Finite Group Databasebeta

← C131×#11512 #45697396

Subgroups — C131×#11512 #45697396

Order 33536.

578 conjugacy classes of subgroups; only the 118 normal subgroups are shown.

normal subgroups only

This group has 578 conjugacy classes of subgroups — too many to draw. Only its 118 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×#384×C131C211yesmaximal, characteristic
2#1463×C131C212yesmaximal
3#1325×C131C214yesmaximal, complemented
4C22×C4⋊C4×C131—22no—
5C22×C4⋊C4×C131C411yescharacteristic
6C22×C4⋊C4×C131C2211yescharacteristic
7C22×C42×C131C411yescharacteristic
8#407×C131—22no—
9#384×C131—22no—
10#384×C131C412yes—
11#384×C131C2212yes—
12#324×C131—22no—
13#324×C131C2214yes—
14C23×C4×C131—21no—
15C23×C4×C131—21no—
16C23×C4×C131C2×C411yescharacteristic
17C23×C4×C131D412yes—
18C2×M16×C131—42no—
19C2×C4⋊C4×C131—24no—
20C2×C4⋊C4×C131—21no—
21C2×C4⋊C4×C131—24no—
22C2×C4⋊C4×C131—41no—
23C2×C4⋊C4×C131—41no—
24C2×C4⋊C4×C131—48no—
25C2×C4⋊C4×C131—41no—
26C2×C4⋊C4×C131—41no—
27C2×C4⋊C4×C131C2×C412yes—
28C2×C4⋊C4×C131C2×C411yescharacteristic
29C2×C4⋊C4×C131D412yes—
30C2×C4⋊C4×C131C2311yescharacteristic
31C2×C42×C131—21no—
32C2×C42×C131—24no—
33C2×C42×C131C2×C412yes—
34C22⋊C8×C131—24no—
35C22⋊C8×C131—42no—
36C24×C131C22⋊C411yescharacteristic
37C22×C4×C131—24no—
38C22×C4×C131—24no—
39C22×C4×C131—24no—
40C22×C4×C131—21no—
41C22×C4×C131—21no—
42C22×C4×C131—22no—
43C22×C4×C131—22no—
44C22×C4×C131—22no—
45C22×C4×C131—22no—
46C22×C4×C131—22no—
47C22×C4×C131—22no—
48C22×C4×C131—44no—
49C22×C4×C131—44no—
50C22×C4×C131—41no—
51C22×C4×C131—41no—
52C22×C4×C131C22⋊C411yescharacteristic
53C22×C4×C131C22⋊C412yes—
54C22×C4×C131C22×C411yescharacteristic
55C22×C4×C131C2×D412yes—
56M16×C131—84no—
57C2×C8×C131—44no—
58C4⋊C4×C131—41no—
59C4⋊C4×C131—42no—
60C4⋊C4×C131—41no—
61C4⋊C4×C131—42no—
62C4⋊C4×C131—48no—
63C4⋊C4×C131—48no—
64C4⋊C4×C131—42no—
65C42×C131—24no—
66C42×C131—22no—
67C42×C131M1614yescomplemented
68C23×C131—22no—
69C23×C131—22no—
70C23×C131—21no—
71C23×C131—21no—
72C23×C131#9911yescharacteristic
73C23×C131#9911yescharacteristic
74C23×C131C2×C22⋊C411yescharacteristic
75C2×C4×C131—24no—
76C2×C4×C131—216no—
77C2×C4×C131—24no—
78C2×C4×C131—24no—
79C2×C4×C131—24no—
80C2×C4×C131—21no—
81C2×C4×C131—24no—
82C2×C4×C131—21no—
83C2×C4×C131—21no—
84C2×C4×C131—21no—
85C2×C4×C131—22no—
86C2×C4×C131—22no—
87C2×C4×C131—44no—
88C2×C4×C131—42no—
89C2×C4×C131—42no—
90C2×C4×C131—44no—
91C2×C4×C131—42no—
92C2×C4×C131—82no—
93C2×C4×C131—82no—
94C2×C4×C131—82no—
95C2×C4×C131#10112yes—
96C2×C4×C131C2×M1612yes—
97C8×C131—84no—
98C22×C131—24no—
99C22×C131—24no—
100C22×C131—21no—
101C22×C131—21no—
102C22×C131—21no—
103C22×C131—21no—
104C22×C131—21no—
105C22×C131—21no—
106C22×C131#35312yes—
107C22×C131#35612yes—
108C22×C131#40711yescharacteristic
109C22×C131C2×#9911yescharacteristic
110C22×C131C2×#10111yescharacteristic
111C4×C131—28no—
112C4×C131—22no—
113C4×C131—22no—
114C4×C131—42no—
115C4×C131—42no—
116C4×C131—82no—
117C2×C131—21no—
118C2×C131—22no—
119C2×C131—22no—
120C2×C131—21no—
121C2×C131#146311yescharacteristic
122C2×C131C2×#35311yescharacteristic
123C2×C131C2×#35611yescharacteristic
