Finite Group Databasebeta

← C3×#67616 #11770876

Subgroups — C3×#67616 #11770876

Order 1152.

581 conjugacy classes of subgroups.

The subgroup lattice has 362 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C32×C4×C22⋊C4C211yesmaximal, characteristic
2C3×#5211C211yesmaximal, characteristic
3C3×#5207C211yesmaximal, characteristic
4C3×#1284—31nomaximal
5#67616C311yesmaximal, characteristic, direct product factor
6C23×C32×C4C2211yescharacteristic
7C2×C32×C22⋊C4—21no—
8C2×C32×C42C412yescomplemented
9C2×C3×#217—21no—
10C2×C3×#208—21no—
11C32×#95—21no—
12C3×C3⋊#95—21no—
13C3×C3⋊#95C412yescomplemented
14C3×#830—21no—
15C3×#830C412yescomplemented
16C3×#407—31no—
17C3×#381—31no—
18C3×C4×C22⋊C4—21no—
19C3×C4×C22⋊C4D311yescharacteristic
20C3×C4×C22⋊C4C2×C311yescharacteristic
21#5211C2×C311yescharacteristic
22#5207C2×C311yescharacteristic
23C24×C32D411yescharacteristic
24C22×C32×C4—22no—
25C22×C32×C4—42no—
26C22×C32×C4C2×C411yescharacteristic
27C22×C32×C4C2×C411yescharacteristic
28C22×C32×C4C2×C411yescharacteristic
29C22×C32×C4D411yescharacteristic
30C22×C32×C4D411yescharacteristic
31C22×C32×C4Q811yescharacteristic
32C22×C3×Dic3—22no—
33C32×C22⋊C4—24no—
34C32×C42—42no—
35C3×#217—42no—
36C3×#208—42no—
37C2×C3×C3⋊C8—22no—
38#1284—31noSylow
39C23×C3×C4—21no—
40C23×C3×C4C2×D311yescharacteristic
41C23×C3×C4C22×C311yescharacteristic
42C2×C3×M16—61no—
43C2×C3×C22⋊C4—22no—
44C2×C3×C22⋊C4—21no—
45C2×C3×C22⋊C4—21no—
46C2×C3×C22⋊C4—61no—
47C2×C3×C42—22no—
48C2×C3×C42Dic312yescomplemented
49C2×C3×C42C3×C412yescomplemented
50C2×#217—21no—
51C2×#208—21no—
52C3×C22⋊C8—32no—
53C3×C22⋊C8—61no—
54C3×#95—22no—
55C3×#95—21no—
56C3×#95—21no—
57C3×#95—32no—
58C3×#95—61no—
59C3⋊#95—21no—
60C3⋊#95C3×C412yescomplemented
61#830—21no—
62#830C3×C412yescomplemented
63C23×C32—22no—
64C23×C32—22no—
65C23×C32—41no—
66C23×C32C22⋊C411yescharacteristic
67C23×C32C22⋊C411yescharacteristic
68C23×C32C4⋊C411yescharacteristic
69C2×C32×C4—22no—
70C2×C32×C4—24no—
71C2×C32×C4—22no—
72C2×C32×C4—41no—
73C2×C32×C4—41no—
74C2×C32×C4—41no—
75C2×C32×C4—41no—
76C2×C32×C4—42no—
77C2×C32×C4—42no—
78C2×C32×C4C4211yescharacteristic
79C2×C32×C4C22⋊C411yescharacteristic
80C2×C32×C4C4⋊C411yescharacteristic
81C2×C32×C4C4⋊C411yescharacteristic
82C2×C3×Dic3—42no—
83C2×C3×Dic3—42no—
84C2×C3×Dic3—42no—
85C3×C3⋊C8—42no—
86#407—31no—
87#381—31no—
88C4×C22⋊C4C3×D311yescharacteristic
89C24×C3—21no—
90C24×C3#6711yescharacteristic
91C24×C3C3×D411yescharacteristic
92C22×C3×C4—24no—
93C22×C3×C4—22no—
94C22×C3×C4—22no—
95C22×C3×C4—21no—
96C22×C3×C4—21no—
97C22×C3×C4—21no—
98C22×C3×C4—21no—
99C22×C3×C4—21no—
100C22×C3×C4—21no—
101C22×C3×C4—42no—
102C22×C3×C4—42no—
103C22×C3×C4—44no—
104C22×C3×C4—62no—
105C22×C3×C4Dic611yescharacteristic
106C22×C3×C4C4×D311yescharacteristic
107C22×C3×C4C4×D311yescharacteristic
108C22×C3×C4D1211yescharacteristic
109C22×C3×C4C2×Dic311yescharacteristic
110C22×C3×C4#6711yescharacteristic
111C22×C3×C4C2×C3×C411yescharacteristic
