Finite Group Databasebeta

← C151×#24650 #50329575

Subgroups — C151×#24650 #50329575

Order 38656.

1120 conjugacy classes of subgroups.

The subgroup lattice has 636 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#459×C151C211yesmaximal, characteristic, complemented
2C2×#431×C151C211yesmaximal, characteristic, complemented
3#2856×C151C211yesmaximal, characteristic, complemented
4C4×#121×C151C211yesmaximal, characteristic, complemented
5#2033×C151C212yesmaximal, complemented
6#1999×C151C212yesmaximal, complemented
7#1982×C151C211yesmaximal, characteristic, complemented
8#1970×C151C212yesmaximal, complemented
9#1947×C151C211yesmaximal, characteristic, complemented
10#1934×C151C212yesmaximal, complemented
11#1802×C151C211yesmaximal, characteristic, complemented
12C22×D8×C151C2212yes—
13C2×#127×C151C2211yescharacteristic
14C2×#121×C151—21no—
15C2×#121×C151—21no—
16C2×#121×C151C2211yescharacteristic
17C2×#121×C151C2212yes—
18C2×C4×D4×C151—21no—
19C2×C4×D4×C151C2211yescharacteristic
20C22×C42×C151C2211yescharacteristic
21#459×C151—24no—
22#431×C151—24no—
23C2×#107×C151C2212yes—
24C2×C4⋊C8×C151C2211yescharacteristic
25C2×C4⋊C8×C151C2211yescharacteristic
26C2×#102×C151C2212yes—
27C2×#102×C151C2212yes—
28C2×#102×C151C2212yes—
29C2×#102×C151C2212yes—
30C2×C22⋊C8×C151C2212yes—
31C2×C4×C8×C151C2212yes—
32#390×C151—21no—
33#390×C151—21no—
34#390×C151C2212yes—
35#390×C151C2211yescharacteristic
36#389×C151C2211yescharacteristic
37#388×C151—21no—
38#386×C151—21no—
39#384×C151C2211yescharacteristic
40#380×C151C2211yescharacteristic
41C4×C4⋊C4×C151C2211yescharacteristic
42C4×C22⋊C4×C151—21no—
43#340×C151C2212yes—
44#340×C151C2212yes—
45C22×D4×C151—21no—
46C22×D4×C151—21no—
47C22×D4×C151—21no—
48C22×D4×C151—22no—
49C22×D4×C151C2312yes—
50C22×D4×C151C2311yescharacteristic
51C23×C4×C151—21no—
52C23×C4×C151D411yescharacteristic
53C23×C4×C151D411yescharacteristic
54C23×C4×C151C2311yescharacteristic
55C2×D8×C151—24no—
56C2×D8×C151—24no—
57C2×D8×C151—42no—
58C22×C8×C151C2312yes—
59C22×C8×C151C2312yes—
60#127×C151—22no—
61#127×C151—22no—
62#121×C151—22no—
63#121×C151—22no—
64#121×C151—42no—
65#121×C151—42no—
66#121×C151—44no—
67#121×C151—44no—
68C4×D4×C151—22no—
69C4×D4×C151—22no—
70C4×D4×C151—44no—
71C2×C4⋊C4×C151—21no—
72C2×C4⋊C4×C151—21no—
73C2×C4⋊C4×C151—21no—
74C2×C4⋊C4×C151C2311yescharacteristic
75C2×C4⋊C4×C151C2312yes—
76C2×C4⋊C4×C151C2311yescharacteristic
77C2×C4⋊C4×C151C2311yescharacteristic
78C2×C22⋊C4×C151—21no—
79C2×C22⋊C4×C151—21no—
80C2×C22⋊C4×C151—21no—
81C2×C22⋊C4×C151—21no—
82C2×C22⋊C4×C151—22no—
83C2×C22⋊C4×C151—22no—
84C2×C22⋊C4×C151—22no—
