Finite Group Databasebeta

← #14649794

Subgroups — #14649794

Order 2816.

524 conjugacy classes of subgroups; only the 127 normal subgroups are shown.

normal subgroups only

This group has 524 conjugacy classes of subgroups — too many to draw. Only its 127 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#13077180C211yesmaximal, characteristic
2#13074382C211yesmaximal, characteristic
3#13067287C212yesmaximal, complemented
4#13066475C212yesmaximal, complemented
5C11×#1458C211yesmaximal, characteristic
6C2×C11×#117C2211yescharacteristic
7C2×#66977—21no—
8C22×#4318—21no—
9C2×#66922C2211yescharacteristic
10C11×#431C2212yes—
11#10622612—24no—
12#10622596—21no—
13#10622596C412yes—
14#10622566—21no—
15#10622566C412yes—
16#10622549C2211yescharacteristic
17#10622542—21no—
18#10622537—21no—
19#10622537C2212yes—
20C11×#324—21no—
21C11×#323—21no—
22#10622124—24no—
23C23×C4×C11D411yescharacteristic
24C22×Dic22—21no—
25C11×#117—22no—
26C11×#117—22no—
27C2×C11×C4⋊C4C2×C411yescharacteristic
28C2×C11×C4⋊C4D411yescharacteristic
29C2×C11×C22⋊C4C2×C411yescharacteristic
30C2×C11×C22⋊C4D411yescharacteristic
31C2×C42×C11D411yescharacteristic
32C2×C42×C11C2311yescharacteristic
33C2×C22⋊Dic11—22no—
34C2×C4⋊Dic11—21no—
35C2×C4⋊Dic11—21no—
36C2×C4⋊Dic11C2×C412yes—
37#66977—42no—
38#66977—42no—
39C2×Dic11⋊C4—22no—
40C2×#4318—22no—
41C2×#4318—22no—
42C2×#4318—42no—
43C2×#4318—42no—
44C22×C11⋊C8—22no—
45#66922—22no—
46#66922—22no—
47C11×C4⋊C8—22no—
48C11×C22⋊C8—22no—
49C4×C8×C11—22no—
50C11⋊#95—22no—
51C11⋊#95—22no—
52C11⋊#95—21no—
53C11⋊#95C2×C412yes—
54C4⋊(C11⋊C8)—24no—
55C4⋊(C11⋊C8)—22no—
56C4⋊(C11⋊C8)D414yes—
57#9195—111nomaximal, Sylow
58C24×C11C22⋊C411yescharacteristic
59C22×C4×C11—21no—
60C22×C4×C11—21no—
61C22×C4×C11—21no—
62C22×C4×C11—21no—
63C22×C4×C11C22⋊C411yescharacteristic
64C22×C4×C11C22⋊C411yescharacteristic
65C22×C4×C11C22⋊C411yescharacteristic
66C22×C4×C11D812yes—
67C22×C4×C11SD1612yes—
68C22×C4×C11C22×C411yescharacteristic
69C22×C4×C11C2×D411yescharacteristic
70C22×C4×C11C2×D411yescharacteristic
71C22×Dic11—22no—
72C22×Dic11—22no—
73C2×Dic22—41no—
74C2×Dic22—41no—
75C2×Dic22—41no—
76C2×Dic22—41no—
77C2×Dic22—41no—
78C2×Dic22—41no—
79C2×C8×C11—42no—
80C11×C4⋊C4—22no—
81C11×C4⋊C4—22no—
82C11×C22⋊C4—22no—
83C11×C22⋊C4—22no—
84C42×C11—21no—
85C42×C11—21no—
86C42×C11C2×D412yes—
87C42×C11#4112yes—
88C22⋊Dic11—44no—
89C4⋊Dic11—24no—
90C4⋊Dic11—42no—
91C4⋊Dic11—41no—
92C4⋊Dic11—41no—
93Dic11⋊C4—44no—
94#4318—44no—
95#4318—42no—
96#4318—42no—
97C2×C11⋊C8—24no—
98C2×C11⋊C8—44no—
99#2905—111no—
100#2621—111no—
101#1546—112no—
102#1458D1111yescharacteristic
103#1286—112no—
