Finite Group Databasebeta

← D11×#2159 #14906803

Subgroups — D11×#2159 #14906803

Order 2816.

718 conjugacy classes of subgroups.

The subgroup lattice has 418 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×D11×M32C211yesmaximal, characteristic
2D11×#427C211yesmaximal, characteristic
3C2×D11×#107C211yesmaximal, characteristic
4#13070405C211yesmaximal, characteristic, complemented
5#13070404C211yesmaximal, characteristic, complemented
6#13070403C212yesmaximal, complemented
7#13070402C211yesmaximal, characteristic, complemented
8#13070401C212yesmaximal, complemented
9D11×#367C212yesmaximal, complemented
10D11×#366C212yesmaximal, complemented
11C11×#2159C211yesmaximal, characteristic, complemented
12C22×C8×D11C2211yescharacteristic
13D11×#117—21no—
14C2×C4⋊C4×D11—21no—
15C2×C11×M32C2211yescharacteristic
16C11×#427C2211yescharacteristic
17C2×C11×#107C2211yescharacteristic
18#10622719C2211yescharacteristic
19C2×#66882C2211yescharacteristic
20C2×#66876C2211yescharacteristic
21#10622611—21no—
22C2×#66871—21no—
23D11×M32C418yescomplemented
24C2×#66862C2212yes—
25C2×C16×D11C2212yes—
26#10622493C2211yescharacteristic
27#10622493C2211yescharacteristic
28D11×#107—21no—
29D11×#107—21no—
30D11×#107C2211yescharacteristic
31D11×#107C2212yes—
32D11×#107C2211yescharacteristic
33D11×#107C2212yes—
34#10622473—21no—
35D11×#106—21no—
36C11×#367C2212yescomplemented
37C11×#366C2212yescomplemented
38#10622143C2212yescomplemented
39#10622142C2212yescomplemented
40#10622128C2212yescomplemented
41#10622128C2212yescomplemented
42#10622127C2212yescomplemented
43#10622127C2212yescomplemented
44C22×C4×D11—41no—
45C22×C4×D11D411yescharacteristic
46C22×C8×C11C2311yescharacteristic
47C11×#117—21no—
48C2×C11×C4⋊C4—21no—
49#66979—21no—
50C2×C4⋊Dic11—21no—
51C2×Dic11⋊C4—41no—
52C22×C11⋊C8D411yescharacteristic
53C2×C8×D11C2×C414yes—
54C2×C8×D11D411yescharacteristic
55C2×C8×D11D411yescharacteristic
56C2×C8×D11Q814yes—
57C2×C8×D11C2311yescharacteristic
58C2×C8×D11C2311yescharacteristic
59#66945—21no—
60#66945—21no—
61C4⋊C4×D11—21no—
62C4⋊C4×D11—21no—
63C4⋊C4×D11—22no—
64C4⋊C4×D11—22no—
65C4⋊C4×D11—41no—
66C4⋊C4×D11—41no—
67C22⋊C4×D11—41no—
68#66930—41no—
69#66925—41no—
70C42×D11—41no—
71C11×M32C2×C414yescomplemented
72C2×C11×C16C2312yes—
73C11×#107—21no—
74C11×#107C2312yes—
75C11×#107C2311yescharacteristic
76C11×#107C2311yescharacteristic
77C11×#106—21no—
78#66882—21no—
79#66882C2312yes—
80#66882C2311yescharacteristic
81#66882C2311yescharacteristic
82#66881—21no—
83#66876C2×C414yescomplemented
84C2×C11⋊C16C2312yes—
85#66872—21no—
86#66872—21no—
87#66871—21no—
88#66871—21no—
89#66871—22no—
90#66871—22no—
91#66862C2×C418yescomplemented
92C16×D11C2×C418yescomplemented
93C2×#2159—111nomaximal, Sylow
94C23×D11D811yescharacteristic
95C22×C4×C11—41no—
96C22×C4×C11C2×D411yescharacteristic
97C22×Dic11—41no—
98C22×Dic11D811yescharacteristic
99C2×C4×D11—41no—
100C2×C4×D11—41no—
101C2×C4×D11—42no—
102C2×C4×D11—42no—
103C2×C4×D11—84no—
104C2×C4×D11C4⋊C414yes—
105C2×C4×D11D811yescharacteristic
106C2×C4×D11D811yescharacteristic
107C2×C4×D11Q1614yes—
108C2×C4×D11C2×D411yescharacteristic
109C2×C4×D11C2×D411yescharacteristic
110C2×C8×C11C22×C412yes—
111C2×C8×C11C2×D411yescharacteristic
