Finite Group Databasebeta

← C131×#16518 #45702402

Subgroups — C131×#16518 #45702402

Order 33536.

1430 conjugacy classes of subgroups.

The subgroup lattice has 660 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#397×C131C211yesmaximal, characteristic
2C2×#396×C131C212yesmaximal
3C2×#389×C131C211yesmaximal, characteristic, complemented
4C2×#388×C131C211yesmaximal, characteristic
5C2×#382×C131C211yesmaximal, characteristic, complemented
6#1445×C131C211yesmaximal, characteristic, complemented
7#1444×C131C211yesmaximal, characteristic, complemented
8#1441×C131C212yesmaximal, complemented
9#1441×C131C212yesmaximal, complemented
10#1440×C131C212yesmaximal
11#1439×C131C211yesmaximal, characteristic
12C22×C4⋊C4×C131C2212yes—
13C22×C4⋊C4×C131C2211yescharacteristic
14C22×C4⋊C4×C131C2211yescharacteristic
15C22×C4⋊C4×C131C2212yes—
16C22×C4⋊C4×C131C2212yes—
17C22×C4⋊C4×C131C2211yescharacteristic
18C22×C22⋊C4×C131C2211yescharacteristic
19C22×C22⋊C4×C131C2212yes—
20C22×C22⋊C4×C131C2212yes—
21C22×C22⋊C4×C131C2211yescharacteristic
22C22×C22⋊C4×C131C2211yescharacteristic
23C22×C42×C131C2211yescharacteristic
24#397×C131—24no—
25#396×C131—28no—
26#389×C131—24no—
27#388×C131—24no—
28#382×C131—24no—
29C2×#95×C131C2211yescharacteristic
30C2×#95×C131C2212yes—
31C2×#95×C131C2211yescharacteristic
32C2×#95×C131C2211yescharacteristic
33C2×#95×C131C2212yes—
34C2×#95×C131C2212yes—
35C2×#95×C131C2212yes—
36C2×#95×C131C2212yes—
37C2×#95×C131C2212yes—
38C2×#95×C131C2212yes—
39C2×#95×C131C2211yescharacteristic
40C25×C131C2311yescharacteristic
41C23×C4×C131C2312yes—
42C23×C4×C131C2311yescharacteristic
43C23×C4×C131C2312yes—
44C23×C4×C131C2311yescharacteristic
45C23×C4×C131C2311yescharacteristic
46C23×C4×C131C2311yescharacteristic
47C23×C4×C131C2312yes—
48C23×C4×C131C2312yes—
49C23×C4×C131C2311yescharacteristic
50C23×C4×C131C2311yescharacteristic
51C2×C4⋊C4×C131—22no—
52C2×C4⋊C4×C131—24no—
53C2×C4⋊C4×C131—22no—
54C2×C4⋊C4×C131—24no—
55C2×C4⋊C4×C131—22no—
56C2×C4⋊C4×C131—24no—
57C2×C4⋊C4×C131—24no—
58C2×C4⋊C4×C131—24no—
59C2×C4⋊C4×C131—22no—
60C2×C4⋊C4×C131—24no—
61C2×C4⋊C4×C131—24no—
62C2×C4⋊C4×C131—24no—
63C2×C4⋊C4×C131—22no—
64C2×C4⋊C4×C131—42no—
65C2×C4⋊C4×C131—42no—
66C2×C4⋊C4×C131—42no—
67C2×C22⋊C4×C131—22no—
68C2×C22⋊C4×C131—22no—
69C2×C22⋊C4×C131—24no—
70C2×C22⋊C4×C131—24no—
71C2×C22⋊C4×C131—22no—
72C2×C22⋊C4×C131—22no—
73C2×C22⋊C4×C131—24no—
74C2×C22⋊C4×C131—22no—
75C2×C22⋊C4×C131—24no—
76C2×C22⋊C4×C131—22no—
77C2×C22⋊C4×C131—42no—
78C2×C22⋊C4×C131—42no—
