Finite Group Databasebeta

← D11×#2242 #14909064

Subgroups — D11×#2242 #14909064

Order 2816.

610 conjugacy classes of subgroups.

The subgroup lattice has 376 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1D11×#499C211yesmaximal, characteristic, complemented
2D11×#495C211yesmaximal, characteristic
3#13070850C211yesmaximal, characteristic, complemented
4#13070849C212yesmaximal, complemented
5#13070848C211yesmaximal, characteristic, complemented
6#13070847C211yesmaximal, characteristic, complemented
7#13070846C212yesmaximal, complemented
8D11×#358C212yesmaximal, complemented
9D11×#357C212yesmaximal
10C4×C16×D11C211yesmaximal, characteristic, complemented
11C11×#2242C211yesmaximal, characteristic, complemented
12C2×Q16×D11C2211yescharacteristic
13C2×SD16×D11—21no—
14C2×D8×D11C2211yescharacteristic
15D11×#125—21no—
16D11×#124—21no—
17C11×#499C2211yescharacteristic, complemented
18C11×#495C2211yescharacteristic
19#10622804C2211yescharacteristic
20#10622781—21no—
21#10622768C2211yescharacteristic
22#10622677—21no—
23#10622672—21no—
24C2×C16×D11C2212yes—
25D11×#107C2212yes—
26#10622491C2212yescomplemented
27D11×#106—21no—
28#10622471—21no—
29#10622309C2211yescharacteristic
30C4×C8×D11C2211yescharacteristic
31#10622296C2211yescharacteristic, complemented
32C11×#358C2212yescomplemented
33C11×#357C2212yes—
34C4×C11×C16C2211yescharacteristic, complemented
35#10622202C2212yescomplemented
36#10622200C2212yes—
37#10622147C2212yes—
38#10622141C2212yescomplemented
39C16×Dic11C2212yescomplemented
40#10622130C2212yescomplemented
41#10622129C2212yes—
42C4×C11⋊C16C2211yescharacteristic, complemented
43C2×Q8×D11—21no—
44C2×D4×D11—21no—
45C2×C11×Q16C2311yescharacteristic
46C2×C11×SD16—21no—
47C2×C11×D8C2311yescharacteristic
48C11×#125—21no—
49C11×#124—21no—
50#67000—21no—
51C2×#4326—21no—
52C2×#4325—21no—
53#66989—21no—
54C2×#4324—21no—
55C2×#4323—21no—
56Q16×D11—24no—
57SD16×D11—44no—
58D8×D11—24no—
59C2×Dic44C2311yescharacteristic
60C2×D88C2311yescharacteristic
61C2×#4314—21no—
62C2×C8×D11D411yescharacteristic
63C2×C8×D11C2311yescharacteristic
64C4⋊C4×D11—22no—
65C4⋊C4×D11—42no—
66#66943—22no—
67#66942—42no—
68#66938—42no—
69C22⋊C4×D11—42no—
70#66928—21no—
71C42×D11D411yescharacteristic
72#66923—21no—
73C2×C11×C16C2312yes—
74C11×#107C2312yes—
75C11×#106—21no—
76C4×C8×C11C2311yescharacteristic
77#66882C2312yes—
78#66881—21no—
79C8×Dic11D411yescharacteristic
80C8×Dic11C2311yescharacteristic
81C2×C11⋊C16C2312yes—
82#66872—22no—
83#66871—22no—
84C4×C11⋊C8D411yescharacteristic
85C16×D11—24no—
86C2×#2242—111nomaximal, Sylow
87C23×D11—41no—
88C2×Q8×C11—21no—
89C2×D4×C11—21no—
90C2×C22⋊D11—41no—
91Q8×D11—42no—
92Q8×D11—42no—
93D4×D11—42no—
94D4×D11—42no—
95C2×D44—21no—
96C2×C4×D11—41no—
97C2×C4×D11—42no—
98C2×C4×D11D812yes—
99C2×C4×D11C2×D411yescharacteristic
100C2×Dic22—21no—
101C2×Dic22—41no—
102C11×Q16—22no—
103C11×SD16—42no—
104C11×D8—22no—
105C2×C8×C11C2×D411yescharacteristic
106C2×C8×C11C2411yescharacteristic
107C11×C4⋊C4—22no—
108C11×C4⋊C4—42no—
109C11×C22⋊C4—42no—
110C42×C11C2×D411yescharacteristic
