Finite Group Databasebeta

← C131×#7308 #45693192

Subgroups — C131×#7308 #45693192

Order 33536.

518 conjugacy classes of subgroups; only the 86 normal subgroups are shown.

normal subgroups only

This group has 518 conjugacy classes of subgroups — too many to draw. Only its 86 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#1446×C131C211yesmaximal, characteristic
3C23×Q8×C131C2211yescharacteristic
4C2×#101×C131—22no—
5C2×#101×C131C414yescomplemented
6#407×C131—22no—
7C2×#95×C131—22no—
8C2×#95×C131C412yes—
9C22×Q8×C131—42no—
10C22×Q8×C131—44no—
11C22×Q8×C131C2×C412yes—
12C22×Q8×C131D411yescharacteristic
13C22×Q8×C131Q811yescharacteristic
14C23×C4×C131—22no—
15C23×C4×C131C2×C411yescharacteristic
16C23×C4×C131D412yes—
17C2×M16×C131—24no—
18#101×C131—44no—
19#101×C131—44no—
20C22⋊C8×C131—44no—
21#95×C131—44no—
22#95×C131—42no—
23C24×C131C22⋊C411yescharacteristic
24C2×Q8×C131—24no—
25C2×Q8×C131—24no—
26C2×Q8×C131—42no—
27C2×Q8×C131—42no—
28C2×Q8×C131—41no—
29C2×Q8×C131—42no—
30C2×Q8×C131—41no—
31C2×Q8×C131—416no—
32C22×C4×C131—22no—
33C22×C4×C131—24no—
34C22×C4×C131—24no—
35C22×C4×C131—24no—
36C22×C4×C131—42no—
37C22×C4×C131—42no—
38C22×C4×C131—44no—
39C22×C4×C131—42no—
40C22×C4×C131—44no—
41C22×C4×C131—42no—
42C22×C4×C131C4211yescharacteristic
43C22×C4×C131C22⋊C412yes—
44C22×C4×C131C4⋊C411yescharacteristic
45C22×C4×C131C4⋊C412yes—
46M16×C131—44no—
47M16×C131—44no—
48C2×C8×C131—44no—
49C23×C131—22no—
50C23×C131—22no—
51C23×C131—22no—
52C23×C131#9511yescharacteristic
53C23×C131#9912yes—
54Q8×C131—44no—
55Q8×C131—48no—
56Q8×C131—44no—
57C2×C4×C131—22no—
58C2×C4×C131—22no—
59C2×C4×C131—22no—
60C2×C4×C131—22no—
61C2×C4×C131—22no—
62C2×C4×C131—22no—
63C2×C4×C131—21no—
64C2×C4×C131—21no—
65C2×C4×C131—22no—
66C2×C4×C131—48no—
67C2×C4×C131—44no—
68C2×C4×C131—48no—
69C2×C4×C131—44no—
70C2×C4×C131—84no—
71C2×C4×C131—82no—
72C2×C4×C131—82no—
73C2×C4×C131#9914yes—
74C8×C131—84no—
75C22×C131—24no—
76C22×C131—22no—
77C22×C131—22no—
78C22×C131—22no—
79C22×C131—22no—
80C22×C131—22no—
81C22×C131#34212yes—
82C22×C131#34211yescharacteristic
83C22×C131#35512yes—
84C22×C131#35612yes—
85C4×C131—24no—
86C4×C131—42no—
87C4×C131—41no—
88C4×C131—41no—
89C4×C131—84no—
90C2×C131—22no—
91C2×C131—22no—
92C2×C131—22no—
93C2×C131#130411yescharacteristic
94C2×C131#139412yes—
95#7308C13111yesmaximal, characteristic, direct product factor, Sylow
96C131#730811yescharacteristic, direct product factor, Sylow
97#1784C2×C13112yes—
98#1446C2×C13111yescharacteristic
99C23×Q8C22×C13111yescharacteristic
100C2×#101—22no—
101C2×#101C4×C13114yescomplemented
102#407—22no—
103C2×#95—22no—
104C2×#95C4×C13112yes—
105C22×Q8—42no—
106C22×Q8—44no—
107C22×Q8C2×C4×C13112yes—
108C22×Q8D4×C13111yescharacteristic
109C22×Q8Q8×C13111yescharacteristic
110C23×C4—22no—
111C23×C4C2×C4×C13111yescharacteristic
112C23×C4D4×C13112yes—
113C2×M16—24no—
114#101—44no—
115#101—44no—
116C22⋊C8—44no—
117#95—42no—
118#95—44no—
119C24C22⋊C4×C13111yescharacteristic
120C2×Q8—24no—
121C2×Q8—24no—
122C2×Q8—42no—
123C2×Q8—42no—
124C2×Q8—41no—
125C2×Q8—41no—
126C2×Q8—42no—
127C2×Q8—416no—
128C22×C4—22no—
129C22×C4—24no—
130C22×C4—24no—
131C22×C4—24no—
132C22×C4—42no—
133C22×C4—42no—
134C22×C4—44no—
135C22×C4—42no—
136C22×C4—44no—
137C22×C4—42no—
138C22×C4C42×C13111yescharacteristic
139C22×C4C22⋊C4×C13112yes—
140C22×C4C4⋊C4×C13111yescharacteristic
141C22×C4C4⋊C4×C13112yes—
142M16—44no—
143M16—44no—
144C2×C8—44no—
145C23—22no—
146C23—22no—
147C23—22no—
148C23#95×C13111yescharacteristic
149C23#99×C13112yes—
150Q8—44no—
151Q8—48no—
152Q8—44no—
153C2×C4—22no—
154C2×C4—22no—
155C2×C4—21no—
156C2×C4—22no—
157C2×C4—21no—
158C2×C4—22no—
159C2×C4—22no—
160C2×C4—22no—
161C2×C4—22no—
162C2×C4—48no—
163C2×C4—44no—
164C2×C4—48no—
165C2×C4—44no—
166C2×C4—84no—
167C2×C4—82no—
168C2×C4—82no—
169C2×C4#99×C13114yes—
170C8—84no—
171C22—24no—
172C22—22no—
173C22—22no—
174C22—22no—
175C22—22no—
176C22—22no—
177C22#342×C13112yes—
178C22#342×C13111yescharacteristic
179C22#355×C13112yes—
180C22#356×C13112yes—
181C4—24no—
182C4—41no—
183C4—42no—
184C4—41no—
185C4—84no—
186C2—22no—
187C2—22no—
188C2—22no—
189C2#1304×C13111yescharacteristic
190C2#1394×C13112yes—
subgroupG/H
center, socleC22×C131#342
commutatorC22×C4C42×C131
Frattini, cosocleC23×Q8C22×C131
prime radicalC24×C131C22⋊C4
LCSG ▷ C22×C4 ▷ C23 ▷ C2 ▷ C1
UCSC1 ◁ C22×C131 ◁ C24×C131 ◁ C23×Q8×C131 ◁ G

Complements

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

NH ≅ G/Ntype
5. C2×#101×C131C4semidirect
95. #7308C131direct (N × H)
96. C131#7308direct (N × H)
101. C2×#101C4×C131semidirect

Maximal subgroups

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

subgroupindex
#1784×C1312
#1446×C1312
#7308131