Finite Group Databasebeta

← C131×#18457 #45704341

Subgroups — C131×#18457 #45704341

Order 33536.

954 conjugacy classes of subgroups.

The subgroup lattice has 674 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#3187×C131C211yesmaximal, characteristic, complemented
4#2817×C131C211yesmaximal, characteristic, complemented
5#1616×C131C212yesmaximal, complemented
6#1615×C131C212yesmaximal, complemented
7#1604×C131C212yesmaximal, complemented
8#1603×C131C212yesmaximal, complemented
9#1516×C131C211yesmaximal, characteristic, complemented
10#1510×C131C211yesmaximal, characteristic, complemented
11#1472×C131C211yesmaximal, characteristic, complemented
12#562×C131—22no—
13#554×C131—21no—
14#548×C131—21no—
15#547×C131—21no—
16#546×C131—21no—
17#546×C131—22no—
18#543×C131—21no—
19#542×C131—21no—
20#539×C131C2212yes—
21#538×C131—21no—
22#537×C131—21no—
23#537×C131C2212yes—
24#525×C131C2211yescharacteristic
25C2×C22⋊Q8×C131C2211yescharacteristic
26C2×C22⋊Q8×C131C2211yescharacteristic
27C2×#121×C131C2211yescharacteristic
28#485×C131—21no—
29#484×C131C2211yescharacteristic, complemented
30#483×C131—21no—
31#481×C131C2212yes—
32#481×C131C2211yescharacteristic, complemented
33#470×C131—21no—
34#468×C131—21no—
35#465×C131—22no—
36#452×C131—21no—
37#451×C131C2211yescharacteristic, complemented
38#450×C131—21no—
39#448×C131C2212yes—
40#448×C131C2211yescharacteristic, complemented
41#407×C131C2211yescharacteristic
42C2×C22⋊C8×C131C2211yescharacteristic
43#400×C131—21no—
44#400×C131C2212yescomplemented
45#397×C131—22no—
46#395×C131—21no—
47#395×C131C2212yescomplemented
48#381×C131C2211yescharacteristic
49#328×C131C2212yescomplemented
50#327×C131C2212yes—
51#327×C131C2212yes—
52#327×C131C2212yescomplemented
53#324×C131C2212yescomplemented
54#324×C131C2212yescomplemented
55C2×#41×C131—21no—
56C2×#41×C131—22no—
57C2×#41×C131D411yescharacteristic
58C22×Q8×C131D411yescharacteristic
59C22×Q8×C131C2311yescharacteristic
60C22×D4×C131—21no—
61C22×D4×C131D411yescharacteristic
62C23×C4×C131C2311yescharacteristic
63C2×Q16×C131—21no—
64C2×SD16×C131—22no—
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—22no—
72#124×C131—21no—
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—22no—
84C22⋊Q8×C131—21no—
85C22⋊Q8×C131—21no—
86C22⋊Q8×C131—21no—
87C22⋊Q8×C131—21no—
88C22⋊Q8×C131—22no—
89C22⋊Q8×C131—22no—
90C22⋊Q8×C131—21no—
91C22⋊Q8×C131—21no—
92C22⋊Q8×C131—21no—
93C22⋊Q8×C131—21no—
94C22⋊Q8×C131D411yescharacteristic
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—21no—
102#121×C131—21no—
103#121×C131—22no—
104#121×C131D412yes—
105#121×C131D411yescharacteristic
106#121×C131C2312yes—
107#121×C131C2311yescharacteristic
108#120×C131—22no—
109#120×C131—21no—
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—22no—
120C2×C4⋊C4×C131D411yescharacteristic
121C2×C4⋊C4×C131D411yescharacteristic
122C2×C4⋊C4×C131C2311yescharacteristic
123C2×C4⋊C4×C131C2312yes—
124C2×C22⋊C4×C131—22no—
125C2×C22⋊C4×C131—21no—
126C2×C22⋊C4×C131—21no—
