Finite Group Databasebeta

← C2×#2200×C131 #45719432

Subgroups — C2×#2200×C131 #45719432

Order 33536.

1328 conjugacy classes of subgroups.

The subgroup lattice has 742 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#560×C131C211yesmaximal, characteristic, complemented
2C2×#458×C131C211yesmaximal, characteristic, complemented
3C2×B(4,𝔽2)×C131C211yesmaximal, characteristic, complemented
4C2×#453×C131C211yesmaximal, characteristic, complemented
5#2200×C131C218yesmaximal, direct product factor
6C2×#353×C131C211yesmaximal, characteristic, complemented
7C2×#352×C131C211yesmaximal, characteristic, complemented
8C2×AΣL(1,𝔽16)×C131C211yesmaximal, characteristic, complemented
9C2×H(5,𝔽2)×C131C2211yescharacteristic
10C2×AGL(1,ℤ/8)×C131—21no—
11#560×C131—22no—
12#560×C131—22no—
13#560×C131—22no—
14#560×C131C2214yescomplemented
15C2×#127×C131C2211yescharacteristic
16C2×#126×C131—21no—
17C2×#123×C131—21no—
18C2×#123×C131—21no—
19C2×#123×C131C2211yescharacteristic
20C2×#121×C131—21no—
21C2×#121×C131—21no—
22C2×#121×C131—21no—
23C2×#120×C131—21no—
24C2×#120×C131—21no—
25C2×#120×C131C2211yescharacteristic
26#458×C131—22no—
27#458×C131C2214yescomplemented
28B(4,𝔽2)×C131—22no—
29B(4,𝔽2)×C131C2214yescomplemented
30#453×C131—22no—
31#453×C131C2214yescomplemented
32C2×#104×C131—21no—
33C2×#100×C131C2211yescharacteristic
34C2×#99×C131—21no—
35C2×#99×C131—21no—
36C2×#99×C131C2211yescharacteristic
37C2×#99×C131C2211yescharacteristic
38#353×C131C2214yescomplemented
39#352×C131C2214yescomplemented
40AΣL(1,𝔽16)×C131C2214yescomplemented
41C25×C131D411yescharacteristic
42H(5,𝔽2)×C131—21no—
43H(5,𝔽2)×C131—21no—
44H(5,𝔽2)×C131—21no—
45H(5,𝔽2)×C131—42no—
46H(5,𝔽2)×C131C2312yes—
47C2×#41×C131—21no—
48C2×#41×C131—41no—
49C22×D4×C131—21no—
50C22×D4×C131—21no—
51C22×D4×C131—21no—
52C22×D4×C131—21no—
53C22×D4×C131—21no—
54C22×D4×C131—21no—
55C22×D4×C131—21no—
56C22×D4×C131—41no—
57C22×D4×C131—41no—
58C22×D4×C131D411yescharacteristic, complemented
59C22×D4×C131C2311yescharacteristic
60C23×C4×C131—21no—
61C23×C4×C131D411yescharacteristic, complemented
62AGL(1,ℤ/8)×C131—24no—
63AGL(1,ℤ/8)×C131—42no—
64C2×SD16×C131—41no—
65C2×D8×C131—41no—
66C2×M16×C131—21no—
67#127×C131—21no—
68#127×C131—21no—
69#127×C131D412yescomplemented
70#127×C131C2312yes—
71#126×C131—24no—
72#126×C131—24no—
73#123×C131—24no—
74#123×C131—21no—
75#123×C131—21no—
76#123×C131—24no—
77#123×C131—24no—
78#123×C131—42no—
79#123×C131D412yescomplemented
80#123×C131C2312yes—
81#121×C131—24no—
