Finite Group Databasebeta

← #24919096

Subgroups — #24919096

Order 10624.

498 conjugacy classes of subgroups.

The subgroup lattice has 418 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14581821C211yesmaximal, characteristic, complemented
2C2×#14581819C211yesmaximal, characteristic, complemented
3#19128363C211yesmaximal, characteristic, complemented
4#19128346C211yesmaximal, characteristic, complemented
5#19128085C211yesmaximal, characteristic, complemented
6#19127960C211yesmaximal, characteristic, complemented
7#19127955C211yesmaximal, characteristic, complemented
8#19127923C211yesmaximal, characteristic, complemented
9#19127916C211yesmaximal, characteristic, complemented
10#19127866C211yesmaximal, characteristic, complemented
11#19127853C211yesmaximal, characteristic, complemented
12#19127847C211yesmaximal, characteristic, complemented
13#19127841C211yesmaximal, characteristic, complemented
14#19127780C211yesmaximal, characteristic, complemented
15C4×SD16×C83C211yesmaximal, characteristic, complemented
16C2×#13050591C2211yescharacteristic
17C2×#13050589C2211yescharacteristic
18C2×Q8×D83C2211yescharacteristic, complemented
19C2×D4×D83C2211yescharacteristic
20#14581821—24no—
21#14581819—24no—
22C2×Dic332C2211yescharacteristic, complemented
23C2×#13050580C2211yescharacteristic, complemented
24C2×#13050579C2211yescharacteristic
25C2×#13050579C2211yescharacteristic, complemented
26C2×#13050578C2211yescharacteristic
27C2×#13050577C2211yescharacteristic
28C2×D664C2211yescharacteristic
29C2×#13050575C2211yescharacteristic
30C2×#13050573C2211yescharacteristic
31C2×#13050573C2211yescharacteristic, complemented
32#14581780—21no—
33#14581780C2211yescharacteristic
34#14581780C2211yescharacteristic, complemented
35#14581776—21no—
36#14581772—21no—
37#14581772C2211yescharacteristic
38#14581772C2211yescharacteristic
39#14581767—21no—
40#14581767C2211yescharacteristic
41#14581767C2211yescharacteristic, complemented
42#14581766—21no—
43#14581762—21no—
44C4×D332—21no—
45C4×D332C2211yescharacteristic
46C2×(C2×D83)⋊C4—21no—
47C4⋊(C83⋊C8)C2211yescharacteristic, complemented
48#14581715C2211yescharacteristic, complemented
49#14581715C2211yescharacteristic, complemented
50#14581712C2211yescharacteristic
51#14581712C2211yescharacteristic, complemented
52(C2×D83)⋊C8C2211yescharacteristic
53(C2×D83)⋊C8C2211yescharacteristic, complemented
54C2×SD16×C83C2211yescharacteristic
55C4×Q8×C83C2211yescharacteristic, complemented
56C4×D4×C83C2211yescharacteristic
57#106×C83C2211yescharacteristic, complemented
58#103×C83C2211yescharacteristic, complemented
59#102×C83C2211yescharacteristic
60C4×C8×C83C2211yescharacteristic, complemented
61C23×D83—21no—
62#13050591—22no—
63#13050591—41no—
64#13050589—22no—
65#13050589—41no—
66C2×Dic166—21no—
67C2×Dic166C2311yescharacteristic
68C2×Dic166C2311yescharacteristic
69Q8×D83—22no—
70Q8×D83—41no—
71C2×D332—21no—
72C2×D332—21no—
73C2×D332—21no—
74C2×D332D411yescharacteristic
75C2×D332C2311yescharacteristic
76C2×D332C2311yescharacteristic
77C2×C22⋊D83—21no—
78C2×C22⋊D83—21no—
79D4×D83—22no—
80D4×D83—41no—
81C22×Dic83—21no—
82C2×C4×D83—21no—
83C2×C4×D83—21no—
84C2×C4×D83C2311yescharacteristic
85C2×C4×D83C2311yescharacteristic
86Dic332—22no—
87#13050580—22no—
88#13050579—41no—
89#13050579—41no—