124#11512C13111yesmaximal, characteristic, direct product factor, Sylow
125C131#1151211yescharacteristic, direct product factor, Sylow
126C2×#384C2×C13111yescharacteristic
127#1463C2×C13112yes—
128#1325C2×C13114yescomplemented
129C22×C4⋊C4—22no—
130C22×C4⋊C4C4×C13111yescharacteristic
131C22×C4⋊C4C22×C13111yescharacteristic
132C22×C42C4×C13111yescharacteristic
133#407—22no—
134#384—22no—
135#384C4×C13112yes—
136#384C22×C13112yes—
137#324—22no—
138#324C22×C13114yes—
139C23×C4—21no—
140C23×C4—21no—
141C23×C4C2×C4×C13111yescharacteristic
142C23×C4D4×C13112yes—
143C2×M16—42no—
144C2×C4⋊C4—24no—
145C2×C4⋊C4—21no—
146C2×C4⋊C4—24no—
147C2×C4⋊C4—41no—
148C2×C4⋊C4—41no—
149C2×C4⋊C4—41no—
150C2×C4⋊C4—41no—
151C2×C4⋊C4—48no—
152C2×C4⋊C4C2×C4×C13112yes—
153C2×C4⋊C4C2×C4×C13111yescharacteristic
154C2×C4⋊C4D4×C13112yes—
155C2×C4⋊C4C23×C13111yescharacteristic
156C2×C42—21no—
157C2×C42—24no—
158C2×C42C2×C4×C13112yes—
159C22⋊C8—24no—
160C22⋊C8—42no—
161C24C22⋊C4×C13111yescharacteristic
162C22×C4—24no—
163C22×C4—24no—
164C22×C4—24no—
165C22×C4—21no—
166C22×C4—21no—
167C22×C4—22no—
168C22×C4—22no—
169C22×C4—22no—
170C22×C4—22no—
171C22×C4—22no—
172C22×C4—22no—
173C22×C4—44no—
174C22×C4—44no—
175C22×C4—41no—
176C22×C4—41no—
177C22×C4C22⋊C4×C13111yescharacteristic
178C22×C4C22⋊C4×C13112yes—
179C22×C4C22×C4×C13111yescharacteristic
180C22×C4C2×D4×C13112yes—
181M16—84no—
182C2×C8—44no—
183C4⋊C4—41no—
184C4⋊C4—42no—
185C4⋊C4—41no—
186C4⋊C4—42no—
187C4⋊C4—48no—
188C4⋊C4—48no—
189C4⋊C4—42no—
190C42—24no—
191C42—22no—
192C42M16×C13114yescomplemented
193C23—21no—
194C23—21no—
195C23—22no—
196C23—22no—
197C23#99×C13111yescharacteristic
198C23#99×C13111yescharacteristic
199C23C2×C22⋊C4×C13111yescharacteristic
200C2×C4—24no—
201C2×C4—216no—
202C2×C4—24no—
203C2×C4—24no—
204C2×C4—24no—
205C2×C4—21no—
206C2×C4—24no—
207C2×C4—21no—
208C2×C4—21no—
209C2×C4—21no—
210C2×C4—22no—
211C2×C4—22no—
212C2×C4—44no—
213C2×C4—42no—
214C2×C4—42no—
215C2×C4—44no—
216C2×C4—42no—
217C2×C4—82no—
218C2×C4—82no—
219C2×C4—82no—
220C2×C4#101×C13112yes—
221C2×C4C2×M16×C13112yes—
222C8—84no—
223C22—24no—
224C22—24no—
225C22—21no—
226C22—21no—
227C22—21no—
228C22—21no—
229C22—21no—
230C22—21no—
231C22#353×C13112yes—
232C22#356×C13112yes—
233C22#407×C13111yescharacteristic
234C22C2×#99×C13111yescharacteristic
235C22C2×#101×C13111yescharacteristic
236C4—28no—
237C4—22no—
238C4—22no—
239C4—42no—
240C4—42no—
241C4—82no—
242C2—21no—
243C2—21no—
244C2—22no—
245C2—22no—
246C2#1463×C13111yescharacteristic
247C2C2×#353×C13111yescharacteristic
248C2C2×#356×C13111yescharacteristic
subgroupG/H
center, socleC22×C131C2×#99
commutatorC22×C4C22×C4×C131
Frattini, cosocleC2×C4⋊C4C23×C131
prime radicalC24×C131C22⋊C4
LCSG ▷ C22×C4 ▷ C22 ▷ C2 ▷ C1
UCSC1 ◁ C22×C131 ◁ C24×C131 ◁ C22×C4⋊C4×C131 ◁ G

Complements

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

NH ≅ G/Ntype
3. #1325×C131C2semidirect
67. C42×C131M16semidirect
124. #11512C131direct (N × H)
125. C131#11512direct (N × H)
128. #1325C2×C131semidirect
192. C42M16×C131semidirect

Maximal subgroups

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

subgroupindex
C2×#384×C1312
#1463×C1312
#1325×C1312
#11512131