Finite Group Databasebeta

← #21434568

Subgroups — #21434568

Order 7552.

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

normal subgroups only

This group has 564 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×#14273757C211yesmaximal, characteristic, complemented
2C2×#14273753C211yesmaximal, characteristic, complemented
3C2×#14273747C211yesmaximal, characteristic, complemented
4C22×#11745670C211yesmaximal, characteristic, complemented
5#16837978C211yesmaximal, characteristic, complemented
6#16837797C212yesmaximal, complemented
7#16837789C212yesmaximal, complemented
8#16837784C212yesmaximal, complemented
9#16837774C212yesmaximal, complemented
10#16837358C211yesmaximal, characteristic, complemented
11C59×#535C211yesmaximal, characteristic, complemented
12C2×#11745685C2211yescharacteristic
13C22×Dic118C2211yescharacteristic
14#14273757—24no—
15#14273753—24no—
16#14273747—24no—
17C2×#11745672C2211yescharacteristic, complemented
18C2×#11745672C2212yescomplemented
19C2×#11745670—24no—
20C2×#11745670C2212yes—
21C2×#11745670C2212yes—
22C2×#11745670C2212yes—
23C2×#11745670C2211yescharacteristic, complemented
24C2×#11745670C2212yescomplemented
25C2×#11745671C2211yescharacteristic, complemented
26C2×#11745669C2212yes—
27C2×#11745669C2211yescharacteristic, complemented
28C2×#11745664C2211yescharacteristic
29C22×C59⋊C8C2211yescharacteristic
30#14273727C2212yescomplemented
31#14273715C2212yescomplemented
32#14273711—22no—
33#14273707—22no—
34#14273638C2212yescomplemented
35C4×C59⋊C8C2212yescomplemented
36C2×#41×C59C2211yescharacteristic
37C22×D4×C59C2211yescharacteristic
38#127×C59C2212yes—
39#124×C59C2212yes—
40#121×C59—22no—
41#120×C59—22no—
42#117×C59C2211yescharacteristic
43C24×C59—21no—
44#41×C59—22no—
45#41×C59—22no—
46C2×Q8×C59C2311yescharacteristic
47C2×D4×C59—21no—
48C2×D4×C59—22no—
49C2×D4×C59—22no—
50C2×D4×C59—21no—
51C2×D4×C59—24no—
52C2×D4×C59C2312yes—
53C2×D4×C59C2311yescharacteristic
54C22×C4×C59—21no—
55C22×C4×C59C2311yescharacteristic
56C2×C22⋊D59—21no—
57C22×Dic59—21no—
58#11745685—22no—
59#11745685—22no—
60C2×D236C2311yescharacteristic
61C2×C4×D59—21no—
62C2×Dic118—22no—
63C2×Dic118—22no—
64C2×Dic118—21no—
65C2×Dic118C2312yes—
66C2×Dic118C2311yescharacteristic
67C4⋊C4×C59D412yes—
68C22⋊C4×C59—24no—
69C22⋊C4×C59D412yes—
70C42×C59C2312yes—
71#11745672—22no—
72#11745672—24no—
73#11745671—22no—
74#11745670—24no—
75#11745670—24no—
76#11745670—24no—
77#11745670—22no—
78#11745670—24no—
79#11745669—24no—
80#11745669—22no—
81(C2×D59)⋊C4—24no—
82C4⋊Dic59—24no—
83#11745664D414yescomplemented
84C2×C59⋊C8D414yescomplemented
85C2×C59⋊C8C2311yescharacteristic
86C2×C59⋊C8C2312yes—
87C2×C59⋊C8C2311yescharacteristic
88C23×C59—22no—
89C23×C59—21no—
90C23×C59—42no—
91C23×C59—82no—
92C23×C59C2×D411yescharacteristic
93C22×D59—21no—
94Q8×C59—21no—
95Q8×C59—21no—
96D4×C59—22no—
97D4×C59—21no—
98D4×C59—22no—
99D4×C59—21no—
100D4×C59—42no—
101D4×C59—42no—
102D4×C59—84no—
103C2×C4×C59—21no—
104C2×C4×C59—42no—
105C2×C4×C59C2×D412yes—
106C2×C4×C59C2×D412yes—
107C2×C4×C59C2×D414yes—
108C2×C4×C59C2×D411yescharacteristic
109C2×C4×C59C2411yescharacteristic
110C22⋊D59—42no—
111C2×Dic59—21no—
112C2×Dic59—22no—
113C2×Dic59—42no—
114D236—21no—
115D236—21no—
116C4×D59—42no—
117Dic118—22no—
118Dic118—21no—
119Dic118—22no—
120Dic118—21no—
121Dic118—42no—
122C59⋊C8C2×D412yes—
123C59⋊C8C2×D412yes—
124C59⋊C8C2×D414yes—
125C22×C59—22no—
126C22×C59—41no—
127C22×C59—42no—
128C22×C59—42no—
129C22×C59—44no—
130C22×C59—84no—
131C22×C59#12712yes—
132C22×C59C22×D411yescharacteristic
133C2×D59—41no—
134C2×D59—42no—
135C4×C59—24no—
136C4×C59—41no—
137C4×C59#12712yes—
138C4×C59C22×D411yescharacteristic
139C4×C59C22×D411yescharacteristic
140Dic59—42no—
141Dic59—41no—
142#3154—591nomaximal, Sylow
