Finite Group Databasebeta

← C131×#14351 #45700235

Subgroups — C131×#14351 #45700235

Order 33536.

1422 conjugacy classes of subgroups.

The subgroup lattice has 632 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C4×C22⋊C4×C131C211yesmaximal, characteristic
2#1443×C131C212yesmaximal, complemented
3#1442×C131C212yesmaximal, complemented
4#1440×C131C212yesmaximal
5#1439×C131C212yesmaximal
6C4⋊#95×C131C211yesmaximal, characteristic, complemented
7#1434×C131C211yesmaximal, characteristic, complemented
8#1434×C131C211yesmaximal, characteristic, complemented
9#1434×C131C211yesmaximal, characteristic, complemented
10C22⋊#95×C131C211yesmaximal, characteristic
11C22⋊#95×C131C211yesmaximal, characteristic
12C24×C4×C131C2211yescharacteristic
13C22×C4⋊C4×C131C2212yes—
14C22×C22⋊C4×C131C2211yescharacteristic
15C22×C22⋊C4×C131C2211yescharacteristic
16C22×C22⋊C4×C131C2212yes—
17C22×C22⋊C4×C131C2212yes—
18C22×C42×C131C2211yescharacteristic
19C22×C42×C131C2211yescharacteristic
20C4×C22⋊C4×C131C418yescomplemented
21C2×#95×C131C2211yescharacteristic
22C2×#95×C131C2211yescharacteristic
23C2×#95×C131C2211yescharacteristic
24C2×#95×C131C2211yescharacteristic
25C2×#95×C131C2212yes—
26C2×#95×C131C2212yes—
27C2×#95×C131C2212yes—
28C2×#95×C131C2212yes—
29C2×#95×C131C2212yes—
30C2×#95×C131C2212yes—
31C2×#95×C131C2212yes—
32C2×#95×C131C2212yes—
33C2×#95×C131C2212yes—
34C2×#95×C131C2211yescharacteristic
35C2×#95×C131C2211yescharacteristic
36C25×C131C2311yescharacteristic
37C23×C4×C131—22no—
38C23×C4×C131—22no—
39C23×C4×C131—42no—
40C23×C4×C131—42no—
41C23×C4×C131C2×C414yes—
42C23×C4×C131C2312yes—
43C23×C4×C131C2312yes—
44C23×C4×C131C2312yes—
45C23×C4×C131C2312yes—
46C23×C4×C131C2311yescharacteristic
47C23×C4×C131C2311yescharacteristic
48C23×C4×C131C2311yescharacteristic
49C23×C4×C131C2311yescharacteristic
50C23×C4×C131C2311yescharacteristic
51C23×C4×C131C2311yescharacteristic
52C2×C4⋊C4×C131—24no—
53C2×C4⋊C4×C131—42no—
54C2×C4⋊C4×C131—42no—
55C2×C22⋊C4×C131—24no—
56C2×C22⋊C4×C131—24no—
57C2×C22⋊C4×C131—24no—
58C2×C22⋊C4×C131—24no—
59C2×C22⋊C4×C131—42no—
60C2×C22⋊C4×C131—42no—
61C2×C22⋊C4×C131—42no—
62C2×C22⋊C4×C131—42no—
63C2×C22⋊C4×C131C2×C414yes—
64C2×C22⋊C4×C131C2×C414yes—
65C2×C42×C131—42no—
66C2×C42×C131—42no—
67C2×C42×C131C2×C414yes—
68C2×C42×C131C2×C414yes—
69#95×C131—22no—
70#95×C131—22no—
71#95×C131—22no—
72#95×C131—22no—
73#95×C131—24no—
74#95×C131—42no—
75#95×C131—42no—
76#95×C131—42no—
77#95×C131—42no—
78#95×C131—42no—
79#95×C131—42no—
80#95×C131—42no—
81#95×C131—42no—
82#95×C131C2×C414yes—
83#95×C131C2×C414yes—
84C24×C131—22no—
85C24×C131—21no—
86C24×C131—21no—
87C24×C131—21no—
88C24×C131—21no—
89C24×C131—22no—
90C24×C131—22no—
91C24×C131—21no—
92C24×C131—21no—
93C24×C131C22×C412yes—
94C24×C131#4114yes—
95C24×C131C2411yescharacteristic
