Finite Group Databasebeta

← #24919486

Subgroups — #24919486

Order 10624.

450 conjugacy classes of subgroups.

The subgroup lattice has 392 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19128391C211yesmaximal, characteristic, complemented
2D4×D332C211yesmaximal, characteristic
3#19128066C211yesmaximal, characteristic, complemented
4#19128026C211yesmaximal, characteristic, complemented
5#19128015C211yesmaximal, characteristic, complemented
6#19128002C211yesmaximal, characteristic, complemented
7#19127947C211yesmaximal, characteristic, complemented
8#19127930C211yesmaximal, characteristic, complemented
9#19127902C211yesmaximal, characteristic, complemented
10#19127854C211yesmaximal, characteristic, complemented
11#19127854C211yesmaximal, characteristic, complemented
12#19127803C211yesmaximal, characteristic, complemented
13#19127707C211yesmaximal, characteristic, complemented
14C2×#14581714C211yesmaximal, characteristic, complemented
15#435×C83C211yesmaximal, characteristic, complemented
16C22×D332C2211yescharacteristic
17C22×D332C2211yescharacteristic
18C2×D4×D83—21no—
19C2×#13050579C2211yescharacteristic
20C2×#13050579C2211yescharacteristic, complemented
21C2×#13050579C2211yescharacteristic, complemented
22#14581789C2211yescharacteristic
23#14581785—21no—
24#14581784C2211yescharacteristic, complemented
25#14581782—21no—
26#14581773—21no—
27#14581771C2211yescharacteristic, complemented
28#14581771C2211yescharacteristic, complemented
29#14581767—21no—
30#14581766C2211yescharacteristic
31#14581766C2211yescharacteristic
32#14581762—21no—
33#14581762—21no—
34C4×Dic166C2211yescharacteristic, complemented
35C4×D332C2211yescharacteristic
36#14581751C2211yescharacteristic, complemented
37#14581748—21no—
38C2×C4⋊Dic83C2211yescharacteristic, complemented
39#14581726C2211yescharacteristic, complemented
40#14581726C2211yescharacteristic, complemented
41#14581724C2211yescharacteristic, complemented
42#14581717C2211yescharacteristic, complemented
43#14581714C2211yescharacteristic
44#14581714C2211yescharacteristic
45#14581714C2211yescharacteristic
46#14581714C2211yescharacteristic, complemented
47#14581714C2211yescharacteristic, complemented
48#14581714C2211yescharacteristic, complemented
49#14581714C2211yescharacteristic, complemented
50#14581714C2211yescharacteristic, complemented
51#14581714C2211yescharacteristic, complemented
52C2×M16×C83C2211yescharacteristic, complemented
53C22×C8×C83C2211yescharacteristic, complemented
54C4×D4×C83C2211yescharacteristic
55C4⋊C8×C83C2211yescharacteristic, complemented
56C22⋊C8×C83C2211yescharacteristic, complemented
57C22⋊C8×C83C2211yescharacteristic, complemented
58#97×C83C2211yescharacteristic, complemented
59C23×D83—21no—
60C23×D83—21no—
61C2×Dic166C2311yescharacteristic
62C2×D332—22no—
63C2×D332—22no—
64C2×D332—21no—
65C2×D332—21no—
66C2×D332—21no—
67C2×D332—21no—
68C2×D332—41no—
69C2×D332—41no—
70C2×D332C2311yescharacteristic
71C2×D332C2311yescharacteristic
72C2×D332C2311yescharacteristic
73C2×C22⋊D83—21no—
74C2×C22⋊D83—21no—
75D4×D83—44no—
76C22×Dic83—21no—
77C2×C4×D83—21no—
78#13050579—22no—
79#13050579—41no—
80#13050579—41no—
81C4⋊Dic83—21no—
82C4⋊Dic83C2311yescharacteristic
