Finite Group Databasebeta

← C131×#10394 #45696278

Subgroups — C131×#10394 #45696278

Order 33536.

772 conjugacy classes of subgroups.

The subgroup lattice has 642 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#2617×C131C211yesmaximal, characteristic
2#1874×C131C211yesmaximal, characteristic, complemented
3#1852×C131C211yesmaximal, characteristic, complemented
4C2×#327×C131C211yesmaximal, characteristic, complemented
5C2×#323×C131C211yesmaximal, characteristic, complemented
6#1439×C131C211yesmaximal, characteristic, complemented
7#1294×C131C211yesmaximal, characteristic, complemented
8C2×#121×C131C2211yescharacteristic
9C2×#120×C131—21no—
10C22×C4⋊C4×C131C2211yescharacteristic
11C22×C22⋊C4×C131—21no—
12C22×C22⋊C4×C131C2211yescharacteristic
13C2×#107×C131—21no—
14C2×#102×C131—21no—
15C2×C22⋊C8×C131C2211yescharacteristic
16C2×C22⋊C8×C131C2211yescharacteristic
17#397×C131—21no—
18#394×C131—21no—
19#394×C131—21no—
20#392×C131—21no—
21#386×C131—21no—
22#380×C131C2211yescharacteristic
23C2×#95×C131—21no—
24C2×#95×C131C2211yescharacteristic
25#340×C131—21no—
26#340×C131—21no—
27#327×C131—22no—
28#323×C131—22no—
29C25×C131D411yescharacteristic
30C22×D4×C131—21no—
31C22×D4×C131—21no—
32C22×D4×C131—21no—
33C22×D4×C131D411yescharacteristic
34C23×C4×C131—21no—
35C23×C4×C131—21no—
36C23×C4×C131D411yescharacteristic
37C23×C4×C131C2311yescharacteristic
38C22×C8×C131—21no—
39C22×C8×C131—21no—
40#121×C131—21no—
41#121×C131—21no—
42#121×C131—21no—
43#121×C131—21no—
44#120×C131—42no—
45#120×C131—42no—
46C2×C4⋊C4×C131—21no—
47C2×C4⋊C4×C131—21no—
48C2×C4⋊C4×C131—42no—
49C2×C4⋊C4×C131D411yescharacteristic
50C2×C4⋊C4×C131D411yescharacteristic
51C2×C4⋊C4×C131D411yescharacteristic
52C2×C22⋊C4×C131—21no—
53C2×C22⋊C4×C131—21no—
54C2×C22⋊C4×C131—21no—
55C2×C22⋊C4×C131—21no—
56C2×C22⋊C4×C131—21no—
57C2×C22⋊C4×C131—21no—
58C2×C22⋊C4×C131—21no—
59C2×C22⋊C4×C131—21no—
60C2×C22⋊C4×C131—21no—
61C2×C22⋊C4×C131—21no—
62C2×C22⋊C4×C131—21no—
63C2×C22⋊C4×C131—21no—
64C2×C22⋊C4×C131—42no—
65C2×C22⋊C4×C131—42no—
66C2×C22⋊C4×C131—42no—
67#107×C131—42no—
68#102×C131—42no—
69C22⋊C8×C131—21no—
70C22⋊C8×C131—21no—
71C22⋊C8×C131—21no—
72C22⋊C8×C131D412yescomplemented
73#95×C131—21no—
74#95×C131—21no—
75#95×C131—21no—
76#95×C131—21no—
77#95×C131—21no—
78#95×C131—42no—
79C24×C131—21no—
80C24×C131—21no—
81C24×C131—21no—
82C24×C131—21no—
83C24×C131—21no—
84C24×C131—21no—
85C24×C131—21no—
86C24×C131—41no—
87C24×C131—41no—
88C24×C131—41no—
89C24×C131—41no—
90C24×C131D812yes—
91C24×C131C2×D411yescharacteristic
92C2×D4×C131—21no—
93C2×D4×C131—21no—
94C2×D4×C131—41no—
95C2×D4×C131—41no—
96C2×D4×C131—42no—
97C2×D4×C131—42no—
98C2×D4×C131—41no—
99C2×D4×C131—41no—
100C2×D4×C131—41no—
101C2×D4×C131—41no—
102C2×D4×C131—41no—
103C2×D4×C131—41no—
104C2×D4×C131—81no—
105C2×D4×C131—81no—
106C2×D4×C131—81no—
107C2×D4×C131—81no—
108C22×C4×C131—22no—
109C22×C4×C131—22no—
110C22×C4×C131—21no—
