Finite Group Databasebeta

← #21457586

Subgroups — #21457586

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#16840574C211yesmaximal, characteristic, complemented
2#16840569C211yesmaximal, characteristic, complemented
3#16840567C211yesmaximal, characteristic, complemented
4#16840564C211yesmaximal, characteristic, complemented
5#16840151C211yesmaximal, characteristic, complemented
6#16840033C211yesmaximal, characteristic, complemented
7#16840032C211yesmaximal, characteristic, complemented
8#16840026C211yesmaximal, characteristic, complemented
9#16840025C211yesmaximal, characteristic, complemented
10#16839941C211yesmaximal, characteristic, complemented
11#16839936C211yesmaximal, characteristic, complemented
12#16839931C211yesmaximal, characteristic, complemented
13#16839931C211yesmaximal, characteristic, complemented
14#16839885C211yesmaximal, characteristic, complemented
15C61×#444C211yesmaximal, characteristic, complemented
16#14519824C2211yescharacteristic, complemented
17#14519823C2211yescharacteristic
18#14519823C2211yescharacteristic, complemented
19#14519823C2211yescharacteristic, complemented
20#14519810—21no—
21#14519810C2211yescharacteristic, complemented
22#14519809—21no—
23#14519807C2211yescharacteristic, complemented
24#14519805—21no—
25#14519805—21no—
26#14519805—21no—
27#14519805C2211yescharacteristic
28#14519805C2211yescharacteristic, complemented
29#14519805C2211yescharacteristic, complemented
30#14519804—21no—
31#14519804—21no—
32#14519802C2211yescharacteristic
33#14519802C2211yescharacteristic, complemented
34#14519802C2211yescharacteristic, complemented
35#14519801—21no—
36#14519800—21no—
37#14519799—21no—
38#14519799—21no—
39#14519799C2211yescharacteristic
40#14519798—21no—
41C2×#11758190—21no—
42C2×#11758190C2211yescharacteristic, complemented
43C2×#11758190C2211yescharacteristic, complemented
44SD16×D61—21no—
45C2×D488—21no—
46C2×D488C2211yescharacteristic, complemented
47C2×D488C2211yescharacteristic, complemented
48D8×D61—21no—
49#14519783C2211yescharacteristic, complemented
50#14519783C2211yescharacteristic, complemented
51#14519774C2211yescharacteristic, complemented
52#14519765C2211yescharacteristic, complemented
53#14519713C2211yescharacteristic, complemented
54#14519705C2211yescharacteristic, complemented
55#14519705C2211yescharacteristic, complemented
56#14519695C2211yescharacteristic, complemented
57#14519693C2211yescharacteristic, complemented
58#14519693C2211yescharacteristic, complemented
59#14519693C2211yescharacteristic, complemented
60#135×C61C2211yescharacteristic
61#131×C61C2211yescharacteristic, complemented
62#131×C61C2211yescharacteristic, complemented
63#108×C61C2211yescharacteristic, complemented
64#104×C61C2211yescharacteristic, complemented
65#104×C61C2211yescharacteristic, complemented
66#97×C61C2211yescharacteristic, complemented
67#41×C61C2311yescharacteristic
68#41×C61C2311yescharacteristic
69#11758226—21no—
70#11758226—21no—
71#11758226—21no—
72Q8×D61—21no—
73#11758224—21no—
74#11758224—41no—
75D4×D61—21no—
76D4×D61—21no—
77D4×D61—21no—
78D4×D61—41no—
79D4×D61—41no—
80D4×D61—41no—
81#11758222—21no—
82#11758222—21no—
83#11758222—21no—
84#11758222—21no—
85#11758222C2311yescharacteristic
86#11758222C2311yescharacteristic
87C2×D244—21no—
88C2×D244—21no—
89C2×D244—21no—
90C2×D244—41no—
91C2×D244C2311yescharacteristic
92C2×D244C2311yescharacteristic
93C2×D244C2311yescharacteristic
94C2×Dic122—21no—
95C2×Dic122C2311yescharacteristic
96Q16×C61D411yescharacteristic, complemented
97SD16×C61D411yescharacteristic, complemented
98SD16×C61D411yescharacteristic, complemented
99D8×C61D411yescharacteristic, complemented
100M16×C61—21no—
101M16×C61—21no—
102M16×C61C2311yescharacteristic
103M16×C61C2311yescharacteristic
104C2×C8×C61—21no—
105C2×C8×C61—21no—
106C2×C8×C61C2311yescharacteristic
107C2×C8×C61C2311yescharacteristic
108C42×C61C2311yescharacteristic
109#11758202—21no—
110#11758201—21no—
111#11758201—21no—
112#11758201—21no—
113#11758200—21no—
114#11758199—21no—
115#11758199—21no—
116#11758199—21no—
117#11758198—41no—
118#11758194C2311yescharacteristic
119#11758194C2311yescharacteristic
120Dic244—21no—
121Dic244D411yescharacteristic, complemented
122D488—21no—
123D488—21no—
124D488—21no—
125D488—21no—
126D488—21no—
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#11758190—21no—
137#11758190—21no—
138#11758190D411yescharacteristic, complemented
139#11758190D411yescharacteristic, complemented
140#11758189—21no—
141#11758189—21no—
142C8×D61—21no—
143C8×D61—21no—
144C22×D61—21no—
145C22×D61—21no—
146C22×D61—21no—
147C22×D61—41no—
148C22×D61—41no—
149C22×D61—41no—
150Q8×C61C2×D411yescharacteristic
151Q8×C61C2×D411yescharacteristic
152D4×C61—21no—
153D4×C61—21no—
154D4×C61C2×D411yescharacteristic
155D4×C61C2×D411yescharacteristic
156C2×C4×C61—21no—
157C2×C4×C61—21no—
158C2×C4×C61—21no—
159C2×C4×C61C2411yescharacteristic
160C22⋊D61—21no—
161C22⋊D61—21no—
162C22⋊D61—41no—
163C22⋊D61—41no—
164C22⋊D61—41no—
165C22⋊D61—41no—
