Finite Group Databasebeta

← C131×#24468 #45710352

Subgroups — C131×#24468 #45710352

Order 33536.

1502 conjugacy classes of subgroups.

The subgroup lattice has 1090 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
5C2×#421×C131C211yesmaximal, characteristic, complemented
6#2619×C131C211yesmaximal, characteristic, complemented
7#2040×C131C211yesmaximal, characteristic, complemented
8#2037×C131C211yesmaximal, characteristic, complemented
9#2006×C131C211yesmaximal, characteristic, complemented
10#2002×C131C211yesmaximal, characteristic, complemented
11#1900×C131C211yesmaximal, characteristic, complemented
12#1897×C131C211yesmaximal, characteristic, complemented
13#1883×C131C211yesmaximal, characteristic, complemented
14#1860×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×C131C2211yescharacteristic
37C2×#121×C131C2211yescharacteristic, complemented
38#520×C131C2211yescharacteristic
39C2×#117×C131C2211yescharacteristic, complemented
40#469×C131—21no—
41#468×C131—21no—
42#466×C131—21no—
43#465×C131—21no—
44#453×C131—24no—
45#449×C131—21no—
46#449×C131—21no—
47#448×C131—21no—
48#447×C131—21no—
49#428×C131C2211yescharacteristic, complemented
50#421×C131—24no—
51C2×#104×C131C2211yescharacteristic
52C2×#104×C131C2211yescharacteristic
53C2×#104×C131C2211yescharacteristic, complemented
54C2×#104×C131C2211yescharacteristic, complemented
55C2×#104×C131C2211yescharacteristic, complemented
56C2×#104×C131C2211yescharacteristic, complemented
57#418×C131C2211yescharacteristic, complemented
58#417×C131C2211yescharacteristic
59#417×C131C2211yescharacteristic, complemented
60#417×C131C2211yescharacteristic, complemented
61C2×#100×C131C2211yescharacteristic, complemented
62C2×#100×C131C2211yescharacteristic, complemented
63#407×C131C2211yescharacteristic, complemented
64#394×C131—22no—
65#392×C131—22no—
66#390×C131C2211yescharacteristic, complemented
67#390×C131C2211yescharacteristic, complemented
68#382×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—21no—
97C22×D4×C131—22no—
98C22×D4×C131D412yes—
99C22×D4×C131D411yescharacteristic, complemented
100C22×D4×C131C2311yescharacteristic
101C22×D4×C131C2311yescharacteristic
102C23×C4×C131—21no—
103C23×C4×C131C2311yescharacteristic
104AGL(1,ℤ/8)×C131—22no—
105AGL(1,ℤ/8)×C131—22no—
106AGL(1,ℤ/8)×C131—22no—
107AGL(1,ℤ/8)×C131—41no—
108AGL(1,ℤ/8)×C131—41no—
109AGL(1,ℤ/8)×C131—41no—
110C2×SD16×C131—21no—
111C2×SD16×C131—21no—
112C2×SD16×C131—21no—
113C2×D8×C131—21no—
114C2×D8×C131—21no—
115C2×D8×C131—21no—
116C2×M16×C131—21no—
117C2×M16×C131—22no—
118C2×M16×C131—41no—
119C2×M16×C131C2311yescharacteristic
120C2×M16×C131C2311yescharacteristic
121C2×M16×C131C2311yescharacteristic
122C2×M16×C131C2311yescharacteristic
123C22×C8×C131—21no—
124#127×C131—22no—
125#127×C131—21no—
126#127×C131—22no—
127#127×C131—41no—
128#124×C131—22no—
129#124×C131—21no—
130#123×C131—22no—
131#123×C131—21no—
132C22⋊Q8×C131—22no—
133C22⋊Q8×C131—21no—
134C22⋊Q8×C131—21no—
135C22⋊Q8×C131D411yescharacteristic, complemented
136C22⋊Q8×C131D411yescharacteristic, complemented
137#121×C131—22no—
138#121×C131—22no—
139#121×C131—22no—
140#121×C131—22no—
141#121×C131—22no—
142#121×C131—21no—
