Finite Group Databasebeta

← #34103321

Subgroups — #34103321

Order 20096.

408 conjugacy classes of subgroups; only the 173 normal subgroups are shown.

normal subgroups only

This group has 408 conjugacy classes of subgroups — too many to draw. Only its 173 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×#19097763C211yesmaximal, characteristic
2#23757170C212yesmaximal
3#23757168C212yesmaximal
4#23757160C212yesmaximal
5#23757158C212yesmaximal
6#23757156C212yesmaximal
7#23757154C212yesmaximal
8#23757139C211yesmaximal, characteristic
9#382×C157C211yesmaximal, characteristic
10#19097763C418yescomplemented
11C2×C4⋊Dic157C2211yescharacteristic
12C2×C4⋊Dic157C2211yescharacteristic
13C2×C4⋊Dic157C2211yescharacteristic
14C2×C4⋊Dic157C2211yescharacteristic
15C2×#14578933C2212yes—
16C2×#14578933C2212yes—
17C2×#14578933C2212yes—
18C2×#14578933C2212yes—
19C2×C4×Dic157C2212yes—
20C2×C4×Dic157C2212yes—
21#19097678C2212yes—
22#19097678C2212yes—
23#19097678C2212yes—
24#19097678C2212yes—
25#19097678C2212yes—
26#19097678C2212yes—
27C2×C4⋊C4×C157C2211yescharacteristic
28C2×C4⋊C4×C157C2211yescharacteristic
29C2×C42×C157C2211yescharacteristic
30#95×C157C2212yes—
31#95×C157C2212yes—
32C22×Dic157C2312yes—
33C22×Dic157C2312yes—
34C22×Dic157C2312yes—
35C22×Dic157C2312yes—
36C4⋊Dic157—41no—
37C4⋊Dic157—41no—
38C4⋊Dic157C2×C414yes—
39C4⋊Dic157C2×C414yes—
40#14578933—42no—
41#14578933—42no—
42#14578933C2×C418yes—
43#14578933C2×C418yes—
44C4×Dic157—42no—
45C4×Dic157—42no—
46C22×C4×C157C2312yes—
47C22×C4×C157C2312yes—
48C22×C4×C157C2311yescharacteristic
49C22×C4×C157C2311yescharacteristic
50C22×C4×C157C2311yescharacteristic
51C4⋊C4×C157—41no—
52C4⋊C4×C157—41no—
53C42×C157C2×C414yes—
54C2×Dic157—22no—
55C2×Dic157—22no—
56C2×Dic157—22no—
57C2×Dic157—22no—
58C2×Dic157—22no—
59C2×Dic157—22no—
60C2×Dic157—22no—
61C2×Dic157—22no—
62C2×Dic157—22no—
63C2×Dic157—22no—
64C2×Dic157C22×C414yes—
65C2×Dic157C22×C414yes—
66C23×C157C2411yescharacteristic
67C2×C4×C157—21no—
68C2×C4×C157—21no—
69C2×C4×C157—21no—
70C2×C4×C157—21no—
71C2×C4×C157—21no—
72C2×C4×C157—21no—
73C2×C4×C157—22no—
74C2×C4×C157—22no—
75C2×C4×C157—22no—
76C2×C4×C157—22no—
77C2×C4×C157—22no—
78C2×C4×C157—22no—
79C2×C4×C157C22×C412yes—
80C2×C4×C157C22×C412yes—
81C2×C4×C157C22×C412yes—
82C22×C157C23×C411yescharacteristic
83C22×C157H(5,𝔽2)11yescharacteristic
84C22×C157H(5,𝔽2)11yescharacteristic
85C22×C1572−1+411yescharacteristic
86C22×C1572−1+411yescharacteristic
87C22×C1572−1+411yescharacteristic
88C22×C1572−1+411yescharacteristic
89C4×C157—22no—
90C4×C157—22no—
91C4×C157—22no—
92C4×C157—42no—
93C4×C157—42no—
94Dic157—24no—
95Dic157—24no—
96Dic157—42no—
97Dic157—42no—
98C2×C157#51911yescharacteristic
99C2×C157#52011yescharacteristic
100C2×C157#52011yescharacteristic
101C2×C157#56211yescharacteristic
102C2×C157#56311yescharacteristic
103C2×C157#56311yescharacteristic
