Finite Group Databasebeta

← D11×#2180 #14907202

Subgroups — D11×#2180 #14907202

Order 2816.

646 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×#510C211yesmaximal, characteristic
2D11×#444C211yesmaximal, characteristic
3D11×#441C211yesmaximal, characteristic, complemented
4#13070510C211yesmaximal, characteristic, complemented
5#13070509C211yesmaximal, characteristic, complemented
6#13070508C211yesmaximal, characteristic, complemented
7#13070507C211yesmaximal, characteristic, complemented
8#13070506C211yesmaximal, characteristic, complemented
9#13070505C211yesmaximal, characteristic, complemented
10#13070504C211yesmaximal, characteristic, complemented
11D11×#365C211yesmaximal, characteristic, complemented
12D11×#362C211yesmaximal, characteristic, complemented
13D11×#360C211yesmaximal, characteristic
14D11×#347C211yesmaximal, characteristic, complemented
15C11×#2180C211yesmaximal, characteristic, complemented
16D11×#135C2211yescharacteristic
17C2×Q16×D11C2211yescharacteristic
18D11×#131—21no—
19C4×Q8×D11—21no—
20C11×#510C2211yescharacteristic
21C11×#444C2211yescharacteristic
22C11×#441C2211yescharacteristic, complemented
23#10622810C2211yescharacteristic
24#10622808C2211yescharacteristic
25#10622797C2211yescharacteristic, complemented
26#10622792C2211yescharacteristic
27#10622758—21no—
28#10622643—21no—
29#10622531C412yescomplemented
30D11×Q32C412yescomplemented
31#10622528C412yescomplemented
32D11×SD32C412yescomplemented
33#10622522C2211yescharacteristic
34D11×M32C2211yescharacteristic
35D11×M32C2211yescharacteristic
36#10622507C2211yescharacteristic
37D11×#108C2211yescharacteristic
38D11×#106C2211yescharacteristic
39#10622466C2211yescharacteristic, complemented
40#10622436—21no—
41D11×#104—21no—
42D11×#103—21no—
43#10622402—21no—
44#10622330C2211yescharacteristic
45#10622329C2211yescharacteristic, complemented
46D11×#97C2211yescharacteristic
47C11×#365C2211yescharacteristic, complemented
48C11×#362C2211yescharacteristic, complemented
49C11×#360C2211yescharacteristic
50C11×#347C2211yescharacteristic, complemented
51#10622204C2211yescharacteristic
52#10622203C2211yescharacteristic, complemented
53#10622156C2211yescharacteristic
54#10622155C2211yescharacteristic, complemented
55#10622151C2211yescharacteristic, complemented
56#10622150C2211yescharacteristic, complemented
57#10622150C2211yescharacteristic, complemented
58#10622134C2211yescharacteristic, complemented
59#10622132C2211yescharacteristic, complemented
60#10622126C2211yescharacteristic
61#10622125C2211yescharacteristic, complemented
62#10622104C2211yescharacteristic, complemented
63#41×D11—21no—
64C2×Q8×D11—21no—
65C11×#135C2311yescharacteristic
66C2×C11×Q16C2311yescharacteristic
67C11×#131—21no—
68C4×Q8×C11—21no—
69#67003—21no—
70#67001—21no—
71Q8×Dic11—21no—
72C2×#4326—21no—
73#66972C2×C411yescharacteristic
74Q16×D11—21no—
75Q16×D11—21no—
76Q16×D11C2×C412yes—
77Q16×D11C2×C412yes—
78Q16×D11C2×C411yescharacteristic
79#66969—21no—
80SD16×D11—21no—
81#66965C2×C411yescharacteristic
82D8×D11C2×C411yescharacteristic
83#66960—21no—
84#66960—41no—
85M16×D11—21no—
86M16×D11—41no—
87C2×Dic44C2311yescharacteristic
88#66957C2311yescharacteristic
89#66954—21no—
90#66954—41no—
