Finite Group Databasebeta

← #34098468

Subgroups — #34098468

Order 20096.

252 conjugacy classes of subgroups; only the 73 normal subgroups are shown.

normal subgroups only

This group has 252 conjugacy classes of subgroups — too many to draw. Only its 73 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×#19097728C211yesmaximal, characteristic
2#23757330C211yesmaximal, characteristic, complemented
3#23756998C212yesmaximal, complemented
4#23756996C212yesmaximal
5#432×C157C211yesmaximal, characteristic, complemented
6C22×C4×D157C411yescharacteristic
7#19097728—21no—
8#19097728—21no—
9#19097728—21no—
10#19097728—21no—
11C2×#14578933C411yescharacteristic
12C2×#14578933C2211yescharacteristic
13C2×#14578931C411yescharacteristic
14C2×#14578931C2211yescharacteristic
15C2×C4×Dic157C411yescharacteristic
16C4⋊#11929434—21no—
17C22⋊#11929434C2212yes—
18#19097682—21no—
19C2×C42×C157C2211yescharacteristic
20C4⋊C8×C157—21no—
21C22⋊C8×C157C2212yes—
22#97×C157—21no—
23C23×D157C2×C411yescharacteristic
24C22×Dic157C2×C411yescharacteristic
25C22×Dic157C2×C411yescharacteristic
26C22×Dic157C2×C411yescharacteristic
27C2×C4×D157—22no—
28C2×C4×D157—22no—
29C2×C4×D157—21no—
30C2×C4×D157—21no—
31C2×#11929434—22no—
32#14578933—21no—
33#14578933—21no—
34#14578933—21no—
35#14578933—21no—
36#14578931—21no—
37#14578931—21no—
38#14578931—21no—
39#14578931—21no—
40C4×Dic157—21no—
41C4×Dic157—21no—
42C22×C4×C157C2×C411yescharacteristic
43C22×C4×C157C2×C411yescharacteristic
44C22×C4×C157C2311yescharacteristic
45C2×C8×C157—22no—
46C42×C157D411yescharacteristic
47C42×C157D411yescharacteristic
48C42×C157D411yescharacteristic
49C42×C157D411yescharacteristic
50C22×D157—21no—
51C22×D157—21no—
52C22×D157—41no—
53C22×D157—41no—
54C22×D157M1612yes—
55C2×Dic157—21no—
56C2×Dic157—21no—
57C2×Dic157—21no—
58C2×Dic157—21no—
59C2×Dic157—41no—
60C2×Dic157—41no—
61C2×Dic157M1612yes—
62C4×D157—24no—
63C4×D157—24no—
64#11929434—42no—
65C23×C157C22×C411yescharacteristic
66C2×C4×C157—21no—
67C2×C4×C157—21no—
68C2×C4×C157—41no—
69C2×C4×C157—41no—
70C2×C4×C157C22⋊C411yescharacteristic
71C2×C4×C157C22⋊C411yescharacteristic
72C2×C4×C157C22⋊C411yescharacteristic
73C2×C4×C157C22⋊C411yescharacteristic
74C2×C4×C157C2×D411yescharacteristic
75C2×C4×C157C2×D411yescharacteristic
76C8×C157—42no—
77C22×C157—21no—
78C22×C157—21no—
79C22×C157C2×C22⋊C411yescharacteristic
80C22×C157C2×M1611yescharacteristic
81C22×C157C2×M1611yescharacteristic
82C2×D157—22no—
83C2×D157—42no—
84C2×D157—41no—
85C2×D157—41no—
86C2×D157—42no—
87C4×C157—21no—
88C4×C157—21no—
89C4×C157—21no—
90C4×C157—21no—
91C4×C157—21no—
92C4×C157—21no—
93Dic157—22no—
94Dic157—41no—
95Dic157—41no—
96C2×C157—21no—
97C2×C157—21no—
98C2×C157#40711yescharacteristic
99C2×C157#41011yescharacteristic
100C2×C157#41311yescharacteristic
