Finite Group Databasebeta

← #13079433

Subgroups — #13079433

Order 1408.

466 conjugacy classes of subgroups; only the 113 normal subgroups are shown.

normal subgroups only

This group has 466 conjugacy classes of subgroups — too many to draw. Only its 113 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×#66991C211yesmaximal, characteristic, complemented
2#10623158C211yesmaximal, characteristic, complemented
3C11×#450C211yesmaximal, characteristic, complemented
4#10622830C211yesmaximal, characteristic, complemented
5#10622787C212yesmaximal, complemented
6#10622785C212yesmaximal, complemented
7#10622656C211yesmaximal, characteristic, complemented
8#10622397C212yesmaximal, complemented
9#10622395C212yesmaximal, complemented
10#10622349C211yesmaximal, characteristic, complemented
11#10622339C211yesmaximal, characteristic, complemented
12C22×D4×C11C2211yescharacteristic
13C22×C22⋊D11—21no—
14C2×#4343C2211yescharacteristic, complemented
15C22×C4×D11C2211yescharacteristic
16C2×C11×SD16C2212yescomplemented
17C11×C22⋊Q8C2211yescharacteristic
18C2×C22⋊Dic11—21no—
19#66999C2211yescharacteristic, complemented
20#66991—21no—
21#66991—21no—
22#66991C2212yes—
23#66991C2212yes—
24C2×#4323C2212yescomplemented
25#66983C2211yescharacteristic
26C2×C4⋊Dic11C2211yescharacteristic
27C2×#4313C2212yescomplemented
28#66948C2211yescharacteristic, complemented
29#66947—21no—
30#66946—21no—
31#66945C2211yescharacteristic, complemented
32#66935—21no—
33(C22⋊D11)⋊C4—21no—
34C11×#102C2212yescomplemented
35C11×C22⋊C8C2211yescharacteristic
36#66899C2212yescomplemented
37#66896C2212yescomplemented
38C22⋊(C11⋊C8)C2211yescharacteristic
39#66885C2212yescomplemented
40(C2×D11)⋊C8C2212yescomplemented
41#66882C2212yescomplemented
42#66872C2212yescomplemented
43C24×C11—21no—
44C23×D11D411yescharacteristic
45C2×Q8×C11C2311yescharacteristic
46C2×D4×C11—21no—
47C2×D4×C11—42no—
48C2×D4×C11C2312yes—
49C22×C4×C11C2311yescharacteristic
50C2×C22⋊D11—21no—
51C2×C22⋊D11—22no—
52C2×C22⋊D11—22no—
53C2×C22⋊D11—44no—
54C22×Dic11—21no—
55C22×Dic11D411yescharacteristic
56#4343—42no—
57C2×D44—21no—
58C2×D44—21no—
59C2×D44C2311yescharacteristic
60C2×C4×D11—21no—
61C2×C4×D11—42no—
62C2×C4×D11D411yescharacteristic
63C2×C4×D11D411yescharacteristic
64C2×C4×D11C2311yescharacteristic
65C2×C4×D11C2311yescharacteristic
66C11×SD16—42no—
67C2×C8×C11C2312yes—
68C11×C4⋊C4—21no—
69C11×C4⋊C4C2311yescharacteristic
70C11×C22⋊C4—21no—
71C22⋊Dic11—22no—
72C22⋊Dic11—22no—
73#4323—42no—
74(C2×D11)⋊C4—21no—
75(C2×D11)⋊C4—21no—
76(C2×D11)⋊C4—21no—
77(C2×D11)⋊C4—21no—
78C4⋊Dic11—21no—
79C4⋊Dic11C2312yes—
80C4⋊Dic11C2311yescharacteristic
81Dic11⋊C4—21no—
82C4×Dic11—21no—
83C2×C11⋊C8C2312yes—
84#4313—42no—
85#3194—111nomaximal, Sylow
