Finite Group Databasebeta

← #14645935

Subgroups — #14645935

Order 2816.

658 conjugacy classes of subgroups; only the 119 normal subgroups are shown.

normal subgroups only

This group has 658 conjugacy classes of subgroups — too many to draw. Only its 119 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
1#13082426C211yesmaximal, characteristic
2#13067314C212yesmaximal
3#13067230C212yesmaximal
4#13066960C211yesmaximal, characteristic
5C11×#1985C211yesmaximal, characteristic
6C2×C4×Q8×C11C2211yescharacteristic
7#10623343C412yes—
8#10623101—22no—
9#10623100—24no—
10Q8×Dic22—22no—
11#10623031—22no—
12#10623031C412yes—
13#10623001—22no—
14#10623001C2212yes—
15C2×C11×C4⋊C8C2211yescharacteristic
16C2×C11×#97C2211yescharacteristic
17#10622539C2212yes—
18C11×#336—22no—
19#10622166—22no—
20#10622124—22no—
21#10622120—22no—
22#10622103—24no—
23C22×Q8×C11C2×C411yescharacteristic
24C22×C8×C11—21no—
25C22×C8×C11—21no—
26C4×Q8×C11—22no—
27C4×Q8×C11—22no—
28C2×C11×C4⋊C4C2×C411yescharacteristic
29C2×C11×C4⋊C4D412yes—
30C2×C42×C11D412yes—
31C2×C42×C11C2311yescharacteristic
32Q8×Dic11—24no—
33Q8×Dic11—24no—
34#66979—24no—
35#66979C2×C414yes—
36#66977—24no—
37#66977—22no—
38#66977—22no—
39#66943—28no—
40#66943—24no—
41#66941—28no—
42#66941—24no—
43#66923—24no—
44#66923D414yes—
45#66922—22no—
46#66922—22no—
47#66922D412yes—
48#66922D412yes—
49C4×Dic22—24no—
50C4×Dic22—24no—
51C4×Dic22—22no—
52C4×Dic22—22no—
53C11×C4⋊C8—22no—
54C11×#97—22no—
55C22⋊(C11⋊C8)—22no—
56C4⋊(C11⋊C8)—22no—
57#66867—22no—
58#8460—111nomaximal, Sylow
59C2×Q8×C11—24no—
60C2×Q8×C11—22no—
61C22×C4×C11C22⋊C412yes—
62C22×C4×C11C22⋊C412yes—
63C22×C4×C11C22×C411yescharacteristic
64C22×C4×C11C2×D411yescharacteristic
65C22×C4×C11C2×D411yescharacteristic
66C2×Dic22—24no—
67C2×Dic22—22no—
68C2×Dic22—22no—
69C2×C8×C11—22no—
70C2×C8×C11—41no—
71C2×C8×C11—42no—
72C2×C8×C11—41no—
73C2×C8×C11—41no—
74C11×C4⋊C4—22no—
75C11×C4⋊C4—24no—
76C42×C11—22no—
77C42×C11—22no—
78C42×C11C2×D412yes—
79C42×C11C2×D412yes—
80C22⋊Dic11—24no—
81C4⋊Dic11—24no—
82C4⋊Dic11—24no—
83C4⋊Dic11—24no—
84C4⋊Dic11—22no—
85C4⋊Dic11—22no—
86C4⋊Dic11C22⋊C414yes—
87C4⋊Dic11C22⋊C414yes—
88Dic11⋊C4—28no—
89Dic11⋊C4—24no—
90Dic11⋊C4—24no—
91C4×Dic11—28no—
92C4×Dic11—24no—
93C2×C11⋊C8—42no—
94#3502—111no—
95#1985D1111yescharacteristic
96#1552—112no—
97#1531—112no—
98#1467—111no—
99C23×C11C2×C22⋊C411yescharacteristic
100Q8×C11—28no—
101C2×C4×C11—22no—
102C2×C4×C11—22no—
103C2×C4×C11—22no—
104C2×C4×C11—21no—
105C2×C4×C11—21no—
106C2×C4×C11—22no—
107C2×C4×C11—41no—
108C2×C4×C11—42no—
109C2×C4×C11#10114yes—
110C2×C4×C11C2×C22⋊C412yes—
111C2×C4×C11#12012yes—
112C2×C4×C11#12011yescharacteristic
113C2×C4×C11#12011yescharacteristic
114C2×Dic11—24no—
115C2×Dic11—24no—
116Dic22—42no—
117Dic22—42no—
118Dic22—82no—
119Dic22—84no—
120C8×C11—42no—
121C8×C11—81no—
122C11⋊C8—82no—
123Q82—222no—
124#557—224no—
125#557—222no—
126#544—112no—
127#544—222no—
128#533—112no—
129#533—222no—
130#519—112no—
131C2×C4×Q8C2×D1111yescharacteristic
132#432—112no—
133C2×C4⋊C8C2×D1111yescharacteristic
134C2×#97C2×D1111yescharacteristic
135#336—22no—
