Finite Group Databasebeta

← #21433362

Subgroups — #21433362

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
2C2×#14273753C211yesmaximal, characteristic, complemented
3C22×#11745669C211yesmaximal, characteristic, complemented
4#16837545C214yesmaximal, complemented
5#16837535C214yesmaximal, complemented
6#16837406C211yesmaximal, characteristic, complemented
7#16837396C211yesmaximal, characteristic, complemented
8#16837369C211yesmaximal, characteristic, complemented
9C59×#535C211yesmaximal, characteristic, complemented
10#14273773—24no—
11#14273773—24no—
12C2×#11745689—21no—
13C2×#11745685C2211yescharacteristic
14C2×#11745685C2212yescomplemented
15C22×D236C2211yescharacteristic
16C22×D236C2212yescomplemented
17C2×D4×D59—21no—
18C2×D4×D59—22no—
19#14273753—24no—
20C2×#11745670C2212yescomplemented
21C2×#11745669—24no—
22C2×#11745669C2214yescomplemented
23C2×#11745669C2212yescomplemented
24C2×#11745664C2211yescharacteristic, complemented
25C22×C59⋊C8C2211yescharacteristic, complemented
26#14273650C2212yescomplemented
27#14273647C2212yescomplemented
28#14273647C2214yescomplemented
29C22⋊(C59⋊C8)C2214yescomplemented
30C2×#41×C59C2211yescharacteristic
31C22×D4×C59C2211yescharacteristic, complemented
32#127×C59—21no—
33#124×C59—21no—
34#121×C59C2214yescomplemented
35#120×C59—22no—
36#117×C59C2211yescharacteristic, complemented
37C24×C59—21no—
38C23×D59—21no—
39C23×D59—22no—
40#41×C59—22no—
41#41×C59—22no—
42C2×Q8×C59D411yescharacteristic
43C2×D4×C59—24no—
44C2×D4×C59—22no—
45C2×D4×C59—22no—
46C2×D4×C59—21no—
47C2×D4×C59D412yes—
48C2×D4×C59D411yescharacteristic
49C2×D4×C59C2312yes—
50C22×C4×C59C2312yes—
51C22×C4×C59C2311yescharacteristic
52C2×C22⋊D59—21no—
53C2×C22⋊D59—22no—
54#11745689—28no—
55D4×D59—216no—
56D4×D59—28no—
57#11745685—22no—
58#11745685—24no—
59#11745685—24no—
60#11745685D414yescomplemented
61C2×D236—21no—
62C2×D236—22no—
63C2×D236—22no—
64C2×D236—24no—
65C2×D236—24no—
66C2×D236D414yescomplemented
67C2×D236C2312yes—
68C2×D236C2311yescharacteristic
69C2×C4×D59—21no—
70C2×C4×D59—22no—
71C2×Dic118C2311yescharacteristic
72C4⋊C4×C59C2312yes—
73C22⋊C4×C59—21no—
74C22⋊C4×C59—24no—
75C42×C59—21no—
76#11745670—24no—
77#11745669—28no—
78#11745669—24no—
79#11745664—22no—
80C2×C59⋊C8—22no—
81C2×C59⋊C8C2312yes—
82C2×C59⋊C8C2312yes—
83C23×C59—22no—
84C23×C59—42no—
85C23×C59—82no—
86C23×C59C2×D412yes—
87C23×C59C2×D411yescharacteristic
88C22×D59—21no—
89C22×D59—22no—
90C22×D59—28no—
91C22×D59—24no—
92C22×D59—82no—
93C22×D59—84no—
94Q8×C59—22no—
95D4×C59—24no—
96D4×C59—22no—
97D4×C59—22no—
98D4×C59—22no—
99D4×C59—42no—
100D4×C59—84no—
101C2×C4×C59—22no—
102C2×C4×C59—22no—
103C2×C4×C59—22no—
104C2×C4×C59C2×D412yes—
105C2×C4×C59C2×D412yes—
106C2×C4×C59C2×D412yes—
107C2×C4×C59C2×D411yescharacteristic
108C2×C4×C59C2411yescharacteristic
109C22⋊D59—28no—
110C22⋊D59—24no—
111C2×Dic59—21no—
112D236—28no—
113D236—24no—
114D236—21no—
115D236—22no—
116D236C2×D412yes—
117D236C2×D414yes—
118C4×D59—28no—
119C4×D59—24no—
120Dic118—21no—
121Dic118C2×D412yes—
122C59⋊C8—22no—
123C59⋊C8—22no—
124C22×C59—22no—
125C22×C59—22no—
126C22×C59—24no—
127C22×C59—42no—
128C22×C59—44no—
129C22×C59—84no—
130C22×C59#12012yes—
131C22×C59C22×D411yescharacteristic
132C2×D59—24no—
133C2×D59—22no—
134C2×D59—44no—
135C2×D59—42no—
136C2×D59—84no—
137C2×D59—88no—
138C4×C59—22no—
139C4×C59—42no—
140C4×C59#12012yes—
141C4×C59C22×D411yescharacteristic
142C4×C59C22×D411yescharacteristic
143Dic59—22no—
144#3008—591nomaximal, Sylow
145C2×C59—22no—
146C2×C59—42no—
147C2×C59—82no—
148C2×C59C2×#12011yescharacteristic
149C2×C59#57612yes—
150D59—44no—
151D59—42no—
152C2×H(5,𝔽2)—591no—
