Finite Group Databasebeta

← #28308222

Subgroups — #28308222

Order 13568.

418 conjugacy classes of subgroups; only the 76 normal subgroups are shown.

normal subgroups only

This group has 418 conjugacy classes of subgroups — too many to draw. Only its 76 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#20289966C211yesmaximal, characteristic
2#20289966C211yesmaximal, characteristic
3#20289660C214yesmaximal
4#20277339C211yesmaximal, characteristic
5#16811643—21no—
6#16811643—21no—
7#16811468—21no—
8#16811468—21no—
9#16811466C2212yes—
10#16811466C2212yes—
11C2×#13133176C411yescharacteristic
12C2×#13133176C2211yescharacteristic
13#16810519—21no—
14#16810519—21no—
15#16810496C412yes—
16#16810496C2212yes—
17#16810492—21no—
18#16810488—21no—
19C22×C4⋊C4×C53C411yescharacteristic
20#13133284—41no—
21#13133284—41no—
22C22⋊#88324—22no—
23C22⋊#88324—22no—
24#13133272—41no—
25#13133272—41no—
26#13133176—24no—
27#13133176—41no—
28#13133176—41no—
29C2×C4⋊Dic53—21no—
30C2×C4⋊Dic53D411yescharacteristic
31C2×C4⋊Dic53D411yescharacteristic
32C2×#11719919—22no—
33C2×#11719919—22no—
34C2×C22⋊Dic53C2×C412yes—
35C2×C22⋊Dic53C2×C411yescharacteristic
36C2×C22⋊Dic53C2311yescharacteristic
37C2×C4×Dic53—21no—
38C2×C4×Dic53D411yescharacteristic
39C2×C4×Dic53D411yescharacteristic
40#13133124—22no—
41#13133124—22no—
42C23×C4×C53C2×C411yescharacteristic
43C23×C4×C53C2×C412yes—
44C2×C4⋊C4×C53—21no—
45C2×C4⋊C4×C53—21no—
46C2×C4⋊C4×C53—41no—
47C2×C4⋊C4×C53—41no—
48C24×C53C22×C411yescharacteristic
49C22×C4×C53—22no—
50C22×C4×C53—21no—
51C22×C4×C53—21no—
52C22×C4×C53—22no—
53C22×C4×C53—22no—
54C22×C4×C53—42no—
55C22×C4×C53—82no—
56C22×C4×C53C22⋊C411yescharacteristic
57C22×C4×C53C22⋊C411yescharacteristic
58C22×Dic53—22no—
59C22×Dic53C22⋊C411yescharacteristic
60C22×Dic53C22⋊C411yescharacteristic
61C22×Dic53C2×D411yescharacteristic
62C22×Dic53C2×D411yescharacteristic
63C2×#88324—42no—
64C2×#88324—42no—
65C4⋊C4×C53—42no—
66C4⋊C4×C53—41no—
67C4⋊C4×C53—41no—
68C22⋊Dic53—22no—
69C22⋊Dic53—41no—
70C22⋊Dic53—41no—
71C22⋊Dic53M1614yes—
72C4⋊Dic53—24no—
73C4⋊Dic53—41no—
74C4⋊Dic53—41no—
75#11719919—82no—
76#11719919—82no—
77C4×Dic53—24no—
78C4×Dic53—21no—
79C4×Dic53—21no—
80C4×Dic53—21no—
81C4×Dic53—21no—
82C23×C53—21no—
83C23×C53—21no—
84C23×C53—41no—
85C23×C53—41no—
86C23×C53C2×C22⋊C411yescharacteristic
87C23×C53C2×M1612yes—
88C2×C4×C53—24no—
89C2×C4×C53—24no—
90C2×C4×C53—21no—
91C2×C4×C53—21no—
92C2×C4×C53—21no—
93C2×C4×C53—21no—
94C2×C4×C53—42no—
95C2×C4×C53—42no—
96C2×C4×C53—42no—
97C2×C4×C53—84no—
98C2×C4×C53#9911yescharacteristic
99C2×C4×C53#9911yescharacteristic
100C2×C4×C53#10112yes—
101C2×Dic53—24no—
102C2×Dic53—21no—
103C2×Dic53—21no—
104C2×Dic53—21no—
105C2×Dic53—21no—
106C2×Dic53—42no—
107C2×Dic53—42no—
108C2×Dic53—41no—
109C2×Dic53—41no—
110C2×Dic53—41no—
111C2×Dic53—41no—
112#88324—82no—
113#88324—82no—
114#11520—531nomaximal, Sylow
115C22×C53—21no—
116C22×C53—21no—
117C22×C53—22no—
118C22×C53—42no—
119C22×C53—42no—
120C22×C53—41no—
121C22×C53—41no—
122C22×C53#40711yescharacteristic
123C22×C53C2×#9911yescharacteristic
124C22×C53C2×#10111yescharacteristic
125C4×C53—21no—
126C4×C53—21no—
127C4×C53—22no—
128C4×C53—82no—
129Dic53—44no—
130Dic53—41no—
131Dic53—41no—
132Dic53—41no—
133Dic53—41no—
