Finite Group Databasebeta

← C151×#18984 #50323909

Subgroups — C151×#18984 #50323909

Order 38656.

990 conjugacy classes of subgroups.

The subgroup lattice has 602 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#3529×C151C211yesmaximal, characteristic, complemented
2#3171×C151C212yesmaximal, complemented
3#3150×C151C211yesmaximal, characteristic, complemented
4#1661×C151C212yesmaximal, complemented
5#1660×C151C211yesmaximal, characteristic, complemented
6#1659×C151C211yesmaximal, characteristic, complemented
7#1657×C151C211yesmaximal, characteristic, complemented
8#1656×C151C212yesmaximal, complemented
9#1655×C151C211yesmaximal, characteristic, complemented
10#1525×C151C211yesmaximal, characteristic, complemented
11#1524×C151C212yesmaximal, complemented
12C2×#135×C151—21no—
13C2×#135×C151—21no—
14#563×C151—21no—
15#563×C151C2211yescharacteristic
16#562×C151—22no—
17#562×C151C2212yes—
18H(3,𝔽4)×C151C2211yescharacteristic
19#560×C151—21no—
20#560×C151—22no—
21#532×C151—21no—
22#532×C151C2211yescharacteristic
23#532×C151C2211yescharacteristic, complemented
24#529×C151—22no—
25#529×C151C2212yes—
26#525×C151—21no—
27#525×C151—22no—
28#501×C151C2212yescomplemented
29#497×C151—21no—
30#497×C151C2211yescharacteristic
31#497×C151C2211yescharacteristic, complemented
32#496×C151—21no—
33#496×C151C2211yescharacteristic
34#496×C151C2212yes—
35#496×C151C2211yescharacteristic, complemented
36#490×C151C2212yescomplemented
37#489×C151C2212yes—
38#469×C151—22no—
39#468×C151—22no—
40C4×SD16×C151—22no—
41C4×D8×C151—22no—
42C4×M16×C151C2212yescomplemented
43C2×#97×C151C2211yescharacteristic, complemented
44#330×C151C2212yescomplemented
45#330×C151C2212yescomplemented
46#329×C151C2211yescharacteristic
47#329×C151C2212yes—
48#329×C151C2212yes—
49#329×C151C2211yescharacteristic
50#329×C151C2212yescomplemented
51C2×#41×C151—21no—
52C2×#41×C151—21no—
53C2×#41×C151D411yescharacteristic
54C2×#41×C151D411yescharacteristic
55C23×C4×C151—21no—
56#135×C151—44no—
57#135×C151—44no—
58C2×Q16×C151—21no—
59C2×Q16×C151—21no—
60C2×SD16×C151—21no—
61C2×SD16×C151—21no—
62C2×SD16×C151—22no—
63C2×SD16×C151—21no—
64C2×SD16×C151—21no—
65C2×D8×C151—22no—
66C2×D8×C151—21no—
67C2×D8×C151—21no—
68C2×M16×C151—22no—
69C22×C8×C151—21no—
70C4⋊Q8×C151—21no—
71C4⋊Q8×C151D411yescharacteristic
72C4⋊Q8×C151C2311yescharacteristic
73#127×C151—21no—
74#127×C151D411yescharacteristic
75#127×C151C2311yescharacteristic
76#126×C151—22no—
77#126×C151—22no—
78#126×C151—22no—
79#125×C151—22no—
80#125×C151C2312yes—
81#124×C151—21no—
82#124×C151—21no—
83#124×C151—22no—
84#124×C151—21no—
85#124×C151C2312yes—
86#124×C151C2311yescharacteristic
87#124×C151C2311yescharacteristic
88#123×C151—22no—
89#123×C151—21no—
90#123×C151—22no—
91#123×C151—21no—
92#123×C151—22no—
93#123×C151—22no—
94#123×C151—22no—
95C22⋊Q8×C151—22no—
96C22⋊Q8×C151—22no—
97C22⋊Q8×C151—22no—
98C22⋊Q8×C151—22no—
99C22⋊Q8×C151D412yes—
100#121×C151—22no—
101#121×C151—22no—
102#121×C151—22no—
103#121×C151—22no—
104#121×C151—22no—
105#121×C151—22no—
106#121×C151—22no—
107#121×C151—22no—
108#121×C151D412yes—
109#120×C151—21no—
110#120×C151—22no—
111#120×C151—21no—
112#120×C151—22no—
113C4×Q8×C151D412yes—
114C4×D4×C151—22no—
115C4×D4×C151—22no—
116C4×D4×C151—22no—
117C4×D4×C151—22no—
