21no—
317C32—21no—
318C32—41no—
319C32C4×D1211yescharacteristic, complemented
320C32#67⋊C411yescharacteristic, complemented
321C32C3×C4×D411yescharacteristic, complemented
322C23—31no—
323C23—91no—
324D4—94no—
325C2×C4—31no—
326C2×C4—31no—
327C2×C4—31no—
328C2×C4—91no—
329C2×C4—182no—
330C2×C4—182no—
331C2×C4C3×D3211yescharacteristic
332C2×C3—21no—
333C2×C3—21no—
334C2×C3—21no—
335C2×C3—21no—
336C2×C3—21no—
337C2×C3—21no—
338C2×C3—21no—
339C2×C3—21no—
340C2×C3—21no—
341C2×C3—41no—
342C2×C3—41no—
343C2×C3—41no—
344C2×C3—62no—
345C2×C3—62no—
346C2×C3—122no—
347C2×C3—182no—
348C2×C3C4×D3211yescharacteristic
349C2×C3D3×D1211yescharacteristic
350C2×C3#380411yescharacteristic
351C2×C3C2×C3×C4×D311yescharacteristic
352C2×C3C2×C3×C4×D311yescharacteristic
353C2×C3C2×C3×D1211yescharacteristic
354C2×C3C3×#23511yescharacteristic
355C2×C3C3×D3×D411yescharacteristic
356C2×C3C3×#23711yescharacteristic
357D3—22no—
358D3—62no—
359D3—62no—
360D3—122no—
361C22—32no—
362C22—61no—
363C22—61no—
364C22—92no—
365C22—181no—
366C22—181no—
367C22C2×C3×D3211yescharacteristic
368C4—21no—
369C4—32no—
370C4—32no—
371C4—61no—
372C4—181no—
373C3—21no—
374C3—21no—
375C3—21no—
376C3—41no—
377C3#6388011yescharacteristic, direct product factor
378C3C3×C4×D1211yescharacteristic, complemented
379C3C3×#67⋊C411yescharacteristic, complemented
380C2—62no—
381C2—182no—
382C2C3×C4×D3211yescharacteristic
383C2C3×D3×D1211yescharacteristic
384C2C3×#380411yescharacteristic
subgroupG/H
centerC22×C3C2×D32
commutatorC2×C32C22×C3×C4
FrattiniC22C2×C3×D32
FittingC2×C33×C4C22
socleC22×C33C23
prime radicalC2×C3×#626C2
cosocleC22×C32C23×C3
hypercenterC2×C3×C4D32
hypocenterC32C3×C4×D4
LCSG ▷ C2×C32 ▷ C32
UCSC1 ◁ C22×C3 ◁ C2×C3×C4

Complements

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

NH ≅ G/Ntype
2. C2×C3×#624C2semidirect
3. C2×C3×D3×Dic3C2semidirect
4. C3×#3752C2semidirect
5. C32×(C2×D3)⋊C4C2semidirect
6. C32×C4×Dic3C2semidirect
7. C3×Dic3⋊Dic3C2semidirect
10. #63880C3direct (N × H)
18. C3×#626C4semidirect
28. C2×#624C2×C3semidirect
29. C2×D3×Dic3C2×C3semidirect
32. #3752C2×C3semidirect
37. C3×(C2×D3)⋊C4D3semidirect
38. C3×(C2×D3)⋊C4C2×C3semidirect
42. C3×C4×Dic3D3semidirect
43. C3×C4×Dic3C2×C3semidirect
44. Dic3⋊Dic3C2×C3semidirect
48. C2×C3×C3⋊D3C2×C4semidirect
51. C2×C32×D3C2×C4semidirect
55. C32×Dic3C2×C4semidirect
56. C32×Dic3D4semidirect
97. #626C3×C4semidirect
125. (C2×D3)⋊C4C3×D3semidirect
128. C4×Dic3C3×D3semidirect
141. C2×C3⋊D3C2×C3×C4semidirect
158. C2×C3×D3C4×D3semidirect
159. C2×C3×D3C2×C3×C4semidirect
179. C3×Dic3C4×D3semidirect
180. C3×Dic3D12semidirect
181. C3×Dic3C2×C3×C4semidirect
182. C3×Dic3C3×D4semidirect
184. C33C4×D4semidirect
291. C2×D3C3×C4×D3semidirect
313. Dic3C3×C4×D3semidirect
314. Dic3C3×D12semidirect
319. C32C4×D12semidirect
320. C32#67⋊C4semidirect
321. C32C3×C4×D4semidirect
377. C3#63880direct (N × H)
378. C3C3×C4×D12semidirect
379. C3C3×#67⋊C4semidirect

Maximal subgroups

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

subgroupindex
C2×C3×#6262
C2×C3×#6242
C2×C3×D3×Dic32
C3×#37522
C32×(C2×D3)⋊C42
C32×C4×Dic32
C3×Dic3⋊Dic32
C3×#67⋊C43
C3×C4×D123
#638803