Finite Group Databasebeta

← D11×#2072 #14782513

Subgroups — D11×#2072 #14782513

Order 2816.

1150 conjugacy classes of subgroups.

The subgroup lattice has 522 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×D11×#103C212yesmaximal
2D11×#391C211yesmaximal, characteristic
3D11×#384C211yesmaximal, characteristic
4#13070028C212yesmaximal, complemented
5#13070027C212yesmaximal, complemented
6#13070026C211yesmaximal, characteristic, complemented
7#13070025C211yesmaximal, characteristic, complemented
8#13070024C211yesmaximal, characteristic, complemented
9D11×#340C212yesmaximal
10D11×#336C211yesmaximal, characteristic
11C11×#2072C211yesmaximal, characteristic, complemented
12C22×Q8×D11C2211yescharacteristic
13C22×C8×D11C2212yes—
14C2×C4⋊C4×D11—21no—
15C2×C4⋊C4×D11—21no—
16C2×C4⋊C4×D11C2211yescharacteristic
17C2×C4⋊C4×D11C2212yes—
18C2×C42×D11C2211yescharacteristic
19C2×C11×#103C2212yes—
20C11×#391C2211yescharacteristic
21C11×#384C2211yescharacteristic
22#10622843C2211yescharacteristic
23C2×#66899C2212yes—
24C2×#66880C2212yes—
25#10622589—21no—
26#10622589—21no—
27#10622589C2212yes—
28#10622587C2211yescharacteristic
29C2×#66874C2212yes—
30#10622548C2211yescharacteristic
31#10622542C2211yescharacteristic
32D11×#103—28no—
33D11×#95—21no—
34D11×#95—21no—
35#10622259—21no—
36#10622259—21no—
37C11×#340C2212yes—
38C11×#336C2211yescharacteristic
39#10622189C2212yes—
40#10622188C2212yes—
41#10622167C2212yes—
42#10622167C2212yes—
43#10622162C2211yescharacteristic
44C22×Q8×C11C2311yescharacteristic
45C2×Q8×D11—22no—
46C2×Q8×D11—24no—
47C2×Q8×D11—24no—
48C2×Q8×D11D414yes—
49C22×C4×D11—21no—
50C22×C4×D11—22no—
51C22×C4×D11—21no—
52C22×C4×D11D411yescharacteristic
53C22×C4×D11D411yescharacteristic
54C22×C4×D11C2311yescharacteristic
55C22×Dic22—21no—
56C22×Dic22C2311yescharacteristic
57C22×C8×C11C2312yes—
58C2×C11×C4⋊C4—21no—
59C2×C11×C4⋊C4—21no—
60C2×C11×C4⋊C4C2311yescharacteristic
61C2×C11×C4⋊C4C2312yes—
62C2×C42×C11C2311yescharacteristic
63C2×C4⋊Dic11—21no—
64C2×C4⋊Dic11—21no—
65C2×C4⋊Dic11C2311yescharacteristic
66C2×C4⋊Dic11C2312yes—
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×D11—24no—
78C4⋊C4×D11—24no—
79C4⋊C4×D11—24no—
80C4⋊C4×D11—24no—
81C4⋊C4×D11—44no—
82C4⋊C4×D11—44no—
83C42×D11—24no—
84C11×#103—24no—
85C11×#95—21no—
86C11×#95—21no—
87#66899—24no—
88C11⋊#95—21no—
89C11⋊#95—21no—
90C11⋊#95—21no—
91C11⋊#95—21no—
92C11⋊#95—21no—
93C11⋊#95—21no—
94#66880—24no—
95#66874—24no—
96C2×#2072—111nomaximal, Sylow
97C23×D11C2×D411yescharacteristic
98C2×Q8×C11—21no—
99C2×Q8×C11—22no—
100C2×Q8×C11—22no—
101C2×Q8×C11C2×D412yes—
102C22×C4×C11—21no—
103C22×C4×C11—21no—
104C22×C4×C11—22no—
105C22×C4×C11C2×D411yescharacteristic
106C22×C4×C11C2×D411yescharacteristic
107C22×C4×C11C2411yescharacteristic
108C22×Dic11—21no—
109C22×Dic11—21no—
110C22×Dic11—22no—
111C22×Dic11C2×D411yescharacteristic
112C22×Dic11C2×D411yescharacteristic
