Finite Group Databasebeta

← C3×#69564 #11775417

Subgroups — C3×#69564 #11775417

Order 1152.

573 conjugacy classes of subgroups.

The subgroup lattice has 374 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#5477C211yesmaximal, characteristic
2C32×#383C211yesmaximal, characteristic, complemented
3C3×#4926C211yesmaximal, characteristic, complemented
4C3×#4451C214yesmaximal, complemented
5C3×#1514—31nomaximal
6#69564C311yesmaximal, characteristic, direct product factor
7C2×C3×#235—21no—
8C2×C32×C42C2211yescharacteristic
9C3×#930—21no—
10C3×#930C2212yes—
11C3×#875—21no—
12C3×#874C411yescharacteristic, complemented
13C3×C4×D12—21no—
14C3×C4×D12C412yescomplemented
15C3×#869C411yescharacteristic, complemented
16C32×#95—21no—
17C32×#95—21no—
18C32×#95C2212yes—
19C3×#830C2212yes—
20C3×C4⋊(C3⋊C8)—21no—
21C3×#803—21no—
22C3×#532—31no—
23#5477C2×C311yescharacteristic
24C3×#432—31no—
25C3×#383—21no—
26C3×#383D311yescharacteristic, complemented
27C3×#383C2×C311yescharacteristic, complemented
28#4926C2×C311yescharacteristic, complemented
29C3×#327—34no—
30#4451C2×C314yescomplemented
31C22×C32×C4—22no—
32C22×C32×C4D411yescharacteristic
33C22×C32×C4D411yescharacteristic
34C22×C32×C4C2311yescharacteristic
35C2×C3×#67—22no—
36C3×#235—44no—
37C2×C3×D12—21no—
38C2×C3×D12—21no—
39C2×C3×D12C2×C412yes—
40C2×C3×C4×D3—22no—
41C2×C3×Dic6—21no—
42C32×C42C2×C411yescharacteristic
43C32×C42C2×C411yescharacteristic
44C32×C42D411yescharacteristic
45C32×C42D411yescharacteristic
46C3×(C2×D3)⋊C4—22no—
47C3×(C2×D3)⋊C4—22no—
48C3×C4⋊Dic3—21no—
49C3×C4⋊Dic3C2×C412yes—
50C2×C3×C3⋊C8—22no—
51#1514—31noSylow
52C2×C3×#41—61no—
53C2×#235—21no—
54C3×C4⋊Q8—31no—
55C3×#127—31no—
56C3×#124—61no—
57C3×#121—32no—
58C3×#121—61no—
59C3×C4×D4—32no—
60C3×C4×D4—61no—
61C2×C3×C42—21no—
62C2×C3×C42C2×D311yescharacteristic
63C2×C3×C42C22×C311yescharacteristic
64#930—21no—
65#930C22×C312yes—
66#875—21no—
67#874C3×C411yescharacteristic, complemented
68C4×D12—21no—
69C4×D12C3×C412yescomplemented
70#869C3×C411yescharacteristic, complemented
71C3×C4⋊C8—61no—
72C3×C22⋊C8—32no—
73C3×#97—61no—
74C3×#95—22no—
75C3×#95—22no—
76C3×#95—21no—
77C3×#95—21no—
78C3×#95—21no—
79C3×#95—21no—
80C3×#95—22no—
81C3×#95C2×D312yes—
82C3×#95C22×C312yes—
83#830C22×C312yes—
84C4⋊(C3⋊C8)—21no—
85#803—21no—
86C23×C32C2×D411yescharacteristic
87C22×C3×D3—22no—
88C2×C32×C4—22no—
89C2×C32×C4—41no—
90C2×C32×C4—41no—
91C2×C32×C4—42no—
92C2×C32×C4—42no—
93C2×C32×C4—42no—
94C2×C32×C4C22⋊C411yescharacteristic
95C2×C32×C4C22⋊C411yescharacteristic
96C2×C32×C4C22⋊C411yescharacteristic
97C2×C32×C4C22⋊C411yescharacteristic
98C2×C32×C4C22×C411yescharacteristic
99C2×C32×C4C2×D411yescharacteristic
100C3×#67—44no—
101C2×C3×Dic3—22no—
102C3×D12—42no—
103C3×D12—42no—
104C3×D12—42no—
105C3×C4×D3—44no—
106C3×Dic6—42no—
107C3×C3⋊C8—42no—
108#532—31no—
109#432—31no—
110#383C3×D311yescharacteristic, complemented
111#327—34no—
112C3×#41—124no—
113C2×C3×Q8—61no—
114C2×C3×D4—32no—
115C2×C3×D4—62no—
116C2×C3×D4—61no—
117C2×C3×D4—61no—
118C22×C3×C4—24no—
119C22×C3×C4—22no—
120C22×C3×C4—22no—
121C22×C3×C4—21no—
122C22×C3×C4—21no—
123C22×C3×C4—21no—
124C22×C3×C4—62no—
