Finite Group Databasebeta

← #13078568

Subgroups — #13078568

Order 1408.

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

normal subgroups only

This group has 418 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#10623358C211yesmaximal, characteristic, complemented
3#10622847C211yesmaximal, characteristic, complemented
4#10622828C211yesmaximal, characteristic, complemented
5C2×#66896C211yesmaximal, characteristic, complemented
6#10622648C212yesmaximal, complemented
7#10622648C212yesmaximal, complemented
8#10622647C212yesmaximal, complemented
9#10622646C212yesmaximal, complemented
10#10622611C211yesmaximal, characteristic, complemented
11#10622608C211yesmaximal, characteristic, complemented
12C2×C11×#41C2211yescharacteristic
13C22×D4×C11C2211yescharacteristic
14C11×#127—21no—
15C11×#124—21no—
16C11×#121C2212yes—
17C11×#121C2212yes—
18C11×#120—22no—
19C11×#117C2211yescharacteristic
20Q8×Dic11—21no—
21D4×Dic11—21no—
22D4×Dic11—22no—
23#66979C2211yescharacteristic
24#66979C2212yescomplemented
25C2×C4⋊Dic11C2211yescharacteristic
26C2×C4⋊Dic11C2212yescomplemented
27C2×#4318C2211yescharacteristic
28C22×C11⋊C8C2211yescharacteristic
29#66896C2212yes—
30#66896C2212yes—
31#66896C2212yes—
32#66896C2212yes—
33C22⋊(C11⋊C8)C2212yescomplemented
34C22⋊(C11⋊C8)C2212yescomplemented
35#66872C2212yescomplemented
36#66872C2211yescharacteristic, complemented
37#66872C2211yescharacteristic, complemented
38#66871C2212yescomplemented
39#66871C2211yescharacteristic, complemented
40#66871C2211yescharacteristic, complemented
41C24×C11—21no—
42C11×#41—22no—
43C11×#41—22no—
44C2×Q8×C11D411yescharacteristic
45C2×D4×C11—22no—
46C2×D4×C11—22no—
47C2×D4×C11—21no—
48C2×D4×C11—22no—
49C2×D4×C11—22no—
50C2×D4×C11D412yes—
51C2×D4×C11D411yescharacteristic
52C2×D4×C11C2312yes—
53C22×C4×C11C2312yes—
54C22×C4×C11C2311yescharacteristic
55C22×Dic11—21no—
56C22×Dic11—22no—
57C11×C4⋊C4C2311yescharacteristic
58C11×C4⋊C4C2311yescharacteristic
59C11×C22⋊C4—21no—
60C11×C22⋊C4—22no—
61C11×C22⋊C4—22no—
62C42×C11—21no—
63C22⋊Dic11—21no—
64C22⋊Dic11—22no—
65C4⋊Dic11—21no—
66C4⋊Dic11—22no—
67C4⋊Dic11C2312yes—
68C4⋊Dic11C2311yescharacteristic
69C4⋊Dic11C2311yescharacteristic
70C4×Dic11—21no—
71C4×Dic11—22no—
72#4318—22no—
73C2×C11⋊C8—22no—
74C2×C11⋊C8C2311yescharacteristic
75C2×C11⋊C8C2312yes—
76C2×C11⋊C8C2311yescharacteristic
77#3096—111nomaximal, Sylow
78C23×C11—22no—
79C23×C11—42no—
80C23×C11—81no—
81C23×C11—81no—
82C23×C11C2×D412yes—
83C23×C11C2×D411yescharacteristic
84Q8×C11—22no—
85D4×C11—24no—
86D4×C11—22no—
87D4×C11—22no—
88D4×C11—22no—
89D4×C11—42no—
90D4×C11—82no—
91D4×C11—82no—
92C2×C4×C11—22no—
93C2×C4×C11—22no—
94C2×C4×C11—21no—
95C2×C4×C11—21no—
96C2×C4×C11C2×D412yes—
97C2×C4×C11C2×D411yescharacteristic
98C2×C4×C11#4112yes—
99C2×C4×C11#4112yes—
100C2×C4×C11C2411yescharacteristic
101C2×Dic11—21no—
102C2×Dic11—21no—
103C2×Dic11—22no—
104C2×Dic11—81no—
105C2×Dic11—82no—
106C11⋊C8—21no—
107C11⋊C8—21no—
108C11⋊C8—22no—
109#535D1111yescharacteristic
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×#102—111no—
119#408—111no—
120C22×C11—21no—
121C22×C11—21no—
122C22×C11—22no—
123C22×C11—22no—
124C22×C11—22no—
125C22×C11—42no—
126C22×C11—42no—
127C22×C11—42no—
128C22×C11—84no—
129C22×C11#12312yes—
130C22×C11C22×D411yescharacteristic
131C4×C11—22no—
132C4×C11—41no—
133C4×C11—41no—
134C4×C11#12312yes—
135C4×C11C2×#4111yescharacteristic
136C4×C11C2×#4111yescharacteristic
137Dic11—41no—
