Finite Group Databasebeta

← C131×#9196 #45695080

Subgroups — C131×#9196 #45695080

Order 33536.

478 conjugacy classes of subgroups; only the 134 normal subgroups are shown.

normal subgroups only

This group has 478 conjugacy classes of subgroups — too many to draw. Only its 134 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#2921×C131C211yesmaximal, characteristic
2#2621×C131C211yesmaximal, characteristic
3#1546×C131C212yesmaximal, complemented
4#1458×C131C211yesmaximal, characteristic
5#1286×C131C212yesmaximal, complemented
6C2×C4⋊Q8×C131C2211yescharacteristic
7C2×C22⋊Q8×C131—21no—
8C2×#117×C131C2211yescharacteristic
9#433×C131—24no—
10#431×C131C2212yes—
11#423×C131C2212yes—
12#407×C131—21no—
13C4×M16×C131—21no—
14#398×C131—21no—
15#398×C131C412yes—
16#397×C131—21no—
17#397×C131C412yes—
18#391×C131—21no—
19#382×C131C2211yescharacteristic
20#332×C131—24no—
21#324×C131—21no—
22#323×C131—21no—
23C22×Q8×C131—21no—
24C23×C4×C131D411yescharacteristic
25C2×M16×C131—22no—
26C4⋊Q8×C131—22no—
27C4⋊Q8×C131—22no—
28C22⋊Q8×C131—44no—
29#117×C131—22no—
30#117×C131—22no—
31C2×C4⋊C4×C131—22no—
32C2×C4⋊C4×C131—21no—
33C2×C4⋊C4×C131—21no—
34C2×C4⋊C4×C131C2×C412yes—
35C2×C4⋊C4×C131C2×C411yescharacteristic
36C2×C4⋊C4×C131D411yescharacteristic
37C2×C22⋊C4×C131—22no—
38C2×C22⋊C4×C131C2×C411yescharacteristic
39C2×C22⋊C4×C131D411yescharacteristic
40C2×C42×C131D411yescharacteristic
41C2×C42×C131C2311yescharacteristic
42C4⋊C8×C131—22no—
43C4⋊C8×C131—22no—
44C4⋊C8×C131D414yes—
45C22⋊C8×C131—24no—
46C22⋊C8×C131—22no—
47#97×C131—22no—
48C4×C8×C131—22no—
49C4×C8×C131—22no—
50#95×C131—22no—
51#95×C131—22no—
52#95×C131—21no—
53#95×C131C2×C412yes—
54C24×C131C22⋊C411yescharacteristic
55C2×Q8×C131—41no—
56C2×Q8×C131—41no—
57C2×Q8×C131—42no—
58C2×Q8×C131—42no—
59C22×C4×C131—21no—
60C22×C4×C131—21no—
61C22×C4×C131—22no—
62C22×C4×C131—22no—
63C22×C4×C131—22no—
64C22×C4×C131—22no—
65C22×C4×C131C22⋊C411yescharacteristic
66C22×C4×C131C22⋊C411yescharacteristic
67C22×C4×C131C22⋊C411yescharacteristic
68C22×C4×C131C22×C411yescharacteristic
69C22×C4×C131C2×D411yescharacteristic
70C22×C4×C131C2×D411yescharacteristic
71M16×C131—42no—
72M16×C131—42no—
73C2×C8×C131—24no—
74C2×C8×C131—42no—
75C4⋊C4×C131—22no—
76C4⋊C4×C131—22no—
77C4⋊C4×C131—24no—
78C4⋊C4×C131—44no—
79C4⋊C4×C131—42no—
80C4⋊C4×C131—42no—
81C22⋊C4×C131—22no—
82C22⋊C4×C131—22no—
83C22⋊C4×C131—44no—
84C42×C131—21no—
85C42×C131—21no—
86C42×C131C2×D412yes—
87C42×C131#4112yes—