127C2×C22⋊C4×C131—21no—
128C2×C22⋊C4×C131D412yes—
129#107×C131—21no—
130#106×C131—22no—
131#106×C131—21no—
132#103×C131—21no—
133#103×C131—22no—
134#103×C131—21no—
135#103×C131—21no—
136#102×C131—22no—
137#102×C131—21no—
138C22⋊C8×C131—21no—
139C22⋊C8×C131—21no—
140C22⋊C8×C131C2312yes—
141C22⋊C8×C131C2311yescharacteristic
142C22⋊C8×C131C2311yescharacteristic
143#95×C131—22no—
144#95×C131—21no—
145#95×C131—22no—
146#95×C131—22no—
147#95×C131C2312yes—
148C24×C131—21no—
149C24×C131C2×D411yescharacteristic
150#41×C131—84no—
151#41×C131—81no—
152#41×C131—82no—
153C2×Q8×C131—22no—
154C2×Q8×C131—21no—
155C2×Q8×C131—21no—
156C2×Q8×C131—21no—
157C2×Q8×C131—21no—
158C2×Q8×C131—81no—
159C2×Q8×C131—81no—
160C2×Q8×C131C2×D411yescharacteristic
161C2×D4×C131—21no—
162C2×D4×C131—21no—
163C2×D4×C131—22no—
164C2×D4×C131—22no—
165C2×D4×C131—22no—
166C2×D4×C131—21no—
167C2×D4×C131—22no—
168C2×D4×C131—21no—
169C2×D4×C131—81no—
170C2×D4×C131—82no—
171C2×D4×C131C2×D411yescharacteristic
172C2×D4×C131C2×D412yes—
173C22×C4×C131—22no—
174C22×C4×C131—22no—
175C22×C4×C131—22no—
176C22×C4×C131—21no—
177C22×C4×C131—21no—
178C22×C4×C131—22no—
179C22×C4×C131—21no—
180C22×C4×C131—21no—
181C22×C4×C131—81no—
182C22×C4×C131C2×D412yes—
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—81no—
191SD16×C131—82no—
192SD16×C131—81no—
193M16×C131—81no—
194C2×C8×C131—22no—
195C2×C8×C131—21no—
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—21no—
205C4⋊C4×C131—21no—
206C4⋊C4×C131—22no—
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×D412yes—
215C4⋊C4×C131C2×D411yescharacteristic
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—21no—
223C22⋊C4×C131—22no—
224C22⋊C4×C131—22no—
225C22⋊C4×C131—21no—
226C22⋊C4×C131—21no—
227C22⋊C4×C131—22no—
228C22⋊C4×C131—21no—
229C22⋊C4×C131—22no—
230C22⋊C4×C131—21no—
231C22⋊C4×C131—41no—
232C22⋊C4×C131—41no—
233C22⋊C4×C131—81no—
234C42×C131—22no—
235C42×C131—21no—
236C23×C131—22no—
237C23×C131—22no—
238C23×C131—21no—
239C23×C131—41no—
240C23×C131—41no—
241C23×C131—42no—
242C23×C131—81no—
243C23×C131—81no—
244C23×C131#12011yescharacteristic
245C23×C131#12011yescharacteristic
246C23×C131C22×D411yescharacteristic
247Q8×C131—41no—
248Q8×C131—42no—
249Q8×C131—42no—
250Q8×C131—41no—
251Q8×C131—41no—
252Q8×C131—81no—
253Q8×C131—82no—
254D4×C131—42no—
255D4×C131—41no—
256D4×C131—42no—
257D4×C131—42no—
258D4×C131—44no—
259D4×C131—42no—
260D4×C131—82no—
261D4×C131—81no—
262D4×C131—82no—
263D4×C131—82no—
264C2×C4×C131—21no—
265C2×C4×C131—22no—
266C2×C4×C131—21no—
267C2×C4×C131—22no—
268C2×C4×C131—21no—
269C2×C4×C131—22no—
270C2×C4×C131—24no—
271C2×C4×C131—41no—
272C2×C4×C131—41no—
273C2×C4×C131—41no—
274C2×C4×C131—41no—
275C2×C4×C131—41no—
276C2×C4×C131—41no—
277C2×C4×C131—42no—
278C2×C4×C131—42no—
279C2×C4×C131—42no—
280C2×C4×C131—42no—
281C2×C4×C131—42no—
282C2×C4×C131—42no—
283C2×C4×C131—41no—
284C2×C4×C131—41no—
285C2×C4×C131—42no—
286C2×C4×C131—81no—
287C2×C4×C131—82no—
288C2×C4×C131—82no—
289C2×C4×C131—82no—
