Finite Group Databasebeta

← D11×#2209 #14908019

Subgroups — D11×#2209 #14908019

Order 2816.

702 conjugacy classes of subgroups.

The subgroup lattice has 426 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×D11×Q32C212yesmaximal
2D11×#494C211yesmaximal, characteristic
3C4×Q16×D11C211yesmaximal, characteristic
4#13070667C211yesmaximal, characteristic, complemented
5#13070666C211yesmaximal, characteristic, complemented
6#13070665C212yesmaximal, complemented
7#13070664C212yesmaximal, complemented
8#13070663C211yesmaximal, characteristic, complemented
9D11×C4⋊C16C211yesmaximal, characteristic
10D11×#358C212yesmaximal
11C11×#2209C211yesmaximal, characteristic, complemented
12C2×Q16×D11—21no—
13C2×Q16×D11C2212yes—
14C2×Q16×D11C2211yescharacteristic
15D11×C4⋊Q8—21no—
16C4×Q8×D11—21no—
17C2×C11×Q32C2212yes—
18C11×#494C2211yescharacteristic
19C4×C11×Q16C2211yescharacteristic
20Q16×Dic11C2211yescharacteristic
21#10622794—21no—
22#10622794C2212yes—
23C2×#66893C2212yes—
24C2×#66893C2212yes—
25#10622705—21no—
26C4×#4326—21no—
27D11×Q32—28no—
28C2×Dic88C2212yes—
29C2×C16×D11C2212yes—
30D11×#107C2211yescharacteristic
31#10622486C2211yescharacteristic
32D11×#103—21no—
33#10622403—21no—
34#10622312C2211yescharacteristic
35C4×Dic44C2211yescharacteristic
36C4×C8×D11C2211yescharacteristic
37C11×C4⋊C16C2211yescharacteristic
38C11×#358C2212yes—
39#10622202C2212yes—
40#10622141C2212yes—
41Dic11⋊C16C2212yes—
42#10622130C2212yes—
43C4⋊(C11⋊C16)C2211yescharacteristic
44C2×Q8×D11—21no—
45C2×Q8×D11—22no—
46C2×C11×Q16—21no—
47C2×C11×Q16C2312yes—
48C2×C11×Q16C2311yescharacteristic
49C11×C4⋊Q8—21no—
50C4×Q8×C11—21no—
51Q8×Dic11—21no—
52#66997—22no—
53C2×#4326—21no—
54C2×#4326—22no—
55C2×#4326—22no—
56Q16×D11—24no—
57Q16×D11—22no—
58Q16×D11—24no—
59Q16×D11—44no—
60Q16×D11D414yes—
61C2×Dic44—21no—
62C2×Dic44C2312yes—
63C2×Dic44C2311yescharacteristic
64C2×C8×D11D411yescharacteristic
65C2×C8×D11C2311yescharacteristic
66C4⋊C4×D11—21no—
67C4⋊C4×D11—41no—
68C4⋊C4×D11—41no—
69C4⋊C4×D11—41no—
70#66941—41no—
71#66941—41no—
72#66940—21no—
73#66940—41no—
74C42×D11—41no—
75C42×D11D411yescharacteristic
76#66922—21no—
77C4×Dic22—21no—
78C4×Dic22—41no—
79C11×Q32—24no—
80C2×C11×C16C2312yes—
81C11×#107C2311yescharacteristic
82C11×#103—21no—
83C4×C8×C11C2311yescharacteristic
84#66899—21no—
85#66893—24no—
86#66893—24no—
87#66882C2311yescharacteristic
88#66880—21no—
89C8×Dic11D411yescharacteristic
90C8×Dic11C2311yescharacteristic
91C2×C11⋊C16C2312yes—
