Finite Group Databasebeta

← C131×#23860 #45709744

Subgroups — C131×#23860 #45709744

Order 33536.

2240 conjugacy classes of subgroups.

The subgroup lattice has 1088 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×AGL(1,ℤ/8)×C131C211yesmaximal, characteristic, complemented
2C2×D42×C131C211yesmaximal, characteristic, complemented
3C2×#449×C131C211yesmaximal, characteristic, complemented
4C2×#450×C131C211yesmaximal, characteristic, complemented
5C2×#447×C131C211yesmaximal, characteristic, complemented
6#2407×C131C211yesmaximal, characteristic, complemented
7#2014×C131C211yesmaximal, characteristic, complemented
8#2011×C131C211yesmaximal, characteristic, complemented
9#2000×C131C211yesmaximal, characteristic, complemented
10#1999×C131C211yesmaximal, characteristic, complemented
11#1895×C131C211yesmaximal, characteristic, complemented
12#1879×C131C211yesmaximal, characteristic, complemented
13#1877×C131C211yesmaximal, characteristic, complemented
14#1870×C131C211yesmaximal, characteristic, complemented
15#1786×C131C211yesmaximal, characteristic, complemented
16C22×#41×C131C2211yescharacteristic, complemented
17C23×D4×C131—21no—
18C23×D4×C131C2211yescharacteristic
19C23×D4×C131C2211yescharacteristic
20C2×AGL(1,ℤ/8)×C131—24no—
21C2×AGL(1,ℤ/8)×C131—24no—
22C2×AGL(1,ℤ/8)×C131—24no—
23C22×SD16×C131C2211yescharacteristic
24C22×SD16×C131C2211yescharacteristic, complemented
25C22×SD16×C131C2211yescharacteristic, complemented
26C22×D8×C131C2211yescharacteristic
27C22×D8×C131C2211yescharacteristic, complemented
28C22×D8×C131C2211yescharacteristic, complemented
29C22×M16×C131C2211yescharacteristic, complemented
30D42×C131—24no—
31D42×C131—24no—
32C2×#127×C131C2211yescharacteristic
33C2×C22⋊Q8×C131C2211yescharacteristic, complemented
34C2×#121×C131—21no—
35C2×#121×C131C2211yescharacteristic
36C2×#121×C131C2211yescharacteristic
37C2×#121×C131C2211yescharacteristic, complemented
38C2×#120×C131—21no—
39C2×#120×C131—21no—
40C2×C4×D4×C131C2211yescharacteristic
41C2×C4×D4×C131C2211yescharacteristic
42#450×C131—24no—
43#449×C131—24no—
44#447×C131—24no—
45C2×#103×C131C2211yescharacteristic, complemented
46C2×#102×C131C2211yescharacteristic
47C2×#102×C131C2211yescharacteristic
48C2×#102×C131C2211yescharacteristic, complemented
49C2×#102×C131C2211yescharacteristic, complemented
50C2×#102×C131C2211yescharacteristic, complemented
51C2×#102×C131C2211yescharacteristic, complemented
52C2×#102×C131C2211yescharacteristic, complemented
53C2×C22⋊C8×C131C2211yescharacteristic, complemented
54C2×C22⋊C8×C131C2211yescharacteristic, complemented
55C2×C22⋊C8×C131C2211yescharacteristic, complemented
56#394×C131—21no—
57#392×C131—21no—
58#391×C131C2211yescharacteristic, complemented
59#390×C131C2211yescharacteristic, complemented
60#386×C131—21no—
61#385×C131—21no—
62#380×C131C2211yescharacteristic, complemented
63#340×C131C2211yescharacteristic, complemented
64#340×C131C2211yescharacteristic, complemented
65#336×C131C2211yescharacteristic, complemented
66#336×C131C2211yescharacteristic, complemented
67C25×C131—21no—
68C25×C131—21no—
69C2×#41×C131—22no—
70C2×#41×C131—22no—
71C2×#41×C131—22no—
72C2×#41×C131—22no—
73C2×#41×C131—41no—
74C2×#41×C131—41no—
75C22×Q8×C131C2311yescharacteristic
76C22×D4×C131—22no—
77C22×D4×C131—22no—
78C22×D4×C131—28no—
79C22×D4×C131—21no—
80C22×D4×C131—21no—
81C22×D4×C131—22no—
82C22×D4×C131—22no—
83C22×D4×C131—22no—
84C22×D4×C131—22no—
85C22×D4×C131—21no—
86C22×D4×C131—21no—
87C22×D4×C131—21no—
88C22×D4×C131—21no—
