Finite Group Databasebeta

← #28303350

Subgroups — #28303350

Order 13568.

554 conjugacy classes of subgroups; only the 100 normal subgroups are shown.

normal subgroups only

This group has 554 conjugacy classes of subgroups — too many to draw. Only its 100 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#20290442C212yesmaximal
2#20289591C214yesmaximal, complemented
3#382×D53C211yesmaximal, characteristic
4C2×#13133274—22no—
5C2×#13133272C2214yes—
6#16811489—22no—
7C2×C4⋊C4×D53C412yes—
8C2×C42×D53C2211yescharacteristic
9#16810489C411yescharacteristic
10#16810488C2212yes—
11#16810487—22no—
12#95×D53—22no—
13C53×#382C411yescharacteristic
14C22×#88324—24no—
15#13133274—28no—
16#13133272—28no—
17C22×C4×D53—22no—
18C22×C4×D53C2×C411yescharacteristic
19C22×C4×D53D412yes—
20C2×C4⋊Dic53C2×C412yes—
21C2×#11719919—22no—
22C4⋊C4×D53—44no—
23C2×C4×Dic53D412yes—
24C2×C4×Dic53C2311yescharacteristic
25C42×D53—24no—
26#13133124—22no—
27#13133124—24no—
28C2×C4⋊C4×C53C2×C412yes—
29C2×C42×C53C2×C411yescharacteristic
30#95×C53—22no—
31C23×D53C22⋊C411yescharacteristic
32C22×C4×C53—22no—
33C22×C4×C53C22⋊C412yes—
34C22×C4×C53C22×C411yescharacteristic
35C22×Dic53—22no—
36C22×Dic53C22⋊C411yescharacteristic
37C22×Dic53C2×D412yes—
38C2×C4×D53—22no—
39C2×C4×D53—22no—
40C2×C4×D53—22no—
41C2×C4×D53—24no—
42C2×C4×D53—24no—
43C2×C4×D53—42no—
44C2×C4×D53—44no—
45C2×C4×D53—44no—
46C2×C4×D53—44no—
47C2×#88324—28no—
48C2×#88324—44no—
49C2×#88324—44no—
50C4⋊C4×C53—42no—
51C42×C53—22no—
52C4⋊Dic53—42no—
53#11719919—44no—
54C4×Dic53—24no—
55C4×Dic53#4114yes—
56C23×C53C2×C22⋊C411yescharacteristic
57C22×D53—21no—
58C22×D53—21no—
59C22×D53—22no—
60C22×D53#10112yes—
61C22×D53#10414yes—
62C2×C4×C53—21no—
63C2×C4×C53—21no—
64C2×C4×C53—22no—
65C2×C4×C53—22no—
66C2×C4×C53—22no—
67C2×C4×C53—42no—
68C2×C4×C53—42no—
69C2×C4×C53—42no—
70C2×C4×C53#11712yes—
71C2×Dic53—21no—
72C2×Dic53—21no—
73C2×Dic53—22no—
74C2×Dic53—22no—
75C2×Dic53—42no—
76C2×Dic53—42no—
77C2×Dic53—42no—
78C2×Dic53#10012yes—
79C2×Dic53#12314yes—
80C4×D53—28no—
81C4×D53—48no—
82C4×D53—88no—
83#88324—48no—
84#8719—531nomaximal, Sylow
85C22×C53#38111yescharacteristic
86C22×C53C2×#10011yescharacteristic
87C22×C53C2×#10111yescharacteristic
88C22×C53C2×#10412yes—
89C22×C53#42112yes—
90C2×D53—22no—
91C2×D53—24no—
92C2×D53—24no—
93C2×D53—22no—
94C2×D53#33014yes—
95C4×C53—22no—
96C4×C53—42no—
97C4×C53—82no—
98Dic53—22no—
99Dic53—24no—
100Dic53—82no—
101C2×#382—531no—
102#1749—532no—
103#1295—534no—
104C2×C53C2×#33011yescharacteristic
105C2×C53#152712yes—
106C2×C53#153411yescharacteristic
