Finite Group Databasebeta

← #14644151

Subgroups — #14644151

Order 2816.

562 conjugacy classes of subgroups.

The subgroup lattice has 362 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13077249C211yesmaximal, characteristic
2#13071014C211yesmaximal, characteristic
3#13066525C214yesmaximal
4C11×#2920C211yesmaximal, characteristic
5C22×C42×C11C2211yescharacteristic
6C11×#432—21no—
7C11×#432C412yescomplemented
8C11×#431—21no—
9C11×#431C412yescomplemented
10C11×#423—21no—
11C11×#407C2212yes—
12C4×C11×M16—21no—
13#10622825C412yes—
14#10622824C2212yes—
15C4×C22⋊Dic11C412yes—
16#10622820C2212yes—
17#10622550—21no—
18#10622549—21no—
19C4×C4⋊Dic11—21no—
20#10622545—21no—
21#10622539—21no—
22#10622539C412yescomplemented
23#10622538—21no—
24#10622538C412yescomplemented
25#10622537—21no—
26C4×#4318—21no—
27C23×C4×C11C2×C411yescharacteristic
28C23×C4×C11C2×C411yescharacteristic
29C23×C4×C11C2311yescharacteristic
30C2×C11×M16—22no—
31C2×C42×C11C2×C411yescharacteristic
32C2×C42×C11C2×C411yescharacteristic
33C2×C42×C11C2×C411yescharacteristic
34C2×C42×C11C2×C411yescharacteristic
35C2×C42×C11D411yescharacteristic
36C2×C42×C11D411yescharacteristic
37C2×C42×C11D411yescharacteristic
38C2×C42×C11D411yescharacteristic
39C2×C42×C11D411yescharacteristic
40C2×C42×C11D411yescharacteristic
41C2×C42×C11Q811yescharacteristic
42C2×C42×C11Q811yescharacteristic
43C2×C22⋊Dic11C2×C414yes—
44C2×C4⋊Dic11—22no—
45C2×C4×Dic11—22no—
46C2×#4318—22no—
47C11×C4⋊C8—22no—
48C11×C4⋊C8—22no—
49C11×C22⋊C8—22no—
50C11×C22⋊C8C2×C414yes—
51C11×#97—22no—
52C4×C8×C11—22no—
53C11⋊#95—22no—
54C11⋊#95—22no—
55C11⋊#95—22no—
56C11⋊#95—22no—
57C22⋊(C11⋊C8)—22no—
58C22⋊(C11⋊C8)C2×C414yes—
59C4⋊(C11⋊C8)—22no—
60C4⋊(C11⋊C8)—22no—
61#66867—22no—
62C4×C11⋊C8—22no—
63#8116—111nomaximal, Sylow
64C24×C11C22×C411yescharacteristic
65C22×C4×C11—42no—
66C22×C4×C11—42no—
67C22×C4×C11—42no—
68C22×C4×C11C4211yescharacteristic
69C22×C4×C11C4211yescharacteristic
70C22×C4×C11C4211yescharacteristic
71C22×C4×C11C4211yescharacteristic
72C22×C4×C11C22⋊C411yescharacteristic
73C22×C4×C11C22⋊C411yescharacteristic
74C22×C4×C11C22⋊C411yescharacteristic
75C22×C4×C11C22⋊C411yescharacteristic
76C22×C4×C11C4⋊C411yescharacteristic
77C22×C4×C11C4⋊C411yescharacteristic
78C22×C4×C11C4⋊C411yescharacteristic
79C22×C4×C11C4⋊C411yescharacteristic
80C22×C4×C11C22×C411yescharacteristic
81C22×C4×C11C22×C411yescharacteristic
82C22×C4×C11C2×D411yescharacteristic
83C22×C4×C11C2×D411yescharacteristic
84C22×C4×C11C2×D411yescharacteristic
85C22×C4×C11C2×Q811yescharacteristic
86C22×Dic11—24no—
87C11×M16—44no—
88C2×C8×C11—24no—
89C42×C11C22⋊C411yescharacteristic
90C42×C11C22⋊C411yescharacteristic
91C42×C11C22⋊C411yescharacteristic
92C42×C11C22⋊C411yescharacteristic
93C42×C11C22⋊C411yescharacteristic
94C42×C11C22⋊C411yescharacteristic
95C42×C11C22⋊C411yescharacteristic
96C42×C11C22⋊C411yescharacteristic
97C42×C11C4⋊C411yescharacteristic
98C42×C11C4⋊C411yescharacteristic
99C42×C11C4⋊C411yescharacteristic
100C42×C11C4⋊C411yescharacteristic
101C42×C11C4⋊C411yescharacteristic
102C42×C11C4⋊C411yescharacteristic
103C42×C11C4⋊C411yescharacteristic
104C42×C11C4⋊C411yescharacteristic
105C22⋊Dic11—44no—
106C4⋊Dic11—44no—
107C4×Dic11—44no—
108#4318—44no—
109C2×C11⋊C8—24no—
110#2920—111no—
111#2920D1111yescharacteristic
