Finite Group Databasebeta

← #28311199

Subgroups — #28311199

Order 13568.

468 conjugacy classes of subgroups; only the 90 normal subgroups are shown.

normal subgroups only

This group has 468 conjugacy classes of subgroups — too many to draw. Only its 90 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
1C2×#16811534C212yesmaximal
2#20290581C212yesmaximal
3#20289812C212yesmaximal
4C4×#13133217C211yesmaximal, characteristic
5#16811626—22no—
6C2×#13133278C2214yes—
7#16811534—24no—
8#16811503—22no—
9C2×#13133217C2211yescharacteristic
10C2×C4×Dic106C411yescharacteristic
11C2×C4×Dic106C2211yescharacteristic
12#16810529C411yescharacteristic
13#16810529C2211yescharacteristic
14#16810521—22no—
15#16810493C411yescharacteristic
16C4×C4⋊Dic53—22no—
17C43×C53C411yescharacteristic
18C2×#11719940—24no—
19#13133284—42no—
20C4⋊#88324—42no—
21#13133278—24no—
22#13133278—24no—
23C22×Dic106C2×C411yescharacteristic
24C22×Dic106C2311yescharacteristic
25#13133217—22no—
26#13133217D412yes—
27#13133217Q812yes—
28C4×Dic106—41no—
29C4×Dic106—41no—
30C4×Dic106—41no—
31C4×Dic106—41no—
32C2×C4⋊Dic53—22no—
33C2×C4⋊Dic53—22no—
34C2×C4⋊Dic53C2×C411yescharacteristic
35C2×C4⋊Dic53C2×C411yescharacteristic
36C2×#11719919—21no—
37C2×#11719919D412yes—
38C2×C4×Dic53—21no—
39C2×C4×Dic53D412yes—
40#13133124—22no—
41#13133124—22no—
42C2×C42×C53—21no—
43C2×C42×C53—21no—
44C2×C42×C53C2×C411yescharacteristic
45C2×C42×C53C2×C411yescharacteristic
46C2×C42×C53C2×C411yescharacteristic
47C22×C4×C53—21no—
48C22×C4×C53—21no—
49C22×C4×C53C22⋊C411yescharacteristic
50C22×C4×C53C22⋊C411yescharacteristic
51C22×C4×C53C22×C411yescharacteristic
52C22×Dic53—21no—
53C22×Dic53—21no—
54C22×Dic53C22⋊C412yes—
55C22×Dic53C2×D412yes—
56C2×Dic106—21no—
57C2×Dic106—41no—
58C2×Dic106—41no—
59C2×Dic106—41no—
60C2×Dic106—41no—
61C2×Dic106C4⋊C412yes—
62C2×Dic106C2×D411yescharacteristic
63C2×Dic106C2×Q811yescharacteristic
64C2×Dic106#4112yes—
65#11719940—44no—
66#11719940—44no—
67C2×#88324—44no—
68C42×C53—24no—
69C42×C53—21no—
70C42×C53—21no—
71C42×C53—21no—
72C42×C53—42no—
73C42×C53—41no—
74C42×C53C4⋊C412yes—
75C4⋊Dic53—24no—
76C4⋊Dic53—24no—
77C4⋊Dic53—41no—
78C4⋊Dic53—44no—
79C4⋊Dic53—41no—
80#11719919—42no—
81#11719919—42no—
82C4×Dic53—22no—
83C4×Dic53—22no—
84C4×Dic53—41no—
85C4×Dic53—41no—
86C23×C53C2×C22⋊C411yescharacteristic
87C2×C4×C53—22no—
88C2×C4×C53—22no—
89C2×C4×C53—22no—
90C2×C4×C53—21no—
91C2×C4×C53—21no—
92C2×C4×C53—22no—
93C2×C4×C53—22no—
94C2×C4×C53—21no—
95C2×C4×C53—41no—
96C2×C4×C53—41no—
97C2×C4×C53—41no—
98C2×C4×C53#9911yescharacteristic
99C2×C4×C53#9911yescharacteristic
100C2×C4×C53C2×C4⋊C411yescharacteristic
101C2×C4×C53#11711yescharacteristic
102C2×Dic53—22no—
103C2×Dic53—22no—
104C2×Dic53—22no—
105C2×Dic53—22no—
106C2×Dic53—41no—
107C2×Dic53—41no—
108C2×Dic53—42no—
109C2×Dic53—42no—
110C2×Dic53—41no—
111C2×Dic53#12112yes—
112C2×Dic53C22⋊Q812yes—
113Dic106—41no—
114Dic106—41no—
115Dic106—42no—
116Dic106—42no—
117Dic106—42no—
118#88324—84no—
119#12802—531nomaximal, Sylow
120C22×C53—21no—
121C22×C53—21no—
122C22×C53#38011yescharacteristic
123C22×C53C2×#9911yescharacteristic
124C22×C53#41011yescharacteristic
125C4×C53—24no—
126C4×C53—21no—
127C4×C53—21no—
128C4×C53—21no—
129C4×C53—42no—
130C4×C53—41no—
131C4×C53#35612yescomplemented
132Dic53—22no—
133Dic53—22no—
134Dic53—42no—
135Dic53—42no—
136Dic53—81no—
137C4×C4⋊Q8—531no—
138C2×#356—532no—
139#1801—532no—
