Finite Group Databasebeta

← C131×#9277 #45695161

Subgroups — C131×#9277 #45695161

Order 33536.

648 conjugacy classes of subgroups.

The subgroup lattice has 540 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#3186×C131C211yesmaximal, characteristic
2#2364×C131C211yesmaximal, characteristic, complemented
3#1964×C131C211yesmaximal, characteristic, complemented
4#1519×C131C211yesmaximal, characteristic, complemented
5C2×#327×C131C211yesmaximal, characteristic, complemented
6#1294×C131C211yesmaximal, characteristic, complemented
7#1282×C131C211yesmaximal, characteristic, complemented
8C2×#121×C131C2211yescharacteristic
9C2×#121×C131C2211yescharacteristic
10C2×C4×D4×C131—21no—
11#480×C131—21no—
12#480×C131C412yescomplemented
13#466×C131—22no—
14#447×C131—21no—
15#447×C131C412yescomplemented
16C2×#99×C131—21no—
17C2×#99×C131—21no—
18C2×C22⋊C8×C131C2211yescharacteristic
19C2×C22⋊C8×C131C2211yescharacteristic
20#388×C131—21no—
21#387×C131—21no—
22#386×C131—21no—
23#386×C131—21no—
24#380×C131C2211yescharacteristic
25C4×C22⋊C4×C131—21no—
26C4×C22⋊C4×C131C2211yescharacteristic
27C2×#95×C131C2211yescharacteristic
28#327×C131—22no—
29#327×C131—21no—
30#327×C131—21no—
31C22×D4×C131—21no—
32C22×D4×C131—21no—
33C22×D4×C131C2×C411yescharacteristic, complemented
34C22×D4×C131D411yescharacteristic
35C23×C4×C131—21no—
36C23×C4×C131—21no—
37C23×C4×C131C2311yescharacteristic
38C2×D8×C131—22no—
39C22×C8×C131—21no—
40C22×C8×C131—21no—
41#121×C131—21no—
42#121×C131—21no—
43#121×C131—21no—
44#121×C131—21no—
45#121×C131—21no—
46#121×C131—21no—
47#121×C131C2×C412yes—
48#121×C131D412yes—
49C4×D4×C131—42no—
50C4×D4×C131—42no—
51C2×C4⋊C4×C131—21no—
52C2×C4⋊C4×C131—21no—
53C2×C4⋊C4×C131C2×C411yescharacteristic, complemented
54C2×C4⋊C4×C131D411yescharacteristic
55C2×C22⋊C4×C131—21no—
56C2×C22⋊C4×C131—21no—
57C2×C22⋊C4×C131—21no—
58C2×C22⋊C4×C131—21no—
59C2×C22⋊C4×C131—21no—
60C2×C22⋊C4×C131—21no—
61C2×C22⋊C4×C131D411yescharacteristic
62C2×C22⋊C4×C131D411yescharacteristic
63C2×C42×C131—21no—
64C2×C42×C131—21no—
65#107×C131—22no—
66#102×C131—22no—
67#102×C131—22no—
68#99×C131—42no—
69#99×C131—42no—
70C22⋊C8×C131—21no—
71C22⋊C8×C131—21no—
72C22⋊C8×C131—21no—
73C22⋊C8×C131C2×C412yescomplemented
74#95×C131—21no—
75#95×C131—21no—
76#95×C131—21no—
77#95×C131—21no—
78#95×C131—21no—
79#95×C131D411yescharacteristic
80#95×C131D411yescharacteristic
81C24×C131—21no—
82C24×C131—21no—
83C24×C131C2×D411yescharacteristic
84C2×D4×C131—22no—
85C2×D4×C131—22no—
86C2×D4×C131—21no—
87C2×D4×C131—21no—
88C2×D4×C131—21no—
89C2×D4×C131—41no—
90C2×D4×C131—41no—
91C2×D4×C131—41no—
