Finite Group Databasebeta

← C151×#18888 #50323813

Subgroups — C151×#18888 #50323813

Order 38656.

964 conjugacy classes of subgroups.

The subgroup lattice has 610 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#3511×C151C211yesmaximal, characteristic, complemented
2#3245×C151C211yesmaximal, characteristic, complemented
3#3227×C151C211yesmaximal, characteristic, complemented
4#3035×C151C211yesmaximal, characteristic, complemented
5#1654×C151C212yesmaximal, complemented
6#1652×C151C212yesmaximal, complemented
7#1628×C151C212yesmaximal, complemented
8#1625×C151C212yesmaximal, complemented
9C2×#332×C151C211yesmaximal, characteristic, complemented
10#1480×C151C211yesmaximal, characteristic, complemented
11#1477×C151C211yesmaximal, characteristic, complemented
12C2×#135×C151—21no—
13#556×C151C2212yes—
14#555×C151—21no—
15#554×C151—21no—
16#553×C151—22no—
17#548×C151—22no—
18#547×C151C2212yes—
19#542×C151—22no—
20#537×C151—21no—
21#533×C151—21no—
22#532×C151—21no—
23#532×C151C2211yescharacteristic
24#532×C151C2211yescharacteristic
25C2×C4⋊Q8×C151C2211yescharacteristic
26#520×C151—21no—
27C4×#41×C151C2211yescharacteristic
28#498×C151C2212yes—
29#486×C151C2212yes—
30#481×C151—22no—
31#476×C151—22no—
32#474×C151—21no—
33#474×C151C2212yes—
34#466×C151—22no—
35#464×C151—21no—
36#463×C151—21no—
37#462×C151C2211yescharacteristic
38#461×C151C2211yescharacteristic
39#460×C151C2211yescharacteristic
40#459×C151—21no—
41#459×C151C2211yescharacteristic
42#459×C151C2212yes—
43#431×C151C2211yescharacteristic
44C2×C4⋊C8×C151C2211yescharacteristic
45C2×C4⋊C8×C151C2211yescharacteristic
46#416×C151—21no—
47#332×C151C2212yes—
48#332×C151C2212yes—
49Q8⋊C8×C151C2212yes—
50D4⋊C8×C151C2212yes—
51D4⋊C8×C151C2212yes—
52D4⋊C8×C151C2212yes—
53C2×#41×C151—21no—
54C2×#41×C151—21no—
55C2×#41×C151—22no—
56C2×#41×C151D411yescharacteristic
57C22×Q8×C151—21no—
58#135×C151—44no—
59C2×Q16×C151—21no—
60C2×SD16×C151—21no—
61C2×SD16×C151—21no—
62C2×D8×C151—21no—
63C2×D8×C151—22no—
64C22×C8×C151—21no—
65C22×C8×C151—21no—
66C4⋊Q8×C151—21no—
67C4⋊Q8×C151—21no—
68C4⋊Q8×C151D411yescharacteristic
69C4⋊Q8×C151D412yes—
70C4⋊Q8×C151C2311yescharacteristic
71C4⋊Q8×C151C2312yes—
72#127×C151D411yescharacteristic
73#127×C151C2311yescharacteristic
74#126×C151—24no—
75#125×C151—22no—
76#124×C151—24no—
77#124×C151—22no—
78#124×C151—21no—
79#124×C151—21no—
80#123×C151—24no—
81C22⋊Q8×C151—22no—
82C22⋊Q8×C151—24no—
83C22⋊Q8×C151—22no—
84C22⋊Q8×C151—22no—
85#121×C151—22no—
86#121×C151—22no—
87#121×C151—24no—
88#121×C151—22no—
89#121×C151—21no—
90#121×C151—21no—
91#121×C151—21no—
92#121×C151D412yes—
93C4×Q8×C151—22no—
94C4×Q8×C151—22no—
95C4×Q8×C151D411yescharacteristic
96C4×Q8×C151C2311yescharacteristic
97C4×D4×C151—22no—
98C4×D4×C151—24no—
99C4×D4×C151—22no—
100C4×D4×C151—21no—
101C4×D4×C151—21no—
102C4×D4×C151—21no—
103C4×D4×C151—21no—
104C4×D4×C151—21no—
105C4×D4×C151D411yescharacteristic
