Finite Group Databasebeta

← D11×#1587 #14723316

Subgroups — D11×#1587 #14723316

Order 2816.

674 conjugacy classes of subgroups.

The subgroup lattice has 572 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1D11×#446C211yesmaximal, characteristic
2C8×Q8×D11C211yesmaximal, characteristic
3C4×Q16×D11C211yesmaximal, characteristic
4#13067490C211yesmaximal, characteristic, complemented
5#13067489C211yesmaximal, characteristic, complemented
6#13067488C211yesmaximal, characteristic, complemented
7#13067487C211yesmaximal, characteristic, complemented
8#13067486C211yesmaximal, characteristic, complemented
9#13067485C211yesmaximal, characteristic, complemented
10#13067484C211yesmaximal, characteristic, complemented
11D11×#334C211yesmaximal, characteristic
12D11×Q8⋊C8C211yesmaximal, characteristic
13D11×Q8⋊C8C211yesmaximal, characteristic
14D11×#322C211yesmaximal, characteristic
15C11×#1587C211yesmaximal, characteristic, complemented
16C2×Q16×D11C411yescharacteristic
17C4×Q8×D11C2211yescharacteristic
18C4×Q8×D11C2211yescharacteristic
19C11×#446C2211yescharacteristic
20C8×Q8×C11C2211yescharacteristic
21C4×C11×Q16C2211yescharacteristic
22Q16×Dic11C411yescharacteristic
23C4×#4326C2211yescharacteristic
24C4×#4326C2211yescharacteristic
25#10622637C2211yescharacteristic
26Q8×C11⋊C8C2211yescharacteristic
27D11×#107C411yescharacteristic
28#10622486C411yescharacteristic
29D11×C4⋊C8—21no—
30D11×C4⋊C8—21no—
31D11×C4⋊C8C2211yescharacteristic
32D11×C4⋊C8C2211yescharacteristic
33#10622444C2211yescharacteristic
34#10622443—21no—
35#10622443C2211yescharacteristic
36#10622441—21no—
37D11×#103C411yescharacteristic
38D11×#103C411yescharacteristic
39#10622403C411yescharacteristic
40#10622403C411yescharacteristic
41D11×#97—21no—
42#10622314—21no—
43C4×Dic44C2211yescharacteristic
44C4×C8×D11—21no—
45C4×C8×D11C2211yescharacteristic
46C4×C8×D11C2211yescharacteristic
47C4×C8×D11C2211yescharacteristic
48#10622292C2211yescharacteristic
49C8×Dic22—21no—
50C8×Dic22C2211yescharacteristic
51C11×#334C2211yescharacteristic
52C11×Q8⋊C8C2211yescharacteristic
53C11×Q8⋊C8C2211yescharacteristic
54C11×#322C2211yescharacteristic
55Q8⋊(C11⋊C8)C2211yescharacteristic
56Q8⋊(C11⋊C8)C2211yescharacteristic
57#10622122C2211yescharacteristic
58#10622122C2211yescharacteristic
59#10622118C2211yescharacteristic
60#10622118C2211yescharacteristic
61#10622095C2211yescharacteristic
62#10622094C2211yescharacteristic
63#10622094C2211yescharacteristic
64#10622093C2211yescharacteristic
65#10622092C2211yescharacteristic
66#10622092C2211yescharacteristic
67C2×Q8×D11C2×C411yescharacteristic
68C2×Q8×D11C2×C411yescharacteristic
69C2×C11×Q16C2×C411yescharacteristic
70C4×Q8×C11C2311yescharacteristic
71C4×Q8×C11C2311yescharacteristic
72Q8×Dic11C2×C411yescharacteristic
73Q8×Dic11C2×C411yescharacteristic
74C2×#4326C2×C411yescharacteristic
