Finite Group Databasebeta

← C131×#24464 #45710348

Subgroups — C131×#24464 #45710348

Order 33536.

1600 conjugacy classes of subgroups.

The subgroup lattice has 1100 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#3488×C131C211yesmaximal, characteristic, complemented
2#3055×C131C211yesmaximal, characteristic, complemented
3C2×#453×C131C211yesmaximal, characteristic, complemented
4#3006×C131C211yesmaximal, characteristic, complemented
5C22×#104×C131C211yesmaximal, characteristic, complemented
6#2856×C131C211yesmaximal, characteristic, complemented
7#2039×C131C211yesmaximal, characteristic, complemented
8#2037×C131C211yesmaximal, characteristic, complemented
9#2006×C131C211yesmaximal, characteristic, complemented
10#2002×C131C211yesmaximal, characteristic, complemented
11#1900×C131C211yesmaximal, characteristic, complemented
12#1896×C131C211yesmaximal, characteristic, complemented
13#1883×C131C211yesmaximal, characteristic, complemented
14#1859×C131C211yesmaximal, characteristic, complemented
15#1792×C131C211yesmaximal, characteristic, complemented
16C2×H(5,𝔽2)×C131C2211yescharacteristic
17C22×#41×C131C2211yescharacteristic
18C2×AGL(1,ℤ/8)×C131C2211yescharacteristic
19C2×AGL(1,ℤ/8)×C131C2211yescharacteristic, complemented
20C2×AGL(1,ℤ/8)×C131C2211yescharacteristic, complemented
21C22×M16×C131C2211yescharacteristic, complemented
22#550×C131—21no—
23#548×C131—21no—
24#546×C131—21no—
25#546×C131—22no—
26D42×C131—22no—
27D42×C131—21no—
28#537×C131—21no—
29#537×C131C2211yescharacteristic
30#535×C131—21no—
31#535×C131C2211yescharacteristic
32C2×#127×C131C2211yescharacteristic, complemented
33#525×C131—21no—
34#525×C131C2211yescharacteristic
35C2×#121×C131—21no—
36C2×#121×C131—22no—
37C2×#121×C131C2211yescharacteristic
38C2×#121×C131C2211yescharacteristic, complemented
39#520×C131C2211yescharacteristic
40C22×C42×C131C2211yescharacteristic, complemented
41#469×C131—21no—
42#468×C131—21no—
43#466×C131—21no—
44#465×C131—21no—
45#453×C131—24no—
46#449×C131—21no—
47#449×C131—21no—
48#448×C131—21no—
49#447×C131—21no—
50#428×C131C2211yescharacteristic, complemented
51C2×#104×C131—24no—
52C2×#104×C131C2211yescharacteristic
53C2×#104×C131C2211yescharacteristic
54C2×#104×C131C2211yescharacteristic, complemented
55C2×#104×C131C2211yescharacteristic, complemented
56C2×#104×C131C2211yescharacteristic, complemented
57C2×#104×C131C2211yescharacteristic, complemented
58#418×C131C2211yescharacteristic, complemented
59#417×C131C2211yescharacteristic
60#417×C131C2211yescharacteristic, complemented
61#417×C131C2211yescharacteristic, complemented
62C2×#100×C131C2211yescharacteristic, complemented
63C2×#100×C131C2211yescharacteristic, complemented
64#407×C131C2211yescharacteristic, complemented
65#390×C131—22no—
66#390×C131C2211yescharacteristic, complemented
67#390×C131C2211yescharacteristic, complemented
68#384×C131C2211yescharacteristic, complemented
69#343×C131C2211yescharacteristic, complemented
70#343×C131C2211yescharacteristic, complemented
71#339×C131C2211yescharacteristic, complemented
72#339×C131C2211yescharacteristic, complemented
73H(5,𝔽2)×C131—22no—
74H(5,𝔽2)×C131—22no—
75H(5,𝔽2)×C131—41no—
76H(5,𝔽2)×C131—41no—
77C2×#41×C131—21no—
78C2×#41×C131—21no—
79C2×#41×C131—21no—
80C2×#41×C131—21no—
81C2×#41×C131—22no—
82C2×#41×C131—22no—
83C2×#41×C131—41no—
84C2×#41×C131—41no—
85C2×#41×C131D411yescharacteristic, complemented
86C2×#41×C131D411yescharacteristic, complemented
87C2×#41×C131C2311yescharacteristic
88C2×#41×C131C2311yescharacteristic
89C2×#41×C131C2311yescharacteristic