112#2283—111no—
113#1306—114no—
114C23×C11—22no—
115C23×C11—41no—
116C23×C11—41no—
117C23×C11C2×C4211yescharacteristic
118C23×C11C2×C22⋊C411yescharacteristic
119C23×C11C2×C4⋊C411yescharacteristic
120C2×C4×C11—22no—
121C2×C4×C11—22no—
122C2×C4×C11—22no—
123C2×C4×C11—22no—
124C2×C4×C11—22no—
125C2×C4×C11—22no—
126C2×C4×C11—22no—
127C2×C4×C11—22no—
128C2×C4×C11—41no—
129C2×C4×C11—41no—
130C2×C4×C11—41no—
131C2×C4×C11—41no—
132C2×C4×C11—41no—
133C2×C4×C11—41no—
134C2×C4×C11—41no—
135C2×C4×C11—41no—
136C2×C4×C11—41no—
137C2×C4×C11—41no—
138C2×C4×C11#9511yescharacteristic
139C2×C4×C11#9511yescharacteristic
140C2×C4×C11#9511yescharacteristic
141C2×C4×C11#9511yescharacteristic
142C2×C4×C11#9511yescharacteristic
143C2×C4×C11#9511yescharacteristic
144C2×C4×C11#9511yescharacteristic
145C2×C4×C11#9511yescharacteristic
146C2×C4×C11C2×C22⋊C411yescharacteristic
147C2×C4×C11C2×C22⋊C411yescharacteristic
148C2×C4×C11C2×C4⋊C411yescharacteristic
149C2×C4×C11C2×C4⋊C411yescharacteristic
150C2×Dic11—44no—
151C2×Dic11—44no—
152C2×Dic11—44no—
153C8×C11—44no—
154C11⋊C8—44no—
155C22×C42C2×D1111yescharacteristic
156#432—21no—
157#432—112no—
158#432—221no—
159#432Dic1112yescomplemented
160#431—21no—
161#431—112no—
162#431—221no—
163#431Dic1112yescomplemented
164#423—21no—
165#423—221no—
166#407—112no—
167#407C2×D1112yes—
168C4×M16—21no—
169C4×M16—221no—
170#383—221no—
171#382—221no—
172#381—112no—
173#380—112no—
174C4×C4⋊C4—221no—
175C4×C22⋊C4—112no—
176#376—221no—
177C22×C11—21no—
178C22×C11—21no—
179C22×C11—21no—
180C22×C11—21no—
181C22×C11—21no—
182C22×C11—21no—
183C22×C11—21no—
184C22×C11—21no—
185C22×C11—44no—
186C22×C11C2×#9511yescharacteristic
187C22×C11#41012yes—
188C4×C11—21no—
189C4×C11—21no—
190C4×C11—21no—
191C4×C11—21no—
192C4×C11—21no—
193C4×C11—21no—
194C4×C11—21no—
195C4×C11—21no—
196C4×C11—21no—
197C4×C11—21no—
198C4×C11#34412yes—
199C4×C11#34412yes—
200Dic11—84no—
201C23×C4C4×D1111yescharacteristic
202C23×C4C4×D1111yescharacteristic
203C23×C4C22×D1111yescharacteristic
204C2×M16—22no—
205C2×M16—222no—
206C2×C4⋊C4—222no—
207C2×C22⋊C4—114no—
208C2×C42—222no—
209C2×C42Dic2211yescharacteristic
210C2×C42Dic2211yescharacteristic
211C2×C42C4×D1111yescharacteristic
212C2×C42C4×D1111yescharacteristic
213C2×C42D4411yescharacteristic
214C2×C42D4411yescharacteristic
215C2×C42C2×Dic1111yescharacteristic
216C2×C42C2×Dic1111yescharacteristic
217C2×C42C22⋊D1111yescharacteristic
218C2×C42C22⋊D1111yescharacteristic
219C2×C42C22⋊D1111yescharacteristic
220C2×C42C22⋊D1111yescharacteristic
221C4⋊C8—22no—
222C4⋊C8—22no—
223C4⋊C8—222no—
224C4⋊C8—222no—
225C22⋊C8—22no—
226C22⋊C8—114no—
227C22⋊C8—222no—
228C22⋊C8C2×Dic1114yes—
229#97—22no—
230#97—222no—
231C4×C8—22no—
232C4×C8—222no—
233#95—222no—
234#95—222no—
235#95—222no—
236#95—222no—
237C2×C11—22no—
238C2×C11—41no—
239C2×C11—41no—
240C2×C11#174011yescharacteristic
241C2×C11C2×#34411yescharacteristic
242C2×C11C2×#34411yescharacteristic
243C24C2×C4×D1111yescharacteristic
244C22×C4—42no—
245C22×C4—42no—
246C22×C4—42no—
247C22×C4—224no—
248C22×C4C4×Dic1111yescharacteristic
249C22×C4C4×Dic1111yescharacteristic
250C22×C4C4×Dic1111yescharacteristic
251C22×C4C4×Dic1111yescharacteristic
252C22×C4Dic11⋊C411yescharacteristic
253C22×C4Dic11⋊C411yescharacteristic
254C22×C4Dic11⋊C411yescharacteristic
