Finite Group Databasebeta

← C131×#9113 #45694997

Subgroups — C131×#9113 #45694997

Order 33536.

1062 conjugacy classes of subgroups.

The subgroup lattice has 592 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C22⋊C8×C131C211yesmaximal, characteristic, complemented
2#2847×C131C211yesmaximal, characteristic
3C2×#327×C131C212yesmaximal, complemented
4C22⋊#95×C131C211yesmaximal, characteristic, complemented
5#1294×C131C212yesmaximal, complemented
6C24×C4×C131C2211yescharacteristic
7C23×C8×C131—21no—
8C2×#121×C131C411yescharacteristic, complemented
9C2×#121×C131C411yescharacteristic, complemented
10C2×#121×C131C2211yescharacteristic
11C2×#120×C131—21no—
12C22×C22⋊C4×C131—21no—
13C2×C22⋊C8×C131—21no—
14C2×C22⋊C8×C131—24no—
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
41C22×C8×C131—24no—
42C22×C8×C131—22no—
43C22×C8×C131—42no—
44C22×C8×C131—42no—
45#121×C131—22no—
46#121×C131—22no—
47#121×C131—42no—
48#121×C131—42no—
49#120×C131—42no—
50#120×C131—42no—
51C2×C4⋊C4×C131C2×C411yescharacteristic
52C2×C4⋊C4×C131C2×C411yescharacteristic
53C2×C4⋊C4×C131C2×C411yescharacteristic
54C2×C22⋊C4×C131—24no—
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×C131—42no—
62C2×C22⋊C4×C131—42no—
63C22⋊C8×C131—24no—
64C22⋊C8×C131—22no—
65C22⋊C8×C131D414yescomplemented
66#95×C131—21no—
67#95×C131—21no—
68#95×C131—21no—
69#95×C131—22no—
70#95×C131—22no—
71#95×C131—42no—
72C24×C131—22no—
73C24×C131—22no—
74C24×C131—22no—
75C24×C131—22no—
76C24×C131—21no—
77C24×C131—41no—
78C24×C131—41no—
79C24×C131C22⋊C411yescharacteristic
80C24×C131C22⋊C411yescharacteristic
81C24×C131D812yes—
82C24×C131SD1612yes—
83C24×C131C2×D411yescharacteristic
84C2×D4×C131—22no—
85C2×D4×C131—41no—
86C2×D4×C131—41no—
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—
96C2×D4×C131—42no—
97C22×C4×C131—22no—
98C22×C4×C131—22no—
99C22×C4×C131—21no—
100C22×C4×C131—21no—
101C22×C4×C131—22no—
102C22×C4×C131—22no—
103C22×C4×C131—22no—
104C22×C4×C131—22no—
105C22×C4×C131—22no—
106C22×C4×C131—22no—
107C22×C4×C131—21no—
108C22×C4×C131—21no—
109C22×C4×C131—24no—
110C22×C4×C131—21no—
111C22×C4×C131—21no—
112C22×C4×C131—21no—
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—41no—
120C22×C4×C131—48no—
121C22×C4×C131—48no—
122C22×C4×C131—42no—
123C22×C4×C131—42no—
124C22×C4×C131—42no—
125C22×C4×C131—42no—
126C22×C4×C131—42no—
127C22×C4×C131—42no—
128C22×C4×C131C22⋊C411yescharacteristic
129C22×C4×C131C22⋊C411yescharacteristic
130C22×C4×C131C22×C411yescharacteristic
131C22×C4×C131C2×D411yescharacteristic
132C22×C4×C131C2×D412yes—
133C22×C4×C131#4112yes—
134C2×C8×C131—24no—
135C2×C8×C131—48no—
136C2×C8×C131—42no—
137C2×C8×C131—42no—
138C4⋊C4×C131—22no—
139C4⋊C4×C131—41no—
140C4⋊C4×C131—41no—
141C22⋊C4×C131—42no—
142C22⋊C4×C131—48no—
143C22⋊C4×C131—42no—
144C22⋊C4×C131—42no—
145C22⋊C4×C131—41no—
146C22⋊C4×C131—41no—
147C22⋊C4×C131—42no—
148C22⋊C4×C131—41no—
149C22⋊C4×C131—41no—
150C23×C131—21no—
151C23×C131—21no—
152C23×C131—21no—
153C23×C131—21no—
154C23×C131—21no—
155C23×C131—21no—
156C23×C131—21no—
