Finite Group Databasebeta

← #28405359

Subgroups — #28405359

Order 14464.

1412 conjugacy classes of subgroups.

The subgroup lattice has 504 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#20299435C211yesmaximal, characteristic, complemented
22−1+4×D113C211yesmaximal, characteristic, complemented
3#20299414C213yesmaximal, complemented
4#20299413C211yesmaximal, characteristic, complemented
5#20299411C213yesmaximal, complemented
6#20299410C211yesmaximal, characteristic, complemented
7#20299407C213yesmaximal, complemented
8#20299406C211yesmaximal, characteristic, complemented
9#20299405C213yesmaximal, complemented
10#20299397C213yesmaximal, complemented
11#20299395C213yesmaximal, complemented
12C2×#16813654C213yesmaximal, complemented
13#137×D113C213yesmaximal, complemented
14#20299363C211yesmaximal, characteristic, complemented
15#578×C113C211yesmaximal, characteristic, complemented
16#16813670—21no—
17#16813670—21no—
18#16813670C2213yescomplemented
19#16813670C2213yescomplemented
20#16813669—23no—
21#16813669C2211yescharacteristic, complemented
22#16813669C2213yescomplemented
23#16813668—23no—
24#16813668C2211yescharacteristic, complemented
25#16813668C2213yescomplemented
26C2×#14268648—21no—
27C2×#14268648C2213yes—
28#41×D113—23no—
29#41×D113—23no—
30#41×D113C2213yes—
31#41×D113C2211yescharacteristic
32#41×D113C2213yescomplemented
33C2×Q8×D113—21no—
34C2×Q8×D113C2213yescomplemented
35#16813655C2213yescomplemented
36#16813654C2216yescomplemented
37#16813654C2213yescomplemented
38#16813654C2216yescomplemented
39#16813654C2216yescomplemented
40#16813654C2213yescomplemented
41#16813653C2213yescomplemented
42#16813653C2213yescomplemented
43#16813652C2213yescomplemented
44#16813651C2213yescomplemented
45#16813651C2213yescomplemented
46#16813650C2213yescomplemented
47#16813649C2213yescomplemented
48#16813649C2213yescomplemented
49#16813647C2213yescomplemented
50#16813646C2211yescharacteristic, complemented
51#16813646C2213yescomplemented
52#16813645C2216yescomplemented
53#16813644C2213yescomplemented
54#16813643C2216yescomplemented
55#16813642C2213yescomplemented
56#16813642C2213yescomplemented
57C2×#14268637C2213yescomplemented
58Q16×D113C2216yescomplemented
59C2×#14268636C2213yescomplemented
60C2×#14268634C2213yescomplemented
61SD16×D113C2216yescomplemented
62#16813630C2213yescomplemented
63#16813629C2211yescharacteristic, complemented
64#16813628C2213yescomplemented
65C2×#14268630C2213yescomplemented
66M16×D113C2213yescomplemented
672−1+4×C113C2211yescharacteristic, complemented
682−1+4×C113C2211yescharacteristic, complemented
69#137×C113C2213yescomplemented
70#137×C113C2213yescomplemented
71#135×C113C2213yescomplemented
72C2×Q16×C113C2213yescomplemented
73#131×C113C2211yescharacteristic, complemented
74#14268648—21no—
75#14268648—23no—
