Finite Group Databasebeta

← C131×#14452 #45700336

Subgroups — C131×#14452 #45700336

Order 33536.

1450 conjugacy classes of subgroups.

The subgroup lattice has 600 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#380×C131C211yesmaximal, characteristic
2#1442×C131C212yesmaximal, complemented
3#1441×C131C212yesmaximal, complemented
4#1439×C131C212yesmaximal
5#1437×C131C212yesmaximal
6#1436×C131C212yesmaximal, complemented
7#1434×C131C212yesmaximal, complemented
8C22⋊#95×C131C211yesmaximal, characteristic
9C22⋊#95×C131C211yesmaximal, characteristic
10C24×C4×C131C2211yescharacteristic
11C22×C4⋊C4×C131C2212yes—
12C22×C4⋊C4×C131C2211yescharacteristic
13C22×C4⋊C4×C131C2211yescharacteristic
14C22×C22⋊C4×C131C2212yes—
15C22×C22⋊C4×C131C2211yescharacteristic
16C22×C22⋊C4×C131C2212yes—
17C22×C22⋊C4×C131C2211yescharacteristic
18C22×C42×C131C2212yes—
19#380×C131C418yescomplemented
20C2×#95×C131C2212yes—
21C2×#95×C131C2212yes—
22C2×#95×C131C2212yes—
23C2×#95×C131C2211yescharacteristic
24C2×#95×C131C2212yes—
25C2×#95×C131C2211yescharacteristic
26C2×#95×C131C2212yes—
27C2×#95×C131C2212yes—
28C2×#95×C131C2212yes—
29C2×#95×C131C2212yes—
30C2×#95×C131C2212yes—
31C2×#95×C131C2212yes—
32C25×C131C2311yescharacteristic
33C23×C4×C131—24no—
34C23×C4×C131—41no—
35C23×C4×C131—41no—
36C23×C4×C131—42no—
37C23×C4×C131C2×C414yes—
38C23×C4×C131C2312yes—
39C23×C4×C131C2312yes—
40C23×C4×C131C2312yes—
41C23×C4×C131C2312yes—
42C23×C4×C131C2311yescharacteristic
43C23×C4×C131C2312yes—
44C23×C4×C131C2312yes—
45C23×C4×C131C2311yescharacteristic
46C2×C4⋊C4×C131—41no—
47C2×C4⋊C4×C131—42no—
48C2×C4⋊C4×C131—41no—
49C2×C4⋊C4×C131—42no—
50C2×C4⋊C4×C131—42no—
51C2×C4⋊C4×C131—42no—
52C2×C4⋊C4×C131C2×C414yes—
53C2×C4⋊C4×C131C2×C414yes—
54C2×C22⋊C4×C131—24no—
55C2×C22⋊C4×C131—22no—
56C2×C22⋊C4×C131—24no—
57C2×C22⋊C4×C131—42no—
58C2×C22⋊C4×C131—42no—
59C2×C22⋊C4×C131—41no—
60C2×C22⋊C4×C131—41no—
61C2×C22⋊C4×C131—42no—
62C2×C22⋊C4×C131—41no—
63C2×C22⋊C4×C131—41no—
64C2×C22⋊C4×C131C2×C418yes—
65C2×C22⋊C4×C131Q814yes—
66C2×C42×C131—24no—
67C2×C42×C131—42no—
68C2×C42×C131—42no—
69#95×C131—24no—
70#95×C131—24no—
71#95×C131—24no—
72#95×C131—42no—
73#95×C131—42no—
74#95×C131—41no—
75#95×C131—42no—
76#95×C131—42no—
77#95×C131—42no—
78#95×C131—42no—
79#95×C131—41no—
80#95×C131C2×C418yes—
81C24×C131—22no—
82C24×C131—22no—
83C24×C131—22no—
84C24×C131—21no—
85C24×C131—21no—
86C24×C131—21no—
87C24×C131—22no—
88C24×C131—21no—
89C24×C131C22×C412yes—
90C24×C131C2×Q812yes—
91C24×C131#4112yes—
92C24×C131C2411yescharacteristic
93C22×C4×C131—21no—
94C22×C4×C131—21no—
95C22×C4×C131—22no—
96C22×C4×C131—22no—
97C22×C4×C131—22no—
98C22×C4×C131—22no—
99C22×C4×C131—22no—
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—22no—
107C22×C4×C131—22no—
108C22×C4×C131—22no—
109C22×C4×C131—22no—
