Finite Group Databasebeta

← C131×#23412 #45709296

Subgroups — C131×#23412 #45709296

Order 33536.

1948 conjugacy classes of subgroups.

The subgroup lattice has 1044 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#575×C131C211yesmaximal, characteristic, complemented
2C2×#575×C131C211yesmaximal, characteristic, complemented
3#3449×C131C211yesmaximal, characteristic, complemented
4C2×#421×C131C211yesmaximal, characteristic, complemented
5#2896×C131C211yesmaximal, characteristic, complemented
6C2×#410×C131C211yesmaximal, characteristic, complemented
7#2009×C131C214yesmaximal, complemented
8#2008×C131C214yesmaximal, complemented
9C2×#344×C131C211yesmaximal, characteristic, complemented
10C22×#41×C131C2211yescharacteristic
11C22×#41×C131C2211yescharacteristic
12C22×#41×C131C2211yescharacteristic
13#575×C131—22no—
14#575×C131—22no—
15#575×C131—22no—
16#575×C131—22no—
17#575×C131—22no—
18#575×C131—22no—
19#575×C131—22no—
20#575×C131C2214yes—
21C2×#137×C131—21no—
22C2×#137×C131—21no—
23C2×#137×C131—21no—
24C2×#137×C131C2212yescomplemented
25C2×AGL(1,ℤ/8)×C131—21no—
26C2×AGL(1,ℤ/8)×C131—21no—
27C2×AGL(1,ℤ/8)×C131—21no—
28C2×AGL(1,ℤ/8)×C131C2212yescomplemented
29C2×#135×C131—22no—
30C2×#135×C131—22no—
31C22×M16×C131C2211yescharacteristic
32C22×M16×C131C2211yescharacteristic
33#537×C131—22no—
34#536×C131—21no—
35#536×C131C2212yescomplemented
36#535×C131—21no—
37#535×C131C2212yescomplemented
38#534×C131—22no—
39#532×C131—22no—
40#525×C131—22no—
41#525×C131—22no—
42C2×#117×C131C2211yescharacteristic
43C2×#117×C131C2211yescharacteristic
44#421×C131—22no—
45#421×C131C2214yescomplemented
46C2×#104×C131—22no—
47#419×C131C2212yescomplemented
48#418×C131C2212yescomplemented
49#417×C131—22no—
50#416×C131—22no—
51#410×C131—22no—
52#410×C131C2214yescomplemented
53C2×#99×C131—22no—
54#344×C131C2214yescomplemented
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×C131—21no—
73C2×#41×C131—21no—
74C2×#41×C131—21no—
75C2×#41×C131—21no—
76C2×#41×C131—21no—
77C2×#41×C131—21no—
78C2×#41×C131—21no—
79C2×#41×C131—21no—
80C2×#41×C131—21no—
81C2×#41×C131—21no—
82C2×#41×C131—21no—
83C2×#41×C131—21no—
84C2×#41×C131—21no—
85C2×#41×C131D412yes—
86C2×#41×C131D412yes—
87C2×#41×C131D412yes—
88C2×#41×C131D412yescomplemented
89C2×#41×C131C2312yes—
90C2×#41×C131C2312yes—
91C22×Q8×C131D411yescharacteristic
92C22×Q8×C131D411yescharacteristic, complemented
93C22×Q8×C131C2311yescharacteristic
94C22×D4×C131—21no—
95C22×D4×C131—21no—
96C22×D4×C131—21no—
97C22×D4×C131D411yescharacteristic
98C22×D4×C131D411yescharacteristic, complemented
99C22×D4×C131C2311yescharacteristic
100C23×C4×C131—21no—
101C23×C4×C131—21no—
102C23×C4×C131—21no—
103C23×C4×C131C2311yescharacteristic
104#137×C131—24no—
105#137×C131—24no—
106#137×C131—24no—
107#137×C131—24no—
108#137×C131—24no—
109#137×C131—24no—
110#137×C131—24no—
111#137×C131—24no—
112AGL(1,ℤ/8)×C131—24no—
113AGL(1,ℤ/8)×C131—24no—
114AGL(1,ℤ/8)×C131—24no—
115AGL(1,ℤ/8)×C131—24no—
116AGL(1,ℤ/8)×C131—24no—
117AGL(1,ℤ/8)×C131—24no—
