Finite Group Databasebeta

← #13080230

Subgroups — #13080230

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
1C2×C11×AGL(1,ℤ/8)C211yesmaximal, characteristic, complemented
2#10623365C211yesmaximal, characteristic, complemented
3D4×C22⋊D11C211yesmaximal, characteristic, complemented
4C2×#66967C211yesmaximal, characteristic, complemented
5#10622851C211yesmaximal, characteristic, complemented
6#10622830C211yesmaximal, characteristic, complemented
7#10622785C211yesmaximal, characteristic, complemented
8#10622776C211yesmaximal, characteristic, complemented
9SD16×Dic11C211yesmaximal, characteristic, complemented
10#10622772C211yesmaximal, characteristic, complemented
11#10622769C211yesmaximal, characteristic, complemented
12#10622764C211yesmaximal, characteristic, complemented
13#10622763C211yesmaximal, characteristic, complemented
14#10622748C211yesmaximal, characteristic, complemented
15#10622741C211yesmaximal, characteristic, complemented
16C2×C11×#41C2211yescharacteristic, complemented
17C22×D4×C11C2211yescharacteristic
18C22×C22⋊D11—21no—
19C2×#4343C2211yescharacteristic, complemented
20C2×D4×D11C2211yescharacteristic
21C11×AGL(1,ℤ/8)—24no—
22C2×C11×SD16C2211yescharacteristic
23C2×C11×SD16C2211yescharacteristic, complemented
24C2×C11×D8C2211yescharacteristic
25C2×C11×D8C2211yescharacteristic, complemented
26C2×C11×M16C2211yescharacteristic, complemented
27#67006—21no—
28Q8×Dic11C2211yescharacteristic, complemented
29C2×#4325C2211yescharacteristic, complemented
30#66993—21no—
31#66993C2211yescharacteristic
32#66993C2211yescharacteristic, complemented
33#66992—21no—
34#66991—21no—
35#66991C2211yescharacteristic
36#66991C2211yescharacteristic, complemented
37#66990—21no—
38D4×Dic11C2211yescharacteristic
39C2×#4323C2211yescharacteristic
40C2×#4323C2211yescharacteristic, complemented
41C2×#4323C2211yescharacteristic, complemented
42#66983—21no—
43#66983C2211yescharacteristic
44#66983C2211yescharacteristic, complemented
45C4×C22⋊D11—21no—
46C4×C22⋊D11C2211yescharacteristic
47#66967—24no—
48C2×D88C2211yescharacteristic, complemented
49C2×#4313C2211yescharacteristic, complemented
50#66899C2211yescharacteristic, complemented
51#66896C2211yescharacteristic
52#66896C2211yescharacteristic, complemented
53#66896C2211yescharacteristic, complemented
54C22⋊(C11⋊C8)C2211yescharacteristic, complemented
55#66885C2211yescharacteristic, complemented
56#66885C2211yescharacteristic, complemented
57(C2×D11)⋊C8C2211yescharacteristic, complemented
58#66881C2211yescharacteristic, complemented
59Dic11⋊C8C2211yescharacteristic, complemented
60C8×Dic11C2211yescharacteristic, complemented
61C24×C11—21no—
62C23×D11—21no—
63C11×#41—22no—
64C11×#41—41no—
65C2×Q8×C11C2311yescharacteristic
66C2×D4×C11—22no—
67C2×D4×C11—21no—
68C2×D4×C11—21no—
69C2×D4×C11—41no—
70C2×D4×C11C2311yescharacteristic
71C2×D4×C11C2311yescharacteristic
72C2×D4×C11C2311yescharacteristic
73C22×C4×C11—21no—
74C22×C4×C11C2311yescharacteristic
75C2×C22⋊D11—21no—
76C2×C22⋊D11—21no—
77C2×C22⋊D11—21no—
78C2×C22⋊D11—21no—
79C2×C22⋊D11—21no—
80C2×C22⋊D11—21no—
81C2×C22⋊D11—21no—
82C2×C22⋊D11—21no—
83C2×C22⋊D11—21no—
84C2×C22⋊D11—44no—
85C2×C22⋊D11D411yescharacteristic
86C22×Dic11—21no—
87#4343—22no—
88#4343—41no—
89D4×D11—22no—
90D4×D11—41no—
91C2×D44—21no—
92C2×D44C2311yescharacteristic
