Finite Group Databasebeta

← C131×#13877 #45699761

Subgroups — C131×#13877 #45699761

Order 33536.

4046 conjugacy classes of subgroups.

The subgroup lattice has 650 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C23×C22⋊C4×C131C211yesmaximal, characteristic
2C23×C22⋊C4×C131C211yesmaximal, characteristic
3C2×#385×C131C212yesmaximal, complemented
4C2×#380×C131C212yesmaximal, complemented
5C2×#379×C131C211yesmaximal, characteristic
6#1439×C131C214yesmaximal, complemented
7C22⋊#95×C131C212yesmaximal, complemented
8C22⋊#95×C131C212yesmaximal, complemented
9C26×C131C2211yescharacteristic
10C24×C4×C131C2212yes—
11C24×C4×C131C2212yes—
12C22×C4⋊C4×C131C2214yescomplemented
13C22×C22⋊C4×C131—24no—
14C22×C22⋊C4×C131—28no—
15C22×C22⋊C4×C131—28no—
16C22×C22⋊C4×C131C418yescomplemented
17C22×C22⋊C4×C131C2211yescharacteristic
18C22×C22⋊C4×C131C2212yes—
19C22×C22⋊C4×C131C2211yescharacteristic
20C22×C22⋊C4×C131C2212yes—
21C22×C22⋊C4×C131C2211yescharacteristic
22C22×C22⋊C4×C131C2212yes—
23C22×C22⋊C4×C131C2212yes—
24C22×C22⋊C4×C131C2212yes—
25C22×C22⋊C4×C131C2211yescharacteristic
26#385×C131—28no—
27#380×C131—28no—
28#379×C131—24no—
29C2×#95×C131C2214yescomplemented
30C2×#95×C131C2214yescomplemented
31C2×#95×C131C2214yescomplemented
32C25×C131—24no—
33C25×C131—24no—
34C25×C131—24no—
35C25×C131—24no—
36C25×C131—44no—
37C25×C131C2×C414yes—
38C25×C131D414yes—
39C25×C131Q814yes—
40C25×C131C2311yescharacteristic
41C25×C131C2311yescharacteristic
42C25×C131C2311yescharacteristic
43C23×C4×C131—24no—
44C23×C4×C131—24no—
45C23×C4×C131—24no—
46C23×C4×C131—28no—
47C23×C4×C131—28no—
48C23×C4×C131—24no—
49C23×C4×C131—24no—
50C23×C4×C131—44no—
51C23×C4×C131—44no—
52C23×C4×C131C2×C418yescomplemented
53C23×C4×C131C2312yes—
54C23×C4×C131C2312yes—
55C23×C4×C131C2312yes—
56C23×C4×C131C2314yes—
57C23×C4×C131C2312yes—
58C2×C4⋊C4×C131—28no—
59C2×C4⋊C4×C131—28no—
60C2×C4⋊C4×C131—44no—
61C2×C22⋊C4×C131—232no—
62C2×C22⋊C4×C131—24no—
63C2×C22⋊C4×C131—24no—
64C2×C22⋊C4×C131—24no—
65C2×C22⋊C4×C131—24no—
66C2×C22⋊C4×C131—28no—
67C2×C22⋊C4×C131—28no—
68C2×C22⋊C4×C131—232no—
69C2×C22⋊C4×C131—24no—
70C2×C22⋊C4×C131—22no—
71C2×C22⋊C4×C131—24no—
72C2×C22⋊C4×C131—22no—
73C2×C22⋊C4×C131—24no—
74C2×C22⋊C4×C131—24no—
75C2×C22⋊C4×C131—24no—
76C2×C22⋊C4×C131—24no—
77C2×C22⋊C4×C131—44no—
78C2×C22⋊C4×C131C2×C414yes—
79C2×C22⋊C4×C131C2×C414yes—
80C2×C22⋊C4×C131C2×C418yescomplemented
81C2×C22⋊C4×C131D418yes—
82C2×C22⋊C4×C131D418yes—
83#95×C131—28no—
84#95×C131—28no—
85#95×C131—44no—
86C24×C131—22no—
87C24×C131—22no—
88C24×C131—22no—
89C24×C131—22no—
90C24×C131—24no—
91C24×C131—24no—
92C24×C131—28no—
93C24×C131—28no—
94C24×C131—216no—
95C24×C131—28no—
96C24×C131—216no—
97C24×C131—216no—
98C24×C131—216no—
99C24×C131—28no—
100C24×C131—22no—
101C24×C131—22no—
102C24×C131—22no—
103C24×C131—22no—
104C24×C131—24no—
105C24×C131—48no—