90C22×Q8×C131D411yescharacteristic, complemented
91C22×D4×C131—21no—
92C22×D4×C131—22no—
93C22×D4×C131—22no—
94C22×D4×C131—21no—
95C22×D4×C131—21no—
96C22×D4×C131—22no—
97C22×D4×C131—21no—
98C22×D4×C131D412yes—
99C22×D4×C131D411yescharacteristic, complemented
100C22×D4×C131C2311yescharacteristic
101C22×D4×C131C2311yescharacteristic
102C23×C4×C131—21no—
103C23×C4×C131—21no—
104C23×C4×C131C2311yescharacteristic
105AGL(1,ℤ/8)×C131—22no—
106AGL(1,ℤ/8)×C131—22no—
107AGL(1,ℤ/8)×C131—22no—
108AGL(1,ℤ/8)×C131—41no—
109AGL(1,ℤ/8)×C131—41no—
110AGL(1,ℤ/8)×C131—41no—
111C2×SD16×C131—21no—
112C2×SD16×C131—21no—
113C2×SD16×C131—21no—
114C2×D8×C131—21no—
115C2×D8×C131—21no—
116C2×D8×C131—21no—
117C2×M16×C131—21no—
118C2×M16×C131—22no—
119C2×M16×C131—41no—
120C2×M16×C131C2311yescharacteristic
121C2×M16×C131C2311yescharacteristic
122C2×M16×C131C2311yescharacteristic
123C2×M16×C131C2311yescharacteristic
124C22×C8×C131—21no—
125#127×C131—22no—
126#127×C131—21no—
127#127×C131—22no—
128#127×C131—41no—
129#124×C131—22no—
130#124×C131—21no—
131#123×C131—22no—
132#123×C131—21no—
133C22⋊Q8×C131—22no—
134C22⋊Q8×C131—21no—
135C22⋊Q8×C131—21no—
136C22⋊Q8×C131D411yescharacteristic, complemented
137C22⋊Q8×C131D411yescharacteristic, complemented
138#121×C131—22no—
139#121×C131—22no—
140#121×C131—22no—
141#121×C131—22no—
142#121×C131—22no—
143#121×C131—21no—
144#121×C131—21no—
145#121×C131—21no—
146#121×C131—21no—
147#121×C131—21no—
148#121×C131—21no—
149#121×C131—22no—
150#121×C131—21no—
151#121×C131—21no—
152#121×C131—21no—
153#121×C131—21no—
154#121×C131—21no—
155#121×C131—21no—
156#121×C131—48no—
157#121×C131D411yescharacteristic, complemented
158#121×C131D411yescharacteristic, complemented
159#120×C131—22no—
160#120×C131—22no—
161#120×C131—22no—
162#120×C131—21no—
163#120×C131—22no—
164C4×Q8×C131—21no—
165C4×D4×C131—22no—
166C4×D4×C131—22no—
167C4×D4×C131—21no—
168C4×D4×C131—22no—
169C4×D4×C131—21no—
170C4×D4×C131—21no—
171#117×C131—21no—
172#117×C131C2311yescharacteristic
173C2×C4⋊C4×C131—21no—
174C2×C4⋊C4×C131—22no—
175C2×C4⋊C4×C131C2311yescharacteristic
176C2×C4⋊C4×C131C2311yescharacteristic
177C2×C22⋊C4×C131—22no—
178C2×C22⋊C4×C131—22no—
179C2×C22⋊C4×C131—21no—
180C2×C22⋊C4×C131—22no—
181C2×C22⋊C4×C131D412yes—
182C2×C42×C131—22no—
183C2×C42×C131—21no—
184C2×C42×C131—41no—
185C2×C42×C131C2311yescharacteristic
186C2×C42×C131C2311yescharacteristic
187#107×C131—21no—
188#106×C131—21no—
189#104×C131—22no—
190#104×C131—22no—
191#104×C131—22no—
192#104×C131—22no—
193#104×C131—41no—
194#104×C131D414yescomplemented
195#103×C131—21no—
196#103×C131—21no—
197#103×C131—21no—
198#102×C131—21no—
199#102×C131—21no—
200#102×C131—21no—
201#102×C131—21no—
202#102×C131—21no—
203#100×C131—22no—
204#100×C131—41no—
205C22⋊C8×C131—21no—
206C22⋊C8×C131—21no—
207C24×C131—22no—
208C24×C131—21no—
209C24×C131—21no—
210C24×C131C2×D411yescharacteristic
211C24×C131C2×D412yes—
212#41×C131—21no—
213#41×C131—21no—
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—42no—
225#41×C131—42no—
226#41×C131—41no—
227#41×C131—41no—
228#41×C131—42no—
229#41×C131—42no—
230#41×C131—42no—
231#41×C131—42no—
232#41×C131—42no—
233#41×C131—42no—
234#41×C131C2×D412yes—
235#41×C131#4112yes—
236C2×Q8×C131—21no—
237C2×Q8×C131—22no—
238C2×Q8×C131—41no—
239C2×Q8×C131C2×D411yescharacteristic
240C2×Q8×C131C2×D411yescharacteristic
241C2×Q8×C131C2×D411yescharacteristic
242C2×D4×C131—21no—
243C2×D4×C131—22no—
244C2×D4×C131—22no—
245C2×D4×C131—22no—
246C2×D4×C131—22no—
247C2×D4×C131—21no—
248C2×D4×C131—21no—
249C2×D4×C131—21no—
250C2×D4×C131—21no—
251C2×D4×C131—21no—