96C22×C4×C131—22no—
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—21no—
105C22×C4×C131—21no—
106C22×C4×C131—21no—
107C22×C4×C131—21no—
108C22×C4×C131—21no—
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—21no—
117C22×C4×C131—28no—
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—22no—
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—22no—
140C22×C4×C131—22no—
141C22×C4×C131—22no—
142C22×C4×C131—22no—
143C22×C4×C131—22no—
144C22×C4×C131—22no—
145C22×C4×C131—22no—
146C22×C4×C131—44no—
147C22×C4×C131—44no—
148C22×C4×C131—48no—
149C22×C4×C131—48no—
150C22×C4×C131C22×C412yes—
151C22×C4×C131C22×C412yes—
152C22×C4×C131C22×C412yes—
153C22×C4×C131C22×C412yes—
154C22×C4×C131C22×C412yes—
155C22×C4×C131C22×C412yes—
156C22×C4×C131#4112yes—
157C22×C4×C131#4112yes—
158C22×C4×C131#4114yes—
159C4⋊C4×C131—48no—
160C22⋊C4×C131—28no—
161C22⋊C4×C131—28no—
162C22⋊C4×C131—48no—
163C22⋊C4×C131—48no—
164C42×C131—44no—
165C42×C131—44no—
166C23×C131—22no—
167C23×C131—22no—
168C23×C131—22no—
169C23×C131—22no—
170C23×C131—22no—
171C23×C131—22no—
172C23×C131—24no—
173C23×C131—24no—
174C23×C131—24no—
175C23×C131—24no—
176C23×C131—24no—
177C23×C131—24no—
178C23×C131—42no—
179C23×C131—42no—
180C23×C131—42no—
181C23×C131—42no—
182C23×C131—41no—
183C23×C131—42no—
184C23×C131—41no—
185C23×C131—41no—
186C23×C131—41no—
187C23×C131—42no—
188C23×C131#11714yes—
189C23×C131C23×C411yescharacteristic
190C23×C131C2×#4112yes—
191C23×C131C2×#4111yescharacteristic
192C23×C131C2×#4111yescharacteristic
193C23×C131C2×#4112yes—
194C23×C131H(5,𝔽2)12yes—
195C23×C131H(5,𝔽2)12yes—
196C23×C131H(5,𝔽2)11yescharacteristic
197C23×C131H(5,𝔽2)11yescharacteristic
198C23×C1312−1+411yescharacteristic
199C23×C1312−1+411yescharacteristic
200C2×C4×C131—22no—
201C2×C4×C131—22no—
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—22no—
209C2×C4×C131—22no—
210C2×C4×C131—22no—
211C2×C4×C131—22no—
212C2×C4×C131—22no—
213C2×C4×C131—22no—
214C2×C4×C131—22no—
215C2×C4×C131—22no—
216C2×C4×C131—22no—
217C2×C4×C131—22no—
218C2×C4×C131—22no—
219C2×C4×C131—22no—
220C2×C4×C131—416no—
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—42no—
245C2×C4×C131—42no—
246C2×C4×C131—42no—
247C2×C4×C131—42no—
248C2×C4×C131—42no—
249C2×C4×C131—42no—
250C2×C4×C131—42no—
251C2×C4×C131—42no—
252C2×C4×C131—42no—
253C2×C4×C131—42no—
254C2×C4×C131—42no—
255C2×C4×C131—42no—
256C2×C4×C131—42no—
257C2×C4×C131#11714yes—
258C2×C4×C131#11714yes—
259C22×C131—24no—
260C22×C131—24no—
261C22×C131—24no—
262C22×C131—42no—
263C22×C131—42no—
264C22×C131—42no—
265C22×C131—42no—
266C22×C131—44no—
267C22×C131—44no—
268C22×C131—44no—
269C22×C131—44no—
270C22×C131C2×#11711yescharacteristic
271C22×C131C2×#11711yescharacteristic
272C22×C131C2×#11711yescharacteristic
273C22×C131#51811yescharacteristic
