Finite Group Databasebeta

← #21435425

Subgroups — #21435425

Order 7552.

398 conjugacy classes of subgroups; only the 115 normal subgroups are shown.

normal subgroups only

This group has 398 conjugacy classes of subgroups — too many to draw. Only its 115 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#16837953C211yesmaximal, characteristic, complemented
2#16837939C211yesmaximal, characteristic, complemented
3#16837705C212yesmaximal, complemented
4#16837689C211yesmaximal, characteristic, complemented
5#16837639C212yesmaximal, complemented
6#16837634C212yesmaximal, complemented
7#16837620C212yesmaximal, complemented
8#16837602C211yesmaximal, characteristic, complemented
9#16837598C211yesmaximal, characteristic, complemented
10C4⋊C8×D59C211yesmaximal, characteristic, complemented
11C59×#477C211yesmaximal, characteristic, complemented
12C2×#11745689—21no—
13C2×#11745671C2212yes—
14C2×D472C2212yes—
15C2×C8×D59C2212yes—
16#14273724C2211yescharacteristic
17#14273722—21no—
18#14273718C2211yescharacteristic
19#14273716—21no—
20#14273716C2211yescharacteristic
21#14273712—21no—
22#14273703C2211yescharacteristic
23#14273702—21no—
24#14273702C2212yes—
25#14273702C2211yescharacteristic
26C4×D236—21no—
27C4×D236C2211yescharacteristic
28#14273689—21no—
29#14273689C2212yes—
30#14273684—21no—
31C42×D59C2211yescharacteristic
32#14273658C2212yes—
33C4⋊(C59⋊C8)C2211yescharacteristic
34Dic59⋊C8C2212yes—
35#14273649C2212yes—
36#14273647C2212yes—
37#14273647C2212yes—
38C4⋊Q8×C59C2211yescharacteristic
39C4×Q8×C59C2211yescharacteristic
40#107×C59C2212yes—
41C4⋊C8×C59C2211yescharacteristic
42#103×C59C2212yes—
43C2×Q8×C59—21no—
44C2×Q8×C59C2311yescharacteristic
45#11745689—44no—
46C2×D236—21no—
47C2×D236—22no—
48C2×D236—21no—
49C2×D236—21no—
50C2×D236C2311yescharacteristic
51C2×D236C2312yes—
52C2×C4×D59—21no—
53C2×C4×D59—22no—
54C2×C4×D59D411yescharacteristic
55C2×C4×D59D411yescharacteristic
56C2×C4×D59C2311yescharacteristic
57C2×C8×C59C2312yes—
58C4⋊C4×C59—21no—
59C4⋊C4×C59—21no—
60C4⋊C4×C59C2312yes—
61C4⋊C4×C59C2311yescharacteristic
62C42×C59—21no—
63C42×C59C2311yescharacteristic
64#11745671—42no—
65(C2×D59)⋊C4—21no—
66(C2×D59)⋊C4—21no—
67(C2×D59)⋊C4—21no—
68(C2×D59)⋊C4—21no—
69(C2×D59)⋊C4—22no—
70(C2×D59)⋊C4—22no—
71(C2×D59)⋊C4—21no—
72C4⋊Dic59—21no—
73C4⋊Dic59C2311yescharacteristic
74Dic59⋊C4—21no—
75Dic59⋊C4—21no—
76C4×Dic59D411yescharacteristic
77C4×Dic59D411yescharacteristic
78C4×Dic59C2311yescharacteristic
79C2×C59⋊C8C2312yes—
80D472—42no—
81C8×D59—42no—
82C22×D59—21no—
83C22×D59—22no—
84C22×D59C2×D411yescharacteristic
85Q8×C59—21no—
86Q8×C59—21no—
87Q8×C59—42no—
88C2×C4×C59—21no—
89C2×C4×C59—21no—
90C2×C4×C59—22no—
91C2×C4×C59C2×D411yescharacteristic
92C2×C4×C59C2×D411yescharacteristic
93C2×C4×C59C2411yescharacteristic
94C2×Dic59—21no—
95C2×Dic59C2×D411yescharacteristic
96C2×Dic59C2×D411yescharacteristic
97C2×Dic59C2×D411yescharacteristic
98D236—21no—
99D236—22no—
100D236—21no—
101D236—22no—
102D236—42no—
103D236—42no—
104D236—44no—
105D236—42no—
106C4×D59—22no—
107C4×D59—22no—
108C4×D59—21no—
109C4×D59—21no—
110C4×D59—44no—
111C4×D59—42no—
112C8×C59—22no—
113C59⋊C8—22no—
114C22×C59C22×D411yescharacteristic
115C2×D59—21no—
116C2×D59—21no—
117C2×D59—41no—
118C2×D59—42no—
119C2×D59—41no—
120C2×D59—42no—
121C2×D59—42no—
122C2×D59—41no—
123C2×D59AGL(1,ℤ/8)12yes—
124C4×C59—21no—
125C4×C59—41no—
126C4×C59—42no—
127C4×C59—41no—
128C4×C59#13512yes—
