Finite Group Databasebeta

← C131×#9424 #45695308

Subgroups — C131×#9424 #45695308

Order 33536.

436 conjugacy classes of subgroups; only the 118 normal subgroups are shown.

normal subgroups only

This group has 436 conjugacy classes of subgroups — too many to draw. Only its 118 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#2987×C131C211yesmaximal, characteristic, complemented
3#1555×C131C212yesmaximal
4#1537×C131C211yesmaximal, characteristic, complemented
5#1291×C131C212yesmaximal, complemented
6#533×C131C2211yescharacteristic
7C2×#127×C131C2211yescharacteristic
8#490×C131—22no—
9#486×C131C414yes—
10#446×C131—24no—
11#433×C131—22no—
12#432×C131C2212yes—
13#432×C131C2212yes—
14#418×C131—22no—
15C4×M16×C131C2211yescharacteristic
16#331×C131—24no—
17#330×C131—22no—
18C22×D4×C131—21no—
19C22×D4×C131—22no—
20C2×M16×C131—21no—
21C4⋊Q8×C131C2×C412yes—
22#127×C131—21no—
23#127×C131—22no—
24#127×C131C2×C412yes—
25#125×C131D412yes—
26C22⋊Q8×C131—22no—
27C4×Q8×C131—22no—
28#117×C131D412yes—
29C2×C42×C131C2311yescharacteristic
30C4⋊C8×C131—24no—
31C4⋊C8×C131—22no—
32C4⋊C8×C131D414yes—
33#102×C131—28no—
34C22⋊C8×C131—22no—
35C22⋊C8×C131—22no—
36#97×C131—22no—
37#97×C131—21no—
38#97×C131—22no—
39#97×C131—22no—
40C4×C8×C131—22no—
41C4×C8×C131C2×C412yes—
42C24×C131—41no—
43C2×Q8×C131—22no—
44C2×D4×C131—22no—
45C2×D4×C131—24no—
46C2×D4×C131—44no—
47C2×D4×C131—41no—
48C2×D4×C131—42no—
49C2×D4×C131—84no—
50C22×C4×C131C2×D411yescharacteristic
51C22×C4×C131#4112yes—
52M16×C131—42no—
53C2×C8×C131—22no—
54C2×C8×C131—24no—
55C2×C8×C131—42no—
56C4⋊C4×C131—22no—
57C4⋊C4×C131—24no—
58C4⋊C4×C131C22⋊C414yes—
59C22⋊C4×C131—22no—
60C42×C131—22no—
61C42×C131C22×C411yescharacteristic
62C42×C131C2×D411yescharacteristic
63C42×C131C2×D412yes—
64C23×C131—42no—
65C23×C131—82no—
66C23×C131—84no—
67C23×C131#12311yescharacteristic
68Q8×C131—82no—
69D4×C131—44no—
70D4×C131—84no—
71D4×C131—84no—
72D4×C131—82no—
73C2×C4×C131—22no—
74C2×C4×C131—24no—
75C2×C4×C131—42no—
76C2×C4×C131C2×C22⋊C411yescharacteristic
77C2×C4×C131C4×D412yes—
78C2×C4×C131#12011yescharacteristic
79C2×C4×C131#12112yes—
80C8×C131—42no—
81C8×C131—44no—
82C8×C131—82no—
83C22×C131—21no—
84C22×C131—22no—
85C22×C131—82no—
86C22×C131—84no—
87C22×C131—164no—
88C22×C131#38611yescharacteristic
89C4×C131—21no—
90C4×C131—22no—
91C4×C131—22no—
92C4×C131—44no—
93C4×C131#45412yes—
94C2×C131—41no—
95C2×C131—162no—
96C2×C131#188811yescharacteristic
97C2×C131#190312yes—
98#9424C13111yesmaximal, characteristic, direct product factor, Sylow
99C131#942411yescharacteristic, direct product factor, Sylow
100#3138C2×C13111yescharacteristic
101#2987C2×C13111yescharacteristic, complemented
102#1555C2×C13112yes—
103#1537C2×C13111yescharacteristic, complemented
104#1291C2×C13112yescomplemented
105#533C22×C13111yescharacteristic
106C2×#127C22×C13111yescharacteristic
107#490—22no—
108#486C4×C13114yes—
109#446—24no—
110#433—22no—
111#432C22×C13112yes—
112#432C22×C13112yes—
113#418—22no—
114C4×M16C22×C13111yescharacteristic
115#331—24no—
116#330—22no—
117C22×D4—21no—
118C22×D4—22no—
119C2×M16—21no—
120C4⋊Q8C2×C4×C13112yes—
121#127—22no—
122#127—21no—
123#127C2×C4×C13112yes—
124#125D4×C13112yes—
125C22⋊Q8—22no—
126C4×Q8—22no—
127#117D4×C13112yes—
128C2×C42C23×C13111yescharacteristic
129C4⋊C8—24no—
130C4⋊C8—22no—
131C4⋊C8D4×C13114yes—
132#102—28no—
133C22⋊C8—22no—
134C22⋊C8—22no—
135#97—22no—
136#97—21no—
137#97—22no—
138#97—22no—
139C4×C8—22no—
140C4×C8C2×C4×C13112yes—
141C24—41no—
142C2×Q8—22no—
143C2×D4—22no—
144C2×D4—24no—
145C2×D4—44no—
146C2×D4—41no—
147C2×D4—42no—
148C2×D4—84no—
149C22×C4C2×D4×C13111yescharacteristic
150C22×C4#41×C13112yes—
151M16—42no—
152C2×C8—22no—
153C2×C8—24no—
154C2×C8—42no—
155C4⋊C4—22no—
156C4⋊C4—24no—
157C4⋊C4C22⋊C4×C13114yes—
158C22⋊C4—22no—
159C42—22no—
160C42C22×C4×C13111yescharacteristic
161C42C2×D4×C13111yescharacteristic
162C42C2×D4×C13112yes—
163C23—42no—
164C23—82no—
165C23—84no—
166C23#123×C13111yescharacteristic
167Q8—82no—
168D4—44no—
169D4—84no—
170D4—84no—
171D4—82no—
172C2×C4—22no—
173C2×C4—24no—
174C2×C4—42no—
175C2×C4C2×C22⋊C4×C13111yescharacteristic
176C2×C4C4×D4×C13112yes—
177C2×C4#120×C13111yescharacteristic
178C2×C4#121×C13112yes—
179C8—42no—
180C8—44no—
181C8—82no—
182C22—21no—
183C22—22no—
184C22—82no—
185C22—84no—
186C22—164no—
187C22#386×C13111yescharacteristic
188C4—21no—
189C4—22no—
190C4—22no—
191C4—44no—
192C4#454×C13112yes—
193C2—41no—
194C2—162no—
195C2#1888×C13111yescharacteristic
196C2#1903×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. #2987×C131C2semidirect
4. #1537×C131C2semidirect
5. #1291×C131C2semidirect
98. #9424C131direct (N × H)
99. C131#9424direct (N × H)
101. #2987C2×C131semidirect
103. #1537C2×C131semidirect
104. #1291C2×C131semidirect

Maximal subgroups

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

subgroupindex
#3138×C1312
#2987×C1312
#1555×C1312
#1537×C1312
#1291×C1312
#9424131