Finite Group Databasebeta

← #14684405

Subgroups — #14684405

Order 2816.

1094 conjugacy classes of subgroups.

The subgroup lattice has 318 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C11⋊#401C211yesmaximal, characteristic
2#13066878C211yesmaximal, characteristic
3#13066874C213yesmaximal
4#13066848C213yesmaximal
5#13066848C213yesmaximal
6#13066840C213yesmaximal
7C11×#1444C211yesmaximal, characteristic
8C22×C11×C4⋊C4C2213yes—
9C22×Dic11⋊C4C2211yescharacteristic
10C22×C4×Dic11C2213yes—
11C2×C11×#95C2213yes—
12C2×C11×#95C2211yescharacteristic
13C2×C11⋊#95C2213yes—
14C2×C11⋊#95C2213yes—
15C2×C11⋊#95C2213yes—
16C2×C11⋊#95C2213yes—
17C2×C11⋊#95C2213yes—
18C2×C11⋊#95C2213yes—
19C2×C11⋊#95C2213yes—
20C2×C11⋊#95C2213yes—
21C11⋊#401C418yescomplemented
22C23×C4×C11C2311yescharacteristic
23C23×C4×C11C2313yes—
24C23×C4×C11C2313yes—
25C23×Dic11C2311yescharacteristic
26C23×Dic11C2313yes—
27C23×Dic11C2311yescharacteristic
28C23×Dic11C2313yes—
29C2×C11×C4⋊C4—26no—
30C2×C11×C4⋊C4—26no—
31C2×C11×C4⋊C4—43no—
32C2×Dic11⋊C4—43no—
33C2×C4×Dic11—26no—
34C2×C4×Dic11—43no—
35C2×C4×Dic11—43no—
36C11×#95—43no—
37C11×#95C2×C414yes—
38C11⋊#95—26no—
39C11⋊#95—26no—
40C11⋊#95—26no—
41C11⋊#95—43no—
42C11⋊#95—43no—
43C11⋊#95—43no—
44C11⋊#95C2×C4112yes—
45C11⋊#95C2×C4112yes—
46#14620—111nomaximal, Sylow
47C24×C11C2411yescharacteristic
48C22×C4×C11—23no—
49C22×C4×C11—23no—
50C22×C4×C11—23no—
51C22×C4×C11—23no—
52C22×C4×C11—23no—
53C22×C4×C11—23no—
54C22×C4×C11—23no—
55C22×C4×C11—23no—
56C22×C4×C11—23no—
57C22×C4×C11—23no—
58C22×C4×C11—23no—
59C22×C4×C11—23no—
60C22×C4×C11—23no—
61C22×C4×C11—23no—
62C22×C4×C11—21no—
63C22×C4×C11C22×C416yes—
64C22×C4×C11#4116yes—
65C22×Dic11—23no—
66C22×Dic11—23no—
67C22×Dic11—23no—
68C22×Dic11—23no—
69C22×Dic11—23no—
70C22×Dic11—23no—
71C22×Dic11—23no—
72C22×Dic11—23no—
73C22×Dic11—23no—
74C22×Dic11—23no—
75C22×Dic11—23no—
76C22×Dic11—23no—
77C22×Dic11—23no—
78C22×Dic11—23no—
79C22×Dic11—23no—
80C22×Dic11—23no—
81C22×Dic11—21no—
82C22×Dic11C22×C416yes—
83C22×Dic11C22×C412yes—
84C22×Dic11#4116yes—
85C11×C4⋊C4—412no—
86Dic11⋊C4—44no—
87C4×Dic11—412no—
88C2×#401—111no—
89#1444D1111yescharacteristic
90#1443—111no—
91#1442—113no—
92#1436—113no—
93#1436—113no—
94#1434—113no—
95C23×C11C23×C411yescharacteristic
96C23×C11C2×#4113yes—
97C23×C11C2×#4113yes—
98C23×C11H(5,𝔽2)13yes—
99C23×C11H(5,𝔽2)11yescharacteristic
100C23×C112−1+413yes—
101C23×C112−1+411yescharacteristic
102C2×C4×C11—26no—
103C2×C4×C11—26no—
104C2×C4×C11—26no—
105C2×C4×C11—26no—
106C2×C4×C11—26no—
107C2×C4×C11—26no—
108C2×C4×C11—43no—
109C2×C4×C11—43no—
110C2×C4×C11—43no—
111C2×C4×C11—43no—
112C2×C4×C11—43no—
113C2×C4×C11—43no—
114C2×C4×C11—43no—
115C2×C4×C11—43no—
116C2×C4×C11—43no—
117C2×C4×C11—43no—
118C2×C4×C11—41no—
119C2×Dic11—26no—
120C2×Dic11—26no—
121C2×Dic11—26no—
122C2×Dic11—26no—
123C2×Dic11—26no—
124C2×Dic11—26no—
125C2×Dic11—26no—
126C2×Dic11—43no—
127C2×Dic11—43no—
128C2×Dic11—43no—
129C2×Dic11—43no—
130C2×Dic11—43no—
131C2×Dic11—43no—
132C2×Dic11—43no—
133C2×Dic11—41no—
134C2×Dic11—43no—
135C2×Dic11—43no—
136C2×Dic11—43no—
137C2×Dic11—43no—
138C2×Dic11—41no—
139C22×C4⋊C4—111no—
140C22×C4⋊C4C2×D1113yes—
141C22×C42—113no—
142#401—118no—
143C2×#95—113no—
144C2×#95—113no—
145C2×#95—113no—
146C2×#95—113no—
147C2×#95—113no—
148C2×#95—113no—
149C2×#95—113no—
150C2×#95—113no—
151C2×#95C2×D1113yes—
152C2×#95C2×D1111yescharacteristic
153C22×C11C4×#4113yes—
154C22×C11#52013yes—
155C22×C11#52011yescharacteristic
156C22×C11#53813yes—
157C22×C11#53913yes—
158C22×C11#54113yes—