76#14268648—23no—
77#14268648—23no—
78#14268648—23no—
79#14268648D411yescharacteristic
80#14268648C2316yes—
81#14268648C2313yes—
82#14268648C2313yes—
83#14268647—26no—
84#14268647—26no—
85#14268647—23no—
86#14268647—23no—
87#14268647—23no—
88#14268647—23no—
89#14268647C2313yes—
90#14268647C2313yes—
91#14268647C2313yes—
92#14268646—23no—
93#14268646—26no—
94#14268646—23no—
95#14268646—23no—
96#14268646D413yes—
97#14268646C2313yes—
98#14268646C2311yescharacteristic
99C2×Dic226—23no—
100C2×Dic226—23no—
101C2×Dic226C2313yes—
102Q8×D113—21no—
103Q8×D113—23no—
104Q8×D113—23no—
105Q8×D113—23no—
106Q8×D113—23no—
107Q8×D113D411yescharacteristic
108Q8×D113C2316yes—
109Q8×D113C2313yes—
110Q8×D113C2313yes—
111C2×D452—23no—
112C2×D452—23no—
113C2×D452C2313yes—
114D4×D113—23no—
115D4×D113—23no—
116D4×D113—23no—
117D4×D113—26no—
118D4×D113D413yes—
119D4×D113C2313yes—
120D4×D113C2311yescharacteristic
121C2×C4×D113—23no—
122C2×C4×D113—23no—
123C2×C4×D113—23no—
124C2×C4×D113—23no—
125C2×C4×D113C2313yes—
126Dic452C2313yes—
127#14268637C2313yes—
128#14268637C2316yes—
129#14268637C2313yes—
130#14268636C2316yes—
131#14268636C2313yes—
132#14268636C2311yescharacteristic
133#14268635C2313yes—
134#14268635C2311yescharacteristic
135#14268634C2316yes—
136#14268634C2313yes—
137#14268634C2313yes—
138D904C2313yes—
139#14268632C2311yescharacteristic
140#14268632C2313yes—
141#14268631C2313yes—
142#14268630C2313yes—
143#14268630C2311yescharacteristic
144#14268630C2313yes—
145#14268630C2313yes—
146C2×#11744751C2313yes—
147C8×D113C2316yes—
148#41×C113—23no—
149#41×C113—23no—
150#41×C113C2313yes—
151#41×C113C2313yes—
152#41×C113C2311yescharacteristic
153C2×Q8×C113—21no—
154C2×Q8×C113—21no—
155C2×Q8×C113C2313yes—
156C2×Q8×C113C2313yes—
157Q16×C113C2316yes—
158Q16×C113C2313yes—
159SD16×C113C2313yes—
160SD16×C113C2313yes—
161D8×C113C2311yescharacteristic
162M16×C113C2313yes—
163C2×C8×C113C2313yes—
164C22×D113—23no—
165C22×D113—21no—
166C22×D113—23no—
167C22×D113C2×D413yes—
168Q8×C113—23no—
169Q8×C113—23no—
170Q8×C113C2×D411yescharacteristic
171Q8×C113C2413yes—
172Q8×C113C2413yes—
173D4×C113—23no—
174D4×C113—23no—
175D4×C113C2×D413yes—
176D4×C113C2411yescharacteristic
177D4×C113C2411yescharacteristic
178C2×C4×C113—23no—
179C2×C4×C113—23no—
180C2×C4×C113—23no—
181C2×C4×C113—23no—
182C2×C4×C113C2413yes—
183C22⋊D113—23no—
184C22⋊D113—23no—
185C22⋊D113—21no—
186C22⋊D113—23no—
187C22⋊D113—23no—
188C22⋊D113—21no—
189C22⋊D113C2×D416yes—
190C2×Dic113—23no—
191C2×Dic113—21no—
192C2×Dic113—23no—
193C2×Dic113C2×D413yes—
194D452—23no—
195D452—26no—
196D452—23no—
197D452—23no—
198D452C2×D413yes—
199D452C2411yescharacteristic
200D452C2413yes—
201C4×D113—23no—
202C4×D113—23no—
203C4×D113—26no—
204C4×D113—23no—
205C4×D113—23no—
206C4×D113—23no—
207C4×D113—26no—
208C4×D113—23no—
209C4×D113C2×D413yes—
