Finite Group Databasebeta

← #21434895

Subgroups — #21434895

Order 7552.

514 conjugacy classes of subgroups; only the 115 normal subgroups are shown.

normal subgroups only

This group has 514 conjugacy classes of subgroups — too many to draw. Only its 115 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14273702C211yesmaximal, characteristic, complemented
2#121×D59C211yesmaximal, characteristic, complemented
3#16837722C212yesmaximal, complemented
4#16837720C211yesmaximal, characteristic, complemented
5#16837656C212yesmaximal, complemented
6#16837654C212yesmaximal, complemented
7#16837538C211yesmaximal, characteristic, complemented
8#16837537C212yesmaximal, complemented
9#16837535C211yesmaximal, characteristic, complemented
10#16837364C211yesmaximal, characteristic, complemented
11C59×#481C211yesmaximal, characteristic, complemented
12C22×D236—21no—
13C22×D236C2211yescharacteristic, complemented
14C2×D4×D59—21no—
15C2×D4×D59C2211yescharacteristic, complemented
16C22×C4×D59C2211yescharacteristic
17C2×D472C2212yescomplemented
18C2×#11745669C2212yescomplemented
19C2×#11745659C2212yescomplemented
20#14273702—21no—
21#14273702—21no—
22#14273702C2212yes—
23#14273702C2211yescharacteristic, complemented
24#14273702C2212yescomplemented
25#14273701C2211yescharacteristic
26#14273700—21no—
27#14273699—21no—
28#14273698C2211yescharacteristic, complemented
29C4⋊C4×D59C2211yescharacteristic, complemented
30C2×(C2×D59)⋊C4—21no—
31C22⋊C4×D59—21no—
32#14273658C2212yescomplemented
33#14273649C2212yescomplemented
34#14273647C2212yescomplemented
35#14273647C2212yescomplemented
36C22⋊(C59⋊C8)C2211yescharacteristic, complemented
37(C2×D59)⋊C8C2212yescomplemented
38#121×C59C2211yescharacteristic
39C2×C4⋊C4×C59C2211yescharacteristic, complemented
40#106×C59C2212yescomplemented
41#102×C59C2212yescomplemented
42C22⋊C8×C59C2211yescharacteristic, complemented
43C23×D59—21no—
44C23×D59—21no—
45C23×D59D411yescharacteristic
46C2×D4×C59—21no—
47C2×D4×C59C2311yescharacteristic
48C22×C4×C59—21no—
49C22×C4×C59C2311yescharacteristic
50C2×C22⋊D59—21no—
51C2×C22⋊D59—21no—
52C2×C22⋊D59—21no—
53C22×Dic59D411yescharacteristic
54D4×D59—42no—
55D4×D59—44no—
56C2×D236—21no—
57C2×D236—22no—
58C2×D236—22no—
59C2×D236—21no—
60C2×D236—42no—
61C2×D236—44no—
62C2×D236C2311yescharacteristic
63C2×D236C2312yes—
64C2×C4×D59—21no—
65C2×C4×D59—42no—
66C2×C4×D59D411yescharacteristic
67C2×C4×D59D411yescharacteristic
68C2×C4×D59C2311yescharacteristic
69C2×C4×D59C2311yescharacteristic
70C2×C8×C59C2312yes—
71C4⋊C4×C59—21no—
72C4⋊C4×C59C2312yes—
73C4⋊C4×C59C2311yescharacteristic
74C22⋊C4×C59—21no—
75C22⋊Dic59—21no—
76#11745669—42no—
77(C2×D59)⋊C4—21no—
78(C2×D59)⋊C4—21no—
79(C2×D59)⋊C4—22no—
80(C2×D59)⋊C4—22no—
81C4⋊Dic59C2311yescharacteristic
82Dic59⋊C4—21no—
83C2×C59⋊C8C2312yes—
84D472—42no—
85#11745659—42no—
86C23×C59—21no—
87C23×C59C2×D411yescharacteristic
88C22×D59—22no—
89C22×D59—22no—
90C22×D59—22no—
91C22×D59—21no—
92C22×D59—41no—
93C22×D59—42no—
94C22×D59—42no—
95C22×D59—42no—
96C22×D59—42no—
97C22×D59—42no—
98C22×D59—42no—
99C22×D59C2×D411yescharacteristic
100C22×D59C2×D411yescharacteristic
101D4×C59—22no—
102D4×C59—42no—
103C2×C4×C59—22no—
104C2×C4×C59—21no—
105C2×C4×C59—22no—
106C2×C4×C59—42no—
107C2×C4×C59C2×D411yescharacteristic
108C2×C4×C59C2411yescharacteristic
109C22⋊D59—42no—
110C22⋊D59—42no—
111C22⋊D59—42no—
112C2×Dic59—21no—
113C2×Dic59—41no—
114C2×Dic59C2×D411yescharacteristic
115C2×Dic59C2×D411yescharacteristic
116D236—22no—
117D236—22no—
118D236—22no—
119D236—42no—
120D236—44no—
121D236—42no—
122D236—44no—
123C4×D59—22no—
124C4×D59—22no—
125C4×D59—41no—
126C4×D59—41no—
127C4×D59—42no—
128C8×C59—22no—
129C59⋊C8—22no—
130C22×C59—21no—
131C22×C59—21no—
132C22×C59—41no—
133C22×C59—41no—
134C22×C59—41no—
135C22×C59AGL(1,ℤ/8)12yes—
136C22×C59C22×D411yescharacteristic
