Finite Group Databasebeta

← #21435061

Subgroups — #21435061

Order 7552.

410 conjugacy classes of subgroups; only the 121 normal subgroups are shown.

normal subgroups only

This group has 410 conjugacy classes of subgroups — too many to draw. Only its 121 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#16837784C212yesmaximal, complemented
3#16837756C212yesmaximal, complemented
4#16837621C212yesmaximal, complemented
5#16837614C212yesmaximal, complemented
6#16837558C211yesmaximal, characteristic, complemented
7#16837553C211yesmaximal, characteristic, complemented
8#16837541C211yesmaximal, characteristic, complemented
9#16837536C211yesmaximal, characteristic
10#16837455C211yesmaximal, characteristic, complemented
11C2×#124×C59C211yesmaximal, characteristic, complemented
12C2×#11745672C2212yescomplemented
13C2×#11745670C2212yes—
14C2×#11745671C2212yescomplemented
15C2×#11745669C2212yes—
16#14273721—21no—
17#14273719C2211yescharacteristic, complemented
18#14273715C2211yescharacteristic, complemented
19#14273710—21no—
20#14273706C2211yescharacteristic
21#14273701C2211yescharacteristic
22C4×Dic118C2211yescharacteristic, complemented
23C4×D236C2211yescharacteristic, complemented
24C4×C22⋊D59—21no—
25#14273684—21no—
26C4⋊(C59⋊C8)C2212yescomplemented
27#14273651C2212yescomplemented
28#14273651C2212yescomplemented
29#14273648C2212yes—
30#14273648C2212yes—
31C22⋊(C59⋊C8)C2211yescharacteristic
32C22⋊(C59⋊C8)C2211yescharacteristic
33C4×C59⋊C8C2212yescomplemented
34C22×Q8×C59C2211yescharacteristic
35C22×D4×C59C2211yescharacteristic
36#124×C59—21no—
37#124×C59—21no—
38#124×C59C2212yes—
39#124×C59C2212yes—
40C2×C22⋊C4×C59—21no—
41C2×C22⋊C4×C59—21no—
42C2×C42×C59C2211yescharacteristic
43C24×C59—21no—
44C2×Q8×C59—21no—
45C2×Q8×C59—42no—
46C2×Q8×C59C2312yes—
47C2×D4×C59—21no—
48C2×D4×C59—42no—
49C2×D4×C59C2312yes—
50C22×C4×C59—21no—
51C22×C4×C59D411yescharacteristic
52C22×C4×C59D411yescharacteristic
53C22×C4×C59C2311yescharacteristic
54C2×C22⋊D59—21no—
55C2×D236C2311yescharacteristic
56C2×C4×D59—21no—
57C2×Dic118C2311yescharacteristic
58C22⋊C4×C59—22no—
59C22⋊C4×C59—22no—
60C22⋊C4×C59—22no—
61C22⋊C4×C59—22no—
62C42×C59D411yescharacteristic
63C42×C59D411yescharacteristic
64C42×C59C2311yescharacteristic
65C42×C59C2311yescharacteristic
66C22⋊Dic59—21no—
67#11745672—42no—
68#11745671—42no—
69#11745670—42no—
70#11745669—42no—
71(C2×D59)⋊C4—21no—
72(C2×D59)⋊C4—21no—
73(C2×D59)⋊C4—21no—
74(C2×D59)⋊C4—21no—
75C4⋊Dic59C2311yescharacteristic
76C4⋊Dic59C2311yescharacteristic
77Dic59⋊C4—21no—
78Dic59⋊C4—21no—
79Dic59⋊C4—21no—
80Dic59⋊C4—21no—
81C4×Dic59—21no—
82C2×C59⋊C8C2312yes—
83C2×C59⋊C8C2312yes—
84C23×C59—22no—
85C23×C59—42no—
86C23×C59—42no—
87C23×C59—42no—
88C23×C59C2×D411yescharacteristic
89C22×D59—21no—
90Q8×C59—22no—
91Q8×C59—22no—
92Q8×C59—42no—
93D4×C59—22no—
94D4×C59—22no—
95D4×C59—42no—
96C2×C4×C59—22no—
97C2×C4×C59—22no—
98C2×C4×C59—22no—
99C2×C4×C59—41no—
100C2×C4×C59—42no—
101C2×C4×C59C2×D411yescharacteristic
102C2×C4×C59C2×D411yescharacteristic
103C2×C4×C59C2×D411yescharacteristic
104C2×C4×C59C2×D411yescharacteristic
105C2×C4×C59C2×D411yescharacteristic
106C2×C4×C59C2411yescharacteristic
107C22⋊D59—42no—
108C2×Dic59—21no—
109C2×Dic59—21no—
110C2×Dic59—21no—
111D236—22no—
112C4×D59—42no—
113Dic118—22no—
114C59⋊C8—22no—
115C59⋊C8—22no—
116C22×C59—21no—
117C22×C59—21no—
118C22×C59—42no—
119C22×C59—42no—
120C22×C59—42no—
121C22×C59—84no—
122C22×C59#13512yes—
123C22×C59C22×D411yescharacteristic
124C2×D59—41no—
125C2×D59—41no—
126C2×D59—41no—
127C4×C59—21no—
128C4×C59—21no—
129C4×C59—21no—
130C4×C59—21no—
131C4×C59—21no—
132C4×C59—42no—
133C4×C59H(5,𝔽2)12yes—
134Dic59—41no—
135Dic59—41no—
136Dic59—41no—
137#3211—591nomaximal, Sylow
138C2×C59—22no—
