Finite Group Databasebeta

← C3×D3×#395 #11808176

Subgroups — C3×D3×#395 #11808176

Order 1152.

1907 conjugacy classes of subgroups.

The subgroup lattice has 351 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C3×D3×Q8C211yesmaximal, characteristic
2C2×C3×D3×C4⋊C4C213yesmaximal
3C32×#395C211yesmaximal, characteristic, complemented
4C3×#5230C211yesmaximal, characteristic, complemented
5C3×#4979C213yesmaximal, complemented
6C3×D3×#95C213yesmaximal
7C3×#4656C213yesmaximal, complemented
8C2×C3×#395—31nomaximal
9D3×#395C311yesmaximal, characteristic, direct product factor
10C22×C32×Q8C2211yescharacteristic
11C2×C3×D3×Q8—212no—
12C22×C3×C4×D3C2211yescharacteristic
13C22×C3×C4×D3C2213yes—
14C22×C3×C4×D3C2213yes—
15C22×C3×Dic6C2213yes—
16C2×C32×C4⋊C4C2213yes—
17C2×C3×C4⋊Dic3C2213yes—
18C2×C3×Dic3⋊C4C2213yes—
19C2×C3×Dic3⋊C4C2213yes—
20C3×D3×C4⋊C4—212no—
21C32×#95C2213yes—
22C3×C3⋊#95C2216yes—
23C3×C3⋊#95C2213yes—
24C23×C3×Q8—31no—
25C22×D3×Q8C2×C311yescharacteristic
26C22×C3×C4⋊C4—33no—
27C2×D3×C4⋊C4C2×C313yes—
28C3×#395—21no—
29C3×#395—31no—
30C3×#395—33no—
31C3×#395—33no—
32C3×#395D311yescharacteristic, direct product factor
33C3×#395C2×C311yescharacteristic, complemented
34C2×C3×#95—33no—
35#5230C2×C311yescharacteristic, complemented
36#4979C2×C313yescomplemented
37D3×#95C2×C313yes—
38#4656C2×C313yescomplemented
39C23×C3×D3C2311yescharacteristic
40C2×C32×Q8—26no—
41C22×C32×C4C2311yescharacteristic
42C22×C32×C4C2313yes—
43C22×C32×C4C2313yes—
44C22×C3×Dic3C2311yescharacteristic
45C22×C3×Dic3C2313yes—
46C22×C3×Dic3C2313yes—
47C3×D3×Q8—232no—
48C2×C3×C4×D3—26no—
49C2×C3×C4×D3—212no—
50C2×C3×C4×D3—26no—
51C2×C3×C4×D3—26no—
52C2×C3×C4×D3D4112yes—
53C2×C3×C4×D3Q8112yescomplemented
54C2×C3×Dic6—26no—
55C2×C3×Dic6—212no—
56C32×C4⋊C4—26no—
57C3×C4⋊Dic3—26no—
58C3×Dic3⋊C4—26no—
59C3×Dic3⋊C4—26no—
60C2×#395—31noSylow
61C22×C3×Q8—21no—
62C22×C3×Q8—33no—
63C22×C3×Q8—612no—
64C22×C3×Q8C2×D311yescharacteristic
65C22×C3×Q8C22×C311yescharacteristic
66C23×C3×C4—33no—
67C23×C3×C4—33no—
68C23×C3×C4—31no—
69C2×D3×Q8—212no—
70C22×C4×D3C22×C311yescharacteristic
71C22×C4×D3C22×C313yes—
72C22×C4×D3C22×C313yes—
73C22×Dic6C22×C313yes—
74C2×C3×C4⋊C4—23no—
75C2×C3×C4⋊C4—33no—
76C2×C3×C4⋊C4—33no—
77C2×C3×C4⋊C4—33no—
78C2×C3×C4⋊C4—612no—
79C2×C3×C4⋊C4C2×D313yes—
80C2×C3×C4⋊C4C22×C313yes—
81C2×C4⋊Dic3C22×C313yes—
82C2×Dic3⋊C4C22×C313yes—
83C2×Dic3⋊C4C22×C313yes—
84D3×C4⋊C4—212no—
85C3×#95—23no—
86C3×#95—33no—
87C3×#95—36no—
88C3×#95C2×D313yes—
89C3×#95C22×C313yes—
90C3⋊#95C22×C316yes—
91C3⋊#95C22×C313yes—
92C23×C32C2411yescharacteristic
93C22×C3×D3C2×D416yes—
94C22×C3×D3C2×Q816yes—
95C22×C3×D3#4112yes—
96C32×Q8—28no—
97C2×C32×C4—23no—
98C2×C32×C4—26no—
