Finite Group Databasebeta

← #13078298

Subgroups — #13078298

Order 1408.

504 conjugacy classes of subgroups; only the 141 normal subgroups are shown.

normal subgroups only

This group has 504 conjugacy classes of subgroups — too many to draw. Only its 141 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
1C11×#537C211yesmaximal, characteristic, complemented
2#10623361C211yesmaximal, characteristic, complemented
3C2×#67002C211yesmaximal, characteristic, complemented
4C2×#67001C211yesmaximal, characteristic, complemented
5#10622846C211yesmaximal, characteristic, complemented
6#10622662C212yesmaximal, complemented
7#10622661C212yesmaximal, complemented
8#10622652C212yesmaximal, complemented
9#10622651C212yesmaximal, complemented
10C2×#66873C211yesmaximal, characteristic, complemented
11#10622577C211yesmaximal, characteristic, complemented
12C2×C11×#41C2211yescharacteristic
13C2×C11×#41C2211yescharacteristic
14C22×D44C2211yescharacteristic
15C11×C22⋊Q8—21no—
16C11×C22⋊Q8C2212yescomplemented
17C11×#121—21no—
18C11×#121—22no—
19C11×#121C2212yescomplemented
20C2×C11×C4⋊C4C2211yescharacteristic
21#67002—24no—
22#67001—24no—
23#67000—21no—
24C2×#4325C2212yes—
25#66993—21no—
26#66990—22no—
27C2×#4323C2212yes—
28#66983C2212yes—
29#66983C2212yes—
30#66979C2211yescharacteristic
31C2×#4318C2211yescharacteristic
32C2×#4318C2212yescomplemented
33C22×C11⋊C8C2211yescharacteristic
34C22×C11⋊C8C2212yescomplemented
35#66899C2211yescharacteristic, complemented
36#66899C2211yescharacteristic, complemented
37#66896C2211yescharacteristic, complemented
38#66896C2211yescharacteristic, complemented
39#66873C2212yes—
40#66873C2212yes—
41#66872C2212yescomplemented
42#66871C2212yescomplemented
43C23×D11—21no—
44C11×#41—22no—
45C11×#41—22no—
46C11×#41—22no—
47C11×#41—22no—
48C2×Q8×C11D411yescharacteristic
49C2×Q8×C11C2311yescharacteristic
50C2×D4×C11—21no—
51C2×D4×C11—22no—
52C2×D4×C11D412yes—
53C2×D4×C11D411yescharacteristic
54C2×D4×C11C2311yescharacteristic
55C22×C4×C11—21no—
56C22×C4×C11—21no—
57C22×C4×C11C2312yes—
58C22×C4×C11C2311yescharacteristic
59C2×C22⋊D11—22no—
60C2×C22⋊D11—22no—
61C2×D44—21no—
62C2×D44—22no—
63C2×D44—22no—
64C2×D44C2312yes—
65C11×C4⋊C4—21no—
66C11×C4⋊C4—22no—
67C11×C4⋊C4C2312yes—
68C11×C22⋊C4—22no—
69C11×C22⋊C4—22no—
70C22⋊Dic11—21no—
71#4325—24no—
72#4323—24no—
73(C2×D11)⋊C4—22no—
74(C2×D11)⋊C4—22no—
75C4⋊Dic11C2311yescharacteristic
76C4⋊Dic11C2311yescharacteristic
77C4×Dic11—21no—
78#4318—24no—
79#4318D414yescomplemented
80C2×C11⋊C8—24no—
81C2×C11⋊C8—22no—
82C2×C11⋊C8C2311yescharacteristic
83C2×C11⋊C8C2311yescharacteristic
84C2×C11⋊C8C2312yes—
