Finite Group Databasebeta

← C131×#7486 #45693370

Subgroups — C131×#7486 #45693370

Order 33536.

286 conjugacy classes of subgroups; only the 66 normal subgroups are shown.

normal subgroups only

This group has 286 conjugacy classes of subgroups — too many to draw. Only its 66 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#2126×C131C211yesmaximal, characteristic
2#1884×C131C211yesmaximal, characteristic
3#1525×C131C211yesmaximal, characteristic
4#568×C131C411yescharacteristic, complemented
5#532×C131C2211yescharacteristic
6#421×C131—21no—
7#410×C131—21no—
8#410×C131C411yescharacteristic, complemented
9C4×M16×C131—21no—
10#354×C131—21no—
11#353×C131C412yescomplemented
12#339×C131—21no—
13#329×C131—21no—
14#329×C131C412yescomplemented
15C2×#41×C131C2×C411yescharacteristic
16C2×#41×C131D411yescharacteristic
17#131×C131—42no—
18C2×M16×C131—21no—
19C2×M16×C131—41no—
20C2×M16×C131—41no—
21C4⋊Q8×C131Q811yescharacteristic
22#127×C131C2×C411yescharacteristic
23#124×C131C2×C411yescharacteristic
24#124×C131D411yescharacteristic
25#121×C131—41no—
26C4×D4×C131—41no—
27#117×C131—21no—
28#117×C131—41no—
29C2×C42×C131D411yescharacteristic
30#104×C131—42no—
31#99×C131—22no—
32#99×C131—41no—
33#99×C131—41no—
34#97×C131—22no—
35C4×C8×C131—41no—
36#41×C131—41no—
37#41×C131—41no—
38#41×C131—41no—
39#41×C131—41no—
40C2×Q8×C131C4⋊C411yescharacteristic
41C2×Q8×C131C4⋊C411yescharacteristic
42C2×D4×C131—21no—
43C2×D4×C131—21no—
44C2×D4×C131—41no—
45C2×D4×C131C4211yescharacteristic
46C2×D4×C131C22⋊C411yescharacteristic
47C22×C4×C131—21no—
48C22×C4×C131—21no—
49C22×C4×C131—21no—
50C22×C4×C131C22⋊C411yescharacteristic
51M16×C131—22no—
52M16×C131—44no—
53M16×C131—42no—
54M16×C131—41no—
55C2×C8×C131—42no—
56C2×C8×C131—41no—
57C2×C8×C131—42no—
58C4⋊C4×C131—41no—
59C4⋊C4×C131—41no—
60C4⋊C4×C131—81no—
61C22⋊C4×C131—41no—
62C22⋊C4×C131—41no—
63C22⋊C4×C131—42no—
64C22⋊C4×C131—41no—
65C42×C131—21no—
66C42×C131—41no—
67C42×C131—81no—
68C42×C131C22⋊C411yescharacteristic
69C42×C131C4⋊C411yescharacteristic
70C23×C131—21no—
71C23×C131—21no—
72C23×C131#9911yescharacteristic
73Q8×C131—41no—
74Q8×C131—41no—
75D4×C131—41no—
76D4×C131—41no—
77D4×C131—42no—
78D4×C131—82no—
79D4×C131—81no—
80C2×C4×C131—21no—
81C2×C4×C131—21no—
82C2×C4×C131—21no—
83C2×C4×C131—21no—
84C2×C4×C131—21no—
85C2×C4×C131—21no—
86C2×C4×C131—42no—
87C2×C4×C131—41no—
88C2×C4×C131—41no—
89C2×C4×C131—41no—
90C2×C4×C131—41no—
91C2×C4×C131—81no—
92C2×C4×C131—82no—
93C2×C4×C131#9511yescharacteristic
94C2×C4×C131#9911yescharacteristic
95C8×C131—44no—
96C8×C131—42no—
97C22×C131—21no—
98C22×C131—41no—
99C22×C131—41no—
100C22×C131—41no—
101C22×C131—81no—
102C22×C131—81no—
103C22×C131#34211yescharacteristic
104C4×C131—22no—
105C4×C131—21no—
106C4×C131—41no—
107C4×C131—41no—
108C4×C131—41no—
109C4×C131—161no—
110C4×C131—162no—
111C4×C131AΣL(1,𝔽16)11yescharacteristic
112C4×C131#35211yescharacteristic
113C2×C131—21no—
114C2×C131—41no—
115C2×C131—81no—
116C2×C131—81no—
117C2×C131#139011yescharacteristic
118#7486C13111yesmaximal, characteristic, direct product factor, Sylow
