Finite Group Databasebeta

← C131×#23876 #45709760

Subgroups — C131×#23876 #45709760

Order 33536.

2012 conjugacy classes of subgroups.

The subgroup lattice has 938 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×AGL(1,ℤ/8)×C131C211yesmaximal, characteristic, complemented
2#3488×C131C211yesmaximal, characteristic, complemented
3C2×#453×C131C212yesmaximal, complemented
4#3003×C131C211yesmaximal, characteristic, complemented
5#2433×C131C211yesmaximal, characteristic, complemented
6#2006×C131C212yesmaximal, complemented
7#2002×C131C212yesmaximal, complemented
8#1900×C131C211yesmaximal, characteristic, complemented
9#1883×C131C212yesmaximal, complemented
10#1871×C131C211yesmaximal, characteristic, complemented
11#1789×C131C211yesmaximal, characteristic, complemented
12C2×H(5,𝔽2)×C131C2211yescharacteristic, complemented
13C22×#41×C131C2211yescharacteristic
14C23×D4×C131C2211yescharacteristic, complemented
15C2×AGL(1,ℤ/8)×C131—21no—
16C2×AGL(1,ℤ/8)×C131—21no—
17C2×AGL(1,ℤ/8)×C131—28no—
18C2×AGL(1,ℤ/8)×C131C2212yes—
19C2×AGL(1,ℤ/8)×C131C2212yescomplemented
20C2×AGL(1,ℤ/8)×C131C2212yescomplemented
21C22×SD16×C131—21no—
22C22×D8×C131—21no—
23C22×M16×C131C2211yescharacteristic, complemented
24#550×C131—21no—
25#548×C131—21no—
26#546×C131—21no—
27#546×C131—22no—
28D42×C131—22no—
29D42×C131—21no—
30#537×C131—21no—
31#537×C131C2211yescharacteristic, complemented
32#535×C131—21no—
33#535×C131C2211yescharacteristic, complemented
34C2×#127×C131C2212yescomplemented
35#525×C131—21no—
36#525×C131C2211yescharacteristic
37C2×#121×C131—21no—
38C2×#121×C131C2211yescharacteristic
39C2×#120×C131—22no—
40#520×C131C2211yescharacteristic, complemented
41#453×C131—28no—
42#450×C131—21no—
43#450×C131—21no—
44#447×C131—21no—
45#447×C131—21no—
46C2×#104×C131C2212yescomplemented
47C2×#104×C131C2212yescomplemented
48C2×#104×C131C2212yescomplemented
49#418×C131C2212yescomplemented
50C2×#100×C131C2212yescomplemented
51#407×C131C2211yescharacteristic, complemented
52#392×C131—22no—
53#390×C131C2212yescomplemented
54C4×C22⋊C4×C131C2211yescharacteristic, complemented
55#343×C131C2212yescomplemented
56#339×C131C2212yescomplemented
57C25×C131—21no—
58H(5,𝔽2)×C131—24no—
59H(5,𝔽2)×C131—42no—
60C2×#41×C131—21no—
61C2×#41×C131—21no—
62C2×#41×C131—21no—
63C2×#41×C131—21no—
64C2×#41×C131—24no—
65C2×#41×C131—42no—
66C2×#41×C131D411yescharacteristic, complemented
67C2×#41×C131D411yescharacteristic, complemented
68C2×#41×C131C2311yescharacteristic
69C2×#41×C131C2311yescharacteristic
70C2×#41×C131C2311yescharacteristic
71C22×Q8×C131D411yescharacteristic, complemented
72C22×D4×C131—24no—
73C22×D4×C131—21no—
74C22×D4×C131—22no—
75C22×D4×C131—22no—
76C22×D4×C131—21no—
77C22×D4×C131—21no—
78C22×D4×C131—24no—
79C22×D4×C131—21no—
80C22×D4×C131—21no—
81C22×D4×C131—21no—
82C22×D4×C131—21no—
83C22×D4×C131—21no—
84C22×D4×C131—42no—
85C22×D4×C131D412yes—
