Finite Group Databasebeta

← #27206926

Subgroups — #27206926

Order 13184.

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

normal subgroups only

This group has 454 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
1#20268605C211yesmaximal, characteristic, complemented
2#20268602C212yesmaximal, complemented
3#20268174C211yesmaximal, characteristic, complemented
4#20268066C211yesmaximal, characteristic, complemented
5#20268058C211yesmaximal, characteristic, complemented
6#20268052C212yesmaximal, complemented
7#20267969C212yesmaximal, complemented
8#20267962C212yesmaximal, complemented
9#20267908C211yesmaximal, characteristic, complemented
10#20267906C211yesmaximal, characteristic, complemented
11#576×C103C211yesmaximal, characteristic, complemented
12#15693068C2212yescomplemented
13#15693051—22no—
14#15693051C2212yes—
15#15693051C2212yescomplemented
16#15693050—22no—
17#15693047—22no—
18#15693047C2212yescomplemented
19#15693041—22no—
20#15693041C2211yescharacteristic
21#15693040—21no—
22C2×Dic412C2211yescharacteristic, complemented
23Q16×D103—21no—
24C2×#13110093—22no—
25C2×#13110093C2212yescomplemented
26#15693028C2212yescomplemented
27#15693027C2211yescharacteristic, complemented
28#15693008C2212yescomplemented
29#15692957C2211yescharacteristic, complemented
30#15692956C2211yescharacteristic, complemented
31#15692948C2211yescharacteristic
32#15692948C2212yescomplemented
33#15692947C2211yescharacteristic, complemented
34#15692939C2212yescomplemented
35#15692938C2212yescomplemented
36C8×Dic103C2211yescharacteristic, complemented
37H(5,𝔽2)×C103C2212yes—
38AGL(1,ℤ/8)×C103—22no—
39AGL(1,ℤ/8)×C103C2212yes—
40#135×C103—21no—
41#135×C103C2211yescharacteristic
42C2×D8×C103—21no—
43C2×D8×C103C2211yescharacteristic
44#131×C103C2211yescharacteristic
45#13110105—22no—
46#13110105C2311yescharacteristic
47#13110104—22no—
48#13110104—42no—
49C2×Dic206—22no—
50C2×Dic206C2312yes—
51Q8×D103—22no—
52Dic412—21no—
53Dic412—21no—
54#13110095—22no—
55#13110095—22no—
56#13110095D411yescharacteristic
57#13110093—22no—
58#13110093—22no—
59#13110093—22no—
60#13110093—22no—
61#13110093—22no—
62#13110093D411yescharacteristic
63#13110092D411yescharacteristic
64#13110090—22no—
65#13110090D411yescharacteristic
66#13110089—22no—
67#13110089C2311yescharacteristic
68#13110089C2312yes—
69#13110088—21no—
70C2×C103⋊C8—22no—
71C2×C103⋊C8C2311yescharacteristic
72C8×D103—21no—
73C22⋊Dic103—42no—
74C4×Dic103C2311yescharacteristic
75#41×C103—22no—
76#41×C103—22no—
77#41×C103C2312yes—
78#41×C103C2311yescharacteristic
79C2×D4×C103—22no—
80C2×D4×C103—22no—
81C2×D4×C103—42no—
82C2×D4×C103C2312yes—
83Q16×C103D411yescharacteristic
84SD16×C103—22no—
85SD16×C103D412yes—
86D8×C103—22no—
87D8×C103—21no—
88D8×C103—21no—
89D8×C103D411yescharacteristic
90M16×C103—21no—
91M16×C103C2311yescharacteristic
92C2×C8×C103—21no—
93C2×C8×C103C2311yescharacteristic
94C23×C103—22no—
95C23×C103—42no—
96Q8×C103C2×D411yescharacteristic
97Q8×C103C2×D412yes—
98D4×C103—21no—
99D4×C103—22no—
100D4×C103—22no—
101D4×C103—22no—
102D4×C103—42no—
103D4×C103—42no—
104D4×C103C2×D411yescharacteristic
105D4×C103C2×D412yes—
106C2×C4×C103—21no—
107C2×C4×C103—22no—
108C2×C4×C103—42no—
109C2×C4×C103C2411yescharacteristic
110C22⋊D103—21no—
111C22⋊D103—42no—
112C2×Dic103—21no—
113C2×Dic103—22no—
114C2×Dic103—42no—
115D412C2×D411yescharacteristic
116C4×D103—21no—
117C4×D103—42no—
118Dic206—22no—
119Dic206—22no—
120Dic206—42no—
121Dic206C2×D411yescharacteristic
122C8×C103—21no—
123C8×C103C2×D411yescharacteristic
124C8×C103C2×D411yescharacteristic
125C103⋊C8—21no—
126C103⋊C8—22no—
127C103⋊C8C2×D411yescharacteristic
128C103⋊C8C2×D411yescharacteristic
129C22×C103—22no—
130C22×C103—21no—
131C22×C103—42no—
132C22×C103—82no—
133C22×C103—162no—
134C22×C103H(5,𝔽2)11yescharacteristic
135C2×D103—21no—
136C4×C103—22no—
137C4×C103—21no—
138C4×C103C22×D411yescharacteristic
139C4×C103C22×D411yescharacteristic
140Dic103—21no—
141Dic103—41no—
142Dic103—42no—
143C2×C103—21no—
144C2×C103—42no—
145C2×C103—41no—
146C2×C103—82no—
