Finite Group Databasebeta

← C131×#9117 #45695001

Subgroups — C131×#9117 #45695001

Order 33536.

1030 conjugacy classes of subgroups.

The subgroup lattice has 588 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#407×C131C211yesmaximal, characteristic, complemented
2#2847×C131C211yesmaximal, characteristic
3C2×#327×C131C212yesmaximal, complemented
4C22⋊#95×C131C211yesmaximal, characteristic, complemented
5#1294×C131C212yesmaximal, complemented
6C24×C4×C131C2211yescharacteristic
7C22×M16×C131—21no—
8C2×#121×C131C411yescharacteristic, complemented
9C2×#121×C131C411yescharacteristic, complemented
10C2×#121×C131C2211yescharacteristic
11C2×#120×C131—21no—
12C22×C22⋊C4×C131—21no—
13#407×C131—24no—
14C2×C22⋊C8×C131—21no—
15C2×C22⋊C8×C131C2212yes—
16#386×C131—21no—
17#386×C131—21no—
18#386×C131—21no—
19#380×C131C411yescharacteristic, complemented
20#380×C131C411yescharacteristic, complemented
21#380×C131C2211yescharacteristic
22C2×#95×C131—21no—
23C2×#95×C131C2212yes—
24#327×C131—24no—
25C25×C131D411yescharacteristic
26C22×D4×C131—21no—
27C22×D4×C131—21no—
28C22×D4×C131—21no—
29C22×D4×C131C2×C411yescharacteristic
30C23×C4×C131—22no—
31C23×C4×C131—22no—
32C23×C4×C131—22no—
33C23×C4×C131—42no—
34C23×C4×C131—42no—
35C23×C4×C131C2×C411yescharacteristic
36C23×C4×C131C2×C411yescharacteristic
37C23×C4×C131D411yescharacteristic
38C23×C4×C131D411yescharacteristic
39C23×C4×C131D411yescharacteristic
40C23×C4×C131C2311yescharacteristic
41C2×M16×C131—24no—
42C2×M16×C131—42no—
43C2×M16×C131—42no—
44C22×C8×C131—22no—
45#121×C131—22no—
46#121×C131—22no—
47#121×C131—42no—
48#121×C131—42no—
49#120×C131—44no—
50C2×C4⋊C4×C131C2×C411yescharacteristic
51C2×C4⋊C4×C131C2×C411yescharacteristic
52C2×C4⋊C4×C131C2×C411yescharacteristic
53C2×C22⋊C4×C131—24no—
54C2×C22⋊C4×C131—21no—
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—42no—
61C2×C22⋊C4×C131—42no—
62C22⋊C8×C131—24no—
63C22⋊C8×C131—22no—
64C22⋊C8×C131D414yescomplemented
65#95×C131—21no—
66#95×C131—21no—
67#95×C131—21no—
68#95×C131—22no—
69#95×C131—22no—
70#95×C131—42no—
71C24×C131—22no—
72C24×C131—22no—
73C24×C131—21no—
74C24×C131—21no—
75C24×C131—22no—
76C24×C131—22no—
77C24×C131—21no—
78C24×C131—41no—
79C24×C131—41no—
80C24×C131C22⋊C411yescharacteristic
81C24×C131C22⋊C411yescharacteristic
82C24×C131C2×D411yescharacteristic
83C2×D4×C131—22no—
84C2×D4×C131—41no—
85C2×D4×C131—41no—
86C2×D4×C131—42no—
87C2×D4×C131—42no—
88C2×D4×C131—42no—
89C2×D4×C131—42no—
90C2×D4×C131—42no—
91C2×D4×C131—42no—
92C2×D4×C131—42no—
93C2×D4×C131—42no—
94C2×D4×C131—41no—
95C2×D4×C131—41no—
96C22×C4×C131—22no—
97C22×C4×C131—22no—
98C22×C4×C131—21no—
99C22×C4×C131—21no—
100C22×C4×C131—22no—
101C22×C4×C131—22no—
