Finite Group Databasebeta

← C131×#9438 #45695322

Subgroups — C131×#9438 #45695322

Order 33536.

452 conjugacy classes of subgroups; only the 126 normal subgroups are shown.

normal subgroups only

This group has 452 conjugacy classes of subgroups — too many to draw. Only its 126 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#3138×C131C211yesmaximal, characteristic
2#2986×C131C211yesmaximal, characteristic, complemented
3#1561×C131C211yesmaximal, characteristic, complemented
4#1545×C131C212yesmaximal
5#1299×C131C212yesmaximal, complemented
6#533×C131C2211yescharacteristic
7C2×#127×C131C2211yescharacteristic
8#490×C131C414yes—
9#486×C131—22no—
10#446×C131—22no—
11C8×Q8×C131—22no—
12#433×C131—22no—
13#431×C131C2212yes—
14#423×C131C2212yes—
15#418×C131—22no—
16C4×M16×C131C2211yescharacteristic
17#332×C131—22no—
18#331×C131—22no—
19#331×C131—22no—
20C22×D4×C131—21no—
21C22×D4×C131—22no—
22C2×M16×C131—21no—
23C2×M16×C131—22no—
24C4⋊Q8×C131D412yes—
25#127×C131—21no—
26#127×C131—22no—
27#127×C131C2×C412yes—
28#125×C131C2×C412yes—
29C22⋊Q8×C131—22no—
30C4×Q8×C131—22no—
31#117×C131D412yes—
32C2×C42×C131C2311yescharacteristic
33C4⋊C8×C131—24no—
34C4⋊C8×C131—22no—
35C4⋊C8×C131—22no—
36C4⋊C8×C131D412yes—
37C4⋊C8×C131D412yes—
38#102×C131—28no—
39C22⋊C8×C131—22no—
40#97×C131—22no—
41#97×C131C2×C412yes—
42C4×C8×C131—22no—
43C4×C8×C131—21no—
44C4×C8×C131—22no—
45C24×C131—41no—
46C2×Q8×C131—22no—
47C2×D4×C131—22no—
48C2×D4×C131—24no—
49C2×D4×C131—44no—
50C2×D4×C131—41no—
51C2×D4×C131—42no—
52C2×D4×C131—82no—
53C2×D4×C131—82no—
54C22×C4×C131C2×D411yescharacteristic
55C22×C4×C131#4112yes—
56M16×C131—42no—
57M16×C131—82no—
58C2×C8×C131—22no—
59C2×C8×C131—22no—
60C2×C8×C131—22no—
61C2×C8×C131—42no—
62C4⋊C4×C131—24no—
63C4⋊C4×C131—22no—
64C4⋊C4×C131C22⋊C414yes—
65C22⋊C4×C131—22no—
66C42×C131—22no—
67C42×C131C22×C411yescharacteristic
68C42×C131C2×D411yescharacteristic
69C42×C131C2×D412yes—
70C23×C131—42no—
71C23×C131—82no—
72C23×C131—84no—
73C23×C131#12311yescharacteristic
74Q8×C131—42no—
75Q8×C131—42no—
76D4×C131—44no—
77D4×C131—84no—
78D4×C131—82no—
79D4×C131—82no—
80D4×C131—82no—
81C2×C4×C131—22no—
82C2×C4×C131—22no—
83C2×C4×C131—22no—
84C2×C4×C131—24no—
85C2×C4×C131C2×C22⋊C411yescharacteristic
86C2×C4×C131C4×D412yes—
87C2×C4×C131#12011yescharacteristic
88C2×C4×C131#12112yes—
89C8×C131—42no—
90C8×C131—42no—
91C8×C131—42no—
92C8×C131—82no—
93C22×C131—21no—
94C22×C131—22no—
95C22×C131—82no—
96C22×C131—84no—
97C22×C131—164no—
98C22×C131#38611yescharacteristic
99C4×C131—21no—
100C4×C131—22no—
101C4×C131—44no—
102C4×C131#45412yes—
103C4×C131#47112yes—
104C4×C131#47212yes—
105C2×C131—41no—
106C2×C131—162no—
107C2×C131#188811yescharacteristic
108C2×C131#190712yes—
109#9438C13111yesmaximal, characteristic, direct product factor, Sylow
