Finite Group Databasebeta

← C151×#24472 #50329397

Subgroups — C151×#24472 #50329397

Order 38656.

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×C151C211yesmaximal, characteristic, complemented
2#3068×C151C211yesmaximal, characteristic, complemented
3#3038×C151C211yesmaximal, characteristic, complemented
4#3021×C151C211yesmaximal, characteristic, complemented
5C2×#453×C151C211yesmaximal, characteristic, complemented
6#2901×C151C211yesmaximal, characteristic, complemented
7#2050×C151C211yesmaximal, characteristic, complemented
8#2048×C151C211yesmaximal, characteristic, complemented
9#2008×C151C211yesmaximal, characteristic, complemented
10#2002×C151C211yesmaximal, characteristic, complemented
11#1906×C151C211yesmaximal, characteristic, complemented
12#1903×C151C211yesmaximal, characteristic, complemented
13#1903×C151C211yesmaximal, characteristic, complemented
14#1861×C151C211yesmaximal, characteristic, complemented
15#1795×C151C211yesmaximal, characteristic, complemented
16#585×C151C2211yescharacteristic
17C2×H(5,𝔽2)×C151C2211yescharacteristic
18#577×C151—22no—
19#577×C151—22no—
20#576×C151—22no—
21#576×C151—22no—
22#575×C151—22no—
23#575×C151C2211yescharacteristic
24#575×C151C2211yescharacteristic
25C2×AGL(1,ℤ/8)×C151—22no—
26C2×AGL(1,ℤ/8)×C151C2211yescharacteristic
27C2×AGL(1,ℤ/8)×C151C2211yescharacteristic
28C2×AGL(1,ℤ/8)×C151C2211yescharacteristic
29C2×AGL(1,ℤ/8)×C151C2211yescharacteristic, complemented
30C2×AGL(1,ℤ/8)×C151C2211yescharacteristic, complemented
31#568×C151C2211yescharacteristic
32#568×C151C2211yescharacteristic, complemented
33#535×C151C2211yescharacteristic, complemented
34C2×#127×C151C2211yescharacteristic, complemented
35C4×#41×C151C2211yescharacteristic, complemented
36#472×C151—22no—
37#471×C151—22no—
38#460×C151—22no—
39#459×C151—22no—
40#454×C151—22no—
41#453×C151—22no—
42#453×C151—22no—
43#453×C151—22no—
44#430×C151C2211yescharacteristic, complemented
45#423×C151C2211yescharacteristic, complemented
46#421×C151—22no—
47#421×C151C2211yescharacteristic
48#421×C151C2211yescharacteristic
49#421×C151C2211yescharacteristic, complemented
50#421×C151C2211yescharacteristic, complemented
51C2×#104×C151—22no—
52C2×#104×C151C2211yescharacteristic
53C2×#104×C151C2211yescharacteristic, complemented
54C2×#104×C151C2211yescharacteristic, complemented
55#418×C151C2211yescharacteristic, complemented
56#418×C151C2211yescharacteristic, complemented
57#418×C151C2211yescharacteristic, complemented
58#413×C151C2211yescharacteristic, complemented
59#413×C151C2211yescharacteristic, complemented
60C2×#100×C151C2211yescharacteristic, complemented
61C2×#100×C151C2211yescharacteristic, complemented
62#410×C151C2211yescharacteristic, complemented
63#344×C151C2211yescharacteristic, complemented
64#344×C151C2211yescharacteristic, complemented
65#339×C151C2211yescharacteristic, complemented
66#338×C151C2211yescharacteristic, complemented
672−1+4×C151—21no—
682−1+4×C151—21no—
692−1+4×C151D412yescomplemented