113C22×Dic11C2×D411yescharacteristic
114Q8×D11—216no—
115Q8×D11—48no—
116C2×C4×D11—24no—
117C2×C4×D11—22no—
118C2×C4×D11—22no—
119C2×C4×D11—22no—
120C2×C4×D11—22no—
121C2×C4×D11—44no—
122C2×C4×D11—42no—
123C2×C4×D11—42no—
124C2×C4×D11—42no—
125C2×C4×D11—44no—
126C2×C4×D11—44no—
127C2×C4×D11—42no—
128C2×C4×D11—42no—
129C2×C4×D11SD1614yes—
130C2×C4×D11Q1614yes—
131C2×C4×D11C2×D412yes—
132C2×C4×D11#4112yes—
133C2×C4×D11#4114yes—
134C2×C4×D11#4114yes—
135C2×Dic22—24no—
136C2×Dic22—22no—
137C2×Dic22—22no—
138C2×Dic22—21no—
139C2×Dic22—42no—
140C2×Dic22—42no—
141C2×Dic22C2×D412yes—
142C2×C8×C11—22no—
143C2×C8×C11—22no—
144C2×C8×C11—22no—
145C11×C4⋊C4—22no—
146C11×C4⋊C4—22no—
147C11×C4⋊C4—22no—
148C11×C4⋊C4—42no—
149C11×C4⋊C4—42no—
150C42×C11—22no—
151C4⋊Dic11—22no—
152C4⋊Dic11—22no—
153C4⋊Dic11—22no—
154C4⋊Dic11—42no—
155C4⋊Dic11—42no—
156Dic11⋊C4—44no—
157Dic11⋊C4—44no—
158Dic11⋊C4—42no—
159Dic11⋊C4—44no—
160C4×Dic11—22no—
161C4×Dic11—22no—
162C4×Dic11—22no—
163C2×C11⋊C8—22no—
164C2×C11⋊C8—22no—
165C2×C11⋊C8—22no—
166C8×D11—48no—
167C22×#103—112no—
168C2×#391—111no—
169C2×#384—111no—
170#2072—112no—
171#2072—111no—
172#2072—111no—
173#2072—112no—
174#2072—111no—
175#2072D1111yescharacteristic, direct product factor
176C2×#340—112no—
177C2×#336—111no—
178C23×C11C22×D411yescharacteristic
179C22×D11#12112yes—
180C22×D11#12312yes—
181C22×D11#12412yes—
182C22×D11C2×SD1612yes—
183C22×D11C2×Q1612yes—
184C22×D11AGL(1,ℤ/8)12yes—
185C22×D11#13712yes—
186Q8×C11—24no—
187Q8×C11—42no—
188C2×C4×C11—21no—
189C2×C4×C11—21no—
190C2×C4×C11—21no—
191C2×C4×C11—21no—
192C2×C4×C11—22no—
193C2×C4×C11—41no—
194C2×C4×C11—41no—
195C2×C4×C11—42no—
196C2×C4×C11—41no—
197C2×C4×C11—42no—
198C2×C4×C11—42no—
199C2×C4×C11—41no—
200C2×C4×C11—41no—
201C2×C4×C11C2×SD1612yes—
202C2×C4×C11C2×Q1612yes—
203C2×C4×C11C22×D411yescharacteristic
204C2×C4×C11C2×#4112yes—
205C2×C4×C11C2×#4112yes—
206C2×C4×C11C2×#4111yescharacteristic
207C2×Dic11—21no—
208C2×Dic11—21no—
209C2×Dic11—21no—
210C2×Dic11—21no—
211C2×Dic11—22no—
212C2×Dic11—41no—
213C2×Dic11—41no—
214C2×Dic11—42no—
215C2×Dic11—41no—
216C2×Dic11—42no—
217C2×Dic11—42no—
218C2×Dic11—41no—
219C2×Dic11—41no—
220C2×Dic11#12112yes—
221C2×Dic11#12312yes—
222C2×Dic11#12412yes—
223C2×Dic11C2×SD1612yes—
224C2×Dic11C2×Q1612yes—
225C4×D11—28no—
226C4×D11—28no—
227C4×D11—48no—
228C4×D11—88no—
229C4×D11—84no—
230C4×D11#12318yes—
231C4×D11#12618yes—
232Dic22—24no—
233Dic22—42no—
234Dic22—48no—
235C8×C11—42no—
236C11⋊C8—42no—
237C23×Q8—111no—
238C23×C8—112no—
239C22×C4⋊C4—112no—
240C22×C4⋊C4—111no—
241C22×C4⋊C4—221no—
242C22×C4⋊C4—221no—
243C22×C42—111no—
244C2×#103—112no—
245C2×#103—112no—
246C2×#103—112no—
247C2×#103—228no—
248C2×#103C2×D1112yes—
249#391—111no—
250#391—111no—
251#391—111no—
252#391—221no—
253#391—221no—
254#391C2×D1111yescharacteristic
255#384—112no—
256#384—111no—
257#384—221no—
258#384—221no—
259#384C2×D1111yescharacteristic
