Finite Group Databasebeta

← #21433569

Subgroups — #21433569

Order 7552.

484 conjugacy classes of subgroups; only the 131 normal subgroups are shown.

normal subgroups only

This group has 484 conjugacy classes of subgroups — too many to draw. Only its 131 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×#14273759C212yesmaximal, complemented
2#16837953C211yesmaximal, characteristic
3C4×Q8×D59C211yesmaximal, characteristic, complemented
4#16837627C212yesmaximal, complemented
5#16837626C212yesmaximal, complemented
6#16837609C211yesmaximal, characteristic, complemented
7#16837603C211yesmaximal, characteristic, complemented
8#16837602C211yesmaximal, characteristic, complemented
9#16837424C211yesmaximal, characteristic, complemented
10#16837402C212yesmaximal, complemented
11C59×#462C211yesmaximal, characteristic, complemented
12C2×#11745689C2212yes—
13C2×Q8×D59C2211yescharacteristic
14#14273759—28no—
15C2×#11745672C2212yes—
16C2×#11745660C2212yes—
17C2×#11745671C2212yes—
18C2×#11745659C2212yes—
19#14273724C2211yescharacteristic
20#14273716C2212yes—
21#14273702—21no—
22#14273702—21no—
23Q8×Dic59C2211yescharacteristic
24C4×Dic118—21no—
25C4×Dic118C2211yescharacteristic
26#14273692—21no—
27#14273692C2211yescharacteristic
28#14273689—21no—
29#14273689—21no—
30C4⋊C4×D59—21no—
31C4⋊C4×D59C2211yescharacteristic
32C42×D59—21no—
33C42×D59C2211yescharacteristic
34C4⋊(C59⋊C8)C2211yescharacteristic
35Dic59⋊C8C2212yes—
36#14273651C2212yes—
37#14273649C2212yes—
38#14273647C2212yes—
39C2×Q16×C59C2212yes—
40C4⋊Q8×C59C2211yescharacteristic
41C4×Q8×C59C2211yescharacteristic
42C4⋊C8×C59C2211yescharacteristic
43#103×C59C2212yes—
44C2×Q8×C59C2312yes—
45C2×Q8×C59C2311yescharacteristic
46#11745689—24no—
47#11745689—24no—
48Q8×D59—22no—
49Q8×D59D414yescomplemented
50C2×D236—22no—
51C2×D236—21no—
52C2×D236—21no—
53C2×D236C2312yes—
54C2×C4×D59—21no—
55C2×C4×D59—21no—
56C2×C4×D59—22no—
57C2×C4×D59D411yescharacteristic
58C2×C4×D59D411yescharacteristic
59C2×C4×D59C2311yescharacteristic
60C2×Dic118—21no—
61C2×Dic118C2311yescharacteristic
62Q16×C59—24no—
63C2×C8×C59C2312yes—
64C4⋊C4×C59—21no—
65C4⋊C4×C59—21no—
66C4⋊C4×C59—21no—
67C4⋊C4×C59C2311yescharacteristic
68C42×C59—21no—
69C42×C59C2311yescharacteristic
70#11745672—24no—
71#11745671—24no—
72(C2×D59)⋊C4—22no—
73(C2×D59)⋊C4—22no—
74C4⋊Dic59—21no—
75C4⋊Dic59C2311yescharacteristic
76Dic59⋊C4—21no—
77Dic59⋊C4—21no—
78Dic59⋊C4—21no—
79C4×Dic59—21no—
80C4×Dic59—21no—
81C4×Dic59—21no—
82C4×Dic59D411yescharacteristic
83C4×Dic59D411yescharacteristic
84C4×Dic59C2311yescharacteristic
85C2×C59⋊C8C2312yes—
86#11745660—24no—
87#11745659—24no—
88C22×D59—22no—
89C22×D59C2×D411yescharacteristic
90Q8×C59—21no—
91Q8×C59—22no—
92Q8×C59—22no—
93Q8×C59C2×D412yes—
94C2×C4×C59—21no—
95C2×C4×C59—21no—
96C2×C4×C59—22no—
97C2×C4×C59C2×D411yescharacteristic
98C2×C4×C59C2×D411yescharacteristic
99C2×C4×C59C2411yescharacteristic
100C2×Dic59—21no—
101C2×Dic59—21no—
102C2×Dic59C2×D411yescharacteristic
103C2×Dic59C2×D411yescharacteristic
104C2×Dic59C2×D411yescharacteristic
105D236—22no—
106D236—22no—
107D236—42no—
108D236—44no—
109D236—42no—
110C4×D59—24no—
111C4×D59—22no—
112C4×D59—41no—
113C4×D59—42no—
114C4×D59—44no—
115C4×D59C2×D412yes—
116C4×D59#4112yes—
117Dic118—21no—
118Dic118—24no—
119Dic118C2×D412yes—
120C8×C59—22no—
121C59⋊C8—22no—
122C22×C59C22×D411yescharacteristic
123C2×D59—21no—
124C2×D59—21no—
125C2×D59—42no—
126C2×D59—42no—
127C2×D59—42no—
128C2×D59#12112yes—
129C4×C59—22no—
130C4×C59—21no—
131C4×C59—42no—
132C4×C59—41no—
133C4×C59#13712yescomplemented
134C4×C59C22×D411yescharacteristic
