Finite Group Databasebeta

← #21427979

Subgroups — #21427979

Order 7552.

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

normal subgroups only

This group has 660 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
1C2×#14273712C212yesmaximal, complemented
2C2×(C22⋊D59)⋊C4C212yesmaximal, complemented
3#16837318C212yesmaximal, complemented
4#16837311C211yesmaximal, characteristic
5#16837298C212yesmaximal, complemented
6#16837294C212yesmaximal, complemented
7#16837274C211yesmaximal, characteristic, complemented
8#16837273C212yesmaximal, complemented
9C59×#399C211yesmaximal, characteristic, complemented
10C22×D236C2211yescharacteristic
11C22×C22⋊D59C2212yes—
12C23×Dic59C2211yescharacteristic
13C22×C4×D59C2212yes—
14#14273712—28no—
15(C22⋊D59)⋊C4—28no—
16C2×C4⋊Dic59C2212yes—
17C2×Dic59⋊C4C2212yes—
18C2×Dic59⋊C4C2212yes—
19C2×C22⋊Dic59C2211yescharacteristic
20C2×(C2×D59)⋊C4C2212yes—
21C2×(C2×D59)⋊C4C2212yes—
22C2×(C2×D59)⋊C4C2212yes—
23C2×(C2×D59)⋊C4C2212yes—
24C2×C4×Dic59C2212yes—
25C59⋊#95C2212yes—
26C59⋊#95C2212yes—
27C59⋊#95C2211yescharacteristic
28C2×C4⋊C4×C59C2212yes—
29C2×C4⋊C4×C59C2211yescharacteristic
30C2×C22⋊C4×C59C2212yes—
31C2×C22⋊C4×C59C2211yescharacteristic
32#95×C59C2211yescharacteristic
33C24×C59C2311yescharacteristic
34C23×D59C2312yes—
35C22×C4×C59C2311yescharacteristic
36C22×C4×C59C2312yes—
37C22×C4×C59C2311yescharacteristic
38C22×C4×C59C2312yes—
39C2×C22⋊D59—24no—
40C2×C22⋊D59—24no—
41C2×C22⋊D59—24no—
42C22×Dic59—24no—
43C22×Dic59—41no—
44C22×Dic59C2312yes—
45C22×Dic59C2312yes—
46C22×Dic59C2312yes—
47C2×D236—24no—
48C2×D236—41no—
49C2×C4×D59—24no—
50C2×C4×D59—24no—
51C2×C4×D59—42no—
52C4⋊C4×C59—24no—
53C4⋊C4×C59—41no—
54C22⋊C4×C59—24no—
55C22⋊C4×C59—41no—
56C22⋊Dic59—22no—
57(C2×D59)⋊C4—24no—
58(C2×D59)⋊C4—24no—
59(C2×D59)⋊C4—24no—
60(C2×D59)⋊C4D418yescomplemented
61C4⋊Dic59—24no—
62Dic59⋊C4—24no—
63Dic59⋊C4—24no—
64C4×Dic59—24no—
65C23×C59—22no—
66C23×C59—22no—
67C23×C59—21no—
68C23×C59—21no—
69C23×C59#4112yes—
70C23×C59C2411yescharacteristic
71C22×D59—22no—
72C22×D59—22no—
73C22×D59—22no—
74C22×D59—22no—
75C22×D59—22no—
76C22×D59—22no—
77C22×D59C2×D414yes—
78C2×C4×C59—22no—
79C2×C4×C59—22no—
80C2×C4×C59—22no—
81C2×C4×C59—22no—
82C2×C4×C59—22no—
83C2×C4×C59—22no—
84C2×C4×C59—21no—
85C2×C4×C59—21no—
86C2×C4×C59—22no—
87C2×C4×C59C2×D414yes—
88C22⋊D59—216no—
89C2×Dic59—22no—
90C2×Dic59—22no—
91C2×Dic59—22no—
92C2×Dic59—22no—
93C2×Dic59—22no—
94C2×Dic59—22no—
95C2×Dic59—22no—
96C2×Dic59—44no—
97C2×Dic59C2×D414yes—
98C2×Dic59#4114yes—
99D236—44no—
100C4×D59—48no—
101C22×C59—24no—
102C22×C59—22no—
103C22×C59—41no—
104C22×C59—42no—
105C22×C59—41no—
106C22×C59C22×D412yes—
107C22×C59C2×#4112yes—
108C22×C59C2×#4111yescharacteristic
109C22×C59H(5,𝔽2)11yescharacteristic
110C22×C592−1+411yescharacteristic
111C2×D59—24no—
112C2×D59—24no—
113C2×D59—24no—
114C2×D59—42no—
115C2×D59—42no—
116C2×D59—42no—
117C2×D59—42no—
118C4×C59—24no—
119C4×C59—42no—
120C4×C59—41no—
121C4×C59—41no—
122Dic59—24no—
123Dic59—24no—
124Dic59—42no—
125#2455—591nomaximal, Sylow
126C2×C59—42no—
127C2×C59#52512yes—
128C2×C59#53911yescharacteristic
