Finite Group Databasebeta

← C131×#16303 #45702187

Subgroups — C131×#16303 #45702187

Order 33536.

1682 conjugacy classes of subgroups.

The subgroup lattice has 634 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#399×C131C211yesmaximal, characteristic
2C2×#395×C131C212yesmaximal, complemented
3C2×#393×C131C211yesmaximal, characteristic
4C2×#380×C131C212yesmaximal
5#1444×C131C212yesmaximal, complemented
6#1442×C131C212yesmaximal, complemented
7#1441×C131C212yesmaximal, complemented
8#1439×C131C212yesmaximal
9C22⋊#95×C131C211yesmaximal, characteristic
10C23×Q8×C131C2211yescharacteristic
11C24×C4×C131C2211yescharacteristic
12C22×C4⋊C4×C131C2212yes—
13C22×C4⋊C4×C131C2212yes—
14C22×C4⋊C4×C131C2212yes—
15C22×C4⋊C4×C131C2212yes—
16C22×C4⋊C4×C131C2211yescharacteristic
17C22×C22⋊C4×C131C2212yes—
18C22×C22⋊C4×C131C2212yes—
19C22×C22⋊C4×C131C2211yescharacteristic
20C22×C22⋊C4×C131C2211yescharacteristic
21#399×C131—24no—
22#395×C131—28no—
23#393×C131—24no—
24#380×C131—28no—
25C2×#95×C131C2212yes—
26C2×#95×C131C2211yescharacteristic
27C2×#95×C131C2212yes—
28C2×#95×C131C2212yes—
29C2×#95×C131C2212yes—
30C2×#95×C131C2211yescharacteristic
31C2×#95×C131C2212yes—
32C2×#95×C131C2212yes—
33C2×#95×C131C2212yes—
34C2×#95×C131C2212yes—
35C25×C131C2311yescharacteristic
36C22×Q8×C131—22no—
37C22×Q8×C131—24no—
38C22×Q8×C131—41no—
39C22×Q8×C131—42no—
40C22×Q8×C131—41no—
41C23×C4×C131—24no—
42C23×C4×C131—24no—
43C23×C4×C131—41no—
44C23×C4×C131—41no—
45C23×C4×C131Q814yescomplemented
46C23×C4×C131C2312yes—
47C23×C4×C131C2312yes—
48C23×C4×C131C2312yes—
49C23×C4×C131C2311yescharacteristic
50C23×C4×C131C2312yes—
51C23×C4×C131C2311yescharacteristic
52C23×C4×C131C2312yes—
53C23×C4×C131C2312yes—
54C2×C4⋊C4×C131—24no—
55C2×C4⋊C4×C131—24no—
56C2×C4⋊C4×C131—24no—
57C2×C4⋊C4×C131—24no—
58C2×C4⋊C4×C131—22no—
59C2×C4⋊C4×C131—24no—
60C2×C4⋊C4×C131—24no—
61C2×C4⋊C4×C131—24no—
62C2×C4⋊C4×C131—42no—
63C2×C4⋊C4×C131—42no—
64C2×C4⋊C4×C131—42no—
65C2×C4⋊C4×C131—42no—
66C2×C4⋊C4×C131—42no—
67C2×C4⋊C4×C131—41no—
68C2×C4⋊C4×C131—41no—
69C2×C22⋊C4×C131—24no—
70C2×C22⋊C4×C131—24no—
71C2×C22⋊C4×C131—24no—
72C2×C22⋊C4×C131—24no—
73C2×C22⋊C4×C131—41no—
74C2×C22⋊C4×C131—41no—
75C2×C22⋊C4×C131—41no—
76C2×C22⋊C4×C131—41no—
77C2×C22⋊C4×C131—42no—
78C2×C22⋊C4×C131—42no—
79C2×C22⋊C4×C131D414yes—
80C2×C22⋊C4×C131Q814yescomplemented
81#95×C131—24no—
82#95×C131—22no—
83#95×C131—24no—
84#95×C131—24no—
85#95×C131—22no—
86#95×C131—24no—
87#95×C131—24no—
88#95×C131—42no—
89#95×C131—42no—
90#95×C131D418yes—
91C24×C131—22no—
92C24×C131—22no—
93C24×C131—21no—
94C24×C131—22no—
95C24×C131—21no—
96C24×C131—21no—
97C24×C131—21no—
98C24×C131—22no—
99C24×C131C2×D412yes—
100C24×C131C2×Q812yes—
101C24×C131C2×Q812yes—
102C24×C131C2411yescharacteristic
103C2×Q8×C131—48no—
104C2×Q8×C131—44no—
105C2×Q8×C131—44no—
106C2×Q8×C131—48no—
107C2×Q8×C131—44no—
108C22×C4×C131—22no—
