Finite Group Databasebeta

← #27205921

Subgroups — #27205921

Order 13184.

420 conjugacy classes of subgroups; only the 125 normal subgroups are shown.

normal subgroups only

This group has 420 conjugacy classes of subgroups — too many to draw. Only its 125 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×#15693000C211yesmaximal, characteristic, complemented
2#20268132C212yesmaximal, complemented
3#20268119C211yesmaximal, characteristic, complemented
4#20268102C211yesmaximal, characteristic, complemented
5#20268030C212yesmaximal, complemented
6#20268018C212yesmaximal, complemented
7#20267953C212yesmaximal, complemented
8#20267946C211yesmaximal, characteristic, complemented
9#20267929C211yesmaximal, characteristic, complemented
10C2×C22⋊(C103⋊C8)C211yesmaximal, characteristic, complemented
11#525×C103C211yesmaximal, characteristic
12C22×Dic206C2211yescharacteristic
13C2×#13110095C2212yescomplemented
14C2×#13110093C2212yescomplemented
15C22×C103⋊C8C2212yes—
16#15693000—21no—
17#15693000—21no—
18#15693000C2212yes—
19#15693000C2212yes—
20C2×C4⋊Dic103C2211yescharacteristic
21C2×Dic103⋊C4—21no—
22C2×C22⋊Dic103—21no—
23#15692954C2212yescomplemented
24#15692952C2212yescomplemented
25#15692945C2212yescomplemented
26#15692944C2212yescomplemented
27#15692944C2212yescomplemented
28#15692942C2212yescomplemented
29C22⋊(C103⋊C8)C2211yescharacteristic
30C22⋊(C103⋊C8)C2211yescharacteristic
31C22⋊(C103⋊C8)C2212yes—
32C2×#41×C103C2211yescharacteristic
33C23×C4×C103C2211yescharacteristic
34#123×C103—21no—
35C22⋊Q8×C103C2211yescharacteristic
36C22⋊Q8×C103C2211yescharacteristic
37#121×C103C2211yescharacteristic
38#121×C103C2211yescharacteristic
39#120×C103—21no—
40C4×D4×C103—21no—
41C4×D4×C103—21no—
42#117×C103C2211yescharacteristic
43C2×Dic206—21no—
44C2×Dic206—42no—
45C2×Dic206C2312yes—
46C22×Dic103—21no—
47C22×Dic103—21no—
48#13110095—42no—
49#13110093—42no—
50C2×C103⋊C8—42no—
51C2×C103⋊C8C2312yes—
52C2×C103⋊C8C2312yes—
53C4⋊Dic103—21no—
54C4⋊Dic103C2312yes—
55Dic103⋊C4—22no—
56Dic103⋊C4—22no—
57C22⋊Dic103—22no—
58C22⋊Dic103—22no—
59C24×C103D411yescharacteristic
60#41×C103—42no—
61C2×Q8×C103C2311yescharacteristic
62C2×D4×C103—21no—
63C2×D4×C103—21no—
64C2×D4×C103—21no—
65C2×D4×C103C2311yescharacteristic
66C22×C4×C103—21no—
67C22×C4×C103—42no—
68C22×C4×C103D411yescharacteristic
69C22×C4×C103D411yescharacteristic
70C22×C4×C103D411yescharacteristic
71C22×C4×C103C2311yescharacteristic
72C22×C4×C103C2311yescharacteristic
73C22×C4×C103C2311yescharacteristic
74C4⋊C4×C103—21no—
75C4⋊C4×C103—21no—
76C4⋊C4×C103C2311yescharacteristic
77C4⋊C4×C103C2311yescharacteristic
78C22⋊C4×C103—21no—
79C22⋊C4×C103—21no—
80C22⋊C4×C103—21no—
81C22⋊C4×C103—21no—
82C22⋊C4×C103—21no—
83C42×C103—21no—
