Finite Group Databasebeta

← D11×#2231 #14908505

Subgroups — D11×#2231 #14908505

Order 2816.

526 conjugacy classes of subgroups.

The subgroup lattice has 428 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1D11×#499C211yesmaximal, characteristic, complemented
2D11×#443C211yesmaximal, characteristic
3#13070793C211yesmaximal, characteristic, complemented
4#13070792C211yesmaximal, characteristic, complemented
5#13070791C212yesmaximal, complemented
6#13070790C212yesmaximal, complemented
7#13070789C211yesmaximal, characteristic, complemented
8D11×#365C212yesmaximal, complemented
9D11×#364C211yesmaximal, characteristic, complemented
10D11×#360C212yesmaximal
11C11×#2231C211yesmaximal, characteristic, complemented
12D11×#135C2211yescharacteristic
13D11×#131—21no—
14D11×#125—21no—
15C11×#499C2211yescharacteristic, complemented
16C11×#443C2211yescharacteristic
17#10622809C2211yescharacteristic
18#10622757—21no—
19#10622677—21no—
20D11×M32C2212yes—
21#10622508C2211yescharacteristic
22D11×#108C2211yescharacteristic
23D11×#107—21no—
24#10622491—21no—
25D11×#106C2212yes—
26#10622471C2212yescomplemented
27#10622437—21no—
28D11×#104—21no—
29#10622313C2211yescharacteristic
30C4×C8×D11C2211yescharacteristic
31#10622296C2211yescharacteristic, 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—
44C11×#135C2311yescharacteristic
45C11×#131—21no—
46C11×#125—21no—
47#67003—21no—
48#67001—21no—
49#66972Q811yescharacteristic
50Q16×D11Q811yescharacteristic
51#66969—21no—
52SD16×D11—21no—
53#66965Q811yescharacteristic
54D8×D11Q811yescharacteristic
55#66960—21no—
56#66960—41no—
57M16×D11—21no—
58M16×D11—41no—
59#66957C2311yescharacteristic
60#66954—21no—
61#66954—41no—
62C2×C8×D11—41no—
63C2×C8×D11D411yescharacteristic
64C2×C8×D11C2311yescharacteristic
65C4⋊C4×D11—22no—
66C4⋊C4×D11—42no—
67#66943—22no—
68#66942—42no—
69C42×D11D411yescharacteristic
70#66923—21no—
71C11×M32C2312yes—
72C11×#108C2311yescharacteristic
73C11×#107—21no—
74C11×#106C2312yes—
75C11×#104—21no—
76C4×C8×C11C2311yescharacteristic
77#66901—21no—
78#66889—21no—
79#66886—21no—
80#66883C2311yescharacteristic
81#66882—21no—
82#66881C2312yes—
83C8×Dic11D411yescharacteristic
84C8×Dic11C2311yescharacteristic
85#66876C2312yes—
86#66872—22no—
87#66871—22no—
88#66869—21no—
89C4×C11⋊C8D411yescharacteristic
90#66862—22no—
91C16×D11—22no—
92C2×#2231—111nomaximal, Sylow
93C11×#41—21no—
94#4343—21no—
95Q8×D11—21no—
96#4341—21no—
97#4341—41no—
98D4×D11—21no—
99D4×D11—41no—
100#4339—21no—
101#4339—41no—
102C2×C4×D11—21no—
103C2×C4×D11—41no—
104C2×C4×D11—42no—
105C2×C4×D11C2×D411yescharacteristic
106C11×Q16C2×Q811yescharacteristic
107C11×SD16—21no—
108C11×D8C2×Q811yescharacteristic
109C11×M16—21no—
110C11×M16—41no—
111C2×C8×C11—41no—
112C2×C8×C11C2×D411yescharacteristic
113C2×C8×C11C2411yescharacteristic
114C11×C4⋊C4—22no—
115C11×C4⋊C4—42no—
116C42×C11C2×D411yescharacteristic
117#4326—21no—
118#4325—21no—
119#4324—21no—
120#4323—21no—
121C4⋊Dic11—22no—
122C4⋊Dic11—42no—
123Dic11⋊C4—42no—
124Dic11⋊C4—42no—
125Dic11⋊C4—42no—
126C4×Dic11—21no—
127C4×Dic11C2×D411yescharacteristic
128#4318—21no—
129#4318—41no—
130C2×C11⋊C8—41no—
131C2×C11⋊C8C2×D411yescharacteristic
132C2×C11⋊C8C2×D411yescharacteristic
133Dic44C2×Q811yescharacteristic
134D88C2×Q811yescharacteristic
135#4314—21no—
136#4313—41no—
137#4313—41no—
138#4313—41no—
139C8×D11—41no—
140C8×D11—41no—
141C8×D11—41no—
