Finite Group Databasebeta

← D11×#2226 #14908378

Subgroups — D11×#2226 #14908378

Order 2816.

638 conjugacy classes of subgroups.

The subgroup lattice has 416 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1D11×#500C211yesmaximal, characteristic, complemented
2C4×D8×D11C211yesmaximal, characteristic
3#13070764C211yesmaximal, characteristic, complemented
4#13070763C211yesmaximal, characteristic, complemented
5#13070762C212yesmaximal, complemented
6#13070761C212yesmaximal, complemented
7#13070760C211yesmaximal, characteristic, complemented
8D11×#367C212yesmaximal, complemented
9D11×C4⋊C16C211yesmaximal, characteristic, complemented
10D11×#357C212yesmaximal
11C11×#2226C211yesmaximal, characteristic, complemented
12C2×D8×D11C2211yescharacteristic
13D11×C4⋊Q8—21no—
14C4×D4×D11—21no—
15C11×#500C2211yescharacteristic, complemented
16C4×C11×D8C2211yescharacteristic
17D8×Dic11C2211yescharacteristic
18#10622691—21no—
19C4×#4323—21no—
20C2×C16×D11C2212yes—
21D11×#107—21no—
22D11×#107C2211yescharacteristic
23D11×#107C2212yes—
24#10622487—21no—
25#10622487C2212yescomplemented
26#10622485C2211yescharacteristic
27D11×#102—21no—
28#10622369—21no—
29C4×D88C2211yescharacteristic
30C4×C8×D11C2211yescharacteristic
31#10622295C2211yescharacteristic, complemented
32C11×#367C2212yescomplemented
33C11×C4⋊C16C2211yescharacteristic, complemented
34C11×#357C2212yes—
35#10622200C2212yes—
36#10622147C2212yes—
37#10622143C2212yescomplemented
38Dic11⋊C16C2212yescomplemented
39#10622129C2212yes—
40#10622128C2212yescomplemented
41#10622128C2212yescomplemented
42C4⋊(C11⋊C16)C2211yescharacteristic, complemented
43C2×Q8×D11—41no—
44C2×D4×D11—21no—
45C22×C4×D11—41no—
46C2×C11×D8C2311yescharacteristic
47C11×C4⋊Q8—21no—
48C4×D4×C11—21no—
49#66997—41no—
50D4×Dic11—21no—
51C2×#4323—21no—
52C4×C22⋊D11—41no—
53D8×D11—22no—
54D8×D11Q814yescomplemented
55C2×D88C2311yescharacteristic
56C2×C8×D11D411yescharacteristic
57C2×C8×D11C2311yescharacteristic
58#66946—21no—
59C4⋊C4×D11—22no—
60C4⋊C4×D11—21no—
61C4⋊C4×D11—41no—
62#66941—22no—
63#66941—41no—
64(C22⋊D11)⋊C4—41no—
65C22⋊C4×D11—41no—
66C4×D44—21no—
67C42×D11D411yescharacteristic
68#66922—21no—
69C2×C11×C16C2312yes—
70C11×#107—21no—
71C11×#107C2312yes—
72C11×#107C2311yescharacteristic
73C11×#102—21no—
74C4×C8×C11C2311yescharacteristic
75#66896—21no—
76#66885—21no—
77#66882—21no—
78#66882C2312yes—
79#66882C2311yescharacteristic
80C8×Dic11D411yescharacteristic
81C8×Dic11C2311yescharacteristic
82C2×C11⋊C16C2312yes—
83#66873—21no—
84#66871—22no—
85#66871—22no—
86#66871—21no—
87C4×C11⋊C8D411yescharacteristic
88C16×D11—24no—
89C2×#2226—111nomaximal, Sylow
90C23×D11—41no—
91C2×Q8×C11—41no—
92C2×D4×C11—21no—
93C22×C4×C11—41no—
94C2×C22⋊D11—41no—
95C22×Dic11—41no—
96Q8×D11—84no—
97D4×D11—24no—
98D4×D11—42no—
99C2×D44—21no—
100C2×C4×D11—41no—
101C2×C4×D11—41no—
102C2×C4×D11—42no—
103C2×C4×D11—41no—
104C2×C4×D11—84no—
105C2×C4×D11D811yescharacteristic
106C2×C4×D11D811yescharacteristic
107C2×C4×D11C2×D411yescharacteristic
108C2×Dic22—42no—
109C2×Dic22—41no—
110C11×D8—21no—
111C11×D8C2×Q812yescomplemented
