Finite Group Databasebeta

← C131×#34348 #45720232

Subgroups — C131×#34348 #45720232

Order 33536.

1898 conjugacy classes of subgroups.

The subgroup lattice has 244 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#533×C131C211yesmaximal, characteristic
2#2382×C131C214yesmaximal, complemented
3#2381×C131C214yesmaximal, complemented
4#2378×C131C218yesmaximal
5#2298×C131C214yesmaximal
6#2295×C131C218yesmaximal, complemented
7#2283×C131C212yesmaximal
8#533×C131C4116yescomplemented
9C2×C4⋊Q8×C131C2212yes—
10C2×#125×C131C2212yes—
11C2×C22⋊Q8×C131C2214yes—
12C2×C4×Q8×C131C2214yes—
13C2×#117×C131C2212yes—
14C22×C42×C131C2211yescharacteristic
15#391×C131C22116yes—
16#389×C131C22116yes—
17#388×C131C22116yes—
18#387×C131C22116yes—
19#387×C131C22116yes—
20#387×C131C22116yes—
21#383×C131C2214yes—
22#382×C131C2214yes—
23#381×C131C2214yes—
24#380×C131C2214yes—
25C4×C4⋊C4×C131C2214yes—
26C4×C4⋊C4×C131C2218yes—
27C4×C22⋊C4×C131C2214yes—
28#376×C131C2214yes—
29#376×C131C2214yes—
30C43×C131C2214yes—
31C22×Q8×C131C2314yes—
32C23×C4×C131C2311yescharacteristic
33C23×C4×C131C2312yes—
34C4⋊Q8×C131C2×C4116yes—
35#125×C131C2×C4116yes—
36C22⋊Q8×C131C2×C4132yes—
37C4×Q8×C131C2×C4132yes—
38#117×C131C2×C4116yes—
39C2×C4⋊C4×C131C23116yes—
40C2×C4⋊C4×C131C2318yes—
41C2×C4⋊C4×C131C2318yes—
42C2×C4⋊C4×C131C2314yes—
43C2×C4⋊C4×C131C2314yes—
44C2×C22⋊C4×C131C2318yes—
45C2×C22⋊C4×C131C2314yes—
46C2×C42×C131C2×C418yes—
47C2×C42×C131C2318yes—
48C2×C42×C131C23116yes—
49C2×C42×C131C2311yescharacteristic
50C2×C42×C131C2311yescharacteristic
51C2×C42×C131C2312yes—
52C2×C42×C131C2314yes—
53#95×C131C23116yes—
54#95×C131C23116yes—
55#95×C131C2318yes—
56#95×C131C2318yes—
57#95×C131C2318yes—
58#95×C131C2318yes—
59C24×C131C2411yescharacteristic
60C2×Q8×C131—48no—
61C2×Q8×C131C22×C4116yes—
62C22×C4×C131—24no—
63C22×C4×C131—44no—
64C22×C4×C131C22×C414yes—
65C22×C4×C131C22×C418yes—
66C22×C4×C131C24116yes—
67C22×C4×C131C2411yescharacteristic
68C22×C4×C131C2412yes—
69C22×C4×C131C2418yes—
70C22×C4×C131C2412yes—
71C22×C4×C131C2411yescharacteristic
72C4⋊C4×C131—416no—
73C4⋊C4×C131—48no—
74C4⋊C4×C131C22×C4116yes—
75C4⋊C4×C131C22×C4132yes—
76C4⋊C4×C131C22×C4116yes—
77C22⋊C4×C131—48no—
78C22⋊C4×C131C22×C4116yes—
79C42×C131—216no—
80C42×C131—416no—
81C42×C131C22×C418yes—
82C42×C131C22×C414yes—
83C42×C131C22×C414yes—
84C42×C131C22×C4116yes—
85C23×C131—22no—
86C23×C131—24no—
87C23×C131C23×C412yes—
88C23×C131C2511yescharacteristic
89Q8×C131—416no—
90C2×C4×C131—22no—
91C2×C4×C131—216no—
92C2×C4×C131—24no—
93C2×C4×C131—24no—
94C2×C4×C131—28no—
95C2×C4×C131—216no—
96C2×C4×C131—216no—
97C2×C4×C131—216no—
98C2×C4×C131—48no—
99C2×C4×C131C23×C412yes—
100C2×C4×C131C23×C414yes—
101C2×C4×C131C23×C414yes—
102C2×C4×C131C23×C4116yes—
103C2×C4×C131C23×C412yes—
104C2×C4×C1312−1+414yes—
105C22×C131—22no—
106C22×C131—24no—
107C22×C131—44no—
108C22×C131C24×C411yescharacteristic
109C22×C131C2×2−1+412yes—
110C22×C131#58514yes—
111C4×C131—22no—
112C4×C131—24no—
113C4×C131—24no—
114C4×C131—216no—
115C4×C131—416no—
116C4×C131#51914yes—
117C2×C131—42no—
118C2×C131C2×#51911yescharacteristic
119C2×C131#342812yes—
120C2×C131#353114yes—
121#34348C13111yesmaximal, characteristic, direct product factor, Sylow
122C131#3434811yescharacteristic, direct product factor, Sylow
123C2×#533C2×C13111yescharacteristic
124#2382C2×C13114yescomplemented
125#2381C2×C13114yescomplemented
126#2378C2×C13118yes—
