Finite Group Databasebeta

← D11×#2075 #14782591

Subgroups — D11×#2075 #14782591

Order 2816.

1270 conjugacy classes of subgroups.

The subgroup lattice has 512 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×D11×#107C211yesmaximal, characteristic, complemented
2C2×D11×C22⋊C8C211yesmaximal, characteristic
3D11×#380C212yesmaximal
4#13070043C212yesmaximal, complemented
5#13070042C212yesmaximal, complemented
6#13070041C211yesmaximal, characteristic, complemented
7#13070040C211yesmaximal, characteristic, complemented
8#13070039C211yesmaximal, characteristic, complemented
9D11×#340C211yesmaximal, characteristic, complemented
10D11×#340C212yesmaximal, complemented
11C11×#2075C211yesmaximal, characteristic, complemented
12C23×C4×D11C2211yescharacteristic
13C22×C8×D11C2211yescharacteristic
14C22×C8×D11C2211yescharacteristic
15C2×C4⋊C4×D11C2212yes—
16C2×C4⋊C4×D11C2212yes—
17C2×C22⋊C4×D11—22no—
18C2×C11×#107C2211yescharacteristic, complemented
19C2×C11×C22⋊C8C2211yescharacteristic
20C11×#380C2212yes—
21#10622825C2212yes—
22C2×C22⋊(C11⋊C8)C2211yescharacteristic
23C2×(C2×D11)⋊C8C2211yescharacteristic
24C2×(C2×D11)⋊C8C2211yescharacteristic
25C2×#66882C2211yescharacteristic, complemented
26#10622600C2212yes—
27#10622600C2212yes—
28C2×#66871C2212yescomplemented
29#10622555—22no—
30D11×#107—24no—
31D11×C22⋊C8—24no—
32#10622280—22no—
33D11×#95—22no—
34C11×#340C2211yescharacteristic, complemented
35C11×#340C2212yescomplemented
36#10622189C2211yescharacteristic, complemented
37#10622189C2212yescomplemented
38#10622167C2212yescomplemented
39#10622167C2212yescomplemented
40#10622167C2212yescomplemented
41C24×D11D411yescharacteristic
42C23×C4×C11C2311yescharacteristic
43C23×Dic11D411yescharacteristic
44C22×C4×D11—22no—
45C22×C4×D11—22no—
46C22×C4×D11—24no—
47C22×C4×D11—24no—
48C22×C4×D11—22no—
49C22×C4×D11—22no—
50C22×C4×D11D411yescharacteristic
51C22×C4×D11D411yescharacteristic
52C22×C4×D11C2311yescharacteristic
53C22×C4×D11C2311yescharacteristic
54C22×C8×C11C2311yescharacteristic
55C22×C8×C11C2311yescharacteristic
56C2×C11×C4⋊C4C2312yes—
57C2×C11×C4⋊C4C2312yes—
58C2×C11×C22⋊C4—22no—
59C2×C22⋊Dic11—22no—
60C2×(C2×D11)⋊C4—22no—
61C2×(C2×D11)⋊C4—22no—
62C2×C4⋊Dic11C2312yes—
63C2×C4⋊Dic11C2312yes—
64C2×Dic11⋊C4—22no—
65C2×Dic11⋊C4—22no—
66C22×C11⋊C8C2311yescharacteristic
67C22×C11⋊C8C2311yescharacteristic
68C2×C8×D11—24no—
69C2×C8×D11—22no—
70C2×C8×D11—24no—
71C2×C8×D11D414yes—
72C4⋊C4×D11—24no—
73C4⋊C4×D11—24no—
74C4⋊C4×D11—24no—
75C4⋊C4×D11—24no—
76C22⋊C4×D11—48no—
77C11×#107—22no—
78C11×C22⋊C8—22no—
79C11×#95—22no—
80C11⋊#95—22no—
81C11⋊#95—22no—
82C11⋊#95—22no—
83C22⋊(C11⋊C8)—22no—
84(C2×D11)⋊C8—22no—
85(C2×D11)⋊C8—22no—
86#66882—22no—
87#66871—24no—
88C2×#2075—111nomaximal, Sylow
89C24×C11C2×D411yescharacteristic
90C23×D11—22no—
91C23×D11—24no—
92C23×D11—22no—
93C23×D11—24no—
94C23×D11D814yes—
95C23×D11C2×D411yescharacteristic
96C23×D11C2×D411yescharacteristic
97C22×C4×C11—21no—
98C22×C4×C11—21no—
99C22×C4×C11—22no—
100C22×C4×C11—22no—
101C22×C4×C11—22no—