91C2×C8×D11—41no—
92C2×C8×D11D411yescharacteristic
93C2×C8×D11C2311yescharacteristic
94C4⋊C4×D11—21no—
95C4⋊C4×D11—41no—
96#66940—21no—
97#66940—41no—
98C42×D11—41no—
99C42×D11D411yescharacteristic
100C4×Dic22—21no—
101C4×Dic22—41no—
102C11×Q32C2×C412yescomplemented
103C11×SD32C2×C412yescomplemented
104C11×M32C2311yescharacteristic
105C11×M32C2311yescharacteristic
106C11×#108C2311yescharacteristic
107C11×#106C2311yescharacteristic
108C11×#104—21no—
109C11×#103—21no—
110C11×#97C2311yescharacteristic
111#66901—21no—
112#66899—21no—
113#66893C2×C412yescomplemented
114#66893C2×C412yescomplemented
115#66892C2×C412yescomplemented
116#66891C2×C412yescomplemented
117#66889—21no—
118#66886—21no—
119#66883C2311yescharacteristic
120#66881C2311yescharacteristic
121#66880—21no—
122#66879D411yescharacteristic
123#66879C2311yescharacteristic
124#66876C2311yescharacteristic
125#66876C2311yescharacteristic
126#66874—21no—
127#66872—21no—
128#66869—21no—
129#66867D411yescharacteristic
130Dic88C2×C412yescomplemented
131#66864C2×C412yescomplemented
132#66862—21no—
133#66862C2×C412yes—
134C16×D11—21no—
135C16×D11C2×C412yes—
136C2×#2180—111nomaximal, Sylow
137C11×#41—21no—
138C2×Q8×C11—21no—
139#4343—21no—
140Q8×D11—21no—
141Q8×D11—22no—
142Q8×D11—22no—
143Q8×D11—41no—
144Q8×D11—41no—
145#4341—21no—
146#4341—41no—
147D4×D11—21no—
148D4×D11—41no—
149#4339—21no—
150#4339—41no—
151C2×C4×D11—21no—
152C2×C4×D11—41no—
153C2×C4×D11—41no—
154C2×C4×D11—41no—
155C2×C4×D11C2×D411yescharacteristic
156C2×Dic22—21no—
157C2×Dic22—41no—
158C11×Q16—21no—
159C11×Q16C22×C412yes—
160C11×Q16C22×C411yescharacteristic
161C11×SD16—21no—
162C11×D8C22×C411yescharacteristic
163C11×M16—21no—
164C11×M16—41no—
165C2×C8×C11—41no—
166C2×C8×C11C2×D411yescharacteristic
167C2×C8×C11C2411yescharacteristic
168C11×C4⋊C4—21no—
169C11×C4⋊C4—41no—
170C42×C11—41no—
171C42×C11C2×D411yescharacteristic
172#4326—21no—
173#4326—22no—
174#4326—22no—
175#4325—21no—
176#4324—21no—
177#4323—21no—
178C4⋊Dic11—21no—
179C4⋊Dic11—41no—
180Dic11⋊C4—41no—
181Dic11⋊C4—41no—
182Dic11⋊C4—41no—
183C4×Dic11—21no—
184C4×Dic11—41no—
185C4×Dic11—41no—
186C4×Dic11—41no—
187C4×Dic11C2×D411yescharacteristic
188#4318—21no—
189#4318—41no—
190C2×C11⋊C8—41no—
191C2×C11⋊C8C2×D411yescharacteristic
192C2×C11⋊C8C2×D411yescharacteristic
193Dic44—21no—
194Dic44C22×C412yes—
195Dic44C22×C411yescharacteristic
196D88C22×C411yescharacteristic
197#4314—21no—
198#4313—41no—
199#4313—41no—
200#4313—41no—
201C8×D11—21no—
202C8×D11—21no—
203C8×D11—41no—
204C8×D11—41no—
205C8×D11—41no—
206C8×D11C22×C411yescharacteristic
207C8×D11C22×C411yescharacteristic
208C8×D11#4111yescharacteristic
209C8×D11#4111yescharacteristic
210C11×C16—21no—
211C11×C16C22×C412yes—
212C11⋊C16—21no—
213C11⋊C16C22×C412yes—
214C2×#510—111no—
215C2×#444—111no—
216C2×#441—111no—
217#2180—111no—
218#2180—111no—
219#2180—111no—
220#2180—111no—
221#2180—111no—
222#2180—111no—
223#2180—111no—
224#2180D1111yescharacteristic, direct product factor
225C2×#365—111no—
226C2×#362—111no—
227C2×#360—111no—
228C2×#347—111no—
229C22×D11—41no—
230C22×D11AGL(1,ℤ/8)11yescharacteristic
231Q8×C11—21no—
232Q8×C11—22no—
233Q8×C11—41no—
234D4×C11—21no—
235D4×C11—41no—
236C2×C4×C11—21no—
