Finite Group Databasebeta

← C151×#18585 #50323510

Subgroups — C151×#18585 #50323510

Order 38656.

938 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#3141×C151C211yesmaximal, characteristic, complemented
4#3106×C151C211yesmaximal, characteristic, complemented
5#1638×C151C212yesmaximal, complemented
6#1635×C151C212yesmaximal, complemented
7#1628×C151C212yesmaximal, complemented
8#1625×C151C212yesmaximal, complemented
9#1546×C151C211yesmaximal, characteristic, complemented
10#1489×C151C211yesmaximal, characteristic, complemented
11#1484×C151C211yesmaximal, characteristic, complemented
12#556×C151C2212yes—
13#555×C151—21no—
14#554×C151—21no—
15#553×C151—22no—
16#548×C151—22no—
17#547×C151C2212yes—
18#542×C151—22no—
19#537×C151—21no—
20#533×C151—21no—
21#532×C151—21no—
22#532×C151C2211yescharacteristic
23#532×C151C2211yescharacteristic
24C2×C4⋊Q8×C151C2211yescharacteristic
25#520×C151—21no—
26C4×#41×C151C2211yescharacteristic
27#489×C151—22no—
28#487×C151C2212yes—
29#486×C151C2212yes—
30#482×C151—21no—
31#477×C151C2211yescharacteristic
32#476×C151—21no—
33#476×C151C2211yescharacteristic
34#476×C151C2212yes—
35#469×C151—22no—
36#460×C151C2211yescharacteristic
37#459×C151—21no—
38#459×C151C2211yescharacteristic
39#459×C151C2212yes—
40#449×C151—21no—
41C4×SD16×C151—21no—
42C4×D8×C151—21no—
43#431×C151C2211yescharacteristic
44#423×C151C2211yescharacteristic
45#417×C151—22no—
46C4×M16×C151C2211yescharacteristic
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—
58C2×SD16×C151—21no—
59C2×D8×C151—21no—
60C2×D8×C151—22no—
61C2×M16×C151—21no—
62C2×M16×C151—21no—
63C4⋊Q8×C151—21no—
64C4⋊Q8×C151—21no—
65C4⋊Q8×C151D411yescharacteristic
66C4⋊Q8×C151D412yes—
67C4⋊Q8×C151C2311yescharacteristic
68C4⋊Q8×C151C2312yes—
69#127×C151D411yescharacteristic
70#127×C151C2311yescharacteristic
71#126×C151—24no—
72#125×C151—22no—
73#124×C151—24no—
74#124×C151—22no—
75#124×C151—21no—
76#124×C151—21no—
77#123×C151—24no—
78C22⋊Q8×C151—22no—
79C22⋊Q8×C151—24no—
80C22⋊Q8×C151—22no—
81C22⋊Q8×C151—22no—
82#121×C151—22no—
83#121×C151—22no—
84#121×C151—24no—
85#121×C151—22no—
86#121×C151—21no—
87#121×C151—21no—
88#121×C151—21no—
89#121×C151D412yes—
90C4×Q8×C151—22no—
91C4×Q8×C151—22no—
92C4×Q8×C151D411yescharacteristic
93C4×Q8×C151C2311yescharacteristic
94C4×D4×C151—22no—
95C4×D4×C151—24no—
96C4×D4×C151—22no—
97C4×D4×C151—21no—
98C4×D4×C151—21no—
99C4×D4×C151—21no—
100C4×D4×C151—21no—
101C4×D4×C151—21no—
102C4×D4×C151D411yescharacteristic
103C4×D4×C151C2311yescharacteristic
104C4×D4×C151C2312yes—
105#117×C151—22no—
106#117×C151—22no—
107#117×C151—21no—
108#117×C151D411yescharacteristic
109C2×C4⋊C4×C151—21no—
110C2×C4⋊C4×C151—22no—
111C2×C4⋊C4×C151D412yes—
112C2×C42×C151—21no—
113C2×C42×C151C2311yescharacteristic
114#107×C151—21no—
115#106×C151—21no—
116#106×C151—22no—