112C2×C8×C11C2×D411yescharacteristic
113C2×C8×C11C2411yescharacteristic
114C11×C4⋊C4—22no—
115C11×C4⋊C4—21no—
116C11×C4⋊C4—41no—
117C11×C22⋊C4—41no—
118C42×C11C2×D411yescharacteristic
119C22⋊Dic11—41no—
120#4323—24no—
121(C2×D11)⋊C4—41no—
122(C2×D11)⋊C4—41no—
123C4⋊Dic11—22no—
124C4⋊Dic11—21no—
125C4⋊Dic11—41no—
126Dic11⋊C4—41no—
127Dic11⋊C4—42no—
128Dic11⋊C4—42no—
129C4×Dic11D811yescharacteristic
130C4×Dic11D811yescharacteristic
131C4×Dic11C2×D411yescharacteristic
132C2×C11⋊C8C2×D411yescharacteristic
133C2×C11⋊C8C2×D411yescharacteristic
134D88—21no—
135D88C2×Q812yescomplemented
136C8×D11—22no—
137C8×D11C2×Q812yes—
138C8×D11#4112yes—
139C11×C16—22no—
140C11⋊C16—22no—
141C2×#500—111no—
142C2×C4×D8—111no—
143#2226—111no—
144#2226—111no—
145#2226—112no—
146#2226—111no—
147#2226—112no—
148#2226D1111yescharacteristic, direct product factor
149C2×#367—112no—
150C2×C4⋊C16—111no—
151C2×#357—112no—
152C23×C11—41no—
153C22×D11—41no—
154C22×D11—44no—
155C22×D11—82no—
156C22×D11—82no—
157C22×D11C2×D811yescharacteristic
158Q8×C11—82no—
159D4×C11—22no—
160D4×C11—41no—
161C2×C4×C11—42no—
162C2×C4×C11—41no—
163C2×C4×C11—82no—
164C2×C4×C11C2×D811yescharacteristic
165C2×C4×C11C2×D811yescharacteristic
166C2×C4×C11C22×D411yescharacteristic
167C22⋊D11—44no—
168C2×Dic11—42no—
169C2×Dic11—41no—
170C2×Dic11—82no—
171C2×Dic11C2×D811yescharacteristic
172C2×Dic11C2×D811yescharacteristic
173C2×Dic11C2×D811yescharacteristic
174D44—22no—
175D44—41no—
176C4×D11—22no—
177C4×D11—82no—
178C4×D11—84no—
179C4×D11—82no—
180C4×D11—82no—
181C4×D11SD3214yes—
182C4×D11C22⋊Q812yes—
183C4×D11#13712yes—
184Dic22—84no—
185Dic22—82no—
186C8×C11—21no—
187C8×C11C22×Q811yescharacteristic
188C8×C11C2×#4111yescharacteristic
189C11⋊C8—21no—
190C11⋊C8C22⋊Q812yes—
191C22×D8—111no—
192C2×C4⋊Q8—221no—
193C2×C4×D4—221no—
194C22×C16—112no—
195#500—112no—
196#500—111no—
197#500—221no—
198#500—221no—
199#500C2×D1111yescharacteristic, complemented
200C4×D8—111no—
201C4×D8—111no—
202C4×D8—111no—
203C4×D8—221no—
204C4×D8—221no—
205C4×D8C2×D1111yescharacteristic
206C2×#107—112no—
207C2×#107—111no—
208C2×#107—221no—
209C2×#102—221no—
210C2×C4×C8—111no—
211#367—112no—
212#367—112no—
213#367—112no—
214#367C2×D1112yescomplemented
215C4⋊C16—112no—
216C4⋊C16—111no—
217C4⋊C16C2×D1111yescharacteristic, complemented
218#357—112no—
219#357—112no—
220#357—112no—
221#357C2×D1112yes—
222C22×C11—42no—
223C22×C11—81no—
224C22×C11—81no—
225C22×C11C22×D811yescharacteristic
226C2×D11—42no—
227C2×D11—81no—
228C2×D11—81no—
229C2×D11—88no—
230C2×D11#47412yes—
231C2×D11C2×SD3212yes—
232C2×D11#50912yes—
233C4×C11—21no—
234C4×C11—81no—
235C4×C11—82no—
236C4×C11C2×SD3212yes—
237C4×C11C2×C22⋊Q811yescharacteristic
238C4×C11C2×#13711yescharacteristic
239Dic11—21no—
240Dic11—81no—
241Dic11—82no—
242Dic11#47412yes—
243Dic11C2×SD3212yes—
244C22×Q8—441no—
245C22×D4—221no—
246C23×C4—441no—
247C2×D8—114no—
248C2×D8—111no—
249C2×D8—222no—
250C2×D8—221no—
251C2×D8C22×D1111yescharacteristic
252C22×C8—111no—
253C22×C8—111no—
254C4⋊Q8—21no—
255C4⋊Q8—222no—
256C4⋊Q8—221no—
257C4⋊Q8—441no—
258C4⋊Q8—441no—
259C4×D4—21no—
