Finite Group Databasebeta

← #14651645

Subgroups — #14651645

Order 2816.

522 conjugacy classes of subgroups; only the 111 normal subgroups are shown.

normal subgroups only

This group has 522 conjugacy classes of subgroups — too many to draw. Only its 111 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#13077701C211yesmaximal, characteristic, complemented
2#13073521C211yesmaximal, characteristic
3#13067040C212yesmaximal
4#13066476C212yesmaximal, complemented
5C11×#1801C211yesmaximal, characteristic, complemented
6C2×C4×Q8×C11C2211yescharacteristic
7C2×#66999—21no—
8C2×C4×D44C2211yescharacteristic
9C11×#423C2212yes—
10C2×C11×#101—21no—
11#10622637—24no—
12#10622604C412yes—
13#10622600—21no—
14#10622596C412yes—
15#10622553—22no—
16#10622549C2211yescharacteristic
17#10622539—22no—
18#10622538C2212yes—
19C11×#343—21no—
20#10622121—24no—
21C22×Q8×C11D411yescharacteristic
22C22×D44C2×C411yescharacteristic
23C22×C4×D11—21no—
24C2×C11×M16—22no—
25C4×Q8×C11—22no—
26C4×Q8×C11—22no—
27C2×C11×C4⋊C4C2×C412yes—
28C2×C11×C4⋊C4D411yescharacteristic
29C2×C42×C11D412yes—
30C2×C42×C11C2311yescharacteristic
31#66999—44no—
32C2×(C2×D11)⋊C4—22no—
33C2×(C2×D11)⋊C4—22no—
34C2×(C2×D11)⋊C4—21no—
35C2×C4⋊Dic11—21no—
36C2×C4⋊Dic11C2×C411yescharacteristic
37C2×Dic11⋊C4—22no—
38C4×D44—22no—
39C4×D44—22no—
40C11×C4⋊C8—22no—
41C11×C4⋊C8—22no—
42C11×#101—42no—
43C11⋊#95—22no—
44C11⋊#95—21no—
45C11⋊#95C2×C412yes—
46C22⋊(C11⋊C8)—22no—
47C4⋊(C11⋊C8)—24no—
48C4⋊(C11⋊C8)—22no—
49#66867—24no—
50C4×C11⋊C8D414yes—
51#9490—111nomaximal, Sylow
52C23×D11—21no—
53C2×Q8×C11—22no—
54C2×Q8×C11—21no—
55C2×Q8×C11—22no—
56C2×Q8×C11—21no—
57C22×C4×C11C22⋊C412yes—
58C22×C4×C11C22⋊C412yes—
59C22×C4×C11C22×C411yescharacteristic
60C22×C4×C11C2×D411yescharacteristic
61C22×C4×C11C2×D411yescharacteristic
62C22×Dic11—22no—
63C22×Dic11—21no—
64C2×D44—22no—
65C2×D44—42no—
66C2×C4×D11—42no—
67C2×C4×D11—42no—
68C2×C4×D11—41no—
69C2×C4×D11—41no—
70C11×M16—42no—
71C11×M16—42no—
72C2×C8×C11—42no—
73C11×C4⋊C4—24no—
74C11×C4⋊C4—22no—
75C42×C11—22no—
76C42×C11—22no—
77C42×C11C2×D412yes—
78C42×C11#4112yes—
79(C2×D11)⋊C4—44no—
80(C2×D11)⋊C4—44no—
81(C2×D11)⋊C4—41no—
82(C2×D11)⋊C4—41no—
83C4⋊Dic11—22no—
84C4⋊Dic11—42no—
85Dic11⋊C4—44no—
86C2×C11⋊C8—24no—
87#2983—111no—
88#2536—111no—
89#1801D1111yescharacteristic, complemented
90#1486—112no—
91#1286—112no—
92C23×C11C2×C22⋊C411yescharacteristic
93C22×D11—22no—
94C22×D11—41no—
95C22×D11—41no—
96C22×D11—41no—
97C22×D11—41no—
98C22×D11—41no—
99C22×D11—41no—
100Q8×C11—42no—
101Q8×C11—42no—
102C2×C4×C11—22no—
103C2×C4×C11—22no—
104C2×C4×C11—22no—
105C2×C4×C11—22no—
106C2×C4×C11—41no—
107C2×C4×C11—41no—
108C2×C4×C11—42no—
109C2×C4×C11C4×D412yes—
110C2×C4×C11#12011yescharacteristic
111C2×C4×C11#12112yes—
112C2×C4×C11#12311yescharacteristic
113C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
114C2×C4×C11AGL(1,ℤ/8)12yes—
115C2×C4×C11#13711yescharacteristic
116C2×Dic11—42no—
117C2×Dic11—42no—
118C2×Dic11—41no—
119C2×Dic11—41no—
120C2×Dic11—41no—
121C2×Dic11—42no—
122D44—24no—
123D44—42no—
124C4×D11—82no—
125C4×D11—82no—
126C8×C11—82no—
127C11⋊C8—44no—
128C2×C22⋊Q8—221no—
129C2×C4×Q8C2×D1111yescharacteristic
130C2×C4×D4—111no—
131#446—224no—
132#432—222no—
133#431—112no—
134#423C2×D1112yes—
135C2×#101—21no—
136#398—112no—
137#394—112no—
138#388—222no—
139#382—111no—
140#380—221no—
141#343—21no—
142D4⋊C8—224no—
143C22×C11—21no—
144C22×C11—21no—
145C22×C11#38611yescharacteristic
146C22×C11#41711yescharacteristic
