Finite Group Databasebeta

← #21431066

Subgroups — #21431066

Order 7552.

512 conjugacy classes of subgroups; only the 129 normal subgroups are shown.

normal subgroups only

This group has 512 conjugacy classes of subgroups — too many to draw. Only its 129 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×#14273705C212yesmaximal, complemented
2#16837343C212yesmaximal, complemented
3#16837331C212yesmaximal, complemented
4#16837319C211yesmaximal, characteristic
5#16837307C211yesmaximal, characteristic, complemented
6#16837292C212yesmaximal, complemented
7#16837280C212yesmaximal
8#16837273C212yesmaximal, complemented
9C59×#398C211yesmaximal, characteristic, complemented
10C22×Dic118C2211yescharacteristic
11C22×D236C2211yescharacteristic
12C22×C4×D59C2212yes—
13#14273705—28no—
14C2×Dic59⋊C4C2212yes—
15C2×Dic59⋊C4C2212yes—
16C2×(C2×D59)⋊C4C2212yes—
17C2×(C2×D59)⋊C4C2212yes—
18C2×(C2×D59)⋊C4C2212yes—
19C2×(C2×D59)⋊C4C2212yes—
20C2×(C2×D59)⋊C4C2212yes—
21C2×C4×Dic59C2211yescharacteristic
22C59⋊#95C2212yes—
23C59⋊#95C2212yes—
24C59⋊#95C2212yes—
25C59⋊#95C2212yes—
26C59⋊#95C2211yescharacteristic
27C2×C4⋊C4×C59C2212yes—
28C2×C4⋊C4×C59C2211yescharacteristic
29C2×C4⋊C4×C59C2211yescharacteristic
30#95×C59C2212yes—
31#95×C59C2211yescharacteristic
32C23×D59C2312yes—
33C22×C4×C59C2311yescharacteristic
34C22×C4×C59C2312yes—
35C22×C4×C59C2311yescharacteristic
36C22×C4×C59C2312yes—
37C22×C4×C59C2311yescharacteristic
38C22×Dic59C2312yes—
39C22×Dic59C2312yes—
40C22×Dic59C2312yes—
41C2×D236—24no—
42C2×D236—41no—
43C2×C4×D59—24no—
44C2×C4×D59—42no—
45C2×C4×D59—42no—
46C2×Dic118—41no—
47C2×Dic118—41no—
48C2×Dic118D414yescomplemented
49C4⋊C4×C59—24no—
50C4⋊C4×C59—41no—
51C4⋊C4×C59—41no—
52(C2×D59)⋊C4—24no—
53(C2×D59)⋊C4—24no—
54(C2×D59)⋊C4—24no—
55(C2×D59)⋊C4—24no—
56(C2×D59)⋊C4—42no—
57Dic59⋊C4—24no—
58Dic59⋊C4—24no—
59C4×Dic59—41no—
60C23×C59C2411yescharacteristic
61C22×D59—22no—
62C22×D59—22no—
63C22×D59—22no—
64C22×D59—22no—
65C22×D59—22no—
66C22×D59—22no—
67C22×D59#4114yes—
68C2×C4×C59—21no—
69C2×C4×C59—21no—
70C2×C4×C59—22no—
71C2×C4×C59—22no—
72C2×C4×C59—22no—
73C2×C4×C59—22no—
74C2×C4×C59—22no—
75C2×C4×C59—22no—
76C2×C4×C59—21no—
77C2×C4×C59—22no—
78C2×C4×C59—21no—
79C2×C4×C59—22no—
80C2×C4×C59C2×D412yes—
81C2×Dic59—22no—
82C2×Dic59—22no—
83C2×Dic59—22no—
84C2×Dic59—22no—
85C2×Dic59—22no—
86C2×Dic59—22no—
87C2×Dic59—22no—
88C2×Dic59—22no—
89C2×Dic59C2×D414yes—
90D236—44no—
91C4×D59—48no—
92Dic118—44no—
93C22×C59C22×D411yescharacteristic
94C22×C59C2×#4112yes—
95C22×C59H(5,𝔽2)11yescharacteristic
96C22×C59H(5,𝔽2)11yescharacteristic
97C22×C592−1+412yes—
98C2×D59—24no—
99C2×D59—24no—
100C2×D59—24no—
101C2×D59—42no—
102C2×D59—42no—
103C2×D59—42no—
104C2×D59—42no—
105C4×C59—22no—
106C4×C59—42no—
107C4×C59—42no—
108C4×C59—41no—
109C4×C59—41no—
110Dic59—24no—
111Dic59—42no—
112Dic59—42no—
113#2728—591nomaximal, Sylow
114C2×C59#53411yescharacteristic