118AGL(1,ℤ/8)×C131—24no—
119AGL(1,ℤ/8)×C131—24no—
120#135×C131—28no—
121#135×C131—28no—
122#135×C131—28no—
123#135×C131—28no—
124C2×Q16×C131—22no—
125C2×Q16×C131—22no—
126C2×SD16×C131—22no—
127C2×SD16×C131—22no—
128C2×SD16×C131—22no—
129C2×SD16×C131—22no—
130C2×D8×C131—22no—
131C2×D8×C131—22no—
132C2×M16×C131—21no—
133C2×M16×C131—21no—
134C2×M16×C131—21no—
135C2×M16×C131—21no—
136C2×M16×C131—21no—
137C2×M16×C131—21no—
138C2×M16×C131—21no—
139C2×M16×C131D412yescomplemented
140C2×M16×C131D412yescomplemented
141C2×M16×C131D412yescomplemented
142C2×M16×C131C2312yes—
143C2×M16×C131C2312yes—
144C22×C8×C131—21no—
145C22×C8×C131D412yescomplemented
146C4⋊Q8×C131—22no—
147#127×C131—22no—
148#124×C131—22no—
149#124×C131—22no—
150#123×C131—24no—
151#123×C131—24no—
152C22⋊Q8×C131—24no—
153C22⋊Q8×C131—24no—
154#121×C131—24no—
155#121×C131—28no—
156#121×C131—24no—
157#120×C131—24no—
158#120×C131—24no—
159C4×D4×C131—28no—
160#117×C131—21no—
161#117×C131—21no—
162#117×C131—21no—
163#117×C131—21no—
164#117×C131—21no—
165#117×C131D412yes—
166#117×C131C2312yes—
167#117×C131C2312yes—
168C2×C4⋊C4×C131—21no—
169C2×C4⋊C4×C131—21no—
170C2×C22⋊C4×C131—21no—
171C2×C22⋊C4×C131D412yes—
172C2×C42×C131—21no—
173C2×C42×C131—21no—
174#104×C131—28no—
175#103×C131—24no—
176#102×C131—24no—
177#99×C131—28no—
178C24×C131—21no—
179C24×C131—21no—
180C24×C131—21no—
181C24×C131C2×D411yescharacteristic
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—22no—
192#41×C131—22no—
193#41×C131—22no—
194#41×C131—22no—
195#41×C131—22no—
196#41×C131—22no—
197#41×C131—22no—
198#41×C131—22no—
199#41×C131—22no—
200#41×C131—22no—
201#41×C131—22no—
202#41×C131—22no—
203#41×C131—22no—
204#41×C131—22no—
205#41×C131—22no—
206#41×C131—41no—
207#41×C131—41no—
208#41×C131—41no—
209#41×C131—41no—
210#41×C131—41no—
211#41×C131—41no—
212#41×C131—41no—
213#41×C131—41no—
214#41×C131—41no—
215#41×C131—41no—
216#41×C131—41no—
217#41×C131—41no—
218#41×C131—41no—
219#41×C131—41no—
220#41×C131—41no—
221#41×C131—41no—
222#41×C131—41no—
223#41×C131—41no—
224#41×C131—41no—
225#41×C131—41no—
226#41×C131—41no—
227#41×C131—41no—
228#41×C131—41no—
229#41×C131—41no—
230C2×Q8×C131—21no—
231C2×Q8×C131—21no—
232C2×Q8×C131—21no—
233C2×Q8×C131—21no—
234C2×Q8×C131—21no—
235C2×Q8×C131—21no—
236C2×Q8×C131—21no—
237C2×Q8×C131—21no—
238C2×Q8×C131—21no—
239C2×Q8×C131—21no—
240C2×Q8×C131—21no—
241C2×Q8×C131—21no—
242C2×Q8×C131—21no—
243C2×Q8×C131—21no—
244C2×Q8×C131—21no—
245C2×Q8×C131C2×D412yes—
246C2×Q8×C131C2×D412yes—
247C2×Q8×C131C2×D412yes—
248C2×D4×C131—22no—
249C2×D4×C131—22no—
250C2×D4×C131—22no—
251C2×D4×C131—22no—
252C2×D4×C131—22no—
253C2×D4×C131—22no—
254C2×D4×C131—28no—
255C2×D4×C131—21no—
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—21no—
270C2×D4×C131—41no—
271C2×D4×C131—41no—
272C2×D4×C131—41no—
273C2×D4×C131—41no—
274C2×D4×C131—41no—
275C2×D4×C131—41no—
276C2×D4×C131—41no—
277C2×D4×C131—41no—
278C2×D4×C131—41no—
279C2×D4×C131—41no—
280C2×D4×C131—41no—
281C2×D4×C131—41no—