112C22×C3×C4C2×C3×C411yescharacteristic
113C22×C3×C4C2×C3×C411yescharacteristic
114C22×C3×C4C3×D411yescharacteristic
115C22×C3×C4C3×D411yescharacteristic
116C22×C3×C4C3×Q811yescharacteristic
117C22×Dic3—22no—
118C3×M16—122no—
119C2×C3×C8—62no—
120C3×C22⋊C4—28no—
121C3×C22⋊C4—24no—
122C3×C22⋊C4—24no—
123C3×C22⋊C4—122no—
124C3×C42—42no—
125C3×C42—42no—
126C3×C42—44no—
127#217—42no—
128#208—42no—
129C2×C3⋊C8—22no—
130C22×C32—21no—
131C22×C32—21no—
132C22×C32—21no—
133C22×C32—21no—
134C22×C32—21no—
135C22×C32—21no—
136C22×C32—21no—
137C22×C32—44no—
138C22×C32#9511yescharacteristic
139C22×C32#9912yes—
140C22×C32#10412yes—
141C32×C4—21no—
142C32×C4—21no—
143C32×C4—21no—
144C32×C4—21no—
145C32×C4—44no—
146C3×Dic3—82no—
147C23×C4C2×C3×D311yescharacteristic
148C2×M16—61no—
149C2×C22⋊C4—21no—
150C2×C22⋊C4—61no—
151C2×C42C3×Dic312yescomplemented
152C22⋊C8—32no—
153C22⋊C8—61no—
154#95—21no—
155#95—32no—
156#95—61no—
157C23×C3—24no—
158C23×C3—22no—
159C23×C3—22no—
160C23×C3—22no—
161C23×C3—22no—
162C23×C3—21no—
163C23×C3—21no—
164C23×C3—21no—
165C23×C3—42no—
166C23×C3—41no—
167C23×C3—41no—
168C23×C3—42no—
169C23×C3Dic3⋊C411yescharacteristic
170C23×C3(C2×D3)⋊C411yescharacteristic
171C23×C3#21711yescharacteristic
172C23×C3C3×C22⋊C411yescharacteristic
173C23×C3C3×C22⋊C411yescharacteristic
174C23×C3C3×C4⋊C411yescharacteristic
175C2×C3×C4—24no—
176C2×C3×C4—22no—
177C2×C3×C4—22no—
178C2×C3×C4—22no—
179C2×C3×C4—22no—
180C2×C3×C4—28no—
181C2×C3×C4—24no—
182C2×C3×C4—24no—
183C2×C3×C4—21no—
184C2×C3×C4—21no—
185C2×C3×C4—21no—
186C2×C3×C4—21no—
187C2×C3×C4—42no—
188C2×C3×C4—41no—
189C2×C3×C4—41no—
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—42no—
200C2×C3×C4—44no—
201C2×C3×C4—44no—
202C2×C3×C4—42no—
203C2×C3×C4—42no—
204C2×C3×C4—42no—
205C2×C3×C4—42no—
206C2×C3×C4—122no—
207C2×C3×C4—122no—
208C2×C3×C4—122no—
209C2×C3×C4C4×Dic311yescharacteristic
210C2×C3×C4Dic3⋊C411yescharacteristic
211C2×C3×C4C4⋊Dic311yescharacteristic
212C2×C3×C4(C2×D3)⋊C411yescharacteristic
213C2×C3×C4C3×C4211yescharacteristic
214C2×C3×C4C3×C22⋊C411yescharacteristic
215C2×C3×C4C3×C4⋊C411yescharacteristic
216C2×C3×C4C3×C4⋊C411yescharacteristic
217C2×Dic3—42no—
218C2×Dic3—42no—
219C2×Dic3—42no—
220C3×C8—122no—
221C3⋊C8—42no—
222C2×C32—22no—
223C2×C32—22no—
224C2×C32—41no—
225C2×C32H(3,ℤ/4)11yescharacteristic
226C2×C32#33911yescharacteristic
227C2×C32#34211yescharacteristic
228C24C3×#6711yescharacteristic
229C22×C4—22no—
230C22×C4—42no—
231C22×C4—62no—
232C22×C4C3×Dic611yescharacteristic
233C22×C4C3×C4×D311yescharacteristic
234C22×C4C3×C4×D311yescharacteristic
235C22×C4C3×D1211yescharacteristic
236C22×C4C2×C3×Dic311yescharacteristic
237C22×C4C3×#6711yescharacteristic
238M16—122no—
239C2×C8—62no—
240C22⋊C4—24no—
241C22⋊C4—122no—
242C42—42no—
243C22×C3—22no—
244C22×C3—22no—
245C22×C3—21no—
246C22×C3—21no—
247C22×C3—21no—
248C22×C3—21no—
249C22×C3—21no—
250C22×C3—21no—
251C22×C3—21no—
252C22×C3—21no—
253C22×C3—22no—
254C22×C3—21no—
