Finite Group Databasebeta

← #24919243

Subgroups — #24919243

Order 10624.

454 conjugacy classes of subgroups.

The subgroup lattice has 454 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19128516C211yesmaximal, characteristic, complemented
2#19128508C211yesmaximal, characteristic, complemented
3#19128504C211yesmaximal, characteristic, complemented
4#19128082C211yesmaximal, characteristic, complemented
5#19127974C211yesmaximal, characteristic, complemented
6#19127969C211yesmaximal, characteristic, complemented
7#19127964C211yesmaximal, characteristic, complemented
8#19127961C211yesmaximal, characteristic, complemented
9#19127879C211yesmaximal, characteristic, complemented
10#19127877C211yesmaximal, characteristic, complemented
11#19127874C211yesmaximal, characteristic, complemented
12#19127872C211yesmaximal, characteristic, complemented
13#19127818C211yesmaximal, characteristic, complemented
14#19127816C211yesmaximal, characteristic, complemented
15#577×C83C211yesmaximal, characteristic, complemented
16#14581839C2211yescharacteristic, complemented
17#14581838C2211yescharacteristic
18#14581824—21no—
19#14581823—21no—
20#14581823C2211yescharacteristic, complemented
21#14581822—21no—
22#14581822C2211yescharacteristic
23#14581822C2211yescharacteristic, complemented
24#14581818—21no—
25#14581818C2211yescharacteristic
26#14581817—21no—
27#14581817C2211yescharacteristic
28#14581817C2211yescharacteristic, complemented
29#14581816—21no—
30#14581813—21no—
31#14581812—21no—
32#14581812—21no—
33#14581812C2211yescharacteristic
34C2×#13050580—21no—
35C2×#13050580C2211yescharacteristic, complemented
36C2×#13050579C2211yescharacteristic, complemented
37SD16×D83—21no—
38C2×#13050575—21no—
39C2×#13050575C2211yescharacteristic
40#14581799C2211yescharacteristic
41#14581799C2211yescharacteristic, complemented
42#14581798C2211yescharacteristic, complemented
43#14581781C2211yescharacteristic, complemented
44#14581779C2211yescharacteristic, complemented
45#14581728C2211yescharacteristic, complemented
46#14581727C2211yescharacteristic, complemented
47#14581719C2211yescharacteristic
48#14581719C2211yescharacteristic, complemented
49#14581719C2211yescharacteristic, complemented
50#14581718C2211yescharacteristic, complemented
51#14581711C2211yescharacteristic, complemented
52#14581710C2211yescharacteristic, complemented
53#14581709C2211yescharacteristic, complemented
54#14581708C2211yescharacteristic, complemented
55C8×Dic83C2211yescharacteristic, complemented
562−1+4×C83C2211yescharacteristic, complemented
57H(5,𝔽2)×C83C2211yescharacteristic
58#137×C83—21no—
59#137×C83C2211yescharacteristic
60AGL(1,ℤ/8)×C83—21no—
61AGL(1,ℤ/8)×C83C2211yescharacteristic, complemented
62#135×C83—21no—
63#135×C83C2211yescharacteristic
64C2×SD16×C83—21no—
65C2×SD16×C83C2211yescharacteristic, complemented
66#131×C83C2211yescharacteristic, complemented
67#13050591—21no—
68#13050590—21no—
69#13050590—21no—
70#13050590C2311yescharacteristic
71#13050589—21no—
72#13050589—41no—
73C2×Dic166—21no—
74C2×Dic166C2311yescharacteristic
75Q8×D83—21no—
76C2×D332—21no—
77C2×D332C2311yescharacteristic
78D4×D83—21no—
79D4×D83—41no—
80#13050580—21no—
81#13050580—21no—
82#13050580—21no—
83#13050580—21no—
84#13050580—21no—
85#13050580D411yescharacteristic
86#13050579—21no—
87#13050579—21no—
88#13050578—21no—
89#13050578—21no—
90#13050578—21no—
91#13050578D411yescharacteristic
92#13050577—21no—
93#13050577—21no—
94#13050577—21no—
95#13050577D411yescharacteristic
96#13050575—21no—
97#13050575—21no—
98#13050575—21no—
