Finite Group Databasebeta

← C151×#20939 #50325864

Subgroups — C151×#20939 #50325864

Order 38656.

1668 conjugacy classes of subgroups.

The subgroup lattice has 820 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
5#2879×C151C211yesmaximal, characteristic, complemented
6#1881×C151C218yesmaximal, complemented
7C2×#344×C151C211yesmaximal, characteristic, complemented
8#1738×C151C211yesmaximal, characteristic, complemented
9C22×#41×C151C2211yescharacteristic
10C22×#41×C151C2211yescharacteristic
11#575×C151—22no—
12#575×C151—22no—
13#575×C151C414yescomplemented
14#575×C151C2214yes—
15C2×#137×C151—21no—
16C2×#137×C151C412yescomplemented
17C2×AGL(1,ℤ/8)×C151—21no—
18C2×AGL(1,ℤ/8)×C151C412yescomplemented
19C2×#135×C151—22no—
20#568×C151—22no—
21#568×C151—22no—
22#568×C151—22no—
23#568×C151C2214yescomplemented
24C2×#131×C151—22no—
25C2×#131×C151—22no—
26C22×M16×C151—22no—
27C22×M16×C151C2211yescharacteristic
28C22×M16×C151C2211yescharacteristic
29C22×M16×C151C2211yescharacteristic
30C22×M16×C151C2211yescharacteristic
31C2×#117×C151C2211yescharacteristic
32#421×C151—22no—
33#421×C151C2214yescomplemented
34C2×#104×C151—22no—
35#419×C151—21no—
36#418×C151—21no—
37#417×C151—22no—
38#416×C151C2214yescomplemented
39#408×C151—22no—
40#408×C151C2214yescomplemented
41#407×C151—22no—
42#344×C151C2214yescomplemented
43#341×C151C2214yescomplemented
44C2×#41×C151—21no—
45C2×#41×C151—21no—
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×C151C2×C412yes—
61C2×#41×C151C2×C412yes—
62C2×#41×C151C2×C412yes—
63C2×#41×C151D412yes—
64C2×#41×C151D412yes—
65C2×#41×C151D412yes—
66C2×#41×C151C2312yes—
67C2×#41×C151C2312yes—
68C22×Q8×C151C2×C411yescharacteristic
69C22×Q8×C151D411yescharacteristic
70C22×D4×C151—21no—
71C22×D4×C151—21no—
72C22×D4×C151C2×C411yescharacteristic
73C22×D4×C151D411yescharacteristic
74C23×C4×C151—21no—
75C23×C4×C151—21no—
76C23×C4×C151C2311yescharacteristic
77#137×C151—24no—
78#137×C151—24no—
79#137×C151—24no—
80#137×C151C2×C418yescomplemented
81AGL(1,ℤ/8)×C151—24no—
82AGL(1,ℤ/8)×C151—24no—
83AGL(1,ℤ/8)×C151—24no—
84AGL(1,ℤ/8)×C151C2×C418yescomplemented
85#135×C151—28no—
86#135×C151—28no—
87C2×Q16×C151—22no—
88C2×SD16×C151—22no—
89C2×SD16×C151—22no—
90C2×D8×C151—22no—
91#131×C151—28no—
92#131×C151—28no—
93#131×C151—28no—
94#131×C151—28no—
95C2×M16×C151—24no—
96C2×M16×C151—28no—
97C2×M16×C151—21no—
98C2×M16×C151—21no—
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—28no—
108C2×M16×C151—21no—
109C2×M16×C151—21no—
110C2×M16×C151—21no—
111C2×M16×C151—21no—
112C2×M16×C151—21no—
113C2×M16×C151—21no—
114C2×M16×C151C2×C412yes—
115C2×M16×C151C2×C412yes—
116C2×M16×C151D412yes—
117C2×M16×C151D412yes—
118C2×M16×C151D412yes—
