Finite Group Databasebeta

← #28303410

Subgroups — #28303410

Order 13568.

450 conjugacy classes of subgroups; only the 80 normal subgroups are shown.

normal subgroups only

This group has 450 conjugacy classes of subgroups — too many to draw. Only its 80 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#20289966C212yesmaximal
2#20289566C214yesmaximal, complemented
3#20277198C211yesmaximal, characteristic
4#16811643C2214yes—
5#16811468—22no—
6#16811466—22no—
7C2×#13133176C411yescharacteristic
8C2×#13133176C2211yescharacteristic
9#16810521—22no—
10#16810496—22no—
11C4×#11719919C412yes—
12C4×#11719919C2212yes—
13C22×C42×C53C411yescharacteristic
14#13133284—24no—
15C22⋊#88324—24no—
16#13133272—24no—
17#13133176—24no—
18#13133176—42no—
19C2×C4⋊Dic53—21no—
20C2×C4⋊Dic53D412yes—
21C2×#11719919—22no—
22C2×#11719919—22no—
23C2×C22⋊Dic53—21no—
24C2×C22⋊Dic53D412yes—
25C2×C4×Dic53C2×C412yes—
26C2×C4×Dic53C2×C411yescharacteristic
27C2×C4×Dic53C2311yescharacteristic
28#13133124—22no—
29#13133124—22no—
30C23×C4×C53—21no—
31C23×C4×C53C2×C411yescharacteristic
32C2×C42×C53—21no—
33C2×C42×C53—42no—
34C2×C42×C53C2×C412yes—
35C24×C53C22⋊C411yescharacteristic
36C22×C4×C53—22no—
37C22×C4×C53—22no—
38C22×C4×C53—22no—
39C22×C4×C53—22no—
40C22×C4×C53—44no—
41C22×C4×C53—42no—
42C22×C4×C53C22⋊C411yescharacteristic
43C22×C4×C53C22×C411yescharacteristic
44C22×Dic53—22no—
45C22×Dic53C22⋊C412yes—
46C22×Dic53C2×D412yes—
47C2×#88324—44no—
48C42×C53—42no—
49C42×C53—42no—
50C22⋊Dic53—24no—
51C22⋊Dic53—42no—
52C4⋊Dic53—24no—
53C4⋊Dic53—42no—
54#11719919—44no—
55#11719919—44no—
56C4×Dic53—22no—
57C4×Dic53—42no—
58C4×Dic53#4114yes—
59C23×C53—21no—
60C23×C53—21no—
61C23×C53—42no—
62C23×C53#10012yes—
63C23×C53C2×C22⋊C411yescharacteristic
64C2×C4×C53—28no—
65C2×C4×C53—21no—
66C2×C4×C53—21no—
67C2×C4×C53—21no—
68C2×C4×C53—21no—
69C2×C4×C53—24no—
70C2×C4×C53—42no—
71C2×C4×C53—48no—
72C2×C4×C53—42no—
73C2×C4×C53#10112yes—
74C2×C4×C53#11712yes—
75C2×Dic53—22no—
76C2×Dic53—42no—
77C2×Dic53—42no—
78C2×Dic53—42no—
79C2×Dic53—42no—
80C2×Dic53—42no—
81C2×Dic53#12314yes—
82#88324—84no—
83#8742—531nomaximal, Sylow
84C22×C53—22no—
85C22×C53—22no—
86C22×C53—42no—
87C22×C53—42no—
88C22×C53—42no—
89C22×C53#38111yescharacteristic
90C22×C53C2×#10011yescharacteristic
91C22×C53C2×#10111yescharacteristic
92C4×C53—22no—
93C4×C53—22no—
94C4×C53—44no—
95Dic53—24no—
96Dic53—42no—
97Dic53—82no—
98#2296—531no—
99#1464—532no—
100#1285—534no—
101C2×C53—21no—
102C2×C53—21no—
103C2×C53—42no—
104C2×C53#182111yescharacteristic
105C2×C53#182712yes—
106C2×#117—531no—
107C2×#117—531no—
108C22×C42#615711yescharacteristic
109#432—534no—
110#389—1062no—
111#385—1062no—
112C4×C4⋊C4—532no—
113C4×C4⋊C4—532no—
114#324—1062no—
115#323—1062no—
116C53#874211yescharacteristic, complemented, Sylow
117C23×C4—21no—
118C23×C4C2×#615711yescharacteristic
119#117—1064no—
120#117—2122no—
121C2×C4⋊C4—532no—
122C2×C4⋊C4—1062no—
123C2×C4⋊C4—1062no—
124C2×C4⋊C4—1061no—
125C2×C22⋊C4—532no—
126C2×C22⋊C4—1061no—
127C2×C42—21no—
128C2×C42—42no—
129C2×C42—531no—
130C2×C42—531no—
131C2×C42—532no—
132C2×C42C2×#615712yes—
133C4⋊C8—1064no—
134C22⋊C8—1064no—
135#97—1064no—
136#95—1062no—
137#95—1062no—
138C24C22⋊#615711yescharacteristic
139C22×C4—22no—
140C22×C4—22no—
141C22×C4—22no—
142C22×C4—22no—
143C22×C4—44no—
144C22×C4—42no—
145C22×C4—532no—
146C22×C4—532no—
147C22×C4—1062no—
148C22×C4C22⋊#615711yescharacteristic
149C22×C4C22×#615711yescharacteristic
150C2×C8—2124no—
151C4⋊C4—1064no—
152C4⋊C4—2122no—
153C4⋊C4—2124no—
154C4⋊C4—2124no—
155C22⋊C4—1064no—
156C22⋊C4—2122no—
157C42—42no—
158C42—42no—
159C42—534no—
160C42—1062no—
161C42—2122no—
162C23—21no—
163C23—21no—
164C23—42no—
165C23#1313327712yes—
166C23C2×C22⋊#615711yescharacteristic
167C2×C4—28no—
168C2×C4—21no—
169C2×C4—21no—
170C2×C4—21no—
171C2×C4—21no—
172C2×C4—24no—
173C2×C4—42no—
174C2×C4—48no—
175C2×C4—42no—
176C2×C4—534no—
177C2×C4—1062no—
178C2×C4—2122no—
179C2×C4—2122no—
180C2×C4—2122no—
181C2×C4—2122no—
182C2×C4—2122no—
183C2×C4#1313327812yes—
184C2×C4#1313329612yes—
185C8—4244no—
186C22—22no—
187C22—22no—
188C22—42no—
189C22—42no—
190C22—42no—
191C22#1681156611yescharacteristic
192C22C2×#1313327711yescharacteristic
193C22C2×#1313327811yescharacteristic
194C4—22no—
195C4—22no—
196C4—44no—
197C4—1064no—
198C4—4242no—
199C4—2122no—
200C2—21no—
201C2—21no—
202C2—42no—
203C2#2029061411yescharacteristic
204C2#2029062412yes—
subgroupG/H
centerC22#16811566
commutatorC22×C4×C53C22×C4
FrattiniC22×C4C22×#6157
FittingC22×C42×C53C4
socleC22×C53#381
prime radicalC24×C53C22⋊C4
cosocleC2×C4×Dic53C23
hypercenterC22×C42#6157
hypocenterC53#8742
LCSG ▷ C22×C4×C53 ▷ C22×C53 ▷ C53
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×C42

Complements

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

NH ≅ G/Ntype
2. #20289566C2semidirect
116. C53#8742semidirect

Maximal subgroups

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

subgroupindex
#202899662
#202895662
#202771982
#874253