110C22×C4×C131—22no—
111C22×C4×C131—22no—
112C22×C4×C131—22no—
113C22×C4×C131—22no—
114C22×C4×C131—21no—
115C22×C4×C131—21no—
116C22×C4×C131—22no—
117C22×C4×C131—22no—
118C22×C4×C131—22no—
119C22×C4×C131—22no—
120C22×C4×C131—22no—
121C22×C4×C131—22no—
122C22×C4×C131—22no—
123C22×C4×C131—22no—
124C22×C4×C131—28no—
125C22×C4×C131—22no—
126C22×C4×C131—22no—
127C22×C4×C131—22no—
128C22×C4×C131—22no—
129C22×C4×C131—22no—
130C22×C4×C131—22no—
131C22×C4×C131—22no—
132C22×C4×C131—22no—
133C22×C4×C131—22no—
134C22×C4×C131—22no—
135C22×C4×C131—22no—
136C22×C4×C131—22no—
137C22×C4×C131—22no—
138C22×C4×C131—22no—
139C22×C4×C131—44no—
140C22×C4×C131—44no—
141C22×C4×C131—48no—
142C22×C4×C131—48no—
143C22×C4×C131C22×C412yes—
144C22×C4×C131C22×C414yes—
145C22×C4×C131C22×C414yes—
146C22×C4×C131C22×C412yes—
147C22×C4×C131C2×Q814yes—
148C22×C4×C131#4114yes—
149C22×C4×C131#4114yes—
150C4⋊C4×C131—44no—
151C4⋊C4×C131—44no—
152C4⋊C4×C131—48no—
153C22⋊C4×C131—48no—
154C22⋊C4×C131—44no—
155C22⋊C4×C131—48no—
156C22⋊C4×C131—44no—
157C42×C131—48no—
158C23×C131—22no—
159C23×C131—22no—
160C23×C131—22no—
161C23×C131—22no—
162C23×C131—22no—
163C23×C131—22no—
164C23×C131—22no—
165C23×C131—22no—
166C23×C131—22no—
167C23×C131—22no—
168C23×C131—24no—
169C23×C131—24no—
170C23×C131—24no—
171C23×C131—24no—
172C23×C131—42no—
173C23×C131—42no—
174C23×C131—42no—
175C23×C131—42no—
176C23×C131—42no—
177C23×C131—42no—
178C23×C131—42no—
179C23×C131—42no—
180C23×C131C4×Q814yes—
181C23×C131C23×C411yescharacteristic
182C23×C131C22×Q811yescharacteristic
183C23×C131C2×#4112yes—
184C23×C131C2×#4111yescharacteristic
185C23×C131C2×#4112yes—
186C23×C131H(5,𝔽2)11yescharacteristic
187C23×C131H(5,𝔽2)11yescharacteristic
188C23×C131H(5,𝔽2)12yes—
189C23×C131H(5,𝔽2)12yes—
190C23×C131H(5,𝔽2)11yescharacteristic
191C23×C1312−1+411yescharacteristic
192C2×C4×C131—22no—
193C2×C4×C131—22no—
194C2×C4×C131—24no—
195C2×C4×C131—24no—
196C2×C4×C131—22no—
197C2×C4×C131—24no—
198C2×C4×C131—24no—
199C2×C4×C131—24no—
200C2×C4×C131—24no—
201C2×C4×C131—24no—
202C2×C4×C131—22no—
203C2×C4×C131—22no—
204C2×C4×C131—24no—
205C2×C4×C131—24no—
206C2×C4×C131—24no—
207C2×C4×C131—24no—
208C2×C4×C131—24no—
209C2×C4×C131—24no—
210C2×C4×C131—24no—
211C2×C4×C131—416no—
212C2×C4×C131—42no—
213C2×C4×C131—42no—
214C2×C4×C131—42no—
215C2×C4×C131—42no—
216C2×C4×C131—42no—
217C2×C4×C131—42no—
218C2×C4×C131—42no—
219C2×C4×C131—42no—
220C2×C4×C131—42no—
221C2×C4×C131—42no—
222C2×C4×C131—42no—
223C2×C4×C131—42no—
224C2×C4×C131—42no—
225C2×C4×C131—42no—
226C2×C4×C131—42no—
227C2×C4×C131—42no—
228C2×C4×C131—42no—
229C2×C4×C131—42no—
230C2×C4×C131—42no—
231C2×C4×C131—42no—
232C2×C4×C131—42no—
233C2×C4×C131—42no—
234C2×C4×C131—42no—
235C2×C4×C131—42no—
236C2×C4×C131—42no—
237C2×C4×C131—42no—
238C2×C4×C131—42no—
239C2×C4×C131—42no—