85C2×C22⋊C4×C151—21no—
86C2×C42×C151—22no—
87C2×C42×C151—22no—
88C2×C42×C151—21no—
89C2×C42×C151D411yescharacteristic
90C2×C42×C151D411yescharacteristic
91C2×C42×C151C2311yescharacteristic
92C2×C42×C151C2311yescharacteristic
93#107×C151—42no—
94C4⋊C8×C151—22no—
95C4⋊C8×C151D414yescomplemented
96#102×C151—24no—
97#102×C151—24no—
98#102×C151—42no—
99#102×C151—42no—
100C22⋊C8×C151—24no—
101C4×C8×C151—24no—
102#95×C151—21no—
103#95×C151—21no—
104#95×C151—21no—
105C24×C151—21no—
106C24×C151—22no—
107C24×C151C2×D411yescharacteristic
108C2×D4×C151—24no—
109C2×D4×C151—21no—
110C2×D4×C151—22no—
111C2×D4×C151—21no—
112C2×D4×C151—21no—
113C2×D4×C151—22no—
114C2×D4×C151—22no—
115C2×D4×C151—22no—
116C2×D4×C151—21no—
117C2×D4×C151—21no—
118C2×D4×C151—22no—
119C2×D4×C151—22no—
120C2×D4×C151—42no—
121C2×D4×C151—42no—
122C2×D4×C151—42no—
123C2×D4×C151—42no—
124C2×D4×C151—44no—
125C2×D4×C151—44no—
126C2×D4×C151—44no—
127C2×D4×C151—42no—
128C2×D4×C151—42no—
129C2×D4×C151—42no—
130C2×D4×C151—42no—
131C2×D4×C151#4112yes—
132C22×C4×C151—22no—
133C22×C4×C151—22no—
134C22×C4×C151—21no—
135C22×C4×C151—22no—
136C22×C4×C151—22no—
137C22×C4×C151—21no—
138C22×C4×C151—21no—
139C22×C4×C151—21no—
140C22×C4×C151—21no—
141C22×C4×C151—21no—
142C22×C4×C151—21no—
143C22×C4×C151—21no—
144C22×C4×C151—21no—
145C22×C4×C151—22no—
146C22×C4×C151—41no—
147C22×C4×C151—42no—
148C22×C4×C151—42no—
149C22×C4×C151—42no—
150C22×C4×C151D814yescomplemented
151C22×C4×C151C2×D411yescharacteristic
152C22×C4×C151C2×D411yescharacteristic
153C22×C4×C151C2×D411yescharacteristic
154C22×C4×C151C2×D411yescharacteristic
155C22×C4×C151C2×D411yescharacteristic
156C22×C4×C151C2411yescharacteristic
157D8×C151—48no—
158C2×C8×C151—22no—
159C2×C8×C151—22no—
160C2×C8×C151—22no—
161C2×C8×C151—22no—
162C2×C8×C151—22no—
163C2×C8×C151C2×D414yes—
164C4⋊C4×C151—21no—
165C4⋊C4×C151—21no—
166C4⋊C4×C151—21no—
167C4⋊C4×C151—21no—
168C4⋊C4×C151—22no—
169C4⋊C4×C151—21no—
170C4⋊C4×C151—22no—
171C4⋊C4×C151—42no—
172C4⋊C4×C151—42no—
173C4⋊C4×C151—42no—
174C4⋊C4×C151#4112yes—
175C22⋊C4×C151—24no—
176C22⋊C4×C151—44no—
177C22⋊C4×C151—42no—
178C22⋊C4×C151—42no—
179C22⋊C4×C151—42no—
180C22⋊C4×C151—44no—
181C22⋊C4×C151—42no—
182C22⋊C4×C151—44no—
183C42×C151—22no—
184C42×C151—22no—
185C42×C151—21no—
186C42×C151—21no—
187C42×C151—42no—
188C42×C151C2×D412yes—
189C42×C151#4112yes—
190C23×C151—21no—
191C23×C151—21no—
192C23×C151—21no—
193C23×C151—21no—
194C23×C151—21no—
195C23×C151—21no—
196C23×C151—22no—
197C23×C151—41no—
198C23×C151—41no—
199C23×C151—41no—
200C23×C151—41no—
201C23×C151—41no—
202C23×C151—41no—
203C23×C151—42no—
204C23×C151—42no—
