Finite Group Databasebeta

← C2×#2008×C131 #45709294

Subgroups — C2×#2008×C131 #45709294

Order 33536.

2118 conjugacy classes of subgroups.

The subgroup lattice has 1002 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#575×C131C211yesmaximal, characteristic, complemented
2C22×AGL(1,ℤ/8)×C131C211yesmaximal, characteristic, complemented
3C2×#535×C131C211yesmaximal, characteristic, complemented
4C2×#421×C131C211yesmaximal, characteristic, complemented
5C2×#418×C131C211yesmaximal, characteristic, complemented
6C2×#410×C131C211yesmaximal, characteristic, complemented
7#2008×C131C218yesmaximal, direct product factor
8C2×#344×C131C211yesmaximal, characteristic, complemented
9C22×#41×C131C2211yescharacteristic
10C22×#41×C131C2211yescharacteristic
11C23×D4×C131C2211yescharacteristic
12#575×C131—22no—
13#575×C131—22no—
14#575×C131—22no—
15#575×C131C2214yescomplemented
16C2×#137×C131—21no—
17C2×#137×C131—21no—
18C2×AGL(1,ℤ/8)×C131—22no—
19C2×AGL(1,ℤ/8)×C131—22no—
20C2×AGL(1,ℤ/8)×C131—22no—
21C2×AGL(1,ℤ/8)×C131—21no—
22C2×AGL(1,ℤ/8)×C131—21no—
23C2×AGL(1,ℤ/8)×C131—22no—
24C2×AGL(1,ℤ/8)×C131—22no—
25C2×AGL(1,ℤ/8)×C131C2214yescomplemented
26C2×#135×C131—22no—
27C22×SD16×C131—21no—
28C22×D8×C131—21no—
29C22×M16×C131C2211yescharacteristic
30C22×M16×C131C2211yescharacteristic
31#535×C131—22no—
32#535×C131—22no—
33#535×C131—22no—
34#535×C131C2214yescomplemented
35C2×#127×C131—21no—
36C2×#124×C131—21no—
37C2×#121×C131—22no—
38C2×#120×C131—22no—
39C2×#117×C131C2211yescharacteristic
40C2×#117×C131C2211yescharacteristic
41#421×C131—22no—
42#421×C131C2214yescomplemented
43C2×#104×C131—22no—
44#418×C131—22no—
45#418×C131C2214yescomplemented
46C2×#102×C131—22no—
47#410×C131—22no—
48#410×C131C2214yescomplemented
49C2×#99×C131—22no—
50#344×C131C2214yescomplemented
51C25×C131—21no—
52C2×#41×C131—21no—
53C2×#41×C131—21no—
54C2×#41×C131—21no—
55C2×#41×C131—21no—
56C2×#41×C131—21no—
57C2×#41×C131—21no—
58C2×#41×C131—21no—
59C2×#41×C131—21no—
60C2×#41×C131—21no—
61C2×#41×C131—21no—
62C2×#41×C131—21no—
63C2×#41×C131—21no—
64C2×#41×C131—21no—
65C2×#41×C131—21no—
66C2×#41×C131—21no—
67C2×#41×C131—21no—
68C2×#41×C131—21no—
69C2×#41×C131—21no—
70C2×#41×C131—21no—
71C2×#41×C131—21no—
72C2×#41×C131D412yes—
73C2×#41×C131D412yescomplemented
74C2×#41×C131C2312yes—
75C2×#41×C131C2312yes—
76C22×Q8×C131D411yescharacteristic
77C22×Q8×C131D411yescharacteristic, complemented
78C22×D4×C131—21no—
79C22×D4×C131—21no—
80C22×D4×C131—24no—
81C22×D4×C131—21no—
82C22×D4×C131—21no—
83C22×D4×C131—21no—
84C22×D4×C131—21no—
85C22×D4×C131—21no—
86C22×D4×C131—21no—
87C22×D4×C131—21no—
88C22×D4×C131—21no—
89C22×D4×C131—21no—
90C22×D4×C131—21no—
91C22×D4×C131—21no—
92C22×D4×C131D412yes—
93C22×D4×C131D411yescharacteristic
94C22×D4×C131D412yes—
95C22×D4×C131D411yescharacteristic, complemented
96C22×D4×C131C2312yes—
97C23×C4×C131—21no—
98C23×C4×C131—21no—
99C23×C4×C131C2311yescharacteristic
100#137×C131—24no—
101#137×C131—24no—
102#137×C131—24no—
103#137×C131—24no—
104AGL(1,ℤ/8)×C131—28no—
