Finite Group Databasebeta

← C131×#7615 #45693499

Subgroups — C131×#7615 #45693499

Order 33536.

428 conjugacy classes of subgroups.

The subgroup lattice has 328 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#2295×C131C211yesmaximal, characteristic
2#1831×C131C211yesmaximal, characteristic
3#1767×C131C211yesmaximal, characteristic
4#1272×C131C212yesmaximal
5#1271×C131C212yesmaximal
6C2×C4×Q8×C131C411yescharacteristic
7C2×C4⋊C8×C131—21no—
8C2×C4⋊C8×C131—21no—
9C2×#97×C131—21no—
10#391×C131C411yescharacteristic
11#391×C131C2211yescharacteristic
12#389×C131C411yescharacteristic
13#389×C131C2211yescharacteristic
14#387×C131—21no—
15#387×C131—21no—
16C4×C4⋊C4×C131—21no—
17C4×C4⋊C4×C131C411yescharacteristic
18#376×C131—21no—
19C43×C131C2211yescharacteristic
20#336×C131—21no—
21#336×C131C2212yes—
22#336×C131C2212yes—
23C22×Q8×C131C2×C411yescharacteristic
24C22×C8×C131—22no—
25C22×C8×C131—22no—
26C4×Q8×C131—22no—
27C4×Q8×C131—22no—
28C2×C4⋊C4×C131—21no—
29C2×C4⋊C4×C131—21no—
30C2×C4⋊C4×C131—21no—
31C2×C4⋊C4×C131C2×C411yescharacteristic
32C2×C4⋊C4×C131C2×C411yescharacteristic
33C2×C4⋊C4×C131C2×C411yescharacteristic
34C2×C42×C131—21no—
35C2×C42×C131—21no—
36C2×C42×C131C2×C411yescharacteristic
37C2×C42×C131C2×C411yescharacteristic
38C2×C42×C131D411yescharacteristic
39C2×C42×C131D411yescharacteristic
40C2×C42×C131D411yescharacteristic
41C2×C42×C131D411yescharacteristic
42C2×C42×C131C2311yescharacteristic
43C4⋊C8×C131—24no—
44C4⋊C8×C131—42no—
45#97×C131—42no—
46#95×C131—21no—
47#95×C131—21no—
48#95×C131—21no—
49#95×C131—21no—
50#95×C131—21no—
51#95×C131—21no—
52#95×C131—21no—
53C2×Q8×C131—21no—
54C2×Q8×C131—41no—
55C2×Q8×C131—41no—
56C2×Q8×C131M1612yes—
57C22×C4×C131—21no—
58C22×C4×C131—21no—
59C22×C4×C131—21no—
60C22×C4×C131—21no—
61C22×C4×C131C22⋊C411yescharacteristic
62C22×C4×C131C22⋊C411yescharacteristic
63C22×C4×C131C22⋊C411yescharacteristic
64C22×C4×C131C22⋊C411yescharacteristic
65C22×C4×C131C22×C411yescharacteristic
66C22×C4×C131C2×D411yescharacteristic
67C22×C4×C131C2×D411yescharacteristic
68C2×C8×C131—24no—
69C2×C8×C131—42no—
70C2×C8×C131—42no—
71C2×C8×C131—42no—
72C2×C8×C131—42no—
73C2×C8×C131—42no—
74C4⋊C4×C131—24no—
75C4⋊C4×C131—21no—
76C4⋊C4×C131—41no—
77C4⋊C4×C131—41no—
78C4⋊C4×C131—42no—
79C4⋊C4×C131—41no—
80C4⋊C4×C131—41no—
81C4⋊C4×C131M1612yes—
82C42×C131—24no—
83C42×C131—22no—
84C42×C131—21no—
85C42×C131—21no—
86C42×C131—21no—
87C42×C131—21no—
88C42×C131—41no—
89C42×C131—41no—
90C42×C131—41no—
91C42×C131—42no—
92C42×C131SD1612yes—
93C42×C131Q1612yes—
94C23×C131C2×C22⋊C411yescharacteristic
95Q8×C131—42no—
96Q8×C131—42no—
97C2×C4×C131—21no—
98C2×C4×C131—21no—
99C2×C4×C131—21no—
100C2×C4×C131—21no—
101C2×C4×C131—21no—
102C2×C4×C131—21no—
103C2×C4×C131—21no—
104C2×C4×C131—21no—
105C2×C4×C131—21no—