119C2×M16×C151C2312yes—
120C2×M16×C151C2312yes—
121C2×M16×C151C2312yes—
122C22×C8×C151—24no—
123C22×C8×C151—21no—
124C22×C8×C151—21no—
125C22×C8×C151D412yes—
126C22×C8×C151C2312yes—
127#117×C151—21no—
128#117×C151—21no—
129#117×C151—21no—
130#117×C151C2312yes—
131C2×C4⋊C4×C151—21no—
132C2×C22⋊C4×C151—21no—
133C2×C42×C151—21no—
134#104×C151—28no—
135#103×C151—24no—
136#102×C151—24no—
137C22⋊C8×C151—28no—
138C24×C151—21no—
139C24×C151—21no—
140C24×C151#4111yescharacteristic
141#41×C151—22no—
142#41×C151—22no—
143#41×C151—22no—
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—41no—
162#41×C151—41no—
163#41×C151—41no—
164#41×C151—41no—
165#41×C151—41no—
166#41×C151—41no—
167#41×C151—41no—
168#41×C151—41no—
169#41×C151C22⋊C414yes—
170#41×C151C22⋊C414yes—
171#41×C151C22×C414yes—
172#41×C151C2×D414yes—
173C2×Q8×C151—21no—
174C2×Q8×C151—21no—
175C2×Q8×C151—21no—
176C2×Q8×C151—21no—
177C2×Q8×C151—21no—
178C2×Q8×C151—21no—
179C2×Q8×C151—21no—
180C2×Q8×C151—21no—
181C2×Q8×C151C22⋊C412yes—
182C2×Q8×C151C22⋊C412yes—
183C2×Q8×C151C22×C412yes—
184C2×Q8×C151C2×D412yes—
185C2×D4×C151—22no—
186C2×D4×C151—22no—
187C2×D4×C151—22no—
188C2×D4×C151—22no—
189C2×D4×C151—22no—
190C2×D4×C151—22no—
191C2×D4×C151—22no—
192C2×D4×C151—22no—
193C2×D4×C151—21no—
194C2×D4×C151—21no—
195C2×D4×C151—21no—
196C2×D4×C151—21no—
197C2×D4×C151—21no—
198C2×D4×C151—21no—
199C2×D4×C151—21no—
200C2×D4×C151—21no—
201C2×D4×C151—41no—
202C2×D4×C151—41no—
203C2×D4×C151—41no—
204C2×D4×C151—41no—
205C2×D4×C151C22⋊C412yes—
206C2×D4×C151C22⋊C412yes—
207C2×D4×C151C22×C412yes—
208C2×D4×C151C2×D412yes—
209C22×C4×C151—21no—
210C22×C4×C151—22no—
211C22×C4×C151—22no—
212C22×C4×C151—22no—
213C22×C4×C151—22no—
214C22×C4×C151—22no—
215C22×C4×C151—22no—
216C22×C4×C151—21no—
217C22×C4×C151—22no—
218C22×C4×C151—22no—
219C22×C4×C151—41no—
220C22×C4×C151—41no—
221C22×C4×C151—41no—
222C22×C4×C151—41no—
223C22×C4×C151—41no—
224C22×C4×C151C22×C411yescharacteristic
225C22×C4×C151C22×C411yescharacteristic
226C22×C4×C151C2×D411yescharacteristic
227C22×C4×C151C2×D411yescharacteristic
228C22×C4×C151C2×D411yescharacteristic
229C22×C4×C151C2×D411yescharacteristic
230C22×C4×C151C2×D411yescharacteristic
231C22×C4×C151C2×D411yescharacteristic
232C22×C4×C151C2×D411yescharacteristic
233C22×C4×C151C2×D411yescharacteristic
234C22×C4×C151#4111yescharacteristic
235C22×C4×C151#4111yescharacteristic
236C22×C4×C151#4111yescharacteristic
237C22×C4×C151C2411yescharacteristic
238Q16×C151—28no—
239SD16×C151—28no—
240SD16×C151—28no—
241D8×C151—28no—
242M16×C151—216no—
243M16×C151—22no—
244M16×C151—22no—
245M16×C151—22no—
246M16×C151—22no—
247M16×C151—22no—
248M16×C151—22no—
249M16×C151—22no—
250M16×C151—22no—