102C22×C4×C11—22no—
103C22×C4×C11C2×D411yescharacteristic
104C22×C4×C11C2411yescharacteristic
105C22×Dic11—22no—
106C22×Dic11—24no—
107C22×Dic11—22no—
108C22×Dic11—22no—
109C22×Dic11C2×D411yescharacteristic
110C22×Dic11C2×D411yescharacteristic
111C2×C4×D11—22no—
112C2×C4×D11—24no—
113C2×C4×D11—22no—
114C2×C4×D11—24no—
115C2×C4×D11—21no—
116C2×C4×D11—22no—
117C2×C4×D11—22no—
118C2×C4×D11—21no—
119C2×C4×D11—44no—
120C2×C4×D11—44no—
121C2×C4×D11—48no—
122C2×C4×D11—44no—
123C2×C4×D11—44no—
124C2×C4×D11—44no—
125C2×C4×D11—44no—
126C2×C4×D11—44no—
127C2×C4×D11—44no—
128C2×C4×D11C2×D412yes—
129C2×C4×D11#4112yes—
130C2×C4×D11#4114yes—
131C2×C4×D11#4114yes—
132C2×C8×C11—21no—
133C2×C8×C11—22no—
134C2×C8×C11—22no—
135C2×C8×C11C2×D412yes—
136C11×C4⋊C4—22no—
137C11×C4⋊C4—22no—
138C11×C4⋊C4—22no—
139C11×C4⋊C4—22no—
140C11×C22⋊C4—44no—
141C22⋊Dic11—44no—
142(C2×D11)⋊C4—44no—
143(C2×D11)⋊C4—44no—
144C4⋊Dic11—22no—
145C4⋊Dic11—22no—
146C4⋊Dic11—22no—
147C4⋊Dic11—22no—
148Dic11⋊C4—44no—
149Dic11⋊C4—44no—
150C2×C11⋊C8—21no—
151C2×C11⋊C8—22no—
152C2×C11⋊C8—22no—
153C2×C11⋊C8C2×D412yes—
154C8×D11—28no—
155C8×D11—44no—
156C22×#107—111no—
157C22×C22⋊C8—111no—
158C2×#380—112no—
159#2075—111no—
160#2075—111no—
161#2075—112no—
162#2075—111no—
163#2075—112no—
164#2075D1111yescharacteristic, direct product factor
165C2×#340—112no—
166C2×#340—111no—
167C23×C11—21no—
168C23×C11—22no—
169C23×C11—21no—
170C23×C11—22no—
171C23×C11C2×D812yes—
172C23×C11C22×D411yescharacteristic
173C22×D11—21no—
174C22×D11—22no—
175C22×D11—21no—
176C22×D11—22no—
177C22×D11—28no—
178C22×D11—216no—
179C22×D11—44no—
180C22×D11—44no—
181C22×D11—48no—
182C22×D11#12112yes—
183C22×D11#12314yes—
184C22×D11C2×D812yes—
185C22×D11C2×D812yes—
186C22×D11#13512yes—
187C22×D11#13714yes—
188C2×C4×C11—21no—
189C2×C4×C11—22no—
190C2×C4×C11—41no—
191C2×C4×C11—41no—
192C2×C4×C11—42no—
193C2×C4×C11—42no—
194C2×C4×C11—42no—
195C2×C4×C11—42no—
196C2×C4×C11—42no—
197C2×C4×C11—42no—
198C2×C4×C11—42no—
199C2×C4×C11C22×D411yescharacteristic
200C2×C4×C11C2×#4112yes—
201C2×C4×C11C2×#4112yes—
202C2×C4×C11C2×#4111yescharacteristic
203C2×Dic11—21no—
204C2×Dic11—22no—
205C2×Dic11—44no—
206C2×Dic11—42no—
207C2×Dic11—42no—
208C2×Dic11—42no—
209C2×Dic11—42no—
210C2×Dic11—42no—
211C2×Dic11—42no—
212C2×Dic11#12112yes—
213C2×Dic11#12314yes—
214C4×D11—44no—
215C4×D11—41no—
216C4×D11—41no—
217C4×D11—42no—
218C4×D11—44no—
219C4×D11—88no—
220C4×D11—88no—
221C4×D11#12314yes—
222C4×D11#12414yes—
223C4×D11#12618yes—
224C8×C11—22no—
225C8×C11—41no—
226C11⋊C8—22no—
227C11⋊C8—41no—
228C24×C4—111no—
229C23×C8—111no—
230C23×C8—111no—
231C22×C4⋊C4—112no—
232C22×C4⋊C4—112no—
233C22×C22⋊C4—222no—
234C2×#107—111no—
235C2×#107—112no—
236C2×#107—224no—
237C2×#107C2×D1111yescharacteristic, complemented
238C2×C22⋊C8—111no—
239C2×C22⋊C8—111no—
240C2×C22⋊C8—111no—
241C2×C22⋊C8—224no—
242C2×C22⋊C8C2×D1111yescharacteristic
243#380—112no—
244#380—112no—
245#380—112no—
246#380—222no—
247#380—222no—
248#380C2×D1112yes—
249C2×#95—222no—
250#340—111no—
