Finite Group Databasebeta

← C131×#18453 #45704337

Subgroups — C131×#18453 #45704337

Order 33536.

970 conjugacy classes of subgroups.

The subgroup lattice has 680 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#3536×C131C211yesmaximal, characteristic
2#3196×C131C211yesmaximal, characteristic, complemented
3#3189×C131C211yesmaximal, characteristic, complemented
4#2816×C131C211yesmaximal, characteristic, complemented
5#1618×C131C212yesmaximal, complemented
6#1614×C131C212yesmaximal, complemented
7#1606×C131C212yesmaximal, complemented
8#1602×C131C212yesmaximal, complemented
9#1516×C131C211yesmaximal, characteristic, complemented
10#1511×C131C211yesmaximal, characteristic, complemented
11#1471×C131C211yesmaximal, characteristic, complemented
12#562×C131—22no—
13#554×C131—21no—
14#548×C131—21no—
15#547×C131—21no—
16#546×C131—22no—
17#546×C131—21no—
18#543×C131C2212yes—
19#542×C131—21no—
20#539×C131—21no—
21#538×C131C2212yes—
22#537×C131—21no—
23#537×C131—21no—
24#525×C131C2211yescharacteristic
25C2×C22⋊Q8×C131C2211yescharacteristic
26C2×C22⋊Q8×C131C2211yescharacteristic
27C2×#121×C131C2211yescharacteristic
28#485×C131—21no—
29#484×C131—21no—
30#484×C131C2211yescharacteristic
31#484×C131C2212yes—
32#481×C131C2211yescharacteristic
33#470×C131—21no—
34#468×C131—21no—
35#467×C131—22no—
36#452×C131—21no—
37#451×C131—21no—
38#451×C131C2211yescharacteristic
39#451×C131C2212yes—
40#448×C131C2211yescharacteristic
41#407×C131C2211yescharacteristic
42C2×C22⋊C8×C131C2211yescharacteristic
43#399×C131C2212yes—
44#398×C131—21no—
45#394×C131—22no—
46#394×C131—21no—
47#393×C131C2212yes—
48#381×C131C2211yescharacteristic
49#328×C131C2212yes—
50#328×C131C2212yes—
51#328×C131C2212yes—
52#327×C131C2212yes—
53#323×C131C2212yes—
54#323×C131C2212yes—
55C2×#41×C131—22no—
56C2×#41×C131—21no—
57C2×#41×C131D411yescharacteristic
58C22×Q8×C131D411yescharacteristic
59C22×Q8×C131C2311yescharacteristic
60C22×D4×C131D412yes—
61C22×D4×C131D411yescharacteristic
62C23×C4×C131C2311yescharacteristic
63C2×Q16×C131—22no—
64C2×Q16×C131—21no—
65C2×SD16×C131—21no—
66C2×M16×C131—21no—
67C22×C8×C131—21no—
68C4⋊Q8×C131—21no—
69#126×C131—22no—
70#125×C131—22no—
71#124×C131—21no—
72#124×C131—22no—
73#124×C131—22no—
74#123×C131—22no—
75#123×C131—22no—
76#123×C131—22no—
77#123×C131—21no—
78#123×C131—22no—
79C22⋊Q8×C131—21no—
80C22⋊Q8×C131—22no—
81C22⋊Q8×C131—22no—
82C22⋊Q8×C131—22no—
83C22⋊Q8×C131—21no—
84C22⋊Q8×C131—21no—
85C22⋊Q8×C131—22no—
86C22⋊Q8×C131—22no—
87C22⋊Q8×C131—22no—
88C22⋊Q8×C131—21no—
89C22⋊Q8×C131—21no—
90C22⋊Q8×C131—21no—
91C22⋊Q8×C131—21no—
92C22⋊Q8×C131D412yes—
93C22⋊Q8×C131D411yescharacteristic