92C2×D4×C131—41no—
93C2×D4×C131—41no—
94C2×D4×C131—41no—
95C2×D4×C131—41no—
96C2×D4×C131—41no—
97C2×D4×C131—41no—
98C2×D4×C131—41no—
99C2×D4×C131—81no—
100C2×D4×C131—81no—
101C2×D4×C131C22⋊C412yes—
102C22×C4×C131—21no—
103C22×C4×C131—21no—
104C22×C4×C131—21no—
105C22×C4×C131—21no—
106C22×C4×C131—21no—
107C22×C4×C131—21no—
108C22×C4×C131—42no—
109C22×C4×C131—42no—
110C22×C4×C131—42no—
111C22×C4×C131—41no—
112C22×C4×C131—41no—
113C22×C4×C131—41no—
114C22×C4×C131—81no—
115C22×C4×C131—81no—
116C22×C4×C131—81no—
117C22×C4×C131C22×C411yescharacteristic
118C22×C4×C131C2×D411yescharacteristic
119C22×C4×C131C2×D411yescharacteristic
120C22×C4×C131C2×D411yescharacteristic
121C22×C4×C131#4111yescharacteristic
122C22×C4×C131#4111yescharacteristic
123D8×C131—82no—
124C2×C8×C131—22no—
125C2×C8×C131—41no—
126C2×C8×C131—81no—
127C2×C8×C131—81no—
128C4⋊C4×C131—21no—
129C4⋊C4×C131—21no—
130C4⋊C4×C131—21no—
131C4⋊C4×C131—42no—
132C4⋊C4×C131—81no—
133C4⋊C4×C131C22⋊C412yes—
134C22⋊C4×C131—21no—
135C22⋊C4×C131—22no—
136C22⋊C4×C131—22no—
137C22⋊C4×C131—21no—
138C22⋊C4×C131—21no—
139C22⋊C4×C131—42no—
140C22⋊C4×C131—42no—
141C22⋊C4×C131—41no—
142C22⋊C4×C131—41no—
143C22⋊C4×C131—41no—
144C22⋊C4×C131—41no—
145C22⋊C4×C131—81no—
146C22⋊C4×C131D812yescomplemented
147C42×C131—42no—
148C42×C131—81no—
149C23×C131—22no—
150C23×C131—41no—
151C23×C131—41no—
152C23×C131—41no—
153C23×C131—41no—
154C23×C131—41no—
155C23×C131—41no—
156C23×C131—41no—
157C23×C131—41no—
158C23×C131—41no—
159C23×C131—41no—
160C23×C131—41no—
161C23×C131—81no—
162C23×C131—81no—
163C23×C131C4×D411yescharacteristic
164C23×C131#12011yescharacteristic
165C23×C131#12111yescharacteristic
166C23×C131C2×D811yescharacteristic
167C23×C131#13511yescharacteristic
168C23×C131AGL(1,ℤ/8)11yescharacteristic
169C23×C131AGL(1,ℤ/8)11yescharacteristic
170D4×C131—42no—
171D4×C131—42no—
172D4×C131—42no—
173D4×C131—42no—
174D4×C131—42no—
175D4×C131—42no—
176D4×C131—81no—
177D4×C131—81no—
178D4×C131—81no—
179D4×C131—81no—
180D4×C131—81no—
181D4×C131—81no—
182C2×C4×C131—22no—
183C2×C4×C131—22no—
184C2×C4×C131—22no—
185C2×C4×C131—41no—
186C2×C4×C131—41no—
187C2×C4×C131—41no—
188C2×C4×C131—41no—
189C2×C4×C131—41no—
190C2×C4×C131—41no—
191C2×C4×C131—41no—
192C2×C4×C131—41no—
193C2×C4×C131—41no—
194C2×C4×C131—41no—
195C2×C4×C131—41no—
196C2×C4×C131—41no—
197C2×C4×C131—41no—
198C2×C4×C131—41no—
199C2×C4×C131—41no—
200C2×C4×C131—41no—
201C2×C4×C131—41no—
202C2×C4×C131—41no—
203C2×C4×C131—41no—
204C2×C4×C131—41no—
205C2×C4×C131—41no—
206C2×C4×C131—84no—
207C2×C4×C131—82no—
208C2×C4×C131—82no—
209C2×C4×C131—81no—
210C2×C4×C131—81no—
