Finite Group Databasebeta

← #28303449

Subgroups — #28303449

Order 13568.

394 conjugacy classes of subgroups; only the 72 normal subgroups are shown.

normal subgroups only

This group has 394 conjugacy classes of subgroups — too many to draw. Only its 72 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#20289963C212yesmaximal
2#20289616C214yesmaximal
3#20277316C211yesmaximal, characteristic
4#16811593C2214yes—
5#16811468—22no—
6#16811468—22no—
7C22×C4⋊Dic53C2211yescharacteristic
8#16810508—22no—
9#16810506—22no—
10#16810486C411yescharacteristic
11#16810481C2212yes—
12C22⋊C4×Dic53C412yes—
13C53×#381C411yescharacteristic
14C2×#11719940—24no—
15C22⋊#88324—24no—
16C22⋊#88324—24no—
17C23×Dic53C2×C411yescharacteristic
18C23×Dic53C2311yescharacteristic
19C2×C4⋊Dic53—24no—
20C2×C4⋊Dic53D412yes—
21C2×C4⋊Dic53D412yes—
22C2×#11719919—22no—
23C2×C22⋊Dic53C2×C412yes—
24C2×C4×Dic53—22no—
25#13133124—21no—
26#13133124—21no—
27#13133124—22no—
28#13133124—22no—
29C23×C4×C53C2×C411yescharacteristic
30C2×C22⋊C4×C53C2×C412yes—
31#95×C53—21no—
32#95×C53—21no—
33C24×C53C22×C411yescharacteristic
34C22×C4×C53—22no—
35C22×C4×C53—22no—
36C22×C4×C53—42no—
37C22×C4×C53C22⋊C411yescharacteristic
38C22×C4×C53C22⋊C411yescharacteristic
39C22×Dic53—22no—
40C22×Dic53—22no—
41C22×Dic53—81no—
42C22×Dic53—81no—
43C22×Dic53C22⋊C412yes—
44C22×Dic53C2×D412yes—
45C22×Dic53#4114yes—
46#11719940—84no—
47C2×#88324—44no—
48C22⋊C4×C53—42no—
49C22⋊Dic53—42no—
50C4⋊Dic53—24no—
51C4⋊Dic53—24no—
52#11719919—82no—
53C4×Dic53—82no—
54C23×C53—22no—
55C23×C53—41no—
56C23×C53—41no—
57C23×C53C2×C22⋊C411yescharacteristic
58C23×C53#11712yes—
59C2×C4×C53—21no—
60C2×C4×C53—21no—
61C2×C4×C53—22no—
62C2×C4×C53—22no—
63C2×C4×C53—44no—
64C2×C4×C53—42no—
65C2×C4×C53—42no—
66C2×C4×C53—42no—
67C2×Dic53—22no—
68C2×Dic53—44no—
69C2×Dic53—42no—
70C2×Dic53—42no—
71C2×Dic53—42no—
72C2×Dic53—42no—
73C2×Dic53—42no—
74C2×Dic53—82no—
75C2×Dic53#12314yes—
76#88324—84no—
77#8758—531nomaximal, Sylow
78C22×C53—21no—
79C22×C53—21no—
80C22×C53—22no—
81C22×C53—22no—
82C22×C53—22no—
83C22×C53—44no—
84C22×C53#38111yescharacteristic
85C22×C53#41312yes—
86C4×C53—41no—
87C4×C53—41no—
88C4×C53—82no—
89Dic53—24no—
90Dic53—42no—
91Dic53—82no—
92#2313—531no—
93#1463—532no—
94#1305—534no—
95C2×C53—22no—
96C2×C53—42no—
97C2×C53#182211yescharacteristic
98C2×C53#182811yescharacteristic
99C2×C53#183011yescharacteristic
100C22×C4⋊C4—531no—
101#407—534no—
102#387—1062no—
103#387—1062no—
104#381—531no—
105#381#615711yescharacteristic
106#380—532no—
107C4×C22⋊C4—532no—
108#324—1062no—
109#324—1062no—
110C53#875811yescharacteristic, complemented, Sylow
111C23×C4—531no—
112C23×C4—531no—
113C23×C4C2×#615711yescharacteristic
114C2×M16—1064no—
115C2×C4⋊C4—532no—
116C2×C4⋊C4—532no—
117C2×C4⋊C4—1064no—
118C2×C4⋊C4—1062no—
119C2×C22⋊C4—532no—
120C2×C22⋊C4C2×#615712yes—
121C2×C42—1062no—
122C22⋊C8—1064no—
123C22⋊C8—1064no—
124#95—21no—
125#95—21no—
126#95—1062no—
127#95—1062no—
128#95—1061no—
129#95—1061no—
130C24C22×#615711yescharacteristic
131C22×C4—22no—
132C22×C4—22no—
133C22×C4—42no—
134C22×C4—532no—
135C22×C4—534no—
136C22×C4—532no—
137C22×C4—1062no—
138C22×C4—1062no—
139C22×C4—4241no—
140C22×C4—4241no—
141C22×C4C22⋊#615711yescharacteristic
142C22×C4C22⋊#615711yescharacteristic
143M16—4244no—
144C2×C8—2124no—
145C4⋊C4—1064no—
146C4⋊C4—1064no—
147C4⋊C4—4242no—
148C22⋊C4—42no—
149C22⋊C4—2122no—
150C42—4242no—
151C23—22no—
152C23—41no—
153C23—41no—
154C23C2×C22⋊#615711yescharacteristic
155C23#1313329612yes—
156C2×C4—21no—
157C2×C4—21no—
158C2×C4—22no—
159C2×C4—22no—
160C2×C4—44no—
161C2×C4—42no—
162C2×C4—42no—
163C2×C4—42no—
164C2×C4—534no—
165C2×C4—1062no—
166C2×C4—4242no—
167C2×C4—2122no—
168C2×C4—2124no—
169C2×C4—2122no—
170C2×C4—2122no—
171C2×C4—2122no—
172C2×C4—2122no—
173C8—4244no—
174C22—21no—
175C22—21no—
176C22—22no—
177C22—22no—
178C22—22no—
179C22—44no—
180C22#1681156611yescharacteristic
181C22#1681161012yes—
182C4—41no—
183C4—41no—
184C4—82no—
185C4—1064no—
186C4—4242no—
187C4—2122no—
188C2—22no—
189C2—42no—
190C2#2029061711yescharacteristic
191C2#2029062711yescharacteristic
192C2#2029062911yescharacteristic
subgroupG/H
centerC22#16811566
commutator, prime radicalC24×C53C22×C4
FrattiniC24C22×#6157
FittingC53×#381C4
socleC22×C53#381
cosocleC23×Dic53C23
hypercenter#381#6157
hypocenterC53#8758
LCSG ▷ C24×C53 ▷ C22×C53 ▷ C53
UCSC1 ◁ C22 ◁ C24 ◁ #381

Complements

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

NH ≅ G/Ntype
110. C53#8758semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
#202899632
#202896162
#202773162
#875853