Finite Group Databasebeta

← C131×#10525 #45696409

Subgroups — C131×#10525 #45696409

Order 33536.

370 conjugacy classes of subgroups; only the 90 normal subgroups are shown.

normal subgroups only

This group has 370 conjugacy classes of subgroups — too many to draw. Only its 90 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#3253×C131C211yesmaximal, characteristic
2#1838×C131C211yesmaximal, characteristic, complemented
3#1557×C131C212yesmaximal, complemented
4#1530×C131C212yesmaximal, complemented
5#1307×C131C211yesmaximal, characteristic, complemented
6#532×C131C2212yes—
7#476×C131—22no—
8#469×C131—22no—
9#459×C131—22no—
10#432×C131C2212yes—
11#423×C131C2211yescharacteristic
12#423×C131C2211yescharacteristic
13C2×#97×C131C2211yescharacteristic
14#341×C131—22no—
15#332×C131—22no—
16#331×C131—22no—
17#329×C131—24no—
18C2×#41×C131—22no—
19C2×D8×C131—22no—
20C2×M16×C131—21no—
21C2×M16×C131D412yes—
22C22×C8×C131—21no—
23C4⋊Q8×C131D412yes—
24#127×C131D412yes—
25#124×C131—22no—
26#121×C131—22no—
27#121×C131—22no—
28C4×D4×C131—22no—
29C4×D4×C131—22no—
30C2×C42×C131C2311yescharacteristic
31#106×C131—22no—
32C4⋊C8×C131—22no—
33C4⋊C8×C131—22no—
34C4⋊C8×C131—22no—
35#102×C131—24no—
36C22⋊C8×C131—22no—
37#97×C131—22no—
38#97×C131—21no—
39#97×C131D412yes—
40#41×C131—84no—
41C2×Q8×C131—22no—
42C2×D4×C131—22no—
43C2×D4×C131—22no—
44C2×D4×C131—22no—
45C2×D4×C131—42no—
46C22×C4×C131—42no—
47C22×C4×C131C2×D411yescharacteristic
48C22×C4×C131#4112yes—
49D8×C131—82no—
50M16×C131—42no—
51M16×C131—42no—
52C2×C8×C131—22no—
53C2×C8×C131—22no—
54C2×C8×C131—41no—
55C2×C8×C131—41no—
56C2×C8×C131—41no—
57C2×C8×C131—42no—
58C4⋊C4×C131—22no—
59C4⋊C4×C131—22no—
60C22⋊C4×C131—42no—
61C22⋊C4×C131—42no—
62C42×C131C2×D412yes—
63C42×C131C2×D411yescharacteristic
64C42×C131#4111yescharacteristic
65C23×C131—42no—
66C23×C131#12411yescharacteristic
67Q8×C131—82no—
68D4×C131—42no—
69D4×C131—42no—
70D4×C131—82no—
71D4×C131—82no—
72D4×C131—84no—
73C2×C4×C131—21no—
74C2×C4×C131—21no—
75C2×C4×C131—42no—
76C2×C4×C131—42no—
77C2×C4×C131—84no—
78C2×C4×C131#12011yescharacteristic
79C2×C4×C131#12112yes—
80C2×C4×C131#12111yescharacteristic
81C2×C4×C131#12312yes—
82C8×C131—42no—
83C8×C131—42no—
84C8×C131—82no—
85C8×C131—81no—
86C22×C131—22no—
87C22×C131—21no—
88C22×C131—82no—
89C22×C131—82no—
90C22×C131—82no—
91C22×C131#39411yescharacteristic
92C4×C131—22no—
93C4×C131—22no—
94C4×C131—21no—
95C4×C131—82no—
96C4×C131#45411yescharacteristic
97C4×C131#45511yescharacteristic
98C2×C131—41no—
99C2×C131—162no—
100C2×C131#204011yescharacteristic
101C2×C131#204812yes—
102#10525C13111yesmaximal, characteristic, direct product factor, Sylow
