Finite Group Databasebeta

← #21435795

Subgroups — #21435795

Order 7552.

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

normal subgroups only

This group has 546 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
1C2×SD16×D59C212yesmaximal, complemented
2#16838067C211yesmaximal, characteristic, complemented
3D4×D236C211yesmaximal, characteristic
4#16837776C211yesmaximal, characteristic, complemented
5#16837634C212yesmaximal, complemented
6#16837603C211yesmaximal, characteristic, complemented
7#16837551C212yesmaximal, complemented
8#16837542C212yesmaximal, complemented
9C4×#11745670C211yesmaximal, characteristic, complemented
10#16837467C211yesmaximal, characteristic, complemented
11C59×#461C211yesmaximal, characteristic, complemented
12C2×Q8×D59C2212yescomplemented
13C22×D236—21no—
14C2×D4×D59C2212yes—
15C2×#11745660C2212yescomplemented
16C2×#11745670C2211yescharacteristic
17C2×#11745671C2212yescomplemented
18C2×#11745671C2212yescomplemented
19SD16×D59—28no—
20C2×C8×D59C2212yescomplemented
21#14273726—21no—
22#14273724C2211yescharacteristic
23#14273705—22no—
24#14273703C2212yescomplemented
25#14273702C2212yes—
26#14273701—21no—
27#14273697—22no—
28C4×Dic118C2211yescharacteristic, complemented
29C4×D236C2211yescharacteristic
30#14273689—21no—
31#14273658C2211yescharacteristic, complemented
32#14273650C2211yescharacteristic, complemented
33#14273649C2212yescomplemented
34#14273648C2211yescharacteristic
35(C2×D59)⋊C8C2212yescomplemented
36C4×C59⋊C8C2211yescharacteristic, complemented
37C2×SD16×C59C2212yes—
38C4⋊Q8×C59C2211yescharacteristic, complemented
39C4×D4×C59C2211yescharacteristic
40C4⋊C8×C59C2211yescharacteristic, complemented
41#103×C59C2212yescomplemented
42C23×D59—22no—
43C2×Q8×C59C2312yes—
44C2×D4×C59C2311yescharacteristic
45C22×C4×C59—21no—
46C2×C22⋊D59—22no—
47Q8×D59—24no—
48Q8×D59—42no—
49D4×D59—24no—
50D4×D59—42no—
51C2×D236—22no—
52C2×D236—21no—
53C2×D236—21no—
54C2×D236—44no—
55C2×D236D411yescharacteristic
56C2×D236C2312yes—
57C2×C4×D59—22no—
58C2×C4×D59C2312yes—
59C2×Dic118—22no—
60C2×Dic118C2311yescharacteristic
61SD16×C59—24no—
62C2×C8×C59C2312yes—
63C4⋊C4×C59—21no—
64C4⋊C4×C59—21no—
65C4⋊C4×C59C2311yescharacteristic
66C22⋊C4×C59—21no—
67C42×C59C2311yescharacteristic
68#11745671—24no—
69#11745671—42no—
70#11745670D414yescomplemented
71(C2×D59)⋊C4—22no—
72(C2×D59)⋊C4—22no—
73(C2×D59)⋊C4D412yes—
74C4⋊Dic59D411yescharacteristic
75C4⋊Dic59C2311yescharacteristic
76Dic59⋊C4—21no—
77Dic59⋊C4—22no—
78C4×Dic59—21no—
79C2×C59⋊C8C2311yescharacteristic
80C2×C59⋊C8C2311yescharacteristic
81#11745660—24no—
82C8×D59—24no—
83C23×C59—21no—
84C22×D59—22no—
85C22×D59—44no—
86C22×D59—44no—
87C22×D59—82no—
88C22×D59C2×D412yes—
89Q8×C59—22no—
90Q8×C59—22no—
91D4×C59—21no—
92D4×C59C2×D412yes—
93C2×C4×C59—22no—
94C2×C4×C59—21no—
95C2×C4×C59—42no—
96C2×C4×C59C2×D411yescharacteristic
97C2×C4×C59C2×D411yescharacteristic
98C2×C4×C59C2411yescharacteristic
99C22⋊D59—44no—
100C2×Dic59—21no—
101C2×Dic59—21no—
102C2×Dic59C2×D412yes—
103D236—22no—
104D236—22no—
105D236—44no—
106D236—42no—
107D236—81no—
108D236SD1614yescomplemented
109C4×D59—22no—
110C4×D59—22no—
111C4×D59—44no—
112Dic118—21no—
113Dic118—44no—
114Dic118C2×D412yescomplemented
115C8×C59—22no—
116C59⋊C8—21no—
117C59⋊C8C2×D412yescomplemented
118C22×C59—22no—
119C22×C59—41no—
120C22×C59—41no—
121C22×C59C22×D411yescharacteristic
122C2×D59—22no—
