Finite Group Databasebeta

← D11×#2916 #15617467

Subgroups — D11×#2916 #15617467

Order 2816.

2586 conjugacy classes of subgroups.

The subgroup lattice has 386 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1D11×#568C212yesmaximal
2C2×D11×#131C211yesmaximal, characteristic
3#13077227C211yesmaximal, characteristic, complemented
4#13077226C216yesmaximal, complemented
5#13077225C212yesmaximal, complemented
6#13077224C216yesmaximal, complemented
7D11×#430C216yesmaximal, complemented
8C2×D11×#108C216yesmaximal, complemented
9C11×#2916C211yesmaximal, characteristic, complemented
10C2×#41×D11C2211yescharacteristic
11C11×#568C2212yes—
12C2×C11×#131C2211yescharacteristic
13#10623350C2212yes—
14C2×#67001C2211yescharacteristic
15#10623281—28no—
16D11×#131—28no—
17D11×#131C418yes—
18D11×#131C418yes—
19#10623276C22112yes—
20C2×#66960C2213yes—
21C2×M16×D11C22112yes—
22C2×M16×D11C2213yes—
23C2×#66954C2213yes—
24C22×C8×D11C2213yes—
25C11×#430C2216yescomplemented
26C2×C11×#108C2216yescomplemented
27#10622738C2216yescomplemented
28#10622737C22112yescomplemented
29C2×#66886C22112yescomplemented
30C2×#66883C2216yescomplemented
31#10622506C22124yescomplemented
32D11×#108C2214yes—
33D11×#108C22112yes—
34D11×#108C22112yescomplemented
35D11×#108C22112yescomplemented
36C2×C11×#41C2311yescharacteristic
37#41×D11C2×C414yes—
38#41×D11C2×C414yes—
39#41×D11D414yes—
40#41×D11D414yes—
41C2×#4343Q811yescharacteristic
42C2×Q8×D11Q811yescharacteristic
43C2×#4341Q813yes—
44C2×D4×D11Q813yes—
45C2×#4339C2313yes—
46C22×C4×D11C2313yes—
47C11×#131—28no—
48C11×#131C2×C418yes—
49C2×C11×M16C23112yes—
50C2×C11×M16C2313yes—
51C22×C8×C11C2313yes—
52#67001—28no—
53#67001C2×C418yes—
54C2×#4318C23112yes—
55C2×#4318C2313yes—
56C22×C11⋊C8C2313yes—
57#66960—224no—
58#66960C2×C4124yes—
59M16×D11—212no—
60M16×D11—212no—
61M16×D11C2×C4112yes—
62M16×D11C2×C4112yes—
63M16×D11C2318yes—
64M16×D11C23124yes—
65#66954—224no—
66#66954C2×C4124yes—
67C2×#4313—212no—
68C2×#4313C2316yes—
69C2×C8×D11—212no—
70C2×C8×D11C2×C4112yes—
71C2×C8×D11C2×C4112yes—
72C2×C8×D11C2311yescharacteristic
73C2×C8×D11C2313yes—
74C2×C8×D11C2313yes—
75C2×C8×D11C2313yes—
76C11×#108C2314yes—
77C11×#108C23112yes—
78#66886C2318yes—
79#66886C23124yes—
80#66883C2314yes—
81#66883C23112yes—
82C2×#2916—111nomaximal, Sylow
83C23×D11C2×Q813yes—
84C11×#41C22×C414yes—
85C11×#41C2×D414yes—
86C2×Q8×C11C2×Q811yescharacteristic
87C2×D4×C11C2×Q813yes—
88C22×C4×C11C2413yes—
89C2×C22⋊D11C2×Q816yes—
90C22×Dic11C2×Q813yes—
91#4343C4⋊C414yes—
92#4343C4⋊C414yes—
93Q8×D11C4⋊C414yes—
94Q8×D11C4⋊C414yes—
95#4341C4⋊C4112yes—
96#4341C4⋊C4112yes—
97D4×D11C4⋊C4112yes—
98D4×D11C4⋊C4112yes—
99#4339C22×C4112yes—
100#4339C2×D4112yes—
101C2×D44C2×Q813yes—
102C2×C4×D11C22×C416yes—
103C2×C4×D11C22×C416yes—
104C2×C4×D11C2×D416yes—
105C2×C4×D11C2×D416yes—
106C2×C4×D11C2×Q813yes—
107C2×C4×D11C2×Q813yes—
108C2×C4×D11C2411yescharacteristic
109C2×C4×D11C2413yes—
110C2×Dic22C2×Q813yes—
111C11×M16—212no—
112C11×M16C22×C4112yes—
113C11×M16C2418yes—
114C2×C8×C11—212no—
115C2×C8×C11C22×C4112yes—
116C2×C8×C11C2411yescharacteristic
117C2×C8×C11C2413yes—
118#4318—212no—
119#4318C22×C4112yes—
120#4318C2418yes—
121C2×C11⋊C8—212no—
122C2×C11⋊C8C22×C4112yes—