251#340—112no—
252#340—112no—
253#340—112no—
254#340—112no—
255#340C2×D1111yescharacteristic, complemented
256#340C2×D1112yescomplemented
257C22×C11—24no—
258C22×C11—22no—
259C22×C11—42no—
260C22×C11—41no—
261C22×C11—41no—
262C22×C11C2×#12111yescharacteristic
263C22×C11C2×#12312yes—
264C22×C11C22×D811yescharacteristic
265C22×C11C2×#13511yescharacteristic
266C22×C11C2×#13712yes—
267C2×D11—24no—
268C2×D11—22no—
269C2×D11—42no—
270C2×D11—41no—
271C2×D11—41no—
272C2×D11—416no—
273C2×D11#39714yes—
274C2×D11#46614yes—
275C2×D11#47014yes—
276C2×D11#48018yes—
277C2×D11#48518yes—
278C4×C11—41no—
279C4×C11—82no—
280C4×C11—82no—
281C4×C11C2×#12311yescharacteristic
282C4×C11C2×#12411yescharacteristic
283C4×C11C2×#12612yes—
284Dic11—41no—
285Dic11—82no—
286Dic11—82no—
287Dic11#39714yes—
288C25—111no—
289C23×C4—111no—
290C23×C4—111no—
291C23×C4—111no—
292C23×C4—111no—
293C23×C4—111no—
294C23×C4—222no—
295C23×C4—222no—
296C23×C4—224no—
297C23×C4—224no—
298C23×C4—222no—
299C23×C4—222no—
300C23×C4C22×D1111yescharacteristic
301C22×C8—111no—
302C22×C8—114no—
303C22×C8—111no—
304C22×C8—224no—
305C22×C8—224no—
306C22×C8—222no—
307C22×C8C22×D1111yescharacteristic
308C22×C8C22×D1111yescharacteristic
309C2×C4⋊C4—112no—
310C2×C4⋊C4—112no—
311C2×C4⋊C4—224no—
312C2×C4⋊C4—224no—
313C2×C4⋊C4—224no—
314C2×C4⋊C4—224no—
315C2×C4⋊C4—222no—
316C2×C4⋊C4—222no—
317C2×C4⋊C4C22×D1112yes—
318C2×C4⋊C4C22×D1112yes—
319C2×C22⋊C4—22no—
320C2×C22⋊C4—222no—
321C2×C22⋊C4—222no—
322C2×C22⋊C4—222no—
323C2×C22⋊C4—448no—
324#107—22no—
325#107—224no—
326#107—222no—
327C22⋊C8—22no—
328C22⋊C8—222no—
329C22⋊C8—222no—
330C22⋊C8—222no—
331#95—22no—
332#95—222no—
333#95—222no—
334#95—222no—
335C2×C11—42no—
336C2×C11C2×#39711yescharacteristic
337C2×C11C2×#46611yescharacteristic
338C2×C11C2×#47011yescharacteristic
339C2×C11C2×#48012yes—
340C2×C11C2×#48512yes—
341D11—42no—
342D11#207518yesdirect product factor
343C24—111no—
344C24—114no—
345C24—111no—
346C24—222no—
347C24—224no—
348C24—222no—
349C24—224no—
350C24D4×D1111yescharacteristic
351C22×C4—21no—
352C22×C4—21no—
353C22×C4—22no—
354C22×C4—22no—
355C22×C4—22no—
356C22×C4—22no—
357C22×C4—111no—
358C22×C4—112no—
359C22×C4—112no—
360C22×C4—114no—
361C22×C4—114no—
362C22×C4—111no—
363C22×C4—222no—
364C22×C4—224no—
365C22×C4—222no—
366C22×C4—224no—
367C22×C4—222no—
368C22×C4—224no—
369C22×C4—221no—
370C22×C4—221no—
371C22×C4—222no—
372C22×C4—222no—
373C22×C4—222no—
374C22×C4—222no—
375C22×C4—448no—
376C22×C4—444no—
377C22×C4—444no—
378C22×C4—444no—
379C22×C4—444no—
380C22×C4—444no—
381C22×C4—444no—
382C22×C4—444no—
383C22×C4—444no—
384C22×C4D4×D1111yescharacteristic
385C22×C4C23×D1111yescharacteristic
386C2×C8—22no—
387C2×C8—21no—
388C2×C8—22no—
389C2×C8—112no—
390C2×C8—228no—
391C2×C8—222no—
392C2×C8—221no—
393C2×C8—222no—
394C2×C8—444no—
395C2×C8D4×D1112yes—
396C4⋊C4—22no—
397C4⋊C4—22no—
398C4⋊C4—22no—
399C4⋊C4—22no—
400C4⋊C4—222no—
401C4⋊C4—222no—
402C4⋊C4—222no—
403C4⋊C4—222no—
404C4⋊C4—444no—
405C4⋊C4—444no—
406C22⋊C4—44no—
407C22⋊C4—444no—
