Finite Group Databasebeta

← #21433360

Subgroups — #21433360

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×#14273772C211yesmaximal, characteristic, complemented
2C2×#14273753C211yesmaximal, characteristic, complemented
3#16837969C211yesmaximal, characteristic, complemented
4#16837544C214yesmaximal, complemented
5#16837534C214yesmaximal, complemented
6#16837407C211yesmaximal, characteristic, complemented
7#16837399C211yesmaximal, characteristic, complemented
8#16837368C211yesmaximal, characteristic, complemented
9C22×D8×C59C211yesmaximal, characteristic, complemented
10#14273772—24no—
11#14273772—24no—
12C2×#11745685C2211yescharacteristic
13C2×#11745685C2211yescharacteristic
14C2×#11745687—21no—
15C2×#11745687C2212yescomplemented
16C22×C22⋊D59—22no—
17C2×D4×D59—21no—
18C2×D4×D59C2212yescomplemented
19#14273753—24no—
20C2×#11745670C2212yescomplemented
21C2×#11745669C2212yescomplemented
22C2×#11745664C2211yescharacteristic, complemented
23#14273723—21no—
24#14273714—21no—
25#14273698C2214yescomplemented
26#14273696—22no—
27#14273686C2211yescharacteristic, complemented
28#14273652C2212yescomplemented
29#14273649C2212yescomplemented
30#14273648C2214yescomplemented
31(C2×D59)⋊C8C2214yescomplemented
32C22×D4×C59C2211yescharacteristic
33C22×D4×C59C2211yescharacteristic, complemented
34C2×D8×C59—24no—
35C2×D8×C59C2214yescomplemented
36C22×C8×C59C2211yescharacteristic, complemented
37C24×C59—21no—
38C24×C59—21no—
39C23×D59—22no—
40C2×D4×C59—21no—
41C2×D4×C59—22no—
42C2×D4×C59—22no—
43C2×D4×C59—22no—
44C2×D4×C59—21no—
45C2×D4×C59D414yescomplemented
46C2×D4×C59C2312yes—
47C2×D4×C59C2312yes—
48C22×C4×C59C2311yescharacteristic
49C2×C22⋊D59—216no—
50C2×C22⋊D59—21no—
51C2×C22⋊D59—22no—
52C2×C22⋊D59—24no—
53C2×C22⋊D59—22no—
54C2×C22⋊D59D412yes—
55C22×Dic59—22no—
56#11745687—28no—
57#11745687—24no—
58#11745687—24no—
59D4×D59—28no—
60D4×D59—24no—
61D4×D59—24no—
62#11745685—22no—
63#11745685—22no—
64#11745685—22no—
65#11745685D414yescomplemented
66C2×D236D411yescharacteristic
67C2×D236C2311yescharacteristic
68C2×C4×D59—21no—
69C2×C4×D59C2312yes—
70C2×Dic118D411yescharacteristic
71C2×Dic118C2311yescharacteristic
72D8×C59—28no—
73C2×C8×C59—22no—
74C2×C8×C59C2312yes—
75C22⋊Dic59—21no—
76C22⋊Dic59—24no—
77#11745670—24no—
78#11745669—24no—
79C4⋊Dic59C2312yes—
80C4×Dic59—21no—
81#11745664—22no—
82C2×C59⋊C8C2312yes—
83C23×C59—22no—
84C23×C59—24no—
85C23×C59—22no—
86C23×C59—42no—
87C23×C59—82no—
88C23×C59—82no—
89C23×C59C2×D411yescharacteristic
90C22×D59—21no—
91C22×D59—28no—
92C22×D59—84no—
93C22×D59C2×D412yes—
94D4×C59—24no—
95D4×C59—22no—
96D4×C59—22no—
97D4×C59—22no—
98D4×C59—42no—
99D4×C59C2×D414yes—
100C2×C4×C59C2×D411yescharacteristic
101C2×C4×C59C2×D412yes—
102C2×C4×C59C2×D412yes—
103C2×C4×C59C2411yescharacteristic
104C22⋊D59—28no—
105C22⋊D59—28no—
106C22⋊D59—24no—
107C22⋊D59—24no—
108C22⋊D59—84no—
109C2×Dic59—28no—
110C2×Dic59—21no—
111C2×Dic59—22no—
112C2×Dic59C2×D412yes—
113D236—22no—
114D236—21no—
115D236C2×D412yes—
116C4×D59—24no—
117C4×D59—22no—
118C4×D59—22no—
119Dic118—22no—
120Dic118—21no—
121Dic118C2×D412yes—
122C8×C59—22no—
123C59⋊C8—22no—
124C22×C59—22no—
125C22×C59—24no—
126C22×C59—44no—
127C22×C59—42no—
128C22×C59—44no—
129C22×C59—84no—
130C22×C59—84no—
131C22×C59#12012yes—
132C22×C59C22×D411yescharacteristic
133C2×D59—22no—
134C2×D59—22no—
135C2×D59—24no—
136C2×D59—42no—
137C2×D59—88no—
138C4×C59#12012yes—
139C4×C59C22×D411yescharacteristic
140C4×C59C22×D411yescharacteristic
141Dic59—22no—
142Dic59—22no—
143Dic59—42no—
144#3008—591nomaximal, Sylow
145C2×C59—22no—
146C2×C59—44no—
147C2×C59—82no—
148C2×C59C2×#12011yescharacteristic
149C2×C59#57612yes—
150D59—42no—
151D59—42no—
152C2×H(5,𝔽2)—591no—
