Finite Group Databasebeta

← C3×#67685 #11771230

Subgroups — C3×#67685 #11771230

Order 1152.

495 conjugacy classes of subgroups.

The subgroup lattice has 366 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C32×#407C211yesmaximal, characteristic
2C3×#5212C211yesmaximal, characteristic
3C3×#5207C211yesmaximal, characteristic
4C3×#1305—31nomaximal
5#67685C311yesmaximal, characteristic, direct product factor
6C23×C32×C4C2211yescharacteristic
7C2×C32×M16—21no—
8C2×C3×#217C412yes—
9C2×C3×C4⋊Dic3—21no—
10C2×C3×#208C412yescomplemented
11C32×C22⋊C8—21no—
12C32×C22⋊C8C412yescomplemented
13C3×C3⋊#95—21no—
14C3×#830—21no—
15C3×#830—21no—
16C3×#407—21no—
17C3×#407—31no—
18C3×#407D311yescharacteristic
19C3×#407C2×C311yescharacteristic
20C3×#380—31no—
21#5212C2×C311yescharacteristic
22#5207C2×C311yescharacteristic
23C24×C32C2×C411yescharacteristic
24C22×C32×C4—42no—
25C22×C32×C4C2×C411yescharacteristic
26C22×C32×C4C2×C411yescharacteristic
27C22×C32×C4D411yescharacteristic
28C22×C32×C4D411yescharacteristic
29C22×C32×C4D411yescharacteristic
30C22×C32×C4Q811yescharacteristic
31C22×C3×Dic3—22no—
32C32×M16—42no—
33C2×C32×C8—22no—
34C3×#217—42no—
35C3×C4⋊Dic3—42no—
36C3×#208—42no—
37C2×C3×C3⋊C8—22no—
38#1305—31noSylow
39C23×C3×C4—21no—
40C23×C3×C4C2×D311yescharacteristic
41C23×C3×C4C22×C311yescharacteristic
42C2×C3×M16—22no—
43C2×C3×M16—21no—
44C2×C3×M16—21no—
45C2×C3×M16—32no—
46C2×C3×C4⋊C4—61no—
47C2×C3×C22⋊C4—32no—
48C2×#217C3×C412yes—
49C2×C4⋊Dic3—21no—
50C2×#208C3×C412yescomplemented
51C3×C22⋊C8—22no—
52C3×C22⋊C8—21no—
53C3×C22⋊C8—21no—
54C3×C22⋊C8—22no—
55C3×C22⋊C8—61no—
56C3×C22⋊C8—61no—
57C3×C22⋊C8Dic312yescomplemented
58C3×C22⋊C8C3×C412yescomplemented
59C3×#95—61no—
60C3⋊#95—21no—
61#830—21no—
62#830—21no—
63C23×C32—21no—
64C23×C32—21no—
65C23×C32—41no—
66C23×C32—41no—
67C23×C32C4211yescharacteristic
68C23×C32C22⋊C411yescharacteristic
69C23×C32C4⋊C411yescharacteristic
70C2×C32×C4—22no—
71C2×C32×C4—22no—
72C2×C32×C4—22no—
73C2×C32×C4—41no—
74C2×C32×C4—41no—
75C2×C32×C4—41no—
76C2×C32×C4C22⋊C411yescharacteristic
77C2×C32×C4C22⋊C411yescharacteristic
78C2×C32×C4C4⋊C411yescharacteristic
79C2×C32×C4C4⋊C411yescharacteristic
80C2×C3×Dic3—42no—
81C2×C3×Dic3—42no—
82C2×C3×Dic3—42no—
83C32×C8—42no—
84C3×C3⋊C8—42no—
85#407—31no—
86#407C3×D311yescharacteristic
87#380—31no—
88C24×C3—21no—
89C24×C3C4×D311yescharacteristic
90C24×C3C2×C3×C411yescharacteristic
91C22×C3×C4—21no—
92C22×C3×C4—21no—
93C22×C3×C4—21no—
94C22×C3×C4—21no—
95C22×C3×C4—21no—
96C22×C3×C4—21no—
97C22×C3×C4—42no—
98C22×C3×C4—42no—
99C22×C3×C4—44no—
100C22×C3×C4—62no—
101C22×C3×C4Dic611yescharacteristic
102C22×C3×C4C4×D311yescharacteristic
103C22×C3×C4D1211yescharacteristic
104C22×C3×C4C2×Dic311yescharacteristic
105C22×C3×C4#6711yescharacteristic
106C22×C3×C4#6711yescharacteristic
107C22×C3×C4C2×C3×C411yescharacteristic
108C22×C3×C4C2×C3×C411yescharacteristic
109C22×C3×C4C3×D411yescharacteristic
110C22×C3×C4C3×D411yescharacteristic
111C22×C3×C4C3×D411yescharacteristic
