Finite Group Databasebeta

← C131×#23894 #45709778

Subgroups — C131×#23894 #45709778

Order 33536.

1642 conjugacy classes of subgroups.

The subgroup lattice has 1018 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#3586×C131C211yesmaximal, characteristic, complemented
2#3585×C131C211yesmaximal, characteristic, complemented
3#3020×C131C211yesmaximal, characteristic, complemented
4#3019×C131C211yesmaximal, characteristic, complemented
5#3010×C131C211yesmaximal, characteristic, complemented
6#3009×C131C211yesmaximal, characteristic, complemented
7#2019×C131C211yesmaximal, characteristic, complemented
8#2017×C131C211yesmaximal, characteristic, complemented
9#2009×C131C211yesmaximal, characteristic, complemented
10#2008×C131C211yesmaximal, characteristic, complemented
11#1903×C131C211yesmaximal, characteristic, complemented
12#1902×C131C211yesmaximal, characteristic, complemented
13#1881×C131C211yesmaximal, characteristic, complemented
14#1881×C131C211yesmaximal, characteristic, complemented
15#1794×C131C211yesmaximal, characteristic, complemented
16#585×C131C2211yescharacteristic
17C2×2−1+4×C131C2211yescharacteristic, complemented
18C2×H(5,𝔽2)×C131C2211yescharacteristic
19#578×C131—22no—
20#578×C131—22no—
21#577×C131—22no—
22#577×C131—22no—
23#577×C131—22no—
24#577×C131—22no—
25#576×C131—22no—
26#576×C131—22no—
27#575×C131—22no—
28#575×C131—22no—
29#575×C131C2211yescharacteristic
30#575×C131C2211yescharacteristic
31#575×C131C2211yescharacteristic
32#575×C131C2211yescharacteristic, complemented
33#575×C131C2211yescharacteristic, complemented
34C2×#137×C131—22no—
35C2×#137×C131C2211yescharacteristic
36C2×#137×C131C2211yescharacteristic, complemented
37C2×AGL(1,ℤ/8)×C131—22no—
38C2×AGL(1,ℤ/8)×C131C2211yescharacteristic
39C2×AGL(1,ℤ/8)×C131C2211yescharacteristic
40C22×SD16×C131C2211yescharacteristic, complemented
41#568×C131C2211yescharacteristic
42#568×C131C2211yescharacteristic, complemented
43#536×C131C2211yescharacteristic, complemented
44#535×C131C2211yescharacteristic, complemented
45#456×C131—22no—
46#455×C131—22no—
47#454×C131—22no—
48#453×C131—22no—
49#452×C131—22no—
50#450×C131—22no—
51#449×C131—22no—
52#448×C131—22no—
53#421×C131C2211yescharacteristic
54#421×C131C2211yescharacteristic, complemented
55#421×C131C2211yescharacteristic, complemented
56#421×C131C2211yescharacteristic, complemented
57#419×C131C2211yescharacteristic, complemented
58#418×C131C2211yescharacteristic, complemented
59#416×C131C2211yescharacteristic
60#416×C131C2211yescharacteristic, complemented
61C2×#101×C131C2211yescharacteristic, complemented
62C2×#100×C131C2211yescharacteristic, complemented
63#410×C131C2211yescharacteristic, complemented
64#408×C131C2211yescharacteristic, complemented
65#408×C131C2211yescharacteristic, complemented
66#408×C131C2211yescharacteristic, complemented
67#344×C131C2211yescharacteristic, complemented
68#344×C131C2211yescharacteristic, complemented
69#341×C131C2211yescharacteristic, complemented
70#338×C131C2211yescharacteristic, complemented
712−1+4×C131—22no—
722−1+4×C131—21no—
732−1+4×C131—22no—
742−1+4×C131—21no—
752−1+4×C131—22no—
762−1+4×C131—41no—
772−1+4×C131D412yescomplemented
78H(5,𝔽2)×C131—22no—
79H(5,𝔽2)×C131—21no—