260C4×D4—221no—
261C4×D4—221no—
262C4×D4—221no—
263C4×D4—441no—
264C4×D4—441no—
265C2×C4⋊C4—221no—
266C2×C4⋊C4—222no—
267C2×C4⋊C4—441no—
268C2×C22⋊C4—441no—
269C2×C42—111no—
270C2×C16—112no—
271C2×C16—224no—
272C2×C16C22×D1112yes—
273#107—21no—
274#107—112no—
275#107—111no—
276#107—221no—
277#107—222no—
278#107—222no—
279#107—221no—
280#107C22×D1112yes—
281#107C22×D1111yescharacteristic
282#102—21no—
283#102—221no—
284#102—221no—
285#102—221no—
286C4×C8—111no—
287C4×C8—111no—
288C4×C8—111no—
289C4×C8C22×D1111yescharacteristic
290C2×C11—82no—
291C2×C11C2×#47411yescharacteristic
292C2×C11C22×SD3211yescharacteristic
293C2×C11C2×#50911yescharacteristic
294D11—82no—
295D11#222614yesdirect product factor
296C24—441no—
297C2×Q8—41no—
298C2×Q8—442no—
299C2×Q8—441no—
300C2×Q8—884no—
301C2×D4—21no—
302C2×D4—224no—
303C2×D4—221no—
304C2×D4—442no—
305C2×D4—441no—
306C22×C4—41no—
307C22×C4—111no—
308C22×C4—111no—
309C22×C4—111no—
310C22×C4—441no—
311C22×C4—441no—
312C22×C4—442no—
313C22×C4—441no—
314C22×C4—441no—
315C22×C4—884no—
316D8—21no—
317D8—112no—
318D8—224no—
319D8—221no—
320D8Q8×D1112yescomplemented
321C2×C8—111no—
322C2×C8—112no—
323C2×C8—112no—
324C2×C8—111no—
325C2×C8—222no—
326C2×C8D4×D1111yescharacteristic
327C2×C8C23×D1111yescharacteristic
328C4⋊C4—21no—
329C4⋊C4—22no—
330C4⋊C4—41no—
331C4⋊C4—221no—
332C4⋊C4—222no—
333C4⋊C4—441no—
334C4⋊C4—442no—
335C4⋊C4—442no—
336C4⋊C4—441no—
337C22⋊C4—41no—
338C22⋊C4—441no—
339C22⋊C4—441no—
340C22⋊C4—441no—
341C42—111no—
342C42—111no—
343C42—111no—
344C42D4×D1111yescharacteristic
345C16—22no—
346C16—222no—
347C11C2×#222611yescharacteristic, complemented, Sylow
348C23—41no—
349C23—111no—
350C23—444no—
351C23—441no—
352C23—882no—
353C23—882no—
354Q8—82no—
355Q8—882no—
356Q8—884no—
357D4—22no—
358D4—41no—
359D4—222no—
360D4—444no—
361D4—441no—
362C2×C4—41no—
363C2×C4—42no—
364C2×C4—82no—
365C2×C4—111no—
366C2×C4—111no—
367C2×C4—114no—
368C2×C4—112no—
369C2×C4—112no—
370C2×C4—111no—
371C2×C4—222no—
372C2×C4—441no—
373C2×C4—442no—
374C2×C4—882no—
375C2×C4—882no—
376C2×C4—884no—
377C2×C4—882no—
378C2×C4—882no—
379C2×C4D8×D1111yescharacteristic
380C2×C4D8×D1111yescharacteristic
381C2×C4C2×D4×D1111yescharacteristic
382C8—21no—
383C8—112no—
384C8—221no—
385C8C2×Q8×D1111yescharacteristic
386C8#41×D1111yescharacteristic
387C22—42no—
388C22—81no—
389C22—81no—
390C22—112no—
391C22—112no—
392C22—112no—
393C22—442no—
394C22—888no—
395C22—881no—
396C22—881no—
397C22C2×D8×D1111yescharacteristic
398C4—21no—
399C4—81no—
400C4—82no—
401C4—112no—
402C4—112no—
403C4—221no—
404C4—881no—
405C4—882no—
406C4D11×SD3212yes—
407C4D11×C22⋊Q811yescharacteristic
408C4D11×#13711yescharacteristic
409C2—82no—
410C2—114no—
411C2—882no—
412C2D11×#47411yescharacteristic
413C2C2×D11×SD3211yescharacteristic
414C2D11×#50911yescharacteristic
subgroupG/H
centerC22C2×D8×D11
commutator, cosocleC2×C8×C11C24
FrattiniC2×C8C23×D11
FittingC11×#2226C2
socleC22×C11C22×D8
prime radicalC2×D8×D11C22
hypercenter#2226D11
hypocenterC11C2×#2226
LCSG ▷ C2×C8×C11 ▷ C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C42 ◁ C4×C8 ◁ #2226