79C2×C22⋊C4×C131—42no—
80C2×C22⋊C4×C131D414yes—
81C2×C42×C131—22no—
82C2×C42×C131—22no—
83C2×C42×C131D414yes—
84#95×C131—22no—
85#95×C131—22no—
86#95×C131—24no—
87#95×C131—24no—
88#95×C131—24no—
89#95×C131—24no—
90#95×C131—22no—
91#95×C131—42no—
92#95×C131—42no—
93#95×C131—42no—
94#95×C131D414yes—
95C24×C131—21no—
96C24×C131—21no—
97C24×C131—21no—
98C24×C131—22no—
99C24×C131—21no—
100C24×C131—21no—
101C24×C131—22no—
102C24×C131—22no—
103C24×C131—22no—
104C24×C131—21no—
105C24×C131C2×D412yes—
106C24×C131C2411yescharacteristic
107C22×C4×C131—21no—
108C22×C4×C131—21no—
109C22×C4×C131—22no—
110C22×C4×C131—21no—
111C22×C4×C131—22no—
112C22×C4×C131—21no—
113C22×C4×C131—21no—
114C22×C4×C131—21no—
115C22×C4×C131—22no—
116C22×C4×C131—22no—
117C22×C4×C131—22no—
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—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—21no—
134C22×C4×C131—21no—
135C22×C4×C131—22no—
136C22×C4×C131—21no—
137C22×C4×C131—22no—
138C22×C4×C131—22no—
139C22×C4×C131—22no—
140C22×C4×C131—22no—
141C22×C4×C131—21no—
142C22×C4×C131—22no—
143C22×C4×C131—22no—
144C22×C4×C131—22no—
145C22×C4×C131—21no—
146C22×C4×C131—22no—
147C22×C4×C131—22no—
148C22×C4×C131—22no—
149C22×C4×C131—22no—
150C22×C4×C131—22no—
151C22×C4×C131—22no—
152C22×C4×C131—22no—
153C22×C4×C131—22no—
154C22×C4×C131—22no—
155C22×C4×C131—22no—
156C22×C4×C131—21no—
157C22×C4×C131C2×D414yes—
158C22×C4×C131C2×D412yes—
159C22×C4×C131C2×D412yes—
160C22×C4×C131C2×D412yes—
161C22×C4×C131C2×D412yes—
162C22×C4×C131C2×D412yes—
163C22×C4×C131C2×D412yes—
164C22×C4×C131#4114yes—
165C22×C4×C131#4112yes—
166C22×C4×C131#4112yes—
167C4⋊C4×C131—28no—
168C4⋊C4×C131—48no—
169C4⋊C4×C131—48no—
170C4⋊C4×C131—44no—
171C4⋊C4×C131—48no—
172C4⋊C4×C131—44no—
173C22⋊C4×C131—28no—
174C22⋊C4×C131—48no—
175C22⋊C4×C131—48no—
176C22⋊C4×C131—44no—
177C22⋊C4×C131—44no—
178C42×C131—28no—
179C23×C131—22no—
180C23×C131—24no—
181C23×C131—22no—
182C23×C131—24no—
183C23×C131—22no—
184C23×C131—41no—
185C23×C131—41no—
186C23×C131—41no—
187C23×C131—41no—
188C23×C131—41no—
189C23×C131—41no—
190C23×C131—42no—
191C23×C131—42no—
192C23×C131—42no—
193C23×C131—42no—
194C23×C131—42no—
195C23×C131—42no—
196C23×C131—41no—
197C23×C131—42no—
198C23×C131—41no—
199C23×C131—42no—
200C23×C131—42no—
201C23×C131—42no—
202C23×C131C22×D411yescharacteristic
203C23×C131C22×D411yescharacteristic
204C23×C131C22×D411yescharacteristic
205C23×C131C2×#4111yescharacteristic
206C23×C131C2×#4111yescharacteristic
207C23×C131C2×#4112yes—
208C23×C131H(5,𝔽2)12yes—