93C2×D44C2311yescharacteristic
94C2×C4×D11—21no—
95C2×C4×D11C2311yescharacteristic
96C11×SD16—22no—
97C11×SD16D414yescomplemented
98C11×D8—22no—
99C11×D8—22no—
100C11×M16—22no—
101C2×C8×C11C2311yescharacteristic
102C2×C8×C11C2311yescharacteristic
103C22⋊Dic11—21no—
104C22⋊Dic11—21no—
105C22⋊Dic11—21no—
106C22⋊Dic11D411yescharacteristic
107#4325—22no—
108#4323—22no—
109#4323—41no—
110#4323—41no—
111(C2×D11)⋊C4—21no—
112(C2×D11)⋊C4—21no—
113(C2×D11)⋊C4D411yescharacteristic
114C4⋊Dic11—21no—
115C4⋊Dic11C2311yescharacteristic
116C4⋊Dic11C2311yescharacteristic
117Dic11⋊C4D411yescharacteristic
118C4×Dic11—21no—
119C4×Dic11C2311yescharacteristic
120C2×C11⋊C8C2311yescharacteristic
121C2×C11⋊C8C2311yescharacteristic
122D88—22no—
123#4313—22no—
124#3274—111nomaximal, Sylow
125C23×C11—21no—
126C23×C11—21no—
127C23×C11—21no—
128C23×C11—42no—
129C23×C11—42no—
130C23×C11—81no—
131C23×C11C2×D411yescharacteristic
132C22×D11—21no—
133C22×D11—21no—
134C22×D11—42no—
135C22×D11—42no—
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—21no—
145D4×C11—42no—
146D4×C11—42no—
147D4×C11C2×D412yes—
148C2×C4×C11—21no—
149C2×C4×C11—21no—
150C2×C4×C11—21no—
151C2×C4×C11—42no—
152C2×C4×C11C2×D411yescharacteristic
153C2×C4×C11C2411yescharacteristic
154C22⋊D11—22no—
155C22⋊D11—42no—
156C22⋊D11—42no—
157C22⋊D11—42no—
158C22⋊D11—42no—
159C22⋊D11—42no—
160C22⋊D11—81no—
161C22⋊D11—81no—
162C22⋊D11—81no—
163C22⋊D11—81no—
164C2×Dic11—21no—
165C2×Dic11—21no—
166C2×Dic11—42no—
167C2×Dic11C2×D411yescharacteristic
168C2×Dic11C2×D411yescharacteristic
169C2×Dic11C2×D411yescharacteristic
170D44—21no—
171D44—21no—
172D44—21no—
173D44—21no—
174D44—42no—
175C4×D11—21no—
176C4×D11—21no—
177C4×D11—42no—
178C8×C11—21no—
179C8×C11C2×D412yescomplemented
180C11⋊C8—21no—
181C11⋊C8—21no—
182C2×AGL(1,ℤ/8)—111no—
183C2×AGL(1,ℤ/8)D1111yescharacteristic, complemented
184#550—111no—
185D42—111no—
186#493—111no—
187#469—111no—
188#469—111no—
189#460—111no—
190#459—111no—
191#449—111no—
192#449—111no—
193#447—111no—
194#447—111no—
195C4×SD16—111no—
196#436—111no—
197C22×C11—21no—
198C22×C11—22no—
199C22×C11—21no—
200C22×C11—21no—
201C22×C11—41no—
202C22×C11—41no—
203C22×C11—41no—
204C22×C11—41no—
205C22×C11—41no—
206C22×C11—41no—
207C22×C11—41no—
208C22×C11—41no—
209C22×C11—84no—
210C22×C11C22×D411yescharacteristic
211C2×D11—21no—
212C2×D11—21no—
213C2×D11—21no—
214C2×D11—41no—
215C2×D11—41no—
216C2×D11—41no—
217C2×D11—41no—
218C2×D11—41no—
219C2×D11—41no—
220C2×D11—84no—
221C4×C11—21no—
222C4×C11—22no—
223C4×C11C22×D411yescharacteristic
224C4×C11H(5,𝔽2)11yescharacteristic
225Dic11—21no—
226Dic11—21no—
227Dic11—41no—
228Dic11—41no—
229Dic11AGL(1,ℤ/8)12yescomplemented
230C2×#41—111no—
231C2×#41C2×D1111yescharacteristic, complemented
232C22×D4—111no—
233C22×D4—221no—
234C22×D4C2×D1111yescharacteristic
235AGL(1,ℤ/8)—24no—
236AGL(1,ℤ/8)—224no—
237C2×SD16—111no—
238C2×SD16C2×D1111yescharacteristic
239C2×SD16C2×D1111yescharacteristic, complemented
240C2×D8—111no—
241C2×D8—111no—
242C2×D8—111no—
243C2×D8—111no—
244C2×D8C2×D1111yescharacteristic
245C2×D8C2×D1111yescharacteristic, complemented
246C2×M16—111no—
247C2×M16C2×D1111yescharacteristic, complemented
248#127—111no—
249#127—111no—
250#127—221no—
251#121—111no—
252#121—111no—
253#121—111no—
254#121—111no—
255#121—221no—
256#121—221no—