112C22×C3×C4C3×Q811yescharacteristic
113C22×Dic3—22no—
114C3×M16—44no—
115C3×M16—42no—
116C3×M16—42no—
117C3×M16—122no—
118C2×C3×C8—24no—
119C2×C3×C8—22no—
120C2×C3×C8—22no—
121C2×C3×C8—62no—
122C3×C4⋊C4—122no—
123C3×C22⋊C4—122no—
124#217—42no—
125C4⋊Dic3—42no—
126#208—42no—
127C2×C3⋊C8—22no—
128C22×C32—21no—
129C22×C32—21no—
130C22×C32—21no—
131C22×C32—21no—
132C22×C32—21no—
133C22×C32—21no—
134C22×C32—21no—
135C22×C32—21no—
136C22×C32—42no—
137C22×C32—42no—
138C22×C32#9511yescharacteristic
139C22×C32#10011yescharacteristic
140C22×C32#10111yescharacteristic
141C32×C4—21no—
142C32×C4—21no—
143C32×C4—21no—
144C32×C4#9912yes—
145C3×Dic3—82no—
146C23×C4C2×C3×D311yescharacteristic
147C2×M16—21no—
148C2×M16—32no—
149C2×C4⋊C4—61no—
150C2×C22⋊C4—32no—
151C22⋊C8—21no—
152C22⋊C8—61no—
153C22⋊C8—61no—
154C22⋊C8C3×Dic312yescomplemented
155#95—61no—
156C23×C3—21no—
157C23×C3—21no—
158C23×C3—21no—
159C23×C3—21no—
160C23×C3—21no—
161C23×C3—21no—
162C23×C3—21no—
163C23×C3—41no—
164C23×C3—41no—
165C23×C3—41no—
166C23×C3—41no—
167C23×C3—41no—
168C23×C3—41no—
169C23×C3—42no—
170C23×C3—42no—
171C23×C3C4×Dic311yescharacteristic
172C23×C3Dic3⋊C411yescharacteristic
173C23×C3(C2×D3)⋊C411yescharacteristic
174C23×C3C3×C4211yescharacteristic
175C23×C3C3×C22⋊C411yescharacteristic
176C23×C3C3×C4⋊C411yescharacteristic
177C2×C3×C4—24no—
178C2×C3×C4—22no—
179C2×C3×C4—22no—
180C2×C3×C4—22no—
181C2×C3×C4—22no—
182C2×C3×C4—22no—
183C2×C3×C4—22no—
184C2×C3×C4—21no—
185C2×C3×C4—21no—
186C2×C3×C4—21no—
187C2×C3×C4—21no—
188C2×C3×C4—42no—
189C2×C3×C4—42no—
190C2×C3×C4—41no—
191C2×C3×C4—41no—
192C2×C3×C4—41no—
193C2×C3×C4—41no—
194C2×C3×C4—41no—
195C2×C3×C4—41no—
196C2×C3×C4—42no—
197C2×C3×C4—42no—
198C2×C3×C4—42no—
199C2×C3×C4—122no—
200C2×C3×C4—122no—
201C2×C3×C4—122no—
202C2×C3×C4Dic3⋊C411yescharacteristic
203C2×C3×C4C4⋊Dic311yescharacteristic
204C2×C3×C4(C2×D3)⋊C411yescharacteristic
205C2×C3×C4#21711yescharacteristic
206C2×C3×C4C3×C22⋊C411yescharacteristic
207C2×C3×C4C3×C22⋊C411yescharacteristic
208C2×C3×C4C3×C4⋊C411yescharacteristic
209C2×C3×C4C3×C4⋊C411yescharacteristic
210C2×Dic3—42no—
211C2×Dic3—42no—
212C2×Dic3—42no—
213C3×C8—44no—
214C3×C8—42no—
215C3×C8—42no—
216C3×C8—122no—
217C3⋊C8—42no—
218C2×C32—21no—
219C2×C32—21no—
220C2×C32—41no—
221C2×C32—41no—
222C2×C32#34211yescharacteristic
223C2×C32#34311yescharacteristic
224C2×C32#34411yescharacteristic
225C24C3×C4×D311yescharacteristic
226C22×C4—42no—
227C22×C4—62no—
228C22×C4C3×Dic611yescharacteristic
229C22×C4C3×C4×D311yescharacteristic
230C22×C4C3×D1211yescharacteristic
231C22×C4C2×C3×Dic311yescharacteristic
232C22×C4C3×#6711yescharacteristic
233C22×C4C3×#6711yescharacteristic
234M16—42no—
235M16—122no—
236C2×C8—22no—
237C2×C8—62no—
238C4⋊C4—122no—
239C22⋊C4—122no—
240C22×C3—21no—
241C22×C3—21no—
242C22×C3—21no—
243C22×C3—21no—
244C22×C3—22no—
245C22×C3—22no—
246C22×C3—21no—
247C22×C3—21no—
248C22×C3—21no—
249C22×C3—21no—
250C22×C3—21no—
251C22×C3—21no—
252C22×C3—21no—
253C22×C3—21no—
254C22×C3—21no—
255C22×C3—21no—
