Finite Group Databasebeta

← #21457580

Subgroups — #21457580

Order 7808.

464 conjugacy classes of subgroups.

The subgroup lattice has 462 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#16840573C211yesmaximal, characteristic, complemented
2#16840572C211yesmaximal, characteristic, complemented
3#16840566C211yesmaximal, characteristic, complemented
4#16840565C211yesmaximal, characteristic, complemented
5#16840149C211yesmaximal, characteristic, complemented
6#16840031C211yesmaximal, characteristic, complemented
7#16840030C211yesmaximal, characteristic, complemented
8#16840024C211yesmaximal, characteristic, complemented
9#16840023C211yesmaximal, characteristic, complemented
10#16839941C211yesmaximal, characteristic, complemented
11#16839936C211yesmaximal, characteristic, complemented
12#16839929C211yesmaximal, characteristic, complemented
13#16839881C211yesmaximal, characteristic, complemented
14#16839881C211yesmaximal, characteristic, complemented
15C61×#453C211yesmaximal, characteristic, complemented
16#14519824C2211yescharacteristic, complemented
17#14519823C2211yescharacteristic
18#14519822C2211yescharacteristic, complemented
19#14519810C2211yescharacteristic, complemented
20#14519807—21no—
21#14519807C2211yescharacteristic, complemented
22#14519806—21no—
23#14519805C2211yescharacteristic, complemented
24#14519804—21no—
25#14519803—21no—
26#14519803—21no—
27#14519803C2211yescharacteristic
28#14519803C2211yescharacteristic, complemented
29#14519802—21no—
30#14519802C2211yescharacteristic, complemented
31#14519801—21no—
32#14519801—21no—
33#14519798—21no—
34#14519797—21no—
35#14519797—21no—
36#14519797C2211yescharacteristic
37#14519797C2211yescharacteristic
38#14519796—21no—
39C2×#11758200—21no—
40C2×#11758200C2211yescharacteristic, complemented
41C2×#11758200C2211yescharacteristic, complemented
42SD16×D61—21no—
43C2×#11758199—21no—
44C2×#11758199C2211yescharacteristic, complemented
45C2×#11758199C2211yescharacteristic, complemented
46D8×D61—21no—
47#14519785C2211yescharacteristic, complemented
48#14519785C2211yescharacteristic, complemented
49#14519784C2211yescharacteristic, complemented
50#14519784C2211yescharacteristic, complemented
51#14519765C2211yescharacteristic, complemented
52#14519712C2211yescharacteristic, complemented
53#14519712C2211yescharacteristic, complemented
54#14519705C2211yescharacteristic, complemented
55#14519705C2211yescharacteristic, complemented
56#14519695C2211yescharacteristic, complemented
57#14519694C2211yescharacteristic, complemented
58#14519693C2211yescharacteristic, complemented
59#14519688C2211yescharacteristic, complemented
60H(5,𝔽2)×C61C2211yescharacteristic, complemented
61AGL(1,ℤ/8)×C61C2211yescharacteristic
62AGL(1,ℤ/8)×C61C2211yescharacteristic, complemented
63#127×C61C2211yescharacteristic, complemented
64#104×C61C2211yescharacteristic, complemented
65#104×C61C2211yescharacteristic, complemented
66#100×C61C2211yescharacteristic, complemented
67#41×C61—21no—
68#41×C61—21no—
69#41×C61C2311yescharacteristic
70#41×C61C2311yescharacteristic
71C2×D4×C61—21no—
72C2×D4×C61—21no—
73C2×D4×C61—41no—
74C2×D4×C61—41no—
75C2×D4×C61C2311yescharacteristic
76C2×D4×C61C2311yescharacteristic
77C2×C22⋊D61—41no—
78#11758226—21no—
79Q8×D61—21no—
80#11758224—21no—
81#11758224—21no—
82#11758224—21no—
83#11758224—41no—
84D4×D61—21no—
85D4×D61—21no—
86D4×D61—21no—
87D4×D61—41no—
88#11758222—21no—
89#11758222—21no—
90#11758222C2311yescharacteristic
91#11758222C2311yescharacteristic
92C2×D244—21no—
93C2×D244C2311yescharacteristic
94C2×Dic122—21no—
95C2×Dic122C2311yescharacteristic
96SD16×C61—21no—
97SD16×C61—21no—
