Finite Group Databasebeta

← C131×#7690 #45693574

Subgroups — C131×#7690 #45693574

Order 33536.

600 conjugacy classes of subgroups.

The subgroup lattice has 402 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#2850×C131C211yesmaximal, characteristic
2#1749×C131C211yesmaximal, characteristic, complemented
3C2×#336×C131C211yesmaximal, characteristic, complemented
4#1272×C131C212yesmaximal, complemented
5#1270×C131C212yesmaximal, complemented
6C23×C8×C131—21no—
7C2×#124×C131C411yescharacteristic
8C2×C22⋊Q8×C131C411yescharacteristic
9C2×#121×C131C411yescharacteristic
10C22×C42×C131C2211yescharacteristic
11C2×C22⋊C8×C131—21no—
12C2×#97×C131—21no—
13#391×C131C2211yescharacteristic
14#390×C131C2211yescharacteristic
15#388×C131—21no—
16#388×C131—21no—
17#386×C131—21no—
18#386×C131—21no—
19#382×C131C411yescharacteristic
20#336×C131—21no—
21#336×C131C2212yes—
22#336×C131C2212yes—
23C22×Q8×C131C2×C411yescharacteristic
24C22×D4×C131—21no—
25C22×D4×C131C2×C411yescharacteristic
26C23×C4×C131C2×C411yescharacteristic
27C23×C4×C131D411yescharacteristic
28C23×C4×C131D411yescharacteristic
29C22×C8×C131—24no—
30C22×C8×C131—22no—
31C22×C8×C131—22no—
32C22×C8×C131—42no—
33C22×C8×C131—42no—
34#124×C131—42no—
35C22⋊Q8×C131—42no—
36#121×C131—42no—
37C2×C4⋊C4×C131—21no—
38C2×C4⋊C4×C131C2×C411yescharacteristic
39C2×C4⋊C4×C131C2×C411yescharacteristic
40C2×C22⋊C4×C131—21no—
41C2×C22⋊C4×C131—21no—
42C2×C22⋊C4×C131—21no—
43C2×C22⋊C4×C131—21no—
44C2×C22⋊C4×C131—21no—
45C2×C22⋊C4×C131—21no—
46C2×C42×C131—42no—
47C2×C42×C131C2×C411yescharacteristic
48C2×C42×C131D411yescharacteristic
49C2×C42×C131D411yescharacteristic
50C2×C42×C131C2311yescharacteristic
51C22⋊C8×C131—24no—
52#97×C131—42no—
53#95×C131—21no—
54#95×C131—21no—
55#95×C131—21no—
56#95×C131—21no—
57C24×C131—21no—
58C24×C131C22⋊C411yescharacteristic
59C2×Q8×C131—22no—
60C2×Q8×C131—41no—
61C2×Q8×C131—41no—
62C2×D4×C131—22no—
63C2×D4×C131—41no—
64C2×D4×C131—41no—
65C2×D4×C131—42no—
66C2×D4×C131—42no—
67C2×D4×C131—42no—
68C22×C4×C131—22no—
69C22×C4×C131—22no—
70C22×C4×C131—21no—
71C22×C4×C131—21no—
72C22×C4×C131—22no—
73C22×C4×C131—22no—
74C22×C4×C131—22no—
75C22×C4×C131—22no—
76C22×C4×C131—21no—
77C22×C4×C131—21no—
78C22×C4×C131—21no—
79C22×C4×C131—41no—
80C22×C4×C131—41no—
81C22×C4×C131C22⋊C411yescharacteristic
82C22×C4×C131C22⋊C411yescharacteristic
83C22×C4×C131C22⋊C411yescharacteristic
84C22×C4×C131C22×C411yescharacteristic
85C22×C4×C131C2×D411yescharacteristic
86C22×C4×C131C2×D411yescharacteristic
87C2×C8×C131—24no—
88C2×C8×C131—24no—
89C2×C8×C131—42no—
90C2×C8×C131—48no—
91C2×C8×C131—42no—
92C2×C8×C131—42no—
93C2×C8×C131—42no—
94C4⋊C4×C131—41no—
95C4⋊C4×C131—41no—
96C4⋊C4×C131—42no—
97C22⋊C4×C131—42no—
98C22⋊C4×C131—42no—
99C22⋊C4×C131—42no—
100C22⋊C4×C131—42no—
101C22⋊C4×C131—42no—
102C22⋊C4×C131—41no—
103C22⋊C4×C131—41no—
104C42×C131—22no—
105C42×C131—22no—
106C42×C131—41no—
107C42×C131—41no—
108C23×C131—21no—
109C23×C131—21no—
110C23×C131—21no—
111C23×C131—21no—
112C23×C131—41no—
113C23×C131—41no—
114C23×C131—41no—
115C23×C131—41no—
116C23×C131—41no—
117C23×C131—41no—
118C23×C131—41no—
119C23×C131#10012yes—
120C23×C131#10412yes—
121C23×C131#10412yes—
122C23×C131C2×C22⋊C411yescharacteristic
123Q8×C131—82no—
124D4×C131—82no—
125D4×C131—84no—
126C2×C4×C131—24no—