99#13050575—21no—
100#13050575—21no—
101#13050575D411yescharacteristic
102#13050574—21no—
103#13050574—21no—
104#13050574C2311yescharacteristic
105#13050574C2311yescharacteristic
106#13050574C2311yescharacteristic
107#13050573—21no—
108C2×C83⋊C8—21no—
109C2×C83⋊C8—21no—
110C2×C83⋊C8C2311yescharacteristic
111C8×D83—21no—
112C22⋊Dic83—41no—
113(C2×D83)⋊C4—41no—
114C4×Dic83C2311yescharacteristic
115#41×C83—21no—
116#41×C83—21no—
117#41×C83—21no—
118#41×C83—21no—
119#41×C83—41no—
120#41×C83C2311yescharacteristic
121#41×C83C2311yescharacteristic
122#41×C83C2311yescharacteristic
123C2×Q8×C83—21no—
124C2×Q8×C83—21no—
125C2×Q8×C83C2311yescharacteristic
126C2×D4×C83—21no—
127C2×D4×C83—21no—
128C2×D4×C83—41no—
129C2×D4×C83C2311yescharacteristic
130Q16×C83—21no—
131Q16×C83D411yescharacteristic
132SD16×C83—21no—
133SD16×C83—21no—
134SD16×C83—21no—
135SD16×C83—21no—
136SD16×C83D411yescharacteristic
137SD16×C83D411yescharacteristic
138D8×C83—21no—
139D8×C83D411yescharacteristic
140M16×C83—21no—
141M16×C83C2311yescharacteristic
142C2×C8×C83—21no—
143C2×C8×C83C2311yescharacteristic
144C23×C83—21no—
145C23×C83—41no—
146C22×D83—21no—
147C22×D83—41no—
148Q8×C83—21no—
149Q8×C83—21no—
150Q8×C83—41no—
151Q8×C83C2×D411yescharacteristic
152Q8×C83C2×D411yescharacteristic
153Q8×C83C2×D411yescharacteristic
154D4×C83—21no—
155D4×C83—21no—
156D4×C83—21no—
157D4×C83—21no—
158D4×C83—21no—
159D4×C83—41no—
160D4×C83—41no—
161D4×C83—41no—
162D4×C83C2×D411yescharacteristic
163D4×C83C2×D411yescharacteristic
164D4×C83C2×D411yescharacteristic
165C2×C4×C83—21no—
166C2×C4×C83—21no—
167C2×C4×C83—21no—
168C2×C4×C83—21no—
169C2×C4×C83—41no—
170C2×C4×C83—41no—
171C2×C4×C83—41no—
172C2×C4×C83C2411yescharacteristic
173C22⋊D83—21no—
174C22⋊D83—41no—
175C22⋊D83—41no—
176C2×Dic83—21no—
177C2×Dic83—21no—
178C2×Dic83—41no—
179D332—21no—
180D332—21no—
181D332—41no—
182D332C2×D411yescharacteristic
183C4×D83—21no—
184C4×D83—41no—
185C4×D83—41no—
186Dic166—21no—
187Dic166—21no—
188Dic166—41no—
189Dic166C2×D411yescharacteristic
190C8×C83—21no—
191C8×C83C2×D411yescharacteristic
192C8×C83C2×D411yescharacteristic
193C83⋊C8—21no—
194C83⋊C8—21no—
195C83⋊C8—21no—
196C83⋊C8C2×D411yescharacteristic
197C83⋊C8C2×D411yescharacteristic
198C22×C83—21no—
199C22×C83—21no—
200C22×C83—21no—
201C22×C83—41no—
202C22×C83—81no—
203C22×C83—161no—
204C22×C83H(5,𝔽2)11yescharacteristic
205C2×D83—21no—
206C2×D83—41no—
207C2×D83—81no—
208C2×D83—161no—
209C4×C83—21no—
210C4×C83—21no—
211C4×C83—21no—
212C4×C83—41no—
213C4×C83C22×D411yescharacteristic
214C4×C83C22×D411yescharacteristic
215Dic83—21no—
216Dic83—41no—
217Dic83—41no—
218C2×C83—21no—
219C2×C83—41no—
220C2×C83—41no—
221C2×C83—41no—
222C2×C83—81no—
223C2×C83D4211yescharacteristic
224D83—41no—
225D83—81no—
226#3290—831nomaximal, Sylow
227C83#329011yescharacteristic, complemented, Sylow
228#578—831no—
229#577—831no—
230#577D8311yescharacteristic, complemented
231#576—831no—
232#495—831no—
233#473—831no—
234#472—831no—
235#471—831no—
236#471—831no—
237#455—831no—
238#455—831no—
239#454—831no—
240#454—831no—
241#443—831no—
242#443—831no—
2432−1+4—831no—
2442−1+4C2×D8311yescharacteristic, complemented
245H(5,𝔽2)—831no—
246H(5,𝔽2)C2×D8311yescharacteristic
247#137—21no—
248#137—831no—
249#137—831no—
250#137—831no—
251#137—1661no—
252#137—1661no—
253#137—1661no—
254#137C2×D8311yescharacteristic
255AGL(1,ℤ/8)—21no—
256AGL(1,ℤ/8)—831no—
257AGL(1,ℤ/8)—831no—
258AGL(1,ℤ/8)—831no—
259AGL(1,ℤ/8)—1661no—
260AGL(1,ℤ/8)—1661no—
261AGL(1,ℤ/8)—1661no—
262AGL(1,ℤ/8)C2×D8311yescharacteristic, complemented
263#135—21no—
