Finite Group Databasebeta

← #24918559

Subgroups — #24918559

Order 10624.

408 conjugacy classes of subgroups.

The subgroup lattice has 394 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19128322C211yesmaximal, characteristic, complemented
2#19128270C211yesmaximal, characteristic, complemented
3#19128090C211yesmaximal, characteristic, complemented
4#19128085C211yesmaximal, characteristic, complemented
5#19128061C211yesmaximal, characteristic, complemented
6#19128048C211yesmaximal, characteristic, complemented
7#19127924C211yesmaximal, characteristic, complemented
8#19127917C211yesmaximal, characteristic, complemented
9#19127902C211yesmaximal, characteristic, complemented
10#19127897C211yesmaximal, characteristic, complemented
11#19127865C211yesmaximal, characteristic, complemented
12#19127854C211yesmaximal, characteristic, complemented
13#19127848C211yesmaximal, characteristic, complemented
14#19127837C211yesmaximal, characteristic, complemented
15#433×C83C211yesmaximal, characteristic, complemented
16C2×#13050590C2211yescharacteristic
17C22×D332C2211yescharacteristic
18C2×Dic332C2211yescharacteristic, complemented
19C2×#13050579C2211yescharacteristic
20C2×#13050579C2211yescharacteristic
21C2×#13050579C2211yescharacteristic, complemented
22C2×#13050579C2211yescharacteristic, complemented
23C2×D664C2211yescharacteristic
24C2×D664C2211yescharacteristic
25C2×D664C2211yescharacteristic, complemented
26#14581792C2211yescharacteristic, complemented
27#14581789C2211yescharacteristic
28#14581789C2211yescharacteristic
29#14581787—21no—
30#14581780C2211yescharacteristic
31#14581780C2211yescharacteristic
32#14581780C2211yescharacteristic, complemented
33#14581778—21no—
34#14581774—21no—
35#14581771C2211yescharacteristic
36#14581770—21no—
37#14581767—21no—
38#14581767—21no—
39#14581766C2211yescharacteristic
40#14581762—21no—
41#14581762—21no—
42C4×Dic166C2211yescharacteristic, complemented
43C4×D332C2211yescharacteristic, complemented
44#14581717C2211yescharacteristic, complemented
45#14581717C2211yescharacteristic, complemented
46#14581714C2211yescharacteristic
47#14581714C2211yescharacteristic
48#14581714C2211yescharacteristic
49#14581714C2211yescharacteristic
50#14581714C2211yescharacteristic, complemented
51#14581714C2211yescharacteristic, complemented
52#117×C83C2211yescharacteristic
53C4⋊C8×C83C2211yescharacteristic, complemented
54C4⋊C8×C83C2211yescharacteristic, complemented
55C22⋊C8×C83C2211yescharacteristic
56C22⋊C8×C83C2211yescharacteristic
57#97×C83C2211yescharacteristic, complemented
58C4×C8×C83C2211yescharacteristic, complemented
59C23×D83—21no—
60#13050590—41no—
61#13050590—41no—
62C2×Dic166—21no—
63C2×Dic166C2311yescharacteristic
64C2×Dic166C2311yescharacteristic
65C2×D332—21no—
66C2×D332—21no—
67C2×D332—21no—
68C2×D332—21no—
69C2×D332—21no—
70C2×D332—41no—
71C2×D332—41no—
72C2×D332C2311yescharacteristic
73C2×D332C2311yescharacteristic
74C2×D332C2311yescharacteristic
75C2×D332C2311yescharacteristic
76C2×C22⋊D83—21no—
77C2×C22⋊D83—21no—
78C2×C4×D83—21no—
79C2×C4×D83—21no—
80Dic332—41no—
81#13050579—41no—
82#13050579—41no—
83#13050579—41no—
84#13050579—41no—
85D664—41no—
86D664—41no—
87D664—41no—
88C4⋊Dic83—21no—
89C4⋊Dic83C2311yescharacteristic
90C4⋊Dic83C2311yescharacteristic
91Dic83⋊C4—21no—
92Dic83⋊C4—21no—
93C22⋊Dic83—21no—
94(C2×D83)⋊C4—21no—
95(C2×D83)⋊C4—21no—
96(C2×D83)⋊C4—21no—
97(C2×D83)⋊C4—21no—
98(C2×D83)⋊C4—21no—
99(C2×D83)⋊C4—21no—
100(C2×D83)⋊C4—21no—
101(C2×D83)⋊C4—21no—
102C4×Dic83—21no—
103C22×C4×C83C2311yescharacteristic
104C2×C8×C83C2311yescharacteristic
105C2×C8×C83C2311yescharacteristic
106C2×C8×C83C2311yescharacteristic
107C2×C8×C83C2311yescharacteristic
108C4⋊C4×C83D411yescharacteristic
109C4⋊C4×C83D411yescharacteristic
110C22⋊C4×C83D411yescharacteristic
111C22⋊C4×C83D411yescharacteristic
112C42×C83C2311yescharacteristic
113C42×C83C2311yescharacteristic
114C23×C83C2×D411yescharacteristic
115C22×D83—21no—
116C22×D83—21no—
117C22×D83—21no—
118C22×D83—21no—
119C22×D83—42no—
120C22×D83—81no—
121C22×D83—81no—
122C2×C4×C83—21no—
123C2×C4×C83—21no—
124C2×C4×C83C2×D411yescharacteristic
125C2×C4×C83C2×D411yescharacteristic
126C2×C4×C83C2×D411yescharacteristic
127C2×C4×C83C2×D411yescharacteristic
128C2×C4×C83C2×D411yescharacteristic
129C2×C4×C83C2411yescharacteristic
130C22⋊D83—42no—
131C22⋊D83—81no—
132C2×Dic83—21no—
133C2×Dic83—21no—
134C2×Dic83—21no—
135C2×Dic83—21no—
136D332—21no—
137D332—21no—
138D332—21no—
139D332—21no—
140D332—21no—
141D332—21no—
142D332—21no—
143D332—21no—
144D332—42no—
145D332—81no—
146D332—81no—
147D332—81no—
148D332—81no—
149C4×D83—42no—
150C4×D83—81no—
151Dic166—21no—
152Dic166—21no—
153Dic166—21no—
