Finite Group Databasebeta

← #24918557

Subgroups — #24918557

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#19128088C211yesmaximal, characteristic, complemented
3#19128083C211yesmaximal, characteristic, complemented
4#19128060C211yesmaximal, characteristic, complemented
5#19128047C211yesmaximal, characteristic, complemented
6#19127920C211yesmaximal, characteristic, complemented
7#19127913C211yesmaximal, characteristic, complemented
8#19127898C211yesmaximal, characteristic, complemented
9#19127893C211yesmaximal, characteristic, complemented
10#19127863C211yesmaximal, characteristic, complemented
11#19127852C211yesmaximal, characteristic, complemented
12#19127846C211yesmaximal, characteristic, complemented
13#19127835C211yesmaximal, characteristic, complemented
14#19127762C211yesmaximal, characteristic, complemented
15#535×C83C211yesmaximal, characteristic, complemented
16C2×#13050580C2211yescharacteristic, complemented
17C2×#13050578C2211yescharacteristic
18C2×#13050578C2211yescharacteristic
19C2×#13050578C2211yescharacteristic, complemented
20C2×#13050577C2211yescharacteristic, complemented
21C2×#13050575C2211yescharacteristic
22C2×#13050575C2211yescharacteristic
23C2×#13050575C2211yescharacteristic, complemented
24#14581792C2211yescharacteristic, complemented
25#14581787—21no—
26#14581780C2211yescharacteristic, complemented
27#14581778—21no—
28#14581774—21no—
29#14581771C2211yescharacteristic
30#14581770—21no—
31#14581766C2211yescharacteristic
32C4×Dic166C2211yescharacteristic, complemented
33C4×D332C2211yescharacteristic, complemented
34C4⋊(C83⋊C8)C2211yescharacteristic, complemented
35C4⋊(C83⋊C8)C2211yescharacteristic, complemented
36#14581716C2211yescharacteristic, complemented
37#14581716C2211yescharacteristic, complemented
38#14581713C2211yescharacteristic
39#14581713C2211yescharacteristic
40#14581713C2211yescharacteristic
41#14581713C2211yescharacteristic
42#14581713C2211yescharacteristic, complemented
43#14581713C2211yescharacteristic, complemented
44C22⋊(C83⋊C8)C2211yescharacteristic
45C22⋊(C83⋊C8)C2211yescharacteristic
46#14581703C2211yescharacteristic, complemented
47C4×C83⋊C8C2211yescharacteristic, complemented
48C2×#41×C83C2211yescharacteristic
49C22×D4×C83C2211yescharacteristic
50#127×C83C2211yescharacteristic
51#127×C83C2211yescharacteristic
52#124×C83C2211yescharacteristic
53#124×C83C2211yescharacteristic
54#121×C83—21no—
55#121×C83—21no—
56#120×C83—21no—
57#120×C83—21no—
58#117×C83C2211yescharacteristic
59C2×Dic166—21no—
60C2×Dic166C2311yescharacteristic
61C2×D332C2311yescharacteristic
62C2×C22⋊D83—21no—
63C2×C4×D83—21no—
64#13050580—41no—
65#13050578—41no—
66#13050578—41no—
67#13050578—41no—
68#13050577—41no—
69#13050575—41no—
70#13050575—41no—
71#13050575—41no—
72C2×C83⋊C8C2311yescharacteristic
73C2×C83⋊C8C2311yescharacteristic
74C2×C83⋊C8C2311yescharacteristic
75C2×C83⋊C8C2311yescharacteristic
76C4⋊Dic83—21no—
77C4⋊Dic83C2311yescharacteristic
78C4⋊Dic83C2311yescharacteristic
79Dic83⋊C4—21no—
80Dic83⋊C4—21no—
81C22⋊Dic83—21no—
82(C2×D83)⋊C4—21no—
83(C2×D83)⋊C4—21no—
84(C2×D83)⋊C4—21no—
85(C2×D83)⋊C4—21no—
86C4×Dic83—21no—
87C24×C83—21no—
88#41×C83—41no—
89#41×C83—41no—
90C2×Q8×C83C2311yescharacteristic
91C2×D4×C83—21no—
92C2×D4×C83—21no—
93C2×D4×C83—21no—
94C2×D4×C83—21no—
95C2×D4×C83—21no—
96C2×D4×C83—21no—
97C2×D4×C83—41no—
98C2×D4×C83—41no—
99C2×D4×C83C2311yescharacteristic
100C2×D4×C83C2311yescharacteristic
101C2×D4×C83C2311yescharacteristic
102C22×C4×C83—21no—
103C22×C4×C83C2311yescharacteristic
104C4⋊C4×C83D411yescharacteristic
105C4⋊C4×C83D411yescharacteristic
106C22⋊C4×C83—21no—
107C22⋊C4×C83—21no—
108C22⋊C4×C83—21no—
109C22⋊C4×C83—21no—
110C22⋊C4×C83D411yescharacteristic
111C22⋊C4×C83D411yescharacteristic
112C42×C83C2311yescharacteristic
113C42×C83C2311yescharacteristic
114C23×C83—21no—
115C23×C83—21no—
116C23×C83—21no—
117C23×C83—42no—
118C23×C83—81no—
119C23×C83—81no—
120C23×C83C2×D411yescharacteristic
121C22×D83—21no—
122Q8×C83—21no—
123Q8×C83—21no—
124D4×C83—21no—
125D4×C83—21no—
126D4×C83—21no—
127D4×C83—21no—
128D4×C83—21no—
129D4×C83—21no—
130D4×C83—42no—
131D4×C83—42no—
132D4×C83—81no—
133D4×C83—81no—
134D4×C83—81no—
135D4×C83—81no—
136C2×C4×C83—21no—
137C2×C4×C83—21no—
138C2×C4×C83—21no—
139C2×C4×C83—42no—
140C2×C4×C83C2×D411yescharacteristic
141C2×C4×C83C2×D411yescharacteristic
142C2×C4×C83C2×D411yescharacteristic
143C2×C4×C83C2×D411yescharacteristic
144C2×C4×C83C2×D411yescharacteristic
145C2×C4×C83C2411yescharacteristic
