Finite Group Databasebeta

← #14907236

Subgroups — #14907236

Order 2816.

632 conjugacy classes of subgroups.

The subgroup lattice has 568 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1D11×#510C211yesmaximal, characteristic
2#13077530C211yesmaximal, characteristic
3#13077481C211yesmaximal, 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
11#13070387C211yesmaximal, characteristic, complemented
12D11×#362C211yesmaximal, characteristic, complemented
13#13070350C211yesmaximal, characteristic
14#13070219C211yesmaximal, characteristic, complemented
15C11×#2180C211yesmaximal, characteristic, complemented
16D11×#135C2211yescharacteristic
17C2×Q16×D11C2211yescharacteristic
18#10623281—21no—
19#10623103—21no—
20C11×#510C2211yescharacteristic
21C11×#444C2211yescharacteristic
22C11×#441C2211yescharacteristic, complemented
23#10622810C2211yescharacteristic
24#10622808C2211yescharacteristic
25#10622797C2211yescharacteristic, complemented
26#10622792C2211yescharacteristic
27#10622757—21no—
28C4×#4326—21no—
29#10622531C412yescomplemented
30D11×Q32C412yescomplemented
31#10622528C412yescomplemented
32D11×SD32C412yescomplemented
33#10622522C2211yescharacteristic
34D11×M32C2211yescharacteristic
35D11×M32C2211yescharacteristic
36#10622507C2211yescharacteristic
37D11×#108C2211yescharacteristic
38#10622473C2211yescharacteristic
39#10622466C2211yescharacteristic, complemented
40#10622437—21no—
41#10622434—21no—
42#10622415—21no—
43#10622403—21no—
44#10622330C2211yescharacteristic
45#10622329C2211yescharacteristic, complemented
46#10622321C2211yescharacteristic
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×#4313—41no—
92C2×#4313D411yescharacteristic
93C2×C8×D11C2311yescharacteristic
94#66945—21no—
95#66945—41no—
96#66940—21no—
97#66940—41no—
98#66925—41no—
99#66925D411yescharacteristic
100C4×Dic22—21no—
101C4×Dic22—41no—
102C11×Q32C2×C412yes—
103C11×SD32C2×C412yes—
104C11×M32C2311yescharacteristic
105C11×M32C2311yescharacteristic
106C11×#108C2311yescharacteristic
107C11×#106C2311yescharacteristic
108C11×#104—21no—
109C11×#103—21no—
110C11×#97C2311yescharacteristic
111#66901—21no—
112#66899—21no—
113#66893C2×C412yes—
114#66893C2×C412yes—
115#66892C2×C412yes—
116#66891C2×C412yes—
117#66889—21no—
118#66886—21no—
119#66883C2311yescharacteristic
120#66881C2311yescharacteristic
121#66880—21no—
122#66879C2311yescharacteristic
123C8×Dic11D411yescharacteristic
124#66876C2311yescharacteristic
125#66876C2311yescharacteristic
126#66874—21no—
127#66871—21no—
128#66869—21no—
129C4×C11⋊C8D411yescharacteristic
130Dic88C2×C412yes—
131#66864C2×C412yes—
132#66862—21no—
133#66862C2×C412yes—
134C16×D11—21no—
135C16×D11C2×C412yes—
136#33470—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—41no—
152C2×C4×D11—41no—
153C2×C4×D11C2×D411yescharacteristic
154C2×Dic22—21no—
155C2×Dic22—41no—
156C11×Q16—21no—
157C11×Q16C22×C412yes—
158C11×Q16C22×C411yescharacteristic
159C11×SD16—21no—
160C11×D8C22×C411yescharacteristic
161C11×M16—21no—
162C11×M16—41no—
163C2×C8×C11—41no—
164C2×C8×C11C2×D411yescharacteristic
165C2×C8×C11C2411yescharacteristic
166C11×C4⋊C4—21no—
167C11×C4⋊C4—41no—
168C42×C11—41no—
169C42×C11C2×D411yescharacteristic
170#4326—21no—
171#4326—22no—
172#4326—22no—
173#4325—21no—
174#4324—21no—
175#4323—21no—
176(C2×D11)⋊C4—21no—
177(C2×D11)⋊C4—41no—
178C4⋊Dic11—21no—
179C4⋊Dic11—41no—
180Dic11⋊C4—21no—
181Dic11⋊C4—41no—
182Dic11⋊C4—41no—
183C4×Dic11—41no—
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—21no—
199#4313—21no—
200#4313—41no—
201#4313—41no—