282C2×D4×C131C2×D412yes—
283C2×D4×C131C2×D412yes—
284C2×D4×C131C2×D412yes—
285C22×C4×C131—21no—
286C22×C4×C131—21no—
287C22×C4×C131—21no—
288C22×C4×C131—22no—
289C22×C4×C131—22no—
290C22×C4×C131—22no—
291C22×C4×C131—22no—
292C22×C4×C131—22no—
293C22×C4×C131—22no—
294C22×C4×C131—22no—
295C22×C4×C131—41no—
296C22×C4×C131—41no—
297C22×C4×C131—41no—
298C22×C4×C131—41no—
299C22×C4×C131—41no—
300C22×C4×C131—41no—
301C22×C4×C131—41no—
302C22×C4×C131—41no—
303C22×C4×C131—41no—
304C22×C4×C131—41no—
305C22×C4×C131—41no—
306C22×C4×C131—41no—
307C22×C4×C131—41no—
308C22×C4×C131C2×D411yescharacteristic
309C22×C4×C131C2×D411yescharacteristic
310C22×C4×C131C2×D411yescharacteristic
311C22×C4×C131C2×D411yescharacteristic
312C22×C4×C131C2×D411yescharacteristic
313C22×C4×C131C2×D411yescharacteristic
314C22×C4×C131C2×D411yescharacteristic
315C22×C4×C131C2×D411yescharacteristic
316C22×C4×C131C2×D411yescharacteristic
317C22×C4×C131C2×D411yescharacteristic
318C22×C4×C131C2×D411yescharacteristic
319C22×C4×C131#4111yescharacteristic
320C22×C4×C131#4111yescharacteristic
321C22×C4×C131C2411yescharacteristic
322Q16×C131—28no—
323Q16×C131—28no—
324SD16×C131—28no—
325SD16×C131—28no—
326SD16×C131—28no—
327SD16×C131—28no—
328D8×C131—28no—
329D8×C131—28no—
330M16×C131—22no—
331M16×C131—22no—
332M16×C131—22no—
333M16×C131—22no—
334M16×C131—22no—
335M16×C131—22no—
336M16×C131—22no—
337M16×C131C2×D414yes—
338C2×C8×C131—22no—
339C2×C8×C131—22no—
340C2×C8×C131—22no—
341C2×C8×C131—22no—
342C2×C8×C131—22no—
343C2×C8×C131C2×D414yes—
344C4⋊C4×C131—28no—
345C4⋊C4×C131—22no—
346C4⋊C4×C131—22no—
347C4⋊C4×C131—22no—
348C4⋊C4×C131—41no—
349C22⋊C4×C131—28no—
350C22⋊C4×C131—28no—
351C22⋊C4×C131—22no—
352C22⋊C4×C131—22no—
353C22⋊C4×C131—41no—
354C22⋊C4×C131C2×D414yes—
355C42×C131—22no—
356C42×C131—22no—
357C42×C131—22no—
358C42×C131—41no—
359C23×C131—22no—
360C23×C131—22no—
361C23×C131—22no—
362C23×C131—41no—
363C23×C131—41no—
364C23×C131—41no—
365C23×C131—41no—
366C23×C131—41no—
367C23×C131—41no—
368C23×C131—81no—
369C23×C131—82no—
370C23×C131—82no—
371C23×C131—82no—
372C23×C131#12011yescharacteristic
373C23×C131#12011yescharacteristic
374C23×C131#12111yescharacteristic
375C23×C131#12111yescharacteristic
376C23×C131#12711yescharacteristic
377C23×C131#12711yescharacteristic
378C23×C131C22×D411yescharacteristic
379Q8×C131—22no—
380Q8×C131—22no—
381Q8×C131—22no—
382Q8×C131—22no—
383Q8×C131—22no—
384Q8×C131—22no—
385Q8×C131—41no—
386Q8×C131—41no—
387Q8×C131—41no—
388Q8×C131—41no—
389Q8×C131—41no—
390Q8×C131—41no—
391D4×C131—22no—
392D4×C131—22no—
393D4×C131—22no—
394D4×C131—22no—
395D4×C131—22no—
396D4×C131—22no—
397D4×C131—42no—
398D4×C131—42no—
399D4×C131—42no—
400D4×C131—42no—
401D4×C131—42no—
402D4×C131—42no—
403D4×C131—42no—
404D4×C131—42no—
405D4×C131—42no—
406D4×C131—42no—
407D4×C131—42no—
408D4×C131—42no—
409D4×C131—41no—
410D4×C131—41no—
411D4×C131—41no—
412D4×C131—41no—
413D4×C131—41no—
414D4×C131—41no—
415D4×C131—88no—
416C2×C4×C131—24no—
417C2×C4×C131—22no—
418C2×C4×C131—22no—
