Finite Group Databasebeta

← #21433475

Subgroups — #21433475

Order 7552.

704 conjugacy classes of subgroups; only the 161 normal subgroups are shown.

normal subgroups only

This group has 704 conjugacy classes of subgroups — too many to draw. Only its 161 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×#14273757C212yesmaximal, complemented
2#16837973C211yesmaximal, characteristic, complemented
3#16837585C214yesmaximal, complemented
4#16837580C214yesmaximal, complemented
5#16837419C212yesmaximal, complemented
6#16837386C211yesmaximal, characteristic, complemented
7C59×#585C211yesmaximal, characteristic
8C22×Dic118C2211yescharacteristic, complemented
9#14273757—24no—
10#14273757C2218yescomplemented
11C2×#11745672—22no—
12C2×#11745670—22no—
13C2×#11745664C2212yescomplemented
14#14273725C2212yescomplemented
15#14273714C2212yescomplemented
16#14273708—22no—
17#14273706—22no—
18#14273686C2211yescharacteristic, complemented
19#14273654C2218yescomplemented
20#14273646C2212yescomplemented
21#14273644C2212yescomplemented
222−1+4×C59—22no—
232−1+4×C59C2212yes—
24H(5,𝔽2)×C59—22no—
25H(5,𝔽2)×C59—22no—
26H(5,𝔽2)×C59C2212yes—
27C2×#41×C59—24no—
28C2×#41×C59—22no—
29C2×#41×C59C2212yes—
30C2×#41×C59C2211yescharacteristic
31#41×C59—24no—
32#41×C59—28no—
33#41×C59—24no—
34#41×C59—24no—
35#41×C59—24no—
36#41×C59—22no—
37#41×C59—22no—
38#41×C59—24no—
39#41×C59—22no—
40#41×C59—22no—
41#41×C59D414yes—
42#41×C59C2314yes—
43C2×Q8×C59—22no—
44C2×Q8×C59—24no—
45C2×Q8×C59D412yes—
46C2×Q8×C59C2311yescharacteristic
47C2×D4×C59—28no—
48C2×D4×C59—22no—
49C2×D4×C59—24no—
50C2×D4×C59—22no—
51C2×D4×C59—24no—
52C2×D4×C59D412yes—
53C2×D4×C59D412yes—
54C2×D4×C59C2311yescharacteristic
55C22×C4×C59—24no—
56C22×C4×C59—22no—
57C22×C4×C59D412yes—
58C22×C4×C59C2311yescharacteristic
59C22×Dic59—21no—
60C2×Dic118—22no—
61C2×Dic118—22no—
62C2×Dic118—21no—
63C2×Dic118C2312yes—
64C22⋊Dic59—21no—
65C22⋊Dic59—24no—
66#11745672—28no—
67#11745670—28no—
68C4⋊Dic59—21no—
69Dic59⋊C4—24no—
70C4×Dic59C2312yes—
71#11745664—22no—
72#11745664C2314yes—
73C2×C59⋊C8—22no—
74C23×C59—24no—
75C23×C59—22no—
76C23×C59C2×D412yes—
77C23×C59C2×D411yescharacteristic
78Q8×C59—24no—
79Q8×C59—22no—
80Q8×C59—22no—
81Q8×C59C2×D414yes—
82D4×C59—28no—
83D4×C59—24no—
84D4×C59—24no—
85D4×C59—24no—
86D4×C59—24no—
87D4×C59—22no—
88D4×C59—22no—
89D4×C59C2×D414yes—
90C2×C4×C59—24no—
91C2×C4×C59—28no—
92C2×C4×C59—22no—
93C2×C4×C59—24no—
94C2×C4×C59—22no—
95C2×C4×C59—22no—
96C2×C4×C59—24no—
97C2×C4×C59C2×D412yes—
98C2×C4×C59C2×D411yescharacteristic
99C2×C4×C59C2×D412yes—
100C2×C4×C59C2×D412yes—
101C2×C4×C59C2411yescharacteristic
102C2×Dic59—22no—
103C2×Dic59—22no—
104C2×Dic59—42no—
105Dic118—24no—
106Dic118—41no—
107Dic118—41no—
108C59⋊C8—24no—
109C22×C59—22no—
110C22×C59—24no—
111C22×C59—41no—
112C22×C59—42no—
113C22×C59—82no—
114C22×C59—84no—
115C22×C59#12012yes—
116C22×C59C22×D411yescharacteristic
117C4×C59—24no—
118C4×C59—22no—
119C4×C59#12011yescharacteristic
120C4×C59#12011yescharacteristic
121C4×C59C22×D412yes—
122Dic59—42no—
123Dic59—42no—
124#3022—591nomaximal, Sylow
125C2×C59—21no—
126C2×C59—22no—
