Finite Group Databasebeta

← D11×#2084 #14782745

Subgroups — D11×#2084 #14782745

Order 2816.

1086 conjugacy classes of subgroups.

The subgroup lattice has 502 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×D11×#106C212yesmaximal
2D11×#389C211yesmaximal, characteristic
3D11×#384C211yesmaximal, characteristic
4#13070096C212yesmaximal, complemented
5#13070095C212yesmaximal, complemented
6#13070094C211yesmaximal, characteristic, complemented
7#13070093C211yesmaximal, characteristic, complemented
8#13070092C211yesmaximal, characteristic, complemented
9D11×#340C212yesmaximal
10D11×#336C211yesmaximal, characteristic
11C11×#2084C211yesmaximal, characteristic, complemented
12C22×C8×D11C2212yes—
13C2×C4⋊C4×D11—21no—
14C2×C4⋊C4×D11—21no—
15C2×C4⋊C4×D11—21no—
16C2×C4⋊C4×D11C2211yescharacteristic
17C2×C4⋊C4×D11C2212yes—
18C2×C4⋊C4×D11C2211yescharacteristic
19C2×C42×D11C2211yescharacteristic
20C2×C11×#106C2212yes—
21C11×#389C2211yescharacteristic
22C11×#384C2211yescharacteristic
23C2×#66881C2212yes—
24#10622598C2211yescharacteristic
25#10622589—21no—
26#10622589—21no—
27#10622589C2212yes—
28#10622586C2211yescharacteristic
29#10622585—21no—
30C2×#66872C2212yes—
31C2×#66872C2212yes—
32#10622548C2211yescharacteristic
33#10622541C2211yescharacteristic
34D11×#106—28no—
35D11×#95—21no—
36#10622260—21no—
37C11×#340C2212yes—
38C11×#336C2211yescharacteristic
39#10622189C2212yes—
40#10622188C2212yes—
41#10622167C2212yes—
42#10622167C2212yes—
43#10622162C2211yescharacteristic
44C22×C4×D11—21no—
45C22×C4×D11—22no—
46C22×C4×D11—21no—
47C22×C4×D11D411yescharacteristic
48C22×C4×D11D411yescharacteristic
49C22×C4×D11C2311yescharacteristic
50C22×C8×C11C2312yes—
51C2×C11×C4⋊C4—21no—
52C2×C11×C4⋊C4—21no—
53C2×C11×C4⋊C4—21no—
54C2×C11×C4⋊C4C2311yescharacteristic
55C2×C11×C4⋊C4C2312yes—
56C2×C11×C4⋊C4C2311yescharacteristic
57C2×C42×C11C2311yescharacteristic
58C2×C4⋊Dic11—21no—
59C2×C4⋊Dic11—21no—
60C2×C4⋊Dic11—21no—
61C2×C4⋊Dic11C2311yescharacteristic
62C2×C4⋊Dic11C2312yes—
63C2×C4⋊Dic11C2311yescharacteristic
64C2×Dic11⋊C4—21no—
65C2×Dic11⋊C4—21no—
66C2×Dic11⋊C4—21no—
67C2×Dic11⋊C4—21no—
68C2×Dic11⋊C4—22no—
69C2×Dic11⋊C4—22no—
70C2×Dic11⋊C4—22no—
71C2×C4×Dic11D411yescharacteristic
72C2×C4×Dic11D411yescharacteristic
73C2×C4×Dic11C2311yescharacteristic
74C22×C11⋊C8C2312yes—
75C2×C8×D11—24no—
76C2×C8×D11—24no—
77C2×C8×D11Q818yes—
78C4⋊C4×D11—22no—
79C4⋊C4×D11—24no—
80C4⋊C4×D11—24no—
81C4⋊C4×D11—24no—
82C4⋊C4×D11—44no—
83C4⋊C4×D11—44no—
84C4⋊C4×D11—44no—
85C4⋊C4×D11D414yes—
86C42×D11—24no—
87C11×#106—24no—
88C11×#95—21no—
89C11⋊#95—21no—
90C11⋊#95—21no—
91C11⋊#95—21no—
92#66881—24no—
93#66872—24no—
94#66872—24no—
95C2×#2084—111nomaximal, Sylow
96C23×D11C2×D411yescharacteristic
97C22×C4×C11—21no—
98C22×C4×C11—21no—
99C22×C4×C11—22no—
100C22×C4×C11C2×D411yescharacteristic
101C22×C4×C11C2×D411yescharacteristic
102C22×C4×C11C2411yescharacteristic
