Finite Group Databasebeta

← C131×#24472 #45710356

Subgroups — C131×#24472 #45710356

Order 33536.

1372 conjugacy classes of subgroups.

The subgroup lattice has 912 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#3585×C131C211yesmaximal, characteristic, complemented
2#3068×C131C211yesmaximal, characteristic, complemented
3#3038×C131C211yesmaximal, characteristic, complemented
4#3021×C131C211yesmaximal, characteristic, complemented
5C2×#453×C131C211yesmaximal, characteristic, complemented
6#2901×C131C211yesmaximal, characteristic, complemented
7#2050×C131C211yesmaximal, characteristic, complemented
8#2048×C131C211yesmaximal, characteristic, complemented
9#2008×C131C211yesmaximal, characteristic, complemented
10#2002×C131C211yesmaximal, characteristic, complemented
11#1906×C131C211yesmaximal, characteristic, complemented
12#1903×C131C211yesmaximal, characteristic, complemented
13#1903×C131C211yesmaximal, characteristic, complemented
14#1861×C131C211yesmaximal, characteristic, complemented
15#1795×C131C211yesmaximal, characteristic, complemented
16#585×C131C2211yescharacteristic
17C2×H(5,𝔽2)×C131C2211yescharacteristic
18#577×C131—22no—
19#577×C131—22no—
20#576×C131—22no—
21#576×C131—22no—
22#575×C131—22no—
23#575×C131C2211yescharacteristic
24#575×C131C2211yescharacteristic
25C2×AGL(1,ℤ/8)×C131—22no—
26C2×AGL(1,ℤ/8)×C131C2211yescharacteristic
27C2×AGL(1,ℤ/8)×C131C2211yescharacteristic
28C2×AGL(1,ℤ/8)×C131C2211yescharacteristic
29C2×AGL(1,ℤ/8)×C131C2211yescharacteristic, complemented
30C2×AGL(1,ℤ/8)×C131C2211yescharacteristic, complemented
31#568×C131C2211yescharacteristic
32#568×C131C2211yescharacteristic, complemented
33#535×C131C2211yescharacteristic, complemented
34C2×#127×C131C2211yescharacteristic, complemented
35C4×#41×C131C2211yescharacteristic, complemented
36#472×C131—22no—
37#471×C131—22no—
38#460×C131—22no—
39#459×C131—22no—
40#454×C131—22no—
41#453×C131—22no—
42#453×C131—22no—
43#453×C131—22no—
44#430×C131C2211yescharacteristic, complemented
45#423×C131C2211yescharacteristic, complemented
46#421×C131—22no—
47#421×C131C2211yescharacteristic
48#421×C131C2211yescharacteristic
49#421×C131C2211yescharacteristic, complemented
50#421×C131C2211yescharacteristic, complemented
51C2×#104×C131—22no—
52C2×#104×C131C2211yescharacteristic
53C2×#104×C131C2211yescharacteristic, complemented
54C2×#104×C131C2211yescharacteristic, complemented
55#418×C131C2211yescharacteristic, complemented
56#418×C131C2211yescharacteristic, complemented
57#418×C131C2211yescharacteristic, complemented
58#413×C131C2211yescharacteristic, complemented
59#413×C131C2211yescharacteristic, complemented
60C2×#100×C131C2211yescharacteristic, complemented
61C2×#100×C131C2211yescharacteristic, complemented
62#410×C131C2211yescharacteristic, complemented
63#344×C131C2211yescharacteristic, complemented
64#344×C131C2211yescharacteristic, complemented
65#339×C131C2211yescharacteristic, complemented
66#338×C131C2211yescharacteristic, complemented
672−1+4×C131—21no—