106C2×C4×C131—21no—
107C2×C4×C131—21no—
108C2×C4×C131—21no—
109C2×C4×C131—21no—
110C2×C4×C131—22no—
111C2×C4×C131—22no—
112C2×C4×C131—21no—
113C2×C4×C131—21no—
114C2×C4×C131—41no—
115C2×C4×C131—41no—
116C2×C4×C131—41no—
117C2×C4×C131—41no—
118C2×C4×C131—41no—
119C2×C4×C131—41no—
120C2×C4×C131—41no—
121C2×C4×C131—41no—
122C2×C4×C131—41no—
123C2×C4×C131—41no—
124C2×C4×C131#10312yes—
125C2×C4×C131#10312yes—
126C2×C4×C131#10412yes—
127C2×C4×C131C2×M1611yescharacteristic
128C2×C4×C131C2×M1611yescharacteristic
129C2×C4×C131C2×SD1611yescharacteristic
130C2×C4×C131C2×Q1611yescharacteristic
131C2×C4×C131AGL(1,ℤ/8)11yescharacteristic
132C2×C4×C131#13711yescharacteristic
133C8×C131—44no—
134C8×C131—82no—
135C22×C131#40711yescharacteristic
136C22×C131#41011yescharacteristic
137C22×C131#41311yescharacteristic
138C22×C131C2×#10311yescharacteristic
139C22×C131#41711yescharacteristic
140C22×C131C2×#10411yescharacteristic
141C22×C131#42111yescharacteristic
142C4×C131—22no—
143C4×C131—21no—
144C4×C131—21no—
145C4×C131—22no—
146C4×C131—21no—
147C4×C131—21no—
148C4×C131—21no—
149C4×C131—21no—
150C4×C131—22no—
151C4×C131—42no—
152C4×C131—41no—
153C4×C131—42no—
154C4×C131—81no—
155C4×C131—81no—
156C2×C131#146411yescharacteristic
157C2×C131#148711yescharacteristic
158C2×C131#148911yescharacteristic
159C2×C131#150311yescharacteristic
160C2×C131#151211yescharacteristic
161C2×C131#153211yescharacteristic
162C2×C131#155011yescharacteristic
163#7615C13111yesmaximal, characteristic, direct product factor, Sylow
164C131#761511yescharacteristic, direct product factor, Sylow
165#2295C2×C13111yescharacteristic
166#1831C2×C13111yescharacteristic
167#1767C2×C13111yescharacteristic
168#1272C2×C13112yes—
169#1271C2×C13112yes—
170C2×C4×Q8C4×C13111yescharacteristic
171C2×C4⋊C8—21no—
172C2×C4⋊C8—21no—
173C2×#97—21no—
174#391C4×C13111yescharacteristic
175#391C22×C13111yescharacteristic
176#389C4×C13111yescharacteristic
177#389C22×C13111yescharacteristic
178#387—21no—
179#387—21no—
180C4×C4⋊C4—21no—
181C4×C4⋊C4C4×C13111yescharacteristic
182#376—21no—
183C43C22×C13111yescharacteristic
184#336—21no—
185#336C22×C13112yes—
186#336C22×C13112yes—
187C22×Q8C2×C4×C13111yescharacteristic
188C22×C8—22no—
189C22×C8—22no—
190C4×Q8—22no—
191C4×Q8—22no—
192C2×C4⋊C4—21no—
193C2×C4⋊C4—21no—
194C2×C4⋊C4—21no—
195C2×C4⋊C4C2×C4×C13111yescharacteristic
196C2×C4⋊C4C2×C4×C13111yescharacteristic
197C2×C4⋊C4C2×C4×C13111yescharacteristic
198C2×C42—21no—
199C2×C42—21no—
200C2×C42C2×C4×C13111yescharacteristic
201C2×C42C2×C4×C13111yescharacteristic
202C2×C42D4×C13111yescharacteristic
203C2×C42D4×C13111yescharacteristic
204C2×C42D4×C13111yescharacteristic
205C2×C42D4×C13111yescharacteristic
206C2×C42C23×C13111yescharacteristic
207C4⋊C8—24no—
208C4⋊C8—42no—
209#97—42no—
