Finite Group Databasebeta

← #27204054

Subgroups — #27204054

Order 13184.

458 conjugacy classes of subgroups; only the 217 normal subgroups are shown.

normal subgroups only

This group has 458 conjugacy classes of subgroups — too many to draw. Only its 217 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#20268558C212yesmaximal, complemented
2#20267913C214yesmaximal, complemented
3#20267908C214yesmaximal, complemented
4#20267840C211yesmaximal, characteristic, complemented
5C2×#15692948C212yesmaximal, complemented
6M16×Dic103C211yesmaximal, characteristic, complemented
7#575×C103C211yesmaximal, characteristic
8#15693028—24no—
9#15693028C2218yescomplemented
10C2×#13110089—24no—
11C2×#13110089C2212yes—
12C2×#13110089C2211yescharacteristic
13C2×C4×Dic103C2211yescharacteristic
14#15692957C2214yescomplemented
15#15692948C2214yescomplemented
16#15692948C2214yescomplemented
17#15692931C2212yescomplemented
18C8×Dic103C2212yescomplemented
19C2×#41×C103C2212yes—
20#137×C103C414yescomplemented
21AGL(1,ℤ/8)×C103C414yescomplemented
22#135×C103C2214yes—
23C2×M16×C103C2211yescharacteristic
24C22×Dic103—21no—
25#13110089—22no—
26#13110089—28no—
27#13110089D414yes—
28#13110089C2314yes—
29C2×C103⋊C8—22no—
30C2×C103⋊C8—28no—
31C2×C103⋊C8C2312yes—
32C4×Dic103—21no—
33C4×Dic103C2311yescharacteristic
34C4×Dic103C2311yescharacteristic
35#41×C103—22no—
36#41×C103—22no—
37#41×C103C2×C414yes—
38#41×C103C2314yes—
39C2×Q8×C103C2×C412yes—
40C2×D4×C103—22no—
41C2×D4×C103C2×C412yes—
42C22×C4×C103—22no—
43C22×C4×C103C2311yescharacteristic
44Q16×C103C2×C414yescomplemented
45SD16×C103C2×C418yescomplemented
46D8×C103C2×C414yescomplemented
47M16×C103C2×C414yes—
48C2×C8×C103C2312yes—
49C23×C103—22no—
50C23×C103#4111yescharacteristic
51Q8×C103—22no—
52Q8×C103C22×C414yes—
53D4×C103—24no—
54D4×C103—24no—
55D4×C103—22no—
56D4×C103C22×C414yes—
57C2×C4×C103—22no—
58C2×C4×C103—24no—
59C2×C4×C103—24no—
60C2×C4×C103C22×C412yes—
61C2×C4×C103C2×D412yes—
62C2×C4×C103#4111yescharacteristic
63C2×C4×C103C2411yescharacteristic
64C2×Dic103—21no—
65C2×Dic103—21no—
66C2×Dic103—42no—
67C8×C103C22×C414yes—
68C103⋊C8—24no—
69C103⋊C8C2×D414yes—
70C22×C103—24no—
71C22×C103—41no—
72C22×C103—82no—
73C22×C103C4×D412yes—
74C22×C103C2×#4111yescharacteristic
75C4×C103—24no—
76C4×C103C4×D412yes—
77C4×C103C23×C411yescharacteristic
78C4×C103C22×D411yescharacteristic
79Dic103—22no—
80Dic103—41no—
81C2×C103—21no—
82C2×C103—22no—
83C2×C103—44no—
84C2×C103C2×C4×D411yescharacteristic
85#2956—1031nomaximal, Sylow
86C103#295611yescharacteristic, complemented, Sylow
87#575D10311yescharacteristic
88#568—1032no—
89#444—1034no—
90#443—1034no—
91#430—1031no—
92C2×#104—1032no—
93C4×M16—1031no—