119C131#748611yescharacteristic, direct product factor, Sylow
120#2126C2×C13111yescharacteristic
121#1884C2×C13111yescharacteristic
122#1525C2×C13111yescharacteristic
123#568C4×C13111yescharacteristic, complemented
124#532C22×C13111yescharacteristic
125#421—21no—
126#410—21no—
127#410C4×C13111yescharacteristic, complemented
128C4×M16—21no—
129#354—21no—
130#353C4×C13112yescomplemented
131#339—21no—
132#329—21no—
133#329C4×C13112yescomplemented
134C2×#41C2×C4×C13111yescharacteristic
135C2×#41D4×C13111yescharacteristic
136#131—42no—
137C2×M16—21no—
138C2×M16—41no—
139C2×M16—41no—
140C4⋊Q8Q8×C13111yescharacteristic
141#127C2×C4×C13111yescharacteristic
142#124C2×C4×C13111yescharacteristic
143#124D4×C13111yescharacteristic
144#121—41no—
145C4×D4—41no—
146#117—21no—
147#117—41no—
148C2×C42D4×C13111yescharacteristic
149#104—42no—
150#99—22no—
151#99—41no—
152#99—41no—
153#97—22no—
154C4×C8—41no—
155#41—41no—
156#41—41no—
157#41—41no—
158#41—41no—
159C2×Q8C4⋊C4×C13111yescharacteristic
160C2×Q8C4⋊C4×C13111yescharacteristic
161C2×D4—21no—
162C2×D4—21no—
163C2×D4—41no—
164C2×D4C42×C13111yescharacteristic
165C2×D4C22⋊C4×C13111yescharacteristic
166C22×C4—21no—
167C22×C4—21no—
168C22×C4—21no—
169C22×C4C22⋊C4×C13111yescharacteristic
170M16—22no—
171M16—44no—
172M16—42no—
173M16—41no—
174C2×C8—42no—
175C2×C8—41no—
176C2×C8—42no—
177C4⋊C4—41no—
178C4⋊C4—41no—
179C4⋊C4—81no—
180C22⋊C4—41no—
181C22⋊C4—41no—
182C22⋊C4—42no—
183C22⋊C4—41no—
184C42—21no—
185C42—41no—
186C42—81no—
187C42C22⋊C4×C13111yescharacteristic
188C42C4⋊C4×C13111yescharacteristic
189C23—21no—
190C23—21no—
191C23#99×C13111yescharacteristic
192Q8—41no—
193Q8—41no—
194D4—41no—
195D4—41no—
196D4—42no—
197D4—82no—
198D4—81no—
199C2×C4—21no—
200C2×C4—21no—
201C2×C4—21no—
202C2×C4—21no—
203C2×C4—21no—
204C2×C4—21no—
205C2×C4—42no—
206C2×C4—41no—
207C2×C4—41no—
208C2×C4—41no—
209C2×C4—41no—
210C2×C4—81no—
211C2×C4—82no—
212C2×C4#95×C13111yescharacteristic
213C2×C4#99×C13111yescharacteristic
214C8—44no—
215C8—42no—
216C22—21no—
217C22—41no—
218C22—41no—
219C22—41no—
220C22—81no—
221C22—81no—
222C22#342×C13111yescharacteristic
223C4—22no—
224C4—21no—
225C4—41no—
226C4—41no—
227C4—41no—
228C4—161no—
229C4—162no—
230C4AΣL(1,𝔽16)×C13111yescharacteristic
231C4#352×C13111yescharacteristic
232C2—21no—
233C2—41no—
234C2—81no—
235C2—81no—
236C2#1390×C13111yescharacteristic
subgroupG/H
centerC4×C131AΣL(1,𝔽16)
commutatorC2×D4C42×C131
Frattini, cosocle#532C22×C131
socleC2×C131#1390
prime radical#532×C131C22
LCSG ▷ C2×D4 ▷ C2×C4 ▷ C22 ▷ C2 ▷ C1
UCSC1 ◁ C4×C131 ◁ C2×C4×C131 ◁ C22×C4×C131 ◁ #532×C131 ◁ G

Complements

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

NH ≅ G/Ntype
4. #568×C131C4semidirect
8. #410×C131C4semidirect
11. #353×C131C4semidirect
14. #329×C131C4semidirect
118. #7486C131direct (N × H)
119. C131#7486direct (N × H)
123. #568C4×C131semidirect
127. #410C4×C131semidirect
130. #353C4×C131semidirect
133. #329C4×C131semidirect

Maximal subgroups

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

subgroupindex
#2126×C1312
#1884×C1312
#1525×C1312
#7486131