99C2×C32×C4—23no—
100C2×C32×C4—23no—
101C2×C32×C4C2×D416yes—
102C2×C32×C4C2×Q816yescomplemented
103C2×C3×Dic3—23no—
104C2×C3×Dic3—26no—
105C2×C3×Dic3—23no—
106C2×C3×Dic3—23no—
107C2×C3×Dic3C2×D416yes—
108C2×C3×Dic3C2×Q816yescomplemented
109C3×C4×D3—224no—
110C3×C4×D3—224no—
111C3×C4×D3—44no—
112C3×Dic6—224no—
113C23×Q8—31no—
114C22×C4⋊C4—33no—
115#395—31no—
116#395—33no—
117#395—33no—
118#395C3×D311yescharacteristic, direct product factor
119C2×#95—33no—
120C24×C3—31no—
121C23×D3C23×C311yescharacteristic
122C2×C3×Q8—26no—
123C2×C3×Q8—26no—
124C2×C3×Q8—46no—
125C2×C3×Q8—612no—
126C2×C3×Q8—632no—
127C2×C3×Q8—66no—
128C22×C3×C4—23no—
129C22×C3×C4—23no—
130C22×C3×C4—21no—
131C22×C3×C4—33no—
132C22×C3×C4—33no—
133C22×C3×C4—312no—
134C22×C3×C4—312no—
135C22×C3×C4—31no—
136C22×C3×C4—66no—
137C22×C3×C4—66no—
138C22×C3×C4—612no—
139C22×C3×C4—66no—
140C22×C3×C4C22×D311yescharacteristic
141C22×C3×C4C22×D313yes—
142C22×C3×C4C22×D313yes—
143C22×C3×C4C23×C311yescharacteristic
144C22×C3×C4C23×C313yes—
145C22×C3×C4C23×C313yes—
146C22×Dic3C23×C311yescharacteristic
147C22×Dic3C23×C313yes—
148C22×Dic3C23×C313yes—
149D3×Q8—232no—
150C2×C4×D3—26no—
151C2×C4×D3—212no—
152C2×C4×D3—26no—
153C2×C4×D3—26no—
154C2×C4×D3C3×D4112yes—
155C2×C4×D3C3×Q8112yescomplemented
156C2×Dic6—26no—
157C2×Dic6—212no—
158C3×C4⋊C4—26no—
159C3×C4⋊C4—26no—
160C3×C4⋊C4—46no—
161C3×C4⋊C4—66no—
162C3×C4⋊C4—66no—
163C3×C4⋊C4—66no—
164C4⋊Dic3—26no—
165Dic3⋊C4—26no—
166Dic3⋊C4—26no—
167C22×C32C22×D413yes—
168C22×C32C22×Q813yes—
169C22×C32C2×#4111yescharacteristic
170C2×C3×D3#12014yes—
171C2×C3×D3C22⋊Q8112yes—
172C2×C3×D3C4⋊Q8112yes—
173C32×C4—26no—
174C32×C4—26no—
175C32×C4—41no—
176C3×Dic3—26no—
177C3×Dic3—26no—
178C3×Dic3—41no—
179C22×Q8—33no—
180C22×Q8—612no—
181C22×Q8C2×C3×D311yescharacteristic
182C23×C4—33no—
183C23×C4—33no—
184C23×C4—31no—
185C2×C4⋊C4—33no—
186C2×C4⋊C4—33no—
187C2×C4⋊C4—33no—
188C2×C4⋊C4—612no—
189C2×C4⋊C4C2×C3×D313yes—
190#95—33no—
191#95—36no—
192#95C2×C3×D313yes—
193C23×C3—21no—
194C23×C3—36no—
195C23×C3—36no—
196C23×C3—32no—
197C23×C3C23×D311yescharacteristic
198C23×C3C24×C311yescharacteristic
199C22×D3C2×C3×D416yes—
200C22×D3C2×C3×Q816yes—
201C22×D3C3×#4112yes—
202C3×Q8—28no—
203C3×Q8—28no—
204C3×Q8—48no—
205C3×Q8—624no—
206C2×C3×C4—23no—
207C2×C3×C4—26no—
208C2×C3×C4—23no—
209C2×C3×C4—23no—
210C2×C3×C4—26no—
211C2×C3×C4—23no—
212C2×C3×C4—23no—
213C2×C3×C4—23no—
214C2×C3×C4—26no—
215C2×C3×C4—26no—
216C2×C3×C4—36no—
217C2×C3×C4—36no—
218C2×C3×C4—43no—
219C2×C3×C4—43no—
220C2×C3×C4—46no—
221C2×C3×C4—43no—
222C2×C3×C4—624no—
223C2×C3×C4—624no—
224C2×C3×C4—63no—
225C2×C3×C4—66no—
226C2×C3×C4—63no—
227C2×C3×C4—63no—
228C2×C3×C4—124no—
229C2×C3×C4D3×D416yes—
