Finite Group Databasebeta

← C131×#7495 #45693379

Subgroups — C131×#7495 #45693379

Order 33536.

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

normal subgroups only

This group has 280 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
1C2×#355×C131C211yesmaximal, characteristic
2#1885×C131C211yesmaximal, characteristic
3#1533×C131C211yesmaximal, characteristic
4C2×#124×C131C2211yescharacteristic
5#518×C131C411yescharacteristic
6#432×C131—21no—
7#419×C131—21no—
8C2×#101×C131—21no—
9C2×#100×C131C411yescharacteristic
10#355×C131—21no—
11#355×C131C412yescomplemented
12#339×C131—21no—
13#329×C131—21no—
14#329×C131C412yescomplemented
15C22×Q8×C131D411yescharacteristic
16C22×D4×C131C2×C411yescharacteristic
17C2×M16×C131—21no—
18C2×M16×C131—41no—
19#124×C131—41no—
20#124×C131C2×C411yescharacteristic
21#124×C131C2×C411yescharacteristic
22#124×C131D411yescharacteristic
23#124×C131Q811yescharacteristic
24C4×D4×C131—42no—
25#117×C131—21no—
26C2×C22⋊C4×C131—41no—
27C2×C22⋊C4×C131—41no—
28C2×C42×C131D411yescharacteristic
29C4⋊C8×C131—41no—
30#103×C131—42no—
31#101×C131—22no—
32#101×C131—41no—
33#100×C131—41no—
34C22⋊C8×C131—41no—
35#97×C131—22no—
36C24×C131—21no—
37C2×Q8×C131—21no—
38C2×Q8×C131—41no—
39C2×Q8×C131—41no—
40C2×Q8×C131C22⋊C411yescharacteristic
41C2×Q8×C131C4⋊C411yescharacteristic
42C2×D4×C131—21no—
43C2×D4×C131—41no—
44C2×D4×C131—41no—
45C2×D4×C131C4211yescharacteristic
46C2×D4×C131C4⋊C411yescharacteristic
47C22×C4×C131—21no—
48C22×C4×C131—21no—
49C22×C4×C131—42no—
50C22×C4×C131C22⋊C411yescharacteristic
51M16×C131—42no—
52M16×C131—41no—
53M16×C131—41no—
54M16×C131—81no—
55C2×C8×C131—42no—
56C2×C8×C131—41no—
57C2×C8×C131—81no—
58C4⋊C4×C131—22no—
59C22⋊C4×C131—41no—
60C22⋊C4×C131—41no—
61C22⋊C4×C131—41no—
62C22⋊C4×C131—41no—
63C22⋊C4×C131—41no—
64C22⋊C4×C131—42no—
65C42×C131—21no—
66C42×C131—41no—
67C42×C131C22⋊C411yescharacteristic
68C42×C131C4⋊C411yescharacteristic
69C23×C131—21no—
70C23×C131—21no—
71C23×C131—41no—
72C23×C131—41no—
73C23×C131—82no—
74C23×C131#9911yescharacteristic
75Q8×C131—41no—
76Q8×C131—41no—
77Q8×C131—81no—
78D4×C131—41no—
79D4×C131—41no—
80D4×C131—42no—
81C2×C4×C131—21no—
82C2×C4×C131—21no—
83C2×C4×C131—21no—
84C2×C4×C131—21no—
85C2×C4×C131—21no—
86C2×C4×C131—21no—
87C2×C4×C131—41no—
88C2×C4×C131—41no—
89C2×C4×C131—42no—
90C2×C4×C131—81no—
91C2×C4×C131—162no—
92C2×C4×C131#9511yescharacteristic
93C2×C4×C131#9911yescharacteristic
94C8×C131—81no—
95C8×C131—82no—
96C8×C131—82no—
97C22×C131—41no—
98C22×C131—41no—
99C22×C131—41no—
100C22×C131—81no—
101C22×C131—81no—
102C22×C131—82no—
103C22×C131—161no—
104C22×C131#34211yescharacteristic
105C22×C131AΣL(1,𝔽16)11yescharacteristic
106C22×C131#35211yescharacteristic
107C4×C131—21no—
108C4×C131—21no—
109C4×C131—41no—
110C4×C131—41no—
111C4×C131—41no—
112C4×C131—41no—
113C4×C131—82no—
114C2×C131—21no—
115C2×C131—21no—
116C2×C131—21no—
117C2×C131—81no—
118C2×C131—81no—
119C2×C131#139011yescharacteristic
120#7495C13111yesmaximal, characteristic, direct product factor, Sylow