111C22×C4×C131—21no—
112C22×C4×C131—21no—
113C22×C4×C131—21no—
114C22×C4×C131—21no—
115C22×C4×C131—21no—
116C22×C4×C131—41no—
117C22×C4×C131—41no—
118C22×C4×C131—41no—
119C22×C4×C131—41no—
120C22×C4×C131—41no—
121C22×C4×C131—41no—
122C22×C4×C131—41no—
123C22×C4×C131—41no—
124C22×C4×C131—41no—
125C22×C4×C131—41no—
126C22×C4×C131—41no—
127C22×C4×C131—41no—
128C22×C4×C131—41no—
129C22×C4×C131—41no—
130C22×C4×C131—41no—
131C22×C4×C131—41no—
132C22×C4×C131C2×D411yescharacteristic
133C22×C4×C131C2×D411yescharacteristic
134C22×C4×C131C2×D411yescharacteristic
135C22×C4×C131#4111yescharacteristic
136C22×C4×C131#4111yescharacteristic
137C22×C4×C131#4111yescharacteristic
138C2×C8×C131—22no—
139C2×C8×C131—41no—
140C2×C8×C131—41no—
141C2×C8×C131—41no—
142C2×C8×C131—41no—
143C2×C8×C131—41no—
144C4⋊C4×C131—22no—
145C4⋊C4×C131—22no—
146C4⋊C4×C131—21no—
147C4⋊C4×C131—21no—
148C4⋊C4×C131—41no—
149C4⋊C4×C131—41no—
150C4⋊C4×C131—41no—
151C4⋊C4×C131—41no—
152C22⋊C4×C131—42no—
153C22⋊C4×C131—42no—
154C22⋊C4×C131—48no—
155C22⋊C4×C131—41no—
156C22⋊C4×C131—41no—
157C22⋊C4×C131—41no—
158C22⋊C4×C131—41no—
159C22⋊C4×C131—41no—
160C22⋊C4×C131—41no—
161C22⋊C4×C131—41no—
162C22⋊C4×C131—41no—
163C22⋊C4×C131—81no—
164C22⋊C4×C131—81no—
165C23×C131—21no—
166C23×C131—21no—
167C23×C131—21no—
168C23×C131—21no—
169C23×C131—22no—
170C23×C131—22no—
171C23×C131—22no—
172C23×C131—42no—
173C23×C131—42no—
174C23×C131—42no—
175C23×C131—42no—
176C23×C131—42no—
177C23×C131—42no—
178C23×C131—41no—
179C23×C131—41no—
180C23×C131—41no—
181C23×C131—41no—
182C23×C131—41no—
183C23×C131—41no—
184C23×C131—41no—
185C23×C131—41no—
186C23×C131—41no—
187C23×C131—41no—
188C23×C131—41no—
189C23×C131—41no—
190C23×C131—41no—
191C23×C131—41no—
192C23×C131—41no—
193C23×C131—81no—
194C23×C131—81no—
195C23×C131—81no—
196C23×C131—81no—
197C23×C131—81no—
198C23×C131—81no—
199C23×C131#12011yescharacteristic
200C23×C131#12111yescharacteristic
201C23×C131#12311yescharacteristic
202C23×C131C2×D811yescharacteristic
203C23×C131#13511yescharacteristic
204C23×C131AGL(1,ℤ/8)11yescharacteristic
205C23×C131#13711yescharacteristic
206D4×C131—42no—
207D4×C131—81no—
208D4×C131—84no—
209D4×C131—84no—
210D4×C131—81no—
211D4×C131—81no—
212D4×C131—81no—
213D4×C131—81no—
214C2×C4×C131—21no—
215C2×C4×C131—21no—
216C2×C4×C131—21no—
217C2×C4×C131—21no—
218C2×C4×C131—41no—
219C2×C4×C131—41no—
220C2×C4×C131—41no—
221C2×C4×C131—41no—
222C2×C4×C131—42no—
223C2×C4×C131—42no—
224C2×C4×C131—42no—
225C2×C4×C131—42no—
226C2×C4×C131—42no—
227C2×C4×C131—42no—
228C2×C4×C131—41no—
229C2×C4×C131—41no—
230C2×C4×C131—41no—
231C2×C4×C131—41no—
232C2×C4×C131—41no—
233C2×C4×C131—41no—
234C2×C4×C131—41no—
235C2×C4×C131—41no—
236C2×C4×C131—41no—
237C2×C4×C131—41no—
238C2×C4×C131—42no—
239C2×C4×C131—41no—
240C2×C4×C131—41no—
241C2×C4×C131—81no—
242C2×C4×C131—81no—
243C2×C4×C131—81no—
244C2×C4×C131—81no—
245C2×C4×C131—81no—
246C2×C4×C131—81no—
247C2×C4×C131—81no—
