Finite Group Databasebeta

← C151×#24231 #50329156

Subgroups — C151×#24231 #50329156

Order 38656.

1368 conjugacy classes of subgroups.

The subgroup lattice has 722 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#3499×C151C211yesmaximal, characteristic, complemented
2#3036×C151C211yesmaximal, characteristic, complemented
3C2×#454×C151C212yesmaximal, complemented
4C4×AGL(1,ℤ/8)×C151C211yesmaximal, characteristic, complemented
5#2547×C151C211yesmaximal, characteristic, complemented
6#2038×C151C212yesmaximal, complemented
7#2003×C151C212yesmaximal, complemented
8#1980×C151C211yesmaximal, characteristic, complemented
9#1966×C151C211yesmaximal, characteristic, complemented
10#1806×C151C211yesmaximal, characteristic, complemented
11#1793×C151C212yesmaximal, complemented
12C2×2−1+4×C151C2212yes—
13C2×AGL(1,ℤ/8)×C151C2212yes—
14C2×AGL(1,ℤ/8)×C151C2211yescharacteristic
15D4×Q8×C151—21no—
16D4×Q8×C151—21no—
17#547×C151—21no—
18#547×C151—21no—
19#547×C151—22no—
20#547×C151—22no—
21#536×C151—22no—
22#536×C151C2212yes—
23#532×C151—21no—
24#532×C151C2211yescharacteristic
25C2×C4⋊Q8×C151—21no—
26C2×C4⋊Q8×C151C2211yescharacteristic
27C2×#124×C151C2212yes—
28C4×#41×C151C2211yescharacteristic
29C2×C4×D4×C151C2211yescharacteristic
30#463×C151—22no—
31#461×C151—21no—
32#459×C151—21no—
33#454×C151—28no—
34#442×C151—21no—
35#440×C151—21no—
36C4×SD16×C151—21no—
37C4×D8×C151—21no—
38#428×C151C2211yescharacteristic
39#423×C151C2211yescharacteristic
40C2×#104×C151C2212yes—
41C2×#104×C151C2212yes—
42C2×#104×C151C2212yes—
43#418×C151C2211yescharacteristic
44#417×C151C2211yescharacteristic
45#417×C151C2212yes—
46C2×#101×C151C2212yes—
47C2×#101×C151C2212yes—
48C4×M16×C151C2211yescharacteristic
49#397×C151—22no—
50#391×C151C2212yes—
51#380×C151—22no—
52C4×C4⋊C4×C151C2211yescharacteristic
53#339×C151C2212yes—
542−1+4×C151—24no—
552−1+4×C151—24no—
562−1+4×C151—42no—
572−1+4×C151—42no—
58C2×#41×C151—22no—
59C2×#41×C151—22no—
60C2×#41×C151—24no—
61C2×#41×C151C2312yes—
62C2×#41×C151C2311yescharacteristic
63C22×Q8×C151—22no—
64C22×Q8×C151—22no—
65C22×Q8×C151C2312yes—
66C22×D4×C151C2311yescharacteristic
67C23×C4×C151—21no—
68AGL(1,ℤ/8)×C151—24no—
69AGL(1,ℤ/8)×C151—22no—
70AGL(1,ℤ/8)×C151—42no—
71AGL(1,ℤ/8)×C151D414yescomplemented
72C2×SD16×C151—21no—
73C2×SD16×C151—22no—
74C2×D8×C151—21no—
75C2×D8×C151—22no—
76C2×M16×C151C2312yes—
77C2×M16×C151C2311yescharacteristic
78C2×M16×C151C2311yescharacteristic
79C4⋊Q8×C151—22no—
80C4⋊Q8×C151—22no—
81C4⋊Q8×C151—21no—
82C4⋊Q8×C151—21no—
83C4⋊Q8×C151—21no—
84C4⋊Q8×C151—21no—
85C4⋊Q8×C151—22no—
86C4⋊Q8×C151D411yescharacteristic
87#127×C151D411yescharacteristic
88#124×C151—22no—
89#124×C151—24no—
90#124×C151—42no—
91#124×C151D412yes—
92#123×C151—24no—
93#123×C151—24no—
94#123×C151—24no—
95C22⋊Q8×C151—24no—
96C22⋊Q8×C151—24no—
97C22⋊Q8×C151—22no—
98C22⋊Q8×C151—22no—
99#121×C151—22no—
100#121×C151—22no—
101#121×C151—21no—
102#121×C151—21no—
103C4×Q8×C151D411yescharacteristic
104C4×Q8×C151D411yescharacteristic
105C4×D4×C151—22no—
106C4×D4×C151—22no—
107C4×D4×C151—21no—
108C4×D4×C151—21no—
109C4×D4×C151—21no—
110C4×D4×C151—21no—
111C4×D4×C151—21no—
112C4×D4×C151—21no—
113C4×D4×C151—21no—
114C4×D4×C151—21no—