86C22×D4×C131D411yescharacteristic, complemented
87C22×D4×C131C2311yescharacteristic
88C22×D4×C131C2312yes—
89C23×C4×C131—21no—
90C23×C4×C131C2311yescharacteristic
91AGL(1,ℤ/8)×C131—28no—
92AGL(1,ℤ/8)×C131—28no—
93AGL(1,ℤ/8)×C131—24no—
94AGL(1,ℤ/8)×C131—24no—
95AGL(1,ℤ/8)×C131—24no—
96AGL(1,ℤ/8)×C131—24no—
97AGL(1,ℤ/8)×C131—42no—
98AGL(1,ℤ/8)×C131D418yescomplemented
99C2×SD16×C131—28no—
100C2×SD16×C131—22no—
101C2×SD16×C131—22no—
102C2×SD16×C131—22no—
103C2×D8×C131—28no—
104C2×D8×C131—22no—
105C2×D8×C131—22no—
106C2×D8×C131—22no—
107C2×M16×C131—21no—
108C2×M16×C131—24no—
109C2×M16×C131C2312yes—
110C2×M16×C131C2312yes—
111C22×C8×C131—21no—
112#127×C131—22no—
113#127×C131—21no—
114#127×C131—24no—
115#127×C131—42no—
116#124×C131—22no—
117#124×C131—21no—
118#123×C131—22no—
119#123×C131—21no—
120C22⋊Q8×C131—22no—
121C22⋊Q8×C131—21no—
122C22⋊Q8×C131—21no—
123C22⋊Q8×C131D411yescharacteristic, complemented
124C22⋊Q8×C131D411yescharacteristic, complemented
125#121×C131—22no—
126#121×C131—22no—
127#121×C131—22no—
128#121×C131—22no—
129#121×C131—22no—
130#121×C131—21no—
131#121×C131—21no—
132#121×C131—21no—
133#121×C131—21no—
134#121×C131—21no—
135#121×C131—21no—
136#121×C131—22no—
137#121×C131—21no—
138#121×C131—21no—
139#121×C131D411yescharacteristic, complemented
140#121×C131D411yescharacteristic, complemented
141#120×C131—22no—
142#120×C131—22no—
143#120×C131—22no—
144#120×C131—21no—
145#120×C131—22no—
146#120×C131—48no—
147C4×Q8×C131—21no—
148C4×D4×C131—22no—
149C4×D4×C131—22no—
150C4×D4×C131—21no—
151C4×D4×C131—22no—
152C4×D4×C131—21no—
153C4×D4×C131—21no—
154#117×C131—21no—
155#117×C131C2311yescharacteristic
156C2×C4⋊C4×C131—21no—
157C2×C4⋊C4×C131C2311yescharacteristic
158C2×C22⋊C4×C131—22no—
159C2×C22⋊C4×C131—21no—
160C2×C22⋊C4×C131—24no—
161C2×C22⋊C4×C131D412yes—
162C2×C42×C131C2312yes—
163#104×C131—24no—
164#104×C131—24no—
165#104×C131—42no—
166#102×C131—22no—
167#102×C131—22no—
168#100×C131—24no—
169C22⋊C8×C131—21no—
170C22⋊C8×C131—21no—
171#95×C131—21no—
172C24×C131—22no—
173C24×C131—22no—
174C24×C131—21no—
175C24×C131—44no—
176C24×C131—44no—
177C24×C131—41no—
178C24×C131—41no—
179C24×C131—82no—
180C24×C131C2×D411yescharacteristic
181C24×C131C2×D412yes—
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—44no—
190#41×C131—41no—
191#41×C131—41no—
192#41×C131—44no—
193#41×C131—44no—
194#41×C131—42no—
195#41×C131—42no—
196#41×C131C2×D414yes—
197C2×Q8×C131—21no—
198C2×Q8×C131—22no—
199C2×Q8×C131—41no—
200C2×Q8×C131C2×D411yescharacteristic
201C2×Q8×C131C2×D411yescharacteristic
202C2×Q8×C131C2×D411yescharacteristic
203C2×D4×C131—21no—
204C2×D4×C131—24no—
205C2×D4×C131—24no—
206C2×D4×C131—22no—
207C2×D4×C131—22no—
208C2×D4×C131—22no—
209C2×D4×C131—22no—
210C2×D4×C131—21no—
211C2×D4×C131—21no—
212C2×D4×C131—21no—
213C2×D4×C131—21no—
214C2×D4×C131—21no—
215C2×D4×C131—22no—
216C2×D4×C131—22no—
217C2×D4×C131—22no—
218C2×D4×C131—21no—
