Finite Group Databasebeta

← C131×#7676 #45693560

Subgroups — C131×#7676 #45693560

Order 33536.

458 conjugacy classes of subgroups.

The subgroup lattice has 344 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#2861×C131C211yesmaximal, characteristic
2C4×C4⋊C8×C131C211yesmaximal, characteristic, complemented
3#1745×C131C211yesmaximal, characteristic, complemented
4#1272×C131C212yesmaximal, complemented
5#1270×C131C212yesmaximal
6C2×#125×C131C411yescharacteristic
7C2×#124×C131C411yescharacteristic
8C2×C4⋊C8×C131—21no—
9C2×#97×C131—21no—
10C2×C4×C8×C131—21no—
11#391×C131C411yescharacteristic
12#391×C131C2211yescharacteristic
13#390×C131C411yescharacteristic
14#390×C131C2211yescharacteristic
15#388×C131—21no—
16#388×C131—21no—
17#388×C131—21no—
18#388×C131—21no—
19C43×C131C2211yescharacteristic
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#97×C131—24no—
48C4×C8×C131—42no—
49#95×C131—21no—
50#95×C131—21no—
51#95×C131—21no—
52#95×C131—21no—
53C24×C131—21no—
54C2×Q8×C131—22no—
55C2×Q8×C131—41no—
56C2×Q8×C131—41no—
57C2×D4×C131—22no—
58C2×D4×C131—41no—
59C2×D4×C131—41no—
60C22×C4×C131—21no—
61C22×C4×C131—21no—
62C22×C4×C131—21no—
63C22×C4×C131C22⋊C411yescharacteristic
64C22×C4×C131C22⋊C411yescharacteristic
65C22×C4×C131C22⋊C411yescharacteristic
66C22×C4×C131C22⋊C411yescharacteristic
67C22×C4×C131C22×C411yescharacteristic
68C22×C4×C131C2×D411yescharacteristic
69C22×C4×C131C2×D411yescharacteristic
70C2×C8×C131—24no—
71C2×C8×C131—24no—
72C2×C8×C131—42no—
73C2×C8×C131—42no—
74C2×C8×C131—42no—
75C2×C8×C131—42no—
76C4⋊C4×C131—41no—
77C4⋊C4×C131—41no—
78C4⋊C4×C131—42no—
79C4⋊C4×C131—42no—
80C22⋊C4×C131—42no—
81C22⋊C4×C131—42no—
82C22⋊C4×C131—42no—
83C22⋊C4×C131—42no—
84C22⋊C4×C131—42no—
85C22⋊C4×C131—41no—
86C22⋊C4×C131—41no—
87C42×C131—22no—
88C42×C131—22no—
89C42×C131—22no—
90C42×C131—22no—
91C42×C131—22no—
92C42×C131—21no—
93C42×C131—21no—
94C42×C131—41no—
95C23×C131—41no—
96C23×C131—41no—
97C23×C131—41no—
98C23×C131—41no—
99C23×C131—41no—
100C23×C131—41no—
101C23×C131—41no—
102C23×C131C2×C22⋊C411yescharacteristic
103Q8×C131—82no—
104D4×C131—82no—
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—21no—
119C2×C4×C131—21no—
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—41no—
128C2×C4×C131—41no—
129C2×C4×C131#10012yes—
130C2×C4×C131#10412yes—
131C2×C4×C131#10412yes—
132C2×C4×C131#13112yes—
133C2×C4×C131#13512yes—
134C2×C4×C131AGL(1,ℤ/8)11yescharacteristic
135C2×C4×C131#13711yescharacteristic
136C8×C131—44no—
137C8×C131—44no—
138C22×C131—81no—
139C22×C131—81no—
140C22×C131—81no—
141C22×C131—81no—
142C22×C131—81no—
143C22×C131—81no—
144C22×C131—81no—
145C22×C131#40811yescharacteristic
146C22×C131#41011yescharacteristic
147C22×C131C2×#10011yescharacteristic
148C22×C131#41611yescharacteristic
149C22×C131#41711yescharacteristic
150C22×C131C2×#10411yescharacteristic
151C22×C131C2×#10411yescharacteristic
152C4×C131—22no—
153C4×C131—22no—
154C4×C131—22no—
155C4×C131—22no—
156C4×C131—22no—
157C4×C131—21no—
158C4×C131—21no—
159C4×C131—41no—
160C4×C131—81no—
161C4×C131—81no—
162C4×C131—81no—
163C2×C131—161no—
164C2×C131#146911yescharacteristic
165C2×C131#148311yescharacteristic
166C2×C131#149411yescharacteristic
167C2×C131#150011yescharacteristic
168C2×C131#150911yescharacteristic
169C2×C131#152511yescharacteristic
170C2×C131#155111yescharacteristic
171#7676C13111yesmaximal, characteristic, direct product factor, Sylow
172C131#767611yescharacteristic, direct product factor, Sylow
173#2861C2×C13111yescharacteristic
174C4×C4⋊C8C2×C13111yescharacteristic, complemented
175#1745C2×C13111yescharacteristic, complemented
176#1272C2×C13112yescomplemented
177#1270C2×C13112yes—
178C2×#125C4×C13111yescharacteristic
