Finite Group Databasebeta

← #13083398

Subgroups — #13083398

Order 1408.

1412 conjugacy classes of subgroups.

The subgroup lattice has 504 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1D11×2−1+4C211yesmaximal, characteristic, complemented
2#10623455C211yesmaximal, characteristic, complemented
3C11×#577C211yesmaximal, characteristic, complemented
4#10623369C211yesmaximal, characteristic, complemented
5#10623367C211yesmaximal, characteristic, complemented
6#10623310C213yesmaximal, complemented
7D11×#137C213yesmaximal, complemented
8#10623306C213yesmaximal, complemented
9#10623304C213yesmaximal, complemented
10#10623302C213yesmaximal, complemented
11#10623299C213yesmaximal, complemented
12#10623293C213yesmaximal, complemented
13C2×#66968C213yesmaximal, complemented
14#10623284C211yesmaximal, characteristic, complemented
15#10623281C211yesmaximal, characteristic, complemented
16C11×2−1+4C2211yescharacteristic, complemented
17C11×H(5,𝔽2)C2211yescharacteristic, complemented
18#67043—21no—
19#67043—23no—
20#67043C2213yescomplemented
21#67043C2213yescomplemented
22#67043C2211yescharacteristic, complemented
23#67043C2211yescharacteristic, complemented
24#41×D11—21no—
25#41×D11—23no—
26#41×D11C2213yes—
27#41×D11C2211yescharacteristic
28#41×D11C2213yescomplemented
29#67040—21no—
30#67040C2213yescomplemented
31C2×Q8×D11—21no—
32C2×Q8×D11C2213yescomplemented
33#67037—23no—
34#67037C2213yescomplemented
35C2×#4341—23no—
36C2×#4341C2213yes—
37C11×#137C2213yescomplemented
38C11×AGL(1,ℤ/8)C2213yescomplemented
39C11×#135C2213yescomplemented
40C2×C11×SD16C2213yescomplemented
41C11×#131C2211yescharacteristic, complemented
42#67004C2213yescomplemented
43#67004C2213yescomplemented
44#67003C2213yescomplemented
45#67003C2213yescomplemented
46#67001C2211yescharacteristic, complemented
47C2×#4326C2213yescomplemented
48#66995C2213yescomplemented
49C2×#4324C2213yescomplemented
50#66985C2213yescomplemented
51#66971C2213yescomplemented
52#66971C2213yescomplemented
53Q16×D11C2216yescomplemented
54#66969C2216yescomplemented
55#66968C2213yescomplemented
56#66968C2216yescomplemented
57#66968C2216yescomplemented
58#66968C2216yescomplemented
59#66968C2213yescomplemented
60#66967C2213yescomplemented
61#66967C2211yescharacteristic, complemented
62SD16×D11C2216yescomplemented
63#66965C2216yescomplemented
64#66964C2213yescomplemented
65#66964C2213yescomplemented
66#66962C2213yescomplemented
67#66962C2213yescomplemented
68#66960C2213yescomplemented
69M16×D11C2213yescomplemented
70C2×Dic44C2213yescomplemented
71#66957C2213yescomplemented
72#66954C2213yescomplemented
73C2×#4313C2213yescomplemented
74C11×#41—21no—
75C11×#41—23no—
76C11×#41C2313yes—
77C11×#41C2313yes—
78C11×#41C2311yescharacteristic
79C2×Q8×C11—21no—
80C2×Q8×C11C2313yes—
81C2×D4×C11—23no—
82C2×D4×C11C2313yes—
83C2×C22⋊D11—26no—
84C2×C22⋊D11—23no—
85C22×Dic11—23no—
86#4343—23no—
87#4343D411yescharacteristic
88#4343C2313yes—
89#4343C2311yescharacteristic
90Q8×D11—23no—
91Q8×D11—23no—
92Q8×D11—23no—
93Q8×D11—21no—
94Q8×D11—21no—
95Q8×D11D411yescharacteristic
96Q8×D11C2316yes—
97Q8×D11C2313yes—
98Q8×D11C2313yes—
99#4341—26no—
100#4341—26no—
101#4341—23no—
102#4341—23no—
103#4341—23no—
104#4341—23no—
105#4341—23no—
106#4341—23no—
107#4341—23no—
108#4341D413yes—
109#4341C2313yes—
110#4341C2313yes—
111#4341C2316yes—
112D4×D11—23no—
113D4×D11—23no—
114D4×D11—23no—
115D4×D11D413yes—
116D4×D11C2311yescharacteristic
117D4×D11C2313yes—
118#4339—26no—
119#4339—23no—
120#4339—23no—
121#4339—23no—
122#4339—23no—
