Finite Group Databasebeta

← #14680784

Subgroups — #14680784

Order 2816.

1590 conjugacy classes of subgroups.

The subgroup lattice has 340 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622290C211yesmaximal, characteristic
2C2×#10622541C213yesmaximal, complemented
3C2×#10622553C213yesmaximal
4#13066883C213yesmaximal, complemented
5#13066881C211yesmaximal, characteristic, complemented
6#13066862C213yesmaximal
7C4×C11×#95C211yesmaximal, characteristic, complemented
8C22×C42×C11C2213yes—
9C22×(C2×D11)⋊C4C2211yescharacteristic
10C22×(C2×D11)⋊C4C2213yes—
11C22×(C2×D11)⋊C4C2213yes—
12C22×C4⋊Dic11C2213yes—
13C22×C4⋊Dic11C2213yes—
14C22×Dic11⋊C4C2213yes—
15C2×C11×#95C2213yes—
16C2×C11×#95C2211yescharacteristic
17C2×C11⋊#95C2216yes—
18C2×C11⋊#95C2213yes—
19C2×C11⋊#95C2213yes—
20#10622553—212no—
21#10622541—212no—
22#10622290C418yescomplemented
23C24×D11C2311yescharacteristic
24C23×C4×C11C2313yes—
25C23×C4×C11C2313yes—
26C23×C4×C11C2311yescharacteristic
27C23×Dic11C2313yes—
28C23×Dic11C2311yescharacteristic
29C23×Dic11C2313yes—
30C2×C42×C11—46no—
31C2×C42×C11D4112yes—
32C2×(C2×D11)⋊C4—26no—
33C2×(C2×D11)⋊C4—26no—
34C2×(C2×D11)⋊C4—26no—
35C2×(C2×D11)⋊C4—26no—
36C2×(C2×D11)⋊C4—46no—
37C2×(C2×D11)⋊C4C2×C4112yes—
38C2×C4⋊Dic11—26no—
39C2×C4⋊Dic11—26no—
40C2×C4⋊Dic11—26no—
41C2×C4⋊Dic11—46no—
42C2×C4⋊Dic11C2×C4112yes—
43C2×Dic11⋊C4—212no—
44C2×Dic11⋊C4—26no—
45C11×#95—26no—
46C11×#95C2×C414yes—
47C11⋊#95—212no—
48C11⋊#95—26no—
49C11⋊#95—26no—
50#14322—111nomaximal, Sylow
51C24×C11C2411yescharacteristic
52C23×D11—23no—
53C23×D11—23no—
54C23×D11—23no—
55C23×D11—21no—
56C23×D11—21no—
57C23×D11—23no—
58C23×D11C22×C412yes—
59C22×C4×C11—26no—
60C22×C4×C11—23no—
61C22×C4×C11—26no—
62C22×C4×C11—21no—
63C22×C4×C11—26no—
64C22×C4×C11—26no—
65C22×C4×C11—23no—
66C22×C4×C11—23no—
67C22×C4×C11C22×C416yes—
68C22×C4×C11C2×D416yes—
69C22×C4×C11C2×D416yes—
70C22×C4×C11C2×D416yes—
71C22×C4×C11#4116yes—
72C22×Dic11—26no—
73C22×Dic11—23no—
74C22×Dic11—23no—
75C22×Dic11—26no—
76C22×Dic11—23no—
77C22×Dic11—26no—
78C22×Dic11—23no—
79C22×Dic11—23no—
80C22×Dic11—26no—
81C22×Dic11—23no—
82C22×Dic11—21no—
83C22×Dic11—23no—
84C22×Dic11C22×C416yes—
85C42×C11—412no—
86(C2×D11)⋊C4—224no—
87(C2×D11)⋊C4—412no—
88(C2×D11)⋊C4—44no—
89C4⋊Dic11—224no—
90C4⋊Dic11—412no—
91Dic11⋊C4—412no—
92C2×#399—111no—
93C2×#389—113no—
94C2×#388—113no—
95#1445—113no—
96#1444—111no—
97#1439—113no—
98C4×#95D1111yescharacteristic, complemented
99C23×C11C23×C411yescharacteristic
100C23×C11C22×D413yes—
101C23×C11C2×#4113yes—
102C23×C11H(5,𝔽2)13yes—
103C23×C112−1+411yescharacteristic