143C2×C59—22no—
144C2×C59—81no—
145C2×C59—82no—
146C2×C59C2×#12711yescharacteristic
147C2×C59#57712yes—
148D59—81no—
149C2×#137—591no—
150C2×AGL(1,ℤ/8)—591no—
151C2×#135—591no—
152C22×SD16—591no—
153#536—591no—
154#535D5911yescharacteristic, complemented
155#497—592no—
156#496—592no—
157#495—592no—
158#492—592no—
159#405—591no—
160C59#315411yescharacteristic, complemented, Sylow
161C2×#41—591no—
162C2×#41C2×D5911yescharacteristic
163C22×Q8—591no—
164C22×D4C2×D5911yescharacteristic
165#137—1184no—
166AGL(1,ℤ/8)—1184no—
167#135—1184no—
168C2×Q16—591no—
169C2×Q16—592no—
170C2×SD16—591no—
171C2×SD16—592no—
172C2×SD16—592no—
173C2×SD16—591no—
174C2×SD16—592no—
175C2×SD16—592no—
176C2×SD16—1184no—
177C2×D8—591no—
178C2×D8—592no—
179C2×M16—591no—
180C22×C8—591no—
181C4⋊Q8—592no—
182#127C2×D5912yes—
183#124—592no—
184#124C2×D5912yes—
185#123—1182no—
186C22⋊Q8—1182no—
187#121—22no—
188#120—22no—
189#117C2×D5911yescharacteristic
190#97—592no—
191C4×C8—592no—
192C24—21no—
193#41—22no—
194#41—22no—
195#41—1182no—
196#41—1182no—
197C2×Q8—592no—
198C2×Q8—591no—
199C2×Q8—1181no—
200C2×Q8—1182no—
201C2×Q8—1182no—
202C2×Q8C22×D5911yescharacteristic
203C2×D4—21no—
204C2×D4—22no—
205C2×D4—22no—
206C2×D4—21no—
207C2×D4—24no—
208C2×D4—591no—
209C2×D4—1181no—
210C2×D4C22×D5912yes—
211C2×D4C22×D5911yescharacteristic
212C22×C4—21no—
213C22×C4—1181no—
214C22×C4—1181no—
215C22×C4C22×D5911yescharacteristic
216Q16—1182no—
217Q16—1184no—
218SD16—1184no—
219SD16—1184no—
220SD16—1182no—
221SD16—1184no—
222SD16—1184no—
223SD16—1182no—
224D8—1182no—
225D8—1184no—
226M16—594no—
227C2×C8—594no—
228C2×C8—591no—
229C2×C8—592no—
230C2×C8—591no—
231C4⋊C4—1184no—
232C4⋊C4C22⋊D5912yes—
233C22⋊C4—24no—
234C22⋊C4—1184no—
235C22⋊C4C22⋊D5912yes—
236C42C22×D5912yes—
237C23—22no—
238C23—21no—
239C23—42no—
240C23—82no—
241C23—1181no—
242C23C2×C22⋊D5911yescharacteristic
243Q8—21no—
244Q8—21no—
245Q8—1182no—
246Q8—1181no—
247Q8—1182no—
248Q8—1181no—
249Q8—2362no—
250D4—22no—
251D4—21no—
252D4—22no—
253D4—21no—
254D4—42no—
255D4—42no—
256D4—84no—
257D4—1181no—
258D4—1181no—
259D4—2362no—
260C2×C4—21no—
261C2×C4—42no—
262C2×C4—1182no—
263C2×C4—1181no—
264C2×C4—2362no—
265C2×C4—2362no—
266C2×C4D4×D5912yes—
267C2×C4D4×D5912yes—
268C2×C4C2×C22⋊D5914yes—
269C2×C4C2×C22⋊D5911yescharacteristic
270C2×C4C23×D5911yescharacteristic
271C8—592no—
272C8—592no—
273C8—594no—
274C22—22no—
275C22—41no—
276C22—42no—
277C22—42no—
278C22—44no—
279C22—84no—
280C22—2361no—
281C22—2362no—
282C22#1427372312yes—
283C22C22×C22⋊D5911yescharacteristic
284C4—24no—
285C4—41no—
286C4—2361no—
287C4—2362no—
288C4#1427372312yes—
289C4C2×D4×D5911yescharacteristic
290C4C2×D4×D5911yescharacteristic
291C2—22no—
292C2—82no—
293C2—81no—
294C2—4721no—
295C2C2×#1427372311yescharacteristic
296C2#1683821312yes—
subgroupG/H
centerC22C22×C22⋊D59
commutatorC2×C4×C59C24
FrattiniC2×C4C23×D59
FittingC59×#535C2
socleC22×C59C22×D4
hypercenter#535D59
hypocenterC59#3154
LCSG ▷ C2×C4×C59 ▷ C2×C59 ▷ C59
UCSC1 ◁ C22 ◁ #117 ◁ #535

Complements

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

NH ≅ G/Ntype
1. C2×#14273757C2semidirect
2. C2×#14273753C2semidirect
3. C2×#14273747C2semidirect
4. C22×#11745670C2semidirect
5. #16837978C2semidirect
6. #16837797C2semidirect
7. #16837789C2semidirect
8. #16837784C2semidirect
9. #16837774C2semidirect
10. #16837358C2semidirect
11. C59×#535C2semidirect
17. C2×#11745672C22semidirect
18. C2×#11745672C22semidirect
23. C2×#11745670C22semidirect
24. C2×#11745670C22semidirect
25. C2×#11745671C22semidirect
27. C2×#11745669C22semidirect
30. #14273727C22semidirect
31. #14273715C22semidirect
34. #14273638C22semidirect
35. C4×C59⋊C8C22semidirect
83. #11745664D4semidirect
84. C2×C59⋊C8D4semidirect
154. #535D59semidirect
160. C59#3154semidirect