252C2×D4×C131—22no—
253C2×D4×C131—22no—
254C2×D4×C131—22no—
255C2×D4×C131—21no—
256C2×D4×C131—22no—
257C2×D4×C131—21no—
258C2×D4×C131—21no—
259C2×D4×C131—21no—
260C2×D4×C131—21no—
261C2×D4×C131—21no—
262C2×D4×C131—21no—
263C2×D4×C131—21no—
264C2×D4×C131—21no—
265C2×D4×C131—21no—
266C2×D4×C131—21no—
267C2×D4×C131—21no—
268C2×D4×C131—21no—
269C2×D4×C131—21no—
270C2×D4×C131—41no—
271C2×D4×C131—42no—
272C2×D4×C131—42no—
273C2×D4×C131—44no—
274C2×D4×C131—44no—
275C2×D4×C131—44no—
276C2×D4×C131—42no—
277C2×D4×C131—42no—
278C2×D4×C131—44no—
279C2×D4×C131—44no—
280C2×D4×C131—42no—
281C2×D4×C131—42no—
282C2×D4×C131—44no—
283C2×D4×C131—44no—
284C2×D4×C131—41no—
285C2×D4×C131—41no—
286C2×D4×C131—84no—
287C2×D4×C131C2×D411yescharacteristic
288C2×D4×C131C2×D411yescharacteristic
289C2×D4×C131C2×D411yescharacteristic
290C22×C4×C131—21no—
291C22×C4×C131—21no—
292C22×C4×C131—21no—
293C22×C4×C131—21no—
294C22×C4×C131—21no—
295C22×C4×C131—21no—
296C22×C4×C131—22no—
297C22×C4×C131—24no—
298C22×C4×C131—21no—
299C22×C4×C131—21no—
300C22×C4×C131—22no—
301C22×C4×C131—21no—
302C22×C4×C131—21no—
303C22×C4×C131—21no—
304C22×C4×C131—21no—
305C22×C4×C131—21no—
306C22×C4×C131—42no—
307C22×C4×C131—42no—
308C22×C4×C131—42no—
309C22×C4×C131—42no—
310C22×C4×C131C2×D411yescharacteristic
311C22×C4×C131C2×D411yescharacteristic
312C22×C4×C131C2×D411yescharacteristic
313C22×C4×C131C2×D411yescharacteristic
314C22×C4×C131C2×D411yescharacteristic
315C22×C4×C131C2×D412yes—
316C22×C4×C131C2411yescharacteristic
317SD16×C131—42no—
318SD16×C131—42no—
319SD16×C131—42no—
320D8×C131—42no—
321D8×C131—42no—
322D8×C131—42no—
323M16×C131—21no—
324M16×C131—21no—
325M16×C131—21no—
326M16×C131—21no—
327M16×C131—21no—
328M16×C131—21no—
329M16×C131—21no—
330M16×C131—42no—
331M16×C131C2×D412yescomplemented
332C2×C8×C131—21no—
333C2×C8×C131—21no—
334C2×C8×C131—21no—
335C2×C8×C131—21no—
336C2×C8×C131—42no—
337C4⋊C4×C131—22no—
338C4⋊C4×C131—22no—
339C4⋊C4×C131—21no—
340C4⋊C4×C131—21no—
341C4⋊C4×C131—21no—
342C4⋊C4×C131—21no—
343C4⋊C4×C131—21no—
344C4⋊C4×C131—21no—
345C4⋊C4×C131—44no—
346C4⋊C4×C131C2×D411yescharacteristic
347C4⋊C4×C131C2×D411yescharacteristic
348C22⋊C4×C131—22no—
349C22⋊C4×C131—22no—
350C22⋊C4×C131—22no—
351C22⋊C4×C131—22no—
352C22⋊C4×C131—22no—
353C22⋊C4×C131—21no—
354C22⋊C4×C131—21no—
355C22⋊C4×C131—21no—
356C22⋊C4×C131—21no—
357C22⋊C4×C131—22no—
358C22⋊C4×C131—22no—
359C22⋊C4×C131—21no—
360C22⋊C4×C131—44no—
361C22⋊C4×C131—44no—
362C22⋊C4×C131—41no—
363C22⋊C4×C131—41no—
364C42×C131—22no—
365C42×C131—21no—
366C42×C131—21no—
367C42×C131—21no—
368C42×C131—21no—
369C42×C131—42no—
370C42×C131C2×D412yescomplemented
371C23×C131—21no—
372C23×C131—21no—
373C23×C131—21no—
374C23×C131—22no—
375C23×C131—22no—
376C23×C131—21no—
377C23×C131—21no—
378C23×C131—22no—
379C23×C131—22no—
380C23×C131—41no—
381C23×C131—42no—
382C23×C131—44no—
383C23×C131—42no—
384C23×C131—42no—
385C23×C131—42no—
386C23×C131—42no—
387C23×C131—42no—
388C23×C131—41no—
389C23×C131—41no—
390C23×C131—41no—
391C23×C131—81no—
392C23×C131—82no—
393C23×C131—82no—
394C23×C131#12011yescharacteristic
395C23×C131#12011yescharacteristic
396C23×C131C22×D411yescharacteristic
397Q8×C131—21no—
398Q8×C131—21no—
399Q8×C131—21no—
400Q8×C131—21no—
401Q8×C131—21no—
402Q8×C131—42no—
403Q8×C131#12112yescomplemented
404D4×C131—22no—
405D4×C131—22no—
406D4×C131—21no—
407D4×C131—21no—
408D4×C131—21no—
409D4×C131—21no—
410D4×C131—21no—
411D4×C131—42no—
412D4×C131—42no—
413D4×C131—44no—
414D4×C131—42no—
415D4×C131—44no—
416D4×C131—41no—
417D4×C131—41no—
418D4×C131—41no—