264#135—831no—
265#135—1661no—
266#135—1661no—
267#135—1661no—
268#135C2×D8311yescharacteristic
269C2×Q16—831no—
270C2×Q16—1661no—
271C2×SD16—21no—
272C2×SD16—831no—
273C2×SD16—1661no—
274C2×SD16C2×D8311yescharacteristic, complemented
275C2×D8—831no—
276C2×D8—1661no—
277#131—831no—
278#131—831no—
279#131—831no—
280#131C2×D8311yescharacteristic, complemented
281#124—831no—
282#124—831no—
283#108—831no—
284#108—831no—
285#104—831no—
286#104—831no—
287#104—831no—
288#104—831no—
289#101—831no—
290#101—831no—
291#100—831no—
292#100—831no—
293C4×C8—831no—
294#41—21no—
295#41—21no—
296#41—21no—
297#41—21no—
298#41—41no—
299#41—3321no—
300#41—831no—
301#41—1661no—
302#41—1661no—
303#41—1661no—
304#41—1661no—
305#41C22×D8311yescharacteristic
306#41C22×D8311yescharacteristic
307#41C22×D8311yescharacteristic
308C2×Q8—21no—
309C2×Q8—21no—
310C2×Q8—831no—
311C2×Q8—1661no—
312C2×Q8—1661no—
313C2×Q8C22×D8311yescharacteristic
314C2×D4—21no—
315C2×D4—21no—
316C2×D4—41no—
317C2×D4—3321no—
318C2×D4—831no—
319C2×D4—1661no—
320C2×D4—1661no—
321C2×D4C22×D8311yescharacteristic
322Q16—21no—
323Q16—831no—
324Q16—1661no—
325Q16—1661no—
326Q16—1661no—
327Q16—1661no—
328Q16—1661no—
329Q16C22⋊D8311yescharacteristic
330SD16—21no—
331SD16—21no—
332SD16—21no—
333SD16—21no—
334SD16—831no—
335SD16—831no—
336SD16—1661no—
337SD16—1661no—
338SD16—1661no—
339SD16—1661no—
340SD16—1661no—
341SD16—1661no—
342SD16—1661no—
343SD16—1661no—
344SD16C22⋊D8311yescharacteristic
345SD16C22⋊D8311yescharacteristic
346D8—21no—
347D8—831no—
348D8—1661no—
349D8—1661no—
350D8—1661no—
351D8—1661no—
352D8—1661no—
353D8C22⋊D8311yescharacteristic
354M16—21no—
355M16—831no—
356M16—831no—
357M16—831no—
358M16—1661no—
359M16—1661no—
360M16—1661no—
361M16C22×D8311yescharacteristic
362C2×C8—21no—
363C2×C8—831no—
364C2×C8—1661no—
365C2×C8—1661no—
366C2×C8—1661no—
367C2×C8C22×D8311yescharacteristic
368C22⋊C4—3321no—
369C22⋊C4—3321no—
370C42—831no—
371C23—21no—
372C23—41no—
373C23—3321no—
374C23—1661no—
375Q8—21no—
376Q8—21no—
377Q8—41no—
378Q8—3321no—
379Q8—831no—
380Q8—1661no—
381Q8—1661no—
382Q8D4×D8311yescharacteristic
383Q8C2×C22⋊D8311yescharacteristic
384Q8C2×C22⋊D8311yescharacteristic
385D4—21no—
386D4—21no—
387D4—21no—
388D4—21no—
389D4—21no—
390D4—41no—
391D4—41no—
392D4—41no—
393D4—3321no—
394D4—3321no—
395D4—3321no—
396D4—831no—
397D4—1661no—
398D4—1661no—
399D4—1661no—
400D4D4×D8311yescharacteristic
401D4C2×C22⋊D8311yescharacteristic
402D4C2×C22⋊D8311yescharacteristic
403C2×C4—21no—
404C2×C4—21no—
405C2×C4—21no—
406C2×C4—21no—
407C2×C4—41no—
408C2×C4—41no—
409C2×C4—41no—
410C2×C4—3321no—
411C2×C4—3321no—
412C2×C4—3321no—
413C2×C4—1661no—
414C2×C4—1661no—
415C2×C4—1661no—
416C2×C4C23×D8311yescharacteristic
417C8—21no—
418C8—831no—
419C8—831no—
420C8—1661no—
421C8—1661no—
422C8—1661no—
423C8C2×C22⋊D8311yescharacteristic
424C8C2×C22⋊D8311yescharacteristic
425C22—21no—
426C22—21no—
427C22—21no—
428C22—41no—
429C22—81no—
430C22—161no—
431C22—13281no—
432C22—3321no—
433C22—6641no—
434C22—1661no—
435C22#1458183711yescharacteristic
436C4—21no—
437C4—21no—
438C4—21no—
439C4—41no—
440C4—3321no—
441C4—3321no—
442C4—1661no—
443C4C2×D4×D8311yescharacteristic
444C4C22×C22⋊D8311yescharacteristic
445C2—21no—
446C2—41no—
447C2—41no—
448C2—41no—
449C2—81no—
450C2—3321no—
451C2—6641no—
452C2D4×C22⋊D8311yescharacteristic
subgroupG/H
centerC2D4×C22⋊D83
commutator, cosocleC2×C4×C83C24
FrattiniC2×C4C23×D83
Fitting#577×C83C2
socleC2×C83D42
hypercenter#577D83
hypocenterC83#3290
LCSG ▷ C2×C4×C83 ▷ C2×C83 ▷ C83
UCSC1 ◁ C2 ◁ C2×C4 ◁ #577

