Finite Group Databasebeta

← C151×#24573 #50329498

Subgroups — C151×#24573 #50329498

Order 38656.

936 conjugacy classes of subgroups.

The subgroup lattice has 618 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#481×C151C211yesmaximal, characteristic, complemented
2#3006×C151C211yesmaximal, characteristic
3C2×#417×C151C211yesmaximal, characteristic, complemented
4#2880×C151C211yesmaximal, characteristic, complemented
5#2079×C151C212yesmaximal, complemented
6#2051×C151C212yesmaximal, complemented
7#1907×C151C212yesmaximal, complemented
8#1900×C151C211yesmaximal, characteristic, complemented
9#1855×C151C211yesmaximal, characteristic, complemented
10#1821×C151C211yesmaximal, characteristic, complemented
11#1815×C151C212yesmaximal, complemented
12C22×#41×C151C2211yescharacteristic
13C2×AGL(1,ℤ/8)×C151C2211yescharacteristic
14C2×AGL(1,ℤ/8)×C151C2211yescharacteristic
15C2×#131×C151C2212yes—
16C22×M16×C151C2211yescharacteristic
17C2×#121×C151C2211yescharacteristic
18C22×C4⋊C4×C151C2211yescharacteristic
19#481×C151—21no—
20#481×C151—21no—
21#481×C151—22no—
22#449×C151—21no—
23#449×C151—21no—
24#448×C151—21no—
25#447×C151—21no—
26C2×#108×C151C2212yescomplemented
27C2×#106×C151C2212yescomplemented
28#417×C151—21no—
29#417×C151—21no—
30#417×C151C2211yescharacteristic
31#417×C151C2212yes—
32#417×C151C2212yes—
33#417×C151C2211yescharacteristic
34C2×#103×C151—21no—
35C2×#102×C151—21no—
36C2×#102×C151C2212yescomplemented
37C2×#100×C151C2212yescomplemented
38#408×C151—22no—
39#408×C151C2212yes—
40#407×C151—21no—
41#407×C151C2211yescharacteristic
42#407×C151C2211yescharacteristic
43C2×C22⋊C8×C151—21no—
44C2×C22⋊C8×C151C2211yescharacteristic
45#343×C151C2212yescomplemented
46#343×C151C2212yescomplemented
47#343×C151C2212yescomplemented
48#341×C151C2212yescomplemented
49C2×#41×C151—24no—
50C2×#41×C151—21no—
51C2×#41×C151—21no—
52C2×#41×C151—42no—
53C2×#41×C151D411yescharacteristic
54C2×#41×C151D411yescharacteristic
55C2×#41×C151C2311yescharacteristic
56C2×#41×C151C2311yescharacteristic
57C22×Q8×C151D411yescharacteristic
58C22×D4×C151—21no—
59C22×D4×C151—21no—
60C22×D4×C151D411yescharacteristic
61C22×D4×C151C2311yescharacteristic
62C23×C4×C151—21no—
63C23×C4×C151—21no—
64C23×C4×C151C2311yescharacteristic
65AGL(1,ℤ/8)×C151—24no—
66AGL(1,ℤ/8)×C151—42no—
67C2×SD16×C151—21no—
68C2×SD16×C151—21no—
69C2×D8×C151—21no—
70C2×D8×C151—21no—
71#131×C151—24no—
72#131×C151—42no—
73C2×M16×C151—21no—
74C2×M16×C151—22no—
75C2×M16×C151—42no—
76C2×M16×C151C2311yescharacteristic
77C2×M16×C151C2312yes—