102C22×C4×C131—22no—
103C22×C4×C131—22no—
104C22×C4×C131—22no—
105C22×C4×C131—22no—
106C22×C4×C131—21no—
107C22×C4×C131—21no—
108C22×C4×C131—24no—
109C22×C4×C131—21no—
110C22×C4×C131—21no—
111C22×C4×C131—21no—
112C22×C4×C131—41no—
113C22×C4×C131—41no—
114C22×C4×C131—41no—
115C22×C4×C131—41no—
116C22×C4×C131—41no—
117C22×C4×C131—41no—
118C22×C4×C131—41no—
119C22×C4×C131—48no—
120C22×C4×C131—48no—
121C22×C4×C131—42no—
122C22×C4×C131—42no—
123C22×C4×C131—42no—
124C22×C4×C131—42no—
125C22×C4×C131—42no—
126C22×C4×C131—42no—
127C22×C4×C131C22⋊C411yescharacteristic
128C22×C4×C131C22⋊C411yescharacteristic
129C22×C4×C131C22×C411yescharacteristic
130C22×C4×C131C2×D411yescharacteristic
131C22×C4×C131C2×D412yes—
132C22×C4×C131#4112yes—
133M16×C131—48no—
134C2×C8×C131—24no—
135C2×C8×C131—42no—
136C2×C8×C131—42no—
137C4⋊C4×C131—22no—
138C4⋊C4×C131—41no—
139C4⋊C4×C131—41no—
140C22⋊C4×C131—42no—
141C22⋊C4×C131—48no—
142C22⋊C4×C131—42no—
143C22⋊C4×C131—42no—
144C22⋊C4×C131—42no—
145C22⋊C4×C131—42no—
146C22⋊C4×C131—41no—
147C22⋊C4×C131—41no—
148C23×C131—21no—
149C23×C131—21no—
150C23×C131—21no—
151C23×C131—21no—
152C23×C131—24no—
153C23×C131—24no—
154C23×C131—21no—
155C23×C131—21no—
156C23×C131—21no—
157C23×C131—21no—
158C23×C131—21no—
159C23×C131—21no—
160C23×C131—21no—
161C23×C131—21no—
162C23×C131—21no—
163C23×C131—21no—
164C23×C131—21no—
165C23×C131—21no—
166C23×C131—44no—
167C23×C131—44no—
168C23×C131—44no—
169C23×C131—44no—
170C23×C131—42no—
171C23×C131—42no—
172C23×C131—42no—
173C23×C131—42no—
174C23×C131—41no—
175C23×C131—41no—
176C23×C131—41no—
177C23×C131—41no—
178C23×C131—41no—
179C23×C131—41no—
180C23×C131—41no—
181C23×C131#9912yes—
182C23×C131#10412yes—
183C23×C131C2×C22⋊C411yescharacteristic
184C23×C131#12112yes—
185C23×C131AGL(1,ℤ/8)11yescharacteristic
186C23×C131AGL(1,ℤ/8)12yes—
187C23×C131#13711yescharacteristic
188D4×C131—82no—
189D4×C131—84no—
190D4×C131—84no—
191D4×C131—82no—
192D4×C131—82no—
193C2×C4×C131—24no—
194C2×C4×C131—24no—
195C2×C4×C131—21no—
196C2×C4×C131—21no—
197C2×C4×C131—21no—
198C2×C4×C131—21no—
199C2×C4×C131—21no—
200C2×C4×C131—21no—
201C2×C4×C131—21no—
202C2×C4×C131—21no—
203C2×C4×C131—21no—
204C2×C4×C131—42no—
205C2×C4×C131—42no—
206C2×C4×C131—44no—
207C2×C4×C131—44no—
208C2×C4×C131—44no—
209C2×C4×C131—42no—
210C2×C4×C131—42no—
211C2×C4×C131—44no—
212C2×C4×C131—44no—
213C2×C4×C131—44no—
214C2×C4×C131—41no—
215C2×C4×C131—41no—
216C2×C4×C131—41no—
217C2×C4×C131—41no—
218C2×C4×C131—41no—
219C2×C4×C131—41no—
220C2×C4×C131—41no—
221C2×C4×C131—41no—
222C2×C4×C131—41no—
223C2×C4×C131—82no—
224C2×C4×C131—82no—
225C2×C4×C131—82no—
226C2×C4×C131—82no—
227C2×C4×C131#9912yes—
228C2×C4×C131C4×D412yes—
229C2×C4×C131#12011yescharacteristic
