Finite Group Databasebeta

← #13080378

Subgroups — #13080378

Order 1408.

464 conjugacy classes of subgroups.

The subgroup lattice has 462 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C11×#577C211yesmaximal, characteristic, complemented
2#10623368C211yesmaximal, characteristic, complemented
3#10623366C211yesmaximal, characteristic, complemented
4#10623300C211yesmaximal, characteristic, complemented
5#10622858C211yesmaximal, characteristic, complemented
6#10622854C211yesmaximal, characteristic, complemented
7#10622816C211yesmaximal, characteristic, complemented
8#10622815C211yesmaximal, characteristic, complemented
9#10622812C211yesmaximal, characteristic, complemented
10#10622811C211yesmaximal, characteristic, complemented
11#10622810C211yesmaximal, characteristic, complemented
12#10622790C211yesmaximal, characteristic, complemented
13#10622789C211yesmaximal, characteristic, complemented
14#10622758C211yesmaximal, characteristic, complemented
15#10622755C211yesmaximal, characteristic, complemented
16C11×2−1+4C2211yescharacteristic, complemented
17C11×H(5,𝔽2)C2211yescharacteristic, complemented
18#67042C2211yescharacteristic
19#67042C2211yescharacteristic, complemented
20C11×#137—21no—
21C11×#137C2211yescharacteristic, complemented
22C11×AGL(1,ℤ/8)—21no—
23C11×AGL(1,ℤ/8)C2211yescharacteristic, complemented
24C11×#135—21no—
25C11×#135C2211yescharacteristic
26C2×C11×SD16—21no—
27C2×C11×SD16C2211yescharacteristic, complemented
28C11×#131C2211yescharacteristic, complemented
29#67003—21no—
30#67003—21no—
31#67003C2211yescharacteristic
32#67002—21no—
33#67002—21no—
34#67002C2211yescharacteristic
35#67002C2211yescharacteristic, complemented
36#67002C2211yescharacteristic, complemented
37#67002C2211yescharacteristic, complemented
38#67001C2211yescharacteristic, complemented
39#67001C2211yescharacteristic, complemented
40#67000C2211yescharacteristic, complemented
41#66995—21no—
42#66995C2211yescharacteristic, complemented
43C2×#4325—21no—
44C2×#4325C2211yescharacteristic, complemented
45#66993C2211yescharacteristic, complemented
46#66985—21no—
47#66985C2211yescharacteristic
48C2×#4323—21no—
49C2×#4323C2211yescharacteristic, complemented
50#66972—21no—
51#66967—21no—
52#66967—21no—
53D8×D11—21no—
54C2×D88C2211yescharacteristic, complemented
55#66954C2211yescharacteristic, complemented
56#66901C2211yescharacteristic, complemented
57#66901C2211yescharacteristic, complemented
58#66901C2211yescharacteristic, complemented
59#66900C2211yescharacteristic, complemented
60#66897C2211yescharacteristic, complemented
61#66889C2211yescharacteristic, complemented
62#66887C2211yescharacteristic, complemented
63#66887C2211yescharacteristic, complemented
64#66886C2211yescharacteristic, complemented
65#66883C2211yescharacteristic, complemented
66#66879C2211yescharacteristic, complemented
67C11×#41—21no—
68C11×#41—21no—
69C11×#41—21no—
70C11×#41—21no—
71C11×#41—41no—
72C11×#41C2311yescharacteristic
73C11×#41C2311yescharacteristic
74C11×#41C2311yescharacteristic
75C2×Q8×C11—21no—
76C2×Q8×C11—21no—
77C2×Q8×C11C2311yescharacteristic
78C2×D4×C11—21no—
79C2×D4×C11—21no—
80C2×D4×C11—41no—
81C2×D4×C11C2311yescharacteristic
82C2×C22⋊D11—41no—
83#4343—21no—
84#4343—21no—
85D4×D11—21no—
86D4×D11—21no—
87D4×D11—41no—
88D4×D11—41no—
89#4339—21no—
90#4339—21no—
91#4339C2311yescharacteristic
92C2×D44—21no—
93C2×D44—21no—
94C2×D44C2311yescharacteristic
95C2×D44C2311yescharacteristic
96C11×Q16—21no—
97C11×Q16D411yescharacteristic, complemented
98C11×SD16—21no—
99C11×SD16—21no—
100C11×SD16—21no—
101C11×SD16—21no—
