Finite Group Databasebeta

← #24919099

Subgroups — #24919099

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×#14581825C211yesmaximal, characteristic, complemented
2C2×#14581820C211yesmaximal, characteristic, complemented
3#19128360C211yesmaximal, characteristic, complemented
4#19128347C211yesmaximal, characteristic, complemented
5#19128085C211yesmaximal, characteristic, complemented
6#19127959C211yesmaximal, characteristic, complemented
7#19127954C211yesmaximal, characteristic, complemented
8#19127924C211yesmaximal, characteristic, complemented
9#19127917C211yesmaximal, characteristic, complemented
10#19127865C211yesmaximal, characteristic, complemented
11#19127854C211yesmaximal, characteristic, complemented
12#19127848C211yesmaximal, characteristic, complemented
13#19127842C211yesmaximal, characteristic, complemented
14C4×#13050579C211yesmaximal, characteristic, complemented
15#436×C83C211yesmaximal, characteristic, complemented
16C2×#13050590C2211yescharacteristic
17C2×#13050590C2211yescharacteristic
18C22×Dic166C2211yescharacteristic, complemented
19C22×D332C2211yescharacteristic
20#14581825—24no—
21#14581820—24no—
22C2×Dic332C2211yescharacteristic, complemented
23C2×Dic332C2211yescharacteristic, complemented
24C2×#13050579C2211yescharacteristic
25C2×#13050579C2211yescharacteristic
26C2×#13050579C2211yescharacteristic
27C2×#13050579C2211yescharacteristic
28C2×#13050579C2211yescharacteristic, complemented
29C2×D664C2211yescharacteristic
30C2×D664C2211yescharacteristic
31#14581780C2211yescharacteristic
32#14581780C2211yescharacteristic, complemented
33#14581778—21no—
34#14581777—21no—
35#14581771C2211yescharacteristic
36#14581771C2211yescharacteristic
37#14581770—21no—
38#14581766C2211yescharacteristic
39#14581766C2211yescharacteristic, complemented
40#14581765—21no—
41#14581764—21no—
42#14581760—21no—
43C4×Dic166C2211yescharacteristic, complemented
44C4×D332C2211yescharacteristic
45(C22⋊D83)⋊C4—21no—
46C22⋊C4×D83—21no—
47#14581724C2211yescharacteristic, complemented
48#14581717C2211yescharacteristic, complemented
49#14581717C2211yescharacteristic, complemented
50#14581717C2211yescharacteristic, complemented
51#14581714C2211yescharacteristic
52#14581714C2211yescharacteristic
53#14581714C2211yescharacteristic, complemented
54C2×M16×C83C2211yescharacteristic
55C2×M16×C83C2211yescharacteristic, complemented
56C4×D4×C83C2211yescharacteristic
57C4⋊C8×C83C2211yescharacteristic, complemented
58C22⋊C8×C83C2211yescharacteristic
59C22⋊C8×C83C2211yescharacteristic, complemented
60C4×C8×C83C2211yescharacteristic, complemented
61C23×D83—21no—
62#13050590—22no—
63#13050590—22no—
64#13050590—41no—
65#13050590—41no—
66C2×Dic166—22no—
67C2×Dic166—21no—
68C2×Dic166—41no—
69C2×Dic166C2311yescharacteristic
70C2×Dic166C2311yescharacteristic
71C2×Dic166C2311yescharacteristic
72C2×D332—22no—
73C2×D332—21no—
74C2×D332—41no—
75C2×D332C2311yescharacteristic
76C2×D332C2311yescharacteristic
77C2×D332C2311yescharacteristic
78C2×C22⋊D83—21no—
79C2×C22⋊D83—21no—
80C2×C22⋊D83—21no—
81C2×C22⋊D83—21no—
82C22×Dic83—21no—
83C2×C4×D83—21no—
84C2×C4×D83—21no—
85C2×C4×D83—21no—
86Dic332—22no—
87Dic332—22no—
88#13050579—22no—
89#13050579—22no—
90#13050579—41no—
91#13050579—41no—
92#13050579D414yescomplemented
93D664—22no—
94D664—22no—
95C4⋊Dic83C2311yescharacteristic
96C4⋊Dic83C2311yescharacteristic
97Dic83⋊C4—21no—
98Dic83⋊C4—21no—
99Dic83⋊C4—21no—
100C22⋊Dic83—21no—
101C22⋊Dic83—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—
109C4×Dic83—21no—
110C2×D4×C83D411yescharacteristic
111C22×C4×C83C2311yescharacteristic
112C22×C4×C83C2311yescharacteristic
113M16×C83—22no—
114M16×C83—22no—
115C2×C8×C83C2311yescharacteristic
116C2×C8×C83C2311yescharacteristic
117C2×C8×C83C2311yescharacteristic
118C2×C8×C83C2311yescharacteristic
119C4⋊C4×C83D411yescharacteristic
120C22⋊C4×C83D411yescharacteristic
121C22⋊C4×C83D411yescharacteristic
122C42×C83C2311yescharacteristic
123C23×C83C2×D411yescharacteristic
124C23×C83C2×D411yescharacteristic
125C22×D83—21no—
126C22×D83—21no—
127C22×D83—21no—
128C22×D83—42no—
129C22×D83—42no—
130C22×D83—81no—
131D4×C83—41no—
132C2×C4×C83—21no—
133C2×C4×C83—21no—
134C2×C4×C83—21no—
135C2×C4×C83—21no—
136C2×C4×C83C2×D411yescharacteristic
137C2×C4×C83C2×D411yescharacteristic
138C2×C4×C83C2×D411yescharacteristic
139C2×C4×C83C2×D411yescharacteristic
140C2×C4×C83C2411yescharacteristic
141C22⋊D83—42no—
142C22⋊D83—42no—
143C22⋊D83—42no—
144C22⋊D83—81no—
145C2×Dic83—21no—
146C2×Dic83—21no—
147C2×Dic83—21no—
148C2×Dic83—21no—
149C2×Dic83—21no—
