Finite Group Databasebeta

← #490×D103 #27205476

Subgroups — #490×D103 #27205476

Order 13184.

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

normal subgroups only

This group has 488 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#127×D103C211yesmaximal, characteristic
2#125×D103C211yesmaximal, characteristic, complemented
3#20268157C211yesmaximal, characteristic, complemented
4#20268156C211yesmaximal, characteristic, complemented
5#20268155C211yesmaximal, characteristic, complemented
6#20268154C214yesmaximal, complemented
7#102×D103C214yesmaximal, complemented
8#97×D103C211yesmaximal, characteristic, complemented
9#490×C103C211yesmaximal, characteristic, complemented
10C2×D4×D103—22no—
11C2×D4×D103C2212yes—
12C2×C8×D103C2212yes—
13#15693018C2211yescharacteristic
14#15693017—22no—
15#15693017C2212yes—
16#15693013C2211yescharacteristic, complemented
17#15693012C2212yescomplemented
18#15693011—22no—
19C4⋊C4×D103—22no—
20C4⋊C4×D103C2212yes—
21C42×D103C2211yescharacteristic
22#15692943C2214yescomplemented
23#15692942C2214yescomplemented
24#15692941C2214yescomplemented
25#15692932C2211yescharacteristic, complemented
26#15692931C2212yescomplemented
27#127×C103C2211yescharacteristic
28#125×C103C2211yescharacteristic, complemented
29#102×C103C2214yescomplemented
30#97×C103C2211yescharacteristic, complemented
31C23×D103—22no—
32C2×D412—22no—
33C2×D412C2312yes—
34C2×C22⋊D103—24no—
35C2×C22⋊D103—22no—
36D4×D103—28no—
37D4×D103—48no—
38C2×C4×D103—22no—
39C2×C4×D103D412yes—
40C2×C4×D103C2311yescharacteristic
41C2×C103⋊C8C2312yes—
42C8×D103—24no—
43C4⋊Dic103—22no—
44C4⋊Dic103C2312yes—
45Dic103⋊C4—22no—
46Dic103⋊C4—22no—
47Dic103⋊C4—22no—
48C4×Dic103D412yes—
49C4×Dic103C2311yescharacteristic
50C2×D4×C103—22no—
51C2×D4×C103C2312yes—
52C2×C8×C103C2312yes—
53C4⋊C4×C103—22no—
54C4⋊C4×C103C2312yes—
55C42×C103C2311yescharacteristic
56C23×C103—22no—
57C22×D103—22no—
58C22×D103—44no—
59C22×D103—48no—
60C22×D103C2×D411yescharacteristic
61D4×C103—24no—
62D4×C103—44no—
63C2×C4×C103—22no—
64C2×C4×C103C2×D412yes—
65C2×C4×C103C2411yescharacteristic
66C22⋊D103—48no—
67C22⋊D103—44no—
68C2×Dic103—22no—
69C2×Dic103C2×D412yes—
70C2×Dic103C2×D411yescharacteristic
71D412—24no—
72D412—44no—
73C4×D103—24no—
74C4×D103—44no—
75C4×D103#4114yes—
76C8×C103—22no—
77C103⋊C8—22no—
78C22×C103—42no—
79C22×C103—44no—
80C22×C103C22×D411yescharacteristic
81C2×D103—42no—
82C2×D103—44no—
83C2×D103—88no—
84C2×D103#12412yes—
85C2×D103AGL(1,ℤ/8)14yes—
86C4×C103—22no—
87C4×C103—42no—
88C4×C103C2×#4112yes—
89Dic103—22no—
90Dic103—42no—
91Dic103#12412yes—
92C2×C103—82no—
93C2×C103C2×#12411yescharacteristic
94C2×C103C2×AGL(1,ℤ/8)12yes—
95D103—82no—
96D103#49014yesdirect product factor
97C2×#490—1031nomaximal, Sylow
98C103C2×#49011yescharacteristic, complemented, Sylow
99C2×#127—1031no—
100C2×#125—1031no—
101#490—1031no—
102#490—1031no—
103#490—1034no—