104C23×C112−1+411yescharacteristic
105C23×C112−1+413yes—
106C22×D11—26no—
107C22×D11—22no—
108C22×D11—26no—
109C22×D11—41no—
110C22×D11—43no—
111C22×D11—43no—
112C22×D11—43no—
113C22×D11—43no—
114C22×D11—43no—
115C22×D11—46no—
116C22×D11—43no—
117C22×D11—43no—
118C2×C4×C11—212no—
119C2×C4×C11—26no—
120C2×C4×C11—26no—
121C2×C4×C11—26no—
122C2×C4×C11—26no—
123C2×C4×C11—212no—
124C2×C4×C11—26no—
125C2×C4×C11—26no—
126C2×C4×C11—26no—
127C2×C4×C11—46no—
128C2×C4×C11—46no—
129C2×C4×C11C4×D4112yes—
130C2×C4×C11#12714yes—
131C2×Dic11—212no—
132C2×Dic11—26no—
133C2×Dic11—43no—
134C2×Dic11—46no—
135C2×Dic11—43no—
136C2×Dic11—43no—
137C2×Dic11—41no—
138C2×Dic11—46no—
139C2×Dic11—43no—
140C2×Dic11—43no—
141C2×Dic11—43no—
142C2×Dic11—46no—
143C2×Dic11—43no—
144C22×C4⋊C4—113no—
145C22×C4⋊C4—113no—
146C22×C4⋊C4—113no—
147C22×C22⋊C4—113no—
148C22×C22⋊C4—111no—
149C22×C22⋊C4—113no—
150C22×C42C2×D1113yes—
151#399—118no—
152#389—2212no—
153#388—2212no—
154C2×#95—116no—
155C2×#95—113no—
156C2×#95—113no—
157C2×#95C2×D1113yes—
158C2×#95C2×D1111yescharacteristic
159C22×C11C2×C4×D413yes—
160C22×C11#51911yescharacteristic
161C22×C11#52013yes—
162C22×C11C2×#12711yescharacteristic
163C22×C11#53213yes—
164C22×C11#53413yes—
165C22×C11#53613yes—
166C22×C11#53613yes—
167C22×C11#53713yes—
168C22×C11#53916yes—
169C22×C11#54113yes—
170C22×C11#54213yes—
171C2×D11—42no—
172C2×D11—46no—
173C2×D11—46no—
174C2×D11—81no—
175C2×D11—81no—
176C2×D11—83no—
177C2×D11—83no—
178C4×C11—212no—
179C4×C11—24no—
180C4×C11—46no—
181Dic11—46no—
182Dic11—83no—
183Dic11—81no—
184C25—111no—
185C23×C4—113no—
186C23×C4—113no—
187C23×C4—111no—
188C23×C4C22×D1113yes—
189C23×C4C22×D1113yes—
190C23×C4C22×D1111yescharacteristic
191C2×C4⋊C4—1112no—
192C2×C4⋊C4—226no—
193C2×C4⋊C4—226no—
194C2×C4⋊C4—226no—
195C2×C4⋊C4—2212no—
196C2×C4⋊C4—226no—
197C2×C4⋊C4—446no—
198C2×C22⋊C4—1112no—
199C2×C22⋊C4—226no—
200C2×C22⋊C4—226no—
201C2×C22⋊C4—226no—
202C2×C22⋊C4—226no—
203C2×C22⋊C4—446no—
204C2×C42—46no—
205C2×C42D44112yes—
206#95—26no—
207#95—226no—
208#95—226no—
209#95—2212no—
210#95C4×D1114yes—
211C2×C11C4×#12711yescharacteristic
212C2×C11#232213yes—
213C2×C11#232313yes—
214C2×C11#265611yescharacteristic
215C2×C11#265811yescharacteristic
216C2×C11#266313yes—
217C2×C11#266413yes—
218D11—82no—
219C24—112no—
220C24—223no—
221C24—223no—
222C24—223no—
223C24—221no—
224C24—223no—
225C24—221no—
226C24C23×D1111yescharacteristic
227C22×C4—23no—
228C22×C4—26no—
229C22×C4—21no—
230C22×C4—26no—
231C22×C4—26no—
232C22×C4—26no—
233C22×C4—23no—
234C22×C4—23no—
235C22×C4—116no—
236C22×C4—223no—
237C22×C4—226no—
