Finite Group Databasebeta

← C131×#8729 #45694613

Subgroups — C131×#8729 #45694613

Order 33536.

514 conjugacy classes of subgroups; only the 166 normal subgroups are shown.

normal subgroups only

This group has 514 conjugacy classes of subgroups — too many to draw. Only its 166 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#2285×C131C211yesmaximal, characteristic
2#1797×C131C212yesmaximal
3#1296×C131C214yesmaximal, complemented
4C2×#117×C131C412yes—
5C22×C42×C131C2211yescharacteristic
6C2×C4⋊C8×C131C2214yes—
7C2×C22⋊C8×C131—22no—
8#384×C131C2212yes—
9#382×C131C412yes—
10#380×C131—22no—
11C4×C4⋊C4×C131—22no—
12#336×C131—22no—
13C23×C4×C131C2×C411yescharacteristic
14C23×C4×C131D412yes—
15C22×C8×C131—24no—
16#117×C131—44no—
17C2×C4⋊C4×C131—22no—
18C2×C4⋊C4×C131—22no—
19C2×C4⋊C4×C131C2×C414yes—
20C2×C22⋊C4×C131—22no—
21C2×C42×C131—24no—
22C2×C42×C131—22no—
23C2×C42×C131C2×C411yescharacteristic
24C2×C42×C131D412yes—
25C2×C42×C131C2311yescharacteristic
26C4⋊C8×C131—28no—
27C22⋊C8×C131—44no—
28#95×C131—24no—
29C24×C131C22⋊C411yescharacteristic
30C22×C4×C131—22no—
31C22×C4×C131—22no—
32C22×C4×C131—22no—
33C22×C4×C131—24no—
34C22×C4×C131—24no—
35C22×C4×C131—22no—
36C22×C4×C131—22no—
37C22×C4×C131—24no—
38C22×C4×C131C22⋊C412yes—
39C22×C4×C131C22⋊C411yescharacteristic
40C22×C4×C131C22×C411yescharacteristic
41C22×C4×C131C2×D412yes—
42C2×C8×C131—44no—
43C2×C8×C131—44no—
44C2×C8×C131—44no—
45C4⋊C4×C131—44no—
46C4⋊C4×C131—44no—
47C4⋊C4×C131—42no—
48C4⋊C4×C131—42no—
49C22⋊C4×C131—44no—
50C42×C131—22no—
51C42×C131—24no—
52C42×C131—44no—
53C42×C131#4114yes—
54C23×C131—21no—
55C23×C131—21no—
56C23×C131—22no—
57C23×C131—22no—
58C23×C131#10012yes—
59C23×C131C2×C22⋊C411yescharacteristic
60C2×C4×C131—28no—
61C2×C4×C131—21no—
62C2×C4×C131—21no—
63C2×C4×C131—21no—
64C2×C4×C131—21no—
65C2×C4×C131—22no—
66C2×C4×C131—22no—
67C2×C4×C131—22no—
68C2×C4×C131—44no—
69C2×C4×C131—44no—
70C2×C4×C131—44no—
71C2×C4×C131—44no—
72C2×C4×C131—44no—
73C2×C4×C131#10112yes—
74C2×C4×C131#11712yes—
75C2×C4×C131#12314yes—
76C2×C4×C131#13514yes—
77C2×C4×C131AGL(1,ℤ/8)12yes—
78C2×C4×C131#13712yes—
79C8×C131—84no—
80C22×C131—24no—
81C22×C131—22no—
82C22×C131—41no—
83C22×C131—41no—
84C22×C131—42no—
85C22×C131#38111yescharacteristic
86C22×C131C2×#10011yescharacteristic
87C22×C131C2×#10111yescharacteristic
88C22×C131#41612yes—
89C22×C131#41712yes—
90C4×C131—22no—
91C4×C131—22no—
92C4×C131—42no—
93C4×C131—84no—
94C4×C131#48214yes—
95C4×C131#48514yes—
96C2×C131—42no—
97C2×C131#154411yescharacteristic
98C2×C131#155112yes—
99C2×C131#156111yescharacteristic
100C2×C131#182111yescharacteristic
101C2×C131#182512yes—
102#8729C13111yesmaximal, characteristic, direct product factor, Sylow