89C22×D4×C131—21no—
90C22×D4×C131—22no—
91C22×D4×C131—21no—
92C22×D4×C131—41no—
93C22×D4×C131—41no—
94C22×D4×C131—41no—
95C22×D4×C131—41no—
96C22×D4×C131—44no—
97C22×D4×C131—44no—
98C22×D4×C131D411yescharacteristic
99C22×D4×C131D414yescomplemented
100C22×D4×C131C2311yescharacteristic
101C22×D4×C131C2311yescharacteristic
102C22×D4×C131C2311yescharacteristic
103C22×D4×C131C2311yescharacteristic
104C23×C4×C131—21no—
105C23×C4×C131—21no—
106C23×C4×C131C2311yescharacteristic
107C23×C4×C131C2311yescharacteristic
108AGL(1,ℤ/8)×C131—232no—
109C2×SD16×C131—22no—
110C2×SD16×C131—22no—
111C2×SD16×C131—22no—
112C2×SD16×C131—22no—
113C2×SD16×C131—22no—
114C2×SD16×C131—22no—
115C2×SD16×C131—22no—
116C2×SD16×C131—41no—
117C2×SD16×C131D414yescomplemented
118C2×D8×C131—22no—
119C2×D8×C131—22no—
120C2×D8×C131—22no—
121C2×D8×C131—22no—
122C2×D8×C131—22no—
123C2×D8×C131—22no—
124C2×D8×C131—22no—
125C2×D8×C131—41no—
126C2×D8×C131D414yescomplemented
127C2×M16×C131—22no—
128C2×M16×C131—22no—
129C2×M16×C131—22no—
130C22×C8×C131C2311yescharacteristic
131C22×C8×C131C2311yescharacteristic
132C22×C8×C131C2311yescharacteristic
133C22×C8×C131C2311yescharacteristic
134#127×C131—22no—
135#127×C131—22no—
136C22⋊Q8×C131—22no—
137C22⋊Q8×C131—41no—
138#121×C131—28no—
139#121×C131—22no—
140#121×C131—22no—
141#121×C131—22no—
142#121×C131—22no—
143#121×C131—41no—
144#121×C131D414yescomplemented
145#120×C131—28no—
146#120×C131—28no—
147C4×D4×C131—22no—
148C4×D4×C131—22no—
149C4×D4×C131—22no—
150C4×D4×C131—22no—
151C2×C4⋊C4×C131—21no—
152C2×C4⋊C4×C131D411yescharacteristic
153C2×C4⋊C4×C131C2311yescharacteristic
154C2×C4⋊C4×C131C2311yescharacteristic
155C2×C4⋊C4×C131C2311yescharacteristic
156C2×C22⋊C4×C131—21no—
157C2×C22⋊C4×C131—21no—
158C2×C22⋊C4×C131—21no—
159C2×C22⋊C4×C131—21no—
160C2×C22⋊C4×C131—21no—
161C2×C22⋊C4×C131—21no—
162C2×C22⋊C4×C131—21no—
163C2×C22⋊C4×C131—21no—
164C2×C22⋊C4×C131D411yescharacteristic
165C2×C22⋊C4×C131D411yescharacteristic
166C2×C42×C131C2311yescharacteristic
167#103×C131—22no—
168#102×C131—22no—
169#102×C131—22no—
170#102×C131—22no—
171#102×C131—22no—
172#102×C131—22no—
173#102×C131—41no—
174#102×C131—41no—
175C22⋊C8×C131—22no—
176C22⋊C8×C131—22no—
177C22⋊C8×C131—22no—
178#95×C131—21no—
179#95×C131—21no—
180#95×C131—21no—
181C24×C131—21no—
182C24×C131—24no—
183C24×C131—21no—
184C24×C131—21no—
185C24×C131—21no—
186C24×C131—24no—
187C24×C131—42no—
188C24×C131—42no—
189C24×C131—42no—
190C24×C131—42no—
191C24×C131—42no—
192C24×C131—42no—
193C24×C131—42no—
194C24×C131—42no—
195C24×C131—81no—
196C24×C131—81no—
197C24×C131—81no—
198C24×C131—81no—
199C24×C131C2×D411yescharacteristic
200C24×C131C2×D411yescharacteristic
201#41×C131—28no—
202#41×C131—44no—
203#41×C131—44no—
204#41×C131—44no—
205C2×Q8×C131—21no—
206C2×Q8×C131—21no—
207C2×Q8×C131—21no—
208C2×Q8×C131—21no—
209C2×Q8×C131—21no—
210C2×Q8×C131C2×D412yescomplemented
211C2×D4×C131—22no—
212C2×D4×C131—22no—
213C2×D4×C131—28no—
214C2×D4×C131—24no—
215C2×D4×C131—24no—
216C2×D4×C131—24no—
217C2×D4×C131—24no—
218C2×D4×C131—24no—
219C2×D4×C131—24no—
220C2×D4×C131—22no—
221C2×D4×C131—21no—
222C2×D4×C131—21no—
223C2×D4×C131—21no—
224C2×D4×C131—21no—
225C2×D4×C131—21no—
226C2×D4×C131—21no—
227C2×D4×C131—21no—
228C2×D4×C131—21no—
229C2×D4×C131—21no—
230C2×D4×C131—21no—
231C2×D4×C131—21no—
232C2×D4×C131—21no—
233C2×D4×C131—21no—
234C2×D4×C131—21no—
235C2×D4×C131—21no—
236C2×D4×C131—21no—
237C2×D4×C131—21no—
238C2×D4×C131—21no—
239C2×D4×C131—44no—
240C2×D4×C131—44no—
241C2×D4×C131—44no—
