Finite Group Databasebeta

← #13080229

Subgroups — #13080229

Order 1408.

556 conjugacy classes of subgroups.

The subgroup lattice has 450 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10623365C211yesmaximal, characteristic, complemented
2C2×#67002C211yesmaximal, characteristic, complemented
3C2×#66967C211yesmaximal, characteristic, complemented
4#10623140C211yesmaximal, characteristic, complemented
5C11×#449C211yesmaximal, characteristic, complemented
6#10622776C211yesmaximal, characteristic, complemented
7#10622769C211yesmaximal, characteristic, complemented
8#10622764C211yesmaximal, characteristic, complemented
9#10622652C211yesmaximal, characteristic, complemented
10#10622424C211yesmaximal, characteristic, complemented
11#10622401C211yesmaximal, characteristic, complemented
12#10622399C211yesmaximal, characteristic, complemented
13#10622395C211yesmaximal, characteristic, complemented
14#10622345C211yesmaximal, characteristic, complemented
15#10622342C211yesmaximal, characteristic, complemented
16C2×C11×#41C2211yescharacteristic, complemented
17C2×#4343C2211yescharacteristic, complemented
18C2×D4×D11—21no—
19C2×D4×D11C2211yescharacteristic
20C22×D44C2211yescharacteristic
21C2×C11×SD16C2211yescharacteristic, complemented
22C2×C11×D8C2211yescharacteristic, complemented
23C11×#121C2211yescharacteristic
24#67002—24no—
25Q8×Dic11C2211yescharacteristic, complemented
26C2×#4325C2211yescharacteristic
27C2×#4325C2211yescharacteristic, complemented
28#66993—21no—
29#66993C2211yescharacteristic
30#66993C2211yescharacteristic, complemented
31#66991—21no—
32#66991C2211yescharacteristic, complemented
33#66990—21no—
34C2×#4323C2211yescharacteristic
35C2×#4323C2211yescharacteristic, complemented
36C2×#4323C2211yescharacteristic, complemented
37#66983—21no—
38#66983C2211yescharacteristic, complemented
39C4×C22⋊D11—21no—
40C4×C22⋊D11C2211yescharacteristic
41C2×#4318C2211yescharacteristic, complemented
42#66967—24no—
43C2×D88C2211yescharacteristic
44C2×D88C2211yescharacteristic, complemented
45C2×#4313C2211yescharacteristic, complemented
46#66948C2211yescharacteristic
47#66946C2211yescharacteristic
48#66937—21no—
49#66935—21no—
50C11×#103C2211yescharacteristic, complemented
51C11×#102C2211yescharacteristic, complemented
52C11×C22⋊C8C2211yescharacteristic, complemented
53#66896C2211yescharacteristic, complemented
54#66885C2211yescharacteristic
55#66885C2211yescharacteristic, complemented
56(C2×D11)⋊C8C2211yescharacteristic, complemented
57Dic11⋊C8C2211yescharacteristic, complemented
58C8×Dic11C2211yescharacteristic, complemented
59#66873C2211yescharacteristic, complemented
60#66872C2211yescharacteristic, complemented
61C23×D11—21no—
62C23×D11—21no—
63C11×#41—22no—
64C11×#41—41no—
65C2×Q8×C11C2311yescharacteristic
66C2×D4×C11—21no—
67C2×D4×C11—21no—
68C2×D4×C11C2311yescharacteristic
69C2×D4×C11C2311yescharacteristic
70C22×C4×C11—21no—
71C22×C4×C11C2311yescharacteristic
72C2×C22⋊D11—21no—
73C2×C22⋊D11—21no—
74C2×C22⋊D11—21no—
75C2×C22⋊D11—21no—
76C2×C22⋊D11—21no—
77C2×C22⋊D11—21no—
78C2×C22⋊D11—21no—
79C2×C22⋊D11D411yescharacteristic
80#4343—22no—
81#4343—41no—
82D4×D11—22no—
83D4×D11—41no—
84D4×D11—44no—
85C2×D44—21no—
86C2×D44—21no—
87C2×D44—22no—
88C2×D44—21no—
89C2×D44—41no—
90C2×D44C2311yescharacteristic
91C2×D44C2311yescharacteristic
92C2×D44C2311yescharacteristic
93C2×C4×D11—21no—
94C2×C4×D11—21no—
95C2×C4×D11C2311yescharacteristic
