Finite Group Databasebeta

← C131×#7283 #45693167

Subgroups — C131×#7283 #45693167

Order 33536.

402 conjugacy classes of subgroups; only the 82 normal subgroups are shown.

normal subgroups only

This group has 402 conjugacy classes of subgroups — too many to draw. Only its 82 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#1955×C131C211yesmaximal, characteristic
2C4×#99×C131C212yesmaximal
3C2×C4×D4×C131C2211yescharacteristic
4C2×C4⋊C8×C131C411yescharacteristic, complemented
5C2×#99×C131—22no—
6C2×C22⋊C8×C131—22no—
7C2×#97×C131C411yescharacteristic, complemented
8C4×C22⋊C4×C131—22no—
9#342×C131C414yescomplemented
10C22×D4×C131D411yescharacteristic
11C23×C4×C131D412yes—
12C22×C8×C131—21no—
13C22×C8×C131—21no—
14C4×D4×C131—41no—
15C4×D4×C131—41no—
16C2×C4⋊C4×C131Q811yescharacteristic
17C2×C22⋊C4×C131—24no—
18C2×C22⋊C4×C131C2×C412yes—
19C2×C42×C131—42no—
20C2×C42×C131C2×C411yescharacteristic
21C4⋊C8×C131—41no—
22#99×C131—28no—
23C22⋊C8×C131—44no—
24#97×C131—41no—
25#95×C131—42no—
26C24×C131C22⋊C412yes—
27C2×D4×C131—24no—
28C2×D4×C131—41no—
29C22×C4×C131—22no—
30C22×C4×C131—22no—
31C22×C4×C131—42no—
32C22×C4×C131—42no—
33C22×C4×C131—44no—
34C22×C4×C131C4211yescharacteristic
35C22×C4×C131C22⋊C411yescharacteristic
36C22×C4×C131C4⋊C411yescharacteristic
37C22×C4×C131C4⋊C412yes—
38C2×C8×C131—22no—
39C2×C8×C131—41no—
40C2×C8×C131—41no—
41C2×C8×C131—42no—
42C2×C8×C131—41no—
43C4⋊C4×C131—41no—
44C22⋊C4×C131—28no—
45C22⋊C4×C131—42no—
46C22⋊C4×C131—44no—
47C42×C131—21no—
48C42×C131—21no—
49C42×C131—82no—
50C42×C131—82no—
51C23×C131—22no—
52C23×C131—22no—
53C23×C131—42no—
54C23×C131—42no—
55C23×C131#9511yescharacteristic
56C23×C131#10414yes—
57D4×C131—44no—
58C2×C4×C131—21no—
59C2×C4×C131—21no—
60C2×C4×C131—22no—
61C2×C4×C131—21no—
62C2×C4×C131—21no—
63C2×C4×C131—22no—
64C2×C4×C131—42no—
65C2×C4×C131—42no—
66C2×C4×C131—42no—
67C2×C4×C131—41no—
68C2×C4×C131—48no—
69C2×C4×C131—82no—
70C2×C4×C131—84no—
71C2×C4×C131—84no—
72C2×C4×C131#9911yescharacteristic
73C2×C4×C131#9911yescharacteristic
74C8×C131—42no—
75C8×C131—81no—
76C22×C131—21no—
77C22×C131—21no—
78C22×C131—24no—
79C22×C131—44no—
80C22×C131—42no—
81C22×C131—42no—
82C22×C131—82no—
83C22×C131#33912yes—
84C22×C131#34211yescharacteristic
85C4×C131—21no—
86C4×C131—41no—
87C4×C131—41no—
88C4×C131—42no—
89C4×C131—88no—
90C4×C131#35311yescharacteristic
91C4×C131#35411yescharacteristic
92C2×C131—22no—
93C2×C131—44no—
94C2×C131#129711yescharacteristic
95C2×C131#139111yescharacteristic
96C2×C131#139311yescharacteristic
97#7283C13111yesmaximal, characteristic, direct product factor, Sylow
