Finite Group Databasebeta

← C131×#9386 #45695270

Subgroups — C131×#9386 #45695270

Order 33536.

618 conjugacy classes of subgroups.

The subgroup lattice has 432 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#2973×C131C211yesmaximal, characteristic, complemented
2#2543×C131C211yesmaximal, characteristic
3#1799×C131C211yesmaximal, characteristic, complemented
4#1519×C131C212yesmaximal, complemented
5#1294×C131C212yesmaximal, complemented
6C2×#121×C131—21no—
7C2×#121×C131C2211yescharacteristic
8C2×C4×D4×C131C2211yescharacteristic
9#435×C131—24no—
10#432×C131—21no—
11C2×#99×C131—21no—
12#407×C131—21no—
13C2×C22⋊C8×C131C2212yes—
14#398×C131C411yescharacteristic, complemented
15#397×C131C411yescharacteristic, complemented
16#394×C131C411yescharacteristic, complemented
17#392×C131C411yescharacteristic, complemented
18#388×C131—21no—
19#386×C131—21no—
20#386×C131—21no—
21#380×C131C2212yes—
22C2×#95×C131C2211yescharacteristic
23#342×C131—21no—
24#327×C131—24no—
25C22×D4×C131—21no—
26C22×D4×C131—21no—
27C22×D4×C131C2×C411yescharacteristic
28C22×D4×C131D411yescharacteristic
29C23×C4×C131—21no—
30C23×C4×C131D411yescharacteristic
31C23×C4×C131C2311yescharacteristic
32C2×M16×C131—22no—
33C22×C8×C131—22no—
34#121×C131—22no—
35#121×C131—22no—
36#121×C131—44no—
37C4×D4×C131—22no—
38C4×D4×C131—22no—
39C2×C4⋊C4×C131—21no—
40C2×C4⋊C4×C131—22no—
41C2×C4⋊C4×C131C2×C411yescharacteristic
42C2×C4⋊C4×C131C2×C411yescharacteristic
43C2×C22⋊C4×C131—21no—
44C2×C22⋊C4×C131—21no—
45C2×C22⋊C4×C131—21no—
46C2×C22⋊C4×C131—21no—
47C2×C22⋊C4×C131—22no—
48C2×C22⋊C4×C131—21no—
49C2×C22⋊C4×C131C2×C411yescharacteristic
50C2×C22⋊C4×C131D411yescharacteristic
51C2×C42×C131D411yescharacteristic
52C4⋊C8×C131—22no—
53#99×C131—42no—
54C22⋊C8×C131—22no—
55C22⋊C8×C131—22no—
56C22⋊C8×C131D414yescomplemented
57#97×C131—22no—
58#95×C131—21no—
59#95×C131—21no—
60#95×C131—21no—
61#95×C131—22no—
62#95×C131C2×C411yescharacteristic
63#95×C131C2×C411yescharacteristic
64C24×C131—21no—
65C24×C131C22⋊C411yescharacteristic
66C24×C131C2×D411yescharacteristic
67C2×D4×C131—22no—
68C2×D4×C131—21no—
69C2×D4×C131—22no—
70C2×D4×C131—21no—
71C2×D4×C131—22no—
72C2×D4×C131—42no—
73C2×D4×C131—42no—
74C2×D4×C131—42no—
75C2×D4×C131—42no—
76C2×D4×C131—41no—
77C2×D4×C131—41no—
78C2×D4×C131—81no—
79C2×D4×C131—81no—
80C22×C4×C131—21no—
81C22×C4×C131—21no—
82C22×C4×C131—21no—
83C22×C4×C131—21no—
84C22×C4×C131—21no—
85C22×C4×C131—42no—
86C22×C4×C131—42no—
87C22×C4×C131—42no—
88C22×C4×C131—81no—
89C22×C4×C131—81no—
90C22×C4×C131—81no—
91C22×C4×C131C22⋊C411yescharacteristic
92C22×C4×C131C22⋊C411yescharacteristic
93C22×C4×C131C22⋊C411yescharacteristic