142C8×D11SD1611yescharacteristic
143C8×D11SD1611yescharacteristic
144C8×D11SD1611yescharacteristic
145C8×D11SD1611yescharacteristic
146C8×D11C2×Q811yescharacteristic
147C8×D11C2×Q811yescharacteristic
148C8×D11#4111yescharacteristic
149C8×D11#4111yescharacteristic
150C11×C16—22no—
151C11⋊C16—22no—
152C2×#499—111no—
153C2×#443—111no—
154#2231—111no—
155#2231—111no—
156#2231—112no—
157#2231—111no—
158#2231—112no—
159#2231D1111yescharacteristic, direct product factor
160C2×#365—112no—
161C2×#364—111no—
162C2×#360—112no—
163C22×D11—41no—
164C22×D11AGL(1,ℤ/8)11yescharacteristic
165Q8×C11—21no—
166D4×C11—21no—
167D4×C11—41no—
168C2×C4×C11—21no—
169C2×C4×C11—41no—
170C2×C4×C11—42no—
171C2×C4×C11C22×D411yescharacteristic
172C22⋊D11—41no—
173C22⋊D11—41no—
174C22⋊D11—41no—
175C2×Dic11—21no—
176C2×Dic11—41no—
177C2×Dic11—42no—
178C2×Dic11AGL(1,ℤ/8)11yescharacteristic
179D44—21no—
180D44—41no—
181C4×D11—42no—
182C4×D11—41no—
183C4×D11—41no—
184C4×D11—41no—
185C4×D11—84no—
186C4×D11C22⋊Q811yescharacteristic
187C4×D11C22⋊Q811yescharacteristic
188C4×D11C2×SD1611yescharacteristic
189C4×D11C2×SD1611yescharacteristic
190Dic22—21no—
191Dic22—41no—
192C8×C11—41no—
193C8×C11C2×SD1611yescharacteristic
194C8×C11C2×SD1611yescharacteristic
195C8×C11C22×Q811yescharacteristic
196C8×C11C2×#4111yescharacteristic
197C11⋊C8—41no—
198C11⋊C8C22⋊Q811yescharacteristic
199C11⋊C8C22⋊Q811yescharacteristic
200C11⋊C8C2×SD1611yescharacteristic
201C11⋊C8C2×SD1611yescharacteristic
202C2×#135—111no—
203C2×#131—221no—
204C2×#125—221no—
205C2×M32—112no—
206#499—112no—
207#499—111no—
208#499—221no—
209#499—221no—
210#499C2×D1111yescharacteristic, complemented
211#443—111no—
212#443—111no—
213#443—111no—
214#443—221no—
215#443—221no—
216#443C2×D1111yescharacteristic
217C2×#108—111no—
218C2×#107—221no—
219C2×#106—112no—
220C2×#104—221no—
221C2×C4×C8—111no—
222#365—112no—
223#365—112no—
224#365—112no—
225#365C2×D1112yescomplemented
226#364—112no—
227#364—111no—
228#364C2×D1111yescharacteristic, complemented
229#360—112no—
230#360—112no—
231#360—112no—
232#360C2×D1112yes—
233C22×C11—41no—
234C22×C11C2×AGL(1,ℤ/8)11yescharacteristic
235C2×D11—22no—
236C2×D11—41no—
237C2×D11—82no—
238C2×D11#47611yescharacteristic
239C2×D11#47611yescharacteristic
240C4×C11—41no—
241C4×C11—41no—
242C4×C11—82no—
243C4×C11C2×C22⋊Q811yescharacteristic
244C4×C11C22×SD1611yescharacteristic
245Dic11—41no—
246Dic11—41no—
247Dic11—82no—
248Dic11#47611yescharacteristic
249Dic11#47611yescharacteristic
250C2×#41—221no—
251#135—111no—
252#135—111no—
253#135—111no—
254#135—221no—
255#135—221no—
256#135C22×D1111yescharacteristic
257C2×Q16—111no—
258C2×SD16—221no—
259C2×D8—111no—
260#131—21no—
261#131—221no—
262#131—221no—
263#131—221no—
264#131—441no—
265#131—441no—
266C2×M16—221no—
267C2×M16—441no—
268C22×C8—111no—
269C22×C8—111no—
270C22×C8—441no—
271#125—21no—
272#125—222no—
273#125—221no—
274#125—442no—
275C2×C4⋊C4—222no—
276C2×C4⋊C4—442no—
277C2×C42—111no—
278M32—112no—
279M32—222no—
280M32C22×D1112yes—
281C2×C16—222no—
282#108—111no—
283#108—221no—
284#108C22×D1111yescharacteristic
285#107—21no—
286#107—222no—
287#107—221no—
288#106—112no—
289#106—222no—
290#106C22×D1112yes—
291#104—21no—
292#104—221no—
293#104—221no—
294#104—221no—
295C4×C8—111no—
296C4×C8—111no—
297C4×C8—111no—
298C4×C8C22×D1111yescharacteristic
299C2×C11—21no—
300C2×C11—81no—
301C2×C11C2×#47611yescharacteristic
302D11—21no—