102C11×SD16D411yescharacteristic, complemented
103C11×SD16D411yescharacteristic, complemented
104C11×D8—21no—
105C11×D8D411yescharacteristic, complemented
106C11×M16—21no—
107C11×M16C2311yescharacteristic
108C2×C8×C11—21no—
109C2×C8×C11C2311yescharacteristic
110#4326—21no—
111#4326D411yescharacteristic, complemented
112#4325—21no—
113#4325—21no—
114#4325—21no—
115#4325—21no—
116#4325—21no—
117#4325—21no—
118#4325—21no—
119#4325D411yescharacteristic, complemented
120#4324—21no—
121#4324D411yescharacteristic, complemented
122#4323—21no—
123#4323—21no—
124#4323—21no—
125#4323—21no—
126#4323—21no—
127#4323—21no—
128#4323—21no—
129#4323D411yescharacteristic, complemented
130(C2×D11)⋊C4—41no—
131C4×Dic11C2311yescharacteristic
132#4318—21no—
133#4318—21no—
134#4318C2311yescharacteristic
135#4318C2311yescharacteristic
136#4318C2311yescharacteristic
137C2×C11⋊C8—21no—
138C2×C11⋊C8—21no—
139C2×C11⋊C8C2311yescharacteristic
140D88—21no—
141D88—21no—
142#4313—21no—
143C8×D11—21no—
144#3288—111nomaximal, Sylow
145C23×C11—21no—
146C23×C11—41no—
147C22×D11—21no—
148C22×D11—21no—
149C22×D11—41no—
150C22×D11—41no—
151Q8×C11—21no—
152Q8×C11—21no—
153Q8×C11—41no—
154Q8×C11C2×D411yescharacteristic
155Q8×C11C2×D411yescharacteristic
156Q8×C11C2×D411yescharacteristic
157D4×C11—21no—
158D4×C11—21no—
159D4×C11—21no—
160D4×C11—21no—
161D4×C11—21no—
162D4×C11—41no—
163D4×C11—41no—
164D4×C11—41no—
165D4×C11C2×D411yescharacteristic
166D4×C11C2×D411yescharacteristic
167D4×C11C2×D411yescharacteristic
168C2×C4×C11—21no—
169C2×C4×C11—21no—
170C2×C4×C11—21no—
171C2×C4×C11—21no—
172C2×C4×C11—41no—
173C2×C4×C11—41no—
174C2×C4×C11—41no—
175C2×C4×C11C2411yescharacteristic
176C22⋊D11—21no—
177C22⋊D11—41no—
178C22⋊D11—41no—
179C22⋊D11—82no—
180C2×Dic11—21no—
181D44—21no—
182D44—21no—
183D44—21no—
184D44—21no—
185D44—41no—
186D44—41no—
187D44C2×D411yescharacteristic
188C4×D11—21no—
189C4×D11—41no—
190C4×D11—41no—
191Dic22C2×D411yescharacteristic
192C8×C11—21no—
193C8×C11C2×D411yescharacteristic
194C8×C11C2×D411yescharacteristic
195C11⋊C8—21no—
196C11⋊C8—21no—
197C11⋊C8—21no—
198C11⋊C8C2×D411yescharacteristic
199C11⋊C8C2×D411yescharacteristic
200#577—111no—
201#577D1111yescharacteristic, complemented
202#576—111no—
203#576—111no—
204#496—111no—
205#472—111no—
206#472—111no—
207#471—111no—
208#471—111no—
209#455—111no—
210#454—111no—
211#453—111no—
212#453—111no—
213#444—111no—
214#444—111no—
215C22×C11—21no—
216C22×C11—21no—
217C22×C11—21no—
218C22×C11—41no—
219C22×C11—81no—
220C22×C11—161no—
221C22×C11H(5,𝔽2)11yescharacteristic
222C2×D11—21no—
223C2×D11—41no—
224C2×D11—41no—
225C2×D11—81no—
226C2×D11—81no—
227C2×D11—161no—
228C2×D11—161no—
229C4×C11—21no—
230C4×C11—21no—
231C4×C11—21no—
232C4×C11—41no—
233C4×C11C22×D411yescharacteristic
234C4×C11C22×D411yescharacteristic
235Dic11—21no—
236Dic11—41no—
2372−1+4C2×D1111yescharacteristic, complemented
238H(5,𝔽2)—111no—
239H(5,𝔽2)—111no—
240H(5,𝔽2)C2×D1111yescharacteristic, complemented
241#137—21no—
242#137—111no—
243#137—221no—
244#137C2×D1111yescharacteristic, complemented
245AGL(1,ℤ/8)—21no—
246AGL(1,ℤ/8)—111no—
247AGL(1,ℤ/8)—111no—
248AGL(1,ℤ/8)—111no—
249AGL(1,ℤ/8)—111no—
250AGL(1,ℤ/8)—111no—
251AGL(1,ℤ/8)—221no—
252AGL(1,ℤ/8)—221no—
253AGL(1,ℤ/8)—221no—
254AGL(1,ℤ/8)—221no—
255AGL(1,ℤ/8)—221no—
256AGL(1,ℤ/8)C2×D1111yescharacteristic, complemented
257#135—21no—
258#135—111no—
259#135—221no—
260#135—221no—
261#135—221no—
262#135C2×D1111yescharacteristic
263C2×SD16—21no—
264C2×SD16—111no—
265C2×SD16—221no—
266C2×SD16C2×D1111yescharacteristic, complemented
267C2×D8—111no—