104C23×C11—21no—
105C23×C11—21no—
106C23×C11—41no—
107C23×C11—41no—
108C23×C11#10212yes—
109C23×C11C2×C22⋊C411yescharacteristic
110C2×C4×C11—21no—
111C2×C4×C11—21no—
112C2×C4×C11—22no—
113C2×C4×C11—22no—
114C2×C4×C11—22no—
115C2×C4×C11—22no—
116C2×C4×C11—21no—
117C2×C4×C11—21no—
118C2×C4×C11—41no—
119C2×C4×C11—41no—
120C2×C4×C11—41no—
121C2×C4×C11—41no—
122C2×C4×C11#10212yes—
123C2×C4×C11C4×D412yes—
124C2×C4×C11#12011yescharacteristic
125C2×C4×C11#12112yes—
126C2×C4×C11#12311yescharacteristic
127C2×C4×C11C2×D811yescharacteristic
128C2×C4×C11C2×SD1611yescharacteristic
129C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
130C2×C4×C11#13711yescharacteristic
131C2×Dic11—42no—
132C2×Dic11—42no—
133C2×Dic11—42no—
134C2×Dic11—42no—
135C2×Dic11—42no—
136C2×Dic11—42no—
137Dic22—81no—
138Dic22—81no—
139Dic22—81no—
140Dic22—81no—
141C8×C11—82no—
142C11⋊C8—44no—
143C22×M16—221no—
144C2×C4⋊Q8—111no—
145C2×C22⋊Q8—221no—
146C2×#117C2×D1111yescharacteristic
147#431C2×D1112yes—
148#424—224no—
149#423—112no—
150#423—221no—
151#398—112no—
152#398—221no—
153#397—112no—
154#397—221no—
155#391—221no—
156#382—111no—
157#332—224no—
158#324—21no—
159#323—21no—
160C22×C11—21no—
161C22×C11—21no—
162C22×C11—22no—
163C22×C11—42no—
164C22×C11—41no—
165C22×C11—41no—
166C22×C11—81no—
167C22×C11#38611yescharacteristic
168C22×C11C2×#10211yescharacteristic
169C22×C11#41711yescharacteristic
170C4×C11—22no—
171C4×C11—22no—
172C4×C11—22no—
173C4×C11—41no—
174C4×C11—41no—
175C4×C11#44711yescharacteristic
176C4×C11#44811yescharacteristic
177C4×C11#48011yescharacteristic
178C4×C11#48111yescharacteristic
179Dic11—82no—
180Dic11—82no—
181C22×Q8—221no—
182C23×C4D4411yescharacteristic
183C2×M16—222no—
184C2×M16—222no—
185C2×M16—442no—
186C2×M16—442no—
187C22×C8—222no—
188C4⋊Q8—222no—
189C4⋊Q8—222no—
190C22⋊Q8—442no—
191C22⋊Q8—442no—
192#117—22no—
193#117—22no—
194C2×C4⋊C4—112no—
195C2×C4⋊C4—222no—
196C2×C4⋊C4—221no—
197C2×C4⋊C4—221no—
198C2×C4⋊C4C4×D1111yescharacteristic
199C2×C4⋊C4C22⋊D1111yescharacteristic
200C2×C22⋊C4—222no—
201C2×C22⋊C4C4×D1111yescharacteristic
202C2×C22⋊C4C22⋊D1111yescharacteristic
203C2×C42D4411yescharacteristic
204C2×C42C22×D1111yescharacteristic
205C4⋊C8—22no—
206C4⋊C8—114no—
207C4⋊C8—224no—
208C4⋊C8—222no—
209C22⋊C8—22no—
210C4×C8—22no—
211#95—112no—
212#95—222no—
213#95—222no—
214#95—221no—
215C2×C11—21no—
216C2×C11—21no—
217C2×C11—42no—
218C2×C11#187411yescharacteristic
219C2×C11#190911yescharacteristic
220C2×C11#191511yescharacteristic
221C24(C2×D11)⋊C411yescharacteristic
222C2×Q8—441no—
223C2×Q8—441no—
224C2×Q8—441no—
225C2×Q8—441no—
226C2×Q8—441no—
227C2×Q8—441no—
