Finite Group Databasebeta

← #21433341

Subgroups — #21433341

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×#11745685C211yesmaximal, characteristic, complemented
2C2×#14273760C211yesmaximal, characteristic, complemented
3C2×#14273755C211yesmaximal, characteristic, complemented
4#16837913C211yesmaximal, characteristic, complemented
5#16837566C214yesmaximal, complemented
6#16837549C214yesmaximal, complemented
7#16837412C211yesmaximal, characteristic, complemented
8#16837408C211yesmaximal, characteristic, complemented
9C59×#407C211yesmaximal, characteristic, complemented
10C2×#11745685—22no—
11C2×#11745685—24no—
12C2×#11745685—24no—
13C2×#11745685C2211yescharacteristic
14C2×#11745685C2214yes—
15C22×Dic118C2211yescharacteristic
16C22×D236C2211yescharacteristic
17C22×C22⋊D59—21no—
18C22×C4×D59—21no—
19#14273760—24no—
20#14273755—24no—
21C2×Dic236C2212yescomplemented
22C2×#11745660C2212yescomplemented
23C2×#11745660C2212yescomplemented
24C2×D472C2212yescomplemented
25#14273710—21no—
26#14273706C2212yescomplemented
27#14273701C2212yescomplemented
28#14273696—21no—
29C4×C22⋊D59—22no—
30#14273686C2211yescharacteristic
31#14273652C2214yescomplemented
32#14273649C2214yescomplemented
33C23×C4×C59C2211yescharacteristic
34C2×M16×C59C2211yescharacteristic
35C2×M16×C59C2211yescharacteristic
36C22⋊C8×C59C2214yescomplemented
37C24×C59D411yescharacteristic
38C23×D59—21no—
39C22×C4×C59—22no—
40C22×C4×C59—22no—
41C22×C4×C59D412yes—
42C22×C4×C59D411yescharacteristic
43C22×C4×C59C2312yes—
44C22×C4×C59C2311yescharacteristic
45C2×C22⋊D59—28no—
46C2×C22⋊D59—24no—
47C2×C22⋊D59—22no—
48C2×C22⋊D59—21no—
49C22×Dic59—21no—
50#11745685—216no—
51#11745685—28no—
52#11745685—22no—
53#11745685—22no—
54#11745685—28no—
55C2×D236—21no—
56C2×D236—22no—
57C2×D236D414yescomplemented
58C2×D236C2311yescharacteristic
59C2×D236C2312yes—
60C2×C4×D59—28no—
61C2×C4×D59—24no—
62C2×C4×D59—21no—
63C2×Dic118—21no—
64C2×Dic118—22no—
65C2×Dic118D414yescomplemented
66C2×Dic118C2311yescharacteristic
67C2×Dic118C2312yes—
68M16×C59—22no—
69M16×C59—22no—
70C2×C8×C59C2312yes—
71C2×C8×C59C2312yes—
72C22⋊Dic59—21no—
73C22⋊Dic59—22no—
74(C2×D59)⋊C4—22no—
75C4⋊Dic59C2312yes—
76Dic59⋊C4—22no—
77C4×Dic59—21no—
78Dic236—24no—
79D472—24no—
80#11745660—24no—
81#11745660—24no—
82C23×C59—22no—
83C23×C59—42no—
84C23×C59C2×D412yes—
85C23×C59C2×D411yescharacteristic
86C22×D59—24no—
87C22×D59—22no—
88C22×D59—21no—
89C22×D59—44no—
90C2×C4×C59—22no—
91C2×C4×C59—24no—
92C2×C4×C59—22no—
93C2×C4×C59—22no—
94C2×C4×C59C2×D412yes—
95C2×C4×C59C2×D411yescharacteristic
96C2×C4×C59C2×D412yes—
97C2×C4×C59C2×D412yes—
98C2×C4×C59C2411yescharacteristic
99C22⋊D59—216no—
100C22⋊D59—44no—
101C22⋊D59—42no—
102C2×Dic59—24no—
103C2×Dic59—22no—
104C2×Dic59—22no—
105C2×Dic59—21no—
106D236—24no—
107D236—22no—
108D236—21no—
109D236—21no—
110D236C2×D414yes—
111C4×D59—216no—
112C4×D59—42no—
113Dic118—24no—
114Dic118—22no—
115Dic118—21no—
116Dic118—21no—
117Dic118C2×D414yes—
118C8×C59—22no—
119C8×C59—22no—
120C22×C59—22no—
121C22×C59—22no—
122C22×C59—22no—
123C22×C59—22no—
124C22×C59—44no—
125C22×C59#12012yes—
126C22×C59C22×D411yescharacteristic
127C2×D59—24no—
128C2×D59—48no—
129C2×D59—44no—
130C2×D59—41no—
131C2×D59—42no—
132C4×C59—22no—
133C4×C59#12012yes—
134C4×C59C22×D411yescharacteristic
135C4×C59C22×D411yescharacteristic
136Dic59—24no—
137Dic59—41no—
138Dic59—42no—
139#3005—591nomaximal, Sylow
140C2×C59—22no—
141C2×C59—42no—
142C2×C59C2×#12011yescharacteristic
143C2×C59#57512yes—
