Finite Group Databasebeta

← C131×#7692 #45693576

Subgroups — C131×#7692 #45693576

Order 33536.

444 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#2860×C131C211yesmaximal, characteristic
2#1745×C131C211yesmaximal, characteristic, complemented
3#1744×C131C211yesmaximal, characteristic, complemented
4#1271×C131C212yesmaximal, complemented
5#1270×C131C212yesmaximal
6C2×#126×C131—21no—
7C2×#97×C131—21no—
8C2×C4×C8×C131—21no—
9#390×C131C411yescharacteristic
10#390×C131C411yescharacteristic
11#390×C131C2211yescharacteristic
12#389×C131C411yescharacteristic
13#389×C131C411yescharacteristic
14#389×C131C2211yescharacteristic
15#388×C131—21no—
16#388×C131—21no—
17#388×C131—21no—
18C43×C131C2211yescharacteristic
19#336×C131—21no—
20#336×C131—21no—
21#336×C131C2212yes—
22#336×C131C2212yes—
23C22×D4×C131C2×C411yescharacteristic
24C22×C8×C131—22no—
25C22×C8×C131—22no—
26#126×C131—44no—
27C2×C4⋊C4×C131—21no—
28C2×C4⋊C4×C131—21no—
29C2×C4⋊C4×C131—21no—
30C2×C4⋊C4×C131C2×C411yescharacteristic
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
46#97×C131—24no—
47C4×C8×C131—24no—
48#95×C131—21no—
49#95×C131—21no—
50#95×C131—21no—
51C24×C131—21no—
52C2×D4×C131—22no—
53C2×D4×C131—41no—
54C2×D4×C131—41no—
55C22×C4×C131—21no—
56C22×C4×C131—21no—
57C22×C4×C131—21no—
58C22×C4×C131C22⋊C411yescharacteristic
59C22×C4×C131C22⋊C411yescharacteristic
60C22×C4×C131C22⋊C411yescharacteristic
61C22×C4×C131C22⋊C411yescharacteristic
62C22×C4×C131C22×C411yescharacteristic
63C22×C4×C131C2×D411yescharacteristic
64C22×C4×C131C2×D411yescharacteristic
65C2×C8×C131—24no—
66C2×C8×C131—24no—
67C2×C8×C131—42no—
68C2×C8×C131—42no—
69C2×C8×C131—42no—
70C2×C8×C131—42no—
71C4⋊C4×C131—22no—
72C4⋊C4×C131—41no—
73C4⋊C4×C131—41no—
74C4⋊C4×C131—42no—
75C4⋊C4×C131—42no—
76C4⋊C4×C131—42no—
77C22⋊C4×C131—42no—
78C22⋊C4×C131—42no—
79C22⋊C4×C131—42no—
80C22⋊C4×C131—42no—
81C22⋊C4×C131—42no—
82C22⋊C4×C131—42no—
83C42×C131—22no—
84C42×C131—22no—
85C42×C131—22no—
86C42×C131—22no—
87C42×C131—22no—
88C42×C131—41no—
89C42×C131—41no—
90C23×C131—41no—
91C23×C131—41no—
92C23×C131—41no—
93C23×C131—41no—
94C23×C131—41no—
95C23×C131—41no—
96C23×C131—41no—
97C23×C131C2×C22⋊C411yescharacteristic
98D4×C131—82no—
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—21no—
111C2×C4×C131—21no—
112C2×C4×C131—21no—
113C2×C4×C131—21no—
114C2×C4×C131—21no—
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#10412yes—
125C2×C4×C131#10412yes—
126C2×C4×C131#13112yes—
127C2×C4×C131#13512yes—
128C2×C4×C131AGL(1,ℤ/8)12yes—
129C8×C131—44no—
130C8×C131—44no—
131C22×C131—81no—
132C22×C131—81no—
133C22×C131—81no—
134C22×C131—81no—
135C22×C131—81no—
136C22×C131—81no—
137C22×C131—81no—
138C22×C131#40811yescharacteristic
139C22×C131#41011yescharacteristic
140C22×C131#41311yescharacteristic
141C22×C131#41611yescharacteristic
142C22×C131#41811yescharacteristic
143C22×C131C2×#10411yescharacteristic
144C22×C131C2×#10411yescharacteristic
145C4×C131—22no—
146C4×C131—22no—
147C4×C131—22no—
148C4×C131—22no—
149C4×C131—22no—
150C4×C131—41no—
151C4×C131—41no—
152C4×C131—81no—
153C4×C131—81no—
154C4×C131—81no—
155C2×C131—161no—
156C2×C131#147311yescharacteristic
157C2×C131#148411yescharacteristic
158C2×C131#149411yescharacteristic
159C2×C131#150011yescharacteristic
160C2×C131#150511yescharacteristic
161C2×C131#152411yescharacteristic
162C2×C131#155311yescharacteristic
163#7692C13111yesmaximal, characteristic, direct product factor, Sylow
164C131#769211yescharacteristic, direct product factor, Sylow
165#2860C2×C13111yescharacteristic
166#1745C2×C13111yescharacteristic, complemented