210C4×D113C2×D413yes—
211C4×D113C2413yes—
212C4×D113C2411yescharacteristic
213Dic226—23no—
214Dic226—26no—
215Dic226—23no—
216Dic226—23no—
217Dic226C2×D413yes—
218Dic226C2413yes—
219Dic226C2411yescharacteristic
220C8×C113C2411yescharacteristic
221C8×C113C2413yes—
222#11744751C2413yes—
223#11744751C2411yescharacteristic
224C22×C113—21no—
225C22×C113—21no—
226C22×C113C22×D413yes—
227C2×D113—21no—
228C2×D113—23no—
229C2×D113—43no—
230C2×D113—42no—
231C2×D113—83no—
232C2×D113—83no—
233C2×D113C22×D411yescharacteristic
234C2×D113C22×D413yes—
235C4×C113—23no—
236C4×C113—23no—
237C4×C113C22×D413yes—
238C4×C113C2511yescharacteristic
239Dic113—23no—
240Dic113—21no—
241Dic113C22×D413yes—
242Dic113C22×D411yescharacteristic
243C2×C113—23no—
244C2×C113—41no—
245C2×C113—41no—
246C2×C113C23×D411yescharacteristic
247D113—21no—
248D113—23no—
249D113—41no—
250D113—43no—
251#3586—1131nomaximal, Sylow
252C113#358611yescharacteristic, complemented, Sylow
253#585—1131no—
254C2×2−1+4—1131no—
255#578—1131no—
256#578—1133no—
257#578—1133no—
258#578D11311yescharacteristic, complemented
259#577—1131no—
260#577—1133no—
261#577—1133no—
262#577—1131no—
263#575—1133no—
264#575—1133no—
265C2×#137—1133no—
266C2×#137—1133no—
267#568—1131no—
2682−1+4—1133no—
2692−1+4—1131no—
2702−1+4—1133no—
2712−1+4—1133no—
2722−1+4—2261no—
2732−1+4—2261no—
2742−1+4—2263no—
2752−1+4C2×D11311yescharacteristic, complemented
2762−1+4C2×D11311yescharacteristic, complemented
277H(5,𝔽2)—1133no—
278H(5,𝔽2)—1131no—
279H(5,𝔽2)—2263no—
280C2×#41—1131no—
281C2×#41—1133no—
282C2×#41—1133no—
283C2×#41—1133no—
284C2×#41—2263no—
285C2×#41—2261no—
286C2×#41—2263no—
287C22×Q8—1133no—
288C22×Q8—2261no—
289#137—1133no—
290#137—1133no—
291#137—1133no—
292#137—1136no—
293#137—1133no—
294#137—1136no—
295#137—1136no—
296#137—1133no—
297#137—1133no—
298#137—1133no—
299#137—1133no—
300#137C2×D11313yescomplemented
301#137C2×D11313yescomplemented
302AGL(1,ℤ/8)—1133no—
303AGL(1,ℤ/8)—1133no—
304AGL(1,ℤ/8)—1133no—
305AGL(1,ℤ/8)—1131no—
306AGL(1,ℤ/8)—1133no—
307AGL(1,ℤ/8)—1133no—
308#135—1133no—
309#135—1133no—
310#135—1136no—
311#135—1136no—
312#135—1133no—
313#135C2×D11313yescomplemented
314C2×Q16—1133no—
315C2×Q16—1136no—
316C2×Q16C2×D11313yescomplemented
317C2×SD16—1133no—
318C2×SD16—1136no—
319C2×SD16—1133no—
320#131—1131no—
321#131—1133no—
322#131—1133no—
323#131C2×D11311yescharacteristic, complemented
324C2×M16—1133no—
325C2×M16—1133no—
326#41—23no—
327#41—23no—
328#41—1131no—
329#41—1133no—
330#41—1133no—
331#41—1133no—
332#41—1136no—
333#41—1133no—
334#41—1133no—
335#41—1131no—
336#41—1133no—
337#41—1133no—
338#41—2263no—
339#41—2263no—
340#41—2266no—
341#41—2266no—
342#41—2263no—
343#41—2263no—
344#41—2263no—
345#41—2263no—
346#41—2263no—
347#41—2263no—
348#41—2266no—
349#41—2263no—
350#41—2263no—