90#13050578—22no—
91#13050577—22no—
92D664—22no—
93#13050575—22no—
94#13050573—22no—
95#13050573—22no—
96C2×C83⋊C8C2311yescharacteristic
97C2×C83⋊C8C2311yescharacteristic
98C4⋊Dic83—21no—
99C4⋊Dic83—21no—
100C4⋊Dic83D411yescharacteristic
101(C2×D83)⋊C4—21no—
102(C2×D83)⋊C4—21no—
103(C2×D83)⋊C4—21no—
104(C2×D83)⋊C4—21no—
105(C2×D83)⋊C4—21no—
106(C2×D83)⋊C4—21no—
107(C2×D83)⋊C4—21no—
108(C2×D83)⋊C4—21no—
109(C2×D83)⋊C4D411yescharacteristic
110(C2×D83)⋊C4D411yescharacteristic
111C2×Q8×C83C2311yescharacteristic
112C2×D4×C83C2311yescharacteristic
113C22×C4×C83—21no—
114SD16×C83D414yescomplemented
115C2×C8×C83C2311yescharacteristic
116C2×C8×C83C2311yescharacteristic
117C4⋊C4×C83—21no—
118C4⋊C4×C83C2311yescharacteristic
119C4⋊C4×C83C2311yescharacteristic
120C22⋊C4×C83—21no—
121C42×C83—21no—
122C42×C83C2311yescharacteristic
123C23×C83—21no—
124C22×D83—21no—
125C22×D83—21no—
126C22×D83—42no—
127C22×D83—42no—
128C22×D83—81no—
129C22×D83C2×D411yescharacteristic
130C22×D83C2×D411yescharacteristic
131Q8×C83—21no—
132Q8×C83C2×D412yes—
133D4×C83—21no—
134D4×C83C2×D412yes—
135C2×C4×C83—21no—
136C2×C4×C83—21no—
137C2×C4×C83—21no—
138C2×C4×C83—81no—
139C2×C4×C83C2×D411yescharacteristic
140C2×C4×C83C2×D411yescharacteristic
141C2×C4×C83C2411yescharacteristic
142C22⋊D83—42no—
143C22⋊D83—42no—
144C2×Dic83—21no—
145C2×Dic83—21no—
146C2×Dic83—42no—
147C2×Dic83C2×D411yescharacteristic
148C2×Dic83C2×D411yescharacteristic
149D332—21no—
150D332—21no—
151D332—21no—
152D332—21no—
153D332—41no—
154D332—42no—
155D332—42no—
156D332—81no—
157C4×D83—21no—
158C4×D83—21no—
159C4×D83—21no—
160C4×D83—21no—
161C4×D83—42no—
162C4×D83—42no—
163Dic166—21no—
164Dic166—21no—
165Dic166—21no—
166Dic166—21no—
167Dic166—42no—
168C8×C83—21no—
169C8×C83C2×D412yes—
170C83⋊C8—21no—
171C83⋊C8—21no—
172C22×C83—22no—
173C22×C83—41no—
174C22×C83—41no—
175C22×C83C22×D411yescharacteristic
176C2×D83—21no—
177C2×D83—21no—
178C2×D83—21no—
179C2×D83—21no—
180C2×D83—21no—
181C2×D83—21no—
182C2×D83—41no—
183C2×D83—41no—
184C2×D83—41no—
185C2×D83—41no—
186C2×D83—41no—
187C2×D83—41no—
188C2×D83—84no—
189C4×C83—22no—
190C4×C83—21no—
191C4×C83—21no—
192C4×C83—41no—
193C4×C83—41no—
194C4×C83C22×D411yescharacteristic
195C4×C83H(5,𝔽2)11yescharacteristic
196Dic83—21no—
197Dic83—21no—
198Dic83—41no—
199Dic83—41no—
200C2×C83—42no—
201C2×C83D4211yescharacteristic
202C2×C83#57511yescharacteristic
203C2×C83#57711yescharacteristic
204D83—41no—
205D83—41no—
206D83—81no—
207D83—81no—
208#3275—831nomaximal, Sylow
209C83#327511yescharacteristic, complemented, Sylow
210C2×#137—831no—
211C2×AGL(1,ℤ/8)—831no—
212#548—831no—
213#546—831no—
214#495—831no—
215#470—831no—
216#469—831no—
217#464—831no—
218#463—831no—
219#452—831no—
220#450—831no—
221#449—831no—
222#448—831no—
223C4×SD16D8311yescharacteristic, complemented
224#436—831no—
225C2×#41—831no—
226C2×#41—831no—
227C22×Q8—831no—
228C22×D4—831no—
229#137—1664no—
230AGL(1,ℤ/8)—1664no—
231C2×Q16—831no—
232C2×Q16—831no—
233C2×SD16—831no—
234C2×SD16—831no—
235C2×SD16—831no—
236C2×SD16—831no—
237C2×SD16C2×D8311yescharacteristic
238C2×D8—831no—
239C2×D8—831no—
240C2×M16—831no—
241C2×M16—831no—
242#124—831no—
243#124—831no—
244#124—1661no—
245#123—1661no—
246C22⋊Q8—831no—
247C22⋊Q8—831no—
248C22⋊Q8—1661no—
249#121—831no—
250#121—831no—