80H(5,𝔽2)×C131—22no—
81H(5,𝔽2)×C131—21no—
82H(5,𝔽2)×C131—22no—
83H(5,𝔽2)×C131—41no—
84H(5,𝔽2)×C131—41no—
85H(5,𝔽2)×C131D412yescomplemented
86C2×#41×C131—22no—
87C2×#41×C131—22no—
88C2×#41×C131—21no—
89C2×#41×C131—21no—
90C2×#41×C131—21no—
91C2×#41×C131—21no—
92C2×#41×C131—41no—
93C2×#41×C131—41no—
94C2×#41×C131C2311yescharacteristic
95C2×#41×C131C2311yescharacteristic
96C2×#41×C131C2311yescharacteristic
97C2×#41×C131C2311yescharacteristic
98C2×#41×C131C2311yescharacteristic
99C22×Q8×C131—21no—
100C22×Q8×C131—21no—
101C22×Q8×C131C2311yescharacteristic
102C22×D4×C131—21no—
103C22×D4×C131—21no—
104C22×D4×C131—41no—
105C22×D4×C131C2311yescharacteristic
106#137×C131—24no—
107#137×C131—24no—
108#137×C131—24no—
109#137×C131—24no—
110#137×C131—22no—
111#137×C131—22no—
112#137×C131—21no—
113#137×C131—22no—
114#137×C131—21no—
115#137×C131—21no—
116#137×C131—21no—
117#137×C131—21no—
118#137×C131—21no—
119#137×C131—21no—
120#137×C131—21no—
121#137×C131—22no—
122#137×C131D412yes—
123#137×C131D412yescomplemented
124AGL(1,ℤ/8)×C131—24no—
125AGL(1,ℤ/8)×C131—24no—
126AGL(1,ℤ/8)×C131—24no—
127AGL(1,ℤ/8)×C131—24no—
128AGL(1,ℤ/8)×C131—22no—
129AGL(1,ℤ/8)×C131—22no—
130AGL(1,ℤ/8)×C131—21no—
131AGL(1,ℤ/8)×C131—22no—
132AGL(1,ℤ/8)×C131—21no—
133AGL(1,ℤ/8)×C131—21no—
134AGL(1,ℤ/8)×C131—21no—
135AGL(1,ℤ/8)×C131—21no—
136AGL(1,ℤ/8)×C131—21no—
137AGL(1,ℤ/8)×C131—21no—
138AGL(1,ℤ/8)×C131—21no—
139AGL(1,ℤ/8)×C131—22no—
140AGL(1,ℤ/8)×C131D412yes—
141AGL(1,ℤ/8)×C131D412yescomplemented
142#135×C131—24no—
143#135×C131—24no—
144#135×C131—24no—
145#135×C131—24no—
146#135×C131—22no—
147#135×C131—22no—
148#135×C131—22no—
149#135×C131—22no—
150#135×C131—41no—
151C2×Q16×C131—24no—
152C2×Q16×C131—21no—
153C2×Q16×C131D412yescomplemented
154C2×SD16×C131—24no—
155C2×SD16×C131—24no—
156C2×SD16×C131—21no—
157C2×SD16×C131—21no—
158C2×SD16×C131—22no—
159C2×SD16×C131—22no—
160C2×SD16×C131—41no—
161C2×SD16×C131D412yes—
162C2×SD16×C131D412yescomplemented
163C2×D8×C131—24no—
164C2×D8×C131—21no—
165C2×D8×C131D412yes—
166#131×C131—22no—
167#131×C131—22no—
168#131×C131—22no—
169#131×C131—22no—
170C2×M16×C131—22no—
171C2×M16×C131—22no—
172C2×M16×C131C2311yescharacteristic
173C2×M16×C131C2311yescharacteristic
174C2×M16×C131C2311yescharacteristic
175C2×M16×C131C2311yescharacteristic
176C2×M16×C131C2311yescharacteristic
177C22×C8×C131C2311yescharacteristic
178C4⋊Q8×C131—21no—
179#127×C131—21no—
180#124×C131—21no—
181#124×C131—21no—
182#123×C131—41no—
183C22⋊Q8×C131—22no—
184#121×C131—22no—
185#120×C131—41no—
186#117×C131C2311yescharacteristic
187#117×C131C2311yescharacteristic
188#104×C131—22no—
189#104×C131—22no—
190#104×C131—22no—
191#104×C131—22no—
192#103×C131—21no—
193#103×C131—21no—
194#103×C131—22no—
195#102×C131—21no—
196#102×C131—21no—
197#102×C131—22no—
198#101×C131—22no—
199#100×C131—22no—
200#99×C131—41no—
201C22⋊C8×C131—22no—
202C22⋊C8×C131—22no—
203C22⋊C8×C131—41no—
204C24×C131—21no—
205C24×C131—41no—
206#41×C131—21no—
207#41×C131—21no—
208#41×C131—21no—
209#41×C131—21no—
210#41×C131—24no—
211#41×C131—24no—
212#41×C131—22no—
213#41×C131—22no—
214#41×C131—22no—
215#41×C131—22no—
216#41×C131—21no—
217#41×C131—21no—
218#41×C131—21no—
219#41×C131—21no—
220#41×C131—21no—
