Finite Group Databasebeta

← C3×#78019 #11808743

Subgroups — C3×#78019 #11808743

Order 1152.

1773 conjugacy classes of subgroups.

The subgroup lattice has 378 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#893C213yesmaximal, complemented
2C2×C3×#67⋊C4C213yesmaximal, complemented
3C32×#399C211yesmaximal, characteristic, complemented
4C3×#4993C213yesmaximal, complemented
5C3×#4960C213yesmaximal, complemented
6C3×#4671C211yesmaximal, characteristic, complemented
7C3×#4648C211yesmaximal, characteristic, complemented
8C3×#2397—31nomaximal
9#78019C311yesmaximal, characteristic, direct product factor
10C22×C3×#67C2213yes—
11C23×C3×Dic3C2211yescharacteristic
12C22×C3×D12C2213yes—
13C22×C3×C4×D3C2213yes—
14C2×C32×C4⋊C4C2213yes—
15C2×C32×C22⋊C4C2213yes—
16C2×C3×(C2×D3)⋊C4C2216yes—
17C2×C3×(C2×D3)⋊C4C2213yes—
18C2×C3×Dic3⋊C4C2213yes—
19C2×C3×C4×Dic3C2213yes—
20C3×#893—212no—
21C3×#67⋊C4—212no—
22C32×#95C2211yescharacteristic
23C3×C3⋊#95C2213yes—
24C2×C3×C4×D4—33no—
25C2×C3×C4×D4—33no—
26C2×#893C2×C313yescomplemented
27C2×#67⋊C4C2×C313yescomplemented
28C3×#399—21no—
29C3×#399—33no—
30C3×#399D311yescharacteristic, complemented
31C3×#399C2×C311yescharacteristic, complemented
32C3×#392—33no—
33C3×#392—31no—
34C3×#376—31no—
35#4993C2×C313yescomplemented
36#4960C2×C313yescomplemented
37#4671C2×C311yescharacteristic, complemented
38#4648C2×C311yescharacteristic, complemented
39C24×C32C2311yescharacteristic
40C23×C3×D3C2313yes—
41C22×C32×C4C2313yes—
42C22×C32×C4C2313yes—
43C2×C3×#67—26no—
44C2×C3×#67—26no—
45C2×C3×#67—26no—
46C22×C3×Dic3—26no—
47C22×C3×Dic3C2311yescharacteristic
48C22×C3×Dic3C2313yes—
49C22×C3×Dic3C2311yescharacteristic
50C2×C3×D12—212no—
51C2×C3×D12—26no—
52C2×C3×C4×D3—26no—
53C2×C3×C4×D3—212no—
54C32×C4⋊C4—26no—
55C32×C22⋊C4—26no—
56C3×(C2×D3)⋊C4—26no—
57C3×(C2×D3)⋊C4—212no—
58C3×Dic3⋊C4—26no—
59C3×C4×Dic3D4112yescomplemented
60#2397—31noSylow
61C22×C3×D4—33no—
62C22×C3×D4—33no—
63C23×C3×C4—31no—
64C23×C3×C4—33no—
65C22×#67C22×C313yes—
66C23×Dic3C22×C311yescharacteristic
67C22×D12C22×C313yes—
68C22×C4×D3C22×C313yes—
69C3×C4×D4—612no—
70C3×C4×D4—612no—
71C2×C3×C4⋊C4—23no—
72C2×C3×C4⋊C4—33no—
73C2×C3×C4⋊C4C2×D313yes—
74C2×C3×C4⋊C4C22×C313yes—
75C2×C3×C22⋊C4—23no—
76C2×C3×C22⋊C4—36no—
77C2×C3×C22⋊C4—33no—
78C2×C3×C22⋊C4C2×D313yes—
79C2×C3×C22⋊C4C22×C313yes—
80C2×C3×C42—33no—
81C2×(C2×D3)⋊C4C22×C313yes—
82C2×(C2×D3)⋊C4C22×C316yes—
83C2×Dic3⋊C4C22×C313yes—
84C2×C4×Dic3C22×C313yes—
85#893—212no—
86#67⋊C4—212no—
87C3×#95—21no—
88C3×#95—33no—
89C3×#95C2×D311yescharacteristic
90C3×#95C22×C311yescharacteristic
91C3⋊#95C22×C313yes—
92C23×C32—23no—
93C23×C32—23no—
94C23×C32#4112yes—
95C23×C32C2411yescharacteristic
96C22×C3×D3—26no—
97C22×C3×D3—23no—
98C22×C3×D3—26no—
99C22×C3×D3—23no—
100C22×C3×D3#4116yes—
101C2×C32×C4—26no—
102C2×C32×C4—23no—
103C2×C32×C4—26no—
104C2×C32×C4C2×D416yes—
105C3×#67—224no—
106C2×C3×Dic3—23no—
107C2×C3×Dic3—23no—
108C2×C3×Dic3—23no—
109C2×C3×Dic3—44no—
110C2×C3×Dic3C2×D416yes—
111C2×C3×Dic3C2×D416yes—
112C3×D12—224no—
