Finite Group Databasebeta

← C131×#7055 #45692939

Subgroups — C131×#7055 #45692939

Order 33536.

240 conjugacy classes of subgroups; only the 62 normal subgroups are shown.

normal subgroups only

This group has 240 conjugacy classes of subgroups — too many to draw. Only its 62 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#1817×C131C211yesmaximal, characteristic
2#1314×C131C212yesmaximal
3C22×C42×C131C411yescharacteristic
4C2×C22⋊C8×C131C411yescharacteristic
5C2×C22⋊C8×C131C2211yescharacteristic
6C22⋊C16×C131—22no—
7#336×C131—22no—
8C23×C4×C131C811yescharacteristic
9C23×C4×C131C811yescharacteristic
10C23×C4×C131C2×C411yescharacteristic
11C22×C8×C131—21no—
12C22×C8×C131D412yes—
13C2×C42×C131—21no—
14C2×C42×C131—21no—
15C2×C42×C131—41no—
16C2×C42×C131—41no—
17C2×C16×C131—42no—
18C22⋊C8×C131—41no—
19C22⋊C8×C131—41no—
20C24×C131C2×C811yescharacteristic
21C22×C4×C131—21no—
22C22×C4×C131—21no—
23C22×C4×C131—21no—
24C22×C4×C131—21no—
25C22×C4×C131—21no—
26C22×C4×C131—42no—
27C22×C4×C131—42no—
28C22×C4×C131—41no—
29C22×C4×C131—41no—
30C22×C4×C131—41no—
31C22×C4×C131C1612yescomplemented
32C22×C4×C131C22⋊C411yescharacteristic
33C22×C4×C131M1611yescharacteristic
34C2×C8×C131—22no—
35C2×C8×C131—42no—
36C2×C8×C131—42no—
37C2×C8×C131—41no—
38C42×C131—42no—
39C42×C131—41no—
40C42×C131—41no—
41C16×C131—82no—
42C23×C131—21no—
43C23×C131—21no—
44C23×C131—41no—
45C23×C131—41no—
46C23×C131C22⋊C811yescharacteristic
47C23×C131C2×C1611yescharacteristic
48C23×C131M3211yescharacteristic
49C2×C4×C131—22no—
50C2×C4×C131—22no—
51C2×C4×C131—21no—
52C2×C4×C131—22no—
53C2×C4×C131—42no—
54C2×C4×C131—42no—
55C2×C4×C131—41no—
56C2×C4×C131—42no—
57C2×C4×C131—41no—
58C2×C4×C131—41no—
59C2×C4×C131—41no—
60C2×C4×C131—42no—
61C2×C4×C131—42no—
62C2×C4×C131—41no—
63C2×C4×C131—42no—
64C2×C4×C131#9911yescharacteristic
65C2×C4×C131#10011yescharacteristic
66C8×C131—42no—
67C8×C131—81no—
68C22×C131—21no—
69C22×C131—21no—
70C22×C131—21no—
71C22×C131—21no—
72C22×C131—41no—
73C22×C131—41no—
74C22×C131—42no—
75C22×C131—41no—
76C22×C131—41no—
77C22×C131#32311yescharacteristic
78C22×C131C22⋊C1611yescharacteristic
79C22×C131#34911yescharacteristic
80C4×C131—21no—
81C4×C131—42no—
82C4×C131—41no—
83C4×C131—42no—
84C4×C131#35212yes—
85C2×C131—21no—
86C2×C131—21no—
87C2×C131—41no—
88C2×C131—41no—
89C2×C131#131411yescharacteristic
90C2×C131#131711yescharacteristic
91C2×C131#132011yescharacteristic
92#7055C13111yesmaximal, characteristic, direct product factor, Sylow
93C131#705511yescharacteristic, direct product factor, Sylow
94#1817C2×C13111yescharacteristic
95#1314C2×C13112yes—
96C22×C42C4×C13111yescharacteristic
97C2×C22⋊C8C4×C13111yescharacteristic
98C2×C22⋊C8C22×C13111yescharacteristic
99C22⋊C16—22no—
100#336—22no—
101C23×C4C8×C13111yescharacteristic
102C23×C4C8×C13111yescharacteristic
103C23×C4C2×C4×C13111yescharacteristic
104C22×C8—21no—
105C22×C8D4×C13112yes—
106C2×C42—21no—
107C2×C42—21no—
108C2×C42—41no—
109C2×C42—41no—
110C2×C16—42no—
111C22⋊C8—41no—
112C22⋊C8—41no—
113C24C2×C8×C13111yescharacteristic
114C22×C4—21no—
115C22×C4—21no—
116C22×C4—21no—
117C22×C4—21no—
118C22×C4—21no—
119C22×C4—42no—
120C22×C4—42no—
121C22×C4—41no—
122C22×C4—41no—
123C22×C4—41no—
124C22×C4C16×C13112yescomplemented
125C22×C4C22⋊C4×C13111yescharacteristic
126C22×C4M16×C13111yescharacteristic
127C2×C8—22no—
128C2×C8—42no—
129C2×C8—42no—
130C2×C8—41no—
131C42—42no—
132C42—41no—
133C42—41no—
134C16—82no—
135C23—21no—
136C23—21no—
137C23—41no—
138C23—41no—
139C23C22⋊C8×C13111yescharacteristic
140C23C2×C16×C13111yescharacteristic
141C23M32×C13111yescharacteristic
142C2×C4—22no—
143C2×C4—22no—
144C2×C4—21no—
145C2×C4—22no—
146C2×C4—42no—
147C2×C4—42no—
148C2×C4—41no—
149C2×C4—42no—
150C2×C4—41no—
151C2×C4—41no—
152C2×C4—41no—
153C2×C4—42no—
154C2×C4—42no—
155C2×C4—41no—
156C2×C4—42no—
157C2×C4#99×C13111yescharacteristic
158C2×C4#100×C13111yescharacteristic
159C8—42no—
160C8—81no—
161C22—21no—
162C22—21no—
163C22—21no—
164C22—21no—
165C22—41no—
166C22—41no—
167C22—42no—
168C22—41no—
169C22—41no—
170C22#323×C13111yescharacteristic
171C22C22⋊C16×C13111yescharacteristic
172C22#349×C13111yescharacteristic
173C4—21no—
174C4—42no—
175C4—41no—
176C4—42no—
177C4#352×C13112yes—
178C2—21no—
179C2—21no—
180C2—41no—
181C2—41no—
182C2#1314×C13111yescharacteristic
183C2#1317×C13111yescharacteristic
184C2#1320×C13111yescharacteristic
subgroupG/H
centerC2×C4×C131#99
commutatorC23C2×C16×C131
Frattini, cosocleC2×C22⋊C8C22×C131
socleC22×C131#323
prime radicalC24×C131C2×C8
LCSG ▷ C23 ▷ C22 ▷ C2 ▷ C1
UCSC1 ◁ C2×C4×C131 ◁ C22×C4×C131 ◁ C2×C22⋊C8×C131 ◁ G

Complements

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

NH ≅ G/Ntype
31. C22×C4×C131C16semidirect
92. #7055C131direct (N × H)
93. C131#7055direct (N × H)
124. C22×C4C16×C131semidirect

Maximal subgroups

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

subgroupindex
#1817×C1312
#1314×C1312
#7055131