Finite Group Databasebeta

← #21436306

Subgroups — #21436306

Order 7552.

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#16838048C211yesmaximal, characteristic
2#16837759C211yesmaximal, characteristic, complemented
3#16837743C211yesmaximal, characteristic, complemented
4#16837720C211yesmaximal, characteristic, complemented
5#16837699C211yesmaximal, characteristic, complemented
6#16837658C211yesmaximal, characteristic, complemented
7#16837650C211yesmaximal, characteristic, complemented
8#16837624C211yesmaximal, characteristic, complemented
9#16837562C211yesmaximal, characteristic, complemented
10#16837552C211yesmaximal, characteristic, complemented
11C4×#11745671C211yesmaximal, characteristic, complemented
12#16837480C211yesmaximal, characteristic, complemented
13#16837406C211yesmaximal, characteristic, complemented
14#16837401C211yesmaximal, characteristic, complemented
15C59×#552C211yesmaximal, characteristic, complemented
16C2×#11745685C2211yescharacteristic
17C22×D236C2211yescharacteristic
18C2×#11745672C2211yescharacteristic, complemented
19C2×#11745671C2211yescharacteristic
20C2×#11745671C2211yescharacteristic
21C2×#11745664C2211yescharacteristic
22C2×#11745664C2211yescharacteristic, complemented
23#14273715C2211yescharacteristic
24#14273712—21no—
25#14273706C2211yescharacteristic
26#14273701C2211yescharacteristic
27#14273700—21no—
28#14273695—21no—
29C4×D236C2211yescharacteristic
30C22⋊C4×D59—21no—
31#14273660C2211yescharacteristic, complemented
32#14273658C2211yescharacteristic, complemented
33#14273658C2211yescharacteristic, complemented
34C4⋊(C59⋊C8)C2211yescharacteristic, complemented
35#14273651C2211yescharacteristic, complemented
36#14273650C2211yescharacteristic, complemented
37#14273650C2211yescharacteristic, complemented
38#14273650C2211yescharacteristic, complemented
39#14273647C2211yescharacteristic
40#14273647C2211yescharacteristic
41#14273647C2211yescharacteristic
42#14273647C2211yescharacteristic
43#14273647C2211yescharacteristic
44#14273647C2211yescharacteristic
45C22⋊(C59⋊C8)C2211yescharacteristic
46C22⋊(C59⋊C8)C2211yescharacteristic, complemented
47C4×C59⋊C8C2211yescharacteristic, complemented
48#126×C59—21no—
49#125×C59—21no—
50#125×C59C2211yescharacteristic, complemented
51#123×C59—21no—
52C22⋊Q8×C59C2211yescharacteristic
53C22⋊Q8×C59C2211yescharacteristic, complemented
54C4×Q8×C59C2211yescharacteristic, complemented
55C4×D4×C59C2211yescharacteristic
56#117×C59—21no—
57#117×C59C2211yescharacteristic
58C2×C4⋊C4×C59C2211yescharacteristic, complemented
59C23×D59—21no—
60C2×Q8×C59C2311yescharacteristic
61C2×D4×C59D411yescharacteristic
62C22×C4×C59—21no—
63C22×C4×C59C2311yescharacteristic
64C22×C4×C59C2311yescharacteristic
65C2×C22⋊D59—21no—
66C2×C22⋊D59—21no—
67#11745685—22no—
68#11745685—41no—
69C2×D236—22no—
70C2×D236—21no—
71C2×D236—41no—
72C2×D236C2311yescharacteristic
73C2×D236C2311yescharacteristic
74C2×C4×D59—21no—
75C2×C4×D59—21no—
76C2×Dic118C2311yescharacteristic
77C4⋊C4×C59—21no—
78C4⋊C4×C59—21no—
79C4⋊C4×C59—21no—
80C4⋊C4×C59—21no—
81C4⋊C4×C59—21no—
82C4⋊C4×C59—21no—
83C4⋊C4×C59D411yescharacteristic
84C4⋊C4×C59C2311yescharacteristic
85C4⋊C4×C59C2311yescharacteristic
86C4⋊C4×C59C2311yescharacteristic
87C22⋊C4×C59—21no—
88C22⋊C4×C59—21no—
89C22⋊C4×C59—21no—
90C22⋊C4×C59D411yescharacteristic
91C22⋊C4×C59D411yescharacteristic
92C42×C59—21no—
93C42×C59—21no—
94C42×C59C2311yescharacteristic
95C22⋊Dic59—21no—
96#11745672—41no—
97#11745671—22no—
98#11745671—41no—
99(C2×D59)⋊C4—21no—
100(C2×D59)⋊C4—21no—
101(C2×D59)⋊C4—21no—
102(C2×D59)⋊C4—21no—
103C4⋊Dic59C2311yescharacteristic
104Dic59⋊C4—21no—
105#11745664—41no—
106#11745664—41no—
107C2×C59⋊C8C2311yescharacteristic
108C2×C59⋊C8C2311yescharacteristic
109C2×C59⋊C8C2311yescharacteristic
110C2×C59⋊C8C2311yescharacteristic
111C23×C59C2×D411yescharacteristic
112C23×C59C2×D411yescharacteristic
113C22×D59—21no—
114C22×D59—21no—
115C22×D59—42no—
116C22×D59—42no—
117C22×D59—81no—
118Q8×C59—21no—
119Q8×C59—21no—
120D4×C59—41no—
121C2×C4×C59—21no—
122C2×C4×C59—21no—
123C2×C4×C59—21no—
124C2×C4×C59—21no—
125C2×C4×C59—21no—
126C2×C4×C59—21no—
127C2×C4×C59—21no—
128C2×C4×C59—21no—
129C2×C4×C59—42no—
130C2×C4×C59C2×D411yescharacteristic
131C2×C4×C59C2×D411yescharacteristic
132C2×C4×C59C2×D411yescharacteristic
133C2×C4×C59C2×D411yescharacteristic
134C2×C4×C59C2411yescharacteristic
135C22⋊D59—42no—
136C22⋊D59—81no—
137C2×Dic59—21no—
138C2×Dic59—21no—
139D236—21no—
140D236—21no—
141D236—21no—
142D236—42no—
143D236#4112yes—
144C4×D59—42no—
145C4×D59—81no—
