Finite Group Databasebeta

← #13078290

Subgroups — #13078290

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
1C2×C11×AGL(1,ℤ/8)C211yesmaximal, characteristic, complemented
2#10623364C211yesmaximal, characteristic, complemented
3#10623336C211yesmaximal, characteristic, complemented
4C2×#66960C211yesmaximal, characteristic, complemented
5#10622846C211yesmaximal, characteristic, complemented
6C2×#66896C211yesmaximal, characteristic, complemented
7#10622787C212yesmaximal, complemented
8#10622784C212yesmaximal, complemented
9#10622772C212yesmaximal, complemented
10#10622770C212yesmaximal, complemented
11#10622734C211yesmaximal, characteristic, complemented
12C2×C11×#41C2211yescharacteristic
13C22×D4×C11C2211yescharacteristic
14C2×#4339C2211yescharacteristic
15C11×AGL(1,ℤ/8)—24no—
16C2×C11×SD16C2212yes—
17C2×C11×D8C2212yes—
18C2×C11×M16C2211yescharacteristic
19#67006—22no—
20#66999C2212yescomplemented
21#66993—21no—
22#66992—22no—
23#66991C2212yes—
24#66991C2212yes—
25#66991C2212yescomplemented
26#66989—21no—
27#66983—21no—
28#66979C2211yescharacteristic
29C2×C4⋊Dic11C2211yescharacteristic
30#66977—21no—
31C22×C11⋊C8C2211yescharacteristic
32#66960—24no—
33C2×#4313C2212yescomplemented
34C2×C8×D11C2212yescomplemented
35#66899C2211yescharacteristic, complemented
36#66899C2211yescharacteristic, complemented
37#66896C2212yes—
38#66896C2212yes—
39#66896C2211yescharacteristic, complemented
40#66896C2211yescharacteristic, complemented
41#66882C2212yescomplemented
42#66881C2212yescomplemented
43C24×C11—21no—
44C11×#41—22no—
45C11×#41—22no—
46C2×Q8×C11C2311yescharacteristic
47C2×D4×C11—21no—
48C2×D4×C11—22no—
49C2×D4×C11—21no—
50C2×D4×C11—22no—
51C2×D4×C11C2312yes—
52C2×D4×C11C2311yescharacteristic
53C22×C4×C11—21no—
54C22×C4×C11C2311yescharacteristic
55C2×C22⋊D11—22no—
56C2×C22⋊D11—22no—
57C2×C22⋊D11—22no—
58C2×C22⋊D11D412yes—
59C22×Dic11—21no—
60#4339—22no—
61#4339—22no—
62C2×D44D411yescharacteristic
63C2×C4×D11C2312yes—
64C2×Dic22D411yescharacteristic
65C11×SD16—24no—
66C11×D8—24no—
67C11×M16D414yescomplemented
68C2×C8×C11C2312yes—
69C22⋊Dic11—22no—
70C22⋊Dic11—22no—
71C22⋊Dic11—22no—
72C22⋊Dic11—21no—
73(C2×D11)⋊C4—22no—
74C4⋊Dic11—21no—
75C4⋊Dic11C2311yescharacteristic
76C4⋊Dic11C2312yes—
77C4⋊Dic11C2311yescharacteristic
78Dic11⋊C4—22no—
79C4×Dic11—21no—
80C2×C11⋊C8—22no—
81C2×C11⋊C8C2311yescharacteristic
82C2×C11⋊C8C2311yescharacteristic
83#4313—24no—
84C8×D11—24no—
85#3062—111nomaximal, Sylow
86C23×C11—21no—
87C23×C11—22no—
88C23×C11—42no—
89C23×C11—81no—
90C23×C11—81no—
91C23×C11C2×D411yescharacteristic
92C22×D11C2×D412yes—
93Q8×C11—21no—
94Q8×C11—21no—
95D4×C11—21no—
96D4×C11—22no—
97D4×C11—22no—
98D4×C11—21no—
99D4×C11—42no—
100D4×C11—42no—
101C2×C4×C11—21no—
102C2×C4×C11—42no—
103C2×C4×C11C2×D411yescharacteristic
104C2×C4×C11C2×D412yes—
105C2×C4×C11#4112yes—
106C2×C4×C11C2411yescharacteristic
107C22⋊D11—24no—
108C22⋊D11—82no—
109C22⋊D11—82no—
110C22⋊D11—82no—
111C2×Dic11—21no—
112C2×Dic11—21no—
113C2×Dic11—22no—
114C2×Dic11—81no—
115C2×Dic11C2×D412yes—
116D44—22no—
117C4×D11—22no—
118C4×D11—22no—
119Dic22—22no—
120C8×C11C2×D414yes—
121C11⋊C8—21no—
122C11⋊C8—21no—
123C2×AGL(1,ℤ/8)D1111yescharacteristic, complemented
124C2×#131—111no—
125#537—111no—
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—41no—
137C22×C11—42no—
138C22×C11—42no—
139C22×C11—41no—
140C22×C11—41no—
141C22×C11—42no—
142C22×C11—84no—
143C22×C11#12112yes—
144C22×C11C22×D411yescharacteristic
145C2×D11—22no—
146C2×D11—22no—
147C2×D11—22no—
148C4×C11—41no—
149C4×C11#12112yes—
150C4×C11C22×D411yescharacteristic
151C4×C11C2×#4111yescharacteristic
152Dic11—22no—
153Dic11—42no—
154Dic11—41no—
155Dic11—41no—
156C2×#41—111no—
157C2×#41C2×D1111yescharacteristic
158C22×D4C2×D1111yescharacteristic
