Finite Group Databasebeta

← C131×#33347 #45719231

Subgroups — C131×#33347 #45719231

Order 33536.

1236 conjugacy classes of subgroups.

The subgroup lattice has 872 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#3449×C131C211yesmaximal, characteristic
2C2×#413×C131C211yesmaximal, characteristic, complemented
3C2×#410×C131C211yesmaximal, characteristic, complemented
4#2123×C131C212yesmaximal, complemented
5#2122×C131C212yesmaximal, complemented
6#2121×C131C214yesmaximal, complemented
7#2120×C131C214yesmaximal, complemented
8C22×#41×C131C411yescharacteristic, complemented
9C22×#41×C131C2211yescharacteristic
10C22×M16×C131—21no—
11#537×C131—21no—
12#537×C131—21no—
13#536×C131—21no—
14#536×C131C411yescharacteristic, complemented
15#536×C131C2211yescharacteristic
16#535×C131—21no—
17#535×C131C411yescharacteristic, complemented
18#535×C131C2211yescharacteristic
19#534×C131C412yescomplemented
20#534×C131C2212yes—
21#532×C131—21no—
22#532×C131—21no—
23#525×C131—21no—
24#525×C131—21no—
25#525×C131C412yescomplemented
26#525×C131C2212yes—
27C2×#117×C131—21no—
28C2×#117×C131C411yescharacteristic, complemented
29#413×C131—21no—
30#413×C131—21no—
31#413×C131C2212yes—
32#413×C131C2212yes—
33C2×#101×C131—21no—
34C2×#100×C131C2212yes—
35#410×C131—21no—
36#410×C131—21no—
37#410×C131C2212yes—
38#410×C131C2212yes—
39C2×#99×C131—21no—
40C2×#99×C131C2212yes—
41#352×C131C2218yescomplemented
42AΣL(1,𝔽16)×C131C2218yescomplemented
43C2×#41×C131—21no—
44C2×#41×C131—21no—
45C2×#41×C131—21no—
46C2×#41×C131—21no—
47C2×#41×C131—41no—
48C2×#41×C131—41no—
49C2×#41×C131—41no—
50C2×#41×C131—41no—
51C2×#41×C131—41no—
52C2×#41×C131—41no—
53C2×#41×C131—41no—
54C2×#41×C131—41no—
55C2×#41×C131C2×C411yescharacteristic
56C2×#41×C131C2×C411yescharacteristic
57C2×#41×C131D411yescharacteristic
58C2×#41×C131D411yescharacteristic
59C2×#41×C131D411yescharacteristic
60C2×#41×C131D411yescharacteristic
61C2×#41×C131C2311yescharacteristic
62C2×#41×C131C2311yescharacteristic
63C22×Q8×C131C2×C411yescharacteristic, complemented
64C22×Q8×C131D411yescharacteristic
65C22×D4×C131C2×C411yescharacteristic
66C22×D4×C131C2×C412yes—
67C22×D4×C131C2×C411yescharacteristic, complemented
68C22×D4×C131D411yescharacteristic
69C22×D4×C131C2311yescharacteristic
70C23×C4×C131C2×C411yescharacteristic
71C23×C4×C131C2×C412yescomplemented
72C23×C4×C131D411yescharacteristic
73C23×C4×C131D411yescharacteristic
74C2×M16×C131—22no—
75C2×M16×C131—22no—
76C2×M16×C131—22no—
77C2×M16×C131—41no—
78C2×M16×C131—41no—
79C2×M16×C131—41no—
80C22×C8×C131—41no—
81C4⋊Q8×C131—21no—
82C4⋊Q8×C131—21no—
83#127×C131—21no—
84#127×C131—21no—
85#124×C131—21no—
86#124×C131—21no—
87#124×C131—21no—
88#124×C131—21no—
89#123×C131—22no—
90#123×C131—22no—
