Finite Group Databasebeta

← #21457611

Subgroups — #21457611

Order 7808.

460 conjugacy classes of subgroups.

The subgroup lattice has 456 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#16840574C211yesmaximal, characteristic, complemented
2#16840572C211yesmaximal, characteristic, complemented
3#16840571C211yesmaximal, characteristic, complemented
4#16840568C211yesmaximal, characteristic, complemented
5#16840133C211yesmaximal, characteristic, complemented
6#16840028C211yesmaximal, characteristic, complemented
7#16840026C211yesmaximal, characteristic, complemented
8#16840024C211yesmaximal, characteristic, complemented
9#16839947C211yesmaximal, characteristic, complemented
10#16839943C211yesmaximal, characteristic, complemented
11#16839932C211yesmaximal, characteristic, complemented
12#16839928C211yesmaximal, characteristic, complemented
13#16839878C211yesmaximal, characteristic, complemented
14#16839877C211yesmaximal, characteristic, complemented
15C61×#471C211yesmaximal, characteristic, complemented
16#14519825C2211yescharacteristic
17#14519824C2211yescharacteristic
18#14519823C2211yescharacteristic, complemented
19#14519822C2211yescharacteristic, complemented
20#14519810—21no—
21#14519810C2211yescharacteristic, complemented
22#14519810C2211yescharacteristic, complemented
23#14519809—21no—
24#14519808C2211yescharacteristic, complemented
25#14519806—21no—
26#14519806—21no—
27#14519805—21no—
28#14519805C2211yescharacteristic
29#14519805C2211yescharacteristic
30#14519804—21no—
31#14519804—21no—
32#14519803C2211yescharacteristic
33#14519801—21no—
34#14519800—21no—
35#14519799—21no—
36#14519799C2211yescharacteristic
37#14519798—21no—
38#14519797C2211yescharacteristic
39#14519796—21no—
40C2×#11758190—21no—
41C2×#11758190C2211yescharacteristic, complemented
42C2×#11758200C2211yescharacteristic, complemented
43C2×#11758201C2211yescharacteristic, complemented
44SD16×D61—21no—
45SD16×D61—21no—
46SD16×D61—21no—
47#14519785C2211yescharacteristic, complemented
48#14519785C2211yescharacteristic, complemented
49#14519783C2211yescharacteristic, complemented
50#14519775C2211yescharacteristic, complemented
51#14519773C2211yescharacteristic
52#14519712C2211yescharacteristic, complemented
53#14519704C2211yescharacteristic, complemented
54#14519703C2211yescharacteristic, complemented
55#14519703C2211yescharacteristic, complemented
56#14519703C2211yescharacteristic, complemented
57#14519695C2211yescharacteristic, complemented
58#14519693C2211yescharacteristic, complemented
59C8×Dic61C2211yescharacteristic, complemented
60#137×C61C2211yescharacteristic, complemented
61AGL(1,ℤ/8)×C61C2211yescharacteristic
62C2×SD16×C61C2211yescharacteristic, complemented
63#131×C61C2211yescharacteristic, complemented
64#108×C61C2211yescharacteristic, complemented
65#101×C61C2211yescharacteristic, complemented
66#100×C61C2211yescharacteristic, complemented
67#41×C61C2311yescharacteristic
68C2×Q8×C61C2311yescharacteristic
69C2×D4×C61C2311yescharacteristic
70C2×C22⋊D61—41no—
71C2×C22⋊D61—41no—
72#11758226—21no—
73#11758226—21no—
74#11758226—21no—
75Q8×D61—21no—
76Q8×D61—21no—
77Q8×D61—21no—
78#11758224—21no—
79#11758224—21no—
80#11758224—21no—
81#11758224—41no—
82D4×D61—21no—
83D4×D61—21no—
84D4×D61—21no—
85D4×D61—41no—
86#11758222—21no—
87#11758222—21no—
88#11758222—41no—
89#11758222C2311yescharacteristic
90#11758222C2311yescharacteristic
91#11758222C2311yescharacteristic
92C2×D244—21no—
93C2×D244C2311yescharacteristic
94C2×Dic122—21no—
95C2×Dic122C2311yescharacteristic