682−1+4×C131—21no—
692−1+4×C131D412yescomplemented
70H(5,𝔽2)×C131—22no—
71H(5,𝔽2)×C131—21no—
72H(5,𝔽2)×C131—22no—
73H(5,𝔽2)×C131—21no—
74H(5,𝔽2)×C131—22no—
75H(5,𝔽2)×C131—41no—
76H(5,𝔽2)×C131—41no—
77H(5,𝔽2)×C131D412yescomplemented
78C2×#41×C131—22no—
79C2×#41×C131—22no—
80C2×#41×C131—21no—
81C2×#41×C131—21no—
82C2×#41×C131—41no—
83C2×#41×C131C2311yescharacteristic
84C2×#41×C131C2311yescharacteristic
85C2×#41×C131C2311yescharacteristic
86C2×#41×C131C2311yescharacteristic
87C22×D4×C131—21no—
88C22×D4×C131—21no—
89C22×D4×C131—41no—
90C22×D4×C131—41no—
91C22×D4×C131C2311yescharacteristic
92C22×D4×C131C2311yescharacteristic
93#137×C131—24no—
94#137×C131—21no—
95#137×C131—21no—
96#137×C131—21no—
97#137×C131D412yescomplemented
98AGL(1,ℤ/8)×C131—24no—
99AGL(1,ℤ/8)×C131—24no—
100AGL(1,ℤ/8)×C131—24no—
101AGL(1,ℤ/8)×C131—22no—
102AGL(1,ℤ/8)×C131—22no—
103AGL(1,ℤ/8)×C131—21no—
104AGL(1,ℤ/8)×C131—22no—
105AGL(1,ℤ/8)×C131—21no—
106AGL(1,ℤ/8)×C131—21no—
107AGL(1,ℤ/8)×C131—22no—
108AGL(1,ℤ/8)×C131—22no—
109AGL(1,ℤ/8)×C131—22no—
110AGL(1,ℤ/8)×C131—22no—
111AGL(1,ℤ/8)×C131—22no—
112AGL(1,ℤ/8)×C131—22no—
113AGL(1,ℤ/8)×C131—41no—
114AGL(1,ℤ/8)×C131D412yescomplemented
115#135×C131—24no—
116#135×C131—24no—
117#135×C131—22no—
118#135×C131—22no—
119C2×SD16×C131—24no—
120C2×SD16×C131—21no—
121C2×SD16×C131—21no—
122C2×SD16×C131—21no—
123C2×SD16×C131—21no—
124C2×SD16×C131D412yescomplemented
125C2×D8×C131—24no—
126C2×D8×C131—21no—
127C2×D8×C131—21no—
128C2×D8×C131—21no—
129C2×D8×C131—21no—
130C2×D8×C131D412yescomplemented
131#131×C131—22no—
132#131×C131—22no—
133#131×C131—22no—
134#131×C131—41no—
135C2×M16×C131—22no—
136C2×M16×C131—22no—
137C2×M16×C131C2311yescharacteristic
138C2×M16×C131C2311yescharacteristic
139C2×M16×C131C2311yescharacteristic
140C2×M16×C131C2311yescharacteristic
141C2×M16×C131C2311yescharacteristic
142C2×M16×C131C2311yescharacteristic
143#127×C131—21no—
144#127×C131—22no—
145#127×C131—21no—
146#127×C131—21no—
147#124×C131—21no—
148#121×C131—41no—
149#120×C131—41no—
150C4×Q8×C131—21no—
151C4×D4×C131—21no—
152C4×D4×C131—41no—
153#117×C131—21no—
154#117×C131C2311yescharacteristic
155#117×C131C2311yescharacteristic
156C2×C42×C131—21no—
157C2×C42×C131C2311yescharacteristic
158#108×C131—22no—
159C4⋊C8×C131—22no—
160#104×C131—22no—
161#104×C131—22no—
162#104×C131—22no—
163#104×C131—22no—
164#104×C131—21no—
165#104×C131—21no—
166#104×C131—21no—
167#104×C131—21no—
168#104×C131D412yescomplemented
169#104×C131D412yescomplemented
170#102×C131—22no—
171#102×C131—22no—
172#102×C131—41no—
173#101×C131—21no—
174#101×C131—21no—
175#100×C131—21no—
176#100×C131—21no—
177#100×C131—22no—
178#100×C131—22no—
179#99×C131—41no—
180C24×C131—21no—
181C24×C131—21no—
182C24×C131—41no—
183#41×C131—21no—
184#41×C131—21no—
185#41×C131—21no—
186#41×C131—21no—
187#41×C131—24no—
188#41×C131—22no—
189#41×C131—22no—
190#41×C131—22no—
191#41×C131—22no—
192#41×C131—21no—
193#41×C131—21no—
194#41×C131—21no—
195#41×C131—21no—
196#41×C131—21no—
197#41×C131—21no—
198#41×C131—21no—