105AGL(1,ℤ/8)×C131—28no—
106AGL(1,ℤ/8)×C131—24no—
107AGL(1,ℤ/8)×C131—24no—
108AGL(1,ℤ/8)×C131—28no—
109AGL(1,ℤ/8)×C131—24no—
110AGL(1,ℤ/8)×C131—24no—
111AGL(1,ℤ/8)×C131—28no—
112#135×C131—28no—
113#135×C131—28no—
114C2×Q16×C131—22no—
115C2×SD16×C131—24no—
116C2×SD16×C131—24no—
117C2×SD16×C131—22no—
118C2×SD16×C131—22no—
119C2×SD16×C131—24no—
120C2×D8×C131—24no—
121C2×D8×C131—24no—
122C2×D8×C131—22no—
123C2×D8×C131—24no—
124C2×M16×C131—21no—
125C2×M16×C131—21no—
126C2×M16×C131—21no—
127C2×M16×C131—21no—
128C2×M16×C131—21no—
129C2×M16×C131—21no—
130C2×M16×C131—21no—
131C2×M16×C131D412yescomplemented
132C2×M16×C131D412yescomplemented
133C2×M16×C131D412yescomplemented
134C2×M16×C131C2312yes—
135C2×M16×C131C2312yes—
136C22×C8×C131—21no—
137C22×C8×C131D412yescomplemented
138#127×C131—24no—
139#127×C131—24no—
140#124×C131—24no—
141#124×C131—24no—
142#121×C131—28no—
143#121×C131—28no—
144#120×C131—28no—
145#120×C131—28no—
146#117×C131—21no—
147#117×C131—21no—
148#117×C131—21no—
149#117×C131—21no—
150#117×C131—21no—
151#117×C131D412yes—
152#117×C131C2312yes—
153#117×C131C2312yes—
154C2×C4⋊C4×C131—21no—
155C2×C4⋊C4×C131—21no—
156C2×C22⋊C4×C131—24no—
157C2×C22⋊C4×C131—21no—
158C2×C22⋊C4×C131D412yes—
159C2×C42×C131—21no—
160C2×C42×C131—21no—
161#104×C131—28no—
162#102×C131—28no—
163#99×C131—28no—
164C24×C131—22no—
165C24×C131—21no—
166C24×C131—22no—
167C24×C131—21no—
168C24×C131—22no—
169C24×C131—41no—
170C24×C131—41no—
171C24×C131—41no—
172C24×C131—41no—
173C24×C131—84no—
174C24×C131C2×D411yescharacteristic
175#41×C131—22no—
176#41×C131—22no—
177#41×C131—22no—
178#41×C131—22no—
179#41×C131—22no—
180#41×C131—22no—
181#41×C131—22no—
182#41×C131—22no—
183#41×C131—22no—
184#41×C131—22no—
185#41×C131—22no—
186#41×C131—22no—
187#41×C131—22no—
188#41×C131—22no—
189#41×C131—22no—
190#41×C131—22no—
191#41×C131—41no—
192#41×C131—41no—
193#41×C131—41no—
194#41×C131—41no—
195#41×C131—41no—
196#41×C131—41no—
197#41×C131—41no—
198#41×C131—41no—
199#41×C131—41no—
200#41×C131—41no—
201#41×C131—41no—
202#41×C131—41no—
203#41×C131—41no—
204#41×C131—41no—
205#41×C131—41no—
206#41×C131—41no—
207C2×Q8×C131—21no—
208C2×Q8×C131—21no—
209C2×Q8×C131—21no—
210C2×Q8×C131—21no—
211C2×Q8×C131—21no—
212C2×Q8×C131—21no—
213C2×Q8×C131—21no—
214C2×Q8×C131—21no—
215C2×Q8×C131—21no—
216C2×Q8×C131—21no—
217C2×Q8×C131C2×D412yes—
218C2×Q8×C131C2×D412yescomplemented
219C2×D4×C131—22no—
220C2×D4×C131—22no—
221C2×D4×C131—22no—
222C2×D4×C131—22no—
223C2×D4×C131—216no—
224C2×D4×C131—21no—
225C2×D4×C131—21no—
226C2×D4×C131—22no—
227C2×D4×C131—22no—
228C2×D4×C131—21no—
229C2×D4×C131—21no—
230C2×D4×C131—22no—
231C2×D4×C131—22no—
232C2×D4×C131—21no—
233C2×D4×C131—21no—
234C2×D4×C131—22no—
235C2×D4×C131—22no—
236C2×D4×C131—21no—
237C2×D4×C131—22no—
238C2×D4×C131—22no—
239C2×D4×C131—22no—
240C2×D4×C131—22no—
241C2×D4×C131—21no—
242C2×D4×C131—21no—
243C2×D4×C131—21no—
244C2×D4×C131—22no—
245C2×D4×C131—22no—
246C2×D4×C131—22no—
247C2×D4×C131—22no—
248C2×D4×C131—22no—