103C22×Dic11—21no—
104C22×Dic11—21no—
105C22×Dic11—22no—
106C22×Dic11C2×D411yescharacteristic
107C22×Dic11C2×D411yescharacteristic
108C22×Dic11C2×D411yescharacteristic
109C2×C4×D11—24no—
110C2×C4×D11—22no—
111C2×C4×D11—22no—
112C2×C4×D11—22no—
113C2×C4×D11—22no—
114C2×C4×D11—44no—
115C2×C4×D11—42no—
116C2×C4×D11—42no—
117C2×C4×D11—44no—
118C2×C4×D11—42no—
119C2×C4×D11—44no—
120C2×C4×D11—42no—
121C2×C4×D11—42no—
122C2×C4×D11SD1614yes—
123C2×C4×D11SD1614yes—
124C2×C4×D11C2×D412yes—
125C2×C4×D11C2×Q814yes—
126C2×C4×D11#4112yes—
127C2×C4×D11#4114yes—
128C2×C8×C11—22no—
129C2×C8×C11—22no—
130C2×C8×C11C2×Q814yes—
131C11×C4⋊C4—21no—
132C11×C4⋊C4—22no—
133C11×C4⋊C4—22no—
134C11×C4⋊C4—22no—
135C11×C4⋊C4—42no—
136C11×C4⋊C4—42no—
137C11×C4⋊C4—42no—
138C11×C4⋊C4C2×D412yes—
139C42×C11—22no—
140C4⋊Dic11—22no—
141C4⋊Dic11—21no—
142C4⋊Dic11—22no—
143C4⋊Dic11—22no—
144C4⋊Dic11—42no—
145C4⋊Dic11—42no—
146C4⋊Dic11—42no—
147C4⋊Dic11C2×D412yes—
148Dic11⋊C4—24no—
149Dic11⋊C4—44no—
150Dic11⋊C4—44no—
151Dic11⋊C4—42no—
152Dic11⋊C4—42no—
153Dic11⋊C4—44no—
154Dic11⋊C4—42no—
155C4×Dic11—22no—
156C4×Dic11—22no—
157C4×Dic11—22no—
158C2×C11⋊C8—22no—
159C2×C11⋊C8—22no—
160C2×C11⋊C8C2×Q814yes—
161C8×D11—216no—
162C22×#106—112no—
163C2×#389—111no—
164C2×#384—111no—
165#2084—112no—
166#2084—111no—
167#2084—111no—
168#2084—112no—
169#2084—111no—
170#2084D1111yescharacteristic, direct product factor
171C2×#340—112no—
172C2×#336—111no—
173C23×C11C22×D411yescharacteristic
174C22×D11#12112yes—
175C22×D11#12312yes—
176C22×D11C4⋊Q812yes—
177C22×D11C2×SD1612yes—
178C22×D11C2×SD1612yes—
179C22×D11AGL(1,ℤ/8)12yes—
180C22×D11#13712yes—
181C2×C4×C11—21no—
182C2×C4×C11—21no—
183C2×C4×C11—21no—
184C2×C4×C11—21no—
185C2×C4×C11—22no—
186C2×C4×C11—41no—
187C2×C4×C11—41no—
188C2×C4×C11—42no—
189C2×C4×C11—41no—
190C2×C4×C11—41no—
191C2×C4×C11—42no—
192C2×C4×C11—42no—
193C2×C4×C11—41no—
194C2×C4×C11C2×SD1612yes—
195C2×C4×C11C2×SD1612yes—
196C2×C4×C11C22×D411yescharacteristic
197C2×C4×C11C22×Q812yes—
198C2×C4×C11C2×#4112yes—
199C2×C4×C11C2×#4111yescharacteristic
200C2×Dic11—21no—
201C2×Dic11—21no—
202C2×Dic11—21no—
203C2×Dic11—21no—
204C2×Dic11—22no—
205C2×Dic11—41no—
206C2×Dic11—41no—
207C2×Dic11—42no—
208C2×Dic11—41no—
209C2×Dic11—41no—
210C2×Dic11—42no—
211C2×Dic11—42no—
212C2×Dic11—41no—
213C2×Dic11#12112yes—
214C2×Dic11#12312yes—
215C2×Dic11C4⋊Q812yes—
216C2×Dic11C2×SD1612yes—
217C2×Dic11C2×SD1612yes—
218C4×D11—28no—
219C4×D11—28no—
220C4×D11—48no—
221C4×D11—88no—
222C4×D11—84no—
223C4×D11C22⋊Q818yes—
224C4×D11#12518yes—
225C8×C11—24no—
226C11⋊C8—24no—
227C23×C8—112no—
228C22×C4⋊C4—111no—
229C22×C4⋊C4—112no—
230C22×C4⋊C4—111no—
231C22×C4⋊C4—221no—
232C22×C4⋊C4—221no—
233C22×C4⋊C4—221no—
234C22×C42—111no—
235C2×#106—112no—
236C2×#106—112no—
237C2×#106—112no—
238C2×#106—228no—
239C2×#106C2×D1112yes—
240#389—111no—
241#389—111no—
242#389—111no—
243#389—221no—
244#389—221no—
