Finite Group Databasebeta

← C151×#24520 #50329445

Subgroups — C151×#24520 #50329445

Order 38656.

1002 conjugacy classes of subgroups.

The subgroup lattice has 592 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#3094×C151C211yesmaximal, characteristic, complemented
2C2×#447×C151C211yesmaximal, characteristic
3#2924×C151C211yesmaximal, characteristic, complemented
4C2×#418×C151C211yesmaximal, characteristic, complemented
5#2063×C151C212yesmaximal, complemented
6#2045×C151C212yesmaximal, complemented
7#1978×C151C212yesmaximal, complemented
8#1931×C151C212yesmaximal, complemented
9#1900×C151C211yesmaximal, characteristic, complemented
10#1855×C151C211yesmaximal, characteristic, complemented
11#1783×C151C211yesmaximal, characteristic, complemented
12C23×D4×C151C2211yescharacteristic
13C22×D8×C151C2212yes—
14C22×M16×C151C2211yescharacteristic
15C2×#121×C151C2211yescharacteristic
16C2×#117×C151C2211yescharacteristic
17#482×C151—21no—
18#482×C151—21no—
19#481×C151—21no—
20#480×C151—21no—
21#447×C151—21no—
22#447×C151—21no—
23#447×C151—22no—
24#433×C151—22no—
25#432×C151—21no—
26#431×C151—21no—
27C2×#108×C151C2212yescomplemented
28#428×C151C2211yescharacteristic, complemented
29#428×C151C2211yescharacteristic, complemented
30#424×C151C2212yescomplemented
31#418×C151—21no—
32#418×C151—21no—
33#418×C151C2212yes—
34#418×C151C2212yes—
35#418×C151C2211yescharacteristic, complemented
36#418×C151C2211yescharacteristic, complemented
37C2×#102×C151—21no—
38C2×#102×C151—21no—
39C2×#102×C151C2212yes—
40C2×#100×C151C2212yes—
41C2×#100×C151C2212yes—
42C2×#100×C151C2212yescomplemented
43#407×C151C2211yescharacteristic
44#407×C151C2211yescharacteristic
45C2×C22⋊C8×C151C2211yescharacteristic
46#405×C151C2212yescomplemented
47#343×C151C2212yescomplemented
48#341×C151C2212yescomplemented
49C25×C151—21no—
50C22×D4×C151—21no—
51C22×D4×C151—21no—
52C22×D4×C151—24no—
53C22×D4×C151—21no—
54C22×D4×C151—21no—
55C22×D4×C151—21no—
56C22×D4×C151—21no—
57C22×D4×C151—42no—
58C22×D4×C151C2311yescharacteristic
59C22×D4×C151C2312yes—
60C23×C4×C151C2311yescharacteristic
61C2×D8×C151—24no—
62C2×D8×C151—22no—
63C2×D8×C151—22no—
64C2×D8×C151—42no—
65C2×M16×C151—21no—
66C2×M16×C151—42no—
67C2×M16×C151C2311yescharacteristic
68C2×M16×C151C2312yes—
69C2×M16×C151C2312yes—
70C2×M16×C151C2311yescharacteristic
71C22×C8×C151—21no—
72C22×C8×C151C2312yes—
73#121×C151—21no—
74#121×C151—21no—
75#121×C151—21no—
76#121×C151—21no—
77#117×C151—21no—
78#117×C151—21no—
79#117×C151D411yescharacteristic
80#117×C151D411yescharacteristic
81#117×C151C2311yescharacteristic
82#117×C151C2311yescharacteristic
83C2×C4⋊C4×C151D411yescharacteristic
84C2×C4⋊C4×C151D411yescharacteristic
85C2×C4⋊C4×C151C2311yescharacteristic
86C2×C22⋊C4×C151—21no—
87C2×C22⋊C4×C151—21no—
88C2×C42×C151—21no—
89#108×C151—42no—
90#107×C151—21no—
91#107×C151—21no—
92#106×C151—21no—
93#106×C151—21no—
94C4⋊C8×C151—22no—
95C4⋊C8×C151—22no—
96#102×C151—22no—
97#102×C151—22no—
98#102×C151—22no—
99#102×C151—22no—
100#102×C151—22no—
101#102×C151—22no—
102#102×C151—21no—
103#102×C151—21no—
104#102×C151—21no—
105#102×C151—21no—
106#100×C151—24no—
107#100×C151—42no—
108#100×C151—42no—
109C22⋊C8×C151—21no—
110C22⋊C8×C151—21no—
111C22⋊C8×C151—21no—
112C22⋊C8×C151—21no—
113C22⋊C8×C151D411yescharacteristic
114C22⋊C8×C151D411yescharacteristic
115C22⋊C8×C151D412yes—
116#97×C151—22no—
