Finite Group Databasebeta

← C151×#24039 #50328964

Subgroups — C151×#24039 #50328964

Order 38656.

1484 conjugacy classes of subgroups.

The subgroup lattice has 648 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#546×C151C211yesmaximal, characteristic
2C2×#484×C151C211yesmaximal, characteristic, complemented
3C22×#102×C151C211yesmaximal, characteristic, complemented
4#2487×C151C211yesmaximal, characteristic, complemented
5#2042×C151C212yesmaximal, complemented
6#2033×C151C212yesmaximal, complemented
7#1892×C151C211yesmaximal, characteristic, complemented
8#1869×C151C211yesmaximal, characteristic, complemented
9#1862×C151C212yesmaximal, complemented
10#1788×C151C212yesmaximal, complemented
11#1786×C151C211yesmaximal, characteristic, complemented
12C22×#41×C151C2211yescharacteristic
13C23×D4×C151C2211yescharacteristic
14C23×C8×C151C2211yescharacteristic
15#546×C151—24no—
16#546×C151—24no—
17C2×#124×C151C2211yescharacteristic
18C2×#123×C151—21no—
19C2×C22⋊Q8×C151C2211yescharacteristic
20C2×#121×C151—21no—
21C2×#121×C151C2211yescharacteristic
22C2×#120×C151—21no—
23C2×C4×D4×C151C2211yescharacteristic
24C2×C4×D4×C151C2211yescharacteristic
25C22×C4⋊C4×C151C2211yescharacteristic
26C22×C22⋊C4×C151—21no—
27#484×C151—24no—
28C2×#107×C151C2212yescomplemented
29C2×#103×C151C2212yescomplemented
30C2×#103×C151C2212yescomplemented
31C2×#102×C151—24no—
32C2×#102×C151C2212yes—
33C2×#102×C151C2212yes—
34C2×#102×C151C2212yes—
35C2×#102×C151C2212yes—
36C2×C22⋊C8×C151C2211yescharacteristic
37C2×C22⋊C8×C151C2212yescomplemented
38#400×C151—21no—
39#399×C151—21no—
40#389×C151C2212yescomplemented
41#386×C151—21no—
42#385×C151—21no—
43#380×C151C2211yescharacteristic
44#380×C151C2212yescomplemented
45#340×C151C2212yescomplemented
46#336×C151C2212yescomplemented
47C25×C151—21no—
48C2×#41×C151—22no—
49C2×#41×C151—24no—
50C2×#41×C151—22no—
51C2×#41×C151—42no—
52C22×Q8×C151C2311yescharacteristic
53C22×D4×C151—21no—
54C22×D4×C151—22no—
55C22×D4×C151—21no—
56C22×D4×C151—21no—
57C22×D4×C151—24no—
58C22×D4×C151—42no—
59C22×D4×C151D414yes—
60C22×D4×C151D411yescharacteristic
61C22×D4×C151C2311yescharacteristic
62C22×D4×C151C2311yescharacteristic
63C23×C4×C151—21no—
64C23×C4×C151—21no—
65C23×C4×C151—21no—
66C23×C4×C151C2311yescharacteristic
67C23×C4×C151C2311yescharacteristic
68C22×C8×C151—22no—
69C22×C8×C151—42no—
70C22×C8×C151C2312yes—
71C22×C8×C151C2312yes—
72#124×C151—22no—
73#124×C151—22no—
74#123×C151—28no—
75C22⋊Q8×C151—22no—
76C22⋊Q8×C151D414yes—
77#121×C151—28no—
78#121×C151—22no—