115C4×D4×C151D411yescharacteristic
116C4×D4×C151D411yescharacteristic
117#117×C151—21no—
118#117×C151C2311yescharacteristic
119C2×C4⋊C4×C151—22no—
120C2×C4⋊C4×C151—22no—
121C2×C4⋊C4×C151—21no—
122C2×C4⋊C4×C151D412yes—
123C2×C4⋊C4×C151D412yes—
124C2×C4⋊C4×C151C2311yescharacteristic
125C2×C22⋊C4×C151—24no—
126C2×C22⋊C4×C151—21no—
127C2×C42×C151—21no—
128C2×C42×C151C2312yes—
129C2×C42×C151C2311yescharacteristic
130#107×C151—21no—
131#106×C151—21no—
132C4⋊C8×C151—21no—
133C4⋊C8×C151—21no—
134#104×C151—24no—
135#104×C151—24no—
136#104×C151—42no—
137#103×C151—21no—
138#103×C151—22no—
139#102×C151—21no—
140#102×C151—22no—
141#102×C151—21no—
142#102×C151—21no—
143#101×C151—24no—
144#101×C151—42no—
145#97×C151—21no—
146C4×C8×C151—21no—
147#95×C151—21no—
148#95×C151—24no—
149C24×C151—21no—
150#41×C151—21no—
151#41×C151—21no—
152#41×C151—22no—
153#41×C151—22no—
154#41×C151—22no—
155#41×C151—22no—
156#41×C151—44no—
157#41×C151—44no—
158#41×C151—48no—
159#41×C151—48no—
160#41×C151—44no—
161#41×C151—44no—
162#41×C151C2×D412yes—
163#41×C151#4112yes—
164C2×Q8×C151—24no—
165C2×Q8×C151—22no—
166C2×Q8×C151—22no—
167C2×Q8×C151—22no—
168C2×Q8×C151—22no—
169C2×Q8×C151—22no—
170C2×Q8×C151—22no—
171C2×Q8×C151—44no—
172C2×Q8×C151—44no—
173C2×Q8×C151—44no—
174C2×Q8×C151—44no—
175C2×Q8×C151C2×D412yes—
176C2×Q8×C151C2×D411yescharacteristic
177C2×D4×C151—21no—
178C2×D4×C151—24no—
179C2×D4×C151—22no—
180C2×D4×C151—21no—
181C2×D4×C151—21no—
182C2×D4×C151—21no—
183C2×D4×C151—21no—
184C2×D4×C151—21no—
185C2×D4×C151—21no—
186C2×D4×C151—21no—
187C2×D4×C151C2×D412yes—
188C2×D4×C151C2×D412yes—
189C2×D4×C151C2×D411yescharacteristic
190C22×C4×C151—21no—
191C22×C4×C151—24no—
192C22×C4×C151—24no—
193C22×C4×C151—21no—
194C22×C4×C151—21no—
195C22×C4×C151—22no—
196C22×C4×C151—21no—
197C22×C4×C151—22no—
198C22×C4×C151—44no—
199C22×C4×C151—41no—
200C22×C4×C151—41no—
201C22×C4×C151C2×D414yes—
202C22×C4×C151C2×D411yescharacteristic
203C22×C4×C151C2×D411yescharacteristic
204C22×C4×C151C2411yescharacteristic
205SD16×C151—24no—
206SD16×C151—44no—
207D8×C151—24no—
208D8×C151—44no—
209M16×C151—21no—
210M16×C151—22no—
211M16×C151—21no—
212M16×C151—22no—
213M16×C151—21no—
214M16×C151C2×D412yes—
215C2×C8×C151—21no—
216C2×C8×C151—21no—
217C2×C8×C151—22no—
218C4⋊C4×C151—24no—
219C4⋊C4×C151—24no—
220C4⋊C4×C151—21no—
221C4⋊C4×C151—21no—
222C4⋊C4×C151—22no—
223C4⋊C4×C151—22no—
224C4⋊C4×C151—22no—
225C4⋊C4×C151—22no—
226C4⋊C4×C151—21no—
227C4⋊C4×C151—21no—
228C4⋊C4×C151—21no—
229C4⋊C4×C151—21no—
230C4⋊C4×C151—42no—
231C4⋊C4×C151C2×D411yescharacteristic
232C4⋊C4×C151C2×D411yescharacteristic
233C22⋊C4×C151—24no—
234C22⋊C4×C151—24no—
235C22⋊C4×C151—21no—
236C22⋊C4×C151—21no—
237C22⋊C4×C151—21no—
238C22⋊C4×C151—22no—
239C22⋊C4×C151—22no—
240C22⋊C4×C151—48no—
241C22⋊C4×C151—41no—
242C22⋊C4×C151—41no—
243C42×C151—21no—
244C42×C151—21no—
245C42×C151—21no—
246C42×C151—22no—
247C42×C151—22no—
248C42×C151C2×D411yescharacteristic
249C42×C151C2×D411yescharacteristic
250C42×C151C2×D411yescharacteristic
251C42×C151C2×D411yescharacteristic
252C23×C151—21no—
253C23×C151—22no—
254C23×C151—22no—
255C23×C151—42no—
256C23×C151—42no—
257C23×C151—41no—
258C23×C151—41no—
259C23×C151C22×D411yescharacteristic
