Finite Group Databasebeta

← #34109046

Subgroups — #34109046

Order 20096.

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#23758040C212yesmaximal, complemented
2#23757395C214yesmaximal, complemented
3#23757390C214yesmaximal, complemented
4#23757322C211yesmaximal, characteristic, complemented
5C2×#19097698C212yesmaximal, complemented
6M16×Dic157C211yesmaximal, characteristic, complemented
7#575×C157C211yesmaximal, characteristic
8#19097778—24no—
9#19097778C2218yescomplemented
10C2×#14578938—24no—
11C2×#14578938C2212yes—
12C2×#14578938C2211yescharacteristic
13C2×C4×Dic157C2211yescharacteristic
14#19097707C2214yescomplemented
15#19097698C2214yescomplemented
16#19097698C2214yescomplemented
17#19097681C2212yescomplemented
18C8×Dic157C2212yescomplemented
19C2×#41×C157C2212yes—
20#137×C157C414yescomplemented
21AGL(1,ℤ/8)×C157C414yescomplemented
22#135×C157C2214yes—
23C2×M16×C157C2211yescharacteristic
24C22×Dic157—21no—
25#14578938—28no—
26#14578938—22no—
27#14578938D414yes—
28#14578938C2314yes—
29C2×#11929434—28no—
30C2×#11929434—22no—
31C2×#11929434C2312yes—
32C4×Dic157—21no—
33C4×Dic157C2311yescharacteristic
34C4×Dic157C2311yescharacteristic
35#41×C157—22no—
36#41×C157—22no—
37#41×C157C2×C414yes—
38#41×C157C2314yes—
39C2×Q8×C157C2×C412yes—
40C2×D4×C157—22no—
41C2×D4×C157C2×C412yes—
42C22×C4×C157—22no—
43C22×C4×C157C2311yescharacteristic
44Q16×C157C2×C414yescomplemented
45SD16×C157C2×C418yescomplemented
46D8×C157C2×C414yescomplemented
47M16×C157C2×C414yes—
48C2×C8×C157C2312yes—
49C2×Dic157—21no—
50C2×Dic157—21no—
51C2×Dic157—42no—
52#11929434—24no—
53#11929434C2×D414yes—
54C23×C157—22no—
55C23×C157#4111yescharacteristic
56Q8×C157—22no—
57Q8×C157C22×C414yes—
58D4×C157—24no—
59D4×C157—24no—
60D4×C157—22no—
61D4×C157C22×C414yes—
62C2×C4×C157—22no—
63C2×C4×C157—24no—
64C2×C4×C157—24no—
65C2×C4×C157C22×C412yes—
66C2×C4×C157C2×D412yes—
67C2×C4×C157#4111yescharacteristic
68C2×C4×C157C2411yescharacteristic
69C8×C157C22×C414yes—
70C22×C157—24no—
71C22×C157—41no—
72C22×C157—82no—
73C22×C157C4×D412yes—
74C22×C157C2×#4111yescharacteristic
75C4×C157—24no—
76C4×C157C4×D412yes—
77C4×C157C23×C411yescharacteristic
78C4×C157C22×D411yescharacteristic
79Dic157—22no—
80Dic157—41no—
81C2×C157—21no—
82C2×C157—22no—
83C2×C157—44no—
84C2×C157C2×C4×D411yescharacteristic
85C157#295611yescharacteristic, complemented, Sylow
86#2956—1571nomaximal, Sylow
87#575D15711yescharacteristic
88#568—1572no—
89#444—1574no—
90#443—1574no—
91#430—1571no—
92C2×#104—1572no—
93C4×M16—1571no—
94C2×#41C2×D15712yes—
95#137Dic15714yescomplemented
96AGL(1,ℤ/8)Dic15714yescomplemented
97#135C2×D15714yes—
98#131—3144no—
99#131—1578no—
100C2×M16—3144no—
101C2×M16—1572no—
102C2×M16—1571no—
103C2×M16C2×D15711yescharacteristic
104C2×C42—1571no—
105#108—1574no—
106#104—1574no—
107#104—1574no—
108#97—1572no—
109C4×C8—1572no—
110#41—22no—
111#41—22no—
112#41C2×Dic15714yes—
113#41C22×D15714yes—
114C2×Q8C2×Dic15712yes—
115C2×D4—22no—
116C2×D4C2×Dic15712yes—
117C22×C4—22no—
118C22×C4—3141no—
119C22×C4C22×D15711yescharacteristic
120Q16C2×Dic15714yescomplemented
121SD16C2×Dic15718yescomplemented
122D8C2×Dic15714yescomplemented
123M16—3142no—
124M16—3148no—
125M16—1574no—
126M16—1574no—
127M16C2×Dic15714yes—
128C2×C8—3142no—
129C2×C8—3148no—
130C2×C8—1572no—
131C2×C8C22×D15712yes—
132C42—3141no—
133C42—1571no—
134C42—1571no—
135C23—22no—
136C23#1457895311yescharacteristic
137Q8—22no—
138Q8C22×Dic15714yes—
139D4—24no—
140D4—24no—
141D4—22no—
142D4C22×Dic15714yes—
143C2×C4—22no—
144C2×C4—24no—
145C2×C4—24no—
146C2×C4—3141no—
147C2×C4—3141no—
148C2×C4—6282no—
149C2×C4C22×Dic15712yes—
150C2×C4D4×D15712yes—
151C2×C4#1457895311yescharacteristic
152C2×C4C23×D15711yescharacteristic
153C8—3144no—
154C8—1574no—
155C8C22×Dic15714yes—
156C22—24no—
157C22—41no—
158C22—82no—
159C22D4×Dic15712yes—
160C22C2×#1457895311yescharacteristic
161C4—24no—
162C4—3142no—
163C4—6281no—
164C4D4×Dic15712yes—
165C4C23×Dic15711yescharacteristic
166C4C2×D4×D15711yescharacteristic
167C2—21no—
168C2—22no—
169C2—44no—
170C2C2×D4×Dic15711yescharacteristic
subgroupG/H
centerC4C2×D4×D157
commutatorC4×C157C23×C4
FrattiniC2×C4C23×D157
Fitting, prime radical#575×C157C2
socleC2×C157C2×C4×D4
cosocleC2×C4×C157C24
hypercenter#575D157
hypocenterC157#2956
LCSG ▷ C4×C157 ▷ C2×C157 ▷ C157
UCSC1 ◁ C4 ◁ C22×C4 ◁ #575

Complements

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

NH ≅ G/Ntype
1. #23758040C2semidirect
2. #23757395C2semidirect
3. #23757390C2semidirect
4. #23757322C2semidirect
5. C2×#19097698C2semidirect
6. M16×Dic157C2semidirect
9. #19097778C22semidirect
14. #19097707C22semidirect
15. #19097698C22semidirect
16. #19097698C22semidirect
17. #19097681C22semidirect
18. C8×Dic157C22semidirect
20. #137×C157C4semidirect
21. AGL(1,ℤ/8)×C157C4semidirect
44. Q16×C157C2×C4semidirect
45. SD16×C157C2×C4semidirect
46. D8×C157C2×C4semidirect
85. C157#2956semidirect
95. #137Dic157semidirect
96. AGL(1,ℤ/8)Dic157semidirect
120. Q16C2×Dic157semidirect
121. SD16C2×Dic157semidirect
122. D8C2×Dic157semidirect

Maximal subgroups

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

subgroupindex
#237580402
#237573952
#237573902
#237573222
C2×#190976982
M16×Dic1572
#575×C1572
#2956157