Finite Group Databasebeta

← C151×#14820 #50319745

Subgroups — C151×#14820 #50319745

Order 38656.

3350 conjugacy classes of subgroups.

The subgroup lattice has 626 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C23×C22⋊C4×C151C211yesmaximal, characteristic
2C2×#397×C151C212yesmaximal, complemented
3C2×#380×C151C211yesmaximal, characteristic, complemented
4C2×#379×C151C212yesmaximal
5#1440×C151C214yesmaximal, complemented
6#1439×C151C212yesmaximal, complemented
7C22⋊#95×C151C211yesmaximal, characteristic, complemented
8C22⋊#95×C151C212yesmaximal, complemented
9C26×C151C2211yescharacteristic
10C24×C4×C151C2211yescharacteristic
11C24×C4×C151C2211yescharacteristic
12C22×C4⋊C4×C151C2211yescharacteristic, complemented
13C22×C4⋊C4×C151C2211yescharacteristic, complemented
14C22×C22⋊C4×C151—24no—
15C22×C22⋊C4×C151—28no—
16C22×C22⋊C4×C151C2214yes—
17C22×C22⋊C4×C151C2212yes—
18C22×C22⋊C4×C151C2212yes—
19C22×C22⋊C4×C151C2212yes—
20C22×C22⋊C4×C151C2212yes—
21C22×C22⋊C4×C151C2214yes—
22#397×C151—28no—
23#380×C151—24no—
24#379×C151—28no—
25C2×#95×C151C2212yescomplemented
26C2×#95×C151C2214yescomplemented
27C2×#95×C151C2212yescomplemented
28C2×#95×C151C2214yescomplemented
29C2×#95×C151C2212yescomplemented
30C25×C151—24no—
31C25×C151—22no—
32C25×C151—24no—
33C25×C151—22no—
34C25×C151—24no—
35C25×C151—24no—
36C25×C151—42no—
37C25×C151—42no—
38C25×C151D414yes—
39C25×C151C2312yes—
40C25×C151C2311yescharacteristic
41C23×C4×C151—24no—
42C23×C4×C151—24no—
43C23×C4×C151—22no—
44C23×C4×C151—24no—
45C23×C4×C151—24no—
46C23×C4×C151—42no—
47C23×C4×C151—42no—
48C23×C4×C151D414yes—
49C23×C4×C151C2314yes—
50C23×C4×C151C2312yes—
51C23×C4×C151C2312yes—
52C23×C4×C151C2311yescharacteristic
53C23×C4×C151C2312yes—
54C23×C4×C151C2311yescharacteristic
55C2×C4⋊C4×C151—22no—
56C2×C4⋊C4×C151—22no—
57C2×C4⋊C4×C151—24no—
58C2×C4⋊C4×C151—42no—
59C2×C22⋊C4×C151—232no—
60C2×C22⋊C4×C151—24no—
61C2×C22⋊C4×C151—24no—
62C2×C22⋊C4×C151—24no—
63C2×C22⋊C4×C151—24no—
64C2×C22⋊C4×C151—24no—
65C2×C22⋊C4×C151—28no—
66C2×C22⋊C4×C151—28no—
67C2×C22⋊C4×C151—24no—
68C2×C22⋊C4×C151—24no—
69C2×C22⋊C4×C151—24no—
70C2×C22⋊C4×C151—28no—
71C2×C22⋊C4×C151—28no—
72C2×C22⋊C4×C151—24no—
73C2×C22⋊C4×C151—24no—
74C2×C22⋊C4×C151—24no—
75C2×C22⋊C4×C151—44no—
76C2×C22⋊C4×C151—44no—
77C2×C22⋊C4×C151D418yes—
78#95×C151—24no—
79#95×C151—24no—
80#95×C151—28no—
81#95×C151—44no—
82#95×C151—42no—
83C24×C151—22no—
84C24×C151—22no—
85C24×C151—22no—
86C24×C151—22no—
87C24×C151—28no—
88C24×C151—28no—
89C24×C151—216no—
90C24×C151—216no—
91C24×C151—28no—
92C24×C151—22no—
93C24×C151—22no—
94C24×C151—22no—
95C24×C151—22no—
96C24×C151—24no—
97C24×C151—24no—
98C24×C151—24no—
99C24×C151—24no—
100C24×C151—216no—
101C24×C151—48no—
102C24×C151—416no—
103C24×C151—416no—
104C24×C151—416no—
105C24×C151—416no—
106C24×C151—44no—
107C24×C151—44no—
108C24×C151—48no—
109C24×C151—44no—
110C24×C151—44no—
111C24×C151—48no—
112C24×C151C2×D414yes—
113C24×C151C2×D414yes—
114C24×C151C2×D412yes—
115C24×C151C2×D412yes—
116C24×C151#4114yes—
117C24×C151#4112yes—
118C24×C151#4114yes—
119C24×C151#4114yes—
120C24×C151C2411yescharacteristic
121C22×C4×C151—22no—
122C22×C4×C151—22no—
123C22×C4×C151—28no—
124C22×C4×C151—28no—
125C22×C4×C151—22no—
126C22×C4×C151—22no—
127C22×C4×C151—22no—
128C22×C4×C151—22no—
129C22×C4×C151—24no—
130C22×C4×C151—22no—
131C22×C4×C151—24no—
132C22×C4×C151—28no—
133C22×C4×C151—24no—
