Finite Group Databasebeta

← #13078309

Subgroups — #13078309

Order 1408.

472 conjugacy classes of subgroups; only the 141 normal subgroups are shown.

normal subgroups only

This group has 472 conjugacy classes of subgroups — too many to draw. Only its 141 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×#537C211yesmaximal, characteristic
2#10623356C211yesmaximal, characteristic, complemented
3C2×#67004C211yesmaximal, characteristic, complemented
4C2×#67001C211yesmaximal, characteristic, complemented
5#10622846C211yesmaximal, characteristic, complemented
6#10622665C212yesmaximal, complemented
7#10622664C212yesmaximal, complemented
8#10622655C212yesmaximal, complemented
9#10622654C212yesmaximal, complemented
10C2×#66874C211yesmaximal, characteristic, complemented
11#10622577C211yesmaximal, characteristic, complemented
12C2×C11×#41C2211yescharacteristic
13C2×C11×#41C2211yescharacteristic
14C22×Dic22C2211yescharacteristic
15C11×C22⋊Q8—21no—
16C11×C22⋊Q8C2212yes—
17C11×#121—21no—
18C11×#121—22no—
19C11×#121C2212yes—
20C2×C11×C4⋊C4C2211yescharacteristic
21#67004—24no—
22#67001—24no—
23#66997—21no—
24C2×#4326C2212yes—
25#66989—21no—
26#66988—22no—
27C2×#4324C2212yes—
28#66979C2211yescharacteristic
29#66977C2212yes—
30#66977C2212yes—
31C2×#4318C2212yes—
32C2×#4318C2211yescharacteristic
33C22×C11⋊C8C2211yescharacteristic
34C22×C11⋊C8C2212yes—
35#66899C2211yescharacteristic
36#66899C2211yescharacteristic
37#66896C2211yescharacteristic
38#66896C2211yescharacteristic
39#66874C2212yes—
40#66874C2212yes—
41#66872C2212yes—
42#66871C2212yes—
43C11×#41—22no—
44C11×#41—22no—
45C11×#41—22no—
46C11×#41—22no—
47C2×Q8×C11D411yescharacteristic
48C2×Q8×C11C2311yescharacteristic
49C2×D4×C11—21no—
50C2×D4×C11—22no—
51C2×D4×C11D412yes—
52C2×D4×C11D411yescharacteristic
53C2×D4×C11C2311yescharacteristic
54C22×C4×C11—21no—
55C22×C4×C11—21no—
56C22×C4×C11C2312yes—
57C22×C4×C11C2311yescharacteristic
58C22×Dic11—21no—
59C2×Dic22—22no—
60C2×Dic22—21no—
61C2×Dic22—22no—
62C2×Dic22C2312yes—
63C11×C4⋊C4—21no—
64C11×C4⋊C4—22no—
65C11×C4⋊C4C2312yes—
66C11×C22⋊C4—22no—
67C11×C22⋊C4—22no—
68C22⋊Dic11—22no—
69C22⋊Dic11—22no—
70C22⋊Dic11—21no—
71#4326—24no—
72#4324—24no—
73C4⋊Dic11C2311yescharacteristic
74C4⋊Dic11C2311yescharacteristic
75Dic11⋊C4—22no—
76Dic11⋊C4—22no—
77C4×Dic11—21no—
78#4318—24no—
79#4318D414yescomplemented
80C2×C11⋊C8—24no—
81C2×C11⋊C8—22no—
82C2×C11⋊C8C2311yescharacteristic
83C2×C11⋊C8C2311yescharacteristic
84C2×C11⋊C8C2312yes—
85#3063—111nomaximal, Sylow
86C23×C11—21no—
87C23×C11C2×D412yes—
88C23×C11C2×D411yescharacteristic
89Q8×C11—22no—
90Q8×C11—21no—
91Q8×C11—21no—
92D4×C11—24no—
93D4×C11—22no—
94D4×C11—21no—
95D4×C11—21no—
96D4×C11—42no—
97D4×C11—82no—
98C2×C4×C11—22no—
99C2×C4×C11—22no—
100C2×C4×C11—22no—
101C2×C4×C11—21no—
102C2×C4×C11—42no—
103C2×C4×C11—81no—
104C2×C4×C11C2×D412yes—
105C2×C4×C11C2×D412yes—
106C2×C4×C11C2×D411yescharacteristic
107C2×C4×C11#4112yes—
108C2×C4×C11C2411yescharacteristic
109C2×Dic11—21no—
110C2×Dic11—21no—
111C2×Dic11—22no—
112C2×Dic11—42no—
113Dic22—22no—
114Dic22—22no—
115Dic22—42no—
116C11⋊C8—21no—
117C11⋊C8—21no—
118C11⋊C8C2×D414yes—
119C2×#137—111no—
120C2×#131—111no—
121#537D1111yescharacteristic
122#536—111no—
123#470—112no—
124#468—112no—
125#467—112no—
126#465—112no—
127#428—111no—
128#416—111no—
129C2×#103—111no—
130C22×C11—21no—
131C22×C11—21no—
132C22×C11—22no—
133C22×C11—22no—
134C22×C11—22no—
135C22×C11—41no—
136C22×C11—41no—
137C22×C11—41no—
138C22×C11#12112yes—
139C22×C11C22×D411yescharacteristic
140C4×C11—22no—
141C4×C11—41no—