221#41×C131—21no—
222#41×C131—21no—
223#41×C131—21no—
224#41×C131—21no—
225#41×C131—21no—
226#41×C131—21no—
227#41×C131—21no—
228#41×C131—42no—
229#41×C131—42no—
230#41×C131—42no—
231#41×C131—42no—
232#41×C131—42no—
233#41×C131—44no—
234#41×C131—42no—
235#41×C131—42no—
236#41×C131—42no—
237#41×C131—41no—
238#41×C131—41no—
239#41×C131—44no—
240#41×C131—42no—
241#41×C131—42no—
242#41×C131C2×D412yes—
243#41×C131C2×D412yes—
244#41×C131C2×D412yes—
245#41×C131C2×D412yes—
246C2×Q8×C131—21no—
247C2×Q8×C131—24no—
248C2×Q8×C131—22no—
249C2×Q8×C131—22no—
250C2×Q8×C131—21no—
251C2×Q8×C131—21no—
252C2×Q8×C131—21no—
253C2×Q8×C131—21no—
254C2×Q8×C131—41no—
255C2×Q8×C131—42no—
256C2×Q8×C131—42no—
257C2×Q8×C131—41no—
258C2×Q8×C131—42no—
259C2×Q8×C131C2×D412yes—
260C2×Q8×C131C2×D411yescharacteristic
261C2×Q8×C131C2×D411yescharacteristic
262C2×Q8×C131C2×D411yescharacteristic
263C2×Q8×C131C2×D411yescharacteristic
264C2×Q8×C131C2×D411yescharacteristic
265C2×D4×C131—21no—
266C2×D4×C131—21no—
267C2×D4×C131—24no—
268C2×D4×C131—22no—
269C2×D4×C131—22no—
270C2×D4×C131—21no—
271C2×D4×C131—21no—
272C2×D4×C131—21no—
273C2×D4×C131—21no—
274C2×D4×C131—21no—
275C2×D4×C131—21no—
276C2×D4×C131—21no—
277C2×D4×C131—21no—
278C2×D4×C131—42no—
279C2×D4×C131—41no—
280C2×D4×C131—41no—
281C2×D4×C131—42no—
282C2×D4×C131—42no—
283C2×D4×C131—41no—
284C2×D4×C131—44no—
285C2×D4×C131—42no—
286C2×D4×C131—42no—
287C2×D4×C131—44no—
288C2×D4×C131—41no—
289C2×D4×C131—42no—
290C2×D4×C131—42no—
291C2×D4×C131C2×D412yes—
292C2×D4×C131C2×D411yescharacteristic
293C2×D4×C131C2×D411yescharacteristic
294C2×D4×C131C2×D411yescharacteristic
295C2×D4×C131C2×D411yescharacteristic
296C2×D4×C131C2×D411yescharacteristic
297C22×C4×C131—21no—
298C22×C4×C131—21no—
299C22×C4×C131—21no—
300C22×C4×C131—21no—
301C22×C4×C131—21no—
302C22×C4×C131—21no—
303C22×C4×C131—41no—
304C22×C4×C131—42no—
305C22×C4×C131—41no—
306C22×C4×C131—41no—
307C22×C4×C131C2411yescharacteristic
308Q16×C131—24no—
309Q16×C131—22no—
310Q16×C131—22no—
311Q16×C131—22no—
312Q16×C131—24no—
313Q16×C131—22no—
314Q16×C131—41no—
315SD16×C131—24no—
316SD16×C131—22no—
317SD16×C131—24no—
318SD16×C131—22no—
319SD16×C131—22no—
320SD16×C131—22no—
321SD16×C131—22no—
322SD16×C131—24no—
323SD16×C131—22no—
324SD16×C131—22no—
325SD16×C131—24no—
326SD16×C131—22no—
327SD16×C131—44no—
328SD16×C131—41no—
329SD16×C131—41no—
330D8×C131—24no—
331D8×C131—22no—
332D8×C131—22no—
333D8×C131—22no—
334D8×C131—24no—
335D8×C131—22no—
336D8×C131—41no—
337M16×C131—24no—
338M16×C131—24no—
339M16×C131—21no—
340M16×C131—21no—
341M16×C131—21no—
342M16×C131—21no—
343M16×C131—21no—
344M16×C131—21no—
345M16×C131—21no—
346M16×C131—21no—
347M16×C131C2×D412yes—
348M16×C131C2×D412yes—
349C2×C8×C131—24no—
350C2×C8×C131—24no—
351C2×C8×C131—21no—
352C2×C8×C131—21no—
353C2×C8×C131—21no—
354C2×C8×C131—21no—
355C2×C8×C131—21no—
356C2×C8×C131—21no—
357C2×C8×C131C2×D412yes—
358C2×C8×C131C2×D412yes—
359C4⋊C4×C131—21no—
360C4⋊C4×C131—21no—
361C4⋊C4×C131—42no—
362C22⋊C4×C131—21no—
363C22⋊C4×C131—21no—
364C22⋊C4×C131—42no—
365C22⋊C4×C131—42no—
366C42×C131—21no—
367C42×C131—21no—
368C23×C131—21no—
369C23×C131—21no—
370C23×C131—21no—
371C23×C131—21no—
372C23×C131—21no—
373C23×C131—22no—
374C23×C131—42no—