123C2×D59—22no—
124C2×D59—42no—
125C2×D59—42no—
126C2×D59—42no—
127C2×D59—88no—
128C2×D59C2×SD1614yescomplemented
129C4×C59—21no—
130C4×C59—42no—
131C4×C59—41no—
132C4×C59C2×SD1612yescomplemented
133C4×C59C22×D411yescharacteristic
134C4×C59H(5,𝔽2)11yescharacteristic
135Dic59—22no—
136Dic59—22no—
137Dic59—41no—
138D4×SD16—591nomaximal, Sylow
139C2×C59—42no—
140C2×C59D4211yescharacteristic
141C2×C59C22×SD1611yescharacteristic
142C2×C59#57711yescharacteristic
143D59—24no—
144D59—82no—
145C22×SD16—592no—
146D4×Q8—591no—
147D42—591no—
148#492—591no—
149#465—592no—
150#461D5911yescharacteristic, complemented
151#460—591no—
152#450—592no—
153#448—592no—
154C4×SD16—591no—
155C8×D4—591no—
156C59D4×SD1611yescharacteristic, complemented, Sylow
157C22×Q8—592no—
158C22×D4—592no—
159C22×D4—1181no—
160C2×SD16—591no—
161C2×SD16—592no—
162C2×SD16—592no—
163C2×SD16—592no—
164C2×SD16—1188no—
165C2×SD16C2×D5912yes—
166C22×C8—592no—
167C4⋊Q8—1181no—
168C4⋊Q8C2×D5911yescharacteristic, complemented
169#127—591no—
170C22⋊Q8—592no—
171C22⋊Q8—1182no—
172#121—592no—
173#121—1181no—
174#120—1182no—
175C4×Q8—591no—
176C4×D4—591no—
177C4×D4—1181no—
178C4×D4C2×D5911yescharacteristic
179#106—591no—
180C4⋊C8C2×D5911yescharacteristic, complemented
181#103—591no—
182#103C2×D5912yescomplemented
183#102—591no—
184#102—592no—
185C22⋊C8—592no—
186C4×C8—591no—
187C24—1182no—
188C2×Q8—591no—
189C2×Q8—1182no—
190C2×Q8—1184no—
191C2×Q8—2362no—
192C2×Q8C22×D5912yes—
193C2×D4—591no—
194C2×D4—592no—
195C2×D4—1182no—
196C2×D4—1182no—
197C2×D4—1184no—
198C2×D4—1181no—
199C2×D4—1181no—
200C2×D4—2364no—
201C2×D4—2362no—
202C2×D4C22×D5911yescharacteristic
203C22×C4—21no—
204C22×C4—592no—
205C22×C4—1182no—
206SD16—24no—
207SD16—594no—
208SD16—1184no—
209SD16—1184no—
210SD16—2362no—
211C2×C8—591no—
212C2×C8—591no—
213C2×C8—1184no—
214C2×C8C22×D5912yes—
215C4⋊C4—21no—
216C4⋊C4—21no—
217C4⋊C4—591no—
218C4⋊C4—591no—
219C4⋊C4—1182no—
220C4⋊C4—1181no—
221C4⋊C4C22×D5911yescharacteristic
222C22⋊C4—21no—
223C22⋊C4—592no—
224C22⋊C4—1182no—
225C22⋊C4—1182no—
226C42—1181no—
227C42C22×D5911yescharacteristic
228C23—21no—
229C23—592no—
230C23—1182no—
231C23—4722no—
232C23—2364no—
233C23—2364no—
234Q8—22no—
235Q8—22no—
236Q8—592no—
237Q8—1181no—
238Q8—2364no—
239D4—21no—
240D4—594no—
241D4—1182no—
242D4—1182no—
243D4—4721no—
244D4—2364no—
245D4—2364no—
246D4—2362no—
247D4D4×D5912yes—
248C2×C4—21no—
249C2×C4—22no—
250C2×C4—42no—
251C2×C4—592no—
252C2×C4—1181no—
253C2×C4—1182no—
254C2×C4—1182no—
255C2×C4—1181no—
256C2×C4—2364no—
257C2×C4D4×D5911yescharacteristic
258C2×C4D4×D5911yescharacteristic
259C2×C4C23×D5911yescharacteristic
260C8—22no—
261C8—592no—
262C8—1181no—
263C22—22no—
264C22—41no—
265C22—41no—
266C22—594no—
267C22—1182no—
268C22—1182no—
269C22—4728no—
270C22—2362no—
271C22—2362no—
272C22—2362no—
273C22C2×D4×D5911yescharacteristic
274C4—21no—
275C4—41no—
276C4—42no—
277C4—1182no—
278C4—1182no—
279C4—2361no—
280C4SD16×D5912yescomplemented
281C4C2×D4×D5911yescharacteristic
282C4#1427377311yescharacteristic
283C2—42no—
284C2—1184no—
285C2—4722no—
286C2#1683803611yescharacteristic
287C2C2×SD16×D5911yescharacteristic
288C2#1683821111yescharacteristic
subgroupG/H
centerC22C2×D4×D59
commutatorC2×C4×C59C24
FrattiniC2×C4C23×D59
FittingC59×#461C2
socleC22×C59C22×D4
hypercenter#461D59
hypocenterC59D4×SD16
LCSG ▷ C2×C4×C59 ▷ C2×C59 ▷ C59
UCSC1 ◁ C22 ◁ C42 ◁ #461