91#123×C131C2×C412yes—
92#123×C131C2×C412yescomplemented
93#123×C131C2×C412yescomplemented
94#123×C131C2312yes—
95C22⋊Q8×C131—22no—
96C22⋊Q8×C131—22no—
97C22⋊Q8×C131—21no—
98C22⋊Q8×C131—21no—
99C22⋊Q8×C131—21no—
100C22⋊Q8×C131—21no—
101#121×C131—22no—
102#121×C131—22no—
103#121×C131—22no—
104#121×C131—22no—
105#121×C131—22no—
106#121×C131—22no—
107#121×C131—21no—
108#121×C131—21no—
109#121×C131—21no—
110#121×C131—21no—
111#120×C131—22no—
112#120×C131—22no—
113#120×C131C2×C412yes—
114#120×C131C2×C412yescomplemented
115#120×C131C2×C412yescomplemented
116#120×C131C2312yes—
117C4×D4×C131—22no—
118C4×D4×C131—22no—
119C4×D4×C131—22no—
120C4×D4×C131—22no—
121#117×C131—21no—
122#117×C131—21no—
123#117×C131—22no—
124#117×C131—22no—
125#117×C131—41no—
126#117×C131—41no—
127#117×C131C2×C412yescomplemented
128#117×C131C2×C411yescharacteristic, complemented
129#117×C131C2×C411yescharacteristic, complemented
130C2×C4⋊C4×C131—21no—
131C2×C4⋊C4×C131—41no—
132C2×C22⋊C4×C131—22no—
133C2×C22⋊C4×C131C2×C412yes—
134C2×C42×C131—21no—
135C2×C42×C131—41no—
136#101×C131—22no—
137#101×C131—22no—
138#100×C131—22no—
139#100×C131C2314yes—
140#99×C131—22no—
141#99×C131—22no—
142#99×C131—22no—
143#99×C131C2314yes—
144C24×C131C22⋊C411yescharacteristic
145C24×C131C22×C411yescharacteristic
146C24×C131C22×C412yes—
147C24×C131C2×D411yescharacteristic
148#41×C131—41no—
149#41×C131—41no—
150#41×C131—41no—
151#41×C131—41no—
152#41×C131—41no—
153#41×C131—41no—
154#41×C131—41no—
155#41×C131—41no—
156#41×C131—41no—
157#41×C131—41no—
158#41×C131—41no—
159#41×C131—41no—
160#41×C131—41no—
161#41×C131—41no—
162#41×C131—41no—
163#41×C131—41no—
164#41×C131—42no—
165#41×C131—42no—
166#41×C131—42no—
167#41×C131—42no—
168#41×C131—42no—
169#41×C131—42no—
170#41×C131—41no—
171#41×C131—41no—
172#41×C131—41no—
173#41×C131—41no—
174C2×Q8×C131—21no—
175C2×Q8×C131—21no—
176C2×Q8×C131—41no—
177C2×Q8×C131—41no—
178C2×Q8×C131—41no—
179C2×Q8×C131—41no—
180C2×Q8×C131C22⋊C411yescharacteristic
181C2×Q8×C131C22⋊C411yescharacteristic
182C2×Q8×C131C2×D411yescharacteristic
183C2×Q8×C131C2×D411yescharacteristic
184C2×D4×C131—22no—
185C2×D4×C131—22no—
186C2×D4×C131—22no—
187C2×D4×C131—22no—
188C2×D4×C131—22no—
189C2×D4×C131—22no—
190C2×D4×C131—21no—
191C2×D4×C131—21no—
192C2×D4×C131—41no—
193C2×D4×C131—41no—
194C2×D4×C131—41no—
195C2×D4×C131—41no—
196C2×D4×C131—41no—
197C2×D4×C131—41no—
198C2×D4×C131—41no—
199C2×D4×C131—41no—
200C2×D4×C131—42no—
201C2×D4×C131—42no—
202C2×D4×C131C22⋊C411yescharacteristic
203C2×D4×C131C22⋊C411yescharacteristic
204C2×D4×C131C22⋊C411yescharacteristic
205C2×D4×C131C22⋊C411yescharacteristic
206C2×D4×C131C22×C411yescharacteristic
207C2×D4×C131C22×C411yescharacteristic
208C2×D4×C131C22×C411yescharacteristic
