Finite Group Databasebeta

← C131×#29672 #45715556

Subgroups — C131×#29672 #45715556

Order 33536.

1096 conjugacy classes of subgroups.

The subgroup lattice has 588 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#542×C131C211yesmaximal, characteristic
2C2×#462×C131C211yesmaximal, characteristic, complemented
3C2×#461×C131C211yesmaximal, characteristic, complemented
4#2621×C131C211yesmaximal, characteristic, complemented
5#2024×C131C212yesmaximal, complemented
6#2015×C131C212yesmaximal, complemented
7#2001×C131C212yesmaximal, complemented
8#2000×C131C212yesmaximal
9#1805×C131C211yesmaximal, characteristic, complemented
10#1804×C131C211yesmaximal, characteristic, complemented
11#1798×C131C211yesmaximal, characteristic, complemented
12C22×Q16×C131C2212yes—
13C22×SD16×C131C2212yes—
14#542×C131—24no—
15#542×C131—24no—
16C2×C4⋊Q8×C131C2211yescharacteristic
17C2×C4⋊Q8×C131C2211yescharacteristic
18C2×#126×C131—21no—
19C2×#124×C131—21no—
20C2×#124×C131C2211yescharacteristic
21C2×#123×C131—21no—
22C2×C22⋊Q8×C131—21no—
23C2×C22⋊Q8×C131C2211yescharacteristic
24C2×C22⋊Q8×C131C2212yes—
25C2×#121×C131C2211yescharacteristic
26C2×C4×Q8×C131C2211yescharacteristic
27C2×C4×D4×C131C2211yescharacteristic
28C2×#117×C131C2211yescharacteristic
29#462×C131—24no—
30#461×C131—24no—
31C2×C4⋊C8×C131C2211yescharacteristic
32C2×C4⋊C8×C131C2211yescharacteristic
33C2×#103×C131C2212yes—
34C2×#103×C131C2212yes—
35C2×#103×C131C2212yes—
36C2×#102×C131C2212yes—
37C2×C22⋊C8×C131C2212yes—
38#398×C131—21no—
39#398×C131—21no—
40#397×C131—21no—
41#397×C131—21no—
42#391×C131C2212yes—
43#382×C131C2211yescharacteristic
44#340×C131C2212yes—
45#340×C131C2212yes—
46#336×C131C2212yes—
47C22×Q8×C131—21no—
48C22×Q8×C131C2312yes—
49C22×Q8×C131C2311yescharacteristic
50C22×D4×C131—21no—
51C22×D4×C131C2311yescharacteristic
52C23×C4×C131—21no—
53C23×C4×C131C2311yescharacteristic
54C2×Q16×C131—24no—
55C2×Q16×C131—42no—
56C2×Q16×C131—42no—
57C2×SD16×C131—24no—
58C2×SD16×C131—42no—
59C2×SD16×C131—42no—
60C22×C8×C131C2312yes—
61C22×C8×C131C2312yes—
62C4⋊Q8×C131—22no—
63C4⋊Q8×C131—22no—
64C4⋊Q8×C131—22no—
65C4⋊Q8×C131—22no—
66#126×C131—28no—
67#124×C131—28no—
68#124×C131—22no—
69#124×C131—22no—
70#123×C131—28no—
71C22⋊Q8×C131—28no—
72C22⋊Q8×C131—22no—
73C22⋊Q8×C131—22no—
74C22⋊Q8×C131—42no—
75C22⋊Q8×C131—42no—
76#121×C131—22no—
77#121×C131—22no—
78C4×Q8×C131—22no—
79C4×Q8×C131D414yes—
80C4×D4×C131—22no—
81C4×D4×C131D414yes—
82#117×C131—22no—
83#117×C131—22no—
84C2×C4⋊C4×C131—21no—
85C2×C4⋊C4×C131—21no—
86C2×C4⋊C4×C131—21no—
87C2×C4⋊C4×C131—21no—
88C2×C4⋊C4×C131—21no—
89C2×C4⋊C4×C131—22no—
90C2×C4⋊C4×C131D411yescharacteristic
91C2×C4⋊C4×C131D411yescharacteristic
92C2×C4⋊C4×C131C2312yes—
93C2×C4⋊C4×C131C2311yescharacteristic
94C2×C4⋊C4×C131C2311yescharacteristic
95C2×C22⋊C4×C131—21no—
96C2×C22⋊C4×C131—21no—
97C2×C22⋊C4×C131—21no—
