Finite Group Databasebeta

← #21433337

Subgroups — #21433337

Order 7552.

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

normal subgroups only

This group has 758 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
1C22×#11745689C211yesmaximal, characteristic, complemented
2C2×#14273752C211yesmaximal, characteristic, complemented
3#16837909C211yesmaximal, characteristic, complemented
4#16837563C214yesmaximal, complemented
5#16837546C214yesmaximal, complemented
6#16837411C211yesmaximal, characteristic, complemented
7#16837408C211yesmaximal, characteristic, complemented
8#16837365C211yesmaximal, characteristic, complemented
9C2×#137×C59C211yesmaximal, characteristic, complemented
10C2×#11745689—24no—
11C2×#11745689—24no—
12C2×#11745689—22no—
13C2×#11745689C2214yes—
14C22×D236—21no—
15C22×D236C2211yescharacteristic
16C22×C4×D59—21no—
17C22×C4×D59C2211yescharacteristic
18#14273752—24no—
19C2×#11745671C2212yescomplemented
20C2×#11745669C2212yescomplemented
21C2×#11745664C2211yescharacteristic
22#14273708—21no—
23#14273703C2212yescomplemented
24#14273698C2212yescomplemented
25#14273695—21no—
26C4×C22⋊D59—22no—
27#14273686C2211yescharacteristic
28#14273651C2214yescomplemented
29#14273649C2214yescomplemented
30(C2×D59)⋊C8C2214yescomplemented
31C2×#41×C59C2211yescharacteristic
32C22×Q8×C59C2211yescharacteristic
33#137×C59—24no—
34C2×Q16×C59C2212yescomplemented
35C2×SD16×C59C2212yescomplemented
36C2×M16×C59C2211yescharacteristic
37C23×D59—21no—
38C23×D59D411yescharacteristic
39#41×C59—22no—
40#41×C59—22no—
41C2×Q8×C59—22no—
42C2×Q8×C59—21no—
43C2×Q8×C59D414yescomplemented
44C2×Q8×C59C2311yescharacteristic
45C2×Q8×C59C2312yes—
46C2×D4×C59—21no—
47C2×D4×C59C2311yescharacteristic
48C22×C4×C59—21no—
49C22×C4×C59—21no—
50C22×C4×C59C2311yescharacteristic
51C2×C22⋊D59—22no—
52C22×Dic59D411yescharacteristic
53#11745689—216no—
54#11745689—28no—
55#11745689—28no—
56C2×D236—28no—
57C2×D236—24no—
58C2×D236—21no—
59C2×D236—22no—
60C2×D236D414yescomplemented
61C2×D236C2312yes—
62C2×C4×D59—28no—
63C2×C4×D59—22no—
64C2×C4×D59—22no—
65C2×C4×D59—24no—
66C2×C4×D59D412yes—
67C2×C4×D59C2312yes—
68Q16×C59—24no—
69SD16×C59—24no—
70M16×C59—22no—
71C2×C8×C59C2312yes—
72C22⋊Dic59—21no—
73C22⋊Dic59—22no—
74#11745671—24no—
75#11745669—24no—
76(C2×D59)⋊C4—22no—
77C4⋊Dic59C2312yes—
78Dic59⋊C4—22no—
79C4×Dic59—21no—
80#11745664—22no—
81C2×C59⋊C8C2312yes—
82C23×C59—21no—
83C23×C59C2×D411yescharacteristic
84C22×D59—22no—
85C22×D59—24no—
86C22×D59—22no—
87C22×D59—42no—
88C22×D59—44no—
89C22×D59C2×D412yes—
90Q8×C59—24no—
91Q8×C59—22no—
92Q8×C59—21no—
93Q8×C59—21no—
94Q8×C59C2×D414yes—
95D4×C59—21no—
96D4×C59—21no—
97D4×C59—42no—
98C2×C4×C59—24no—
99C2×C4×C59—22no—
100C2×C4×C59—21no—
101C2×C4×C59—42no—
102C2×C4×C59C2×D411yescharacteristic
103C2×C4×C59C2×D412yes—
104C2×C4×C59C2×D412yes—
105C2×C4×C59C2411yescharacteristic
106C22⋊D59—44no—
107C2×Dic59—22no—
108C2×Dic59—22no—
109C2×Dic59C2×D412yes—
110D236—216no—
111D236—24no—
112D236—22no—
113D236C2×D414yes—
114C4×D59—216no—
115C4×D59—24no—
116C4×D59—22no—
117C4×D59—22no—
118C8×C59—22no—
119C59⋊C8—22no—
120C22×C59—22no—
121C22×C59—41no—
122C22×C59—42no—
123C22×C59#12012yes—
124C22×C59C22×D411yescharacteristic
125C2×D59—22no—
126C2×D59—24no—
127C2×D59—22no—
128C2×D59—22no—
129C2×D59—44no—
130C2×D59—48no—
131C2×D59—44no—
132C4×C59—24no—
133C4×C59—41no—
134C4×C59#12012yes—
135C4×C59C22×D411yescharacteristic
136C4×C59C22×D411yescharacteristic
137Dic59—22no—
138Dic59—42no—
139#3005—591nomaximal, Sylow
140C2×C59—22no—
141C2×C59—81no—
142C2×C59C2×#12011yescharacteristic
143C2×C59#57512yes—
144D59—42no—
145D59—44no—
146C22×#41—591no—
