Finite Group Databasebeta

← #21435409

Subgroups — #21435409

Order 7552.

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

normal subgroups only

This group has 392 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#16837957C211yesmaximal, characteristic, complemented
2#16837949C211yesmaximal, characteristic
3#16837693C211yesmaximal, characteristic, complemented
4#16837692C211yesmaximal, characteristic, complemented
5#16837685C212yesmaximal, complemented
6#16837634C212yesmaximal, complemented
7#16837628C212yesmaximal, complemented
8#16837604C211yesmaximal, characteristic, complemented
9#16837600C212yesmaximal, complemented
10C4⋊C8×D59C211yesmaximal, characteristic, complemented
11C59×#461C211yesmaximal, characteristic, complemented
12C2×#11745685—21no—
13C2×#11745671C2212yes—
14C2×C8×D59C2212yes—
15#14273727C2211yescharacteristic
16#14273726C2211yescharacteristic
17#14273723C2211yescharacteristic
18#14273718—21no—
19#14273713—21no—
20#14273707—21no—
21#14273703C2212yes—
22#14273702C2211yescharacteristic
23#14273700—21no—
24#14273698C2211yescharacteristic
25Q8×Dic59C2212yes—
26#14273692—21no—
27C4×D236C2211yescharacteristic
28C4×C22⋊D59—21no—
29#14273685—21no—
30C42×D59C2211yescharacteristic
31#14273659C2212yes—
32#14273658C2212yes—
33C4⋊(C59⋊C8)C2211yescharacteristic
34Dic59⋊C8C2212yes—
35#14273651C2212yes—
36#14273649C2212yes—
37#14273648C2212yes—
38C2×SD16×C59C2212yes—
39C4⋊Q8×C59C2211yescharacteristic
40C4×D4×C59C2211yescharacteristic
41C4⋊C8×C59C2211yescharacteristic
42#103×C59C2212yes—
43C2×Q8×C59C2312yes—
44C2×D4×C59C2311yescharacteristic
45C22×C4×C59—21no—
46C2×C22⋊D59—21no—
47C2×C22⋊D59—21no—
48C2×C22⋊D59—21no—
49#11745685—44no—
50C2×D236—21no—
51C2×D236C2311yescharacteristic
52C2×C4×D59—21no—
53C2×C4×D59D411yescharacteristic
54C2×C4×D59D411yescharacteristic
55C2×C4×D59C2311yescharacteristic
56C2×Dic118—21no—
57C2×Dic118—21no—
58SD16×C59—42no—
59C2×C8×C59C2312yes—
60C4⋊C4×C59—21no—
61C4⋊C4×C59—21no—
62C4⋊C4×C59C2311yescharacteristic
63C22⋊C4×C59—21no—
64C42×C59C2311yescharacteristic
65C22⋊Dic59—21no—
66#11745671—42no—
67(C2×D59)⋊C4—22no—
68(C2×D59)⋊C4—21no—
69(C2×D59)⋊C4—21no—
70C4⋊Dic59—21no—
71C4⋊Dic59—22no—
72C4⋊Dic59C2312yes—
73C4⋊Dic59C2311yescharacteristic
74Dic59⋊C4—21no—
75Dic59⋊C4—22no—
76C4×Dic59—22no—
77C4×Dic59D411yescharacteristic
78C4×Dic59D411yescharacteristic
79C4×Dic59C2311yescharacteristic
80C2×C59⋊C8C2312yes—
81C8×D59—42no—
82C23×C59—21no—
83C22×D59—21no—
84C22×D59C2×D411yescharacteristic
85Q8×C59—22no—
86Q8×C59—22no—
87D4×C59—21no—
88D4×C59—21no—
89C2×C4×C59—22no—
90C2×C4×C59—21no—
91C2×C4×C59—42no—
92C2×C4×C59C2×D411yescharacteristic
93C2×C4×C59C2×D411yescharacteristic
94C2×C4×C59C2411yescharacteristic
95C22⋊D59—42no—
96C22⋊D59—42no—
97C22⋊D59—42no—
98C2×Dic59—22no—
99C2×Dic59—21no—
100C2×Dic59C2×D411yescharacteristic
101C2×Dic59C2×D411yescharacteristic
102C2×Dic59C2×D411yescharacteristic
103D236—21no—
104D236—21no—
105D236—42no—
106C4×D59—21no—
107C4×D59—21no—
108C4×D59—41no—
109C4×D59—42no—
110C4×D59SD1614yescomplemented
111Dic118—42no—
112Dic118—42no—
113C8×C59—22no—
114C59⋊C8—22no—
115C22×C59—41no—
116C22×C59—41no—
117C22×C59—41no—
118C22×C59C22×D411yescharacteristic
119C2×D59—21no—
120C2×D59—21no—
121C2×D59—41no—
122C2×D59—41no—
123C2×D59—41no—
124C2×D59C2×SD1612yes—
125C4×C59—21no—
126C4×C59—42no—
127C4×C59—41no—
128C4×C59C2×SD1612yes—
129C4×C59H(5,𝔽2)11yescharacteristic
130C4×C592−1+411yescharacteristic