248C2×C4×C131—81no—
249C2×C4×C131—81no—
250C2×C4×C131#12111yescharacteristic
251C2×C4×C131#12111yescharacteristic
252C2×C4×C131#12311yescharacteristic
253C2×C4×C131#12411yescharacteristic
254C8×C131—42no—
255C8×C131—81no—
256C22×C131—21no—
257C22×C131—21no—
258C22×C131—21no—
259C22×C131—21no—
260C22×C131—21no—
261C22×C131—21no—
262C22×C131—21no—
263C22×C131—21no—
264C22×C131—21no—
265C22×C131—21no—
266C22×C131—21no—
267C22×C131—21no—
268C22×C131—44no—
269C22×C131—42no—
270C22×C131—42no—
271C22×C131—42no—
272C22×C131—82no—
273C22×C131—82no—
274C22×C131—82no—
275C22×C131—81no—
276C22×C131—81no—
277C22×C131—81no—
278C22×C131—81no—
279C22×C131—81no—
280C22×C131—81no—
281C22×C131—81no—
282C22×C131—81no—
283C22×C131—81no—
284C22×C131—81no—
285C22×C131—81no—
286C22×C131#39411yescharacteristic
287C22×C131#44711yescharacteristic
288C22×C131#45211yescharacteristic
289C22×C131#45311yescharacteristic
290C22×C131#45511yescharacteristic
291C22×C131B(4,𝔽2)11yescharacteristic
292C22×C131#45811yescharacteristic
293C22×C131#46611yescharacteristic
294C22×C131#46811yescharacteristic
295C22×C131#48011yescharacteristic
296C22×C131#48211yescharacteristic
297C4×C131—21no—
298C4×C131—21no—
299C4×C131—21no—
300C4×C131—21no—
301C4×C131—82no—
302C4×C131—82no—
303C4×C131—81no—
304C4×C131—81no—
305C4×C131—81no—
306C4×C131—81no—
307C2×C131—21no—
308C2×C131—21no—
309C2×C131—21no—
310C2×C131—21no—
311C2×C131—82no—
312C2×C131—161no—
313C2×C131#159511yescharacteristic
314C2×C131#160611yescharacteristic
315C2×C131#160711yescharacteristic
316C2×C131#161811yescharacteristic
317C2×C131#203311yescharacteristic
318C2×C131#203711yescharacteristic
319C2×C131#204411yescharacteristic
320#10394C13111yesmaximal, characteristic, direct product factor, Sylow
321C131#1039411yescharacteristic, direct product factor, Sylow
322#2617C2×C13111yescharacteristic
323#1874C2×C13111yescharacteristic, complemented
324#1852C2×C13111yescharacteristic, complemented
325C2×#327C2×C13111yescharacteristic, complemented
326C2×#323C2×C13111yescharacteristic, complemented
327#1439C2×C13111yescharacteristic, complemented
328#1294C2×C13111yescharacteristic, complemented
329C2×#121C22×C13111yescharacteristic
330C2×#120—21no—
331C22×C4⋊C4C22×C13111yescharacteristic
332C22×C22⋊C4—21no—
333C22×C22⋊C4C22×C13111yescharacteristic
334C2×#107—21no—
335C2×#102—21no—
336C2×C22⋊C8C22×C13111yescharacteristic
337C2×C22⋊C8C22×C13111yescharacteristic
338#397—21no—
339#394—21no—
340#394—21no—
341#392—21no—
342#386—21no—
343#380C22×C13111yescharacteristic
344C2×#95—21no—
345C2×#95C22×C13111yescharacteristic
346#340—21no—
347#340—21no—
348#327—22no—
349#323—22no—
350C25D4×C13111yescharacteristic
351C22×D4—21no—
352C22×D4—21no—
353C22×D4—21no—
354C22×D4D4×C13111yescharacteristic
355C23×C4—21no—
356C23×C4—21no—
357C23×C4D4×C13111yescharacteristic
358C23×C4C23×C13111yescharacteristic
359C22×C8—21no—
360C22×C8—21no—
361#121—21no—