106C24×C131—48no—
107C24×C131—48no—
108C24×C131—416no—
109C24×C131—416no—
110C24×C131—416no—
111C24×C131—416no—
112C24×C131C4⋊C4116yescomplemented
113C24×C131C22×C412yes—
114C24×C131C22×C412yes—
115C24×C131C22×C412yes—
116C24×C131C2×D412yes—
117C24×C131C2×D414yes—
118C24×C131C2×D412yes—
119C24×C131C2×D412yes—
120C24×C131C2×D414yes—
121C24×C131C2×Q812yes—
122C24×C131C2×Q812yes—
123C24×C131C2×Q812yes—
124C24×C131#4114yes—
125C24×C131#4114yes—
126C24×C131C2411yescharacteristic
127C22×C4×C131—22no—
128C22×C4×C131—22no—
129C22×C4×C131—24no—
130C22×C4×C131—216no—
131C22×C4×C131—216no—
132C22×C4×C131—22no—
133C22×C4×C131—24no—
134C22×C4×C131—24no—
135C22×C4×C131—24no—
136C22×C4×C131—24no—
137C22×C4×C131—22no—
138C22×C4×C131—24no—
139C22×C4×C131—24no—
140C22×C4×C131—24no—
141C22×C4×C131—24no—
142C22×C4×C131—216no—
143C22×C4×C131—22no—
144C22×C4×C131—24no—
145C22×C4×C131—22no—
146C22×C4×C131—22no—
147C22×C4×C131—22no—
148C22×C4×C131—22no—
149C22×C4×C131—22no—
150C22×C4×C131—24no—
151C22×C4×C131—24no—
152C22×C4×C131—24no—
153C22×C4×C131—48no—
154C22×C4×C131—416no—
155C22×C4×C131—416no—
156C22×C4×C131—416no—
157C22×C4×C131—416no—
158C22×C4×C131—48no—
159C22×C4×C131—48no—
160C22×C4×C131C22×C414yes—
161C22×C4×C131C22×C414yes—
162C22×C4×C131C2×D418yes—
163C22×C4×C131C2×D418yes—
164C4⋊C4×C131—416no—
165C22⋊C4×C131—216no—
166C22⋊C4×C131—28no—
167C22⋊C4×C131—216no—
168C22⋊C4×C131—216no—
169C22⋊C4×C131—48no—
170C22⋊C4×C131—44no—
171C22⋊C4×C131—48no—
172C22⋊C4×C131—44no—
173C22⋊C4×C131C22⋊C4116yescomplemented
174C23×C131—22no—
175C23×C131—22no—
176C23×C131—24no—
177C23×C131—24no—
178C23×C131—24no—
179C23×C131—22no—
180C23×C131—24no—
181C23×C131—24no—
182C23×C131—24no—
183C23×C131—22no—
184C23×C131—24no—
185C23×C131—24no—
186C23×C131—24no—
187C23×C131—24no—
188C23×C131—28no—
189C23×C131—28no—
190C23×C131—28no—
191C23×C131—28no—
192C23×C131—28no—
193C23×C131—28no—
194C23×C131—28no—
195C23×C131—28no—
196C23×C131—22no—
197C23×C131—22no—
198C23×C131—24no—
199C23×C131—24no—
200C23×C131—22no—
201C23×C131—24no—
202C23×C131—24no—
203C23×C131—24no—
204C23×C131—22no—
205C23×C131—24no—
206C23×C131—24no—
207C23×C131—232no—
208C23×C131—232no—
209C23×C131—416no—
210C23×C131—432no—
211C23×C131—432no—
212C23×C131—432no—
213C23×C131—432no—
214C23×C131—464no—
215C23×C131—44no—
216C23×C131—44no—
217C23×C131—44no—
218C23×C131—44no—
219C23×C131C2×C22⋊C414yes—
220C23×C131C2×C4⋊C414yes—
221C23×C131C2×C4⋊C414yes—
222C23×C131C2×C4⋊C414yes—
223C23×C131#11714yes—
224C23×C131C4×D418yes—
225C23×C131#12014yes—
226C23×C131#12118yes—
227C23×C131C22⋊Q818yes—
228C23×C131C22⋊Q818yes—
229C23×C131#12314yes—
230C23×C131C23×C411yescharacteristic
231C23×C131C22×D412yes—
232C23×C131C22×D411yescharacteristic
233C23×C131C22×D412yes—
234C23×C131C22×Q811yescharacteristic
235C23×C131C2×#4112yes—
236C23×C131C2×#4112yes—
