Finite Group Databasebeta

← C151×#20995 #50325920

Subgroups — C151×#20995 #50325920

Order 38656.

1664 conjugacy classes of subgroups.

The subgroup lattice has 826 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#575×C151C211yesmaximal, characteristic
2C2×#568×C151C211yesmaximal, characteristic, complemented
3C2×#421×C151C211yesmaximal, characteristic, complemented
4#2896×C151C211yesmaximal, characteristic, complemented
5C2×#413×C151C211yesmaximal, characteristic, complemented
6#1903×C151C214yesmaximal, complemented
7#1902×C151C214yesmaximal, complemented
8C2×#344×C151C211yesmaximal, characteristic, complemented
9C2×#338×C151C211yesmaximal, characteristic, complemented
10C22×#41×C151C2211yescharacteristic
11C22×#41×C151C2211yescharacteristic
12#575×C151—22no—
13#575×C151—22no—
14#575×C151—22no—
15#575×C151—22no—
16C2×#137×C151C412yescomplemented
17C2×#137×C151C2212yes—
18C2×AGL(1,ℤ/8)×C151C412yescomplemented
19C2×AGL(1,ℤ/8)×C151C2212yes—
20C2×#135×C151C414yescomplemented
21#568×C151—22no—
22#568×C151—22no—
23#568×C151—22no—
24#568×C151C2214yes—
25C2×#131×C151—22no—
26C2×#131×C151—22no—
27C22×M16×C151—22no—
28C22×M16×C151C2211yescharacteristic
29C22×M16×C151C2211yescharacteristic
30C22×M16×C151C2211yescharacteristic
31C22×M16×C151C2211yescharacteristic
32C2×#117×C151C2211yescharacteristic
33#421×C151—22no—
34#421×C151C2214yes—
35C2×#104×C151—22no—
36#419×C151C2212yescomplemented
37#418×C151C2212yescomplemented
38#417×C151—22no—
39#416×C151—22no—
40#413×C151—22no—
41#413×C151—22no—
42C2×#101×C151C2212yescomplemented
43C2×#100×C151C2212yescomplemented
44#344×C151C2214yescomplemented
45#338×C151C2214yescomplemented
46C2×#41×C151—21no—
47C2×#41×C151—21no—
48C2×#41×C151—21no—
49C2×#41×C151—21no—
50C2×#41×C151—21no—
51C2×#41×C151—21no—
52C2×#41×C151—21no—
53C2×#41×C151—21no—
54C2×#41×C151—21no—
55C2×#41×C151—21no—
56C2×#41×C151—21no—
57C2×#41×C151—21no—
58C2×#41×C151—21no—
59C2×#41×C151—21no—
60C2×#41×C151—21no—
61C2×#41×C151—21no—
62C2×#41×C151C2×C412yes—
63C2×#41×C151C2×C412yes—
64C2×#41×C151C2×C412yes—
65C2×#41×C151D412yes—
66C2×#41×C151D412yes—
67C2×#41×C151D412yes—
68C2×#41×C151D412yes—
69C2×#41×C151C2312yes—
70C22×Q8×C151C2×C411yescharacteristic
71C22×Q8×C151C2311yescharacteristic
72C22×D4×C151—21no—
73C22×D4×C151—21no—
74C22×D4×C151C2×C411yescharacteristic
75C22×D4×C151C2311yescharacteristic
76C23×C4×C151—21no—
77C23×C4×C151—21no—
78C23×C4×C151C2311yescharacteristic
79#137×C151—24no—
80#137×C151—24no—
81#137×C151—24no—
82#137×C151—24no—
83AGL(1,ℤ/8)×C151—24no—
84AGL(1,ℤ/8)×C151—24no—
85AGL(1,ℤ/8)×C151—24no—
86AGL(1,ℤ/8)×C151—24no—
87#135×C151—28no—