139C2×C59—82no—
140C2×C59#53511yescharacteristic
141C2×C59C2×#13511yescharacteristic
142C2×C59#57511yescharacteristic
143D59—81no—
144#529—591no—
145C2×#124D5911yescharacteristic, complemented
146#495—592no—
147#488—592no—
148#464—592no—
149#463—592no—
150#451—591no—
151#450—591no—
152#448—591no—
153#447—591no—
154#431—591no—
155C59#321111yescharacteristic, complemented, Sylow
156C22×Q8C2×D5911yescharacteristic
157C22×D4C2×D5911yescharacteristic
158C2×Q16—592no—
159C2×SD16—592no—
160C2×SD16—592no—
161C2×D8—592no—
162#126—1181no—
163#125—591no—
164#124—21no—
165#124—21no—
166#124—591no—
167#124C2×D5912yes—
168#124C2×D5912yes—
169#123—1181no—
170C22⋊Q8—591no—
171#121—591no—
172C4×Q8—591no—
173C4×D4—591no—
174C4×D4—1181no—
175#117—1181no—
176C2×C22⋊C4—21no—
177C2×C22⋊C4—21no—
178C2×C42C2×D5911yescharacteristic
179C4⋊C8—592no—
180#103—592no—
181#103—592no—
182#102—592no—
183#102—592no—
184C22⋊C8—591no—
185C22⋊C8—591no—
186C4×C8—592no—
187C24—21no—
188C2×Q8—21no—
189C2×Q8—42no—
190C2×Q8—591no—
191C2×Q8C22×D5912yes—
192C2×D4—21no—
193C2×D4—42no—
194C2×D4—591no—
195C2×D4—1181no—
196C2×D4C22×D5912yes—
197C22×C4—21no—
198C22×C4—1181no—
199C22×C4C22⋊D5911yescharacteristic
200C22×C4C22⋊D5911yescharacteristic
201C22×C4C22×D5911yescharacteristic
202Q16—2362no—
203SD16—2362no—
204SD16—2362no—
205D8—2362no—
206C2×C8—592no—
207C2×C8—592no—
208C4⋊C4—591no—
209C4⋊C4—591no—
210C4⋊C4—1181no—
211C4⋊C4—1181no—
212C4⋊C4—1181no—
213C4⋊C4—1181no—
214C22⋊C4—22no—
215C22⋊C4—22no—
216C22⋊C4—22no—
217C22⋊C4—22no—
218C22⋊C4—1181no—
219C22⋊C4—1181no—
220C22⋊C4—1181no—
221C22⋊C4—1181no—
222C22⋊C4—1181no—
223C42—1181no—
224C42C22⋊D5911yescharacteristic
225C42C22⋊D5911yescharacteristic
226C42C22×D5911yescharacteristic
227C42C22×D5911yescharacteristic
228C23—22no—
229C23—42no—
230C23—42no—
231C23—42no—
232C23—1181no—
233C23C2×C22⋊D5911yescharacteristic
234Q8—22no—
235Q8—22no—
236Q8—42no—
237Q8—1182no—
238D4—22no—
239D4—22no—
240D4—42no—
241D4—1182no—
242D4—2362no—
243C2×C4—22no—
244C2×C4—22no—
245C2×C4—22no—
246C2×C4—41no—
247C2×C4—42no—
248C2×C4—1181no—
249C2×C4—1181no—
250C2×C4—1181no—
251C2×C4—2362no—
252C2×C4C2×C22⋊D5911yescharacteristic
253C2×C4C2×C22⋊D5911yescharacteristic
254C2×C4C2×C22⋊D5911yescharacteristic
255C2×C4C2×C22⋊D5911yescharacteristic
256C2×C4C2×C22⋊D5911yescharacteristic
257C2×C4C23×D5911yescharacteristic
258C8—1182no—
259C8—1182no—
260C22—21no—
261C22—21no—
262C22—42no—
263C22—42no—
264C22—42no—
265C22—84no—
266C22—2361no—
267C22—2361no—
268C22—2361no—
269C22#1427374712yes—
270C22C22×C22⋊D5911yescharacteristic
271C4—21no—
272C4—21no—
273C4—21no—
274C4—21no—
275C4—21no—
276C4—42no—
277C4—2361no—
278C4—2361no—
279C4—2361no—
280C4#1427377212yes—
281C2—22no—
282C2—82no—
283C2—4721no—
284C2#1683796911yescharacteristic
285C2C2×#1427374711yescharacteristic
286C2#1683820011yescharacteristic
subgroupG/H
centerC22C22×C22⋊D59
commutatorC2×C4×C59C24
FrattiniC2×C4C23×D59
FittingC2×#124×C59C2
socleC22×C59C22×D4
hypercenterC2×#124D59
hypocenterC59#3211
LCSG ▷ C2×C4×C59 ▷ C2×C59 ▷ C59
UCSC1 ◁ C22 ◁ C2×C42 ◁ C2×#124

Complements

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

NH ≅ G/Ntype
1. #16837936C2semidirect
2. #16837784C2semidirect
3. #16837756C2semidirect
4. #16837621C2semidirect
5. #16837614C2semidirect
6. #16837558C2semidirect
7. #16837553C2semidirect
8. #16837541C2semidirect
10. #16837455C2semidirect
11. C2×#124×C59C2semidirect
12. C2×#11745672C22semidirect
14. C2×#11745671C22semidirect
17. #14273719C22semidirect
18. #14273715C22semidirect
22. C4×Dic118C22semidirect
23. C4×D236C22semidirect
26. C4⋊(C59⋊C8)C22semidirect
27. #14273651C22semidirect
28. #14273651C22semidirect
33. C4×C59⋊C8C22semidirect
145. C2×#124D59semidirect
155. C59#3211semidirect