375C23×C131—44no—
376C23×C131—41no—
377C23×C131—41no—
378C23×C131—161no—
379C23×C131—162no—
380C23×C131H(5,𝔽2)11yescharacteristic
381Q8×C131—21no—
382Q8×C131—21no—
383Q8×C131—21no—
384Q8×C131—21no—
385Q8×C131—22no—
386Q8×C131—21no—
387Q8×C131—21no—
388Q8×C131—22no—
389Q8×C131—21no—
390Q8×C131—21no—
391Q8×C131—42no—
392Q8×C131—44no—
393Q8×C131—41no—
394Q8×C131—41no—
395Q8×C131#12012yes—
396Q8×C131#12012yes—
397D4×C131—22no—
398D4×C131—22no—
399D4×C131—22no—
400D4×C131—22no—
401D4×C131—21no—
402D4×C131—21no—
403D4×C131—22no—
404D4×C131—21no—
405D4×C131—21no—
406D4×C131—21no—
407D4×C131—21no—
408D4×C131—21no—
409D4×C131—21no—
410D4×C131—22no—
411D4×C131—42no—
412D4×C131—42no—
413D4×C131—44no—
414D4×C131—42no—
415D4×C131—44no—
416D4×C131—44no—
417D4×C131—41no—
418D4×C131—41no—
419D4×C131—41no—
420D4×C131—41no—
421D4×C131—41no—
422D4×C131—41no—
423D4×C131—41no—
424D4×C131—41no—
425D4×C131—162no—
426D4×C131#12012yes—
427D4×C131#12012yes—
428C2×C4×C131—21no—
429C2×C4×C131—21no—
430C2×C4×C131—22no—
431C2×C4×C131—22no—
432C2×C4×C131—22no—
433C2×C4×C131—22no—
434C2×C4×C131—21no—
435C2×C4×C131—21no—
436C2×C4×C131—22no—
437C2×C4×C131—21no—
438C2×C4×C131—42no—
439C2×C4×C131—42no—
440C2×C4×C131—42no—
441C2×C4×C131—44no—
442C2×C4×C131—44no—
443C2×C4×C131—44no—
444C2×C4×C131—41no—
445C2×C4×C131—41no—
446C2×C4×C131—41no—
447C2×C4×C131—41no—
448C2×C4×C131—41no—
449C2×C4×C131—41no—
450C2×C4×C131—41no—
451C2×C4×C131—41no—
452C2×C4×C131—41no—
453C2×C4×C131—41no—
454C2×C4×C131C22×D411yescharacteristic
455C2×C4×C131C22×D411yescharacteristic
456C2×C4×C131C22×D411yescharacteristic
457C2×C4×C131C22×D411yescharacteristic
458C2×C4×C131C22×D411yescharacteristic
459C2×C4×C131H(5,𝔽2)11yescharacteristic
460C8×C131—22no—
461C8×C131—22no—
462C8×C131—22no—
463C8×C131—22no—
464C8×C131—41no—
465C8×C131—41no—
466C22×C131—22no—
467C22×C131—22no—
468C22×C131—41no—
469C22×C131—42no—
470C22×C131—42no—
471C22×C131—41no—
472C22×C131—41no—
473C22×C131—41no—
474C22×C131—42no—
475C22×C131—81no—
476C22×C131—81no—
477C22×C131—82no—
478C22×C131—81no—
479C22×C131—82no—
480C22×C131—161no—
481C22×C131—162no—
482C22×C131—164no—
483C22×C131#53411yescharacteristic
484C22×C131D4211yescharacteristic
485C22×C131D4211yescharacteristic
486C4×C131—22no—
487C4×C131—22no—
488C4×C131—41no—
489C4×C131—41no—
490C4×C131—41no—
491C4×C131—42no—
492C4×C131—81no—
493C4×C131—81no—
494C4×C131C2×#12011yescharacteristic
495C4×C131C2×#12011yescharacteristic
496C4×C131D4211yescharacteristic
497C4×C131D4211yescharacteristic
498C2×C131—21no—
499C2×C131—21no—
500C2×C131—21no—
501C2×C131—42no—
502C2×C131—42no—
503C2×C131—81no—
504C2×C131—81no—
505C2×C131—82no—
506C2×C131—81no—
507C2×C131#240311yescharacteristic
508#23894C13111yesmaximal, characteristic, direct product factor, Sylow
509C131#2389411yescharacteristic, direct product factor, Sylow
510#3586C2×C13111yescharacteristic, complemented
511#3585C2×C13111yescharacteristic, complemented
512#3020C2×C13111yescharacteristic, complemented
513#3019C2×C13111yescharacteristic, complemented
514#3010C2×C13111yescharacteristic, complemented
515#3009C2×C13111yescharacteristic, complemented
516#2019C2×C13111yescharacteristic, complemented
517#2017C2×C13111yescharacteristic, complemented