199#41×C131—21no—
200#41×C131—42no—
201#41×C131—42no—
202#41×C131—42no—
203#41×C131—42no—
204#41×C131—42no—
205#41×C131—42no—
206#41×C131—41no—
207#41×C131—41no—
208#41×C131—42no—
209#41×C131C2×D412yes—
210#41×C131C2×D412yes—
211#41×C131C2×D412yes—
212#41×C131C2×D412yes—
213C2×Q8×C131—22no—
214C2×Q8×C131—22no—
215C2×Q8×C131—41no—
216C2×Q8×C131C2×D411yescharacteristic
217C2×Q8×C131C2×D411yescharacteristic
218C2×Q8×C131C2×D411yescharacteristic
219C2×Q8×C131#4111yescharacteristic
220C2×D4×C131—21no—
221C2×D4×C131—21no—
222C2×D4×C131—24no—
223C2×D4×C131—22no—
224C2×D4×C131—22no—
225C2×D4×C131—21no—
226C2×D4×C131—21no—
227C2×D4×C131—21no—
228C2×D4×C131—21no—
229C2×D4×C131—21no—
230C2×D4×C131—21no—
231C2×D4×C131—21no—
232C2×D4×C131—21no—
233C2×D4×C131—21no—
234C2×D4×C131—21no—
235C2×D4×C131—21no—
236C2×D4×C131—21no—
237C2×D4×C131—21no—
238C2×D4×C131—42no—
239C2×D4×C131—41no—
240C2×D4×C131—41no—
241C2×D4×C131—42no—
242C2×D4×C131—42no—
243C2×D4×C131—42no—
244C2×D4×C131—42no—
245C2×D4×C131—41no—
246C2×D4×C131—44no—
247C2×D4×C131—42no—
248C2×D4×C131—42no—
249C2×D4×C131—44no—
250C2×D4×C131—42no—
251C2×D4×C131—42no—
252C2×D4×C131—84no—
253C2×D4×C131C2×D411yescharacteristic
254C2×D4×C131C2×D411yescharacteristic
255C2×D4×C131C2×D412yes—
256C2×D4×C131C2×D411yescharacteristic
257C2×D4×C131#4111yescharacteristic
258C22×C4×C131—21no—
259C22×C4×C131—21no—
260C22×C4×C131—21no—
261C22×C4×C131—21no—
262C22×C4×C131—21no—
263C22×C4×C131—41no—
264C22×C4×C131—42no—
265C22×C4×C131—41no—
266C22×C4×C131C2411yescharacteristic
267Q16×C131—22no—
268Q16×C131—22no—
269SD16×C131—24no—
270SD16×C131—22no—
271SD16×C131—22no—
272SD16×C131—22no—
273SD16×C131—24no—
274SD16×C131—22no—
275SD16×C131—42no—
276SD16×C131—42no—
277SD16×C131—42no—
278D8×C131—24no—
279D8×C131—22no—
280D8×C131—22no—
281D8×C131—24no—
282D8×C131—42no—
283D8×C131—42no—
284D8×C131—42no—
285M16×C131—24no—
286M16×C131—21no—
287M16×C131—21no—
288M16×C131—21no—
289M16×C131—21no—
290M16×C131—21no—
291M16×C131—21no—
292M16×C131—21no—
293M16×C131—21no—
294M16×C131—21no—
295M16×C131—21no—
296M16×C131—42no—
297M16×C131C2×D412yes—
298M16×C131C2×D412yes—
299C2×C8×C131—24no—
300C2×C8×C131—21no—
301C2×C8×C131—21no—
302C2×C8×C131—21no—
303C2×C8×C131—21no—
304C2×C8×C131—21no—
305C2×C8×C131—42no—
306C2×C8×C131C2×D412yes—
307C4⋊C4×C131—21no—
308C4⋊C4×C131—21no—
309C4⋊C4×C131—41no—
310C22⋊C4×C131—21no—
311C22⋊C4×C131—21no—
312C22⋊C4×C131—41no—
313C22⋊C4×C131—42no—
314C42×C131—21no—
315C42×C131—21no—
316C42×C131—21no—
317C42×C131—41no—
318C42×C131C2×D411yescharacteristic
319C42×C131C2×D411yescharacteristic
320C23×C131—21no—
321C23×C131—21no—
322C23×C131—21no—
323C23×C131—22no—
324C23×C131—21no—
325C23×C131—42no—
326C23×C131—44no—
327C23×C131—41no—
328C23×C131—41no—
329C23×C131—41no—
330C23×C131—41no—
331C23×C131—41no—
332C23×C131—82no—
333C23×C131—82no—
334C23×C131—162no—
335C23×C131H(5,𝔽2)11yescharacteristic
336Q8×C131—21no—
337Q8×C131—21no—
338Q8×C131—21no—
339Q8×C131—21no—
340Q8×C131—21no—
341Q8×C131—21no—
342Q8×C131—42no—
