Finite Group Databasebeta

← C151×#24475 #50329400

Subgroups — C151×#24475 #50329400

Order 38656.

1324 conjugacy classes of subgroups.

The subgroup lattice has 894 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#3585×C151C211yesmaximal, characteristic
2#3069×C151C211yesmaximal, characteristic, complemented
3#3040×C151C211yesmaximal, characteristic, complemented
4#3022×C151C211yesmaximal, characteristic, complemented
5C2×#455×C151C211yesmaximal, characteristic, complemented
6#2901×C151C211yesmaximal, characteristic, complemented
7#2050×C151C211yesmaximal, characteristic, complemented
8#2048×C151C211yesmaximal, characteristic, complemented
9#2009×C151C211yesmaximal, characteristic, complemented
10#2003×C151C211yesmaximal, characteristic, complemented
11#1906×C151C211yesmaximal, characteristic, complemented
12#1903×C151C211yesmaximal, characteristic, complemented
13#1902×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×#137×C151C2211yescharacteristic
26C2×#137×C151C2211yescharacteristic, complemented
27C2×#137×C151C2211yescharacteristic, complemented
28C2×AGL(1,ℤ/8)×C151—22no—
29C2×AGL(1,ℤ/8)×C151C2211yescharacteristic
30C2×AGL(1,ℤ/8)×C151C2211yescharacteristic
31#568×C151C2211yescharacteristic
32#568×C151C2211yescharacteristic, complemented
33#536×C151C2211yescharacteristic, complemented
34C2×#124×C151C2211yescharacteristic, complemented
35C4×#41×C151C2211yescharacteristic, complemented
36#473×C151—22no—
37#471×C151—22no—
38#464×C151—22no—
39#463×C151—22no—
40#456×C151—22no—
41#455×C151—22no—
42#455×C151—22no—
43#455×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#419×C151C2211yescharacteristic, complemented
56#418×C151C2211yescharacteristic, complemented
57#418×C151C2211yescharacteristic, complemented
58#413×C151C2211yescharacteristic, complemented
59#413×C151C2211yescharacteristic, complemented
60C2×#101×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×C151D412yes—
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)×C151D412yes—
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×Q8×C151C2311yescharacteristic
88C22×D4×C151—21no—
89C22×D4×C151—21no—
90C22×D4×C151—41no—
91C22×D4×C151C2311yescharacteristic
92#137×C151—24no—
93#137×C151—22no—
94#137×C151—22no—
95#137×C151—22no—
96#137×C151—22no—
97#137×C151—22no—
98#137×C151—21no—
99#137×C151—21no—
100#137×C151—21no—
101#137×C151—41no—
102#137×C151D412yes—
103AGL(1,ℤ/8)×C151—24no—
104AGL(1,ℤ/8)×C151—24no—
105AGL(1,ℤ/8)×C151—24no—
106AGL(1,ℤ/8)×C151—21no—
107AGL(1,ℤ/8)×C151—22no—
108AGL(1,ℤ/8)×C151—21no—
109AGL(1,ℤ/8)×C151—21no—
110AGL(1,ℤ/8)×C151—22no—
111AGL(1,ℤ/8)×C151—22no—
112AGL(1,ℤ/8)×C151—22no—
113AGL(1,ℤ/8)×C151D412yes—
114#135×C151—24no—
115#135×C151—24no—
116#135×C151—22no—
117#135×C151—22no—
118C2×Q16×C151—21no—
119C2×Q16×C151—21no—
120C2×Q16×C151—21no—
121C2×SD16×C151—24no—
122C2×SD16×C151—21no—
123C2×SD16×C151—21no—
124C2×SD16×C151—21no—
125C2×SD16×C151—21no—
126C2×SD16×C151D412yes—
127C2×D8×C151—24no—
128C2×D8×C151—21no—
129C2×D8×C151D412yes—
