Finite Group Databasebeta

← #13079791

Subgroups — #13079791

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×#529C211yesmaximal, characteristic
2#10623001C211yesmaximal, characteristic, complemented
3#10622677C212yesmaximal, complemented
4#10622669C212yesmaximal, complemented
5#10622658C212yesmaximal, complemented
6#10622648C212yesmaximal
7#10622634C211yesmaximal, characteristic, complemented
8#10622633C211yesmaximal, characteristic, complemented
9#10622621C211yesmaximal, characteristic, complemented
10#10622620C211yesmaximal, characteristic, complemented
11#10622538C211yesmaximal, characteristic, complemented
12C11×#126—21no—
13C11×#125C2211yescharacteristic
14C11×#124C2211yescharacteristic
15C11×#123—21no—
16C11×C22⋊Q8C2211yescharacteristic
17C11×#121C2211yescharacteristic
18C4×Q8×C11C2211yescharacteristic
19C4×D4×C11—21no—
20C4×D4×C11C2211yescharacteristic
21C11×#117—21no—
22C2×C42×C11C2211yescharacteristic
23#66979C2212yes—
24#66977—21no—
25#66977—21no—
26#66923C2212yes—
27#66922C2211yescharacteristic
28#66922C2211yescharacteristic
29C4×Dic22—21no—
30C4×Dic22—21no—
31#66899C2212yes—
32#66899C2212yes—
33#66896C2212yes—
34#66896C2212yes—
35C22⋊(C11⋊C8)C2212yes—
36#66872C2212yes—
37#66872C2212yes—
38#66871C2212yes—
39#66871C2212yes—
40C4⋊(C11⋊C8)C2211yescharacteristic
41C4⋊(C11⋊C8)C2211yescharacteristic
42C4×C11⋊C8C2212yes—
43C2×Q8×C11C2311yescharacteristic
44C2×D4×C11—21no—
45C2×D4×C11C2311yescharacteristic
46C22×C4×C11—21no—
47C22×C4×C11D411yescharacteristic
48C22×C4×C11D411yescharacteristic
49C22×C4×C11C2311yescharacteristic
50C2×Dic22—21no—
51C2×Dic22—21no—
52C11×C4⋊C4—21no—
53C11×C4⋊C4—21no—
54C11×C4⋊C4—21no—
55C11×C4⋊C4—21no—
56C11×C4⋊C4C2311yescharacteristic
57C11×C4⋊C4C2311yescharacteristic
58C11×C22⋊C4—21no—
59C11×C22⋊C4—21no—
60C11×C22⋊C4—21no—
61C11×C22⋊C4—21no—
62C11×C22⋊C4—21no—
63C42×C11—21no—
64C42×C11D411yescharacteristic
65C42×C11D411yescharacteristic
66C42×C11C2311yescharacteristic
67C42×C11C2311yescharacteristic
68C22⋊Dic11—22no—
69C4⋊Dic11—21no—
70C4⋊Dic11—21no—
71C4⋊Dic11C2312yes—
72C4⋊Dic11C2312yes—
73Dic11⋊C4—22no—
74Dic11⋊C4—22no—
75C4×Dic11—22no—
76C2×C11⋊C8C2312yes—
77C2×C11⋊C8C2312yes—
78#3233—111nomaximal, Sylow
79C23×C11—21no—
80C23×C11C2×D411yescharacteristic
81Q8×C11—21no—
82Q8×C11—21no—
83D4×C11—21no—
84D4×C11—21no—
85D4×C11—42no—
86C2×C4×C11—22no—
87C2×C4×C11—21no—
88C2×C4×C11—21no—
89C2×C4×C11—21no—
90C2×C4×C11—21no—
91C2×C4×C11—21no—
92C2×C4×C11—41no—
93C2×C4×C11—42no—
94C2×C4×C11C2×D411yescharacteristic
95C2×C4×C11C2×D411yescharacteristic
96C2×C4×C11C2×D411yescharacteristic
97C2×C4×C11C2×D411yescharacteristic
98C2×C4×C11C2×D411yescharacteristic
99C2×C4×C11C2411yescharacteristic
100C2×Dic11—22no—
101C2×Dic11—22no—
102Dic22—42no—
103Dic22—42no—
104C11⋊C8—22no—
105C11⋊C8—22no—
106#533—111no—
107#529D1111yescharacteristic
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×C11—41no—
121C22×C11—41no—
122C22×C11—41no—
123C22×C11C22×D411yescharacteristic
124C4×C11—21no—
125C4×C11—21no—
126C4×C11—21no—
127C4×C11—21no—
128C4×C11—41no—
