Finite Group Databasebeta

← C131×#7706 #45693590

Subgroups — C131×#7706 #45693590

Order 33536.

426 conjugacy classes of subgroups.

The subgroup lattice has 336 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#2860×C131C211yesmaximal, characteristic
2#1831×C131C211yesmaximal, characteristic, complemented
3#1745×C131C211yesmaximal, characteristic, complemented
4#1271×C131C212yesmaximal, complemented
5#1270×C131C212yesmaximal
6C2×#126×C131—21no—
7C2×C4⋊C8×C131—21no—
8C2×#97×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
46C4⋊C8×C131—42no—
47#97×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—42no—
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—41no—
82C22⋊C4×C131—42no—
83C22⋊C4×C131—41no—
84C42×C131—22no—
85C42×C131—22no—
86C42×C131—21no—
87C42×C131—22no—
88C42×C131—21no—
89C42×C131—41no—
90C42×C131—41no—
91C42×C131—41no—
92C23×C131—41no—
93C23×C131—41no—
94C23×C131—41no—
95C23×C131—41no—
96C23×C131—41no—
97C23×C131—41no—
98C23×C131—41no—
99C23×C131C2×C22⋊C411yescharacteristic
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—21no—
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—41no—
127C2×C4×C131#10412yes—
128C2×C4×C131#13112yes—
129C2×C4×C131AGL(1,ℤ/8)11yescharacteristic
130C2×C4×C131AGL(1,ℤ/8)12yes—
131C2×C4×C131#13711yescharacteristic
132C8×C131—44no—
133C8×C131—82no—
134C22×C131—81no—
135C22×C131—81no—
136C22×C131—81no—
137C22×C131—81no—
138C22×C131—81no—
139C22×C131—81no—
140C22×C131—81no—
141C22×C131#40811yescharacteristic
142C22×C131#41011yescharacteristic
143C22×C131#41311yescharacteristic
144C22×C131#41711yescharacteristic
145C22×C131#41811yescharacteristic
146C22×C131C2×#10411yescharacteristic
147C22×C131#42111yescharacteristic
148C4×C131—22no—
149C4×C131—22no—
150C4×C131—22no—
151C4×C131—21no—
152C4×C131—21no—
153C4×C131—41no—
154C4×C131—41no—
155C4×C131—41no—
156C4×C131—81no—
157C4×C131—81no—
158C4×C131—81no—
159C2×C131—161no—
160C2×C131#147311yescharacteristic
161C2×C131#148311yescharacteristic
162C2×C131#149611yescharacteristic
163C2×C131#150511yescharacteristic
164C2×C131#151211yescharacteristic
165C2×C131#152911yescharacteristic
166C2×C131#155711yescharacteristic
167#7706C13111yesmaximal, characteristic, direct product factor, Sylow
168C131#770611yescharacteristic, direct product factor, Sylow
169#2860C2×C13111yescharacteristic
170#1831C2×C13111yescharacteristic, complemented
171#1745C2×C13111yescharacteristic, complemented
172#1271C2×C13112yescomplemented
173#1270C2×C13112yes—
174C2×#126—21no—
175C2×C4⋊C8—21no—
176C2×#97—21no—
177#390C4×C13111yescharacteristic
178#390C4×C13111yescharacteristic
179#390C22×C13111yescharacteristic
180#389C4×C13111yescharacteristic
181#389C4×C13111yescharacteristic
182#389C22×C13111yescharacteristic
183#388—21no—
184#388—21no—
185#388—21no—
186C43C22×C13111yescharacteristic
187#336—21no—
188#336—21no—
189#336C22×C13112yes—
190#336C22×C13112yes—
191C22×D4C2×C4×C13111yescharacteristic
192C22×C8—22no—
193C22×C8—22no—
194#126—44no—
195C2×C4⋊C4—21no—
196C2×C4⋊C4—21no—
197C2×C4⋊C4—21no—
