Finite Group Databasebeta

← C151×#15061 #50319986

Subgroups — C151×#15061 #50319986

Order 38656.

1526 conjugacy classes of subgroups.

The subgroup lattice has 650 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#397×C151C212yesmaximal
2C2×#380×C151C211yesmaximal, characteristic
3C2×C4×C22⋊C4×C151C211yesmaximal, characteristic
4#1445×C151C211yesmaximal, characteristic, complemented
5#1445×C151C211yesmaximal, characteristic, complemented
6#1444×C151C211yesmaximal, characteristic, complemented
7#1442×C151C211yesmaximal, characteristic, complemented
8#1440×C151C212yesmaximal
9#1436×C151C212yesmaximal, complemented
10#1434×C151C212yesmaximal, complemented
11C22⋊#95×C151C211yesmaximal, characteristic
12C24×C4×C151C2211yescharacteristic
13C22×C4⋊C4×C151C2211yescharacteristic
14C22×C4⋊C4×C151C2212yes—
15C22×C4⋊C4×C151C2211yescharacteristic
16C22×C22⋊C4×C151C2212yes—
17C22×C22⋊C4×C151C2211yescharacteristic
18C22×C22⋊C4×C151C2212yes—
19C22×C22⋊C4×C151C2211yescharacteristic
20C22×C42×C151C2211yescharacteristic
21C22×C42×C151C2211yescharacteristic
22#397×C151—28no—
23#380×C151—24no—
24C4×C22⋊C4×C151—24no—
25C2×#95×C151C2212yes—
26C2×#95×C151C2212yes—
27C2×#95×C151C2212yes—
28C2×#95×C151C2212yes—
29C2×#95×C151C2211yescharacteristic
30C2×#95×C151C2211yescharacteristic
31C2×#95×C151C2212yes—
32C2×#95×C151C2212yes—
33C2×#95×C151C2212yes—
34C2×#95×C151C2212yes—
35C2×#95×C151C2211yescharacteristic
36C2×#95×C151C2211yescharacteristic
37C2×#95×C151C2212yes—
38C25×C151C2311yescharacteristic
39C23×C4×C151—24no—
40C23×C4×C151—22no—
41C23×C4×C151—22no—
42C23×C4×C151—42no—
43C23×C4×C151D414yes—
44C23×C4×C151C2312yes—
45C23×C4×C151C2312yes—
46C23×C4×C151C2312yes—
47C23×C4×C151C2311yescharacteristic
48C23×C4×C151C2311yescharacteristic
49C23×C4×C151C2311yescharacteristic
50C23×C4×C151C2311yescharacteristic
51C23×C4×C151C2312yes—
52C23×C4×C151C2311yescharacteristic
53C23×C4×C151C2311yescharacteristic
54C2×C4⋊C4×C151—22no—
55C2×C4⋊C4×C151—22no—
56C2×C4⋊C4×C151—24no—
57C2×C4⋊C4×C151—24no—
58C2×C4⋊C4×C151—22no—
59C2×C4⋊C4×C151—22no—
60C2×C4⋊C4×C151—42no—
61C2×C4⋊C4×C151—42no—
62C2×C22⋊C4×C151—22no—
63C2×C22⋊C4×C151—22no—
64C2×C22⋊C4×C151—24no—
65C2×C22⋊C4×C151—22no—
66C2×C22⋊C4×C151—22no—
67C2×C22⋊C4×C151—24no—
68C2×C22⋊C4×C151—24no—
69C2×C22⋊C4×C151—24no—
70C2×C22⋊C4×C151—22no—
71C2×C22⋊C4×C151—24no—
72C2×C22⋊C4×C151—42no—
73C2×C22⋊C4×C151D414yes—
74C2×C42×C151—22no—
75C2×C42×C151—22no—
76C2×C42×C151—24no—
77C2×C42×C151—42no—
78#95×C151—22no—
79#95×C151—22no—
80#95×C151—24no—
81#95×C151—24no—
82#95×C151—24no—
83#95×C151—24no—