408C22⋊C4—444no—
409C22⋊C4—444no—
410C11C2×#207511yescharacteristic, complemented, Sylow
411C23—21no—
412C23—22no—
413C23—21no—
414C23—22no—
415C23—112no—
416C23—112no—
417C23—114no—
418C23—112no—
419C23—114no—
420C23—112no—
421C23—228no—
422C23—2216no—
423C23—221no—
424C23—222no—
425C23—221no—
426C23—222no—
427C23—444no—
428C23—444no—
429C23—448no—
430C23D8×D1112yes—
431C23C2×D4×D1111yescharacteristic
432C2×C4—21no—
433C2×C4—22no—
434C2×C4—42no—
435C2×C4—41no—
436C2×C4—41no—
437C2×C4—42no—
438C2×C4—42no—
439C2×C4—42no—
440C2×C4—42no—
441C2×C4—42no—
442C2×C4—42no—
443C2×C4—112no—
444C2×C4—114no—
445C2×C4—118no—
446C2×C4—114no—
447C2×C4—114no—
448C2×C4—221no—
449C2×C4—222no—
450C2×C4—444no—
451C2×C4—444no—
452C2×C4—444no—
453C2×C4—442no—
454C2×C4—441no—
455C2×C4—441no—
456C2×C4—442no—
457C2×C4—442no—
458C2×C4—442no—
459C2×C4—442no—
460C2×C4—442no—
461C2×C4—442no—
462C2×C4—888no—
463C2×C4—888no—
464C2×C4C2×D4×D1111yescharacteristic
465C2×C4#41×D1111yescharacteristic
466C2×C4#41×D1112yes—
467C2×C4#41×D1112yes—
468C8—22no—
469C8—41no—
470C8—222no—
471C8—441no—
472C22—22no—
473C22—24no—
474C22—41no—
475C22—41no—
476C22—42no—
477C22—114no—
478C22—114no—
479C22—118no—
480C22—114no—
481C22—118no—
482C22—222no—
483C22—224no—
484C22—4416no—
485C22—441no—
486C22—441no—
487C22—442no—
488C22D11×#12111yescharacteristic
489C22D11×#12312yes—
490C22C2×D8×D1111yescharacteristic
491C22D11×#13511yescharacteristic
492C22D11×#13712yes—
493C4—41no—
494C4—82no—
495C4—82no—
496C4—114no—
497C4—441no—
498C4—882no—
499C4—882no—
500C4D11×#12311yescharacteristic
501C4D11×#12411yescharacteristic
502C4D11×#12612yes—
503C2—42no—
504C2—118no—
505C2—442no—
506C2D11×#39711yescharacteristic
507C2D11×#46611yescharacteristic
508C2D11×#47011yescharacteristic
509C2D11×#48012yes—
510C2D11×#48512yes—
subgroupG/H
centerC23C2×D4×D11
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC11×#2075C2
socleC23×C11C22×D4
prime radicalC24×D11D4
hypercenter#2075D11
hypocenterC11C2×#2075
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C23×C4 ◁ #2075

Complements

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

NH ≅ G/Ntype
1. C2×D11×#107C2semidirect
4. #13070043C2semidirect
5. #13070042C2semidirect
6. #13070041C2semidirect
7. #13070040C2semidirect
8. #13070039C2semidirect
9. D11×#340C2semidirect
10. D11×#340C2semidirect
11. C11×#2075C2semidirect
18. C2×C11×#107C22semidirect
25. C2×#66882C22semidirect
28. C2×#66871C22semidirect
34. C11×#340C22semidirect
35. C11×#340C22semidirect
36. #10622189C22semidirect
37. #10622189C22semidirect
38. #10622167C22semidirect
39. #10622167C22semidirect
40. #10622167C22semidirect
164. #2075D11direct (N × H)
237. C2×#107C2×D11semidirect
255. #340C2×D11semidirect
256. #340C2×D11semidirect
342. D11#2075direct (N × H)
410. C11C2×#2075semidirect

Maximal subgroups

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

subgroupindex
C2×D11×#1072
C2×D11×C22⋊C82
D11×#3802
#130700432
#130700422
#130700412
#130700402
#130700392
D11×#3402
C11×#20752
C2×#207511