Finite Group Databasebeta

← C131×#29894 #45715778

Subgroups — C131×#29894 #45715778

Order 33536.

1050 conjugacy classes of subgroups.

The subgroup lattice has 606 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#2848×C131C211yesmaximal, characteristic
2C2×#380×C131C211yesmaximal, characteristic
3#2077×C131C212yesmaximal, complemented
4#2075×C131C212yesmaximal, complemented
5#2036×C131C212yesmaximal, complemented
6#2035×C131C212yesmaximal, complemented
7#1872×C131C211yesmaximal, characteristic, complemented
8#1872×C131C211yesmaximal, characteristic, complemented
9#1853×C131C211yesmaximal, characteristic, complemented
10#1852×C131C211yesmaximal, characteristic, complemented
11#1779×C131C211yesmaximal, characteristic
12C24×C4×C131C2211yescharacteristic
13C2×C22⋊Q8×C131C2211yescharacteristic
14C2×C22⋊Q8×C131C2211yescharacteristic
15C2×C22⋊Q8×C131C2211yescharacteristic
16C22×C4⋊C4×C131C2211yescharacteristic
17C22×C4⋊C4×C131C2211yescharacteristic
18C22×C22⋊C4×C131—21no—
19C2×#107×C131C2212yescomplemented
20C2×#106×C131C2212yescomplemented
21C2×#103×C131C2212yescomplemented
22C2×#103×C131C2212yescomplemented
23C2×C22⋊C8×C131C2211yescharacteristic
24C2×C22⋊C8×C131C2211yescharacteristic
25C2×C22⋊C8×C131C2212yes—
26C2×C22⋊C8×C131C2212yes—
27#385×C131—21no—
28#385×C131—21no—
29#385×C131—21no—
30#380×C131—21no—
31#380×C131—21no—
32#380×C131C2212yes—
33#380×C131C2212yes—
34#380×C131C2211yescharacteristic
35#380×C131C2211yescharacteristic
36#380×C131C2211yescharacteristic
37#379×C131—21no—
38C2×#95×C131—21no—
39#340×C131C2212yescomplemented
40#340×C131C2212yescomplemented
41#340×C131C2212yescomplemented
42#340×C131C2212yescomplemented
43C25×C131D411yescharacteristic
44C22×Q8×C131C2311yescharacteristic
45C23×C4×C131—22no—
46C23×C4×C131—22no—
47C23×C4×C131—21no—
48C23×C4×C131—21no—
49C23×C4×C131—42no—
50C23×C4×C131—42no—
51C23×C4×C131D411yescharacteristic
52C23×C4×C131D411yescharacteristic
53C23×C4×C131D411yescharacteristic
54C23×C4×C131C2311yescharacteristic
55C23×C4×C131C2311yescharacteristic
56C23×C4×C131C2311yescharacteristic
57C22×C8×C131C2312yes—
58C22×C8×C131C2312yes—
59C22⋊Q8×C131—22no—
60C22⋊Q8×C131—22no—
61C22⋊Q8×C131—42no—
62C22⋊Q8×C131—42no—
63C2×C4⋊C4×C131—21no—
64C2×C4⋊C4×C131—21no—
65C2×C4⋊C4×C131—21no—
66C2×C4⋊C4×C131—21no—
67C2×C4⋊C4×C131—21no—
68C2×C4⋊C4×C131—42no—
69C2×C4⋊C4×C131—42no—
70C2×C4⋊C4×C131C2312yes—
71C2×C4⋊C4×C131C2312yes—
72C2×C4⋊C4×C131C2311yescharacteristic
73C2×C4⋊C4×C131C2311yescharacteristic
74C2×C4⋊C4×C131C2311yescharacteristic
75C2×C22⋊C4×C131—22no—
76C2×C22⋊C4×C131—22no—
77C2×C22⋊C4×C131—21no—
78C2×C22⋊C4×C131—21no—
79C2×C22⋊C4×C131—21no—
80C2×C22⋊C4×C131—21no—
81C2×C22⋊C4×C131—21no—
82C2×C22⋊C4×C131—21no—
83C2×C22⋊C4×C131—44no—
84#107×C131—42no—
85#106×C131—42no—
86#103×C131—42no—