117C4×C8×C151—22no—
118C24×C151—22no—
119C24×C151—21no—
120C24×C151—44no—
121C24×C151—41no—
122C24×C151—41no—
123C24×C151—82no—
124C24×C151—82no—
125C24×C151#4111yescharacteristic
126C2×D4×C151—24no—
127C2×D4×C151—24no—
128C2×D4×C151—22no—
129C2×D4×C151—22no—
130C2×D4×C151—21no—
131C2×D4×C151—21no—
132C2×D4×C151—22no—
133C2×D4×C151—22no—
134C2×D4×C151—22no—
135C2×D4×C151—22no—
136C2×D4×C151—22no—
137C2×D4×C151—44no—
138C2×D4×C151—44no—
139C2×D4×C151—44no—
140C2×D4×C151—42no—
141C2×D4×C151—42no—
142C2×D4×C151—41no—
143C2×D4×C151—41no—
144C2×D4×C151—41no—
145C2×D4×C151—41no—
146C2×D4×C151—82no—
147C2×D4×C151#4114yes—
148C22×C4×C151—22no—
149C22×C4×C151—22no—
150C22×C4×C151—21no—
151C22×C4×C151—21no—
152C22×C4×C151—21no—
153C22×C4×C151C2×D411yescharacteristic
154C22×C4×C151C2×D411yescharacteristic
155C22×C4×C151C2×D411yescharacteristic
156C22×C4×C151C2×D411yescharacteristic
157C22×C4×C151#4111yescharacteristic
158C22×C4×C151C2411yescharacteristic
159D8×C151—44no—
160D8×C151—44no—
161M16×C151—22no—
162M16×C151—22no—
163M16×C151—22no—
164M16×C151—22no—
165M16×C151—22no—
166M16×C151—22no—
167M16×C151—42no—
168C2×C8×C151—22no—
169C2×C8×C151—22no—
170C2×C8×C151—22no—
171C2×C8×C151—21no—
172C2×C8×C151—21no—
173C2×C8×C151—22no—
174C2×C8×C151—42no—
175C2×C8×C151C2×D412yes—
176C2×C8×C151C2×D412yes—
177C4⋊C4×C151—21no—
178C4⋊C4×C151—21no—
179C4⋊C4×C151—21no—
180C4⋊C4×C151—21no—
181C4⋊C4×C151C2×D411yescharacteristic
182C4⋊C4×C151C2×D411yescharacteristic
183C4⋊C4×C151C2×D411yescharacteristic
184C4⋊C4×C151C2×D411yescharacteristic
185C22⋊C4×C151—21no—
186C22⋊C4×C151—21no—
187C22⋊C4×C151—21no—
188C22⋊C4×C151—21no—
189C22⋊C4×C151—41no—
190C22⋊C4×C151—41no—
191C42×C151—21no—
192C42×C151—21no—
193C42×C151—21no—
194C42×C151—21no—
195C23×C151—22no—
196C23×C151—22no—
197C23×C151—24no—
198C23×C151—41no—
199C23×C151—44no—
200C23×C151—44no—
201C23×C151—42no—
202C23×C151—42no—
203C23×C151—41no—
204C23×C151—42no—
205C23×C151—82no—
206C23×C151—82no—
207C23×C151—82no—
208C23×C151—82no—
209C23×C151—82no—
210C23×C151—81no—
211C23×C151—81no—
212C23×C151—816no—
213C23×C151—82no—
214C23×C151#12111yescharacteristic
215C23×C151#12111yescharacteristic
216C23×C151C2×#4111yescharacteristic
217D4×C151—24no—
218D4×C151—24no—
219D4×C151—44no—
220D4×C151—44no—
221D4×C151—41no—
222D4×C151—42no—
223D4×C151—41no—
224D4×C151—42no—
225D4×C151—42no—
226D4×C151—82no—
227D4×C151—82no—
228C2×C4×C151—22no—
229C2×C4×C151—21no—
230C2×C4×C151—21no—
231C2×C4×C151—21no—
232C2×C4×C151—21no—
233C2×C4×C151—22no—
234C2×C4×C151—22no—
235C2×C4×C151—21no—
236C2×C4×C151—21no—
237C2×C4×C151—21no—
238C2×C4×C151—21no—
239C2×C4×C151—42no—
240C2×C4×C151—41no—
241C2×C4×C151—81no—
242C2×C4×C151—81no—
243C2×C4×C151#12111yescharacteristic
244C2×C4×C151#12111yescharacteristic
245C2×C4×C151C22×D411yescharacteristic
246C2×C4×C151C22×D411yescharacteristic
247C2×C4×C151C2×#4112yes—
248C2×C4×C151H(5,𝔽2)12yes—
249C8×C151—22no—
250C8×C151—22no—
251C8×C151—41no—
252C8×C151—42no—
253C8×C151—41no—
254C8×C151—42no—
255C22×C151—21no—
256C22×C151—21no—
257C22×C151—21no—
258C22×C151—21no—
259C22×C151—21no—
260C22×C151—21no—
261C22×C151—21no—
262C22×C151—44no—
263C22×C151—44no—
264C22×C151—84no—
265C22×C151—84no—
266C22×C151—88no—
267C22×C151—88no—
268C22×C151—82no—
269C22×C151—82no—
270C22×C151—81no—
271C22×C151—81no—
272C22×C151—81no—
273C22×C151—162no—
274C22×C151#47212yes—