82#121×C131—24no—
83#121×C131—24no—
84#121×C131—24no—
85#121×C131—24no—
86#121×C131—24no—
87#120×C131—24no—
88#120×C131—24no—
89#120×C131—21no—
90#120×C131—21no—
91#120×C131—24no—
92#120×C131—42no—
93#120×C131D412yes—
94#120×C131C2312yes—
95C2×C4⋊C4×C131—21no—
96C2×C4⋊C4×C131—21no—
97C2×C4⋊C4×C131—21no—
98C2×C4⋊C4×C131—41no—
99C2×C22⋊C4×C131—21no—
100C2×C22⋊C4×C131—21no—
101C2×C22⋊C4×C131—21no—
102C2×C22⋊C4×C131—21no—
103C2×C22⋊C4×C131—21no—
104C2×C22⋊C4×C131—21no—
105C2×C22⋊C4×C131—21no—
106C2×C22⋊C4×C131—41no—
107C2×C22⋊C4×C131—41no—
108C2×C22⋊C4×C131D411yescharacteristic
109C2×C22⋊C4×C131D411yescharacteristic, complemented
110C2×C42×C131D411yescharacteristic, complemented
111#104×C131—24no—
112#100×C131—21no—
113#100×C131C2312yes—
114#99×C131—21no—
115#99×C131—21no—
116#99×C131—24no—
117#99×C131—24no—
118#99×C131C2312yes—
119#99×C131C2312yes—
120C24×C131—21no—
121C24×C131—21no—
122C24×C131—21no—
123C24×C131—21no—
124C24×C131—21no—
125C24×C131—41no—
126C24×C131—41no—
127C24×C131—82no—
128C24×C131C2×D411yescharacteristic
129C24×C131C2×D411yescharacteristic
130C24×C131C2×D412yes—
131#41×C131—22no—
132#41×C131—22no—
133#41×C131—42no—
134#41×C131—41no—
135#41×C131—42no—
136#41×C131—42no—
137#41×C131—42no—
138#41×C131—41no—
139C2×Q8×C131—21no—
140C2×D4×C131—21no—
141C2×D4×C131—22no—
142C2×D4×C131—22no—
143C2×D4×C131—22no—
144C2×D4×C131—22no—
145C2×D4×C131—24no—
146C2×D4×C131—24no—
147C2×D4×C131—22no—
148C2×D4×C131—22no—
149C2×D4×C131—22no—
150C2×D4×C131—22no—
151C2×D4×C131—22no—
152C2×D4×C131—22no—
153C2×D4×C131—21no—
154C2×D4×C131—41no—
155C2×D4×C131—41no—
156C2×D4×C131—41no—
157C2×D4×C131—41no—
158C2×D4×C131—42no—
159C2×D4×C131—42no—
160C2×D4×C131—41no—
161C2×D4×C131—41no—
162C2×D4×C131—41no—
163C2×D4×C131—41no—
164C2×D4×C131—42no—
165C2×D4×C131—42no—
166C2×D4×C131—41no—
167C2×D4×C131—41no—
168C2×D4×C131—41no—
169C2×D4×C131—44no—
170C2×D4×C131—82no—
171C2×D4×C131—82no—
172C2×D4×C131—82no—
173C2×D4×C131—82no—
174C2×D4×C131—81no—
175C2×D4×C131—81no—
176C2×D4×C131—84no—
177C2×D4×C131C2×D411yescharacteristic
178C2×D4×C131C2×D411yescharacteristic
179C2×D4×C131C2×D411yescharacteristic
180C2×D4×C131C2×D412yescomplemented
181C2×D4×C131C2411yescharacteristic
182C22×C4×C131—21no—
183C22×C4×C131—21no—
184C22×C4×C131—21no—
185C22×C4×C131—21no—
186C22×C4×C131—21no—
187C22×C4×C131—21no—
188C22×C4×C131—24no—
189C22×C4×C131—21no—
190C22×C4×C131—41no—
191C22×C4×C131—41no—
192C22×C4×C131—41no—
193C22×C4×C131—41no—
194C22×C4×C131—41no—
195C22×C4×C131—82no—
