Finite Group Databasebeta

← #14651485

Subgroups — #14651485

Order 2816.

536 conjugacy classes of subgroups; only the 103 normal subgroups are shown.

normal subgroups only

This group has 536 conjugacy classes of subgroups — too many to draw. Only its 103 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#13077701C211yesmaximal, characteristic, complemented
2#13073615C211yesmaximal, characteristic
3#13067329C212yesmaximal
4#13066471C212yesmaximal, complemented
5C11×#1467C211yesmaximal, characteristic, complemented
6C2×C4×Q8×C11C2211yescharacteristic
7C2×#67000C412yes—
8C2×#66927C2211yescharacteristic
9C11×#432C2212yes—
10#10622637—24no—
11#10622604—21no—
12#10622604—21no—
13#10622601C412yes—
14#10622552—21no—
15#10622552—21no—
16C4×C4⋊Dic11C2211yescharacteristic
17#10622539—21no—
18#10622539C2212yes—
19#10622538—21no—
20C11×#324—21no—
21C11×#324—21no—
22#10622123—24no—
23C22×Q8×C11C2×C411yescharacteristic
24C22×D44—21no—
25C22×D44—21no—
26C22×D44C2×C412yes—
27C4×Q8×C11—22no—
28C4×Q8×C11—22no—
29C2×C11×C4⋊C4C2×C411yescharacteristic
30C2×C11×C4⋊C4D411yescharacteristic
31C2×C11×C4⋊C4D411yescharacteristic
32C2×C42×C11D411yescharacteristic
33C2×C42×C11D411yescharacteristic
34C2×C42×C11C2311yescharacteristic
35#67000—44no—
36C2×(C2×D11)⋊C4—22no—
37C2×(C2×D11)⋊C4—22no—
38C2×(C2×D11)⋊C4—22no—
39C2×(C2×D11)⋊C4—22no—
40C2×C4⋊Dic11—21no—
41C2×C4×Dic11C2×C412yes—
42#66927—22no—
43#66927—22no—
44C11×C4⋊C8—22no—
45C11×C22⋊C8—22no—
46C11×#97—22no—
47C11⋊#95—21no—
48C22⋊(C11⋊C8)—22no—
49C4⋊(C11⋊C8)—22no—
50C4⋊(C11⋊C8)—22no—
51C4⋊(C11⋊C8)D414yes—
52#66867—22no—
53#66867—22no—
54C4×C11⋊C8—22no—
55#9458—111nomaximal, Sylow
56C23×D11—22no—
57C2×Q8×C11—22no—
58C2×Q8×C11—22no—
59C2×Q8×C11—41no—
60C22×C4×C11C22⋊C411yescharacteristic
61C22×C4×C11C22⋊C411yescharacteristic
62C22×C4×C11C22⋊C411yescharacteristic
63C22×C4×C11C22⋊C411yescharacteristic
64C22×C4×C11C22×C411yescharacteristic
65C22×C4×C11C2×D411yescharacteristic
66C22×C4×C11C2×D411yescharacteristic
67C22×Dic11—22no—
68C2×D44—24no—
69C2×D44—42no—
70C2×D44—42no—
71C2×D44—42no—
72C2×D44—42no—
73C2×D44—41no—
74C2×D44—42no—
75C2×D44—41no—
76C2×D44—82no—
77C2×C8×C11—42no—
78C11×C4⋊C4—22no—
79C11×C4⋊C4—22no—
80C11×C4⋊C4—22no—
81C42×C11—21no—
82C42×C11—21no—
83C42×C11—21no—
84C42×C11—21no—
85C42×C11C2×D412yes—
86C42×C11#4112yes—
87(C2×D11)⋊C4—44no—
88(C2×D11)⋊C4—44no—
89(C2×D11)⋊C4—82no—
90(C2×D11)⋊C4—82no—
91C4⋊Dic11—42no—
92C4×Dic11—42no—
93C2×C11⋊C8—24no—
94#2983—111no—
95#2548—111no—
96#1555—112no—
97#1467D1111yescharacteristic, complemented
98#1285—112no—
99C23×C11C2×C22⋊C411yescharacteristic
100C22×D11—42no—
101C22×D11—42no—
102C22×D11—42no—
103C22×D11—42no—
104C22×D11—42no—
105C22×D11—42no—
106C22×D11—42no—
107Q8×C11—44no—
108C2×C4×C11—21no—
109C2×C4×C11—21no—
110C2×C4×C11—21no—
111C2×C4×C11—21no—
112C2×C4×C11—22no—
113C2×C4×C11—21no—
114C2×C4×C11—21no—
115C2×C4×C11—21no—
116C2×C4×C11—21no—
117C2×C4×C11—21no—
118C2×C4×C11—41no—
119C2×C4×C11—41no—
120C2×C4×C11—41no—
121C2×C4×C11#10012yes—
122C2×C4×C11C4×D412yes—
123C2×C4×C11#12011yescharacteristic
124C2×C4×C11#12112yes—
125C2×C4×C11#12311yescharacteristic
126C2×Dic11—42no—
127C2×Dic11—42no—
128C2×Dic11—42no—
129D44—84no—
130D44—82no—
131D44—84no—
132D44—82no—
133C8×C11—82no—
134C11⋊C8—44no—
135C2×#127—111no—
136C2×#124—112no—
137C2×C4×Q8C2×D1111yescharacteristic
138#446—224no—
139#432—112no—
140#432—221no—
141#432C2×D1112yes—
142#431—221no—
143#394—221no—
144#394—221no—
145#390—112no—
146#390—221no—
147#390—221no—
148C4×C4⋊C4—111no—
149#331—224no—
150#324—21no—
151#324—21no—
152C22×C11—21no—
153C22×C11—21no—
154C22×C11#38611yescharacteristic
155C22×C11C2×#10011yescharacteristic