130#131×C151—22no—
131#131×C151—22no—
132#131×C151—22no—
133#131×C151—41no—
134C2×M16×C151—22no—
135C2×M16×C151—22no—
136C2×M16×C151C2311yescharacteristic
137C2×M16×C151C2311yescharacteristic
138C2×M16×C151C2311yescharacteristic
139C2×M16×C151C2311yescharacteristic
140C2×M16×C151C2311yescharacteristic
141C2×M16×C151C2311yescharacteristic
142C4⋊Q8×C151—21no—
143#124×C151—21no—
144#124×C151—22no—
145#124×C151—21no—
146#124×C151—21no—
147#123×C151—41no—
148C22⋊Q8×C151—41no—
149C4×Q8×C151—21no—
150C4×D4×C151—21no—
151C4×D4×C151—41no—
152#117×C151—21no—
153#117×C151C2311yescharacteristic
154#117×C151C2311yescharacteristic
155C2×C22⋊C4×C151—41no—
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×C151D412yes—
169#104×C151D412yes—
170#103×C151—22no—
171#102×C151—22no—
172#102×C151—41no—
173#101×C151—22no—
174#101×C151—21no—
175#101×C151—21no—
176#100×C151—21no—
177#100×C151—21no—
178#100×C151—22no—
179#99×C151—41no—
180C24×C151—21no—
181C24×C151—41no—
182#41×C151—21no—
183#41×C151—21no—
184#41×C151—21no—
185#41×C151—21no—
186#41×C151—24no—
187#41×C151—22no—
188#41×C151—22no—
189#41×C151—22no—
190#41×C151—22no—
191#41×C151—21no—
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—42no—
200#41×C151—42no—
201#41×C151—42no—
202#41×C151—42no—
203#41×C151—42no—
204#41×C151—42no—
205#41×C151—41no—
206#41×C151—41no—
207#41×C151—42no—
208#41×C151C2×D412yes—
209#41×C151C2×D412yes—
210#41×C151C2×D412yes—
211#41×C151C2×D412yes—
212C2×Q8×C151—22no—
213C2×Q8×C151—22no—
214C2×Q8×C151—21no—
215C2×Q8×C151—21no—
216C2×Q8×C151—21no—
217C2×Q8×C151—21no—
218C2×Q8×C151—21no—
219C2×Q8×C151—21no—
220C2×Q8×C151—41no—
221C2×Q8×C151C2×D411yescharacteristic
222C2×Q8×C151C2×D411yescharacteristic
223C2×Q8×C151C2×D411yescharacteristic
224C2×Q8×C151#4111yescharacteristic
225C2×D4×C151—21no—
226C2×D4×C151—21no—
227C2×D4×C151—24no—
228C2×D4×C151—22no—
229C2×D4×C151—22no—
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—42no—
238C2×D4×C151—41no—
239C2×D4×C151—41no—
240C2×D4×C151—42no—
241C2×D4×C151—42no—
242C2×D4×C151—41no—
243C2×D4×C151—44no—
244C2×D4×C151—42no—
245C2×D4×C151—42no—
246C2×D4×C151—44no—
247C2×D4×C151—42no—
248C2×D4×C151C2×D411yescharacteristic
249C2×D4×C151C2×D411yescharacteristic
250C2×D4×C151C2×D412yes—
251C2×D4×C151C2×D411yescharacteristic
252C2×D4×C151#4111yescharacteristic
253C22×C4×C151—21no—
254C22×C4×C151—21no—
255C22×C4×C151—21no—
256C22×C4×C151—21no—
257C22×C4×C151—21no—
258C22×C4×C151—21no—
259C22×C4×C151—41no—
260C22×C4×C151—42no—
261C22×C4×C151—41no—
262C22×C4×C151C2411yescharacteristic
263Q16×C151—22no—
264Q16×C151—22no—
265Q16×C151—42no—
266Q16×C151—42no—
267Q16×C151—42no—
268SD16×C151—24no—
269SD16×C151—22no—
270SD16×C151—22no—
271SD16×C151—22no—
272SD16×C151—24no—
273SD16×C151—22no—
274SD16×C151—42no—
275SD16×C151—42no—
276SD16×C151—42no—
277D8×C151—24no—
278D8×C151—22no—
279D8×C151—22no—
280D8×C151—24no—
281M16×C151—24no—
282M16×C151—21no—
283M16×C151—21no—
284M16×C151—21no—
285M16×C151—21no—
286M16×C151—21no—
