Finite Group Databasebeta

← #14652263

Subgroups — #14652263

Order 2816.

312 conjugacy classes of subgroups; only the 95 normal subgroups are shown.

normal subgroups only

This group has 312 conjugacy classes of subgroups — too many to draw. Only its 95 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#13067405C211yesmaximal, characteristic, complemented
2#13067067C211yesmaximal, characteristic
3#13067033C211yesmaximal, characteristic
4#13066900C211yesmaximal, characteristic, complemented
5#13066507C211yesmaximal, characteristic, complemented
6#13066452C211yesmaximal, characteristic, complemented
7C11×#1543C211yesmaximal, characteristic
8C11×#532C2211yescharacteristic
9C11×#431C2211yescharacteristic
10C11×#431C2211yescharacteristic
11#10622538C2211yescharacteristic
12#10622537C2211yescharacteristic
13C4×#4318C2211yescharacteristic
14C2×C4×C11⋊C8C2211yescharacteristic
15C11×#333C411yescharacteristic
16C11×#333C411yescharacteristic
17C11×#331C411yescharacteristic
18C11×#331C411yescharacteristic
19D4⋊(C11⋊C8)—21no—
20D4⋊(C11⋊C8)—21no—
21D4⋊(C11⋊C8)—21no—
22D4⋊(C11⋊C8)—21no—
23#10622096—21no—
24#10622095—21no—
25#10622092—21no—
26C8×C11⋊C8—21no—
27C2×C11×#41—21no—
28C11×C4⋊Q8C2×C411yescharacteristic
29C11×#127C2×C411yescharacteristic
30C11×#124—21no—
31C11×#121—21no—
32C11×#121—21no—
33C4×D4×C11—21no—
34C4×D4×C11—21no—
35C2×C42×C11C2311yescharacteristic
36C2×#4318—21no—
37C2×#4318—21no—
38C22×C11⋊C8—21no—
39C11×C4⋊C8C2×C411yescharacteristic
40C11×C4⋊C8C2×C411yescharacteristic
41C11×C4⋊C8C2×C411yescharacteristic
42C11×C4⋊C8C2×C411yescharacteristic
43C11×C22⋊C8—21no—
44C11×C22⋊C8—21no—
45C4×C8×C11—21no—
46C4×C8×C11—21no—
47C22⋊(C11⋊C8)—21no—
48C4⋊(C11⋊C8)—21no—
49C4⋊(C11⋊C8)—21no—
50C4⋊(C11⋊C8)D411yescharacteristic
51C4⋊(C11⋊C8)D411yescharacteristic
52#66867—21no—
53C4×C11⋊C8—21no—
54C4×C11⋊C8—21no—
55C4×C11⋊C8—21no—
56C4×C11⋊C8D411yescharacteristic
57C4×C11⋊C8D411yescharacteristic
58#9586—111nomaximal, Sylow
59C11×#41—81no—
60C11×#41—81no—
61C2×Q8×C11—21no—
62C2×D4×C11—21no—
63C2×D4×C11—21no—
64C2×D4×C11—21no—
65C2×D4×C11—41no—
66C22×C4×C11—41no—
67C22×C4×C11#4111yescharacteristic
68C22×C4×C11#4111yescharacteristic
69C22×C4×C11#4111yescharacteristic
70C2×C8×C11—21no—
71C2×C8×C11—21no—
72C2×C8×C11—21no—
73C2×C8×C11—21no—
74C11×C4⋊C4—21no—
75C11×C4⋊C4—21no—
76C11×C22⋊C4—41no—
77C11×C22⋊C4—41no—
78C42×C11C22×C411yescharacteristic
79C42×C11C2×D411yescharacteristic
80C42×C11C2×D411yescharacteristic
81C42×C11#4111yescharacteristic
82#4318—22no—
83#4318—41no—
84#4318—81no—
85C2×C11⋊C8—22no—
86C2×C11⋊C8—22no—
87C2×C11⋊C8—21no—
88C2×C11⋊C8—21no—
89C2×C11⋊C8—21no—
90C2×C11⋊C8—21no—
91C2×C11⋊C8—41no—
92C2×C11⋊C8—41no—
93#1574—111no—
94#1543D1111yescharacteristic
95#1492—111no—
96#1484—111no—
97#1450—111no—
98#1299—111no—
99#1278—111no—
100C23×C11—41no—
101C23×C11#12611yescharacteristic
102Q8×C11—81no—
103D4×C11—41no—
104D4×C11—41no—
105D4×C11—41no—
106D4×C11—41no—
107D4×C11—81no—
108D4×C11—82no—
109C2×C4×C11—21no—
110C2×C4×C11—21no—
111C2×C4×C11—21no—
112C2×C4×C11—21no—
113C2×C4×C11—21no—
114C2×C4×C11—21no—
115C2×C4×C11—41no—
116C2×C4×C11—81no—
117C2×C4×C11—81no—
118C2×C4×C11#11711yescharacteristic
119C2×C4×C11C4×D411yescharacteristic
120C2×C4×C11C4×D411yescharacteristic
121C2×C4×C11#12111yescharacteristic
122C2×C4×C11#12311yescharacteristic
123C2×C4×C11#12411yescharacteristic
124C8×C11—41no—
125C8×C11—41no—
126C8×C11—41no—
127C8×C11—41no—
128C11⋊C8—22no—
129C11⋊C8—22no—
130C11⋊C8—42no—
131C11⋊C8—41no—
132C11⋊C8—41no—
133C11⋊C8—81no—
134#532C2×D1111yescharacteristic
135#431—111no—
136#431C2×D1111yescharacteristic
137#431C2×D1111yescharacteristic
138#423—111no—
139C4×M16—111no—
140C2×C4×C8—111no—
141#335—221no—
142#334—221no—
143#333Dic1111yescharacteristic
144#333Dic1111yescharacteristic