242C2×D4×C131—42no—
243C2×D4×C131—42no—
244C2×D4×C131—42no—
245C2×D4×C131—42no—
246C2×D4×C131—42no—
247C2×D4×C131—42no—
248C2×D4×C131—44no—
249C2×D4×C131—44no—
250C2×D4×C131—432no—
251C2×D4×C131—44no—
252C2×D4×C131—42no—
253C2×D4×C131—42no—
254C2×D4×C131—42no—
255C2×D4×C131—42no—
256C2×D4×C131—42no—
257C2×D4×C131—42no—
258C2×D4×C131—44no—
259C2×D4×C131—42no—
260C2×D4×C131—42no—
261C2×D4×C131—42no—
262C2×D4×C131—81no—
263C2×D4×C131—81no—
264C2×D4×C131—81no—
265C2×D4×C131C2×D412yes—
266C2×D4×C131C2×D412yes—
267C2×D4×C131C2×D412yes—
268C2×D4×C131C2×D412yes—
269C2×D4×C131C2×D412yes—
270C2×D4×C131C2×D412yescomplemented
271C22×C4×C131—21no—
272C22×C4×C131—21no—
273C22×C4×C131—21no—
274C22×C4×C131—21no—
275C22×C4×C131—24no—
276C22×C4×C131—21no—
277C22×C4×C131—21no—
278C22×C4×C131—21no—
279C22×C4×C131—21no—
280C22×C4×C131—21no—
281C22×C4×C131—21no—
282C22×C4×C131—21no—
283C22×C4×C131—21no—
284C22×C4×C131—21no—
285C22×C4×C131—21no—
286C22×C4×C131—42no—
287C22×C4×C131—42no—
288C22×C4×C131—42no—
289C22×C4×C131—42no—
290C22×C4×C131—42no—
291C22×C4×C131C2×D411yescharacteristic
292C22×C4×C131C2×D411yescharacteristic
293C22×C4×C131C2×D411yescharacteristic
294C22×C4×C131C2×D412yes—
295C22×C4×C131C2×D412yes—
296C22×C4×C131C2×D411yescharacteristic
297C22×C4×C131C2411yescharacteristic
298SD16×C131—28no—
299SD16×C131—28no—
300SD16×C131—44no—
301D8×C131—28no—
302D8×C131—28no—
303D8×C131—44no—
304M16×C131—28no—
305C2×C8×C131—21no—
306C2×C8×C131—21no—
307C2×C8×C131—21no—
308C2×C8×C131—21no—
309C2×C8×C131—21no—
310C2×C8×C131—21no—
311C2×C8×C131—21no—
312C2×C8×C131—21no—
313C2×C8×C131—21no—
314C2×C8×C131—21no—
315C2×C8×C131C2×D412yescomplemented
316C2×C8×C131C2×D412yescomplemented
317C4⋊C4×C131—22no—
318C4⋊C4×C131—21no—
319C4⋊C4×C131—21no—
320C4⋊C4×C131—21no—
321C4⋊C4×C131—21no—
322C4⋊C4×C131—21no—
323C4⋊C4×C131—42no—
324C4⋊C4×C131C2×D412yes—
325C22⋊C4×C131—24no—
326C22⋊C4×C131—24no—
327C22⋊C4×C131—22no—
328C22⋊C4×C131—24no—
329C22⋊C4×C131—22no—
330C22⋊C4×C131—42no—
331C22⋊C4×C131—42no—
332C22⋊C4×C131—42no—
333C22⋊C4×C131—81no—
334C22⋊C4×C131—81no—
335C42×C131—21no—
336C42×C131—21no—
337C23×C131—21no—
338C23×C131—22no—
339C23×C131—21no—
340C23×C131—21no—
341C23×C131—21no—
342C23×C131—21no—
343C23×C131—22no—
344C23×C131—22no—
345C23×C131—21no—
346C23×C131—21no—
347C23×C131—21no—
348C23×C131—21no—
349C23×C131—21no—
350C23×C131—21no—
351C23×C131—21no—
352C23×C131—22no—
353C23×C131—22no—
354C23×C131—22no—
355C23×C131—48no—
356C23×C131—48no—
357C23×C131—48no—
358C23×C131—48no—
359C23×C131—41no—
360C23×C131—41no—
361C23×C131—41no—
362C23×C131—41no—
363C23×C131—41no—
364C23×C131—41no—
365C23×C131—41no—
366C23×C131—41no—
367C23×C131—41no—
368C23×C131—41no—
369C23×C131—41no—
370C23×C131—41no—
371C23×C131—41no—
372C23×C131—41no—
373C23×C131—41no—
374C23×C131—41no—
375C23×C131—41no—
376C23×C131—41no—
377C23×C131—41no—
378C23×C131—41no—
379C23×C131—41no—
380C23×C131—41no—
381C23×C131—84no—
382C23×C131—84no—
383C23×C131—84no—
384C23×C131—84no—
385C23×C131—84no—
386C23×C131—84no—
387C23×C131—84no—
388C23×C131—84no—
389C23×C131—84no—
390C23×C131—84no—
391C23×C131#12012yes—
392C23×C131AGL(1,ℤ/8)12yescomplemented
393C23×C131C22×D411yescharacteristic
394Q8×C131—22no—
395Q8×C131—22no—
396Q8×C131—41no—
397Q8×C131—41no—
398D4×C131—28no—
399D4×C131—22no—
400D4×C131—22no—
401D4×C131—22no—
402D4×C131—22no—
403D4×C131—22no—
404D4×C131—22no—
405D4×C131—22no—
406D4×C131—22no—
407D4×C131—22no—
408D4×C131—48no—
409D4×C131—48no—
410D4×C131—48no—
411D4×C131—48no—
412D4×C131—48no—