237C23×C131H(5,𝔽2)14yes—
238C2×C4×C131—24no—
239C2×C4×C131—24no—
240C2×C4×C131—28no—
241C2×C4×C131—28no—
242C2×C4×C131—24no—
243C2×C4×C131—24no—
244C2×C4×C131—24no—
245C2×C4×C131—28no—
246C2×C4×C131—28no—
247C2×C4×C131—28no—
248C2×C4×C131—432no—
249C2×C4×C131—432no—
250C2×C4×C131—44no—
251C2×C4×C131—44no—
252C2×C4×C131—44no—
253C2×C4×C131—44no—
254C2×C4×C131—44no—
255C2×C4×C131—44no—
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—44no—
263C2×C4×C131—44no—
264C2×C4×C131—44no—
265C2×C4×C131—44no—
266C2×C4×C131C2×C22⋊C418yescomplemented
267C22×C131—24no—
268C22×C131—24no—
269C22×C131—28no—
270C22×C131—28no—
271C22×C131—28no—
272C22×C131—28no—
273C22×C131—28no—
274C22×C131—28no—
275C22×C131—28no—
276C22×C131—28no—
277C22×C131—216no—
278C22×C131—216no—
279C22×C131—24no—
280C22×C131—24no—
281C22×C131—24no—
282C22×C131—24no—
283C22×C131—24no—
284C22×C131—464no—
285C22×C131—44no—
286C22×C131—44no—
287C22×C131—44no—
288C22×C131—44no—
289C22×C131—48no—
290C22×C131#38018yescomplemented
291C22×C131#38518yescomplemented
292C22×C131C22×C22⋊C411yescharacteristic
293C22×C131C22×C4⋊C411yescharacteristic
294C22×C131C2×#11711yescharacteristic
295C22×C131C2×C4×D412yes—
296C22×C131#51812yes—
297C22×C131C2×#12011yescharacteristic
298C22×C131C2×#12112yes—
299C22×C131C2×C22⋊Q812yes—
300C22×C131C2×C22⋊Q812yes—
301C22×C131C2×#12311yescharacteristic
302C22×C131#53412yes—
303C22×C131#54312yes—
304C22×C131D4214yes—
305C22×C131#54614yes—
306C22×C131#54614yes—
307C22×C131#55114yes—
308C4×C131—28no—
309C4×C131—44no—
310C4×C131—48no—
311C4×C131—82no—
312C4×C131—82no—
313C2×C131—28no—
314C2×C131—28no—
315C2×C131—44no—
316C2×C131C2×#38011yescharacteristic
317C2×C131C2×#38511yescharacteristic
318C2×C131#231511yescharacteristic
319C2×C131D4×C22⋊C412yes—
320C2×C131#234212yes—
321C2×C131#241012yes—
322C2×C131#241212yes—
323C2×C131#243714yes—
324#13877C13111yesmaximal, characteristic, direct product factor, Sylow
325C131#1387711yescharacteristic, direct product factor, Sylow
326C23×C22⋊C4C2×C13111yescharacteristic
327C23×C22⋊C4C2×C13111yescharacteristic
328C2×#385C2×C13112yescomplemented
329C2×#380C2×C13112yescomplemented
330C2×#379C2×C13111yescharacteristic
331#1439C2×C13114yescomplemented
332C22⋊#95C2×C13112yescomplemented
333C22⋊#95C2×C13112yescomplemented
334C26C22×C13111yescharacteristic
335C24×C4C22×C13112yes—
336C24×C4C22×C13112yes—
337C22×C4⋊C4C22×C13114yescomplemented
338C22×C22⋊C4—24no—
339C22×C22⋊C4—28no—
340C22×C22⋊C4—28no—
341C22×C22⋊C4C4×C13118yescomplemented
342C22×C22⋊C4C22×C13112yes—
343C22×C22⋊C4C22×C13111yescharacteristic
344C22×C22⋊C4C22×C13112yes—
345C22×C22⋊C4C22×C13111yescharacteristic
346C22×C22⋊C4C22×C13111yescharacteristic
347C22×C22⋊C4C22×C13112yes—
348C22×C22⋊C4C22×C13112yes—
349C22×C22⋊C4C22×C13112yes—
350C22×C22⋊C4C22×C13111yescharacteristic
351#385—28no—
352#380—28no—
