Finite Group Databasebeta

← C131×#10432 #45696316

Subgroups — C131×#10432 #45696316

Order 33536.

630 conjugacy classes of subgroups; only the 146 normal subgroups are shown.

normal subgroups only

This group has 630 conjugacy classes of subgroups — too many to draw. Only its 146 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#2537×C131C211yesmaximal, characteristic
2#1844×C131C211yesmaximal, characteristic, complemented
3#1802×C131C212yesmaximal, complemented
4C2×D4⋊C8×C131C212yesmaximal, complemented
5#1296×C131C211yesmaximal, characteristic, complemented
6C2×#121×C131—22no—
7C2×C4×D4×C131C2212yes—
8C2×#106×C131—22no—
9C2×C4⋊C8×C131C2212yes—
10C2×#102×C131—22no—
11C2×C4×C8×C131C2211yescharacteristic
12#394×C131—22no—
13#384×C131C2211yescharacteristic
14#384×C131C2211yescharacteristic
15#380×C131—22no—
16#340×C131—22no—
17D4⋊C8×C131—24no—
18C22×D4×C131—22no—
19C22×D4×C131D412yes—
20C23×C4×C131—22no—
21C22×C8×C131—21no—
22C22×C8×C131—22no—
23#121×C131—44no—
24#121×C131—44no—
25C4×D4×C131—22no—
26C4×D4×C131—22no—
27C4×D4×C131—22no—
28C4×D4×C131—22no—
29C2×C4⋊C4×C131—22no—
30C2×C4⋊C4×C131—22no—
31C2×C4⋊C4×C131—21no—
32C2×C4⋊C4×C131D412yes—
33C2×C4⋊C4×C131D412yes—
34C2×C22⋊C4×C131—24no—
35C2×C22⋊C4×C131—22no—
36C2×C42×C131C2311yescharacteristic
37#106×C131—44no—
38C4⋊C8×C131—22no—
39C4⋊C8×C131—22no—
40#102×C131—44no—
41C4×C8×C131—21no—
42C4×C8×C131D412yescomplemented
43#95×C131—22no—
44C24×C131—22no—
45C2×D4×C131—22no—
46C2×D4×C131—22no—
47C2×D4×C131—22no—
48C2×D4×C131—22no—
49C2×D4×C131—22no—
50C2×D4×C131—48no—
51C2×D4×C131—82no—
52C2×D4×C131SD1614yes—
53C22×C4×C131—22no—
54C22×C4×C131—22no—
55C22×C4×C131—42no—
56C22×C4×C131—42no—
57C22×C4×C131—42no—
58C22×C4×C131—42no—
59C22×C4×C131—42no—
60C22×C4×C131—42no—
61C22×C4×C131—41no—
62C22×C4×C131C2×D411yescharacteristic
63C22×C4×C131C2×D412yes—
64C2×C8×C131—22no—
65C2×C8×C131—22no—
66C2×C8×C131—22no—
67C2×C8×C131—42no—
68C2×C8×C131—42no—
69C2×C8×C131—42no—
70C4⋊C4×C131—22no—
71C4⋊C4×C131—22no—
72C4⋊C4×C131—42no—
73C4⋊C4×C131—42no—
74C4⋊C4×C131—42no—
75C4⋊C4×C131—42no—
76C4⋊C4×C131—42no—
77C4⋊C4×C131—42no—
78C22⋊C4×C131—48no—
79C22⋊C4×C131—42no—
80C22⋊C4×C131—42no—
81C42×C131C2×D411yescharacteristic
82C42×C131#4111yescharacteristic
83C42×C131#4112yes—
84C23×C131—24no—
85C23×C131—42no—
86C23×C131—42no—
87C23×C131—42no—
88C23×C131—42no—
89C23×C131—42no—
90C23×C131—42no—
91C23×C131#12011yescharacteristic
92D4×C131—24no—
93D4×C131—24no—
94D4×C131—42no—
