Finite Group Databasebeta

← C131×#8746 #45694630

Subgroups — C131×#8746 #45694630

Order 33536.

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

normal subgroups only

This group has 814 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#1781×C131C212yesmaximal
3#1304×C131C214yesmaximal, complemented
4C23×D4×C131C2211yescharacteristic
5C22×C22⋊C4×C131C412yescomplemented
6C2×#99×C131—24no—
7#386×C131—24no—
8#381×C131C412yescomplemented
9#379×C131C2214yes—
10#379×C131C2212yes—
11C25×C131C2×C411yescharacteristic
12C25×C131C2311yescharacteristic
13C22×D4×C131—24no—
14C22×D4×C131—44no—
15C22×D4×C131D414yes—
16C23×C4×C131—22no—
17C23×C4×C131C2×C411yescharacteristic
18C2×C22⋊C4×C131—22no—
19C2×C22⋊C4×C131—24no—
20C2×C22⋊C4×C131—24no—
21C2×C22⋊C4×C131—28no—
22C2×C22⋊C4×C131—44no—
23C2×C22⋊C4×C131C2×C414yes—
24#99×C131—48no—
25#95×C131—24no—
26C24×C131—24no—
27C24×C131—22no—
28C24×C131—42no—
29C24×C131—82no—
30C24×C131—82no—
31C24×C131C22⋊C412yes—
32C24×C131C22×C411yescharacteristic
33C24×C131C2×D412yes—
34C24×C131#4114yes—
35C2×D4×C131—28no—
36C2×D4×C131—28no—
37C2×D4×C131—44no—
38C2×D4×C131—416no—
39C22×C4×C131—22no—
40C22×C4×C131—24no—
41C22×C4×C131—42no—
42C22×C4×C131—44no—
43C22×C4×C131—44no—
44C22×C4×C131—84no—
45C22×C4×C131C22⋊C412yes—
46C22⋊C4×C131—44no—
47C22⋊C4×C131—44no—
48C22⋊C4×C131—48no—
49C22⋊C4×C131—84no—
50C22⋊C4×C131—88no—
51C23×C131—28no—
52C23×C131—22no—
53C23×C131—22no—
54C23×C131—22no—
55C23×C131—24no—
56C23×C131—42no—
57C23×C131—44no—
58C23×C131—48no—
59C23×C131—44no—
60C23×C131—44no—
61C23×C131—84no—
62C23×C131—88no—
63C23×C131—88no—
64C23×C131#9914yes—
65C23×C131C2×C22⋊C411yescharacteristic
66C23×C131#11712yes—
67C23×C131#12314yes—
68D4×C131—416no—
69C2×C4×C131—22no—
70C2×C4×C131—24no—
71C2×C4×C131—44no—
72C2×C4×C131—48no—
73C2×C4×C131—44no—
74C2×C4×C131—88no—
75C2×C4×C131—84no—
76C2×C4×C131—88no—
77C22×C131—22no—
78C22×C131—22no—
79C22×C131—24no—
80C22×C131—24no—
81C22×C131—28no—
82C22×C131—24no—
83C22×C131—44no—
84C22×C131—44no—
85C22×C131—44no—
86C22×C131—44no—
87C22×C131—84no—
88C22×C131—88no—
89C22×C131—88no—
90C22×C131#38111yescharacteristic
91C22×C131C2×#9912yes—
92C4×C131—42no—
93C4×C131—84no—
94C4×C131—164no—
95C2×C131—22no—
96C2×C131—44no—
97C2×C131—42no—
98C2×C131—44no—
99C2×C131#181911yescharacteristic
100C2×C131#182812yes—
101#8746C13111yesmaximal, characteristic, direct product factor, Sylow
102C131#874611yescharacteristic, direct product factor, Sylow
103#2308C2×C13111yescharacteristic
104#1781C2×C13112yes—
105#1304C2×C13114yescomplemented
106C23×D4C22×C13111yescharacteristic
107C22×C22⋊C4C4×C13112yescomplemented
108C2×#99—24no—
109#386—24no—
110#381C4×C13112yescomplemented
111#379C22×C13114yes—
112#379C22×C13112yes—
113C25C2×C4×C13111yescharacteristic
114C25C23×C13111yescharacteristic
115C22×D4—24no—
116C22×D4—44no—
117C22×D4D4×C13114yes—
118C23×C4—22no—
119C23×C4C2×C4×C13111yescharacteristic
120C2×C22⋊C4—22no—
121C2×C22⋊C4—24no—
122C2×C22⋊C4—24no—
123C2×C22⋊C4—28no—
124C2×C22⋊C4—44no—
125C2×C22⋊C4C2×C4×C13114yes—
126#99—48no—
127#95—24no—
128C24—24no—
129C24—22no—
130C24—42no—
131C24—82no—
132C24—82no—
133C24C22⋊C4×C13112yes—
134C24C22×C4×C13111yescharacteristic
135C24C2×D4×C13112yes—
136C24#41×C13114yes—
137C2×D4—28no—
138C2×D4—28no—
139C2×D4—44no—
140C2×D4—416no—
141C22×C4—22no—
142C22×C4—24no—
143C22×C4—42no—
144C22×C4—44no—
145C22×C4—44no—
146C22×C4—84no—
147C22×C4C22⋊C4×C13112yes—
148C22⋊C4—44no—
149C22⋊C4—44no—
150C22⋊C4—48no—
151C22⋊C4—84no—
152C22⋊C4—88no—
153C23—28no—
154C23—22no—
155C23—22no—
156C23—22no—
157C23—24no—
158C23—42no—
159C23—44no—
160C23—48no—
161C23—44no—
162C23—44no—
163C23—84no—
164C23—88no—
165C23—88no—
166C23#99×C13114yes—
167C23C2×C22⋊C4×C13111yescharacteristic
168C23#117×C13112yes—
169C23#123×C13114yes—
170D4—416no—
171C2×C4—24no—
172C2×C4—22no—
173C2×C4—44no—
174C2×C4—48no—
175C2×C4—44no—
176C2×C4—88no—
177C2×C4—84no—
178C2×C4—88no—
179C22—22no—
180C22—22no—
181C22—24no—
182C22—24no—
183C22—28no—
184C22—24no—
185C22—44no—
186C22—44no—
187C22—44no—
188C22—44no—
189C22—84no—
190C22—88no—
191C22—88no—
192C22#381×C13111yescharacteristic
193C22C2×#99×C13112yes—
194C4—42no—
195C4—84no—
196C4—164no—
197C2—22no—
198C2—44no—
199C2—42no—
200C2—44no—
201C2#1819×C13111yescharacteristic
202C2#1828×C13112yes—
subgroupG/H
center, socleC22×C131#381
commutatorC24C22×C4×C131
Frattini, cosocleC25C23×C131
prime radicalC23×D4×C131C22
LCSG ▷ C24 ▷ C22 ▷ C1
UCSC1 ◁ C22×C131 ◁ C25×C131 ◁ G

Complements

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

NH ≅ G/Ntype
3. #1304×C131C2semidirect
5. C22×C22⋊C4×C131C4semidirect
8. #381×C131C4semidirect
101. #8746C131direct (N × H)
102. C131#8746direct (N × H)
105. #1304C2×C131semidirect
107. C22×C22⋊C4C4×C131semidirect
110. #381C4×C131semidirect

Maximal subgroups

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

subgroupindex
#2308×C1312
#1781×C1312
#1304×C1312
#8746131