Finite Group Databasebeta

← #21434012

Subgroups — #21434012

Order 7552.

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

normal subgroups only

This group has 420 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#16837915C211yesmaximal, characteristic
2C2×#14273685C211yesmaximal, characteristic, complemented
3#16837742C212yesmaximal, complemented
4#16837730C211yesmaximal, characteristic, complemented
5#16837729C212yesmaximal, complemented
6#16837720C211yesmaximal, characteristic, complemented
7#16837716C211yesmaximal, characteristic, complemented
8#16837439C212yesmaximal, complemented
9#16837397C212yesmaximal, complemented
10C22⋊C8×D59C211yesmaximal, characteristic, complemented
11C59×#484C211yesmaximal, characteristic, complemented
12C2×#11745689C2211yescharacteristic
13C22×C4×D59C2211yescharacteristic
14C2×C8×D59C2212yes—
15#14273712—21no—
16#14273703C2211yescharacteristic
17#14273702C2211yescharacteristic
18#14273701C2211yescharacteristic
19#14273697—21no—
20#14273689—21no—
21(C22⋊D59)⋊C4—21no—
22#14273685—21no—
23#14273685—21no—
24#14273685C2212yes—
25#14273685C2211yescharacteristic
26#14273685C2212yes—
27C2×C4⋊Dic59C2211yescharacteristic
28C2×(C2×D59)⋊C4—21no—
29C2×C4×Dic59—21no—
30#14273661C2212yescomplemented
31#14273658C2212yescomplemented
32#14273658C2212yescomplemented
33#14273651C2212yescomplemented
34#14273649C2212yescomplemented
35#14273647C2212yescomplemented
36C22⋊(C59⋊C8)C2211yescharacteristic
37(C2×D59)⋊C8C2212yes—
38C22⋊Q8×C59C2211yescharacteristic
39C2×C4⋊C4×C59C2211yescharacteristic
40#107×C59C2212yescomplemented
41#103×C59C2212yescomplemented
42C22⋊C8×C59C2211yescharacteristic
43C23×D59D411yescharacteristic
44C2×Q8×C59C2311yescharacteristic
45C22×C4×C59—21no—
46C22×C4×C59C2311yescharacteristic
47C2×C22⋊D59—21no—
48C22×Dic59—21no—
49C22×Dic59D411yescharacteristic
50#11745689—24no—
51C2×D236—21no—
52C2×D236—21no—
53C2×D236C2311yescharacteristic
54C2×C4×D59—24no—
55C2×C4×D59—21no—
56C2×C4×D59D411yescharacteristic
57C2×C4×D59D411yescharacteristic
58C2×C4×D59C2311yescharacteristic
59C2×C4×D59C2311yescharacteristic
60C2×C8×C59C2312yes—
61C4⋊C4×C59—21no—
62C4⋊C4×C59—21no—
63C4⋊C4×C59C2312yes—
64C4⋊C4×C59C2311yescharacteristic
65C22⋊C4×C59—21no—
66(C2×D59)⋊C4—22no—
67(C2×D59)⋊C4—22no—
68(C2×D59)⋊C4—21no—
69(C2×D59)⋊C4—21no—
70(C2×D59)⋊C4—21no—
71(C2×D59)⋊C4—21no—
72C4⋊Dic59—21no—
73C4⋊Dic59C2312yes—
74C4⋊Dic59C2311yescharacteristic
75Dic59⋊C4—21no—
76C4×Dic59—22no—
77C4×Dic59—22no—
78C4×Dic59—21no—
79C2×C59⋊C8C2312yes—
80C8×D59—24no—
81C23×C59C2×D411yescharacteristic
82C22×D59—22no—
83C22×D59—22no—
84C22×D59—21no—
85C22×D59—41no—
86C22×D59C2×D411yescharacteristic
87C22×D59C2×D411yescharacteristic
88Q8×C59—22no—
89C2×C4×C59—22no—
90C2×C4×C59—22no—
91C2×C4×C59—21no—
92C2×C4×C59—21no—
93C2×C4×C59—42no—
94C2×C4×C59C2×D411yescharacteristic
95C2×C4×C59C2411yescharacteristic
96C22⋊D59—42no—
97C2×Dic59—22no—
98C2×Dic59—22no—
99C2×Dic59—21no—
100C2×Dic59—42no—
101C2×Dic59C2×D411yescharacteristic
102C2×Dic59C2×D411yescharacteristic
103D236—22no—
104D236—42no—
105D236—42no—
106C4×D59—22no—
107C4×D59—22no—
108C4×D59—22no—
109C4×D59—42no—
110C4×D59#4114yes—
111C8×C59—22no—
112C59⋊C8—22no—
113C22×C59—21no—
114C22×C59—21no—
115C22×C59#13512yes—
116C22×C59C22×D411yescharacteristic
117C2×D59—21no—
118C2×D59—21no—
119C2×D59—21no—
120C2×D59—21no—
121C2×D59—21no—
122C2×D59—44no—
123C2×D59—41no—
124C2×D59—41no—
125C2×D59—41no—
126C2×D59#12312yes—
127C4×C59—21no—
128C4×C59—41no—
129C4×C59—41no—
130C4×C59—42no—
131C4×C59C2×#4112yes—
132Dic59—21no—
133Dic59—42no—
134Dic59—41no—
135Dic59#12312yes—
136#3091—591nomaximal, Sylow
137C2×C59—22no—