78C2×M16×C151C2312yes—
79C2×M16×C151C2311yescharacteristic
80C22×C8×C151—21no—
81C22×C8×C151—22no—
82C22×C8×C151C2312yes—
83#121×C151—21no—
84#121×C151—21no—
85#121×C151—21no—
86#121×C151—21no—
87C2×C4⋊C4×C151—21no—
88C2×C4⋊C4×C151—21no—
89C2×C4⋊C4×C151—21no—
90C2×C4⋊C4×C151—21no—
91C2×C4⋊C4×C151—21no—
92C2×C4⋊C4×C151C2312yes—
93C2×C4⋊C4×C151C2311yescharacteristic
94C2×C22⋊C4×C151—21no—
95#108×C151—42no—
96#106×C151—22no—
97#106×C151—22no—
98#103×C151—22no—
99#103×C151—22no—
100#103×C151—21no—
101#103×C151—21no—
102#102×C151—22no—
103#102×C151—22no—
104#102×C151—21no—
105#102×C151—21no—
106#102×C151—22no—
107#102×C151—22no—
108#100×C151—42no—
109C22⋊C8×C151—21no—
110C22⋊C8×C151—21no—
111C22⋊C8×C151—21no—
112C22⋊C8×C151—21no—
113C22⋊C8×C151—22no—
114C22⋊C8×C151—22no—
115C22⋊C8×C151D411yescharacteristic
116C22⋊C8×C151D411yescharacteristic
117C22⋊C8×C151D412yes—
118C24×C151—21no—
119C24×C151—21no—
120C24×C151#4111yescharacteristic
121#41×C151—22no—
122#41×C151—22no—
123#41×C151—22no—
124#41×C151—22no—
125#41×C151—22no—
126#41×C151—44no—
127#41×C151—41no—
128#41×C151—41no—
129#41×C151—44no—
130#41×C151#4114yes—
131C2×Q8×C151—21no—
132C2×Q8×C151—22no—
133C2×Q8×C151—41no—
134C2×Q8×C151C2×D411yescharacteristic
135C2×Q8×C151C2×D411yescharacteristic
136C2×D4×C151—21no—
137C2×D4×C151—22no—
138C2×D4×C151—21no—
139C2×D4×C151—21no—
140C2×D4×C151—21no—
141C2×D4×C151—21no—
142C2×D4×C151—21no—
143C2×D4×C151—21no—
144C2×D4×C151—22no—
145C2×D4×C151—22no—
146C2×D4×C151—41no—
147C2×D4×C151—44no—
148C2×D4×C151—41no—
149C2×D4×C151—41no—
150C2×D4×C151—82no—
151C2×D4×C151C2×D411yescharacteristic
152C2×D4×C151C2×D411yescharacteristic
153C22×C4×C151—21no—
154C22×C4×C151—22no—
155C22×C4×C151—22no—
156C22×C4×C151—21no—
157C22×C4×C151—21no—
158C22×C4×C151—21no—
159C22×C4×C151—21no—
160C22×C4×C151—21no—
161C22×C4×C151—22no—
162C22×C4×C151—44no—
163C22×C4×C151—41no—
164C22×C4×C151—41no—
165C22×C4×C151—82no—
166C22×C4×C151C2×D411yescharacteristic
167C22×C4×C151C2×D411yescharacteristic
168C22×C4×C151C2×D411yescharacteristic
169C22×C4×C151C2×D411yescharacteristic
170C22×C4×C151#4111yescharacteristic
171C22×C4×C151C2411yescharacteristic
172SD16×C151—42no—
173SD16×C151—42no—
174D8×C151—42no—
175D8×C151—42no—
176M16×C151—22no—
177M16×C151—22no—
178M16×C151—22no—
179M16×C151—22no—
180M16×C151—22no—
181M16×C151—22no—
182M16×C151—44no—
183M16×C151—42no—
184C2×C8×C151—22no—
185C2×C8×C151—22no—
186C2×C8×C151—22no—
187C2×C8×C151—21no—
188C2×C8×C151—21no—
189C2×C8×C151—22no—
190C2×C8×C151—44no—
191C2×C8×C151—42no—
192C2×C8×C151C2×D412yes—