84#95×C151—22no—
85#95×C151—24no—
86#95×C151—24no—
87#95×C151—24no—
88#95×C151—24no—
89#95×C151—22no—
90#95×C151—42no—
91C24×C151—21no—
92C24×C151—21no—
93C24×C151—22no—
94C24×C151—21no—
95C24×C151—21no—
96C24×C151—22no—
97C24×C151—22no—
98C24×C151—22no—
99C24×C151C2×D412yes—
100C24×C151C2×D412yes—
101C24×C151#4112yes—
102C24×C151C2411yescharacteristic
103C22×C4×C151—22no—
104C22×C4×C151—21no—
105C22×C4×C151—21no—
106C22×C4×C151—22no—
107C22×C4×C151—22no—
108C22×C4×C151—21no—
109C22×C4×C151—21no—
110C22×C4×C151—21no—
111C22×C4×C151—21no—
112C22×C4×C151—22no—
113C22×C4×C151—22no—
114C22×C4×C151—22no—
115C22×C4×C151—22no—
116C22×C4×C151—22no—
117C22×C4×C151—22no—
118C22×C4×C151—22no—
119C22×C4×C151—21no—
120C22×C4×C151—21no—
121C22×C4×C151—21no—
122C22×C4×C151—21no—
123C22×C4×C151—22no—
124C22×C4×C151—22no—
125C22×C4×C151—22no—
126C22×C4×C151—22no—
127C22×C4×C151—22no—
128C22×C4×C151—22no—
129C22×C4×C151—22no—
130C22×C4×C151—28no—
131C22×C4×C151—28no—
132C22×C4×C151—22no—
133C22×C4×C151—22no—
134C22×C4×C151—22no—
135C22×C4×C151—22no—
136C22×C4×C151—22no—
137C22×C4×C151—22no—
138C22×C4×C151—22no—
139C22×C4×C151—22no—
140C22×C4×C151—22no—
141C22×C4×C151—22no—
142C22×C4×C151—22no—
143C22×C4×C151—22no—
144C22×C4×C151—22no—
145C22×C4×C151—22no—
146C22×C4×C151—22no—
147C22×C4×C151—22no—
148C22×C4×C151—22no—
149C22×C4×C151—22no—
150C22×C4×C151—22no—
151C22×C4×C151—22no—
152C22×C4×C151—22no—
153C22×C4×C151—44no—
154C22×C4×C151—48no—
155C22×C4×C151—48no—
156C22×C4×C151C2×D412yes—
157C22×C4×C151C2×D412yes—
158C22×C4×C151C2×D412yes—
159C22×C4×C151C2×D412yes—
160C22×C4×C151#4112yes—
161C22×C4×C151#4112yes—
162C22×C4×C151#4114yes—
163C22×C4×C151#4114yes—
164C22×C4×C151#4112yes—
165C22×C4×C151#4112yes—
166C4⋊C4×C151—48no—
167C4⋊C4×C151—44no—
168C4⋊C4×C151—44no—
169C22⋊C4×C151—28no—
170C22⋊C4×C151—28no—
171C22⋊C4×C151—48no—
172C22⋊C4×C151—48no—
173C42×C151—44no—
174C42×C151—44no—
175C23×C151—22no—
176C23×C151—22no—
177C23×C151—22no—
178C23×C151—22no—
179C23×C151—22no—
180C23×C151—22no—
181C23×C151—22no—
182C23×C151—22no—
183C23×C151—22no—
184C23×C151—22no—
185C23×C151—24no—
186C23×C151—24no—
187C23×C151—24no—
188C23×C151—24no—
189C23×C151—42no—
190C23×C151—42no—
191C23×C151—42no—
192C23×C151—42no—
193C23×C151—42no—
194C23×C151—42no—
195C23×C151—42no—
196C23×C151—42no—
197C23×C151#12114yes—
198C23×C151C22×D411yescharacteristic
199C23×C151C22×D411yescharacteristic
200C23×C151C2×#4111yescharacteristic
201C23×C151C2×#4112yes—
202C23×C151C2×#4111yescharacteristic
203C23×C151C2×#4111yescharacteristic
