Finite Group Databasebeta

← C131×#9428 #45695312

Subgroups — C131×#9428 #45695312

Order 33536.

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

normal subgroups only

This group has 620 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
1#3151×C131C211yesmaximal, characteristic
2#2380×C131C211yesmaximal, characteristic, complemented
3#1555×C131C211yesmaximal, characteristic, complemented
4#1514×C131C212yesmaximal, complemented
5#1288×C131C212yesmaximal, complemented
6C2×AGL(1,ℤ/8)×C131—22no—
7#532×C131C2211yescharacteristic
8C2×#127×C131C2211yescharacteristic
9#496×C131—22no—
10#493×C131C412yescomplemented
11#492×C131C412yescomplemented
12#432×C131C2212yes—
13C4×M16×C131C2211yescharacteristic
14#386×C131—22no—
15#386×C131—24no—
16#383×C131C2212yes—
17#331×C131—22no—
18#327×C131—24no—
19C2×#41×C131—21no—
20C22×D4×C131—22no—
21C22×D4×C131D412yes—
22C23×C4×C131—22no—
23AGL(1,ℤ/8)×C131—44no—
24AGL(1,ℤ/8)×C131—44no—
25C2×SD16×C131—24no—
26C2×D8×C131—24no—
27C2×M16×C131—21no—
28C4⋊Q8×C131C2×C411yescharacteristic, complemented
29#127×C131—22no—
30#127×C131C2×C412yes—
31#127×C131C2×C411yescharacteristic, complemented
32#127×C131D412yes—
33#124×C131—21no—
34#121×C131—22no—
35C4×D4×C131—22no—
36C2×C22⋊C4×C131—24no—
37C2×C22⋊C4×C131—22no—
38C2×C42×C131C2311yescharacteristic
39C4⋊C8×C131—22no—
40C22⋊C8×C131—22no—
41#97×C131—21no—
42#97×C131—22no—
43C4×C8×C131C2×C412yescomplemented
44#95×C131—22no—
45#95×C131—22no—
46#95×C131D414yes—
47C24×C131—22no—
48#41×C131—42no—
49#41×C131—42no—
50C2×Q8×C131—21no—
51C2×D4×C131—21no—
52C2×D4×C131—24no—
53C2×D4×C131—22no—
54C2×D4×C131—24no—
55C2×D4×C131—22no—
56C2×D4×C131—42no—
57C2×D4×C131—42no—
58C2×D4×C131—41no—
59C2×D4×C131—82no—
60C2×D4×C131—82no—
61C2×D4×C131C22⋊C414yes—
62C22×C4×C131—24no—
63C22×C4×C131—41no—
64C22×C4×C131—84no—
65C22×C4×C131—82no—
66C22×C4×C131C2×D411yescharacteristic
67C22×C4×C131C2×D412yes—
68SD16×C131—48no—
69D8×C131—48no—
70M16×C131—24no—
71C2×C8×C131—22no—
72C2×C8×C131—42no—
73C4⋊C4×C131—22no—
74C22⋊C4×C131—42no—
75C22⋊C4×C131—84no—
76C22⋊C4×C131—82no—
77C42×C131C22×C411yescharacteristic
78C42×C131C2×D411yescharacteristic
79C42×C131#4112yes—
80C23×C131—24no—
81C23×C131—44no—
82C23×C131—44no—
83C23×C131—42no—
84C23×C131—42no—
85C23×C131—41no—
86C23×C131#12011yescharacteristic
87Q8×C131—42no—
88D4×C131—44no—
89D4×C131—42no—
90D4×C131—82no—
91D4×C131—84no—
92D4×C131—84no—
93D4×C131—82no—
94D4×C131—82no—
95C2×C4×C131—22no—
96C2×C4×C131—42no—
97C2×C4×C131—48no—
98C2×C4×C131—41no—
99C2×C4×C131—44no—
100C2×C4×C131—81no—
101C2×C4×C131—81no—
102C2×C4×C131—88no—
103C2×C4×C131C2×C22⋊C411yescharacteristic
104C2×C4×C131C4×D412yes—
105C2×C4×C131#12112yes—
106C2×C4×C131#12311yescharacteristic
107C8×C131—24no—
108C8×C131—82no—
109C22×C131—22no—
110C22×C131—44no—
111C22×C131—48no—
112C22×C131—82no—
113C22×C131—82no—
114C22×C131—84no—
115C22×C131—81no—
116C22×C131—82no—
117C22×C131#38611yescharacteristic
118C22×C131#45312yes—
119C4×C131—21no—
120C4×C131—21no—
121C4×C131—22no—
122C4×C131—22no—
123C4×C131—84no—
124C4×C131—81no—
125C2×C131—22no—
126C2×C131—84no—
127C2×C131—161no—
128C2×C131#188711yescharacteristic
129C2×C131#190412yes—
130#9428C13111yesmaximal, characteristic, direct product factor, Sylow
131C131#942811yescharacteristic, direct product factor, Sylow
132#3151C2×C13111yescharacteristic
133#2380C2×C13111yescharacteristic, complemented