106C4×D4×C151C2311yescharacteristic
107C4×D4×C151C2312yes—
108#117×C151—22no—
109#117×C151—22no—
110#117×C151—21no—
111#117×C151D411yescharacteristic
112C2×C4⋊C4×C151—21no—
113C2×C4⋊C4×C151—22no—
114C2×C4⋊C4×C151D412yes—
115C2×C42×C151—21no—
116C2×C42×C151C2311yescharacteristic
117#107×C151—22no—
118#106×C151—24no—
119C4⋊C8×C151—21no—
120C4⋊C8×C151—21no—
121C4⋊C8×C151—21no—
122C4⋊C8×C151C2311yescharacteristic
123C4⋊C8×C151C2312yes—
124C4⋊C8×C151C2311yescharacteristic
125#103×C151—21no—
126#103×C151—21no—
127#102×C151—22no—
128#102×C151—21no—
129#102×C151—21no—
130#102×C151—22no—
131#102×C151—24no—
132C22⋊C8×C151—21no—
133C4×C8×C151C2312yes—
134#41×C151—22no—
135#41×C151—22no—
136#41×C151—42no—
137#41×C151—42no—
138#41×C151—42no—
139#41×C151—42no—
140#41×C151—82no—
141#41×C151—82no—
142C2×Q8×C151—21no—
143C2×Q8×C151—22no—
144C2×Q8×C151—22no—
145C2×Q8×C151—21no—
146C2×Q8×C151—81no—
147C2×Q8×C151—81no—
148C2×Q8×C151C2×D411yescharacteristic
149C2×D4×C151—21no—
150C2×D4×C151—22no—
151C2×D4×C151—24no—
152C2×D4×C151—21no—
153C2×D4×C151—21no—
154C2×D4×C151—21no—
155C2×D4×C151—21no—
156C2×D4×C151—21no—
157C2×D4×C151—41no—
158C2×D4×C151C2×D412yes—
159C2×D4×C151C2×D411yescharacteristic
160C22×C4×C151—24no—
161C22×C4×C151—22no—
162C22×C4×C151—21no—
163C22×C4×C151—21no—
164C22×C4×C151—21no—
165C22×C4×C151—22no—
166C22×C4×C151—41no—
167C22×C4×C151C2×D411yescharacteristic
168C22×C4×C151C2×D411yescharacteristic
169C22×C4×C151C2×D411yescharacteristic
170Q16×C151—42no—
171SD16×C151—42no—
172SD16×C151—42no—
173D8×C151—42no—
174D8×C151—82no—
175C2×C8×C151—22no—
176C2×C8×C151—22no—
177C2×C8×C151—21no—
178C2×C8×C151—21no—
179C2×C8×C151—42no—
180C2×C8×C151—81no—
181C4⋊C4×C151—24no—
182C4⋊C4×C151—24no—
183C4⋊C4×C151—22no—
184C4⋊C4×C151—22no—
185C4⋊C4×C151—21no—
186C4⋊C4×C151—21no—
187C4⋊C4×C151—22no—
188C4⋊C4×C151—21no—
189C4⋊C4×C151—21no—
190C4⋊C4×C151—21no—
191C4⋊C4×C151C2×D411yescharacteristic
192C4⋊C4×C151C2×D411yescharacteristic
193C4⋊C4×C151C2×D414yes—
194C4⋊C4×C151C2×D412yes—
195C22⋊C4×C151—24no—
196C22⋊C4×C151—24no—
197C22⋊C4×C151—24no—
198C22⋊C4×C151—21no—
199C22⋊C4×C151—21no—
200C22⋊C4×C151—22no—
201C22⋊C4×C151—21no—
202C22⋊C4×C151—22no—
203C22⋊C4×C151—41no—
204C22⋊C4×C151—41no—
205C42×C151—24no—
206C42×C151—21no—
207C42×C151—21no—
208C42×C151—21no—
209C42×C151C2×D411yescharacteristic
210C42×C151C2×D411yescharacteristic
211C42×C151C2×D411yescharacteristic
212C42×C151C2411yescharacteristic
213C23×C151—21no—
214C23×C151—22no—
215C23×C151—41no—
216C23×C151#12011yescharacteristic
217Q8×C151—21no—
218Q8×C151—21no—
219Q8×C151—42no—
220Q8×C151—42no—
221Q8×C151—42no—
222Q8×C151—41no—
223Q8×C151—41no—
224Q8×C151—82no—
225D4×C151—21no—
226D4×C151—21no—
227D4×C151—22no—
228D4×C151—22no—
229D4×C151—42no—
230D4×C151—42no—
231D4×C151—42no—
232D4×C151—44no—
233D4×C151—41no—
234D4×C151—41no—
235D4×C151—41no—
236D4×C151—41no—
237D4×C151—42no—
238D4×C151—84no—
239D4×C151—82no—