219C2×D4×C131—22no—
220C2×D4×C131—21no—
221C2×D4×C131—22no—
222C2×D4×C131—22no—
223C2×D4×C131—22no—
224C2×D4×C131—22no—
225C2×D4×C131—21no—
226C2×D4×C131—21no—
227C2×D4×C131—22no—
228C2×D4×C131—22no—
229C2×D4×C131—22no—
230C2×D4×C131—41no—
231C2×D4×C131—44no—
232C2×D4×C131—44no—
233C2×D4×C131—44no—
234C2×D4×C131—44no—
235C2×D4×C131—42no—
236C2×D4×C131—42no—
237C2×D4×C131—48no—
238C2×D4×C131—44no—
239C2×D4×C131—48no—
240C2×D4×C131—42no—
241C2×D4×C131—42no—
242C2×D4×C131—44no—
243C2×D4×C131—48no—
244C2×D4×C131—41no—
245C2×D4×C131—41no—
246C2×D4×C131—84no—
247C2×D4×C131—84no—
248C2×D4×C131C2×D411yescharacteristic
249C2×D4×C131C2×D411yescharacteristic
250C2×D4×C131C2×D411yescharacteristic
251C2×D4×C131C2×D414yescomplemented
252C22×C4×C131—21no—
253C22×C4×C131—22no—
254C22×C4×C131—22no—
255C22×C4×C131—22no—
256C22×C4×C131—21no—
257C22×C4×C131—22no—
258C22×C4×C131—22no—
259C22×C4×C131—21no—
260C22×C4×C131—21no—
261C22×C4×C131—21no—
262C22×C4×C131—21no—
263C22×C4×C131—44no—
264C22×C4×C131C2×D411yescharacteristic
265C22×C4×C131C2×D411yescharacteristic
266C22×C4×C131C2×D411yescharacteristic
267C22×C4×C131C2×D411yescharacteristic
268C22×C4×C131C2×D411yescharacteristic
269C22×C4×C131C2×D412yes—
270C22×C4×C131C2411yescharacteristic
271SD16×C131—28no—
272SD16×C131—28no—
273SD16×C131—44no—
274D8×C131—28no—
275D8×C131—28no—
276D8×C131—44no—
277M16×C131—24no—
278M16×C131—22no—
279M16×C131—22no—
280M16×C131—22no—
281M16×C131C2×D414yescomplemented
282C2×C8×C131—24no—
283C2×C8×C131—22no—
284C2×C8×C131—22no—
285C4⋊C4×C131—22no—
286C4⋊C4×C131—22no—
287C4⋊C4×C131—21no—
288C4⋊C4×C131—21no—
289C4⋊C4×C131—21no—
290C4⋊C4×C131—21no—
291C4⋊C4×C131C2×D411yescharacteristic
292C4⋊C4×C131C2×D411yescharacteristic
293C22⋊C4×C131—22no—
294C22⋊C4×C131—22no—
295C22⋊C4×C131—24no—
296C22⋊C4×C131—22no—
297C22⋊C4×C131—22no—
298C22⋊C4×C131—22no—
299C22⋊C4×C131—21no—
300C22⋊C4×C131—21no—
301C22⋊C4×C131—21no—
302C22⋊C4×C131—21no—
303C22⋊C4×C131—22no—
304C22⋊C4×C131—22no—
305C22⋊C4×C131—21no—
306C22⋊C4×C131—48no—
307C42×C131—22no—
308C42×C131—21no—
309C42×C131—22no—
310C42×C131—22no—
311C23×C131—21no—
312C23×C131—22no—
313C23×C131—22no—
314C23×C131—22no—
315C23×C131—21no—
316C23×C131—21no—
317C23×C131—24no—
318C23×C131—24no—
319C23×C131—41no—
320C23×C131—42no—
321C23×C131—44no—
322C23×C131—44no—
323C23×C131—44no—
324C23×C131—44no—
325C23×C131—44no—
326C23×C131—42no—
327C23×C131—42no—
328C23×C131—42no—
329C23×C131—42no—
330C23×C131—42no—
331C23×C131—81no—
332C23×C131—82no—
333C23×C131—82no—
334C23×C131—82no—
335C23×C131—82no—
336C23×C131—82no—
337C23×C131—816no—
338C23×C131—82no—
339C23×C131#12011yescharacteristic
340C23×C131#12011yescharacteristic
341C23×C131C22×D411yescharacteristic
342Q8×C131—21no—
343Q8×C131—21no—
344Q8×C131—21no—
345Q8×C131—22no—
346Q8×C131—42no—
347Q8×C131#12012yescomplemented
348D4×C131—24no—
349D4×C131—21no—
350D4×C131—24no—
351D4×C131—21no—
