Finite Group Databasebeta

← #21435010

Subgroups — #21435010

Order 7552.

532 conjugacy classes of subgroups; only the 125 normal subgroups are shown.

normal subgroups only

This group has 532 conjugacy classes of subgroups — too many to draw. Only its 125 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#127×D59C211yesmaximal, characteristic, complemented
3#16837778C211yesmaximal, characteristic, complemented
4#16837749C211yesmaximal, characteristic, complemented
5#16837748C211yesmaximal, characteristic, complemented
6#16837595C214yesmaximal, complemented
7#16837534C214yesmaximal, complemented
8#16837453C211yesmaximal, characteristic, complemented
9C59×#493C211yesmaximal, characteristic, complemented
10C2×#11745687—21no—
11C2×D4×D59—21no—
12C2×D4×D59—21no—
13C2×D4×D59C2212yes—
14C2×#11745669C2214yescomplemented
15#14273727C2211yescharacteristic, complemented
16#14273724C2211yescharacteristic
17#14273723—21no—
18#14273723—21no—
19#14273723C2212yes—
20#14273714—21no—
21#14273698—21no—
22#14273698C2212yes—
23D4×Dic59—21no—
24D4×Dic59C2212yescomplemented
25C42×D59C2211yescharacteristic
26Dic59⋊C8C2212yescomplemented
27#14273649C2214yescomplemented
28#14273648C2214yescomplemented
29(C2×D59)⋊C8C2212yes—
30C4×C59⋊C8C2211yescharacteristic, complemented
31C2×D8×C59C2214yescomplemented
32#127×C59C2211yescharacteristic
33#127×C59C2211yescharacteristic, complemented
34C4×C8×C59C2211yescharacteristic, complemented
35C23×D59—22no—
36C2×D4×C59—21no—
37C2×D4×C59—21no—
38C2×D4×C59—21no—
39C2×D4×C59—21no—
40C2×D4×C59C2312yes—
41C2×D4×C59C2312yes—
42C2×C22⋊D59—22no—
43C2×C22⋊D59—22no—
44C2×C22⋊D59—22no—
45C2×C22⋊D59—22no—
46C22×Dic59—22no—
47#11745687—44no—
48D4×D59—44no—
49D4×D59—44no—
50D4×D59—44no—
51C2×D236—21no—
52C2×D236—21no—
53C2×D236C2312yes—
54C2×C4×D59D411yescharacteristic
55C2×C4×D59D411yescharacteristic
56C2×C4×D59C2311yescharacteristic
57C2×Dic118—21no—
58D8×C59—44no—
59C2×C8×C59C2312yes—
60C42×C59C2311yescharacteristic
61C22⋊Dic59—22no—
62C22⋊Dic59—22no—
63#11745669—44no—
64C4⋊Dic59—21no—
65C4⋊Dic59C2312yes—
66C4×Dic59D411yescharacteristic
67C4×Dic59D411yescharacteristic
68C4×Dic59C2311yescharacteristic
69C2×C59⋊C8C2312yes—
70C23×C59—22no—
71C23×C59—22no—
72C22×D59—22no—
73C22×D59—44no—
74C22×D59—44no—
75C22×D59—44no—
76C22×D59C2×D411yescharacteristic
77D4×C59—24no—
78D4×C59—24no—
79D4×C59—42no—
80D4×C59—42no—
81D4×C59—42no—
82D4×C59—42no—
83C2×C4×C59C2×D411yescharacteristic
84C2×C4×C59C2×D411yescharacteristic
85C2×C4×C59C2411yescharacteristic
86C22⋊D59—44no—
87C22⋊D59—44no—
88C22⋊D59—44no—
89C22⋊D59—44no—
90C2×Dic59—22no—
91C2×Dic59—44no—
92C2×Dic59C2×D411yescharacteristic
93C2×Dic59C2×D411yescharacteristic
94C2×Dic59C2×D411yescharacteristic
95D236—24no—
96D236—42no—
97D236—42no—
98C4×D59—22no—
99C4×D59—22no—
100C4×D59D814yescomplemented
101Dic118—42no—
102C8×C59—22no—
103C59⋊C8—22no—
104C22×C59—42no—
105C22×C59—42no—
106C22×C59—42no—
107C22×C59—42no—
108C22×C59—42no—
109C22×C59—42no—
110C22×C59C22×D411yescharacteristic
111C2×D59—21no—
112C2×D59—21no—
113C2×D59—42no—
114C2×D59—42no—
115C2×D59—42no—
116C2×D59—88no—
117C2×D59C2×D812yes—
118C4×C59C2×D812yes—
119C4×C59AGL(1,ℤ/8)12yes—
120C4×C59H(5,𝔽2)12yes—
121Dic59—21no—
122Dic59—21no—
123Dic59—42no—
124Dic59C2×D812yes—
125#3205—591nomaximal, Sylow
126C2×C59—82no—
127C2×C59—82no—