83C4⋊Dic83C2311yescharacteristic
84C4⋊Dic83C2311yescharacteristic
85C4⋊Dic83C2311yescharacteristic
86Dic83⋊C4—21no—
87Dic83⋊C4—21no—
88Dic83⋊C4—21no—
89Dic83⋊C4—21no—
90Dic83⋊C4—21no—
91C22⋊Dic83—21no—
92C22⋊Dic83—21no—
93C22⋊Dic83—21no—
94(C2×D83)⋊C4—21no—
95(C2×D83)⋊C4—21no—
96(C2×D83)⋊C4—21no—
97C4×Dic83—21no—
98C4×Dic83—21no—
99C2×D4×C83D411yescharacteristic
100C22×C4×C83C2311yescharacteristic
101C22×C4×C83C2311yescharacteristic
102M16×C83—41no—
103C2×C8×C83—41no—
104C2×C8×C83C2311yescharacteristic
105C2×C8×C83C2311yescharacteristic
106C2×C8×C83C2311yescharacteristic
107C2×C8×C83C2311yescharacteristic
108C4⋊C4×C83D411yescharacteristic
109C22⋊C4×C83D411yescharacteristic
110C22⋊C4×C83D411yescharacteristic
111C42×C83C2311yescharacteristic
112C23×C83C2×D411yescharacteristic
113C23×C83C2×D411yescharacteristic
114C22×D83—21no—
115C22×D83—21no—
116C22×D83—21no—
117C22×D83—42no—
118C22×D83—42no—
119C22×D83—42no—
120C22×D83—42no—
121C22×D83—81no—
122C22×D83—81no—
123D4×C83—22no—
124C2×C4×C83—21no—
125C2×C4×C83—21no—
126C2×C4×C83—21no—
127C2×C4×C83—21no—
128C2×C4×C83C2×D411yescharacteristic
129C2×C4×C83C2×D411yescharacteristic
130C2×C4×C83C2×D411yescharacteristic
131C2×C4×C83C2×D411yescharacteristic
132C2×C4×C83C2411yescharacteristic
133C22⋊D83—42no—
134C22⋊D83—42no—
135C2×Dic83—21no—
136C2×Dic83—21no—
137C2×Dic83—21no—
138C2×Dic83—21no—
139C2×Dic83—21no—
140C2×Dic83—42no—
141D332—21no—
142D332—21no—
143D332—21no—
144D332—21no—
145D332—21no—
146D332—42no—
147D332—42no—
148D332—42no—
149D332—81no—
150D332#4112yes—
151C4×D83—42no—
152Dic166—21no—
153Dic166—21no—
154C8×C83—21no—
155C8×C83—21no—
156C8×C83—21no—
157C8×C83—21no—
158C22×C83—21no—
159C22×C83—21no—
160C22×C83—21no—
161C22×C83—21no—
162C22×C83—21no—
163C22×C83AGL(1,ℤ/8)12yes—
164C22×C83C22×D411yescharacteristic
165C2×D83—22no—
166C2×D83—41no—
167C2×D83—41no—
168C2×D83—41no—
169C2×D83—41no—
170C2×D83—41no—
171C2×D83—41no—
172C2×D83—41no—
173C2×D83—41no—
174C2×D83—84no—
175C2×D83—84no—
176C4×C83—21no—
177C4×C83—21no—
178C4×C83—21no—
179C4×C83—21no—
180C4×C83C2×#4111yescharacteristic
181C4×C83H(5,𝔽2)11yescharacteristic
182Dic83—41no—
183Dic83—41no—
184Dic83—41no—
185Dic83—41no—
186Dic83—41no—
187C2×C83—22no—
188C2×C83—41no—
189C2×C83#54611yescharacteristic
190C2×C83C2×AGL(1,ℤ/8)11yescharacteristic
191C2×C83#57711yescharacteristic
192D83—42no—
193D83—81no—
194D83—81no—
195#3310—831nomaximal, Sylow
196C83#331011yescharacteristic, complemented, Sylow
197#552—831no—
198D42—831no—
199#490—831no—
200#482—831no—
201#480—831no—
202#478—831no—
203#468—831no—
204#465—831no—
205#460—831no—
206#450—831no—
207#450—831no—
208#440—831no—
209#435D8311yescharacteristic, complemented
210#418—831no—
211C2×#102—831no—
212C22×D4—831no—
213C22×D4—831no—
214C22×D4—1661no—
215C2×SD16—831no—
216C2×SD16—831no—
217C2×SD16—831no—
218C2×M16C2×D8311yescharacteristic, complemented
219C22×C8C2×D8311yescharacteristic, complemented
220#127—831no—
221#126—1661no—
222#125—831no—
223#125—1661no—
224#123—1661no—
225C22⋊Q8—831no—
226C22⋊Q8—831no—
227#121—831no—
228#121—831no—
229#121—1661no—
230#120—1661no—
231#120—1661no—
232C4×Q8—831no—
233C4×D4—831no—
234C4×D4C2×D8311yescharacteristic
235#117—831no—
236#117—1661no—
