Finite Group Databasebeta

← C131×#7249 #45693133

Subgroups — C131×#7249 #45693133

Order 33536.

312 conjugacy classes of subgroups; only the 78 normal subgroups are shown.

normal subgroups only

This group has 312 conjugacy classes of subgroups — too many to draw. Only its 78 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#1954×C131C211yesmaximal, characteristic
2#1465×C131C212yesmaximal
3C2×C4×D4×C131C2211yescharacteristic
4C2×C4⋊C8×C131C411yescharacteristic
5#407×C131—22no—
6C2×C22⋊C8×C131—22no—
7C2×C4×C8×C131C411yescharacteristic
8#324×C131—22no—
9#323×C131C414yes—
10C22×D4×C131Q811yescharacteristic
11C23×C4×C131D412yes—
12C2×M16×C131—42no—
13C22×C8×C131—21no—
14C22×C8×C131—21no—
15C4×D4×C131—41no—
16C4×D4×C131—41no—
17C2×C4⋊C4×C131D411yescharacteristic
18C2×C22⋊C4×C131C2×C412yes—
19C2×C42×C131C2×C411yescharacteristic
20C4⋊C8×C131—41no—
21C22⋊C8×C131—24no—
22C22⋊C8×C131—44no—
23C22⋊C8×C131—42no—
24C4×C8×C131—41no—
25C24×C131C4⋊C412yes—
26C2×D4×C131—22no—
27C2×D4×C131—41no—
28C2×D4×C131—41no—
29C22×C4×C131—22no—
30C22×C4×C131—22no—
31C22×C4×C131—42no—
32C22×C4×C131—42no—
33C22×C4×C131C4211yescharacteristic
34C22×C4×C131C22⋊C412yes—
35C22×C4×C131C22⋊C411yescharacteristic
36C22×C4×C131C4⋊C411yescharacteristic
37M16×C131—82no—
38M16×C131—82no—
39C2×C8×C131—22no—
40C2×C8×C131—41no—
41C2×C8×C131—41no—
42C2×C8×C131—44no—
43C2×C8×C131—42no—
44C2×C8×C131—41no—
45C4⋊C4×C131—41no—
46C22⋊C4×C131—42no—
47C42×C131—21no—
48C42×C131—21no—
49C23×C131—22no—
50C23×C131—22no—
51C23×C131—22no—
52C23×C131—42no—
53C23×C131—42no—
54C23×C131#9511yescharacteristic
55D4×C131—44no—
56C2×C4×C131—21no—
57C2×C4×C131—21no—
58C2×C4×C131—21no—
59C2×C4×C131—21no—
60C2×C4×C131—21no—
61C2×C4×C131—22no—
62C2×C4×C131—42no—
63C2×C4×C131—42no—
64C2×C4×C131—42no—
65C2×C4×C131—41no—
66C2×C4×C131—82no—
67C2×C4×C131#9911yescharacteristic
68C2×C4×C131#9911yescharacteristic
69C2×C4×C131#10812yes—
70C8×C131—42no—
71C8×C131—84no—
72C8×C131—81no—
73C22×C131—21no—
74C22×C131—21no—
75C22×C131—44no—
76C22×C131—42no—
77C22×C131—42no—
78C22×C131—42no—
79C22×C131—82no—
80C22×C131#33811yescharacteristic
81C22×C131#34111yescharacteristic
82C22×C131#34211yescharacteristic
83C4×C131—22no—
84C4×C131—21no—
85C4×C131—41no—
86C4×C131—42no—
87C4×C131#35311yescharacteristic
88C4×C131#35411yescharacteristic
89C2×C131—21no—
90C2×C131—21no—
91C2×C131—82no—
92C2×C131#129311yescharacteristic
93C2×C131#139211yescharacteristic
94C2×C131#139311yescharacteristic
95#7249C13111yesmaximal, characteristic, direct product factor, Sylow
96C131#724911yescharacteristic, direct product factor, Sylow
97#1954C2×C13111yescharacteristic
98#1465C2×C13112yes—
99C2×C4×D4C22×C13111yescharacteristic
100C2×C4⋊C8C4×C13111yescharacteristic
101#407—22no—
102C2×C22⋊C8—22no—
103C2×C4×C8C4×C13111yescharacteristic
104#324—22no—
105#323C4×C13114yes—
106C22×D4Q8×C13111yescharacteristic
107C23×C4D4×C13112yes—
108C2×M16—42no—
109C22×C8—21no—
110C22×C8—21no—
111C4×D4—41no—
112C4×D4—41no—
113C2×C4⋊C4D4×C13111yescharacteristic
114C2×C22⋊C4C2×C4×C13112yes—
115C2×C42C2×C4×C13111yescharacteristic
116C4⋊C8—41no—
117C22⋊C8—24no—
118C22⋊C8—44no—
119C22⋊C8—42no—
120C4×C8—41no—
121C24C4⋊C4×C13112yes—
122C2×D4—22no—
123C2×D4—41no—
124C2×D4—41no—
125C22×C4—22no—
126C22×C4—22no—
127C22×C4—42no—
128C22×C4—42no—
129C22×C4C42×C13111yescharacteristic
130C22×C4C22⋊C4×C13111yescharacteristic
131C22×C4C22⋊C4×C13112yes—
132C22×C4C4⋊C4×C13111yescharacteristic
133M16—82no—
134M16—82no—
135C2×C8—22no—
136C2×C8—41no—
137C2×C8—41no—
138C2×C8—44no—
139C2×C8—42no—
140C2×C8—41no—
141C4⋊C4—41no—
142C22⋊C4—42no—
143C42—21no—
144C42—21no—
145C23—22no—
146C23—22no—
147C23—22no—
148C23—42no—
149C23—42no—
150C23#95×C13111yescharacteristic
151D4—44no—
152C2×C4—21no—
153C2×C4—21no—
154C2×C4—21no—
155C2×C4—21no—
156C2×C4—21no—
157C2×C4—22no—
158C2×C4—42no—
159C2×C4—42no—
160C2×C4—42no—
161C2×C4—41no—
162C2×C4—82no—
163C2×C4#99×C13111yescharacteristic
164C2×C4#99×C13111yescharacteristic
165C2×C4#108×C13112yes—
166C8—42no—
167C8—84no—
168C8—81no—
169C22—21no—
170C22—21no—
171C22—44no—
172C22—42no—
173C22—42no—
174C22—42no—
175C22—82no—
176C22#338×C13111yescharacteristic
177C22#341×C13111yescharacteristic
178C22#342×C13111yescharacteristic
179C4—22no—
180C4—21no—
181C4—41no—
182C4—42no—
183C4#353×C13111yescharacteristic
184C4#354×C13111yescharacteristic
185C2—21no—
186C2—21no—
187C2—82no—
188C2#1293×C13111yescharacteristic
189C2#1392×C13111yescharacteristic
190C2#1393×C13111yescharacteristic
subgroupG/H
center, socleC22×C131#342
commutatorC22×C4C42×C131
Frattini, cosocleC2×C4×D4C22×C131
prime radicalC22×D4×C131Q8
LCSG ▷ C22×C4 ▷ C22 ▷ C2 ▷ C1
UCSC1 ◁ C22×C131 ◁ C22×C4×C131 ◁ C2×C4×D4×C131 ◁ G

Complements

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

NH ≅ G/Ntype
95. #7249C131direct (N × H)
96. C131#7249direct (N × H)

Maximal subgroups

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

subgroupindex
#1954×C1312
#1465×C1312
#7249131