204C23×C151C2×#4111yescharacteristic
205C23×C151C2×#4111yescharacteristic
206C23×C151C2×#4112yes—
207C23×C151H(5,𝔽2)12yes—
208C23×C1512−1+412yes—
209C2×C4×C151—22no—
210C2×C4×C151—22no—
211C2×C4×C151—22no—
212C2×C4×C151—22no—
213C2×C4×C151—24no—
214C2×C4×C151—24no—
215C2×C4×C151—24no—
216C2×C4×C151—24no—
217C2×C4×C151—22no—
218C2×C4×C151—22no—
219C2×C4×C151—22no—
220C2×C4×C151—22no—
221C2×C4×C151—24no—
222C2×C4×C151—24no—
223C2×C4×C151—24no—
224C2×C4×C151—24no—
225C2×C4×C151—24no—
226C2×C4×C151—24no—
227C2×C4×C151—24no—
228C2×C4×C151—416no—
229C2×C4×C151—41no—
230C2×C4×C151—41no—
231C2×C4×C151—42no—
232C2×C4×C151—41no—
233C2×C4×C151—41no—
234C2×C4×C151—42no—
235C2×C4×C151—41no—
236C2×C4×C151—41no—
237C2×C4×C151—41no—
238C2×C4×C151—41no—
239C2×C4×C151—42no—
240C2×C4×C151—42no—
241C2×C4×C151—42no—
242C2×C4×C151—42no—
243C2×C4×C151—42no—
244C2×C4×C151—42no—
245C2×C4×C151—42no—
246C2×C4×C151—42no—
247C2×C4×C151—42no—
248C2×C4×C151—42no—
249C2×C4×C151—42no—
250C2×C4×C151—42no—
251C2×C4×C151—42no—
252C2×C4×C151—42no—
253C2×C4×C151—42no—
254C2×C4×C151—42no—
255C2×C4×C151—42no—
256C2×C4×C151—42no—
257C2×C4×C151—42no—
258C2×C4×C151—42no—
259C2×C4×C151—42no—
260C2×C4×C151—42no—
261C2×C4×C151—42no—
262C2×C4×C151—42no—
263C2×C4×C151—42no—
264C2×C4×C151—42no—
265C2×C4×C151—42no—
266C2×C4×C151#12314yes—
267C2×C4×C151#12314yes—
268C22×C151—24no—
269C22×C151—24no—
270C22×C151—24no—
271C22×C151—44no—
272C22×C151—42no—
273C22×C151—42no—
274C22×C151—42no—
275C22×C151—42no—
276C22×C151—44no—
277C22×C151—44no—
278C22×C151—44no—
279C22×C151C2×#12111yescharacteristic
280C22×C151C2×#12311yescharacteristic
281C22×C151C2×#12311yescharacteristic
282C22×C151#52511yescharacteristic
283C22×C151#52911yescharacteristic
284C22×C151#52912yes—
285C22×C151#52911yescharacteristic
286C22×C151#52912yes—
287C22×C151#53211yescharacteristic
288C22×C151#53211yescharacteristic
289C22×C151#53211yescharacteristic
290C22×C151#53411yescharacteristic
291C22×C151#53611yescharacteristic
292C22×C151#53912yes—
293C22×C151#54212yes—
294C22×C151#54612yes—
295C22×C151#54712yes—
296C22×C151#55112yes—
297C22×C151#55112yes—
298C22×C151#55212yes—
299C22×C151#55212yes—
300C22×C151#55312yes—
301C22×C151#55612yes—
302C4×C151—24no—
303C4×C151—24no—
304C4×C151—42no—
305C4×C151—42no—
306C4×C151—42no—
307C4×C151—42no—
308C4×C151—44no—
309C4×C151—82no—
310C4×C151—82no—
311C4×C151—82no—
312C2×C151—44no—
313C2×C151#239511yescharacteristic
314C2×C151#248311yescharacteristic
315C2×C151#248611yescharacteristic
316C2×C151#249911yescharacteristic
317C2×C151#252112yes—
318C2×C151#253012yes—