237C2×C4×C11—41no—
238C2×C4×C11—41no—
239C2×C4×C11—41no—
240C2×C4×C11C22×D411yescharacteristic
241C22⋊D11—41no—
242C22⋊D11—41no—
243C22⋊D11—41no—
244C2×Dic11—21no—
245C2×Dic11—41no—
246C2×Dic11—41no—
247C2×Dic11—41no—
248C2×Dic11AGL(1,ℤ/8)11yescharacteristic
249D44—21no—
250D44—41no—
251C4×D11—42no—
252C4×D11—41no—
253C4×D11—42no—
254C4×D11—42no—
255C4×D11—41no—
256C4×D11—41no—
257C4×D11—82no—
258C4×D11C4×D411yescharacteristic
259C4×D11C4×D411yescharacteristic
260C4×D11AGL(1,ℤ/8)11yescharacteristic
261C4×D11AGL(1,ℤ/8)11yescharacteristic
262Dic22—21no—
263Dic22—22no—
264Dic22—41no—
265Dic22—42no—
266Dic22—42no—
267Dic22—41no—
268C8×C11—21no—
269C8×C11—41no—
270C8×C11C23×C411yescharacteristic
271C8×C11C2×#4111yescharacteristic
272C11⋊C8—21no—
273C11⋊C8—41no—
274C11⋊C8C4×D411yescharacteristic
275C11⋊C8C4×D411yescharacteristic
276C2×#135—111no—
277C22×Q16—111no—
278C2×#131—221no—
279C2×C4×Q8—221no—
280#510—111no—
281#510—111no—
282#510—112no—
283#510—112no—
284#510—111no—
285#510C2×D1111yescharacteristic
286C2×Q32—112no—
287C2×SD32—112no—
288C2×M32—111no—
289C2×M32—111no—
290#444—111no—
291#444—111no—
292#444—111no—
293#444—221no—
294#444—221no—
295#444C2×D1111yescharacteristic
296#441—111no—
297#441—111no—
298#441—111no—
299#441—221no—
300#441—221no—
301#441C2×D1111yescharacteristic, complemented
302C2×#108—111no—
303C2×#106—111no—
304C2×#104—221no—
305C2×#103—221no—
306C2×#97—111no—
307#365—111no—
308#365—111no—
309#365—111no—
310#365C2×D1111yescharacteristic, complemented
311#362—111no—
312#362—111no—
313#362—111no—
314#362C2×D1111yescharacteristic, complemented
315#360—111no—
316#360—111no—
317#360—111no—
318#360C2×D1111yescharacteristic
319#347—111no—
320#347—111no—
321#347—111no—
322#347C2×D1111yescharacteristic, complemented
323C22×C11—41no—
324C22×C11C2×AGL(1,ℤ/8)11yescharacteristic
325C2×D11—22no—
326C2×D11—41no—
327C2×D11—82no—
328C2×D11#44211yescharacteristic
329C2×D11#44211yescharacteristic
330C4×C11—41no—
331C4×C11—41no—
332C4×C11—42no—
333C4×C11—81no—
334C4×C11C2×C4×D411yescharacteristic
335C4×C11C2×AGL(1,ℤ/8)11yescharacteristic
336Dic11—41no—
337Dic11—42no—
338Dic11—41no—
339Dic11—81no—
340Dic11#44211yescharacteristic
341Dic11#44211yescharacteristic
342C2×#41—221no—
343C22×Q8—221no—
344#135—111no—
345#135—111no—
346#135—111no—
347#135—221no—
348#135—221no—
349#135C22×D1111yescharacteristic
350C2×Q16—112no—
351C2×Q16—112no—
352C2×Q16—111no—
353C2×Q16—111no—
354C2×Q16—221no—
355C2×Q16—221no—
356C2×Q16—221no—
357C2×Q16C22×D1111yescharacteristic
358C2×SD16—221no—
359C2×D8—111no—
360#131—21no—
361#131—221no—
362#131—221no—
363#131—221no—
364#131—441no—
365#131—441no—
366C2×M16—221no—
367C2×M16—441no—
368C22×C8—111no—
369C22×C8—111no—
370C22×C8—441no—
371C4×Q8—21no—
372C4×Q8—221no—
373C4×Q8—221no—
374C4×Q8—221no—
375C4×Q8—441no—
376C4×Q8—441no—
377C2×C4⋊C4—221no—
378C2×C4⋊C4—441no—
379C2×C42—111no—
380C2×C42—441no—
381Q32—112no—
382Q32—112no—
383Q32—112no—
384Q32C4×D1112yescomplemented
385SD32—112no—
386SD32—112no—
387SD32—112no—
388SD32C4×D1112yescomplemented
389M32—111no—
390M32—112no—
391M32—111no—
392M32—221no—
393M32C22×D1111yescharacteristic
394M32C22×D1111yescharacteristic
395C2×C16—112no—
396C2×C16—221no—
397#108—111no—