251M16×C151—22no—
252M16×C151—22no—
253M16×C151—41no—
254M16×C151—41no—
255M16×C151—41no—
256M16×C151—41no—
257M16×C151C22×C414yes—
258M16×C151C2×D414yes—
259C2×C8×C151—216no—
260C2×C8×C151—22no—
261C2×C8×C151—22no—
262C2×C8×C151—22no—
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×C151C2×D414yes—
272C4⋊C4×C151—22no—
273C4⋊C4×C151—41no—
274C22⋊C4×C151—22no—
275C22⋊C4×C151—41no—
276C42×C151—22no—
277C42×C151—41no—
278C23×C151—22no—
279C23×C151—22no—
280C23×C151—22no—
281C23×C151—22no—
282C23×C151—41no—
283C23×C151—41no—
284C23×C151—81no—
285C23×C151—82no—
286C23×C151—82no—
287C23×C151C4×D411yescharacteristic
288C23×C151C4×D411yescharacteristic
289C23×C151#12111yescharacteristic
290C23×C151#12111yescharacteristic
291C23×C151#12311yescharacteristic
292C23×C151#12311yescharacteristic
293C23×C151C2×#4111yescharacteristic
294Q8×C151—22no—
295Q8×C151—22no—
296Q8×C151—22no—
297Q8×C151—22no—
298Q8×C151—22no—
299Q8×C151—41no—
300Q8×C151—41no—
301Q8×C151C2×C22⋊C414yes—
302D4×C151—24no—
303D4×C151—24no—
304D4×C151—24no—
305D4×C151—24no—
306D4×C151—22no—
307D4×C151—22no—
308D4×C151—22no—
309D4×C151—22no—
310D4×C151—22no—
311D4×C151—42no—
312D4×C151—42no—
313D4×C151—42no—
314D4×C151—42no—
315D4×C151—41no—
316D4×C151—41no—
317D4×C151C2×C22⋊C414yes—
318C2×C4×C151—22no—
319C2×C4×C151—22no—
320C2×C4×C151—22no—
321C2×C4×C151—24no—
322C2×C4×C151—24no—
323C2×C4×C151—24no—
324C2×C4×C151—24no—
325C2×C4×C151—22no—
326C2×C4×C151—41no—
327C2×C4×C151—41no—
328C2×C4×C151—42no—
329C2×C4×C151—42no—
330C2×C4×C151—42no—
331C2×C4×C151—42no—
332C2×C4×C151—42no—
333C2×C4×C151—82no—
334C2×C4×C151C2×C22⋊C411yescharacteristic
335C2×C4×C151C2×C22⋊C411yescharacteristic
336C2×C4×C151C2×C22⋊C411yescharacteristic
337C2×C4×C151C2×C22⋊C411yescharacteristic
338C2×C4×C151C4×D411yescharacteristic
339C2×C4×C151C4×D411yescharacteristic
340C2×C4×C151C4×D411yescharacteristic
341C2×C4×C151C4×D411yescharacteristic
342C2×C4×C151C4×D411yescharacteristic
343C2×C4×C151C4×D411yescharacteristic
344C2×C4×C151#12011yescharacteristic
345C2×C4×C151#12011yescharacteristic
346C2×C4×C151#12011yescharacteristic
347C2×C4×C151#12011yescharacteristic
348C2×C4×C151#12111yescharacteristic
349C2×C4×C151#12111yescharacteristic
350C2×C4×C151#12111yescharacteristic
351C2×C4×C151#12111yescharacteristic
352C2×C4×C151#12111yescharacteristic
353C2×C4×C151#12111yescharacteristic
354C2×C4×C151#12311yescharacteristic
355C2×C4×C151#12311yescharacteristic
356C2×C4×C151C23×C411yescharacteristic
357C2×C4×C151C22×D411yescharacteristic
358C2×C4×C151C22×D411yescharacteristic
359C2×C4×C151C22×D411yescharacteristic
360C2×C4×C151C22×D411yescharacteristic
361C2×C4×C151C2×#4111yescharacteristic
362C8×C151—24no—