290C2×C4×C131#12011yescharacteristic
291C2×C4×C131#12011yescharacteristic
292C2×C4×C131C22×D411yescharacteristic
293C2×C4×C131C22×D411yescharacteristic
294C8×C131—42no—
295C8×C131—41no—
296C8×C131—41no—
297C22×C131—21no—
298C22×C131—21no—
299C22×C131—21no—
300C22×C131—21no—
301C22×C131—21no—
302C22×C131—21no—
303C22×C131—21no—
304C22×C131—21no—
305C22×C131—41no—
306C22×C131—42no—
307C22×C131—41no—
308C22×C131—42no—
309C22×C131—41no—
310C22×C131—42no—
311C22×C131—82no—
312C22×C131—162no—
313C22×C131C2×#12011yescharacteristic
314C22×C131#57712yes—
315C4×C131—21no—
316C4×C131—21no—
317C4×C131—21no—
318C4×C131—21no—
319C4×C131—42no—
320C4×C131—42no—
321C4×C131—41no—
322C4×C131—41no—
323C4×C131—41no—
324C4×C131—42no—
325C4×C131—82no—
326C4×C131—81no—
327C4×C131—81no—
328C2×C131—22no—
329C2×C131—41no—
330C2×C131—41no—
331C2×C131—81no—
332C2×C131—82no—
333C2×C131#300911yescharacteristic
334C2×C131#302011yescharacteristic
335C2×C131#302611yescharacteristic
336#18457C13111yesmaximal, characteristic, direct product factor, Sylow
337C131#1845711yescharacteristic, direct product factor, Sylow
338#3536C2×C13111yescharacteristic
339#3196C2×C13111yescharacteristic, complemented
340#3187C2×C13111yescharacteristic, complemented
341#2817C2×C13111yescharacteristic, complemented
342#1616C2×C13112yescomplemented
343#1615C2×C13112yescomplemented
344#1604C2×C13112yescomplemented
345#1603C2×C13112yescomplemented
346#1516C2×C13111yescharacteristic, complemented
347#1510C2×C13111yescharacteristic, complemented
348#1472C2×C13111yescharacteristic, complemented
349#562—22no—
350#554—21no—
351#548—21no—
352#547—21no—
353#546—21no—
354#546—22no—
355#543—21no—
356#542—21no—
357#539C22×C13112yes—
358#538—21no—
359#537—21no—
360#537C22×C13112yes—
361#525C22×C13111yescharacteristic
362C2×C22⋊Q8C22×C13111yescharacteristic
363C2×C22⋊Q8C22×C13111yescharacteristic
364C2×#121C22×C13111yescharacteristic
365#485—21no—
366#484C22×C13111yescharacteristic, complemented
367#483—21no—
368#481C22×C13112yes—
369#481C22×C13111yescharacteristic, complemented
370#470—21no—
371#468—21no—
372#465—22no—
373#452—21no—
374#451C22×C13111yescharacteristic, complemented
375#450—21no—
376#448C22×C13112yes—
377#448C22×C13111yescharacteristic, complemented
378#407C22×C13111yescharacteristic
379C2×C22⋊C8C22×C13111yescharacteristic
380#400—21no—
381#400C22×C13112yescomplemented
382#397—22no—
383#395—21no—
384#395C22×C13112yescomplemented
385#381C22×C13111yescharacteristic
386#328C22×C13112yescomplemented
387#327C22×C13112yes—
388#327C22×C13112yes—
389#327C22×C13112yescomplemented
390#324C22×C13112yescomplemented
391#324C22×C13112yescomplemented
392C2×#41—21no—
393C2×#41—22no—
394C2×#41D4×C13111yescharacteristic
395C22×Q8D4×C13111yescharacteristic
396C22×Q8C23×C13111yescharacteristic
397C22×D4—21no—
398C22×D4D4×C13111yescharacteristic
399C23×C4C23×C13111yescharacteristic
400C2×Q16—21no—
401C2×SD16—22no—
402C2×SD16—21no—
403C2×M16—21no—
404C22×C8—21no—
405C4⋊Q8—21no—
406#126—22no—
407#125—22no—
