Finite Group Databasebeta

← #21434933

Subgroups — #21434933

Order 7552.

418 conjugacy classes of subgroups.

The subgroup lattice has 396 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#16837913C211yesmaximal, characteristic, complemented
2#16837743C211yesmaximal, characteristic, complemented
3#16837740C211yesmaximal, characteristic, complemented
4#16837726C211yesmaximal, characteristic, complemented
5#16837723C211yesmaximal, characteristic, complemented
6#16837658C211yesmaximal, characteristic, complemented
7#16837653C211yesmaximal, characteristic, complemented
8#16837650C211yesmaximal, characteristic, complemented
9#16837646C211yesmaximal, characteristic, complemented
10#16837564C211yesmaximal, characteristic, complemented
11#16837562C211yesmaximal, characteristic, complemented
12#16837547C211yesmaximal, characteristic, complemented
13#16837545C211yesmaximal, characteristic, complemented
14#16837366C211yesmaximal, characteristic, complemented
15C59×#525C211yesmaximal, characteristic, complemented
16C2×#11745685C2211yescharacteristic
17C2×#11745672C2211yescharacteristic, complemented
18C2×#11745670C2211yescharacteristic, complemented
19C2×#11745671C2211yescharacteristic, complemented
20C2×#11745669C2211yescharacteristic, complemented
21C2×#11745664C2211yescharacteristic
22C2×#11745664C2211yescharacteristic
23#14273710—21no—
24#14273706C2211yescharacteristic
25#14273706C2211yescharacteristic
26#14273701C2211yescharacteristic
27#14273701C2211yescharacteristic
28#14273696—21no—
29C4×C22⋊D59—21no—
30C4×C22⋊D59—21no—
31#14273686C2211yescharacteristic
32#14273660C2211yescharacteristic, complemented
33#14273660C2211yescharacteristic, complemented
34#14273658C2211yescharacteristic, complemented
35#14273658C2211yescharacteristic, complemented
36#14273651C2211yescharacteristic, complemented
37#14273651C2211yescharacteristic, complemented
38#14273650C2211yescharacteristic, complemented
39#14273650C2211yescharacteristic, complemented
40#14273648C2211yescharacteristic, complemented
41#14273648C2211yescharacteristic, complemented
42#14273647C2211yescharacteristic, complemented
43#14273647C2211yescharacteristic, complemented
44C22⋊(C59⋊C8)C2211yescharacteristic
45C22⋊(C59⋊C8)C2211yescharacteristic
46C22⋊(C59⋊C8)C2211yescharacteristic
47C22⋊(C59⋊C8)C2211yescharacteristic
48C2×#41×C59C2211yescharacteristic
49C23×C4×C59C2211yescharacteristic
50#123×C59—21no—
51C22⋊Q8×C59C2211yescharacteristic
52C22⋊Q8×C59C2211yescharacteristic
53#121×C59C2211yescharacteristic
54#121×C59C2211yescharacteristic
55#120×C59—21no—
56C4×D4×C59—21no—
57C4×D4×C59—21no—
58#117×C59C2211yescharacteristic
59C24×C59D411yescharacteristic
60#41×C59—41no—
61#41×C59—41no—
62C2×Q8×C59C2311yescharacteristic
63C2×D4×C59—21no—
64C2×D4×C59—21no—
65C2×D4×C59—21no—
66C2×D4×C59C2311yescharacteristic
67C22×C4×C59—21no—
68C22×C4×C59—41no—
69C22×C4×C59—41no—
70C22×C4×C59D411yescharacteristic
71C22×C4×C59D411yescharacteristic
72C22×C4×C59D411yescharacteristic
73C22×C4×C59C2311yescharacteristic
74C22×C4×C59C2311yescharacteristic
75C22×C4×C59C2311yescharacteristic
76C2×C22⋊D59—21no—
77C2×C22⋊D59—21no—
78C2×C22⋊D59—21no—
79#11745685—41no—
80#11745685—41no—
81C2×D236C2311yescharacteristic
82C2×C4×D59—21no—
83C2×Dic118C2311yescharacteristic
84C4⋊C4×C59—21no—
85C4⋊C4×C59—21no—
86C4⋊C4×C59C2311yescharacteristic
87C4⋊C4×C59C2311yescharacteristic
88C22⋊C4×C59—21no—
89C22⋊C4×C59—21no—
90C22⋊C4×C59—21no—
91C22⋊C4×C59—21no—
92C22⋊C4×C59—21no—
93C42×C59—21no—