79#121×C151—22no—
80#120×C151—28no—
81C4×D4×C151—22no—
82C4×D4×C151—22no—
83C4×D4×C151—22no—
84C4×D4×C151—22no—
85C2×C4⋊C4×C151—21no—
86C2×C4⋊C4×C151—22no—
87C2×C4⋊C4×C151—22no—
88C2×C4⋊C4×C151—21no—
89C2×C4⋊C4×C151—22no—
90C2×C4⋊C4×C151D411yescharacteristic
91C2×C4⋊C4×C151C2312yes—
92C2×C4⋊C4×C151C2312yes—
93C2×C4⋊C4×C151C2311yescharacteristic
94C2×C22⋊C4×C151—28no—
95C2×C22⋊C4×C151—21no—
96C2×C22⋊C4×C151—21no—
97C2×C22⋊C4×C151—21no—
98C2×C22⋊C4×C151—21no—
99C2×C22⋊C4×C151—21no—
100C2×C22⋊C4×C151—21no—
101C2×C22⋊C4×C151—22no—
102C2×C22⋊C4×C151D411yescharacteristic
103C2×C22⋊C4×C151D411yescharacteristic
104C2×C42×C151C2311yescharacteristic
105#107×C151—24no—
106#103×C151—24no—
107#103×C151—42no—
108#102×C151—24no—
109#102×C151—24no—
110#102×C151—24no—
111#102×C151—42no—
112C22⋊C8×C151—22no—
113C22⋊C8×C151—42no—
114#95×C151—21no—
115#95×C151—22no—
116#95×C151—22no—
117C24×C151—21no—
118C24×C151—21no—
119C24×C151—24no—
120C24×C151—44no—
121C24×C151—42no—
122C24×C151—42no—
123C24×C151—82no—
124C24×C151C2×D411yescharacteristic
125C24×C151C2×D411yescharacteristic
126#41×C151—48no—
127#41×C151—44no—
128#41×C151—44no—
129C2×Q8×C151—21no—
130C2×Q8×C151—22no—
131C2×Q8×C151—22no—
132C2×Q8×C151C2×D412yes—
133C2×D4×C151—28no—
134C2×D4×C151—24no—
135C2×D4×C151—22no—
136C2×D4×C151—22no—
137C2×D4×C151—22no—
138C2×D4×C151—24no—
139C2×D4×C151—24no—
140C2×D4×C151—21no—
141C2×D4×C151—21no—
142C2×D4×C151—22no—
143C2×D4×C151—22no—
144C2×D4×C151—22no—
145C2×D4×C151—44no—
146C2×D4×C151—48no—
147C2×D4×C151—44no—
148C2×D4×C151—44no—
149C2×D4×C151—82no—
150C2×D4×C151C2×D412yes—
151C2×D4×C151C2×D412yes—
152C2×D4×C151#4114yes—
153C22×C4×C151—22no—
154C22×C4×C151—22no—
155C22×C4×C151—24no—
156C22×C4×C151—21no—
157C22×C4×C151—21no—
158C22×C4×C151—24no—
159C22×C4×C151—21no—
160C22×C4×C151—21no—
161C22×C4×C151—22no—
162C22×C4×C151—22no—
163C22×C4×C151—22no—
164C22×C4×C151—22no—
165C22×C4×C151—44no—
166C22×C4×C151—42no—
167C22×C4×C151—82no—
168C22×C4×C151—82no—
169C22×C4×C151C2×D411yescharacteristic
170C22×C4×C151C2×D411yescharacteristic
171C22×C4×C151C2×D411yescharacteristic
172C22×C4×C151C2×D411yescharacteristic
173C22×C4×C151C2×D412yes—
174C22×C4×C151C2×D412yes—
175C22×C4×C151C2411yescharacteristic
176C2×C8×C151—22no—
177C2×C8×C151—22no—
178C2×C8×C151—22no—
179C2×C8×C151—22no—
180C2×C8×C151—22no—
181C2×C8×C151—22no—
182C2×C8×C151—44no—
183C4⋊C4×C151—24no—
184C4⋊C4×C151—22no—
185C4⋊C4×C151—21no—
186C4⋊C4×C151—22no—
187C4⋊C4×C151—22no—
188C4⋊C4×C151—22no—
189C4⋊C4×C151—22no—
190C4⋊C4×C151—42no—
191C4⋊C4×C151—82no—