75C2×#4326C2×C411yescharacteristic
76Q16×D11—24no—
77C2×Dic44C2×C411yescharacteristic
78C2×C8×D11—21no—
79C2×C8×D11—21no—
80C2×C8×D11—21no—
81C2×C8×D11C2×C411yescharacteristic
82C2×C8×D11C2×C411yescharacteristic
83C2×C8×D11D411yescharacteristic
84C2×C8×D11D411yescharacteristic
85C4⋊C4×D11—21no—
86C4⋊C4×D11—21no—
87C4⋊C4×D11C2×C411yescharacteristic
88C4⋊C4×D11C2×C411yescharacteristic
89#66940—21no—
90#66940—21no—
91#66940C2×C411yescharacteristic
92#66940C2×C411yescharacteristic
93C42×D11—21no—
94C42×D11—21no—
95C42×D11C2311yescharacteristic
96C4×Dic22—21no—
97C4×Dic22—21no—
98C4×Dic22C2311yescharacteristic
99C4×Dic22C2311yescharacteristic
100C11×#107C2×C411yescharacteristic
101C11×C4⋊C8—21no—
102C11×C4⋊C8—21no—
103C11×C4⋊C8C2311yescharacteristic
104C11×C4⋊C8C2311yescharacteristic
105C11×#103C2×C411yescharacteristic
106C11×#103C2×C411yescharacteristic
107C11×#97—21no—
108C4×C8×C11—21no—
109C4×C8×C11C2311yescharacteristic
110C4×C8×C11C2311yescharacteristic
111C4×C8×C11C2311yescharacteristic
112#66899C2×C411yescharacteristic
113#66899C2×C411yescharacteristic
114#66882C2×C411yescharacteristic
115#66880C2×C411yescharacteristic
116#66880C2×C411yescharacteristic
117#66879—21no—
118#66879—21no—
119Dic11⋊C8—21no—
120Dic11⋊C8—21no—
121Dic11⋊C8—21no—
122Dic11⋊C8—21no—
123Dic11⋊C8—21no—
124Dic11⋊C8—21no—
125C8×Dic11—21no—
126C8×Dic11—21no—
127C8×Dic11—21no—
128C8×Dic11C2×C411yescharacteristic
129C8×Dic11C2×C411yescharacteristic
130C8×Dic11D411yescharacteristic
131C8×Dic11D411yescharacteristic
132#66874C2×C411yescharacteristic
133#66874C2×C411yescharacteristic
134#66871C2×C411yescharacteristic
135#66871C2×C411yescharacteristic
136C4⋊(C11⋊C8)—21no—
137C4⋊(C11⋊C8)—21no—
138C4⋊(C11⋊C8)C2311yescharacteristic
139C4⋊(C11⋊C8)C2311yescharacteristic
140#66867—21no—
141C4×C11⋊C8—21no—
142C4×C11⋊C8C2311yescharacteristic
143C4×C11⋊C8C2311yescharacteristic
144C4×C11⋊C8C2311yescharacteristic
145C2×#1587—111nomaximal, Sylow
146C2×Q8×C11C22×C411yescharacteristic
147C2×Q8×C11C22×C411yescharacteristic
148Q8×D11—22no—
149Q8×D11—22no—
150Q8×D11—22no—
151Q8×D11M1614yes—
152C2×C4×D11—21no—
153C2×C4×D11—21no—
154C2×C4×D11—21no—
155C2×C4×D11—21no—
156C2×C4×D11C22×C411yescharacteristic
157C2×C4×D11C2×D411yescharacteristic
158C2×C4×D11#4111yescharacteristic
159C2×Dic22—21no—
160C2×Dic22—21no—
161C2×Dic22C22×C411yescharacteristic
162C2×Dic22C22×C411yescharacteristic
163C11×Q16—22no—
164C2×C8×C11—21no—
165C2×C8×C11—21no—
166C2×C8×C11—21no—
167C2×C8×C11C22×C411yescharacteristic
168C2×C8×C11C22×C411yescharacteristic
169C2×C8×C11C2×D411yescharacteristic
170C2×C8×C11C2×D411yescharacteristic
171C11×C4⋊C4—21no—
172C11×C4⋊C4—21no—
173C11×C4⋊C4C22×C411yescharacteristic
174C11×C4⋊C4C22×C411yescharacteristic
175C42×C11—21no—
176C42×C11—21no—
177C42×C11C2411yescharacteristic
178#4326—22no—
179#4326—22no—