103C131#1052511yescharacteristic, direct product factor, Sylow
104#3253C2×C13111yescharacteristic
105#1838C2×C13111yescharacteristic, complemented
106#1557C2×C13112yescomplemented
107#1530C2×C13112yescomplemented
108#1307C2×C13111yescharacteristic, complemented
109#532C22×C13112yes—
110#476—22no—
111#469—22no—
112#459—22no—
113#432C22×C13112yes—
114#423C22×C13111yescharacteristic
115#423C22×C13111yescharacteristic
116C2×#97C22×C13111yescharacteristic
117#341—22no—
118#332—22no—
119#331—22no—
120#329—24no—
121C2×#41—22no—
122C2×D8—22no—
123C2×M16—21no—
124C2×M16D4×C13112yes—
125C22×C8—21no—
126C4⋊Q8D4×C13112yes—
127#127D4×C13112yes—
128#124—22no—
129#121—22no—
130#121—22no—
131C4×D4—22no—
132C4×D4—22no—
133C2×C42C23×C13111yescharacteristic
134#106—22no—
135C4⋊C8—22no—
136C4⋊C8—22no—
137C4⋊C8—22no—
138#102—24no—
139C22⋊C8—22no—
140#97—22no—
141#97—21no—
142#97D4×C13112yes—
143#41—84no—
144C2×Q8—22no—
145C2×D4—22no—
146C2×D4—22no—
147C2×D4—22no—
148C2×D4—42no—
149C22×C4—42no—
150C22×C4C2×D4×C13111yescharacteristic
151C22×C4#41×C13112yes—
152D8—82no—
153M16—42no—
154M16—42no—
155C2×C8—22no—
156C2×C8—22no—
157C2×C8—41no—
158C2×C8—41no—
159C2×C8—41no—
160C2×C8—42no—
161C4⋊C4—22no—
162C4⋊C4—22no—
163C22⋊C4—42no—
164C22⋊C4—42no—
165C42C2×D4×C13112yes—
166C42C2×D4×C13111yescharacteristic
167C42#41×C13111yescharacteristic
168C23—42no—
169C23#124×C13111yescharacteristic
170Q8—82no—
171D4—42no—
172D4—42no—
173D4—82no—
174D4—82no—
175D4—84no—
176C2×C4—21no—
177C2×C4—21no—
178C2×C4—42no—
179C2×C4—42no—
180C2×C4—84no—
181C2×C4#120×C13111yescharacteristic
182C2×C4#121×C13112yes—
183C2×C4#121×C13111yescharacteristic
184C2×C4#123×C13112yes—
185C8—42no—
186C8—42no—
187C8—82no—
188C8—81no—
189C22—21no—
190C22—22no—
191C22—82no—
192C22—82no—
193C22—82no—
194C22#394×C13111yescharacteristic
195C4—21no—
196C4—22no—
197C4—22no—
198C4—82no—
199C4#454×C13111yescharacteristic
200C4#455×C13111yescharacteristic
201C2—41no—
202C2—162no—
203C2#2040×C13111yescharacteristic
204C2#2048×C13112yes—
subgroupG/H
center, socleC22×C131#394
commutator, Frattini, cosocleC2×C42C23×C131
prime radical#3253×C131C2
LCSG ▷ C2×C42 ▷ C22 ▷ C1
UCSC1 ◁ C22×C131 ◁ C2×C42×C131 ◁ G

Complements

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

NH ≅ G/Ntype
2. #1838×C131C2semidirect
3. #1557×C131C2semidirect
4. #1530×C131C2semidirect
5. #1307×C131C2semidirect
102. #10525C131direct (N × H)
103. C131#10525direct (N × H)
105. #1838C2×C131semidirect
106. #1557C2×C131semidirect
107. #1530C2×C131semidirect
108. #1307C2×C131semidirect

Maximal subgroups

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

subgroupindex
#3253×C1312
#1838×C1312
#1557×C1312
#1530×C1312
#1307×C1312
#10525131