Finite Group Databasebeta

← #28399823

Subgroups — #28399823

Order 14464.

806 conjugacy classes of subgroups.

The subgroup lattice has 496 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#41×D113C211yesmaximal, characteristic, complemented
2C2×#16813649C211yesmaximal, characteristic, complemented
3C2×#16813646C211yesmaximal, characteristic, complemented
4#121×D113C211yesmaximal, characteristic, complemented
5#20298745C211yesmaximal, characteristic, complemented
6#20298743C211yesmaximal, characteristic, complemented
7#20298741C211yesmaximal, characteristic, complemented
8#20298738C211yesmaximal, characteristic, complemented
9#20298735C211yesmaximal, characteristic, complemented
10#20298733C211yesmaximal, characteristic, complemented
11#20298730C211yesmaximal, characteristic, complemented
12#20298598C211yesmaximal, characteristic, complemented
13#20298596C211yesmaximal, characteristic, complemented
14#20298560C211yesmaximal, characteristic, complemented
15#449×C113C211yesmaximal, characteristic, complemented
16C2×#14268648C2211yescharacteristic
17C2×#14268647—21no—
18C2×#14268647C2211yescharacteristic, complemented
19C2×#14268646—21no—
20C2×#14268646C2211yescharacteristic
21#41×D113—24no—
22#41×D113—24no—
23C2×Q8×D113C2211yescharacteristic, complemented
24C2×D4×D113—21no—
25C2×D4×D113—21no—
26C2×D4×D113C2211yescharacteristic, complemented
27C2×D4×D113C2211yescharacteristic, complemented
28C22×C4×D113—21no—
29C22×C4×D113C2211yescharacteristic
30#16813649—24no—
31#16813646—24no—
32C2×#14268636C2211yescharacteristic, complemented
33C2×#14268635C2211yescharacteristic, complemented
34C2×#14268634C2211yescharacteristic, complemented
35C2×D904C2211yescharacteristic, complemented
36C2×#14268632C2211yescharacteristic, complemented
37C2×#14268632C2211yescharacteristic, complemented
38C2×#14268630C2211yescharacteristic, complemented
39C2×#14268630C2211yescharacteristic, complemented
40#16813597C2211yescharacteristic
41#16813596C2211yescharacteristic, complemented
42#16813595—21no—
43#16813594—21no—
44#16813593C2211yescharacteristic
45C4⋊C4×D113C2211yescharacteristic, complemented
46C22⋊C4×D113—21no—
47#16813547C2211yescharacteristic, complemented
48#16813546C2211yescharacteristic, complemented
49#16813545C2211yescharacteristic, complemented
50#16813544C2211yescharacteristic, complemented
51#16813543C2211yescharacteristic, complemented
52#16813542C2211yescharacteristic, complemented
53C22⋊#11744751C2211yescharacteristic, complemented
54#16813534C2211yescharacteristic, complemented
55#16813534C2211yescharacteristic, complemented
56C2×#41×C113C2211yescharacteristic, complemented
57C2×SD16×C113C2211yescharacteristic, complemented
58C2×D8×C113C2211yescharacteristic, complemented
59#121×C113C2211yescharacteristic, complemented
60#103×C113C2211yescharacteristic, complemented
61#102×C113C2211yescharacteristic, complemented
62C22⋊C8×C113C2211yescharacteristic, complemented