111C22⋊Dic11—42no—
112#4326—42no—
113#4325—42no—
114#4324—42no—
115#4323—42no—
116(C2×D11)⋊C4—42no—
117(C2×D11)⋊C4—42no—
118C4⋊Dic11—22no—
119C4⋊Dic11—42no—
120Dic11⋊C4—42no—
121Dic11⋊C4—42no—
122Dic11⋊C4—42no—
123C4×Dic11D812yes—
124C4×Dic11C2×D411yescharacteristic
125C2×C11⋊C8C2×D411yescharacteristic
126C2×C11⋊C8C2×D411yescharacteristic
127Dic44—22no—
128D88—22no—
129#4314—42no—
130C8×D11SD1614yes—
131C8×D11#4114yes—
132C11×C16—22no—
133C11⋊C16—22no—
134C2×#499—111no—
135C2×#495—111no—
136#2242—111no—
137#2242—111no—
138#2242—112no—
139#2242—112no—
140#2242—111no—
141#2242D1111yescharacteristic, direct product factor
142C2×#358—112no—
143C2×#357—112no—
144C2×C4×C16—111no—
145C23×C11—41no—
146C22×D11—41no—
147C22×D11—82no—
148C22×D11—84no—
149C22×D11C2×D811yescharacteristic
150Q8×C11—41no—
151Q8×C11—41no—
152D4×C11—41no—
153D4×C11—41no—
154C2×C4×C11—42no—
155C2×C4×C11—41no—
156C2×C4×C11C2×D812yes—
157C2×C4×C11C22×D411yescharacteristic
158C22⋊D11—82no—
159C2×Dic11—42no—
160C2×Dic11—41no—
161C2×Dic11C2×D812yes—
162C2×Dic11C2×D811yescharacteristic
163D44—41no—
164D44—41no—
165C4×D11—24no—
166C4×D11—82no—
167C4×D11—84no—
168C4×D11#12412yes—
169C4×D11C2×SD1612yes—
170Dic22—41no—
171Dic22—41no—
172Dic22—82no—
173C8×C11C2×SD1612yes—
174C8×C11C2×#4112yes—
175C11⋊C8#12412yes—
176C11⋊C8C2×SD1612yes—
177C22×Q16—111no—
178C22×SD16—221no—
179C22×D8—111no—
180C2×#125—221no—
181C2×#124—221no—
182C22×C16—112no—
183#499—112no—
184#499—111no—
185#499—221no—
186#499—221no—
187#499C2×D1111yescharacteristic, complemented
188#495—111no—
189#495—111no—
190#495—111no—
191#495—221no—
192#495—221no—
193#495C2×D1111yescharacteristic
194C2×#107—112no—
195C2×#106—221no—
196C2×C4×C8—111no—
197#358—112no—
198#358—112no—
199#358—112no—
200#358C2×D1112yescomplemented
201#357—112no—
202#357—112no—
203#357—112no—
204#357C2×D1112yes—
205C4×C16—112no—
206C4×C16—111no—
207C4×C16C2×D1111yescharacteristic, complemented
208C22×C11—81no—
209C22×C11—82no—
210C22×C11C22×D811yescharacteristic
211C2×D11—81no—
212C2×D11—82no—
213C2×D11—164no—
214C2×D11#48612yes—
215C2×D11#50814yes—
216C4×C11—22no—
217C4×C11—81no—
218C4×C11—82no—
219C4×C11C2×#12411yescharacteristic
220C4×C11C22×SD1611yescharacteristic
221Dic11—22no—
222Dic11—81no—
223Dic11—82no—
224Dic11#48612yes—
225C22×Q8—221no—
226C22×D4—221no—
227C2×Q16—111no—
228C2×Q16—224no—
229C2×Q16—221no—
230C2×Q16C22×D1111yescharacteristic
231C2×SD16—21no—
232C2×SD16—221no—
233C2×SD16—221no—
234C2×SD16—221no—
235C2×SD16—444no—
236C2×D8—111no—
237C2×D8—224no—
238C2×D8—221no—
239C2×D8C22×D1111yescharacteristic
240C22×C8—111no—
241C22×C8—111no—
242#125—21no—
243#125—222no—
244#125—221no—
245#125—442no—
246#124—21no—
247#124—221no—
248#124—221no—
249#124—221no—
250#124—442no—
251C2×C4⋊C4—222no—
252C2×C4⋊C4—442no—
253C2×C22⋊C4—442no—
254C2×C42—111no—
255C2×C16—112no—
256C2×C16—224no—
257C2×C16C22×D1112yes—
258#107—112no—
259#107—222no—
260#107C22×D1112yes—
261#106—21no—
262#106—222no—
263#106—221no—
264C4×C8—111no—
265C4×C8—111no—
266C4×C8—111no—
267C4×C8C22×D1111yescharacteristic
268C2×C11—161no—
