Finite Group Databasebeta

← C131×#7635 #45693519

Subgroups — C131×#7635 #45693519

Order 33536.

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

normal subgroups only

This group has 520 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
1C4×#124×C131C211yesmaximal, characteristic
2#1767×C131C212yesmaximal, complemented
3#1272×C131C212yesmaximal, complemented
4#1270×C131C212yesmaximal
5C2×#124×C131C411yescharacteristic
6C2×C4×Q8×C131C411yescharacteristic
7C2×C4×D4×C131C411yescharacteristic
8C2×C4⋊C8×C131—22no—
9C2×#97×C131—22no—
10#391×C131C2211yescharacteristic
11#390×C131C2211yescharacteristic
12#388×C131—22no—
13#382×C131C411yescharacteristic
14C4×C22⋊C4×C131—22no—
15C43×C131C2211yescharacteristic
16#336×C131C2214yes—
17C22×Q8×C131C2×C411yescharacteristic
18C22×D4×C131C2×C411yescharacteristic
19C23×C4×C131—21no—
20C22×C8×C131—24no—
21#124×C131—22no—
22#124×C131—22no—
23C4×Q8×C131—42no—
24C4×D4×C131—42no—
25C2×C4⋊C4×C131—21no—
26C2×C4⋊C4×C131C2×C411yescharacteristic
27C2×C4⋊C4×C131C2×C411yescharacteristic
28C2×C22⋊C4×C131—22no—
29C2×C22⋊C4×C131—21no—
30C2×C22⋊C4×C131—22no—
31C2×C42×C131—21no—
32C2×C42×C131C2×C411yescharacteristic
33C2×C42×C131C2×C411yescharacteristic
34C2×C42×C131D412yes—
35C2×C42×C131D412yes—
36C2×C42×C131C2311yescharacteristic
37C4⋊C8×C131—28no—
38#97×C131—44no—
39#95×C131—22no—
40#95×C131—22no—
41C24×C131—21no—
42C2×Q8×C131—21no—
43C2×Q8×C131—41no—
44C2×Q8×C131—41no—
45C2×Q8×C131M1612yes—
46C2×D4×C131—21no—
47C2×D4×C131—41no—
48C2×D4×C131—41no—
49C2×D4×C131M1612yes—
50C22×C4×C131—21no—
51C22×C4×C131—21no—
52C22×C4×C131—21no—
53C22×C4×C131—42no—
54C22×C4×C131—44no—
55C22×C4×C131C22⋊C412yes—
56C22×C4×C131C22⋊C411yescharacteristic
57C22×C4×C131C22⋊C411yescharacteristic
58C22×C4×C131C22×C411yescharacteristic
59C22×C4×C131C2×D412yes—
60C2×C8×C131—28no—
61C2×C8×C131—44no—
62C2×C8×C131—44no—
63C4⋊C4×C131—41no—
64C4⋊C4×C131—41no—
65C4⋊C4×C131—42no—
66C22⋊C4×C131—28no—
67C22⋊C4×C131—42no—
68C22⋊C4×C131—42no—
69C22⋊C4×C131—42no—
70C42×C131—22no—
71C42×C131—24no—
72C42×C131—21no—
73C42×C131—21no—
74C42×C131—22no—
75C42×C131—22no—
76C42×C131—41no—
77C42×C131—42no—
78C23×C131—22no—
79C23×C131—41no—
80C23×C131—41no—
81C23×C131—42no—
82C23×C131—42no—
83C23×C131C2×C22⋊C411yescharacteristic
84Q8×C131—42no—
85Q8×C131—42no—
86D4×C131—42no—
87D4×C131—42no—
88C2×C4×C131—22no—
89C2×C4×C131—21no—
90C2×C4×C131—21no—
91C2×C4×C131—22no—
92C2×C4×C131—22no—
93C2×C4×C131—22no—
94C2×C4×C131—21no—
95C2×C4×C131—22no—
96C2×C4×C131—22no—
97C2×C4×C131—22no—
98C2×C4×C131—41no—
99C2×C4×C131—41no—
100C2×C4×C131—41no—
101C2×C4×C131—41no—
102C2×C4×C131—42no—
103C2×C4×C131—42no—
104C2×C4×C131—84no—
105C2×C4×C131#10012yes—
106C2×C4×C131#10414yes—
107C2×C4×C131C2×M1611yescharacteristic
108C2×C4×C131C2×M1611yescharacteristic
109C2×C4×C131AGL(1,ℤ/8)12yes—
110C2×C4×C131#13712yes—
111C8×C131—48no—
112C22×C131—42no—
113C22×C131—44no—
114C22×C131—81no—
115C22×C131—82no—
116C22×C131—81no—
117C22×C131#40711yescharacteristic
118C22×C131#41011yescharacteristic
119C22×C131C2×#10011yescharacteristic
120C22×C131#41712yes—
121C22×C131C2×#10412yes—
122C4×C131—21no—
123C4×C131—21no—
124C4×C131—22no—
125C4×C131—22no—
126C4×C131—41no—
127C4×C131—42no—
128C4×C131—42no—
129C4×C131—81no—
130C4×C131—81no—
131C4×C131#32914yes—
132C2×C131—82no—
133C2×C131#146611yescharacteristic
134C2×C131#148912yes—
135C2×C131#150912yes—
136C2×C131C2×#32911yescharacteristic
137C2×C131#156011yescharacteristic
138#7635C13111yesmaximal, characteristic, direct product factor, Sylow