Complements

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

NH ≅ G/Ntype
1. #19128516C2semidirect
2. #19128508C2semidirect
3. #19128504C2semidirect
4. #19128082C2semidirect
5. #19127974C2semidirect
6. #19127969C2semidirect
7. #19127964C2semidirect
8. #19127961C2semidirect
9. #19127879C2semidirect
10. #19127877C2semidirect
11. #19127874C2semidirect
12. #19127872C2semidirect
13. #19127818C2semidirect
14. #19127816C2semidirect
15. #577×C83C2semidirect
16. #14581839C22semidirect
20. #14581823C22semidirect
23. #14581822C22semidirect
28. #14581817C22semidirect
35. C2×#13050580C22semidirect
36. C2×#13050579C22semidirect
41. #14581799C22semidirect
42. #14581798C22semidirect
43. #14581781C22semidirect
44. #14581779C22semidirect
45. #14581728C22semidirect
46. #14581727C22semidirect
48. #14581719C22semidirect
49. #14581719C22semidirect
50. #14581718C22semidirect
51. #14581711C22semidirect
52. #14581710C22semidirect
53. #14581709C22semidirect
54. #14581708C22semidirect
55. C8×Dic83C22semidirect
56. 2−1+4×C83C22semidirect
61. AGL(1,ℤ/8)×C83C22semidirect
65. C2×SD16×C83C22semidirect
66. #131×C83C22semidirect
227. C83#3290semidirect
230. #577D83semidirect
244. 2−1+4C2×D83semidirect
262. AGL(1,ℤ/8)C2×D83semidirect
274. C2×SD16C2×D83semidirect
280. #131C2×D83semidirect

Maximal subgroups

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

subgroupindex
#191285162
#191285082
#191285042
#191280822
#191279742
#191279692
#191279642
#191279612
#191278792
#191278772
#191278742
#191278722
#191278182
#191278162
#577×C832
#329083