Finite Group Databasebeta

← #14664757

Subgroups — #14664757

Order 2816.

306 conjugacy classes of subgroups; only the 75 normal subgroups are shown.

normal subgroups only

This group has 306 conjugacy classes of subgroups — too many to draw. Only its 75 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#13079187C211yesmaximal, characteristic
2#13070416C211yesmaximal, characteristic, complemented
3#13068752C211yesmaximal, characteristic, complemented
4#13066634C211yesmaximal, characteristic, complemented
5#13066632C211yesmaximal, characteristic
6#13066630C211yesmaximal, characteristic
7C11×#1350C211yesmaximal, characteristic, complemented
8#10623155—21no—
9C11×#467C2211yescharacteristic
10#10622804C411yescharacteristic
11Q16×Dic11C411yescharacteristic
12#10622731—21no—
13#10622728C2211yescharacteristic
14C2×C8×Dic11C2211yescharacteristic
15#10622661—21no—
16#10622491C411yescharacteristic
17#10622485C411yescharacteristic
18#10622413—21no—
19#10622401—21no—
20C11×C22⋊C16C2211yescharacteristic
21C11×#341C2211yescharacteristic
22#10622196—21no—
23#10622190C2211yescharacteristic
24C22⋊(C11⋊C16)C2211yescharacteristic
25#10622140—21no—
26Dic11⋊C16—21no—
27C2×C11×Q16C2×C411yescharacteristic
28C2×C11×M16—21no—
29C22×C8×C11C2311yescharacteristic
30C11×C22⋊Q8—21no—
31#67000—21no—
32Q8×Dic11—21no—
33C2×#4325—21no—
34#66983—21no—
35C2×C4×Dic11D411yescharacteristic
36C2×#4318—21no—
37C22×C11⋊C8D411yescharacteristic
38C2×D88C2×C411yescharacteristic
39#66951—41no—
40#66946—21no—
41#66945—41no—
42#66943—21no—
43#66939—41no—
44(C22⋊D11)⋊C4—41no—
45C2×C11×C16—21no—
46C11×#107C2×C411yescharacteristic
47C11×#103—21no—
48#66899—21no—
49#66885—21no—
50#66882C2×C411yescharacteristic
51Dic11⋊C8—41no—
52Dic11⋊C8—41no—
53C8×Dic11C2×C411yescharacteristic
54C8×Dic11C2×C411yescharacteristic
55C8×Dic11D411yescharacteristic
56C8×Dic11D411yescharacteristic
57C2×C11⋊C16—21no—
58#66873—21no—
59#66872—21no—
60#11866—111nomaximal, Sylow
61C2×Q8×C11—21no—
62C22×C4×C11C2×D411yescharacteristic
63C2×C22⋊D11—41no—
64C22×Dic11SD1611yescharacteristic
65C22×Dic11SD1611yescharacteristic
66C2×D44—21no—
67C2×C4×D11—41no—
68C11×Q16—41no—
69C11×M16—41no—
70C11×M16—41no—
71C2×C8×C11—41no—
72C2×C8×C11—41no—
73C2×C8×C11C22×C411yescharacteristic
74C2×C8×C11C2×D411yescharacteristic
75C11×C4⋊C4—21no—
76C11×C4⋊C4—41no—
77C11×C22⋊C4—41no—
78#4325—42no—
79(C2×D11)⋊C4—41no—
80(C2×D11)⋊C4—41no—
81(C2×D11)⋊C4—41no—
82(C2×D11)⋊C4—41no—
83C4⋊Dic11—21no—
84C4⋊Dic11—41no—
85C4⋊Dic11—41no—
86Dic11⋊C4—41no—
87C4×Dic11—41no—
88C4×Dic11C22⋊C411yescharacteristic
89C4×Dic11C22⋊C411yescharacteristic
90C4×Dic11D811yescharacteristic
91C4×Dic11D811yescharacteristic
92#4318—41no—
93#4318—41no—
94C2×C11⋊C8—41no—
95C2×C11⋊C8—41no—
96C2×C11⋊C8C22⋊C411yescharacteristic
97C2×C11⋊C8C22⋊C411yescharacteristic
98D88—41no—
99C11×C16—41no—
100C11⋊C16—41no—
101#3168—111no—
102#2163—111no—
103#1837—111no—
104#1350—111no—
105#1350D1111yescharacteristic, complemented
106#1349—111no—
107#1349—111no—
108C23×C11C2×SD1611yescharacteristic
109C22×D11—41no—
110Q8×C11—41no—
111Q8×C11—41no—
112C2×C4×C11—21no—
113C2×C4×C11—21no—
114C2×C4×C11—41no—
115C2×C4×C11—41no—
116C2×C4×C11C2×C22⋊C411yescharacteristic
117C2×C4×C11C2×D811yescharacteristic
118C22⋊D11—82no—
119C2×Dic11—41no—
120C2×Dic11—41no—
121C2×Dic11—41no—
122C2×Dic11#10211yescharacteristic
123C2×Dic11#10211yescharacteristic
124C2×Dic11#10211yescharacteristic
125C2×Dic11#10211yescharacteristic
126D44—41no—
127D44—41no—
128C4×D11—82no—
129C8×C11—21no—
130C8×C11—21no—
131C8×C11—81no—
132C11⋊C8—21no—
133C11⋊C8—21no—
134C11⋊C8—81no—
135#529—221no—
136#499—111no—
137#495—111no—