94C22⋊Dic59—21no—
95C22⋊Dic59—21no—
96C22⋊Dic59—21no—
97#11745672—41no—
98#11745671—41no—
99#11745670—41no—
100#11745669—41no—
101(C2×D59)⋊C4—21no—
102(C2×D59)⋊C4—21no—
103C4⋊Dic59C2311yescharacteristic
104C4⋊Dic59C2311yescharacteristic
105Dic59⋊C4—21no—
106Dic59⋊C4—21no—
107C4×Dic59—21no—
108#11745664—41no—
109#11745664—41no—
110C2×C59⋊C8C2311yescharacteristic
111C2×C59⋊C8C2311yescharacteristic
112C2×C59⋊C8C2311yescharacteristic
113C2×C59⋊C8C2311yescharacteristic
114C23×C59—21no—
115C23×C59—41no—
116C23×C59—41no—
117C23×C59—41no—
118C23×C59C2×D411yescharacteristic
119C23×C59C2×D411yescharacteristic
120C23×C59C2×D411yescharacteristic
121C22×D59—21no—
122Q8×C59—21no—
123Q8×C59—21no—
124D4×C59—21no—
125D4×C59—21no—
126D4×C59—42no—
127D4×C59—42no—
128D4×C59—42no—
129C2×C4×C59—21no—
130C2×C4×C59—21no—
131C2×C4×C59—21no—
132C2×C4×C59—21no—
133C2×C4×C59—21no—
134C2×C4×C59—21no—
135C2×C4×C59—21no—
136C2×C4×C59—21no—
137C2×C4×C59—21no—
138C2×C4×C59—41no—
139C2×C4×C59—41no—
140C2×C4×C59—41no—
141C2×C4×C59—42no—
142C2×C4×C59C2×D411yescharacteristic
143C2×C4×C59C2×D411yescharacteristic
144C2×C4×C59C2×D411yescharacteristic
145C2×C4×C59C2411yescharacteristic
146C22⋊D59—42no—
147C22⋊D59—42no—
148C22⋊D59—42no—
149C2×Dic59—21no—
150C2×Dic59—21no—
151C2×Dic59—21no—
152D236—21no—
153D236—21no—
154C4×D59—42no—
155Dic118—21no—
156Dic118—21no—
157C59⋊C8—21no—
158C59⋊C8—21no—
159C59⋊C8—21no—
160C59⋊C8—21no—
161C22×C59—21no—
162C22×C59—21no—
163C22×C59—21no—
164C22×C59—21no—
165C22×C59—21no—
166C22×C59—21no—
167C22×C59—21no—
168C22×C59—21no—
169C22×C59—21no—
170C22×C59—44no—
171C22×C59—41no—
172C22×C59—41no—
173C22×C59—41no—
174C22×C59C22×D411yescharacteristic
175C2×D59—41no—
176C2×D59—41no—
177C2×D59—41no—
178C4×C59—21no—
179C4×C59—21no—
180C4×C59—21no—
181C4×C59—41no—
182C4×C59—41no—
183C4×C59—41no—
184C4×C59H(5,𝔽2)11yescharacteristic
185C4×C59H(5,𝔽2)11yescharacteristic
186Dic59—41no—
187Dic59—41no—
188Dic59—41no—
189#3197—591nomaximal, Sylow
190C2×C59—41no—
191C2×C59—41no—
192C2×C59—41no—
193C2×C59—81no—
194C2×C59#53411yescharacteristic
195C2×C59#57511yescharacteristic
196C2×C59#57511yescharacteristic
197D59—81no—
198#525—591no—
199#525D5911yescharacteristic, complemented
200#485—591no—
201#485—591no—
202#482—591no—
203#482—591no—
204#470—591no—
205#469—591no—
206#468—591no—
207#468—591no—
208#452—591no—
209#452—591no—
210#449—591no—
211#449—591no—
212#407—591no—
213C59#319711yescharacteristic, complemented, Sylow
214C2×#41—591no—
215C2×#41C2×D5911yescharacteristic
216C23×C4C2×D5911yescharacteristic
217C2×Q16—591no—
218C2×SD16—591no—
219C2×SD16—591no—
220C2×D8—591no—
221C2×M16—591no—
222C2×M16—591no—
223#123—21no—
224#123—1181no—
225C22⋊Q8—591no—
226C22⋊Q8—591no—
227C22⋊Q8C2×D5911yescharacteristic
228C22⋊Q8C2×D5911yescharacteristic
229#121—591no—
230#121—591no—
231#121C2×D5911yescharacteristic
232#121C2×D5911yescharacteristic
233#120—21no—
234#120—1181no—
235C4×D4—21no—
236C4×D4—21no—
237C4×D4—1181no—
238C4×D4—1181no—
239#117—591no—
240#117C2×D5911yescharacteristic
241#107—591no—
242#107—591no—
243#106—591no—
244#106—591no—
245#103—591no—
246#103—591no—
247#103—591no—
248#103—591no—
249#102—591no—
250#102—591no—
251#102—591no—
252#102—591no—
253C22⋊C8—591no—
254C22⋊C8—591no—
255C22⋊C8—591no—
256C22⋊C8—591no—
257C24C22⋊D5911yescharacteristic
258#41—41no—
259#41—41no—
260#41—2361no—
261#41—2361no—
262C2×Q8—591no—
263C2×Q8C22×D5911yescharacteristic
264C2×D4—21no—
265C2×D4—21no—
266C2×D4—21no—
267C2×D4—591no—
268C2×D4—1181no—
