Finite Group Databasebeta

← #13080098

Subgroups — #13080098

Order 1408.

568 conjugacy classes of subgroups.

The subgroup lattice has 452 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#66964C211yesmaximal, characteristic, complemented
2C2×D8×D11C211yesmaximal, characteristic, complemented
3#10623085C211yesmaximal, characteristic, complemented
4D4×D44C211yesmaximal, characteristic, complemented
5C11×#442C211yesmaximal, characteristic, complemented
6#10622629C211yesmaximal, characteristic, complemented
7#10622628C211yesmaximal, characteristic, complemented
8#10622478C211yesmaximal, characteristic, complemented
9#10622477C211yesmaximal, characteristic, complemented
10#10622394C211yesmaximal, characteristic, complemented
11#10622389C211yesmaximal, characteristic, complemented
12#10622386C211yesmaximal, characteristic, complemented
13#10622386C211yesmaximal, characteristic, complemented
14#10622325C211yesmaximal, characteristic, complemented
15#10622319C211yesmaximal, characteristic, complemented
16C2×#4341C2211yescharacteristic, complemented
17C2×D4×D11C2211yescharacteristic
18C2×D4×D11C2211yescharacteristic, complemented
19C2×D4×D11C2211yescharacteristic, complemented
20C22×D44—21no—
21C2×C11×D8C2211yescharacteristic
22C4×D4×C11C2211yescharacteristic, complemented
23C4×D4×C11C2211yescharacteristic, complemented
24C2×#4324C2211yescharacteristic, complemented
25C2×#4323C2211yescharacteristic
26C2×#4323C2211yescharacteristic, complemented
27C2×#4323C2211yescharacteristic, complemented
28#66983—21no—
29#66983—21no—
30C2×(C2×D11)⋊C4—21no—
31#66964—24no—
32D8×D11—24no—
33C2×D88C2211yescharacteristic, complemented
34C2×D88C2211yescharacteristic, complemented
35C2×#4314C2211yescharacteristic, complemented
36C2×#4314C2211yescharacteristic, complemented
37C2×#4313C2211yescharacteristic, complemented
38C2×C8×D11C2211yescharacteristic, complemented
39#66950C2211yescharacteristic, complemented
40#66948C2211yescharacteristic
41#66948C2211yescharacteristic, complemented
42#66948C2211yescharacteristic, complemented
43#66939—21no—
44#66935—21no—
45#66935—21no—
46#66935—21no—
47#66928C2211yescharacteristic, complemented
48#66927C2211yescharacteristic, complemented
49C4×D44C2211yescharacteristic
50C11×#106C2211yescharacteristic, complemented
51C11×#102C2211yescharacteristic, complemented
52C11×#102C2211yescharacteristic, complemented
53C11×#97C2211yescharacteristic, complemented
54(C2×D11)⋊C8C2211yescharacteristic, complemented
55(C2×D11)⋊C8C2211yescharacteristic, complemented
56#66874C2211yescharacteristic, complemented
57#66873C2211yescharacteristic, complemented
58#66873C2211yescharacteristic, complemented
59#66873C2211yescharacteristic, complemented
60C4⋊(C11⋊C8)C2211yescharacteristic, complemented
61C23×D11—21no—
62C23×D11—21no—
63C23×D11—21no—
64C2×D4×C11C2311yescharacteristic
65C2×D4×C11C2311yescharacteristic
66C22×C4×C11—21no—
67C22×C4×C11—21no—
68C2×C22⋊D11—21no—
69C2×C22⋊D11—21no—
70C2×C22⋊D11—21no—
71C2×C22⋊D11—21no—
72C22×Dic11—21no—
73#4341—22no—
74#4341—41no—
75D4×D11—22no—
76D4×D11—22no—
77D4×D11—22no—
78D4×D11—41no—
79D4×D11—41no—
80D4×D11—41no—
81C2×D44—21no—
82C2×D44—21no—
83C2×D44—21no—
84C2×D44—21no—
85C2×D44—21no—
86C2×D44—44no—
87C2×D44D411yescharacteristic
88C2×D44C2311yescharacteristic
89C2×D44C2311yescharacteristic
90C2×D44C2311yescharacteristic
91C2×C4×D11C2311yescharacteristic
92C2×C4×D11C2311yescharacteristic
93C2×Dic22C2311yescharacteristic
