Finite Group Databasebeta

← C151×#13888 #50318813

Subgroups — C151×#13888 #50318813

Order 38656.

1602 conjugacy classes of subgroups.

The subgroup lattice has 654 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#382×C151C211yesmaximal, characteristic, complemented
2C2×C4×C22⋊C4×C151C211yesmaximal, characteristic
3C2×C4×C22⋊C4×C151C211yesmaximal, characteristic
4#1440×C151C212yesmaximal
5#1439×C151C212yesmaximal
6#1436×C151C212yesmaximal, complemented
7#1434×C151C211yesmaximal, characteristic, complemented
8#1434×C151C211yesmaximal, characteristic, complemented
9#1434×C151C212yesmaximal, complemented
10#1434×C151C211yesmaximal, characteristic, complemented
11C22⋊#95×C151C211yesmaximal, characteristic
12C24×C4×C151C2211yescharacteristic
13C22×C4⋊C4×C151C2212yes—
14C22×C22⋊C4×C151C2212yes—
15C22×C22⋊C4×C151C2211yescharacteristic
16C22×C22⋊C4×C151C2211yescharacteristic
17C22×C22⋊C4×C151C2212yes—
18C22×C42×C151C2212yes—
19C22×C42×C151C2211yescharacteristic
20C22×C42×C151C2211yescharacteristic
21#382×C151—24no—
22C4×C22⋊C4×C151—24no—
23C4×C22⋊C4×C151C418yescomplemented
24C2×#95×C151C2211yescharacteristic
25C2×#95×C151C2212yes—
26C2×#95×C151C2211yescharacteristic
27C2×#95×C151C2212yes—
28C2×#95×C151C2212yes—
29C2×#95×C151C2211yescharacteristic
30C2×#95×C151C2212yes—
31C2×#95×C151C2212yes—
32C2×#95×C151C2212yes—
33C2×#95×C151C2212yes—
34C2×#95×C151C2212yes—
35C2×#95×C151C2211yescharacteristic
36C2×#95×C151C2211yescharacteristic
37C2×#95×C151C2211yescharacteristic
38C25×C151C2311yescharacteristic
39C23×C4×C151—22no—
40C23×C4×C151—24no—
41C23×C4×C151—22no—
42C23×C4×C151—42no—
43C23×C4×C151C2×C414yes—
44C23×C4×C151C2312yes—
45C23×C4×C151C2312yes—
46C23×C4×C151C2311yescharacteristic
47C23×C4×C151C2311yescharacteristic
48C23×C4×C151C2311yescharacteristic
49C23×C4×C151C2312yes—
50C23×C4×C151C2312yes—
51C23×C4×C151C2311yescharacteristic
52C23×C4×C151C2311yescharacteristic
53C23×C4×C151C2311yescharacteristic
54C2×C4⋊C4×C151—24no—
55C2×C4⋊C4×C151—24no—
56C2×C4⋊C4×C151—42no—
57C2×C22⋊C4×C151—24no—
58C2×C22⋊C4×C151—24no—
59C2×C22⋊C4×C151—22no—
60C2×C22⋊C4×C151—22no—
61C2×C22⋊C4×C151—24no—
62C2×C22⋊C4×C151—24no—
63C2×C22⋊C4×C151—24no—
64C2×C22⋊C4×C151—42no—
65C2×C22⋊C4×C151—42no—
66C2×C22⋊C4×C151C2×C414yes—
67C2×C22⋊C4×C151C2×C414yes—
68C2×C42×C151—22no—
69C2×C42×C151—22no—
70C2×C42×C151—24no—
71C2×C42×C151—24no—
72C2×C42×C151—42no—
73C2×C42×C151—42no—
74C2×C42×C151C2×C414yes—
75C2×C42×C151C2×C414yes—
76#95×C151—22no—
77#95×C151—24no—
78#95×C151—22no—
79#95×C151—24no—
80#95×C151—24no—
81#95×C151—24no—
82#95×C151—24no—
83#95×C151—22no—
84#95×C151—42no—
85#95×C151—42no—
86#95×C151—42no—
87#95×C151C2×C414yes—
88#95×C151C2×C414yes—
89#95×C151D414yes—
90C24×C151—21no—
91C24×C151—21no—
92C24×C151—21no—
93C24×C151—22no—
94C24×C151—22no—
95C24×C151—21no—
96C24×C151—21no—
