Finite Group Databasebeta

← #24919677

Subgroups — #24919677

Order 10624.

402 conjugacy classes of subgroups.

The subgroup lattice has 372 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19128390C211yesmaximal, characteristic, complemented
2#19128342C211yesmaximal, characteristic
3#19128057C211yesmaximal, characteristic, complemented
4#19128021C211yesmaximal, characteristic, complemented
5#19128004C211yesmaximal, characteristic, complemented
6#19127957C211yesmaximal, characteristic, complemented
7#19127948C211yesmaximal, characteristic, complemented
8#19127926C211yesmaximal, characteristic, complemented
9#19127866C211yesmaximal, characteristic, complemented
10#19127854C211yesmaximal, characteristic, complemented
11#19127788C211yesmaximal, characteristic, complemented
12#19127776C211yesmaximal, characteristic, complemented
13#19127705C211yesmaximal, characteristic, complemented
14#19127701C211yesmaximal, characteristic, complemented
15#485×C83C211yesmaximal, characteristic, complemented
16C2×#13050591C2211yescharacteristic
17C22×D332C2211yescharacteristic
18C2×#13050580C2211yescharacteristic, complemented
19C2×#13050579C2211yescharacteristic
20C2×#13050579C2211yescharacteristic
21C2×#13050574C2211yescharacteristic
22C2×#13050573C2211yescharacteristic, complemented
23#14581785—21no—
24#14581784—21no—
25#14581783C2211yescharacteristic, complemented
26#14581781C2211yescharacteristic
27#14581777—21no—
28#14581774—21no—
29#14581772C2211yescharacteristic, complemented
30#14581771C2211yescharacteristic
31#14581767—21no—
32#14581767C2211yescharacteristic
33#14581762—21no—
34#14581757C2211yescharacteristic, complemented
35#14581754C2211yescharacteristic
36C4×C22⋊D83C2211yescharacteristic
37#14581749—21no—
38C4⋊C4×D83C2211yescharacteristic, complemented
39C22⋊C4×D83—21no—
40#14581723C2211yescharacteristic, complemented
41Dic83⋊C8C2211yescharacteristic, complemented
42#14581716C2211yescharacteristic, complemented
43#14581715C2211yescharacteristic, complemented
44#14581714C2211yescharacteristic
45#14581714C2211yescharacteristic
46#14581712C2211yescharacteristic
47#14581712C2211yescharacteristic
48#14581712C2211yescharacteristic
49#14581712C2211yescharacteristic
50(C2×D83)⋊C8C2211yescharacteristic, complemented
51C8×Dic83C2211yescharacteristic, complemented
52C22⋊Q8×C83C2211yescharacteristic
53#117×C83C2211yescharacteristic
54#107×C83C2211yescharacteristic, complemented
55#106×C83C2211yescharacteristic, complemented
56#103×C83C2211yescharacteristic, complemented
57#103×C83C2211yescharacteristic, complemented
58C22⋊C8×C83C2211yescharacteristic
59C23×D83—21no—
60#13050591—22no—
61#13050591—41no—
62C2×Dic166C2311yescharacteristic
63C2×D332—22no—
64C2×D332—21no—
65C2×D332—21no—
66C2×D332—21no—
67C2×D332—41no—
68C2×D332C2311yescharacteristic
69C2×D332C2311yescharacteristic
70C2×C22⋊D83D411yescharacteristic
71C2×C4×D83—21no—
72C2×C4×D83—21no—
73C2×C4×D83—21no—
74C2×C4×D83C2311yescharacteristic
75#13050580—41no—
76#13050579—22no—
77#13050579—41no—
78#13050574—41no—
79#13050573—41no—
80C2×C83⋊C8C2311yescharacteristic
81C2×C83⋊C8C2311yescharacteristic
82C4⋊Dic83—21no—
83C4⋊Dic83—21no—
84C4⋊Dic83C2311yescharacteristic
85Dic83⋊C4—21no—
86Dic83⋊C4—21no—
87Dic83⋊C4—21no—
88Dic83⋊C4—21no—
89Dic83⋊C4D411yescharacteristic
90C22⋊Dic83—21no—
91C22⋊Dic83D411yescharacteristic
92(C2×D83)⋊C4—21no—
93(C2×D83)⋊C4—21no—
94(C2×D83)⋊C4—21no—
95(C2×D83)⋊C4—21no—
96(C2×D83)⋊C4—21no—
97(C2×D83)⋊C4D411yescharacteristic
98C4×Dic83—21no—
99C4×Dic83C2311yescharacteristic
100C2×Q8×C83C2311yescharacteristic
101C22×C4×C83C2311yescharacteristic
102C2×C8×C83C2311yescharacteristic
103C2×C8×C83C2311yescharacteristic
104C4⋊C4×C83—21no—
105C4⋊C4×C83C2311yescharacteristic
106C4⋊C4×C83C2311yescharacteristic
107C4⋊C4×C83C2311yescharacteristic
108C22⋊C4×C83—21no—
109C22⋊C4×C83—21no—
110C42×C83—21no—
111C23×C83C2×D411yescharacteristic
112C22×D83—21no—
113C22×D83—21no—
114C22×D83—42no—
115C22×D83—42no—
116C22×D83—81no—
117C22×D83C2×D411yescharacteristic
118Q8×C83—21no—
119Q8×C83—21no—
120C2×C4×C83—21no—
121C2×C4×C83—21no—
122C2×C4×C83—21no—
123C2×C4×C83—21no—
124C2×C4×C83—21no—
125C2×C4×C83—21no—
126C2×C4×C83C2×D411yescharacteristic
127C2×C4×C83C2411yescharacteristic
128C22⋊D83—41no—
129C2×Dic83—21no—
130C2×Dic83—21no—
131C2×Dic83C2×D411yescharacteristic
132C2×Dic83C2×D411yescharacteristic
133C2×Dic83C2×D411yescharacteristic
134D332—21no—
135D332—21no—
136D332—21no—
137D332—42no—
138D332—42no—
139D332—81no—
140D332#4112yes—
141C4×D83—21no—
