Finite Group Databasebeta

← #21435339

Subgroups — #21435339

Order 7552.

328 conjugacy classes of subgroups; only the 109 normal subgroups are shown.

normal subgroups only

This group has 328 conjugacy classes of subgroups — too many to draw. Only its 109 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#16837937C211yesmaximal, characteristic
3#16837812C211yesmaximal, characteristic, complemented
4#16837764C211yesmaximal, characteristic, complemented
5#16837762C211yesmaximal, characteristic, complemented
6#16837746C212yesmaximal, complemented
7#16837729C212yesmaximal
8#16837708C212yesmaximal, complemented
9#16837701C212yesmaximal, complemented
10#16837457C211yesmaximal, characteristic, complemented
11C59×#501C211yesmaximal, characteristic, complemented
12#14273727C2211yescharacteristic
13#14273722—21no—
14#14273718C2212yes—
15#14273715C2211yescharacteristic
16#14273712—21no—
17#14273707—21no—
18#14273707C2211yescharacteristic
19#14273703—21no—
20#14273702C2211yescharacteristic
21Q8×Dic59—21no—
22#14273692—21no—
23#14273692C2211yescharacteristic
24#14273689—21no—
25#14273689C2211yescharacteristic
26#14273685—21no—
27#14273685C2212yes—
28C42×D59C2211yescharacteristic
29#14273660C2212yes—
30#14273658C2212yes—
31Dic59⋊C8C2212yes—
32#14273652C2212yes—
33#14273650C2212yes—
34#14273649C2212yes—
35#14273647C2212yes—
36(C2×D59)⋊C8C2212yes—
37#14273638C2211yescharacteristic
38C4⋊Q8×C59C2211yescharacteristic
39#125×C59C2211yescharacteristic
40#107×C59C2212yes—
41#106×C59C2212yes—
42#97×C59C2211yescharacteristic
43C2×Q8×C59—21no—
44C2×D236—21no—
45C2×D236C2311yescharacteristic
46C2×C4×D59—21no—
47C2×C4×D59D411yescharacteristic
48C2×C4×D59D411yescharacteristic
49C2×C4×D59C2311yescharacteristic
50C2×Dic118—21no—
51C2×Dic118C2311yescharacteristic
52C2×C8×C59C2312yes—
53C4⋊C4×C59—21no—
54C4⋊C4×C59—21no—
55C4⋊C4×C59—21no—
56C4⋊C4×C59C2311yescharacteristic
57C4⋊C4×C59C2312yes—
58C4⋊C4×C59C2311yescharacteristic
59C42×C59C2311yescharacteristic
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—22no—
69C4⋊Dic59C2312yes—
70Dic59⋊C4—22no—
71Dic59⋊C4—21no—
72C4×Dic59—21no—
73C4×Dic59—22no—
74C4×Dic59D411yescharacteristic
75C4×Dic59D411yescharacteristic
76C4×Dic59C2311yescharacteristic
77C2×C59⋊C8C2312yes—
78C22×D59—21no—
79C22×D59C2×D411yescharacteristic
80Q8×C59—42no—
81C2×C4×C59—22no—
82C2×C4×C59—21no—
83C2×C4×C59—21no—
84C2×C4×C59C2×D411yescharacteristic
85C2×C4×C59C2×D411yescharacteristic
86C2×C4×C59C2411yescharacteristic
87C2×Dic59—22no—
88C2×Dic59—21no—
89C2×Dic59C2×D411yescharacteristic
90C2×Dic59C2×D411yescharacteristic
91C2×Dic59C2×D411yescharacteristic
92D236—22no—
93D236—42no—
94C4×D59—22no—
95C4×D59—41no—
96C4×D59—41no—
97C4×D59—42no—
98Dic118—22no—
99Dic118—42no—
100C8×C59—22no—
101C59⋊C8—22no—
102C22×C59C22×D411yescharacteristic
103C2×D59—21no—
104C2×D59—21no—
105C2×D59—21no—
106C2×D59—41no—
107C2×D59—41no—
108C2×D59—41no—
109C4×C59—21no—
110C4×C59—21no—
111C4×C59—41no—
112C4×C59—41no—
113C4×C59—42no—
114C4×C592−1+412yes—
115Dic59—21no—
116Dic59—21no—
117Dic59—21no—