136#332—222no—
137#332—222no—
138#330—224no—
139#324—222no—
140C22×C11—21no—
141C22×C11—21no—
142C22×C11#37911yescharacteristic
143C22×C11C2×#10112yes—
144C4×C11—21no—
145C4×C11—22no—
146C4×C11—24no—
147C4×C11—22no—
148C4×C11—42no—
149C4×C11#45411yescharacteristic
150C4×C11#45611yescharacteristic
151Dic11—44no—
152Dic11—44no—
153C22×Q8C4×D1111yescharacteristic
154C22×C8—21no—
155C22×C8—21no—
156C4⋊Q8—112no—
157C4⋊Q8—112no—
158C4⋊Q8—222no—
159C4⋊Q8—222no—
160C4⋊Q8—224no—
161C4⋊Q8—228no—
162#125—114no—
163#125—224no—
164#125—224no—
165#125—228no—
166C22⋊Q8—224no—
167C22⋊Q8—222no—
168C22⋊Q8—222no—
169C4×Q8—22no—
170C4×Q8—22no—
171C4×Q8—224no—
172C4×Q8—224no—
173C4×Q8—224no—
174C4×Q8—224no—
175C4×Q8—222no—
176C4×Q8—222no—
177#117—114no—
178#117—224no—
179C2×C4⋊C4C4×D1111yescharacteristic
180C2×C4⋊C4D4412yes—
181C2×C42C22⋊D1112yes—
182C2×C42C22×D1111yescharacteristic
183C4⋊C8—22no—
184C4⋊C8—222no—
185C22⋊C8—222no—
186#97—22no—
187#97—222no—
188C2×C11—22no—
189C2×C11#178411yescharacteristic
190C2×C11#179311yescharacteristic
191C2×C11#179411yescharacteristic
192C2×Q8—24no—
193C2×Q8—22no—
194C2×Q8—224no—
195C2×Q8—222no—
196C2×Q8—222no—
197C22×C4(C2×D11)⋊C412yes—
198C22×C4(C2×D11)⋊C412yes—
199C22×C4C2×C4×D1111yescharacteristic
200C22×C4C2×D4411yescharacteristic
201C22×C4C2×C22⋊D1111yescharacteristic
202C2×C8—22no—
203C2×C8—41no—
204C2×C8—41no—
205C2×C8—42no—
206C2×C8—41no—
207C2×C8—442no—
208C4⋊C4—22no—
209C4⋊C4—24no—
210C4⋊C4—114no—
211C4⋊C4—114no—
212C4⋊C4—224no—
213C4⋊C4—224no—
214C4⋊C4—224no—
215C4⋊C4—228no—
216C4⋊C4—224no—
217C4⋊C4—222no—
218C4⋊C4—224no—
219C4⋊C4—222no—
220C22⋊C4—224no—
221C42—22no—
222C42—22no—
223C42—228no—
224C42—224no—
225C42D4×D1112yes—
226C42D4×D1112yes—
227C11#846011yescharacteristic, complemented, Sylow
228C23C2×(C2×D11)⋊C411yescharacteristic
229Q8—28no—
230Q8—442no—
231Q8—442no—
232Q8—882no—
233Q8—884no—
234C2×C4—22no—
235C2×C4—22no—
236C2×C4—22no—
237C2×C4—21no—
238C2×C4—21no—
239C2×C4—22no—
240C2×C4—41no—
241C2×C4—42no—
242C2×C4—224no—
243C2×C4—224no—
244C2×C4#6688814yes—
245C2×C4C22⋊C4×D1112yes—
246C2×C4#6693512yes—
247C2×C4#6699011yescharacteristic
248C2×C4#6699011yescharacteristic
249C8—42no—
250C8—81no—
251C8—882no—
252C22—21no—
253C22—21no—
254C22#1062256811yescharacteristic
255C22C2×#6688812yes—
256C4—21no—
257C4—22no—
258C4—24no—
259C4—22no—
260C4—42no—
261C4—444no—
262C4—444no—
263C4#1062267511yescharacteristic
264C4#1062270811yescharacteristic
265C2—22no—
266C2#1306853911yescharacteristic
267C2#1306857411yescharacteristic
268C2#1306857911yescharacteristic
subgroupG/H
centerC22#10622568
commutatorC22×C4×C11C22×C4
FrattiniC2×C42C22×D11
FittingC11×#1985C2
socleC22×C11#379
prime radicalC23×C11C2×C22⋊C4
cosocleC2×C42×C11C23
hypercenter#1985D11
hypocenterC11#8460
LCSG ▷ C22×C4×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1985

Complements

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

NH ≅ G/Ntype
227. C11#8460semidirect

Maximal subgroups

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

subgroupindex
#130824262
#130673142
#130672302
#130669602
C11×#19852
#846011