343Q8×C131#12012yes—
344Q8×C131#12112yes—
345D4×C131—22no—
346D4×C131—22no—
347D4×C131—22no—
348D4×C131—22no—
349D4×C131—21no—
350D4×C131—21no—
351D4×C131—22no—
352D4×C131—21no—
353D4×C131—21no—
354D4×C131—21no—
355D4×C131—21no—
356D4×C131—22no—
357D4×C131—42no—
358D4×C131—42no—
359D4×C131—44no—
360D4×C131—42no—
361D4×C131—44no—
362D4×C131—41no—
363D4×C131—41no—
364D4×C131—41no—
365D4×C131—41no—
366D4×C131—41no—
367D4×C131—41no—
368D4×C131—41no—
369D4×C131—41no—
370D4×C131—41no—
371D4×C131—41no—
372D4×C131—84no—
373D4×C131—84no—
374D4×C131—162no—
375D4×C131#12012yes—
376D4×C131#12112yes—
377C2×C4×C131—21no—
378C2×C4×C131—21no—
379C2×C4×C131—21no—
380C2×C4×C131—22no—
381C2×C4×C131—22no—
382C2×C4×C131—22no—
383C2×C4×C131—22no—
384C2×C4×C131—21no—
385C2×C4×C131—21no—
386C2×C4×C131—21no—
387C2×C4×C131—42no—
388C2×C4×C131—42no—
389C2×C4×C131—42no—
390C2×C4×C131—42no—
391C2×C4×C131—44no—
392C2×C4×C131—41no—
393C2×C4×C131—41no—
394C2×C4×C131—41no—
395C2×C4×C131—41no—
396C2×C4×C131—41no—
397C2×C4×C131—41no—
398C2×C4×C131—82no—
399C2×C4×C131C22×D411yescharacteristic
400C2×C4×C131C22×D411yescharacteristic
401C2×C4×C131C22×D411yescharacteristic
402C2×C4×C131C22×D411yescharacteristic
403C2×C4×C131C2×#4111yescharacteristic
404C2×C4×C131H(5,𝔽2)11yescharacteristic
405C8×C131—22no—
406C8×C131—22no—
407C8×C131—22no—
408C8×C131—41no—
409C8×C131—41no—
410C8×C131—41no—
411C22×C131—22no—
412C22×C131—22no—
413C22×C131—41no—
414C22×C131—41no—
415C22×C131—42no—
416C22×C131—41no—
417C22×C131—81no—
418C22×C131—81no—
419C22×C131—82no—
420C22×C131—81no—
421C22×C131—81no—
422C22×C131—82no—
423C22×C131—82no—
424C22×C131—82no—
425C22×C131—81no—
426C22×C131—161no—
427C22×C131—161no—
428C22×C131—162no—
429C22×C131—164no—
430C22×C131#53411yescharacteristic
431C22×C131D4211yescharacteristic
432C22×C131#54611yescharacteristic
433C4×C131—22no—
434C4×C131—22no—
435C4×C131—22no—
436C4×C131—41no—
437C4×C131—41no—
438C4×C131—41no—
439C4×C131—81no—
440C4×C131—81no—
441C4×C131C2×#12011yescharacteristic
442C4×C131C2×#12111yescharacteristic
443C4×C131D4211yescharacteristic
444C4×C131#54611yescharacteristic
445C2×C131—21no—
446C2×C131—21no—
447C2×C131—21no—
448C2×C131—42no—
449C2×C131—42no—
450C2×C131—82no—
451C2×C131—81no—
452C2×C131—81no—
453C2×C131—161no—
454C2×C131#241011yescharacteristic
455#24472C13111yesmaximal, characteristic, direct product factor, Sylow
456C131#2447211yescharacteristic, direct product factor, Sylow
457#3585C2×C13111yescharacteristic, complemented
458#3068C2×C13111yescharacteristic, complemented
459#3038C2×C13111yescharacteristic, complemented
460#3021C2×C13111yescharacteristic, complemented
461C2×#453C2×C13111yescharacteristic, complemented
462#2901C2×C13111yescharacteristic, complemented
463#2050C2×C13111yescharacteristic, complemented
464#2048C2×C13111yescharacteristic, complemented
465#2008C2×C13111yescharacteristic, complemented
466#2002C2×C13111yescharacteristic, complemented
467#1906C2×C13111yescharacteristic, complemented
468#1903C2×C13111yescharacteristic, complemented