125C22×C3×C4#6711yescharacteristic
126C22×C3×C4#6711yescharacteristic
127C22×C3×C4C3×D411yescharacteristic
128C22×C3×C4C3×D411yescharacteristic
129C22×C3×C4C22×D311yescharacteristic
130C22×C3×C4C23×C311yescharacteristic
131C2×#67—22no—
132#235—44no—
133C2×D12—21no—
134C2×D12—21no—
135C2×D12C2×C3×C412yes—
136C2×C4×D3—22no—
137C2×Dic6—21no—
138C2×C3×C8—62no—
139C3×C4⋊C4—32no—
140C3×C4⋊C4—61no—
141C3×C22⋊C4—62no—
142C3×C22⋊C4—62no—
143C3×C42—21no—
144C3×C42—21no—
145C3×C42—21no—
146C3×C42—21no—
147C3×C42C4×D311yescharacteristic
148C3×C42C4×D311yescharacteristic
149C3×C42D1211yescharacteristic
150C3×C42D1211yescharacteristic
151C3×C42C2×C3×C411yescharacteristic
152C3×C42C2×C3×C411yescharacteristic
153C3×C42C3×D411yescharacteristic
154C3×C42C3×D411yescharacteristic
155(C2×D3)⋊C4—22no—
156(C2×D3)⋊C4—22no—
157C4⋊Dic3—21no—
158C4⋊Dic3C2×C3×C412yes—
159C2×C3⋊C8—22no—
160C22×C32—21no—
161C22×C32—21no—
162C22×C32C2×C22⋊C411yescharacteristic
163C22×C32AGL(1,ℤ/8)12yes—
164C2×C3×D3—42no—
165C2×C3×D3—42no—
166C2×C3×D3—42no—
167C32×C4—21no—
168C32×C4—21no—
169C32×C4—21no—
170C32×C4—21no—
171C32×C4—21no—
172C32×C4—21no—
173C32×C4—82no—
174C3×Dic3—42no—
175C2×#41—61no—
176C4⋊Q8—31no—
177#127—31no—
178#124—61no—
179#121—32no—
180#121—61no—
181C4×D4—32no—
182C4×D4—61no—
183C2×C42C2×C3×D311yescharacteristic
184C4⋊C8—61no—
185C22⋊C8—32no—
186#97—61no—
187#95—21no—
188#95—21no—
189#95C2×C3×D312yes—
190C23×C3—21no—
191C23×C3—62no—
192C23×C3C2×#6711yescharacteristic
193C23×C3C2×C3×D411yescharacteristic
194C22×D3—22no—
195C3×Q8—122no—
196C3×D4—122no—
197C3×D4—122no—
198C3×D4—122no—
199C3×D4—124no—
200C2×C3×C4—22no—
201C2×C3×C4—22no—
202C2×C3×C4—21no—
203C2×C3×C4—21no—
204C2×C3×C4—21no—
205C2×C3×C4—21no—
206C2×C3×C4—21no—
207C2×C3×C4—21no—
208C2×C3×C4—42no—
209C2×C3×C4—41no—
210C2×C3×C4—41no—
211C2×C3×C4—41no—
212C2×C3×C4—41no—
213C2×C3×C4—42no—
214C2×C3×C4—42no—
215C2×C3×C4—44no—
216C2×C3×C4—44no—
217C2×C3×C4—42no—
218C2×C3×C4—42no—
219C2×C3×C4—42no—
220C2×C3×C4—42no—
221C2×C3×C4—44no—
222C2×C3×C4—42no—
223C2×C3×C4—42no—
224C2×C3×C4—62no—
225C2×C3×C4—124no—
226C2×C3×C4(C2×D3)⋊C411yescharacteristic
227C2×C3×C4(C2×D3)⋊C411yescharacteristic
228C2×C3×C4(C2×D3)⋊C411yescharacteristic
229C2×C3×C4(C2×D3)⋊C411yescharacteristic
230C2×C3×C4C3×C22⋊C411yescharacteristic
231C2×C3×C4C3×C22⋊C411yescharacteristic
232C2×C3×C4C3×C22⋊C411yescharacteristic
233C2×C3×C4C3×C22⋊C411yescharacteristic
234C2×C3×C4C2×C4×D311yescharacteristic
235C2×C3×C4C2×D1211yescharacteristic
236C2×C3×C4C22×C3×C411yescharacteristic
237C2×C3×C4C2×C3×D411yescharacteristic
238#67—44no—
239C2×Dic3—22no—
240D12—42no—
241D12—42no—
242D12—42no—
243C4×D3—44no—
244Dic6—42no—
245C3×C8—122no—
246C3⋊C8—42no—
247C2×C32—22no—
248C2×C32#41011yescharacteristic
249C2×C32#41811yescharacteristic
250C2×C32#42111yescharacteristic
251C3×D3—82no—
252#41—124no—
253C2×Q8—61no—
254C2×D4—32no—
255C2×D4—62no—
256C2×D4—61no—
257C2×D4—61no—
258C22×C4—22no—
259C22×C4—62no—
260C22×C4C3×#6711yescharacteristic
261C22×C4C3×#6711yescharacteristic
262C22×C4C22×C3×D311yescharacteristic
263C2×C8—62no—
264C4⋊C4—32no—
265C4⋊C4—61no—
266C22⋊C4—62no—
267C22⋊C4—62no—
