Finite Group Databasebeta

← C151×#18569 #50323494

Subgroups — C151×#18569 #50323494

Order 38656.

1002 conjugacy classes of subgroups.

The subgroup lattice has 600 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#3511×C151C211yesmaximal, characteristic, complemented
2#3253×C151C211yesmaximal, characteristic, complemented
3#3152×C151C211yesmaximal, characteristic, complemented
4#3106×C151C211yesmaximal, characteristic, complemented
5#1634×C151C212yesmaximal, complemented
6#1632×C151C212yesmaximal, complemented
7#1624×C151C212yesmaximal, complemented
8#1622×C151C212yesmaximal, complemented
9#1548×C151C211yesmaximal, characteristic, complemented
10#1489×C151C211yesmaximal, characteristic, complemented
11#1484×C151C211yesmaximal, characteristic, complemented
12C2×#137×C151—22no—
13#556×C151—21no—
14#555×C151C2212yes—
15#554×C151C2212yes—
16#553×C151—22no—
17#548×C151—22no—
18#547×C151—21no—
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#497×C151—22no—
29#494×C151C2212yes—
30#492×C151C2212yes—
31#482×C151—21no—
32#477×C151C2211yescharacteristic
33#476×C151—21no—
34#476×C151C2211yescharacteristic
35#476×C151C2212yes—
36#469×C151—22no—
37#460×C151C2211yescharacteristic
38#459×C151—21no—
39#459×C151C2211yescharacteristic
40#459×C151C2212yes—
41#449×C151—21no—
42C4×SD16×C151—21no—
43C4×D8×C151—21no—
44#431×C151C2211yescharacteristic
45#423×C151C2211yescharacteristic
46C4×M16×C151C2211yescharacteristic
47#333×C151C2212yes—
48#333×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×C151D412yes—
58#137×C151—48no—
59C2×Q16×C151—24no—
60C2×SD16×C151—21no—
61C2×SD16×C151—24no—
62C2×D8×C151—21no—
63C2×D8×C151—22no—
64C2×M16×C151—21no—
65C2×M16×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—22no—
77#124×C151—21no—
78#124×C151—21no—
79#124×C151—24no—
80#123×C151—24no—
81C22⋊Q8×C151—22no—
82C22⋊Q8×C151—22no—
83C22⋊Q8×C151—22no—
84C22⋊Q8×C151—24no—
85#121×C151—22no—
86#121×C151—24no—
87#121×C151—22no—
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—21no—
114C2×C4⋊C4×C151—22no—
115C2×C42×C151—21no—
116C2×C42×C151C2311yescharacteristic
117#107×C151—21no—
118#106×C151—21no—
119#106×C151—22no—
120C4⋊C8×C151—21no—
121C4⋊C8×C151C2312yes—
122C4⋊C8×C151C2311yescharacteristic
123C4⋊C8×C151C2311yescharacteristic
124#103×C151—21no—
125#102×C151—21no—
126#102×C151—22no—
127#102×C151—21no—
128#102×C151—21no—
129#102×C151—22no—
130C22⋊C8×C151—21no—
131#97×C151—21no—
132C4×C8×C151—21no—
133C4×C8×C151C2312yes—
134#41×C151—41no—
135#41×C151—41no—
136#41×C151—42no—
137#41×C151—42no—
138#41×C151—44no—
139#41×C151—84no—
140C2×Q8×C151—21no—