134C22×C4×C151—22no—
135C22×C4×C151—24no—
136C22×C4×C151—22no—
137C22×C4×C151—22no—
138C22×C4×C151—24no—
139C22×C4×C151—22no—
140C22×C4×C151—22no—
141C22×C4×C151—24no—
142C22×C4×C151—22no—
143C22×C4×C151—24no—
144C22×C4×C151—24no—
145C22×C4×C151—24no—
146C22×C4×C151—24no—
147C22×C4×C151—24no—
148C22×C4×C151—24no—
149C22×C4×C151—24no—
150C22×C4×C151—44no—
151C22×C4×C151—416no—
152C22×C4×C151—416no—
153C22×C4×C151—44no—
154C22×C4×C151—44no—
155C22×C4×C151C2×D412yes—
156C22×C4×C151C2×D414yes—
157C22×C4×C151C2×D414yes—
158C22×C4×C151C2×D412yes—
159C4⋊C4×C151—44no—
160C4⋊C4×C151—44no—
161C22⋊C4×C151—216no—
162C22⋊C4×C151—216no—
163C22⋊C4×C151—416no—
164C22⋊C4×C151—416no—
165C22⋊C4×C151—48no—
166C22⋊C4×C151—48no—
167C23×C151—22no—
168C23×C151—24no—
169C23×C151—22no—
170C23×C151—24no—
171C23×C151—24no—
172C23×C151—22no—
173C23×C151—22no—
174C23×C151—24no—
175C23×C151—28no—
176C23×C151—28no—
177C23×C151—28no—
178C23×C151—28no—
179C23×C151—232no—
180C23×C151—24no—
181C23×C151—24no—
182C23×C151—24no—
183C23×C151—28no—
184C23×C151—24no—
185C23×C151—24no—
186C23×C151—24no—
187C23×C151—28no—
188C23×C151—28no—
189C23×C151—28no—
190C23×C151—28no—
191C23×C151—28no—
192C23×C151—464no—
193C23×C151—416no—
194C23×C151—416no—
195C23×C151—416no—
196C23×C151—416no—
197C23×C151—464no—
198C23×C151—416no—
199C23×C151—42no—
200C23×C151—42no—
201C23×C151—44no—
202C23×C151—42no—
203C23×C151—42no—
204C23×C151—44no—
205C23×C151—44no—
206C23×C151—44no—
207C23×C151—44no—
208C23×C151—44no—
209C23×C151—416no—
210C23×C151#12118yes—
211C23×C151#12114yes—
212C23×C151#12318yes—
213C23×C151#12314yes—
214C23×C151#12414yes—
215C23×C151#12618yes—
216C23×C151C22×D411yescharacteristic
217C23×C151C22×D412yes—
218C23×C151C22×D411yescharacteristic
219C23×C151C2×#4111yescharacteristic
220C23×C151C2×#4112yes—
221C23×C151C2×#4112yes—
222C23×C151C2×#4112yes—
223C23×C151H(5,𝔽2)12yes—
224C23×C151H(5,𝔽2)12yes—
225C2×C4×C151—22no—
226C2×C4×C151—22no—
227C2×C4×C151—28no—
228C2×C4×C151—22no—
229C2×C4×C151—24no—
230C2×C4×C151—22no—
231C2×C4×C151—22no—
232C2×C4×C151—28no—
233C2×C4×C151—416no—
234C2×C4×C151—416no—
235C2×C4×C151—42no—
236C2×C4×C151—42no—
237C2×C4×C151—44no—
238C2×C4×C151—44no—
239C2×C4×C151—42no—
240C2×C4×C151—42no—
241C2×C4×C151—44no—
242C2×C4×C151—42no—
243C2×C4×C151—44no—
244C2×C4×C151—44no—
245C2×C4×C151—42no—
246C2×C4×C151—44no—
247C2×C4×C151—44no—
248C2×C4×C151—44no—
249C2×C4×C151—42no—
250C2×C4×C151—42no—
251C2×C4×C151—44no—
252C2×C4×C151—44no—
253C2×C4×C151—44no—
254C2×C4×C151—44no—
255C2×C4×C151—44no—
256C2×C4×C151#12014yes—
257C22×C151—24no—
258C22×C151—24no—
259C22×C151—24no—
260C22×C151—24no—
261C22×C151—216no—
262C22×C151—24no—
263C22×C151—216no—
264C22×C151—24no—
265C22×C151—28no—
266C22×C151—216no—
267C22×C151—464no—
268C22×C151—44no—
269C22×C151—44no—
270C22×C151—44no—
271C22×C151—44no—
272C22×C151—48no—
273C22×C151—44no—
274C22×C151—48no—
275C22×C151—48no—
276C22×C151—44no—
277C22×C151#39718yescomplemented
278C22×C151C2×#12011yescharacteristic
279C22×C151C2×#12111yescharacteristic
280C22×C151C2×#12112yes—
281C22×C151C2×#12311yescharacteristic
282C22×C151C2×#12312yes—
283C22×C151#52511yescharacteristic
284C22×C151#52512yes—
285C22×C151C2×#12411yescharacteristic
286C22×C151C2×#12612yes—
287C22×C151#53411yescharacteristic
288C22×C151#53412yes—
289C22×C151#53511yescharacteristic
290C22×C151#53812yes—
291C22×C151#54614yes—