159AGL(1,ℤ/8)—24no—
160C2×SD16C2×D1112yes—
161C2×D8C2×D1112yes—
162#131—224no—
163C2×M16—112no—
164C2×M16C2×D1111yescharacteristic
165C22×C8—111no—
166C22×C8—112no—
167#127—221no—
168#124—221no—
169C22⋊Q8—112no—
170C22⋊Q8—221no—
171#121—112no—
172#121—112no—
173#121—112no—
174#121—221no—
175#121—222no—
176#120—222no—
177#117—111no—
178C2×C4⋊C4—111no—
179#107—112no—
180#106—112no—
181#103—111no—
182#103—111no—
183#102—112no—
184#102—112no—
185#102—111no—
186#102—111no—
187C2×C11—22no—
188C2×C11—81no—
189C2×C11—82no—
190C2×C11C2×#12111yescharacteristic
191C2×C11#57611yescharacteristic
192C2×C11#57711yescharacteristic
193D11—42no—
194C24—21no—
195#41—22no—
196#41—22no—
197#41—222no—
198#41—222no—
199C2×Q8—111no—
200C2×Q8C22×D1111yescharacteristic
201C2×D4—21no—
202C2×D4—21no—
203C2×D4—22no—
204C2×D4—22no—
205C2×D4—112no—
206C2×D4—111no—
207C2×D4—222no—
208C2×D4—222no—
209C2×D4—222no—
210C2×D4C22×D1111yescharacteristic
211C2×D4C22×D1112yes—
212C22×C4—21no—
213C22×C4—112no—
214C22×C4—221no—
215C22×C4C22×D1111yescharacteristic
216SD16—24no—
217D8—24no—
218M16—224no—
219M16C22⋊D1114yescomplemented
220C2×C8—111no—
221C2×C8—111no—
222C2×C8—222no—
223C2×C8—224no—
224C2×C8C22×D1112yes—
225C4⋊C4—112no—
226C4⋊C4—111no—
227C4⋊C4—111no—
228C4⋊C4—222no—
229C4⋊C4—221no—
230C22⋊C4—222no—
231C22⋊C4—222no—
232C22⋊C4—222no—
233C22⋊C4—222no—
234C22⋊C4—221no—
235C42—221no—
236C11#306211yescharacteristic, complemented, Sylow
237C23—21no—
238C23—22no—
239C23—42no—
240C23—81no—
241C23—81no—
242C23—112no—
243C23D4×D1111yescharacteristic
244Q8—21no—
245Q8—21no—
246Q8—222no—
247D4—22no—
248D4—21no—
249D4—21no—
250D4—22no—
251D4—42no—
252D4—42no—
253D4—224no—
254D4—222no—
255D4—882no—
256D4—882no—
257D4—882no—
258C2×C4—21no—
259C2×C4—42no—
260C2×C4—112no—
261C2×C4—222no—
262C2×C4—222no—
263C2×C4—221no—
264C2×C4—221no—
265C2×C4—222no—
266C2×C4—881no—
267C2×C4D4×D1111yescharacteristic
268C2×C4#434112yes—
269C2×C4C2×C22⋊D1112yes—
270C2×C4C23×D1111yescharacteristic
271C8—221no—
272C8—221no—
273C8C2×C22⋊D1114yes—
274C22—21no—
275C22—21no—
276C22—41no—
277C22—42no—
278C22—42no—
279C22—41no—
280C22—41no—
281C22—42no—
282C22—84no—
283C22—222no—
284C22—222no—
285C22—222no—
286C22#6699112yes—
287C22C2×D4×D1111yescharacteristic
288C4—41no—
289C4—222no—
290C4—442no—
291C4—441no—
292C4—441no—
293C4#6699112yes—
294C4C2×#434111yescharacteristic
295C4C22×C22⋊D1111yescharacteristic
296C2—22no—
297C2—82no—
298C2—81no—
299C2—442no—
300C2#1062330511yescharacteristic
301C2#1062330611yescharacteristic
302C2C2×#6699111yescharacteristic
subgroupG/H
centerC22C2×D4×D11
commutator, cosocleC2×C4×C11C24
FrattiniC2×C4C23×D11
FittingC2×C11×AGL(1,ℤ/8)C2
socleC22×C11C22×D4
hypercenterC2×AGL(1,ℤ/8)D11
hypocenterC11#3062
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×AGL(1,ℤ/8)

Complements

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

NH ≅ G/Ntype
1. C2×C11×AGL(1,ℤ/8)C2semidirect
2. #10623364C2semidirect
3. #10623336C2semidirect
4. C2×#66960C2semidirect
5. #10622846C2semidirect
6. C2×#66896C2semidirect
7. #10622787C2semidirect
8. #10622784C2semidirect
9. #10622772C2semidirect
10. #10622770C2semidirect
11. #10622734C2semidirect
20. #66999C22semidirect
25. #66991C22semidirect
33. C2×#4313C22semidirect
34. C2×C8×D11C22semidirect
35. #66899C22semidirect
36. #66899C22semidirect
39. #66896C22semidirect
40. #66896C22semidirect
41. #66882C22semidirect
42. #66881C22semidirect
67. C11×M16D4semidirect
123. C2×AGL(1,ℤ/8)D11semidirect
219. M16C22⋊D11semidirect
236. C11#3062semidirect

Maximal subgroups

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

subgroupindex
C2×C11×AGL(1,ℤ/8)2
#106233642
#106233362
C2×#669602
#106228462
C2×#668962
#106227872
#106227842
#106227722
#106227702
#106227342
#306211