238C22×C4—223no—
239C22×C4—226no—
240C22×C4—223no—
241C22×C4—223no—
242C22×C4—226no—
243C22×C4—226no—
244C22×C4—223no—
245C22×C4—223no—
246C22×C4—223no—
247C22×C4—221no—
248C22×C4C2×C4×D1116yes—
249C22×C4C2×D4416yes—
250C22×C4C2×D4416yes—
251C22×C4C2×D4416yes—
252C22×C4#433916yes—
253C4⋊C4—2224no—
254C4⋊C4—4412no—
255C4⋊C4—4412no—
256C22⋊C4—2224no—
257C22⋊C4—4412no—
258C22⋊C4—444no—
259C42—412no—
260C11#1432211yescharacteristic, complemented, Sylow
261C23—226no—
262C23—226no—
263C23—222no—
264C23—441no—
265C23—443no—
266C23—443no—
267C23—443no—
268C23—443no—
269C23—443no—
270C23—443no—
271C23—446no—
272C23—443no—
273C23C22×C4×D1111yescharacteristic
274C23C22×D4413yes—
275C23C2×#433913yes—
276C23#6703713yes—
277C23#6704011yescharacteristic
278C23#6704313yes—
279C23#6704311yescharacteristic
280C2×C4—26no—
281C2×C4—26no—
282C2×C4—26no—
283C2×C4—26no—
284C2×C4—212no—
285C2×C4—212no—
286C2×C4—26no—
287C2×C4—26no—
288C2×C4—26no—
289C2×C4—46no—
290C2×C4—46no—
291C2×C4—226no—
292C2×C4—2212no—
293C2×C4—443no—
294C2×C4—443no—
295C2×C4—446no—
296C2×C4—441no—
297C2×C4—443no—
298C2×C4—443no—
299C2×C4—446no—
300C2×C4—443no—
301C2×C4—446no—
302C2×C4—443no—
303C2×C4—443no—
304C2×C4C4×D44112yes—
305C2×C4#6692714yes—
306C22—442no—
307C22—446no—
308C22—446no—
309C22—881no—
310C22—881no—
311C22—883no—
312C22—883no—
313C22C2×C4×D4413yes—
314C22C2×#6692711yescharacteristic
315C22#1062300813yes—
316C22#1062302413yes—
317C22#1062304113yes—
318C22#1062305713yes—
319C22#1062305713yes—
320C22#1062307713yes—
321C22#1062309213yes—
322C22#1062309516yes—
323C22#1062310311yescharacteristic
324C22#1062311413yes—
325C4—24no—
326C4—212no—
327C4—46no—
328C4—446no—
329C4—883no—
330C4—881no—
331C2—882no—
332C2C4×#6692711yescharacteristic
333C2#1307128713yes—
334C2#1307129913yes—
335C2#1307471811yescharacteristic
336C2#1307472611yescharacteristic
337C2#1307476413yes—
338C2#1307477513yes—
subgroupG/H
center, FrattiniC24C23×D11
commutatorC23×C11C23×C4
FittingC4×C11×#95C2
socle, cosocleC24×C11C24
prime radicalC24×D11C23
hypercenterC4×#95D11
hypocenterC11#14322
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C24 ◁ C4×#95

Complements

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

NH ≅ G/Ntype
2. C2×#10622541C2semidirect
4. #13066883C2semidirect
5. #13066881C2semidirect
7. C4×C11×#95C2semidirect
22. #10622290C4semidirect
98. C4×#95D11semidirect
260. C11#14322semidirect

Maximal subgroups

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

subgroupindex
C2×#106222902
C2×#106225412
C2×#106225532
#130668832
#130668812
#130668622
C4×C11×#952
#1432211