260Q8×C151—21no—
261Q8×C151—22no—
262Q8×C151—22no—
263Q8×C151—48no—
264Q8×C151—42no—
265Q8×C151—42no—
266Q8×C151—42no—
267Q8×C151—42no—
268Q8×C151#12112yes—
269D4×C151—22no—
270D4×C151—22no—
271D4×C151—22no—
272D4×C151—21no—
273D4×C151—22no—
274D4×C151—22no—
275D4×C151—22no—
276D4×C151—42no—
277D4×C151—48no—
278D4×C151—42no—
279D4×C151—42no—
280D4×C151—41no—
281D4×C151—41no—
282D4×C151—42no—
283D4×C151#12112yes—
284C2×C4×C151—21no—
285C2×C4×C151—22no—
286C2×C4×C151—22no—
287C2×C4×C151—22no—
288C2×C4×C151—24no—
289C2×C4×C151—22no—
290C2×C4×C151—21no—
291C2×C4×C151—21no—
292C2×C4×C151—24no—
293C2×C4×C151—24no—
294C2×C4×C151—41no—
295C2×C4×C151—48no—
296C2×C4×C151—42no—
297C2×C4×C151—48no—
298C2×C4×C151—42no—
299C2×C4×C151—42no—
300C2×C4×C151—42no—
301C2×C4×C151—42no—
302C2×C4×C151—42no—
303C2×C4×C151—42no—
304C2×C4×C151—41no—
305C2×C4×C151—42no—
306C2×C4×C151—82no—
307C2×C4×C151—82no—
308C2×C4×C151#12011yescharacteristic
309C2×C4×C151#12011yescharacteristic
310C2×C4×C151#12011yescharacteristic
311C2×C4×C151#12011yescharacteristic
312C2×C4×C151C22×D411yescharacteristic
313C2×C4×C151C22×D411yescharacteristic
314C2×C4×C151C22×D411yescharacteristic
315C2×C4×C151C2×#4111yescharacteristic
316C2×C4×C151H(5,𝔽2)11yescharacteristic
317C2×C4×C151H(5,𝔽2)11yescharacteristic
318C8×C151—22no—
319C8×C151—41no—
320C8×C151—42no—
321C22×C151—21no—
322C22×C151—21no—
323C22×C151—22no—
324C22×C151—44no—
325C22×C151—41no—
326C22×C151—41no—
327C22×C151—42no—
328C22×C151—42no—
329C22×C151—42no—
330C22×C151—42no—
331C22×C151—82no—
332C22×C151—81no—
333C22×C151—81no—
334C22×C151C2×#12011yescharacteristic
335C22×C151D4211yescharacteristic
336C22×C151#54611yescharacteristic
337C4×C151—22no—
338C4×C151—21no—
339C4×C151—21no—
340C4×C151—21no—
341C4×C151—44no—
342C4×C151—42no—
343C4×C151—41no—
344C4×C151—41no—
345C4×C151—82no—
346C4×C151—81no—
347C4×C151#45412yescomplemented
348C4×C151C2×#12111yescharacteristic
349C4×C151#53511yescharacteristic
350C4×C151D4211yescharacteristic
351C4×C151#54611yescharacteristic
352C2×C151—21no—
353C2×C151—21no—
354C2×C151—42no—
355C2×C151—82no—
356C2×C151—82no—
357C2×C151#240811yescharacteristic
358C2×C151C2×#45411yescharacteristic
359C2×C151#302011yescharacteristic
360#24231C15111yesmaximal, characteristic, direct product factor, Sylow
361C151#2423111yescharacteristic, direct product factor, Sylow
362#3499C2×C15111yescharacteristic, complemented
363#3036C2×C15111yescharacteristic, complemented
364C2×#454C2×C15112yescomplemented
365C4×AGL(1,ℤ/8)C2×C15111yescharacteristic, complemented
366#2547C2×C15111yescharacteristic, complemented
367#2038C2×C15112yescomplemented
368#2003C2×C15112yescomplemented
369#1980C2×C15111yescharacteristic, complemented
370#1966C2×C15111yescharacteristic, complemented
371#1806C2×C15111yescharacteristic, complemented
372#1793C2×C15112yescomplemented
373C2×2−1+4C22×C15112yes—
374C2×AGL(1,ℤ/8)C22×C15112yes—
375C2×AGL(1,ℤ/8)C22×C15111yescharacteristic
376D4×Q8—21no—
377D4×Q8—21no—
378#547—21no—
379#547—21no—
380#547—22no—
381#547—22no—
382#536—22no—
383#536C22×C15112yes—
384#532—21no—
385#532C22×C15111yescharacteristic
386C2×C4⋊Q8—21no—
387C2×C4⋊Q8C22×C15111yescharacteristic
388C2×#124C22×C15112yes—