192C4⋊C4×C151C2×D412yes—
193C22⋊C4×C151—24no—
194C22⋊C4×C151—24no—
195C22⋊C4×C151—24no—
196C22⋊C4×C151—24no—
197C22⋊C4×C151—22no—
198C22⋊C4×C151—24no—
199C22⋊C4×C151—22no—
200C22⋊C4×C151—42no—
201C22⋊C4×C151—82no—
202C42×C151—21no—
203C42×C151—21no—
204C23×C151—22no—
205C23×C151—22no—
206C23×C151—22no—
207C23×C151—24no—
208C23×C151—22no—
209C23×C151—21no—
210C23×C151—22no—
211C23×C151—21no—
212C23×C151—21no—
213C23×C151—22no—
214C23×C151—48no—
215C23×C151—41no—
216C23×C151—41no—
217C23×C151—42no—
218C23×C151—42no—
219C23×C151—41no—
220C23×C151—41no—
221C23×C151—42no—
222C23×C151—48no—
223C23×C151—84no—
224C23×C151—88no—
225C23×C151—88no—
226C23×C151#12012yes—
227C23×C151#13512yes—
228C23×C151#13712yes—
229C23×C151C22×D411yescharacteristic
230Q8×C151—24no—
231Q8×C151—41no—
232Q8×C151—41no—
233D4×C151—22no—
234D4×C151—22no—
235D4×C151—22no—
236D4×C151—24no—
237D4×C151—48no—
238D4×C151—48no—
239D4×C151—44no—
240D4×C151—42no—
241D4×C151—84no—
242D4×C151#12314yes—
243C2×C4×C151—22no—
244C2×C4×C151—22no—
245C2×C4×C151—22no—
246C2×C4×C151—24no—
247C2×C4×C151—22no—
248C2×C4×C151—21no—
249C2×C4×C151—21no—
250C2×C4×C151—22no—
251C2×C4×C151—21no—
252C2×C4×C151—22no—
253C2×C4×C151—21no—
254C2×C4×C151—21no—
255C2×C4×C151—22no—
256C2×C4×C151—48no—
257C2×C4×C151—42no—
258C2×C4×C151—42no—
259C2×C4×C151—41no—
260C2×C4×C151—41no—
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—42no—
268C2×C4×C151—84no—
269C2×C4×C151—84no—
270C2×C4×C151#12012yes—
271C2×C4×C151C22×D411yescharacteristic
272C2×C4×C151C22×D411yescharacteristic
273C2×C4×C151C2×#4112yes—
274C2×C4×C151H(5,𝔽2)12yes—
275C8×C151—42no—
276C8×C151—42no—
277C22×C151—22no—
278C22×C151—22no—
279C22×C151—24no—
280C22×C151—24no—
281C22×C151—24no—
282C22×C151—42no—
283C22×C151—42no—
284C22×C151—44no—
285C22×C151—44no—
286C22×C151—41no—
287C22×C151—42no—
288C22×C151—41no—
289C22×C151—42no—
290C22×C151—41no—
291C22×C151—42no—
292C22×C151—42no—
293C22×C151—42no—
294C22×C151—816no—
295C22×C151—82no—
296C22×C151—82no—
297C22×C151#45214yes—
298C22×C151C2×#12011yescharacteristic
299C22×C151#54612yes—
300C22×C151C2×#13511yescharacteristic
301C22×C151C2×#13711yescharacteristic
302C22×C151#57612yes—
303C4×C151—22no—
304C4×C151—41no—
305C4×C151—42no—
306C4×C151—41no—
307C4×C151—41no—
308C4×C151—42no—
309C4×C151—82no—
310C4×C151—82no—
311C4×C151C2×#12311yescharacteristic
312C4×C151#53411yescharacteristic
313C4×C151#54612yes—
314C2×C151—24no—
315C2×C151—44no—
316C2×C151—81no—
317C2×C151—82no—
318C2×C151#240511yescharacteristic