109C22×C4×C131—22no—
110C22×C4×C131—22no—
111C22×C4×C131—22no—
112C22×C4×C131—22no—
113C22×C4×C131—22no—
114C22×C4×C131—22no—
115C22×C4×C131—22no—
116C22×C4×C131—22no—
117C22×C4×C131—22no—
118C22×C4×C131—22no—
119C22×C4×C131—22no—
120C22×C4×C131—22no—
121C22×C4×C131—22no—
122C22×C4×C131—22no—
123C22×C4×C131—21no—
124C22×C4×C131—21no—
125C22×C4×C131—22no—
126C22×C4×C131—22no—
127C22×C4×C131—21no—
128C22×C4×C131—21no—
129C22×C4×C131—22no—
130C22×C4×C131—22no—
131C22×C4×C131—22no—
132C22×C4×C131—22no—
133C22×C4×C131—22no—
134C22×C4×C131—22no—
135C22×C4×C131—22no—
136C22×C4×C131—22no—
137C22×C4×C131—22no—
138C22×C4×C131—216no—
139C22×C4×C131—22no—
140C22×C4×C131—22no—
141C22×C4×C131—22no—
142C22×C4×C131—22no—
143C22×C4×C131—22no—
144C22×C4×C131—22no—
145C22×C4×C131—22no—
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—44no—
154C22×C4×C131—44no—
155C22×C4×C131—48no—
156C22×C4×C131—44no—
157C22×C4×C131C2×D412yes—
158C22×C4×C131C2×D414yes—
159C22×C4×C131C2×D412yes—
160C22×C4×C131C2×D414yes—
161C22×C4×C131C2×D414yes—
162C22×C4×C131C2×Q814yes—
163C22×C4×C131C2×Q814yes—
164C22×C4×C131#4114yes—
165C4⋊C4×C131—48no—
166C4⋊C4×C131—48no—
167C4⋊C4×C131—48no—
168C4⋊C4×C131—44no—
169C4⋊C4×C131—48no—
170C22⋊C4×C131—44no—
171C22⋊C4×C131—44no—
172C22⋊C4×C131—48no—
173C22⋊C4×C131—48no—
174C23×C131—24no—
175C23×C131—22no—
176C23×C131—22no—
177C23×C131—22no—
178C23×C131—22no—
179C23×C131—22no—
180C23×C131—22no—
181C23×C131—24no—
182C23×C131—24no—
183C23×C131—24no—
184C23×C131—24no—
185C23×C131—24no—
186C23×C131—42no—
187C23×C131—42no—
188C23×C131—42no—
189C23×C131—42no—
190C23×C131—41no—
191C23×C131—42no—
192C23×C131—41no—
193C23×C131—41no—
194C23×C131—42no—
195C23×C131—41no—
196C23×C131C4⋊Q814yes—
197C23×C131C22×D412yes—
198C23×C131C22×D411yescharacteristic
199C23×C131C22×Q811yescharacteristic
200C23×C131C22×Q811yescharacteristic
201C23×C131C2×#4112yes—
202C23×C131H(5,𝔽2)11yescharacteristic
203C23×C131H(5,𝔽2)11yescharacteristic
204C23×C131H(5,𝔽2)12yes—
205C23×C131H(5,𝔽2)11yescharacteristic
206C23×C1312−1+411yescharacteristic
207C23×C1312−1+412yes—
208Q8×C131—416no—
209C2×C4×C131—24no—
210C2×C4×C131—24no—
211C2×C4×C131—24no—
212C2×C4×C131—24no—
213C2×C4×C131—24no—
214C2×C4×C131—24no—
215C2×C4×C131—22no—
216C2×C4×C131—22no—
217C2×C4×C131—24no—
218C2×C4×C131—24no—
219C2×C4×C131—24no—
220C2×C4×C131—24no—
221C2×C4×C131—24no—
222C2×C4×C131—24no—
223C2×C4×C131—24no—
224C2×C4×C131—24no—
225C2×C4×C131—24no—
226C2×C4×C131—24no—
227C2×C4×C131—24no—
228C2×C4×C131—416no—
229C2×C4×C131—42no—
230C2×C4×C131—42no—
231C2×C4×C131—42no—
232C2×C4×C131—42no—
233C2×C4×C131—42no—
234C2×C4×C131—42no—
235C2×C4×C131—42no—
236C2×C4×C131—42no—
237C2×C4×C131—42no—
238C2×C4×C131—41no—
239C2×C4×C131—42no—
240C2×C4×C131—42no—
241C2×C4×C131—41no—
242C2×C4×C131—41no—
243C2×C4×C131—42no—
244C2×C4×C131—42no—
245C2×C4×C131—42no—
246C2×C4×C131—41no—