249C2×D4×C131—41no—
250C2×D4×C131—41no—
251C2×D4×C131—41no—
252C2×D4×C131—41no—
253C2×D4×C131—41no—
254C2×D4×C131—41no—
255C2×D4×C131—41no—
256C2×D4×C131—41no—
257C2×D4×C131—41no—
258C2×D4×C131—41no—
259C2×D4×C131—41no—
260C2×D4×C131—41no—
261C2×D4×C131—41no—
262C2×D4×C131—41no—
263C2×D4×C131—41no—
264C2×D4×C131—41no—
265C2×D4×C131—41no—
266C2×D4×C131—41no—
267C2×D4×C131—41no—
268C2×D4×C131—41no—
269C2×D4×C131—88no—
270C2×D4×C131C2×D414yes—
271C2×D4×C131C2×D412yes—
272C2×D4×C131C2×D412yescomplemented
273C22×C4×C131—22no—
274C22×C4×C131—21no—
275C22×C4×C131—21no—
276C22×C4×C131—22no—
277C22×C4×C131—22no—
278C22×C4×C131—22no—
279C22×C4×C131—22no—
280C22×C4×C131—41no—
281C22×C4×C131—41no—
282C22×C4×C131—41no—
283C22×C4×C131—41no—
284C22×C4×C131—41no—
285C22×C4×C131—41no—
286C22×C4×C131—41no—
287C22×C4×C131—41no—
288C22×C4×C131—41no—
289C22×C4×C131C2×D411yescharacteristic
290C22×C4×C131C2×D411yescharacteristic
291C22×C4×C131C2×D411yescharacteristic
292C22×C4×C131C2×D411yescharacteristic
293C22×C4×C131C2×D411yescharacteristic
294C22×C4×C131C2×D411yescharacteristic
295C22×C4×C131C2×D411yescharacteristic
296C22×C4×C131C2×D411yescharacteristic
297C22×C4×C131C2×D411yescharacteristic
298C22×C4×C131C2×D411yescharacteristic
299C22×C4×C131C2×D411yescharacteristic
300C22×C4×C131#4111yescharacteristic
301C22×C4×C131#4111yescharacteristic
302C22×C4×C131C2411yescharacteristic
303Q16×C131—28no—
304SD16×C131—216no—
305SD16×C131—28no—
306SD16×C131—28no—
307D8×C131—216no—
308D8×C131—28no—
309M16×C131—22no—
310M16×C131—22no—
311M16×C131—22no—
312M16×C131—22no—
313M16×C131—22no—
314M16×C131—22no—
315M16×C131—22no—
316M16×C131C2×D414yescomplemented
317C2×C8×C131—22no—
318C2×C8×C131—22no—
319C2×C8×C131—22no—
320C2×C8×C131—22no—
321C2×C8×C131—22no—
322C2×C8×C131C2×D414yescomplemented
323C4⋊C4×C131—22no—
324C4⋊C4×C131—22no—
325C4⋊C4×C131—22no—
326C4⋊C4×C131—41no—
327C22⋊C4×C131—216no—
328C22⋊C4×C131—22no—
329C22⋊C4×C131—22no—
330C22⋊C4×C131—41no—
331C22⋊C4×C131C2×D414yes—
332C42×C131—22no—
333C42×C131—22no—
334C42×C131—22no—
335C42×C131—41no—
336C23×C131—24no—
337C23×C131—22no—
338C23×C131—22no—
339C23×C131—42no—
340C23×C131—44no—
341C23×C131—48no—
342C23×C131—42no—
343C23×C131—42no—
344C23×C131—41no—
345C23×C131—41no—
346C23×C131—42no—
347C23×C131—42no—
348C23×C131—42no—
349C23×C131—41no—
350C23×C131—41no—
351C23×C131—42no—
352C23×C131—82no—
353C23×C131—84no—
354C23×C131—84no—
355C23×C131—84no—
356C23×C131—84no—
357C23×C131—84no—
358C23×C131—84no—
359C23×C131#12011yescharacteristic
360C23×C131#12011yescharacteristic
361C23×C131#12111yescharacteristic
362C23×C131#12111yescharacteristic
363C23×C131#12711yescharacteristic
364C23×C131#12711yescharacteristic
365C23×C131C22×D411yescharacteristic
366Q8×C131—22no—
367Q8×C131—22no—
368Q8×C131—22no—
369Q8×C131—22no—
370Q8×C131—41no—
371Q8×C131—41no—
372Q8×C131—41no—
373Q8×C131—41no—
374D4×C131—22no—
375D4×C131—24no—
376D4×C131—22no—
377D4×C131—22no—
378D4×C131—24no—
379D4×C131—22no—
380D4×C131—42no—
381D4×C131—42no—