353#379—24no—
354C2×#95C22×C13114yescomplemented
355C2×#95C22×C13114yescomplemented
356C2×#95C22×C13114yescomplemented
357C25—24no—
358C25—24no—
359C25—24no—
360C25—24no—
361C25—44no—
362C25C2×C4×C13114yes—
363C25D4×C13114yes—
364C25Q8×C13114yes—
365C25C23×C13111yescharacteristic
366C25C23×C13111yescharacteristic
367C25C23×C13111yescharacteristic
368C23×C4—24no—
369C23×C4—24no—
370C23×C4—24no—
371C23×C4—28no—
372C23×C4—28no—
373C23×C4—24no—
374C23×C4—24no—
375C23×C4—44no—
376C23×C4—44no—
377C23×C4C2×C4×C13118yescomplemented
378C23×C4C23×C13112yes—
379C23×C4C23×C13112yes—
380C23×C4C23×C13112yes—
381C23×C4C23×C13114yes—
382C23×C4C23×C13112yes—
383C2×C4⋊C4—28no—
384C2×C4⋊C4—28no—
385C2×C4⋊C4—44no—
386C2×C22⋊C4—232no—
387C2×C22⋊C4—24no—
388C2×C22⋊C4—24no—
389C2×C22⋊C4—24no—
390C2×C22⋊C4—24no—
391C2×C22⋊C4—28no—
392C2×C22⋊C4—28no—
393C2×C22⋊C4—232no—
394C2×C22⋊C4—24no—
395C2×C22⋊C4—22no—
396C2×C22⋊C4—24no—
397C2×C22⋊C4—22no—
398C2×C22⋊C4—24no—
399C2×C22⋊C4—24no—
400C2×C22⋊C4—24no—
401C2×C22⋊C4—24no—
402C2×C22⋊C4—44no—
403C2×C22⋊C4C2×C4×C13114yes—
404C2×C22⋊C4C2×C4×C13114yes—
405C2×C22⋊C4C2×C4×C13118yescomplemented
406C2×C22⋊C4D4×C13118yes—
407C2×C22⋊C4D4×C13118yes—
408#95—28no—
409#95—28no—
410#95—44no—
411C24—22no—
412C24—22no—
413C24—22no—
414C24—22no—
415C24—24no—
416C24—24no—
417C24—28no—
418C24—28no—
419C24—216no—
420C24—28no—
421C24—216no—
422C24—216no—
423C24—216no—
424C24—28no—
425C24—22no—
426C24—22no—
427C24—22no—
428C24—22no—
429C24—24no—
430C24—48no—
431C24—48no—
432C24—48no—
433C24—416no—
434C24—416no—
435C24—416no—
436C24—416no—
437C24C4⋊C4×C131116yescomplemented
438C24C22×C4×C13112yes—
439C24C22×C4×C13112yes—
440C24C22×C4×C13112yes—
441C24C2×D4×C13112yes—
442C24C2×D4×C13114yes—
443C24C2×D4×C13112yes—
444C24C2×D4×C13112yes—
445C24C2×D4×C13114yes—
446C24C2×Q8×C13112yes—
447C24C2×Q8×C13112yes—
448C24C2×Q8×C13112yes—
449C24#41×C13114yes—
450C24#41×C13114yes—
451C24C24×C13111yescharacteristic
452C22×C4—22no—
453C22×C4—22no—
454C22×C4—24no—
455C22×C4—216no—
456C22×C4—216no—
457C22×C4—22no—
458C22×C4—24no—
459C22×C4—24no—
460C22×C4—24no—
461C22×C4—24no—
462C22×C4—22no—
463C22×C4—24no—
464C22×C4—24no—
465C22×C4—24no—
466C22×C4—24no—
467C22×C4—216no—
468C22×C4—22no—
469C22×C4—24no—
470C22×C4—22no—
471C22×C4—22no—
472C22×C4—22no—
473C22×C4—22no—
474C22×C4—22no—
475C22×C4—24no—
476C22×C4—24no—
477C22×C4—24no—
478C22×C4—48no—
479C22×C4—416no—
480C22×C4—416no—
481C22×C4—416no—
482C22×C4—416no—
483C22×C4—48no—
484C22×C4—48no—
485C22×C4C22×C4×C13114yes—
486C22×C4C22×C4×C13114yes—
487C22×C4C2×D4×C13118yes—
488C22×C4C2×D4×C13118yes—
489C4⋊C4—416no—
490C22⋊C4—216no—
491C22⋊C4—28no—
492C22⋊C4—216no—
493C22⋊C4—216no—
494C22⋊C4—48no—
495C22⋊C4—44no—
496C22⋊C4—48no—
497C22⋊C4—44no—
498C22⋊C4C22⋊C4×C131116yescomplemented
499C23—22no—
500C23—22no—
501C23—24no—
502C23—24no—
503C23—24no—
