Finite Group Databasebeta

← #14663411

Subgroups — #14663411

Order 2816.

462 conjugacy classes of subgroups; only the 87 normal subgroups are shown.

normal subgroups only

This group has 462 conjugacy classes of subgroups — too many to draw. Only its 87 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#13073615C211yesmaximal, characteristic
2#13066960C211yesmaximal, characteristic, complemented
3#13066547C214yesmaximal, complemented
4C11×#1461C211yesmaximal, characteristic, complemented
5C2×C4×Q8×C11C2211yescharacteristic
6C2×#67000C412yes—
7C2×#66927C411yescharacteristic
8C11×#431—21no—
9#10622604—21no—
10#10622604—21no—
11#10622601C2212yes—
12#10622552—21no—
13#10622552—21no—
14C4×C4⋊Dic11C411yescharacteristic
15#10622539—21no—
16C11×#324—21no—
17C11×#324C2212yes—
18#10622166—21no—
19#10622166C2212yes—
20C22×Q8×C11C2×C411yescharacteristic
21C22×D44—21no—
22C22×D44—21no—
23C22×D44C2×C412yes—
24C4×Q8×C11—41no—
25C4×Q8×C11—41no—
26C2×C11×C4⋊C4D411yescharacteristic
27C2×C11×C4⋊C4D411yescharacteristic
28C2×C11×C4⋊C4C2311yescharacteristic
29C2×C42×C11C2×C411yescharacteristic
30C2×C42×C11D411yescharacteristic
31C2×C42×C11D411yescharacteristic
32#67000—44no—
33C2×(C2×D11)⋊C4—22no—
34C2×(C2×D11)⋊C4—22no—
35C2×(C2×D11)⋊C4—22no—
36C2×(C2×D11)⋊C4—22no—
37C2×C4⋊Dic11—21no—
38C2×C4×Dic11C2×C412yes—
39#66927—41no—
40#66927—41no—
41C11×C4⋊C8—41no—
42C11×C22⋊C8—22no—
43C4×C8×C11—41no—
44C11⋊#95—21no—
45C22⋊(C11⋊C8)—22no—
46C4⋊(C11⋊C8)—41no—
47#66867—41no—
48#11567—111nomaximal, Sylow
49C23×D11—22no—
50C2×Q8×C11—22no—
51C2×Q8×C11—22no—
52C2×Q8×C11—41no—
53C22×C4×C11C22⋊C411yescharacteristic
54C22×C4×C11C22⋊C411yescharacteristic
55C22×C4×C11C22⋊C411yescharacteristic
56C22×C4×C11C22⋊C411yescharacteristic
57C22×C4×C11C22×C411yescharacteristic
58C22×C4×C11C2×D411yescharacteristic
59C22×C4×C11C2×D411yescharacteristic
60C22×Dic11—22no—
61C2×D44—24no—
62C2×D44—42no—
63C2×D44—42no—
64C2×D44—42no—
65C2×D44—42no—
66C2×D44—42no—
67C2×D44—41no—
68C2×D44—41no—
69C2×D44—82no—
70C2×C8×C11—42no—
71C11×C4⋊C4—41no—
72C11×C4⋊C4—41no—
73C11×C4⋊C4—41no—
74C42×C11—21no—
75C42×C11—21no—
76C42×C11—21no—
77C42×C11—21no—
78C42×C11—21no—
79C42×C11—21no—
80(C2×D11)⋊C4—44no—
81(C2×D11)⋊C4—44no—
82(C2×D11)⋊C4—82no—
83(C2×D11)⋊C4—82no—
84C4⋊Dic11—42no—
85C4×Dic11—42no—
86C2×C11⋊C8—42no—
87#2548—111no—
88#1467—111no—
89#1461D1111yescharacteristic, complemented
90#1318—114no—
91C23×C11C2×C22⋊C411yescharacteristic
92C22×D11—42no—
93C22×D11—42no—
94C22×D11—42no—
95C22×D11—42no—
96C22×D11—42no—
97C22×D11—42no—
98C22×D11—42no—
99Q8×C11—44no—
100C2×C4×C11—21no—
101C2×C4×C11—21no—
102C2×C4×C11—21no—
103C2×C4×C11—21no—
104C2×C4×C11—22no—
105C2×C4×C11—21no—
106C2×C4×C11—21no—
107C2×C4×C11—21no—
108C2×C4×C11—21no—
109C2×C4×C11—21no—
110C2×C4×C11—21no—
111C2×C4×C11—41no—
112C2×C4×C11—41no—
113C2×C4×C11—41no—
114C2×C4×C11#9911yescharacteristic
115C2×C4×C11#9911yescharacteristic
116C2×C4×C11#10012yes—
117C2×C4×C11#13112yes—
118C2×Dic11—42no—
119C2×Dic11—42no—
120C2×Dic11—42no—
121D44—84no—
122D44—82no—
123D44—84no—
124D44—82no—
125C8×C11—82no—
126C11⋊C8—82no—
127C2×#127—111no—
128C2×#124—112no—
129C2×C4×Q8C2×D1111yescharacteristic
130#432—221no—
131#431—21no—
132#394—221no—
133#394—221no—
134#390—112no—
135#390—221no—
136#390—221no—
137C4×C4⋊C4—111no—
138#324—21no—
139#324—112no—
140#324—221no—
141#324C2×D1112yes—
142C22×C11—21no—
143C22×C11—21no—
144C22×C11#40811yescharacteristic
145C22×C11C2×#9911yescharacteristic
146C22×C11C2×#10011yescharacteristic
147C2×D11—82no—
148C2×D11—82no—
