Finite Group Databasebeta

← #13078975

Subgroups — #13078975

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×#544C211yesmaximal, characteristic, complemented
2#10623056C211yesmaximal, characteristic
3#10622702C212yesmaximal, complemented
4#10622701C212yesmaximal, complemented
5#10622681C212yesmaximal, complemented
6#10622680C212yesmaximal, complemented
7#10622615C211yesmaximal, characteristic, complemented
8#10622614C211yesmaximal, characteristic, complemented
9#10622610C211yesmaximal, characteristic, complemented
10#10622579C211yesmaximal, characteristic, complemented
11C2×#66873C211yesmaximal, characteristic, complemented
12C2×#4339C2211yescharacteristic
13C22×D44C2211yescharacteristic
14C11×C4⋊Q8—21no—
15C11×C4⋊Q8C2212yescomplemented
16C11×#125—21no—
17C11×#125C2212yescomplemented
18C11×C22⋊Q8—22no—
19C11×#117C2211yescharacteristic
20C11×#117C2211yescharacteristic
21C2×C11×C4⋊C4C2211yescharacteristic
22C2×#4318C2211yescharacteristic
23C22×C11⋊C8C2211yescharacteristic
24#66948—21no—
25#66948—21no—
26#66935—22no—
27#66928C2212yes—
28#66927C2212yes—
29#66874C2212yescomplemented
30#66874C2211yescharacteristic, complemented
31#66874C2211yescharacteristic, complemented
32#66873C2212yes—
33#66873C2212yes—
34#66873C2212yes—
35#66873C2212yes—
36#66873C2212yescomplemented
37#66873C2211yescharacteristic, complemented
38#66873C2211yescharacteristic, complemented
39#66867C2212yescomplemented
40C4×C11⋊C8C2212yescomplemented
41C23×D11—21no—
42C2×Q8×C11—22no—
43C22×C4×C11—21no—
44C22×C4×C11C2311yescharacteristic
45C2×C22⋊D11—21no—
46#4339—22no—
47#4339—22no—
48C2×D44—21no—
49C2×D44—22no—
50C2×D44—22no—
51C2×D44—22no—
52C2×D44—22no—
53C2×D44C2312yes—
54C2×D44C2311yescharacteristic
55C2×C4×D11—21no—
56C2×Dic22C2311yescharacteristic
57C11×C4⋊C4—21no—
58C11×C4⋊C4—22no—
59C11×C4⋊C4—22no—
60C11×C4⋊C4—22no—
61C11×C4⋊C4D411yescharacteristic
62C11×C4⋊C4D411yescharacteristic
63C11×C4⋊C4C2312yes—
64C11×C4⋊C4C2311yescharacteristic
65C11×C4⋊C4C2311yescharacteristic
66C11×C22⋊C4—21no—
67C11×C22⋊C4D412yes—
68C42×C11—21no—
69C42×C11C2312yes—
70(C2×D11)⋊C4—22no—
71(C2×D11)⋊C4—22no—
72#4318—22no—
73C2×C11⋊C8—22no—
74C2×C11⋊C8C2311yescharacteristic
75C2×C11⋊C8C2312yes—
76C2×C11⋊C8C2311yescharacteristic
77#3136—111nomaximal, Sylow
78C23×C11C2×D411yescharacteristic
79C22×D11—22no—
80C22×D11—21no—
81C22×D11—42no—
82C22×D11—81no—
83C22×D11—81no—
84Q8×C11—82no—
85C2×C4×C11—21no—
86C2×C4×C11—21no—
87C2×C4×C11—22no—
88C2×C4×C11—81no—
89C2×C4×C11C2×D412yes—
90C2×C4×C11C2×D412yes—
91C2×C4×C11C2×D411yescharacteristic
92C2×C4×C11#4112yes—
93C2×C4×C11#4112yes—
94C2×C4×C11C2411yescharacteristic
95C22⋊D11—42no—
96C2×Dic11—21no—
97D44—22no—
98D44—22no—
99D44—21no—
100D44—21no—
101D44—42no—
102D44—82no—
103D44—82no—
104C4×D11—42no—
105Dic22—21no—
106Dic22—21no—
107C11⋊C8—21no—
108C11⋊C8—21no—
109C11⋊C8—22no—
110#544D1111yescharacteristic, complemented
111#535—111no—
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#12412yes—
124C22×C11C22×D411yescharacteristic
125C2×D11—42no—
126C2×D11—41no—
127C2×D11—42no—
128C2×D11—41no—
129C2×D11—42no—
130C2×D11—41no—
131C2×D11—84no—
132C4×C11—22no—
133C4×C11—22no—
134C4×C11—42no—
135C4×C11—41no—
136C4×C11—41no—
137C4×C11#12412yes—
138C4×C11C2×#4111yescharacteristic