382D4×C131—42no—
383D4×C131—42no—
384D4×C131—42no—
385D4×C131—42no—
386D4×C131—42no—
387D4×C131—42no—
388D4×C131—42no—
389D4×C131—42no—
390D4×C131—42no—
391D4×C131—42no—
392D4×C131—42no—
393D4×C131—42no—
394D4×C131—41no—
395D4×C131—41no—
396D4×C131—41no—
397D4×C131—41no—
398D4×C131—816no—
399C2×C4×C131—24no—
400C2×C4×C131—22no—
401C2×C4×C131—22no—
402C2×C4×C131—44no—
403C2×C4×C131—41no—
404C2×C4×C131—41no—
405C2×C4×C131—41no—
406C2×C4×C131—41no—
407C2×C4×C131—42no—
408C2×C4×C131—42no—
409C2×C4×C131—42no—
410C2×C4×C131—42no—
411C2×C4×C131—42no—
412C2×C4×C131—42no—
413C2×C4×C131—42no—
414C2×C4×C131—42no—
415C2×C4×C131—42no—
416C2×C4×C131—82no—
417C2×C4×C131#12011yescharacteristic
418C2×C4×C131#12011yescharacteristic
419C2×C4×C131#12011yescharacteristic
420C2×C4×C131#12011yescharacteristic
421C2×C4×C131#12011yescharacteristic
422C2×C4×C131#12011yescharacteristic
423C2×C4×C131#12011yescharacteristic
424C2×C4×C131#12011yescharacteristic
425C2×C4×C131#12011yescharacteristic
426C2×C4×C131#12011yescharacteristic
427C2×C4×C131#12111yescharacteristic
428C2×C4×C131#12111yescharacteristic
429C2×C4×C131#12111yescharacteristic
430C2×C4×C131#12111yescharacteristic
431C2×C4×C131#12111yescharacteristic
432C2×C4×C131#12111yescharacteristic
433C2×C4×C131#12111yescharacteristic
434C2×C4×C131#12111yescharacteristic
435C2×C4×C131#12111yescharacteristic
436C2×C4×C131#12111yescharacteristic
437C2×C4×C131#12711yescharacteristic
438C2×C4×C131#12711yescharacteristic
439C2×C4×C131C22×D411yescharacteristic
440C2×C4×C131C22×D411yescharacteristic
441C2×C4×C131C22×D411yescharacteristic
442C2×C4×C131C22×D411yescharacteristic
443C2×C4×C131C22×D411yescharacteristic
444C2×C4×C131C2×#4111yescharacteristic
445C8×C131—24no—
446C8×C131—24no—
447C22×C131—22no—
448C22×C131—22no—
449C22×C131—22no—
450C22×C131—41no—
451C22×C131—41no—
452C22×C131—41no—
453C22×C131—41no—
454C22×C131—44no—
455C22×C131—48no—
456C22×C131—42no—
457C22×C131—42no—
458C22×C131—44no—
459C22×C131—82no—
460C22×C131—82no—
461C22×C131—84no—
462C22×C131—82no—
463C22×C131—84no—
464C22×C131—84no—
465C22×C131—84no—
466C22×C131—84no—
467C22×C131—82no—
468C22×C131—84no—
469C22×C131—82no—
470C22×C131#39211yescharacteristic
471C22×C131#39211yescharacteristic
472C22×C131#39211yescharacteristic
473C22×C131#39211yescharacteristic
474C22×C131C2×#12011yescharacteristic
475C22×C131C2×#12111yescharacteristic
476C22×C131C2×#12711yescharacteristic
477C4×C131—44no—
478C4×C131—42no—
479C4×C131—42no—
480C4×C131—82no—
481C4×C131#39211yescharacteristic
482C4×C131#39211yescharacteristic
483C4×C131#39211yescharacteristic
484C4×C131#39211yescharacteristic
485C4×C131C2×#12011yescharacteristic
486C4×C131C2×#12011yescharacteristic
487C4×C131C2×#12111yescharacteristic
488C4×C131C2×#12111yescharacteristic
489C2×C131—21no—
490C2×C131—21no—
491C2×C131—21no—
492C2×C131—21no—
493C2×C131—21no—
494C2×C131—21no—
495C2×C131—82no—
496C2×C131—84no—
497C2×C131—82no—
498C2×C131#200812yesdirect product factor
499C2×C131C2×#39211yescharacteristic