134#1555C2×C13111yescharacteristic, complemented
135#1514C2×C13112yescomplemented
136#1288C2×C13112yescomplemented
137C2×AGL(1,ℤ/8)—22no—
138#532C22×C13111yescharacteristic
139C2×#127C22×C13111yescharacteristic
140#496—22no—
141#493C4×C13112yescomplemented
142#492C4×C13112yescomplemented
143#432C22×C13112yes—
144C4×M16C22×C13111yescharacteristic
145#386—22no—
146#386—24no—
147#383C22×C13112yes—
148#331—22no—
149#327—24no—
150C2×#41—21no—
151C22×D4—22no—
152C22×D4D4×C13112yes—
153C23×C4—22no—
154AGL(1,ℤ/8)—44no—
155AGL(1,ℤ/8)—44no—
156C2×SD16—24no—
157C2×D8—24no—
158C2×M16—21no—
159C4⋊Q8C2×C4×C13111yescharacteristic, complemented
160#127—22no—
161#127C2×C4×C13112yes—
162#127C2×C4×C13111yescharacteristic, complemented
163#127D4×C13112yes—
164#124—21no—
165#121—22no—
166C4×D4—22no—
167C2×C22⋊C4—24no—
168C2×C22⋊C4—22no—
169C2×C42C23×C13111yescharacteristic
170C4⋊C8—22no—
171C22⋊C8—22no—
172#97—21no—
173#97—22no—
174C4×C8C2×C4×C13112yescomplemented
175#95—22no—
176#95—22no—
177#95D4×C13114yes—
178C24—22no—
179#41—42no—
180#41—42no—
181C2×Q8—21no—
182C2×D4—21no—
183C2×D4—24no—
184C2×D4—22no—
185C2×D4—24no—
186C2×D4—22no—
187C2×D4—42no—
188C2×D4—42no—
189C2×D4—41no—
190C2×D4—82no—
191C2×D4—82no—
192C2×D4C22⋊C4×C13114yes—
193C22×C4—24no—
194C22×C4—41no—
195C22×C4—84no—
196C22×C4—82no—
197C22×C4C2×D4×C13111yescharacteristic
198C22×C4C2×D4×C13112yes—
199SD16—48no—
200D8—48no—
201M16—24no—
202C2×C8—22no—
203C2×C8—42no—
204C4⋊C4—22no—
205C22⋊C4—42no—
206C22⋊C4—84no—
207C22⋊C4—82no—
208C42C22×C4×C13111yescharacteristic
209C42C2×D4×C13111yescharacteristic
210C42#41×C13112yes—
211C23—24no—
212C23—44no—
213C23—44no—
214C23—42no—
215C23—42no—
216C23—41no—
217C23#120×C13111yescharacteristic
218Q8—42no—
219D4—44no—
220D4—42no—
221D4—82no—
222D4—84no—
223D4—84no—
224D4—82no—
225D4—82no—
226C2×C4—22no—
227C2×C4—42no—
228C2×C4—48no—
229C2×C4—44no—
230C2×C4—41no—
231C2×C4—81no—
232C2×C4—81no—
233C2×C4—88no—
234C2×C4C2×C22⋊C4×C13111yescharacteristic
235C2×C4C4×D4×C13112yes—
236C2×C4#121×C13112yes—
237C2×C4#123×C13111yescharacteristic
238C8—24no—
239C8—82no—
240C22—22no—
241C22—44no—
242C22—48no—
243C22—82no—
244C22—82no—
245C22—84no—
246C22—81no—
247C22—82no—
248C22#386×C13111yescharacteristic
249C22#453×C13112yes—
250C4—21no—
251C4—21no—
252C4—22no—
253C4—22no—
254C4—84no—
255C4—81no—
256C2—22no—
257C2—84no—
258C2—161no—
259C2#1887×C13111yescharacteristic
260C2#1904×C13112yes—
subgroupG/H
center, socleC22×C131#386
commutatorC42C22×C4×C131
Frattini, cosocleC2×C42C23×C131
prime radical#3151×C131C2
LCSG ▷ C42 ▷ C22 ▷ C1
UCSC1 ◁ C22×C131 ◁ C2×C42×C131 ◁ G

Complements

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

NH ≅ G/Ntype
2. #2380×C131C2semidirect
3. #1555×C131C2semidirect
4. #1514×C131C2semidirect
5. #1288×C131C2semidirect
10. #493×C131C4semidirect
11. #492×C131C4semidirect
28. C4⋊Q8×C131C2×C4semidirect
31. #127×C131C2×C4semidirect
43. C4×C8×C131C2×C4semidirect
130. #9428C131direct (N × H)
131. C131#9428direct (N × H)
133. #2380C2×C131semidirect
134. #1555C2×C131semidirect
135. #1514C2×C131semidirect
136. #1288C2×C131semidirect
141. #493C4×C131semidirect
142. #492C4×C131semidirect
159. C4⋊Q8C2×C4×C131semidirect
162. #127C2×C4×C131semidirect
174. C4×C8C2×C4×C131semidirect

Maximal subgroups

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

subgroupindex
#3151×C1312
#2380×C1312
#1555×C1312
#1514×C1312
#1288×C1312
#9428131