Finite Group Databasebeta

← #21435024

Subgroups — #21435024

Order 7552.

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

normal subgroups only

This group has 438 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#16837950C211yesmaximal, characteristic, complemented
2#16837950C211yesmaximal, characteristic, complemented
3#16837774C211yesmaximal, characteristic, complemented
4#16837753C211yesmaximal, characteristic, complemented
5#16837748C211yesmaximal, characteristic, complemented
6#16837615C214yesmaximal, complemented
7#16837544C214yesmaximal, complemented
8#16837453C211yesmaximal, characteristic, complemented
9C59×#493C211yesmaximal, characteristic, complemented
10C2×#11745687—21no—
11C2×#11745687C2212yes—
12C2×#11745670C2214yes—
13#14273727C2211yescharacteristic
14#14273727C2211yescharacteristic
15#14273714—21no—
16#14273714C2212yes—
17#14273698—21no—
18#14273698—21no—
19#14273698—21no—
20#14273698C2212yes—
21D4×Dic59—21no—
22D4×Dic59—21no—
23D4×Dic59—21no—
24D4×Dic59C2212yes—
25C42×D59C2211yescharacteristic
26Dic59⋊C8C2212yes—
27#14273652C2214yes—
28#14273648C2214yes—
29(C2×D59)⋊C8C2212yes—
30C4×C59⋊C8C2211yescharacteristic
31C2×D8×C59C2214yes—
32#127×C59C2211yescharacteristic
33#127×C59C2211yescharacteristic
34C4×C8×C59C2211yescharacteristic
35C2×D4×C59—21no—
36C2×D4×C59—21no—
37C2×D4×C59—21no—
38C2×D4×C59—21no—
39C2×D4×C59C2312yes—
40C2×D4×C59C2312yes—
41C2×C22⋊D59—22no—
42C2×C22⋊D59—22no—
43C22×Dic59—22no—
44C22×Dic59—22no—
45#11745687—44no—
46#11745687—44no—
47C2×C4×D59D411yescharacteristic
48C2×C4×D59D411yescharacteristic
49C2×C4×D59C2311yescharacteristic
50C2×Dic118—21no—
51C2×Dic118C2312yes—
52D8×C59—44no—
53C2×C8×C59C2312yes—
54C42×C59C2311yescharacteristic
55C22⋊Dic59—22no—
56C22⋊Dic59—22no—
57C22⋊Dic59—22no—
58C22⋊Dic59—22no—
59#11745670—44no—
60C4⋊Dic59—21no—
61C4⋊Dic59—21no—
62C4⋊Dic59—21no—
63C4⋊Dic59C2312yes—
64C4×Dic59D411yescharacteristic
65C4×Dic59D411yescharacteristic
66C4×Dic59C2311yescharacteristic
67C2×C59⋊C8C2312yes—
68C23×C59—22no—
69C23×C59—22no—
70C22×D59C2×D411yescharacteristic
71D4×C59—24no—
72D4×C59—24no—
73D4×C59—42no—
74D4×C59—42no—
75D4×C59—42no—
76D4×C59—42no—
77C2×C4×C59C2×D411yescharacteristic
78C2×C4×C59C2×D411yescharacteristic
79C2×C4×C59C2411yescharacteristic
80C22⋊D59—44no—
81C22⋊D59—44no—
82C2×Dic59—22no—
83C2×Dic59—22no—
84C2×Dic59—44no—
85C2×Dic59—44no—
86C2×Dic59C2×D411yescharacteristic
87C2×Dic59C2×D411yescharacteristic
88C2×Dic59C2×D411yescharacteristic
89C4×D59—22no—
90C4×D59—22no—
91C4×D59—22no—
92Dic118—24no—
93Dic118—42no—
94C8×C59—22no—
95C59⋊C8—22no—
96C22×C59—42no—
97C22×C59—42no—
98C22×C59—42no—
99C22×C59—42no—
100C22×C59—42no—
101C22×C59—42no—
102C22×C59C22×D411yescharacteristic
103C2×D59—21no—
104C2×D59—21no—
105C2×D59—21no—
106C4×C59#13512yes—
107C4×C59AGL(1,ℤ/8)12yes—
108C4×C59H(5,𝔽2)12yes—
109Dic59—21no—
110Dic59—21no—
111Dic59—21no—
112Dic59—42no—
113Dic59—42no—