101D157—42no—
102C157#146411yescharacteristic, complemented, Sylow
103#1464—1571nomaximal, Sylow
104C2×#117—1571no—
105#432—1571no—
106#432D15711yescharacteristic, complemented
107#324—1572no—
108#323—1572no—
109C23×C4—1571no—
110#117—3141no—
111#117—3141no—
112#117—3141no—
113#117—3141no—
114C2×C4⋊C4—1571no—
115C2×C4⋊C4—1571no—
116C2×C22⋊C4—1571no—
117C2×C22⋊C4—1571no—
118C2×C42—1571no—
119C2×C42C2×D15711yescharacteristic
120C4⋊C8—21no—
121C4⋊C8—3141no—
122C22⋊C8—1572no—
123C22⋊C8C2×D15712yes—
124#97—21no—
125#97—3141no—
126C24—1571no—
127C22×C4—3142no—
128C22×C4—3142no—
129C22×C4—3141no—
130C22×C4—3141no—
131C22×C4—1571no—
132C22×C4—1571no—
133C22×C4—1571no—
134C22×C4C4×D15711yescharacteristic
135C22×C4C4×D15711yescharacteristic
136C22×C4C22×D15711yescharacteristic
137C2×C8—22no—
138C2×C8—3142no—
139C4⋊C4—3141no—
140C4⋊C4—3141no—
141C4⋊C4—3141no—
142C4⋊C4—3141no—
143C22⋊C4—3141no—
144C22⋊C4—3141no—
145C22⋊C4—3141no—
146C22⋊C4—3141no—
147C42—3141no—
148C42—3141no—
149C42C22⋊D15711yescharacteristic
150C42C22⋊D15711yescharacteristic
151C42D62811yescharacteristic
152C42D62811yescharacteristic
153C23—3141no—
154C23—3141no—
155C23—6281no—
156C23—6281no—
157C23—1572no—
158C23C2×C4×D15711yescharacteristic
159C2×C4—21no—
160C2×C4—21no—
161C2×C4—41no—
162C2×C4—41no—
163C2×C4—3144no—
164C2×C4—3144no—
165C2×C4—3141no—
166C2×C4—3141no—
167C2×C4—3141no—
168C2×C4—3141no—
169C2×C4—6281no—
170C2×C4—6281no—
171C2×C4—1572no—
172C2×C4#1457893111yescharacteristic
173C2×C4#1457893111yescharacteristic
174C2×C4#1457893111yescharacteristic
175C2×C4#1457893111yescharacteristic
176C2×C4C2×C22⋊D15711yescharacteristic
177C2×C4C2×D62811yescharacteristic
178C8—42no—
179C8—6282no—
180C22—21no—
181C22—21no—
182C22—3142no—
183C22—6282no—
184C22—6282no—
185C22—6281no—
186C22—6281no—
187C22C2×#1457893111yescharacteristic
188C22M16×D15711yescharacteristic
189C22M16×D15711yescharacteristic
190C4—21no—
191C4—21no—
192C4—21no—
193C4—21no—
194C4—21no—
195C4—21no—
196C4—3142no—
197C4—6281no—
198C4—6281no—
199C2—21no—
200C2—21no—
201C2—6282no—
202C2#2375723611yescharacteristic
203C2#2375724611yescharacteristic
204C2#2375725511yescharacteristic
subgroupG/H
centerC22C2×#14578931
commutatorC23×C157C22×C4
FrattiniC22×C4C22×D157
Fitting#432×C157C2
socleC22×C157C2×C22⋊C4
prime radicalC23×D157C2×C4
cosocleC22×C4×C157C23
hypercenter#432D157
hypocenterC157#1464
LCSG ▷ C23×C157 ▷ C2×C157 ▷ C157
UCSC1 ◁ C22 ◁ C2×C42 ◁ #432

Complements

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

NH ≅ G/Ntype
2. #23757330C2semidirect
3. #23756998C2semidirect
5. #432×C157C2semidirect
102. C157#1464semidirect
106. #432D157semidirect

Maximal subgroups

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

subgroupindex
C2×#190977282
#237573302
#237569982
#237569962
#432×C1572
#1464157