139C131#763511yescharacteristic, direct product factor, Sylow
140C4×#124C2×C13111yescharacteristic
141#1767C2×C13112yescomplemented
142#1272C2×C13112yescomplemented
143#1270C2×C13112yes—
144C2×#124C4×C13111yescharacteristic
145C2×C4×Q8C4×C13111yescharacteristic
146C2×C4×D4C4×C13111yescharacteristic
147C2×C4⋊C8—22no—
148C2×#97—22no—
149#391C22×C13111yescharacteristic
150#390C22×C13111yescharacteristic
151#388—22no—
152#382C4×C13111yescharacteristic
153C4×C22⋊C4—22no—
154C43C22×C13111yescharacteristic
155#336C22×C13114yes—
156C22×Q8C2×C4×C13111yescharacteristic
157C22×D4C2×C4×C13111yescharacteristic
158C23×C4—21no—
159C22×C8—24no—
160#124—22no—
161#124—22no—
162C4×Q8—42no—
163C4×D4—42no—
164C2×C4⋊C4—21no—
165C2×C4⋊C4C2×C4×C13111yescharacteristic
166C2×C4⋊C4C2×C4×C13111yescharacteristic
167C2×C22⋊C4—22no—
168C2×C22⋊C4—21no—
169C2×C22⋊C4—22no—
170C2×C42—21no—
171C2×C42C2×C4×C13111yescharacteristic
172C2×C42C2×C4×C13111yescharacteristic
173C2×C42D4×C13112yes—
174C2×C42D4×C13112yes—
175C2×C42C23×C13111yescharacteristic
176C4⋊C8—28no—
177#97—44no—
178#95—22no—
179#95—22no—
180C24—21no—
181C2×Q8—21no—
182C2×Q8—41no—
183C2×Q8—41no—
184C2×Q8M16×C13112yes—
185C2×D4—21no—
186C2×D4—41no—
187C2×D4—41no—
188C2×D4M16×C13112yes—
189C22×C4—21no—
190C22×C4—21no—
191C22×C4—21no—
192C22×C4—42no—
193C22×C4—44no—
194C22×C4C22⋊C4×C13112yes—
195C22×C4C22⋊C4×C13111yescharacteristic
196C22×C4C22⋊C4×C13111yescharacteristic
197C22×C4C22×C4×C13111yescharacteristic
198C22×C4C2×D4×C13112yes—
199C2×C8—28no—
200C2×C8—44no—
201C2×C8—44no—
202C4⋊C4—41no—
203C4⋊C4—41no—
204C4⋊C4—42no—
205C22⋊C4—28no—
206C22⋊C4—42no—
207C22⋊C4—42no—
208C22⋊C4—42no—
209C42—22no—
210C42—24no—
211C42—21no—
212C42—21no—
213C42—22no—
214C42—22no—
215C42—41no—
216C42—42no—
217C23—22no—
218C23—41no—
219C23—41no—
220C23—42no—
221C23—42no—
222C23C2×C22⋊C4×C13111yescharacteristic
223Q8—42no—
224Q8—42no—
225D4—42no—
226D4—42no—
227C2×C4—22no—
228C2×C4—21no—
229C2×C4—21no—
230C2×C4—22no—
231C2×C4—22no—
232C2×C4—22no—
233C2×C4—21no—
234C2×C4—22no—
235C2×C4—22no—
236C2×C4—22no—
237C2×C4—41no—
238C2×C4—41no—
239C2×C4—41no—
240C2×C4—41no—
241C2×C4—42no—
242C2×C4—42no—
243C2×C4—84no—
244C2×C4#100×C13112yes—
245C2×C4#104×C13114yes—
246C2×C4C2×M16×C13111yescharacteristic
247C2×C4C2×M16×C13111yescharacteristic
248C2×C4AGL(1,ℤ/8)×C13112yes—
249C2×C4#137×C13112yes—
250C8—48no—
251C22—42no—
252C22—44no—
253C22—82no—
254C22—81no—
255C22—81no—
256C22#407×C13111yescharacteristic
257C22#410×C13111yescharacteristic
258C22C2×#100×C13111yescharacteristic
259C22#417×C13112yes—
260C22C2×#104×C13112yes—
261C4—21no—
262C4—21no—
263C4—22no—
264C4—22no—
265C4—42no—
266C4—42no—
267C4—41no—
268C4—81no—
269C4—81no—
270C4#329×C13114yes—
271C2—82no—
272C2#1466×C13111yescharacteristic
273C2#1489×C13112yes—
274C2#1509×C13112yes—
275C2C2×#329×C13111yescharacteristic
276C2#1560×C13111yescharacteristic
subgroupG/H
center, socleC23×C131C2×C22⋊C4
commutatorC22×C4C22×C4×C131
Frattini, cosocleC2×C42C23×C131
prime radicalC22×D4×C131C2×C4
LCSG ▷ C22×C4 ▷ C22 ▷ C1
UCSC1 ◁ C23×C131 ◁ C43×C131 ◁ G

Complements

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

NH ≅ G/Ntype
2. #1767×C131C2semidirect
3. #1272×C131C2semidirect
138. #7635C131direct (N × H)
139. C131#7635direct (N × H)
141. #1767C2×C131semidirect
142. #1272C2×C131semidirect

Maximal subgroups

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

subgroupindex
C4×#124×C1312
#1767×C1312
#1272×C1312
#1270×C1312
#7635131