63C23×D113—21no—
64C23×D113—21no—
65C23×D113D411yescharacteristic
66#14268648—22no—
67#14268648D414yescomplemented
68#14268647—28no—
69#14268647—22no—
70#14268647—22no—
71#14268646—28no—
72#14268646—22no—
73#14268646D414yescomplemented
74C2×Dic226—21no—
75C2×Dic226C2311yescharacteristic
76Q8×D113—22no—
77Q8×D113—22no—
78C2×D452—21no—
79C2×D452—21no—
80C2×D452C2311yescharacteristic
81C2×D452C2311yescharacteristic
82C2×C22⋊D113—21no—
83C2×C22⋊D113—21no—
84C2×C22⋊D113—21no—
85C2×C22⋊D113—21no—
86C2×C22⋊D113—21no—
87C2×C22⋊D113—21no—
88D4×D113—28no—
89D4×D113—22no—
90D4×D113—22no—
91D4×D113—22no—
92D4×D113—22no—
93D4×D113—44no—
94C22×Dic113—21no—
95C22×Dic113D411yescharacteristic
96C2×C4×D113—28no—
97C2×C4×D113—21no—
98C2×C4×D113—21no—
99C2×C4×D113—21no—
100C2×C4×D113—22no—
101C2×C4×D113—22no—
102C2×C4×D113—21no—
103C2×C4×D113D411yescharacteristic
104C2×C4×D113D411yescharacteristic
105C2×C4×D113C2311yescharacteristic
106C2×C4×D113C2311yescharacteristic
107#14268636—22no—
108#14268635—22no—
109#14268634—22no—
110D904—22no—
111#14268632—22no—
112#14268632—22no—
113#14268630—22no—
114#14268630—22no—
115C2×#11744751C2311yescharacteristic
116C2×#11744751C2311yescharacteristic
117C4⋊Dic113C2311yescharacteristic
118#14268626—21no—
119C22⋊Dic113—21no—
120#14268624—21no—
121#14268624—21no—
122#41×C113—22no—
123#41×C113—22no—
124C2×Q8×C113C2311yescharacteristic
125C2×D4×C113—21no—
126C2×D4×C113—21no—
127C2×D4×C113C2311yescharacteristic
128C2×D4×C113C2311yescharacteristic
129C22×C4×C113—21no—
130C22×C4×C113C2311yescharacteristic
131SD16×C113—22no—
132D8×C113—22no—
133C2×C8×C113C2311yescharacteristic
134C2×C8×C113C2311yescharacteristic
135C4⋊C4×C113C2311yescharacteristic
136C22⋊C4×C113—21no—
137C23×C113—21no—
138C23×C113—21no—
139C23×C113C2×D411yescharacteristic
140C22×D113—24no—
141C22×D113—21no—
142C22×D113—22no—
143C22×D113—22no—
144C22×D113—21no—
145C22×D113—41no—
146C22×D113—42no—
147C22×D113—42no—
148C22×D113—42no—
149C22×D113—42no—
150C22×D113—42no—
151C22×D113C2×D411yescharacteristic
152C22×D113C2×D411yescharacteristic
153Q8×C113—21no—
154Q8×C113C2×D412yescomplemented
155D4×C113—24no—
156D4×C113—21no—
157D4×C113—21no—
158D4×C113—21no—
159D4×C113—42no—
160D4×C113C2×D412yescomplemented
161C2×C4×C113—24no—
162C2×C4×C113—21no—
163C2×C4×C113—21no—
164C2×C4×C113—21no—
165C2×C4×C113—21no—
166C2×C4×C113C2×D411yescharacteristic
167C2×C4×C113C2411yescharacteristic
168C22⋊D113—24no—
169C22⋊D113—24no—
170C22⋊D113—24no—
171C22⋊D113—42no—
172C22⋊D113—42no—
173C22⋊D113—42no—
174C2×Dic113—21no—
175C2×Dic113—24no—
176C2×Dic113—22no—
177C2×Dic113—21no—
178C2×Dic113C2×D411yescharacteristic
179C2×Dic113C2×D411yescharacteristic
180D452—24no—
181D452—21no—
182D452—21no—
183D452—21no—
184D452—42no—
185D452C2×D412yescomplemented
186C4×D113—24no—
187C4×D113—24no—
188C4×D113—22no—
189C4×D113—21no—
190C4×D113—21no—
191C4×D113—22no—
192C4×D113—24no—
193C4×D113—42no—
194C4×D113C2×D412yes—
195C4×D113C2×D412yes—