504C23—22no—
505C23—24no—
506C23—24no—
507C23—24no—
508C23—22no—
509C23—24no—
510C23—24no—
511C23—24no—
512C23—24no—
513C23—28no—
514C23—28no—
515C23—28no—
516C23—28no—
517C23—28no—
518C23—28no—
519C23—28no—
520C23—28no—
521C23—22no—
522C23—22no—
523C23—24no—
524C23—24no—
525C23—22no—
526C23—24no—
527C23—24no—
528C23—24no—
529C23—22no—
530C23—24no—
531C23—24no—
532C23—232no—
533C23—232no—
534C23—416no—
535C23—432no—
536C23—432no—
537C23—432no—
538C23—432no—
539C23—464no—
540C23—44no—
541C23—44no—
542C23—44no—
543C23—44no—
544C23C2×C22⋊C4×C13114yes—
545C23C2×C4⋊C4×C13114yes—
546C23C2×C4⋊C4×C13114yes—
547C23C2×C4⋊C4×C13114yes—
548C23#117×C13114yes—
549C23C4×D4×C13118yes—
550C23#120×C13114yes—
551C23#121×C13118yes—
552C23C22⋊Q8×C13118yes—
553C23C22⋊Q8×C13118yes—
554C23#123×C13114yes—
555C23C23×C4×C13111yescharacteristic
556C23C22×D4×C13112yes—
557C23C22×D4×C13111yescharacteristic
558C23C22×D4×C13112yes—
559C23C22×Q8×C13111yescharacteristic
560C23C2×#41×C13112yes—
561C23C2×#41×C13112yes—
562C23H(5,𝔽2)×C13114yes—
563C2×C4—24no—
564C2×C4—24no—
565C2×C4—28no—
566C2×C4—28no—
567C2×C4—24no—
568C2×C4—24no—
569C2×C4—24no—
570C2×C4—28no—
571C2×C4—28no—
572C2×C4—28no—
573C2×C4—432no—
574C2×C4—432no—
575C2×C4—44no—
576C2×C4—44no—
577C2×C4—44no—
578C2×C4—44no—
579C2×C4—44no—
580C2×C4—44no—
581C2×C4—42no—
582C2×C4—42no—
583C2×C4—42no—
584C2×C4—42no—
585C2×C4—42no—
586C2×C4—42no—
587C2×C4—44no—
588C2×C4—44no—
589C2×C4—44no—
590C2×C4—44no—
591C2×C4C2×C22⋊C4×C13118yescomplemented
592C22—24no—
593C22—24no—
594C22—24no—
595C22—24no—
596C22—28no—
597C22—28no—
598C22—28no—
599C22—28no—
600C22—28no—
601C22—28no—
602C22—28no—
603C22—28no—
604C22—216no—
605C22—216no—
606C22—24no—
607C22—24no—
608C22—24no—
609C22—464no—
610C22—44no—
611C22—44no—
612C22—44no—
613C22—44no—
614C22—48no—
615C22#380×C13118yescomplemented
616C22#385×C13118yescomplemented
617C22C22×C22⋊C4×C13111yescharacteristic
618C22C22×C4⋊C4×C13111yescharacteristic
619C22C2×#117×C13111yescharacteristic
620C22C2×C4×D4×C13112yes—
621C22#518×C13112yes—
622C22C2×#120×C13111yescharacteristic
623C22C2×#121×C13112yes—
624C22C2×C22⋊Q8×C13112yes—
625C22C2×C22⋊Q8×C13112yes—
626C22C2×#123×C13111yescharacteristic
627C22#534×C13112yes—
628C22#543×C13112yes—
629C22D42×C13114yes—
630C22#546×C13114yes—
631C22#546×C13114yes—
632C22#551×C13114yes—
633C4—28no—
634C4—44no—
635C4—48no—
636C4—82no—
637C4—82no—
638C2—28no—
639C2—28no—
640C2—44no—
641C2C2×#380×C13111yescharacteristic
642C2C2×#385×C13111yescharacteristic
643C2#2315×C13111yescharacteristic
644C2D4×C22⋊C4×C13112yes—
645C2#2342×C13112yes—
646C2#2410×C13112yes—
647C2#2412×C13112yes—
648C2#2437×C13114yes—
subgroupG/H
center, socleC24×C131C24
commutatorC23C23×C4×C131
Frattini, cosocleC24C24×C131
prime radicalC26×C131C22
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C24×C131 ◁ G