193C2×C8×C151C2×D412yes—
194C4⋊C4×C151—22no—
195C4⋊C4×C151—21no—
196C4⋊C4×C151—22no—
197C4⋊C4×C151—21no—
198C4⋊C4×C151—41no—
199C4⋊C4×C151—41no—
200C22⋊C4×C151—41no—
201C22⋊C4×C151—41no—
202C23×C151—21no—
203C23×C151—22no—
204C23×C151—22no—
205C23×C151—21no—
206C23×C151—41no—
207C23×C151—42no—
208C23×C151—42no—
209C23×C151—41no—
210C23×C151—42no—
211C23×C151—81no—
212C23×C151—81no—
213C23×C151—81no—
214C23×C151#12111yescharacteristic
215C23×C151#12111yescharacteristic
216C23×C151C2×#4111yescharacteristic
217Q8×C151—21no—
218Q8×C151—21no—
219Q8×C151—21no—
220Q8×C151—42no—
221Q8×C151#12312yes—
222D4×C151—24no—
223D4×C151—21no—
224D4×C151—21no—
225D4×C151—21no—
226D4×C151—42no—
227D4×C151—42no—
228D4×C151—42no—
229D4×C151—42no—
230D4×C151—41no—
231D4×C151—41no—
232D4×C151—42no—
233D4×C151—82no—
234D4×C151—82no—
235D4×C151#12312yes—
236C2×C4×C151—21no—
237C2×C4×C151—22no—
238C2×C4×C151—21no—
239C2×C4×C151—21no—
240C2×C4×C151—21no—
241C2×C4×C151—21no—
242C2×C4×C151—24no—
243C2×C4×C151—22no—
244C2×C4×C151—22no—
245C2×C4×C151—21no—
246C2×C4×C151—42no—
247C2×C4×C151—42no—
248C2×C4×C151—42no—
249C2×C4×C151—42no—
250C2×C4×C151—41no—
251C2×C4×C151—42no—
252C2×C4×C151—82no—
253C2×C4×C151—82no—
254C2×C4×C151—82no—
255C2×C4×C151—81no—
256C2×C4×C151#12111yescharacteristic
257C2×C4×C151#12111yescharacteristic
258C2×C4×C151C22×D411yescharacteristic
259C2×C4×C151C22×D411yescharacteristic
260C2×C4×C151C2×#4112yes—
261C2×C4×C151H(5,𝔽2)12yes—
262C8×C151—22no—
263C8×C151—22no—
264C8×C151—41no—
265C8×C151—42no—
266C8×C151—41no—
267C8×C151—42no—
268C22×C151—21no—
269C22×C151—21no—
270C22×C151—21no—
271C22×C151—21no—
272C22×C151—21no—
273C22×C151—22no—
274C22×C151—21no—
275C22×C151—21no—
276C22×C151—44no—
277C22×C151—41no—
278C22×C151—41no—
279C22×C151—41no—
280C22×C151—41no—
281C22×C151—41no—
282C22×C151—84no—
283C22×C151—81no—
284C22×C151—81no—
285C22×C151—81no—
286C22×C151—162no—
287C22×C151#47112yes—
288C22×C151C2×#12111yescharacteristic
289C22×C151#55112yes—
290C4×C151—21no—
291C4×C151—21no—
292C4×C151—22no—
293C4×C151—41no—
294C4×C151—81no—
295C4×C151—82no—
296C4×C151C2×#12311yescharacteristic
297C4×C151#53411yescharacteristic
298C4×C151#54612yes—
299C2×C151—22no—
300C2×C151—22no—
301C2×C151—41no—
302C2×C151—42no—
303C2×C151—81no—
304C2×C151—161no—
305C2×C151#241211yescharacteristic
306C2×C151C2×#47111yescharacteristic
307C2×C151#306811yescharacteristic
308#24573C15111yesmaximal, characteristic, direct product factor, Sylow
309C151#2457311yescharacteristic, direct product factor, Sylow
