Finite Group Databasebeta

← #14663389

Subgroups — #14663389

Order 2816.

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

normal subgroups only

This group has 444 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#13072924C211yesmaximal, characteristic
2#13066954C211yesmaximal, characteristic
3#13066545C214yesmaximal, complemented
4C11×#1460C211yesmaximal, characteristic
5C2×C4×D4×C11C2211yescharacteristic
6C2×#66988C412yes—
7C22×C4⋊Dic11C411yescharacteristic
8C11×#431—21no—
9#10622825—21no—
10#10622825C411yescharacteristic
11#10622820—21no—
12#10622596—21no—
13#10622566—21no—
14#10622556C2212yes—
15#10622541—21no—
16C11×#323—21no—
17C11×#323C2212yes—
18#10622166—21no—
19#10622163C2212yes—
20C22×D4×C11C2×C411yescharacteristic
21C23×C4×C11C2×C411yescharacteristic
22C23×C4×C11D411yescharacteristic
23C23×Dic11C2×C412yes—
24C4×D4×C11—41no—
25C4×D4×C11—41no—
26C2×C11×C4⋊C4D411yescharacteristic
27C2×C11×C22⋊C4D411yescharacteristic
28C2×C11×C22⋊C4C2311yescharacteristic
29C2×C42×C11D411yescharacteristic
30C2×C22⋊Dic11—22no—
31C2×C22⋊Dic11C2×C412yes—
32#66988—44no—
33C2×C4⋊Dic11—21no—
34C2×C4⋊Dic11—21no—
35C2×C4⋊Dic11—21no—
36C2×C4⋊Dic11—41no—
37C2×C4⋊Dic11—41no—
38C2×Dic11⋊C4—22no—
39C2×#4318—41no—
40C11×C4⋊C8—41no—
41C11×C22⋊C8—22no—
42C4×C8×C11—41no—
43C11⋊#95—21no—
44C11⋊#95—22no—
45C11⋊#95—22no—
46C22⋊(C11⋊C8)—22no—
47C22⋊(C11⋊C8)—41no—
48#11562—111nomaximal, Sylow
49C24×C11C22⋊C411yescharacteristic
50C24×C11C22×C411yescharacteristic
51C2×D4×C11—22no—
52C2×D4×C11—22no—
53C2×D4×C11—41no—
54C22×C4×C11—21no—
55C22×C4×C11—21no—
56C22×C4×C11—21no—
57C22×C4×C11—21no—
58C22×C4×C11—42no—
59C22×C4×C11—42no—
60C22×C4×C11C22⋊C411yescharacteristic
61C22×C4×C11C22⋊C411yescharacteristic
62C22×C4×C11C22⋊C411yescharacteristic
63C22×C4×C11C2×D411yescharacteristic
64C22×C4×C11C2×D411yescharacteristic
65C22×Dic11—22no—
66C22×Dic11—22no—
67C22×Dic11—24no—
68C22×Dic11—42no—
69C22×Dic11—42no—
70C2×C8×C11—42no—
71C11×C4⋊C4—41no—
72C11×C22⋊C4—41no—
73C11×C22⋊C4—41no—
74C42×C11—21no—
75C42×C11—21no—
76C22⋊Dic11—42no—
77C22⋊Dic11—44no—
78C4⋊Dic11—42no—
79C4⋊Dic11—42no—
80C4⋊Dic11—41no—
81C4⋊Dic11—41no—
82Dic11⋊C4—44no—
83#4318—82no—
84C2×C11⋊C8—42no—
85#2486—111no—
86#1465—111no—
87#1460D1111yescharacteristic
88#1317—114no—
89C23×C11—21no—
90C23×C11—21no—
91C23×C11—21no—
92C23×C11—21no—
93C23×C11—21no—
94C23×C11—41no—
95C23×C11—41no—
96C23×C11—41no—
97C23×C11—41no—
98C23×C11C2×C22⋊C411yescharacteristic
99C23×C11#13112yes—
100D4×C11—44no—
101C2×C4×C11—21no—
102C2×C4×C11—21no—
103C2×C4×C11—22no—
104C2×C4×C11—21no—
105C2×C4×C11—21no—
106C2×C4×C11—21no—
107C2×C4×C11—42no—
108C2×C4×C11—42no—
109C2×C4×C11—42no—
110C2×C4×C11—41no—
111C2×C4×C11—41no—
112C2×C4×C11—41no—
113C2×C4×C11—81no—
114C2×C4×C11#9911yescharacteristic
115C2×C4×C11#9911yescharacteristic
116C2×C4×C11#10012yes—
117C2×Dic11—42no—
118C2×Dic11—42no—
119C2×Dic11—42no—
120C2×Dic11—42no—
121C2×Dic11—42no—
122C2×Dic11—42no—
123C2×Dic11—84no—
124C8×C11—82no—
125C11⋊C8—82no—
126C2×#123—112no—
127C2×C4×D4C2×D1111yescharacteristic
128C22×C4⋊C4—111no—
129#431—21no—
130#407—221no—
131#398—221no—
132#397—221no—
133#389—221no—
134#381—112no—
135#380—111no—
136#380—221no—
137#324—221no—
138#323—21no—
139#323—112no—
140#323C2×D1112yes—
141C22×C11—21no—
142C22×C11—21no—
143C22×C11—22no—
144C22×C11—42no—
145C22×C11—42no—
146C22×C11—42no—
147C22×C11—41no—
148C22×C11—41no—
149C22×C11—41no—
150C22×C11—41no—
151C22×C11—41no—
152C22×C11—81no—
153C22×C11#40811yescharacteristic
