Finite Group Databasebeta

← #28303441

Subgroups — #28303441

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#20277317C211yesmaximal, characteristic
4#16811593C2214yes—
5#16811503—22no—
6#16811503—22no—
7C22×#11719919C2211yescharacteristic
8#16810510—22no—
9#16810504—22no—
10#16810484C2212yes—
11#16810483C411yescharacteristic
12C22⋊C4×Dic53C412yes—
13C53×#380C411yescharacteristic
14C2×#11719940—24no—
15C22⋊#88324—28no—
16C23×Dic53C2×C411yescharacteristic
17C23×Dic53C2311yescharacteristic
18C2×C4⋊Dic53—21no—
19C2×#11719919—24no—
20C2×#11719919D412yes—
21C2×#11719919D412yes—
22C2×C22⋊Dic53C2×C412yes—
23C2×C4×Dic53—22no—
24#13133124—21no—
25#13133124—22no—
26#13133124—24no—
27C23×C4×C53C2×C411yescharacteristic
28C2×C4⋊C4×C53—21no—
29C2×C22⋊C4×C53C2×C412yes—
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—41no—
40C22×Dic53—41no—
41C22×Dic53—81no—
42C22×Dic53C22⋊C412yes—
43C22×Dic53C2×D412yes—
44C22×Dic53#4114yes—
45#11719940—44no—
46#11719940—44no—
47C2×#88324—44no—
48C4⋊C4×C53—81no—
49C22⋊C4×C53—42no—
50C22⋊Dic53—42no—
51C4⋊Dic53—81no—
52#11719919—24no—
53#11719919—24no—
54C4×Dic53—82no—
55C23×C53—21no—
56C23×C53—21no—
57C23×C53—41no—
58C23×C53—41no—
59C23×C53C2×C22⋊C411yescharacteristic
60C23×C53#11712yes—
61C2×C4×C53—21no—
62C2×C4×C53—21no—
63C2×C4×C53—41no—
64C2×C4×C53—41no—
65C2×C4×C53—42no—
66C2×C4×C53—42no—
67C2×C4×C53—42no—
68C2×C4×C53—82no—
69C2×Dic53—22no—
70C2×Dic53—22no—
71C2×Dic53—22no—
72C2×Dic53—44no—
73C2×Dic53—42no—
74C2×Dic53—42no—
75C2×Dic53—42no—
76C2×Dic53—42no—
77C2×Dic53—82no—
78C2×Dic53#12314yes—
79#88324—84no—
80#8755—531nomaximal, Sylow
81C22×C53—21no—
82C22×C53—21no—
83C22×C53—22no—
84C22×C53—22no—
85C22×C53—22no—
86C22×C53—42no—
87C22×C53—42no—
88C22×C53#38111yescharacteristic
89C22×C53#41011yescharacteristic
90C22×C53#41011yescharacteristic
91C4×C53—41no—
92C4×C53—41no—
93C4×C53—82no—
94Dic53—24no—
95Dic53—42no—
96Dic53—82no—
97#2313—531no—
98#1821—532no—
99#1306—534no—
100C2×C53—21no—
101C2×C53—21no—
102C2×C53—42no—
103C2×C53#182011yescharacteristic
104C2×C53#182911yescharacteristic
105C2×C53#183011yescharacteristic
106C22×C4⋊C4—531no—
107#407—534no—
108#387—1062no—
109#387—1062no—
110#381—532no—
111#380—531no—
112#380#615711yescharacteristic
113C4×C22⋊C4—532no—
114#343—1062no—
115#343—1062no—
116C53#875511yescharacteristic, complemented, Sylow
117C23×C4—531no—
118C23×C4—531no—
119C23×C4C2×#615711yescharacteristic
120C2×M16—1064no—
121C2×C4⋊C4—21no—
122C2×C4⋊C4—532no—
123C2×C4⋊C4—532no—
124C2×C4⋊C4—1064no—
125C2×C4⋊C4—1061no—
126C2×C22⋊C4—532no—
127C2×C22⋊C4C2×#615712yes—
128C2×C42—1062no—
129C22⋊C8—1068no—
130#95—21no—
131#95—1062no—
132#95—1064no—
133#95—1061no—
134C24C22×#615711yescharacteristic
135C22×C4—22no—
136C22×C4—22no—
137C22×C4—81no—
138C22×C4—532no—
139C22×C4—534no—
140C22×C4—532no—
141C22×C4—1062no—
142C22×C4—1062no—
143C22×C4—4241no—
144C22×C4—2121no—
145C22×C4—2121no—
146C22×C4C22⋊#615711yescharacteristic
147C22×C4C22⋊#615711yescharacteristic
148M16—2124no—
149M16—2124no—
150C2×C8—2124no—
151C4⋊C4—81no—
152C4⋊C4—1064no—
153C4⋊C4—1064no—
154C4⋊C4—4241no—
155C22⋊C4—42no—
156C22⋊C4—2122no—
157C42—4242no—
158C23—21no—
159C23—21no—
160C23—41no—
161C23—41no—
162C23C2×C22⋊#615711yescharacteristic
163C23#1313329612yes—
164C2×C4—21no—
165C2×C4—21no—
166C2×C4—41no—
167C2×C4—41no—
168C2×C4—42no—
169C2×C4—42no—
170C2×C4—42no—
171C2×C4—82no—
172C2×C4—534no—
173C2×C4—1062no—
174C2×C4—1062no—
175C2×C4—1062no—
176C2×C4—4242no—
177C2×C4—2124no—
178C2×C4—2122no—
179C2×C4—2122no—
180C2×C4—2122no—
181C2×C4—2122no—
182C8—4244no—
183C22—21no—
184C22—21no—
185C22—22no—
186C22—22no—
187C22—22no—
188C22—42no—
189C22—42no—
190C22#1681156611yescharacteristic
191C22#1681160311yescharacteristic
192C22#1681160411yescharacteristic
193C4—41no—
194C4—41no—
195C4—82no—
196C4—1064no—
197C4—4242no—
198C4—2122no—
199C2—21no—
200C2—21no—
201C2—42no—
202C2#2029061311yescharacteristic
203C2#2029062811yescharacteristic
204C2#2029062911yescharacteristic
subgroupG/H
centerC22#16811566
commutator, prime radicalC24×C53C22×C4
FrattiniC24C22×#6157
FittingC53×#380C4
socleC22×C53#381
cosocleC23×Dic53C23
hypercenter#380#6157
hypocenterC53#8755
LCSG ▷ C24×C53 ▷ C22×C53 ▷ C53
UCSC1 ◁ C22 ◁ C24 ◁ #380

Complements

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

NH ≅ G/Ntype
116. C53#8755semidirect

Maximal subgroups

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

subgroupindex
#202906142
#202896182
#202773172
#875553