Finite Group Databasebeta

← #21433358

Subgroups — #21433358

Order 7552.

754 conjugacy classes of subgroups; only the 153 normal subgroups are shown.

normal subgroups only

This group has 754 conjugacy classes of subgroups — too many to draw. Only its 153 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
1C22×#11745685C211yesmaximal, characteristic
2C2×#14273760C212yesmaximal, complemented
3C2×#14273706C211yesmaximal, characteristic, complemented
4#16837566C214yesmaximal, complemented
5#16837560C212yesmaximal, complemented
6#16837555C212yesmaximal, complemented
7#16837404C212yesmaximal, complemented
8C59×#407C211yesmaximal, characteristic, complemented
9C2×#11745685—21no—
10C2×#11745685—21no—
11C2×#11745685—28no—
12C2×#11745685C2212yes—
13C2×#11745685C2212yes—
14C22×Dic118C2211yescharacteristic
15C22×Dic118C2211yescharacteristic, complemented
16C22×D236C2211yescharacteristic
17C22×C22⋊D59—21no—
18C22×C4×D59—21no—
19#14273760—28no—
20C2×Dic236C2214yescomplemented
21C2×#11745660C2214yescomplemented
22#14273706—21no—
23#14273706—21no—
24#14273706C2212yes—
25#14273706C2212yescomplemented
26C2×C4⋊Dic59C2211yescharacteristic, complemented
27C2×Dic59⋊C4—21no—
28C2×C22⋊Dic59—21no—
29#14273652C2214yescomplemented
30#14273649C2214yescomplemented
31C23×C4×C59C2211yescharacteristic
32C2×M16×C59C2212yescomplemented
33C22⋊C8×C59C2212yes—
34C22⋊C8×C59C2212yescomplemented
35C24×C59D411yescharacteristic
36C23×D59—21no—
37C22×C4×C59—24no—
38C22×C4×C59D411yescharacteristic
39C22×C4×C59D411yescharacteristic
40C22×C4×C59D411yescharacteristic
41C22×C4×C59C2311yescharacteristic
42C22×C4×C59C2311yescharacteristic
43C22×C4×C59C2311yescharacteristic
44C2×C22⋊D59—28no—
45C2×C22⋊D59—22no—
46C2×C22⋊D59—22no—
47C22×Dic59—21no—
48C22×Dic59—21no—
49C22×Dic59—21no—
50#11745685—28no—
51#11745685—28no—
52#11745685—24no—
53#11745685—24no—
54#11745685—24no—
55#11745685D418yes—
56C2×D236—21no—
57C2×D236—24no—
58C2×D236C2312yes—
59C2×C4×D59—28no—
60C2×C4×D59—22no—
61C2×C4×D59—22no—
62C2×Dic118—21no—
63C2×Dic118—24no—
64C2×Dic118—24no—
65C2×Dic118—21no—
66C2×Dic118C2312yes—
67C2×Dic118C2312yes—
68M16×C59—24no—
69C2×C8×C59C2314yes—
70C22⋊Dic59—22no—
71C22⋊Dic59—22no—
72C4⋊Dic59—21no—
73C4⋊Dic59C2312yes—
74Dic59⋊C4—22no—
75Dic59⋊C4—22no—
76Dic236—28no—
77#11745660—28no—
78C23×C59—22no—
79C23×C59—22no—
80C23×C59—41no—
81C23×C59C2×D411yescharacteristic
82C23×C59C2×D411yescharacteristic
83C23×C59C2×D411yescharacteristic
84C22×D59—24no—
85C22×D59—22no—
86C22×D59—42no—
87C22×D59—42no—
88C2×C4×C59—22no—
89C2×C4×C59—22no—
90C2×C4×C59—22no—
91C2×C4×C59—22no—
92C2×C4×C59—22no—
93C2×C4×C59C2×D411yescharacteristic
94C2×C4×C59C2×D411yescharacteristic
95C2×C4×C59C2×D411yescharacteristic
96C2×C4×C59C2×D414yes—
97C2×C4×C59C2411yescharacteristic
98C22⋊D59—28no—
99C22⋊D59—28no—
100C2×Dic59—24no—
101C2×Dic59—22no—
102C2×Dic59—22no—
103C2×Dic59—22no—
104C2×Dic59—42no—
105C2×Dic59—42no—
106D236—24no—
107D236—22no—
108D236C2×D414yes—
109C4×D59—28no—
110C4×D59—28no—
111Dic118—24no—
112Dic118—22no—
113Dic118—24no—
114Dic118—42no—
115Dic118C2×D414yes—
116C8×C59—24no—
117C22×C59—21no—
118C22×C59—21no—
119C22×C59—21no—
120C22×C59—21no—
121C22×C59—21no—
122C22×C59—21no—
123C22×C59—21no—
124C22×C59—44no—
125C22×C59#12012yes—
126C22×C59#13712yescomplemented
127C22×C59C22×D411yescharacteristic
128C2×D59—24no—
129C2×D59—48no—
130C2×D59—42no—
131C2×D59—42no—
132C4×C59—21no—
133C4×C59—21no—
134C4×C59#12012yes—
135C4×C59C22×D412yes—
136Dic59—24no—
137Dic59—42no—
138Dic59—42no—
139#3007—591nomaximal, Sylow
140C2×C59—22no—
141C2×C59—22no—
142C2×C59—41no—
143C2×C59C2×#12011yescharacteristic
144C2×C59C2×#13711yescharacteristic