275C22×C151C2×#12111yescharacteristic
276C22×C151#55112yes—
277C4×C151—21no—
278C4×C151—21no—
279C4×C151—41no—
280C4×C151—41no—
281C4×C151—41no—
282C4×C151—41no—
283C4×C151—81no—
284C4×C151#52511yescharacteristic
285C4×C151#53511yescharacteristic
286C4×C151#54612yes—
287C2×C151—22no—
288C2×C151—22no—
289C2×C151—41no—
290C2×C151—84no—
291C2×C151—161no—
292C2×C151#241111yescharacteristic
293C2×C151C2×#47211yescharacteristic
294C2×C151#306811yescharacteristic
295#24520C15111yesmaximal, characteristic, direct product factor, Sylow
296C151#2452011yescharacteristic, direct product factor, Sylow
297#3094C2×C15111yescharacteristic, complemented
298C2×#447C2×C15111yescharacteristic
299#2924C2×C15111yescharacteristic, complemented
300C2×#418C2×C15111yescharacteristic, complemented
301#2063C2×C15112yescomplemented
302#2045C2×C15112yescomplemented
303#1978C2×C15112yescomplemented
304#1931C2×C15112yescomplemented
305#1900C2×C15111yescharacteristic, complemented
306#1855C2×C15111yescharacteristic, complemented
307#1783C2×C15111yescharacteristic, complemented
308C23×D4C22×C15111yescharacteristic
309C22×D8C22×C15112yes—
310C22×M16C22×C15111yescharacteristic
311C2×#121C22×C15111yescharacteristic
312C2×#117C22×C15111yescharacteristic
313#482—21no—
314#482—21no—
315#481—21no—
316#480—21no—
317#447—21no—
318#447—21no—
319#447—22no—
320#433—22no—
321#432—21no—
322#431—21no—
323C2×#108C22×C15112yescomplemented
324#428C22×C15111yescharacteristic, complemented
325#428C22×C15111yescharacteristic, complemented
326#424C22×C15112yescomplemented
327#418—21no—
328#418—21no—
329#418C22×C15112yes—
330#418C22×C15112yes—
331#418C22×C15111yescharacteristic, complemented
332#418C22×C15111yescharacteristic, complemented
333C2×#102—21no—
334C2×#102—21no—
335C2×#102C22×C15112yes—
336C2×#100C22×C15112yes—
337C2×#100C22×C15112yes—
338C2×#100C22×C15112yescomplemented
339#407C22×C15111yescharacteristic
340#407C22×C15111yescharacteristic
341C2×C22⋊C8C22×C15111yescharacteristic
342#405C22×C15112yescomplemented
343#343C22×C15112yescomplemented
344#341C22×C15112yescomplemented
345C25—21no—
346C22×D4—24no—
347C22×D4—21no—
348C22×D4—21no—
349C22×D4—21no—
350C22×D4—21no—
351C22×D4—21no—
352C22×D4—21no—
353C22×D4—42no—
354C22×D4C23×C15111yescharacteristic
355C22×D4C23×C15112yes—
356C23×C4C23×C15111yescharacteristic
357C2×D8—24no—
358C2×D8—22no—
359C2×D8—22no—
360C2×D8—42no—
361C2×M16—21no—
362C2×M16—42no—
363C2×M16C23×C15112yes—
364C2×M16C23×C15111yescharacteristic
365C2×M16C23×C15112yes—
366C2×M16C23×C15111yescharacteristic
367C22×C8—21no—
368C22×C8C23×C15112yes—
369#121—21no—
370#121—21no—
371#121—21no—
372#121—21no—
373#117—21no—
374#117—21no—
375#117D4×C15111yescharacteristic
376#117D4×C15111yescharacteristic
377#117C23×C15111yescharacteristic
378#117C23×C15111yescharacteristic
379C2×C4⋊C4D4×C15111yescharacteristic
380C2×C4⋊C4D4×C15111yescharacteristic
381C2×C4⋊C4C23×C15111yescharacteristic
382C2×C22⋊C4—21no—
383C2×C22⋊C4—21no—
384C2×C42—21no—
385#108—42no—
386#107—21no—
387#107—21no—
388#106—21no—
389#106—21no—
390C4⋊C8—22no—
391C4⋊C8—22no—
392#102—22no—
393#102—22no—
394#102—22no—
395#102—22no—
396#102—22no—
397#102—22no—
398#102—21no—
399#102—21no—
400#102—21no—
401#102—21no—
402#100—24no—
403#100—42no—
404#100—42no—
405C22⋊C8—21no—
406C22⋊C8—21no—
407C22⋊C8—21no—
408C22⋊C8—21no—
409C22⋊C8D4×C15111yescharacteristic
