Finite Group Databasebeta

← #21433363

Subgroups — #21433363

Order 7552.

784 conjugacy classes of subgroups; only the 149 normal subgroups are shown.

normal subgroups only

This group has 784 conjugacy classes of subgroups — too many to draw. Only its 149 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×#14273773C211yesmaximal, characteristic, complemented
2C22×#11745669C211yesmaximal, characteristic, complemented
3#16837969C211yesmaximal, characteristic, complemented
4#16837546C214yesmaximal, complemented
5#16837534C214yesmaximal, complemented
6#16837408C211yesmaximal, characteristic, complemented
7#16837398C211yesmaximal, characteristic, complemented
8#16837370C211yesmaximal, characteristic, complemented
9C2×AGL(1,ℤ/8)×C59C211yesmaximal, characteristic, complemented
10#14273773—24no—
11#14273773—24no—
12C2×#11745689C2212yescomplemented
13C2×#11745685—21no—
14C2×#11745685C2211yescharacteristic
15C22×D236—21no—
16C22×D236C2211yescharacteristic
17C2×D4×D59—22no—
18C2×D4×D59C2212yescomplemented
19C2×#11745669—24no—
20C2×#11745669C2214yescomplemented
21C22×C59⋊C8C2211yescharacteristic, complemented
22#14273723—21no—
23#14273714—21no—
24#14273698C2214yescomplemented
25#14273696—22no—
26#14273686C2211yescharacteristic, complemented
27#14273651C2212yescomplemented
28#14273649C2214yescomplemented
29#14273648C2212yescomplemented
30(C2×D59)⋊C8C2214yescomplemented
31C2×#41×C59C2211yescharacteristic
32C22×D4×C59C2211yescharacteristic, complemented
33AGL(1,ℤ/8)×C59—24no—
34C2×SD16×C59C2212yescomplemented
35C2×D8×C59C2212yescomplemented
36C2×M16×C59C2211yescharacteristic, complemented
37C24×C59—21no—
38C23×D59—21no—
39C23×D59—22no—
40#41×C59—22no—
41#41×C59D414yescomplemented
42C2×Q8×C59C2311yescharacteristic
43C2×D4×C59—21no—
44C2×D4×C59—22no—
45C2×D4×C59—22no—
46C2×D4×C59—21no—
47C2×D4×C59C2312yes—
48C2×D4×C59C2311yescharacteristic
49C22×C4×C59—21no—
50C22×C4×C59C2311yescharacteristic
51C2×C22⋊D59—24no—
52C2×C22⋊D59—22no—
53C2×C22⋊D59D412yes—
54#11745689—24no—
55#11745689—24no—
56D4×D59—216no—
57D4×D59—24no—
58D4×D59—24no—
59#11745685—28no—
60#11745685—22no—
61#11745685—22no—
62C2×D236—28no—
63C2×D236—22no—
64C2×D236—21no—
65C2×D236—22no—
66C2×D236D411yescharacteristic
67C2×D236D414yescomplemented
68C2×D236C2312yes—
69C2×C4×D59—22no—
70C2×C4×D59C2312yes—
71C2×Dic118D411yescharacteristic
72SD16×C59—24no—
73D8×C59—24no—
74M16×C59—22no—
75C2×C8×C59C2312yes—
76C22⋊Dic59—21no—
77C22⋊Dic59—24no—
78#11745669—28no—
79C4⋊Dic59C2312yes—
80C4×Dic59—21no—
81C2×C59⋊C8—22no—
82C2×C59⋊C8C2312yes—
83C23×C59—21no—
84C23×C59—22no—
85C23×C59—42no—
86C23×C59—82no—
87C23×C59C2×D411yescharacteristic
88C22×D59—22no—
89C22×D59—28no—
90C22×D59—24no—
91C22×D59—84no—
92C22×D59—82no—
93C22×D59C2×D412yes—
94Q8×C59—21no—
95Q8×C59C2×D412yes—
96D4×C59—24no—
97D4×C59—21no—
98D4×C59—22no—
99D4×C59—22no—
100D4×C59—42no—
101D4×C59C2×D412yes—
102C2×C4×C59—21no—
103C2×C4×C59—24no—
104C2×C4×C59C2×D411yescharacteristic
105C2×C4×C59C2×D412yes—
106C2×C4×C59C2×D412yes—
107C2×C4×C59C2411yescharacteristic
108C22⋊D59—28no—
109C22⋊D59—24no—
110C22⋊D59—84no—
111C2×Dic59—22no—
112C2×Dic59C2×D412yes—
113D236—28no—
114D236—22no—
115D236—24no—
116D236—22no—
117D236C2×D414yes—
118C4×D59—28no—
119C4×D59—22no—
120C4×D59—22no—
121Dic118—22no—
122C8×C59—22no—
123C59⋊C8—22no—
124C22×C59—22no—
125C22×C59—22no—
126C22×C59—42no—
127C22×C59—42no—
128C22×C59—44no—
129C22×C59—84no—
130C22×C59#12012yes—
131C22×C59C22×D411yescharacteristic
