Finite Group Databasebeta

← #28402060

Subgroups — #28402060

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×#16813649C211yesmaximal, characteristic, complemented
2C2×D8×D113C211yesmaximal, characteristic, complemented
3#20299241C211yesmaximal, characteristic, complemented
4D4×D452C211yesmaximal, characteristic, complemented
5#20298988C211yesmaximal, characteristic, complemented
6#20298850C211yesmaximal, characteristic, complemented
7#20298830C211yesmaximal, characteristic, complemented
8#20298794C211yesmaximal, characteristic, complemented
9#20298747C211yesmaximal, characteristic, complemented
10#20298746C211yesmaximal, characteristic, complemented
11#20298733C211yesmaximal, characteristic, complemented
12#20298730C211yesmaximal, characteristic, complemented
13#20298708C211yesmaximal, characteristic, complemented
14#20298668C211yesmaximal, characteristic, complemented
15#463×C113C211yesmaximal, characteristic, complemented
16C2×#14268648C2211yescharacteristic, complemented
17C22×D452—21no—
18C2×D4×D113C2211yescharacteristic
19C2×D4×D113C2211yescharacteristic, complemented
20C2×D4×D113C2211yescharacteristic, complemented
21#16813649—24no—
22C2×#14268634C2211yescharacteristic, complemented
23C2×#14268634C2211yescharacteristic, complemented
24C2×D904C2211yescharacteristic, complemented
25C2×D904C2211yescharacteristic, complemented
26C2×#14268632C2211yescharacteristic
27C2×#14268632C2211yescharacteristic, complemented
28C2×#14268632C2211yescharacteristic, complemented
29D8×D113—24no—
30C2×#14268630C2211yescharacteristic, complemented
31C2×C8×D113C2211yescharacteristic, complemented
32#16813619C2211yescharacteristic, complemented
33#16813604—21no—
34#16813598C2211yescharacteristic, complemented
35#16813597C2211yescharacteristic
36#16813597C2211yescharacteristic, complemented
37#16813596—21no—
38#16813595—21no—
39#16813593C2211yescharacteristic, complemented
40#16813592—21no—
41#16813592—21no—
42#16813592—21no—
43C4×D452C2211yescharacteristic
44C4×D452C2211yescharacteristic, complemented
45C22⋊C4×D113—21no—
46#16813553C2211yescharacteristic, complemented
47#16813544C2211yescharacteristic, complemented
48#16813544C2211yescharacteristic, complemented
49#16813543C2211yescharacteristic, complemented
50#16813542C2211yescharacteristic, complemented
51#16813534C2211yescharacteristic, complemented
52#16813534C2211yescharacteristic, complemented
53#16813533C2211yescharacteristic, complemented
54C2×SD16×C113C2211yescharacteristic, complemented
55C2×D8×C113C2211yescharacteristic
56#124×C113C2211yescharacteristic, complemented
57C4×D4×C113C2211yescharacteristic, complemented
58C4⋊C8×C113C2211yescharacteristic, complemented
59#103×C113C2211yescharacteristic, complemented
60#102×C113C2211yescharacteristic, complemented
61C23×D113—21no—
62C23×D113—21no—
63C23×D113—21no—
64#14268648—22no—
65#14268648—41no—
66C2×D452—21no—
67C2×D452—21no—
68C2×D452—21no—
69C2×D452—21no—
70C2×D452—21no—
71C2×D452—44no—
72C2×D452D411yescharacteristic
73C2×D452C2311yescharacteristic
74C2×D452C2311yescharacteristic
75C2×D452C2311yescharacteristic
76C2×C22⋊D113—21no—
77C2×C22⋊D113—21no—
78C2×C22⋊D113—21no—
79C2×C22⋊D113—21no—
80D4×D113—22no—
81D4×D113—22no—
82D4×D113—22no—
83D4×D113—41no—
84D4×D113—41no—
85D4×D113—41no—
86C2×C4×D113—21no—
87C2×C4×D113—21no—
88C2×C4×D113C2311yescharacteristic
89C2×C4×D113C2311yescharacteristic
90#14268634—22no—
91#14268634—41no—
92D904—22no—
93D904—22no—
94#14268632—22no—
95#14268632—41no—
96#14268632D414yescomplemented
97#14268630—22no—
98C2×#11744751C2311yescharacteristic
99C2×#11744751C2311yescharacteristic
100C8×D113—22no—
101C4⋊Dic113D411yescharacteristic
102C4⋊Dic113C2311yescharacteristic
103#14268626—21no—
104C22⋊Dic113—21no—
105#14268624—21no—
106#14268624—21no—
107#14268624—21no—
108#14268624—21no—
109#14268624D411yescharacteristic
110#14268624D411yescharacteristic
111C2×Q8×C113C2311yescharacteristic
112C2×D4×C113C2311yescharacteristic
113C2×D4×C113C2311yescharacteristic
114C22×C4×C113—21no—
115SD16×C113—22no—
116D8×C113—22no—
117C2×C8×C113C2311yescharacteristic
118C2×C8×C113C2311yescharacteristic
119C4⋊C4×C113C2311yescharacteristic
120C22⋊C4×C113—21no—
121C22⋊C4×C113—21no—
122C22⋊C4×C113—21no—
123C42×C113C2311yescharacteristic
124C23×C113—21no—
125C23×C113—21no—
126C22×D113—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
140Q8×C113—21no—
141Q8×C113—21no—
142D4×C113—21no—
143D4×C113—21no—
144D4×C113—21no—
