Finite Group Databasebeta

← #21434545

Subgroups — #21434545

Order 7552.

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

normal subgroups only

This group has 656 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×#14273754C212yesmaximal, complemented
2C2×#14273751C212yesmaximal, complemented
3#16837951C211yesmaximal, characteristic, complemented
4#127×D59C211yesmaximal, characteristic, complemented
5#16837792C211yesmaximal, characteristic, complemented
6#16837791C211yesmaximal, characteristic, complemented
7#16837789C211yesmaximal, characteristic, complemented
8#16837777C212yesmaximal, complemented
9#16837773C212yesmaximal, complemented
10#16837354C211yesmaximal, characteristic, complemented
11C59×#496C211yesmaximal, characteristic, complemented
12C2×#11745689C2211yescharacteristic
13C2×#11745687C2211yescharacteristic
14C2×D4×D59—22no—
15C2×D4×D59C2212yes—
16#14273754—28no—
17#14273751—28no—
18C2×#11745660C2212yescomplemented
19C2×#11745670C2212yescomplemented
20C2×#11745671C2212yescomplemented
21C2×D472C2212yescomplemented
22C2×#11745669C2212yescomplemented
23C2×#11745669C2212yescomplemented
24C2×#11745659C2212yes—
25#14273725C2211yescharacteristic, complemented
26#14273724C2211yescharacteristic
27#14273723—22no—
28#14273723C2212yes—
29#14273723C2211yescharacteristic, complemented
30#14273715C2211yescharacteristic, complemented
31#14273700—22no—
32(C22⋊D59)⋊C4—22no—
33C42×D59C2211yescharacteristic
34#14273638C2211yescharacteristic, complemented
35C8×Dic59C2212yescomplemented
36C2×SD16×C59C2212yescomplemented
37C2×D8×C59C2212yescomplemented
38#127×C59C2211yescharacteristic
39#124×C59C2211yescharacteristic, complemented
40#97×C59C2211yescharacteristic, complemented
41C23×D59—22no—
42C2×Q8×C59C2311yescharacteristic
43C2×D4×C59—22no—
44C2×D4×C59C2311yescharacteristic
45C2×D4×C59C2312yes—
46C2×C22⋊D59—21no—
47C2×C22⋊D59—22no—
48C2×C22⋊D59—22no—
49C2×C22⋊D59—24no—
50C22×Dic59—21no—
51#11745689—24no—
52#11745687—24no—
53D4×D59—24no—
54D4×D59—24no—
55D4×D59—48no—
56C2×D236—21no—
57C2×D236—22no—
58C2×D236C2311yescharacteristic
59C2×D236C2312yes—
60C2×C4×D59—21no—
61C2×C4×D59D412yes—
62C2×C4×D59C2311yescharacteristic
63C2×Dic118C2311yescharacteristic
64SD16×C59—24no—
65D8×C59—24no—
66C2×C8×C59C2312yes—
67C22⋊C4×C59—22no—
68C42×C59C2311yescharacteristic
69#11745671—24no—
70#11745670—24no—
71#11745669—24no—
72#11745669—24no—
73(C2×D59)⋊C4—22no—
74Dic59⋊C4—22no—
75C4×Dic59D412yes—
76C4×Dic59C2311yescharacteristic
77C2×C59⋊C8C2312yes—
78D472—24no—
79#11745660—24no—
80#11745659D418yescomplemented
81C23×C59—21no—
82C23×C59—22no—
83C22×D59—21no—
84C22×D59—22no—
85C22×D59—48no—
86C22×D59—44no—
87C22×D59C2×D411yescharacteristic
88Q8×C59—22no—
89D4×C59—22no—
90D4×C59—22no—
91D4×C59—22no—
92D4×C59—44no—
93C2×C4×C59—21no—
94C2×C4×C59C2×D412yes—
95C2×C4×C59C2411yescharacteristic
96C22⋊D59—42no—
97C22⋊D59—44no—
98C22⋊D59—48no—
99C22⋊D59—44no—
100C2×Dic59—21no—
101C2×Dic59—42no—
102C2×Dic59C2×D411yescharacteristic
103C2×Dic59C2×D412yes—
104D236—22no—
105D236—22no—
106D236—22no—
107D236—44no—
108D236—42no—
109C4×D59—24no—
110C4×D59—42no—
111C4×D59C2×D414yes—
112Dic118—22no—
113C8×C59C2×D414yescomplemented
114C59⋊C8C2×D414yescomplemented
115C22×C59—41no—
116C22×C59—42no—
117C22×C59—44no—
118C22×C59—42no—
119C22×C59C22×D411yescharacteristic
120C2×D59—22no—
121C2×D59—41no—
122C2×D59—42no—
123C2×D59—44no—
124C2×D59—42no—
125C2×D59—88no—
126C2×D59#12712yes—
127C4×C59—22no—
128C4×C59—41no—
129C4×C59C22×D412yes—
130Dic59—41no—
131Dic59#12712yes—
132Dic59AGL(1,ℤ/8)14yescomplemented
133#3151—591nomaximal, Sylow
134C2×C59—82no—
135C2×C59—81no—
136C2×C59C2×#12711yescharacteristic
137C2×C59C2×AGL(1,ℤ/8)12yes—
138D59—22no—
139D59—81no—
140D59—82no—
141C2×AGL(1,ℤ/8)—592no—
142C2×AGL(1,ℤ/8)—592no—
143#532—591no—
144C2×#127—591no—
145#496—591no—
146#496—591no—
147#496—591no—
148#496D5911yescharacteristic, complemented
149#493—592no—
150#492—592no—
151C4×M16—591no—
152C59#315111yescharacteristic, complemented, Sylow
153C2×#41—591no—
154C2×#41—591no—
155C22×D4—592no—
156C22×D4—1182no—
157AGL(1,ℤ/8)—1188no—
158AGL(1,ℤ/8)—1188no—
159C2×SD16—592no—
160C2×SD16—592no—
161C2×SD16—592no—
162C2×SD16C2×D5912yescomplemented
163C2×D8—592no—
164C2×D8—592no—
165C2×D8—592no—
166C2×D8C2×D5912yescomplemented
167C2×M16—592no—
168C4⋊Q8—591no—
169#127—592no—
170#127—591no—
171#127—591no—
172#127—1182no—
173#127C2×D5911yescharacteristic
174#124—591no—
175#124C2×D5911yescharacteristic, complemented
176#121—1182no—
177C4×D4—1182no—
178C2×C42—591no—
179#97—591no—
180#97C2×D5911yescharacteristic, complemented
181C4×C8—592no—
182C24—1182no—
183#41—1184no—
184#41—1184no—
185C2×Q8—591no—
186C2×Q8C22×D5911yescharacteristic
187C2×D4—22no—
188C2×D4—591no—
189C2×D4—592no—
190C2×D4—1181no—
191C2×D4—1184no—
192C2×D4—1184no—
193C2×D4—1182no—
194C2×D4—1184no—
195C2×D4—1182no—
196C2×D4—1181no—
197C2×D4—1182no—
198C2×D4—2368no—
199C2×D4C22×D5911yescharacteristic
200C2×D4C22×D5912yes—
201C22×C4—591no—
202C22×C4—592no—
203C22×C4—1181no—
204C22×C4—1181no—
205SD16—24no—
206SD16—1184no—
207SD16—1184no—
208SD16—1184no—
209D8—24no—
210D8—1184no—
211D8—1184no—
212D8—1184no—
213M16—598no—
214C2×C8—592no—
215C2×C8C22×D5912yes—
216C4⋊C4—1182no—
217C22⋊C4—22no—
218C22⋊C4—1182no—
219C42—592no—
220C42—591no—
221C42C22×D5911yescharacteristic
222C23—21no—
223C23—22no—
224C23—591no—
225C23—1181no—
226C23—1182no—
227C23—2364no—
228C23—2368no—
229Q8—22no—
230Q8—1182no—
231D4—22no—
232D4—22no—
233D4—22no—
234D4—44no—
235D4—1182no—
236D4—1182no—
237D4—1182no—
238D4—2364no—
239D4—2362no—
240D4—2364no—
241D4—2364no—
242D4—2368no—
243D4—2362no—
244C2×C4—21no—
245C2×C4—592no—
246C2×C4—591no—
247C2×C4—594no—
248C2×C4—1184no—
249C2×C4—1181no—
250C2×C4—2362no—
251C2×C4—2362no—
252C2×C4D4×D5912yes—
253C2×C4C23×D5911yescharacteristic
254C8—594no—
255C8D4×D5914yescomplemented
256C22—44no—
257C22—42no—
258C22—41no—
259C22—42no—
260C22—592no—
261C22—1182no—
262C22—4728no—
263C22—2364no—
264C22—2362no—
265C22—2361no—
266C22—2362no—
267C22C2×D4×D5911yescharacteristic
268C4—22no—
269C4—41no—
270C4—594no—
271C4—592no—
272C4—2361no—
273C4C2×D4×D5912yes—
274C2—82no—
275C2—81no—
276C2—1182no—
277C2—4722no—
278C2—4721no—
279C2#127×D5911yescharacteristic
280C2AGL(1,ℤ/8)×D5912yes—
subgroupG/H
centerC22C2×D4×D59
commutatorC2×C4×C59C24
FrattiniC2×C4C23×D59
FittingC59×#496C2
socleC22×C59C22×D4
hypercenter#496D59
hypocenterC59#3151
LCSG ▷ C2×C4×C59 ▷ C2×C59 ▷ C59
UCSC1 ◁ C22 ◁ C42 ◁ #496

