Finite Group Databasebeta

← C3×#78445 #11861335

Subgroups — C3×#78445 #11861335

Order 1152.

809 conjugacy classes of subgroups.

The subgroup lattice has 311 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#5470C211yesmaximal, characteristic
2C2×C32×C4×C8C211yesmaximal, characteristic
3C3×#5102C212yesmaximal
4C3×#5101C212yesmaximal
5C3×#4924C211yesmaximal, characteristic
6C3×#4679C214yesmaximal, complemented
7C3×C8×Dic6C214yesmaximal, complemented
8C3×#2960—31nomaximal
9#78445C311yesmaximal, characteristic, direct product factor
10C22×C32×C8C2211yescharacteristic
11C22×C32×C8C2211yescharacteristic
12C2×C32×C42C2211yescharacteristic
13C3×#926C2212yes—
14C3×#924C414yes—
15C2×C3×#208C2212yes—
16C3×#870C412yes—
17C3×#869C412yes—
18C3×C4×Dic6C2214yes—
19C32×C4×C8C2212yes—
20C32×C4×C8C2212yes—
21C3×#815C2214yes—
22C3×Dic3⋊C8C2218yes—
23C3×C8×Dic3C2214yes—
24C3×C4⋊(C3⋊C8)C2214yes—
25C3×#533—31no—
26#5470C2×C311yescharacteristic
27C3×#446—34no—
28C3×C8×Q8—34no—
29C3×#424—32no—
30C3×#423—31no—
31C3×#405—32no—
32C2×C3×C4×C8—21no—
33C2×C3×C4×C8D311yescharacteristic
34C2×C3×C4×C8C2×C311yescharacteristic
35#5102C2×C312yes—
36#5101C2×C312yes—
37#4924C2×C311yescharacteristic
38#4679C2×C314yescomplemented
39C8×Dic6C2×C314yescomplemented
40C22×C32×C4C2×C412yes—
41C22×C32×C4C2311yescharacteristic
42C2×C3×Dic6C2×C414yes—
43C2×C32×C8—22no—
44C2×C32×C8Q814yescomplemented
45C2×C32×C8C2312yes—
46C2×C32×C8C2311yescharacteristic
47C2×C32×C8C2311yescharacteristic
48C32×C42C2×C411yescharacteristic
49C32×C42C2×C411yescharacteristic
50C32×C42C2312yes—
51C3×#217C2×C414yes—
52C3×C4⋊Dic3C2×C414yes—
53C3×C4⋊Dic3C2×C414yes—
54C3×Dic3⋊C4C2×C418yes—
55C3×C4×Dic3C2314yes—
56C3×#208—24no—
57C2×C3×C3⋊C8C2314yes—
58#2960—31noSylow
59C2×C3×M16—32no—
60C22×C3×C8—21no—
61C22×C3×C8—21no—
62C22×C3×C8C2×D311yescharacteristic
63C22×C3×C8C2×D311yescharacteristic
64C22×C3×C8C22×C311yescharacteristic
65C22×C3×C8C22×C311yescharacteristic
66C3×C4⋊Q8—32no—
67C3×#125—32no—
68C3×C22⋊Q8—34no—
69C3×C4×Q8—34no—
70C3×#117—32no—
71C2×C3×C42—21no—
72C2×C3×C42C2×D311yescharacteristic
73C2×C3×C42C22×C311yescharacteristic
74#926C22×C312yes—
75#924C3×C414yes—
76C2×#208C22×C312yes—
77#870C3×C412yes—
78#869C3×C412yes—
79C4×Dic6C22×C314yes—
80C3×C4⋊C8—38no—
81C3×C4⋊C8—34no—
82C3×#97—34no—
83C3×C4×C8—22no—
84C3×C4×C8—22no—
85C3×C4×C8—34no—
86C3×C4×C8C2×D312yes—
87C3×C4×C8C2×D312yes—
88C3×C4×C8C22×C312yes—
89C3×C4×C8C22×C312yes—
90#815C22×C314yes—
91Dic3⋊C8C22×C318yes—
92C8×Dic3C22×C314yes—
93C4⋊(C3⋊C8)C22×C314yes—
94C23×C32C22×C411yescharacteristic
95C2×C32×C4—24no—
96C2×C32×C4C22×C412yes—
97C2×C32×C4C22×C411yescharacteristic
98C2×C32×C4C22×C412yes—
99C2×C32×C4C2×Q812yes—
100C2×C32×C4#4112yes—
101C2×C32×C4C2411yescharacteristic
102C2×C3×Dic3C22×C418yes—
103C3×Dic6—28no—
104C32×C8—22no—
