Finite Group Databasebeta

← C3×#67680 #11771108

Subgroups — C3×#67680 #11771108

Order 1152.

481 conjugacy classes of subgroups.

The subgroup lattice has 330 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C32×C22⋊C8C211yesmaximal, characteristic
2C3×#5207C211yesmaximal, characteristic
3C2×C3×#830C211yesmaximal, characteristic
4C3×#1298—31nomaximal
5#67680C311yesmaximal, characteristic, direct product factor
6C23×C32×C4C2211yescharacteristic
7C22×C32×C8—21no—
8C2×C3×#208C412yes—
9C22×C3×C3⋊C8—21no—
10C32×C22⋊C8—21no—
11C32×C22⋊C8C412yes—
12C3×#830—21no—
13C3×#830—21no—
14C3×#830—21no—
15C3×#830C412yes—
16C3×#407—31no—
17C2×C3×C22⋊C8—21no—
18C2×C3×C22⋊C8—31no—
19C2×C3×C22⋊C8D311yescharacteristic
20C2×C3×C22⋊C8C2×C311yescharacteristic
21#5207C2×C311yescharacteristic
22C2×#830C2×C311yescharacteristic
23C24×C32Q811yescharacteristic
24C22×C32×C4—42no—
25C22×C32×C4C2×C411yescharacteristic
26C22×C32×C4C2×C411yescharacteristic
27C22×C32×C4C2×C411yescharacteristic
28C22×C32×C4D411yescharacteristic
29C22×C32×C4D411yescharacteristic
30C22×C32×C4D411yescharacteristic
31C2×C32×C8—22no—
32C2×C32×C8—42no—
33C3×#208—42no—
34C2×C3×C3⋊C8—22no—
35C2×C3×C3⋊C8—22no—
36C2×C3×C3⋊C8—42no—
37#1298—31noSylow
38C23×C3×C4—21no—
39C23×C3×C4C2×D311yescharacteristic
40C23×C3×C4C22×C311yescharacteristic
41C2×C3×M16—32no—
42C22×C3×C8—22no—
43C22×C3×C8—21no—
44C22×C3×C8—21no—
45C22×C3×C8—61no—
46C2×#208C3×C412yes—
47C22×C3⋊C8—21no—
48C3×C22⋊C8—22no—
49C3×C22⋊C8—21no—
50C3×C22⋊C8—21no—
51C3×C22⋊C8—22no—
52C3×C22⋊C8—32no—
53C3×C22⋊C8—61no—
54C3×C22⋊C8—61no—
55C3×C22⋊C8—61no—
56C3×C22⋊C8Dic312yes—
57C3×C22⋊C8C3×C412yes—
58#830—21no—
59#830—21no—
60#830—21no—
61#830C3×C412yes—
62C23×C32—22no—
63C23×C32—22no—
64C23×C32—41no—
65C23×C32C4⋊C411yescharacteristic
66C23×C32C4⋊C411yescharacteristic
67C23×C32C4⋊C411yescharacteristic
68C2×C32×C4—22no—
69C2×C32×C4—22no—
70C2×C32×C4—22no—
71C2×C32×C4—41no—
72C2×C32×C4—41no—
73C2×C32×C4—41no—
74C2×C32×C4C4211yescharacteristic
75C2×C32×C4C22⋊C411yescharacteristic
76C2×C32×C4C22⋊C411yescharacteristic
77C2×C32×C4C22⋊C411yescharacteristic
78C32×C8—42no—
79C3×C3⋊C8—42no—
80C3×C3⋊C8—42no—
81#407—31no—
82C2×C22⋊C8—31no—
83C2×C22⋊C8C3×D311yescharacteristic
84C24×C3—21no—
85C24×C3Dic611yescharacteristic
86C24×C3C3×Q811yescharacteristic
87C22×C3×C4—21no—
88C22×C3×C4—21no—
89C22×C3×C4—21no—
90C22×C3×C4—21no—
91C22×C3×C4—21no—
92C22×C3×C4—21no—
93C22×C3×C4—42no—
94C22×C3×C4—42no—
95C22×C3×C4—44no—
96C22×C3×C4C4×D311yescharacteristic
97C22×C3×C4C4×D311yescharacteristic
98C22×C3×C4D1211yescharacteristic
99C22×C3×C4C2×Dic311yescharacteristic
100C22×C3×C4#6711yescharacteristic
101C22×C3×C4#6711yescharacteristic
102C22×C3×C4C2×C3×C411yescharacteristic