94C22×C4×C131C22×C411yescharacteristic
95C22×C4×C131C2×D412yes—
96C22×C4×C131C2×D411yescharacteristic
97C22×C4×C131#4112yes—
98M16×C131—82no—
99C2×C8×C131—24no—
100C2×C8×C131—82no—
101C4⋊C4×C131—22no—
102C4⋊C4×C131—22no—
103C4⋊C4×C131—42no—
104C4⋊C4×C131—82no—
105C22⋊C4×C131—22no—
106C22⋊C4×C131—22no—
107C22⋊C4×C131—42no—
108C22⋊C4×C131—42no—
109C22⋊C4×C131—42no—
110C22⋊C4×C131—41no—
111C22⋊C4×C131—41no—
112C22⋊C4×C131—42no—
113C22⋊C4×C131—42no—
114C22⋊C4×C131—81no—
115C42×C131—21no—
116C42×C131—21no—
117C23×C131—21no—
118C23×C131—21no—
119C23×C131—21no—
120C23×C131—41no—
121C23×C131—41no—
122C23×C131—41no—
123C23×C131—41no—
124C23×C131—41no—
125C23×C131—41no—
126C23×C131—41no—
127C23×C131—41no—
128C23×C131—41no—
129C23×C131—41no—
130C23×C131—41no—
131C23×C131C2×C22⋊C411yescharacteristic
132C23×C131#12112yes—
133C23×C131AGL(1,ℤ/8)11yescharacteristic
134C23×C131AGL(1,ℤ/8)12yes—
135C23×C131#13711yescharacteristic
136D4×C131—42no—
137D4×C131—42no—
138D4×C131—82no—
139D4×C131—84no—
140D4×C131—82no—
141D4×C131—82no—
142C2×C4×C131—22no—
143C2×C4×C131—21no—
144C2×C4×C131—21no—
145C2×C4×C131—21no—
146C2×C4×C131—21no—
147C2×C4×C131—21no—
148C2×C4×C131—42no—
149C2×C4×C131—42no—
150C2×C4×C131—41no—
151C2×C4×C131—41no—
152C2×C4×C131—42no—
153C2×C4×C131—41no—
154C2×C4×C131—41no—
155C2×C4×C131—41no—
156C2×C4×C131—41no—
157C2×C4×C131—41no—
158C2×C4×C131—41no—
159C2×C4×C131—41no—
160C2×C4×C131—41no—
161C2×C4×C131—41no—
162C2×C4×C131—41no—
163C2×C4×C131—81no—
164C2×C4×C131—84no—
165C2×C4×C131—82no—
166C2×C4×C131—82no—
167C2×C4×C131—82no—
168C2×C4×C131C4×D412yes—
169C2×C4×C131#12011yescharacteristic
170C2×C4×C131#12311yescharacteristic
171C8×C131—44no—
172C22×C131—21no—
173C22×C131—22no—
174C22×C131—21no—
175C22×C131—22no—
176C22×C131—42no—
177C22×C131—41no—
178C22×C131—41no—
179C22×C131—42no—
180C22×C131—41no—
181C22×C131—41no—
182C22×C131—41no—
183C22×C131—81no—
184C22×C131—81no—
185C22×C131—81no—
186C22×C131—81no—
187C22×C131—81no—
188C22×C131—81no—
189C22×C131—81no—
190C22×C131—81no—
191C22×C131#38611yescharacteristic
192C22×C131#41711yescharacteristic
193C22×C131#41811yescharacteristic
194C22×C131#46812yes—
195C22×C131#46912yes—
196C4×C131—21no—
197C4×C131—21no—
198C4×C131—22no—
199C4×C131—42no—
200C4×C131—41no—
201C4×C131—41no—
202C4×C131—41no—
203C4×C131—81no—
204C4×C131—81no—
205C4×C131—162no—
206C2×C131—21no—
207C2×C131—22no—
208C2×C131—21no—
209C2×C131—22no—
210C2×C131—81no—
211C2×C131—161no—
212C2×C131#188411yescharacteristic
213C2×C131#189511yescharacteristic
214C2×C131#191311yescharacteristic
215#9386C13111yesmaximal, characteristic, direct product factor, Sylow