88#135×C151—28no—
89C2×Q16×C151C2×C414yescomplemented
90C2×SD16×C151C2×C414yescomplemented
91C2×SD16×C151C2×C414yescomplemented
92C2×D8×C151C2×C414yescomplemented
93#131×C151—28no—
94#131×C151—28no—
95#131×C151—28no—
96#131×C151—28no—
97C2×M16×C151—24no—
98C2×M16×C151—28no—
99C2×M16×C151—21no—
100C2×M16×C151—21no—
101C2×M16×C151—21no—
102C2×M16×C151—21no—
103C2×M16×C151—21no—
104C2×M16×C151—21no—
105C2×M16×C151—21no—
106C2×M16×C151—21no—
107C2×M16×C151—21no—
108C2×M16×C151—21no—
109C2×M16×C151—21no—
110C2×M16×C151—28no—
111C2×M16×C151—21no—
112C2×M16×C151—21no—
113C2×M16×C151—21no—
114C2×M16×C151—21no—
115C2×M16×C151—21no—
116C2×M16×C151C2×C412yes—
117C2×M16×C151D412yes—
118C2×M16×C151D412yes—
119C2×M16×C151D412yes—
120C2×M16×C151C2312yes—
121C2×M16×C151C2312yes—
122C2×M16×C151C2312yes—
123C2×M16×C151C2312yes—
124C22×C8×C151—24no—
125C22×C8×C151—21no—
126C22×C8×C151—21no—
127C22×C8×C151C2×C412yes—
128C22×C8×C151D412yes—
129#117×C151—21no—
130#117×C151—21no—
131#117×C151—21no—
132#117×C151C2312yes—
133C2×C4⋊C4×C151—21no—
134C2×C22⋊C4×C151—21no—
135C2×C42×C151—21no—
136#104×C151—28no—
137#103×C151—24no—
138#102×C151—24no—
139#101×C151—24no—
140#100×C151—24no—
141C24×C151—21no—
142C24×C151—21no—
143C24×C151#4111yescharacteristic
144#41×C151—22no—
145#41×C151—22no—
146#41×C151—22no—
147#41×C151—22no—
148#41×C151—22no—
149#41×C151—22no—
150#41×C151—22no—
151#41×C151—22no—
152#41×C151—22no—
153#41×C151—22no—
154#41×C151—22no—
155#41×C151—22no—
156#41×C151—22no—
157#41×C151—22no—
158#41×C151—22no—
159#41×C151—22no—
160#41×C151—22no—
161#41×C151—22no—
162#41×C151—22no—
163#41×C151—22no—
164#41×C151—41no—
165#41×C151—41no—
166#41×C151—41no—
167#41×C151—41no—
168#41×C151—41no—
169#41×C151—41no—
170#41×C151—41no—
171#41×C151—41no—
172#41×C151C22⋊C414yes—
173#41×C151C22⋊C414yes—
174#41×C151C2×D414yes—
175#41×C151C2×D414yes—
176C2×Q8×C151—21no—
177C2×Q8×C151—21no—
178C2×Q8×C151—21no—
179C2×Q8×C151—21no—
180C2×Q8×C151—21no—
181C2×Q8×C151—21no—
182C2×Q8×C151—21no—
183C2×Q8×C151—21no—
184C2×Q8×C151C22⋊C412yes—
185C2×Q8×C151C22⋊C412yes—
186C2×Q8×C151C22×C412yes—
187C2×Q8×C151C22×C412yes—
188C2×D4×C151—22no—
189C2×D4×C151—22no—
190C2×D4×C151—22no—
191C2×D4×C151—22no—
192C2×D4×C151—22no—
193C2×D4×C151—22no—
194C2×D4×C151—22no—
195C2×D4×C151—22no—
196C2×D4×C151—21no—
197C2×D4×C151—21no—
198C2×D4×C151—21no—
199C2×D4×C151—21no—
200C2×D4×C151—21no—
201C2×D4×C151—21no—
202C2×D4×C151—21no—
203C2×D4×C151—21no—
204C2×D4×C151—41no—
205C2×D4×C151—41no—
206C2×D4×C151—41no—
207C2×D4×C151—41no—
208C2×D4×C151C22⋊C412yes—
209C2×D4×C151C22⋊C412yes—
210C2×D4×C151C22×C412yes—