363C8×C151—24no—
364C8×C151—24no—
365C8×C151—42no—
366C22×C151—24no—
367C22×C151—41no—
368C22×C151—41no—
369C22×C151—41no—
370C22×C151—41no—
371C22×C151—41no—
372C22×C151—41no—
373C22×C151—41no—
374C22×C151—44no—
375C22×C151—44no—
376C22×C151—42no—
377C22×C151—82no—
378C22×C151—82no—
379C22×C151—82no—
380C22×C151—82no—
381C22×C151#38611yescharacteristic
382C22×C151#38611yescharacteristic
383C22×C151#38611yescharacteristic
384C22×C151#38611yescharacteristic
385C22×C151C2×C4×D411yescharacteristic
386C22×C151C2×#12111yescharacteristic
387C22×C151C2×#12311yescharacteristic
388C4×C151—24no—
389C4×C151—42no—
390C4×C151—82no—
391C4×C151#38611yescharacteristic
392C4×C151#38611yescharacteristic
393C4×C151#38611yescharacteristic
394C4×C151#38611yescharacteristic
395C4×C151C22×C22⋊C411yescharacteristic
396C4×C151C2×C4×D411yescharacteristic
397C4×C151C2×#12011yescharacteristic
398C4×C151C2×#12111yescharacteristic
399C2×C151—21no—
400C2×C151—21no—
401C2×C151—21no—
402C2×C151—21no—
403C2×C151—21no—
404C2×C151—21no—
405C2×C151—21no—
406C2×C151—44no—
407C2×C151—82no—
408C2×C151C2×#38611yescharacteristic
409#20939C15111yesmaximal, characteristic, direct product factor, Sylow
410C151#2093911yescharacteristic, direct product factor, Sylow
411C2×#575C2×C15111yescharacteristic
412C2×#568C2×C15111yescharacteristic, complemented
413C2×#421C2×C15111yescharacteristic, complemented
414#2896C2×C15111yescharacteristic, complemented
415#2879C2×C15111yescharacteristic, complemented
416#1881C2×C15118yescomplemented
417C2×#344C2×C15111yescharacteristic, complemented
418#1738C2×C15111yescharacteristic, complemented
419C22×#41C22×C15111yescharacteristic
420C22×#41C22×C15111yescharacteristic
421#575—22no—
422#575—22no—
423#575C4×C15114yescomplemented
424#575C22×C15114yes—
425C2×#137—21no—
426C2×#137C4×C15112yescomplemented
427C2×AGL(1,ℤ/8)—21no—
428C2×AGL(1,ℤ/8)C4×C15112yescomplemented
429C2×#135—22no—
430#568—22no—
431#568—22no—
432#568—22no—
433#568C22×C15114yescomplemented
434C2×#131—22no—
435C2×#131—22no—
436C22×M16—22no—
437C22×M16C22×C15111yescharacteristic
438C22×M16C22×C15111yescharacteristic
439C22×M16C22×C15111yescharacteristic
440C22×M16C22×C15111yescharacteristic
441C2×#117C22×C15111yescharacteristic
442#421—22no—
443#421C22×C15114yescomplemented
444C2×#104—22no—
445#419—21no—
446#418—21no—
447#417—22no—
448#416C22×C15114yescomplemented
449#408—22no—
450#408C22×C15114yescomplemented
451#407—22no—
452#344C22×C15114yescomplemented
453#341C22×C15114yescomplemented
454C2×#41—21no—
455C2×#41—21no—
456C2×#41—21no—
457C2×#41—21no—
458C2×#41—21no—
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×#41C2×C4×C15112yes—
471C2×#41C2×C4×C15112yes—