Complements

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

NH ≅ G/Ntype
1. C2×#14273754C2semidirect
2. C2×#14273751C2semidirect
3. #16837951C2semidirect
4. #127×D59C2semidirect
5. #16837792C2semidirect
6. #16837791C2semidirect
7. #16837789C2semidirect
8. #16837777C2semidirect
9. #16837773C2semidirect
10. #16837354C2semidirect
11. C59×#496C2semidirect
18. C2×#11745660C22semidirect
19. C2×#11745670C22semidirect
20. C2×#11745671C22semidirect
21. C2×D472C22semidirect
22. C2×#11745669C22semidirect
23. C2×#11745669C22semidirect
25. #14273725C22semidirect
29. #14273723C22semidirect
30. #14273715C22semidirect
34. #14273638C22semidirect
35. C8×Dic59C22semidirect
36. C2×SD16×C59C22semidirect
37. C2×D8×C59C22semidirect
39. #124×C59C22semidirect
40. #97×C59C22semidirect
80. #11745659D4semidirect
113. C8×C59C2×D4semidirect
114. C59⋊C8C2×D4semidirect
132. Dic59AGL(1,ℤ/8)semidirect
148. #496D59semidirect
152. C59#3151semidirect
162. C2×SD16C2×D59semidirect
166. C2×D8C2×D59semidirect
175. #124C2×D59semidirect
180. #97C2×D59semidirect
255. C8D4×D59semidirect