138Dic11—42no—
139Dic11—41no—
140C2×#41C2×D1111yescharacteristic
141C22×D4C2×D1111yescharacteristic
142C2×M16—111no—
143C22×C8—111no—
144#127—21no—
145#124—21no—
146#121C2×D1112yes—
147#121C2×D1112yes—
148#120—22no—
149C4×Q8—221no—
150C4×D4—222no—
151C4×D4—221no—
152#117—111no—
153#117—112no—
154#117C2×D1111yescharacteristic
155C2×C4⋊C4—111no—
156C2×C4⋊C4—112no—
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#102—112no—
166#102—112no—
167C22⋊C8—112no—
168C22⋊C8—112no—
169C2×C11—22no—
170C2×C11—42no—
171C2×C11—82no—
172C2×C11C2×#12311yescharacteristic
173C2×C11#57611yescharacteristic
174C2×C11#57711yescharacteristic
175C24—21no—
176#41—22no—
177#41—22no—
178C2×Q8C22⋊D1111yescharacteristic
179C2×D4—22no—
180C2×D4—22no—
181C2×D4—22no—
182C2×D4—22no—
183C2×D4—21no—
184C2×D4C22⋊D1112yes—
185C2×D4C22⋊D1111yescharacteristic
186C2×D4C22×D1112yes—
187C22×C4—222no—
188C22×C4—221no—
189C22×C4C22×D1112yes—
190C22×C4C22×D1111yescharacteristic
191M16—222no—
192C2×C8—111no—
193C2×C8—112no—
194C2×C8—111no—
195C2×C8—222no—
196C4⋊C4—112no—
197C4⋊C4—111no—
198C4⋊C4—111no—
199C4⋊C4—222no—
200C4⋊C4—221no—
201C4⋊C4C22×D1111yescharacteristic
202C4⋊C4C22×D1111yescharacteristic
203C22⋊C4—21no—
204C22⋊C4—22no—
205C22⋊C4—22no—
206C22⋊C4—222no—
207C22⋊C4—221no—
208C42—21no—
209C42—222no—
210C42—221no—
211C11#309611yescharacteristic, complemented, Sylow
212C23—22no—
213C23—42no—
214C23—81no—
215C23—81no—
216C23C2×C22⋊D1112yes—
217C23C2×C22⋊D1111yescharacteristic
218Q8—22no—
219D4—24no—
220D4—22no—
221D4—22no—
222D4—22no—
223D4—42no—
224D4—82no—
225D4—82no—
226C2×C4—22no—
227C2×C4—22no—
228C2×C4—21no—
229C2×C4—21no—
230C2×C4—221no—
231C2×C4—222no—
232C2×C4—221no—
233C2×C4—881no—
234C2×C4—882no—
235C2×C4#434112yes—
236C2×C4#434112yes—
237C2×C4C2×C22⋊D1112yes—
238C2×C4C2×C22⋊D1111yescharacteristic
239C2×C4C23×D1111yescharacteristic
240C8—221no—
241C8—221no—
242C8—222no—
243C22—21no—
244C22—21no—
245C22—22no—
246C22—22no—
247C22—22no—
248C22—42no—
249C22—42no—
250C22—42no—
251C22—84no—
252C22#6698812yes—
253C22C22×C22⋊D1111yescharacteristic
254C4—22no—
255C4—41no—
256C4—41no—
257C4—442no—
258C4—441no—
259C4—441no—
260C4#6698812yes—
261C4C2×#434111yescharacteristic
262C4C2×#434111yescharacteristic
263C2—22no—
264C2—42no—
265C2—82no—
266C2C2×#6698811yescharacteristic
267C2#1062336611yescharacteristic
268C2#1062336711yescharacteristic
subgroupG/H
centerC22C22×C22⋊D11
commutator, cosocleC2×C4×C11C24
FrattiniC2×C4C23×D11
Fitting, prime radicalC11×#535C2
socleC22×C11C22×D4
hypercenter#535D11
hypocenterC11#3096
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×#41 ◁ #535

Complements

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

NH ≅ G/Ntype
2. #10623358C2semidirect
3. #10622847C2semidirect
4. #10622828C2semidirect
5. C2×#66896C2semidirect
6. #10622648C2semidirect
7. #10622648C2semidirect
8. #10622647C2semidirect
9. #10622646C2semidirect
10. #10622611C2semidirect
11. #10622608C2semidirect
24. #66979C22semidirect
26. C2×C4⋊Dic11C22semidirect
33. C22⋊(C11⋊C8)C22semidirect
34. C22⋊(C11⋊C8)C22semidirect
35. #66872C22semidirect
36. #66872C22semidirect
37. #66872C22semidirect
38. #66871C22semidirect
39. #66871C22semidirect
40. #66871C22semidirect
211. C11#3096semidirect

Maximal subgroups

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

subgroupindex
C11×#5352
#106233582
#106228472
#106228282
C2×#668962
#106226482
#106226472
#106226462
#106226112
#106226082
#309611