Finite Group Databasebeta

← #21435135

Subgroups — #21435135

Order 7552.

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

normal subgroups only

This group has 396 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#16837952C211yesmaximal, characteristic, complemented
2#16837936C211yesmaximal, characteristic, complemented
3#16837796C211yesmaximal, characteristic, complemented
4#16837791C211yesmaximal, characteristic, complemented
5#16837771C211yesmaximal, characteristic, complemented
6#16837767C211yesmaximal, characteristic, complemented
7#16837625C212yesmaximal, complemented
8#16837618C212yesmaximal, complemented
9#16837566C212yesmaximal, complemented
10#16837549C212yesmaximal, complemented
11C59×#432C211yesmaximal, characteristic, complemented
12C2×#11745685C2212yes—
13C2×Dic236C2212yes—
14C2×#11745660C2212yes—
15C2×#11745660C2212yes—
16C2×D472C2212yes—
17#14273727C2211yescharacteristic
18#14273724C2211yescharacteristic
19#14273721—21no—
20#14273719C2211yescharacteristic
21#14273715C2211yescharacteristic
22#14273715C2212yes—
23#14273710—21no—
24#14273706C2211yescharacteristic
25#14273701—21no—
26#14273701—21no—
27#14273701C2211yescharacteristic
28C4×Dic118C2211yescharacteristic
29C4×D236—21no—
30C4×D236—21no—
31C4×D236C2211yescharacteristic
32C4×C22⋊D59—21no—
33#14273684—21no—
34#14273652C2212yes—
35#14273652C2212yes—
36#14273649C2212yes—
37#14273649C2212yes—
38C2×C42×C59C2211yescharacteristic
39C4⋊C8×C59C2212yes—
40C22⋊C8×C59C2212yes—
41#97×C59C2211yescharacteristic
42#97×C59C2211yescharacteristic
43C22×C4×C59D411yescharacteristic
44C22×C4×C59D411yescharacteristic
45C22×C4×C59C2311yescharacteristic
46C2×C22⋊D59—21no—
47C2×C22⋊D59—22no—
48#11745685—42no—
49#11745685—42no—
50C2×D236—21no—
51C2×D236—21no—
52C2×D236C2312yes—
53C2×D236C2311yescharacteristic
54C2×C4×D59—21no—
55C2×C4×D59—22no—
56C2×Dic118C2312yes—
57C2×Dic118C2311yescharacteristic
58C2×C8×C59C2312yes—
59C2×C8×C59C2312yes—
60C42×C59D411yescharacteristic
61C42×C59D411yescharacteristic
62C42×C59C2311yescharacteristic
63C42×C59C2311yescharacteristic
64C22⋊Dic59—21no—
65(C2×D59)⋊C4—21no—
66(C2×D59)⋊C4—21no—
67(C2×D59)⋊C4—21no—
68(C2×D59)⋊C4—22no—
69(C2×D59)⋊C4—22no—
70(C2×D59)⋊C4—21no—
71C4⋊Dic59—21no—
72C4⋊Dic59—21no—
73C4⋊Dic59C2311yescharacteristic
74C4⋊Dic59C2311yescharacteristic
75Dic59⋊C4—21no—
76Dic59⋊C4—21no—
77Dic59⋊C4—21no—
78Dic59⋊C4—21no—
79C4×Dic59—21no—
80Dic236—42no—
81D472—42no—
82#11745660—42no—
83#11745660—42no—
84C23×C59C2×D411yescharacteristic
85C22×D59—21no—
86C22×D59—22no—
87C2×C4×C59—22no—
88C2×C4×C59—41no—
89C2×C4×C59—41no—
90C2×C4×C59C2×D411yescharacteristic
91C2×C4×C59C2×D411yescharacteristic
92C2×C4×C59C2×D411yescharacteristic
93C2×C4×C59C2×D411yescharacteristic
94C2×C4×C59C2×D411yescharacteristic
95C2×C4×C59C2411yescharacteristic
96C22⋊D59—44no—
97C22⋊D59—42no—
98C2×Dic59—21no—
99C2×Dic59—21no—
100C2×Dic59—21no—
101C2×Dic59—22no—
102D236—22no—
103D236—22no—
104D236—22no—
105D236—42no—
106D236—42no—
107C4×D59—42no—
108C4×D59—44no—
109Dic118—22no—
110Dic118—22no—
111Dic118—22no—
112C8×C59—22no—
113C8×C59—22no—
114C22×C59—21no—
115C22×C59—21no—
116C22×C59—21no—
117C22×C59C22×D411yescharacteristic
118C2×D59—42no—
119C2×D59—41no—
120C2×D59—41no—
121C2×D59—42no—
122C2×D59—42no—
123C2×D59—41no—
124C4×C59—21no—
125C4×C59—21no—
126C4×C59—21no—
127C4×C59—21no—
128C4×C59—21no—
129C4×C59H(5,𝔽2)12yes—
130Dic59—42no—
131Dic59—41no—
132Dic59—41no—
133Dic59—41no—