251#121—1661no—
252#121—1661no—
253#120—1661no—
254C4×Q8C2×D8311yescharacteristic, complemented
255C4×D4—831no—
256C4×D4—1661no—
257C4×D4C2×D8311yescharacteristic
258C2×C22⋊C4—1661no—
259#106C2×D8311yescharacteristic, complemented
260C4⋊C8—831no—
261#103—831no—
262#103—831no—
263#103C2×D8311yescharacteristic, complemented
264#102—831no—
265#102—831no—
266#102C2×D8311yescharacteristic
267C22⋊C8—831no—
268C22⋊C8—831no—
269C4×C8C2×D8311yescharacteristic, complemented
270C24—1661no—
271#41—3321no—
272#41—3321no—
273#41—1662no—
274#41—1662no—
275C2×Q8—3321no—
276C2×Q8—831no—
277C2×Q8—831no—
278C2×Q8—1661no—
279C2×Q8—1662no—
280C2×Q8C22×D8311yescharacteristic
281C2×D4—3321no—
282C2×D4—831no—
283C2×D4—831no—
284C2×D4—831no—
285C2×D4—1661no—
286C2×D4—1661no—
287C2×D4—1661no—
288C2×D4—1661no—
289C2×D4—1661no—
290C2×D4—1662no—
291C2×D4C22×D8311yescharacteristic
292C22×C4—21no—
293C22×C4—831no—
294C22×C4—831no—
295C22×C4—1661no—
296C22×C4—1661no—
297C22×C4—1661no—
298Q16—1662no—
299Q16—1662no—
300SD16—3321no—
301SD16—3321no—
302SD16—1662no—
303SD16—1662no—
304SD16D33214yescomplemented
305D8—1662no—
306D8—1662no—
307M16—1662no—
308M16—1662no—
309C2×C8—831no—
310C2×C8—831no—
311C2×C8C22×D8311yescharacteristic
312C2×C8C22×D8311yescharacteristic
313C4⋊C4—21no—
314C4⋊C4—831no—
315C4⋊C4—1661no—
316C4⋊C4—1661no—
317C4⋊C4C22×D8311yescharacteristic
318C4⋊C4C22×D8311yescharacteristic
319C22⋊C4—21no—
320C22⋊C4—831no—
321C22⋊C4—831no—
322C22⋊C4—1661no—
323C22⋊C4—1661no—
324C22⋊C4—1661no—
325C22⋊C4—1661no—
326C22⋊C4—1661no—
327C22⋊C4—1661no—
328C22⋊C4—1661no—
329C22⋊C4—1661no—
330C42—21no—
331C42C22×D8311yescharacteristic
332C23—21no—
333C23—3322no—
334C23—3322no—
335C23—831no—
336C23—831no—
337C23—6641no—
338C23—1661no—
339C23—1661no—
340Q8—21no—
341Q8—3322no—
342Q8—1661no—
343Q8—1661no—
344Q8—1661no—
345Q8—1661no—
346Q8C2×D33212yes—
347D4—21no—
348D4—3322no—
349D4—3321no—
350D4—3322no—
351D4—3322no—
352D4—3322no—
353D4—6641no—
354D4—1661no—
355D4—1661no—
356D4—1661no—
357D4—1661no—
358D4C2×D33212yes—
359C2×C4—21no—
360C2×C4—21no—
361C2×C4—21no—
362C2×C4—81no—
363C2×C4—3322no—
364C2×C4—3322no—
365C2×C4—3322no—
366C2×C4—831no—
367C2×C4—831no—
368C2×C4—1661no—
369C2×C4—1661no—
370C2×C4—1661no—
371C2×C4—1661no—
372C2×C4—1661no—
373C2×C4—1661no—
374C2×C4D4×D8311yescharacteristic
375C2×C4D4×D8311yescharacteristic
376C2×C4C23×D8311yescharacteristic
377C8—21no—
378C8—1661no—
379C8—1661no—
380C8C2×D33212yes—
381C22—22no—
382C22—41no—
383C22—41no—
384C22—3321no—
385C22—3321no—
386C22—3321no—
387C22—3321no—
388C22—3321no—
389C22—3321no—
390C22—6644no—
391C22—1661no—
392C22—1661no—
393C22—1661no—
394C22—1661no—
395C22—1661no—
396C22—1661no—
397C22C2×D4×D8311yescharacteristic
398C4—22no—
399C4—21no—
400C4—21no—
401C4—41no—
402C4—41no—
403C4—3321no—
404C4—3321no—
405C4—1661no—
406C4—1661no—
407C4C22×D33211yescharacteristic
408C4#1458183811yescharacteristic
409C2—42no—
410C2—3321no—
411C2—3321no—
412C2—6641no—
413C2—6641no—
414C2D4×D33211yescharacteristic
415C2#1912849811yescharacteristic
416C2#1912850711yescharacteristic
subgroupG/H
centerC22C2×D4×D83
commutator, cosocleC2×C4×C83C24
FrattiniC2×C4C23×D83
FittingC4×SD16×C83C2
socleC22×C83C22×D4
hypercenterC4×SD16D83
hypocenterC83#3275
LCSG ▷ C2×C4×C83 ▷ C2×C83 ▷ C83
UCSC1 ◁ C22 ◁ C42 ◁ C4×SD16