180C4⋊Dic11—21no—
181C4⋊Dic11—21no—
182C4⋊Dic11C22×C411yescharacteristic
183C4⋊Dic11C22×C411yescharacteristic
184Dic11⋊C4—21no—
185Dic11⋊C4—21no—
186Dic11⋊C4—21no—
187Dic11⋊C4—21no—
188Dic11⋊C4—21no—
189Dic11⋊C4—21no—
190C4×Dic11—21no—
191C4×Dic11—21no—
192C4×Dic11—21no—
193C4×Dic11—21no—
194C4×Dic11—21no—
195C4×Dic11—21no—
196C4×Dic11C22×C411yescharacteristic
197C4×Dic11C2×D411yescharacteristic
198C4×Dic11#4111yescharacteristic
199C2×C11⋊C8—21no—
200C2×C11⋊C8—21no—
201C2×C11⋊C8—21no—
202C2×C11⋊C8C22×C411yescharacteristic
203C2×C11⋊C8C22×C411yescharacteristic
204C2×C11⋊C8C2×D411yescharacteristic
205C2×C11⋊C8C2×D411yescharacteristic
206Dic44—22no—
207C8×D11—24no—
208C8×D11—22no—
209C8×D11—22no—
210C8×D11—22no—
211C8×D11—22no—
212C8×D11—42no—
213C8×D11—42no—
214C2×#446—111no—
215C2×C8×Q8—111no—
216C2×C4×Q16—111no—
217#1587—111no—
218#1587—111no—
219#1587—111no—
220#1587—111no—
221#1587—111no—
222#1587—111no—
223#1587—111no—
224#1587D1111yescharacteristic, direct product factor
225C2×#334—111no—
226C2×Q8⋊C8—111no—
227C2×Q8⋊C8—111no—
228C2×#322—111no—
229C22×D11C4×D411yescharacteristic
230Q8×C11—21no—
231Q8×C11—21no—
232Q8×C11—21no—
233Q8×C11C2×M1612yes—
234C2×C4×C11—21no—
235C2×C4×C11—21no—
236C2×C4×C11—21no—
237C2×C4×C11—21no—
238C2×C4×C11C23×C411yescharacteristic
239C2×C4×C11C22×D411yescharacteristic
240C2×C4×C11C2×#4111yescharacteristic
241C2×Dic11—21no—
242C2×Dic11—21no—
243C2×Dic11—21no—
244C2×Dic11—21no—
245C2×Dic11C4×D411yescharacteristic
246C2×Dic11C4×D411yescharacteristic
247C2×Dic11C4×D411yescharacteristic
248C4×D11—24no—
249C4×D11—22no—
250C4×D11—42no—
251C4×D11—42no—
252C4×D11—42no—
253C4×D11C2×M1612yes—
254C4×D11#13112yes—
255C4×D11#13712yes—
256C4×D11#13712yes—
257Dic22—21no—
258Dic22—24no—
259Dic22—21no—
260Dic22—21no—
261Dic22—42no—
262Dic22C2×M1612yes—
263C8×C11—22no—
264C8×C11—21no—
265C8×C11—21no—
266C8×C11—21no—
267C8×C11—21no—
268C8×C11—41no—
269C8×C11—41no—
270C11⋊C8—22no—
271C11⋊C8—21no—
272C11⋊C8—21no—
273C11⋊C8—21no—
274C11⋊C8—21no—
275C11⋊C8—41no—
276C11⋊C8—41no—
277C22×Q16—111no—
278C2×C4×Q8—111no—
279C2×C4×Q8—111no—
280#446—111no—
281#446—111no—
282#446—111no—
283#446—221no—
284#446—221no—
285#446C2×D1111yescharacteristic
286C8×Q8—111no—
287C8×Q8—111no—
288C8×Q8—111no—
289C8×Q8—221no—
290C8×Q8—221no—
291C8×Q8C2×D1111yescharacteristic
292C4×Q16—111no—
293C4×Q16—111no—
294C4×Q16—111no—
295C4×Q16—111no—
296C4×Q16—111no—
297C4×Q16—111no—
298C4×Q16—111no—
299C4×Q16C2×D1111yescharacteristic
300C2×#107—111no—
301C2×C4⋊C8—111no—
302C2×C4⋊C8—111no—
303C2×C4⋊C8—221no—
304C2×C4⋊C8—221no—
305C2×#103—111no—
306C2×#103—111no—
307C2×#97—221no—
308C2×C4×C8—111no—
309C2×C4×C8—111no—
310C2×C4×C8—111no—
311C2×C4×C8—221no—
312#334—111no—
313#334—111no—
314#334—111no—
315#334C2×D1111yescharacteristic
316Q8⋊C8—111no—
317Q8⋊C8—111no—
318Q8⋊C8—111no—
319Q8⋊C8—111no—