413D4×C131—48no—
414D4×C131—41no—
415D4×C131—41no—
416D4×C131—41no—
417D4×C131—41no—
418D4×C131—41no—
419D4×C131—41no—
420D4×C131—84no—
421D4×C131—84no—
422D4×C131#12014yes—
423C2×C4×C131—21no—
424C2×C4×C131—21no—
425C2×C4×C131—21no—
426C2×C4×C131—21no—
427C2×C4×C131—22no—
428C2×C4×C131—22no—
429C2×C4×C131—22no—
430C2×C4×C131—22no—
431C2×C4×C131—21no—
432C2×C4×C131—21no—
433C2×C4×C131—22no—
434C2×C4×C131—21no—
435C2×C4×C131—22no—
436C2×C4×C131—21no—
437C2×C4×C131—21no—
438C2×C4×C131—21no—
439C2×C4×C131—48no—
440C2×C4×C131—48no—
441C2×C4×C131—41no—
442C2×C4×C131—41no—
443C2×C4×C131—41no—
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×C131—41no—
455C2×C4×C131#12012yes—
456C2×C4×C131AGL(1,ℤ/8)12yescomplemented
457C2×C4×C131C22×D411yescharacteristic
458C2×C4×C131C22×D411yescharacteristic
459C2×C4×C131C22×D411yescharacteristic
460C2×C4×C131C22×D411yescharacteristic
461C2×C4×C131H(5,𝔽2)11yescharacteristic
462C2×C4×C131H(5,𝔽2)11yescharacteristic
463C8×C131—22no—
464C8×C131—22no—
465C8×C131—41no—
466C8×C131—41no—
467C22×C131—22no—
468C22×C131—24no—
469C22×C131—22no—
470C22×C131—22no—
471C22×C131—22no—
472C22×C131—22no—
473C22×C131—22no—
474C22×C131—41no—
475C22×C131—42no—
476C22×C131—41no—
477C22×C131—42no—
478C22×C131—41no—
479C22×C131—42no—
480C22×C131—41no—
481C22×C131—42no—
482C22×C131—41no—
483C22×C131—41no—
484C22×C131—42no—
485C22×C131—41no—
486C22×C131—41no—
487C22×C131—42no—
488C22×C131—42no—
489C22×C131—42no—
490C22×C131—42no—
491C22×C131—42no—
492C22×C131—42no—
493C22×C131—42no—
494C22×C131—42no—
495C22×C131—42no—
496C22×C131—42no—
497C22×C131—816no—
498C22×C131—816no—
499C22×C131—81no—
500C22×C131—81no—
501C22×C131—81no—
502C22×C131—81no—
503C22×C131—81no—
504C22×C131—81no—
505C22×C131—81no—
506C22×C131—81no—
507C22×C131—81no—
508C22×C131—81no—
509C22×C131—81no—
510C22×C131—81no—
511C22×C131C2×#12011yescharacteristic
512C22×C131D4211yescharacteristic
513C22×C131D4211yescharacteristic
514C22×C131C2×AGL(1,ℤ/8)11yescharacteristic
515C22×C131C2×AGL(1,ℤ/8)11yescharacteristic
516C22×C131#57611yescharacteristic
517C22×C131#57711yescharacteristic
518C4×C131—22no—
519C4×C131—22no—
520C4×C131—41no—
521C4×C131—42no—
522C4×C131—42no—
523C4×C131—41no—
524C4×C131—81no—
525C4×C131—81no—
526C4×C131C2×#12011yescharacteristic
527C4×C131#53411yescharacteristic
528C4×C131D4211yescharacteristic
529C4×C131D4211yescharacteristic
530C2×C131—42no—
531C2×C131—42no—
532C2×C131—44no—
533C2×C131—82no—
534C2×C131—82no—
535C2×C131—82no—
536C2×C131#240311yescharacteristic
537C2×C131#300311yescharacteristic
538C2×C131#301211yescharacteristic
539C2×C131#326411yescharacteristic
540C2×C131#326511yescharacteristic
541C2×C131#327211yescharacteristic
542C2×C131#327411yescharacteristic
543#23860C13111yesmaximal, characteristic, direct product factor, Sylow
544C131#2386011yescharacteristic, direct product factor, Sylow
545C22×AGL(1,ℤ/8)C2×C13111yescharacteristic, complemented
546C2×D42C2×C13111yescharacteristic, complemented
547C2×#449C2×C13111yescharacteristic, complemented
548C2×#450C2×C13111yescharacteristic, complemented
549C2×#447C2×C13111yescharacteristic, complemented
550#2407C2×C13111yescharacteristic, complemented
551#2014C2×C13111yescharacteristic, complemented
552#2011C2×C13111yescharacteristic, complemented
553#2000C2×C13111yescharacteristic, complemented
554#1999C2×C13111yescharacteristic, complemented
555#1895C2×C13111yescharacteristic, complemented
556#1879C2×C13111yescharacteristic, complemented
557#1877C2×C13111yescharacteristic, complemented