230C2×C3×C4D3×Q816yescomplemented
231C2×C3×C4C2×C3×D416yes—
232C2×C3×C4C2×C3×Q816yescomplemented
233C2×Dic3—23no—
234C2×Dic3—26no—
235C2×Dic3—23no—
236C2×Dic3—23no—
237C2×Dic3C2×C3×D416yes—
238C2×Dic3C2×C3×Q816yescomplemented
239C4×D3—224no—
240C4×D3—224no—
241C4×D3—44no—
242Dic6—224no—
243C2×C32C2×#12011yescharacteristic
244C2×C32C2×C22⋊Q813yes—
245C2×C32C2×C4⋊Q813yes—
246C3×D3#39518yesdirect product factor
247C24—31no—
248C2×Q8—26no—
249C2×Q8—612no—
250C2×Q8—632no—
251C2×Q8—66no—
252C22×C4—33no—
253C22×C4—33no—
254C22×C4—312no—
255C22×C4—312no—
256C22×C4—31no—
257C22×C4—66no—
258C22×C4—612no—
259C22×C4—66no—
260C22×C4—66no—
261C22×C4C22×C3×D311yescharacteristic
262C22×C4C22×C3×D313yes—
263C22×C4C22×C3×D313yes—
264C4⋊C4—26no—
265C4⋊C4—66no—
266C4⋊C4—66no—
267C4⋊C4—66no—
268C22×C3—23no—
269C22×C3—23no—
270C22×C3—21no—
271C22×C3—312no—
272C22×C3—34no—
273C22×C3—312no—
274C22×C3C2×D3×D413yes—
275C22×C3C2×D3×Q813yes—
276C22×C3D3×#4111yescharacteristic
277C22×C3C22×C3×D413yes—
278C22×C3C22×C3×Q813yes—
279C22×C3C2×C3×#4111yescharacteristic
280C2×D3C3×#12014yes—
281C2×D3C3×C22⋊Q8112yes—
282C2×D3C3×C4⋊Q8112yes—
283C3×C4—26no—
284C3×C4—26no—
285C3×C4—26no—
286C3×C4—26no—
287C3×C4—46no—
288C3×C4—46no—
289C3×C4—41no—
290C3×C4—41no—
291C3×C4—66no—
292C3×C4—66no—
293C3×C4—81no—
294C3×C4—121no—
295Dic3—26no—
296Dic3—26no—
297Dic3—41no—
298C32C2×#39511yescharacteristic, complemented, Sylow
299C23—36no—
300C23—36no—
301C23—32no—
302C23C23×C3×D311yescharacteristic
303Q8—28no—
304Q8—624no—
305C2×C4—23no—
306C2×C4—26no—
307C2×C4—23no—
308C2×C4—23no—
309C2×C4—36no—
310C2×C4—36no—
311C2×C4—624no—
312C2×C4—624no—
313C2×C4—63no—
314C2×C4—66no—
315C2×C4—63no—
316C2×C4—63no—
317C2×C4—124no—
318C2×C4C3×D3×D416yes—
319C2×C4C3×D3×Q816yescomplemented
320C2×C3—21no—
321C2×C3—23no—
322C2×C3—23no—
323C2×C3—38no—
324C2×C3D3×#12011yescharacteristic
325C2×C3D3×C22⋊Q813yes—
326C2×C3D3×C4⋊Q813yes—
327C2×C3C2×C3×#12011yescharacteristic
328C2×C3C2×C3×C22⋊Q813yes—
329C2×C3C2×C3×C4⋊Q813yes—
330D3C3×#39518yesdirect product factor
331C22—34no—
332C22—312no—
333C22—312no—
334C22C2×C3×D3×D413yes—
335C22C2×C3×D3×Q813yes—
336C22C3×D3×#4111yescharacteristic
337C4—26no—
338C4—26no—
339C4—41no—
340C4—66no—
341C4—66no—
342C4—121no—
343C3—21no—
344C3D3×#39511yescharacteristic, direct product factor
345C3C2×C3×#39511yescharacteristic, complemented
346C2—38no—
347C2C3×D3×#12011yescharacteristic
348C2C3×D3×C22⋊Q813yes—
349C2C3×D3×C4⋊Q813yes—
subgroupG/H
centerC23×C3C23×D3
commutator, cosocleC23×C3C24×C3
FrattiniC23C23×C3×D3
FittingC32×#395C2
socleC23×C32C24
prime radicalC23×C3×D3C23
hypercenterC3×#395D3
hypocenterC3C2×C3×#395
LCSG ▷ C23×C3 ▷ C3
UCSC1 ◁ C23×C3 ◁ C3×#395

