Finite Group Databasebeta

← D11×#2264 #14911909

Subgroups — D11×#2264 #14911909

Order 2816.

462 conjugacy classes of subgroups.

The subgroup lattice has 380 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1D11×#508C211yesmaximal, characteristic
2C2×D11×Q32C211yesmaximal, characteristic, complemented
3#13070936C211yesmaximal, characteristic, complemented
4#13070935C212yesmaximal, complemented
5#13070934C211yesmaximal, characteristic, complemented
6#13070933C211yesmaximal, characteristic, complemented
7#13070932C212yesmaximal, complemented
8D11×Q64C212yesmaximal, complemented
9D11×SD64C212yesmaximal, complemented
10D11×M64C211yesmaximal, characteristic, complemented
11C11×#2264C211yesmaximal, characteristic, complemented
12D11×#135—21no—
13C2×Q16×D11—21no—
14C11×#508C2211yescharacteristic
15C2×C11×Q32C2211yescharacteristic, complemented
16#10622807—21no—
17C2×#66893—21no—
18#10622532C2211yescharacteristic
19D11×Q32—21no—
20D11×Q32—21no—
21D11×Q32C2212yes—
22D11×Q32C2211yescharacteristic
23D11×Q32C2212yescomplemented
24#10622529—21no—
25D11×SD32—21no—
26#10622525C2211yescharacteristic
27D11×D16C2211yescharacteristic
28C2×Dic88C2211yescharacteristic, complemented
29#10622517C2211yescharacteristic
30C2×C16×D11C2211yescharacteristic
31C11×Q64C2212yescomplemented
32C11×SD64C2212yescomplemented
33C11×M64C2211yescharacteristic, complemented
34#10622160C2212yescomplemented
35#10622160C2212yescomplemented
36#10622159C2212yescomplemented
37#10622158C2212yescomplemented
38#10622137C2211yescharacteristic, complemented
39Dic176C2212yescomplemented
40#10622087C2212yescomplemented
41#10622085C2212yescomplemented
42D11×C32C2212yes—
43#41×D11—41no—
44C2×Q8×D11—41no—
45C11×#135—21no—
46C2×C11×Q16—21no—
47#67003—41no—
48C2×#4326—41no—
49#66972—21no—
50Q16×D11—21no—
51Q16×D11—22no—
52Q16×D11—22no—
53Q16×D11—41no—
54Q16×D11—41no—
55#66969—41no—
56SD16×D11—41no—
57#66965—21no—
58D8×D11—21no—
59C2×Dic44—21no—
60#66957—21no—
61C2×C8×D11D411yescharacteristic
62C11×Q32—21no—
63C11×Q32C2312yes—
64C11×Q32C2311yescharacteristic
65C11×SD32—21no—
66C11×D16C2311yescharacteristic
67C2×C11×C16C2311yescharacteristic
68#66893—21no—
69#66893—22no—
70#66893—22no—
71#66892—21no—
72#66891—21no—
73#66890—21no—
74C2×C11⋊C16D411yescharacteristic
75Dic88—21no—
76Dic88C2311yescharacteristic
77Dic88C2312yes—
78#66864—21no—
79D176C2311yescharacteristic
80C16×D11D411yescharacteristic
81C16×D11D411yescharacteristic
82C16×D11C2311yescharacteristic
83C16×D11C2311yescharacteristic
84C11×C32C2312yes—
85C11⋊C32C2312yes—
86C2×#2264—111nomaximal, Sylow
87C11×#41—41no—
88C2×Q8×C11—41no—
89#4343—41no—
90Q8×D11—41no—
91Q8×D11—42no—
92Q8×D11—42no—
93Q8×D11—81no—
94Q8×D11—81no—
95#4341—41no—
96#4341—81no—
97D4×D11—41no—
98D4×D11—81no—
99#4339—41no—
100#4339—81no—
101C2×C4×D11—81no—
102C2×C4×D11—81no—
103C2×C4×D11D811yescharacteristic
104C2×Dic22—41no—
105C2×Dic22—81no—
106C11×Q16—21no—
107C11×Q16—22no—
108C11×Q16—41no—
109C11×SD16—41no—
110C11×D8—21no—
111C2×C8×C11C2×D411yescharacteristic
112#4326—41no—
113#4326—42no—
114#4326—42no—
115#4325—41no—
116#4324—41no—
117#4323—41no—
118C2×C11⋊C8D811yescharacteristic
119Dic44—21no—
120Dic44—22no—
121Dic44—41no—
122D88—21no—
123#4314—41no—
124C8×D11D811yescharacteristic
125C8×D11D811yescharacteristic
126C8×D11C2×D411yescharacteristic
127C8×D11C2×D411yescharacteristic
128C11×C16C2×D411yescharacteristic
129C11×C16C2411yescharacteristic
130C11⋊C16C2×D411yescharacteristic
131C11⋊C16C2×D411yescharacteristic
132C2×#508—111no—
133C22×Q32—111no—
134#2264—111no—
135#2264—111no—
136#2264—112no—
137#2264—112no—
138#2264—111no—
139#2264D1111yescharacteristic, direct product factor
140C2×Q64—112no—
141C2×SD64—112no—
142C2×M64—111no—
143C22×D11—81no—
144C22×D11D1611yescharacteristic
145Q8×C11—41no—
146Q8×C11—42no—
147Q8×C11—81no—
148D4×C11—41no—
149D4×C11—81no—
150C2×C4×C11—81no—
151C2×C4×C11—81no—
152C2×C4×C11C2×D811yescharacteristic
153C22⋊D11—81no—
154C22⋊D11—81no—
155C22⋊D11—81no—
156C2×Dic11—81no—
157C2×Dic11—81no—
158C2×Dic11D1611yescharacteristic
159D44—41no—
160D44—81no—
161C4×D11—81no—
162C4×D11—82no—
163C4×D11—82no—
164C4×D11—81no—
165C4×D11—81no—
166C4×D11D1611yescharacteristic
167C4×D11D1611yescharacteristic