500C2×#2008C13111yesmaximal, characteristic, direct product factor, Sylow
501C131C2×#200811yescharacteristic, direct product factor, Sylow
502C2×#575C2×C13111yescharacteristic, complemented
503C22×AGL(1,ℤ/8)C2×C13111yescharacteristic, complemented
504C2×#535C2×C13111yescharacteristic, complemented
505C2×#421C2×C13111yescharacteristic, complemented
506C2×#418C2×C13111yescharacteristic, complemented
507C2×#410C2×C13111yescharacteristic, complemented
508#2008C2×C13118yesdirect product factor
509C2×#344C2×C13111yescharacteristic, complemented
510C22×#41C22×C13111yescharacteristic
511C22×#41C22×C13111yescharacteristic
512C23×D4C22×C13111yescharacteristic
513#575—22no—
514#575—22no—
515#575—22no—
516#575C22×C13114yescomplemented
517C2×#137—21no—
518C2×#137—21no—
519C2×AGL(1,ℤ/8)—22no—
520C2×AGL(1,ℤ/8)—22no—
521C2×AGL(1,ℤ/8)—22no—
522C2×AGL(1,ℤ/8)—21no—
523C2×AGL(1,ℤ/8)—21no—
524C2×AGL(1,ℤ/8)—22no—
525C2×AGL(1,ℤ/8)—22no—
526C2×AGL(1,ℤ/8)C22×C13114yescomplemented
527C2×#135—22no—
528C22×SD16—21no—
529C22×D8—21no—
530C22×M16C22×C13111yescharacteristic
531C22×M16C22×C13111yescharacteristic
532#535—22no—
533#535—22no—
534#535—22no—
535#535C22×C13114yescomplemented
536C2×#127—21no—
537C2×#124—21no—
538C2×#121—22no—
539C2×#120—22no—
540C2×#117C22×C13111yescharacteristic
541C2×#117C22×C13111yescharacteristic
542#421—22no—
543#421C22×C13114yescomplemented
544C2×#104—22no—
545#418—22no—
546#418C22×C13114yescomplemented
547C2×#102—22no—
548#410—22no—
549#410C22×C13114yescomplemented
550C2×#99—22no—
551#344C22×C13114yescomplemented
552C25—21no—
553C2×#41—21no—
554C2×#41—21no—
555C2×#41—21no—
556C2×#41—21no—
557C2×#41—21no—
558C2×#41—21no—
559C2×#41—21no—
560C2×#41—21no—
561C2×#41—21no—
562C2×#41—21no—
563C2×#41—21no—
564C2×#41—21no—
565C2×#41—21no—
566C2×#41—21no—
567C2×#41—21no—
568C2×#41—21no—
569C2×#41—21no—
570C2×#41—21no—
571C2×#41—21no—
572C2×#41—21no—
573C2×#41D4×C13112yes—
574C2×#41D4×C13112yescomplemented
575C2×#41C23×C13112yes—
576C2×#41C23×C13112yes—
577C22×Q8D4×C13111yescharacteristic
578C22×Q8D4×C13111yescharacteristic, complemented
579C22×D4—21no—
580C22×D4—21no—
581C22×D4—24no—
582C22×D4—21no—
583C22×D4—21no—
584C22×D4—21no—
585C22×D4—21no—
586C22×D4—21no—
587C22×D4—21no—
588C22×D4—21no—
589C22×D4—21no—
590C22×D4—21no—
591C22×D4—21no—
592C22×D4—21no—
593C22×D4D4×C13112yes—
594C22×D4D4×C13111yescharacteristic
595C22×D4D4×C13112yes—
596C22×D4D4×C13111yescharacteristic, complemented
597C22×D4C23×C13112yes—
598C23×C4—21no—
599C23×C4—21no—
600C23×C4C23×C13111yescharacteristic
601#137—24no—
602#137—24no—
603#137—24no—
604#137—24no—
605AGL(1,ℤ/8)—28no—
606AGL(1,ℤ/8)—28no—
607AGL(1,ℤ/8)—24no—
608AGL(1,ℤ/8)—24no—
609AGL(1,ℤ/8)—28no—
610AGL(1,ℤ/8)—24no—
611AGL(1,ℤ/8)—24no—
612AGL(1,ℤ/8)—28no—
613#135—28no—
614#135—28no—
615C2×Q16—22no—
616C2×SD16—24no—
617C2×SD16—24no—
618C2×SD16—22no—
619C2×SD16—22no—
620C2×SD16—24no—
621C2×D8—24no—
622C2×D8—24no—
623C2×D8—22no—
624C2×D8—24no—
625C2×M16—21no—
626C2×M16—21no—
627C2×M16—21no—