211C2×C4×C131—81no—
212C2×C4×C131C2×C22⋊C411yescharacteristic
213C2×C4×C131C4×D411yescharacteristic
214C2×C4×C131#12111yescharacteristic
215C2×C4×C131#12311yescharacteristic
216C8×C131—42no—
217C8×C131—81no—
218C22×C131—21no—
219C22×C131—21no—
220C22×C131—21no—
221C22×C131—21no—
222C22×C131—21no—
223C22×C131—21no—
224C22×C131—41no—
225C22×C131—41no—
226C22×C131—41no—
227C22×C131—41no—
228C22×C131—42no—
229C22×C131—42no—
230C22×C131—42no—
231C22×C131—81no—
232C22×C131—81no—
233C22×C131—81no—
234C22×C131—81no—
235C22×C131—81no—
236C22×C131—81no—
237C22×C131—81no—
238C22×C131—161no—
239C22×C131—161no—
240C22×C131#38611yescharacteristic
241C22×C131C4×D811yescharacteristic
242C22×C131#44211yescharacteristic
243C22×C131#44711yescharacteristic
244C22×C131#44911yescharacteristic
245C22×C131#45911yescharacteristic
246C22×C131#46311yescharacteristic
247C4×C131—21no—
248C4×C131—21no—
249C4×C131—21no—
250C4×C131—21no—
251C4×C131—42no—
252C4×C131—42no—
253C4×C131—42no—
254C4×C131—81no—
255C4×C131—81no—
256C4×C131—81no—
257C4×C131—161no—
258C2×C131—21no—
259C2×C131—21no—
260C2×C131—21no—
261C2×C131—21no—
262C2×C131—21no—
263C2×C131—21no—
264C2×C131—82no—
265C2×C131—161no—
266C2×C131#187911yescharacteristic
267C2×C131#190611yescharacteristic
268C2×C131#191311yescharacteristic
269#9277C13111yesmaximal, characteristic, direct product factor, Sylow
270C131#927711yescharacteristic, direct product factor, Sylow
271#3186C2×C13111yescharacteristic
272#2364C2×C13111yescharacteristic, complemented
273#1964C2×C13111yescharacteristic, complemented
274#1519C2×C13111yescharacteristic, complemented
275C2×#327C2×C13111yescharacteristic, complemented
276#1294C2×C13111yescharacteristic, complemented
277#1282C2×C13111yescharacteristic, complemented
278C2×#121C22×C13111yescharacteristic
279C2×#121C22×C13111yescharacteristic
280C2×C4×D4—21no—
281#480—21no—
282#480C4×C13112yescomplemented
283#466—22no—
284#447—21no—
285#447C4×C13112yescomplemented
286C2×#99—21no—
287C2×#99—21no—
288C2×C22⋊C8C22×C13111yescharacteristic
289C2×C22⋊C8C22×C13111yescharacteristic
290#388—21no—
291#387—21no—
292#386—21no—
293#386—21no—
294#380C22×C13111yescharacteristic
295C4×C22⋊C4—21no—
296C4×C22⋊C4C22×C13111yescharacteristic
297C2×#95C22×C13111yescharacteristic
298#327—22no—
299#327—21no—
300#327—21no—
301C22×D4—21no—
302C22×D4—21no—
303C22×D4C2×C4×C13111yescharacteristic, complemented
304C22×D4D4×C13111yescharacteristic
305C23×C4—21no—
306C23×C4—21no—
307C23×C4C23×C13111yescharacteristic
308C2×D8—22no—
309C22×C8—21no—
310C22×C8—21no—
311#121—21no—
312#121—21no—
313#121—21no—
314#121—21no—
