Finite Group Databasebeta

← C131×#7656 #45693540

Subgroups — C131×#7656 #45693540

Order 33536.

432 conjugacy classes of subgroups.

The subgroup lattice has 332 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#2861×C131C211yesmaximal, characteristic
2#1839×C131C211yesmaximal, characteristic, complemented
3#1744×C131C211yesmaximal, characteristic, complemented
4#1272×C131C212yesmaximal, complemented
5#1270×C131C212yesmaximal
6C2×#125×C131C411yescharacteristic
7C2×#124×C131C411yescharacteristic
8C2×C4×C8×C131—21no—
9#391×C131C411yescharacteristic
10#391×C131C2211yescharacteristic
11#390×C131C411yescharacteristic
12#390×C131C2211yescharacteristic
13#388×C131—21no—
14#388×C131—21no—
15#388×C131—21no—
16#388×C131—21no—
17C43×C131C2211yescharacteristic
18#336×C131—21no—
19#336×C131—21no—
20#336×C131—21no—
21#336×C131C2212yes—
22#336×C131C2212yes—
23C22×Q8×C131C2×C411yescharacteristic
24C22×D4×C131C2×C411yescharacteristic
25C22×C8×C131—22no—
26C22×C8×C131—22no—
27#125×C131—42no—
28#124×C131—42no—
29C2×C4⋊C4×C131—21no—
30C2×C4⋊C4×C131—21no—
31C2×C4⋊C4×C131C2×C411yescharacteristic
32C2×C4⋊C4×C131C2×C411yescharacteristic
33C2×C22⋊C4×C131—21no—
34C2×C22⋊C4×C131—21no—
35C2×C22⋊C4×C131—21no—
36C2×C22⋊C4×C131—21no—
37C2×C22⋊C4×C131—21no—
38C2×C22⋊C4×C131—21no—
39C2×C42×C131C2×C411yescharacteristic
40C2×C42×C131C2×C411yescharacteristic
41C2×C42×C131D411yescharacteristic
42C2×C42×C131D411yescharacteristic
43C2×C42×C131D411yescharacteristic
44C2×C42×C131D411yescharacteristic
45C2×C42×C131C2311yescharacteristic
46C4×C8×C131—24no—
47#95×C131—21no—
48#95×C131—21no—
49#95×C131—21no—
50#95×C131—21no—
51C24×C131—21no—
52C2×Q8×C131—22no—
53C2×Q8×C131—41no—
54C2×Q8×C131—41no—
55C2×D4×C131—22no—
56C2×D4×C131—41no—
57C2×D4×C131—41no—
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—41no—
75C4⋊C4×C131—41no—
76C4⋊C4×C131—42no—
77C4⋊C4×C131—42no—
78C22⋊C4×C131—42no—
79C22⋊C4×C131—42no—
80C22⋊C4×C131—42no—
81C22⋊C4×C131—42no—
82C22⋊C4×C131—42no—
83C22⋊C4×C131—42no—
84C42×C131—22no—
85C42×C131—22no—
86C42×C131—22no—
87C42×C131—22no—
88C42×C131—22no—
89C42×C131—41no—
90C42×C131—41no—
91C23×C131—41no—
92C23×C131—41no—
93C23×C131—41no—
94C23×C131—41no—
95C23×C131—41no—
96C23×C131—41no—
97C23×C131—41no—
98C23×C131C2×C22⋊C411yescharacteristic
99Q8×C131—82no—
100D4×C131—82no—
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—21no—
111C2×C4×C131—21no—
112C2×C4×C131—21no—
113C2×C4×C131—21no—
114C2×C4×C131—21no—
115C2×C4×C131—21no—
116C2×C4×C131—21no—
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—41no—
125C2×C4×C131—41no—
126C2×C4×C131#10012yes—
127C2×C4×C131#10412yes—
128C2×C4×C131#13112yes—
129C2×C4×C131#13512yes—
130C2×C4×C131#13512yes—
131C8×C131—44no—
132C8×C131—82no—
133C22×C131—81no—
134C22×C131—81no—
135C22×C131—81no—
136C22×C131—81no—
137C22×C131—81no—
138C22×C131—81no—
139C22×C131—81no—
140C22×C131#40811yescharacteristic
141C22×C131#41011yescharacteristic
142C22×C131C2×#10011yescharacteristic
143C22×C131#41611yescharacteristic
144C22×C131#41611yescharacteristic
145C22×C131C2×#10411yescharacteristic
146C22×C131#42111yescharacteristic
147C4×C131—22no—
148C4×C131—22no—
149C4×C131—22no—
150C4×C131—22no—
151C4×C131—22no—
152C4×C131—41no—
153C4×C131—41no—
154C4×C131—81no—
155C4×C131—81no—
156C4×C131—81no—
157C2×C131—161no—
158C2×C131#146911yescharacteristic
159C2×C131#148211yescharacteristic
160C2×C131#149411yescharacteristic
161C2×C131#150011yescharacteristic
162C2×C131#152111yescharacteristic
163C2×C131#153011yescharacteristic
164C2×C131#154311yescharacteristic
165#7656C13111yesmaximal, characteristic, direct product factor, Sylow
166C131#765611yescharacteristic, direct product factor, Sylow
167#2861C2×C13111yescharacteristic
168#1839C2×C13111yescharacteristic, complemented
