Finite Group Databasebeta

← #21435712

Subgroups — #21435712

Order 7552.

556 conjugacy classes of subgroups; only the 133 normal subgroups are shown.

normal subgroups only

This group has 556 conjugacy classes of subgroups — too many to draw. Only its 133 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×#14273753C212yesmaximal, complemented
2#16838073C211yesmaximal, characteristic, complemented
3#16837778C211yesmaximal, characteristic, complemented
4#16837653C212yesmaximal, complemented
5#16837599C211yesmaximal, characteristic, complemented
6#16837597C211yesmaximal, characteristic, complemented
7#16837545C212yesmaximal, complemented
8#16837536C212yesmaximal, complemented
9C4×#11745670C211yesmaximal, characteristic, complemented
10#16837480C211yesmaximal, characteristic, complemented
11D42×C59C211yesmaximal, characteristic, complemented
12C2×#11745685C2212yescomplemented
13#14273753—28no—
14C2×#11745670C2211yescharacteristic
15C2×#11745670C2212yescomplemented
16C2×#11745669C2212yes—
17C2×#11745669C2212yescomplemented
18C2×#11745669C2212yescomplemented
19C2×#11745664C2212yescomplemented
20#14273724C2211yescharacteristic, complemented
21#14273723—21no—
22#14273701C2212yescomplemented
23#14273700—22no—
24C4×Dic118C2211yescharacteristic, complemented
25#14273689—21no—
26#14273658C2211yescharacteristic, complemented
27C4⋊(C59⋊C8)C2211yescharacteristic, complemented
28#14273650C2211yescharacteristic, complemented
29#14273648C2211yescharacteristic
30#14273648C2212yescomplemented
31#14273647C2212yescomplemented
32C22⋊(C59⋊C8)C2212yescomplemented
33C4×C59⋊C8C2211yescharacteristic, complemented
34C22×D4×C59—21no—
35C22×D4×C59C2212yes—
36#127×C59C2211yescharacteristic
37#121×C59—21no—
38#121×C59C2212yes—
39#120×C59—22no—
40C4×D4×C59C2211yescharacteristic
41C4×D4×C59C2211yescharacteristic
42C24×C59—22no—
43C2×D4×C59—24no—
44C2×D4×C59—22no—
45C2×D4×C59—22no—
46C2×D4×C59—21no—
47C2×D4×C59—21no—
48C2×D4×C59—42no—
49C2×D4×C59—44no—
50C2×D4×C59D411yescharacteristic
51C2×D4×C59C2312yes—
52C2×D4×C59C2311yescharacteristic
53C22×C4×C59—21no—
54C22×C4×C59C2312yes—
55C2×C22⋊D59—22no—
56C2×C22⋊D59—22no—
57#11745685—24no—
58#11745685—42no—
59C2×D236—21no—
60C2×D236—21no—
61C2×D236C2312yes—
62C2×C4×D59—22no—
63C2×Dic118C2311yescharacteristic
64C4⋊C4×C59D411yescharacteristic
65C4⋊C4×C59C2311yescharacteristic
66C22⋊C4×C59—21no—
67C22⋊C4×C59—22no—
68C22⋊C4×C59D412yes—
69C42×C59C2311yescharacteristic
70#11745670—24no—
71#11745670D414yescomplemented
72#11745669—24no—
73#11745669—24no—
74#11745669—42no—
75(C2×D59)⋊C4—22no—
76C4⋊Dic59C2311yescharacteristic
77Dic59⋊C4—21no—
78C4×Dic59—21no—
79#11745664—24no—
80C2×C59⋊C8C2311yescharacteristic
81C2×C59⋊C8C2312yes—
82C2×C59⋊C8C2311yescharacteristic
83C23×C59—21no—
84C23×C59—22no—
85C23×C59—44no—
86C23×C59—44no—
87C23×C59—82no—
88C23×C59C2×D412yes—
89C22×D59—22no—
90D4×C59—22no—
91D4×C59—22no—
92D4×C59—21no—
93D4×C59—22no—
94D4×C59—44no—
95D4×C59—44no—
96D4×C59—42no—
97D4×C59—81no—
98D4×C59C2×D412yes—
99C2×C4×C59—22no—
100C2×C4×C59—22no—
101C2×C4×C59—21no—
102C2×C4×C59—42no—
103C2×C4×C59C2×D411yescharacteristic
104C2×C4×C59C2×D412yes—
105C2×C4×C59C2×D411yescharacteristic
106C2×C4×C59C2411yescharacteristic
107C22⋊D59—44no—
108C22⋊D59—82no—
109C2×Dic59—21no—
110C2×Dic59—21no—
111D236—22no—
112D236—22no—
113D236—42no—
114D236—81no—
115C4×D59—44no—
116Dic118—21no—
117Dic118C2×D412yescomplemented
118C59⋊C8—22no—
119C59⋊C8—21no—
120C59⋊C8C2×D412yescomplemented
121C22×C59—22no—
122C22×C59—22no—
123C22×C59—22no—