94C22⋊Q8×C131C2312yes—
95C22⋊Q8×C131C2311yescharacteristic
96#121×C131—21no—
97#121×C131—22no—
98#121×C131—22no—
99#121×C131—22no—
100#121×C131—22no—
101#121×C131—22no—
102#121×C131—21no—
103#121×C131—21no—
104#121×C131—21no—
105#121×C131—21no—
106#121×C131D411yescharacteristic
107#121×C131C2311yescharacteristic
108#120×C131—21no—
109#120×C131—22no—
110C4×Q8×C131—21no—
111C4×D4×C131—22no—
112C4×D4×C131—21no—
113C4×D4×C131—21no—
114C4×D4×C131—21no—
115C4×D4×C131—22no—
116#117×C131D411yescharacteristic
117C2×C4⋊C4×C131—21no—
118C2×C4⋊C4×C131—21no—
119C2×C4⋊C4×C131—21no—
120C2×C4⋊C4×C131—22no—
121C2×C4⋊C4×C131D411yescharacteristic
122C2×C4⋊C4×C131D411yescharacteristic
123C2×C4⋊C4×C131C2311yescharacteristic
124C2×C22⋊C4×C131—21no—
125C2×C22⋊C4×C131—22no—
126C2×C22⋊C4×C131—21no—
127C2×C22⋊C4×C131—22no—
128C2×C22⋊C4×C131—22no—
129C2×C22⋊C4×C131—21no—
130C2×C22⋊C4×C131C2312yes—
131#107×C131—22no—
132#107×C131—21no—
133#106×C131—21no—
134#103×C131—22no—
135#103×C131—21no—
136#103×C131—21no—
137#103×C131—22no—
138#103×C131—21no—
139#102×C131—21no—
140C22⋊C8×C131—21no—
141C22⋊C8×C131—21no—
142C22⋊C8×C131C2312yes—
143C22⋊C8×C131C2311yescharacteristic
144C22⋊C8×C131C2311yescharacteristic
145#95×C131—22no—
146#95×C131—21no—
147#95×C131C2312yes—
148C24×C131C2×D412yes—
149C24×C131C2×D411yescharacteristic
150#41×C131—81no—
151#41×C131—84no—
152#41×C131—82no—
153C2×Q8×C131—22no—
154C2×Q8×C131—21no—
155C2×Q8×C131—21no—
156C2×Q8×C131—21no—
157C2×Q8×C131—81no—
158C2×Q8×C131—81no—
159C2×Q8×C131C2×D411yescharacteristic
160C2×Q8×C131C2×D412yes—
161C2×D4×C131—21no—
162C2×D4×C131—22no—
163C2×D4×C131—21no—
164C2×D4×C131—22no—
165C2×D4×C131—22no—
166C2×D4×C131—21no—
167C2×D4×C131—22no—
168C2×D4×C131—21no—
169C2×D4×C131—21no—
170C2×D4×C131—81no—
171C2×D4×C131—82no—
172C2×D4×C131C2×D411yescharacteristic
173C22×C4×C131—21no—
174C22×C4×C131—22no—
175C22×C4×C131—22no—
176C22×C4×C131—22no—
177C22×C4×C131—21no—
178C22×C4×C131—21no—
179C22×C4×C131—22no—
180C22×C4×C131—21no—
181C22×C4×C131—21no—
182C22×C4×C131—81no—
183C22×C4×C131C2×D412yes—
184C22×C4×C131C2×D411yescharacteristic
185C22×C4×C131C2×D411yescharacteristic
186C22×C4×C131C2×D411yescharacteristic
187C22×C4×C131C2×D411yescharacteristic
188C22×C4×C131C2×D411yescharacteristic
189C22×C4×C131C2411yescharacteristic
190Q16×C131—82no—
191Q16×C131—81no—
192SD16×C131—81no—
193M16×C131—81no—
194C2×C8×C131—21no—
195C2×C8×C131—22no—
196C2×C8×C131—21no—
197C2×C8×C131—81no—
198C4⋊C4×C131—22no—
199C4⋊C4×C131—22no—
200C4⋊C4×C131—22no—
201C4⋊C4×C131—22no—
202C4⋊C4×C131—21no—
203C4⋊C4×C131—21no—
204C4⋊C4×C131—22no—
205C4⋊C4×C131—21no—
