Finite Group Databasebeta

← #21460591

Subgroups — #21460591

Order 7808.

1424 conjugacy classes of subgroups.

The subgroup lattice has 506 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#16840599C211yesmaximal, characteristic, complemented
2#16840597C211yesmaximal, characteristic, complemented
3#16840578C213yesmaximal, complemented
4#16840577C211yesmaximal, characteristic, complemented
5#16840574C211yesmaximal, characteristic, complemented
6#16840569C213yesmaximal, complemented
7#16840568C213yesmaximal, complemented
8#16840566C213yesmaximal, complemented
9#16840565C211yesmaximal, characteristic, complemented
10#16840561C213yesmaximal, complemented
11#16840558C213yesmaximal, complemented
12C2×#14519798C213yesmaximal, complemented
13#135×D61C213yesmaximal, complemented
14#131×D61C211yesmaximal, characteristic, complemented
15C61×#577C211yesmaximal, characteristic, complemented
16#14519825—21no—
17#14519825C2213yescomplemented
18#14519824—21no—
19#14519824C2213yescomplemented
20#14519824C2211yescharacteristic, complemented
21#14519823—23no—
22#14519823C2213yescomplemented
23#14519823C2211yescharacteristic, complemented
24#14519822—23no—
25#14519822C2213yescomplemented
26C2×#11758226—21no—
27C2×#11758226C2213yescomplemented
28C2×#11758224—23no—
29C2×#11758224C2213yescomplemented
30#41×D61—21no—
31#41×D61—23no—
32#41×D61C2211yescharacteristic
33#41×D61C2213yescomplemented
34#41×D61C2213yescomplemented
35#14519810C2213yescomplemented
36#14519809C2216yescomplemented
37#14519808C2213yescomplemented
38#14519807C2213yescomplemented
39#14519806C2216yescomplemented
40#14519805C2213yescomplemented
41#14519804C2216yescomplemented
42#14519803C2213yescomplemented
43#14519802C2213yescomplemented
44#14519801C2216yescomplemented
45#14519800C2213yescomplemented
46#14519799C2213yescomplemented
47#14519798C2211yescharacteristic, complemented
48#14519798C2213yescomplemented
49#14519798C2216yescomplemented
50#14519798C2216yescomplemented
51#14519798C2216yescomplemented
52#14519797C2213yescomplemented
53#14519797C2213yescomplemented
54#14519796C2213yescomplemented
55C2×#11758202C2213yescomplemented
56Q16×D61C2213yescomplemented
57C2×#11758190C2213yescomplemented
58SD16×D61C2213yescomplemented
59SD16×D61C2213yescomplemented
60C2×#11758199C2213yescomplemented
61D8×D61C2213yescomplemented
62#14519785C2213yescomplemented
63#14519784C2211yescharacteristic, complemented
64#14519783C2213yescomplemented
65M16×D61C2213yescomplemented
66C2×C8×D61C2213yescomplemented
672−1+4×C61C2211yescharacteristic, complemented
68H(5,𝔽2)×C61C2211yescharacteristic, complemented
69#137×C61C2213yescomplemented
70AGL(1,ℤ/8)×C61C2213yescomplemented
71#135×C61C2213yescomplemented
72C2×SD16×C61C2213yescomplemented
73#131×C61C2211yescharacteristic, complemented
74#41×C61—21no—
75#41×C61—23no—
76#41×C61C2313yes—
77#41×C61C2313yes—
78#41×C61C2311yescharacteristic
79C2×Q8×C61—21no—
80C2×Q8×C61C2313yes—
81C2×D4×C61—23no—
82C2×D4×C61C2313yes—
83C2×C22⋊D61—23no—
84C2×C22⋊D61—26no—
85C22×Dic61—23no—
86#11758226—21no—
87#11758226—23no—
88#11758226—23no—
89#11758226—23no—
90#11758226D411yescharacteristic
91#11758226C2316yes—
92#11758226C2311yescharacteristic
93#11758226C2313yes—
94Q8×D61—21no—
95Q8×D61—23no—
96Q8×D61D411yescharacteristic
97Q8×D61C2313yes—
98Q8×D61C2313yes—
99#11758224—23no—
100#11758224—26no—
101#11758224—23no—
102#11758224—23no—
103#11758224—23no—
104#11758224—23no—
105#11758224—23no—
106#11758224D413yes—
107#11758224C2311yescharacteristic
108#11758224C2313yes—
109#11758224C2316yes—
110D4×D61—23no—
111D4×D61—23no—
112D4×D61—23no—
113D4×D61—26no—
114D4×D61—23no—
115D4×D61D413yes—
116D4×D61C2313yes—
117D4×D61C2313yes—