132C2×D59—22no—
133C2×D59—24no—
134C2×D59—24no—
135C2×D59—44no—
136C2×D59—84no—
137C2×D59—88no—
138C4×C59—22no—
139C4×C59#12012yes—
140C4×C59C22×D411yescharacteristic
141C4×C59C22×D411yescharacteristic
142Dic59—22no—
143Dic59—42no—
144#3008—591nomaximal, Sylow
145C2×C59—22no—
146C2×C59—42no—
147C2×C59—82no—
148C2×C59C2×#12011yescharacteristic
149C2×C59#57612yes—
150D59—42no—
151D59—44no—
152C2×H(5,𝔽2)—591no—
153C2×AGL(1,ℤ/8)D5911yescharacteristic, complemented
154C22×D8—591no—
155#535—591no—
156#449—594no—
157#447—594no—
158#418—591no—
159#416—591no—
160#408—591no—
161C59#300811yescharacteristic, complemented, Sylow
162H(5,𝔽2)—1184no—
163H(5,𝔽2)—1184no—
164C2×#41—591no—
165C2×#41—592no—
166C2×#41—1181no—
167C2×#41C2×D5911yescharacteristic
168C22×D4—592no—
169C22×D4—591no—
170C22×D4—1181no—
171C22×D4—1182no—
172C22×D4C2×D5911yescharacteristic, complemented
173AGL(1,ℤ/8)—24no—
174C2×SD16C2×D5912yescomplemented
175C2×D8—594no—
176C2×D8—1184no—
177C2×D8C2×D5912yescomplemented
178C2×M16C2×D5911yescharacteristic, complemented
179C22×C8—591no—
180#127—1181no—
181#124—1181no—
182#121—594no—
183#120—1182no—
184#117—591no—
185#103—592no—
186#102—592no—
187#102—594no—
188C22⋊C8—594no—
189C24—21no—
190C24—1182no—
191C24—1181no—
192#41—22no—
193#41—1188no—
194#41—1184no—
195#41—1184no—
196#41—1182no—
197#41—1182no—
198#41C22⋊D5914yescomplemented
199C2×Q8—591no—
200C2×Q8C22×D5911yescharacteristic
201C2×D4—21no—
202C2×D4—22no—
203C2×D4—21no—
204C2×D4—22no—
205C2×D4—592no—
206C2×D4—594no—
207C2×D4—591no—
208C2×D4—592no—
209C2×D4—1182no—
210C2×D4—1188no—
211C2×D4—1182no—
212C2×D4—1184no—
213C2×D4—11816no—
214C2×D4—1184no—
215C2×D4—1184no—
216C2×D4—1181no—
217C2×D4—1182no—
218C2×D4C22×D5912yes—
219C2×D4C22×D5911yescharacteristic
220C22×C4—21no—
221C22×C4—592no—
222C22×C4—1182no—
223C22×C4C22×D5911yescharacteristic
224SD16—24no—
225D8—24no—
226D8—1188no—
227M16—22no—
228C2×C8—592no—
229C2×C8—1182no—
230C2×C8C22×D5912yes—
231C4⋊C4—592no—
232C22⋊C4—1184no—
233C22⋊C4—1181no—
234C42—1181no—
235C23—21no—
236C23—22no—
237C23—42no—
238C23—82no—
239C23—592no—
240C23—1188no—
241C23—1184no—
242C23—1182no—
243C23—4722no—
244C23—4724no—
245C23D4×D5911yescharacteristic
246Q8—21no—
247Q8—1182no—
248Q8C2×C22⋊D5912yes—
249D4—24no—
250D4—21no—
251D4—22no—
252D4—22no—
253D4—42no—
254D4—594no—
255D4—1188no—
256D4—1188no—
257D4—1184no—
258D4—1184no—
259D4—1182no—
260D4—1182no—
261D4—4724no—
262D4C2×C22⋊D5912yes—
263C2×C4—21no—
264C2×C4—24no—
265C2×C4—592no—
266C2×C4—1188no—
267C2×C4—1182no—
268C2×C4—1182no—
269C2×C4—1182no—
270C2×C4D4×D5911yescharacteristic
271C2×C4D4×D5912yes—
272C2×C4C2×C22⋊D5912yes—
273C2×C4C23×D5911yescharacteristic
274C8—22no—
275C8—1182no—
276C22—22no—
277C22—22no—
278C22—42no—
279C22—44no—
280C22—42no—
281C22—84no—
282C22—1184no—
283C22—1184no—
284C22—1182no—
285C22—4724no—
286C22—4728no—
287C22—2364no—
288C22#1427369512yes—
289C22C2×D4×D5911yescharacteristic
290C4—22no—
291C4—1182no—
292C4—2362no—
293C4#1427369512yes—
294C4C2×D4×D5911yescharacteristic
295C4C22×C22⋊D5911yescharacteristic
296C2—22no—
297C2—42no—
298C2—82no—
299C2—2362no—
300C2—2364no—
301C2C2×#1427369511yescharacteristic
302C2#1683820612yes—
subgroupG/H
centerC22C2×D4×D59
commutatorC2×C4×C59C24
FrattiniC2×C4C23×D59
FittingC2×AGL(1,ℤ/8)×C59C2
socleC22×C59C22×D4
hypercenterC2×AGL(1,ℤ/8)D59
hypocenterC59#3008
LCSG ▷ C2×C4×C59 ▷ C2×C59 ▷ C59
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×AGL(1,ℤ/8)