209C2×D4×C131C2×D411yescharacteristic
210C2×D4×C131C2×D411yescharacteristic
211C2×D4×C131C2×D411yescharacteristic
212C2×D4×C131C2×D411yescharacteristic
213C2×D4×C131C2411yescharacteristic
214C22×C4×C131—21no—
215C22×C4×C131—21no—
216C22×C4×C131—21no—
217C22×C4×C131—21no—
218C22×C4×C131—21no—
219C22×C4×C131—21no—
220C22×C4×C131—21no—
221C22×C4×C131—21no—
222C22×C4×C131—21no—
223C22×C4×C131—21no—
224C22×C4×C131—21no—
225C22×C4×C131—21no—
226C22×C4×C131—22no—
227C22×C4×C131—22no—
228C22×C4×C131—22no—
229C22×C4×C131—42no—
230C22×C4×C131—42no—
231C22×C4×C131—42no—
232C22×C4×C131C22⋊C411yescharacteristic
233C22×C4×C131C22⋊C411yescharacteristic
234C22×C4×C131C22⋊C411yescharacteristic
235C22×C4×C131C22⋊C411yescharacteristic
236C22×C4×C131C22⋊C411yescharacteristic
237C22×C4×C131C22⋊C411yescharacteristic
238C22×C4×C131C22⋊C411yescharacteristic
239C22×C4×C131C22⋊C411yescharacteristic
240C22×C4×C131C22⋊C411yescharacteristic
241C22×C4×C131C22×C411yescharacteristic
242C22×C4×C131C22×C411yescharacteristic
243C22×C4×C131C22×C412yes—
244C22×C4×C131C2×D411yescharacteristic
245C22×C4×C131C2×D411yescharacteristic
246C22×C4×C131C2×D411yescharacteristic
247C22×C4×C131C2×D411yescharacteristic
248C22×C4×C131C2×D411yescharacteristic
249M16×C131—24no—
250M16×C131—42no—
251M16×C131—42no—
252M16×C131—42no—
253C2×C8×C131—42no—
254C2×C8×C131—42no—
255C2×C8×C131—42no—
256C4⋊C4×C131—22no—
257C4⋊C4×C131—21no—
258C4⋊C4×C131—21no—
259C4⋊C4×C131—22no—
260C4⋊C4×C131—22no—
261C4⋊C4×C131—22no—
262C4⋊C4×C131—22no—
263C4⋊C4×C131—42no—
264C4⋊C4×C131—42no—
265C22⋊C4×C131—22no—
266C22⋊C4×C131—22no—
267C22⋊C4×C131—22no—
268C22⋊C4×C131—22no—
269C22⋊C4×C131—22no—
270C22⋊C4×C131—22no—
271C22⋊C4×C131—22no—
272C22⋊C4×C131—22no—
273C22⋊C4×C131—22no—
274C22⋊C4×C131—24no—
275C22⋊C4×C131—42no—
276C22⋊C4×C131C22×C412yes—
277C22⋊C4×C131C22×C412yes—
278C42×C131—22no—
279C42×C131—21no—
280C42×C131—21no—
281C42×C131—42no—
282C42×C131—42no—
283C23×C131—21no—
284C23×C131—21no—
285C23×C131—21no—
286C23×C131—21no—
287C23×C131—21no—
288C23×C131—21no—
289C23×C131—22no—
290C23×C131—42no—
291C23×C131—81no—
292C23×C131—81no—
293C23×C131—81no—
294C23×C131—82no—
295C23×C131C2×C22⋊C411yescharacteristic
296C23×C131C2×C22⋊C411yescharacteristic
297C23×C131C2×C22⋊C411yescharacteristic
298C23×C131C2×C22⋊C411yescharacteristic
299C23×C131C2×C22⋊C411yescharacteristic
300C23×C131C23×C411yescharacteristic
301C23×C131C22×D411yescharacteristic
302Q8×C131—41no—
303Q8×C131—41no—
304Q8×C131—41no—
305Q8×C131—41no—
306Q8×C131—42no—
307Q8×C131—41no—
308Q8×C131—41no—
309D4×C131—41no—
310D4×C131—41no—
311D4×C131—41no—
312D4×C131—41no—
313D4×C131—41no—
314D4×C131—41no—
315D4×C131—41no—
316D4×C131—41no—
317D4×C131—41no—
318D4×C131—41no—
319D4×C131—41no—