287M16×C151—21no—
288M16×C151—21no—
289M16×C151—21no—
290M16×C151—21no—
291M16×C151—21no—
292M16×C151—42no—
293M16×C151C2×D412yes—
294M16×C151C2×D412yes—
295C2×C8×C151—24no—
296C2×C8×C151—21no—
297C2×C8×C151—21no—
298C2×C8×C151—21no—
299C2×C8×C151—21no—
300C2×C8×C151—21no—
301C2×C8×C151—42no—
302C2×C8×C151C2×D412yes—
303C4⋊C4×C151—21no—
304C4⋊C4×C151—21no—
305C4⋊C4×C151—41no—
306C4⋊C4×C151—42no—
307C22⋊C4×C151—21no—
308C22⋊C4×C151—21no—
309C22⋊C4×C151—42no—
310C22⋊C4×C151—42no—
311C22⋊C4×C151—41no—
312C22⋊C4×C151—42no—
313C42×C151—21no—
314C42×C151—21no—
315C42×C151—21no—
316C42×C151—41no—
317C42×C151C2×D411yescharacteristic
318C42×C151C2×D411yescharacteristic
319C23×C151—21no—
320C23×C151—21no—
321C23×C151—21no—
322C23×C151—22no—
323C23×C151—21no—
324C23×C151—42no—
325C23×C151—44no—
326C23×C151—41no—
327C23×C151—41no—
328C23×C151—82no—
329C23×C151—162no—
330C23×C151H(5,𝔽2)11yescharacteristic
331Q8×C151—21no—
332Q8×C151—21no—
333Q8×C151—21no—
334Q8×C151—21no—
335Q8×C151—21no—
336Q8×C151—21no—
337Q8×C151—42no—
338Q8×C151—41no—
339Q8×C151—41no—
340Q8×C151—41no—
341Q8×C151—41no—
342Q8×C151#12012yes—
343Q8×C151#12112yes—
344D4×C151—22no—
345D4×C151—22no—
346D4×C151—22no—
347D4×C151—22no—
348D4×C151—21no—
349D4×C151—22no—
350D4×C151—21no—
351D4×C151—21no—
352D4×C151—21no—
353D4×C151—21no—
354D4×C151—21no—
355D4×C151—22no—
356D4×C151—42no—
357D4×C151—42no—
358D4×C151—44no—
359D4×C151—42no—
360D4×C151—44no—
361D4×C151—41no—
362D4×C151—41no—
363D4×C151—41no—
364D4×C151—41no—
365D4×C151—41no—
366D4×C151—41no—
367D4×C151#12012yes—
368D4×C151#12112yes—
369C2×C4×C151—21no—
370C2×C4×C151—21no—
371C2×C4×C151—22no—
372C2×C4×C151—22no—
373C2×C4×C151—22no—
374C2×C4×C151—22no—
375C2×C4×C151—21no—
376C2×C4×C151—21no—
377C2×C4×C151—21no—
378C2×C4×C151—21no—
379C2×C4×C151—42no—
380C2×C4×C151—42no—
381C2×C4×C151—42no—
382C2×C4×C151—44no—
383C2×C4×C151—41no—
384C2×C4×C151—41no—
385C2×C4×C151—41no—
386C2×C4×C151—41no—
387C2×C4×C151—41no—
388C2×C4×C151—41no—
389C2×C4×C151—41no—
390C2×C4×C151—41no—
391C2×C4×C151—41no—
392C2×C4×C151—81no—
393C2×C4×C151—82no—
394C2×C4×C151C22×D411yescharacteristic
395C2×C4×C151C22×D411yescharacteristic
396C2×C4×C151C22×D411yescharacteristic
397C2×C4×C151C22×D411yescharacteristic
398C2×C4×C151C2×#4111yescharacteristic
399C2×C4×C151H(5,𝔽2)11yescharacteristic
400C8×C151—22no—
401C8×C151—22no—
402C8×C151—22no—
403C8×C151—41no—
404C8×C151—41no—
405C8×C151—41no—
406C22×C151—22no—
407C22×C151—22no—
408C22×C151—41no—
409C22×C151—41no—
410C22×C151—42no—
411C22×C151—41no—
412C22×C151—81no—
413C22×C151—81no—
414C22×C151—81no—
415C22×C151—82no—
416C22×C151—81no—
417C22×C151—82no—
418C22×C151—161no—
419C22×C151—162no—
420C22×C151—164no—
421C22×C151#53411yescharacteristic
422C22×C151D4211yescharacteristic
423C22×C151#54611yescharacteristic
424C4×C151—22no—
425C4×C151—22no—
426C4×C151—41no—
427C4×C151—41no—
428C4×C151—41no—
429C4×C151—41no—
430C4×C151—81no—
431C4×C151—81no—
432C4×C151—81no—
433C4×C151C2×#12011yescharacteristic