230C2×C4×C131#12311yescharacteristic
231C8×C131—44no—
232C22×C131—22no—
233C22×C131—22no—
234C22×C131—21no—
235C22×C131—21no—
236C22×C131—22no—
237C22×C131—22no—
238C22×C131—21no—
239C22×C131—21no—
240C22×C131—22no—
241C22×C131—22no—
242C22×C131—22no—
243C22×C131—22no—
244C22×C131—22no—
245C22×C131—22no—
246C22×C131—48no—
247C22×C131—48no—
248C22×C131—41no—
249C22×C131—41no—
250C22×C131—41no—
251C22×C131—41no—
252C22×C131—41no—
253C22×C131—41no—
254C22×C131—41no—
255C22×C131—41no—
256C22×C131—81no—
257C22×C131—81no—
258C22×C131—81no—
259C22×C131—81no—
260C22×C131—81no—
261C22×C131—81no—
262C22×C131—81no—
263C22×C131#38611yescharacteristic
264C22×C131C2×#9911yescharacteristic
265C22×C131C2×#9911yescharacteristic
266C22×C131#41711yescharacteristic
267C22×C131#41811yescharacteristic
268C22×C131C2×#10411yescharacteristic
269C22×C131#42111yescharacteristic
270C22×C131#46812yes—
271C22×C131#46912yes—
272C4×C131—21no—
273C4×C131—22no—
274C4×C131—21no—
275C4×C131—22no—
276C4×C131—41no—
277C4×C131—84no—
278C4×C131—81no—
279C4×C131—81no—
280C4×C131—81no—
281C2×C131—22no—
282C2×C131—22no—
283C2×C131—42no—
284C2×C131—42no—
285C2×C131—161no—
286C2×C131#150411yescharacteristic
287C2×C131#150711yescharacteristic
288C2×C131#151011yescharacteristic
289C2×C131#151311yescharacteristic
290C2×C131#187111yescharacteristic
291C2×C131#189511yescharacteristic
292C2×C131#189811yescharacteristic
293#9117C13111yesmaximal, characteristic, direct product factor, Sylow
294C131#911711yescharacteristic, direct product factor, Sylow
295C2×#407C2×C13111yescharacteristic, complemented
296#2847C2×C13111yescharacteristic
297C2×#327C2×C13112yescomplemented
298C22⋊#95C2×C13111yescharacteristic, complemented
299#1294C2×C13112yescomplemented
300C24×C4C22×C13111yescharacteristic
301C22×M16—21no—
302C2×#121C4×C13111yescharacteristic, complemented
303C2×#121C4×C13111yescharacteristic, complemented
304C2×#121C22×C13111yescharacteristic
305C2×#120—21no—
306C22×C22⋊C4—21no—
307#407—24no—
308C2×C22⋊C8—21no—
309C2×C22⋊C8C22×C13112yes—
310#386—21no—
311#386—21no—
312#386—21no—
313#380C4×C13111yescharacteristic, complemented
314#380C4×C13111yescharacteristic, complemented
315#380C22×C13111yescharacteristic
316C2×#95—21no—
317C2×#95C22×C13112yes—
318#327—24no—
319C25D4×C13111yescharacteristic
320C22×D4—21no—
321C22×D4—21no—
322C22×D4—21no—
323C22×D4C2×C4×C13111yescharacteristic
324C23×C4—22no—
325C23×C4—22no—
326C23×C4—22no—
327C23×C4—42no—
328C23×C4—42no—
329C23×C4C2×C4×C13111yescharacteristic
330C23×C4C2×C4×C13111yescharacteristic
331C23×C4D4×C13111yescharacteristic
332C23×C4D4×C13111yescharacteristic
333C23×C4D4×C13111yescharacteristic
334C23×C4C23×C13111yescharacteristic
