Finite Group Databasebeta

← #14664730

Subgroups — #14664730

Order 2816.

336 conjugacy classes of subgroups; only the 99 normal subgroups are shown.

normal subgroups only

This group has 336 conjugacy classes of subgroups — too many to draw. Only its 99 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#13079186C211yesmaximal, characteristic
2#13070419C211yesmaximal, characteristic, complemented
3#13066627C212yesmaximal, complemented
4#13066624C212yesmaximal
5C11×#1834C211yesmaximal, characteristic, complemented
6#10623010—21no—
7C2×C4×C8×C11C2211yescharacteristic
8C11×#384—21no—
9#10622729C2211yescharacteristic
10#10622728C2211yescharacteristic
11#10622727—21no—
12C4×Dic44C411yescharacteristic, complemented
13#10622310—21no—
14#10622309C411yescharacteristic, complemented
15C4×D88C411yescharacteristic, complemented
16C4×#4314—21no—
17#10622296C411yescharacteristic, complemented
18C11×#340—21no—
19C11×#340C2212yes—
20C22⋊(C11⋊C16)C2212yes—
21C4⋊(C11⋊C16)—21no—
22#10622099—21no—
23C22×C8×C11D411yescharacteristic
24C22×C8×C11C2311yescharacteristic
25C2×C11×C4⋊C4—22no—
26C2×C11×C4⋊C4—41no—
27C2×C11×C4⋊C4—41no—
28C2×C42×C11D411yescharacteristic
29#66983—21no—
30#66982—41no—
31C4×C22⋊D11—41no—
32#66977—21no—
33C2×Dic44C2×C411yescharacteristic
34C2×D88C2×C411yescharacteristic
35C2×#4314—21no—
36#66929—41no—
37#66928—21no—
38C4×D44—21no—
39#66925—41no—
40#66923—21no—
41C4×Dic22—21no—
42C4×C8×C11C2×C411yescharacteristic
43C4×C8×C11C2×C411yescharacteristic
44C4×C8×C11D411yescharacteristic
45C4×C8×C11D411yescharacteristic
46#66885—21no—
47#66885—21no—
48#66882C2×C411yescharacteristic
49#66882C2×C411yescharacteristic
50#66881—21no—
51#66880—21no—
52#66880—21no—
53C2×C11⋊C16—22no—
54#11860—111nomaximal, Sylow
55C22×C4×C11—42no—
56C22×C4×C11D811yescharacteristic
57C22×C4×C11D811yescharacteristic
58C22×C4×C11C2×D411yescharacteristic
59C2×C22⋊D11—41no—
60C2×D44—21no—
61C2×C4×D11—41no—
62C2×Dic22—21no—
63C2×C8×C11—41no—
64C2×C8×C11—41no—
65C2×C8×C11C22⋊C411yescharacteristic
66C2×C8×C11C22⋊C411yescharacteristic
67C2×C8×C11C22×C411yescharacteristic
68C2×C8×C11C2×D411yescharacteristic
69C11×C4⋊C4—42no—
70C11×C4⋊C4—42no—
71C11×C4⋊C4—82no—
72C11×C4⋊C4—82no—
73C42×C11C22⋊C411yescharacteristic
74C42×C11C22⋊C411yescharacteristic
75C42×C11SD1611yescharacteristic
76C42×C11SD1611yescharacteristic
77C22⋊Dic11—41no—
78(C2×D11)⋊C4—41no—
79(C2×D11)⋊C4—41no—
80(C2×D11)⋊C4—41no—
81(C2×D11)⋊C4—41no—
82C4⋊Dic11—21no—
83C4⋊Dic11—21no—
84Dic11⋊C4—41no—
85Dic11⋊C4—41no—
86Dic11⋊C4—41no—
87Dic11⋊C4—41no—
88C4×Dic11—41no—
89Dic44—41no—
90D88—41no—
91#4314—42no—
92C11⋊C16—42no—
93#3168—111no—
94#2163—111no—
95#1834D1111yescharacteristic, complemented
96#1348—112no—
97#1347—112no—
98C23×C11C2×D811yescharacteristic
99C22×D11—41no—
100C2×C4×C11—21no—
101C2×C4×C11—21no—
102C2×C4×C11—22no—
103C2×C4×C11—21no—
104C2×C4×C11—21no—
105C2×C4×C11—82no—
106C2×C4×C11—82no—
107C2×C4×C11—82no—
108C2×C4×C11#10211yescharacteristic
109C2×C4×C11#10211yescharacteristic
110C2×C4×C11#10211yescharacteristic
111C2×C4×C11#10211yescharacteristic
112C2×C4×C11C2×C22⋊C411yescharacteristic
113C2×C4×C11C2×SD1611yescharacteristic
114C22⋊D11—81no—
115C22⋊D11—81no—
116C2×Dic11—41no—
117C2×Dic11—41no—
118C2×Dic11—41no—
119D44—41no—
120D44—41no—
121C4×D11—82no—
122Dic22—41no—
123Dic22—41no—
124C8×C11—21no—
125C8×C11—21no—
126C8×C11—21no—
127C8×C11—21no—
128#529—221no—
129#499—111no—
130#495—111no—
131#488—221no—
132#467—111no—
133#466—111no—
134#465—221no—
135C4×Q16—111no—
136C4×SD16—221no—
137C4×D8—111no—
138C2×C4×C8C2×D1111yescharacteristic
139#384—21no—
140C4⋊C16—221no—
141C22⋊C16—112no—
142#346—221no—
143#340—21no—
144#340C2×D1112yes—
145C22×C11—21no—
146C22×C11—21no—
147C22×C11C2×#10211yescharacteristic
148C22×C11#50911yescharacteristic