211C2×D4×C151C22×C412yes—
212C22×C4×C151—21no—
213C22×C4×C151—22no—
214C22×C4×C151—22no—
215C22×C4×C151—22no—
216C22×C4×C151—22no—
217C22×C4×C151—22no—
218C22×C4×C151—22no—
219C22×C4×C151—21no—
220C22×C4×C151—22no—
221C22×C4×C151—22no—
222C22×C4×C151—41no—
223C22×C4×C151—41no—
224C22×C4×C151—41no—
225C22×C4×C151—41no—
226C22×C4×C151—41no—
227C22×C4×C151C22×C411yescharacteristic
228C22×C4×C151C22×C411yescharacteristic
229C22×C4×C151C2×D411yescharacteristic
230C22×C4×C151C2×D411yescharacteristic
231C22×C4×C151C2×D411yescharacteristic
232C22×C4×C151C2×D411yescharacteristic
233C22×C4×C151C2×D411yescharacteristic
234C22×C4×C151C2×D411yescharacteristic
235C22×C4×C151C2×D411yescharacteristic
236C22×C4×C151C2×D411yescharacteristic
237C22×C4×C151#4111yescharacteristic
238C22×C4×C151#4111yescharacteristic
239C22×C4×C151#4111yescharacteristic
240C22×C4×C151C2411yescharacteristic
241Q16×C151—28no—
242SD16×C151—28no—
243SD16×C151—28no—
244D8×C151—28no—
245M16×C151—216no—
246M16×C151—22no—
247M16×C151—22no—
248M16×C151—22no—
249M16×C151—22no—
250M16×C151—22no—
251M16×C151—22no—
252M16×C151—22no—
253M16×C151—22no—
254M16×C151—22no—
255M16×C151—22no—
256M16×C151—22no—
257M16×C151—22no—
258M16×C151—22no—
259M16×C151—41no—
260M16×C151—41no—
261M16×C151C2×D414yes—
262C2×C8×C151—216no—
263C2×C8×C151—22no—
264C2×C8×C151—22no—
265C2×C8×C151—22no—
266C2×C8×C151—22no—
267C2×C8×C151—22no—
268C2×C8×C151—22no—
269C2×C8×C151—22no—
270C2×C8×C151—22no—
271C2×C8×C151—41no—
272C2×C8×C151—41no—
273C2×C8×C151C22×C414yes—
274C2×C8×C151C2×D414yes—
275C4⋊C4×C151—22no—
276C4⋊C4×C151—41no—
277C22⋊C4×C151—22no—
278C22⋊C4×C151—41no—
279C42×C151—22no—
280C42×C151—41no—
281C23×C151—22no—
282C23×C151—22no—
283C23×C151—22no—
284C23×C151—22no—
285C23×C151—41no—
286C23×C151—41no—
287C23×C151—81no—
288C23×C151—82no—
289C23×C151—82no—
290C23×C151C4×D411yescharacteristic
291C23×C151C4×D411yescharacteristic
292C23×C151#12111yescharacteristic
293C23×C151#12111yescharacteristic
294C23×C151#12311yescharacteristic
295C23×C151#12311yescharacteristic
296C23×C151C2×#4111yescharacteristic
297Q8×C151—22no—
298Q8×C151—22no—
299Q8×C151—22no—
300Q8×C151—22no—
301Q8×C151—22no—
302Q8×C151—41no—
303Q8×C151—41no—
304Q8×C151C2×C22⋊C414yes—
305D4×C151—24no—
306D4×C151—24no—
307D4×C151—24no—
308D4×C151—24no—
309D4×C151—22no—
310D4×C151—22no—
311D4×C151—22no—
312D4×C151—22no—
313D4×C151—22no—
314D4×C151—42no—
315D4×C151—42no—
316D4×C151—42no—
317D4×C151—42no—
318D4×C151—41no—
319D4×C151—41no—
320D4×C151C2×C22⋊C414yes—
321C2×C4×C151—22no—
322C2×C4×C151—22no—
323C2×C4×C151—22no—
324C2×C4×C151—24no—
325C2×C4×C151—24no—
326C2×C4×C151—24no—