196Dic226—24no—
197Dic226—21no—
198Dic226C2×D412yescomplemented
199C8×C113—21no—
200C8×C113—21no—
201#11744751—21no—
202#11744751—21no—
203C22×C113—21no—
204C22×C113—22no—
205C22×C113—21no—
206C22×C113—21no—
207C22×C113—41no—
208C22×C113—41no—
209C22×C113—41no—
210C22×C113—41no—
211C22×C113—41no—
212C22×C113C22×D411yescharacteristic
213C2×D113—21no—
214C2×D113—21no—
215C2×D113—21no—
216C2×D113—21no—
217C2×D113—22no—
218C2×D113—44no—
219C2×D113—48no—
220C2×D113—41no—
221C2×D113—41no—
222C2×D113—41no—
223C2×D113—41no—
224C2×D113—41no—
225C2×D113—84no—
226C2×D113#12012yes—
227C2×D113AGL(1,ℤ/8)12yescomplemented
228C4×C113—22no—
229C4×C113—21no—
230C4×C113—41no—
231C4×C113C22×D411yescharacteristic
232C4×C113C22×D411yescharacteristic
233Dic113—21no—
234Dic113—22no—
235Dic113—41no—
236Dic113#12012yes—
237C2×C113—41no—
238C2×C113—42no—
239C2×C113—81no—
240C2×C113C2×#12011yescharacteristic
241C2×C113C2×AGL(1,ℤ/8)11yescharacteristic
242C2×C113#57511yescharacteristic
243D113—22no—
244D113—22no—
245D113—42no—
246D113—81no—
247#3006—1131nomaximal, Sylow
248C113#300611yescharacteristic, complemented, Sylow
249C22×#41—1131no—
250C2×AGL(1,ℤ/8)—1131no—
251C2×AGL(1,ℤ/8)—1131no—
252C2×#121—1131no—
253#449—1131no—
254#449—1131no—
255#449—1131no—
256#449D11311yescharacteristic, complemented
257#448—1131no—
258#448—1131no—
259#447—1131no—
260#447—1131no—
261#417—1131no—
262#417—1131no—
263#407—1131no—
264C2×#41—1131no—
265C2×#41—1131no—
266C2×#41—1131no—
267C2×#41—2261no—
268C2×#41—2261no—
269C2×#41—2264no—
270C2×#41—2264no—
271C2×#41C2×D11311yescharacteristic, complemented
272C22×Q8—1131no—
273C22×D4—1131no—
274C22×D4—1131no—
275C22×D4—2261no—
276C22×D4—2261no—
277C23×C4—1131no—
278C23×C4—2261no—
279AGL(1,ℤ/8)—2264no—
280AGL(1,ℤ/8)—2264no—
281C2×SD16—1131no—
282C2×SD16—1131no—
283C2×SD16—1131no—
284C2×SD16C2×D11311yescharacteristic, complemented
285C2×D8—1131no—
286C2×D8—1131no—
287C2×D8—1131no—
288C2×D8C2×D11311yescharacteristic, complemented
289C2×M16—1131no—
290C2×M16—1131no—
291#121—1131no—
292#121—1131no—
293#121—1131no—
294#121—2261no—
295#121—2261no—
296#121C2×D11311yescharacteristic, complemented
297C2×C4⋊C4—1131no—
298C2×C22⋊C4—2261no—
299#103—1131no—
300#103—1131no—
301#103—1131no—
302#103C2×D11311yescharacteristic, complemented
303#102—1131no—
304#102—1131no—
305#102—1131no—
306#102C2×D11311yescharacteristic, complemented
307C22⋊C8—1131no—
308C22⋊C8—1131no—
309C22⋊C8—1131no—
310C22⋊C8C2×D11311yescharacteristic, complemented
311C24—1131no—
312C24—2261no—
313C24—2261no—
314#41—22no—
315#41—22no—
316#41—1134no—
317#41—1134no—
318#41—2262no—
319#41—2262no—
320#41—2268no—
321#41—2262no—
322#41—2262no—
323#41—2268no—
324C2×Q8—1131no—
325C2×Q8—2261no—
326C2×Q8—2262no—
327C2×Q8—2262no—
328C2×Q8C22×D11311yescharacteristic
329C2×D4—21no—
330C2×D4—21no—
331C2×D4—1131no—
332C2×D4—1131no—
333C2×D4—4524no—
334C2×D4—2261no—
335C2×D4—2261no—
336C2×D4—2262no—
337C2×D4—2262no—
338C2×D4—2261no—
