Finite Group Databasebeta

← #21435032

Subgroups — #21435032

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#16837953C211yesmaximal, characteristic, complemented
2#16837953C211yesmaximal, characteristic, complemented
3#16837779C211yesmaximal, characteristic, complemented
4#16837776C211yesmaximal, characteristic, complemented
5#16837750C211yesmaximal, characteristic, complemented
6#16837620C214yesmaximal, complemented
7#16837550C214yesmaximal, complemented
8#16837453C211yesmaximal, characteristic, complemented
9C59×#487C211yesmaximal, characteristic, complemented
10C2×#11745689—21no—
11C2×#11745689C2212yes—
12C2×#11745671C2214yes—
13C2×D472C2214yes—
14#14273724C2211yescharacteristic
15#14273724C2211yescharacteristic
16#14273716—21no—
17#14273716C2212yes—
18#14273702—21no—
19#14273702—21no—
20#14273702—21no—
21#14273702C2212yes—
22#14273689—21no—
23#14273689—21no—
24#14273689—21no—
25#14273689C2212yes—
26C42×D59C2211yescharacteristic
27Dic59⋊C8C2212yes—
28#14273647C2214yes—
29(C2×D59)⋊C8C2212yes—
30C4×C59⋊C8C2211yescharacteristic
31C4⋊Q8×C59C2211yescharacteristic
32C4⋊Q8×C59C2211yescharacteristic
33#103×C59C2214yes—
34C4×C8×C59C2211yescharacteristic
35C2×Q8×C59—21no—
36C2×Q8×C59C2312yes—
37#11745689—44no—
38#11745689—44no—
39C2×D236—22no—
40C2×D236—22no—
41C2×D236—21no—
42C2×D236—21no—
43C2×D236—21no—
44C2×D236—21no—
45C2×D236C2312yes—
46C2×D236C2312yes—
47C2×C4×D59—22no—
48C2×C4×D59—22no—
49C2×C4×D59D411yescharacteristic
50C2×C4×D59D411yescharacteristic
51C2×C4×D59C2311yescharacteristic
52C2×C8×C59C2312yes—
53C4⋊C4×C59—21no—
54C4⋊C4×C59—21no—
55C4⋊C4×C59—21no—
56C4⋊C4×C59C2312yes—
57C42×C59C2311yescharacteristic
58#11745671—44no—
59(C2×D59)⋊C4—22no—
60(C2×D59)⋊C4—22no—
61(C2×D59)⋊C4—22no—
62(C2×D59)⋊C4—22no—
63C4×Dic59D411yescharacteristic
64C4×Dic59D411yescharacteristic
65C4×Dic59C2311yescharacteristic
66C2×C59⋊C8C2312yes—
67D472—44no—
68C22×D59—22no—
69C22×D59—22no—
70C22×D59C2×D411yescharacteristic
71Q8×C59—24no—
72Q8×C59—42no—
73C2×C4×C59—22no—
74C2×C4×C59—22no—
75C2×C4×C59C2×D411yescharacteristic
76C2×C4×C59C2×D411yescharacteristic
77C2×C4×C59C2411yescharacteristic
78C2×Dic59C2×D411yescharacteristic
79C2×Dic59C2×D411yescharacteristic
80C2×Dic59C2×D411yescharacteristic
81D236—24no—
82D236—24no—
83D236—44no—
84D236—44no—
85D236—42no—
86D236—42no—
87D236—42no—
88D236—42no—
89C4×D59—22no—
90C4×D59—22no—
91C4×D59—22no—
92C4×D59—44no—
93C4×D59—44no—
94C8×C59—22no—
95C59⋊C8—22no—
96C22×C59C22×D411yescharacteristic
97C2×D59—21no—
98C2×D59—21no—
99C2×D59—21no—
100C2×D59—42no—
101C2×D59—42no—
102C2×D59—42no—
103C2×D59—42no—
104C2×D59—42no—
105C2×D59—42no—
106C4×C59—42no—