146Dic118—21no—
147Dic118—21no—
148C59⋊C8—21no—
149C59⋊C8—21no—
150C59⋊C8—21no—
151C59⋊C8—21no—
152C22×C59—21no—
153C22×C59—21no—
154C22×C59—21no—
155C22×C59—21no—
156C22×C59—21no—
157C22×C59—21no—
158C22×C59C22×D411yescharacteristic
159C2×D59—22no—
160C2×D59—41no—
161C2×D59—41no—
162C2×D59—41no—
163C2×D59—41no—
164C2×D59—41no—
165C2×D59—84no—
166C4×C59—21no—
167C4×C59—21no—
168C4×C59—21no—
169C4×C59—21no—
170C4×C59—41no—
171C4×C59—41no—
172C4×C59—41no—
173C4×C59—41no—
174C4×C59C2×#4111yescharacteristic
175C4×C59H(5,𝔽2)11yescharacteristic
176Dic59—41no—
177Dic59—41no—
178#3323—591nomaximal, Sylow
179C2×C59—41no—
180C2×C59—41no—
181C2×C59#54611yescharacteristic
182C2×C59#57511yescharacteristic
183C2×C59#57711yescharacteristic
184D59—42no—
185D59—81no—
186#552D5911yescharacteristic, complemented
187#546—591no—
188#488—591no—
189#485—591no—
190#481—591no—
191#478—591no—
192#470—591no—
193#468—591no—
194#464—591no—
195#452—591no—
196#450—591no—
197C4×SD16—591no—
198#436—591no—
199#418—591no—
200#417—591no—
201C59#332311yescharacteristic, complemented, Sylow
202C2×#41—591no—
203C22×D4—591no—
204C2×Q16—591no—
205C2×SD16—591no—
206C2×SD16—591no—
207C2×M16—591no—
208C2×M16—591no—
209#126—21no—
210#125—21no—
211#125C2×D5911yescharacteristic, complemented
212#124—591no—
213#123—21no—
214#123—1181no—
215C22⋊Q8—591no—
216C22⋊Q8C2×D5911yescharacteristic
217C22⋊Q8C2×D5911yescharacteristic, complemented
218#121—591no—
219#121—1181no—
220#120—1181no—
221C4×Q8C2×D5911yescharacteristic, complemented
222C4×D4—591no—
223C4×D4C2×D5911yescharacteristic
224#117—21no—
225#117C2×D5911yescharacteristic
226C2×C4⋊C4C2×D5911yescharacteristic, complemented
227C2×C22⋊C4—1181no—
228#107—591no—
229#106—591no—
230#106—591no—
231C4⋊C8—591no—
232#103—591no—
233#103—591no—
234#103—591no—
235#103—591no—
236#102—591no—
237#102—591no—
238#102—591no—
239#102—591no—
240#102—591no—
241#102—591no—
242C22⋊C8—591no—
243C22⋊C8—591no—
244C4×C8—591no—
245C24—1181no—
246#41—1182no—
247#41—2361no—
248C2×Q8—591no—
249C2×Q8C22×D5911yescharacteristic
250C2×D4—591no—
251C2×D4—591no—
252C2×D4—1182no—
253C2×D4—1181no—
254C2×D4—1181no—
255C2×D4—1181no—
256C2×D4—2361no—
257C2×D4C22⋊D5911yescharacteristic
258C22×C4—21no—
259C22×C4—1181no—
260C22×C4—1181no—
261C22×C4C22×D5911yescharacteristic
262C22×C4C22×D5911yescharacteristic
263Q16—2361no—
264SD16—1182no—
265SD16—2361no—
266M16—2361no—
267M16—2361no—
268C2×C8—591no—
269C2×C8—591no—
270C2×C8—591no—
271C2×C8—591no—
272C4⋊C4—21no—
273C4⋊C4—21no—
274C4⋊C4—21no—
275C4⋊C4—21no—
276C4⋊C4—21no—
277C4⋊C4—21no—
278C4⋊C4—591no—
279C4⋊C4—1181no—
280C4⋊C4C22⋊D5911yescharacteristic
281C4⋊C4C22×D5911yescharacteristic
282C4⋊C4C22×D5911yescharacteristic
283C4⋊C4C22×D5911yescharacteristic
284C22⋊C4—21no—
285C22⋊C4—21no—
286C22⋊C4—21no—
287C22⋊C4—1181no—
288C22⋊C4—1181no—
289C22⋊C4—1181no—
290C22⋊C4—1181no—
291C22⋊C4—1181no—
292C22⋊C4C22⋊D5911yescharacteristic
293C22⋊C4C22⋊D5911yescharacteristic
294C42—21no—
295C42—21no—
296C42C22×D5911yescharacteristic
297C23—1181no—
298C23—1181no—
299C23—4721no—
300C23—2362no—
301C23—2362no—
302C23C2×C22⋊D5911yescharacteristic
303C23C2×C22⋊D5911yescharacteristic
304Q8—21no—
305Q8—21no—
306Q8—1181no—
307Q8—1181no—
308D4—41no—
309D4—592no—
310D4—1181no—
311D4—1181no—
312D4—1181no—
313D4—4721no—
314D4—2362no—
315D4—2362no—
316C2×C4—21no—
317C2×C4—21no—
318C2×C4—21no—
319C2×C4—21no—
320C2×C4—21no—
321C2×C4—21no—
322C2×C4—21no—
323C2×C4—21no—
324C2×C4—42no—
325C2×C4—1181no—
326C2×C4—1181no—
327C2×C4—4721no—
328C2×C4—2362no—
329C2×C4C2×C22⋊D5911yescharacteristic
330C2×C4C2×C22⋊D5911yescharacteristic
331C2×C4C2×C22⋊D5911yescharacteristic
332C2×C4C2×C22⋊D5911yescharacteristic
333C2×C4C23×D5911yescharacteristic
334C8—1181no—
335C8—1181no—
336C8—1181no—
337C8—1181no—
338C22—21no—
339C22—21no—
340C22—21no—
341C22—21no—
342C22—21no—
343C22—21no—
344C22—1182no—
345C22—4724no—
346C22—2361no—
347C22—2361no—
348C22—2361no—
349C22—2361no—
350C22—2361no—
351C22C22×C22⋊D5911yescharacteristic
352C4—21no—
353C4—21no—
354C4—21no—
355C4—21no—
356C4—41no—
357C4—41no—
358C4—41no—
359C4—41no—
360C4—2361no—
361C4—2361no—
362C4#41×D5911yescharacteristic
363C4#1427377311yescharacteristic
364C2—41no—
365C2—41no—
366C2—4721no—
367C2—2362no—
368C2#1683804011yescharacteristic
369C2#1683820011yescharacteristic
370C2#1683821011yescharacteristic
subgroupG/H
centerC22C22×C22⋊D59
commutatorC2×C4×C59C24
FrattiniC2×C4C23×D59
FittingC59×#552C2
socleC22×C59C22×D4
hypercenter#552D59
hypocenterC59#3323
LCSG ▷ C2×C4×C59 ▷ C2×C59 ▷ C59
UCSC1 ◁ C22 ◁ C4×D4 ◁ #552

