Finite Group Databasebeta

← #489×D103 #27205470

Subgroups — #489×D103 #27205470

Order 13184.

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

normal subgroups only

This group has 436 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
1C4⋊Q8×D103C211yesmaximal, characteristic, complemented
2#124×D103C211yesmaximal, characteristic
3#20268153C211yesmaximal, characteristic, complemented
4#20268152C212yesmaximal, complemented
5#20268151C211yesmaximal, characteristic, complemented
6#20268150C211yesmaximal, characteristic, complemented
7#20268149C212yesmaximal, complemented
8#103×D103C212yesmaximal, complemented
9#102×D103C212yesmaximal
10#97×D103C211yesmaximal, characteristic, complemented
11#489×C103C211yesmaximal, characteristic, complemented
12C2×Q8×D103—21no—
13C2×Q8×D103C2211yescharacteristic
14C2×D4×D103C2211yescharacteristic
15C2×C8×D103C2212yes—
16#15693021C2211yescharacteristic, complemented
17#15693020—21no—
18#15693020C2212yescomplemented
19#15693019—21no—
20#15693010C2211yescharacteristic
21#15693009C2211yescharacteristic
22#15693008C2211yescharacteristic
23#15693007—21no—
24#15693007—21no—
25C4⋊C4×D103—21no—
26C4⋊C4×D103C2212yes—
27C22⋊C4×D103—21no—
28C22⋊C4×D103—21no—
29C42×D103C2211yescharacteristic
30#15692946C2212yescomplemented
31#15692945C2212yescomplemented
32#15692944C2212yescomplemented
33#15692943C2212yes—
34#15692942C2212yes—
35#15692941C2212yes—
36#15692932C2211yescharacteristic, complemented
37#15692931C2212yescomplemented
38C4⋊Q8×C103C2211yescharacteristic, complemented
39#124×C103C2211yescharacteristic
40#103×C103C2212yescomplemented
41#102×C103C2212yes—
42#97×C103C2211yescharacteristic, complemented
43C23×D103—21no—
44C2×Dic206—21no—
45C2×Dic206—22no—
46C2×Dic206—21no—
47C2×Dic206C2311yescharacteristic
48Q8×D103—24no—
49Q8×D103—44no—
50C2×D412C2311yescharacteristic
51C2×C22⋊D103—21no—
52D4×D103—24no—
53C2×C4×D103—22no—
54C2×C4×D103—21no—
55C2×C4×D103D411yescharacteristic
56C2×C4×D103D411yescharacteristic
57C2×C4×D103C2311yescharacteristic
58C2×C103⋊C8C2312yes—
59C8×D103—24no—
60C4⋊Dic103—21no—
61C4⋊Dic103C2312yes—
62Dic103⋊C4—22no—
63Dic103⋊C4—22no—
64C22⋊Dic103—21no—
65C22⋊Dic103—21no—
66(C2×D103)⋊C4—21no—
67(C2×D103)⋊C4—21no—
68(C2×D103)⋊C4—21no—
69(C2×D103)⋊C4—21no—
70C4×Dic103D411yescharacteristic
71C4×Dic103D411yescharacteristic
72C4×Dic103C2311yescharacteristic
73C2×Q8×C103—21no—
74C2×Q8×C103C2311yescharacteristic
75C2×D4×C103C2311yescharacteristic
76C2×C8×C103C2312yes—
77C4⋊C4×C103—21no—
78C4⋊C4×C103C2312yes—
79C22⋊C4×C103—21no—
80C22⋊C4×C103—21no—
81C42×C103C2311yescharacteristic
82C23×C103—21no—
83C22×D103—21no—
84C22×D103—42no—
85C22×D103—42no—
86C22×D103—42no—
87C22×D103C2×D411yescharacteristic
88Q8×C103—22no—
89Q8×C103—42no—
90D4×C103—22no—
91C2×C4×C103—21no—
92C2×C4×C103—22no—
93C2×C4×C103C2×D411yescharacteristic
94C2×C4×C103C2×D411yescharacteristic
95C2×C4×C103C2411yescharacteristic
96C22⋊D103—42no—
97C2×Dic103—21no—
98C2×Dic103—22no—
99C2×Dic103C2×D411yescharacteristic
100C2×Dic103C2×D411yescharacteristic
101C2×Dic103C2×D411yescharacteristic
102D412—22no—
103C4×D103—22no—
104C4×D103—22no—
105C4×D103—42no—
106C4×D103—44no—
107C4×D103#4114yes—
108Dic206—22no—
109Dic206—44no—
110Dic206—42no—
111Dic206—42no—
112C8×C103—22no—
113C103⋊C8—22no—
114C22×C103—41no—
115C22×C103—41no—
116C22×C103—41no—
117C22×C103C22×D411yescharacteristic
118C2×D103—41no—
119C2×D103—41no—
120C2×D103—41no—
121C2×D103—84no—
122C2×D103#12412yes—
123C2×D103AGL(1,ℤ/8)12yes—
124C2×D103#13712yes—
125C4×C103—21no—
126C4×C103—21no—
127C4×C103—41no—
128C4×C103—42no—
129C4×C103C2×#4112yes—
130Dic103—21no—
131Dic103—21no—
132Dic103—41no—
133Dic103—42no—
134Dic103#12412yes—
135C2×C103—81no—
136C2×C103C2×#12411yescharacteristic
137C2×C103C2×AGL(1,ℤ/8)11yescharacteristic
138C2×C103C2×#13711yescharacteristic
139D103—81no—
140D103#48914yesdirect product factor
141C2×#489—1031nomaximal, Sylow