145C2×C59#57511yescharacteristic
146D59—44no—
147C22×#41—591no—
148C2×#137—592no—
149C2×C22⋊Q8—591no—
150#452—594no—
151#451—592no—
152#450—592no—
153#417—592no—
154#407D5911yescharacteristic, complemented
155C59#300711yescharacteristic, complemented, Sylow
156C2×#41—592no—
157C2×#41—592no—
158C2×#41—1188no—
159C2×#41—1181no—
160C2×#41—1181no—
161C22×Q8—591no—
162C22×Q8—591no—
163C22×D4—591no—
164C22×D4—1181no—
165C23×C4—1181no—
166C23×C4C2×D5911yescharacteristic
167#137—1188no—
168C2×Q16—594no—
169C2×SD16—594no—
170C2×M16C2×D5912yescomplemented
171C22⋊Q8—592no—
172C22⋊Q8—592no—
173C22⋊Q8—1181no—
174C22⋊Q8—1181no—
175C2×C4⋊C4—591no—
176C2×C4⋊C4—1181no—
177C2×C22⋊C4—1181no—
178#103—594no—
179#102—594no—
180C22⋊C8C2×D5912yes—
181C22⋊C8C2×D5912yescomplemented
182C24—1181no—
183C24D23611yescharacteristic
184#41—598no—
185#41—1184no—
186#41—1184no—
187#41—1188no—
188#41—1188no—
189#41—1184no—
190C2×Q8—592no—
191C2×Q8—592no—
192C2×Q8—1184no—
193C2×Q8—1181no—
194C2×Q8—1181no—
195C2×Q8—1184no—
196C2×D4—592no—
197C2×D4—1184no—
198C2×D4—1188no—
199C2×D4—1182no—
200C2×D4—1182no—
201C2×D4—1181no—
202C22×C4—24no—
203C22×C4—1188no—
204C22×C4—1181no—
205C22×C4—1182no—
206C22×C4—1182no—
207C22×C4—1181no—
208C22×C4—1181no—
209C22×C4D23611yescharacteristic
210C22×C4D23611yescharacteristic
211C22×C4D23611yescharacteristic
212C22×C4C22×D5911yescharacteristic
213C22×C4C22×D5911yescharacteristic
214C22×C4C22×D5911yescharacteristic
215Q16—1188no—
216SD16—1188no—
217M16—24no—
218C2×C8C22×D5914yes—
219C4⋊C4—592no—
220C4⋊C4—1181no—
221C4⋊C4—1182no—
222C4⋊C4—1182no—
223C22⋊C4—1182no—
224C22⋊C4—1182no—
225C23—22no—
226C23—22no—
227C23—41no—
228C23—1184no—
229C23—1182no—
230C23—2362no—
231C23—2362no—
232C23C2×D23611yescharacteristic
233C23C2×D23611yescharacteristic
234C23C2×D23611yescharacteristic
235Q8—594no—
236Q8—1184no—
237Q8—1182no—
238Q8—1184no—
239Q8—2362no—
240D4—594no—
241D4—1184no—
242D4—1188no—
243D4—1188no—
244D4—1182no—
245C2×C4—22no—
246C2×C4—22no—
247C2×C4—22no—
248C2×C4—22no—
249C2×C4—22no—
250C2×C4—1188no—
251C2×C4—1184no—
252C2×C4—1182no—
253C2×C4—1188no—
254C2×C4—1182no—
255C2×C4—1182no—
256C2×C4—2362no—
257C2×C4—2362no—
258C2×C4C2×D23611yescharacteristic
259C2×C4C2×D23611yescharacteristic
260C2×C4C2×D23611yescharacteristic
261C2×C4D4×D5914yes—
262C2×C4C23×D5911yescharacteristic
263C8—24no—
264C22—21no—
265C22—21no—
266C22—21no—
267C22—21no—
268C22—21no—
269C22—21no—
270C22—21no—
271C22—44no—
272C22—1184no—
273C22—2368no—
274C22—2362no—
275C22—2362no—
276C22#1427369712yes—
277C22#1427376012yescomplemented
278C22C22×D23611yescharacteristic
279C4—21no—
280C4—21no—
281C4—1184no—
282C4—2362no—
283C4—2362no—
284C4#1427369712yes—
285C4C2×D4×D5912yes—
286C2—22no—
287C2—22no—
288C2—41no—
289C2—2364no—
290C2C2×#1427369711yescharacteristic
291C2C2×#1427376011yescharacteristic
292C2#1683820211yescharacteristic
subgroupG/H
centerC22C22×D236
commutatorC2×C4×C59C24
FrattiniC2×C4C23×D59
FittingC59×#407C2
socleC22×C59C22×D4
hypercenter#407D59
hypocenterC59#3007
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. C2×#14273760C2semidirect
3. C2×#14273706C2semidirect
4. #16837566C2semidirect
5. #16837560C2semidirect
6. #16837555C2semidirect
7. #16837404C2semidirect
8. C59×#407C2semidirect
15. C22×Dic118C22semidirect
20. C2×Dic236C22semidirect
21. C2×#11745660C22semidirect
25. #14273706C22semidirect
26. C2×C4⋊Dic59C22semidirect
29. #14273652C22semidirect
30. #14273649C22semidirect
32. C2×M16×C59C22semidirect
34. C22⋊C8×C59C22semidirect
126. C22×C59#137semidirect
154. #407D59semidirect
155. C59#3007semidirect
170. C2×M16C2×D59semidirect
181. C22⋊C8C2×D59semidirect
277. C22#14273760semidirect