168C4×D11C2×D811yescharacteristic
169C4×D11C2×D811yescharacteristic
170Dic22—41no—
171Dic22—42no—
172Dic22—81no—
173Dic22—82no—
174Dic22—82no—
175Dic22—81no—
176C8×C11C2×D811yescharacteristic
177C8×C11C22×D411yescharacteristic
178C11⋊C8C2×D811yescharacteristic
179C11⋊C8C2×D811yescharacteristic
180C2×#135—221no—
181C22×Q16—221no—
182#508—111no—
183#508—111no—
184#508—111no—
185#508—221no—
186#508—221no—
187#508C2×D1111yescharacteristic
188C2×Q32—112no—
189C2×Q32—111no—
190C2×Q32—112no—
191C2×Q32—111no—
192C2×Q32—221no—
193C2×Q32—221no—
194C2×Q32—221no—
195C2×Q32C2×D1111yescharacteristic, complemented
196C2×SD32—221no—
197C2×D16—111no—
198C22×C16—111no—
199Q64—112no—
200Q64—112no—
201Q64—112no—
202Q64C2×D1112yescomplemented
203SD64—112no—
204SD64—112no—
205SD64—112no—
206SD64C2×D1112yescomplemented
207M64—111no—
208M64—112no—
209M64C2×D1111yescharacteristic, complemented
210C2×C32—112no—
211C22×C11—81no—
212C22×C11C2×D1611yescharacteristic
213C2×D11—22no—
214C2×D11—81no—
215C2×D11—162no—
216C2×D11C2×D1611yescharacteristic
217C2×D11C2×D1611yescharacteristic
218C4×C11—81no—
219C4×C11—82no—
220C4×C11C2×D1611yescharacteristic
221C4×C11C22×D811yescharacteristic
222Dic11—82no—
223Dic11—81no—
224Dic11C2×D1611yescharacteristic
225Dic11C2×D1611yescharacteristic
226C2×#41—441no—
227C22×Q8—441no—
228#135—21no—
229#135—221no—
230#135—221no—
231#135—221no—
232#135—441no—
233#135—441no—
234C2×Q16—21no—
235C2×Q16—222no—
236C2×Q16—222no—
237C2×Q16—221no—
238C2×Q16—221no—
239C2×Q16—441no—
240C2×Q16—441no—
241C2×Q16—441no—
242C2×SD16—441no—
243C2×D8—221no—
244C22×C8—111no—
245Q32—21no—
246Q32—112no—
247Q32—111no—
248Q32—222no—
249Q32—222no—
250Q32—221no—
251Q32—221no—
252Q32C22×D1112yes—
253Q32C22×D1111yescharacteristic
254SD32—21no—
255SD32—221no—
256SD32—221no—
257SD32—221no—
258D16—111no—
259D16—221no—
260D16C22×D1111yescharacteristic
261C2×C16—111no—
262C2×C16—111no—
263C2×C16—111no—
264C2×C16—111no—
265C2×C16—111no—
266C2×C16C22×D1111yescharacteristic
267C32—112no—
268C32C22×D1112yes—
269C2×C11—21no—
270C2×C11—161no—
271C2×C11C22×D1611yescharacteristic
272D11—21no—
273D11—161no—
274D11#226412yesdirect product factor
275#41—41no—
276#41—441no—
277#41—441no—
278#41—441no—
279#41—881no—
280#41—881no—
281C2×Q8—41no—
282C2×Q8—441no—
283C2×Q8—442no—
284C2×Q8—442no—
285C2×Q8—441no—
286C2×Q8—881no—
287C2×Q8—881no—
288C2×Q8—881no—
289C2×D4—441no—
290C2×D4—881no—
291C22×C4—111no—
292C22×C4—881no—
293C22×C4—881no—
294Q16—21no—
295Q16—22no—
296Q16—41no—
297Q16—221no—
298Q16—222no—
299Q16—442no—
300Q16—442no—
301Q16—441no—
302Q16—441no—
303SD16—41no—
304SD16—441no—
305SD16—441no—
306SD16—441no—
307D8—21no—
308D8—221no—
309D8—441no—
310C2×C8—111no—
311C2×C8—111no—
312C2×C8—111no—
313C2×C8—111no—
314C2×C8—111no—
315C2×C8D4×D1111yescharacteristic
316C16—111no—
317C16—111no—
318C16D4×D1111yescharacteristic
319C16C23×D1111yescharacteristic
320C11C2×#226411yescharacteristic, complemented, Sylow
321C23—111no—
322C23—881no—
323Q8—41no—
324Q8—42no—
325Q8—81no—
326Q8—441no—
327Q8—442no—
328Q8—882no—
329Q8—882no—
330Q8—881no—
331Q8—881no—
332D4—41no—
333D4—81no—
334D4—441no—
335D4—881no—
336D4—881no—
337D4—881no—
338D4—881no—
339C2×C4—81no—
340C2×C4—81no—
341C2×C4—111no—
342C2×C4—111no—
343C2×C4—111no—
344C2×C4—111no—
345C2×C4—111no—
346C2×C4—881no—
347C2×C4—881no—
348C2×C4—882no—
349C2×C4—882no—
350C2×C4—881no—
351C2×C4—881no—
352C2×C4—881no—
353C2×C4D8×D1111yescharacteristic
354C8—111no—
355C8—111no—
356C8D8×D1111yescharacteristic
357C8C2×D4×D1111yescharacteristic
358C22—81no—
359C22—111no—
360C22—111no—
361C22—222no—
362C22—881no—
363C22—1762no—
364C22D11×D1611yescharacteristic
365C4—81no—
366C4—82no—
367C4—111no—
368C4—111no—
369C4—881no—
370C4—882no—
371C4D11×D1611yescharacteristic
372C4C2×D8×D1111yescharacteristic
373C2—21no—
374C2—112no—
375C2—161no—
376C2—221no—
377C2—1761no—
378C2C2×D11×D1611yescharacteristic
subgroupG/H
centerC2C2×D11×D16
commutator, cosocleC11×C16C24
FrattiniC16C23×D11
FittingC11×#2264C2
socleC2×C11C22×D16
prime radicalD11×#508C2
hypercenter#2264D11
hypocenterC11C2×#2264
LCSG ▷ C11×C16 ▷ C8×C11 ▷ C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C2 ◁ C2×C4 ◁ C2×C8 ◁ C2×C16 ◁ #2264