143#121×C131—21no—
144#121×C131—21no—
145#121×C131—21no—
146#121×C131—21no—
147#121×C131—21no—
148#121×C131—22no—
149#121×C131—21no—
150#121×C131—21no—
151#121×C131—21no—
152#121×C131—21no—
153#121×C131—21no—
154#121×C131—21no—
155#121×C131D411yescharacteristic, complemented
156#121×C131D411yescharacteristic, complemented
157#120×C131—22no—
158#120×C131—22no—
159#120×C131—22no—
160#120×C131—21no—
161#120×C131—22no—
162C4×Q8×C131—21no—
163C4×D4×C131—22no—
164C4×D4×C131—22no—
165C4×D4×C131—21no—
166C4×D4×C131—22no—
167C4×D4×C131—21no—
168C4×D4×C131—21no—
169#117×C131—21no—
170#117×C131—22no—
171#117×C131—41no—
172#117×C131C2311yescharacteristic
173C2×C4⋊C4×C131—21no—
174C2×C4⋊C4×C131—21no—
175C2×C4⋊C4×C131C2311yescharacteristic
176C2×C4⋊C4×C131C2311yescharacteristic
177C2×C22⋊C4×C131—22no—
178C2×C22⋊C4×C131—21no—
179C2×C22⋊C4×C131—21no—
180C2×C22⋊C4×C131—22no—
181C2×C22⋊C4×C131—22no—
182C2×C22⋊C4×C131D412yes—
183C2×C42×C131C2311yescharacteristic
184C2×C42×C131C2311yescharacteristic
185#107×C131—21no—
186#106×C131—21no—
187#104×C131—22no—
188#104×C131—22no—
189#104×C131—22no—
190#104×C131—22no—
191#104×C131—41no—
192#104×C131D414yescomplemented
193#103×C131—21no—
194#103×C131—21no—
195#103×C131—21no—
196#102×C131—21no—
197#102×C131—21no—
198#102×C131—21no—
199#102×C131—21no—
200#102×C131—21no—
201#100×C131—22no—
202#100×C131—41no—
203C22⋊C8×C131—21no—
204C22⋊C8×C131—21no—
205#95×C131—22no—
206C24×C131—22no—
207C24×C131—21no—
208C24×C131—21no—
209C24×C131C2×D412yes—
210C24×C131C2×D411yescharacteristic
211#41×C131—21no—
212#41×C131—21no—
213#41×C131—22no—
214#41×C131—22no—
215#41×C131—21no—
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—42no—
224#41×C131—42no—
225#41×C131—41no—
226#41×C131—41no—
227#41×C131—42no—
228#41×C131—42no—
229#41×C131—42no—
230#41×C131—42no—
231#41×C131—42no—
232#41×C131—42no—
233#41×C131C2×D412yes—
234#41×C131#4112yes—
235C2×Q8×C131—21no—
236C2×Q8×C131—22no—
237C2×Q8×C131—41no—
238C2×Q8×C131C2×D411yescharacteristic
239C2×Q8×C131C2×D411yescharacteristic
240C2×Q8×C131C2×D411yescharacteristic
241C2×D4×C131—21no—
242C2×D4×C131—22no—
243C2×D4×C131—22no—
244C2×D4×C131—22no—
245C2×D4×C131—22no—
246C2×D4×C131—21no—
247C2×D4×C131—21no—
248C2×D4×C131—21no—
249C2×D4×C131—21no—
250C2×D4×C131—21no—
251C2×D4×C131—22no—
252C2×D4×C131—22no—
253C2×D4×C131—22no—
254C2×D4×C131—21no—
255C2×D4×C131—22no—
256C2×D4×C131—21no—
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—41no—
270C2×D4×C131—42no—
271C2×D4×C131—42no—
272C2×D4×C131—44no—
273C2×D4×C131—42no—
274C2×D4×C131—42no—
275C2×D4×C131—44no—
276C2×D4×C131—44no—
277C2×D4×C131—42no—
278C2×D4×C131—42no—
279C2×D4×C131—41no—
280C2×D4×C131—41no—
281C2×D4×C131—82no—
282C2×D4×C131—82no—
283C2×D4×C131—82no—
284C2×D4×C131—82no—
285C2×D4×C131—84no—
286C2×D4×C131C2×D411yescharacteristic
287C2×D4×C131C2×D411yescharacteristic
288C2×D4×C131C2×D411yescharacteristic
289C22×C4×C131—21no—
290C22×C4×C131—21no—
291C22×C4×C131—21no—
292C22×C4×C131—21no—
293C22×C4×C131—21no—
294C22×C4×C131—22no—
295C22×C4×C131—21no—
296C22×C4×C131—21no—
297C22×C4×C131—22no—
298C22×C4×C131—21no—
299C22×C4×C131—21no—
300C22×C4×C131—21no—
301C22×C4×C131—21no—
