Finite Group Databasebeta

← C131×#7315 #45693199

Subgroups — C131×#7315 #45693199

Order 33536.

432 conjugacy classes of subgroups; only the 74 normal subgroups are shown.

normal subgroups only

This group has 432 conjugacy classes of subgroups — too many to draw. Only its 74 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#1784×C131C212yesmaximal
2#1784×C131C211yesmaximal, characteristic
3C23×Q8×C131C2211yescharacteristic
4C2×#101×C131—22no—
5C2×#101×C131—22no—
6C2×#101×C131C414yes—
7#407×C131—22no—
8#407×C131C412yes—
9C22×Q8×C131—42no—
10C22×Q8×C131—44no—
11C22×Q8×C131C2×C412yes—
12C22×Q8×C131D412yes—
13C23×C4×C131C2×C411yescharacteristic
14C23×C4×C131D411yescharacteristic
15C23×C4×C131Q811yescharacteristic
16C2×M16×C131—24no—
17C2×M16×C131—22no—
18#101×C131—44no—
19#101×C131—44no—
20#101×C131—44no—
21C22⋊C8×C131—44no—
22C22⋊C8×C131—42no—
23C24×C131C4⋊C411yescharacteristic
24C2×Q8×C131—24no—
25C2×Q8×C131—24no—
26C2×Q8×C131—24no—
27C2×Q8×C131—42no—
28C2×Q8×C131—42no—
29C2×Q8×C131—42no—
30C2×Q8×C131—416no—
31C22×C4×C131—22no—
32C22×C4×C131—24no—
33C22×C4×C131—42no—
34C22×C4×C131—41no—
35C22×C4×C131—42no—
36C22×C4×C131—41no—
37C22×C4×C131C4211yescharacteristic
38C22×C4×C131C22⋊C411yescharacteristic
39C22×C4×C131C22⋊C412yes—
40C22×C4×C131C4⋊C412yes—
41M16×C131—44no—
42M16×C131—44no—
43M16×C131—44no—
44C2×C8×C131—44no—
45C2×C8×C131—42no—
46C23×C131—21no—
47C23×C131—22no—
48C23×C131—42no—
49C23×C131#9511yescharacteristic
50Q8×C131—48no—
51Q8×C131—48no—
52C2×C4×C131—22no—
53C2×C4×C131—22no—
54C2×C4×C131—22no—
55C2×C4×C131—21no—
56C2×C4×C131—22no—
57C2×C4×C131—22no—
58C2×C4×C131—22no—
59C2×C4×C131—22no—
60C2×C4×C131—44no—
61C2×C4×C131—44no—
62C2×C4×C131—44no—
63C2×C4×C131#9912yes—
64C2×C4×C131#9914yes—
65C8×C131—84no—
66C8×C131—82no—
67C22×C131—22no—
68C22×C131—24no—
69C22×C131—41no—
70C22×C131—41no—
71C22×C131—42no—
72C22×C131—41no—
73C22×C131#34212yes—
74C22×C131#34211yescharacteristic
75C4×C131—24no—
76C4×C131—22no—
77C4×C131—41no—
78C4×C131—42no—
79C2×C131—22no—
80C2×C131—21no—
81C2×C131—42no—
82C2×C131#130411yescharacteristic
83#7315C13111yesmaximal, characteristic, direct product factor, Sylow
84C131#731511yescharacteristic, direct product factor, Sylow
85#1784C2×C13112yes—
86#1784C2×C13111yescharacteristic
87C23×Q8C22×C13111yescharacteristic
88C2×#101—22no—
89C2×#101—22no—
90C2×#101C4×C13114yes—
91#407—22no—
92#407C4×C13112yes—
93C22×Q8—42no—
94C22×Q8—44no—
95C22×Q8C2×C4×C13112yes—
96C22×Q8D4×C13112yes—
97C23×C4C2×C4×C13111yescharacteristic
98C23×C4D4×C13111yescharacteristic
99C23×C4Q8×C13111yescharacteristic
100C2×M16—24no—
101C2×M16—22no—
102#101—44no—
103#101—44no—
104#101—44no—
105C22⋊C8—44no—
106C22⋊C8—42no—
107C24C4⋊C4×C13111yescharacteristic
108C2×Q8—24no—
109C2×Q8—24no—
110C2×Q8—24no—
111C2×Q8—42no—
112C2×Q8—42no—
113C2×Q8—42no—
114C2×Q8—416no—
115C22×C4—22no—
116C22×C4—24no—
117C22×C4—42no—
118C22×C4—41no—
119C22×C4—42no—
120C22×C4—41no—
121C22×C4C42×C13111yescharacteristic
122C22×C4C22⋊C4×C13111yescharacteristic
123C22×C4C22⋊C4×C13112yes—
124C22×C4C4⋊C4×C13112yes—
125M16—44no—
126M16—44no—
127M16—44no—
128C2×C8—44no—
129C2×C8—42no—
130C23—21no—
131C23—22no—
132C23—42no—
133C23#95×C13111yescharacteristic
134Q8—48no—
135Q8—48no—
136C2×C4—22no—
137C2×C4—22no—
138C2×C4—22no—
139C2×C4—21no—
140C2×C4—22no—
141C2×C4—22no—
142C2×C4—22no—
143C2×C4—22no—
144C2×C4—44no—
145C2×C4—44no—
146C2×C4—44no—
147C2×C4#99×C13112yes—
148C2×C4#99×C13114yes—
149C8—84no—
150C8—82no—
151C22—22no—
152C22—24no—
153C22—41no—
154C22—41no—
155C22—42no—
156C22—41no—
157C22#342×C13112yes—
158C22#342×C13111yescharacteristic
159C4—24no—
160C4—22no—
161C4—41no—
162C4—42no—
163C2—22no—
164C2—21no—
165C2—42no—
166C2#1304×C13111yescharacteristic
subgroupG/H
center, socleC2×C131#1304
commutatorC22×C4C42×C131
Frattini, cosocleC23×Q8C22×C131
prime radicalC24×C131C4⋊C4
LCSG ▷ C22×C4 ▷ C23 ▷ C2 ▷ C1
UCSC1 ◁ C2×C131 ◁ C23×C131 ◁ C23×Q8×C131 ◁ G

Complements

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

NH ≅ G/Ntype
83. #7315C131direct (N × H)
84. C131#7315direct (N × H)

Maximal subgroups

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

subgroupindex
#1784×C1312
#7315131