98C2×C22⋊C4×C131—21no—
99C2×C22⋊C4×C131—21no—
100C2×C22⋊C4×C131—22no—
101C2×C22⋊C4×C131D411yescharacteristic
102C2×C22⋊C4×C131D411yescharacteristic
103C2×C42×C131—21no—
104C2×C42×C131C2311yescharacteristic
105C2×C42×C131C2311yescharacteristic
106C4⋊C8×C131—22no—
107C4⋊C8×C131—22no—
108#103×C131—24no—
109#103×C131—24no—
110#103×C131—42no—
111#102×C131—42no—
112C22⋊C8×C131—42no—
113#95×C131—22no—
114#95×C131—22no—
115#95×C131—21no—
116#95×C131—21no—
117C24×C131—21no—
118C24×C131C2×D411yescharacteristic
119C2×Q8×C131—24no—
120C2×Q8×C131—21no—
121C2×Q8×C131—22no—
122C2×Q8×C131—22no—
123C2×Q8×C131—21no—
124C2×Q8×C131—21no—
125C2×Q8×C131—21no—
126C2×Q8×C131—22no—
127C2×Q8×C131—22no—
128C2×Q8×C131—22no—
129C2×Q8×C131—21no—
130C2×Q8×C131—22no—
131C2×Q8×C131—82no—
132C2×Q8×C131C2×D412yes—
133C2×D4×C131—24no—
134C2×D4×C131—21no—
135C2×D4×C131—21no—
136C2×D4×C131—21no—
137C2×D4×C131—21no—
138C2×D4×C131—21no—
139C2×D4×C131—82no—
140C2×D4×C131C2×D412yes—
141C22×C4×C131—21no—
142C22×C4×C131—21no—
143C22×C4×C131—21no—
144C22×C4×C131—21no—
145C22×C4×C131—21no—
146C22×C4×C131—21no—
147C22×C4×C131—21no—
148C22×C4×C131—21no—
149C22×C4×C131—21no—
150C22×C4×C131—24no—
151C22×C4×C131—22no—
152C22×C4×C131—22no—
153C22×C4×C131—82no—
154C22×C4×C131C2×D411yescharacteristic
155C22×C4×C131C2×D411yescharacteristic
156C22×C4×C131C2×D411yescharacteristic
157C22×C4×C131C2×D411yescharacteristic
158C22×C4×C131C2×D411yescharacteristic
159C22×C4×C131C2411yescharacteristic
160Q16×C131—48no—
161SD16×C131—48no—
162C2×C8×C131—22no—
163C2×C8×C131—22no—
164C2×C8×C131—22no—
165C2×C8×C131—22no—
166C2×C8×C131—22no—
167C2×C8×C131—22no—
168C4⋊C4×C131—24no—
169C4⋊C4×C131—24no—
170C4⋊C4×C131—24no—
171C4⋊C4×C131—22no—
172C4⋊C4×C131—22no—
173C4⋊C4×C131—21no—
174C4⋊C4×C131—21no—
175C4⋊C4×C131—22no—
176C4⋊C4×C131—22no—
177C4⋊C4×C131—44no—
178C4⋊C4×C131—42no—
179C4⋊C4×C131—42no—
180C4⋊C4×C131C2×D412yes—
181C4⋊C4×C131C2×D412yes—
182C22⋊C4×C131—24no—
183C22⋊C4×C131—24no—
184C22⋊C4×C131—24no—
185C22⋊C4×C131—24no—
186C22⋊C4×C131—24no—
187C22⋊C4×C131—22no—
188C22⋊C4×C131—22no—
189C22⋊C4×C131—44no—
190C42×C131—24no—
191C42×C131—21no—
192C42×C131—21no—
193C42×C131C2×D412yes—
194C42×C131C2×D412yes—
195C23×C131—21no—
196C23×C131—22no—
197C23×C131—21no—
198C23×C131—21no—
199C23×C131—22no—
200C23×C131—22no—
201C23×C131—41no—
202C23×C131—41no—
203C23×C131—42no—
204C23×C131—42no—
205C23×C131C22×D411yescharacteristic
206Q8×C131—22no—
207Q8×C131—22no—
208Q8×C131—41no—
209Q8×C131—41no—
210Q8×C131—42no—
211Q8×C131—42no—
212Q8×C131—42no—
213Q8×C131—42no—
214Q8×C131—84no—
215D4×C131—22no—
216D4×C131—22no—
217D4×C131—41no—
218D4×C131—41no—
219D4×C131—84no—
220C2×C4×C131—22no—
221C2×C4×C131—22no—
222C2×C4×C131—21no—
223C2×C4×C131—22no—
224C2×C4×C131—21no—
225C2×C4×C131—22no—
226C2×C4×C131—21no—
227C2×C4×C131—22no—
228C2×C4×C131—21no—
229C2×C4×C131—21no—