269C2×D4—1181no—
270C2×D4—1181no—
271C2×D4C22×D5911yescharacteristic
272C22×C4—21no—
273C22×C4—41no—
274C22×C4—41no—
275C22×C4—1181no—
276C22×C4C22⋊D5911yescharacteristic
277C22×C4C22⋊D5911yescharacteristic
278C22×C4C22⋊D5911yescharacteristic
279C22×C4C22×D5911yescharacteristic
280C22×C4C22×D5911yescharacteristic
281C22×C4C22×D5911yescharacteristic
282Q16—2361no—
283SD16—2361no—
284SD16—2361no—
285D8—2361no—
286M16—2361no—
287M16—2361no—
288C2×C8—591no—
289C2×C8—591no—
290C2×C8—591no—
291C2×C8—591no—
292C4⋊C4—21no—
293C4⋊C4—21no—
294C4⋊C4—591no—
295C4⋊C4—591no—
296C4⋊C4—1181no—
297C4⋊C4—1181no—
298C4⋊C4C22×D5911yescharacteristic
299C4⋊C4C22×D5911yescharacteristic
300C22⋊C4—21no—
301C22⋊C4—21no—
302C22⋊C4—21no—
303C22⋊C4—21no—
304C22⋊C4—21no—
305C22⋊C4—1181no—
306C22⋊C4—1181no—
307C22⋊C4—1181no—
308C22⋊C4—1181no—
309C22⋊C4—1181no—
310C42—21no—
311C42—1181no—
312C23—21no—
313C23—41no—
314C23—41no—
315C23—41no—
316C23—1181no—
317C23C2×C22⋊D5911yescharacteristic
318C23C2×C22⋊D5911yescharacteristic
319C23C2×C22⋊D5911yescharacteristic
320Q8—21no—
321Q8—21no—
322Q8—1181no—
323Q8—1181no—
324D4—21no—
325D4—21no—
326D4—42no—
327D4—42no—
328D4—42no—
329D4—1181no—
330D4—1181no—
331D4—2362no—
332D4—2362no—
333D4—2362no—
334C2×C4—21no—
335C2×C4—21no—
336C2×C4—21no—
337C2×C4—21no—
338C2×C4—21no—
339C2×C4—21no—
340C2×C4—21no—
341C2×C4—21no—
342C2×C4—21no—
343C2×C4—41no—
344C2×C4—41no—
345C2×C4—41no—
346C2×C4—42no—
347C2×C4—1181no—
348C2×C4—1181no—
349C2×C4—1181no—
350C2×C4—2362no—
351C2×C4C2×C22⋊D5911yescharacteristic
352C2×C4C2×C22⋊D5911yescharacteristic
353C2×C4C2×C22⋊D5911yescharacteristic
354C2×C4C23×D5911yescharacteristic
355C8—1181no—
356C8—1181no—
357C8—1181no—
358C8—1181no—
359C22—21no—
360C22—21no—
361C22—21no—
362C22—21no—
363C22—21no—
364C22—21no—
365C22—21no—
366C22—21no—
367C22—21no—
368C22—44no—
369C22—41no—
370C22—41no—
371C22—41no—
372C22—2361no—
373C22—2361no—
374C22—2361no—
375C22C22×C22⋊D5911yescharacteristic
376C4—21no—
377C4—21no—
378C4—21no—
379C4—41no—
380C4—41no—
381C4—41no—
382C4—2361no—
383C4—2361no—
384C4—2361no—
385C4#1427377211yescharacteristic
386C4#1427377211yescharacteristic
387C2—41no—
388C2—41no—
389C2—41no—
390C2—81no—
391C2—4721no—
392C2#1683796111yescharacteristic
393C2#1683820011yescharacteristic
394C2#1683820011yescharacteristic
subgroupG/H
centerC22C22×C22⋊D59
commutatorC2×C4×C59C24
FrattiniC2×C4C23×D59
FittingC59×#525C2
socleC22×C59C22×D4
hypercenter#525D59
hypocenterC59#3197
LCSG ▷ C2×C4×C59 ▷ C2×C59 ▷ C59
UCSC1 ◁ C22 ◁ C23×C4 ◁ #525

Complements

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

NH ≅ G/Ntype
1. #16837913C2semidirect
2. #16837743C2semidirect
3. #16837740C2semidirect
4. #16837726C2semidirect
5. #16837723C2semidirect
6. #16837658C2semidirect
7. #16837653C2semidirect
8. #16837650C2semidirect
9. #16837646C2semidirect
10. #16837564C2semidirect
11. #16837562C2semidirect
12. #16837547C2semidirect
13. #16837545C2semidirect
14. #16837366C2semidirect
15. C59×#525C2semidirect
17. C2×#11745672C22semidirect
18. C2×#11745670C22semidirect
19. C2×#11745671C22semidirect
20. C2×#11745669C22semidirect
32. #14273660C22semidirect
33. #14273660C22semidirect
34. #14273658C22semidirect
35. #14273658C22semidirect
36. #14273651C22semidirect
37. #14273651C22semidirect
38. #14273650C22semidirect
39. #14273650C22semidirect
40. #14273648C22semidirect
41. #14273648C22semidirect
42. #14273647C22semidirect
43. #14273647C22semidirect
199. #525D59semidirect
213. C59#3197semidirect