96Q16×C61—21no—
97SD16×C61—21no—
98SD16×C61—21no—
99SD16×C61—21no—
100SD16×C61—21no—
101D8×C61—21no—
102M16×C61—21no—
103M16×C61C2311yescharacteristic
104M16×C61C2311yescharacteristic
105M16×C61C2311yescharacteristic
106C2×C8×C61—21no—
107C2×C8×C61C2311yescharacteristic
108#11758202—21no—
109#11758202D411yescharacteristic, complemented
110#11758201—21no—
111#11758201—21no—
112#11758201—21no—
113#11758201D411yescharacteristic, complemented
114#11758200—21no—
115#11758200—21no—
116#11758200—21no—
117#11758200D411yescharacteristic, complemented
118#11758199—21no—
119#11758199D411yescharacteristic, complemented
120#11758196—41no—
121C4×Dic61C2311yescharacteristic
122#11758194C2311yescharacteristic
123C2×#92418C2311yescharacteristic
124Dic244—21no—
125Dic244—21no—
126Dic244D411yescharacteristic, complemented
127D488—21no—
128D488—21no—
129D488D411yescharacteristic, complemented
130#11758190—21no—
131#11758190—21no—
132#11758190—21no—
133#11758190—21no—
134#11758190—21no—
135#11758190—21no—
136#11758190D411yescharacteristic, complemented
137#11758190D411yescharacteristic, complemented
138#11758189—21no—
139#11758189—21no—
140#11758189—21no—
141C8×D61—21no—
142C8×D61—21no—
143C8×D61—21no—
144C23×C61—21no—
145C22×D61—21no—
146C22×D61—41no—
147C22×D61—41no—
148Q8×C61—21no—
149Q8×C61—21no—
150Q8×C61C2×D411yescharacteristic
151D4×C61—21no—
152D4×C61—21no—
153D4×C61—21no—
154D4×C61C2×D411yescharacteristic
155C2×C4×C61—21no—
156C2×C4×C61—21no—
157C2×C4×C61C2411yescharacteristic
158C22⋊D61—21no—
159C22⋊D61—21no—
160C22⋊D61—21no—
161C22⋊D61—41no—
162C22⋊D61—41no—
163C22⋊D61—41no—
164C22⋊D61—41no—
165C22⋊D61—82no—
166C2×Dic61—21no—
167C2×Dic61—21no—
168C2×Dic61—41no—
169C2×Dic61—41no—
170D244—21no—
171D244—21no—
172D244—41no—
173D244—41no—
174D244C2×D411yescharacteristic
175D244C2×D411yescharacteristic
176D244C2×D411yescharacteristic
177C4×D61—21no—
178C4×D61—21no—
179C4×D61—21no—
180C4×D61—41no—
181C4×D61—41no—
182C4×D61—41no—
183C4×D61—41no—
184Dic122—21no—
185Dic122—21no—
186Dic122—41no—
187Dic122—41no—
188Dic122C2×D411yescharacteristic
189Dic122C2×D411yescharacteristic
190Dic122C2×D411yescharacteristic
191C8×C61—21no—
192C8×C61—21no—
193C8×C61—21no—
194C8×C61C2×D411yescharacteristic
195C8×C61C2×D411yescharacteristic
196#92418—21no—
197#92418C2×D411yescharacteristic
198#92418C2×D411yescharacteristic
199C22×C61—21no—
200C22×C61—41no—
201C22×C61—81no—
202C22×C61H(5,𝔽2)11yescharacteristic
203C2×D61—21no—
204C2×D61—21no—
205C2×D61—21no—
206C2×D61—41no—
207C2×D61—81no—
208C2×D61—161no—
209C2×D61—161no—
210C4×C61—21no—
211C4×C61—41no—
212C4×C61C22×D411yescharacteristic
213C4×C61C22×D411yescharacteristic
214Dic61—22no—
215Dic61—21no—
216Dic61—21no—
217Dic61—21no—
218Dic61—41no—
219#3291—611nomaximal, Sylow
220C2×C61—21no—
221C2×C61—41no—
222C2×C61—81no—
223C2×C61D4211yescharacteristic
224D61—41no—
225D61—41no—
226D61—41no—
227D61—81no—
228#577—611no—
229#577—611no—
230#577—611no—
231#577—611no—
232#492—611no—
233#471—611no—
234#471—611no—
235#471—611no—
236#471D6111yescharacteristic, complemented
237#456—611no—
238#456—611no—
239#453—611no—
240#453—611no—
241#443—611no—
242#443—611no—
243C61#329111yescharacteristic, complemented, Sylow
2442−1+4—611no—
2452−1+4—611no—
246H(5,𝔽2)—611no—
247H(5,𝔽2)—611no—
248#137—611no—
249#137—611no—
250#137—611no—
251#137—1221no—
252#137—1221no—
253#137—1221no—
254#137—1221no—
255#137C2×D6111yescharacteristic, complemented
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)C2×D6111yescharacteristic
264#135—611no—
