Finite Group Databasebeta

← D11×#2230 #14908499

Subgroups — D11×#2230 #14908499

Order 2816.

558 conjugacy classes of subgroups.

The subgroup lattice has 444 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1D11×#498C211yesmaximal, characteristic, complemented
2D11×#443C211yesmaximal, characteristic
3#13070788C211yesmaximal, characteristic, complemented
4#13070787C211yesmaximal, characteristic, complemented
5#13070786C212yesmaximal, complemented
6#13070785C212yesmaximal, complemented
7#13070784C211yesmaximal, characteristic, complemented
8D11×#365C212yesmaximal, complemented
9D11×#364C211yesmaximal, characteristic, complemented
10D11×#360C212yesmaximal
11C11×#2230C211yesmaximal, characteristic, complemented
12D11×#135C2211yescharacteristic
13D11×#131—21no—
14D11×C4⋊Q8—21no—
15C11×#498C2211yescharacteristic, complemented
16C11×#443C2211yescharacteristic
17#10622809C2211yescharacteristic
18#10622757—21no—
19#10622692—21no—
20D11×M32C2212yes—
21#10622508C2211yescharacteristic
22D11×#108C2211yescharacteristic
23D11×#106—21no—
24D11×#106C2212yes—
25#10622468—21no—
26#10622468C2212yescomplemented
27#10622437—21no—
28D11×#104—21no—
29#10622313C2211yescharacteristic
30C4×C8×D11C2211yescharacteristic
31#10622293C2211yescharacteristic, complemented
32C11×#365C2212yescomplemented
33C11×#364C2211yescharacteristic, complemented
34C11×#360C2212yes—
35#10622204C2212yes—
36#10622156C2212yes—
37#10622151C2212yescomplemented
38#10622149C2212yescomplemented
39#10622132C2212yescomplemented
40#10622126C2212yes—
41#10622125C2212yescomplemented
42#10622101C2211yescharacteristic, complemented
43#41×D11—21no—
44C2×Q8×D11—41no—
45C11×#135C2311yescharacteristic
46C11×#131—21no—
47C11×C4⋊Q8—21no—
48#67003—21no—
49#67001—21no—
50#66997—41no—
51#66972Q811yescharacteristic, complemented
52Q16×D11Q811yescharacteristic, complemented
53#66969—21no—
54SD16×D11—21no—
55#66965Q811yescharacteristic, complemented
56D8×D11Q811yescharacteristic, complemented
57#66960—21no—
58#66960—41no—
59M16×D11—21no—
60M16×D11—41no—
61#66957C2311yescharacteristic
62#66954—21no—
63#66954—41no—
64C2×C8×D11—41no—
65C2×C8×D11D411yescharacteristic
66C2×C8×D11C2311yescharacteristic
67C4⋊C4×D11—22no—
68C4⋊C4×D11—41no—
69#66941—22no—
70#66941—41no—
71C42×D11D411yescharacteristic
72#66922—21no—
73C11×M32C2312yes—
74C11×#108C2311yescharacteristic
75C11×#106—21no—
76C11×#106C2312yes—
77C11×#104—21no—
78C4×C8×C11C2311yescharacteristic
79#66901—21no—
80#66889—21no—
81#66886—21no—
82#66883C2311yescharacteristic
83#66881—21no—
84#66881C2312yes—
85C8×Dic11D411yescharacteristic
86C8×Dic11C2311yescharacteristic
87#66876C2312yes—
88#66872—22no—
89#66872—22no—
90#66869—21no—
91C4×C11⋊C8D411yescharacteristic
92#66862—22no—
93C16×D11—22no—
94C2×#2230—111nomaximal, Sylow
95C11×#41—21no—
96C2×Q8×C11—41no—
97#4343—21no—
98Q8×D11—21no—
99Q8×D11—84no—
100#4341—21no—
101#4341—41no—
102D4×D11—21no—
103D4×D11—41no—
104#4339—21no—
105#4339—41no—
106C2×C4×D11—21no—
107C2×C4×D11—41no—
108C2×C4×D11—42no—
109C2×C4×D11C2×D411yescharacteristic
110C2×Dic22—41no—
111C2×Dic22—42no—
112C11×Q16C2×Q811yescharacteristic, complemented
113C11×SD16—21no—
114C11×D8C2×Q811yescharacteristic, complemented
115C11×M16—21no—
116C11×M16—41no—
117C2×C8×C11—41no—
118C2×C8×C11C2×D411yescharacteristic
119C2×C8×C11C2411yescharacteristic