628C2×M16—21no—
629C2×M16—21no—
630C2×M16—21no—
631C2×M16—21no—
632C2×M16D4×C13112yescomplemented
633C2×M16D4×C13112yescomplemented
634C2×M16D4×C13112yescomplemented
635C2×M16C23×C13112yes—
636C2×M16C23×C13112yes—
637C22×C8—21no—
638C22×C8D4×C13112yescomplemented
639#127—24no—
640#127—24no—
641#124—24no—
642#124—24no—
643#121—28no—
644#121—28no—
645#120—28no—
646#120—28no—
647#117—21no—
648#117—21no—
649#117—21no—
650#117—21no—
651#117—21no—
652#117D4×C13112yes—
653#117C23×C13112yes—
654#117C23×C13112yes—
655C2×C4⋊C4—21no—
656C2×C4⋊C4—21no—
657C2×C22⋊C4—24no—
658C2×C22⋊C4—21no—
659C2×C22⋊C4D4×C13112yes—
660C2×C42—21no—
661C2×C42—21no—
662#104—28no—
663#102—28no—
664#99—28no—
665C24—22no—
666C24—21no—
667C24—22no—
668C24—21no—
669C24—22no—
670C24—41no—
671C24—41no—
672C24—41no—
673C24—41no—
674C24—84no—
675C24C2×D4×C13111yescharacteristic
676#41—22no—
677#41—22no—
678#41—22no—
679#41—22no—
680#41—22no—
681#41—22no—
682#41—22no—
683#41—22no—
684#41—22no—
685#41—22no—
686#41—22no—
687#41—22no—
688#41—22no—
689#41—22no—
690#41—22no—
691#41—22no—
692#41—41no—
693#41—41no—
694#41—41no—
695#41—41no—
696#41—41no—
697#41—41no—
698#41—41no—
699#41—41no—
700#41—41no—
701#41—41no—
702#41—41no—
703#41—41no—
704#41—41no—
705#41—41no—
706#41—41no—
707#41—41no—
708C2×Q8—21no—
709C2×Q8—21no—
710C2×Q8—21no—
711C2×Q8—21no—
712C2×Q8—21no—
713C2×Q8—21no—
714C2×Q8—21no—
715C2×Q8—21no—
716C2×Q8—21no—
717C2×Q8—21no—
718C2×Q8C2×D4×C13112yes—
719C2×Q8C2×D4×C13112yescomplemented
720C2×D4—22no—
721C2×D4—22no—
722C2×D4—22no—
723C2×D4—22no—
724C2×D4—216no—
725C2×D4—21no—
726C2×D4—21no—
727C2×D4—22no—
728C2×D4—22no—
729C2×D4—21no—
730C2×D4—21no—
731C2×D4—22no—
732C2×D4—22no—
733C2×D4—21no—
734C2×D4—21no—
735C2×D4—22no—
736C2×D4—22no—
737C2×D4—21no—
738C2×D4—22no—
739C2×D4—22no—
740C2×D4—22no—
741C2×D4—22no—
742C2×D4—21no—
743C2×D4—21no—
744C2×D4—21no—
745C2×D4—22no—
746C2×D4—22no—
747C2×D4—22no—
748C2×D4—22no—
749C2×D4—22no—
750C2×D4—41no—
751C2×D4—41no—
752C2×D4—41no—
753C2×D4—41no—
754C2×D4—41no—
755C2×D4—41no—
756C2×D4—41no—
757C2×D4—41no—
758C2×D4—41no—
759C2×D4—41no—
760C2×D4—41no—
761C2×D4—41no—
762C2×D4—41no—
763C2×D4—41no—
764C2×D4—41no—
765C2×D4—41no—
766C2×D4—41no—
767C2×D4—41no—
768C2×D4—41no—
769C2×D4—41no—
770C2×D4—88no—
771C2×D4C2×D4×C13114yes—
772C2×D4C2×D4×C13112yes—
773C2×D4C2×D4×C13112yescomplemented
774C22×C4—22no—
775C22×C4—21no—
776C22×C4—21no—
777C22×C4—22no—
778C22×C4—22no—
779C22×C4—22no—
780C22×C4—22no—
781C22×C4—41no—
782C22×C4—41no—
783C22×C4—41no—
784C22×C4—41no—
785C22×C4—41no—
786C22×C4—41no—
787C22×C4—41no—
788C22×C4—41no—
789C22×C4—41no—
790C22×C4C2×D4×C13111yescharacteristic
791C22×C4C2×D4×C13111yescharacteristic
792C22×C4C2×D4×C13111yescharacteristic
793C22×C4C2×D4×C13111yescharacteristic
794C22×C4C2×D4×C13111yescharacteristic
795C22×C4C2×D4×C13111yescharacteristic
796C22×C4C2×D4×C13111yescharacteristic
797C22×C4C2×D4×C13111yescharacteristic
798C22×C4C2×D4×C13111yescharacteristic
799C22×C4C2×D4×C13111yescharacteristic