320D4×C131—41no—
321D4×C131—42no—
322D4×C131—44no—
323D4×C131—42no—
324D4×C131—42no—
325D4×C131—41no—
326D4×C131—41no—
327D4×C131—82no—
328D4×C131—82no—
329D4×C131—82no—
330D4×C131—82no—
331C2×C4×C131—21no—
332C2×C4×C131—21no—
333C2×C4×C131—21no—
334C2×C4×C131—21no—
335C2×C4×C131—21no—
336C2×C4×C131—21no—
337C2×C4×C131—21no—
338C2×C4×C131—21no—
339C2×C4×C131—21no—
340C2×C4×C131—21no—
341C2×C4×C131—21no—
342C2×C4×C131—21no—
343C2×C4×C131—21no—
344C2×C4×C131—21no—
345C2×C4×C131—21no—
346C2×C4×C131—21no—
347C2×C4×C131—21no—
348C2×C4×C131—21no—
349C2×C4×C131—21no—
350C2×C4×C131—21no—
351C2×C4×C131—21no—
352C2×C4×C131—21no—
353C2×C4×C131—21no—
354C2×C4×C131—21no—
355C2×C4×C131—21no—
356C2×C4×C131—21no—
357C2×C4×C131—21no—
358C2×C4×C131—21no—
359C2×C4×C131—21no—
360C2×C4×C131—21no—
361C2×C4×C131—22no—
362C2×C4×C131—22no—
363C2×C4×C131—22no—
364C2×C4×C131—44no—
365C2×C4×C131—42no—
366C2×C4×C131—42no—
367C2×C4×C131—42no—
368C2×C4×C131—44no—
369C2×C4×C131—82no—
370C2×C4×C131—84no—
371C2×C4×C131#9911yescharacteristic
372C2×C4×C131#9911yescharacteristic
373C2×C4×C131#9911yescharacteristic
374C2×C4×C131#9911yescharacteristic
375C2×C4×C131C2×C22⋊C411yescharacteristic
376C2×C4×C131C2×C22⋊C411yescharacteristic
377C2×C4×C131C2×C22⋊C411yescharacteristic
378C2×C4×C131C2×C22⋊C411yescharacteristic
379C2×C4×C131C2×C22⋊C411yescharacteristic
380C2×C4×C131C2×C22⋊C411yescharacteristic
381C2×C4×C131C2×C22⋊C411yescharacteristic
382C2×C4×C131C22×D411yescharacteristic
383C8×C131—44no—
384C22×C131—21no—
385C22×C131—21no—
386C22×C131—21no—
387C22×C131—21no—
388C22×C131—21no—
389C22×C131—21no—
390C22×C131—41no—
391C22×C131—41no—
392C22×C131—41no—
393C22×C131—41no—
394C22×C131—41no—
395C22×C131—41no—
396C22×C131—41no—
397C22×C131—42no—
398C22×C131—42no—
399C22×C131—42no—
400C22×C131—42no—
401C22×C131—42no—
402C22×C131—81no—
403C22×C131—81no—
404C22×C131—81no—
405C22×C131—81no—
406C22×C131—84no—
407C22×C131C2×#9911yescharacteristic
408C22×C131C2×#9911yescharacteristic
409C22×C131C22×C22⋊C411yescharacteristic
410C4×C131—21no—
411C4×C131—21no—
412C4×C131—21no—
413C4×C131—21no—
414C4×C131—21no—
415C4×C131—21no—
416C4×C131—42no—
417C4×C131—42no—
418C4×C131—42no—
419C4×C131—84no—
420C4×C131C2×#9911yescharacteristic
421C4×C131C2×#9911yescharacteristic
422C4×C131C2×#9911yescharacteristic
423C4×C131C2×#9911yescharacteristic
424C2×C131—21no—
425C2×C131—21no—
426C2×C131—21no—
427C2×C131—41no—
428C2×C131—41no—
429C2×C131—41no—
430C2×C131—41no—
431C2×C131—41no—
432C2×C131—41no—
433C2×C131—82no—
434C2×C131C22×#9911yescharacteristic
435#33347C13111yesmaximal, characteristic, direct product factor, Sylow
436C131#3334711yescharacteristic, direct product factor, Sylow
437#3449C2×C13111yescharacteristic