327C2×C4×C151—24no—
328C2×C4×C151—22no—
329C2×C4×C151—41no—
330C2×C4×C151—41no—
331C2×C4×C151—42no—
332C2×C4×C151—42no—
333C2×C4×C151—42no—
334C2×C4×C151—42no—
335C2×C4×C151—42no—
336C2×C4×C151—82no—
337C2×C4×C151C2×C22⋊C411yescharacteristic
338C2×C4×C151C2×C22⋊C411yescharacteristic
339C2×C4×C151C2×C22⋊C411yescharacteristic
340C2×C4×C151C2×C22⋊C411yescharacteristic
341C2×C4×C151C4×D411yescharacteristic
342C2×C4×C151C4×D411yescharacteristic
343C2×C4×C151C4×D411yescharacteristic
344C2×C4×C151C4×D411yescharacteristic
345C2×C4×C151C4×D411yescharacteristic
346C2×C4×C151C4×D411yescharacteristic
347C2×C4×C151#12011yescharacteristic
348C2×C4×C151#12011yescharacteristic
349C2×C4×C151#12011yescharacteristic
350C2×C4×C151#12011yescharacteristic
351C2×C4×C151#12111yescharacteristic
352C2×C4×C151#12111yescharacteristic
353C2×C4×C151#12111yescharacteristic
354C2×C4×C151#12111yescharacteristic
355C2×C4×C151#12111yescharacteristic
356C2×C4×C151#12111yescharacteristic
357C2×C4×C151#12311yescharacteristic
358C2×C4×C151#12311yescharacteristic
359C2×C4×C151C23×C411yescharacteristic
360C2×C4×C151C22×D411yescharacteristic
361C2×C4×C151C22×D411yescharacteristic
362C2×C4×C151C22×D411yescharacteristic
363C2×C4×C151C22×D411yescharacteristic
364C2×C4×C151C2×#4111yescharacteristic
365C8×C151—24no—
366C8×C151—24no—
367C8×C151—24no—
368C8×C151—42no—
369C22×C151—24no—
370C22×C151—41no—
371C22×C151—41no—
372C22×C151—41no—
373C22×C151—41no—
374C22×C151—41no—
375C22×C151—41no—
376C22×C151—41no—
377C22×C151—44no—
378C22×C151—42no—
379C22×C151—82no—
380C22×C151—82no—
381C22×C151—82no—
382C22×C151—82no—
383C22×C151—82no—
384C22×C151#38611yescharacteristic
385C22×C151#38611yescharacteristic
386C22×C151#38611yescharacteristic
387C22×C151#38611yescharacteristic
388C22×C151C2×C4×D411yescharacteristic
389C22×C151C2×#12111yescharacteristic
390C22×C151C2×#12311yescharacteristic
391C4×C151—24no—
392C4×C151—42no—
393C4×C151—82no—
394C4×C151#38611yescharacteristic
395C4×C151#38611yescharacteristic
396C4×C151#38611yescharacteristic
397C4×C151#38611yescharacteristic
398C4×C151C22×C22⋊C411yescharacteristic
399C4×C151C2×C4×D411yescharacteristic
400C4×C151C2×#12011yescharacteristic
401C4×C151C2×#12111yescharacteristic
402C2×C151—21no—
403C2×C151—21no—
404C2×C151—21no—
405C2×C151—21no—
406C2×C151—21no—
407C2×C151—21no—
408C2×C151—21no—
409C2×C151—44no—
410C2×C151—82no—
411C2×C151C2×#38611yescharacteristic
412#20995C15111yesmaximal, characteristic, direct product factor, Sylow
413C151#2099511yescharacteristic, direct product factor, Sylow
414C2×#575C2×C15111yescharacteristic
415C2×#568C2×C15111yescharacteristic, complemented