Complements

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

NH ≅ G/Ntype
1. D11×#500C2semidirect
3. #13070764C2semidirect
4. #13070763C2semidirect
5. #13070762C2semidirect
6. #13070761C2semidirect
7. #13070760C2semidirect
8. D11×#367C2semidirect
9. D11×C4⋊C16C2semidirect
11. C11×#2226C2semidirect
15. C11×#500C22semidirect
25. #10622487C22semidirect
31. #10622295C22semidirect
32. C11×#367C22semidirect
33. C11×C4⋊C16C22semidirect
37. #10622143C22semidirect
38. Dic11⋊C16C22semidirect
40. #10622128C22semidirect
41. #10622128C22semidirect
42. C4⋊(C11⋊C16)C22semidirect
54. D8×D11Q8semidirect
111. C11×D8C2×Q8semidirect
135. D88C2×Q8semidirect
148. #2226D11direct (N × H)
199. #500C2×D11semidirect
214. #367C2×D11semidirect
217. C4⋊C16C2×D11semidirect
295. D11#2226direct (N × H)
320. D8Q8×D11semidirect
347. C11C2×#2226semidirect

Maximal subgroups

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

subgroupindex
D11×#5002
C4×D8×D112
#130707642
#130707632
#130707622
#130707612
#130707602
D11×#3672
D11×C4⋊C162
D11×#3572
C11×#22262
C2×#222611