94C11×D8D414yescomplemented
95C2×C8×C11C2311yescharacteristic
96C2×C8×C11C2311yescharacteristic
97C11×C4⋊C4C2311yescharacteristic
98C11×C4⋊C4C2311yescharacteristic
99C11×C22⋊C4—21no—
100C11×C22⋊C4—21no—
101C42×C11C2311yescharacteristic
102#4324—22no—
103#4323—22no—
104#4323—22no—
105#4323—22no—
106(C2×D11)⋊C4—21no—
107(C2×D11)⋊C4—21no—
108(C2×D11)⋊C4—21no—
109(C2×D11)⋊C4—21no—
110(C2×D11)⋊C4—21no—
111(C2×D11)⋊C4—21no—
112(C2×D11)⋊C4D411yescharacteristic
113(C2×D11)⋊C4D411yescharacteristic
114C4⋊Dic11—21no—
115C4⋊Dic11D411yescharacteristic
116C2×C11⋊C8C2311yescharacteristic
117C2×C11⋊C8C2311yescharacteristic
118D88—22no—
119D88—41no—
120#4314—22no—
121#4314—41no—
122#4313—22no—
123C8×D11—22no—
124#3264—111nomaximal, Sylow
125C23×C11—21no—
126C23×C11—21no—
127C22×D11—21no—
128C22×D11—21no—
129C22×D11—21no—
130C22×D11—42no—
131C22×D11—42no—
132C22×D11—42no—
133C22×D11—42no—
134C22×D11—42no—
135C22×D11—42no—
136C22×D11—81no—
137C22×D11—81no—
138C22×D11—81no—
139C22×D11C2×D411yescharacteristic
140C22×D11C2×D411yescharacteristic
141D4×C11—21no—
142D4×C11—21no—
143D4×C11C2×D412yes—
144D4×C11C2×D412yescomplemented
145C2×C4×C11—21no—
146C2×C4×C11—21no—
147C2×C4×C11—42no—
148C2×C4×C11—81no—
149C2×C4×C11C2×D411yescharacteristic
150C2×C4×C11C2×D411yescharacteristic
151C2×C4×C11C2411yescharacteristic
152C22⋊D11—42no—
153C22⋊D11—42no—
154C22⋊D11—42no—
155C22⋊D11—42no—
156C2×Dic11—21no—
157C2×Dic11—42no—
158C2×Dic11C2×D411yescharacteristic
159C2×Dic11C2×D411yescharacteristic
160D44—22no—
161D44—21no—
162D44—21no—
163D44—21no—
164D44—21no—
165D44—21no—
166D44—21no—
167D44—42no—
168D44—42no—
169D44—42no—
170D44—81no—
171D44—81no—
172C4×D11—21no—
173C4×D11—21no—
174C4×D11—21no—
175C4×D11—21no—
176Dic22—21no—
177Dic22—21no—
178C8×C11—21no—
179C8×C11C2×D412yescomplemented
180C11⋊C8—21no—
181C11⋊C8—21no—
182C2×AGL(1,ℤ/8)—111no—
183C22×D8—111no—
184#546—111no—
185D42—111no—
186#496—111no—
187#469—111no—
188#465—111no—
189#463—111no—
190#459—111no—
191#450—111no—
192#449—111no—
193#447—111no—
194#447—111no—
195#442D1111yescharacteristic, complemented
196#435—111no—
197C22×C11—22no—
198C22×C11—22no—
199C22×C11—41no—
200C22×C11—41no—
201C22×C11—41no—
202C22×C11—41no—
203C22×C11C22×D411yescharacteristic
204C2×D11—21no—
205C2×D11—21no—
206C2×D11—21no—
207C2×D11—21no—
208C2×D11—21no—
209C2×D11—41no—
210C2×D11—41no—
211C2×D11—41no—
212C2×D11—41no—
213C2×D11—41no—
214C2×D11—41no—
215C2×D11—41no—
216C2×D11—41no—
217C2×D11—41no—
218C2×D11—84no—
219C2×D11—84no—
220C2×D11—84no—
221C2×D11AGL(1,ℤ/8)12yescomplemented
222C4×C11—21no—
223C4×C11—21no—
224C4×C11—41no—
225C4×C11—41no—
226C4×C11C22×D411yescharacteristic
227C4×C11H(5,𝔽2)11yescharacteristic
228Dic11—21no—
229Dic11—21no—
230Dic11—41no—
231C2×#41—111no—
232C22×D4—111no—
233C22×D4—111no—
234C22×D4—111no—
235C22×D4—221no—
236AGL(1,ℤ/8)—224no—
237C2×SD16—111no—
238C2×SD16—111no—
239C2×SD16—111no—
240C2×D8—111no—
241C2×D8—111no—
242C2×D8—111no—
243C2×D8—111no—
244C2×D8—111no—
245C2×D8—224no—
246C2×D8C2×D1111yescharacteristic
247C2×M16—111no—
248C22×C8—111no—
249#127—111no—
250#124—111no—
251#123—221no—
252C22⋊Q8—111no—
253#121—111no—
254#121—111no—
255#121—111no—
256#121—221no—
257#121—221no—
258#120—221no—
259#120—221no—
260#120—221no—
261C4×D4—111no—
262C4×D4C2×D1111yescharacteristic, complemented
263C4×D4C2×D1111yescharacteristic, complemented
264C2×C22⋊C4—221no—
265#106C2×D1111yescharacteristic, complemented
266C4⋊C8—111no—
267#103—111no—