416C2×#421C2×C15111yescharacteristic, complemented
417#2896C2×C15111yescharacteristic, complemented
418C2×#413C2×C15111yescharacteristic, complemented
419#1903C2×C15114yescomplemented
420#1902C2×C15114yescomplemented
421C2×#344C2×C15111yescharacteristic, complemented
422C2×#338C2×C15111yescharacteristic, complemented
423C22×#41C22×C15111yescharacteristic
424C22×#41C22×C15111yescharacteristic
425#575—22no—
426#575—22no—
427#575—22no—
428#575—22no—
429C2×#137C4×C15112yescomplemented
430C2×#137C22×C15112yes—
431C2×AGL(1,ℤ/8)C4×C15112yescomplemented
432C2×AGL(1,ℤ/8)C22×C15112yes—
433C2×#135C4×C15114yescomplemented
434#568—22no—
435#568—22no—
436#568—22no—
437#568C22×C15114yes—
438C2×#131—22no—
439C2×#131—22no—
440C22×M16—22no—
441C22×M16C22×C15111yescharacteristic
442C22×M16C22×C15111yescharacteristic
443C22×M16C22×C15111yescharacteristic
444C22×M16C22×C15111yescharacteristic
445C2×#117C22×C15111yescharacteristic
446#421—22no—
447#421C22×C15114yes—
448C2×#104—22no—
449#419C22×C15112yescomplemented
450#418C22×C15112yescomplemented
451#417—22no—
452#416—22no—
453#413—22no—
454#413—22no—
455C2×#101C22×C15112yescomplemented
456C2×#100C22×C15112yescomplemented
457#344C22×C15114yescomplemented
458#338C22×C15114yescomplemented
459C2×#41—21no—
460C2×#41—21no—
461C2×#41—21no—
462C2×#41—21no—
463C2×#41—21no—
464C2×#41—21no—
465C2×#41—21no—
466C2×#41—21no—
467C2×#41—21no—
468C2×#41—21no—
469C2×#41—21no—
470C2×#41—21no—
471C2×#41—21no—
472C2×#41—21no—
473C2×#41—21no—
474C2×#41—21no—
475C2×#41C2×C4×C15112yes—
476C2×#41C2×C4×C15112yes—
477C2×#41C2×C4×C15112yes—
478C2×#41D4×C15112yes—
479C2×#41D4×C15112yes—
480C2×#41D4×C15112yes—
481C2×#41D4×C15112yes—
482C2×#41C23×C15112yes—
483C22×Q8C2×C4×C15111yescharacteristic
484C22×Q8C23×C15111yescharacteristic
485C22×D4—21no—
486C22×D4—21no—
487C22×D4C2×C4×C15111yescharacteristic
488C22×D4C23×C15111yescharacteristic
489C23×C4—21no—
490C23×C4—21no—
491C23×C4C23×C15111yescharacteristic
492#137—24no—
493#137—24no—
494#137—24no—
495#137—24no—
496AGL(1,ℤ/8)—24no—
497AGL(1,ℤ/8)—24no—
498AGL(1,ℤ/8)—24no—
499AGL(1,ℤ/8)—24no—
500#135—28no—
501#135—28no—
502C2×Q16C2×C4×C15114yescomplemented
503C2×SD16C2×C4×C15114yescomplemented
504C2×SD16C2×C4×C15114yescomplemented
505C2×D8C2×C4×C15114yescomplemented
506#131—28no—
507#131—28no—
508#131—28no—
509#131—28no—
510C2×M16—24no—
511C2×M16—28no—
512C2×M16—21no—
513C2×M16—21no—
514C2×M16—21no—
515C2×M16—21no—
516C2×M16—21no—
517C2×M16—21no—
518C2×M16—21no—
519C2×M16—21no—
520C2×M16—21no—
521C2×M16—21no—
522C2×M16—21no—
523C2×M16—28no—
524C2×M16—21no—
525C2×M16—21no—
526C2×M16—21no—
