Finite Group Databasebeta

← #34116094

Subgroups — #34116094

Order 20096.

252 conjugacy classes of subgroups; only the 66 normal subgroups are shown.

normal subgroups only

This group has 252 conjugacy classes of subgroups — too many to draw. Only its 66 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#23758353C211yesmaximal, characteristic
2#23758288C212yesmaximal, complemented
3#23758248C211yesmaximal, characteristic
4#23758148C212yesmaximal, complemented
5#23757256C211yesmaximal, characteristic
6#19097859—22no—
7#19097859—22no—
8C2×#14578964C2211yescharacteristic
9D157⋊M16—22no—
10D157⋊M16C2212yes—
11C2×D157⋊C8C2211yescharacteristic
12#19097842—22no—
13#19097841—22no—
14#19097828—22no—
15C2×#14578955C2211yescharacteristic
16M16×D157C2212yes—
17#19097690C411yescharacteristic
18#19097687C412yes—
19#101×C157C411yescharacteristic
20#14578964—22no—
21#14578964—22no—
22#14578964—22no—
23#14578964D412yes—
24#14578964D412yes—
25#14578963—22no—
26D157⋊C8—24no—
27D157⋊C8—22no—
28D157⋊C8—22no—
29C2×#11929441—21no—
30C2×#11929441—21no—
31#14578955—22no—
32#14578955—22no—
33C2×D628C2×C411yescharacteristic
34C2×D628Q812yes—
35C2×C4×D157D412yes—
36C2×C4×D157C2311yescharacteristic
37#14578938C2×C412yes—
38#14578937—22no—
39C8×D157—22no—
40C2×Q8×C157C2×C411yescharacteristic
41M16×C157C2×C412yes—
42#11929441—22no—
43#11929441—22no—
44#11929441—41no—
45#11929441—41no—
46C22×D157C4⋊C412yes—
47C22×D157C2×Q811yescharacteristic
48D628—24no—
49D628—22no—
50C2×Dic157C2×D411yescharacteristic
51C4×D157—22no—
52C4×D157—22no—
53C4×D157C2×D412yes—
54C4×D157#4112yes—
55#11929434—22no—
56Q8×C157—22no—
57C2×C4×C157C4⋊C412yes—
58C2×C4×C157C22×C411yescharacteristic
59C8×C157—22no—
60C22×C157C2×C4⋊C411yescharacteristic
61C2×D157—22no—
62C2×D157—41no—
63C2×D157—42no—
64C2×D157C22⋊Q812yes—
65C4×C157—22no—
66C4×C157C4×D412yes—
67Dic157#12011yescharacteristic
68Dic157#12311yescharacteristic
69C2×C157—21no—
70C2×C157#38511yescharacteristic
71D157—22no—
72D157—42no—
73C157#185811yescharacteristic, complemented, Sylow
74#1858—1571nomaximal, Sylow
75#568—1571no—
76#430—1572no—
77#413—1571no—
78#408—1571no—
79#341—1572no—
80C2×#41—1571no—
81#131—3142no—
82#131—3142no—
83C2×M16—3142no—
84C2×M16—1571no—
85C2×M16—1572no—
86C2×M16—1572no—
87C22×C8—1571no—
88#108—3142no—
89#108—3142no—
90#101—1571no—
91#101#1059784511yescharacteristic
92#100—1572no—
93C22⋊C8—3142no—
94#41—3142no—
95#41—3142no—
96C2×Q8C2×#1059784511yescharacteristic
97C2×D4—1572no—
98C2×D4—1571no—
99C22×C4—1572no—
100C22×C4—1571no—
101M16—3142no—
102M16—3142no—
103M16—3142no—
104M16—3142no—
105M16—3142no—
106M16—1572no—
107M16—1572no—
108M16—1572no—
109M16C2×#1059784512yes—
110C2×C8—3142no—
111C2×C8—3144no—
112C2×C8—3142no—
113C2×C8—3141no—
114C2×C8—3141no—
115C2×C8—3142no—
116C23—1572no—
117C23—1571no—
118Q8—22no—
119D4—3144no—
120D4—3142no—
121C2×C4—3142no—
122C2×C4—3142no—
123C2×C4—1571no—
124C2×C4—1572no—
125C2×C4—1572no—
126C2×C4C4⋊#1059784512yes—
127C2×C4C22×#1059784511yescharacteristic
128C8—22no—
129C8—3142no—
130C8—3142no—
131C8—3142no—
132C8—6281no—
133C8—6281no—
134C22—3142no—
135C22—6281no—
136C22—6282no—
137C22—1572no—
138C22C2×C4⋊#1059784511yescharacteristic
139C4—22no—
140C4—1571no—
141C4—1571no—
142C4D4×#1059784512yes—
143C2—21no—
144C2—3142no—
145C2—6282no—
146C2#2375822011yescharacteristic
subgroupG/H
centerC2#23758220
commutatorC2×C4×C157C22×C4
FrattiniC2×C4C22×#10597845
Fitting#101×C157C4
socleC2×C157#385
prime radicalC2×#14578955C22
cosocleC2×C4×D157C23
hypercenter#101#10597845
hypocenterC157#1858
LCSG ▷ C2×C4×C157 ▷ C2×C157 ▷ C157
UCSC1 ◁ C2 ◁ C2×C4 ◁ #101

Complements

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

NH ≅ G/Ntype
2. #23758288C2semidirect
4. #23758148C2semidirect
73. C157#1858semidirect

Maximal subgroups

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

subgroupindex
#237583532
#237582882
#237582482
#237581482
#237572562
#1858157