141C2×Q8×C151—22no—
142C2×Q8×C151—21no—
143C2×Q8×C151—44no—
144C2×Q8×C151C2×D411yescharacteristic
145C2×Q8×C151C2×D414yes—
146C2×D4×C151—21no—
147C2×D4×C151—22no—
148C2×D4×C151—24no—
149C2×D4×C151—21no—
150C2×D4×C151—21no—
151C2×D4×C151—21no—
152C2×D4×C151—21no—
153C2×D4×C151—21no—
154C2×D4×C151—41no—
155C2×D4×C151C2×D412yes—
156C2×D4×C151C2×D411yescharacteristic
157C22×C4×C151—24no—
158C22×C4×C151—22no—
159C22×C4×C151—21no—
160C22×C4×C151—21no—
161C22×C4×C151—21no—
162C22×C4×C151—22no—
163C22×C4×C151—41no—
164C22×C4×C151C2×D411yescharacteristic
165C22×C4×C151C2×D411yescharacteristic
166C22×C4×C151C2×D411yescharacteristic
167Q16×C151—48no—
168SD16×C151—48no—
169SD16×C151—42no—
170D8×C151—42no—
171D8×C151—82no—
172M16×C151—24no—
173M16×C151—81no—
174C2×C8×C151—22no—
175C2×C8×C151—21no—
176C2×C8×C151—21no—
177C2×C8×C151—22no—
178C4⋊C4×C151—24no—
179C4⋊C4×C151—24no—
180C4⋊C4×C151—22no—
181C4⋊C4×C151—22no—
182C4⋊C4×C151—21no—
183C4⋊C4×C151—21no—
184C4⋊C4×C151—22no—
185C4⋊C4×C151—22no—
186C4⋊C4×C151—21no—
187C4⋊C4×C151—21no—
188C4⋊C4×C151—21no—
189C4⋊C4×C151C2×D411yescharacteristic
190C4⋊C4×C151C2×D412yes—
191C4⋊C4×C151C2×D411yescharacteristic
192C22⋊C4×C151—24no—
193C22⋊C4×C151—24no—
194C22⋊C4×C151—24no—
195C22⋊C4×C151—21no—
196C22⋊C4×C151—21no—
197C22⋊C4×C151—22no—
198C22⋊C4×C151—21no—
199C22⋊C4×C151—22no—
200C22⋊C4×C151—41no—
201C22⋊C4×C151—41no—
202C42×C151—24no—
203C42×C151—21no—
204C42×C151—21no—
205C42×C151—21no—
206C42×C151C2×D411yescharacteristic
207C42×C151C2×D411yescharacteristic
208C42×C151C2×D411yescharacteristic
209C42×C151C2411yescharacteristic
210C23×C151—21no—
211C23×C151—22no—
212C23×C151—41no—
213C23×C151#12011yescharacteristic
214Q8×C151—21no—
215Q8×C151—21no—
216Q8×C151—44no—
217Q8×C151—42no—
218Q8×C151—42no—
219Q8×C151—44no—
220D4×C151—21no—
221D4×C151—21no—
222D4×C151—22no—
223D4×C151—22no—
224D4×C151—42no—
225D4×C151—42no—
226D4×C151—42no—
227D4×C151—44no—
228D4×C151—41no—
229D4×C151—41no—
230D4×C151—41no—
231D4×C151—41no—
232D4×C151—42no—
233D4×C151—84no—
234D4×C151—82no—
235C2×C4×C151—21no—
236C2×C4×C151—21no—
237C2×C4×C151—21no—
238C2×C4×C151—21no—
239C2×C4×C151—22no—
240C2×C4×C151—24no—
241C2×C4×C151—22no—
242C2×C4×C151—21no—
243C2×C4×C151—21no—
244C2×C4×C151—21no—
245C2×C4×C151—42no—
246C2×C4×C151—42no—
247C2×C4×C151—42no—
248C2×C4×C151—41no—
249C2×C4×C151—41no—
250C2×C4×C151—42no—
251C2×C4×C151—41no—
252C2×C4×C151—82no—
253C2×C4×C151—84no—
254C2×C4×C151—82no—
255C2×C4×C151#12011yescharacteristic
256C2×C4×C151#12011yescharacteristic
257C2×C4×C151#12011yescharacteristic
258C2×C4×C151C22×D411yescharacteristic