260C2×#95—221no—
261C2×#95—221no—
262#340—112no—
263#340—112no—
264#340—112no—
265#340C2×D1112yes—
266#336—112no—
267#336—111no—
268#336C2×D1111yescharacteristic
269C22×C11C2×#12111yescharacteristic
270C22×C11C2×#12311yescharacteristic
271C22×C11C2×#12411yescharacteristic
272C22×C11C22×SD1611yescharacteristic
273C22×C11C22×Q1611yescharacteristic
274C22×C11C2×AGL(1,ℤ/8)11yescharacteristic
275C22×C11C2×#13711yescharacteristic
276C2×D11#39714yes—
277C2×D11#46014yes—
278C2×D11#46214yes—
279C2×D11#48314yes—
280C2×D11#48414yes—
281C2×D11#48714yes—
282C2×D11#48914yes—
283C4×C11—22no—
284C4×C11—22no—
285C4×C11—42no—
286C4×C11—81no—
287C4×C11—82no—
288C4×C11C2×#12312yes—
289C4×C11C2×#12612yes—
290Dic11—22no—
291Dic11—22no—
292Dic11—42no—
293Dic11—81no—
294Dic11—82no—
295Dic11#39714yes—
296C22×Q8—114no—
297C22×Q8—111no—
298C22×Q8—221no—
299C22×Q8—222no—
300C22×Q8—224no—
301C22×Q8—224no—
302C22×Q8C22×D1111yescharacteristic
303C23×C4—111no—
304C23×C4—111no—
305C23×C4—111no—
306C23×C4—221no—
307C23×C4—222no—
308C23×C4—221no—
309C22×C8—112no—
310C22×C8—224no—
311C22×C8—224no—
312C22×C8—224no—
313C22×C8C22×D1112yes—
314C2×C4⋊C4—21no—
315C2×C4⋊C4—21no—
316C2×C4⋊C4—111no—
317C2×C4⋊C4—112no—
318C2×C4⋊C4—224no—
319C2×C4⋊C4—224no—
320C2×C4⋊C4—224no—
321C2×C4⋊C4—222no—
322C2×C4⋊C4—221no—
323C2×C4⋊C4—222no—
324C2×C4⋊C4—222no—
325C2×C4⋊C4—221no—
326C2×C4⋊C4—221no—
327C2×C4⋊C4—444no—
328C2×C4⋊C4—444no—
329C2×C4⋊C4C22×D1111yescharacteristic
330C2×C4⋊C4C22×D1112yes—
331C2×C42—111no—
332C2×C42—111no—
333C2×C42—111no—
334C2×C42—224no—
335C2×C42C22×D1111yescharacteristic
336#103—24no—
337#103—224no—
338#103—224no—
339#103—224no—
340#95—21no—
341#95—21no—
342#95—221no—
343#95—221no—
344#95—221no—
345#95—221no—
346#95—221no—
347#95—221no—
348C2×C11C2×#39711yescharacteristic
349C2×C11C2×#46011yescharacteristic
350C2×C11C2×#46211yescharacteristic
351C2×C11C2×#48311yescharacteristic
352C2×C11C2×#48411yescharacteristic
353C2×C11C2×#48711yescharacteristic
354C2×C11C2×#48911yescharacteristic
355D11#207218yesdirect product factor
356C24—111no—
357C2×Q8—21no—
358C2×Q8—22no—
359C2×Q8—22no—
360C2×Q8—112no—
361C2×Q8—224no—
362C2×Q8—2216no—
363C2×Q8—221no—
364C2×Q8—222no—
365C2×Q8—222no—
366C2×Q8—442no—
367C2×Q8—442no—
368C2×Q8—448no—
369C2×Q8D4×D1112yes—
370C22×C4—21no—
371C22×C4—21no—
372C22×C4—22no—
373C22×C4—111no—
374C22×C4—112no—
375C22×C4—114no—
376C22×C4—112no—
377C22×C4—114no—
378C22×C4—111no—
379C22×C4—111no—
380C22×C4—114no—
381C22×C4—114no—
382C22×C4—222no—
383C22×C4—222no—
384C22×C4—222no—
385C22×C4—222no—
386C22×C4—224no—
387C22×C4—221no—
388C22×C4—221no—
389C22×C4—222no—
390C22×C4—442no—
391C22×C4—442no—
392C22×C4—444no—
393C22×C4—442no—
394C22×C4—444no—
395C22×C4—444no—
396C22×C4—442no—
397C22×C4—442no—
398C22×C4D4×D1111yescharacteristic
399C22×C4D4×D1111yescharacteristic
400C22×C4C23×D1111yescharacteristic
401C2×C8—22no—
402C2×C8—22no—