98D8×C61—21no—
99D8×C61—21no—
100M16×C61C2311yescharacteristic
101M16×C61C2311yescharacteristic
102C42×C61C2311yescharacteristic
103#11758202—21no—
104#11758202D411yescharacteristic, complemented
105#11758202D411yescharacteristic, complemented
106#11758201—21no—
107#11758201D411yescharacteristic, complemented
108#11758201D411yescharacteristic, complemented
109#11758200—21no—
110#11758200—21no—
111#11758200—21no—
112#11758200—21no—
113#11758200—21no—
114#11758200—21no—
115#11758200—21no—
116#11758200D411yescharacteristic, complemented
117#11758200D411yescharacteristic, complemented
118#11758199—21no—
119#11758199—21no—
120#11758199—21no—
121#11758199—21no—
122#11758199—21no—
123#11758199—21no—
124#11758199—21no—
125#11758199D411yescharacteristic, complemented
126#11758199D411yescharacteristic, complemented
127#11758198—41no—
128#11758194—21no—
129#11758194—21no—
130#11758194C2311yescharacteristic
131#11758194C2311yescharacteristic
132C2×#92418—21no—
133C2×#92418—21no—
134C2×#92418C2311yescharacteristic
135C2×#92418C2311yescharacteristic
136Dic244—21no—
137D488—21no—
138#11758190—21no—
139#11758190—21no—
140#11758189—21no—
141#11758189—21no—
142C8×D61—21no—
143C8×D61—21no—
144C23×C61—21no—
145C23×C61—21no—
146C23×C61—41no—
147C22×D61—21no—
148C22×D61—41no—
149C22×D61—41no—
150Q8×C61C2×D411yescharacteristic
151Q8×C61C2×D411yescharacteristic
152D4×C61—21no—
153D4×C61—21no—
154D4×C61—21no—
155D4×C61—21no—
156D4×C61—21no—
157D4×C61—21no—
158D4×C61—41no—
159D4×C61—41no—
160D4×C61—82no—
161D4×C61C2×D411yescharacteristic
162D4×C61C2×D411yescharacteristic
163C2×C4×C61—21no—
164C2×C4×C61—21no—
165C2×C4×C61—21no—
166C2×C4×C61—41no—
167C2×C4×C61C2411yescharacteristic
168C22⋊D61—21no—
169C22⋊D61—21no—
170C22⋊D61—41no—
171C22⋊D61—41no—
172C22⋊D61—41no—
173C22⋊D61—41no—
174C2×Dic61—21no—
175C2×Dic61—41no—
176C2×Dic61—41no—
177D244—21no—
178D244—21no—
179D244—41no—
180D244C2×D411yescharacteristic
181D244C2×D411yescharacteristic
182C4×D61—21no—
183C4×D61—21no—
184C4×D61—41no—
185C4×D61—41no—
186Dic122—21no—
187Dic122—21no—
188Dic122—41no—
189Dic122C2×D411yescharacteristic
190Dic122C2×D411yescharacteristic
191C8×C61—21no—
192C8×C61—21no—
193#92418—21no—
194#92418—21no—
195#92418C2×D411yescharacteristic
196#92418C2×D411yescharacteristic
197#92418C2×D411yescharacteristic
198#92418C2×D411yescharacteristic
199C22×C61—21no—
200C22×C61—21no—
201C22×C61—41no—
202C22×C61—41no—
203C22×C61—81no—
204C22×C61—81no—
205C22×C61—161no—
206C22×C61H(5,𝔽2)11yescharacteristic
207C2×D61—21no—
208C2×D61—21no—
209C2×D61—41no—
210C2×D61—81no—
211C2×D61—161no—
212C2×D61—161no—
213C4×C61—21no—
214C4×C61—21no—
215C4×C61—41no—
216C4×C61C22×D411yescharacteristic
217C4×C61C22×D411yescharacteristic
218Dic61—21no—
219Dic61—21no—
220Dic61—41no—
221#3288—611nomaximal, Sylow
222C2×C61—21no—
223C2×C61—41no—
224C2×C61—41no—
225C2×C61—81no—
226C2×C61—81no—
227C2×C61D4211yescharacteristic
228D61—41no—
229D61—41no—
230D61—81no—
231#577—611no—
232#577—611no—
233#576—611no—
234#576—611no—
235#496—611no—
236#472—611no—
237#472—611no—
238#471—611no—
239#471—611no—
240#455—611no—
241#454—611no—
242#453—611no—
243#453D6111yescharacteristic, complemented
244#444—611no—
245#444—611no—
246C61#328811yescharacteristic, complemented, Sylow
2472−1+4—611no—
248H(5,𝔽2)—611no—
249H(5,𝔽2)—611no—
250H(5,𝔽2)C2×D6111yescharacteristic, complemented
251#137—611no—
252#137—611no—
253#137—1221no—
254#137—1221no—
255AGL(1,ℤ/8)—611no—
256AGL(1,ℤ/8)—611no—
257AGL(1,ℤ/8)—611no—
258AGL(1,ℤ/8)—611no—
259AGL(1,ℤ/8)—1221no—
260AGL(1,ℤ/8)—1221no—
261AGL(1,ℤ/8)—1221no—
262AGL(1,ℤ/8)—1221no—
263AGL(1,ℤ/8)—1221no—