196C22×C4×C131C2×D411yescharacteristic
197C22×C4×C131C2×D412yescomplemented
198SD16×C131—44no—
199D8×C131—44no—
200M16×C131—22no—
201M16×C131—41no—
202C2×C8×C131—41no—
203C4⋊C4×C131—24no—
204C4⋊C4×C131—24no—
205C4⋊C4×C131—22no—
206C4⋊C4×C131—22no—
207C4⋊C4×C131—44no—
208C22⋊C4×C131—24no—
209C22⋊C4×C131—24no—
210C22⋊C4×C131—24no—
211C22⋊C4×C131—22no—
212C22⋊C4×C131—21no—
213C22⋊C4×C131—21no—
214C22⋊C4×C131—22no—
215C22⋊C4×C131—22no—
216C22⋊C4×C131—22no—
217C22⋊C4×C131—22no—
218C22⋊C4×C131—22no—
219C22⋊C4×C131—44no—
220C22⋊C4×C131—41no—
221C22⋊C4×C131—41no—
222C22⋊C4×C131—44no—
223C22⋊C4×C131C2×D412yes—
224C22⋊C4×C131C2×D412yescomplemented
225C42×C131—21no—
226C42×C131C2×D412yescomplemented
227C23×C131—21no—
228C23×C131—21no—
229C23×C131—21no—
230C23×C131—21no—
231C23×C131—22no—
232C23×C131—22no—
233C23×C131—22no—
234C23×C131—22no—
235C23×C131—42no—
236C23×C131—42no—
237C23×C131—42no—
238C23×C131—42no—
239C23×C131—42no—
240C23×C131—42no—
241C23×C131—42no—
242C23×C131—41no—
243C23×C131—41no—
244C23×C131—44no—
245C23×C131—41no—
246C23×C131—41no—
247C23×C131—41no—
248C23×C131—41no—
249C23×C131—41no—
250C23×C131—81no—
251C23×C131—82no—
252C23×C131—82no—
253C23×C131—82no—
254C23×C131—84no—
255C23×C131—82no—
256C23×C131—82no—
257C23×C131#12011yescharacteristic
258C23×C131#12011yescharacteristic
259C23×C131#12011yescharacteristic
260C23×C131C22×D411yescharacteristic
261C23×C131C22×D411yescharacteristic
262Q8×C131—22no—
263Q8×C131—41no—
264D4×C131—22no—
265D4×C131—41no—
266D4×C131—41no—
267D4×C131—41no—
268D4×C131—41no—
269D4×C131—42no—
270D4×C131—41no—
271D4×C131—42no—
272D4×C131—42no—
273D4×C131—42no—
274D4×C131—42no—
275D4×C131—42no—
276D4×C131—42no—
277D4×C131—81no—
278D4×C131—82no—
279D4×C131—82no—
280D4×C131—84no—
281D4×C131—82no—
282D4×C131—82no—
283D4×C131—82no—
284D4×C131—82no—
285D4×C131—84no—
286D4×C131—88no—
287C2×C4×C131—21no—
288C2×C4×C131—21no—
289C2×C4×C131—22no—
290C2×C4×C131—22no—
291C2×C4×C131—22no—
292C2×C4×C131—22no—
293C2×C4×C131—22no—
294C2×C4×C131—22no—
295C2×C4×C131—42no—
296C2×C4×C131—42no—
297C2×C4×C131—42no—
298C2×C4×C131—42no—
299C2×C4×C131—41no—
300C2×C4×C131—41no—
301C2×C4×C131—42no—
302C2×C4×C131—41no—
303C2×C4×C131—41no—
304C2×C4×C131—41no—
305C2×C4×C131—42no—
306C2×C4×C131—42no—
307C2×C4×C131—42no—
308C2×C4×C131—81no—
309C2×C4×C131—84no—
310C2×C4×C131—82no—
311C2×C4×C131—82no—
312C2×C4×C131#12011yescharacteristic
313C2×C4×C131C22×D411yescharacteristic
314C8×C131—42no—
315C22×C131—22no—
316C22×C131—21no—
317C22×C131—21no—