302C22×C4×C131—21no—
303C22×C4×C131—21no—
304C22×C4×C131—42no—
305C22×C4×C131—42no—
306C22×C4×C131C2×D411yescharacteristic
307C22×C4×C131C2×D411yescharacteristic
308C22×C4×C131C2×D411yescharacteristic
309C22×C4×C131C2×D411yescharacteristic
310C22×C4×C131C2×D411yescharacteristic
311C22×C4×C131C2×D412yes—
312C22×C4×C131C2411yescharacteristic
313SD16×C131—42no—
314SD16×C131—42no—
315SD16×C131—42no—
316D8×C131—42no—
317D8×C131—42no—
318D8×C131—42no—
319M16×C131—21no—
320M16×C131—21no—
321M16×C131—21no—
322M16×C131—21no—
323M16×C131—21no—
324M16×C131—21no—
325M16×C131—21no—
326M16×C131—42no—
327M16×C131C2×D412yescomplemented
328C2×C8×C131—21no—
329C2×C8×C131—21no—
330C2×C8×C131—21no—
331C2×C8×C131—21no—
332C2×C8×C131—42no—
333C4⋊C4×C131—22no—
334C4⋊C4×C131—22no—
335C4⋊C4×C131—21no—
336C4⋊C4×C131—21no—
337C4⋊C4×C131—21no—
338C4⋊C4×C131—21no—
339C4⋊C4×C131—21no—
340C4⋊C4×C131—21no—
341C4⋊C4×C131—42no—
342C4⋊C4×C131C2×D411yescharacteristic
343C4⋊C4×C131C2×D411yescharacteristic
344C22⋊C4×C131—22no—
345C22⋊C4×C131—22no—
346C22⋊C4×C131—22no—
347C22⋊C4×C131—22no—
348C22⋊C4×C131—22no—
349C22⋊C4×C131—21no—
350C22⋊C4×C131—21no—
351C22⋊C4×C131—21no—
352C22⋊C4×C131—21no—
353C22⋊C4×C131—22no—
354C22⋊C4×C131—22no—
355C22⋊C4×C131—21no—
356C22⋊C4×C131—42no—
357C22⋊C4×C131—41no—
358C22⋊C4×C131—41no—
359C22⋊C4×C131—82no—
360C22⋊C4×C131—82no—
361C42×C131—22no—
362C42×C131—21no—
363C42×C131—21no—
364C42×C131—21no—
365C42×C131—21no—
366C42×C131C2×D412yescomplemented
367C23×C131—21no—
368C23×C131—21no—
369C23×C131—21no—
370C23×C131—22no—
371C23×C131—21no—
372C23×C131—21no—
373C23×C131—22no—
374C23×C131—22no—
375C23×C131—41no—
376C23×C131—41no—
377C23×C131—42no—
378C23×C131—42no—
379C23×C131—44no—
380C23×C131—42no—
381C23×C131—42no—
382C23×C131—42no—
383C23×C131—42no—
384C23×C131—41no—
385C23×C131—41no—
386C23×C131—41no—
387C23×C131—81no—
388C23×C131—82no—
389C23×C131—82no—
390C23×C131#12011yescharacteristic
391C23×C131#12011yescharacteristic
392C23×C131C22×D411yescharacteristic
393Q8×C131—21no—
394Q8×C131—21no—
395Q8×C131—21no—
396Q8×C131—21no—
397Q8×C131—21no—
398Q8×C131—42no—
399Q8×C131#12112yes—
400D4×C131—22no—
401D4×C131—22no—
402D4×C131—21no—
403D4×C131—21no—
404D4×C131—21no—
405D4×C131—21no—
406D4×C131—21no—
407D4×C131—42no—
408D4×C131—42no—
409D4×C131—44no—
410D4×C131—42no—
411D4×C131—44no—
412D4×C131—44no—
413D4×C131—42no—
414D4×C131—41no—
415D4×C131—41no—
416D4×C131—41no—
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—41no—
426D4×C131—81no—
427D4×C131—82no—
428D4×C131—82no—
429D4×C131—82no—
430D4×C131—82no—
431D4×C131—88no—
432D4×C131—82no—
433D4×C131—82no—
434D4×C131#12112yes—
435C2×C4×C131—21no—
436C2×C4×C131—21no—
437C2×C4×C131—21no—
438C2×C4×C131—21no—
439C2×C4×C131—21no—
440C2×C4×C131—21no—
441C2×C4×C131—21no—
442C2×C4×C131—21no—
443C2×C4×C131—21no—
444C2×C4×C131—22no—
445C2×C4×C131—21no—
446C2×C4×C131—21no—
447C2×C4×C131—22no—
448C2×C4×C131—21no—
449C2×C4×C131—22no—
450C2×C4×C131—21no—
451C2×C4×C131—21no—
452C2×C4×C131—21no—
453C2×C4×C131—22no—
454C2×C4×C131—42no—
455C2×C4×C131—42no—
456C2×C4×C131—42no—
457C2×C4×C131—44no—
458C2×C4×C131—41no—
459C2×C4×C131—41no—
460C2×C4×C131—41no—
461C2×C4×C131—41no—