70H(5,𝔽2)×C151—21no—
71H(5,𝔽2)×C151—22no—
72H(5,𝔽2)×C151—21no—
73H(5,𝔽2)×C151—22no—
74H(5,𝔽2)×C151—22no—
75H(5,𝔽2)×C151—41no—
76H(5,𝔽2)×C151—41no—
77H(5,𝔽2)×C151D412yescomplemented
78C2×#41×C151—22no—
79C2×#41×C151—22no—
80C2×#41×C151—21no—
81C2×#41×C151—21no—
82C2×#41×C151—41no—
83C2×#41×C151C2311yescharacteristic
84C2×#41×C151C2311yescharacteristic
85C2×#41×C151C2311yescharacteristic
86C2×#41×C151C2311yescharacteristic
87C22×D4×C151—21no—
88C22×D4×C151—21no—
89C22×D4×C151—41no—
90C22×D4×C151—41no—
91C22×D4×C151C2311yescharacteristic
92C22×D4×C151C2311yescharacteristic
93#137×C151—24no—
94#137×C151—21no—
95#137×C151—21no—
96#137×C151—21no—
97#137×C151D412yescomplemented
98AGL(1,ℤ/8)×C151—24no—
99AGL(1,ℤ/8)×C151—24no—
100AGL(1,ℤ/8)×C151—24no—
101AGL(1,ℤ/8)×C151—21no—
102AGL(1,ℤ/8)×C151—22no—
103AGL(1,ℤ/8)×C151—21no—
104AGL(1,ℤ/8)×C151—21no—
105AGL(1,ℤ/8)×C151—22no—
106AGL(1,ℤ/8)×C151—22no—
107AGL(1,ℤ/8)×C151—22no—
108AGL(1,ℤ/8)×C151—22no—
109AGL(1,ℤ/8)×C151—22no—
110AGL(1,ℤ/8)×C151—22no—
111AGL(1,ℤ/8)×C151—22no—
112AGL(1,ℤ/8)×C151—22no—
113AGL(1,ℤ/8)×C151—41no—
114AGL(1,ℤ/8)×C151D412yescomplemented
115#135×C151—24no—
116#135×C151—24no—
117#135×C151—22no—
118#135×C151—22no—
119C2×SD16×C151—24no—
120C2×SD16×C151—21no—
121C2×SD16×C151—21no—
122C2×SD16×C151—21no—
123C2×SD16×C151—21no—
124C2×SD16×C151D412yescomplemented
125C2×D8×C151—24no—
126C2×D8×C151—21no—
127C2×D8×C151—21no—
128C2×D8×C151—21no—
129C2×D8×C151—21no—
130C2×D8×C151D412yescomplemented
131#131×C151—22no—
132#131×C151—22no—
133#131×C151—22no—
134#131×C151—41no—
135C2×M16×C151—22no—
136C2×M16×C151—22no—
137C2×M16×C151C2311yescharacteristic
138C2×M16×C151C2311yescharacteristic
139C2×M16×C151C2311yescharacteristic
140C2×M16×C151C2311yescharacteristic
141C2×M16×C151C2311yescharacteristic
142C2×M16×C151C2311yescharacteristic
143#127×C151—21no—
144#127×C151—22no—
145#127×C151—21no—
146#127×C151—21no—
147#124×C151—21no—
148#121×C151—41no—
149#120×C151—41no—
150C4×Q8×C151—21no—
151C4×D4×C151—21no—
152C4×D4×C151—41no—
153#117×C151—21no—
154#117×C151C2311yescharacteristic
155#117×C151C2311yescharacteristic
156C2×C42×C151—21no—
157C2×C42×C151C2311yescharacteristic
158#108×C151—22no—
159C4⋊C8×C151—22no—
160#104×C151—22no—
161#104×C151—21no—
162#104×C151—21no—
163#104×C151—21no—
164#104×C151—21no—
165#104×C151—22no—
166#104×C151—22no—
167#104×C151—22no—
168#104×C151D412yescomplemented
169#104×C151D412yescomplemented
170#102×C151—22no—
171#102×C151—22no—
172#102×C151—41no—
173#101×C151—21no—
174#101×C151—21no—
175#100×C151—21no—
176#100×C151—21no—
177#100×C151—22no—
178#100×C151—22no—
179#99×C151—41no—
180C24×C151—21no—
181C24×C151—21no—
182C24×C151—41no—
183#41×C151—21no—
184#41×C151—21no—
185#41×C151—21no—
186#41×C151—21no—
187#41×C151—24no—
188#41×C151—22no—
189#41×C151—22no—
190#41×C151—22no—
191#41×C151—22no—
192#41×C151—21no—
193#41×C151—21no—
194#41×C151—21no—
195#41×C151—21no—
196#41×C151—21no—
197#41×C151—21no—
198#41×C151—21no—