558#1870C2×C13111yescharacteristic, complemented
559#1786C2×C13111yescharacteristic, complemented
560C22×#41C22×C13111yescharacteristic, complemented
561C23×D4—21no—
562C23×D4C22×C13111yescharacteristic
563C23×D4C22×C13111yescharacteristic
564C2×AGL(1,ℤ/8)—24no—
565C2×AGL(1,ℤ/8)—24no—
566C2×AGL(1,ℤ/8)—24no—
567C22×SD16C22×C13111yescharacteristic
568C22×SD16C22×C13111yescharacteristic, complemented
569C22×SD16C22×C13111yescharacteristic, complemented
570C22×D8C22×C13111yescharacteristic
571C22×D8C22×C13111yescharacteristic, complemented
572C22×D8C22×C13111yescharacteristic, complemented
573C22×M16C22×C13111yescharacteristic, complemented
574D42—24no—
575D42—24no—
576C2×#127C22×C13111yescharacteristic
577C2×C22⋊Q8C22×C13111yescharacteristic, complemented
578C2×#121—21no—
579C2×#121C22×C13111yescharacteristic
580C2×#121C22×C13111yescharacteristic
581C2×#121C22×C13111yescharacteristic, complemented
582C2×#120—21no—
583C2×#120—21no—
584C2×C4×D4C22×C13111yescharacteristic
585C2×C4×D4C22×C13111yescharacteristic
586#450—24no—
587#449—24no—
588#447—24no—
589C2×#103C22×C13111yescharacteristic, complemented
590C2×#102C22×C13111yescharacteristic
591C2×#102C22×C13111yescharacteristic
592C2×#102C22×C13111yescharacteristic, complemented
593C2×#102C22×C13111yescharacteristic, complemented
594C2×#102C22×C13111yescharacteristic, complemented
595C2×#102C22×C13111yescharacteristic, complemented
596C2×#102C22×C13111yescharacteristic, complemented
597C2×C22⋊C8C22×C13111yescharacteristic, complemented
598C2×C22⋊C8C22×C13111yescharacteristic, complemented
599C2×C22⋊C8C22×C13111yescharacteristic, complemented
600#394—21no—
601#392—21no—
602#391C22×C13111yescharacteristic, complemented
603#390C22×C13111yescharacteristic, complemented
604#386—21no—
605#385—21no—
606#380C22×C13111yescharacteristic, complemented
607#340C22×C13111yescharacteristic, complemented
608#340C22×C13111yescharacteristic, complemented
609#336C22×C13111yescharacteristic, complemented
610#336C22×C13111yescharacteristic, complemented
611C25—21no—
612C25—21no—
613C2×#41—22no—
614C2×#41—22no—
615C2×#41—22no—
616C2×#41—22no—
617C2×#41—41no—
618C2×#41—41no—
619C22×Q8C23×C13111yescharacteristic
620C22×D4—22no—
621C22×D4—22no—
622C22×D4—28no—
623C22×D4—21no—
624C22×D4—21no—
625C22×D4—22no—
626C22×D4—22no—
627C22×D4—22no—
628C22×D4—22no—
629C22×D4—21no—
630C22×D4—21no—
631C22×D4—21no—
632C22×D4—21no—
633C22×D4—21no—
634C22×D4—22no—
635C22×D4—21no—
636C22×D4—41no—
637C22×D4—41no—
638C22×D4—41no—
639C22×D4—41no—
640C22×D4—44no—
641C22×D4—44no—
642C22×D4D4×C13111yescharacteristic
643C22×D4D4×C13114yescomplemented
644C22×D4C23×C13111yescharacteristic
645C22×D4C23×C13111yescharacteristic
646C22×D4C23×C13111yescharacteristic
647C22×D4C23×C13111yescharacteristic
648C23×C4—21no—
649C23×C4—21no—
650C23×C4C23×C13111yescharacteristic
651C23×C4C23×C13111yescharacteristic
652AGL(1,ℤ/8)—232no—
653C2×SD16—22no—
654C2×SD16—22no—
655C2×SD16—22no—
656C2×SD16—22no—
657C2×SD16—22no—
658C2×SD16—22no—
659C2×SD16—22no—
660C2×SD16—41no—
661C2×SD16D4×C13114yescomplemented
662C2×D8—22no—
663C2×D8—22no—
664C2×D8—22no—
665C2×D8—22no—
666C2×D8—22no—
667C2×D8—22no—
668C2×D8—22no—
669C2×D8—41no—
670C2×D8D4×C13114yescomplemented
671C2×M16—22no—
672C2×M16—22no—
673C2×M16—22no—
674C22×C8C23×C13111yescharacteristic
675C22×C8C23×C13111yescharacteristic
676C22×C8C23×C13111yescharacteristic
677C22×C8C23×C13111yescharacteristic
678#127—22no—
679#127—22no—
680C22⋊Q8—22no—
681C22⋊Q8—41no—
682#121—28no—
