Finite Group Databasebeta

← C131×#7632 #45693516

Subgroups — C131×#7632 #45693516

Order 33536.

590 conjugacy classes of subgroups; only the 142 normal subgroups are shown.

normal subgroups only

This group has 590 conjugacy classes of subgroups — too many to draw. Only its 142 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#2296×C131C211yesmaximal, characteristic
2#1728×C131C212yesmaximal
3#1271×C131C214yesmaximal, complemented
4C22×M16×C131—22no—
5C2×#117×C131C411yescharacteristic
6C2×#117×C131C411yescharacteristic
7C22×C42×C131C2211yescharacteristic
8#389×C131C412yes—
9#389×C131C2212yes—
10#385×C131—22no—
11C4×C4⋊C4×C131—22no—
12#336×C131—22no—
13#336×C131C2214yes—
14C23×C4×C131C2×C411yescharacteristic
15C23×C4×C131D412yes—
16C2×M16×C131—28no—
17C2×M16×C131—44no—
18C2×M16×C131—44no—
19C22×C8×C131—24no—
20#117×C131—24no—
21#117×C131—42no—
22C2×C4⋊C4×C131—22no—
23C2×C4⋊C4×C131—22no—
24C2×C4⋊C4×C131C2×C412yes—
25C2×C4⋊C4×C131C2×C412yes—
26C2×C22⋊C4×C131—21no—
27C2×C22⋊C4×C131—21no—
28C2×C42×C131—21no—
29C2×C42×C131—21no—
30C2×C42×C131—42no—
31C2×C42×C131C2×C411yescharacteristic
32C2×C42×C131D412yes—
33C2×C42×C131C2311yescharacteristic
34#95×C131—22no—
35#95×C131—22no—
36C24×C131C22⋊C411yescharacteristic
37C22×C4×C131—22no—
38C22×C4×C131—24no—
39C22×C4×C131—22no—
40C22×C4×C131—24no—
41C22×C4×C131—22no—
42C22×C4×C131—22no—
43C22×C4×C131—22no—
44C22×C4×C131—22no—
45C22×C4×C131—22no—
46C22×C4×C131C22⋊C411yescharacteristic
47C22×C4×C131C22⋊C412yes—
48C22×C4×C131C22×C411yescharacteristic
49C22×C4×C131C2×D412yes—
50M16×C131—416no—
51C2×C8×C131—28no—
52C2×C8×C131—44no—
53C2×C8×C131—44no—
54C4⋊C4×C131—22no—
55C4⋊C4×C131—42no—
56C4⋊C4×C131—44no—
57C4⋊C4×C131—42no—
58C4⋊C4×C131—42no—
59C4⋊C4×C131M1614yescomplemented
60C22⋊C4×C131—24no—
61C22⋊C4×C131—42no—
62C42×C131—24no—
63C42×C131—41no—
64C42×C131—42no—
65C42×C131—41no—
66C42×C131—42no—
67C23×C131—21no—
68C23×C131—21no—
69C23×C131—22no—
70C23×C131—22no—
71C23×C131#9912yes—
72C23×C131C2×C22⋊C411yescharacteristic
73C2×C4×C131—28no—
74C2×C4×C131—28no—
75C2×C4×C131—28no—
76C2×C4×C131—21no—
77C2×C4×C131—21no—
78C2×C4×C131—21no—
79C2×C4×C131—22no—
80C2×C4×C131—22no—
81C2×C4×C131—21no—
82C2×C4×C131—22no—
83C2×C4×C131—22no—
84C2×C4×C131—24no—
85C2×C4×C131—42no—
86C2×C4×C131—42no—
87C2×C4×C131—42no—
88C2×C4×C131—42no—
89C2×C4×C131—42no—
90C2×C4×C131#10112yes—
91C2×C4×C131#10414yes—
92C2×C4×C131C2×M1612yes—
93C2×C4×C131AGL(1,ℤ/8)12yes—
94C2×C4×C131#13712yes—
95C8×C131—48no—
96C22×C131—22no—
97C22×C131—24no—
98C22×C131—41no—
99C22×C131—42no—
100C22×C131—41no—
101C22×C131#40711yescharacteristic
102C22×C131C2×#9911yescharacteristic
103C22×C131C2×#10111yescharacteristic
104C22×C131#41712yes—
105C22×C131C2×#10412yes—
106C4×C131—22no—
107C4×C131—22no—
108C4×C131—22no—
109C4×C131—24no—
110C4×C131—22no—
111C4×C131—44no—
112C4×C131—82no—
113C2×C131—42no—
114C2×C131#146311yescharacteristic
115C2×C131#148912yes—
