Finite Group Databasebeta

← #496×D103 #27205574

Subgroups — #496×D103 #27205574

Order 13184.

668 conjugacy classes of subgroups; only the 145 normal subgroups are shown.

normal subgroups only

This group has 668 conjugacy classes of subgroups — too many to draw. Only its 145 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×SD16×D103C212yesmaximal, complemented
2C2×D8×D103C212yesmaximal, complemented
3#127×D103C211yesmaximal, characteristic, complemented
4#124×D103C211yesmaximal, characteristic, complemented
5#20268181C211yesmaximal, characteristic, complemented
6#20268180C211yesmaximal, characteristic, complemented
7#20268179C212yesmaximal, complemented
8#20268178C211yesmaximal, characteristic, complemented
9#20268177C212yesmaximal, complemented
10#97×D103C211yesmaximal, characteristic, complemented
11#496×C103C211yesmaximal, characteristic, complemented
12C2×Q8×D103C2211yescharacteristic
13C2×D4×D103—22no—
14C2×D4×D103C2211yescharacteristic
15C2×D4×D103C2212yes—
16C2×#13110094C2212yescomplemented
17C2×#13110093C2212yescomplemented
18C2×#13110092C2212yescomplemented
19SD16×D103—28no—
20C2×D824C2212yescomplemented
21C2×#13110090C2212yescomplemented
22C2×#13110090C2212yescomplemented
23D8×D103—28no—
24C2×C8×D103C2212yes—
25#15693018C2211yescharacteristic, complemented
26#15693017—22no—
27#15693017C2212yescomplemented
28#15693010C2211yescharacteristic, complemented
29#15693009C2211yescharacteristic, complemented
30#15693008C2211yescharacteristic, complemented
31#15693007—22no—
32C22⋊C4×D103—22no—
33C42×D103C2211yescharacteristic
34#15692932C2211yescharacteristic, complemented
35#15692931C2212yescomplemented
36C2×SD16×C103C2212yescomplemented
37C2×D8×C103C2212yescomplemented
38#127×C103C2211yescharacteristic, complemented
39#124×C103C2211yescharacteristic, complemented
40#97×C103C2211yescharacteristic, complemented
41C23×D103—22no—
42C23×D103—21no—
43C2×Dic206—21no—
44C2×Dic206C2311yescharacteristic
45Q8×D103—24no—
46C2×D412—22no—
47C2×D412C2311yescharacteristic
48C2×D412C2312yes—
49C2×C22⋊D103—24no—
50C2×C22⋊D103—21no—
51C2×C22⋊D103—22no—
52D4×D103—24no—
53D4×D103—24no—
54D4×D103—24no—
55D4×D103—48no—
56C2×C4×D103—21no—
57C2×C4×D103D412yes—
58C2×C4×D103C2311yescharacteristic
59#13110094—24no—
60#13110093—24no—
61#13110092—24no—
62D824—24no—
63#13110090—24no—
64#13110090—24no—
65C2×C103⋊C8C2312yes—
66C8×D103D418yescomplemented
67C22⋊Dic103—22no—
68(C2×D103)⋊C4—22no—
69(C2×D103)⋊C4—22no—
70C4×Dic103D412yes—
71C4×Dic103C2311yescharacteristic
72C2×Q8×C103C2311yescharacteristic
73C2×D4×C103—22no—
74C2×D4×C103C2311yescharacteristic
75C2×D4×C103C2312yes—
76SD16×C103—24no—
77D8×C103—24no—
78C2×C8×C103C2312yes—
79C22⋊C4×C103—22no—
80C42×C103C2311yescharacteristic
81C23×C103—21no—
82C23×C103—22no—
83C22×D103—21no—
84C22×D103—22no—
85C22×D103—42no—
86C22×D103—44no—
87C22×D103—48no—
88C22×D103—44no—
89C22×D103C2×D411yescharacteristic
90Q8×C103—22no—
91D4×C103—22no—
92D4×C103—22no—
93D4×C103—22no—
94D4×C103—44no—
95C2×C4×C103—21no—
96C2×C4×C103C2×D412yes—
97C2×C4×C103C2411yescharacteristic
98C22⋊D103—48no—
99C22⋊D103—42no—
100C22⋊D103—44no—
101C2×Dic103—21no—
102C2×Dic103C2×D412yes—
103C2×Dic103C2×D411yescharacteristic
104D412—22no—
105D412—22no—
106D412—22no—
107D412—44no—
108C4×D103—24no—
109C4×D103—42no—
110C4×D103C2×D414yes—
111Dic206—22no—
112Dic206—42no—
113C8×C103C2×D414yescomplemented
114C103⋊C8C2×D414yescomplemented