419C2×C4×C131—22no—
420C2×C4×C131—41no—
421C2×C4×C131—41no—
422C2×C4×C131—41no—
423C2×C4×C131—41no—
424C2×C4×C131—41no—
425C2×C4×C131—41no—
426C2×C4×C131—42no—
427C2×C4×C131—42no—
428C2×C4×C131—42no—
429C2×C4×C131—42no—
430C2×C4×C131—42no—
431C2×C4×C131—42no—
432C2×C4×C131—42no—
433C2×C4×C131—42no—
434C2×C4×C131—42no—
435C2×C4×C131—42no—
436C2×C4×C131—42no—
437C2×C4×C131—42no—
438C2×C4×C131—42no—
439C2×C4×C131—82no—
440C2×C4×C131—82no—
441C2×C4×C131#12011yescharacteristic
442C2×C4×C131#12011yescharacteristic
443C2×C4×C131#12011yescharacteristic
444C2×C4×C131#12011yescharacteristic
445C2×C4×C131#12011yescharacteristic
446C2×C4×C131#12011yescharacteristic
447C2×C4×C131#12011yescharacteristic
448C2×C4×C131#12011yescharacteristic
449C2×C4×C131#12011yescharacteristic
450C2×C4×C131#12011yescharacteristic
451C2×C4×C131#12111yescharacteristic
452C2×C4×C131#12111yescharacteristic
453C2×C4×C131#12111yescharacteristic
454C2×C4×C131#12111yescharacteristic
455C2×C4×C131#12111yescharacteristic
456C2×C4×C131#12111yescharacteristic
457C2×C4×C131#12111yescharacteristic
458C2×C4×C131#12111yescharacteristic
459C2×C4×C131#12111yescharacteristic
460C2×C4×C131#12111yescharacteristic
461C2×C4×C131#12711yescharacteristic
462C2×C4×C131#12711yescharacteristic
463C2×C4×C131C22×D411yescharacteristic
464C2×C4×C131C22×D411yescharacteristic
465C2×C4×C131C22×D411yescharacteristic
466C2×C4×C131C22×D411yescharacteristic
467C2×C4×C131C22×D411yescharacteristic
468C2×C4×C131C2×#4111yescharacteristic
469C8×C131—24no—
470C8×C131—24no—
471C22×C131—41no—
472C22×C131—41no—
473C22×C131—41no—
474C22×C131—41no—
475C22×C131—41no—
476C22×C131—41no—
477C22×C131—41no—
478C22×C131—44no—
479C22×C131—44no—
480C22×C131—42no—
481C22×C131—42no—
482C22×C131—42no—
483C22×C131—82no—
484C22×C131—82no—
485C22×C131—82no—
486C22×C131—82no—
487C22×C131—82no—
488C22×C131—82no—
489C22×C131—82no—
490C22×C131#39211yescharacteristic
491C22×C131#39211yescharacteristic
492C22×C131#39211yescharacteristic
493C22×C131#39211yescharacteristic
494C22×C131C2×#12011yescharacteristic
495C22×C131C2×#12111yescharacteristic
496C22×C131C2×#12711yescharacteristic
497C4×C131—44no—
498C4×C131—42no—
499C4×C131—42no—
500C4×C131—42no—
501C4×C131—82no—
502C4×C131#39211yescharacteristic
503C4×C131#39211yescharacteristic
504C4×C131#39211yescharacteristic
505C4×C131#39211yescharacteristic
506C4×C131C2×#12011yescharacteristic
507C4×C131C2×#12011yescharacteristic
508C4×C131C2×#12111yescharacteristic
509C4×C131C2×#12111yescharacteristic
510C2×C131—21no—
511C2×C131—21no—
512C2×C131—21no—
513C2×C131—21no—
514C2×C131—21no—
515C2×C131—21no—
516C2×C131—21no—
517C2×C131—82no—
518C2×C131—82no—
519C2×C131—82no—
520C2×C131C2×#39211yescharacteristic
521#23412C13111yesmaximal, characteristic, direct product factor, Sylow
522C131#2341211yescharacteristic, direct product factor, Sylow
523C2×#575C2×C13111yescharacteristic, complemented
524C2×#575C2×C13111yescharacteristic, complemented
525#3449C2×C13111yescharacteristic, complemented