96C11×SD16—22no—
97C11×D8—41no—
98C2×C8×C11C2311yescharacteristic
99C2×C8×C11C2311yescharacteristic
100C11×C4⋊C4C2311yescharacteristic
101C11×C22⋊C4—21no—
102C22⋊Dic11—21no—
103C22⋊Dic11D411yescharacteristic
104#4325—22no—
105#4325D414yescomplemented
106#4323—22no—
107#4323—22no—
108#4323—22no—
109(C2×D11)⋊C4—21no—
110(C2×D11)⋊C4—21no—
111(C2×D11)⋊C4—21no—
112(C2×D11)⋊C4D411yescharacteristic
113C4⋊Dic11—21no—
114C4⋊Dic11C2311yescharacteristic
115Dic11⋊C4D411yescharacteristic
116C4×Dic11—21no—
117C4×Dic11C2311yescharacteristic
118#4318—22no—
119C2×C11⋊C8C2311yescharacteristic
120C2×C11⋊C8C2311yescharacteristic
121D88—22no—
122D88—41no—
123#4313—22no—
124#3274—111nomaximal, Sylow
125C23×C11—21no—
126C23×C11—21no—
127C23×C11C2×D411yescharacteristic
128C22×D11—21no—
129C22×D11—21no—
130C22×D11—21no—
131C22×D11—42no—
132C22×D11—42no—
133C22×D11—42no—
134C22×D11—42no—
135C22×D11—81no—
136C22×D11—81no—
137C22×D11C2×D411yescharacteristic
138Q8×C11—21no—
139Q8×C11C2×D412yescomplemented
140D4×C11—21no—
141D4×C11—21no—
142D4×C11—21no—
143D4×C11—21no—
144D4×C11—42no—
145D4×C11—42no—
146C2×C4×C11—21no—
147C2×C4×C11—21no—
148C2×C4×C11—21no—
149C2×C4×C11—21no—
150C2×C4×C11—42no—
151C2×C4×C11C2×D411yescharacteristic
152C2×C4×C11C2411yescharacteristic
153C22⋊D11—22no—
154C22⋊D11—42no—
155C22⋊D11—42no—
156C22⋊D11—42no—
157C22⋊D11—81no—
158C22⋊D11—81no—
159C22⋊D11—81no—
160C22⋊D11—81no—
161C2×Dic11—21no—
162C2×Dic11C2×D411yescharacteristic
163C2×Dic11C2×D411yescharacteristic
164C2×Dic11C2×D411yescharacteristic
165D44—21no—
166D44—21no—
167D44—21no—
168D44—21no—
169D44—21no—
170D44—42no—
171D44—42no—
172D44—42no—
173D44C2×D412yes—
174C4×D11—21no—
175C4×D11—21no—
176C4×D11—42no—
177C4×D11—42no—
178C8×C11—21no—
179C8×C11—21no—
180C11⋊C8—21no—
181C11⋊C8C2×D412yescomplemented
182C2×AGL(1,ℤ/8)—111no—
183C2×AGL(1,ℤ/8)—111no—
184#550—111no—
185D42—111no—
186#493—111no—
187#469—111no—
188#469—111no—
189#460—111no—
190#459—111no—
191#449—111no—
192#449D1111yescharacteristic, complemented
193#447—111no—
194#447—111no—
195C4×SD16—111no—
196#436—111no—
197C22×C11—21no—
198C22×C11—21no—
199C22×C11—21no—
200C22×C11—41no—
201C22×C11—41no—
202C22×C11—41no—
203C22×C11—41no—
204C22×C11—41no—
205C22×C11—41no—
206C22×C11C22×D411yescharacteristic
207C2×D11—22no—
208C2×D11—21no—
209C2×D11—21no—
210C2×D11—21no—
211C2×D11—41no—
212C2×D11—41no—
213C2×D11—41no—
214C2×D11—41no—
215C2×D11—41no—
216C2×D11—41no—
217C2×D11—41no—
218C2×D11—41no—
219C2×D11—84no—
220C2×D11—84no—
221C4×C11—21no—
222C4×C11—22no—
223C4×C11—41no—
224C4×C11C22×D411yescharacteristic
225C4×C11H(5,𝔽2)11yescharacteristic
226Dic11—21no—
227Dic11—21no—
228Dic11—41no—
229Dic11AGL(1,ℤ/8)12yescomplemented
230C2×#41—111no—
231C2×#41C2×D1111yescharacteristic, complemented
232C22×D4—111no—
233C22×D4—111no—
234C22×D4—221no—
235AGL(1,ℤ/8)—224no—
236AGL(1,ℤ/8)—224no—
237C2×SD16—111no—
238C2×SD16—111no—
239C2×SD16C2×D1111yescharacteristic, complemented
240C2×D8—111no—
241C2×D8—111no—
242C2×D8—111no—
243C2×D8—111no—
244C2×D8—111no—
245C2×D8C2×D1111yescharacteristic, complemented
246C2×M16—111no—
247C2×M16—111no—
248#127—111no—
249#127—111no—
250#127—221no—
251#121—111no—
252#121—111no—
253#121—111no—
254#121—221no—
255#121—221no—
256#121—221no—
257#121C2×D1111yescharacteristic
258#120—221no—
259#120—221no—
260C4×Q8—111no—
261C4×D4—111no—
262C4×D4—111no—
263C4×D4—221no—
264#106—111no—
265C4⋊C8—111no—
