Finite Group Databasebeta

← C131×#8723 #45694607

Subgroups — C131×#8723 #45694607

Order 33536.

630 conjugacy classes of subgroups; only the 206 normal subgroups are shown.

normal subgroups only

This group has 630 conjugacy classes of subgroups — too many to draw. Only its 206 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×#384×C131C211yesmaximal, characteristic
2#1797×C131C212yesmaximal
3#1296×C131C214yesmaximal, complemented
4C22×C4⋊C4×C131—22no—
5C22×C4⋊C4×C131C412yes—
6C22×C42×C131C2211yescharacteristic
7C2×C4⋊C8×C131C2214yes—
8C2×C22⋊C8×C131—22no—
9#384×C131—22no—
10#384×C131C412yes—
11#384×C131C2212yes—
12#336×C131—22no—
13C23×C4×C131—22no—
14C23×C4×C131C2×C411yescharacteristic
15C23×C4×C131D412yes—
16C22×C8×C131—24no—
17C2×C4⋊C4×C131—24no—
18C2×C4⋊C4×C131—22no—
19C2×C4⋊C4×C131—24no—
20C2×C4⋊C4×C131—44no—
21C2×C4⋊C4×C131—44no—
22C2×C4⋊C4×C131—44no—
23C2×C4⋊C4×C131C2×C414yes—
24C2×C42×C131—24no—
25C2×C42×C131C2×C411yescharacteristic
26C2×C42×C131D412yes—
27C2×C42×C131C2311yescharacteristic
28C4⋊C8×C131—28no—
29C22⋊C8×C131—44no—
30C24×C131C22⋊C411yescharacteristic
31C22×C4×C131—22no—
32C22×C4×C131—22no—
33C22×C4×C131—22no—
34C22×C4×C131—24no—
35C22×C4×C131—24no—
36C22×C4×C131—24no—
37C22×C4×C131—44no—
38C22×C4×C131—48no—
39C22×C4×C131C22⋊C411yescharacteristic
40C22×C4×C131C22⋊C412yes—
41C22×C4×C131D814yes—
42C22×C4×C131SD1614yes—
43C22×C4×C131C22×C411yescharacteristic
44C22×C4×C131C2×D412yes—
45C2×C8×C131—44no—
46C2×C8×C131—44no—
47C2×C8×C131—44no—
48C4⋊C4×C131—44no—
49C4⋊C4×C131—44no—
50C4⋊C4×C131—48no—
51C4⋊C4×C131—44no—
52C4⋊C4×C131—44no—
53C42×C131—22no—
54C42×C131—24no—
55C42×C131#4114yes—
56C23×C131—21no—
57C23×C131—21no—
58C23×C131—22no—
59C23×C131#10012yes—
60C23×C131#10214yes—
61C23×C131C2×C22⋊C411yescharacteristic
62C2×C4×C131—28no—
63C2×C4×C131—21no—
64C2×C4×C131—22no—
65C2×C4×C131—21no—
66C2×C4×C131—21no—
67C2×C4×C131—21no—
68C2×C4×C131—22no—
69C2×C4×C131—28no—
70C2×C4×C131—28no—
71C2×C4×C131—44no—
72C2×C4×C131—48no—
73C2×C4×C131—88no—
74C2×C4×C131#10112yes—
75C2×C4×C131#10214yes—
76C2×C4×C131#11712yes—
77C2×C4×C131#12314yes—
78C2×C4×C131C2×D812yes—
79C2×C4×C131C2×SD1612yes—
80C2×C4×C131#13714yes—
81C8×C131—84no—
82C22×C131—24no—
83C22×C131—22no—
84C22×C131—22no—
85C22×C131—24no—
86C22×C131#33114yes—
87C22×C131#38111yescharacteristic
88C22×C131C2×#10011yescharacteristic
89C22×C131C2×#10111yescharacteristic
90C22×C131C2×#10212yes—
91C22×C131#41912yes—
92C4×C131—22no—
93C4×C131—22no—
94C4×C131—24no—
95C4×C131—84no—
96C4×C131#48014yes—
97C4×C131#48314yes—
98C2×C131—24no—
99C2×C131C2×#33111yescharacteristic
100C2×C131#154612yes—
101C2×C131#155811yescharacteristic
