Finite Group Databasebeta

← C3×#82209 #11858866

Subgroups — C3×#82209 #11858866

Order 1152.

949 conjugacy classes of subgroups.

The subgroup lattice has 317 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C32×#117C211yesmaximal, characteristic
2C3×#5207C212yesmaximal
3C3×#5000C218yesmaximal, complemented
4C3×#4924C212yesmaximal, complemented
5C3×C4×#208C212yesmaximal, complemented
6C3×#2921—31nomaximal
7#82209C311yesmaximal, characteristic, direct product factor
8C23×C32×C4C2211yescharacteristic
9C32×#117C414yes—
10C32×#117C2214yes—
11C2×C32×C4⋊C4C412yes—
12C2×C32×C22⋊C4C412yes—
13C2×C32×C42C2211yescharacteristic
14C2×C32×C42C2211yescharacteristic
15C2×C3×#208C2214yes—
16C3×#830C2218yes—
17C3×C4⋊(C3⋊C8)C2218yescomplemented
18C3×#803C2214yescomplemented
19C3×C4×C3⋊C8C2214yescomplemented
20C2×C3×#117—21no—
21C2×C3×#117D311yescharacteristic
22C2×C3×#117C2×C311yescharacteristic
23C3×#433—38no—
24C3×#423—32no—
25C3×#407—32no—
26C3×C4×M16—32no—
27#5207C2×C312yes—
28#5000C2×C318yescomplemented
29#4924C2×C312yescomplemented
30C4×#208C2×C312yescomplemented
31C24×C32C2×C411yescharacteristic
32C22×C32×C4—24no—
33C22×C32×C4C2×C411yescharacteristic
34C22×C32×C4C2×C412yes—
35C22×C32×C4C2×C412yes—
36C22×C32×C4C2×C412yes—
37C22×C32×C4C2312yes—
38C22×C32×C4C2311yescharacteristic
39C32×C4⋊C4C2×C418yes—
40C32×C22⋊C4C2×C418yes—
41C32×C42C2×C412yes—
42C32×C42C2×C412yes—
43C32×C42C2312yes—
44C32×C42C2312yes—
45C3×#208—28no—
46C2×C3×C3⋊C8C2318yes—
47#2921—31noSylow
48C23×C3×C4—21no—
49C23×C3×C4C2×D311yescharacteristic
50C23×C3×C4C22×C311yescharacteristic
51C2×C3×M16—34no—
52C3×#117—24no—
53C3×#117—24no—
54C3×#117Dic314yes—
55C3×#117C3×C414yes—
56C3×#117C2×D314yes—
57C3×#117C22×C314yes—
58C2×C3×C4⋊C4—22no—
59C2×C3×C4⋊C4Dic312yes—
60C2×C3×C4⋊C4C3×C412yes—
61C2×C3×C22⋊C4—22no—
62C2×C3×C22⋊C4Dic312yes—
63C2×C3×C22⋊C4C3×C412yes—
64C2×C3×C42—21no—
65C2×C3×C42—21no—
66C2×C3×C42C2×D311yescharacteristic
67C2×C3×C42C2×D311yescharacteristic
68C2×C3×C42C22×C311yescharacteristic
69C2×C3×C42C22×C311yescharacteristic
70C2×#208C22×C314yes—
71C3×C4⋊C8—38no—
72C3×C22⋊C8—38no—
73C3×#97—34no—
74C3×C4×C8—34no—
75#830C22×C318yes—
76C4⋊(C3⋊C8)C22×C318yescomplemented
77#803C22×C314yescomplemented
78C4×C3⋊C8C22×C314yescomplemented
79C23×C32—22no—
80C23×C32—42no—
81C23×C32C22×C412yes—
82C23×C32C22×C411yescharacteristic
83C2×C32×C4—22no—
84C2×C32×C4—24no—
85C2×C32×C4—24no—
86C2×C32×C4—42no—
87C2×C32×C4—42no—
88C2×C32×C4C22×C414yes—
89C2×C32×C4C22×C414yes—
90C2×C32×C4C22×C412yes—
91C2×C32×C4C22×C411yescharacteristic
92C2×C32×C4#4114yes—
93C2×C32×C4C2411yescharacteristic
94C3×C3⋊C8—28no—
95C2×#117C3×D311yescharacteristic
96#433—38no—
97#423—32no—
98#407—32no—
99C4×M16—32no—
100C24×C3—21no—
101C24×C3C2×Dic311yescharacteristic
