Finite Group Databasebeta

← #21433702

Subgroups — #21433702

Order 7552.

500 conjugacy classes of subgroups; only the 141 normal subgroups are shown.

normal subgroups only

This group has 500 conjugacy classes of subgroups — too many to draw. Only its 141 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×#14273747C211yesmaximal, characteristic, complemented
2C22×#11745664C211yesmaximal, characteristic, complemented
3#16837913C211yesmaximal, characteristic, complemented
4#16837658C212yesmaximal, complemented
5#16837653C212yesmaximal, complemented
6#16837650C212yesmaximal, complemented
7#16837646C212yesmaximal, complemented
8#16837438C211yesmaximal, characteristic, complemented
9#16837398C211yesmaximal, characteristic, complemented
10#16837396C211yesmaximal, characteristic, complemented
11C59×#525C211yesmaximal, characteristic, complemented
12C2×#11745685C2211yescharacteristic
13#14273747—24no—
14C2×#11745672C2211yescharacteristic, complemented
15C2×#11745670C2211yescharacteristic, complemented
16C2×#11745671C2211yescharacteristic, complemented
17C2×#11745669C2211yescharacteristic, complemented
18C2×#11745664—24no—
19C2×#11745664C2212yes—
20C2×#11745664C2212yes—
21C22×C59⋊C8C2211yescharacteristic
22C22×C59⋊C8C2211yescharacteristic
23#14273710—21no—
24#14273706C2212yes—
25#14273701C2212yes—
26#14273696—21no—
27C4×C22⋊D59—22no—
28#14273686C2211yescharacteristic
29#14273660C2212yescomplemented
30#14273658C2212yescomplemented
31#14273651C2212yescomplemented
32#14273650C2212yescomplemented
33#14273648C2212yescomplemented
34#14273647C2212yescomplemented
35C2×#41×C59C2211yescharacteristic
36C23×C4×C59C2211yescharacteristic
37#123×C59—21no—
38C22⋊Q8×C59C2212yes—
39#121×C59C2212yes—
40#120×C59—21no—
41C4×D4×C59—22no—
42#117×C59C2211yescharacteristic
43C24×C59D411yescharacteristic
44#41×C59—22no—
45#41×C59—22no—
46C2×Q8×C59C2311yescharacteristic
47C2×D4×C59—22no—
48C2×D4×C59—21no—
49C2×D4×C59C2311yescharacteristic
50C22×C4×C59—22no—
51C22×C4×C59—22no—
52C22×C4×C59—21no—
53C22×C4×C59D412yes—
54C22×C4×C59D411yescharacteristic
55C22×C4×C59C2312yes—
56C22×C4×C59C2311yescharacteristic
57C2×C22⋊D59—22no—
58C2×C22⋊D59—21no—
59#11745685—22no—
60#11745685—22no—
61C2×D236C2311yescharacteristic
62C2×C4×D59—21no—
63C2×Dic118C2311yescharacteristic
64C4⋊C4×C59—22no—
65C4⋊C4×C59C2312yes—
66C22⋊C4×C59—21no—
67C22⋊C4×C59—22no—
68C22⋊C4×C59—22no—
69C42×C59—21no—
70C22⋊Dic59—21no—
71C22⋊Dic59—22no—
72#11745672—22no—
73#11745671—22no—
74#11745670—22no—
75#11745669—22no—
76(C2×D59)⋊C4—22no—
77C4⋊Dic59C2312yes—
78Dic59⋊C4—22no—
79C4×Dic59—21no—
80#11745664—24no—
81#11745664—24no—
82C2×C59⋊C8—22no—
83C2×C59⋊C8D414yescomplemented
84C2×C59⋊C8C2312yes—
85C2×C59⋊C8C2311yescharacteristic
86C2×C59⋊C8C2311yescharacteristic
87C23×C59—22no—
88C23×C59—21no—
89C23×C59—42no—
90C23×C59C2×D412yes—
91C23×C59C2×D411yescharacteristic
92C22×D59—21no—
93Q8×C59—21no—
94Q8×C59—21no—
95D4×C59—21no—
96D4×C59—21no—
97D4×C59—44no—
98D4×C59—42no—
99C2×C4×C59—22no—
100C2×C4×C59—24no—
101C2×C4×C59—22no—
102C2×C4×C59—22no—
103C2×C4×C59—22no—
104C2×C4×C59—21no—
105C2×C4×C59—42no—
106C2×C4×C59C2×D412yes—
107C2×C4×C59C2×D412yes—
108C2×C4×C59C2×D411yescharacteristic
109C2×C4×C59#4112yes—
110C2×C4×C59C2411yescharacteristic
111C22⋊D59—44no—
112C22⋊D59—42no—
113C2×Dic59—22no—
114C2×Dic59—21no—
115D236—21no—
116D236—21no—
117C4×D59—42no—
118Dic118—21no—
119Dic118—21no—
120C59⋊C8—22no—
121C59⋊C8C2×D412yes—
122C59⋊C8C2×D412yes—
123C22×C59—22no—
124C22×C59—22no—
125C22×C59—22no—
126C22×C59—22no—
127C22×C59—44no—
128C22×C59—41no—
129C22×C59—42no—
130C22×C59#12112yes—
131C22×C59C22×D411yescharacteristic
132C2×D59—41no—
133C2×D59—42no—
134C4×C59—22no—
135C4×C59—41no—
136C4×C59—42no—
137C4×C59#12112yes—
138C4×C59C22×D411yescharacteristic
139C4×C59C2×#4111yescharacteristic
