Finite Group Databasebeta

← #34115235

Subgroups — #34115235

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#23758260C211yesmaximal, characteristic
2#23758247C211yesmaximal, characteristic
3#23757245C211yesmaximal, characteristic
4C2×#14578964C411yescharacteristic, complemented
5C2×#14578963—21no—
6C2×D157⋊C8C411yescharacteristic, complemented
7#19097832C412yescomplemented
8#19097831—21no—
9C22⋊#11929441—21no—
10C22⋊#11929441—21no—
11C2×#14578953C2211yescharacteristic
12#19097727—21no—
13#19097686C411yescharacteristic
14#19097685—21no—
15#99×C157C411yescharacteristic
16#14578964—41no—
17#14578963—22no—
18#14578963—41no—
19D157⋊C8—41no—
20C2×#11929441—21no—
21C2×#11929441—21no—
22C2×#11929441—41no—
23#14578953—41no—
24#14578953—41no—
25C2×Dic314C2×C411yescharacteristic
26C2×C22⋊D157D411yescharacteristic
27C2×C22⋊D157Q811yescharacteristic
28C22×Dic157D411yescharacteristic
29C22×Dic157D411yescharacteristic
30C2×C4×D157C2×C411yescharacteristic
31#14578933—41no—
32C22⋊Dic157—21no—
33C4×Dic157—41no—
34C2×D4×C157C2×C411yescharacteristic
35C22⋊C4×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×Dic157—41no—
48C2×Dic157C22⋊C411yescharacteristic
49C2×Dic157C22⋊C411yescharacteristic
50C2×Dic157C4⋊C411yescharacteristic
51C4×D157—21no—
52C4×D157—21no—
53C23×C157C22⋊C411yescharacteristic
54C23×C157C4⋊C411yescharacteristic
55D4×C157—41no—
56C2×C4×C157—41no—
57C2×C4×C157C4211yescharacteristic
58C22×C157—21no—
59C22×C157—21no—
60C22×C157—41no—
61C22×C157—41no—
62C22×C157#9511yescharacteristic
63C2×D157—21no—
64C2×D157—41no—
65C4×C157—21no—
66C4×C157—81no—
67Dic157—21no—
68Dic157—21no—
69Dic157—81no—
70Dic157#9911yescharacteristic
71Dic157#9911yescharacteristic
72C2×C157—21no—
73C2×C157—41no—
74C2×C157—41no—
75C2×C157#34211yescharacteristic
76D157—41no—
77C157#139511yescharacteristic, complemented, Sylow
78#1395—1571nomaximal, Sylow
79#413—1571no—
80#410—1571no—
81#408—1571no—
82C2×#41—1571no—
83C2×M16—3141no—
84C2×M16—1571no—
85C22×C8—1571no—
86#117—3141no—
87#101—1572no—
88#100—3141no—
89#99—3141no—
90#99—1571no—
91#99#1059784511yescharacteristic
92C22⋊C8—3141no—
93C22⋊C8—3141no—
94#41—6281no—
95#41—6281no—
96C2×Q8—1571no—
97C2×D4—1571no—
98C2×D4—1571no—
99C2×D4C2×#1059784511yescharacteristic
100C22×C4—1571no—
101C22×C4—1571no—
102C22×C4—1571no—
103M16—3142no—
104M16—6281no—
105M16—6281no—
106C2×C8—3141no—
107C2×C8—3141no—
108C2×C8—6281no—
109C2×C8—6281no—
110C4⋊C4—6281no—
111C22⋊C4—21no—
112C22⋊C4—3141no—
113C42—6281no—
114C23—1571no—
115C23C22⋊#1059784511yescharacteristic
116C23C4⋊#1059784511yescharacteristic
117Q8—6281no—
118D4—41no—
119D4—6281no—
120D4—6281no—
121C2×C4—41no—
122C2×C4—3141no—
123C2×C4—3141no—
124C2×C4—3141no—
125C2×C4—3141no—
126C2×C4—3141no—
127C2×C4—3141no—
128C2×C4—6281no—
129C2×C4—1571no—
130C2×C4—1571no—
131C2×C4—1571no—
132C2×C4C4×#1059784511yescharacteristic
133C8—6282no—
134C8—6281no—
135C8—6281no—
136C22—21no—
137C22—21no—
138C22—41no—
139C22—41no—
140C22—3141no—
141C22—6281no—
142C22(C2×#10597845)⋊C411yescharacteristic
143C4—21no—
144C4—81no—
145C4—3141no—
146C4—3141no—
147C4—1571no—
148C4—1571no—
149C4—12561no—
150C2—21no—
151C2—41no—
152C2—41no—
153C2—6281no—
154C2#2375815011yescharacteristic
subgroupG/H
centerC2#23758150
commutatorC2×C4×C157C42
FrattiniC2×D4C2×#10597845
Fitting#99×C157C4
socleC2×C157#342
prime radical, cosocleC2×#14578953C22
hypercenter#99#10597845
hypocenterC157#1395
LCSG ▷ C2×C4×C157 ▷ C22×C157 ▷ C2×C157 ▷ C157
UCSC1 ◁ C2 ◁ C22 ◁ C2×D4 ◁ #99

Complements

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

NH ≅ G/Ntype
4. C2×#14578964C4semidirect
6. C2×D157⋊C8C4semidirect
7. #19097832C4semidirect
77. C157#1395semidirect

Maximal subgroups

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

subgroupindex
#237582602
#237582472
#237572452
#1395157