Finite Group Databasebeta

← #13078299

Subgroups — #13078299

Order 1408.

504 conjugacy classes of subgroups; only the 133 normal subgroups are shown.

normal subgroups only

This group has 504 conjugacy classes of subgroups — too many to draw. Only its 133 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#10623364C211yesmaximal, characteristic, complemented
2C2×#67002C211yesmaximal, characteristic, complemented
3C2×#66954C211yesmaximal, characteristic, complemented
4#10623056C211yesmaximal, characteristic, complemented
5C11×#416C211yesmaximal, characteristic, complemented
6C2×#66885C211yesmaximal, characteristic, complemented
7#10622608C211yesmaximal, characteristic, complemented
8#10622425C212yesmaximal, complemented
9#10622420C212yesmaximal, complemented
10#10622395C212yesmaximal, complemented
11#10622388C212yesmaximal, complemented
12C2×C11×#41C2211yescharacteristic
13C2×#4339C2211yescharacteristic
14C22×D44C2211yescharacteristic
15C22×C8×C11C2211yescharacteristic
16C11×#117C2211yescharacteristic
17#67002—24no—
18#66999C2212yescomplemented
19C2×#4325C2212yes—
20#66992—22no—
21#66991C2212yescomplemented
22C2×#4323C2212yes—
23#66983—21no—
24C2×C4⋊Dic11C2211yescharacteristic
25#66977—21no—
26C2×#4318C2211yescharacteristic
27#66954—24no—
28C2×#4313C2212yescomplemented
29C2×C8×D11C2212yescomplemented
30#66948C2212yes—
31#66948C2212yes—
32#66935—22no—
33#66928—21no—
34#66927—21no—
35C11×#103C2211yescharacteristic, complemented
36C11×#103C2211yescharacteristic, complemented
37C11×#102C2211yescharacteristic, complemented
38C11×#102C2211yescharacteristic, complemented
39#66885C2212yes—
40#66885C2212yes—
41#66872C2212yescomplemented
42#66871C2212yescomplemented
43C23×D11—21no—
44C11×#41—22no—
45C11×#41—22no—
46C2×Q8×C11C2311yescharacteristic
47C2×D4×C11—21no—
48C2×D4×C11C2311yescharacteristic
49C22×C4×C11—21no—
50C22×C4×C11C2311yescharacteristic
51C2×C22⋊D11—22no—
52C2×C22⋊D11D412yes—
53C22×Dic11—21no—
54#4339—22no—
55#4339—22no—
56C2×D44—22no—
57C2×D44—22no—
58C2×D44—21no—
59C2×D44—22no—
60C2×D44—22no—
61C2×D44D411yescharacteristic
62C2×D44C2312yes—
63C2×C4×D11C2312yes—
64C2×Dic22D411yescharacteristic
65C2×C8×C11—22no—
66C2×C8×C11C2311yescharacteristic
67C2×C8×C11C2311yescharacteristic
68C11×C4⋊C4C2311yescharacteristic
69C11×C4⋊C4C2311yescharacteristic
70C11×C22⋊C4—21no—
71C42×C11—21no—
72C22⋊Dic11—22no—
73#4325—24no—
74#4323—24no—
75(C2×D11)⋊C4—22no—
76(C2×D11)⋊C4—22no—
77(C2×D11)⋊C4—22no—
78C4⋊Dic11—21no—
79C4⋊Dic11C2312yes—
80Dic11⋊C4—22no—
81#4318D414yescomplemented
82C2×C11⋊C8C2312yes—
83#4313—24no—
84C8×D11—24no—
85#3062—111nomaximal, Sylow
86C23×C11—21no—
87C23×C11C2×D411yescharacteristic
88C22×D11—22no—
89C22×D11—42no—
90C22×D11—81no—
91C22×D11—81no—
92C22×D11C2×D412yes—
93Q8×C11—21no—
94Q8×C11—21no—
95D4×C11—21no—
96D4×C11—21no—
97D4×C11—42no—
98C2×C4×C11—21no—
99C2×C4×C11—21no—
100C2×C4×C11—21no—
101C2×C4×C11—42no—
102C2×C4×C11C2×D411yescharacteristic
103C2×C4×C11C2×D412yes—
104C2×C4×C11#4112yes—
105C2×C4×C11C2411yescharacteristic
106C22⋊D11—24no—
107C22⋊D11—82no—
108C2×Dic11—22no—
109C2×Dic11—81no—
110C2×Dic11C2×D412yes—
111D44—22no—
112D44—22no—
113D44—22no—
114D44—42no—
115D44—82no—
116D44—82no—
117C4×D11—22no—
118C4×D11—22no—
119Dic22—22no—
120C8×C11—21no—
121C8×C11—21no—
122C11⋊C8C2×D414yes—
123C2×AGL(1,ℤ/8)—111no—
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#416D1111yescharacteristic, complemented
133C2×#102—111no—
134C22×C11—21no—
135C22×C11—21no—
136C22×C11—41no—
137C22×C11—41no—
138C22×C11—41no—
139C22×C11#12112yes—
140C22×C11C22×D411yescharacteristic
141C2×D11—22no—
142C2×D11—22no—
143C2×D11—22no—
144C2×D11—42no—
145C2×D11—42no—
146C2×D11—42no—
147C2×D11—84no—
148C4×C11—41no—
149C4×C11—41no—
150C4×C11—41no—
151C4×C11#12112yes—
152C4×C11C22×D411yescharacteristic
153C4×C11C2×#4111yescharacteristic
154Dic11—22no—