259C2×C4×C151C22×D411yescharacteristic
260C2×C4×C151C22×D411yescharacteristic
261C8×C151—24no—
262C8×C151—41no—
263C8×C151—41no—
264C8×C151—42no—
265C22×C151—21no—
266C22×C151—21no—
267C22×C151—21no—
268C22×C151—41no—
269C22×C151—42no—
270C22×C151—41no—
271C22×C151—42no—
272C22×C151—41no—
273C22×C151—42no—
274C22×C151—81no—
275C22×C151—81no—
276C22×C151—81no—
277C22×C151C2×#12011yescharacteristic
278C4×C151—21no—
279C4×C151—21no—
280C4×C151—21no—
281C4×C151—41no—
282C4×C151—42no—
283C4×C151—41no—
284C4×C151—41no—
285C4×C151—44no—
286C4×C151—81no—
287C4×C151#45312yes—
288C4×C151#57511yescharacteristic
289C4×C151#57511yescharacteristic
290C4×C151#57711yescharacteristic
291C4×C151#57811yescharacteristic
292C2×C151—41no—
293C2×C151—81no—
294C2×C151—82no—
295C2×C151—161no—
296C2×C151#300511yescharacteristic
297C2×C151#301311yescharacteristic
298C2×C151C2×#45311yescharacteristic
299#18569C15111yesmaximal, characteristic, direct product factor, Sylow
300C151#1856911yescharacteristic, direct product factor, Sylow
301#3511C2×C15111yescharacteristic, complemented
302#3253C2×C15111yescharacteristic, complemented
303#3152C2×C15111yescharacteristic, complemented
304#3106C2×C15111yescharacteristic, complemented
305#1634C2×C15112yescomplemented
306#1632C2×C15112yescomplemented
307#1624C2×C15112yescomplemented
308#1622C2×C15112yescomplemented
309#1548C2×C15111yescharacteristic, complemented
310#1489C2×C15111yescharacteristic, complemented
311#1484C2×C15111yescharacteristic, complemented
312C2×#137—22no—
313#556—21no—
314#555C22×C15112yes—
315#554C22×C15112yes—
316#553—22no—
317#548—22no—
318#547—21no—
319#542—22no—
320#537—21no—
321#533—21no—
322#532—21no—
323#532C22×C15111yescharacteristic
324#532C22×C15111yescharacteristic
325C2×C4⋊Q8C22×C15111yescharacteristic
326#520—21no—
327C4×#41C22×C15111yescharacteristic
328#497—22no—
329#494C22×C15112yes—
330#492C22×C15112yes—
331#482—21no—
332#477C22×C15111yescharacteristic
333#476—21no—
334#476C22×C15111yescharacteristic
335#476C22×C15112yes—
336#469—22no—
337#460C22×C15111yescharacteristic
338#459—21no—
339#459C22×C15111yescharacteristic
340#459C22×C15112yes—
341#449—21no—
342C4×SD16—21no—
343C4×D8—21no—
344#431C22×C15111yescharacteristic
345#423C22×C15111yescharacteristic
346C4×M16C22×C15111yescharacteristic
347#333C22×C15112yes—
348#333C22×C15112yes—
349Q8⋊C8C22×C15112yes—
350D4⋊C8C22×C15112yes—
351D4⋊C8C22×C15112yes—
352D4⋊C8C22×C15112yes—
353C2×#41—22no—
354C2×#41—21no—
355C2×#41—21no—
356C2×#41D4×C15111yescharacteristic
357C22×Q8D4×C15112yes—
358#137—48no—
359C2×Q16—24no—
360C2×SD16—24no—
361C2×SD16—21no—