102C24×C3C2×C3×C411yescharacteristic
103C22×C3×C4—28no—
104C22×C3×C4—24no—
105C22×C3×C4—24no—
106C22×C3×C4—21no—
107C22×C3×C4—22no—
108C22×C3×C4—22no—
109C22×C3×C4—22no—
110C22×C3×C4—21no—
111C22×C3×C4—22no—
112C22×C3×C4C2×Dic311yescharacteristic
113C22×C3×C4C2×Dic312yes—
114C22×C3×C4C2×Dic312yes—
115C22×C3×C4C2×Dic312yes—
116C22×C3×C4C2×C3×C411yescharacteristic
117C22×C3×C4C2×C3×C412yes—
118C22×C3×C4C2×C3×C412yes—
119C22×C3×C4C2×C3×C412yes—
120C22×C3×C4C22×D312yes—
121C22×C3×C4C22×D311yescharacteristic
122C22×C3×C4C23×C312yes—
123C22×C3×C4C23×C311yescharacteristic
124C3×M16—68no—
125C2×C3×C8—38no—
126C3×C4⋊C4—28no—
127C3×C4⋊C4C2×Dic318yes—
128C3×C4⋊C4C2×C3×C418yes—
129C3×C22⋊C4—28no—
130C3×C22⋊C4C2×Dic318yes—
131C3×C22⋊C4C2×C3×C418yes—
132C3×C42—22no—
133C3×C42—22no—
134C3×C42—22no—
135C3×C42—22no—
136C3×C42C2×Dic312yes—
137C3×C42C2×Dic312yes—
138C3×C42C2×C3×C412yes—
139C3×C42C2×C3×C412yes—
140C3×C42C22×D312yes—
141C3×C42C22×D312yes—
142C3×C42C23×C312yes—
143C3×C42C23×C312yes—
144#208—28no—
145C2×C3⋊C8C23×C318yes—
146C22×C32—22no—
147C22×C32—22no—
148C22×C32—24no—
149C22×C32—44no—
150C22×C32#11712yes—
151C22×C32C23×C411yescharacteristic
152C32×C4—22no—
153C32×C4—24no—
154C32×C4—24no—
155C32×C4#11712yes—
156C32×C4C2×#4112yes—
157C23×C4C2×C3×D311yescharacteristic
158C2×M16—34no—
159#117C3×Dic314yes—
160#117C2×C3×D314yes—
161C2×C4⋊C4C3×Dic312yes—
162C2×C22⋊C4C3×Dic312yes—
163C2×C42C2×C3×D311yescharacteristic
164C2×C42C2×C3×D311yescharacteristic
165C4⋊C8—38no—
166C22⋊C8—38no—
167#97—34no—
168C4×C8—34no—
169C23×C3—24no—
170C23×C3—22no—
171C23×C3—22no—
172C23×C3—21no—
173C23×C3—22no—
174C23×C3—42no—
175C23×C3—42no—
176C23×C3—44no—
177C23×C3C22×Dic312yes—
178C23×C3C22×Dic311yescharacteristic
179C23×C3C22×C3×C412yes—
180C23×C3C22×C3×C411yescharacteristic
181C2×C3×C4—24no—
182C2×C3×C4—28no—
183C2×C3×C4—28no—
184C2×C3×C4—22no—
185C2×C3×C4—22no—
186C2×C3×C4—24no—
187C2×C3×C4—24no—
188C2×C3×C4—24no—
189C2×C3×C4—24no—
190C2×C3×C4—21no—
191C2×C3×C4—24no—
192C2×C3×C4—21no—
193C2×C3×C4—22no—
194C2×C3×C4—24no—
195C2×C3×C4—24no—
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#23514yes—
203C2×C3×C4C22×Dic314yes—
204C2×C3×C4C22×Dic314yes—
205C2×C3×C4C22×Dic312yes—
206C2×C3×C4C22×Dic311yescharacteristic
207C2×C3×C4C22×C3×C414yes—
208C2×C3×C4C22×C3×C414yes—
209C2×C3×C4C22×C3×C412yes—
210C2×C3×C4C22×C3×C411yescharacteristic
211C2×C3×C4C3×#4114yes—
212C2×C3×C4C23×D311yescharacteristic
213C2×C3×C4C24×C311yescharacteristic
214C3×C8—68no—
215C3⋊C8—28no—
216C2×C32—22no—
217C2×C32—42no—
218C2×C32C2×#11711yescharacteristic
219C2×C32#56812yes—
220C24C2×C3×Dic311yescharacteristic
221C22×C4—24no—
222C22×C4C2×C3×Dic311yescharacteristic
223C22×C4C2×C3×Dic312yes—
224C22×C4C2×C3×Dic312yes—
225C22×C4C2×C3×Dic312yes—
226C22×C4C22×C3×D312yes—