134#2317—531no—
135#1464—531no—
136#1464—531no—
137#1326—534no—
138C2×C53—21no—
139C2×C53—21no—
140C2×C53—42no—
141C2×C53#146311yescharacteristic
142C2×C53#212211yescharacteristic
143C2×C53#212311yescharacteristic
144C2×#117—531no—
145C2×#117—531no—
146C22×C4⋊C4#615711yescharacteristic
147#432—1061no—
148#432—1061no—
149#389—1061no—
150#389—1061no—
151#385—532no—
152#385—532no—
153#384—1061no—
154#382—1061no—
155#324—1061no—
156#324—1061no—
157#323—532no—
158#323—532no—
159C53#1152011yescharacteristic, complemented, Sylow
160C23×C4C2×#615712yes—
161C23×C4C2×#615711yescharacteristic
162#117—1064no—
163#117—2121no—
164#117—2121no—
165C2×C4⋊C4—21no—
166C2×C4⋊C4—21no—
167C2×C4⋊C4—41no—
168C2×C4⋊C4—41no—
169C2×C4⋊C4—531no—
170C2×C4⋊C4—531no—
171C2×C4⋊C4—1061no—
172C2×C4⋊C4—1062no—
173C2×C4⋊C4—1062no—
174C2×C22⋊C4—532no—
175C2×C22⋊C4—531no—
176C2×C22⋊C4—531no—
177C2×C42—531no—
178C2×C42—531no—
179C2×C42—1061no—
180C4⋊C8—2121no—
181C4⋊C8—2121no—
182C22⋊C8—1062no—
183C22⋊C8—1062no—
184#97—2121no—
185#97—2121no—
186#95—1062no—
187#95—1062no—
188C24C22×#615711yescharacteristic
189C22×C4—22no—
190C22×C4—21no—
191C22×C4—21no—
192C22×C4—22no—
193C22×C4—22no—
194C22×C4—42no—
195C22×C4—82no—
196C22×C4—531no—
197C22×C4—531no—
198C22×C4—531no—
199C22×C4—531no—
200C22×C4—1062no—
201C22×C4C22⋊#615711yescharacteristic
202C22×C4C22⋊#615711yescharacteristic
203C2×C8—2122no—
204C2×C8—2122no—
205C4⋊C4—42no—
206C4⋊C4—41no—
207C4⋊C4—41no—
208C4⋊C4—1064no—
209C4⋊C4—4242no—
210C4⋊C4—4242no—
211C4⋊C4—2121no—
212C4⋊C4—2121no—
213C22⋊C4—534no—
214C22⋊C4—1062no—
215C22⋊C4—2121no—
216C22⋊C4—2121no—
217C42—1064no—
218C42—1061no—
219C42—1061no—
220C42—1061no—
221C42—1061no—
222C23—21no—
223C23—21no—
224C23—41no—
225C23—41no—
226C23C2×C22⋊#615711yescharacteristic
227C23D53⋊M1612yes—
228C2×C4—24no—
229C2×C4—24no—
230C2×C4—21no—
231C2×C4—21no—
232C2×C4—21no—
233C2×C4—21no—
234C2×C4—42no—
235C2×C4—42no—
236C2×C4—42no—
237C2×C4—84no—
238C2×C4—1064no—
239C2×C4—1061no—
240C2×C4—1061no—
241C2×C4—1061no—
242C2×C4—1061no—
243C2×C4—2122no—
244C2×C4—2122no—
245C2×C4—2121no—
246C2×C4—2121no—
247C2×C4—2121no—
248C2×C4—2121no—
249C2×C4#1313327511yescharacteristic
250C2×C4#1313327511yescharacteristic
251C2×C4#1313327812yes—
252C8—4242no—
253C8—4242no—
254C22—21no—
255C22—21no—
256C22—22no—
257C22—42no—
258C22—42no—
259C22—41no—
260C22—41no—
261C22#1681159511yescharacteristic
262C22C2×#1313327511yescharacteristic
263C22C2×#1313327811yescharacteristic
264C4—21no—
265C4—21no—
266C4—22no—
267C4—82no—
268C4—2124no—
269C4—2121no—
270C4—2121no—
271C4—2121no—
272C4—2121no—
273C2—21no—
274C2—21no—
275C2—42no—
276C2#2028996511yescharacteristic
277C2#2029097411yescharacteristic
278C2#2029097711yescharacteristic
subgroupG/H
centerC22C2×#13133275
commutator, prime radicalC24×C53C22×C4
FrattiniC24C22×#6157
FittingC22×C4⋊C4×C53C4
socleC22×C53C2×#99
cosocleC2×C22⋊Dic53C23
hypercenterC22×C4⋊C4#6157
hypocenterC53#11520
LCSG ▷ C24×C53 ▷ C22×C53 ▷ C2×C53 ▷ C53
UCSC1 ◁ C22 ◁ C22×C4 ◁ C23×C4 ◁ C22×C4⋊C4

Complements

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

NH ≅ G/Ntype
159. C53#11520semidirect

Maximal subgroups

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

subgroupindex
#202899662
#202896602
#202773392
#1152053