129C4×C11—41no—
130C4×C11—41no—
131C4×C11#13512yes—
132C4×C112−1+411yescharacteristic
133C4×C112−1+411yescharacteristic
134Dic11—42no—
135Dic11—42no—
136C4⋊Q8—111no—
137C4⋊Q8—111no—
138#126—21no—
139#125—112no—
140#125C2×D1111yescharacteristic
141#124C2×D1111yescharacteristic
142#123—21no—
143C22⋊Q8—221no—
144C22⋊Q8—221no—
145C22⋊Q8C2×D1111yescharacteristic
146#121C2×D1111yescharacteristic
147C4×Q8—221no—
148C4×Q8—221no—
149C4×Q8C2×D1111yescharacteristic
150C4×D4—21no—
151C4×D4C2×D1111yescharacteristic
152#117—21no—
153#117—112no—
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—81no—
169C2×C11#53611yescharacteristic
170C2×C11C2×#13511yescharacteristic
171C2×C11#57511yescharacteristic
172C2×Q8—221no—
173C2×Q8—221no—
174C2×Q8C22×D1111yescharacteristic
175C2×D4—21no—
176C2×D4C22×D1111yescharacteristic
177C22×C4—21no—
178C22×C4C22⋊D1111yescharacteristic
179C22×C4C22⋊D1111yescharacteristic
180C22×C4C22×D1111yescharacteristic
181C2×C8—112no—
182C2×C8—112no—
183C4⋊C4—21no—
184C4⋊C4—21no—
185C4⋊C4—21no—
186C4⋊C4—21no—
187C4⋊C4—112no—
188C4⋊C4—112no—
189C4⋊C4—222no—
190C4⋊C4—222no—
191C4⋊C4—221no—
192C4⋊C4—221no—
193C4⋊C4C22×D1111yescharacteristic
194C4⋊C4C22×D1111yescharacteristic
195C22⋊C4—21no—
196C22⋊C4—21no—
197C22⋊C4—21no—
198C22⋊C4—21no—
199C22⋊C4—21no—
200C22⋊C4—222no—
201C42—21no—
202C42—222no—
203C42C22⋊D1111yescharacteristic
204C42C22⋊D1111yescharacteristic
205C42C22×D1111yescharacteristic
206C42C22×D1111yescharacteristic
207C11#323311yescharacteristic, complemented, Sylow
208C23—21no—
209C23C2×C22⋊D1111yescharacteristic
210Q8—21no—
211Q8—21no—
212Q8—442no—
213Q8—442no—
214D4—21no—
215D4—21no—
216D4—42no—
217C2×C4—22no—
218C2×C4—21no—
219C2×C4—21no—
220C2×C4—21no—
221C2×C4—21no—
222C2×C4—21no—
223C2×C4—41no—
224C2×C4—42no—
225C2×C4—222no—
226C2×C4—222no—
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—41no—
239C22—41no—
240C22—41no—
241C22C22×C22⋊D1111yescharacteristic
242C4—21no—
243C4—21no—
244C4—21no—
245C4—21no—
246C4—41no—
247C4—41no—
248C4—41no—
249C4—442no—
250C4—442no—
251C4#6700312yes—
252C4#6704311yescharacteristic
253C4#6704311yescharacteristic
254C2—41no—
255C2—81no—
256C2C2×#6700311yescharacteristic
257C2#1062335311yescharacteristic
258C2#1062335611yescharacteristic
subgroupG/H
centerC22C22×C22⋊D11
commutator, cosocleC2×C4×C11C24
FrattiniC2×C4C23×D11
FittingC11×#529C2
socleC22×C11C22×D4
prime radicalC11×#121C22
hypercenter#529D11
hypocenterC11#3233
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #529

Complements

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

NH ≅ G/Ntype
2. #10623001C2semidirect
3. #10622677C2semidirect
4. #10622669C2semidirect
5. #10622658C2semidirect
7. #10622634C2semidirect
8. #10622633C2semidirect
9. #10622621C2semidirect
10. #10622620C2semidirect
11. #10622538C2semidirect
207. C11#3233semidirect

Maximal subgroups

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

subgroupindex
C11×#5292
#106230012
#106226772
#106226692
#106226582
#106226482
#106226342
#106226332
#106226212
#106226202
#106225382
#323311