527C2×M16—21no—
528C2×M16—21no—
529C2×M16C2×C4×C15112yes—
530C2×M16D4×C15112yes—
531C2×M16D4×C15112yes—
532C2×M16D4×C15112yes—
533C2×M16C23×C15112yes—
534C2×M16C23×C15112yes—
535C2×M16C23×C15112yes—
536C2×M16C23×C15112yes—
537C22×C8—24no—
538C22×C8—21no—
539C22×C8—21no—
540C22×C8C2×C4×C15112yes—
541C22×C8D4×C15112yes—
542#117—21no—
543#117—21no—
544#117—21no—
545#117C23×C15112yes—
546C2×C4⋊C4—21no—
547C2×C22⋊C4—21no—
548C2×C42—21no—
549#104—28no—
550#103—24no—
551#102—24no—
552#101—24no—
553#100—24no—
554C24—21no—
555C24—21no—
556C24#41×C15111yescharacteristic
557#41—22no—
558#41—22no—
559#41—22no—
560#41—22no—
561#41—22no—
562#41—22no—
563#41—22no—
564#41—22no—
565#41—22no—
566#41—22no—
567#41—22no—
568#41—22no—
569#41—22no—
570#41—22no—
571#41—22no—
572#41—22no—
573#41—22no—
574#41—22no—
575#41—22no—
576#41—22no—
577#41—41no—
578#41—41no—
579#41—41no—
580#41—41no—
581#41—41no—
582#41—41no—
583#41—41no—
584#41—41no—
585#41C22⋊C4×C15114yes—
586#41C22⋊C4×C15114yes—
587#41C2×D4×C15114yes—
588#41C2×D4×C15114yes—
589C2×Q8—21no—
590C2×Q8—21no—
591C2×Q8—21no—
592C2×Q8—21no—
593C2×Q8—21no—
594C2×Q8—21no—
595C2×Q8—21no—
596C2×Q8—21no—
597C2×Q8C22⋊C4×C15112yes—
598C2×Q8C22⋊C4×C15112yes—
599C2×Q8C22×C4×C15112yes—
600C2×Q8C22×C4×C15112yes—
601C2×D4—22no—
602C2×D4—22no—
603C2×D4—22no—
604C2×D4—22no—
605C2×D4—22no—
606C2×D4—22no—
607C2×D4—22no—
608C2×D4—22no—
609C2×D4—21no—
610C2×D4—21no—
611C2×D4—21no—
612C2×D4—21no—
613C2×D4—21no—
614C2×D4—21no—
615C2×D4—21no—
616C2×D4—21no—
617C2×D4—41no—
618C2×D4—41no—
619C2×D4—41no—
620C2×D4—41no—
621C2×D4C22⋊C4×C15112yes—
622C2×D4C22⋊C4×C15112yes—
623C2×D4C22×C4×C15112yes—
624C2×D4C22×C4×C15112yes—
625C22×C4—21no—
626C22×C4—22no—
627C22×C4—22no—
628C22×C4—22no—
629C22×C4—22no—
630C22×C4—22no—
631C22×C4—22no—
632C22×C4—21no—
633C22×C4—22no—
634C22×C4—22no—
635C22×C4—41no—
636C22×C4—41no—
637C22×C4—41no—
638C22×C4—41no—
639C22×C4—41no—
640C22×C4C22×C4×C15111yescharacteristic
641C22×C4C22×C4×C15111yescharacteristic
642C22×C4C2×D4×C15111yescharacteristic
643C22×C4C2×D4×C15111yescharacteristic
644C22×C4C2×D4×C15111yescharacteristic
645C22×C4C2×D4×C15111yescharacteristic
646C22×C4C2×D4×C15111yescharacteristic
647C22×C4C2×D4×C15111yescharacteristic
648C22×C4C2×D4×C15111yescharacteristic
649C22×C4C2×D4×C15111yescharacteristic
650C22×C4#41×C15111yescharacteristic
651C22×C4#41×C15111yescharacteristic
652C22×C4#41×C15111yescharacteristic
653C22×C4C24×C15111yescharacteristic
654Q16—28no—
655SD16—28no—
656SD16—28no—
657D8—28no—
658M16—216no—
659M16—22no—
660M16—22no—
661M16—22no—
662M16—22no—
663M16—22no—
664M16—22no—
665M16—22no—
666M16—22no—