149C22×C11#51011yescharacteristic
150C2×D11—81no—
151C2×D11—81no—
152C2×D11—81no—
153C4×C11—21no—
154C4×C11—21no—
155C4×C11—21no—
156C4×C11—21no—
157C4×C11—162no—
158C4×C11#36012yes—
159C4×C11#41011yescharacteristic
160C4×C11#42111yescharacteristic
161Dic11—81no—
162Dic11—81no—
163Dic11—81no—
164C2×Q16—111no—
165C2×SD16—221no—
166C2×D8—111no—
167C22×C8C22⋊D1111yescharacteristic
168C22×C8C22×D1111yescharacteristic
169#126—441no—
170#125—221no—
171#124—221no—
172#123—441no—
173C22⋊Q8—221no—
174#121—221no—
175C4×Q8—221no—
176C4×D4—221no—
177C4×D4—441no—
178#117—441no—
179C2×C4⋊C4—22no—
180C2×C4⋊C4—41no—
181C2×C4⋊C4—41no—
182C2×C42C22⋊D1111yescharacteristic
183C2×C16—222no—
184#107—111no—
185#107—111no—
186#106—221no—
187#103—221no—
188#103—221no—
189#102—221no—
190#102—221no—
191C4×C8C4×D1111yescharacteristic
192C4×C8C4×D1111yescharacteristic
193C4×C8D4411yescharacteristic
194C4×C8D4411yescharacteristic
195C2×C11—21no—
196C2×C11—21no—
197C2×C11#151711yescharacteristic
198C2×C11#213911yescharacteristic
199C2×C11C2×#36011yescharacteristic
200D11—161no—
201C2×Q8—221no—
202C2×D4—221no—
203C2×D4—441no—
204C22×C4—42no—
205C22×C4—441no—
206C22×C4#432311yescharacteristic
207C22×C4#432311yescharacteristic
208C22×C4C2×C22⋊D1111yescharacteristic
209Q16—441no—
210SD16—442no—
211D8—441no—
212C2×C8—41no—
213C2×C8—41no—
214C2×C8(C2×D11)⋊C411yescharacteristic
215C2×C8(C2×D11)⋊C411yescharacteristic
216C2×C8C2×C4×D1111yescharacteristic
217C2×C8C2×D4411yescharacteristic
218C4⋊C4—42no—
219C4⋊C4—42no—
220C4⋊C4—82no—
221C4⋊C4—82no—
222C4⋊C4—221no—
223C4⋊C4—221no—
224C4⋊C4—441no—
225C4⋊C4—441no—
226C4⋊C4—441no—
227C4⋊C4—441no—
228C22⋊C4—441no—
229C22⋊C4—441no—
230C22⋊C4—441no—
231C22⋊C4—441no—
232C22⋊C4—441no—
233C42—441no—
234C42(C2×D11)⋊C411yescharacteristic
235C42(C2×D11)⋊C411yescharacteristic
236C42#432511yescharacteristic
237C42#432511yescharacteristic
238C16—442no—
239C11#1186011yescharacteristic, complemented, Sylow
240C23—441no—
241C23C2×#432311yescharacteristic
242Q8—441no—
243Q8—441no—
244D4—441no—
245D4—441no—
246D4—881no—
247D4—881no—
248C2×C4—21no—
249C2×C4—21no—
250C2×C4—21no—
251C2×C4—21no—
252C2×C4—22no—
253C2×C4—82no—
254C2×C4—82no—
255C2×C4—82no—
256C2×C4—441no—
257C2×C4—441no—
258C2×C4—441no—
259C2×C4—882no—
260C2×C4#6687311yescharacteristic
261C2×C4#6687311yescharacteristic
262C2×C4#6687311yescharacteristic
263C2×C4#6687311yescharacteristic
264C2×C4C2×(C2×D11)⋊C411yescharacteristic
265C2×C4C2×#432511yescharacteristic
266C8—21no—
267C8—21no—
268C8—21no—
269C8—21no—
270C22—21no—
271C22—21no—
272C22—881no—
273C22—881no—
274C22—881no—
275C22C2×#6687311yescharacteristic
276C22#1062276011yescharacteristic
277C22#1062279211yescharacteristic
278C4—21no—
279C4—21no—
280C4—21no—
281C4—21no—
282C4—162no—
283C4—881no—
284C4—881no—
285C4—881no—
286C4#1062212612yes—
287C4#1062261811yescharacteristic
288C4#1062261911yescharacteristic
289C2—21no—
290C2—21no—
291C2—1761no—
292C2#1306717511yescharacteristic
293C2#1307032611yescharacteristic
294C2C2×#1062212611yescharacteristic
subgroupG/H
centerC22C2×#66873
commutatorC2×C8×C11C22×C4
FrattiniC22×C8C22×D11
FittingC11×#1834C2
socleC22×C11C2×#102
prime radical#10622728C22
cosocleC22×C8×C11C23
hypercenter#1834D11
hypocenterC11#11860
LCSG ▷ C2×C8×C11 ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ C2×C4×C8 ◁ #1834

Complements

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

NH ≅ G/Ntype
2. #13070419C2semidirect
3. #13066627C2semidirect
5. C11×#1834C2semidirect
12. C4×Dic44C4semidirect
14. #10622309C4semidirect
15. C4×D88C4semidirect
17. #10622296C4semidirect
95. #1834D11semidirect
239. C11#11860semidirect

Maximal subgroups

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

subgroupindex
#130791862
#130704192
#130666272
#130666242
C11×#18342
#1186011