166C2×Dic61—21no—
167C2×Dic61—41no—
168D244—21no—
169D244—21no—
170D244—21no—
171D244—21no—
172D244—21no—
173D244—21no—
174D244—41no—
175D244—41no—
176D244—41no—
177D244—82no—
178D244C2×D411yescharacteristic
179D244C2×D411yescharacteristic
180C4×D61—21no—
181C4×D61—21no—
182C4×D61—41no—
183C4×D61—41no—
184C4×D61—41no—
185C4×D61—41no—
186Dic122—21no—
187Dic122—21no—
188Dic122—41no—
189Dic122C2×D411yescharacteristic
190Dic122C2×D411yescharacteristic
191C8×C61—21no—
192C8×C61—21no—
193C8×C61C2×D411yescharacteristic
194C8×C61C2×D411yescharacteristic
195C8×C61C2×D411yescharacteristic
196C8×C61C2×D411yescharacteristic
197#92418—21no—
198#92418—21no—
199C22×C61—21no—
200C22×C61—21no—
201C22×C61H(5,𝔽2)11yescharacteristic
202C2×D61—21no—
203C2×D61—21no—
204C2×D61—41no—
205C2×D61—41no—
206C2×D61—41no—
207C2×D61—81no—
208C2×D61—81no—
209C2×D61—81no—
210C2×D61—161no—
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×C61D4211yescharacteristic
226D61—41no—
227D61—41no—
228D61—81no—
229D61—81no—
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#453—611no—
244#444—611no—
245#444D6111yescharacteristic, complemented
246C61#328811yescharacteristic, complemented, Sylow
2472−1+4—611no—
248H(5,𝔽2)—611no—
249H(5,𝔽2)—611no—
250H(5,𝔽2)—611no—
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)—611no—
260AGL(1,ℤ/8)—611no—
261AGL(1,ℤ/8)—1221no—
262AGL(1,ℤ/8)—1221no—
263AGL(1,ℤ/8)—1221no—
264AGL(1,ℤ/8)—1221no—
265AGL(1,ℤ/8)—1221no—
266AGL(1,ℤ/8)—1221no—
267#135—611no—
268#135—1221no—
269#135—1221no—
270#135—1221no—
271#135—1221no—
272#135C2×D6111yescharacteristic
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#131C2×D6111yescharacteristic, complemented
284#131C2×D6111yescharacteristic, complemented
285#127—611no—
286#124—611no—
287#108—611no—
288#108C2×D6111yescharacteristic, complemented
289#104—611no—
290#104—611no—
291#104C2×D6111yescharacteristic, complemented
292#104C2×D6111yescharacteristic, complemented
293#101—611no—
294#100—611no—
295#100—611no—
296#100—611no—
297#97C2×D6111yescharacteristic, complemented
298#41—611no—
299#41—611no—
300#41—1221no—
301#41—1221no—
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—611no—
315C2×D4—611no—
316C2×D4—611no—
317C2×D4—1221no—
318C2×D4—1221no—
319C2×D4—1221no—
320C2×D4—1221no—
321C2×D4—1221no—
322C2×D4—1221no—
323C2×D4—2441no—
324C2×D4—2441no—
325C2×D4—2441no—
326C2×D4—2441no—
327Q16—611no—
328Q16—1221no—
329Q16—1221no—
330Q16D24411yescharacteristic, complemented
331SD16—611no—
332SD16—611no—
333SD16—1221no—
334SD16—1221no—
335SD16—1221no—
336SD16—1221no—
337SD16—1221no—
338SD16—1221no—
339SD16—1221no—
340SD16—1221no—
341SD16—1221no—
342SD16—1221no—
343SD16—1221no—
344SD16—1221no—
345SD16D24411yescharacteristic, complemented
346SD16D24411yescharacteristic, complemented
347D8—611no—
348D8—1221no—
349D8—1221no—
350D8—1221no—
351D8—1221no—
352D8—1221no—
353D8—1221no—
354D8—1221no—
355D8—1221no—
356D8—1221no—
357D8—1221no—
358D8D24411yescharacteristic, complemented
359M16—21no—
360M16—21no—
361M16—611no—
362M16—611no—
363M16—1221no—
364M16—1221no—
365M16C22×D6111yescharacteristic
366M16C22×D6111yescharacteristic
367C2×C8—21no—
368C2×C8—21no—
369C2×C8—1221no—
370C2×C8—1221no—
371C2×C8C22×D6111yescharacteristic
372C2×C8C22×D6111yescharacteristic
373C22⋊C4—2441no—
374C42C22×D6111yescharacteristic
375C23—1221no—
376C23—1221no—
377C23—1221no—
378C23—2441no—
379C23—2441no—
380C23—2441no—
381Q8—611no—
382Q8—611no—
383Q8—1221no—
384Q8—1221no—
385Q8—2441no—
386Q8C2×D24411yescharacteristic
387Q8C2×D24411yescharacteristic
388D4—21no—
389D4—21no—
390D4—611no—
391D4—611no—
392D4—1221no—
393D4—1221no—
394D4—1221no—
395D4—1221no—
396D4—1221no—
397D4—1221no—
398D4—1221no—
399D4—1221no—
400D4—4882no—
401D4—2441no—
402D4—2441no—
403D4—2441no—
404D4—2441no—
405D4—2441no—
406D4—2441no—
407D4—2441no—
408D4C2×D24411yescharacteristic
409D4C2×D24411yescharacteristic
410C2×C4—21no—
411C2×C4—21no—
412C2×C4—21no—
413C2×C4—1221no—
414C2×C4—1221no—
415C2×C4—1221no—
416C2×C4—2441no—
417C2×C4—2441no—
418C2×C4—2441no—
419C2×C4—2441no—
420C2×C4—2441no—
421C2×C4C23×D6111yescharacteristic
422C8—21no—
423C8—21no—
424C8—1221no—
425C8—1221no—
426C8C2×D24411yescharacteristic
427C8C2×D24411yescharacteristic
428C8D4×D6111yescharacteristic
429C8D4×D6111yescharacteristic
430C22—21no—
431C22—21no—
432C22—1221no—
433C22—1221no—
434C22—9761no—
435C22—9761no—
436C22—9761no—
437C22—4881no—
438C22—4881no—
439C22—4881no—
440C22—2441no—
441C22—2441no—
442C22—2441no—
443C22#1451982311yescharacteristic
444C4—21no—
445C4—21no—
446C4—41no—
447C4—1221no—
448C4—1221no—
449C4—2441no—
450C4C2×D4×D6111yescharacteristic
451C4C22×D24411yescharacteristic
452C2—21no—
453C2—41no—
454C2—41no—
455C2—4881no—
456C2—4881no—
457C2—4881no—
458C2—2441no—
459C2—2441no—
460C2D4×D24411yescharacteristic
subgroupG/H
centerC2D4×D244
commutatorC2×C4×C61C24
FrattiniC2×C4C23×D61
FittingC61×#444C2
socleC2×C61D42
hypercenter#444D61
hypocenterC61#3288
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C2 ◁ C2×C4 ◁ #444