120C11×C4⋊C4—22no—
121C11×C4⋊C4—41no—
122C42×C11C2×D411yescharacteristic
123#4326—21no—
124#4325—21no—
125#4324—21no—
126#4323—21no—
127C4⋊Dic11—22no—
128C4⋊Dic11—41no—
129Dic11⋊C4—42no—
130Dic11⋊C4—42no—
131C4×Dic11—21no—
132C4×Dic11C2×D411yescharacteristic
133#4318—21no—
134#4318—41no—
135C2×C11⋊C8—41no—
136C2×C11⋊C8C2×D411yescharacteristic
137C2×C11⋊C8C2×D411yescharacteristic
138Dic44C2×Q811yescharacteristic, complemented
139D88C2×Q811yescharacteristic, complemented
140#4314—21no—
141#4313—41no—
142#4313—41no—
143#4313—41no—
144C8×D11—41no—
145C8×D11—41no—
146C8×D11—41no—
147C8×D11SD1611yescharacteristic
148C8×D11SD1611yescharacteristic
149C8×D11SD1611yescharacteristic
150C8×D11SD1611yescharacteristic
151C8×D11C2×Q811yescharacteristic
152C8×D11C2×Q811yescharacteristic
153C8×D11#4111yescharacteristic
154C8×D11#4111yescharacteristic
155C11×C16—22no—
156C11⋊C16—22no—
157C2×#498—111no—
158C2×#443—111no—
159#2230—111no—
160#2230—111no—
161#2230—112no—
162#2230—111no—
163#2230—112no—
164#2230D1111yescharacteristic, direct product factor
165C2×#365—112no—
166C2×#364—111no—
167C2×#360—112no—
168C22×D11—41no—
169C22×D11AGL(1,ℤ/8)11yescharacteristic
170Q8×C11—21no—
171Q8×C11—82no—
172D4×C11—21no—
173D4×C11—41no—
174C2×C4×C11—21no—
175C2×C4×C11—41no—
176C2×C4×C11—42no—
177C2×C4×C11C22×D411yescharacteristic
178C22⋊D11—41no—
179C22⋊D11—41no—
180C22⋊D11—41no—
181C2×Dic11—21no—
182C2×Dic11—41no—
183C2×Dic11—42no—
184C2×Dic11AGL(1,ℤ/8)11yescharacteristic
185D44—21no—
186D44—41no—
187C4×D11—24no—
188C4×D11—41no—
189C4×D11—41no—
190C4×D11—41no—
191C4×D11—84no—
192C4×D11C22⋊Q811yescharacteristic
193C4×D11C22⋊Q811yescharacteristic
194C4×D11C2×SD1611yescharacteristic
195C4×D11C2×SD1611yescharacteristic
196Dic22—21no—
197Dic22—41no—
198Dic22—84no—
199Dic22—82no—
200C8×C11—41no—
201C8×C11C2×SD1611yescharacteristic
202C8×C11C2×SD1611yescharacteristic
203C8×C11C22×Q811yescharacteristic
204C8×C11C2×#4111yescharacteristic
205C11⋊C8—41no—
206C11⋊C8C22⋊Q811yescharacteristic
207C11⋊C8C22⋊Q811yescharacteristic
208C11⋊C8C2×SD1611yescharacteristic
209C11⋊C8C2×SD1611yescharacteristic
210C2×#135—111no—
211C2×#131—221no—
212C2×C4⋊Q8—221no—
213C2×M32—112no—
214#498—112no—
215#498—111no—
216#498—221no—
217#498—221no—
218#498C2×D1111yescharacteristic, complemented
219#443—111no—
220#443—111no—
221#443—111no—
222#443—221no—
223#443—221no—
224#443C2×D1111yescharacteristic
225C2×#108—111no—
226C2×#106—112no—
227C2×#106—221no—
228C2×#104—221no—
229C2×C4×C8—111no—
230#365—112no—
231#365—112no—
232#365—112no—
233#365C2×D1112yescomplemented
234#364—112no—
235#364—111no—
236#364C2×D1111yescharacteristic, complemented
237#360—112no—
238#360—112no—
239#360—112no—
240#360C2×D1112yes—
241C22×C11—41no—
242C22×C11C2×AGL(1,ℤ/8)11yescharacteristic
243C2×D11—22no—
244C2×D11—41no—
245C2×D11—82no—
246C2×D11#47611yescharacteristic
247C2×D11#47611yescharacteristic
248C4×C11—22no—
249C4×C11—41no—
250C4×C11—82no—
251C4×C11C2×C22⋊Q811yescharacteristic
252C4×C11C22×SD1611yescharacteristic
253Dic11—22no—
254Dic11—41no—
255Dic11—82no—
256Dic11#47611yescharacteristic
257Dic11#47611yescharacteristic
258C2×#41—221no—
259C22×Q8—441no—
260#135—111no—
261#135—111no—
262#135—111no—
263#135—221no—
264#135—221no—
265#135C22×D1111yescharacteristic
266C2×Q16—111no—
267C2×SD16—221no—
268C2×D8—111no—