Complements

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

NH ≅ G/Ntype
2. C2×D11×Q32C2semidirect
3. #13070936C2semidirect
4. #13070935C2semidirect
5. #13070934C2semidirect
6. #13070933C2semidirect
7. #13070932C2semidirect
8. D11×Q64C2semidirect
9. D11×SD64C2semidirect
10. D11×M64C2semidirect
11. C11×#2264C2semidirect
15. C2×C11×Q32C22semidirect
23. D11×Q32C22semidirect
28. C2×Dic88C22semidirect
31. C11×Q64C22semidirect
32. C11×SD64C22semidirect
33. C11×M64C22semidirect
34. #10622160C22semidirect
35. #10622160C22semidirect
36. #10622159C22semidirect
37. #10622158C22semidirect
38. #10622137C22semidirect
39. Dic176C22semidirect
40. #10622087C22semidirect
41. #10622085C22semidirect
139. #2264D11direct (N × H)
195. C2×Q32C2×D11semidirect
202. Q64C2×D11semidirect
206. SD64C2×D11semidirect
209. M64C2×D11semidirect
274. D11#2264direct (N × H)
320. C11C2×#2264semidirect

Maximal subgroups

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

subgroupindex
D11×#5082
C2×D11×Q322
#130709362
#130709352
#130709342
#130709332
#130709322
D11×Q642
D11×SD642
D11×M642
C11×#22642
C2×#226411