339C2×D4—2261no—
340C2×D4—2262no—
341C2×D4—2268no—
342C2×D4—2261no—
343C2×D4—2261no—
344C2×D4—2261no—
345C2×D4—2261no—
346C2×D4—2262no—
347C2×D4C22×D11311yescharacteristic
348C2×D4C22×D11311yescharacteristic
349C22×C4—21no—
350C22×C4—1131no—
351C22×C4—1131no—
352C22×C4—1131no—
353C22×C4—1131no—
354C22×C4—1131no—
355C22×C4—2262no—
356C22×C4—2262no—
357C22×C4—2261no—
358C22×C4—2261no—
359C22×C4—2261no—
360C22×C4—2268no—
361C22×C4—2261no—
362C22×C4—2261no—
363C22×C4C22×D11311yescharacteristic
364SD16—22no—
365SD16—2262no—
366SD16—2262no—
367SD16—2262no—
368D8—22no—
369D8—2262no—
370D8—2262no—
371D8—2262no—
372M16—2262no—
373M16—2262no—
374C2×C8—1131no—
375C2×C8—1131no—
376C2×C8C22×D11311yescharacteristic
377C2×C8C22×D11311yescharacteristic
378C4⋊C4—1131no—
379C4⋊C4—2261no—
380C4⋊C4C22×D11311yescharacteristic
381C22⋊C4—21no—
382C22⋊C4—2261no—
383C22⋊C4—2261no—
384C22⋊C4—2261no—
385C23—21no—
386C23—21no—
387C23—1131no—
388C23—1131no—
389C23—4521no—
390C23—4522no—
391C23—4522no—
392C23—4522no—
393C23—4522no—
394C23—4522no—
395C23—2262no—
396C23—2262no—
397C23—2264no—
398C23—2261no—
399C23—2261no—
400C23D4×D11311yescharacteristic
401Q8—21no—
402Q8—1132no—
403Q8—2264no—
404Q8—2261no—
405Q8D4×D11312yescomplemented
406D4—24no—
407D4—21no—
408D4—21no—
409D4—21no—
410D4—42no—
411D4—1132no—
412D4—4522no—
413D4—4522no—
414D4—4522no—
415D4—4522no—
416D4—2264no—
417D4—2264no—
418D4—2264no—
419D4—2264no—
420D4—2261no—
421D4—2261no—
422D4—2261no—
423D4D4×D11312yescomplemented
424C2×C4—24no—
425C2×C4—21no—
426C2×C4—21no—
427C2×C4—21no—
428C2×C4—21no—
429C2×C4—1131no—
430C2×C4—1132no—
431C2×C4—1132no—
432C2×C4—1131no—
433C2×C4—4522no—
434C2×C4—2262no—
435C2×C4—2264no—
436C2×C4—2262no—
437C2×C4—2264no—
438C2×C4—2264no—
439C2×C4—2262no—
440C2×C4—2264no—
441C2×C4—2261no—
442C2×C4—2261no—
443C2×C4—2261no—
444C2×C4—2261no—
445C2×C4D4×D11311yescharacteristic
446C2×C4C23×D11311yescharacteristic
447C8—21no—
448C8—21no—
449C8—2261no—
450C8—2261no—
451C22—21no—
452C22—22no—
453C22—21no—
454C22—21no—
455C22—41no—
456C22—41no—
457C22—41no—
458C22—41no—
459C22—41no—
460C22—1132no—
461C22—1132no—
462C22—9044no—
463C22—4528no—
464C22—4524no—
465C22—4521no—
466C22—4521no—
467C22—4521no—
468C22—4521no—
469C22—4521no—
470C22—2262no—
471C22—2261no—
472C22—2261no—
473C22—2261no—
474C22—2261no—
475C22C2×D4×D11311yescharacteristic
476C4—21no—
477C4—22no—
478C4—41no—
479C4—1132no—
480C4—4521no—
481C4—2261no—
482C4—2262no—
483C4C2×D4×D11311yescharacteristic
484C4C2×D4×D11311yescharacteristic
485C2—41no—
486C2—42no—
487C2—81no—
488C2—9041no—
489C2—4522no—
490C2—2262no—
491C2—2262no—
492C2#120×D11311yescharacteristic
493C2AGL(1,ℤ/8)×D11311yescharacteristic
494C2#2029939511yescharacteristic
subgroupG/H
centerC22C2×D4×D113
commutator, cosocleC2×C4×C113C24
FrattiniC2×C4C23×D113
Fitting#449×C113C2
socleC22×C113C22×D4
hypercenter#449D113
hypocenterC113#3006
LCSG ▷ C2×C4×C113 ▷ C2×C113 ▷ C113
UCSC1 ◁ C22 ◁ C22×C4 ◁ #449