97C24×C151—22no—
98C24×C151—21no—
99C24×C151C22×C412yes—
100C24×C151#4114yes—
101C24×C151C2411yescharacteristic
102C22×C4×C151—21no—
103C22×C4×C151—21no—
104C22×C4×C151—21no—
105C22×C4×C151—22no—
106C22×C4×C151—21no—
107C22×C4×C151—22no—
108C22×C4×C151—22no—
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—21no—
117C22×C4×C151—22no—
118C22×C4×C151—22no—
119C22×C4×C151—22no—
120C22×C4×C151—22no—
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—21no—
128C22×C4×C151—22no—
129C22×C4×C151—22no—
130C22×C4×C151—22no—
131C22×C4×C151—22no—
132C22×C4×C151—22no—
133C22×C4×C151—21no—
134C22×C4×C151—22no—
135C22×C4×C151—28no—
136C22×C4×C151—28no—
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—44no—
152C22×C4×C151—48no—
153C22×C4×C151—48no—
154C22×C4×C151C22×C412yes—
155C22×C4×C151C22×C412yes—
156C22×C4×C151C22×C412yes—
157C22×C4×C151C22×C412yes—
158C22×C4×C151C22×C412yes—
159C22×C4×C151C22×C412yes—
160C22×C4×C151C2×D414yes—
161C22×C4×C151C2×D412yes—
162C22×C4×C151#4114yes—
163C22×C4×C151#4112yes—
164C22×C4×C151#4114yes—
165C22×C4×C151#4112yes—
166C22×C4×C151#4112yes—
167C4⋊C4×C151—48no—
168C22⋊C4×C151—216no—
169C22⋊C4×C151—28no—
170C22⋊C4×C151—28no—
171C22⋊C4×C151—48no—
172C42×C151—28no—
173C42×C151—44no—
174C42×C151—48no—
175C23×C151—22no—
176C23×C151—22no—
177C23×C151—22no—
178C23×C151—22no—
179C23×C151—22no—
180C23×C151—22no—
181C23×C151—24no—
182C23×C151—24no—
183C23×C151—24no—
184C23×C151—24no—
185C23×C151—24no—
186C23×C151—24no—
187C23×C151—41no—
188C23×C151—42no—
189C23×C151—41no—
190C23×C151—42no—
191C23×C151—42no—
192C23×C151—41no—
193C23×C151—41no—
194C23×C151—42no—
195C23×C151—42no—
196C23×C151—42no—
197C23×C151#11714yes—
198C23×C151C23×C411yescharacteristic
199C23×C151C22×D411yescharacteristic
200C23×C151C2×#4112yes—
201C23×C151C2×#4112yes—
202C23×C151C2×#4111yescharacteristic
203C23×C151C2×#4111yescharacteristic
204C23×C151C2×#4111yescharacteristic
205C23×C151C2×#4112yes—
206C23×C151H(5,𝔽2)12yes—
207C23×C151H(5,𝔽2)11yescharacteristic
208C23×C1512−1+411yescharacteristic
209C2×C4×C151—22no—
210C2×C4×C151—22no—
211C2×C4×C151—22no—
212C2×C4×C151—22no—
213C2×C4×C151—22no—
214C2×C4×C151—22no—
215C2×C4×C151—24no—
216C2×C4×C151—22no—
217C2×C4×C151—24no—
218C2×C4×C151—22no—
219C2×C4×C151—24no—
220C2×C4×C151—24no—
221C2×C4×C151—22no—
222C2×C4×C151—22no—
223C2×C4×C151—22no—
224C2×C4×C151—22no—
225C2×C4×C151—22no—
226C2×C4×C151—22no—
227C2×C4×C151—22no—
228C2×C4×C151—22no—
229C2×C4×C151—22no—
230C2×C4×C151—22no—
231C2×C4×C151—22no—
232C2×C4×C151—24no—
233C2×C4×C151—24no—
234C2×C4×C151—24no—
235C2×C4×C151—24no—
236C2×C4×C151—24no—
237C2×C4×C151—24no—
238C2×C4×C151—416no—
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—42no—
267C2×C4×C151#11714yes—
268C2×C4×C151#11714yes—
269C2×C4×C151C4×D414yes—
270C22×C151—24no—
271C22×C151—24no—
272C22×C151—24no—
