Finite Group Databasebeta

← #34100456

Subgroups — #34100456

Order 20096.

412 conjugacy classes of subgroups; only the 105 normal subgroups are shown.

normal subgroups only

This group has 412 conjugacy classes of subgroups — too many to draw. Only its 105 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×#19097745C211yesmaximal, characteristic
2C2×#19097730C211yesmaximal, characteristic, complemented
3C2×#19097693C212yesmaximal, complemented
4#23757036C212yesmaximal, complemented
5C2×C22⋊C8×C157C211yesmaximal, characteristic, complemented
6C22×D628C2211yescharacteristic
7C22×C22⋊D157—21no—
8#19097745—22no—
9#19097745C414yescomplemented
10#19097730—24no—
11C2×C4⋊Dic157C2211yescharacteristic
12C2×C4⋊Dic157C2212yes—
13C2×C22⋊Dic157—21no—
14C2×#14578931—21no—
15C2×C4×Dic157—21no—
16#19097693—24no—
17C23×C4×C157C2211yescharacteristic
18C22×C8×C157C2212yes—
19C22⋊C8×C157—22no—
20C23×D157—21no—
21C2×D628—22no—
22C2×D628—21no—
23C2×D628—22no—
24C2×D628C2×C412yes—
25C2×C22⋊D157—24no—
26C2×C22⋊D157—44no—
27C22×Dic157—22no—
28C22×Dic157—21no—
29C4⋊Dic157—22no—
30C4⋊Dic157—21no—
31C4⋊Dic157C2×C412yes—
32C4⋊Dic157D414yescomplemented
33C22⋊Dic157—24no—
34#14578931—24no—
35C4×Dic157—24no—
36C24×C157D411yescharacteristic
37C22×C4×C157—22no—
38C22×C4×C157—22no—
39C22×C4×C157C2×C412yes—
40C22×C4×C157D412yes—
41C22×C4×C157D411yescharacteristic
42C22×C4×C157C2311yescharacteristic
43C2×C8×C157—22no—
44C2×C8×C157—22no—
45C2×C8×C157—22no—
46C22×D157—22no—
47C22×D157—41no—
48C22×D157—41no—
49C22×D157—42no—
50C22×D157—42no—
51D628—24no—
52D628—42no—
53C22⋊D157—48no—
54C2×Dic157—22no—
55C2×Dic157—24no—
56C2×Dic157—42no—
57C2×Dic157—42no—
58C2×Dic157—42no—
59C23×C157—21no—
60C23×C157—21no—
61C23×C157—22no—
62C23×C157—22no—
63C23×C157C22⋊C412yes—
64C23×C157C2×D411yescharacteristic
65C2×C4×C157—21no—
66C2×C4×C157—21no—
67C2×C4×C157—24no—
68C2×C4×C157—24no—
69C2×C4×C157C22⋊C412yes—
70C2×C4×C157C22×C411yescharacteristic
71C2×C4×C157C2×D412yes—
72C2×C4×C157C2×D411yescharacteristic
73C2×C4×C157#4112yes—
74C8×C157—42no—
75C22×C157—22no—
76C22×C157—22no—
77C22×C157—22no—
78C22×C157—42no—
79C22×C157—42no—
80C22×C157C2×C22⋊C411yescharacteristic
81C22×C157#12011yescharacteristic
82C22×C157#12311yescharacteristic
83C22×C157#13512yes—
84C22×C157AGL(1,ℤ/8)12yes—
85C2×D157—42no—
86C2×D157—42no—
87C2×D157—42no—
88C2×D157—82no—
89C2×D157—82no—
90C4×C157—22no—
91C4×C157C4×D412yes—
92C4×C157#12112yes—
93Dic157—42no—
94Dic157—44no—
95C2×C157—42no—
96C2×C157#38611yescharacteristic
97C2×C157#41611yescharacteristic
98C2×C157#41811yescharacteristic
99C2×C157#44912yes—
100C2×C157#48212yes—
101D157—82no—
102C157#187511yescharacteristic, complemented, Sylow
103#1875—1571nomaximal, Sylow
104C2×#121—1571no—