121C131#749511yescharacteristic, direct product factor, Sylow
122C2×#355C2×C13111yescharacteristic
123#1885C2×C13111yescharacteristic
124#1533C2×C13111yescharacteristic
125C2×#124C22×C13111yescharacteristic
126#518C4×C13111yescharacteristic
127#432—21no—
128#419—21no—
129C2×#101—21no—
130C2×#100C4×C13111yescharacteristic
131#355—21no—
132#355C4×C13112yescomplemented
133#339—21no—
134#329—21no—
135#329C4×C13112yescomplemented
136C22×Q8D4×C13111yescharacteristic
137C22×D4C2×C4×C13111yescharacteristic
138C2×M16—21no—
139C2×M16—41no—
140#124—41no—
141#124C2×C4×C13111yescharacteristic
142#124C2×C4×C13111yescharacteristic
143#124D4×C13111yescharacteristic
144#124Q8×C13111yescharacteristic
145C4×D4—42no—
146#117—21no—
147C2×C22⋊C4—41no—
148C2×C22⋊C4—41no—
149C2×C42D4×C13111yescharacteristic
150C4⋊C8—41no—
151#103—42no—
152#101—22no—
153#101—41no—
154#100—41no—
155C22⋊C8—41no—
156#97—22no—
157C24—21no—
158C2×Q8—21no—
159C2×Q8—41no—
160C2×Q8—41no—
161C2×Q8C22⋊C4×C13111yescharacteristic
162C2×Q8C4⋊C4×C13111yescharacteristic
163C2×D4—21no—
164C2×D4—41no—
165C2×D4—41no—
166C2×D4C42×C13111yescharacteristic
167C2×D4C4⋊C4×C13111yescharacteristic
168C22×C4—21no—
169C22×C4—21no—
170C22×C4—42no—
171C22×C4C22⋊C4×C13111yescharacteristic
172M16—42no—
173M16—41no—
174M16—41no—
175M16—81no—
176C2×C8—42no—
177C2×C8—41no—
178C2×C8—81no—
179C4⋊C4—22no—
180C22⋊C4—41no—
181C22⋊C4—41no—
182C22⋊C4—41no—
183C22⋊C4—41no—
184C22⋊C4—41no—
185C22⋊C4—42no—
186C42—21no—
187C42—41no—
188C42C22⋊C4×C13111yescharacteristic
189C42C4⋊C4×C13111yescharacteristic
190C23—21no—
191C23—21no—
192C23—41no—
193C23—41no—
194C23—82no—
195C23#99×C13111yescharacteristic
196Q8—41no—
197Q8—41no—
198Q8—81no—
199D4—41no—
200D4—41no—
201D4—42no—
202C2×C4—21no—
203C2×C4—21no—
204C2×C4—21no—
205C2×C4—21no—
206C2×C4—21no—
207C2×C4—21no—
208C2×C4—41no—
209C2×C4—41no—
210C2×C4—42no—
211C2×C4—81no—
212C2×C4—162no—
213C2×C4#95×C13111yescharacteristic
214C2×C4#99×C13111yescharacteristic
215C8—81no—
216C8—82no—
217C8—82no—
218C22—41no—
219C22—41no—
220C22—41no—
221C22—81no—
222C22—81no—
223C22—82no—
224C22—161no—
225C22#342×C13111yescharacteristic
226C22AΣL(1,𝔽16)×C13111yescharacteristic
227C22#352×C13111yescharacteristic
228C4—21no—
229C4—21no—
230C4—41no—
231C4—41no—
232C4—41no—
233C4—41no—
234C4—82no—
235C2—21no—
236C2—21no—
237C2—21no—
238C2—81no—
239C2—81no—
240C2#1390×C13111yescharacteristic
subgroupG/H
center, socleC2×C131#1390
commutatorC2×D4C42×C131
Frattini, cosocleC2×#124C22×C131
prime radicalC22×D4×C131C2×C4
LCSG ▷ C2×D4 ▷ C2×C4 ▷ C22 ▷ C2 ▷ C1
UCSC1 ◁ C2×C131 ◁ C23×C131 ◁ C22×C4×C131 ◁ C2×#124×C131 ◁ G

Complements

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

NH ≅ G/Ntype
11. #355×C131C4semidirect
14. #329×C131C4semidirect
120. #7495C131direct (N × H)
121. C131#7495direct (N × H)
132. #355C4×C131semidirect
135. #329C4×C131semidirect

Maximal subgroups

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

subgroupindex
C2×#355×C1312
#1885×C1312
#1533×C1312
#7495131