Finite Group Databasebeta

← #28303348

Subgroups — #28303348

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#20289591C212yesmaximal, complemented
3#20289591C212yesmaximal, complemented
4#382×D53C211yesmaximal, characteristic
5C2×#13133274—22no—
6C2×#13133272C2214yes—
7#16811489—22no—
8C2×C4⋊C4×D53C411yescharacteristic
9C2×C4⋊C4×D53C411yescharacteristic
10C2×C42×D53C2211yescharacteristic
11#16810489C411yescharacteristic
12#16810488C2211yescharacteristic
13#16810488C2211yescharacteristic
14#16810487—22no—
15#95×D53—22no—
16C53×#382C411yescharacteristic
17C22×#88324—24no—
18#13133274—28no—
19#13133272—28no—
20C22×C4×D53—21no—
21C22×C4×D53—21no—
22C22×C4×D53C2×C411yescharacteristic
23C22×C4×D53D412yes—
24C2×C4⋊Dic53C2×C411yescharacteristic
25C2×C4⋊Dic53C2×C411yescharacteristic
26C2×#11719919—21no—
27C2×#11719919—21no—
28C4⋊C4×D53—42no—
29C4⋊C4×D53—42no—
30C2×C4×Dic53D412yes—
31C2×C4×Dic53C2311yescharacteristic
32C42×D53—24no—
33#13133124—22no—
34#13133124—22no—
35#13133124—22no—
36C2×C4⋊C4×C53C2×C411yescharacteristic
37C2×C4⋊C4×C53C2×C411yescharacteristic
38C2×C42×C53C2×C411yescharacteristic
39#95×C53—22no—
40C23×D53C22⋊C411yescharacteristic
41C22×C4×C53—21no—
42C22×C4×C53—21no—
43C22×C4×C53C22⋊C412yes—
44C22×C4×C53C22×C411yescharacteristic
45C22×Dic53—21no—
46C22×Dic53—21no—
47C22×Dic53C22⋊C411yescharacteristic
48C22×Dic53C2×D412yes—
49C2×C4×D53—22no—
50C2×C4×D53—22no—
51C2×C4×D53—22no—
52C2×C4×D53—24no—
53C2×C4×D53—24no—
54C2×C4×D53—42no—
55C2×C4×D53—44no—
56C2×C4×D53—42no—
57C2×C4×D53—42no—
58C2×C4×D53—44no—
59C2×#88324—28no—
60C2×#88324—44no—
61C2×#88324—44no—
62C4⋊C4×C53—41no—
63C4⋊C4×C53—41no—
64C42×C53—22no—
65C4⋊Dic53—41no—
66C4⋊Dic53—41no—
67#11719919—42no—
68#11719919—42no—
69C4×Dic53—24no—
70C4×Dic53#4114yes—
71C23×C53C2×C22⋊C411yescharacteristic
72C22×D53—21no—
73C22×D53—21no—
74C22×D53—22no—
75C22×D53#10012yes—
76C22×D53#10414yes—
77C2×C4×C53—21no—
78C2×C4×C53—21no—
79C2×C4×C53—22no—
80C2×C4×C53—22no—
81C2×C4×C53—22no—
82C2×C4×C53—41no—
83C2×C4×C53—41no—
84C2×C4×C53—42no—
85C2×C4×C53—42no—
86C2×C4×C53#11712yes—
87C2×Dic53—21no—
88C2×Dic53—21no—
89C2×Dic53—22no—
90C2×Dic53—22no—
91C2×Dic53—41no—
92C2×Dic53—41no—
93C2×Dic53—42no—
94C2×Dic53—42no—
95C2×Dic53#10112yes—
96C2×Dic53#12314yes—
97C4×D53—28no—
98C4×D53—48no—
99C4×D53—84no—
100C4×D53—84no—
101#88324—48no—
102#8718—531nomaximal, Sylow
103C22×C53#38111yescharacteristic
104C22×C53C2×#10011yescharacteristic
105C22×C53C2×#10111yescharacteristic
106C22×C53C2×#10412yes—
107C22×C53#42112yes—
108C2×D53—22no—
109C2×D53—24no—
110C2×D53—24no—
111C2×D53—22no—
112C2×D53#32914yes—
113C4×C53—22no—
114C4×C53—42no—
115C4×C53—81no—
116C4×C53—81no—
117Dic53—22no—
118Dic53—24no—
119Dic53—81no—
120Dic53—81no—
121C2×#382—531no—
122#1749—532no—