320Q8⋊C8—111no—
321Q8⋊C8—111no—
322Q8⋊C8C2×D1111yescharacteristic
323Q8⋊C8C2×D1111yescharacteristic
324#322—111no—
325#322—111no—
326#322—111no—
327#322C2×D1111yescharacteristic
328C22×C11C2×C4×D411yescharacteristic
329C2×D11#43512yes—
330C2×D11#44112yes—
331C2×D11#44312yes—
332C4×C11—22no—
333C4×C11—21no—
334C4×C11—41no—
335C4×C11—41no—
336C4×C11—41no—
337C4×C11C22×M1611yescharacteristic
338C4×C11C2×#13111yescharacteristic
339C4×C11C2×#13711yescharacteristic
340C4×C11C2×#13711yescharacteristic
341Dic11—22no—
342Dic11—21no—
343Dic11—41no—
344Dic11—41no—
345Dic11—41no—
346Dic11#43512yes—
347Dic11#44112yes—
348C22×Q8—111no—
349C22×Q8—111no—
350C2×Q16—111no—
351C2×Q16—111no—
352C2×Q16—111no—
353C2×Q16—224no—
354C2×Q16C4×D1111yescharacteristic
355C22×C8—111no—
356C22×C8—111no—
357C22×C8—111no—
358C22×C8—111no—
359C22×C8—221no—
360C22×C8—221no—
361C22×C8—221no—
362C4×Q8—111no—
363C4×Q8—111no—
364C4×Q8—111no—
365C4×Q8—111no—
366C4×Q8—111no—
367C4×Q8—111no—
368C4×Q8—221no—
369C4×Q8—221no—
370C4×Q8—221no—
371C4×Q8—221no—
372C4×Q8C22×D1111yescharacteristic
373C4×Q8C22×D1111yescharacteristic
374C2×C4⋊C4—111no—
375C2×C4⋊C4—111no—
376C2×C4⋊C4—221no—
377C2×C4⋊C4—221no—
378C2×C42—111no—
379C2×C42—221no—
380C2×C42—221no—
381#107—111no—
382#107—111no—
383#107—111no—
384#107C4×D1111yescharacteristic
385C4⋊C8—21no—
386C4⋊C8—21no—
387C4⋊C8—111no—
388C4⋊C8—111no—
389C4⋊C8—221no—
390C4⋊C8—221no—
391C4⋊C8—221no—
392C4⋊C8—221no—
393C4⋊C8—221no—
394C4⋊C8—221no—
395C4⋊C8—221no—
396C4⋊C8—221no—
397C4⋊C8C22×D1111yescharacteristic
398C4⋊C8C22×D1111yescharacteristic
399#103—111no—
400#103—111no—
401#103—111no—
402#103—111no—
403#103—111no—
404#103—111no—
405#103C4×D1111yescharacteristic
406#103C4×D1111yescharacteristic
407#97—21no—
408#97—221no—
409#97—221no—
410#97—221no—
411C4×C8—21no—
412C4×C8—111no—
413C4×C8—111no—
414C4×C8—111no—
415C4×C8—111no—
416C4×C8—111no—
417C4×C8—111no—
418C4×C8—111no—
419C4×C8—221no—
420C4×C8—221no—
421C4×C8—221no—
422C4×C8—221no—
423C4×C8C22×D1111yescharacteristic
424C4×C8C22×D1111yescharacteristic
425C4×C8C22×D1111yescharacteristic
426C2×C11C2×#43511yescharacteristic
427C2×C11C2×#44111yescharacteristic
428C2×C11C2×#44311yescharacteristic
429D11#158714yesdirect product factor
430C2×Q8—114no—
431C2×Q8—111no—
432C2×Q8—111no—
433C2×Q8—221no—
434C2×Q8—221no—
435C2×Q8—222no—
436C2×Q8—222no—
437C2×Q8—222no—
438C2×Q8C2×C4×D1111yescharacteristic
439C2×Q8C2×C4×D1111yescharacteristic
440C22×C4—111no—
441C22×C4—111no—
442C22×C4—111no—
443C22×C4—221no—
444C22×C4—221no—
445C22×C4—221no—
446C22×C4—221no—
447Q16—22no—
448Q16—222no—
449Q16—222no—
450Q16—222no—
451C2×C8—21no—
452C2×C8—21no—
453C2×C8—21no—
454C2×C8—111no—
455C2×C8—111no—
456C2×C8—111no—
457C2×C8—111no—
458C2×C8—222no—
459C2×C8—222no—
460C2×C8—222no—
461C2×C8—222no—
462C2×C8—224no—
463C2×C8—221no—
464C2×C8—221no—