150C2×Dic83—42no—
151D332—21no—
152D332—21no—
153D332—21no—
154D332—21no—
155D332—21no—
156D332—42no—
157D332C2×D412yes—
158C4×D83—42no—
159C4×D83—42no—
160C4×D83—81no—
161Dic166—21no—
162Dic166—21no—
163Dic166—21no—
164Dic166—21no—
165Dic166—21no—
166Dic166—42no—
167Dic166C2×D412yes—
168C8×C83—21no—
169C8×C83—21no—
170C8×C83—21no—
171C8×C83C2×D412yes—
172C22×C83—21no—
173C22×C83—21no—
174C22×C83—21no—
175C22×C83—21no—
176C22×C83—21no—
177C22×C83—21no—
178C22×C83C22×D411yescharacteristic
179C2×D83—22no—
180C2×D83—41no—
181C2×D83—41no—
182C2×D83—41no—
183C2×D83—41no—
184C2×D83—41no—
185C2×D83—41no—
186C2×D83—41no—
187C2×D83—41no—
188C2×D83—84no—
189C4×C83—21no—
190C4×C83—21no—
191C4×C83—21no—
192C4×C83—21no—
193C4×C83C22×D411yescharacteristic
194C4×C83H(5,𝔽2)11yescharacteristic
195Dic83—22no—
196Dic83—41no—
197Dic83—41no—
198Dic83—41no—
199Dic83—41no—
200C2×C83—41no—
201C2×C83—41no—
202C2×C83D4211yescharacteristic
203C2×C83#57511yescharacteristic
204C2×C83#57711yescharacteristic
205D83—42no—
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×SD16—831no—
224#436D8311yescharacteristic, complemented
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×SD16—831no—
238C2×D8—831no—
239C2×D8—831no—
240C2×M16C2×D8311yescharacteristic
241C2×M16C2×D8311yescharacteristic, complemented
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×Q8—831no—
255C4×D4—831no—
256C4×D4—1661no—
257C4×D4C2×D8311yescharacteristic
258C2×C22⋊C4—1661no—
259#106—831no—
260C4⋊C8C2×D8311yescharacteristic, complemented
261#103—831no—
262#103—831no—
263#103—831no—
264#102—831no—
265#102—831no—
266#102—831no—
267C22⋊C8C2×D8311yescharacteristic
268C22⋊C8C2×D8311yescharacteristic, complemented
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—831no—
279C2×Q8—1662no—
280C2×Q8—1661no—
281C2×D4—3321no—
282C2×D4—831no—
283C2×D4—831no—
284C2×D4—831no—
285C2×D4—1662no—
286C2×D4—1661no—
287C2×D4—1661no—
288C2×D4—1661no—
289C2×D4—1661no—
290C2×D4—1661no—
291C2×D4D33211yescharacteristic
292C22×C4—1661no—
293C22×C4—1661no—
294C22×C4—1661no—
295C22×C4—1661no—
296C22×C4C22×D8311yescharacteristic
297C22×C4C22×D8311yescharacteristic
298Q16—1662no—
299Q16—1662no—
300SD16—3321no—
301SD16—3321no—
302SD16—834no—
303SD16—1662no—
304SD16—1662no—
305D8—1662no—
306D8—1662no—
307M16—22no—
308M16—22no—
309C2×C8C22×D8311yescharacteristic
310C2×C8C22×D8311yescharacteristic
311C2×C8C22×D8311yescharacteristic
312C2×C8C22×D8311yescharacteristic
313C4⋊C4—831no—
314C4⋊C4—831no—
315C4⋊C4—1661no—
316C4⋊C4—1661no—
317C4⋊C4—1661no—
318C4⋊C4D33211yescharacteristic
319C22⋊C4—1661no—
320C22⋊C4—1661no—
321C22⋊C4—1661no—
322C22⋊C4—1661no—
323C22⋊C4—1661no—
324C22⋊C4—1661no—
325C22⋊C4—1661no—
326C22⋊C4—1661no—
327C22⋊C4—1661no—
328C22⋊C4D33211yescharacteristic
329C22⋊C4D33211yescharacteristic
330C42—1661no—
331C42C22×D8311yescharacteristic
332C23—3322no—
333C23—3322no—
334C23—6641no—
335C23—1661no—
336C23—1661no—
337C23—1661no—
338C23C2×D33211yescharacteristic
339C23C2×D33211yescharacteristic
340Q8—3322no—
341Q8—832no—
342Q8—1661no—
343Q8—1661no—
344Q8—1661no—
345Q8—1661no—
346Q8—1661no—
347D4—41no—
348D4—3322no—
349D4—3322no—
350D4—3322no—
351D4—3322no—
352D4—832no—
353D4—6641no—
354D4—1661no—
355D4—1661no—
356D4—1661no—
357D4—1661no—
358D4—1661no—
359C2×C4—21no—
360C2×C4—21no—
361C2×C4—21no—
362C2×C4—21no—
363C2×C4—3322no—
364C2×C4—3322no—
365C2×C4—3322no—
366C2×C4—6641no—
367C2×C4—1661no—
368C2×C4—1661no—
369C2×C4—1661no—
370C2×C4—1661no—
371C2×C4—1661no—
372C2×C4C2×D33211yescharacteristic
373C2×C4C2×D33211yescharacteristic
374C2×C4C2×D33211yescharacteristic
375C2×C4C2×D33211yescharacteristic
376C2×C4C23×D8311yescharacteristic
377C8—21no—
378C8—21no—
379C8—21no—
380C8D4×D8312yes—
381C22—21no—
382C22—21no—
383C22—21no—
384C22—21no—
385C22—21no—
386C22—21no—
387C22—3321no—
388C22—3321no—
389C22—3321no—
390C22—3321no—
391C22—3321no—
392C22—3321no—
393C22—3321no—
394C22—3321no—
395C22—6644no—
396C22—1662no—
397C22C22×D33211yescharacteristic
398C4—21no—
399C4—21no—
400C4—21no—
401C4—21no—
402C4—3321no—
403C4—3321no—
404C4—3321no—
405C4—3321no—
406C4—1662no—
407C4C2×D4×D8311yescharacteristic
408C4#1458183811yescharacteristic
409C2—41no—
410C2—41no—
411C2—3322no—
412C2—6641no—
413C2—6641no—
414C2D4×D33211yescharacteristic
415C2#1912850111yescharacteristic
416C2#1912851311yescharacteristic
subgroupG/H
centerC22C22×D332
commutator, cosocleC2×C4×C83C24
FrattiniC2×C4C23×D83
Fitting#436×C83C2
socleC22×C83C22×D4
hypercenter#436D83
hypocenterC83#3275
LCSG ▷ C2×C4×C83 ▷ C2×C83 ▷ C83
UCSC1 ◁ C22 ◁ C4×D4 ◁ #436