268#102—111no—
269#102—111no—
270#102—111no—
271#102C2×D1111yescharacteristic, complemented
272#102C2×D1111yescharacteristic, complemented
273C22⋊C8—111no—
274C22⋊C8—111no—
275#97C2×D1111yescharacteristic, complemented
276C2×C11—42no—
277C2×C11—42no—
278C2×C11D4211yescharacteristic
279C2×C11C2×AGL(1,ℤ/8)11yescharacteristic
280C2×C11#57611yescharacteristic
281D11—22no—
282D11—41no—
283D11—81no—
284D11—81no—
285D11—81no—
286C24—221no—
287C24—221no—
288C24—221no—
289#41—222no—
290#41—441no—
291C2×Q8—111no—
292C2×D4—111no—
293C2×D4—111no—
294C2×D4—111no—
295C2×D4—111no—
296C2×D4—221no—
297C2×D4—221no—
298C2×D4—221no—
299C2×D4—221no—
300C2×D4—221no—
301C2×D4—221no—
302C2×D4—222no—
303C2×D4—222no—
304C2×D4—222no—
305C2×D4—221no—
306C2×D4—221no—
307C2×D4—221no—
308C2×D4—444no—
309C2×D4—441no—
310C2×D4—441no—
311C2×D4—441no—
312C2×D4C22×D1111yescharacteristic
313C2×D4C22×D1111yescharacteristic
314C22×C4—21no—
315C22×C4—21no—
316C22×C4—111no—
317C22×C4—111no—
318C22×C4—221no—
319SD16—222no—
320SD16—222no—
321SD16—441no—
322D8—222no—
323D8—222no—
324D8—222no—
325D8—222no—
326D8—441no—
327D8D4414yescomplemented
328M16—222no—
329C2×C8—111no—
330C2×C8—111no—
331C2×C8—222no—
332C2×C8C22×D1111yescharacteristic
333C2×C8C22×D1111yescharacteristic
334C4⋊C4—111no—
335C4⋊C4—221no—
336C4⋊C4C22×D1111yescharacteristic
337C4⋊C4C22×D1111yescharacteristic
338C22⋊C4—21no—
339C22⋊C4—21no—
340C22⋊C4—111no—
341C22⋊C4—111no—
342C22⋊C4—221no—
343C22⋊C4—221no—
344C22⋊C4—221no—
345C22⋊C4—221no—
346C22⋊C4—221no—
347C22⋊C4—221no—
348C42C22×D1111yescharacteristic
349C11#326411yescharacteristic, complemented, Sylow
350C23—21no—
351C23—21no—
352C23—111no—
353C23—111no—
354C23—221no—
355C23—221no—
356C23—221no—
357C23—442no—
358C23—442no—
359C23—442no—
360C23—442no—
361C23—442no—
362C23—442no—
363C23—881no—
364C23—881no—
365C23—881no—
366Q8—221no—
367Q8—221no—
368D4—21no—
369D4—21no—
370D4—222no—
371D4—221no—
372D4—221no—
373D4—221no—
374D4—221no—
375D4—221no—
376D4—221no—
377D4—442no—
378D4—442no—
379D4—442no—
380D4—442no—
381D4—442no—
382D4—442no—
383D4—442no—
384D4—881no—
385D4—881no—
386D4C2×D4412yes—
387D4C2×D4412yescomplemented
388C2×C4—21no—
389C2×C4—21no—
390C2×C4—42no—
391C2×C4—81no—
392C2×C4—111no—
393C2×C4—111no—
394C2×C4—221no—
395C2×C4—221no—
396C2×C4—221no—
397C2×C4—221no—
398C2×C4—221no—
399C2×C4—442no—
400C2×C4D4×D1111yescharacteristic
401C2×C4D4×D1111yescharacteristic
402C2×C4C23×D1111yescharacteristic
403C8—21no—
404C8—221no—
405C8—221no—
406C8C2×D4412yescomplemented
407C22—22no—
408C22—22no—
409C22—41no—
410C22—41no—
411C22—41no—
412C22—41no—
413C22—112no—
414C22—221no—
415C22—221no—
416C22—221no—
417C22—221no—
418C22—221no—
419C22—441no—
420C22—441no—
421C22—441no—
422C22—441no—
423C22—441no—
424C22—441no—
425C22—441no—
426C22—441no—
427C22—441no—
428C22—884no—
429C22—884no—
430C22—884no—
431C22C2×D4×D1111yescharacteristic
432C4—21no—
433C4—21no—
434C4—41no—
435C4—41no—
436C4—221no—
437C4—221no—
438C4—441no—
439C4C22×D4411yescharacteristic
440C4#6704211yescharacteristic
441C2—42no—
442C2—42no—
443C2—222no—
444C2—441no—
445C2—881no—
446C2—881no—
447C2—881no—
448C2D4×D4411yescharacteristic
449C2D11×AGL(1,ℤ/8)11yescharacteristic
450C2#1062330511yescharacteristic
subgroupG/H
centerC22C2×D4×D11
commutator, cosocleC2×C4×C11C24
FrattiniC2×C4C23×D11
FittingC11×#442C2
socleC22×C11C22×D4
hypercenter#442D11
hypocenterC11#3264
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C42 ◁ #442