88C23×C131—21no—
89C23×C131—21no—
90C23×C131—21no—
91C23×C131—41no—
92C23×C131—41no—
93C23×C131C2×C22⋊C411yescharacteristic
94Q8×C131—82no—
95Q8×C131—82no—
96C2×C4×C131—21no—
97C2×C4×C131—21no—
98C2×C4×C131—21no—
99C2×C4×C131—21no—
100C2×C4×C131—21no—
101C2×C4×C131—41no—
102C2×C4×C131—41no—
103C2×C4×C131—42no—
104C2×C4×C131—42no—
105C2×C4×C131—41no—
106C2×C4×C131—41no—
107C2×C4×C131—42no—
108C2×C4×C131—42no—
109C2×C4×C131—42no—
110C2×C4×C131—42no—
111C2×C4×C131—42no—
112C2×C4×C131—42no—
113C2×C4×C131C4×D412yes—
114C2×C4×C131#12011yescharacteristic
115C2×C4×C131#12112yes—
116C2×C4×C131#12311yescharacteristic
117C2×C4×C131#13512yes—
118C2×C4×C131AGL(1,ℤ/8)12yes—
119C8×C131—44no—
120C8×C131—82no—
121C22×C131—21no—
122C22×C131—21no—
123C22×C131—42no—
124C22×C131—41no—
125C22×C131—41no—
126C22×C131—41no—
127C22×C131—81no—
128C22×C131#38611yescharacteristic
129C22×C131#41611yescharacteristic
130C22×C131#41811yescharacteristic
131C4×C131—22no—
132C4×C131—22no—
133C4×C131—41no—
134C4×C131—41no—
135C4×C131—41no—
136C4×C131—82no—
137C4×C131—82no—
138C4×C131#44912yes—
139C4×C131#48212yes—
140C2×C131—21no—
141C2×C131—21no—
142C2×C131—81no—
143C2×C131#187511yescharacteristic
144C2×C131#190911yescharacteristic
145C2×C131#191511yescharacteristic
146#9196C13111yesmaximal, characteristic, direct product factor, Sylow
147C131#919611yescharacteristic, direct product factor, Sylow
148#2921C2×C13111yescharacteristic
149#2621C2×C13111yescharacteristic
150#1546C2×C13112yescomplemented
151#1458C2×C13111yescharacteristic
152#1286C2×C13112yescomplemented
153C2×C4⋊Q8C22×C13111yescharacteristic
154C2×C22⋊Q8—21no—
155C2×#117C22×C13111yescharacteristic
156#433—24no—
157#431C22×C13112yes—
158#423C22×C13112yes—
159#407—21no—
160C4×M16—21no—
161#398—21no—
162#398C4×C13112yes—
163#397—21no—
164#397C4×C13112yes—
165#391—21no—
166#382C22×C13111yescharacteristic
167#332—24no—
168#324—21no—
169#323—21no—
170C22×Q8—21no—
171C23×C4D4×C13111yescharacteristic
172C2×M16—22no—
173C4⋊Q8—22no—
174C4⋊Q8—22no—
175C22⋊Q8—44no—
176#117—22no—
177#117—22no—
178C2×C4⋊C4—22no—
179C2×C4⋊C4—21no—
180C2×C4⋊C4—21no—
181C2×C4⋊C4C2×C4×C13112yes—
182C2×C4⋊C4C2×C4×C13111yescharacteristic
183C2×C4⋊C4D4×C13111yescharacteristic
184C2×C22⋊C4—22no—
185C2×C22⋊C4C2×C4×C13111yescharacteristic
186C2×C22⋊C4D4×C13111yescharacteristic
187C2×C42D4×C13111yescharacteristic
188C2×C42C23×C13111yescharacteristic
189C4⋊C8—22no—
190C4⋊C8—22no—
191C4⋊C8D4×C13114yes—
192C22⋊C8—24no—
193C22⋊C8—22no—