800C22×C4C2×D4×C13111yescharacteristic
801C22×C4#41×C13111yescharacteristic
802C22×C4#41×C13111yescharacteristic
803C22×C4C24×C13111yescharacteristic
804Q16—28no—
805SD16—216no—
806SD16—28no—
807SD16—28no—
808D8—216no—
809D8—28no—
810M16—22no—
811M16—22no—
812M16—22no—
813M16—22no—
814M16—22no—
815M16—22no—
816M16—22no—
817M16C2×D4×C13114yescomplemented
818C2×C8—22no—
819C2×C8—22no—
820C2×C8—22no—
821C2×C8—22no—
822C2×C8—22no—
823C2×C8C2×D4×C13114yescomplemented
824C4⋊C4—22no—
825C4⋊C4—22no—
826C4⋊C4—22no—
827C4⋊C4—41no—
828C22⋊C4—216no—
829C22⋊C4—22no—
830C22⋊C4—22no—
831C22⋊C4—41no—
832C22⋊C4C2×D4×C13114yes—
833C42—22no—
834C42—22no—
835C42—22no—
836C42—41no—
837C23—24no—
838C23—22no—
839C23—22no—
840C23—42no—
841C23—44no—
842C23—48no—
843C23—41no—
844C23—41no—
845C23—41no—
846C23—41no—
847C23—42no—
848C23—42no—
849C23—42no—
850C23—42no—
851C23—42no—
852C23—42no—
853C23—82no—
854C23—84no—
855C23—84no—
856C23—84no—
857C23—84no—
858C23—84no—
859C23—84no—
860C23#120×C13111yescharacteristic
861C23#120×C13111yescharacteristic
862C23#121×C13111yescharacteristic
863C23#121×C13111yescharacteristic
864C23#127×C13111yescharacteristic
865C23#127×C13111yescharacteristic
866C23C22×D4×C13111yescharacteristic
867Q8—22no—
868Q8—22no—
869Q8—22no—
870Q8—22no—
871Q8—41no—
872Q8—41no—
873Q8—41no—
874Q8—41no—
875D4—22no—
876D4—24no—
877D4—22no—
878D4—22no—
879D4—24no—
880D4—22no—
881D4—42no—
882D4—42no—
883D4—42no—
884D4—42no—
885D4—42no—
886D4—42no—
887D4—42no—
888D4—42no—
889D4—42no—
890D4—42no—
891D4—42no—
892D4—42no—
893D4—41no—
894D4—41no—
895D4—41no—
896D4—41no—
897D4—42no—
898D4—42no—
899D4—816no—
900C2×C4—24no—
901C2×C4—22no—
902C2×C4—22no—
903C2×C4—44no—
904C2×C4—41no—
905C2×C4—41no—
906C2×C4—41no—
907C2×C4—41no—
908C2×C4—42no—
909C2×C4—42no—
910C2×C4—42no—
911C2×C4—42no—
912C2×C4—42no—
913C2×C4—42no—
914C2×C4—42no—
915C2×C4—42no—
916C2×C4—42no—
917C2×C4—82no—
918C2×C4#120×C13111yescharacteristic
919C2×C4#120×C13111yescharacteristic
920C2×C4#120×C13111yescharacteristic
921C2×C4#120×C13111yescharacteristic
922C2×C4#120×C13111yescharacteristic
923C2×C4#120×C13111yescharacteristic
924C2×C4#120×C13111yescharacteristic
925C2×C4#120×C13111yescharacteristic
926C2×C4#120×C13111yescharacteristic
927C2×C4#120×C13111yescharacteristic
928C2×C4#121×C13111yescharacteristic
929C2×C4#121×C13111yescharacteristic
930C2×C4#121×C13111yescharacteristic
931C2×C4#121×C13111yescharacteristic
932C2×C4#121×C13111yescharacteristic
933C2×C4#121×C13111yescharacteristic
934C2×C4#121×C13111yescharacteristic
935C2×C4#121×C13111yescharacteristic
936C2×C4#121×C13111yescharacteristic
937C2×C4#121×C13111yescharacteristic
938C2×C4#127×C13111yescharacteristic
939C2×C4#127×C13111yescharacteristic
940C2×C4C22×D4×C13111yescharacteristic
941C2×C4C22×D4×C13111yescharacteristic
942C2×C4C22×D4×C13111yescharacteristic
943C2×C4C22×D4×C13111yescharacteristic
944C2×C4C22×D4×C13111yescharacteristic
945C2×C4C2×#41×C13111yescharacteristic
946C8—24no—
947C8—24no—
948C22—22no—
