Finite Group Databasebeta

← #24918533

Subgroups — #24918533

Order 10624.

396 conjugacy classes of subgroups.

The subgroup lattice has 382 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19128311C211yesmaximal, characteristic, complemented
2#19128265C211yesmaximal, characteristic
3#19128094C211yesmaximal, characteristic, complemented
4#19128072C211yesmaximal, characteristic, complemented
5#19128064C211yesmaximal, characteristic, complemented
6#19128057C211yesmaximal, characteristic, complemented
7#19127926C211yesmaximal, characteristic, complemented
8#19127925C211yesmaximal, characteristic, complemented
9#19127900C211yesmaximal, characteristic, complemented
10#19127899C211yesmaximal, characteristic, complemented
11#19127863C211yesmaximal, characteristic, complemented
12#19127854C211yesmaximal, characteristic, complemented
13#19127851C211yesmaximal, characteristic, complemented
14#19127759C211yesmaximal, characteristic, complemented
15#452×C83C211yesmaximal, characteristic, complemented
16C22×D332C2211yescharacteristic
17C2×#13050580C2211yescharacteristic, complemented
18C2×#13050579C2211yescharacteristic
19C2×#13050579C2211yescharacteristic
20C2×#13050578C2211yescharacteristic, complemented
21C2×#13050577C2211yescharacteristic
22C2×#13050577C2211yescharacteristic
23#14581790C2211yescharacteristic, complemented
24#14581788C2211yescharacteristic
25#14581788C2211yescharacteristic
26#14581785—21no—
27#14581785—21no—
28#14581783—21no—
29#14581783C2211yescharacteristic, complemented
30#14581782—21no—
31#14581781C2211yescharacteristic
32#14581781C2211yescharacteristic
33#14581771C2211yescharacteristic
34#14581766—21no—
35#14581766—21no—
36#14581760—21no—
37#14581760—21no—
38Q8×Dic83C2211yescharacteristic, complemented
39#14581757C2211yescharacteristic, complemented
40#14581751C2211yescharacteristic
41Dic83⋊C8C2211yescharacteristic, complemented
42Dic83⋊C8C2211yescharacteristic, complemented
43#14581716C2211yescharacteristic, complemented
44#14581714C2211yescharacteristic
45#14581714C2211yescharacteristic
46#14581713C2211yescharacteristic, complemented
47#14581712C2211yescharacteristic
48#14581712C2211yescharacteristic
49C22⋊(C83⋊C8)C2211yescharacteristic
50#14581702C2211yescharacteristic, complemented
51C8×Dic83C2211yescharacteristic, complemented
52C2×#41×C83C2211yescharacteristic
53C2×Q16×C83C2211yescharacteristic, complemented
54C2×SD16×C83C2211yescharacteristic, complemented
55C22⋊Q8×C83C2211yescharacteristic
56#103×C83C2211yescharacteristic, complemented
57#102×C83C2211yescharacteristic, complemented
58C22⋊C8×C83C2211yescharacteristic
59C23×D83—21no—
60C2×Dic166C2311yescharacteristic
61C2×D332—21no—
62C2×D332—41no—
63C2×D332—41no—
64C2×D332C2311yescharacteristic
65C2×D332C2311yescharacteristic
66C2×C22⋊D83—21no—
67C2×C22⋊D83—21no—
68C2×C22⋊D83—21no—
69C2×C22⋊D83—21no—
70#13050580—41no—
71#13050579—41no—
72#13050579—41no—
73#13050578—41no—
74#13050577—41no—
75#13050577—41no—
76C2×C83⋊C8C2311yescharacteristic
77C2×C83⋊C8C2311yescharacteristic
78C4⋊Dic83—21no—
79C4⋊Dic83—21no—
80C4⋊Dic83D411yescharacteristic
81C4⋊Dic83D411yescharacteristic
82C4⋊Dic83C2311yescharacteristic
83Dic83⋊C4—21no—
84Dic83⋊C4—21no—
85Dic83⋊C4—21no—
86Dic83⋊C4—21no—
87Dic83⋊C4—21no—
88C22⋊Dic83—21no—
89C22⋊Dic83D411yescharacteristic
90C22⋊Dic83D411yescharacteristic
91(C2×D83)⋊C4—21no—
92(C2×D83)⋊C4—21no—
93(C2×D83)⋊C4—21no—
94(C2×D83)⋊C4—21no—
95C4×Dic83—21no—
96C4×Dic83—21no—
97C4×Dic83C2311yescharacteristic
98C4×Dic83C2311yescharacteristic
99#41×C83—41no—
100#41×C83—41no—
101C2×Q8×C83C2311yescharacteristic
102C2×Q8×C83C2311yescharacteristic
103C2×D4×C83—21no—
104C2×D4×C83C2311yescharacteristic
105C22×C4×C83—21no—
106C22×C4×C83C2311yescharacteristic
107Q16×C83—41no—
108SD16×C83—41no—
109C2×C8×C83C2311yescharacteristic
110C2×C8×C83C2311yescharacteristic
111C4⋊C4×C83—21no—
112C4⋊C4×C83C2311yescharacteristic
113C22⋊C4×C83—21no—
114C23×C83—21no—
115C23×C83C2×D411yescharacteristic
116C22×D83—21no—
117C22×D83—21no—
118C22×D83—42no—
119C22×D83—81no—
120C22×D83—81no—
121Q8×C83—21no—
122Q8×C83—21no—
123Q8×C83—21no—
124Q8×C83—21no—
125D4×C83—21no—
126D4×C83—21no—
127D4×C83—42no—
128C2×C4×C83—21no—
129C2×C4×C83—21no—
130C2×C4×C83—21no—
131C2×C4×C83—21no—
132C2×C4×C83—21no—
133C2×C4×C83—42no—
134C2×C4×C83C2×D411yescharacteristic
135C2×C4×C83C2411yescharacteristic
136C22⋊D83—81no—
137C22⋊D83—81no—
138C22⋊D83—81no—
139C22⋊D83—81no—
140C2×Dic83—21no—
141C2×Dic83—21no—
142C2×Dic83C2×D411yescharacteristic
143C2×Dic83C2×D411yescharacteristic
144C2×Dic83C2×D411yescharacteristic
