Finite Group Databasebeta

← #28402059

Subgroups — #28402059

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×#16813650C211yesmaximal, characteristic, complemented
2C22×D904C211yesmaximal, characteristic, complemented
3#20299244C211yesmaximal, characteristic, complemented
4D4×D452C211yesmaximal, characteristic, complemented
5#20298987C211yesmaximal, characteristic, complemented
6#20298851C211yesmaximal, characteristic, complemented
7#20298827C211yesmaximal, characteristic, complemented
8#20298814C211yesmaximal, characteristic, complemented
9#20298794C211yesmaximal, characteristic, complemented
10#20298751C211yesmaximal, characteristic, complemented
11#20298745C211yesmaximal, characteristic, complemented
12#20298734C211yesmaximal, characteristic, complemented
13#20298734C211yesmaximal, characteristic, complemented
14#20298711C211yesmaximal, characteristic, complemented
15#435×C113C211yesmaximal, characteristic, complemented
16C2×#14268647C2211yescharacteristic, complemented
17C22×D452C2211yescharacteristic
18C22×D452C2211yescharacteristic, complemented
19C22×D452C2211yescharacteristic, complemented
20C2×D4×D113—21no—
21#16813650—24no—
22C2×#14268636C2211yescharacteristic, complemented
23C2×#14268636C2211yescharacteristic, complemented
24C2×#14268636C2211yescharacteristic, complemented
25C2×D904—24no—
26C2×D904C2211yescharacteristic
27C2×D904C2211yescharacteristic
28C2×D904C2211yescharacteristic, complemented
29C2×D904C2211yescharacteristic, complemented
30C2×D904C2211yescharacteristic, complemented
31C2×D904C2211yescharacteristic, complemented
32#16813619C2211yescharacteristic, complemented
33#16813610C2211yescharacteristic, complemented
34#16813607—21no—
35#16813601C2211yescharacteristic, complemented
36#16813597—21no—
37#16813596C2211yescharacteristic
38#16813596C2211yescharacteristic, complemented
39#16813596C2211yescharacteristic, complemented
40#16813595—21no—
41#16813592—21no—
42#16813592—21no—
43#16813590—21no—
44C4×D452C2211yescharacteristic, complemented
45C4×D452C2211yescharacteristic, complemented
46C22⋊C4×D113—21no—
47#16813554C2211yescharacteristic, complemented
48#16813547C2211yescharacteristic, complemented
49#16813544C2211yescharacteristic, complemented
50#16813544C2211yescharacteristic, complemented
51#16813544C2211yescharacteristic, complemented
52#16813544C2211yescharacteristic, complemented
53#16813544C2211yescharacteristic, complemented
54C2×M16×C113C2211yescharacteristic, complemented
55C22×C8×C113C2211yescharacteristic, complemented
56C4×D4×C113C2211yescharacteristic
57C4⋊C8×C113C2211yescharacteristic, complemented
58C22⋊C8×C113C2211yescharacteristic, complemented
59C22⋊C8×C113C2211yescharacteristic, complemented
60#97×C113C2211yescharacteristic, complemented
61C23×D113—21no—
62C23×D113—21no—
63C23×D113—21no—
64#14268647—22no—
65#14268647—41no—
66C2×Dic226C2311yescharacteristic
67C2×D452—22no—
68C2×D452—22no—
69C2×D452—22no—
70C2×D452—21no—
71C2×D452—21no—
72C2×D452—21no—
73C2×D452—21no—
74C2×D452—21no—
75C2×D452—41no—
76C2×D452—41no—
77C2×D452—41no—
78C2×D452C2311yescharacteristic
79C2×D452C2311yescharacteristic
80C2×D452C2311yescharacteristic
81C2×D452C2311yescharacteristic
82C2×D452C2311yescharacteristic
83C2×C22⋊D113—21no—
84C2×C22⋊D113—21no—
85C2×C22⋊D113—21no—
86C2×C22⋊D113—21no—
87D4×D113—44no—
88C2×C4×D113—21no—
89C2×C4×D113—21no—
90C2×C4×D113—21no—
91#14268636—22no—