137C2×D59—21no—
138C2×D59—21no—
139C2×D59—21no—
140C2×D59—21no—
141C2×D59—21no—
142C2×D59—44no—
143C2×D59—42no—
144C2×D59—41no—
145C2×D59—42no—
146C2×D59—41no—
147C2×D59—41no—
148C2×D59—42no—
149C2×D59—84no—
150C2×D59—84no—
151C2×D59AGL(1,ℤ/8)12yes—
152C4×C59—21no—
153C4×C59—41no—
154C4×C59—42no—
155C4×C59H(5,𝔽2)12yes—
156Dic59—21no—
157Dic59—21no—
158Dic59—41no—
159#3192—591nomaximal, Sylow
160C2×C59—22no—
161C2×C59—81no—
162C2×C59#53411yescharacteristic
163C2×C59C2×AGL(1,ℤ/8)11yescharacteristic
164C2×C59C2×AGL(1,ℤ/8)11yescharacteristic
165D59—22no—
166D59—41no—
167D59—82no—
168D59—81no—
169C2×#121—591no—
170C2×#121—591no—
171#481—591no—
172#481—592no—
173#481D5911yescharacteristic, complemented
174#469—592no—
175#469—592no—
176#447—591no—
177#447—592no—
178#447—591no—
179#407—591no—
180C59#319211yescharacteristic, complemented, Sylow
181C22×D4—591no—
182C22×D4—591no—
183C22×D4—1181no—
184C22×D4—1181no—
185C23×C4—591no—
186C2×D8—592no—
187C2×D8—592no—
188C2×M16—592no—
189#121—591no—
190#121—591no—
191#121—592no—
192#121—591no—
193#121—592no—
194#121—1181no—
195#121—1181no—
196#121—1181no—
197#121—1181no—
198#121C2×D5911yescharacteristic
199C2×C4⋊C4—591no—
200C2×C4⋊C4C2×D5911yescharacteristic, complemented
201C2×C22⋊C4—1181no—
202C2×C22⋊C4—1181no—
203#106—592no—
204#106C2×D5912yescomplemented
205#102—592no—
206#102—592no—
207#102—592no—
208#102C2×D5912yescomplemented
209C22⋊C8—591no—
210C22⋊C8—592no—
211C22⋊C8C2×D5911yescharacteristic, complemented
212C24—591no—
213C24—1181no—
214C24—1181no—
215C2×D4—21no—
216C2×D4—592no—
217C2×D4—591no—
218C2×D4—1181no—
219C2×D4—1182no—
220C2×D4—1182no—
221C2×D4—1181no—
222C2×D4—1181no—
223C2×D4—1181no—
224C2×D4—1181no—
225C2×D4—2362no—
226C2×D4—2364no—
227C2×D4—2362no—
228C2×D4—2364no—
229C2×D4C22×D5911yescharacteristic
230C22×C4—21no—
231C22×C4—591no—
232C22×C4—591no—
233C22×C4—591no—
234C22×C4—591no—
235C22×C4—591no—
236C22×C4—1181no—
237C22×C4—2362no—
238C22×C4C22×D5911yescharacteristic
239D8—2362no—
240D8—2362no—
241M16—2362no—
242C2×C8—592no—
243C2×C8C22×D5912yes—
244C4⋊C4—21no—
245C4⋊C4—591no—
246C4⋊C4—1181no—
247C4⋊C4C22×D5911yescharacteristic
248C4⋊C4C22×D5912yes—
249C22⋊C4—21no—
250C22⋊C4—1181no—
251C22⋊C4—1182no—
252C22⋊C4—1182no—
253C22⋊C4—1181no—
254C22⋊C4—1181no—
255C23—21no—
256C23—591no—
257C23—591no—
258C23—1182no—
259C23—1182no—
260C23—1182no—
261C23—1181no—
262C23—2361no—
263C23—2362no—
264C23—2362no—
265C23—2362no—
266C23—2362no—
267C23—2362no—
268C23—2362no—
269C23D4×D5911yescharacteristic
270D4—22no—
271D4—42no—
272D4—1182no—
273D4—1182no—
274D4—1182no—
275D4—2362no—
276D4—2364no—
277D4—2364no—
278D4—2362no—
279D4—2362no—
280D4—2362no—
281D4—2362no—
282C2×C4—22no—
283C2×C4—21no—
284C2×C4—22no—
285C2×C4—42no—
286C2×C4—591no—
287C2×C4—591no—
288C2×C4—1182no—
289C2×C4—1182no—
290C2×C4—1181no—
291C2×C4—2361no—
292C2×C4—2361no—
293C2×C4—2362no—
294C2×C4—2361no—
295C2×C4D4×D5911yescharacteristic
296C2×C4C23×D5911yescharacteristic
297C8—22no—
298C8—1182no—
299C22—21no—
300C22—21no—
301C22—41no—
302C22—41no—
303C22—41no—
304C22—592no—
305C22—1181no—
306C22—1181no—
307C22—1181no—
308C22—1181no—
309C22—1181no—
310C22—4724no—
311C22—4724no—
312C22—2364no—
313C22—2362no—
314C22—2361no—
315C22—2361no—
316C22—2362no—
317C22—2362no—
318C22—2361no—
319C22#1427375412yes—
320C22C2×D4×D5911yescharacteristic
321C4—21no—
322C4—42no—
323C4—41no—
324C4—1181no—
325C4—1181no—
326C4—2361no—
327C4#1427377312yes—
328C2—22no—
329C2—81no—
330C2—1182no—
331C2—4722no—
332C2—4721no—
333C2—2361no—
334C2#1683796311yescharacteristic
335C2AGL(1,ℤ/8)×D5911yescharacteristic
336C2C2×#1427375411yescharacteristic
subgroupG/H
centerC22C2×D4×D59
commutatorC2×C4×C59C24
FrattiniC2×C4C23×D59
FittingC59×#481C2
socleC22×C59C22×D4
hypercenter#481D59
hypocenterC59#3192
LCSG ▷ C2×C4×C59 ▷ C2×C59 ▷ C59
UCSC1 ◁ C22 ◁ C22×C4 ◁ #481