240C2×C4×C131—42no—
241C2×C4×C131—42no—
242C2×C4×C131—42no—
243C2×C4×C131—42no—
244C2×C4×C131#11714yes—
245C22×C131—24no—
246C22×C131—24no—
247C22×C131—24no—
248C22×C131—42no—
249C22×C131—42no—
250C22×C131—42no—
251C22×C131—42no—
252C22×C131—44no—
253C22×C131—44no—
254C22×C131—44no—
255C22×C131—44no—
256C22×C131C2×#11711yescharacteristic
257C22×C131C2×C4×Q811yescharacteristic
258C22×C131C4×#4111yescharacteristic
259C22×C131#51811yescharacteristic
260C22×C131#51811yescharacteristic
261C22×C131#51811yescharacteristic
262C22×C131#52011yescharacteristic
263C22×C131#53812yes—
264C22×C131#53812yes—
265C22×C131#53811yescharacteristic
266C22×C131#53812yes—
267C22×C131#53911yescharacteristic
268C22×C131#54012yes—
269C22×C131#54311yescharacteristic
270C22×C131#54411yescharacteristic
271C22×C131#55112yes—
272C22×C131#55212yes—
273C22×C131#55312yes—
274C22×C131#55412yes—
275C22×C131#55412yes—
276C22×C131#55512yes—
277C22×C131#56012yes—
278C22×C131#56212yes—
279C4×C131—24no—
280C4×C131—42no—
281C4×C131—44no—
282C4×C131—44no—
283C4×C131—44no—
284C4×C131—44no—
285C4×C131—82no—
286C4×C131—82no—
287C2×C131—44no—
288C2×C131#231211yescharacteristic
289C2×C131#232911yescharacteristic
290C2×C131#233311yescharacteristic
291C2×C131#234511yescharacteristic
292C2×C131#234611yescharacteristic
293C2×C131#236811yescharacteristic
294C2×C131#237711yescharacteristic
295C2×C131#275012yes—
296C2×C131#275612yes—
297C2×C131#276812yes—
298C2×C131#278412yes—
299#14452C13111yesmaximal, characteristic, direct product factor, Sylow
300C131#1445211yescharacteristic, direct product factor, Sylow
301C2×#380C2×C13111yescharacteristic
302#1442C2×C13112yescomplemented
303#1441C2×C13112yescomplemented
304#1439C2×C13112yes—
305#1437C2×C13112yes—
306#1436C2×C13112yescomplemented
307#1434C2×C13112yescomplemented
308C22⋊#95C2×C13111yescharacteristic
309C22⋊#95C2×C13111yescharacteristic
310C24×C4C22×C13111yescharacteristic
311C22×C4⋊C4C22×C13112yes—
312C22×C4⋊C4C22×C13111yescharacteristic
313C22×C4⋊C4C22×C13111yescharacteristic
314C22×C22⋊C4C22×C13112yes—
315C22×C22⋊C4C22×C13111yescharacteristic
316C22×C22⋊C4C22×C13112yes—
317C22×C22⋊C4C22×C13111yescharacteristic
318C22×C42C22×C13112yes—
319#380C4×C13118yescomplemented
320C2×#95C22×C13112yes—
321C2×#95C22×C13112yes—
322C2×#95C22×C13112yes—
323C2×#95C22×C13111yescharacteristic
324C2×#95C22×C13112yes—
325C2×#95C22×C13111yescharacteristic
326C2×#95C22×C13112yes—
327C2×#95C22×C13112yes—
328C2×#95C22×C13112yes—
329C2×#95C22×C13112yes—
330C2×#95C22×C13112yes—
331C2×#95C22×C13112yes—
332C25C23×C13111yescharacteristic
333C23×C4—24no—
334C23×C4—41no—
335C23×C4—41no—
336C23×C4—42no—
337C23×C4C2×C4×C13114yes—
338C23×C4C23×C13112yes—
339C23×C4C23×C13112yes—
340C23×C4C23×C13112yes—
341C23×C4C23×C13112yes—
342C23×C4C23×C13111yescharacteristic