255C22×C4Dic11⋊C411yescharacteristic
256C22×C4(C2×D11)⋊C411yescharacteristic
257C22×C4(C2×D11)⋊C411yescharacteristic
258C22×C4(C2×D11)⋊C411yescharacteristic
259C22×C4(C2×D11)⋊C411yescharacteristic
260C22×C4C2×Dic2211yescharacteristic
261C22×C4C2×C4×D1111yescharacteristic
262C22×C4C2×D4411yescharacteristic
263C22×C4C22×Dic1111yescharacteristic
264C22×C4C2×C22⋊D1111yescharacteristic
265C22×C4C2×C22⋊D1111yescharacteristic
266M16—44no—
267M16—444no—
268C2×C8—24no—
269C2×C8—224no—
270C4⋊C4—444no—
271C22⋊C4—444no—
272C42—444no—
273C42Dic11⋊C411yescharacteristic
274C42Dic11⋊C411yescharacteristic
275C42Dic11⋊C411yescharacteristic
276C42Dic11⋊C411yescharacteristic
277C42C4⋊Dic1111yescharacteristic
278C42C4⋊Dic1111yescharacteristic
279C42C4⋊Dic1111yescharacteristic
280C42C4⋊Dic1111yescharacteristic
281C42(C2×D11)⋊C411yescharacteristic
282C42(C2×D11)⋊C411yescharacteristic
283C42(C2×D11)⋊C411yescharacteristic
284C42(C2×D11)⋊C411yescharacteristic
285C42C22⋊Dic1111yescharacteristic
286C42C22⋊Dic1111yescharacteristic
287C42C22⋊Dic1111yescharacteristic
288C42C22⋊Dic1111yescharacteristic
289C11#811611yescharacteristic, complemented, Sylow
290C23—22no—
291C23—41no—
292C23—41no—
293C23C2×C4×Dic1111yescharacteristic
294C23C2×Dic11⋊C411yescharacteristic
295C23C2×(C2×D11)⋊C411yescharacteristic
296C2×C4—22no—
297C2×C4—22no—
298C2×C4—22no—
299C2×C4—22no—
300C2×C4—22no—
301C2×C4—22no—
302C2×C4—22no—
303C2×C4—22no—
304C2×C4—41no—
305C2×C4—41no—
306C2×C4—41no—
307C2×C4—41no—
308C2×C4—41no—
309C2×C4—41no—
310C2×C4—41no—
311C2×C4—41no—
312C2×C4—41no—
313C2×C4—41no—
314C2×C4—444no—
315C2×C4—444no—
316C2×C4—444no—
317C2×C4C11⋊#9511yescharacteristic
318C2×C4C11⋊#9511yescharacteristic
319C2×C4C11⋊#9511yescharacteristic
320C2×C4C11⋊#9511yescharacteristic
321C2×C4C11⋊#9511yescharacteristic
322C2×C4C11⋊#9511yescharacteristic
323C2×C4C11⋊#9511yescharacteristic
324C2×C4C11⋊#9511yescharacteristic
325C2×C4C2×Dic11⋊C411yescharacteristic
326C2×C4C2×C4⋊Dic1111yescharacteristic
327C2×C4C2×(C2×D11)⋊C411yescharacteristic
328C2×C4C2×C22⋊Dic1111yescharacteristic
329C8—44no—
330C8—444no—
331C22—21no—
332C22—21no—
333C22—21no—
334C22—21no—
335C22—21no—
336C22—21no—
337C22—21no—
338C22—21no—
339C22—44no—
340C22#1062261912yes—
341C22C2×C11⋊#9511yescharacteristic
342C4—21no—
343C4—21no—
344C4—21no—
345C4—21no—
346C4—21no—
347C4—21no—
348C4—21no—
349C4—21no—
350C4—21no—
351C4—21no—
352C4—884no—
353C4#1062219412yes—
354C4#1062219712yes—
355C2—22no—
356C2—41no—
357C2—41no—
358C2#1306834811yescharacteristic
359C2C2×#1062219411yescharacteristic
360C2C2×#1062219711yescharacteristic
subgroupG/H
centerC22C2×C11⋊#95
commutatorC23×C11C2×C42
FrattiniC23×C4C22×D11
FittingC11×#2920C2
socleC22×C11C2×#95
prime radicalC24×C11C22×C4
cosocleC23×C4×C11C23
hypercenter#2920D11
hypocenterC11#8116
LCSG ▷ C23×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C22×C42 ◁ #2920

Complements

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

NH ≅ G/Ntype
7. C11×#432C4semidirect
9. C11×#431C4semidirect
22. #10622539C4semidirect
24. #10622538C4semidirect
159. #432Dic11semidirect
163. #431Dic11semidirect
289. C11#8116semidirect

Maximal subgroups

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

subgroupindex
#130772492
#130710142
#130665252
C11×#29202
#811611