154Dic166—21no—
155Dic166—81no—
156C8×C83—21no—
157C8×C83—21no—
158C8×C83—21no—
159C8×C83—21no—
160C22×C83—21no—
161C22×C83—21no—
162C22×C83—21no—
163C22×C83C22×D411yescharacteristic
164C2×D83—41no—
165C2×D83—41no—
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—41no—
175C2×D83—41no—
176C2×D83—84no—
177C4×C83—21no—
178C4×C83—21no—
179C4×C83—21no—
180C4×C83—21no—
181C4×C83—21no—
182C4×C83H(5,𝔽2)11yescharacteristic
183C4×C83H(5,𝔽2)11yescharacteristic
184Dic83—41no—
185Dic83—41no—
186Dic83—41no—
187Dic83—41no—
188C2×C83—41no—
189C2×C83#53511yescharacteristic
190C2×C83#57611yescharacteristic
191C2×C83#57711yescharacteristic
192D83—81no—
193D83—81no—
194D83—81no—
195D83—81no—
196#3224—831nomaximal, Sylow
197C83#322411yescharacteristic, complemented, Sylow
198#542—831no—
199#535—831no—
200#496—831no—
201#495—831no—
202#489—831no—
203#486—831no—
204#464—831no—
205#463—831no—
206#460—831no—
207#459—831no—
208#452—831no—
209#450—831no—
210#449—831no—
211#447—831no—
212#433D8311yescharacteristic, complemented
213C2×#41—831no—
214C22×D4—831no—
215C2×Q16—831no—
216C2×SD16—831no—
217C2×SD16—831no—
218C2×SD16—831no—
219C2×SD16—831no—
220C2×D8—831no—
221C2×D8—831no—
222C2×D8—831no—
223C4⋊Q8—831no—
224#127—831no—
225#127—831no—
226#126—1661no—
227#124—831no—
228#124—831no—
229#124—831no—
230#124—1661no—
231#123—1661no—
232C22⋊Q8—831no—
233C22⋊Q8—1661no—
234#121—831no—
235#121—1661no—
236#121—1661no—
237#120—1661no—
238#120—1661no—
239C4×Q8—831no—
240C4×D4—831no—
241#117C2×D8311yescharacteristic
242C4⋊C8C2×D8311yescharacteristic, complemented
243C4⋊C8C2×D8311yescharacteristic, complemented
244#103—831no—
245#103—831no—
246#102—831no—
247#102—831no—
248#102—831no—
249#102—831no—
250#102—831no—
251#102—831no—
252C22⋊C8C2×D8311yescharacteristic
253C22⋊C8C2×D8311yescharacteristic
254#97C2×D8311yescharacteristic, complemented
255C4×C8C2×D8311yescharacteristic, complemented
256C24—1661no—
257#41—3321no—
258#41—3321no—
259C2×Q8—831no—
260C2×Q8—831no—
261C2×Q8—1661no—
262C2×D4—3321no—
263C2×D4—3321no—
264C2×D4—831no—
265C2×D4—831no—
266C2×D4—831no—
267C2×D4—831no—
268C2×D4—1661no—
269C2×D4—1661no—
270C2×D4—1661no—
271C2×D4—1661no—
272C2×D4—1661no—
273C2×D4—1661no—
274C2×D4—1661no—
275C22×C4—1661no—
276C22×C4—1661no—
277C22×C4C22×D8311yescharacteristic
278Q16—3321no—
279SD16—3321no—
280SD16—3321no—
281SD16—3321no—
282SD16—3321no—
283D8—3321no—
284D8—3321no—
285D8—3321no—
286C2×C8C22×D8311yescharacteristic
287C2×C8C22×D8311yescharacteristic
288C2×C8C22×D8311yescharacteristic
289C2×C8C22×D8311yescharacteristic
290C4⋊C4—831no—
291C4⋊C4—831no—
292C4⋊C4—1661no—
293C4⋊C4—1661no—
294C4⋊C4—1661no—
295C4⋊C4D33211yescharacteristic
296C4⋊C4D33211yescharacteristic
297C22⋊C4—1661no—
298C22⋊C4—1661no—
299C22⋊C4—1661no—
300C22⋊C4—1661no—
301C22⋊C4—1661no—
302C22⋊C4—1661no—
303C22⋊C4—1661no—
304C22⋊C4—1661no—
305C22⋊C4—1661no—
306C22⋊C4D33211yescharacteristic
307C22⋊C4D33211yescharacteristic
308C42—1661no—
309C42C22×D8311yescharacteristic
310C42C22×D8311yescharacteristic
311C23—3322no—
312C23—6641no—
313C23—6641no—
314C23—1661no—
315C23—1661no—
316C23—1661no—
317C23—1661no—
318C23C2×D33211yescharacteristic
319Q8—6641no—
320Q8—1661no—
321Q8—1661no—
322Q8—1661no—
323Q8—1661no—
324D4—3322no—
325D4—3322no—
326D4—6641no—
327D4—6641no—
328D4—6641no—
329D4—6641no—
330D4—6641no—
331D4—1661no—
332D4—1661no—
333D4—1661no—
334D4—1661no—
335D4—1661no—
336D4—1661no—
337D4—1661no—
338D4—1661no—
339C2×C4—21no—
340C2×C4—21no—
341C2×C4—3322no—
342C2×C4—6641no—
343C2×C4—1661no—
344C2×C4—1661no—
345C2×C4—1661no—
346C2×C4—1661no—
347C2×C4C2×D33211yescharacteristic
348C2×C4C2×D33211yescharacteristic
349C2×C4C2×D33211yescharacteristic
350C2×C4C2×D33211yescharacteristic
351C2×C4C2×D33211yescharacteristic
352C2×C4C23×D8311yescharacteristic
353C8—21no—
354C8—21no—
355C8—21no—
356C8—21no—
357C22—21no—
358C22—21no—
359C22—21no—
360C22—3321no—
361C22—3321no—
362C22—3321no—
363C22—3321no—
364C22—3321no—
365C22—3321no—
366C22—3321no—
367C22—3321no—
368C22—3321no—
369C22—3321no—
370C22—3321no—
371C22—3321no—
372C22—6644no—
373C22C22×D33211yescharacteristic
374C4—21no—
375C4—21no—
376C4—21no—
377C4—21no—
378C4—21no—
379C4—3321no—
380C4—3321no—
381C4—3321no—
382C4—3321no—
383C4#1458183811yescharacteristic
384C4#1458183811yescharacteristic
385C2—41no—
386C2—6641no—
387C2—6641no—
388C2—6641no—
389C2—6641no—
390C2#1912827011yescharacteristic
391C2#1912850611yescharacteristic
392C2#1912851311yescharacteristic
subgroupG/H
centerC22C22×D332
commutator, cosocleC2×C4×C83C24
FrattiniC2×C4C23×D83
Fitting#433×C83C2
socleC22×C83C22×D4
hypercenter#433D83
hypocenterC83#3224
LCSG ▷ C2×C4×C83 ▷ C2×C83 ▷ C83
UCSC1 ◁ C22 ◁ #117 ◁ #433