205C23×C151—42no—
206C23×C151—42no—
207C23×C151—42no—
208C23×C151—42no—
209C23×C151—42no—
210C23×C151C2×D812yes—
211C23×C151C22×D411yescharacteristic
212D4×C151—22no—
213D4×C151—22no—
214D4×C151—48no—
215D4×C151—42no—
216D4×C151—41no—
217D4×C151—42no—
218D4×C151—42no—
219D4×C151—41no—
220D4×C151—42no—
221D4×C151—84no—
222D4×C151—88no—
223D4×C151—84no—
224C2×C4×C151—21no—
225C2×C4×C151—21no—
226C2×C4×C151—21no—
227C2×C4×C151—21no—
228C2×C4×C151—21no—
229C2×C4×C151—21no—
230C2×C4×C151—28no—
231C2×C4×C151—21no—
232C2×C4×C151—21no—
233C2×C4×C151—22no—
234C2×C4×C151—21no—
235C2×C4×C151—44no—
236C2×C4×C151—41no—
237C2×C4×C151—41no—
238C2×C4×C151—41no—
239C2×C4×C151—41no—
240C2×C4×C151—41no—
241C2×C4×C151—41no—
242C2×C4×C151—41no—
243C2×C4×C151—42no—
244C2×C4×C151—41no—
245C2×C4×C151—41no—
246C2×C4×C151—41no—
247C2×C4×C151—42no—
248C2×C4×C151—41no—
249C2×C4×C151—42no—
250C2×C4×C151—41no—
251C2×C4×C151—84no—
252C2×C4×C151#12112yes—
253C2×C4×C151#12112yes—
254C2×C4×C151C2×D812yes—
255C2×C4×C151C2×D812yes—
256C2×C4×C151#13512yes—
257C2×C4×C151AGL(1,ℤ/8)12yes—
258C2×C4×C151C22×D411yescharacteristic
259C2×C4×C151C2×#4111yescharacteristic
260C2×C4×C151C2×#4111yescharacteristic
261C2×C4×C151C2×#4111yescharacteristic
262C2×C4×C151H(5,𝔽2)11yescharacteristic
263C2×C4×C151H(5,𝔽2)11yescharacteristic
264C8×C151—24no—
265C8×C151—42no—
266C22×C151—22no—
267C22×C151—22no—
268C22×C151—22no—
269C22×C151—41no—
270C22×C151—41no—
271C22×C151—41no—
272C22×C151—41no—
273C22×C151—42no—
274C22×C151—42no—
275C22×C151—42no—
276C22×C151—81no—
277C22×C151—81no—
278C22×C151—81no—
279C22×C151—81no—
280C22×C151—82no—
281C22×C151—82no—
282C22×C151—82no—
283C22×C151—82no—
284C22×C151—82no—
285C22×C151—82no—
286C22×C151—82no—
287C22×C151C2×#12111yescharacteristic
288C22×C151#52511yescharacteristic
289C22×C151#53511yescharacteristic
290C22×C151C22×D811yescharacteristic
291C22×C151C2×#13511yescharacteristic
292C22×C151C2×AGL(1,ℤ/8)11yescharacteristic
293C22×C151#57511yescharacteristic
294C4×C151—22no—
295C4×C151—22no—
296C4×C151—22no—
297C4×C151—42no—
298C4×C151—41no—
299C4×C151—81no—
300C4×C151—82no—
301C4×C151—81no—
302C4×C151#46614yes—
303C4×C151#54611yescharacteristic
304C4×C151#55011yescharacteristic
305C4×C151#55311yescharacteristic
306C4×C151#55511yescharacteristic
307C2×C151—42no—
308C2×C151—82no—
309C2×C151—162no—
310C2×C151#241411yescharacteristic
311C2×C151C2×#46611yescharacteristic
312C2×C151#305511yescharacteristic
313C2×C151#310011yescharacteristic
314C2×C151#310611yescharacteristic
315C2×C151#320511yescharacteristic
316C2×C151#321211yescharacteristic