124C22×C59—22no—
125C22×C59—41no—
126C22×C59—41no—
127C22×C59—42no—
128C22×C59—42no—
129C22×C59—42no—
130C22×C59—88no—
131C22×C59C22×D411yescharacteristic
132C2×D59—42no—
133C2×D59—42no—
134C2×D59—42no—
135C4×C59—22no—
136C4×C59—21no—
137C4×C59—41no—
138C4×C59AGL(1,ℤ/8)12yescomplemented
139C4×C59C22×D411yescharacteristic
140C4×C59H(5,𝔽2)11yescharacteristic
141Dic59—22no—
142Dic59—41no—
143#3274—591nomaximal, Sylow
144C2×C59—42no—
145C2×C59—42no—
146C2×C59—82no—
147C2×C59D4211yescharacteristic
148C2×C59C2×AGL(1,ℤ/8)11yescharacteristic
149C2×C59#57611yescharacteristic
150D59—82no—
151C2×AGL(1,ℤ/8)—592no—
152#550—591no—
153D42D5911yescharacteristic, complemented
154#493—591no—
155#469—592no—
156#460—591no—
157#459—591no—
158#449—592no—
159#447—592no—
160C4×SD16—591no—
161#436—591no—
162C59#327411yescharacteristic, complemented, Sylow
163C2×#41—592no—
164C22×D4—21no—
165C22×D4C2×D5912yes—
166AGL(1,ℤ/8)—1188no—
167C2×SD16—591no—
168C2×SD16—592no—
169C2×D8—592no—
170C2×D8—592no—
171C2×D8—592no—
172C2×M16—592no—
173#127—591no—
174#127—1181no—
175#127C2×D5911yescharacteristic
176#121—21no—
177#121—592no—
178#121—1182no—
179#121C2×D5912yes—
180#120—22no—
181C4×Q8—591no—
182C4×D4—1181no—
183C4×D4C2×D5911yescharacteristic
184C4×D4C2×D5911yescharacteristic
185#106—591no—
186C4⋊C8—591no—
187#103—591no—
188#102—591no—
189#102—592no—
190#102—592no—
191C22⋊C8—592no—
192C4×C8—591no—
193C24—22no—
194#41—1184no—
195#41—2362no—
196C2×Q8—591no—
197C2×D4—24no—
198C2×D4—22no—
199C2×D4—22no—
200C2×D4—21no—
201C2×D4—21no—
202C2×D4—42no—
203C2×D4—44no—
204C2×D4—592no—
205C2×D4—1182no—
206C2×D4—1182no—
207C2×D4—1181no—
208C2×D4—1181no—
209C2×D4C22⋊D5911yescharacteristic
210C2×D4C22×D5912yes—
211C2×D4C22×D5911yescharacteristic
212C22×C4—21no—
213C22×C4—1182no—
214C22×C4C22×D5912yes—
215SD16—594no—
216SD16—1184no—
217D8—1184no—
218D8—1184no—
219D8—2362no—
220M16—1184no—
221C2×C8—591no—
222C2×C8—591no—
223C2×C8—592no—
224C4⋊C4—591no—
225C4⋊C4—1181no—
226C4⋊C4C22⋊D5911yescharacteristic
227C4⋊C4C22×D5911yescharacteristic
228C22⋊C4—21no—
229C22⋊C4—22no—
230C22⋊C4—1182no—
231C22⋊C4C22⋊D5912yes—
232C42—1181no—
233C42C22×D5911yescharacteristic
234C23—21no—
235C23—22no—
236C23—44no—
237C23—44no—
238C23—82no—
239C23—1182no—
240C23C2×C22⋊D5912yes—
241Q8—592no—
242Q8—1181no—
243D4—22no—
244D4—22no—
245D4—21no—
246D4—22no—
247D4—44no—
248D4—44no—
249D4—42no—
250D4—81no—
251D4—1182no—
252D4—1182no—
253D4—4721no—
254D4—4722no—
255D4—2364no—
256D4—2362no—
257D4D4×D5912yes—
258C2×C4—22no—
259C2×C4—22no—
260C2×C4—21no—
261C2×C4—42no—
262C2×C4—1181no—
263C2×C4—1181no—
264C2×C4—2364no—
265C2×C4C2×C22⋊D5911yescharacteristic
266C2×C4C2×C22⋊D5912yes—
267C2×C4C2×C22⋊D5911yescharacteristic
268C2×C4C23×D5911yescharacteristic
269C8—592no—
270C8—1182no—
271C8—1181no—
272C22—22no—
273C22—22no—
274C22—22no—
275C22—22no—
276C22—41no—
277C22—41no—
278C22—42no—
279C22—42no—
280C22—42no—
281C22—88no—
282C22—2362no—
283C22—2362no—
284C22—2362no—
285C22C22×C22⋊D5911yescharacteristic
286C4—21no—
287C4—22no—
288C4—41no—
289C4—1182no—
290C4—2361no—
291C4#1427375312yescomplemented
292C4C2×D4×D5911yescharacteristic
293C4#1427377211yescharacteristic
294C2—42no—
295C2—42no—
296C2—82no—
297C2—4722no—
298C2D4×C22⋊D5911yescharacteristic
299C2C2×#1427375311yescharacteristic
300C2#1683820511yescharacteristic
subgroupG/H
centerC22C22×C22⋊D59
commutatorC2×C4×C59C24
FrattiniC2×C4C23×D59
FittingD42×C59C2
socleC22×C59C22×D4
hypercenterD42D59
hypocenterC59#3274
LCSG ▷ C2×C4×C59 ▷ C2×C59 ▷ C59
UCSC1 ◁ C22 ◁ C4×D4 ◁ D42