92#14268636—22no—
93#14268636—41no—
94D904—22no—
95D904—22no—
96D904—22no—
97D904—22no—
98D904—41no—
99D904D414yescomplemented
100C4⋊Dic113C2311yescharacteristic
101C4⋊Dic113C2311yescharacteristic
102#14268626—21no—
103C22⋊Dic113—21no—
104#14268624—21no—
105#14268624—21no—
106#14268624—21no—
107#14268624—21no—
108#14268624—21no—
109#14268624—21no—
110#14268624—21no—
111C2×D4×C113D411yescharacteristic
112C22×C4×C113C2311yescharacteristic
113C22×C4×C113C2311yescharacteristic
114M16×C113—22no—
115C2×C8×C113—22no—
116C2×C8×C113C2311yescharacteristic
117C2×C8×C113C2311yescharacteristic
118C2×C8×C113C2311yescharacteristic
119C2×C8×C113C2311yescharacteristic
120C4⋊C4×C113D411yescharacteristic
121C22⋊C4×C113D411yescharacteristic
122C22⋊C4×C113D411yescharacteristic
123C42×C113C2311yescharacteristic
124C23×C113C2×D411yescharacteristic
125C23×C113C2×D411yescharacteristic
126C22×D113—21no—
127C22×D113—21no—
128C22×D113—21no—
129C22×D113—21no—
130C22×D113—21no—
131C22×D113—42no—
132C22×D113—42no—
133C22×D113—42no—
134C22×D113—42no—
135C22×D113—42no—
136C22×D113—42no—
137C22×D113—81no—
138C22×D113—81no—
139C22×D113—81no—
140D4×C113—22no—
141C2×C4×C113—21no—
142C2×C4×C113—21no—
143C2×C4×C113—21no—
144C2×C4×C113—21no—
145C2×C4×C113C2×D411yescharacteristic
146C2×C4×C113C2×D411yescharacteristic
147C2×C4×C113C2×D411yescharacteristic
148C2×C4×C113C2×D411yescharacteristic
149C2×C4×C113C2411yescharacteristic
150C22⋊D113—42no—
151C22⋊D113—42no—
152C22⋊D113—42no—
153C22⋊D113—81no—
154C2×Dic113—21no—
155C2×Dic113—21no—
156C2×Dic113—21no—
157D452—21no—
158D452—21no—
159D452—21no—
160D452—21no—
161D452—21no—
162D452—21no—
163D452—21no—
164D452—21no—
165D452—42no—
166D452—42no—
167D452—42no—
168D452—42no—
169D452—81no—
170D452C2×D412yes—
171D452C2×D412yescomplemented
172C4×D113—42no—
173C4×D113—42no—
174C4×D113—81no—
175Dic226—21no—
176Dic226—21no—
177C8×C113—21no—
178C8×C113—21no—
179C8×C113—21no—
180C8×C113C2×D412yescomplemented
181C22×C113—21no—
182C22×C113—21no—
183C22×C113—21no—
184C22×C113—21no—
185C22×C113—21no—
186C22×C113AGL(1,ℤ/8)12yescomplemented
187C22×C113C22×D411yescharacteristic
188C2×D113—22no—
189C2×D113—22no—
190C2×D113—41no—
191C2×D113—41no—
192C2×D113—41no—
193C2×D113—41no—
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—41no—
203C2×D113—84no—
204C2×D113—84no—
205C2×D113—84no—
206C4×C113—21no—
207C4×C113—21no—
208C4×C113—21no—
209C4×C113—21no—
210C4×C113C22×D411yescharacteristic
211C4×C113H(5,𝔽2)11yescharacteristic
212Dic113—41no—
213Dic113—41no—
214Dic113—41no—
215C2×C113—22no—
216C2×C113—41no—
217C2×C113D4211yescharacteristic
218C2×C113C2×AGL(1,ℤ/8)11yescharacteristic
219C2×C113#57611yescharacteristic
220D113—42no—
221D113—42no—
222D113—81no—
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#463—1131no—
235#459—1131no—
236#450—1131no—
237#449—1131no—
238#447—1131no—
239#447—1131no—
240#442—1131no—
241#435D11311yescharacteristic, complemented
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—1131no—
256C2×D8—1131no—
257C2×D8—2264no—
258C2×M16C2×D11311yescharacteristic, complemented
259C22×C8C2×D11311yescharacteristic, complemented
260#127—1131no—
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
275C2×C22⋊C4—2261no—
276#106—1131no—
277C4⋊C8C2×D11311yescharacteristic, complemented
278#103—1131no—
279#102—1131no—
280#102—1131no—
281#102—1131no—
282#102—1131no—
283#102—1131no—