112C2×C8×C11C2×Q812yes—
113C2×C8×C11C2411yescharacteristic
114C11×C4⋊C4—22no—
115C11×C4⋊C4—21no—
116C11×C4⋊C4—21no—
117C11×C4⋊C4—41no—
118C11×C22⋊C4—41no—
119C42×C11—41no—
120C22⋊Dic11—41no—
121(C2×D11)⋊C4—41no—
122(C2×D11)⋊C4—41no—
123C4⋊Dic11—22no—
124C4⋊Dic11—21no—
125C4⋊Dic11—21no—
126C4⋊Dic11—41no—
127Dic11⋊C4—41no—
128Dic11⋊C4—41no—
129Dic11⋊C4—42no—
130Dic11⋊C4—42no—
131C4×Dic11—41no—
132C4×Dic11—41no—
133C4×Dic11—41no—
134C2×C11⋊C8C4⋊C414yes—
135C2×C11⋊C8C2×D411yescharacteristic
136C2×C11⋊C8C2×D411yescharacteristic
137C8×D11C4⋊C414yes—
138C8×D11C4⋊C414yes—
139C8×D11C22×C412yes—
140C8×D11C22×C412yes—
141C8×D11C2×Q812yes—
142C8×D11C2×Q812yes—
143C11×C16C22×C414yescomplemented
144C11⋊C16C22×C414yescomplemented
145C22×M32—111no—
146C2×#427—111no—
147C22×#107—111no—
148#2159—111no—
149#2159—111no—
150#2159—111no—
151#2159—112no—
152#2159—112no—
153#2159D1111yescharacteristic, direct product factor
154C2×#367—112no—
155C2×#366—112no—
156C23×C11C2×D811yescharacteristic
157C22×D11—22no—
158C22×D11—22no—
159C22×D11#10714yes—
160C22×D11C2×D811yescharacteristic
161C22×D11C2×D811yescharacteristic
162C2×C4×C11—41no—
163C2×C4×C11—41no—
164C2×C4×C11—42no—
165C2×C4×C11—82no—
166C2×C4×C11C2×C4⋊C412yes—
167C2×C4×C11C2×D811yescharacteristic
168C2×C4×C11C2×Q1612yes—
169C2×C4×C11C22×D411yescharacteristic
170C2×Dic11—41no—
171C2×Dic11—41no—
172C2×Dic11—42no—
173C2×Dic11—82no—
174C2×Dic11#10714yes—
175C2×Dic11C2×D811yescharacteristic
176C2×Dic11C2×D811yescharacteristic
177C4×D11—84no—
178C4×D11—82no—
179C4×D11—84no—
180C4×D11—82no—
181C4×D11#10714yes—
182C4×D11#10714yes—
183C4×D11C2×C4⋊C412yes—
184C4×D11C2×C4⋊C412yes—
185C4×D11C2×Q1612yes—
186C4×D11C2×Q1612yes—
187C8×C11C2×C4⋊C412yes—
188C8×C11C23×C411yescharacteristic
189C8×C11C22×Q811yescharacteristic
190C11⋊C8C2×C4⋊C412yes—
191C11⋊C8C2×C4⋊C412yes—
192C23×C8—111no—
193C2×#117—221no—
194C22×C4⋊C4—221no—
195C2×M32—111no—
196C2×M32—118no—
197C2×M32—112no—
198C2×M32C2×D1111yescharacteristic
199C22×C16—112no—
200#427—111no—
201#427—111no—
202#427—111no—
203#427—221no—
204#427—221no—
205#427C2×D1111yescharacteristic
206C2×#107—111no—
207C2×#107—112no—
208C2×#107—112no—
209C2×#107—111no—
210C2×#107—111no—
211C2×#107—221no—
212C2×#107—221no—
213C2×#107—221no—
214C2×#107C2×D1111yescharacteristic
215C2×#106—221no—
216#367—112no—
217#367—112no—
218#367—112no—
219#367C2×D1112yescomplemented
220#366—112no—
221#366—112no—
222#366—112no—
223#366C2×D1112yescomplemented
224C22×C11—21no—
225C22×C11—21no—
226C22×C11C2×#10712yes—
227C22×C11C22×D811yescharacteristic
228C2×D11—21no—
229C2×D11—21no—
230C2×D11—28no—
231C2×D11C2×#10712yes—
232C2×D11C2×#10712yes—
233C2×D11#50912yes—
234C2×D11#51012yes—
235C4×C11—82no—
236C4×C11—81no—
237C4×C11—81no—
238C4×C11C2×#10712yes—
239C4×C11C22×C4⋊C411yescharacteristic
240C4×C11C22×Q1611yescharacteristic
241Dic11—82no—
242Dic11—81no—
243Dic11—81no—
244Dic11C2×#10712yes—
245Dic11C2×#10712yes—
246C23×C4—111no—
247C23×C4—441no—
248C22×C8—111no—
249C22×C8—114no—
250C22×C8—111no—
251C22×C8—111no—
252C22×C8—114no—
253C22×C8—111no—
254C22×C8—111no—
255C22×C8C22×D1111yescharacteristic
256#117—21no—
257#117—221no—
258#117—221no—
259#117—221no—
260#117—441no—
261#117—441no—
