Finite Group Databasebeta

← C131×#8757 #45694641

Subgroups — C131×#8757 #45694641

Order 33536.

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

normal subgroups only

This group has 438 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#2316×C131C211yesmaximal, characteristic
2#1463×C131C212yesmaximal
3#1305×C131C214yesmaximal
4C2×#117×C131C411yescharacteristic
5C2×#117×C131C411yescharacteristic
6C22×C4⋊C4×C131C2211yescharacteristic
7#407×C131C2214yes—
8#389×C131—22no—
9#389×C131—22no—
10#380×C131C412yes—
11#380×C131C2212yes—
12#324×C131—22no—
13#324×C131—22no—
14C23×C4×C131C2×C411yescharacteristic
15C23×C4×C131C2×C411yescharacteristic
16C23×C4×C131C2311yescharacteristic
17C2×M16×C131—24no—
18#117×C131—42no—
19#117×C131—42no—
20C2×C4⋊C4×C131—24no—
21C2×C4⋊C4×C131—21no—
22C2×C4⋊C4×C131—21no—
23C2×C4⋊C4×C131—22no—
24C2×C4⋊C4×C131—22no—
25C2×C4⋊C4×C131D412yes—
26C2×C4⋊C4×C131D412yes—
27C2×C22⋊C4×C131C2×C412yes—
28C2×C22⋊C4×C131C2×C412yes—
29C2×C42×C131—21no—
30C2×C42×C131—21no—
31C22⋊C8×C131—24no—
32C22⋊C8×C131—24no—
33#95×C131—22no—
34#95×C131—22no—
35C24×C131C22×C411yescharacteristic
36C22×C4×C131—22no—
37C22×C4×C131—22no—
38C22×C4×C131—22no—
39C22×C4×C131—22no—
40C22×C4×C131—22no—
41C22×C4×C131—22no—
42C22×C4×C131—81no—
43C22×C4×C131—81no—
44C22×C4×C131C22⋊C411yescharacteristic
45C22×C4×C131C22⋊C411yescharacteristic
46C22×C4×C131C22⋊C412yes—
47C22×C4×C131C2×D412yes—
48C22×C4×C131#4114yes—
49M16×C131—84no—
50C2×C8×C131—44no—
51C4⋊C4×C131—24no—
52C4⋊C4×C131—24no—
53C4⋊C4×C131—42no—
54C4⋊C4×C131—42no—
55C4⋊C4×C131—82no—
56C4⋊C4×C131—82no—
57C22⋊C4×C131—42no—
58C22⋊C4×C131—42no—
59C42×C131—42no—
60C42×C131—42no—
61C23×C131—21no—
62C23×C131—21no—
63C23×C131—41no—
64C23×C131—41no—
65C23×C131C2×C22⋊C411yescharacteristic
66C23×C131#11712yes—
67C2×C4×C131—28no—
68C2×C4×C131—21no—
69C2×C4×C131—21no—
70C2×C4×C131—21no—
71C2×C4×C131—21no—
72C2×C4×C131—22no—
73C2×C4×C131—42no—
74C2×C4×C131—44no—
75C2×C4×C131—42no—
76C2×C4×C131—42no—
77C2×C4×C131—42no—
78C2×C4×C131—42no—
79C2×C4×C131—42no—
80C2×C4×C131—42no—
81C2×C4×C131—42no—
82C2×C4×C131—82no—
83C2×C4×C131#10012yes—
84C2×C4×C131#10112yes—
85C2×C4×C131#12314yes—
86C8×C131—84no—
87C22×C131—21no—
88C22×C131—21no—
89C22×C131—22no—
90C22×C131—22no—
91C22×C131—22no—
92C22×C131—42no—
93C22×C131—42no—
94C22×C131#38111yescharacteristic
95C22×C131C2×#10011yescharacteristic
96C22×C131C2×#10111yescharacteristic
97C4×C131—22no—
98C4×C131—22no—
99C4×C131—24no—
100C4×C131—42no—
101C4×C131—82no—
102C4×C131—82no—
103C2×C131—21no—
104C2×C131—21no—
105C2×C131—42no—
106C2×C131#182111yescharacteristic
107C2×C131#182811yescharacteristic
