Finite Group Databasebeta

← #21433487

Subgroups — #21433487

Order 7552.

766 conjugacy classes of subgroups; only the 145 normal subgroups are shown.

normal subgroups only

This group has 766 conjugacy classes of subgroups — too many to draw. Only its 145 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#16838238C211yesmaximal, characteristic, complemented
2#16837913C212yesmaximal, complemented
3#16837591C214yesmaximal, complemented
4#16837588C214yesmaximal, complemented
5#16837376C211yesmaximal, characteristic, complemented
6#16837375C212yesmaximal, complemented
7C59×#525C211yesmaximal, characteristic, complemented
8#14273775—21no—
9#14273774—22no—
10#14273773—22no—
11#14273772—21no—
12#14273772C2214yes—
13C2×#11745685—22no—
14C2×#11745685C2212yes—
15#41×D59—24no—
16#14273710C2214yescomplemented
17#14273706—22no—
18#14273701—22no—
19#14273696C2214yescomplemented
20C4×C22⋊D59—24no—
21#14273686C2212yescomplemented
22#14273642C2214yescomplemented
23#14273641C2218yescomplemented
24C2×#41×C59C2211yescharacteristic
25C23×C4×C59C2211yescharacteristic, complemented
26#123×C59C2212yescomplemented
27C22⋊Q8×C59—21no—
28#121×C59—21no—
29#120×C59C2212yescomplemented
30C4×D4×C59—22no—
31#117×C59C2211yescharacteristic, complemented
32C24×C59C2311yescharacteristic
33#41×C59—22no—
34#41×C59—22no—
35C2×Q8×C59D411yescharacteristic, complemented
36C2×D4×C59—22no—
37C2×D4×C59D411yescharacteristic, complemented
38C2×D4×C59C2312yes—
39C22×C4×C59—21no—
40C22×C4×C59—21no—
41C22×C4×C59—22no—
42C22×C4×C59—22no—
43C22×C4×C59D412yescomplemented
44C22×C4×C59C2311yescharacteristic
45C22×C4×C59C2311yescharacteristic
46C2×C22⋊D59—24no—
47C2×C22⋊D59—24no—
48C2×C22⋊D59C2314yes—
49#11745689—24no—
50Q8×D59—24no—
51#11745687—24no—
52#11745687—28no—
53D4×D59—24no—
54D4×D59—28no—
55#11745685—24no—
56#11745685—24no—
57#11745685—22no—
58#11745685—22no—
59#11745685—24no—
60#11745685—22no—
61#11745685—22no—
62C2×D236—22no—
63C2×D236D412yescomplemented
64C2×C4×D59—24no—
65C2×C4×D59D414yescomplemented
66C2×Dic118—22no—
67C2×Dic118D412yescomplemented
68C4⋊C4×C59—21no—
69C4⋊C4×C59—22no—
70C22⋊C4×C59—22no—
71C22⋊C4×C59—22no—
72C22⋊C4×C59C2312yes—
73C42×C59—21no—
74C22⋊Dic59—24no—
75C22⋊Dic59C2314yes—
76(C2×D59)⋊C4—24no—
77C4⋊Dic59—22no—
78Dic59⋊C4—24no—
79C4×Dic59—22no—
80C23×C59—22no—
81C23×C59—21no—
82C23×C59—42no—
83C23×C59C2×D412yes—
84C23×C59C2411yescharacteristic
85C22×D59—24no—
86C22×D59C2×D414yes—
87Q8×C59—22no—
88D4×C59—24no—
89D4×C59—22no—
90D4×C59—44no—
91C2×C4×C59—22no—
92C2×C4×C59—22no—
93C2×C4×C59—22no—
94C2×C4×C59—22no—
95C2×C4×C59—21no—
96C2×C4×C59—41no—
97C2×C4×C59—42no—
98C2×C4×C59—41no—
99C2×C4×C59C2×D412yes—
100C2×C4×C59C2×D412yes—
101C2×C4×C59C2×D412yes—
102C2×C4×C59C2×D411yescharacteristic
103C2×C4×C59C2×D411yescharacteristic
104C22⋊D59—28no—
105C22⋊D59—24no—
106C22⋊D59—24no—
107C22⋊D59—48no—
108C2×Dic59—24no—
109C2×Dic59—24no—
110C2×Dic59C2×D414yes—
111D236—24no—
112D236—22no—
113D236—22no—
114C4×D59—28no—
115C4×D59—24no—
116C4×D59—24no—
117Dic118—24no—
118Dic118—22no—
119Dic118—22no—
120C22×C59—24no—
121C22×C59—22no—
122C22×C59—22no—
123C22×C59—41no—
124C22×C59—42no—
125C22×C59—42no—
126C22×C59—41no—
127C22×C59—41no—
128C22×C59C22×D412yes—
129C22×C59C22×D411yescharacteristic
130C2×D59—24no—
131C2×D59—44no—
132C2×D59—84no—
133C4×C59—22no—
134C4×C59—42no—
135C4×C59—41no—
136C4×C59#12011yescharacteristic
137C4×C59#12012yes—
138C4×C59#12011yescharacteristic
139Dic59—24no—
140Dic59—44no—
141#3025—591nomaximal, Sylow
142C2×C59—22no—
143C2×C59—21no—
144C2×C59—42no—
145C2×C59—42no—
146C2×C59C2×#12011yescharacteristic
147D59—44no—
148#585—591no—
149#525—592no—
150#525D5911yescharacteristic, complemented
151#458—594no—
152B(4,𝔽2)—594no—
153#410—591no—
154#410—592no—