98C131#728311yescharacteristic, direct product factor, Sylow
99#1955C2×C13111yescharacteristic
100C4×#99C2×C13112yes—
101C2×C4×D4C22×C13111yescharacteristic
102C2×C4⋊C8C4×C13111yescharacteristic, complemented
103C2×#99—22no—
104C2×C22⋊C8—22no—
105C2×#97C4×C13111yescharacteristic, complemented
106C4×C22⋊C4—22no—
107#342C4×C13114yescomplemented
108C22×D4D4×C13111yescharacteristic
109C23×C4D4×C13112yes—
110C22×C8—21no—
111C22×C8—21no—
112C4×D4—41no—
113C4×D4—41no—
114C2×C4⋊C4Q8×C13111yescharacteristic
115C2×C22⋊C4—24no—
116C2×C22⋊C4C2×C4×C13112yes—
117C2×C42—42no—
118C2×C42C2×C4×C13111yescharacteristic
119C4⋊C8—41no—
120#99—28no—
121C22⋊C8—44no—
122#97—41no—
123#95—42no—
124C24C22⋊C4×C13112yes—
125C2×D4—24no—
126C2×D4—41no—
127C22×C4—22no—
128C22×C4—22no—
129C22×C4—42no—
130C22×C4—42no—
131C22×C4—44no—
132C22×C4C42×C13111yescharacteristic
133C22×C4C22⋊C4×C13111yescharacteristic
134C22×C4C4⋊C4×C13111yescharacteristic
135C22×C4C4⋊C4×C13112yes—
136C2×C8—22no—
137C2×C8—41no—
138C2×C8—41no—
139C2×C8—42no—
140C2×C8—41no—
141C4⋊C4—41no—
142C22⋊C4—28no—
143C22⋊C4—42no—
144C22⋊C4—44no—
145C42—21no—
146C42—21no—
147C42—82no—
148C42—82no—
149C23—22no—
150C23—22no—
151C23—42no—
152C23—42no—
153C23#95×C13111yescharacteristic
154C23#104×C13114yes—
155D4—44no—
156C2×C4—21no—
157C2×C4—21no—
158C2×C4—22no—
159C2×C4—21no—
160C2×C4—21no—
161C2×C4—22no—
162C2×C4—42no—
163C2×C4—42no—
164C2×C4—42no—
165C2×C4—41no—
166C2×C4—48no—
167C2×C4—82no—
168C2×C4—84no—
169C2×C4—84no—
170C2×C4#99×C13111yescharacteristic
171C2×C4#99×C13111yescharacteristic
172C8—42no—
173C8—81no—
174C22—21no—
175C22—21no—
176C22—24no—
177C22—44no—
178C22—42no—
179C22—42no—
180C22—82no—
181C22#339×C13112yes—
182C22#342×C13111yescharacteristic
183C4—21no—
184C4—41no—
185C4—41no—
186C4—42no—
187C4—88no—
188C4#353×C13111yescharacteristic
189C4#354×C13111yescharacteristic
190C2—22no—
191C2—44no—
192C2#1297×C13111yescharacteristic
193C2#1391×C13111yescharacteristic
194C2#1393×C13111yescharacteristic
subgroupG/H
centerC2×C4×C131#99
commutatorC22×C4C42×C131
Frattini, cosocleC2×C4×D4C22×C131
socleC22×C131#342
prime radicalC22×D4×C131D4
LCSG ▷ C22×C4 ▷ C23 ▷ C2 ▷ C1
UCSC1 ◁ C2×C4×C131 ◁ C22×C4×C131 ◁ C2×C4×D4×C131 ◁ G

Complements

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

NH ≅ G/Ntype
4. C2×C4⋊C8×C131C4semidirect
7. C2×#97×C131C4semidirect
9. #342×C131C4semidirect
97. #7283C131direct (N × H)
98. C131#7283direct (N × H)
102. C2×C4⋊C8C4×C131semidirect
105. C2×#97C4×C131semidirect
107. #342C4×C131semidirect

Maximal subgroups

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

subgroupindex
#1955×C1312
C4×#99×C1312
#7283131