434C4×C151C2×#12111yescharacteristic
435C4×C151D4211yescharacteristic
436C4×C151#54611yescharacteristic
437C2×C151—21no—
438C2×C151—21no—
439C2×C151—21no—
440C2×C151—42no—
441C2×C151—42no—
442C2×C151—82no—
443C2×C151—81no—
444C2×C151—81no—
445C2×C151#241011yescharacteristic
446#24475C15111yesmaximal, characteristic, direct product factor, Sylow
447C151#2447511yescharacteristic, direct product factor, Sylow
448#3585C2×C15111yescharacteristic
449#3069C2×C15111yescharacteristic, complemented
450#3040C2×C15111yescharacteristic, complemented
451#3022C2×C15111yescharacteristic, complemented
452C2×#455C2×C15111yescharacteristic, complemented
453#2901C2×C15111yescharacteristic, complemented
454#2050C2×C15111yescharacteristic, complemented
455#2048C2×C15111yescharacteristic, complemented
456#2009C2×C15111yescharacteristic, complemented
457#2003C2×C15111yescharacteristic, complemented
458#1906C2×C15111yescharacteristic, complemented
459#1903C2×C15111yescharacteristic, complemented
460#1902C2×C15111yescharacteristic, complemented
461#1861C2×C15111yescharacteristic, complemented
462#1795C2×C15111yescharacteristic, complemented
463#585C22×C15111yescharacteristic
464C2×H(5,𝔽2)C22×C15111yescharacteristic
465#577—22no—
466#577—22no—
467#576—22no—
468#576—22no—
469#575—22no—
470#575C22×C15111yescharacteristic
471#575C22×C15111yescharacteristic
472C2×#137C22×C15111yescharacteristic
473C2×#137C22×C15111yescharacteristic, complemented
474C2×#137C22×C15111yescharacteristic, complemented
475C2×AGL(1,ℤ/8)—22no—
476C2×AGL(1,ℤ/8)C22×C15111yescharacteristic
477C2×AGL(1,ℤ/8)C22×C15111yescharacteristic
478#568C22×C15111yescharacteristic
479#568C22×C15111yescharacteristic, complemented
480#536C22×C15111yescharacteristic, complemented
481C2×#124C22×C15111yescharacteristic, complemented
482C4×#41C22×C15111yescharacteristic, complemented
483#473—22no—
484#471—22no—
485#464—22no—
486#463—22no—
487#456—22no—
488#455—22no—
489#455—22no—
490#455—22no—
491#430C22×C15111yescharacteristic, complemented
492#423C22×C15111yescharacteristic, complemented
493#421—22no—
494#421C22×C15111yescharacteristic
495#421C22×C15111yescharacteristic
496#421C22×C15111yescharacteristic, complemented
497#421C22×C15111yescharacteristic, complemented
498C2×#104—22no—
499C2×#104C22×C15111yescharacteristic
500C2×#104C22×C15111yescharacteristic, complemented
501C2×#104C22×C15111yescharacteristic, complemented
502#419C22×C15111yescharacteristic, complemented
503#418C22×C15111yescharacteristic, complemented
504#418C22×C15111yescharacteristic, complemented
505#413C22×C15111yescharacteristic, complemented
506#413C22×C15111yescharacteristic, complemented
507C2×#101C22×C15111yescharacteristic, complemented
508C2×#100C22×C15111yescharacteristic, complemented
509#410C22×C15111yescharacteristic, complemented
510#344C22×C15111yescharacteristic, complemented
511#344C22×C15111yescharacteristic, complemented
512#339C22×C15111yescharacteristic, complemented
513#338C22×C15111yescharacteristic, complemented