129C2×C59D4211yescharacteristic
130C2×C59#54712yes—
131C2×C59#55911yescharacteristic
132D59—44no—
133C2×#123—592no—
134C2×C4×D4—592no—
135#399D5911yescharacteristic, complemented
136#394—592no—
137#392—591no—
138#389—592no—
139#388—592no—
140#385—592no—
141#385—591no—
142C59#245511yescharacteristic, complemented, Sylow
143C22×D4—592no—
144C22×D4—591no—
145C23×C4—591no—
146C23×C4—592no—
147#123—1188no—
148C4×D4—1188no—
149C2×C4⋊C4—592no—
150C2×C4⋊C4—592no—
151C2×C4⋊C4—592no—
152C2×C4⋊C4C2×D5912yes—
153C2×C4⋊C4C2×D5911yescharacteristic
154C2×C22⋊C4—592no—
155C2×C22⋊C4—591no—
156C2×C22⋊C4—592no—
157C2×C22⋊C4—592no—
158C2×C22⋊C4—592no—
159C2×C22⋊C4C2×D5912yes—
160C2×C22⋊C4C2×D5911yescharacteristic
161C2×C42—592no—
162#95—592no—
163#95—592no—
164#95—591no—
165#95C2×D5911yescharacteristic
166C24—592no—
167C24C22×D5911yescharacteristic
168C2×D4—1184no—
169C2×D4—1184no—
170C2×D4—1184no—
171C2×D4—1184no—
172C2×D4—2361no—
173C22×C4—592no—
174C22×C4—592no—
175C22×C4—592no—
176C22×C4—1184no—
177C22×C4—1184no—
178C22×C4—1184no—
179C22×C4—2362no—
180C22×C4—2361no—
181C22×C4C22×D5911yescharacteristic
182C22×C4C22×D5912yes—
183C22×C4C22×D5911yescharacteristic
184C22×C4C22×D5912yes—
185C4⋊C4—24no—
186C4⋊C4—41no—
187C4⋊C4—1184no—
188C4⋊C4—1184no—
189C4⋊C4—1184no—
190C22⋊C4—24no—
191C22⋊C4—41no—
192C22⋊C4—598no—
193C22⋊C4—1184no—
194C22⋊C4—1184no—
195C22⋊C4—1182no—
196C22⋊C4—1184no—
197C42—1184no—
198C23—22no—
199C23—22no—
200C23—21no—
201C23—21no—
202C23—594no—
203C23—1182no—
204C23—1182no—
205C23—1182no—
206C23—1182no—
207C23—1182no—
208C23—1182no—
209C23#1174568912yes—
210C23C23×D5911yescharacteristic
211D4—11816no—
212D4—2364no—
213C2×C4—22no—
214C2×C4—22no—
215C2×C4—22no—
216C2×C4—22no—
217C2×C4—22no—
218C2×C4—22no—
219C2×C4—21no—
220C2×C4—21no—
221C2×C4—22no—
222C2×C4—594no—
223C2×C4—594no—
224C2×C4—1182no—
225C2×C4—1182no—
226C2×C4—1182no—
227C2×C4—1182no—
228C2×C4—1182no—
229C2×C4—1182no—
230C2×C4—1182no—
231C2×C4—2368no—
232C2×C4—2364no—
233C2×C4D4×D5914yes—
234C22—24no—
235C22—22no—
236C22—41no—
237C22—42no—
238C22—41no—
239C22—1184no—
240C22—1184no—
241C22—1184no—
242C22—2362no—
243C22—2362no—
244C22—2362no—
245C22—2362no—
246C22C2×D4×D5912yes—
247C22#41×D5912yes—
248C22C2×#1174568911yescharacteristic
249C22#1427377211yescharacteristic
250C22#1427377411yescharacteristic
251C4—24no—
252C4—42no—
253C4—41no—
254C4—41no—
255C4—1184no—
256C4—1184no—
257C4—2362no—
258C2—42no—
259C2—2364no—
260C2#1683791512yes—
261C2#1683800111yescharacteristic
262C2#1683803711yescharacteristic
263C2#1683805012yes—
264C2#1683813611yescharacteristic
subgroupG/H
center, FrattiniC23C23×D59
commutator, socleC23×C59C24
FittingC59×#399C2
hypercenter#399D59
hypocenterC59#2455
LCSG ▷ C23×C59 ▷ C59
UCSC1 ◁ C23 ◁ #399

Complements

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

NH ≅ G/Ntype
1. C2×#14273712C2semidirect
2. C2×(C22⋊D59)⋊C4C2semidirect
3. #16837318C2semidirect
5. #16837298C2semidirect
6. #16837294C2semidirect
7. #16837274C2semidirect
8. #16837273C2semidirect
9. C59×#399C2semidirect
60. (C2×D59)⋊C4D4semidirect
135. #399D59semidirect
142. C59#2455semidirect