274C22×C131#51811yescharacteristic
275C22×C131#52011yescharacteristic
276C22×C131#52011yescharacteristic
277C22×C131#52912yes—
278C22×C131#52912yes—
279C22×C131#53812yes—
280C22×C131#53812yes—
281C22×C131#53812yes—
282C22×C131#53812yes—
283C22×C131#53812yes—
284C22×C131#53912yes—
285C22×C131#53912yes—
286C22×C131#53912yes—
287C22×C131#54011yescharacteristic
288C22×C131#54012yes—
289C22×C131#54111yescharacteristic
290C22×C131#54211yescharacteristic
291C22×C131#54211yescharacteristic
292C22×C131#54212yes—
293C4×C131—24no—
294C4×C131—24no—
295C4×C131—42no—
296C4×C131—42no—
297C4×C131—42no—
298C4×C131—42no—
299C4×C131—82no—
300C4×C131—82no—
301C4×C131—82no—
302C4×C131—82no—
303C2×C131—44no—
304C2×C131#228311yescharacteristic
305C2×C131#231211yescharacteristic
306C2×C131#231411yescharacteristic
307C2×C131#231811yescharacteristic
308C2×C131#231811yescharacteristic
309C2×C131#231811yescharacteristic
310C2×C131#231911yescharacteristic
311C2×C131#264812yes—
312C2×C131#264912yes—
313C2×C131#265212yes—
314C2×C131#265312yes—
315#14351C13111yesmaximal, characteristic, direct product factor, Sylow
316C131#1435111yescharacteristic, direct product factor, Sylow
317C2×C4×C22⋊C4C2×C13111yescharacteristic
318#1443C2×C13112yescomplemented
319#1442C2×C13112yescomplemented
320#1440C2×C13112yes—
321#1439C2×C13112yes—
322C4⋊#95C2×C13111yescharacteristic, complemented
323#1434C2×C13111yescharacteristic, complemented
324#1434C2×C13111yescharacteristic, complemented
325#1434C2×C13111yescharacteristic, complemented
326C22⋊#95C2×C13111yescharacteristic
327C22⋊#95C2×C13111yescharacteristic
328C24×C4C22×C13111yescharacteristic
329C22×C4⋊C4C22×C13112yes—
330C22×C22⋊C4C22×C13111yescharacteristic
331C22×C22⋊C4C22×C13111yescharacteristic
332C22×C22⋊C4C22×C13112yes—
333C22×C22⋊C4C22×C13112yes—
334C22×C42C22×C13111yescharacteristic
335C22×C42C22×C13111yescharacteristic
336C4×C22⋊C4C4×C13118yescomplemented
337C2×#95C22×C13111yescharacteristic
338C2×#95C22×C13111yescharacteristic
339C2×#95C22×C13111yescharacteristic
340C2×#95C22×C13111yescharacteristic
341C2×#95C22×C13112yes—
342C2×#95C22×C13112yes—
343C2×#95C22×C13112yes—
344C2×#95C22×C13112yes—
345C2×#95C22×C13112yes—
346C2×#95C22×C13112yes—
347C2×#95C22×C13112yes—
348C2×#95C22×C13112yes—
349C2×#95C22×C13112yes—
350C2×#95C22×C13111yescharacteristic
351C2×#95C22×C13111yescharacteristic
352C25C23×C13111yescharacteristic
353C23×C4—22no—
354C23×C4—22no—
355C23×C4—42no—
356C23×C4—42no—
357C23×C4C2×C4×C13114yes—
358C23×C4C23×C13112yes—
359C23×C4C23×C13112yes—
360C23×C4C23×C13112yes—
361C23×C4C23×C13112yes—
362C23×C4C23×C13111yescharacteristic
363C23×C4C23×C13111yescharacteristic
364C23×C4C23×C13111yescharacteristic
365C23×C4C23×C13111yescharacteristic
366C23×C4C23×C13111yescharacteristic