127C2×C4×C131—24no—
128C2×C4×C131—21no—
129C2×C4×C131—21no—
130C2×C4×C131—21no—
131C2×C4×C131—21no—
132C2×C4×C131—21no—
133C2×C4×C131—21no—
134C2×C4×C131—21no—
135C2×C4×C131—21no—
136C2×C4×C131—21no—
137C2×C4×C131—21no—
138C2×C4×C131—21no—
139C2×C4×C131—21no—
140C2×C4×C131—21no—
141C2×C4×C131—21no—
142C2×C4×C131—44no—
143C2×C4×C131—44no—
144C2×C4×C131—41no—
145C2×C4×C131—41no—
146C2×C4×C131—41no—
147C2×C4×C131—41no—
148C2×C4×C131—41no—
149C2×C4×C131—41no—
150C2×C4×C131—41no—
151C2×C4×C131—41no—
152C2×C4×C131—41no—
153C2×C4×C131#9912yes—
154C2×C4×C131#13112yes—
155C2×C4×C131#13512yes—
156C2×C4×C131AGL(1,ℤ/8)11yescharacteristic
157C2×C4×C131#13711yescharacteristic
158C8×C131—44no—
159C8×C131—44no—
160C22×C131—22no—
161C22×C131—22no—
162C22×C131—22no—
163C22×C131—22no—
164C22×C131—22no—
165C22×C131—22no—
166C22×C131—81no—
167C22×C131—81no—
168C22×C131—81no—
169C22×C131—81no—
170C22×C131—81no—
171C22×C131—81no—
172C22×C131—81no—
173C22×C131#32914yes—
174C22×C131#40811yescharacteristic
175C22×C131C2×#9911yescharacteristic
176C22×C131C2×#10011yescharacteristic
177C22×C131#41611yescharacteristic
178C22×C131#41711yescharacteristic
179C22×C131C2×#10411yescharacteristic
180C22×C131C2×#10411yescharacteristic
181C4×C131—22no—
182C4×C131—22no—
183C4×C131—21no—
184C4×C131—22no—
185C4×C131—21no—
186C4×C131—41no—
187C4×C131—41no—
188C4×C131—81no—
189C4×C131—81no—
190C4×C131—81no—
191C2×C131—24no—
192C2×C131—161no—
193C2×C131#147111yescharacteristic
194C2×C131#148311yescharacteristic
195C2×C131#149411yescharacteristic
196C2×C131#150111yescharacteristic
197C2×C131#150411yescharacteristic
198C2×C131C2×#32911yescharacteristic
199C2×C131#155111yescharacteristic
200#7690C13111yesmaximal, characteristic, direct product factor, Sylow
201C131#769011yescharacteristic, direct product factor, Sylow
202#2850C2×C13111yescharacteristic
203#1749C2×C13111yescharacteristic, complemented
204C2×#336C2×C13111yescharacteristic, complemented
205#1272C2×C13112yescomplemented
206#1270C2×C13112yescomplemented
207C23×C8—21no—
208C2×#124C4×C13111yescharacteristic
209C2×C22⋊Q8C4×C13111yescharacteristic
210C2×#121C4×C13111yescharacteristic
211C22×C42C22×C13111yescharacteristic
212C2×C22⋊C8—21no—
213C2×#97—21no—
214#391C22×C13111yescharacteristic
215#390C22×C13111yescharacteristic
216#388—21no—
217#388—21no—
218#386—21no—
219#386—21no—
220#382C4×C13111yescharacteristic
221#336—21no—
222#336C22×C13112yes—
223#336C22×C13112yes—
224C22×Q8C2×C4×C13111yescharacteristic
225C22×D4—21no—
226C22×D4C2×C4×C13111yescharacteristic
227C23×C4C2×C4×C13111yescharacteristic
228C23×C4D4×C13111yescharacteristic
229C23×C4D4×C13111yescharacteristic
230C22×C8—24no—
231C22×C8—22no—
232C22×C8—22no—
233C22×C8—42no—
234C22×C8—42no—
235#124—42no—
236C22⋊Q8—42no—
237#121—42no—
238C2×C4⋊C4—21no—
239C2×C4⋊C4C2×C4×C13111yescharacteristic
240C2×C4⋊C4C2×C4×C13111yescharacteristic
241C2×C22⋊C4—21no—
242C2×C22⋊C4—21no—
243C2×C22⋊C4—21no—
244C2×C22⋊C4—21no—
245C2×C22⋊C4—21no—
246C2×C22⋊C4—21no—
247C2×C42—42no—
248C2×C42C2×C4×C13111yescharacteristic
249C2×C42D4×C13111yescharacteristic
250C2×C42D4×C13111yescharacteristic
251C2×C42C23×C13111yescharacteristic
252C22⋊C8—24no—
253#97—42no—
254#95—21no—
255#95—21no—
256#95—21no—
257#95—21no—
258C24—21no—
259C24C22⋊C4×C13111yescharacteristic
260C2×Q8—22no—