438C2×#413C2×C13111yescharacteristic, complemented
439C2×#410C2×C13111yescharacteristic, complemented
440#2123C2×C13112yescomplemented
441#2122C2×C13112yescomplemented
442#2121C2×C13114yescomplemented
443#2120C2×C13114yescomplemented
444C22×#41C4×C13111yescharacteristic, complemented
445C22×#41C22×C13111yescharacteristic
446C22×M16—21no—
447#537—21no—
448#537—21no—
449#536—21no—
450#536C4×C13111yescharacteristic, complemented
451#536C22×C13111yescharacteristic
452#535—21no—
453#535C4×C13111yescharacteristic, complemented
454#535C22×C13111yescharacteristic
455#534C4×C13112yescomplemented
456#534C22×C13112yes—
457#532—21no—
458#532—21no—
459#525—21no—
460#525—21no—
461#525C4×C13112yescomplemented
462#525C22×C13112yes—
463C2×#117—21no—
464C2×#117C4×C13111yescharacteristic, complemented
465#413—21no—
466#413—21no—
467#413C22×C13112yes—
468#413C22×C13112yes—
469C2×#101—21no—
470C2×#100C22×C13112yes—
471#410—21no—
472#410—21no—
473#410C22×C13112yes—
474#410C22×C13112yes—
475C2×#99—21no—
476C2×#99C22×C13112yes—
477#352C22×C13118yescomplemented
478AΣL(1,𝔽16)C22×C13118yescomplemented
479C2×#41—21no—
480C2×#41—21no—
481C2×#41—21no—
482C2×#41—21no—
483C2×#41—41no—
484C2×#41—41no—
485C2×#41—41no—
486C2×#41—41no—
487C2×#41—41no—
488C2×#41—41no—
489C2×#41—41no—
490C2×#41—41no—
491C2×#41C2×C4×C13111yescharacteristic
492C2×#41C2×C4×C13111yescharacteristic
493C2×#41D4×C13111yescharacteristic
494C2×#41D4×C13111yescharacteristic
495C2×#41D4×C13111yescharacteristic
496C2×#41D4×C13111yescharacteristic
497C2×#41C23×C13111yescharacteristic
498C2×#41C23×C13111yescharacteristic
499C22×Q8C2×C4×C13111yescharacteristic, complemented
500C22×Q8D4×C13111yescharacteristic
501C22×D4C2×C4×C13111yescharacteristic
502C22×D4C2×C4×C13112yes—
503C22×D4C2×C4×C13111yescharacteristic, complemented
504C22×D4D4×C13111yescharacteristic
505C22×D4C23×C13111yescharacteristic
506C23×C4C2×C4×C13111yescharacteristic
507C23×C4C2×C4×C13112yescomplemented
508C23×C4D4×C13111yescharacteristic
509C23×C4D4×C13111yescharacteristic
510C2×M16—22no—
511C2×M16—22no—
512C2×M16—22no—
513C2×M16—41no—
514C2×M16—41no—
515C2×M16—41no—
516C22×C8—41no—
517C4⋊Q8—21no—
518C4⋊Q8—21no—
519#127—21no—
520#127—21no—
521#124—21no—
522#124—21no—
523#124—21no—
524#124—21no—
525#123—22no—
526#123—22no—
527#123C2×C4×C13112yes—
528#123C2×C4×C13112yescomplemented
529#123C2×C4×C13112yescomplemented
530#123C23×C13112yes—
531C22⋊Q8—22no—
532C22⋊Q8—22no—
533C22⋊Q8—21no—
534C22⋊Q8—21no—
535C22⋊Q8—21no—
536C22⋊Q8—21no—
537#121—22no—
538#121—22no—
539#121—22no—
540#121—22no—
541#121—22no—
542#121—22no—
543#121—21no—
544#121—21no—
545#121—21no—
546#121—21no—
547#120—22no—
548#120—22no—
549#120C2×C4×C13112yes—
550#120C2×C4×C13112yescomplemented