131Dic59—21no—
132Dic59—21no—
133Dic59—41no—
134Dic59—42no—
135Dic59C2×SD1612yes—
136#3246—591nomaximal, Sylow
137C2×C59—81no—
138C2×C59#53711yescharacteristic
139C2×C59C22×SD1611yescharacteristic
140C2×C59#57511yescharacteristic
141D59—22no—
142D59—81no—
143#533—591no—
144#532—591no—
145#476—591no—
146#476—591no—
147#475—592no—
148#465—592no—
149#465—592no—
150#461—591no—
151#461D5911yescharacteristic, complemented
152#460—592no—
153C2×C4⋊C8—591no—
154C59#324611yescharacteristic, complemented, Sylow
155C2×#41—1181no—
156C2×SD16—592no—
157C2×SD16C2×D5912yes—
158C22×C8—592no—
159C4⋊Q8—591no—
160C4⋊Q8—591no—
161C4⋊Q8C2×D5911yescharacteristic
162#127—591no—
163#125—1181no—
164#124—1181no—
165C22⋊Q8—592no—
166C22⋊Q8—1181no—
167#121—591no—
168#121—591no—
169#121—1181no—
170C4×Q8—592no—
171C4×Q8—1181no—
172C4×D4—591no—
173C4×D4—1181no—
174C4×D4C2×D5911yescharacteristic
175#117—1181no—
176C2×C42—591no—
177#106—592no—
178#106—592no—
179C4⋊C8—592no—
180C4⋊C8—591no—
181C4⋊C8C2×D5911yescharacteristic
182#103—592no—
183#103C2×D5912yes—
184#102—592no—
185#102—592no—
186#41—2364no—
187C2×Q8—1181no—
188C2×Q8—1181no—
189C2×Q8C22×D5912yes—
190C2×D4—591no—
191C2×D4—1181no—
192C2×D4—1181no—
193C2×D4—1181no—
194C2×D4—1181no—
195C2×D4C22×D5911yescharacteristic
196C22×C4—21no—
197C22×C4—591no—
198C22×C4—591no—
199C22×C4—591no—
200C22×C4—1181no—
201SD16—42no—
202SD16—2362no—
203C2×C8—592no—
204C2×C8—2362no—
205C2×C8C22×D5912yes—
206C4⋊C4—21no—
207C4⋊C4—21no—
208C4⋊C4—592no—
209C4⋊C4—591no—
210C4⋊C4—1181no—
211C4⋊C4—1182no—
212C4⋊C4—1182no—
213C4⋊C4—1181no—
214C4⋊C4C22×D5911yescharacteristic
215C22⋊C4—21no—
216C22⋊C4—1181no—
217C22⋊C4—1182no—
218C22⋊C4—1181no—
219C22⋊C4—1181no—
220C42—591no—
221C42—591no—
222C42—591no—
223C42—1182no—
224C42C22×D5911yescharacteristic
225C23—21no—
226C23—591no—
227C23—1181no—
228Q8—22no—
229Q8—22no—
230Q8—2362no—
231Q8—2362no—
232D4—21no—
233D4—21no—
234D4—1181no—
235D4—1181no—
236D4—2362no—
237D4—2362no—
238D4—2362no—
239D4—2362no—
240C2×C4—22no—
241C2×C4—21no—
242C2×C4—42no—
243C2×C4—591no—
244C2×C4—594no—
245C2×C4—591no—
246C2×C4—591no—
247C2×C4—1181no—
248C2×C4—1181no—
249C2×C4—1182no—
250C2×C4—1181no—
251C2×C4—2361no—
252C2×C4—2362no—
253C2×C4D4×D5911yescharacteristic
254C2×C4D4×D5911yescharacteristic
255C2×C4C23×D5911yescharacteristic
256C8—22no—
257C8—1182no—
258C22—41no—
259C22—41no—
260C22—41no—
261C22—592no—
262C22—1181no—
263C22—1181no—
264C22—2361no—
265C22—2361no—
266C22—2361no—
267C22C2×D4×D5911yescharacteristic
268C4—21no—
269C4—41no—
270C4—42no—
271C4—592no—
272C4—1181no—
273C4—1181no—
274C4—2361no—
275C4—2362no—
276C4SD16×D5912yes—
277C4#1427377211yescharacteristic
278C4#1427377411yescharacteristic
279C2—81no—
280C2—1182no—
281C2—4721no—
282C2#1683798111yescharacteristic
283C2C2×SD16×D5911yescharacteristic
284C2#1683820111yescharacteristic
subgroupG/H
centerC22C2×D4×D59
commutatorC2×C4×C59C24
FrattiniC2×C4C23×D59
FittingC59×#461C2
socleC22×C59C22×D4
hypercenter#461D59
hypocenterC59#3246
LCSG ▷ C2×C4×C59 ▷ C2×C59 ▷ C59
UCSC1 ◁ C22 ◁ C42 ◁ #461

Complements

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

NH ≅ G/Ntype
1. #16837957C2semidirect
3. #16837693C2semidirect
4. #16837692C2semidirect
5. #16837685C2semidirect
6. #16837634C2semidirect
7. #16837628C2semidirect
8. #16837604C2semidirect
9. #16837600C2semidirect
10. C4⋊C8×D59C2semidirect
11. C59×#461C2semidirect
110. C4×D59SD16semidirect
151. #461D59semidirect
154. C59#3246semidirect