230C2×C4×C131—22no—
231C2×C4×C131—22no—
232C2×C4×C131—41no—
233C2×C4×C131—41no—
234C2×C4×C131—42no—
235C2×C4×C131—42no—
236C2×C4×C131—41no—
237C2×C4×C131—41no—
238C2×C4×C131—41no—
239C2×C4×C131—41no—
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—84no—
247C2×C4×C131#12012yes—
248C2×C4×C131#12012yes—
249C2×C4×C131C22×D411yescharacteristic
250C2×C4×C131C22×D411yescharacteristic
251C2×C4×C131H(5,𝔽2)11yescharacteristic
252C2×C4×C131H(5,𝔽2)11yescharacteristic
253C2×C4×C131H(5,𝔽2)11yescharacteristic
254C2×C4×C1312−1+411yescharacteristic
255C8×C131—42no—
256C8×C131—42no—
257C22×C131—41no—
258C22×C131—42no—
259C22×C131—42no—
260C22×C131—42no—
261C22×C131—42no—
262C22×C131—41no—
263C22×C131—41no—
264C22×C131—42no—
265C22×C131—82no—
266C22×C131—82no—
267C22×C131C2×#12011yescharacteristic
268C22×C131#53511yescharacteristic
269C22×C131#53711yescharacteristic
270C22×C131#57712yes—
271C22×C131#57812yes—
272C4×C131—22no—
273C4×C131—22no—
274C4×C131—41no—
275C4×C131—42no—
276C4×C131—41no—
277C4×C131—42no—
278C4×C131—42no—
279C4×C131—41no—
280C4×C131—82no—
281C4×C131—82no—
282C4×C131#53511yescharacteristic
283C4×C131#53511yescharacteristic
284C4×C131#53711yescharacteristic
285C4×C131#53711yescharacteristic
286C2×C131—81no—
287C2×C131—82no—
288C2×C131#261511yescharacteristic
289C2×C131#300911yescharacteristic
290C2×C131#301111yescharacteristic
291C2×C131#322512yes—
292C2×C131#325812yes—
293#29672C13111yesmaximal, characteristic, direct product factor, Sylow
294C131#2967211yescharacteristic, direct product factor, Sylow
295C2×#542C2×C13111yescharacteristic
296C2×#462C2×C13111yescharacteristic, complemented
297C2×#461C2×C13111yescharacteristic, complemented
298#2621C2×C13111yescharacteristic, complemented
299#2024C2×C13112yescomplemented
300#2015C2×C13112yescomplemented
301#2001C2×C13112yescomplemented
302#2000C2×C13112yes—
303#1805C2×C13111yescharacteristic, complemented
304#1804C2×C13111yescharacteristic, complemented
305#1798C2×C13111yescharacteristic, complemented
306C22×Q16C22×C13112yes—
307C22×SD16C22×C13112yes—
308#542—24no—
309#542—24no—
310C2×C4⋊Q8C22×C13111yescharacteristic
311C2×C4⋊Q8C22×C13111yescharacteristic
312C2×#126—21no—
313C2×#124—21no—
314C2×#124C22×C13111yescharacteristic
315C2×#123—21no—
316C2×C22⋊Q8—21no—
317C2×C22⋊Q8C22×C13111yescharacteristic
318C2×C22⋊Q8C22×C13112yes—
319C2×#121C22×C13111yescharacteristic
320C2×C4×Q8C22×C13111yescharacteristic
321C2×C4×D4C22×C13111yescharacteristic
322C2×#117C22×C13111yescharacteristic
323#462—24no—
324#461—24no—
325C2×C4⋊C8C22×C13111yescharacteristic
326C2×C4⋊C8C22×C13111yescharacteristic
327C2×#103C22×C13112yes—
328C2×#103C22×C13112yes—
329C2×#103C22×C13112yes—
330C2×#102C22×C13112yes—
331C2×C22⋊C8C22×C13112yes—
332#398—21no—
333#398—21no—
334#397—21no—
335#397—21no—
336#391C22×C13112yes—
337#382C22×C13111yescharacteristic
338#340C22×C13112yes—