389C4×#41C22×C15111yescharacteristic
390C2×C4×D4C22×C15111yescharacteristic
391#463—22no—
392#461—21no—
393#459—21no—
394#454—28no—
395#442—21no—
396#440—21no—
397C4×SD16—21no—
398C4×D8—21no—
399#428C22×C15111yescharacteristic
400#423C22×C15111yescharacteristic
401C2×#104C22×C15112yes—
402C2×#104C22×C15112yes—
403C2×#104C22×C15112yes—
404#418C22×C15111yescharacteristic
405#417C22×C15111yescharacteristic
406#417C22×C15112yes—
407C2×#101C22×C15112yes—
408C2×#101C22×C15112yes—
409C4×M16C22×C15111yescharacteristic
410#397—22no—
411#391C22×C15112yes—
412#380—22no—
413C4×C4⋊C4C22×C15111yescharacteristic
414#339C22×C15112yes—
4152−1+4—24no—
4162−1+4—24no—
4172−1+4—42no—
4182−1+4—42no—
419C2×#41—22no—
420C2×#41—22no—
421C2×#41—24no—
422C2×#41C23×C15112yes—
423C2×#41C23×C15111yescharacteristic
424C22×Q8—22no—
425C22×Q8—22no—
426C22×Q8C23×C15112yes—
427C22×D4C23×C15111yescharacteristic
428C23×C4—21no—
429AGL(1,ℤ/8)—22no—
430AGL(1,ℤ/8)—24no—
431AGL(1,ℤ/8)—42no—
432AGL(1,ℤ/8)D4×C15114yescomplemented
433C2×SD16—21no—
434C2×SD16—22no—
435C2×D8—21no—
436C2×D8—22no—
437C2×M16C23×C15112yes—
438C2×M16C23×C15111yescharacteristic
439C2×M16C23×C15111yescharacteristic
440C4⋊Q8—22no—
441C4⋊Q8—22no—
442C4⋊Q8—22no—
443C4⋊Q8—21no—
444C4⋊Q8—21no—
445C4⋊Q8—21no—
446C4⋊Q8—21no—
447C4⋊Q8D4×C15111yescharacteristic
448#127D4×C15111yescharacteristic
449#124—22no—
450#124—24no—
451#124—42no—
452#124D4×C15112yes—
453#123—24no—
454#123—24no—
455#123—24no—
456C22⋊Q8—24no—
457C22⋊Q8—24no—
458C22⋊Q8—22no—
459C22⋊Q8—22no—
460#121—22no—
461#121—22no—
462#121—21no—
463#121—21no—
464C4×Q8D4×C15111yescharacteristic
465C4×Q8D4×C15111yescharacteristic
466C4×D4—22no—
467C4×D4—22no—
468C4×D4—21no—
469C4×D4—21no—
470C4×D4—21no—
471C4×D4—21no—
472C4×D4—21no—
473C4×D4—21no—
474C4×D4—21no—
475C4×D4—21no—
476C4×D4D4×C15111yescharacteristic
477C4×D4D4×C15111yescharacteristic
478#117—21no—
479#117C23×C15111yescharacteristic
480C2×C4⋊C4—22no—
481C2×C4⋊C4—22no—
482C2×C4⋊C4—21no—
483C2×C4⋊C4D4×C15112yes—
484C2×C4⋊C4D4×C15112yes—
485C2×C4⋊C4C23×C15111yescharacteristic
486C2×C22⋊C4—21no—
487C2×C22⋊C4—24no—
488C2×C42—21no—
489C2×C42C23×C15112yes—
490C2×C42C23×C15111yescharacteristic
491#107—21no—
492#106—21no—
493C4⋊C8—21no—
494C4⋊C8—21no—
495#104—24no—
496#104—24no—
497#104—42no—
498#103—21no—
499#103—22no—
500#102—21no—
501#102—22no—
502#102—21no—
503#102—21no—
504#101—24no—
505#101—42no—
506#97—21no—
507C4×C8—21no—
508#95—21no—
509#95—24no—
510C24—21no—
511#41—21no—
512#41—21no—
513#41—22no—
514#41—22no—
515#41—22no—
516#41—22no—
517#41—44no—
518#41—44no—
519#41—48no—
520#41—48no—
521#41—44no—
522#41—44no—
523#41C2×D4×C15112yes—
524#41#41×C15112yes—
525C2×Q8—24no—
526C2×Q8—22no—
527C2×Q8—22no—
528C2×Q8—22no—
529C2×Q8—22no—
530C2×Q8—22no—
531C2×Q8—22no—
532C2×Q8—44no—
533C2×Q8—44no—
534C2×Q8—44no—
535C2×Q8—44no—
536C2×Q8C2×D4×C15112yes—
537C2×Q8C2×D4×C15111yescharacteristic
538C2×D4—21no—
539C2×D4—24no—
540C2×D4—22no—
541C2×D4—21no—
542C2×D4—21no—
543C2×D4—21no—
544C2×D4—21no—
545C2×D4—21no—
546C2×D4—21no—
547C2×D4—21no—
548C2×D4C2×D4×C15112yes—
549C2×D4C2×D4×C15112yes—
550C2×D4C2×D4×C15111yescharacteristic
551C22×C4—21no—
552C22×C4—24no—
553C22×C4—24no—
554C22×C4—21no—
555C22×C4—21no—
