Finite Group Databasebeta

← #21435470

Subgroups — #21435470

Order 7552.

348 conjugacy classes of subgroups; only the 121 normal subgroups are shown.

normal subgroups only

This group has 348 conjugacy classes of subgroups — too many to draw. Only its 121 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#16837959C211yesmaximal, characteristic, complemented
2#16837936C211yesmaximal, characteristic
3#16837710C212yesmaximal, complemented
4#16837698C211yesmaximal, characteristic, complemented
5#16837693C211yesmaximal, characteristic, complemented
6#16837660C212yesmaximal, complemented
7#16837648C212yesmaximal
8#16837625C212yesmaximal, complemented
9#16837613C211yesmaximal, characteristic, complemented
10#16837608C211yesmaximal, characteristic, complemented
11C59×#423C211yesmaximal, characteristic, complemented
12C2×Dic236C2212yes—
13C2×#11745660C2212yes—
14#14273727C2211yescharacteristic
15#14273727C2211yescharacteristic
16#14273721—21no—
17#14273719—21no—
18#14273719C2211yescharacteristic
19#14273715C2211yescharacteristic
20#14273710—21no—
21#14273706—21no—
22#14273706C2212yes—
23#14273706C2211yescharacteristic
24#14273701C2211yescharacteristic
25C4×Dic118—21no—
26C4×Dic118C2211yescharacteristic
27C4×Dic118C2212yes—
28C4×D236C2211yescharacteristic
29C4×C22⋊D59—21no—
30#14273686—21no—
31#14273684—21no—
32#14273661C2212yes—
33#14273659C2212yes—
34#14273652C2212yes—
35#14273652C2212yes—
36#14273652C2212yes—
37#14273649C2212yes—
38C2×M16×C59C2212yes—
39C2×C42×C59C2211yescharacteristic
40C4⋊C8×C59C2211yescharacteristic
41C4⋊C8×C59C2211yescharacteristic
42C4⋊C8×C59C2212yes—
43C22×C4×C59D411yescharacteristic
44C22×C4×C59D411yescharacteristic
45C22×C4×C59C2311yescharacteristic
46C2×C22⋊D59—21no—
47C2×D236C2311yescharacteristic
48C2×C4×D59—21no—
49C2×Dic118—21no—
50C2×Dic118C2311yescharacteristic
51C2×Dic118C2312yes—
52M16×C59—42no—
53C2×C8×C59C2312yes—
54C2×C8×C59C2312yes—
55C42×C59D411yescharacteristic
56C42×C59D411yescharacteristic
57C42×C59C2311yescharacteristic
58C42×C59C2311yescharacteristic
59C22⋊Dic59—22no—
60C22⋊Dic59—21no—
61(C2×D59)⋊C4—21no—
62(C2×D59)⋊C4—21no—
63(C2×D59)⋊C4—21no—
64(C2×D59)⋊C4—21no—
65C4⋊Dic59—21no—
66C4⋊Dic59—21no—
67C4⋊Dic59—21no—
68C4⋊Dic59C2312yes—
69C4⋊Dic59C2311yescharacteristic
70C4⋊Dic59C2311yescharacteristic
71Dic59⋊C4—21no—
72Dic59⋊C4—21no—
73Dic59⋊C4—21no—
74Dic59⋊C4—22no—
75Dic59⋊C4—22no—
76Dic59⋊C4—21no—
77C4×Dic59—21no—
78C4×Dic59—22no—
79Dic236—42no—
80#11745660—42no—
81C23×C59C2×D411yescharacteristic
82C22×D59—21no—
83C2×C4×C59—22no—
84C2×C4×C59—21no—
85C2×C4×C59—21no—
86C2×C4×C59—41no—
87C2×C4×C59C2×D411yescharacteristic
88C2×C4×C59C2×D411yescharacteristic
89C2×C4×C59C2×D411yescharacteristic
90C2×C4×C59C2×D411yescharacteristic
91C2×C4×C59C2×D411yescharacteristic
92C2×C4×C59C2411yescharacteristic
93C22⋊D59—42no—
94C2×Dic59—21no—
95C2×Dic59—22no—
96C2×Dic59—22no—
97C2×Dic59—21no—
98C2×Dic59—21no—
99D236—21no—
100D236—21no—
101C4×D59—42no—
102Dic118—22no—
103Dic118—21no—
104Dic118—21no—
105Dic118—22no—
106Dic118—42no—
107C8×C59—22no—
108C8×C59—22no—
109C22×C59—21no—
110C22×C59—21no—
111C22×C59—21no—
112C22×C59C22×D411yescharacteristic
113C2×D59—41no—
114C2×D59—41no—
115C2×D59—41no—
116C4×C59—21no—
117C4×C59—21no—
118C4×C59—21no—
119C4×C59—21no—
120C4×C59#13712yes—
121C4×C59H(5,𝔽2)11yescharacteristic