155C59#302511yescharacteristic, complemented, Sylow
1562−1+4—1182no—
1572−1+4—1181no—
158H(5,𝔽2)—594no—
159H(5,𝔽2)—1182no—
160H(5,𝔽2)—1181no—
161C2×#41—592no—
162C2×#41—1184no—
163C2×#41—1182no—
164C2×#41C2×D5911yescharacteristic
165C23×C4C2×D5911yescharacteristic, complemented
166#123—594no—
167#123C2×D5912yescomplemented
168C22⋊Q8—21no—
169C22⋊Q8—1182no—
170#121—21no—
171#121—1182no—
172#120—594no—
173#120C2×D5912yescomplemented
174C4×D4—22no—
175C4×D4—1184no—
176#117—592no—
177#117C2×D5911yescharacteristic, complemented
178#99—594no—
179#99—598no—
180C24C22×D5911yescharacteristic
181#41—22no—
182#41—22no—
183#41—1184no—
184#41—1184no—
185#41—1188no—
186#41—1184no—
187#41—1184no—
188#41—1182no—
189#41—1182no—
190#41—1182no—
191#41—1182no—
192#41—1184no—
193C2×Q8—592no—
194C2×Q8—1182no—
195C2×Q8—1184no—
196C2×Q8C22⋊D5911yescharacteristic, complemented
197C2×D4—22no—
198C2×D4—594no—
199C2×D4—592no—
200C2×D4—1182no—
201C2×D4—1188no—
202C2×D4—1184no—
203C2×D4—1184no—
204C2×D4—1184no—
205C2×D4C22⋊D5911yescharacteristic, complemented
206C2×D4C22×D5912yes—
207C22×C4—22no—
208C22×C4—22no—
209C22×C4—21no—
210C22×C4—21no—
211C22×C4—594no—
212C22×C4—1184no—
213C22×C4C22⋊D5912yescomplemented
214C22×C4C22×D5911yescharacteristic
215C22×C4C22×D5911yescharacteristic
216C4⋊C4—21no—
217C4⋊C4—22no—
218C4⋊C4—1184no—
219C4⋊C4—1182no—
220C22⋊C4—22no—
221C22⋊C4—22no—
222C22⋊C4—594no—
223C22⋊C4—1184no—
224C22⋊C4—1184no—
225C22⋊C4C22×D5912yes—
226C42—21no—
227C42—1182no—
228C23—22no—
229C23—21no—
230C23—42no—
231C23—594no—
232C23—1184no—
233C23C2×C22⋊D5912yes—
234C23C23×D5911yescharacteristic
235Q8—22no—
236Q8—1184no—
237Q8—1182no—
238Q8—1182no—
239D4—24no—
240D4—22no—
241D4—44no—
242D4—1184no—
243D4—1188no—
244D4—1184no—
245D4—1184no—
246D4—1182no—
247D4—1182no—
248D4—2368no—
249C2×C4—22no—
250C2×C4—22no—
251C2×C4—22no—
252C2×C4—22no—
253C2×C4—21no—
254C2×C4—41no—
255C2×C4—42no—
256C2×C4—41no—
257C2×C4—594no—
258C2×C4—1188no—
259C2×C4—1184no—
260C2×C4—1184no—
261C2×C4—1184no—
262C2×C4—1184no—
263C2×C4D4×D5912yes—
264C2×C4D4×D5912yes—
265C2×C4C2×C22⋊D5912yes—
266C2×C4C2×C22⋊D5911yescharacteristic
267C2×C4C2×C22⋊D5911yescharacteristic
268C22—22no—
269C22—24no—
270C22—22no—
271C22—41no—
272C22—42no—
273C22—41no—
274C22—42no—
275C22—41no—
276C22—1184no—
277C22—4724no—
278C22—2364no—
279C22C2×D4×D5912yes—
280C22C22×C22⋊D5911yescharacteristic
281C4—22no—
282C4—42no—
283C4—41no—
284C4—1184no—
285C4—2364no—
286C4#1427369511yescharacteristic
287C4#1427369512yes—
288C4#1427369511yescharacteristic
289C2—21no—
290C2—22no—
291C2—42no—
292C2—42no—
293C2—2364no—
294C2C2×#1427369511yescharacteristic
subgroupG/H
centerC4#14273695
commutatorC23×C59C24
FrattiniC23C23×D59
FittingC59×#525C2
socleC2×C59C2×#120
hypercenter#525D59
hypocenterC59#3025
LCSG ▷ C23×C59 ▷ C2×C59 ▷ C59
UCSC1 ◁ C4 ◁ C22×C4 ◁ #525

Complements

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

NH ≅ G/Ntype
1. #16838238C2semidirect
2. #16837913C2semidirect
3. #16837591C2semidirect
4. #16837588C2semidirect
5. #16837376C2semidirect
6. #16837375C2semidirect
7. C59×#525C2semidirect
16. #14273710C22semidirect
19. #14273696C22semidirect
21. #14273686C22semidirect
22. #14273642C22semidirect
23. #14273641C22semidirect
25. C23×C4×C59C22semidirect
26. #123×C59C22semidirect
29. #120×C59C22semidirect
31. #117×C59C22semidirect
35. C2×Q8×C59D4semidirect
37. C2×D4×C59D4semidirect
43. C22×C4×C59D4semidirect
63. C2×D236D4semidirect
65. C2×C4×D59D4semidirect
67. C2×Dic118D4semidirect
150. #525D59semidirect
155. C59#3025semidirect
165. C23×C4C2×D59semidirect
167. #123C2×D59semidirect
173. #120C2×D59semidirect
177. #117C2×D59semidirect
196. C2×Q8C22⋊D59semidirect
205. C2×D4C22⋊D59semidirect
213. C22×C4C22⋊D59semidirect