127#2298C2×C13114yes—
128#2295C2×C13118yescomplemented
129#2283C2×C13112yes—
130#533C4×C131116yescomplemented
131C2×C4⋊Q8C22×C13112yes—
132C2×#125C22×C13112yes—
133C2×C22⋊Q8C22×C13114yes—
134C2×C4×Q8C22×C13114yes—
135C2×#117C22×C13112yes—
136C22×C42C22×C13111yescharacteristic
137#391C22×C131116yes—
138#389C22×C131116yes—
139#388C22×C131116yes—
140#387C22×C131116yes—
141#387C22×C131116yes—
142#387C22×C131116yes—
143#383C22×C13114yes—
144#382C22×C13114yes—
145#381C22×C13114yes—
146#380C22×C13114yes—
147C4×C4⋊C4C22×C13114yes—
148C4×C4⋊C4C22×C13118yes—
149C4×C22⋊C4C22×C13114yes—
150#376C22×C13114yes—
151#376C22×C13114yes—
152C43C22×C13114yes—
153C22×Q8C23×C13114yes—
154C23×C4C23×C13111yescharacteristic
155C23×C4C23×C13112yes—
156C4⋊Q8C2×C4×C131116yes—
157#125C2×C4×C131116yes—
158C22⋊Q8C2×C4×C131132yes—
159C4×Q8C2×C4×C131132yes—
160#117C2×C4×C131116yes—
161C2×C4⋊C4C23×C13118yes—
162C2×C4⋊C4C23×C131116yes—
163C2×C4⋊C4C23×C13114yes—
164C2×C4⋊C4C23×C13118yes—
165C2×C4⋊C4C23×C13114yes—
166C2×C22⋊C4C23×C13118yes—
167C2×C22⋊C4C23×C13114yes—
168C2×C42C2×C4×C13118yes—
169C2×C42C23×C13118yes—
170C2×C42C23×C131116yes—
171C2×C42C23×C13114yes—
172C2×C42C23×C13112yes—
173C2×C42C23×C13111yescharacteristic
174C2×C42C23×C13111yescharacteristic
175#95C23×C13118yes—
176#95C23×C13118yes—
177#95C23×C131116yes—
178#95C23×C13118yes—
179#95C23×C13118yes—
180#95C23×C131116yes—
181C24C24×C13111yescharacteristic
182C2×Q8—48no—
183C2×Q8C22×C4×C131116yes—
184C22×C4—24no—
185C22×C4—44no—
186C22×C4C22×C4×C13114yes—
187C22×C4C22×C4×C13118yes—
188C22×C4C24×C131116yes—
189C22×C4C24×C13111yescharacteristic
190C22×C4C24×C13112yes—
191C22×C4C24×C13118yes—
192C22×C4C24×C13112yes—
193C22×C4C24×C13111yescharacteristic
194C4⋊C4—416no—
195C4⋊C4—48no—
196C4⋊C4C22×C4×C131116yes—
197C4⋊C4C22×C4×C131132yes—
198C4⋊C4C22×C4×C131116yes—
199C22⋊C4—48no—
200C22⋊C4C22×C4×C131116yes—
201C42—216no—
202C42—416no—
203C42C22×C4×C13118yes—
204C42C22×C4×C13114yes—
205C42C22×C4×C13114yes—
206C42C22×C4×C131116yes—
207C23—22no—
208C23—24no—
209C23C23×C4×C13112yes—
210C23C25×C13111yescharacteristic
211Q8—416no—
212C2×C4—22no—
213C2×C4—216no—
214C2×C4—24no—
215C2×C4—24no—
216C2×C4—28no—
217C2×C4—216no—
218C2×C4—216no—
219C2×C4—216no—
220C2×C4—48no—
221C2×C4C23×C4×C13112yes—
222C2×C4C23×C4×C13114yes—
223C2×C4C23×C4×C13114yes—
224C2×C4C23×C4×C131116yes—
225C2×C4C23×C4×C13112yes—
226C2×C42−1+4×C13114yes—
227C22—22no—
228C22—24no—
229C22—44no—
230C22C24×C4×C13111yescharacteristic
231C22C2×2−1+4×C13112yes—
232C22#585×C13114yes—
233C4—22no—
234C4—24no—
235C4—24no—
236C4—216no—
237C4—416no—
238C4#519×C13114yes—
239C2—42no—
240C2C2×#519×C13111yescharacteristic
241C2#3428×C13112yes—
242C2#3531×C13114yes—
subgroupG/H
centerC22×C4×C131C24
commutatorC22C24×C4×C131
Frattini, cosocleC23C25×C131
socleC23×C131C25
prime radicalC24×C131C24
LCSG ▷ C22 ▷ C1
UCSC1 ◁ C22×C4×C131 ◁ G

Complements

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

NH ≅ G/Ntype
2. #2382×C131C2semidirect
3. #2381×C131C2semidirect
6. #2295×C131C2semidirect
8. #533×C131C4semidirect
121. #34348C131direct (N × H)
122. C131#34348direct (N × H)
124. #2382C2×C131semidirect
125. #2381C2×C131semidirect
128. #2295C2×C131semidirect
130. #533C4×C131semidirect

Maximal subgroups

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

subgroupindex
C2×#533×C1312
#2382×C1312
#2381×C1312
#2378×C1312
#2298×C1312
#2295×C1312
#2283×C1312
#34348131