155Dic11—42no—
156C2×#41—111no—
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—112no—
166C22×C8C2×D1111yescharacteristic
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#117C2×D1111yescharacteristic
178C2×C4⋊C4—111no—
179#107—112no—
180#106—112no—
181#103C2×D1111yescharacteristic, complemented
182#103C2×D1111yescharacteristic, complemented
183#102—112no—
184#102—112no—
185#102C2×D1111yescharacteristic, complemented
186#102C2×D1111yescharacteristic, complemented
187C2×C11—22no—
188C2×C11—81no—
189C2×C11C2×#12111yescharacteristic
190C2×C11#57611yescharacteristic
191C2×C11#57711yescharacteristic
192D11—42no—
193D11—82no—
194C24—221no—
195#41—22no—
196#41—22no—
197#41—222no—
198#41—222no—
199C2×Q8—111no—
200C2×Q8C22×D1111yescharacteristic
201C2×D4—21no—
202C2×D4—112no—
203C2×D4—111no—
204C2×D4—112no—
205C2×D4—222no—
206C2×D4—222no—
207C2×D4—222no—
208C2×D4—222no—
209C2×D4—222no—
210C2×D4—221no—
211C2×D4C22×D1111yescharacteristic
212C22×C4—21no—
213C22×C4—112no—
214C22×C4—221no—
215C22×C4C22×D1111yescharacteristic
216SD16—224no—
217D8—224no—
218M16—114no—
219M16—224no—
220C2×C8—22no—
221C2×C8—112no—
222C2×C8—224no—
223C2×C8C22×D1111yescharacteristic
224C2×C8C22×D1111yescharacteristic
225C4⋊C4—112no—
226C4⋊C4—222no—
227C4⋊C4—221no—
228C4⋊C4C22×D1111yescharacteristic
229C4⋊C4C22×D1111yescharacteristic
230C22⋊C4—21no—
231C22⋊C4—222no—
232C22⋊C4—222no—
233C22⋊C4—222no—
234C22⋊C4—222no—
235C42—21no—
236C11#306211yescharacteristic, complemented, Sylow
237C23—21no—
238C23—112no—
239C23—222no—
240C23—442no—
241C23—881no—
242C23—881no—
243C23D4×D1111yescharacteristic
244Q8—21no—
245Q8—21no—
246Q8—222no—
247D4—21no—
248D4—21no—
249D4—42no—
250D4—224no—
251D4—222no—
252D4—222no—
253D4—222no—
254D4—442no—
255D4—882no—
256D4—882no—
257D4—882no—
258C2×C4—21no—
259C2×C4—21no—
260C2×C4—21no—
261C2×C4—42no—
262C2×C4—112no—
263C2×C4—222no—
264C2×C4—222no—
265C2×C4—222no—
266C2×C4—881no—
267C2×C4#433912yes—
268C2×C4D4×D1111yescharacteristic
269C2×C4D4×D1112yes—
270C2×C4C23×D1111yescharacteristic
271C8—21no—
272C8—21no—
273C8—114no—
274C22—21no—
275C22—21no—
276C22—41no—
277C22—41no—
278C22—41no—
279C22—222no—
280C22—222no—
281C22—222no—
282C22—442no—
283C22—442no—
284C22—442no—
285C22—884no—
286C22#6693712yes—
287C22C2×D4×D1111yescharacteristic
288C4—41no—
289C4—41no—
290C4—41no—
291C4—222no—
292C4—442no—
293C4#6693712yes—
294C4C2×#433911yescharacteristic
295C4C2×D4×D1111yescharacteristic
296C2—22no—
297C2—81no—
298C2—442no—
299C2—882no—
300C2C2×#6693711yescharacteristic
301C2#1062330011yescharacteristic
302C2#1062330111yescharacteristic
subgroupG/H
centerC22C2×D4×D11
commutator, cosocleC2×C4×C11C24
FrattiniC2×C4C23×D11
FittingC11×#416C2
socleC22×C11C22×D4
hypercenter#416D11
hypocenterC11#3062
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C22×C4 ◁ #416

Complements

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

NH ≅ G/Ntype
1. #10623364C2semidirect
2. C2×#67002C2semidirect
3. C2×#66954C2semidirect
4. #10623056C2semidirect
5. C11×#416C2semidirect
6. C2×#66885C2semidirect
7. #10622608C2semidirect
8. #10622425C2semidirect
9. #10622420C2semidirect
10. #10622395C2semidirect
11. #10622388C2semidirect
18. #66999C22semidirect
21. #66991C22semidirect
28. C2×#4313C22semidirect
29. C2×C8×D11C22semidirect
35. C11×#103C22semidirect
36. C11×#103C22semidirect
37. C11×#102C22semidirect
38. C11×#102C22semidirect
41. #66872C22semidirect
42. #66871C22semidirect
81. #4318D4semidirect
132. #416D11semidirect
181. #103C2×D11semidirect
182. #103C2×D11semidirect
185. #102C2×D11semidirect
186. #102C2×D11semidirect
236. C11#3062semidirect

Maximal subgroups

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

subgroupindex
#106233642
C2×#670022
C2×#669542
#106230562
C11×#4162
C2×#668852
#106226082
#106224252
#106224202
#106223952
#106223882
#306211