462C2×C4×C131—41no—
463C2×C4×C131—41no—
464C2×C4×C131—42no—
465C2×C4×C131—41no—
466C2×C4×C131—41no—
467C2×C4×C131—42no—
468C2×C4×C131—41no—
469C2×C4×C131—41no—
470C2×C4×C131—82no—
471C2×C4×C131#12011yescharacteristic
472C2×C4×C131#12011yescharacteristic
473C2×C4×C131C22×D411yescharacteristic
474C2×C4×C131C22×D411yescharacteristic
475C2×C4×C131C22×D411yescharacteristic
476C2×C4×C131C2×#4111yescharacteristic
477C2×C4×C131H(5,𝔽2)11yescharacteristic
478C2×C4×C131H(5,𝔽2)11yescharacteristic
479C8×C131—22no—
480C8×C131—41no—
481C8×C131—41no—
482C8×C131—41no—
483C22×C131—21no—
484C22×C131—21no—
485C22×C131—21no—
486C22×C131—21no—
487C22×C131—22no—
488C22×C131—21no—
489C22×C131—21no—
490C22×C131—21no—
491C22×C131—21no—
492C22×C131—41no—
493C22×C131—41no—
494C22×C131—41no—
495C22×C131—41no—
496C22×C131—42no—
497C22×C131—42no—
498C22×C131—41no—
499C22×C131—41no—
500C22×C131—41no—
501C22×C131—42no—
502C22×C131—41no—
503C22×C131—81no—
504C22×C131—81no—
505C22×C131—82no—
506C22×C131—82no—
507C22×C131—82no—
508C22×C131—82no—
509C22×C131—84no—
510C22×C131—81no—
511C22×C131—81no—
512C22×C131—81no—
513C22×C131—164no—
514C22×C131C2×#12011yescharacteristic
515C22×C131D4211yescharacteristic
516C22×C131#54611yescharacteristic
517C4×C131—21no—
518C4×C131—21no—
519C4×C131—22no—
520C4×C131—42no—
521C4×C131—41no—
522C4×C131—41no—
523C4×C131—42no—
524C4×C131—41no—
525C4×C131—41no—
526C4×C131—81no—
527C4×C131—81no—
528C4×C131C2×#12111yescharacteristic
529C4×C131#53411yescharacteristic
530C4×C131D4211yescharacteristic
531C4×C131#54611yescharacteristic
532C2×C131—21no—
533C2×C131—21no—
534C2×C131—41no—
535C2×C131—41no—
536C2×C131—42no—
537C2×C131—81no—
538C2×C131—82no—
539C2×C131—81no—
540C2×C131—161no—
541C2×C131#241011yescharacteristic
542C2×C131#301911yescharacteristic
543C2×C131#302111yescharacteristic
544#24468C13111yesmaximal, characteristic, direct product factor, Sylow
545C131#2446811yescharacteristic, direct product factor, Sylow
546#3488C2×C13111yescharacteristic, complemented
547#3055C2×C13111yescharacteristic, complemented
548C2×#453C2×C13111yescharacteristic, complemented
549#3006C2×C13111yescharacteristic, complemented
550C2×#421C2×C13111yescharacteristic, complemented
551#2619C2×C13111yescharacteristic, complemented
552#2040C2×C13111yescharacteristic, complemented
553#2037C2×C13111yescharacteristic, complemented
554#2006C2×C13111yescharacteristic, complemented
555#2002C2×C13111yescharacteristic, complemented
556#1900C2×C13111yescharacteristic, complemented
557#1897C2×C13111yescharacteristic, complemented
558#1883C2×C13111yescharacteristic, complemented
559#1860C2×C13111yescharacteristic, complemented
560#1792C2×C13111yescharacteristic, complemented
561C2×H(5,𝔽2)C22×C13111yescharacteristic
562C22×#41C22×C13111yescharacteristic
563C2×AGL(1,ℤ/8)C22×C13111yescharacteristic
564C2×AGL(1,ℤ/8)C22×C13111yescharacteristic, complemented
565C2×AGL(1,ℤ/8)C22×C13111yescharacteristic, complemented
566C22×M16C22×C13111yescharacteristic, complemented
567#550—21no—
568#548—21no—
569#546—21no—
570#546—22no—
571D42—22no—
572D42—21no—
573#537—21no—
574#537C22×C13111yescharacteristic
575#535—21no—
