Finite Group Databasebeta

← #14667050

Subgroups — #14667050

Order 2816.

316 conjugacy classes of subgroups; only the 61 normal subgroups are shown.

normal subgroups only

This group has 316 conjugacy classes of subgroups — too many to draw. Only its 61 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#13079969C211yesmaximal, characteristic
2#13070811C211yesmaximal, characteristic, complemented
3#13070797C211yesmaximal, characteristic
4#13070106C211yesmaximal, characteristic, complemented
5#13066624C211yesmaximal, characteristic
6#13066555C211yesmaximal, characteristic, complemented
7C11×#1348C211yesmaximal, characteristic, complemented
8#10623155—21no—
9C11×#467C2211yescharacteristic
10#10622798—21no—
11#10622728C2211yescharacteristic
12C2×#66882C2211yescharacteristic
13C2×Dic11⋊C8C2211yescharacteristic
14#10622661—21no—
15#10622598—21no—
16#10622504—21no—
17#10622432—21no—
18#10622409—21no—
19C11×C22⋊C16C2211yescharacteristic
20C11×#340C2211yescharacteristic
21#10622202—21no—
22C22⋊(C11⋊C16)C2211yescharacteristic
23#10622167—21no—
24#10622147—21no—
25#10622142—21no—
26#10622128—21no—
27C2×C11×Q16D411yescharacteristic
28C22×C8×C11C2311yescharacteristic
29C11×C22⋊Q8—21no—
30C2×C11×C4⋊C4—21no—
31#67000—21no—
32Q8×Dic11—21no—
33C2×#4325—21no—
34#66983—21no—
35C2×C4⋊Dic11—21no—
36C2×C4⋊Dic11—41no—
37C2×C4×Dic11D411yescharacteristic
38C22×C11⋊C8D411yescharacteristic
39C2×D88D411yescharacteristic
40#66951—41no—
41#66946—21no—
42#66945—41no—
43#66943—21no—
44#66939—41no—
45(C22⋊D11)⋊C4—41no—
46C2×C11×C16—21no—
47C11×#107D411yescharacteristic
48C11×#103—21no—
49#66899—21no—
50C11⋊#95—41no—
51#66885—21no—
52#66882—21no—
53#66882—21no—
54#66882D411yescharacteristic
55Dic11⋊C8—21no—
56Dic11⋊C8—21no—
57C2×C11⋊C16—21no—
58#66873—21no—
59#66872—21no—
60#12290—111nomaximal, Sylow
61C2×Q8×C11—21no—
62C22×C4×C11—41no—
63C22×C4×C11C2×D411yescharacteristic
64C2×C22⋊D11—41no—
65C22×Dic11—41no—
66C22×Dic11D811yescharacteristic
67C22×Dic11D811yescharacteristic
68C2×D44—21no—
69C2×C4×D11—41no—
70C11×Q16—41no—
71C2×C8×C11—41no—
72C2×C8×C11C2×D411yescharacteristic
73C2×C8×C11C2×D411yescharacteristic
74C11×C4⋊C4—22no—
75C11×C4⋊C4—21no—
76C11×C4⋊C4—41no—
77C11×C4⋊C4—41no—
78C11×C22⋊C4—41no—
79#4325—81no—
80(C2×D11)⋊C4—41no—
81(C2×D11)⋊C4—41no—
82(C2×D11)⋊C4—41no—
83(C2×D11)⋊C4—41no—
84C4⋊Dic11—21no—
85C4⋊Dic11—41no—
86C4⋊Dic11—41no—
87C4⋊Dic11—41no—
88C4⋊Dic11—41no—
89C4⋊Dic11—82no—
90Dic11⋊C4—41no—
91C4×Dic11—21no—
92C4×Dic11—21no—
93C4×Dic11—41no—
94C2×C11⋊C8—21no—
95C2×C11⋊C8—41no—
96D88—41no—
97C11×C16—41no—
98C11⋊C16—41no—
99#3250—111no—
100#2235—111no—
101#2232—111no—
102#2086—111no—
103#1348D1111yescharacteristic, complemented
104#1347—111no—
105#1322—111no—
106C23×C11C2×D811yescharacteristic
107C22×D11—41no—
108Q8×C11—41no—
109Q8×C11—41no—
110C2×C4×C11—21no—
111C2×C4×C11—21no—
112C2×C4×C11—42no—
113C2×C4×C11—41no—
114C2×C4×C11—41no—
115C2×C4×C11—81no—
116C2×C4×C11—81no—
117C2×C4×C11#12011yescharacteristic
118C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
119C22⋊D11—81no—
120C22⋊D11—81no—
121C2×Dic11—21no—
122C2×Dic11—21no—
123C2×Dic11—21no—
124C2×Dic11—21no—
125C2×Dic11—41no—
126C2×Dic11—41no—
127C2×Dic11—81no—
128C2×Dic11—81no—
129C2×Dic11—81no—
130D44—41no—
131D44—41no—
132C4×D11—82no—
133C8×C11—21no—
134C8×C11—21no—
135C11⋊C8—41no—
136#529—221no—
137#479—221no—
138#478—221no—
139#467C2×D1111yescharacteristic
140#466—111no—
141#465—221no—
142#464—221no—
143#463—221no—
144C2×#107—111no—
145C2×C4⋊C8—111no—