Complements

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

NH ≅ G/Ntype
3. C32×#395C2semidirect
4. C3×#5230C2semidirect
5. C3×#4979C2semidirect
7. C3×#4656C2semidirect
9. D3×#395C3direct (N × H)
32. C3×#395D3direct (N × H)
33. C3×#395C2×C3semidirect
35. #5230C2×C3semidirect
36. #4979C2×C3semidirect
38. #4656C2×C3semidirect
53. C2×C3×C4×D3Q8semidirect
102. C2×C32×C4C2×Q8semidirect
108. C2×C3×Dic3C2×Q8semidirect
118. #395C3×D3direct (N × H)
155. C2×C4×D3C3×Q8semidirect
230. C2×C3×C4D3×Q8semidirect
232. C2×C3×C4C2×C3×Q8semidirect
238. C2×Dic3C2×C3×Q8semidirect
246. C3×D3#395direct (N × H)
298. C32C2×#395semidirect
319. C2×C4C3×D3×Q8semidirect
330. D3C3×#395direct (N × H)
344. C3D3×#395direct (N × H)
345. C3C2×C3×#395semidirect

Maximal subgroups

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

subgroupindex
C22×C3×D3×Q82
C2×C3×D3×C4⋊C42
C32×#3952
C3×#52302
C3×#49792
C3×D3×#952
C3×#46562
C2×C3×#3953
D3×#3953