202#4313—41no—
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—
215#2957—111no—
216#2950—111no—
217#2180—111no—
218#2180—111no—
219#2180—111no—
220#2180—111no—
221#2180—111no—
222#2180—111no—
223#2180—111no—
224#2180D1111yescharacteristic, complemented
225#2155—111no—
226C2×#362—111no—
227#2145—111no—
228#2110—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—41no—
252C4×D11—42no—
253C4×D11—42no—
254C4×D11—41no—
255C4×D11—41no—
256C4×D11C4×D411yescharacteristic
257C4×D11C4×D411yescharacteristic
258C4×D11AGL(1,ℤ/8)11yescharacteristic
259C4×D11AGL(1,ℤ/8)11yescharacteristic
260Dic22—21no—
261Dic22—22no—
262Dic22—41no—
263Dic22—42no—
264Dic22—42no—
265Dic22—41no—
266C8×C11—21no—
267C8×C11—41no—
268C8×C11C23×C411yescharacteristic
269C8×C11C2×#4111yescharacteristic
270C11⋊C8—21no—
271C11⋊C8—41no—
272C11⋊C8C4×D411yescharacteristic
273C11⋊C8C4×D411yescharacteristic
274C2×#135—111no—
275C22×Q16—111no—
276#568—221no—
277#519—221no—
278#510—111no—
279#510—111no—
280#510—112no—
281#510—112no—
282#510—111no—
283#510C2×D1111yescharacteristic
284C2×Q32—112no—
285C2×SD32—112no—
286C2×M32—111no—
287C2×M32—111no—
288#444—111no—
289#444—111no—
290#444—111no—
291#444C2×D1111yescharacteristic
292#443—221no—
293#443—221no—
294#441—111no—
295#441—111no—
296#441—111no—
297#441C2×D1111yescharacteristic, complemented
298C4×Q16—221no—
299C4×Q16—221no—
300C2×#108—111no—
301#427—111no—
302#421—221no—
303#419—221no—
304#405—111no—
305#365—111no—
306#365—111no—
307#365—111no—
308#365C2×D1111yescharacteristic, complemented
309#362—111no—
310#362—111no—
311#362—111no—
312#362C2×D1111yescharacteristic, complemented
313#360—111no—
314#360—111no—
315#360—111no—
316#360C2×D1111yescharacteristic
317#347—111no—
318#347—111no—
319#347—111no—
320#347C2×D1111yescharacteristic, complemented
321C22×C11—41no—
322C22×C11C2×AGL(1,ℤ/8)11yescharacteristic
323C2×D11—41no—
324C2×D11—41no—
325C2×D11—161no—
326C2×D11#44211yescharacteristic
327C2×D11#44211yescharacteristic
328C4×C11—41no—
329C4×C11—41no—
330C4×C11—42no—
331C4×C11—81no—
332C4×C11C2×C4×D411yescharacteristic
333C4×C11C2×AGL(1,ℤ/8)11yescharacteristic
334Dic11—41no—
335Dic11—42no—
336Dic11—41no—
337Dic11—81no—
338Dic11#44211yescharacteristic
339Dic11#44211yescharacteristic
340C2×#41—221no—
341C22×Q8—221no—
342#135—111no—
343#135—111no—
344#135—111no—
345#135—221no—
346#135—221no—
347#135C22×D1111yescharacteristic
348C2×Q16—112no—
349C2×Q16—112no—
350C2×Q16—111no—
351C2×Q16—111no—
352C2×Q16—221no—
353C2×Q16—221no—
354C2×Q16—221no—
355C2×Q16C22×D1111yescharacteristic
356C2×SD16—221no—
357C2×D8—111no—
358#131—21no—
359#131—221no—
360#131—221no—
361#131—221no—
362#131—441no—
363#131—441no—
364C2×M16—111no—
365C2×M16—221no—
366C2×M16—441no—
367C2×M16—441no—
368C22×C8—111no—
369C4×Q8—21no—
370C4×Q8—221no—
371C4×Q8—221no—
372C4×Q8—221no—
373C4×Q8—441no—
374C4×Q8—441no—
375#117—111no—
376#117—221no—
377#117—441no—
378#117—441no—
379Q32—112no—
380Q32—112no—
381Q32—112no—
382Q32C4×D1112yes—
383SD32—112no—
384SD32—112no—
385SD32—112no—
386SD32C4×D1112yes—
387M32—111no—
388M32—112no—
389M32—111no—
390M32—221no—
391M32C22×D1111yescharacteristic
392M32C22×D1111yescharacteristic
393C2×C16—112no—
394C2×C16—221no—
395#108—111no—
396#108—221no—
397#108C22×D1111yescharacteristic
398#107—221no—
399#106—111no—
400#106C22×D1111yescharacteristic
401#104—21no—
402#104—221no—
403#104—221no—
404#104—221no—
405#103—21no—
406#103—221no—
407#103—221no—
408#103—221no—
409#97—111no—
410#97C22×D1111yescharacteristic
411C4×C8—111no—
412C4×C8—111no—
413C2×C11—21no—
