Finite Group Databasebeta

← #21422444

Subgroups — #21422444

Order 7552.

280 conjugacy classes of subgroups; only the 81 normal subgroups are shown.

normal subgroups only

This group has 280 conjugacy classes of subgroups — too many to draw. Only its 81 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
1#16837366C211yesmaximal, characteristic, complemented
2C2×C22⋊(C59⋊C8)C211yesmaximal, characteristic, complemented
3#16837128C212yesmaximal, complemented
4#16837126C212yesmaximal, complemented
5C2×#123×C59C211yesmaximal, characteristic
6C2×#11745664—21no—
7C22×C59⋊C8—21no—
8C22⋊(C59⋊C8)—21no—
9C22⋊(C59⋊C8)—21no—
10C22⋊(C59⋊C8)C2212yes—
11C22⋊(C59⋊C8)C2212yes—
12C22×D4×C59C411yescharacteristic
13C23×C4×C59C2211yescharacteristic
14#123×C59—21no—
15#123×C59—21no—
16#123×C59—21no—
17#123×C59—21no—
18C2×C4⋊C4×C59C411yescharacteristic
19C2×C4⋊C4×C59C2211yescharacteristic
20C2×C22⋊C4×C59C411yescharacteristic
21C2×C22⋊C4×C59C411yescharacteristic
22C2×C22⋊C4×C59C2211yescharacteristic
23C24×C59C2×C411yescharacteristic
24C24×C59C2×C411yescharacteristic
25C2×D4×C59—21no—
26C2×D4×C59—21no—
27C2×D4×C59—42no—
28C22×C4×C59—42no—
29C22×C4×C59C2×C411yescharacteristic
30C22×C4×C59C2×C411yescharacteristic
31C22×C4×C59C2×C411yescharacteristic
32C22×C4×C59C2×C411yescharacteristic
33C22×C4×C59D411yescharacteristic
34C22×C4×C59D411yescharacteristic
35C22×C4×C59D411yescharacteristic
36C22×C4×C59D411yescharacteristic
37C22×C4×C59C2311yescharacteristic
38C4⋊C4×C59—21no—
39C4⋊C4×C59—21no—
40C4⋊C4×C59—21no—
41C4⋊C4×C59—21no—
42C22⋊C4×C59—21no—
43C22⋊C4×C59—21no—
44C22⋊C4×C59—21no—
45C22⋊C4×C59—21no—
46C22⋊C4×C59—21no—
47C22⋊C4×C59—21no—
48#11745664—42no—
49C2×C59⋊C8—22no—
50C2×C59⋊C8—22no—
51C2×C59⋊C8—42no—
52C23×C59—22no—
53C23×C59—22no—
54C23×C59—21no—
55C23×C59—22no—
56C23×C59—41no—
57C23×C59—41no—
58C23×C59—41no—
59C23×C59C22⋊C411yescharacteristic
60C23×C59C22⋊C411yescharacteristic
61C23×C59C22×C411yescharacteristic
62D4×C59—42no—
63D4×C59—42no—
64C2×C4×C59—22no—
65C2×C4×C59—22no—
66C2×C4×C59—21no—
67C2×C4×C59—21no—
68C2×C4×C59—21no—
69C2×C4×C59—22no—
70C2×C4×C59—41no—
71C2×C4×C59—41no—
72C2×C4×C59—41no—
73C2×C4×C59—41no—
74C2×C4×C59—41no—
75C2×C4×C59—41no—
76C2×C4×C59C22⋊C411yescharacteristic
77C2×C4×C59C22⋊C411yescharacteristic
78C2×C4×C59C2×D411yescharacteristic
79C2×C4×C59C2×D411yescharacteristic
80C59⋊C8—42no—
81C59⋊C8—42no—
82C22×C59—21no—
83C22×C59—21no—
84C22×C59—21no—
85C22×C59—21no—
86C22×C59—21no—
87C22×C59—21no—
88C22×C59—21no—
89C22×C59—44no—
90C22×C59—41no—
91C22×C59—41no—
92C22×C59—41no—
93C22×C59—82no—
94C22×C59#9912yes—
95C22×C59C2×C22⋊C411yescharacteristic
96C22×C59#13112yes—
97C4×C59—21no—
98C4×C59—21no—
99C4×C59—21no—
100C4×C59—21no—
101C4×C59—41no—
102C4×C59—41no—
103C4×C59—41no—
104#1468—591nomaximal, Sylow
105C2×C59—22no—
106C2×C59—22no—
107C2×C59—41no—
108C2×C59—81no—