206C4⋊C4×C131—21no—
207C4⋊C4×C131—22no—
208C4⋊C4×C131—21no—
209C4⋊C4×C131—21no—
210C4⋊C4×C131—21no—
211C4⋊C4×C131—41no—
212C4⋊C4×C131—41no—
213C4⋊C4×C131—82no—
214C4⋊C4×C131C2×D411yescharacteristic
215C4⋊C4×C131C2×D412yes—
216C4⋊C4×C131C2×D411yescharacteristic
217C22⋊C4×C131—22no—
218C22⋊C4×C131—22no—
219C22⋊C4×C131—22no—
220C22⋊C4×C131—22no—
221C22⋊C4×C131—22no—
222C22⋊C4×C131—22no—
223C22⋊C4×C131—21no—
224C22⋊C4×C131—21no—
225C22⋊C4×C131—22no—
226C22⋊C4×C131—21no—
227C22⋊C4×C131—21no—
228C22⋊C4×C131—22no—
229C22⋊C4×C131—22no—
230C22⋊C4×C131—21no—
231C22⋊C4×C131—41no—
232C22⋊C4×C131—41no—
233C22⋊C4×C131—81no—
234C22⋊C4×C131—82no—
235C22⋊C4×C131—82no—
236C42×C131—22no—
237C42×C131—21no—
238C23×C131—22no—
239C23×C131—22no—
240C23×C131—21no—
241C23×C131—24no—
242C23×C131—41no—
243C23×C131—41no—
244C23×C131—42no—
245C23×C131—42no—
246C23×C131#12011yescharacteristic
247C23×C131#12011yescharacteristic
248C23×C131C22×D411yescharacteristic
249Q8×C131—42no—
250Q8×C131—41no—
251Q8×C131—42no—
252Q8×C131—41no—
253Q8×C131—41no—
254Q8×C131—42no—
255Q8×C131—82no—
256D4×C131—41no—
257D4×C131—42no—
258D4×C131—44no—
259D4×C131—42no—
260D4×C131—42no—
261D4×C131—81no—
262D4×C131—82no—
263D4×C131—81no—
264D4×C131—82no—
265D4×C131—82no—
266C2×C4×C131—21no—
267C2×C4×C131—22no—
268C2×C4×C131—21no—
269C2×C4×C131—22no—
270C2×C4×C131—21no—
271C2×C4×C131—22no—
272C2×C4×C131—41no—
273C2×C4×C131—41no—
274C2×C4×C131—41no—
275C2×C4×C131—41no—
276C2×C4×C131—41no—
277C2×C4×C131—41no—
278C2×C4×C131—42no—
279C2×C4×C131—42no—
280C2×C4×C131—42no—
281C2×C4×C131—42no—
282C2×C4×C131—41no—
283C2×C4×C131—42no—
284C2×C4×C131—42no—
285C2×C4×C131—41no—
286C2×C4×C131—41no—
287C2×C4×C131—41no—
288C2×C4×C131—42no—
289C2×C4×C131—81no—
290C2×C4×C131—82no—
291C2×C4×C131—82no—
292C2×C4×C131—82no—
293C2×C4×C131#12011yescharacteristic
294C2×C4×C131#12011yescharacteristic
295C2×C4×C131C22×D411yescharacteristic
296C2×C4×C131C22×D411yescharacteristic
297C8×C131—42no—
298C8×C131—41no—
299C8×C131—41no—
300C22×C131—21no—
301C22×C131—21no—
302C22×C131—21no—
303C22×C131—21no—
304C22×C131—21no—
305C22×C131—21no—
306C22×C131—21no—
307C22×C131—21no—
308C22×C131—41no—
309C22×C131—42no—
310C22×C131—41no—
311C22×C131—42no—
312C22×C131—41no—
313C22×C131—42no—
314C22×C131—82no—
315C22×C131—84no—
316C22×C131C2×#12011yescharacteristic
317C22×C131#57812yes—
318C4×C131—21no—
319C4×C131—21no—
320C4×C131—21no—
321C4×C131—21no—
322C4×C131—41no—
323C4×C131—42no—
324C4×C131—42no—
325C4×C131—41no—
326C4×C131—41no—
327C4×C131—42no—
328C4×C131—82no—
329C4×C131—81no—
330C4×C131—81no—
331C2×C131—22no—
332C2×C131—41no—
333C2×C131—41no—