102C2×C131#182111yescharacteristic
103C2×C131#182312yes—
104#8723C13111yesmaximal, characteristic, direct product factor, Sylow
105C131#872311yescharacteristic, direct product factor, Sylow
106C2×#384C2×C13111yescharacteristic
107#1797C2×C13112yes—
108#1296C2×C13114yescomplemented
109C22×C4⋊C4—22no—
110C22×C4⋊C4C4×C13112yes—
111C22×C42C22×C13111yescharacteristic
112C2×C4⋊C8C22×C13114yes—
113C2×C22⋊C8—22no—
114#384—22no—
115#384C4×C13112yes—
116#384C22×C13112yes—
117#336—22no—
118C23×C4—22no—
119C23×C4C2×C4×C13111yescharacteristic
120C23×C4D4×C13112yes—
121C22×C8—24no—
122C2×C4⋊C4—24no—
123C2×C4⋊C4—22no—
124C2×C4⋊C4—24no—
125C2×C4⋊C4—44no—
126C2×C4⋊C4—44no—
127C2×C4⋊C4—44no—
128C2×C4⋊C4C2×C4×C13114yes—
129C2×C42—24no—
130C2×C42C2×C4×C13111yescharacteristic
131C2×C42D4×C13112yes—
132C2×C42C23×C13111yescharacteristic
133C4⋊C8—28no—
134C22⋊C8—44no—
135C24C22⋊C4×C13111yescharacteristic
136C22×C4—22no—
137C22×C4—22no—
138C22×C4—22no—
139C22×C4—24no—
140C22×C4—24no—
141C22×C4—24no—
142C22×C4—44no—
143C22×C4—48no—
144C22×C4C22⋊C4×C13111yescharacteristic
145C22×C4C22⋊C4×C13112yes—
146C22×C4D8×C13114yes—
147C22×C4SD16×C13114yes—
148C22×C4C22×C4×C13111yescharacteristic
149C22×C4C2×D4×C13112yes—
150C2×C8—44no—
151C2×C8—44no—
152C2×C8—44no—
153C4⋊C4—44no—
154C4⋊C4—44no—
155C4⋊C4—48no—
156C4⋊C4—44no—
157C4⋊C4—44no—
158C42—22no—
159C42—24no—
160C42#41×C13114yes—
161C23—21no—
162C23—22no—
163C23—21no—
164C23#100×C13112yes—
165C23#102×C13114yes—
166C23C2×C22⋊C4×C13111yescharacteristic
167C2×C4—28no—
168C2×C4—21no—
169C2×C4—21no—
170C2×C4—21no—
171C2×C4—22no—
172C2×C4—21no—
173C2×C4—22no—
174C2×C4—28no—
175C2×C4—28no—
176C2×C4—44no—
177C2×C4—48no—
178C2×C4—88no—
179C2×C4#101×C13112yes—
180C2×C4#102×C13114yes—
181C2×C4#117×C13112yes—
182C2×C4#123×C13114yes—
183C2×C4C2×D8×C13112yes—
184C2×C4C2×SD16×C13112yes—
185C2×C4#137×C13114yes—
186C8—84no—
187C22—24no—
188C22—22no—
189C22—22no—
190C22—24no—
191C22#331×C13114yes—
192C22#381×C13111yescharacteristic
193C22C2×#100×C13111yescharacteristic
194C22C2×#101×C13111yescharacteristic
195C22C2×#102×C13112yes—
196C22#419×C13112yes—
197C4—22no—
198C4—22no—
199C4—24no—
200C4—84no—
201C4#480×C13114yes—
202C4#483×C13114yes—
203C2—24no—
204C2C2×#331×C13111yescharacteristic
205C2#1546×C13112yes—
206C2#1558×C13111yescharacteristic
207C2#1821×C13111yescharacteristic
208C2#1823×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
104. #8723C131direct (N × H)
105. C131#8723direct (N × H)
108. #1296C2×C131semidirect

Maximal subgroups

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

subgroupindex
C2×#384×C1312
#1797×C1312
#1296×C1312
#8723131