245#389C2×D1111yescharacteristic
246#384—112no—
247#384—111no—
248#384—221no—
249#384—221no—
250#384C2×D1111yescharacteristic
251C2×#95—221no—
252#340—112no—
253#340—112no—
254#340—112no—
255#340C2×D1112yes—
256#336—112no—
257#336—111no—
258#336C2×D1111yescharacteristic
259C22×C11C2×#12111yescharacteristic
260C22×C11C2×#12311yescharacteristic
261C22×C11C2×C4⋊Q811yescharacteristic
262C22×C11C22×SD1611yescharacteristic
263C22×C11C22×SD1611yescharacteristic
264C22×C11C2×AGL(1,ℤ/8)11yescharacteristic
265C22×C11C2×#13711yescharacteristic
266C2×D11#39814yes—
267C2×D11#46014yes—
268C2×D11#46114yes—
269C2×D11#48114yes—
270C2×D11#48314yes—
271C2×D11#49814yes—
272C2×D11#50114yes—
273C4×C11—22no—
274C4×C11—22no—
275C4×C11—42no—
276C4×C11—81no—
277C4×C11—82no—
278C4×C11C2×C22⋊Q812yes—
279C4×C11C2×#12512yes—
280Dic11—22no—
281Dic11—22no—
282Dic11—42no—
283Dic11—81no—
284Dic11—82no—
285Dic11#39814yes—
286C23×C4—111no—
287C23×C4—111no—
288C23×C4—111no—
289C23×C4—221no—
290C23×C4—222no—
291C23×C4—221no—
292C22×C8—112no—
293C22×C8—118no—
294C22×C8—224no—
295C22×C8—224no—
296C22×C8C22×D1112yes—
297C2×C4⋊C4—21no—
298C2×C4⋊C4—21no—
299C2×C4⋊C4—21no—
300C2×C4⋊C4—111no—
301C2×C4⋊C4—114no—
302C2×C4⋊C4—111no—
303C2×C4⋊C4—112no—
304C2×C4⋊C4—222no—
305C2×C4⋊C4—224no—
306C2×C4⋊C4—224no—
307C2×C4⋊C4—224no—
308C2×C4⋊C4—221no—
309C2×C4⋊C4—222no—
310C2×C4⋊C4—221no—
311C2×C4⋊C4—222no—
312C2×C4⋊C4—222no—
313C2×C4⋊C4—221no—
314C2×C4⋊C4—221no—
315C2×C4⋊C4—221no—
316C2×C4⋊C4—221no—
317C2×C4⋊C4—221no—
318C2×C4⋊C4—444no—
319C2×C4⋊C4—444no—
320C2×C4⋊C4—444no—
321C2×C4⋊C4C22×D1111yescharacteristic
322C2×C4⋊C4C22×D1112yes—
323C2×C4⋊C4C22×D1111yescharacteristic
324C2×C42—111no—
325C2×C42—111no—
326C2×C42—111no—
327C2×C42—224no—
328C2×C42C22×D1111yescharacteristic
329#106—24no—
330#106—224no—
331#106—224no—
332#106—224no—
333#95—21no—
334#95—221no—
335#95—221no—
336#95—221no—
337C2×C11C2×#39811yescharacteristic
338C2×C11C2×#46111yescharacteristic
339C2×C11C2×#46011yescharacteristic
340C2×C11C2×#48311yescharacteristic
341C2×C11C2×#48111yescharacteristic
342C2×C11C2×#49811yescharacteristic
343C2×C11C2×#50111yescharacteristic
344D11#208418yesdirect product factor
345C24—111no—
346C22×C4—21no—
347C22×C4—21no—
348C22×C4—22no—
349C22×C4—111no—
350C22×C4—112no—
351C22×C4—114no—
352C22×C4—114no—
353C22×C4—112no—
354C22×C4—111no—
355C22×C4—111no—
356C22×C4—114no—
357C22×C4—114no—
358C22×C4—222no—
359C22×C4—222no—
360C22×C4—222no—
361C22×C4—222no—
362C22×C4—224no—
363C22×C4—221no—
364C22×C4—221no—
365C22×C4—222no—
366C22×C4—442no—
367C22×C4—442no—
368C22×C4—444no—
369C22×C4—442no—
370C22×C4—444no—
371C22×C4—442no—
372C22×C4—444no—
373C22×C4—442no—
374C22×C4D4×D1111yescharacteristic
375C22×C4D4×D1111yescharacteristic
376C22×C4C23×D1111yescharacteristic
377C2×C8—22no—
378C2×C8—22no—
379C2×C8—114no—
380C2×C8—2216no—
381C2×C8—222no—
382C2×C8—222no—
383C2×C8Q8×D1114yes—
384C4⋊C4—21no—