157C23×C131—21no—
158C23×C131—24no—
159C23×C131—24no—
160C23×C131—21no—
161C23×C131—21no—
162C23×C131—21no—
163C23×C131—21no—
164C23×C131—21no—
165C23×C131—21no—
166C23×C131—24no—
167C23×C131—24no—
168C23×C131—42no—
169C23×C131—42no—
170C23×C131—44no—
171C23×C131—44no—
172C23×C131—44no—
173C23×C131—44no—
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#10212yes—
183C23×C131#10212yes—
184C23×C131#10412yes—
185C23×C131C2×C22⋊C411yescharacteristic
186C23×C131#12112yes—
187C23×C131C2×D811yescharacteristic
188C23×C131C2×SD1611yescharacteristic
189C23×C131#13512yes—
190D4×C131—82no—
191D4×C131—84no—
192D4×C131—84no—
193D4×C131—82no—
194D4×C131—82no—
195C2×C4×C131—24no—
196C2×C4×C131—24no—
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—21no—
205C2×C4×C131—21no—
206C2×C4×C131—42no—
207C2×C4×C131—42no—
208C2×C4×C131—44no—
209C2×C4×C131—44no—
210C2×C4×C131—44no—
211C2×C4×C131—42no—
212C2×C4×C131—42no—
213C2×C4×C131—44no—
214C2×C4×C131—44no—
215C2×C4×C131—44no—
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—41no—
224C2×C4×C131—41no—
225C2×C4×C131—82no—
226C2×C4×C131—82no—
227C2×C4×C131—82no—
228C2×C4×C131—82no—
229C2×C4×C131#9912yes—
230C2×C4×C131C4×D412yes—
231C2×C4×C131#12011yescharacteristic
232C2×C4×C131#12311yescharacteristic
233C8×C131—44no—
234C22×C131—22no—
235C22×C131—22no—
236C22×C131—22no—
237C22×C131—22no—
238C22×C131—22no—
239C22×C131—21no—
240C22×C131—21no—
241C22×C131—22no—
242C22×C131—22no—
243C22×C131—22no—
244C22×C131—22no—
245C22×C131—21no—
246C22×C131—22no—
247C22×C131—21no—
248C22×C131—22no—
249C22×C131—22no—
250C22×C131—22no—
251C22×C131—48no—
252C22×C131—48no—
253C22×C131—41no—
254C22×C131—41no—
255C22×C131—41no—
256C22×C131—41no—
257C22×C131—81no—
258C22×C131—81no—
259C22×C131—81no—
260C22×C131—81no—
261C22×C131—81no—
262C22×C131—81no—
263C22×C131—81no—
264C22×C131#32714yescomplemented
265C22×C131#38611yescharacteristic
266C22×C131C2×#9911yescharacteristic
267C22×C131C2×#9911yescharacteristic
268C22×C131C2×#10211yescharacteristic
269C22×C131#41611yescharacteristic
270C22×C131C2×#10411yescharacteristic
271C22×C131#42111yescharacteristic
272C22×C131#46512yes—
273C22×C131#46612yes—
274C4×C131—21no—
275C4×C131—22no—
276C4×C131—21no—
277C4×C131—22no—
278C4×C131—41no—
279C4×C131—84no—
280C4×C131—81no—
281C4×C131—81no—
282C4×C131—81no—
283C2×C131—22no—
284C2×C131—24no—
285C2×C131—22no—
286C2×C131—42no—
287C2×C131—161no—
288C2×C131C2×#32711yescharacteristic
289C2×C131#150111yescharacteristic
290C2×C131#151611yescharacteristic
291C2×C131#151911yescharacteristic
292C2×C131#187111yescharacteristic
293C2×C131#189311yescharacteristic
294C2×C131#189811yescharacteristic
295#9113C13111yesmaximal, characteristic, direct product factor, Sylow
296C131#911311yescharacteristic, direct product factor, Sylow
297C22×C22⋊C8C2×C13111yescharacteristic, complemented
298#2847C2×C13111yescharacteristic
299C2×#327C2×C13112yescomplemented
300C22⋊#95C2×C13111yescharacteristic, complemented
301#1294C2×C13112yescomplemented
302C24×C4C22×C13111yescharacteristic
303C23×C8—21no—