86C23×C11—22no—
87C23×C11—42no—
88C23×C11—42no—
89C23×C11—42no—
90C23×C11C2×D411yescharacteristic
91C22×D11—22no—
92C22×D11—21no—
93C22×D11—41no—
94C22×D11—41no—
95C22×D11C2×D411yescharacteristic
96C22×D11C2×D411yescharacteristic
97Q8×C11—22no—
98D4×C11—22no—
99D4×C11—22no—
100D4×C11—42no—
101C2×C4×C11—22no—
102C2×C4×C11—21no—
103C2×C4×C11—21no—
104C2×C4×C11C2×D411yescharacteristic
105C2×C4×C11C2411yescharacteristic
106C22⋊D11—44no—
107C22⋊D11—44no—
108C22⋊D11—42no—
109C2×Dic11—21no—
110C2×Dic11—22no—
111C2×Dic11—41no—
112C2×Dic11—42no—
113C2×Dic11C2×D411yescharacteristic
114C2×Dic11C2×D411yescharacteristic
115D44—22no—
116D44—42no—
117D44—42no—
118C4×D11—22no—
119C4×D11—22no—
120C4×D11—41no—
121C4×D11—41no—
122C4×D11—42no—
123C8×C11—22no—
124C11⋊C8—22no—
125#525—111no—
126C2×#121—111no—
127#483—111no—
128#482—112no—
129#480—111no—
130#469—112no—
131#468—112no—
132#450D1111yescharacteristic, complemented
133#449—112no—
134#447—111no—
135#407—111no—
136C22×C11—21no—
137C22×C11—21no—
138C22×C11—42no—
139C22×C11—42no—
140C22×C11—42no—
141C22×C11—84no—
142C22×C11AGL(1,ℤ/8)12yes—
143C22×C11C22×D411yescharacteristic
144C2×D11—21no—
145C2×D11—21no—
146C2×D11—21no—
147C2×D11—21no—
148C2×D11—21no—
149C2×D11—21no—
150C2×D11—44no—
151C2×D11—41no—
152C2×D11—41no—
153C2×D11—41no—
154C4×C11—21no—
155C4×C11—41no—
156C4×C11—41no—
157C4×C11H(5,𝔽2)12yes—
158Dic11—21no—
159Dic11—21no—
160Dic11—42no—
161Dic11—41no—
162C2×#41—111no—
163C22×D4—221no—
164C22×D4C2×D1111yescharacteristic
165C23×C4—111no—
166C2×SD16C2×D1112yescomplemented
167C2×D8—112no—
168C2×M16—112no—
169#123—221no—
170C22⋊Q8—111no—
171C22⋊Q8C2×D1111yescharacteristic
172#121—112no—
173#121—112no—
174#121—111no—
175#121—111no—
176#121—221no—
177#121—221no—
178#120—221no—
179C4×D4—221no—
180C4×D4—221no—
181#117—111no—
182C2×C4⋊C4—111no—
183C2×C22⋊C4—221no—
184#107—112no—
185#106—112no—
186#103—112no—
187#102—112no—
188#102—112no—
189#102C2×D1112yescomplemented
190C22⋊C8—111no—
191C22⋊C8—112no—
192C22⋊C8C2×D1111yescharacteristic
193C2×C11—22no—
194C2×C11—82no—
195C2×C11#53411yescharacteristic
196C2×C11C2×AGL(1,ℤ/8)11yescharacteristic
197C2×C11#57511yescharacteristic
198D11—41no—
199D11—41no—
200D11—81no—
201C24—21no—
202C24—111no—
203#41—442no—
204C2×Q8C22×D1111yescharacteristic
205C2×D4—21no—
206C2×D4—42no—
207C2×D4—111no—
208C2×D4—221no—
209C2×D4—221no—
210C2×D4—222no—
211C2×D4—222no—
212C2×D4—221no—
213C2×D4—444no—
214C2×D4C22×D1112yes—
215C22×C4—111no—
216C22×C4—111no—
217C22×C4—111no—
218C22×C4—111no—
219C22×C4—111no—
220C22×C4—221no—
221C22×C4—221no—
222C22×C4—442no—
223C22×C4C22×D1111yescharacteristic
224SD16—42no—
225D8—442no—
226M16—442no—
227C2×C8—112no—
228C2×C8C22×D1112yes—
229C4⋊C4—21no—