414C2×C11—81no—
415C2×C11C2×#44211yescharacteristic
416D11—21no—
417D11—21no—
418D11—81no—
419#41—21no—
420#41—221no—
421#41—221no—
422#41—221no—
423#41—441no—
424#41—441no—
425C2×Q8—21no—
426C2×Q8—221no—
427C2×Q8—222no—
428C2×Q8—222no—
429C2×Q8—221no—
430C2×Q8—441no—
431C2×Q8—441no—
432C2×Q8—441no—
433C2×D4—221no—
434C2×D4—441no—
435C22×C4—111no—
436C22×C4—441no—
437C22×C4—441no—
438Q16—21no—
439Q16—112no—
440Q16—111no—
441Q16—222no—
442Q16—222no—
443Q16—221no—
444Q16—221no—
445Q16C2×C4×D1112yes—
446Q16C2×C4×D1111yescharacteristic
447SD16—21no—
448SD16—221no—
449SD16—221no—
450SD16—221no—
451D8—111no—
452D8—221no—
453D8C2×C4×D1111yescharacteristic
454M16—21no—
455M16—41no—
456M16—221no—
457M16—221no—
458M16—221no—
459M16—441no—
460M16—441no—
461M16—441no—
462M16—441no—
463C2×C8—41no—
464C2×C8—111no—
465C2×C8—111no—
466C2×C8—111no—
467C2×C8—111no—
468C2×C8—111no—
469C2×C8—111no—
470C2×C8—441no—
471C2×C8—441no—
472C2×C8—441no—
473C2×C8—441no—
474C2×C8D4×D1111yescharacteristic
475C2×C8C23×D1111yescharacteristic
476C4⋊C4—21no—
477C4⋊C4—41no—
478C4⋊C4—221no—
479C4⋊C4—221no—
480C4⋊C4—441no—
481C4⋊C4—441no—
482C4⋊C4—441no—
483C22⋊C4—221no—
484C22⋊C4—441no—
485C42—41no—
486C42—111no—
487C42—441no—
488C42—441no—
489C42—441no—
490C42—441no—
491C42D4×D1111yescharacteristic
492C16—21no—
493C16—112no—
494C16—221no—
495C16C2×C4×D1112yes—
496C11#3347011yescharacteristic, complemented, Sylow
497C23—111no—
498C23—441no—
499Q8—21no—
500Q8—22no—
501Q8—41no—
502Q8—221no—
503Q8—222no—
504Q8—442no—
505Q8—442no—
506Q8—441no—
507Q8—441no—
508D4—21no—
509D4—41no—
510D4—221no—
511D4—441no—
512D4—441no—
513D4—441no—
514D4—441no—
515C2×C4—21no—
516C2×C4—41no—
517C2×C4—41no—
518C2×C4—41no—
519C2×C4—111no—
520C2×C4—111no—
521C2×C4—111no—
522C2×C4—111no—
523C2×C4—111no—
524C2×C4—221no—
525C2×C4—441no—
526C2×C4—441no—
527C2×C4—442no—
528C2×C4—442no—
529C2×C4—441no—
530C2×C4—441no—
531C2×C4—441no—
532C2×C4—441no—
533C2×C4C2×D4×D1111yescharacteristic
534C8—21no—
535C8—41no—
536C8—111no—
537C8—111no—
538C8—221no—
539C8—441no—
540C8C22×C4×D1111yescharacteristic
541C8#41×D1111yescharacteristic
542C22—41no—
543C22—111no—
544C22—111no—
545C22—441no—
546C22—441no—
547C22—1761no—
548C22D11×AGL(1,ℤ/8)11yescharacteristic
549C4—41no—
550C4—41no—
551C4—42no—
552C4—81no—
553C4—111no—
554C4—111no—
555C4—441no—
556C4—441no—
557C4—442no—
558C4—881no—
559C4C4×D4×D1111yescharacteristic
560C4D11×AGL(1,ℤ/8)11yescharacteristic
561C2—21no—
562C2—81no—
563C2—221no—
564C2—221no—
565C2—881no—
566C2D11×#44211yescharacteristic
subgroupG/H
centerC2D11×#442
commutatorC8×C11C23×C4
FrattiniC2×C8C23×D11
FittingC11×#2180C2
socleC2×C11C2×#442
prime radicalD11×#135C22
cosocleC2×C8×C11C24
hypercenter#2180D11
hypocenterC11#33470
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. #13077481C2semidirect
4. #13070510C2semidirect
5. #13070509C2semidirect
6. #13070508C2semidirect
7. #13070507C2semidirect
8. #13070506C2semidirect
9. #13070505C2semidirect
10. #13070504C2semidirect
11. #13070387C2semidirect
12. D11×#362C2semidirect
14. #13070219C2semidirect
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
224. #2180D11semidirect
297. #441C2×D11semidirect
308. #365C2×D11semidirect
312. #362C2×D11semidirect
320. #347C2×D11semidirect
496. C11#33470semidirect

Maximal subgroups

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

subgroupindex
D11×#5102
#130775302
#130774812
#130705102
#130705092
#130705082
#130705072
#130705062
#130705052
#130705042
#130703872
D11×#3622
#130703502
#130702192
C11×#21802
#3347011