92#66874—21no—
93#66871—21no—
94C4×C11⋊C8D411yescharacteristic
95Dic88—24no—
96C16×D11—24no—
97C2×#2209—111nomaximal, Sylow
98C2×Q8×C11—21no—
99C2×Q8×C11—22no—
100Q8×D11—24no—
101Q8×D11—42no—
102Q8×D11—44no—
103Q8×D11—44no—
104C2×C4×D11—41no—
105C2×C4×D11—41no—
106C2×C4×D11—42no—
107C2×C4×D11D811yescharacteristic
108C2×C4×D11D811yescharacteristic
109C2×C4×D11C2×D411yescharacteristic
110C2×Dic22—21no—
111C2×Dic22—22no—
112C2×Dic22—41no—
113C2×Dic22—42no—
114C11×Q16—21no—
115C11×Q16—22no—
116C11×Q16—22no—
117C11×Q16—42no—
118C11×Q16C2×D412yes—
119C2×C8×C11C2×D411yescharacteristic
120C2×C8×C11C2411yescharacteristic
121C11×C4⋊C4—21no—
122C11×C4⋊C4—41no—
123C11×C4⋊C4—41no—
124C11×C4⋊C4—41no—
125C42×C11—41no—
126C42×C11C2×D411yescharacteristic
127#4326—24no—
128#4326—44no—
129#4326—44no—
130C4⋊Dic11—21no—
131C4⋊Dic11—41no—
132C4⋊Dic11—41no—
133C4⋊Dic11—41no—
134Dic11⋊C4—41no—
135Dic11⋊C4—41no—
136Dic11⋊C4—42no—
137Dic11⋊C4—42no—
138Dic11⋊C4—41no—
139C4×Dic11—41no—
140C4×Dic11—41no—
141C4×Dic11—41no—
142C4×Dic11D811yescharacteristic
143C4×Dic11D811yescharacteristic
144C4×Dic11C2×D411yescharacteristic
145C2×C11⋊C8C2×D411yescharacteristic
146C2×C11⋊C8C2×D411yescharacteristic
147Dic44—22no—
148Dic44—21no—
149Dic44—22no—
150Dic44—42no—
151Dic44C2×D412yes—
152C8×D11—22no—
153C8×D11C2×D412yes—
154C8×D11#4112yes—
155C11×C16—22no—
156C11⋊C16—22no—
157C22×Q32—112no—
158C2×#494—111no—
159C2×C4×Q16—111no—
160#2209—112no—
161#2209—111no—
162#2209—111no—
163#2209—111no—
164#2209—112no—
165#2209D1111yescharacteristic, direct product factor
166C2×C4⋊C16—111no—
167C2×#358—112no—
168C22×D11C2×D811yescharacteristic
169Q8×C11—22no—
170Q8×C11—41no—
171Q8×C11—42no—
172Q8×C11—42no—
173C2×C4×C11—41no—
174C2×C4×C11—41no—
175C2×C4×C11—42no—
176C2×C4×C11C2×D811yescharacteristic
177C2×C4×C11C2×D811yescharacteristic
178C2×C4×C11C22×D411yescharacteristic
179C2×Dic11—41no—
180C2×Dic11—41no—
181C2×Dic11—42no—
182C2×Dic11C2×D811yescharacteristic
183C2×Dic11C2×D811yescharacteristic
184C2×Dic11C2×D811yescharacteristic
185C4×D11—22no—
186C4×D11—44no—
187C4×D11—84no—
188C4×D11—82no—
189C4×D11Q3214yescomplemented
190C4×D11#12112yes—
191C4×D11AGL(1,ℤ/8)12yes—
192Dic22—22no—
193Dic22—41no—
194Dic22—44no—
195Dic22—42no—
196Dic22—42no—
197Dic22—84no—
198C8×C11—21no—
199C8×C11C22×D411yescharacteristic
200C8×C11C2×#4111yescharacteristic
201C11⋊C8—21no—
202C11⋊C8#12112yes—
203C22×Q16—111no—
204C22×Q16—112no—
205C22×Q16—221no—
206C2×C4⋊Q8—221no—
207C2×C4×Q8—221no—