Complements

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

NH ≅ G/Ntype
1. #16840574C2semidirect
2. #16840569C2semidirect
3. #16840567C2semidirect
4. #16840564C2semidirect
5. #16840151C2semidirect
6. #16840033C2semidirect
7. #16840032C2semidirect
8. #16840026C2semidirect
9. #16840025C2semidirect
10. #16839941C2semidirect
11. #16839936C2semidirect
12. #16839931C2semidirect
13. #16839931C2semidirect
14. #16839885C2semidirect
15. C61×#444C2semidirect
16. #14519824C22semidirect
18. #14519823C22semidirect
19. #14519823C22semidirect
21. #14519810C22semidirect
23. #14519807C22semidirect
28. #14519805C22semidirect
29. #14519805C22semidirect
33. #14519802C22semidirect
34. #14519802C22semidirect
42. C2×#11758190C22semidirect
43. C2×#11758190C22semidirect
46. C2×D488C22semidirect
47. C2×D488C22semidirect
49. #14519783C22semidirect
50. #14519783C22semidirect
51. #14519774C22semidirect
52. #14519765C22semidirect
53. #14519713C22semidirect
54. #14519705C22semidirect
55. #14519705C22semidirect
56. #14519695C22semidirect
57. #14519693C22semidirect
58. #14519693C22semidirect
59. #14519693C22semidirect
61. #131×C61C22semidirect
62. #131×C61C22semidirect
63. #108×C61C22semidirect
64. #104×C61C22semidirect
65. #104×C61C22semidirect
66. #97×C61C22semidirect
96. Q16×C61D4semidirect
97. SD16×C61D4semidirect
98. SD16×C61D4semidirect
99. D8×C61D4semidirect
121. Dic244D4semidirect
129. D488D4semidirect
138. #11758190D4semidirect
139. #11758190D4semidirect
245. #444D61semidirect
246. C61#3288semidirect
283. #131C2×D61semidirect
284. #131C2×D61semidirect
288. #108C2×D61semidirect
291. #104C2×D61semidirect
292. #104C2×D61semidirect
297. #97C2×D61semidirect
330. Q16D244semidirect
345. SD16D244semidirect
346. SD16D244semidirect
358. D8D244semidirect