140#1394—532no—
141C2×C53—21no—
142C2×C53—21no—
143C2×C53#179911yescharacteristic
144C2×C53C2×#35611yescharacteristic
145C2×C53#213211yescharacteristic
146C2×C4⋊Q8—531no—
147C2×C4×Q8—531no—
148C2×C4×Q8—531no—
149#423—1062no—
150C2×#101—534no—
151#391—531no—
152#391—531no—
153#389—1062no—
154#384—531no—
155C4×C4⋊C4—1062no—
156C43#615711yescharacteristic
157#356—1064no—
158#343—1062no—
159C53#1280211yescharacteristic, complemented, Sylow
160C22×Q8—531no—
161C22×Q8—531no—
162C2×M16—1064no—
163C4⋊Q8—532no—
164C4⋊Q8—532no—
165C4⋊Q8—1062no—
166C4×Q8—2121no—
167C4×Q8—2121no—
168C4×Q8—2121no—
169C4×Q8—2121no—
170C2×C4⋊C4—532no—
171C2×C4⋊C4—531no—
172C2×C4⋊C4—531no—
173C2×C4⋊C4—1062no—
174C2×C4⋊C4—1062no—
175C2×C4⋊C4—1061no—
176C2×C42—21no—
177C2×C42—21no—
178C2×C42—532no—
179C2×C42—1061no—
180C2×C42C2×#615711yescharacteristic
181C2×C42C2×#615711yescharacteristic
182C2×C42C2×#615711yescharacteristic
183C4⋊C8—2122no—
184C4⋊C8—2122no—
185#101—1064no—
186#101—1064no—
187#95—1062no—
188#95—1062no—
189C2×Q8—531no—
190C2×Q8—531no—
191C2×Q8—532no—
192C2×Q8—532no—
193C2×Q8—1061no—
194C2×Q8—2121no—
195C2×Q8—2121no—
196C2×Q8—2121no—
197C2×Q8—2121no—
198C22×C4—21no—
199C22×C4—21no—
200C22×C4—532no—
201C22×C4—532no—
202C22×C4—1061no—
203C22×C4—1061no—
204C22×C4C22⋊#615711yescharacteristic
205C22×C4C22⋊#615711yescharacteristic
206C22×C4C22×#615711yescharacteristic
207M16—2124no—
208M16—2124no—
209C2×C8—2124no—
210C4⋊C4—1064no—
211C4⋊C4—1064no—
212C4⋊C4—2122no—
213C4⋊C4—2121no—
214C4⋊C4—2121no—
215C4⋊C4—2122no—
216C4⋊C4—2124no—
217C42—24no—
218C42—21no—
219C42—21no—
220C42—21no—
221C42—41no—
222C42—42no—
223C42—1062no—
224C42—1062no—
225C42—2121no—
226C42—2121no—
227C42C4⋊#615712yes—
228C23C2×C22⋊#615711yescharacteristic
229Q8—2121no—
230Q8—2121no—
231Q8—2122no—
232Q8—2122no—
233Q8—2122no—
234C2×C4—22no—
235C2×C4—22no—
236C2×C4—22no—
237C2×C4—21no—
238C2×C4—21no—
239C2×C4—22no—
240C2×C4—22no—
241C2×C4—21no—
242C2×C4—41no—
243C2×C4—41no—
244C2×C4—41no—
245C2×C4—532no—
246C2×C4—532no—
247C2×C4—1062no—
248C2×C4—1062no—
249C2×C4—1062no—
250C2×C4—1062no—
251C2×C4—2122no—
252C2×C4—2121no—
253C2×C4—2121no—
254C2×C4—2121no—
255C2×C4—2122no—
256C2×C4#1313327611yescharacteristic
257C2×C4#1313327611yescharacteristic
258C2×C4C2×C4⋊#615711yescharacteristic
259C2×C4#1313329611yescharacteristic
260C8—4244no—
261C22—21no—
262C22—21no—
263C22#1681156511yescharacteristic
264C22C2×#1313327611yescharacteristic
265C22#1681160211yescharacteristic
266C4—24no—
267C4—21no—
268C4—21no—
269C4—21no—
270C4—42no—
271C4—41no—
272C4—1062no—
273C4—1062no—
274C4—4241no—
275C4—2122no—
276C4—2122no—
277C4#1681153412yescomplemented
278C2—21no—
279C2—21no—
280C2#2029057611yescharacteristic
281C2C2×#1681153411yescharacteristic
282C2#2029100811yescharacteristic
subgroupG/H
centerC22C2×#13133276
commutatorC22×C4×C53C22×C4
FrattiniC22×C4C22×#6157
FittingC43×C53C4
socleC22×C53C2×#99
prime radicalC23×C53C2×C22⋊C4
cosocleC22×Dic106C23
hypercenterC43#6157
hypocenterC53#12802
LCSG ▷ C22×C4×C53 ▷ C22×C53 ▷ C2×C53 ▷ C53
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×C42 ◁ C43

Complements

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

NH ≅ G/Ntype
131. C4×C53#356semidirect
159. C53#12802semidirect
277. C4#16811534semidirect

Maximal subgroups

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

subgroupindex
C2×#168115342
#202905812
#202898122
C4×#131332172
#1280253