Complements

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

NH ≅ G/Ntype
1. C2×SD16×D59C2semidirect
2. #16838067C2semidirect
4. #16837776C2semidirect
5. #16837634C2semidirect
6. #16837603C2semidirect
7. #16837551C2semidirect
8. #16837542C2semidirect
9. C4×#11745670C2semidirect
10. #16837467C2semidirect
11. C59×#461C2semidirect
12. C2×Q8×D59C22semidirect
15. C2×#11745660C22semidirect
17. C2×#11745671C22semidirect
18. C2×#11745671C22semidirect
20. C2×C8×D59C22semidirect
24. #14273703C22semidirect
28. C4×Dic118C22semidirect
31. #14273658C22semidirect
32. #14273650C22semidirect
33. #14273649C22semidirect
35. (C2×D59)⋊C8C22semidirect
36. C4×C59⋊C8C22semidirect
38. C4⋊Q8×C59C22semidirect
40. C4⋊C8×C59C22semidirect
41. #103×C59C22semidirect
70. #11745670D4semidirect
108. D236SD16semidirect
114. Dic118C2×D4semidirect
117. C59⋊C8C2×D4semidirect
128. C2×D59C2×SD16semidirect
132. C4×C59C2×SD16semidirect
150. #461D59semidirect
156. C59D4×SD16semidirect
168. C4⋊Q8C2×D59semidirect
180. C4⋊C8C2×D59semidirect
182. #103C2×D59semidirect
280. C4SD16×D59semidirect