310C2×#481C2×C15111yescharacteristic, complemented
311#3006C2×C15111yescharacteristic
312C2×#417C2×C15111yescharacteristic, complemented
313#2880C2×C15111yescharacteristic, complemented
314#2079C2×C15112yescomplemented
315#2051C2×C15112yescomplemented
316#1907C2×C15112yescomplemented
317#1900C2×C15111yescharacteristic, complemented
318#1855C2×C15111yescharacteristic, complemented
319#1821C2×C15111yescharacteristic, complemented
320#1815C2×C15112yescomplemented
321C22×#41C22×C15111yescharacteristic
322C2×AGL(1,ℤ/8)C22×C15111yescharacteristic
323C2×AGL(1,ℤ/8)C22×C15111yescharacteristic
324C2×#131C22×C15112yes—
325C22×M16C22×C15111yescharacteristic
326C2×#121C22×C15111yescharacteristic
327C22×C4⋊C4C22×C15111yescharacteristic
328#481—21no—
329#481—21no—
330#481—22no—
331#449—21no—
332#449—21no—
333#448—21no—
334#447—21no—
335C2×#108C22×C15112yescomplemented
336C2×#106C22×C15112yescomplemented
337#417—21no—
338#417—21no—
339#417C22×C15112yes—
340#417C22×C15111yescharacteristic
341#417C22×C15112yes—
342#417C22×C15111yescharacteristic
343C2×#103—21no—
344C2×#102—21no—
345C2×#102C22×C15112yescomplemented
346C2×#100C22×C15112yescomplemented
347#408—22no—
348#408C22×C15112yes—
349#407—21no—
350#407C22×C15111yescharacteristic
351#407C22×C15111yescharacteristic
352C2×C22⋊C8—21no—
353C2×C22⋊C8C22×C15111yescharacteristic
354#343C22×C15112yescomplemented
355#343C22×C15112yescomplemented
356#343C22×C15112yescomplemented
357#341C22×C15112yescomplemented
358C2×#41—21no—
359C2×#41—21no—
360C2×#41—24no—
361C2×#41—42no—
362C2×#41D4×C15111yescharacteristic
363C2×#41D4×C15111yescharacteristic
364C2×#41C23×C15111yescharacteristic
365C2×#41C23×C15111yescharacteristic
366C22×Q8D4×C15111yescharacteristic
367C22×D4—21no—
368C22×D4—21no—
369C22×D4D4×C15111yescharacteristic
370C22×D4C23×C15111yescharacteristic
371C23×C4—21no—
372C23×C4—21no—
373C23×C4C23×C15111yescharacteristic
374AGL(1,ℤ/8)—24no—
375AGL(1,ℤ/8)—42no—
376C2×SD16—21no—
377C2×SD16—21no—
378C2×D8—21no—
379C2×D8—21no—
380#131—24no—
381#131—42no—
382C2×M16—21no—
383C2×M16—22no—
384C2×M16—42no—
385C2×M16C23×C15112yes—
386C2×M16C23×C15112yes—
387C2×M16C23×C15111yescharacteristic
388C2×M16C23×C15111yescharacteristic
389C22×C8—21no—
390C22×C8—22no—
391C22×C8C23×C15112yes—
392#121—21no—
393#121—21no—
394#121—21no—
395#121—21no—
396C2×C4⋊C4—21no—
397C2×C4⋊C4—21no—
398C2×C4⋊C4—21no—
399C2×C4⋊C4—21no—
400C2×C4⋊C4—21no—
401C2×C4⋊C4C23×C15112yes—
402C2×C4⋊C4C23×C15111yescharacteristic
403C2×C22⋊C4—21no—
404#108—42no—
405#106—22no—
406#106—22no—
407#103—22no—
408#103—22no—