576#535C22×C13111yescharacteristic
577C2×#127C22×C13111yescharacteristic, complemented
578#525—21no—
579#525C22×C13111yescharacteristic
580C2×#121—21no—
581C2×#121C22×C13111yescharacteristic
582C2×#121C22×C13111yescharacteristic, complemented
583#520C22×C13111yescharacteristic
584C2×#117C22×C13111yescharacteristic, complemented
585#469—21no—
586#468—21no—
587#466—21no—
588#465—21no—
589#453—24no—
590#449—21no—
591#449—21no—
592#448—21no—
593#447—21no—
594#428C22×C13111yescharacteristic, complemented
595#421—24no—
596C2×#104C22×C13111yescharacteristic
597C2×#104C22×C13111yescharacteristic
598C2×#104C22×C13111yescharacteristic, complemented
599C2×#104C22×C13111yescharacteristic, complemented
600C2×#104C22×C13111yescharacteristic, complemented
601C2×#104C22×C13111yescharacteristic, complemented
602#418C22×C13111yescharacteristic, complemented
603#417C22×C13111yescharacteristic
604#417C22×C13111yescharacteristic, complemented
605#417C22×C13111yescharacteristic, complemented
606C2×#100C22×C13111yescharacteristic, complemented
607C2×#100C22×C13111yescharacteristic, complemented
608#407C22×C13111yescharacteristic, complemented
609#394—22no—
610#392—22no—
611#390C22×C13111yescharacteristic, complemented
612#390C22×C13111yescharacteristic, complemented
613#382C22×C13111yescharacteristic, complemented
614#343C22×C13111yescharacteristic, complemented
615#343C22×C13111yescharacteristic, complemented
616#339C22×C13111yescharacteristic, complemented
617#339C22×C13111yescharacteristic, complemented
618H(5,𝔽2)—22no—
619H(5,𝔽2)—22no—
620H(5,𝔽2)—41no—
621H(5,𝔽2)—41no—
622C2×#41—21no—
623C2×#41—21no—
624C2×#41—21no—
625C2×#41—21no—
626C2×#41—22no—
627C2×#41—22no—
628C2×#41—41no—
629C2×#41—41no—
630C2×#41D4×C13111yescharacteristic, complemented
631C2×#41D4×C13111yescharacteristic, complemented
632C2×#41C23×C13111yescharacteristic
633C2×#41C23×C13111yescharacteristic
634C2×#41C23×C13111yescharacteristic
635C22×Q8D4×C13111yescharacteristic, complemented
636C22×D4—21no—
637C22×D4—22no—
638C22×D4—22no—
639C22×D4—21no—
640C22×D4—21no—
641C22×D4—21no—
642C22×D4—22no—
643C22×D4D4×C13112yes—
644C22×D4D4×C13111yescharacteristic, complemented
645C22×D4C23×C13111yescharacteristic
646C22×D4C23×C13111yescharacteristic
647C23×C4—21no—
648C23×C4C23×C13111yescharacteristic
649AGL(1,ℤ/8)—22no—
650AGL(1,ℤ/8)—22no—
651AGL(1,ℤ/8)—22no—
652AGL(1,ℤ/8)—41no—
653AGL(1,ℤ/8)—41no—
654AGL(1,ℤ/8)—41no—
655C2×SD16—21no—
656C2×SD16—21no—
657C2×SD16—21no—
658C2×D8—21no—
659C2×D8—21no—
660C2×D8—21no—
661C2×M16—21no—
662C2×M16—22no—
663C2×M16—41no—
664C2×M16C23×C13111yescharacteristic
665C2×M16C23×C13111yescharacteristic
666C2×M16C23×C13111yescharacteristic
667C2×M16C23×C13111yescharacteristic
668C22×C8—21no—
669#127—22no—
670#127—21no—
671#127—22no—
672#127—41no—
673#124—22no—
674#124—21no—
675#123—22no—
676#123—21no—
677C22⋊Q8—22no—
678C22⋊Q8—21no—
679C22⋊Q8—21no—
680C22⋊Q8D4×C13111yescharacteristic, complemented
681C22⋊Q8D4×C13111yescharacteristic, complemented
682#121—22no—
683#121—22no—
684#121—22no—
685#121—22no—
686#121—22no—
687#121—21no—
688#121—21no—
689#121—21no—
690#121—21no—
691#121—21no—
692#121—21no—
693#121—22no—
694#121—21no—
695#121—21no—