419D4×C131—41no—
420D4×C131—44no—
421D4×C131—42no—
422D4×C131—41no—
423D4×C131—41no—
424D4×C131—41no—
425D4×C131—41no—
426D4×C131—41no—
427D4×C131—41no—
428D4×C131—41no—
429D4×C131—41no—
430D4×C131—88no—
431D4×C131—81no—
432D4×C131—82no—
433D4×C131—82no—
434D4×C131—82no—
435D4×C131—82no—
436D4×C131—82no—
437D4×C131—82no—
438D4×C131#12112yescomplemented
439C2×C4×C131—22no—
440C2×C4×C131—22no—
441C2×C4×C131—21no—
442C2×C4×C131—22no—
443C2×C4×C131—21no—
444C2×C4×C131—21no—
445C2×C4×C131—21no—
446C2×C4×C131—21no—
447C2×C4×C131—21no—
448C2×C4×C131—21no—
449C2×C4×C131—21no—
450C2×C4×C131—21no—
451C2×C4×C131—22no—
452C2×C4×C131—21no—
453C2×C4×C131—21no—
454C2×C4×C131—22no—
455C2×C4×C131—22no—
456C2×C4×C131—21no—
457C2×C4×C131—22no—
458C2×C4×C131—21no—
459C2×C4×C131—21no—
460C2×C4×C131—21no—
461C2×C4×C131—42no—
462C2×C4×C131—42no—
463C2×C4×C131—42no—
464C2×C4×C131—48no—
465C2×C4×C131—44no—
466C2×C4×C131—41no—
467C2×C4×C131—41no—
468C2×C4×C131—41no—
469C2×C4×C131—41no—
470C2×C4×C131—41no—
471C2×C4×C131—41no—
472C2×C4×C131—42no—
473C2×C4×C131—42no—
474C2×C4×C131—41no—
475C2×C4×C131—82no—
476C2×C4×C131#12011yescharacteristic
477C2×C4×C131#12011yescharacteristic
478C2×C4×C131C22×D411yescharacteristic
479C2×C4×C131C22×D411yescharacteristic
480C2×C4×C131C22×D411yescharacteristic
481C2×C4×C131C2×#4111yescharacteristic
482C2×C4×C131H(5,𝔽2)11yescharacteristic
483C2×C4×C131H(5,𝔽2)11yescharacteristic
484C8×C131—22no—
485C8×C131—41no—
486C8×C131—41no—
487C8×C131—41no—
488C22×C131—21no—
489C22×C131—21no—
490C22×C131—21no—
491C22×C131—21no—
492C22×C131—21no—
493C22×C131—22no—
494C22×C131—21no—
495C22×C131—21no—
496C22×C131—42no—
497C22×C131—42no—
498C22×C131—41no—
499C22×C131—41no—
500C22×C131—41no—
501C22×C131—41no—
502C22×C131—42no—
503C22×C131—42no—
504C22×C131—41no—
505C22×C131—41no—
506C22×C131—41no—
507C22×C131—42no—
508C22×C131—41no—
509C22×C131—84no—
510C22×C131—82no—
511C22×C131—82no—
512C22×C131—82no—
513C22×C131—82no—
514C22×C131—81no—
515C22×C131—81no—
516C22×C131—81no—
517C22×C131—164no—
518C22×C131#45312yescomplemented
519C22×C131C2×#12011yescharacteristic
520C22×C131D4211yescharacteristic
521C22×C131#54611yescharacteristic
522C4×C131—24no—
523C4×C131—21no—
524C4×C131—21no—
525C4×C131—22no—
526C4×C131—42no—
527C4×C131—41no—
528C4×C131—41no—
529C4×C131—42no—
530C4×C131—41no—
531C4×C131—41no—
532C4×C131—81no—
533C4×C131C2×#12111yescharacteristic
534C4×C131#53411yescharacteristic
535C4×C131D4211yescharacteristic
536C4×C131#54611yescharacteristic
537C2×C131—21no—
538C2×C131—21no—
539C2×C131—22no—
540C2×C131—41no—
541C2×C131—42no—
542C2×C131—81no—
543C2×C131—82no—
544C2×C131—81no—
545C2×C131—161no—
546C2×C131#241011yescharacteristic
547C2×C131C2×#45311yescharacteristic
548C2×C131#301811yescharacteristic
549#24464C13111yesmaximal, characteristic, direct product factor, Sylow
550C131#2446411yescharacteristic, direct product factor, Sylow
551#3488C2×C13111yescharacteristic, complemented
552#3055C2×C13111yescharacteristic, complemented
553C2×#453C2×C13111yescharacteristic, complemented
554#3006C2×C13111yescharacteristic, complemented
555C22×#104C2×C13111yescharacteristic, complemented
556#2856C2×C13111yescharacteristic, complemented
557#2039C2×C13111yescharacteristic, complemented
558#2037C2×C13111yescharacteristic, complemented
559#2006C2×C13111yescharacteristic, complemented
560#2002C2×C13111yescharacteristic, complemented
561#1900C2×C13111yescharacteristic, complemented
562#1896C2×C13111yescharacteristic, complemented
563#1883C2×C13111yescharacteristic, complemented
564#1859C2×C13111yescharacteristic, complemented