683#121—22no—
684#121—22no—
685#121—22no—
686#121—22no—
687#121—41no—
688#121D4×C13114yescomplemented
689#120—28no—
690#120—28no—
691C4×D4—22no—
692C4×D4—22no—
693C4×D4—22no—
694C4×D4—22no—
695C2×C4⋊C4—21no—
696C2×C4⋊C4D4×C13111yescharacteristic
697C2×C4⋊C4C23×C13111yescharacteristic
698C2×C4⋊C4C23×C13111yescharacteristic
699C2×C4⋊C4C23×C13111yescharacteristic
700C2×C22⋊C4—21no—
701C2×C22⋊C4—21no—
702C2×C22⋊C4—21no—
703C2×C22⋊C4—21no—
704C2×C22⋊C4—21no—
705C2×C22⋊C4—21no—
706C2×C22⋊C4—21no—
707C2×C22⋊C4—21no—
708C2×C22⋊C4D4×C13111yescharacteristic
709C2×C22⋊C4D4×C13111yescharacteristic
710C2×C42C23×C13111yescharacteristic
711#103—22no—
712#102—22no—
713#102—22no—
714#102—22no—
715#102—22no—
716#102—22no—
717#102—41no—
718#102—41no—
719C22⋊C8—22no—
720C22⋊C8—22no—
721C22⋊C8—22no—
722#95—21no—
723#95—21no—
724#95—21no—
725C24—21no—
726C24—24no—
727C24—21no—
728C24—21no—
729C24—21no—
730C24—24no—
731C24—42no—
732C24—42no—
733C24—42no—
734C24—42no—
735C24—42no—
736C24—42no—
737C24—42no—
738C24—42no—
739C24—81no—
740C24—81no—
741C24—81no—
742C24—81no—
743C24C2×D4×C13111yescharacteristic
744C24C2×D4×C13111yescharacteristic
745#41—28no—
746#41—44no—
747#41—44no—
748#41—44no—
749C2×Q8—21no—
750C2×Q8—21no—
751C2×Q8—21no—
752C2×Q8—21no—
753C2×Q8—21no—
754C2×Q8C2×D4×C13112yescomplemented
755C2×D4—22no—
756C2×D4—22no—
757C2×D4—28no—
758C2×D4—24no—
759C2×D4—24no—
760C2×D4—24no—
761C2×D4—24no—
762C2×D4—24no—
763C2×D4—24no—
764C2×D4—22no—
765C2×D4—21no—
766C2×D4—21no—
767C2×D4—21no—
768C2×D4—21no—
769C2×D4—21no—
770C2×D4—21no—
771C2×D4—21no—
772C2×D4—21no—
773C2×D4—21no—
774C2×D4—21no—
775C2×D4—21no—
776C2×D4—21no—
777C2×D4—21no—
778C2×D4—21no—
779C2×D4—21no—
780C2×D4—21no—
781C2×D4—21no—
782C2×D4—21no—
783C2×D4—44no—
784C2×D4—44no—
785C2×D4—44no—
786C2×D4—42no—
787C2×D4—42no—
788C2×D4—42no—
789C2×D4—42no—
790C2×D4—42no—
791C2×D4—42no—
792C2×D4—44no—
793C2×D4—44no—
794C2×D4—432no—
795C2×D4—44no—
796C2×D4—42no—
797C2×D4—42no—
798C2×D4—42no—
799C2×D4—42no—
800C2×D4—42no—
801C2×D4—42no—
802C2×D4—44no—
803C2×D4—42no—
804C2×D4—42no—
805C2×D4—42no—
806C2×D4—81no—
807C2×D4—81no—
808C2×D4—81no—
809C2×D4C2×D4×C13112yes—
810C2×D4C2×D4×C13112yes—
811C2×D4C2×D4×C13112yes—
812C2×D4C2×D4×C13112yes—
813C2×D4C2×D4×C13112yes—
814C2×D4C2×D4×C13112yescomplemented
815C22×C4—21no—
816C22×C4—21no—
817C22×C4—21no—
818C22×C4—21no—
819C22×C4—24no—
820C22×C4—21no—
821C22×C4—21no—
822C22×C4—21no—
823C22×C4—21no—
824C22×C4—21no—
825C22×C4—21no—
826C22×C4—21no—
827C22×C4—21no—
828C22×C4—21no—
829C22×C4—21no—
830C22×C4—42no—
831C22×C4—42no—
832C22×C4—42no—
833C22×C4—42no—
834C22×C4—42no—
835C22×C4C2×D4×C13111yescharacteristic
836C22×C4C2×D4×C13111yescharacteristic
837C22×C4C2×D4×C13111yescharacteristic
838C22×C4C2×D4×C13112yes—
839C22×C4C2×D4×C13112yes—
840C22×C4C2×D4×C13111yescharacteristic
841C22×C4C24×C13111yescharacteristic
842SD16—28no—
843SD16—28no—
844SD16—44no—
845D8—28no—
846D8—28no—
847D8—44no—
848M16—28no—
849C2×C8—21no—
850C2×C8—21no—
851C2×C8—21no—
852C2×C8—21no—
853C2×C8—21no—
854C2×C8—21no—
855C2×C8—21no—
856C2×C8—21no—
857C2×C8—21no—
858C2×C8—21no—
859C2×C8C2×D4×C13112yescomplemented
860C2×C8C2×D4×C13112yescomplemented
861C4⋊C4—22no—
862C4⋊C4—21no—
863C4⋊C4—21no—
864C4⋊C4—21no—
865C4⋊C4—21no—
866C4⋊C4—21no—
867C4⋊C4—42no—
868C4⋊C4C2×D4×C13112yes—
869C22⋊C4—24no—
870C22⋊C4—24no—
871C22⋊C4—22no—
872C22⋊C4—24no—
873C22⋊C4—22no—
874C22⋊C4—42no—
875C22⋊C4—42no—
876C22⋊C4—42no—
877C22⋊C4—81no—
878C22⋊C4—81no—
879C42—21no—
880C42—21no—
881C23—21no—