261C2×Q8—41no—
262C2×Q8—41no—
263C2×D4—22no—
264C2×D4—41no—
265C2×D4—41no—
266C2×D4—42no—
267C2×D4—42no—
268C2×D4—42no—
269C22×C4—22no—
270C22×C4—22no—
271C22×C4—21no—
272C22×C4—21no—
273C22×C4—22no—
274C22×C4—22no—
275C22×C4—22no—
276C22×C4—22no—
277C22×C4—21no—
278C22×C4—21no—
279C22×C4—21no—
280C22×C4—41no—
281C22×C4—41no—
282C22×C4C22⋊C4×C13111yescharacteristic
283C22×C4C22⋊C4×C13111yescharacteristic
284C22×C4C22⋊C4×C13111yescharacteristic
285C22×C4C22×C4×C13111yescharacteristic
286C22×C4C2×D4×C13111yescharacteristic
287C22×C4C2×D4×C13111yescharacteristic
288C2×C8—24no—
289C2×C8—24no—
290C2×C8—42no—
291C2×C8—48no—
292C2×C8—42no—
293C2×C8—42no—
294C2×C8—42no—
295C4⋊C4—41no—
296C4⋊C4—41no—
297C4⋊C4—42no—
298C22⋊C4—42no—
299C22⋊C4—42no—
300C22⋊C4—42no—
301C22⋊C4—42no—
302C22⋊C4—42no—
303C22⋊C4—41no—
304C22⋊C4—41no—
305C42—22no—
306C42—22no—
307C42—41no—
308C42—41no—
309C23—21no—
310C23—21no—
311C23—21no—
312C23—21no—
313C23—41no—
314C23—41no—
315C23—41no—
316C23—41no—
317C23—41no—
318C23—41no—
319C23—41no—
320C23#100×C13112yes—
321C23#104×C13112yes—
322C23#104×C13112yes—
323C23C2×C22⋊C4×C13111yescharacteristic
324Q8—82no—
325D4—82no—
326D4—84no—
327C2×C4—24no—
328C2×C4—24no—
329C2×C4—21no—
330C2×C4—21no—
331C2×C4—21no—
332C2×C4—21no—
333C2×C4—21no—
334C2×C4—21no—
335C2×C4—21no—
336C2×C4—21no—
337C2×C4—21no—
338C2×C4—21no—
339C2×C4—21no—
340C2×C4—21no—
341C2×C4—21no—
342C2×C4—21no—
343C2×C4—44no—
344C2×C4—44no—
345C2×C4—41no—
346C2×C4—41no—
347C2×C4—41no—
348C2×C4—41no—
349C2×C4—41no—
350C2×C4—41no—
351C2×C4—41no—
352C2×C4—41no—
353C2×C4—41no—
354C2×C4#99×C13112yes—
355C2×C4#131×C13112yes—
356C2×C4#135×C13112yes—
357C2×C4AGL(1,ℤ/8)×C13111yescharacteristic
358C2×C4#137×C13111yescharacteristic
359C8—44no—
360C8—44no—
361C22—22no—
362C22—22no—
363C22—22no—
364C22—22no—
365C22—22no—
366C22—22no—
367C22—81no—
368C22—81no—
369C22—81no—
370C22—81no—
371C22—81no—
372C22—81no—
373C22—81no—
374C22#329×C13114yes—
375C22#408×C13111yescharacteristic
376C22C2×#99×C13111yescharacteristic
377C22C2×#100×C13111yescharacteristic
378C22#416×C13111yescharacteristic
379C22#417×C13111yescharacteristic
380C22C2×#104×C13111yescharacteristic
381C22C2×#104×C13111yescharacteristic
382C4—22no—
383C4—22no—
384C4—21no—
385C4—22no—
386C4—21no—
387C4—41no—
388C4—41no—
389C4—81no—
390C4—81no—
391C4—81no—
392C2—24no—
393C2—161no—
394C2#1471×C13111yescharacteristic
395C2#1483×C13111yescharacteristic
396C2#1494×C13111yescharacteristic
397C2#1501×C13111yescharacteristic
398C2#1504×C13111yescharacteristic
399C2C2×#329×C13111yescharacteristic
400C2#1551×C13111yescharacteristic
subgroupG/H
center, socleC23×C131C2×C22⋊C4
commutatorC22×C4C22×C4×C131
Frattini, cosocleC2×C42C23×C131
prime radicalC2×#121×C131C4
LCSG ▷ C22×C4 ▷ C22 ▷ C1
UCSC1 ◁ C23×C131 ◁ C22×C42×C131 ◁ G

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
2. #1749×C131C2semidirect
3. C2×#336×C131C2semidirect
4. #1272×C131C2semidirect
5. #1270×C131C2semidirect
200. #7690C131direct (N × H)
201. C131#7690direct (N × H)
203. #1749C2×C131semidirect
204. C2×#336C2×C131semidirect
205. #1272C2×C131semidirect
206. #1270C2×C131semidirect

Maximal subgroups

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

subgroupindex
#2850×C1312
#1749×C1312
C2×#336×C1312
#1272×C1312
#1270×C1312
#7690131