247C2×C4×C131—42no—
248C2×C4×C131—42no—
249C2×C4×C131—42no—
250C2×C4×C131—42no—
251C2×C4×C131—42no—
252C2×C4×C131—42no—
253C2×C4×C131—42no—
254C2×C4×C131—42no—
255C2×C4×C131—42no—
256C2×C4×C131—42no—
257C2×C4×C131—42no—
258C2×C4×C131—42no—
259C2×C4×C131—42no—
260C2×C4×C131—42no—
261C2×C4×C131C22⋊Q818yes—
262C22×C131—24no—
263C22×C131—28no—
264C22×C131—42no—
265C22×C131—44no—
266C22×C131—42no—
267C22×C131—44no—
268C22×C131—42no—
269C22×C131—44no—
270C22×C131—42no—
271C22×C131—42no—
272C22×C131—42no—
273C22×C131C2×C22⋊Q812yes—
274C22×C131C2×C4⋊Q811yescharacteristic
275C22×C131#53411yescharacteristic
276C22×C131#53512yes—
277C22×C131#53612yes—
278C22×C131#53711yescharacteristic
279C22×C131#54212yes—
280C22×C131#54212yes—
281C22×C131#54311yescharacteristic
282C22×C131#54311yescharacteristic
283C22×C131#54412yes—
284C22×C131#54411yescharacteristic
285C22×C131#54411yescharacteristic
286C22×C131D4212yes—
287C22×C131D4211yescharacteristic
288C22×C131#54612yes—
289C22×C131#54712yes—
290C22×C131D4×Q812yes—
291C22×C131#55111yescharacteristic
292C22×C131#55412yes—
293C22×C131#56011yescharacteristic
294C22×C131#56212yes—
295C22×C131#56311yescharacteristic
296C4×C131—28no—
297C4×C131—42no—
298C4×C131—44no—
299C4×C131—44no—
300C4×C131—44no—
301C4×C131—42no—
302C4×C131—82no—
303C4×C131—82no—
304C2×C131—44no—
305C2×C131#243711yescharacteristic
306C2×C131#244012yes—
307C2×C131#262812yes—
308C2×C131#265911yescharacteristic
309C2×C131#266911yescharacteristic
310C2×C131#267212yes—
311C2×C131#267711yescharacteristic
312C2×C131#269212yes—
313C2×C131#271711yescharacteristic
314C2×C131#274211yescharacteristic
315C2×C131#284111yescharacteristic
316#16303C13111yesmaximal, characteristic, direct product factor, Sylow
317C131#1630311yescharacteristic, direct product factor, Sylow
318C2×#399C2×C13111yescharacteristic
319C2×#395C2×C13112yescomplemented
320C2×#393C2×C13111yescharacteristic
321C2×#380C2×C13112yes—
322#1444C2×C13112yescomplemented
323#1442C2×C13112yescomplemented
324#1441C2×C13112yescomplemented
325#1439C2×C13112yes—
326C22⋊#95C2×C13111yescharacteristic
327C23×Q8C22×C13111yescharacteristic
328C24×C4C22×C13111yescharacteristic
329C22×C4⋊C4C22×C13112yes—
330C22×C4⋊C4C22×C13112yes—
331C22×C4⋊C4C22×C13112yes—
332C22×C4⋊C4C22×C13112yes—
333C22×C4⋊C4C22×C13111yescharacteristic
334C22×C22⋊C4C22×C13112yes—
335C22×C22⋊C4C22×C13112yes—
336C22×C22⋊C4C22×C13111yescharacteristic
337C22×C22⋊C4C22×C13111yescharacteristic
338#399—24no—
339#395—28no—
340#393—24no—
341#380—28no—
342C2×#95C22×C13111yescharacteristic
343C2×#95C22×C13112yes—
344C2×#95C22×C13112yes—
345C2×#95C22×C13112yes—
346C2×#95C22×C13111yescharacteristic
347C2×#95C22×C13112yes—
348C2×#95C22×C13112yes—
349C2×#95C22×C13112yes—
350C2×#95C22×C13112yes—
351C2×#95C22×C13112yes—
352C25C23×C13111yescharacteristic
353C22×Q8—22no—
354C22×Q8—24no—
355C22×Q8—41no—
