Finite Group Databasebeta

← #21435148

Subgroups — #21435148

Order 7552.

420 conjugacy classes of subgroups; only the 117 normal subgroups are shown.

normal subgroups only

This group has 420 conjugacy classes of subgroups — too many to draw. Only its 117 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
1#16838007C211yesmaximal, characteristic, complemented
2#16837971C211yesmaximal, characteristic, complemented
3#16837791C211yesmaximal, characteristic, complemented
4#16837779C211yesmaximal, characteristic, complemented
5#16837767C211yesmaximal, characteristic, complemented
6#16837757C211yesmaximal, characteristic, complemented
7#16837618C212yesmaximal, complemented
8#16837598C212yesmaximal, complemented
9#16837549C212yesmaximal, complemented
10#16837538C212yesmaximal, complemented
11C59×#433C211yesmaximal, characteristic, complemented
12C2×#11745685C2211yescharacteristic
13C22×D236C2211yescharacteristic
14C2×#11745660C2212yescomplemented
15C2×D472C2212yes—
16C2×D472C2212yes—
17C2×D472C2212yescomplemented
18#14273724C2211yescharacteristic
19#14273724C2211yescharacteristic
20#14273724C2211yescharacteristic, complemented
21#14273719C2211yescharacteristic, complemented
22#14273715C2211yescharacteristic
23#14273715C2211yescharacteristic
24#14273712—22no—
25#14273702—22no—
26#14273701C2212yes—
27#14273700—22no—
28#14273697—22no—
29C4×D236C2212yescomplemented
30#14273652C2212yescomplemented
31#14273649C2212yes—
32#14273649C2212yes—
33#14273649C2212yescomplemented
34#117×C59C2211yescharacteristic
35C4⋊C8×C59C2212yescomplemented
36C22⋊C8×C59C2212yes—
37#97×C59C2211yescharacteristic, complemented
38C4×C8×C59C2211yescharacteristic, complemented
39C23×D59—21no—
40C22×C4×C59C2311yescharacteristic
41C2×C22⋊D59—21no—
42C2×C22⋊D59—22no—
43#11745685—42no—
44C2×D236—21no—
45C2×D236—22no—
46C2×D236—22no—
47C2×D236—22no—
48C2×D236—42no—
49C2×D236C2311yescharacteristic
50C2×D236C2311yescharacteristic
51C2×D236C2311yescharacteristic
52C2×D236C2312yes—
53C2×C4×D59—21no—
54C2×C4×D59—22no—
55C2×Dic118C2311yescharacteristic
56C2×C8×C59C2312yes—
57C2×C8×C59C2312yes—
58C4⋊C4×C59D412yes—
59C22⋊C4×C59D412yes—
60C42×C59C2311yescharacteristic
61C42×C59C2311yescharacteristic
62(C2×D59)⋊C4—22no—
63(C2×D59)⋊C4—22no—
64(C2×D59)⋊C4—22no—
65(C2×D59)⋊C4—22no—
66C4⋊Dic59C2312yes—
67Dic59⋊C4—22no—
68D472—42no—
69D472—42no—
70D472—42no—
71#11745660—42no—
72C23×C59C2×D411yescharacteristic
73C22×D59—22no—
74C22×D59—21no—
75C22×D59—21no—
76C22×D59—21no—
77C22×D59—42no—
78C22×D59—82no—
79C2×C4×C59—22no—
80C2×C4×C59C2×D412yes—
81C2×C4×C59C2×D412yes—
82C2×C4×C59C2×D411yescharacteristic
83C2×C4×C59C2411yescharacteristic
84C22⋊D59—42no—
85C22⋊D59—82no—
86C2×Dic59—22no—
87C2×Dic59—21no—
88D236—22no—
89D236—22no—
90D236—22no—
91D236—22no—
92D236—22no—
93D236—42no—
94D236—82no—
95D236—82no—
96D236—82no—
97C4×D59—42no—
98C4×D59—82no—
99Dic118—22no—
100C8×C59—22no—
101C8×C59—22no—
102C22×C59—21no—
103C22×C59—22no—
104C22×C59C22×D411yescharacteristic
105C2×D59—41no—
106C2×D59—41no—
107C2×D59—41no—
108C2×D59—42no—
109C2×D59—42no—
110C2×D59—42no—
111C2×D59—42no—
112C2×D59—42no—
113C2×D59—42no—
114C2×D59—84no—
115C4×C59—21no—
116C4×C59—22no—
117C4×C59—22no—
118C4×C59H(5,𝔽2)12yes—
119Dic59—41no—
120Dic59—42no—
121#3220—591nomaximal, Sylow
122C2×C59—41no—
123C2×C59#53511yescharacteristic
124C2×C59#57612yes—