142C103C2×#48911yescharacteristic, complemented, Sylow
143C2×C4⋊Q8—1031no—
144C2×#124—1031no—
145#489—1031no—
146#489—1031no—
147#489—1032no—
148#489—1032no—
149#489—1031no—
150#489D10311yescharacteristic, direct product factor
151C2×#103—1032no—
152C2×#102—1032no—
153C2×#97—1031no—
154C22×Q8—1031no—
155C22×Q8—2061no—
156C22×D4—1031no—
157C22×C8—1032no—
158C4⋊Q8—1032no—
159C4⋊Q8—1031no—
160C4⋊Q8—2061no—
161C4⋊Q8—2061no—
162C4⋊Q8C2×D10311yescharacteristic, complemented
163#124—1031no—
164#124—1031no—
165#124—1031no—
166#124—2061no—
167#124—2061no—
168#124C2×D10311yescharacteristic
169C2×C4⋊C4—1032no—
170C2×C4⋊C4—2061no—
171C2×C22⋊C4—2061no—
172C2×C22⋊C4—2061no—
173C2×C42—1031no—
174#103—1032no—
175#103—1032no—
176#103—1032no—
177#103C2×D10312yescomplemented
178#102—1032no—
179#102—1032no—
180#102—1032no—
181#102C2×D10312yes—
182#97—1032no—
183#97—1031no—
184#97C2×D10311yescharacteristic, complemented
185C24—2061no—
186C2×Q8—21no—
187C2×Q8—1031no—
188C2×Q8—4124no—
189C2×Q8—2061no—
190C2×Q8—2062no—
191C2×Q8—2064no—
192C2×Q8—2061no—
193C2×Q8C22×D10311yescharacteristic
194C2×D4—1031no—
195C2×D4—2064no—
196C2×D4—2061no—
197C2×D4C22×D10311yescharacteristic
198C22×C4—1031no—
199C22×C4—1031no—
200C22×C4—1031no—
201C22×C4—2061no—
202C22×C4—2062no—
203C2×C8—1032no—
204C2×C8—2064no—
205C2×C8C22×D10312yes—
206C4⋊C4—21no—
207C4⋊C4—1032no—
208C4⋊C4—2062no—
209C4⋊C4—2062no—
210C4⋊C4—2061no—
211C4⋊C4C22×D10312yes—
212C22⋊C4—21no—
213C22⋊C4—21no—
214C22⋊C4—2061no—
215C22⋊C4—2061no—
216C22⋊C4—2061no—
217C22⋊C4—2061no—
218C22⋊C4—2061no—
219C22⋊C4—2061no—
220C42—1031no—
221C42—1031no—
222C42—1031no—
223C42C22×D10311yescharacteristic
224C23—21no—
225C23—1031no—
226C23—4122no—
227C23—4122no—
228C23—4122no—
229C23—2061no—
230Q8—22no—
231Q8—42no—
232Q8—4122no—
233Q8—4122no—
234Q8—4124no—
235Q8—2062no—
236D4—22no—
237D4—4122no—
238D4—2062no—
239C2×C4—21no—
240C2×C4—22no—
241C2×C4—1031no—
242C2×C4—1034no—
243C2×C4—1031no—
244C2×C4—1031no—
245C2×C4—4124no—
246C2×C4—4122no—
247C2×C4—2062no—
248C2×C4—2062no—
249C2×C4—2061no—
250C2×C4—2062no—
251C2×C4D4×D10311yescharacteristic
252C2×C4D4×D10311yescharacteristic
253C2×C4C23×D10311yescharacteristic
254C8—22no—
255C8—2062no—
256C22—41no—
257C22—41no—
258C22—41no—
259C22—8244no—
260C22—1032no—
261C22—1032no—
262C22—1032no—
263C22—4121no—
264C22—4121no—
265C22—4121no—
266C22C2×D4×D10311yescharacteristic
267C4—21no—
268C4—21no—
269C4—41no—
270C4—42no—
271C4—1032no—
272C4—4121no—
273C4—4122no—
274C4—2061no—
275C4—2061no—
276C4#41×D10312yes—
277C2—81no—
278C2—8241no—
279C2—1034no—
280C2#124×D10311yescharacteristic
281C2AGL(1,ℤ/8)×D10311yescharacteristic
282C2#137×D10311yescharacteristic
subgroupG/H
centerC22C2×D4×D103
commutator, cosocleC2×C4×C103C24
FrattiniC2×C4C23×D103
Fitting#489×C103C2
socleC22×C103C22×D4
prime radicalC2×D4×D103C22
hypercenter#489D103
hypocenterC103C2×#489
LCSG ▷ C2×C4×C103 ▷ C2×C103 ▷ C103
UCSC1 ◁ C22 ◁ C42 ◁ #489

Complements

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

NH ≅ G/Ntype
1. C4⋊Q8×D103C2semidirect
3. #20268153C2semidirect
4. #20268152C2semidirect
5. #20268151C2semidirect
6. #20268150C2semidirect
7. #20268149C2semidirect
8. #103×D103C2semidirect
10. #97×D103C2semidirect
11. #489×C103C2semidirect
16. #15693021C22semidirect
18. #15693020C22semidirect
30. #15692946C22semidirect
31. #15692945C22semidirect
32. #15692944C22semidirect
36. #15692932C22semidirect
37. #15692931C22semidirect
38. C4⋊Q8×C103C22semidirect
40. #103×C103C22semidirect
42. #97×C103C22semidirect
140. D103#489direct (N × H)
142. C103C2×#489semidirect
150. #489D103direct (N × H)
162. C4⋊Q8C2×D103semidirect
177. #103C2×D103semidirect
184. #97C2×D103semidirect

Maximal subgroups

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

subgroupindex
C4⋊Q8×D1032
#124×D1032
#202681532
#202681522
#202681512
#202681502
#202681492
#103×D1032
#102×D1032
#97×D1032
#489×C1032
C2×#489103