565#1792C2×C13111yescharacteristic, complemented
566C2×H(5,𝔽2)C22×C13111yescharacteristic
567C22×#41C22×C13111yescharacteristic
568C2×AGL(1,ℤ/8)C22×C13111yescharacteristic
569C2×AGL(1,ℤ/8)C22×C13111yescharacteristic, complemented
570C2×AGL(1,ℤ/8)C22×C13111yescharacteristic, complemented
571C22×M16C22×C13111yescharacteristic, complemented
572#550—21no—
573#548—21no—
574#546—21no—
575#546—22no—
576D42—22no—
577D42—21no—
578#537—21no—
579#537C22×C13111yescharacteristic
580#535—21no—
581#535C22×C13111yescharacteristic
582C2×#127C22×C13111yescharacteristic, complemented
583#525—21no—
584#525C22×C13111yescharacteristic
585C2×#121—21no—
586C2×#121—22no—
587C2×#121C22×C13111yescharacteristic
588C2×#121C22×C13111yescharacteristic, complemented
589#520C22×C13111yescharacteristic
590C22×C42C22×C13111yescharacteristic, complemented
591#469—21no—
592#468—21no—
593#466—21no—
594#465—21no—
595#453—24no—
596#449—21no—
597#449—21no—
598#448—21no—
599#447—21no—
600#428C22×C13111yescharacteristic, complemented
601C2×#104—24no—
602C2×#104C22×C13111yescharacteristic
603C2×#104C22×C13111yescharacteristic
604C2×#104C22×C13111yescharacteristic, complemented
605C2×#104C22×C13111yescharacteristic, complemented
606C2×#104C22×C13111yescharacteristic, complemented
607C2×#104C22×C13111yescharacteristic, complemented
608#418C22×C13111yescharacteristic, complemented
609#417C22×C13111yescharacteristic
610#417C22×C13111yescharacteristic, complemented
611#417C22×C13111yescharacteristic, complemented
612C2×#100C22×C13111yescharacteristic, complemented
613C2×#100C22×C13111yescharacteristic, complemented
614#407C22×C13111yescharacteristic, complemented
615#390—22no—
616#390C22×C13111yescharacteristic, complemented
617#390C22×C13111yescharacteristic, complemented
618#384C22×C13111yescharacteristic, complemented
619#343C22×C13111yescharacteristic, complemented
620#343C22×C13111yescharacteristic, complemented
621#339C22×C13111yescharacteristic, complemented
622#339C22×C13111yescharacteristic, complemented
623H(5,𝔽2)—22no—
624H(5,𝔽2)—22no—
625H(5,𝔽2)—41no—
626H(5,𝔽2)—41no—
627C2×#41—21no—
628C2×#41—21no—
629C2×#41—21no—
630C2×#41—21no—
631C2×#41—22no—
632C2×#41—22no—
633C2×#41—41no—
634C2×#41—41no—
635C2×#41D4×C13111yescharacteristic, complemented
636C2×#41D4×C13111yescharacteristic, complemented
637C2×#41C23×C13111yescharacteristic
638C2×#41C23×C13111yescharacteristic
639C2×#41C23×C13111yescharacteristic
640C22×Q8D4×C13111yescharacteristic, complemented
641C22×D4—21no—
642C22×D4—22no—
643C22×D4—22no—
644C22×D4—21no—
645C22×D4—21no—
646C22×D4—21no—
647C22×D4—22no—
648C22×D4D4×C13112yes—
649C22×D4D4×C13111yescharacteristic, complemented
650C22×D4C23×C13111yescharacteristic
651C22×D4C23×C13111yescharacteristic
652C23×C4—21no—
653C23×C4—21no—
654C23×C4C23×C13111yescharacteristic
655AGL(1,ℤ/8)—22no—
656AGL(1,ℤ/8)—22no—
657AGL(1,ℤ/8)—22no—
658AGL(1,ℤ/8)—41no—
659AGL(1,ℤ/8)—41no—
660AGL(1,ℤ/8)—41no—
661C2×SD16—21no—
662C2×SD16—21no—
663C2×SD16—21no—
664C2×D8—21no—
665C2×D8—21no—
666C2×D8—21no—
667C2×M16—21no—
668C2×M16—22no—
669C2×M16—41no—
670C2×M16C23×C13111yescharacteristic
671C2×M16C23×C13111yescharacteristic
672C2×M16C23×C13111yescharacteristic
673C2×M16C23×C13111yescharacteristic
674C22×C8—21no—
675#127—22no—
676#127—21no—
677#127—22no—
678#127—41no—
679#124—22no—
680#124—21no—
681#123—22no—
682#123—21no—
683C22⋊Q8—22no—
684C22⋊Q8—21no—
685C22⋊Q8—21no—
686C22⋊Q8D4×C13111yescharacteristic, complemented
687C22⋊Q8D4×C13111yescharacteristic, complemented
688#121—22no—
689#121—22no—
690#121—22no—