118C4×D4×C151—22no—
119C4×D4×C151D412yes—
120#117×C151—21no—
121#117×C151—22no—
122C2×C42×C151—21no—
123C2×C42×C151C2311yescharacteristic
124#107×C151—22no—
125#106×C151—22no—
126#103×C151—22no—
127#102×C151—22no—
128#102×C151—22no—
129#102×C151—22no—
130#97×C151—21no—
131#97×C151C2311yescharacteristic
132#97×C151C2311yescharacteristic
133#97×C151C2312yes—
134#97×C151C2312yes—
135C4×C8×C151—22no—
136C24×C151—21no—
137#41×C151—42no—
138#41×C151—42no—
139#41×C151—42no—
140#41×C151—42no—
141#41×C151—82no—
142C2×Q8×C151—21no—
143C2×Q8×C151—21no—
144C2×Q8×C151C2×D412yes—
145C2×Q8×C151C2×D411yescharacteristic
146C2×Q8×C151C2×D411yescharacteristic
147C2×D4×C151—22no—
148C2×D4×C151—22no—
149C2×D4×C151—21no—
150C2×D4×C151—22no—
151C2×D4×C151—22no—
152C2×D4×C151—21no—
153C2×D4×C151—21no—
154C2×D4×C151—22no—
155C2×D4×C151—22no—
156C2×D4×C151—21no—
157C2×D4×C151—41no—
158C2×D4×C151C2×D412yes—
159C2×D4×C151C2×D411yescharacteristic
160C2×D4×C151C2×D411yescharacteristic
161C22×C4×C151—22no—
162C22×C4×C151—21no—
163C22×C4×C151—22no—
164C22×C4×C151—21no—
165C22×C4×C151—21no—
166C22×C4×C151—22no—
167C22×C4×C151—41no—
168C22×C4×C151—82no—
169C22×C4×C151C2×D411yescharacteristic
170C22×C4×C151C2×D412yes—
171Q16×C151—42no—
172Q16×C151—42no—
173SD16×C151—44no—
174SD16×C151—42no—
175SD16×C151—42no—
176SD16×C151—42no—
177SD16×C151—42no—
178D8×C151—44no—
179D8×C151—42no—
180D8×C151—42no—
181M16×C151—44no—
182C2×C8×C151—24no—
183C2×C8×C151—22no—
184C2×C8×C151—21no—
185C2×C8×C151—21no—
186C2×C8×C151—22no—
187C4⋊C4×C151—22no—
188C4⋊C4×C151—22no—
189C4⋊C4×C151—22no—
190C4⋊C4×C151—22no—
191C4⋊C4×C151—22no—
192C4⋊C4×C151—22no—
193C4⋊C4×C151—22no—
194C4⋊C4×C151—22no—
195C4⋊C4×C151—22no—
196C4⋊C4×C151C2×D412yes—
197C4⋊C4×C151C2×D412yes—
198C22⋊C4×C151—21no—
199C22⋊C4×C151—21no—
200C22⋊C4×C151—22no—
201C22⋊C4×C151—22no—
202C22⋊C4×C151—22no—
203C22⋊C4×C151—22no—
204C22⋊C4×C151—22no—
205C22⋊C4×C151—22no—
206C22⋊C4×C151—22no—
207C22⋊C4×C151—22no—
208C22⋊C4×C151—22no—
209C22⋊C4×C151—22no—
210C22⋊C4×C151—22no—
211C22⋊C4×C151—42no—
212C42×C151—21no—
213C42×C151—21no—
214C42×C151—22no—
215C42×C151C2×D411yescharacteristic
216C42×C151C2×D412yes—
217C42×C151C2411yescharacteristic
218C23×C151—21no—
219C23×C151—22no—
220C23×C151—21no—
221C23×C151—41no—
222C23×C151—82no—
223C23×C151—81no—
224C23×C151#12011yescharacteristic
225Q8×C151—41no—
226Q8×C151—41no—
227Q8×C151—42no—
228Q8×C151—41no—
229Q8×C151—41no—
230Q8×C151—81no—
231D4×C151—41no—
232D4×C151—41no—
233D4×C151—42no—
234D4×C151—41no—
235D4×C151—41no—
236D4×C151—42no—
237D4×C151—42no—
238D4×C151—82no—
239D4×C151—81no—
240D4×C151—81no—
241D4×C151—82no—
242D4×C151—82no—
243D4×C151—81no—
244D4×C151—82no—
245D4×C151—82no—
246D4×C151—82no—
247C2×C4×C151—22no—
248C2×C4×C151—21no—
249C2×C4×C151—22no—
250C2×C4×C151—22no—
251C2×C4×C151—21no—
252C2×C4×C151—22no—
253C2×C4×C151—42no—
254C2×C4×C151—42no—
255C2×C4×C151—42no—
256C2×C4×C151—44no—
257C2×C4×C151—41no—
258C2×C4×C151—82no—
259C2×C4×C151—82no—
260C2×C4×C151—81no—
261C2×C4×C151—82no—
262C2×C4×C151#12012yes—
263C2×C4×C151#12011yescharacteristic
264C2×C4×C151C22×D411yescharacteristic
265C2×C4×C151C22×D412yes—
266C8×C151—22no—
267C8×C151—22no—
268C8×C151—24no—
269C8×C151—42no—
270C22×C151—21no—
271C22×C151—22no—
272C22×C151—41no—