319C2×C151#254311yescharacteristic
320C2×C151#255312yes—
321C2×C151#257712yes—
322C2×C151#263811yescharacteristic
323C2×C151#285411yescharacteristic
324#15061C15111yesmaximal, characteristic, direct product factor, Sylow
325C151#1506111yescharacteristic, direct product factor, Sylow
326C2×#397C2×C15112yes—
327C2×#380C2×C15111yescharacteristic
328C2×C4×C22⋊C4C2×C15111yescharacteristic
329#1445C2×C15111yescharacteristic, complemented
330#1445C2×C15111yescharacteristic, complemented
331#1444C2×C15111yescharacteristic, complemented
332#1442C2×C15111yescharacteristic, complemented
333#1440C2×C15112yes—
334#1436C2×C15112yescomplemented
335#1434C2×C15112yescomplemented
336C22⋊#95C2×C15111yescharacteristic
337C24×C4C22×C15111yescharacteristic
338C22×C4⋊C4C22×C15111yescharacteristic
339C22×C4⋊C4C22×C15112yes—
340C22×C4⋊C4C22×C15111yescharacteristic
341C22×C22⋊C4C22×C15112yes—
342C22×C22⋊C4C22×C15111yescharacteristic
343C22×C22⋊C4C22×C15112yes—
344C22×C22⋊C4C22×C15111yescharacteristic
345C22×C42C22×C15111yescharacteristic
346C22×C42C22×C15111yescharacteristic
347#397—28no—
348#380—24no—
349C4×C22⋊C4—24no—
350C2×#95C22×C15112yes—
351C2×#95C22×C15112yes—
352C2×#95C22×C15112yes—
353C2×#95C22×C15112yes—
354C2×#95C22×C15111yescharacteristic
355C2×#95C22×C15111yescharacteristic
356C2×#95C22×C15112yes—
357C2×#95C22×C15112yes—
358C2×#95C22×C15112yes—
359C2×#95C22×C15112yes—
360C2×#95C22×C15111yescharacteristic
361C2×#95C22×C15111yescharacteristic
362C2×#95C22×C15112yes—
363C25C23×C15111yescharacteristic
364C23×C4—24no—
365C23×C4—22no—
366C23×C4—22no—
367C23×C4—42no—
368C23×C4D4×C15114yes—
369C23×C4C23×C15112yes—
370C23×C4C23×C15112yes—
371C23×C4C23×C15112yes—
372C23×C4C23×C15112yes—
373C23×C4C23×C15111yescharacteristic
374C23×C4C23×C15111yescharacteristic
375C23×C4C23×C15111yescharacteristic
376C23×C4C23×C15111yescharacteristic
377C23×C4C23×C15111yescharacteristic
378C23×C4C23×C15111yescharacteristic
379C2×C4⋊C4—24no—
380C2×C4⋊C4—22no—
381C2×C4⋊C4—22no—
382C2×C4⋊C4—22no—
383C2×C4⋊C4—22no—
384C2×C4⋊C4—24no—
385C2×C4⋊C4—42no—
386C2×C4⋊C4—42no—
387C2×C22⋊C4—22no—
388C2×C22⋊C4—22no—
389C2×C22⋊C4—22no—
390C2×C22⋊C4—22no—
391C2×C22⋊C4—22no—
392C2×C22⋊C4—24no—
393C2×C22⋊C4—24no—
394C2×C22⋊C4—24no—
395C2×C22⋊C4—24no—
396C2×C22⋊C4—24no—
397C2×C22⋊C4—42no—
398C2×C22⋊C4D4×C15114yes—
399C2×C42—24no—
400C2×C42—22no—
401C2×C42—22no—
402C2×C42—42no—
403#95—22no—
404#95—24no—
405#95—24no—
406#95—24no—
407#95—24no—
408#95—22no—
409#95—22no—
410#95—22no—
411#95—24no—
412#95—24no—
413#95—24no—
414#95—24no—
415#95—42no—
416C24—21no—
