Finite Group Databasebeta

← #13078308

Subgroups — #13078308

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
1C2×#66962C211yesmaximal, characteristic, complemented
2C2×#66960C211yesmaximal, characteristic, complemented
3#10623057C211yesmaximal, characteristic, complemented
4#10623041C211yesmaximal, characteristic
5C11×#428C211yesmaximal, characteristic, complemented
6#10622615C211yesmaximal, characteristic, complemented
7C2×#66874C211yesmaximal, characteristic, complemented
8#10622500C212yesmaximal, complemented
9#10622499C212yesmaximal, complemented
10#10622481C212yesmaximal, complemented
11#10622477C212yesmaximal, complemented
12C2×#4339C2211yescharacteristic
13C2×#4339C2211yescharacteristic
14C22×Dic22C2211yescharacteristic
15C2×C11×M16C2211yescharacteristic
16C11×#117C2211yescharacteristic
17C2×C11×C4⋊C4C2211yescharacteristic
18#66983—22no—
19C22×C11⋊C8C2211yescharacteristic
20#66962—24no—
21#66960—24no—
22C2×Dic44C2212yes—
23C2×#4314C2212yes—
24C2×#4313C2212yes—
25C2×C8×D11C2212yes—
26#66950—21no—
27#66950C2212yes—
28#66950C2212yes—
29#66950C2212yes—
30#66948—21no—
31#66948C2212yes—
32#66939—22no—
33#66928—21no—
34#66922—21no—
35C11×#107C2212yes—
36C11×#106C2212yes—
37#66874C2212yes—
38#66874C2211yescharacteristic
39#66874C2212yes—
40#66874C2211yescharacteristic
41#66873C2211yescharacteristic
42#66873C2211yescharacteristic
43C22×C4×C11—21no—
44C22×C4×C11C2311yescharacteristic
45C2×C22⋊D11—21no—
46C2×C22⋊D11D412yes—
47C22×Dic11—21no—
48#4339—22no—
49#4339—22no—
50#4339—22no—
51#4339—22no—
52C2×D44—22no—
53C2×D44D411yescharacteristic
54C2×D44C2311yescharacteristic
55C2×C4×D11—21no—
56C2×C4×D11C2312yes—
57C2×Dic22—22no—
58C2×Dic22—21no—
59C2×Dic22—22no—
60C2×Dic22D411yescharacteristic
61C2×Dic22C2312yes—
62C2×Dic22C2311yescharacteristic
63C11×M16D414yescomplemented
64C2×C8×C11C2312yes—
65C11×C4⋊C4—21no—
66C11×C4⋊C4C2311yescharacteristic
67C11×C4⋊C4C2311yescharacteristic
68C11×C4⋊C4C2312yes—
69C11×C22⋊C4—21no—
70C42×C11—21no—
71(C2×D11)⋊C4—22no—
72(C2×D11)⋊C4—22no—
73(C2×D11)⋊C4—22no—
74(C2×D11)⋊C4—22no—
75C4⋊Dic11—22no—
76C4⋊Dic11—22no—
77C4⋊Dic11—22no—
78C2×C11⋊C8—22no—
79C2×C11⋊C8C2311yescharacteristic
80C2×C11⋊C8C2311yescharacteristic
81Dic44—24no—
82#4314—24no—
83#4313—24no—
84C8×D11—24no—
85#3063—111nomaximal, Sylow
86C23×C11C2×D411yescharacteristic
87C22×D11—21no—
88C22×D11C2×D412yes—
89C2×C4×C11—21no—
90C2×C4×C11—21no—
91C2×C4×C11—22no—
92C2×C4×C11—81no—
93C2×C4×C11C2×D412yes—
94C2×C4×C11C2×D411yescharacteristic
95C2×C4×C11#4112yes—
96C2×C4×C11C2411yescharacteristic
97C22⋊D11—24no—
98C22⋊D11—42no—
99C2×Dic11—22no—
100C2×Dic11—21no—
101C2×Dic11—42no—
102C2×Dic11C2×D412yes—
103D44—22no—
104D44—21no—
105D44—21no—
106D44—82no—
107C4×D11—22no—
108C4×D11—22no—
109C4×D11—42no—
110Dic22—22no—
111Dic22—22no—
112Dic22—21no—
113Dic22—22no—
114Dic22—21no—
115Dic22—42no—
116C8×C11C2×D414yes—
117C11⋊C8—21no—
118C11⋊C8—21no—
119C2×#137—111no—
120C2×#131—111no—
121#537—111no—
122#536—111no—
123#470—112no—
124#468—112no—
125#467—112no—
126#465—112no—
127#428D1111yescharacteristic, complemented
128#416—111no—
129C2×#103—111no—
130C22×C11—21no—
131C22×C11—21no—
132C22×C11#12112yes—
133C22×C11C22×D411yescharacteristic
134C2×D11—22no—
135C2×D11—22no—
136C2×D11—22no—
137C2×D11—41no—
138C2×D11—41no—
139C2×D11—41no—
140C4×C11—41no—
141C4×C11—42no—
142C4×C11—41no—
143C4×C11#12112yes—
144C4×C11C22×D411yescharacteristic
145C4×C11C2×#4111yescharacteristic
146Dic11—22no—