265#135—611no—
266#135—1221no—
267#135—1221no—
268#135—1221no—
269#135—1221no—
270C2×SD16—611no—
271C2×SD16—611no—
272C2×SD16—611no—
273C2×SD16—1221no—
274C2×SD16—1221no—
275C2×SD16—1221no—
276C2×SD16—1221no—
277C2×SD16C2×D6111yescharacteristic, complemented
278#131—611no—
279#131—611no—
280#131—611no—
281#131C2×D6111yescharacteristic, complemented
282C4⋊Q8—611no—
283#127—611no—
284#108—611no—
285#108C2×D6111yescharacteristic, complemented
286#104—611no—
287#104—611no—
288#104—611no—
289#104—611no—
290#101—611no—
291#101C2×D6111yescharacteristic, complemented
292#100—611no—
293#100C2×D6111yescharacteristic, complemented
294C4×C8—611no—
295#41—611no—
296#41—611no—
297#41—611no—
298#41—1221no—
299#41—1221no—
300#41—1221no—
301#41—1221no—
302#41—1221no—
303#41—1221no—
304#41—1221no—
305#41—1221no—
306#41—2441no—
307#41—2441no—
308#41C22×D6111yescharacteristic
309C2×Q8—611no—
310C2×Q8—1221no—
311C2×Q8—1221no—
312C2×Q8—1221no—
313C2×Q8—1221no—
314C2×Q8C22×D6111yescharacteristic
315C2×D4—611no—
316C2×D4—1221no—
317C2×D4—1221no—
318C2×D4—1221no—
319C2×D4—1221no—
320C2×D4—2441no—
321C2×D4—2441no—
322C2×D4—2441no—
323C2×D4C22×D6111yescharacteristic
324Q16—21no—
325Q16—611no—
326Q16—611no—
327Q16—1221no—
328Q16—1221no—
329Q16—1221no—
330SD16—21no—
331SD16—21no—
332SD16—21no—
333SD16—21no—
334SD16—611no—
335SD16—611no—
336SD16—611no—
337SD16—611no—
338SD16—1221no—
339SD16—1221no—
340SD16—1221no—
341SD16—1221no—
342SD16—1221no—
343SD16—1221no—
344SD16—1221no—
345SD16—1221no—
346SD16—1221no—
347SD16—1221no—
348SD16—1221no—
349SD16—1221no—
350D8—21no—
351D8—611no—
352D8—611no—
353D8—1221no—
354D8—1221no—
355D8—1221no—
356M16—21no—
357M16—611no—
358M16—1221no—
359M16—1221no—
360M16—1221no—
361M16C22×D6111yescharacteristic
362M16C22×D6111yescharacteristic
363M16C22×D6111yescharacteristic
364C2×C8—21no—
365C2×C8—611no—
366C2×C8—1221no—
367C2×C8—1221no—
368C2×C8—1221no—
369C2×C8C22×D6111yescharacteristic
370C4⋊C4—2441no—
371C42—611no—
372C23—21no—
373C23—1221no—
374C23—2441no—
375C23—2441no—
376Q8—21no—
377Q8—21no—
378Q8—611no—
379Q8—611no—
380Q8—611no—
381Q8—1221no—
382Q8—1221no—
383Q8—2441no—
384Q8—2441no—
385Q8D4×D6111yescharacteristic
386D4—21no—
387D4—21no—
388D4—21no—
389D4—611no—
390D4—611no—
391D4—611no—
392D4—1221no—
393D4—1221no—
394D4—1221no—
395D4—1221no—
396D4—1221no—
397D4—4882no—
398D4—2441no—
399D4—2441no—
400D4—2441no—
401D4—2441no—
402D4—2441no—
403D4—2441no—
404D4D4×D6111yescharacteristic
405C2×C4—21no—
406C2×C4—21no—
407C2×C4—1221no—
408C2×C4—1221no—
409C2×C4—1221no—
410C2×C4—1221no—
411C2×C4—1221no—
412C2×C4—2441no—
413C2×C4—2441no—
414C2×C4—2441no—
415C2×C4—2441no—
416C2×C4—2441no—
417C2×C4—2441no—
418C2×C4C23×D6111yescharacteristic
419C8—21no—
420C8—21no—
421C8—21no—
422C8—611no—
423C8—611no—
424C8—1221no—
425C8D4×D6111yescharacteristic
426C8D4×D6111yescharacteristic
427C22—21no—
428C22—41no—
429C22—81no—
430C22—1221no—
431C22—1221no—
432C22—1221no—
433C22—9761no—
434C22—9761no—
435C22—4881no—
436C22—2441no—
437C22#1451982311yescharacteristic
438C4—21no—
439C4—41no—
440C4—1222no—
441C4—1221no—
442C4—1221no—
443C4—1221no—
444C4—2441no—
445C4C2×D4×D6111yescharacteristic
446C4C2×D4×D6111yescharacteristic
447C2—21no—
448C2—41no—
449C2—81no—
450C2—4881no—
451C2—2441no—
452C2—2441no—
453C2—2441no—
454C2#1684039611yescharacteristic
subgroupG/H
centerC2#16840396
commutatorC2×C4×C61C24
FrattiniC2×C4C23×D61
FittingC61×#471C2
socleC2×C61D42
hypercenter#471D61
hypocenterC61#3291
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C2 ◁ C2×C4 ◁ #471