109C2×C59#40811yescharacteristic
110C2×C59C2×#9911yescharacteristic
111C2×C59#41311yescharacteristic
112C2×#123D5911yescharacteristic
113#407—591no—
114C2×C22⋊C8—591no—
115#324—592no—
116#323—592no—
117C59#146811yescharacteristic, complemented, Sylow
118C22×D4Dic5911yescharacteristic
119C23×C4C2×D5911yescharacteristic
120C2×M16—1181no—
121C22×C8—1181no—
122#123—21no—
123#123—21no—
124#123—21no—
125#123—21no—
126C2×C4⋊C4Dic5911yescharacteristic
127C2×C4⋊C4C2×D5911yescharacteristic
128C2×C22⋊C4Dic5911yescharacteristic
129C2×C22⋊C4Dic5911yescharacteristic
130C2×C22⋊C4C2×D5911yescharacteristic
131C22⋊C8—592no—
132C22⋊C8—592no—
133C22⋊C8—1181no—
134C22⋊C8—1181no—
135C24C2×Dic5911yescharacteristic
136C24C2×Dic5911yescharacteristic
137C2×D4—21no—
138C2×D4—21no—
139C2×D4—42no—
140C22×C4—42no—
141C22×C4C2×Dic5911yescharacteristic
142C22×C4C2×Dic5911yescharacteristic
143C22×C4C2×Dic5911yescharacteristic
144C22×C4C2×Dic5911yescharacteristic
145C22×C4C22⋊D5911yescharacteristic
146C22×C4C22⋊D5911yescharacteristic
147C22×C4C22⋊D5911yescharacteristic
148C22×C4C22⋊D5911yescharacteristic
149C22×C4C22×D5911yescharacteristic
150M16—2362no—
151C2×C8—1182no—
152C2×C8—1182no—
153C2×C8—2362no—
154C4⋊C4—21no—
155C4⋊C4—21no—
156C4⋊C4—21no—
157C4⋊C4—21no—
158C22⋊C4—21no—
159C22⋊C4—21no—
160C22⋊C4—21no—
161C22⋊C4—21no—
162C22⋊C4—21no—
163C22⋊C4—21no—
164C23—22no—
165C23—22no—
166C23—21no—
167C23—22no—
168C23—41no—
169C23—41no—
170C23—41no—
171C23C22⋊Dic5911yescharacteristic
172C23C22⋊Dic5911yescharacteristic
173C23C22×Dic5911yescharacteristic
174D4—42no—
175D4—42no—
176C2×C4—22no—
177C2×C4—22no—
178C2×C4—21no—
179C2×C4—21no—
180C2×C4—21no—
181C2×C4—22no—
182C2×C4—41no—
183C2×C4—41no—
184C2×C4—41no—
185C2×C4—41no—
186C2×C4—41no—
187C2×C4—41no—
188C2×C4C22⋊Dic5911yescharacteristic
189C2×C4C22⋊Dic5911yescharacteristic
190C2×C4C2×C22⋊D5911yescharacteristic
191C2×C4C2×C22⋊D5911yescharacteristic
192C8—2362no—
193C8—2362no—
194C22—21no—
195C22—21no—
196C22—21no—
197C22—21no—
198C22—21no—
199C22—21no—
200C22—21no—
201C22—44no—
202C22—41no—
203C22—41no—
204C22—41no—
205C22—82no—
206C22#1427364212yes—
207C22C2×C22⋊Dic5911yescharacteristic
208C22#1427373412yes—
209C4—21no—
210C4—21no—
211C4—21no—
212C4—21no—
213C4—41no—
214C4—41no—
215C4—41no—
216C2—22no—
217C2—22no—
218C2—41no—
219C2—81no—
220C2#1683736911yescharacteristic
221C2C2×#1427364211yescharacteristic
222C2#1683738611yescharacteristic
subgroupG/H
centerC22C2×C22⋊Dic59
commutatorC23×C59C22×C4
FrattiniC22×C4C22×D59
FittingC2×#123×C59C2
socleC22×C59C2×C22⋊C4
hypercenterC2×#123D59
hypocenterC59#1468
LCSG ▷ C23×C59 ▷ C2×C59 ▷ C59
UCSC1 ◁ C22 ◁ C23×C4 ◁ C2×#123

Complements

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

NH ≅ G/Ntype
1. #16837366C2semidirect
2. C2×C22⋊(C59⋊C8)C2semidirect
3. #16837128C2semidirect
4. #16837126C2semidirect
117. C59#1468semidirect