Finite Group Databasebeta

← #13079759

Subgroups — #13079759

Order 1408.

360 conjugacy classes of subgroups; only the 123 normal subgroups are shown.

normal subgroups only

This group has 360 conjugacy classes of subgroups — too many to draw. Only its 123 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
1D11×C4⋊Q8C211yesmaximal, characteristic
2#10623109C211yesmaximal, characteristic
3C11×#475C211yesmaximal, characteristic, complemented
4#10622707C211yesmaximal, characteristic, complemented
5#10622633C211yesmaximal, characteristic, complemented
6#10622475C212yesmaximal
7#10622468C212yesmaximal, complemented
8#10622464C211yesmaximal, characteristic, complemented
9#10622446C211yesmaximal, characteristic
10#10622418C212yesmaximal
11#10622405C212yesmaximal, complemented
12C2×Q8×D11—21no—
13C11×C4⋊Q8C2211yescharacteristic
14C4×Q8×C11C2211yescharacteristic
15#66999C2211yescharacteristic
16#66997—21no—
17#66997C2211yescharacteristic
18#66950C2211yescharacteristic
19#66949—21no—
20C4⋊C4×D11—21no—
21C4⋊C4×D11C2212yes—
22#66942—21no—
23#66941—21no—
24#66941C2211yescharacteristic
25#66941C2212yes—
26#66925—21no—
27C42×D11C2211yescharacteristic
28#66922C2211yescharacteristic
29C4×Dic22—21no—
30C4×Dic22C2211yescharacteristic
31C11×#106C2212yes—
32C11×C4⋊C8C2211yescharacteristic
33C11×#103C2212yes—
34#66899C2212yes—
35(C2×D11)⋊C8C2212yes—
36#66881C2212yes—
37#66880C2212yes—
38C8×Dic11C2212yes—
39#66874C2212yes—
40#66872C2212yes—
41#66872C2212yes—
42C4⋊(C11⋊C8)C2211yescharacteristic
43C2×Q8×C11—21no—
44C2×Q8×C11C2311yescharacteristic
45Q8×D11—44no—
46C2×C4×D11—22no—
47C2×C4×D11D411yescharacteristic
48C2×C4×D11D411yescharacteristic
49C2×C4×D11C2311yescharacteristic
50C2×Dic22—21no—
51C2×Dic22—22no—
52C2×Dic22—21no—
53C2×Dic22C2311yescharacteristic
54C2×C8×C11C2312yes—
55C11×C4⋊C4—21no—
56C11×C4⋊C4—21no—
57C11×C4⋊C4C2311yescharacteristic
58C11×C4⋊C4C2312yes—
59C42×C11—21no—
60C42×C11C2311yescharacteristic
61(C2×D11)⋊C4—21no—
62(C2×D11)⋊C4—21no—
63C4⋊Dic11—21no—
64C4⋊Dic11—21no—
65C4⋊Dic11C2311yescharacteristic
66C4⋊Dic11C2312yes—
67Dic11⋊C4—21no—
68Dic11⋊C4—21no—
69Dic11⋊C4—21no—
70Dic11⋊C4—21no—
71Dic11⋊C4—22no—
72Dic11⋊C4—22no—
73Dic11⋊C4—21no—
74C4×Dic11—21no—
75C4×Dic11D411yescharacteristic
76C4×Dic11D411yescharacteristic
77C4×Dic11C2311yescharacteristic
78C2×C11⋊C8C2312yes—
79#3229—111nomaximal, Sylow
80C22×D11C2×D411yescharacteristic
81Q8×C11—21no—
82Q8×C11—21no—
83Q8×C11—42no—
84C2×C4×C11—21no—
85C2×C4×C11—22no—
86C2×C4×C11—21no—
87C2×C4×C11C2×D411yescharacteristic
88C2×C4×C11C2×D411yescharacteristic
89C2×C4×C11C2411yescharacteristic
90C2×Dic11—21no—
91C2×Dic11—21no—
92C2×Dic11—22no—
93C2×Dic11C2×D411yescharacteristic
94C2×Dic11C2×D411yescharacteristic
95C2×Dic11C2×D411yescharacteristic
96C4×D11—21no—
97C4×D11—21no—
98C4×D11—22no—
99C4×D11—44no—
100C4×D11SD1614yes—
101Dic22—21no—
102Dic22—21no—
103Dic22—42no—
104Dic22—44no—
105Dic22—42no—
106C8×C11—22no—
107C11⋊C8—22no—
108#533—111no—
109C2×C4⋊Q8—111no—
110#498—112no—
111#487—112no—
112#483—112no—
113#483—112no—
114#475—111no—
115#475—111no—
116#475—111no—
117#475D1111yescharacteristic, complemented
118#431—111no—
119C22×C11C22×D411yescharacteristic
120C2×D11—21no—
121C2×D11—21no—
122C2×D11C2×SD1612yes—
123C4×C11—21no—