696#121—21no—
697#121—21no—
698#121—21no—
699#121—21no—
700#121D4×C13111yescharacteristic, complemented
701#121D4×C13111yescharacteristic, complemented
702#120—22no—
703#120—22no—
704#120—22no—
705#120—21no—
706#120—22no—
707C4×Q8—21no—
708C4×D4—22no—
709C4×D4—22no—
710C4×D4—21no—
711C4×D4—22no—
712C4×D4—21no—
713C4×D4—21no—
714#117—21no—
715#117—22no—
716#117—41no—
717#117C23×C13111yescharacteristic
718C2×C4⋊C4—21no—
719C2×C4⋊C4—21no—
720C2×C4⋊C4C23×C13111yescharacteristic
721C2×C4⋊C4C23×C13111yescharacteristic
722C2×C22⋊C4—22no—
723C2×C22⋊C4—21no—
724C2×C22⋊C4—21no—
725C2×C22⋊C4—22no—
726C2×C22⋊C4—22no—
727C2×C22⋊C4D4×C13112yes—
728C2×C42C23×C13111yescharacteristic
729C2×C42C23×C13111yescharacteristic
730#107—21no—
731#106—21no—
732#104—22no—
733#104—22no—
734#104—22no—
735#104—22no—
736#104—41no—
737#104D4×C13114yescomplemented
738#103—21no—
739#103—21no—
740#103—21no—
741#102—21no—
742#102—21no—
743#102—21no—
744#102—21no—
745#102—21no—
746#100—22no—
747#100—41no—
748C22⋊C8—21no—
749C22⋊C8—21no—
750#95—22no—
751C24—22no—
752C24—21no—
753C24—21no—
754C24C2×D4×C13112yes—
755C24C2×D4×C13111yescharacteristic
756#41—21no—
757#41—21no—
758#41—22no—
759#41—22no—
760#41—21no—
761#41—21no—
762#41—21no—
763#41—21no—
764#41—21no—
765#41—21no—
766#41—21no—
767#41—21no—
768#41—42no—
769#41—42no—
770#41—41no—
771#41—41no—
772#41—42no—
773#41—42no—
774#41—42no—
775#41—42no—
776#41—42no—
777#41—42no—
778#41C2×D4×C13112yes—
779#41#41×C13112yes—
780C2×Q8—21no—
781C2×Q8—22no—
782C2×Q8—41no—
783C2×Q8C2×D4×C13111yescharacteristic
784C2×Q8C2×D4×C13111yescharacteristic
785C2×Q8C2×D4×C13111yescharacteristic
786C2×D4—21no—
787C2×D4—22no—
788C2×D4—22no—
789C2×D4—22no—
790C2×D4—22no—
791C2×D4—21no—
792C2×D4—21no—
793C2×D4—21no—
794C2×D4—21no—
795C2×D4—21no—
796C2×D4—22no—
797C2×D4—22no—
798C2×D4—22no—
799C2×D4—21no—
800C2×D4—22no—
801C2×D4—21no—
802C2×D4—21no—
803C2×D4—21no—
804C2×D4—21no—
805C2×D4—21no—
806C2×D4—21no—
807C2×D4—21no—
808C2×D4—21no—
809C2×D4—21no—
810C2×D4—21no—
811C2×D4—21no—
812C2×D4—21no—
813C2×D4—21no—
814C2×D4—41no—
815C2×D4—42no—
816C2×D4—42no—
817C2×D4—44no—
818C2×D4—42no—
819C2×D4—42no—
820C2×D4—44no—
821C2×D4—44no—
822C2×D4—42no—
823C2×D4—42no—
824C2×D4—41no—
825C2×D4—41no—
826C2×D4—82no—
827C2×D4—82no—
828C2×D4—82no—
829C2×D4—82no—
830C2×D4—84no—
831C2×D4C2×D4×C13111yescharacteristic
832C2×D4C2×D4×C13111yescharacteristic
833C2×D4C2×D4×C13111yescharacteristic
834C22×C4—21no—
835C22×C4—21no—
836C22×C4—21no—
837C22×C4—21no—
838C22×C4—21no—
839C22×C4—22no—
840C22×C4—21no—
841C22×C4—21no—
842C22×C4—22no—
843C22×C4—21no—
844C22×C4—21no—
845C22×C4—21no—
846C22×C4—21no—
847C22×C4—21no—
848C22×C4—21no—
849C22×C4—42no—
850C22×C4—42no—
851C22×C4C2×D4×C13111yescharacteristic
852C22×C4C2×D4×C13111yescharacteristic
853C22×C4C2×D4×C13111yescharacteristic
854C22×C4C2×D4×C13111yescharacteristic
855C22×C4C2×D4×C13111yescharacteristic
856C22×C4C2×D4×C13112yes—
857C22×C4C24×C13111yescharacteristic
858SD16—42no—
859SD16—42no—
860SD16—42no—
861D8—42no—
862D8—42no—
863D8—42no—
864M16—21no—
865M16—21no—
866M16—21no—
867M16—21no—
868M16—21no—
869M16—21no—
870M16—21no—
871M16—42no—
872M16C2×D4×C13112yescomplemented