949C22—22no—
950C22—22no—
951C22—41no—
952C22—41no—
953C22—41no—
954C22—41no—
955C22—44no—
956C22—48no—
957C22—42no—
958C22—42no—
959C22—44no—
960C22—82no—
961C22—84no—
962C22—82no—
963C22—84no—
964C22—84no—
965C22—84no—
966C22—84no—
967C22—82no—
968C22—84no—
969C22—82no—
970C22—82no—
971C22#392×C13111yescharacteristic
972C22#392×C13111yescharacteristic
973C22#392×C13111yescharacteristic
974C22#392×C13111yescharacteristic
975C22C2×#120×C13111yescharacteristic
976C22C2×#121×C13111yescharacteristic
977C22C2×#127×C13111yescharacteristic
978C4—44no—
979C4—42no—
980C4—42no—
981C4—82no—
982C4#392×C13111yescharacteristic
983C4#392×C13111yescharacteristic
984C4#392×C13111yescharacteristic
985C4#392×C13111yescharacteristic
986C4C2×#120×C13111yescharacteristic
987C4C2×#120×C13111yescharacteristic
988C4C2×#121×C13111yescharacteristic
989C4C2×#121×C13111yescharacteristic
990C2—21no—
991C2—21no—
992C2—21no—
993C2—21no—
994C2—21no—
995C2—21no—
996C2—84no—
997C2—82no—
998C2—82no—
999C2#2008×C13112yesdirect product factor
1000C2C2×#392×C13111yescharacteristic
subgroupG/H
center, socleC22×C131#392
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. C2×#575×C131C2semidirect
2. C22×AGL(1,ℤ/8)×C131C2semidirect
3. C2×#535×C131C2semidirect
4. C2×#421×C131C2semidirect
5. C2×#418×C131C2semidirect
6. C2×#410×C131C2semidirect
7. #2008×C131C2direct (N × H)
8. C2×#344×C131C2semidirect
15. #575×C131C22semidirect
25. C2×AGL(1,ℤ/8)×C131C22semidirect
34. #535×C131C22semidirect
42. #421×C131C22semidirect
45. #418×C131C22semidirect
48. #410×C131C22semidirect
50. #344×C131C22semidirect
73. C2×#41×C131D4semidirect
77. C22×Q8×C131D4semidirect
95. C22×D4×C131D4semidirect
131. C2×M16×C131D4semidirect
132. C2×M16×C131D4semidirect
133. C2×M16×C131D4semidirect
137. C22×C8×C131D4semidirect
218. C2×Q8×C131C2×D4semidirect
272. C2×D4×C131C2×D4semidirect
316. M16×C131C2×D4semidirect
322. C2×C8×C131C2×D4semidirect
498. C2×C131#2008direct (N × H)
500. C2×#2008C131direct (N × H)
501. C131C2×#2008direct (N × H)
502. C2×#575C2×C131semidirect
503. C22×AGL(1,ℤ/8)C2×C131semidirect
504. C2×#535C2×C131semidirect
505. C2×#421C2×C131semidirect
506. C2×#418C2×C131semidirect
507. C2×#410C2×C131semidirect
508. #2008C2×C131direct (N × H)
509. C2×#344C2×C131semidirect
516. #575C22×C131semidirect
526. C2×AGL(1,ℤ/8)C22×C131semidirect
535. #535C22×C131semidirect
543. #421C22×C131semidirect
546. #418C22×C131semidirect
549. #410C22×C131semidirect
551. #344C22×C131semidirect
574. C2×#41D4×C131semidirect
578. C22×Q8D4×C131semidirect
596. C22×D4D4×C131semidirect
632. C2×M16D4×C131semidirect
633. C2×M16D4×C131semidirect
634. C2×M16D4×C131semidirect
638. C22×C8D4×C131semidirect
719. C2×Q8C2×D4×C131semidirect
773. C2×D4C2×D4×C131semidirect
817. M16C2×D4×C131semidirect
823. C2×C8C2×D4×C131semidirect
999. C2#2008×C131direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#575×C1312
C22×AGL(1,ℤ/8)×C1312
C2×#535×C1312
C2×#421×C1312
C2×#418×C1312
C2×#410×C1312
#2008×C1312
C2×#344×C1312
C2×#2008131