107C2×C53#182111yescharacteristic
108C2×C53#182612yes—
109D53—24no—
110C22×C4⋊C4—532no—
111C22×C42—531no—
112C2×C22⋊C8—1062no—
113C2×#97—534no—
114#382—532no—
115#382—531no—
116#382—1062no—
117#382#615711yescharacteristic
118C2×#95—1062no—
119#336—1062no—
120C53#871911yescharacteristic, complemented, Sylow
121C23×C4—531no—
122C23×C4—532no—
123C23×C4—1062no—
124C22×C8—1064no—
125C2×C4⋊C4—532no—
126C2×C4⋊C4—1062no—
127C2×C4⋊C4—2124no—
128C2×C4⋊C4C2×#615712yes—
129C2×C42—531no—
130C2×C42—532no—
131C2×C42—1064no—
132C2×C42C2×#615711yescharacteristic
133C22⋊C8—1068no—
134#97—1068no—
135#95—22no—
136#95—1064no—
137#95—1062no—
138C24—531no—
139C22×C4—22no—
140C22×C4—531no—
141C22×C4—532no—
142C22×C4—1062no—
143C22×C4—1064no—
144C22×C4—1062no—
145C22×C4—1064no—
146C22×C4—1062no—
147C22×C4—1062no—
148C22×C4—2122no—
149C22×C4—2124no—
150C22×C4—2124no—
151C22×C4—2124no—
152C22×C4C22⋊#615712yes—
153C22×C4C22×#615711yescharacteristic
154C2×C8—1068no—
155C2×C8—2124no—
156C2×C8—2124no—
157C4⋊C4—42no—
158C4⋊C4—2122no—
159C4⋊C4—2124no—
160C42—22no—
161C42—534no—
162C42—1064no—
163C23—532no—
164C23—534no—
165C23—1061no—
166C23—1061no—
167C23—1062no—
168C23C2×C22⋊#615711yescharacteristic
169C2×C4—21no—
170C2×C4—21no—
171C2×C4—22no—
172C2×C4—22no—
173C2×C4—22no—
174C2×C4—42no—
175C2×C4—42no—
176C2×C4—42no—
177C2×C4—534no—
178C2×C4—532no—
179C2×C4—1068no—
180C2×C4—1061no—
181C2×C4—1061no—
182C2×C4—1062no—
183C2×C4—1062no—
184C2×C4—4248no—
185C2×C4—2128no—
186C2×C4—2122no—
187C2×C4—2122no—
188C2×C4—2122no—
189C2×C4#1313329612yes—
190C8—2128no—
191C22—534no—
192C22—1062no—
193C22—1064no—
194C22—1064no—
195C22—1062no—
196C22#1681156611yescharacteristic
197C22D53⋊#10011yescharacteristic
198C22D53⋊#10111yescharacteristic
199C22D53⋊#10412yes—
200C22#1681162012yes—
201C4—22no—
202C4—42no—
203C4—82no—
204C4—1062no—
205C4—1064no—
206C4—4242no—
207C2—1064no—
208C2D53⋊#33011yescharacteristic
209C2#2029017512yes—
210C2#2029019811yescharacteristic
211C2#2029061511yescharacteristic
212C2#2029062312yes—
subgroupG/H
centerC23C2×C22⋊#6157
commutatorC22×C4×C53C22×C4
FrattiniC22×C4C22×#6157
FittingC53×#382C4
socleC23×C53C2×C22⋊C4
prime radicalC23×D53C22⋊C4
cosocleC2×C4×Dic53C23
hypercenter#382#6157
hypocenterC53#8719
LCSG ▷ C22×C4×C53 ▷ C22×C53 ▷ C53
UCSC1 ◁ C23 ◁ C2×C42 ◁ #382

Complements

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

NH ≅ G/Ntype
2. #20289591C2semidirect
120. C53#8719semidirect

Maximal subgroups

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

subgroupindex
#202904422
#202895912
#382×D532
#871953