Finite Group Databasebeta

← #34115238

Subgroups — #34115238

Order 20096.

162 conjugacy classes of subgroups; only the 38 normal subgroups are shown.

normal subgroups only

This group has 162 conjugacy classes of subgroups — too many to draw. Only its 38 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#23758254C211yesmaximal, characteristic
2#23758248C211yesmaximal, characteristic
3#23757256C211yesmaximal, characteristic
4C2×#14578964C411yescharacteristic, complemented
5C2×D157⋊C8C411yescharacteristic, complemented
6#19097850—21no—
7#19097830—21no—
8#19097830C412yes—
9#19097828—21no—
10#19097828—21no—
11C2×#14578955C2211yescharacteristic
12M16×D157—21no—
13#19097690C411yescharacteristic, complemented
14#19097687—21no—
15#101×C157C411yescharacteristic, complemented
16#14578964—41no—
17D157⋊C8—41no—
18C2×#11929441—21no—
19C2×#11929441—21no—
20C4⋊#10597845—41no—
21C22⋊#10597845—22no—
22C4×#10597845—41no—
23#14578955—41no—
24#14578955—41no—
25C2×D628C2×C411yescharacteristic
26C2×D628D411yescharacteristic
27C2×D628Q811yescharacteristic
28C2×C4×D157C2×C411yescharacteristic
29C2×C4×D157D411yescharacteristic
30C2×C4×D157D411yescharacteristic
31#14578938—21no—
32#14578937—41no—
33C8×D157—41no—
34C2×Q8×C157C2×C411yescharacteristic
35M16×C157—21no—
36C2×#10597845—42no—
37#11929441—41no—
38#11929441—41no—
39C22×D157C22⋊C411yescharacteristic
40C22×D157C4⋊C411yescharacteristic
41C22×D157C4⋊C411yescharacteristic
42D628—41no—
43D628—41no—
44D628—41no—
45C2×Dic157C22⋊C411yescharacteristic
46C4×D157—21no—
47C4×D157—21no—
48C4×D157—21no—
49C4×D157—21no—
50C4×D157—21no—
51C4×D157—21no—
52#11929434—41no—
53Q8×C157—41no—
54C2×C4×C157C4211yescharacteristic
55C2×C4×C157C22⋊C411yescharacteristic
56C2×C4×C157C4⋊C411yescharacteristic
57C8×C157—41no—
58C22×C157#9511yescharacteristic
59C2×D157—21no—
60C2×D157—21no—
61C2×D157—21no—
62C2×D157—41no—
63C2×D157—41no—
64C2×D157—41no—
65#10597845—82no—
66C4×C157—21no—
67C4×C157—21no—
68C4×C157—21no—
69Dic157#9911yescharacteristic
70Dic157#9911yescharacteristic
71C2×C157—21no—
72C2×C157#34211yescharacteristic
73D157—41no—
74D157—41no—
75D157—41no—
76C157#139511yescharacteristic, complemented, Sylow
77#1395—1571nomaximal, Sylow
78#413—1571no—
79#410—1571no—
80#408—1571no—
81C2×#41—1571no—
82C2×M16—3141no—
83C2×M16—1571no—
84C22×C8—1571no—
85#117—3141no—
86#101—1571no—
87#101#1059784511yescharacteristic, complemented
88#100—3141no—
89#99—3141no—
90#99—1572no—
91C22⋊C8—3141no—
92C22⋊C8—3141no—
93#41—6281no—
94#41—6281no—
95C2×Q8C2×#1059784511yescharacteristic
96C2×D4—1571no—
97C2×D4—1571no—
98C2×D4—1571no—
99C22×C4—1571no—
100C22×C4—1571no—
101C22×C4—1571no—
102M16—21no—
103M16—3141no—
104M16—6281no—
105M16—6281no—
106C2×C8—3141no—
107C2×C8—3141no—
108C2×C8—6281no—
109C2×C8—6281no—
110C4⋊C4—6281no—
111C22⋊C4—3142no—
112C42—6281no—
113C23—1571no—
114C23—1571no—
115C23—1571no—
116Q8—41no—
117D4—6281no—
118D4—6281no—
119D4—6281no—
120C2×C4—3141no—
121C2×C4—3141no—
122C2×C4—3141no—
123C2×C4—3141no—
124C2×C4—3141no—
125C2×C4—3141no—
126C2×C4—6282no—
127C2×C4—1571no—
128C2×C4C4×#1059784511yescharacteristic
129C2×C4C22⋊#1059784511yescharacteristic
130C2×C4C4⋊#1059784511yescharacteristic
131C8—41no—
132C8—6281no—
133C8—6281no—
134C8—6281no—
135C22—3141no—
136C22—3141no—
137C22—3141no—
138C22—6281no—
139C22—6281no—
140C22—6281no—
141C22(C2×#10597845)⋊C411yescharacteristic
142C4—21no—
143C4—21no—
144C4—21no—
145C4—1571no—
146C4—1571no—
147C4—12562no—
148C2—21no—
149C2—6281no—
150C2—6281no—
151C2—6281no—
152C2#2375815011yescharacteristic
subgroupG/H
centerC2#23758150
commutatorC2×C4×C157C42
FrattiniC2×Q8C2×#10597845
Fitting#101×C157C4
socleC2×C157#342
prime radical, cosocleC2×#14578955C22
hypercenter#101#10597845
hypocenterC157#1395
LCSG ▷ C2×C4×C157 ▷ C22×C157 ▷ C2×C157 ▷ C157
UCSC1 ◁ C2 ◁ C22 ◁ C2×Q8 ◁ #101

Complements

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

NH ≅ G/Ntype
4. C2×#14578964C4semidirect
5. C2×D157⋊C8C4semidirect
13. #19097690C4semidirect
15. #101×C157C4semidirect
76. C157#1395semidirect
87. #101#10597845semidirect

Maximal subgroups

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

subgroupindex
#237582542
#237582482
#237572562
#1395157