Finite Group Databasebeta

← #21435472

Subgroups — #21435472

Order 7552.

348 conjugacy classes of subgroups; only the 113 normal subgroups are shown.

normal subgroups only

This group has 348 conjugacy classes of subgroups — too many to draw. Only its 113 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, complemented
2#16837939C211yesmaximal, characteristic
3#16837708C212yesmaximal, complemented
4#16837689C211yesmaximal, characteristic, complemented
5#16837659C212yesmaximal, complemented
6#16837649C212yesmaximal
7#16837627C212yesmaximal, complemented
8#16837612C211yesmaximal, characteristic, complemented
9#16837608C211yesmaximal, characteristic, complemented
10#16837424C211yesmaximal, characteristic, complemented
11C59×#477C211yesmaximal, characteristic, complemented
12C2×#11745672C2212yes—
13C2×#11745660C2212yes—
14C2×#11745659C2212yes—
15#14273727C2211yescharacteristic
16#14273722—21no—
17#14273718—21no—
18#14273718C2211yescharacteristic
19#14273716C2211yescharacteristic
20#14273712—21no—
21#14273707C2212yes—
22#14273703—21no—
23#14273703C2211yescharacteristic
24#14273702C2211yescharacteristic
25Q8×Dic59—21no—
26#14273692C2212yes—
27C4×D236—21no—
28C4×D236C2211yescharacteristic
29#14273685—21no—
30#14273684—21no—
31C42×D59C2211yescharacteristic
32#14273658C2212yes—
33C4⋊(C59⋊C8)C2211yescharacteristic
34Dic59⋊C8C2212yes—
35#14273652C2212yes—
36#14273650C2212yes—
37#14273647C2212yes—
38C4⋊Q8×C59C2211yescharacteristic
39C4×Q8×C59C2211yescharacteristic
40#107×C59C2212yes—
41C4⋊C8×C59C2211yescharacteristic
42#103×C59C2212yes—
43C2×Q8×C59—21no—
44C2×Q8×C59C2311yescharacteristic
45C2×D236—21no—
46C2×D236C2311yescharacteristic
47C2×C4×D59—21no—
48C2×C4×D59D411yescharacteristic
49C2×C4×D59D411yescharacteristic
50C2×C4×D59C2311yescharacteristic
51C2×Dic118C2312yes—
52C2×C8×C59C2312yes—
53C4⋊C4×C59—21no—
54C4⋊C4×C59—21no—
55C4⋊C4×C59C2312yes—
56C4⋊C4×C59C2311yescharacteristic
57C42×C59—21no—
58C42×C59C2311yescharacteristic
59#11745672—42no—
60(C2×D59)⋊C4—22no—
61(C2×D59)⋊C4—21no—
62(C2×D59)⋊C4—21no—
63(C2×D59)⋊C4—21no—
64(C2×D59)⋊C4—21no—
65(C2×D59)⋊C4—21no—
66C4⋊Dic59—21no—
67C4⋊Dic59—21no—
68C4⋊Dic59—21no—
69C4⋊Dic59—22no—
70C4⋊Dic59C2311yescharacteristic
71Dic59⋊C4—21no—
72Dic59⋊C4—21no—
73Dic59⋊C4—22no—
74C4×Dic59—22no—
75C4×Dic59D411yescharacteristic
76C4×Dic59D411yescharacteristic
77C4×Dic59C2311yescharacteristic
78C2×C59⋊C8C2312yes—
79#11745660—42no—
80#11745659—42no—
81C22×D59—21no—
82C22×D59C2×D411yescharacteristic
83Q8×C59—21no—
84Q8×C59—21no—
85Q8×C59—42no—
86C2×C4×C59—22no—
87C2×C4×C59—21no—
88C2×C4×C59—21no—
89C2×C4×C59C2×D411yescharacteristic
90C2×C4×C59C2×D411yescharacteristic
91C2×C4×C59C2411yescharacteristic
92C2×Dic59—22no—
93C2×Dic59—21no—
94C2×Dic59C2×D411yescharacteristic
95C2×Dic59C2×D411yescharacteristic
96C2×Dic59C2×D411yescharacteristic
97D236—21no—
98D236—21no—
99D236—42no—
100C4×D59—22no—
101C4×D59—21no—
102C4×D59—21no—
103C4×D59—41no—
104C4×D59—42no—
105Dic118—22no—
106Dic118—22no—
107C8×C59—22no—
108C59⋊C8—22no—
109C22×C59C22×D411yescharacteristic
110C2×D59—21no—
111C2×D59—21no—
112C2×D59—21no—
113C2×D59—41no—
114C2×D59—41no—
115C2×D59—41no—
116C4×C59—21no—
117C4×C59—41no—
118C4×C59—41no—
119C4×C59—42no—
120C4×C59#13712yes—
121C4×C59H(5,𝔽2)11yescharacteristic