518#2009C2×C13111yescharacteristic, complemented
519#2008C2×C13111yescharacteristic, complemented
520#1903C2×C13111yescharacteristic, complemented
521#1902C2×C13111yescharacteristic, complemented
522#1881C2×C13111yescharacteristic, complemented
523#1881C2×C13111yescharacteristic, complemented
524#1794C2×C13111yescharacteristic, complemented
525#585C22×C13111yescharacteristic
526C2×2−1+4C22×C13111yescharacteristic, complemented
527C2×H(5,𝔽2)C22×C13111yescharacteristic
528#578—22no—
529#578—22no—
530#577—22no—
531#577—22no—
532#577—22no—
533#577—22no—
534#576—22no—
535#576—22no—
536#575—22no—
537#575—22no—
538#575C22×C13111yescharacteristic
539#575C22×C13111yescharacteristic
540#575C22×C13111yescharacteristic
541#575C22×C13111yescharacteristic, complemented
542#575C22×C13111yescharacteristic, complemented
543C2×#137—22no—
544C2×#137C22×C13111yescharacteristic
545C2×#137C22×C13111yescharacteristic, complemented
546C2×AGL(1,ℤ/8)—22no—
547C2×AGL(1,ℤ/8)C22×C13111yescharacteristic
548C2×AGL(1,ℤ/8)C22×C13111yescharacteristic
549C22×SD16C22×C13111yescharacteristic, complemented
550#568C22×C13111yescharacteristic
551#568C22×C13111yescharacteristic, complemented
552#536C22×C13111yescharacteristic, complemented
553#535C22×C13111yescharacteristic, complemented
554#456—22no—
555#455—22no—
556#454—22no—
557#453—22no—
558#452—22no—
559#450—22no—
560#449—22no—
561#448—22no—
562#421C22×C13111yescharacteristic
563#421C22×C13111yescharacteristic, complemented
564#421C22×C13111yescharacteristic, complemented
565#421C22×C13111yescharacteristic, complemented
566#419C22×C13111yescharacteristic, complemented
567#418C22×C13111yescharacteristic, complemented
568#416C22×C13111yescharacteristic
569#416C22×C13111yescharacteristic, complemented
570C2×#101C22×C13111yescharacteristic, complemented
571C2×#100C22×C13111yescharacteristic, complemented
572#410C22×C13111yescharacteristic, complemented
573#408C22×C13111yescharacteristic, complemented
574#408C22×C13111yescharacteristic, complemented
575#408C22×C13111yescharacteristic, complemented
576#344C22×C13111yescharacteristic, complemented
577#344C22×C13111yescharacteristic, complemented
578#341C22×C13111yescharacteristic, complemented
579#338C22×C13111yescharacteristic, complemented
5802−1+4—22no—
5812−1+4—21no—
5822−1+4—22no—
5832−1+4—21no—
5842−1+4—22no—
5852−1+4—41no—
5862−1+4D4×C13112yescomplemented
587H(5,𝔽2)—22no—
588H(5,𝔽2)—21no—
589H(5,𝔽2)—22no—
590H(5,𝔽2)—21no—
591H(5,𝔽2)—22no—
592H(5,𝔽2)—41no—
593H(5,𝔽2)—41no—
594H(5,𝔽2)D4×C13112yescomplemented
595C2×#41—22no—
596C2×#41—22no—
597C2×#41—21no—
598C2×#41—21no—
599C2×#41—21no—
600C2×#41—21no—
601C2×#41—41no—
602C2×#41—41no—
603C2×#41C23×C13111yescharacteristic
604C2×#41C23×C13111yescharacteristic
605C2×#41C23×C13111yescharacteristic
606C2×#41C23×C13111yescharacteristic
607C2×#41C23×C13111yescharacteristic
608C22×Q8—21no—
609C22×Q8—21no—
610C22×Q8C23×C13111yescharacteristic
611C22×D4—21no—
612C22×D4—21no—
613C22×D4—41no—
614C22×D4C23×C13111yescharacteristic
615#137—24no—
616#137—24no—
617#137—24no—
618#137—24no—
619#137—22no—
620#137—22no—
621#137—21no—
622#137—22no—
623#137—21no—
624#137—21no—
625#137—21no—
626#137—21no—
627#137—21no—
628#137—21no—