138#488—221no—
139#467C2×D1111yescharacteristic
140#466—111no—
141#465—221no—
142C4×Q16—111no—
143C4×SD16—221no—
144C4×D8—111no—
145#423—221no—
146C2×C4×C8—111no—
147C4⋊C16—221no—
148C22⋊C16—111no—
149C22⋊C16C2×D1111yescharacteristic
150#346—221no—
151#341—111no—
152#341—221no—
153#341C2×D1111yescharacteristic
154C22×C11—21no—
155C22×C11—21no—
156C22×C11—21no—
157C22×C11C2×#10211yescharacteristic
158C2×D11—81no—
159C2×D11—81no—
160C2×D11—81no—
161C4×C11—21no—
162C4×C11—81no—
163C4×C11—81no—
164C4×C11#41011yescharacteristic
165C4×C11#42111yescharacteristic
166Dic11—21no—
167Dic11—21no—
168Dic11—21no—
169Dic11—21no—
170Dic11—81no—
171C2×Q16C4×D1111yescharacteristic
172C2×SD16—221no—
173C2×D8—111no—
174C2×M16—21no—
175C2×M16—221no—
176C22×C8—111no—
177C22×C8C22×D1111yescharacteristic
178#126—441no—
179#125—221no—
180#124—221no—
181#123—441no—
182C22⋊Q8—21no—
183#121—221no—
184C4×Q8—221no—
185C4×D4—221no—
186C4×D4—441no—
187#117—441no—
188C2×C42—111no—
189C2×C16—21no—
190C2×C16—221no—
191#107—111no—
192#107C4×D1111yescharacteristic
193#106—221no—
194C4⋊C8—441no—
195C4⋊C8—441no—
196#103—21no—
197#103—221no—
198#102—221no—
199#102—221no—
200C4×C8—111no—
201C4×C8—111no—
202C4×C8—111no—
203C4×C8—111no—
204C2×C11—41no—
205C2×C11#151711yescharacteristic
206C2×C11#214311yescharacteristic
207C2×C11#214811yescharacteristic
208D11—161no—
209C2×Q8—21no—
210C2×D4—221no—
211C2×D4—441no—
212C22×C4—111no—
213C22×C4—111no—
214C22×C4—441no—
215C22×C4D4×D1111yescharacteristic
216Q16—41no—
217SD16—442no—
218D8—441no—
219M16—41no—
220M16—41no—
221M16—441no—
222M16—441no—
223C2×C8—41no—
224C2×C8—41no—
225C2×C8—111no—
226C2×C8—111no—
227C2×C8—441no—
228C2×C8—441no—
229C2×C8C2×C4×D1111yescharacteristic
230C2×C8D4×D1111yescharacteristic
231C4⋊C4—21no—
232C4⋊C4—41no—
233C4⋊C4—221no—
234C4⋊C4—441no—
235C4⋊C4—441no—
236C4⋊C4—441no—
237C22⋊C4—41no—
238C22⋊C4—441no—
239C22⋊C4—441no—
240C22⋊C4—441no—
241C22⋊C4—441no—
242C42—111no—
243C42—111no—
244C42—111no—
245C42—111no—
246C42—441no—
247C16—41no—
248C16—441no—
249C11#1186611yescharacteristic, complemented, Sylow
250C23—441no—
251C23SD16×D1111yescharacteristic
252Q8—41no—
253Q8—41no—
254D4—441no—
255D4—441no—
256D4—882no—
257C2×C4—21no—
258C2×C4—21no—
259C2×C4—41no—
260C2×C4—41no—
261C2×C4—111no—
262C2×C4—111no—
263C2×C4—111no—
264C2×C4—111no—
265C2×C4—441no—
266C2×C4—441no—
267C2×C4—441no—
268C2×C4—882no—
269C2×C4C22⋊C4×D1111yescharacteristic
270C2×C4D8×D1111yescharacteristic
271C8—21no—
272C8—21no—
273C8—81no—
274C8—221no—
275C8—221no—
276C8—881no—
277C22—21no—
278C22—21no—
279C22—21no—
280C22—881no—
281C22—881no—
282C22—881no—
283C22D11×#10211yescharacteristic
284C4—21no—
285C4—81no—
286C4—81no—
287C4—221no—
288C4—221no—
289C4—221no—
290C4—221no—
291C4—881no—
292C4#1062235311yescharacteristic
293C4#1062243411yescharacteristic
294C2—41no—
295C2—1761no—
296C2#1306717411yescharacteristic
297C2#1307034211yescharacteristic
298C2#1307036411yescharacteristic
subgroupG/H
centerC22D11×#102
commutatorC2×C8×C11C22×C4
FrattiniC22×C8C22×D11
FittingC11×#1350C2
socleC22×C11C2×#102
prime radical#10622728C22
cosocleC22×C8×C11C23
hypercenter#1350D11
hypocenterC11#11866
LCSG ▷ C2×C8×C11 ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×C8 ◁ #1350

Complements

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

NH ≅ G/Ntype
2. #13070416C2semidirect
3. #13068752C2semidirect
4. #13066634C2semidirect
7. C11×#1350C2semidirect
105. #1350D11semidirect
249. C11#11866semidirect

Maximal subgroups

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

subgroupindex
#130791872
#130704162
#130687522
#130666342
#130666322
#130666302
C11×#13502
#1186611