Finite Group Databasebeta

← #13078968

Subgroups — #13078968

Order 1408.

404 conjugacy classes of subgroups; only the 125 normal subgroups are shown.

normal subgroups only

This group has 404 conjugacy classes of subgroups — too many to draw. Only its 125 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
2#10623031C211yesmaximal, characteristic, complemented
3C2×C11×#102C211yesmaximal, characteristic, complemented
4#10622828C211yesmaximal, characteristic, complemented
5#10622726C211yesmaximal, characteristic, complemented
6#10622714C211yesmaximal, characteristic, complemented
7#10622579C211yesmaximal, characteristic, complemented
8#10622381C212yesmaximal, complemented
9#10622378C212yesmaximal, complemented
10#10622377C212yesmaximal, complemented
11#10622373C212yesmaximal, complemented
12C22×D4×C11C2211yescharacteristic
13C2×#4339C2211yescharacteristic
14C22×C8×C11C2211yescharacteristic
15C2×C11×C4⋊C4C2211yescharacteristic
16#67006—22no—
17#66993C2212yes—
18#66991—21no—
19#66991—21no—
20#66989C2212yes—
21#66979C2211yescharacteristic
22#66979C2211yescharacteristic
23#66977—22no—
24C2×#4318C2211yescharacteristic
25#66943—21no—
26#66943C2212yescomplemented
27#66941—21no—
28#66941C2212yescomplemented
29C11×#102C2212yes—
30C11×#102C2212yes—
31#66896C2212yes—
32#66896C2212yes—
33#66885C2211yescharacteristic, complemented
34#66885C2211yescharacteristic, complemented
35#66880C2211yescharacteristic, complemented
36#66880C2211yescharacteristic, complemented
37#66879C2212yescomplemented
38C8×Dic11C2212yescomplemented
39#66874C2212yescomplemented
40#66873C2212yescomplemented
41C24×C11—21no—
42C2×D4×C11—21no—
43C2×D4×C11—22no—
44C2×D4×C11—22no—
45C2×D4×C11C2312yes—
46C22×C4×C11—21no—
47C22×C4×C11C2311yescharacteristic
48C2×C22⋊D11—22no—
49C2×C22⋊D11—22no—
50C2×C22⋊D11—21no—
51#4339—22no—
52#4339—22no—
53C2×D44C2311yescharacteristic
54C2×C4×D11—21no—
55C2×Dic22—22no—
56C2×Dic22C2311yescharacteristic
57C2×C8×C11—22no—
58C2×C8×C11C2311yescharacteristic
59C2×C8×C11C2311yescharacteristic
60C11×C4⋊C4—21no—
61C11×C4⋊C4C2312yes—
62C22⋊Dic11—22no—
63C22⋊Dic11—22no—
64C22⋊Dic11—21no—
65C22⋊Dic11D412yes—
66C4⋊Dic11—22no—
67C4⋊Dic11D411yescharacteristic
68C4⋊Dic11D411yescharacteristic
69C4⋊Dic11C2311yescharacteristic
70C4⋊Dic11C2311yescharacteristic
71Dic11⋊C4—22no—
72Dic11⋊C4—22no—
73C4×Dic11—21no—
74C4×Dic11C2312yes—
75#4318—22no—
76C2×C11⋊C8C2312yes—
77#3136—111nomaximal, Sylow
78C23×C11—22no—
79C23×C11—42no—
80C23×C11—81no—
81C23×C11—81no—
82C23×C11C2×D411yescharacteristic
83C22×D11—21no—
84D4×C11—22no—
85D4×C11—22no—
86D4×C11—42no—
87C2×C4×C11—22no—
88C2×C4×C11—81no—
89C2×C4×C11C2×D411yescharacteristic
90C2×C4×C11#4112yes—
91C2×C4×C11#4112yes—
92C2×C4×C11C2411yescharacteristic
93C22⋊D11—42no—
94C22⋊D11—82no—
95C22⋊D11—82no—
96C2×Dic11—21no—
97C2×Dic11—21no—
98C2×Dic11—21no—
99C2×Dic11C2×D412yes—
100C2×Dic11C2×D412yes—
101D44—21no—
102D44—21no—
103C4×D11—42no—
104Dic22—21no—
105Dic22—21no—
106Dic22—82no—
107C8×C11—21no—
108C8×C11—21no—
109C11⋊C8—22no—
110#544—111no—
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×#102D1111yescharacteristic, complemented
120#405—111no—
121C22×C11—21no—
122C22×C11—21no—
123C22×C11—42no—
124C22×C11—42no—
125C22×C11—42no—
126C22×C11—84no—
127C22×C11#12412yes—
128C22×C11C22×D411yescharacteristic
129C2×D11—41no—
130C2×D11—41no—
131C2×D11—41no—
132C4×C11—42no—
133C4×C11#12412yes—
134C4×C11C2×#4111yescharacteristic
135C4×C11C2×#4111yescharacteristic
