Finite Group Databasebeta

← #13078247

Subgroups — #13078247

Order 1408.

496 conjugacy classes of subgroups; only the 143 normal subgroups are shown.

normal subgroups only

This group has 496 conjugacy classes of subgroups — too many to draw. Only its 143 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
1C2×#66962C211yesmaximal, characteristic, complemented
2C2×M16×D11C211yesmaximal, characteristic, complemented
3#10623055C211yesmaximal, characteristic
4C2×#66950C211yesmaximal, characteristic, complemented
5C11×#428C211yesmaximal, characteristic, complemented
6#10622617C211yesmaximal, characteristic, complemented
7#10622579C211yesmaximal, characteristic, complemented
8#10622500C212yesmaximal, complemented
9#10622499C212yesmaximal, complemented
10#10622481C212yesmaximal, complemented
11#10622477C212yesmaximal, complemented
12C2×#4339C2211yescharacteristic
13C22×C4×D11C2211yescharacteristic
14C22×Dic22C2211yescharacteristic
15C2×C11×M16C2211yescharacteristic
16C11×#117C2211yescharacteristic
17C2×C11×C4⋊C4C2211yescharacteristic
18C2×(C2×D11)⋊C4—21no—
19C2×C4⋊Dic11—21no—
20C2×#4318C2211yescharacteristic
21#66962—24no—
22M16×D11—24no—
23C2×Dic44C2212yescomplemented
24C2×#4314C2212yescomplemented
25C2×#4313C2212yes—
26C2×C8×D11C2212yes—
27#66950—21no—
28#66950—21no—
29#66950C2212yes—
30#66950C2211yescharacteristic
31#66950C2212yes—
32#66950C2211yescharacteristic
33#66948C2211yescharacteristic
34#66948C2211yescharacteristic
35#66939—21no—
36#66935—21no—
37C4×D44—21no—
38C4×D44—21no—
39C11×#107C2212yescomplemented
40C11×#106C2212yescomplemented
41#66874C2212yescomplemented
42#66874C2212yescomplemented
43#66874C2212yescomplemented
44#66873C2212yescomplemented
45C23×D11D411yescharacteristic
46C22×C4×C11—21no—
47C22×C4×C11C2311yescharacteristic
48C2×C22⋊D11—21no—
49C22×Dic11—21no—
50C22×Dic11D411yescharacteristic
51#4339—22no—
52#4339—22no—
53C2×D44—21no—
54C2×D44—21no—
55C2×D44C2311yescharacteristic
56C2×C4×D11—22no—
57C2×C4×D11—21no—
58C2×C4×D11—22no—
59C2×C4×D11D411yescharacteristic
60C2×C4×D11D411yescharacteristic
61C2×C4×D11C2311yescharacteristic
62C2×C4×D11C2311yescharacteristic
63C2×Dic22—22no—
64C2×Dic22—21no—
65C2×Dic22—22no—
66C2×Dic22C2312yes—
67C2×Dic22C2311yescharacteristic
68C11×M16D414yescomplemented
69C2×C8×C11C2312yes—
70C11×C4⋊C4—21no—
71C11×C4⋊C4C2312yes—
72C11×C4⋊C4C2311yescharacteristic
73C11×C4⋊C4C2311yescharacteristic
74C11×C22⋊C4—21no—
75C42×C11—21no—
76(C2×D11)⋊C4—21no—
77(C2×D11)⋊C4—21no—
78(C2×D11)⋊C4—21no—
79(C2×D11)⋊C4—21no—
80(C2×D11)⋊C4—22no—
81(C2×D11)⋊C4—22no—
82C4⋊Dic11—21no—
83C4⋊Dic11—21no—
84C4⋊Dic11—22no—
85C4⋊Dic11—22no—
86#4318—22no—
87C2×C11⋊C8C2312yes—
88Dic44—24no—
89#4314—24no—
90#4313—24no—
91C8×D11—24no—
92#3056—111nomaximal, Sylow
93C23×C11C2×D411yescharacteristic