398#108—221no—
399#108C22×D1111yescharacteristic
400#106—111no—
401#106—221no—
402#106C22×D1111yescharacteristic
403#104—21no—
404#104—221no—
405#104—221no—
406#104—221no—
407#103—21no—
408#103—221no—
409#103—221no—
410#103—221no—
411#97—111no—
412#97—111no—
413#97—111no—
414#97C22×D1111yescharacteristic
415C2×C11—21no—
416C2×C11—81no—
417C2×C11C2×#44211yescharacteristic
418D11—21no—
419D11—81no—
420D11#218012yesdirect product factor
421#41—21no—
422#41—221no—
423#41—221no—
424#41—221no—
425#41—441no—
426#41—441no—
427C2×Q8—21no—
428C2×Q8—221no—
429C2×Q8—222no—
430C2×Q8—222no—
431C2×Q8—221no—
432C2×Q8—441no—
433C2×Q8—441no—
434C2×Q8—441no—
435C2×D4—221no—
436C2×D4—441no—
437C22×C4—111no—
438C22×C4—221no—
439C22×C4—441no—
440C22×C4—441no—
441C22×C4—441no—
442Q16—21no—
443Q16—112no—
444Q16—111no—
445Q16—222no—
446Q16—222no—
447Q16—221no—
448Q16—221no—
449Q16C2×C4×D1112yes—
450Q16C2×C4×D1111yescharacteristic
451SD16—21no—
452SD16—221no—
453SD16—221no—
454SD16—221no—
455D8—111no—
456D8—221no—
457D8C2×C4×D1111yescharacteristic
458M16—21no—
459M16—41no—
460M16—221no—
461M16—441no—
462M16—441no—
463M16—441no—
464M16—441no—
465C2×C8—41no—
466C2×C8—111no—
467C2×C8—111no—
468C2×C8—111no—
469C2×C8—111no—
470C2×C8—111no—
471C2×C8—111no—
472C2×C8—221no—
473C2×C8—221no—
474C2×C8—441no—
475C2×C8—441no—
476C2×C8—441no—
477C2×C8—441no—
478C2×C8D4×D1111yescharacteristic
479C2×C8C23×D1111yescharacteristic
480C4⋊C4—21no—
481C4⋊C4—41no—
482C4⋊C4—221no—
483C4⋊C4—441no—
484C4⋊C4—441no—
485C4⋊C4—441no—
486C4⋊C4—441no—
487C42—41no—
488C42—111no—
489C42—221no—
490C42—441no—
491C42—441no—
492C42—441no—
493C42D4×D1111yescharacteristic
494C16—21no—
495C16—112no—
496C16—221no—
497C16C2×C4×D1112yes—
498C11C2×#218011yescharacteristic, complemented, Sylow
499C23—111no—
500C23—441no—
501Q8—21no—
502Q8—22no—
503Q8—41no—
504Q8—221no—
505Q8—222no—
506Q8—442no—
507Q8—442no—
508Q8—441no—
509Q8—441no—
510D4—21no—
511D4—41no—
512D4—221no—
513D4—441no—
514D4—441no—
515D4—441no—
516D4—441no—
517C2×C4—21no—
518C2×C4—41no—
519C2×C4—41no—
520C2×C4—41no—
521C2×C4—111no—
522C2×C4—111no—
523C2×C4—111no—
524C2×C4—111no—
525C2×C4—111no—
526C2×C4—221no—
527C2×C4—441no—
528C2×C4—441no—
529C2×C4—442no—
530C2×C4—442no—
531C2×C4—442no—
532C2×C4—441no—
533C2×C4—441no—
534C2×C4—441no—
535C2×C4—441no—
536C2×C4—882no—
537C2×C4C2×D4×D1111yescharacteristic
538C8—21no—
539C8—41no—
540C8—111no—
541C8—111no—
542C8—221no—
543C8—441no—
544C8C22×C4×D1111yescharacteristic
545C8#41×D1111yescharacteristic
546C22—41no—
547C22—111no—
548C22—111no—
549C22—222no—
550C22—441no—
551C22—882no—
552C22D11×AGL(1,ℤ/8)11yescharacteristic
553C4—41no—
554C4—41no—
555C4—42no—
556C4—81no—
557C4—111no—
558C4—111no—
559C4—441no—
560C4—441no—
561C4—442no—
562C4—881no—
563C4C4×D4×D1111yescharacteristic
564C4D11×AGL(1,ℤ/8)11yescharacteristic
565C2—21no—
566C2—81no—
567C2—112no—
568C2—221no—
569C2—881no—
570C2D11×#44211yescharacteristic
subgroupG/H
centerC2D11×#442
commutatorC8×C11C23×C4
FrattiniC2×C8C23×D11
FittingC11×#2180C2
socleC2×C11C2×#442
prime radicalD11×#135C22
cosocleC2×C8×C11C24
hypercenter#2180D11
hypocenterC11C2×#2180
LCSG ▷ C8×C11 ▷ C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C2 ◁ C2×C4 ◁ #97 ◁ #2180