Complements

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

NH ≅ G/Ntype
1. C2×#14273753C2semidirect
2. #16838073C2semidirect
3. #16837778C2semidirect
4. #16837653C2semidirect
5. #16837599C2semidirect
6. #16837597C2semidirect
7. #16837545C2semidirect
8. #16837536C2semidirect
9. C4×#11745670C2semidirect
10. #16837480C2semidirect
11. D42×C59C2semidirect
12. C2×#11745685C22semidirect
15. C2×#11745670C22semidirect
17. C2×#11745669C22semidirect
18. C2×#11745669C22semidirect
19. C2×#11745664C22semidirect
20. #14273724C22semidirect
22. #14273701C22semidirect
24. C4×Dic118C22semidirect
26. #14273658C22semidirect
27. C4⋊(C59⋊C8)C22semidirect
28. #14273650C22semidirect
30. #14273648C22semidirect
31. #14273647C22semidirect
32. C22⋊(C59⋊C8)C22semidirect
33. C4×C59⋊C8C22semidirect
71. #11745670D4semidirect
117. Dic118C2×D4semidirect
120. C59⋊C8C2×D4semidirect
138. C4×C59AGL(1,ℤ/8)semidirect
153. D42D59semidirect
162. C59#3274semidirect
291. C4#14273753semidirect