Finite Group Databasebeta

← #21435303

Subgroups — #21435303

Order 7552.

324 conjugacy classes of subgroups; only the 111 normal subgroups are shown.

normal subgroups only

This group has 324 conjugacy classes of subgroups — too many to draw. Only its 111 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#16837957C211yesmaximal, characteristic
2#125×D59C211yesmaximal, characteristic
3#16837808C211yesmaximal, characteristic, complemented
4#16837772C211yesmaximal, characteristic, complemented
5#16837771C211yesmaximal, characteristic, complemented
6#16837739C212yesmaximal
7#16837734C212yesmaximal
8#16837712C212yesmaximal, complemented
9#16837708C212yesmaximal, complemented
10#16837457C211yesmaximal, characteristic
11C59×#501C211yesmaximal, characteristic, complemented
12#14273727C2211yescharacteristic
13#14273719C2211yescharacteristic
14#14273718—21no—
15#14273718C2211yescharacteristic
16#14273718C2211yescharacteristic
17#14273717—21no—
18#14273717—21no—
19#14273707C2212yes—
20#14273703—21no—
21Q8×Dic59—21no—
22#14273692C2212yes—
23#14273685—21no—
24C4⋊C4×D59—21no—
25C4⋊C4×D59—21no—
26C4⋊C4×D59C2211yescharacteristic
27C4⋊C4×D59C2211yescharacteristic
28C42×D59C2211yescharacteristic
29#14273660C2212yes—
30#14273658C2212yes—
31Dic59⋊C8C2212yes—
32#14273652C2212yes—
33#14273652C2212yes—
34#14273650C2212yes—
35#14273650C2212yes—
36(C2×D59)⋊C8C2212yes—
37#14273638C2211yescharacteristic
38C4⋊Q8×C59C2211yescharacteristic
39#125×C59C2211yescharacteristic
40#107×C59C2212yes—
41#106×C59C2212yes—
42#97×C59C2211yescharacteristic
43C2×Q8×C59—21no—
44C2×C4×D59—21no—
45C2×C4×D59—21no—
46C2×C4×D59D411yescharacteristic
47C2×C4×D59D411yescharacteristic
48C2×C4×D59C2311yescharacteristic
49C2×Dic118C2312yes—
50C2×C8×C59C2312yes—
51C4⋊C4×C59—21no—
52C4⋊C4×C59—21no—
53C4⋊C4×C59—21no—
54C4⋊C4×C59C2311yescharacteristic
55C4⋊C4×C59C2312yes—
56C4⋊C4×C59C2311yescharacteristic
57C42×C59C2311yescharacteristic
58(C2×D59)⋊C4—22no—
59C4⋊Dic59—21no—
60C4⋊Dic59—21no—
61C4⋊Dic59—21no—
62C4⋊Dic59—21no—
63C4⋊Dic59—22no—
64C4⋊Dic59C2311yescharacteristic
65C4⋊Dic59C2311yescharacteristic
66Dic59⋊C4—21no—
67Dic59⋊C4—21no—
68Dic59⋊C4—21no—
69Dic59⋊C4—21no—
70Dic59⋊C4—21no—
71Dic59⋊C4—21no—
72Dic59⋊C4—22no—
73C4×Dic59—22no—
74C4×Dic59D411yescharacteristic
75C4×Dic59D411yescharacteristic
76C4×Dic59C2311yescharacteristic
77C2×C59⋊C8C2312yes—
78C22×D59C2×D411yescharacteristic
79Q8×C59—42no—
80C2×C4×C59—22no—
81C2×C4×C59—21no—
82C2×C4×C59—21no—
83C2×C4×C59C2×D411yescharacteristic
84C2×C4×C59C2×D411yescharacteristic
85C2×C4×C59C2411yescharacteristic
86C2×Dic59—22no—
87C2×Dic59—21no—
88C2×Dic59—21no—
89C2×Dic59C2×D411yescharacteristic
90C2×Dic59C2×D411yescharacteristic
91C2×Dic59C2×D411yescharacteristic
92C4×D59—22no—
93C4×D59—22no—
94C4×D59—41no—
95C4×D59—42no—
96C4×D59—42no—
97Dic118—24no—
98C8×C59—22no—
99C59⋊C8—22no—
100C22×C59C22×D411yescharacteristic
101C2×D59—21no—
102C2×D59—21no—
103C2×D59#13712yes—
104C4×C59—21no—
105C4×C59—21no—
106C4×C59—41no—