149C2×D11—82no—
150C2×D11—82no—
151C2×D11—82no—
152C2×D11—82no—
153C2×D11—82no—
154C4×C11—21no—
155C4×C11—22no—
156C4×C11—22no—
157C4×C11—41no—
158C4×C11—41no—
159C4×C11—41no—
160C4×C11—41no—
161C4×C11#35512yes—
162Dic11—82no—
163C22×Q8C4×D1111yescharacteristic
164C22×D4—112no—
165C22×D4—221no—
166C22×D4—221no—
167#127—441no—
168#127—441no—
169#124—444no—
170C4×Q8—41no—
171C4×Q8—41no—
172C2×C4⋊C4—221no—
173C2×C4⋊C4D4411yescharacteristic
174C2×C4⋊C4C22⋊D1111yescharacteristic
175C2×C4⋊C4C22×D1111yescharacteristic
176C2×C22⋊C4—222no—
177C2×C22⋊C4—222no—
178C2×C22⋊C4—222no—
179C2×C22⋊C4—222no—
180C2×C42—112no—
181C2×C42C4×D1111yescharacteristic
182C2×C42D4411yescharacteristic
183C2×C42C22⋊D1111yescharacteristic
184C4⋊C8—41no—
185C4⋊C8—441no—
186C22⋊C8—22no—
187C22⋊C8—222no—
188#97—441no—
189C4×C8—41no—
190#95—221no—
191C2×C11—21no—
192C2×C11—21no—
193C2×C11#147111yescharacteristic
194C2×C11#212811yescharacteristic
195C2×C11C2×#35511yescharacteristic
196D11—162no—
197C24—222no—
198C2×Q8—22no—
199C2×Q8—22no—
200C2×Q8—41no—
201C2×D4—224no—
202C2×D4—442no—
203C2×D4—442no—
204C2×D4—442no—
205C2×D4—442no—
206C2×D4—442no—
207C2×D4—441no—
208C2×D4—441no—
209C2×D4—882no—
210C22×C4—222no—
211C22×C4(C2×D11)⋊C411yescharacteristic
212C22×C4(C2×D11)⋊C411yescharacteristic
213C22×C4(C2×D11)⋊C411yescharacteristic
214C22×C4(C2×D11)⋊C411yescharacteristic
215C22×C4C2×C4×D1111yescharacteristic
216C22×C4C2×D4411yescharacteristic
217C22×C4C2×C22⋊D1111yescharacteristic
218C2×C8—42no—
219C2×C8—442no—
220C4⋊C4—41no—
221C4⋊C4—41no—
222C4⋊C4—41no—
223C4⋊C4—442no—
224C22⋊C4—444no—
225C22⋊C4—444no—
226C22⋊C4—882no—
227C22⋊C4—882no—
228C42—21no—
229C42—21no—
230C42—21no—
231C42—21no—
232C42—21no—
233C42—21no—
234C42—442no—
235C11#1156711yescharacteristic, complemented, Sylow
236C23—442no—
237C23—442no—
238C23—442no—
239C23—442no—
240C23—442no—
241C23—442no—
242C23—442no—
243C23C2×(C2×D11)⋊C411yescharacteristic
244Q8—44no—
245D4—884no—
246D4—882no—
247D4—884no—
248D4—882no—
249C2×C4—21no—
250C2×C4—21no—
251C2×C4—21no—
252C2×C4—21no—
253C2×C4—22no—
254C2×C4—21no—
255C2×C4—21no—
256C2×C4—21no—
257C2×C4—21no—
258C2×C4—21no—
259C2×C4—21no—
260C2×C4—41no—
261C2×C4—41no—
262C2×C4—41no—
263C2×C4—442no—
264C2×C4—442no—
265C2×C4—442no—
266C2×C4#6687011yescharacteristic
267C2×C4#6687011yescharacteristic
268C2×C4#6688712yes—
269C2×C4#6695412yes—
270C8—82no—
271C8—882no—
272C22—21no—
273C22—21no—
274C22—882no—
275C22—882no—
276C22—882no—
277C22—882no—
278C22—882no—
279C22—882no—
280C22—882no—
281C22C2×#6687011yescharacteristic
282C22#1062272311yescharacteristic
283C22C2×#6688711yescharacteristic
284C4—21no—
285C4—22no—
286C4—22no—
287C4—41no—
288C4—41no—
289C4—41no—
290C4—41no—
291C4—882no—
292C4#1062211512yes—
293C2—21no—
294C2—21no—
295C2—1762no—
296C2#1306697511yescharacteristic
297C2#1307028711yescharacteristic
298C2C2×#1062211511yescharacteristic
subgroupG/H
centerC22C2×#66870
commutatorC22×C4×C11C22×C4
FrattiniC2×C4⋊C4C22×D11
FittingC11×#1461C2
socleC22×C11C2×#99
prime radicalC2×#66927C4
cosocleC2×C11×C4⋊C4C23
hypercenter#1461D11
hypocenterC11#11567
LCSG ▷ C22×C4×C11 ▷ C22×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×C4×Q8 ◁ #1461

Complements

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

NH ≅ G/Ntype
2. #13066960C2semidirect
3. #13066547C2semidirect
4. C11×#1461C2semidirect
89. #1461D11semidirect
235. C11#11567semidirect

Maximal subgroups

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

subgroupindex
#130736152
#130669602
#130665472
C11×#14612
#1156711