Finite Group Databasebeta

← #34100534

Subgroups — #34100534

Order 20096.

444 conjugacy classes of subgroups; only the 93 normal subgroups are shown.

normal subgroups only

This group has 444 conjugacy classes of subgroups — too many to draw. Only its 93 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×#19097767C211yesmaximal, characteristic
2#23757277C212yesmaximal, complemented
3C2×#19097688C211yesmaximal, characteristic, complemented
4#23757032C212yesmaximal, complemented
5#518×C157C211yesmaximal, characteristic, complemented
6C22×D628C2211yescharacteristic
7C22×C22⋊D157—22no—
8C2×#14578938C2212yes—
9#19097767—22no—
10#19097767C414yescomplemented
11C2×C4×Dic157C2211yescharacteristic
12#19097691—24no—
13#19097688—22no—
14C22×D4×C157C2211yescharacteristic
15C4×D4×C157—24no—
16#117×C157C2212yes—
17C2×C22⋊C4×C157—22no—
18C23×D157—21no—
19C2×D628—22no—
20C2×D628—21no—
21C2×D628—22no—
22C2×D628C2×C412yescomplemented
23C2×C22⋊D157—28no—
24C2×C22⋊D157—48no—
25C22×Dic157—21no—
26#14578938—22no—
27#14578938—22no—
28C2×#11929434—22no—
29C4×Dic157—21no—
30C4×Dic157C2×C412yescomplemented
31C24×C157D412yes—
32C2×D4×C157—22no—
33C2×D4×C157—22no—
34C2×D4×C157C2×C412yes—
35C2×D4×C157D412yes—
36C22×C4×C157—24no—
37C22×C4×C157C2311yescharacteristic
38C4⋊C4×C157D414yescomplemented
39C22⋊C4×C157—24no—
40C22⋊C4×C157—22no—
41C42×C157—22no—
42C22×D157—22no—
43C22×D157—44no—
44C22×D157—41no—
45C22×D157—41no—
46D628—24no—
47D628—42no—
48C22⋊D157—416no—
49C2×Dic157—24no—
50C2×Dic157—22no—
51#11929434—42no—
52C23×C157—22no—
53C23×C157—22no—
54C23×C157—44no—
55C23×C157C22⋊C414yes—
56C23×C157C2×D411yescharacteristic
57D4×C157—24no—
58D4×C157—24no—
59C2×C4×C157—24no—
60C2×C4×C157—84no—
61C2×C4×C157C22×C411yescharacteristic
62C2×C4×C157C2×D412yes—
63C2×C4×C157C2×D411yescharacteristic
64C2×C4×C157#4112yes—
65C22×C157—22no—
66C22×C157—24no—
67C22×C157—44no—
68C22×C157—44no—
69C22×C157—82no—
70C22×C157C2×C22⋊C411yescharacteristic
71C22×C157#12011yescharacteristic
72C22×C157#12311yescharacteristic
73C2×D157—44no—
74C2×D157—42no—
75C2×D157—82no—
76C2×D157—82no—
77C4×C157—44no—
78C4×C157C4×D412yes—
79C4×C157#12112yes—
80Dic157—24no—
81C2×C157—21no—
82C2×C157—21no—
83C2×C157—44no—
84C2×C157#38611yescharacteristic
85C2×C157#45312yes—
86D157—82no—
87C157#188711yescharacteristic, complemented, Sylow
88#1887—1571nomaximal, Sylow
89C2×#127—1571no—
90#518D15711yescharacteristic, complemented
91#418—1572no—
92C2×#100—1571no—
93#339—1572no—
94C22×D4—3142no—
95C22×D4—1571no—
96C22×D4C2×D15711yescharacteristic
97C2×M16—1572no—
98#127—3142no—
99#127—1574no—
100C4×D4—24no—
101#117C2×D15712yes—
102C2×C22⋊C4—22no—
103C2×C42—1571no—
104#102—3144no—
105#100—3142no—
106C24—3141no—
107C24C22⋊D15712yes—
108C2×D4—22no—
109C2×D4—22no—
110C2×D4—3148no—
111C2×D4—3142no—
112C2×D4—3141no—
113C2×D4—3142no—
114C2×D4—6288no—
115C2×D4—1572no—
116C2×D4C4×D15712yes—
117C2×D4D62812yes—
118C22×C4—24no—
119C22×C4—3141no—
120C22×C4C22×D15711yescharacteristic
121M16—3142no—
122M16—3142no—
123C2×C8—3142no—
124C4⋊C4C22⋊D15714yescomplemented
125C22⋊C4—24no—
126C22⋊C4—22no—
127C42—22no—
128C42—3141no—
129C42—1572no—
130C23—22no—
131C23—22no—
132C23—44no—
133C23—3142no—
134C23—6284no—
135C23—6281no—
136C23—6281no—
137C23#1457893114yes—
138C23C2×C22⋊D15711yescharacteristic
139D4—24no—
140D4—24no—
141D4—3144no—
142D4—62816no—
143D4—6282no—
144C2×C4—24no—
145C2×C4—84no—
146C2×C4—3144no—
147C2×C4—3142no—
148C2×C4C2×C4×D15711yescharacteristic
149C2×C4C2×C22⋊D15712yes—
150C2×C4C2×D62811yescharacteristic
151C2×C4#1457895412yes—
152C8—6282no—
153C22—22no—
154C22—24no—
155C22—44no—
156C22—44no—
157C22—82no—
158C22—6284no—
159C22—6282no—
160C22—12562no—
161C22—12562no—
162C22C2×#1457893111yescharacteristic
163C22#1909774011yescharacteristic
164C22#1909775411yescharacteristic
165C4—44no—
166C4—3144no—
167C4C4×C22⋊D15712yes—
168C4#1909774512yes—
169C2—21no—
170C2—21no—
171C2—44no—
172C2—12562no—
173C2#2375715211yescharacteristic
174C2#2375744112yes—
subgroupG/H
centerC22#19097740
commutatorC2×C4×C157C22×C4
FrattiniC22×C4C22×D157
Fitting#518×C157C2
socleC22×C157#120
prime radicalC2×#19097767C2
cosocleC22×C4×C157C23
hypercenter#518D157
hypocenterC157#1887
LCSG ▷ C2×C4×C157 ▷ C2×C157 ▷ C157
UCSC1 ◁ C22 ◁ C22×C4 ◁ #518

Complements

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

NH ≅ G/Ntype
2. #23757277C2semidirect
3. C2×#19097688C2semidirect
4. #23757032C2semidirect
5. #518×C157C2semidirect
10. #19097767C4semidirect
22. C2×D628C2×C4semidirect
30. C4×Dic157C2×C4semidirect
38. C4⋊C4×C157D4semidirect
87. C157#1887semidirect
90. #518D157semidirect
124. C4⋊C4C22⋊D157semidirect

Maximal subgroups

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

subgroupindex
C2×#190977672
#237572772
C2×#190976882
#237570322
#518×C1572
#1887157