352D4×C131—21no—
353D4×C131—22no—
354D4×C131—24no—
355D4×C131—42no—
356D4×C131—42no—
357D4×C131—44no—
358D4×C131—44no—
359D4×C131—44no—
360D4×C131—42no—
361D4×C131—44no—
362D4×C131—42no—
363D4×C131—42no—
364D4×C131—44no—
365D4×C131—42no—
366D4×C131—41no—
367D4×C131—42no—
368D4×C131—41no—
369D4×C131—42no—
370D4×C131—42no—
371D4×C131—81no—
372D4×C131—82no—
373D4×C131—82no—
374D4×C131—82no—
375D4×C131—82no—
376D4×C131—816no—
377D4×C131#12012yescomplemented
378C2×C4×C131—21no—
379C2×C4×C131—22no—
380C2×C4×C131—21no—
381C2×C4×C131—21no—
382C2×C4×C131—21no—
383C2×C4×C131—21no—
384C2×C4×C131—22no—
385C2×C4×C131—22no—
386C2×C4×C131—24no—
387C2×C4×C131—24no—
388C2×C4×C131—21no—
389C2×C4×C131—22no—
390C2×C4×C131—21no—
391C2×C4×C131—21no—
392C2×C4×C131—21no—
393C2×C4×C131—42no—
394C2×C4×C131—42no—
395C2×C4×C131—42no—
396C2×C4×C131—44no—
397C2×C4×C131—42no—
398C2×C4×C131—42no—
399C2×C4×C131—41no—
400C2×C4×C131—41no—
401C2×C4×C131—42no—
402C2×C4×C131—42no—
403C2×C4×C131—82no—
404C2×C4×C131#12011yescharacteristic
405C2×C4×C131#12011yescharacteristic
406C2×C4×C131C22×D411yescharacteristic
407C2×C4×C131C22×D412yes—
408C2×C4×C131C22×D411yescharacteristic
409C2×C4×C131H(5,𝔽2)12yes—
410C8×C131—24no—
411C8×C131—42no—
412C22×C131—21no—
413C22×C131—21no—
414C22×C131—21no—
415C22×C131—21no—
416C22×C131—21no—
417C22×C131—22no—
418C22×C131—21no—
419C22×C131—21no—
420C22×C131—44no—
421C22×C131—48no—
422C22×C131—41no—
423C22×C131—41no—
424C22×C131—41no—
425C22×C131—41no—
426C22×C131—42no—
427C22×C131—44no—
428C22×C131—42no—
429C22×C131—41no—
430C22×C131—41no—
431C22×C131—41no—
432C22×C131—42no—
433C22×C131—41no—
434C22×C131—84no—
435C22×C131—84no—
436C22×C131—84no—
437C22×C131—88no—
438C22×C131—88no—
439C22×C131—82no—
440C22×C131—82no—
441C22×C131—164no—
442C22×C131#45312yescomplemented
443C22×C131C2×#12011yescharacteristic
444C22×C131D4212yes—
445C4×C131—21no—
446C4×C131—21no—
447C4×C131—22no—
448C4×C131—44no—
449C4×C131—41no—
450C4×C131—41no—
451C4×C131—42no—
452C4×C131—41no—
453C4×C131—41no—
454C4×C131C2×#12011yescharacteristic
455C4×C131#53411yescharacteristic
456C4×C131D4212yes—
457C2×C131—22no—
458C2×C131—22no—
459C2×C131—41no—
460C2×C131—42no—
461C2×C131—81no—
462C2×C131—84no—
463C2×C131—82no—
464C2×C131—81no—
465C2×C131#240311yescharacteristic
466C2×C131C2×#45311yescharacteristic
467C2×C131#302111yescharacteristic
468#23876C13111yesmaximal, characteristic, direct product factor, Sylow
469C131#2387611yescharacteristic, direct product factor, Sylow
470C22×AGL(1,ℤ/8)C2×C13111yescharacteristic, complemented
471#3488C2×C13111yescharacteristic, complemented
472C2×#453C2×C13112yescomplemented
473#3003C2×C13111yescharacteristic, complemented
474#2433C2×C13111yescharacteristic, complemented
475#2006C2×C13112yescomplemented
476#2002C2×C13112yescomplemented
477#1900C2×C13111yescharacteristic, complemented
478#1883C2×C13112yescomplemented