5142−1+4—21no—
5152−1+4—21no—
5162−1+4D4×C15112yes—
517H(5,𝔽2)—22no—
518H(5,𝔽2)—21no—
519H(5,𝔽2)—21no—
520H(5,𝔽2)—22no—
521H(5,𝔽2)—22no—
522H(5,𝔽2)—41no—
523H(5,𝔽2)—41no—
524H(5,𝔽2)D4×C15112yes—
525C2×#41—22no—
526C2×#41—22no—
527C2×#41—21no—
528C2×#41—21no—
529C2×#41—41no—
530C2×#41C23×C15111yescharacteristic
531C2×#41C23×C15111yescharacteristic
532C2×#41C23×C15111yescharacteristic
533C2×#41C23×C15111yescharacteristic
534C22×Q8C23×C15111yescharacteristic
535C22×D4—21no—
536C22×D4—21no—
537C22×D4—41no—
538C22×D4C23×C15111yescharacteristic
539#137—24no—
540#137—21no—
541#137—21no—
542#137—21no—
543#137—22no—
544#137—22no—
545#137—22no—
546#137—22no—
547#137—22no—
548#137—41no—
549#137D4×C15112yes—
550AGL(1,ℤ/8)—24no—
551AGL(1,ℤ/8)—24no—
552AGL(1,ℤ/8)—24no—
553AGL(1,ℤ/8)—22no—
554AGL(1,ℤ/8)—22no—
555AGL(1,ℤ/8)—21no—
556AGL(1,ℤ/8)—22no—
557AGL(1,ℤ/8)—21no—
558AGL(1,ℤ/8)—21no—
559AGL(1,ℤ/8)—22no—
560AGL(1,ℤ/8)D4×C15112yes—
561#135—24no—
562#135—24no—
563#135—22no—
564#135—22no—
565C2×Q16—21no—
566C2×Q16—21no—
567C2×Q16—21no—
568C2×SD16—24no—
569C2×SD16—21no—
570C2×SD16—21no—
571C2×SD16—21no—
572C2×SD16—21no—
573C2×SD16D4×C15112yes—
574C2×D8—24no—
575C2×D8—21no—
576C2×D8D4×C15112yes—
577#131—22no—
578#131—22no—
579#131—22no—
580#131—41no—
581C2×M16—22no—
582C2×M16—22no—
583C2×M16C23×C15111yescharacteristic
584C2×M16C23×C15111yescharacteristic
585C2×M16C23×C15111yescharacteristic
586C2×M16C23×C15111yescharacteristic
587C2×M16C23×C15111yescharacteristic
588C2×M16C23×C15111yescharacteristic
589C4⋊Q8—21no—
590#124—22no—
591#124—21no—
592#124—21no—
593#124—21no—
594#123—41no—
595C22⋊Q8—41no—
596C4×Q8—21no—
597C4×D4—21no—
598C4×D4—41no—
599#117—21no—
600#117C23×C15111yescharacteristic
601#117C23×C15111yescharacteristic
602C2×C22⋊C4—41no—
603C2×C42—21no—
604C2×C42C23×C15111yescharacteristic
605#108—22no—
606C4⋊C8—22no—
607#104—22no—
608#104—22no—
609#104—22no—
610#104—22no—
611#104—21no—
612#104—21no—
613#104—21no—
614#104—21no—
615#104D4×C15112yes—
616#104D4×C15112yes—
617#103—22no—
618#102—22no—
619#102—41no—
620#101—21no—
621#101—21no—
622#101—22no—
623#100—21no—
624#100—21no—
625#100—22no—
626#99—41no—
627C24—21no—
628C24—41no—
629#41—21no—
630#41—21no—
631#41—21no—
632#41—21no—
633#41—24no—
634#41—22no—
635#41—22no—
636#41—22no—
637#41—22no—
638#41—21no—
639#41—21no—
640#41—21no—
641#41—21no—
642#41—21no—
643#41—21no—
644#41—21no—
645#41—21no—
646#41—42no—
647#41—42no—
648#41—42no—
649#41—42no—
650#41—42no—
651#41—42no—
652#41—41no—
653#41—41no—
654#41—42no—
655#41C2×D4×C15112yes—
656#41C2×D4×C15112yes—
657#41C2×D4×C15112yes—
658#41C2×D4×C15112yes—
659C2×Q8—22no—
660C2×Q8—22no—
661C2×Q8—21no—
662C2×Q8—21no—
663C2×Q8—21no—
664C2×Q8—21no—
665C2×Q8—21no—
666C2×Q8—21no—
667C2×Q8—41no—
668C2×Q8C2×D4×C15111yescharacteristic
669C2×Q8C2×D4×C15111yescharacteristic
670C2×Q8C2×D4×C15111yescharacteristic
671C2×Q8#41×C15111yescharacteristic
672C2×D4—21no—
673C2×D4—21no—
674C2×D4—24no—
675C2×D4—22no—
676C2×D4—22no—
677C2×D4—21no—
678C2×D4—21no—