273C22×C151—42no—
274C22×C151—42no—
275C22×C151—42no—
276C22×C151—42no—
277C22×C151—44no—
278C22×C151—44no—
279C22×C151—44no—
280C22×C151—44no—
281C22×C151C2×#11711yescharacteristic
282C22×C151C2×#11711yescharacteristic
283C22×C151C2×#11711yescharacteristic
284C22×C151C2×C4×D411yescharacteristic
285C22×C151C4×#4111yescharacteristic
286C22×C151#51811yescharacteristic
287C22×C151#52011yescharacteristic
288C22×C151#52512yes—
289C22×C151#52912yes—
290C22×C151#52912yes—
291C22×C151#52912yes—
292C22×C151#53812yes—
293C22×C151#53912yes—
294C22×C151#54612yes—
295C22×C151#54611yescharacteristic
296C22×C151#54811yescharacteristic
297C22×C151#55112yes—
298C22×C151#55212yes—
299C22×C151#55211yescharacteristic
300C22×C151#55311yescharacteristic
301C22×C151#55312yes—
302C22×C151#55512yes—
303C22×C151#55912yes—
304C4×C151—24no—
305C4×C151—24no—
306C4×C151—24no—
307C4×C151—42no—
308C4×C151—42no—
309C4×C151—44no—
310C4×C151—44no—
311C4×C151—42no—
312C4×C151—82no—
313C4×C151—82no—
314C2×C151—44no—
315C2×C151#228311yescharacteristic
316C2×C151#229011yescharacteristic
317C2×C151#231811yescharacteristic
318C2×C151#234211yescharacteristic
319C2×C151#234611yescharacteristic
320C2×C151#235211yescharacteristic
321C2×C151#235711yescharacteristic
322C2×C151#245912yes—
323C2×C151#246012yes—
324C2×C151#251712yes—
325C2×C151#251812yes—
326#13888C15111yesmaximal, characteristic, direct product factor, Sylow
327C151#1388811yescharacteristic, direct product factor, Sylow
328C2×#382C2×C15111yescharacteristic, complemented
329C2×C4×C22⋊C4C2×C15111yescharacteristic
330C2×C4×C22⋊C4C2×C15111yescharacteristic
331#1440C2×C15112yes—
332#1439C2×C15112yes—
333#1436C2×C15112yescomplemented
334#1434C2×C15111yescharacteristic, complemented
335#1434C2×C15111yescharacteristic, complemented
336#1434C2×C15112yescomplemented
337#1434C2×C15111yescharacteristic, complemented
338C22⋊#95C2×C15111yescharacteristic
339C24×C4C22×C15111yescharacteristic
340C22×C4⋊C4C22×C15112yes—
341C22×C22⋊C4C22×C15112yes—
342C22×C22⋊C4C22×C15111yescharacteristic
343C22×C22⋊C4C22×C15111yescharacteristic
344C22×C22⋊C4C22×C15112yes—
345C22×C42C22×C15112yes—
346C22×C42C22×C15111yescharacteristic
347C22×C42C22×C15111yescharacteristic
348#382—24no—
349C4×C22⋊C4—24no—
350C4×C22⋊C4C4×C15118yescomplemented
351C2×#95C22×C15111yescharacteristic
352C2×#95C22×C15112yes—
353C2×#95C22×C15111yescharacteristic
354C2×#95C22×C15112yes—
355C2×#95C22×C15112yes—
356C2×#95C22×C15111yescharacteristic
357C2×#95C22×C15112yes—
358C2×#95C22×C15112yes—
359C2×#95C22×C15112yes—
360C2×#95C22×C15112yes—
361C2×#95C22×C15112yes—
362C2×#95C22×C15111yescharacteristic
363C2×#95C22×C15111yescharacteristic
364C2×#95C22×C15111yescharacteristic
365C25C23×C15111yescharacteristic
366C23×C4—24no—
367C23×C4—22no—
368C23×C4—22no—
369C23×C4—42no—
370C23×C4C2×C4×C15114yes—
371C23×C4C23×C15112yes—