94C22×D11—22no—
95C22×D11—22no—
96C22×D11—21no—
97C22×D11—41no—
98C22×D11C2×D411yescharacteristic
99C22×D11C2×D411yescharacteristic
100C2×C4×C11—22no—
101C2×C4×C11—21no—
102C2×C4×C11—21no—
103C2×C4×C11—42no—
104C2×C4×C11C2×D412yes—
105C2×C4×C11C2×D411yescharacteristic
106C2×C4×C11#4112yes—
107C2×C4×C11C2411yescharacteristic
108C22⋊D11—42no—
109C2×Dic11—22no—
110C2×Dic11—22no—
111C2×Dic11—21no—
112C2×Dic11—42no—
113C2×Dic11C2×D411yescharacteristic
114C2×Dic11C2×D411yescharacteristic
115D44—21no—
116D44—21no—
117D44—42no—
118D44—42no—
119C4×D11—22no—
120C4×D11—22no—
121C4×D11—21no—
122C4×D11—21no—
123C4×D11—21no—
124C4×D11—21no—
125C4×D11—42no—
126Dic22—22no—
127Dic22—21no—
128Dic22—22no—
129Dic22—21no—
130Dic22—42no—
131C8×C11C2×D414yes—
132C11⋊C8—22no—
133C2×#137—111no—
134C22×M16—111no—
135#525—111no—
136C2×C22⋊Q8—111no—
137#470—112no—
138#468—112no—
139#467—112no—
140#465—112no—
141#428D1111yescharacteristic, complemented
142#419—111no—
143#417—111no—
144C22×C11—21no—
145C22×C11—21no—
146C22×C11#12112yes—
147C22×C11C22×D411yescharacteristic
148C2×D11—21no—
149C2×D11—21no—
150C2×D11—21no—
151C2×D11—21no—
152C2×D11—21no—
153C2×D11—44no—
154C2×D11—41no—
155C2×D11—41no—
156C2×D11—41no—
157C2×D11#13712yescomplemented
158C4×C11—41no—
159C4×C11—42no—
160C4×C11—41no—
161C4×C11#12112yes—
162C4×C11C22×D411yescharacteristic
163C4×C11C2×#4111yescharacteristic
164Dic11—21no—
165Dic11—21no—
166Dic11—42no—
167Dic11—41no—
168C2×#41—111no—
169C22×Q8—111no—
170C23×C4—111no—
171#137—224no—
172C2×Q16—112no—
173C2×SD16—112no—
174C2×M16—111no—
175C2×M16—112no—
176C2×M16—224no—
177C2×M16C2×D1111yescharacteristic
178C22×C8—112no—
179#123—221no—
180C22⋊Q8—112no—
181C22⋊Q8—112no—
182C22⋊Q8—111no—
183C22⋊Q8—111no—
184C22⋊Q8—221no—
185C22⋊Q8—221no—
186#121—111no—
187#121—111no—
188#120—221no—
189C4×D4—221no—
190C4×D4—221no—
191#117C2×D1111yescharacteristic
192C2×C4⋊C4—221no—
193C2×C4⋊C4C2×D1111yescharacteristic
194C2×C22⋊C4—221no—
195#107C2×D1112yescomplemented
196#106C2×D1112yescomplemented
197#103—112no—
198#103—112no—
199#103—112no—
200#102—112no—
201C2×C11—22no—
202C2×C11C2×#12111yescharacteristic
203C2×C11C2×#13711yescharacteristic
204C2×C11#57511yescharacteristic
205D11—22no—
206D11—41no—
207D11—81no—
208C24—111no—
209#41—222no—
210#41—222no—
211C2×Q8—112no—
212C2×Q8—111no—
213C2×Q8—221no—
214C2×Q8—222no—
215C2×Q8—222no—
216C2×D4—111no—
217C2×D4—221no—
218C2×D4—221no—
219C2×D4—221no—
220C22×C4—21no—
221C22×C4—111no—
222C22×C4—111no—
223C22×C4—111no—
224C22×C4—111no—
225C22×C4—111no—
226C22×C4—222no—
227C22×C4—222no—
228C22×C4—221no—
229C22×C4—221no—
230C22×C4C22×D1111yescharacteristic
231Q16—224no—
232SD16—224no—
233M16—222no—
234M16—224no—
235M16D4414yescomplemented
236C2×C8—112no—
237C2×C8—224no—