146C22⋊D83—81no—
147C2×Dic83—21no—
148C2×Dic83—21no—
149C2×Dic83—21no—
150D332—21no—
151D332—21no—
152C4×D83—81no—
153Dic166—21no—
154Dic166—21no—
155Dic166—81no—
156C83⋊C8—21no—
157C83⋊C8—21no—
158C83⋊C8—21no—
159C83⋊C8—21no—
160C22×C83—21no—
161C22×C83—21no—
162C22×C83—21no—
163C22×C83—41no—
164C22×C83—41no—
165C22×C83—41no—
166C22×C83—41no—
167C22×C83—41no—
168C22×C83—41no—
169C22×C83—41no—
170C22×C83—41no—
171C22×C83—41no—
172C22×C83—84no—
173C22×C83C22×D411yescharacteristic
174C2×D83—41no—
175C2×D83—41no—
176C2×D83—41no—
177C4×C83—21no—
178C4×C83—21no—
179C4×C83—21no—
180C4×C83—21no—
181C4×C83—21no—
182C4×C83—41no—
183C4×C83H(5,𝔽2)11yescharacteristic
184C4×C83H(5,𝔽2)11yescharacteristic
185Dic83—41no—
186Dic83—41no—
187Dic83—41no—
188C2×C83—41no—
189C2×C83—81no—
190C2×C83—81no—
191C2×C83—81no—
192C2×C83#53511yescharacteristic
193C2×C83#57611yescharacteristic
194C2×C83#57711yescharacteristic
195D83—81no—
196#3224—831nomaximal, Sylow
197C83#322411yescharacteristic, complemented, Sylow
198#542—831no—
199#535D8311yescharacteristic, complemented
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#433—831no—
213C2×#41C2×D8311yescharacteristic
214C22×D4C2×D8311yescharacteristic
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#127C2×D8311yescharacteristic
225#127C2×D8311yescharacteristic
226#126—1661no—
227#124—831no—
228#124—1661no—
229#124C2×D8311yescharacteristic
230#124C2×D8311yescharacteristic
231#123—1661no—
232C22⋊Q8—831no—
233C22⋊Q8—1661no—
234#121—21no—
235#121—21no—
236#121—831no—
237#120—21no—
238#120—21no—
239C4×Q8—831no—
240C4×D4—831no—
241#117C2×D8311yescharacteristic
242C4⋊C8—831no—
243C4⋊C8—831no—
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⋊C8—831no—
253C22⋊C8—831no—
254#97—831no—
255C4×C8—831no—
256C24—21no—
257#41—41no—
258#41—41no—
259C2×Q8—831no—
260C2×Q8—1661no—
261C2×Q8C22×D8311yescharacteristic
262C2×D4—21no—
263C2×D4—21no—
264C2×D4—21no—
265C2×D4—21no—
266C2×D4—21no—
267C2×D4—21no—
268C2×D4—41no—
269C2×D4—41no—
270C2×D4—831no—
271C2×D4—1661no—
272C2×D4C22×D8311yescharacteristic
273C2×D4C22×D8311yescharacteristic
274C2×D4C22×D8311yescharacteristic
275C22×C4—21no—
276C22×C4—1661no—
277C22×C4C22×D8311yescharacteristic
278Q16—3321no—
279SD16—3321no—
280SD16—3321no—
281SD16—3321no—
282SD16—3321no—
283D8—3321no—
284D8—3321no—
285D8—3321no—
286C2×C8—831no—
287C2×C8—831no—
288C2×C8—831no—
289C2×C8—831no—
290C4⋊C4—831no—
291C4⋊C4—831no—
292C4⋊C4—1661no—
293C4⋊C4—1661no—
294C4⋊C4—1661no—
295C4⋊C4C22⋊D8311yescharacteristic
296C4⋊C4C22⋊D8311yescharacteristic
297C22⋊C4—21no—
298C22⋊C4—21no—
299C22⋊C4—21no—
300C22⋊C4—21no—
301C22⋊C4—1661no—
302C22⋊C4—1661no—
303C22⋊C4—1661no—
304C22⋊C4—1661no—
305C22⋊C4—1661no—
306C22⋊C4C22⋊D8311yescharacteristic
307C22⋊C4C22⋊D8311yescharacteristic
308C42—1661no—
309C42C22×D8311yescharacteristic
310C42C22×D8311yescharacteristic
311C23—21no—
312C23—21no—
313C23—21no—
314C23—42no—
315C23—81no—
316C23—81no—
317C23—1661no—
318C23C2×C22⋊D8311yescharacteristic
319Q8—21no—
320Q8—21no—
321Q8—6641no—
322Q8—1661no—
323Q8—1661no—
324D4—21no—
325D4—21no—
326D4—21no—
327D4—21no—
328D4—21no—
329D4—21no—
330D4—42no—
331D4—42no—
332D4—81no—
333D4—81no—
334D4—81no—
335D4—81no—
336D4—6641no—
337D4—1661no—
338D4—1661no—
339C2×C4—21no—
340C2×C4—21no—
341C2×C4—21no—
342C2×C4—42no—
343C2×C4—6641no—
344C2×C4—1661no—
345C2×C4—1661no—
346C2×C4—1661no—
347C2×C4C2×C22⋊D8311yescharacteristic
348C2×C4C2×C22⋊D8311yescharacteristic
349C2×C4C2×C22⋊D8311yescharacteristic
350C2×C4C2×C22⋊D8311yescharacteristic
351C2×C4C2×C22⋊D8311yescharacteristic
352C2×C4C23×D8311yescharacteristic
353C8—1661no—
354C8—1661no—
355C8—1661no—
356C8—1661no—
357C22—21no—
358C22—21no—
359C22—21no—
360C22—41no—
361C22—41no—
362C22—41no—
363C22—41no—
364C22—41no—
365C22—41no—
366C22—41no—
367C22—41no—
368C22—41no—
369C22—84no—
370C22—3321no—
371C22—3321no—
372C22—3321no—
373C22C22×C22⋊D8311yescharacteristic
374C4—21no—
375C4—21no—
376C4—21no—
377C4—21no—
378C4—21no—
379C4—41no—
380C4—3321no—
381C4—3321no—
382C4—3321no—
383C4#1458183711yescharacteristic
384C4#1458183711yescharacteristic
385C2—41no—
386C2—81no—
387C2—81no—
388C2—81no—
389C2—6641no—
390C2#1912826811yescharacteristic
391C2#1912850411yescharacteristic
392C2#1912851211yescharacteristic
subgroupG/H
centerC22C22×C22⋊D83
commutator, cosocleC2×C4×C83C24
FrattiniC2×C4C23×D83
Fitting#535×C83C2
socleC22×C83C22×D4
hypercenter#535D83
hypocenterC83#3224
LCSG ▷ C2×C4×C83 ▷ C2×C83 ▷ C83
UCSC1 ◁ C22 ◁ #117 ◁ #535

