Finite Group Databasebeta

← #13078160

Subgroups — #13078160

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×#66957C211yesmaximal, characteristic, complemented
4#10623035C211yesmaximal, characteristic, complemented
5C2×C11×#102C211yesmaximal, characteristic, complemented
6#10622715C211yesmaximal, characteristic, complemented
7#10622579C211yesmaximal, characteristic, complemented
8#10622400C212yesmaximal, complemented
9#10622399C212yesmaximal, complemented
10#10622380C212yesmaximal, complemented
11#10622375C212yesmaximal, complemented
12C22×D4×C11C2211yescharacteristic
13C2×#4339C2211yescharacteristic
14C2×#4339C2211yescharacteristic
15C22×C8×C11C2211yescharacteristic
16C2×C11×C4⋊C4C2211yescharacteristic
17#67006—22no—
18#66993C2212yes—
19#66991—21no—
20#66991—21no—
21#66989C2212yes—
22C2×#4324C2212yes—
23#66985—24no—
24C2×#4323C2212yes—
25C4×C22⋊D11—22no—
26#66979C2211yescharacteristic
27C2×#4318C2211yescharacteristic
28C2×Dic44C2211yescharacteristic, complemented
29#66957—24no—
30C2×D88C2211yescharacteristic, complemented
31C2×#4314C2211yescharacteristic, complemented
32C2×#4314C2211yescharacteristic, complemented
33#66946C2212yescomplemented
34#66945—21no—
35C4⋊C4×D11—21no—
36#66940C2212yescomplemented
37C11×#102C2212yes—
38C11×#102C2212yes—
39Dic11⋊C8C2212yescomplemented
40Dic11⋊C8C2212yescomplemented
41#66874C2212yescomplemented
42#66873C2212yescomplemented
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—22no—
51C2×C22⋊D11—22no—
52C2×C22⋊D11—21no—
53C2×C22⋊D11—21no—
54#4339—22no—
55#4339—22no—
56#4339—22no—
57#4339D414yescomplemented
58C2×D44C2311yescharacteristic
59C2×D44C2311yescharacteristic
60C2×C4×D11—22no—
61C2×C4×D11—21no—
62C2×C4×D11—21no—
63C2×Dic22C2311yescharacteristic
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⋊Dic11D412yes—
73#4324—24no—
74#4323—24no—
75(C2×D11)⋊C4—22no—
76C4⋊Dic11D411yescharacteristic
77C4⋊Dic11D411yescharacteristic
78Dic11⋊C4—22no—
79C4×Dic11—22no—
80C4×Dic11C2312yes—
81#4318—22no—
82C2×C11⋊C8C2312yes—
83Dic44—22no—
84D88—22no—
85#4314—22no—
86#4314—22no—
87#3045—111nomaximal, Sylow
88C23×C11—22no—
89C23×C11—42no—
90C23×C11—81no—
91C23×C11—81no—
92C23×C11C2×D411yescharacteristic
93C22×D11—21no—
94C22×D11—21no—
95D4×C11—22no—
96D4×C11—22no—
97D4×C11—42no—
98C2×C4×C11—22no—
99C2×C4×C11—81no—
100C2×C4×C11C2×D411yescharacteristic
101C2×C4×C11C2×D412yes—
102C2×C4×C11#4112yes—
103C2×C4×C11C2411yescharacteristic
104C22⋊D11—24no—
105C22⋊D11—42no—
106C22⋊D11—82no—
107C22⋊D11—82no—
108C2×Dic11—21no—
109C2×Dic11—21no—
110C2×Dic11C2×D412yes—
111C2×Dic11C2×D412yes—
112D44—21no—
113D44—21no—
114D44—21no—
115D44C2×D412yes—
116C4×D11—24no—
117C4×D11—42no—
118C4×D11—82no—
119Dic22—21no—
120Dic22—21no—
121Dic22—21no—
122Dic22C2×D412yes—
123C8×C11—21no—
124C8×C11—21no—
125C11⋊C8—22no—
126C2×AGL(1,ℤ/8)—111no—
127C2×#135—111no—
128#535—111no—
129#520—111no—
130#464—112no—
131#463—112no—
132#460—112no—
133#459—112no—
134#424—111no—
135#417—111no—
136C2×#102D1111yescharacteristic, complemented
137C22×C11—21no—
138C22×C11—21no—
139C22×C11—42no—
140C22×C11—42no—
141C22×C11—42no—
142C22×C11—84no—
143C22×C11#12112yes—
144C22×C11C22×D411yescharacteristic
145C2×D11—22no—
146C2×D11—41no—
147C2×D11—41no—
148C2×D11—41no—
149C2×D11—41no—
150C2×D11—41no—
151C4×C11—42no—
152C4×C11#12112yes—
153C4×C11C22×D411yescharacteristic
154C4×C11C2×#4111yescharacteristic
155Dic11—22no—
156Dic11—22no—
157Dic11—22no—
158Dic11—41no—
159C2×#41—111no—
160C2×#41—111no—
161C22×D4C2×D1111yescharacteristic
162AGL(1,ℤ/8)—224no—
163#135—224no—