156C22×C11#41311yescharacteristic
157C2×D11—82no—
158C2×D11—82no—
159C2×D11—82no—
160C2×D11—82no—
161C2×D11—82no—
162C2×D11—82no—
163C2×D11—82no—
164C4×C11—21no—
165C4×C11—22no—
166C4×C11—22no—
167C4×C11—22no—
168C4×C11—41no—
169C4×C11—41no—
170C4×C11—41no—
171C4×C11#45412yes—
172Dic11—82no—
173C22×Q8C4×D1111yescharacteristic
174C22×D4—112no—
175C22×D4—221no—
176C22×D4—221no—
177#127—222no—
178#127—222no—
179#124—444no—
180C4×Q8—22no—
181C4×Q8—22no—
182C2×C4⋊C4—221no—
183C2×C4⋊C4C4×D1111yescharacteristic
184C2×C4⋊C4C22⋊D1111yescharacteristic
185C2×C4⋊C4C22⋊D1111yescharacteristic
186C2×C22⋊C4—222no—
187C2×C22⋊C4—222no—
188C2×C22⋊C4—222no—
189C2×C22⋊C4—222no—
190C2×C42—112no—
191C2×C42D4411yescharacteristic
192C2×C42D4411yescharacteristic
193C2×C42C22×D1111yescharacteristic
194C4⋊C8—22no—
195C4⋊C8—114no—
196C4⋊C8—222no—
197C4⋊C8—222no—
198C22⋊C8—22no—
199C22⋊C8—222no—
200#97—22no—
201#97—222no—
202#97—222no—
203C4×C8—222no—
204#95—221no—
205C2×C11—21no—
206C2×C11—21no—
207C2×C11#188811yescharacteristic
208C2×C11#190011yescharacteristic
209C2×C11#191011yescharacteristic
210D11—162no—
211C24—222no—
212C2×Q8—22no—
213C2×Q8—22no—
214C2×Q8—41no—
215C2×D4—224no—
216C2×D4—442no—
217C2×D4—442no—
218C2×D4—442no—
219C2×D4—442no—
220C2×D4—441no—
221C2×D4—441no—
222C2×D4—442no—
223C2×D4—882no—
224C22×C4—222no—
225C22×C4(C2×D11)⋊C411yescharacteristic
226C22×C4(C2×D11)⋊C411yescharacteristic
227C22×C4(C2×D11)⋊C411yescharacteristic
228C22×C4(C2×D11)⋊C411yescharacteristic
229C22×C4C2×C4×D1111yescharacteristic
230C22×C4C2×D4411yescharacteristic
231C22×C4C2×C22⋊D1111yescharacteristic
232C2×C8—42no—
233C2×C8—224no—
234C4⋊C4—22no—
235C4⋊C4—22no—
236C4⋊C4—22no—
237C4⋊C4—442no—
238C22⋊C4—444no—
239C22⋊C4—444no—
240C22⋊C4—882no—
241C22⋊C4—882no—
242C42—21no—
243C42—21no—
244C42—21no—
245C42—21no—
246C42—442no—
247C42D4×D1112yes—
248C42#434112yes—
249C11#945811yescharacteristic, complemented, Sylow
250C23—442no—
251C23—442no—
252C23—442no—
253C23—442no—
254C23—442no—
255C23—442no—
256C23—442no—
257C23C2×(C2×D11)⋊C411yescharacteristic
258Q8—44no—
259D4—884no—
260D4—882no—
261D4—884no—
262D4—882no—
263C2×C4—21no—
264C2×C4—21no—
265C2×C4—21no—
266C2×C4—21no—
267C2×C4—22no—
268C2×C4—21no—
269C2×C4—21no—
270C2×C4—21no—
271C2×C4—21no—
272C2×C4—21no—
273C2×C4—41no—
274C2×C4—41no—
275C2×C4—41no—
276C2×C4—442no—
277C2×C4—442no—
278C2×C4—442no—
279C2×C4#6688712yes—
280C2×C4(C22⋊D11)⋊C412yes—
281C2×C4#6693511yescharacteristic
282C2×C4#6693911yescharacteristic
283C2×C4#6699212yes—
284C8—82no—
285C8—444no—
286C22—21no—
287C22—21no—
288C22—882no—
289C22—882no—
290C22—882no—
291C22—882no—
292C22—882no—
293C22—882no—
294C22—882no—
295C22#1062257111yescharacteristic
296C22C2×#6688711yescharacteristic
297C22#1062274511yescharacteristic
298C4—22no—
299C4—22no—
300C4—22no—
301C4—21no—
302C4—41no—
303C4—41no—
304C4—41no—
305C4—882no—
306C4#1062236612yes—
307C2—21no—
308C2—21no—
309C2—1762no—
310C2#1306901711yescharacteristic
311C2#1306907711yescharacteristic
312C2#1306914111yescharacteristic
subgroupG/H
centerC22#10622571
commutatorC22×C4×C11C22×C4
FrattiniC2×C42C22×D11
FittingC11×#1467C2
socleC22×C11#386
prime radicalC2×#66927C22
cosocleC2×C42×C11C23
hypercenter#1467D11
hypocenterC11#9458
LCSG ▷ C22×C4×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1467

Complements

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

NH ≅ G/Ntype
1. #13077701C2semidirect
4. #13066471C2semidirect
5. C11×#1467C2semidirect
97. #1467D11semidirect
249. C11#9458semidirect

Maximal subgroups

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

subgroupindex
#130777012
#130736152
#130673292
#130664712
C11×#14672
#945811