142C4×D83—21no—
143C4×D83—42no—
144C4×D83—42no—
145C4×D83—81no—
146Dic166—21no—
147Dic166—21no—
148C8×C83—21no—
149C8×C83—21no—
150C83⋊C8—21no—
151C83⋊C8—21no—
152C22×C83—21no—
153C22×C83—21no—
154C22×C83—21no—
155C22×C83C22×D411yescharacteristic
156C2×D83—21no—
157C2×D83—22no—
158C2×D83—21no—
159C2×D83—21no—
160C2×D83—41no—
161C2×D83—41no—
162C2×D83—41no—
163C2×D83—41no—
164C2×D83—41no—
165C2×D83—84no—
166C4×C83—21no—
167C4×C83—41no—
168C4×C83—41no—
169C4×C83—41no—
170C4×C83—41no—
171C4×C83C2×#4111yescharacteristic
172C4×C83H(5,𝔽2)11yescharacteristic
173Dic83—21no—
174Dic83—21no—
175Dic83—21no—
176Dic83—41no—
177Dic83—41no—
178C2×C83—41no—
179C2×C83#54611yescharacteristic
180C2×C83#57511yescharacteristic
181C2×C83#57711yescharacteristic
182D83—41no—
183D83—42no—
184D83—81no—
185#3323—831nomaximal, Sylow
186C83#332311yescharacteristic, complemented, Sylow
187#552—831no—
188#546—831no—
189#488—831no—
190#485D8311yescharacteristic, complemented
191#481—831no—
192#478—831no—
193#470—831no—
194#468—831no—
195#464—831no—
196#452—831no—
197#450—831no—
198C4×SD16—831no—
199#436—831no—
200#418—831no—
201#417—831no—
202C2×#41—831no—
203C22×D4—831no—
204C2×Q16—831no—
205C2×SD16—831no—
206C2×SD16—831no—
207C2×M16—831no—
208C2×M16—831no—
209#126—1661no—
210#125—831no—
211#125—1661no—
212#124—831no—
213#123—1661no—
214#123—1661no—
215C22⋊Q8—831no—
216C22⋊Q8—831no—
217C22⋊Q8C2×D8311yescharacteristic
218#121—831no—
219#121—1661no—
220#120—1661no—
221C4×Q8—831no—
222C4×D4—831no—
223C4×D4—831no—
224#117—1661no—
225#117C2×D8311yescharacteristic
226C2×C4⋊C4—831no—
227C2×C22⋊C4—1661no—
228#107C2×D8311yescharacteristic, complemented
229#106—831no—
230#106C2×D8311yescharacteristic, complemented
231C4⋊C8—831no—
232#103—831no—
233#103—831no—
234#103C2×D8311yescharacteristic, complemented
235#103C2×D8311yescharacteristic, complemented
236#102—831no—
237#102—831no—
238#102—831no—
239#102—831no—
240#102—831no—
241#102—831no—
242C22⋊C8—831no—
243C22⋊C8C2×D8311yescharacteristic
244C4×C8—831no—
245C24—1661no—
246#41—3321no—
247#41—1662no—
248C2×Q8—831no—
249C2×Q8C22×D8311yescharacteristic
250C2×D4—3321no—
251C2×D4—831no—
252C2×D4—831no—
253C2×D4—831no—
254C2×D4—1661no—
255C2×D4—1662no—
256C2×D4—1661no—
257C2×D4—1661no—
258C22×C4—831no—
259C22×C4—1661no—
260C22×C4—1661no—
261C22×C4—1661no—
262C22×C4C22×D8311yescharacteristic
263Q16—3321no—
264SD16—3321no—
265SD16—1662no—
266M16—3321no—
267M16—3321no—
268C2×C8—831no—
269C2×C8—831no—
270C2×C8C22×D8311yescharacteristic
271C2×C8C22×D8311yescharacteristic
272C4⋊C4—21no—
273C4⋊C4—831no—
274C4⋊C4—831no—
275C4⋊C4—1661no—
276C4⋊C4—1661no—
277C4⋊C4—1661no—
278C4⋊C4—1661no—
279C4⋊C4—1661no—
280C4⋊C4—1661no—
281C4⋊C4C22×D8311yescharacteristic
282C4⋊C4C22×D8311yescharacteristic
283C4⋊C4C22×D8311yescharacteristic
284C22⋊C4—21no—
285C22⋊C4—21no—
286C22⋊C4—831no—
287C22⋊C4—831no—
288C22⋊C4—1661no—
289C22⋊C4—1661no—
290C22⋊C4—1661no—
291C22⋊C4—1661no—
292C22⋊C4—1661no—
293C22⋊C4—1661no—
294C42—21no—
295C42—831no—
296C42—1661no—
297C23—3322no—
298C23—3322no—
299C23—831no—
300C23—6641no—
301C23—1661no—
302C23—1661no—
303C23D4×D8311yescharacteristic
304Q8—21no—
305Q8—21no—
306Q8—1661no—
307Q8—1661no—
308D4—3322no—
309D4—3322no—
310D4—3321no—
311D4—832no—
312D4—6641no—
313D4—1661no—
314D4—1661no—
315D4—1661no—
316C2×C4—21no—
317C2×C4—21no—
318C2×C4—21no—
319C2×C4—21no—
320C2×C4—21no—
321C2×C4—21no—
322C2×C4—3322no—
323C2×C4—3322no—
324C2×C4—831no—
325C2×C4—831no—
326C2×C4—831no—
327C2×C4—6641no—
328C2×C4—1661no—
329C2×C4—1661no—
330C2×C4—1661no—
331C2×C4—1661no—
332C2×C4D4×D8311yescharacteristic
333C2×C4C23×D8311yescharacteristic
334C8—21no—
335C8—21no—
336C8—1661no—
337C8—1661no—
338C22—21no—
339C22—21no—
340C22—21no—
341C22—3321no—
342C22—3321no—
343C22—3321no—
344C22—3321no—
345C22—3321no—
346C22—6644no—
347C22—1662no—
348C22—1661no—
349C22—1661no—
350C22—1661no—
351C22C2×D4×D8311yescharacteristic
352C4—21no—
353C4—41no—
354C4—41no—
355C4—41no—
356C4—41no—
357C4—3321no—
358C4—3321no—
359C4—1661no—
360C4—1661no—
361C4—1661no—
362C4#41×D8311yescharacteristic
363C4#1458183811yescharacteristic
364C2—41no—
365C2—3322no—
366C2—3321no—
367C2—6641no—
368C2#1912834311yescharacteristic
369C2#1912850011yescharacteristic
370C2#1912850811yescharacteristic
subgroupG/H
centerC22C2×D4×D83
commutator, cosocleC2×C4×C83C24
FrattiniC2×C4C23×D83
Fitting#485×C83C2
socleC22×C83C22×D4
prime radical#19128342C2
hypercenter#485D83
hypocenterC83#3323
LCSG ▷ C2×C4×C83 ▷ C2×C83 ▷ C83
UCSC1 ◁ C22 ◁ C22×C4 ◁ #485