472C2×#41C2×C4×C15112yes—
473C2×#41D4×C15112yes—
474C2×#41D4×C15112yes—
475C2×#41D4×C15112yes—
476C2×#41C23×C15112yes—
477C2×#41C23×C15112yes—
478C22×Q8C2×C4×C15111yescharacteristic
479C22×Q8D4×C15111yescharacteristic
480C22×D4—21no—
481C22×D4—21no—
482C22×D4C2×C4×C15111yescharacteristic
483C22×D4D4×C15111yescharacteristic
484C23×C4—21no—
485C23×C4—21no—
486C23×C4C23×C15111yescharacteristic
487#137—24no—
488#137—24no—
489#137—24no—
490#137C2×C4×C15118yescomplemented
491AGL(1,ℤ/8)—24no—
492AGL(1,ℤ/8)—24no—
493AGL(1,ℤ/8)—24no—
494AGL(1,ℤ/8)C2×C4×C15118yescomplemented
495#135—28no—
496#135—28no—
497C2×Q16—22no—
498C2×SD16—22no—
499C2×SD16—22no—
500C2×D8—22no—
501#131—28no—
502#131—28no—
503#131—28no—
504#131—28no—
505C2×M16—24no—
506C2×M16—28no—
507C2×M16—21no—
508C2×M16—21no—
509C2×M16—21no—
510C2×M16—21no—
511C2×M16—21no—
512C2×M16—21no—
513C2×M16—21no—
514C2×M16—21no—
515C2×M16—21no—
516C2×M16—21no—
517C2×M16—28no—
518C2×M16—21no—
519C2×M16—21no—
520C2×M16—21no—
521C2×M16—21no—
522C2×M16—21no—
523C2×M16—21no—
524C2×M16C2×C4×C15112yes—
525C2×M16C2×C4×C15112yes—
526C2×M16D4×C15112yes—
527C2×M16D4×C15112yes—
528C2×M16D4×C15112yes—
529C2×M16C23×C15112yes—
530C2×M16C23×C15112yes—
531C2×M16C23×C15112yes—
532C22×C8—24no—
533C22×C8—21no—
534C22×C8—21no—
535C22×C8D4×C15112yes—
536C22×C8C23×C15112yes—
537#117—21no—
538#117—21no—
539#117—21no—
540#117C23×C15112yes—
541C2×C4⋊C4—21no—
542C2×C22⋊C4—21no—
543C2×C42—21no—
544#104—28no—
545#103—24no—
546#102—24no—
547C22⋊C8—28no—
548C24—21no—
549C24—21no—
550C24#41×C15111yescharacteristic
551#41—22no—
552#41—22no—
553#41—22no—
554#41—22no—
555#41—22no—
556#41—22no—
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—41no—
572#41—41no—
573#41—41no—
574#41—41no—
575#41—41no—
576#41—41no—
577#41—41no—
578#41—41no—
579#41C22⋊C4×C15114yes—
580#41C22⋊C4×C15114yes—
581#41C22×C4×C15114yes—
582#41C2×D4×C15114yes—
583C2×Q8—21no—
584C2×Q8—21no—
585C2×Q8—21no—
586C2×Q8—21no—
587C2×Q8—21no—
588C2×Q8—21no—
589C2×Q8—21no—
590C2×Q8—21no—
591C2×Q8C22⋊C4×C15112yes—
592C2×Q8C22⋊C4×C15112yes—
593C2×Q8C22×C4×C15112yes—
594C2×Q8C2×D4×C15112yes—
595C2×D4—22no—
596C2×D4—22no—
597C2×D4—22no—
598C2×D4—22no—
599C2×D4—22no—
600C2×D4—22no—
601C2×D4—22no—
602C2×D4—22no—
603C2×D4—21no—
604C2×D4—21no—
605C2×D4—21no—
606C2×D4—21no—
607C2×D4—21no—
608C2×D4—21no—
609C2×D4—21no—
610C2×D4—21no—
611C2×D4—41no—
612C2×D4—41no—
613C2×D4—41no—
614C2×D4—41no—
615C2×D4C22⋊C4×C15112yes—
616C2×D4C22⋊C4×C15112yes—
617C2×D4C22×C4×C15112yes—
618C2×D4C2×D4×C15112yes—
619C22×C4—21no—
620C22×C4—22no—
621C22×C4—22no—
622C22×C4—22no—
623C22×C4—22no—
624C22×C4—22no—
625C22×C4—22no—
626C22×C4—21no—
627C22×C4—22no—
628C22×C4—22no—
629C22×C4—41no—