266#103C2×D1111yescharacteristic, complemented
267#102—111no—
268#102—111no—
269#102—111no—
270#102—111no—
271#102C2×D1111yescharacteristic, complemented
272C22⋊C8—111no—
273C22⋊C8C2×D1111yescharacteristic, complemented
274C4×C8—111no—
275C2×C11—41no—
276C2×C11—81no—
277C2×C11—81no—
278C2×C11D4211yescharacteristic
279C2×C11C2×AGL(1,ℤ/8)11yescharacteristic
280C2×C11#57611yescharacteristic
281D11—41no—
282D11—42no—
283D11—81no—
284D11—81no—
285C24—221no—
286C24—221no—
287#41—22no—
288#41—41no—
289#41—222no—
290#41—441no—
291C2×Q8C22×D1111yescharacteristic
292C2×D4—21no—
293C2×D4—21no—
294C2×D4—111no—
295C2×D4—111no—
296C2×D4—111no—
297C2×D4—111no—
298C2×D4—222no—
299C2×D4—221no—
300C2×D4—221no—
301C2×D4—221no—
302C2×D4—221no—
303C2×D4—221no—
304C2×D4—221no—
305C2×D4—221no—
306C2×D4—222no—
307C2×D4—221no—
308C2×D4—221no—
309C2×D4—221no—
310C2×D4—441no—
311C2×D4—441no—
312C2×D4—444no—
313C2×D4C22×D1111yescharacteristic
314C2×D4C22×D1111yescharacteristic
315C22×C4—21no—
316C22×C4—111no—
317C22×C4—221no—
318C22×C4—221no—
319C22×C4C22×D1111yescharacteristic
320SD16—22no—
321SD16—114no—
322SD16—222no—
323D8—41no—
324D8—222no—
325D8—222no—
326D8—222no—
327D8—222no—
328D8—441no—
329M16—222no—
330M16—222no—
331C2×C8—111no—
332C2×C8—111no—
333C2×C8C22×D1111yescharacteristic
334C2×C8C22×D1111yescharacteristic
335C4⋊C4—111no—
336C4⋊C4—111no—
337C4⋊C4—221no—
338C4⋊C4C22×D1111yescharacteristic
339C22⋊C4—21no—
340C22⋊C4—111no—
341C22⋊C4—111no—
342C22⋊C4—221no—
343C22⋊C4—221no—
344C22⋊C4—221no—
345C22⋊C4—221no—
346C42—111no—
347C42—221no—
348C11#327411yescharacteristic, complemented, Sylow
349C23—21no—
350C23—21no—
351C23—111no—
352C23—221no—
353C23—221no—
354C23—221no—
355C23—442no—
356C23—442no—
357C23—442no—
358C23—442no—
359C23—881no—
360C23—881no—
361C23D4×D1111yescharacteristic
362Q8—21no—
363Q8D4×D1112yescomplemented
364D4—21no—
365D4—21no—
366D4—21no—
367D4—21no—
368D4—42no—
369D4—42no—
370D4—112no—
371D4—222no—
372D4—221no—
373D4—221no—
374D4—221no—
375D4—221no—
376D4—221no—
377D4—442no—
378D4—442no—
379D4—442no—
380D4—442no—
381D4—442no—
382D4—442no—
383D4—881no—
384D4—881no—
385D4—881no—
386D4—881no—
387C2×C4—21no—
388C2×C4—21no—
389C2×C4—21no—
390C2×C4—21no—
391C2×C4—42no—
392C2×C4—111no—
393C2×C4—111no—
394C2×C4—111no—
395C2×C4—221no—
396C2×C4—221no—
397C2×C4—221no—
398C2×C4—442no—
399C2×C4—442no—
400C2×C4D4×D1111yescharacteristic
401C2×C4C23×D1111yescharacteristic
402C8—21no—
403C8—21no—
404C8—112no—
405C8—221no—
406C22—21no—
407C22—21no—
408C22—21no—
409C22—41no—
410C22—41no—
411C22—41no—
412C22—41no—
413C22—41no—
414C22—41no—
415C22—221no—
416C22—221no—
417C22—221no—
418C22—222no—
419C22—441no—
420C22—441no—
421C22—441no—
422C22—441no—
423C22—441no—
424C22—441no—
425C22—441no—
426C22—441no—
427C22—884no—
428C22—884no—
429C22C2×D4×D1111yescharacteristic
430C4—21no—
431C4—22no—
432C4—41no—
433C4—112no—
434C4—221no—
435C4—221no—
436C4—441no—
437C4C2×D4×D1111yescharacteristic
438C4#6703711yescharacteristic
439C2—41no—
440C2—81no—
441C2—81no—
442C2—441no—
443C2—442no—
444C2—881no—
445C2—881no—
446C2#1062312111yescharacteristic
447C2#1062330011yescharacteristic
448C2D11×AGL(1,ℤ/8)11yescharacteristic
subgroupG/H
centerC22C2×D4×D11
commutator, cosocleC2×C4×C11C24
FrattiniC2×C4C23×D11
FittingC11×#449C2
socleC22×C11C22×D4
hypercenter#449D11
hypocenterC11#3274
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C22×C4 ◁ #449

