Finite Group Databasebeta

← #13079795

Subgroups — #13079795

Order 1408.

332 conjugacy classes of subgroups; only the 121 normal subgroups are shown.

normal subgroups only

This group has 332 conjugacy classes of subgroups — too many to draw. Only its 121 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×#533C211yesmaximal, characteristic, complemented
2#10623010C211yesmaximal, characteristic
3#10622707C211yesmaximal, characteristic, complemented
4#10622704C211yesmaximal, characteristic, complemented
5#10622700C211yesmaximal, characteristic, complemented
6#10622697C211yesmaximal, characteristic, complemented
7#10622681C212yesmaximal, complemented
8#10622677C212yesmaximal, complemented
9#10622616C212yesmaximal
10#10622609C212yesmaximal, complemented
11#10622538C211yesmaximal, characteristic, complemented
12C11×C4⋊Q8C2211yescharacteristic
13C11×C4⋊Q8C2211yescharacteristic
14C11×#125C2212yes—
15C11×C22⋊Q8—21no—
16C11×C22⋊Q8—21no—
17C4×Q8×C11—21no—
18C4×Q8×C11—21no—
19C11×#117C2212yes—
20C2×C42×C11C2211yescharacteristic
21#66983C2211yescharacteristic
22#66982—21no—
23C4×C22⋊D11—21no—
24#66977C2211yescharacteristic
25#66929—21no—
26#66928C2211yescharacteristic
27C4×D44C2211yescharacteristic
28#66925—21no—
29#66923C2211yescharacteristic
30C4×Dic22C2211yescharacteristic
31C22⋊(C11⋊C8)C2212yes—
32#66874C2212yes—
33#66874C2212yes—
34#66873C2212yes—
35#66873C2212yes—
36#66872C2212yes—
37#66872C2212yes—
38#66871C2212yes—
39#66871C2212yes—
40C4⋊(C11⋊C8)C2211yescharacteristic
41C4⋊(C11⋊C8)C2211yescharacteristic
42C4×C11⋊C8C2212yes—
43C2×Q8×C11—21no—
44C2×Q8×C11—21no—
45C22×C4×C11D411yescharacteristic
46C22×C4×C11D411yescharacteristic
47C22×C4×C11C2311yescharacteristic
48C2×C22⋊D11—21no—
49C2×D44C2311yescharacteristic
50C2×C4×D11—21no—
51C2×Dic22C2311yescharacteristic
52C11×C4⋊C4—22no—
53C11×C4⋊C4—22no—
54C11×C4⋊C4—21no—
55C11×C4⋊C4—21no—
56C11×C4⋊C4C2312yes—
57C11×C4⋊C4C2312yes—
58C11×C22⋊C4—22no—
59C42×C11—22no—
60C42×C11D411yescharacteristic
61C42×C11D411yescharacteristic
62C42×C11C2311yescharacteristic
63C42×C11C2311yescharacteristic
64C22⋊Dic11—21no—
65(C2×D11)⋊C4—21no—
66(C2×D11)⋊C4—21no—
67(C2×D11)⋊C4—21no—
68(C2×D11)⋊C4—21no—
69C4⋊Dic11C2311yescharacteristic
70C4⋊Dic11C2311yescharacteristic
71Dic11⋊C4—21no—
72Dic11⋊C4—21no—
73Dic11⋊C4—21no—
74Dic11⋊C4—21no—
75C4×Dic11—21no—
76C2×C11⋊C8C2312yes—
77C2×C11⋊C8C2312yes—
78#3233—111nomaximal, Sylow
79C23×C11C2×D411yescharacteristic
80C22×D11—21no—
81Q8×C11—42no—
82Q8×C11—42no—
83C2×C4×C11—22no—
84C2×C4×C11—21no—
85C2×C4×C11—21no—
86C2×C4×C11—22no—
87C2×C4×C11—22no—
88C2×C4×C11—41no—
89C2×C4×C11C2×D411yescharacteristic
90C2×C4×C11C2×D411yescharacteristic
91C2×C4×C11C2×D411yescharacteristic
92C2×C4×C11C2×D411yescharacteristic
93C2×C4×C11C2×D411yescharacteristic
94C2×C4×C11C2411yescharacteristic
95C22⋊D11—42no—
96C2×Dic11—21no—
97C2×Dic11—21no—
98C2×Dic11—21no—
99D44—21no—
100D44—21no—
101C4×D11—42no—
102Dic22—21no—
103Dic22—21no—
104C11⋊C8—22no—
105C11⋊C8—22no—
106#533D1111yescharacteristic, complemented
107#529—111no—
108#499—112no—
109#488—112no—
110#485—112no—
111#482—112no—
112#477—111no—
113#476—111no—
114#475—111no—
115#474—111no—
116#431—111no—
117C22×C11—21no—
118C22×C11—21no—
119C22×C11—21no—
120C22×C11C22×D411yescharacteristic
121C2×D11—41no—
122C2×D11—41no—
123C2×D11—41no—
124C4×C11—21no—
125C4×C11—21no—
126C4×C11—21no—
127C4×C11—21no—
128C4×C11—42no—