629#137—21no—
630#137—22no—
631#137D4×C13112yes—
632#137D4×C13112yescomplemented
633AGL(1,ℤ/8)—24no—
634AGL(1,ℤ/8)—24no—
635AGL(1,ℤ/8)—24no—
636AGL(1,ℤ/8)—24no—
637AGL(1,ℤ/8)—22no—
638AGL(1,ℤ/8)—22no—
639AGL(1,ℤ/8)—21no—
640AGL(1,ℤ/8)—22no—
641AGL(1,ℤ/8)—21no—
642AGL(1,ℤ/8)—21no—
643AGL(1,ℤ/8)—21no—
644AGL(1,ℤ/8)—21no—
645AGL(1,ℤ/8)—21no—
646AGL(1,ℤ/8)—21no—
647AGL(1,ℤ/8)—21no—
648AGL(1,ℤ/8)—22no—
649AGL(1,ℤ/8)D4×C13112yes—
650AGL(1,ℤ/8)D4×C13112yescomplemented
651#135—24no—
652#135—24no—
653#135—24no—
654#135—24no—
655#135—22no—
656#135—22no—
657#135—22no—
658#135—22no—
659#135—41no—
660C2×Q16—24no—
661C2×Q16—21no—
662C2×Q16D4×C13112yescomplemented
663C2×SD16—24no—
664C2×SD16—24no—
665C2×SD16—21no—
666C2×SD16—21no—
667C2×SD16—22no—
668C2×SD16—22no—
669C2×SD16—41no—
670C2×SD16D4×C13112yes—
671C2×SD16D4×C13112yescomplemented
672C2×D8—24no—
673C2×D8—21no—
674C2×D8D4×C13112yes—
675#131—22no—
676#131—22no—
677#131—22no—
678#131—22no—
679C2×M16—22no—
680C2×M16—22no—
681C2×M16C23×C13111yescharacteristic
682C2×M16C23×C13111yescharacteristic
683C2×M16C23×C13111yescharacteristic
684C2×M16C23×C13111yescharacteristic
685C2×M16C23×C13111yescharacteristic
686C22×C8C23×C13111yescharacteristic
687C4⋊Q8—21no—
688#127—21no—
689#124—21no—
690#124—21no—
691#123—41no—
692C22⋊Q8—22no—
693#121—22no—
694#120—41no—
695#117C23×C13111yescharacteristic
696#117C23×C13111yescharacteristic
697#104—22no—
698#104—22no—
699#104—22no—
700#104—22no—
701#103—21no—
702#103—21no—
703#103—22no—
704#102—21no—
705#102—21no—
706#102—22no—
707#101—22no—
708#100—22no—
709#99—41no—
710C22⋊C8—22no—
711C22⋊C8—22no—
712C22⋊C8—41no—
713C24—21no—
714C24—41no—
715#41—21no—
716#41—21no—
717#41—21no—
718#41—21no—
719#41—24no—
720#41—24no—
721#41—22no—
722#41—22no—
723#41—22no—
724#41—22no—
725#41—21no—
726#41—21no—
727#41—21no—
728#41—21no—
729#41—21no—
730#41—21no—
731#41—21no—
732#41—21no—
733#41—21no—
734#41—21no—
735#41—21no—
736#41—21no—
737#41—42no—
738#41—42no—
739#41—42no—
740#41—42no—
741#41—42no—
742#41—44no—
743#41—42no—
744#41—42no—
745#41—42no—
746#41—41no—
747#41—41no—
748#41—44no—
749#41—42no—
750#41—42no—
751#41C2×D4×C13112yes—
752#41C2×D4×C13112yes—
753#41C2×D4×C13112yes—
754#41C2×D4×C13112yes—
755C2×Q8—21no—
756C2×Q8—24no—
757C2×Q8—22no—
758C2×Q8—22no—
759C2×Q8—21no—
760C2×Q8—21no—
761C2×Q8—21no—
762C2×Q8—21no—
763C2×Q8—41no—
764C2×Q8—42no—
765C2×Q8—42no—
766C2×Q8—41no—
767C2×Q8—42no—
768C2×Q8C2×D4×C13112yes—
769C2×Q8C2×D4×C13111yescharacteristic
770C2×Q8C2×D4×C13111yescharacteristic
771C2×Q8C2×D4×C13111yescharacteristic
772C2×Q8C2×D4×C13111yescharacteristic
773C2×Q8C2×D4×C13111yescharacteristic
774C2×D4—21no—
775C2×D4—21no—
776C2×D4—24no—
777C2×D4—22no—
778C2×D4—22no—
779C2×D4—21no—
780C2×D4—21no—
781C2×D4—21no—
782C2×D4—21no—
783C2×D4—21no—
784C2×D4—21no—
785C2×D4—21no—
786C2×D4—21no—
787C2×D4—42no—
788C2×D4—41no—
789C2×D4—41no—
790C2×D4—42no—
791C2×D4—42no—
792C2×D4—41no—
793C2×D4—44no—
794C2×D4—42no—
795C2×D4—42no—
796C2×D4—44no—
797C2×D4—41no—
798C2×D4—42no—
799C2×D4—42no—
800C2×D4C2×D4×C13112yes—
801C2×D4C2×D4×C13111yescharacteristic
802C2×D4C2×D4×C13111yescharacteristic
803C2×D4C2×D4×C13111yescharacteristic
804C2×D4C2×D4×C13111yescharacteristic
805C2×D4C2×D4×C13111yescharacteristic