110C131#943811yescharacteristic, direct product factor, Sylow
111#3138C2×C13111yescharacteristic
112#2986C2×C13111yescharacteristic, complemented
113#1561C2×C13111yescharacteristic, complemented
114#1545C2×C13112yes—
115#1299C2×C13112yescomplemented
116#533C22×C13111yescharacteristic
117C2×#127C22×C13111yescharacteristic
118#490C4×C13114yes—
119#486—22no—
120#446—22no—
121C8×Q8—22no—
122#433—22no—
123#431C22×C13112yes—
124#423C22×C13112yes—
125#418—22no—
126C4×M16C22×C13111yescharacteristic
127#332—22no—
128#331—22no—
129#331—22no—
130C22×D4—21no—
131C22×D4—22no—
132C2×M16—21no—
133C2×M16—22no—
134C4⋊Q8D4×C13112yes—
135#127—22no—
136#127—21no—
137#127C2×C4×C13112yes—
138#125C2×C4×C13112yes—
139C22⋊Q8—22no—
140C4×Q8—22no—
141#117D4×C13112yes—
142C2×C42C23×C13111yescharacteristic
143C4⋊C8—24no—
144C4⋊C8—22no—
145C4⋊C8—22no—
146C4⋊C8D4×C13112yes—
147C4⋊C8D4×C13112yes—
148#102—28no—
149C22⋊C8—22no—
150#97—22no—
151#97C2×C4×C13112yes—
152C4×C8—22no—
153C4×C8—21no—
154C4×C8—22no—
155C24—41no—
156C2×Q8—22no—
157C2×D4—22no—
158C2×D4—24no—
159C2×D4—44no—
160C2×D4—41no—
161C2×D4—42no—
162C2×D4—82no—
163C2×D4—82no—
164C22×C4C2×D4×C13111yescharacteristic
165C22×C4#41×C13112yes—
166M16—42no—
167M16—82no—
168C2×C8—22no—
169C2×C8—22no—
170C2×C8—22no—
171C2×C8—42no—
172C4⋊C4—24no—
173C4⋊C4—22no—
174C4⋊C4C22⋊C4×C13114yes—
175C22⋊C4—22no—
176C42—22no—
177C42C22×C4×C13111yescharacteristic
178C42C2×D4×C13111yescharacteristic
179C42C2×D4×C13112yes—
180C23—42no—
181C23—82no—
182C23—84no—
183C23#123×C13111yescharacteristic
184Q8—42no—
185Q8—42no—
186D4—44no—
187D4—84no—
188D4—82no—
189D4—82no—
190D4—82no—
191C2×C4—22no—
192C2×C4—22no—
193C2×C4—22no—
194C2×C4—24no—
195C2×C4C2×C22⋊C4×C13111yescharacteristic
196C2×C4C4×D4×C13112yes—
197C2×C4#120×C13111yescharacteristic
198C2×C4#121×C13112yes—
199C8—42no—
200C8—42no—
201C8—42no—
202C8—82no—
203C22—21no—
204C22—22no—
205C22—82no—
206C22—84no—
207C22—164no—
208C22#386×C13111yescharacteristic
209C4—21no—
210C4—22no—
211C4—44no—
212C4#454×C13112yes—
213C4#471×C13112yes—
214C4#472×C13112yes—
215C2—41no—
216C2—162no—
217C2#1888×C13111yescharacteristic
218C2#1907×C13112yes—
subgroupG/H
center, socleC22×C131#386
commutatorC42C22×C4×C131
Frattini, cosocleC2×C42C23×C131
prime radicalC2×#127×C131C22
LCSG ▷ C42 ▷ C22 ▷ C1
UCSC1 ◁ C22×C131 ◁ C2×C42×C131 ◁ G

Complements

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

NH ≅ G/Ntype
2. #2986×C131C2semidirect
3. #1561×C131C2semidirect
5. #1299×C131C2semidirect
109. #9438C131direct (N × H)
110. C131#9438direct (N × H)
112. #2986C2×C131semidirect
113. #1561C2×C131semidirect
115. #1299C2×C131semidirect

Maximal subgroups

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

subgroupindex
#3138×C1312
#2986×C1312
#1561×C1312
#1545×C1312
#1299×C1312
#9438131