Finite Group Databasebeta

← #13078970

Subgroups — #13078970

Order 1408.

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

normal subgroups only

This group has 404 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
1C11×#535C211yesmaximal, characteristic
2#10623050C211yesmaximal, characteristic, complemented
3#10622846C211yesmaximal, characteristic, complemented
4#10622845C211yesmaximal, characteristic, complemented
5#10622828C211yesmaximal, characteristic, complemented
6C2×#66896C211yesmaximal, characteristic, complemented
7#10622684C212yesmaximal, complemented
8#10622683C212yesmaximal, complemented
9#10622669C212yesmaximal, complemented
10#10622668C212yesmaximal, complemented
11#10622610C211yesmaximal, characteristic, complemented
12C2×C11×#41C2211yescharacteristic
13C22×D4×C11C2211yescharacteristic
14C11×#127C2212yes—
15C11×#124C2212yes—
16C11×#121—21no—
17C11×#121—21no—
18C11×#120—22no—
19C11×#117C2211yescharacteristic
20#66979C2211yescharacteristic
21C2×C4⋊Dic11C2211yescharacteristic
22C2×#4318C2211yescharacteristic
23C22×C11⋊C8C2211yescharacteristic
24#66943—21no—
25#66941—21no—
26#66931—22no—
27#66923C2212yescomplemented
28#66922C2212yescomplemented
29#66899C2212yescomplemented
30#66899C2211yescharacteristic, complemented
31#66899C2211yescharacteristic, complemented
32#66896C2212yes—
33#66896C2212yes—
34#66896C2212yes—
35#66896C2212yes—
36#66896C2212yescomplemented
37#66896C2211yescharacteristic, complemented
38#66896C2211yescharacteristic, complemented
39#66867C2212yescomplemented
40C4×C11⋊C8C2212yescomplemented
41C24×C11—21no—
42C11×#41—22no—
43C11×#41—22no—
44C2×Q8×C11C2311yescharacteristic
45C2×D4×C11—21no—
46C2×D4×C11—21no—
47C2×D4×C11—22no—
48C2×D4×C11—22no—
49C2×D4×C11—22no—
50C2×D4×C11—22no—
51C2×D4×C11C2312yes—
52C2×D4×C11C2311yescharacteristic
53C22×C4×C11—21no—
54C22×C4×C11C2311yescharacteristic
55C22×Dic11—21no—
56C2×Dic22—22no—
57C11×C4⋊C4D411yescharacteristic
58C11×C4⋊C4D411yescharacteristic
59C11×C22⋊C4—22no—
60C11×C22⋊C4—22no—
61C11×C22⋊C4D412yes—
62C42×C11C2312yes—
63C22⋊Dic11—21no—
64C4⋊Dic11—22no—
65C4⋊Dic11—21no—
66C4⋊Dic11C2311yescharacteristic
67C4⋊Dic11C2312yes—
68C4⋊Dic11C2311yescharacteristic
69Dic11⋊C4—22no—
70Dic11⋊C4—22no—
71C4×Dic11—21no—
72#4318—22no—
73C2×C11⋊C8—22no—
74C2×C11⋊C8C2311yescharacteristic
75C2×C11⋊C8C2312yes—
76C2×C11⋊C8C2311yescharacteristic
77#3136—111nomaximal, Sylow
78C23×C11—22no—
79C23×C11—21no—
80C23×C11—42no—
81C23×C11—81no—
82C23×C11—81no—
83C23×C11C2×D411yescharacteristic
84Q8×C11—21no—
85Q8×C11—21no—
86D4×C11—22no—
87D4×C11—22no—
88D4×C11—21no—
89D4×C11—21no—
90D4×C11—42no—
91D4×C11—42no—
92D4×C11—82no—
93D4×C11—82no—
94C2×C4×C11—21no—
95C2×C4×C11—42no—
96C2×C4×C11C2×D412yes—
97C2×C4×C11C2×D412yes—
98C2×C4×C11C2×D411yescharacteristic
99C2×C4×C11#4112yes—
100C2×C4×C11#4112yes—
101C2×C4×C11C2411yescharacteristic
102C2×Dic11—21no—
103C2×Dic11—21no—
104C2×Dic11—22no—
105C2×Dic11—81no—
106Dic22—82no—
107C11⋊C8—21no—
108C11⋊C8—21no—
109C11⋊C8—22no—
110#544—111no—
111#535D1111yescharacteristic
112#490—112no—
113#489—112no—
114#488—112no—
115#486—112no—
116#418—111no—
117#417—111no—
118#416—111no—
119C2×#102—111no—
120#405—111no—
121C22×C11—21no—
122C22×C11—21no—
123C22×C11—41no—
124C22×C11—42no—
125C22×C11—41no—
126C22×C11—42no—
127C22×C11—41no—
128C22×C11—42no—
129C22×C11—84no—
130C22×C11#12412yes—
131C22×C11C22×D411yescharacteristic
132C4×C11—22no—
133C4×C11—22no—
134C4×C11—41no—
135C4×C11#12412yes—
136C4×C11C2×#4111yescharacteristic
137C4×C11C2×#4111yescharacteristic