125D59—81no—
126D59—82no—
127D59—81no—
128D59—81no—
129#540—591no—
130#535—591no—
131#496—591no—
132#493—591no—
133#490—591no—
134#488—591no—
135#463—592no—
136#459—592no—
137#449—592no—
138#447—592no—
139#433D5911yescharacteristic, complemented
140C59#322011yescharacteristic, complemented, Sylow
141C2×#41—591no—
142C22×D4—591no—
143C2×SD16—592no—
144C2×D8—592no—
145C2×D8—592no—
146C2×D8—592no—
147#127—591no—
148#127—591no—
149#127—591no—
150#125—591no—
151#124—591no—
152#124—591no—
153#123—1182no—
154#121—592no—
155#121—1182no—
156#121—1182no—
157#120—1182no—
158C4×D4—592no—
159#117C2×D5911yescharacteristic
160C4⋊C8C2×D5912yescomplemented
161#103—592no—
162#102—592no—
163#102—592no—
164#102—592no—
165C22⋊C8C2×D5912yes—
166#97C2×D5911yescharacteristic, complemented
167C4×C8C2×D5911yescharacteristic, complemented
168C24—1181no—
169#41—2362no—
170C2×Q8—591no—
171C2×D4—591no—
172C2×D4—591no—
173C2×D4—591no—
174C2×D4—592no—
175C2×D4—1182no—
176C2×D4—1181no—
177C2×D4—1182no—
178C2×D4—1182no—
179C2×D4—1182no—
180C2×D4—1181no—
181C2×D4—2362no—
182C22×C4—1182no—
183C22×C4—1181no—
184C22×C4C22×D5911yescharacteristic
185SD16—2362no—
186D8—2362no—
187D8—2362no—
188D8—2362no—
189C2×C8C22×D5912yes—
190C2×C8C22×D5912yes—
191C4⋊C4—592no—
192C4⋊C4—1182no—
193C4⋊C4D23612yes—
194C22⋊C4—1182no—
195C22⋊C4—1182no—
196C22⋊C4—1182no—
197C22⋊C4—1182no—
198C22⋊C4D23612yes—
199C42C22×D5911yescharacteristic
200C42C22×D5911yescharacteristic
201C23—1182no—
202C23—1181no—
203C23—1181no—
204C23—1181no—
205C23—4722no—
206C23—2362no—
207C23C2×D23611yescharacteristic
208Q8—1182no—
209D4—1182no—
210D4—1182no—
211D4—1182no—
212D4—1182no—
213D4—1182no—
214D4—4722no—
215D4—4722no—
216D4—4722no—
217D4—4722no—
218D4—2362no—
219D4—2362no—
220C2×C4—22no—
221C2×C4—1181no—
222C2×C4—1182no—
223C2×C4—4722no—
224C2×C4—2362no—
225C2×C4C2×D23612yes—
226C2×C4C2×D23612yes—
227C2×C4C2×D23611yescharacteristic
228C2×C4C23×D5911yescharacteristic
229C8—22no—
230C8—22no—
231C22—22no—
232C22—21no—
233C22—4724no—
234C22—2362no—
235C22—2362no—
236C22—2362no—
237C22—2362no—
238C22—2362no—
239C22—2361no—
240C22—2361no—
241C22—2361no—
242C22—2362no—
243C22C22×D23611yescharacteristic
244C4—22no—
245C4—22no—
246C4—21no—
247C4—2362no—
248C4—2361no—
249C4#1427377312yes—
250C2—41no—
251C2—4721no—
252C2—4721no—
253C2—4722no—
254C2—4721no—
255C2#1683797111yescharacteristic
256C2#1683820712yes—
subgroupG/H
centerC22C22×D236
commutatorC2×C4×C59C24
FrattiniC2×C4C23×D59
FittingC59×#433C2
socleC22×C59C22×D4
hypercenter#433D59
hypocenterC59#3220
LCSG ▷ C2×C4×C59 ▷ C2×C59 ▷ C59
UCSC1 ◁ C22 ◁ #117 ◁ #433

Complements

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

NH ≅ G/Ntype
1. #16838007C2semidirect
2. #16837971C2semidirect
3. #16837791C2semidirect
4. #16837779C2semidirect
5. #16837767C2semidirect
6. #16837757C2semidirect
7. #16837618C2semidirect
8. #16837598C2semidirect
9. #16837549C2semidirect
10. #16837538C2semidirect
11. C59×#433C2semidirect
14. C2×#11745660C22semidirect
17. C2×D472C22semidirect
20. #14273724C22semidirect
21. #14273719C22semidirect
29. C4×D236C22semidirect
30. #14273652C22semidirect
33. #14273649C22semidirect
35. C4⋊C8×C59C22semidirect
37. #97×C59C22semidirect
38. C4×C8×C59C22semidirect
139. #433D59semidirect
140. C59#3220semidirect
160. C4⋊C8C2×D59semidirect
166. #97C2×D59semidirect
167. C4×C8C2×D59semidirect