240C2×C4×C151—21no—
241C2×C4×C151—21no—
242C2×C4×C151—24no—
243C2×C4×C151—22no—
244C2×C4×C151—21no—
245C2×C4×C151—21no—
246C2×C4×C151—21no—
247C2×C4×C151—41no—
248C2×C4×C151—42no—
249C2×C4×C151—42no—
250C2×C4×C151—42no—
251C2×C4×C151—41no—
252C2×C4×C151—41no—
253C2×C4×C151—42no—
254C2×C4×C151—41no—
255C2×C4×C151—82no—
256C2×C4×C151—84no—
257C2×C4×C151—82no—
258C2×C4×C151#12011yescharacteristic
259C2×C4×C151#12011yescharacteristic
260C2×C4×C151#12011yescharacteristic
261C2×C4×C151#13512yes—
262C2×C4×C151AGL(1,ℤ/8)12yes—
263C2×C4×C151C22×D411yescharacteristic
264C2×C4×C151C22×D411yescharacteristic
265C2×C4×C151C22×D411yescharacteristic
266C8×C151—42no—
267C8×C151—41no—
268C8×C151—41no—
269C8×C151—42no—
270C22×C151—21no—
271C22×C151—21no—
272C22×C151—41no—
273C22×C151—42no—
274C22×C151—41no—
275C22×C151—42no—
276C22×C151—41no—
277C22×C151—42no—
278C22×C151—81no—
279C22×C151—81no—
280C22×C151—81no—
281C22×C151#44912yes—
282C22×C151C2×#12011yescharacteristic
283C4×C151—21no—
284C4×C151—21no—
285C4×C151—21no—
286C4×C151—41no—
287C4×C151—42no—
288C4×C151—41no—
289C4×C151—44no—
290C4×C151—41no—
291C4×C151—81no—
292C4×C151#44912yes—
293C4×C151C2×#13511yescharacteristic
294C4×C151C2×AGL(1,ℤ/8)11yescharacteristic
295C4×C151#57611yescharacteristic
296C4×C151#57711yescharacteristic
297C2×C151—22no—
298C2×C151—81no—
299C2×C151—82no—
300C2×C151—161no—
301C2×C151C2×#44911yescharacteristic
302C2×C151#301211yescharacteristic
303C2×C151#302011yescharacteristic
304#18888C15111yesmaximal, characteristic, direct product factor, Sylow
305C151#1888811yescharacteristic, direct product factor, Sylow
306#3511C2×C15111yescharacteristic, complemented
307#3245C2×C15111yescharacteristic, complemented
308#3227C2×C15111yescharacteristic, complemented
309#3035C2×C15111yescharacteristic, complemented
310#1654C2×C15112yescomplemented
311#1652C2×C15112yescomplemented
312#1628C2×C15112yescomplemented
313#1625C2×C15112yescomplemented
314C2×#332C2×C15111yescharacteristic, complemented
315#1480C2×C15111yescharacteristic, complemented
316#1477C2×C15111yescharacteristic, complemented
317C2×#135—21no—
318#556C22×C15112yes—
319#555—21no—
320#554—21no—
321#553—22no—
322#548—22no—
323#547C22×C15112yes—
324#542—22no—
325#537—21no—
326#533—21no—
327#532—21no—
328#532C22×C15111yescharacteristic
329#532C22×C15111yescharacteristic
330C2×C4⋊Q8C22×C15111yescharacteristic
331#520—21no—
332C4×#41C22×C15111yescharacteristic
333#498C22×C15112yes—
334#486C22×C15112yes—
335#481—22no—
336#476—22no—
337#474—21no—
338#474C22×C15112yes—
339#466—22no—
340#464—21no—
341#463—21no—
342#462C22×C15111yescharacteristic
343#461C22×C15111yescharacteristic
344#460C22×C15111yescharacteristic
345#459—21no—
346#459C22×C15111yescharacteristic
347#459C22×C15112yes—
348#431C22×C15111yescharacteristic
349C2×C4⋊C8C22×C15111yescharacteristic
350C2×C4⋊C8C22×C15111yescharacteristic
351#416—21no—
352#332C22×C15112yes—