104C2×C157#56411yescharacteristic
105C157#238211yescharacteristic, complemented, Sylow
106#2382—1571nomaximal, Sylow
107C2×#125—1571no—
108#389—1572no—
109#389—1572no—
110#387—1572no—
111#387—1572no—
112#387—1572no—
113#387—1572no—
114#382—1571no—
115#382D15711yescharacteristic
116#125—1578no—
117C2×C4⋊C4—1572no—
118C2×C4⋊C4—1572no—
119C2×C4⋊C4—1571no—
120C2×C4⋊C4—1571no—
121C2×C4⋊C4—1572no—
122C2×C4⋊C4—1572no—
123C2×C4⋊C4—1571no—
124C2×C4⋊C4—1571no—
125C2×C4⋊C4C2×D15711yescharacteristic
126C2×C4⋊C4C2×D15711yescharacteristic
127C2×C42—1572no—
128C2×C42—1572no—
129C2×C42C2×D15711yescharacteristic
130#95—1572no—
131#95—1572no—
132#95—1572no—
133#95—1572no—
134#95—1572no—
135#95—1572no—
136#95C2×D15712yes—
137#95C2×D15712yes—
138C22×C4—1572no—
139C22×C4—1572no—
140C22×C4—1572no—
141C22×C4—1572no—
142C22×C4C22×D15712yes—
143C22×C4C22×D15712yes—
144C22×C4C22×D15711yescharacteristic
145C22×C4C22×D15711yescharacteristic
146C22×C4C22×D15711yescharacteristic
147C4⋊C4—41no—
148C4⋊C4—41no—
149C4⋊C4—6282no—
150C4⋊C4—6282no—
151C4⋊C4—6281no—
152C4⋊C4—6281no—
153C4⋊C4—1578no—
154C4⋊C4—1578no—
155C4⋊C4—1574no—
156C4⋊C4—1574no—
157C42—6282no—
158C42—6282no—
159C42C4×D15714yes—
160C23C23×D15711yescharacteristic
161C2×C4—21no—
162C2×C4—21no—
163C2×C4—21no—
164C2×C4—21no—
165C2×C4—21no—
166C2×C4—21no—
167C2×C4—22no—
168C2×C4—22no—
169C2×C4—22no—
170C2×C4—22no—
171C2×C4—22no—
172C2×C4—22no—
173C2×C4—3142no—
174C2×C4—3142no—
175C2×C4—3142no—
176C2×C4—3142no—
177C2×C4—3142no—
178C2×C4—3142no—
179C2×C4—3142no—
180C2×C4—3142no—
181C2×C4—3142no—
182C2×C4—3142no—
183C2×C4—1574no—
184C2×C4—1574no—
185C2×C4C2×C4×D15712yes—
186C2×C4C2×C4×D15712yes—
187C2×C4C2×C4×D15712yes—
188C22C22×C4×D15711yescharacteristic
189C22#1909781611yescharacteristic
190C22#1909781711yescharacteristic
191C22#1909781811yescharacteristic
192C22#1909781811yescharacteristic
193C22#1909781811yescharacteristic
194C22#1909781911yescharacteristic
195C4—22no—
196C4—22no—
197C4—22no—
198C4—42no—
199C4—42no—
200C4—3144no—
201C4—3144no—
202C4—6282no—
203C4—6282no—
204C2#2375775011yescharacteristic
205C2#2375775311yescharacteristic
206C2#2375775411yescharacteristic
207C2#2375801711yescharacteristic
208C2#2375802311yescharacteristic
209C2#2375802711yescharacteristic
210C2C157⋊#56411yescharacteristic
subgroupG/H
center, FrattiniC23C23×D157
commutatorC22×C157C23×C4
Fitting#382×C157C2
socle, prime radical, cosocleC23×C157C24
hypercenter#382D157
hypocenterC157#2382
LCSG ▷ C22×C157 ▷ C157
UCSC1 ◁ C23 ◁ #382

Complements

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

NH ≅ G/Ntype
10. #19097763C4semidirect
105. C157#2382semidirect

Maximal subgroups

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

subgroupindex
C2×#190977632
#237571702
#237571682
#237571602
#237571582
#237571562
#237571542
#237571392
#382×C1572
#2382157