Finite Group Databasebeta

← #21434143

Subgroups — #21434143

Order 7552.

454 conjugacy classes of subgroups; only the 133 normal subgroups are shown.

normal subgroups only

This group has 454 conjugacy classes of subgroups — too many to draw. Only its 133 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#16837936C211yesmaximal, characteristic, complemented
2#16837737C211yesmaximal, characteristic, complemented
3#16837720C211yesmaximal, characteristic, complemented
4#16837702C212yesmaximal, complemented
5#16837617C212yesmaximal, complemented
6#16837553C211yesmaximal, characteristic, complemented
7#16837536C211yesmaximal, characteristic
8C4×#11745670C212yesmaximal, complemented
9C4×#11745669C212yesmaximal, complemented
10#16837455C211yesmaximal, characteristic, complemented
11C2×C4×D4×C59C211yesmaximal, characteristic, complemented
12C2×#11745670C2212yes—
13C2×#11745669C2212yes—
14#14273721—21no—
15#14273719C2211yescharacteristic, complemented
16#14273715C2211yescharacteristic, complemented
17#14273710—21no—
18#14273706C2211yescharacteristic
19#14273701C2211yescharacteristic
20C4×Dic118C2211yescharacteristic, complemented
21C4×D236C2211yescharacteristic, complemented
22C4×C22⋊D59—21no—
23#14273684—21no—
24#14273660C2212yescomplemented
25#14273658C2212yescomplemented
26C4⋊(C59⋊C8)C2212yescomplemented
27#14273650C2212yescomplemented
28#14273648C2212yes—
29#14273648C2212yes—
30#14273647C2212yescomplemented
31C22⋊(C59⋊C8)C2211yescharacteristic
32C22⋊(C59⋊C8)C2211yescharacteristic
33C4×C59⋊C8C2212yescomplemented
34C22×D4×C59C2211yescharacteristic
35C23×C4×C59—21no—
36C4×D4×C59—21no—
37C4×D4×C59—21no—
38C4×D4×C59C2212yes—
39C4×D4×C59C2212yes—
40C2×C4⋊C4×C59C2211yescharacteristic
41C2×C22⋊C4×C59—21no—
42C2×C42×C59C2211yescharacteristic
43C24×C59—21no—
44C2×D4×C59—24no—
45C2×D4×C59—21no—
46C2×D4×C59C2312yes—
47C22×C4×C59—21no—
48C22×C4×C59—22no—
49C22×C4×C59—22no—
50C22×C4×C59—44no—
51C22×C4×C59D411yescharacteristic
52C22×C4×C59D411yescharacteristic
53C22×C4×C59C2311yescharacteristic
54C2×C22⋊D59—21no—
55C2×D236C2311yescharacteristic
56C2×C4×D59—21no—
57C2×Dic118C2311yescharacteristic
58C4⋊C4×C59—21no—
59C4⋊C4×C59C2312yes—
60C22⋊C4×C59—22no—
61C22⋊C4×C59—22no—
62C42×C59D411yescharacteristic
63C42×C59D411yescharacteristic
64C42×C59C2311yescharacteristic
65C42×C59C2311yescharacteristic
66C22⋊Dic59—21no—
67#11745670—24no—
68#11745669—24no—
69(C2×D59)⋊C4—21no—
70(C2×D59)⋊C4—21no—
71(C2×D59)⋊C4—21no—
72(C2×D59)⋊C4—21no—
73C4⋊Dic59C2311yescharacteristic
74C4⋊Dic59C2311yescharacteristic
75Dic59⋊C4—21no—
76Dic59⋊C4—21no—
77Dic59⋊C4—21no—
78Dic59⋊C4—21no—
79C4×Dic59—21no—
80C2×C59⋊C8C2312yes—
81C2×C59⋊C8C2312yes—
82C23×C59—24no—
83C23×C59—22no—
84C23×C59—42no—
85C23×C59—42no—
86C23×C59C2×D411yescharacteristic
87C22×D59—21no—
88D4×C59—24no—
89D4×C59—22no—
90D4×C59#4114yes—
91C2×C4×C59—22no—
92C2×C4×C59—22no—
93C2×C4×C59—22no—
94C2×C4×C59—22no—
95C2×C4×C59—44no—
96C2×C4×C59—42no—
97C2×C4×C59—44no—
98C2×C4×C59C2×D411yescharacteristic
99C2×C4×C59C2×D411yescharacteristic
100C2×C4×C59C2×D411yescharacteristic
101C2×C4×C59C2×D411yescharacteristic
102C2×C4×C59C2×D411yescharacteristic
103C2×C4×C59C2411yescharacteristic
104C22⋊D59—42no—
105C2×Dic59—21no—
106C2×Dic59—21no—
107C2×Dic59—21no—
108D236—22no—
109C4×D59—42no—
110Dic118—22no—
111C59⋊C8—22no—
112C59⋊C8—22no—
113C22×C59—21no—
114C22×C59—21no—
115C22×C59—24no—
116C22×C59—48no—
117C22×C59—42no—
118C22×C59—42no—
119C22×C59#13512yes—
120C22×C59C22×D411yescharacteristic
121C2×D59—41no—
122C2×D59—41no—
123C2×D59—41no—
124C4×C59—21no—
125C4×C59—21no—
126C4×C59—21no—
127C4×C59—21no—
128C4×C59—42no—
129C4×C59AGL(1,ℤ/8)12yes—
130C4×C59C2×#4112yes—
131Dic59—41no—
132Dic59—41no—
133Dic59—41no—
134#3105—591nomaximal, Sylow
135C2×C59—22no—