208C2×Q32—112no—
209C2×Q32—112no—
210C2×Q32—112no—
211C2×Q32—228no—
212C2×Q32C2×D1112yes—
213C22×C16—112no—
214#494—112no—
215#494—111no—
216#494—221no—
217#494—221no—
218#494C2×D1111yescharacteristic
219C4×Q16—111no—
220C4×Q16—111no—
221C4×Q16—111no—
222C4×Q16—221no—
223C4×Q16—221no—
224C4×Q16C2×D1111yescharacteristic
225C2×#107—111no—
226C2×#103—221no—
227C2×C4×C8—111no—
228C4⋊C16—112no—
229C4⋊C16—111no—
230C4⋊C16C2×D1111yescharacteristic
231#358—112no—
232#358—112no—
233#358—112no—
234#358C2×D1112yes—
235C22×C11C22×D811yescharacteristic
236C2×D11#45912yes—
237C2×D11C2×Q3212yes—
238C2×D11#51012yes—
239C4×C11—21no—
240C4×C11—42no—
241C4×C11—81no—
242C4×C11—82no—
243C4×C11C2×Q3212yescomplemented
244C4×C11C2×#12111yescharacteristic
245C4×C11C2×AGL(1,ℤ/8)11yescharacteristic
246Dic11—21no—
247Dic11—42no—
248Dic11—81no—
249Dic11—82no—
250Dic11#45912yes—
251Dic11C2×Q3212yescomplemented
252C22×Q8—221no—
253C22×Q8—222no—
254C2×Q16—21no—
255C2×Q16—114no—
256C2×Q16—111no—
257C2×Q16—112no—
258C2×Q16—222no—
259C2×Q16—224no—
260C2×Q16—224no—
261C2×Q16—221no—
262C2×Q16—222no—
263C2×Q16—222no—
264C2×Q16—221no—
265C2×Q16—444no—
266C2×Q16C22×D1112yes—
267C2×Q16C22×D1111yescharacteristic
268C22×C8—111no—
269C22×C8—111no—
270C4⋊Q8—21no—
271C4⋊Q8—222no—
272C4⋊Q8—221no—
273C4⋊Q8—441no—
274C4⋊Q8—441no—
275C4×Q8—21no—
276C4×Q8—221no—
277C4×Q8—221no—
278C4×Q8—221no—
279C4×Q8—441no—
280C4×Q8—441no—
281C2×C4⋊C4—221no—
282C2×C4⋊C4—441no—
283C2×C4⋊C4—441no—
284C2×C4⋊C4—441no—
285C2×C42—111no—
286C2×C42—441no—
287Q32—24no—
288Q32—224no—
289Q32—224no—
290Q32—224no—
291C2×C16—112no—
292C2×C16—224no—
293C2×C16C22×D1112yes—
294#107—111no—
295#107—221no—
296#107C22×D1111yescharacteristic
297#103—21no—
298#103—221no—
299#103—221no—
300#103—221no—
301C4×C8—111no—
302C4×C8—111no—
303C4×C8—111no—
304C4×C8C22×D1111yescharacteristic
305C2×C11C2×#45911yescharacteristic
306C2×C11C22×Q3211yescharacteristic
307C2×C11C2×#51011yescharacteristic
308D11#220914yesdirect product factor
309C2×Q8—21no—
310C2×Q8—22no—
311C2×Q8—224no—
312C2×Q8—221no—
313C2×Q8—222no—
314C2×Q8—441no—
315C2×Q8—442no—
316C2×Q8—442no—
317C2×Q8—444no—
318C2×Q8—444no—
319C22×C4—111no—
320C22×C4—111no—
321C22×C4—111no—
322C22×C4—441no—
323C22×C4—441no—
324C22×C4—442no—
325Q16—22no—
326Q16—21no—
327Q16—22no—
328Q16—42no—
329Q16—112no—
330Q16—224no—
331Q16—222no—
332Q16—221no—
333Q16—222no—
334Q16—442no—
335Q16—444no—
336Q16—444no—
337Q16D4×D1112yes—
338C2×C8—111no—
339C2×C8—112no—
340C2×C8—112no—
