Finite Group Databasebeta

← #11785442

Subgroups — #11785442

Order 1152.

679 conjugacy classes of subgroups.

The subgroup lattice has 312 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C23×C3×C3⋊C8C211yesmaximal, characteristic
2#10592906C211yesmaximal, characteristic
3C3×#5207C211yesmaximal, characteristic
4C2×#63577C212yesmaximal, complemented
5#10589166C212yesmaximal, complemented
6#71977—31nomaximal
7#69982—31nomaximal
8C23×C32×C4C2211yescharacteristic
9C2×#3748C2212yes—
10C2×C3×#208C2212yes—
11C22×C3×C3⋊C8—24no—
12C22×C3×C3⋊C8C414yes—
13C22×C3×C3⋊C8C2211yescharacteristic
14C22×C3×C3⋊C8C2211yescharacteristic
15#63657—22no—
16C3×#830—22no—
17#63577—24no—
18C23×C3×C8—31no—
19C23×C3⋊C8D311yescharacteristic
20C3×#407—31no—
21#5207—31no—
22#5207—31no—
23#5207—61no—
24#5207D311yescharacteristic
25C2×#822—32no—
26C2×#819—32no—
27#4558—32no—
28#4552—32no—
29C24×C32Q811yescharacteristic
30C22×C32×C4—22no—
31C22×C32×C4—22no—
32C22×C32×C4C2×C412yes—
33C22×C32×C4D412yes—
34C22×C32×C4Q811yescharacteristic
35C22×C32×C4C2311yescharacteristic
36#3748—22no—
37#3748—22no—
38C2×C3⋊(C3⋊C8)—22no—
39C3×#208—22no—
40C3×#208—22no—
41C2×C3×C3⋊C8—22no—
42C2×C3×C3⋊C8—28no—
43C2×C3×C3⋊C8—22no—
44C2×C3×C3⋊C8C2×C412yes—
45C2×C3×C3⋊C8C2×C412yes—
46C2×C3×C3⋊C8D414yes—
47#1810—91noSylow
48C23×C3×C4—21no—
49C23×C3×C4C2×D311yescharacteristic
50C23×C3×C4C2×D311yescharacteristic
51C2×C3×M16—32no—
52C22×C3×C8—31no—
53C22×C3×C8—34no—
54C22×C3×C8—31no—
55C22×C3×C8—64no—
56C2×#208—32no—
57C2×#208—32no—
58C2×#208—62no—
59C2×#208C2×D312yes—
60C22×C3⋊C8—24no—
61C22×C3⋊C8Dic314yes—
62C22×C3⋊C8C2×D311yescharacteristic
63C22×C3⋊C8C2×D311yescharacteristic
64C3×C22⋊C8—62no—
65#830—22no—
66#830—64no—
67#830—62no—
68#830—62no—
69#822—64no—
70#819—64no—
71C23×C32—24no—
72C23×C32—22no—
73C23×C32C4⋊C412yes—
74C23×C32C2×Q811yescharacteristic
75C2×C32×C4—22no—
76C2×C32×C4—22no—
77C2×C32×C4—22no—
78C2×C32×C4—24no—
79C2×C32×C4C4⋊C412yes—
80C2×C32×C4C22×C411yescharacteristic
81C2×C32×C4C2×D411yescharacteristic
82C2×C32×C4C2×D412yes—
83C2×C32×C4#4112yes—
84C3⋊(C3⋊C8)—42no—
85C3×C3⋊C8—22no—
86C3×C3⋊C8—42no—
87C3×C3⋊C8C22⋊C414yes—
88C23×C8—31no—
89C2×#108—92no—
90#407—31no—
91#407—91no—
92#341—92no—
93C24×C3—21no—
94C24×C3Dic611yescharacteristic
95C24×C3Dic611yescharacteristic
96C22×C3×C4—22no—
97C22×C3×C4—22no—
98C22×C3×C4—22no—
99C22×C3×C4—22no—
100C22×C3×C4—22no—
101C22×C3×C4—22no—
102C22×C3×C4—21no—
103C22×C3×C4—21no—
104C22×C3×C4—42no—
105C22×C3×C4—42no—
106C22×C3×C4Dic611yescharacteristic