136Dic11—22no—
137Dic11—22no—
138Dic11—41no—
139Dic11—41no—
140Dic11—41no—
141C2×#41—111no—
142C22×D4C2×D1111yescharacteristic
143C2×M16—111no—
144C22×C8C2×D1111yescharacteristic
145C4⋊Q8—112no—
146C4⋊Q8—221no—
147#127—112no—
148#125—112no—
149#125—221no—
150#124—112no—
151C22⋊Q8—222no—
152#121—221no—
153#121—221no—
154#120—222no—
155#117—111no—
156#117—111no—
157C2×C4⋊C4C2×D1111yescharacteristic
158#103—111no—
159#103—111no—
160#103—112no—
161#102—112no—
162#102—112no—
163#102—111no—
164#102—111no—
165#102—112no—
166#102C2×D1112yes—
167#102C2×D1112yes—
168#97—112no—
169C4×C8—112no—
170C2×C11—22no—
171C2×C11—82no—
172C2×C11C2×#12411yescharacteristic
173C2×C11#57611yescharacteristic
174C2×C11#57711yescharacteristic
175D11—81no—
176C24—21no—
177#41—222no—
178#41—222no—
179C2×Q8—111no—
180C2×Q8—222no—
181C2×D4—22no—
182C2×D4—21no—
183C2×D4—22no—
184C2×D4—111no—
185C2×D4—222no—
186C2×D4—222no—
187C2×D4—221no—
188C2×D4C22×D1112yes—
189C22×C4—21no—
190C22×C4—221no—
191C22×C4C22×D1111yescharacteristic
192M16—222no—
193C2×C8—22no—
194C2×C8—112no—
195C2×C8C22×D1111yescharacteristic
196C2×C8C22×D1111yescharacteristic
197C4⋊C4—21no—
198C4⋊C4—111no—
199C4⋊C4—111no—
200C4⋊C4—111no—
201C4⋊C4—111no—
202C4⋊C4—222no—
203C4⋊C4—222no—
204C4⋊C4—222no—
205C4⋊C4C22×D1112yes—
206C22⋊C4—112no—
207C22⋊C4—222no—
208C22⋊C4—222no—
209C22⋊C4—221no—
210C42—112no—
211C42—221no—
212C11#313611yescharacteristic, complemented, Sylow
213C23—22no—
214C23—42no—
215C23—81no—
216C23—81no—
217C23—221no—
218C23D4×D1111yescharacteristic
219Q8—221no—
220Q8—221no—
221Q8—882no—
222D4—22no—
223D4—22no—
224D4—42no—
225D4—221no—
226D4—221no—
227D4—442no—
228D4—882no—
229D4—882no—
230C2×C4—22no—
231C2×C4—81no—
232C2×C4—112no—
233C2×C4—112no—
234C2×C4—221no—
235C2×C4—221no—
236C2×C4—221no—
237C2×C4—442no—
238C2×C4#433912yes—
239C2×C4D4×D1111yescharacteristic
240C2×C4#434112yes—
241C2×C4C23×D1111yescharacteristic
242C8—21no—
243C8—21no—
244C8—222no—
245C22—21no—
246C22—21no—
247C22—42no—
248C22—42no—
249C22—42no—
250C22—84no—
251C22—441no—
252C22—441no—
253C22—441no—
254C22#6693812yes—
255C22C2×D4×D1111yescharacteristic
256C4—42no—
257C4—222no—
258C4—222no—
259C4—441no—
260C4—441no—
261C4—441no—
262C4#6693812yes—
263C4C2×#433911yescharacteristic
264C4C2×#434111yescharacteristic
265C2—22no—
266C2—82no—
267C2—881no—
268C2C2×#6693811yescharacteristic
269C2#1062328811yescharacteristic
270C2#1062329311yescharacteristic
subgroupG/H
centerC22C2×D4×D11
commutator, cosocleC2×C4×C11C24
FrattiniC2×C4C23×D11
FittingC2×C11×#102C2
socleC22×C11C22×D4
prime radical#10623336C2
hypercenterC2×#102D11
hypocenterC11#3136
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
2. #10623031C2semidirect
3. C2×C11×#102C2semidirect
4. #10622828C2semidirect
5. #10622726C2semidirect
6. #10622714C2semidirect
7. #10622579C2semidirect
8. #10622381C2semidirect
9. #10622378C2semidirect
10. #10622377C2semidirect
11. #10622373C2semidirect
26. #66943C22semidirect
28. #66941C22semidirect
33. #66885C22semidirect
34. #66885C22semidirect
35. #66880C22semidirect
36. #66880C22semidirect
37. #66879C22semidirect
38. C8×Dic11C22semidirect
39. #66874C22semidirect
40. #66873C22semidirect
119. C2×#102D11semidirect
212. C11#3136semidirect

Maximal subgroups

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

subgroupindex
#106233362
#106230312
C2×C11×#1022
#106228282
#106227262
#106227142
#106225792
#106223812
#106223782
#106223772
#106223732
#313611