630C22×C4—41no—
631C22×C4—41no—
632C22×C4—41no—
633C22×C4—41no—
634C22×C4C22×C4×C15111yescharacteristic
635C22×C4C22×C4×C15111yescharacteristic
636C22×C4C2×D4×C15111yescharacteristic
637C22×C4C2×D4×C15111yescharacteristic
638C22×C4C2×D4×C15111yescharacteristic
639C22×C4C2×D4×C15111yescharacteristic
640C22×C4C2×D4×C15111yescharacteristic
641C22×C4C2×D4×C15111yescharacteristic
642C22×C4C2×D4×C15111yescharacteristic
643C22×C4C2×D4×C15111yescharacteristic
644C22×C4#41×C15111yescharacteristic
645C22×C4#41×C15111yescharacteristic
646C22×C4#41×C15111yescharacteristic
647C22×C4C24×C15111yescharacteristic
648Q16—28no—
649SD16—28no—
650SD16—28no—
651D8—28no—
652M16—216no—
653M16—22no—
654M16—22no—
655M16—22no—
656M16—22no—
657M16—22no—
658M16—22no—
659M16—22no—
660M16—22no—
661M16—22no—
662M16—22no—
663M16—41no—
664M16—41no—
665M16—41no—
666M16—41no—
667M16C22×C4×C15114yes—
668M16C2×D4×C15114yes—
669C2×C8—216no—
670C2×C8—22no—
671C2×C8—22no—
672C2×C8—22no—
673C2×C8—22no—
674C2×C8—22no—
675C2×C8—22no—
676C2×C8—22no—
677C2×C8—22no—
678C2×C8—22no—
679C2×C8—22no—
680C2×C8—22no—
681C2×C8C2×D4×C15114yes—
682C4⋊C4—22no—
683C4⋊C4—41no—
684C22⋊C4—22no—
685C22⋊C4—41no—
686C42—22no—
687C42—41no—
688C23—22no—
689C23—22no—
690C23—22no—
691C23—22no—
692C23—41no—
693C23—41no—
694C23—81no—
695C23—82no—
696C23—82no—
697C23C4×D4×C15111yescharacteristic
698C23C4×D4×C15111yescharacteristic
699C23#121×C15111yescharacteristic
700C23#121×C15111yescharacteristic
701C23#123×C15111yescharacteristic
702C23#123×C15111yescharacteristic
703C23C2×#41×C15111yescharacteristic
704Q8—22no—
705Q8—22no—
706Q8—22no—
707Q8—22no—
708Q8—22no—
709Q8—41no—
710Q8—41no—
711Q8C2×C22⋊C4×C15114yes—
712D4—24no—
713D4—24no—
714D4—24no—
715D4—24no—
716D4—22no—
717D4—22no—
718D4—22no—
719D4—22no—
720D4—22no—
721D4—42no—
722D4—42no—
723D4—42no—
724D4—42no—
725D4—41no—
726D4—41no—
727D4C2×C22⋊C4×C15114yes—
728C2×C4—22no—
729C2×C4—22no—
730C2×C4—22no—
731C2×C4—24no—
732C2×C4—24no—
733C2×C4—24no—
734C2×C4—24no—
735C2×C4—22no—
736C2×C4—41no—
737C2×C4—41no—
738C2×C4—42no—
739C2×C4—42no—
740C2×C4—42no—
741C2×C4—42no—
742C2×C4—42no—
743C2×C4—82no—
744C2×C4C2×C22⋊C4×C15111yescharacteristic
745C2×C4C2×C22⋊C4×C15111yescharacteristic
746C2×C4C2×C22⋊C4×C15111yescharacteristic
747C2×C4C2×C22⋊C4×C15111yescharacteristic
748C2×C4C4×D4×C15111yescharacteristic
749C2×C4C4×D4×C15111yescharacteristic
750C2×C4C4×D4×C15111yescharacteristic
751C2×C4C4×D4×C15111yescharacteristic
752C2×C4C4×D4×C15111yescharacteristic
753C2×C4C4×D4×C15111yescharacteristic
754C2×C4#120×C15111yescharacteristic
755C2×C4#120×C15111yescharacteristic
756C2×C4#120×C15111yescharacteristic
757C2×C4#120×C15111yescharacteristic