87#103×C131—42no—
88C22⋊C8×C131—22no—
89C22⋊C8×C131—22no—
90C22⋊C8×C131—42no—
91C22⋊C8×C131—42no—
92#95×C131—22no—
93#95×C131—22no—
94#95×C131—21no—
95#95×C131—21no—
96#95×C131—21no—
97C24×C131—22no—
98C24×C131—22no—
99C24×C131—22no—
100C24×C131—22no—
101C24×C131—22no—
102C24×C131—41no—
103C24×C131—41no—
104C24×C131C2×D411yescharacteristic
105C24×C131C2×D411yescharacteristic
106C24×C131C2×D411yescharacteristic
107C2×Q8×C131—21no—
108C2×Q8×C131—21no—
109C2×Q8×C131—22no—
110C2×Q8×C131—22no—
111C22×C4×C131—22no—
112C22×C4×C131—22no—
113C22×C4×C131—22no—
114C22×C4×C131—22no—
115C22×C4×C131—22no—
116C22×C4×C131—21no—
117C22×C4×C131—21no—
118C22×C4×C131—21no—
119C22×C4×C131—21no—
120C22×C4×C131—22no—
121C22×C4×C131—22no—
122C22×C4×C131—22no—
123C22×C4×C131—22no—
124C22×C4×C131—21no—
125C22×C4×C131—21no—
126C22×C4×C131—21no—
127C22×C4×C131—22no—
128C22×C4×C131—22no—
129C22×C4×C131—21no—
130C22×C4×C131—41no—
131C22×C4×C131—41no—
132C22×C4×C131—41no—
133C22×C4×C131—41no—
134C22×C4×C131—41no—
135C22×C4×C131—41no—
136C22×C4×C131—48no—
137C22×C4×C131—48no—
138C22×C4×C131—42no—
139C22×C4×C131—42no—
140C22×C4×C131—42no—
141C22×C4×C131—42no—
142C22×C4×C131—42no—
143C22×C4×C131—42no—
144C22×C4×C131C2×D411yescharacteristic
145C22×C4×C131C2×D411yescharacteristic
146C22×C4×C131C2×D411yescharacteristic
147C22×C4×C131#4112yes—
148C22×C4×C131#4112yes—
149C22×C4×C131C2411yescharacteristic
150C2×C8×C131—22no—
151C2×C8×C131—22no—
152C2×C8×C131—22no—
153C2×C8×C131—22no—
154C2×C8×C131—22no—
155C2×C8×C131—22no—
156C4⋊C4×C131—21no—
157C4⋊C4×C131—21no—
158C4⋊C4×C131—22no—
159C4⋊C4×C131—22no—
160C4⋊C4×C131—22no—
161C4⋊C4×C131—22no—
162C4⋊C4×C131—22no—
163C4⋊C4×C131—22no—
164C4⋊C4×C131—42no—
165C4⋊C4×C131—42no—
166C4⋊C4×C131—42no—
167C4⋊C4×C131—42no—
168C4⋊C4×C131—42no—
169C22⋊C4×C131—44no—
170C22⋊C4×C131—42no—
171C22⋊C4×C131—42no—
172C22⋊C4×C131—42no—
173C22⋊C4×C131—42no—
174C22⋊C4×C131—42no—
175C22⋊C4×C131—44no—
176C22⋊C4×C131—42no—
177C23×C131—21no—
178C23×C131—21no—
179C23×C131—21no—
180C23×C131—21no—
181C23×C131—28no—
182C23×C131—21no—
183C23×C131—21no—
184C23×C131—21no—
185C23×C131—21no—
186C23×C131—21no—
187C23×C131—21no—
188C23×C131—21no—
189C23×C131—21no—
190C23×C131—21no—
191C23×C131—21no—
192C23×C131—21no—
193C23×C131—21no—
194C23×C131—44no—
195C23×C131—44no—
196C23×C131—44no—
197C23×C131—44no—
198C23×C131—44no—
199C23×C131—44no—
200C23×C131#12312yes—
201C23×C131#13512yes—
202C23×C131AGL(1,ℤ/8)12yes—
203C23×C131#13712yes—
204C23×C131#13712yes—
205C23×C131C22×D411yescharacteristic
206Q8×C131—42no—
207Q8×C131—42no—
208C2×C4×C131—21no—
209C2×C4×C131—21no—
210C2×C4×C131—24no—
211C2×C4×C131—24no—
212C2×C4×C131—21no—
213C2×C4×C131—21no—
214C2×C4×C131—21no—
215C2×C4×C131—21no—
216C2×C4×C131—21no—
217C2×C4×C131—21no—
218C2×C4×C131—44no—