882C23—22no—
883C23—21no—
884C23—21no—
885C23—21no—
886C23—21no—
887C23—22no—
888C23—22no—
889C23—21no—
890C23—21no—
891C23—21no—
892C23—21no—
893C23—21no—
894C23—21no—
895C23—21no—
896C23—22no—
897C23—22no—
898C23—22no—
899C23—48no—
900C23—48no—
901C23—48no—
902C23—48no—
903C23—41no—
904C23—41no—
905C23—41no—
906C23—41no—
907C23—41no—
908C23—41no—
909C23—41no—
910C23—41no—
911C23—41no—
912C23—41no—
913C23—41no—
914C23—41no—
915C23—41no—
916C23—41no—
917C23—41no—
918C23—41no—
919C23—41no—
920C23—41no—
921C23—41no—
922C23—41no—
923C23—41no—
924C23—41no—
925C23—84no—
926C23—84no—
927C23—84no—
928C23—84no—
929C23—84no—
930C23—84no—
931C23—84no—
932C23—84no—
933C23—84no—
934C23—84no—
935C23#120×C13112yes—
936C23AGL(1,ℤ/8)×C13112yescomplemented
937C23C22×D4×C13111yescharacteristic
938Q8—22no—
939Q8—22no—
940Q8—41no—
941Q8—41no—
942D4—28no—
943D4—22no—
944D4—22no—
945D4—22no—
946D4—22no—
947D4—22no—
948D4—22no—
949D4—22no—
950D4—22no—
951D4—22no—
952D4—48no—
953D4—48no—
954D4—48no—
955D4—48no—
956D4—48no—
957D4—48no—
958D4—41no—
959D4—41no—
960D4—41no—
961D4—41no—
962D4—41no—
963D4—41no—
964D4—84no—
965D4—84no—
966D4#120×C13114yes—
967C2×C4—21no—
968C2×C4—21no—
969C2×C4—21no—
970C2×C4—21no—
971C2×C4—22no—
972C2×C4—22no—
973C2×C4—22no—
974C2×C4—22no—
975C2×C4—21no—
976C2×C4—21no—
977C2×C4—22no—
978C2×C4—21no—
979C2×C4—22no—
980C2×C4—21no—
981C2×C4—21no—
982C2×C4—21no—
983C2×C4—48no—
984C2×C4—48no—
985C2×C4—41no—
986C2×C4—41no—
987C2×C4—41no—
988C2×C4—41no—
989C2×C4—41no—
990C2×C4—41no—
991C2×C4—41no—
992C2×C4—41no—
993C2×C4—41no—
994C2×C4—41no—
995C2×C4—41no—
996C2×C4—41no—
997C2×C4—41no—
998C2×C4—41no—
999C2×C4#120×C13112yes—
1000C2×C4AGL(1,ℤ/8)×C13112yescomplemented
1001C2×C4C22×D4×C13111yescharacteristic
1002C2×C4C22×D4×C13111yescharacteristic
1003C2×C4C22×D4×C13111yescharacteristic
1004C2×C4C22×D4×C13111yescharacteristic
1005C2×C4H(5,𝔽2)×C13111yescharacteristic
1006C2×C4H(5,𝔽2)×C13111yescharacteristic
1007C8—22no—
1008C8—22no—
1009C8—41no—
1010C8—41no—
1011C22—22no—
1012C22—22no—
1013C22—22no—
1014C22—22no—
1015C22—22no—
1016C22—22no—
1017C22—24no—
1018C22—42no—
1019C22—41no—
1020C22—42no—
1021C22—41no—
1022C22—42no—
1023C22—41no—
1024C22—42no—
1025C22—41no—
1026C22—41no—
1027C22—42no—
1028C22—41no—
1029C22—41no—
1030C22—42no—
1031C22—41no—
1032C22—42no—
1033C22—42no—
1034C22—42no—
1035C22—42no—
1036C22—42no—
1037C22—42no—
1038C22—42no—
1039C22—42no—
1040C22—42no—
1041C22—816no—
1042C22—816no—
1043C22—81no—
1044C22—81no—
1045C22—81no—
1046C22—81no—
1047C22—81no—
1048C22—81no—
1049C22—81no—
1050C22—81no—
1051C22—81no—
1052C22—81no—
1053C22—81no—
1054C22—81no—
1055C22C2×#120×C13111yescharacteristic
1056C22D42×C13111yescharacteristic
1057C22D42×C13111yescharacteristic
1058C22C2×AGL(1,ℤ/8)×C13111yescharacteristic
1059C22C2×AGL(1,ℤ/8)×C13111yescharacteristic
1060C22#576×C13111yescharacteristic
1061C22#577×C13111yescharacteristic
1062C4—22no—
1063C4—22no—
1064C4—42no—
1065C4—41no—
1066C4—41no—
1067C4—42no—
1068C4—81no—
1069C4—81no—
1070C4C2×#120×C13111yescharacteristic
1071C4#534×C13111yescharacteristic
1072C4D42×C13111yescharacteristic
1073C4D42×C13111yescharacteristic
1074C2—42no—
1075C2—42no—
1076C2—44no—
1077C2—82no—
1078C2—82no—
1079C2—82no—
1080C2#2403×C13111yescharacteristic
1081C2#3003×C13111yescharacteristic
1082C2#3012×C13111yescharacteristic
1083C2#3264×C13111yescharacteristic
1084C2#3265×C13111yescharacteristic
1085C2#3272×C13111yescharacteristic
1086C2#3274×C13111yescharacteristic
subgroupG/H
