Finite Group Databasebeta

← #21434892

Subgroups — #21434892

Order 7552.

514 conjugacy classes of subgroups; only the 113 normal subgroups are shown.

normal subgroups only

This group has 514 conjugacy classes of subgroups — too many to draw. Only its 113 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#121×D59C212yesmaximal, complemented
2#16837722C212yesmaximal, complemented
3#16837719C212yesmaximal, complemented
4#16837655C211yesmaximal, characteristic, complemented
5#16837653C212yesmaximal, complemented
6#16837537C212yesmaximal, complemented
7#16837534C212yesmaximal, complemented
8#16837365C211yesmaximal, characteristic, complemented
9C59×#469C211yesmaximal, characteristic, complemented
10C2×D4×D59—22no—
11C2×D4×D59C2212yescomplemented
12C22×C4×D59C2211yescharacteristic
13C2×D472C2211yescharacteristic, complemented
14C2×#11745669C2212yescomplemented
15C2×#11745664C2211yescharacteristic, complemented
16#14273702C2212yes—
17#14273701C2212yescomplemented
18#14273700—22no—
19#14273699—22no—
20#14273698C2212yes—
21C4⋊C4×D59C2212yescomplemented
22C22⋊C4×D59—22no—
23#14273659C2211yescharacteristic, complemented
24#14273658C2212yescomplemented
25#14273649C2212yescomplemented
26#14273648C2212yescomplemented
27#14273647C2212yescomplemented
28(C2×D59)⋊C8C2212yescomplemented
29(C2×D59)⋊C8C2212yescomplemented
30C2×D8×C59C2211yescharacteristic, complemented
31C2×M16×C59C2211yescharacteristic, complemented
32#121×C59C2212yescomplemented
33#106×C59C2211yescharacteristic, complemented
34#102×C59C2212yescomplemented
35C23×D59—22no—
36C23×D59D411yescharacteristic
37C2×D4×C59—22no—
38C2×D4×C59C2312yes—
39C22×C4×C59C2311yescharacteristic
40C2×C22⋊D59—22no—
41C2×C22⋊D59—22no—
42C2×C22⋊D59—22no—
43C22×Dic59D411yescharacteristic
44D4×D59—42no—
45D4×D59—42no—
46D4×D59—48no—
47C2×D236—22no—
48C2×D236C2312yes—
49C2×C4×D59—22no—
50C2×C4×D59—41no—
51C2×C4×D59—41no—
52C2×C4×D59D412yes—
53C2×C4×D59C2312yes—
54D8×C59—41no—
55M16×C59—41no—
56C2×C8×C59C2311yescharacteristic
57C2×C8×C59C2311yescharacteristic
58C4⋊C4×C59C2312yes—
59C22⋊C4×C59—22no—
60C22⋊Dic59—22no—
61#11745669—42no—
62(C2×D59)⋊C4—22no—
63(C2×D59)⋊C4—22no—
64C4⋊Dic59C2312yes—
65Dic59⋊C4—22no—
66#11745664—41no—
67C2×C59⋊C8C2312yes—
68D472—41no—
69C23×C59—22no—
70C23×C59C2×D411yescharacteristic
71C22×D59—24no—
72C22×D59—22no—
73C22×D59—41no—
74C22×D59—44no—
75C22×D59—44no—
76C22×D59—44no—
77C22×D59C2×D412yes—
78D4×C59—22no—
79D4×C59—22no—
80D4×C59—44no—
81C2×C4×C59—21no—
82C2×C4×C59—21no—
83C2×C4×C59—22no—
84C2×C4×C59C2×D411yescharacteristic
85C2×C4×C59C2411yescharacteristic
86C22⋊D59—44no—
87C22⋊D59—44no—
88C22⋊D59—44no—
89C2×Dic59—22no—
90C2×Dic59—41no—
91C2×Dic59C2×D412yes—
92D236—22no—
93D236—22no—
94D236—44no—
95C4×D59—22no—
96C4×D59—22no—
97C4×D59—42no—
98C4×D59—44no—
99C8×C59—21no—
100C8×C59—21no—
101C59⋊C8—22no—
102C22×C59—21no—
103C22×C59—22no—
104C22×C59—42no—
105C22×C59—42no—
106C22×C59—42no—
107C22×C59C22×D411yescharacteristic
108C2×D59—22no—
109C2×D59—22no—
110C2×D59—44no—
111C2×D59—42no—
112C2×D59—42no—
113C2×D59—42no—
114C2×D59—88no—
115C2×D59AGL(1,ℤ/8)14yes—
116C4×C59—21no—
117C4×C59—42no—
118C4×C59H(5,𝔽2)11yescharacteristic
119C4×C59H(5,𝔽2)11yescharacteristic
120Dic59—22no—
121Dic59—42no—
122#3192—591nomaximal, Sylow
123C2×C59—41no—
124C2×C59—82no—
125C2×C59#53411yescharacteristic
126C2×C59C2×AGL(1,ℤ/8)12yes—
127D59—24no—
128D59—82no—
129C2×#121—592no—
130#481—592no—
131#481—592no—
132#469—591no—
133#469—592no—
134#469D5911yescharacteristic, complemented
135#447—592no—
136#447—592no—
137#407—591no—
138C59#319211yescharacteristic, complemented, Sylow
139C22×D4—592no—
140C22×D4—1182no—
141C23×C4—591no—
142C2×D8—592no—
143C2×D8—591no—
144C2×D8C2×D5911yescharacteristic, complemented
145C2×M16—591no—
146C2×M16C2×D5911yescharacteristic, complemented
147#121—592no—
148#121—592no—
149#121—592no—
150#121—1182no—
151#121—1182no—
152#121C2×D5912yescomplemented
153C2×C4⋊C4—592no—
154C2×C22⋊C4—1182no—
155#106—591no—
156#106—592no—
157#106C2×D5911yescharacteristic, complemented
158#102—592no—
159#102—592no—
160#102—592no—
161#102C2×D5912yescomplemented
162C22⋊C8—592no—
163C22⋊C8—592no—
164C24—591no—
165C24—1182no—
166C2×D4—22no—
167C2×D4—592no—
168C2×D4—1182no—
169C2×D4—1182no—
170C2×D4—1182no—
171C2×D4—1182no—
172C2×D4—2362no—
173C2×D4—2362no—
174C2×D4—2368no—
175C2×D4C22×D5912yes—
176C22×C4—591no—
177C22×C4—592no—
178C22×C4—592no—
179C22×C4—1182no—
180C22×C4—2361no—
181C22×C4—2361no—
182C22×C4C22×D5911yescharacteristic
183D8—41no—
184D8—2361no—
185D8—2362no—
186M16—41no—
187M16—2361no—
188C2×C8—592no—
189C2×C8C22×D5911yescharacteristic
190C2×C8C22×D5911yescharacteristic
191C4⋊C4—592no—
192C4⋊C4—1182no—
193C4⋊C4C22×D5912yes—
194C22⋊C4—22no—
195C22⋊C4—1182no—
196C22⋊C4—1182no—
197C22⋊C4—1182no—
198C23—22no—
199C23—592no—
200C23—1184no—
201C23—1182no—
202C23—2361no—
203C23—2364no—
204C23—2364no—
205C23—2364no—
206C23D4×D5911yescharacteristic
207D4—22no—
208D4—22no—
209D4—44no—
210D4—1182no—
211D4—1182no—
212D4—2364no—
213D4—2364no—
214D4—2364no—
215D4—2364no—
216C2×C4—21no—
217C2×C4—21no—
218C2×C4—22no—
219C2×C4—592no—
220C2×C4—1182no—
221C2×C4—1182no—
222C2×C4—1182no—
223C2×C4—2362no—
224C2×C4—2364no—
225C2×C4—2361no—
226C2×C4D4×D5911yescharacteristic
227C2×C4C23×D5911yescharacteristic
228C8—21no—
229C8—21no—
230C8—1182no—
231C22—22no—
232C22—21no—
233C22—42no—
234C22—42no—
235C22—42no—
236C22—594no—
237C22—1182no—
238C22—1182no—
239C22—4728no—
240C22—2364no—
241C22—2362no—
242C22—2362no—
243C22—2362no—
244C22C2×D4×D5911yescharacteristic
245C4—21no—
246C4—42no—
247C4—1182no—
248C4—2362no—
249C4#1427377211yescharacteristic
250C4#1427377311yescharacteristic
251C2—41no—
252C2—82no—
253C2—1184no—
254C2—4722no—
255C2#1683796011yescharacteristic
256C2AGL(1,ℤ/8)×D5912yes—
subgroupG/H
centerC22C2×D4×D59
commutatorC2×C4×C59C24
FrattiniC2×C4C23×D59
FittingC59×#469C2
socleC22×C59C22×D4
hypercenter#469D59
hypocenterC59#3192
LCSG ▷ C2×C4×C59 ▷ C2×C59 ▷ C59
UCSC1 ◁ C22 ◁ C22×C4 ◁ #469