167#1744C2×C13111yescharacteristic, complemented
168#1271C2×C13112yescomplemented
169#1270C2×C13112yes—
170C2×#126—21no—
171C2×#97—21no—
172C2×C4×C8—21no—
173#390C4×C13111yescharacteristic
174#390C4×C13111yescharacteristic
175#390C22×C13111yescharacteristic
176#389C4×C13111yescharacteristic
177#389C4×C13111yescharacteristic
178#389C22×C13111yescharacteristic
179#388—21no—
180#388—21no—
181#388—21no—
182C43C22×C13111yescharacteristic
183#336—21no—
184#336—21no—
185#336C22×C13112yes—
186#336C22×C13112yes—
187C22×D4C2×C4×C13111yescharacteristic
188C22×C8—22no—
189C22×C8—22no—
190#126—44no—
191C2×C4⋊C4—21no—
192C2×C4⋊C4—21no—
193C2×C4⋊C4—21no—
194C2×C4⋊C4C2×C4×C13111yescharacteristic
195C2×C4⋊C4C2×C4×C13111yescharacteristic
196C2×C4⋊C4C2×C4×C13111yescharacteristic
197C2×C22⋊C4—21no—
198C2×C22⋊C4—21no—
199C2×C22⋊C4—21no—
200C2×C22⋊C4—21no—
201C2×C22⋊C4—21no—
202C2×C22⋊C4—21no—
203C2×C42C2×C4×C13111yescharacteristic
204C2×C42C2×C4×C13111yescharacteristic
205C2×C42D4×C13111yescharacteristic
206C2×C42D4×C13111yescharacteristic
207C2×C42D4×C13111yescharacteristic
208C2×C42D4×C13111yescharacteristic
209C2×C42C23×C13111yescharacteristic
210#97—24no—
211C4×C8—24no—
212#95—21no—
213#95—21no—
214#95—21no—
215C24—21no—
216C2×D4—22no—
217C2×D4—41no—
218C2×D4—41no—
219C22×C4—21no—
220C22×C4—21no—
221C22×C4—21no—
222C22×C4C22⋊C4×C13111yescharacteristic
223C22×C4C22⋊C4×C13111yescharacteristic
224C22×C4C22⋊C4×C13111yescharacteristic
225C22×C4C22⋊C4×C13111yescharacteristic
226C22×C4C22×C4×C13111yescharacteristic
227C22×C4C2×D4×C13111yescharacteristic
228C22×C4C2×D4×C13111yescharacteristic
229C2×C8—24no—
230C2×C8—24no—
231C2×C8—42no—
232C2×C8—42no—
233C2×C8—42no—
234C2×C8—42no—
235C4⋊C4—22no—
236C4⋊C4—41no—
237C4⋊C4—41no—
238C4⋊C4—42no—
239C4⋊C4—42no—
240C4⋊C4—42no—
241C22⋊C4—42no—
242C22⋊C4—42no—
243C22⋊C4—42no—
244C22⋊C4—42no—
245C22⋊C4—42no—
246C22⋊C4—42no—
247C42—22no—
248C42—22no—
249C42—22no—
250C42—22no—
251C42—22no—
252C42—41no—
253C42—41no—
254C23—41no—
255C23—41no—
256C23—41no—
257C23—41no—
258C23—41no—
259C23—41no—
260C23—41no—
261C23C2×C22⋊C4×C13111yescharacteristic
262D4—82no—
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—21no—
275C2×C4—21no—
276C2×C4—21no—
277C2×C4—21no—
278C2×C4—21no—
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#104×C13112yes—
289C2×C4#104×C13112yes—
290C2×C4#131×C13112yes—
291C2×C4#135×C13112yes—
292C2×C4AGL(1,ℤ/8)×C13112yes—
293C8—44no—
294C8—44no—
295C22—81no—
296C22—81no—
297C22—81no—
298C22—81no—
299C22—81no—
300C22—81no—
301C22—81no—
302C22#408×C13111yescharacteristic
303C22#410×C13111yescharacteristic
304C22#413×C13111yescharacteristic
305C22#416×C13111yescharacteristic
306C22#418×C13111yescharacteristic
307C22C2×#104×C13111yescharacteristic
308C22C2×#104×C13111yescharacteristic
309C4—22no—
310C4—22no—
311C4—22no—
312C4—22no—
313C4—22no—
314C4—41no—
315C4—41no—
316C4—81no—
317C4—81no—
318C4—81no—
319C2—161no—
320C2#1473×C13111yescharacteristic
321C2#1484×C13111yescharacteristic
322C2#1494×C13111yescharacteristic
323C2#1500×C13111yescharacteristic
324C2#1505×C13111yescharacteristic
325C2#1524×C13111yescharacteristic
326C2#1553×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. #1745×C131C2semidirect
3. #1744×C131C2semidirect
4. #1271×C131C2semidirect
163. #7692C131direct (N × H)
164. C131#7692direct (N × H)
166. #1745C2×C131semidirect
167. #1744C2×C131semidirect
168. #1271C2×C131semidirect

Maximal subgroups

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

subgroupindex
#2860×C1312
#1745×C1312
#1744×C1312
#1271×C1312
#1270×C1312
#7692131