115C2×C59#53912yes—
116C2×C59#54812yes—
117C2×C59#55111yescharacteristic
118C2×C59#56311yescharacteristic
119D59—44no—
120C2×C22⋊Q8—592no—
121#400—592no—
122#398D5911yescharacteristic, complemented
123#397—592no—
124#394—591no—
125#391—591no—
126#388—592no—
127#386—592no—
128#385—592no—
129C59#272811yescharacteristic, complemented, Sylow
130C22×Q8—591no—
131C22×D4—591no—
132C23×C4—592no—
133C22⋊Q8—1188no—
134C2×C4⋊C4—592no—
135C2×C4⋊C4—592no—
136C2×C4⋊C4C2×D5912yes—
137C2×C4⋊C4C2×D5911yescharacteristic
138C2×C4⋊C4C2×D5911yescharacteristic
139C2×C22⋊C4—592no—
140C2×C22⋊C4—592no—
141C2×C22⋊C4—592no—
142C2×C22⋊C4—592no—
143C2×C22⋊C4—592no—
144C2×C42—591no—
145#95—592no—
146#95—592no—
147#95—592no—
148#95—592no—
149#95—591no—
150#95C2×D5912yes—
151#95C2×D5911yescharacteristic
152C24—592no—
153C2×Q8—594no—
154C2×Q8—2361no—
155C2×Q8—2361no—
156C2×D4—1184no—
157C2×D4—2361no—
158C22×C4—592no—
159C22×C4—592no—
160C22×C4—592no—
161C22×C4—1184no—
162C22×C4—2362no—
163C22×C4—2362no—
164C22×C4C22×D5911yescharacteristic
165C22×C4C22×D5911yescharacteristic
166C22×C4C22×D5912yes—
167C22×C4C22×D5912yes—
168C22×C4C22×D5911yescharacteristic
169C4⋊C4—24no—
170C4⋊C4—41no—
171C4⋊C4—41no—
172C4⋊C4—1184no—
173C4⋊C4—1184no—
174C22⋊C4—1184no—
175C22⋊C4—1184no—
176C22⋊C4—1184no—
177C22⋊C4—1184no—
178C22⋊C4—2362no—
179C42—2361no—
180C23—594no—
181C23—1182no—
182C23—1182no—
183C23—1182no—
184C23—1182no—
185C23—1182no—
186C23—1182no—
187C23C23×D5911yescharacteristic
188Q8—2364no—
189D4—2364no—
190C2×C4—21no—
191C2×C4—21no—
192C2×C4—22no—
193C2×C4—22no—
194C2×C4—22no—
195C2×C4—22no—
196C2×C4—22no—
197C2×C4—21no—
198C2×C4—22no—
199C2×C4—21no—
200C2×C4—22no—
201C2×C4—22no—
202C2×C4—594no—
203C2×C4—1182no—
204C2×C4—1182no—
205C2×C4—1182no—
206C2×C4—1182no—
207C2×C4—1182no—
208C2×C4—1182no—
209C2×C4—1182no—
210C2×C4—1182no—
211C2×C4—2368no—
212C2×C4D4×D5912yes—
213C22—1184no—
214C22—1184no—
215C22—1184no—
216C22—2362no—
217C22—2362no—
218C22—2362no—
219C22—2362no—
220C22C2×D4×D5911yescharacteristic
221C22#41×D5912yes—
222C22#1427377211yescharacteristic
223C22#1427377311yescharacteristic
224C22#1427377512yes—
225C4—22no—
226C4—42no—
227C4—42no—
228C4—41no—
229C4—41no—
230C4—1184no—
231C4—2362no—
232C4—2362no—
233C2—2364no—
234C2#1683796011yescharacteristic
235C2#1683800012yes—
236C2#1683806212yes—
237C2#1683808011yescharacteristic
238C2#1683815111yescharacteristic
subgroupG/H
center, FrattiniC23C23×D59
commutator, socleC23×C59C24
FittingC59×#398C2
hypercenter#398D59
hypocenterC59#2728
LCSG ▷ C23×C59 ▷ C59
UCSC1 ◁ C23 ◁ #398

Complements

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

NH ≅ G/Ntype
1. C2×#14273705C2semidirect
2. #16837343C2semidirect
3. #16837331C2semidirect
5. #16837307C2semidirect
6. #16837292C2semidirect
8. #16837273C2semidirect
9. C59×#398C2semidirect
48. C2×Dic118D4semidirect
122. #398D59semidirect
129. C59#2728semidirect