Finite Group Databasebeta

← #13078297

Subgroups — #13078297

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×#66961C211yesmaximal, characteristic, complemented
2C2×#66960C211yesmaximal, characteristic, complemented
3#10623056C211yesmaximal, characteristic, complemented
4#10623041C211yesmaximal, characteristic, complemented
5C11×#428C211yesmaximal, characteristic, complemented
6#10622615C211yesmaximal, characteristic, complemented
7C2×#66873C211yesmaximal, characteristic, complemented
8#10622499C212yesmaximal, complemented
9#10622496C212yesmaximal, complemented
10#10622478C212yesmaximal, complemented
11#10622477C212yesmaximal, complemented
12C2×#4339C2211yescharacteristic
13C2×#4339C2211yescharacteristic
14C22×D44C2211yescharacteristic
15C2×C11×M16C2211yescharacteristic
16C11×#117C2211yescharacteristic
17C2×C11×C4⋊C4C2211yescharacteristic
18#66983—22no—
19C22×C11⋊C8C2211yescharacteristic
20#66961—24no—
21#66960—24no—
22C2×D88C2212yes—
23C2×#4314C2212yes—
24C2×#4313C2212yescomplemented
25C2×C8×D11C2212yescomplemented
26#66950—21no—
27#66950C2212yescomplemented
28#66948—21no—
29#66948C2212yes—
30#66948C2212yes—
31#66948C2212yescomplemented
32#66935—22no—
33#66928—21no—
34#66927—21no—
35C11×#107C2212yescomplemented
36C11×#106C2212yescomplemented
37#66874C2211yescharacteristic, complemented
38#66874C2211yescharacteristic, complemented
39#66873C2212yes—
40#66873C2212yes—
41#66873C2211yescharacteristic, complemented
42#66873C2211yescharacteristic, complemented
43C23×D11—21no—
44C22×C4×C11—21no—
45C22×C4×C11C2311yescharacteristic
46C2×C22⋊D11—21no—
47C2×C22⋊D11D412yes—
48#4339—22no—
49#4339—22no—
50#4339—22no—
51#4339—22no—
52C2×D44—22no—
53C2×D44—22no—
54C2×D44—22no—
55C2×D44—21no—
56C2×D44—22no—
57C2×D44—22no—
58C2×D44D411yescharacteristic
59C2×D44C2312yes—
60C2×D44C2311yescharacteristic
61C2×C4×D11—21no—
62C2×C4×D11C2312yes—
63C2×Dic22D411yescharacteristic
64C2×Dic22C2311yescharacteristic
65C11×M16D414yescomplemented
66C2×C8×C11C2312yes—
67C11×C4⋊C4—21no—
68C11×C4⋊C4C2312yes—
69C11×C4⋊C4C2311yescharacteristic
70C11×C4⋊C4C2311yescharacteristic
71C11×C22⋊C4—21no—
72C42×C11—21no—
73(C2×D11)⋊C4—22no—
74(C2×D11)⋊C4—22no—
75(C2×D11)⋊C4—22no—
76(C2×D11)⋊C4—22no—
77C4⋊Dic11—22no—
78C2×C11⋊C8—22no—
79C2×C11⋊C8C2311yescharacteristic
80C2×C11⋊C8C2311yescharacteristic
81D88—24no—
82#4314—24no—
83#4313—24no—
84C8×D11—24no—
85#3062—111nomaximal, Sylow
86C23×C11C2×D411yescharacteristic
87C22×D11—21no—
88C22×D11—22no—
89C22×D11—42no—
90C22×D11—81no—
91C22×D11—81no—
92C22×D11C2×D412yes—
93C2×C4×C11—22no—
94C2×C4×C11—21no—
95C2×C4×C11—21no—
96C2×C4×C11—81no—
97C2×C4×C11C2×D412yes—
98C2×C4×C11C2×D411yescharacteristic
99C2×C4×C11#4112yes—
100C2×C4×C11C2411yescharacteristic
101C22⋊D11—24no—
102C22⋊D11—42no—
103C2×Dic11—21no—
104C2×Dic11C2×D412yes—
105D44—22no—
106D44—22no—
107D44—21no—
108D44—22no—
109D44—21no—
110D44—42no—
111D44—82no—
112D44—82no—
113D44—82no—
114C4×D11—22no—
115C4×D11—22no—
116C4×D11—42no—
117Dic22—22no—
118Dic22—21no—
119Dic22—21no—
120C8×C11C2×D414yes—
121C11⋊C8—21no—
122C11⋊C8—21no—
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#428D1111yescharacteristic, complemented
132#416—111no—
133C2×#102—111no—
134C22×C11—21no—
135C22×C11—21no—
136C22×C11#12112yes—
137C22×C11C22×D411yescharacteristic
138C2×D11—22no—
139C2×D11—22no—
140C2×D11—22no—
141C2×D11—42no—
142C2×D11—41no—
143C2×D11—42no—
144C2×D11—41no—
145C2×D11—41no—
146C2×D11—42no—
147C2×D11—84no—
148C4×C11—42no—
149C4×C11—41no—
150C4×C11—41no—
151C4×C11#12112yes—
152C4×C11C22×D411yescharacteristic