147C22×C11#41811yescharacteristic
148C2×D11—42no—
149C2×D11—42no—
150C2×D11—42no—
151C2×D11—81no—
152C2×D11—81no—
153C2×D11—81no—
154C2×D11—81no—
155C4×C11—22no—
156C4×C11—21no—
157C4×C11—21no—
158C4×C11—42no—
159C4×C11—42no—
160C4×C11#46812yes—
161C4×C11#46912yes—
162Dic11—82no—
163Dic11—81no—
164C22×Q8C22⋊D1111yescharacteristic
165C22×D4—111no—
166C23×C4—221no—
167C2×M16—22no—
168C22⋊Q8—444no—
169C4×Q8—22no—
170C4×Q8—22no—
171C4×D4—222no—
172C4×D4—222no—
173C2×C4⋊C4—111no—
174C2×C4⋊C4—222no—
175C2×C4⋊C4—221no—
176C2×C4⋊C4C4×D1112yes—
177C2×C4⋊C4C22⋊D1111yescharacteristic
178C2×C22⋊C4—222no—
179C2×C22⋊C4—222no—
180C2×C22⋊C4—221no—
181C2×C42D4412yes—
182C2×C42C22×D1111yescharacteristic
183C4⋊C8—22no—
184C4⋊C8—22no—
185C4⋊C8—224no—
186C4⋊C8—222no—
187#101—42no—
188C22⋊C8—222no—
189#97—224no—
190C4×C8—114no—
191#95—112no—
192#95—222no—
193#95—221no—
194C2×C11—21no—
195C2×C11—21no—
196C2×C11#189111yescharacteristic
197C2×C11#189511yescharacteristic
198C2×C11#191211yescharacteristic
199D11—82no—
200C24—221no—
201C2×Q8—21no—
202C2×Q8—22no—
203C2×Q8—21no—
204C2×Q8—22no—
205C2×D4—222no—
206C2×D4—442no—
207C22×C4—222no—
208C22×C4—221no—
209C22×C4—441no—
210C22×C4—442no—
211C22×C4—441no—
212C22×C4—442no—
213C22×C4(C2×D11)⋊C412yes—
214C22×C4(C2×D11)⋊C412yes—
215C22×C4C2×C4×D1111yescharacteristic
216C22×C4C2×D4411yescharacteristic
217C22×C4C2×C22⋊D1111yescharacteristic
218M16—42no—
219M16—42no—
220C2×C8—42no—
221C2×C8—224no—
222C4⋊C4—24no—
223C4⋊C4—22no—
224C4⋊C4—222no—
225C4⋊C4—444no—
226C4⋊C4—442no—
227C22⋊C4—444no—
228C22⋊C4—444no—
229C22⋊C4—441no—
230C22⋊C4—441no—
231C42—22no—
232C42—22no—
233C42D4×D1112yes—
234C42#434112yes—
235C11#949011yescharacteristic, complemented, Sylow
236C23—222no—
237C23—441no—
238C23—441no—
239C23—441no—
240C23—441no—
241C23—441no—
242C23—441no—
243C23C2×(C2×D11)⋊C411yescharacteristic
244Q8—42no—
245Q8—42no—
246D4—224no—
247D4—442no—
248C2×C4—22no—
249C2×C4—22no—
250C2×C4—22no—
251C2×C4—22no—
252C2×C4—41no—
253C2×C4—41no—
254C2×C4—42no—
255C2×C4—442no—
256C2×C4—442no—
257C2×C4—441no—
258C2×C4—441no—
259C2×C4—442no—
260C2×C4—441no—
261C2×C4—882no—
262C2×C4—882no—
263C2×C4(C22⋊D11)⋊C412yes—
264C2×C4#6693511yescharacteristic
265C2×C4#6693911yescharacteristic
266C2×C4#6698511yescharacteristic
267C2×C4#6699212yes—
268C2×C4#6699511yescharacteristic
269C2×C4#6700212yes—
270C8—82no—
271C8—444no—
272C22—21no—
273C22—21no—
274C22—442no—
275C22—442no—
276C22—442no—
277C22—881no—
278C22—881no—
279C22—881no—
280C22—881no—
281C22#1062257111yescharacteristic
282C22#1062257911yescharacteristic
283C22#1062261411yescharacteristic
284C4—21no—
285C4—21no—
286C4—22no—
287C4—42no—
288C4—42no—
289C4—882no—
290C4—881no—
291C4#1062265212yes—
292C4#1062266212yes—
293C2—21no—
294C2—21no—
295C2—882no—
296C2#1306903211yescharacteristic
297C2#1306905211yescharacteristic
298C2#1306915111yescharacteristic
subgroupG/H
centerC22#10622571
commutatorC22×C4×C11C22×C4
FrattiniC2×C42C22×D11
FittingC11×#1801C2
socleC22×C11#386
prime radicalC22×D44C2×C4
cosocleC2×C42×C11C23
hypercenter#1801D11
hypocenterC11#9490
LCSG ▷ C22×C4×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1801

Complements

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

NH ≅ G/Ntype
1. #13077701C2semidirect
4. #13066476C2semidirect
5. C11×#1801C2semidirect
89. #1801D11semidirect
235. C11#9490semidirect

Maximal subgroups

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

subgroupindex
#130777012
#130735212
#130670402
#130664762
C11×#18012
#949011