Finite Group Databasebeta

← C151×#24653 #50329578

Subgroups — C151×#24653 #50329578

Order 38656.

1036 conjugacy classes of subgroups.

The subgroup lattice has 596 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#460×C151C211yesmaximal, characteristic, complemented
2C2×#431×C151C211yesmaximal, characteristic, complemented
3#2856×C151C211yesmaximal, characteristic
4C4×C22⋊Q8×C151C211yesmaximal, characteristic, complemented
5#2034×C151C212yesmaximal, complemented
6#2000×C151C212yesmaximal, complemented
7#1982×C151C211yesmaximal, characteristic, complemented
8#1968×C151C212yesmaximal, complemented
9#1948×C151C211yesmaximal, characteristic, complemented
10#1934×C151C212yesmaximal, complemented
11#1803×C151C211yesmaximal, characteristic, complemented
12C22×SD16×C151C2212yes—
13C2×#127×C151C2211yescharacteristic
14C2×C22⋊Q8×C151C2211yescharacteristic
15C2×#121×C151—21no—
16C2×#121×C151—21no—
17C2×#121×C151C2212yes—
18C2×C4×Q8×C151C2211yescharacteristic
19C22×C42×C151C2211yescharacteristic
20#460×C151—24no—
21#431×C151—24no—
22C2×#106×C151C2212yes—
23C2×C4⋊C8×C151C2211yescharacteristic
24C2×C4⋊C8×C151C2211yescharacteristic
25C2×#103×C151C2212yes—
26C2×#102×C151C2212yes—
27C2×#102×C151C2212yes—
28C2×#102×C151C2212yes—
29C2×C22⋊C8×C151C2212yes—
30C2×C4×C8×C151C2212yes—
31#391×C151C2211yescharacteristic
32#390×C151—21no—
33#390×C151—21no—
34#390×C151C2212yes—
35#389×C151C2211yescharacteristic
36#387×C151—21no—
37#385×C151—21no—
38#384×C151C2211yescharacteristic
39#380×C151C2211yescharacteristic
40C4×C4⋊C4×C151—21no—
41C4×C4⋊C4×C151C2211yescharacteristic
42C4×C22⋊C4×C151—21no—
43#340×C151C2212yes—
44#340×C151C2212yes—
45C22×Q8×C151C2311yescharacteristic
46C22×D4×C151—21no—
47C22×D4×C151—21no—
48C22×D4×C151—22no—
49C22×D4×C151C2312yes—
50C23×C4×C151D411yescharacteristic
51C23×C4×C151D411yescharacteristic
52C23×C4×C151C2311yescharacteristic
53C2×SD16×C151—24no—
54C2×SD16×C151—24no—
55C2×SD16×C151—42no—
56C22×C8×C151C2312yes—
57C22×C8×C151C2312yes—
58#127×C151—22no—
59#127×C151—22no—
60C22⋊Q8×C151—22no—
61C22⋊Q8×C151—22no—
62#121×C151—42no—
63#121×C151—42no—
64#121×C151—44no—
65#121×C151—44no—
66C4×Q8×C151—22no—
67C4×Q8×C151—22no—
68C2×C4⋊C4×C151—21no—
69C2×C4⋊C4×C151—21no—
70C2×C4⋊C4×C151—21no—
71C2×C4⋊C4×C151—21no—
72C2×C4⋊C4×C151—21no—
73C2×C4⋊C4×C151C2311yescharacteristic
74C2×C4⋊C4×C151C2312yes—
75C2×C4⋊C4×C151C2311yescharacteristic
76C2×C4⋊C4×C151C2311yescharacteristic
77C2×C22⋊C4×C151—22no—
78C2×C22⋊C4×C151—22no—
79C2×C22⋊C4×C151—22no—
