Finite Group Databasebeta

← #21428093

Subgroups — #21428093

Order 7552.

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

normal subgroups only

This group has 668 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×#14273703C212yesmaximal, complemented
2C2×(C22⋊D59)⋊C4C212yesmaximal, complemented
3#16837318C212yesmaximal, complemented
4#16837311C211yesmaximal, characteristic
5#16837291C212yesmaximal, complemented
6#16837289C212yesmaximal, complemented
7#16837280C212yesmaximal, complemented
8#16837274C211yesmaximal, characteristic, complemented
9C59×#393C211yesmaximal, characteristic, complemented
10C22×D236C2211yescharacteristic
11C22×C22⋊D59C2212yes—
12C23×Dic59C2211yescharacteristic
13C22×C4×D59C2212yes—
14#14273703—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⋊#95C2211yescharacteristic
27C59⋊#95C2212yes—
28C22×Q8×C59C2211yescharacteristic
29C2×C22⋊C4×C59C2212yes—
30C2×C22⋊C4×C59C2211yescharacteristic
31#95×C59C2212yes—
32#95×C59C2211yescharacteristic
33C24×C59C2311yescharacteristic
34C23×D59C2312yes—
35C2×Q8×C59—24no—
36C2×Q8×C59—41no—
37C22×C4×C59C2311yescharacteristic
38C22×C4×C59C2312yes—
39C22×C4×C59C2311yescharacteristic
40C22×C4×C59C2312yes—
41C2×C22⋊D59—24no—
42C2×C22⋊D59—24no—
43C2×C22⋊D59—24no—
44C22×Dic59—24no—
45C22×Dic59—41no—
46C22×Dic59C2312yes—
47C22×Dic59C2312yes—
48C22×Dic59C2312yes—
49C2×D236—24no—
50C2×D236—41no—
51C2×C4×D59—24no—
52C2×C4×D59—24no—
53C2×C4×D59—42no—
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)⋊C4—24no—
61C4⋊Dic59—24no—
62Dic59⋊C4—24no—
63Dic59⋊C4D418yescomplemented
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×D59#4114yes—
78Q8×C59—44no—
79C2×C4×C59—22no—
80C2×C4×C59—22no—
81C2×C4×C59—22no—
82C2×C4×C59—22no—
83C2×C4×C59—22no—
84C2×C4×C59—22no—
85C2×C4×C59—21no—
86C2×C4×C59—21no—
87C2×C4×C59—22no—
88C2×C4×C59C2×D414yes—
89C22⋊D59—216no—
90C2×Dic59—22no—
91C2×Dic59—22no—
92C2×Dic59—22no—
93C2×Dic59—22no—
94C2×Dic59—22no—
95C2×Dic59—22no—
96C2×Dic59—22no—
97C2×Dic59—44no—
98C2×Dic59C2×D414yes—
99C2×Dic59C2×D414yes—
100D236—44no—
101C4×D59—48no—
102C22×C59—24no—
103C22×C59—22no—
104C22×C59—41no—
105C22×C59—42no—
106C22×C59—41no—
107C22×C59C22×D412yes—
108C22×C59C2×#4112yes—
109C22×C59C2×#4111yescharacteristic
110C22×C59H(5,𝔽2)11yescharacteristic
111C22×C592−1+411yescharacteristic
112C2×D59—24no—
113C2×D59—24no—
114C2×D59—24no—
115C2×D59—42no—
116C2×D59—42no—
117C2×D59—42no—
118C2×D59—42no—
119C4×C59—24no—
120C4×C59—41no—
121C4×C59—42no—
122C4×C59—41no—
123Dic59—24no—
124Dic59—24no—
125Dic59—42no—
126#2463—591nomaximal, Sylow
127C2×C59—42no—
128C2×C59#52512yes—
129C2×C59#53911yescharacteristic
130C2×C59D4211yescharacteristic
131C2×C59#54812yes—
132C2×C59#55111yescharacteristic
133D59—44no—
134C2×C22⋊Q8—592no—
135C2×C4×D4—592no—
136#394—592no—
137#393D5911yescharacteristic, complemented