273C22×C151—42no—
274C22×C151—41no—
275C22×C151—42no—
276C22×C151—42no—
277C22×C151—42no—
278C22×C151—42no—
279C22×C151—84no—
280C22×C151—81no—
281C22×C151—82no—
282C22×C151C2×#12011yescharacteristic
283C4×C151—21no—
284C4×C151—22no—
285C4×C151—22no—
286C4×C151—41no—
287C4×C151—42no—
288C4×C151—41no—
289C4×C151—42no—
290C4×C151—42no—
291C4×C151—81no—
292C4×C151#45312yes—
293C2×C151—41no—
294C2×C151—81no—
295C2×C151—81no—
296C2×C151—82no—
297C2×C151—161no—
298C2×C151C2×#45311yescharacteristic
299C2×C151#301812yes—
300#18984C15111yesmaximal, characteristic, direct product factor, Sylow
301C151#1898411yescharacteristic, direct product factor, Sylow
302#3529C2×C15111yescharacteristic, complemented
303#3171C2×C15112yescomplemented
304#3150C2×C15111yescharacteristic, complemented
305#1661C2×C15112yescomplemented
306#1660C2×C15111yescharacteristic, complemented
307#1659C2×C15111yescharacteristic, complemented
308#1657C2×C15111yescharacteristic, complemented
309#1656C2×C15112yescomplemented
310#1655C2×C15111yescharacteristic, complemented
311#1525C2×C15111yescharacteristic, complemented
312#1524C2×C15112yescomplemented
313C2×#135—21no—
314C2×#135—21no—
315#563—21no—
316#563C22×C15111yescharacteristic
317#562—22no—
318#562C22×C15112yes—
319H(3,𝔽4)C22×C15111yescharacteristic
320#560—21no—
321#560—22no—
322#532—21no—
323#532C22×C15111yescharacteristic
324#532C22×C15111yescharacteristic, complemented
325#529—22no—
326#529C22×C15112yes—
327#525—21no—
328#525—22no—
329#501C22×C15112yescomplemented
330#497—21no—
331#497C22×C15111yescharacteristic
332#497C22×C15111yescharacteristic, complemented
333#496—21no—
334#496C22×C15111yescharacteristic
335#496C22×C15112yes—
336#496C22×C15111yescharacteristic, complemented
337#490C22×C15112yescomplemented
338#489C22×C15112yes—
339#469—22no—
340#468—22no—
341C4×SD16—22no—
342C4×D8—22no—
343C4×M16C22×C15112yescomplemented
344C2×#97C22×C15111yescharacteristic, complemented
345#330C22×C15112yescomplemented
346#330C22×C15112yescomplemented
347#329C22×C15111yescharacteristic
348#329C22×C15112yes—
349#329C22×C15112yes—
350#329C22×C15111yescharacteristic
351#329C22×C15112yescomplemented
352C2×#41—21no—
353C2×#41—21no—
354C2×#41D4×C15111yescharacteristic
355C2×#41D4×C15111yescharacteristic
356C23×C4—21no—
357#135—44no—
358#135—44no—
359C2×Q16—21no—
360C2×Q16—21no—
361C2×SD16—21no—
362C2×SD16—21no—
363C2×SD16—22no—
364C2×SD16—21no—
365C2×SD16—21no—
366C2×D8—21no—
367C2×D8—21no—
368C2×D8—22no—
369C2×M16—22no—
370C22×C8—21no—
371C4⋊Q8—21no—
372C4⋊Q8D4×C15111yescharacteristic
373C4⋊Q8C23×C15111yescharacteristic
374#127—21no—
375#127D4×C15111yescharacteristic
376#127C23×C15111yescharacteristic
377#126—22no—
378#126—22no—
379#126—22no—
380#125—22no—
381#125C23×C15112yes—
382#124—21no—
383#124—22no—
384#124—21no—
385#124—21no—
386#124C23×C15112yes—
387#124C23×C15111yescharacteristic
388#124C23×C15111yescharacteristic
389#123—22no—
390#123—21no—
391#123—22no—
392#123—21no—
393#123—22no—
394#123—22no—
395#123—22no—
396C22⋊Q8—22no—
397C22⋊Q8—22no—
398C22⋊Q8—22no—
399C22⋊Q8—22no—
400C22⋊Q8D4×C15112yes—
401#121—22no—
402#121—22no—
403#121—22no—
404#121—22no—
405#121—22no—
406#121—22no—
407#121—22no—
408#121—22no—
409#121D4×C15112yes—
410#120—21no—
411#120—22no—
412#120—21no—