353#332C22×C15112yes—
354Q8⋊C8C22×C15112yes—
355D4⋊C8C22×C15112yes—
356D4⋊C8C22×C15112yes—
357D4⋊C8C22×C15112yes—
358C2×#41—22no—
359C2×#41—21no—
360C2×#41—21no—
361C2×#41D4×C15111yescharacteristic
362C22×Q8—21no—
363#135—44no—
364C2×Q16—21no—
365C2×SD16—21no—
366C2×SD16—21no—
367C2×D8—21no—
368C2×D8—22no—
369C22×C8—21no—
370C22×C8—21no—
371C4⋊Q8—21no—
372C4⋊Q8—21no—
373C4⋊Q8D4×C15112yes—
374C4⋊Q8D4×C15111yescharacteristic
375C4⋊Q8C23×C15111yescharacteristic
376C4⋊Q8C23×C15112yes—
377#127D4×C15111yescharacteristic
378#127C23×C15111yescharacteristic
379#126—24no—
380#125—22no—
381#124—24no—
382#124—22no—
383#124—21no—
384#124—21no—
385#123—24no—
386C22⋊Q8—22no—
387C22⋊Q8—24no—
388C22⋊Q8—22no—
389C22⋊Q8—22no—
390#121—22no—
391#121—22no—
392#121—24no—
393#121—22no—
394#121—21no—
395#121—21no—
396#121—21no—
397#121D4×C15112yes—
398C4×Q8—22no—
399C4×Q8—22no—
400C4×Q8D4×C15111yescharacteristic
401C4×Q8C23×C15111yescharacteristic
402C4×D4—22no—
403C4×D4—24no—
404C4×D4—22no—
405C4×D4—21no—
406C4×D4—21no—
407C4×D4—21no—
408C4×D4—21no—
409C4×D4—21no—
410C4×D4D4×C15111yescharacteristic
411C4×D4C23×C15111yescharacteristic
412C4×D4C23×C15112yes—
413#117—22no—
414#117—22no—
415#117—21no—
416#117D4×C15111yescharacteristic
417C2×C4⋊C4—21no—
418C2×C4⋊C4—22no—
419C2×C4⋊C4D4×C15112yes—
420C2×C42—21no—
421C2×C42C23×C15111yescharacteristic
422#107—22no—
423#106—24no—
424C4⋊C8—21no—
425C4⋊C8—21no—
426C4⋊C8—21no—
427C4⋊C8C23×C15111yescharacteristic
428C4⋊C8C23×C15111yescharacteristic
429C4⋊C8C23×C15112yes—
430#103—21no—
431#103—21no—
432#102—22no—
433#102—21no—
434#102—21no—
435#102—22no—
436#102—24no—
437C22⋊C8—21no—
438C4×C8C23×C15112yes—
439#41—22no—
440#41—22no—
441#41—42no—
442#41—42no—
443#41—42no—
444#41—42no—
445#41—82no—
446#41—82no—
447C2×Q8—21no—
448C2×Q8—22no—
449C2×Q8—22no—
450C2×Q8—21no—
451C2×Q8—81no—
452C2×Q8—81no—
453C2×Q8C2×D4×C15111yescharacteristic
454C2×D4—21no—
455C2×D4—22no—
456C2×D4—24no—
457C2×D4—21no—
458C2×D4—21no—
459C2×D4—21no—
460C2×D4—21no—
461C2×D4—21no—
462C2×D4—41no—
463C2×D4C2×D4×C15112yes—
464C2×D4C2×D4×C15111yescharacteristic
465C22×C4—24no—
466C22×C4—22no—
467C22×C4—21no—
468C22×C4—21no—
469C22×C4—21no—
470C22×C4—22no—
471C22×C4—41no—
472C22×C4C2×D4×C15111yescharacteristic
473C22×C4C2×D4×C15111yescharacteristic
474C22×C4C2×D4×C15111yescharacteristic
475Q16—42no—
476SD16—42no—
477SD16—42no—
478D8—42no—
479D8—82no—
480C2×C8—22no—
481C2×C8—22no—
482C2×C8—21no—
483C2×C8—21no—
484C2×C8—42no—
485C2×C8—81no—
486C4⋊C4—24no—
487C4⋊C4—24no—
488C4⋊C4—22no—
489C4⋊C4—22no—
490C4⋊C4—21no—
491C4⋊C4—21no—
492C4⋊C4—22no—
493C4⋊C4—21no—
494C4⋊C4—21no—
495C4⋊C4—21no—
496C4⋊C4C2×D4×C15111yescharacteristic
497C4⋊C4C2×D4×C15111yescharacteristic
498C4⋊C4C2×D4×C15114yes—
499C4⋊C4C2×D4×C15112yes—
500C22⋊C4—24no—
501C22⋊C4—24no—
502C22⋊C4—24no—
503C22⋊C4—21no—
504C22⋊C4—21no—
505C22⋊C4—22no—
506C22⋊C4—21no—
507C22⋊C4—22no—
508C22⋊C4—41no—
509C22⋊C4—41no—