144D59—44no—
145D59—81no—
146C22×#41—591no—
147C2×#137—591no—
148C2×AGL(1,ℤ/8)—591no—
149#525—591no—
150#452—594no—
151#449—594no—
152#419—591no—
153#418—591no—
154#407D5911yescharacteristic, complemented
155C59#300511yescharacteristic, complemented, Sylow
156C2×#41—591no—
157C2×#41—594no—
158C2×#41—1184no—
159C2×#41—1184no—
160C2×#41—1182no—
161C22×Q8—591no—
162C22×D4—591no—
163C22×D4—1181no—
164C23×C4—1181no—
165C23×C4C2×D5911yescharacteristic
166#137—1184no—
167AGL(1,ℤ/8)—1184no—
168C2×Q16—592no—
169C2×SD16—592no—
170C2×SD16—592no—
171C2×D8—592no—
172C2×M16C2×D5911yescharacteristic
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⋊C8C2×D5914yescomplemented
183C24—1181no—
184C24D23611yescharacteristic
185#41—1188no—
186#41—1188no—
187#41—11816no—
188#41—1182no—
189#41—1182no—
190C2×Q8—594no—
191C2×Q8—592no—
192C2×Q8—591no—
193C2×Q8—1181no—
194C2×Q8—1182no—
195C2×D4—594no—
196C2×D4—592no—
197C2×D4—591no—
198C2×D4—1188no—
199C2×D4—1184no—
200C2×D4—1182no—
201C2×D4—1181no—
202C2×D4—1181no—
203C2×D4—1182no—
204C22×C4—22no—
205C22×C4—22no—
206C22×C4—1188no—
207C22×C4—1181no—
208C22×C4—1184no—
209C22×C4—1181no—
210C22×C4D23612yes—
211C22×C4D23611yescharacteristic
212C22×C4C22×D5912yes—
213C22×C4C22×D5911yescharacteristic
214Q16—1184no—
215SD16—1184no—
216SD16—1184no—
217D8—1184no—
218M16—22no—
219M16—22no—
220C2×C8C22×D5912yes—
221C2×C8C22×D5912yes—
222C4⋊C4—592no—
223C4⋊C4—1182no—
224C22⋊C4—1181no—
225C22⋊C4—1182no—
226C22⋊C4—1182no—
227C42—1181no—
228C23—22no—
229C23—42no—
230C23—1184no—
231C23—1182no—
232C23—1181no—
233C23—2364no—
234C23C2×D23612yes—
235C23C2×D23611yescharacteristic
236Q8—594no—
237Q8—1184no—
238Q8—1182no—
239Q8—1181no—
240Q8—1181no—
241D4—594no—
242D4—11816no—
243D4—1184no—
244D4—1182no—
245D4—1181no—
246D4—1181no—
247D4—2364no—
248D4—2362no—
249C2×C4—22no—
250C2×C4—24no—
251C2×C4—22no—
252C2×C4—22no—
253C2×C4—11816no—
254C2×C4—1184no—
255C2×C4—1182no—
256C2×C4—1182no—
257C2×C4—1181no—
258C2×C4—2362no—
259C2×C4C2×D23612yes—
260C2×C4C2×D23611yescharacteristic
261C2×C4D4×D5912yes—
262C2×C4D4×D5912yes—
263C2×C4C23×D5911yescharacteristic
264C8—22no—
265C8—22no—
266C22—22no—
267C22—22no—
268C22—22no—
269C22—22no—
270C22—44no—
271C22—1184no—
272C22—2368no—
273C22—2361no—
274C22—2362no—
275C22—2364no—
276C22#1427369712yes—
277C22C22×D23611yescharacteristic
278C4—22no—
279C4—1184no—
280C4—2361no—
281C4—2362no—
282C4#1427369712yes—
283C4C2×D4×D5911yescharacteristic
284C4C2×D4×D5911yescharacteristic
285C2—22no—
286C2—42no—
287C2—4721no—
288C2—2364no—
289C2C2×#1427369711yescharacteristic
290C2#1683820212yes—
subgroupG/H
centerC22C22×D236
commutatorC2×C4×C59C24
FrattiniC2×C4C23×D59
FittingC59×#407C2
socleC22×C59C22×D4
hypercenter#407D59
hypocenterC59#3005
LCSG ▷ C2×C4×C59 ▷ C2×C59 ▷ C59
UCSC1 ◁ C22 ◁ C23×C4 ◁ #407

Complements

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

NH ≅ G/Ntype
1. C22×#11745685C2semidirect
2. C2×#14273760C2semidirect
3. C2×#14273755C2semidirect
4. #16837913C2semidirect
5. #16837566C2semidirect
6. #16837549C2semidirect
7. #16837412C2semidirect
8. #16837408C2semidirect
9. C59×#407C2semidirect
21. C2×Dic236C22semidirect
22. C2×#11745660C22semidirect
23. C2×#11745660C22semidirect
24. C2×D472C22semidirect
26. #14273706C22semidirect
27. #14273701C22semidirect
31. #14273652C22semidirect
32. #14273649C22semidirect
36. C22⋊C8×C59C22semidirect
57. C2×D236D4semidirect
65. C2×Dic118D4semidirect
154. #407D59semidirect
155. C59#3005semidirect
182. C22⋊C8C2×D59semidirect