140Dic59—41no—
141Dic59—42no—
142#3054—591nomaximal, Sylow
143C2×C59—22no—
144C2×C59—42no—
145C2×C59—81no—
146C2×C59C2×#12111yescharacteristic
147C2×C59#57512yes—
148D59—81no—
149C2×#135—591no—
150C22×M16—591no—
151#525—591no—
152#525D5911yescharacteristic, complemented
153#470—592no—
154#469—592no—
155#468—592no—
156#468—592no—
157#427—591no—
158#416—591no—
159#416—591no—
160C59#305411yescharacteristic, complemented, Sylow
161C2×#41—591no—
162C2×#41C2×D5911yescharacteristic
163C23×C4C2×D5911yescharacteristic
164#135—1184no—
165C2×Q16—591no—
166C2×SD16—591no—
167C2×SD16—591no—
168C2×D8—591no—
169C2×M16—592no—
170C2×M16—592no—
171C2×M16—1184no—
172C22×C8—591no—
173C22×C8—591no—
174#123—21no—
175#123—1181no—
176C22⋊Q8—592no—
177C22⋊Q8C2×D5912yes—
178#121—592no—
179#121C2×D5912yes—
180#120—21no—
181#120—1181no—
182C4×D4—22no—
183C4×D4—1182no—
184#117—591no—
185#117C2×D5911yescharacteristic
186#107—592no—
187#106—592no—
188#103—592no—
189#103—592no—
190#102—592no—
191#102—592no—
192C24C22⋊D5911yescharacteristic
193#41—22no—
194#41—22no—
195#41—1182no—
196#41—1182no—
197C2×Q8—591no—
198C2×Q8C22×D5911yescharacteristic
199C2×D4—22no—
200C2×D4—21no—
201C2×D4—591no—
202C2×D4—1182no—
203C2×D4—1181no—
204C2×D4C22×D5911yescharacteristic
205C22×C4—22no—
206C22×C4—22no—
207C22×C4—21no—
208C22×C4—1181no—
209C22×C4C22⋊D5911yescharacteristic
210C22×C4C22⋊D5912yes—
211C22×C4C22×D5912yes—
212C22×C4C22×D5911yescharacteristic
213Q16—1182no—
214SD16—1182no—
215SD16—1182no—
216D8—1182no—
217M16—1184no—
218M16—1184no—
219C2×C8—594no—
220C2×C8—591no—
221C2×C8—591no—
222C2×C8—592no—
223C2×C8—1182no—
224C4⋊C4—22no—
225C4⋊C4—592no—
226C4⋊C4—1182no—
227C4⋊C4C22×D5912yes—
228C22⋊C4—21no—
229C22⋊C4—22no—
230C22⋊C4—22no—
231C22⋊C4—1181no—
232C22⋊C4—1182no—
233C22⋊C4—1182no—
234C42—21no—
235C42—1181no—
236C23—22no—
237C23—21no—
238C23—42no—
239C23—1181no—
240C23C2×C22⋊D5912yes—
241C23C2×C22⋊D5911yescharacteristic
242Q8—21no—
243Q8—21no—
244Q8—1181no—
245Q8—1181no—
246D4—21no—
247D4—21no—
248D4—44no—
249D4—42no—
250D4—1181no—
251D4—1181no—
252D4—2364no—
253D4—2362no—
254C2×C4—22no—
255C2×C4—24no—
256C2×C4—22no—
257C2×C4—22no—
258C2×C4—22no—
259C2×C4—21no—
260C2×C4—42no—
261C2×C4—1182no—
262C2×C4—1181no—
263C2×C4—2362no—
264C2×C4D4×D5912yes—
265C2×C4#1174568712yes—
266C2×C4C2×C22⋊D5912yes—
267C2×C4C2×C22⋊D5911yescharacteristic
268C2×C4C23×D5911yescharacteristic
269C8—592no—
270C8—592no—
271C8—1182no—
272C22—22no—
273C22—22no—
274C22—22no—
275C22—22no—
276C22—44no—
277C22—41no—
278C22—42no—
279C22—2361no—
280C22—2362no—
281C22#1427369912yes—
282C22C22×C22⋊D5911yescharacteristic
283C4—22no—
284C4—41no—
285C4—42no—
286C4—2361no—
287C4—2362no—
288C4#1427369912yes—
289C4C2×D4×D5911yescharacteristic
290C4C2×#1174568711yescharacteristic
291C2—22no—
292C2—42no—
293C2—81no—
294C2—4721no—
295C2C2×#1427369911yescharacteristic
296C2#1683820012yes—
subgroupG/H
centerC2×C4C2×C22⋊D59
commutatorC2×C4×C59C24
FrattiniC2×C4C23×D59
FittingC59×#525C2
socleC22×C59C22×D4
hypercenter#525D59
hypocenterC59#3054
LCSG ▷ C2×C4×C59 ▷ C2×C59 ▷ C59
UCSC1 ◁ C2×C4 ◁ C23×C4 ◁ #525

Complements

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

NH ≅ G/Ntype
1. C2×#14273747C2semidirect
2. C22×#11745664C2semidirect
3. #16837913C2semidirect
4. #16837658C2semidirect
5. #16837653C2semidirect
6. #16837650C2semidirect
7. #16837646C2semidirect
8. #16837438C2semidirect
9. #16837398C2semidirect
10. #16837396C2semidirect
11. C59×#525C2semidirect
14. C2×#11745672C22semidirect
15. C2×#11745670C22semidirect
16. C2×#11745671C22semidirect
17. C2×#11745669C22semidirect
29. #14273660C22semidirect
30. #14273658C22semidirect
31. #14273651C22semidirect
32. #14273650C22semidirect
33. #14273648C22semidirect
34. #14273647C22semidirect
83. C2×C59⋊C8D4semidirect
152. #525D59semidirect
160. C59#3054semidirect