122C4×C592−1+411yescharacteristic
123Dic59—42no—
124Dic59—41no—
125Dic59—41no—
126Dic59—42no—
127Dic59—41no—
128#3252—591nomaximal, Sylow
129C2×C59—41no—
130C2×C59#53711yescharacteristic
131C2×C59C2×#13711yescharacteristic
132C2×C59#57511yescharacteristic
133D59—81no—
134#533—591no—
135#529—591no—
136#479—592no—
137#477—591no—
138#476—591no—
139#470—592no—
140#468—592no—
141#464—592no—
142#462—591no—
143#461—591no—
144#423D5911yescharacteristic, complemented
145C59#325211yescharacteristic, complemented, Sylow
146C2×Q16—592no—
147C2×SD16—592no—
148C2×M16C2×D5912yes—
149C4⋊Q8—591no—
150C4⋊Q8—591no—
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—591no—
161C4×Q8—592no—
162C4×Q8—1181no—
163C4×D4—591no—
164C4×D4—1181no—
165#117—1181no—
166#117—1181no—
167C2×C42C2×D5911yescharacteristic
168#107—592no—
169#106—592no—
170C4⋊C8C2×D5911yescharacteristic
171C4⋊C8C2×D5911yescharacteristic
172C4⋊C8C2×D5912yes—
173#103—592no—
174#103—592no—
175#103—592no—
176#102—592no—
177C2×Q8—591no—
178C2×Q8—592no—
179C2×Q8—1181no—
180C2×D4—591no—
181C2×D4—1181no—
182C22×C4—1181no—
183C22×C4D23611yescharacteristic
184C22×C4D23611yescharacteristic
185C22×C4C22×D5911yescharacteristic
186Q16—2362no—
187SD16—2362no—
188M16—42no—
189C2×C8C22×D5912yes—
190C2×C8C22×D5912yes—
191C4⋊C4—592no—
192C4⋊C4—591no—
193C4⋊C4—591no—
194C4⋊C4—1181no—
195C4⋊C4—1181no—
196C4⋊C4—1181no—
197C4⋊C4—1181no—
198C4⋊C4—1181no—
199C4⋊C4—1182no—
200C4⋊C4—1181no—
201C4⋊C4—1182no—
202C4⋊C4—1181no—
203C22⋊C4—1182no—
204C22⋊C4—1181no—
205C22⋊C4—1181no—
206C22⋊C4—1181no—
207C22⋊C4—1181no—
208C22⋊C4—1181no—
209C42—1181no—
210C42—1182no—
211C42D23611yescharacteristic
212C42D23611yescharacteristic
213C42C22×D5911yescharacteristic
214C42C22×D5911yescharacteristic
215C23—1181no—
216C23C2×D23611yescharacteristic
217Q8—1182no—
218Q8—1181no—
219Q8—1181no—
220Q8—1182no—
221Q8—2362no—
222D4—1181no—
223D4—1181no—
224D4—2362no—
225C2×C4—22no—
226C2×C4—21no—
227C2×C4—21no—
228C2×C4—41no—
229C2×C4—1181no—
230C2×C4—1181no—
231C2×C4—1182no—
232C2×C4—1182no—
233C2×C4—1181no—
234C2×C4—2362no—
235C2×C4C2×D23611yescharacteristic
236C2×C4C2×D23611yescharacteristic
237C2×C4C2×D23611yescharacteristic
238C2×C4C2×D23611yescharacteristic
239C2×C4C2×D23611yescharacteristic
240C2×C4C23×D5911yescharacteristic
241C8—22no—
242C8—22no—
243C22—21no—
244C22—21no—
245C22—21no—
246C22—2361no—
247C22—2361no—
248C22—2361no—
249C22C22×D23611yescharacteristic
250C4—21no—
251C4—21no—
252C4—21no—
253C4—21no—
254C4—2361no—
255C4—2361no—
256C4—2362no—
257C4—2361no—
258C4—2362no—
259C4#1427376012yes—
260C4#1427377211yescharacteristic
261C4#1427377511yescharacteristic
262C2—41no—
263C2—4721no—
264C2#1683798311yescharacteristic
265C2C2×#1427376011yescharacteristic
266C2#1683820211yescharacteristic
subgroupG/H
centerC22C22×D236
commutatorC2×C4×C59C24
FrattiniC2×C4C23×D59
FittingC59×#423C2
socleC22×C59C22×D4
hypercenter#423D59
hypocenterC59#3252
LCSG ▷ C2×C4×C59 ▷ C2×C59 ▷ C59
UCSC1 ◁ C22 ◁ C2×C42 ◁ #423

Complements

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

NH ≅ G/Ntype
1. #16837959C2semidirect
3. #16837710C2semidirect
4. #16837698C2semidirect
5. #16837693C2semidirect
6. #16837660C2semidirect
8. #16837625C2semidirect
9. #16837613C2semidirect
10. #16837608C2semidirect
11. C59×#423C2semidirect
144. #423D59semidirect
145. C59#3252semidirect