80C2×C22⋊C4×C151—21no—
81C2×C22⋊C4×C151—21no—
82C2×C42×C151—22no—
83C2×C42×C151—22no—
84C2×C42×C151—21no—
85C2×C42×C151—21no—
86C2×C42×C151D411yescharacteristic
87C2×C42×C151D411yescharacteristic
88C2×C42×C151C2311yescharacteristic
89C2×C42×C151C2311yescharacteristic
90#106×C151—42no—
91C4⋊C8×C151—22no—
92C4⋊C8×C151D414yescomplemented
93#103×C151—42no—
94#102×C151—24no—
95#102×C151—24no—
96#102×C151—42no—
97C22⋊C8×C151—24no—
98C4×C8×C151—24no—
99#95×C151—21no—
100#95×C151—21no—
101#95×C151—21no—
102#95×C151—21no—
103#95×C151—21no—
104C24×C151—22no—
105C24×C151C2×D411yescharacteristic
106C2×Q8×C151—21no—
107C2×Q8×C151—21no—
108C2×Q8×C151—21no—
109C2×Q8×C151—21no—
110C2×Q8×C151—21no—
111C2×Q8×C151#4112yes—
112C2×D4×C151—22no—
113C2×D4×C151—22no—
114C2×D4×C151—22no—
115C2×D4×C151—22no—
116C2×D4×C151—22no—
117C2×D4×C151—22no—
118C2×D4×C151—42no—
119C2×D4×C151—42no—
120C2×D4×C151—44no—
121C2×D4×C151—44no—
122C2×D4×C151—44no—
123C2×D4×C151—42no—
124C2×D4×C151—42no—
125C2×D4×C151—42no—
126C2×D4×C151—42no—
127C22×C4×C151—22no—
128C22×C4×C151—22no—
129C22×C4×C151—21no—
130C22×C4×C151—21no—
131C22×C4×C151—22no—
132C22×C4×C151—22no—
133C22×C4×C151—21no—
134C22×C4×C151—21no—
135C22×C4×C151—21no—
136C22×C4×C151—21no—
137C22×C4×C151—21no—
138C22×C4×C151—21no—
139C22×C4×C151—21no—
140C22×C4×C151—21no—
141C22×C4×C151—22no—
142C22×C4×C151—41no—
143C22×C4×C151SD1614yescomplemented
144C22×C4×C151C2×D411yescharacteristic
145C22×C4×C151C2×D411yescharacteristic
146C22×C4×C151C2×D411yescharacteristic
147C22×C4×C151C2×D411yescharacteristic
148C22×C4×C151C2×D411yescharacteristic
149C22×C4×C151C2411yescharacteristic
150SD16×C151—48no—
151C2×C8×C151—22no—
152C2×C8×C151—22no—
153C2×C8×C151—22no—
154C2×C8×C151—22no—
155C2×C8×C151—22no—
156C2×C8×C151C2×D414yes—
157C4⋊C4×C151—24no—
158C4⋊C4×C151—21no—
159C4⋊C4×C151—21no—
160C4⋊C4×C151—21no—
161C4⋊C4×C151—21no—
162C4⋊C4×C151—22no—
163C4⋊C4×C151—21no—
164C4⋊C4×C151—22no—
165C4⋊C4×C151—42no—
166C4⋊C4×C151—42no—
167C4⋊C4×C151—42no—
168C4⋊C4×C151—42no—
169C4⋊C4×C151#4112yes—
170C22⋊C4×C151—24no—
171C22⋊C4×C151—44no—
172C22⋊C4×C151—42no—
173C22⋊C4×C151—44no—
174C22⋊C4×C151—44no—
175C42×C151—22no—
176C42×C151—22no—
177C42×C151—21no—
178C42×C151—21no—
179C42×C151—42no—
180C42×C151—42no—
181C42×C151C2×D412yes—
182C42×C151#4112yes—
183C23×C151—21no—
184C23×C151—21no—
185C23×C151—21no—
186C23×C151—21no—
187C23×C151—21no—
188C23×C151—21no—
189C23×C151—42no—
190C23×C151—42no—
191C23×C151—42no—
192C23×C151—42no—
193C23×C151—42no—
