Finite Group Databasebeta

← C131×#7435 #45693319

Subgroups — C131×#7435 #45693319

Order 33536.

224 conjugacy classes of subgroups; only the 46 normal subgroups are shown.

normal subgroups only

This group has 224 conjugacy classes of subgroups — too many to draw. Only its 46 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#2094×C131C211yesmaximal, characteristic
2#1393×C131C211yesmaximal, characteristic
3#1318×C131C211yesmaximal, characteristic
4C2×#106×C131—21no—
5C2×#102×C131—21no—
6C2×#99×C131—21no—
7#390×C131C2211yescharacteristic
8#384×C131C411yescharacteristic, complemented
9#336×C131C411yescharacteristic, complemented
10#324×C131—21no—
11C22×D4×C131D411yescharacteristic
12C22×C8×C131—21no—
13C2×C4⋊C4×C131—21no—
14C2×C4⋊C4×C131—41no—
15C2×C4⋊C4×C131D411yescharacteristic
16C2×C22⋊C4×C131—41no—
17C2×C22⋊C4×C131—41no—
18C2×C42×C131C2×C411yescharacteristic
19#106×C131—42no—
20#102×C131—42no—
21#99×C131—22no—
22#99×C131—41no—
23C22⋊C8×C131—41no—
24C24×C131—21no—
25C2×D4×C131—21no—
26C2×D4×C131—41no—
27C2×D4×C131—41no—
28C2×D4×C131SD1611yescharacteristic
29C2×D4×C131Q1611yescharacteristic
30C22×C4×C131—21no—
31C22×C4×C131—21no—
32C22×C4×C131—41no—
33C22×C4×C131—81no—
34C22×C4×C131C22⋊C411yescharacteristic
35C2×C8×C131—22no—
36C2×C8×C131—41no—
37C2×C8×C131—41no—
38C2×C8×C131—81no—
39C4⋊C4×C131—41no—
40C4⋊C4×C131—41no—
41C4⋊C4×C131—41no—
42C4⋊C4×C131—82no—
43C22⋊C4×C131—42no—
44C22⋊C4×C131—82no—
45C22⋊C4×C131—81no—
46C42×C131—41no—
47C23×C131—21no—
48C23×C131—21no—
49C23×C131—41no—
50C23×C131—41no—
51C23×C131—81no—
52C23×C131—81no—
53C23×C131#9911yescharacteristic
54D4×C131—41no—
55D4×C131—41no—
56D4×C131—81no—
57C2×C4×C131—21no—
58C2×C4×C131—21no—
59C2×C4×C131—22no—
60C2×C4×C131—41no—
61C2×C4×C131—41no—
62C2×C4×C131—41no—
63C2×C4×C131—81no—
64C2×C4×C131—82no—
65C2×C4×C131—82no—
66C2×C4×C131—81no—
67C2×C4×C131—161no—
68C2×C4×C131—161no—
69C2×C4×C131#10311yescharacteristic
70C2×C4×C131#10411yescharacteristic
71C8×C131—42no—
72C8×C131—161no—
73C22×C131—21no—
74C22×C131—21no—
75C22×C131—41no—
76C22×C131—41no—
77C22×C131—81no—
78C22×C131—81no—
79C22×C131—81no—
80C22×C131—81no—
81C22×C131—161no—
82C22×C131#32811yescharacteristic
83C22×C131#35211yescharacteristic
84C22×C131#35311yescharacteristic
85C4×C131—21no—
86C4×C131—21no—
87C4×C131—42no—
88C4×C131—81no—
89C4×C131—162no—
90C4×C131—161no—
91C2×C131—21no—
92C2×C131—21no—
93C2×C131—81no—
94C2×C131—81no—
95C2×C131#135211yescharacteristic
96C2×C131#140611yescharacteristic
97C2×C131#140911yescharacteristic
98#7435C13111yesmaximal, characteristic, direct product factor, Sylow
99C131#743511yescharacteristic, direct product factor, Sylow
100#2094C2×C13111yescharacteristic
101#1393C2×C13111yescharacteristic
102#1318C2×C13111yescharacteristic
103C2×#106—21no—
104C2×#102—21no—
105C2×#99—21no—
106#390C22×C13111yescharacteristic
107#384C4×C13111yescharacteristic, complemented
108#336C4×C13111yescharacteristic, complemented
109#324—21no—
110C22×D4D4×C13111yescharacteristic
111C22×C8—21no—
112C2×C4⋊C4—21no—
113C2×C4⋊C4—41no—
114C2×C4⋊C4D4×C13111yescharacteristic
115C2×C22⋊C4—41no—
116C2×C22⋊C4—41no—
117C2×C42C2×C4×C13111yescharacteristic
118#106—42no—
119#102—42no—
120#99—22no—
121#99—41no—
122C22⋊C8—41no—
123C24—21no—
124C2×D4—21no—
125C2×D4—41no—
126C2×D4—41no—
127C2×D4SD16×C13111yescharacteristic
128C2×D4Q16×C13111yescharacteristic
129C22×C4—21no—
130C22×C4—21no—
131C22×C4—41no—
132C22×C4—81no—
133C22×C4C22⋊C4×C13111yescharacteristic
134C2×C8—22no—
135C2×C8—41no—
136C2×C8—41no—
137C2×C8—81no—
138C4⋊C4—41no—
139C4⋊C4—41no—
140C4⋊C4—41no—
141C4⋊C4—82no—
142C22⋊C4—42no—
143C22⋊C4—82no—
144C22⋊C4—81no—
145C42—41no—
146C23—21no—
147C23—21no—
148C23—41no—
149C23—41no—
150C23—81no—
151C23—81no—
152C23#99×C13111yescharacteristic
153D4—41no—
154D4—41no—
155D4—81no—
156C2×C4—21no—
157C2×C4—21no—
158C2×C4—22no—
159C2×C4—41no—
160C2×C4—41no—
161C2×C4—41no—
162C2×C4—81no—
163C2×C4—82no—
164C2×C4—82no—
165C2×C4—81no—
166C2×C4—161no—
167C2×C4—161no—
168C2×C4#103×C13111yescharacteristic
169C2×C4#104×C13111yescharacteristic
170C8—42no—
171C8—161no—
172C22—21no—
173C22—21no—
174C22—41no—
175C22—41no—
176C22—81no—
177C22—81no—
178C22—81no—
179C22—81no—
180C22—161no—
181C22#328×C13111yescharacteristic
182C22#352×C13111yescharacteristic
183C22#353×C13111yescharacteristic
184C4—21no—
185C4—21no—
186C4—42no—
187C4—81no—
188C4—162no—
189C4—161no—
190C2—21no—
191C2—21no—
192C2—81no—
193C2—81no—
194C2#1352×C13111yescharacteristic
195C2#1406×C13111yescharacteristic
196C2#1409×C13111yescharacteristic
subgroupG/H
center, socleC22×C131#353
commutatorC2×C42C2×C4×C131
Frattini, cosocle#390C22×C131
prime radicalC22×D4×C131D4
LCSG ▷ C2×C42 ▷ C22×C4 ▷ C22 ▷ C2 ▷ C1
UCSC1 ◁ C22×C131 ◁ C23×C131 ◁ C22×C4×C131 ◁ #390×C131 ◁ G

Complements

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

NH ≅ G/Ntype
8. #384×C131C4semidirect
9. #336×C131C4semidirect
98. #7435C131direct (N × H)
99. C131#7435direct (N × H)
107. #384C4×C131semidirect
108. #336C4×C131semidirect

Maximal subgroups

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

subgroupindex
#2094×C1312
#1393×C1312
#1318×C1312
#7435131