123#4339C2313yes—
124#4339C2313yes—
125#4339C2313yes—
126C2×C4×D11—23no—
127C2×C4×D11—23no—
128C2×C4×D11—23no—
129C2×C4×D11C2313yes—
130C2×Dic22—23no—
131C2×Dic22—23no—
132C2×Dic22—23no—
133C2×Dic22C2313yes—
134C2×Dic22C2313yes—
135C11×Q16C2313yes—
136C11×SD16C2316yes—
137C11×SD16C2313yes—
138C11×SD16C2311yescharacteristic
139C11×D8C2313yes—
140C11×M16C2313yes—
141C2×C8×C11C2313yes—
142#4326C2313yes—
143#4326C2316yes—
144#4326C2313yes—
145#4325C2313yes—
146#4325C2311yescharacteristic
147#4324C2313yes—
148#4324C2313yes—
149#4324C2316yes—
150#4323C2311yescharacteristic
151#4323C2313yes—
152#4318C2313yes—
153C2×C11⋊C8C2313yes—
154Dic44C2313yes—
155Dic44C2316yes—
156D88C2311yescharacteristic
157#4314C2313yes—
158#4314C2313yes—
159#4313C2311yescharacteristic
160#4313C2313yes—
161#4313C2313yes—
162#4313C2313yes—
163C8×D11C2316yes—
164#3586—111nomaximal, Sylow
165C23×C11—23no—
166C22×D11—21no—
167C22×D11—23no—
168C22×D11C2×D413yes—
169Q8×C11—23no—
170Q8×C11C2×D411yescharacteristic
171Q8×C11C2413yes—
172Q8×C11C2411yescharacteristic
173D4×C11—23no—
174D4×C11—23no—
175D4×C11—23no—
176D4×C11C2×D413yes—
177D4×C11C2411yescharacteristic
178D4×C11C2413yes—
179C2×C4×C11—23no—
180C2×C4×C11—23no—
181C2×C4×C11—23no—
182C2×C4×C11C2413yes—
183C22⋊D11—23no—
184C22⋊D11—23no—
185C22⋊D11—23no—
186C22⋊D11—23no—
187C22⋊D11—26no—
188C22⋊D11—21no—
189C22⋊D11—23no—
190C22⋊D11C2×D416yes—
191C2×Dic11—23no—
192C2×Dic11—23no—
193C2×Dic11—23no—
194C2×Dic11—26no—
195C2×Dic11—23no—
196C2×Dic11C2×D413yes—
197D44—21no—
198D44—23no—
199D44C2×D413yes—
200D44C2411yescharacteristic
201D44C2411yescharacteristic
202C4×D11—23no—
203C4×D11—23no—
204C4×D11—26no—
205C4×D11—23no—
206C4×D11—23no—
207C4×D11—21no—
208C4×D11—23no—
209C4×D11C2×D413yes—
210C4×D11C2×D413yes—
211C4×D11C2413yes—
212C4×D11C2411yescharacteristic
213Dic22—23no—
214Dic22—23no—
215Dic22—23no—
216Dic22—26no—
217Dic22—23no—
218Dic22C2×D413yes—
219Dic22C2413yes—
220Dic22C2413yes—
221C8×C11C2413yes—
222C8×C11C2411yescharacteristic
223C11⋊C8C2413yes—
224C11⋊C8C2411yescharacteristic
225#585—111no—
226C2×2−1+4—111no—
227#578—111no—
228#578—113no—
229#578—113no—
230#578—111no—
231#577—111no—
232#577—113no—
233#577—113no—
234#577D1111yescharacteristic, complemented
235#575—113no—
236#575—113no—
237C2×#137—113no—
238C2×#137—113no—
239#568—111no—
240C22×C11—21no—
241C22×C11—23no—
242C22×C11—83no—
243C22×C11C22×D413yes—
244C2×D11—21no—
245C2×D11—21no—
246C2×D11—43no—
247C2×D11—42no—
248C2×D11—83no—
249C2×D11C22×D411yescharacteristic
250C2×D11C22×D413yes—
251C4×C11—21no—
252C4×C11—23no—
253C4×C11C22×D413yes—
254C4×C11C2511yescharacteristic
255Dic11—23no—
256Dic11—23no—
257Dic11C22×D413yes—
258Dic11C22×D411yescharacteristic
2592−1+4—113no—
2602−1+4—113no—
2612−1+4—111no—
2622−1+4—111no—
2632−1+4—113no—
2642−1+4—221no—
2652−1+4—221no—
2662−1+4—223no—
2672−1+4C2×D1111yescharacteristic, complemented
268H(5,𝔽2)—113no—
269H(5,𝔽2)—223no—
270H(5,𝔽2)C2×D1111yescharacteristic, complemented
271C2×#41—111no—
272C2×#41—113no—
273C2×#41—113no—
274C2×#41—113no—
275C2×#41—223no—
276C2×#41—223no—
277C2×#41—221no—
278C22×Q8—113no—
279C22×Q8—221no—
280#137—113no—
281#137—113no—
282#137—113no—
283#137—113no—
284#137—113no—
285#137—116no—
286#137—113no—
287#137—116no—
288#137—116no—
289#137—113no—
290#137—113no—
291#137—113no—
292#137C2×D1113yescomplemented
293AGL(1,ℤ/8)—113no—
294AGL(1,ℤ/8)—111no—
295AGL(1,ℤ/8)—113no—
296AGL(1,ℤ/8)—113no—
297AGL(1,ℤ/8)—113no—
298AGL(1,ℤ/8)C2×D1113yescomplemented
299#135—113no—
300#135—113no—
301#135—116no—
302#135—116no—