362#121—21no—
363#121—21no—
364#121—21no—
365#120—42no—
366#120—42no—
367C2×C4⋊C4—21no—
368C2×C4⋊C4—21no—
369C2×C4⋊C4—42no—
370C2×C4⋊C4D4×C13111yescharacteristic
371C2×C4⋊C4D4×C13111yescharacteristic
372C2×C4⋊C4D4×C13111yescharacteristic
373C2×C22⋊C4—21no—
374C2×C22⋊C4—21no—
375C2×C22⋊C4—21no—
376C2×C22⋊C4—21no—
377C2×C22⋊C4—21no—
378C2×C22⋊C4—21no—
379C2×C22⋊C4—21no—
380C2×C22⋊C4—21no—
381C2×C22⋊C4—21no—
382C2×C22⋊C4—21no—
383C2×C22⋊C4—21no—
384C2×C22⋊C4—21no—
385C2×C22⋊C4—42no—
386C2×C22⋊C4—42no—
387C2×C22⋊C4—42no—
388#107—42no—
389#102—42no—
390C22⋊C8—21no—
391C22⋊C8—21no—
392C22⋊C8—21no—
393C22⋊C8D4×C13112yescomplemented
394#95—21no—
395#95—21no—
396#95—21no—
397#95—21no—
398#95—21no—
399#95—42no—
400C24—21no—
401C24—21no—
402C24—21no—
403C24—21no—
404C24—21no—
405C24—21no—
406C24—21no—
407C24—41no—
408C24—41no—
409C24—41no—
410C24—41no—
411C24D8×C13112yes—
412C24C2×D4×C13111yescharacteristic
413C2×D4—21no—
414C2×D4—21no—
415C2×D4—41no—
416C2×D4—41no—
417C2×D4—42no—
418C2×D4—42no—
419C2×D4—41no—
420C2×D4—41no—
421C2×D4—41no—
422C2×D4—41no—
423C2×D4—41no—
424C2×D4—41no—
425C2×D4—81no—
426C2×D4—81no—
427C2×D4—81no—
428C2×D4—81no—
429C22×C4—22no—
430C22×C4—22no—
431C22×C4—21no—
432C22×C4—21no—
433C22×C4—21no—
434C22×C4—21no—
435C22×C4—21no—
436C22×C4—21no—
437C22×C4—41no—
438C22×C4—41no—
439C22×C4—41no—
440C22×C4—41no—
441C22×C4—41no—
442C22×C4—41no—
443C22×C4—41no—
444C22×C4—41no—
445C22×C4—41no—
446C22×C4—41no—
447C22×C4—41no—
448C22×C4—41no—
449C22×C4—41no—
450C22×C4—41no—
451C22×C4—41no—
452C22×C4—41no—
453C22×C4C2×D4×C13111yescharacteristic
454C22×C4C2×D4×C13111yescharacteristic
455C22×C4C2×D4×C13111yescharacteristic
456C22×C4#41×C13111yescharacteristic
457C22×C4#41×C13111yescharacteristic
458C22×C4#41×C13111yescharacteristic
459C2×C8—22no—
460C2×C8—41no—
461C2×C8—41no—
462C2×C8—41no—
463C2×C8—41no—
464C2×C8—41no—
465C4⋊C4—22no—
466C4⋊C4—22no—
467C4⋊C4—21no—
468C4⋊C4—21no—
469C4⋊C4—41no—
470C4⋊C4—41no—
471C4⋊C4—41no—
472C4⋊C4—41no—
473C22⋊C4—42no—
474C22⋊C4—42no—
475C22⋊C4—48no—
476C22⋊C4—41no—
477C22⋊C4—41no—
478C22⋊C4—41no—
479C22⋊C4—41no—
480C22⋊C4—41no—
481C22⋊C4—41no—
482C22⋊C4—41no—
483C22⋊C4—41no—
484C22⋊C4—81no—
485C22⋊C4—81no—
486C23—21no—
487C23—21no—
488C23—21no—
489C23—21no—
490C23—22no—
491C23—22no—
492C23—22no—
493C23—42no—
494C23—42no—
495C23—42no—
496C23—42no—
497C23—42no—
498C23—42no—
499C23—41no—
500C23—41no—
501C23—41no—
502C23—41no—
503C23—41no—
504C23—41no—
505C23—41no—
506C23—41no—
507C23—41no—
508C23—41no—
509C23—41no—
510C23—41no—
511C23—41no—
512C23—41no—
513C23—41no—
514C23—81no—
515C23—81no—
516C23—81no—
517C23—81no—
518C23—81no—
519C23—81no—
520C23#120×C13111yescharacteristic
521C23#121×C13111yescharacteristic
522C23#123×C13111yescharacteristic
523C23C2×D8×C13111yescharacteristic
524C23#135×C13111yescharacteristic
525C23AGL(1,ℤ/8)×C13111yescharacteristic
526C23#137×C13111yescharacteristic
527D4—42no—