153C4×C11C2×#4111yescharacteristic
154Dic11—22no—
155Dic11—41no—
156C2×#41—111no—
157C2×#41—111no—
158C22×D4—111no—
159AGL(1,ℤ/8)—224no—
160C2×SD16—112no—
161C2×D8—112no—
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#117C2×D1111yescharacteristic
178C2×C4⋊C4C2×D1111yescharacteristic
179#107C2×D1112yescomplemented
180#106C2×D1112yescomplemented
181#103—111no—
182#103—111no—
183#102—112no—
184#102—112no—
185#102—111no—
186#102—111no—
187C2×C11—22no—
188C2×C11C2×#12111yescharacteristic
189C2×C11#57611yescharacteristic
190C2×C11#57711yescharacteristic
191D11—42no—
192D11—81no—
193D11—82no—
194C24—221no—
195#41—222no—
196#41—222no—
197#41—222no—
198#41—222no—
199C2×Q8—111no—
200C2×Q8—111no—
201C2×D4—112no—
202C2×D4—111no—
203C2×D4—111no—
204C2×D4—112no—
205C2×D4—222no—
206C2×D4—222no—
207C2×D4—222no—
208C2×D4—221no—
209C2×D4—222no—
210C2×D4—221no—
211C2×D4—222no—
212C22×C4—21no—
213C22×C4—112no—
214C22×C4—221no—
215C22×C4C22×D1111yescharacteristic
216SD16—224no—
217D8—224no—
218M16—224no—
219M16D4414yescomplemented
220C2×C8—111no—
221C2×C8—111no—
222C2×C8—222no—
223C2×C8—224no—
224C2×C8C22×D1112yes—
225C4⋊C4—21no—
226C4⋊C4—222no—
227C4⋊C4C22×D1112yes—
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—112no—
238C23—221no—
239C23—222no—
240C23—442no—
241C23—881no—
242C23—881no—
243C23D4×D1111yescharacteristic
244Q8—222no—
245Q8—221no—
246Q8—221no—
247D4—224no—
248D4—222no—
249D4—221no—
250D4—222no—
251D4—222no—
252D4—221no—
253D4—442no—
254D4—442no—
255D4—882no—
256D4—882no—
257D4—882no—
258C2×C4—21no—
259C2×C4—21no—
260C2×C4—22no—
261C2×C4—81no—
262C2×C4—112no—
263C2×C4—222no—
264C2×C4—222no—
265C2×C4—221no—
266C2×C4—442no—
267C2×C4C2×D4412yes—
268C2×C4D4×D1111yescharacteristic
269C2×C4#434312yes—
270C2×C4C23×D1111yescharacteristic
271C8—221no—
272C8—221no—
273C8C2×D4414yes—
274C22—21no—
275C22—21no—
276C22—222no—
277C22—222no—
278C22—222no—
279C22—441no—
280C22—442no—
281C22—441no—
282C22—442no—
283C22—442no—
284C22—441no—
285C22—884no—
286C22#6694812yes—
287C22C2×D4×D1111yescharacteristic
288C4—42no—
289C4—41no—
290C4—41no—
291C4—222no—
292C4—441no—
293C4#6694812yes—
294C4C22×D4411yescharacteristic
295C4C2×#434311yescharacteristic
296C2—22no—
297C2—442no—
298C2—882no—
299C2—881no—
300C2C2×#6694811yescharacteristic
301C2#1062330511yescharacteristic
302C2#1062330911yescharacteristic
subgroupG/H
centerC22C2×D4×D11
commutator, cosocleC2×C4×C11C24
FrattiniC2×C4C23×D11
FittingC11×#428C2
socleC22×C11C22×D4
hypercenter#428D11
hypocenterC11#3062
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C22×C4 ◁ #428

Complements

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

NH ≅ G/Ntype
1. C2×#66961C2semidirect
2. C2×#66960C2semidirect
3. #10623056C2semidirect
4. #10623041C2semidirect
5. C11×#428C2semidirect
6. #10622615C2semidirect
7. C2×#66873C2semidirect
8. #10622499C2semidirect
9. #10622496C2semidirect
10. #10622478C2semidirect
11. #10622477C2semidirect
24. C2×#4313C22semidirect
25. C2×C8×D11C22semidirect
27. #66950C22semidirect
31. #66948C22semidirect
35. C11×#107C22semidirect
36. C11×#106C22semidirect
37. #66874C22semidirect
38. #66874C22semidirect
41. #66873C22semidirect
42. #66873C22semidirect
65. C11×M16D4semidirect
131. #428D11semidirect
179. #107C2×D11semidirect
180. #106C2×D11semidirect
219. M16D44semidirect
236. C11#3062semidirect

Maximal subgroups

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

subgroupindex
C2×#669612
C2×#669602
#106230562
#106230412
C11×#4282
#106226152
C2×#668732
#106224992
#106224962
#106224782
#106224772
#306211