526C2×#421C2×C13111yescharacteristic, complemented
527#2896C2×C13111yescharacteristic, complemented
528C2×#410C2×C13111yescharacteristic, complemented
529#2009C2×C13114yescomplemented
530#2008C2×C13114yescomplemented
531C2×#344C2×C13111yescharacteristic, complemented
532C22×#41C22×C13111yescharacteristic
533C22×#41C22×C13111yescharacteristic
534C22×#41C22×C13111yescharacteristic
535#575—22no—
536#575—22no—
537#575—22no—
538#575—22no—
539#575—22no—
540#575—22no—
541#575—22no—
542#575C22×C13114yes—
543C2×#137—21no—
544C2×#137—21no—
545C2×#137—21no—
546C2×#137C22×C13112yescomplemented
547C2×AGL(1,ℤ/8)—21no—
548C2×AGL(1,ℤ/8)—21no—
549C2×AGL(1,ℤ/8)—21no—
550C2×AGL(1,ℤ/8)C22×C13112yescomplemented
551C2×#135—22no—
552C2×#135—22no—
553C22×M16C22×C13111yescharacteristic
554C22×M16C22×C13111yescharacteristic
555#537—22no—
556#536—21no—
557#536C22×C13112yescomplemented
558#535—21no—
559#535C22×C13112yescomplemented
560#534—22no—
561#532—22no—
562#525—22no—
563#525—22no—
564C2×#117C22×C13111yescharacteristic
565C2×#117C22×C13111yescharacteristic
566#421—22no—
567#421C22×C13114yescomplemented
568C2×#104—22no—
569#419C22×C13112yescomplemented
570#418C22×C13112yescomplemented
571#417—22no—
572#416—22no—
573#410—22no—
574#410C22×C13114yescomplemented
575C2×#99—22no—
576#344C22×C13114yescomplemented
577C2×#41—21no—
578C2×#41—21no—
579C2×#41—21no—
580C2×#41—21no—
581C2×#41—21no—
582C2×#41—21no—
583C2×#41—21no—
584C2×#41—21no—
585C2×#41—21no—
586C2×#41—21no—
587C2×#41—21no—
588C2×#41—21no—
589C2×#41—21no—
590C2×#41—21no—
591C2×#41—21no—
592C2×#41—21no—
593C2×#41—21no—
594C2×#41—21no—
595C2×#41—21no—
596C2×#41—21no—
597C2×#41—21no—
598C2×#41—21no—
599C2×#41—21no—
600C2×#41—21no—
601C2×#41—21no—
602C2×#41—21no—
603C2×#41—21no—
604C2×#41—21no—
605C2×#41—21no—
606C2×#41—21no—
607C2×#41D4×C13112yes—
608C2×#41D4×C13112yes—
609C2×#41D4×C13112yes—
610C2×#41D4×C13112yescomplemented
611C2×#41C23×C13112yes—
612C2×#41C23×C13112yes—
613C22×Q8D4×C13111yescharacteristic
614C22×Q8D4×C13111yescharacteristic, complemented
615C22×Q8C23×C13111yescharacteristic
616C22×D4—21no—
617C22×D4—21no—
618C22×D4—21no—
619C22×D4D4×C13111yescharacteristic
620C22×D4D4×C13111yescharacteristic, complemented
621C22×D4C23×C13111yescharacteristic
622C23×C4—21no—
623C23×C4—21no—
624C23×C4—21no—
625C23×C4C23×C13111yescharacteristic
626#137—24no—
627#137—24no—
628#137—24no—
629#137—24no—
630#137—24no—
631#137—24no—
632#137—24no—
633#137—24no—
634AGL(1,ℤ/8)—24no—
635AGL(1,ℤ/8)—24no—
636AGL(1,ℤ/8)—24no—
637AGL(1,ℤ/8)—24no—
638AGL(1,ℤ/8)—24no—
639AGL(1,ℤ/8)—24no—
640AGL(1,ℤ/8)—24no—
641AGL(1,ℤ/8)—24no—
642#135—28no—
643#135—28no—
644#135—28no—
645#135—28no—
646C2×Q16—22no—
647C2×Q16—22no—
648C2×SD16—22no—
649C2×SD16—22no—
650C2×SD16—22no—
651C2×SD16—22no—
652C2×D8—22no—
653C2×D8—22no—
654C2×M16—21no—
655C2×M16—21no—
656C2×M16—21no—
657C2×M16—21no—
658C2×M16—21no—
659C2×M16—21no—
660C2×M16—21no—
661C2×M16D4×C13112yescomplemented
662C2×M16D4×C13112yescomplemented
