Finite Group Databasebeta

← C131×#8751 #45694635

Subgroups — C131×#8751 #45694635

Order 33536.

754 conjugacy classes of subgroups; only the 118 normal subgroups are shown.

normal subgroups only

This group has 754 conjugacy classes of subgroups — too many to draw. Only its 118 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#2308×C131C211yesmaximal, characteristic
2#1783×C131C212yesmaximal
3#1306×C131C214yesmaximal, complemented
4C23×D4×C131C2211yescharacteristic
5C22×C22⋊C4×C131C412yes—
6C2×#100×C131—24no—
7#407×C131C2214yes—
8#386×C131—24no—
9#381×C131C2212yes—
10#379×C131C412yes—
11C25×C131C2×C411yescharacteristic
12C25×C131C2×C411yescharacteristic
13C22×D4×C131—24no—
14C22×D4×C131—44no—
15C22×D4×C131D414yes—
16C23×C4×C131—22no—
17C23×C4×C131C2311yescharacteristic
18C2×M16×C131—24no—
19C2×C22⋊C4×C131—22no—
20C2×C22⋊C4×C131—24no—
21C2×C22⋊C4×C131—44no—
22C2×C22⋊C4×C131C2×C414yes—
23#100×C131—48no—
24C22⋊C8×C131—28no—
25#95×C131—24no—
26C24×C131—24no—
27C24×C131—22no—
28C24×C131—22no—
29C24×C131—42no—
30C24×C131—82no—
31C24×C131—82no—
32C24×C131C22⋊C412yes—
33C24×C131C22⋊C412yes—
34C24×C131C22×C411yescharacteristic
35C2×D4×C131—28no—
36C2×D4×C131—28no—
37C2×D4×C131—44no—
38C2×D4×C131—416no—
39C22×C4×C131—24no—
40C22×C4×C131—42no—
41C22×C4×C131—44no—
42C22×C4×C131—84no—
43C22×C4×C131C2×D412yes—
44C22×C4×C131#4114yes—
45M16×C131—48no—
46C2×C8×C131—44no—
47C22⋊C4×C131—44no—
48C22⋊C4×C131—44no—
49C22⋊C4×C131—84no—
50C23×C131—28no—
51C23×C131—22no—
52C23×C131—22no—
53C23×C131—22no—
54C23×C131—22no—
55C23×C131—24no—
56C23×C131—42no—
57C23×C131—44no—
58C23×C131—44no—
59C23×C131—44no—
60C23×C131—84no—
61C23×C131—84no—
62C23×C131—88no—
63C23×C131—88no—
64C23×C131#9914yes—
65C23×C131C2×C22⋊C411yescharacteristic
66C23×C131#11712yes—
67D4×C131—416no—
68C2×C4×C131—24no—
69C2×C4×C131—44no—
70C2×C4×C131—48no—
71C2×C4×C131—44no—
72C2×C4×C131—88no—
73C2×C4×C131#12314yes—
74C8×C131—84no—
75C22×C131—22no—
76C22×C131—22no—
77C22×C131—24no—
78C22×C131—24no—
79C22×C131—44no—
80C22×C131—44no—
81C22×C131—44no—
82C22×C131—44no—
83C22×C131—42no—
84C22×C131—44no—
85C22×C131—84no—
86C22×C131—88no—
87C22×C131—88no—
88C22×C131#38111yescharacteristic
89C22×C131C2×#9912yes—
90C4×C131—24no—
91C4×C131—84no—
92C2×C131—22no—
93C2×C131—42no—
94C2×C131—44no—
95C2×C131—82no—
96C2×C131#181911yescharacteristic
97C2×C131#182912yes—
98#8751C13111yesmaximal, characteristic, direct product factor, Sylow
99C131#875111yescharacteristic, direct product factor, Sylow
100#2308C2×C13111yescharacteristic
101#1783C2×C13112yes—
102#1306C2×C13114yescomplemented
103C23×D4C22×C13111yescharacteristic
104C22×C22⋊C4C4×C13112yes—
105C2×#100—24no—
106#407C22×C13114yes—
107#386—24no—
108#381C22×C13112yes—
109#379C4×C13112yes—
110C25C2×C4×C13111yescharacteristic
111C25C2×C4×C13111yescharacteristic
112C22×D4—24no—
113C22×D4—44no—
114C22×D4D4×C13114yes—
115C23×C4—22no—
116C23×C4C23×C13111yescharacteristic
117C2×M16—24no—
118C2×C22⋊C4—22no—
119C2×C22⋊C4—24no—
120C2×C22⋊C4—44no—
121C2×C22⋊C4C2×C4×C13114yes—
122#100—48no—
123C22⋊C8—28no—
124#95—24no—
125C24—24no—
126C24—22no—
127C24—22no—
128C24—42no—
129C24—82no—
130C24—82no—
131C24C22⋊C4×C13112yes—
132C24C22⋊C4×C13112yes—
133C24C22×C4×C13111yescharacteristic
134C2×D4—28no—
135C2×D4—28no—
136C2×D4—44no—
137C2×D4—416no—
138C22×C4—24no—
139C22×C4—42no—
140C22×C4—44no—
141C22×C4—84no—
142C22×C4C2×D4×C13112yes—
143C22×C4#41×C13114yes—
144M16—48no—
145C2×C8—44no—
146C22⋊C4—44no—
147C22⋊C4—44no—
148C22⋊C4—84no—
149C23—28no—
150C23—22no—
151C23—22no—
152C23—22no—
153C23—22no—
154C23—24no—
155C23—42no—
156C23—44no—
157C23—44no—
158C23—44no—
159C23—84no—
160C23—84no—
161C23—88no—
162C23—88no—
163C23#99×C13114yes—
164C23C2×C22⋊C4×C13111yescharacteristic
165C23#117×C13112yes—
166D4—416no—
167C2×C4—24no—
168C2×C4—44no—
169C2×C4—48no—
170C2×C4—44no—
171C2×C4—88no—
172C2×C4#123×C13114yes—
173C8—84no—
174C22—22no—
175C22—22no—
176C22—24no—
177C22—24no—
178C22—44no—
179C22—44no—
180C22—44no—
181C22—44no—
182C22—42no—
183C22—44no—
184C22—84no—
185C22—88no—
186C22—88no—
187C22#381×C13111yescharacteristic
188C22C2×#99×C13112yes—
189C4—24no—
190C4—84no—
191C2—22no—
192C2—42no—
193C2—44no—
194C2—82no—
195C2#1819×C13111yescharacteristic
196C2#1829×C13112yes—
subgroupG/H
center, socleC22×C131#381
commutatorC24C22×C4×C131
Frattini, cosocleC23×C4C23×C131
prime radicalC23×D4×C131C22
LCSG ▷ C24 ▷ C22 ▷ C1
UCSC1 ◁ C22×C131 ◁ C23×C4×C131 ◁ G

Complements

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

NH ≅ G/Ntype
3. #1306×C131C2semidirect
98. #8751C131direct (N × H)
99. C131#8751direct (N × H)
102. #1306C2×C131semidirect

Maximal subgroups

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

subgroupindex
#2308×C1312
#1783×C1312
#1306×C1312
#8751131