135C4×C59C2×#4111yescharacteristic
136Dic59—22no—
137Dic59—21no—
138Dic59—21no—
139Dic59—41no—
140Dic59#12112yes—
141#3037—591nomaximal, Sylow
142C2×C59C2×#12111yescharacteristic
143C2×C59C2×#13711yescharacteristic
144C2×C59#57511yescharacteristic
145D59—22no—
146D59—82no—
147C2×#137—592no—
148#532—591no—
149C2×C4×Q8—591no—
150#464—592no—
151#464—592no—
152#462—591no—
153#462D5911yescharacteristic, complemented
154#460—591no—
155#460—591no—
156#423—591no—
157#417—592no—
158C59#303711yescharacteristic, complemented, Sylow
159C2×#41—592no—
160C22×Q8—591no—
161#137—1188no—
162C2×Q16—592no—
163C2×Q16C2×D5912yes—
164C2×SD16—592no—
165C2×SD16—592no—
166C2×M16—592no—
167C4⋊Q8C2×D5911yescharacteristic
168#127—591no—
169#124—592no—
170#121—1181no—
171#121—1181no—
172C4×Q8—591no—
173C4×Q8—591no—
174C4×Q8—591no—
175C4×Q8—1181no—
176C4×Q8—1181no—
177C4×Q8C2×D5911yescharacteristic
178C4×D4—1181no—
179C4×D4—1181no—
180C2×C4⋊C4—591no—
181C2×C4⋊C4—1181no—
182C2×C42—591no—
183C2×C42—1181no—
184C4⋊C8—592no—
185C4⋊C8—591no—
186C4⋊C8C2×D5911yescharacteristic
187#103—592no—
188#103C2×D5912yes—
189#102—592no—
190#102—592no—
191#41—1184no—
192#41—1184no—
193C2×Q8—594no—
194C2×Q8—591no—
195C2×Q8—1181no—
196C2×Q8—1182no—
197C2×Q8C22×D5912yes—
198C2×Q8C22×D5911yescharacteristic
199C2×D4—592no—
200C2×D4—1182no—
201C2×D4—1181no—
202C2×D4—1181no—
203C22×C4—591no—
204C22×C4—591no—
205C22×C4—591no—
206C22×C4—1182no—
207C22×C4—1181no—
208C22×C4—1181no—
209Q16—24no—
210Q16—1184no—
211SD16—1184no—
212SD16—1184no—
213M16—1184no—
214C2×C8—592no—
215C2×C8C22×D5912yes—
216C4⋊C4—21no—
217C4⋊C4—21no—
218C4⋊C4—21no—
219C4⋊C4—591no—
220C4⋊C4—1181no—
221C4⋊C4—1181no—
222C4⋊C4—1181no—
223C4⋊C4—1181no—
224C4⋊C4C22×D5911yescharacteristic
225C22⋊C4—1182no—
226C22⋊C4—1182no—
227C42—21no—
228C42—591no—
229C42—591no—
230C42—591no—
231C42—1181no—
232C42—1181no—
233C42—1181no—
234C42C22×D5911yescharacteristic
235C23—591no—
236C23—1182no—
237Q8—21no—
238Q8—22no—
239Q8—22no—
240Q8—592no—
241Q8—1184no—
242Q8—1181no—
243Q8D4×D5912yes—
244D4—1182no—
245D4—1182no—
246D4—2362no—
247D4—2364no—
248D4—2362no—
249C2×C4—21no—
250C2×C4—21no—
251C2×C4—22no—
252C2×C4—591no—
253C2×C4—592no—
254C2×C4—592no—
255C2×C4—591no—
256C2×C4—591no—
257C2×C4—1184no—
258C2×C4—1181no—
259C2×C4—1182no—
260C2×C4—1181no—
261C2×C4—2361no—
262C2×C4—2364no—
263C2×C4—2362no—
264C2×C4D4×D5911yescharacteristic
265C2×C4D4×D5911yescharacteristic
266C2×C4C23×D5911yescharacteristic
267C8—22no—
268C8—1182no—
269C22—592no—
270C22—1181no—
271C22—1181no—
272C22—2362no—
273C22—2362no—
274C22—2362no—
275C22C2×D4×D5911yescharacteristic
276C4—22no—
277C4—21no—
278C4—42no—
279C4—41no—
280C4—592no—
281C4—1182no—
282C4—1181no—
283C4—1181no—
284C4—2361no—
285C4#1427375912yescomplemented
286C4C2×D4×D5911yescharacteristic
287C4#41×D5911yescharacteristic
288C2—1182no—
289C2—4722no—
290C2#121×D5911yescharacteristic
291C2C2×#1427375911yescharacteristic
292C2#1683820111yescharacteristic
subgroupG/H
centerC22C2×D4×D59
commutatorC2×C4×C59C24
FrattiniC2×C4C23×D59
FittingC59×#462C2
socleC22×C59C22×D4
hypercenter#462D59
hypocenterC59#3037
LCSG ▷ C2×C4×C59 ▷ C2×C59 ▷ C59
UCSC1 ◁ C22 ◁ C42 ◁ #462

Complements

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

NH ≅ G/Ntype
1. C2×#14273759C2semidirect
3. C4×Q8×D59C2semidirect
4. #16837627C2semidirect
5. #16837626C2semidirect
6. #16837609C2semidirect
7. #16837603C2semidirect
8. #16837602C2semidirect
9. #16837424C2semidirect
10. #16837402C2semidirect
11. C59×#462C2semidirect
49. Q8×D59D4semidirect
133. C4×C59#137semidirect
153. #462D59semidirect
158. C59#3037semidirect
285. C4#14273759semidirect