198C2×C4⋊C4C2×C4×C13111yescharacteristic
199C2×C4⋊C4C2×C4×C13111yescharacteristic
200C2×C4⋊C4C2×C4×C13111yescharacteristic
201C2×C22⋊C4—21no—
202C2×C22⋊C4—21no—
203C2×C22⋊C4—21no—
204C2×C22⋊C4—21no—
205C2×C22⋊C4—21no—
206C2×C22⋊C4—21no—
207C2×C42C2×C4×C13111yescharacteristic
208C2×C42C2×C4×C13111yescharacteristic
209C2×C42D4×C13111yescharacteristic
210C2×C42D4×C13111yescharacteristic
211C2×C42D4×C13111yescharacteristic
212C2×C42D4×C13111yescharacteristic
213C2×C42C23×C13111yescharacteristic
214C4⋊C8—42no—
215#97—24no—
216#95—21no—
217#95—21no—
218#95—21no—
219C24—21no—
220C2×D4—22no—
221C2×D4—41no—
222C2×D4—41no—
223C22×C4—21no—
224C22×C4—21no—
225C22×C4—21no—
226C22×C4C22⋊C4×C13111yescharacteristic
227C22×C4C22⋊C4×C13111yescharacteristic
228C22×C4C22⋊C4×C13111yescharacteristic
229C22×C4C22⋊C4×C13111yescharacteristic
230C22×C4C22×C4×C13111yescharacteristic
231C22×C4C2×D4×C13111yescharacteristic
232C22×C4C2×D4×C13111yescharacteristic
233C2×C8—24no—
234C2×C8—42no—
235C2×C8—42no—
236C2×C8—42no—
237C2×C8—42no—
238C2×C8—42no—
239C4⋊C4—22no—
240C4⋊C4—41no—
241C4⋊C4—41no—
242C4⋊C4—42no—
243C4⋊C4—42no—
244C4⋊C4—42no—
245C22⋊C4—42no—
246C22⋊C4—42no—
247C22⋊C4—42no—
248C22⋊C4—42no—
249C22⋊C4—41no—
250C22⋊C4—42no—
251C22⋊C4—41no—
252C42—22no—
253C42—22no—
254C42—21no—
255C42—22no—
256C42—21no—
257C42—41no—
258C42—41no—
259C42—41no—
260C23—41no—
261C23—41no—
262C23—41no—
263C23—41no—
264C23—41no—
265C23—41no—
266C23—41no—
267C23C2×C22⋊C4×C13111yescharacteristic
268D4—82no—
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—21no—
284C2×C4—21no—
285C2×C4—21no—
286C2×C4—41no—
287C2×C4—41no—
288C2×C4—41no—
289C2×C4—41no—
290C2×C4—41no—
291C2×C4—41no—
292C2×C4—41no—
293C2×C4—41no—
294C2×C4—41no—
295C2×C4#104×C13112yes—
296C2×C4#131×C13112yes—
297C2×C4AGL(1,ℤ/8)×C13111yescharacteristic
298C2×C4AGL(1,ℤ/8)×C13112yes—
299C2×C4#137×C13111yescharacteristic
300C8—44no—
301C8—82no—
302C22—81no—
303C22—81no—
304C22—81no—
305C22—81no—
306C22—81no—
307C22—81no—
308C22—81no—
309C22#408×C13111yescharacteristic
310C22#410×C13111yescharacteristic
311C22#413×C13111yescharacteristic
312C22#417×C13111yescharacteristic
313C22#418×C13111yescharacteristic
314C22C2×#104×C13111yescharacteristic
315C22#421×C13111yescharacteristic
316C4—22no—
317C4—22no—
318C4—22no—
319C4—21no—
320C4—21no—
321C4—41no—
322C4—41no—
323C4—41no—
324C4—81no—
325C4—81no—
326C4—81no—
327C2—161no—
328C2#1473×C13111yescharacteristic
329C2#1483×C13111yescharacteristic
330C2#1496×C13111yescharacteristic
331C2#1505×C13111yescharacteristic
332C2#1512×C13111yescharacteristic
333C2#1529×C13111yescharacteristic
334C2#1557×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. #1831×C131C2semidirect
3. #1745×C131C2semidirect
4. #1271×C131C2semidirect
167. #7706C131direct (N × H)
168. C131#7706direct (N × H)
170. #1831C2×C131semidirect
171. #1745C2×C131semidirect
172. #1271C2×C131semidirect

Maximal subgroups

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

subgroupindex
#2860×C1312
#1831×C1312
#1745×C1312
#1271×C1312
#1270×C1312
#7706131