413#120—22no—
414C4×Q8D4×C15112yes—
415C4×D4—22no—
416C4×D4—22no—
417C4×D4—22no—
418C4×D4—22no—
419C4×D4—22no—
420C4×D4D4×C15112yes—
421#117—21no—
422#117—22no—
423C2×C42—21no—
424C2×C42C23×C15111yescharacteristic
425#107—22no—
426#106—22no—
427#103—22no—
428#102—22no—
429#102—22no—
430#102—22no—
431#97—21no—
432#97C23×C15112yes—
433#97C23×C15112yes—
434#97C23×C15111yescharacteristic
435#97C23×C15111yescharacteristic
436C4×C8—22no—
437C24—21no—
438#41—42no—
439#41—42no—
440#41—42no—
441#41—42no—
442#41—82no—
443C2×Q8—21no—
444C2×Q8—21no—
445C2×Q8C2×D4×C15112yes—
446C2×Q8C2×D4×C15111yescharacteristic
447C2×Q8C2×D4×C15111yescharacteristic
448C2×D4—22no—
449C2×D4—22no—
450C2×D4—21no—
451C2×D4—22no—
452C2×D4—22no—
453C2×D4—21no—
454C2×D4—21no—
455C2×D4—22no—
456C2×D4—22no—
457C2×D4—21no—
458C2×D4—41no—
459C2×D4C2×D4×C15112yes—
460C2×D4C2×D4×C15111yescharacteristic
461C2×D4C2×D4×C15111yescharacteristic
462C22×C4—22no—
463C22×C4—22no—
464C22×C4—21no—
465C22×C4—21no—
466C22×C4—21no—
467C22×C4—22no—
468C22×C4—41no—
469C22×C4—82no—
470C22×C4C2×D4×C15111yescharacteristic
471C22×C4C2×D4×C15112yes—
472Q16—42no—
473Q16—42no—
474SD16—42no—
475SD16—42no—
476SD16—42no—
477SD16—42no—
478SD16—44no—
479D8—42no—
480D8—42no—
481D8—44no—
482M16—44no—
483C2×C8—24no—
484C2×C8—22no—
485C2×C8—21no—
486C2×C8—21no—
487C2×C8—22no—
488C4⋊C4—22no—
489C4⋊C4—22no—
490C4⋊C4—22no—
491C4⋊C4—22no—
492C4⋊C4—22no—
493C4⋊C4—22no—
494C4⋊C4—22no—
495C4⋊C4—22no—
496C4⋊C4—22no—
497C4⋊C4C2×D4×C15112yes—
498C4⋊C4C2×D4×C15112yes—
499C22⋊C4—21no—
500C22⋊C4—21no—
501C22⋊C4—22no—
502C22⋊C4—22no—
503C22⋊C4—22no—
504C22⋊C4—22no—
505C22⋊C4—22no—
506C22⋊C4—22no—
507C22⋊C4—22no—
508C22⋊C4—22no—
509C22⋊C4—22no—
510C22⋊C4—22no—
511C22⋊C4—22no—
512C22⋊C4—42no—
513C42—21no—
514C42—21no—
515C42—22no—
516C42C2×D4×C15112yes—
517C42C2×D4×C15111yescharacteristic
518C42C24×C15111yescharacteristic
519C23—21no—
520C23—22no—
521C23—21no—
522C23—41no—
523C23—81no—
524C23—82no—
525C23#120×C15111yescharacteristic
526Q8—41no—
527Q8—41no—
528Q8—42no—
529Q8—41no—
530Q8—41no—
531Q8—81no—
532D4—41no—
533D4—41no—
534D4—42no—
535D4—41no—
536D4—41no—
537D4—42no—
538D4—42no—
539D4—82no—
540D4—81no—
541D4—81no—
542D4—82no—
543D4—82no—
544D4—81no—
545D4—82no—
546D4—82no—
547D4—82no—
548C2×C4—22no—
549C2×C4—22no—
550C2×C4—22no—
551C2×C4—21no—
552C2×C4—21no—
553C2×C4—22no—
554C2×C4—42no—
555C2×C4—42no—
556C2×C4—44no—
557C2×C4—42no—
558C2×C4—41no—
559C2×C4—82no—
560C2×C4—81no—
561C2×C4—82no—
562C2×C4—82no—
563C2×C4#120×C15112yes—
564C2×C4#120×C15111yescharacteristic
565C2×C4C22×D4×C15112yes—
566C2×C4C22×D4×C15111yescharacteristic
567C8—22no—
568C8—22no—
569C8—24no—
570C8—42no—
571C22—21no—
572C22—22no—
573C22—41no—
574C22—42no—
575C22—41no—
576C22—42no—
577C22—42no—
578C22—42no—
579C22—42no—
580C22—84no—
581C22—81no—
582C22—82no—
583C22C2×#120×C15111yescharacteristic
584C4—21no—
585C4—22no—
586C4—22no—
587C4—41no—
588C4—42no—
589C4—41no—
590C4—42no—
591C4—42no—
592C4—81no—
593C4#453×C15112yes—
594C2—41no—
595C2—81no—
596C2—82no—
597C2—81no—
598C2—161no—
599C2C2×#453×C15111yescharacteristic
600C2#3018×C15112yes—
subgroupG/H
centerC2×C4×C151#120
commutator, Frattini, cosocleC42C24×C151
socleC22×C151C2×#120
LCSG ▷ C42 ▷ C22 ▷ C1
UCSC1 ◁ C2×C4×C151 ◁ C2×C42×C151 ◁ G