104#490—1031no—
105#490D10311yescharacteristic, direct product factor
106C2×#102—1034no—
107C2×#97—1031no—
108C22×D4—1032no—
109C22×D4—2062no—
110C22×C8—1032no—
111#127—1032no—
112#127—1031no—
113#127—2062no—
114#127C2×D10311yescharacteristic
115#125—1032no—
116#125—1031no—
117#125—2062no—
118#125C2×D10311yescharacteristic, complemented
119C2×C4⋊C4—1032no—
120C2×C4⋊C4—2062no—
121C2×C42—1031no—
122#102—1034no—
123#102—1034no—
124#102—1034no—
125#102C2×D10314yescomplemented
126#97—1032no—
127#97—1031no—
128#97C2×D10311yescharacteristic, complemented
129C24—2062no—
130C2×D4—22no—
131C2×D4—1032no—
132C2×D4—4128no—
133C2×D4—2068no—
134C2×D4—2064no—
135C2×D4—2062no—
136C2×D4—2062no—
137C2×D4C22×D10312yes—
138C22×C4—1031no—
139C22×C4—1032no—
140C22×C4—2062no—
141C2×C8—1032no—
142C2×C8—2064no—
143C2×C8C22×D10312yes—
144C4⋊C4—22no—
145C4⋊C4—1032no—
146C4⋊C4—2062no—
147C4⋊C4—2062no—
148C4⋊C4—2062no—
149C4⋊C4—2062no—
150C4⋊C4C22×D10312yes—
151C42—1032no—
152C42—1031no—
153C42C22×D10311yescharacteristic
154C23—22no—
155C23—1031no—
156C23—4128no—
157C23—4124no—
158C23—2062no—
159D4—24no—
160D4—44no—
161D4—4124no—
162D4—4124no—
163D4—4128no—
164D4—2064no—
165C2×C4—22no—
166C2×C4—1031no—
167C2×C4—1034no—
168C2×C4—1032no—
169C2×C4—4124no—
170C2×C4—2064no—
171C2×C4—2062no—
172C2×C4D4×D10312yes—
173C2×C4C23×D10311yescharacteristic
174C8—22no—
175C8—2062no—
176C22—42no—
177C22—44no—
178C22—8248no—
179C22—1032no—
180C22—1034no—
181C22—4122no—
182C22—4124no—
183C22C2×D4×D10311yescharacteristic
184C4—22no—
185C4—42no—
186C4—1032no—
187C4—4122no—
188C4—2062no—
189C4#41×D10312yes—
190C2—82no—
191C2—8242no—
192C2—1034no—
193C2#124×D10311yescharacteristic
194C2AGL(1,ℤ/8)×D10312yes—
subgroupG/H
centerC22C2×D4×D103
commutator, cosocleC2×C4×C103C24
FrattiniC2×C4C23×D103
Fitting#490×C103C2
socleC22×C103C22×D4
prime radical#127×D103C2
hypercenter#490D103
hypocenterC103C2×#490
LCSG ▷ C2×C4×C103 ▷ C2×C103 ▷ C103
UCSC1 ◁ C22 ◁ C42 ◁ #490

Complements

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

NH ≅ G/Ntype
2. #125×D103C2semidirect
3. #20268157C2semidirect
4. #20268156C2semidirect
5. #20268155C2semidirect
6. #20268154C2semidirect
7. #102×D103C2semidirect
8. #97×D103C2semidirect
9. #490×C103C2semidirect
16. #15693013C22semidirect
17. #15693012C22semidirect
22. #15692943C22semidirect
23. #15692942C22semidirect
24. #15692941C22semidirect
25. #15692932C22semidirect
26. #15692931C22semidirect
28. #125×C103C22semidirect
29. #102×C103C22semidirect
30. #97×C103C22semidirect
96. D103#490direct (N × H)
98. C103C2×#490semidirect
105. #490D103direct (N × H)
118. #125C2×D103semidirect
125. #102C2×D103semidirect
128. #97C2×D103semidirect

Maximal subgroups

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

subgroupindex
#127×D1032
#125×D1032
#202681572
#202681562
#202681552
#202681542
#102×D1032
#97×D1032
#490×C1032
C2×#490103