667M16—22no—
668M16—22no—
669M16—22no—
670M16—22no—
671M16—22no—
672M16—41no—
673M16—41no—
674M16C2×D4×C15114yes—
675C2×C8—216no—
676C2×C8—22no—
677C2×C8—22no—
678C2×C8—22no—
679C2×C8—22no—
680C2×C8—22no—
681C2×C8—22no—
682C2×C8—22no—
683C2×C8—22no—
684C2×C8—41no—
685C2×C8—41no—
686C2×C8C22×C4×C15114yes—
687C2×C8C2×D4×C15114yes—
688C4⋊C4—22no—
689C4⋊C4—41no—
690C22⋊C4—22no—
691C22⋊C4—41no—
692C42—22no—
693C42—41no—
694C23—22no—
695C23—22no—
696C23—22no—
697C23—22no—
698C23—41no—
699C23—41no—
700C23—81no—
701C23—82no—
702C23—82no—
703C23C4×D4×C15111yescharacteristic
704C23C4×D4×C15111yescharacteristic
705C23#121×C15111yescharacteristic
706C23#121×C15111yescharacteristic
707C23#123×C15111yescharacteristic
708C23#123×C15111yescharacteristic
709C23C2×#41×C15111yescharacteristic
710Q8—22no—
711Q8—22no—
712Q8—22no—
713Q8—22no—
714Q8—22no—
715Q8—41no—
716Q8—41no—
717Q8C2×C22⋊C4×C15114yes—
718D4—24no—
719D4—24no—
720D4—24no—
721D4—24no—
722D4—22no—
723D4—22no—
724D4—22no—
725D4—22no—
726D4—22no—
727D4—42no—
728D4—42no—
729D4—42no—
730D4—42no—
731D4—41no—
732D4—41no—
733D4C2×C22⋊C4×C15114yes—
734C2×C4—22no—
735C2×C4—22no—
736C2×C4—22no—
737C2×C4—24no—
738C2×C4—24no—
739C2×C4—24no—
740C2×C4—24no—
741C2×C4—22no—
742C2×C4—41no—
743C2×C4—41no—
744C2×C4—42no—
745C2×C4—42no—
746C2×C4—42no—
747C2×C4—42no—
748C2×C4—42no—
749C2×C4—82no—
750C2×C4C2×C22⋊C4×C15111yescharacteristic
751C2×C4C2×C22⋊C4×C15111yescharacteristic
752C2×C4C2×C22⋊C4×C15111yescharacteristic
753C2×C4C2×C22⋊C4×C15111yescharacteristic
754C2×C4C4×D4×C15111yescharacteristic
755C2×C4C4×D4×C15111yescharacteristic
756C2×C4C4×D4×C15111yescharacteristic
757C2×C4C4×D4×C15111yescharacteristic
758C2×C4C4×D4×C15111yescharacteristic
759C2×C4C4×D4×C15111yescharacteristic
760C2×C4#120×C15111yescharacteristic
761C2×C4#120×C15111yescharacteristic
762C2×C4#120×C15111yescharacteristic
763C2×C4#120×C15111yescharacteristic
764C2×C4#121×C15111yescharacteristic
765C2×C4#121×C15111yescharacteristic
766C2×C4#121×C15111yescharacteristic
767C2×C4#121×C15111yescharacteristic
768C2×C4#121×C15111yescharacteristic
769C2×C4#121×C15111yescharacteristic
770C2×C4#123×C15111yescharacteristic
771C2×C4#123×C15111yescharacteristic
772C2×C4C23×C4×C15111yescharacteristic
773C2×C4C22×D4×C15111yescharacteristic
774C2×C4C22×D4×C15111yescharacteristic
775C2×C4C22×D4×C15111yescharacteristic
776C2×C4C22×D4×C15111yescharacteristic
777C2×C4C2×#41×C15111yescharacteristic
778C8—24no—
779C8—24no—
780C8—24no—
781C8—42no—
782C22—24no—
783C22—41no—
784C22—41no—
785C22—41no—
786C22—41no—
787C22—41no—
788C22—41no—
789C22—41no—
790C22—44no—
791C22—42no—