Complements

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

NH ≅ G/Ntype
1. C2×#66964C2semidirect
2. C2×D8×D11C2semidirect
3. #10623085C2semidirect
4. D4×D44C2semidirect
5. C11×#442C2semidirect
6. #10622629C2semidirect
7. #10622628C2semidirect
8. #10622478C2semidirect
9. #10622477C2semidirect
10. #10622394C2semidirect
11. #10622389C2semidirect
12. #10622386C2semidirect
13. #10622386C2semidirect
14. #10622325C2semidirect
15. #10622319C2semidirect
16. C2×#4341C22semidirect
18. C2×D4×D11C22semidirect
19. C2×D4×D11C22semidirect
22. C4×D4×C11C22semidirect
23. C4×D4×C11C22semidirect
24. C2×#4324C22semidirect
26. C2×#4323C22semidirect
27. C2×#4323C22semidirect
33. C2×D88C22semidirect
34. C2×D88C22semidirect
35. C2×#4314C22semidirect
36. C2×#4314C22semidirect
37. C2×#4313C22semidirect
38. C2×C8×D11C22semidirect
39. #66950C22semidirect
41. #66948C22semidirect
42. #66948C22semidirect
47. #66928C22semidirect
48. #66927C22semidirect
50. C11×#106C22semidirect
51. C11×#102C22semidirect
52. C11×#102C22semidirect
53. C11×#97C22semidirect
54. (C2×D11)⋊C8C22semidirect
55. (C2×D11)⋊C8C22semidirect
56. #66874C22semidirect
57. #66873C22semidirect
58. #66873C22semidirect
59. #66873C22semidirect
60. C4⋊(C11⋊C8)C22semidirect
94. C11×D8D4semidirect
144. D4×C11C2×D4semidirect
179. C8×C11C2×D4semidirect
195. #442D11semidirect
221. C2×D11AGL(1,ℤ/8)semidirect
262. C4×D4C2×D11semidirect
263. C4×D4C2×D11semidirect
265. #106C2×D11semidirect
271. #102C2×D11semidirect
272. #102C2×D11semidirect
275. #97C2×D11semidirect
327. D8D44semidirect
349. C11#3264semidirect
387. D4C2×D44semidirect
406. C8C2×D44semidirect

Maximal subgroups

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

subgroupindex
C2×#669642
C2×D8×D112
#106230852
D4×D442
C11×#4422
#106226292
#106226282
#106224782
#106224772
#106223942
#106223892
#106223862
#106223252
#106223192
#326411