145D4×C113C2×D412yes—
146C2×C4×C113—21no—
147C2×C4×C113—21no—
148C2×C4×C113—42no—
149C2×C4×C113C2×D411yescharacteristic
150C2×C4×C113C2×D411yescharacteristic
151C2×C4×C113C2411yescharacteristic
152C22⋊D113—42no—
153C22⋊D113—42no—
154C22⋊D113—42no—
155C22⋊D113—81no—
156C2×Dic113—21no—
157C2×Dic113C2×D411yescharacteristic
158C2×Dic113C2×D411yescharacteristic
159D452—22no—
160D452—21no—
161D452—21no—
162D452—21no—
163D452—21no—
164D452—21no—
165D452—42no—
166D452—42no—
167D452—42no—
168D452—42no—
169D452—81no—
170D452C2×D412yescomplemented
171C4×D113—21no—
172C4×D113—21no—
173C4×D113—21no—
174C4×D113—21no—
175C4×D113—42no—
176C4×D113—81no—
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×C113C22×D411yescharacteristic
188C2×D113—21no—
189C2×D113—21no—
190C2×D113—21no—
191C2×D113—22no—
192C2×D113—21no—
193C2×D113—21no—
194C2×D113—41no—
195C2×D113—41no—
196C2×D113—41no—
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×C113—41no—
210C4×C113C22×D411yescharacteristic
211C4×C113H(5,𝔽2)11yescharacteristic
212Dic113—21no—
213Dic113—21no—
214Dic113—41no—
215C2×C113—42no—
216C2×C113—81no—
217C2×C113D4211yescharacteristic
218C2×C113C2×AGL(1,ℤ/8)11yescharacteristic
219C2×C113#57611yescharacteristic
220D113—22no—
221D113—41no—
222D113—42no—
223D113—81no—
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#463D11311yescharacteristic, complemented
235#459—1131no—
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×SD16C2×D11311yescharacteristic, complemented
251C2×D8—1131no—
252C2×D8—1131no—
253C2×D8—1131no—
254C2×D8—1131no—
255C2×D8—1131no—
256C2×D8—2264no—
257C2×D8C2×D11311yescharacteristic
258C2×M16—1131no—
259C22×C8—1131no—
260#127—1131no—
261#124C2×D11311yescharacteristic, complemented
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#103C2×D11311yescharacteristic, complemented
279#102—1131no—
280#102—1131no—
281#102—1131no—
282#102—1131no—
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×Q8C22×D11311yescharacteristic
293C2×D4—1131no—
294C2×D4—1131no—
295C2×D4—1131no—
296C2×D4—1131no—
297C2×D4—4524no—
298C2×D4—4521no—
299C2×D4—4521no—
300C2×D4—4521no—
301C2×D4—2261no—
302C2×D4—2261no—
303C2×D4—2261no—
304C2×D4—2261no—
305C2×D4—2261no—
306C2×D4—2261no—
307C2×D4—2262no—
308C2×D4—2261no—
309C2×D4—2262no—
310C2×D4—2262no—
311C2×D4—2261no—
312C2×D4—2261no—
313C2×D4C22×D11311yescharacteristic
314C2×D4C22×D11311yescharacteristic
315C22×C4—21no—
316C22×C4—1131no—
317C22×C4—1131no—
318C22×C4—2261no—
319C22×C4—2261no—
320SD16—22no—
321SD16—4521no—
322SD16—2262no—
323D8—22no—
324D8—1134no—
325D8—4521no—
326D8—2262no—
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—21no—
341C22⋊C4—21no—
342C22⋊C4—1131no—
343C22⋊C4—1131no—
344C22⋊C4—2261no—
345C22⋊C4—2261no—
346C22⋊C4—2261no—
347C22⋊C4—2261no—
348C22⋊C4—2261no—
349C42C22×D11311yescharacteristic
350C23—21no—
351C23—21no—
352C23—1131no—
353C23—1131no—
354C23—9041no—
355C23—9041no—
356C23—9041no—
357C23—4522no—
358C23—4522no—
359C23—4522no—
360C23—4522no—
361C23—4522no—
362C23—4522no—
363C23—2261no—
364C23—2261no—
365C23—2261no—
366Q8—21no—
367Q8—21no—
368D4—21no—
369D4—21no—
370D4—21no—
371D4—1132no—
372D4—9041no—
373D4—9041no—
374D4—4522no—
375D4—4522no—
376D4—4522no—
377D4—4522no—
378D4—4522no—
379D4—4522no—
380D4—4522no—
381D4—2262no—
382D4—2261no—
383D4—2261no—
384D4—2261no—
385D4—2261no—
386D4—2261no—
387D4D4×D11312yes—
388C2×C4—21no—
389C2×C4—21no—
390C2×C4—42no—
391C2×C4—1131no—
392C2×C4—1131no—
393C2×C4—9041no—
394C2×C4—4522no—
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—1132no—
414C22—9044no—
415C22—9044no—
416C22—9044no—
417C22—4521no—
418C22—4521no—
419C22—4521no—
420C22—4521no—
421C22—4521no—
422C22—4521no—
423C22—4521no—
424C22—4521no—
425C22—2261no—
426C22—2261no—
427C22—2262no—
428C22—2261no—
429C22—2261no—
430C22—2261no—
431C22C2×D4×D11311yescharacteristic
432C4—21no—
433C4—21no—
434C4—41no—
435C4—41no—
436C4—4521no—
437C4—2261no—
438C4—2261no—
439C4C2×D4×D11311yescharacteristic
440C4#1681366811yescharacteristic
441C2—42no—
442C2—81no—
443C2—9041no—
444C2—9041no—
445C2—4521no—
446C2—4522no—
447C2—2262no—
448C2#2029923211yescharacteristic
449C2AGL(1,ℤ/8)×D11311yescharacteristic
450C2#2029940011yescharacteristic
subgroupG/H
centerC22C2×D4×D113
commutator, cosocleC2×C4×C113C24
FrattiniC2×C4C23×D113
Fitting#463×C113C2
socleC22×C113C22×D4
hypercenter#463D113
hypocenterC113#3264
LCSG ▷ C2×C4×C113 ▷ C2×C113 ▷ C113
UCSC1 ◁ C22 ◁ C42 ◁ #463