199#41×C151—21no—
200#41×C151—42no—
201#41×C151—42no—
202#41×C151—42no—
203#41×C151—42no—
204#41×C151—42no—
205#41×C151—42no—
206#41×C151—41no—
207#41×C151—41no—
208#41×C151—42no—
209#41×C151C2×D412yes—
210#41×C151C2×D412yes—
211#41×C151C2×D412yes—
212#41×C151C2×D412yes—
213C2×Q8×C151—22no—
214C2×Q8×C151—22no—
215C2×Q8×C151—41no—
216C2×Q8×C151C2×D411yescharacteristic
217C2×Q8×C151C2×D411yescharacteristic
218C2×Q8×C151C2×D411yescharacteristic
219C2×Q8×C151#4111yescharacteristic
220C2×D4×C151—21no—
221C2×D4×C151—21no—
222C2×D4×C151—24no—
223C2×D4×C151—22no—
224C2×D4×C151—22no—
225C2×D4×C151—21no—
226C2×D4×C151—21no—
227C2×D4×C151—21no—
228C2×D4×C151—21no—
229C2×D4×C151—21no—
230C2×D4×C151—21no—
231C2×D4×C151—21no—
232C2×D4×C151—21no—
233C2×D4×C151—21no—
234C2×D4×C151—21no—
235C2×D4×C151—21no—
236C2×D4×C151—21no—
237C2×D4×C151—21no—
238C2×D4×C151—42no—
239C2×D4×C151—41no—
240C2×D4×C151—41no—
241C2×D4×C151—42no—
242C2×D4×C151—42no—
243C2×D4×C151—42no—
244C2×D4×C151—42no—
245C2×D4×C151—41no—
246C2×D4×C151—44no—
247C2×D4×C151—42no—
248C2×D4×C151—42no—
249C2×D4×C151—44no—
250C2×D4×C151—42no—
251C2×D4×C151—42no—
252C2×D4×C151—84no—
253C2×D4×C151C2×D411yescharacteristic
254C2×D4×C151C2×D411yescharacteristic
255C2×D4×C151C2×D412yes—
256C2×D4×C151C2×D411yescharacteristic
257C2×D4×C151#4111yescharacteristic
258C22×C4×C151—21no—
259C22×C4×C151—21no—
260C22×C4×C151—21no—
261C22×C4×C151—21no—
262C22×C4×C151—21no—
263C22×C4×C151—41no—
264C22×C4×C151—42no—
265C22×C4×C151—41no—
266C22×C4×C151C2411yescharacteristic
267Q16×C151—22no—
268Q16×C151—22no—
269SD16×C151—24no—
270SD16×C151—22no—
271SD16×C151—22no—
272SD16×C151—22no—
273SD16×C151—24no—
274SD16×C151—22no—
275SD16×C151—42no—
276SD16×C151—42no—
277SD16×C151—42no—
278D8×C151—24no—
279D8×C151—22no—
280D8×C151—22no—
281D8×C151—24no—
282D8×C151—42no—
283D8×C151—42no—
284D8×C151—42no—
285M16×C151—24no—
286M16×C151—21no—
287M16×C151—21no—
288M16×C151—21no—
289M16×C151—21no—
290M16×C151—21no—
291M16×C151—21no—
292M16×C151—21no—
293M16×C151—21no—
294M16×C151—21no—
295M16×C151—21no—
296M16×C151—42no—
297M16×C151C2×D412yes—
298M16×C151C2×D412yes—
299C2×C8×C151—24no—
300C2×C8×C151—21no—
301C2×C8×C151—21no—
302C2×C8×C151—21no—
303C2×C8×C151—21no—
304C2×C8×C151—21no—
305C2×C8×C151—42no—
306C2×C8×C151C2×D412yes—
307C4⋊C4×C151—21no—
308C4⋊C4×C151—21no—
309C4⋊C4×C151—41no—
310C22⋊C4×C151—21no—
311C22⋊C4×C151—21no—
312C22⋊C4×C151—41no—
313C22⋊C4×C151—42no—
314C42×C151—21no—
315C42×C151—21no—
316C42×C151—21no—
317C42×C151—41no—
318C42×C151C2×D411yescharacteristic
319C42×C151C2×D411yescharacteristic
320C23×C151—21no—
321C23×C151—21no—
322C23×C151—21no—
323C23×C151—22no—
324C23×C151—21no—
325C23×C151—42no—
326C23×C151—44no—
327C23×C151—41no—
328C23×C151—41no—
329C23×C151—41no—
330C23×C151—41no—
331C23×C151—41no—
332C23×C151—82no—
333C23×C151—82no—
334C23×C151—162no—
335C23×C151H(5,𝔽2)11yescharacteristic
336Q8×C151—21no—
337Q8×C151—21no—
338Q8×C151—21no—
339Q8×C151—21no—