469#1903C2×C13111yescharacteristic, complemented
470#1861C2×C13111yescharacteristic, complemented
471#1795C2×C13111yescharacteristic, complemented
472#585C22×C13111yescharacteristic
473C2×H(5,𝔽2)C22×C13111yescharacteristic
474#577—22no—
475#577—22no—
476#576—22no—
477#576—22no—
478#575—22no—
479#575C22×C13111yescharacteristic
480#575C22×C13111yescharacteristic
481C2×AGL(1,ℤ/8)—22no—
482C2×AGL(1,ℤ/8)C22×C13111yescharacteristic
483C2×AGL(1,ℤ/8)C22×C13111yescharacteristic
484C2×AGL(1,ℤ/8)C22×C13111yescharacteristic
485C2×AGL(1,ℤ/8)C22×C13111yescharacteristic, complemented
486C2×AGL(1,ℤ/8)C22×C13111yescharacteristic, complemented
487#568C22×C13111yescharacteristic
488#568C22×C13111yescharacteristic, complemented
489#535C22×C13111yescharacteristic, complemented
490C2×#127C22×C13111yescharacteristic, complemented
491C4×#41C22×C13111yescharacteristic, complemented
492#472—22no—
493#471—22no—
494#460—22no—
495#459—22no—
496#454—22no—
497#453—22no—
498#453—22no—
499#453—22no—
500#430C22×C13111yescharacteristic, complemented
501#423C22×C13111yescharacteristic, complemented
502#421—22no—
503#421C22×C13111yescharacteristic
504#421C22×C13111yescharacteristic
505#421C22×C13111yescharacteristic, complemented
506#421C22×C13111yescharacteristic, complemented
507C2×#104—22no—
508C2×#104C22×C13111yescharacteristic
509C2×#104C22×C13111yescharacteristic, complemented
510C2×#104C22×C13111yescharacteristic, complemented
511#418C22×C13111yescharacteristic, complemented
512#418C22×C13111yescharacteristic, complemented
513#418C22×C13111yescharacteristic, complemented
514#413C22×C13111yescharacteristic, complemented
515#413C22×C13111yescharacteristic, complemented
516C2×#100C22×C13111yescharacteristic, complemented
517C2×#100C22×C13111yescharacteristic, complemented
518#410C22×C13111yescharacteristic, complemented
519#344C22×C13111yescharacteristic, complemented
520#344C22×C13111yescharacteristic, complemented
521#339C22×C13111yescharacteristic, complemented
522#338C22×C13111yescharacteristic, complemented
5232−1+4—21no—
5242−1+4—21no—
5252−1+4D4×C13112yescomplemented
526H(5,𝔽2)—22no—
527H(5,𝔽2)—21no—
528H(5,𝔽2)—22no—
529H(5,𝔽2)—21no—
530H(5,𝔽2)—22no—
531H(5,𝔽2)—41no—
532H(5,𝔽2)—41no—
533H(5,𝔽2)D4×C13112yescomplemented
534C2×#41—22no—
535C2×#41—22no—
536C2×#41—21no—
537C2×#41—21no—
538C2×#41—41no—
539C2×#41C23×C13111yescharacteristic
540C2×#41C23×C13111yescharacteristic
541C2×#41C23×C13111yescharacteristic
542C2×#41C23×C13111yescharacteristic
543C22×D4—21no—
544C22×D4—21no—
545C22×D4—41no—
546C22×D4—41no—
547C22×D4C23×C13111yescharacteristic
548C22×D4C23×C13111yescharacteristic
549#137—24no—
550#137—21no—
551#137—21no—
552#137—21no—
553#137D4×C13112yescomplemented
554AGL(1,ℤ/8)—24no—
555AGL(1,ℤ/8)—24no—
556AGL(1,ℤ/8)—24no—
557AGL(1,ℤ/8)—22no—
558AGL(1,ℤ/8)—22no—
559AGL(1,ℤ/8)—21no—
560AGL(1,ℤ/8)—22no—
561AGL(1,ℤ/8)—21no—
562AGL(1,ℤ/8)—21no—
563AGL(1,ℤ/8)—22no—
564AGL(1,ℤ/8)—22no—
565AGL(1,ℤ/8)—22no—
566AGL(1,ℤ/8)—22no—
567AGL(1,ℤ/8)—22no—
