Finite Group Databasebeta

← #21434021

Subgroups — #21434021

Order 7552.

458 conjugacy classes of subgroups; only the 141 normal subgroups are shown.

normal subgroups only

This group has 458 conjugacy classes of subgroups — too many to draw. Only its 141 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#16837913C211yesmaximal, characteristic
2C22×C4⋊Dic59C211yesmaximal, characteristic, complemented
3#16837738C212yesmaximal, complemented
4#16837733C212yesmaximal, complemented
5#16837721C212yesmaximal, complemented
6#16837716C212yesmaximal, complemented
7#16837444C212yesmaximal, complemented
8#16837404C212yesmaximal, complemented
9C59×#407C211yesmaximal, characteristic, complemented
10C2×#11745685C2211yescharacteristic
11C23×Dic59—21no—
12#14273710—21no—
13#14273706C2211yescharacteristic
14#14273706C2211yescharacteristic
15#14273701C2211yescharacteristic
16#14273701C2211yescharacteristic
17#14273696—21no—
18C4×C22⋊D59—21no—
19C4×C22⋊D59—21no—
20#14273686C2211yescharacteristic
21C2×C4⋊Dic59—21no—
22C2×C4⋊Dic59—21no—
23C2×C4⋊Dic59—21no—
24C2×C4⋊Dic59C2212yes—
25C2×C4⋊Dic59C2212yes—
26C2×C4⋊Dic59C2212yes—
27#14273661C2214yescomplemented
28#14273659C2214yescomplemented
29#14273652C2214yescomplemented
30#14273649C2214yescomplemented
31C23×C4×C59C2211yescharacteristic
32C2×M16×C59C2212yes—
33C22⋊C8×C59C2212yes—
34C22⋊C8×C59C2212yes—
35C24×C59D411yescharacteristic
36C22×C4×C59—24no—
37C22×C4×C59D411yescharacteristic
38C22×C4×C59D411yescharacteristic
39C22×C4×C59D411yescharacteristic
40C22×C4×C59C2311yescharacteristic
41C22×C4×C59C2311yescharacteristic
42C22×C4×C59C2311yescharacteristic
43C2×C22⋊D59—21no—
44C2×C22⋊D59—21no—
45C2×C22⋊D59—21no—
46C22×Dic59—22no—
47C22×Dic59—22no—
48C22×Dic59—22no—
49C22×Dic59—44no—
50#11745685—24no—
51C2×D236C2311yescharacteristic
52C2×C4×D59—21no—
53C2×Dic118C2311yescharacteristic
54M16×C59—24no—
55C2×C8×C59C2314yes—
56C22⋊Dic59—21no—
57C22⋊Dic59—21no—
58C22⋊Dic59—21no—
59(C2×D59)⋊C4—21no—
60(C2×D59)⋊C4—21no—
61C4⋊Dic59—22no—
62C4⋊Dic59—22no—
63C4⋊Dic59—22no—
64C4⋊Dic59C2314yes—
65C4⋊Dic59C2311yescharacteristic
66C4⋊Dic59C2311yescharacteristic
67Dic59⋊C4—21no—
68Dic59⋊C4—21no—
69C4×Dic59—21no—
70C23×C59—22no—
71C23×C59—22no—
72C23×C59—22no—
73C23×C59C2×D411yescharacteristic
74C23×C59C2×D411yescharacteristic
75C23×C59C2×D411yescharacteristic
76C22×D59—21no—
77C2×C4×C59—22no—
78C2×C4×C59—22no—
79C2×C4×C59—22no—
80C2×C4×C59—22no—
81C2×C4×C59—22no—
82C2×C4×C59C2×D411yescharacteristic
83C2×C4×C59C2×D411yescharacteristic
84C2×C4×C59C2×D411yescharacteristic
85C2×C4×C59#4114yes—
86C2×C4×C59C2411yescharacteristic
87C22⋊D59—42no—
88C22⋊D59—42no—
89C22⋊D59—42no—
90C2×Dic59—21no—
91C2×Dic59—21no—
92C2×Dic59—21no—
93C2×Dic59—24no—
94C2×Dic59—44no—
95C2×Dic59—44no—
96C2×Dic59—44no—
97D236—22no—
98C4×D59—42no—
99Dic118—22no—
100C8×C59—24no—
101C22×C59—28no—
102C22×C59—21no—
103C22×C59—21no—
104C22×C59—21no—
105C22×C59—21no—
106C22×C59—21no—
107C22×C59—21no—
108C22×C59#12312yes—
109C22×C59AGL(1,ℤ/8)12yes—
110C22×C59#13712yes—
111C22×C59C22×D411yescharacteristic
112C2×D59—41no—
113C2×D59—41no—
114C2×D59—41no—
115C4×C59—21no—
116C4×C59—21no—
117C4×C59#12312yes—
118C4×C59C2×#4112yes—
119Dic59—41no—
120Dic59—44no—
121Dic59—41no—
122Dic59—41no—
123#3092—591nomaximal, Sylow
124C2×C59—22no—
125C2×C59—22no—
126C2×C59—22no—