114#3207—591nomaximal, Sylow
115C2×C59—82no—
116C2×C59—82no—
117C2×C59#53511yescharacteristic
118C2×C59C2×#13511yescharacteristic
119C2×C59C2×AGL(1,ℤ/8)11yescharacteristic
120D59—41no—
121#532—591no—
122#532—591no—
123#493D5911yescharacteristic, complemented
124#492—591no—
125#487—591no—
126#486—591no—
127#463—594no—
128#449—594no—
129#431—591no—
130C59#320711yescharacteristic, complemented, Sylow
131C2×#41—592no—
132C2×#41—1181no—
133C2×SD16—594no—
134C2×D8C2×D5914yes—
135C4⋊Q8—591no—
136C4⋊Q8—591no—
137#127C2×D5911yescharacteristic
138#127C2×D5911yescharacteristic
139#124—592no—
140#124—1181no—
141#121—592no—
142#121—1181no—
143#121—1181no—
144#121—1181no—
145C4×D4—592no—
146C4×D4—1181no—
147C4×D4—1181no—
148C4×D4—1181no—
149C2×C42—591no—
150C4⋊C8—592no—
151#103—594no—
152#102—594no—
153C22⋊C8—592no—
154C4×C8—591no—
155C4×C8C2×D5911yescharacteristic
156#41—2364no—
157#41—2364no—
158C2×Q8—592no—
159C2×Q8—1181no—
160C2×D4—21no—
161C2×D4—21no—
162C2×D4—21no—
163C2×D4—21no—
164C2×D4—1182no—
165C2×D4—1182no—
166C2×D4C22×D5912yes—
167C2×D4C22×D5912yes—
168C22×C4—591no—
169C22×C4—591no—
170C22×C4—591no—
171C22×C4—1182no—
172C22×C4—1182no—
173SD16—2364no—
174D8—44no—
175C2×C8—592no—
176C2×C8C22×D5912yes—
177C4⋊C4—592no—
178C4⋊C4—1181no—
179C4⋊C4—1181no—
180C4⋊C4—1181no—
181C22⋊C4—1182no—
182C22⋊C4—1182no—
183C22⋊C4—1182no—
184C22⋊C4—1182no—
185C42—591no—
186C42—591no—
187C42—591no—
188C42C22×D5911yescharacteristic
189C23—22no—
190C23—22no—
191C23—591no—
192Q8—1184no—
193Q8—2362no—
194D4—24no—
195D4—24no—
196D4—42no—
197D4—42no—
198D4—42no—
199D4—42no—
200D4—2364no—
201D4—2364no—
202C2×C4—591no—
203C2×C4—591no—
204C2×C4—591no—
205C2×C4—1182no—
206C2×C4—1182no—
207C2×C4—1182no—
208C2×C4—1182no—
209C2×C4—1182no—
210C2×C4—2364no—
211C2×C4—2364no—
212C2×C4D4×D5911yescharacteristic
213C2×C4D4×D5911yescharacteristic
214C2×C4C23×D5911yescharacteristic
215C8—22no—
216C8—1182no—
217C22—42no—
218C22—42no—
219C22—42no—
220C22—42no—
221C22—42no—
222C22—42no—
223C22—1181no—
224C22—1181no—
225C22—1181no—
226C22C2×D4×D5911yescharacteristic
227C4—1181no—
228C4—1181no—
229C4—1181no—
230C4—2362no—
231C4—2362no—
232C4#1427374612yes—
233C4#1427375112yes—
234C4#1427377212yes—
235C2—82no—
236C2—82no—
237C2—2361no—
238C2#1683796511yescharacteristic
239C2C2×#1427374611yescharacteristic
240C2C2×#1427375111yescharacteristic
subgroupG/H
centerC22C2×D4×D59
commutatorC2×C4×C59C24
FrattiniC2×C4C23×D59
FittingC59×#493C2
socleC22×C59C22×D4
hypercenter#493D59
hypocenterC59#3207
LCSG ▷ C2×C4×C59 ▷ C2×C59 ▷ C59
UCSC1 ◁ C22 ◁ C42 ◁ #493

Complements

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

NH ≅ G/Ntype
1. #16837950C2semidirect
2. #16837950C2semidirect
3. #16837774C2semidirect
4. #16837753C2semidirect
5. #16837748C2semidirect
6. #16837615C2semidirect
7. #16837544C2semidirect
8. #16837453C2semidirect
9. C59×#493C2semidirect
123. #493D59semidirect
130. C59#3207semidirect