209C23×C131H(5,𝔽2)11yescharacteristic
210C23×C1312−1+412yes—
211C23×C1312−1+412yes—
212C23×C1312−1+411yescharacteristic
213C2×C4×C131—22no—
214C2×C4×C131—22no—
215C2×C4×C131—22no—
216C2×C4×C131—22no—
217C2×C4×C131—22no—
218C2×C4×C131—24no—
219C2×C4×C131—22no—
220C2×C4×C131—22no—
221C2×C4×C131—24no—
222C2×C4×C131—22no—
223C2×C4×C131—22no—
224C2×C4×C131—22no—
225C2×C4×C131—24no—
226C2×C4×C131—22no—
227C2×C4×C131—22no—
228C2×C4×C131—24no—
229C2×C4×C131—24no—
230C2×C4×C131—24no—
231C2×C4×C131—24no—
232C2×C4×C131—24no—
233C2×C4×C131—24no—
234C2×C4×C131—42no—
235C2×C4×C131—41no—
236C2×C4×C131—41no—
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—41no—
248C2×C4×C131—42no—
249C2×C4×C131—42no—
250C2×C4×C131—41no—
251C2×C4×C131—41no—
252C2×C4×C131—41no—
253C2×C4×C131—41no—
254C2×C4×C131—42no—
255C2×C4×C131—41no—
256C2×C4×C131—42no—
257C2×C4×C131—42no—
258C2×C4×C131—42no—
259C2×C4×C131—42no—
260C2×C4×C131—42no—
261C2×C4×C131—42no—
262C2×C4×C131—42no—
263C2×C4×C131—42no—
264C2×C4×C131—42no—
265C2×C4×C131—42no—
266C2×C4×C131—42no—
267C2×C4×C131—42no—
268C2×C4×C131—42no—
269C2×C4×C131—42no—
270C2×C4×C131—42no—
271C2×C4×C131#12114yes—
272C2×C4×C131#12114yes—
273C22×C131—42no—
274C22×C131—42no—
275C22×C131—44no—
276C22×C131—44no—
277C22×C131—42no—
278C22×C131—81no—
279C22×C131—81no—
280C22×C131—81no—
281C22×C131—81no—
282C22×C131—82no—
283C22×C131—82no—
284C22×C131C2×#12111yescharacteristic
285C22×C131C2×#12111yescharacteristic
286C22×C131#52511yescharacteristic
287C22×C131#53511yescharacteristic
288C22×C131#53611yescharacteristic
289C22×C131#53611yescharacteristic
290C22×C131#53612yes—
291C22×C131#53711yescharacteristic
292C22×C131#53712yes—
293C22×C131#54112yes—
294C22×C131#54112yes—
295C22×C131#54212yes—
296C22×C131#54212yes—
297C22×C131D4211yescharacteristic
298C22×C131#54612yes—
299C22×C131#54712yes—
300C22×C131#54711yescharacteristic
301C22×C131#54811yescharacteristic
302C22×C131#55212yes—
303C22×C131#55311yescharacteristic
304C22×C131#55312yes—
305C22×C131#56212yes—
306C22×C131#56312yes—
307C4×C131—24no—
308C4×C131—24no—
309C4×C131—42no—
310C4×C131—44no—
311C4×C131—42no—
312C4×C131—44no—
313C4×C131—81no—
314C4×C131—81no—
315C4×C131—82no—
316C4×C131—82no—
317C2×C131—82no—
318C2×C131#241311yescharacteristic
319C2×C131#241611yescharacteristic
320C2×C131#253511yescharacteristic
321C2×C131#262011yescharacteristic
322C2×C131#262111yescharacteristic
323C2×C131#263711yescharacteristic
324C2×C131#267212yes—
325C2×C131#269812yes—
326C2×C131#272512yes—