568AGL(1,ℤ/8)—22no—
569AGL(1,ℤ/8)—41no—
570AGL(1,ℤ/8)D4×C13112yescomplemented
571#135—24no—
572#135—24no—
573#135—22no—
574#135—22no—
575C2×SD16—24no—
576C2×SD16—21no—
577C2×SD16—21no—
578C2×SD16—21no—
579C2×SD16—21no—
580C2×SD16D4×C13112yescomplemented
581C2×D8—24no—
582C2×D8—21no—
583C2×D8—21no—
584C2×D8—21no—
585C2×D8—21no—
586C2×D8D4×C13112yescomplemented
587#131—22no—
588#131—22no—
589#131—22no—
590#131—41no—
591C2×M16—22no—
592C2×M16—22no—
593C2×M16C23×C13111yescharacteristic
594C2×M16C23×C13111yescharacteristic
595C2×M16C23×C13111yescharacteristic
596C2×M16C23×C13111yescharacteristic
597C2×M16C23×C13111yescharacteristic
598C2×M16C23×C13111yescharacteristic
599#127—22no—
600#127—21no—
601#127—21no—
602#127—21no—
603#124—21no—
604#121—41no—
605#120—41no—
606C4×Q8—21no—
607C4×D4—21no—
608C4×D4—41no—
609#117—21no—
610#117C23×C13111yescharacteristic
611#117C23×C13111yescharacteristic
612C2×C42—21no—
613C2×C42C23×C13111yescharacteristic
614#108—22no—
615C4⋊C8—22no—
616#104—22no—
617#104—22no—
618#104—22no—
619#104—22no—
620#104—21no—
621#104—21no—
622#104—21no—
623#104—21no—
624#104D4×C13112yescomplemented
625#104D4×C13112yescomplemented
626#102—22no—
627#102—22no—
628#102—41no—
629#101—21no—
630#101—21no—
631#100—21no—
632#100—21no—
633#100—22no—
634#100—22no—
635#99—41no—
636C24—21no—
637C24—21no—
638C24—41no—
639#41—21no—
640#41—21no—
641#41—21no—
642#41—21no—
643#41—24no—
644#41—22no—
645#41—22no—
646#41—22no—
647#41—22no—
648#41—21no—
649#41—21no—
650#41—21no—
651#41—21no—
652#41—21no—
653#41—21no—
654#41—21no—
655#41—21no—
656#41—42no—
657#41—42no—
658#41—42no—
659#41—42no—
660#41—42no—
661#41—42no—
662#41—41no—
663#41—41no—
664#41—42no—
665#41C2×D4×C13112yes—
666#41C2×D4×C13112yes—
667#41C2×D4×C13112yes—
668#41C2×D4×C13112yes—
669C2×Q8—22no—
670C2×Q8—22no—
671C2×Q8—41no—
672C2×Q8C2×D4×C13111yescharacteristic
673C2×Q8C2×D4×C13111yescharacteristic
674C2×Q8C2×D4×C13111yescharacteristic
675C2×Q8#41×C13111yescharacteristic
676C2×D4—21no—
677C2×D4—21no—
678C2×D4—24no—
679C2×D4—22no—
680C2×D4—22no—
681C2×D4—21no—
682C2×D4—21no—
683C2×D4—21no—
684C2×D4—21no—
685C2×D4—21no—
686C2×D4—21no—
687C2×D4—21no—
688C2×D4—21no—
689C2×D4—21no—
690C2×D4—21no—
691C2×D4—21no—
692C2×D4—21no—
693C2×D4—21no—
694C2×D4—42no—
695C2×D4—41no—
696C2×D4—41no—
697C2×D4—42no—
698C2×D4—42no—
699C2×D4—42no—
700C2×D4—42no—
701C2×D4—41no—
702C2×D4—44no—
703C2×D4—42no—
704C2×D4—42no—
705C2×D4—44no—
706C2×D4—42no—
707C2×D4—42no—
708C2×D4—84no—
709C2×D4C2×D4×C13111yescharacteristic
710C2×D4C2×D4×C13111yescharacteristic
711C2×D4C2×D4×C13112yes—
712C2×D4C2×D4×C13111yescharacteristic
713C2×D4#41×C13111yescharacteristic
714C22×C4—21no—
715C22×C4—21no—
716C22×C4—21no—
717C22×C4—21no—
718C22×C4—21no—
719C22×C4—41no—
720C22×C4—42no—
721C22×C4—41no—
722C22×C4C24×C13111yescharacteristic
723Q16—22no—
724Q16—22no—
725SD16—24no—
726SD16—22no—
727SD16—22no—
728SD16—22no—
729SD16—24no—
730SD16—22no—
731SD16—42no—
732SD16—42no—
733SD16—42no—
734D8—24no—
735D8—22no—
736D8—22no—
737D8—24no—