117C4⋊C8×C151—21no—
118C4⋊C8×C151C2312yes—
119C4⋊C8×C151C2311yescharacteristic
120C4⋊C8×C151C2311yescharacteristic
121#103×C151—24no—
122#103×C151—21no—
123#102×C151—21no—
124#102×C151—22no—
125#102×C151—24no—
126#102×C151—21no—
127#102×C151—21no—
128#102×C151—22no—
129C22⋊C8×C151—21no—
130#97×C151—21no—
131C4×C8×C151—21no—
132C4×C8×C151C2312yes—
133#41×C151—41no—
134#41×C151—41no—
135#41×C151—42no—
136#41×C151—42no—
137#41×C151—44no—
138#41×C151—82no—
139#41×C151—82no—
140C2×Q8×C151—21no—
141C2×Q8×C151—22no—
142C2×Q8×C151—22no—
143C2×Q8×C151—21no—
144C2×Q8×C151—81no—
145C2×Q8×C151—81no—
146C2×Q8×C151C2×D411yescharacteristic
147C2×D4×C151—21no—
148C2×D4×C151—22no—
149C2×D4×C151—24no—
150C2×D4×C151—21no—
151C2×D4×C151—21no—
152C2×D4×C151—21no—
153C2×D4×C151—21no—
154C2×D4×C151—21no—
155C2×D4×C151—41no—
156C2×D4×C151C2×D411yescharacteristic
157C2×D4×C151C2×D412yes—
158C22×C4×C151—24no—
159C22×C4×C151—22no—
160C22×C4×C151—21no—
161C22×C4×C151—21no—
162C22×C4×C151—21no—
163C22×C4×C151—22no—
164C22×C4×C151—41no—
165C22×C4×C151C2×D411yescharacteristic
166C22×C4×C151C2×D411yescharacteristic
167C22×C4×C151C2×D411yescharacteristic
168SD16×C151—42no—
169D8×C151—42no—
170D8×C151—82no—
171M16×C151—42no—
172M16×C151—81no—
173C2×C8×C151—21no—
174C2×C8×C151—21no—
175C2×C8×C151—22no—
176C2×C8×C151—22no—
177C4⋊C4×C151—24no—
178C4⋊C4×C151—24no—
179C4⋊C4×C151—22no—
180C4⋊C4×C151—22no—
181C4⋊C4×C151—21no—
182C4⋊C4×C151—21no—
183C4⋊C4×C151—22no—
184C4⋊C4×C151—21no—
185C4⋊C4×C151—21no—
186C4⋊C4×C151—21no—
187C4⋊C4×C151C2×D414yes—
188C4⋊C4×C151C2×D411yescharacteristic
189C4⋊C4×C151C2×D412yes—
190C4⋊C4×C151C2×D411yescharacteristic
191C22⋊C4×C151—24no—
192C22⋊C4×C151—24no—
193C22⋊C4×C151—24no—
194C22⋊C4×C151—21no—
195C22⋊C4×C151—21no—
196C22⋊C4×C151—22no—
197C22⋊C4×C151—21no—
198C22⋊C4×C151—22no—
199C22⋊C4×C151—41no—
200C22⋊C4×C151—41no—
201C42×C151—24no—
202C42×C151—21no—
203C42×C151—21no—
204C42×C151—21no—
205C42×C151C2×D411yescharacteristic
206C42×C151C2×D411yescharacteristic
207C42×C151C2×D411yescharacteristic
208C42×C151C2411yescharacteristic
209C23×C151—21no—
210C23×C151—22no—
211C23×C151—41no—
212C23×C151#12011yescharacteristic
213Q8×C151—21no—
214Q8×C151—21no—
215Q8×C151—42no—
216Q8×C151—42no—
217Q8×C151—42no—
218Q8×C151—42no—
219Q8×C151—82no—
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—42no—
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—44no—
285C4×C151—41no—
286C4×C151—81no—
287C4×C151#45412yes—
288C4×C151#57511yescharacteristic
289C4×C151#57511yescharacteristic
290C4×C151#57611yescharacteristic
291C4×C151#57711yescharacteristic
292C2×C151—41no—
293C2×C151—81no—
294C2×C151—82no—
295C2×C151—161no—
296C2×C151#300511yescharacteristic
297C2×C151#301211yescharacteristic
298C2×C151C2×#45411yescharacteristic
299#18585C15111yesmaximal, characteristic, direct product factor, Sylow