343C23×C4C23×C13112yes—
344C23×C4C23×C13112yes—
345C23×C4C23×C13111yescharacteristic
346C2×C4⋊C4—41no—
347C2×C4⋊C4—42no—
348C2×C4⋊C4—41no—
349C2×C4⋊C4—42no—
350C2×C4⋊C4—42no—
351C2×C4⋊C4—42no—
352C2×C4⋊C4C2×C4×C13114yes—
353C2×C4⋊C4C2×C4×C13114yes—
354C2×C22⋊C4—24no—
355C2×C22⋊C4—22no—
356C2×C22⋊C4—24no—
357C2×C22⋊C4—42no—
358C2×C22⋊C4—42no—
359C2×C22⋊C4—41no—
360C2×C22⋊C4—41no—
361C2×C22⋊C4—42no—
362C2×C22⋊C4—41no—
363C2×C22⋊C4—41no—
364C2×C22⋊C4C2×C4×C13118yes—
365C2×C22⋊C4Q8×C13114yes—
366C2×C42—24no—
367C2×C42—42no—
368C2×C42—42no—
369#95—24no—
370#95—24no—
371#95—24no—
372#95—42no—
373#95—42no—
374#95—41no—
375#95—42no—
376#95—42no—
377#95—42no—
378#95—42no—
379#95—41no—
380#95C2×C4×C13118yes—
381C24—22no—
382C24—22no—
383C24—22no—
384C24—21no—
385C24—21no—
386C24—21no—
387C24—22no—
388C24—21no—
389C24C22×C4×C13112yes—
390C24C2×Q8×C13112yes—
391C24#41×C13112yes—
392C24C24×C13111yescharacteristic
393C22×C4—21no—
394C22×C4—21no—
395C22×C4—22no—
396C22×C4—22no—
397C22×C4—22no—
398C22×C4—22no—
399C22×C4—22no—
400C22×C4—22no—
401C22×C4—22no—
402C22×C4—22no—
403C22×C4—22no—
404C22×C4—22no—
405C22×C4—22no—
406C22×C4—22no—
407C22×C4—22no—
408C22×C4—22no—
409C22×C4—22no—
410C22×C4—22no—
411C22×C4—22no—
412C22×C4—22no—
413C22×C4—22no—
414C22×C4—21no—
415C22×C4—21no—
416C22×C4—22no—
417C22×C4—22no—
418C22×C4—22no—
419C22×C4—22no—
420C22×C4—22no—
421C22×C4—22no—
422C22×C4—22no—
423C22×C4—22no—
424C22×C4—28no—
425C22×C4—22no—
426C22×C4—22no—
427C22×C4—22no—
428C22×C4—22no—
429C22×C4—22no—
430C22×C4—22no—
431C22×C4—22no—
432C22×C4—22no—
433C22×C4—22no—
434C22×C4—22no—
435C22×C4—22no—
436C22×C4—22no—
437C22×C4—22no—
438C22×C4—22no—
439C22×C4—44no—
440C22×C4—44no—
441C22×C4—48no—
442C22×C4—48no—
443C22×C4C22×C4×C13112yes—
444C22×C4C22×C4×C13114yes—
445C22×C4C22×C4×C13114yes—
446C22×C4C22×C4×C13112yes—
447C22×C4C2×Q8×C13114yes—
448C22×C4#41×C13114yes—
449C22×C4#41×C13114yes—
450C4⋊C4—44no—
451C4⋊C4—44no—
452C4⋊C4—48no—
453C22⋊C4—48no—
454C22⋊C4—44no—
455C22⋊C4—48no—
456C22⋊C4—44no—
457C42—48no—
458C23—22no—
459C23—22no—
460C23—22no—
461C23—22no—
462C23—22no—
463C23—22no—
464C23—22no—
465C23—22no—
466C23—22no—
467C23—22no—
468C23—24no—
469C23—24no—
470C23—24no—
471C23—24no—
472C23—42no—
473C23—42no—
474C23—42no—
475C23—42no—
476C23—42no—
477C23—42no—
478C23—42no—
479C23—42no—
480C23C4×Q8×C13114yes—
481C23C23×C4×C13111yescharacteristic
482C23C22×Q8×C13111yescharacteristic
483C23C2×#41×C13112yes—
484C23C2×#41×C13111yescharacteristic
485C23C2×#41×C13112yes—
486C23H(5,𝔽2)×C13111yescharacteristic
487C23H(5,𝔽2)×C13111yescharacteristic
488C23H(5,𝔽2)×C13112yes—
489C23H(5,𝔽2)×C13112yes—
490C23H(5,𝔽2)×C13111yescharacteristic
491C232−1+4×C13111yescharacteristic
492C2×C4—22no—
493C2×C4—22no—
494C2×C4—24no—
495C2×C4—24no—