351#41—2261no—
352#41—2263no—
353#41C22×D11313yes—
354#41C22×D11313yes—
355#41C22×D11311yescharacteristic
356C2×Q8—21no—
357C2×Q8—21no—
358C2×Q8—1131no—
359C2×Q8—1136no—
360C2×Q8—1133no—
361C2×Q8—1133no—
362C2×Q8—1133no—
363C2×Q8—2263no—
364C2×Q8—2263no—
365C2×Q8—2263no—
366C2×Q8—2263no—
367C2×Q8—2263no—
368C2×Q8—2263no—
369C2×Q8—2261no—
370C2×Q8C22×D11313yes—
371C2×Q8C22×D11313yes—
372C2×D4—1133no—
373C2×D4—1133no—
374C2×D4—1131no—
375C2×D4—1133no—
376C2×D4—2263no—
377C2×D4—2263no—
378C2×D4—2266no—
379C2×D4—2263no—
380C2×D4—2263no—
381C2×D4—2263no—
382C22×C4—1133no—
383C22×C4—2263no—
384C22×C4—2263no—
385C22×C4—2263no—
386C22×C4—2263no—
387Q16—1133no—
388Q16—1136no—
389Q16—1133no—
390Q16—1133no—
391Q16C22×D11316yes—
392Q16C22×D11313yes—
393SD16—1133no—
394SD16—1136no—
395SD16—1133no—
396SD16—1133no—
397SD16—1131no—
398SD16—1136no—
399SD16—1133no—
400SD16—1131no—
401SD16C22×D11313yes—
402SD16C22×D11313yes—
403D8—1131no—
404D8—1133no—
405D8—1133no—
406D8C22×D11311yescharacteristic
407M16—1133no—
408M16—1133no—
409M16—1131no—
410M16—1133no—
411M16—1133no—
412M16C22×D11313yes—
413C2×C8—1133no—
414C2×C8—1136no—
415C2×C8C22×D11313yes—
416C23—1133no—
417C23—2263no—
418C23—2261no—
419C23—2263no—
420Q8—23no—
421Q8—23no—
422Q8—1133no—
423Q8—1133no—
424Q8—1131no—
425Q8—2263no—
426Q8—2266no—
427Q8—2263no—
428Q8—2263no—
429Q8D4×D11311yescharacteristic
430Q8C23×D11313yes—
431Q8C23×D11313yes—
432D4—23no—
433D4—23no—
434D4—1136no—
435D4—1133no—
436D4—1131no—
437D4—1133no—
438D4—2263no—
439D4—2266no—
440D4—2263no—
441D4—2263no—
442D4—2261no—
443D4—2261no—
444D4—2263no—
445D4—2263no—
446D4—2263no—
447D4—2263no—
448D4D4×D11313yes—
449D4C23×D11311yescharacteristic
450D4C23×D11311yescharacteristic
451C2×C4—23no—
452C2×C4—23no—
453C2×C4—23no—
454C2×C4—23no—
455C2×C4—1133no—
456C2×C4—1133no—
457C2×C4—1133no—
458C2×C4—1133no—
459C2×C4—1131no—
460C2×C4—2263no—
461C2×C4—2266no—
462C2×C4—2263no—
463C2×C4—2263no—
464C2×C4—2263no—
465C2×C4—2266no—
466C2×C4—2261no—
467C2×C4—2263no—
468C2×C4—2263no—
469C2×C4—2263no—
470C2×C4—2263no—
471C2×C4C23×D11313yes—
472C8—1131no—
473C8—1133no—
474C8C23×D11313yes—
475C8C23×D11311yescharacteristic
476C22—21no—
477C22—21no—
478C22—1131no—
479C22—1133no—
480C22—9043no—
481C22—9043no—
482C22—4523no—
483C22—4522no—
484C22—2261no—
485C22—2263no—
486C22C2×D4×D11313yes—
487C4—23no—
488C4—23no—
489C4—1131no—
490C4—1133no—
491C4—2261no—
492C4—2263no—
493C4C2×D4×D11313yes—
494C4C24×D11311yescharacteristic
495C2—23no—
496C2—41no—
497C2—41no—
498C2—4523no—
499C2—4521no—
500C2—2263no—
501C2—2261no—
502C2C22×D4×D11311yescharacteristic
subgroupG/H
centerC2C22×D4×D113
commutator, cosocleC4×C113C25
FrattiniC4C24×D113
Fitting#578×C113C2
socleC2×C113C23×D4
hypercenter#578D113
hypocenterC113#3586
LCSG ▷ C4×C113 ▷ C2×C113 ▷ C113
UCSC1 ◁ C2 ◁ #41 ◁ #578