292C22×C151#54614yes—
293C22×C151#55114yes—
294C22×C151#55114yes—
295C4×C151—24no—
296C4×C151—42no—
297C4×C151—44no—
298C4×C151—82no—
299C4×C151—82no—
300C4×C151—84no—
301C2×C151—28no—
302C2×C151—48no—
303C2×C151C2×#39711yescharacteristic
304C2×C151#240511yescharacteristic
305C2×C151#241214yes—
306C2×C151#243511yescharacteristic
307C2×C151#248014yes—
308C2×C151#248211yescharacteristic
309C2×C151#256111yescharacteristic
310C2×C151#261711yescharacteristic
311C2×C151#284711yescharacteristic
312#14820C15111yesmaximal, characteristic, direct product factor, Sylow
313C151#1482011yescharacteristic, direct product factor, Sylow
314C23×C22⋊C4C2×C15111yescharacteristic
315C2×#397C2×C15112yescomplemented
316C2×#380C2×C15111yescharacteristic, complemented
317C2×#379C2×C15112yes—
318#1440C2×C15114yescomplemented
319#1439C2×C15112yescomplemented
320C22⋊#95C2×C15111yescharacteristic, complemented
321C22⋊#95C2×C15112yescomplemented
322C26C22×C15111yescharacteristic
323C24×C4C22×C15111yescharacteristic
324C24×C4C22×C15111yescharacteristic
325C22×C4⋊C4C22×C15111yescharacteristic, complemented
326C22×C4⋊C4C22×C15111yescharacteristic, complemented
327C22×C22⋊C4—24no—
328C22×C22⋊C4—28no—
329C22×C22⋊C4C22×C15114yes—
330C22×C22⋊C4C22×C15112yes—
331C22×C22⋊C4C22×C15112yes—
332C22×C22⋊C4C22×C15112yes—
333C22×C22⋊C4C22×C15112yes—
334C22×C22⋊C4C22×C15114yes—
335#397—28no—
336#380—24no—
337#379—28no—
338C2×#95C22×C15112yescomplemented
339C2×#95C22×C15114yescomplemented
340C2×#95C22×C15112yescomplemented
341C2×#95C22×C15114yescomplemented
342C2×#95C22×C15112yescomplemented
343C25—24no—
344C25—22no—
345C25—24no—
346C25—22no—
347C25—24no—
348C25—24no—
349C25—42no—
350C25—42no—
351C25D4×C15114yes—
352C25C23×C15112yes—
353C25C23×C15111yescharacteristic
354C23×C4—24no—
355C23×C4—22no—
356C23×C4—24no—
357C23×C4—24no—
358C23×C4—24no—
359C23×C4—42no—
360C23×C4—42no—
361C23×C4D4×C15114yes—
362C23×C4C23×C15112yes—
363C23×C4C23×C15112yes—
364C23×C4C23×C15114yes—
365C23×C4C23×C15111yescharacteristic
366C23×C4C23×C15112yes—
367C23×C4C23×C15111yescharacteristic
368C2×C4⋊C4—22no—
369C2×C4⋊C4—22no—
370C2×C4⋊C4—24no—
371C2×C4⋊C4—42no—
372C2×C22⋊C4—232no—
373C2×C22⋊C4—24no—
374C2×C22⋊C4—24no—
375C2×C22⋊C4—24no—
376C2×C22⋊C4—24no—
377C2×C22⋊C4—24no—
378C2×C22⋊C4—28no—
379C2×C22⋊C4—24no—
380C2×C22⋊C4—24no—
381C2×C22⋊C4—24no—
382C2×C22⋊C4—28no—
383C2×C22⋊C4—28no—
384C2×C22⋊C4—24no—
385C2×C22⋊C4—24no—
386C2×C22⋊C4—24no—
387C2×C22⋊C4—28no—
388C2×C22⋊C4—44no—
389C2×C22⋊C4—44no—
390C2×C22⋊C4D4×C15118yes—
391#95—24no—
392#95—24no—
393#95—28no—
394#95—44no—
395#95—42no—
396C24—22no—
397C24—22no—
398C24—22no—
399C24—22no—
400C24—28no—
401C24—216no—
402C24—28no—
403C24—216no—
404C24—28no—
405C24—22no—
406C24—22no—
407C24—22no—
408C24—22no—
409C24—24no—
410C24—24no—
411C24—24no—
412C24—24no—
413C24—216no—
414C24—48no—
415C24—416no—
416C24—416no—
417C24—416no—
418C24—416no—
419C24—44no—
420C24—44no—
421C24—48no—
422C24—44no—
423C24—44no—
424C24—48no—
425C24C2×D4×C15114yes—
426C24C2×D4×C15114yes—
427C24C2×D4×C15112yes—
428C24C2×D4×C15112yes—
429C24#41×C15114yes—
430C24#41×C15112yes—
431C24#41×C15114yes—
432C24#41×C15114yes—
433C24C24×C15111yescharacteristic
434C22×C4—22no—
435C22×C4—22no—
436C22×C4—28no—
437C22×C4—28no—
438C22×C4—22no—
439C22×C4—22no—
440C22×C4—22no—
441C22×C4—22no—
442C22×C4—24no—
443C22×C4—22no—
444C22×C4—24no—
445C22×C4—28no—