551#120C2×C4×C13112yescomplemented
552#120C23×C13112yes—
553C4×D4—22no—
554C4×D4—22no—
555C4×D4—22no—
556C4×D4—22no—
557#117—21no—
558#117—21no—
559#117—22no—
560#117—22no—
561#117—41no—
562#117—41no—
563#117C2×C4×C13112yescomplemented
564#117C2×C4×C13111yescharacteristic, complemented
565#117C2×C4×C13111yescharacteristic, complemented
566C2×C4⋊C4—21no—
567C2×C4⋊C4—41no—
568C2×C22⋊C4—22no—
569C2×C22⋊C4C2×C4×C13112yes—
570C2×C42—21no—
571C2×C42—41no—
572#101—22no—
573#101—22no—
574#100—22no—
575#100C23×C13114yes—
576#99—22no—
577#99—22no—
578#99—22no—
579#99C23×C13114yes—
580C24C22⋊C4×C13111yescharacteristic
581C24C22×C4×C13111yescharacteristic
582C24C22×C4×C13112yes—
583C24C2×D4×C13111yescharacteristic
584#41—41no—
585#41—41no—
586#41—41no—
587#41—41no—
588#41—41no—
589#41—41no—
590#41—41no—
591#41—41no—
592#41—41no—
593#41—41no—
594#41—41no—
595#41—41no—
596#41—41no—
597#41—41no—
598#41—41no—
599#41—41no—
600#41—42no—
601#41—42no—
602#41—42no—
603#41—42no—
604#41—42no—
605#41—42no—
606#41—41no—
607#41—41no—
608#41—41no—
609#41—41no—
610C2×Q8—21no—
611C2×Q8—21no—
612C2×Q8—41no—
613C2×Q8—41no—
614C2×Q8—41no—
615C2×Q8—41no—
616C2×Q8C22⋊C4×C13111yescharacteristic
617C2×Q8C22⋊C4×C13111yescharacteristic
618C2×Q8C2×D4×C13111yescharacteristic
619C2×Q8C2×D4×C13111yescharacteristic
620C2×D4—22no—
621C2×D4—22no—
622C2×D4—22no—
623C2×D4—22no—
624C2×D4—22no—
625C2×D4—22no—
626C2×D4—21no—
627C2×D4—21no—
628C2×D4—41no—
629C2×D4—41no—
630C2×D4—41no—
631C2×D4—41no—
632C2×D4—41no—
633C2×D4—41no—
634C2×D4—41no—
635C2×D4—41no—
636C2×D4—42no—
637C2×D4—42no—
638C2×D4C22⋊C4×C13111yescharacteristic
639C2×D4C22⋊C4×C13111yescharacteristic
640C2×D4C22⋊C4×C13111yescharacteristic
641C2×D4C22⋊C4×C13111yescharacteristic
642C2×D4C22×C4×C13111yescharacteristic
643C2×D4C22×C4×C13111yescharacteristic
644C2×D4C22×C4×C13111yescharacteristic
645C2×D4C2×D4×C13111yescharacteristic
646C2×D4C2×D4×C13111yescharacteristic
647C2×D4C2×D4×C13111yescharacteristic
648C2×D4C2×D4×C13111yescharacteristic
649C2×D4C24×C13111yescharacteristic
650C22×C4—21no—
651C22×C4—21no—
652C22×C4—21no—
653C22×C4—21no—
654C22×C4—21no—
655C22×C4—21no—
656C22×C4—21no—
657C22×C4—21no—
658C22×C4—21no—
659C22×C4—21no—
660C22×C4—21no—
661C22×C4—21no—
662C22×C4—22no—
663C22×C4—22no—
664C22×C4—22no—
665C22×C4—42no—
666C22×C4—42no—
667C22×C4—42no—
668C22×C4C22⋊C4×C13111yescharacteristic
669C22×C4C22⋊C4×C13111yescharacteristic
670C22×C4C22⋊C4×C13111yescharacteristic
671C22×C4C22⋊C4×C13111yescharacteristic
672C22×C4C22⋊C4×C13111yescharacteristic
673C22×C4C22⋊C4×C13111yescharacteristic
674C22×C4C22⋊C4×C13111yescharacteristic
675C22×C4C22⋊C4×C13111yescharacteristic
676C22×C4C22⋊C4×C13111yescharacteristic
677C22×C4C22×C4×C13111yescharacteristic