339#340C22×C13112yes—
340#336C22×C13112yes—
341C22×Q8—21no—
342C22×Q8C23×C13112yes—
343C22×Q8C23×C13111yescharacteristic
344C22×D4—21no—
345C22×D4C23×C13111yescharacteristic
346C23×C4—21no—
347C23×C4C23×C13111yescharacteristic
348C2×Q16—24no—
349C2×Q16—42no—
350C2×Q16—42no—
351C2×SD16—24no—
352C2×SD16—42no—
353C2×SD16—42no—
354C22×C8C23×C13112yes—
355C22×C8C23×C13112yes—
356C4⋊Q8—22no—
357C4⋊Q8—22no—
358C4⋊Q8—22no—
359C4⋊Q8—22no—
360#126—28no—
361#124—28no—
362#124—22no—
363#124—22no—
364#123—28no—
365C22⋊Q8—28no—
366C22⋊Q8—22no—
367C22⋊Q8—22no—
368C22⋊Q8—42no—
369C22⋊Q8—42no—
370#121—22no—
371#121—22no—
372C4×Q8—22no—
373C4×Q8D4×C13114yes—
374C4×D4—22no—
375C4×D4D4×C13114yes—
376#117—22no—
377#117—22no—
378C2×C4⋊C4—21no—
379C2×C4⋊C4—21no—
380C2×C4⋊C4—21no—
381C2×C4⋊C4—22no—
382C2×C4⋊C4—21no—
383C2×C4⋊C4—21no—
384C2×C4⋊C4D4×C13111yescharacteristic
385C2×C4⋊C4D4×C13111yescharacteristic
386C2×C4⋊C4C23×C13112yes—
387C2×C4⋊C4C23×C13111yescharacteristic
388C2×C4⋊C4C23×C13111yescharacteristic
389C2×C22⋊C4—21no—
390C2×C22⋊C4—21no—
391C2×C22⋊C4—21no—
392C2×C22⋊C4—21no—
393C2×C22⋊C4—21no—
394C2×C22⋊C4—22no—
395C2×C22⋊C4D4×C13111yescharacteristic
396C2×C22⋊C4D4×C13111yescharacteristic
397C2×C42—21no—
398C2×C42C23×C13111yescharacteristic
399C2×C42C23×C13111yescharacteristic
400C4⋊C8—22no—
401C4⋊C8—22no—
402#103—24no—
403#103—24no—
404#103—42no—
405#102—42no—
406C22⋊C8—42no—
407#95—21no—
408#95—21no—
409#95—22no—
410#95—22no—
411C24—21no—
412C24C2×D4×C13111yescharacteristic
413C2×Q8—24no—
414C2×Q8—21no—
415C2×Q8—22no—
416C2×Q8—22no—
417C2×Q8—21no—
418C2×Q8—21no—
419C2×Q8—21no—
420C2×Q8—22no—
421C2×Q8—22no—
422C2×Q8—22no—
423C2×Q8—21no—
424C2×Q8—22no—
425C2×Q8—82no—
426C2×Q8C2×D4×C13112yes—
427C2×D4—24no—
428C2×D4—21no—
429C2×D4—21no—
430C2×D4—21no—
431C2×D4—21no—
432C2×D4—21no—
433C2×D4—82no—
434C2×D4C2×D4×C13112yes—
435C22×C4—21no—
436C22×C4—21no—
437C22×C4—21no—
438C22×C4—21no—
439C22×C4—21no—
440C22×C4—21no—
441C22×C4—21no—
442C22×C4—21no—
443C22×C4—21no—
444C22×C4—24no—
445C22×C4—22no—
446C22×C4—22no—
447C22×C4—82no—
448C22×C4C2×D4×C13111yescharacteristic
449C22×C4C2×D4×C13111yescharacteristic
450C22×C4C2×D4×C13111yescharacteristic
451C22×C4C2×D4×C13111yescharacteristic
452C22×C4C2×D4×C13111yescharacteristic
453C22×C4C24×C13111yescharacteristic
454Q16—48no—
455SD16—48no—
456C2×C8—22no—
457C2×C8—22no—
458C2×C8—22no—
459C2×C8—22no—
460C2×C8—22no—
461C2×C8—22no—
462C4⋊C4—24no—
463C4⋊C4—24no—
464C4⋊C4—24no—
465C4⋊C4—22no—
466C4⋊C4—22no—
467C4⋊C4—21no—
468C4⋊C4—21no—
469C4⋊C4—22no—
470C4⋊C4—22no—
471C4⋊C4—44no—
472C4⋊C4—42no—
473C4⋊C4—42no—
474C4⋊C4C2×D4×C13112yes—
475C4⋊C4C2×D4×C13112yes—
476C22⋊C4—24no—
477C22⋊C4—24no—
478C22⋊C4—24no—
479C22⋊C4—24no—
480C22⋊C4—24no—
481C22⋊C4—22no—
482C22⋊C4—22no—
483C22⋊C4—44no—
484C42—24no—
485C42—21no—
486C42—21no—
487C42C2×D4×C13112yes—
488C42C2×D4×C13112yes—