103C131#872911yescharacteristic, direct product factor, Sylow
104#2285C2×C13111yescharacteristic
105#1797C2×C13112yes—
106#1296C2×C13114yescomplemented
107C2×#117C4×C13112yes—
108C22×C42C22×C13111yescharacteristic
109C2×C4⋊C8C22×C13114yes—
110C2×C22⋊C8—22no—
111#384C22×C13112yes—
112#382C4×C13112yes—
113#380—22no—
114C4×C4⋊C4—22no—
115#336—22no—
116C23×C4C2×C4×C13111yescharacteristic
117C23×C4D4×C13112yes—
118C22×C8—24no—
119#117—44no—
120C2×C4⋊C4—22no—
121C2×C4⋊C4—22no—
122C2×C4⋊C4C2×C4×C13114yes—
123C2×C22⋊C4—22no—
124C2×C42—24no—
125C2×C42—22no—
126C2×C42C2×C4×C13111yescharacteristic
127C2×C42D4×C13112yes—
128C2×C42C23×C13111yescharacteristic
129C4⋊C8—28no—
130C22⋊C8—44no—
131#95—24no—
132C24C22⋊C4×C13111yescharacteristic
133C22×C4—22no—
134C22×C4—22no—
135C22×C4—22no—
136C22×C4—24no—
137C22×C4—24no—
138C22×C4—22no—
139C22×C4—22no—
140C22×C4—24no—
141C22×C4C22⋊C4×C13112yes—
142C22×C4C22⋊C4×C13111yescharacteristic
143C22×C4C22×C4×C13111yescharacteristic
144C22×C4C2×D4×C13112yes—
145C2×C8—44no—
146C2×C8—44no—
147C2×C8—44no—
148C4⋊C4—44no—
149C4⋊C4—44no—
150C4⋊C4—42no—
151C4⋊C4—42no—
152C22⋊C4—44no—
153C42—22no—
154C42—24no—
155C42—44no—
156C42#41×C13114yes—
157C23—21no—
158C23—22no—
159C23—22no—
160C23—21no—
161C23#100×C13112yes—
162C23C2×C22⋊C4×C13111yescharacteristic
163C2×C4—28no—
164C2×C4—21no—
165C2×C4—21no—
166C2×C4—21no—
167C2×C4—21no—
168C2×C4—22no—
169C2×C4—22no—
170C2×C4—22no—
171C2×C4—44no—
172C2×C4—44no—
173C2×C4—44no—
174C2×C4—44no—
175C2×C4—44no—
176C2×C4#101×C13112yes—
177C2×C4#117×C13112yes—
178C2×C4#123×C13114yes—
179C2×C4#135×C13114yes—
180C2×C4AGL(1,ℤ/8)×C13112yes—
181C2×C4#137×C13112yes—
182C8—84no—
183C22—24no—
184C22—22no—
185C22—41no—
186C22—41no—
187C22—42no—
188C22#381×C13111yescharacteristic
189C22C2×#100×C13111yescharacteristic
190C22C2×#101×C13111yescharacteristic
191C22#416×C13112yes—
192C22#417×C13112yes—
193C4—22no—
194C4—22no—
195C4—42no—
196C4—84no—
197C4#482×C13114yes—
198C4#485×C13114yes—
199C2—42no—
200C2#1544×C13111yescharacteristic
201C2#1551×C13112yes—
202C2#1561×C13111yescharacteristic
203C2#1821×C13111yescharacteristic
204C2#1825×C13112yes—
subgroupG/H
center, socleC23×C131C2×C22⋊C4
commutatorC22×C4C22×C4×C131
Frattini, cosocleC2×C42C23×C131
prime radicalC24×C131C22⋊C4
LCSG ▷ C22×C4 ▷ C22 ▷ C1
UCSC1 ◁ C23×C131 ◁ C22×C42×C131 ◁ G

Complements

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

NH ≅ G/Ntype
3. #1296×C131C2semidirect
102. #8729C131direct (N × H)
103. C131#8729direct (N × H)
106. #1296C2×C131semidirect

Maximal subgroups

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

subgroupindex
#2285×C1312
#1797×C1312
#1296×C1312
#8729131