268C2×D8—111no—
269C2×D8—221no—
270C2×D8—221no—
271#131—111no—
272#131—111no—
273#131—111no—
274#131C2×D1111yescharacteristic, complemented
275#127—111no—
276#124—111no—
277#108—111no—
278#108—111no—
279#104—111no—
280#104—111no—
281#104—111no—
282#104—111no—
283#101—111no—
284#100—111no—
285#100—111no—
286#100—111no—
287#97—111no—
288C2×C11—21no—
289C2×C11—41no—
290C2×C11—41no—
291C2×C11—41no—
292C2×C11—81no—
293C2×C11D4211yescharacteristic
294D11—41no—
295D11—81no—
296D11—81no—
297#41—21no—
298#41—21no—
299#41—21no—
300#41—21no—
301#41—41no—
302#41—111no—
303#41—221no—
304#41—221no—
305#41—221no—
306#41—221no—
307#41C22×D1111yescharacteristic
308#41C22×D1111yescharacteristic
309#41C22×D1111yescharacteristic
310C2×Q8—21no—
311C2×Q8—21no—
312C2×Q8C22×D1111yescharacteristic
313C2×D4—21no—
314C2×D4—21no—
315C2×D4—41no—
316C2×D4—111no—
317C2×D4—111no—
318C2×D4—221no—
319C2×D4—221no—
320C2×D4—221no—
321C2×D4—221no—
322C2×D4—441no—
323C2×D4—441no—
324C2×D4—441no—
325C2×D4C22×D1111yescharacteristic
326Q16—21no—
327Q16—111no—
328Q16—221no—
329Q16C22⋊D1111yescharacteristic, complemented
330SD16—21no—
331SD16—21no—
332SD16—21no—
333SD16—21no—
334SD16—111no—
335SD16—111no—
336SD16—221no—
337SD16—221no—
338SD16—221no—
339SD16—221no—
340SD16—221no—
341SD16—221no—
342SD16—221no—
343SD16—221no—
344SD16C22⋊D1111yescharacteristic, complemented
345SD16C22⋊D1111yescharacteristic, complemented
346D8—21no—
347D8—111no—
348D8—221no—
349D8—221no—
350D8—221no—
351D8—221no—
352D8—221no—
353D8—221no—
354D8—221no—
355D8—221no—
356D8—221no—
357D8C22⋊D1111yescharacteristic, complemented
358M16—21no—
359M16—111no—
360M16—111no—
361M16—111no—
362M16—221no—
363M16—221no—
364M16—221no—
365M16C22×D1111yescharacteristic
366C2×C8—21no—
367C2×C8—111no—
368C2×C8—221no—
369C2×C8—221no—
370C2×C8—221no—
371C2×C8C22×D1111yescharacteristic
372C22⋊C4—441no—
373C42—111no—
374C11#328811yescharacteristic, complemented, Sylow
375C23—21no—
376C23—41no—
377C23—221no—
378C23—221no—
379C23—441no—
380C23—441no—
381Q8—21no—
382Q8—21no—
383Q8—41no—
384Q8—111no—
385Q8D4×D1111yescharacteristic
386Q8C2×C22⋊D1111yescharacteristic
387Q8C2×C22⋊D1111yescharacteristic
388D4—21no—
389D4—21no—
390D4—21no—
391D4—21no—
392D4—21no—
393D4—41no—
394D4—41no—
395D4—41no—
396D4—111no—
397D4—221no—
398D4—221no—
399D4—221no—
400D4—221no—
401D4—221no—
402D4—441no—
403D4—441no—
404D4—441no—
405D4—441no—
406D4—882no—
407D4D4×D1111yescharacteristic
408D4C2×C22⋊D1111yescharacteristic
409D4C2×C22⋊D1111yescharacteristic
410C2×C4—21no—
411C2×C4—21no—
412C2×C4—21no—
413C2×C4—21no—
414C2×C4—41no—
415C2×C4—41no—
416C2×C4—41no—
417C2×C4—221no—
418C2×C4—221no—
419C2×C4—441no—
420C2×C4—441no—
421C2×C4C23×D1111yescharacteristic
422C8—21no—
423C8—111no—
424C8—111no—
425C8—221no—
426C8—221no—
427C8—221no—
428C8C2×C22⋊D1111yescharacteristic
429C8C2×C22⋊D1111yescharacteristic
430C22—21no—
431C22—21no—
432C22—21no—
433C22—41no—
434C22—81no—
435C22—161no—
436C22—221no—
437C22—441no—
438C22—441no—
439C22—881no—
440C22—881no—
441C22—1761no—
442C22—1761no—
443C22#6703711yescharacteristic
444C4—21no—
445C4—21no—
446C4—21no—
447C4—41no—
448C4—221no—
449C4—441no—
450C4C2×D4×D1111yescharacteristic
451C4C22×C22⋊D1111yescharacteristic
452C2—21no—
453C2—41no—
454C2—41no—
455C2—41no—
456C2—81no—
457C2—441no—
458C2—881no—
459C2—881no—
460C2D4×C22⋊D1111yescharacteristic
subgroupG/H
centerC2D4×C22⋊D11
commutator, cosocleC2×C4×C11C24
FrattiniC2×C4C23×D11
FittingC11×#577C2
socleC2×C11D42
hypercenter#577D11
hypocenterC11#3288
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C2 ◁ C2×C4 ◁ #577