216C131#938611yescharacteristic, direct product factor, Sylow
217#2973C2×C13111yescharacteristic, complemented
218#2543C2×C13111yescharacteristic
219#1799C2×C13111yescharacteristic, complemented
220#1519C2×C13112yescomplemented
221#1294C2×C13112yescomplemented
222C2×#121—21no—
223C2×#121C22×C13111yescharacteristic
224C2×C4×D4C22×C13111yescharacteristic
225#435—24no—
226#432—21no—
227C2×#99—21no—
228#407—21no—
229C2×C22⋊C8C22×C13112yes—
230#398C4×C13111yescharacteristic, complemented
231#397C4×C13111yescharacteristic, complemented
232#394C4×C13111yescharacteristic, complemented
233#392C4×C13111yescharacteristic, complemented
234#388—21no—
235#386—21no—
236#386—21no—
237#380C22×C13112yes—
238C2×#95C22×C13111yescharacteristic
239#342—21no—
240#327—24no—
241C22×D4—21no—
242C22×D4—21no—
243C22×D4C2×C4×C13111yescharacteristic
244C22×D4D4×C13111yescharacteristic
245C23×C4—21no—
246C23×C4D4×C13111yescharacteristic
247C23×C4C23×C13111yescharacteristic
248C2×M16—22no—
249C22×C8—22no—
250#121—22no—
251#121—22no—
252#121—44no—
253C4×D4—22no—
254C4×D4—22no—
255C2×C4⋊C4—21no—
256C2×C4⋊C4—22no—
257C2×C4⋊C4C2×C4×C13111yescharacteristic
258C2×C4⋊C4C2×C4×C13111yescharacteristic
259C2×C22⋊C4—21no—
260C2×C22⋊C4—21no—
261C2×C22⋊C4—21no—
262C2×C22⋊C4—21no—
263C2×C22⋊C4—22no—
264C2×C22⋊C4—21no—
265C2×C22⋊C4C2×C4×C13111yescharacteristic
266C2×C22⋊C4D4×C13111yescharacteristic
267C2×C42D4×C13111yescharacteristic
268C4⋊C8—22no—
269#99—42no—
270C22⋊C8—22no—
271C22⋊C8—22no—
272C22⋊C8D4×C13114yescomplemented
273#97—22no—
274#95—21no—
275#95—21no—
276#95—21no—
277#95—22no—
278#95C2×C4×C13111yescharacteristic
279#95C2×C4×C13111yescharacteristic
280C24—21no—
281C24C22⋊C4×C13111yescharacteristic
282C24C2×D4×C13111yescharacteristic
283C2×D4—22no—
284C2×D4—21no—
285C2×D4—22no—
286C2×D4—21no—
287C2×D4—22no—
288C2×D4—42no—
289C2×D4—42no—
290C2×D4—42no—
291C2×D4—42no—
292C2×D4—41no—
293C2×D4—41no—
294C2×D4—81no—
295C2×D4—81no—
296C22×C4—21no—
297C22×C4—21no—
298C22×C4—21no—
299C22×C4—21no—
300C22×C4—21no—
301C22×C4—42no—
302C22×C4—42no—
303C22×C4—42no—
304C22×C4—81no—
305C22×C4—81no—
306C22×C4—81no—
307C22×C4C22⋊C4×C13111yescharacteristic
308C22×C4C22⋊C4×C13111yescharacteristic
309C22×C4C22⋊C4×C13111yescharacteristic
310C22×C4C22×C4×C13111yescharacteristic
311C22×C4C2×D4×C13112yes—
312C22×C4C2×D4×C13111yescharacteristic
313C22×C4#41×C13112yes—
314M16—82no—
315C2×C8—24no—
316C2×C8—82no—
317C4⋊C4—22no—
318C4⋊C4—22no—
319C4⋊C4—42no—
320C4⋊C4—82no—
321C22⋊C4—22no—
322C22⋊C4—22no—
323C22⋊C4—42no—
324C22⋊C4—42no—
325C22⋊C4—42no—
326C22⋊C4—41no—
327C22⋊C4—41no—
328C22⋊C4—42no—
329C22⋊C4—42no—
330C22⋊C4—81no—