403C2×C8—22no—
404C2×C8—222no—
405C2×C8—222no—
406C2×C8—222no—
407C2×C8—448no—
408C4⋊C4—22no—
409C4⋊C4—22no—
410C4⋊C4—22no—
411C4⋊C4—42no—
412C4⋊C4—42no—
413C4⋊C4—222no—
414C4⋊C4—222no—
415C4⋊C4—222no—
416C4⋊C4—442no—
417C4⋊C4—444no—
418C4⋊C4—442no—
419C4⋊C4—444no—
420C4⋊C4—444no—
421C4⋊C4—442no—
422C42—22no—
423C42—222no—
424C42—222no—
425C42—222no—
426C11C2×#207211yescharacteristic, complemented, Sylow
427C23—112no—
428C23—112no—
429C23—112no—
430C23—112no—
431C23—112no—
432C23—112no—
433C23—112no—
434C23C2×D4×D1111yescharacteristic
435Q8—24no—
436Q8—42no—
437Q8—224no—
438Q8—448no—
439Q8—442no—
440C2×C4—21no—
441C2×C4—21no—
442C2×C4—21no—
443C2×C4—21no—
444C2×C4—22no—
445C2×C4—41no—
446C2×C4—41no—
447C2×C4—42no—
448C2×C4—42no—
449C2×C4—41no—
450C2×C4—41no—
451C2×C4—42no—
452C2×C4—41no—
453C2×C4—112no—
454C2×C4—112no—
455C2×C4—112no—
456C2×C4—118no—
457C2×C4—118no—
458C2×C4—112no—
459C2×C4—112no—
460C2×C4—228no—
461C2×C4—228no—
462C2×C4—221no—
463C2×C4—221no—
464C2×C4—221no—
465C2×C4—221no—
466C2×C4—222no—
467C2×C4—448no—
468C2×C4—441no—
469C2×C4—441no—
470C2×C4—442no—
471C2×C4—442no—
472C2×C4—441no—
473C2×C4—441no—
474C2×C4—442no—
475C2×C4—441no—
476C2×C4—888no—
477C2×C4—884no—
478C2×C4SD16×D1112yes—
479C2×C4Q16×D1112yes—
480C2×C4C2×D4×D1111yescharacteristic
481C2×C4#41×D1111yescharacteristic
482C2×C4#41×D1112yes—
483C2×C4#41×D1112yes—
484C8—42no—
485C8—442no—
486C22—114no—
487C22—114no—
488C22—114no—
489C22—114no—
490C22—114no—
491C22—114no—
492C22—114no—
493C22D11×#12111yescharacteristic
494C22D11×#12311yescharacteristic
495C22D11×#12411yescharacteristic
496C22C2×SD16×D1111yescharacteristic
497C22C2×Q16×D1111yescharacteristic
498C22D11×AGL(1,ℤ/8)11yescharacteristic
499C22D11×#13711yescharacteristic
500C4—22no—
501C4—22no—
502C4—42no—
503C4—82no—
504C4—81no—
505C4—114no—
506C4—222no—
507C4—222no—
508C4—442no—
509C4—882no—
510C4—881no—
511C4D11×#12312yes—
512C4D11×#12612yes—
513C2—118no—
514C2D11×#39711yescharacteristic
515C2D11×#46011yescharacteristic
516C2D11×#46211yescharacteristic
517C2D11×#48311yescharacteristic
518C2D11×#48411yescharacteristic
519C2D11×#48711yescharacteristic
520C2D11×#48911yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC11×#2072C2
socleC23×C11C22×D4
prime radicalC23×D11C2×D4
hypercenter#2072D11
hypocenterC11C2×#2072
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ #2072

Complements

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

NH ≅ G/Ntype
4. #13070028C2semidirect
5. #13070027C2semidirect
6. #13070026C2semidirect
7. #13070025C2semidirect
8. #13070024C2semidirect
11. C11×#2072C2semidirect
175. #2072D11direct (N × H)
355. D11#2072direct (N × H)
426. C11C2×#2072semidirect

Maximal subgroups

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

subgroupindex
C2×D11×#1032
D11×#3912
D11×#3842
#130700282
#130700272
#130700262
#130700252
#130700242
D11×#3402
D11×#3362
C11×#20722
C2×#207211