145#331Dic1111yescharacteristic
146#331Dic1111yescharacteristic
147D4⋊C8—221no—
148D4⋊C8—221no—
149D4⋊C8—221no—
150D4⋊C8—221no—
151#322—221no—
152C82—221no—
153C22×C11—21no—
154C22×C11—21no—
155C22×C11—21no—
156C22×C11—81no—
157C22×C11—81no—
158C22×C11—81no—
159C22×C11#38811yescharacteristic
160C4×C11—21no—
161C4×C11—21no—
162C4×C11—21no—
163C4×C11—81no—
164C4×C11#44311yescharacteristic
165C4×C11#44311yescharacteristic
166C4×C11#44311yescharacteristic
167C4×C11#44411yescharacteristic
168C4×C11#47111yescharacteristic
169C4×C11#47211yescharacteristic
170C2×#41—21no—
171C2×M16—221no—
172C2×M16—221no—
173C22×C8—221no—
174C4⋊Q8C2×Dic1111yescharacteristic
175#127C2×Dic1111yescharacteristic
176#124—21no—
177#121—21no—
178#121—21no—
179C4×D4—21no—
180C4×D4—21no—
181C2×C42C22×D1111yescharacteristic
182C4⋊C8—111no—
183C4⋊C8—111no—
184C4⋊C8—221no—
185C4⋊C8—221no—
186C4⋊C8C2×Dic1111yescharacteristic
187C4⋊C8C2×Dic1111yescharacteristic
188C4⋊C8C2×Dic1111yescharacteristic
189C4⋊C8C2×Dic1111yescharacteristic
190C22⋊C8—21no—
191C22⋊C8—21no—
192C22⋊C8—221no—
193#97—221no—
194C4×C8—21no—
195C4×C8—21no—
196C4×C8—111no—
197C4×C8—111no—
198C4×C8—221no—
199C4×C8—221no—
200C4×C8—221no—
201C2×C11—41no—
202C2×C11—161no—
203C2×C11#192911yescharacteristic
204C2×C11#193111yescharacteristic
205C2×C11#193711yescharacteristic
206#41—81no—
207#41—81no—
208C2×Q8—21no—
209C2×D4—21no—
210C2×D4—21no—
211C2×D4—21no—
212C2×D4—41no—
213C22×C4—41no—
214C22×C4#433911yescharacteristic
215C22×C4#434111yescharacteristic
216C22×C4#434111yescharacteristic
217M16—222no—
218M16—441no—
219M16—881no—
220C2×C8—21no—
221C2×C8—21no—
222C2×C8—21no—
223C2×C8—21no—
224C2×C8—222no—
225C2×C8—222no—
226C2×C8—221no—
227C2×C8—221no—
228C2×C8—221no—
229C2×C8—221no—
230C2×C8—441no—
231C2×C8—441no—
232C4⋊C4—21no—
233C4⋊C4—21no—
234C22⋊C4—41no—
235C22⋊C4—41no—
236C42#433911yescharacteristic
237C42D4×D1111yescharacteristic
238C42D4×D1111yescharacteristic
239C42C22×Dic1111yescharacteristic
240C11#958611yescharacteristic, complemented, Sylow
241C23—41no—
242C23#6693211yescharacteristic
243Q8—81no—
244D4—41no—
245D4—41no—
246D4—41no—
247D4—41no—
248D4—81no—
249D4—82no—
250C2×C4—21no—
251C2×C4—21no—
252C2×C4—21no—
253C2×C4—21no—
254C2×C4—21no—
255C2×C4—21no—
256C2×C4—41no—
257C2×C4—81no—
258C2×C4—81no—
259C2×C4#6693611yescharacteristic
260C2×C4#6693711yescharacteristic
261C2×C4#6693811yescharacteristic
262C2×C4#6697911yescharacteristic
263C2×C4D4×Dic1111yescharacteristic
264C2×C4D4×Dic1111yescharacteristic
265C8—41no—
266C8—41no—
267C8—41no—
268C8—41no—
269C8—222no—
270C8—222no—
271C8—442no—
272C8—441no—
273C8—441no—
274C8—881no—
275C22—21no—
276C22—21no—
277C22—21no—
278C22—81no—
279C22—81no—
280C22—81no—
281C22#1062256411yescharacteristic
282C4—21no—
283C4—21no—
284C4—21no—
285C4—81no—
286C4#1062236111yescharacteristic
287C4#1062236211yescharacteristic
288C4#1062280911yescharacteristic
289C4#1062280911yescharacteristic
290C4#1062280911yescharacteristic
291C4#1062281011yescharacteristic
292C2—41no—
293C2—161no—
294C2#1306926611yescharacteristic
295C2#1306928011yescharacteristic
296C2#1306932211yescharacteristic
subgroupG/H
centerC2×C4#66937
commutatorC42×C11C22×C4
FrattiniC2×C42C22×D11
FittingC11×#1543C2
socleC22×C11#388
prime radicalC11×#532C22
cosocleC2×C42×C11C23
hypercenter#1543D11
hypocenterC11#9586
LCSG ▷ C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #1543

Complements

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

NH ≅ G/Ntype
1. #13067405C2semidirect
4. #13066900C2semidirect
5. #13066507C2semidirect
6. #13066452C2semidirect
240. C11#9586semidirect

Maximal subgroups

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

subgroupindex
#130674052
#130670672
#130670332
#130669002
#130665072
#130664522
C11×#15432
#958611