284C22⋊C8C2×D11311yescharacteristic, complemented
285C22⋊C8C2×D11311yescharacteristic, complemented
286#97C2×D11311yescharacteristic, complemented
287C24—2261no—
288C24—2261no—
289C24—2261no—
290#41—4521no—
291#41—2262no—
292C2×Q8—1131no—
293C2×D4—1131no—
294C2×D4—1131no—
295C2×D4—1131no—
296C2×D4—1131no—
297C2×D4—1131no—
298C2×D4—4521no—
299C2×D4—4521no—
300C2×D4—4521no—
301C2×D4—4524no—
302C2×D4—2262no—
303C2×D4—2262no—
304C2×D4—2262no—
305C2×D4—2261no—
306C2×D4—2261no—
307C2×D4—2261no—
308C2×D4—2261no—
309C2×D4—2261no—
310C2×D4—2261no—
311C2×D4—2261no—
312C2×D4—2261no—
313C2×D4—2261no—
314C2×D4D45211yescharacteristic
315C22×C4—2261no—
316C22×C4—2261no—
317C22×C4—2261no—
318C22×C4C22×D11311yescharacteristic
319C22×C4C22×D11311yescharacteristic
320SD16—4521no—
321SD16—2262no—
322SD16—2262no—
323D8—1134no—
324D8—4521no—
325D8—2262no—
326D8—2262no—
327D8—2262no—
328D8—2262no—
329M16—22no—
330C2×C8—22no—
331C2×C8C22×D11311yescharacteristic
332C2×C8C22×D11311yescharacteristic
333C2×C8C22×D11311yescharacteristic
334C2×C8C22×D11311yescharacteristic
335C4⋊C4—1131no—
336C4⋊C4—1131no—
337C4⋊C4—2261no—
338C4⋊C4D45211yescharacteristic
339C22⋊C4—2261no—
340C22⋊C4—2261no—
341C22⋊C4—2261no—
342C22⋊C4—2261no—
343C22⋊C4—2261no—
344C22⋊C4—2261no—
345C22⋊C4—2261no—
346C22⋊C4—2261no—
347C22⋊C4D45211yescharacteristic
348C22⋊C4D45211yescharacteristic
349C42C22×D11311yescharacteristic
350C23—9041no—
351C23—9041no—
352C23—9041no—
353C23—4522no—
354C23—4522no—
355C23—4522no—
356C23—4522no—
357C23—4522no—
358C23—4522no—
359C23—2261no—
360C23—2261no—
361C23—2261no—
362C23—2261no—
363C23—2261no—
364C23C2×D45211yescharacteristic
365C23C2×D45211yescharacteristic
366Q8—2261no—
367Q8—2261no—
368D4—22no—
369D4—1132no—
370D4—1132no—
371D4—9041no—
372D4—9041no—
373D4—4522no—
374D4—4522no—
375D4—4522no—
376D4—4522no—
377D4—4522no—
378D4—4522no—
379D4—4522no—
380D4—2261no—
381D4—2261no—
382D4—2261no—
383D4—2261no—
384D4—2261no—
385D4—2261no—
386D4—2261no—
387D4—2261no—
388C2×C4—21no—
389C2×C4—21no—
390C2×C4—21no—
391C2×C4—21no—
392C2×C4—9041no—
393C2×C4—4522no—
394C2×C4—4522no—
395C2×C4—2261no—
396C2×C4—2261no—
397C2×C4—2261no—
398C2×C4C2×D45211yescharacteristic
399C2×C4C2×D45211yescharacteristic
400C2×C4C2×D45211yescharacteristic
401C2×C4C2×D45211yescharacteristic
402C2×C4C23×D11311yescharacteristic
403C8—21no—
404C8—21no—
405C8—21no—
406C8D4×D11312yescomplemented
407C22—21no—
408C22—21no—
409C22—21no—
410C22—21no—
411C22—21no—
412C22—9044no—
413C22—9044no—
414C22—9044no—
415C22—4521no—
416C22—4521no—
417C22—4521no—
418C22—4521no—
419C22—4521no—
420C22—4521no—
421C22—4521no—
422C22—4521no—
423C22—4521no—
424C22—4521no—
425C22—4521no—
426C22—4521no—
427C22—4521no—
428C22—2262no—
429C22—2262no—
430C22#1681365012yescomplemented
431C22C22×D45211yescharacteristic
432C4—21no—
433C4—21no—
434C4—21no—
435C4—21no—
436C4—4521no—
437C4—4521no—
438C4—4521no—
439C4C2×D4×D11311yescharacteristic
440C4#1681366811yescharacteristic
441C2—22no—
442C2—41no—
443C2—9041no—
444C2—9041no—
445C2—9041no—
446C2—4522no—
447C2—4522no—
448C2D4×D45211yescharacteristic
449C2C2×#1681365011yescharacteristic
450C2#2029940311yescharacteristic
subgroupG/H
centerC22C22×D452
commutator, cosocleC2×C4×C113C24
FrattiniC2×C4C23×D113
Fitting#435×C113C2
socleC22×C113C22×D4
hypercenter#435D113
hypocenterC113#3264
LCSG ▷ C2×C4×C113 ▷ C2×C113 ▷ C113
UCSC1 ◁ C22 ◁ C4×D4 ◁ #435