317#24650C15111yesmaximal, characteristic, direct product factor, Sylow
318C151#2465011yescharacteristic, direct product factor, Sylow
319C2×#459C2×C15111yescharacteristic, complemented
320C2×#431C2×C15111yescharacteristic, complemented
321#2856C2×C15111yescharacteristic, complemented
322C4×#121C2×C15111yescharacteristic, complemented
323#2033C2×C15112yescomplemented
324#1999C2×C15112yescomplemented
325#1982C2×C15111yescharacteristic, complemented
326#1970C2×C15112yescomplemented
327#1947C2×C15111yescharacteristic, complemented
328#1934C2×C15112yescomplemented
329#1802C2×C15111yescharacteristic, complemented
330C22×D8C22×C15112yes—
331C2×#127C22×C15111yescharacteristic
332C2×#121—21no—
333C2×#121—21no—
334C2×#121C22×C15111yescharacteristic
335C2×#121C22×C15112yes—
336C2×C4×D4—21no—
337C2×C4×D4C22×C15111yescharacteristic
338C22×C42C22×C15111yescharacteristic
339#459—24no—
340#431—24no—
341C2×#107C22×C15112yes—
342C2×C4⋊C8C22×C15111yescharacteristic
343C2×C4⋊C8C22×C15111yescharacteristic
344C2×#102C22×C15112yes—
345C2×#102C22×C15112yes—
346C2×#102C22×C15112yes—
347C2×#102C22×C15112yes—
348C2×C22⋊C8C22×C15112yes—
349C2×C4×C8C22×C15112yes—
350#390—21no—
351#390—21no—
352#390C22×C15112yes—
353#390C22×C15111yescharacteristic
354#389C22×C15111yescharacteristic
355#388—21no—
356#386—21no—
357#384C22×C15111yescharacteristic
358#380C22×C15111yescharacteristic
359C4×C4⋊C4C22×C15111yescharacteristic
360C4×C22⋊C4—21no—
361#340C22×C15112yes—
362#340C22×C15112yes—
363C22×D4—21no—
364C22×D4—22no—
365C22×D4—21no—
366C22×D4—21no—
367C22×D4C23×C15112yes—
368C22×D4C23×C15111yescharacteristic
369C23×C4—21no—
370C23×C4D4×C15111yescharacteristic
371C23×C4D4×C15111yescharacteristic
372C23×C4C23×C15111yescharacteristic
373C2×D8—24no—
374C2×D8—24no—
375C2×D8—42no—
376C22×C8C23×C15112yes—
377C22×C8C23×C15112yes—
378#127—22no—
379#127—22no—
380#121—22no—
381#121—22no—
382#121—42no—
383#121—42no—
384#121—44no—
385#121—44no—
386C4×D4—22no—
387C4×D4—22no—
388C4×D4—44no—
389C2×C4⋊C4—21no—
390C2×C4⋊C4—21no—
391C2×C4⋊C4—21no—
392C2×C4⋊C4C23×C15111yescharacteristic
393C2×C4⋊C4C23×C15112yes—
394C2×C4⋊C4C23×C15111yescharacteristic
395C2×C4⋊C4C23×C15111yescharacteristic
396C2×C22⋊C4—21no—
397C2×C22⋊C4—21no—
398C2×C22⋊C4—21no—
399C2×C22⋊C4—21no—
400C2×C22⋊C4—22no—
401C2×C22⋊C4—22no—
402C2×C22⋊C4—22no—
403C2×C22⋊C4—21no—
404C2×C42—22no—
405C2×C42—22no—
406C2×C42—21no—
407C2×C42D4×C15111yescharacteristic
408C2×C42D4×C15111yescharacteristic
409C2×C42C23×C15111yescharacteristic
410C2×C42C23×C15111yescharacteristic
411#107—42no—
412C4⋊C8—22no—
413C4⋊C8D4×C15114yescomplemented
414#102—24no—
415#102—24no—
416#102—42no—