340Q8×C151—21no—
341Q8×C151—21no—
342Q8×C151—42no—
343Q8×C151#12012yes—
344Q8×C151#12112yes—
345D4×C151—22no—
346D4×C151—22no—
347D4×C151—22no—
348D4×C151—22no—
349D4×C151—21no—
350D4×C151—22no—
351D4×C151—21no—
352D4×C151—21no—
353D4×C151—21no—
354D4×C151—21no—
355D4×C151—21no—
356D4×C151—22no—
357D4×C151—42no—
358D4×C151—42no—
359D4×C151—44no—
360D4×C151—42no—
361D4×C151—44no—
362D4×C151—41no—
363D4×C151—41no—
364D4×C151—41no—
365D4×C151—41no—
366D4×C151—41no—
367D4×C151—41no—
368D4×C151—41no—
369D4×C151—41no—
370D4×C151—41no—
371D4×C151—41no—
372D4×C151—84no—
373D4×C151—84no—
374D4×C151—162no—
375D4×C151#12012yes—
376D4×C151#12112yes—
377C2×C4×C151—21no—
378C2×C4×C151—21no—
379C2×C4×C151—21no—
380C2×C4×C151—22no—
381C2×C4×C151—22no—
382C2×C4×C151—22no—
383C2×C4×C151—22no—
384C2×C4×C151—21no—
385C2×C4×C151—21no—
386C2×C4×C151—21no—
387C2×C4×C151—42no—
388C2×C4×C151—42no—
389C2×C4×C151—42no—
390C2×C4×C151—44no—
391C2×C4×C151—42no—
392C2×C4×C151—41no—
393C2×C4×C151—41no—
394C2×C4×C151—41no—
395C2×C4×C151—41no—
396C2×C4×C151—41no—
397C2×C4×C151—41no—
398C2×C4×C151—82no—
399C2×C4×C151C22×D411yescharacteristic
400C2×C4×C151C22×D411yescharacteristic
401C2×C4×C151C22×D411yescharacteristic
402C2×C4×C151C22×D411yescharacteristic
403C2×C4×C151C2×#4111yescharacteristic
404C2×C4×C151H(5,𝔽2)11yescharacteristic
405C8×C151—22no—
406C8×C151—22no—
407C8×C151—22no—
408C8×C151—41no—
409C8×C151—41no—
410C8×C151—41no—
411C22×C151—22no—
412C22×C151—22no—
413C22×C151—41no—
414C22×C151—41no—
415C22×C151—42no—
416C22×C151—41no—
417C22×C151—81no—
418C22×C151—81no—
419C22×C151—82no—
420C22×C151—81no—
421C22×C151—81no—
422C22×C151—82no—
423C22×C151—82no—
424C22×C151—82no—
425C22×C151—81no—
426C22×C151—161no—
427C22×C151—161no—
428C22×C151—162no—
429C22×C151—164no—
430C22×C151#53411yescharacteristic
431C22×C151D4211yescharacteristic
432C22×C151#54611yescharacteristic
433C4×C151—22no—
434C4×C151—22no—
435C4×C151—22no—
436C4×C151—41no—
437C4×C151—41no—
438C4×C151—41no—
439C4×C151—81no—
440C4×C151—81no—
441C4×C151C2×#12011yescharacteristic
442C4×C151C2×#12111yescharacteristic
443C4×C151D4211yescharacteristic
444C4×C151#54611yescharacteristic
445C2×C151—21no—
446C2×C151—21no—
447C2×C151—21no—
448C2×C151—42no—
449C2×C151—42no—
450C2×C151—82no—
451C2×C151—81no—
452C2×C151—81no—
453C2×C151—161no—
454C2×C151#241011yescharacteristic
455#24472C15111yesmaximal, characteristic, direct product factor, Sylow
456C151#2447211yescharacteristic, direct product factor, Sylow
457#3585C2×C15111yescharacteristic, complemented
458#3068C2×C15111yescharacteristic, complemented
459#3038C2×C15111yescharacteristic, complemented
460#3021C2×C15111yescharacteristic, complemented
461C2×#453C2×C15111yescharacteristic, complemented
462#2901C2×C15111yescharacteristic, complemented
463#2050C2×C15111yescharacteristic, complemented
464#2048C2×C15111yescharacteristic, complemented
465#2008C2×C15111yescharacteristic, complemented
466#2002C2×C15111yescharacteristic, complemented