Complements

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

NH ≅ G/Ntype
1. C2×#16813650C2semidirect
2. C22×D904C2semidirect
3. #20299244C2semidirect
4. D4×D452C2semidirect
5. #20298987C2semidirect
6. #20298851C2semidirect
7. #20298827C2semidirect
8. #20298814C2semidirect
9. #20298794C2semidirect
10. #20298751C2semidirect
11. #20298745C2semidirect
12. #20298734C2semidirect
13. #20298734C2semidirect
14. #20298711C2semidirect
15. #435×C113C2semidirect
16. C2×#14268647C22semidirect
18. C22×D452C22semidirect
19. C22×D452C22semidirect
22. C2×#14268636C22semidirect
23. C2×#14268636C22semidirect
24. C2×#14268636C22semidirect
28. C2×D904C22semidirect
29. C2×D904C22semidirect
30. C2×D904C22semidirect
31. C2×D904C22semidirect
32. #16813619C22semidirect
33. #16813610C22semidirect
35. #16813601C22semidirect
38. #16813596C22semidirect
39. #16813596C22semidirect
44. C4×D452C22semidirect
45. C4×D452C22semidirect
47. #16813554C22semidirect
48. #16813547C22semidirect
49. #16813544C22semidirect
50. #16813544C22semidirect
51. #16813544C22semidirect
52. #16813544C22semidirect
53. #16813544C22semidirect
54. C2×M16×C113C22semidirect
55. C22×C8×C113C22semidirect
57. C4⋊C8×C113C22semidirect
58. C22⋊C8×C113C22semidirect
59. C22⋊C8×C113C22semidirect
60. #97×C113C22semidirect
99. D904D4semidirect
171. D452C2×D4semidirect
180. C8×C113C2×D4semidirect
186. C22×C113AGL(1,ℤ/8)semidirect
226. C113#3264semidirect
241. #435D113semidirect
258. C2×M16C2×D113semidirect
259. C22×C8C2×D113semidirect
277. C4⋊C8C2×D113semidirect
284. C22⋊C8C2×D113semidirect
285. C22⋊C8C2×D113semidirect
286. #97C2×D113semidirect
406. C8D4×D113semidirect
430. C22#16813650semidirect

Maximal subgroups

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

subgroupindex
C2×#168136502
C22×D9042
#202992442
D4×D4522
#202989872
#202988512
#202988272
#202988142
#202987942
#202987512
#202987452
#202987342
#202987112
#435×C1132
#3264113