678C22×C4C22×C4×C13111yescharacteristic
679C22×C4C22×C4×C13112yes—
680C22×C4C2×D4×C13111yescharacteristic
681C22×C4C2×D4×C13111yescharacteristic
682C22×C4C2×D4×C13111yescharacteristic
683C22×C4C2×D4×C13111yescharacteristic
684C22×C4C2×D4×C13111yescharacteristic
685M16—24no—
686M16—42no—
687M16—42no—
688M16—42no—
689C2×C8—42no—
690C2×C8—42no—
691C2×C8—42no—
692C4⋊C4—22no—
693C4⋊C4—21no—
694C4⋊C4—21no—
695C4⋊C4—22no—
696C4⋊C4—22no—
697C4⋊C4—22no—
698C4⋊C4—22no—
699C4⋊C4—42no—
700C4⋊C4—42no—
701C22⋊C4—22no—
702C22⋊C4—22no—
703C22⋊C4—22no—
704C22⋊C4—22no—
705C22⋊C4—22no—
706C22⋊C4—22no—
707C22⋊C4—22no—
708C22⋊C4—22no—
709C22⋊C4—22no—
710C22⋊C4—24no—
711C22⋊C4—42no—
712C22⋊C4C22×C4×C13112yes—
713C22⋊C4C22×C4×C13112yes—
714C42—22no—
715C42—21no—
716C42—21no—
717C42—42no—
718C42—42no—
719C23—21no—
720C23—21no—
721C23—21no—
722C23—21no—
723C23—21no—
724C23—21no—
725C23—22no—
726C23—42no—
727C23—81no—
728C23—81no—
729C23—81no—
730C23—82no—
731C23C2×C22⋊C4×C13111yescharacteristic
732C23C2×C22⋊C4×C13111yescharacteristic
733C23C2×C22⋊C4×C13111yescharacteristic
734C23C2×C22⋊C4×C13111yescharacteristic
735C23C2×C22⋊C4×C13111yescharacteristic
736C23C23×C4×C13111yescharacteristic
737C23C22×D4×C13111yescharacteristic
738Q8—41no—
739Q8—41no—
740Q8—41no—
741Q8—41no—
742Q8—42no—
743Q8—41no—
744Q8—41no—
745D4—41no—
746D4—41no—
747D4—41no—
748D4—41no—
749D4—41no—
750D4—41no—
751D4—41no—
752D4—41no—
753D4—41no—
754D4—41no—
755D4—41no—
756D4—41no—
757D4—42no—
758D4—44no—
759D4—42no—
760D4—42no—
761D4—41no—
762D4—41no—
763D4—82no—
764D4—82no—
765D4—82no—
766D4—82no—
767C2×C4—21no—
768C2×C4—21no—
769C2×C4—21no—
770C2×C4—21no—
771C2×C4—21no—
772C2×C4—21no—
773C2×C4—21no—
774C2×C4—21no—
775C2×C4—21no—
776C2×C4—21no—
777C2×C4—21no—
778C2×C4—21no—
779C2×C4—21no—
780C2×C4—21no—
781C2×C4—21no—
782C2×C4—21no—
783C2×C4—21no—
784C2×C4—21no—
785C2×C4—21no—
786C2×C4—21no—
787C2×C4—21no—
788C2×C4—21no—
789C2×C4—21no—
790C2×C4—21no—
791C2×C4—21no—
792C2×C4—21no—
793C2×C4—21no—
794C2×C4—21no—
795C2×C4—21no—
796C2×C4—21no—
797C2×C4—22no—
798C2×C4—22no—
799C2×C4—22no—
800C2×C4—44no—
801C2×C4—42no—
802C2×C4—42no—
803C2×C4—42no—
804C2×C4—44no—
805C2×C4—82no—
806C2×C4—84no—
807C2×C4#99×C13111yescharacteristic
808C2×C4#99×C13111yescharacteristic
809C2×C4#99×C13111yescharacteristic
810C2×C4#99×C13111yescharacteristic
811C2×C4C2×C22⋊C4×C13111yescharacteristic
812C2×C4C2×C22⋊C4×C13111yescharacteristic
813C2×C4C2×C22⋊C4×C13111yescharacteristic
814C2×C4C2×C22⋊C4×C13111yescharacteristic
815C2×C4C2×C22⋊C4×C13111yescharacteristic
816C2×C4C2×C22⋊C4×C13111yescharacteristic
817C2×C4C2×C22⋊C4×C13111yescharacteristic
818C2×C4C22×D4×C13111yescharacteristic
819C8—44no—
820C22—21no—
821C22—21no—
822C22—21no—
823C22—21no—