138#392—591no—
139#388—592no—
140#387—592no—
141#386—592no—
142#385—591no—
143C59#246311yescharacteristic, complemented, Sylow
144C22×Q8C2×D5911yescharacteristic
145C22×D4—592no—
146C22×D4—591no—
147C23×C4—591no—
148C23×C4—592no—
149C22⋊Q8—1188no—
150C4×D4—1188no—
151C2×C4⋊C4—592no—
152C2×C4⋊C4—592no—
153C2×C4⋊C4—592no—
154C2×C22⋊C4—591no—
155C2×C22⋊C4—592no—
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—591no—
164#95—592no—
165#95C2×D5912yes—
166#95C2×D5911yescharacteristic
167C24—592no—
168C24C22×D5911yescharacteristic
169C2×Q8—24no—
170C2×Q8—41no—
171C2×D4—1184no—
172C2×D4—1184no—
173C2×D4—1184no—
174C2×D4—1184no—
175C2×D4—2361no—
176C22×C4—592no—
177C22×C4—592no—
178C22×C4—592no—
179C22×C4—1184no—
180C22×C4—1184no—
181C22×C4—1184no—
182C22×C4—2362no—
183C22×C4—2361no—
184C22×C4C22×D5911yescharacteristic
185C22×C4C22×D5912yes—
186C22×C4C22×D5911yescharacteristic
187C22×C4C22×D5912yes—
188C4⋊C4—598no—
189C4⋊C4—1184no—
190C4⋊C4—1184no—
191C22⋊C4—24no—
192C22⋊C4—41no—
193C22⋊C4—1184no—
194C22⋊C4—1184no—
195C22⋊C4—1184no—
196C22⋊C4—1182no—
197C22⋊C4—1184no—
198C42—1184no—
199C23—22no—
200C23—22no—
201C23—21no—
202C23—21no—
203C23—594no—
204C23—1182no—
205C23—1182no—
206C23—1182no—
207C23—1182no—
208C23—1182no—
209C23—1182no—
210C23#1174568912yes—
211C23C23×D5911yescharacteristic
212Q8—44no—
213D4—11816no—
214D4—2364no—
215C2×C4—22no—
216C2×C4—22no—
217C2×C4—22no—
218C2×C4—22no—
219C2×C4—22no—
220C2×C4—22no—
221C2×C4—21no—
222C2×C4—21no—
223C2×C4—22no—
224C2×C4—594no—
225C2×C4—594no—
226C2×C4—1182no—
227C2×C4—1182no—
228C2×C4—1182no—
229C2×C4—1182no—
230C2×C4—1182no—
231C2×C4—1182no—
232C2×C4—1182no—
233C2×C4—2368no—
234C2×C4—2364no—
235C2×C4D4×D5914yes—
236C22—24no—
237C22—22no—
238C22—41no—
239C22—42no—
240C22—41no—
241C22—1184no—
242C22—1184no—
243C22—1184no—
244C22—2362no—
245C22—2362no—
246C22—2362no—
247C22—2362no—
248C22C2×D4×D5912yes—
249C22#41×D5912yes—
250C22C2×#1174568911yescharacteristic
251C22#1427377211yescharacteristic
252C22#1427377411yescharacteristic
253C4—24no—
254C4—41no—
255C4—42no—
256C4—41no—
257C4—1184no—
258C4—1184no—
259C4—2362no—
260C2—42no—
261C2—2364no—
262C2#1683791512yes—
263C2#1683800111yescharacteristic
264C2#1683803411yescharacteristic
265C2#1683806012yes—
266C2#1683808211yescharacteristic
subgroupG/H
center, FrattiniC23C23×D59
commutator, socleC23×C59C24
FittingC59×#393C2
hypercenter#393D59
hypocenterC59#2463
LCSG ▷ C23×C59 ▷ C59
UCSC1 ◁ C23 ◁ #393

Complements

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

NH ≅ G/Ntype
1. C2×#14273703C2semidirect
2. C2×(C22⋊D59)⋊C4C2semidirect
3. #16837318C2semidirect
5. #16837291C2semidirect
6. #16837289C2semidirect
7. #16837280C2semidirect
8. #16837274C2semidirect
9. C59×#393C2semidirect
63. Dic59⋊C4D4semidirect
137. #393D59semidirect
143. C59#2463semidirect