262C2×C4⋊C4—21no—
263C2×C4⋊C4—222no—
264C2×C4⋊C4—222no—
265C2×C4⋊C4—221no—
266C2×C4⋊C4—221no—
267C2×C4⋊C4—221no—
268C2×C4⋊C4—441no—
269C2×C4⋊C4—441no—
270C2×C4⋊C4—441no—
271C2×C22⋊C4—441no—
272C2×C42—441no—
273M32—114no—
274M32—118no—
275M32C4×D1114yescomplemented
276C2×C16—112no—
277C2×C16—118no—
278C2×C16C22×D1112yes—
279#107—21no—
280#107—111no—
281#107—112no—
282#107—111no—
283#107—222no—
284#107—222no—
285#107—221no—
286#107—221no—
287#107—221no—
288#107C22×D1111yescharacteristic
289#107C22×D1112yes—
290#107C22×D1111yescharacteristic
291#106—21no—
292#106—221no—
293#106—221no—
294#106—221no—
295C2×C11—22no—
296C2×C11C22×#10711yescharacteristic
297C2×C11C2×#50911yescharacteristic
298C2×C11C2×#51011yescharacteristic
299D11—22no—
300D11#215914yesdirect product factor
301C24—111no—
302C22×C4—41no—
303C22×C4—111no—
304C22×C4—114no—
305C22×C4—111no—
306C22×C4—111no—
307C22×C4—114no—
308C22×C4—111no—
309C22×C4—111no—
310C22×C4—441no—
311C22×C4—441no—
312C22×C4—442no—
313C22×C4—442no—
314C22×C4—441no—
315C22×C4—884no—
316C22×C4D4×D1111yescharacteristic
317C2×C8—114no—
318C2×C8—111no—
319C2×C8—111no—
320C2×C8—114no—
321C2×C8—114no—
322C2×C8—112no—
323C2×C8—112no—
324C2×C8—112no—
325C2×C8—112no—
326C2×C8C2×C4×D1112yes—
327C2×C8D4×D1111yescharacteristic
328C2×C8Q8×D1112yes—
329C2×C8C23×D1111yescharacteristic
330C4⋊C4—21no—
331C4⋊C4—21no—
332C4⋊C4—22no—
333C4⋊C4—41no—
334C4⋊C4—221no—
335C4⋊C4—221no—
336C4⋊C4—222no—
337C4⋊C4—442no—
338C4⋊C4—442no—
339C4⋊C4—441no—
340C4⋊C4—441no—
341C4⋊C4—441no—
342C22⋊C4—41no—
343C22⋊C4—441no—
344C22⋊C4—441no—
345C22⋊C4—441no—
346C42—41no—
347C42—441no—
348C42—441no—
349C42—441no—
350C16—114no—
351C16C2×C4×D1114yescomplemented
352C11C2×#215911yescharacteristic, complemented, Sylow
353C23—111no—
354C23—114no—
355C23—111no—
356C23—222no—
357C23—222no—
358C23D8×D1111yescharacteristic
359C2×C4—41no—
360C2×C4—41no—
361C2×C4—42no—
362C2×C4—82no—
363C2×C4—114no—
364C2×C4—111no—
365C2×C4—111no—
366C2×C4—114no—
367C2×C4—114no—
368C2×C4—112no—
369C2×C4—112no—
370C2×C4—112no—
371C2×C4—112no—
372C2×C4—441no—
373C2×C4—441no—
374C2×C4—442no—
375C2×C4—884no—
376C2×C4—882no—
377C2×C4—882no—
378C2×C4—884no—
379C2×C4—882no—
380C2×C4C4⋊C4×D1112yes—
381C2×C4D8×D1111yescharacteristic
382C2×C4Q16×D1112yes—
383C2×C4C2×D4×D1111yescharacteristic
384C8—112no—
385C8—112no—
386C8C4⋊C4×D1112yes—
387C8C22×C4×D1111yescharacteristic
388C8C2×Q8×D1111yescharacteristic
389C22—21no—
390C22—21no—
391C22—112no—
392C22—112no—
393C22—112no—
394C22—112no—
395C22—228no—
396C22—221no—
397C22—221no—
398C22D11×#10712yes—
399C22C2×D8×D1111yescharacteristic
400C4—82no—
401C4—81no—
402C4—81no—
403C4—112no—
404C4—112no—
405C4—882no—
406C4—881no—
407C4—881no—
408C4D11×#10712yes—
409C4C2×C4⋊C4×D1111yescharacteristic
410C4C2×Q16×D1111yescharacteristic
411C2—22no—
412C2—114no—
413C2—222no—
414C2C2×D11×#10711yescharacteristic
415C2D11×#50911yescharacteristic
416C2D11×#51011yescharacteristic
subgroupG/H
centerC22C2×D8×D11
commutatorC8×C11C23×C4
FrattiniC2×C8C23×D11
FittingC11×#2159C2
socleC22×C11C22×D8
prime radicalC23×D11D8
cosocleC2×C8×C11C24
hypercenter#2159D11
hypocenterC11C2×#2159
LCSG ▷ C8×C11 ▷ C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×C8 ◁ #2159