227C22×C4C22×C3×D311yescharacteristic
228M16—68no—
229C2×C8—38no—
230C4⋊C4C2×C3×Dic318yes—
231C22⋊C4C2×C3×Dic318yes—
232C42C2×C3×Dic312yes—
233C42C2×C3×Dic312yes—
234C42C22×C3×D312yes—
235C42C22×C3×D312yes—
236C22×C3—24no—
237C22×C3—22no—
238C22×C3—22no—
239C22×C3—24no—
240C22×C3—24no—
241C22×C3—22no—
242C22×C3—24no—
243C22×C3—22no—
244C22×C3—22no—
245C22×C3—21no—
246C22×C3—44no—
247C22×C3—48no—
248C22×C3—44no—
249C22×C3—44no—
250C22×C3#92612yes—
251C22×C3C3×#11712yes—
252C22×C3C23×Dic311yescharacteristic
253C22×C3C23×C3×C411yescharacteristic
254C3×C4—24no—
255C3×C4—24no—
256C3×C4—24no—
257C3×C4—22no—
258C3×C4—24no—
259C3×C4—24no—
260C3×C4—22no—
261C3×C4—22no—
262C3×C4—22no—
263C3×C4—44no—
264C3×C4—44no—
265C3×C4#92612yes—
266C3×C4C3×#11712yes—
267C3×C4C2×#23512yes—
268C3×C4C2×C3×#4112yes—
269C32#292111yescharacteristic, complemented, Sylow
270C23—22no—
271C23—42no—
272C23C22×C3×Dic312yes—
273C23C22×C3×Dic311yescharacteristic
274C2×C4—22no—
275C2×C4—24no—
276C2×C4—24no—
277C2×C4—42no—
278C2×C4—42no—
279C2×C4C3×#23514yes—
280C2×C4C22×C3×Dic314yes—
281C2×C4C22×C3×Dic314yes—
282C2×C4C22×C3×Dic312yes—
283C2×C4C22×C3×Dic311yescharacteristic
284C2×C4C23×C3×D311yescharacteristic
285C8—68no—
286C2×C3—24no—
287C2×C3—22no—
288C2×C3—22no—
289C2×C3—21no—
290C2×C3—22no—
291C2×C3—44no—
292C2×C3—42no—
293C2×C3—42no—
294C2×C3C2×#92611yescharacteristic
295C2×C3#581912yes—
296C2×C3C2×C3×#11711yescharacteristic
297C2×C3C3×#56812yes—
298C22—22no—
299C22—22no—
300C22—24no—
301C22—44no—
302C22C3×#92612yes—
303C22C23×C3×Dic311yescharacteristic
304C4—22no—
305C4—24no—
306C4—24no—
307C4C3×#92612yes—
308C4C2×C3×#23512yes—
309C3—21no—
310C3#8220911yescharacteristic, direct product factor
311C3C3×#292111yescharacteristic, complemented
312C2—22no—
313C2—42no—
314C2C2×C3×#92611yescharacteristic
315C2C3×#581912yes—
subgroupG/H
centerC2×C3×C4C23×D3
commutatorC22×C3C23×C3×C4
FrattiniC2×C4C23×C3×D3
FittingC2×C32×#117C2
socleC22×C32C23×C4
prime radicalC24×C32C2×C4
cosocleC2×C3×C4C24×C3
hypercenterC2×C3×#117D3
hypocenterC3C3×#2921
LCSG ▷ C22×C3 ▷ C3
UCSC1 ◁ C2×C3×C4 ◁ C2×C3×#117

Complements

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

NH ≅ G/Ntype
3. C3×#5000C2semidirect
4. C3×#4924C2semidirect
5. C3×C4×#208C2semidirect
7. #82209C3direct (N × H)
17. C3×C4⋊(C3⋊C8)C22semidirect
18. C3×#803C22semidirect
19. C3×C4×C3⋊C8C22semidirect
28. #5000C2×C3semidirect
29. #4924C2×C3semidirect
30. C4×#208C2×C3semidirect
76. C4⋊(C3⋊C8)C22×C3semidirect
77. #803C22×C3semidirect
78. C4×C3⋊C8C22×C3semidirect
269. C32#2921semidirect
310. C3#82209direct (N × H)
311. C3C3×#2921semidirect

Maximal subgroups

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

subgroupindex
C2×C32×#1172
C3×#52072
C3×#50002
C3×#49242
C3×C4×#2082
C3×#29213
#822093