318C22×C131—21no—
319C22×C131—21no—
320C22×C131—41no—
321C22×C131—41no—
322C22×C131—41no—
323C22×C131—41no—
324C22×C131—42no—
325C22×C131—42no—
326C22×C131—42no—
327C22×C131—42no—
328C22×C131—42no—
329C22×C131—42no—
330C22×C131—44no—
331C22×C131—42no—
332C22×C131—42no—
333C22×C131—42no—
334C22×C131—81no—
335C22×C131—81no—
336C22×C131—82no—
337C22×C131—82no—
338C22×C131—82no—
339C22×C131—82no—
340C22×C131—82no—
341C22×C131—84no—
342C22×C131—82no—
343C22×C131—82no—
344C22×C131—82no—
345C22×C131—161no—
346C22×C131—161no—
347C22×C131B(4,𝔽2)11yescharacteristic
348C22×C131B(4,𝔽2)11yescharacteristic
349C22×C131C2×#12011yescharacteristic
350C4×C131—21no—
351C4×C131—21no—
352C4×C131—42no—
353C4×C131—42no—
354C4×C131—42no—
355C4×C131—42no—
356C4×C131—42no—
357C4×C131—82no—
358C4×C131—82no—
359C2×C131—21no—
360C2×C131—21no—
361C2×C131—41no—
362C2×C131—41no—
363C2×C131—41no—
364C2×C131—41no—
365C2×C131—82no—
366C2×C131—82no—
367C2×C131—82no—
368C2×C131#220012yesdirect product factor
369C2×C131C2×B(4,𝔽2)11yescharacteristic
370C2×#2200C13111yesmaximal, characteristic, direct product factor, Sylow
371C131C2×#220011yescharacteristic, direct product factor, Sylow
372C2×#560C2×C13111yescharacteristic, complemented
373C2×#458C2×C13111yescharacteristic, complemented
374C2×B(4,𝔽2)C2×C13111yescharacteristic, complemented
375C2×#453C2×C13111yescharacteristic, complemented
376#2200C2×C13118yesdirect product factor
377C2×#353C2×C13111yescharacteristic, complemented
378C2×#352C2×C13111yescharacteristic, complemented
379C2×AΣL(1,𝔽16)C2×C13111yescharacteristic, complemented
380C2×H(5,𝔽2)C22×C13111yescharacteristic
381C2×AGL(1,ℤ/8)—21no—
382#560—22no—
383#560—22no—
384#560—22no—
385#560C22×C13114yescomplemented
386C2×#127C22×C13111yescharacteristic
387C2×#126—21no—
388C2×#123—21no—
389C2×#123—21no—
390C2×#123C22×C13111yescharacteristic
391C2×#121—21no—
392C2×#121—21no—
393C2×#121—21no—
394C2×#120—21no—
395C2×#120—21no—
396C2×#120C22×C13111yescharacteristic
397#458—22no—
398#458C22×C13114yescomplemented
399B(4,𝔽2)—22no—
400B(4,𝔽2)C22×C13114yescomplemented
401#453—22no—
402#453C22×C13114yescomplemented
403C2×#104—21no—
404C2×#100C22×C13111yescharacteristic
405C2×#99—21no—
406C2×#99—21no—
407C2×#99C22×C13111yescharacteristic
408C2×#99C22×C13111yescharacteristic
409#353C22×C13114yescomplemented
410#352C22×C13114yescomplemented
411AΣL(1,𝔽16)C22×C13114yescomplemented
412C25D4×C13111yescharacteristic
413H(5,𝔽2)—21no—
414H(5,𝔽2)—21no—
415H(5,𝔽2)—21no—
416H(5,𝔽2)—42no—