256C22×C3—21no—
257C22×C3—21no—
258C22×C3—21no—
259C22×C3—21no—
260C22×C3—21no—
261C22×C3—41no—
262C22×C3—41no—
263C22×C3—41no—
264C22×C3—41no—
265C22×C3—41no—
266C22×C3—41no—
267C22×C3—42no—
268C22×C3—42no—
269C22×C3—42no—
270C22×C3—42no—
271C22×C3—44no—
272C22×C3—44no—
273C22×C3#82311yescharacteristic
274C22×C3#82411yescharacteristic
275C22×C3C3⋊#9511yescharacteristic
276C22×C3C3×#9511yescharacteristic
277C22×C3C3×#10011yescharacteristic
278C22×C3C3×#10111yescharacteristic
279C3×C4—22no—
280C3×C4—21no—
281C3×C4—21no—
282C3×C4—21no—
283C3×C4—21no—
284C3×C4—21no—
285C3×C4—21no—
286C3×C4—22no—
287C3×C4—41no—
288C3×C4—41no—
289C3×C4—242no—
290C3×C4#80612yes—
291C3×C4C3×#9912yes—
292Dic3—82no—
293C32#130511yescharacteristic, complemented, Sylow
294C23—21no—
295C23—21no—
296C23—41no—
297C23—41no—
298C23C3×C4×Dic311yescharacteristic
299C23C3×Dic3⋊C411yescharacteristic
300C23C3×(C2×D3)⋊C411yescharacteristic
301C2×C4—22no—
302C2×C4—22no—
303C2×C4—22no—
304C2×C4—41no—
305C2×C4—41no—
306C2×C4—41no—
307C2×C4—122no—
308C2×C4—122no—
309C2×C4—122no—
310C2×C4C3×Dic3⋊C411yescharacteristic
311C2×C4C3×C4⋊Dic311yescharacteristic
312C2×C4C3×(C2×D3)⋊C411yescharacteristic
313C2×C4C3×#21711yescharacteristic
314C8—42no—
315C8—122no—
316C2×C3—21no—
317C2×C3—21no—
318C2×C3—21no—
319C2×C3—21no—
320C2×C3—21no—
321C2×C3—21no—
322C2×C3—21no—
323C2×C3—41no—
324C2×C3—41no—
325C2×C3—42no—
326C2×C3—42no—
327C2×C3—41no—
328C2×C3—41no—
329C2×C3—41no—
330C2×C3—41no—
331C2×C3#452711yescharacteristic
332C2×C3#455411yescharacteristic
333C2×C3#455611yescharacteristic
334C2×C3C3×#34211yescharacteristic
335C2×C3C3×#34311yescharacteristic
336C2×C3C3×#34411yescharacteristic
337C22—21no—
338C22—21no—
339C22—21no—
340C22—21no—
341C22—21no—
342C22—21no—
343C22—21no—
344C22—21no—
345C22—42no—
346C22—42no—
347C22C3×#82311yescharacteristic
348C22C3×#82411yescharacteristic
349C22C3×C3⋊#9511yescharacteristic
350C4—21no—
351C4—21no—
352C4—21no—
353C4—242no—
354C4C3×#80612yes—
355C3—21no—
356C3#6768511yescharacteristic, direct product factor
357C3C3×#130511yescharacteristic, complemented
358C2—21no—
359C2—21no—
360C2—41no—
361C2—41no—
362C2C3×#452711yescharacteristic
363C2C3×#455411yescharacteristic
364C2C3×#455611yescharacteristic
subgroupG/H
centerC22×C3C3⋊#95
commutatorC23×C3C3×C42
FrattiniC23×C4C2×C3×D3
FittingC32×#407C2
socleC22×C32#95
prime radicalC24×C32C2×C4
cosocleC23×C3×C4C22×C3
hypercenterC3×#407D3
hypocenterC3C3×#1305
LCSG ▷ C23×C3 ▷ C22×C3 ▷ C3
UCSC1 ◁ C22×C3 ◁ C23×C3×C4 ◁ C3×#407

Complements

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

NH ≅ G/Ntype
5. #67685C3direct (N × H)
10. C2×C3×#208C4semidirect
12. C32×C22⋊C8C4semidirect
50. C2×#208C3×C4semidirect
57. C3×C22⋊C8Dic3semidirect
58. C3×C22⋊C8C3×C4semidirect
154. C22⋊C8C3×Dic3semidirect
293. C32#1305semidirect
356. C3#67685direct (N × H)
357. C3C3×#1305semidirect

Maximal subgroups

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

subgroupindex
C32×#4072
C3×#52122
C3×#52072
C3×#13053
#676853