Complements

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

NH ≅ G/Ntype
1. #16840574C2semidirect
2. #16840572C2semidirect
3. #16840571C2semidirect
4. #16840568C2semidirect
5. #16840133C2semidirect
6. #16840028C2semidirect
7. #16840026C2semidirect
8. #16840024C2semidirect
9. #16839947C2semidirect
10. #16839943C2semidirect
11. #16839932C2semidirect
12. #16839928C2semidirect
13. #16839878C2semidirect
14. #16839877C2semidirect
15. C61×#471C2semidirect
18. #14519823C22semidirect
19. #14519822C22semidirect
21. #14519810C22semidirect
22. #14519810C22semidirect
24. #14519808C22semidirect
41. C2×#11758190C22semidirect
42. C2×#11758200C22semidirect
43. C2×#11758201C22semidirect
47. #14519785C22semidirect
48. #14519785C22semidirect
49. #14519783C22semidirect
50. #14519775C22semidirect
52. #14519712C22semidirect
53. #14519704C22semidirect
54. #14519703C22semidirect
55. #14519703C22semidirect
56. #14519703C22semidirect
57. #14519695C22semidirect
58. #14519693C22semidirect
59. C8×Dic61C22semidirect
60. #137×C61C22semidirect
62. C2×SD16×C61C22semidirect
63. #131×C61C22semidirect
64. #108×C61C22semidirect
65. #101×C61C22semidirect
66. #100×C61C22semidirect
109. #11758202D4semidirect
113. #11758201D4semidirect
117. #11758200D4semidirect
119. #11758199D4semidirect
126. Dic244D4semidirect
129. D488D4semidirect
136. #11758190D4semidirect
137. #11758190D4semidirect
236. #471D61semidirect
243. C61#3291semidirect
255. #137C2×D61semidirect
277. C2×SD16C2×D61semidirect
281. #131C2×D61semidirect
285. #108C2×D61semidirect
291. #101C2×D61semidirect
293. #100C2×D61semidirect