142C4×C11—42no—
143C4×C11#12112yes—
144C4×C11C22×D411yescharacteristic
145C4×C11C2×#4111yescharacteristic
146Dic11—42no—
147Dic11—41no—
148Dic11—41no—
149C2×#41C2×D1111yescharacteristic
150C2×#41C2×D1111yescharacteristic
151C22×Q8—111no—
152#137—224no—
153C2×Q16—112no—
154C2×SD16—112no—
155#131—224no—
156C2×M16—111no—
157C2×M16—112no—
158C22×C8—111no—
159C22×C8—112no—
160C4⋊Q8—221no—
161#124—221no—
162#123—222no—
163C22⋊Q8—21no—
164C22⋊Q8—112no—
165C22⋊Q8—112no—
166C22⋊Q8C2×D1112yes—
167#121—21no—
168#121—22no—
169#121C2×D1112yes—
170#117—111no—
171C2×C4⋊C4C2×D1111yescharacteristic
172#107—112no—
173#106—112no—
174#103—111no—
175#103—111no—
176#103—112no—
177#103—112no—
178#102—111no—
179#102—111no—
180C2×C11—22no—
181C2×C11—42no—
182C2×C11—81no—
183C2×C11C2×#12111yescharacteristic
184C2×C11#57711yescharacteristic
185C2×C11#57811yescharacteristic
186#41—22no—
187#41—22no—
188#41—22no—
189#41—22no—
190C2×Q8—112no—
191C2×Q8—221no—
192C2×Q8—222no—
193C2×Q8—222no—
194C2×Q8C22⋊D1111yescharacteristic
195C2×Q8C22×D1111yescharacteristic
196C2×D4—21no—
197C2×D4—22no—
198C2×D4C22⋊D1112yes—
199C2×D4C22⋊D1111yescharacteristic
200C2×D4C22×D1111yescharacteristic
201C22×C4—21no—
202C22×C4—21no—
203C22×C4—221no—
204C22×C4C22×D1112yes—
205C22×C4C22×D1111yescharacteristic
206Q16—224no—
207SD16—224no—
208M16—114no—
209M16—224no—
210C2×C8—112no—
211C2×C8—111no—
212C2×C8—111no—
213C2×C8—224no—
214C2×C8—222no—
215C4⋊C4—21no—
216C4⋊C4—22no—
217C4⋊C4—111no—
218C4⋊C4—111no—
219C4⋊C4—222no—
220C4⋊C4—222no—
221C4⋊C4C22×D1112yes—
222C22⋊C4—22no—
223C22⋊C4—22no—
224C22⋊C4—221no—
225C22⋊C4—222no—
226C22⋊C4—222no—
227C42—221no—
228C11#306311yescharacteristic, complemented, Sylow
229C23—21no—
230C23C2×C22⋊D1112yes—
231C23C2×C22⋊D1111yescharacteristic
232Q8—22no—
233Q8—21no—
234Q8—21no—
235Q8—222no—
236Q8—222no—
237Q8—442no—
238D4—24no—
239D4—22no—
240D4—21no—
241D4—21no—
242D4—42no—
243D4—82no—
244C2×C4—22no—
245C2×C4—22no—
246C2×C4—22no—
247C2×C4—21no—
248C2×C4—42no—
249C2×C4—81no—
250C2×C4—221no—
251C2×C4—221no—
252C2×C4—222no—
253C2×C4—442no—
254C2×C4D4×D1112yes—
255C2×C4#434112yes—
256C2×C4C2×C22⋊D1112yes—
257C2×C4C2×C22⋊D1111yescharacteristic
258C2×C4C23×D1111yescharacteristic
259C8—114no—
260C8—221no—
261C8—221no—
262C22—21no—
263C22—21no—
264C22—22no—
265C22—22no—
266C22—22no—
267C22—41no—
268C22—41no—
269C22—41no—
270C22#6699212yes—
271C22C22×C22⋊D1111yescharacteristic
272C4—22no—
273C4—41no—
274C4—42no—
275C4—442no—
276C4—441no—
277C4—441no—
278C4#6699212yes—
279C4C2×D4×D1111yescharacteristic
280C4C2×#434111yescharacteristic
281C2—22no—
282C2—42no—
283C2—81no—
284C2C2×#6699211yescharacteristic
285C2#1062336711yescharacteristic
286C2#1062336911yescharacteristic
subgroupG/H
centerC22C22×C22⋊D11
commutator, cosocleC2×C4×C11C24
FrattiniC2×C4C23×D11
Fitting, prime radicalC11×#537C2
socleC22×C11C22×D4
hypercenter#537D11
hypocenterC11#3063
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×#41 ◁ #537

Complements

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

NH ≅ G/Ntype
2. #10623356C2semidirect
3. C2×#67004C2semidirect
4. C2×#67001C2semidirect
5. #10622846C2semidirect
6. #10622665C2semidirect
7. #10622664C2semidirect
8. #10622655C2semidirect
9. #10622654C2semidirect
10. C2×#66874C2semidirect
11. #10622577C2semidirect
79. #4318D4semidirect
228. C11#3063semidirect

Maximal subgroups

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

subgroupindex
C11×#5372
#106233562
C2×#670042
C2×#670012
#106228462
#106226652
#106226642
#106226552
#106226542
C2×#668742
#106225772
#306311