300C151#1858511yescharacteristic, direct product factor, Sylow
301#3511C2×C15111yescharacteristic, complemented
302#3253C2×C15111yescharacteristic, complemented
303#3141C2×C15111yescharacteristic, complemented
304#3106C2×C15111yescharacteristic, complemented
305#1638C2×C15112yescomplemented
306#1635C2×C15112yescomplemented
307#1628C2×C15112yescomplemented
308#1625C2×C15112yescomplemented
309#1546C2×C15111yescharacteristic, complemented
310#1489C2×C15111yescharacteristic, complemented
311#1484C2×C15111yescharacteristic, complemented
312#556C22×C15112yes—
313#555—21no—
314#554—21no—
315#553—22no—
316#548—22no—
317#547C22×C15112yes—
318#542—22no—
319#537—21no—
320#533—21no—
321#532—21no—
322#532C22×C15111yescharacteristic
323#532C22×C15111yescharacteristic
324C2×C4⋊Q8C22×C15111yescharacteristic
325#520—21no—
326C4×#41C22×C15111yescharacteristic
327#489—22no—
328#487C22×C15112yes—
329#486C22×C15112yes—
330#482—21no—
331#477C22×C15111yescharacteristic
332#476—21no—
333#476C22×C15111yescharacteristic
334#476C22×C15112yes—
335#469—22no—
336#460C22×C15111yescharacteristic
337#459—21no—
338#459C22×C15111yescharacteristic
339#459C22×C15112yes—
340#449—21no—
341C4×SD16—21no—
342C4×D8—21no—
343#431C22×C15111yescharacteristic
344#423C22×C15111yescharacteristic
345#417—22no—
346C4×M16C22×C15111yescharacteristic
347#332C22×C15112yes—
348#332C22×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×Q8—21no—
358C2×SD16—21no—
359C2×D8—21no—
360C2×D8—22no—
361C2×M16—21no—
362C2×M16—21no—
363C4⋊Q8—21no—
364C4⋊Q8—21no—
365C4⋊Q8D4×C15112yes—
366C4⋊Q8D4×C15111yescharacteristic
367C4⋊Q8C23×C15111yescharacteristic
368C4⋊Q8C23×C15112yes—
369#127D4×C15111yescharacteristic
370#127C23×C15111yescharacteristic
371#126—24no—
372#125—22no—
373#124—24no—
374#124—22no—
375#124—21no—
376#124—21no—
377#123—24no—
378C22⋊Q8—22no—
379C22⋊Q8—24no—
380C22⋊Q8—22no—
381C22⋊Q8—22no—
382#121—22no—
383#121—22no—
384#121—24no—
385#121—22no—
386#121—21no—
387#121—21no—
388#121—21no—
389#121D4×C15112yes—
390C4×Q8—22no—
391C4×Q8—22no—
392C4×Q8D4×C15111yescharacteristic
393C4×Q8C23×C15111yescharacteristic
394C4×D4—22no—
395C4×D4—24no—
396C4×D4—22no—
397C4×D4—21no—
398C4×D4—21no—
399C4×D4—21no—
400C4×D4—21no—
401C4×D4—21no—
402C4×D4D4×C15111yescharacteristic
403C4×D4C23×C15111yescharacteristic
404C4×D4C23×C15112yes—
405#117—22no—
406#117—22no—
407#117—21no—
408#117D4×C15111yescharacteristic
409C2×C4⋊C4—21no—
410C2×C4⋊C4—22no—
411C2×C4⋊C4D4×C15112yes—
412C2×C42—21no—
413C2×C42C23×C15111yescharacteristic
414#107—21no—
415#106—21no—
416#106—22no—
417C4⋊C8—21no—
418C4⋊C8C23×C15111yescharacteristic
419C4⋊C8C23×C15111yescharacteristic
420C4⋊C8C23×C15112yes—
421#103—21no—
422#103—24no—
423#102—21no—
424#102—22no—
425#102—24no—
426#102—21no—
427#102—21no—
428#102—22no—
429C22⋊C8—21no—