873C2×C8—21no—
874C2×C8—21no—
875C2×C8—21no—
876C2×C8—21no—
877C2×C8—42no—
878C4⋊C4—22no—
879C4⋊C4—22no—
880C4⋊C4—21no—
881C4⋊C4—21no—
882C4⋊C4—21no—
883C4⋊C4—21no—
884C4⋊C4—21no—
885C4⋊C4—21no—
886C4⋊C4—42no—
887C4⋊C4C2×D4×C13111yescharacteristic
888C4⋊C4C2×D4×C13111yescharacteristic
889C22⋊C4—22no—
890C22⋊C4—22no—
891C22⋊C4—22no—
892C22⋊C4—22no—
893C22⋊C4—22no—
894C22⋊C4—21no—
895C22⋊C4—21no—
896C22⋊C4—21no—
897C22⋊C4—21no—
898C22⋊C4—22no—
899C22⋊C4—22no—
900C22⋊C4—21no—
901C22⋊C4—42no—
902C22⋊C4—41no—
903C22⋊C4—41no—
904C22⋊C4—82no—
905C22⋊C4—82no—
906C42—22no—
907C42—21no—
908C42—21no—
909C42—21no—
910C42—21no—
911C42C2×D4×C13112yescomplemented
912C23—21no—
913C23—21no—
914C23—21no—
915C23—22no—
916C23—21no—
917C23—21no—
918C23—22no—
919C23—22no—
920C23—41no—
921C23—41no—
922C23—42no—
923C23—42no—
924C23—44no—
925C23—42no—
926C23—42no—
927C23—42no—
928C23—42no—
929C23—41no—
930C23—41no—
931C23—41no—
932C23—81no—
933C23—82no—
934C23—82no—
935C23#120×C13111yescharacteristic
936C23#120×C13111yescharacteristic
937C23C22×D4×C13111yescharacteristic
938Q8—21no—
939Q8—21no—
940Q8—21no—
941Q8—21no—
942Q8—21no—
943Q8—42no—
944Q8#121×C13112yes—
945D4—22no—
946D4—22no—
947D4—21no—
948D4—21no—
949D4—21no—
950D4—21no—
951D4—21no—
952D4—42no—
953D4—42no—
954D4—44no—
955D4—42no—
956D4—44no—
957D4—44no—
958D4—42no—
959D4—41no—
960D4—41no—
961D4—41no—
962D4—41no—
963D4—41no—
964D4—41no—
965D4—41no—
966D4—41no—
967D4—41no—
968D4—41no—
969D4—41no—
970D4—41no—
971D4—82no—
972D4—81no—
973D4—82no—
974D4—82no—
975D4—82no—
976D4—88no—
977D4—82no—
978D4—82no—
979D4#121×C13112yes—
980C2×C4—21no—
981C2×C4—21no—
982C2×C4—21no—
983C2×C4—21no—
984C2×C4—21no—
985C2×C4—21no—
986C2×C4—21no—
987C2×C4—21no—
988C2×C4—21no—
989C2×C4—22no—
990C2×C4—21no—
991C2×C4—21no—
992C2×C4—22no—
993C2×C4—21no—
994C2×C4—22no—
995C2×C4—21no—
996C2×C4—21no—
997C2×C4—21no—
998C2×C4—22no—
999C2×C4—42no—
1000C2×C4—42no—
1001C2×C4—42no—
1002C2×C4—44no—
1003C2×C4—41no—
1004C2×C4—41no—
1005C2×C4—41no—
1006C2×C4—41no—
1007C2×C4—41no—
1008C2×C4—41no—
1009C2×C4—42no—
1010C2×C4—41no—
1011C2×C4—41no—
1012C2×C4—42no—
1013C2×C4—41no—
1014C2×C4—41no—
1015C2×C4—82no—
1016C2×C4#120×C13111yescharacteristic
1017C2×C4#120×C13111yescharacteristic
1018C2×C4C22×D4×C13111yescharacteristic
1019C2×C4C22×D4×C13111yescharacteristic
1020C2×C4C22×D4×C13111yescharacteristic
1021C2×C4C2×#41×C13111yescharacteristic
1022C2×C4H(5,𝔽2)×C13111yescharacteristic
1023C2×C4H(5,𝔽2)×C13111yescharacteristic
1024C8—22no—
1025C8—41no—
1026C8—41no—
1027C8—41no—
1028C22—21no—
1029C22—21no—
1030C22—21no—
1031C22—21no—
1032C22—21no—
1033C22—21no—
1034C22—21no—
1035C22—21no—
1036C22—22no—
1037C22—41no—
1038C22—41no—
1039C22—42no—
1040C22—41no—
1041C22—41no—
1042C22—41no—
1043C22—42no—
1044C22—41no—
1045C22—41no—
1046C22—41no—
1047C22—42no—
1048C22—81no—
1049C22—81no—
1050C22—82no—
1051C22—82no—
1052C22—82no—
1053C22—82no—
1054C22—84no—
1055C22—81no—
1056C22—81no—
1057C22—81no—
1058C22—164no—
1059C22C2×#120×C13111yescharacteristic
1060C22D42×C13111yescharacteristic
1061C22#546×C13111yescharacteristic
1062C4—21no—
1063C4—21no—
1064C4—22no—
1065C4—42no—
1066C4—42no—
1067C4—41no—
1068C4—41no—