327C2×C131#277212yes—
328C2×C131#282011yescharacteristic
329#16518C13111yesmaximal, characteristic, direct product factor, Sylow
330C131#1651811yescharacteristic, direct product factor, Sylow
331C2×#397C2×C13111yescharacteristic
332C2×#396C2×C13112yes—
333C2×#389C2×C13111yescharacteristic, complemented
334C2×#388C2×C13111yescharacteristic
335C2×#382C2×C13111yescharacteristic, complemented
336#1445C2×C13111yescharacteristic, complemented
337#1444C2×C13111yescharacteristic, complemented
338#1441C2×C13112yescomplemented
339#1441C2×C13112yescomplemented
340#1440C2×C13112yes—
341#1439C2×C13111yescharacteristic
342C22×C4⋊C4C22×C13112yes—
343C22×C4⋊C4C22×C13111yescharacteristic
344C22×C4⋊C4C22×C13111yescharacteristic
345C22×C4⋊C4C22×C13112yes—
346C22×C4⋊C4C22×C13112yes—
347C22×C4⋊C4C22×C13111yescharacteristic
348C22×C22⋊C4C22×C13111yescharacteristic
349C22×C22⋊C4C22×C13112yes—
350C22×C22⋊C4C22×C13112yes—
351C22×C22⋊C4C22×C13111yescharacteristic
352C22×C22⋊C4C22×C13111yescharacteristic
353C22×C42C22×C13111yescharacteristic
354#397—24no—
355#396—28no—
356#389—24no—
357#388—24no—
358#382—24no—
359C2×#95C22×C13112yes—
360C2×#95C22×C13112yes—
361C2×#95C22×C13111yescharacteristic
362C2×#95C22×C13112yes—
363C2×#95C22×C13112yes—
364C2×#95C22×C13111yescharacteristic
365C2×#95C22×C13111yescharacteristic
366C2×#95C22×C13112yes—
367C2×#95C22×C13112yes—
368C2×#95C22×C13112yes—
369C2×#95C22×C13111yescharacteristic
370C25C23×C13111yescharacteristic
371C23×C4C23×C13112yes—
372C23×C4C23×C13111yescharacteristic
373C23×C4C23×C13112yes—
374C23×C4C23×C13111yescharacteristic
375C23×C4C23×C13111yescharacteristic
376C23×C4C23×C13112yes—
377C23×C4C23×C13111yescharacteristic
378C23×C4C23×C13112yes—
379C23×C4C23×C13111yescharacteristic
380C23×C4C23×C13111yescharacteristic
381C2×C4⋊C4—22no—
382C2×C4⋊C4—24no—
383C2×C4⋊C4—24no—
384C2×C4⋊C4—22no—
385C2×C4⋊C4—24no—
386C2×C4⋊C4—22no—
387C2×C4⋊C4—24no—
388C2×C4⋊C4—24no—
389C2×C4⋊C4—24no—
390C2×C4⋊C4—22no—
391C2×C4⋊C4—24no—
392C2×C4⋊C4—24no—
393C2×C4⋊C4—22no—
394C2×C4⋊C4—42no—
395C2×C4⋊C4—42no—
396C2×C4⋊C4—42no—
397C2×C22⋊C4—22no—
398C2×C22⋊C4—22no—
399C2×C22⋊C4—24no—
400C2×C22⋊C4—24no—
401C2×C22⋊C4—22no—
402C2×C22⋊C4—22no—
403C2×C22⋊C4—24no—
404C2×C22⋊C4—22no—
405C2×C22⋊C4—24no—
406C2×C22⋊C4—22no—
407C2×C22⋊C4—42no—
408C2×C22⋊C4—42no—
409C2×C22⋊C4—42no—
410C2×C22⋊C4D4×C13114yes—
411C2×C42—22no—
412C2×C42—22no—
413C2×C42D4×C13114yes—
414#95—24no—
415#95—22no—
416#95—22no—
417#95—22no—
418#95—24no—
419#95—24no—
420#95—24no—
421#95—42no—
422#95—42no—