Complements

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

NH ≅ G/Ntype
1. #3529×C151C2semidirect
2. #3171×C151C2semidirect
3. #3150×C151C2semidirect
4. #1661×C151C2semidirect
5. #1660×C151C2semidirect
6. #1659×C151C2semidirect
7. #1657×C151C2semidirect
8. #1656×C151C2semidirect
9. #1655×C151C2semidirect
10. #1525×C151C2semidirect
11. #1524×C151C2semidirect
23. #532×C151C22semidirect
28. #501×C151C22semidirect
31. #497×C151C22semidirect
35. #496×C151C22semidirect
36. #490×C151C22semidirect
42. C4×M16×C151C22semidirect
43. C2×#97×C151C22semidirect
44. #330×C151C22semidirect
45. #330×C151C22semidirect
50. #329×C151C22semidirect
300. #18984C151direct (N × H)
301. C151#18984direct (N × H)
302. #3529C2×C151semidirect
303. #3171C2×C151semidirect
304. #3150C2×C151semidirect
305. #1661C2×C151semidirect
306. #1660C2×C151semidirect
307. #1659C2×C151semidirect
308. #1657C2×C151semidirect
309. #1656C2×C151semidirect
310. #1655C2×C151semidirect
311. #1525C2×C151semidirect
312. #1524C2×C151semidirect
324. #532C22×C151semidirect
329. #501C22×C151semidirect
332. #497C22×C151semidirect
336. #496C22×C151semidirect
337. #490C22×C151semidirect
343. C4×M16C22×C151semidirect
344. C2×#97C22×C151semidirect
345. #330C22×C151semidirect
346. #330C22×C151semidirect
351. #329C22×C151semidirect

Maximal subgroups

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

subgroupindex
#3529×C1512
#3171×C1512
#3150×C1512
#1661×C1512
#1660×C1512
#1659×C1512
#1657×C1512
#1656×C1512
#1655×C1512
#1525×C1512
#1524×C1512
#18984151