154C22×C11C2×#9911yescharacteristic
155C22×C11C2×#10011yescharacteristic
156C4×C11—21no—
157C4×C11—22no—
158C4×C11—41no—
159C4×C11—41no—
160C4×C11—41no—
161C4×C11#35212yes—
162Dic11—82no—
163Dic11—82no—
164C22×D4C4×D1111yescharacteristic
165C23×C4—112no—
166C23×C4C4×D1111yescharacteristic
167C23×C4D4411yescharacteristic
168C2×M16—441no—
169#123—444no—
170C4×D4—41no—
171C4×D4—41no—
172C2×C4⋊C4—221no—
173C2×C4⋊C4—222no—
174C2×C4⋊C4—221no—
175C2×C4⋊C4—221no—
176C2×C4⋊C4—441no—
177C2×C4⋊C4—441no—
178C2×C4⋊C4D4411yescharacteristic
179C2×C22⋊C4—112no—
180C2×C22⋊C4—222no—
181C2×C22⋊C4C22⋊D1111yescharacteristic
182C2×C22⋊C4C22×D1111yescharacteristic
183C2×C42C22⋊D1111yescharacteristic
184C4⋊C8—41no—
185C22⋊C8—22no—
186C22⋊C8—222no—
187C22⋊C8—441no—
188C4×C8—41no—
189#95—221no—
190#95—222no—
191#95—222no—
192C2×C11—21no—
193C2×C11—21no—
194C2×C11—42no—
195C2×C11—81no—
196C2×C11#147111yescharacteristic
197C2×C11C2×#35211yescharacteristic
198C2×C11#212311yescharacteristic
199C24(C2×D11)⋊C411yescharacteristic
200C24C2×C4×D1111yescharacteristic
201C2×D4—22no—
202C2×D4—22no—
203C2×D4—41no—
204C22×C4—21no—
205C22×C4—21no—
206C22×C4—21no—
207C22×C4—21no—
208C22×C4—42no—
209C22×C4—42no—
210C22×C4—222no—
211C22×C4—222no—
212C22×C4—224no—
213C22×C4—442no—
214C22×C4—442no—
215C22×C4(C2×D11)⋊C411yescharacteristic
216C22×C4(C2×D11)⋊C411yescharacteristic
217C22×C4(C2×D11)⋊C411yescharacteristic
218C22×C4C2×D4411yescharacteristic
219C22×C4C2×C22⋊D1111yescharacteristic
220M16—882no—
221C2×C8—42no—
222C2×C8—442no—
223C4⋊C4—41no—
224C4⋊C4—442no—
225C4⋊C4—442no—
226C4⋊C4—441no—
227C4⋊C4—441no—
228C4⋊C4—444no—
229C22⋊C4—41no—
230C22⋊C4—41no—
231C22⋊C4—444no—
232C22⋊C4—442no—
233C42—21no—
234C42—21no—
235C11#1156211yescharacteristic, complemented, Sylow
236C23—21no—
237C23—21no—
238C23—21no—
239C23—21no—
240C23—21no—
241C23—41no—
242C23—41no—
243C23—41no—
244C23—41no—
245C23#6695412yes—
246C23C2×(C2×D11)⋊C411yescharacteristic
247D4—44no—
248C2×C4—21no—
249C2×C4—21no—
250C2×C4—22no—
251C2×C4—21no—
252C2×C4—21no—
253C2×C4—21no—
254C2×C4—42no—
255C2×C4—42no—
256C2×C4—42no—
257C2×C4—41no—
258C2×C4—41no—
259C2×C4—41no—
260C2×C4—81no—
261C2×C4—442no—
262C2×C4—442no—
263C2×C4—442no—
264C2×C4—442no—
265C2×C4—442no—
266C2×C4—442no—
267C2×C4—884no—
268C2×C4#6687011yescharacteristic
269C2×C4#6687011yescharacteristic
270C2×C4#6688712yes—
271C8—82no—
272C8—882no—
273C22—21no—
274C22—21no—
275C22—22no—
276C22—42no—
277C22—42no—
278C22—42no—
279C22—41no—
280C22—41no—
281C22—41no—
282C22—41no—
283C22—41no—
284C22—81no—
285C22C2×#6687011yescharacteristic
286C22#1062272311yescharacteristic
287C22C2×#6688711yescharacteristic
288C4—21no—
289C4—22no—
290C4—41no—
291C4—41no—
292C4—41no—
293C4—882no—
294C4—882no—
295C4#1062211412yes—
296C2—21no—
297C2—21no—
298C2—42no—
299C2—81no—
300C2#1306697511yescharacteristic
301C2C2×#1062211411yescharacteristic
302C2#1307026911yescharacteristic
subgroupG/H
centerC22C2×#66870
commutatorC24×C11C22×C4
FrattiniC2×C22⋊C4C22×D11
FittingC11×#1460C2
socleC22×C11C2×#99
prime radicalC22×D4×C11C2×C4
cosocleC2×C11×C22⋊C4C23
hypercenter#1460D11
hypocenterC11#11562
LCSG ▷ C24×C11 ▷ C22×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×C4×D4 ◁ #1460

Complements

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

NH ≅ G/Ntype
3. #13066545C2semidirect
235. C11#11562semidirect

Maximal subgroups

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

subgroupindex
#130729242
#130669542
#130665452
C11×#14602
#1156211