423#95—42no—
424#95D4×C13114yes—
425C24—21no—
426C24—21no—
427C24—21no—
428C24—22no—
429C24—21no—
430C24—21no—
431C24—22no—
432C24—22no—
433C24—22no—
434C24—21no—
435C24C2×D4×C13112yes—
436C24C24×C13111yescharacteristic
437C22×C4—21no—
438C22×C4—21no—
439C22×C4—22no—
440C22×C4—21no—
441C22×C4—22no—
442C22×C4—21no—
443C22×C4—21no—
444C22×C4—21no—
445C22×C4—22no—
446C22×C4—22no—
447C22×C4—22no—
448C22×C4—21no—
449C22×C4—21no—
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—22no—
463C22×C4—21no—
464C22×C4—21no—
465C22×C4—22no—
466C22×C4—21no—
467C22×C4—22no—
468C22×C4—22no—
469C22×C4—22no—
470C22×C4—22no—
471C22×C4—21no—
472C22×C4—22no—
473C22×C4—22no—
474C22×C4—22no—
475C22×C4—21no—
476C22×C4—22no—
477C22×C4—22no—
478C22×C4—22no—
479C22×C4—22no—
480C22×C4—22no—
481C22×C4—22no—
482C22×C4—22no—
483C22×C4—22no—
484C22×C4—22no—
485C22×C4—22no—
486C22×C4—21no—
487C22×C4C2×D4×C13114yes—
488C22×C4C2×D4×C13112yes—
489C22×C4C2×D4×C13112yes—
490C22×C4C2×D4×C13112yes—
491C22×C4C2×D4×C13112yes—
492C22×C4C2×D4×C13112yes—
493C22×C4C2×D4×C13112yes—
494C22×C4#41×C13114yes—
495C22×C4#41×C13112yes—
496C22×C4#41×C13112yes—
497C4⋊C4—28no—
498C4⋊C4—48no—
499C4⋊C4—48no—
500C4⋊C4—44no—
501C4⋊C4—48no—
502C4⋊C4—44no—
503C22⋊C4—28no—
504C22⋊C4—48no—
505C22⋊C4—48no—
506C22⋊C4—44no—
507C22⋊C4—44no—
508C42—28no—
509C23—22no—
510C23—24no—
511C23—22no—
512C23—24no—
513C23—22no—
514C23—41no—
515C23—41no—
516C23—41no—
517C23—41no—
518C23—41no—
519C23—41no—
520C23—42no—
521C23—42no—
522C23—42no—
523C23—42no—
524C23—42no—
525C23—42no—
526C23—41no—
527C23—42no—
528C23—42no—
529C23—41no—
530C23—42no—
531C23—42no—
532C23C22×D4×C13111yescharacteristic
533C23C22×D4×C13111yescharacteristic
534C23C22×D4×C13111yescharacteristic
535C23C2×#41×C13111yescharacteristic
536C23C2×#41×C13111yescharacteristic
537C23C2×#41×C13112yes—
538C23H(5,𝔽2)×C13112yes—
539C23H(5,𝔽2)×C13111yescharacteristic
540C232−1+4×C13112yes—
541C232−1+4×C13112yes—
542C232−1+4×C13111yescharacteristic
543C2×C4—22no—
544C2×C4—22no—
545C2×C4—22no—
546C2×C4—22no—
547C2×C4—22no—
548C2×C4—24no—
549C2×C4—22no—
550C2×C4—22no—
551C2×C4—24no—
552C2×C4—22no—
553C2×C4—22no—
554C2×C4—22no—
555C2×C4—24no—
556C2×C4—22no—
557C2×C4—22no—
558C2×C4—24no—
559C2×C4—24no—
560C2×C4—24no—
561C2×C4—24no—
562C2×C4—24no—
563C2×C4—24no—
564C2×C4—42no—
565C2×C4—41no—
566C2×C4—41no—
567C2×C4—42no—
568C2×C4—42no—
569C2×C4—42no—
570C2×C4—42no—
571C2×C4—42no—
572C2×C4—42no—
573C2×C4—42no—
574C2×C4—42no—
575C2×C4—42no—
576C2×C4—42no—
577C2×C4—41no—