127C2×C59C2×#12311yescharacteristic
128C2×C59C2×AGL(1,ℤ/8)11yescharacteristic
129C2×C59C2×#13711yescharacteristic
130D59—81no—
131#525—591no—
132C22×C4⋊C4—591no—
133#484—592no—
134#483—592no—
135#481—592no—
136#480—592no—
137#428—592no—
138#417—592no—
139#407D5911yescharacteristic, complemented
140C59#309211yescharacteristic, complemented, Sylow
141C2×#41—591no—
142C23×C4—1181no—
143C23×C4C2×D5911yescharacteristic
144C2×M16C2×D5912yes—
145#123—1181no—
146C22⋊Q8—591no—
147C22⋊Q8—591no—
148#121—591no—
149#121—591no—
150#120—1181no—
151C4×D4—1181no—
152C4×D4—1181no—
153#117—591no—
154C2×C4⋊C4—592no—
155C2×C4⋊C4—592no—
156C2×C4⋊C4—592no—
157C2×C4⋊C4—1181no—
158C2×C4⋊C4—1181no—
159C2×C4⋊C4—1181no—
160#107—594no—
161#106—594no—
162#103—594no—
163#102—594no—
164C22⋊C8C2×D5912yes—
165C22⋊C8C2×D5912yes—
166C24D23611yescharacteristic
167#41—1184no—
168C2×Q8—591no—
169C2×D4—591no—
170C2×D4—1181no—
171C2×D4—1181no—
172C2×D4—1181no—
173C22×C4—24no—
174C22×C4—1182no—
175C22×C4—1182no—
176C22×C4—1182no—
177C22×C4—1181no—
178C22×C4—2364no—
179C22×C4D23611yescharacteristic
180C22×C4D23611yescharacteristic
181C22×C4D23611yescharacteristic
182C22×C4C22×D5911yescharacteristic
183C22×C4C22×D5911yescharacteristic
184C22×C4C22×D5911yescharacteristic
185M16—24no—
186C2×C8C22×D5914yes—
187C4⋊C4—594no—
188C4⋊C4—591no—
189C4⋊C4—591no—
190C4⋊C4—1182no—
191C4⋊C4—1182no—
192C4⋊C4—1182no—
193C4⋊C4—1181no—
194C4⋊C4—1181no—
195C22⋊C4—1181no—
196C22⋊C4—1181no—
197C22⋊C4—1181no—
198C22⋊C4—1181no—
199C22⋊C4—1181no—
200C42—1181no—
201C23—22no—
202C23—22no—
203C23—22no—
204C23—1181no—
205C23C2×D23611yescharacteristic
206C23C2×D23611yescharacteristic
207C23C2×D23611yescharacteristic
208Q8—1182no—
209D4—1182no—
210D4—2362no—
211D4—2362no—
212D4—2362no—
213C2×C4—22no—
214C2×C4—22no—
215C2×C4—22no—
216C2×C4—22no—
217C2×C4—22no—
218C2×C4—1181no—
219C2×C4—1181no—
220C2×C4—1181no—
221C2×C4—1184no—
222C2×C4—2364no—
223C2×C4—2364no—
224C2×C4—2364no—
225C2×C4—2362no—
226C2×C4C2×D23611yescharacteristic
227C2×C4C2×D23611yescharacteristic
228C2×C4C2×D23611yescharacteristic
229C2×C4#1174568714yes—
230C2×C4C23×D5911yescharacteristic
231C8—24no—
232C22—28no—
233C22—21no—
234C22—21no—
235C22—21no—
236C22—21no—
237C22—21no—
238C22—21no—
239C22—2361no—
240C22—2361no—
241C22—2361no—
242C22#1427371112yes—
243C22#1427375512yes—
244C22#1427376012yes—
245C22C22×D23611yescharacteristic
246C4—21no—
247C4—21no—
248C4—2361no—
249C4—2364no—
250C4—2361no—
251C4—2361no—
252C4#1427371112yes—
253C4C2×#1174568712yes—
254C2—22no—
255C2—22no—
256C2—22no—
257C2—4721no—
258C2C2×#1427371111yescharacteristic
259C2C2×#1427375511yescharacteristic
260C2C2×#1427376011yescharacteristic
subgroupG/H
centerC22C22×D236
commutatorC2×C4×C59C24
FrattiniC2×C4C23×D59
FittingC59×#407C2
socleC22×C59C22×D4
hypercenter#407D59
hypocenterC59#3092
LCSG ▷ C2×C4×C59 ▷ C2×C59 ▷ C59
UCSC1 ◁ C22 ◁ C23×C4 ◁ #407

Complements

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

NH ≅ G/Ntype
2. C22×C4⋊Dic59C2semidirect
3. #16837738C2semidirect
4. #16837733C2semidirect
5. #16837721C2semidirect
6. #16837716C2semidirect
7. #16837444C2semidirect
8. #16837404C2semidirect
9. C59×#407C2semidirect
27. #14273661C22semidirect
28. #14273659C22semidirect
29. #14273652C22semidirect
30. #14273649C22semidirect
139. #407D59semidirect
140. C59#3092semidirect