238C2×C8C22×D1112yes—
239C4⋊C4—21no—
240C4⋊C4—222no—
241C4⋊C4—222no—
242C4⋊C4—221no—
243C4⋊C4—221no—
244C4⋊C4C22×D1112yes—
245C4⋊C4C22×D1111yescharacteristic
246C4⋊C4C22×D1111yescharacteristic
247C22⋊C4—21no—
248C22⋊C4—221no—
249C22⋊C4—221no—
250C22⋊C4—222no—
251C22⋊C4—222no—
252C22⋊C4—221no—
253C22⋊C4—221no—
254C42—21no—
255C11#305611yescharacteristic, complemented, Sylow
256C23—111no—
257C23—111no—
258C23—222no—
259C23—222no—
260C23—221no—
261C23—441no—
262C23D4×D1111yescharacteristic
263Q8—222no—
264Q8—221no—
265Q8—222no—
266Q8—221no—
267Q8—442no—
268D4—221no—
269D4—221no—
270D4—442no—
271D4—442no—
272D4—442no—
273C2×C4—21no—
274C2×C4—21no—
275C2×C4—22no—
276C2×C4—42no—
277C2×C4—111no—
278C2×C4—111no—
279C2×C4—222no—
280C2×C4—222no—
281C2×C4—222no—
282C2×C4—221no—
283C2×C4—221no—
284C2×C4—221no—
285C2×C4—221no—
286C2×C4—221no—
287C2×C4—222no—
288C2×C4—442no—
289C2×C4—442no—
290C2×C4C2×D4412yes—
291C2×C4D4×D1111yescharacteristic
292C2×C4#434312yes—
293C2×C4C23×D1111yescharacteristic
294C8—222no—
295C8C2×D4414yes—
296C22—21no—
297C22—21no—
298C22—112no—
299C22—221no—
300C22—221no—
301C22—221no—
302C22—221no—
303C22—221no—
304C22—444no—
305C22—441no—
306C22—441no—
307C22—441no—
308C22#6694812yes—
309C22C2×D4×D1111yescharacteristic
310C4—42no—
311C4—41no—
312C4—41no—
313C4—221no—
314C4—221no—
315C4—441no—
316C4—442no—
317C4#6694812yes—
318C4C22×D4411yescharacteristic
319C4C2×#434311yescharacteristic
320C2—22no—
321C2—222no—
322C2—441no—
323C2—881no—
324C2C2×#6694811yescharacteristic
325C2#1062330411yescharacteristic
326C2D11×#13711yescharacteristic
subgroupG/H
centerC22C2×D4×D11
commutator, cosocleC2×C4×C11C24
FrattiniC2×C4C23×D11
FittingC11×#428C2
socleC22×C11C22×D4
prime radical#10623055C2
hypercenter#428D11
hypocenterC11#3056
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C22×C4 ◁ #428

Complements

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

NH ≅ G/Ntype
1. C2×#66962C2semidirect
2. C2×M16×D11C2semidirect
4. C2×#66950C2semidirect
5. C11×#428C2semidirect
6. #10622617C2semidirect
7. #10622579C2semidirect
8. #10622500C2semidirect
9. #10622499C2semidirect
10. #10622481C2semidirect
11. #10622477C2semidirect
23. C2×Dic44C22semidirect
24. C2×#4314C22semidirect
39. C11×#107C22semidirect
40. C11×#106C22semidirect
41. #66874C22semidirect
42. #66874C22semidirect
43. #66874C22semidirect
44. #66873C22semidirect
68. C11×M16D4semidirect
141. #428D11semidirect
157. C2×D11#137semidirect
195. #107C2×D11semidirect
196. #106C2×D11semidirect
235. M16D44semidirect
255. C11#3056semidirect

Maximal subgroups

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

subgroupindex
C2×#669622
C2×M16×D112
#106230552
C2×#669502
C11×#4282
#106226172
#106225792
#106225002
#106224992
#106224812
#106224772
#305611