Complements

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

NH ≅ G/Ntype
1. C2×#14581821C2semidirect
2. C2×#14581819C2semidirect
3. #19128363C2semidirect
4. #19128346C2semidirect
5. #19128085C2semidirect
6. #19127960C2semidirect
7. #19127955C2semidirect
8. #19127923C2semidirect
9. #19127916C2semidirect
10. #19127866C2semidirect
11. #19127853C2semidirect
12. #19127847C2semidirect
13. #19127841C2semidirect
14. #19127780C2semidirect
15. C4×SD16×C83C2semidirect
18. C2×Q8×D83C22semidirect
22. C2×Dic332C22semidirect
23. C2×#13050580C22semidirect
25. C2×#13050579C22semidirect
31. C2×#13050573C22semidirect
34. #14581780C22semidirect
41. #14581767C22semidirect
47. C4⋊(C83⋊C8)C22semidirect
48. #14581715C22semidirect
49. #14581715C22semidirect
51. #14581712C22semidirect
53. (C2×D83)⋊C8C22semidirect
55. C4×Q8×C83C22semidirect
57. #106×C83C22semidirect
58. #103×C83C22semidirect
60. C4×C8×C83C22semidirect
114. SD16×C83D4semidirect
209. C83#3275semidirect
223. C4×SD16D83semidirect
254. C4×Q8C2×D83semidirect
259. #106C2×D83semidirect
263. #103C2×D83semidirect
269. C4×C8C2×D83semidirect
304. SD16D332semidirect

Maximal subgroups

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

subgroupindex
C2×#145818212
C2×#145818192
#191283632
#191283462
#191280852
#191279602
#191279552
#191279232
#191279162
#191278662
#191278532
#191278472
#191278412
#191277802
C4×SD16×C832
#327583