356C22×Q8—42no—
357C22×Q8—41no—
358C23×C4—24no—
359C23×C4—24no—
360C23×C4—41no—
361C23×C4—41no—
362C23×C4Q8×C13114yescomplemented
363C23×C4C23×C13112yes—
364C23×C4C23×C13112yes—
365C23×C4C23×C13112yes—
366C23×C4C23×C13111yescharacteristic
367C23×C4C23×C13112yes—
368C23×C4C23×C13111yescharacteristic
369C23×C4C23×C13112yes—
370C23×C4C23×C13112yes—
371C2×C4⋊C4—24no—
372C2×C4⋊C4—24no—
373C2×C4⋊C4—24no—
374C2×C4⋊C4—24no—
375C2×C4⋊C4—24no—
376C2×C4⋊C4—24no—
377C2×C4⋊C4—22no—
378C2×C4⋊C4—24no—
379C2×C4⋊C4—42no—
380C2×C4⋊C4—42no—
381C2×C4⋊C4—42no—
382C2×C4⋊C4—42no—
383C2×C4⋊C4—42no—
384C2×C4⋊C4—41no—
385C2×C4⋊C4—41no—
386C2×C22⋊C4—24no—
387C2×C22⋊C4—24no—
388C2×C22⋊C4—24no—
389C2×C22⋊C4—24no—
390C2×C22⋊C4—41no—
391C2×C22⋊C4—41no—
392C2×C22⋊C4—41no—
393C2×C22⋊C4—41no—
394C2×C22⋊C4—42no—
395C2×C22⋊C4—42no—
396C2×C22⋊C4D4×C13114yes—
397C2×C22⋊C4Q8×C13114yescomplemented
398#95—24no—
399#95—24no—
400#95—22no—
401#95—24no—
402#95—24no—
403#95—22no—
404#95—24no—
405#95—42no—
406#95—42no—
407#95D4×C13118yes—
408C24—22no—
409C24—22no—
410C24—21no—
411C24—22no—
412C24—21no—
413C24—21no—
414C24—21no—
415C24—22no—
416C24C2×D4×C13112yes—
417C24C2×Q8×C13112yes—
418C24C2×Q8×C13112yes—
419C24C24×C13111yescharacteristic
420C2×Q8—48no—
421C2×Q8—44no—
422C2×Q8—44no—
423C2×Q8—48no—
424C2×Q8—44no—
425C22×C4—22no—
426C22×C4—22no—
427C22×C4—22no—
428C22×C4—22no—
429C22×C4—22no—
430C22×C4—22no—
431C22×C4—22no—
432C22×C4—22no—
433C22×C4—22no—
434C22×C4—22no—
435C22×C4—22no—
436C22×C4—22no—
437C22×C4—22no—
438C22×C4—22no—
439C22×C4—22no—
440C22×C4—21no—
441C22×C4—21no—
442C22×C4—22no—
443C22×C4—22no—
444C22×C4—21no—
445C22×C4—21no—
446C22×C4—22no—
447C22×C4—22no—
448C22×C4—22no—
449C22×C4—22no—
450C22×C4—22no—
451C22×C4—22no—
452C22×C4—22no—
453C22×C4—22no—
454C22×C4—22no—
455C22×C4—216no—
456C22×C4—22no—
457C22×C4—22no—
458C22×C4—22no—
459C22×C4—22no—
460C22×C4—22no—
461C22×C4—22no—
462C22×C4—22no—
463C22×C4—22no—
464C22×C4—22no—
465C22×C4—22no—
466C22×C4—22no—
467C22×C4—22no—
468C22×C4—22no—
469C22×C4—22no—
470C22×C4—44no—
471C22×C4—44no—
472C22×C4—48no—
473C22×C4—44no—
474C22×C4C2×D4×C13112yes—
475C22×C4C2×D4×C13114yes—
476C22×C4C2×D4×C13112yes—
477C22×C4C2×D4×C13114yes—
478C22×C4C2×D4×C13114yes—
479C22×C4C2×Q8×C13114yes—
480C22×C4C2×Q8×C13114yes—
481C22×C4#41×C13114yes—
482C4⋊C4—48no—
483C4⋊C4—48no—
484C4⋊C4—48no—
485C4⋊C4—44no—
486C4⋊C4—48no—
487C22⋊C4—44no—
488C22⋊C4—44no—
489C22⋊C4—48no—
490C22⋊C4—48no—
491C23—24no—
492C23—22no—
493C23—22no—
494C23—22no—
495C23—22no—
496C23—22no—
497C23—22no—
498C23—24no—
499C23—24no—
500C23—24no—
501C23—24no—
502C23—24no—
503C23—42no—
504C23—42no—
505C23—42no—
506C23—42no—
507C23—41no—
508C23—42no—
509C23—41no—
510C23—41no—
511C23—42no—
512C23—41no—
513C23C4⋊Q8×C13114yes—
514C23C22×D4×C13112yes—
515C23C22×D4×C13111yescharacteristic
516C23C22×Q8×C13111yescharacteristic
