Finite Group Databasebeta

← #13078756

Subgroups — #13078756

Order 1408.

450 conjugacy classes of subgroups; only the 125 normal subgroups are shown.

normal subgroups only

This group has 450 conjugacy classes of subgroups — too many to draw. Only its 125 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10623010C211yesmaximal, characteristic, complemented
2C2×C4×D44C211yesmaximal, characteristic, complemented
3C11×#432C211yesmaximal, characteristic, complemented
4#10622460C212yesmaximal, complemented
5#10622457C212yesmaximal, complemented
6#10622349C211yesmaximal, characteristic, complemented
7#10622345C211yesmaximal, characteristic
8#10622344C211yesmaximal, characteristic, complemented
9#10622334C211yesmaximal, characteristic, complemented
10#10622324C212yesmaximal, complemented
11#10622323C212yesmaximal, complemented
12C22×D44C2211yescharacteristic
13C22×C4×D11—21no—
14C2×C42×C11C2211yescharacteristic
15#66983C2211yescharacteristic
16#66982—21no—
17C4×C22⋊D11—21no—
18C2×(C2×D11)⋊C4—21no—
19C2×C4⋊Dic11C2211yescharacteristic
20#66977C2211yescharacteristic
21C2×D88C2212yes—
22C2×#4314C2212yes—
23#66929—21no—
24#66928C2211yescharacteristic, complemented
25C4×D44—21no—
26C4×D44—21no—
27C4×D44C2212yes—
28C4×D44C2212yes—
29C4×D44C2211yescharacteristic, complemented
30#66925—21no—
31#66923C2211yescharacteristic, complemented
32C4×Dic22C2211yescharacteristic, complemented
33C11×C4⋊C8C2212yescomplemented
34C11×C22⋊C8C2211yescharacteristic
35C11×C22⋊C8C2211yescharacteristic
36C11×#97C2212yescomplemented
37#66885C2212yes—
38#66885C2212yes—
39#66885C2212yescomplemented
40#66882C2212yescomplemented
41#66881C2212yescomplemented
42#66880C2212yescomplemented
43C23×D11—21no—
44C22×C4×C11D411yescharacteristic
45C22×C4×C11D411yescharacteristic
46C22×C4×C11C2311yescharacteristic
47C2×C22⋊D11—21no—
48C22×Dic11—21no—
49C2×D44—24no—
50C2×D44—21no—
51C2×D44C2311yescharacteristic
52C2×D44C2312yes—
53C2×C4×D11—21no—
54C2×C4×D11—22no—
55C2×C4×D11—22no—
56C2×C4×D11—44no—
57C2×Dic22C2311yescharacteristic
58C2×C8×C11C2312yes—
59C2×C8×C11C2312yes—
60C42×C11D411yescharacteristic
61C42×C11D411yescharacteristic
62C42×C11C2311yescharacteristic
63C42×C11C2311yescharacteristic
64C22⋊Dic11—21no—
65(C2×D11)⋊C4—21no—
66(C2×D11)⋊C4—21no—
67(C2×D11)⋊C4—22no—
68(C2×D11)⋊C4—22no—
69(C2×D11)⋊C4—21no—
70(C2×D11)⋊C4—21no—
71C4⋊Dic11—21no—
72C4⋊Dic11C2312yes—
73C4⋊Dic11C2311yescharacteristic
74C4⋊Dic11C2311yescharacteristic
75Dic11⋊C4—21no—
76Dic11⋊C4—21no—
77Dic11⋊C4—21no—
78Dic11⋊C4—21no—
79C4×Dic11—21no—
80D88—24no—
81#4314—24no—
82#3114—111nomaximal, Sylow
83C23×C11C2×D411yescharacteristic
84C22×D11—24no—
85C22×D11—22no—
86C22×D11—21no—
87C22×D11—42no—
88C22×D11—42no—
89C2×C4×C11—22no—
90C2×C4×C11—22no—
91C2×C4×C11—41no—
92C2×C4×C11C2×D411yescharacteristic
93C2×C4×C11C2×D411yescharacteristic
94C2×C4×C11C2×D411yescharacteristic
95C2×C4×C11C2×D411yescharacteristic
96C2×C4×C11C2×D411yescharacteristic
97C2×C4×C11C2411yescharacteristic
98C22⋊D11—42no—
99C2×Dic11—21no—
100C2×Dic11—21no—
101C2×Dic11—21no—
102C2×Dic11—22no—
103C2×Dic11—42no—
104D44—24no—
105D44—22no—
106D44—22no—
107D44#4114yes—
108C4×D11—42no—
109C4×D11—44no—
110C4×D11—44no—
111Dic22—22no—
112C8×C11—22no—
113C8×C11—22no—
114#529—111no—
115C2×C4×D4—111no—
116#483—111no—
117#480—111no—
118#478—112no—
119#463—112no—
120#450—111no—
121#447—111no—
122#442—112no—
123#440—112no—
124#432D1111yescharacteristic, complemented
125C22×C11—21no—
126C22×C11—21no—
127C22×C11AGL(1,ℤ/8)12yes—
128C22×C11C22×D411yescharacteristic
129C2×D11—24no—
130C2×D11—48no—
131C2×D11—42no—
132C2×D11—42no—
133C2×D11—41no—
134C2×D11—41no—
135C2×D11—41no—
136C4×C11—21no—
137C4×C11—21no—
138C4×C11—21no—
139C4×C11—21no—
140C4×C11—21no—
141C4×C11C2×#4112yes—
142Dic11—41no—
143Dic11—42no—