367C23×C4C23×C13111yescharacteristic
368C2×C4⋊C4—24no—
369C2×C4⋊C4—42no—
370C2×C4⋊C4—42no—
371C2×C22⋊C4—24no—
372C2×C22⋊C4—24no—
373C2×C22⋊C4—24no—
374C2×C22⋊C4—24no—
375C2×C22⋊C4—42no—
376C2×C22⋊C4—42no—
377C2×C22⋊C4—42no—
378C2×C22⋊C4—42no—
379C2×C22⋊C4C2×C4×C13114yes—
380C2×C22⋊C4C2×C4×C13114yes—
381C2×C42—42no—
382C2×C42—42no—
383C2×C42C2×C4×C13114yes—
384C2×C42C2×C4×C13114yes—
385#95—22no—
386#95—22no—
387#95—22no—
388#95—22no—
389#95—24no—
390#95—42no—
391#95—42no—
392#95—42no—
393#95—42no—
394#95—42no—
395#95—42no—
396#95—42no—
397#95—42no—
398#95C2×C4×C13114yes—
399#95C2×C4×C13114yes—
400C24—22no—
401C24—21no—
402C24—21no—
403C24—21no—
404C24—21no—
405C24—22no—
406C24—22no—
407C24—21no—
408C24—21no—
409C24C22×C4×C13112yes—
410C24#41×C13114yes—
411C24C24×C13111yescharacteristic
412C22×C4—22no—
413C22×C4—22no—
414C22×C4—22no—
415C22×C4—21no—
416C22×C4—21no—
417C22×C4—22no—
418C22×C4—22no—
419C22×C4—22no—
420C22×C4—21no—
421C22×C4—21no—
422C22×C4—21no—
423C22×C4—21no—
424C22×C4—21no—
425C22×C4—22no—
426C22×C4—22no—
427C22×C4—22no—
428C22×C4—22no—
429C22×C4—22no—
430C22×C4—21no—
431C22×C4—21no—
432C22×C4—21no—
433C22×C4—28no—
434C22×C4—22no—
435C22×C4—22no—
436C22×C4—22no—
437C22×C4—22no—
438C22×C4—22no—
439C22×C4—22no—
440C22×C4—22no—
441C22×C4—22no—
442C22×C4—22no—
443C22×C4—22no—
444C22×C4—22no—
445C22×C4—22no—
446C22×C4—22no—
447C22×C4—22no—
448C22×C4—22no—
449C22×C4—22no—
450C22×C4—22no—
451C22×C4—22no—
452C22×C4—22no—
453C22×C4—22no—
454C22×C4—22no—
455C22×C4—22no—
456C22×C4—22no—
457C22×C4—22no—
458C22×C4—22no—
459C22×C4—22no—
460C22×C4—22no—
461C22×C4—22no—
462C22×C4—44no—
463C22×C4—44no—
464C22×C4—48no—
465C22×C4—48no—
466C22×C4C22×C4×C13112yes—
467C22×C4C22×C4×C13112yes—
468C22×C4C22×C4×C13112yes—
469C22×C4C22×C4×C13112yes—
470C22×C4C22×C4×C13112yes—
471C22×C4C22×C4×C13112yes—
472C22×C4#41×C13112yes—
473C22×C4#41×C13112yes—
474C22×C4#41×C13114yes—
475C4⋊C4—48no—
476C22⋊C4—28no—
477C22⋊C4—28no—
478C22⋊C4—48no—
479C22⋊C4—48no—
480C42—44no—
481C42—44no—
482C23—22no—
483C23—22no—
484C23—22no—
485C23—22no—
486C23—22no—
487C23—22no—
488C23—24no—
489C23—24no—
490C23—24no—
491C23—24no—
492C23—24no—
493C23—24no—
494C23—42no—
495C23—42no—
496C23—42no—
497C23—42no—
498C23—41no—
499C23—42no—
500C23—41no—
501C23—41no—
502C23—41no—
503C23—42no—
504C23#117×C13114yes—
505C23C23×C4×C13111yescharacteristic
506C23C2×#41×C13112yes—
507C23C2×#41×C13111yescharacteristic
508C23C2×#41×C13111yescharacteristic
509C23C2×#41×C13112yes—
510C23H(5,𝔽2)×C13112yes—
511C23H(5,𝔽2)×C13112yes—
512C23H(5,𝔽2)×C13111yescharacteristic
513C23H(5,𝔽2)×C13111yescharacteristic
514C232−1+4×C13111yescharacteristic
515C232−1+4×C13111yescharacteristic
516C2×C4—22no—
517C2×C4—22no—
518C2×C4—22no—
519C2×C4—22no—
520C2×C4—24no—
521C2×C4—24no—
522C2×C4—24no—