Complements

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

NH ≅ G/Ntype
1. C2×#41×D113C2semidirect
2. C2×#16813649C2semidirect
3. C2×#16813646C2semidirect
4. #121×D113C2semidirect
5. #20298745C2semidirect
6. #20298743C2semidirect
7. #20298741C2semidirect
8. #20298738C2semidirect
9. #20298735C2semidirect
10. #20298733C2semidirect
11. #20298730C2semidirect
12. #20298598C2semidirect
13. #20298596C2semidirect
14. #20298560C2semidirect
15. #449×C113C2semidirect
18. C2×#14268647C22semidirect
23. C2×Q8×D113C22semidirect
26. C2×D4×D113C22semidirect
27. C2×D4×D113C22semidirect
32. C2×#14268636C22semidirect
33. C2×#14268635C22semidirect
34. C2×#14268634C22semidirect
35. C2×D904C22semidirect
36. C2×#14268632C22semidirect
37. C2×#14268632C22semidirect
38. C2×#14268630C22semidirect
39. C2×#14268630C22semidirect
41. #16813596C22semidirect
45. C4⋊C4×D113C22semidirect
47. #16813547C22semidirect
48. #16813546C22semidirect
49. #16813545C22semidirect
50. #16813544C22semidirect
51. #16813543C22semidirect
52. #16813542C22semidirect
53. C22⋊#11744751C22semidirect
54. #16813534C22semidirect
55. #16813534C22semidirect
56. C2×#41×C113C22semidirect
57. C2×SD16×C113C22semidirect
58. C2×D8×C113C22semidirect
59. #121×C113C22semidirect
60. #103×C113C22semidirect
61. #102×C113C22semidirect
62. C22⋊C8×C113C22semidirect
67. #14268648D4semidirect
73. #14268646D4semidirect
154. Q8×C113C2×D4semidirect
160. D4×C113C2×D4semidirect
185. D452C2×D4semidirect
198. Dic226C2×D4semidirect
227. C2×D113AGL(1,ℤ/8)semidirect
248. C113#3006semidirect
256. #449D113semidirect
271. C2×#41C2×D113semidirect
284. C2×SD16C2×D113semidirect
288. C2×D8C2×D113semidirect
296. #121C2×D113semidirect
302. #103C2×D113semidirect
306. #102C2×D113semidirect
310. C22⋊C8C2×D113semidirect
405. Q8D4×D113semidirect
423. D4D4×D113semidirect

Maximal subgroups

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

subgroupindex
C2×#41×D1132
C2×#168136492
C2×#168136462
#121×D1132
#202987452
#202987432
#202987412
#202987382
#202987352
#202987332
#202987302
#202985982
#202985962
#202985602
#449×C1132
#3006113