118Dic59—41no—
119Dic59—42no—
120#3240—591nomaximal, Sylow
121C2×C59#53611yescharacteristic
122C2×C59#57511yescharacteristic
123C2×C59#57511yescharacteristic
124D59—41no—
125D59—81no—
126#533—591no—
127#529—591no—
128#501—591no—
129#501D5911yescharacteristic, complemented
130#489—591no—
131#489—591no—
132#485—592no—
133#482—592no—
134#479—592no—
135#478—592no—
136#432—591no—
137C59#324011yescharacteristic, complemented, Sylow
138C4⋊Q8—591no—
139C4⋊Q8C2×D5911yescharacteristic
140#126—1181no—
141#125—592no—
142#125C2×D5911yescharacteristic
143#124—591no—
144#123—1181no—
145C22⋊Q8—591no—
146C22⋊Q8—1181no—
147C22⋊Q8—1181no—
148#121—591no—
149C4×Q8—591no—
150C4×Q8—1181no—
151C4×Q8—1181no—
152C4×D4—591no—
153C4×D4—1181no—
154#117—592no—
155#117—1181no—
156C2×C42—591no—
157#107—592no—
158#107C2×D5912yes—
159#106—592no—
160#106C2×D5912yes—
161C4⋊C8—592no—
162#103—592no—
163#103—592no—
164#102—592no—
165#102—592no—
166C22⋊C8—592no—
167#97—591no—
168#97C2×D5911yescharacteristic
169C2×Q8—21no—
170C2×Q8—591no—
171C2×Q8—1181no—
172C2×D4—591no—
173C2×D4—1181no—
174C22×C4—591no—
175C22×C4—591no—
176C22×C4—591no—
177C22×C4—1181no—
178C2×C8—592no—
179C2×C8C22×D5912yes—
180C4⋊C4—21no—
181C4⋊C4—21no—
182C4⋊C4—21no—
183C4⋊C4—592no—
184C4⋊C4—1181no—
185C4⋊C4—1181no—
186C4⋊C4—1182no—
187C4⋊C4—1182no—
188C4⋊C4—1181no—
189C4⋊C4C22×D5912yes—
190C4⋊C4C22×D5911yescharacteristic
191C4⋊C4C22×D5911yescharacteristic
192C22⋊C4—1181no—
193C22⋊C4—1181no—
194C22⋊C4—1182no—
195C22⋊C4—1181no—
196C22⋊C4—1181no—
197C22⋊C4—1181no—
198C42—591no—
199C42—591no—
200C42—591no—
201C42—1182no—
202C42—1181no—
203C42C22×D5911yescharacteristic
204C23—591no—
205C23—1181no—
206Q8—42no—
207Q8—1182no—
208Q8—2362no—
209D4—1182no—
210D4—2362no—
211C2×C4—21no—
212C2×C4—22no—
213C2×C4—21no—
214C2×C4—591no—
215C2×C4—591no—
216C2×C4—591no—
217C2×C4—1182no—
218C2×C4—1181no—
219C2×C4—1182no—
220C2×C4—2361no—
221C2×C4—2361no—
222C2×C4—2362no—
223C2×C4D4×D5911yescharacteristic
224C2×C4D4×D5911yescharacteristic
225C2×C4C23×D5911yescharacteristic
226C8—22no—
227C8—1182no—
228C22—1181no—
229C22—1181no—
230C22—1181no—
231C22—2361no—
232C22—2361no—
233C22—2361no—
234C22C2×D4×D5911yescharacteristic
235C4—21no—
236C4—21no—
237C4—41no—
238C4—42no—
239C4—41no—
240C4—1181no—
241C4—1181no—
242C4—1181no—
243C4—2362no—
244C4—2361no—
245C4#1427377512yes—
246C2—4721no—
247C2—2361no—
248C2#1683797711yescharacteristic
249C2#1683819811yescharacteristic
250C2#1683820111yescharacteristic
subgroupG/H
centerC22C2×D4×D59
commutatorC2×C4×C59C24
FrattiniC2×C4C23×D59
FittingC59×#501C2
socleC22×C59C22×D4
hypercenter#501D59
hypocenterC59#3240
LCSG ▷ C2×C4×C59 ▷ C2×C59 ▷ C59
UCSC1 ◁ C22 ◁ C42 ◁ #501

Complements

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

NH ≅ G/Ntype
1. #16837957C2semidirect
3. #16837812C2semidirect
4. #16837764C2semidirect
5. #16837762C2semidirect
6. #16837746C2semidirect
8. #16837708C2semidirect
9. #16837701C2semidirect
10. #16837457C2semidirect
11. C59×#501C2semidirect
129. #501D59semidirect
137. C59#3240semidirect