136C2×C59—44no—
137C2×C59#52511yescharacteristic
138C2×C59C2×#13511yescharacteristic
139C2×C59C2×AGL(1,ℤ/8)11yescharacteristic
140D59—81no—
141#529—591no—
142C2×C4×D4D5911yescharacteristic, complemented
143#484—591no—
144#481—591no—
145#478—592no—
146#463—592no—
147#450—591no—
148#447—591no—
149C4×SD16—592no—
150C4×D8—592no—
151#431—591no—
152C59#310511yescharacteristic, complemented, Sylow
153C22×D4C2×D5911yescharacteristic
154C23×C4—21no—
155C2×SD16—592no—
156C2×D8—592no—
157#126—1181no—
158#125—591no—
159#124—591no—
160#123—1181no—
161C22⋊Q8—591no—
162#121—591no—
163C4×Q8—591no—
164C4×D4—21no—
165C4×D4—21no—
166C4×D4—591no—
167C4×D4—1181no—
168C4×D4C2×D5912yes—
169C4×D4C2×D5912yes—
170#117—1181no—
171C2×C4⋊C4C2×D5911yescharacteristic
172C2×C22⋊C4—21no—
173C2×C42C2×D5911yescharacteristic
174#107—592no—
175#106—592no—
176C4⋊C8—592no—
177#103—592no—
178#102—592no—
179#102—592no—
180#102—592no—
181C22⋊C8—591no—
182C22⋊C8—591no—
183C4×C8—592no—
184C24—21no—
185C2×Q8—591no—
186C2×D4—24no—
187C2×D4—21no—
188C2×D4—591no—
189C2×D4—1181no—
190C2×D4C22×D5912yes—
191C22×C4—21no—
192C22×C4—22no—
193C22×C4—22no—
194C22×C4—44no—
195C22×C4—1181no—
196C22×C4C22⋊D5911yescharacteristic
197C22×C4C22⋊D5911yescharacteristic
198C22×C4C22×D5911yescharacteristic
199SD16—1184no—
200D8—1184no—
201C2×C8—592no—
202C2×C8—592no—
203C4⋊C4—21no—
204C4⋊C4—591no—
205C4⋊C4—591no—
206C4⋊C4—1181no—
207C4⋊C4—1181no—
208C4⋊C4—1181no—
209C4⋊C4—1181no—
210C4⋊C4C22×D5912yes—
211C22⋊C4—22no—
212C22⋊C4—22no—
213C22⋊C4—1181no—
214C22⋊C4—1181no—
215C22⋊C4—1181no—
216C22⋊C4—1181no—
217C22⋊C4—1181no—
218C42—1181no—
219C42C22⋊D5911yescharacteristic
220C42C22⋊D5911yescharacteristic
221C42C22×D5911yescharacteristic
222C42C22×D5911yescharacteristic
223C23—24no—
224C23—22no—
225C23—42no—
226C23—42no—
227C23—1181no—
228C23C2×C22⋊D5911yescharacteristic
229Q8—1182no—
230D4—24no—
231D4—22no—
232D4—1182no—
233D4—2362no—
234D4#1174568514yes—
235C2×C4—22no—
236C2×C4—22no—
237C2×C4—22no—
238C2×C4—22no—
239C2×C4—44no—
240C2×C4—42no—
241C2×C4—44no—
242C2×C4—1181no—
243C2×C4—1181no—
244C2×C4—1181no—
245C2×C4—2362no—
246C2×C4C2×C22⋊D5911yescharacteristic
247C2×C4C2×C22⋊D5911yescharacteristic
248C2×C4C2×C22⋊D5911yescharacteristic
249C2×C4C2×C22⋊D5911yescharacteristic
250C2×C4C2×C22⋊D5911yescharacteristic
251C2×C4C23×D5911yescharacteristic
252C8—1182no—
253C8—1182no—
254C22—21no—
255C22—21no—
256C22—24no—
257C22—48no—
258C22—42no—
259C22—42no—
260C22—2361no—
261C22—2361no—
262C22—2361no—
263C22#1427374712yes—
264C22C22×C22⋊D5911yescharacteristic
265C4—21no—
266C4—21no—
267C4—21no—
268C4—21no—
269C4—42no—
270C4—2361no—
271C4—2361no—
272C4—2361no—
273C4#1427375312yes—
274C4C2×#1174568512yes—
275C2—22no—
276C2—44no—
277C2—4721no—
278C2#1683791311yescharacteristic
279C2C2×#1427374711yescharacteristic
280C2C2×#1427375311yescharacteristic
subgroupG/H
centerC2×C4C2×C22⋊D59
commutatorC2×C4×C59C24
FrattiniC2×C4C23×D59
FittingC2×C4×D4×C59C2
socleC22×C59C22×D4
hypercenterC2×C4×D4D59
hypocenterC59#3105
LCSG ▷ C2×C4×C59 ▷ C2×C59 ▷ C59
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ C2×C4×D4

Complements

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

NH ≅ G/Ntype
1. #16837936C2semidirect
2. #16837737C2semidirect
3. #16837720C2semidirect
4. #16837702C2semidirect
5. #16837617C2semidirect
6. #16837553C2semidirect
8. C4×#11745670C2semidirect
9. C4×#11745669C2semidirect
10. #16837455C2semidirect
11. C2×C4×D4×C59C2semidirect
15. #14273719C22semidirect
16. #14273715C22semidirect
20. C4×Dic118C22semidirect
21. C4×D236C22semidirect
24. #14273660C22semidirect
25. #14273658C22semidirect
26. C4⋊(C59⋊C8)C22semidirect
27. #14273650C22semidirect
30. #14273647C22semidirect
33. C4×C59⋊C8C22semidirect
142. C2×C4×D4D59semidirect
152. C59#3105semidirect