303#135—113no—
304#135C2×D1113yescomplemented
305C2×Q16—113no—
306C2×Q16—116no—
307C2×Q16—113no—
308C2×SD16—113no—
309C2×SD16—116no—
310C2×SD16C2×D1113yescomplemented
311#131—111no—
312#131—113no—
313#131—113no—
314#131C2×D1111yescharacteristic, complemented
315C2×M16—113no—
316C2×M16—113no—
317C2×C11—23no—
318C2×C11—41no—
319C2×C11—43no—
320C2×C11C23×D411yescharacteristic
321D11—21no—
322D11—23no—
323D11—41no—
324D11—41no—
325#41—21no—
326#41—23no—
327#41—111no—
328#41—113no—
329#41—113no—
330#41—113no—
331#41—111no—
332#41—113no—
333#41—116no—
334#41—113no—
335#41—113no—
336#41—113no—
337#41—223no—
338#41—223no—
339#41—223no—
340#41—226no—
341#41—223no—
342#41—223no—
343#41—223no—
344#41—223no—
345#41—223no—
346#41—226no—
347#41—226no—
348#41—223no—
349#41—223no—
350#41—223no—
351#41—223no—
352#41C22×D1113yes—
353#41C22×D1113yes—
354#41C22×D1111yescharacteristic
355C2×Q8—21no—
356C2×Q8—111no—
357C2×Q8—116no—
358C2×Q8—113no—
359C2×Q8—113no—
360C2×Q8—113no—
361C2×Q8—113no—
362C2×Q8—223no—
363C2×Q8—223no—
364C2×Q8—223no—
365C2×Q8—223no—
366C2×Q8—223no—
367C2×Q8—223no—
368C2×Q8—221no—
369C2×Q8—221no—
370C2×Q8C22×D1113yes—
371C2×D4—23no—
372C2×D4—113no—
373C2×D4—113no—
374C2×D4—111no—
375C2×D4—223no—
376C2×D4—223no—
377C2×D4—223no—
378C2×D4—226no—
379C2×D4—223no—
380C2×D4C22×D1113yes—
381C22×C4—113no—
382C22×C4—223no—
383C22×C4—223no—
384C22×C4—223no—
385C22×C4—223no—
386Q16—113no—
387Q16—113no—
388Q16—116no—
389Q16—116no—
390Q16—113no—
391Q16C22×D1113yes—
392SD16—113no—
393SD16—111no—
394SD16—113no—
395SD16—116no—
396SD16—113no—
397SD16—113no—
398SD16—113no—
399SD16C22×D1116yes—
400SD16C22×D1113yes—
401SD16C22×D1111yescharacteristic
402D8—113no—
403D8—111no—
404D8—111no—
405D8C22×D1113yes—
406M16—113no—
407M16—113no—
408M16—111no—
409M16—113no—
410M16—113no—
411M16C22×D1113yes—
412C2×C8—113no—
413C2×C8—116no—
414C2×C8C22×D1113yes—
415C11#358611yescharacteristic, complemented, Sylow
416C23—23no—
417C23—113no—
418C23—221no—
419C23—223no—
420Q8—23no—
421Q8—113no—
422Q8—113no—
423Q8—113no—
424Q8—223no—
425Q8—226no—
426Q8—223no—
427Q8—223no—
428Q8—223no—
429Q8D4×D1111yescharacteristic
430Q8C23×D1113yes—
431Q8C23×D1111yescharacteristic
432D4—23no—
433D4—23no—
434D4—23no—
435D4—116no—
436D4—113no—
437D4—111no—
438D4—111no—
439D4—221no—
440D4—223no—
441D4—223no—
442D4—221no—
443D4—223no—
444D4—226no—
445D4—223no—
446D4—223no—
447D4—223no—
448D4D4×D1113yes—
449D4C23×D1111yescharacteristic
450D4C23×D1113yes—
451C2×C4—23no—
452C2×C4—23no—
453C2×C4—23no—
454C2×C4—113no—
455C2×C4—113no—
456C2×C4—113no—
457C2×C4—113no—
458C2×C4—111no—
459C2×C4—221no—
460C2×C4—223no—
461C2×C4—223no—
462C2×C4—223no—
463C2×C4—226no—
464C2×C4—223no—
465C2×C4—226no—
466C2×C4—223no—
467C2×C4—223no—
468C2×C4—223no—
469C2×C4—223no—
470C2×C4—223no—
471C2×C4C23×D1113yes—
472C8—111no—
473C8—113no—
474C8C23×D1113yes—
475C8C23×D1111yescharacteristic
476C22—21no—
477C22—23no—
478C22—83no—
479C22—111no—
480C22—113no—
481C22—221no—
482C22—221no—
483C22—443no—
484C22—442no—
485C22—883no—
486C22C2×D4×D1113yes—
487C4—21no—
488C4—23no—
489C4—111no—
490C4—113no—
491C4—223no—
492C4—223no—
493C4C2×D4×D1113yes—
494C4C24×D1111yescharacteristic
495C2—23no—
496C2—43no—
497C2—41no—
498C2—221no—
499C2—223no—
500C2—441no—
501C2—441no—
502C2C22×D4×D1111yescharacteristic
subgroupG/H
centerC2C22×D4×D11
commutator, cosocleC4×C11C25
FrattiniC4C24×D11
FittingC11×#577C2
socleC2×C11C23×D4
hypercenter#577D11
hypocenterC11#3586
LCSG ▷ C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C2 ◁ #41 ◁ #577