116C2×C131#150412yes—
117C2×C131#152611yescharacteristic
118C2×C131#156111yescharacteristic
119#7632C13111yesmaximal, characteristic, direct product factor, Sylow
120C131#763211yescharacteristic, direct product factor, Sylow
121#2296C2×C13111yescharacteristic
122#1728C2×C13112yes—
123#1271C2×C13114yescomplemented
124C22×M16—22no—
125C2×#117C4×C13111yescharacteristic
126C2×#117C4×C13111yescharacteristic
127C22×C42C22×C13111yescharacteristic
128#389C4×C13112yes—
129#389C22×C13112yes—
130#385—22no—
131C4×C4⋊C4—22no—
132#336—22no—
133#336C22×C13114yes—
134C23×C4C2×C4×C13111yescharacteristic
135C23×C4D4×C13112yes—
136C2×M16—28no—
137C2×M16—44no—
138C2×M16—44no—
139C22×C8—24no—
140#117—24no—
141#117—42no—
142C2×C4⋊C4—22no—
143C2×C4⋊C4—22no—
144C2×C4⋊C4C2×C4×C13112yes—
145C2×C4⋊C4C2×C4×C13112yes—
146C2×C22⋊C4—21no—
147C2×C22⋊C4—21no—
148C2×C42—21no—
149C2×C42—21no—
150C2×C42—42no—
151C2×C42C2×C4×C13111yescharacteristic
152C2×C42D4×C13112yes—
153C2×C42C23×C13111yescharacteristic
154#95—22no—
155#95—22no—
156C24C22⋊C4×C13111yescharacteristic
157C22×C4—22no—
158C22×C4—24no—
159C22×C4—22no—
160C22×C4—24no—
161C22×C4—22no—
162C22×C4—22no—
163C22×C4—22no—
164C22×C4—22no—
165C22×C4—22no—
166C22×C4C22⋊C4×C13111yescharacteristic
167C22×C4C22⋊C4×C13112yes—
168C22×C4C22×C4×C13111yescharacteristic
169C22×C4C2×D4×C13112yes—
170M16—416no—
171C2×C8—28no—
172C2×C8—44no—
173C2×C8—44no—
174C4⋊C4—22no—
175C4⋊C4—42no—
176C4⋊C4—44no—
177C4⋊C4—42no—
178C4⋊C4—42no—
179C4⋊C4M16×C13114yescomplemented
180C22⋊C4—24no—
181C22⋊C4—42no—
182C42—24no—
183C42—41no—
184C42—42no—
185C42—41no—
186C42—42no—
187C23—21no—
188C23—21no—
189C23—22no—
190C23—22no—
191C23#99×C13112yes—
192C23C2×C22⋊C4×C13111yescharacteristic
193C2×C4—28no—
194C2×C4—28no—
195C2×C4—28no—
196C2×C4—21no—
197C2×C4—21no—
198C2×C4—21no—
199C2×C4—22no—
200C2×C4—22no—
201C2×C4—21no—
202C2×C4—22no—
203C2×C4—22no—
204C2×C4—24no—
205C2×C4—42no—
206C2×C4—42no—
207C2×C4—42no—
208C2×C4—42no—
209C2×C4—42no—
210C2×C4#101×C13112yes—
211C2×C4#104×C13114yes—
212C2×C4C2×M16×C13112yes—
213C2×C4AGL(1,ℤ/8)×C13112yes—
214C2×C4#137×C13112yes—
215C8—48no—
216C22—22no—
217C22—24no—
218C22—42no—
219C22—41no—
220C22—41no—
221C22#407×C13111yescharacteristic
222C22C2×#99×C13111yescharacteristic
223C22C2×#101×C13111yescharacteristic
224C22#417×C13112yes—
225C22C2×#104×C13112yes—
226C4—22no—
227C4—22no—
228C4—22no—
229C4—24no—
230C4—22no—
231C4—44no—
232C4—82no—
233C2—42no—
234C2#1463×C13111yescharacteristic
235C2#1489×C13112yes—
236C2#1504×C13112yes—
237C2#1526×C13111yescharacteristic
238C2#1561×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. #1271×C131C2semidirect
59. C4⋊C4×C131M16semidirect
119. #7632C131direct (N × H)
120. C131#7632direct (N × H)
123. #1271C2×C131semidirect
179. C4⋊C4M16×C131semidirect

Maximal subgroups

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

subgroupindex
#2296×C1312
#1728×C1312
#1271×C1312
#7632131