362C2×D8—21no—
363C2×D8—22no—
364C2×M16—21no—
365C2×M16—21no—
366C4⋊Q8—21no—
367C4⋊Q8—21no—
368C4⋊Q8D4×C15112yes—
369C4⋊Q8D4×C15111yescharacteristic
370C4⋊Q8C23×C15111yescharacteristic
371C4⋊Q8C23×C15112yes—
372#127D4×C15111yescharacteristic
373#127C23×C15111yescharacteristic
374#126—24no—
375#125—22no—
376#124—22no—
377#124—24no—
378#124—21no—
379#124—21no—
380#123—24no—
381C22⋊Q8—22no—
382C22⋊Q8—22no—
383C22⋊Q8—22no—
384C22⋊Q8—24no—
385#121—22no—
386#121—24no—
387#121—22no—
388#121—22no—
389#121—21no—
390#121—21no—
391#121—21no—
392#121D4×C15112yes—
393C4×Q8—22no—
394C4×Q8—22no—
395C4×Q8D4×C15111yescharacteristic
396C4×Q8C23×C15111yescharacteristic
397C4×D4—22no—
398C4×D4—24no—
399C4×D4—22no—
400C4×D4—21no—
401C4×D4—21no—
402C4×D4—21no—
403C4×D4—21no—
404C4×D4—21no—
405C4×D4D4×C15111yescharacteristic
406C4×D4C23×C15111yescharacteristic
407C4×D4C23×C15112yes—
408#117—22no—
409#117—22no—
410#117—21no—
411#117D4×C15111yescharacteristic
412C2×C4⋊C4—21no—
413C2×C4⋊C4—21no—
414C2×C4⋊C4—22no—
415C2×C42—21no—
416C2×C42C23×C15111yescharacteristic
417#107—21no—
418#106—21no—
419#106—22no—
420C4⋊C8—21no—
421C4⋊C8C23×C15111yescharacteristic
422C4⋊C8C23×C15111yescharacteristic
423C4⋊C8C23×C15112yes—
424#103—21no—
425#102—21no—
426#102—22no—
427#102—21no—
428#102—21no—
429#102—22no—
430C22⋊C8—21no—
431#97—21no—
432C4×C8—21no—
433C4×C8C23×C15112yes—
434#41—41no—
435#41—41no—
436#41—42no—
437#41—42no—
438#41—44no—
439#41—84no—
440C2×Q8—21no—
441C2×Q8—22no—
442C2×Q8—21no—
443C2×Q8—44no—
444C2×Q8C2×D4×C15111yescharacteristic
445C2×Q8C2×D4×C15114yes—
446C2×D4—21no—
447C2×D4—22no—
448C2×D4—24no—
449C2×D4—21no—
450C2×D4—21no—
451C2×D4—21no—
452C2×D4—21no—
453C2×D4—21no—
454C2×D4—41no—
455C2×D4C2×D4×C15112yes—
456C2×D4C2×D4×C15111yescharacteristic
457C22×C4—24no—
458C22×C4—22no—
459C22×C4—21no—
460C22×C4—21no—
461C22×C4—21no—
462C22×C4—22no—
463C22×C4—41no—
464C22×C4C2×D4×C15111yescharacteristic
465C22×C4C2×D4×C15111yescharacteristic
466C22×C4C2×D4×C15111yescharacteristic
467Q16—48no—
468SD16—48no—
469SD16—42no—
470D8—42no—
471D8—82no—
472M16—24no—
473M16—81no—
474C2×C8—22no—
475C2×C8—21no—
476C2×C8—21no—
477C2×C8—22no—
478C4⋊C4—24no—
479C4⋊C4—24no—
480C4⋊C4—22no—
481C4⋊C4—22no—
482C4⋊C4—21no—
483C4⋊C4—21no—
484C4⋊C4—22no—
485C4⋊C4—22no—
486C4⋊C4—21no—
487C4⋊C4—21no—
488C4⋊C4—21no—
489C4⋊C4C2×D4×C15111yescharacteristic
490C4⋊C4C2×D4×C15112yes—
491C4⋊C4C2×D4×C15111yescharacteristic
492C22⋊C4—24no—
493C22⋊C4—24no—
494C22⋊C4—24no—
495C22⋊C4—21no—
496C22⋊C4—21no—
497C22⋊C4—22no—
498C22⋊C4—21no—
499C22⋊C4—22no—
500C22⋊C4—41no—
501C22⋊C4—41no—
502C42—24no—