372C23×C4C23×C15112yes—
373C23×C4C23×C15112yes—
374C23×C4C23×C15111yescharacteristic
375C23×C4C23×C15111yescharacteristic
376C23×C4C23×C15111yescharacteristic
377C23×C4C23×C15112yes—
378C23×C4C23×C15111yescharacteristic
379C23×C4C23×C15111yescharacteristic
380C23×C4C23×C15111yescharacteristic
381C2×C4⋊C4—24no—
382C2×C4⋊C4—24no—
383C2×C4⋊C4—42no—
384C2×C22⋊C4—24no—
385C2×C22⋊C4—24no—
386C2×C22⋊C4—24no—
387C2×C22⋊C4—22no—
388C2×C22⋊C4—22no—
389C2×C22⋊C4—24no—
390C2×C22⋊C4—24no—
391C2×C22⋊C4—42no—
392C2×C22⋊C4—42no—
393C2×C22⋊C4C2×C4×C15114yes—
394C2×C22⋊C4C2×C4×C15114yes—
395C2×C42—22no—
396C2×C42—22no—
397C2×C42—24no—
398C2×C42—24no—
399C2×C42—42no—
400C2×C42—42no—
401C2×C42C2×C4×C15114yes—
402C2×C42C2×C4×C15114yes—
403#95—24no—
404#95—24no—
405#95—24no—
406#95—24no—
407#95—22no—
408#95—22no—
409#95—24no—
410#95—22no—
411#95—42no—
412#95—42no—
413#95—42no—
414#95C2×C4×C15114yes—
415#95C2×C4×C15114yes—
416#95D4×C15114yes—
417C24—21no—
418C24—21no—
419C24—21no—
420C24—22no—
421C24—22no—
422C24—21no—
423C24—21no—
424C24—22no—
425C24—21no—
426C24C22×C4×C15112yes—
427C24#41×C15114yes—
428C24C24×C15111yescharacteristic
429C22×C4—21no—
430C22×C4—21no—
431C22×C4—21no—
432C22×C4—22no—
433C22×C4—21no—
434C22×C4—22no—
435C22×C4—22no—
436C22×C4—21no—
437C22×C4—21no—
438C22×C4—21no—
439C22×C4—22no—
440C22×C4—22no—
441C22×C4—22no—
442C22×C4—22no—
443C22×C4—21no—
444C22×C4—22no—
445C22×C4—22no—
446C22×C4—22no—
447C22×C4—22no—
448C22×C4—21no—
449C22×C4—21no—
450C22×C4—22no—
451C22×C4—22no—
452C22×C4—22no—
453C22×C4—22no—
454C22×C4—21no—
455C22×C4—22no—
456C22×C4—22no—
457C22×C4—22no—
458C22×C4—22no—
459C22×C4—22no—
460C22×C4—21no—
461C22×C4—22no—
462C22×C4—28no—
463C22×C4—28no—
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×C4C22×C4×C15112yes—
482C22×C4C22×C4×C15112yes—
483C22×C4C22×C4×C15112yes—
484C22×C4C22×C4×C15112yes—
485C22×C4C22×C4×C15112yes—
486C22×C4C22×C4×C15112yes—
487C22×C4C2×D4×C15114yes—
488C22×C4C2×D4×C15112yes—
489C22×C4#41×C15114yes—
490C22×C4#41×C15112yes—
491C22×C4#41×C15114yes—
492C22×C4#41×C15112yes—
493C22×C4#41×C15112yes—
494C4⋊C4—48no—
495C22⋊C4—216no—
496C22⋊C4—28no—
497C22⋊C4—28no—
498C22⋊C4—48no—
499C42—28no—
500C42—44no—
501C42—48no—
502C23—22no—
503C23—22no—
504C23—22no—
505C23—22no—
506C23—22no—
507C23—22no—
508C23—24no—
509C23—24no—
510C23—24no—
511C23—24no—
512C23—24no—
513C23—24no—
514C23—42no—
515C23—41no—
516C23—41no—
517C23—42no—
518C23—42no—
519C23—41no—
520C23—41no—
521C23—42no—
522C23—42no—
523C23—42no—
524C23#117×C15114yes—
525C23C23×C4×C15111yescharacteristic
526C23C22×D4×C15111yescharacteristic
527C23C2×#41×C15112yes—
528C23C2×#41×C15112yes—
529C23C2×#41×C15111yescharacteristic
530C23C2×#41×C15111yescharacteristic
531C23C2×#41×C15111yescharacteristic
532C23C2×#41×C15112yes—
533C23H(5,𝔽2)×C15112yes—
534C23H(5,𝔽2)×C15111yescharacteristic