115C22×C103—41no—
116C22×C103—42no—
117C22×C103—44no—
118C22×C103—42no—
119C22×C103C22×D411yescharacteristic
120C2×D103—41no—
121C2×D103—42no—
122C2×D103—44no—
123C2×D103—42no—
124C2×D103—88no—
125C2×D103—84no—
126C2×D103#12712yes—
127C2×D103AGL(1,ℤ/8)14yes—
128C4×C103—22no—
129C4×C103—41no—
130C4×C103C22×D412yes—
131Dic103—22no—
132Dic103—41no—
133Dic103#12712yes—
134C2×C103—82no—
135C2×C103—81no—
136C2×C103C2×#12711yescharacteristic
137C2×C103C2×AGL(1,ℤ/8)12yes—
138D103—82no—
139D103—81no—
140D103#49614yesdirect product factor
141C2×#496—1031nomaximal, Sylow
142C103C2×#49611yescharacteristic, complemented, Sylow
143C22×SD16—1032no—
144C22×D8—1032no—
145C2×#127—1031no—
146C2×#124—1031no—
147#496—1032no—
148#496—1032no—
149#496—1031no—
150#496—1031no—
151#496—1031no—
152#496D10311yescharacteristic, direct product factor
153C2×#97—1031no—
154C22×Q8—1031no—
155C22×D4—1031no—
156C22×D4—1032no—
157C22×D4—2062no—
158C2×SD16—1032no—
159C2×SD16—1032no—
160C2×SD16—1032no—
161C2×SD16—2068no—
162C2×SD16C2×D10312yescomplemented
163C2×D8—1032no—
164C2×D8—1032no—
165C2×D8—1032no—
166C2×D8—2068no—
167C2×D8C2×D10312yescomplemented
168C22×C8—1032no—
169#127—1032no—
170#127—1031no—
171#127—2062no—
172#127C2×D10311yescharacteristic, complemented
173#124—1031no—
174#124—1031no—
175#124—1031no—
176#124—2062no—
177#124C2×D10311yescharacteristic, complemented
178C2×C22⋊C4—2062no—
179C2×C42—1031no—
180#97—1032no—
181#97—1031no—
182#97C2×D10311yescharacteristic, complemented
183C24—2061no—
184C24—2062no—
185C2×Q8—1031no—
186C2×Q8—2061no—
187C2×Q8—2064no—
188C2×Q8C22×D10311yescharacteristic
189C2×D4—22no—
190C2×D4—1031no—
191C2×D4—1032no—
192C2×D4—4128no—
193C2×D4—2064no—
194C2×D4—2064no—
195C2×D4—2064no—
196C2×D4—2061no—
197C2×D4—2064no—
198C2×D4—2062no—
199C2×D4—2062no—
200C2×D4C22×D10311yescharacteristic
201C2×D4C22×D10312yes—
202C22×C4—1031no—
203C22×C4—1032no—
204C22×C4—2061no—
205SD16—24no—
206SD16—2064no—
207SD16—2064no—
208SD16—2064no—
209D8—24no—
210D8—2064no—
211D8—2064no—
212D8—2064no—
213C2×C8—1032no—
214C2×C8—1038no—
215C2×C8C22×D10312yes—
216C22⋊C4—22no—
217C22⋊C4—2062no—
218C22⋊C4—2062no—
219C22⋊C4—2062no—
220C42—1032no—
221C42—1031no—
222C42C22×D10311yescharacteristic
223C23—21no—
224C23—22no—
225C23—1031no—
226C23—4128no—
227C23—4122no—
228C23—4124no—
229C23—4124no—
230C23—2061no—
231C23—2062no—
232Q8—22no—
233Q8—4122no—
234Q8—2062no—
235D4—22no—
236D4—22no—
237D4—22no—
238D4—44no—
239D4—4124no—
240D4—4122no—
241D4—4124no—
242D4—4128no—
243D4—2062no—
244D4—2062no—
245D4—2062no—
246C2×C4—21no—
247C2×C4—1031no—
248C2×C4—1034no—
249C2×C4—1032no—
250C2×C4—4122no—
251C2×C4—2064no—
252C2×C4—2061no—
253C2×C4D4×D10312yes—
254C2×C4C23×D10311yescharacteristic
255C8—1034no—
256C8D4×D10314yescomplemented
257C22—44no—
258C22—42no—
259C22—41no—
260C22—42no—
261C22—8248no—
262C22—8244no—
263C22—1034no—
264C22—1032no—
265C22—4124no—
266C22—4122no—
267C22—4121no—
268C22—4122no—
269C22C2×D4×D10311yescharacteristic
270C4—22no—
271C4—41no—
272C4—1032no—
273C4—4121no—
274C4—2062no—
275C4C2×D4×D10312yes—
276C2—82no—
277C2—81no—
278C2—8242no—
279C2—8241no—
280C2—1034no—
281C2#127×D10311yescharacteristic
282C2AGL(1,ℤ/8)×D10312yes—
subgroupG/H
centerC22C2×D4×D103
commutator, cosocleC2×C4×C103C24
FrattiniC2×C4C23×D103
Fitting#496×C103C2
socleC22×C103C22×D4
hypercenter#496D103
hypocenterC103C2×#496
LCSG ▷ C2×C4×C103 ▷ C2×C103 ▷ C103
UCSC1 ◁ C22 ◁ C42 ◁ #496