194C23×C151—42no—
195C23×C151—42no—
196C23×C151C2×SD1612yes—
197C23×C151C22×D411yescharacteristic
198Q8×C151—22no—
199Q8×C151—22no—
200Q8×C151—41no—
201Q8×C151—41no—
202D4×C151—42no—
203D4×C151—42no—
204D4×C151—42no—
205D4×C151—42no—
206D4×C151—84no—
207D4×C151—88no—
208D4×C151—84no—
209C2×C4×C151—21no—
210C2×C4×C151—21no—
211C2×C4×C151—21no—
212C2×C4×C151—21no—
213C2×C4×C151—21no—
214C2×C4×C151—21no—
215C2×C4×C151—28no—
216C2×C4×C151—21no—
217C2×C4×C151—22no—
218C2×C4×C151—22no—
219C2×C4×C151—21no—
220C2×C4×C151—21no—
221C2×C4×C151—44no—
222C2×C4×C151—41no—
223C2×C4×C151—41no—
224C2×C4×C151—41no—
225C2×C4×C151—41no—
226C2×C4×C151—41no—
227C2×C4×C151—41no—
228C2×C4×C151—41no—
229C2×C4×C151—41no—
230C2×C4×C151—41no—
231C2×C4×C151—42no—
232C2×C4×C151—41no—
233C2×C4×C151—42no—
234C2×C4×C151—41no—
235C2×C4×C151—42no—
236C2×C4×C151—41no—
237C2×C4×C151—41no—
238C2×C4×C151—41no—
239C2×C4×C151#12112yes—
240C2×C4×C151#12112yes—
241C2×C4×C151C2×SD1612yes—
242C2×C4×C151C2×SD1612yes—
243C2×C4×C151#13512yes—
244C2×C4×C151AGL(1,ℤ/8)12yes—
245C2×C4×C151C22×D411yescharacteristic
246C2×C4×C151C2×#4111yescharacteristic
247C2×C4×C151C2×#4111yescharacteristic
248C2×C4×C151C2×#4111yescharacteristic
249C2×C4×C151H(5,𝔽2)11yescharacteristic
250C2×C4×C151H(5,𝔽2)11yescharacteristic
251C8×C151—24no—
252C8×C151—42no—
253C22×C151—22no—
254C22×C151—22no—
255C22×C151—22no—
256C22×C151—41no—
257C22×C151—41no—
258C22×C151—41no—
259C22×C151—41no—
260C22×C151—82no—
261C22×C151—82no—
262C22×C151—82no—
263C22×C151—82no—
264C22×C151—82no—
265C22×C151—82no—
266C22×C151—82no—
267C22×C151C2×#12111yescharacteristic
268C22×C151#52511yescharacteristic
269C22×C151#53511yescharacteristic
270C22×C151C22×SD1611yescharacteristic
271C22×C151C2×#13511yescharacteristic
272C22×C151C2×AGL(1,ℤ/8)11yescharacteristic
273C22×C151#57511yescharacteristic
274C4×C151—22no—
275C4×C151—22no—
276C4×C151—22no—
277C4×C151—42no—
278C4×C151—41no—
279C4×C151—42no—
280C4×C151—82no—
281C4×C151—81no—
282C4×C151—81no—
283C4×C151#46514yes—
284C4×C151#54611yescharacteristic
285C4×C151#55011yescharacteristic
286C4×C151#55311yescharacteristic
287C4×C151#55511yescharacteristic
288C2×C151—42no—
289C2×C151—162no—
290C2×C151#241411yescharacteristic
291C2×C151C2×#46511yescharacteristic
292C2×C151#305511yescharacteristic
293C2×C151#310311yescharacteristic
294C2×C151#310611yescharacteristic
295C2×C151#320811yescharacteristic
296C2×C151#321211yescharacteristic
297#24653C15111yesmaximal, characteristic, direct product factor, Sylow