85#3062—111nomaximal, Sylow
86C23×C11—21no—
87C23×C11C2×D412yes—
88C23×C11C2×D411yescharacteristic
89C22×D11—22no—
90C22×D11—42no—
91C22×D11—81no—
92C22×D11—81no—
93Q8×C11—22no—
94Q8×C11—21no—
95Q8×C11—21no—
96D4×C11—24no—
97D4×C11—22no—
98D4×C11—21no—
99D4×C11—21no—
100D4×C11—42no—
101D4×C11—82no—
102C2×C4×C11—22no—
103C2×C4×C11—22no—
104C2×C4×C11—22no—
105C2×C4×C11—21no—
106C2×C4×C11—42no—
107C2×C4×C11—81no—
108C2×C4×C11C2×D412yes—
109C2×C4×C11C2×D412yes—
110C2×C4×C11C2×D411yescharacteristic
111C2×C4×C11#4112yes—
112C2×C4×C11C2411yescharacteristic
113C22⋊D11—82no—
114C22⋊D11—82no—
115C2×Dic11—21no—
116C2×Dic11—21no—
117D44—22no—
118D44—22no—
119D44—42no—
120C11⋊C8—21no—
121C11⋊C8—21no—
122C11⋊C8C2×D414yes—
123C2×AGL(1,ℤ/8)—111no—
124C2×#131—111no—
125#537D1111yescharacteristic, complemented
126#535—111no—
127#469—112no—
128#468—112no—
129#466—112no—
130#465—112no—
131#428—111no—
132#416—111no—
133C2×#102—111no—
134C22×C11—21no—
135C22×C11—21no—
136C22×C11—22no—
137C22×C11—22no—
138C22×C11—22no—
139C22×C11—41no—
140C22×C11—41no—
141C22×C11—41no—
142C22×C11#12112yes—
143C22×C11C22×D411yescharacteristic
144C2×D11—42no—
145C2×D11—42no—
146C2×D11—42no—
147C2×D11—84no—
148C4×C11—22no—
149C4×C11—41no—
150C4×C11—42no—
151C4×C11#12112yes—
152C4×C11C22×D411yescharacteristic
153C4×C11C2×#4111yescharacteristic
154Dic11—41no—
155Dic11—41no—
156C2×#41C2×D1111yescharacteristic
157C2×#41C2×D1111yescharacteristic
158C22×D4—111no—
159AGL(1,ℤ/8)—224no—
160C2×SD16—112no—
161C2×D8—112no—
162#131—224no—
163C2×M16—111no—
164C2×M16—112no—
165C22×C8—111no—
166C22×C8—112no—
167#127—221no—
168#124—221no—
169C22⋊Q8—21no—
170C22⋊Q8C2×D1112yescomplemented
171#121—21no—
172#121—22no—
173#121—112no—
174#121—112no—
175#121C2×D1112yescomplemented
176#120—222no—
177#117—111no—
178C2×C4⋊C4C2×D1111yescharacteristic
179#107—112no—
180#106—112no—
181#103—111no—
182#103—111no—
183#102—111no—
184#102—111no—
185#102—112no—
186#102—112no—
187C2×C11—22no—
188C2×C11—42no—
189C2×C11—81no—
190C2×C11C2×#12111yescharacteristic
191C2×C11#57611yescharacteristic
192C2×C11#57711yescharacteristic
193D11—82no—
194C24—221no—
195#41—22no—
196#41—22no—
197#41—22no—
198#41—22no—
199C2×Q8C22⋊D1111yescharacteristic
200C2×Q8C22×D1111yescharacteristic
201C2×D4—21no—
202C2×D4—22no—
203C2×D4—112no—
204C2×D4—222no—
205C2×D4—222no—
206C2×D4—222no—
207C2×D4—222no—
208C2×D4—221no—
209C2×D4C22⋊D1112yes—
210C2×D4C22⋊D1111yescharacteristic
211C2×D4C22×D1111yescharacteristic
212C22×C4—21no—
213C22×C4—21no—
214C22×C4C22×D1112yes—
215C22×C4C22×D1111yescharacteristic
216SD16—224no—
217D8—224no—
218M16—114no—
219M16—224no—