159C22×C11#54213yes—
160C22×C11#55113yes—
161C22×C11#55213yes—
162C22×C11#55313yes—
163C22×C11#55613yes—
164C22×C11#56011yescharacteristic
165C22×C11#56313yes—
166C4×C11—46no—
167C4×C11—46no—
168C4×C11—81no—
169Dic11—46no—
170Dic11—42no—
171Dic11—46no—
172Dic11—81no—
173C23×C4—111no—
174C23×C4—113no—
175C23×C4—113no—
176C23×C4—111no—
177C23×C4C22×D1111yescharacteristic
178C23×C4C22×D1113yes—
179C23×C4C22×D1113yes—
180C2×C4⋊C4—26no—
181C2×C4⋊C4—26no—
182C2×C4⋊C4—43no—
183C2×C4⋊C4—443no—
184C2×C42—226no—
185C2×C42—443no—
186C2×C42—443no—
187#95—43no—
188#95—1112no—
189#95—1112no—
190#95—226no—
191#95—226no—
192#95—226no—
193#95—443no—
194#95—443no—
195#95—443no—
196#95C4×D1114yes—
197C2×C11#233413yes—
198C2×C11#237313yes—
199C2×C11#238311yescharacteristic
200C2×C11#276011yescharacteristic
201C2×C11#276213yes—
202C2×C11#278713yes—
203C2×C11#280111yescharacteristic
204C24C23×D1111yescharacteristic
205C22×C4—23no—
206C22×C4—23no—
207C22×C4—23no—
208C22×C4—23no—
209C22×C4—23no—
210C22×C4—23no—
211C22×C4—23no—
212C22×C4—23no—
213C22×C4—23no—
214C22×C4—23no—
215C22×C4—23no—
216C22×C4—23no—
217C22×C4—23no—
218C22×C4—21no—
219C22×C4—23no—
220C22×C4—112no—
221C22×C4—116no—
222C22×C4—116no—
223C22×C4—223no—
224C22×C4—223no—
225C22×C4—223no—
226C22×C4—223no—
227C22×C4—223no—
228C22×C4—223no—
229C22×C4—223no—
230C22×C4—223no—
231C22×C4—223no—
232C22×C4—223no—
233C22×C4—223no—
234C22×C4—223no—
235C22×C4—223no—
236C22×C4—223no—
237C22×C4—223no—
238C22×C4—221no—
239C22×C4—223no—
240C22×C4C2×C4×D1116yes—
241C22×C4#434116yes—
242C4⋊C4—412no—
243C4⋊C4—444no—
244C42—4412no—
245C11#1462011yescharacteristic, complemented, Sylow
246C23C22×C4×D1111yescharacteristic
247C23C2×#434113yes—
248C23#6703713yes—
249C23#6704011yescharacteristic
250C23#6704013yes—
251C23#41×D1113yes—
252C23#6704211yescharacteristic
253C2×C4—26no—
254C2×C4—26no—
255C2×C4—26no—
256C2×C4—26no—
257C2×C4—26no—
258C2×C4—26no—
259C2×C4—43no—
260C2×C4—43no—
261C2×C4—43no—
262C2×C4—43no—
263C2×C4—43no—
264C2×C4—43no—
265C2×C4—43no—
266C2×C4—43no—
267C2×C4—41no—
268C2×C4—43no—
269C2×C4—43no—
270C2×C4—226no—
271C2×C4—226no—
272C2×C4—226no—
273C2×C4—226no—
274C2×C4—226no—
275C2×C4—226no—
276C2×C4—226no—
277C2×C4—441no—
278C2×C4—443no—
279C2×C4—443no—
280C2×C4—443no—
281C2×C4—443no—
282C2×C4—443no—
283C2×C4—443no—
284C2×C4—443no—
285C2×C4—443no—
286C2×C4—443no—
287C2×C4—441no—
288C2×C4—443no—
289C2×C4—443no—
290C22#1062303513yes—
291C22C4×#434113yes—
292C22#1062310511yescharacteristic
293C22#1062311813yes—
294C22#1062314813yes—
295C22#1062317013yes—
296C22#1062317113yes—
297C22#1062317213yes—
298C22#1062319213yes—
299C22#1062322313yes—
300C22#1062325111yescharacteristic
301C22#1062326213yes—
302C22#1062326613yes—
303C4—46no—
304C4—46no—
305C4—81no—
306C4—446no—
307C4—446no—
308C4—442no—
309C4—881no—
310C2#1307138413yes—
311C2#1307173113yes—
312C2#1307180911yescharacteristic
313C2#1307599511yescharacteristic
314C2#1307602013yes—
315C2#1307634913yes—
316C2#1307652411yescharacteristic
subgroupG/H
center, FrattiniC24C23×D11
commutatorC23×C11C23×C4
FittingC11×#1444C2
socle, prime radical, cosocleC24×C11C24
hypercenter#1444D11
hypocenterC11#14620
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C24 ◁ #1444

Complements

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

NH ≅ G/Ntype
21. C11⋊#401C4semidirect
245. C11#14620semidirect

Maximal subgroups

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

subgroupindex
C2×C11⋊#4012
#130668782
#130668742
#130668482
#130668402
C11×#14442
#1462011