410C22⋊C8D4×C15111yescharacteristic
411C22⋊C8D4×C15112yes—
412#97—22no—
413C4×C8—22no—
414C24—22no—
415C24—21no—
416C24—44no—
417C24—41no—
418C24—41no—
419C24—82no—
420C24—82no—
421C24#41×C15111yescharacteristic
422C2×D4—24no—
423C2×D4—24no—
424C2×D4—22no—
425C2×D4—22no—
426C2×D4—21no—
427C2×D4—21no—
428C2×D4—22no—
429C2×D4—22no—
430C2×D4—22no—
431C2×D4—22no—
432C2×D4—22no—
433C2×D4—44no—
434C2×D4—44no—
435C2×D4—44no—
436C2×D4—42no—
437C2×D4—42no—
438C2×D4—41no—
439C2×D4—41no—
440C2×D4—41no—
441C2×D4—41no—
442C2×D4—82no—
443C2×D4#41×C15114yes—
444C22×C4—22no—
445C22×C4—22no—
446C22×C4—21no—
447C22×C4—21no—
448C22×C4—21no—
449C22×C4C2×D4×C15111yescharacteristic
450C22×C4C2×D4×C15111yescharacteristic
451C22×C4C2×D4×C15111yescharacteristic
452C22×C4C2×D4×C15111yescharacteristic
453C22×C4#41×C15111yescharacteristic
454C22×C4C24×C15111yescharacteristic
455D8—44no—
456D8—44no—
457M16—22no—
458M16—22no—
459M16—22no—
460M16—22no—
461M16—22no—
462M16—22no—
463M16—42no—
464C2×C8—22no—
465C2×C8—22no—
466C2×C8—22no—
467C2×C8—21no—
468C2×C8—21no—
469C2×C8—22no—
470C2×C8—42no—
471C2×C8C2×D4×C15112yes—
472C2×C8C2×D4×C15112yes—
473C4⋊C4—21no—
474C4⋊C4—21no—
475C4⋊C4—21no—
476C4⋊C4—21no—
477C4⋊C4C2×D4×C15111yescharacteristic
478C4⋊C4C2×D4×C15111yescharacteristic
479C4⋊C4C2×D4×C15111yescharacteristic
480C4⋊C4C2×D4×C15111yescharacteristic
481C22⋊C4—21no—
482C22⋊C4—21no—
483C22⋊C4—21no—
484C22⋊C4—21no—
485C22⋊C4—41no—
486C22⋊C4—41no—
487C42—21no—
488C42—21no—
489C42—21no—
490C42—21no—
491C23—22no—
492C23—22no—
493C23—24no—
494C23—41no—
495C23—44no—
496C23—44no—
497C23—42no—
498C23—42no—
499C23—41no—
500C23—42no—
501C23—82no—
502C23—82no—
503C23—82no—
504C23—82no—
505C23—82no—
506C23—81no—
507C23—81no—
508C23—816no—
509C23—82no—
510C23#121×C15111yescharacteristic
511C23#121×C15111yescharacteristic
512C23C2×#41×C15111yescharacteristic
513D4—24no—
514D4—24no—
515D4—44no—
516D4—44no—
517D4—41no—
518D4—42no—
519D4—41no—
520D4—42no—
521D4—42no—
522D4—82no—
523D4—82no—
524C2×C4—22no—
525C2×C4—21no—
526C2×C4—21no—
527C2×C4—21no—
528C2×C4—21no—
529C2×C4—22no—
530C2×C4—22no—
531C2×C4—21no—
532C2×C4—21no—
533C2×C4—21no—
534C2×C4—21no—
535C2×C4—42no—
536C2×C4—41no—
537C2×C4—81no—
538C2×C4—81no—
539C2×C4#121×C15111yescharacteristic
540C2×C4#121×C15111yescharacteristic
541C2×C4C22×D4×C15111yescharacteristic
542C2×C4C22×D4×C15111yescharacteristic
543C2×C4C2×#41×C15112yes—
544C2×C4H(5,𝔽2)×C15112yes—
545C8—22no—
546C8—22no—
547C8—41no—
548C8—42no—
549C8—41no—
550C8—42no—
551C22—21no—
552C22—21no—
553C22—21no—
554C22—21no—
555C22—21no—
556C22—21no—
557C22—21no—
558C22—44no—
559C22—44no—
560C22—84no—
561C22—84no—
562C22—88no—
563C22—88no—
564C22—82no—
565C22—82no—
566C22—81no—
567C22—81no—
568C22—81no—
569C22—162no—
570C22#472×C15112yes—
571C22C2×#121×C15111yescharacteristic
572C22#551×C15112yes—
573C4—21no—
574C4—21no—
575C4—41no—
576C4—41no—
577C4—41no—
578C4—41no—
579C4—81no—
580C4#525×C15111yescharacteristic
581C4#535×C15111yescharacteristic
582C4#546×C15112yes—
583C2—22no—
584C2—22no—
585C2—41no—
586C2—84no—
587C2—161no—
588C2#2411×C15111yescharacteristic
589C2C2×#472×C15111yescharacteristic
590C2#3068×C15111yescharacteristic
subgroupG/H
center, socleC22×C151C2×#121
commutator, Frattini, cosocleC22×C4C24×C151
prime radicalC2×#447×C151C2
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C151 ◁ C23×C4×C151 ◁ G