107C22×C3×C4Dic611yescharacteristic
108C22×C3×C4C4×D312yes—
109C22×C3×C4D1212yes—
110C22×C3×C4C2×Dic312yes—
111C22×C3×C4#6712yes—
112C22×C3×C4C22×D311yescharacteristic
113C22×C3×C4C22×D311yescharacteristic
114C3×M16—62no—
115C3×M16—62no—
116C2×C3×C8—32no—
117C2×C3×C8—34no—
118C2×C3×C8—32no—
119C2×C3×C8—68no—
120C2×C3×C8—62no—
121C2×C3×C8—62no—
122#208—22no—
123#208—22no—
124#208—62no—
125#208—62no—
126#208—62no—
127#208—62no—
128#208—122no—
129#208—122no—
130C2×C3⋊C8—22no—
131C2×C3⋊C8—28no—
132C2×C3⋊C8—22no—
133C2×C3⋊C8—64no—
134C2×C3⋊C8—62no—
135C2×C3⋊C8—62no—
136C2×C3⋊C8C2×Dic312yes—
137C2×C3⋊C8C2×Dic312yes—
138C2×C3⋊C8#6714yes—
139C22×C32—28no—
140C22×C32—22no—
141C22×C32—22no—
142C22×C32—22no—
143C22×C32#10814yescomplemented
144C22×C32C2×C4⋊C411yescharacteristic
145C22×C32C22⋊Q812yes—
146C32×C4—22no—
147C32×C4C2×C22⋊C411yescharacteristic
148C32×C4#11711yescharacteristic
149C32×C4#12112yes—
150C23×C4D3211yescharacteristic
151C2×M16—32no—
152C2×M16—92no—
153C22×C8—31no—
154C22×C8—34no—
155C22×C8—31no—
156C22×C8—64no—
157#108—184no—
158C22⋊C8—62no—
159C22⋊C8—182no—
160C23×C3—24no—
161C23×C3—24no—
162C23×C3—22no—
163C23×C3—22no—
164C23×C3—22no—
165C23×C3—21no—
166C23×C3—42no—
167C23×C3—44no—
168C23×C3Dic3⋊C412yes—
169C23×C3C4⋊Dic312yes—
170C23×C3C2×Dic611yescharacteristic
171C23×C3C2×Dic611yescharacteristic
172C2×C3×C4—22no—
173C2×C3×C4—22no—
174C2×C3×C4—22no—
175C2×C3×C4—22no—
176C2×C3×C4—22no—
177C2×C3×C4—24no—
178C2×C3×C4—24no—
179C2×C3×C4—22no—
180C2×C3×C4—22no—
181C2×C3×C4—21no—
182C2×C3×C4—22no—
183C2×C3×C4—21no—
184C2×C3×C4—22no—
185C2×C3×C4—42no—
186C2×C3×C4—42no—
187C2×C3×C4—44no—
188C2×C3×C4—42no—
189C2×C3×C4Dic3⋊C412yes—
190C2×C3×C4C4⋊Dic312yes—
191C2×C3×C4C2×C4×D311yescharacteristic
192C2×C3×C4C2×D1211yescharacteristic
193C2×C3×C4#23512yes—
194C2×C3×C4D3×D412yes—
195C2×C3×C4#23712yes—
196C2×C3×C4C22×Dic311yescharacteristic
197C2×C3×C4C2×#6711yescharacteristic
198C2×C3×C4C2×#6712yes—
199C3×C8—34no—
200C3×C8—62no—
201C3×C8—122no—
202C3⋊C8—22no—
203C3⋊C8—42no—
204C3⋊C8—124no—
205C3⋊C8—122no—
206C3⋊C8—122no—
207C3⋊C8#21714yes—
208C2×C32—24no—
209C2×C32—22no—
210C2×C32#38011yescharacteristic
211C2×C32C2×#10812yes—
212C24#62711yescharacteristic
213C22×C4—22no—
214C22×C4—22no—
215C22×C4D3×Dic312yes—
216C22×C4#62612yes—
217C22×C4#62711yescharacteristic
218C22×C4C2×D3211yescharacteristic
219M16—62no—
220M16—62no—
221M16—182no—
222M16—182no—
223C2×C8—32no—
224C2×C8—34no—
225C2×C8—32no—
226C2×C8—68no—
227C2×C8—62no—