Complements

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

NH ≅ G/Ntype
3. C2×#385×C131C2semidirect
4. C2×#380×C131C2semidirect
6. #1439×C131C2semidirect
7. C22⋊#95×C131C2semidirect
8. C22⋊#95×C131C2semidirect
12. C22×C4⋊C4×C131C22semidirect
16. C22×C22⋊C4×C131C4semidirect
29. C2×#95×C131C22semidirect
30. C2×#95×C131C22semidirect
31. C2×#95×C131C22semidirect
52. C23×C4×C131C2×C4semidirect
80. C2×C22⋊C4×C131C2×C4semidirect
112. C24×C131C4⋊C4semidirect
173. C22⋊C4×C131C22⋊C4semidirect
266. C2×C4×C131C2×C22⋊C4semidirect
290. C22×C131#380semidirect
291. C22×C131#385semidirect
324. #13877C131direct (N × H)
325. C131#13877direct (N × H)
328. C2×#385C2×C131semidirect
329. C2×#380C2×C131semidirect
331. #1439C2×C131semidirect
332. C22⋊#95C2×C131semidirect
333. C22⋊#95C2×C131semidirect
337. C22×C4⋊C4C22×C131semidirect
341. C22×C22⋊C4C4×C131semidirect
354. C2×#95C22×C131semidirect
355. C2×#95C22×C131semidirect
356. C2×#95C22×C131semidirect
377. C23×C4C2×C4×C131semidirect
405. C2×C22⋊C4C2×C4×C131semidirect
437. C24C4⋊C4×C131semidirect
498. C22⋊C4C22⋊C4×C131semidirect
591. C2×C4C2×C22⋊C4×C131semidirect
615. C22#380×C131semidirect
616. C22#385×C131semidirect

Maximal subgroups

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

subgroupindex
C23×C22⋊C4×C1312
C2×#385×C1312
C2×#380×C1312
C2×#379×C1312
#1439×C1312
C22⋊#95×C1312
#13877131