Finite Group Databasebeta

← C131×#21795 #45707679

Subgroups — C131×#21795 #45707679

Order 33536.

1538 conjugacy classes of subgroups; only the 366 normal subgroups are shown.

normal subgroups only

This group has 1538 conjugacy classes of subgroups — too many to draw. Only its 366 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
1C2×#534×C131C211yesmaximal, characteristic
2#2312×C131C212yesmaximal, complemented
3#1964×C131C218yesmaximal, complemented
4#1781×C131C214yesmaximal, complemented
5C23×D4×C131C2212yes—
6#534×C131—28no—
7C2×#123×C131C414yescomplemented
8C2×#121×C131C2214yes—
9C2×#120×C131C414yescomplemented
10C22×C22⋊C4×C131C2211yescharacteristic
11C2×#99×C131C22116yescomplemented
12#388×C131—28no—
13#380×C131C2214yescomplemented
14#379×C131C2214yes—
15C4×C22⋊C4×C131C2214yescomplemented
16C25×C131C2×C412yes—
17C25×C131C2311yescharacteristic
18C22×D4×C131—28no—
19C22×D4×C131—48no—
20C22×D4×C131C2×C414yes—
21C22×D4×C131C2×C414yes—
22C22×D4×C131C2314yes—
23C23×C4×C131C2×C412yes—
24C23×C4×C131C2312yes—
25#123×C131—216no—
26#121×C131—28no—
27#121×C131—28no—
28#120×C131—216no—
29C2×C4⋊C4×C131—24no—
30C2×C4⋊C4×C131C2×C414yes—
31C2×C22⋊C4×C131—24no—
32C2×C22⋊C4×C131—24no—
33C2×C22⋊C4×C131C2×C418yes—
34C2×C22⋊C4×C131C2×C414yes—
35C2×C22⋊C4×C131D418yes—
36C2×C22⋊C4×C131C2318yes—
37C2×C42×C131—24no—
38#99×C131—416no—
39#95×C131—24no—
40#95×C131—24no—
41C24×C131—24no—
42C24×C131—24no—
43C24×C131—44no—
44C24×C131—82no—
45C24×C131—84no—
46C24×C131C22×C414yes—
47C24×C131C22×C412yes—
48C24×C131C2×D414yes—
49C24×C131C2411yescharacteristic
50C2×D4×C131—28no—
51C2×D4×C131—28no—
52C2×D4×C131—216no—
53C2×D4×C131—28no—
54C2×D4×C131—48no—
55C2×D4×C131—432no—
56C2×D4×C131—84no—
57C22×C4×C131—24no—
58C22×C4×C131—28no—
59C22×C4×C131—44no—
60C22×C4×C131—82no—
61C22×C4×C131C22×C414yes—
62C22×C4×C131C22×C414yes—
63C22×C4×C131C2×D414yes—
64C22×C4×C131C2×D414yes—
65C4⋊C4×C131—28no—
66C4⋊C4×C131—84no—
67C22⋊C4×C131—216no—
68C22⋊C4×C131—216no—
69C22⋊C4×C131—84no—
70C22⋊C4×C131—84no—
71C22⋊C4×C131C22⋊C4116yes—
72C42×C131—84no—
73C23×C131—24no—
74C23×C131—28no—
75C23×C131—24no—
76C23×C131—28no—
77C23×C131—42no—
78C23×C131—44no—
79C23×C131—44no—
80C23×C131—44no—
81C23×C131—48no—
82C23×C131—48no—
83C23×C131—88no—
84C23×C131—88no—
85C23×C131—816no—
86C23×C131C2×C22⋊C414yes—
87C23×C131C23×C411yescharacteristic
88C23×C131C22×D412yes—
89C23×C131H(5,𝔽2)14yes—
90D4×C131—416no—
91D4×C131—416no—
92D4×C131—88no—
93C2×C4×C131—24no—
94C2×C4×C131—28no—
95C2×C4×C131—44no—
96C2×C4×C131—44no—
97C2×C4×C131—44no—
98C2×C4×C131—48no—
99C2×C4×C131—48no—
100C2×C4×C131—48no—
101C2×C4×C131—48no—
102C2×C4×C131C2×C22⋊C418yes—
103C22×C131—22no—
104C22×C131—22no—
105C22×C131—22no—
106C22×C131—24no—
107C22×C131—28no—
108C22×C131—44no—
109C22×C131—48no—
110C22×C131—44no—
111C22×C131—48no—
112C22×C131—88no—
113C22×C131—88no—
114C22×C131—816no—
115C22×C131C22×C22⋊C411yescharacteristic
116C22×C131#51812yes—
117C22×C131#53514yes—
118C4×C131—28no—
119C4×C131—44no—
120C4×C131—88no—
121C2×C131—24no—
122C2×C131—22no—
123C2×C131—44no—
124C2×C131—84no—
125C2×C131#230911yescharacteristic
126C2×C131#288312yes—
127#21795C13111yesmaximal, characteristic, direct product factor, Sylow
128C131#2179511yescharacteristic, direct product factor, Sylow
129C2×#534C2×C13111yescharacteristic
130#2312C2×C13112yescomplemented