228C22×C4—21no—
229C22×C4—21no—
230C22×C4—21no—
231C22×C4—21no—
232C22×C4—222no—
233C22×C4—222no—
234C22×C4#431412yes—
235C22×C4D8812yes—
236C22×C4(C2×D11)⋊C411yescharacteristic
237C22×C4(C2×D11)⋊C411yescharacteristic
238C22×C4(C2×D11)⋊C411yescharacteristic
239C22×C4C2×C4×D1111yescharacteristic
240C22×C4C2×D4411yescharacteristic
241C22×C4C2×C22⋊D1111yescharacteristic
242M16—444no—
243M16—442no—
244M16—442no—
245C2×C8—42no—
246C2×C8—224no—
247C2×C8—444no—
248C4⋊C4—22no—
249C4⋊C4—22no—
250C4⋊C4—224no—
251C4⋊C4—444no—
252C4⋊C4—441no—
253C4⋊C4—441no—
254C4⋊C4—442no—
255C22⋊C4—22no—
256C22⋊C4—22no—
257C22⋊C4—444no—
258C42—21no—
259C42—21no—
260C42D4×D1112yes—
261C42#434112yes—
262C11#919511yescharacteristic, complemented, Sylow
263C23—21no—
264C23—21no—
265C23—41no—
266C23—41no—
267C23#6688512yes—
268C23C2×(C2×D11)⋊C411yescharacteristic
269Q8—881no—
270Q8—881no—
271Q8—881no—
272Q8—881no—
273C2×C4—21no—
274C2×C4—21no—
275C2×C4—22no—
276C2×C4—22no—
277C2×C4—22no—
278C2×C4—22no—
279C2×C4—21no—
280C2×C4—21no—
281C2×C4—41no—
282C2×C4—41no—
283C2×C4—41no—
284C2×C4—41no—
285C2×C4—442no—
286C2×C4—442no—
287C2×C4—442no—
288C2×C4—442no—
289C2×C4—442no—
290C2×C4—442no—
291C2×C4#6688512yes—
292C2×C4(C22⋊D11)⋊C412yes—
293C2×C4#6693511yescharacteristic
294C2×C4#6693911yescharacteristic
295C2×C4C2×#431411yescharacteristic
296C2×C4C2×D8811yescharacteristic
297C2×C4#6696111yescharacteristic
298C2×C4#6696211yescharacteristic
299C2×C4#6699212yes—
300C8—82no—
301C8—444no—
302C22—21no—
303C22—21no—
304C22—22no—
305C22—42no—
306C22—41no—
307C22—41no—
308C22—81no—
309C22#1062257111yescharacteristic
310C22C2×#6688511yescharacteristic
311C22#1062274611yescharacteristic
312C4—22no—
313C4—22no—
314C4—22no—
315C4—41no—
316C4—41no—
317C4—882no—
318C4—882no—
319C4#1062234511yescharacteristic
320C4#1062234811yescharacteristic
321C4#1062234911yescharacteristic
322C4#1062235111yescharacteristic
323C2—21no—
324C2—21no—
325C2—42no—
326C2#1306893111yescharacteristic
327C2#1306913611yescharacteristic
328C2#1306916611yescharacteristic
subgroupG/H
centerC22#10622571
commutatorC22×C4×C11C22×C4
FrattiniC2×C42C22×D11
FittingC11×#1458C2
socleC22×C11#386
prime radicalC24×C11C22⋊C4
cosocleC2×C42×C11C23
hypercenter#1458D11
hypocenterC11#9195
LCSG ▷ C22×C4×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1458

Complements

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

NH ≅ G/Ntype
3. #13067287C2semidirect
4. #13066475C2semidirect
262. C11#9195semidirect

Maximal subgroups

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

subgroupindex
#130771802
#130743822
#130672872
#130664752
C11×#14582
#919511