220C2×C8—112no—
221C2×C8—111no—
222C2×C8—111no—
223C2×C8—224no—
224C2×C8—222no—
225C4⋊C4—21no—
226C4⋊C4—22no—
227C4⋊C4—111no—
228C4⋊C4—111no—
229C4⋊C4C22×D1112yes—
230C22⋊C4—22no—
231C22⋊C4—22no—
232C22⋊C4—221no—
233C22⋊C4—222no—
234C22⋊C4—222no—
235C42—221no—
236C11#306211yescharacteristic, complemented, Sylow
237C23—21no—
238C23—222no—
239C23—442no—
240C23—881no—
241C23—881no—
242C23C2×C22⋊D1112yes—
243C23C2×C22⋊D1111yescharacteristic
244Q8—22no—
245Q8—21no—
246Q8—21no—
247D4—24no—
248D4—22no—
249D4—21no—
250D4—21no—
251D4—42no—
252D4—82no—
253D4—222no—
254D4—222no—
255D4—442no—
256D4—882no—
257D4—882no—
258C2×C4—22no—
259C2×C4—22no—
260C2×C4—22no—
261C2×C4—21no—
262C2×C4—42no—
263C2×C4—81no—
264C2×C4—221no—
265C2×C4—221no—
266C2×C4D4×D1112yes—
267C2×C4#434112yes—
268C2×C4C2×C22⋊D1112yes—
269C2×C4C2×C22⋊D1111yescharacteristic
270C2×C4C23×D1111yescharacteristic
271C8—114no—
272C8—221no—
273C8—221no—
274C22—21no—
275C22—21no—
276C22—22no—
277C22—22no—
278C22—22no—
279C22—41no—
280C22—41no—
281C22—41no—
282C22—442no—
283C22—442no—
284C22—442no—
285C22—884no—
286C22#6699212yes—
287C22C22×C22⋊D1111yescharacteristic
288C4—22no—
289C4—41no—
290C4—42no—
291C4—441no—
292C4—441no—
293C4#6699212yes—
294C4C2×D4×D1111yescharacteristic
295C4C2×#434111yescharacteristic
296C2—22no—
297C2—42no—
298C2—81no—
299C2—882no—
300C2C2×#6699211yescharacteristic
301C2#1062336611yescharacteristic
302C2#1062336811yescharacteristic
subgroupG/H
centerC22C22×C22⋊D11
commutator, cosocleC2×C4×C11C24
FrattiniC2×C4C23×D11
FittingC11×#537C2
socleC22×C11C22×D4
hypercenter#537D11
hypocenterC11#3062
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×#41 ◁ #537

Complements

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

NH ≅ G/Ntype
1. C11×#537C2semidirect
2. #10623361C2semidirect
3. C2×#67002C2semidirect
4. C2×#67001C2semidirect
5. #10622846C2semidirect
6. #10622662C2semidirect
7. #10622661C2semidirect
8. #10622652C2semidirect
9. #10622651C2semidirect
10. C2×#66873C2semidirect
11. #10622577C2semidirect
16. C11×C22⋊Q8C22semidirect
19. C11×#121C22semidirect
32. C2×#4318C22semidirect
34. C22×C11⋊C8C22semidirect
35. #66899C22semidirect
36. #66899C22semidirect
37. #66896C22semidirect
38. #66896C22semidirect
41. #66872C22semidirect
42. #66871C22semidirect
79. #4318D4semidirect
125. #537D11semidirect
170. C22⋊Q8C2×D11semidirect
175. #121C2×D11semidirect
236. C11#3062semidirect

Maximal subgroups

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

subgroupindex
C11×#5372
#106233612
C2×#670022
C2×#670012
#106228462
#106226622
#106226612
#106226522
#106226512
C2×#668732
#106225772
#306211