Finite Group Databasebeta

← #13078570

Subgroups — #13078570

Order 1408.

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

normal subgroups only

This group has 418 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#10623035C211yesmaximal, characteristic, complemented
3C2×C11×#102C211yesmaximal, characteristic, complemented
4#10622828C211yesmaximal, characteristic, complemented
5#10622723C211yesmaximal, characteristic, complemented
6#10622719C211yesmaximal, characteristic, complemented
7#10622577C211yesmaximal, characteristic, complemented
8#10622397C212yesmaximal, complemented
9#10622392C212yesmaximal, complemented
10#10622390C212yesmaximal, complemented
11#10622387C212yesmaximal, complemented
12C22×D4×C11C2211yescharacteristic
13C2×#4339C2211yescharacteristic
14C22×C8×C11C2211yescharacteristic
15C2×C11×C4⋊C4C2211yescharacteristic
16#67006—22no—
17#66993—21no—
18#66991C2212yes—
19#66991C2212yes—
20#66989—21no—
21C4×C22⋊D11—22no—
22#66979C2211yescharacteristic
23#66979C2211yescharacteristic
24C2×#4318C2211yescharacteristic
25#66946—21no—
26#66945C2212yescomplemented
27C4⋊C4×D11C2212yescomplemented
28#66940—21no—
29C11×#102C2212yes—
30C11×#102C2212yes—
31#66896C2212yes—
32#66896C2212yes—
33(C2×D11)⋊C8C2212yescomplemented
34(C2×D11)⋊C8C2212yescomplemented
35#66882C2211yescharacteristic, complemented
36#66882C2211yescharacteristic, complemented
37#66881C2211yescharacteristic, complemented
38#66881C2211yescharacteristic, complemented
39#66872C2212yescomplemented
40#66871C2212yescomplemented
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⋊D11D412yes—
51#4339—22no—
52#4339—22no—
53C2×D44D411yescharacteristic
54C2×C4×D11—22no—
55C2×C4×D11C2312yes—
56C2×Dic22D411yescharacteristic
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⋊Dic11—21no—
66(C2×D11)⋊C4—22no—
67C4⋊Dic11C2311yescharacteristic
68C4⋊Dic11C2311yescharacteristic
69C4⋊Dic11C2311yescharacteristic
70C4⋊Dic11C2311yescharacteristic
71Dic11⋊C4—22no—
72C4×Dic11—22no—
73C4×Dic11—21no—
74C4×Dic11—21no—
75#4318—22no—
76C2×C11⋊C8C2312yes—
77#3096—111nomaximal, Sylow
78C23×C11—22no—
79C23×C11—42no—
80C23×C11—81no—
81C23×C11—81no—
82C23×C11C2×D411yescharacteristic
83C22×D11C2×D412yes—
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—24no—
94C22⋊D11—82no—
95C22⋊D11—82no—
96C2×Dic11—21no—
97C2×Dic11—21no—
98C2×Dic11—21no—
99C2×Dic11—21no—
100C2×Dic11C2×D412yes—
101D44—22no—
102C4×D11—22no—
103C4×D11—22no—
104C4×D11—82no—
105Dic22—22no—
106C8×C11—21no—
107C8×C11—21no—
108C11⋊C8—22no—
109#535—111no—
110#520—111no—
111#482—112no—
112#482—112no—
113#481—112no—
114#480—112no—
115#428—111no—
116#427—111no—
117#418—111no—
118C2×#102D1111yescharacteristic, complemented
119#408—111no—
120C22×C11—21no—
121C22×C11—21no—
122C22×C11—42no—
123C22×C11—42no—
124C22×C11—42no—
125C22×C11—84no—
126C22×C11#12312yes—
127C22×C11C22×D411yescharacteristic
128C2×D11—22no—
129C2×D11—22no—
130C2×D11—22no—
131C4×C11—42no—
132C4×C11#12312yes—
133C4×C11C2×#4111yescharacteristic
134C4×C11C2×#4111yescharacteristic
135Dic11—22no—
136Dic11—41no—
137Dic11—41no—
138Dic11—41no—
139Dic11—41no—
140C2×#41—111no—
141C22×D4C2×D1111yescharacteristic