467#1906C2×C15111yescharacteristic, complemented
468#1903C2×C15111yescharacteristic, complemented
469#1903C2×C15111yescharacteristic, complemented
470#1861C2×C15111yescharacteristic, complemented
471#1795C2×C15111yescharacteristic, complemented
472#585C22×C15111yescharacteristic
473C2×H(5,𝔽2)C22×C15111yescharacteristic
474#577—22no—
475#577—22no—
476#576—22no—
477#576—22no—
478#575—22no—
479#575C22×C15111yescharacteristic
480#575C22×C15111yescharacteristic
481C2×AGL(1,ℤ/8)—22no—
482C2×AGL(1,ℤ/8)C22×C15111yescharacteristic
483C2×AGL(1,ℤ/8)C22×C15111yescharacteristic
484C2×AGL(1,ℤ/8)C22×C15111yescharacteristic
485C2×AGL(1,ℤ/8)C22×C15111yescharacteristic, complemented
486C2×AGL(1,ℤ/8)C22×C15111yescharacteristic, complemented
487#568C22×C15111yescharacteristic
488#568C22×C15111yescharacteristic, complemented
489#535C22×C15111yescharacteristic, complemented
490C2×#127C22×C15111yescharacteristic, complemented
491C4×#41C22×C15111yescharacteristic, 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×C15111yescharacteristic, complemented
501#423C22×C15111yescharacteristic, complemented
502#421—22no—
503#421C22×C15111yescharacteristic
504#421C22×C15111yescharacteristic
505#421C22×C15111yescharacteristic, complemented
506#421C22×C15111yescharacteristic, complemented
507C2×#104—22no—
508C2×#104C22×C15111yescharacteristic
509C2×#104C22×C15111yescharacteristic, complemented
510C2×#104C22×C15111yescharacteristic, complemented
511#418C22×C15111yescharacteristic, complemented
512#418C22×C15111yescharacteristic, complemented
513#418C22×C15111yescharacteristic, complemented
514#413C22×C15111yescharacteristic, complemented
515#413C22×C15111yescharacteristic, complemented
516C2×#100C22×C15111yescharacteristic, complemented
517C2×#100C22×C15111yescharacteristic, complemented
518#410C22×C15111yescharacteristic, complemented
519#344C22×C15111yescharacteristic, complemented
520#344C22×C15111yescharacteristic, complemented
521#339C22×C15111yescharacteristic, complemented
522#338C22×C15111yescharacteristic, complemented
5232−1+4—21no—
5242−1+4—21no—
5252−1+4D4×C15112yescomplemented
526H(5,𝔽2)—22no—
527H(5,𝔽2)—21no—
528H(5,𝔽2)—21no—
529H(5,𝔽2)—22no—
530H(5,𝔽2)—22no—
531H(5,𝔽2)—41no—
532H(5,𝔽2)—41no—
533H(5,𝔽2)D4×C15112yescomplemented
534C2×#41—22no—
535C2×#41—22no—
536C2×#41—21no—
537C2×#41—21no—
538C2×#41—41no—
539C2×#41C23×C15111yescharacteristic
540C2×#41C23×C15111yescharacteristic
541C2×#41C23×C15111yescharacteristic
542C2×#41C23×C15111yescharacteristic
543C22×D4—21no—
544C22×D4—21no—
545C22×D4—41no—
546C22×D4—41no—
547C22×D4C23×C15111yescharacteristic
548C22×D4C23×C15111yescharacteristic
549#137—24no—
550#137—21no—
551#137—21no—
552#137—21no—
553#137D4×C15112yescomplemented
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×C15112yescomplemented
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×C15112yescomplemented
581C2×D8—24no—
582C2×D8—21no—
583C2×D8—21no—
584C2×D8—21no—
585C2×D8—21no—