164C2×Q16—111no—
165C2×SD16—112no—
166C2×SD16—111no—
167C2×SD16—111no—
168C2×D8—112no—
169C2×D8—111no—
170C2×M16—111no—
171C22×C8C2×D1111yescharacteristic
172#127—112no—
173#124—112no—
174#121—221no—
175#121—221no—
176#120—222no—
177C4×Q8—112no—
178C4×D4—112no—
179C4×D4—222no—
180#117—111no—
181#117—221no—
182C2×C4⋊C4—221no—
183C2×C4⋊C4C2×D1111yescharacteristic
184C4⋊C8—112no—
185C4⋊C8—112no—
186#103—112no—
187#102—112no—
188#102C2×D1112yes—
189#102C2×D1112yes—
190C2×C11—22no—
191C2×C11—82no—
192C2×C11C2×#12111yescharacteristic
193C2×C11#57611yescharacteristic
194C2×C11#57711yescharacteristic
195D11—42no—
196D11—81no—
197C24—21no—
198#41—114no—
199#41—222no—
200#41—222no—
201#41—222no—
202C2×Q8—111no—
203C2×Q8—111no—
204C2×D4—22no—
205C2×D4—22no—
206C2×D4—21no—
207C2×D4—111no—
208C2×D4—111no—
209C2×D4—222no—
210C2×D4—222no—
211C2×D4—221no—
212C2×D4—221no—
213C2×D4C22×D1112yes—
214C22×C4—21no—
215C22×C4—222no—
216C22×C4—221no—
217C22×C4—221no—
218C22×C4C22×D1111yescharacteristic
219Q16—222no—
220SD16—222no—
221SD16—222no—
222SD16—224no—
223D8—222no—
224D8—224no—
225M16—222no—
226C2×C8—22no—
227C2×C8—112no—
228C2×C8C22×D1111yescharacteristic
229C2×C8C22×D1111yescharacteristic
230C4⋊C4—21no—
231C4⋊C4—111no—
232C4⋊C4—111no—
233C4⋊C4—222no—
234C4⋊C4C22×D1112yes—
235C22⋊C4—112no—
236C22⋊C4—222no—
237C22⋊C4—222no—
238C22⋊C4—222no—
239C42—112no—
240C42—222no—
241C11#304511yescharacteristic, complemented, Sylow
242C23—22no—
243C23—42no—
244C23—81no—
245C23—81no—
246C23—221no—
247C23—221no—
248C23D4×D1111yescharacteristic
249Q8—112no—
250Q8—221no—
251Q8—221no—
252Q8—221no—
253D4—22no—
254D4—22no—
255D4—42no—
256D4—112no—
257D4—224no—
258D4—221no—
259D4—221no—
260D4—221no—
261D4—442no—
262D4—882no—
263D4—882no—
264C2×C4—22no—
265C2×C4—81no—
266C2×C4—112no—
267C2×C4—112no—
268C2×C4—221no—
269C2×C4—224no—
270C2×C4—221no—
271C2×C4—442no—
272C2×C4—882no—
273C2×C4#433912yes—
274C2×C4D4×D1111yescharacteristic
275C2×C4D4×D1112yes—
276C2×C4C23×D1111yescharacteristic
277C8—21no—
278C8—21no—
279C8—222no—
280C22—21no—
281C22—21no—
282C22—42no—
283C22—42no—
284C22—42no—
285C22—84no—
286C22—222no—
287C22—441no—
288C22—441no—
289C22—441no—
290C22—441no—
291C22—441no—
292C22#6693712yes—
293C22C2×D4×D1111yescharacteristic
294C4—42no—
295C4—222no—
296C4—222no—
297C4—222no—
298C4—441no—
299C4#6693712yes—
300C4C2×#433911yescharacteristic
301C4C2×D4×D1111yescharacteristic
302C2—22no—
303C2—82no—
304C2—442no—
305C2—881no—
306C2C2×#6693711yescharacteristic
307C2#1062328811yescharacteristic
308C2#1062329311yescharacteristic
subgroupG/H
centerC22C2×D4×D11
commutator, cosocleC2×C4×C11C24
FrattiniC2×C4C23×D11
FittingC2×C11×#102C2
socleC22×C11C22×D4
hypercenterC2×#102D11
hypocenterC11#3045
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×#66957C2semidirect
4. #10623035C2semidirect
5. C2×C11×#102C2semidirect
6. #10622715C2semidirect
7. #10622579C2semidirect
8. #10622400C2semidirect
9. #10622399C2semidirect
10. #10622380C2semidirect
11. #10622375C2semidirect
28. C2×Dic44C22semidirect
30. C2×D88C22semidirect
31. C2×#4314C22semidirect
32. C2×#4314C22semidirect
33. #66946C22semidirect
36. #66940C22semidirect
39. Dic11⋊C8C22semidirect
40. Dic11⋊C8C22semidirect
41. #66874C22semidirect
42. #66873C22semidirect
57. #4339D4semidirect
136. C2×#102D11semidirect
241. C11#3045semidirect

Maximal subgroups

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

subgroupindex
#106233362
C2×#669852
C2×#669572
#106230352
C2×C11×#1022
#106227152
#106225792
#106224002
#106223992
#106223802
#106223752
#304511