523C2×C4—24no—
524C2×C4—22no—
525C2×C4—22no—
526C2×C4—22no—
527C2×C4—22no—
528C2×C4—22no—
529C2×C4—22no—
530C2×C4—22no—
531C2×C4—22no—
532C2×C4—22no—
533C2×C4—22no—
534C2×C4—22no—
535C2×C4—22no—
536C2×C4—416no—
537C2×C4—42no—
538C2×C4—42no—
539C2×C4—42no—
540C2×C4—42no—
541C2×C4—42no—
542C2×C4—42no—
543C2×C4—42no—
544C2×C4—42no—
545C2×C4—42no—
546C2×C4—42no—
547C2×C4—42no—
548C2×C4—42no—
549C2×C4—42no—
550C2×C4—42no—
551C2×C4—42no—
552C2×C4—42no—
553C2×C4—42no—
554C2×C4—42no—
555C2×C4—42no—
556C2×C4—42no—
557C2×C4—42no—
558C2×C4—42no—
559C2×C4—42no—
560C2×C4—42no—
561C2×C4—42no—
562C2×C4—42no—
563C2×C4—42no—
564C2×C4—42no—
565C2×C4—42no—
566C2×C4—42no—
567C2×C4—42no—
568C2×C4—42no—
569C2×C4—42no—
570C2×C4—42no—
571C2×C4—42no—
572C2×C4—42no—
573C2×C4#117×C13114yes—
574C2×C4#117×C13114yes—
575C22—24no—
576C22—24no—
577C22—24no—
578C22—42no—
579C22—42no—
580C22—42no—
581C22—42no—
582C22—44no—
583C22—44no—
584C22—44no—
585C22—44no—
586C22C2×#117×C13111yescharacteristic
587C22C2×#117×C13111yescharacteristic
588C22C2×#117×C13111yescharacteristic
589C22#518×C13111yescharacteristic
590C22#518×C13111yescharacteristic
591C22#520×C13111yescharacteristic
592C22#520×C13111yescharacteristic
593C22#529×C13112yes—
594C22#529×C13112yes—
595C22#538×C13112yes—
596C22#538×C13112yes—
597C22#538×C13112yes—
598C22#538×C13112yes—
599C22#538×C13112yes—
600C22#539×C13112yes—
601C22#539×C13112yes—
602C22#539×C13112yes—
603C22#540×C13111yescharacteristic
604C22#540×C13112yes—
605C22#541×C13111yescharacteristic
606C22#542×C13111yescharacteristic
607C22#542×C13111yescharacteristic
608C22#542×C13112yes—
609C4—24no—
610C4—24no—
611C4—42no—
612C4—42no—
613C4—42no—
614C4—42no—
615C4—82no—
616C4—82no—
617C4—82no—
618C4—82no—
619C2—44no—
620C2#2283×C13111yescharacteristic
621C2#2312×C13111yescharacteristic
622C2#2314×C13111yescharacteristic
623C2#2318×C13111yescharacteristic
624C2#2318×C13111yescharacteristic
625C2#2318×C13111yescharacteristic
626C2#2319×C13111yescharacteristic
627C2#2648×C13112yes—
628C2#2649×C13112yes—
629C2#2652×C13112yes—
630C2#2653×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. #1443×C131C2semidirect
3. #1442×C131C2semidirect
6. C4⋊#95×C131C2semidirect
7. #1434×C131C2semidirect
8. #1434×C131C2semidirect
9. #1434×C131C2semidirect
20. C4×C22⋊C4×C131C4semidirect
315. #14351C131direct (N × H)
316. C131#14351direct (N × H)
318. #1443C2×C131semidirect
319. #1442C2×C131semidirect
322. C4⋊#95C2×C131semidirect
323. #1434C2×C131semidirect
324. #1434C2×C131semidirect
325. #1434C2×C131semidirect
336. C4×C22⋊C4C4×C131semidirect

Maximal subgroups

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

subgroupindex
C2×C4×C22⋊C4×C1312
#1443×C1312
#1442×C1312
#1440×C1312
#1439×C1312
C4⋊#95×C1312
#1434×C1312
C22⋊#95×C1312
#14351131