129C4×C11—42no—
130C4×C11#13512yes—
131C4×C112−1+411yescharacteristic
132C4×C112−1+411yescharacteristic
133Dic11—41no—
134Dic11—41no—
135Dic11—41no—
136C4⋊Q8C2×D1111yescharacteristic
137C4⋊Q8C2×D1111yescharacteristic
138#126—221no—
139#125—111no—
140#125C2×D1112yes—
141#124—111no—
142#123—221no—
143C22⋊Q8—21no—
144C22⋊Q8—21no—
145C22⋊Q8—111no—
146#121—111no—
147C4×Q8—21no—
148C4×Q8—21no—
149C4×Q8—111no—
150C4×D4—111no—
151C4×D4—221no—
152#117—221no—
153#117C2×D1112yes—
154C2×C42C2×D1111yescharacteristic
155#107—112no—
156#107—112no—
157#106—112no—
158#106—112no—
159C4⋊C8—111no—
160C4⋊C8—111no—
161#103—112no—
162#103—112no—
163#102—112no—
164#102—112no—
165C22⋊C8—112no—
166C4×C8—112no—
167C2×C11—41no—
168C2×C11#53611yescharacteristic
169C2×C11C2×#13511yescharacteristic
170C2×C11#57511yescharacteristic
171D11—81no—
172C2×Q8—21no—
173C2×Q8—21no—
174C2×Q8—111no—
175C2×D4—111no—
176C2×D4—221no—
177C22×C4—221no—
178C22×C4C22⋊D1111yescharacteristic
179C22×C4C22⋊D1111yescharacteristic
180C22×C4C22×D1111yescharacteristic
181C2×C8—112no—
182C2×C8—112no—
183C4⋊C4—22no—
184C4⋊C4—22no—
185C4⋊C4—21no—
186C4⋊C4—21no—
187C4⋊C4—111no—
188C4⋊C4—111no—
189C4⋊C4—221no—
190C4⋊C4—221no—
191C4⋊C4—221no—
192C4⋊C4—221no—
193C4⋊C4C22×D1112yes—
194C4⋊C4C22×D1112yes—
195C22⋊C4—22no—
196C22⋊C4—221no—
197C22⋊C4—221no—
198C22⋊C4—221no—
199C22⋊C4—221no—
200C22⋊C4—221no—
201C42—22no—
202C42—221no—
203C42C22⋊D1111yescharacteristic
204C42C22⋊D1111yescharacteristic
205C42C22×D1111yescharacteristic
206C42C22×D1111yescharacteristic
207C11#323311yescharacteristic, complemented, Sylow
208C23—221no—
209C23C2×C22⋊D1111yescharacteristic
210Q8—42no—
211Q8—42no—
212Q8—221no—
213Q8—221no—
214D4—221no—
215D4—221no—
216D4—442no—
217C2×C4—22no—
218C2×C4—21no—
219C2×C4—21no—
220C2×C4—22no—
221C2×C4—22no—
222C2×C4—41no—
223C2×C4—221no—
224C2×C4—221no—
225C2×C4—221no—
226C2×C4—442no—
227C2×C4C2×C22⋊D1111yescharacteristic
228C2×C4C2×C22⋊D1111yescharacteristic
229C2×C4C2×C22⋊D1111yescharacteristic
230C2×C4C2×C22⋊D1111yescharacteristic
231C2×C4C2×C22⋊D1111yescharacteristic
232C2×C4C23×D1111yescharacteristic
233C8—222no—
234C8—222no—
235C22—21no—
236C22—21no—
237C22—21no—
238C22—441no—
239C22—441no—
240C22—441no—
241C22C22×C22⋊D1111yescharacteristic
242C4—21no—
243C4—21no—
244C4—21no—
245C4—21no—
246C4—42no—
247C4—42no—
248C4—441no—
249C4—441no—
250C4—441no—
251C4#6700312yes—
252C4#6704011yescharacteristic
253C4#6704011yescharacteristic
254C2—41no—
255C2—881no—
256C2#1062334711yescharacteristic
257C2C2×#6700311yescharacteristic
258C2#1062335311yescharacteristic
subgroupG/H
centerC22C22×C22⋊D11
commutator, cosocleC2×C4×C11C24
FrattiniC2×C4C23×D11
FittingC11×#533C2
socleC22×C11C22×D4
prime radical#66983C22
hypercenter#533D11
hypocenterC11#3233
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #533

Complements

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

NH ≅ G/Ntype
1. C11×#533C2semidirect
3. #10622707C2semidirect
4. #10622704C2semidirect
5. #10622700C2semidirect
6. #10622697C2semidirect
7. #10622681C2semidirect
8. #10622677C2semidirect
10. #10622609C2semidirect
11. #10622538C2semidirect
106. #533D11semidirect
207. C11#3233semidirect

Maximal subgroups

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

subgroupindex
C11×#5332
#106230102
#106227072
#106227042
#106227002
#106226972
#106226812
#106226772
#106226162
#106226092
#106225382
#323311