417#102—42no—
418C22⋊C8—24no—
419C4×C8—24no—
420#95—21no—
421#95—21no—
422#95—21no—
423C24—21no—
424C24—22no—
425C24C2×D4×C15111yescharacteristic
426C2×D4—24no—
427C2×D4—21no—
428C2×D4—22no—
429C2×D4—21no—
430C2×D4—21no—
431C2×D4—22no—
432C2×D4—22no—
433C2×D4—22no—
434C2×D4—21no—
435C2×D4—21no—
436C2×D4—22no—
437C2×D4—22no—
438C2×D4—42no—
439C2×D4—42no—
440C2×D4—42no—
441C2×D4—42no—
442C2×D4—44no—
443C2×D4—44no—
444C2×D4—44no—
445C2×D4—42no—
446C2×D4—42no—
447C2×D4—42no—
448C2×D4—42no—
449C2×D4#41×C15112yes—
450C22×C4—22no—
451C22×C4—22no—
452C22×C4—21no—
453C22×C4—22no—
454C22×C4—22no—
455C22×C4—21no—
456C22×C4—21no—
457C22×C4—21no—
458C22×C4—21no—
459C22×C4—21no—
460C22×C4—21no—
461C22×C4—21no—
462C22×C4—21no—
463C22×C4—22no—
464C22×C4—41no—
465C22×C4—42no—
466C22×C4—42no—
467C22×C4—42no—
468C22×C4D8×C15114yescomplemented
469C22×C4C2×D4×C15111yescharacteristic
470C22×C4C2×D4×C15111yescharacteristic
471C22×C4C2×D4×C15111yescharacteristic
472C22×C4C2×D4×C15111yescharacteristic
473C22×C4C2×D4×C15111yescharacteristic
474C22×C4C24×C15111yescharacteristic
475D8—48no—
476C2×C8—22no—
477C2×C8—22no—
478C2×C8—22no—
479C2×C8—22no—
480C2×C8—22no—
481C2×C8C2×D4×C15114yes—
482C4⋊C4—21no—
483C4⋊C4—21no—
484C4⋊C4—21no—
485C4⋊C4—21no—
486C4⋊C4—22no—
487C4⋊C4—21no—
488C4⋊C4—22no—
489C4⋊C4—42no—
490C4⋊C4—42no—
491C4⋊C4—42no—
492C4⋊C4#41×C15112yes—
493C22⋊C4—24no—
494C22⋊C4—44no—
495C22⋊C4—42no—
496C22⋊C4—42no—
497C22⋊C4—42no—
498C22⋊C4—44no—
499C22⋊C4—44no—
500C22⋊C4—42no—
501C42—22no—
502C42—22no—
503C42—21no—
504C42—21no—
505C42—42no—
506C42C2×D4×C15112yes—
507C42#41×C15112yes—
508C23—21no—
509C23—21no—
510C23—21no—
511C23—21no—
512C23—21no—
513C23—21no—
514C23—22no—
515C23—41no—
516C23—41no—
517C23—41no—
518C23—41no—
519C23—41no—
520C23—41no—
521C23—42no—
522C23—42no—
523C23—42no—
524C23—42no—
525C23—42no—
526C23—42no—
527C23—42no—
528C23C2×D8×C15112yes—
529C23C22×D4×C15111yescharacteristic
530D4—22no—
531D4—22no—
532D4—48no—
533D4—42no—
534D4—41no—
535D4—42no—
536D4—42no—
537D4—41no—
538D4—42no—
539D4—84no—
540D4—88no—
541D4—84no—
542C2×C4—21no—
543C2×C4—21no—
544C2×C4—21no—
545C2×C4—21no—
546C2×C4—21no—
547C2×C4—21no—
548C2×C4—28no—
549C2×C4—21no—
550C2×C4—21no—
551C2×C4—22no—
552C2×C4—21no—
553C2×C4—44no—
554C2×C4—41no—
555C2×C4—41no—
556C2×C4—41no—
557C2×C4—41no—
558C2×C4—41no—
559C2×C4—41no—
560C2×C4—41no—
561C2×C4—42no—
562C2×C4—41no—
563C2×C4—41no—
564C2×C4—41no—
565C2×C4—42no—
566C2×C4—41no—
567C2×C4—42no—
568C2×C4—41no—
569C2×C4—84no—
570C2×C4#121×C15112yes—
571C2×C4#121×C15112yes—
572C2×C4C2×D8×C15112yes—
573C2×C4C2×D8×C15112yes—
574C2×C4#135×C15112yes—