496C2×C4—22no—
497C2×C4—24no—
498C2×C4—24no—
499C2×C4—24no—
500C2×C4—24no—
501C2×C4—24no—
502C2×C4—22no—
503C2×C4—22no—
504C2×C4—24no—
505C2×C4—24no—
506C2×C4—24no—
507C2×C4—24no—
508C2×C4—24no—
509C2×C4—24no—
510C2×C4—24no—
511C2×C4—416no—
512C2×C4—42no—
513C2×C4—42no—
514C2×C4—42no—
515C2×C4—42no—
516C2×C4—42no—
517C2×C4—42no—
518C2×C4—42no—
519C2×C4—42no—
520C2×C4—42no—
521C2×C4—42no—
522C2×C4—42no—
523C2×C4—42no—
524C2×C4—42no—
525C2×C4—42no—
526C2×C4—42no—
527C2×C4—42no—
528C2×C4—42no—
529C2×C4—42no—
530C2×C4—42no—
531C2×C4—42no—
532C2×C4—42no—
533C2×C4—42no—
534C2×C4—42no—
535C2×C4—42no—
536C2×C4—42no—
537C2×C4—42no—
538C2×C4—42no—
539C2×C4—42no—
540C2×C4—42no—
541C2×C4—42no—
542C2×C4—42no—
543C2×C4—42no—
544C2×C4#117×C13114yes—
545C22—24no—
546C22—24no—
547C22—24no—
548C22—44no—
549C22—44no—
550C22—44no—
551C22—44no—
552C22—42no—
553C22—42no—
554C22—42no—
555C22—42no—
556C22C2×#117×C13111yescharacteristic
557C22C2×C4×Q8×C13111yescharacteristic
558C22C4×#41×C13111yescharacteristic
559C22#518×C13111yescharacteristic
560C22#518×C13111yescharacteristic
561C22#518×C13111yescharacteristic
562C22#520×C13111yescharacteristic
563C22#538×C13112yes—
564C22#538×C13112yes—
565C22#538×C13111yescharacteristic
566C22#538×C13112yes—
567C22#539×C13111yescharacteristic
568C22#540×C13112yes—
569C22#543×C13111yescharacteristic
570C22#544×C13111yescharacteristic
571C22#551×C13112yes—
572C22#552×C13112yes—
573C22#553×C13112yes—
574C22#554×C13112yes—
575C22#554×C13112yes—
576C22#555×C13112yes—
577C22#560×C13112yes—
578C22#562×C13112yes—
579C4—24no—
580C4—44no—
581C4—44no—
582C4—42no—
583C4—44no—
584C4—44no—
585C4—82no—
586C4—82no—
587C2—44no—
588C2#2312×C13111yescharacteristic
589C2#2329×C13111yescharacteristic
590C2#2333×C13111yescharacteristic
591C2#2345×C13111yescharacteristic
592C2#2346×C13111yescharacteristic
593C2#2368×C13111yescharacteristic
594C2#2377×C13111yescharacteristic
595C2#2750×C13112yes—
596C2#2756×C13112yes—
597C2#2768×C13112yes—
598C2#2784×C13112yes—
subgroupG/H
center, socleC24×C131C24
commutatorC23C23×C4×C131
Frattini, cosocleC24C24×C131
prime radicalC25×C131C23
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C24×C131 ◁ G

Complements

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

NH ≅ G/Ntype
2. #1442×C131C2semidirect
3. #1441×C131C2semidirect
6. #1436×C131C2semidirect
7. #1434×C131C2semidirect
19. #380×C131C4semidirect
299. #14452C131direct (N × H)
300. C131#14452direct (N × H)
302. #1442C2×C131semidirect
303. #1441C2×C131semidirect
306. #1436C2×C131semidirect
307. #1434C2×C131semidirect
319. #380C4×C131semidirect

Maximal subgroups

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

subgroupindex
C2×#380×C1312
#1442×C1312
#1441×C1312
#1439×C1312
#1437×C1312
#1436×C1312
#1434×C1312
C22⋊#95×C1312
#14452131