118#11758222—26no—
119#11758222—23no—
120#11758222—23no—
121#11758222—23no—
122#11758222—23no—
123#11758222C2313yes—
124#11758222C2313yes—
125#11758222C2313yes—
126C2×D244—23no—
127C2×D244—23no—
128C2×D244C2313yes—
129C2×C4×D61—23no—
130C2×C4×D61—23no—
131C2×C4×D61—23no—
132C2×C4×D61C2313yes—
133C2×Dic122—23no—
134C2×Dic122C2313yes—
135Q16×C61C2313yes—
136SD16×C61C2313yes—
137SD16×C61C2316yes—
138SD16×C61C2311yescharacteristic
139D8×C61C2313yes—
140M16×C61C2313yes—
141C2×C8×C61C2313yes—
142#11758202C2316yes—
143#11758202C2311yescharacteristic
144#11758202C2313yes—
145#11758201C2313yes—
146#11758201C2313yes—
147#11758200C2313yes—
148#11758200C2313yes—
149#11758199C2311yescharacteristic
150#11758199C2313yes—
151#11758199C2316yes—
152#11758194C2313yes—
153C2×#92418C2313yes—
154Dic244C2313yes—
155D488C2313yes—
156#11758190C2316yes—
157#11758190C2311yescharacteristic
158#11758190C2313yes—
159#11758189C2316yes—
160C8×D61C2311yescharacteristic
161C8×D61C2313yes—
162C8×D61C2313yes—
163C8×D61C2313yes—
164C23×C61—23no—
165C22×D61—23no—
166C22×D61—23no—
167C22×D61—23no—
168C22×D61C2×D413yes—
169Q8×C61—23no—
170Q8×C61C2×D411yescharacteristic
171Q8×C61C2411yescharacteristic
172Q8×C61C2413yes—
173D4×C61—23no—
174D4×C61—23no—
175D4×C61—23no—
176D4×C61C2×D413yes—
177D4×C61C2413yes—
178D4×C61C2411yescharacteristic
179C2×C4×C61—23no—
180C2×C4×C61—23no—
181C2×C4×C61—23no—
182C2×C4×C61C2413yes—
183C22⋊D61—23no—
184C22⋊D61—23no—
185C22⋊D61—21no—
186C22⋊D61—26no—
187C22⋊D61—23no—
188C22⋊D61—23no—
189C22⋊D61—23no—
190C22⋊D61C2×D416yes—
191C2×Dic61—23no—
192C2×Dic61—26no—
193C2×Dic61—21no—
194C2×Dic61—23no—
195C2×Dic61C2×D413yes—
196D244—26no—
197D244—23no—
198D244—21no—
199D244—23no—
200D244C2×D413yes—
201D244C2413yes—
202D244C2411yescharacteristic
203C4×D61—23no—
204C4×D61—23no—
205C4×D61—23no—
206C4×D61—23no—
207C4×D61—21no—
208C4×D61—23no—
209C4×D61—26no—
210C4×D61C2×D413yes—
211C4×D61C2×D413yes—
212C4×D61C2411yescharacteristic
213C4×D61C2413yes—
214Dic122—23no—
215Dic122—23no—
216Dic122—23no—
217Dic122C2×D413yes—
218Dic122C2413yes—
219Dic122C2411yescharacteristic
220C8×C61C2411yescharacteristic
221C8×C61C2413yes—
222#92418C2411yescharacteristic
223#92418C2413yes—
224C22×C61—23no—
225C22×C61—21no—
226C22×C61—83no—
227C22×C61C22×D413yes—
228C2×D61—23no—
229C2×D61—21no—
230C2×D61—43no—
231C2×D61—83no—
232C2×D61—83no—
233C2×D61—83no—
234C2×D61C22×D413yes—
235C2×D61C22×D411yescharacteristic
236C4×C61—21no—
237C4×C61—23no—
238C4×C61C22×D413yes—
239C4×C61C2511yescharacteristic
240Dic61—21no—
241Dic61—23no—
242Dic61C22×D413yes—
243Dic61C22×D411yescharacteristic
244#3584—611nomaximal, Sylow
245C2×C61—23no—
246C2×C61—41no—
247C2×C61—43no—
248C2×C61C23×D411yescharacteristic
249D61—21no—
250D61—23no—
251D61—43no—
252D61—41no—
253#585—611no—
254#585—611no—
255#578—611no—
256#578—613no—
257#577—613no—
258#577—613no—
259#577—611no—
260#577D6111yescharacteristic, complemented
261#576—611no—
262#576—613no—
263#575—613no—
264#575—613no—
265C2×#135—613no—
266C2×#135—613no—
267C2×#131—611no—
268C61#358411yescharacteristic, complemented, Sylow
2692−1+4—613no—
2702−1+4—611no—
2712−1+4—613no—
2722−1+4—1221no—
2732−1+4—1221no—
2742−1+4C2×D6111yescharacteristic, complemented
275H(5,𝔽2)—613no—
276H(5,𝔽2)—611no—
277H(5,𝔽2)—613no—
278H(5,𝔽2)—1223no—
279H(5,𝔽2)—1223no—
280H(5,𝔽2)C2×D6111yescharacteristic, complemented
281C2×#41—611no—
282C2×#41—613no—
283C2×#41—613no—
284C2×#41—613no—
285C2×#41—613no—
286C2×#41—1223no—
287C2×#41—1221no—
288C2×#41—1221no—
289C2×#41—1223no—
290#137—613no—
291#137—613no—
292#137—616no—
293#137—616no—
294#137—613no—
295#137C2×D6113yescomplemented
296AGL(1,ℤ/8)—613no—
297AGL(1,ℤ/8)—613no—