107C4×C59—41no—
108C4×C59—42no—
109C4×C592−1+412yes—
110Dic59—21no—
111Dic59—21no—
112Dic59—21no—
113Dic59—42no—
114Dic59—41no—
115Dic59—41no—
116#3236—591nomaximal, Sylow
117C2×C59#53611yescharacteristic
118C2×C59C2×#13711yescharacteristic
119C2×C59#57511yescharacteristic
120D59—22no—
121#533—591no—
122C2×#125—591no—
123#501—591no—
124#501D5911yescharacteristic, complemented
125#491—591no—
126#491—591no—
127#484—592no—
128#483—592no—
129#479—592no—
130#479—592no—
131#432—591no—
132C59#323611yescharacteristic, complemented, Sylow
133C4⋊Q8—591no—
134C4⋊Q8C2×D5911yescharacteristic
135#125—591no—
136#125—591no—
137#125—591no—
138#125—1181no—
139#125—1181no—
140#125—1181no—
141#125C2×D5911yescharacteristic
142C22⋊Q8—592no—
143C22⋊Q8—1181no—
144C4×Q8—592no—
145C4×Q8—1181no—
146#117—1181no—
147C2×C4⋊C4—591no—
148C2×C4⋊C4—591no—
149C2×C4⋊C4—1181no—
150C2×C4⋊C4—1181no—
151C2×C42—591no—
152#107—592no—
153#107C2×D5912yes—
154#106—592no—
155#106C2×D5912yes—
156C4⋊C8—592no—
157#103—592no—
158#103—592no—
159#103—592no—
160#103—592no—
161C22⋊C8—592no—
162#97—591no—
163#97C2×D5911yescharacteristic
164C2×Q8—21no—
165C2×Q8—592no—
166C22×C4—591no—
167C22×C4—591no—
168C22×C4—591no—
169C22×C4—1181no—
170C22×C4—1181no—
171C2×C8—592no—
172C2×C8C22×D5912yes—
173C4⋊C4—21no—
174C4⋊C4—21no—
175C4⋊C4—21no—
176C4⋊C4—591no—
177C4⋊C4—591no—
178C4⋊C4—1181no—
179C4⋊C4—1181no—
180C4⋊C4—1181no—
181C4⋊C4—1181no—
182C4⋊C4—1181no—
183C4⋊C4—1181no—
184C4⋊C4—1182no—
185C4⋊C4—1182no—
186C4⋊C4—1181no—
187C4⋊C4—1181no—
188C4⋊C4—1181no—
189C4⋊C4—1181no—
190C4⋊C4C22×D5911yescharacteristic
191C4⋊C4C22×D5911yescharacteristic
192C4⋊C4C22×D5912yes—
193C22⋊C4—1182no—
194C42—591no—
195C42—591no—
196C42—591no—
197C42—1182no—
198C42C22×D5911yescharacteristic
199C23—591no—
200Q8—42no—
201Q8—1184no—
202C2×C4—22no—
203C2×C4—21no—
204C2×C4—21no—
205C2×C4—591no—
206C2×C4—591no—
207C2×C4—591no—
208C2×C4—1182no—
209C2×C4—1182no—
210C2×C4—1182no—
211C2×C4—1181no—
212C2×C4—1181no—
213C2×C4—2361no—
214C2×C4—2362no—
215C2×C4—2362no—
216C2×C4D4×D5911yescharacteristic
217C2×C4D4×D5911yescharacteristic
218C2×C4C23×D5911yescharacteristic
219C8—22no—
220C8—1182no—
221C22—592no—
222C22—1181no—
223C22—1181no—
224C22C2×D4×D5911yescharacteristic
225C4—21no—
226C4—21no—
227C4—41no—
228C4—41no—
229C4—42no—
230C4—1181no—
231C4—1181no—
232C4—1181no—
233C4—2361no—
234C4—2361no—
235C4—2362no—
236C4#1427377512yes—
237C2—1182no—
238C2#1683797711yescharacteristic
239C2#137×D5911yescharacteristic
240C2#1683819811yescharacteristic
subgroupG/H
centerC22C2×D4×D59
commutatorC2×C4×C59C24
FrattiniC2×C4C23×D59
FittingC59×#501C2
socleC22×C59C22×D4
hypercenter#501D59
hypocenterC59#3236
LCSG ▷ C2×C4×C59 ▷ C2×C59 ▷ C59
UCSC1 ◁ C22 ◁ C42 ◁ #501

Complements

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

NH ≅ G/Ntype
3. #16837808C2semidirect
4. #16837772C2semidirect
5. #16837771C2semidirect
8. #16837712C2semidirect
9. #16837708C2semidirect
11. C59×#501C2semidirect
124. #501D59semidirect
132. C59#3236semidirect