145C2×Dic83C2×D411yescharacteristic
146D332—21no—
147D332—21no—
148D332—21no—
149D332—21no—
150D332—42no—
151Dic166—21no—
152Dic166—21no—
153C8×C83—21no—
154C8×C83—21no—
155C83⋊C8—21no—
156C83⋊C8—21no—
157C22×C83—21no—
158C22×C83—21no—
159C22×C83—21no—
160C22×C83—41no—
161C22×C83—41no—
162C22×C83—41no—
163C22×C83C22×D411yescharacteristic
164C2×D83—41no—
165C2×D83—41no—
166C2×D83—41no—
167C2×D83—41no—
168C2×D83—41no—
169C2×D83—41no—
170C2×D83—84no—
171C4×C83—21no—
172C4×C83—41no—
173C4×C83—41no—
174C4×C83—41no—
175C4×C83H(5,𝔽2)11yescharacteristic
176C4×C83H(5,𝔽2)11yescharacteristic
177Dic83—21no—
178Dic83—21no—
179Dic83—21no—
180Dic83—21no—
181Dic83—41no—
182Dic83—41no—
183C2×C83—41no—
184C2×C83—81no—
185C2×C83#53511yescharacteristic
186C2×C83#57711yescharacteristic
187C2×C83#57711yescharacteristic
188D83—81no—
189D83—81no—
190#3222—831nomaximal, Sylow
191C83#322211yescharacteristic, complemented, Sylow
192#541—831no—
193#535—831no—
194#497—831no—
195#492—831no—
196#490—831no—
197#488—831no—
198#464—831no—
199#464—831no—
200#460—831no—
201#460—831no—
202#452—831no—
203#452D8311yescharacteristic, complemented
204#450—831no—
205#450—831no—
206#433—831no—
207C2×#41C2×D8311yescharacteristic
208C22×D4—831no—
209C2×Q16—831no—
210C2×Q16C2×D8311yescharacteristic, complemented
211C2×SD16—831no—
212C2×SD16—831no—
213C2×SD16—831no—
214C2×SD16—831no—
215C2×SD16—831no—
216C2×SD16C2×D8311yescharacteristic, complemented
217C4⋊Q8—831no—
218#127—831no—
219#127—831no—
220#126—1661no—
221#126—1661no—
222#125—831no—
223#125—1661no—
224#125—1661no—
225#124—831no—
226#124—831no—
227C22⋊Q8—831no—
228C22⋊Q8C2×D8311yescharacteristic
229#121—1661no—
230#121—1661no—
231#120—1661no—
232#120—1661no—
233C4×Q8—831no—
234C4×Q8—831no—
235#117—831no—
236C4⋊C8—831no—
237C4⋊C8—831no—
238#103—831no—
239#103C2×D8311yescharacteristic, complemented
240#102—831no—
241#102—831no—
242#102—831no—
243#102—831no—
244#102—831no—
245#102C2×D8311yescharacteristic, complemented
246C22⋊C8—831no—
247C22⋊C8C2×D8311yescharacteristic
248#97—831no—
249C4×C8—831no—
250C24—1661no—
251#41—41no—
252#41—41no—
253C2×Q8—831no—
254C2×Q8C22×D8311yescharacteristic
255C2×Q8C22×D8311yescharacteristic
256C2×D4—21no—
257C2×D4—3321no—
258C2×D4—3321no—
259C2×D4—831no—
260C2×D4—831no—
261C2×D4—1661no—
262C2×D4—1661no—
263C2×D4—1661no—
264C2×D4—1661no—
265C2×D4—1661no—
266C2×D4C22×D8311yescharacteristic
267C22×C4—21no—
268C22×C4C22×D8311yescharacteristic
269Q16—41no—
270Q16—3321no—
271SD16—41no—
272SD16—3321no—
273SD16—3321no—
274SD16—3321no—
275SD16—3321no—
276SD16—3321no—
277C2×C8—831no—
278C2×C8—831no—
279C2×C8C22×D8311yescharacteristic
280C2×C8C22×D8311yescharacteristic
281C4⋊C4—21no—
282C4⋊C4—831no—
283C4⋊C4—831no—
284C4⋊C4—831no—
285C4⋊C4—1661no—
286C4⋊C4—1661no—
287C4⋊C4—1661no—
288C4⋊C4—1661no—
289C4⋊C4—1661no—
290C4⋊C4—1661no—
291C4⋊C4—1661no—
292C4⋊C4C22×D8311yescharacteristic
293C22⋊C4—21no—
294C22⋊C4—831no—
295C22⋊C4—831no—
296C22⋊C4—1661no—
297C22⋊C4—1661no—
298C22⋊C4—1661no—
299C22⋊C4—1661no—
300C22⋊C4—1661no—
301C42—831no—
302C42—831no—
303C42—1661no—
304C42—1661no—
305C23—21no—
306C23—3322no—
307C23—6641no—
308C23—6641no—
309C23—1661no—
310C23—1661no—
311C23D4×D8311yescharacteristic
312Q8—21no—
313Q8—21no—
314Q8—21no—
315Q8—21no—
316Q8—1661no—
317Q8—1661no—
318D4—21no—
319D4—21no—
320D4—42no—
321D4—3322no—
322D4—6641no—
323D4—6641no—
324D4—6641no—
325D4—6641no—
326D4—1661no—
327D4—1661no—
328D4—1661no—
329D4—1661no—
330C2×C4—21no—
331C2×C4—21no—
332C2×C4—21no—
333C2×C4—21no—
334C2×C4—21no—
335C2×C4—42no—
336C2×C4—831no—
337C2×C4—831no—
338C2×C4—831no—
339C2×C4—831no—
340C2×C4—1661no—
341C2×C4—1661no—
342C2×C4D4×D8311yescharacteristic
343C2×C4C23×D8311yescharacteristic
344C8—21no—
345C8—21no—
346C8—1661no—
347C8—1661no—
348C22—21no—
349C22—21no—
350C22—21no—
351C22—41no—
352C22—41no—
353C22—41no—
354C22—3321no—
355C22—3321no—
356C22—3321no—
357C22—3321no—
358C22—3321no—
359C22—3321no—
360C22—6644no—
361C22C2×D4×D8311yescharacteristic
362C4—21no—
363C4—41no—
364C4—41no—
365C4—41no—
366C4—3321no—
367C4—3321no—
368C4—1661no—
369C4—1661no—
370C4—1661no—
371C4—1661no—
372C4#1458183711yescharacteristic
373C4#1458183711yescharacteristic
374C2—41no—
375C2—81no—
376C2—6641no—
377C2—6641no—
378C2#1912826611yescharacteristic
379C2#1912850811yescharacteristic
380C2#1912851011yescharacteristic
subgroupG/H
centerC22C2×D4×D83
commutator, cosocleC2×C4×C83C24
FrattiniC2×C4C23×D83
Fitting#452×C83C2
socleC22×C83C22×D4
prime radical#19128265C2
hypercenter#452D83
hypocenterC83#3222
LCSG ▷ C2×C4×C83 ▷ C2×C83 ▷ C83
UCSC1 ◁ C22 ◁ C22×C4 ◁ #452