269#131—21no—
270#131—221no—
271#131—221no—
272#131—221no—
273#131—441no—
274#131—441no—
275C2×M16—221no—
276C2×M16—441no—
277C22×C8—111no—
278C22×C8—111no—
279C22×C8—441no—
280C4⋊Q8—21no—
281C4⋊Q8—222no—
282C4⋊Q8—221no—
283C4⋊Q8—441no—
284C4⋊Q8—441no—
285C2×C4⋊C4—222no—
286C2×C4⋊C4—441no—
287C2×C42—111no—
288M32—112no—
289M32—222no—
290M32C22×D1112yes—
291C2×C16—222no—
292#108—111no—
293#108—221no—
294#108C22×D1111yescharacteristic
295#106—21no—
296#106—112no—
297#106—222no—
298#106—222no—
299#106—221no—
300#106C22×D1112yes—
301#104—21no—
302#104—221no—
303#104—221no—
304#104—221no—
305C4×C8—111no—
306C4×C8—111no—
307C4×C8—111no—
308C4×C8C22×D1111yescharacteristic
309C2×C11—21no—
310C2×C11—81no—
311C2×C11C2×#47611yescharacteristic
312D11—21no—
313D11—81no—
314D11#223012yesdirect product factor
315#41—21no—
316#41—221no—
317#41—221no—
318#41—221no—
319#41—441no—
320#41—441no—
321C2×Q8—41no—
322C2×Q8—221no—
323C2×Q8—441no—
324C2×Q8—442no—
325C2×Q8—884no—
326C2×D4—221no—
327C2×D4—441no—
328C22×C4—111no—
329C22×C4—221no—
330C22×C4—441no—
331C22×C4—442no—
332Q16—111no—
333Q16—221no—
334Q16Q8×D1111yescharacteristic, complemented
335SD16—21no—
336SD16—221no—
337SD16—221no—
338SD16—221no—
339D8—111no—
340D8—221no—
341D8Q8×D1111yescharacteristic, complemented
342M16—21no—
343M16—41no—
344M16—221no—
345M16—441no—
346M16—441no—
347M16—441no—
348M16—441no—
349C2×C8—41no—
350C2×C8—111no—
351C2×C8—111no—
352C2×C8—111no—
353C2×C8—111no—
354C2×C8—111no—
355C2×C8—111no—
356C2×C8—111no—
357C2×C8—111no—
358C2×C8—111no—
359C2×C8—111no—
360C2×C8—441no—
361C2×C8—441no—
362C2×C8—441no—
363C2×C8—441no—
364C2×C8D4×D1111yescharacteristic
365C2×C8C23×D1111yescharacteristic
366C4⋊C4—22no—
367C4⋊C4—41no—
368C4⋊C4—222no—
369C4⋊C4—441no—
370C4⋊C4—442no—
371C4⋊C4—442no—
372C42—111no—
373C42—221no—
374C42D4×D1111yescharacteristic
375C16—22no—
376C16—222no—
377C11C2×#223011yescharacteristic, complemented, Sylow
378C23—111no—
379C23—441no—
380Q8—21no—
381Q8—82no—
382Q8—221no—
383Q8—441no—
384Q8—882no—
385Q8—884no—
386D4—21no—
387D4—41no—
388D4—221no—
389D4—441no—
390D4—441no—
391D4—441no—
392D4—441no—
393C2×C4—21no—
394C2×C4—41no—
395C2×C4—42no—
396C2×C4—111no—
397C2×C4—111no—
398C2×C4—111no—
399C2×C4—111no—
400C2×C4—111no—
401C2×C4—224no—
402C2×C4—221no—
403C2×C4—441no—
404C2×C4—441no—
405C2×C4—441no—
406C2×C4—441no—
407C2×C4—442no—
408C2×C4—884no—
409C2×C4C2×D4×D1111yescharacteristic
410C8—41no—
411C8—111no—
412C8—111no—
413C8—111no—
414C8—111no—
415C8—441no—
416C8SD16×D1111yescharacteristic
417C8SD16×D1111yescharacteristic
418C8C2×Q8×D1111yescharacteristic
419C8#41×D1111yescharacteristic
420C22—41no—
421C22—111no—
422C22—111no—
423C22—222no—
424C22—441no—
425C22—882no—
426C22D11×AGL(1,ℤ/8)11yescharacteristic
427C4—22no—
428C4—41no—
429C4—82no—
430C4—111no—
431C4—111no—
432C4—222no—
433C4—441no—
434C4—882no—
435C4D11×C22⋊Q811yescharacteristic
436C4C2×SD16×D1111yescharacteristic
437C2—21no—
438C2—81no—
439C2—112no—
440C2—221no—
441C2—881no—
442C2D11×#47611yescharacteristic
subgroupG/H
centerC2D11×#476
commutator, cosocleC2×C8×C11C24
FrattiniC2×C8C23×D11
FittingC11×#2230C2
socleC2×C11C2×#476
prime radicalD11×#135C22
hypercenter#2230D11
hypocenterC11C2×#2230
LCSG ▷ C2×C8×C11 ▷ C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C2 ◁ C2×C4 ◁ C4×C8 ◁ #2230