105C32×C8C2×Q812yes—
106C32×C8C2×Q812yes—
107C3×C3⋊C8—24no—
108#533—31no—
109#446—34no—
110C8×Q8—34no—
111#424—32no—
112#423—31no—
113#405—32no—
114C2×C4×C8C3×D311yescharacteristic
115C2×C3×Q8—34no—
116C22×C3×C4—22no—
117C22×C3×C4—21no—
118C22×C3×C4C4×D312yes—
119C22×C3×C4C2×C3×C412yes—
120C22×C3×C4C22×D311yescharacteristic
121C22×C3×C4C23×C311yescharacteristic
122C2×Dic6C2×C3×C414yes—
123C3×M16—64no—
124C2×C3×C8—24no—
125C2×C3×C8—22no—
126C2×C3×C8—22no—
127C2×C3×C8—24no—
128C2×C3×C8—22no—
129C2×C3×C8—21no—
130C2×C3×C8—21no—
131C2×C3×C8—34no—
132C2×C3×C8Dic614yescomplemented
133C2×C3×C8C3×Q814yescomplemented
134C2×C3×C8C22×D312yes—
135C2×C3×C8C22×D311yescharacteristic
136C2×C3×C8C22×D311yescharacteristic
137C2×C3×C8C23×C312yes—
138C2×C3×C8C23×C311yescharacteristic
139C2×C3×C8C23×C311yescharacteristic
140C3×C4⋊C4—38no—
141C3×C4⋊C4—34no—
142C3×C4⋊C4—34no—
143C3×C22⋊C4—34no—
144C3×C42—21no—
145C3×C42—21no—
146C3×C42—22no—
147C3×C42—34no—
148C3×C42C4×D311yescharacteristic
149C3×C42C4×D311yescharacteristic
150C3×C42C2×C3×C411yescharacteristic
151C3×C42C2×C3×C411yescharacteristic
152C3×C42C22×D312yes—
153C3×C42C23×C312yes—
154#217C2×C3×C414yes—
155C4⋊Dic3C2×C3×C414yes—
156C4⋊Dic3C2×C3×C414yes—
157Dic3⋊C4C2×C3×C418yes—
158C4×Dic3C23×C314yes—
159#208—24no—
160C2×C3⋊C8C23×C314yes—
161C22×C32—22no—
162C22×C32C4×Q812yes—
163C22×C32C23×C411yescharacteristic
164C32×C4—22no—
165C32×C4C4×Q812yes—
166C32×C4#13114yes—
167C32×C4C22×Q811yescharacteristic
168C32×C4C2×#4111yescharacteristic
169C3×Dic3—28no—
170C2×M16—32no—
171C22×C8C2×C3×D311yescharacteristic
172C22×C8C2×C3×D311yescharacteristic
173C4⋊Q8—32no—
174#125—32no—
175C22⋊Q8—34no—
176C4×Q8—34no—
177#117—32no—
178C2×C42C2×C3×D311yescharacteristic
179C4⋊C8—38no—
180C4⋊C8—34no—
181#97—34no—
182C4×C8—34no—
183C4×C8C2×C3×D312yes—
184C4×C8C2×C3×D312yes—
185C23×C3—21no—
186C23×C3C2×C4×D311yescharacteristic
187C23×C3C22×C3×C411yescharacteristic
188C3×Q8—68no—
189C2×C3×C4—28no—
190C2×C3×C4—24no—
191C2×C3×C4—24no—
192C2×C3×C4—21no—
193C2×C3×C4—22no—
194C2×C3×C4—22no—
195C2×C3×C4—22no—
196C2×C3×C4—21no—
197C2×C3×C4—22no—
198C2×C3×C4—38no—
199C2×C3×C4C2×Dic612yes—
200C2×C3×C4C2×C4×D312yes—
201C2×C3×C4C2×C4×D311yescharacteristic
202C2×C3×C4C2×C4×D312yes—
203C2×C3×C4#23512yes—
204C2×C3×C4C22×C3×C412yes—
205C2×C3×C4C22×C3×C411yescharacteristic
206C2×C3×C4C22×C3×C412yes—
207C2×C3×C4C2×C3×Q812yes—
208C2×C3×C4C3×#4112yes—
209C2×C3×C4C23×D311yescharacteristic
210C2×C3×C4C24×C311yescharacteristic
211C2×Dic3C22×C3×C418yes—
212Dic6—28no—
213C3×C8—24no—
214C3×C8—22no—
215C3×C8—22no—
216C3×C8—22no—
217C3×C8—22no—
218C3×C8—64no—
219C3×C8C2×Dic612yes—
220C3×C8C2×Dic612yes—
221C3×C8C2×C3×Q812yes—
222C3×C8C2×C3×Q812yes—
223C3⋊C8—24no—
224C2×C32—22no—
225C2×C32C2×C4×Q811yescharacteristic
226C2×C32C2×#13112yes—
227C2×Q8—34no—
