Finite Group Databasebeta

← #14919939

Subgroups — #14919939

Order 2816.

2488 conjugacy classes of subgroups.

The subgroup lattice has 352 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13071790C213yesmaximal, complemented
2#13071691C216yesmaximal, complemented
3#13071600C216yesmaximal, complemented
4#13071431C216yesmaximal, complemented
5#13071277C216yesmaximal, complemented
6#124×Dic11C213yesmaximal, complemented
7C2×C11×H(3,𝔽4)C211yesmaximal, characteristic
8C11×H(3,𝔽4)C4116yescomplemented
9C2×C11×#124C2213yes—
10C2×C11×#124C2216yes—
11C2×C11×#120C2216yes—
12C22×C22⋊Dic11C2216yescomplemented
13C2×Q8×Dic11C2213yescomplemented
14C2×D4×Dic11C2213yes—
15C2×D4×Dic11C2216yes—
16#10622860C2212yescomplemented
17#10622843C2213yescomplemented
18#10622843C2216yescomplemented
19#10622834C2213yes—
20#10622834C2216yes—
21#10622833C2216yes—
22#10622833C2216yes—
23#10622833C2216yes—
24#10622564C2216yescomplemented
25#10622564C2216yescomplemented
26#10622564C2216yescomplemented
27#10622564C2216yescomplemented
28#10622564C2216yescomplemented
29#10622564C2216yescomplemented
30#10622563C2216yescomplemented
31#10622563C2216yescomplemented
32#10622563C2216yescomplemented
33C22⋊C4×Dic11C2216yescomplemented
34C22⋊C4×Dic11C2216yescomplemented
35C22⋊C4×Dic11C2216yescomplemented
36#10622550C2212yescomplemented
37#10622549C2213yescomplemented
38C4×C4⋊Dic11C2216yescomplemented
39C42×Dic11C2211yescharacteristic, complemented
40C25×C11C2312yes—
41C22×Q8×C11C2313yes—
42C22×D4×C11C2313yes—
43C22×D4×C11C2316yes—
44C23×Dic11C2316yes—
45C23×Dic11C2316yes—
46C11×#124C2×C4124yescomplemented
47C11×#124C2×C4148yescomplemented
48C11×#120C2×C4148yescomplemented
49C2×C11×C22⋊C4C2316yes—
50C2×C11×C22⋊C4C2316yes—
51C2×C11×C22⋊C4C2316yes—
52C2×C42×C11C2311yescharacteristic
53C2×C42×C11C2312yes—
54C2×C22⋊Dic11—412no—
55C2×C22⋊Dic11C2316yes—
56C2×C22⋊Dic11C2316yes—
57C2×C22⋊Dic11C2316yes—
58C2×C22⋊Dic11C2316yes—
59C2×C22⋊Dic11C2316yes—
60C2×C22⋊Dic11C2316yes—
61Q8×Dic11—46no—
62D4×Dic11—46no—
63D4×Dic11—412no—
64C2×C4⋊Dic11C2316yes—
65C2×C4⋊Dic11C2316yes—
66C2×C4⋊Dic11C2313yes—
67C2×C4⋊Dic11C2313yes—
68C2×C4×Dic11C2313yes—
69C2×C4×Dic11C2313yes—
70C2×C4×Dic11C2316yes—
71C2×C4×Dic11C2316yes—
72C11⋊#95C2316yes—
73C11⋊#95C2316yes—
74C11⋊#95C2316yes—
75C11⋊#95C2316yes—
76C11⋊#95C2316yes—
77C11⋊#95C2316yes—
78#34529—111nomaximal, Sylow
79C24×C11—46no—
80C24×C11—46no—
81C24×C11C22×C418yes—
82C24×C11C2416yes—
83C2×Q8×C11—43no—
84C2×Q8×C11—43no—
85C2×Q8×C11C22×C4112yes—
86C2×D4×C11—43no—
87C2×D4×C11—46no—
88C2×D4×C11—43no—
89C2×D4×C11—46no—
90C2×D4×C11C22×C4112yes—
91C2×D4×C11C22×C4124yes—
92C22×C4×C11C2413yes—
93C22×C4×C11C2416yes—
94C22×Dic11—212no—
95C22×Dic11—46no—
96C22×Dic11—46no—
97C22×Dic11—46no—
98C22×Dic11—46no—
99C22×Dic11—46no—
100C22×Dic11C2411yescharacteristic
101C22×Dic11C2416yes—
102C22×Dic11C2416yes—
103C22×Dic11C2413yes—
104C11×C22⋊C4C22×C4124yes—
105C11×C22⋊C4C22×C4124yes—
106C11×C22⋊C4C22×C4124yes—
107C42×C11C22×C414yes—
108C42×C11C22×C418yes—
109C22⋊Dic11—212no—
110C22⋊Dic11—212no—
111C22⋊Dic11—46no—
112C22⋊Dic11—46no—
113C22⋊Dic11—46no—
114C22⋊Dic11—46no—
115C4⋊Dic11—212no—
116C4⋊Dic11—46no—
117C4⋊Dic11—43no—
118C4⋊Dic11—43no—
119C4×Dic11—26no—
120C4×Dic11—43no—
121C4×Dic11—46no—
122C4×Dic11—46no—
123C2×H(3,𝔽4)D1111yescharacteristic
124#2379—113no—
125#2367—116no—
126#2358—116no—
127#2337—116no—
128#2321—116no—
129C4×#124—113no—
130C23×C11—26no—
131C23×C11—26no—
132C23×C11—26no—
133C23×C11—26no—
134C23×C11—26no—
135C23×C11—26no—
136C23×C11—424no—
137C23×C11—812no—
138C23×C11—84no—
139C23×C11C23×C4112yes—
140C23×C11C2511yescharacteristic
141Q8×C11—412no—
142D4×C11—412no—
143D4×C11—424no—
144C2×C4×C11—23no—
145C2×C4×C11—26no—
146C2×C4×C11—23no—
147C2×C4×C11—26no—
148C2×C4×C11C23×C416yes—
149C2×C4×C11C23×C4112yes—
150C2×Dic11—23no—
151C2×Dic11—23no—
152C2×Dic11—26no—
153C2×Dic11—26no—
154C2×Dic11—26no—