408#124—22no—
409#124—21no—
410#124—22no—
411#123—22no—
412#123—22no—
413#123—22no—
414#123—21no—
415#123—22no—
416C22⋊Q8—21no—
417C22⋊Q8—22no—
418C22⋊Q8—22no—
419C22⋊Q8—22no—
420C22⋊Q8—22no—
421C22⋊Q8—21no—
422C22⋊Q8—21no—
423C22⋊Q8—21no—
424C22⋊Q8—21no—
425C22⋊Q8—22no—
426C22⋊Q8—22no—
427C22⋊Q8—21no—
428C22⋊Q8—21no—
429C22⋊Q8—21no—
430C22⋊Q8—21no—
431C22⋊Q8D4×C13111yescharacteristic
432C22⋊Q8C23×C13111yescharacteristic
433#121—21no—
434#121—22no—
435#121—22no—
436#121—22no—
437#121—22no—
438#121—21no—
439#121—21no—
440#121—22no—
441#121D4×C13112yes—
442#121D4×C13111yescharacteristic
443#121C23×C13112yes—
444#121C23×C13111yescharacteristic
445#120—22no—
446#120—21no—
447C4×Q8—21no—
448C4×D4—22no—
449C4×D4—21no—
450C4×D4—21no—
451C4×D4—21no—
452C4×D4—22no—
453#117D4×C13111yescharacteristic
454C2×C4⋊C4—21no—
455C2×C4⋊C4—21no—
456C2×C4⋊C4—22no—
457C2×C4⋊C4D4×C13111yescharacteristic
458C2×C4⋊C4D4×C13111yescharacteristic
459C2×C4⋊C4C23×C13111yescharacteristic
460C2×C4⋊C4C23×C13112yes—
461C2×C22⋊C4—22no—
462C2×C22⋊C4—21no—
463C2×C22⋊C4—21no—
464C2×C22⋊C4—21no—
465C2×C22⋊C4D4×C13112yes—
466#107—21no—
467#106—22no—
468#106—21no—
469#103—21no—
470#103—22no—
471#103—21no—
472#103—21no—
473#102—22no—
474#102—21no—
475C22⋊C8—21no—
476C22⋊C8—21no—
477C22⋊C8C23×C13111yescharacteristic
478C22⋊C8C23×C13111yescharacteristic
479C22⋊C8C23×C13112yes—
480#95—21no—
481#95—22no—
482#95—22no—
483#95—22no—
484#95C23×C13112yes—
485C24—21no—
486C24C2×D4×C13111yescharacteristic
487#41—84no—
488#41—81no—
489#41—82no—
490C2×Q8—22no—
491C2×Q8—21no—
492C2×Q8—21no—
493C2×Q8—21no—
494C2×Q8—21no—
495C2×Q8—81no—
496C2×Q8—81no—
497C2×Q8C2×D4×C13111yescharacteristic
498C2×D4—21no—
499C2×D4—21no—
500C2×D4—22no—
501C2×D4—22no—
502C2×D4—22no—
503C2×D4—21no—
504C2×D4—22no—
505C2×D4—21no—
506C2×D4—81no—
507C2×D4—82no—
508C2×D4C2×D4×C13111yescharacteristic
509C2×D4C2×D4×C13112yes—
510C22×C4—22no—
511C22×C4—22no—
512C22×C4—22no—
513C22×C4—21no—
514C22×C4—21no—
515C22×C4—22no—
516C22×C4—21no—
517C22×C4—21no—
518C22×C4—81no—
519C22×C4C2×D4×C13112yes—
520C22×C4C2×D4×C13112yes—
521C22×C4C2×D4×C13111yescharacteristic
522C22×C4C2×D4×C13111yescharacteristic
523C22×C4C2×D4×C13111yescharacteristic
524C22×C4C2×D4×C13111yescharacteristic
525C22×C4C2×D4×C13111yescharacteristic
526C22×C4C24×C13111yescharacteristic
527Q16—81no—
528SD16—82no—
529SD16—81no—
530M16—81no—
531C2×C8—22no—
532C2×C8—21no—
533C2×C8—21no—
534C2×C8—81no—
535C4⋊C4—22no—
536C4⋊C4—22no—
537C4⋊C4—22no—
538C4⋊C4—22no—
539C4⋊C4—21no—
540C4⋊C4—21no—
541C4⋊C4—21no—
542C4⋊C4—21no—
543C4⋊C4—22no—
544C4⋊C4—22no—
545C4⋊C4—21no—
546C4⋊C4—21no—
547C4⋊C4—21no—
548C4⋊C4—41no—
549C4⋊C4—41no—
550C4⋊C4—82no—
551C4⋊C4C2×D4×C13112yes—
552C4⋊C4C2×D4×C13111yescharacteristic
553C4⋊C4C2×D4×C13111yescharacteristic
554C22⋊C4—22no—
555C22⋊C4—22no—
556C22⋊C4—22no—
557C22⋊C4—22no—
558C22⋊C4—22no—
559C22⋊C4—21no—
560C22⋊C4—22no—
561C22⋊C4—22no—
562C22⋊C4—21no—
563C22⋊C4—21no—
564C22⋊C4—22no—
565C22⋊C4—21no—
566C22⋊C4—22no—
567C22⋊C4—21no—