146#389—221no—
147#367—221no—
148#366—221no—
149#358—221no—
150#357—221no—
151C22⋊C16—111no—
152C22⋊C16C2×D1111yescharacteristic
153#340—221no—
154#340C2×D1111yescharacteristic
155C22×C11—21no—
156C22×C11—21no—
157C22×C11#44711yescharacteristic
158C22×C11#50811yescharacteristic
159C22×C11#50911yescharacteristic
160C2×D11—81no—
161C2×D11—81no—
162C2×D11—81no—
163C4×C11—21no—
164C4×C11—82no—
165C4×C11—81no—
166C4×C11—81no—
167C4×C11#45611yescharacteristic
168C4×C11#45811yescharacteristic
169Dic11—41no—
170Dic11—41no—
171Dic11—81no—
172Dic11—161no—
173C2×Q16D4411yescharacteristic
174C2×SD16—221no—
175C2×D8—111no—
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×C4⋊C4—21no—
189C2×C4⋊C4—221no—
190C2×C4⋊C4—441no—
191C2×C42—111no—
192C2×C16—21no—
193C2×C16—221no—
194#107—111no—
195#107—221no—
196#107—221no—
197#107D4411yescharacteristic
198#106—221no—
199C4⋊C8—221no—
200C4⋊C8—221no—
201#103—21no—
202#103—221no—
203#102—221no—
204#102—221no—
205#95—441no—
206C2×C11—21no—
207C2×C11—21no—
208C2×C11#161011yescharacteristic
209C2×C11#218611yescharacteristic
210C2×C11#219111yescharacteristic
211D11—161no—
212C2×Q8—21no—
213C2×D4—221no—
214C2×D4—441no—
215C22×C4—41no—
216C22×C4—111no—
217C22×C4—111no—
218C22×C4—441no—
219C22×C4—441no—
220C22×C4D4×D1111yescharacteristic
221Q16—41no—
222SD16—881no—
223D8—441no—
224C2×C8—41no—
225C2×C8—221no—
226C2×C8—441no—
227C2×C8C2×D4411yescharacteristic
228C2×C8D4×D1111yescharacteristic
229C4⋊C4—22no—
230C4⋊C4—21no—
231C4⋊C4—41no—
232C4⋊C4—41no—
233C4⋊C4—221no—
234C4⋊C4—441no—
235C4⋊C4—441no—
236C4⋊C4—441no—
237C4⋊C4—441no—
238C4⋊C4—441no—
239C4⋊C4—882no—
240C22⋊C4—41no—
241C22⋊C4—441no—
242C22⋊C4—441no—
243C22⋊C4—441no—
244C22⋊C4—441no—
245C42—221no—
246C42—221no—
247C42—441no—
248C16—41no—
249C16—441no—
250C11#1229011yescharacteristic, complemented, Sylow
251C23—441no—
252C23D8×D1111yescharacteristic
253Q8—41no—
254Q8—41no—
255D4—441no—
256D4—441no—
257D4—881no—
258D4—881no—
259C2×C4—21no—
260C2×C4—21no—
261C2×C4—42no—
262C2×C4—41no—
263C2×C4—41no—
264C2×C4—81no—
265C2×C4—81no—
266C2×C4—221no—
267C2×C4—221no—
268C2×C4—221no—
269C2×C4—221no—
270C2×C4—441no—
271C2×C4—441no—
272C2×C4—882no—
273C2×C4—881no—
274C2×C4—881no—
275C2×C4—881no—
276C2×C4#6693511yescharacteristic
277C2×C4#6696711yescharacteristic
278C8—21no—
279C8—21no—
280C8—441no—
281C22—21no—
282C22—21no—
283C22—881no—
284C22—881no—
285C22—881no—
286C22#1062238611yescharacteristic
287C22#1062252711yescharacteristic
288C22#1062253211yescharacteristic
289C4—21no—
290C4—82no—
291C4—81no—
292C4—81no—
293C4—441no—
294C4—441no—
295C4—881no—
296C4—1761no—
297C4#1062235511yescharacteristic
298C4#1062243911yescharacteristic
299C2—21no—
300C2—21no—
301C2—1761no—
302C2#1306762011yescharacteristic
303C2#1307054211yescharacteristic
304C2#1307056811yescharacteristic
subgroupG/H
centerC22#10622386
commutator, cosocleC22×C8×C11C23
FrattiniC22×C8C22×D11
FittingC11×#1348C2
socleC22×C11#447
prime radical#10622728C22
hypercenter#1348D11
hypocenterC11#12290
LCSG ▷ C22×C8×C11 ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×C8 ◁ #1348

Complements

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

NH ≅ G/Ntype
2. #13070811C2semidirect
4. #13070106C2semidirect
6. #13066555C2semidirect
7. C11×#1348C2semidirect
103. #1348D11semidirect
250. C11#12290semidirect

Maximal subgroups

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

subgroupindex
#130799692
#130708112
#130707972
#130701062
#130666242
#130665552
C11×#13482
#1229011