691#121—22no—
692#121—22no—
693#121—21no—
694#121—21no—
695#121—21no—
696#121—21no—
697#121—21no—
698#121—21no—
699#121—22no—
700#121—21no—
701#121—21no—
702#121—21no—
703#121—21no—
704#121—21no—
705#121—21no—
706#121—48no—
707#121D4×C13111yescharacteristic, complemented
708#121D4×C13111yescharacteristic, complemented
709#120—22no—
710#120—22no—
711#120—22no—
712#120—21no—
713#120—22no—
714C4×Q8—21no—
715C4×D4—22no—
716C4×D4—22no—
717C4×D4—21no—
718C4×D4—22no—
719C4×D4—21no—
720C4×D4—21no—
721#117—21no—
722#117C23×C13111yescharacteristic
723C2×C4⋊C4—21no—
724C2×C4⋊C4—22no—
725C2×C4⋊C4C23×C13111yescharacteristic
726C2×C4⋊C4C23×C13111yescharacteristic
727C2×C22⋊C4—22no—
728C2×C22⋊C4—22no—
729C2×C22⋊C4—22no—
730C2×C22⋊C4—21no—
731C2×C22⋊C4D4×C13112yes—
732C2×C42—22no—
733C2×C42—21no—
734C2×C42—41no—
735C2×C42C23×C13111yescharacteristic
736C2×C42C23×C13111yescharacteristic
737#107—21no—
738#106—21no—
739#104—22no—
740#104—22no—
741#104—22no—
742#104—22no—
743#104—41no—
744#104D4×C13114yescomplemented
745#103—21no—
746#103—21no—
747#103—21no—
748#102—21no—
749#102—21no—
750#102—21no—
751#102—21no—
752#102—21no—
753#100—22no—
754#100—41no—
755C22⋊C8—21no—
756C22⋊C8—21no—
757C24—22no—
758C24—21no—
759C24—21no—
760C24C2×D4×C13111yescharacteristic
761C24C2×D4×C13112yes—
762#41—21no—
763#41—21no—
764#41—22no—
765#41—22no—
766#41—21no—
767#41—21no—
768#41—21no—
769#41—21no—
770#41—21no—
771#41—21no—
772#41—21no—
773#41—21no—
774#41—42no—
775#41—42no—
776#41—41no—
777#41—41no—
778#41—42no—
779#41—42no—
780#41—42no—
781#41—42no—
782#41—42no—
783#41—42no—
784#41C2×D4×C13112yes—
785#41#41×C13112yes—
786C2×Q8—21no—
787C2×Q8—22no—
788C2×Q8—41no—
789C2×Q8C2×D4×C13111yescharacteristic
790C2×Q8C2×D4×C13111yescharacteristic
791C2×Q8C2×D4×C13111yescharacteristic
792C2×D4—21no—
793C2×D4—22no—
794C2×D4—22no—
795C2×D4—22no—
796C2×D4—22no—
797C2×D4—21no—
798C2×D4—21no—
799C2×D4—21no—
800C2×D4—21no—
801C2×D4—21no—
802C2×D4—22no—
803C2×D4—22no—
804C2×D4—22no—
805C2×D4—21no—
806C2×D4—22no—
807C2×D4—21no—
808C2×D4—21no—
809C2×D4—21no—
810C2×D4—21no—
811C2×D4—21no—
812C2×D4—21no—
813C2×D4—21no—
814C2×D4—21no—
815C2×D4—21no—
816C2×D4—21no—
817C2×D4—21no—
818C2×D4—21no—
819C2×D4—21no—
820C2×D4—41no—
821C2×D4—42no—
822C2×D4—42no—
823C2×D4—44no—
824C2×D4—44no—
825C2×D4—44no—
826C2×D4—42no—
827C2×D4—42no—
828C2×D4—44no—
829C2×D4—44no—
830C2×D4—42no—
831C2×D4—42no—
832C2×D4—44no—
833C2×D4—44no—
834C2×D4—41no—
835C2×D4—41no—
836C2×D4—84no—
837C2×D4C2×D4×C13111yescharacteristic
838C2×D4C2×D4×C13111yescharacteristic
839C2×D4C2×D4×C13111yescharacteristic
840C22×C4—21no—
841C22×C4—21no—
842C22×C4—21no—
843C22×C4—21no—
844C22×C4—21no—
845C22×C4—21no—
846C22×C4—22no—
847C22×C4—24no—
848C22×C4—21no—
849C22×C4—21no—
850C22×C4—22no—
851C22×C4—21no—
852C22×C4—21no—
853C22×C4—21no—
854C22×C4—21no—
855C22×C4—21no—
856C22×C4—42no—
857C22×C4—42no—
858C22×C4—42no—
859C22×C4—42no—
860C22×C4C2×D4×C13111yescharacteristic
861C22×C4C2×D4×C13111yescharacteristic
862C22×C4C2×D4×C13111yescharacteristic
863C22×C4C2×D4×C13111yescharacteristic
864C22×C4C2×D4×C13111yescharacteristic
865C22×C4C2×D4×C13112yes—
866C22×C4C24×C13111yescharacteristic
867SD16—42no—
868SD16—42no—
869SD16—42no—
870D8—42no—
871D8—42no—
872D8—42no—
873M16—21no—
874M16—21no—
875M16—21no—
876M16—21no—
877M16—21no—
878M16—21no—
879M16—21no—
880M16—42no—
881M16C2×D4×C13112yescomplemented
882C2×C8—21no—
883C2×C8—21no—
884C2×C8—21no—
885C2×C8—21no—
886C2×C8—42no—
887C4⋊C4—22no—
888C4⋊C4—22no—
889C4⋊C4—21no—
890C4⋊C4—21no—
891C4⋊C4—21no—
892C4⋊C4—21no—
893C4⋊C4—21no—
