Finite Group Databasebeta

← #13078294

Subgroups — #13078294

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#10623336C211yesmaximal, characteristic, complemented
2C2×#66985C211yesmaximal, characteristic, complemented
3C2×#66954C211yesmaximal, characteristic, complemented
4#10623041C211yesmaximal, characteristic, complemented
5C2×C11×#102C211yesmaximal, characteristic, complemented
6#10622726C211yesmaximal, characteristic, complemented
7#10622577C211yesmaximal, characteristic, complemented
8#10622395C212yesmaximal, complemented
9#10622393C212yesmaximal, complemented
10#10622391C212yesmaximal, complemented
11#10622388C212yesmaximal, complemented
12C22×D4×C11C2211yescharacteristic
13C2×#4339C2211yescharacteristic
14C2×#4339C2211yescharacteristic
15C22×C8×C11C2211yescharacteristic
16C2×C11×C4⋊C4C2211yescharacteristic
17#67006—22no—
18#66993—21no—
19#66991C2212yes—
20#66991C2212yes—
21#66989—21no—
22C2×#4324C2212yes—
23#66985—24no—
24C2×#4323C2212yes—
25#66983—22no—
26#66979C2211yescharacteristic
27C2×#4318C2211yescharacteristic
28#66954—24no—
29C2×#4313C2212yescomplemented
30C2×C8×D11C2212yescomplemented
31#66950—21no—
32#66950C2212yescomplemented
33#66948—21no—
34#66948C2212yescomplemented
35C11×#102C2212yes—
36C11×#102C2212yes—
37#66885C2211yescharacteristic, complemented
38#66885C2211yescharacteristic, complemented
39#66880C2211yescharacteristic, complemented
40#66880C2211yescharacteristic, complemented
41#66872C2212yescomplemented
42#66871C2212yescomplemented
43C24×C11—21no—
44C2×D4×C11—22no—
45C2×D4×C11—21no—
46C2×D4×C11—22no—
47C2×D4×C11C2312yes—
48C22×C4×C11—21no—
49C22×C4×C11C2311yescharacteristic
50C2×C22⋊D11—21no—
51C2×C22⋊D11—22no—
52C2×C22⋊D11—22no—
53C2×C22⋊D11D412yes—
54#4339—22no—
55#4339—22no—
56#4339—22no—
57#4339—22no—
58C2×D44—22no—
59C2×D44D411yescharacteristic
60C2×D44C2311yescharacteristic
61C2×C4×D11—21no—
62C2×C4×D11C2312yes—
63C2×Dic22D411yescharacteristic
64C2×Dic22C2311yescharacteristic
65C2×C8×C11—22no—
66C2×C8×C11C2311yescharacteristic
67C2×C8×C11C2311yescharacteristic
68C11×C4⋊C4—21no—
69C11×C4⋊C4C2312yes—
70C22⋊Dic11—22no—
71C22⋊Dic11—22no—
72C22⋊Dic11—21no—
73#4324—24no—
74#4323—24no—
75(C2×D11)⋊C4—22no—
76(C2×D11)⋊C4—22no—
77C4⋊Dic11—22no—
78C4⋊Dic11C2311yescharacteristic
79C4⋊Dic11C2311yescharacteristic
80C4×Dic11—21no—
81#4318D414yescomplemented
82C2×C11⋊C8C2312yes—
83#4313—24no—
84C8×D11—24no—
85#3062—111nomaximal, Sylow
86C23×C11—22no—
87C23×C11—42no—
88C23×C11—81no—
89C23×C11—81no—
90C23×C11C2×D411yescharacteristic
91C22×D11—21no—
92C22×D11C2×D412yes—
93D4×C11—22no—
94D4×C11—22no—
95D4×C11—42no—
96C2×C4×C11—22no—
97C2×C4×C11—81no—
98C2×C4×C11C2×D411yescharacteristic
99C2×C4×C11C2×D412yes—
100C2×C4×C11#4112yes—
101C2×C4×C11C2411yescharacteristic
102C22⋊D11—24no—
103C22⋊D11—42no—
104C22⋊D11—82no—
105C22⋊D11—82no—
106C2×Dic11—21no—
107C2×Dic11—21no—
108C2×Dic11—21no—
109C2×Dic11C2×D412yes—
110D44—22no—
111D44—21no—
112D44—21no—
113D44—82no—
114C4×D11—22no—
115C4×D11—22no—
116C4×D11—42no—
117Dic22—22no—
118Dic22—21no—
119Dic22—21no—
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#416—111no—
133C2×#102D1111yescharacteristic, complemented
134C22×C11—21no—
135C22×C11—21no—
136C22×C11—42no—
137C22×C11—42no—
138C22×C11—42no—
139C22×C11—84no—
140C22×C11#12112yes—
141C22×C11C22×D411yescharacteristic
142C2×D11—22no—
143C2×D11—22no—
144C2×D11—22no—
145C2×D11—41no—