417H(5,𝔽2)C23×C13112yes—
418C2×#41—21no—
419C2×#41—41no—
420C22×D4—21no—
421C22×D4—21no—
422C22×D4—21no—
423C22×D4—21no—
424C22×D4—21no—
425C22×D4—21no—
426C22×D4—21no—
427C22×D4—41no—
428C22×D4—41no—
429C22×D4D4×C13111yescharacteristic, complemented
430C22×D4C23×C13111yescharacteristic
431C23×C4—21no—
432C23×C4D4×C13111yescharacteristic, complemented
433AGL(1,ℤ/8)—24no—
434AGL(1,ℤ/8)—42no—
435C2×SD16—41no—
436C2×D8—41no—
437C2×M16—21no—
438#127—21no—
439#127—21no—
440#127D4×C13112yescomplemented
441#127C23×C13112yes—
442#126—24no—
443#126—24no—
444#123—24no—
445#123—21no—
446#123—21no—
447#123—24no—
448#123—24no—
449#123—42no—
450#123D4×C13112yescomplemented
451#123C23×C13112yes—
452#121—24no—
453#121—24no—
454#121—24no—
455#121—24no—
456#121—24no—
457#121—24no—
458#120—24no—
459#120—24no—
460#120—21no—
461#120—21no—
462#120—24no—
463#120—42no—
464#120D4×C13112yes—
465#120C23×C13112yes—
466C2×C4⋊C4—21no—
467C2×C4⋊C4—21no—
468C2×C4⋊C4—21no—
469C2×C4⋊C4—41no—
470C2×C22⋊C4—21no—
471C2×C22⋊C4—21no—
472C2×C22⋊C4—21no—
473C2×C22⋊C4—21no—
474C2×C22⋊C4—21no—
475C2×C22⋊C4—21no—
476C2×C22⋊C4—21no—
477C2×C22⋊C4—41no—
478C2×C22⋊C4—41no—
479C2×C22⋊C4D4×C13111yescharacteristic
480C2×C22⋊C4D4×C13111yescharacteristic, complemented
481C2×C42D4×C13111yescharacteristic, complemented
482#104—24no—
483#100—21no—
484#100C23×C13112yes—
485#99—21no—
486#99—21no—
487#99—24no—
488#99—24no—
489#99C23×C13112yes—
490#99C23×C13112yes—
491C24—21no—
492C24—21no—
493C24—21no—
494C24—21no—
495C24—21no—
496C24—41no—
497C24—41no—
498C24—82no—
499C24C2×D4×C13111yescharacteristic
500C24C2×D4×C13111yescharacteristic
501C24C2×D4×C13112yes—
502#41—22no—
503#41—22no—
504#41—42no—
505#41—41no—
506#41—42no—
507#41—42no—
508#41—42no—
509#41—41no—
510C2×Q8—21no—
511C2×D4—21no—
512C2×D4—22no—
513C2×D4—22no—
514C2×D4—22no—
515C2×D4—22no—
516C2×D4—24no—
517C2×D4—24no—
518C2×D4—22no—
519C2×D4—22no—
520C2×D4—22no—
521C2×D4—22no—
522C2×D4—22no—
523C2×D4—22no—
524C2×D4—21no—
525C2×D4—41no—
526C2×D4—41no—
527C2×D4—41no—
528C2×D4—41no—
529C2×D4—42no—
530C2×D4—42no—
531C2×D4—41no—
532C2×D4—41no—
533C2×D4—41no—
534C2×D4—41no—
535C2×D4—42no—
536C2×D4—42no—
537C2×D4—41no—
538C2×D4—41no—
539C2×D4—41no—
540C2×D4—44no—
541C2×D4—82no—
542C2×D4—82no—
543C2×D4—82no—
544C2×D4—82no—
545C2×D4—81no—
546C2×D4—81no—
547C2×D4—84no—
548C2×D4C2×D4×C13111yescharacteristic
549C2×D4C2×D4×C13111yescharacteristic
550C2×D4C2×D4×C13111yescharacteristic
551C2×D4C2×D4×C13112yescomplemented