269C2×C11C2×#48611yescharacteristic
270C2×C11C2×#50812yes—
271D11—161no—
272D11#224214yesdirect product factor
273C24—441no—
274C2×Q8—21no—
275C2×Q8—221no—
276C2×Q8—441no—
277C2×Q8—442no—
278C2×Q8—442no—
279C2×D4—21no—
280C2×D4—221no—
281C2×D4—442no—
282C2×D4—442no—
283C2×D4—441no—
284C22×C4—111no—
285C22×C4—112no—
286C22×C4—441no—
287C22×C4—442no—
288Q16—22no—
289Q16—222no—
290Q16—442no—
291SD16—42no—
292SD16—442no—
293SD16—442no—
294SD16—442no—
295D8—22no—
296D8—222no—
297D8—442no—
298C2×C8—111no—
299C2×C8—111no—
300C2×C8—114no—
301C2×C8—114no—
302C2×C8D4×D1111yescharacteristic
303C2×C8C23×D1111yescharacteristic
304C4⋊C4—22no—
305C4⋊C4—42no—
306C4⋊C4—222no—
307C4⋊C4—442no—
308C4⋊C4—442no—
309C4⋊C4—442no—
310C4⋊C4—442no—
311C22⋊C4—42no—
312C22⋊C4—442no—
313C22⋊C4—442no—
314C22⋊C4—442no—
315C42—112no—
316C42—111no—
317C42D4×D1111yescharacteristic
318C16—22no—
319C16—222no—
320C11C2×#224211yescharacteristic, complemented, Sylow
321C23—41no—
322C23—111no—
323C23—441no—
324C23—882no—
325C23—884no—
326Q8—41no—
327Q8—41no—
328Q8—441no—
329Q8—441no—
330Q8—882no—
331D4—41no—
332D4—41no—
333D4—441no—
334D4—441no—
335D4—882no—
336C2×C4—41no—
337C2×C4—42no—
338C2×C4—111no—
339C2×C4—112no—
340C2×C4—112no—
341C2×C4—112no—
342C2×C4—224no—
343C2×C4—441no—
344C2×C4—442no—
345C2×C4—882no—
346C2×C4—884no—
347C2×C4D8×D1112yes—
348C2×C4C2×D4×D1111yescharacteristic
349C8—112no—
350C8—112no—
351C8SD16×D1112yes—
352C8#41×D1112yes—
353C22—82no—
354C22—81no—
355C22—114no—
356C22—112no—
357C22—882no—
358C22—881no—
359C22—1764no—
360C22C2×D8×D1111yescharacteristic
361C4—22no—
362C4—82no—
363C4—81no—
364C4—112no—
365C4—222no—
366C4—882no—
367C4—881no—
368C4D11×#12411yescharacteristic
369C4C2×SD16×D1111yescharacteristic
370C2—114no—
371C2—161no—
372C2—1761no—
373C2D11×#48611yescharacteristic
374C2D11×#50812yes—
subgroupG/H
centerC22C2×D8×D11
commutator, cosocleC2×C8×C11C24
FrattiniC2×C8C23×D11
FittingC11×#2242C2
socleC22×C11C22×D8
prime radicalC2×D8×D11C22
hypercenter#2242D11
hypocenterC11C2×#2242
LCSG ▷ C2×C8×C11 ▷ C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C42 ◁ C4×C8 ◁ #2242

Complements

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

NH ≅ G/Ntype
1. D11×#499C2semidirect
3. #13070850C2semidirect
4. #13070849C2semidirect
5. #13070848C2semidirect
6. #13070847C2semidirect
7. #13070846C2semidirect
8. D11×#358C2semidirect
10. C4×C16×D11C2semidirect
11. C11×#2242C2semidirect
17. C11×#499C22semidirect
26. #10622491C22semidirect
31. #10622296C22semidirect
32. C11×#358C22semidirect
34. C4×C11×C16C22semidirect
35. #10622202C22semidirect
38. #10622141C22semidirect
39. C16×Dic11C22semidirect
40. #10622130C22semidirect
42. C4×C11⋊C16C22semidirect
141. #2242D11direct (N × H)
187. #499C2×D11semidirect
200. #358C2×D11semidirect
207. C4×C16C2×D11semidirect
272. D11#2242direct (N × H)
320. C11C2×#2242semidirect

Maximal subgroups

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

subgroupindex
D11×#4992
D11×#4952
#130708502
#130708492
#130708482
#130708472
#130708462
D11×#3582
D11×#3572
C4×C16×D112
C11×#22422
C2×#224211