663C2×M16D4×C13112yescomplemented
664C2×M16C23×C13112yes—
665C2×M16C23×C13112yes—
666C22×C8—21no—
667C22×C8D4×C13112yescomplemented
668C4⋊Q8—22no—
669#127—22no—
670#124—22no—
671#124—22no—
672#123—24no—
673#123—24no—
674C22⋊Q8—24no—
675C22⋊Q8—24no—
676#121—24no—
677#121—28no—
678#121—24no—
679#120—24no—
680#120—24no—
681C4×D4—28no—
682#117—21no—
683#117—21no—
684#117—21no—
685#117—21no—
686#117—21no—
687#117D4×C13112yes—
688#117C23×C13112yes—
689#117C23×C13112yes—
690C2×C4⋊C4—21no—
691C2×C4⋊C4—21no—
692C2×C22⋊C4—21no—
693C2×C22⋊C4D4×C13112yes—
694C2×C42—21no—
695C2×C42—21no—
696#104—28no—
697#103—24no—
698#102—24no—
699#99—28no—
700C24—21no—
701C24—21no—
702C24—21no—
703C24C2×D4×C13111yescharacteristic
704#41—22no—
705#41—22no—
706#41—22no—
707#41—22no—
708#41—22no—
709#41—22no—
710#41—22no—
711#41—22no—
712#41—22no—
713#41—22no—
714#41—22no—
715#41—22no—
716#41—22no—
717#41—22no—
718#41—22no—
719#41—22no—
720#41—22no—
721#41—22no—
722#41—22no—
723#41—22no—
724#41—22no—
725#41—22no—
726#41—22no—
727#41—22no—
728#41—41no—
729#41—41no—
730#41—41no—
731#41—41no—
732#41—41no—
733#41—41no—
734#41—41no—
735#41—41no—
736#41—41no—
737#41—41no—
738#41—41no—
739#41—41no—
740#41—41no—
741#41—41no—
742#41—41no—
743#41—41no—
744#41—41no—
745#41—41no—
746#41—41no—
747#41—41no—
748#41—41no—
749#41—41no—
750#41—41no—
751#41—41no—
752C2×Q8—21no—
753C2×Q8—21no—
754C2×Q8—21no—
755C2×Q8—21no—
756C2×Q8—21no—
757C2×Q8—21no—
758C2×Q8—21no—
759C2×Q8—21no—
760C2×Q8—21no—
761C2×Q8—21no—
762C2×Q8—21no—
763C2×Q8—21no—
764C2×Q8—21no—
765C2×Q8—21no—
766C2×Q8—21no—
767C2×Q8C2×D4×C13112yes—
768C2×Q8C2×D4×C13112yes—
769C2×Q8C2×D4×C13112yes—
770C2×D4—22no—
771C2×D4—22no—
772C2×D4—22no—
773C2×D4—22no—
774C2×D4—22no—
775C2×D4—22no—
776C2×D4—28no—
777C2×D4—21no—
778C2×D4—21no—
779C2×D4—21no—
780C2×D4—21no—
781C2×D4—21no—
782C2×D4—21no—
783C2×D4—21no—
784C2×D4—21no—
785C2×D4—21no—
786C2×D4—21no—
787C2×D4—21no—
788C2×D4—21no—
789C2×D4—21no—
790C2×D4—21no—
791C2×D4—21no—
792C2×D4—41no—
793C2×D4—41no—
794C2×D4—41no—
795C2×D4—41no—
796C2×D4—41no—
797C2×D4—41no—
798C2×D4—41no—
799C2×D4—41no—
800C2×D4—41no—
801C2×D4—41no—
802C2×D4—41no—
803C2×D4—41no—
804C2×D4C2×D4×C13112yes—
805C2×D4C2×D4×C13112yes—
806C2×D4C2×D4×C13112yes—
807C22×C4—21no—
808C22×C4—21no—
809C22×C4—21no—
810C22×C4—22no—
811C22×C4—22no—
812C22×C4—22no—
813C22×C4—22no—
814C22×C4—22no—
815C22×C4—22no—
816C22×C4—22no—
817C22×C4—41no—
818C22×C4—41no—
819C22×C4—41no—
820C22×C4—41no—
821C22×C4—41no—
822C22×C4—41no—
823C22×C4—41no—
824C22×C4—41no—
825C22×C4—41no—
826C22×C4—41no—
827C22×C4—41no—
828C22×C4—41no—
829C22×C4—41no—
830C22×C4C2×D4×C13111yescharacteristic
831C22×C4C2×D4×C13111yescharacteristic
832C22×C4C2×D4×C13111yescharacteristic
833C22×C4C2×D4×C13111yescharacteristic
834C22×C4C2×D4×C13111yescharacteristic
835C22×C4C2×D4×C13111yescharacteristic
836C22×C4C2×D4×C13111yescharacteristic
837C22×C4C2×D4×C13111yescharacteristic
838C22×C4C2×D4×C13111yescharacteristic
839C22×C4C2×D4×C13111yescharacteristic