792C22—82no—
793C22—82no—
794C22—82no—
795C22—82no—
796C22—82no—
797C22#386×C15111yescharacteristic
798C22#386×C15111yescharacteristic
799C22#386×C15111yescharacteristic
800C22#386×C15111yescharacteristic
801C22C2×C4×D4×C15111yescharacteristic
802C22C2×#121×C15111yescharacteristic
803C22C2×#123×C15111yescharacteristic
804C4—24no—
805C4—42no—
806C4—82no—
807C4#386×C15111yescharacteristic
808C4#386×C15111yescharacteristic
809C4#386×C15111yescharacteristic
810C4#386×C15111yescharacteristic
811C4C22×C22⋊C4×C15111yescharacteristic
812C4C2×C4×D4×C15111yescharacteristic
813C4C2×#120×C15111yescharacteristic
814C4C2×#121×C15111yescharacteristic
815C2—21no—
816C2—21no—
817C2—21no—
818C2—21no—
819C2—21no—
820C2—21no—
821C2—21no—
822C2—44no—
823C2—82no—
824C2C2×#386×C15111yescharacteristic
subgroupG/H
centerC4×C151#386
commutatorC2×C4C23×C4×C151
Frattini, cosocleC22×C4C24×C151
socleC2×C151C2×#386
prime radicalC2×#575×C151C2
LCSG ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C4×C151 ◁ C23×C4×C151 ◁ G

Complements

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

NH ≅ G/Ntype
2. C2×#568×C151C2semidirect
3. C2×#421×C151C2semidirect
4. #2896×C151C2semidirect
5. C2×#413×C151C2semidirect
6. #1903×C151C2semidirect
7. #1902×C151C2semidirect
8. C2×#344×C151C2semidirect
9. C2×#338×C151C2semidirect
16. C2×#137×C151C4semidirect
18. C2×AGL(1,ℤ/8)×C151C4semidirect
20. C2×#135×C151C4semidirect
36. #419×C151C22semidirect
37. #418×C151C22semidirect
42. C2×#101×C151C22semidirect
43. C2×#100×C151C22semidirect
44. #344×C151C22semidirect
45. #338×C151C22semidirect
89. C2×Q16×C151C2×C4semidirect
90. C2×SD16×C151C2×C4semidirect
91. C2×SD16×C151C2×C4semidirect
92. C2×D8×C151C2×C4semidirect
412. #20995C151direct (N × H)
413. C151#20995direct (N × H)
415. C2×#568C2×C151semidirect
416. C2×#421C2×C151semidirect
417. #2896C2×C151semidirect
418. C2×#413C2×C151semidirect
419. #1903C2×C151semidirect
420. #1902C2×C151semidirect
421. C2×#344C2×C151semidirect
422. C2×#338C2×C151semidirect
429. C2×#137C4×C151semidirect
431. C2×AGL(1,ℤ/8)C4×C151semidirect
433. C2×#135C4×C151semidirect
449. #419C22×C151semidirect
450. #418C22×C151semidirect
455. C2×#101C22×C151semidirect
456. C2×#100C22×C151semidirect
457. #344C22×C151semidirect
458. #338C22×C151semidirect
502. C2×Q16C2×C4×C151semidirect
503. C2×SD16C2×C4×C151semidirect
504. C2×SD16C2×C4×C151semidirect
505. C2×D8C2×C4×C151semidirect

Maximal subgroups

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

subgroupindex
C2×#575×C1512
C2×#568×C1512
C2×#421×C1512
#2896×C1512
C2×#413×C1512
#1903×C1512
#1902×C1512
C2×#344×C1512
C2×#338×C1512
#20995151