334C2×C131—81no—
335C2×C131—82no—
336C2×C131#301111yescharacteristic
337C2×C131#301911yescharacteristic
338C2×C131#302611yescharacteristic
339#18453C13111yesmaximal, characteristic, direct product factor, Sylow
340C131#1845311yescharacteristic, direct product factor, Sylow
341#3536C2×C13111yescharacteristic
342#3196C2×C13111yescharacteristic, complemented
343#3189C2×C13111yescharacteristic, complemented
344#2816C2×C13111yescharacteristic, complemented
345#1618C2×C13112yescomplemented
346#1614C2×C13112yescomplemented
347#1606C2×C13112yescomplemented
348#1602C2×C13112yescomplemented
349#1516C2×C13111yescharacteristic, complemented
350#1511C2×C13111yescharacteristic, complemented
351#1471C2×C13111yescharacteristic, complemented
352#562—22no—
353#554—21no—
354#548—21no—
355#547—21no—
356#546—22no—
357#546—21no—
358#543C22×C13112yes—
359#542—21no—
360#539—21no—
361#538C22×C13112yes—
362#537—21no—
363#537—21no—
364#525C22×C13111yescharacteristic
365C2×C22⋊Q8C22×C13111yescharacteristic
366C2×C22⋊Q8C22×C13111yescharacteristic
367C2×#121C22×C13111yescharacteristic
368#485—21no—
369#484—21no—
370#484C22×C13111yescharacteristic
371#484C22×C13112yes—
372#481C22×C13111yescharacteristic
373#470—21no—
374#468—21no—
375#467—22no—
376#452—21no—
377#451—21no—
378#451C22×C13111yescharacteristic
379#451C22×C13112yes—
380#448C22×C13111yescharacteristic
381#407C22×C13111yescharacteristic
382C2×C22⋊C8C22×C13111yescharacteristic
383#399C22×C13112yes—
384#398—21no—
385#394—21no—
386#394—22no—
387#393C22×C13112yes—
388#381C22×C13111yescharacteristic
389#328C22×C13112yes—
390#328C22×C13112yes—
391#328C22×C13112yes—
392#327C22×C13112yes—
393#323C22×C13112yes—
394#323C22×C13112yes—
395C2×#41—22no—
396C2×#41—21no—
397C2×#41D4×C13111yescharacteristic
398C22×Q8D4×C13111yescharacteristic
399C22×Q8C23×C13111yescharacteristic
400C22×D4D4×C13112yes—
401C22×D4D4×C13111yescharacteristic
402C23×C4C23×C13111yescharacteristic
403C2×Q16—22no—
404C2×Q16—21no—
405C2×SD16—21no—
406C2×M16—21no—
407C22×C8—21no—
408C4⋊Q8—21no—
409#126—22no—
410#125—22no—
411#124—21no—
412#124—22no—
413#124—22no—
414#123—22no—
415#123—22no—
416#123—22no—
417#123—21no—
418#123—22no—
419C22⋊Q8—21no—
420C22⋊Q8—22no—
421C22⋊Q8—22no—
422C22⋊Q8—22no—
423C22⋊Q8—21no—
424C22⋊Q8—21no—
425C22⋊Q8—22no—
426C22⋊Q8—22no—
427C22⋊Q8—22no—
428C22⋊Q8—21no—
429C22⋊Q8—21no—
430C22⋊Q8—21no—
431C22⋊Q8—21no—
432C22⋊Q8D4×C13112yes—
433C22⋊Q8D4×C13111yescharacteristic
434C22⋊Q8C23×C13112yes—
435C22⋊Q8C23×C13111yescharacteristic
436#121—21no—
437#121—22no—
438#121—22no—
439#121—22no—
440#121—22no—
441#121—22no—
442#121—21no—
443#121—21no—
444#121—21no—