Complements

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

NH ≅ G/Ntype
2. #16837759C2semidirect
3. #16837743C2semidirect
4. #16837720C2semidirect
5. #16837699C2semidirect
6. #16837658C2semidirect
7. #16837650C2semidirect
8. #16837624C2semidirect
9. #16837562C2semidirect
10. #16837552C2semidirect
11. C4×#11745671C2semidirect
12. #16837480C2semidirect
13. #16837406C2semidirect
14. #16837401C2semidirect
15. C59×#552C2semidirect
18. C2×#11745672C22semidirect
22. C2×#11745664C22semidirect
31. #14273660C22semidirect
32. #14273658C22semidirect
33. #14273658C22semidirect
34. C4⋊(C59⋊C8)C22semidirect
35. #14273651C22semidirect
36. #14273650C22semidirect
37. #14273650C22semidirect
38. #14273650C22semidirect
46. C22⋊(C59⋊C8)C22semidirect
47. C4×C59⋊C8C22semidirect
50. #125×C59C22semidirect
53. C22⋊Q8×C59C22semidirect
54. C4×Q8×C59C22semidirect
58. C2×C4⋊C4×C59C22semidirect
186. #552D59semidirect
201. C59#3323semidirect
211. #125C2×D59semidirect
217. C22⋊Q8C2×D59semidirect
221. C4×Q8C2×D59semidirect
226. C2×C4⋊C4C2×D59semidirect