517C23C22×Q8×C13111yescharacteristic
518C23C2×#41×C13112yes—
519C23H(5,𝔽2)×C13111yescharacteristic
520C23H(5,𝔽2)×C13111yescharacteristic
521C23H(5,𝔽2)×C13112yes—
522C23H(5,𝔽2)×C13111yescharacteristic
523C232−1+4×C13111yescharacteristic
524C232−1+4×C13112yes—
525Q8—416no—
526C2×C4—24no—
527C2×C4—24no—
528C2×C4—24no—
529C2×C4—24no—
530C2×C4—24no—
531C2×C4—24no—
532C2×C4—22no—
533C2×C4—22no—
534C2×C4—24no—
535C2×C4—24no—
536C2×C4—24no—
537C2×C4—24no—
538C2×C4—24no—
539C2×C4—24no—
540C2×C4—24no—
541C2×C4—24no—
542C2×C4—24no—
543C2×C4—24no—
544C2×C4—24no—
545C2×C4—416no—
546C2×C4—42no—
547C2×C4—42no—
548C2×C4—42no—
549C2×C4—42no—
550C2×C4—42no—
551C2×C4—42no—
552C2×C4—42no—
553C2×C4—42no—
554C2×C4—42no—
555C2×C4—41no—
556C2×C4—42no—
557C2×C4—42no—
558C2×C4—41no—
559C2×C4—41no—
560C2×C4—42no—
561C2×C4—42no—
562C2×C4—42no—
563C2×C4—41no—
564C2×C4—42no—
565C2×C4—42no—
566C2×C4—42no—
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—42no—
578C2×C4C22⋊Q8×C13118yes—
579C22—24no—
580C22—28no—
581C22—42no—
582C22—42no—
583C22—44no—
584C22—42no—
585C22—44no—
586C22—42no—
587C22—44no—
588C22—42no—
589C22—42no—
590C22C2×C22⋊Q8×C13112yes—
591C22C2×C4⋊Q8×C13111yescharacteristic
592C22#534×C13111yescharacteristic
593C22#535×C13112yes—
594C22#536×C13112yes—
595C22#537×C13111yescharacteristic
596C22#542×C13112yes—
597C22#542×C13112yes—
598C22#543×C13111yescharacteristic
599C22#543×C13111yescharacteristic
600C22#544×C13111yescharacteristic
601C22#544×C13112yes—
602C22#544×C13111yescharacteristic
603C22D42×C13112yes—
604C22D42×C13111yescharacteristic
605C22#546×C13112yes—
606C22#547×C13112yes—
607C22D4×Q8×C13112yes—
608C22#551×C13111yescharacteristic
609C22#554×C13112yes—
610C22#560×C13111yescharacteristic
611C22#562×C13112yes—
612C22#563×C13111yescharacteristic
613C4—28no—
614C4—42no—
615C4—44no—
616C4—44no—
617C4—44no—
618C4—42no—
619C4—82no—
620C4—82no—
621C2—44no—
622C2#2437×C13111yescharacteristic
623C2#2440×C13112yes—
624C2#2628×C13112yes—
625C2#2659×C13111yescharacteristic
626C2#2669×C13111yescharacteristic
627C2#2672×C13112yes—
628C2#2677×C13111yescharacteristic
629C2#2692×C13112yes—
630C2#2717×C13111yescharacteristic
631C2#2742×C13111yescharacteristic
632C2#2841×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
2. C2×#395×C131C2semidirect
5. #1444×C131C2semidirect
6. #1442×C131C2semidirect
7. #1441×C131C2semidirect
45. C23×C4×C131Q8semidirect
80. C2×C22⋊C4×C131Q8semidirect
316. #16303C131direct (N × H)
317. C131#16303direct (N × H)
319. C2×#395C2×C131semidirect
322. #1444C2×C131semidirect
323. #1442C2×C131semidirect
324. #1441C2×C131semidirect
362. C23×C4Q8×C131semidirect
397. C2×C22⋊C4Q8×C131semidirect

Maximal subgroups

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

subgroupindex
C2×#399×C1312
C2×#395×C1312
C2×#393×C1312
C2×#380×C1312
#1444×C1312
#1442×C1312
#1441×C1312
#1439×C1312
C22⋊#95×C1312
#16303131