147C2×#137D5911yescharacteristic, complemented
148C2×AGL(1,ℤ/8)—591no—
149#525—591no—
150#452—594no—
151#449—594no—
152#419—591no—
153#418—591no—
154#407—591no—
155C59#300511yescharacteristic, complemented, Sylow
156C2×#41—594no—
157C2×#41—1182no—
158C2×#41—1184no—
159C2×#41—1184no—
160C2×#41C2×D5911yescharacteristic
161C22×Q8C2×D5911yescharacteristic
162C22×D4—591no—
163C22×D4—1181no—
164C23×C4—591no—
165C23×C4—1181no—
166#137—24no—
167AGL(1,ℤ/8)—1184no—
168C2×Q16C2×D5912yescomplemented
169C2×SD16—592no—
170C2×SD16C2×D5912yescomplemented
171C2×D8—592no—
172C2×M16—591no—
173C2×M16C2×D5911yescharacteristic
174#123—1181no—
175C22⋊Q8—592no—
176#121—592no—
177#120—1181no—
178C4×D4—1182no—
179#117—591no—
180#103—594no—
181#102—594no—
182C22⋊C8—594no—
183C24—591no—
184C24—1181no—
185#41—22no—
186#41—22no—
187#41—1188no—
188#41—11816no—
189#41—1188no—
190C2×Q8—22no—
191C2×Q8—21no—
192C2×Q8C22⋊D5914yescomplemented
193C2×Q8C22×D5911yescharacteristic
194C2×Q8C22×D5912yes—
195C2×D4—21no—
196C2×D4—594no—
197C2×D4—592no—
198C2×D4—1184no—
199C2×D4—1188no—
200C2×D4—1182no—
201C2×D4—1181no—
202C2×D4—1182no—
203C2×D4C22×D5911yescharacteristic
204C22×C4—21no—
205C22×C4—21no—
206C22×C4—591no—
207C22×C4—592no—
208C22×C4—592no—
209C22×C4—1184no—
210C22×C4—1188no—
211C22×C4—1182no—
212C22×C4—1182no—
213C22×C4C22×D5911yescharacteristic
214Q16—24no—
215SD16—24no—
216SD16—1184no—
217D8—1184no—
218M16—22no—
219M16—1182no—
220C2×C8—592no—
221C2×C8C22×D5912yes—
222C4⋊C4—592no—
223C4⋊C4—1182no—
224C22⋊C4—1182no—
225C22⋊C4—1182no—
226C22⋊C4—1181no—
227C42—1181no—
228C23—21no—
229C23—592no—
230C23—1184no—
231C23—1182no—
232C23—1182no—
233C23—2362no—
234C23—2364no—
235C23D4×D5911yescharacteristic
236Q8—24no—
237Q8—22no—
238Q8—21no—
239Q8—21no—
240Q8C2×C22⋊D5914yes—
241D4—21no—
242D4—21no—
243D4—42no—
244D4—594no—
245D4—11816no—
246D4—1184no—
247D4—1182no—
248D4—2364no—
249C2×C4—24no—
250C2×C4—22no—
251C2×C4—21no—
252C2×C4—42no—
253C2×C4—592no—
254C2×C4—11816no—
255C2×C4—1182no—
256C2×C4—1184no—
257C2×C4—1182no—
258C2×C4—1182no—
259C2×C4—1182no—
260C2×C4D4×D5911yescharacteristic
261C2×C4D4×D5912yes—
262C2×C4C2×C22⋊D5912yes—
263C2×C4C23×D5911yescharacteristic
264C8—22no—
265C8—1182no—
266C22—22no—
267C22—42no—
268C22—41no—
269C22—1182no—
270C22—1182no—
271C22—1184no—
272C22—1182no—
273C22—2364no—
274C22—2368no—
275C22—2364no—
276C22#1427369512yes—
277C22C2×D4×D5911yescharacteristic
278C4—24no—
279C4—41no—
280C4—1182no—
281C4—2362no—
282C4#1427369512yes—
283C4C2×D4×D5911yescharacteristic
284C4C22×C22⋊D5911yescharacteristic
285C2—22no—
286C2—81no—
287C2—2362no—
288C2—2364no—
289C2C2×#1427369511yescharacteristic
290C2#1683820112yes—
subgroupG/H
centerC22C2×D4×D59
commutatorC2×C4×C59C24
FrattiniC2×C4C23×D59
FittingC2×#137×C59C2
socleC22×C59C22×D4
hypercenterC2×#137D59
hypocenterC59#3005
LCSG ▷ C2×C4×C59 ▷ C2×C59 ▷ C59
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×#137

Complements

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

NH ≅ G/Ntype
1. C22×#11745689C2semidirect
2. C2×#14273752C2semidirect
3. #16837909C2semidirect
4. #16837563C2semidirect
5. #16837546C2semidirect
6. #16837411C2semidirect
7. #16837408C2semidirect
8. #16837365C2semidirect
9. C2×#137×C59C2semidirect
19. C2×#11745671C22semidirect
20. C2×#11745669C22semidirect
23. #14273703C22semidirect
24. #14273698C22semidirect
28. #14273651C22semidirect
29. #14273649C22semidirect
30. (C2×D59)⋊C8C22semidirect
34. C2×Q16×C59C22semidirect
35. C2×SD16×C59C22semidirect
43. C2×Q8×C59D4semidirect
60. C2×D236D4semidirect
147. C2×#137D59semidirect
155. C59#3005semidirect
168. C2×Q16C2×D59semidirect
170. C2×SD16C2×D59semidirect
192. C2×Q8C22⋊D59semidirect