123C2×C11⋊C8C2411yescharacteristic
124C2×C11⋊C8C2413yes—
125#4313—28no—
126#4313—224no—
127#4313C22×C4124yes—
128C8×D11—28no—
129C8×D11—224no—
130C8×D11C22×C412yes—
131C8×D11C22×C412yes—
132C8×D11C22×C4112yes—
133C8×D11C22×C416yes—
134C8×D11C22×C416yes—
135C8×D11C22×C4112yes—
136C2×#568—112no—
137C22×#131—111no—
138#2916—116no—
139#2916—116no—
140#2916—112no—
141#2916—111no—
142#2916D1111yescharacteristic, direct product factor
143C2×#430—116no—
144C22×#108—116no—
145C23×C11C22×Q813yes—
146C22×D11—46no—
147C22×D11C2×C4⋊C416yes—
148C22×D11C2×C4⋊C416yes—
149C22×D11C22×Q811yescharacteristic
150C22×D11C22×Q813yes—
151Q8×C11C2×C4⋊C414yes—
152D4×C11C2×C4⋊C4112yes—
153C2×C4×C11C23×C416yes—
154C2×C4×C11C22×D416yes—
155C2×C4×C11C22×Q813yes—
156C2×C4×C11C2511yescharacteristic
157C22⋊D11C2×C4⋊C4124yes—
158C2×Dic11C2×C4⋊C416yes—
159C2×Dic11C2×C4⋊C416yes—
160C2×Dic11C22×Q813yes—
161C2×Dic11C22×Q811yescharacteristic
162D44C2×C4⋊C4112yes—
163C4×D11C2×C4⋊C416yes—
164C4×D11C2×C4⋊C416yes—
165C4×D11C2×C4⋊C416yes—
166C4×D11C2×C4⋊C416yes—
167C4×D11C23×C411yescharacteristic
168C4×D11C23×C411yescharacteristic
169C4×D11C23×C416yes—
170C4×D11C22×D411yescharacteristic
171C4×D11C22×D416yes—
172C4×D11C22×D411yescharacteristic
173Dic22C2×C4⋊C4112yes—
174C8×C11—28no—
175C8×C11C23×C412yes—
176C8×C11C23×C416yes—
177C11⋊C8—28no—
178C11⋊C8C23×C412yes—
179C11⋊C8C23×C416yes—
180C22×#41—111no—
181#568—112no—
182#568—1112no—
183#568—228no—
184#568C2×D1112yes—
185C2×#131—111no—
186C2×#131—118no—
187C2×#131—118no—
188C2×#131—113no—
189C2×#131—113no—
190C2×#131—228no—
191C2×#131C2×D1111yescharacteristic
192C22×M16—113no—
193C22×M16—1112no—
194C23×C8—113no—
195#430—1112no—
196#430—116no—
197#430—1124no—
198#430C2×D1116yescomplemented
199C2×#108—1112no—
200C2×#108—116no—
201C2×#108—114no—
202C2×#108—1112no—
203C2×#108—1112no—
204C2×#108—1112no—
205C2×#108C2×D1116yescomplemented
206C22×C11—43no—
207C22×C11C22×C4⋊C416yes—
208C22×C11C23×Q811yescharacteristic
209C2×D11—22no—
210C2×D11—212no—
211C2×D11—46no—
212C2×D11—43no—
213C2×D11C22×C4⋊C411yescharacteristic
214C2×D11C22×C4⋊C416yes—
215C2×D11C22×C4⋊C411yescharacteristic
216C4×C11C22×C4⋊C416yes—
217C4×C11C24×C411yescharacteristic
218C4×C11C23×D411yescharacteristic
219Dic11C22×C4⋊C416yes—
220Dic11C22×C4⋊C411yescharacteristic
221Dic11C22×C4⋊C411yescharacteristic
222C2×#41—114no—
223C2×#41—114no—
224C2×#41—114no—
225C2×#41—114no—
226C2×#41—111no—
227C2×#41—113no—
228C2×#41—113no—
229C2×#41C22×D1111yescharacteristic
230C22×Q8—111no—
231C22×D4—113no—
232C23×C4—113no—
233#131—28no—
234#131—118no—
235#131—1124no—
236#131—1124no—
237#131—2224no—
238#131—2224no—
239#131—228no—
240#131C4×D1118yes—
241C2×M16—113no—
242C2×M16—1112no—
243C2×M16—1112no—
244C2×M16—116no—
245C2×M16—1112no—
246C2×M16—118no—
247C2×M16—1124no—
248C2×M16—2212no—
249C2×M16—2212no—
250C2×M16—2212no—
251C2×M16C22×D11112yes—
252C2×M16C22×D1113yes—
253C22×C8—113no—
254C22×C8—1112no—
255C22×C8—1112no—
256C22×C8—111no—
257C22×C8—113no—
258C22×C8—113no—
259C22×C8—113no—
260C22×C8—2212no—
261C22×C8C22×D1113yes—
262#108—118no—
263#108—1124no—
264#108—114no—
265#108—1112no—
266#108C22×D1114yes—
267#108C22×D11112yes—
268C2×C11—21no—
269C2×C11—26no—
270C2×C11C23×C4⋊C411yescharacteristic