479#1871C2×C13111yescharacteristic, complemented
480#1789C2×C13111yescharacteristic, complemented
481C2×H(5,𝔽2)C22×C13111yescharacteristic, complemented
482C22×#41C22×C13111yescharacteristic
483C23×D4C22×C13111yescharacteristic, complemented
484C2×AGL(1,ℤ/8)—21no—
485C2×AGL(1,ℤ/8)—21no—
486C2×AGL(1,ℤ/8)—28no—
487C2×AGL(1,ℤ/8)C22×C13112yes—
488C2×AGL(1,ℤ/8)C22×C13112yescomplemented
489C2×AGL(1,ℤ/8)C22×C13112yescomplemented
490C22×SD16—21no—
491C22×D8—21no—
492C22×M16C22×C13111yescharacteristic, complemented
493#550—21no—
494#548—21no—
495#546—21no—
496#546—22no—
497D42—22no—
498D42—21no—
499#537—21no—
500#537C22×C13111yescharacteristic, complemented
501#535—21no—
502#535C22×C13111yescharacteristic, complemented
503C2×#127C22×C13112yescomplemented
504#525—21no—
505#525C22×C13111yescharacteristic
506C2×#121—21no—
507C2×#121C22×C13111yescharacteristic
508C2×#120—22no—
509#520C22×C13111yescharacteristic, complemented
510#453—28no—
511#450—21no—
512#450—21no—
513#447—21no—
514#447—21no—
515C2×#104C22×C13112yescomplemented
516C2×#104C22×C13112yescomplemented
517C2×#104C22×C13112yescomplemented
518#418C22×C13112yescomplemented
519C2×#100C22×C13112yescomplemented
520#407C22×C13111yescharacteristic, complemented
521#392—22no—
522#390C22×C13112yescomplemented
523C4×C22⋊C4C22×C13111yescharacteristic, complemented
524#343C22×C13112yescomplemented
525#339C22×C13112yescomplemented
526C25—21no—
527H(5,𝔽2)—24no—
528H(5,𝔽2)—42no—
529C2×#41—21no—
530C2×#41—21no—
531C2×#41—21no—
532C2×#41—21no—
533C2×#41—24no—
534C2×#41—42no—
535C2×#41D4×C13111yescharacteristic, complemented
536C2×#41D4×C13111yescharacteristic, complemented
537C2×#41C23×C13111yescharacteristic
538C2×#41C23×C13111yescharacteristic
539C2×#41C23×C13111yescharacteristic
540C22×Q8D4×C13111yescharacteristic, complemented
541C22×D4—24no—
542C22×D4—21no—
543C22×D4—22no—
544C22×D4—22no—
545C22×D4—21no—
546C22×D4—21no—
547C22×D4—24no—
548C22×D4—21no—
549C22×D4—21no—
550C22×D4—21no—
551C22×D4—21no—
552C22×D4—21no—
553C22×D4—42no—
554C22×D4D4×C13112yes—
555C22×D4D4×C13111yescharacteristic, complemented
556C22×D4C23×C13111yescharacteristic
557C22×D4C23×C13112yes—
558C23×C4—21no—
559C23×C4C23×C13111yescharacteristic
560AGL(1,ℤ/8)—28no—
561AGL(1,ℤ/8)—28no—
562AGL(1,ℤ/8)—24no—
563AGL(1,ℤ/8)—24no—
564AGL(1,ℤ/8)—24no—
565AGL(1,ℤ/8)—24no—
566AGL(1,ℤ/8)—42no—
567AGL(1,ℤ/8)D4×C13118yescomplemented
568C2×SD16—28no—
569C2×SD16—22no—
570C2×SD16—22no—
571C2×SD16—22no—
572C2×D8—28no—
573C2×D8—22no—
574C2×D8—22no—
575C2×D8—22no—
576C2×M16—21no—
577C2×M16—24no—
578C2×M16C23×C13112yes—
579C2×M16C23×C13112yes—
580C22×C8—21no—
581#127—22no—
582#127—21no—
583#127—24no—
584#127—42no—
585#124—22no—
586#124—21no—
587#123—22no—
588#123—21no—
589C22⋊Q8—22no—
590C22⋊Q8—21no—
591C22⋊Q8—21no—
592C22⋊Q8D4×C13111yescharacteristic, complemented
593C22⋊Q8D4×C13111yescharacteristic, complemented
594#121—22no—