445#121—21no—
446#121D4×C13111yescharacteristic
447#121C23×C13111yescharacteristic
448#120—21no—
449#120—22no—
450C4×Q8—21no—
451C4×D4—22no—
452C4×D4—21no—
453C4×D4—21no—
454C4×D4—21no—
455C4×D4—22no—
456#117D4×C13111yescharacteristic
457C2×C4⋊C4—21no—
458C2×C4⋊C4—21no—
459C2×C4⋊C4—21no—
460C2×C4⋊C4—22no—
461C2×C4⋊C4D4×C13111yescharacteristic
462C2×C4⋊C4D4×C13111yescharacteristic
463C2×C4⋊C4C23×C13111yescharacteristic
464C2×C22⋊C4—21no—
465C2×C22⋊C4—22no—
466C2×C22⋊C4—21no—
467C2×C22⋊C4—21no—
468C2×C22⋊C4—22no—
469C2×C22⋊C4—22no—
470C2×C22⋊C4C23×C13112yes—
471#107—22no—
472#107—21no—
473#106—21no—
474#103—22no—
475#103—21no—
476#103—21no—
477#103—22no—
478#103—21no—
479#102—21no—
480C22⋊C8—21no—
481C22⋊C8—21no—
482C22⋊C8C23×C13112yes—
483C22⋊C8C23×C13111yescharacteristic
484C22⋊C8C23×C13111yescharacteristic
485#95—21no—
486#95—22no—
487#95C23×C13112yes—
488C24C2×D4×C13112yes—
489C24C2×D4×C13111yescharacteristic
490#41—81no—
491#41—84no—
492#41—82no—
493C2×Q8—22no—
494C2×Q8—21no—
495C2×Q8—21no—
496C2×Q8—21no—
497C2×Q8—81no—
498C2×Q8—81no—
499C2×Q8C2×D4×C13111yescharacteristic
500C2×Q8C2×D4×C13112yes—
501C2×D4—21no—
502C2×D4—22no—
503C2×D4—21no—
504C2×D4—22no—
505C2×D4—22no—
506C2×D4—21no—
507C2×D4—22no—
508C2×D4—21no—
509C2×D4—21no—
510C2×D4—81no—
511C2×D4—82no—
512C2×D4C2×D4×C13111yescharacteristic
513C22×C4—21no—
514C22×C4—22no—
515C22×C4—22no—
516C22×C4—22no—
517C22×C4—21no—
518C22×C4—21no—
519C22×C4—22no—
520C22×C4—21no—
521C22×C4—21no—
522C22×C4—81no—
523C22×C4C2×D4×C13112yes—
524C22×C4C2×D4×C13111yescharacteristic
525C22×C4C2×D4×C13111yescharacteristic
526C22×C4C2×D4×C13111yescharacteristic
527C22×C4C2×D4×C13111yescharacteristic
528C22×C4C2×D4×C13111yescharacteristic
529C22×C4C24×C13111yescharacteristic
530Q16—82no—
531Q16—81no—
532SD16—81no—
533M16—81no—
534C2×C8—21no—
535C2×C8—22no—
536C2×C8—21no—
537C2×C8—81no—
538C4⋊C4—22no—
539C4⋊C4—22no—
540C4⋊C4—22no—
541C4⋊C4—22no—
542C4⋊C4—21no—
543C4⋊C4—21no—
544C4⋊C4—22no—
545C4⋊C4—21no—
546C4⋊C4—21no—
547C4⋊C4—22no—
548C4⋊C4—21no—
549C4⋊C4—21no—
550C4⋊C4—21no—
551C4⋊C4—41no—
552C4⋊C4—41no—
553C4⋊C4—82no—
554C4⋊C4C2×D4×C13111yescharacteristic
555C4⋊C4C2×D4×C13112yes—
556C4⋊C4C2×D4×C13111yescharacteristic
557C22⋊C4—22no—
558C22⋊C4—22no—
559C22⋊C4—22no—
560C22⋊C4—22no—
561C22⋊C4—22no—
562C22⋊C4—22no—
563C22⋊C4—21no—
564C22⋊C4—21no—
565C22⋊C4—22no—
566C22⋊C4—21no—
567C22⋊C4—21no—
568C22⋊C4—22no—
569C22⋊C4—22no—
570C22⋊C4—21no—
571C22⋊C4—41no—
572C22⋊C4—41no—
573C22⋊C4—81no—
574C22⋊C4—82no—
575C22⋊C4—82no—
576C42—22no—
577C42—21no—
578C23—22no—
579C23—22no—
580C23—21no—
581C23—24no—
582C23—41no—
583C23—41no—
