Finite Group Databasebeta

← #34111929

Subgroups — #34111929

Order 20096.

460 conjugacy classes of subgroups; only the 117 normal subgroups are shown.

normal subgroups only

This group has 460 conjugacy classes of subgroups — too many to draw. Only its 117 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#23758079C214yesmaximal, complemented
2#23757533C214yesmaximal, complemented
3#23757455C212yesmaximal, complemented
4#23757440C212yesmaximal, complemented
5#23757391C212yesmaximal, complemented
6#492×C157C211yesmaximal, characteristic, complemented
7#19097819C2212yes—
8#19097816C2212yescomplemented
9#19097802C2214yescomplemented
10#19097800—24no—
11#19097798—24no—
12#19097797C2214yes—
13#19097793C2212yes—
14#19097792—24no—
15SD16×D157—24no—
16#19097777C2214yescomplemented
17#19097707C2212yescomplemented
18#19097699C2214yescomplemented
19#19097690C2212yescomplemented
20#19097688C2212yescomplemented
21C2×SD16×C157C2214yescomplemented
22C4⋊Q8×C157C2211yescharacteristic, complemented
23#127×C157C2211yescharacteristic
24C4×C8×C157C2211yescharacteristic, complemented
25#14578955—24no—
26#14578954—42no—
27#14578954C2314yes—
28#14578953—24no—
29Q8×D157—24no—
30C2×C22⋊D157—42no—
31D4×D157—24no—
32Dic628D412yescomplemented
33#14578944—24no—
34#14578943D414yescomplemented
35#14578942—24no—
36#14578941—24no—
37D1256D412yescomplemented
38#14578939—24no—
39#14578938C2314yes—
40#14578937—24no—
41C8×D157—24no—
42C2×Q8×C157C2312yes—
43C2×D4×C157—41no—
44C2×D4×C157C2312yes—
45SD16×C157—24no—
46SD16×C157—24no—
47C2×C8×C157C2312yes—
48C4⋊C4×C157—41no—
49C42×C157C2311yescharacteristic
50C22×D157—42no—
51Dic314—42no—
52Dic314C2×D414yes—
53D628—42no—
54D628C2×D414yes—
55C22⋊D157—24no—
56C22⋊D157—44no—
57C2×Dic157—42no—
58C4×D157—24no—
59C4×D157—44no—
60#11929434—24no—
61C23×C157—22no—
62Q8×C157—24no—
63D4×C157—24no—
64D4×C157—82no—
65C2×C4×C157—21no—
66C2×C4×C157—22no—
67C2×C4×C157C2411yescharacteristic
68C8×C157C2×D412yes—
69C8×C157C2×D412yes—
70C22×C157—42no—
71C22×C157—82no—
72C22×C157H(5,𝔽2)11yescharacteristic
73C2×D157—24no—
74C2×D157—162no—
75C4×C157—22no—
76C4×C157—42no—
77C4×C157C22×D412yes—
78Dic157—24no—
79C2×C157—21no—
80C2×C157—82no—
81C2×C157D4211yescharacteristic
82D157—44no—
83C157#329111yescharacteristic, complemented, Sylow
84#3291—1571nomaximal, Sylow
85#577—1574no—
86#492D15711yescharacteristic, complemented
87#471—1574no—
88#456—1572no—
89#453—1572no—
90#443—1572no—
912−1+4—1572no—
92H(5,𝔽2)—1572no—
93#137—3144no—
94#137—1574no—
95AGL(1,ℤ/8)—3144no—
96AGL(1,ℤ/8)—1574no—
97#135—3144no—
98#135—1572no—
99C2×SD16—3144no—
100C2×SD16C2×D15714yescomplemented
101#131—1574no—
102C4⋊Q8C2×D15711yescharacteristic, complemented
103#127C2×D15711yescharacteristic
104#108—1572no—
105#104—1574no—
106#101—1572no—
107#100—1572no—
108C4×C8C2×D15711yescharacteristic, complemented
109#41—3144no—
110#41—3144no—
111#41—6282no—
112#41—1574no—
113C2×Q8—3144no—
114C2×Q8C22×D15712yes—
115C2×D4—41no—
116C2×D4—3144no—
117C2×D4—6282no—
118C2×D4C22×D15712yes—
119Q16—3144no—
120Q16—1572no—
121SD16—24no—
122SD16—24no—
123SD16—3144no—
124SD16—3144no—
125SD16—1574no—
126D8—3144no—
127D8—1572no—
128M16—3144no—
129M16—1574no—
130C2×C8—3144no—
131C2×C8C22×D15712yes—
132C4⋊C4—41no—
133C42C22×D15711yescharacteristic
134C23—22no—
135C23—6282no—
136Q8—24no—
137Q8—6282no—
138Q8—1574no—
139D4—24no—
140D4—82no—
141D4—3144no—
142D4—6282no—
143D4—6284no—
144D4—1574no—
145C2×C4—21no—
146C2×C4—22no—
147C2×C4—3144no—
148C2×C4—6284no—
149C2×C4—6282no—
150C2×C4C23×D15711yescharacteristic
151C8—3144no—
152C8D4×D15712yes—
153C8D4×D15712yes—
154C22—42no—
155C22—82no—
156C22—3144no—
157C22—25122no—
158C22#1909781611yescharacteristic
159C4—22no—
160C4—42no—
161C4—3144no—
162C4C2×D4×D15712yes—
163C2—21no—
164C2—82no—
165C2—6284no—
166C2#2375790811yescharacteristic
subgroupG/H
centerC2#23757908
commutator, cosocleC2×C4×C157C24
FrattiniC2×C4C23×D157
Fitting#492×C157C2
socleC2×C157D42
hypercenter#492D157
hypocenterC157#3291
LCSG ▷ C2×C4×C157 ▷ C2×C157 ▷ C157
UCSC1 ◁ C2 ◁ C2×C4 ◁ #492

Complements

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

NH ≅ G/Ntype
1. #23758079C2semidirect
2. #23757533C2semidirect
3. #23757455C2semidirect
4. #23757440C2semidirect
5. #23757391C2semidirect
6. #492×C157C2semidirect
8. #19097816C22semidirect
9. #19097802C22semidirect
16. #19097777C22semidirect
17. #19097707C22semidirect
18. #19097699C22semidirect
19. #19097690C22semidirect
20. #19097688C22semidirect
21. C2×SD16×C157C22semidirect
22. C4⋊Q8×C157C22semidirect
24. C4×C8×C157C22semidirect
32. Dic628D4semidirect
34. #14578943D4semidirect
37. D1256D4semidirect
83. C157#3291semidirect
86. #492D157semidirect
100. C2×SD16C2×D157semidirect
102. C4⋊Q8C2×D157semidirect
108. C4×C8C2×D157semidirect

Maximal subgroups

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

subgroupindex
#237580792
#237575332
#237574552
#237574402
#237573912
#492×C1572
#3291157