568C22⋊C4—41no—
569C22⋊C4—41no—
570C22⋊C4—81no—
571C42—22no—
572C42—21no—
573C23—22no—
574C23—22no—
575C23—21no—
576C23—41no—
577C23—41no—
578C23—42no—
579C23—81no—
580C23—81no—
581C23#120×C13111yescharacteristic
582C23#120×C13111yescharacteristic
583C23C22×D4×C13111yescharacteristic
584Q8—41no—
585Q8—42no—
586Q8—42no—
587Q8—41no—
588Q8—41no—
589Q8—81no—
590Q8—82no—
591D4—42no—
592D4—41no—
593D4—42no—
594D4—42no—
595D4—44no—
596D4—42no—
597D4—82no—
598D4—81no—
599D4—82no—
600D4—82no—
601C2×C4—21no—
602C2×C4—22no—
603C2×C4—21no—
604C2×C4—22no—
605C2×C4—21no—
606C2×C4—22no—
607C2×C4—24no—
608C2×C4—41no—
609C2×C4—41no—
610C2×C4—41no—
611C2×C4—41no—
612C2×C4—41no—
613C2×C4—41no—
614C2×C4—42no—
615C2×C4—42no—
616C2×C4—42no—
617C2×C4—42no—
618C2×C4—42no—
619C2×C4—42no—
620C2×C4—41no—
621C2×C4—41no—
622C2×C4—42no—
623C2×C4—81no—
624C2×C4—82no—
625C2×C4—82no—
626C2×C4—82no—
627C2×C4#120×C13111yescharacteristic
628C2×C4#120×C13111yescharacteristic
629C2×C4C22×D4×C13111yescharacteristic
630C2×C4C22×D4×C13111yescharacteristic
631C8—42no—
632C8—41no—
633C8—41no—
634C22—21no—
635C22—21no—
636C22—21no—
637C22—21no—
638C22—21no—
639C22—21no—
640C22—21no—
641C22—21no—
642C22—41no—
643C22—42no—
644C22—41no—
645C22—42no—
646C22—41no—
647C22—42no—
648C22—82no—
649C22—162no—
650C22C2×#120×C13111yescharacteristic
651C22#577×C13112yes—
652C4—21no—
653C4—21no—
654C4—21no—
655C4—21no—
656C4—42no—
657C4—42no—
658C4—41no—
659C4—41no—
660C4—41no—
661C4—42no—
662C4—82no—
663C4—81no—
664C4—81no—
665C2—22no—
666C2—41no—
667C2—41no—
668C2—82no—
669C2—81no—
670C2#3009×C13111yescharacteristic
671C2#3020×C13111yescharacteristic
672C2#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. #3187×C131C2semidirect
4. #2817×C131C2semidirect
5. #1616×C131C2semidirect
6. #1615×C131C2semidirect
7. #1604×C131C2semidirect
8. #1603×C131C2semidirect
9. #1516×C131C2semidirect
10. #1510×C131C2semidirect
11. #1472×C131C2semidirect
29. #484×C131C22semidirect
32. #481×C131C22semidirect
37. #451×C131C22semidirect
40. #448×C131C22semidirect
44. #400×C131C22semidirect
47. #395×C131C22semidirect
49. #328×C131C22semidirect
52. #327×C131C22semidirect
53. #324×C131C22semidirect
54. #324×C131C22semidirect
336. #18457C131direct (N × H)
337. C131#18457direct (N × H)
339. #3196C2×C131semidirect
340. #3187C2×C131semidirect
341. #2817C2×C131semidirect
342. #1616C2×C131semidirect
343. #1615C2×C131semidirect
344. #1604C2×C131semidirect
345. #1603C2×C131semidirect
346. #1516C2×C131semidirect
347. #1510C2×C131semidirect
348. #1472C2×C131semidirect
366. #484C22×C131semidirect
369. #481C22×C131semidirect
374. #451C22×C131semidirect
377. #448C22×C131semidirect
381. #400C22×C131semidirect
384. #395C22×C131semidirect
386. #328C22×C131semidirect
389. #327C22×C131semidirect
390. #324C22×C131semidirect
391. #324C22×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
#3187×C1312
#2817×C1312
#1616×C1312
#1615×C1312
#1604×C1312
#1603×C1312
#1516×C1312
#1510×C1312
#1472×C1312
#18457131