Complements

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

NH ≅ G/Ntype
4. #13070405C2semidirect
5. #13070404C2semidirect
6. #13070403C2semidirect
7. #13070402C2semidirect
8. #13070401C2semidirect
9. D11×#367C2semidirect
10. D11×#366C2semidirect
11. C11×#2159C2semidirect
23. D11×M32C4semidirect
36. C11×#367C22semidirect
37. C11×#366C22semidirect
38. #10622143C22semidirect
39. #10622142C22semidirect
40. #10622128C22semidirect
41. #10622128C22semidirect
42. #10622127C22semidirect
43. #10622127C22semidirect
71. C11×M32C2×C4semidirect
83. #66876C2×C4semidirect
91. #66862C2×C4semidirect
92. C16×D11C2×C4semidirect
143. C11×C16C22×C4semidirect
144. C11⋊C16C22×C4semidirect
153. #2159D11direct (N × H)
219. #367C2×D11semidirect
223. #366C2×D11semidirect
275. M32C4×D11semidirect
300. D11#2159direct (N × H)
351. C16C2×C4×D11semidirect
352. C11C2×#2159semidirect

Maximal subgroups

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

subgroupindex
C2×D11×M322
D11×#4272
C2×D11×#1072
#130704052
#130704042
#130704032
#130704022
#130704012
D11×#3672
D11×#3662
C11×#21592
C2×#215911