134#3219—591nomaximal, Sylow
135C2×C59—41no—
136C2×C59#53511yescharacteristic
137C2×C59#57511yescharacteristic
138C2×C59#57511yescharacteristic
139D59—82no—
140D59—81no—
141#532—591no—
142#529—591no—
143#497—591no—
144#496—591no—
145#491—591no—
146#490—591no—
147#464—592no—
148#463—592no—
149#452—592no—
150#449—592no—
151#432D5911yescharacteristic, complemented
152C59#321911yescharacteristic, complemented, Sylow
153C2×#41—592no—
154C2×Q16—592no—
155C2×SD16—592no—
156C2×SD16—592no—
157C2×D8—592no—
158C4⋊Q8—591no—
159#127—591no—
160#126—1181no—
161#125—591no—
162#124—591no—
163#124—592no—
164#123—1181no—
165C22⋊Q8—591no—
166#121—591no—
167#121—1181no—
168#121—1181no—
169C4×Q8—591no—
170C4×D4—591no—
171C4×D4—1181no—
172C4×D4—1181no—
173C4×D4—1181no—
174#117—1181no—
175C2×C42C2×D5911yescharacteristic
176C4⋊C8C2×D5912yes—
177#103—592no—
178#103—592no—
179#102—592no—
180#102—592no—
181C22⋊C8C2×D5912yes—
182#97C2×D5911yescharacteristic
183#97C2×D5911yescharacteristic
184#41—2362no—
185#41—2362no—
186C2×Q8—592no—
187C2×Q8—591no—
188C2×D4—592no—
189C2×D4—591no—
190C2×D4—1181no—
191C2×D4—1182no—
192C2×D4—1181no—
193C2×D4—1181no—
194C22×C4—1181no—
195C22×C4—1182no—
196C22×C4D23611yescharacteristic
197C22×C4D23611yescharacteristic
198C22×C4C22×D5911yescharacteristic
199Q16—2362no—
200SD16—2362no—
201SD16—2362no—
202D8—2362no—
203C2×C8C22×D5912yes—
204C2×C8C22×D5912yes—
205C4⋊C4—591no—
206C4⋊C4—591no—
207C4⋊C4—1181no—
208C4⋊C4—1181no—
209C4⋊C4—1181no—
210C4⋊C4—1181no—
211C4⋊C4—1181no—
212C4⋊C4—1181no—
213C22⋊C4—1181no—
214C22⋊C4—1181no—
215C22⋊C4—1181no—
216C22⋊C4—1181no—
217C22⋊C4—1182no—
218C22⋊C4—1182no—
219C22⋊C4—1181no—
220C42—1181no—
221C42D23611yescharacteristic
222C42D23611yescharacteristic
223C42C22×D5911yescharacteristic
224C42C22×D5911yescharacteristic
225C23—1181no—
226C23—1182no—
227C23C2×D23611yescharacteristic
228Q8—1182no—
229Q8—1182no—
230Q8—1182no—
231D4—1182no—
232D4—1182no—
233D4—1182no—
234D4—2362no—
235D4—2362no—
236D4—2362no—
237D4—2364no—
238C2×C4—22no—
239C2×C4—41no—
240C2×C4—41no—
241C2×C4—1181no—
242C2×C4—1181no—
243C2×C4—1181no—
244C2×C4—1182no—
245C2×C4—2362no—
246C2×C4—2364no—
247C2×C4C2×D23611yescharacteristic
248C2×C4C2×D23611yescharacteristic
249C2×C4C2×D23611yescharacteristic
250C2×C4C2×D23611yescharacteristic
251C2×C4C2×D23611yescharacteristic
252C2×C4C23×D5911yescharacteristic
253C8—22no—
254C8—22no—
255C22—21no—
256C22—21no—
257C22—21no—
258C22—2361no—
259C22—2362no—
260C22—2362no—
261C22—2361no—
262C22—2362no—
263C22—2361no—
264C22C22×D23611yescharacteristic
265C4—21no—
266C4—21no—
267C4—21no—
268C4—21no—
269C4—21no—
270C4—2361no—
271C4—2361no—
272C4—2362no—
273C4—2361no—
274C4#1427377312yes—
275C2—41no—
276C2—4721no—
277C2—4722no—
278C2#1683797111yescharacteristic
279C2#1683820211yescharacteristic
280C2#1683820211yescharacteristic
subgroupG/H
centerC22C22×D236
commutatorC2×C4×C59C24
FrattiniC2×C4C23×D59
FittingC59×#432C2
socleC22×C59C22×D4
hypercenter#432D59
hypocenterC59#3219
LCSG ▷ C2×C4×C59 ▷ C2×C59 ▷ C59
UCSC1 ◁ C22 ◁ C2×C42 ◁ #432

Complements

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

NH ≅ G/Ntype
1. #16837952C2semidirect
2. #16837936C2semidirect
3. #16837796C2semidirect
4. #16837791C2semidirect
5. #16837771C2semidirect
6. #16837767C2semidirect
7. #16837625C2semidirect
8. #16837618C2semidirect
9. #16837566C2semidirect
10. #16837549C2semidirect
11. C59×#432C2semidirect
151. #432D59semidirect
152. C59#3219semidirect