840C22×C4C2×D4×C13111yescharacteristic
841C22×C4#41×C13111yescharacteristic
842C22×C4#41×C13111yescharacteristic
843C22×C4C24×C13111yescharacteristic
844Q16—28no—
845Q16—28no—
846SD16—28no—
847SD16—28no—
848SD16—28no—
849SD16—28no—
850D8—28no—
851D8—28no—
852M16—22no—
853M16—22no—
854M16—22no—
855M16—22no—
856M16—22no—
857M16—22no—
858M16—22no—
859M16C2×D4×C13114yes—
860C2×C8—22no—
861C2×C8—22no—
862C2×C8—22no—
863C2×C8—22no—
864C2×C8—22no—
865C2×C8C2×D4×C13114yes—
866C4⋊C4—28no—
867C4⋊C4—22no—
868C4⋊C4—22no—
869C4⋊C4—22no—
870C4⋊C4—41no—
871C22⋊C4—28no—
872C22⋊C4—28no—
873C22⋊C4—22no—
874C22⋊C4—22no—
875C22⋊C4—41no—
876C22⋊C4C2×D4×C13114yes—
877C42—22no—
878C42—22no—
879C42—22no—
880C42—41no—
881C23—22no—
882C23—22no—
883C23—22no—
884C23—41no—
885C23—41no—
886C23—41no—
887C23—41no—
888C23—41no—
889C23—41no—
890C23—81no—
891C23—82no—
892C23—82no—
893C23—82no—
894C23#120×C13111yescharacteristic
895C23#120×C13111yescharacteristic
896C23#121×C13111yescharacteristic
897C23#121×C13111yescharacteristic
898C23#127×C13111yescharacteristic
899C23#127×C13111yescharacteristic
900C23C22×D4×C13111yescharacteristic
901Q8—22no—
902Q8—22no—
903Q8—22no—
904Q8—22no—
905Q8—22no—
906Q8—22no—
907Q8—41no—
908Q8—41no—
909Q8—41no—
910Q8—41no—
911Q8—41no—
912Q8—41no—
913D4—22no—
914D4—22no—
915D4—22no—
916D4—22no—
917D4—22no—
918D4—22no—
919D4—42no—
920D4—42no—
921D4—42no—
922D4—42no—
923D4—42no—
924D4—42no—
925D4—42no—
926D4—42no—
927D4—42no—
928D4—42no—
929D4—42no—
930D4—42no—
931D4—41no—
932D4—41no—
933D4—41no—
934D4—41no—
935D4—41no—
936D4—41no—
937D4—88no—
938C2×C4—24no—
939C2×C4—22no—
940C2×C4—22no—
941C2×C4—22no—
942C2×C4—41no—
943C2×C4—41no—
944C2×C4—41no—
945C2×C4—41no—
946C2×C4—41no—
947C2×C4—41no—
948C2×C4—42no—
949C2×C4—42no—
950C2×C4—42no—
951C2×C4—42no—
952C2×C4—42no—
953C2×C4—42no—
954C2×C4—42no—
955C2×C4—42no—
956C2×C4—42no—
957C2×C4—42no—
958C2×C4—42no—
959C2×C4—42no—
960C2×C4—42no—
961C2×C4—82no—
962C2×C4—82no—
963C2×C4#120×C13111yescharacteristic
964C2×C4#120×C13111yescharacteristic
965C2×C4#120×C13111yescharacteristic
966C2×C4#120×C13111yescharacteristic
967C2×C4#120×C13111yescharacteristic
968C2×C4#120×C13111yescharacteristic
969C2×C4#120×C13111yescharacteristic
970C2×C4#120×C13111yescharacteristic
971C2×C4#120×C13111yescharacteristic
972C2×C4#120×C13111yescharacteristic
973C2×C4#121×C13111yescharacteristic
974C2×C4#121×C13111yescharacteristic
975C2×C4#121×C13111yescharacteristic
976C2×C4#121×C13111yescharacteristic
977C2×C4#121×C13111yescharacteristic
978C2×C4#121×C13111yescharacteristic
979C2×C4#121×C13111yescharacteristic
980C2×C4#121×C13111yescharacteristic
981C2×C4#121×C13111yescharacteristic
982C2×C4#121×C13111yescharacteristic
983C2×C4#127×C13111yescharacteristic
984C2×C4#127×C13111yescharacteristic
985C2×C4C22×D4×C13111yescharacteristic
986C2×C4C22×D4×C13111yescharacteristic
987C2×C4C22×D4×C13111yescharacteristic
988C2×C4C22×D4×C13111yescharacteristic
989C2×C4C22×D4×C13111yescharacteristic
990C2×C4C2×#41×C13111yescharacteristic