556C22×C4—22no—
557C22×C4—21no—
558C22×C4—22no—
559C22×C4—44no—
560C22×C4—41no—
561C22×C4—41no—
562C22×C4C2×D4×C15114yes—
563C22×C4C2×D4×C15111yescharacteristic
564C22×C4C2×D4×C15111yescharacteristic
565C22×C4C24×C15111yescharacteristic
566SD16—24no—
567SD16—44no—
568D8—24no—
569D8—44no—
570M16—21no—
571M16—22no—
572M16—21no—
573M16—22no—
574M16—21no—
575M16C2×D4×C15112yes—
576C2×C8—21no—
577C2×C8—21no—
578C2×C8—22no—
579C4⋊C4—24no—
580C4⋊C4—24no—
581C4⋊C4—21no—
582C4⋊C4—21no—
583C4⋊C4—22no—
584C4⋊C4—22no—
585C4⋊C4—22no—
586C4⋊C4—22no—
587C4⋊C4—21no—
588C4⋊C4—21no—
589C4⋊C4—21no—
590C4⋊C4—21no—
591C4⋊C4—42no—
592C4⋊C4C2×D4×C15111yescharacteristic
593C4⋊C4C2×D4×C15111yescharacteristic
594C22⋊C4—24no—
595C22⋊C4—24no—
596C22⋊C4—21no—
597C22⋊C4—21no—
598C22⋊C4—21no—
599C22⋊C4—22no—
600C22⋊C4—22no—
601C22⋊C4—48no—
602C22⋊C4—41no—
603C22⋊C4—41no—
604C42—21no—
605C42—21no—
606C42—21no—
607C42—22no—
608C42—22no—
609C42C2×D4×C15111yescharacteristic
610C42C2×D4×C15111yescharacteristic
611C42C2×D4×C15111yescharacteristic
612C42C2×D4×C15111yescharacteristic
613C23—21no—
614C23—22no—
615C23—22no—
616C23—42no—
617C23—42no—
618C23—41no—
619C23—41no—
620C23C22×D4×C15111yescharacteristic
621Q8—21no—
622Q8—22no—
623Q8—22no—
624Q8—48no—
625Q8—42no—
626Q8—42no—
627Q8—42no—
628Q8—42no—
629Q8#121×C15112yes—
630D4—22no—
631D4—22no—
632D4—22no—
633D4—21no—
634D4—22no—
635D4—22no—
636D4—22no—
637D4—42no—
638D4—48no—
639D4—42no—
640D4—42no—
641D4—42no—
642D4—41no—
643D4—41no—
644D4#121×C15112yes—
645C2×C4—21no—
646C2×C4—22no—
647C2×C4—22no—
648C2×C4—22no—
649C2×C4—21no—
650C2×C4—21no—
651C2×C4—22no—
652C2×C4—24no—
653C2×C4—24no—
654C2×C4—24no—
655C2×C4—41no—
656C2×C4—48no—
657C2×C4—42no—
658C2×C4—48no—
659C2×C4—42no—
660C2×C4—42no—
661C2×C4—42no—
662C2×C4—42no—
663C2×C4—42no—
664C2×C4—42no—
665C2×C4—41no—
666C2×C4—42no—
667C2×C4—82no—
668C2×C4—82no—
669C2×C4#120×C15111yescharacteristic
670C2×C4#120×C15111yescharacteristic
671C2×C4#120×C15111yescharacteristic
672C2×C4#120×C15111yescharacteristic
673C2×C4C22×D4×C15111yescharacteristic
674C2×C4C22×D4×C15111yescharacteristic
675C2×C4C22×D4×C15111yescharacteristic
676C2×C4C2×#41×C15111yescharacteristic
677C2×C4H(5,𝔽2)×C15111yescharacteristic
678C2×C4H(5,𝔽2)×C15111yescharacteristic
679C8—22no—
680C8—41no—
681C8—42no—
682C22—21no—
683C22—21no—
684C22—22no—
685C22—44no—
686C22—41no—
687C22—41no—
688C22—42no—
689C22—42no—
690C22—42no—
691C22—42no—
692C22—82no—
693C22—81no—
694C22—81no—
695C22C2×#120×C15111yescharacteristic
696C22D42×C15111yescharacteristic
697C22#546×C15111yescharacteristic
698C4—22no—
699C4—21no—
700C4—21no—
701C4—21no—
702C4—44no—
703C4—42no—
704C4—41no—
705C4—41no—
706C4—82no—
707C4—81no—
708C4#454×C15112yescomplemented
709C4C2×#121×C15111yescharacteristic
710C4#535×C15111yescharacteristic
711C4D42×C15111yescharacteristic
712C4#546×C15111yescharacteristic
713C2—21no—
714C2—21no—
715C2—42no—
716C2—82no—
717C2—82no—
718C2#2408×C15111yescharacteristic
719C2C2×#454×C15111yescharacteristic
720C2#3020×C15111yescharacteristic
subgroupG/H
center, socleC22×C151C2×#120
commutator, Frattini, cosocleC22×C4C24×C151
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C151 ◁ C2×C42×C151 ◁ G