146C2×D11—41no—
147C2×D11—41no—
148C4×C11—42no—
149C4×C11#12112yes—
150C4×C11C22×D411yescharacteristic
151C4×C11C2×#4111yescharacteristic
152Dic11—22no—
153Dic11—41no—
154Dic11—41no—
155Dic11—41no—
156C2×#41—111no—
157C2×#41—111no—
158C22×D4C2×D1111yescharacteristic
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#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#102C2×D1112yes—
186#102C2×D1112yes—
187C2×C11—22no—
188C2×C11—82no—
189C2×C11C2×#12111yescharacteristic
190C2×C11#57611yescharacteristic
191C2×C11#57711yescharacteristic
192D11—42no—
193D11—81no—
194C24—21no—
195#41—222no—
196#41—222no—
197#41—222no—
198#41—222no—
199C2×Q8—111no—
200C2×Q8—111no—
201C2×D4—22no—
202C2×D4—22no—
203C2×D4—21no—
204C2×D4—112no—
205C2×D4—111no—
206C2×D4—111no—
207C2×D4—222no—
208C2×D4—221no—
209C2×D4—222no—
210C2×D4—222no—
211C2×D4C22×D1112yes—
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—21no—
226C4⋊C4—111no—
227C4⋊C4—111no—
228C4⋊C4—222no—
229C4⋊C4C22×D1112yes—
230C22⋊C4—222no—
231C22⋊C4—222no—
232C22⋊C4—222no—
233C22⋊C4—222no—
234C22⋊C4—221no—
235C42—221no—
236C11#306211yescharacteristic, complemented, Sylow
237C23—22no—
238C23—42no—
239C23—81no—
240C23—81no—
241C23—112no—
242C23—221no—
243C23D4×D1111yescharacteristic
244Q8—222no—
245Q8—221no—
246Q8—221no—
247D4—22no—
248D4—22no—
249D4—42no—
250D4—224no—
251D4—222no—
252D4—221no—
253D4—221no—
254D4—442no—
255D4—882no—
256D4—882no—
257D4—882no—
258C2×C4—22no—
259C2×C4—81no—
260C2×C4—112no—
261C2×C4—222no—
262C2×C4—222no—
263C2×C4—221no—
264C2×C4—221no—
265C2×C4—221no—
266C2×C4—442no—
267C2×C4#433912yes—
268C2×C4D4×D1111yescharacteristic
269C2×C4D4×D1112yes—
270C2×C4C23×D1111yescharacteristic
271C8—21no—
272C8—21no—
273C8—114no—
274C22—21no—
275C22—21no—
276C22—42no—
277C22—42no—
278C22—42no—
279C22—84no—
280C22—222no—
281C22—222no—
282C22—222no—
283C22—441no—
284C22—441no—
285C22—441no—
286C22#6693712yes—
287C22C2×D4×D1111yescharacteristic
288C4—42no—
289C4—222no—
290C4—441no—
291C4—441no—
292C4—441no—
293C4#6693712yes—
294C4C2×#433911yescharacteristic
295C4C2×D4×D1111yescharacteristic
296C2—22no—
297C2—82no—
298C2—442no—
299C2—881no—
300C2C2×#6693711yescharacteristic
301C2#1062328811yescharacteristic
302C2#1062329311yescharacteristic
subgroupG/H
centerC22C2×D4×D11
commutator, cosocleC2×C4×C11C24
FrattiniC2×C4C23×D11
FittingC2×C11×#102C2
socleC22×C11C22×D4
hypercenterC2×#102D11
hypocenterC11#3062
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×#102

Complements

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

NH ≅ G/Ntype
1. #10623336C2semidirect
2. C2×#66985C2semidirect
3. C2×#66954C2semidirect
4. #10623041C2semidirect
5. C2×C11×#102C2semidirect
6. #10622726C2semidirect
7. #10622577C2semidirect
8. #10622395C2semidirect
9. #10622393C2semidirect
10. #10622391C2semidirect
11. #10622388C2semidirect
29. C2×#4313C22semidirect
30. C2×C8×D11C22semidirect
32. #66950C22semidirect
34. #66948C22semidirect
37. #66885C22semidirect
38. #66885C22semidirect
39. #66880C22semidirect
40. #66880C22semidirect
41. #66872C22semidirect
42. #66871C22semidirect
81. #4318D4semidirect
133. C2×#102D11semidirect
236. C11#3062semidirect

Maximal subgroups

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

subgroupindex
#106233362
C2×#669852
C2×#669542
#106230412
C2×C11×#1022
#106227262
#106225772
#106223952
#106223932
#106223912
#106223882
#306211