417C24—21no—
418C24—22no—
419C24—21no—
420C24—21no—
421C24—22no—
422C24—22no—
423C24—22no—
424C24C2×D4×C15112yes—
425C24C2×D4×C15112yes—
426C24#41×C15112yes—
427C24C24×C15111yescharacteristic
428C22×C4—22no—
429C22×C4—21no—
430C22×C4—21no—
431C22×C4—22no—
432C22×C4—22no—
433C22×C4—21no—
434C22×C4—21no—
435C22×C4—21no—
436C22×C4—21no—
437C22×C4—22no—
438C22×C4—22no—
439C22×C4—22no—
440C22×C4—22no—
441C22×C4—22no—
442C22×C4—22no—
443C22×C4—22no—
444C22×C4—21no—
445C22×C4—21no—
446C22×C4—21no—
447C22×C4—21no—
448C22×C4—22no—
449C22×C4—22no—
450C22×C4—22no—
451C22×C4—22no—
452C22×C4—22no—
453C22×C4—22no—
454C22×C4—22no—
455C22×C4—28no—
456C22×C4—28no—
457C22×C4—22no—
458C22×C4—22no—
459C22×C4—22no—
460C22×C4—22no—
461C22×C4—22no—
462C22×C4—22no—
463C22×C4—22no—
464C22×C4—22no—
465C22×C4—22no—
466C22×C4—22no—
467C22×C4—22no—
468C22×C4—22no—
469C22×C4—22no—
470C22×C4—22no—
471C22×C4—22no—
472C22×C4—22no—
473C22×C4—22no—
474C22×C4—22no—
475C22×C4—22no—
476C22×C4—22no—
477C22×C4—22no—
478C22×C4—44no—
479C22×C4—48no—
480C22×C4—48no—
481C22×C4C2×D4×C15112yes—
482C22×C4C2×D4×C15112yes—
483C22×C4C2×D4×C15112yes—
484C22×C4C2×D4×C15112yes—
485C22×C4#41×C15112yes—
486C22×C4#41×C15112yes—
487C22×C4#41×C15114yes—
488C22×C4#41×C15114yes—
489C22×C4#41×C15112yes—
490C22×C4#41×C15112yes—
491C4⋊C4—48no—
492C4⋊C4—44no—
493C4⋊C4—44no—
494C22⋊C4—28no—
495C22⋊C4—28no—
496C22⋊C4—48no—
497C22⋊C4—48no—
498C42—44no—
499C42—44no—
500C23—22no—
501C23—22no—
502C23—22no—
503C23—22no—
504C23—22no—
505C23—22no—
506C23—22no—
507C23—22no—
508C23—22no—
509C23—22no—
510C23—24no—
511C23—24no—
512C23—24no—
513C23—24no—
514C23—42no—
515C23—42no—
516C23—42no—
517C23—42no—
518C23—42no—
519C23—42no—
520C23—42no—
521C23—42no—
522C23#121×C15114yes—
523C23C22×D4×C15111yescharacteristic
524C23C22×D4×C15111yescharacteristic
525C23C2×#41×C15111yescharacteristic
526C23C2×#41×C15112yes—
527C23C2×#41×C15111yescharacteristic
528C23C2×#41×C15111yescharacteristic
529C23C2×#41×C15111yescharacteristic
530C23C2×#41×C15111yescharacteristic
531C23C2×#41×C15112yes—
532C23H(5,𝔽2)×C15112yes—
533C232−1+4×C15112yes—
534C2×C4—22no—
535C2×C4—22no—
536C2×C4—22no—
537C2×C4—22no—
538C2×C4—24no—
539C2×C4—24no—
540C2×C4—24no—
541C2×C4—24no—
542C2×C4—22no—
543C2×C4—22no—
544C2×C4—22no—
545C2×C4—22no—
546C2×C4—24no—
547C2×C4—24no—
548C2×C4—24no—
549C2×C4—24no—
550C2×C4—24no—
551C2×C4—24no—
552C2×C4—24no—
553C2×C4—416no—
554C2×C4—41no—
555C2×C4—41no—
556C2×C4—42no—
557C2×C4—41no—
558C2×C4—41no—
559C2×C4—42no—
560C2×C4—41no—
561C2×C4—41no—
562C2×C4—41no—
563C2×C4—41no—
564C2×C4—42no—