194#97—22no—
195C4×C8—22no—
196C4×C8—22no—
197#95—22no—
198#95—22no—
199#95—21no—
200#95C2×C4×C13112yes—
201C24C22⋊C4×C13111yescharacteristic
202C2×Q8—41no—
203C2×Q8—41no—
204C2×Q8—42no—
205C2×Q8—42no—
206C22×C4—21no—
207C22×C4—21no—
208C22×C4—22no—
209C22×C4—22no—
210C22×C4—22no—
211C22×C4—22no—
212C22×C4C22⋊C4×C13111yescharacteristic
213C22×C4C22⋊C4×C13111yescharacteristic
214C22×C4C22⋊C4×C13111yescharacteristic
215C22×C4C22×C4×C13111yescharacteristic
216C22×C4C2×D4×C13111yescharacteristic
217C22×C4C2×D4×C13111yescharacteristic
218M16—42no—
219M16—42no—
220C2×C8—24no—
221C2×C8—42no—
222C4⋊C4—22no—
223C4⋊C4—22no—
224C4⋊C4—24no—
225C4⋊C4—44no—
226C4⋊C4—42no—
227C4⋊C4—42no—
228C22⋊C4—22no—
229C22⋊C4—22no—
230C22⋊C4—44no—
231C42—21no—
232C42—21no—
233C42C2×D4×C13112yes—
234C42#41×C13112yes—
235C23—21no—
236C23—21no—
237C23—21no—
238C23—41no—
239C23—41no—
240C23C2×C22⋊C4×C13111yescharacteristic
241Q8—82no—
242Q8—82no—
243C2×C4—21no—
244C2×C4—21no—
245C2×C4—21no—
246C2×C4—21no—
247C2×C4—21no—
248C2×C4—41no—
249C2×C4—41no—
250C2×C4—42no—
251C2×C4—42no—
252C2×C4—41no—
253C2×C4—41no—
254C2×C4—42no—
255C2×C4—42no—
256C2×C4—42no—
257C2×C4—42no—
258C2×C4—42no—
259C2×C4—42no—
260C2×C4C4×D4×C13112yes—
261C2×C4#120×C13111yescharacteristic
262C2×C4#121×C13112yes—
263C2×C4#123×C13111yescharacteristic
264C2×C4#135×C13112yes—
265C2×C4AGL(1,ℤ/8)×C13112yes—
266C8—44no—
267C8—82no—
268C22—21no—
269C22—21no—
270C22—42no—
271C22—41no—
272C22—41no—
273C22—41no—
274C22—81no—
275C22#386×C13111yescharacteristic
276C22#416×C13111yescharacteristic
277C22#418×C13111yescharacteristic
278C4—22no—
279C4—22no—
280C4—41no—
281C4—41no—
282C4—41no—
283C4—82no—
284C4—82no—
285C4#449×C13112yes—
286C4#482×C13112yes—
287C2—21no—
288C2—21no—
289C2—81no—
290C2#1875×C13111yescharacteristic
291C2#1909×C13111yescharacteristic
292C2#1915×C13111yescharacteristic
subgroupG/H
center, socleC22×C131#386
commutatorC22×C4C22×C4×C131
Frattini, cosocleC2×C42C23×C131
prime radicalC24×C131C22⋊C4
LCSG ▷ C22×C4 ▷ C22 ▷ C1
UCSC1 ◁ C22×C131 ◁ C2×C42×C131 ◁ G

Complements

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

NH ≅ G/Ntype
3. #1546×C131C2semidirect
5. #1286×C131C2semidirect
146. #9196C131direct (N × H)
147. C131#9196direct (N × H)
150. #1546C2×C131semidirect
152. #1286C2×C131semidirect

Maximal subgroups

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

subgroupindex
#2921×C1312
#2621×C1312
#1546×C1312
#1458×C1312
#1286×C1312
#9196131