446C22×C4—24no—
447C22×C4—22no—
448C22×C4—24no—
449C22×C4—22no—
450C22×C4—22no—
451C22×C4—24no—
452C22×C4—22no—
453C22×C4—22no—
454C22×C4—24no—
455C22×C4—22no—
456C22×C4—24no—
457C22×C4—24no—
458C22×C4—24no—
459C22×C4—24no—
460C22×C4—24no—
461C22×C4—24no—
462C22×C4—24no—
463C22×C4—44no—
464C22×C4—416no—
465C22×C4—416no—
466C22×C4—44no—
467C22×C4—44no—
468C22×C4C2×D4×C15112yes—
469C22×C4C2×D4×C15114yes—
470C22×C4C2×D4×C15114yes—
471C22×C4C2×D4×C15112yes—
472C4⋊C4—44no—
473C4⋊C4—44no—
474C22⋊C4—216no—
475C22⋊C4—216no—
476C22⋊C4—416no—
477C22⋊C4—416no—
478C22⋊C4—48no—
479C22⋊C4—48no—
480C23—22no—
481C23—24no—
482C23—24no—
483C23—22no—
484C23—22no—
485C23—24no—
486C23—22no—
487C23—24no—
488C23—28no—
489C23—28no—
490C23—28no—
491C23—28no—
492C23—232no—
493C23—24no—
494C23—24no—
495C23—24no—
496C23—28no—
497C23—24no—
498C23—24no—
499C23—24no—
500C23—28no—
501C23—28no—
502C23—28no—
503C23—28no—
504C23—28no—
505C23—464no—
506C23—416no—
507C23—416no—
508C23—416no—
509C23—464no—
510C23—416no—
511C23—416no—
512C23—416no—
513C23—42no—
514C23—42no—
515C23—44no—
516C23—42no—
517C23—42no—
518C23—44no—
519C23—44no—
520C23—44no—
521C23—44no—
522C23—44no—
523C23#121×C15118yes—
524C23#121×C15114yes—
525C23#123×C15118yes—
526C23#123×C15114yes—
527C23#124×C15114yes—
528C23#126×C15118yes—
529C23C22×D4×C15111yescharacteristic
530C23C22×D4×C15112yes—
531C23C22×D4×C15111yescharacteristic
532C23C2×#41×C15111yescharacteristic
533C23C2×#41×C15112yes—
534C23C2×#41×C15112yes—
535C23C2×#41×C15112yes—
536C23H(5,𝔽2)×C15112yes—
537C23H(5,𝔽2)×C15112yes—
538C2×C4—22no—
539C2×C4—22no—
540C2×C4—28no—
541C2×C4—22no—
542C2×C4—24no—
543C2×C4—22no—
544C2×C4—22no—
545C2×C4—28no—
546C2×C4—416no—
547C2×C4—416no—
548C2×C4—42no—
549C2×C4—42no—
550C2×C4—44no—
551C2×C4—44no—
552C2×C4—42no—
553C2×C4—42no—
554C2×C4—44no—
555C2×C4—42no—
556C2×C4—44no—
557C2×C4—44no—
558C2×C4—44no—
559C2×C4—42no—
560C2×C4—44no—
561C2×C4—44no—
562C2×C4—42no—
563C2×C4—42no—
564C2×C4—44no—
565C2×C4—44no—
566C2×C4—44no—
567C2×C4—44no—
568C2×C4—44no—
569C2×C4#120×C15114yes—
570C22—24no—
571C22—24no—
572C22—24no—
573C22—216no—
574C22—24no—
575C22—216no—
576C22—24no—
577C22—24no—
578C22—28no—
579C22—216no—
580C22—464no—
581C22—44no—
582C22—44no—
583C22—44no—
584C22—48no—
585C22—44no—
586C22—48no—
587C22—48no—
588C22—44no—
589C22—44no—
590C22#397×C15118yescomplemented
591C22C2×#120×C15111yescharacteristic
592C22C2×#121×C15111yescharacteristic
593C22C2×#121×C15112yes—
594C22C2×#123×C15111yescharacteristic
595C22C2×#123×C15112yes—
596C22#525×C15112yes—
597C22#525×C15111yescharacteristic
598C22C2×#124×C15111yescharacteristic
599C22C2×#126×C15112yes—
600C22#534×C15111yescharacteristic
601C22#534×C15112yes—
602C22#535×C15111yescharacteristic
603C22#538×C15112yes—
604C22#546×C15114yes—
605C22#546×C15114yes—
606C22#551×C15114yes—
607C22#551×C15114yes—
608C4—24no—
609C4—42no—
610C4—44no—
611C4—82no—
612C4—82no—
613C4—84no—
614C2—28no—
615C2—48no—
616C2C2×#397×C15111yescharacteristic
617C2#2405×C15111yescharacteristic
618C2#2412×C15114yes—
619C2#2435×C15111yescharacteristic
620C2#2480×C15114yes—
621C2#2482×C15111yescharacteristic
622C2#2561×C15111yescharacteristic
623C2#2617×C15111yescharacteristic
624C2#2847×C15111yescharacteristic
subgroupG/H
center, socleC24×C151C24
commutator, Frattini, cosocleC24C24×C151
prime radicalC26×C151C22
LCSG ▷ C24 ▷ C1
UCSC1 ◁ C24×C151 ◁ G