341C2×C8—111no—
342C2×C8—222no—
343C2×C8D4×D1111yescharacteristic
344C2×C8C23×D1111yescharacteristic
345C4⋊C4—21no—
346C4⋊C4—41no—
347C4⋊C4—41no—
348C4⋊C4—41no—
349C4⋊C4—221no—
350C4⋊C4—441no—
351C4⋊C4—441no—
352C4⋊C4—441no—
353C4⋊C4—442no—
354C4⋊C4—442no—
355C4⋊C4—441no—
356C4⋊C4—441no—
357C4⋊C4—441no—
358C42—41no—
359C42—111no—
360C42—111no—
361C42—111no—
362C42—441no—
363C42—441no—
364C42—441no—
365C42D4×D1111yescharacteristic
366C16—22no—
367C16—222no—
368C11C2×#220911yescharacteristic, complemented, Sylow
369C23—111no—
370Q8—22no—
371Q8—41no—
372Q8—42no—
373Q8—42no—
374Q8—222no—
375Q8—444no—
376Q8—441no—
377Q8—442no—
378Q8—442no—
379Q8—884no—
380C2×C4—41no—
381C2×C4—41no—
382C2×C4—42no—
383C2×C4—111no—
384C2×C4—111no—
385C2×C4—114no—
386C2×C4—112no—
387C2×C4—112no—
388C2×C4—111no—
389C2×C4—222no—
390C2×C4—444no—
391C2×C4—441no—
392C2×C4—441no—
393C2×C4—442no—
394C2×C4—884no—
395C2×C4—882no—
396C2×C4D8×D1111yescharacteristic
397C2×C4D8×D1111yescharacteristic
398C2×C4C2×D4×D1111yescharacteristic
399C8—21no—
400C8—112no—
401C8—221no—
402C8C2×D4×D1111yescharacteristic
403C8#41×D1111yescharacteristic
404C22—112no—
405C22—112no—
406C22—112no—
407C22C2×D8×D1111yescharacteristic
408C4—21no—
409C4—42no—
410C4—82no—
411C4—81no—
412C4—112no—
413C4—112no—
414C4—221no—
415C4—442no—
416C4—882no—
417C4—881no—
418C4D11×Q3212yescomplemented
419C4D11×#12111yescharacteristic
420C4D11×AGL(1,ℤ/8)11yescharacteristic
421C2—114no—
422C2D11×#45911yescharacteristic
423C2C2×D11×Q3211yescharacteristic
424C2D11×#51011yescharacteristic
subgroupG/H
centerC22C2×D8×D11
commutator, cosocleC2×C8×C11C24
FrattiniC2×C8C23×D11
FittingC11×#2209C2
socleC22×C11C22×D8
prime radicalC22×D11C2×D8
hypercenter#2209D11
hypocenterC11C2×#2209
LCSG ▷ C2×C8×C11 ▷ C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C42 ◁ C4×C8 ◁ #2209

Complements

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

NH ≅ G/Ntype
4. #13070667C2semidirect
5. #13070666C2semidirect
6. #13070665C2semidirect
7. #13070664C2semidirect
8. #13070663C2semidirect
11. C11×#2209C2semidirect
165. #2209D11direct (N × H)
189. C4×D11Q32semidirect
243. C4×C11C2×Q32semidirect
251. Dic11C2×Q32semidirect
308. D11#2209direct (N × H)
368. C11C2×#2209semidirect
418. C4D11×Q32semidirect

Maximal subgroups

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

subgroupindex
C2×D11×Q322
D11×#4942
C4×Q16×D112
#130706672
#130706662
#130706652
#130706642
#130706632
D11×C4⋊C162
D11×#3582
C11×#22092
C2×#220911