147C2×C103D4211yescharacteristic
148D103—41no—
149#3290—1031nomaximal, Sylow
150C103#329011yescharacteristic, complemented, Sylow
151#578—1031no—
152#577—1032no—
153#576D10311yescharacteristic, complemented
154#495—1031no—
155#473—1031no—
156#472—1031no—
157#471—1032no—
158#455—1032no—
159#454—1032no—
160#443—1031no—
161#443—1031no—
1622−1+4—1032no—
163H(5,𝔽2)C2×D10312yes—
164#137—1032no—
165#137—1032no—
166#137—2062no—
167#137—2062no—
168AGL(1,ℤ/8)—22no—
169AGL(1,ℤ/8)—1032no—
170AGL(1,ℤ/8)—2062no—
171AGL(1,ℤ/8)C2×D10312yes—
172#135—21no—
173#135—1031no—
174#135—2062no—
175#135—2061no—
176#135C2×D10311yescharacteristic
177C2×Q16—1031no—
178C2×Q16—2061no—
179C2×SD16—1032no—
180C2×SD16—2062no—
181C2×D8—21no—
182C2×D8C2×D10311yescharacteristic
183#131—1032no—
184#131—1031no—
185#131C2×D10311yescharacteristic
186#124—1032no—
187#108—1031no—
188#108—1031no—
189#104—1031no—
190#104—1032no—
191#104—1031no—
192#101—1032no—
193#100—1032no—
194C4×C8—1031no—
195#41—22no—
196#41—22no—
197#41—1031no—
198#41—4122no—
199#41—2062no—
200#41—2062no—
201#41C22×D10311yescharacteristic
202#41C22×D10312yes—
203C2×Q8—1032no—
204C2×Q8—2062no—
205C2×Q8—2062no—
206C2×D4—22no—
207C2×D4—22no—
208C2×D4—42no—
209C2×D4C22×D10312yes—
210Q16—1031no—
211Q16—2062no—
212Q16—2062no—
213Q16—2061no—
214Q16—2061no—
215Q16C22⋊D10311yescharacteristic
216SD16—22no—
217SD16—1031no—
218SD16—1031no—
219SD16—2062no—
220SD16—2062no—
221SD16—2062no—
222SD16—2062no—
223SD16—2062no—
224SD16C22⋊D10312yes—
225D8—22no—
226D8—21no—
227D8—21no—
228D8—1031no—
229D8—2062no—
230D8C22⋊D10311yescharacteristic
231M16—21no—
232M16—1031no—
233M16—1032no—
234M16—2062no—
235M16—2061no—
236M16C22×D10311yescharacteristic
237C2×C8—21no—
238C2×C8—1031no—
239C2×C8—2062no—
240C2×C8—2061no—
241C2×C8C22×D10311yescharacteristic
242C22⋊C4—4122no—
243C42—1031no—
244C23—22no—
245C23—42no—
246Q8—1031no—
247Q8—4122no—
248Q8—2062no—
249Q8—2062no—
250Q8D4×D10311yescharacteristic
251Q8C2×C22⋊D10312yes—
252D4—21no—
253D4—22no—
254D4—22no—
255D4—22no—
256D4—42no—
257D4—42no—
258D4—1031no—
259D4—4122no—
260D4—2061no—
261D4D4×D10311yescharacteristic
262D4C2×C22⋊D10312yes—
263C2×C4—22no—
264C2×C4—21no—
265C2×C4—42no—
266C2×C4—4122no—
267C2×C4—4122no—
268C2×C4—2061no—
269C2×C4—2062no—
270C2×C4—2061no—
271C2×C4C23×D10311yescharacteristic
272C8—21no—
273C8—1031no—
274C8—1031no—
275C8—2062no—
276C8—2061no—
277C8C2×C22⋊D10311yescharacteristic
278C8C2×C22⋊D10311yescharacteristic
279C22—22no—
280C22—21no—
281C22—42no—
282C22—82no—
283C22—162no—
284C22—2061no—
285C22#1569306611yescharacteristic
286C4—21no—
287C4—22no—
288C4—4121no—
289C4—4122no—
290C4—2061no—
291C4C2×D4×D10311yescharacteristic
292C4C22×C22⋊D10311yescharacteristic
293C2—21no—
294C2—41no—
295C2—42no—
296C2—82no—
297C2—4121no—
298C2D4×C22⋊D10311yescharacteristic
subgroupG/H
centerC2D4×C22⋊D103
commutator, cosocleC2×C4×C103C24
FrattiniC2×C4C23×D103
Fitting#576×C103C2
socleC2×C103D42
hypercenter#576D103
hypocenterC103#3290
LCSG ▷ C2×C4×C103 ▷ C2×C103 ▷ C103
UCSC1 ◁ C2 ◁ C2×C4 ◁ #576

Complements

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

NH ≅ G/Ntype
1. #20268605C2semidirect
2. #20268602C2semidirect
3. #20268174C2semidirect
4. #20268066C2semidirect
5. #20268058C2semidirect
6. #20268052C2semidirect
7. #20267969C2semidirect
8. #20267962C2semidirect
9. #20267908C2semidirect
10. #20267906C2semidirect
11. #576×C103C2semidirect
12. #15693068C22semidirect
15. #15693051C22semidirect
18. #15693047C22semidirect
22. C2×Dic412C22semidirect
25. C2×#13110093C22semidirect
26. #15693028C22semidirect
27. #15693027C22semidirect
28. #15693008C22semidirect
29. #15692957C22semidirect
30. #15692956C22semidirect
32. #15692948C22semidirect
33. #15692947C22semidirect
34. #15692939C22semidirect
35. #15692938C22semidirect
36. C8×Dic103C22semidirect
150. C103#3290semidirect
153. #576D103semidirect

Maximal subgroups

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

subgroupindex
#202686052
#202686022
#202681742
#202680662
#202680582
#202680522
#202679692
#202679622
#202679082
#202679062
#576×C1032
#3290103