552C2×D4C24×C13111yescharacteristic
553C22×C4—21no—
554C22×C4—21no—
555C22×C4—21no—
556C22×C4—21no—
557C22×C4—21no—
558C22×C4—21no—
559C22×C4—24no—
560C22×C4—21no—
561C22×C4—41no—
562C22×C4—41no—
563C22×C4—41no—
564C22×C4—41no—
565C22×C4—41no—
566C22×C4—82no—
567C22×C4C2×D4×C13111yescharacteristic
568C22×C4C2×D4×C13112yescomplemented
569SD16—44no—
570D8—44no—
571M16—22no—
572M16—41no—
573C2×C8—41no—
574C4⋊C4—24no—
575C4⋊C4—24no—
576C4⋊C4—22no—
577C4⋊C4—22no—
578C4⋊C4—44no—
579C22⋊C4—24no—
580C22⋊C4—24no—
581C22⋊C4—24no—
582C22⋊C4—22no—
583C22⋊C4—21no—
584C22⋊C4—21no—
585C22⋊C4—22no—
586C22⋊C4—22no—
587C22⋊C4—22no—
588C22⋊C4—22no—
589C22⋊C4—22no—
590C22⋊C4—44no—
591C22⋊C4—41no—
592C22⋊C4—41no—
593C22⋊C4—44no—
594C22⋊C4C2×D4×C13112yes—
595C22⋊C4C2×D4×C13112yescomplemented
596C42—21no—
597C42C2×D4×C13112yescomplemented
598C23—21no—
599C23—21no—
600C23—21no—
601C23—21no—
602C23—22no—
603C23—22no—
604C23—22no—
605C23—22no—
606C23—42no—
607C23—42no—
608C23—42no—
609C23—42no—
610C23—42no—
611C23—42no—
612C23—42no—
613C23—41no—
614C23—41no—
615C23—44no—
616C23—41no—
617C23—41no—
618C23—41no—
619C23—41no—
620C23—41no—
621C23—81no—
622C23—82no—
623C23—82no—
624C23—82no—
625C23—84no—
626C23—82no—
627C23—82no—
628C23#120×C13111yescharacteristic
629C23#120×C13111yescharacteristic
630C23#120×C13111yescharacteristic
631C23C22×D4×C13111yescharacteristic
632C23C22×D4×C13111yescharacteristic
633Q8—22no—
634Q8—41no—
635D4—22no—
636D4—41no—
637D4—41no—
638D4—41no—
639D4—41no—
640D4—42no—
641D4—41no—
642D4—42no—
643D4—42no—
644D4—42no—
645D4—42no—
646D4—42no—
647D4—42no—
648D4—81no—
649D4—82no—
650D4—82no—
651D4—84no—
652D4—82no—
653D4—82no—
654D4—82no—
655D4—82no—
656D4—84no—
657D4—88no—
658C2×C4—21no—
659C2×C4—21no—
660C2×C4—22no—
661C2×C4—22no—
662C2×C4—22no—
663C2×C4—22no—
664C2×C4—22no—
665C2×C4—22no—
666C2×C4—42no—
667C2×C4—42no—
668C2×C4—42no—
669C2×C4—42no—
670C2×C4—41no—
671C2×C4—41no—
672C2×C4—42no—
673C2×C4—41no—
674C2×C4—41no—
675C2×C4—41no—
676C2×C4—42no—
677C2×C4—42no—
678C2×C4—42no—
679C2×C4—81no—
680C2×C4—84no—
681C2×C4—82no—
682C2×C4—82no—
683C2×C4#120×C13111yescharacteristic
684C2×C4C22×D4×C13111yescharacteristic
685C8—42no—
686C22—22no—
687C22—21no—
688C22—21no—
689C22—21no—
690C22—21no—
691C22—41no—
692C22—41no—
693C22—41no—
694C22—41no—
695C22—42no—
696C22—42no—
697C22—42no—
698C22—42no—
699C22—42no—
700C22—42no—
701C22—44no—
702C22—42no—
703C22—42no—
704C22—42no—
705C22—81no—
706C22—81no—
707C22—82no—
708C22—82no—
709C22—82no—
710C22—82no—
711C22—82no—