1069C4—41no—
1070C4—41no—
1071C4—81no—
1072C4—81no—
1073C4C2×#121×C13111yescharacteristic
1074C4#534×C13111yescharacteristic
1075C4D42×C13111yescharacteristic
1076C4#546×C13111yescharacteristic
1077C2—21no—
1078C2—21no—
1079C2—41no—
1080C2—41no—
1081C2—42no—
1082C2—81no—
1083C2—82no—
1084C2—81no—
1085C2—161no—
1086C2#2410×C13111yescharacteristic
1087C2#3019×C13111yescharacteristic
1088C2#3021×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. C2×#421×C131C2semidirect
6. #2619×C131C2semidirect
7. #2040×C131C2semidirect
8. #2037×C131C2semidirect
9. #2006×C131C2semidirect
10. #2002×C131C2semidirect
11. #1900×C131C2semidirect
12. #1897×C131C2semidirect
13. #1883×C131C2semidirect
14. #1860×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
37. C2×#121×C131C22semidirect
39. C2×#117×C131C22semidirect
49. #428×C131C22semidirect
53. C2×#104×C131C22semidirect
54. C2×#104×C131C22semidirect
55. C2×#104×C131C22semidirect
56. C2×#104×C131C22semidirect
57. #418×C131C22semidirect
59. #417×C131C22semidirect
60. #417×C131C22semidirect
61. C2×#100×C131C22semidirect
62. C2×#100×C131C22semidirect
63. #407×C131C22semidirect
66. #390×C131C22semidirect
67. #390×C131C22semidirect
68. #382×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
135. C22⋊Q8×C131D4semidirect
136. C22⋊Q8×C131D4semidirect
155. #121×C131D4semidirect
156. #121×C131D4semidirect
192. #104×C131D4semidirect
327. M16×C131C2×D4semidirect
366. C42×C131C2×D4semidirect
544. #24468C131direct (N × H)
545. C131#24468direct (N × H)
546. #3488C2×C131semidirect
547. #3055C2×C131semidirect
548. C2×#453C2×C131semidirect
549. #3006C2×C131semidirect
550. C2×#421C2×C131semidirect
551. #2619C2×C131semidirect
552. #2040C2×C131semidirect
553. #2037C2×C131semidirect
554. #2006C2×C131semidirect
555. #2002C2×C131semidirect
556. #1900C2×C131semidirect
557. #1897C2×C131semidirect
558. #1883C2×C131semidirect
559. #1860C2×C131semidirect
560. #1792C2×C131semidirect
564. C2×AGL(1,ℤ/8)C22×C131semidirect
565. C2×AGL(1,ℤ/8)C22×C131semidirect
566. C22×M16C22×C131semidirect
577. C2×#127C22×C131semidirect
582. C2×#121C22×C131semidirect
584. C2×#117C22×C131semidirect
594. #428C22×C131semidirect
598. C2×#104C22×C131semidirect
599. C2×#104C22×C131semidirect
600. C2×#104C22×C131semidirect
601. C2×#104C22×C131semidirect
602. #418C22×C131semidirect
604. #417C22×C131semidirect
605. #417C22×C131semidirect
606. C2×#100C22×C131semidirect
607. C2×#100C22×C131semidirect
608. #407C22×C131semidirect
611. #390C22×C131semidirect
612. #390C22×C131semidirect
613. #382C22×C131semidirect
614. #343C22×C131semidirect
615. #343C22×C131semidirect
616. #339C22×C131semidirect
617. #339C22×C131semidirect
630. C2×#41D4×C131semidirect
631. C2×#41D4×C131semidirect
635. C22×Q8D4×C131semidirect
644. C22×D4D4×C131semidirect
680. C22⋊Q8D4×C131semidirect
681. C22⋊Q8D4×C131semidirect
700. #121D4×C131semidirect
701. #121D4×C131semidirect
737. #104D4×C131semidirect
872. M16C2×D4×C131semidirect
911. C42C2×D4×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
C2×#421×C1312
#2619×C1312
#2040×C1312
#2037×C1312
#2006×C1312
#2002×C1312
#1900×C1312
#1897×C1312
#1883×C1312
#1860×C1312
#1792×C1312
#24468131