Finite Group Databasebeta

← #34101268

Subgroups — #34101268

Order 20096.

430 conjugacy classes of subgroups; only the 75 normal subgroups are shown.

normal subgroups only

This group has 430 conjugacy classes of subgroups — too many to draw. Only its 75 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#23757835C211yesmaximal, characteristic
2C2×#19097755C212yesmaximal, complemented
3C2×#19097685C212yesmaximal, complemented
4#23757134C211yesmaximal, characteristic, complemented
5#342×C157C211yesmaximal, characteristic, complemented
6C22×C22⋊D157C2212yes—
7C23×Dic157C2211yescharacteristic
8#19097755—24no—
9#19097755—22no—
10#19097755—24no—
11#19097745—22no—
12#19097741—22no—
13C2×C4⋊Dic157—22no—
14C2×C22⋊Dic157C2211yescharacteristic
15C2×#14578931—22no—
16#19097685—24no—
17#19097678—22no—
18C2×C22⋊C4×C157C2211yescharacteristic
19C2×C22⋊C4×C157C2212yes—
20C23×D157D412yes—
21C2×D628—22no—
22C2×C22⋊D157—22no—
23C2×C22⋊D157—22no—
24C2×C22⋊D157—22no—
25C2×C22⋊D157—22no—
26C2×C22⋊D157—22no—
27C2×C22⋊D157—22no—
28C22×Dic157—21no—
29C22×Dic157—22no—
30C22×Dic157—22no—
31C22×Dic157—21no—
32C22×Dic157—21no—
33C22×Dic157D412yes—
34C22×Dic157D412yescomplemented
35C4⋊Dic157—28no—
36C4⋊Dic157—22no—
37C22⋊Dic157—22no—
38#14578931—28no—
39#14578931—24no—
40C24×C157C2311yescharacteristic
41C22×C4×C157—22no—
42C22×C4×C157D412yes—
43C22⋊C4×C157—22no—
44C22⋊C4×C157—22no—
45C22⋊C4×C157D414yescomplemented
46C22×D157—22no—
47C22×D157—22no—
48C22×D157—22no—
49C22×D157—44no—
50D628—82no—
51C22⋊D157—42no—
52C22⋊D157—42no—
53C22⋊D157—42no—
54C22⋊D157—42no—
55C2×Dic157—24no—
56C2×Dic157—22no—
57C2×Dic157—22no—
58C2×Dic157—22no—
59C2×Dic157—22no—
60C2×Dic157—41no—
61C2×Dic157—42no—
62C2×Dic157—41no—
63C2×Dic157—42no—
64C2×Dic157—41no—
65C23×C157—42no—
66C23×C157C2×D412yes—
67C23×C157C2×D411yescharacteristic
68C23×C157C2×D411yescharacteristic
69C23×C157C2×D412yes—
70C23×C157#4111yescharacteristic
71C2×C4×C157—22no—
72C2×C4×C157—24no—
73C2×C4×C157—44no—
74C2×C4×C157—42no—
75C22×C157—22no—
76C22×C157—24no—
77C22×C157—41no—
78C22×C157—42no—
79C22×C157—41no—
80C22×C157#12012yes—
81C22×C157#12011yescharacteristic
82C22×C157#12111yescharacteristic
83C22×C157#12112yes—
84C22×C157#12711yescharacteristic
85C2×D157—44no—
86C2×D157—42no—
87C2×D157—44no—
88C2×D157—82no—
89C4×C157—44no—
90C4×C157—42no—
91Dic157—42no—
92Dic157—42no—
93Dic157—81no—
94C2×C157—21no—
95C2×C157—22no—
96C2×C157—22no—
97C2×C157—21no—
98C2×C157#39211yescharacteristic
99C2×C157#45812yes—
100D157—82no—
101C157#202211yescharacteristic, complemented, Sylow
102#2022—1571nomaximal, Sylow
103#534—1571no—
104C2×#123—1572no—
105C2×#99—1572no—
106#381—1571no—
107#342D15711yescharacteristic, complemented
108C22×D4—1572no—
109C23×C4—1571no—
110#123—3144no—
111#123—3142no—
112#123—3144no—
113#121—3142no—
114#120—3142no—
115C2×C4⋊C4—3142no—
116C2×C22⋊C4—3142no—
117C2×C22⋊C4—1571no—
118C2×C22⋊C4C2×D15711yescharacteristic
119C2×C22⋊C4C2×D15712yes—
120#99—3144no—
121#95—3142no—
122C24—1572no—
123C24C22×D15711yescharacteristic
124C2×D4—3142no—
125C2×D4—3142no—
126C2×D4—3142no—
127C2×D4—3142no—
128C2×D4—3142no—
129C2×D4—3142no—
130C2×D4—3142no—
131C22×C4—22no—
132C22×C4—3142no—
133C22×C4—3141no—
134C22×C4—3142no—
135C22×C4—3141no—
136C22×C4—3141no—
137C22×C4—1572no—
138C22×C4—1572no—
139C22×C4D62812yes—
140C4⋊C4—3148no—
141C4⋊C4—3142no—
142C22⋊C4—22no—
143C22⋊C4—22no—
144C22⋊C4—3148no—
145C22⋊C4—3144no—
146C22⋊C4—3142no—
147C22⋊C4D62814yescomplemented
148C23—42no—
149C23—3142no—
150C23—3142no—
151C23—3142no—
152C23—6284no—
153C23D4×D15712yes—
154C23D4×D15711yescharacteristic
155C23C2×D62811yescharacteristic
156C23C2×D62812yes—
157C23#1457895511yescharacteristic
158D4—6282no—
159D4—6282no—
160D4—6282no—
161D4—6282no—
162D4—12562no—
163C2×C4—24no—
164C2×C4—22no—
165C2×C4—44no—
166C2×C4—42no—
167C2×C4—3144no—
168C2×C4—3142no—
169C2×C4—3142no—
170C2×C4—3142no—
171C2×C4—3142no—
172C2×C4—6281no—
173C2×C4—6282no—
174C2×C4—6281no—
175C2×C4—6282no—
176C2×C4—6281no—
177C22—22no—
178C22—24no—
179C22—41no—
180C22—42no—
181C22—41no—
182C22—6284no—
183C22—6282no—
184C22—6284no—
185C22—12562no—
186C22#1909774112yes—
187C22#1909774111yescharacteristic
188C22#1909774611yescharacteristic
189C22#1909774612yes—
190C22#1909776811yescharacteristic
191C4—44no—
192C4—42no—
193C4—6282no—
194C4—6282no—
195C4—12561no—
196C2—22no—
197C2—21no—
198C2—22no—
199C2—21no—
200C2—12562no—
201C2#2375718311yescharacteristic
202C2#2375746412yes—
subgroupG/H
centerC22#19097741
commutator, cosocleC24×C157C23
FrattiniC24C22×D157
Fitting#342×C157C2
socleC22×C157#120
prime radical#23757835C2
hypercenter#342D157
hypocenterC157#2022
LCSG ▷ C24×C157 ▷ C2×C157 ▷ C157
UCSC1 ◁ C22 ◁ C24 ◁ #342

Complements

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

NH ≅ G/Ntype
2. C2×#19097755C2semidirect
3. C2×#19097685C2semidirect
4. #23757134C2semidirect
5. #342×C157C2semidirect
34. C22×Dic157D4semidirect
45. C22⋊C4×C157D4semidirect
101. C157#2022semidirect
107. #342D157semidirect
147. C22⋊C4D628semidirect

Maximal subgroups

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

subgroupindex
#237578352
C2×#190977552
C2×#190976852
#237571342
#342×C1572
#2022157