210#95—21no—
211#95—21no—
212#95—21no—
213#95—21no—
214#95—21no—
215#95—21no—
216#95—21no—
217C2×Q8—21no—
218C2×Q8—41no—
219C2×Q8—41no—
220C2×Q8M16×C13112yes—
221C22×C4—21no—
222C22×C4—21no—
223C22×C4—21no—
224C22×C4—21no—
225C22×C4C22⋊C4×C13111yescharacteristic
226C22×C4C22⋊C4×C13111yescharacteristic
227C22×C4C22⋊C4×C13111yescharacteristic
228C22×C4C22⋊C4×C13111yescharacteristic
229C22×C4C22×C4×C13111yescharacteristic
230C22×C4C2×D4×C13111yescharacteristic
231C22×C4C2×D4×C13111yescharacteristic
232C2×C8—24no—
233C2×C8—42no—
234C2×C8—42no—
235C2×C8—42no—
236C2×C8—42no—
237C2×C8—42no—
238C4⋊C4—24no—
239C4⋊C4—21no—
240C4⋊C4—41no—
241C4⋊C4—41no—
242C4⋊C4—42no—
243C4⋊C4—41no—
244C4⋊C4—41no—
245C4⋊C4M16×C13112yes—
246C42—24no—
247C42—22no—
248C42—21no—
249C42—21no—
250C42—21no—
251C42—21no—
252C42—41no—
253C42—41no—
254C42—41no—
255C42—42no—
256C42SD16×C13112yes—
257C42Q16×C13112yes—
258C23C2×C22⋊C4×C13111yescharacteristic
259Q8—42no—
260Q8—42no—
261C2×C4—21no—
262C2×C4—21no—
263C2×C4—21no—
264C2×C4—21no—
265C2×C4—21no—
266C2×C4—21no—
267C2×C4—21no—
268C2×C4—21no—
269C2×C4—21no—
270C2×C4—21no—
271C2×C4—21no—
272C2×C4—21no—
273C2×C4—21no—
274C2×C4—22no—
275C2×C4—22no—
276C2×C4—21no—
277C2×C4—21no—
278C2×C4—41no—
279C2×C4—41no—
280C2×C4—41no—
281C2×C4—41no—
282C2×C4—41no—
283C2×C4—41no—
284C2×C4—41no—
285C2×C4—41no—
286C2×C4—41no—
287C2×C4—41no—
288C2×C4#103×C13112yes—
289C2×C4#103×C13112yes—
290C2×C4#104×C13112yes—
291C2×C4C2×M16×C13111yescharacteristic
292C2×C4C2×M16×C13111yescharacteristic
293C2×C4C2×SD16×C13111yescharacteristic
294C2×C4C2×Q16×C13111yescharacteristic
295C2×C4AGL(1,ℤ/8)×C13111yescharacteristic
296C2×C4#137×C13111yescharacteristic
297C8—44no—
298C8—82no—
299C22#407×C13111yescharacteristic
300C22#410×C13111yescharacteristic
301C22#413×C13111yescharacteristic
302C22C2×#103×C13111yescharacteristic
303C22#417×C13111yescharacteristic
304C22C2×#104×C13111yescharacteristic
305C22#421×C13111yescharacteristic
306C4—21no—
307C4—21no—
308C4—22no—
309C4—21no—
310C4—21no—
311C4—21no—
312C4—21no—
313C4—22no—
314C4—22no—
315C4—42no—
316C4—41no—
317C4—42no—
318C4—81no—
319C4—81no—
320C2#1464×C13111yescharacteristic
321C2#1487×C13111yescharacteristic
322C2#1489×C13111yescharacteristic
323C2#1503×C13111yescharacteristic
324C2#1512×C13111yescharacteristic
325C2#1532×C13111yescharacteristic
326C2#1550×C13111yescharacteristic
subgroupG/H
center, socle, prime radicalC23×C131C2×C22⋊C4
commutatorC22×C4C22×C4×C131
Frattini, cosocleC2×C42C23×C131
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
163. #7615C131direct (N × H)
164. C131#7615direct (N × H)

Maximal subgroups

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

subgroupindex
#2295×C1312
#1831×C1312
#1767×C1312
#1272×C1312
#1271×C1312
#7615131