824C22—21no—
825C22—21no—
826C22—41no—
827C22—41no—
828C22—41no—
829C22—41no—
830C22—41no—
831C22—41no—
832C22—41no—
833C22—42no—
834C22—42no—
835C22—42no—
836C22—42no—
837C22—42no—
838C22—81no—
839C22—81no—
840C22—81no—
841C22—81no—
842C22—84no—
843C22C2×#99×C13111yescharacteristic
844C22C2×#99×C13111yescharacteristic
845C22C22×C22⋊C4×C13111yescharacteristic
846C4—21no—
847C4—21no—
848C4—21no—
849C4—21no—
850C4—21no—
851C4—21no—
852C4—42no—
853C4—42no—
854C4—42no—
855C4—84no—
856C4C2×#99×C13111yescharacteristic
857C4C2×#99×C13111yescharacteristic
858C4C2×#99×C13111yescharacteristic
859C4C2×#99×C13111yescharacteristic
860C2—21no—
861C2—21no—
862C2—21no—
863C2—41no—
864C2—41no—
865C2—41no—
866C2—41no—
867C2—41no—
868C2—41no—
869C2—82no—
870C2C22×#99×C13111yescharacteristic
subgroupG/H
centerC4×C131C2×#99
commutatorC23C23×C4×C131
Frattini, cosocleC2×D4C24×C131
socleC2×C131C22×#99
prime radical#3449×C131C2
LCSG ▷ C23 ▷ C22 ▷ C2 ▷ C1
UCSC1 ◁ C4×C131 ◁ C22×C4×C131 ◁ C22×#41×C131 ◁ G

Complements

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

NH ≅ G/Ntype
2. C2×#413×C131C2semidirect
3. C2×#410×C131C2semidirect
4. #2123×C131C2semidirect
5. #2122×C131C2semidirect
6. #2121×C131C2semidirect
7. #2120×C131C2semidirect
8. C22×#41×C131C4semidirect
14. #536×C131C4semidirect
17. #535×C131C4semidirect
19. #534×C131C4semidirect
25. #525×C131C4semidirect
28. C2×#117×C131C4semidirect
41. #352×C131C22semidirect
42. AΣL(1,𝔽16)×C131C22semidirect
63. C22×Q8×C131C2×C4semidirect
67. C22×D4×C131C2×C4semidirect
71. C23×C4×C131C2×C4semidirect
92. #123×C131C2×C4semidirect
93. #123×C131C2×C4semidirect
114. #120×C131C2×C4semidirect
115. #120×C131C2×C4semidirect
127. #117×C131C2×C4semidirect
128. #117×C131C2×C4semidirect
129. #117×C131C2×C4semidirect
435. #33347C131direct (N × H)
436. C131#33347direct (N × H)
438. C2×#413C2×C131semidirect
439. C2×#410C2×C131semidirect
440. #2123C2×C131semidirect
441. #2122C2×C131semidirect
442. #2121C2×C131semidirect
443. #2120C2×C131semidirect
444. C22×#41C4×C131semidirect
450. #536C4×C131semidirect
453. #535C4×C131semidirect
455. #534C4×C131semidirect
461. #525C4×C131semidirect
464. C2×#117C4×C131semidirect
477. #352C22×C131semidirect
478. AΣL(1,𝔽16)C22×C131semidirect
499. C22×Q8C2×C4×C131semidirect
503. C22×D4C2×C4×C131semidirect
507. C23×C4C2×C4×C131semidirect
528. #123C2×C4×C131semidirect
529. #123C2×C4×C131semidirect
550. #120C2×C4×C131semidirect
551. #120C2×C4×C131semidirect
563. #117C2×C4×C131semidirect
564. #117C2×C4×C131semidirect
565. #117C2×C4×C131semidirect

Maximal subgroups

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

subgroupindex
#3449×C1312
C2×#413×C1312
C2×#410×C1312
#2123×C1312
#2122×C1312
#2121×C1312
#2120×C1312
#33347131