228C22×C4C3×C4×D312yes—
229C22×C4C22×C3×D311yescharacteristic
230M16—64no—
231C2×C8—22no—
232C2×C8—34no—
233C2×C8C3×Dic614yescomplemented
234C2×C8C22×C3×D312yes—
235C2×C8C22×C3×D311yescharacteristic
236C2×C8C22×C3×D311yescharacteristic
237C4⋊C4—34no—
238C4⋊C4—38no—
239C4⋊C4—34no—
240C22⋊C4—34no—
241C42—34no—
242C42C3×C4×D311yescharacteristic
243C42C3×C4×D311yescharacteristic
244C42C22×C3×D312yes—
245C22×C3—24no—
246C22×C3—22no—
247C22×C3—22no—
248C22×C3—21no—
249C22×C3—22no—
250C22×C3C4×Dic612yes—
251C22×C3C3×C4×Q812yes—
252C22×C3C22×C4×D311yescharacteristic
253C22×C3C23×C3×C411yescharacteristic
254C3×C4—24no—
255C3×C4—22no—
256C3×C4—22no—
257C3×C4—24no—
258C3×C4—21no—
259C3×C4—21no—
260C3×C4—22no—
261C3×C4—68no—
262C3×C4C4×Dic612yes—
263C3×C4#90114yes—
264C3×C4C3×C4×Q812yes—
265C3×C4C3×#13114yes—
266C3×C4C22×Dic611yescharacteristic
267C3×C4C2×#23511yescharacteristic
268C3×C4C22×C3×Q811yescharacteristic
269C3×C4C2×C3×#4111yescharacteristic
270Dic3—28no—
271C32#296011yescharacteristic, complemented, Sylow
272C23C2×C3×C4×D311yescharacteristic
273Q8—68no—
274C2×C4—24no—
275C2×C4—38no—
276C2×C4C2×C3×Dic612yes—
277C2×C4C2×C3×C4×D312yes—
278C2×C4C2×C3×C4×D312yes—
279C2×C4C2×C3×C4×D311yescharacteristic
280C2×C4C3×#23512yes—
281C2×C4C23×C3×D311yescharacteristic
282C8—22no—
283C8—64no—
284C8C2×C3×Dic612yes—
285C8C2×C3×Dic612yes—
286C2×C3—24no—
287C2×C3—22no—
288C2×C3—22no—
289C2×C3—21no—
290C2×C3—22no—
291C2×C3C2×C4×Dic611yescharacteristic
292C2×C3C2×#90112yes—
293C2×C3C2×C3×C4×Q811yescharacteristic
294C2×C3C2×C3×#13112yes—
295C22—22no—
296C22C3×C4×Dic612yes—
297C22C22×C3×C4×D311yescharacteristic
298C4—22no—
299C4—68no—
300C4C3×C4×Dic612yes—
301C4C3×#90114yes—
302C4C22×C3×Dic611yescharacteristic
303C4C2×C3×#23511yescharacteristic
304C3—21no—
305C3#7844511yescharacteristic, direct product factor
306C3C3×#296011yescharacteristic, complemented
307C2—22no—
308C2C2×C3×C4×Dic611yescharacteristic
309C2C2×C3×#90112yes—
subgroupG/H
centerC2×C3×C8C22×D3
commutatorC22×C3C23×C3×C4
FrattiniC2×C4C23×C3×D3
FittingC2×C32×C4×C8C2
socleC22×C32C23×C4
prime radicalC23×C32C22×C4
cosocleC2×C3×C4C24×C3
hypercenterC2×C3×C4×C8D3
hypocenterC3C3×#2960
LCSG ▷ C22×C3 ▷ C3
UCSC1 ◁ C2×C3×C8 ◁ C2×C3×C4×C8

Complements

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

NH ≅ G/Ntype
6. C3×#4679C2semidirect
7. C3×C8×Dic6C2semidirect
9. #78445C3direct (N × H)
38. #4679C2×C3semidirect
39. C8×Dic6C2×C3semidirect
44. C2×C32×C8Q8semidirect
132. C2×C3×C8Dic6semidirect
133. C2×C3×C8C3×Q8semidirect
233. C2×C8C3×Dic6semidirect
271. C32#2960semidirect
305. C3#78445direct (N × H)
306. C3C3×#2960semidirect

Maximal subgroups

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

subgroupindex
C3×#54702
C2×C32×C4×C82
C3×#51022
C3×#51012
C3×#49242
C3×#46792
C3×C8×Dic62
C3×#29603
#784453