113C3×C4×D3—412no—
114C2×C4×D4—33no—
115C2×C4×D4—33no—
116#399—33no—
117#399C3×D311yescharacteristic, complemented
118#392—33no—
119#392—31no—
120#376—31no—
121C24×C3—21no—
122C24×C3—33no—
123C24×C3C22×D311yescharacteristic
124C24×C3C23×C311yescharacteristic
125C23×D3C23×C313yes—
126C2×C3×D4—612no—
127C2×C3×D4—66no—
128C2×C3×D4—66no—
129C2×C3×D4—66no—
130C2×C3×D4—66no—
131C22×C3×C4—23no—
132C22×C3×C4—23no—
133C22×C3×C4—31no—
134C22×C3×C4—33no—
135C22×C3×C4—31no—
136C22×C3×C4—66no—
137C22×C3×C4—612no—
138C22×C3×C4—66no—
139C22×C3×C4C22×D313yes—
140C22×C3×C4C22×D313yes—
141C22×C3×C4C23×C313yes—
142C22×C3×C4C23×C313yes—
143C2×#67—26no—
144C2×#67—26no—
145C2×#67—26no—
146C22×Dic3—26no—
147C22×Dic3C23×C311yescharacteristic
148C22×Dic3C23×C313yes—
149C22×Dic3C23×C311yescharacteristic
150C2×D12—212no—
151C2×D12—26no—
152C2×C4×D3—26no—
153C2×C4×D3—212no—
154C3×C4⋊C4—26no—
155C3×C4⋊C4—26no—
156C3×C4⋊C4—46no—
157C3×C4⋊C4—66no—
158C3×C22⋊C4—26no—
159C3×C22⋊C4—26no—
160C3×C22⋊C4—46no—
161C3×C22⋊C4—612no—
162C3×C22⋊C4—66no—
163C3×C42—312no—
164(C2×D3)⋊C4—26no—
165(C2×D3)⋊C4—212no—
166Dic3⋊C4—26no—
167C4×Dic3C3×D4112yescomplemented
168C22×C32—26no—
169C22×C32—43no—
170C22×C32—41no—
171C22×C32C22×D413yes—
172C22×C32C2×#4111yescharacteristic
173C22×C32C2×#4113yes—
174C2×C3×D3—212no—
175C2×C3×D3—26no—
176C2×C3×D3—43no—
177C2×C3×D3—46no—
178C2×C3×D3—43no—
179C32×C4—26no—
180C32×C4—43no—
181C3×Dic3—26no—
182C3×Dic3—41no—
183C3×Dic3#12714yes—
184C22×D4—33no—
185C22×D4—33no—
186C23×C4—31no—
187C23×C4—33no—
188C4×D4—612no—
189C4×D4—612no—
190C2×C4⋊C4—33no—
191C2×C4⋊C4C2×C3×D313yes—
192C2×C22⋊C4—36no—
193C2×C22⋊C4—33no—
194C2×C22⋊C4C2×C3×D313yes—
195C2×C42—33no—
196#95—33no—
197#95C2×C3×D311yescharacteristic
198C23×C3—23no—
199C23×C3—23no—
200C23×C3—23no—
201C23×C3—23no—
202C23×C3—21no—
203C23×C3—22no—
204C23×C3—36no—
205C23×C3—43no—
206C23×C3—43no—
207C23×C3—66no—
208C23×C3—63no—
209C23×C3—63no—
210C23×C3—66no—
211C23×C3#23912yes—
212C23×C3C3×#4112yes—
213C23×C3C23×D311yescharacteristic
214C23×C3C24×C311yescharacteristic
215C22×D3—26no—
216C22×D3—23no—
217C22×D3—26no—
218C22×D3—23no—
219C22×D3C3×#4116yes—
220C3×D4—624no—
221C3×D4—624no—
222C2×C3×C4—26no—
223C2×C3×C4—26no—
224C2×C3×C4—23no—
225C2×C3×C4—26no—
226C2×C3×C4—23no—
227C2×C3×C4—26no—
228C2×C3×C4—26no—
229C2×C3×C4—36no—
230C2×C3×C4—36no—
231C2×C3×C4—46no—
232C2×C3×C4—43no—
233C2×C3×C4—46no—
234C2×C3×C4—63no—
235C2×C3×C4—63no—
236C2×C3×C4—63no—
237C2×C3×C4—1212no—
238C2×C3×C4—124no—
239C2×C3×C4D3×D416yes—
240C2×C3×C4C2×C3×D416yes—
241#67—224no—
242C2×Dic3—23no—
243C2×Dic3—23no—
244C2×Dic3—23no—
245C2×Dic3—44no—
246C2×Dic3C2×C3×D416yes—
247C2×Dic3C2×C3×D416yes—
248D12—224no—
249C4×D3—412no—
250C2×C32—42no—
251C2×C32#52513yes—
252C2×C32#52513yes—
253C2×C32C2×#12711yescharacteristic
254C3×D3—46no—
255C24—33no—
256C24C22×C3×D311yescharacteristic
257C2×D4—612no—
258C2×D4—66no—
259C2×D4—66no—
260C2×D4—66no—
261C2×D4—66no—
262C22×C4—31no—
263C22×C4—33no—
264C22×C4—31no—
265C22×C4—66no—
266C22×C4—612no—
267C22×C4—66no—
268C22×C4C22×C3×D313yes—