298C151#2465311yescharacteristic, direct product factor, Sylow
299C2×#460C2×C15111yescharacteristic, complemented
300C2×#431C2×C15111yescharacteristic, complemented
301#2856C2×C15111yescharacteristic
302C4×C22⋊Q8C2×C15111yescharacteristic, complemented
303#2034C2×C15112yescomplemented
304#2000C2×C15112yescomplemented
305#1982C2×C15111yescharacteristic, complemented
306#1968C2×C15112yescomplemented
307#1948C2×C15111yescharacteristic, complemented
308#1934C2×C15112yescomplemented
309#1803C2×C15111yescharacteristic, complemented
310C22×SD16C22×C15112yes—
311C2×#127C22×C15111yescharacteristic
312C2×C22⋊Q8C22×C15111yescharacteristic
313C2×#121—21no—
314C2×#121—21no—
315C2×#121C22×C15112yes—
316C2×C4×Q8C22×C15111yescharacteristic
317C22×C42C22×C15111yescharacteristic
318#460—24no—
319#431—24no—
320C2×#106C22×C15112yes—
321C2×C4⋊C8C22×C15111yescharacteristic
322C2×C4⋊C8C22×C15111yescharacteristic
323C2×#103C22×C15112yes—
324C2×#102C22×C15112yes—
325C2×#102C22×C15112yes—
326C2×#102C22×C15112yes—
327C2×C22⋊C8C22×C15112yes—
328C2×C4×C8C22×C15112yes—
329#391C22×C15111yescharacteristic
330#390—21no—
331#390—21no—
332#390C22×C15112yes—
333#389C22×C15111yescharacteristic
334#387—21no—
335#385—21no—
336#384C22×C15111yescharacteristic
337#380C22×C15111yescharacteristic
338C4×C4⋊C4—21no—
339C4×C4⋊C4C22×C15111yescharacteristic
340C4×C22⋊C4—21no—
341#340C22×C15112yes—
342#340C22×C15112yes—
343C22×Q8C23×C15111yescharacteristic
344C22×D4—22no—
345C22×D4—21no—
346C22×D4—21no—
347C22×D4C23×C15112yes—
348C23×C4D4×C15111yescharacteristic
349C23×C4D4×C15111yescharacteristic
350C23×C4C23×C15111yescharacteristic
351C2×SD16—24no—
352C2×SD16—24no—
353C2×SD16—42no—
354C22×C8C23×C15112yes—
355C22×C8C23×C15112yes—
356#127—22no—
357#127—22no—
358C22⋊Q8—22no—
359C22⋊Q8—22no—
360#121—42no—
361#121—42no—
362#121—44no—
363#121—44no—
364C4×Q8—22no—
365C4×Q8—22no—
366C2×C4⋊C4—21no—
367C2×C4⋊C4—21no—
368C2×C4⋊C4—21no—
369C2×C4⋊C4—21no—
370C2×C4⋊C4—21no—
371C2×C4⋊C4C23×C15111yescharacteristic
372C2×C4⋊C4C23×C15112yes—
373C2×C4⋊C4C23×C15111yescharacteristic
374C2×C4⋊C4C23×C15111yescharacteristic
375C2×C22⋊C4—21no—
376C2×C22⋊C4—21no—
377C2×C22⋊C4—22no—
378C2×C22⋊C4—22no—
379C2×C22⋊C4—22no—
380C2×C42—22no—
381C2×C42—22no—
382C2×C42—21no—
383C2×C42—21no—
384C2×C42D4×C15111yescharacteristic
385C2×C42D4×C15111yescharacteristic
386C2×C42C23×C15111yescharacteristic
387C2×C42C23×C15111yescharacteristic
388#106—42no—
389C4⋊C8—22no—
390C4⋊C8D4×C15114yescomplemented
391#103—42no—