139C4×C11C2×#4111yescharacteristic
140Dic11—41no—
141C2×#41—111no—
142C22×D4—111no—
143C2×M16—111no—
144C22×C8—111no—
145C4⋊Q8—21no—
146C4⋊Q8C2×D1112yescomplemented
147#127—112no—
148#125—21no—
149#125C2×D1112yescomplemented
150#124—112no—
151C22⋊Q8—22no—
152#121—221no—
153#121—221no—
154#120—222no—
155#117C2×D1111yescharacteristic
156#117C2×D1111yescharacteristic
157C2×C4⋊C4C2×D1111yescharacteristic
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×C11C2×#12411yescharacteristic
172C2×C11#57611yescharacteristic
173C2×C11#57711yescharacteristic
174D11—81no—
175D11—82no—
176C24—221no—
177#41—222no—
178#41—222no—
179C2×Q8—22no—
180C2×Q8—111no—
181C2×D4—112no—
182C2×D4—111no—
183C2×D4—221no—
184C2×D4—222no—
185C2×D4—222no—
186C2×D4—221no—
187C2×D4—222no—
188C2×D4—222no—
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—21no—
198C4⋊C4—22no—
199C4⋊C4—22no—
200C4⋊C4—22no—
201C4⋊C4C22⋊D1111yescharacteristic
202C4⋊C4C22⋊D1111yescharacteristic
203C4⋊C4C22×D1112yes—
204C4⋊C4C22×D1111yescharacteristic
205C4⋊C4C22×D1111yescharacteristic
206C22⋊C4—21no—
207C22⋊C4—222no—
208C22⋊C4—222no—
209C22⋊C4C22⋊D1112yes—
210C42—21no—
211C42C22×D1112yes—
212C11#313611yescharacteristic, complemented, Sylow
213C23—222no—
214C23—221no—
215C23—442no—
216C23—881no—
217C23—881no—
218C23C2×C22⋊D1111yescharacteristic
219Q8—82no—
220Q8—221no—
221Q8—221no—
222D4—222no—
223D4—222no—
224D4—221no—
225D4—221no—
226D4—442no—
227D4—442no—
228D4—882no—
229D4—882no—
230C2×C4—21no—
231C2×C4—21no—
232C2×C4—22no—
233C2×C4—81no—
234C2×C4—221no—
235C2×C4—442no—
236C2×C4#434312yes—
237C2×C4#434312yes—
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—441no—
248C22—442no—
249C22—441no—
250C22—442no—
251C22—441no—
252C22—442no—
253C22—884no—
254C22#6700012yes—
255C22C22×C22⋊D1111yescharacteristic
256C4—22no—
257C4—22no—
258C4—42no—
259C4—41no—
260C4—41no—
261C4—441no—
262C4#6700012yes—
263C4C2×#434311yescharacteristic
264C4C2×#434311yescharacteristic
265C2—22no—
266C2—882no—
267C2—881no—
268C2C2×#6700011yescharacteristic
269C2#1062336611yescharacteristic
270C2#1062336811yescharacteristic
subgroupG/H
centerC22C22×C22⋊D11
commutator, cosocleC2×C4×C11C24
FrattiniC2×C4C23×D11
FittingC11×#544C2
socleC22×C11C22×D4
prime radical#10623056C2
hypercenter#544D11
hypocenterC11#3136
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ #117 ◁ #544

Complements

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

NH ≅ G/Ntype
1. C11×#544C2semidirect
3. #10622702C2semidirect
4. #10622701C2semidirect
5. #10622681C2semidirect
6. #10622680C2semidirect
7. #10622615C2semidirect
8. #10622614C2semidirect
9. #10622610C2semidirect
10. #10622579C2semidirect
11. C2×#66873C2semidirect
15. C11×C4⋊Q8C22semidirect
17. C11×#125C22semidirect
29. #66874C22semidirect
30. #66874C22semidirect
31. #66874C22semidirect
36. #66873C22semidirect
37. #66873C22semidirect
38. #66873C22semidirect
39. #66867C22semidirect
40. C4×C11⋊C8C22semidirect
110. #544D11semidirect
146. C4⋊Q8C2×D11semidirect
149. #125C2×D11semidirect
212. C11#3136semidirect

Maximal subgroups

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

subgroupindex
C11×#5442
#106230562
#106227022
#106227012
#106226812
#106226802
#106226152
#106226142
#106226102
#106225792
C2×#668732
#313611