Complements

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

NH ≅ G/Ntype
1. #3094×C151C2semidirect
3. #2924×C151C2semidirect
4. C2×#418×C151C2semidirect
5. #2063×C151C2semidirect
6. #2045×C151C2semidirect
7. #1978×C151C2semidirect
8. #1931×C151C2semidirect
9. #1900×C151C2semidirect
10. #1855×C151C2semidirect
11. #1783×C151C2semidirect
27. C2×#108×C151C22semidirect
28. #428×C151C22semidirect
29. #428×C151C22semidirect
30. #424×C151C22semidirect
35. #418×C151C22semidirect
36. #418×C151C22semidirect
42. C2×#100×C151C22semidirect
46. #405×C151C22semidirect
47. #343×C151C22semidirect
48. #341×C151C22semidirect
295. #24520C151direct (N × H)
296. C151#24520direct (N × H)
297. #3094C2×C151semidirect
299. #2924C2×C151semidirect
300. C2×#418C2×C151semidirect
301. #2063C2×C151semidirect
302. #2045C2×C151semidirect
303. #1978C2×C151semidirect
304. #1931C2×C151semidirect
305. #1900C2×C151semidirect
306. #1855C2×C151semidirect
307. #1783C2×C151semidirect
323. C2×#108C22×C151semidirect
324. #428C22×C151semidirect
325. #428C22×C151semidirect
326. #424C22×C151semidirect
331. #418C22×C151semidirect
332. #418C22×C151semidirect
338. C2×#100C22×C151semidirect
342. #405C22×C151semidirect
343. #343C22×C151semidirect
344. #341C22×C151semidirect

Maximal subgroups

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

subgroupindex
#3094×C1512
C2×#447×C1512
#2924×C1512
C2×#418×C1512
#2063×C1512
#2045×C1512
#1978×C1512
#1931×C1512
#1900×C1512
#1855×C1512
#1783×C1512
#24520151