237C2×C4⋊C4—831no—
238#107—831no—
239#107—831no—
240#106—831no—
241C4⋊C8C2×D8311yescharacteristic, complemented
242#103—831no—
243#102—831no—
244#102—831no—
245#102—831no—
246#102—831no—
247#102—831no—
248#102—831no—
249#102—831no—
250#102—831no—
251#102—831no—
252C22⋊C8C2×D8311yescharacteristic, complemented
253C22⋊C8C2×D8311yescharacteristic, complemented
254#97C2×D8311yescharacteristic, complemented
255C24—1661no—
256C24—1661no—
257C2×Q8—831no—
258C2×D4—3321no—
259C2×D4—3321no—
260C2×D4—3324no—
261C2×D4—831no—
262C2×D4—831no—
263C2×D4—831no—
264C2×D4—1662no—
265C2×D4—1662no—
266C2×D4—1661no—
267C2×D4—1661no—
268C2×D4—1661no—
269C2×D4—1661no—
270C2×D4—1661no—
271C2×D4—1661no—
272C2×D4D33211yescharacteristic
273C22×C4—1661no—
274C22×C4—1661no—
275C22×C4C22×D8311yescharacteristic
276C22×C4C22×D8311yescharacteristic
277SD16—3321no—
278SD16—3321no—
279SD16—1662no—
280M16—41no—
281C2×C8—41no—
282C2×C8C22×D8311yescharacteristic
283C2×C8C22×D8311yescharacteristic
284C2×C8C22×D8311yescharacteristic
285C2×C8C22×D8311yescharacteristic
286C4⋊C4—831no—
287C4⋊C4—831no—
288C4⋊C4—831no—
289C4⋊C4—831no—
290C4⋊C4—1661no—
291C4⋊C4—1661no—
292C4⋊C4—1661no—
293C4⋊C4—1661no—
294C4⋊C4—1661no—
295C4⋊C4—1661no—
296C4⋊C4D33211yescharacteristic
297C22⋊C4—1661no—
298C22⋊C4—1661no—
299C22⋊C4—1661no—
300C22⋊C4—1661no—
301C22⋊C4—1661no—
302C22⋊C4—1661no—
303C22⋊C4D33211yescharacteristic
304C22⋊C4D33211yescharacteristic
305C42—1661no—
306C42—1661no—
307C42C22×D8311yescharacteristic
308C23—3322no—
309C23—3322no—
310C23—3322no—
311C23—3322no—
312C23—6641no—
313C23—6641no—
314C23—1661no—
315C23—1661no—
316C23—1661no—
317C23C2×D33211yescharacteristic
318C23C2×D33211yescharacteristic
319Q8—1661no—
320Q8—1661no—
321D4—22no—
322D4—3322no—
323D4—3322no—
324D4—3322no—
325D4—3322no—
326D4—3322no—
327D4—832no—
328D4—6641no—
329D4—1661no—
330D4—1661no—
331D4—1661no—
332D4—1661no—
333D4—1661no—
334C2×C4—21no—
335C2×C4—21no—
336C2×C4—21no—
337C2×C4—21no—
338C2×C4—3322no—
339C2×C4—3322no—
340C2×C4—1661no—
341C2×C4—1661no—
342C2×C4—1661no—
343C2×C4—1661no—
344C2×C4—1661no—
345C2×C4C2×D33211yescharacteristic
346C2×C4C2×D33211yescharacteristic
347C2×C4C2×D33211yescharacteristic
348C2×C4C2×D33211yescharacteristic
349C2×C4C23×D8311yescharacteristic
350C8—21no—
351C8—21no—
352C8—21no—
353C8—21no—
354C22—21no—
355C22—21no—
356C22—21no—
357C22—21no—
358C22—21no—
359C22—3321no—
360C22—3321no—
361C22—3321no—
362C22—3321no—
363C22—3321no—
364C22—3321no—
365C22—3321no—
366C22—3321no—
367C22—6644no—
368C22—6644no—
369C22—1662no—
370C22#1458182012yes—
371C22C22×D33211yescharacteristic
372C4—21no—
373C4—21no—
374C4—21no—
375C4—21no—
376C4—3321no—
377C4—3321no—
378C4—3321no—
379C4—3321no—
380C4—3321no—
381C4#41×D8311yescharacteristic
382C4#1458183711yescharacteristic
383C2—22no—
384C2—41no—
385C2—3322no—
386C2—6641no—
387C2—6641no—
388C2#1912834611yescharacteristic
389C2C2×#1458182011yescharacteristic
390C2#1912851311yescharacteristic
subgroupG/H
centerC22C22×D332
commutator, cosocleC2×C4×C83C24
FrattiniC2×C4C23×D83
Fitting#435×C83C2
socleC22×C83C22×D4
prime radicalD4×D332C2
hypercenter#435D83
hypocenterC83#3310
LCSG ▷ C2×C4×C83 ▷ C2×C83 ▷ C83
UCSC1 ◁ C22 ◁ C4×D4 ◁ #435