Complements

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

NH ≅ G/Ntype
1. #19128390C2semidirect
3. #19128057C2semidirect
4. #19128021C2semidirect
5. #19128004C2semidirect
6. #19127957C2semidirect
7. #19127948C2semidirect
8. #19127926C2semidirect
9. #19127866C2semidirect
10. #19127854C2semidirect
11. #19127788C2semidirect
12. #19127776C2semidirect
13. #19127705C2semidirect
14. #19127701C2semidirect
15. #485×C83C2semidirect
18. C2×#13050580C22semidirect
22. C2×#13050573C22semidirect
25. #14581783C22semidirect
29. #14581772C22semidirect
34. #14581757C22semidirect
38. C4⋊C4×D83C22semidirect
40. #14581723C22semidirect
41. Dic83⋊C8C22semidirect
42. #14581716C22semidirect
43. #14581715C22semidirect
50. (C2×D83)⋊C8C22semidirect
51. C8×Dic83C22semidirect
54. #107×C83C22semidirect
55. #106×C83C22semidirect
56. #103×C83C22semidirect
57. #103×C83C22semidirect
186. C83#3323semidirect
190. #485D83semidirect
228. #107C2×D83semidirect
230. #106C2×D83semidirect
234. #103C2×D83semidirect
235. #103C2×D83semidirect

Maximal subgroups

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

subgroupindex
#191283902
#191283422
#191280572
#191280212
#191280042
#191279572
#191279482
#191279262
#191278662
#191278542
#191277882
#191277762
#191277052
#191277012
#485×C832
#332383