Complements

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

NH ≅ G/Ntype
1. #19128322C2semidirect
2. #19128088C2semidirect
3. #19128083C2semidirect
4. #19128060C2semidirect
5. #19128047C2semidirect
6. #19127920C2semidirect
7. #19127913C2semidirect
8. #19127898C2semidirect
9. #19127893C2semidirect
10. #19127863C2semidirect
11. #19127852C2semidirect
12. #19127846C2semidirect
13. #19127835C2semidirect
14. #19127762C2semidirect
15. #535×C83C2semidirect
16. C2×#13050580C22semidirect
19. C2×#13050578C22semidirect
20. C2×#13050577C22semidirect
23. C2×#13050575C22semidirect
24. #14581792C22semidirect
26. #14581780C22semidirect
32. C4×Dic166C22semidirect
33. C4×D332C22semidirect
34. C4⋊(C83⋊C8)C22semidirect
35. C4⋊(C83⋊C8)C22semidirect
36. #14581716C22semidirect
37. #14581716C22semidirect
42. #14581713C22semidirect
43. #14581713C22semidirect
46. #14581703C22semidirect
47. C4×C83⋊C8C22semidirect
197. C83#3224semidirect
199. #535D83semidirect

Maximal subgroups

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

subgroupindex
#191283222
#191280882
#191280832
#191280602
#191280472
#191279202
#191279132
#191278982
#191278932
#191278632
#191278522
#191278462
#191278352
#191277622
#535×C832
#322483