268C42C3×C4×D311yescharacteristic
269C42C3×C4×D311yescharacteristic
270C42C3×D1211yescharacteristic
271C42C3×D1211yescharacteristic
272C22×C3—22no—
273C22×C3—22no—
274C22×C3—21no—
275C22×C3—21no—
276C22×C3—21no—
277C22×C3—21no—
278C22×C3—21no—
279C22×C3—22no—
280C22×C3—122no—
281C22×C3—122no—
282C22×C3—122no—
283C22×C3C2×(C2×D3)⋊C411yescharacteristic
284C22×C3#94912yes—
285C22×C3C2×C3×C22⋊C411yescharacteristic
286C22×C3C3×AGL(1,ℤ/8)12yes—
287C2×D3—42no—
288C2×D3—42no—
289C2×D3—42no—
290C3×C4—21no—
291C3×C4—21no—
292C3×C4—21no—
293C3×C4—21no—
294C3×C4—21no—
295C3×C4—21no—
296C3×C4—21no—
297C3×C4—21no—
298C3×C4—21no—
299C3×C4—21no—
300C3×C4—21no—
301C3×C4—21no—
302C3×C4—41no—
303C3×C4—41no—
304C3×C4—41no—
305C3×C4—41no—
306C3×C4—41no—
307C3×C4—41no—
308C3×C4—84no—
309C3×C4—82no—
310C3×C4—82no—
311C3×C4—122no—
312Dic3—42no—
313C32#151411yescharacteristic, complemented, Sylow
314C23—62no—
315C23C2×C3×#6711yescharacteristic
316Q8—122no—
317D4—122no—
318D4—122no—
319D4—122no—
320D4—124no—
321C2×C4—22no—
322C2×C4—41no—
323C2×C4—41no—
324C2×C4—42no—
325C2×C4—42no—
326C2×C4—42no—
327C2×C4—62no—
328C2×C4—124no—
329C2×C4C3×(C2×D3)⋊C411yescharacteristic
330C2×C4C3×(C2×D3)⋊C411yescharacteristic
331C2×C4C3×(C2×D3)⋊C411yescharacteristic
332C2×C4C3×(C2×D3)⋊C411yescharacteristic
333C2×C4C2×C3×C4×D311yescharacteristic
334C2×C4C2×C3×D1211yescharacteristic
335C8—122no—
336C2×C3—24no—
337C2×C3—22no—
338C2×C3—22no—
339C2×C3—21no—
340C2×C3—21no—
341C2×C3—21no—
342C2×C3—242no—
343C2×C3#500111yescharacteristic
344C2×C3#500511yescharacteristic
345C2×C3#500611yescharacteristic
346C2×C3C3×#41011yescharacteristic
347C2×C3C3×#41811yescharacteristic
348C2×C3C3×#42111yescharacteristic
349D3—82no—
350C22—21no—
351C22—21no—
352C22—122no—
353C22—122no—
354C22—122no—
355C22C2×C3×(C2×D3)⋊C411yescharacteristic
356C22C3×#94912yes—
357C4—21no—
358C4—21no—
359C4—21no—
360C4—21no—
361C4—21no—
362C4—21no—
363C4—82no—
364C4—122no—
365C3—21no—
366C3#6956411yescharacteristic, direct product factor
367C3C3×#151411yescharacteristic, complemented
368C2—22no—
369C2—242no—
370C2C3×#500111yescharacteristic
371C2C3×#500511yescharacteristic
372C2C3×#500611yescharacteristic
subgroupG/H
centerC22×C3C2×(C2×D3)⋊C4
commutatorC2×C3×C4C22×C3×C4
FrattiniC22×C4C22×C3×D3
FittingC32×#383C2
socleC22×C32C2×C22⋊C4
prime radicalC3×#5477C2
cosocleC22×C3×C4C23×C3
hypercenterC3×#383D3
hypocenterC3C3×#1514
LCSG ▷ C2×C3×C4 ▷ C22×C3 ▷ C3
UCSC1 ◁ C22×C3 ◁ C2×C3×C42 ◁ C3×#383

Complements

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

NH ≅ G/Ntype
2. C32×#383C2semidirect
3. C3×#4926C2semidirect
4. C3×#4451C2semidirect
6. #69564C3direct (N × H)
12. C3×#874C4semidirect
14. C3×C4×D12C4semidirect
15. C3×#869C4semidirect
26. C3×#383D3semidirect
27. C3×#383C2×C3semidirect
28. #4926C2×C3semidirect
30. #4451C2×C3semidirect
67. #874C3×C4semidirect
69. C4×D12C3×C4semidirect
70. #869C3×C4semidirect
110. #383C3×D3semidirect
313. C32#1514semidirect
366. C3#69564direct (N × H)
367. C3C3×#1514semidirect

Maximal subgroups

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

subgroupindex
C3×#54772
C32×#3832
C3×#49262
C3×#44512
C3×#15143
#695643