679C2×D4—21no—
680C2×D4—21no—
681C2×D4—21no—
682C2×D4—21no—
683C2×D4—21no—
684C2×D4—42no—
685C2×D4—41no—
686C2×D4—41no—
687C2×D4—42no—
688C2×D4—42no—
689C2×D4—41no—
690C2×D4—44no—
691C2×D4—42no—
692C2×D4—42no—
693C2×D4—44no—
694C2×D4—42no—
695C2×D4C2×D4×C15111yescharacteristic
696C2×D4C2×D4×C15111yescharacteristic
697C2×D4C2×D4×C15112yes—
698C2×D4C2×D4×C15111yescharacteristic
699C2×D4#41×C15111yescharacteristic
700C22×C4—21no—
701C22×C4—21no—
702C22×C4—21no—
703C22×C4—21no—
704C22×C4—21no—
705C22×C4—21no—
706C22×C4—41no—
707C22×C4—42no—
708C22×C4—41no—
709C22×C4C24×C15111yescharacteristic
710Q16—22no—
711Q16—22no—
712Q16—42no—
713Q16—42no—
714Q16—42no—
715SD16—24no—
716SD16—22no—
717SD16—22no—
718SD16—22no—
719SD16—24no—
720SD16—22no—
721SD16—42no—
722SD16—42no—
723SD16—42no—
724D8—24no—
725D8—22no—
726D8—22no—
727D8—24no—
728M16—24no—
729M16—21no—
730M16—21no—
731M16—21no—
732M16—21no—
733M16—21no—
734M16—21no—
735M16—21no—
736M16—21no—
737M16—21no—
738M16—21no—
739M16—42no—
740M16C2×D4×C15112yes—
741M16C2×D4×C15112yes—
742C2×C8—24no—
743C2×C8—21no—
744C2×C8—21no—
745C2×C8—21no—
746C2×C8—21no—
747C2×C8—21no—
748C2×C8—42no—
749C2×C8C2×D4×C15112yes—
750C4⋊C4—21no—
751C4⋊C4—21no—
752C4⋊C4—41no—
753C4⋊C4—42no—
754C22⋊C4—21no—
755C22⋊C4—21no—
756C22⋊C4—42no—
757C22⋊C4—42no—
758C22⋊C4—41no—
759C22⋊C4—42no—
760C42—21no—
761C42—21no—
762C42—21no—
763C42—41no—
764C42C2×D4×C15111yescharacteristic
765C42C2×D4×C15111yescharacteristic
766C23—21no—
767C23—21no—
768C23—21no—
769C23—22no—
770C23—21no—
771C23—42no—
772C23—44no—
773C23—41no—
774C23—41no—
775C23—82no—
776C23—162no—
777C23H(5,𝔽2)×C15111yescharacteristic
778Q8—21no—
779Q8—21no—
780Q8—21no—
781Q8—21no—
782Q8—21no—
783Q8—21no—
784Q8—42no—
785Q8—41no—
786Q8—41no—
787Q8—41no—
788Q8—41no—
789Q8#120×C15112yes—
790Q8#121×C15112yes—
791D4—22no—
792D4—22no—
793D4—22no—
794D4—22no—
795D4—21no—
796D4—21no—
797D4—22no—
798D4—21no—
799D4—21no—
800D4—21no—
801D4—21no—
802D4—22no—
803D4—42no—
804D4—42no—
805D4—44no—
806D4—42no—
807D4—44no—
808D4—41no—
809D4—41no—
810D4—41no—
811D4—41no—
812D4—41no—
813D4—41no—
814D4#120×C15112yes—
815D4#121×C15112yes—
816C2×C4—21no—
817C2×C4—21no—
818C2×C4—22no—
819C2×C4—22no—
820C2×C4—22no—
821C2×C4—22no—
822C2×C4—21no—
823C2×C4—21no—
824C2×C4—21no—
825C2×C4—21no—
826C2×C4—42no—
827C2×C4—42no—
828C2×C4—42no—
829C2×C4—44no—
830C2×C4—41no—
831C2×C4—41no—
832C2×C4—41no—
833C2×C4—41no—
834C2×C4—41no—
835C2×C4—41no—
836C2×C4—41no—
837C2×C4—41no—
838C2×C4—41no—
839C2×C4—81no—
840C2×C4—82no—
841C2×C4C22×D4×C15111yescharacteristic
842C2×C4C22×D4×C15111yescharacteristic
843C2×C4C22×D4×C15111yescharacteristic
844C2×C4C22×D4×C15111yescharacteristic
845C2×C4C2×#41×C15111yescharacteristic
846C2×C4H(5,𝔽2)×C15111yescharacteristic
847C8—22no—
848C8—22no—
849C8—22no—
850C8—41no—
851C8—41no—
852C8—41no—
853C22—22no—
854C22—22no—
855C22—41no—
856C22—41no—
857C22—42no—
858C22—41no—
859C22—81no—
860C22—81no—
861C22—82no—
862C22—81no—
863C22—81no—
864C22—82no—
865C22—161no—