228C2×C8—62no—
229C2×C8—182no—
230C22×C3—28no—
231C22×C3—28no—
232C22×C3—22no—
233C22×C3—22no—
234C22×C3—22no—
235C22×C3—22no—
236C22×C3—22no—
237C22×C3—22no—
238C22×C3—24no—
239C22×C3—22no—
240C22×C3—21no—
241C22×C3—42no—
242C22×C3—42no—
243C22×C3—42no—
244C22×C3—48no—
245C22×C3#81914yescomplemented
246C22×C3#82214yescomplemented
247C22×C3#87812yes—
248C22×C3C2×Dic3⋊C411yescharacteristic
249C22×C3#92412yes—
250C22×C3C2×C4⋊Dic311yescharacteristic
251C3×C4—22no—
252C3×C4—22no—
253C3×C4—21no—
254C3×C4—21no—
255C3×C4—22no—
256C3×C4—42no—
257C3×C4#87711yescharacteristic
258C3×C4D3×C22⋊C411yescharacteristic
259C3×C4#92611yescharacteristic
260C3×C4#93012yes—
261C3×C4#93912yes—
262C3×C4C2×#21711yescharacteristic
263C32#181011yescharacteristic, complemented, Sylow
264C23—24no—
265C23—22no—
266C23Dic3⋊Dic312yes—
267C23C2×#62711yescharacteristic
268C2×C4—22no—
269C2×C4—22no—
270C2×C4—22no—
271C2×C4—24no—
272C2×C4Dic3⋊Dic312yes—
273C2×C4C2×D3×Dic311yescharacteristic
274C2×C4#380412yes—
275C2×C4C2×#62611yescharacteristic
276C2×C4D3×#6712yes—
277C8—34no—
278C8—62no—
279C8—122no—
280C8—362no—
281C2×C3—24no—
282C2×C3—22no—
283C2×C3—24no—
284C2×C3—22no—
285C2×C3—22no—
286C2×C3—21no—
287C2×C3—44no—
288C2×C3—42no—
289C2×C3#494211yescharacteristic
290C2×C3C2×#81912yes—
291C2×C3C2×#82212yes—
292C2×C3#521211yescharacteristic
293C22—28no—
294C22—22no—
295C22—22no—
296C22—22no—
297C22#6357714yescomplemented
298C22#6396412yes—
299C22C2×Dic3⋊Dic311yescharacteristic
300C4—22no—
301C4#6395511yescharacteristic
302C4D3×#21711yescharacteristic
303C4#6397812yes—
304C3—21no—
305C3#6998211yescharacteristic, complemented
306C3#7197711yescharacteristic, complemented
307C2—24no—
308C2—22no—
309C2C2×#6357712yes—
310C2#1059171611yescharacteristic
subgroupG/H
centerC2×C4C2×#626
commutatorC2×C32×C4C22×C4
FrattiniC22×C4C2×D32
FittingC23×C32×C4C22
socleC22×C32C2×C4⋊C4
prime radicalC24×C32Q8
cosocleC22×C32×C4C23
hypercenterC23×C4D32
hypocenterC32#1810
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C2×C4 ◁ C23×C4

Complements

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

NH ≅ G/Ntype
4. C2×#63577C2semidirect
5. #10589166C2semidirect
143. C22×C32#108semidirect
245. C22×C3#819semidirect
246. C22×C3#822semidirect
263. C32#1810semidirect
297. C22#63577semidirect
305. C3#69982semidirect
306. C3#71977semidirect

Maximal subgroups

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

subgroupindex
C23×C3×C3⋊C82
#105929062
C3×#52072
C2×#635772
#105891662
#719773
#699823