103C22×C3×C4C2×C3×C411yescharacteristic
104C22×C3×C4C2×C3×C411yescharacteristic
105C22×C3×C4C3×D411yescharacteristic
106C22×C3×C4C3×D411yescharacteristic
107C22×C3×C4C3×D411yescharacteristic
108C3×M16—122no—
109C2×C3×C8—24no—
110C2×C3×C8—22no—
111C2×C3×C8—22no—
112C2×C3×C8—44no—
113C2×C3×C8—42no—
114C2×C3×C8—42no—
115C2×C3×C8—62no—
116C2×C3×C8—62no—
117C2×C3×C8—122no—
118#208—42no—
119C2×C3⋊C8—22no—
120C2×C3⋊C8—22no—
121C2×C3⋊C8—42no—
122C22×C32—21no—
123C22×C32—21no—
124C22×C32—21no—
125C22×C32—21no—
126C22×C32—21no—
127C22×C32—21no—
128C22×C32—21no—
129C22×C32—44no—
130C22×C32#9511yescharacteristic
131C22×C32#10812yes—
132C22×C32#10812yes—
133C32×C4—21no—
134C32×C4—21no—
135C32×C4—21no—
136C32×C4#9912yes—
137C23×C4C2×C3×D311yescharacteristic
138C2×M16—32no—
139C22×C8—21no—
140C22×C8—61no—
141C22⋊C8—21no—
142C22⋊C8—32no—
143C22⋊C8—61no—
144C22⋊C8—61no—
145C22⋊C8—61no—
146C22⋊C8C3×Dic312yes—
147C23×C3—24no—
148C23×C3—22no—
149C23×C3—22no—
150C23×C3—22no—
151C23×C3—22no—
152C23×C3—21no—
153C23×C3—21no—
154C23×C3—21no—
155C23×C3—42no—
156C23×C3—41no—
157C23×C3—41no—
158C23×C3—42no—
159C23×C3Dic3⋊C411yescharacteristic
160C23×C3Dic3⋊C411yescharacteristic
161C23×C3C4⋊Dic311yescharacteristic
162C23×C3C3×C4⋊C411yescharacteristic
163C23×C3C3×C4⋊C411yescharacteristic
164C23×C3C3×C4⋊C411yescharacteristic
165C2×C3×C4—24no—
166C2×C3×C4—22no—
167C2×C3×C4—22no—
168C2×C3×C4—22no—
169C2×C3×C4—22no—
170C2×C3×C4—22no—
171C2×C3×C4—22no—
172C2×C3×C4—21no—
173C2×C3×C4—21no—
174C2×C3×C4—21no—
175C2×C3×C4—21no—
176C2×C3×C4—42no—
177C2×C3×C4—42no—
178C2×C3×C4—41no—
179C2×C3×C4—41no—
180C2×C3×C4—41no—
181C2×C3×C4—41no—
182C2×C3×C4—41no—
183C2×C3×C4—41no—
184C2×C3×C4—42no—
185C2×C3×C4—42no—
186C2×C3×C4—42no—
187C2×C3×C4C4×Dic311yescharacteristic
188C2×C3×C4(C2×D3)⋊C411yescharacteristic
189C2×C3×C4(C2×D3)⋊C411yescharacteristic
190C2×C3×C4#21711yescharacteristic
191C2×C3×C4C3×C4211yescharacteristic
192C2×C3×C4C3×C22⋊C411yescharacteristic
193C2×C3×C4C3×C22⋊C411yescharacteristic
194C2×C3×C4C3×C22⋊C411yescharacteristic
195C3×C8—44no—
196C3×C8—42no—
197C3×C8—42no—
198C3×C8—122no—
199C3×C8—122no—
200C3⋊C8—42no—
201C3⋊C8—42no—
202C2×C32—22no—
203C2×C32—22no—
204C2×C32—41no—
205C2×C32#34111yescharacteristic
206C2×C32#34111yescharacteristic
207C2×C32#34211yescharacteristic
208C24C3×Dic611yescharacteristic
209C22×C4—42no—
210C22×C4C3×C4×D311yescharacteristic
211C22×C4C3×C4×D311yescharacteristic
212C22×C4C3×D1211yescharacteristic
213C22×C4C2×C3×Dic311yescharacteristic
214C22×C4C3×#6711yescharacteristic
215C22×C4C3×#6711yescharacteristic
216M16—122no—
217C2×C8—22no—
218C2×C8—42no—
219C2×C8—62no—
220C2×C8—62no—
221C2×C8—122no—
222C22×C3—22no—
223C22×C3—22no—
224C22×C3—21no—