257#121—221no—
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#103—111no—
267#102—111no—
268#102—111no—
269#102—111no—
270#102—111no—
271#102—111no—
272C22⋊C8—111no—
273C22⋊C8—111no—
274C4×C8—111no—
275C2×C11—42no—
276C2×C11—41no—
277C2×C11—81no—
278C2×C11—81no—
279C2×C11D4211yescharacteristic
280C2×C11C2×AGL(1,ℤ/8)11yescharacteristic
281C2×C11#57611yescharacteristic
282D11—41no—
283D11—81no—
284D11—81no—
285C24—21no—
286C24—221no—
287#41—22no—
288#41—41no—
289#41—222no—
290#41—441no—
291C2×Q8C22×D1111yescharacteristic
292C2×D4—22no—
293C2×D4—21no—
294C2×D4—21no—
295C2×D4—41no—
296C2×D4—111no—
297C2×D4—111no—
298C2×D4—111no—
299C2×D4—221no—
300C2×D4—221no—
301C2×D4—221no—
302C2×D4—221no—
303C2×D4—221no—
304C2×D4—221no—
305C2×D4—222no—
306C2×D4—221no—
307C2×D4—221no—
308C2×D4—221no—
309C2×D4—221no—
310C2×D4—441no—
311C2×D4—444no—
312C2×D4C22×D1111yescharacteristic
313C2×D4C22×D1111yescharacteristic
314C2×D4C22×D1111yescharacteristic
315C22×C4—21no—
316C22×C4—111no—
317C22×C4—221no—
318C22×C4—221no—
319C22×C4C22×D1111yescharacteristic
320SD16—22no—
321SD16—222no—
322SD16C22⋊D1114yescomplemented
323D8—22no—
324D8—22no—
325D8—222no—
326D8—222no—
327D8—441no—
328D8—441no—
329M16—22no—
330M16—222no—
331C2×C8—111no—
332C2×C8—111no—
333C2×C8C22×D1111yescharacteristic
334C2×C8C22×D1111yescharacteristic
335C4⋊C4—111no—
336C4⋊C4—111no—
337C4⋊C4—111no—
338C4⋊C4—221no—
339C22⋊C4—111no—
340C22⋊C4—111no—
341C22⋊C4—221no—
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—21no—
352C23—42no—
353C23—42no—
354C23—81no—
355C23—111no—
356C23—221no—
357C23—221no—
358C23—442no—
359C23—442no—
360C23—881no—
361C23D4×D1111yescharacteristic
362Q8—21no—
363Q8C2×C22⋊D1112yescomplemented
364D4—21no—
365D4—21no—
366D4—21no—
367D4—21no—
368D4—21no—
369D4—42no—
370D4—42no—
371D4—222no—
372D4—221no—
373D4—221no—
374D4—221no—
375D4—221no—
376D4—442no—
377D4—442no—
378D4—442no—
379D4—442no—
380D4—442no—
381D4—442no—
382D4—881no—
383D4—881no—
384D4—881no—
385D4—881no—
386D4C2×C22⋊D1112yes—
387C2×C4—21no—
388C2×C4—21no—
389C2×C4—21no—
390C2×C4—42no—
391C2×C4—111no—
392C2×C4—111no—
393C2×C4—111no—
394C2×C4—221no—
395C2×C4—221no—
396C2×C4—221no—
397C2×C4—221no—
398C2×C4—442no—
399C2×C4—442no—
400C2×C4D4×D1111yescharacteristic
401C2×C4C23×D1111yescharacteristic
402C8—21no—
403C8—221no—
404C8—221no—
405C8C2×C22⋊D1112yescomplemented
406C22—21no—
407C22—21no—
408C22—21no—
409C22—22no—
410C22—41no—
411C22—41no—
412C22—41no—
413C22—41no—
414C22—41no—
415C22—41no—
416C22—41no—
417C22—41no—
418C22—84no—
419C22—221no—
420C22—221no—
421C22—221no—
422C22—441no—
423C22—441no—
424C22—441no—
425C22—441no—
426C22—441no—
427C22—441no—
428C22—884no—
429C22C2×D4×D1111yescharacteristic
430C4—21no—
431C4—22no—
432C4—112no—
433C4—221no—
434C4—221no—
435C4—441no—
436C4—441no—
437C4#6703711yescharacteristic
438C4C22×C22⋊D1111yescharacteristic
439C2—41no—
440C2—42no—
441C2—81no—
442C2—81no—
443C2—441no—
444C2—881no—
445C2—881no—
446C2D11×AGL(1,ℤ/8)11yescharacteristic
447C2#1062330511yescharacteristic
448C2D4×C22⋊D1111yescharacteristic
subgroupG/H
centerC22C2×D4×D11
commutator, cosocleC2×C4×C11C24
FrattiniC2×C4C23×D11
FittingC2×C11×AGL(1,ℤ/8)C2
socleC22×C11C22×D4
hypercenterC2×AGL(1,ℤ/8)D11
hypocenterC11#3274
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×AGL(1,ℤ/8)