392#102—24no—
393#102—24no—
394#102—42no—
395C22⋊C8—24no—
396C4×C8—24no—
397#95—21no—
398#95—21no—
399#95—21no—
400#95—21no—
401#95—21no—
402C24—22no—
403C24C2×D4×C15111yescharacteristic
404C2×Q8—21no—
405C2×Q8—21no—
406C2×Q8—21no—
407C2×Q8—21no—
408C2×Q8—21no—
409C2×Q8#41×C15112yes—
410C2×D4—22no—
411C2×D4—22no—
412C2×D4—22no—
413C2×D4—22no—
414C2×D4—22no—
415C2×D4—22no—
416C2×D4—42no—
417C2×D4—42no—
418C2×D4—44no—
419C2×D4—44no—
420C2×D4—44no—
421C2×D4—42no—
422C2×D4—42no—
423C2×D4—42no—
424C2×D4—42no—
425C22×C4—22no—
426C22×C4—22no—
427C22×C4—21no—
428C22×C4—21no—
429C22×C4—22no—
430C22×C4—22no—
431C22×C4—21no—
432C22×C4—21no—
433C22×C4—21no—
434C22×C4—21no—
435C22×C4—21no—
436C22×C4—21no—
437C22×C4—21no—
438C22×C4—21no—
439C22×C4—22no—
440C22×C4—41no—
441C22×C4SD16×C15114yescomplemented
442C22×C4C2×D4×C15111yescharacteristic
443C22×C4C2×D4×C15111yescharacteristic
444C22×C4C2×D4×C15111yescharacteristic
445C22×C4C2×D4×C15111yescharacteristic
446C22×C4C2×D4×C15111yescharacteristic
447C22×C4C24×C15111yescharacteristic
448SD16—48no—
449C2×C8—22no—
450C2×C8—22no—
451C2×C8—22no—
452C2×C8—22no—
453C2×C8—22no—
454C2×C8C2×D4×C15114yes—
455C4⋊C4—24no—
456C4⋊C4—21no—
457C4⋊C4—21no—
458C4⋊C4—21no—
459C4⋊C4—21no—
460C4⋊C4—22no—
461C4⋊C4—21no—
462C4⋊C4—22no—
463C4⋊C4—42no—
464C4⋊C4—42no—
465C4⋊C4—42no—
466C4⋊C4—42no—
467C4⋊C4#41×C15112yes—
468C22⋊C4—24no—
469C22⋊C4—44no—
470C22⋊C4—42no—
471C22⋊C4—44no—
472C22⋊C4—44no—
473C42—22no—
474C42—22no—
475C42—21no—
476C42—21no—
477C42—42no—
478C42—42no—
479C42C2×D4×C15112yes—
480C42#41×C15112yes—
481C23—21no—
482C23—21no—
483C23—21no—
484C23—21no—
485C23—21no—
486C23—21no—
487C23—42no—
488C23—42no—
489C23—42no—
490C23—42no—
491C23—42no—
492C23—42no—
493C23—42no—
494C23C2×SD16×C15112yes—
495C23C22×D4×C15111yescharacteristic
496Q8—22no—
497Q8—22no—
498Q8—41no—
499Q8—41no—
500D4—42no—
501D4—42no—
502D4—42no—
503D4—42no—
504D4—84no—
505D4—88no—
506D4—84no—
507C2×C4—21no—
508C2×C4—21no—
509C2×C4—21no—
510C2×C4—21no—
511C2×C4—21no—
512C2×C4—21no—
513C2×C4—28no—
514C2×C4—21no—
515C2×C4—22no—
516C2×C4—22no—
517C2×C4—21no—
518C2×C4—21no—
519C2×C4—44no—
520C2×C4—41no—
521C2×C4—41no—
522C2×C4—41no—
523C2×C4—41no—
524C2×C4—41no—
525C2×C4—41no—
526C2×C4—41no—
527C2×C4—41no—
528C2×C4—41no—
529C2×C4—42no—
530C2×C4—41no—
531C2×C4—42no—
532C2×C4—41no—
533C2×C4—42no—
534C2×C4—41no—
535C2×C4—41no—
536C2×C4—41no—
537C2×C4#121×C15112yes—
538C2×C4#121×C15112yes—
539C2×C4C2×SD16×C15112yes—
540C2×C4C2×SD16×C15112yes—
541C2×C4#135×C15112yes—