108C2×C131#183011yescharacteristic
109#8757C13111yesmaximal, characteristic, direct product factor, Sylow
110C131#875711yescharacteristic, direct product factor, Sylow
111#2316C2×C13111yescharacteristic
112#1463C2×C13112yes—
113#1305C2×C13114yes—
114C2×#117C4×C13111yescharacteristic
115C2×#117C4×C13111yescharacteristic
116C22×C4⋊C4C22×C13111yescharacteristic
117#407C22×C13114yes—
118#389—22no—
119#389—22no—
120#380C4×C13112yes—
121#380C22×C13112yes—
122#324—22no—
123#324—22no—
124C23×C4C2×C4×C13111yescharacteristic
125C23×C4C2×C4×C13111yescharacteristic
126C23×C4C23×C13111yescharacteristic
127C2×M16—24no—
128#117—42no—
129#117—42no—
130C2×C4⋊C4—24no—
131C2×C4⋊C4—21no—
132C2×C4⋊C4—21no—
133C2×C4⋊C4—22no—
134C2×C4⋊C4—22no—
135C2×C4⋊C4D4×C13112yes—
136C2×C4⋊C4D4×C13112yes—
137C2×C22⋊C4C2×C4×C13112yes—
138C2×C22⋊C4C2×C4×C13112yes—
139C2×C42—21no—
140C2×C42—21no—
141C22⋊C8—24no—
142C22⋊C8—24no—
143#95—22no—
144#95—22no—
145C24C22×C4×C13111yescharacteristic
146C22×C4—22no—
147C22×C4—22no—
148C22×C4—22no—
149C22×C4—22no—
150C22×C4—22no—
151C22×C4—22no—
152C22×C4—81no—
153C22×C4—81no—
154C22×C4C22⋊C4×C13111yescharacteristic
155C22×C4C22⋊C4×C13111yescharacteristic
156C22×C4C22⋊C4×C13112yes—
157C22×C4C2×D4×C13112yes—
158C22×C4#41×C13114yes—
159M16—84no—
160C2×C8—44no—
161C4⋊C4—24no—
162C4⋊C4—24no—
163C4⋊C4—42no—
164C4⋊C4—42no—
165C4⋊C4—82no—
166C4⋊C4—82no—
167C22⋊C4—42no—
168C22⋊C4—42no—
169C42—42no—
170C42—42no—
171C23—21no—
172C23—21no—
173C23—41no—
174C23—41no—
175C23C2×C22⋊C4×C13111yescharacteristic
176C23#117×C13112yes—
177C2×C4—28no—
178C2×C4—21no—
179C2×C4—21no—
180C2×C4—21no—
181C2×C4—21no—
182C2×C4—22no—
183C2×C4—42no—
184C2×C4—44no—
185C2×C4—42no—
186C2×C4—42no—
187C2×C4—42no—
188C2×C4—42no—
189C2×C4—42no—
190C2×C4—42no—
191C2×C4—42no—
192C2×C4—82no—
193C2×C4#100×C13112yes—
194C2×C4#101×C13112yes—
195C2×C4#123×C13114yes—
196C8—84no—
197C22—21no—
198C22—21no—
199C22—22no—
200C22—22no—
201C22—22no—
202C22—42no—
203C22—42no—
204C22#381×C13111yescharacteristic
205C22C2×#100×C13111yescharacteristic
206C22C2×#101×C13111yescharacteristic
207C4—22no—
208C4—22no—
209C4—24no—
210C4—42no—
211C4—82no—
212C4—82no—
213C2—21no—
214C2—21no—
215C2—42no—
216C2#1821×C13111yescharacteristic
217C2#1828×C13111yescharacteristic
218C2#1830×C13111yescharacteristic
subgroupG/H
center, socleC22×C131#381
commutatorC24C22×C4×C131
Frattini, cosocleC23×C4C23×C131
prime radicalC24×C131C22×C4
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
109. #8757C131direct (N × H)
110. C131#8757direct (N × H)

Maximal subgroups

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

subgroupindex
#2316×C1312
#1463×C1312
#1305×C1312
#8757131