84C23×C103—22no—
85C23×C103—22no—
86C23×C103—21no—
87C23×C103—41no—
88C23×C103C2×D411yescharacteristic
89C23×C103C2×D411yescharacteristic
90C23×C103C2×D411yescharacteristic
91Q8×C103—22no—
92D4×C103—22no—
93D4×C103—42no—
94D4×C103—42no—
95D4×C103—42no—
96C2×C4×C103—22no—
97C2×C4×C103—22no—
98C2×C4×C103—22no—
99C2×C4×C103—21no—
100C2×C4×C103—21no—
101C2×C4×C103—21no—
102C2×C4×C103—41no—
103C2×C4×C103—41no—
104C2×C4×C103—41no—
105C2×C4×C103—42no—
106C2×C4×C103C2×D411yescharacteristic
107C2×C4×C103C2×D411yescharacteristic
108C2×C4×C103C2×D411yescharacteristic
109C2×C4×C103C2411yescharacteristic
110C2×Dic103—22no—
111C2×Dic103—22no—
112C2×Dic103—42no—
113C2×Dic103—42no—
114Dic206—22no—
115Dic206—22no—
116Dic206—42no—
117C103⋊C8—22no—
118C103⋊C8—22no—
119C22×C103—21no—
120C22×C103—21no—
121C22×C103—21no—
122C22×C103—21no—
123C22×C103—21no—
124C22×C103—21no—
125C22×C103—21no—
126C22×C103—44no—
127C22×C103—41no—
128C22×C103—41no—
129C22×C103—41no—
130C22×C103#13512yes—
131C22×C103#13712yes—
132C22×C103C22×D411yescharacteristic
133C4×C103—21no—
134C4×C103—21no—
135C4×C103—21no—
136C4×C103—41no—
137C4×C103—41no—
138C4×C103—41no—
139C4×C103H(5,𝔽2)12yes—
140Dic103—42no—
141Dic103—42no—
142C2×C103—22no—
143C2×C103—22no—
144C2×C103—41no—
145C2×C103—81no—
146C2×C103#53411yescharacteristic
147C2×C103C2×#13511yescharacteristic
148C2×C103C2×#13711yescharacteristic
149#3190—1031nomaximal, Sylow
150C103#319011yescharacteristic, complemented, Sylow
151#525D10311yescharacteristic
152C2×C22⋊Q8—1031no—
153#485—1032no—
154#483—1031no—
155#480—1031no—
156#467—1032no—
157#465—1032no—
158#452—1032no—
159#451—1031no—
160#448—1031no—
161C2×C22⋊C8—1031no—
162C2×#41C2×D10311yescharacteristic
163C22×Q8—1031no—
164C23×C4C2×D10311yescharacteristic
165C2×Q16—1032no—
166C2×SD16—1032no—
167C22×C8—1032no—
168#123—21no—
169C22⋊Q8—1032no—
170C22⋊Q8—1032no—
171C22⋊Q8—2061no—
172C22⋊Q8—2061no—
173C22⋊Q8C2×D10311yescharacteristic
174C22⋊Q8C2×D10311yescharacteristic
175#121C2×D10311yescharacteristic
176#121C2×D10311yescharacteristic
177#120—21no—
178C4×D4—21no—
179C4×D4—21no—
180#117C2×D10311yescharacteristic
181C2×C4⋊C4—1031no—
182C2×C4⋊C4—2061no—
183C2×C22⋊C4—2061no—
184#107—1032no—
185#106—1032no—
186#103—1032no—
187#103—1032no—
188#103—1032no—
189#102—1032no—
190C22⋊C8—1031no—
191C22⋊C8—1031no—
192C22⋊C8—1032no—
193C24C22⋊D10311yescharacteristic
194#41—42no—
195C2×Q8—1032no—
196C2×Q8—4122no—
197C2×Q8—2061no—
198C2×Q8C22×D10311yescharacteristic
199C2×D4—21no—
200C2×D4—21no—
201C2×D4—21no—
202C2×D4C22×D10311yescharacteristic
203C22×C4—21no—
204C22×C4—42no—
205C22×C4—2061no—
206C22×C4—2061no—
207C22×C4C22⋊D10311yescharacteristic
208C22×C4C22⋊D10311yescharacteristic
209C22×C4C22⋊D10311yescharacteristic