131#1964C2×C13118yescomplemented
132#1781C2×C13114yescomplemented
133C23×D4C22×C13112yes—
134#534—28no—
135C2×#123C4×C13114yescomplemented
136C2×#121C22×C13114yes—
137C2×#120C4×C13114yescomplemented
138C22×C22⋊C4C22×C13111yescharacteristic
139C2×#99C22×C131116yescomplemented
140#388—28no—
141#380C22×C13114yescomplemented
142#379C22×C13114yes—
143C4×C22⋊C4C22×C13114yescomplemented
144C25C2×C4×C13112yes—
145C25C23×C13111yescharacteristic
146C22×D4—28no—
147C22×D4—48no—
148C22×D4C2×C4×C13114yes—
149C22×D4C2×C4×C13114yes—
150C22×D4C23×C13114yes—
151C23×C4C2×C4×C13112yes—
152C23×C4C23×C13112yes—
153#123—216no—
154#121—28no—
155#121—28no—
156#120—216no—
157C2×C4⋊C4—24no—
158C2×C4⋊C4C2×C4×C13114yes—
159C2×C22⋊C4—24no—
160C2×C22⋊C4—24no—
161C2×C22⋊C4C2×C4×C13118yes—
162C2×C22⋊C4C2×C4×C13114yes—
163C2×C22⋊C4D4×C13118yes—
164C2×C22⋊C4C23×C13118yes—
165C2×C42—24no—
166#99—416no—
167#95—24no—
168#95—24no—
169C24—24no—
170C24—24no—
171C24—44no—
172C24—82no—
173C24—84no—
174C24C22×C4×C13114yes—
175C24C22×C4×C13112yes—
176C24C2×D4×C13114yes—
177C24C24×C13111yescharacteristic
178C2×D4—28no—
179C2×D4—28no—
180C2×D4—216no—
181C2×D4—28no—
182C2×D4—48no—
183C2×D4—432no—
184C2×D4—84no—
185C22×C4—24no—
186C22×C4—28no—
187C22×C4—44no—
188C22×C4—82no—
189C22×C4C22×C4×C13114yes—
190C22×C4C22×C4×C13114yes—
191C22×C4C2×D4×C13114yes—
192C22×C4C2×D4×C13114yes—
193C4⋊C4—28no—
194C4⋊C4—84no—
195C22⋊C4—216no—
196C22⋊C4—216no—
197C22⋊C4—84no—
198C22⋊C4—84no—
199C22⋊C4C22⋊C4×C131116yes—
200C42—84no—
201C23—24no—
202C23—28no—
203C23—24no—
204C23—28no—
205C23—42no—
206C23—44no—
207C23—44no—
208C23—44no—
209C23—48no—
210C23—48no—
211C23—88no—
212C23—88no—
213C23—816no—
214C23C2×C22⋊C4×C13114yes—
215C23C23×C4×C13111yescharacteristic
216C23C22×D4×C13112yes—
217C23H(5,𝔽2)×C13114yes—
218D4—416no—
219D4—416no—
220D4—88no—
221C2×C4—24no—
222C2×C4—28no—
223C2×C4—44no—
224C2×C4—44no—
225C2×C4—44no—
226C2×C4—48no—
227C2×C4—48no—
228C2×C4—48no—
229C2×C4—48no—
230C2×C4C2×C22⋊C4×C13118yes—
231C22—22no—
232C22—22no—
233C22—22no—
234C22—24no—
235C22—28no—
236C22—44no—
237C22—48no—
238C22—44no—
239C22—48no—
240C22—88no—
241C22—88no—
242C22—816no—
243C22C22×C22⋊C4×C13111yescharacteristic
244C22#518×C13112yes—
245C22#535×C13114yes—
246C4—28no—
247C4—44no—
248C4—88no—
249C2—24no—
250C2—22no—
251C2—44no—
252C2—84no—
253C2#2309×C13111yescharacteristic
254C2#2883×C13112yes—
subgroupG/H
center, socleC22×C131C22×C22⋊C4
commutatorC23C23×C4×C131
Frattini, cosocleC24C24×C131
prime radicalC2×#534×C131C2
LCSG ▷ C23 ▷ C2 ▷ C1
UCSC1 ◁ C22×C131 ◁ C22×C22⋊C4×C131 ◁ G

Complements

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

NH ≅ G/Ntype
2. #2312×C131C2semidirect
3. #1964×C131C2semidirect
4. #1781×C131C2semidirect
7. C2×#123×C131C4semidirect
9. C2×#120×C131C4semidirect
11. C2×#99×C131C22semidirect
13. #380×C131C22semidirect
15. C4×C22⋊C4×C131C22semidirect
127. #21795C131direct (N × H)
128. C131#21795direct (N × H)
130. #2312C2×C131semidirect
131. #1964C2×C131semidirect
132. #1781C2×C131semidirect
135. C2×#123C4×C131semidirect
137. C2×#120C4×C131semidirect
139. C2×#99C22×C131semidirect
141. #380C22×C131semidirect
143. C4×C22⋊C4C22×C131semidirect

Maximal subgroups

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

subgroupindex
C2×#534×C1312
#2312×C1312
#1964×C1312
#1781×C1312
#21795131