586C2×D8D4×C15112yescomplemented
587#131—22no—
588#131—22no—
589#131—22no—
590#131—41no—
591C2×M16—22no—
592C2×M16—22no—
593C2×M16C23×C15111yescharacteristic
594C2×M16C23×C15111yescharacteristic
595C2×M16C23×C15111yescharacteristic
596C2×M16C23×C15111yescharacteristic
597C2×M16C23×C15111yescharacteristic
598C2×M16C23×C15111yescharacteristic
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×C15111yescharacteristic
611#117C23×C15111yescharacteristic
612C2×C42—21no—
613C2×C42C23×C15111yescharacteristic
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×C15112yescomplemented
625#104D4×C15112yescomplemented
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×C15112yes—
666#41C2×D4×C15112yes—
667#41C2×D4×C15112yes—
668#41C2×D4×C15112yes—
669C2×Q8—22no—
670C2×Q8—22no—
671C2×Q8—41no—
672C2×Q8C2×D4×C15111yescharacteristic
673C2×Q8C2×D4×C15111yescharacteristic
674C2×Q8C2×D4×C15111yescharacteristic
675C2×Q8#41×C15111yescharacteristic
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×C15111yescharacteristic
710C2×D4C2×D4×C15111yescharacteristic
711C2×D4C2×D4×C15112yes—
712C2×D4C2×D4×C15111yescharacteristic
713C2×D4#41×C15111yescharacteristic
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×C15111yescharacteristic
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×C15112yes—
754M16C2×D4×C15112yes—
755C2×C8—24no—
756C2×C8—21no—
757C2×C8—21no—
758C2×C8—21no—
759C2×C8—21no—
760C2×C8—21no—
761C2×C8—42no—
762C2×C8C2×D4×C15112yes—
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×C15111yescharacteristic
775C42C2×D4×C15111yescharacteristic
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)×C15111yescharacteristic
792Q8—21no—
793Q8—21no—
794Q8—21no—
795Q8—21no—
796Q8—21no—
797Q8—21no—
798Q8—42no—
799Q8#120×C15112yes—
800Q8#121×C15112yes—
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×C15112yes—
832D4#121×C15112yes—
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×C15111yescharacteristic
856C2×C4C22×D4×C15111yescharacteristic
857C2×C4C22×D4×C15111yescharacteristic
858C2×C4C22×D4×C15111yescharacteristic
859C2×C4C2×#41×C15111yescharacteristic
860C2×C4H(5,𝔽2)×C15111yescharacteristic
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×C15111yescharacteristic
887C22D42×C15111yescharacteristic
888C22#546×C15111yescharacteristic
889C4—22no—
890C4—22no—
891C4—22no—
892C4—41no—
893C4—41no—
894C4—41no—
895C4—81no—
896C4—81no—
897C4C2×#120×C15111yescharacteristic
898C4C2×#121×C15111yescharacteristic
899C4D42×C15111yescharacteristic
900C4#546×C15111yescharacteristic
901C2—21no—
902C2—21no—
903C2—21no—
904C2—42no—
905C2—42no—
906C2—82no—
907C2—81no—
908C2—81no—
909C2—161no—
910C2#2410×C15111yescharacteristic
subgroupG/H
center, socleC2×C151#2410
commutator, Frattini, cosocleC22×C4C24×C151
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C2×C151 ◁ C22×C4×C151 ◁ G

Complements

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

NH ≅ G/Ntype
1. #3585×C151C2semidirect
2. #3068×C151C2semidirect