303D11—81no—
304D11#223112yesdirect product factor
305#41—21no—
306#41—221no—
307#41—221no—
308#41—221no—
309#41—441no—
310#41—441no—
311C2×Q8—221no—
312C2×D4—221no—
313C2×D4—441no—
314C22×C4—111no—
315C22×C4—221no—
316C22×C4—441no—
317C22×C4—442no—
318Q16—111no—
319Q16—221no—
320Q16Q8×D1111yescharacteristic
321SD16—21no—
322SD16—221no—
323SD16—221no—
324SD16—221no—
325D8—111no—
326D8—221no—
327D8Q8×D1111yescharacteristic
328M16—21no—
329M16—41no—
330M16—221no—
331M16—441no—
332M16—441no—
333M16—441no—
334M16—441no—
335C2×C8—41no—
336C2×C8—111no—
337C2×C8—111no—
338C2×C8—111no—
339C2×C8—111no—
340C2×C8—111no—
341C2×C8—111no—
342C2×C8—111no—
343C2×C8—111no—
344C2×C8—111no—
345C2×C8—111no—
346C2×C8—441no—
347C2×C8—441no—
348C2×C8—441no—
349C2×C8—441no—
350C2×C8D4×D1111yescharacteristic
351C2×C8C23×D1111yescharacteristic
352C4⋊C4—22no—
353C4⋊C4—42no—
354C4⋊C4—222no—
355C4⋊C4—442no—
356C4⋊C4—442no—
357C4⋊C4—442no—
358C4⋊C4—442no—
359C42—111no—
360C42—221no—
361C42D4×D1111yescharacteristic
362C16—22no—
363C16—222no—
364C11C2×#223111yescharacteristic, complemented, Sylow
365C23—111no—
366C23—441no—
367Q8—21no—
368Q8—221no—
369Q8—441no—
370D4—21no—
371D4—41no—
372D4—221no—
373D4—441no—
374D4—441no—
375D4—441no—
376D4—441no—
377C2×C4—21no—
378C2×C4—41no—
379C2×C4—42no—
380C2×C4—111no—
381C2×C4—111no—
382C2×C4—111no—
383C2×C4—111no—
384C2×C4—111no—
385C2×C4—221no—
386C2×C4—441no—
387C2×C4—441no—
388C2×C4—442no—
389C2×C4—441no—
390C2×C4—441no—
391C2×C4—442no—
392C2×C4—884no—
393C2×C4C2×D4×D1111yescharacteristic
394C8—41no—
395C8—111no—
396C8—111no—
397C8—111no—
398C8—111no—
399C8—441no—
400C8SD16×D1111yescharacteristic
401C8SD16×D1111yescharacteristic
402C8C2×Q8×D1111yescharacteristic
403C8#41×D1111yescharacteristic
404C22—41no—
405C22—111no—
406C22—111no—
407C22—222no—
408C22—441no—
409C22—882no—
410C22D11×AGL(1,ℤ/8)11yescharacteristic
411C4—41no—
412C4—41no—
413C4—82no—
414C4—111no—
415C4—111no—
416C4—441no—
417C4—441no—
418C4—882no—
419C4D11×C22⋊Q811yescharacteristic
420C4C2×SD16×D1111yescharacteristic
421C2—21no—
422C2—81no—
423C2—112no—
424C2—221no—
425C2—881no—
426C2D11×#47611yescharacteristic
subgroupG/H
centerC2D11×#476
commutator, cosocleC2×C8×C11C24
FrattiniC2×C8C23×D11
FittingC11×#2231C2
socleC2×C11C2×#476
prime radicalD11×#135C22
hypercenter#2231D11
hypocenterC11C2×#2231
LCSG ▷ C2×C8×C11 ▷ C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C2 ◁ C2×C4 ◁ C4×C8 ◁ #2231

Complements

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

NH ≅ G/Ntype
1. D11×#499C2semidirect
3. #13070793C2semidirect
4. #13070792C2semidirect
5. #13070791C2semidirect
6. #13070790C2semidirect
7. #13070789C2semidirect
8. D11×#365C2semidirect
9. D11×#364C2semidirect
11. C11×#2231C2semidirect
15. C11×#499C22semidirect
26. #10622471C22semidirect
31. #10622296C22semidirect
32. C11×#365C22semidirect
33. C11×#364C22semidirect
37. #10622151C22semidirect
38. #10622149C22semidirect
39. #10622132C22semidirect
41. #10622125C22semidirect
42. #10622101C22semidirect
159. #2231D11direct (N × H)
210. #499C2×D11semidirect
225. #365C2×D11semidirect
228. #364C2×D11semidirect
304. D11#2231direct (N × H)
364. C11C2×#2231semidirect

Maximal subgroups

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

subgroupindex
D11×#4992
D11×#4432
#130707932
#130707922
#130707912
#130707902
#130707892
D11×#3652
D11×#3642
D11×#3602
C11×#22312
C2×#223111