758C2×C4#121×C15111yescharacteristic
759C2×C4#121×C15111yescharacteristic
760C2×C4#121×C15111yescharacteristic
761C2×C4#121×C15111yescharacteristic
762C2×C4#121×C15111yescharacteristic
763C2×C4#121×C15111yescharacteristic
764C2×C4#123×C15111yescharacteristic
765C2×C4#123×C15111yescharacteristic
766C2×C4C23×C4×C15111yescharacteristic
767C2×C4C22×D4×C15111yescharacteristic
768C2×C4C22×D4×C15111yescharacteristic
769C2×C4C22×D4×C15111yescharacteristic
770C2×C4C22×D4×C15111yescharacteristic
771C2×C4C2×#41×C15111yescharacteristic
772C8—24no—
773C8—24no—
774C8—24no—
775C8—42no—
776C22—24no—
777C22—41no—
778C22—41no—
779C22—41no—
780C22—41no—
781C22—41no—
782C22—41no—
783C22—41no—
784C22—44no—
785C22—44no—
786C22—42no—
787C22—82no—
788C22—82no—
789C22—82no—
790C22—82no—
791C22#386×C15111yescharacteristic
792C22#386×C15111yescharacteristic
793C22#386×C15111yescharacteristic
794C22#386×C15111yescharacteristic
795C22C2×C4×D4×C15111yescharacteristic
796C22C2×#121×C15111yescharacteristic
797C22C2×#123×C15111yescharacteristic
798C4—24no—
799C4—42no—
800C4—82no—
801C4#386×C15111yescharacteristic
802C4#386×C15111yescharacteristic
803C4#386×C15111yescharacteristic
804C4#386×C15111yescharacteristic
805C4C22×C22⋊C4×C15111yescharacteristic
806C4C2×C4×D4×C15111yescharacteristic
807C4C2×#120×C15111yescharacteristic
808C4C2×#121×C15111yescharacteristic
809C2—21no—
810C2—21no—
811C2—21no—
812C2—21no—
813C2—21no—
814C2—21no—
815C2—21no—
816C2—44no—
817C2—82no—
818C2C2×#386×C15111yescharacteristic
subgroupG/H
centerC4×C151C2×#120
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. #2879×C151C2semidirect
6. #1881×C151C2semidirect
7. C2×#344×C151C2semidirect
8. #1738×C151C2semidirect
13. #575×C151C4semidirect
16. C2×#137×C151C4semidirect
18. C2×AGL(1,ℤ/8)×C151C4semidirect
23. #568×C151C22semidirect
33. #421×C151C22semidirect
38. #416×C151C22semidirect
40. #408×C151C22semidirect
42. #344×C151C22semidirect
43. #341×C151C22semidirect
80. #137×C151C2×C4semidirect
84. AGL(1,ℤ/8)×C151C2×C4semidirect
409. #20939C151direct (N × H)
410. C151#20939direct (N × H)
412. C2×#568C2×C151semidirect
413. C2×#421C2×C151semidirect
414. #2896C2×C151semidirect
415. #2879C2×C151semidirect
416. #1881C2×C151semidirect
417. C2×#344C2×C151semidirect
418. #1738C2×C151semidirect
423. #575C4×C151semidirect
426. C2×#137C4×C151semidirect
428. C2×AGL(1,ℤ/8)C4×C151semidirect
433. #568C22×C151semidirect
443. #421C22×C151semidirect
448. #416C22×C151semidirect
450. #408C22×C151semidirect
452. #344C22×C151semidirect
453. #341C22×C151semidirect
490. #137C2×C4×C151semidirect
494. AGL(1,ℤ/8)C2×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
#2879×C1512
#1881×C1512
C2×#344×C1512
#1738×C1512
#20939151