3. #3038×C151C2semidirect
4. #3021×C151C2semidirect
5. C2×#453×C151C2semidirect
6. #2901×C151C2semidirect
7. #2050×C151C2semidirect
8. #2048×C151C2semidirect
9. #2008×C151C2semidirect
10. #2002×C151C2semidirect
11. #1906×C151C2semidirect
12. #1903×C151C2semidirect
13. #1903×C151C2semidirect
14. #1861×C151C2semidirect
15. #1795×C151C2semidirect
29. C2×AGL(1,ℤ/8)×C151C22semidirect
30. C2×AGL(1,ℤ/8)×C151C22semidirect
32. #568×C151C22semidirect
33. #535×C151C22semidirect
34. C2×#127×C151C22semidirect
35. C4×#41×C151C22semidirect
44. #430×C151C22semidirect
45. #423×C151C22semidirect
49. #421×C151C22semidirect
50. #421×C151C22semidirect
53. C2×#104×C151C22semidirect
54. C2×#104×C151C22semidirect
55. #418×C151C22semidirect
56. #418×C151C22semidirect
57. #418×C151C22semidirect
58. #413×C151C22semidirect
59. #413×C151C22semidirect
60. C2×#100×C151C22semidirect
61. C2×#100×C151C22semidirect
62. #410×C151C22semidirect
63. #344×C151C22semidirect
64. #344×C151C22semidirect
65. #339×C151C22semidirect
66. #338×C151C22semidirect
69. 2−1+4×C151D4semidirect
77. H(5,𝔽2)×C151D4semidirect
97. #137×C151D4semidirect
114. AGL(1,ℤ/8)×C151D4semidirect
124. C2×SD16×C151D4semidirect
130. C2×D8×C151D4semidirect
168. #104×C151D4semidirect
169. #104×C151D4semidirect
455. #24472C151direct (N × H)
456. C151#24472direct (N × H)
457. #3585C2×C151semidirect
458. #3068C2×C151semidirect
459. #3038C2×C151semidirect
460. #3021C2×C151semidirect
461. C2×#453C2×C151semidirect
462. #2901C2×C151semidirect
463. #2050C2×C151semidirect
464. #2048C2×C151semidirect
465. #2008C2×C151semidirect
466. #2002C2×C151semidirect
467. #1906C2×C151semidirect
468. #1903C2×C151semidirect
469. #1903C2×C151semidirect
470. #1861C2×C151semidirect
471. #1795C2×C151semidirect
485. C2×AGL(1,ℤ/8)C22×C151semidirect
486. C2×AGL(1,ℤ/8)C22×C151semidirect
488. #568C22×C151semidirect
489. #535C22×C151semidirect
490. C2×#127C22×C151semidirect
491. C4×#41C22×C151semidirect
500. #430C22×C151semidirect
501. #423C22×C151semidirect
505. #421C22×C151semidirect
506. #421C22×C151semidirect
509. C2×#104C22×C151semidirect
510. C2×#104C22×C151semidirect
511. #418C22×C151semidirect
512. #418C22×C151semidirect
513. #418C22×C151semidirect
514. #413C22×C151semidirect
515. #413C22×C151semidirect
516. C2×#100C22×C151semidirect
517. C2×#100C22×C151semidirect
518. #410C22×C151semidirect
519. #344C22×C151semidirect
520. #344C22×C151semidirect
521. #339C22×C151semidirect
522. #338C22×C151semidirect
525. 2−1+4D4×C151semidirect
533. H(5,𝔽2)D4×C151semidirect
553. #137D4×C151semidirect
570. AGL(1,ℤ/8)D4×C151semidirect
580. C2×SD16D4×C151semidirect
586. C2×D8D4×C151semidirect
624. #104D4×C151semidirect
625. #104D4×C151semidirect

Maximal subgroups

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

subgroupindex
#3585×C1512
#3068×C1512
#3038×C1512
#3021×C1512
C2×#453×C1512
#2901×C1512
#2050×C1512
#2048×C1512
#2008×C1512
#2002×C1512
#1906×C1512
#1903×C1512
#1861×C1512
#1795×C1512
#24472151