Finite Group Databasebeta

← #27205924

Subgroups — #27205924

Order 13184.

420 conjugacy classes of subgroups; only the 115 normal subgroups are shown.

normal subgroups only

This group has 420 conjugacy classes of subgroups — too many to draw. Only its 115 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#20268301C211yesmaximal, characteristic
2C2×#15693001C211yesmaximal, characteristic, complemented
3#20268134C212yesmaximal, complemented
4#20268121C211yesmaximal, characteristic, complemented
5#20268033C212yesmaximal, complemented
6#20268019C212yesmaximal, complemented
7#20267954C212yesmaximal, complemented
8#20267949C211yesmaximal, characteristic, complemented
9#20267929C211yesmaximal, characteristic, complemented
10C22⋊C8×D103C211yesmaximal, characteristic, complemented
11#480×C103C211yesmaximal, characteristic, complemented
12C2×#13110104C2211yescharacteristic
13C22×Dic206C2211yescharacteristic
14C22×C4×D103C2211yescharacteristic
15C2×Dic412C2212yescomplemented
16C2×#13110093C2212yescomplemented
17C2×C8×D103C2212yes—
18#15693003—21no—
19#15693001—21no—
20#15693001—21no—
21#15693001C2211yescharacteristic
22#15693001C2212yes—
23#15693001C2212yes—
24#15693000C2211yescharacteristic
25#15692992C2211yescharacteristic
26#15692989—21no—
27D4×Dic103—21no—
28(C22⋊D103)⋊C4—21no—
29#15692979C2211yescharacteristic
30C2×C4⋊Dic103—21no—
31C2×(C2×D103)⋊C4—21no—
32#15692952C2212yescomplemented
33#15692946C2212yescomplemented
34#15692944C2212yescomplemented
35#15692944C2212yescomplemented
36C22⋊(C103⋊C8)C2211yescharacteristic
37(C2×D103)⋊C8C2212yes—
38#121×C103C2211yescharacteristic
39C2×C4⋊C4×C103C2211yescharacteristic
40#107×C103C2212yescomplemented
41#102×C103C2212yescomplemented
42C22⋊C8×C103C2211yescharacteristic
43C23×D103D411yescharacteristic
44#13110104—42no—
45C2×Dic206—21no—
46C2×Dic206—42no—
47C2×Dic206C2312yes—
48C2×Dic206C2311yescharacteristic
49C2×C22⋊D103—21no—
50C2×C22⋊D103—21no—
51C22×Dic103—21no—
52C22×Dic103—21no—
53C22×Dic103D411yescharacteristic
54C2×C4×D103—42no—
55C2×C4×D103D411yescharacteristic
56C2×C4×D103D411yescharacteristic
57C2×C4×D103C2311yescharacteristic
58C2×C4×D103C2311yescharacteristic
59Dic412—42no—
60#13110093—42no—
61C2×C103⋊C8C2312yes—
62C8×D103—42no—
63C4⋊Dic103—22no—
64C4⋊Dic103—22no—
65C4⋊Dic103—21no—
66C4⋊Dic103C2311yescharacteristic
67Dic103⋊C4—21no—
68C22⋊Dic103—21no—
69C22⋊Dic103—21no—
70(C2×D103)⋊C4—22no—
71(C2×D103)⋊C4—22no—
72(C2×D103)⋊C4—21no—
73(C2×D103)⋊C4—21no—
74C4×Dic103—21no—
75C2×D4×C103—21no—
76C2×D4×C103C2311yescharacteristic
77C22×C4×C103—21no—
78C22×C4×C103C2311yescharacteristic
79C2×C8×C103C2312yes—
80C4⋊C4×C103—21no—
81C4⋊C4×C103C2312yes—
