Finite Group Databasebeta

← #21428374

Subgroups — #21428374

Order 7552.

700 conjugacy classes of subgroups; only the 165 normal subgroups are shown.

normal subgroups only

This group has 700 conjugacy classes of subgroups — too many to draw. Only its 165 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
1C22×C22⋊Dic59C211yesmaximal, characteristic
2#16837330C214yesmaximal, complemented
3#16837275C212yesmaximal, complemented
4#16837274C212yesmaximal, complemented
5#16837265C212yesmaximal, complemented
6#16837263C212yesmaximal, complemented
7#16837258C211yesmaximal, characteristic
8C22×C22⋊C4×C59C211yesmaximal, characteristic
9C23×Dic59C2211yescharacteristic
10C23×Dic59C2211yescharacteristic
11C2×Dic59⋊C4C2214yescomplemented
12C2×C22⋊Dic59—24no—
13C2×C22⋊Dic59C2212yes—
14C2×C22⋊Dic59C2212yes—
15C2×C22⋊Dic59C2212yes—
16C2×C22⋊Dic59C2212yes—
17C2×C22⋊Dic59C2212yes—
18C59⋊#95C2214yescomplemented
19C59⋊#95C2214yescomplemented
20C59⋊#95C2214yescomplemented
21C25×C59C2211yescharacteristic
22C23×C4×C59C2211yescharacteristic
23C23×C4×C59C2211yescharacteristic
24C2×C22⋊C4×C59—24no—
25C2×C22⋊C4×C59C2212yes—
26C2×C22⋊C4×C59C2212yes—
27C24×C59—24no—
28C24×C59—24no—
29C24×C59—42no—
30C24×C59D414yes—
31C24×C59C2311yescharacteristic
32C24×C59C2311yescharacteristic
33C24×C59C2311yescharacteristic
34C22×C4×C59—22no—
35C22×C4×C59—22no—
36C22×C4×C59—24no—
37C22×C4×C59—42no—
38C22×C4×C59C2312yes—
39C22×C4×C59C2312yes—
40C22×Dic59—22no—
41C22×Dic59—22no—
42C22×Dic59—24no—
43C22×Dic59—42no—
44C22×Dic59C2312yes—
45C22×Dic59C2314yes—
46C22×Dic59C2312yes—
47C22⋊C4×C59—24no—
48C22⋊C4×C59—24no—
49C22⋊Dic59—24no—
50C22⋊Dic59—24no—
51C22⋊Dic59—24no—
52C22⋊Dic59—24no—
53C22⋊Dic59—42no—
54Dic59⋊C4—44no—
55C23×C59—22no—
56C23×C59—22no—
57C23×C59—22no—
58C23×C59—22no—
59C23×C59—28no—
60C23×C59—28no—
61C23×C59—22no—
62C23×C59—22no—
63C23×C59—22no—
64C23×C59—44no—
65C23×C59—416no—
66C23×C59C2×D412yes—
67C23×C59C2×D412yes—
68C23×C59C2×D412yes—
69C23×C59#4114yes—
70C23×C59#4114yes—
71C23×C59C2411yescharacteristic
72C2×C4×C59—22no—
73C2×C4×C59—22no—
74C2×C4×C59—24no—
75C2×C4×C59—24no—
76C2×C4×C59—44no—
77C2×C4×C59—44no—
78C2×Dic59—22no—
79C2×Dic59—22no—
80C2×Dic59—24no—
81C2×Dic59—24no—
82C2×Dic59—24no—
83C2×Dic59—24no—
84C2×Dic59—24no—
85C2×Dic59—44no—
86C2×Dic59—44no—
87C22×C59—22no—
88C22×C59—22no—
89C22×C59—22no—
90C22×C59—22no—
91C22×C59—28no—
92C22×C59—28no—
93C22×C59—22no—
94C22×C59—22no—
95C22×C59—22no—
96C22×C59—416no—
97C22×C59—44no—
98C22×C59#12314yes—
99C22×C59#12314yes—
100C22×C59C22×D411yescharacteristic
101C22×C59C2×#4112yes—
102C22×C59C2×#4112yes—
103C22×C59H(5,𝔽2)12yes—
104C4×C59—42no—
105C4×C59—42no—
106Dic59—42no—
107Dic59—42no—
108Dic59—44no—
109#2483—591nomaximal, Sylow
110C2×C59—24no—
111C2×C59—24no—
112C2×C59—42no—
113C2×C59C2×#12311yescharacteristic
