Finite Group Databasebeta

← C3×D3×#491 #11873596

Subgroups — C3×D3×#491 #11873596

Order 1152.

813 conjugacy classes of subgroups.

The subgroup lattice has 377 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×D3×C4⋊Q8C211yesmaximal, characteristic
2C3×D3×#125C211yesmaximal, characteristic
3C32×#491C211yesmaximal, characteristic, complemented
4C3×#5082C211yesmaximal, characteristic, complemented
5C3×#5069C211yesmaximal, characteristic, complemented
6C3×D3×#103C214yesmaximal
7C3×#4797C214yesmaximal, complemented
8C3×D3×#97C211yesmaximal, characteristic
9C3×#4703C211yesmaximal, characteristic, complemented
10C2×C3×#491—31nomaximal
11D3×#491C311yesmaximal, characteristic, direct product factor
12C2×C3×D3×Q8C2212yes—
13C32×C4⋊Q8C2211yescharacteristic
14C32×#125C2211yescharacteristic
15C3×#944C2212yes—
16C2×C3×D3×C8C2212yes—
17C3×D3×C4⋊C4—22no—
18C3×D3×C4⋊C4—22no—
19C3×D3×C4⋊C4C2212yes—
20C3×#890C2212yes—
21C3×#889—22no—
22C3×#888—22no—
23C3×C42×D3C2211yescharacteristic
24C3×#870C2211yescharacteristic
25C3×#869C2211yescharacteristic
26C32×#103C2214yes—
27C32×#97C2211yescharacteristic
28C3×#835C2214yes—
29C3×#816C2214yes—
30C3×#815C2212yes—
31C3×#810C2214yes—
32C3×#803C2211yescharacteristic
33C2×C3×C4⋊Q8—31no—
34C2×C3×#125—31no—
35D3×C4⋊Q8C2×C311yescharacteristic
36D3×#125C2×C311yescharacteristic
37C3×#491—21no—
38C3×#491—31no—
39C3×#491—31no—
40C3×#491—34no—
41C3×#491—31no—
42C3×#491D311yescharacteristic, direct product factor
43C3×#491C2×C311yescharacteristic, complemented
44C2×C3×#103—34no—
45C2×C3×#97—31no—
46#5082C2×C311yescharacteristic, complemented
47#5069C2×C311yescharacteristic, complemented
48D3×#103C2×C314yes—
49#4797C2×C314yescomplemented
50D3×#97C2×C311yescharacteristic
51#4703C2×C311yescharacteristic, complemented
52C2×C32×Q8C2312yes—
53C3×D3×Q8—28no—
54C2×C3×C4×D3—22no—
55C2×C3×C4×D3—22no—
56C2×C3×C4×D3D412yes—
57C2×C3×C4×D3C2311yescharacteristic
58C2×C3×Dic6—22no—
59C2×C3×Dic6C2312yes—
60C2×C32×C8C2312yes—
61C32×C4⋊C4—22no—
62C32×C4⋊C4—22no—
63C32×C4⋊C4C2312yes—
64C32×C42C2311yescharacteristic
65C3×C4⋊Dic3—22no—
66C3×C4⋊Dic3—22no—
67C3×C4⋊Dic3C2312yes—
68C3×Dic3⋊C4—22no—
69C3×Dic3⋊C4—24no—
70C3×Dic3⋊C4—22no—
71C3×Dic3⋊C4—22no—
72C3×C4×Dic3D412yes—
73C3×C4×Dic3C2311yescharacteristic
74C2×C3×C3⋊C8C2312yes—
75C3×D3×C8—24no—
76C2×#491—31noSylow
77C22×C3×Q8—32no—
78C2×D3×Q8C22×C312yes—