Complements

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

NH ≅ G/Ntype
1. C2×SD16×D103C2semidirect
2. C2×D8×D103C2semidirect
3. #127×D103C2semidirect
4. #124×D103C2semidirect
5. #20268181C2semidirect
6. #20268180C2semidirect
7. #20268179C2semidirect
8. #20268178C2semidirect
9. #20268177C2semidirect
10. #97×D103C2semidirect
11. #496×C103C2semidirect
16. C2×#13110094C22semidirect
17. C2×#13110093C22semidirect
18. C2×#13110092C22semidirect
20. C2×D824C22semidirect
21. C2×#13110090C22semidirect
22. C2×#13110090C22semidirect
25. #15693018C22semidirect
27. #15693017C22semidirect
28. #15693010C22semidirect
29. #15693009C22semidirect
30. #15693008C22semidirect
34. #15692932C22semidirect
35. #15692931C22semidirect
36. C2×SD16×C103C22semidirect
37. C2×D8×C103C22semidirect
38. #127×C103C22semidirect
39. #124×C103C22semidirect
40. #97×C103C22semidirect
66. C8×D103D4semidirect
113. C8×C103C2×D4semidirect
114. C103⋊C8C2×D4semidirect
140. D103#496direct (N × H)
142. C103C2×#496semidirect
152. #496D103direct (N × H)
162. C2×SD16C2×D103semidirect
167. C2×D8C2×D103semidirect
172. #127C2×D103semidirect
177. #124C2×D103semidirect
182. #97C2×D103semidirect
256. C8D4×D103semidirect

Maximal subgroups

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

subgroupindex
C2×SD16×D1032
C2×D8×D1032
#127×D1032
#124×D1032
#202681812
#202681802
#202681792
#202681782
#202681772
#97×D1032
#496×C1032
C2×#496103