385C4⋊C4—22no—
386C4⋊C4—22no—
387C4⋊C4—22no—
388C4⋊C4—42no—
389C4⋊C4—42no—
390C4⋊C4—42no—
391C4⋊C4—112no—
392C4⋊C4—224no—
393C4⋊C4—221no—
394C4⋊C4—222no—
395C4⋊C4—222no—
396C4⋊C4—222no—
397C4⋊C4—442no—
398C4⋊C4—444no—
399C4⋊C4—442no—
400C4⋊C4—442no—
401C4⋊C4—444no—
402C4⋊C4—442no—
403C4⋊C4—444no—
404C4⋊C4—442no—
405C4⋊C4—442no—
406C4⋊C4D4×D1112yes—
407C42—22no—
408C42—222no—
409C42—222no—
410C42—222no—
411C11C2×#208411yescharacteristic, complemented, Sylow
412C23—112no—
413C23—112no—
414C23—112no—
415C23—112no—
416C23—112no—
417C23—112no—
418C23—112no—
419C23C2×D4×D1111yescharacteristic
420C2×C4—21no—
421C2×C4—21no—
422C2×C4—21no—
423C2×C4—21no—
424C2×C4—22no—
425C2×C4—41no—
426C2×C4—41no—
427C2×C4—42no—
428C2×C4—41no—
429C2×C4—42no—
430C2×C4—41no—
431C2×C4—42no—
432C2×C4—41no—
433C2×C4—112no—
434C2×C4—112no—
435C2×C4—112no—
436C2×C4—118no—
437C2×C4—118no—
438C2×C4—112no—
439C2×C4—112no—
440C2×C4—228no—
441C2×C4—228no—
442C2×C4—221no—
443C2×C4—221no—
444C2×C4—221no—
445C2×C4—221no—
446C2×C4—222no—
447C2×C4—448no—
448C2×C4—441no—
449C2×C4—441no—
450C2×C4—442no—
451C2×C4—441no—
452C2×C4—442no—
453C2×C4—441no—
454C2×C4—442no—
455C2×C4—441no—
456C2×C4—888no—
457C2×C4—884no—
458C2×C4SD16×D1112yes—
459C2×C4SD16×D1112yes—
460C2×C4C2×D4×D1111yescharacteristic
461C2×C4C2×Q8×D1112yes—
462C2×C4#41×D1112yes—
463C2×C4#41×D1111yescharacteristic
464C8—24no—
465C8—224no—
466C22—114no—
467C22—114no—
468C22—114no—
469C22—114no—
470C22—114no—
471C22—114no—
472C22—114no—
473C22D11×#12111yescharacteristic
474C22D11×#12311yescharacteristic
475C22D11×C4⋊Q811yescharacteristic
476C22C2×SD16×D1111yescharacteristic
477C22C2×SD16×D1111yescharacteristic
478C22D11×AGL(1,ℤ/8)11yescharacteristic
479C22D11×#13711yescharacteristic
480C4—22no—
481C4—22no—
482C4—42no—
483C4—82no—
484C4—81no—
485C4—114no—
486C4—222no—
487C4—222no—
488C4—442no—
489C4—882no—
490C4—881no—
491C4D11×C22⋊Q812yes—
492C4D11×#12512yes—
493C2—118no—
494C2D11×#39811yescharacteristic
495C2D11×#46111yescharacteristic
496C2D11×#46011yescharacteristic
497C2D11×#48311yescharacteristic
498C2D11×#48111yescharacteristic
499C2D11×#49811yescharacteristic
500C2D11×#50111yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC11×#2084C2
socleC23×C11C22×D4
prime radicalC23×D11C2×D4
hypercenter#2084D11
hypocenterC11C2×#2084
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ #2084

Complements

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

NH ≅ G/Ntype
4. #13070096C2semidirect
5. #13070095C2semidirect
6. #13070094C2semidirect
7. #13070093C2semidirect
8. #13070092C2semidirect
11. C11×#2084C2semidirect
170. #2084D11direct (N × H)
344. D11#2084direct (N × H)
411. C11C2×#2084semidirect

Maximal subgroups

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

subgroupindex
C2×D11×#1062
D11×#3892
D11×#3842
#130700962
#130700952
#130700942
#130700932
#130700922
D11×#3402
D11×#3362
C11×#20842
C2×#208411