82C4⋊C4×C103C2311yescharacteristic
83C22⋊C4×C103—21no—
84C23×C103—21no—
85C23×C103C2×D411yescharacteristic
86C22×D103—22no—
87C22×D103—22no—
88C22×D103—41no—
89C22×D103C2×D411yescharacteristic
90C22×D103C2×D411yescharacteristic
91D4×C103—22no—
92D4×C103—42no—
93C2×C4×C103—22no—
94C2×C4×C103—21no—
95C2×C4×C103—22no—
96C2×C4×C103—42no—
97C2×C4×C103C2×D411yescharacteristic
98C2×C4×C103C2411yescharacteristic
99C22⋊D103—42no—
100C22⋊D103—42no—
101C2×Dic103—21no—
102C2×Dic103—22no—
103C2×Dic103—21no—
104C2×Dic103—41no—
105C2×Dic103—42no—
106C2×Dic103—42no—
107C2×Dic103C2×D411yescharacteristic
108C2×Dic103C2×D411yescharacteristic
109C4×D103—22no—
110C4×D103—22no—
111C4×D103—41no—
112C4×D103—41no—
113Dic206—22no—
114Dic206—22no—
115Dic206—22no—
116Dic206—42no—
117C8×C103—22no—
118C103⋊C8—22no—
119C22×C103—21no—
120C22×C103—21no—
121C22×C103—41no—
122C22×C103—41no—
123C22×C103—41no—
124C22×C103#13512yes—
125C22×C103C22×D411yescharacteristic
126C2×D103—21no—
127C2×D103—21no—
128C2×D103—21no—
129C2×D103—21no—
130C2×D103—21no—
131C2×D103—44no—
132C2×D103#13712yes—
133C4×C103—21no—
134C4×C103—42no—
135C4×C103—41no—
136C4×C103H(5,𝔽2)12yes—
137Dic103—21no—
138Dic103—21no—
139Dic103—42no—
140Dic103—41no—
141Dic103—41no—
142C2×C103—22no—
143C2×C103—81no—
144C2×C103#53411yescharacteristic
145C2×C103C2×#13511yescharacteristic
146C2×C103C2×#13711yescharacteristic
147D103—22no—
148D103—41no—
149#3190—1031nomaximal, Sylow
150C103#319011yescharacteristic, complemented, Sylow
151#525—1031no—
152C2×C22⋊Q8—1031no—
153#485—1032no—
154#483—1031no—
155#480D10311yescharacteristic, complemented
156#467—1032no—
157#465—1032no—
158#452—1032no—
159#451—1031no—
160#448—1031no—
161C2×C22⋊C8—1031no—
162C2×#41—1031no—
163C22×Q8—1031no—
164C23×C4—1031no—
165C2×Q16—1032no—
166C2×SD16—1032no—
167C22×C8—1032no—
168#123—2061no—
169C22⋊Q8—1031no—
170C22⋊Q8—1032no—
171C22⋊Q8—1032no—
172C22⋊Q8—1031no—
173C22⋊Q8—2061no—
174C22⋊Q8—2061no—
175#121—1031no—
176#121C2×D10311yescharacteristic
177#120—2061no—
178C4×D4—2061no—
179C4×D4—2061no—
180#117—1031no—
181C2×C4⋊C4—2061no—
182C2×C4⋊C4C2×D10311yescharacteristic
183C2×C22⋊C4—2061no—
184#107C2×D10312yescomplemented
185#106—1032no—
186#103—1032no—
187#103—1032no—
188#103—1032no—
189#102C2×D10312yescomplemented
190C22⋊C8—1031no—
191C22⋊C8—1032no—
192C22⋊C8C2×D10311yescharacteristic
193C24—1031no—
194#41—4122no—
195C2×Q8—1032no—
196C2×Q8—1031no—
197C2×Q8—4122no—
198C2×Q8—2061no—
199C2×D4—21no—
200C2×D4—2061no—
201C2×D4—2061no—
202C2×D4C22×D10311yescharacteristic
203C22×C4—21no—
204C22×C4—1031no—
205C22×C4—1031no—
206C22×C4—1031no—
207C22×C4—1031no—
208C22×C4—1031no—
209C22×C4—4122no—
210C22×C4—2061no—
211C22×C4—2061no—