210C22×C4C22×D10311yescharacteristic
211C22×C4C22×D10311yescharacteristic
212C22×C4C22×D10311yescharacteristic
213Q16—4122no—
214SD16—4122no—
215C2×C8—1032no—
216C2×C8—1032no—
217C2×C8—4122no—
218C4⋊C4—21no—
219C4⋊C4—21no—
220C4⋊C4—1032no—
221C4⋊C4—2062no—
222C4⋊C4—2062no—
223C4⋊C4—2061no—
224C4⋊C4C22×D10311yescharacteristic
225C4⋊C4C22×D10311yescharacteristic
226C22⋊C4—21no—
227C22⋊C4—21no—
228C22⋊C4—21no—
229C22⋊C4—21no—
230C22⋊C4—21no—
231C22⋊C4—2062no—
232C22⋊C4—2062no—
233C42—21no—
234C23—22no—
235C23—22no—
236C23—21no—
237C23—41no—
238C23C2×C22⋊D10311yescharacteristic
239C23C2×C22⋊D10311yescharacteristic
240C23C2×C22⋊D10311yescharacteristic
241Q8—22no—
242Q8—4122no—
243Q8—2062no—
244Q8—2062no—
245D4—22no—
246D4—42no—
247D4—42no—
248D4—42no—
249C2×C4—22no—
250C2×C4—22no—
251C2×C4—22no—
252C2×C4—21no—
253C2×C4—21no—
254C2×C4—21no—
255C2×C4—41no—
256C2×C4—41no—
257C2×C4—41no—
258C2×C4—42no—
259C2×C4—4122no—
260C2×C4—4122no—
261C2×C4—2062no—
262C2×C4—2062no—
263C2×C4C2×C22⋊D10311yescharacteristic
264C2×C4C2×C22⋊D10311yescharacteristic
265C2×C4C2×C22⋊D10311yescharacteristic
266C2×C4C23×D10311yescharacteristic
267C8—2062no—
268C8—2062no—
269C22—21no—
270C22—21no—
271C22—21no—
272C22—21no—
273C22—21no—
274C22—21no—
275C22—21no—
276C22—44no—
277C22—41no—
278C22—41no—
279C22—41no—
280C22#1569304112yes—
281C22#1569305112yes—
282C22C22×C22⋊D10311yescharacteristic
283C4—21no—
284C4—21no—
285C4—21no—
286C4—41no—
287C4—41no—
288C4—41no—
289C4—4122no—
290C4—4122no—
291C4#1569306612yes—
292C2—22no—
293C2—22no—
294C2—41no—
295C2—81no—
296C2#2026835011yescharacteristic
297C2C2×#1569304111yescharacteristic
298C2C2×#1569305111yescharacteristic
subgroupG/H
centerC22C22×C22⋊D103
commutator, cosocleC2×C4×C103C24
FrattiniC2×C4C23×D103
Fitting, prime radical#525×C103C2
socleC22×C103C22×D4
hypercenter#525D103
hypocenterC103#3190
LCSG ▷ C2×C4×C103 ▷ C2×C103 ▷ C103
UCSC1 ◁ C22 ◁ C23×C4 ◁ #525

Complements

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

NH ≅ G/Ntype
1. C2×#15693000C2semidirect
2. #20268132C2semidirect
3. #20268119C2semidirect
4. #20268102C2semidirect
5. #20268030C2semidirect
6. #20268018C2semidirect
7. #20267953C2semidirect
8. #20267946C2semidirect
9. #20267929C2semidirect
10. C2×C22⋊(C103⋊C8)C2semidirect
13. C2×#13110095C22semidirect
14. C2×#13110093C22semidirect
23. #15692954C22semidirect
24. #15692952C22semidirect
25. #15692945C22semidirect
26. #15692944C22semidirect
27. #15692944C22semidirect
28. #15692942C22semidirect
150. C103#3190semidirect

Maximal subgroups

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

subgroupindex
C2×#156930002
#202681322
#202681192
#202681022
#202680302
#202680182
#202679532
#202679462
#202679292
C2×C22⋊(C103⋊C8)2
#525×C1032
#3190103