894C4⋊C4—21no—
895C4⋊C4—44no—
896C4⋊C4C2×D4×C13111yescharacteristic
897C4⋊C4C2×D4×C13111yescharacteristic
898C22⋊C4—22no—
899C22⋊C4—22no—
900C22⋊C4—22no—
901C22⋊C4—22no—
902C22⋊C4—22no—
903C22⋊C4—21no—
904C22⋊C4—21no—
905C22⋊C4—21no—
906C22⋊C4—21no—
907C22⋊C4—22no—
908C22⋊C4—22no—
909C22⋊C4—21no—
910C22⋊C4—44no—
911C22⋊C4—44no—
912C22⋊C4—41no—
913C22⋊C4—41no—
914C42—22no—
915C42—21no—
916C42—21no—
917C42—21no—
918C42—21no—
919C42—42no—
920C42C2×D4×C13112yescomplemented
921C23—22no—
922C23—21no—
923C23—21no—
924C23—21no—
925C23—22no—
926C23—21no—
927C23—21no—
928C23—22no—
929C23—22no—
930C23—41no—
931C23—42no—
932C23—44no—
933C23—42no—
934C23—42no—
935C23—42no—
936C23—42no—
937C23—42no—
938C23—41no—
939C23—41no—
940C23—41no—
941C23—81no—
942C23—82no—
943C23—82no—
944C23#120×C13111yescharacteristic
945C23#120×C13111yescharacteristic
946C23C22×D4×C13111yescharacteristic
947Q8—21no—
948Q8—21no—
949Q8—21no—
950Q8—21no—
951Q8—21no—
952Q8—42no—
953Q8#121×C13112yescomplemented
954D4—22no—
955D4—22no—
956D4—21no—
957D4—21no—
958D4—21no—
959D4—21no—
960D4—21no—
961D4—42no—
962D4—42no—
963D4—44no—
964D4—42no—
965D4—44no—
966D4—44no—
967D4—42no—
968D4—41no—
969D4—41no—
970D4—41no—
971D4—41no—
972D4—41no—
973D4—41no—
974D4—41no—
975D4—41no—
976D4—41no—
977D4—41no—
978D4—41no—
979D4—41no—
980D4—88no—
981D4—82no—
982D4—81no—
983D4—82no—
984D4—82no—
985D4—82no—
986D4—82no—
987D4—82no—
988D4#121×C13112yescomplemented
989C2×C4—22no—
990C2×C4—22no—
991C2×C4—21no—
992C2×C4—22no—
993C2×C4—21no—
994C2×C4—21no—
995C2×C4—21no—
996C2×C4—21no—
997C2×C4—21no—
998C2×C4—21no—
999C2×C4—21no—
1000C2×C4—21no—
1001C2×C4—22no—
1002C2×C4—21no—
1003C2×C4—21no—
1004C2×C4—22no—
1005C2×C4—22no—
1006C2×C4—21no—
1007C2×C4—22no—
1008C2×C4—21no—
1009C2×C4—21no—
1010C2×C4—21no—
1011C2×C4—42no—
1012C2×C4—42no—
1013C2×C4—42no—
1014C2×C4—48no—
1015C2×C4—44no—
1016C2×C4—41no—
1017C2×C4—41no—
1018C2×C4—41no—
1019C2×C4—41no—
1020C2×C4—41no—
1021C2×C4—41no—
1022C2×C4—42no—
1023C2×C4—42no—
1024C2×C4—41no—
1025C2×C4—82no—
1026C2×C4#120×C13111yescharacteristic
1027C2×C4#120×C13111yescharacteristic
1028C2×C4C22×D4×C13111yescharacteristic
1029C2×C4C22×D4×C13111yescharacteristic
1030C2×C4C22×D4×C13111yescharacteristic
1031C2×C4C2×#41×C13111yescharacteristic
1032C2×C4H(5,𝔽2)×C13111yescharacteristic
1033C2×C4H(5,𝔽2)×C13111yescharacteristic
1034C8—22no—
1035C8—41no—
1036C8—41no—
1037C8—41no—
1038C22—21no—
1039C22—21no—
1040C22—21no—
1041C22—21no—
1042C22—21no—
1043C22—21no—
1044C22—21no—
1045C22—22no—
1046C22—42no—
1047C22—42no—
1048C22—41no—
1049C22—41no—
1050C22—42no—
1051C22—41no—
1052C22—41no—
1053C22—41no—
1054C22—42no—
1055C22—41no—
1056C22—41no—
1057C22—41no—
1058C22—42no—
1059C22—84no—
1060C22—82no—
1061C22—82no—
1062C22—82no—
1063C22—82no—
1064C22—81no—
1065C22—81no—
1066C22—81no—
1067C22—164no—
1068C22#453×C13112yescomplemented
1069C22C2×#120×C13111yescharacteristic
1070C22D42×C13111yescharacteristic
1071C22#546×C13111yescharacteristic
1072C4—24no—
1073C4—21no—
1074C4—21no—
1075C4—22no—
1076C4—42no—
1077C4—42no—
1078C4—41no—
1079C4—41no—
1080C4—41no—
1081C4—41no—
1082C4—81no—
1083C4C2×#121×C13111yescharacteristic
1084C4#534×C13111yescharacteristic
1085C4D42×C13111yescharacteristic
1086C4#546×C13111yescharacteristic
1087C2—21no—
1088C2—21no—
1089C2—22no—
1090C2—41no—
1091C2—42no—
1092C2—81no—
1093C2—82no—
1094C2—81no—
1095C2—161no—
1096C2#2410×C13111yescharacteristic
1097C2C2×#453×C13111yescharacteristic
1098C2#3018×C13111yescharacteristic
subgroupG/H
center, socleC22×C131C2×#120
commutator, Frattini, cosocleC22×C4C24×C131