489C23—21no—
490C23—22no—
491C23—21no—
492C23—21no—
493C23—22no—
494C23—22no—
495C23—41no—
496C23—41no—
497C23—42no—
498C23—42no—
499C23C22×D4×C13111yescharacteristic
500Q8—22no—
501Q8—22no—
502Q8—41no—
503Q8—41no—
504Q8—42no—
505Q8—42no—
506Q8—42no—
507Q8—42no—
508Q8—84no—
509D4—22no—
510D4—22no—
511D4—41no—
512D4—41no—
513D4—84no—
514C2×C4—22no—
515C2×C4—22no—
516C2×C4—21no—
517C2×C4—22no—
518C2×C4—21no—
519C2×C4—22no—
520C2×C4—21no—
521C2×C4—22no—
522C2×C4—21no—
523C2×C4—21no—
524C2×C4—22no—
525C2×C4—22no—
526C2×C4—41no—
527C2×C4—41no—
528C2×C4—42no—
529C2×C4—42no—
530C2×C4—41no—
531C2×C4—41no—
532C2×C4—41no—
533C2×C4—41no—
534C2×C4—42no—
535C2×C4—42no—
536C2×C4—42no—
537C2×C4—42no—
538C2×C4—42no—
539C2×C4—42no—
540C2×C4—84no—
541C2×C4#120×C13112yes—
542C2×C4#120×C13112yes—
543C2×C4C22×D4×C13111yescharacteristic
544C2×C4C22×D4×C13111yescharacteristic
545C2×C4H(5,𝔽2)×C13111yescharacteristic
546C2×C4H(5,𝔽2)×C13111yescharacteristic
547C2×C4H(5,𝔽2)×C13111yescharacteristic
548C2×C42−1+4×C13111yescharacteristic
549C8—42no—
550C8—42no—
551C22—42no—
552C22—42no—
553C22—41no—
554C22—41no—
555C22—42no—
556C22—41no—
557C22—42no—
558C22—42no—
559C22—82no—
560C22—82no—
561C22C2×#120×C13111yescharacteristic
562C22#535×C13111yescharacteristic
563C22#537×C13111yescharacteristic
564C22#577×C13112yes—
565C22#578×C13112yes—
566C4—22no—
567C4—22no—
568C4—41no—
569C4—42no—
570C4—42no—
571C4—41no—
572C4—41no—
573C4—42no—
574C4—82no—
575C4—82no—
576C4#535×C13111yescharacteristic
577C4#535×C13111yescharacteristic
578C4#537×C13111yescharacteristic
579C4#537×C13111yescharacteristic
580C2—81no—
581C2—82no—
582C2#2615×C13111yescharacteristic
583C2#3009×C13111yescharacteristic
584C2#3011×C13111yescharacteristic
585C2#3225×C13112yes—
586C2#3258×C13112yes—
subgroupG/H
center, socleC23×C131C22×D4
commutator, Frattini, cosocleC22×C4C24×C131
prime radicalC2×#121×C131C22
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C131 ◁ C2×#117×C131 ◁ G

Complements

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

NH ≅ G/Ntype
2. C2×#462×C131C2semidirect
3. C2×#461×C131C2semidirect
4. #2621×C131C2semidirect
5. #2024×C131C2semidirect
6. #2015×C131C2semidirect
7. #2001×C131C2semidirect
9. #1805×C131C2semidirect
10. #1804×C131C2semidirect
11. #1798×C131C2semidirect
293. #29672C131direct (N × H)
294. C131#29672direct (N × H)
296. C2×#462C2×C131semidirect
297. C2×#461C2×C131semidirect
298. #2621C2×C131semidirect
299. #2024C2×C131semidirect
300. #2015C2×C131semidirect
301. #2001C2×C131semidirect
303. #1805C2×C131semidirect
304. #1804C2×C131semidirect
305. #1798C2×C131semidirect

Maximal subgroups

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

subgroupindex
C2×#542×C1312
C2×#462×C1312
C2×#461×C1312
#2621×C1312
#2024×C1312
#2015×C1312
#2001×C1312
#2000×C1312
#1805×C1312
#1804×C1312
#1798×C1312
#29672131