465C2×C8—221no—
466C2×C8—442no—
467C2×C8—442no—
468C2×C8C2×C4×D1111yescharacteristic
469C2×C8C2×C4×D1111yescharacteristic
470C2×C8D4×D1111yescharacteristic
471C2×C8D4×D1111yescharacteristic
472C4⋊C4—21no—
473C4⋊C4—21no—
474C4⋊C4—111no—
475C4⋊C4—111no—
476C4⋊C4—221no—
477C4⋊C4—221no—
478C4⋊C4—221no—
479C4⋊C4—221no—
480C4⋊C4—221no—
481C4⋊C4—221no—
482C4⋊C4—221no—
483C4⋊C4—221no—
484C4⋊C4C2×C4×D1111yescharacteristic
485C4⋊C4C2×C4×D1111yescharacteristic
486C42—21no—
487C42—21no—
488C42—111no—
489C42—111no—
490C42—111no—
491C42—221no—
492C42—221no—
493C42—221no—
494C42—221no—
495C42—221no—
496C42—221no—
497C42C23×D1111yescharacteristic
498C11C2×#158711yescharacteristic, complemented, Sylow
499C23—111no—
500Q8—21no—
501Q8—21no—
502Q8—21no—
503Q8—112no—
504Q8—224no—
505Q8—221no—
506Q8—221no—
507Q8—221no—
508Q8—442no—
509Q8M16×D1112yes—
510C2×C4—21no—
511C2×C4—21no—
512C2×C4—21no—
513C2×C4—21no—
514C2×C4—111no—
515C2×C4—111no—
516C2×C4—112no—
517C2×C4—112no—
518C2×C4—112no—
519C2×C4—112no—
520C2×C4—111no—
521C2×C4—222no—
522C2×C4—224no—
523C2×C4—221no—
524C2×C4—221no—
525C2×C4—221no—
526C2×C4—221no—
527C2×C4—442no—
528C2×C4—442no—
529C2×C4—442no—
530C2×C4C22×C4×D1111yescharacteristic
531C2×C4C2×D4×D1111yescharacteristic
532C2×C4#41×D1111yescharacteristic
533C8—22no—
534C8—21no—
535C8—21no—
536C8—21no—
537C8—21no—
538C8—41no—
539C8—41no—
540C8—222no—
541C8—221no—
542C8—221no—
543C8—221no—
544C8—221no—
545C8—441no—
546C8—441no—
547C22—112no—
548C22—112no—
549C22—112no—
550C22C4×D4×D1111yescharacteristic
551C4—22no—
552C4—21no—
553C4—41no—
554C4—41no—
555C4—41no—
556C4—112no—
557C4—112no—
558C4—222no—
559C4—221no—
560C4—441no—
561C4—441no—
562C4—441no—
563C4C2×M16×D1111yescharacteristic
564C4D11×#13111yescharacteristic
565C4D11×#13711yescharacteristic
566C4D11×#13711yescharacteristic
567C2—114no—
568C2D11×#43511yescharacteristic
569C2D11×#44111yescharacteristic
570C2D11×#44311yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D11
commutatorC2×C4×C11C23×C4
FrattiniC42C23×D11
FittingC11×#1587C2
socleC22×C11C2×C4×D4
prime radicalC22×D11C4×D4
cosocleC42×C11C24
hypercenter#1587D11
hypocenterC11C2×#1587
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C2×C4 ◁ C4×C8 ◁ #1587

Complements

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

NH ≅ G/Ntype
4. #13067490C2semidirect
5. #13067489C2semidirect
6. #13067488C2semidirect
7. #13067487C2semidirect
8. #13067486C2semidirect
9. #13067485C2semidirect
10. #13067484C2semidirect
15. C11×#1587C2semidirect
224. #1587D11direct (N × H)
429. D11#1587direct (N × H)
498. C11C2×#1587semidirect

Maximal subgroups

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

subgroupindex
D11×#4462
C8×Q8×D112
C4×Q16×D112
#130674902
#130674892
#130674882
#130674872
#130674862
#130674852
#130674842
D11×#3342
D11×Q8⋊C82
D11×#3222
C11×#15872
C2×#158711