142C2×M16—111no—
143C22×C8C2×D1111yescharacteristic
144#127—221no—
145#124—221no—
146#121—112no—
147#121—112no—
148#120—222no—
149C4×Q8—221no—
150C4×D4—221no—
151C4×D4—222no—
152#117—111no—
153#117—111no—
154#117—112no—
155C2×C4⋊C4—112no—
156C2×C4⋊C4C2×D1111yescharacteristic
157#107—111no—
158#107—111no—
159#107—112no—
160#106—111no—
161#106—111no—
162#106—112no—
163#102—112no—
164#102—112no—
165#102C2×D1112yes—
166#102C2×D1112yes—
167C22⋊C8—112no—
168C22⋊C8—112no—
169C2×C11—22no—
170C2×C11—82no—
171C2×C11C2×#12311yescharacteristic
172C2×C11#57611yescharacteristic
173C2×C11#57711yescharacteristic
174D11—42no—
175C24—21no—
176#41—222no—
177#41—222no—
178C2×Q8—111no—
179C2×D4—22no—
180C2×D4—21no—
181C2×D4—22no—
182C2×D4—112no—
183C2×D4—111no—
184C2×D4—222no—
185C2×D4—222no—
186C2×D4C22×D1112yes—
187C22×C4—21no—
188C22×C4—112no—
189C22×C4—222no—
190C22×C4C22×D1111yescharacteristic
191M16—222no—
192C2×C8—22no—
193C2×C8—112no—
194C2×C8C22×D1111yescharacteristic
195C2×C8C22×D1111yescharacteristic
196C4⋊C4—21no—
197C4⋊C4—111no—
198C4⋊C4—111no—
199C4⋊C4—111no—
200C4⋊C4—111no—
201C4⋊C4—222no—
202C4⋊C4C22×D1112yes—
203C22⋊C4—222no—
204C22⋊C4—222no—
205C22⋊C4—222no—
206C22⋊C4—221no—
207C22⋊C4—221no—
208C42—222no—
209C42—221no—
210C42—221no—
211C11#309611yescharacteristic, complemented, Sylow
212C23—22no—
213C23—42no—
214C23—81no—
215C23—81no—
216C23—112no—
217C23D4×D1111yescharacteristic
218Q8—222no—
219D4—22no—
220D4—22no—
221D4—42no—
222D4—224no—
223D4—222no—
224D4—882no—
225D4—882no—
226C2×C4—22no—
227C2×C4—81no—
228C2×C4—112no—
229C2×C4—222no—
230C2×C4—222no—
231C2×C4—221no—
232C2×C4—221no—
233C2×C4—221no—
234C2×C4—221no—
235C2×C4—882no—
236C2×C4#433912yes—
237C2×C4D4×D1111yescharacteristic
238C2×C4#434112yes—
239C2×C4C23×D1111yescharacteristic
240C8—21no—
241C8—21no—
242C8—222no—
243C22—21no—
244C22—21no—
245C22—42no—
246C22—42no—
247C22—42no—
248C22—84no—
249C22—222no—
250C22—222no—
251C22—222no—
252C22#6693612yes—
253C22C2×D4×D1111yescharacteristic
254C4—42no—
255C4—222no—
256C4—441no—
257C4—441no—
258C4—441no—
259C4—441no—
260C4#6693612yes—
261C4C2×#433911yescharacteristic
262C4C2×#434111yescharacteristic
263C2—22no—
264C2—82no—
265C2—442no—
266C2C2×#6693611yescharacteristic
267C2#1062328811yescharacteristic
268C2#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#3096
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. #10623035C2semidirect
3. C2×C11×#102C2semidirect
4. #10622828C2semidirect
5. #10622723C2semidirect
6. #10622719C2semidirect
7. #10622577C2semidirect
8. #10622397C2semidirect
9. #10622392C2semidirect
10. #10622390C2semidirect
11. #10622387C2semidirect
26. #66945C22semidirect
27. C4⋊C4×D11C22semidirect
33. (C2×D11)⋊C8C22semidirect
34. (C2×D11)⋊C8C22semidirect
35. #66882C22semidirect
36. #66882C22semidirect
37. #66881C22semidirect
38. #66881C22semidirect
39. #66872C22semidirect
40. #66871C22semidirect
118. C2×#102D11semidirect
211. C11#3096semidirect

Maximal subgroups

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

subgroupindex
#106233362
#106230352
C2×C11×#1022
#106228282
#106227232
#106227192
#106225772
#106223972
#106223922
#106223902
#106223872
#309611