Complements

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

NH ≅ G/Ntype
1. C2×#14273702C2semidirect
2. #121×D59C2semidirect
3. #16837722C2semidirect
4. #16837720C2semidirect
5. #16837656C2semidirect
6. #16837654C2semidirect
7. #16837538C2semidirect
8. #16837537C2semidirect
9. #16837535C2semidirect
10. #16837364C2semidirect
11. C59×#481C2semidirect
13. C22×D236C22semidirect
15. C2×D4×D59C22semidirect
17. C2×D472C22semidirect
18. C2×#11745669C22semidirect
19. C2×#11745659C22semidirect
23. #14273702C22semidirect
24. #14273702C22semidirect
28. #14273698C22semidirect
29. C4⋊C4×D59C22semidirect
32. #14273658C22semidirect
33. #14273649C22semidirect
34. #14273647C22semidirect
35. #14273647C22semidirect
36. C22⋊(C59⋊C8)C22semidirect
37. (C2×D59)⋊C8C22semidirect
39. C2×C4⋊C4×C59C22semidirect
40. #106×C59C22semidirect
41. #102×C59C22semidirect
42. C22⋊C8×C59C22semidirect
173. #481D59semidirect
180. C59#3192semidirect
200. C2×C4⋊C4C2×D59semidirect
204. #106C2×D59semidirect
208. #102C2×D59semidirect
211. C22⋊C8C2×D59semidirect