105C2×#117—1571no—
106C2×#102—1572no—
107C2×C22⋊C8D15711yescharacteristic, complemented
108#340—1572no—
109C22×D4—3141no—
110C22×D4—1571no—
111C23×C4C2×D15711yescharacteristic
112C22×C8C2×D15712yes—
113#121—3142no—
114#121—1574no—
115#117—3144no—
116C2×C4⋊C4—1572no—
117C2×C4⋊C4—1571no—
118C2×C22⋊C4—3141no—
119C2×C22⋊C4—3141no—
120C2×C42—3141no—
121#102—3144no—
122C22⋊C8—22no—
123C24—3141no—
124C24D62811yescharacteristic
125C2×D4—3144no—
126C2×D4—3142no—
127C2×D4—3141no—
128C2×D4—3142no—
129C2×D4—6284no—
130C2×D4—1572no—
131C22×C4—22no—
132C22×C4—22no—
133C22×C4—3142no—
134C22×C4—3141no—
135C22×C4C4×D15712yes—
136C22×C4C22⋊D15712yes—
137C22×C4D62811yescharacteristic
138C22×C4C22×D15711yescharacteristic
139C2×C8—22no—
140C2×C8—22no—
141C2×C8—22no—
142C4⋊C4—3142no—
143C4⋊C4—3141no—
144C4⋊C4—1572no—
145C4⋊C4—1574no—
146C22⋊C4—3144no—
147C22⋊C4—3144no—
148C42—3144no—
149C23—21no—
150C23—21no—
151C23—22no—
152C23—22no—
153C23—3142no—
154C23—6281no—
155C23—6281no—
156C23—6282no—
157C23—6282no—
158C23#1457893112yes—
159C23C2×D62811yescharacteristic
160D4—3144no—
161D4—6288no—
162D4—6282no—
163C2×C4—21no—
164C2×C4—21no—
165C2×C4—24no—
166C2×C4—24no—
167C2×C4—3142no—
168C2×C4—3144no—
169C2×C4—6282no—
170C2×C4—6282no—
171C2×C4—6282no—
172C2×C4#1457893112yes—
173C2×C4C2×C4×D15711yescharacteristic
174C2×C4D4×D15712yes—
175C2×C4C2×C22⋊D15711yescharacteristic
176C2×C4#1457895312yes—
177C8—42no—
178C22—22no—
179C22—22no—
180C22—22no—
181C22—42no—
182C22—42no—
183C22—6282no—
184C22—6282no—
185C22—6282no—
186C22—12562no—
187C22—12562no—
188C22C2×#1457893111yescharacteristic
189C22#1909774111yescharacteristic
190C22#1909775511yescharacteristic
191C22#1909779312yes—
192C22#1909779912yes—
193C4—22no—
194C4—6284no—
195C4—6282no—
196C4#1909773112yes—
197C4#1909774312yes—
198C2—42no—
199C2—12562no—
200C2#2375715011yescharacteristic
201C2#2375727011yescharacteristic
202C2#2375727911yescharacteristic
203C2#2375742012yes—
204C2#2375759812yes—
subgroupG/H
centerC23C2×D628
commutatorC2×C4×C157C22×C4
FrattiniC22×C4C22×D157
FittingC2×C22⋊C8×C157C2
socleC23×C157C2×D4
prime radicalC2×#19097745C2
cosocleC22×C4×C157C23
hypercenterC2×C22⋊C8D157
hypocenterC157#1875
LCSG ▷ C2×C4×C157 ▷ C2×C157 ▷ C157
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×C22⋊C8

Complements

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

NH ≅ G/Ntype
2. C2×#19097730C2semidirect
3. C2×#19097693C2semidirect
4. #23757036C2semidirect
5. C2×C22⋊C8×C157C2semidirect
9. #19097745C4semidirect
32. C4⋊Dic157D4semidirect
102. C157#1875semidirect
107. C2×C22⋊C8D157semidirect

Maximal subgroups

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

subgroupindex
C2×#190977452
C2×#190977302
C2×#190976932
#237570362
C2×C22⋊C8×C1572
#1875157