Finite Group Databasebeta

← #13079947

Subgroups — #13079947

Order 1408.

354 conjugacy classes of subgroups; only the 125 normal subgroups are shown.

normal subgroups only

This group has 354 conjugacy classes of subgroups — too many to draw. Only its 125 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#10622703C211yesmaximal, characteristic, complemented
5#10622700C211yesmaximal, characteristic, complemented
6#10622696C211yesmaximal, characteristic, complemented
7#10622664C212yesmaximal, complemented
8#10622661C212yesmaximal
9#10622641C212yesmaximal, complemented
10#10622635C212yesmaximal, complemented
11C2×C4⋊(C11⋊C8)C211yesmaximal, characteristic, complemented
12C11×C4⋊Q8C2211yescharacteristic
13C11×C4⋊Q8C2211yescharacteristic
14C11×#125—21no—
15C11×C22⋊Q8—21no—
16C11×C22⋊Q8C2212yes—
17C4×Q8×C11—21no—
18C4×Q8×C11C2212yes—
19C11×#117—21no—
20C2×C42×C11C2211yescharacteristic
21C2×#4326C2212yes—
22C2×#4325C2212yes—
23#66983C2211yescharacteristic
24#66982—21no—
25C4×C22⋊D11—21no—
26#66977C2211yescharacteristic
27C22×C11⋊C8C2212yes—
28#66929—21no—
29#66928C2211yescharacteristic
30C4×D44C2211yescharacteristic
31#66925—21no—
32#66923C2211yescharacteristic
33C4×Dic22C2211yescharacteristic
34#66899C2212yes—
35#66899C2212yes—
36#66874C2212yes—
37#66873C2212yes—
38#66872C2212yes—
39#66871C2212yes—
40C4⋊(C11⋊C8)C2212yes—
41C4⋊(C11⋊C8)C2211yescharacteristic
42C4⋊(C11⋊C8)C2211yescharacteristic
43C2×Q8×C11—21no—
44C2×Q8×C11C2312yes—
45C22×C4×C11D411yescharacteristic
46C22×C4×C11D411yescharacteristic
47C22×C4×C11C2311yescharacteristic
48C2×C22⋊D11—21no—
49C2×D44C2311yescharacteristic
50C2×C4×D11—21no—
51C2×Dic22C2311yescharacteristic
52C11×C4⋊C4—21no—
53C11×C4⋊C4—21no—
54C11×C4⋊C4—21no—
55C11×C4⋊C4—22no—
56C11×C4⋊C4—22no—
57C11×C4⋊C4C2312yes—
58C11×C22⋊C4—22no—
59C42×C11—22no—
60C42×C11D411yescharacteristic
61C42×C11D411yescharacteristic
62C42×C11C2311yescharacteristic
63C42×C11C2311yescharacteristic
64C22⋊Dic11—21no—
65#4326—42no—
66#4325—42no—
67(C2×D11)⋊C4—21no—
68(C2×D11)⋊C4—21no—
69(C2×D11)⋊C4—21no—
70(C2×D11)⋊C4—21no—
71C4⋊Dic11C2311yescharacteristic
72C4⋊Dic11C2311yescharacteristic
73Dic11⋊C4—21no—
74Dic11⋊C4—21no—
75Dic11⋊C4—21no—
76Dic11⋊C4—21no—
77C4×Dic11—21no—
78C2×C11⋊C8—42no—
79C2×C11⋊C8C2312yes—
80C2×C11⋊C8C2312yes—
81#3248—111nomaximal, Sylow
82C23×C11C2×D411yescharacteristic
83C22×D11—21no—
84Q8×C11—22no—
85Q8×C11—22no—
86Q8×C11—42no—
87C2×C4×C11—22no—
88C2×C4×C11—22no—
89C2×C4×C11—21no—
90C2×C4×C11—21no—
91C2×C4×C11—22no—
92C2×C4×C11—22no—
93C2×C4×C11C2×D411yescharacteristic
94C2×C4×C11C2×D411yescharacteristic
95C2×C4×C11C2×D411yescharacteristic
96C2×C4×C11C2×D411yescharacteristic
97C2×C4×C11C2×D411yescharacteristic
98C2×C4×C11C2411yescharacteristic
99C22⋊D11—42no—
100C2×Dic11—21no—
101C2×Dic11—21no—
102C2×Dic11—21no—
103D44—21no—
104D44—21no—
105C4×D11—42no—
106Dic22—21no—
107Dic22—21no—
108C11⋊C8—22no—
109C11⋊C8—22no—
110#533D1111yescharacteristic, complemented
111#529—111no—
112#479—112no—
113#475—111no—
114#474—111no—
115#467—112no—
116#465—112no—
117#464—112no—
118#462—111no—
119#461—111no—
120C2×C4⋊C8—111no—
121C22×C11—21no—
122C22×C11—21no—
123C22×C11#13712yes—
124C22×C11C22×D411yescharacteristic
125C2×D11—41no—
126C2×D11—41no—
127C2×D11—41no—
128C4×C11—21no—
129C4×C11—21no—
130C4×C11—21no—
131C4×C11—21no—
132C4×C11—42no—