Complements

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

NH ≅ G/Ntype
2. C2×#397×C151C2semidirect
3. C2×#380×C151C2semidirect
5. #1440×C151C2semidirect
6. #1439×C151C2semidirect
7. C22⋊#95×C151C2semidirect
8. C22⋊#95×C151C2semidirect
12. C22×C4⋊C4×C151C22semidirect
13. C22×C4⋊C4×C151C22semidirect
25. C2×#95×C151C22semidirect
26. C2×#95×C151C22semidirect
27. C2×#95×C151C22semidirect
28. C2×#95×C151C22semidirect
29. C2×#95×C151C22semidirect
277. C22×C151#397semidirect
312. #14820C151direct (N × H)
313. C151#14820direct (N × H)
315. C2×#397C2×C151semidirect
316. C2×#380C2×C151semidirect
318. #1440C2×C151semidirect
319. #1439C2×C151semidirect
320. C22⋊#95C2×C151semidirect
321. C22⋊#95C2×C151semidirect
325. C22×C4⋊C4C22×C151semidirect
326. C22×C4⋊C4C22×C151semidirect
338. C2×#95C22×C151semidirect
339. C2×#95C22×C151semidirect
340. C2×#95C22×C151semidirect
341. C2×#95C22×C151semidirect
342. C2×#95C22×C151semidirect
590. C22#397×C151semidirect

Maximal subgroups

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

subgroupindex
C23×C22⋊C4×C1512
C2×#397×C1512
C2×#380×C1512
C2×#379×C1512
#1440×C1512
#1439×C1512
C22⋊#95×C1512
#14820151