264AGL(1,ℤ/8)—1221no—
265AGL(1,ℤ/8)C2×D6111yescharacteristic
266AGL(1,ℤ/8)C2×D6111yescharacteristic, complemented
267#135—611no—
268#135—611no—
269#135—1221no—
270#135—1221no—
271#135—1221no—
272#135—1221no—
273C2×SD16—611no—
274C2×SD16—611no—
275C2×SD16—1221no—
276C2×SD16—1221no—
277C2×D8—611no—
278C2×D8—611no—
279C2×D8—1221no—
280C2×D8—1221no—
281#131—611no—
282#131—611no—
283#131—611no—
284#131—611no—
285#127C2×D6111yescharacteristic, complemented
286#124—611no—
287#108—611no—
288#108—611no—
289#104—611no—
290#104—611no—
291#104C2×D6111yescharacteristic, complemented
292#104C2×D6111yescharacteristic, complemented
293#101—611no—
294#100—611no—
295#100—611no—
296#100C2×D6111yescharacteristic, complemented
297#97—611no—
298#41—21no—
299#41—21no—
300#41—611no—
301#41—611no—
302#41—1221no—
303#41—1221no—
304#41—1221no—
305#41—1221no—
306#41—1221no—
307#41—1221no—
308#41—2441no—
309#41C22×D6111yescharacteristic
310#41C22×D6111yescharacteristic
311C2×Q8—611no—
312C2×Q8—1221no—
313C2×Q8—1221no—
314C2×D4—21no—
315C2×D4—21no—
316C2×D4—41no—
317C2×D4—41no—
318C2×D4—611no—
319C2×D4—1221no—
320C2×D4—1221no—
321C2×D4—1221no—
322C2×D4—1221no—
323C2×D4—2441no—
324C2×D4—2441no—
325C2×D4C22×D6111yescharacteristic
326C2×D4C22×D6111yescharacteristic
327Q16—611no—
328Q16—611no—
329Q16—1221no—
330Q16—1221no—
331SD16—21no—
332SD16—21no—
333SD16—611no—
334SD16—611no—
335SD16—611no—
336SD16—611no—
337SD16—1221no—
338SD16—1221no—
339SD16—1221no—
340SD16—1221no—
341SD16—1221no—
342SD16—1221no—
343SD16—1221no—
344SD16—1221no—
345SD16—1221no—
346SD16—1221no—
347D8—21no—
348D8—21no—
349D8—611no—
350D8—611no—
351D8—1221no—
352D8—1221no—
353D8—1221no—
354D8—1221no—
355D8—1221no—
356D8—1221no—
357D8—1221no—
358D8—1221no—
359M16—611no—
360M16—611no—
361M16—1221no—
362M16—1221no—
363M16—1221no—
364M16—1221no—
365M16C22×D6111yescharacteristic
366M16C22×D6111yescharacteristic
367C2×C8—611no—
368C2×C8—611no—
369C2×C8—1221no—
370C2×C8—1221no—
371C2×C8—1221no—
372C2×C8—1221no—
373C22⋊C4—2441no—
374C42C22×D6111yescharacteristic
375C23—21no—
376C23—21no—
377C23—41no—
378C23—1221no—
379C23—2441no—
380C23—2441no—
381Q8—611no—
382Q8—611no—
383Q8—1221no—
384Q8—1221no—
385Q8—2441no—
386Q8D4×D6111yescharacteristic
387Q8D4×D6111yescharacteristic
388D4—21no—
389D4—21no—
390D4—21no—
391D4—21no—
392D4—21no—
393D4—21no—
394D4—41no—
395D4—41no—
396D4—82no—
397D4—611no—
398D4—611no—
399D4—1221no—
400D4—1221no—
401D4—1221no—
402D4—1221no—
403D4—2441no—
404D4—2441no—
405D4—2441no—
406D4—2441no—
407D4—2441no—
408D4D4×D6111yescharacteristic
409D4D4×D6111yescharacteristic
410C2×C4—21no—
411C2×C4—21no—
412C2×C4—21no—
413C2×C4—41no—
414C2×C4—1221no—
415C2×C4—1221no—
416C2×C4—1221no—
417C2×C4—2441no—
418C2×C4—2441no—
419C2×C4—2441no—
420C2×C4—2441no—
421C2×C4C23×D6111yescharacteristic
422C8—21no—
423C8—21no—
424C8—611no—
425C8—611no—
426C8—611no—
427C8—611no—
428C8—1221no—
429C8—1221no—
430C22—21no—
431C22—21no—
432C22—41no—
433C22—41no—
434C22—81no—
435C22—81no—
436C22—161no—
437C22—1221no—
438C22—1221no—
439C22—9761no—
440C22—9761no—
441C22—4881no—
442C22—2441no—
443C22#1451982211yescharacteristic
444C4—21no—
445C4—21no—
446C4—41no—
447C4—1221no—
448C4—1221no—
449C4—2441no—
450C4C2×D4×D6111yescharacteristic
451C4C2×D4×D6111yescharacteristic
452C2—21no—
453C2—41no—
454C2—41no—
455C2—81no—
456C2—81no—
457C2—4881no—
458C2—2441no—
459C2—2441no—
460C2#1684039411yescharacteristic
subgroupG/H
centerC2#16840394
commutatorC2×C4×C61C24
FrattiniC2×C4C23×D61
FittingC61×#453C2
socleC2×C61D42
hypercenter#453D61
hypocenterC61#3288
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C2 ◁ C2×C4 ◁ #453