128C2×C59#53511yescharacteristic
129C2×C59C22×D811yescharacteristic
130C2×C59C2×AGL(1,ℤ/8)11yescharacteristic
131D59—22no—
132D59—82no—
133#532—591no—
134C2×#127—591no—
135#493—591no—
136#493D5911yescharacteristic, complemented
137#486—591no—
138#486—591no—
139#459—594no—
140#447—594no—
141#431—591no—
142C59#320511yescharacteristic, complemented, Sylow
143C2×#41—1181no—
144C22×D4—592no—
145C22×D4—1181no—
146C22×D4—1181no—
147C2×D8—594no—
148C2×D8C2×D5914yescomplemented
149C4⋊Q8—591no—
150#127—592no—
151#127—591no—
152#127—1181no—
153#127—1181no—
154#127C2×D5911yescharacteristic
155#127C2×D5911yescharacteristic, complemented
156#124—1181no—
157#121—592no—
158#121—1181no—
159C4×D4—592no—
160C4×D4—1181no—
161C2×C42—591no—
162C4⋊C8—592no—
163#102—594no—
164#102—594no—
165C22⋊C8—592no—
166C4×C8—591no—
167C4×C8C2×D5911yescharacteristic, complemented
168C24—1182no—
169#41—2364no—
170C2×Q8—1181no—
171C2×D4—21no—
172C2×D4—21no—
173C2×D4—21no—
174C2×D4—21no—
175C2×D4—592no—
176C2×D4—1182no—
177C2×D4—1182no—
178C2×D4—1182no—
179C2×D4—1182no—
180C2×D4—1181no—
181C2×D4—1181no—
182C2×D4—2364no—
183C2×D4—2364no—
184C2×D4—2364no—
185C2×D4C22×D5912yes—
186C2×D4C22×D5912yes—
187C22×C4—591no—
188C22×C4—591no—
189C22×C4—591no—
190C22×C4—1182no—
191D8—44no—
192D8—2364no—
193C2×C8—592no—
194C2×C8C22×D5912yes—
195C4⋊C4—592no—
196C4⋊C4—1181no—
197C22⋊C4—1182no—
198C22⋊C4—1182no—
199C42—591no—
200C42—591no—
201C42—591no—
202C42C22×D5911yescharacteristic
203C23—22no—
204C23—22no—
205C23—591no—
206C23—1182no—
207C23—2364no—
208C23—2364no—
209C23—2364no—
210Q8—2362no—
211D4—24no—
212D4—24no—
213D4—42no—
214D4—42no—
215D4—42no—
216D4—42no—
217D4—1184no—
218D4—2364no—
219D4—2364no—
220D4—2364no—
221D4—2364no—
222D4—2362no—
223D4—2362no—
224C2×C4—591no—
225C2×C4—594no—
226C2×C4—591no—
227C2×C4—591no—
228C2×C4—1182no—
229C2×C4—1182no—
230C2×C4—1182no—
231C2×C4—2364no—
232C2×C4D4×D5911yescharacteristic
233C2×C4D4×D5911yescharacteristic
234C2×C4C23×D5911yescharacteristic
235C8—22no—
236C8—1182no—
237C22—42no—
238C22—42no—
239C22—42no—
240C22—42no—
241C22—42no—
242C22—42no—
243C22—592no—
244C22—1181no—
245C22—1181no—
246C22—4728no—
247C22—2362no—
248C22—2362no—
249C22—2362no—
250C22C2×D4×D5911yescharacteristic
251C4—592no—
252C4—1181no—
253C4—1181no—
254C4—2362no—
255C4D8×D5912yes—
256C4#1427375112yes—
257C4#1427377212yes—
258C2—82no—
259C2—82no—
260C2—1182no—
261C2—4722no—
262C2#1683796511yescharacteristic
263C2C2×D8×D5911yescharacteristic
264C2C2×#1427375111yescharacteristic
subgroupG/H
centerC22C2×D4×D59
commutatorC2×C4×C59C24
FrattiniC2×C4C23×D59
FittingC59×#493C2
socleC22×C59C22×D4
hypercenter#493D59
hypocenterC59#3205
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. #127×D59C2semidirect
3. #16837778C2semidirect
4. #16837749C2semidirect
5. #16837748C2semidirect
6. #16837595C2semidirect
7. #16837534C2semidirect
8. #16837453C2semidirect
9. C59×#493C2semidirect
14. C2×#11745669C22semidirect
15. #14273727C22semidirect
24. D4×Dic59C22semidirect
26. Dic59⋊C8C22semidirect
27. #14273649C22semidirect
28. #14273648C22semidirect
30. C4×C59⋊C8C22semidirect
31. C2×D8×C59C22semidirect
33. #127×C59C22semidirect
34. C4×C8×C59C22semidirect
100. C4×D59D8semidirect
136. #493D59semidirect
142. C59#3205semidirect
148. C2×D8C2×D59semidirect
155. #127C2×D59semidirect
167. C4×C8C2×D59semidirect