315#121—21no—
316#121—21no—
317#121C2×C4×C13112yes—
318#121D4×C13112yes—
319C4×D4—42no—
320C4×D4—42no—
321C2×C4⋊C4—21no—
322C2×C4⋊C4—21no—
323C2×C4⋊C4C2×C4×C13111yescharacteristic, complemented
324C2×C4⋊C4D4×C13111yescharacteristic
325C2×C22⋊C4—21no—
326C2×C22⋊C4—21no—
327C2×C22⋊C4—21no—
328C2×C22⋊C4—21no—
329C2×C22⋊C4—21no—
330C2×C22⋊C4—21no—
331C2×C22⋊C4D4×C13111yescharacteristic
332C2×C22⋊C4D4×C13111yescharacteristic
333C2×C42—21no—
334C2×C42—21no—
335#107—22no—
336#102—22no—
337#102—22no—
338#99—42no—
339#99—42no—
340C22⋊C8—21no—
341C22⋊C8—21no—
342C22⋊C8—21no—
343C22⋊C8C2×C4×C13112yescomplemented
344#95—21no—
345#95—21no—
346#95—21no—
347#95—21no—
348#95—21no—
349#95D4×C13111yescharacteristic
350#95D4×C13111yescharacteristic
351C24—21no—
352C24—21no—
353C24C2×D4×C13111yescharacteristic
354C2×D4—22no—
355C2×D4—22no—
356C2×D4—21no—
357C2×D4—21no—
358C2×D4—21no—
359C2×D4—41no—
360C2×D4—41no—
361C2×D4—41no—
362C2×D4—41no—
363C2×D4—41no—
364C2×D4—41no—
365C2×D4—41no—
366C2×D4—41no—
367C2×D4—41no—
368C2×D4—41no—
369C2×D4—81no—
370C2×D4—81no—
371C2×D4C22⋊C4×C13112yes—
372C22×C4—21no—
373C22×C4—21no—
374C22×C4—21no—
375C22×C4—21no—
376C22×C4—21no—
377C22×C4—21no—
378C22×C4—42no—
379C22×C4—42no—
380C22×C4—42no—
381C22×C4—41no—
382C22×C4—41no—
383C22×C4—41no—
384C22×C4—81no—
385C22×C4—81no—
386C22×C4—81no—
387C22×C4C22×C4×C13111yescharacteristic
388C22×C4C2×D4×C13111yescharacteristic
389C22×C4C2×D4×C13111yescharacteristic
390C22×C4C2×D4×C13111yescharacteristic
391C22×C4#41×C13111yescharacteristic
392C22×C4#41×C13111yescharacteristic
393D8—82no—
394C2×C8—22no—
395C2×C8—41no—
396C2×C8—81no—
397C2×C8—81no—
398C4⋊C4—21no—
399C4⋊C4—21no—
400C4⋊C4—21no—
401C4⋊C4—42no—
402C4⋊C4—81no—
403C4⋊C4C22⋊C4×C13112yes—
404C22⋊C4—21no—
405C22⋊C4—22no—
406C22⋊C4—22no—
407C22⋊C4—21no—
408C22⋊C4—21no—
409C22⋊C4—42no—
410C22⋊C4—42no—
411C22⋊C4—41no—
412C22⋊C4—41no—
413C22⋊C4—41no—
414C22⋊C4—41no—
415C22⋊C4—81no—
416C22⋊C4D8×C13112yescomplemented
417C42—42no—
418C42—81no—
419C23—22no—
420C23—41no—
421C23—41no—
422C23—41no—
423C23—41no—
424C23—41no—
425C23—41no—
426C23—41no—
427C23—41no—
428C23—41no—
429C23—41no—
430C23—41no—
431C23—81no—
432C23—81no—
433C23C4×D4×C13111yescharacteristic
434C23#120×C13111yescharacteristic
435C23#121×C13111yescharacteristic
436C23C2×D8×C13111yescharacteristic
437C23#135×C13111yescharacteristic
438C23AGL(1,ℤ/8)×C13111yescharacteristic
439C23AGL(1,ℤ/8)×C13111yescharacteristic
440D4—42no—
441D4—42no—
442D4—42no—
443D4—42no—
444D4—42no—
445D4—42no—
446D4—81no—
447D4—81no—
448D4—81no—
449D4—81no—
450D4—81no—
451D4—81no—
452C2×C4—22no—