123#1295—532no—
124#1295—532no—
125C2×C53C2×#32911yescharacteristic
126C2×C53#152812yes—
127C2×C53#153311yescharacteristic
128C2×C53#182111yescharacteristic
129C2×C53#182612yes—
130D53—24no—
131C22×C4⋊C4—531no—
132C22×C4⋊C4—531no—
133C22×C42—531no—
134C2×C22⋊C8—1062no—
135C2×#97—534no—
136#382—531no—
137#382—531no—
138#382—531no—
139#382—1062no—
140#382#615711yescharacteristic
141C2×#95—1062no—
142#336—1062no—
143C53#871811yescharacteristic, complemented, Sylow
144C23×C4—531no—
145C23×C4—532no—
146C23×C4—1061no—
147C23×C4—1061no—
148C22×C8—1064no—
149C2×C4⋊C4—531no—
150C2×C4⋊C4—531no—
151C2×C4⋊C4—1061no—
152C2×C4⋊C4—1061no—
153C2×C4⋊C4—2122no—
154C2×C4⋊C4—2122no—
155C2×C4⋊C4C2×#615711yescharacteristic
156C2×C4⋊C4C2×#615711yescharacteristic
157C2×C42—531no—
158C2×C42—532no—
159C2×C42—1064no—
160C2×C42C2×#615711yescharacteristic
161C22⋊C8—1068no—
162#97—1068no—
163#95—22no—
164#95—1062no—
165#95—1062no—
166#95—1062no—
167C24—531no—
168C22×C4—21no—
169C22×C4—21no—
170C22×C4—531no—
171C22×C4—532no—
172C22×C4—1062no—
173C22×C4—1064no—
174C22×C4—1062no—
175C22×C4—1064no—
176C22×C4—1062no—
177C22×C4—1061no—
178C22×C4—1061no—
179C22×C4—2122no—
180C22×C4—2122no—
181C22×C4—2122no—
182C22×C4—2124no—
183C22×C4—2124no—
184C22×C4C22⋊#615712yes—
185C22×C4C22×#615711yescharacteristic
186C2×C8—1068no—
187C2×C8—2124no—
188C2×C8—2124no—
189C4⋊C4—41no—
190C4⋊C4—41no—
191C4⋊C4—2121no—
192C4⋊C4—2121no—
193C4⋊C4—2122no—
194C4⋊C4—2122no—
195C42—22no—
196C42—534no—
197C42—1064no—
198C23—532no—
199C23—534no—
200C23—1061no—
201C23—1061no—
202C23—1062no—
203C23C2×C22⋊#615711yescharacteristic
204C2×C4—21no—
205C2×C4—21no—
206C2×C4—22no—
207C2×C4—22no—
208C2×C4—22no—
209C2×C4—41no—
210C2×C4—41no—
211C2×C4—42no—
212C2×C4—42no—
213C2×C4—534no—
214C2×C4—532no—
215C2×C4—1068no—
216C2×C4—1061no—
217C2×C4—1061no—
218C2×C4—1062no—
219C2×C4—1062no—
220C2×C4—4244no—
221C2×C4—4244no—
222C2×C4—2128no—
223C2×C4—2121no—
224C2×C4—2121no—
225C2×C4—2122no—
226C2×C4—2122no—
227C2×C4#1313329612yes—
228C8—2128no—
229C22—534no—
230C22—1062no—
231C22—1064no—
232C22—1064no—
233C22—1062no—
234C22#1681156611yescharacteristic
235C22D53⋊#10011yescharacteristic
236C22D53⋊#10111yescharacteristic
237C22D53⋊#10412yes—
238C22#1681162012yes—
239C4—22no—
240C4—42no—
241C4—81no—
242C4—81no—
243C4—1062no—
244C4—1064no—
245C4—4241no—
246C4—4241no—
247C2—1064no—
248C2D53⋊#32911yescharacteristic
249C2#2029017812yes—
250C2#2029019511yescharacteristic
251C2#2029061511yescharacteristic
252C2#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#8718
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
3. #20289591C2semidirect
143. C53#8718semidirect

Maximal subgroups

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

subgroupindex
#202904422
#202895912
#382×D532
#871853