Finite Group Databasebeta

← #21427762

Subgroups — #21427762

Order 7552.

780 conjugacy classes of subgroups; only the 181 normal subgroups are shown.

normal subgroups only

This group has 780 conjugacy classes of subgroups — too many to draw. Only its 181 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×#14273704C212yesmaximal, complemented
2C22×C22⋊Dic59C212yesmaximal
3#16837338C211yesmaximal, characteristic, complemented
4#16837325C212yesmaximal, complemented
5#16837314C211yesmaximal, characteristic, complemented
6#16837277C212yesmaximal, complemented
7#16837274C212yesmaximal, complemented
8#16837260C212yesmaximal, complemented
9C59×#379C211yesmaximal, characteristic
10C22×Dic118C2211yescharacteristic, complemented
11C23×Dic59C2212yes—
12C23×Dic59C2212yes—
13#14273704—28no—
14C2×C4⋊Dic59C2212yescomplemented
15C2×C4⋊Dic59C2211yescharacteristic, complemented
16C2×Dic59⋊C4C2212yescomplemented
17C2×Dic59⋊C4C2212yescomplemented
18C2×Dic59⋊C4C2212yescomplemented
19C2×C22⋊Dic59—28no—
20C2×C22⋊Dic59C2212yes—
21C2×C22⋊Dic59C2212yes—
22C2×C22⋊Dic59C2212yes—
23C2×C22⋊Dic59C2212yes—
24C59⋊#95C2211yescharacteristic, complemented
25C59⋊#95C2212yescomplemented
26C59⋊#95C2211yescharacteristic, complemented
27C59⋊#95C2212yescomplemented
28C25×C59C2211yescharacteristic
29C2×C22⋊C4×C59C2212yes—
30C2×C22⋊C4×C59C2212yes—
31C2×C22⋊C4×C59C2211yescharacteristic
32C2×C22⋊C4×C59C2211yescharacteristic
33C24×C59—24no—
34C24×C59—24no—
35C24×C59—41no—
36C24×C59—41no—
37C24×C59Q814yescomplemented
38C24×C59C2311yescharacteristic
39C24×C59C2312yes—
40C22×C4×C59C2311yescharacteristic
41C22×C4×C59C2312yes—
42C22×C4×C59C2311yescharacteristic
43C22×Dic59—24no—
44C22×Dic59—24no—
45C22×Dic59—24no—
46C22×Dic59—24no—
47C22×Dic59—42no—
48C22×Dic59—42no—
49C22×Dic59C2312yes—
50C22×Dic59C2312yes—
51C22×Dic59C2312yes—
52C22×Dic59C2312yes—
53C2×Dic118—24no—
54C2×Dic118—41no—
55C22⋊C4×C59—24no—
56C22⋊C4×C59—24no—
57C22⋊C4×C59—41no—
58C22⋊C4×C59—41no—
59C22⋊Dic59—24no—
60C22⋊Dic59—24no—
61C22⋊Dic59—24no—
62C22⋊Dic59D418yes—
63C4⋊Dic59—24no—
64C4⋊Dic59—41no—
65Dic59⋊C4—24no—
66Dic59⋊C4—24no—
67Dic59⋊C4—42no—
68C23×C59—22no—
69C23×C59—22no—
70C23×C59—22no—
71C23×C59—22no—
72C23×C59—216no—
73C23×C59—22no—
74C23×C59—22no—
75C23×C59—21no—
76C23×C59—21no—
77C23×C59—44no—
78C23×C59—44no—
79C23×C59—48no—
80C23×C59—44no—
81C23×C59C2×D414yes—
82C23×C59C2×Q812yes—
83C23×C59C2×Q814yes—
84C23×C59#4114yes—
85C23×C59C2411yescharacteristic
86C2×C4×C59—22no—
87C2×C4×C59—22no—
88C2×C4×C59—22no—
89C2×C4×C59—22no—
90C2×C4×C59—22no—
91C2×C4×C59—21no—
92C2×C4×C59—21no—
93C2×Dic59—22no—
94C2×Dic59—22no—
95C2×Dic59—22no—
96C2×Dic59—22no—
97C2×Dic59—22no—
98C2×Dic59—22no—
99C2×Dic59—22no—
100C2×Dic59—22no—
101C2×Dic59—22no—
102C2×Dic59—22no—
103C2×Dic59—48no—
104C2×Dic59—48no—
105C2×Dic59C2×D414yes—
106C2×Dic59C2×D414yes—
107Dic118—44no—
108C22×C59—24no—
109C22×C59—24no—
110C22×C59—24no—
111C22×C59—24no—
112C22×C59—24no—
113C22×C59—24no—
114C22×C59—24no—
115C22×C59—22no—
116C22×C59—416no—
117C22×C59—41no—
118C22×C59—42no—
119C22×C59—41no—
120C22×C59C22⋊Q818yescomplemented
121C22×C59C22×D412yes—
122C22×C59C22×Q811yescharacteristic
123C22×C59C2×#4112yes—
124C22×C59H(5,𝔽2)11yescharacteristic
125C22×C59H(5,𝔽2)11yescharacteristic
126C4×C59—41no—
127C4×C59—42no—
128C4×C59—41no—
129Dic59—24no—
130Dic59—24no—
131Dic59—42no—
132Dic59—42no—
133#2437—591nomaximal, Sylow
134C2×C59—28no—
135C2×C59—42no—
136C2×C59C2×C22⋊Q812yes—
137C2×C59#54311yescharacteristic
138C2×C59D4211yescharacteristic