595#121—22no—
596#121—22no—
597#121—22no—
598#121—22no—
599#121—21no—
600#121—21no—
601#121—21no—
602#121—21no—
603#121—21no—
604#121—21no—
605#121—22no—
606#121—21no—
607#121—21no—
608#121D4×C13111yescharacteristic, complemented
609#121D4×C13111yescharacteristic, complemented
610#120—22no—
611#120—22no—
612#120—22no—
613#120—21no—
614#120—22no—
615#120—48no—
616C4×Q8—21no—
617C4×D4—22no—
618C4×D4—22no—
619C4×D4—21no—
620C4×D4—22no—
621C4×D4—21no—
622C4×D4—21no—
623#117—21no—
624#117C23×C13111yescharacteristic
625C2×C4⋊C4—21no—
626C2×C4⋊C4C23×C13111yescharacteristic
627C2×C22⋊C4—22no—
628C2×C22⋊C4—21no—
629C2×C22⋊C4—24no—
630C2×C22⋊C4D4×C13112yes—
631C2×C42C23×C13112yes—
632#104—24no—
633#104—24no—
634#104—42no—
635#102—22no—
636#102—22no—
637#100—24no—
638C22⋊C8—21no—
639C22⋊C8—21no—
640#95—21no—
641C24—22no—
642C24—22no—
643C24—21no—
644C24—44no—
645C24—44no—
646C24—41no—
647C24—41no—
648C24—82no—
649C24C2×D4×C13111yescharacteristic
650C24C2×D4×C13112yes—
651#41—22no—
652#41—22no—
653#41—22no—
654#41—22no—
655#41—22no—
656#41—22no—
657#41—22no—
658#41—44no—
659#41—41no—
660#41—41no—
661#41—44no—
662#41—44no—
663#41—42no—
664#41—42no—
665#41C2×D4×C13114yes—
666C2×Q8—21no—
667C2×Q8—22no—
668C2×Q8—41no—
669C2×Q8C2×D4×C13111yescharacteristic
670C2×Q8C2×D4×C13111yescharacteristic
671C2×Q8C2×D4×C13111yescharacteristic
672C2×D4—21no—
673C2×D4—24no—
674C2×D4—24no—
675C2×D4—22no—
676C2×D4—22no—
677C2×D4—22no—
678C2×D4—22no—
679C2×D4—21no—
680C2×D4—21no—
681C2×D4—21no—
682C2×D4—21no—
683C2×D4—21no—
684C2×D4—22no—
685C2×D4—22no—
686C2×D4—22no—
687C2×D4—21no—
688C2×D4—22no—
689C2×D4—21no—
690C2×D4—22no—
691C2×D4—22no—
692C2×D4—22no—
693C2×D4—22no—
694C2×D4—21no—
695C2×D4—21no—
696C2×D4—22no—
697C2×D4—22no—
698C2×D4—22no—
699C2×D4—41no—
700C2×D4—44no—
701C2×D4—44no—
702C2×D4—44no—
703C2×D4—44no—
704C2×D4—42no—
705C2×D4—42no—
706C2×D4—48no—
707C2×D4—44no—
708C2×D4—48no—
709C2×D4—42no—
710C2×D4—42no—
711C2×D4—44no—
712C2×D4—48no—
713C2×D4—41no—
714C2×D4—41no—
715C2×D4—84no—
716C2×D4—84no—
717C2×D4C2×D4×C13111yescharacteristic
718C2×D4C2×D4×C13111yescharacteristic
719C2×D4C2×D4×C13111yescharacteristic
720C2×D4C2×D4×C13114yescomplemented
721C22×C4—21no—
722C22×C4—22no—
723C22×C4—22no—
724C22×C4—22no—
725C22×C4—21no—
726C22×C4—22no—
727C22×C4—22no—
728C22×C4—21no—
729C22×C4—21no—
730C22×C4—21no—
731C22×C4—21no—
732C22×C4—44no—
733C22×C4C2×D4×C13111yescharacteristic
734C22×C4C2×D4×C13111yescharacteristic
735C22×C4C2×D4×C13111yescharacteristic
736C22×C4C2×D4×C13111yescharacteristic
737C22×C4C2×D4×C13111yescharacteristic
738C22×C4C2×D4×C13112yes—
739C22×C4C24×C13111yescharacteristic
740SD16—28no—
741SD16—28no—
742SD16—44no—
743D8—28no—
744D8—28no—
745D8—44no—
746M16—24no—
747M16—22no—
748M16—22no—
749M16—22no—
750M16C2×D4×C13114yescomplemented
751C2×C8—24no—
752C2×C8—22no—
753C2×C8—22no—
754C4⋊C4—22no—
755C4⋊C4—22no—
756C4⋊C4—21no—