155C2×Dic11—26no—
156C2×Dic11—23no—
157C2×Dic11—26no—
158C2×Dic11—26no—
159C2×Dic11—812no—
160C2×Dic11—812no—
161C2×Dic11H(5,𝔽2)16yes—
162H(3,𝔽4)Dic11116yescomplemented
163C2×#124C2×D1116yes—
164C2×#124C2×D1113yes—
165C2×#120C2×D1116yes—
166C2×C4×Q8—113no—
167C2×C4×D4—116no—
168C2×C4×D4—113no—
169C22×C22⋊C4—116no—
170#391—113no—
171#391—116no—
172#390—113no—
173#390—116no—
174#388—116no—
175#388—116no—
176#388—116no—
177#388—116no—
178#388—116no—
179#388—116no—
180#386—116no—
181#386—116no—
182#386—116no—
183#385—116no—
184#385—116no—
185#385—116no—
186#383—112no—
187#382—113no—
188#379—112no—
189C4×C4⋊C4—116no—
190C4×C22⋊C4—116no—
191C4×C22⋊C4—116no—
192C4×C22⋊C4—116no—
193C43—111no—
194C22×C11—212no—
195C22×C11—212no—
196C22×C11—212no—
197C22×C11—46no—
198C22×C11—46no—
199C22×C11—46no—
200C22×C11—46no—
201C22×C11—816no—
202C22×C11C24×C411yescharacteristic
203C22×C11C2×H(5,𝔽2)13yes—
204C22×C11#58513yes—
205C4×C11—26no—
206C4×C11—212no—
207Dic11—26no—
208Dic11—46no—
209Dic11—46no—
210Dic11—41no—
211C25C22×D1112yes—
212C22×Q8C22×D1113yes—
213C22×D4C22×D1116yes—
214C22×D4C22×D1113yes—
215C23×C4—116no—
216C23×C4—116no—
217#124C2×Dic11148yescomplemented
218#124C2×Dic11124yescomplemented
219#120C2×Dic11148yescomplemented
220C4×Q8—446no—
221C4×D4—446no—
222C4×D4—4412no—
223C2×C4⋊C4—116no—
224C2×C4⋊C4—113no—
225C2×C4⋊C4—113no—
226C2×C4⋊C4—116no—
227C2×C22⋊C4—116no—
228C2×C22⋊C4—116no—
229C2×C22⋊C4—116no—
230C2×C22⋊C4—116no—
231C2×C22⋊C4—116no—
232C2×C22⋊C4—116no—
233C2×C22⋊C4—4412no—
234C2×C22⋊C4C22×D1116yes—
235C2×C22⋊C4C22×D1116yes—
236C2×C22⋊C4C22×D1116yes—
237C2×C42—113no—
238C2×C42—116no—
239C2×C42—116no—
240C2×C42—113no—
241C2×C42C22×D1111yescharacteristic
242C2×C42C22×D1112yes—
243#95—116no—
244#95—116no—
245#95—116no—
246#95—116no—
247#95—116no—
248#95—116no—
249C2×C11—412no—
250C2×C11C4×H(5,𝔽2)13yes—
251C2×C11#355813yes—
252C2×C11#356811yescharacteristic
253C24—46no—
254C24—46no—
255C24C22×Dic1118yes—
256C24C23×D1116yes—
257C2×Q8—43no—
258C2×Q8—43no—
259C2×Q8C22×Dic11112yes—
260C2×D4—43no—
261C2×D4—46no—
262C2×D4—43no—
263C2×D4—46no—
264C2×D4C22×Dic11124yes—
265C2×D4C22×Dic11112yes—
266C22×C4—113no—
267C22×C4—111no—
268C22×C4—116no—
269C22×C4—116no—
270C22×C4—2212no—
271C22×C4—446no—
272C22×C4—446no—
273C22×C4—446no—
274C22×C4—446no—
275C22×C4—446no—
276C22×C4C23×D1113yes—
277C22×C4C23×D1116yes—
278C4⋊C4—2212no—
279C4⋊C4—443no—
280C4⋊C4—443no—
281C4⋊C4—446no—
282C22⋊C4—2212no—
283C22⋊C4—2212no—
284C22⋊C4—446no—
285C22⋊C4—446no—
286C22⋊C4—446no—
287C22⋊C4—446no—
288C22⋊C4C22×Dic11124yes—
289C22⋊C4C22×Dic11124yes—
290C22⋊C4C22×Dic11124yes—
291C42—226no—
292C42—446no—
293C42—446no—
294C42—443no—
295C42C22×Dic1114yes—
296C42C22×Dic1118yes—
297C11#3452911yescharacteristic, complemented, Sylow
298C23—26no—
299C23—26no—
300C23—26no—
301C23—26no—
302C23—26no—
303C23—26no—
304C23—424no—
305C23—84no—
306C23—812no—
307C23C23×Dic11112yes—
308C23C24×D1111yescharacteristic
309Q8—412no—
310D4—412no—
311D4—424no—
312C2×C4—23no—
313C2×C4—26no—
314C2×C4—23no—
315C2×C4—26no—
316C2×C4—116no—
317C2×C4—223no—
318C2×C4—223no—
319C2×C4—226no—
320C2×C4—226no—
321C2×C4—226no—
322C2×C4—226no—
323C2×C4—223no—
324C2×C4—226no—
325C2×C4—226no—
326C2×C4—8812no—
327C2×C4—8812no—
328C2×C4C23×Dic1116yes—
329C2×C4C23×Dic11112yes—
330C22—212no—
331C22—212no—
332C22—212no—
333C22—46no—
334C22—46no—
335C22—46no—
336C22—46no—
337C22—816no—
338C22D11×H(5,𝔽2)13yes—
339C22#1062345513yes—
340C22C24×Dic1111yescharacteristic
341C4—26no—
342C4—212no—
343C4—226no—
344C4—441no—
345C4—446no—
346C4—446no—
347C2—412no—
348C2H(5,𝔽2)×Dic1113yes—
349C2#1308312913yes—
350C2#1308331011yescharacteristic
subgroupG/H
center, FrattiniC23C24×D11
commutatorC22×C11C24×C4
Fitting, prime radicalC2×C11×H(3,𝔽4)C2
socle, cosocleC23×C11C25
hypercenterC2×H(3,𝔽4)D11
hypocenterC11#34529
LCSG ▷ C22×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×H(3,𝔽4)