139C2×C59#54612yes—
140C2×C59#55111yescharacteristic
141C2×C22⋊Q8—592no—
142C22×C22⋊C4—592no—
143#399—591no—
144#396—592no—
145#393—591no—
146#385—592no—
147#385—592no—
148#380—592no—
149#379D5911yescharacteristic
150C59#243711yescharacteristic, complemented, Sylow
151C25C2×D5911yescharacteristic
152C22×Q8—591no—
153C23×C4—592no—
154C23×C4—592no—
155C22⋊Q8—1188no—
156C2×C4⋊C4—592no—
157C2×C4⋊C4—592no—
158C2×C4⋊C4—592no—
159C2×C4⋊C4—592no—
160C2×C4⋊C4—591no—
161C2×C22⋊C4—592no—
162C2×C22⋊C4—592no—
163C2×C22⋊C4—592no—
164C2×C22⋊C4—592no—
165C2×C22⋊C4—1188no—
166C2×C22⋊C4C2×D5912yes—
167C2×C22⋊C4C2×D5912yes—
168C2×C22⋊C4C2×D5911yescharacteristic
169C2×C22⋊C4C2×D5911yescharacteristic
170#95—591no—
171#95—592no—
172#95—592no—
173#95—591no—
174C24—24no—
175C24—24no—
176C24—41no—
177C24—41no—
178C24Dic11814yescomplemented
179C24C22×D5911yescharacteristic
180C24C22×D5912yes—
181C2×Q8—1184no—
182C2×Q8—2361no—
183C22×C4—592no—
184C22×C4—592no—
185C22×C4—592no—
186C22×C4—592no—
187C22×C4—1184no—
188C22×C4—1184no—
189C22×C4—1184no—
190C22×C4—1184no—
191C22×C4—2362no—
192C22×C4—2362no—
193C22×C4C22×D5911yescharacteristic
194C22×C4C22×D5912yes—
195C22×C4C22×D5911yescharacteristic
196C4⋊C4—1184no—
197C4⋊C4—1184no—
198C4⋊C4—1184no—
199C4⋊C4—2362no—
200C4⋊C4—2361no—
201C22⋊C4—24no—
202C22⋊C4—24no—
203C22⋊C4—41no—
204C22⋊C4—41no—
205C22⋊C4—598no—
206C22⋊C4—1184no—
207C22⋊C4—1184no—
208C22⋊C4—1184no—
209C23—22no—
210C23—22no—
211C23—22no—
212C23—22no—
213C23—216no—
214C23—22no—
215C23—22no—
216C23—21no—
217C23—21no—
218C23—44no—
219C23—44no—
220C23—48no—
221C23—44no—
222C23C2×Dic11812yes—
223C23C2×Dic11814yes—
224C23D4×D5914yes—
225C23#1174568714yes—
226C23C23×D5911yescharacteristic
227Q8—2364no—
228C2×C4—22no—
229C2×C4—22no—
230C2×C4—22no—
231C2×C4—22no—
232C2×C4—22no—
233C2×C4—21no—
234C2×C4—21no—
235C2×C4—594no—
236C2×C4—594no—
237C2×C4—1182no—
238C2×C4—1182no—
239C2×C4—1182no—
240C2×C4—1182no—
241C2×C4—1182no—
242C2×C4—1182no—
243C2×C4—1182no—
244C2×C4—1182no—
245C2×C4—1182no—
246C2×C4—1182no—
247C2×C4—2368no—
248C2×C4—2368no—
249C22—24no—
250C22—24no—
251C22—24no—
252C22—24no—
253C22—24no—
254C22—24no—
255C22—24no—
256C22—22no—
257C22—416no—
258C22—41no—
259C22—42no—
260C22—41no—
261C22#1427370418yescomplemented
262C22C2×D4×D5912yes—
263C22C22×Dic11811yescharacteristic
264C22C2×#1174568712yes—
265C22#1427377211yescharacteristic
266C22#1427377211yescharacteristic
267C4—41no—
268C4—42no—
269C4—41no—
270C4—1184no—
271C4—1184no—
272C4—2362no—
273C4—2362no—
274C2—28no—
275C2—42no—
276C2C2×#1427370412yes—
277C2#1683802811yescharacteristic
278C2#1683803411yescharacteristic
279C2#1683803912yes—
280C2#1683808311yescharacteristic
subgroupG/H
center, FrattiniC23C23×D59
commutator, socleC23×C59C24
FittingC59×#379C2
hypercenter#379D59
hypocenterC59#2437
LCSG ▷ C23×C59 ▷ C59
UCSC1 ◁ C23 ◁ #379

Complements

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

NH ≅ G/Ntype
1. C2×#14273704C2semidirect
3. #16837338C2semidirect
4. #16837325C2semidirect
5. #16837314C2semidirect
6. #16837277C2semidirect
7. #16837274C2semidirect
8. #16837260C2semidirect
10. C22×Dic118C22semidirect
14. C2×C4⋊Dic59C22semidirect
15. C2×C4⋊Dic59C22semidirect
16. C2×Dic59⋊C4C22semidirect
17. C2×Dic59⋊C4C22semidirect
18. C2×Dic59⋊C4C22semidirect
24. C59⋊#95C22semidirect
25. C59⋊#95C22semidirect
26. C59⋊#95C22semidirect
27. C59⋊#95C22semidirect
37. C24×C59Q8semidirect
120. C22×C59C22⋊Q8semidirect
150. C59#2437semidirect
178. C24Dic118semidirect
261. C22#14273704semidirect