409#103—21no—
410#103—21no—
411#102—22no—
412#102—22no—
413#102—21no—
414#102—21no—
415#102—22no—
416#102—22no—
417#100—42no—
418C22⋊C8—21no—
419C22⋊C8—21no—
420C22⋊C8—21no—
421C22⋊C8—21no—
422C22⋊C8—22no—
423C22⋊C8—22no—
424C22⋊C8D4×C15111yescharacteristic
425C22⋊C8D4×C15111yescharacteristic
426C22⋊C8D4×C15112yes—
427C24—21no—
428C24—21no—
429C24#41×C15111yescharacteristic
430#41—22no—
431#41—22no—
432#41—22no—
433#41—22no—
434#41—22no—
435#41—44no—
436#41—41no—
437#41—41no—
438#41—44no—
439#41#41×C15114yes—
440C2×Q8—21no—
441C2×Q8—22no—
442C2×Q8—41no—
443C2×Q8C2×D4×C15111yescharacteristic
444C2×Q8C2×D4×C15111yescharacteristic
445C2×D4—21no—
446C2×D4—22no—
447C2×D4—21no—
448C2×D4—21no—
449C2×D4—21no—
450C2×D4—21no—
451C2×D4—21no—
452C2×D4—21no—
453C2×D4—22no—
454C2×D4—22no—
455C2×D4—41no—
456C2×D4—44no—
457C2×D4—41no—
458C2×D4—41no—
459C2×D4—82no—
460C2×D4C2×D4×C15111yescharacteristic
461C2×D4C2×D4×C15111yescharacteristic
462C22×C4—21no—
463C22×C4—22no—
464C22×C4—22no—
465C22×C4—21no—
466C22×C4—21no—
467C22×C4—21no—
468C22×C4—21no—
469C22×C4—21no—
470C22×C4—22no—
471C22×C4—44no—
472C22×C4—41no—
473C22×C4—41no—
474C22×C4—82no—
475C22×C4C2×D4×C15111yescharacteristic
476C22×C4C2×D4×C15111yescharacteristic
477C22×C4C2×D4×C15111yescharacteristic
478C22×C4C2×D4×C15111yescharacteristic
479C22×C4#41×C15111yescharacteristic
480C22×C4C24×C15111yescharacteristic
481SD16—42no—
482SD16—42no—
483D8—42no—
484D8—42no—
485M16—22no—
486M16—22no—
487M16—22no—
488M16—22no—
489M16—22no—
490M16—22no—
491M16—44no—
492M16—42no—
493C2×C8—22no—
494C2×C8—22no—
495C2×C8—22no—
496C2×C8—21no—
497C2×C8—21no—
498C2×C8—22no—
499C2×C8—44no—
500C2×C8—42no—
501C2×C8C2×D4×C15112yes—
502C2×C8C2×D4×C15112yes—
503C4⋊C4—22no—
504C4⋊C4—21no—
505C4⋊C4—22no—
506C4⋊C4—21no—
507C4⋊C4—41no—
508C4⋊C4—41no—
509C22⋊C4—41no—
510C22⋊C4—41no—
511C23—22no—
512C23—21no—
513C23—22no—
514C23—21no—
515C23—41no—
516C23—42no—
517C23—42no—
518C23—41no—
519C23—42no—
520C23—81no—
521C23—81no—
522C23—81no—
523C23#121×C15111yescharacteristic
524C23#121×C15111yescharacteristic
525C23C2×#41×C15111yescharacteristic
526Q8—21no—
527Q8—21no—
528Q8—21no—
529Q8—42no—
530Q8#123×C15112yes—
531D4—24no—
532D4—21no—
533D4—21no—
534D4—21no—
535D4—42no—
536D4—42no—
537D4—42no—
538D4—42no—
539D4—41no—
540D4—41no—
541D4—42no—
542D4—82no—
543D4—82no—
544D4#123×C15112yes—
545C2×C4—21no—
546C2×C4—22no—
547C2×C4—21no—
548C2×C4—21no—
549C2×C4—21no—
550C2×C4—21no—
551C2×C4—24no—
552C2×C4—22no—
553C2×C4—22no—
554C2×C4—21no—
555C2×C4—42no—
556C2×C4—42no—
557C2×C4—42no—