133C4×C11—42no—
134C4×C11#13512yes—
135C4×C11H(5,𝔽2)11yescharacteristic
136C4×C112−1+411yescharacteristic
137Dic11—41no—
138Dic11—41no—
139Dic11—41no—
140C2×Q16—112no—
141C2×SD16—112no—
142C22×C8—112no—
143C4⋊Q8C2×D1111yescharacteristic
144C4⋊Q8C2×D1111yescharacteristic
145#126—221no—
146#125—21no—
147#125—111no—
148#124—111no—
149#123—221no—
150C22⋊Q8—21no—
151C22⋊Q8—111no—
152C22⋊Q8C2×D1112yes—
153#121—111no—
154C4×Q8—21no—
155C4×Q8—111no—
156C4×Q8C2×D1112yes—
157C4×D4—111no—
158C4×D4—221no—
159#117—21no—
160#117—221no—
161C2×C42C2×D1111yescharacteristic
162#107—112no—
163#106—112no—
164C4⋊C8—111no—
165C4⋊C8—111no—
166C4⋊C8—112no—
167#103—112no—
168#103—112no—
169#103—112no—
170#102—112no—
171C2×C11—22no—
172C2×C11#53711yescharacteristic
173C2×C11C2×#13511yescharacteristic
174C2×C11C2×#13711yescharacteristic
175D11—81no—
176C2×Q8—21no—
177C2×Q8—111no—
178C2×Q8C22×D1112yes—
179C2×D4—111no—
180C2×D4—221no—
181C22×C4—221no—
182C22×C4C22⋊D1111yescharacteristic
183C22×C4C22⋊D1111yescharacteristic
184C22×C4C22×D1111yescharacteristic
185Q16—442no—
186SD16—442no—
187C2×C8—112no—
188C2×C8—112no—
189C2×C8—442no—
190C4⋊C4—21no—
191C4⋊C4—21no—
192C4⋊C4—21no—
193C4⋊C4—22no—
194C4⋊C4—22no—
195C4⋊C4—111no—
196C4⋊C4—111no—
197C4⋊C4—221no—
198C4⋊C4—221no—
199C4⋊C4—221no—
200C4⋊C4—221no—
201C4⋊C4C22×D1112yes—
202C22⋊C4—22no—
203C22⋊C4—221no—
204C22⋊C4—221no—
205C22⋊C4—221no—
206C22⋊C4—221no—
207C22⋊C4—221no—
208C42—22no—
209C42—221no—
210C42C22⋊D1111yescharacteristic
211C42C22⋊D1111yescharacteristic
212C42C22×D1111yescharacteristic
213C42C22×D1111yescharacteristic
214C11#324811yescharacteristic, complemented, Sylow
215C23—221no—
216C23C2×C22⋊D1111yescharacteristic
217Q8—22no—
218Q8—22no—
219Q8—42no—
220Q8—221no—
221Q8—221no—
222D4—221no—
223D4—221no—
224D4—442no—
225C2×C4—22no—
226C2×C4—22no—
227C2×C4—21no—
228C2×C4—21no—
229C2×C4—22no—
230C2×C4—22no—
231C2×C4—221no—
232C2×C4—221no—
233C2×C4—221no—
234C2×C4—442no—
235C2×C4C2×C22⋊D1111yescharacteristic
236C2×C4C2×C22⋊D1111yescharacteristic
237C2×C4C2×C22⋊D1111yescharacteristic
238C2×C4C2×C22⋊D1111yescharacteristic
239C2×C4C2×C22⋊D1111yescharacteristic
240C2×C4C23×D1111yescharacteristic
241C8—222no—
242C8—222no—
243C22—21no—
244C22—21no—
245C22—441no—
246C22—441no—
247C22—441no—
248C22#6699512yes—
249C22C22×C22⋊D1111yescharacteristic
250C4—21no—
251C4—21no—
252C4—21no—
253C4—21no—
254C4—42no—
255C4—42no—
256C4—441no—
257C4—441no—
258C4—441no—
259C4#6700312yes—
260C4#6704211yescharacteristic
261C4#6704311yescharacteristic
262C2—22no—
263C2—881no—
264C2C2×#6699511yescharacteristic
265C2C2×#6700311yescharacteristic
266C2#1062336411yescharacteristic
subgroupG/H
centerC22C22×C22⋊D11
commutator, cosocleC2×C4×C11C24
FrattiniC2×C4C23×D11
FittingC11×#533C2
socleC22×C11C22×D4
prime radical#66983C22
hypercenter#533D11
hypocenterC11#3248
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. #10622703C2semidirect
5. #10622700C2semidirect
6. #10622696C2semidirect
7. #10622664C2semidirect
9. #10622641C2semidirect
10. #10622635C2semidirect
11. C2×C4⋊(C11⋊C8)C2semidirect
110. #533D11semidirect
214. C11#3248semidirect

Maximal subgroups

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

subgroupindex
C11×#5332
#106230102
#106227072
#106227032
#106227002
#106226962
#106226642
#106226612
#106226412
#106226352
C2×C4⋊(C11⋊C8)2
#324811