335C2×M16—24no—
336C2×M16—42no—
337C2×M16—42no—
338C22×C8—22no—
339#121—22no—
340#121—22no—
341#121—42no—
342#121—42no—
343#120—44no—
344C2×C4⋊C4C2×C4×C13111yescharacteristic
345C2×C4⋊C4C2×C4×C13111yescharacteristic
346C2×C4⋊C4C2×C4×C13111yescharacteristic
347C2×C22⋊C4—24no—
348C2×C22⋊C4—21no—
349C2×C22⋊C4—21no—
350C2×C22⋊C4—21no—
351C2×C22⋊C4—21no—
352C2×C22⋊C4—21no—
353C2×C22⋊C4—21no—
354C2×C22⋊C4—42no—
355C2×C22⋊C4—42no—
356C22⋊C8—24no—
357C22⋊C8—22no—
358C22⋊C8D4×C13114yescomplemented
359#95—21no—
360#95—21no—
361#95—21no—
362#95—22no—
363#95—22no—
364#95—42no—
365C24—22no—
366C24—22no—
367C24—21no—
368C24—21no—
369C24—22no—
370C24—22no—
371C24—21no—
372C24—41no—
373C24—41no—
374C24C22⋊C4×C13111yescharacteristic
375C24C22⋊C4×C13111yescharacteristic
376C24C2×D4×C13111yescharacteristic
377C2×D4—22no—
378C2×D4—41no—
379C2×D4—41no—
380C2×D4—42no—
381C2×D4—42no—
382C2×D4—42no—
383C2×D4—42no—
384C2×D4—42no—
385C2×D4—42no—
386C2×D4—42no—
387C2×D4—42no—
388C2×D4—41no—
389C2×D4—41no—
390C22×C4—22no—
391C22×C4—22no—
392C22×C4—21no—
393C22×C4—21no—
394C22×C4—22no—
395C22×C4—22no—
396C22×C4—22no—
397C22×C4—22no—
398C22×C4—22no—
399C22×C4—22no—
400C22×C4—21no—
401C22×C4—21no—
402C22×C4—24no—
403C22×C4—21no—
404C22×C4—21no—
405C22×C4—21no—
406C22×C4—41no—
407C22×C4—41no—
408C22×C4—41no—
409C22×C4—41no—
410C22×C4—41no—
411C22×C4—41no—
412C22×C4—41no—
413C22×C4—48no—
414C22×C4—48no—
415C22×C4—42no—
416C22×C4—42no—
417C22×C4—42no—
418C22×C4—42no—
419C22×C4—42no—
420C22×C4—42no—
421C22×C4C22⋊C4×C13111yescharacteristic
422C22×C4C22⋊C4×C13111yescharacteristic
423C22×C4C22×C4×C13111yescharacteristic
424C22×C4C2×D4×C13111yescharacteristic
425C22×C4C2×D4×C13112yes—
426C22×C4#41×C13112yes—
427M16—48no—
428C2×C8—24no—
429C2×C8—42no—
430C2×C8—42no—
431C4⋊C4—22no—
432C4⋊C4—41no—
433C4⋊C4—41no—
434C22⋊C4—42no—
435C22⋊C4—48no—
436C22⋊C4—42no—
437C22⋊C4—42no—
438C22⋊C4—42no—
439C22⋊C4—42no—
440C22⋊C4—41no—
441C22⋊C4—41no—
442C23—21no—
443C23—21no—
444C23—21no—
445C23—21no—
446C23—24no—
447C23—24no—
448C23—21no—
449C23—21no—
450C23—21no—
451C23—21no—
452C23—21no—
453C23—21no—
454C23—21no—
455C23—21no—
456C23—21no—
457C23—21no—
458C23—21no—
459C23—21no—
460C23—44no—
461C23—44no—
462C23—44no—
463C23—44no—
464C23—42no—
465C23—42no—
466C23—42no—
467C23—42no—
468C23—41no—
469C23—41no—
470C23—41no—
471C23—41no—
472C23—41no—
473C23—41no—
474C23—41no—
475C23#99×C13112yes—
476C23#104×C13112yes—
477C23C2×C22⋊C4×C13111yescharacteristic
478C23#121×C13112yes—
479C23AGL(1,ℤ/8)×C13111yescharacteristic
480C23AGL(1,ℤ/8)×C13112yes—
481C23#137×C13111yescharacteristic
482D4—82no—
483D4—84no—
484D4—84no—
485D4—82no—
486D4—82no—
487C2×C4—24no—
488C2×C4—24no—
489C2×C4—21no—