219C2×C4×C131—44no—
220C2×C4×C131—44no—
221C2×C4×C131—42no—
222C2×C4×C131—42no—
223C2×C4×C131—42no—
224C2×C4×C131—42no—
225C2×C4×C131—41no—
226C2×C4×C131—41no—
227C2×C4×C131—41no—
228C2×C4×C131—41no—
229C2×C4×C131—41no—
230C2×C4×C131—41no—
231C2×C4×C131—42no—
232C2×C4×C131—42no—
233C2×C4×C131—41no—
234C2×C4×C131—41no—
235C2×C4×C131—42no—
236C2×C4×C131—42no—
237C2×C4×C131—42no—
238C2×C4×C131—41no—
239C2×C4×C131—41no—
240C2×C4×C131—41no—
241C2×C4×C131—41no—
242C2×C4×C131—42no—
243C2×C4×C131—84no—
244C2×C4×C131—84no—
245C2×C4×C131#12312yes—
246C2×C4×C131C2×#4111yescharacteristic
247C2×C4×C131C2×#4111yescharacteristic
248C2×C4×C131H(5,𝔽2)12yes—
249C2×C4×C131H(5,𝔽2)12yes—
250C8×C131—42no—
251C8×C131—42no—
252C22×C131—22no—
253C22×C131—22no—
254C22×C131—22no—
255C22×C131—22no—
256C22×C131—22no—
257C22×C131—22no—
258C22×C131—22no—
259C22×C131—22no—
260C22×C131—22no—
261C22×C131—22no—
262C22×C131—22no—
263C22×C131—22no—
264C22×C131—416no—
265C22×C131—41no—
266C22×C131—41no—
267C22×C131—41no—
268C22×C131—41no—
269C22×C131—41no—
270C22×C131—41no—
271C22×C131—41no—
272C22×C131—41no—
273C22×C131#48514yes—
274C22×C131C2×#12311yescharacteristic
275C22×C131#53411yescharacteristic
276C22×C131#53411yescharacteristic
277C22×C131C2×#13511yescharacteristic
278C22×C131C2×AGL(1,ℤ/8)11yescharacteristic
279C22×C131C2×#13711yescharacteristic
280C22×C131C2×#13711yescharacteristic
281C4×C131—22no—
282C4×C131—41no—
283C4×C131—41no—
284C4×C131—81no—
285C4×C131—81no—
286C4×C131—81no—
287C4×C131—82no—
288C4×C131—81no—
289C4×C131—82no—
290C4×C131#53812yes—
291C4×C131#53812yes—
292C2×C131—24no—
293C2×C131—42no—
294C2×C131—42no—
295C2×C131#262211yescharacteristic
296C2×C131C2×#48511yescharacteristic
297C2×C131#309211yescharacteristic
298C2×C131#318811yescharacteristic
299C2×C131#319011yescharacteristic
300C2×C131#319311yescharacteristic
301C2×C131#319511yescharacteristic
302#29894C13111yesmaximal, characteristic, direct product factor, Sylow
303C131#2989411yescharacteristic, direct product factor, Sylow
304#2848C2×C13111yescharacteristic
305C2×#380C2×C13111yescharacteristic
306#2077C2×C13112yescomplemented
307#2075C2×C13112yescomplemented
308#2036C2×C13112yescomplemented
309#2035C2×C13112yescomplemented
310#1872C2×C13111yescharacteristic, complemented
311#1872C2×C13111yescharacteristic, complemented
312#1853C2×C13111yescharacteristic, complemented
313#1852C2×C13111yescharacteristic, complemented
314#1779C2×C13111yescharacteristic
315C24×C4C22×C13111yescharacteristic
316C2×C22⋊Q8C22×C13111yescharacteristic
317C2×C22⋊Q8C22×C13111yescharacteristic
318C2×C22⋊Q8C22×C13111yescharacteristic
319C22×C4⋊C4C22×C13111yescharacteristic
320C22×C4⋊C4C22×C13111yescharacteristic
321C22×C22⋊C4—21no—
322C2×#107C22×C13112yescomplemented
323C2×#106C22×C13112yescomplemented