738D8—42no—
739D8—42no—
740D8—42no—
741M16—24no—
742M16—21no—
743M16—21no—
744M16—21no—
745M16—21no—
746M16—21no—
747M16—21no—
748M16—21no—
749M16—21no—
750M16—21no—
751M16—21no—
752M16—42no—
753M16C2×D4×C13112yes—
754M16C2×D4×C13112yes—
755C2×C8—24no—
756C2×C8—21no—
757C2×C8—21no—
758C2×C8—21no—
759C2×C8—21no—
760C2×C8—21no—
761C2×C8—42no—
762C2×C8C2×D4×C13112yes—
763C4⋊C4—21no—
764C4⋊C4—21no—
765C4⋊C4—41no—
766C22⋊C4—21no—
767C22⋊C4—21no—
768C22⋊C4—41no—
769C22⋊C4—42no—
770C42—21no—
771C42—21no—
772C42—21no—
773C42—41no—
774C42C2×D4×C13111yescharacteristic
775C42C2×D4×C13111yescharacteristic
776C23—21no—
777C23—21no—
778C23—21no—
779C23—22no—
780C23—21no—
781C23—42no—
782C23—44no—
783C23—41no—
784C23—41no—
785C23—41no—
786C23—41no—
787C23—41no—
788C23—82no—
789C23—82no—
790C23—162no—
791C23H(5,𝔽2)×C13111yescharacteristic
792Q8—21no—
793Q8—21no—
794Q8—21no—
795Q8—21no—
796Q8—21no—
797Q8—21no—
798Q8—42no—
799Q8#120×C13112yes—
800Q8#121×C13112yes—
801D4—22no—
802D4—22no—
803D4—22no—
804D4—22no—
805D4—21no—
806D4—21no—
807D4—22no—
808D4—21no—
809D4—21no—
810D4—21no—
811D4—21no—
812D4—22no—
813D4—42no—
814D4—42no—
815D4—44no—
816D4—42no—
817D4—44no—
818D4—41no—
819D4—41no—
820D4—41no—
821D4—41no—
822D4—41no—
823D4—41no—
824D4—41no—
825D4—41no—
826D4—41no—
827D4—41no—
828D4—84no—
829D4—84no—
830D4—162no—
831D4#120×C13112yes—
832D4#121×C13112yes—
833C2×C4—21no—
834C2×C4—21no—
835C2×C4—21no—
836C2×C4—22no—
837C2×C4—22no—
838C2×C4—22no—
839C2×C4—22no—
840C2×C4—21no—
841C2×C4—21no—
842C2×C4—21no—
843C2×C4—42no—
844C2×C4—42no—
845C2×C4—42no—
846C2×C4—42no—
847C2×C4—44no—
848C2×C4—41no—
849C2×C4—41no—
850C2×C4—41no—
851C2×C4—41no—
852C2×C4—41no—
853C2×C4—41no—
854C2×C4—82no—
855C2×C4C22×D4×C13111yescharacteristic
856C2×C4C22×D4×C13111yescharacteristic
857C2×C4C22×D4×C13111yescharacteristic
858C2×C4C22×D4×C13111yescharacteristic
859C2×C4C2×#41×C13111yescharacteristic
860C2×C4H(5,𝔽2)×C13111yescharacteristic
861C8—22no—
862C8—22no—
863C8—22no—
864C8—41no—
865C8—41no—
866C8—41no—
867C22—22no—
868C22—22no—
869C22—41no—
870C22—41no—
871C22—42no—
872C22—41no—
873C22—81no—
874C22—81no—
875C22—82no—
876C22—81no—
877C22—81no—
878C22—82no—
879C22—82no—
880C22—82no—
881C22—81no—
882C22—161no—
883C22—161no—
884C22—162no—
885C22—164no—
886C22#534×C13111yescharacteristic
887C22D42×C13111yescharacteristic
888C22#546×C13111yescharacteristic
889C4—22no—
890C4—22no—
891C4—22no—
892C4—41no—
893C4—41no—
894C4—41no—
895C4—81no—
896C4—81no—
897C4C2×#120×C13111yescharacteristic
898C4C2×#121×C13111yescharacteristic
899C4D42×C13111yescharacteristic
900C4#546×C13111yescharacteristic
901C2—21no—
902C2—21no—
903C2—21no—
904C2—42no—
905C2—42no—
906C2—82no—
907C2—81no—
908C2—81no—
909C2—161no—
910C2#2410×C13111yescharacteristic
subgroupG/H
center, socleC2×C131#2410
commutator, Frattini, cosocleC22×C4C24×C131
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C2×C131 ◁ C22×C4×C131 ◁ G

Complements

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

NH ≅ G/Ntype