147Dic11—42no—
148Dic11—41no—
149C2×#41—111no—
150C2×#41—111no—
151C22×Q8—111no—
152#137—224no—
153C2×Q16—112no—
154C2×SD16—112no—
155#131—224no—
156C2×M16—112no—
157C2×M16C2×D1111yescharacteristic
158C22×C8—111no—
159C22×C8—112no—
160C4⋊Q8—221no—
161#124—221no—
162#123—222no—
163C22⋊Q8—112no—
164C22⋊Q8—112no—
165C22⋊Q8—112no—
166C22⋊Q8—221no—
167#121—112no—
168#121—221no—
169#121—222no—
170#117C2×D1111yescharacteristic
171C2×C4⋊C4C2×D1111yescharacteristic
172#107C2×D1112yes—
173#106C2×D1112yes—
174#103—112no—
175#103—112no—
176#103—111no—
177#103—111no—
178#102—111no—
179#102—111no—
180C2×C11—22no—
181C2×C11C2×#12111yescharacteristic
182C2×C11#57711yescharacteristic
183C2×C11#57811yescharacteristic
184D11—42no—
185D11—81no—
186#41—222no—
187#41—222no—
188#41—222no—
189#41—222no—
190C2×Q8—111no—
191C2×Q8—112no—
192C2×Q8—111no—
193C2×Q8—221no—
194C2×Q8—222no—
195C2×Q8—222no—
196C2×D4—112no—
197C2×D4—111no—
198C2×D4—111no—
199C2×D4—222no—
200C2×D4—221no—
201C22×C4—21no—
202C22×C4—112no—
203C22×C4—221no—
204C22×C4—221no—
205C22×C4C22×D1111yescharacteristic
206Q16—224no—
207SD16—224no—
208M16—224no—
209M16D4414yescomplemented
210C2×C8—111no—
211C2×C8—111no—
212C2×C8—222no—
213C2×C8—224no—
214C2×C8C22×D1112yes—
215C4⋊C4—21no—
216C4⋊C4—222no—
217C4⋊C4—222no—
218C4⋊C4—222no—
219C4⋊C4C22×D1111yescharacteristic
220C4⋊C4C22×D1111yescharacteristic
221C4⋊C4C22×D1112yes—
222C22⋊C4—21no—
223C22⋊C4—222no—
224C22⋊C4—222no—
225C22⋊C4—222no—
226C22⋊C4—222no—
227C42—21no—
228C11#306311yescharacteristic, complemented, Sylow
229C23—112no—
230C23—221no—
231C23D4×D1111yescharacteristic
232Q8—222no—
233Q8—222no—
234Q8—221no—
235Q8—222no—
236Q8—221no—
237Q8—442no—
238D4—224no—
239D4—222no—
240D4—221no—
241D4—221no—
242D4—442no—
243D4—882no—
244C2×C4—21no—
245C2×C4—21no—
246C2×C4—22no—
247C2×C4—81no—
248C2×C4—112no—
249C2×C4—222no—
250C2×C4—222no—
251C2×C4—221no—
252C2×C4—222no—
253C2×C4—442no—
254C2×C4—442no—
255C2×C4C2×D4412yes—
256C2×C4D4×D1111yescharacteristic
257C2×C4#434312yes—
258C2×C4C23×D1111yescharacteristic
259C8—221no—
260C8—221no—
261C8C2×D4414yes—
262C22—21no—
263C22—21no—
264C22—222no—
265C22—222no—
266C22—222no—
267C22—441no—
268C22—441no—
269C22—441no—
270C22#6694812yes—
271C22C2×D4×D1111yescharacteristic
272C4—42no—
273C4—41no—
274C4—41no—
275C4—222no—
276C4—441no—
277C4—442no—
278C4#6694812yes—
279C4C22×D4411yescharacteristic
280C4C2×#434311yescharacteristic
281C2—22no—
282C2—442no—
283C2—881no—
284C2C2×#6694811yescharacteristic
285C2#1062330611yescharacteristic
286C2#1062331011yescharacteristic
subgroupG/H
centerC22C2×D4×D11
commutator, cosocleC2×C4×C11C24
FrattiniC2×C4C23×D11
FittingC11×#428C2
socleC22×C11C22×D4
prime radical#10623041C2
hypercenter#428D11
hypocenterC11#3063
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C22×C4 ◁ #428

Complements

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

NH ≅ G/Ntype
1. C2×#66962C2semidirect
2. C2×#66960C2semidirect
3. #10623057C2semidirect
5. C11×#428C2semidirect
6. #10622615C2semidirect
7. C2×#66874C2semidirect
8. #10622500C2semidirect
9. #10622499C2semidirect
10. #10622481C2semidirect
11. #10622477C2semidirect
63. C11×M16D4semidirect
127. #428D11semidirect
209. M16D44semidirect
228. C11#3063semidirect

Maximal subgroups

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

subgroupindex
C2×#669622
C2×#669602
#106230572
#106230412
C11×#4282
#106226152
C2×#668742
#106225002
#106224992
#106224812
#106224772
#306311