Finite Group Databasebeta

← #28402049

Subgroups — #28402049

Order 14464.

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×#16813646C211yesmaximal, characteristic, complemented
2C2×D8×D113C211yesmaximal, characteristic, complemented
3#20299243C211yesmaximal, characteristic, complemented
4#20299233C211yesmaximal, characteristic, complemented
5#20298985C211yesmaximal, characteristic, complemented
6#20298850C211yesmaximal, characteristic, complemented
7#20298826C211yesmaximal, characteristic, complemented
8#20298814C211yesmaximal, characteristic, complemented
9#20298750C211yesmaximal, characteristic, complemented
10#20298740C211yesmaximal, characteristic, complemented
11#20298733C211yesmaximal, characteristic, complemented
12#20298730C211yesmaximal, characteristic, complemented
13#20298708C211yesmaximal, characteristic, complemented
14#20298668C211yesmaximal, characteristic, complemented
15#459×C113C211yesmaximal, characteristic, complemented
16C2×#14268646C2211yescharacteristic, complemented
17C2×D4×D113—21no—
18C2×D4×D113C2211yescharacteristic
19C2×D4×D113C2211yescharacteristic, complemented
20C2×D4×D113C2211yescharacteristic, complemented
21#16813646—24no—
22C2×#14268636C2211yescharacteristic, complemented
23C2×#14268635C2211yescharacteristic, complemented
24C2×#14268635C2211yescharacteristic, complemented
25C2×D904C2211yescharacteristic
26C2×#14268632C2211yescharacteristic
27C2×#14268632C2211yescharacteristic, complemented
28C2×#14268632C2211yescharacteristic, complemented
29D8×D113—24no—
30C2×#14268630C2211yescharacteristic, complemented
31C2×C8×D113C2211yescharacteristic, complemented
32#16813610C2211yescharacteristic, complemented
33#16813606—21no—
34#16813602C2211yescharacteristic, complemented
35#16813597C2211yescharacteristic, complemented
36#16813596—21no—
37#16813593—21no—
38#16813593C2211yescharacteristic
39#16813593C2211yescharacteristic, complemented
40#16813592—21no—
41#16813590—21no—
42#16813590—21no—
43C4×D452C2211yescharacteristic
44C4×D452C2211yescharacteristic, complemented
45C2×#14268624—21no—
46#16813553C2211yescharacteristic, complemented
47#16813547C2211yescharacteristic, complemented
48#16813544C2211yescharacteristic, complemented
49#16813543C2211yescharacteristic, complemented
50#16813542C2211yescharacteristic, complemented
51#16813534C2211yescharacteristic, complemented
52#16813534C2211yescharacteristic, complemented
53#16813533C2211yescharacteristic, complemented
54C2×D8×C113C2211yescharacteristic, complemented
55C2×D8×C113C2211yescharacteristic, complemented
56#127×C113C2211yescharacteristic, complemented
57C4×D4×C113C2211yescharacteristic, complemented
58C4⋊C8×C113C2211yescharacteristic, complemented
59#102×C113C2211yescharacteristic, complemented
60#102×C113C2211yescharacteristic, complemented
61C23×D113—21no—
62C23×D113—21no—
63C23×D113—21no—
64#14268646—22no—
65#14268646—41no—
66C2×Dic226C2311yescharacteristic
67C2×D452—21no—
68C2×D452D411yescharacteristic
69C2×D452C2311yescharacteristic
70C2×D452C2311yescharacteristic
71C2×C22⋊D113—21no—
72C2×C22⋊D113—21no—
73C2×C22⋊D113—21no—
74C2×C22⋊D113—21no—
75C2×C22⋊D113—21no—
76C2×C22⋊D113—21no—
77D4×D113—22no—
78D4×D113—22no—
79D4×D113—22no—
80D4×D113—41no—
81D4×D113—41no—
82D4×D113—41no—
83D4×D113—44no—
84C22×Dic113—21no—
85C2×C4×D113—21no—
86C2×C4×D113C2311yescharacteristic
87C2×C4×D113C2311yescharacteristic
88#14268636—22no—
89#14268635—22no—
90#14268635—41no—
91D904—22no—
92#14268632—22no—
93#14268632—41no—
94#14268632D414yescomplemented
95#14268630—22no—
96C2×#11744751C2311yescharacteristic
97C2×#11744751C2311yescharacteristic