Complements

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

NH ≅ G/Ntype
1. C2×#16813649C2semidirect
2. C2×D8×D113C2semidirect
3. #20299241C2semidirect
4. D4×D452C2semidirect
5. #20298988C2semidirect
6. #20298850C2semidirect
7. #20298830C2semidirect
8. #20298794C2semidirect
9. #20298747C2semidirect
10. #20298746C2semidirect
11. #20298733C2semidirect
12. #20298730C2semidirect
13. #20298708C2semidirect
14. #20298668C2semidirect
15. #463×C113C2semidirect
16. C2×#14268648C22semidirect
19. C2×D4×D113C22semidirect
20. C2×D4×D113C22semidirect
22. C2×#14268634C22semidirect
23. C2×#14268634C22semidirect
24. C2×D904C22semidirect
25. C2×D904C22semidirect
27. C2×#14268632C22semidirect
28. C2×#14268632C22semidirect
30. C2×#14268630C22semidirect
31. C2×C8×D113C22semidirect
32. #16813619C22semidirect
34. #16813598C22semidirect
36. #16813597C22semidirect
39. #16813593C22semidirect
44. C4×D452C22semidirect
46. #16813553C22semidirect
47. #16813544C22semidirect
48. #16813544C22semidirect
49. #16813543C22semidirect
50. #16813542C22semidirect
51. #16813534C22semidirect
52. #16813534C22semidirect
53. #16813533C22semidirect
54. C2×SD16×C113C22semidirect
56. #124×C113C22semidirect
57. C4×D4×C113C22semidirect
58. C4⋊C8×C113C22semidirect
59. #103×C113C22semidirect
60. #102×C113C22semidirect
96. #14268632D4semidirect
170. D452C2×D4semidirect
180. #11744751C2×D4semidirect
205. C2×D113AGL(1,ℤ/8)semidirect
226. C113#3264semidirect
234. #463D113semidirect
250. C2×SD16C2×D113semidirect
261. #124C2×D113semidirect
274. C4×D4C2×D113semidirect
277. C4⋊C8C2×D113semidirect
278. #103C2×D113semidirect
283. #102C2×D113semidirect

Maximal subgroups

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

subgroupindex
C2×#168136492
C2×D8×D1132
#202992412
D4×D4522
#202989882
#202988502
#202988302
#202987942
#202987472
#202987462
#202987332
#202987302
#202987082
#202986682
#463×C1132
#3264113