806C22×C4—21no—
807C22×C4—21no—
808C22×C4—21no—
809C22×C4—21no—
810C22×C4—21no—
811C22×C4—21no—
812C22×C4—41no—
813C22×C4—42no—
814C22×C4—41no—
815C22×C4—41no—
816C22×C4C24×C13111yescharacteristic
817Q16—24no—
818Q16—22no—
819Q16—22no—
820Q16—22no—
821Q16—24no—
822Q16—22no—
823Q16—41no—
824SD16—24no—
825SD16—22no—
826SD16—24no—
827SD16—22no—
828SD16—22no—
829SD16—22no—
830SD16—22no—
831SD16—24no—
832SD16—22no—
833SD16—22no—
834SD16—24no—
835SD16—22no—
836SD16—44no—
837SD16—41no—
838SD16—41no—
839D8—24no—
840D8—22no—
841D8—22no—
842D8—22no—
843D8—24no—
844D8—22no—
845D8—41no—
846M16—24no—
847M16—24no—
848M16—21no—
849M16—21no—
850M16—21no—
851M16—21no—
852M16—21no—
853M16—21no—
854M16—21no—
855M16—21no—
856M16C2×D4×C13112yes—
857M16C2×D4×C13112yes—
858C2×C8—24no—
859C2×C8—24no—
860C2×C8—21no—
861C2×C8—21no—
862C2×C8—21no—
863C2×C8—21no—
864C2×C8—21no—
865C2×C8—21no—
866C2×C8C2×D4×C13112yes—
867C2×C8C2×D4×C13112yes—
868C4⋊C4—21no—
869C4⋊C4—21no—
870C4⋊C4—42no—
871C22⋊C4—21no—
872C22⋊C4—21no—
873C22⋊C4—42no—
874C22⋊C4—42no—
875C42—21no—
876C42—21no—
877C23—21no—
878C23—21no—
879C23—21no—
880C23—21no—
881C23—21no—
882C23—22no—
883C23—42no—
884C23—44no—
885C23—41no—
886C23—41no—
887C23—161no—
888C23—162no—
889C23H(5,𝔽2)×C13111yescharacteristic
890Q8—21no—
891Q8—21no—
892Q8—21no—
893Q8—21no—
894Q8—22no—
895Q8—21no—
896Q8—21no—
897Q8—22no—
898Q8—21no—
899Q8—21no—
900Q8—42no—
901Q8—44no—
902Q8—41no—
903Q8—41no—
904Q8#120×C13112yes—
905Q8#120×C13112yes—
906D4—22no—
907D4—22no—
908D4—22no—
909D4—22no—
910D4—21no—
911D4—21no—
912D4—22no—
913D4—21no—
914D4—21no—
915D4—21no—
916D4—21no—
917D4—21no—
918D4—21no—
919D4—22no—
920D4—42no—
921D4—42no—
922D4—44no—
923D4—42no—
924D4—44no—
925D4—44no—
926D4—41no—
927D4—41no—
928D4—41no—
929D4—41no—
930D4—41no—
931D4—41no—
932D4—41no—
933D4—41no—
934D4—162no—
935D4#120×C13112yes—
936D4#120×C13112yes—
937C2×C4—21no—
938C2×C4—21no—
939C2×C4—22no—
940C2×C4—22no—
941C2×C4—22no—
942C2×C4—22no—
943C2×C4—21no—
944C2×C4—21no—
945C2×C4—22no—
946C2×C4—21no—
947C2×C4—42no—
948C2×C4—42no—
949C2×C4—42no—
950C2×C4—44no—
951C2×C4—44no—
952C2×C4—44no—
953C2×C4—41no—
954C2×C4—41no—
955C2×C4—41no—
956C2×C4—41no—
957C2×C4—41no—
958C2×C4—41no—
959C2×C4—41no—
960C2×C4—41no—
961C2×C4—41no—
962C2×C4—41no—
963C2×C4C22×D4×C13111yescharacteristic
964C2×C4C22×D4×C13111yescharacteristic
965C2×C4C22×D4×C13111yescharacteristic
966C2×C4C22×D4×C13111yescharacteristic
967C2×C4C22×D4×C13111yescharacteristic
968C2×C4H(5,𝔽2)×C13111yescharacteristic
969C8—22no—
970C8—22no—
971C8—22no—
972C8—22no—
973C8—41no—
974C8—41no—
975C22—22no—
976C22—22no—
977C22—41no—
978C22—42no—
979C22—42no—
980C22—41no—
981C22—41no—
982C22—41no—
983C22—42no—
984C22—81no—
985C22—81no—
986C22—82no—
987C22—81no—
988C22—82no—
989C22—161no—
990C22—162no—
991C22—164no—
992C22#534×C13111yescharacteristic
993C22D42×C13111yescharacteristic
994C22D42×C13111yescharacteristic
995C4—22no—
996C4—22no—
997C4—41no—
998C4—41no—
999C4—41no—
1000C4—42no—
1001C4—81no—
1002C4—81no—
1003C4C2×#120×C13111yescharacteristic
1004C4C2×#120×C13111yescharacteristic
1005C4D42×C13111yescharacteristic
1006C4D42×C13111yescharacteristic
1007C2—21no—
1008C2—21no—
1009C2—21no—
1010C2—42no—