558C2×C4—42no—
559C2×C4—41no—
560C2×C4—42no—
561C2×C4—82no—
562C2×C4—82no—
563C2×C4—82no—
564C2×C4—81no—
565C2×C4#121×C15111yescharacteristic
566C2×C4#121×C15111yescharacteristic
567C2×C4C22×D4×C15111yescharacteristic
568C2×C4C22×D4×C15111yescharacteristic
569C2×C4C2×#41×C15112yes—
570C2×C4H(5,𝔽2)×C15112yes—
571C8—22no—
572C8—22no—
573C8—41no—
574C8—42no—
575C8—41no—
576C8—42no—
577C22—21no—
578C22—21no—
579C22—21no—
580C22—21no—
581C22—21no—
582C22—22no—
583C22—21no—
584C22—21no—
585C22—44no—
586C22—41no—
587C22—41no—
588C22—41no—
589C22—41no—
590C22—41no—
591C22—84no—
592C22—81no—
593C22—81no—
594C22—81no—
595C22—162no—
596C22#471×C15112yes—
597C22C2×#121×C15111yescharacteristic
598C22#551×C15112yes—
599C4—21no—
600C4—21no—
601C4—22no—
602C4—41no—
603C4—81no—
604C4—82no—
605C4C2×#123×C15111yescharacteristic
606C4#534×C15111yescharacteristic
607C4#546×C15112yes—
608C2—22no—
609C2—22no—
610C2—41no—
611C2—42no—
612C2—81no—
613C2—161no—
614C2#2412×C15111yescharacteristic
615C2C2×#471×C15111yescharacteristic
616C2#3068×C15111yescharacteristic
subgroupG/H
center, socleC22×C151C2×#121
commutator, Frattini, cosocleC22×C4C24×C151
prime radical#3006×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. C2×#481×C151C2semidirect
3. C2×#417×C151C2semidirect
4. #2880×C151C2semidirect
5. #2079×C151C2semidirect
6. #2051×C151C2semidirect
7. #1907×C151C2semidirect
8. #1900×C151C2semidirect
9. #1855×C151C2semidirect
10. #1821×C151C2semidirect
11. #1815×C151C2semidirect
26. C2×#108×C151C22semidirect
27. C2×#106×C151C22semidirect
36. C2×#102×C151C22semidirect
37. C2×#100×C151C22semidirect
45. #343×C151C22semidirect
46. #343×C151C22semidirect
47. #343×C151C22semidirect
48. #341×C151C22semidirect
308. #24573C151direct (N × H)
309. C151#24573direct (N × H)
310. C2×#481C2×C151semidirect
312. C2×#417C2×C151semidirect
313. #2880C2×C151semidirect
314. #2079C2×C151semidirect
315. #2051C2×C151semidirect
316. #1907C2×C151semidirect
317. #1900C2×C151semidirect
318. #1855C2×C151semidirect
319. #1821C2×C151semidirect
320. #1815C2×C151semidirect
335. C2×#108C22×C151semidirect
336. C2×#106C22×C151semidirect
345. C2×#102C22×C151semidirect
346. C2×#100C22×C151semidirect
354. #343C22×C151semidirect
355. #343C22×C151semidirect
356. #343C22×C151semidirect
357. #341C22×C151semidirect

Maximal subgroups

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

subgroupindex
C2×#481×C1512
#3006×C1512
C2×#417×C1512
#2880×C1512
#2079×C1512
#2051×C1512
#1907×C1512
#1900×C1512
#1855×C1512
#1821×C1512
#1815×C1512
#24573151