Complements

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

NH ≅ G/Ntype
1. D11×#498C2semidirect
3. #13070788C2semidirect
4. #13070787C2semidirect
5. #13070786C2semidirect
6. #13070785C2semidirect
7. #13070784C2semidirect
8. D11×#365C2semidirect
9. D11×#364C2semidirect
11. C11×#2230C2semidirect
15. C11×#498C22semidirect
26. #10622468C22semidirect
31. #10622293C22semidirect
32. C11×#365C22semidirect
33. C11×#364C22semidirect
37. #10622151C22semidirect
38. #10622149C22semidirect
39. #10622132C22semidirect
41. #10622125C22semidirect
42. #10622101C22semidirect
51. #66972Q8semidirect
52. Q16×D11Q8semidirect
55. #66965Q8semidirect
56. D8×D11Q8semidirect
112. C11×Q16C2×Q8semidirect
114. C11×D8C2×Q8semidirect
138. Dic44C2×Q8semidirect
139. D88C2×Q8semidirect
164. #2230D11direct (N × H)
218. #498C2×D11semidirect
233. #365C2×D11semidirect
236. #364C2×D11semidirect
314. D11#2230direct (N × H)
334. Q16Q8×D11semidirect
341. D8Q8×D11semidirect
377. C11C2×#2230semidirect

Maximal subgroups

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

subgroupindex
D11×#4982
D11×#4432
#130707882
#130707872
#130707862
#130707852
#130707842
D11×#3652
D11×#3642
D11×#3602
C11×#22302
C2×#223011