Complements

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

NH ≅ G/Ntype
1. #20299435C2semidirect
2. 2−1+4×D113C2semidirect
3. #20299414C2semidirect
4. #20299413C2semidirect
5. #20299411C2semidirect
6. #20299410C2semidirect
7. #20299407C2semidirect
8. #20299406C2semidirect
9. #20299405C2semidirect
10. #20299397C2semidirect
11. #20299395C2semidirect
12. C2×#16813654C2semidirect
13. #137×D113C2semidirect
14. #20299363C2semidirect
15. #578×C113C2semidirect
18. #16813670C22semidirect
19. #16813670C22semidirect
21. #16813669C22semidirect
22. #16813669C22semidirect
24. #16813668C22semidirect
25. #16813668C22semidirect
32. #41×D113C22semidirect
34. C2×Q8×D113C22semidirect
35. #16813655C22semidirect
36. #16813654C22semidirect
37. #16813654C22semidirect
38. #16813654C22semidirect
39. #16813654C22semidirect
40. #16813654C22semidirect
41. #16813653C22semidirect
42. #16813653C22semidirect
43. #16813652C22semidirect
44. #16813651C22semidirect
45. #16813651C22semidirect
46. #16813650C22semidirect
47. #16813649C22semidirect
48. #16813649C22semidirect
49. #16813647C22semidirect
50. #16813646C22semidirect
51. #16813646C22semidirect
52. #16813645C22semidirect
53. #16813644C22semidirect
54. #16813643C22semidirect
55. #16813642C22semidirect
56. #16813642C22semidirect
57. C2×#14268637C22semidirect
58. Q16×D113C22semidirect
59. C2×#14268636C22semidirect
60. C2×#14268634C22semidirect
61. SD16×D113C22semidirect
62. #16813630C22semidirect
63. #16813629C22semidirect
64. #16813628C22semidirect
65. C2×#14268630C22semidirect
66. M16×D113C22semidirect
67. 2−1+4×C113C22semidirect
68. 2−1+4×C113C22semidirect
69. #137×C113C22semidirect
70. #137×C113C22semidirect
71. #135×C113C22semidirect
72. C2×Q16×C113C22semidirect
73. #131×C113C22semidirect
252. C113#3586semidirect
258. #578D113semidirect
275. 2−1+4C2×D113semidirect
276. 2−1+4C2×D113semidirect
300. #137C2×D113semidirect
301. #137C2×D113semidirect
313. #135C2×D113semidirect
316. C2×Q16C2×D113semidirect
323. #131C2×D113semidirect

Maximal subgroups

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

subgroupindex
#202994352
2−1+4×D1132
#202994142
#202994132
#202994112
#202994102
#202994072
#202994062
#202994052
#202993972
#202993952
C2×#168136542
#137×D1132
#202993632
#578×C1132
#3586113