114C2×C59C2×#12311yescharacteristic
115C2×C59#53411yescharacteristic
116C2×C59#55114yes—
117C22×C22⋊C4—591no—
118C22×C22⋊C4D5911yescharacteristic
119#397—594no—
120#385—592no—
121#385—592no—
122#381—592no—
123#381—592no—
124#379—591no—
125C59#248311yescharacteristic, complemented, Sylow
126C25C2×D5911yescharacteristic
127C23×C4—591no—
128C23×C4—591no—
129C23×C4C2×D5911yescharacteristic
130C23×C4C2×D5911yescharacteristic
131C2×C4⋊C4—594no—
132C2×C22⋊C4—24no—
133C2×C22⋊C4—592no—
134C2×C22⋊C4—592no—
135C2×C22⋊C4—592no—
136C2×C22⋊C4—592no—
137C2×C22⋊C4—592no—
138C2×C22⋊C4—1184no—
139C2×C22⋊C4C2×D5912yes—
140C2×C22⋊C4C2×D5912yes—
141#95—594no—
142#95—594no—
143#95—594no—
144C24—24no—
145C24—24no—
146C24—42no—
147C24C22⋊D5914yes—
148C24C22×D5911yescharacteristic
149C24C22×D5911yescharacteristic
150C24C22×D5911yescharacteristic
151C22×C4—24no—
152C22×C4—22no—
153C22×C4—22no—
154C22×C4—42no—
155C22×C4—592no—
156C22×C4—594no—
157C22×C4—592no—
158C22×C4—1184no—
159C22×C4—1182no—
160C22×C4—1182no—
161C22×C4—2362no—
162C22×C4C22×D5912yes—
163C22×C4C22×D5912yes—
164C4⋊C4—2364no—
165C22⋊C4—24no—
166C22⋊C4—24no—
167C22⋊C4—1184no—
168C22⋊C4—1184no—
169C22⋊C4—1184no—
170C22⋊C4—1184no—
171C22⋊C4—2362no—
172C23—22no—
173C23—22no—
174C23—22no—
175C23—22no—
176C23—28no—
177C23—28no—
178C23—22no—
179C23—22no—
180C23—22no—
181C23—44no—
182C23—416no—
183C23#1174568514yes—
184C23#1174568714yes—
185C23C2×C22⋊D5912yes—
186C23C2×C22⋊D5912yes—
187C23C2×C22⋊D5912yes—
188C23C23×D5911yescharacteristic
189C2×C4—22no—
190C2×C4—22no—
191C2×C4—24no—
192C2×C4—24no—
193C2×C4—44no—
194C2×C4—44no—
195C2×C4—1182no—
196C2×C4—1182no—
197C2×C4—1184no—
198C2×C4—1184no—
199C2×C4—1184no—
200C2×C4—1184no—
201C2×C4—1184no—
202C2×C4—2364no—
203C2×C4—2364no—
204C22—22no—
205C22—22no—
206C22—22no—
207C22—22no—
208C22—28no—
209C22—28no—
210C22—22no—
211C22—22no—
212C22—22no—
213C22—416no—
214C22—44no—
215C22#1427370814yes—
216C22#1427371014yes—
217C22C22×C22⋊D5911yescharacteristic
218C22C2×#1174568712yes—
219C22C2×#1174568512yes—
220C22#1427377212yes—
221C4—42no—
222C4—42no—
223C4—2362no—
224C4—2362no—
225C4—2364no—
226C2—24no—
227C2—24no—
228C2—42no—
229C2C2×#1427370811yescharacteristic
230C2C2×#1427371011yescharacteristic
231C2#1683796111yescharacteristic
232C2#1683807814yes—
subgroupG/H
center, FrattiniC23C23×D59
commutator, socleC23×C59C24
FittingC22×C22⋊C4×C59C2
hypercenterC22×C22⋊C4D59
hypocenterC59#2483
LCSG ▷ C23×C59 ▷ C59
UCSC1 ◁ C23 ◁ C22×C22⋊C4

Complements

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

NH ≅ G/Ntype
2. #16837330C2semidirect
3. #16837275C2semidirect
4. #16837274C2semidirect
5. #16837265C2semidirect
6. #16837263C2semidirect
11. C2×Dic59⋊C4C22semidirect
18. C59⋊#95C22semidirect
19. C59⋊#95C22semidirect
20. C59⋊#95C22semidirect
125. C59#2483semidirect