324C2×#103C22×C13112yescomplemented
325C2×#103C22×C13112yescomplemented
326C2×C22⋊C8C22×C13111yescharacteristic
327C2×C22⋊C8C22×C13111yescharacteristic
328C2×C22⋊C8C22×C13112yes—
329C2×C22⋊C8C22×C13112yes—
330#385—21no—
331#385—21no—
332#385—21no—
333#380—21no—
334#380—21no—
335#380C22×C13111yescharacteristic
336#380C22×C13112yes—
337#380C22×C13111yescharacteristic
338#380C22×C13112yes—
339#380C22×C13111yescharacteristic
340#379—21no—
341C2×#95—21no—
342#340C22×C13112yescomplemented
343#340C22×C13112yescomplemented
344#340C22×C13112yescomplemented
345#340C22×C13112yescomplemented
346C25D4×C13111yescharacteristic
347C22×Q8C23×C13111yescharacteristic
348C23×C4—22no—
349C23×C4—22no—
350C23×C4—21no—
351C23×C4—21no—
352C23×C4—42no—
353C23×C4—42no—
354C23×C4D4×C13111yescharacteristic
355C23×C4D4×C13111yescharacteristic
356C23×C4D4×C13111yescharacteristic
357C23×C4C23×C13111yescharacteristic
358C23×C4C23×C13111yescharacteristic
359C23×C4C23×C13111yescharacteristic
360C22×C8C23×C13112yes—
361C22×C8C23×C13112yes—
362C22⋊Q8—22no—
363C22⋊Q8—22no—
364C22⋊Q8—42no—
365C22⋊Q8—42no—
366C2×C4⋊C4—21no—
367C2×C4⋊C4—21no—
368C2×C4⋊C4—21no—
369C2×C4⋊C4—21no—
370C2×C4⋊C4—21no—
371C2×C4⋊C4—42no—
372C2×C4⋊C4—42no—
373C2×C4⋊C4C23×C13112yes—
374C2×C4⋊C4C23×C13112yes—
375C2×C4⋊C4C23×C13111yescharacteristic
376C2×C4⋊C4C23×C13111yescharacteristic
377C2×C4⋊C4C23×C13111yescharacteristic
378C2×C22⋊C4—22no—
379C2×C22⋊C4—22no—
380C2×C22⋊C4—21no—
381C2×C22⋊C4—21no—
382C2×C22⋊C4—21no—
383C2×C22⋊C4—21no—
384C2×C22⋊C4—21no—
385C2×C22⋊C4—21no—
386C2×C22⋊C4—44no—
387#107—42no—
388#106—42no—
389#103—42no—
390#103—42no—
391C22⋊C8—22no—
392C22⋊C8—22no—
393C22⋊C8—42no—
394C22⋊C8—42no—
395#95—22no—
396#95—22no—
397#95—21no—
398#95—21no—
399#95—21no—
400C24—22no—
401C24—22no—
402C24—22no—
403C24—22no—
404C24—22no—
405C24—41no—
406C24—41no—
407C24C2×D4×C13111yescharacteristic
408C24C2×D4×C13111yescharacteristic
409C24C2×D4×C13111yescharacteristic
410C2×Q8—21no—
411C2×Q8—21no—
412C2×Q8—22no—
413C2×Q8—22no—
414C22×C4—22no—
415C22×C4—22no—
416C22×C4—22no—
417C22×C4—22no—
418C22×C4—22no—
419C22×C4—21no—
420C22×C4—21no—
421C22×C4—21no—
422C22×C4—21no—
423C22×C4—22no—
424C22×C4—22no—
425C22×C4—22no—
426C22×C4—22no—
427C22×C4—21no—
428C22×C4—21no—
429C22×C4—21no—
430C22×C4—22no—
431C22×C4—22no—
432C22×C4—21no—
433C22×C4—41no—
434C22×C4—41no—
435C22×C4—41no—
436C22×C4—41no—
437C22×C4—41no—
438C22×C4—41no—
439C22×C4—48no—
440C22×C4—48no—
441C22×C4—42no—
442C22×C4—42no—
443C22×C4—42no—
444C22×C4—42no—
445C22×C4—42no—
446C22×C4—42no—
447C22×C4C2×D4×C13111yescharacteristic
448C22×C4C2×D4×C13111yescharacteristic
449C22×C4C2×D4×C13111yescharacteristic
450C22×C4#41×C13112yes—
451C22×C4#41×C13112yes—
452C22×C4C24×C13111yescharacteristic
453C2×C8—22no—
454C2×C8—22no—
455C2×C8—22no—
