Finite Group Databasebeta

← C131×#10285 #45696169

Subgroups — C131×#10285 #45696169

Order 33536.

542 conjugacy classes of subgroups; only the 130 normal subgroups are shown.

normal subgroups only

This group has 542 conjugacy classes of subgroups — too many to draw. Only its 130 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#3227×C131C212yesmaximal
2#2862×C131C211yesmaximal, characteristic, complemented
3#1962×C131C211yesmaximal, characteristic
4#1549×C131C212yesmaximal, complemented
5#1276×C131C211yesmaximal, characteristic, complemented
6#532×C131C2211yescharacteristic
7C2×C4⋊Q8×C131C2212yes—
8#498×C131—22no—
9#486×C131—22no—
10#481×C131—24no—
11#476×C131—24no—
12#431×C131C2212yes—
13#423×C131C2211yescharacteristic
14C2×#104×C131—22no—
15#391×C131—24no—
16#382×C131—22no—
17C43×C131C2211yescharacteristic
18#332×C131—24no—
19C2×#41×C131—21no—
20C22×Q8×C131—22no—
21C2×M16×C131—21no—
22C4⋊Q8×C131—22no—
23C4⋊Q8×C131—22no—
24C4⋊Q8×C131—22no—
25C4⋊Q8×C131—22no—
26C4⋊Q8×C131D411yescharacteristic
27#127×C131D411yescharacteristic
28#124×C131—21no—
29#121×C131—22no—
30C4×D4×C131—22no—
31C2×C4⋊C4×C131—22no—
32C2×C4⋊C4×C131D414yes—
33C2×C42×C131—22no—
34C2×C42×C131D412yes—
35C2×C42×C131C2311yescharacteristic
36#106×C131—28no—
37C4⋊C8×C131—22no—
38C4⋊C8×C131D414yes—
39#104×C131—44no—
40#102×C131—28no—
41C22⋊C8×C131—22no—
42C4×C8×C131—22no—
43#95×C131—28no—
44#41×C131—42no—
45#41×C131—42no—
46C2×Q8×C131—21no—
47C2×Q8×C131—48no—
48C2×Q8×C131—42no—
49C2×Q8×C131—42no—
50C2×D4×C131—22no—
51C2×D4×C131—21no—
52C2×D4×C131—41no—
53C22×C4×C131—22no—
54C22×C4×C131—24no—
55C22×C4×C131—41no—
56C22×C4×C131C2×D412yes—
57C22×C4×C131C2×D411yescharacteristic
58M16×C131—42no—
59C2×C8×C131—24no—
60C2×C8×C131—41no—
61C4⋊C4×C131—24no—
62C4⋊C4×C131—22no—
63C4⋊C4×C131—24no—
64C4⋊C4×C131—42no—
65C4⋊C4×C131—42no—
66C22⋊C4×C131—42no—
67C42×C131—22no—
68C42×C131—44no—
69C42×C131SD1614yes—
70C42×C131C2×D411yescharacteristic
71C42×C131C2×D412yes—
72C42×C131#4111yescharacteristic
73C23×C131—41no—
74C23×C131#12011yescharacteristic
75Q8×C131—42no—
76Q8×C131—84no—
77Q8×C131—84no—
78D4×C131—44no—
79D4×C131—42no—
80D4×C131—82no—
81C2×C4×C131—24no—
82C2×C4×C131—24no—
83C2×C4×C131—44no—
84C2×C4×C131—48no—
85C2×C4×C131—41no—
86C2×C4×C131—44no—
87C2×C4×C131—81no—
88C2×C4×C131—81no—
89C2×C4×C131#12012yes—
90C2×C4×C131#12112yes—
91C2×C4×C131#12111yescharacteristic
92C2×C4×C131#12711yescharacteristic
93C2×C4×C131C2×SD1612yes—
94C2×C4×C131#13712yes—
95C8×C131—44no—
96C8×C131—81no—
97C22×C131—22no—
98C22×C131—82no—
99C22×C131—81no—
100C22×C131#39211yescharacteristic
101C22×C131#44812yes—
102C4×C131—22no—
103C4×C131—44no—
104C4×C131—84no—
105C4×C131—81no—
106C4×C131#45414yes—
107C4×C131#46112yes—
108C4×C131#49211yescharacteristic
109C4×C131#49711yescharacteristic
110C2×C131—22no—
111C2×C131—161no—
112C2×C131#200312yes—
113C2×C131#201311yescharacteristic