225C22×C3—21no—
226C22×C3—21no—
227C22×C3—21no—
228C22×C3—21no—
229C22×C3—21no—
230C22×C3—21no—
231C22×C3—21no—
232C22×C3—22no—
233C22×C3—21no—
234C22×C3—21no—
235C22×C3—21no—
236C22×C3—21no—
237C22×C3—21no—
238C22×C3—21no—
239C22×C3—22no—
240C22×C3—22no—
241C22×C3—21no—
242C22×C3—41no—
243C22×C3—41no—
244C22×C3—41no—
245C22×C3—41no—
246C22×C3—44no—
247C22×C3—44no—
248C22×C3—48no—
249C22×C3#81912yes—
250C22×C3#82212yes—
251C22×C3C3⋊#9511yescharacteristic
252C22×C3C3×#9511yescharacteristic
253C22×C3C3×#10812yes—
254C22×C3C3×#10812yes—
255C3×C4—22no—
256C3×C4—21no—
257C3×C4—21no—
258C3×C4—21no—
259C3×C4—21no—
260C3×C4—21no—
261C3×C4—21no—
262C3×C4—22no—
263C3×C4—41no—
264C3×C4—41no—
265C3×C4#80612yes—
266C3×C4C3×#9912yes—
267C32#129811yescharacteristic, complemented, Sylow
268C23—22no—
269C23—22no—
270C23—41no—
271C23C3×Dic3⋊C411yescharacteristic
272C23C3×Dic3⋊C411yescharacteristic
273C23C3×C4⋊Dic311yescharacteristic
274C2×C4—22no—
275C2×C4—22no—
276C2×C4—22no—
277C2×C4—41no—
278C2×C4—41no—
279C2×C4—41no—
280C2×C4C3×C4×Dic311yescharacteristic
281C2×C4C3×(C2×D3)⋊C411yescharacteristic
282C2×C4C3×(C2×D3)⋊C411yescharacteristic
283C2×C4C3×#21711yescharacteristic
284C8—42no—
285C8—122no—
286C8—122no—
287C2×C3—24no—
288C2×C3—22no—
289C2×C3—22no—
290C2×C3—22no—
291C2×C3—22no—
292C2×C3—21no—
293C2×C3—21no—
294C2×C3—21no—
295C2×C3—42no—
296C2×C3—42no—
297C2×C3—41no—
298C2×C3—41no—
299C2×C3#452711yescharacteristic
300C2×C3#455211yescharacteristic
301C2×C3#455811yescharacteristic
302C2×C3C3×#34111yescharacteristic
303C2×C3C3×#34111yescharacteristic
304C2×C3C3×#34211yescharacteristic
305C22—21no—
306C22—21no—
307C22—21no—
308C22—21no—
309C22—21no—
310C22—21no—
311C22—21no—
312C22—44no—
313C22C3×#81912yes—
314C22C3×#82212yes—
315C22C3×C3⋊#9511yescharacteristic
316C4—21no—
317C4—21no—
318C4—21no—
319C4C3×#80612yes—
320C3—21no—
321C3#6768011yescharacteristic, direct product factor
322C3C3×#129811yescharacteristic, complemented
323C2—22no—
324C2—22no—
325C2—41no—
326C2C3×#452711yescharacteristic
327C2C3×#455211yescharacteristic
328C2C3×#455811yescharacteristic
subgroupG/H
centerC2×C3×C4(C2×D3)⋊C4
commutatorC2×C3×C4C3×C42
FrattiniC23×C4C2×C3×D3
FittingC2×C32×C22⋊C8C2
socleC22×C32#95
prime radicalC24×C32Q8
cosocleC23×C3×C4C22×C3
hypercenterC2×C3×C22⋊C8D3
hypocenterC3C3×#1298
LCSG ▷ C2×C3×C4 ▷ C22×C3 ▷ C3
UCSC1 ◁ C2×C3×C4 ◁ C23×C3×C4 ◁ C2×C3×C22⋊C8

Complements

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

NH ≅ G/Ntype
5. #67680C3direct (N × H)
267. C32#1298semidirect
321. C3#67680direct (N × H)
322. C3C3×#1298semidirect

Maximal subgroups

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

subgroupindex
C2×C32×C22⋊C82
C3×#52072
C2×C3×#8302
C3×#12983
#676803