Complements

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

NH ≅ G/Ntype
1. #19128391C2semidirect
3. #19128066C2semidirect
4. #19128026C2semidirect
5. #19128015C2semidirect
6. #19128002C2semidirect
7. #19127947C2semidirect
8. #19127930C2semidirect
9. #19127902C2semidirect
10. #19127854C2semidirect
11. #19127854C2semidirect
12. #19127803C2semidirect
13. #19127707C2semidirect
14. C2×#14581714C2semidirect
15. #435×C83C2semidirect
20. C2×#13050579C22semidirect
21. C2×#13050579C22semidirect
24. #14581784C22semidirect
27. #14581771C22semidirect
28. #14581771C22semidirect
34. C4×Dic166C22semidirect
36. #14581751C22semidirect
38. C2×C4⋊Dic83C22semidirect
39. #14581726C22semidirect
40. #14581726C22semidirect
41. #14581724C22semidirect
42. #14581717C22semidirect
46. #14581714C22semidirect
47. #14581714C22semidirect
48. #14581714C22semidirect
49. #14581714C22semidirect
50. #14581714C22semidirect
51. #14581714C22semidirect
52. C2×M16×C83C22semidirect
53. C22×C8×C83C22semidirect
55. C4⋊C8×C83C22semidirect
56. C22⋊C8×C83C22semidirect
57. C22⋊C8×C83C22semidirect
58. #97×C83C22semidirect
196. C83#3310semidirect
209. #435D83semidirect
218. C2×M16C2×D83semidirect
219. C22×C8C2×D83semidirect
241. C4⋊C8C2×D83semidirect
252. C22⋊C8C2×D83semidirect
253. C22⋊C8C2×D83semidirect
254. #97C2×D83semidirect

Maximal subgroups

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

subgroupindex
#191283912
D4×D3322
#191280662
#191280262
#191280152
#191280022
#191279472
#191279302
#191279022
#191278542
#191278032
#191277072
C2×#145817142
#435×C832
#331083