542C2×C4AGL(1,ℤ/8)×C15112yes—
543C2×C4C22×D4×C15111yescharacteristic
544C2×C4C2×#41×C15111yescharacteristic
545C2×C4C2×#41×C15111yescharacteristic
546C2×C4C2×#41×C15111yescharacteristic
547C2×C4H(5,𝔽2)×C15111yescharacteristic
548C2×C4H(5,𝔽2)×C15111yescharacteristic
549C8—24no—
550C8—42no—
551C22—22no—
552C22—22no—
553C22—22no—
554C22—41no—
555C22—41no—
556C22—41no—
557C22—41no—
558C22—82no—
559C22—82no—
560C22—82no—
561C22—82no—
562C22—82no—
563C22—82no—
564C22—82no—
565C22C2×#121×C15111yescharacteristic
566C22#525×C15111yescharacteristic
567C22#535×C15111yescharacteristic
568C22C22×SD16×C15111yescharacteristic
569C22C2×#135×C15111yescharacteristic
570C22C2×AGL(1,ℤ/8)×C15111yescharacteristic
571C22#575×C15111yescharacteristic
572C4—22no—
573C4—22no—
574C4—22no—
575C4—42no—
576C4—41no—
577C4—42no—
578C4—82no—
579C4—81no—
580C4—81no—
581C4#465×C15114yes—
582C4#546×C15111yescharacteristic
583C4#550×C15111yescharacteristic
584C4#553×C15111yescharacteristic
585C4#555×C15111yescharacteristic
586C2—42no—
587C2—162no—
588C2#2414×C15111yescharacteristic
589C2C2×#465×C15111yescharacteristic
590C2#3055×C15111yescharacteristic
591C2#3103×C15111yescharacteristic
592C2#3106×C15111yescharacteristic
593C2#3208×C15111yescharacteristic
594C2#3212×C15111yescharacteristic
subgroupG/H
center, socleC23×C151C22×D4
commutator, Frattini, cosocleC22×C4C24×C151
prime radical#2856×C151C2
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C151 ◁ C22×C42×C151 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×#460×C151C2semidirect
2. C2×#431×C151C2semidirect
4. C4×C22⋊Q8×C151C2semidirect
5. #2034×C151C2semidirect
6. #2000×C151C2semidirect
7. #1982×C151C2semidirect
8. #1968×C151C2semidirect
9. #1948×C151C2semidirect
10. #1934×C151C2semidirect
11. #1803×C151C2semidirect
92. C4⋊C8×C151D4semidirect
143. C22×C4×C151SD16semidirect
297. #24653C151direct (N × H)
298. C151#24653direct (N × H)
299. C2×#460C2×C151semidirect
300. C2×#431C2×C151semidirect
302. C4×C22⋊Q8C2×C151semidirect
303. #2034C2×C151semidirect
304. #2000C2×C151semidirect
305. #1982C2×C151semidirect
306. #1968C2×C151semidirect
307. #1948C2×C151semidirect
308. #1934C2×C151semidirect
309. #1803C2×C151semidirect
390. C4⋊C8D4×C151semidirect
441. C22×C4SD16×C151semidirect

Maximal subgroups

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

subgroupindex
C2×#460×C1512
C2×#431×C1512
#2856×C1512
C4×C22⋊Q8×C1512
#2034×C1512
#2000×C1512
#1982×C1512
#1968×C1512
#1948×C1512
#1934×C1512
#1803×C1512
#24653151