Complements

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

NH ≅ G/Ntype
1. C2×#14273773C2semidirect
2. C22×#11745669C2semidirect
3. #16837969C2semidirect
4. #16837546C2semidirect
5. #16837534C2semidirect
6. #16837408C2semidirect
7. #16837398C2semidirect
8. #16837370C2semidirect
9. C2×AGL(1,ℤ/8)×C59C2semidirect
12. C2×#11745689C22semidirect
18. C2×D4×D59C22semidirect
20. C2×#11745669C22semidirect
21. C22×C59⋊C8C22semidirect
24. #14273698C22semidirect
26. #14273686C22semidirect
27. #14273651C22semidirect
28. #14273649C22semidirect
29. #14273648C22semidirect
30. (C2×D59)⋊C8C22semidirect
32. C22×D4×C59C22semidirect
34. C2×SD16×C59C22semidirect
35. C2×D8×C59C22semidirect
36. C2×M16×C59C22semidirect
41. #41×C59D4semidirect
67. C2×D236D4semidirect
153. C2×AGL(1,ℤ/8)D59semidirect
161. C59#3008semidirect
172. C22×D4C2×D59semidirect
174. C2×SD16C2×D59semidirect
177. C2×D8C2×D59semidirect
178. C2×M16C2×D59semidirect
198. #41C22⋊D59semidirect