138C2×C59C2×#12311yescharacteristic
139C2×C59C2×#13511yescharacteristic
140C2×C59#57511yescharacteristic
141D59—22no—
142D59—41no—
143D59—81no—
144#525—591no—
145C2×#117—591no—
146#485—592no—
147#484D5911yescharacteristic, complemented
148#483—591no—
149#482—592no—
150#481—591no—
151#480—591no—
152#427—592no—
153#416—592no—
154C2×C22⋊C8—591no—
155C59#309111yescharacteristic, complemented, Sylow
156C2×#41—591no—
157C23×C4—591no—
158C22×C8—592no—
159#123—1181no—
160C22⋊Q8—591no—
161C22⋊Q8C2×D5911yescharacteristic
162#121—591no—
163#121—591no—
164#120—1181no—
165C4×D4—1181no—
166C4×D4—1181no—
167#117—592no—
168#117—592no—
169#117—591no—
170#117—1181no—
171#117—1181no—
172C2×C4⋊C4—591no—
173C2×C4⋊C4C2×D5911yescharacteristic
174C2×C22⋊C4—1181no—
175C2×C42—1181no—
176#107—592no—
177#107C2×D5912yescomplemented
178#106—592no—
179#106—592no—
180#103—592no—
181#103C2×D5912yescomplemented
182#102—592no—
183#102—592no—
184C22⋊C8—591no—
185C22⋊C8—592no—
186C22⋊C8C2×D5911yescharacteristic
187C24—591no—
188#41—1184no—
189C2×Q8C22×D5911yescharacteristic
190C2×D4—591no—
191C2×D4—1181no—
192C2×D4—1181no—
193C2×D4—1181no—
194C22×C4—21no—
195C22×C4—591no—
196C22×C4—591no—
197C22×C4—591no—
198C22×C4—591no—
199C22×C4—591no—
200C22×C4—1184no—
201C22×C4—1181no—
202C22×C4—1181no—
203C22×C4C22×D5911yescharacteristic
204C2×C8—592no—
205C2×C8—1184no—
206C2×C8C22×D5912yes—
207C4⋊C4—21no—
208C4⋊C4—21no—
209C4⋊C4—592no—
210C4⋊C4—591no—
211C4⋊C4—1181no—
212C4⋊C4—1181no—
213C4⋊C4C22×D5912yes—
214C4⋊C4C22×D5911yescharacteristic
215C22⋊C4—21no—
216C22⋊C4—1181no—
217C22⋊C4—1182no—
218C22⋊C4—1182no—
219C22⋊C4—1181no—
220C22⋊C4—1181no—
221C22⋊C4—1181no—
222C42—1182no—
223C42—1182no—
224C42—1181no—
225C23—591no—
226C23—591no—
227C23—1182no—
228C23—1182no—
229C23—1181no—
230C23—2361no—
231C23D4×D5911yescharacteristic
232Q8—22no—
233D4—1182no—
234D4—2362no—
235D4—2362no—
236D4—2362no—
237C2×C4—22no—
238C2×C4—22no—
239C2×C4—21no—
240C2×C4—21no—
241C2×C4—42no—
242C2×C4—591no—
243C2×C4—594no—
244C2×C4—591no—
245C2×C4—1182no—
246C2×C4—1182no—
247C2×C4—1182no—
248C2×C4—1182no—
249C2×C4—1182no—
250C2×C4—1181no—
251C2×C4—2362no—
252C2×C4—2362no—
253C2×C4D4×D5911yescharacteristic
254C2×C4C23×D5911yescharacteristic
255C8—22no—
256C8—1182no—
257C22—21no—
258C22—21no—
259C22—592no—
260C22—1181no—
261C22—1181no—
262C22—1181no—
263C22—1181no—
264C22—1181no—
265C22—2364no—
266C22—2361no—
267C22—2361no—
268C22—2361no—
269C22#1427375012yes—
270C22C2×D4×D5911yescharacteristic
271C4—21no—
272C4—41no—
273C4—42no—
274C4—41no—
275C4—592no—
276C4—1181no—
277C4—2362no—
278C4—2361no—
279C4#41×D5912yes—
280C2—22no—
281C2—1182no—
282C2—4721no—
283C2—2361no—
284C2#123×D5911yescharacteristic
285C2C2×#1427375011yescharacteristic
286C2#1683819811yescharacteristic
subgroupG/H
centerC22C2×D4×D59
commutatorC2×C4×C59C24
FrattiniC2×C4C23×D59
FittingC59×#484C2
socleC22×C59C22×D4
hypercenter#484D59
hypocenterC59#3091
LCSG ▷ C2×C4×C59 ▷ C2×C59 ▷ C59
UCSC1 ◁ C22 ◁ C22×C4 ◁ #484

Complements

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

NH ≅ G/Ntype
2. C2×#14273685C2semidirect
3. #16837742C2semidirect
4. #16837730C2semidirect
5. #16837729C2semidirect
6. #16837720C2semidirect
7. #16837716C2semidirect
8. #16837439C2semidirect
9. #16837397C2semidirect
10. C22⋊C8×D59C2semidirect
11. C59×#484C2semidirect
30. #14273661C22semidirect
31. #14273658C22semidirect
32. #14273658C22semidirect
33. #14273651C22semidirect
34. #14273649C22semidirect
35. #14273647C22semidirect
40. #107×C59C22semidirect
41. #103×C59C22semidirect
147. #484D59semidirect
155. C59#3091semidirect
177. #107C2×D59semidirect
181. #103C2×D59semidirect