98C8×D113—22no—
99C4⋊Dic113—21no—
100C4⋊Dic113D411yescharacteristic
101C4⋊Dic113C2311yescharacteristic
102C22⋊Dic113—21no—
103C22⋊Dic113—21no—
104#14268624—21no—
105#14268624—21no—
106#14268624—21no—
107#14268624—21no—
108#14268624—21no—
109#14268624D411yescharacteristic
110#14268624D411yescharacteristic
111C2×D4×C113—21no—
112C2×D4×C113—21no—
113C2×D4×C113C2311yescharacteristic
114C2×D4×C113C2311yescharacteristic
115C2×D4×C113C2311yescharacteristic
116C22×C4×C113—21no—
117D8×C113—22no—
118D8×C113—22no—
119C2×C8×C113C2311yescharacteristic
120C2×C8×C113C2311yescharacteristic
121C4⋊C4×C113C2311yescharacteristic
122C22⋊C4×C113—21no—
123C42×C113C2311yescharacteristic
124C23×C113—21no—
125C23×C113—21no—
126C23×C113—21no—
127C22×D113—21no—
128C22×D113—21no—
129C22×D113—42no—
130C22×D113—42no—
131C22×D113—42no—
132C22×D113—42no—
133C22×D113—42no—
134C22×D113—42no—
135C22×D113—81no—
136C22×D113—81no—
137C22×D113—81no—
138C22×D113C2×D411yescharacteristic
139C22×D113C2×D411yescharacteristic
140D4×C113—21no—
141D4×C113—21no—
142D4×C113—21no—
143D4×C113—21no—
144D4×C113—21no—
145D4×C113—42no—
146D4×C113—81no—
147D4×C113C2×D412yescomplemented
148C2×C4×C113—21no—
149C2×C4×C113—81no—
150C2×C4×C113C2×D411yescharacteristic
151C2×C4×C113C2×D411yescharacteristic
152C2×C4×C113C2411yescharacteristic
153C22⋊D113—42no—
154C22⋊D113—42no—
155C22⋊D113—42no—
156C22⋊D113—42no—
157C22⋊D113—42no—
158C22⋊D113—42no—
159C2×Dic113—21no—
160C2×Dic113—21no—
161C2×Dic113—42no—
162C2×Dic113C2×D411yescharacteristic
163C2×Dic113C2×D411yescharacteristic
164D452—22no—
165D452—21no—
166D452—21no—
167D452—21no—
168D452—81no—
169D452C2×D412yes—
170C4×D113—21no—
171C4×D113—21no—
172C4×D113—21no—
173C4×D113—21no—
174C4×D113—42no—
175Dic226—21no—
176Dic226—21no—
177C8×C113—21no—
178C8×C113—21no—
179#11744751—21no—
180#11744751C2×D412yescomplemented
181C22×C113—22no—
182C22×C113—41no—
183C22×C113—41no—
184C22×C113—41no—
185C22×C113—41no—
186C22×C113—41no—
187C22×C113—41no—
188C22×C113—41no—
189C22×C113—41no—
190C22×C113C22×D411yescharacteristic
191C2×D113—21no—
192C2×D113—21no—
193C2×D113—21no—
194C2×D113—22no—
195C2×D113—21no—
196C2×D113—21no—
197C2×D113—41no—
198C2×D113—41no—
199C2×D113—41no—
200C2×D113—41no—
201C2×D113—41no—
202C2×D113—84no—
203C2×D113—84no—
204C2×D113—84no—
205C2×D113AGL(1,ℤ/8)12yescomplemented
206C4×C113—21no—
207C4×C113—21no—
208C4×C113—41no—
209C4×C113C22×D411yescharacteristic
210C4×C113H(5,𝔽2)11yescharacteristic
211Dic113—21no—
212Dic113—21no—
213Dic113—41no—
214Dic113—41no—
215C2×C113—42no—
216C2×C113—81no—
217C2×C113—81no—
218C2×C113D4211yescharacteristic
219C2×C113C2×AGL(1,ℤ/8)11yescharacteristic
220C2×C113#57611yescharacteristic
221D113—22no—
222D113—41no—
223D113—42no—
224D113—81no—
225#3264—1131nomaximal, Sylow
226C113#326411yescharacteristic, complemented, Sylow
227C2×AGL(1,ℤ/8)—1131no—
228C22×D8—1131no—
229#546—1131no—
230D42—1131no—
231#496—1131no—
232#469—1131no—
233#465—1131no—
234#463—1131no—
235#459D11311yescharacteristic, complemented
236#450—1131no—
237#449—1131no—
238#447—1131no—
239#447—1131no—
240#442—1131no—
241#435—1131no—
242C2×#41—1131no—
243C22×D4—1131no—
244C22×D4—1131no—
245C22×D4—1131no—
246C22×D4—2261no—
247AGL(1,ℤ/8)—2264no—
248C2×SD16—1131no—
249C2×SD16—1131no—
250C2×SD16—1131no—
251C2×D8—1131no—
252C2×D8—1131no—
253C2×D8—1131no—
254C2×D8—1131no—
255C2×D8—2264no—
256C2×D8C2×D11311yescharacteristic, complemented
257C2×D8C2×D11311yescharacteristic, complemented
258C2×M16—1131no—
259C22×C8—1131no—
260#127C2×D11311yescharacteristic, complemented
261#124—1131no—
262#123—2261no—