991C8—24no—
992C8—24no—
993C22—41no—
994C22—41no—
995C22—41no—
996C22—41no—
997C22—41no—
998C22—41no—
999C22—41no—
1000C22—44no—
1001C22—44no—
1002C22—42no—
1003C22—42no—
1004C22—42no—
1005C22—82no—
1006C22—82no—
1007C22—82no—
1008C22—82no—
1009C22—82no—
1010C22—82no—
1011C22—82no—
1012C22#392×C13111yescharacteristic
1013C22#392×C13111yescharacteristic
1014C22#392×C13111yescharacteristic
1015C22#392×C13111yescharacteristic
1016C22C2×#120×C13111yescharacteristic
1017C22C2×#121×C13111yescharacteristic
1018C22C2×#127×C13111yescharacteristic
1019C4—44no—
1020C4—42no—
1021C4—42no—
1022C4—42no—
1023C4—82no—
1024C4#392×C13111yescharacteristic
1025C4#392×C13111yescharacteristic
1026C4#392×C13111yescharacteristic
1027C4#392×C13111yescharacteristic
1028C4C2×#120×C13111yescharacteristic
1029C4C2×#120×C13111yescharacteristic
1030C4C2×#121×C13111yescharacteristic
1031C4C2×#121×C13111yescharacteristic
1032C2—21no—
1033C2—21no—
1034C2—21no—
1035C2—21no—
1036C2—21no—
1037C2—21no—
1038C2—21no—
1039C2—82no—
1040C2—82no—
1041C2—82no—
1042C2C2×#392×C13111yescharacteristic
subgroupG/H
centerC4×C131#392
commutator, Frattini, cosocleC22×C4C24×C131
socleC2×C131C2×#392
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C4×C131 ◁ C23×C4×C131 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×#575×C131C2semidirect
2. C2×#575×C131C2semidirect
3. #3449×C131C2semidirect
4. C2×#421×C131C2semidirect
5. #2896×C131C2semidirect
6. C2×#410×C131C2semidirect
7. #2009×C131C2semidirect
8. #2008×C131C2semidirect
9. C2×#344×C131C2semidirect
24. C2×#137×C131C22semidirect
28. C2×AGL(1,ℤ/8)×C131C22semidirect
35. #536×C131C22semidirect
37. #535×C131C22semidirect
45. #421×C131C22semidirect
47. #419×C131C22semidirect
48. #418×C131C22semidirect
52. #410×C131C22semidirect
54. #344×C131C22semidirect
88. C2×#41×C131D4semidirect
92. C22×Q8×C131D4semidirect
98. C22×D4×C131D4semidirect
139. C2×M16×C131D4semidirect
140. C2×M16×C131D4semidirect
141. C2×M16×C131D4semidirect
145. C22×C8×C131D4semidirect
521. #23412C131direct (N × H)
522. C131#23412direct (N × H)
523. C2×#575C2×C131semidirect
524. C2×#575C2×C131semidirect
525. #3449C2×C131semidirect
526. C2×#421C2×C131semidirect
527. #2896C2×C131semidirect
528. C2×#410C2×C131semidirect
529. #2009C2×C131semidirect
530. #2008C2×C131semidirect
531. C2×#344C2×C131semidirect
546. C2×#137C22×C131semidirect
550. C2×AGL(1,ℤ/8)C22×C131semidirect
557. #536C22×C131semidirect
559. #535C22×C131semidirect
567. #421C22×C131semidirect
569. #419C22×C131semidirect
570. #418C22×C131semidirect
574. #410C22×C131semidirect
576. #344C22×C131semidirect
610. C2×#41D4×C131semidirect
614. C22×Q8D4×C131semidirect
620. C22×D4D4×C131semidirect
661. C2×M16D4×C131semidirect
662. C2×M16D4×C131semidirect
663. C2×M16D4×C131semidirect
667. C22×C8D4×C131semidirect

Maximal subgroups

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

subgroupindex
C2×#575×C1312
#3449×C1312
C2×#421×C1312
#2896×C1312
C2×#410×C1312
#2009×C1312
#2008×C1312
C2×#344×C1312
#23412131