255C22×C3—21no—
256C22×C3—21no—
257C22×C3—21no—
258C22×C3—21no—
259C22×C3—21no—
260C22×C3—22no—
261C22×C3—21no—
262C22×C3—22no—
263C22×C3—41no—
264C22×C3—41no—
265C22×C3—41no—
266C22×C3—41no—
267C22×C3—44no—
268C22×C3—44no—
269C22×C3—48no—
270C22×C3#80512yes—
271C22×C3C3⋊#9511yescharacteristic
272C22×C3#83412yes—
273C22×C3C3×#9511yescharacteristic
274C22×C3C3×#9912yes—
275C22×C3C3×#10412yes—
276C3×C4—22no—
277C3×C4—22no—
278C3×C4—21no—
279C3×C4—21no—
280C3×C4—21no—
281C3×C4—21no—
282C3×C4—21no—
283C3×C4—21no—
284C3×C4—21no—
285C3×C4—21no—
286C3×C4—41no—
287C3×C4—41no—
288C3×C4—48no—
289C3×C4—44no—
290C3×C4—44no—
291C3×C4—242no—
292Dic3—82no—
293C32#128411yescharacteristic, complemented, Sylow
294C23—22no—
295C23—22no—
296C23—41no—
297C23C3×Dic3⋊C411yescharacteristic
298C23C3×(C2×D3)⋊C411yescharacteristic
299C23C3×#21711yescharacteristic
300C2×C4—22no—
301C2×C4—22no—
302C2×C4—24no—
303C2×C4—41no—
304C2×C4—41no—
305C2×C4—41no—
306C2×C4—41no—
307C2×C4—42no—
308C2×C4—42no—
309C2×C4—122no—
310C2×C4—122no—
311C2×C4—122no—
312C2×C4C3×C4×Dic311yescharacteristic
313C2×C4C3×Dic3⋊C411yescharacteristic
314C2×C4C3×C4⋊Dic311yescharacteristic
315C2×C4C3×(C2×D3)⋊C411yescharacteristic
316C8—122no—
317C2×C3—24no—
318C2×C3—22no—
319C2×C3—22no—
320C2×C3—22no—
321C2×C3—22no—
322C2×C3—21no—
323C2×C3—21no—
324C2×C3—21no—
325C2×C3—42no—
326C2×C3—42no—
327C2×C3—41no—
328C2×C3—41no—
329C2×C3#452311yescharacteristic
330C2×C3#452611yescharacteristic
331C2×C3#453111yescharacteristic
332C2×C3C3×H(3,ℤ/4)11yescharacteristic
333C2×C3C3×#33911yescharacteristic
334C2×C3C3×#34211yescharacteristic
335C22—21no—
336C22—21no—
337C22—21no—
338C22—21no—
339C22—21no—
340C22—21no—
341C22—21no—
342C22—44no—
343C22C3×#80512yes—
344C22C3×C3⋊#9511yescharacteristic
345C22C3×#83412yes—
346C4—21no—
347C4—21no—
348C4—21no—
349C4—21no—
350C4—44no—
351C4—242no—
352C3—21no—
353C3#6761611yescharacteristic, direct product factor
354C3C3×#128411yescharacteristic, complemented
355C2—22no—
356C2—22no—
357C2—41no—
358C2C3×#452311yescharacteristic
359C2C3×#452611yescharacteristic
360C2C3×#453111yescharacteristic
subgroupG/H
centerC22×C3C3⋊#95
commutatorC2×C3×C4C3×C42
FrattiniC23×C4C2×C3×D3
FittingC32×C4×C22⋊C4C2
socleC22×C32#95
prime radicalC24×C32D4
cosocleC23×C3×C4C22×C3
hypercenterC3×C4×C22⋊C4D3
hypocenterC3C3×#1284
LCSG ▷ C2×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C22×C3 ◁ C23×C3×C4 ◁ C3×C4×C22⋊C4

Complements

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

NH ≅ G/Ntype
5. #67616C3direct (N × H)
8. C2×C32×C42C4semidirect
13. C3×C3⋊#95C4semidirect
15. C3×#830C4semidirect
48. C2×C3×C42Dic3semidirect
49. C2×C3×C42C3×C4semidirect
60. C3⋊#95C3×C4semidirect
62. #830C3×C4semidirect
151. C2×C42C3×Dic3semidirect
293. C32#1284semidirect
353. C3#67616direct (N × H)
354. C3C3×#1284semidirect

Maximal subgroups

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

subgroupindex
C32×C4×C22⋊C42
C3×#52112
C3×#52072
C3×#12843
#676163