95D4×C131—42no—
96D4×C131—88no—
97C2×C4×C131—21no—
98C2×C4×C131—21no—
99C2×C4×C131—42no—
100C2×C4×C131—42no—
101C2×C4×C131—42no—
102C2×C4×C131—44no—
103C2×C4×C131—42no—
104C2×C4×C131—82no—
105C2×C4×C131—82no—
106C2×C4×C131—82no—
107C2×C4×C131—82no—
108C2×C4×C131—82no—
109C2×C4×C131—81no—
110C2×C4×C131#12111yescharacteristic
111C2×C4×C131#12112yes—
112C2×C4×C131#12312yes—
113C2×C4×C131#12411yescharacteristic
114C2×C4×C131C2×SD1612yes—
115C2×C4×C131#13512yes—
116C2×C4×C131AGL(1,ℤ/8)12yes—
117C2×C4×C131AGL(1,ℤ/8)12yes—
118C8×C131—24no—
119C8×C131—82no—
120C22×C131—44no—
121C22×C131—44no—
122C22×C131—44no—
123C22×C131—82no—
124C22×C131—82no—
125C22×C131—82no—
126C22×C131—82no—
127C22×C131#39411yescharacteristic
128C22×C131#44912yes—
129C22×C131#45012yes—
130C22×C131#45311yescharacteristic
131C22×C131#45611yescharacteristic
132C4×C131—21no—
133C4×C131—21no—
134C4×C131—82no—
135C4×C131—82no—
136C4×C131—161no—
137C4×C131#46512yes—
138C4×C131#46912yes—
139C4×C131#48112yes—
140C4×C131#48212yes—
141C2×C131—84no—
142C2×C131#162411yescharacteristic
143C2×C131#162911yescharacteristic
144C2×C131#165412yes—
145C2×C131#203412yes—
146C2×C131#203911yescharacteristic
147#10432C13111yesmaximal, characteristic, direct product factor, Sylow
148C131#1043211yescharacteristic, direct product factor, Sylow
149#2537C2×C13111yescharacteristic
150#1844C2×C13111yescharacteristic, complemented
151#1802C2×C13112yescomplemented
152C2×D4⋊C8C2×C13112yescomplemented
153#1296C2×C13111yescharacteristic, complemented
154C2×#121—22no—
155C2×C4×D4C22×C13112yes—
156C2×#106—22no—
157C2×C4⋊C8C22×C13112yes—
158C2×#102—22no—
159C2×C4×C8C22×C13111yescharacteristic
160#394—22no—
161#384C22×C13111yescharacteristic
162#384C22×C13111yescharacteristic
163#380—22no—
164#340—22no—
165D4⋊C8—24no—
166C22×D4—22no—
167C22×D4D4×C13112yes—
168C23×C4—22no—
169C22×C8—21no—
170C22×C8—22no—
171#121—44no—
172#121—44no—
173C4×D4—22no—
174C4×D4—22no—
175C4×D4—22no—
176C4×D4—22no—
177C2×C4⋊C4—22no—
178C2×C4⋊C4—22no—
179C2×C4⋊C4—21no—
180C2×C4⋊C4D4×C13112yes—
181C2×C4⋊C4D4×C13112yes—
182C2×C22⋊C4—24no—
183C2×C22⋊C4—22no—
184C2×C42C23×C13111yescharacteristic
185#106—44no—
186C4⋊C8—22no—
187C4⋊C8—22no—
188#102—44no—
189C4×C8—21no—
190C4×C8D4×C13112yescomplemented
191#95—22no—
192C24—22no—
193C2×D4—22no—
194C2×D4—22no—
195C2×D4—22no—
196C2×D4—22no—
197C2×D4—22no—
198C2×D4—48no—
199C2×D4—82no—
200C2×D4SD16×C13114yes—
201C22×C4—22no—
202C22×C4—22no—
203C22×C4—42no—