331C42—21no—
332C42—21no—
333C23—21no—
334C23—21no—
335C23—21no—
336C23—41no—
337C23—41no—
338C23—41no—
339C23—41no—
340C23—41no—
341C23—41no—
342C23—41no—
343C23—41no—
344C23—41no—
345C23—41no—
346C23—41no—
347C23C2×C22⋊C4×C13111yescharacteristic
348C23#121×C13112yes—
349C23AGL(1,ℤ/8)×C13111yescharacteristic
350C23AGL(1,ℤ/8)×C13112yes—
351C23#137×C13111yescharacteristic
352D4—42no—
353D4—42no—
354D4—82no—
355D4—84no—
356D4—82no—
357D4—82no—
358C2×C4—22no—
359C2×C4—21no—
360C2×C4—21no—
361C2×C4—21no—
362C2×C4—21no—
363C2×C4—21no—
364C2×C4—42no—
365C2×C4—42no—
366C2×C4—41no—
367C2×C4—41no—
368C2×C4—42no—
369C2×C4—41no—
370C2×C4—41no—
371C2×C4—41no—
372C2×C4—41no—
373C2×C4—41no—
374C2×C4—41no—
375C2×C4—41no—
376C2×C4—41no—
377C2×C4—41no—
378C2×C4—41no—
379C2×C4—81no—
380C2×C4—84no—
381C2×C4—82no—
382C2×C4—82no—
383C2×C4—82no—
384C2×C4C4×D4×C13112yes—
385C2×C4#120×C13111yescharacteristic
386C2×C4#123×C13111yescharacteristic
387C8—44no—
388C22—21no—
389C22—22no—
390C22—21no—
391C22—22no—
392C22—42no—
393C22—41no—
394C22—41no—
395C22—42no—
396C22—41no—
397C22—41no—
398C22—41no—
399C22—81no—
400C22—81no—
401C22—81no—
402C22—81no—
403C22—81no—
404C22—81no—
405C22—81no—
406C22—81no—
407C22#386×C13111yescharacteristic
408C22#417×C13111yescharacteristic
409C22#418×C13111yescharacteristic
410C22#468×C13112yes—
411C22#469×C13112yes—
412C4—21no—
413C4—21no—
414C4—22no—
415C4—42no—
416C4—41no—
417C4—41no—
418C4—41no—
419C4—81no—
420C4—81no—
421C4—162no—
422C2—21no—
423C2—22no—
424C2—21no—
425C2—22no—
426C2—81no—
427C2—161no—
428C2#1884×C13111yescharacteristic
429C2#1895×C13111yescharacteristic
430C2#1913×C13111yescharacteristic
subgroupG/H
center, socleC22×C131#386
commutatorC22×C4C22×C4×C131
Frattini, cosocleC23×C4C23×C131
prime radical#2543×C131C2
LCSG ▷ C22×C4 ▷ C22 ▷ C1
UCSC1 ◁ C22×C131 ◁ C23×C4×C131 ◁ G

Complements

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

NH ≅ G/Ntype
1. #2973×C131C2semidirect
3. #1799×C131C2semidirect
4. #1519×C131C2semidirect
5. #1294×C131C2semidirect
14. #398×C131C4semidirect
15. #397×C131C4semidirect
16. #394×C131C4semidirect
17. #392×C131C4semidirect
56. C22⋊C8×C131D4semidirect
215. #9386C131direct (N × H)
216. C131#9386direct (N × H)
217. #2973C2×C131semidirect
219. #1799C2×C131semidirect
220. #1519C2×C131semidirect
221. #1294C2×C131semidirect
230. #398C4×C131semidirect
231. #397C4×C131semidirect
232. #394C4×C131semidirect
233. #392C4×C131semidirect
272. C22⋊C8D4×C131semidirect

Maximal subgroups

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

subgroupindex
#2973×C1312
#2543×C1312
#1799×C1312
#1519×C1312
#1294×C1312
#9386131