Finite Group Databasebeta

← C131×#7643 #45693527

Subgroups — C131×#7643 #45693527

Order 33536.

646 conjugacy classes of subgroups; only the 174 normal subgroups are shown.

normal subgroups only

This group has 646 conjugacy classes of subgroups — too many to draw. Only its 174 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×#391×C131C211yesmaximal, characteristic
2#1797×C131C212yesmaximal
3#1272×C131C214yesmaximal, complemented
4C23×Q8×C131C411yescharacteristic
5C22×C4⋊C4×C131C411yescharacteristic
6C22×C42×C131C2211yescharacteristic
7C2×C4⋊C8×C131—22no—
8C2×C22⋊C8×C131—22no—
9#391×C131—22no—
10#391×C131C412yes—
11#391×C131C2212yes—
12C2×#95×C131—22no—
13#336×C131C2214yes—
14C22×Q8×C131—24no—
15C22×Q8×C131—21no—
16C22×Q8×C131—42no—
17C22×Q8×C131—42no—
18C22×Q8×C131C2×C412yes—
19C23×C4×C131—21no—
20C23×C4×C131—21no—
21C23×C4×C131C2×C411yescharacteristic
22C23×C4×C131D412yes—
23C22×C8×C131—24no—
24C2×C4⋊C4×C131—21no—
25C2×C4⋊C4×C131—42no—
26C2×C4⋊C4×C131C2×C412yes—
27C2×C42×C131—42no—
28C2×C42×C131C2×C411yescharacteristic
29C2×C42×C131D412yes—
30C2×C42×C131C2311yescharacteristic
31C4⋊C8×C131—44no—
32C22⋊C8×C131—44no—
33#95×C131—24no—
34#95×C131—24no—
35C24×C131C22⋊C411yescharacteristic
36C2×Q8×C131—24no—
37C2×Q8×C131—22no—
38C2×Q8×C131—416no—
39C2×Q8×C131—42no—
40C2×Q8×C131—42no—
41C2×Q8×C131—42no—
42C2×Q8×C131—42no—
43C2×Q8×C131M1614yes—
44C22×C4×C131—22no—
45C22×C4×C131—22no—
46C22×C4×C131—22no—
47C22×C4×C131—24no—
48C22×C4×C131—22no—
49C22×C4×C131—22no—
50C22×C4×C131—42no—
51C22×C4×C131—42no—
52C22×C4×C131—42no—
53C22×C4×C131—42no—
54C22×C4×C131—44no—
55C22×C4×C131—42no—
56C22×C4×C131C22⋊C411yescharacteristic
57C22×C4×C131C22⋊C412yes—
58C22×C4×C131SD1614yes—
59C22×C4×C131Q1614yes—
60C22×C4×C131C22×C411yescharacteristic
61C22×C4×C131C2×D412yes—
62C2×C8×C131—44no—
63C2×C8×C131—44no—
64C2×C8×C131—44no—
65C4⋊C4×C131—42no—
66C4⋊C4×C131—42no—
67C42×C131—24no—
68C42×C131—41no—
69C42×C131—41no—
70C23×C131—21no—
71C23×C131—21no—
72C23×C131—22no—
73C23×C131#10012yes—
74C23×C131#10314yes—
75C23×C131C2×C22⋊C411yescharacteristic
76Q8×C131—44no—
77Q8×C131—48no—
78Q8×C131—44no—
79C2×C4×C131—28no—
80C2×C4×C131—21no—
81C2×C4×C131—22no—
82C2×C4×C131—22no—
83C2×C4×C131—21no—
84C2×C4×C131—21no—
85C2×C4×C131—21no—
86C2×C4×C131—22no—
87C2×C4×C131—22no—
88C2×C4×C131—24no—
89C2×C4×C131—44no—
90C2×C4×C131—44no—
91C2×C4×C131—48no—
92C2×C4×C131—42no—
93C2×C4×C131—42no—
94C2×C4×C131—42no—
95C2×C4×C131—44no—
96C2×C4×C131—84no—
97C2×C4×C131#9912yes—
98C2×C4×C131#10314yes—
99C2×C4×C131C2×M1612yes—
100C2×C4×C131C2×SD1612yes—
101C2×C4×C131C2×Q1612yes—
102C8×C131—84no—
103C22×C131—22no—
104C22×C131—24no—
105C22×C131—24no—
106C22×C131—22no—
107C22×C131#33314yes—
108C22×C131#40711yescharacteristic
109C22×C131C2×#9911yescharacteristic
110C22×C131C2×#10011yescharacteristic
111C22×C131C2×#10312yes—
112C22×C131#42112yes—
113C4×C131—22no—
114C4×C131—22no—
115C4×C131—22no—
116C4×C131—24no—
117C4×C131—22no—
118C4×C131—44no—
119C4×C131—82no—
120C2×C131—24no—
121C2×C131#146211yescharacteristic
122C2×C131#148712yes—
123C2×C131#152012yes—
124C2×C131#153311yescharacteristic
125C2×C131C2×#33311yescharacteristic