528D4—81no—
529D4—84no—
530D4—84no—
531D4—81no—
532D4—81no—
533D4—81no—
534D4—81no—
535C2×C4—21no—
536C2×C4—21no—
537C2×C4—21no—
538C2×C4—21no—
539C2×C4—41no—
540C2×C4—41no—
541C2×C4—41no—
542C2×C4—41no—
543C2×C4—42no—
544C2×C4—42no—
545C2×C4—42no—
546C2×C4—42no—
547C2×C4—42no—
548C2×C4—42no—
549C2×C4—41no—
550C2×C4—41no—
551C2×C4—41no—
552C2×C4—41no—
553C2×C4—41no—
554C2×C4—41no—
555C2×C4—41no—
556C2×C4—41no—
557C2×C4—41no—
558C2×C4—41no—
559C2×C4—42no—
560C2×C4—41no—
561C2×C4—41no—
562C2×C4—81no—
563C2×C4—81no—
564C2×C4—81no—
565C2×C4—81no—
566C2×C4—81no—
567C2×C4—81no—
568C2×C4—81no—
569C2×C4—81no—
570C2×C4—81no—
571C2×C4#121×C13111yescharacteristic
572C2×C4#121×C13111yescharacteristic
573C2×C4#123×C13111yescharacteristic
574C2×C4#124×C13111yescharacteristic
575C8—42no—
576C8—81no—
577C22—21no—
578C22—21no—
579C22—21no—
580C22—21no—
581C22—21no—
582C22—21no—
583C22—21no—
584C22—21no—
585C22—21no—
586C22—21no—
587C22—21no—
588C22—21no—
589C22—44no—
590C22—42no—
591C22—42no—
592C22—42no—
593C22—82no—
594C22—82no—
595C22—82no—
596C22—81no—
597C22—81no—
598C22—81no—
599C22—81no—
600C22—81no—
601C22—81no—
602C22—81no—
603C22—81no—
604C22—81no—
605C22—81no—
606C22—81no—
607C22#394×C13111yescharacteristic
608C22#447×C13111yescharacteristic
609C22#452×C13111yescharacteristic
610C22#453×C13111yescharacteristic
611C22#455×C13111yescharacteristic
612C22B(4,𝔽2)×C13111yescharacteristic
613C22#458×C13111yescharacteristic
614C22#466×C13111yescharacteristic
615C22#468×C13111yescharacteristic
616C22#480×C13111yescharacteristic
617C22#482×C13111yescharacteristic
618C4—21no—
619C4—21no—
620C4—21no—
621C4—21no—
622C4—82no—
623C4—81no—
624C4—81no—
625C4—82no—
626C4—81no—
627C4—81no—
628C2—21no—
629C2—21no—
630C2—21no—
631C2—21no—
632C2—82no—
633C2—161no—
634C2#1595×C13111yescharacteristic
635C2#1606×C13111yescharacteristic
636C2#1607×C13111yescharacteristic
637C2#1618×C13111yescharacteristic
638C2#2033×C13111yescharacteristic
639C2#2037×C13111yescharacteristic
640C2#2044×C13111yescharacteristic
subgroupG/H
center, socleC23×C131#120
commutator, Frattini, cosocleC23×C4C23×C131
prime radical#2617×C131C2
LCSG ▷ C23×C4 ▷ C22 ▷ C1
UCSC1 ◁ C23×C131 ◁ C23×C4×C131 ◁ G

Complements

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

NH ≅ G/Ntype
2. #1874×C131C2semidirect
3. #1852×C131C2semidirect
4. C2×#327×C131C2semidirect
5. C2×#323×C131C2semidirect
6. #1439×C131C2semidirect
7. #1294×C131C2semidirect
72. C22⋊C8×C131D4semidirect
320. #10394C131direct (N × H)
321. C131#10394direct (N × H)
323. #1874C2×C131semidirect
324. #1852C2×C131semidirect
325. C2×#327C2×C131semidirect
326. C2×#323C2×C131semidirect
327. #1439C2×C131semidirect
328. #1294C2×C131semidirect
393. C22⋊C8D4×C131semidirect

Maximal subgroups

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

subgroupindex
#2617×C1312
#1874×C1312
#1852×C1312
C2×#327×C1312
C2×#323×C1312
#1439×C1312
#1294×C1312
#10394131