79C22×C3×C8—32no—
80C3×C4⋊Q8—21no—
81C3×C4⋊Q8—32no—
82C3×C4⋊Q8—31no—
83C3×C4⋊Q8—62no—
84C3×C4⋊Q8C2×D311yescharacteristic
85C3×C4⋊Q8C22×C311yescharacteristic
86C3×#125—21no—
87C3×#125—32no—
88C3×#125—31no—
89C3×#125—62no—
90C3×#125C2×D311yescharacteristic
91C3×#125C22×C311yescharacteristic
92C2×C3×C4⋊C4—32no—
93C2×C3×C4⋊C4—62no—
94C2×C3×C4⋊C4—62no—
95C2×C3×C42—31no—
96#944C22×C312yes—
97C2×D3×C8C22×C312yes—
98D3×C4⋊C4—22no—
99D3×C4⋊C4—22no—
100D3×C4⋊C4C22×C312yes—
101#890C22×C312yes—
102#889—22no—
103#888—22no—
104C42×D3C22×C311yescharacteristic
105#870C22×C311yescharacteristic
106#869C22×C311yescharacteristic
107C3×#103—24no—
108C3×#103—34no—
109C3×#103—34no—
110C3×#103—34no—
111C3×#103C2×D314yes—
112C3×#103C22×C314yes—
113C3×#97—21no—
114C3×#97—32no—
115C3×#97—31no—
116C3×#97C2×D311yescharacteristic
117C3×#97C22×C311yescharacteristic
118#835C22×C314yes—
119#816C22×C314yes—
120#815C22×C312yes—
121#810C22×C314yes—
122#803C22×C311yescharacteristic
123C22×C3×D3C2×D411yescharacteristic
124C32×Q8—24no—
125C2×C32×C4—22no—
126C2×C32×C4—22no—
127C2×C32×C4C2×D412yes—
128C2×C32×C4C2411yescharacteristic
129C2×C3×Dic3—22no—
130C2×C3×Dic3—22no—
131C2×C3×Dic3C2×D412yes—
132C2×C3×Dic3C2×D411yescharacteristic
133C3×C4×D3—24no—
134C3×C4×D3—44no—
135C3×C4×D3—44no—
136C3×C4×D3#4114yes—
137C3×Dic6—24no—
138C3×Dic6—44no—
139C32×C8—22no—
140C3×C3⋊C8—22no—
141C2×C4⋊Q8—31no—
142C2×#125—31no—
143#491—31no—
144#491—31no—
145#491—34no—
146#491—31no—
147#491C3×D311yescharacteristic, direct product factor
148C2×#103—34no—
149C2×#97—31no—
150C2×C3×Q8—22no—
151C2×C3×Q8—32no—
152C2×C3×Q8—62no—
153C2×C3×Q8—68no—
154C2×C3×Q8C22×D312yes—
155C2×C3×Q8C23×C312yes—
156C22×C3×C4—31no—
157C22×C3×C4—32no—
158C22×C3×C4—62no—
159C22×C3×C4—62no—
160D3×Q8—28no—
161C2×C4×D3—22no—
162C2×C4×D3—22no—
163C2×C4×D3C3×D412yes—
164C2×C4×D3C23×C311yescharacteristic
165C2×Dic6—22no—
166C2×Dic6C23×C312yes—
167C2×C3×C8—22no—
168C2×C3×C8—32no—
169C2×C3×C8—64no—
170C2×C3×C8C22×D312yes—
171C2×C3×C8C23×C312yes—
172C3×C4⋊C4—22no—
173C3×C4⋊C4—22no—
174C3×C4⋊C4—22no—
175C3×C4⋊C4—22no—
176C3×C4⋊C4—22no—
177C3×C4⋊C4—32no—
178C3×C4⋊C4—42no—
179C3×C4⋊C4—42no—
180C3×C4⋊C4—62no—
181C3×C4⋊C4—62no—
182C3×C4⋊C4—64no—
183C3×C4⋊C4—62no—
184C3×C4⋊C4—62no—
185C3×C4⋊C4—62no—
186C3×C4⋊C4C22×D312yes—
187C3×C4⋊C4C23×C312yes—
188C3×C42—21no—
189C3×C42—32no—