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C131 ◁ C23×C4×C131 ◁ G

Complements

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

NH ≅ G/Ntype
1. #3488×C131C2semidirect
2. #3055×C131C2semidirect
3. C2×#453×C131C2semidirect
4. #3006×C131C2semidirect
5. C22×#104×C131C2semidirect
6. #2856×C131C2semidirect
7. #2039×C131C2semidirect
8. #2037×C131C2semidirect
9. #2006×C131C2semidirect
10. #2002×C131C2semidirect
11. #1900×C131C2semidirect
12. #1896×C131C2semidirect
13. #1883×C131C2semidirect
14. #1859×C131C2semidirect
15. #1792×C131C2semidirect
19. C2×AGL(1,ℤ/8)×C131C22semidirect
20. C2×AGL(1,ℤ/8)×C131C22semidirect
21. C22×M16×C131C22semidirect
32. C2×#127×C131C22semidirect
38. C2×#121×C131C22semidirect
40. C22×C42×C131C22semidirect
50. #428×C131C22semidirect
54. C2×#104×C131C22semidirect
55. C2×#104×C131C22semidirect
56. C2×#104×C131C22semidirect
57. C2×#104×C131C22semidirect
58. #418×C131C22semidirect
60. #417×C131C22semidirect
61. #417×C131C22semidirect
62. C2×#100×C131C22semidirect
63. C2×#100×C131C22semidirect
64. #407×C131C22semidirect
66. #390×C131C22semidirect
67. #390×C131C22semidirect
68. #384×C131C22semidirect
69. #343×C131C22semidirect
70. #343×C131C22semidirect
71. #339×C131C22semidirect
72. #339×C131C22semidirect
85. C2×#41×C131D4semidirect
86. C2×#41×C131D4semidirect
90. C22×Q8×C131D4semidirect
99. C22×D4×C131D4semidirect
136. C22⋊Q8×C131D4semidirect
137. C22⋊Q8×C131D4semidirect
157. #121×C131D4semidirect
158. #121×C131D4semidirect
194. #104×C131D4semidirect
331. M16×C131C2×D4semidirect
370. C42×C131C2×D4semidirect
403. Q8×C131#121semidirect
438. D4×C131#121semidirect
518. C22×C131#453semidirect
549. #24464C131direct (N × H)
550. C131#24464direct (N × H)
551. #3488C2×C131semidirect
552. #3055C2×C131semidirect
553. C2×#453C2×C131semidirect
554. #3006C2×C131semidirect
555. C22×#104C2×C131semidirect
556. #2856C2×C131semidirect
557. #2039C2×C131semidirect
558. #2037C2×C131semidirect
559. #2006C2×C131semidirect
560. #2002C2×C131semidirect
561. #1900C2×C131semidirect
562. #1896C2×C131semidirect
563. #1883C2×C131semidirect
564. #1859C2×C131semidirect
565. #1792C2×C131semidirect
569. C2×AGL(1,ℤ/8)C22×C131semidirect
570. C2×AGL(1,ℤ/8)C22×C131semidirect
571. C22×M16C22×C131semidirect
582. C2×#127C22×C131semidirect
588. C2×#121C22×C131semidirect
590. C22×C42C22×C131semidirect
600. #428C22×C131semidirect
604. C2×#104C22×C131semidirect
605. C2×#104C22×C131semidirect
606. C2×#104C22×C131semidirect
607. C2×#104C22×C131semidirect
608. #418C22×C131semidirect
610. #417C22×C131semidirect
611. #417C22×C131semidirect
612. C2×#100C22×C131semidirect
613. C2×#100C22×C131semidirect
614. #407C22×C131semidirect
616. #390C22×C131semidirect
617. #390C22×C131semidirect
618. #384C22×C131semidirect
619. #343C22×C131semidirect
620. #343C22×C131semidirect
621. #339C22×C131semidirect
622. #339C22×C131semidirect
635. C2×#41D4×C131semidirect
636. C2×#41D4×C131semidirect
640. C22×Q8D4×C131semidirect
649. C22×D4D4×C131semidirect
686. C22⋊Q8D4×C131semidirect
687. C22⋊Q8D4×C131semidirect
707. #121D4×C131semidirect
708. #121D4×C131semidirect
744. #104D4×C131semidirect
881. M16C2×D4×C131semidirect
920. C42C2×D4×C131semidirect
953. Q8#121×C131semidirect
988. D4#121×C131semidirect
1068. C22#453×C131semidirect

Maximal subgroups

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

subgroupindex
#3488×C1312
#3055×C1312
C2×#453×C1312
#3006×C1312
C22×#104×C1312
#2856×C1312
#2039×C1312
#2037×C1312
#2006×C1312
#2002×C1312
#1900×C1312
#1896×C1312
#1883×C1312
#1859×C1312
#1792×C1312
#24464131