535C232−1+4×C15111yescharacteristic
536C2×C4—22no—
537C2×C4—22no—
538C2×C4—22no—
539C2×C4—22no—
540C2×C4—22no—
541C2×C4—22no—
542C2×C4—24no—
543C2×C4—22no—
544C2×C4—24no—
545C2×C4—22no—
546C2×C4—24no—
547C2×C4—24no—
548C2×C4—22no—
549C2×C4—22no—
550C2×C4—22no—
551C2×C4—22no—
552C2×C4—22no—
553C2×C4—22no—
554C2×C4—22no—
555C2×C4—22no—
556C2×C4—22no—
557C2×C4—22no—
558C2×C4—22no—
559C2×C4—24no—
560C2×C4—24no—
561C2×C4—24no—
562C2×C4—24no—
563C2×C4—24no—
564C2×C4—24no—
565C2×C4—416no—
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—42no—
592C2×C4—42no—
593C2×C4—42no—
594C2×C4#117×C15114yes—
595C2×C4#117×C15114yes—
596C2×C4C4×D4×C15114yes—
597C22—24no—
598C22—24no—
599C22—24no—
600C22—42no—
601C22—42no—
602C22—42no—
603C22—42no—
604C22—44no—
605C22—44no—
606C22—44no—
607C22—44no—
608C22C2×#117×C15111yescharacteristic
609C22C2×#117×C15111yescharacteristic
610C22C2×#117×C15111yescharacteristic
611C22C2×C4×D4×C15111yescharacteristic
612C22C4×#41×C15111yescharacteristic
613C22#518×C15111yescharacteristic
614C22#520×C15111yescharacteristic
615C22#525×C15112yes—
616C22#529×C15112yes—
617C22#529×C15112yes—
618C22#529×C15112yes—
619C22#538×C15112yes—
620C22#539×C15112yes—
621C22#546×C15112yes—
622C22#546×C15111yescharacteristic
623C22#548×C15111yescharacteristic
624C22#551×C15112yes—
625C22#552×C15112yes—
626C22#552×C15111yescharacteristic
627C22#553×C15111yescharacteristic
628C22#553×C15112yes—
629C22#555×C15112yes—
630C22#559×C15112yes—
631C4—24no—
632C4—24no—
633C4—24no—
634C4—42no—
635C4—44no—
636C4—44no—
637C4—42no—
638C4—42no—
639C4—82no—
640C4—82no—
641C2—44no—
642C2#2283×C15111yescharacteristic
643C2#2290×C15111yescharacteristic
644C2#2318×C15111yescharacteristic
645C2#2342×C15111yescharacteristic
646C2#2346×C15111yescharacteristic
647C2#2352×C15111yescharacteristic
648C2#2357×C15111yescharacteristic
649C2#2459×C15112yes—
650C2#2460×C15112yes—
651C2#2517×C15112yes—
652C2#2518×C15112yes—
subgroupG/H
center, socleC24×C151C24
commutatorC23C23×C4×C151
Frattini, cosocleC24C24×C151
prime radicalC25×C151C23
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C24×C151 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×#382×C151C2semidirect
6. #1436×C151C2semidirect
7. #1434×C151C2semidirect
8. #1434×C151C2semidirect
9. #1434×C151C2semidirect
10. #1434×C151C2semidirect
23. C4×C22⋊C4×C151C4semidirect
326. #13888C151direct (N × H)
327. C151#13888direct (N × H)
328. C2×#382C2×C151semidirect
333. #1436C2×C151semidirect
334. #1434C2×C151semidirect
335. #1434C2×C151semidirect
336. #1434C2×C151semidirect
337. #1434C2×C151semidirect
350. C4×C22⋊C4C4×C151semidirect

Maximal subgroups

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

subgroupindex
C2×#382×C1512
C2×C4×C22⋊C4×C1512
#1440×C1512
#1439×C1512
#1436×C1512
#1434×C1512
C22⋊#95×C1512
#13888151