127C2×C59—42no—
128C2×C59—44no—
129C2×C59C2×#12011yescharacteristic
130#585D5911yescharacteristic
131C2×#137—592no—
132#536—591no—
133#456—594no—
134#455—594no—
135#421—592no—
136#413—591no—
137C59#302211yescharacteristic, complemented, Sylow
1382−1+4—22no—
1392−1+4C2×D5912yes—
140H(5,𝔽2)—22no—
141H(5,𝔽2)—22no—
142H(5,𝔽2)C2×D5912yes—
143C2×#41—24no—
144C2×#41—22no—
145C2×#41C2×D5912yes—
146C2×#41C2×D5911yescharacteristic
147C22×Q8—591no—
148#137—598no—
149#137—1184no—
150C2×Q16—1182no—
151C2×SD16—1182no—
152C2×M16—592no—
153C4⋊Q8—592no—
154#124—592no—
155#123—1182no—
156C22⋊Q8—1182no—
157#117—591no—
158#104—598no—
159#101—592no—
160#100—592no—
161#41—24no—
162#41—28no—
163#41—24no—
164#41—24no—
165#41—24no—
166#41—22no—
167#41—22no—
168#41—24no—
169#41—22no—
170#41—22no—
171#41C22⋊D5914yes—
172#41C22×D5914yes—
173C2×Q8—22no—
174C2×Q8—24no—
175C2×Q8—592no—
176C2×Q8—1181no—
177C2×Q8—1182no—
178C2×Q8—1182no—
179C2×Q8C22⋊D5912yes—
180C2×Q8C22×D5911yescharacteristic
181C2×D4—28no—
182C2×D4—22no—
183C2×D4—24no—
184C2×D4—22no—
185C2×D4—24no—
186C2×D4C22⋊D5912yes—
187C2×D4C22⋊D5912yes—
188C2×D4C22×D5911yescharacteristic
189C22×C4—24no—
190C22×C4—22no—
191C22×C4—1181no—
192C22×C4C22⋊D5912yes—
193C22×C4C22×D5911yescharacteristic
194Q16—1188no—
195SD16—1188no—
196M16—594no—
197M16—1182no—
198C2×C8—1182no—
199C4⋊C4—1181no—
200C4⋊C4—1184no—
201C22⋊C4—1181no—
202C22⋊C4—1184no—
203C42—592no—
204C23—24no—
205C23—22no—
206C23C2×C22⋊D5912yes—
207C23C2×C22⋊D5911yescharacteristic
208Q8—24no—
209Q8—22no—
210Q8—22no—
211Q8—1184no—
212Q8—2361no—
213Q8—2361no—
214Q8C2×C22⋊D5914yes—
215D4—28no—
216D4—24no—
217D4—24no—
218D4—24no—
219D4—24no—
220D4—22no—
221D4—22no—
222D4C2×C22⋊D5914yes—
223C2×C4—24no—
224C2×C4—28no—
225C2×C4—22no—
226C2×C4—24no—
227C2×C4—22no—
228C2×C4—22no—
229C2×C4—24no—
230C2×C4—1182no—
231C2×C4—1182no—
232C2×C4—2362no—
233C2×C4C2×C22⋊D5912yes—
234C2×C4C2×C22⋊D5911yescharacteristic
235C2×C4C2×C22⋊D5912yes—
236C2×C4C2×C22⋊D5912yes—
237C2×C4C23×D5911yescharacteristic
238C8—1184no—
239C22—22no—
240C22—24no—
241C22—41no—
242C22—42no—
243C22—82no—
244C22—84no—
245C22#1427369612yes—
246C22C22×C22⋊D5911yescharacteristic
247C4—24no—
248C4—22no—
249C4—2362no—
250C4—2362no—
251C4#1427369611yescharacteristic
252C4#1427369611yescharacteristic
253C4C22×C22⋊D5912yes—
254C2—21no—
255C2—22no—
256C2—42no—
257C2—44no—
258C2C2×#1427369611yescharacteristic
subgroupG/H
centerC2C2×#14273696
commutatorC2×C4×C59C24
FrattiniC2×C4C23×D59
FittingC59×#585C2
socleC2×C59C2×#120
hypercenter#585D59
hypocenterC59#3022
LCSG ▷ C2×C4×C59 ▷ C2×C59 ▷ C59
UCSC1 ◁ C2 ◁ C22×C4 ◁ #585

Complements

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

NH ≅ G/Ntype
1. C2×#14273757C2semidirect
2. #16837973C2semidirect
3. #16837585C2semidirect
4. #16837580C2semidirect
5. #16837419C2semidirect
6. #16837386C2semidirect
8. C22×Dic118C22semidirect
10. #14273757C22semidirect
13. C2×#11745664C22semidirect
14. #14273725C22semidirect
15. #14273714C22semidirect
18. #14273686C22semidirect
19. #14273654C22semidirect
20. #14273646C22semidirect
21. #14273644C22semidirect
137. C59#3022semidirect