179C2×#124C4×C13111yescharacteristic
180C2×C4⋊C8—21no—
181C2×#97—21no—
182C2×C4×C8—21no—
183#391C4×C13111yescharacteristic
184#391C22×C13111yescharacteristic
185#390C4×C13111yescharacteristic
186#390C22×C13111yescharacteristic
187#388—21no—
188#388—21no—
189#388—21no—
190#388—21no—
191C43C22×C13111yescharacteristic
192#336—21no—
193#336C22×C13112yes—
194#336C22×C13112yes—
195C22×Q8C2×C4×C13111yescharacteristic
196C22×D4C2×C4×C13111yescharacteristic
197C22×C8—22no—
198C22×C8—22no—
199#125—42no—
200#124—42no—
201C2×C4⋊C4—21no—
202C2×C4⋊C4—21no—
203C2×C4⋊C4C2×C4×C13111yescharacteristic
204C2×C4⋊C4C2×C4×C13111yescharacteristic
205C2×C22⋊C4—21no—
206C2×C22⋊C4—21no—
207C2×C22⋊C4—21no—
208C2×C22⋊C4—21no—
209C2×C22⋊C4—21no—
210C2×C22⋊C4—21no—
211C2×C42C2×C4×C13111yescharacteristic
212C2×C42C2×C4×C13111yescharacteristic
213C2×C42D4×C13111yescharacteristic
214C2×C42D4×C13111yescharacteristic
215C2×C42D4×C13111yescharacteristic
216C2×C42D4×C13111yescharacteristic
217C2×C42C23×C13111yescharacteristic
218C4⋊C8—24no—
219#97—24no—
220C4×C8—42no—
221#95—21no—
222#95—21no—
223#95—21no—
224#95—21no—
225C24—21no—
226C2×Q8—22no—
227C2×Q8—41no—
228C2×Q8—41no—
229C2×D4—22no—
230C2×D4—41no—
231C2×D4—41no—
232C22×C4—21no—
233C22×C4—21no—
234C22×C4—21no—
235C22×C4C22⋊C4×C13111yescharacteristic
236C22×C4C22⋊C4×C13111yescharacteristic
237C22×C4C22⋊C4×C13111yescharacteristic
238C22×C4C22⋊C4×C13111yescharacteristic
239C22×C4C22×C4×C13111yescharacteristic
240C22×C4C2×D4×C13111yescharacteristic
241C22×C4C2×D4×C13111yescharacteristic
242C2×C8—24no—
243C2×C8—24no—
244C2×C8—42no—
245C2×C8—42no—
246C2×C8—42no—
247C2×C8—42no—
248C4⋊C4—41no—
249C4⋊C4—41no—
250C4⋊C4—42no—
251C4⋊C4—42no—
252C22⋊C4—42no—
253C22⋊C4—42no—
254C22⋊C4—42no—
255C22⋊C4—42no—
256C22⋊C4—42no—
257C22⋊C4—41no—
258C22⋊C4—41no—
259C42—22no—
260C42—22no—
261C42—22no—
262C42—22no—
263C42—22no—
264C42—21no—
265C42—21no—
266C42—41no—
267C23—41no—
268C23—41no—
269C23—41no—
270C23—41no—
271C23—41no—
272C23—41no—
273C23—41no—
274C23C2×C22⋊C4×C13111yescharacteristic
275Q8—82no—
276D4—82no—
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—21no—
287C2×C4—21no—
288C2×C4—21no—
289C2×C4—21no—
290C2×C4—21no—
291C2×C4—21no—
292C2×C4—41no—
293C2×C4—41no—
294C2×C4—41no—
295C2×C4—41no—
296C2×C4—41no—
297C2×C4—41no—
298C2×C4—41no—
299C2×C4—41no—
300C2×C4—41no—
301C2×C4#100×C13112yes—
302C2×C4#104×C13112yes—
303C2×C4#104×C13112yes—
304C2×C4#131×C13112yes—
305C2×C4#135×C13112yes—
306C2×C4AGL(1,ℤ/8)×C13111yescharacteristic
307C2×C4#137×C13111yescharacteristic
308C8—44no—
309C8—44no—
310C22—81no—
311C22—81no—
312C22—81no—
313C22—81no—
314C22—81no—
315C22—81no—
316C22—81no—
317C22#408×C13111yescharacteristic
318C22#410×C13111yescharacteristic
319C22C2×#100×C13111yescharacteristic
320C22#416×C13111yescharacteristic
321C22#417×C13111yescharacteristic
322C22C2×#104×C13111yescharacteristic
323C22C2×#104×C13111yescharacteristic
324C4—22no—
325C4—22no—
326C4—22no—
327C4—22no—
328C4—21no—
329C4—21no—
330C4—22no—
331C4—41no—
332C4—81no—
333C4—81no—
334C4—81no—
335C2—161no—
336C2#1469×C13111yescharacteristic
337C2#1483×C13111yescharacteristic
338C2#1494×C13111yescharacteristic
339C2#1500×C13111yescharacteristic
340C2#1509×C13111yescharacteristic
341C2#1525×C13111yescharacteristic
342C2#1551×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. C4×C4⋊C8×C131C2semidirect
3. #1745×C131C2semidirect
4. #1272×C131C2semidirect
171. #7676C131direct (N × H)
172. C131#7676direct (N × H)
174. C4×C4⋊C8C2×C131semidirect
175. #1745C2×C131semidirect
176. #1272C2×C131semidirect

Maximal subgroups

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

subgroupindex
#2861×C1312
C4×C4⋊C8×C1312
#1745×C1312
#1272×C1312
#1270×C1312
#7676131