503C42—21no—
504C42—21no—
505C42—21no—
506C42C2×D4×C15111yescharacteristic
507C42C2×D4×C15111yescharacteristic
508C42C2×D4×C15111yescharacteristic
509C42C24×C15111yescharacteristic
510C23—21no—
511C23—22no—
512C23—41no—
513C23#120×C15111yescharacteristic
514Q8—21no—
515Q8—21no—
516Q8—44no—
517Q8—42no—
518Q8—42no—
519Q8—44no—
520D4—21no—
521D4—21no—
522D4—22no—
523D4—22no—
524D4—42no—
525D4—42no—
526D4—42no—
527D4—44no—
528D4—42no—
529D4—41no—
530D4—41no—
531D4—41no—
532D4—41no—
533D4—84no—
534D4—82no—
535C2×C4—22no—
536C2×C4—21no—
537C2×C4—21no—
538C2×C4—21no—
539C2×C4—21no—
540C2×C4—21no—
541C2×C4—21no—
542C2×C4—22no—
543C2×C4—21no—
544C2×C4—24no—
545C2×C4—42no—
546C2×C4—42no—
547C2×C4—42no—
548C2×C4—42no—
549C2×C4—41no—
550C2×C4—41no—
551C2×C4—41no—
552C2×C4—82no—
553C2×C4—84no—
554C2×C4—82no—
555C2×C4#120×C15111yescharacteristic
556C2×C4#120×C15111yescharacteristic
557C2×C4#120×C15111yescharacteristic
558C2×C4C22×D4×C15111yescharacteristic
559C2×C4C22×D4×C15111yescharacteristic
560C2×C4C22×D4×C15111yescharacteristic
561C8—24no—
562C8—41no—
563C8—41no—
564C8—42no—
565C22—21no—
566C22—21no—
567C22—21no—
568C22—41no—
569C22—42no—
570C22—41no—
571C22—42no—
572C22—41no—
573C22—42no—
574C22—81no—
575C22—81no—
576C22—81no—
577C22C2×#120×C15111yescharacteristic
578C4—21no—
579C4—21no—
580C4—21no—
581C4—41no—
582C4—42no—
583C4—41no—
584C4—41no—
585C4—44no—
586C4—81no—
587C4#453×C15112yes—
588C4#575×C15111yescharacteristic
589C4#575×C15111yescharacteristic
590C4#577×C15111yescharacteristic
591C4#578×C15111yescharacteristic
592C2—41no—
593C2—81no—
594C2—82no—
595C2—161no—
596C2#3005×C15111yescharacteristic
597C2#3013×C15111yescharacteristic
598C2C2×#453×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. #3253×C151C2semidirect
3. #3152×C151C2semidirect
4. #3106×C151C2semidirect
5. #1634×C151C2semidirect
6. #1632×C151C2semidirect
7. #1624×C151C2semidirect
8. #1622×C151C2semidirect
9. #1548×C151C2semidirect
10. #1489×C151C2semidirect
11. #1484×C151C2semidirect
299. #18569C151direct (N × H)
300. C151#18569direct (N × H)
301. #3511C2×C151semidirect
302. #3253C2×C151semidirect
303. #3152C2×C151semidirect
304. #3106C2×C151semidirect
305. #1634C2×C151semidirect
306. #1632C2×C151semidirect
307. #1624C2×C151semidirect
308. #1622C2×C151semidirect
309. #1548C2×C151semidirect
310. #1489C2×C151semidirect
311. #1484C2×C151semidirect

Maximal subgroups

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

subgroupindex
#3511×C1512
#3253×C1512
#3152×C1512
#3106×C1512
#1634×C1512
#1632×C1512
#1624×C1512
#1622×C1512
#1548×C1512
#1489×C1512
#1484×C1512
#18569151