169#1744C2×C13111yescharacteristic, complemented
170#1272C2×C13112yescomplemented
171#1270C2×C13112yes—
172C2×#125C4×C13111yescharacteristic
173C2×#124C4×C13111yescharacteristic
174C2×C4×C8—21no—
175#391C4×C13111yescharacteristic
176#391C22×C13111yescharacteristic
177#390C4×C13111yescharacteristic
178#390C22×C13111yescharacteristic
179#388—21no—
180#388—21no—
181#388—21no—
182#388—21no—
183C43C22×C13111yescharacteristic
184#336—21no—
185#336—21no—
186#336—21no—
187#336C22×C13112yes—
188#336C22×C13112yes—
189C22×Q8C2×C4×C13111yescharacteristic
190C22×D4C2×C4×C13111yescharacteristic
191C22×C8—22no—
192C22×C8—22no—
193#125—42no—
194#124—42no—
195C2×C4⋊C4—21no—
196C2×C4⋊C4—21no—
197C2×C4⋊C4C2×C4×C13111yescharacteristic
198C2×C4⋊C4C2×C4×C13111yescharacteristic
199C2×C22⋊C4—21no—
200C2×C22⋊C4—21no—
201C2×C22⋊C4—21no—
202C2×C22⋊C4—21no—
203C2×C22⋊C4—21no—
204C2×C22⋊C4—21no—
205C2×C42C2×C4×C13111yescharacteristic
206C2×C42C2×C4×C13111yescharacteristic
207C2×C42D4×C13111yescharacteristic
208C2×C42D4×C13111yescharacteristic
209C2×C42D4×C13111yescharacteristic
210C2×C42D4×C13111yescharacteristic
211C2×C42C23×C13111yescharacteristic
212C4×C8—24no—
213#95—21no—
214#95—21no—
215#95—21no—
216#95—21no—
217C24—21no—
218C2×Q8—22no—
219C2×Q8—41no—
220C2×Q8—41no—
221C2×D4—22no—
222C2×D4—41no—
223C2×D4—41no—
224C22×C4—21no—
225C22×C4—21no—
226C22×C4—21no—
227C22×C4C22⋊C4×C13111yescharacteristic
228C22×C4C22⋊C4×C13111yescharacteristic
229C22×C4C22⋊C4×C13111yescharacteristic
230C22×C4C22⋊C4×C13111yescharacteristic
231C22×C4C22×C4×C13111yescharacteristic
232C22×C4C2×D4×C13111yescharacteristic
233C22×C4C2×D4×C13111yescharacteristic
234C2×C8—24no—
235C2×C8—42no—
236C2×C8—42no—
237C2×C8—42no—
238C2×C8—42no—
239C2×C8—42no—
240C4⋊C4—41no—
241C4⋊C4—41no—
242C4⋊C4—42no—
243C4⋊C4—42no—
244C22⋊C4—42no—
245C22⋊C4—42no—
246C22⋊C4—42no—
247C22⋊C4—42no—
248C22⋊C4—42no—
249C22⋊C4—42no—
250C42—22no—
251C42—22no—
252C42—22no—
253C42—22no—
254C42—22no—
255C42—41no—
256C42—41no—
257C23—41no—
258C23—41no—
259C23—41no—
260C23—41no—
261C23—41no—
262C23—41no—
263C23—41no—
264C23C2×C22⋊C4×C13111yescharacteristic
265Q8—82no—
266D4—82no—
267C2×C4—21no—
268C2×C4—21no—
269C2×C4—21no—
270C2×C4—21no—
271C2×C4—21no—
272C2×C4—21no—
273C2×C4—21no—
274C2×C4—21no—
275C2×C4—21no—
276C2×C4—21no—
277C2×C4—21no—
278C2×C4—21no—
279C2×C4—21no—
280C2×C4—21no—
281C2×C4—21no—
282C2×C4—21no—
283C2×C4—41no—
284C2×C4—41no—
285C2×C4—41no—
286C2×C4—41no—
287C2×C4—41no—
288C2×C4—41no—
289C2×C4—41no—
290C2×C4—41no—
291C2×C4—41no—
292C2×C4#100×C13112yes—
293C2×C4#104×C13112yes—
294C2×C4#131×C13112yes—
295C2×C4#135×C13112yes—
296C2×C4#135×C13112yes—
297C8—44no—
298C8—82no—
299C22—81no—
300C22—81no—
301C22—81no—
302C22—81no—
303C22—81no—
304C22—81no—
305C22—81no—
306C22#408×C13111yescharacteristic
307C22#410×C13111yescharacteristic
308C22C2×#100×C13111yescharacteristic
309C22#416×C13111yescharacteristic
310C22#416×C13111yescharacteristic
311C22C2×#104×C13111yescharacteristic
312C22#421×C13111yescharacteristic
313C4—22no—
314C4—22no—
315C4—22no—
316C4—22no—
317C4—22no—
318C4—41no—
319C4—41no—
320C4—81no—
321C4—81no—
322C4—81no—
323C2—161no—
324C2#1469×C13111yescharacteristic
325C2#1482×C13111yescharacteristic
326C2#1494×C13111yescharacteristic
327C2#1500×C13111yescharacteristic
328C2#1521×C13111yescharacteristic
329C2#1530×C13111yescharacteristic
330C2#1543×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. #1839×C131C2semidirect
3. #1744×C131C2semidirect
4. #1272×C131C2semidirect
165. #7656C131direct (N × H)
166. C131#7656direct (N × H)
168. #1839C2×C131semidirect
169. #1744C2×C131semidirect
170. #1272C2×C131semidirect

Maximal subgroups

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

subgroupindex
#2861×C1312
#1839×C1312
#1744×C1312
#1272×C1312
#1270×C1312
#7656131