center, socleC23×C131C22×D4
commutator, Frattini, cosocleC22×C4C24×C131
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C131 ◁ C2×C4×D4×C131 ◁ G

Complements

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

NH ≅ G/Ntype
1. C22×AGL(1,ℤ/8)×C131C2semidirect
2. C2×D42×C131C2semidirect
3. C2×#449×C131C2semidirect
4. C2×#450×C131C2semidirect
5. C2×#447×C131C2semidirect
6. #2407×C131C2semidirect
7. #2014×C131C2semidirect
8. #2011×C131C2semidirect
9. #2000×C131C2semidirect
10. #1999×C131C2semidirect
11. #1895×C131C2semidirect
12. #1879×C131C2semidirect
13. #1877×C131C2semidirect
14. #1870×C131C2semidirect
15. #1786×C131C2semidirect
16. C22×#41×C131C22semidirect
24. C22×SD16×C131C22semidirect
25. C22×SD16×C131C22semidirect
27. C22×D8×C131C22semidirect
28. C22×D8×C131C22semidirect
29. C22×M16×C131C22semidirect
33. C2×C22⋊Q8×C131C22semidirect
37. C2×#121×C131C22semidirect
45. C2×#103×C131C22semidirect
48. C2×#102×C131C22semidirect
49. C2×#102×C131C22semidirect
50. C2×#102×C131C22semidirect
51. C2×#102×C131C22semidirect
52. C2×#102×C131C22semidirect
53. C2×C22⋊C8×C131C22semidirect
54. C2×C22⋊C8×C131C22semidirect
55. C2×C22⋊C8×C131C22semidirect
58. #391×C131C22semidirect
59. #390×C131C22semidirect
62. #380×C131C22semidirect
63. #340×C131C22semidirect
64. #340×C131C22semidirect
65. #336×C131C22semidirect
66. #336×C131C22semidirect
99. C22×D4×C131D4semidirect
117. C2×SD16×C131D4semidirect
126. C2×D8×C131D4semidirect
144. #121×C131D4semidirect
210. C2×Q8×C131C2×D4semidirect
270. C2×D4×C131C2×D4semidirect
315. C2×C8×C131C2×D4semidirect
316. C2×C8×C131C2×D4semidirect
392. C23×C131AGL(1,ℤ/8)semidirect
456. C2×C4×C131AGL(1,ℤ/8)semidirect
543. #23860C131direct (N × H)
544. C131#23860direct (N × H)
545. C22×AGL(1,ℤ/8)C2×C131semidirect
546. C2×D42C2×C131semidirect
547. C2×#449C2×C131semidirect
548. C2×#450C2×C131semidirect
549. C2×#447C2×C131semidirect
550. #2407C2×C131semidirect
551. #2014C2×C131semidirect
552. #2011C2×C131semidirect
553. #2000C2×C131semidirect
554. #1999C2×C131semidirect
555. #1895C2×C131semidirect
556. #1879C2×C131semidirect
557. #1877C2×C131semidirect
558. #1870C2×C131semidirect
559. #1786C2×C131semidirect
560. C22×#41C22×C131semidirect
568. C22×SD16C22×C131semidirect
569. C22×SD16C22×C131semidirect
571. C22×D8C22×C131semidirect
572. C22×D8C22×C131semidirect
573. C22×M16C22×C131semidirect
577. C2×C22⋊Q8C22×C131semidirect
581. C2×#121C22×C131semidirect
589. C2×#103C22×C131semidirect
592. C2×#102C22×C131semidirect
593. C2×#102C22×C131semidirect
594. C2×#102C22×C131semidirect
595. C2×#102C22×C131semidirect
596. C2×#102C22×C131semidirect
597. C2×C22⋊C8C22×C131semidirect
598. C2×C22⋊C8C22×C131semidirect
599. C2×C22⋊C8C22×C131semidirect
602. #391C22×C131semidirect
603. #390C22×C131semidirect
606. #380C22×C131semidirect
607. #340C22×C131semidirect
608. #340C22×C131semidirect
609. #336C22×C131semidirect
610. #336C22×C131semidirect
643. C22×D4D4×C131semidirect
661. C2×SD16D4×C131semidirect
670. C2×D8D4×C131semidirect
688. #121D4×C131semidirect
754. C2×Q8C2×D4×C131semidirect
814. C2×D4C2×D4×C131semidirect
859. C2×C8C2×D4×C131semidirect
860. C2×C8C2×D4×C131semidirect
936. C23AGL(1,ℤ/8)×C131semidirect
1000. C2×C4AGL(1,ℤ/8)×C131semidirect

Maximal subgroups

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

subgroupindex
C22×AGL(1,ℤ/8)×C1312
C2×D42×C1312
C2×#449×C1312
C2×#450×C1312
C2×#447×C1312
#2407×C1312
#2014×C1312
#2011×C1312
#2000×C1312
#1999×C1312
#1895×C1312
#1879×C1312
#1877×C1312
#1870×C1312
#1786×C1312
#23860131