Complements

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

NH ≅ G/Ntype
1. C2×C11×AGL(1,ℤ/8)C2semidirect
2. #10623365C2semidirect
3. D4×C22⋊D11C2semidirect
4. C2×#66967C2semidirect
5. #10622851C2semidirect
6. #10622830C2semidirect
7. #10622785C2semidirect
8. #10622776C2semidirect
9. SD16×Dic11C2semidirect
10. #10622772C2semidirect
11. #10622769C2semidirect
12. #10622764C2semidirect
13. #10622763C2semidirect
14. #10622748C2semidirect
15. #10622741C2semidirect
16. C2×C11×#41C22semidirect
19. C2×#4343C22semidirect
23. C2×C11×SD16C22semidirect
25. C2×C11×D8C22semidirect
26. C2×C11×M16C22semidirect
28. Q8×Dic11C22semidirect
29. C2×#4325C22semidirect
32. #66993C22semidirect
36. #66991C22semidirect
40. C2×#4323C22semidirect
41. C2×#4323C22semidirect
44. #66983C22semidirect
48. C2×D88C22semidirect
49. C2×#4313C22semidirect
50. #66899C22semidirect
52. #66896C22semidirect
53. #66896C22semidirect
54. C22⋊(C11⋊C8)C22semidirect
55. #66885C22semidirect
56. #66885C22semidirect
57. (C2×D11)⋊C8C22semidirect
58. #66881C22semidirect
59. Dic11⋊C8C22semidirect
60. C8×Dic11C22semidirect
97. C11×SD16D4semidirect
139. Q8×C11C2×D4semidirect
179. C8×C11C2×D4semidirect
183. C2×AGL(1,ℤ/8)D11semidirect
229. Dic11AGL(1,ℤ/8)semidirect
231. C2×#41C2×D11semidirect
239. C2×SD16C2×D11semidirect
245. C2×D8C2×D11semidirect
247. C2×M16C2×D11semidirect
322. SD16C22⋊D11semidirect
348. C11#3274semidirect
363. Q8C2×C22⋊D11semidirect
405. C8C2×C22⋊D11semidirect

Maximal subgroups

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

subgroupindex
C2×C11×AGL(1,ℤ/8)2
#106233652
D4×C22⋊D112
C2×#669672
#106228512
#106228302
#106227852
#106227762
SD16×Dic112
#106227722
#106227692
#106227642
#106227632
#106227482
#106227412
#327411