124C4×C11—41no—
125C4×C11—42no—
126C4×C11—41no—
127C4×C11C2×SD1612yes—
128C4×C112−1+411yescharacteristic
129C4×C112−1+411yescharacteristic
130Dic11—21no—
131Dic11—41no—
132Dic11—42no—
133Dic11—41no—
134Dic11C2×SD1612yes—
135Dic11#13712yes—
136C22×Q8—221no—
137C4⋊Q8—112no—
138C4⋊Q8—111no—
139C4⋊Q8—111no—
140C4⋊Q8—111no—
141C4⋊Q8—221no—
142C4⋊Q8—221no—
143C4⋊Q8C2×D1111yescharacteristic
144#125—221no—
145C22⋊Q8—111no—
146C22⋊Q8—111no—
147C22⋊Q8—221no—
148C4×Q8—111no—
149C4×Q8—221no—
150C4×Q8C2×D1111yescharacteristic
151#117—221no—
152C2×C4⋊C4—112no—
153C2×C4⋊C4—221no—
154C2×C42—111no—
155#106—112no—
156#106—112no—
157#106—112no—
158#106C2×D1112yes—
159C4⋊C8—111no—
160C4⋊C8C2×D1111yescharacteristic
161#103—112no—
162#103—112no—
163#103—112no—
164#103C2×D1112yes—
165C22⋊C8—112no—
166C4×C8—112no—
167C2×C11#53611yescharacteristic
168C2×C11C22×SD1611yescharacteristic
169C2×C11C2×#13711yescharacteristic
170D11—22no—
171C2×Q8—21no—
172C2×Q8—111no—
173C2×Q8—221no—
174C2×Q8—222no—
175C2×Q8—221no—
176C2×Q8—444no—
177C2×Q8C22×D1111yescharacteristic
178C22×C4—111no—
179C22×C4—111no—
180C22×C4—111no—
181C22×C4—222no—
182C2×C8—112no—
183C2×C8C22×D1112yes—
184C4⋊C4—21no—
185C4⋊C4—21no—
186C4⋊C4—112no—
187C4⋊C4—111no—
188C4⋊C4—222no—
189C4⋊C4—222no—
190C4⋊C4—221no—
191C4⋊C4—221no—
192C4⋊C4—221no—
193C4⋊C4—221no—
194C4⋊C4—221no—
195C4⋊C4—221no—
196C4⋊C4—221no—
197C4⋊C4C22×D1112yes—
198C4⋊C4C22×D1111yescharacteristic
199C22⋊C4—221no—
200C22⋊C4—221no—
201C42—21no—
202C42—111no—
203C42—111no—
204C42—111no—
205C42—221no—
206C42C22×D1111yescharacteristic
207C11#322911yescharacteristic, complemented, Sylow
208C23—111no—
209Q8—21no—
210Q8—21no—
211Q8—42no—
212Q8—221no—
213Q8—221no—
214Q8—444no—
215Q8—442no—
216Q8—442no—
217C2×C4—21no—
218C2×C4—21no—
219C2×C4—22no—
220C2×C4—111no—
221C2×C4—111no—
222C2×C4—114no—
223C2×C4—111no—
224C2×C4—222no—
225C2×C4—221no—
226C2×C4—221no—
227C2×C4—221no—
228C2×C4—221no—
229C2×C4—222no—
230C2×C4—444no—
231C2×C4D4×D1111yescharacteristic
232C2×C4D4×D1111yescharacteristic
233C2×C4C23×D1111yescharacteristic
234C8—22no—
235C8—222no—
236C22—112no—
237C22—221no—
238C22—221no—
239C22C2×D4×D1111yescharacteristic
240C4—21no—
241C4—42no—
242C4—41no—
243C4—41no—
244C4—112no—
245C4—112no—
246C4—221no—
247C4—442no—
248C4—441no—
249C4—441no—
250C4SD16×D1112yes—
251C4#6704011yescharacteristic
252C4#6704311yescharacteristic
253C2—222no—
254C2#1062315911yescharacteristic
255C2C2×SD16×D1111yescharacteristic
256C2D11×#13711yescharacteristic
subgroupG/H
centerC22C2×D4×D11
commutator, cosocleC2×C4×C11C24
FrattiniC2×C4C23×D11
FittingC11×#475C2
socleC22×C11C22×D4
prime radicalC22×D11C2×D4
hypercenter#475D11
hypocenterC11#3229
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C42 ◁ #475

Complements

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

NH ≅ G/Ntype
3. C11×#475C2semidirect
4. #10622707C2semidirect
5. #10622633C2semidirect
7. #10622468C2semidirect
8. #10622464C2semidirect
11. #10622405C2semidirect
117. #475D11semidirect
207. C11#3229semidirect

Maximal subgroups

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

subgroupindex
D11×C4⋊Q82
#106231092
C11×#4752
#106227072
#106226332
#106224752
#106224682
#106224642
#106224462
#106224182
#106224052
#322911