Complements

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

NH ≅ G/Ntype
1. #16840573C2semidirect
2. #16840572C2semidirect
3. #16840566C2semidirect
4. #16840565C2semidirect
5. #16840149C2semidirect
6. #16840031C2semidirect
7. #16840030C2semidirect
8. #16840024C2semidirect
9. #16840023C2semidirect
10. #16839941C2semidirect
11. #16839936C2semidirect
12. #16839929C2semidirect
13. #16839881C2semidirect
14. #16839881C2semidirect
15. C61×#453C2semidirect
16. #14519824C22semidirect
18. #14519822C22semidirect
19. #14519810C22semidirect
21. #14519807C22semidirect
23. #14519805C22semidirect
28. #14519803C22semidirect
30. #14519802C22semidirect
40. C2×#11758200C22semidirect
41. C2×#11758200C22semidirect
44. C2×#11758199C22semidirect
45. C2×#11758199C22semidirect
47. #14519785C22semidirect
48. #14519785C22semidirect
49. #14519784C22semidirect
50. #14519784C22semidirect
51. #14519765C22semidirect
52. #14519712C22semidirect
53. #14519712C22semidirect
54. #14519705C22semidirect
55. #14519705C22semidirect
56. #14519695C22semidirect
57. #14519694C22semidirect
58. #14519693C22semidirect
59. #14519688C22semidirect
60. H(5,𝔽2)×C61C22semidirect
62. AGL(1,ℤ/8)×C61C22semidirect
63. #127×C61C22semidirect
64. #104×C61C22semidirect
65. #104×C61C22semidirect
66. #100×C61C22semidirect
104. #11758202D4semidirect
105. #11758202D4semidirect
107. #11758201D4semidirect
108. #11758201D4semidirect
116. #11758200D4semidirect
117. #11758200D4semidirect
125. #11758199D4semidirect
126. #11758199D4semidirect
243. #453D61semidirect
246. C61#3288semidirect
250. H(5,𝔽2)C2×D61semidirect
266. AGL(1,ℤ/8)C2×D61semidirect
285. #127C2×D61semidirect
291. #104C2×D61semidirect
292. #104C2×D61semidirect
296. #100C2×D61semidirect