866C22—162no—
867C22—164no—
868C22#534×C15111yescharacteristic
869C22D42×C15111yescharacteristic
870C22#546×C15111yescharacteristic
871C4—22no—
872C4—22no—
873C4—41no—
874C4—41no—
875C4—41no—
876C4—41no—
877C4—81no—
878C4—81no—
879C4—81no—
880C4C2×#120×C15111yescharacteristic
881C4C2×#121×C15111yescharacteristic
882C4D42×C15111yescharacteristic
883C4#546×C15111yescharacteristic
884C2—21no—
885C2—21no—
886C2—21no—
887C2—42no—
888C2—42no—
889C2—82no—
890C2—81no—
891C2—81no—
892C2#2410×C15111yescharacteristic
subgroupG/H
center, socleC2×C151#2410
commutator, Frattini, cosocleC22×C4C24×C151
prime radical#3585×C151C2
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
2. #3069×C151C2semidirect
3. #3040×C151C2semidirect
4. #3022×C151C2semidirect
5. C2×#455×C151C2semidirect
6. #2901×C151C2semidirect
7. #2050×C151C2semidirect
8. #2048×C151C2semidirect
9. #2009×C151C2semidirect
10. #2003×C151C2semidirect
11. #1906×C151C2semidirect
12. #1903×C151C2semidirect
13. #1902×C151C2semidirect
14. #1861×C151C2semidirect
15. #1795×C151C2semidirect
26. C2×#137×C151C22semidirect
27. C2×#137×C151C22semidirect
32. #568×C151C22semidirect
33. #536×C151C22semidirect
34. C2×#124×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. #419×C151C22semidirect
56. #418×C151C22semidirect
57. #418×C151C22semidirect
58. #413×C151C22semidirect
59. #413×C151C22semidirect
60. C2×#101×C151C22semidirect
61. C2×#100×C151C22semidirect
62. #410×C151C22semidirect
63. #344×C151C22semidirect
64. #344×C151C22semidirect
65. #339×C151C22semidirect
66. #338×C151C22semidirect
446. #24475C151direct (N × H)
447. C151#24475direct (N × H)
449. #3069C2×C151semidirect
450. #3040C2×C151semidirect
451. #3022C2×C151semidirect
452. C2×#455C2×C151semidirect
453. #2901C2×C151semidirect
454. #2050C2×C151semidirect
455. #2048C2×C151semidirect
456. #2009C2×C151semidirect
457. #2003C2×C151semidirect
458. #1906C2×C151semidirect
459. #1903C2×C151semidirect
460. #1902C2×C151semidirect
461. #1861C2×C151semidirect
462. #1795C2×C151semidirect
473. C2×#137C22×C151semidirect
474. C2×#137C22×C151semidirect
479. #568C22×C151semidirect
480. #536C22×C151semidirect
481. C2×#124C22×C151semidirect
482. C4×#41C22×C151semidirect
491. #430C22×C151semidirect
492. #423C22×C151semidirect
496. #421C22×C151semidirect
497. #421C22×C151semidirect
500. C2×#104C22×C151semidirect
501. C2×#104C22×C151semidirect
502. #419C22×C151semidirect
503. #418C22×C151semidirect
504. #418C22×C151semidirect
505. #413C22×C151semidirect
506. #413C22×C151semidirect
507. C2×#101C22×C151semidirect
508. C2×#100C22×C151semidirect
509. #410C22×C151semidirect
510. #344C22×C151semidirect
511. #344C22×C151semidirect
512. #339C22×C151semidirect
513. #338C22×C151semidirect

Maximal subgroups

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

subgroupindex
#3585×C1512
#3069×C1512
#3040×C1512
#3022×C1512
C2×#455×C1512
#2901×C1512
#2050×C1512
#2048×C1512
#2009×C1512
#2003×C1512
#1906×C1512
#1903×C1512
#1902×C1512
#1861×C1512
#1795×C1512
#24475151