584C23—42no—
585C23—42no—
586C23#120×C13111yescharacteristic
587C23#120×C13111yescharacteristic
588C23C22×D4×C13111yescharacteristic
589Q8—42no—
590Q8—41no—
591Q8—42no—
592Q8—41no—
593Q8—41no—
594Q8—42no—
595Q8—82no—
596D4—41no—
597D4—42no—
598D4—44no—
599D4—42no—
600D4—42no—
601D4—81no—
602D4—82no—
603D4—81no—
604D4—82no—
605D4—82no—
606C2×C4—21no—
607C2×C4—22no—
608C2×C4—21no—
609C2×C4—22no—
610C2×C4—21no—
611C2×C4—22no—
612C2×C4—41no—
613C2×C4—41no—
614C2×C4—41no—
615C2×C4—41no—
616C2×C4—41no—
617C2×C4—41no—
618C2×C4—42no—
619C2×C4—42no—
620C2×C4—42no—
621C2×C4—42no—
622C2×C4—41no—
623C2×C4—42no—
624C2×C4—42no—
625C2×C4—41no—
626C2×C4—41no—
627C2×C4—41no—
628C2×C4—42no—
629C2×C4—81no—
630C2×C4—82no—
631C2×C4—82no—
632C2×C4—82no—
633C2×C4#120×C13111yescharacteristic
634C2×C4#120×C13111yescharacteristic
635C2×C4C22×D4×C13111yescharacteristic
636C2×C4C22×D4×C13111yescharacteristic
637C8—42no—
638C8—41no—
639C8—41no—
640C22—21no—
641C22—21no—
642C22—21no—
643C22—21no—
644C22—21no—
645C22—21no—
646C22—21no—
647C22—21no—
648C22—41no—
649C22—42no—
650C22—41no—
651C22—42no—
652C22—41no—
653C22—42no—
654C22—82no—
655C22—84no—
656C22C2×#120×C13111yescharacteristic
657C22#578×C13112yes—
658C4—21no—
659C4—21no—
660C4—21no—
661C4—21no—
662C4—41no—
663C4—42no—
664C4—42no—
665C4—41no—
666C4—41no—
667C4—42no—
668C4—82no—
669C4—81no—
670C4—81no—
671C2—22no—
672C2—41no—
673C2—41no—
674C2—82no—
675C2—81no—
676C2#3011×C13111yescharacteristic
677C2#3019×C13111yescharacteristic
678C2#3026×C13111yescharacteristic
subgroupG/H
center, socleC22×C131C2×#120
commutator, Frattini, cosocleC22×C4C24×C131
prime radical#3536×C131C2
LCSG ▷ C22×C4 ▷ C22 ▷ C1
UCSC1 ◁ C22×C131 ◁ C23×C4×C131 ◁ G

Complements

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

NH ≅ G/Ntype
2. #3196×C131C2semidirect
3. #3189×C131C2semidirect
4. #2816×C131C2semidirect
5. #1618×C131C2semidirect
6. #1614×C131C2semidirect
7. #1606×C131C2semidirect
8. #1602×C131C2semidirect
9. #1516×C131C2semidirect
10. #1511×C131C2semidirect
11. #1471×C131C2semidirect
339. #18453C131direct (N × H)
340. C131#18453direct (N × H)
342. #3196C2×C131semidirect
343. #3189C2×C131semidirect
344. #2816C2×C131semidirect
345. #1618C2×C131semidirect
346. #1614C2×C131semidirect
347. #1606C2×C131semidirect
348. #1602C2×C131semidirect
349. #1516C2×C131semidirect
350. #1511C2×C131semidirect
351. #1471C2×C131semidirect

Maximal subgroups

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

subgroupindex
#3536×C1312
#3196×C1312
#3189×C1312
#2816×C1312
#1618×C1312
#1614×C1312
#1606×C1312
#1602×C1312
#1516×C1312
#1511×C1312
#1471×C1312
#18453131