263C22⋊Q8—1131no—
264#121—1131no—
265#121—1131no—
266#121—1131no—
267#121—2261no—
268#121—2261no—
269#120—2261no—
270#120—2261no—
271#120—2261no—
272C4×D4—1131no—
273C4×D4—1131no—
274C4×D4C2×D11311yescharacteristic, complemented
275C2×C22⋊C4—2261no—
276#106—1131no—
277C4⋊C8C2×D11311yescharacteristic, complemented
278#103—1131no—
279#102—1131no—
280#102—1131no—
281#102—1131no—
282#102C2×D11311yescharacteristic, complemented
283#102C2×D11311yescharacteristic, complemented
284C22⋊C8—1131no—
285C22⋊C8—1131no—
286#97—1131no—
287C24—2261no—
288C24—2261no—
289C24—2261no—
290#41—4521no—
291#41—2262no—
292C2×Q8—1131no—
293C2×D4—21no—
294C2×D4—21no—
295C2×D4—1131no—
296C2×D4—1131no—
297C2×D4—1131no—
298C2×D4—4524no—
299C2×D4—4521no—
300C2×D4—4521no—
301C2×D4—4521no—
302C2×D4—2261no—
303C2×D4—2261no—
304C2×D4—2261no—
305C2×D4—2261no—
306C2×D4—2262no—
307C2×D4—2262no—
308C2×D4—2261no—
309C2×D4—2261no—
310C2×D4—2261no—
311C2×D4—2262no—
312C2×D4C22×D11311yescharacteristic
313C2×D4C22×D11311yescharacteristic
314C2×D4C22×D11311yescharacteristic
315C22×C4—21no—
316C22×C4—1131no—
317C22×C4—1131no—
318C22×C4—2261no—
319C22×C4—2261no—
320SD16—4521no—
321SD16—2262no—
322SD16—2262no—
323D8—22no—
324D8—22no—
325D8—1134no—
326D8—4521no—
327D8—2262no—
328D8—2262no—
329M16—2262no—
330C2×C8—1131no—
331C2×C8—1131no—
332C2×C8—2262no—
333C2×C8C22×D11311yescharacteristic
334C2×C8C22×D11311yescharacteristic
335C4⋊C4—1131no—
336C4⋊C4—1131no—
337C4⋊C4—2261no—
338C4⋊C4C22×D11311yescharacteristic
339C22⋊C4—21no—
340C22⋊C4—1131no—
341C22⋊C4—1131no—
342C22⋊C4—2261no—
343C22⋊C4—2261no—
344C22⋊C4—2261no—
345C22⋊C4—2261no—
346C22⋊C4—2261no—
347C22⋊C4—2261no—
348C22⋊C4—2261no—
349C42C22×D11311yescharacteristic
350C23—21no—
351C23—21no—
352C23—21no—
353C23—1131no—
354C23—1131no—
355C23—9041no—
356C23—9041no—
357C23—9041no—
358C23—4522no—
359C23—4522no—
360C23—4522no—
361C23—4522no—
362C23—4522no—
363C23—4522no—
364C23—2261no—
365C23—2261no—
366Q8—2261no—
367Q8—2261no—
368D4—21no—
369D4—21no—
370D4—21no—
371D4—21no—
372D4—21no—
373D4—42no—
374D4—81no—
375D4—1132no—
376D4—9041no—
377D4—4522no—
378D4—4522no—
379D4—4522no—
380D4—4522no—
381D4—4522no—
382D4—4522no—
383D4—2262no—
384D4—2261no—
385D4—2261no—
386D4—2261no—
387D4D4×D11312yescomplemented
388C2×C4—21no—
389C2×C4—81no—
390C2×C4—1131no—
391C2×C4—1131no—
392C2×C4—4522no—
393C2×C4—4522no—
394C2×C4—2261no—
395C2×C4—2261no—
396C2×C4—2261no—
397C2×C4—2261no—
398C2×C4—2261no—
399C2×C4—2261no—
400C2×C4D4×D11311yescharacteristic
401C2×C4D4×D11311yescharacteristic
402C2×C4C23×D11311yescharacteristic
403C8—21no—
404C8—21no—
405C8—1132no—
406C8—2261no—
407C22—22no—
408C22—41no—
409C22—41no—
410C22—41no—
411C22—41no—
412C22—41no—
413C22—41no—
414C22—41no—
415C22—41no—
416C22—1132no—
417C22—9044no—
418C22—9044no—
419C22—9044no—
420C22—4521no—
421C22—4521no—
422C22—4521no—
423C22—4521no—
424C22—4521no—
425C22—2261no—
426C22—2261no—
427C22—2261no—
428C22—2262no—
429C22—2261no—
430C22—2261no—
431C22C2×D4×D11311yescharacteristic
432C4—21no—
433C4—21no—
434C4—41no—
435C4—4521no—
436C4—4521no—
437C4—2261no—
438C4—2261no—
439C4C2×D4×D11311yescharacteristic
440C4#1681366811yescharacteristic
441C2—42no—
442C2—81no—
443C2—81no—
444C2—9041no—
445C2—4522no—
446C2—4521no—
447C2—2262no—
448C2#2029923211yescharacteristic
449C2AGL(1,ℤ/8)×D11311yescharacteristic
450C2#2029939911yescharacteristic
subgroupG/H
centerC22C2×D4×D113
commutator, cosocleC2×C4×C113C24
FrattiniC2×C4C23×D113
Fitting#459×C113C2
socleC22×C113C22×D4
hypercenter#459D113
hypocenterC113#3264
LCSG ▷ C2×C4×C113 ▷ C2×C113 ▷ C113
UCSC1 ◁ C22 ◁ C42 ◁ #459