94C2×#41C2×D10312yes—
95#137Dic10314yescomplemented
96AGL(1,ℤ/8)Dic10314yescomplemented
97#135C2×D10314yes—
98#131—1038no—
99#131—2064no—
100C2×M16—1031no—
101C2×M16—1032no—
102C2×M16—2064no—
103C2×M16C2×D10311yescharacteristic
104C2×C42—1031no—
105#108—1034no—
106#104—1034no—
107#104—1034no—
108#97—1032no—
109C4×C8—1032no—
110#41—22no—
111#41—22no—
112#41C2×Dic10314yes—
113#41C22×D10314yes—
114C2×Q8C2×Dic10312yes—
115C2×D4—22no—
116C2×D4C2×Dic10312yes—
117C22×C4—22no—
118C22×C4—2061no—
119C22×C4C22×D10311yescharacteristic
120Q16C2×Dic10314yescomplemented
121SD16C2×Dic10318yescomplemented
122D8C2×Dic10314yescomplemented
123M16—1034no—
124M16—1034no—
125M16—2068no—
126M16—2062no—
127M16C2×Dic10314yes—
128C2×C8—1032no—
129C2×C8—2068no—
130C2×C8—2062no—
131C2×C8C22×D10312yes—
132C42—1031no—
133C42—1031no—
134C42—2061no—
135C23—22no—
136C23#1311010411yescharacteristic
137Q8—22no—
138Q8C22×Dic10314yes—
139D4—24no—
140D4—24no—
141D4—22no—
142D4C22×Dic10314yes—
143C2×C4—22no—
144C2×C4—24no—
145C2×C4—24no—
146C2×C4—4122no—
147C2×C4—2061no—
148C2×C4—2061no—
149C2×C4C22×Dic10312yes—
150C2×C4D4×D10312yes—
151C2×C4#1311010411yescharacteristic
152C2×C4C23×D10311yescharacteristic
153C8—1034no—
154C8—2064no—
155C8C22×Dic10314yes—
156C22—24no—
157C22—41no—
158C22—82no—
159C22D4×Dic10312yes—
160C22C2×#1311010411yescharacteristic
161C4—24no—
162C4—4121no—
163C4—2062no—
164C4D4×Dic10312yes—
165C4C23×Dic10311yescharacteristic
166C4C2×D4×D10311yescharacteristic
167C2—21no—
168C2—22no—
169C2—44no—
170C2C2×D4×Dic10311yescharacteristic
subgroupG/H
centerC4C2×D4×D103
commutatorC4×C103C23×C4
FrattiniC2×C4C23×D103
Fitting, prime radical#575×C103C2
socleC2×C103C2×C4×D4
cosocleC2×C4×C103C24
hypercenter#575D103
hypocenterC103#2956
LCSG ▷ C4×C103 ▷ C2×C103 ▷ C103
UCSC1 ◁ C4 ◁ C22×C4 ◁ #575

Complements

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

NH ≅ G/Ntype
1. #20268558C2semidirect
2. #20267913C2semidirect
3. #20267908C2semidirect
4. #20267840C2semidirect
5. C2×#15692948C2semidirect
6. M16×Dic103C2semidirect
9. #15693028C22semidirect
14. #15692957C22semidirect
15. #15692948C22semidirect
16. #15692948C22semidirect
17. #15692931C22semidirect
18. C8×Dic103C22semidirect
20. #137×C103C4semidirect
21. AGL(1,ℤ/8)×C103C4semidirect
44. Q16×C103C2×C4semidirect
45. SD16×C103C2×C4semidirect
46. D8×C103C2×C4semidirect
86. C103#2956semidirect
95. #137Dic103semidirect
96. AGL(1,ℤ/8)Dic103semidirect
120. Q16C2×Dic103semidirect
121. SD16C2×Dic103semidirect
122. D8C2×Dic103semidirect

Maximal subgroups

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

subgroupindex
#202685582
#202679132
#202679082
#202678402
C2×#156929482
M16×Dic1032
#575×C1032
#2956103