271D11—21no—
272D11—26no—
273D11#291612yesdirect product factor
274C24—113no—
275#41—114no—
276#41—114no—
277#41—1112no—
278#41—1112no—
279#41—1112no—
280#41—1112no—
281#41C2×C4×D1114yes—
282#41D4×D1114yes—
283C2×Q8—114no—
284C2×Q8—114no—
285C2×Q8—113no—
286C2×Q8Q8×D1111yescharacteristic
287C2×D4—116no—
288C2×D4—1112no—
289C2×D4—1112no—
290C2×D4—113no—
291C2×D4Q8×D1113yes—
292C22×C4—113no—
293C22×C4—116no—
294C22×C4—116no—
295C22×C4—116no—
296C22×C4—116no—
297C22×C4—113no—
298C22×C4—113no—
299C22×C4—111no—
300C22×C4—113no—
301C22×C4C23×D1113yes—
302M16—212no—
303M16—1112no—
304M16—1124no—
305M16—118no—
306M16—228no—
307M16—2224no—
308M16—2212no—
309M16C2×C4×D11112yes—
310M16C23×D1118yes—
311C2×C8—212no—
312C2×C8—1112no—
313C2×C8—111no—
314C2×C8—113no—
315C2×C8—112no—
316C2×C8—112no—
317C2×C8—116no—
318C2×C8—116no—
319C2×C8—1112no—
320C2×C8—1112no—
321C2×C8—228no—
322C2×C8—2224no—
323C2×C8—2212no—
324C2×C8C2×C4×D11112yes—
325C2×C8C23×D1111yescharacteristic
326C2×C8C23×D1113yes—
327C11C2×#291611yescharacteristic, complemented, Sylow
328C23—116no—
329C23—111no—
330C23—116no—
331C23—113no—
332C23—446no—
333C23C2×Q8×D1113yes—
334Q8—1112no—
335Q8C4⋊C4×D1114yes—
336D4—1124no—
337D4—1112no—
338D4C4⋊C4×D11112yes—
339C2×C4—116no—
340C2×C4—116no—
341C2×C4—111no—
342C2×C4—113no—
343C2×C4—116no—
344C2×C4—116no—
345C2×C4—116no—
346C2×C4—116no—
347C2×C4—111no—
348C2×C4—111no—
349C2×C4—116no—
350C2×C4—111no—
351C2×C4—116no—
352C2×C4—111no—
353C2×C4C22×C4×D1116yes—
354C2×C4C2×D4×D1116yes—
355C2×C4C2×Q8×D1113yes—
356C2×C4C24×D1111yescharacteristic
357C8—28no—
358C8—112no—
359C8—116no—
360C8—228no—
361C8C22×C4×D1112yes—
362C8C22×C4×D1116yes—
363C22—43no—
364C22—111no—
365C22—111no—
366C22—116no—
367C22—222no—
368C22—2212no—
369C22—443no—
370C22—446no—
371C22C2×C4⋊C4×D1116yes—
372C22C22×Q8×D1111yescharacteristic
373C4—111no—
374C4—111no—
375C4—116no—
376C4C2×C4⋊C4×D1116yes—
377C4C23×C4×D1111yescharacteristic
378C4C22×D4×D1111yescharacteristic
379C2—21no—
380C2—26no—
381C2—112no—
382C2—221no—
383C2—226no—
384C2C22×C4⋊C4×D1111yescharacteristic
subgroupG/H
centerC4C22×D4×D11
commutatorC4×C11C24×C4
FrattiniC2×C4C24×D11
FittingC11×#2916C2
socleC2×C11C23×C4⋊C4
prime radicalC2×#41×D11C22
cosocleC2×C4×C11C25
hypercenter#2916D11
hypocenterC11C2×#2916
LCSG ▷ C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C4 ◁ C2×#41 ◁ #2916

Complements

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

NH ≅ G/Ntype
3. #13077227C2semidirect
4. #13077226C2semidirect
5. #13077225C2semidirect
6. #13077224C2semidirect
7. D11×#430C2semidirect
8. C2×D11×#108C2semidirect
9. C11×#2916C2semidirect
25. C11×#430C22semidirect
26. C2×C11×#108C22semidirect
27. #10622738C22semidirect
28. #10622737C22semidirect
29. C2×#66886C22semidirect
30. C2×#66883C22semidirect
31. #10622506C22semidirect
34. D11×#108C22semidirect
35. D11×#108C22semidirect
142. #2916D11direct (N × H)
198. #430C2×D11semidirect
205. C2×#108C2×D11semidirect
273. D11#2916direct (N × H)
327. C11C2×#2916semidirect

Maximal subgroups

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

subgroupindex
D11×#5682
C2×D11×#1312
#130772272
#130772262
#130772252
#130772242
D11×#4302
C2×D11×#1082
C11×#29162
C2×#291611