190C3×C42—31no—
191C3×C42C22×D311yescharacteristic
192C3×C42C23×C311yescharacteristic
193C4⋊Dic3—22no—
194C4⋊Dic3—22no—
195C4⋊Dic3C23×C312yes—
196Dic3⋊C4—22no—
197Dic3⋊C4—24no—
198Dic3⋊C4—22no—
199Dic3⋊C4—22no—
200C4×Dic3C3×D412yes—
201C4×Dic3C23×C311yescharacteristic
202C2×C3⋊C8C23×C312yes—
203D3×C8—24no—
204C22×C32C22×D411yescharacteristic
205C2×C3×D3#12412yes—
206C2×C3×D3#13714yes—
207C32×C4—22no—
208C32×C4—42no—
209C32×C4—42no—
210C32×C4C2×#4112yes—
211C3×Dic3—22no—
212C3×Dic3—42no—
213C3×Dic3—42no—
214C3×Dic3#12412yes—
215C22×Q8—32no—
216C22×C8—32no—
217C4⋊Q8—32no—
218C4⋊Q8—31no—
219C4⋊Q8—62no—
220C4⋊Q8C2×C3×D311yescharacteristic
221#125—32no—
222#125—31no—
223#125—62no—
224#125C2×C3×D311yescharacteristic
225C2×C4⋊C4—32no—
226C2×C4⋊C4—62no—
227C2×C4⋊C4—62no—
228C2×C42—31no—
229#103—34no—
230#103—34no—
231#103—34no—
232#103C2×C3×D314yes—
233#97—32no—
234#97—31no—
235#97C2×C3×D311yescharacteristic
236C23×C3—31no—
237C22×D3C2×C3×D411yescharacteristic
238C3×Q8—24no—
239C3×Q8—24no—
240C3×Q8—44no—
241C3×Q8—64no—
242C3×Q8—124no—
243C2×C3×C4—22no—
244C2×C3×C4—22no—
245C2×C3×C4—22no—
246C2×C3×C4—22no—
247C2×C3×C4—21no—
248C2×C3×C4—22no—
249C2×C3×C4—31no—
250C2×C3×C4—34no—
251C2×C3×C4—32no—
252C2×C3×C4—42no—
253C2×C3×C4—42no—
254C2×C3×C4—64no—
255C2×C3×C4—62no—
256C2×C3×C4—62no—
257C2×C3×C4—124no—
258C2×C3×C4—124no—
259C2×C3×C4D3×D412yes—
260C2×C3×C4C2×C3×D412yes—
261C2×C3×C4C23×D311yescharacteristic
262C2×C3×C4C24×C311yescharacteristic
263C2×Dic3—22no—
264C2×Dic3—22no—
265C2×Dic3C2×C3×D412yes—
266C2×Dic3C2×C3×D411yescharacteristic
267C4×D3—24no—
268C4×D3—44no—
269C4×D3—44no—
270C4×D3C3×#4114yes—
271Dic6—24no—
272Dic6—44no—
273C3×C8—22no—
274C3×C8—22no—
275C3×C8—42no—
276C3×C8—62no—
277C3⋊C8—22no—
278C2×C32C2×#12411yescharacteristic
279C2×C32C2×#13712yes—
280C3×D3#49114yesdirect product factor
281C2×Q8—32no—
282C2×Q8—62no—
283C2×Q8—68no—
284C2×Q8C22×C3×D312yes—
285C22×C4—31no—
286C22×C4—32no—
287C22×C4—62no—
288C22×C4—62no—
289C2×C8—32no—
290C2×C8—64no—
291C2×C8C22×C3×D312yes—
292C4⋊C4—22no—
293C4⋊C4—22no—
294C4⋊C4—32no—
295C4⋊C4—62no—
296C4⋊C4—62no—
297C4⋊C4—62no—
298C4⋊C4—64no—
299C4⋊C4—62no—
300C4⋊C4—62no—
301C4⋊C4C22×C3×D312yes—
302C42—31no—
303C42—32no—
304C42C22×C3×D311yescharacteristic
305C22×C3—21no—
306C22×C3—32no—
307C22×C3—34no—
308C22×C3C2×D3×D411yescharacteristic
309C22×C3C22×C3×D411yescharacteristic