Complements

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

NH ≅ G/Ntype
1. #10623365C2semidirect
2. C2×#67002C2semidirect
3. C2×#66967C2semidirect
4. #10623140C2semidirect
5. C11×#449C2semidirect
6. #10622776C2semidirect
7. #10622769C2semidirect
8. #10622764C2semidirect
9. #10622652C2semidirect
10. #10622424C2semidirect
11. #10622401C2semidirect
12. #10622399C2semidirect
13. #10622395C2semidirect
14. #10622345C2semidirect
15. #10622342C2semidirect
16. C2×C11×#41C22semidirect
17. C2×#4343C22semidirect
21. C2×C11×SD16C22semidirect
22. C2×C11×D8C22semidirect
25. Q8×Dic11C22semidirect
27. C2×#4325C22semidirect
30. #66993C22semidirect
32. #66991C22semidirect
35. C2×#4323C22semidirect
36. C2×#4323C22semidirect
38. #66983C22semidirect
41. C2×#4318C22semidirect
44. C2×D88C22semidirect
45. C2×#4313C22semidirect
50. C11×#103C22semidirect
51. C11×#102C22semidirect
52. C11×C22⋊C8C22semidirect
53. #66896C22semidirect
55. #66885C22semidirect
56. (C2×D11)⋊C8C22semidirect
57. Dic11⋊C8C22semidirect
58. C8×Dic11C22semidirect
59. #66873C22semidirect
60. #66872C22semidirect
105. #4325D4semidirect
139. Q8×C11C2×D4semidirect
181. C11⋊C8C2×D4semidirect
192. #449D11semidirect
229. Dic11AGL(1,ℤ/8)semidirect
231. C2×#41C2×D11semidirect
239. C2×SD16C2×D11semidirect
245. C2×D8C2×D11semidirect
266. #103C2×D11semidirect
271. #102C2×D11semidirect
273. C22⋊C8C2×D11semidirect
348. C11#3274semidirect
363. Q8D4×D11semidirect

Maximal subgroups

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

subgroupindex
#106233652
C2×#670022
C2×#669672
#106231402
C11×#4492
#106227762
#106227692
#106227642
#106226522
#106224242
#106224012
#106223992
#106223952
#106223452
#106223422
#327411