138Dic11—41no—
139Dic11—42no—
140Dic11—41no—
141C2×#41C2×D1111yescharacteristic
142C22×D4C2×D1111yescharacteristic
143C2×M16—111no—
144C22×C8—111no—
145C4⋊Q8—112no—
146C4⋊Q8—221no—
147#127C2×D1112yes—
148#125—112no—
149#125—221no—
150#124C2×D1112yes—
151C22⋊Q8—222no—
152#121—21no—
153#121—21no—
154#120—22no—
155#117—111no—
156#117C2×D1111yescharacteristic
157C2×C4⋊C4—111no—
158#103—111no—
159#103—111no—
160#103—112no—
161#102—112no—
162#102—112no—
163#102—112no—
164#102—112no—
165#102—111no—
166#102—111no—
167#102—112no—
168#97—112no—
169C4×C8—112no—
170C2×C11—22no—
171C2×C11—81no—
172C2×C11—82no—
173C2×C11C2×#12411yescharacteristic
174C2×C11#57611yescharacteristic
175C2×C11#57711yescharacteristic
176C24—21no—
177#41—22no—
178#41—22no—
179C2×Q8—222no—
180C2×Q8C22×D1111yescharacteristic
181C2×D4—21no—
182C2×D4—22no—
183C2×D4—22no—
184C2×D4—21no—
185C2×D4—22no—
186C2×D4—22no—
187C2×D4C22×D1112yes—
188C2×D4C22×D1111yescharacteristic
189C22×C4—21no—
190C22×C4—221no—
191C22×C4C22×D1111yescharacteristic
192M16—222no—
193C2×C8—111no—
194C2×C8—112no—
195C2×C8—111no—
196C2×C8—222no—
197C4⋊C4—112no—
198C4⋊C4—111no—
199C4⋊C4—111no—
200C4⋊C4—221no—
201C4⋊C4—222no—
202C4⋊C4—222no—
203C4⋊C4—222no—
204C4⋊C4C22⋊D1111yescharacteristic
205C4⋊C4C22⋊D1111yescharacteristic
206C22⋊C4—22no—
207C22⋊C4—22no—
208C22⋊C4—221no—
209C22⋊C4C22⋊D1112yes—
210C42—221no—
211C42C22×D1112yes—
212C11#313611yescharacteristic, complemented, Sylow
213C23—22no—
214C23—21no—
215C23—42no—
216C23—81no—
217C23—81no—
218C23C2×C22⋊D1111yescharacteristic
219Q8—21no—
220Q8—21no—
221Q8—882no—
222D4—22no—
223D4—22no—
224D4—21no—
225D4—21no—
226D4—42no—
227D4—42no—
228D4—82no—
229D4—82no—
230C2×C4—21no—
231C2×C4—42no—
232C2×C4—221no—
233C2×C4—221no—
234C2×C4—222no—
235C2×C4—881no—
236C2×C4#434112yes—
237C2×C4#434112yes—
238C2×C4C2×C22⋊D1112yes—
239C2×C4C2×C22⋊D1112yes—
240C2×C4C2×C22⋊D1111yescharacteristic
241C2×C4C23×D1111yescharacteristic
242C8—221no—
243C8—221no—
244C8—222no—
245C22—21no—
246C22—21no—
247C22—41no—
248C22—42no—
249C22—41no—
250C22—42no—
251C22—41no—
252C22—42no—
253C22—84no—
254C22#6698912yes—
255C22C22×C22⋊D1111yescharacteristic
256C4—22no—
257C4—22no—
258C4—41no—
259C4—442no—
260C4—441no—
261C4—441no—
262C4#6698912yes—
263C4C2×#434111yescharacteristic
264C4C2×#434111yescharacteristic
265C2—22no—
266C2—82no—
267C2—81no—
268C2C2×#6698911yescharacteristic
269C2#1062336611yescharacteristic
270C2#1062336711yescharacteristic
subgroupG/H
centerC22C22×C22⋊D11
commutator, cosocleC2×C4×C11C24
FrattiniC2×C4C23×D11
Fitting, prime radicalC11×#535C2
socleC22×C11C22×D4
hypercenter#535D11
hypocenterC11#3136
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ #117 ◁ #535

Complements

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

NH ≅ G/Ntype
2. #10623050C2semidirect
3. #10622846C2semidirect
4. #10622845C2semidirect
5. #10622828C2semidirect
6. C2×#66896C2semidirect
7. #10622684C2semidirect
8. #10622683C2semidirect
9. #10622669C2semidirect
10. #10622668C2semidirect
11. #10622610C2semidirect
27. #66923C22semidirect
28. #66922C22semidirect
29. #66899C22semidirect
30. #66899C22semidirect
31. #66899C22semidirect
36. #66896C22semidirect
37. #66896C22semidirect
38. #66896C22semidirect
39. #66867C22semidirect
40. C4×C11⋊C8C22semidirect
212. C11#3136semidirect

Maximal subgroups

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

subgroupindex
C11×#5352
#106230502
#106228462
#106228452
#106228282
C2×#668962
#106226842
#106226832
#106226692
#106226682
#106226102
#313611