1. #3585×C131C2semidirect
2. #3068×C131C2semidirect
3. #3038×C131C2semidirect
4. #3021×C131C2semidirect
5. C2×#453×C131C2semidirect
6. #2901×C131C2semidirect
7. #2050×C131C2semidirect
8. #2048×C131C2semidirect
9. #2008×C131C2semidirect
10. #2002×C131C2semidirect
11. #1906×C131C2semidirect
12. #1903×C131C2semidirect
13. #1903×C131C2semidirect
14. #1861×C131C2semidirect
15. #1795×C131C2semidirect
29. C2×AGL(1,ℤ/8)×C131C22semidirect
30. C2×AGL(1,ℤ/8)×C131C22semidirect
32. #568×C131C22semidirect
33. #535×C131C22semidirect
34. C2×#127×C131C22semidirect
35. C4×#41×C131C22semidirect
44. #430×C131C22semidirect
45. #423×C131C22semidirect
49. #421×C131C22semidirect
50. #421×C131C22semidirect
53. C2×#104×C131C22semidirect
54. C2×#104×C131C22semidirect
55. #418×C131C22semidirect
56. #418×C131C22semidirect
57. #418×C131C22semidirect
58. #413×C131C22semidirect
59. #413×C131C22semidirect
60. C2×#100×C131C22semidirect
61. C2×#100×C131C22semidirect
62. #410×C131C22semidirect
63. #344×C131C22semidirect
64. #344×C131C22semidirect
65. #339×C131C22semidirect
66. #338×C131C22semidirect
69. 2−1+4×C131D4semidirect
77. H(5,𝔽2)×C131D4semidirect
97. #137×C131D4semidirect
114. AGL(1,ℤ/8)×C131D4semidirect
124. C2×SD16×C131D4semidirect
130. C2×D8×C131D4semidirect
168. #104×C131D4semidirect
169. #104×C131D4semidirect
455. #24472C131direct (N × H)
456. C131#24472direct (N × H)
457. #3585C2×C131semidirect
458. #3068C2×C131semidirect
459. #3038C2×C131semidirect
460. #3021C2×C131semidirect
461. C2×#453C2×C131semidirect
462. #2901C2×C131semidirect
463. #2050C2×C131semidirect
464. #2048C2×C131semidirect
465. #2008C2×C131semidirect
466. #2002C2×C131semidirect
467. #1906C2×C131semidirect
468. #1903C2×C131semidirect
469. #1903C2×C131semidirect
470. #1861C2×C131semidirect
471. #1795C2×C131semidirect
485. C2×AGL(1,ℤ/8)C22×C131semidirect
486. C2×AGL(1,ℤ/8)C22×C131semidirect
488. #568C22×C131semidirect
489. #535C22×C131semidirect
490. C2×#127C22×C131semidirect
491. C4×#41C22×C131semidirect
500. #430C22×C131semidirect
501. #423C22×C131semidirect
505. #421C22×C131semidirect
506. #421C22×C131semidirect
509. C2×#104C22×C131semidirect
510. C2×#104C22×C131semidirect
511. #418C22×C131semidirect
512. #418C22×C131semidirect
513. #418C22×C131semidirect
514. #413C22×C131semidirect
515. #413C22×C131semidirect
516. C2×#100C22×C131semidirect
517. C2×#100C22×C131semidirect
518. #410C22×C131semidirect
519. #344C22×C131semidirect
520. #344C22×C131semidirect
521. #339C22×C131semidirect
522. #338C22×C131semidirect
525. 2−1+4D4×C131semidirect
533. H(5,𝔽2)D4×C131semidirect
553. #137D4×C131semidirect
570. AGL(1,ℤ/8)D4×C131semidirect
580. C2×SD16D4×C131semidirect
586. C2×D8D4×C131semidirect
624. #104D4×C131semidirect
625. #104D4×C131semidirect

Maximal subgroups

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

subgroupindex
#3585×C1312
#3068×C1312
#3038×C1312
#3021×C1312
C2×#453×C1312
#2901×C1312
#2050×C1312
#2048×C1312
#2008×C1312
#2002×C1312
#1906×C1312
#1903×C1312
#1861×C1312
#1795×C1312
#24472131