212C22×C4C22×D10311yescharacteristic
213Q16—4122no—
214SD16—4122no—
215C2×C8—1032no—
216C2×C8—4122no—
217C2×C8C22×D10312yes—
218C4⋊C4—21no—
219C4⋊C4—1031no—
220C4⋊C4—2062no—
221C4⋊C4—2062no—
222C4⋊C4—2061no—
223C4⋊C4—2061no—
224C4⋊C4C22×D10312yes—
225C4⋊C4C22×D10311yescharacteristic
226C22⋊C4—21no—
227C22⋊C4—2062no—
228C22⋊C4—2062no—
229C22⋊C4—2061no—
230C22⋊C4—2061no—
231C22⋊C4—2061no—
232C22⋊C4—2061no—
233C42—2061no—
234C23—21no—
235C23—1031no—
236C23—1031no—
237C23—4121no—
238C23—2062no—
239C23—2062no—
240C23D4×D10311yescharacteristic
241Q8—4122no—
242Q8—2062no—
243Q8—2062no—
244Q8—2062no—
245D4—22no—
246D4—42no—
247D4—4122no—
248D4—4122no—
249C2×C4—22no—
250C2×C4—21no—
251C2×C4—22no—
252C2×C4—42no—
253C2×C4—1031no—
254C2×C4—1031no—
255C2×C4—4121no—
256C2×C4—4121no—
257C2×C4—4122no—
258C2×C4—4122no—
259C2×C4—4121no—
260C2×C4—2061no—
261C2×C4—2061no—
262C2×C4—2062no—
263C2×C4—2062no—
264C2×C4—2062no—
265C2×C4D4×D10311yescharacteristic
266C2×C4C23×D10311yescharacteristic
267C8—22no—
268C8—2062no—
269C22—21no—
270C22—21no—
271C22—41no—
272C22—41no—
273C22—41no—
274C22—1032no—
275C22—4124no—
276C22—2061no—
277C22—2061no—
278C22—2061no—
279C22—2061no—
280C22—2061no—
281C22#1569304012yes—
282C22C2×D4×D10311yescharacteristic
283C4—21no—
284C4—42no—
285C4—41no—
286C4—4121no—
287C4—4121no—
288C4—4122no—
289C4—2061no—
290C4—2061no—
291C4#1569306712yes—
292C2—22no—
293C2—81no—
294C2—4121no—
295C2—2062no—
296C2#2026835211yescharacteristic
297C2C2×#1569304011yescharacteristic
298C2#137×D10311yescharacteristic
subgroupG/H
centerC22C2×D4×D103
commutator, cosocleC2×C4×C103C24
FrattiniC2×C4C23×D103
Fitting#480×C103C2
socleC22×C103C22×D4
prime radical#20268301C2
hypercenter#480D103
hypocenterC103#3190
LCSG ▷ C2×C4×C103 ▷ C2×C103 ▷ C103
UCSC1 ◁ C22 ◁ C22×C4 ◁ #480

Complements

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

NH ≅ G/Ntype
2. C2×#15693001C2semidirect
3. #20268134C2semidirect
4. #20268121C2semidirect
5. #20268033C2semidirect
6. #20268019C2semidirect
7. #20267954C2semidirect
8. #20267949C2semidirect
9. #20267929C2semidirect
10. C22⋊C8×D103C2semidirect
11. #480×C103C2semidirect
15. C2×Dic412C22semidirect
16. C2×#13110093C22semidirect
32. #15692952C22semidirect
33. #15692946C22semidirect
34. #15692944C22semidirect
35. #15692944C22semidirect
40. #107×C103C22semidirect
41. #102×C103C22semidirect
150. C103#3190semidirect
155. #480D103semidirect
184. #107C2×D103semidirect
189. #102C2×D103semidirect

Maximal subgroups

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

subgroupindex
#202683012
C2×#156930012
#202681342
#202681212
#202680332
#202680192
#202679542
#202679492
#202679292
C22⋊C8×D1032
#480×C1032
#3190103