153C2×AGL(1,ℤ/8)—591no—
154C22×D8—591no—
155#535D5911yescharacteristic, complemented
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—591no—
169C22×D4—592no—
170C22×D4—1182no—
171C22×D4—1181no—
172C22×D4C2×D5911yescharacteristic, complemented
173AGL(1,ℤ/8)—1184no—
174C2×SD16—592no—
175C2×D8—594no—
176C2×D8—592no—
177C2×D8—1184no—
178C2×M16—591no—
179C22×C8—591no—
180#127—21no—
181#124—21no—
182#121C2×D5914yescomplemented
183#120—22no—
184#117C2×D5911yescharacteristic, complemented
185#103—592no—
186#102—592no—
187#102—594no—
188C22⋊C8—594no—
189C24—21no—
190C24—1182no—
191C24—1181no—
192#41—22no—
193#41—22no—
194#41—594no—
195#41—1184no—
196#41—1184no—
197#41—1188no—
198#41—1182no—
199C2×Q8—591no—
200C2×Q8C22⋊D5911yescharacteristic
201C2×D4—24no—
202C2×D4—22no—
203C2×D4—22no—
204C2×D4—21no—
205C2×D4—594no—
206C2×D4—592no—
207C2×D4—591no—
208C2×D4—1184no—
209C2×D4—1184no—
210C2×D4—11816no—
211C2×D4—1188no—
212C2×D4—1182no—
213C2×D4—1181no—
214C2×D4—1182no—
215C2×D4—1182no—
216C2×D4—1181no—
217C2×D4C22⋊D5912yes—
218C2×D4C22⋊D5911yescharacteristic
219C2×D4C22×D5912yes—
220C22×C4—1182no—
221C22×C4—1181no—
222C22×C4C22×D5912yes—
223C22×C4C22×D5911yescharacteristic
224SD16—1184no—
225D8—1188no—
226D8—1184no—
227M16—1182no—
228C2×C8—592no—
229C2×C8—592no—
230C2×C8—1182no—
231C4⋊C4C22×D5912yes—
232C22⋊C4—21no—
233C22⋊C4—24no—
234C42—21no—
235C23—22no—
236C23—42no—
237C23—82no—
238C23—1188no—
239C23—1184no—
240C23—1182no—
241C23—1181no—
242C23—4722no—
243C23—4724no—
244C23C2×C22⋊D5912yes—
245C23C2×C22⋊D5911yescharacteristic
246Q8—22no—
247Q8—592no—
248Q8—1181no—
249D4—24no—
250D4—22no—
251D4—22no—
252D4—22no—
253D4—42no—
254D4—84no—
255D4—594no—
256D4—592no—
257D4—1188no—
258D4—1188no—
259D4—1184no—
260D4—1184no—
261D4—1181no—
262D4—1182no—
263C2×C4—22no—
264C2×C4—22no—
265C2×C4—22no—
266C2×C4—1188no—
267C2×C4—1181no—
268C2×C4—1184no—
269C2×C4D4×D5912yes—
270C2×C4D4×D5912yes—
271C2×C4C2×C22⋊D5912yes—
272C2×C4C2×C22⋊D5911yescharacteristic
273C2×C4C23×D5911yescharacteristic
274C8—1182no—
275C8—1182no—
276C22—22no—
277C22—24no—
278C22—22no—
279C22—44no—
280C22—42no—
281C22—84no—
282C22—1184no—
283C22—1182no—
284C22—4724no—
285C22—4728no—
286C22—2364no—
287C22—2362no—
288C22#1427369512yes—
289C22C22×C22⋊D5911yescharacteristic
290C4—22no—
291C4—42no—
292C4—1182no—
293C4#1427369512yes—
294C4C2×D4×D5911yescharacteristic
295C4C2×D4×D5911yescharacteristic
296C2—22no—
297C2—42no—
298C2—82no—
299C2—2364no—
300C2—2362no—
301C2C2×#1427369511yescharacteristic
302C2#1683820512yes—
subgroupG/H
centerC22C22×C22⋊D59
commutatorC2×C4×C59C24
FrattiniC2×C4C23×D59
FittingC59×#535C2
socleC22×C59C22×D4
hypercenter#535D59
hypocenterC59#3008
LCSG ▷ C2×C4×C59 ▷ C2×C59 ▷ C59
UCSC1 ◁ C22 ◁ C2×#41 ◁ #535

Complements

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

NH ≅ G/Ntype
1. C2×#14273773C2semidirect
2. C2×#14273753C2semidirect
3. C22×#11745669C2semidirect
4. #16837545C2semidirect
5. #16837535C2semidirect
6. #16837406C2semidirect
7. #16837396C2semidirect
8. #16837369C2semidirect
9. C59×#535C2semidirect
14. C2×#11745685C22semidirect
16. C22×D236C22semidirect
20. C2×#11745670C22semidirect
22. C2×#11745669C22semidirect
23. C2×#11745669C22semidirect
24. C2×#11745664C22semidirect
25. C22×C59⋊C8C22semidirect
26. #14273650C22semidirect
27. #14273647C22semidirect
28. #14273647C22semidirect
29. C22⋊(C59⋊C8)C22semidirect
31. C22×D4×C59C22semidirect
34. #121×C59C22semidirect
36. #117×C59C22semidirect
60. #11745685D4semidirect
66. C2×D236D4semidirect
155. #535D59semidirect
161. C59#3008semidirect
172. C22×D4C2×D59semidirect
182. #121C2×D59semidirect
184. #117C2×D59semidirect