Complements

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

NH ≅ G/Ntype
1. #3499×C151C2semidirect
2. #3036×C151C2semidirect
3. C2×#454×C151C2semidirect
4. C4×AGL(1,ℤ/8)×C151C2semidirect
5. #2547×C151C2semidirect
6. #2038×C151C2semidirect
7. #2003×C151C2semidirect
8. #1980×C151C2semidirect
9. #1966×C151C2semidirect
10. #1806×C151C2semidirect
11. #1793×C151C2semidirect
71. AGL(1,ℤ/8)×C151D4semidirect
347. C4×C151#454semidirect
360. #24231C151direct (N × H)
361. C151#24231direct (N × H)
362. #3499C2×C151semidirect
363. #3036C2×C151semidirect
364. C2×#454C2×C151semidirect
365. C4×AGL(1,ℤ/8)C2×C151semidirect
366. #2547C2×C151semidirect
367. #2038C2×C151semidirect
368. #2003C2×C151semidirect
369. #1980C2×C151semidirect
370. #1966C2×C151semidirect
371. #1806C2×C151semidirect
372. #1793C2×C151semidirect
432. AGL(1,ℤ/8)D4×C151semidirect
708. C4#454×C151semidirect

Maximal subgroups

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

subgroupindex
#3499×C1512
#3036×C1512
C2×#454×C1512
C4×AGL(1,ℤ/8)×C1512
#2547×C1512
#2038×C1512
#2003×C1512
#1980×C1512
#1966×C1512
#1806×C1512
#1793×C1512
#24231151