1011C2—42no—
1012C2—81no—
1013C2—81no—
1014C2—82no—
1015C2—81no—
1016C2#2403×C13111yescharacteristic
subgroupG/H
center, socleC2×C131#2403
commutator, Frattini, cosocleC22×C4C24×C131
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C2×C131 ◁ C22×C4×C131 ◁ G

Complements

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

NH ≅ G/Ntype
1. #3586×C131C2semidirect
2. #3585×C131C2semidirect
3. #3020×C131C2semidirect
4. #3019×C131C2semidirect
5. #3010×C131C2semidirect
6. #3009×C131C2semidirect
7. #2019×C131C2semidirect
8. #2017×C131C2semidirect
9. #2009×C131C2semidirect
10. #2008×C131C2semidirect
11. #1903×C131C2semidirect
12. #1902×C131C2semidirect
13. #1881×C131C2semidirect
14. #1881×C131C2semidirect
15. #1794×C131C2semidirect
17. C2×2−1+4×C131C22semidirect
32. #575×C131C22semidirect
33. #575×C131C22semidirect
36. C2×#137×C131C22semidirect
40. C22×SD16×C131C22semidirect
42. #568×C131C22semidirect
43. #536×C131C22semidirect
44. #535×C131C22semidirect
54. #421×C131C22semidirect
55. #421×C131C22semidirect
56. #421×C131C22semidirect
57. #419×C131C22semidirect
58. #418×C131C22semidirect
60. #416×C131C22semidirect
61. C2×#101×C131C22semidirect
62. C2×#100×C131C22semidirect
63. #410×C131C22semidirect
64. #408×C131C22semidirect
65. #408×C131C22semidirect
66. #408×C131C22semidirect
67. #344×C131C22semidirect
68. #344×C131C22semidirect
69. #341×C131C22semidirect
70. #338×C131C22semidirect
77. 2−1+4×C131D4semidirect
85. H(5,𝔽2)×C131D4semidirect
123. #137×C131D4semidirect
141. AGL(1,ℤ/8)×C131D4semidirect
153. C2×Q16×C131D4semidirect
162. C2×SD16×C131D4semidirect
508. #23894C131direct (N × H)
509. C131#23894direct (N × H)
510. #3586C2×C131semidirect
511. #3585C2×C131semidirect
512. #3020C2×C131semidirect
513. #3019C2×C131semidirect
514. #3010C2×C131semidirect
515. #3009C2×C131semidirect
516. #2019C2×C131semidirect
517. #2017C2×C131semidirect
518. #2009C2×C131semidirect
519. #2008C2×C131semidirect
520. #1903C2×C131semidirect
521. #1902C2×C131semidirect
522. #1881C2×C131semidirect
523. #1881C2×C131semidirect
524. #1794C2×C131semidirect
526. C2×2−1+4C22×C131semidirect
541. #575C22×C131semidirect
542. #575C22×C131semidirect
545. C2×#137C22×C131semidirect
549. C22×SD16C22×C131semidirect
551. #568C22×C131semidirect
552. #536C22×C131semidirect
553. #535C22×C131semidirect
563. #421C22×C131semidirect
564. #421C22×C131semidirect
565. #421C22×C131semidirect
566. #419C22×C131semidirect
567. #418C22×C131semidirect
569. #416C22×C131semidirect
570. C2×#101C22×C131semidirect
571. C2×#100C22×C131semidirect
572. #410C22×C131semidirect
573. #408C22×C131semidirect
574. #408C22×C131semidirect
575. #408C22×C131semidirect
576. #344C22×C131semidirect
577. #344C22×C131semidirect
578. #341C22×C131semidirect
579. #338C22×C131semidirect
586. 2−1+4D4×C131semidirect
594. H(5,𝔽2)D4×C131semidirect
632. #137D4×C131semidirect
650. AGL(1,ℤ/8)D4×C131semidirect
662. C2×Q16D4×C131semidirect
671. C2×SD16D4×C131semidirect

Maximal subgroups

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

subgroupindex
#3586×C1312
#3585×C1312
#3020×C1312
#3019×C1312
#3010×C1312
#3009×C1312
#2019×C1312
#2017×C1312
#2009×C1312
#2008×C1312
#1903×C1312
#1902×C1312
#1881×C1312
#1794×C1312
#23894131