Complements

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

NH ≅ G/Ntype
1. C11×#577C2semidirect
2. #10623368C2semidirect
3. #10623366C2semidirect
4. #10623300C2semidirect
5. #10622858C2semidirect
6. #10622854C2semidirect
7. #10622816C2semidirect
8. #10622815C2semidirect
9. #10622812C2semidirect
10. #10622811C2semidirect
11. #10622810C2semidirect
12. #10622790C2semidirect
13. #10622789C2semidirect
14. #10622758C2semidirect
15. #10622755C2semidirect
16. C11×2−1+4C22semidirect
17. C11×H(5,𝔽2)C22semidirect
19. #67042C22semidirect
21. C11×#137C22semidirect
23. C11×AGL(1,ℤ/8)C22semidirect
27. C2×C11×SD16C22semidirect
28. C11×#131C22semidirect
35. #67002C22semidirect
36. #67002C22semidirect
37. #67002C22semidirect
38. #67001C22semidirect
39. #67001C22semidirect
40. #67000C22semidirect
42. #66995C22semidirect
44. C2×#4325C22semidirect
45. #66993C22semidirect
49. C2×#4323C22semidirect
54. C2×D88C22semidirect
55. #66954C22semidirect
56. #66901C22semidirect
57. #66901C22semidirect
58. #66901C22semidirect
59. #66900C22semidirect
60. #66897C22semidirect
61. #66889C22semidirect
62. #66887C22semidirect
63. #66887C22semidirect
64. #66886C22semidirect
65. #66883C22semidirect
66. #66879C22semidirect
97. C11×Q16D4semidirect
102. C11×SD16D4semidirect
103. C11×SD16D4semidirect
105. C11×D8D4semidirect
111. #4326D4semidirect
119. #4325D4semidirect
121. #4324D4semidirect
129. #4323D4semidirect
201. #577D11semidirect
237. 2−1+4C2×D11semidirect
240. H(5,𝔽2)C2×D11semidirect
244. #137C2×D11semidirect
256. AGL(1,ℤ/8)C2×D11semidirect
266. C2×SD16C2×D11semidirect
274. #131C2×D11semidirect
329. Q16C22⋊D11semidirect
344. SD16C22⋊D11semidirect
345. SD16C22⋊D11semidirect
357. D8C22⋊D11semidirect
374. C11#3288semidirect

Maximal subgroups

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

subgroupindex
C11×#5772
#106233682
#106233662
#106233002
#106228582
#106228542
#106228162
#106228152
#106228122
#106228112
#106228102
#106227902
#106227892
#106227582
#106227552
#328811