Complements

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

NH ≅ G/Ntype
1. #121×D59C2semidirect
2. #16837722C2semidirect
3. #16837719C2semidirect
4. #16837655C2semidirect
5. #16837653C2semidirect
6. #16837537C2semidirect
7. #16837534C2semidirect
8. #16837365C2semidirect
9. C59×#469C2semidirect
11. C2×D4×D59C22semidirect
13. C2×D472C22semidirect
14. C2×#11745669C22semidirect
15. C2×#11745664C22semidirect
17. #14273701C22semidirect
21. C4⋊C4×D59C22semidirect
23. #14273659C22semidirect
24. #14273658C22semidirect
25. #14273649C22semidirect
26. #14273648C22semidirect
27. #14273647C22semidirect
28. (C2×D59)⋊C8C22semidirect
29. (C2×D59)⋊C8C22semidirect
30. C2×D8×C59C22semidirect
31. C2×M16×C59C22semidirect
32. #121×C59C22semidirect
33. #106×C59C22semidirect
34. #102×C59C22semidirect
134. #469D59semidirect
138. C59#3192semidirect
144. C2×D8C2×D59semidirect
146. C2×M16C2×D59semidirect
152. #121C2×D59semidirect
157. #106C2×D59semidirect
161. #102C2×D59semidirect