304C2×#121C4×C13111yescharacteristic, complemented
305C2×#121C4×C13111yescharacteristic, complemented
306C2×#121C22×C13111yescharacteristic
307C2×#120—21no—
308C22×C22⋊C4—21no—
309C2×C22⋊C8—21no—
310C2×C22⋊C8—24no—
311C2×C22⋊C8C22×C13112yes—
312#386—21no—
313#386—21no—
314#386—21no—
315#380C4×C13111yescharacteristic, complemented
316#380C4×C13111yescharacteristic, complemented
317#380C22×C13111yescharacteristic
318C2×#95—21no—
319C2×#95C22×C13112yes—
320#327—24no—
321C25D4×C13111yescharacteristic
322C22×D4—21no—
323C22×D4—21no—
324C22×D4—21no—
325C22×D4C2×C4×C13111yescharacteristic
326C23×C4—22no—
327C23×C4—22no—
328C23×C4—22no—
329C23×C4—42no—
330C23×C4—42no—
331C23×C4C2×C4×C13111yescharacteristic
332C23×C4C2×C4×C13111yescharacteristic
333C23×C4D4×C13111yescharacteristic
334C23×C4D4×C13111yescharacteristic
335C23×C4D4×C13111yescharacteristic
336C23×C4C23×C13111yescharacteristic
337C22×C8—24no—
338C22×C8—22no—
339C22×C8—42no—
340C22×C8—42no—
341#121—22no—
342#121—22no—
343#121—42no—
344#121—42no—
345#120—42no—
346#120—42no—
347C2×C4⋊C4C2×C4×C13111yescharacteristic
348C2×C4⋊C4C2×C4×C13111yescharacteristic
349C2×C4⋊C4C2×C4×C13111yescharacteristic
350C2×C22⋊C4—24no—
351C2×C22⋊C4—21no—
352C2×C22⋊C4—21no—
353C2×C22⋊C4—21no—
354C2×C22⋊C4—21no—
355C2×C22⋊C4—21no—
356C2×C22⋊C4—21no—
357C2×C22⋊C4—42no—
358C2×C22⋊C4—42no—
359C22⋊C8—24no—
360C22⋊C8—22no—
361C22⋊C8D4×C13114yescomplemented
362#95—21no—
363#95—21no—
364#95—21no—
365#95—22no—
366#95—22no—
367#95—42no—
368C24—22no—
369C24—22no—
370C24—22no—
371C24—22no—
372C24—21no—
373C24—41no—
374C24—41no—
375C24C22⋊C4×C13111yescharacteristic
376C24C22⋊C4×C13111yescharacteristic
377C24D8×C13112yes—
378C24SD16×C13112yes—
379C24C2×D4×C13111yescharacteristic
380C2×D4—22no—
381C2×D4—41no—
382C2×D4—41no—
383C2×D4—42no—
384C2×D4—42no—
385C2×D4—42no—
386C2×D4—42no—
387C2×D4—42no—
388C2×D4—42no—
389C2×D4—42no—
390C2×D4—41no—
391C2×D4—41no—
392C2×D4—42no—
393C22×C4—22no—
394C22×C4—22no—
395C22×C4—21no—
396C22×C4—21no—
397C22×C4—22no—
398C22×C4—22no—
399C22×C4—22no—
400C22×C4—22no—
401C22×C4—22no—
402C22×C4—22no—
403C22×C4—21no—
404C22×C4—21no—
405C22×C4—24no—
406C22×C4—21no—
407C22×C4—21no—
408C22×C4—21no—
409C22×C4—41no—
410C22×C4—41no—
411C22×C4—41no—
412C22×C4—41no—
413C22×C4—41no—
414C22×C4—41no—
415C22×C4—41no—
416C22×C4—48no—
417C22×C4—48no—
418C22×C4—42no—
419C22×C4—42no—
420C22×C4—42no—
421C22×C4—42no—
422C22×C4—42no—
423C22×C4—42no—
424C22×C4C22⋊C4×C13111yescharacteristic
425C22×C4C22⋊C4×C13111yescharacteristic
426C22×C4C22×C4×C13111yescharacteristic
427C22×C4C2×D4×C13111yescharacteristic
428C22×C4C2×D4×C13112yes—
429C22×C4#41×C13112yes—
430C2×C8—24no—
431C2×C8—48no—
432C2×C8—42no—
433C2×C8—42no—
434C4⋊C4—22no—
435C4⋊C4—41no—
436C4⋊C4—41no—
437C22⋊C4—42no—
438C22⋊C4—48no—
439C22⋊C4—42no—
440C22⋊C4—42no—
441C22⋊C4—41no—
442C22⋊C4—41no—
443C22⋊C4—42no—
444C22⋊C4—41no—
445C22⋊C4—41no—
446C23—21no—
447C23—21no—
448C23—21no—
449C23—21no—
450C23—21no—
451C23—21no—
452C23—21no—
453C23—21no—
454C23—21no—
455C23—21no—
456C23—21no—