Complements

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

NH ≅ G/Ntype
1. C2×#16813646C2semidirect
2. C2×D8×D113C2semidirect
3. #20299243C2semidirect
4. #20299233C2semidirect
5. #20298985C2semidirect
6. #20298850C2semidirect
7. #20298826C2semidirect
8. #20298814C2semidirect
9. #20298750C2semidirect
10. #20298740C2semidirect
11. #20298733C2semidirect
12. #20298730C2semidirect
13. #20298708C2semidirect
14. #20298668C2semidirect
15. #459×C113C2semidirect
16. C2×#14268646C22semidirect
19. C2×D4×D113C22semidirect
20. C2×D4×D113C22semidirect
22. C2×#14268636C22semidirect
23. C2×#14268635C22semidirect
24. C2×#14268635C22semidirect
27. C2×#14268632C22semidirect
28. C2×#14268632C22semidirect
30. C2×#14268630C22semidirect
31. C2×C8×D113C22semidirect
32. #16813610C22semidirect
34. #16813602C22semidirect
35. #16813597C22semidirect
39. #16813593C22semidirect
44. C4×D452C22semidirect
46. #16813553C22semidirect
47. #16813547C22semidirect
48. #16813544C22semidirect
49. #16813543C22semidirect
50. #16813542C22semidirect
51. #16813534C22semidirect
52. #16813534C22semidirect
53. #16813533C22semidirect
54. C2×D8×C113C22semidirect
55. C2×D8×C113C22semidirect
56. #127×C113C22semidirect
57. C4×D4×C113C22semidirect
58. C4⋊C8×C113C22semidirect
59. #102×C113C22semidirect
60. #102×C113C22semidirect
94. #14268632D4semidirect
147. D4×C113C2×D4semidirect
180. #11744751C2×D4semidirect
205. C2×D113AGL(1,ℤ/8)semidirect
226. C113#3264semidirect
235. #459D113semidirect
256. C2×D8C2×D113semidirect
257. C2×D8C2×D113semidirect
260. #127C2×D113semidirect
274. C4×D4C2×D113semidirect
277. C4⋊C8C2×D113semidirect
282. #102C2×D113semidirect
283. #102C2×D113semidirect
387. D4D4×D113semidirect

Maximal subgroups

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

subgroupindex
C2×#168136462
C2×D8×D1132
#202992432
#202992332
#202989852
#202988502
#202988262
#202988142
#202987502
#202987402
#202987332
#202987302
#202987082
#202986682
#459×C1132
#3264113