Finite Group Databasebeta

← C131×#7521 #45693405

Subgroups — C131×#7521 #45693405

Order 33536.

148 conjugacy classes of subgroups; only the 30 normal subgroups are shown.

normal subgroups only

This group has 148 conjugacy classes of subgroups — too many to draw. Only its 30 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#1634×C131C211yesmaximal, characteristic
2#1411×C131C211yesmaximal, characteristic, complemented
3#1358×C131C211yesmaximal, characteristic, complemented
4#555×C131C411yescharacteristic
5#494×C131C2211yescharacteristic
6#476×C131—21no—
7#364×C131—21no—
8#356×C131—21no—
9#333×C131C411yescharacteristic
10D4⋊C8×C131—21no—
11C2×Q16×C131—41no—
12C4⋊Q8×C131C2×C411yescharacteristic
13C4⋊Q8×C131D411yescharacteristic
14#124×C131—41no—
15#121×C131—41no—
16C4×D4×C131—21no—
17#117×C131—41no—
18M32×C131—41no—
19#106×C131—41no—
20C4⋊C8×C131—21no—
21#102×C131—41no—
22#101×C131—41no—
23C4×C8×C131D411yescharacteristic
24C2×Q8×C131—21no—
25C2×Q8×C131—21no—
26C2×D4×C131—21no—
27C2×D4×C131—41no—
28C22×C4×C131—41no—
29Q16×C131—81no—
30Q16×C131—81no—
31M16×C131—81no—
32C2×C8×C131—21no—
33C2×C8×C131—41no—
34C4⋊C4×C131—21no—
35C4⋊C4×C131—41no—
36C4⋊C4×C131—41no—
37C22⋊C4×C131—42no—
38C22⋊C4×C131—41no—
39C42×C131—41no—
40C42×C131C22⋊C411yescharacteristic
41C16×C131—81no—
42C23×C131—41no—
43Q8×C131—81no—
44Q8×C131—81no—
45D4×C131—41no—
46D4×C131—41no—
47D4×C131—161no—
48C2×C4×C131—21no—
49C2×C4×C131—41no—
50C2×C4×C131—41no—
51C2×C4×C131—41no—
52C2×C4×C131—81no—
53C2×C4×C131—81no—
54C2×C4×C131#9911yescharacteristic
55C8×C131—21no—
56C8×C131—21no—
57C8×C131—81no—
58C8×C131—161no—
59C22×C131—81no—
60C22×C131—81no—
61C22×C131—81no—
62C22×C131AΣL(1,𝔽16)11yescharacteristic
63C4×C131—21no—
64C4×C131—21no—
65C4×C131—21no—
66C4×C131—81no—
67C4×C131—81no—
68C4×C131—81no—
69C2×C131—21no—
70C2×C131—161no—
71C2×C131#140211yescharacteristic
72#7521C13111yesmaximal, characteristic, direct product factor, Sylow
73C131#752111yescharacteristic, direct product factor, Sylow
74#1634C2×C13111yescharacteristic
75#1411C2×C13111yescharacteristic, complemented
76#1358C2×C13111yescharacteristic, complemented
77#555C4×C13111yescharacteristic
78#494C22×C13111yescharacteristic
79#476—21no—
80#364—21no—
81#356—21no—
82#333C4×C13111yescharacteristic
83D4⋊C8—21no—
84C2×Q16—41no—
85C4⋊Q8C2×C4×C13111yescharacteristic
86C4⋊Q8D4×C13111yescharacteristic
87#124—41no—
88#121—41no—
89C4×D4—21no—
90#117—41no—
91M32—41no—
92#106—41no—
93C4⋊C8—21no—
94#102—41no—
95#101—41no—
96C4×C8D4×C13111yescharacteristic
97C2×Q8—21no—
98C2×Q8—21no—
99C2×D4—21no—
100C2×D4—41no—
101C22×C4—41no—
102Q16—81no—
103Q16—81no—
104M16—81no—
105C2×C8—21no—
106C2×C8—41no—
107C4⋊C4—21no—
108C4⋊C4—41no—
109C4⋊C4—41no—
110C22⋊C4—42no—
111C22⋊C4—41no—
112C42—41no—
113C42C22⋊C4×C13111yescharacteristic
114C16—81no—
115C23—41no—
116Q8—81no—
117Q8—81no—
118D4—41no—
119D4—41no—
120D4—161no—
121C2×C4—21no—
122C2×C4—41no—
123C2×C4—41no—
124C2×C4—41no—
125C2×C4—81no—
126C2×C4—81no—
127C2×C4#99×C13111yescharacteristic
128C8—21no—
129C8—21no—
130C8—81no—
131C8—161no—
132C22—81no—
133C22—81no—
134C22—81no—
135C22AΣL(1,𝔽16)×C13111yescharacteristic
136C4—21no—
137C4—21no—
138C4—21no—
139C4—81no—
140C4—81no—
141C4—81no—
142C2—21no—
143C2—161no—
144C2#1402×C13111yescharacteristic
subgroupG/H
center, socleC2×C131#1402
commutatorC4⋊Q8C2×C4×C131
Frattini, cosocle#494C22×C131
prime radical#555×C131C4
LCSG ▷ C4⋊Q8 ▷ C42 ▷ C2×C4 ▷ C22 ▷ C2 ▷ C1
UCSC1 ◁ C2×C131 ◁ C22×C131 ◁ C2×C4×C131 ◁ C42×C131 ◁ #494×C131 ◁ G

Complements

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

NH ≅ G/Ntype
2. #1411×C131C2semidirect
3. #1358×C131C2semidirect
72. #7521C131direct (N × H)
73. C131#7521direct (N × H)
75. #1411C2×C131semidirect
76. #1358C2×C131semidirect

Maximal subgroups

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

subgroupindex
#1634×C1312
#1411×C1312
#1358×C1312
#7521131