230C4⋊C4—111no—
231C4⋊C4—112no—
232C4⋊C4—221no—
233C4⋊C4—221no—
234C4⋊C4C22×D1111yescharacteristic
235C22⋊C4—21no—
236C22⋊C4—221no—
237C22⋊C4—221no—
238C22⋊C4—221no—
239C22⋊C4—222no—
240C22⋊C4—222no—
241C22⋊C4—221no—
242C42—221no—
243C11#319411yescharacteristic, complemented, Sylow
244C23—22no—
245C23—42no—
246C23—42no—
247C23—42no—
248C23—111no—
249C23—111no—
250C23—222no—
251C23—221no—
252C23—441no—
253C23—441no—
254C23D4×D1111yescharacteristic
255Q8—22no—
256D4—22no—
257D4—22no—
258D4—42no—
259D4—222no—
260D4—442no—
261D4—442no—
262D4—444no—
263D4—444no—
264D4—442no—
265C2×C4—22no—
266C2×C4—21no—
267C2×C4—21no—
268C2×C4—111no—
269C2×C4—111no—
270C2×C4—222no—
271C2×C4—222no—
272C2×C4—221no—
273C2×C4—222no—
274C2×C4—441no—
275C2×C4—441no—
276C2×C4—442no—
277C2×C4—441no—
278C2×C4—442no—
279C2×C4D4×D1111yescharacteristic
280C2×C4C23×D1111yescharacteristic
281C8—22no—
282C8—222no—
283C22—21no—
284C22—21no—
285C22—42no—
286C22—42no—
287C22—42no—
288C22—84no—
289C22—221no—
290C22—221no—
291C22—221no—
292C22—221no—
293C22—221no—
294C22—221no—
295C22—444no—
296C22—441no—
297C22—441no—
298C22—441no—
299C22#6696712yes—
300C22C2×D4×D1111yescharacteristic
301C4—21no—
302C4—41no—
303C4—41no—
304C4—221no—
305C4—221no—
306C4—442no—
307C4—441no—
308C4#6703712yes—
309C2—22no—
310C2—82no—
311C2—441no—
312C2—441no—
313C2—881no—
314C2#1062312011yescharacteristic
315C2C2×#6696711yescharacteristic
316C2#1062330411yescharacteristic
subgroupG/H
centerC22C2×D4×D11
commutator, cosocleC2×C4×C11C24
FrattiniC2×C4C23×D11
FittingC11×#450C2
socleC22×C11C22×D4
hypercenter#450D11
hypocenterC11#3194
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C22×C4 ◁ #450

Complements

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

NH ≅ G/Ntype
1. C2×#66991C2semidirect
2. #10623158C2semidirect
3. C11×#450C2semidirect
4. #10622830C2semidirect
5. #10622787C2semidirect
6. #10622785C2semidirect
7. #10622656C2semidirect
8. #10622397C2semidirect
9. #10622395C2semidirect
10. #10622349C2semidirect
11. #10622339C2semidirect
14. C2×#4343C22semidirect
16. C2×C11×SD16C22semidirect
19. #66999C22semidirect
24. C2×#4323C22semidirect
27. C2×#4313C22semidirect
28. #66948C22semidirect
31. #66945C22semidirect
34. C11×#102C22semidirect
36. #66899C22semidirect
37. #66896C22semidirect
39. #66885C22semidirect
40. (C2×D11)⋊C8C22semidirect
41. #66882C22semidirect
42. #66872C22semidirect
132. #450D11semidirect
166. C2×SD16C2×D11semidirect
189. #102C2×D11semidirect
243. C11#3194semidirect

Maximal subgroups

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

subgroupindex
C2×#669912
#106231582
C11×#4502
#106228302
#106227872
#106227852
#106226562
#106223972
#106223952
#106223492
#106223392
#319411