Finite Group Databasebeta

← C131×#8722 #45694606

Subgroups — C131×#8722 #45694606

Order 33536.

526 conjugacy classes of subgroups; only the 142 normal subgroups are shown.

normal subgroups only

This group has 526 conjugacy classes of subgroups — too many to draw. Only its 142 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#1749×C131C212yesmaximal
3#1295×C131C214yesmaximal, complemented
4C2×#117×C131C412yes—
5C22×C42×C131C2211yescharacteristic
6C2×C22⋊C8×C131—22no—
7C2×#97×C131C2214yes—
8#384×C131C412yes—
9#382×C131C2212yes—
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
26C22⋊C8×C131—28no—
27#97×C131—28no—
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—24no—
36C22×C4×C131—42no—
37C22×C4×C131C22⋊C411yescharacteristic
38C22×C4×C131C22⋊C412yes—
39C22×C4×C131C22×C411yescharacteristic
40C22×C4×C131C2×D412yes—
41C2×C8×C131—28no—
42C2×C8×C131—44no—
43C2×C8×C131—44no—
44C4⋊C4×C131—44no—
45C4⋊C4×C131—44no—
46C4⋊C4×C131—44no—
47C22⋊C4×C131—44no—
48C42×C131—22no—
49C42×C131—24no—
50C42×C131—44no—
51C42×C131#4114yes—
52C23×C131—21no—
53C23×C131—21no—
54C23×C131—22no—
55C23×C131—22no—
56C23×C131#10012yes—
57C23×C131C2×C22⋊C411yescharacteristic
58C2×C4×C131—28no—
59C2×C4×C131—21no—
60C2×C4×C131—22no—
61C2×C4×C131—21no—
62C2×C4×C131—21no—
63C2×C4×C131—21no—
64C2×C4×C131—22no—
65C2×C4×C131—22no—
66C2×C4×C131—22no—
67C2×C4×C131—48no—
68C2×C4×C131—44no—
69C2×C4×C131—44no—
70C2×C4×C131—44no—
71C2×C4×C131#10112yes—
72C2×C4×C131#10414yes—
73C2×C4×C131#11712yes—
74C2×C4×C131#12314yes—
75C8×C131—48no—
76C22×C131—22no—
77C22×C131—24no—
78C22×C131—41no—
79C22×C131—42no—
80C22×C131—41no—
81C22×C131#38111yescharacteristic
82C22×C131C2×#10011yescharacteristic
83C22×C131C2×#10111yescharacteristic
84C22×C131C2×#10412yes—
85C22×C131#42112yes—
86C4×C131—22no—
87C4×C131—22no—
88C4×C131—24no—
89C4×C131—24no—
90C4×C131—84no—
91C2×C131—42no—
92C2×C131#152611yescharacteristic
93C2×C131#153012yes—
94C2×C131#153711yescharacteristic
95C2×C131#182111yescharacteristic
96C2×C131#182612yes—
97#8722C13111yesmaximal, characteristic, direct product factor, Sylow
98C131#872211yescharacteristic, direct product factor, Sylow
99#2285C2×C13111yescharacteristic
100#1749C2×C13112yes—
101#1295C2×C13114yescomplemented
102C2×#117C4×C13112yes—
103C22×C42C22×C13111yescharacteristic
104C2×C22⋊C8—22no—
105C2×#97C22×C13114yes—
106#384C4×C13112yes—
107#382C22×C13112yes—
108#380—22no—
109C4×C4⋊C4—22no—
110#336—22no—
111C23×C4C2×C4×C13111yescharacteristic
112C23×C4D4×C13112yes—
113C22×C8—24no—
114#117—44no—
115C2×C4⋊C4—22no—
116C2×C4⋊C4—22no—
117C2×C4⋊C4C2×C4×C13114yes—
118C2×C22⋊C4—22no—
119C2×C42—24no—
120C2×C42—22no—
121C2×C42C2×C4×C13111yescharacteristic
122C2×C42D4×C13112yes—
123C2×C42C23×C13111yescharacteristic
124C22⋊C8—28no—
125#97—28no—
126#95—24no—
127C24C22⋊C4×C13111yescharacteristic
128C22×C4—22no—
129C22×C4—22no—
130C22×C4—22no—
131C22×C4—24no—
132C22×C4—24no—
133C22×C4—24no—
134C22×C4—42no—
135C22×C4C22⋊C4×C13111yescharacteristic
136C22×C4C22⋊C4×C13112yes—
137C22×C4C22×C4×C13111yescharacteristic
138C22×C4C2×D4×C13112yes—
139C2×C8—28no—
140C2×C8—44no—
141C2×C8—44no—
142C4⋊C4—44no—
143C4⋊C4—44no—
144C4⋊C4—44no—
145C22⋊C4—44no—
146C42—22no—
147C42—24no—
148C42—44no—
149C42#41×C13114yes—
150C23—21no—
151C23—22no—
152C23—22no—
153C23—21no—
154C23#100×C13112yes—
155C23C2×C22⋊C4×C13111yescharacteristic
156C2×C4—28no—
157C2×C4—21no—
158C2×C4—21no—
159C2×C4—21no—
160C2×C4—22no—
161C2×C4—22no—
162C2×C4—22no—
163C2×C4—21no—
164C2×C4—22no—
165C2×C4—48no—
166C2×C4—44no—
167C2×C4—44no—
168C2×C4—44no—
169C2×C4#101×C13112yes—
170C2×C4#104×C13114yes—
171C2×C4#117×C13112yes—
172C2×C4#123×C13114yes—
173C8—48no—
174C22—24no—
175C22—22no—
176C22—41no—
177C22—41no—
178C22—42no—
179C22#381×C13111yescharacteristic
180C22C2×#100×C13111yescharacteristic
181C22C2×#101×C13111yescharacteristic
182C22C2×#104×C13112yes—
183C22#421×C13112yes—
184C4—22no—
185C4—22no—
186C4—24no—
187C4—24no—
188C4—84no—
189C2—42no—
190C2#1526×C13111yescharacteristic
191C2#1530×C13112yes—
192C2#1537×C13111yescharacteristic
193C2#1821×C13111yescharacteristic
194C2#1826×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. #1295×C131C2semidirect
97. #8722C131direct (N × H)
98. C131#8722direct (N × H)
101. #1295C2×C131semidirect

Maximal subgroups

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

subgroupindex
#2285×C1312
#1749×C1312
#1295×C1312
#8722131