129C4×C59H(5,𝔽2)11yescharacteristic
130C4×C592−1+411yescharacteristic
131Dic59—21no—
132Dic59—21no—
133Dic59—21no—
134Dic59—41no—
135#3247—591nomaximal, Sylow
136C2×C59#53711yescharacteristic
137C2×C59C2×#13511yescharacteristic
138C2×C59C2×AGL(1,ℤ/8)11yescharacteristic
139D59—22no—
140D59—81no—
141D59—82no—
142#532—591no—
143#529—591no—
144#478—592no—
145#477D5911yescharacteristic, complemented
146#476—591no—
147#466—592no—
148#465—592no—
149#463—592no—
150#460—591no—
151#459—591no—
152C2×C4⋊C8—591no—
153C59#324711yescharacteristic, complemented, Sylow
154C2×#41—1181no—
155C2×SD16—592no—
156C2×D8—592no—
157C22×C8—592no—
158C4⋊Q8C2×D5911yescharacteristic
159#127—591no—
160#126—1181no—
161#125—591no—
162#124—591no—
163#124—1181no—
164#123—1181no—
165C22⋊Q8—591no—
166#121—591no—
167#121—592no—
168#121—1181no—
169C4×Q8C2×D5911yescharacteristic
170C4×D4—592no—
171C4×D4—591no—
172C4×D4—1181no—
173C4×D4—1181no—
174#117—1181no—
175C2×C42—591no—
176#107C2×D5912yes—
177#106—592no—
178C4⋊C8—592no—
179C4⋊C8—591no—
180C4⋊C8C2×D5911yescharacteristic
181#103C2×D5912yes—
182#102—592no—
183#102—592no—
184#102—592no—
185#41—2364no—
186C2×Q8—21no—
187C2×Q8C22×D5911yescharacteristic
188C2×D4—591no—
189C2×D4—592no—
190C2×D4—1181no—
191C2×D4—1182no—
192C2×D4—1181no—
193C2×D4—1181no—
194C22×C4—591no—
195C22×C4—591no—
196C22×C4—591no—
197C22×C4—1182no—
198C22×C4—1181no—
199SD16—2362no—
200D8—2362no—
201C2×C8—592no—
202C2×C8—2362no—
203C2×C8C22×D5912yes—
204C4⋊C4—21no—
205C4⋊C4—21no—
206C4⋊C4—591no—
207C4⋊C4—1181no—
208C4⋊C4—1181no—
209C4⋊C4—1181no—
210C4⋊C4C22×D5911yescharacteristic
211C4⋊C4C22×D5912yes—
212C22⋊C4—1181no—
213C22⋊C4—1181no—
214C22⋊C4—1182no—
215C22⋊C4—1182no—
216C22⋊C4—1181no—
217C22⋊C4—1181no—
218C22⋊C4—1181no—
219C42—21no—
220C42—591no—
221C42—591no—
222C42—591no—
223C42C22×D5911yescharacteristic
224C23—591no—
225C23—1181no—
226C23—1182no—
227Q8—21no—
228Q8—21no—
229Q8—42no—
230D4—1181no—
231D4—1182no—
232D4—1181no—
233D4—1182no—
234D4—2362no—
235D4—2362no—
236D4—2364no—
237D4—2362no—
238C2×C4—21no—
239C2×C4—21no—
240C2×C4—22no—
241C2×C4—591no—
242C2×C4—591no—
243C2×C4—591no—
244C2×C4—1182no—
245C2×C4—1182no—
246C2×C4—1181no—
247C2×C4—1181no—
248C2×C4—1181no—
249C2×C4—2364no—
250C2×C4—2362no—
251C2×C4D4×D5911yescharacteristic
252C2×C4D4×D5911yescharacteristic
253C2×C4C23×D5911yescharacteristic
254C8—22no—
255C8—1182no—
256C22—592no—
257C22—1181no—
258C22—1181no—
259C22—2361no—
260C22—2362no—
261C22—2362no—
262C22—2361no—
263C22—2361no—
264C22—2362no—
265C22C2×D4×D5911yescharacteristic
266C4—21no—
267C4—42no—
268C4—41no—
269C4—41no—
270C4—1181no—
271C4—1181no—
272C4—1181no—
273C4—2361no—
274C4#1427375012yes—
275C4#1427377311yescharacteristic
276C4#1427377511yescharacteristic
277C2—1182no—
278C2—4721no—
279C2—4722no—
280C2#1683798211yescharacteristic
281C2C2×#1427375011yescharacteristic
282C2AGL(1,ℤ/8)×D5911yescharacteristic
subgroupG/H
centerC22C2×D4×D59
commutatorC2×C4×C59C24
FrattiniC2×C4C23×D59
FittingC59×#477C2
socleC22×C59C22×D4
hypercenter#477D59
hypocenterC59#3247
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. #16837953C2semidirect
2. #16837939C2semidirect
3. #16837705C2semidirect
4. #16837689C2semidirect
5. #16837639C2semidirect
6. #16837634C2semidirect
7. #16837620C2semidirect
8. #16837602C2semidirect
9. #16837598C2semidirect
10. C4⋊C8×D59C2semidirect
11. C59×#477C2semidirect
145. #477D59semidirect
153. C59#3247semidirect