153C2×AGL(1,ℤ/8)—591no—
154C22×D8D5911yescharacteristic, complemented
155#535—591no—
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—591no—
167C2×#41—1181no—
168C22×D4—592no—
169C22×D4—1181no—
170C22×D4—1182no—
171C22×D4C2×D5911yescharacteristic
172C22×D4C2×D5911yescharacteristic, complemented
173AGL(1,ℤ/8)—1184no—
174C2×SD16—592no—
175C2×D8—24no—
176C2×D8—592no—
177C2×D8C2×D5914yescomplemented
178C2×M16—591no—
179C22×C8C2×D5911yescharacteristic, complemented
180#127—1181no—
181#124—1181no—
182#121—594no—
183#120—1182no—
184#117—591no—
185#103—592no—
186#102—594no—
187#102—592no—
188C22⋊C8—594no—
189C24—21no—
190C24—21no—
191C24—1182no—
192#41—594no—
193#41—1184no—
194#41—1188no—
195#41—1184no—
196#41—1182no—
197#41—1182no—
198#41—1182no—
199C2×Q8—591no—
200C2×Q8—591no—
201C2×D4—21no—
202C2×D4—22no—
203C2×D4—22no—
204C2×D4—21no—
205C2×D4—22no—
206C2×D4—592no—
207C2×D4—591no—
208C2×D4—591no—
209C2×D4—1182no—
210C2×D4—1184no—
211C2×D4—1188no—
212C2×D4—1182no—
213C2×D4—11816no—
214C2×D4—1181no—
215C2×D4—1184no—
216C2×D4—1184no—
217C2×D4C22⋊D5914yescomplemented
218C2×D4C22×D5912yes—
219C2×D4C22×D5912yes—
220C22×C4—592no—
221C22×C4—1182no—
222C22×C4—1181no—
223C22×C4C22×D5911yescharacteristic
224SD16—1184no—
225D8—28no—
226D8—1184no—
227M16—1182no—
228C2×C8—22no—
229C2×C8—592no—
230C2×C8C22×D5912yes—
231C4⋊C4—592no—
232C22⋊C4—1184no—
233C22⋊C4—1181no—
234C42—1181no—
235C23—22no—
236C23—24no—
237C23—22no—
238C23—42no—
239C23—82no—
240C23—82no—
241C23—592no—
242C23—1188no—
243C23—1181no—
244C23—4724no—
245C23D4×D5911yescharacteristic
246Q8—592no—
247Q8—1182no—
248Q8—1181no—
249D4—24no—
250D4—22no—
251D4—22no—
252D4—22no—
253D4—42no—
254D4—592no—
255D4—1188no—
256D4—1188no—
257D4—1184no—
258D4—1184no—
259D4—1182no—
260D4—1181no—
261D4—4724no—
262D4C2×C22⋊D5914yes—
263C2×C4—592no—
264C2×C4—1188no—
265C2×C4—1181no—
266C2×C4—1184no—
267C2×C4—1182no—
268C2×C4—1182no—
269C2×C4—1182no—
270C2×C4D4×D5911yescharacteristic
271C2×C4D4×D5912yes—
272C2×C4C2×C22⋊D5912yes—
273C2×C4C23×D5911yescharacteristic
274C8—22no—
275C8—1182no—
276C22—22no—
277C22—24no—
278C22—44no—
279C22—44no—
280C22—42no—
281C22—84no—
282C22—84no—
283C22—1184no—
284C22—1182no—
285C22—1182no—
286C22—4728no—
287C22—2362no—
288C22#1427369512yes—
289C22C2×D4×D5911yescharacteristic
290C4—1182no—
291C4—1182no—
292C4—2362no—
293C4#1427369512yes—
294C4C2×D4×D5911yescharacteristic
295C4C22×C22⋊D5911yescharacteristic
296C2—22no—
297C2—44no—
298C2—82no—
299C2—2362no—
300C2—2362no—
301C2C2×#1427369511yescharacteristic
302C2#1683820312yes—
subgroupG/H
centerC22C2×D4×D59
commutatorC2×C4×C59C24
FrattiniC2×C4C23×D59
FittingC22×D8×C59C2
socleC22×C59C22×D4
hypercenterC22×D8D59
hypocenterC59#3008
LCSG ▷ C2×C4×C59 ▷ C2×C59 ▷ C59
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×D8

Complements

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

NH ≅ G/Ntype
1. C2×#14273772C2semidirect
2. C2×#14273753C2semidirect
3. #16837969C2semidirect
4. #16837544C2semidirect
5. #16837534C2semidirect
6. #16837407C2semidirect
7. #16837399C2semidirect
8. #16837368C2semidirect
9. C22×D8×C59C2semidirect
15. C2×#11745687C22semidirect
18. C2×D4×D59C22semidirect
20. C2×#11745670C22semidirect
21. C2×#11745669C22semidirect
22. C2×#11745664C22semidirect
25. #14273698C22semidirect
27. #14273686C22semidirect
28. #14273652C22semidirect
29. #14273649C22semidirect
30. #14273648C22semidirect
31. (C2×D59)⋊C8C22semidirect
33. C22×D4×C59C22semidirect
35. C2×D8×C59C22semidirect
36. C22×C8×C59C22semidirect
45. C2×D4×C59D4semidirect
65. #11745685D4semidirect
154. C22×D8D59semidirect
161. C59#3008semidirect
172. C22×D4C2×D59semidirect
177. C2×D8C2×D59semidirect
179. C22×C8C2×D59semidirect
217. C2×D4C22⋊D59semidirect