122C4×C592−1+411yescharacteristic
123Dic59—21no—
124Dic59—21no—
125Dic59—21no—
126Dic59—42no—
127Dic59—41no—
128#3252—591nomaximal, Sylow
129C2×C59#53711yescharacteristic
130C2×C59C2×#13711yescharacteristic
131C2×C59#57511yescharacteristic
132D59—41no—
133D59—81no—
134#533—591no—
135#529—591no—
136#479—592no—
137#477D5911yescharacteristic, complemented
138#476—591no—
139#470—592no—
140#468—592no—
141#464—592no—
142#462—591no—
143#461—591no—
144#423—591no—
145C59#325211yescharacteristic, complemented, Sylow
146C2×Q16—592no—
147C2×SD16—592no—
148C2×M16—592no—
149C4⋊Q8—591no—
150C4⋊Q8C2×D5911yescharacteristic
151#126—1181no—
152#125—591no—
153#125—1181no—
154#124—591no—
155#123—1181no—
156C22⋊Q8—591no—
157C22⋊Q8—592no—
158C22⋊Q8—1181no—
159#121—591no—
160C4×Q8—592no—
161C4×Q8—1181no—
162C4×Q8C2×D5911yescharacteristic
163C4×D4—591no—
164C4×D4—1181no—
165#117—1181no—
166#117—1181no—
167C2×C42—591no—
168#107C2×D5912yes—
169#106—592no—
170C4⋊C8—592no—
171C4⋊C8—591no—
172C4⋊C8C2×D5911yescharacteristic
173#103—592no—
174#103—592no—
175#103C2×D5912yes—
176#102—592no—
177C2×Q8—21no—
178C2×Q8—592no—
179C2×Q8C22×D5911yescharacteristic
180C2×D4—591no—
181C2×D4—1181no—
182C22×C4—591no—
183C22×C4—591no—
184C22×C4—591no—
185C22×C4—1181no—
186Q16—2362no—
187SD16—2362no—
188M16—2362no—
189C2×C8—592no—
190C2×C8C22×D5912yes—
191C4⋊C4—21no—
192C4⋊C4—21no—
193C4⋊C4—591no—
194C4⋊C4—1181no—
195C4⋊C4—1181no—
196C4⋊C4—1181no—
197C4⋊C4—1182no—
198C4⋊C4—1182no—
199C4⋊C4—1181no—
200C4⋊C4—1181no—
201C4⋊C4C22×D5912yes—
202C4⋊C4C22×D5911yescharacteristic
203C22⋊C4—1181no—
204C22⋊C4—1181no—
205C22⋊C4—1181no—
206C22⋊C4—1182no—
207C22⋊C4—1181no—
208C22⋊C4—1181no—
209C42—21no—
210C42—591no—
211C42—591no—
212C42—591no—
213C42—1182no—
214C42C22×D5911yescharacteristic
215C23—591no—
216C23—1181no—
217Q8—21no—
218Q8—21no—
219Q8—42no—
220Q8—1182no—
221Q8—1182no—
222D4—1181no—
223D4—1181no—
224D4—2362no—
225C2×C4—21no—
226C2×C4—21no—
227C2×C4—22no—
228C2×C4—591no—
229C2×C4—591no—
230C2×C4—591no—
231C2×C4—1182no—
232C2×C4—1181no—
233C2×C4—1181no—
234C2×C4—1182no—
235C2×C4—1181no—
236C2×C4—2361no—
237C2×C4—2362no—
238C2×C4D4×D5911yescharacteristic
239C2×C4D4×D5911yescharacteristic
240C2×C4C23×D5911yescharacteristic
241C8—22no—
242C8—1182no—
243C22—1181no—
244C22—1181no—
245C22—1181no—
246C22—2361no—
247C22—2361no—
248C22—2361no—
249C22C2×D4×D5911yescharacteristic
250C4—21no—
251C4—41no—
252C4—42no—
253C4—41no—
254C4—1181no—
255C4—1181no—
256C4—1181no—
257C4—2361no—
258C4—2362no—
259C4#1427375912yes—
260C4#1427377311yescharacteristic
261C4#1427377511yescharacteristic
262C2—4721no—
263C2—2361no—
264C2#1683798211yescharacteristic
265C2C2×#1427375911yescharacteristic
266C2#1683819811yescharacteristic
subgroupG/H
centerC22C2×D4×D59
commutatorC2×C4×C59C24
FrattiniC2×C4C23×D59
FittingC59×#477C2
socleC22×C59C22×D4
hypercenter#477D59
hypocenterC59#3252
LCSG ▷ C2×C4×C59 ▷ C2×C59 ▷ C59
UCSC1 ◁ C22 ◁ C42 ◁ #477

Complements

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

NH ≅ G/Ntype
1. #16837957C2semidirect
3. #16837708C2semidirect
4. #16837689C2semidirect
5. #16837659C2semidirect
7. #16837627C2semidirect
8. #16837612C2semidirect
9. #16837608C2semidirect
10. #16837424C2semidirect
11. C59×#477C2semidirect
137. #477D59semidirect
145. C59#3252semidirect