578C2×C4—42no—
579C2×C4—42no—
580C2×C4—41no—
581C2×C4—41no—
582C2×C4—41no—
583C2×C4—41no—
584C2×C4—42no—
585C2×C4—41no—
586C2×C4—42no—
587C2×C4—42no—
588C2×C4—42no—
589C2×C4—42no—
590C2×C4—42no—
591C2×C4—42no—
592C2×C4—42no—
593C2×C4—42no—
594C2×C4—42no—
595C2×C4—42no—
596C2×C4—42no—
597C2×C4—42no—
598C2×C4—42no—
599C2×C4—42no—
600C2×C4—42no—
601C2×C4#121×C13114yes—
602C2×C4#121×C13114yes—
603C22—42no—
604C22—42no—
605C22—42no—
606C22—44no—
607C22—44no—
608C22—82no—
609C22—81no—
610C22—81no—
611C22—81no—
612C22—81no—
613C22—82no—
614C22C2×#121×C13111yescharacteristic
615C22C2×#121×C13111yescharacteristic
616C22#525×C13111yescharacteristic
617C22#535×C13111yescharacteristic
618C22#536×C13111yescharacteristic
619C22#536×C13111yescharacteristic
620C22#536×C13112yes—
621C22#537×C13111yescharacteristic
622C22#537×C13112yes—
623C22#541×C13112yes—
624C22#541×C13112yes—
625C22#542×C13112yes—
626C22#542×C13112yes—
627C22D42×C13111yescharacteristic
628C22#546×C13112yes—
629C22#547×C13112yes—
630C22#547×C13111yescharacteristic
631C22#548×C13111yescharacteristic
632C22#552×C13112yes—
633C22#553×C13111yescharacteristic
634C22#553×C13112yes—
635C22#562×C13112yes—
636C22#563×C13112yes—
637C4—24no—
638C4—24no—
639C4—42no—
640C4—44no—
641C4—42no—
642C4—44no—
643C4—81no—
644C4—81no—
645C4—82no—
646C4—82no—
647C2—82no—
648C2#2413×C13111yescharacteristic
649C2#2416×C13111yescharacteristic
650C2#2535×C13111yescharacteristic
651C2#2620×C13111yescharacteristic
652C2#2621×C13111yescharacteristic
653C2#2637×C13111yescharacteristic
654C2#2672×C13112yes—
655C2#2698×C13112yes—
656C2#2725×C13112yes—
657C2#2772×C13112yes—
658C2#2820×C13111yescharacteristic
subgroupG/H
center, socleC24×C131C24
commutator, Frattini, cosocleC24C24×C131
prime radicalC25×C131C23
LCSG ▷ C24 ▷ C1
UCSC1 ◁ C24×C131 ◁ G

Complements

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

NH ≅ G/Ntype
3. C2×#389×C131C2semidirect
5. C2×#382×C131C2semidirect
6. #1445×C131C2semidirect
7. #1444×C131C2semidirect
8. #1441×C131C2semidirect
9. #1441×C131C2semidirect
329. #16518C131direct (N × H)
330. C131#16518direct (N × H)
333. C2×#389C2×C131semidirect
335. C2×#382C2×C131semidirect
336. #1445C2×C131semidirect
337. #1444C2×C131semidirect
338. #1441C2×C131semidirect
339. #1441C2×C131semidirect

Maximal subgroups

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

subgroupindex
C2×#397×C1312
C2×#396×C1312
C2×#389×C1312
C2×#388×C1312
C2×#382×C1312
#1445×C1312
#1444×C1312
#1441×C1312
#1440×C1312
#1439×C1312
#16518131