Complements

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

NH ≅ G/Ntype
1. #19128311C2semidirect
3. #19128094C2semidirect
4. #19128072C2semidirect
5. #19128064C2semidirect
6. #19128057C2semidirect
7. #19127926C2semidirect
8. #19127925C2semidirect
9. #19127900C2semidirect
10. #19127899C2semidirect
11. #19127863C2semidirect
12. #19127854C2semidirect
13. #19127851C2semidirect
14. #19127759C2semidirect
15. #452×C83C2semidirect
17. C2×#13050580C22semidirect
20. C2×#13050578C22semidirect
23. #14581790C22semidirect
29. #14581783C22semidirect
38. Q8×Dic83C22semidirect
39. #14581757C22semidirect
41. Dic83⋊C8C22semidirect
42. Dic83⋊C8C22semidirect
43. #14581716C22semidirect
46. #14581713C22semidirect
50. #14581702C22semidirect
51. C8×Dic83C22semidirect
53. C2×Q16×C83C22semidirect
54. C2×SD16×C83C22semidirect
56. #103×C83C22semidirect
57. #102×C83C22semidirect
191. C83#3222semidirect
203. #452D83semidirect
210. C2×Q16C2×D83semidirect
216. C2×SD16C2×D83semidirect
239. #103C2×D83semidirect
245. #102C2×D83semidirect

Maximal subgroups

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

subgroupindex
#191283112
#191282652
#191280942
#191280722
#191280642
#191280572
#191279262
#191279252
#191279002
#191278992
#191278632
#191278542
#191278512
#191277592
#452×C832
#322283