Finite Group Databasebeta

← #14649293

Subgroups — #14649293

Order 2816.

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

normal subgroups only

This group has 474 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#13071332C211yesmaximal, characteristic
2#13067012C212yesmaximal
3#13066940C211yesmaximal, characteristic
4#13066444C212yesmaximal
5C11×#2983C211yesmaximal, characteristic
6C2×C4×Q8×C11C2211yescharacteristic
7C2×#66997C411yescharacteristic
8C2×C4×Dic22C2211yescharacteristic
9C11×#446—24no—
10C11×#432—22no—
11C11×#431C2212yes—
12#10622843C411yescharacteristic
13#10622591—22no—
14#10622590C411yescharacteristic
15#10622587C411yescharacteristic
16#10622546—22no—
17#10622545C2211yescharacteristic
18#10622538C2212yes—
19#10622166—22no—
20#10622094—24no—
21C22×Q8×C11C2×C411yescharacteristic
22C22×Dic22C2×C411yescharacteristic
23C4×Q8×C11—22no—
24C4×Q8×C11—22no—
25C2×C11×C4⋊C4C2×C411yescharacteristic
26C2×C11×C4⋊C4D412yes—
27C2×C42×C11D412yes—
28C2×C42×C11C2311yescharacteristic
29#66997—22no—
30#66997—22no—
31C2×C4⋊Dic11C2×C411yescharacteristic
32C2×Dic11⋊C4—22no—
33C2×Dic11⋊C4—21no—
34C2×C4×Dic11—21no—
35C2×C4×Dic11C2×C411yescharacteristic
36C2×C4×Dic11C2×C411yescharacteristic
37C4×Dic22—22no—
38C4×Dic22—22no—
39C11×C4⋊C8—24no—
40C11×C4⋊C8—22no—
41C11×C22⋊C8—22no—
42C11×#97—24no—
43C4×C8×C11D414yes—
44C11⋊#95—22no—
45C11⋊#95—22no—
46C11⋊#95—22no—
47C11⋊#95—21no—
48C11⋊#95—21no—
49C22⋊(C11⋊C8)—22no—
50C4⋊(C11⋊C8)—22no—
51C4×C11⋊C8—22no—
52#9104—111nomaximal, Sylow
53C2×Q8×C11—22no—
54C2×Q8×C11—21no—
55C2×Q8×C11—21no—
56C2×Q8×C11—22no—
57C22×C4×C11C22⋊C412yes—
58C22×C4×C11C22⋊C412yes—
59C22×C4×C11C22×C411yescharacteristic
60C22×C4×C11C2×D411yescharacteristic
61C22×C4×C11C2×D411yescharacteristic
62C22×Dic11—21no—
63C22×Dic11—21no—
64C22×Dic11—21no—
65C22×Dic11—21no—
66C2×Dic22—22no—
67C2×Dic22—21no—
68C2×Dic22—22no—
69C2×Dic22M1612yes—
70C2×C8×C11—24no—
71C11×C4⋊C4—22no—
72C11×C4⋊C4—24no—
73C42×C11—22no—
74C42×C11—22no—
75C42×C11C2×D412yes—
76C42×C11#4112yes—
77C4⋊Dic11—22no—
78Dic11⋊C4—28no—
79Dic11⋊C4—41no—
80Dic11⋊C4—41no—
81C4×Dic11—21no—
82C4×Dic11—22no—
83C4×Dic11—42no—
84C4×Dic11M1612yes—
85C2×C11⋊C8—42no—
86#2983D1111yescharacteristic
87#2327—111no—
88#1479—112no—
89#1461—111no—
90#1274—112no—
91C23×C11C2×C22⋊C411yescharacteristic
92Q8×C11—42no—
93Q8×C11—42no—
94C2×C4×C11—22no—
95C2×C4×C11—22no—
96C2×C4×C11—22no—
97C2×C4×C11—22no—
98C2×C4×C11—41no—
99C2×C4×C11—41no—
100C2×C4×C11—42no—
101C2×C4×C11C4×D412yes—
102C2×C4×C11#12011yescharacteristic
103C2×C4×C11#12112yes—
104C2×C4×C11#12311yescharacteristic
105C2×C4×C11C2×M1611yescharacteristic
106C2×C4×C11C2×M1611yescharacteristic
107C2×C4×C11#13112yes—
108C2×Dic11—22no—
109C2×Dic11—22no—
110C2×Dic11—41no—
111C2×Dic11—41no—
112C2×Dic11—41no—
113C2×Dic11—41no—
114C2×Dic11—41no—
115C2×Dic11—41no—
116C2×Dic11—42no—
117C2×Dic11—41no—
118C2×Dic11—41no—
119Dic22—24no—
120Dic22—42no—
121C8×C11—44no—
122C11⋊C8—82no—
123C2×C4⋊Q8—111no—
124C2×C4×Q8—111no—
125C2×C4×Q8C2×D1111yescharacteristic
126#446—24no—
127#432—22no—
128#431—112no—
129#431C2×D1112yes—
130#391—111no—
131#391—111no—
132#387—222no—
133#387—222no—
134#382—111no—
135#376—111no—
136Q8⋊C8—224no—
137#324—222no—
138C22×C11—21no—