456C2×C8—22no—
457C2×C8—22no—
458C2×C8—22no—
459C4⋊C4—21no—
460C4⋊C4—21no—
461C4⋊C4—22no—
462C4⋊C4—22no—
463C4⋊C4—22no—
464C4⋊C4—22no—
465C4⋊C4—22no—
466C4⋊C4—22no—
467C4⋊C4—42no—
468C4⋊C4—42no—
469C4⋊C4—42no—
470C4⋊C4—42no—
471C4⋊C4—42no—
472C22⋊C4—44no—
473C22⋊C4—42no—
474C22⋊C4—42no—
475C22⋊C4—42no—
476C22⋊C4—42no—
477C22⋊C4—42no—
478C22⋊C4—44no—
479C22⋊C4—42no—
480C23—21no—
481C23—21no—
482C23—21no—
483C23—21no—
484C23—28no—
485C23—21no—
486C23—21no—
487C23—21no—
488C23—21no—
489C23—21no—
490C23—21no—
491C23—21no—
492C23—21no—
493C23—21no—
494C23—21no—
495C23—21no—
496C23—21no—
497C23—44no—
498C23—44no—
499C23—44no—
500C23—44no—
501C23—44no—
502C23—44no—
503C23#123×C13112yes—
504C23#135×C13112yes—
505C23AGL(1,ℤ/8)×C13112yes—
506C23#137×C13112yes—
507C23#137×C13112yes—
508C23C22×D4×C13111yescharacteristic
509Q8—42no—
510Q8—42no—
511C2×C4—21no—
512C2×C4—21no—
513C2×C4—24no—
514C2×C4—24no—
515C2×C4—21no—
516C2×C4—21no—
517C2×C4—21no—
518C2×C4—21no—
519C2×C4—21no—
520C2×C4—21no—
521C2×C4—44no—
522C2×C4—44no—
523C2×C4—44no—
524C2×C4—42no—
525C2×C4—42no—
526C2×C4—42no—
527C2×C4—42no—
528C2×C4—41no—
529C2×C4—41no—
530C2×C4—41no—
531C2×C4—41no—
532C2×C4—41no—
533C2×C4—41no—
534C2×C4—42no—
535C2×C4—42no—
536C2×C4—41no—
537C2×C4—41no—
538C2×C4—42no—
539C2×C4—42no—
540C2×C4—42no—
541C2×C4—41no—
542C2×C4—41no—
543C2×C4—41no—
544C2×C4—41no—
545C2×C4—42no—
546C2×C4—84no—
547C2×C4—84no—
548C2×C4#123×C13112yes—
549C2×C4C2×#41×C13111yescharacteristic
550C2×C4C2×#41×C13111yescharacteristic
551C2×C4H(5,𝔽2)×C13112yes—
552C2×C4H(5,𝔽2)×C13112yes—
553C8—42no—
554C8—42no—
555C22—22no—
556C22—22no—
557C22—22no—
558C22—22no—
559C22—22no—
560C22—22no—
561C22—22no—
562C22—22no—
563C22—22no—
564C22—22no—
565C22—22no—
566C22—22no—
567C22—416no—
568C22—41no—
569C22—41no—
570C22—41no—
571C22—41no—
572C22—41no—
573C22—41no—
574C22—41no—
575C22—41no—
576C22#485×C13114yes—
577C22C2×#123×C13111yescharacteristic
578C22#534×C13111yescharacteristic
579C22#534×C13111yescharacteristic
580C22C2×#135×C13111yescharacteristic
581C22C2×AGL(1,ℤ/8)×C13111yescharacteristic
582C22C2×#137×C13111yescharacteristic
583C22C2×#137×C13111yescharacteristic
584C4—22no—
585C4—41no—
586C4—41no—
587C4—81no—
588C4—81no—
589C4—82no—
590C4—81no—
591C4—81no—
592C4—82no—
593C4#538×C13112yes—
594C4#538×C13112yes—
595C2—24no—
596C2—42no—
597C2—42no—
598C2#2622×C13111yescharacteristic
599C2C2×#485×C13111yescharacteristic
600C2#3092×C13111yescharacteristic
601C2#3188×C13111yescharacteristic
602C2#3190×C13111yescharacteristic
603C2#3193×C13111yescharacteristic
604C2#3195×C13111yescharacteristic
subgroupG/H
center, socleC23×C131C22×D4
commutator, Frattini, cosocleC22×C4C24×C131
prime radicalC25×C131D4
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C131 ◁ C24×C4×C131 ◁ G

