Finite Group Databasebeta

← #34115226

Subgroups — #34115226

Order 20096.

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

normal subgroups only

This group has 158 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#23758260C211yesmaximal, characteristic
2#23758246C211yesmaximal, characteristic
3#23757254C211yesmaximal, characteristic
4C2×#14578963—21no—
5C2×#14578963C411yescharacteristic
6C22×#11929441C411yescharacteristic
7#19097832—21no—
8#19097831C412yes—
9#19097828—21no—
10C22⋊#11929441—21no—
11C2×#14578953C2211yescharacteristic
12M16×D157—21no—
13#19097689—21no—
14#19097688C411yescharacteristic
15#100×C157C411yescharacteristic
16#14578963—22no—
17#14578963—41no—
18#14578963—41no—
19C2×#11929441—21no—
20C2×#11929441—21no—
21C2×#11929441—41no—
22C2×#11929441—41no—
23#14578953—41no—
24#14578953—41no—
25C2×Dic314D411yescharacteristic
26C2×C22⋊D157C2×C411yescharacteristic
27C2×C22⋊D157Q811yescharacteristic
28C22×Dic157C2×C411yescharacteristic
29C22×Dic157D411yescharacteristic
30C2×C4×D157D411yescharacteristic
31#14578938—21no—
32#14578937—41no—
33C8×D157—41no—
34C2×D4×C157C2×C411yescharacteristic
35M16×C157—21no—
36#11929441—42no—
37#11929441—41no—
38#11929441—41no—
39C22×D157C4⋊C411yescharacteristic
40Dic314—41no—
41C22⋊D157—41no—
42C22⋊D157—41no—
43C2×Dic157—21no—
44C2×Dic157—21no—
45C2×Dic157—21no—
46C2×Dic157—21no—
47C2×Dic157C22⋊C411yescharacteristic
48C2×Dic157C22⋊C411yescharacteristic
49C2×Dic157C4⋊C411yescharacteristic
50C4×D157—21no—
51C4×D157—21no—
52#11929434—41no—
53C23×C157C4211yescharacteristic
54C23×C157C4⋊C411yescharacteristic
55D4×C157—41no—
56C2×C4×C157C22⋊C411yescharacteristic
57C8×C157—41no—
58C22×C157—21no—
59C22×C157—21no—
60C22×C157—41no—
61C22×C157—41no—
62C22×C157#9511yescharacteristic
63C2×D157—21no—
64C2×D157—41no—
65C4×C157—21no—
66Dic157—21no—
67Dic157—21no—
68Dic157#9911yescharacteristic
69Dic157#9911yescharacteristic
70C2×C157—21no—
71C2×C157—41no—
72C2×C157—41no—
73C2×C157#34211yescharacteristic
74D157—41no—
75C157#139211yescharacteristic, complemented, Sylow
76#1392—1571nomaximal, Sylow
77#413—1571no—
78#413—1571no—
79#408—1571no—
80C2×#41—1571no—
81C2×M16—3141no—
82C2×M16—3141no—
83C2×M16—1571no—
84C22×C8—1571no—
85#101—3141no—
86#101—3141no—
87#100—1572no—
88#100—1571no—
89#100#1059784511yescharacteristic
90C22⋊C8—3141no—
91C22⋊C8—3141no—
92#41—6281no—
93#41—6281no—
94C2×Q8—1571no—
95C2×D4—1571no—
96C2×D4—1571no—
97C2×D4C2×#1059784511yescharacteristic
98C22×C4—1571no—
99C22×C4—1571no—
100C22×C4—1571no—
101M16—21no—
102M16—3142no—
103M16—3141no—
104M16—6281no—
105M16—6281no—
106M16—6281no—
107C2×C8—3141no—
108C2×C8—3141no—
109C2×C8—6281no—
110C2×C8—6281no—
111C2×C8—6281no—
112C23—1571no—
113C23C4×#1059784511yescharacteristic
114C23C4⋊#1059784511yescharacteristic
115Q8—6281no—
116D4—41no—
117D4—6281no—
118D4—6281no—
119C2×C4—3141no—
120C2×C4—3141no—
121C2×C4—3141no—
122C2×C4—3141no—
123C2×C4—3141no—
124C2×C4—3141no—
125C2×C4—1571no—
126C2×C4—1571no—
127C2×C4—1571no—
128C2×C4C22⋊#1059784511yescharacteristic
129C8—41no—
130C8—6281no—
131C8—6282no—
132C8—6281no—
133C8—6281no—
134C22—21no—
135C22—21no—
136C22—41no—
137C22—41no—
138C22—3141no—
139C22—6281no—
140C22(C2×#10597845)⋊C411yescharacteristic
141C4—21no—
142C4—3141no—
143C4—3141no—
144C4—1571no—
145C4—1571no—
146C2—21no—
147C2—41no—
148C2—41no—
149C2—6281no—
150C2#2375815011yescharacteristic
subgroupG/H
centerC2#23758150
commutatorC23×C157C42
FrattiniC2×D4C2×#10597845
Fitting#100×C157C4
socleC2×C157#342
prime radical, cosocleC2×#14578953C22
hypercenter#100#10597845
hypocenterC157#1392
LCSG ▷ C23×C157 ▷ C22×C157 ▷ C2×C157 ▷ C157
UCSC1 ◁ C2 ◁ C22 ◁ C2×D4 ◁ #100

Complements

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

NH ≅ G/Ntype
75. C157#1392semidirect

Maximal subgroups

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

subgroupindex
#237582602
#237582462
#237572542
#1392157