490C2×C4—21no—
491C2×C4—21no—
492C2×C4—21no—
493C2×C4—21no—
494C2×C4—21no—
495C2×C4—21no—
496C2×C4—21no—
497C2×C4—21no—
498C2×C4—42no—
499C2×C4—42no—
500C2×C4—44no—
501C2×C4—44no—
502C2×C4—44no—
503C2×C4—42no—
504C2×C4—42no—
505C2×C4—44no—
506C2×C4—44no—
507C2×C4—44no—
508C2×C4—41no—
509C2×C4—41no—
510C2×C4—41no—
511C2×C4—41no—
512C2×C4—41no—
513C2×C4—41no—
514C2×C4—41no—
515C2×C4—41no—
516C2×C4—41no—
517C2×C4—82no—
518C2×C4—82no—
519C2×C4—82no—
520C2×C4—82no—
521C2×C4#99×C13112yes—
522C2×C4C4×D4×C13112yes—
523C2×C4#120×C13111yescharacteristic
524C2×C4#123×C13111yescharacteristic
525C8—44no—
526C22—21no—
527C22—21no—
528C22—22no—
529C22—22no—
530C22—21no—
531C22—21no—
532C22—22no—
533C22—22no—
534C22—22no—
535C22—22no—
536C22—22no—
537C22—22no—
538C22—22no—
539C22—22no—
540C22—48no—
541C22—48no—
542C22—41no—
543C22—41no—
544C22—41no—
545C22—41no—
546C22—41no—
547C22—41no—
548C22—41no—
549C22—41no—
550C22—81no—
551C22—81no—
552C22—81no—
553C22—81no—
554C22—81no—
555C22—81no—
556C22—81no—
557C22#386×C13111yescharacteristic
558C22C2×#99×C13111yescharacteristic
559C22C2×#99×C13111yescharacteristic
560C22#417×C13111yescharacteristic
561C22#418×C13111yescharacteristic
562C22C2×#104×C13111yescharacteristic
563C22#421×C13111yescharacteristic
564C22#468×C13112yes—
565C22#469×C13112yes—
566C4—21no—
567C4—22no—
568C4—21no—
569C4—22no—
570C4—41no—
571C4—84no—
572C4—81no—
573C4—81no—
574C4—81no—
575C2—22no—
576C2—22no—
577C2—42no—
578C2—42no—
579C2—161no—
580C2#1504×C13111yescharacteristic
581C2#1507×C13111yescharacteristic
582C2#1510×C13111yescharacteristic
583C2#1513×C13111yescharacteristic
584C2#1871×C13111yescharacteristic
585C2#1895×C13111yescharacteristic
586C2#1898×C13111yescharacteristic
subgroupG/H
center, socleC23×C131C2×C22⋊C4
commutatorC22×C4C22×C4×C131
Frattini, cosocleC23×C4C23×C131
prime radical#2847×C131C2
LCSG ▷ C22×C4 ▷ C22 ▷ C1
UCSC1 ◁ C23×C131 ◁ C24×C4×C131 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×#407×C131C2semidirect
3. C2×#327×C131C2semidirect
4. C22⋊#95×C131C2semidirect
5. #1294×C131C2semidirect
8. C2×#121×C131C4semidirect
9. C2×#121×C131C4semidirect
19. #380×C131C4semidirect
20. #380×C131C4semidirect
64. C22⋊C8×C131D4semidirect
293. #9117C131direct (N × H)
294. C131#9117direct (N × H)
295. C2×#407C2×C131semidirect
297. C2×#327C2×C131semidirect
298. C22⋊#95C2×C131semidirect
299. #1294C2×C131semidirect
302. C2×#121C4×C131semidirect
303. C2×#121C4×C131semidirect
313. #380C4×C131semidirect
314. #380C4×C131semidirect
358. C22⋊C8D4×C131semidirect

Maximal subgroups

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

subgroupindex
C2×#407×C1312
#2847×C1312
C2×#327×C1312
C22⋊#95×C1312
#1294×C1312
#9117131