114#10285C13111yesmaximal, characteristic, direct product factor, Sylow
115C131#1028511yescharacteristic, direct product factor, Sylow
116#3227C2×C13112yes—
117#2862C2×C13111yescharacteristic, complemented
118#1962C2×C13111yescharacteristic
119#1549C2×C13112yescomplemented
120#1276C2×C13111yescharacteristic, complemented
121#532C22×C13111yescharacteristic
122C2×C4⋊Q8C22×C13112yes—
123#498—22no—
124#486—22no—
125#481—24no—
126#476—24no—
127#431C22×C13112yes—
128#423C22×C13111yescharacteristic
129C2×#104—22no—
130#391—24no—
131#382—22no—
132C43C22×C13111yescharacteristic
133#332—24no—
134C2×#41—21no—
135C22×Q8—22no—
136C2×M16—21no—
137C4⋊Q8—22no—
138C4⋊Q8—22no—
139C4⋊Q8—22no—
140C4⋊Q8—22no—
141C4⋊Q8D4×C13111yescharacteristic
142#127D4×C13111yescharacteristic
143#124—21no—
144#121—22no—
145C4×D4—22no—
146C2×C4⋊C4—22no—
147C2×C4⋊C4D4×C13114yes—
148C2×C42—22no—
149C2×C42D4×C13112yes—
150C2×C42C23×C13111yescharacteristic
151#106—28no—
152C4⋊C8—22no—
153C4⋊C8D4×C13114yes—
154#104—44no—
155#102—28no—
156C22⋊C8—22no—
157C4×C8—22no—
158#95—28no—
159#41—42no—
160#41—42no—
161C2×Q8—21no—
162C2×Q8—48no—
163C2×Q8—42no—
164C2×Q8—42no—
165C2×D4—22no—
166C2×D4—21no—
167C2×D4—41no—
168C22×C4—22no—
169C22×C4—24no—
170C22×C4—41no—
171C22×C4C2×D4×C13112yes—
172C22×C4C2×D4×C13111yescharacteristic
173M16—42no—
174C2×C8—24no—
175C2×C8—41no—
176C4⋊C4—24no—
177C4⋊C4—22no—
178C4⋊C4—24no—
179C4⋊C4—42no—
180C4⋊C4—42no—
181C22⋊C4—42no—
182C42—22no—
183C42—44no—
184C42SD16×C13114yes—
185C42C2×D4×C13111yescharacteristic
186C42C2×D4×C13112yes—
187C42#41×C13111yescharacteristic
188C23—41no—
189C23#120×C13111yescharacteristic
190Q8—42no—
191Q8—84no—
192Q8—84no—
193D4—44no—
194D4—42no—
195D4—82no—
196C2×C4—24no—
197C2×C4—24no—
198C2×C4—44no—
199C2×C4—48no—
200C2×C4—41no—
201C2×C4—44no—
202C2×C4—81no—
203C2×C4—81no—
204C2×C4#120×C13112yes—
205C2×C4#121×C13112yes—
206C2×C4#121×C13111yescharacteristic
207C2×C4#127×C13111yescharacteristic
208C2×C4C2×SD16×C13112yes—
209C2×C4#137×C13112yes—
210C8—44no—
211C8—81no—
212C22—22no—
213C22—82no—
214C22—81no—
215C22#392×C13111yescharacteristic
216C22#448×C13112yes—
217C4—22no—
218C4—44no—
219C4—84no—
220C4—81no—
221C4#454×C13114yes—
222C4#461×C13112yes—
223C4#492×C13111yescharacteristic
224C4#497×C13111yescharacteristic
225C2—22no—
226C2—161no—
227C2#2003×C13112yes—
228C2#2013×C13111yescharacteristic
subgroupG/H
center, socleC22×C131#392
commutator, Frattini, cosocleC2×C42C23×C131
prime radical#532×C131C22
LCSG ▷ C2×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. #2862×C131C2semidirect
4. #1549×C131C2semidirect
5. #1276×C131C2semidirect
114. #10285C131direct (N × H)
115. C131#10285direct (N × H)
117. #2862C2×C131semidirect
119. #1549C2×C131semidirect
120. #1276C2×C131semidirect

Maximal subgroups

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

subgroupindex
#3227×C1312
#2862×C1312
#1962×C1312
#1549×C1312
#1276×C1312
#10285131