310C2×D3C3×#12412yes—
311C2×D3C3×#13714yes—
312C3×C4—22no—
313C3×C4—22no—
314C3×C4—22no—
315C3×C4—32no—
316C3×C4—42no—
317C3×C4—42no—
318C3×C4—42no—
319C3×C4—42no—
320C3×C4—42no—
321C3×C4—62no—
322C3×C4—82no—
323C3×C4—82no—
324C3×C4—122no—
325C3×C4—122no—
326C3×C4D3×#4112yes—
327C3×C4C2×C3×#4112yes—
328Dic3—22no—
329Dic3—42no—
330Dic3—42no—
331Dic3C3×#12412yes—
332C32C2×#49111yescharacteristic, complemented, Sylow
333C23—31no—
334Q8—24no—
335Q8—64no—
336Q8—124no—
337C2×C4—22no—
338C2×C4—22no—
339C2×C4—31no—
340C2×C4—34no—
341C2×C4—32no—
342C2×C4—64no—
343C2×C4—62no—
344C2×C4—62no—
345C2×C4—124no—
346C2×C4—124no—
347C2×C4C3×D3×D412yes—
348C2×C4C23×C3×D311yescharacteristic
349C8—22no—
350C8—62no—
351C2×C3—22no—
352C2×C3—21no—
353C2×C3—34no—
354C2×C3D3×#12411yescharacteristic
355C2×C3D3×#13712yes—
356C2×C3C2×C3×#12411yescharacteristic
357C2×C3C2×C3×#13712yes—
358D3C3×#49114yesdirect product factor
359C22—34no—
360C22—32no—
361C22C2×C3×D3×D411yescharacteristic
362C4—22no—
363C4—32no—
364C4—42no—
365C4—42no—
366C4—62no—
367C4—122no—
368C4—122no—
369C4C3×D3×#4112yes—
370C3—21no—
371C3D3×#49111yescharacteristic, direct product factor
372C3C2×C3×#49111yescharacteristic, complemented
373C2—34no—
374C2C3×D3×#12411yescharacteristic
375C2C3×D3×#13712yes—
subgroupG/H
centerC22×C3C2×D3×D4
commutator, cosocleC2×C3×C4C24×C3
FrattiniC2×C4C23×C3×D3
FittingC32×#491C2
socleC22×C32C22×D4
prime radicalC22×C3×D3C2×D4
hypercenterC3×#491D3
hypocenterC3C2×C3×#491
LCSG ▷ C2×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C22×C3 ◁ C3×C42 ◁ C3×#491

Complements

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

NH ≅ G/Ntype
3. C32×#491C2semidirect
4. C3×#5082C2semidirect
5. C3×#5069C2semidirect
7. C3×#4797C2semidirect
9. C3×#4703C2semidirect
11. D3×#491C3direct (N × H)
42. C3×#491D3direct (N × H)
43. C3×#491C2×C3semidirect
46. #5082C2×C3semidirect
47. #5069C2×C3semidirect
49. #4797C2×C3semidirect
51. #4703C2×C3semidirect
147. #491C3×D3direct (N × H)
280. C3×D3#491direct (N × H)
332. C32C2×#491semidirect
358. D3C3×#491direct (N × H)
371. C3D3×#491direct (N × H)
372. C3C2×C3×#491semidirect

Maximal subgroups

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

subgroupindex
C3×D3×C4⋊Q82
C3×D3×#1252
C32×#4912
C3×#50822
C3×#50692
C3×D3×#1032
C3×#47972
C3×D3×#972
C3×#47032
C2×C3×#4913
D3×#4913