757C4⋊C4—21no—
758C4⋊C4—21no—
759C4⋊C4—21no—
760C4⋊C4C2×D4×C13111yescharacteristic
761C4⋊C4C2×D4×C13111yescharacteristic
762C22⋊C4—22no—
763C22⋊C4—22no—
764C22⋊C4—24no—
765C22⋊C4—22no—
766C22⋊C4—22no—
767C22⋊C4—22no—
768C22⋊C4—21no—
769C22⋊C4—21no—
770C22⋊C4—21no—
771C22⋊C4—21no—
772C22⋊C4—22no—
773C22⋊C4—22no—
774C22⋊C4—21no—
775C22⋊C4—48no—
776C42—22no—
777C42—21no—
778C42—22no—
779C42—22no—
780C23—22no—
781C23—21no—
782C23—22no—
783C23—22no—
784C23—21no—
785C23—21no—
786C23—24no—
787C23—24no—
788C23—41no—
789C23—42no—
790C23—44no—
791C23—44no—
792C23—44no—
793C23—44no—
794C23—44no—
795C23—42no—
796C23—42no—
797C23—42no—
798C23—42no—
799C23—42no—
800C23—81no—
801C23—82no—
802C23—82no—
803C23—82no—
804C23—82no—
805C23—82no—
806C23—816no—
807C23—82no—
808C23#120×C13111yescharacteristic
809C23#120×C13111yescharacteristic
810C23C22×D4×C13111yescharacteristic
811Q8—21no—
812Q8—21no—
813Q8—21no—
814Q8—22no—
815Q8—42no—
816Q8#120×C13112yescomplemented
817D4—24no—
818D4—21no—
819D4—24no—
820D4—21no—
821D4—21no—
822D4—22no—
823D4—24no—
824D4—42no—
825D4—42no—
826D4—44no—
827D4—44no—
828D4—44no—
829D4—42no—
830D4—44no—
831D4—44no—
832D4—42no—
833D4—42no—
834D4—42no—
835D4—41no—
836D4—42no—
837D4—41no—
838D4—42no—
839D4—42no—
840D4—82no—
841D4—81no—
842D4—82no—
843D4—82no—
844D4—82no—
845D4—816no—
846D4#120×C13112yescomplemented
847C2×C4—21no—
848C2×C4—22no—
849C2×C4—21no—
850C2×C4—21no—
851C2×C4—21no—
852C2×C4—21no—
853C2×C4—22no—
854C2×C4—22no—
855C2×C4—24no—
856C2×C4—24no—
857C2×C4—21no—
858C2×C4—22no—
859C2×C4—21no—
860C2×C4—21no—
861C2×C4—21no—
862C2×C4—42no—
863C2×C4—42no—
864C2×C4—42no—
865C2×C4—44no—
866C2×C4—42no—
867C2×C4—42no—
868C2×C4—41no—
869C2×C4—41no—
870C2×C4—42no—
871C2×C4—42no—
872C2×C4—82no—
873C2×C4#120×C13111yescharacteristic
874C2×C4#120×C13111yescharacteristic
875C2×C4C22×D4×C13111yescharacteristic
876C2×C4C22×D4×C13112yes—
877C2×C4C22×D4×C13111yescharacteristic
878C2×C4H(5,𝔽2)×C13112yes—
879C8—24no—
880C8—42no—
881C22—21no—
882C22—21no—
883C22—21no—
884C22—21no—
885C22—21no—
886C22—21no—
887C22—21no—
888C22—22no—
889C22—44no—
890C22—48no—
891C22—41no—
892C22—41no—
893C22—42no—
894C22—41no—
895C22—41no—
896C22—41no—
897C22—42no—
898C22—41no—
899C22—41no—
900C22—41no—
901C22—42no—
902C22—44no—
903C22—84no—
904C22—84no—
905C22—84no—
906C22—88no—
907C22—88no—
908C22—82no—
909C22—82no—
910C22—164no—
911C22#453×C13112yescomplemented
912C22C2×#120×C13111yescharacteristic
913C22D42×C13112yes—
914C4—21no—
915C4—21no—
916C4—22no—
917C4—44no—
918C4—42no—
919C4—41no—
920C4—41no—
921C4—41no—
922C4—41no—
923C4C2×#120×C13111yescharacteristic
924C4#534×C13111yescharacteristic
925C4D42×C13112yes—
926C2—22no—
927C2—22no—
928C2—41no—
929C2—42no—
930C2—84no—
931C2—81no—
932C2—82no—
933C2—81no—
934C2#2403×C13111yescharacteristic
935C2C2×#453×C13111yescharacteristic
936C2#3021×C13111yescharacteristic
subgroupG/H