457C23—21no—
458C23—21no—
459C23—24no—
460C23—24no—
461C23—24no—
462C23—24no—
463C23—21no—
464C23—42no—
465C23—42no—
466C23—44no—
467C23—44no—
468C23—44no—
469C23—44no—
470C23—41no—
471C23—41no—
472C23—41no—
473C23—41no—
474C23—41no—
475C23—41no—
476C23—41no—
477C23#99×C13112yes—
478C23#102×C13112yes—
479C23#102×C13112yes—
480C23#104×C13112yes—
481C23C2×C22⋊C4×C13111yescharacteristic
482C23#121×C13112yes—
483C23C2×D8×C13111yescharacteristic
484C23C2×SD16×C13111yescharacteristic
485C23#135×C13112yes—
486D4—82no—
487D4—84no—
488D4—82no—
489D4—82no—
490D4—84no—
491C2×C4—24no—
492C2×C4—24no—
493C2×C4—21no—
494C2×C4—21no—
495C2×C4—21no—
496C2×C4—21no—
497C2×C4—21no—
498C2×C4—21no—
499C2×C4—21no—
500C2×C4—21no—
501C2×C4—21no—
502C2×C4—42no—
503C2×C4—42no—
504C2×C4—44no—
505C2×C4—44no—
506C2×C4—44no—
507C2×C4—42no—
508C2×C4—42no—
509C2×C4—44no—
510C2×C4—44no—
511C2×C4—44no—
512C2×C4—41no—
513C2×C4—41no—
514C2×C4—41no—
515C2×C4—41no—
516C2×C4—41no—
517C2×C4—41no—
518C2×C4—41no—
519C2×C4—41no—
520C2×C4—41no—
521C2×C4—82no—
522C2×C4—82no—
523C2×C4—82no—
524C2×C4—82no—
525C2×C4#99×C13112yes—
526C2×C4C4×D4×C13112yes—
527C2×C4#120×C13111yescharacteristic
528C2×C4#123×C13111yescharacteristic
529C8—44no—
530C22—21no—
531C22—21no—
532C22—22no—
533C22—22no—
534C22—22no—
535C22—22no—
536C22—21no—
537C22—22no—
538C22—21no—
539C22—22no—
540C22—22no—
541C22—22no—
542C22—22no—
543C22—22no—
544C22—22no—
545C22—22no—
546C22—22no—
547C22—48no—
548C22—48no—
549C22—41no—
550C22—41no—
551C22—41no—
552C22—41no—
553C22—81no—
554C22—81no—
555C22—81no—
556C22—81no—
557C22—81no—
558C22—81no—
559C22—81no—
560C22#327×C13114yescomplemented
561C22#386×C13111yescharacteristic
562C22C2×#99×C13111yescharacteristic
563C22C2×#99×C13111yescharacteristic
564C22C2×#102×C13111yescharacteristic
565C22#416×C13111yescharacteristic
566C22C2×#104×C13111yescharacteristic
567C22#421×C13111yescharacteristic
568C22#465×C13112yes—
569C22#466×C13112yes—
570C4—21no—
571C4—22no—
572C4—21no—
573C4—22no—
574C4—41no—
575C4—84no—
576C4—81no—
577C4—81no—
578C4—81no—
579C2—22no—
580C2—22no—
581C2—24no—
582C2—42no—
583C2—161no—
584C2C2×#327×C13111yescharacteristic
585C2#1501×C13111yescharacteristic
586C2#1516×C13111yescharacteristic
587C2#1519×C13111yescharacteristic
588C2#1871×C13111yescharacteristic
589C2#1893×C13111yescharacteristic
590C2#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. C22×C22⋊C8×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
65. C22⋊C8×C131D4semidirect
264. C22×C131#327semidirect
295. #9113C131direct (N × H)
296. C131#9113direct (N × H)
297. C22×C22⋊C8C2×C131semidirect
299. C2×#327C2×C131semidirect
300. C22⋊#95C2×C131semidirect
301. #1294C2×C131semidirect
304. C2×#121C4×C131semidirect
305. C2×#121C4×C131semidirect
315. #380C4×C131semidirect
316. #380C4×C131semidirect
361. C22⋊C8D4×C131semidirect
560. C22#327×C131semidirect

Maximal subgroups

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

subgroupindex
C22×C22⋊C8×C1312
#2847×C1312
C2×#327×C1312
C22⋊#95×C1312
#1294×C1312
#9113131