Complements

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

NH ≅ G/Ntype
3. D11×#441C2semidirect
4. #13070510C2semidirect
5. #13070509C2semidirect
6. #13070508C2semidirect
7. #13070507C2semidirect
8. #13070506C2semidirect
9. #13070505C2semidirect
10. #13070504C2semidirect
11. D11×#365C2semidirect
12. D11×#362C2semidirect
14. D11×#347C2semidirect
15. C11×#2180C2semidirect
22. C11×#441C22semidirect
25. #10622797C22semidirect
29. #10622531C4semidirect
30. D11×Q32C4semidirect
31. #10622528C4semidirect
32. D11×SD32C4semidirect
39. #10622466C22semidirect
45. #10622329C22semidirect
47. C11×#365C22semidirect
48. C11×#362C22semidirect
50. C11×#347C22semidirect
52. #10622203C22semidirect
54. #10622155C22semidirect
55. #10622151C22semidirect
56. #10622150C22semidirect
57. #10622150C22semidirect
58. #10622134C22semidirect
59. #10622132C22semidirect
61. #10622125C22semidirect
62. #10622104C22semidirect
102. C11×Q32C2×C4semidirect
103. C11×SD32C2×C4semidirect
113. #66893C2×C4semidirect
114. #66893C2×C4semidirect
115. #66892C2×C4semidirect
116. #66891C2×C4semidirect
130. Dic88C2×C4semidirect
131. #66864C2×C4semidirect
224. #2180D11direct (N × H)
301. #441C2×D11semidirect
310. #365C2×D11semidirect
314. #362C2×D11semidirect
322. #347C2×D11semidirect
384. Q32C4×D11semidirect
388. SD32C4×D11semidirect
420. D11#2180direct (N × H)
498. C11C2×#2180semidirect

Maximal subgroups

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

subgroupindex
D11×#5102
D11×#4442
D11×#4412
#130705102
#130705092
#130705082
#130705072
#130705062
#130705052
#130705042
D11×#3652
D11×#3622
D11×#3602
D11×#3472
C11×#21802
C2×#218011