Complements

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

NH ≅ G/Ntype
1. #13071790C2semidirect
2. #13071691C2semidirect
3. #13071600C2semidirect
4. #13071431C2semidirect
5. #13071277C2semidirect
6. #124×Dic11C2semidirect
8. C11×H(3,𝔽4)C4semidirect
12. C22×C22⋊Dic11C22semidirect
13. C2×Q8×Dic11C22semidirect
16. #10622860C22semidirect
17. #10622843C22semidirect
18. #10622843C22semidirect
24. #10622564C22semidirect
25. #10622564C22semidirect
26. #10622564C22semidirect
27. #10622564C22semidirect
28. #10622564C22semidirect
29. #10622564C22semidirect
30. #10622563C22semidirect
31. #10622563C22semidirect
32. #10622563C22semidirect
33. C22⋊C4×Dic11C22semidirect
34. C22⋊C4×Dic11C22semidirect
35. C22⋊C4×Dic11C22semidirect
36. #10622550C22semidirect
37. #10622549C22semidirect
38. C4×C4⋊Dic11C22semidirect
39. C42×Dic11C22semidirect
46. C11×#124C2×C4semidirect
47. C11×#124C2×C4semidirect
48. C11×#120C2×C4semidirect
162. H(3,𝔽4)Dic11semidirect
217. #124C2×Dic11semidirect
218. #124C2×Dic11semidirect
219. #120C2×Dic11semidirect
297. C11#34529semidirect

Maximal subgroups

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

subgroupindex
#130717902
#130716912
#130716002
#130714312
#130712772
#124×Dic112
C2×C11×H(3,𝔽4)2
#3452911