712C22—84no—
713C22—82no—
714C22—82no—
715C22—82no—
716C22—161no—
717C22—161no—
718C22B(4,𝔽2)×C13111yescharacteristic
719C22B(4,𝔽2)×C13111yescharacteristic
720C22C2×#120×C13111yescharacteristic
721C4—21no—
722C4—21no—
723C4—42no—
724C4—42no—
725C4—42no—
726C4—42no—
727C4—42no—
728C4—82no—
729C4—82no—
730C2—21no—
731C2—21no—
732C2—41no—
733C2—41no—
734C2—41no—
735C2—41no—
736C2—82no—
737C2—82no—
738C2—82no—
739C2#2200×C13112yesdirect product factor
740C2C2×B(4,𝔽2)×C13111yescharacteristic
subgroupG/H
center, socleC22×C131B(4,𝔽2)
commutator, Frattini, cosocleC2×D4C24×C131
LCSG ▷ C2×D4 ▷ C22 ▷ C2 ▷ C1
UCSC1 ◁ C22×C131 ◁ C23×C131 ◁ C22×D4×C131 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×#560×C131C2semidirect
2. C2×#458×C131C2semidirect
3. C2×B(4,𝔽2)×C131C2semidirect
4. C2×#453×C131C2semidirect
5. #2200×C131C2direct (N × H)
6. C2×#353×C131C2semidirect
7. C2×#352×C131C2semidirect
8. C2×AΣL(1,𝔽16)×C131C2semidirect
14. #560×C131C22semidirect
27. #458×C131C22semidirect
29. B(4,𝔽2)×C131C22semidirect
31. #453×C131C22semidirect
38. #353×C131C22semidirect
39. #352×C131C22semidirect
40. AΣL(1,𝔽16)×C131C22semidirect
58. C22×D4×C131D4semidirect
61. C23×C4×C131D4semidirect
69. #127×C131D4semidirect
79. #123×C131D4semidirect
109. C2×C22⋊C4×C131D4semidirect
110. C2×C42×C131D4semidirect
180. C2×D4×C131C2×D4semidirect
197. C22×C4×C131C2×D4semidirect
224. C22⋊C4×C131C2×D4semidirect
226. C42×C131C2×D4semidirect
368. C2×C131#2200direct (N × H)
370. C2×#2200C131direct (N × H)
371. C131C2×#2200direct (N × H)
372. C2×#560C2×C131semidirect
373. C2×#458C2×C131semidirect
374. C2×B(4,𝔽2)C2×C131semidirect
375. C2×#453C2×C131semidirect
376. #2200C2×C131direct (N × H)
377. C2×#353C2×C131semidirect
378. C2×#352C2×C131semidirect
379. C2×AΣL(1,𝔽16)C2×C131semidirect
385. #560C22×C131semidirect
398. #458C22×C131semidirect
400. B(4,𝔽2)C22×C131semidirect
402. #453C22×C131semidirect
409. #353C22×C131semidirect
410. #352C22×C131semidirect
411. AΣL(1,𝔽16)C22×C131semidirect
429. C22×D4D4×C131semidirect
432. C23×C4D4×C131semidirect
440. #127D4×C131semidirect
450. #123D4×C131semidirect
480. C2×C22⋊C4D4×C131semidirect
481. C2×C42D4×C131semidirect
551. C2×D4C2×D4×C131semidirect
568. C22×C4C2×D4×C131semidirect
595. C22⋊C4C2×D4×C131semidirect
597. C42C2×D4×C131semidirect
739. C2#2200×C131direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#560×C1312
C2×#458×C1312
C2×B(4,𝔽2)×C1312
C2×#453×C1312
#2200×C1312
C2×#353×C1312
C2×#352×C1312
C2×AΣL(1,𝔽16)×C1312
C2×#2200131