Complements

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

NH ≅ G/Ntype
3. #2077×C131C2semidirect
4. #2075×C131C2semidirect
5. #2036×C131C2semidirect
6. #2035×C131C2semidirect
7. #1872×C131C2semidirect
8. #1872×C131C2semidirect
9. #1853×C131C2semidirect
10. #1852×C131C2semidirect
19. C2×#107×C131C22semidirect
20. C2×#106×C131C22semidirect
21. C2×#103×C131C22semidirect
22. C2×#103×C131C22semidirect
39. #340×C131C22semidirect
40. #340×C131C22semidirect
41. #340×C131C22semidirect
42. #340×C131C22semidirect
302. #29894C131direct (N × H)
303. C131#29894direct (N × H)
306. #2077C2×C131semidirect
307. #2075C2×C131semidirect
308. #2036C2×C131semidirect
309. #2035C2×C131semidirect
310. #1872C2×C131semidirect
311. #1872C2×C131semidirect
312. #1853C2×C131semidirect
313. #1852C2×C131semidirect
322. C2×#107C22×C131semidirect
323. C2×#106C22×C131semidirect
324. C2×#103C22×C131semidirect
325. C2×#103C22×C131semidirect
342. #340C22×C131semidirect
343. #340C22×C131semidirect
344. #340C22×C131semidirect
345. #340C22×C131semidirect

Maximal subgroups

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

subgroupindex
#2848×C1312
C2×#380×C1312
#2077×C1312
#2075×C1312
#2036×C1312
#2035×C1312
#1872×C1312
#1853×C1312
#1852×C1312
#1779×C1312
#29894131