510C42—24no—
511C42—21no—
512C42—21no—
513C42—21no—
514C42C2×D4×C15111yescharacteristic
515C42C2×D4×C15111yescharacteristic
516C42C2×D4×C15111yescharacteristic
517C42C24×C15111yescharacteristic
518C23—21no—
519C23—22no—
520C23—41no—
521C23#120×C15111yescharacteristic
522Q8—21no—
523Q8—21no—
524Q8—42no—
525Q8—42no—
526Q8—42no—
527Q8—41no—
528Q8—41no—
529Q8—82no—
530D4—21no—
531D4—21no—
532D4—22no—
533D4—22no—
534D4—42no—
535D4—42no—
536D4—42no—
537D4—44no—
538D4—42no—
539D4—41no—
540D4—41no—
541D4—41no—
542D4—41no—
543D4—84no—
544D4—82no—
545C2×C4—21no—
546C2×C4—21no—
547C2×C4—21no—
548C2×C4—21no—
549C2×C4—22no—
550C2×C4—21no—
551C2×C4—24no—
552C2×C4—41no—
553C2×C4—42no—
554C2×C4—42no—
555C2×C4—42no—
556C2×C4—42no—
557C2×C4—41no—
558C2×C4—41no—
559C2×C4—41no—
560C2×C4—82no—
561C2×C4—84no—
562C2×C4—82no—
563C2×C4#120×C15111yescharacteristic
564C2×C4#120×C15111yescharacteristic
565C2×C4#120×C15111yescharacteristic
566C2×C4#135×C15112yes—
567C2×C4AGL(1,ℤ/8)×C15112yes—
568C2×C4C22×D4×C15111yescharacteristic
569C2×C4C22×D4×C15111yescharacteristic
570C2×C4C22×D4×C15111yescharacteristic
571C8—42no—
572C8—41no—
573C8—41no—
574C8—42no—
575C22—21no—
576C22—21no—
577C22—41no—
578C22—42no—
579C22—41no—
580C22—42no—
581C22—41no—
582C22—42no—
583C22—81no—
584C22—81no—
585C22—81no—
586C22#449×C15112yes—
587C22C2×#120×C15111yescharacteristic
588C4—21no—
589C4—21no—
590C4—21no—
591C4—41no—
592C4—42no—
593C4—41no—
594C4—44no—
595C4—41no—
596C4—81no—
597C4#449×C15112yes—
598C4C2×#135×C15111yescharacteristic
599C4C2×AGL(1,ℤ/8)×C15111yescharacteristic
600C4#576×C15111yescharacteristic
601C4#577×C15111yescharacteristic
602C2—22no—
603C2—81no—
604C2—82no—
605C2—161no—
606C2C2×#449×C15111yescharacteristic
607C2#3012×C15111yescharacteristic
608C2#3020×C15111yescharacteristic
subgroupG/H
center, socleC22×C151C2×#120
commutator, Frattini, cosocleC42C24×C151
LCSG ▷ C42 ▷ C22 ▷ C1
UCSC1 ◁ C22×C151 ◁ C2×C42×C151 ◁ G

Complements

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

NH ≅ G/Ntype
1. #3511×C151C2semidirect
2. #3245×C151C2semidirect
3. #3227×C151C2semidirect
4. #3035×C151C2semidirect
5. #1654×C151C2semidirect
6. #1652×C151C2semidirect
7. #1628×C151C2semidirect
8. #1625×C151C2semidirect
9. C2×#332×C151C2semidirect
10. #1480×C151C2semidirect
11. #1477×C151C2semidirect
304. #18888C151direct (N × H)
305. C151#18888direct (N × H)
306. #3511C2×C151semidirect
307. #3245C2×C151semidirect
308. #3227C2×C151semidirect
309. #3035C2×C151semidirect
310. #1654C2×C151semidirect
311. #1652C2×C151semidirect
312. #1628C2×C151semidirect
313. #1625C2×C151semidirect
314. C2×#332C2×C151semidirect
315. #1480C2×C151semidirect
316. #1477C2×C151semidirect

Maximal subgroups

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

subgroupindex
#3511×C1512
#3245×C1512
#3227×C1512
#3035×C1512
#1654×C1512
#1652×C1512
#1628×C1512
#1625×C1512
C2×#332×C1512
#1480×C1512
#1477×C1512
#18888151