565C2×C4—42no—
566C2×C4—42no—
567C2×C4—42no—
568C2×C4—42no—
569C2×C4—42no—
570C2×C4—42no—
571C2×C4—42no—
572C2×C4—42no—
573C2×C4—42no—
574C2×C4—42no—
575C2×C4—42no—
576C2×C4—42no—
577C2×C4—42no—
578C2×C4—42no—
579C2×C4—42no—
580C2×C4—42no—
581C2×C4—42no—
582C2×C4—42no—
583C2×C4—42no—
584C2×C4—42no—
585C2×C4—42no—
586C2×C4—42no—
587C2×C4—42no—
588C2×C4—42no—
589C2×C4—42no—
590C2×C4—42no—
591C2×C4#123×C15114yes—
592C2×C4#123×C15114yes—
593C22—24no—
594C22—24no—
595C22—24no—
596C22—42no—
597C22—42no—
598C22—42no—
599C22—42no—
600C22—44no—
601C22—44no—
602C22—44no—
603C22—44no—
604C22C2×#121×C15111yescharacteristic
605C22C2×#123×C15111yescharacteristic
606C22C2×#123×C15111yescharacteristic
607C22#525×C15111yescharacteristic
608C22#529×C15111yescharacteristic
609C22#529×C15111yescharacteristic
610C22#529×C15112yes—
611C22#529×C15112yes—
612C22#532×C15111yescharacteristic
613C22#532×C15111yescharacteristic
614C22#532×C15111yescharacteristic
615C22#534×C15111yescharacteristic
616C22#536×C15111yescharacteristic
617C22#539×C15112yes—
618C22#542×C15112yes—
619C22#546×C15112yes—
620C22#547×C15112yes—
621C22#551×C15112yes—
622C22#551×C15112yes—
623C22#552×C15112yes—
624C22#552×C15112yes—
625C22#553×C15112yes—
626C22#556×C15112yes—
627C4—24no—
628C4—24no—
629C4—42no—
630C4—42no—
631C4—42no—
632C4—42no—
633C4—44no—
634C4—82no—
635C4—82no—
636C4—82no—
637C2—44no—
638C2#2395×C15111yescharacteristic
639C2#2483×C15111yescharacteristic
640C2#2486×C15111yescharacteristic
641C2#2499×C15111yescharacteristic
642C2#2521×C15112yes—
643C2#2530×C15112yes—
644C2#2543×C15111yescharacteristic
645C2#2553×C15112yes—
646C2#2577×C15112yes—
647C2#2638×C15111yescharacteristic
648C2#2854×C15111yescharacteristic
subgroupG/H
center, socleC24×C151C24
commutator, Frattini, cosocleC24C24×C151
prime radicalC25×C151C23
LCSG ▷ C24 ▷ C1
UCSC1 ◁ C24×C151 ◁ G

Complements

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

NH ≅ G/Ntype
4. #1445×C151C2semidirect
5. #1445×C151C2semidirect
6. #1444×C151C2semidirect
7. #1442×C151C2semidirect
9. #1436×C151C2semidirect
10. #1434×C151C2semidirect
324. #15061C151direct (N × H)
325. C151#15061direct (N × H)
329. #1445C2×C151semidirect
330. #1445C2×C151semidirect
331. #1444C2×C151semidirect
332. #1442C2×C151semidirect
334. #1436C2×C151semidirect
335. #1434C2×C151semidirect

Maximal subgroups

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

subgroupindex
C2×#397×C1512
C2×#380×C1512
C2×C4×C22⋊C4×C1512
#1445×C1512
#1444×C1512
#1442×C1512
#1440×C1512
#1436×C1512
#1434×C1512
C22⋊#95×C1512
#15061151