453C2×C4—22no—
454C2×C4—22no—
455C2×C4—41no—
456C2×C4—41no—
457C2×C4—41no—
458C2×C4—41no—
459C2×C4—41no—
460C2×C4—41no—
461C2×C4—41no—
462C2×C4—41no—
463C2×C4—41no—
464C2×C4—41no—
465C2×C4—41no—
466C2×C4—41no—
467C2×C4—41no—
468C2×C4—41no—
469C2×C4—41no—
470C2×C4—41no—
471C2×C4—41no—
472C2×C4—41no—
473C2×C4—41no—
474C2×C4—41no—
475C2×C4—41no—
476C2×C4—84no—
477C2×C4—82no—
478C2×C4—82no—
479C2×C4—81no—
480C2×C4—81no—
481C2×C4—81no—
482C2×C4C2×C22⋊C4×C13111yescharacteristic
483C2×C4C4×D4×C13111yescharacteristic
484C2×C4#121×C13111yescharacteristic
485C2×C4#123×C13111yescharacteristic
486C8—42no—
487C8—81no—
488C22—21no—
489C22—21no—
490C22—21no—
491C22—21no—
492C22—21no—
493C22—21no—
494C22—41no—
495C22—41no—
496C22—41no—
497C22—41no—
498C22—42no—
499C22—42no—
500C22—42no—
501C22—81no—
502C22—81no—
503C22—81no—
504C22—81no—
505C22—81no—
506C22—81no—
507C22—81no—
508C22—161no—
509C22—161no—
510C22#386×C13111yescharacteristic
511C22C4×D8×C13111yescharacteristic
512C22#442×C13111yescharacteristic
513C22#447×C13111yescharacteristic
514C22#449×C13111yescharacteristic
515C22#459×C13111yescharacteristic
516C22#463×C13111yescharacteristic
517C4—21no—
518C4—21no—
519C4—21no—
520C4—21no—
521C4—42no—
522C4—42no—
523C4—42no—
524C4—81no—
525C4—81no—
526C4—81no—
527C4—161no—
528C2—21no—
529C2—21no—
530C2—21no—
531C2—21no—
532C2—21no—
533C2—21no—
534C2—82no—
535C2—161no—
536C2#1879×C13111yescharacteristic
537C2#1906×C13111yescharacteristic
538C2#1913×C13111yescharacteristic
subgroupG/H
center, socleC22×C131#386
commutatorC22×C4C22×C4×C131
Frattini, cosocleC23×C4C23×C131
prime radical#3186×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
2. #2364×C131C2semidirect
3. #1964×C131C2semidirect
4. #1519×C131C2semidirect
5. C2×#327×C131C2semidirect
6. #1294×C131C2semidirect
7. #1282×C131C2semidirect
12. #480×C131C4semidirect
15. #447×C131C4semidirect
33. C22×D4×C131C2×C4semidirect
53. C2×C4⋊C4×C131C2×C4semidirect
73. C22⋊C8×C131C2×C4semidirect
146. C22⋊C4×C131D8semidirect
269. #9277C131direct (N × H)
270. C131#9277direct (N × H)
272. #2364C2×C131semidirect
273. #1964C2×C131semidirect
274. #1519C2×C131semidirect
275. C2×#327C2×C131semidirect
276. #1294C2×C131semidirect
277. #1282C2×C131semidirect
282. #480C4×C131semidirect
285. #447C4×C131semidirect
303. C22×D4C2×C4×C131semidirect
323. C2×C4⋊C4C2×C4×C131semidirect
343. C22⋊C8C2×C4×C131semidirect
416. C22⋊C4D8×C131semidirect

Maximal subgroups

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

subgroupindex
#3186×C1312
#2364×C1312
#1964×C1312
#1519×C1312
C2×#327×C1312
#1294×C1312
#1282×C1312
#9277131