269C22×C4C22×C3×D313yes—
270C4⋊C4—26no—
271C4⋊C4—66no—
272C22⋊C4—26no—
273C22⋊C4—612no—
274C22⋊C4—66no—
275C42—312no—
276C22×C3—26no—
277C22×C3—26no—
278C22×C3—23no—
279C22×C3—21no—
280C22×C3—23no—
281C22×C3—46no—
282C22×C3—43no—
283C22×C3—41no—
284C22×C3—43no—
285C22×C3—41no—
286C22×C3—612no—
287C22×C3—66no—
288C22×C3—83no—
289C22×C3—81no—
290C22×C3—123no—
291C22×C3—123no—
292C22×C3—126no—
293C22×C3C2×D3×D413yes—
294C22×C3C2×#23911yescharacteristic
295C22×C3D3×#4113yes—
296C22×C3C22×C3×D413yes—
297C22×C3C2×C3×#4111yescharacteristic
298C22×C3C2×C3×#4113yes—
299C2×D3—212no—
300C2×D3—26no—
301C2×D3—46no—
302C2×D3—43no—
303C2×D3—43no—
304C3×C4—26no—
305C3×C4—26no—
306C3×C4—34no—
307C3×C4—46no—
308C3×C4—43no—
309C3×C4—43no—
310C3×C4—66no—
311C3×C4—83no—
312C3×C4—121no—
313Dic3—26no—
314Dic3—41no—
315Dic3C3×#12714yes—
316C32#239711yescharacteristic, complemented, Sylow
317C23—23no—
318C23—23no—
319C23—36no—
320C23—63no—
321C23—66no—
322C23—63no—
323C23—66no—
324C23C3×#23912yes—
325C23C23×C3×D311yescharacteristic
326D4—624no—
327D4—624no—
328C2×C4—26no—
329C2×C4—23no—
330C2×C4—26no—
331C2×C4—36no—
332C2×C4—36no—
333C2×C4—63no—
334C2×C4—63no—
335C2×C4—63no—
336C2×C4—1212no—
337C2×C4—124no—
338C2×C4C3×D3×D416yes—
339C2×C3—23no—
340C2×C3—23no—
341C2×C3—21no—
342C2×C3—42no—
343C2×C3—42no—
344C2×C3—82no—
345C2×C3—126no—
346C2×C3#562713yes—
347C2×C3#565613yes—
348C2×C3D3×#12711yescharacteristic
349C2×C3C3×#52513yes—
350C2×C3C3×#52513yes—
351C2×C3C2×C3×#12711yescharacteristic
352D3—46no—
353C22—26no—
354C22—43no—
355C22—41no—
356C22—66no—
357C22—612no—
358C22—126no—
359C22—123no—
360C22—123no—
361C22C2×C3×D3×D413yes—
362C22C2×C3×#23911yescharacteristic
363C22C3×D3×#4113yes—
364C4—26no—
365C4—34no—
366C4—43no—
367C4—66no—
368C4—121no—
369C3—21no—
370C3#7801911yescharacteristic, direct product factor
371C3C3×#239711yescharacteristic, complemented
372C2—42no—
373C2—126no—
374C2C3×#562713yes—
375C2C3×#565613yes—
376C2C3×D3×#12711yescharacteristic
subgroupG/H
centerC23×C3C23×D3
commutator, cosocleC23×C3C24×C3
FrattiniC23C23×C3×D3
FittingC32×#399C2
socleC23×C32C24
hypercenterC3×#399D3
hypocenterC3C3×#2397
LCSG ▷ C23×C3 ▷ C3
UCSC1 ◁ C23×C3 ◁ C3×#399

Complements

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

NH ≅ G/Ntype
1. C2×C3×#893C2semidirect
2. C2×C3×#67⋊C4C2semidirect
3. C32×#399C2semidirect
4. C3×#4993C2semidirect
5. C3×#4960C2semidirect
6. C3×#4671C2semidirect
7. C3×#4648C2semidirect
9. #78019C3direct (N × H)
26. C2×#893C2×C3semidirect
27. C2×#67⋊C4C2×C3semidirect
30. C3×#399D3semidirect
31. C3×#399C2×C3semidirect
35. #4993C2×C3semidirect
36. #4960C2×C3semidirect
37. #4671C2×C3semidirect
38. #4648C2×C3semidirect
59. C3×C4×Dic3D4semidirect
117. #399C3×D3semidirect
167. C4×Dic3C3×D4semidirect
316. C32#2397semidirect
370. C3#78019direct (N × H)
371. C3C3×#2397semidirect

Maximal subgroups

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

subgroupindex
C2×C3×#8932
C2×C3×#67⋊C42
C32×#3992
C3×#49932
C3×#49602
C3×#46712
C3×#46482
C3×#23973
#780193