204C22×C4—42no—
205C22×C4—42no—
206C22×C4—42no—
207C22×C4—42no—
208C22×C4—42no—
209C22×C4—41no—
210C22×C4C2×D4×C13111yescharacteristic
211C22×C4C2×D4×C13112yes—
212C2×C8—22no—
213C2×C8—22no—
214C2×C8—22no—
215C2×C8—42no—
216C2×C8—42no—
217C2×C8—42no—
218C4⋊C4—22no—
219C4⋊C4—22no—
220C4⋊C4—42no—
221C4⋊C4—42no—
222C4⋊C4—42no—
223C4⋊C4—42no—
224C4⋊C4—42no—
225C4⋊C4—42no—
226C22⋊C4—48no—
227C22⋊C4—42no—
228C22⋊C4—42no—
229C42C2×D4×C13111yescharacteristic
230C42#41×C13111yescharacteristic
231C42#41×C13112yes—
232C23—24no—
233C23—42no—
234C23—42no—
235C23—42no—
236C23—42no—
237C23—42no—
238C23—42no—
239C23#120×C13111yescharacteristic
240D4—24no—
241D4—24no—
242D4—42no—
243D4—42no—
244D4—88no—
245C2×C4—21no—
246C2×C4—21no—
247C2×C4—42no—
248C2×C4—42no—
249C2×C4—42no—
250C2×C4—44no—
251C2×C4—42no—
252C2×C4—82no—
253C2×C4—82no—
254C2×C4—82no—
255C2×C4—82no—
256C2×C4—82no—
257C2×C4—81no—
258C2×C4#121×C13111yescharacteristic
259C2×C4#121×C13112yes—
260C2×C4#123×C13112yes—
261C2×C4#124×C13111yescharacteristic
262C2×C4C2×SD16×C13112yes—
263C2×C4#135×C13112yes—
264C2×C4AGL(1,ℤ/8)×C13112yes—
265C2×C4AGL(1,ℤ/8)×C13112yes—
266C8—24no—
267C8—82no—
268C22—44no—
269C22—44no—
270C22—44no—
271C22—82no—
272C22—82no—
273C22—82no—
274C22—82no—
275C22#394×C13111yescharacteristic
276C22#449×C13112yes—
277C22#450×C13112yes—
278C22#453×C13111yescharacteristic
279C22#456×C13111yescharacteristic
280C4—21no—
281C4—21no—
282C4—82no—
283C4—82no—
284C4—161no—
285C4#465×C13112yes—
286C4#469×C13112yes—
287C4#481×C13112yes—
288C4#482×C13112yes—
289C2—84no—
290C2#1624×C13111yescharacteristic
291C2#1629×C13111yescharacteristic
292C2#1654×C13112yes—
293C2#2034×C13112yes—
294C2#2039×C13111yescharacteristic
subgroupG/H
center, socleC23×C131#120
commutator, Frattini, cosocleC2×C42C23×C131
prime radical#2537×C131C2
LCSG ▷ C2×C42 ▷ C22 ▷ C1
UCSC1 ◁ C23×C131 ◁ C2×C42×C131 ◁ G

Complements

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

NH ≅ G/Ntype
2. #1844×C131C2semidirect
3. #1802×C131C2semidirect
4. C2×D4⋊C8×C131C2semidirect
5. #1296×C131C2semidirect
42. C4×C8×C131D4semidirect
147. #10432C131direct (N × H)
148. C131#10432direct (N × H)
150. #1844C2×C131semidirect
151. #1802C2×C131semidirect
152. C2×D4⋊C8C2×C131semidirect
153. #1296C2×C131semidirect
190. C4×C8D4×C131semidirect

Maximal subgroups

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

subgroupindex
#2537×C1312
#1844×C1312
#1802×C1312
C2×D4⋊C8×C1312
#1296×C1312
#10432131