Finite Group Databasebeta

← #28303440

Subgroups — #28303440

Order 13568.

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

normal subgroups only

This group has 398 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#20290614C212yesmaximal
2#20289618C214yesmaximal
3#20277315C211yesmaximal, characteristic
4#16811593C2214yes—
5#16811503—22no—
6#16811503—22no—
7C22×#11719919C2211yescharacteristic
8#16810507—22no—
9#16810505—22no—
10#16810484C2212yes—
11#16810481C412yes—
12C4×C22⋊Dic53C411yescharacteristic
13C4×C22⋊C4×C53C411yescharacteristic
14C2×#11719940—24no—
15C22⋊#88324—28no—
16C23×Dic53C2×C411yescharacteristic
17C23×Dic53C2311yescharacteristic
18C2×#11719919—22no—
19C2×#11719919—24no—
20C2×#11719919D412yes—
21C2×#11719919D412yes—
22C2×C22⋊Dic53C2×C412yes—
23C2×C4×Dic53—21no—
24#13133124—21no—
25#13133124—22no—
26#13133124—24no—
27C23×C4×C53C2×C411yescharacteristic
28C2×C22⋊C4×C53C2×C412yes—
29C2×C42×C53—21no—
30#95×C53—21no—
31C24×C53C22×C411yescharacteristic
32C22×C4×C53—22no—
33C22×C4×C53—22no—
34C22×C4×C53—81no—
35C22×C4×C53C22⋊C411yescharacteristic
36C22×C4×C53C22⋊C411yescharacteristic
37C22×Dic53—22no—
38C22×Dic53—22no—
39C22×Dic53—42no—
40C22×Dic53—81no—
41C22×Dic53C22⋊C412yes—
42C22×Dic53C2×D412yes—
43C22×Dic53#4114yes—
44#11719940—48no—
45C2×#88324—44no—
46C22⋊C4×C53—42no—
47C42×C53—81no—
48C22⋊Dic53—42no—
49#11719919—24no—
50#11719919—24no—
51#11719919—82no—
52C4×Dic53—81no—
53C23×C53—22no—
54C23×C53—41no—
55C23×C53—41no—
56C23×C53C2×C22⋊C411yescharacteristic
57C23×C53#11712yes—
58C2×C4×C53—21no—
59C2×C4×C53—21no—
60C2×C4×C53—41no—
61C2×C4×C53—41no—
62C2×C4×C53—42no—
63C2×C4×C53—42no—
64C2×C4×C53—42no—
65C2×C4×C53—82no—
66C2×Dic53—24no—
67C2×Dic53—22no—
68C2×Dic53—44no—
69C2×Dic53—42no—
70C2×Dic53—42no—
71C2×Dic53—42no—
72C2×Dic53—42no—
73C2×Dic53—82no—
74C2×Dic53#12314yes—
75#88324—84no—
76#8755—531nomaximal, Sylow
77C22×C53—21no—
78C22×C53—21no—
79C22×C53—22no—
80C22×C53—22no—
81C22×C53—22no—
82C22×C53—44no—
83C22×C53#38111yescharacteristic
84C22×C53#41012yes—
85C4×C53—41no—
86C4×C53—41no—
87C4×C53—82no—
88Dic53—24no—
89Dic53—42no—
90Dic53—82no—
91#2313—531no—
92#1821—532no—
93#1306—534no—
94C2×C53—22no—
95C2×C53—42no—
96C2×C53#182011yescharacteristic
97C2×C53#182911yescharacteristic
98C2×C53#183011yescharacteristic
99C22×C4⋊C4—531no—
100#407—534no—
101#387—1062no—
102#387—1062no—
103#381—532no—
104#380—532no—
105C4×C22⋊C4—531no—
106C4×C22⋊C4#615711yescharacteristic
107#343—1062no—
108#343—1062no—
109C53#875511yescharacteristic, complemented, Sylow
110C23×C4—531no—
111C23×C4—531no—
112C23×C4C2×#615711yescharacteristic
113C2×M16—1064no—
114C2×C4⋊C4—532no—
115C2×C4⋊C4—532no—
116C2×C4⋊C4—1064no—
117C2×C4⋊C4—1062no—
118C2×C22⋊C4—532no—
119C2×C22⋊C4C2×#615712yes—
120C2×C42—21no—
121C2×C42—1061no—
122C22⋊C8—1068no—
123#95—21no—
124#95—1062no—
125#95—1064no—
126#95—1061no—
127C24C22×#615711yescharacteristic
128C22×C4—22no—
129C22×C4—22no—
130C22×C4—81no—
131C22×C4—532no—
132C22×C4—534no—
133C22×C4—532no—
134C22×C4—1062no—
135C22×C4—1062no—
136C22×C4—4241no—
137C22×C4—2122no—
138C22×C4C22⋊#615711yescharacteristic
139C22×C4C22⋊#615711yescharacteristic
140M16—2128no—
141C2×C8—2124no—
142C4⋊C4—1064no—
143C4⋊C4—1064no—
144C4⋊C4—4242no—
145C22⋊C4—42no—
146C22⋊C4—2122no—
147C42—81no—
148C42—4241no—
149C23—22no—
150C23—41no—
151C23—41no—
152C23C2×C22⋊#615711yescharacteristic
153C23#1313329612yes—
154C2×C4—21no—
155C2×C4—21no—
156C2×C4—41no—
157C2×C4—41no—
158C2×C4—42no—
159C2×C4—42no—
160C2×C4—42no—
161C2×C4—82no—
162C2×C4—534no—
163C2×C4—1064no—
164C2×C4—1062no—
165C2×C4—4242no—
166C2×C4—2124no—
167C2×C4—2122no—
168C2×C4—2122no—
169C2×C4—2122no—
170C2×C4—2122no—
171C8—4244no—
172C22—21no—
173C22—21no—
174C22—22no—
175C22—22no—
176C22—22no—
177C22—44no—
178C22#1681156611yescharacteristic
179C22#1681160212yes—
180C4—41no—
181C4—41no—
182C4—82no—
183C4—1064no—
184C4—4242no—
185C4—2122no—
186C2—22no—
187C2—42no—
188C2#2029061211yescharacteristic
189C2#2029062811yescharacteristic
190C2#2029062911yescharacteristic
subgroupG/H
centerC22#16811566
commutator, prime radicalC24×C53C22×C4
FrattiniC24C22×#6157
FittingC4×C22⋊C4×C53C4
socleC22×C53#381
cosocleC23×Dic53C23
hypercenterC4×C22⋊C4#6157
hypocenterC53#8755
LCSG ▷ C24×C53 ▷ C22×C53 ▷ C53
UCSC1 ◁ C22 ◁ C24 ◁ C4×C22⋊C4

Complements

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

NH ≅ G/Ntype
109. C53#8755semidirect

Maximal subgroups

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

subgroupindex
#202906142
#202896182
#202773152
#875553