Complements

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

NH ≅ G/Ntype
1. D11×2−1+4C2semidirect
2. #10623455C2semidirect
3. C11×#577C2semidirect
4. #10623369C2semidirect
5. #10623367C2semidirect
6. #10623310C2semidirect
7. D11×#137C2semidirect
8. #10623306C2semidirect
9. #10623304C2semidirect
10. #10623302C2semidirect
11. #10623299C2semidirect
12. #10623293C2semidirect
13. C2×#66968C2semidirect
14. #10623284C2semidirect
15. #10623281C2semidirect
16. C11×2−1+4C22semidirect
17. C11×H(5,𝔽2)C22semidirect
20. #67043C22semidirect
21. #67043C22semidirect
22. #67043C22semidirect
23. #67043C22semidirect
28. #41×D11C22semidirect
30. #67040C22semidirect
32. C2×Q8×D11C22semidirect
34. #67037C22semidirect
37. C11×#137C22semidirect
38. C11×AGL(1,ℤ/8)C22semidirect
39. C11×#135C22semidirect
40. C2×C11×SD16C22semidirect
41. C11×#131C22semidirect
42. #67004C22semidirect
43. #67004C22semidirect
44. #67003C22semidirect
45. #67003C22semidirect
46. #67001C22semidirect
47. C2×#4326C22semidirect
48. #66995C22semidirect
49. C2×#4324C22semidirect
50. #66985C22semidirect
51. #66971C22semidirect
52. #66971C22semidirect
53. Q16×D11C22semidirect
54. #66969C22semidirect
55. #66968C22semidirect
56. #66968C22semidirect
57. #66968C22semidirect
58. #66968C22semidirect
59. #66968C22semidirect
60. #66967C22semidirect
61. #66967C22semidirect
62. SD16×D11C22semidirect
63. #66965C22semidirect
64. #66964C22semidirect
65. #66964C22semidirect
66. #66962C22semidirect
67. #66962C22semidirect
68. #66960C22semidirect
69. M16×D11C22semidirect
70. C2×Dic44C22semidirect
71. #66957C22semidirect
72. #66954C22semidirect
73. C2×#4313C22semidirect
234. #577D11semidirect
267. 2−1+4C2×D11semidirect
270. H(5,𝔽2)C2×D11semidirect
292. #137C2×D11semidirect
298. AGL(1,ℤ/8)C2×D11semidirect
304. #135C2×D11semidirect
310. C2×SD16C2×D11semidirect
314. #131C2×D11semidirect
415. C11#3586semidirect

Maximal subgroups

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

subgroupindex
D11×2−1+42
#106234552
C11×#5772
#106233692
#106233672
#106233102
D11×#1372
#106233062
#106233042
#106233022
#106232992
#106232932
C2×#669682
#106232842
#106232812
#358611