139C22×C11—21no—
140C22×C11#38611yescharacteristic
141C22×C11#40711yescharacteristic
142C22×C11#40811yescharacteristic
143C4×C11—22no—
144C4×C11—21no—
145C4×C11—21no—
146C4×C11—42no—
147C4×C11—42no—
148C4×C11#43512yes—
149C4×C11#43612yes—
150Dic11—42no—
151Dic11—42no—
152Dic11—81no—
153Dic11—81no—
154C22×Q8—111no—
155C22×Q8C4×D1111yescharacteristic
156C4⋊Q8—222no—
157C4⋊Q8—222no—
158C4×Q8—22no—
159C4×Q8—22no—
160C4×Q8—222no—
161C4×Q8—222no—
162C2×C4⋊C4—111no—
163C2×C4⋊C4—222no—
164C2×C4⋊C4—221no—
165C2×C4⋊C4C4×D1111yescharacteristic
166C2×C4⋊C4D4412yes—
167C2×C42—111no—
168C2×C42—111no—
169C2×C42—221no—
170C2×C42C22⋊D1112yes—
171C2×C42C22×D1111yescharacteristic
172C4⋊C8—24no—
173C4⋊C8—22no—
174C4⋊C8—222no—
175C22⋊C8—22no—
176C22⋊C8—222no—
177#97—24no—
178C4×C8—222no—
179C4×C8C22⋊D1114yes—
180#95—222no—
181#95—222no—
182#95—222no—
183#95—221no—
184#95—221no—
185C2×C11—21no—
186C2×C11—21no—
187C2×C11#187011yescharacteristic
188C2×C11#190911yescharacteristic
189C2×C11#191211yescharacteristic
190C2×Q8—21no—
191C2×Q8—21no—
192C2×Q8—22no—
193C2×Q8—22no—
194C2×Q8—112no—
195C2×Q8—221no—
196C2×Q8—222no—
197C2×Q8—222no—
198C22×C4—221no—
199C22×C4—221no—
200C22×C4—221no—
201C22×C4—221no—
202C22×C4(C2×D11)⋊C412yes—
203C22×C4(C2×D11)⋊C412yes—
204C22×C4C2×C4×D1111yescharacteristic
205C22×C4C2×D4411yescharacteristic
206C22×C4C2×C22⋊D1111yescharacteristic
207C2×C8—24no—
208C2×C8—442no—
209C4⋊C4—22no—
210C4⋊C4—24no—
211C4⋊C4—228no—
212C4⋊C4—222no—
213C4⋊C4—441no—
214C4⋊C4—441no—
215C42—22no—
216C42—22no—
217C42—112no—
218C42—221no—
219C42—222no—
220C42—442no—
221C42#433912yes—
222C42C2×C22⋊D1112yes—
223C11#910411yescharacteristic, complemented, Sylow
224C23C2×(C2×D11)⋊C411yescharacteristic
225Q8—42no—
226Q8—42no—
227Q8—224no—
228Q8—442no—
229C2×C4—22no—
230C2×C4—22no—
231C2×C4—22no—
232C2×C4—22no—
233C2×C4—41no—
234C2×C4—41no—
235C2×C4—42no—
236C2×C4—222no—
237C2×C4—222no—
238C2×C4—441no—
239C2×C4—441no—
240C2×C4—441no—
241C2×C4—441no—
242C2×C4—441no—
243C2×C4—441no—
244C2×C4—442no—
245C2×C4—441no—
246C2×C4—441no—
247C2×C4M16×D1111yescharacteristic
248C2×C4M16×D1111yescharacteristic
249C2×C4#6696012yes—
250C2×C4C4×C22⋊D1112yes—
251C2×C4#6698211yescharacteristic
252C2×C4#6698312yes—
253C2×C4#6700611yescharacteristic
254C8—44no—
255C8—882no—
256C22—21no—
257C22—21no—
258C22#1062273911yescharacteristic
259C22#1062274211yescharacteristic
260C22#1062282611yescharacteristic
261C4—22no—
262C4—21no—
263C4—21no—
264C4—42no—
265C4—42no—
266C4—442no—
267C4—442no—
268C4—881no—
269C4—881no—
270C4#1062274012yes—
271C4#1062274112yes—
272C2—21no—
273C2—21no—
274C2#1306891311yescharacteristic
275C2#1306913811yescharacteristic
276C2#1306915311yescharacteristic
subgroupG/H
centerC22#10622826
commutatorC22×C4×C11C22×C4
FrattiniC2×C42C22×D11
FittingC11×#2983C2
socleC22×C11#386
prime radicalC23×C11C2×C22⋊C4
cosocleC2×C42×C11C23
hypercenter#2983D11
hypocenterC11#9104
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #2983

Complements

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

NH ≅ G/Ntype
223. C11#9104semidirect

Maximal subgroups

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

subgroupindex
#130713322
#130670122
#130669402
#130664442
C11×#29832
#910411