144Dic11—41no—
145Dic11—41no—
146C22×D4—111no—
147C23×C4—221no—
148C2×SD16—112no—
149C2×D8—112no—
150#126—221no—
151#125—111no—
152#124—111no—
153#123—221no—
154C22⋊Q8—111no—
155#121—111no—
156C4×Q8—111no—
157C4×D4—112no—
158C4×D4—112no—
159C4×D4—111no—
160C4×D4—221no—
161C4×D4—221no—
162C4×D4—221no—
163#117—221no—
164C2×C4⋊C4—111no—
165C2×C22⋊C4—221no—
166C2×C42C2×D1111yescharacteristic
167#107—112no—
168#106—112no—
169C4⋊C8C2×D1112yescomplemented
170#103—112no—
171#102—112no—
172#102—112no—
173#102—112no—
174C22⋊C8C2×D1111yescharacteristic
175C22⋊C8C2×D1111yescharacteristic
176#97C2×D1112yescomplemented
177C2×C11—22no—
178C2×C11#52511yescharacteristic
179C2×C11C2×AGL(1,ℤ/8)11yescharacteristic
180C2×C11#57511yescharacteristic
181D11—44no—
182D11—81no—
183C24—221no—
184C2×Q8—111no—
185C2×D4—112no—
186C2×D4—111no—
187C2×D4—224no—
188C2×D4—221no—
189C2×D4—221no—
190C22×C4—221no—
191C22×C4—221no—
192C22×C4—222no—
193C22×C4—222no—
194C22×C4—444no—
195C22×C4D4411yescharacteristic
196C22×C4D4411yescharacteristic
197C22×C4C22×D1111yescharacteristic
198SD16—224no—
199D8—224no—
200C2×C8C22×D1112yes—
201C2×C8C22×D1112yes—
202C4⋊C4—111no—
203C4⋊C4—111no—
204C4⋊C4—112no—
205C4⋊C4—221no—
206C4⋊C4—221no—
207C4⋊C4—221no—
208C4⋊C4—221no—
209C4⋊C4—221no—
210C22⋊C4—221no—
211C22⋊C4—222no—
212C22⋊C4—222no—
213C22⋊C4—221no—
214C22⋊C4—221no—
215C22⋊C4—221no—
216C22⋊C4—221no—
217C42—221no—
218C42D4411yescharacteristic
219C42D4411yescharacteristic
220C42C22×D1111yescharacteristic
221C42C22×D1111yescharacteristic
222C11#311411yescharacteristic, complemented, Sylow
223C23—224no—
224C23—222no—
225C23—221no—
226C23—442no—
227C23—442no—
228C23C2×D4411yescharacteristic
229Q8—222no—
230D4—114no—
231D4—224no—
232D4—222no—
233D4—222no—
234D4—442no—
235C2×C4—22no—
236C2×C4—22no—
237C2×C4—41no—
238C2×C4—221no—
239C2×C4—221no—
240C2×C4—221no—
241C2×C4—222no—
242C2×C4—444no—
243C2×C4—444no—
244C2×C4—442no—
245C2×C4—442no—
246C2×C4C2×D4411yescharacteristic
247C2×C4C2×D4411yescharacteristic
248C2×C4C2×D4411yescharacteristic
249C2×C4C2×D4411yescharacteristic
250C2×C4C2×D4411yescharacteristic
251C2×C4C23×D1111yescharacteristic
252C8—22no—
253C8—22no—
254C22—21no—
255C22—21no—
256C22—224no—
257C22—448no—
258C22—442no—
259C22—442no—
260C22—441no—
261C22—441no—
262C22—441no—
263C22#6696112yes—
264C22C22×D4411yescharacteristic
265C4—21no—
266C4—21no—
267C4—21no—
268C4—21no—
269C4—21no—
270C4—442no—
271C4—441no—
272C4—441no—
273C4—441no—
274C4#41×D1112yes—
275C2—22no—
276C2—444no—
277C2—881no—
278C2#1062305511yescharacteristic
279C2C2×#6696111yescharacteristic
280C2#1062327911yescharacteristic
subgroupG/H
centerC22C22×D44
commutator, cosocleC2×C4×C11C24
FrattiniC2×C4C23×D11
FittingC11×#432C2
socleC22×C11C22×D4
prime radical#10622345C2
hypercenter#432D11
hypocenterC11#3114
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #432

Complements

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

NH ≅ G/Ntype
1. #10623010C2semidirect
2. C2×C4×D44C2semidirect
3. C11×#432C2semidirect
4. #10622460C2semidirect
5. #10622457C2semidirect
6. #10622349C2semidirect
8. #10622344C2semidirect
9. #10622334C2semidirect
10. #10622324C2semidirect
11. #10622323C2semidirect
24. #66928C22semidirect
29. C4×D44C22semidirect
31. #66923C22semidirect
32. C4×Dic22C22semidirect
33. C11×C4⋊C8C22semidirect
36. C11×#97C22semidirect
39. #66885C22semidirect
40. #66882C22semidirect
41. #66881C22semidirect
42. #66880C22semidirect
124. #432D11semidirect
169. C4⋊C8C2×D11semidirect
176. #97C2×D11semidirect
222. C11#3114semidirect

Maximal subgroups

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

subgroupindex
#106230102
C2×C4×D442
C11×#4322
#106224602
#106224572
#106223492
#106223452
#106223442
#106223342
#106223242
#106223232
#311411