center, socleC22×C131C2×#120
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. C22×AGL(1,ℤ/8)×C131C2semidirect
2. #3488×C131C2semidirect
3. C2×#453×C131C2semidirect
4. #3003×C131C2semidirect
5. #2433×C131C2semidirect
6. #2006×C131C2semidirect
7. #2002×C131C2semidirect
8. #1900×C131C2semidirect
9. #1883×C131C2semidirect
10. #1871×C131C2semidirect
11. #1789×C131C2semidirect
12. C2×H(5,𝔽2)×C131C22semidirect
14. C23×D4×C131C22semidirect
19. C2×AGL(1,ℤ/8)×C131C22semidirect
20. C2×AGL(1,ℤ/8)×C131C22semidirect
23. C22×M16×C131C22semidirect
31. #537×C131C22semidirect
33. #535×C131C22semidirect
34. C2×#127×C131C22semidirect
40. #520×C131C22semidirect
46. C2×#104×C131C22semidirect
47. C2×#104×C131C22semidirect
48. C2×#104×C131C22semidirect
49. #418×C131C22semidirect
50. C2×#100×C131C22semidirect
51. #407×C131C22semidirect
53. #390×C131C22semidirect
54. C4×C22⋊C4×C131C22semidirect
55. #343×C131C22semidirect
56. #339×C131C22semidirect
66. C2×#41×C131D4semidirect
67. C2×#41×C131D4semidirect
71. C22×Q8×C131D4semidirect
86. C22×D4×C131D4semidirect
98. AGL(1,ℤ/8)×C131D4semidirect
123. C22⋊Q8×C131D4semidirect
124. C22⋊Q8×C131D4semidirect
139. #121×C131D4semidirect
140. #121×C131D4semidirect
251. C2×D4×C131C2×D4semidirect
281. M16×C131C2×D4semidirect
347. Q8×C131#120semidirect
377. D4×C131#120semidirect
442. C22×C131#453semidirect
468. #23876C131direct (N × H)
469. C131#23876direct (N × H)
470. C22×AGL(1,ℤ/8)C2×C131semidirect
471. #3488C2×C131semidirect
472. C2×#453C2×C131semidirect
473. #3003C2×C131semidirect
474. #2433C2×C131semidirect
475. #2006C2×C131semidirect
476. #2002C2×C131semidirect
477. #1900C2×C131semidirect
478. #1883C2×C131semidirect
479. #1871C2×C131semidirect
480. #1789C2×C131semidirect
481. C2×H(5,𝔽2)C22×C131semidirect
483. C23×D4C22×C131semidirect
488. C2×AGL(1,ℤ/8)C22×C131semidirect
489. C2×AGL(1,ℤ/8)C22×C131semidirect
492. C22×M16C22×C131semidirect
500. #537C22×C131semidirect
502. #535C22×C131semidirect
503. C2×#127C22×C131semidirect
509. #520C22×C131semidirect
515. C2×#104C22×C131semidirect
516. C2×#104C22×C131semidirect
517. C2×#104C22×C131semidirect
518. #418C22×C131semidirect
519. C2×#100C22×C131semidirect
520. #407C22×C131semidirect
522. #390C22×C131semidirect
523. C4×C22⋊C4C22×C131semidirect
524. #343C22×C131semidirect
525. #339C22×C131semidirect
535. C2×#41D4×C131semidirect
536. C2×#41D4×C131semidirect
540. C22×Q8D4×C131semidirect
555. C22×D4D4×C131semidirect
567. AGL(1,ℤ/8)D4×C131semidirect
592. C22⋊Q8D4×C131semidirect
593. C22⋊Q8D4×C131semidirect
608. #121D4×C131semidirect
609. #121D4×C131semidirect
720. C2×D4C2×D4×C131semidirect
750. M16C2×D4×C131semidirect
816. Q8#120×C131semidirect
846. D4#120×C131semidirect
911. C22#453×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
#3488×C1312
C2×#453×C1312
#3003×C1312
#2433×C1312
#2006×C1312
#2002×C1312
#1900×C1312
#1883×C1312
#1871×C1312
#1789×C1312
#23876131