107C4×C59—42no—
108C4×C59#13512yes—
109C4×C59AGL(1,ℤ/8)12yes—
110C4×C59H(5,𝔽2)12yes—
111Dic59—21no—
112Dic59—21no—
113Dic59—21no—
114#3207—591nomaximal, Sylow
115C2×C59#53511yescharacteristic
116C2×C59C2×#13511yescharacteristic
117C2×C59C2×AGL(1,ℤ/8)11yescharacteristic
118D59—41no—
119D59—82no—
120D59—82no—
121#532—591no—
122#532—591no—
123#493—591no—
124#492—591no—
125#487D5911yescharacteristic, complemented
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×D8—594no—
135C4⋊Q8C2×D5911yescharacteristic
136C4⋊Q8C2×D5911yescharacteristic
137#127—591no—
138#127—591no—
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#103C2×D5914yes—
152#102—594no—
153C22⋊C8—592no—
154C4×C8—591no—
155C4×C8C2×D5911yescharacteristic
156#41—2364no—
157#41—2364no—
158C2×Q8—21no—
159C2×Q8C22×D5912yes—
160C2×D4—592no—
161C2×D4—592no—
162C2×D4—1182no—
163C2×D4—1182no—
164C2×D4—1181no—
165C2×D4—1181no—
166C2×D4—1181no—
167C2×D4—1181no—
168C22×C4—591no—
169C22×C4—591no—
170C22×C4—591no—
171C22×C4—1182no—
172C22×C4—1182no—
173SD16—2364no—
174D8—2364no—
175C2×C8—592no—
176C2×C8C22×D5912yes—
177C4⋊C4—21no—
178C4⋊C4—21no—
179C4⋊C4—21no—
180C4⋊C4C22×D5912yes—
181C22⋊C4—1182no—
182C22⋊C4—1182no—
183C22⋊C4—1182no—
184C22⋊C4—1182no—
185C42—591no—
186C42—591no—
187C42—591no—
188C42C22×D5911yescharacteristic
189C23—591no—
190C23—1182no—
191C23—1182no—
192Q8—24no—
193Q8—42no—
194D4—1184no—
195D4—1184no—
196D4—2364no—
197D4—2364no—
198D4—2362no—
199D4—2362no—
200D4—2362no—
201D4—2362no—
202C2×C4—22no—
203C2×C4—22no—
204C2×C4—591no—
205C2×C4—591no—
206C2×C4—591no—
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—1181no—
218C22—1181no—
219C22—1181no—
220C22—2362no—
221C22—2362no—
222C22—2362no—
223C22—2362no—
224C22—2362no—
225C22—2362no—
226C22C2×D4×D5911yescharacteristic
227C4—42no—
228C4—42no—
229C4—1181no—
230C4—1181no—
231C4—1181no—
232C4#1427375012yes—
233C4#1427375412yes—
234C4#1427377312yes—
235C2—4722no—
236C2—4722no—
237C2—2361no—
238C2#1683797011yescharacteristic
239C2C2×#1427375011yescharacteristic
240C2C2×#1427375411yescharacteristic
subgroupG/H
centerC22C2×D4×D59
commutatorC2×C4×C59C24
FrattiniC2×C4C23×D59
FittingC59×#487C2
socleC22×C59C22×D4
hypercenter#487D59
hypocenterC59#3207
LCSG ▷ C2×C4×C59 ▷ C2×C59 ▷ C59
UCSC1 ◁ C22 ◁ C42 ◁ #487

Complements

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

NH ≅ G/Ntype
1. #16837953C2semidirect
2. #16837953C2semidirect
3. #16837779C2semidirect
4. #16837776C2semidirect
5. #16837750C2semidirect
6. #16837620C2semidirect
7. #16837550C2semidirect
8. #16837453C2semidirect
9. C59×#487C2semidirect
125. #487D59semidirect
130. C59#3207semidirect