430#97—21no—
431C4×C8—21no—
432C4×C8C23×C15112yes—
433#41—41no—
434#41—41no—
435#41—42no—
436#41—42no—
437#41—44no—
438#41—82no—
439#41—82no—
440C2×Q8—21no—
441C2×Q8—22no—
442C2×Q8—22no—
443C2×Q8—21no—
444C2×Q8—81no—
445C2×Q8—81no—
446C2×Q8C2×D4×C15111yescharacteristic
447C2×D4—21no—
448C2×D4—22no—
449C2×D4—24no—
450C2×D4—21no—
451C2×D4—21no—
452C2×D4—21no—
453C2×D4—21no—
454C2×D4—21no—
455C2×D4—41no—
456C2×D4C2×D4×C15111yescharacteristic
457C2×D4C2×D4×C15112yes—
458C22×C4—24no—
459C22×C4—22no—
460C22×C4—21no—
461C22×C4—21no—
462C22×C4—21no—
463C22×C4—22no—
464C22×C4—41no—
465C22×C4C2×D4×C15111yescharacteristic
466C22×C4C2×D4×C15111yescharacteristic
467C22×C4C2×D4×C15111yescharacteristic
468SD16—42no—
469D8—42no—
470D8—82no—
471M16—42no—
472M16—81no—
473C2×C8—21no—
474C2×C8—21no—
475C2×C8—22no—
476C2×C8—22no—
477C4⋊C4—24no—
478C4⋊C4—24no—
479C4⋊C4—22no—
480C4⋊C4—22no—
481C4⋊C4—21no—
482C4⋊C4—21no—
483C4⋊C4—22no—
484C4⋊C4—21no—
485C4⋊C4—21no—
486C4⋊C4—21no—
487C4⋊C4C2×D4×C15114yes—
488C4⋊C4C2×D4×C15111yescharacteristic
489C4⋊C4C2×D4×C15112yes—
490C4⋊C4C2×D4×C15111yescharacteristic
491C22⋊C4—24no—
492C22⋊C4—24no—
493C22⋊C4—24no—
494C22⋊C4—21no—
495C22⋊C4—21no—
496C22⋊C4—22no—
497C22⋊C4—21no—
498C22⋊C4—22no—
499C22⋊C4—41no—
500C22⋊C4—41no—
501C42—24no—
502C42—21no—
503C42—21no—
504C42—21no—
505C42C2×D4×C15111yescharacteristic
506C42C2×D4×C15111yescharacteristic
507C42C2×D4×C15111yescharacteristic
508C42C24×C15111yescharacteristic
509C23—21no—
510C23—22no—
511C23—41no—
512C23#120×C15111yescharacteristic
513Q8—21no—
514Q8—21no—
515Q8—42no—
516Q8—42no—
517Q8—42no—
518Q8—42no—
519Q8—82no—
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—42no—
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—44no—
585C4—41no—
586C4—81no—
587C4#454×C15112yes—
588C4#575×C15111yescharacteristic
589C4#575×C15111yescharacteristic
590C4#576×C15111yescharacteristic
591C4#577×C15111yescharacteristic
592C2—41no—
593C2—81no—
594C2—82no—
595C2—161no—
596C2#3005×C15111yescharacteristic
597C2#3012×C15111yescharacteristic
598C2C2×#454×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. #3141×C151C2semidirect
4. #3106×C151C2semidirect
5. #1638×C151C2semidirect
6. #1635×C151C2semidirect
7. #1628×C151C2semidirect
8. #1625×C151C2semidirect
9. #1546×C151C2semidirect
10. #1489×C151C2semidirect
11. #1484×C151C2semidirect
299. #18585C151direct (N × H)
300. C151#18585direct (N × H)
301. #3511C2×C151semidirect
302. #3253C2×C151semidirect
303. #3141C2×C151semidirect
304. #3106C2×C151semidirect
305. #1638C2×C151semidirect
306. #1635C2×C151semidirect
307. #1628C2×C151semidirect
308. #1625C2×C151semidirect
309. #1546C2×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
#3141×C1512
#3106×C1512
#1638×C1512
#1635×C1512
#1628×C1512
#1625×C1512
#1546×C1512
#1489×C1512
#1484×C1512
#18585151