298AGL(1,ℤ/8)—616no—
299AGL(1,ℤ/8)—616no—
300AGL(1,ℤ/8)—613no—
301AGL(1,ℤ/8)C2×D6113yescomplemented
302#135—613no—
303#135—613no—
304#135—613no—
305#135—611no—
306#135—613no—
307#135—616no—
308#135—616no—
309#135—616no—
310#135—613no—
311#135—613no—
312#135C2×D6113yescomplemented
313C2×Q16—613no—
314C2×Q16—613no—
315C2×SD16—613no—
316C2×SD16—613no—
317C2×SD16—613no—
318C2×SD16C2×D6113yescomplemented
319C2×D8—613no—
320C2×D8—613no—
321#131—611no—
322#131—613no—
323#131—613no—
324#131C2×D6111yescharacteristic, complemented
325C2×M16—613no—
326C22×C8—613no—
327#41—21no—
328#41—23no—
329#41—611no—
330#41—613no—
331#41—613no—
332#41—611no—
333#41—613no—
334#41—616no—
335#41—613no—
336#41—611no—
337#41—616no—
338#41—613no—
339#41—613no—
340#41—1223no—
341#41—1223no—
342#41—1226no—
343#41—1223no—
344#41—1223no—
345#41—1223no—
346#41—1223no—
347#41—1223no—
348#41—1223no—
349#41—1223no—
350#41—1223no—
351#41—1226no—
352#41—1223no—
353#41—1223no—
354#41—1221no—
355#41—1223no—
356#41C22×D6113yes—
357#41C22×D6113yes—
358#41C22×D6111yescharacteristic
359C2×Q8—21no—
360C2×Q8—611no—
361C2×Q8—613no—
362C2×Q8—613no—
363C2×Q8—613no—
364C2×Q8—1223no—
365C2×Q8—1223no—
366C2×Q8—1221no—
367C2×Q8C22×D6113yes—
368C2×D4—23no—
369C2×D4—613no—
370C2×D4—613no—
371C2×D4—613no—
372C2×D4—613no—
373C2×D4—1223no—
374C2×D4—1223no—
375C2×D4—1226no—
376C2×D4—1223no—
377C2×D4—1223no—
378C2×D4—1223no—
379C2×D4—1226no—
380C2×D4—1223no—
381C2×D4—1223no—
382C2×D4C22×D6113yes—
383C22×C4—613no—
384C22×C4—1223no—
385C22×C4—1223no—
386C22×C4—1223no—
387C22×C4—1223no—
388Q16—611no—
389Q16—613no—
390Q16—616no—
391Q16—613no—
392Q16C22×D6113yes—
393SD16—613no—
394SD16—613no—
395SD16—613no—
396SD16—613no—
397SD16—611no—
398SD16—613no—
399SD16—616no—
400SD16C22×D6111yescharacteristic
401SD16C22×D6113yes—
402SD16C22×D6116yes—
403D8—613no—
404D8—611no—
405D8—616no—
406D8—613no—
407D8C22×D6113yes—
408M16—613no—
409M16—616no—
410M16C22×D6113yes—
411C2×C8—613no—
412C2×C8—611no—
413C2×C8—613no—
414C2×C8—613no—
415C2×C8—613no—
416C2×C8C22×D6113yes—
417C23—23no—
418C23—613no—
419C23—1223no—
420C23—1223no—
421C23—1223no—
422Q8—23no—
423Q8—613no—
424Q8—613no—
425Q8—611no—
426Q8—1223no—
427Q8—1223no—
428Q8—1223no—
429Q8D4×D6111yescharacteristic
430Q8C23×D6111yescharacteristic
431Q8C23×D6113yes—
432D4—23no—
433D4—23no—
434D4—23no—
435D4—616no—
436D4—613no—
437D4—613no—
438D4—611no—
439D4—1221no—
440D4—1223no—
441D4—1226no—
442D4—1223no—
443D4—1223no—
444D4—1221no—
445D4—1223no—
446D4—1226no—
447D4—1223no—
448D4—1223no—
449D4—1223no—
450D4D4×D6113yes—
451D4C23×D6113yes—
452D4C23×D6111yescharacteristic
453C2×C4—23no—
454C2×C4—23no—
455C2×C4—23no—
456C2×C4—613no—
457C2×C4—613no—
458C2×C4—613no—
459C2×C4—611no—
460C2×C4—613no—
461C2×C4—1221no—
462C2×C4—1223no—
463C2×C4—1226no—
464C2×C4—1223no—
465C2×C4—1223no—
466C2×C4—1221no—
467C2×C4—1223no—
468C2×C4—1226no—
469C2×C4—1223no—
470C2×C4—1223no—
471C2×C4—1223no—
472C2×C4C23×D6113yes—
473C8—611no—
474C8—613no—
475C8C23×D6111yescharacteristic
476C8C23×D6113yes—
477C22—21no—
478C22—23no—
479C22—83no—
480C22—611no—
481C22—613no—
482C22—1223no—
483C22—1221no—
484C22—4883no—
485C22—4883no—
486C22—4883no—
487C22—2443no—
488C22C2×D4×D6113yes—
489C4—21no—
490C4—23no—
491C4—611no—
492C4—613no—
493C4—1221no—
494C4—1223no—
495C4C2×D4×D6113yes—
496C4C24×D6111yescharacteristic
497C2—23no—
498C2—43no—
499C2—41no—
500C2—1223no—
501C2—1221no—
502C2—2443no—
503C2—2441no—
504C2C22×D4×D6111yescharacteristic
subgroupG/H
centerC2C22×D4×D61
commutatorC4×C61C25
FrattiniC4C24×D61
FittingC61×#577C2
socleC2×C61C23×D4
hypercenter#577D61
hypocenterC61#3584
LCSG ▷ C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C2 ◁ #41 ◁ #577