126#7643C13111yesmaximal, characteristic, direct product factor, Sylow
127C131#764311yescharacteristic, direct product factor, Sylow
128C2×#391C2×C13111yescharacteristic
129#1797C2×C13112yes—
130#1272C2×C13114yescomplemented
131C23×Q8C4×C13111yescharacteristic
132C22×C4⋊C4C4×C13111yescharacteristic
133C22×C42C22×C13111yescharacteristic
134C2×C4⋊C8—22no—
135C2×C22⋊C8—22no—
136#391—22no—
137#391C4×C13112yes—
138#391C22×C13112yes—
139C2×#95—22no—
140#336C22×C13114yes—
141C22×Q8—24no—
142C22×Q8—21no—
143C22×Q8—42no—
144C22×Q8—42no—
145C22×Q8C2×C4×C13112yes—
146C23×C4—21no—
147C23×C4—21no—
148C23×C4C2×C4×C13111yescharacteristic
149C23×C4D4×C13112yes—
150C22×C8—24no—
151C2×C4⋊C4—21no—
152C2×C4⋊C4—42no—
153C2×C4⋊C4C2×C4×C13112yes—
154C2×C42—42no—
155C2×C42C2×C4×C13111yescharacteristic
156C2×C42D4×C13112yes—
157C2×C42C23×C13111yescharacteristic
158C4⋊C8—44no—
159C22⋊C8—44no—
160#95—24no—
161#95—24no—
162C24C22⋊C4×C13111yescharacteristic
163C2×Q8—24no—
164C2×Q8—22no—
165C2×Q8—416no—
166C2×Q8—42no—
167C2×Q8—42no—
168C2×Q8—42no—
169C2×Q8—42no—
170C2×Q8M16×C13114yes—
171C22×C4—22no—
172C22×C4—22no—
173C22×C4—22no—
174C22×C4—24no—
175C22×C4—22no—
176C22×C4—22no—
177C22×C4—42no—
178C22×C4—42no—
179C22×C4—42no—
180C22×C4—42no—
181C22×C4—44no—
182C22×C4—42no—
183C22×C4C22⋊C4×C13111yescharacteristic
184C22×C4C22⋊C4×C13112yes—
185C22×C4SD16×C13114yes—
186C22×C4Q16×C13114yes—
187C22×C4C22×C4×C13111yescharacteristic
188C22×C4C2×D4×C13112yes—
189C2×C8—44no—
190C2×C8—44no—
191C2×C8—44no—
192C4⋊C4—42no—
193C4⋊C4—42no—
194C42—24no—
195C42—41no—
196C42—41no—
197C23—21no—
198C23—21no—
199C23—22no—
200C23#100×C13112yes—
201C23#103×C13114yes—
202C23C2×C22⋊C4×C13111yescharacteristic
203Q8—44no—
204Q8—48no—
205Q8—44no—
206C2×C4—28no—
207C2×C4—21no—
208C2×C4—22no—
209C2×C4—22no—
210C2×C4—21no—
211C2×C4—21no—
212C2×C4—21no—
213C2×C4—22no—
214C2×C4—22no—
215C2×C4—24no—
216C2×C4—44no—
217C2×C4—44no—
218C2×C4—48no—
219C2×C4—42no—
220C2×C4—42no—
221C2×C4—42no—
222C2×C4—44no—
223C2×C4—84no—
224C2×C4#99×C13112yes—
225C2×C4#103×C13114yes—
226C2×C4C2×M16×C13112yes—
227C2×C4C2×SD16×C13112yes—
228C2×C4C2×Q16×C13112yes—
229C8—84no—
230C22—22no—
231C22—24no—
232C22—24no—
233C22—22no—
234C22#333×C13114yes—
235C22#407×C13111yescharacteristic
236C22C2×#99×C13111yescharacteristic
237C22C2×#100×C13111yescharacteristic
238C22C2×#103×C13112yes—
239C22#421×C13112yes—
240C4—22no—
241C4—22no—
242C4—22no—
243C4—24no—
244C4—22no—
245C4—44no—
246C4—82no—
247C2—24no—
248C2#1462×C13111yescharacteristic
249C2#1487×C13112yes—
250C2#1520×C13112yes—
251C2#1533×C13111yescharacteristic
252C2C2×#333×C13111yescharacteristic
subgroupG/H
center, socleC23×C131C2×C22⋊C4
commutatorC22×C4C22×C4×C131
Frattini, cosocleC2×C42C23×C131
prime radicalC24×C131C22⋊C4
LCSG ▷ C22×C4 ▷ C22 ▷ C1
UCSC1 ◁ C23×C131 ◁ C22×C42×C131 ◁ G

Complements

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

NH ≅ G/Ntype
3. #1272×C131C2semidirect
126. #7643C131direct (N × H)
127. C131#7643direct (N × H)
130. #1272C2×C131semidirect

Maximal subgroups

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

subgroupindex
C2×#391×C1312
#1797×C1312
#1272×C1312
#7643131