Finite Group Databasebeta

← #34108458

Subgroups — #34108458

Order 20096.

582 conjugacy classes of subgroups; only the 165 normal subgroups are shown.

normal subgroups only

This group has 582 conjugacy classes of subgroups — too many to draw. Only its 165 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
1C2×#19097754C211yesmaximal, characteristic
2#23757164C214yesmaximal, complemented
3#23757157C214yesmaximal, complemented
4#23757152C212yesmaximal
5#23757146C212yesmaximal, complemented
6#23757136C211yesmaximal, characteristic, complemented
7C22×C42×C157C211yesmaximal, characteristic, complemented
8C22×C22⋊D157C2211yescharacteristic
9#19097754—24no—
10C2×#14578933C2214yes—
11C2×#14578933C2212yes—
12C2×C22⋊Dic157C2212yes—
13C2×C22⋊Dic157C2211yescharacteristic
14C2×#14578931C2214yes—
15C2×#14578931C2212yes—
16#19097678C2214yes—
17#19097678C2214yes—
18#19097678C2214yes—
19C23×C4×C157C2212yes—
20C23×C4×C157C2211yescharacteristic
21C2×C42×C157—24no—
22C2×C42×C157C2214yes—
23C23×D157C2311yescharacteristic
24C2×C22⋊D157—22no—
25C2×C22⋊D157—24no—
26C22×Dic157C2314yes—
27C22×Dic157C2311yescharacteristic
28C22×Dic157C2312yes—
29#14578933—24no—
30#14578933—28no—
31C22⋊Dic157—22no—
32C22⋊Dic157—24no—
33#14578931—24no—
34#14578931—28no—
35C24×C157C2311yescharacteristic
36C22×C4×C157—24no—
37C22×C4×C157—24no—
38C22×C4×C157—28no—
39C22×C4×C157D414yes—
40C22×C4×C157C2312yes—
41C22×C4×C157C2314yes—
42C42×C157—28no—
43C22×D157—21no—
44C22×D157—22no—
45C22×D157—24no—
46C22⋊D157—44no—
47C2×Dic157—21no—
48C2×Dic157—22no—
49C2×Dic157—22no—
50C2×Dic157—24no—
51C2×Dic157—24no—
52C2×Dic157—24no—
53C2×Dic157—24no—
54C23×C157—24no—
55C23×C157C2×D412yes—
56C23×C157#4114yes—
57C23×C157C2411yescharacteristic
58C2×C4×C157—216no—
59C2×C4×C157—28no—
60C2×C4×C157—24no—
61C2×C4×C157—24no—
62C2×C4×C157—24no—
63C2×C4×C157C2×D414yes—
64C2×C4×C157#4118yes—
65C22×C157—24no—
66C22×C157—28no—
67C22×C157#12314yes—
68C22×C157C22×D411yescharacteristic
69C22×C157C2×#4112yes—
70C22×C157C2×#4114yes—
71C2×D157—41no—
72C2×D157—42no—
73C2×D157—44no—
74C4×C157—24no—
75C4×C157—28no—
76Dic157—41no—
77Dic157—42no—
78Dic157—44no—
79C2×C157—24no—
80C2×C157C2×#12311yescharacteristic
81C2×C157#52512yes—
82C2×C157#52914yes—
83D157—81no—
84C157#285311yescharacteristic, complemented, Sylow
85#2853—1571nomaximal, Sylow
86C2×#123—1571no—
87C22×C42D15711yescharacteristic, complemented
88#388—1574no—
89#387—1574no—
90#386—1572no—
91#385—1572no—
92#381—1571no—
93C22×D4—1571no—
94C23×C4C2×D15712yes—
95C23×C4C2×D15711yescharacteristic
96#123—3144no—
97C2×C4⋊C4—1572no—
98C2×C4⋊C4—1574no—
99C2×C22⋊C4—1571no—
100C2×C22⋊C4—1572no—
101C2×C22⋊C4—1572no—
102C2×C22⋊C4—1574no—
103C2×C42—24no—
104C2×C42C2×D15714yes—
105#95—1574no—
106#95—1574no—
107#95—1574no—
108C24—1571no—
109C24C22×D15711yescharacteristic
110C2×D4—3142no—
111C2×D4—3144no—
112C22×C4—24no—
113C22×C4—24no—
114C22×C4—28no—
115C22×C4—1574no—
116C22×C4—1571no—
117C22×C4—1572no—
118C22×C4C22⋊D15714yes—
119C22×C4C22×D15712yes—
120C22×C4C22×D15714yes—
121C4⋊C4—3144no—
122C4⋊C4—3148no—
123C22⋊C4—3142no—
124C22⋊C4—3144no—
125C22⋊C4—3144no—
126C22⋊C4—3148no—
127C42—28no—
128C23—24no—
129C23—3141no—
130C23—3144no—
131C23—3142no—
132C23C2×C22⋊D15712yes—
133C23#1457895414yes—
134C23C23×D15711yescharacteristic
135D4—6284no—
136C2×C4—216no—
137C2×C4—28no—
138C2×C4—24no—
139C2×C4—24no—
140C2×C4—24no—
141C2×C4—3142no—
142C2×C4—3141no—
143C2×C4—3144no—
144C2×C4—3144no—
145C2×C4—3144no—
146C2×C4—3144no—
147C2×C4—3142no—
148C2×C4C2×C22⋊D15714yes—
149C2×C4#1457895418yes—
150C22—24no—
151C22—28no—
152C22—6281no—
153C22—6282no—
154C22—6284no—
155C22#1909775414yes—
156C22C22×C22⋊D15711yescharacteristic
157C22C2×#1457895412yes—
158C22C2×#1457895414yes—
159C4—24no—
160C4—28no—
161C4—6281no—
162C4—6282no—
163C4—6284no—
164C2—24no—
165C2—12561no—
166C2C2×#1909775411yescharacteristic
167C2#2375778412yes—
168C2#2375780714yes—
subgroupG/H
center, FrattiniC23C23×D157
commutator, socle, cosocleC23×C157C24
FittingC22×C42×C157C2
prime radicalC22×C22⋊D157C22
hypercenterC22×C42D157
hypocenterC157#2853
LCSG ▷ C23×C157 ▷ C157
UCSC1 ◁ C23 ◁ C22×C42

Complements

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

NH ≅ G/Ntype
2. #23757164C2semidirect
3. #23757157C2semidirect
5. #23757146C2semidirect
6. #23757136C2semidirect
7. C22×C42×C157C2semidirect
84. C157#2853semidirect
87. C22×C42D157semidirect

Maximal subgroups

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

subgroupindex
C2×#190977542
#237571642
#237571572
#237571522
#237571462
#237571362
C22×C42×C1572
#2853157