Complements

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

NH ≅ G/Ntype
1. #16840599C2semidirect
2. #16840597C2semidirect
3. #16840578C2semidirect
4. #16840577C2semidirect
5. #16840574C2semidirect
6. #16840569C2semidirect
7. #16840568C2semidirect
8. #16840566C2semidirect
9. #16840565C2semidirect
10. #16840561C2semidirect
11. #16840558C2semidirect
12. C2×#14519798C2semidirect
13. #135×D61C2semidirect
14. #131×D61C2semidirect
15. C61×#577C2semidirect
17. #14519825C22semidirect
19. #14519824C22semidirect
20. #14519824C22semidirect
22. #14519823C22semidirect
23. #14519823C22semidirect
25. #14519822C22semidirect
27. C2×#11758226C22semidirect
29. C2×#11758224C22semidirect
33. #41×D61C22semidirect
34. #41×D61C22semidirect
35. #14519810C22semidirect
36. #14519809C22semidirect
37. #14519808C22semidirect
38. #14519807C22semidirect
39. #14519806C22semidirect
40. #14519805C22semidirect
41. #14519804C22semidirect
42. #14519803C22semidirect
43. #14519802C22semidirect
44. #14519801C22semidirect
45. #14519800C22semidirect
46. #14519799C22semidirect
47. #14519798C22semidirect
48. #14519798C22semidirect
49. #14519798C22semidirect
50. #14519798C22semidirect
51. #14519798C22semidirect
52. #14519797C22semidirect
53. #14519797C22semidirect
54. #14519796C22semidirect
55. C2×#11758202C22semidirect
56. Q16×D61C22semidirect
57. C2×#11758190C22semidirect
58. SD16×D61C22semidirect
59. SD16×D61C22semidirect
60. C2×#11758199C22semidirect
61. D8×D61C22semidirect
62. #14519785C22semidirect
63. #14519784C22semidirect
64. #14519783C22semidirect
65. M16×D61C22semidirect
66. C2×C8×D61C22semidirect
67. 2−1+4×C61C22semidirect
68. H(5,𝔽2)×C61C22semidirect
69. #137×C61C22semidirect
70. AGL(1,ℤ/8)×C61C22semidirect
71. #135×C61C22semidirect
72. C2×SD16×C61C22semidirect
73. #131×C61C22semidirect
260. #577D61semidirect
268. C61#3584semidirect
274. 2−1+4C2×D61semidirect
280. H(5,𝔽2)C2×D61semidirect
295. #137C2×D61semidirect
301. AGL(1,ℤ/8)C2×D61semidirect
312. #135C2×D61semidirect
318. C2×SD16C2×D61semidirect
324. #131C2×D61semidirect