575C2×C4AGL(1,ℤ/8)×C15112yes—
576C2×C4C22×D4×C15111yescharacteristic
577C2×C4C2×#41×C15111yescharacteristic
578C2×C4C2×#41×C15111yescharacteristic
579C2×C4C2×#41×C15111yescharacteristic
580C2×C4H(5,𝔽2)×C15111yescharacteristic
581C2×C4H(5,𝔽2)×C15111yescharacteristic
582C8—24no—
583C8—42no—
584C22—22no—
585C22—22no—
586C22—22no—
587C22—41no—
588C22—41no—
589C22—41no—
590C22—41no—
591C22—42no—
592C22—42no—
593C22—42no—
594C22—81no—
595C22—81no—
596C22—81no—
597C22—81no—
598C22—82no—
599C22—82no—
600C22—82no—
601C22—82no—
602C22—82no—
603C22—82no—
604C22—82no—
605C22C2×#121×C15111yescharacteristic
606C22#525×C15111yescharacteristic
607C22#535×C15111yescharacteristic
608C22C22×D8×C15111yescharacteristic
609C22C2×#135×C15111yescharacteristic
610C22C2×AGL(1,ℤ/8)×C15111yescharacteristic
611C22#575×C15111yescharacteristic
612C4—22no—
613C4—22no—
614C4—22no—
615C4—42no—
616C4—41no—
617C4—82no—
618C4—81no—
619C4—81no—
620C4#466×C15114yes—
621C4#546×C15111yescharacteristic
622C4#550×C15111yescharacteristic
623C4#553×C15111yescharacteristic
624C4#555×C15111yescharacteristic
625C2—42no—
626C2—82no—
627C2—162no—
628C2#2414×C15111yescharacteristic
629C2C2×#466×C15111yescharacteristic
630C2#3055×C15111yescharacteristic
631C2#3100×C15111yescharacteristic
632C2#3106×C15111yescharacteristic
633C2#3205×C15111yescharacteristic
634C2#3212×C15111yescharacteristic
subgroupG/H
center, socleC23×C151C22×D4
commutator, Frattini, cosocleC22×C4C24×C151
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C151 ◁ C22×C42×C151 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×#459×C151C2semidirect
2. C2×#431×C151C2semidirect
3. #2856×C151C2semidirect
4. C4×#121×C151C2semidirect
5. #2033×C151C2semidirect
6. #1999×C151C2semidirect
7. #1982×C151C2semidirect
8. #1970×C151C2semidirect
9. #1947×C151C2semidirect
10. #1934×C151C2semidirect
11. #1802×C151C2semidirect
95. C4⋊C8×C151D4semidirect
150. C22×C4×C151D8semidirect
317. #24650C151direct (N × H)
318. C151#24650direct (N × H)
319. C2×#459C2×C151semidirect
320. C2×#431C2×C151semidirect
321. #2856C2×C151semidirect
322. C4×#121C2×C151semidirect
323. #2033C2×C151semidirect
324. #1999C2×C151semidirect
325. #1982C2×C151semidirect
326. #1970C2×C151semidirect
327. #1947C2×C151semidirect
328. #1934C2×C151semidirect
329. #1802C2×C151semidirect
413. C4⋊C8D4×C151semidirect
468. C22×C4D8×C151semidirect

Maximal subgroups

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

subgroupindex
C2×#459×C1512
C2×#431×C1512
#2856×C1512
C4×#121×C1512
#2033×C1512
#1999×C1512
#1982×C1512
#1970×C1512
#1947×C1512
#1934×C1512
#1802×C1512
#24650151