Complements

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

NH ≅ G/Ntype
1. #19128322C2semidirect
2. #19128270C2semidirect
3. #19128090C2semidirect
4. #19128085C2semidirect
5. #19128061C2semidirect
6. #19128048C2semidirect
7. #19127924C2semidirect
8. #19127917C2semidirect
9. #19127902C2semidirect
10. #19127897C2semidirect
11. #19127865C2semidirect
12. #19127854C2semidirect
13. #19127848C2semidirect
14. #19127837C2semidirect
15. #433×C83C2semidirect
18. C2×Dic332C22semidirect
21. C2×#13050579C22semidirect
22. C2×#13050579C22semidirect
25. C2×D664C22semidirect
26. #14581792C22semidirect
32. #14581780C22semidirect
42. C4×Dic166C22semidirect
43. C4×D332C22semidirect
44. #14581717C22semidirect
45. #14581717C22semidirect
50. #14581714C22semidirect
51. #14581714C22semidirect
53. C4⋊C8×C83C22semidirect
54. C4⋊C8×C83C22semidirect
57. #97×C83C22semidirect
58. C4×C8×C83C22semidirect
197. C83#3224semidirect
212. #433D83semidirect
242. C4⋊C8C2×D83semidirect
243. C4⋊C8C2×D83semidirect
254. #97C2×D83semidirect
255. C4×C8C2×D83semidirect

Maximal subgroups

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

subgroupindex
#191283222
#191282702
#191280902
#191280852
#191280612
#191280482
#191279242
#191279172
#191279022
#191278972
#191278652
#191278542
#191278482
#191278372
#433×C832
#322483