Complements

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

NH ≅ G/Ntype
1. C2×#14581825C2semidirect
2. C2×#14581820C2semidirect
3. #19128360C2semidirect
4. #19128347C2semidirect
5. #19128085C2semidirect
6. #19127959C2semidirect
7. #19127954C2semidirect
8. #19127924C2semidirect
9. #19127917C2semidirect
10. #19127865C2semidirect
11. #19127854C2semidirect
12. #19127848C2semidirect
13. #19127842C2semidirect
14. C4×#13050579C2semidirect
15. #436×C83C2semidirect
18. C22×Dic166C22semidirect
22. C2×Dic332C22semidirect
23. C2×Dic332C22semidirect
28. C2×#13050579C22semidirect
32. #14581780C22semidirect
39. #14581766C22semidirect
43. C4×Dic166C22semidirect
47. #14581724C22semidirect
48. #14581717C22semidirect
49. #14581717C22semidirect
50. #14581717C22semidirect
53. #14581714C22semidirect
55. C2×M16×C83C22semidirect
57. C4⋊C8×C83C22semidirect
59. C22⋊C8×C83C22semidirect
60. C4×C8×C83C22semidirect
92. #13050579D4semidirect
209. C83#3275semidirect
224. #436D83semidirect
241. C2×M16C2×D83semidirect
260. C4⋊C8C2×D83semidirect
268. C22⋊C8C2×D83semidirect
269. C4×C8C2×D83semidirect

Maximal subgroups

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

subgroupindex
C2×#145818252
C2×#145818202
#191283602
#191283472
#191280852
#191279592
#191279542
#191279242
#191279172
#191278652
#191278542
#191278482
#191278422
C4×#130505792
#436×C832
#327583