319C2×C151C2×#45211yescharacteristic
320C2×C151#300811yescharacteristic
321C2×C151#329712yes—
322C2×C151#331412yes—
323#24039C15111yesmaximal, characteristic, direct product factor, Sylow
324C151#2403911yescharacteristic, direct product factor, Sylow
325C2×#546C2×C15111yescharacteristic
326C2×#484C2×C15111yescharacteristic, complemented
327C22×#102C2×C15111yescharacteristic, complemented
328#2487C2×C15111yescharacteristic, complemented
329#2042C2×C15112yescomplemented
330#2033C2×C15112yescomplemented
331#1892C2×C15111yescharacteristic, complemented
332#1869C2×C15111yescharacteristic, complemented
333#1862C2×C15112yescomplemented
334#1788C2×C15112yescomplemented
335#1786C2×C15111yescharacteristic, complemented
336C22×#41C22×C15111yescharacteristic
337C23×D4C22×C15111yescharacteristic
338C23×C8C22×C15111yescharacteristic
339#546—24no—
340#546—24no—
341C2×#124C22×C15111yescharacteristic
342C2×#123—21no—
343C2×C22⋊Q8C22×C15111yescharacteristic
344C2×#121—21no—
345C2×#121C22×C15111yescharacteristic
346C2×#120—21no—
347C2×C4×D4C22×C15111yescharacteristic
348C2×C4×D4C22×C15111yescharacteristic
349C22×C4⋊C4C22×C15111yescharacteristic
350C22×C22⋊C4—21no—
351#484—24no—
352C2×#107C22×C15112yescomplemented
353C2×#103C22×C15112yescomplemented
354C2×#103C22×C15112yescomplemented
355C2×#102—24no—
356C2×#102C22×C15112yes—
357C2×#102C22×C15112yes—
358C2×#102C22×C15112yes—
359C2×#102C22×C15112yes—
360C2×C22⋊C8C22×C15111yescharacteristic
361C2×C22⋊C8C22×C15112yescomplemented
362#400—21no—
363#399—21no—
364#389C22×C15112yescomplemented
365#386—21no—
366#385—21no—
367#380C22×C15111yescharacteristic
368#380C22×C15112yescomplemented
369#340C22×C15112yescomplemented
370#336C22×C15112yescomplemented
371C25—21no—
372C2×#41—22no—
373C2×#41—22no—
374C2×#41—24no—
375C2×#41—42no—
376C22×Q8C23×C15111yescharacteristic
377C22×D4—24no—
378C22×D4—21no—
379C22×D4—21no—
380C22×D4—21no—
381C22×D4—22no—
382C22×D4—42no—
383C22×D4D4×C15111yescharacteristic
384C22×D4D4×C15114yes—
385C22×D4C23×C15111yescharacteristic
386C22×D4C23×C15111yescharacteristic
387C23×C4—21no—
388C23×C4—21no—
389C23×C4—21no—
390C23×C4C23×C15111yescharacteristic
391C23×C4C23×C15111yescharacteristic
392C22×C8—22no—
393C22×C8—42no—
394C22×C8C23×C15112yes—
395C22×C8C23×C15112yes—
396#124—22no—
397#124—22no—
398#123—28no—
399C22⋊Q8—22no—
400C22⋊Q8D4×C15114yes—
401#121—28no—
402#121—22no—
403#121—22no—
404#120—28no—
405C4×D4—22no—
406C4×D4—22no—
407C4×D4—22no—
408C4×D4—22no—
409C2×C4⋊C4—21no—
410C2×C4⋊C4—22no—
411C2×C4⋊C4—22no—
412C2×C4⋊C4—21no—
413C2×C4⋊C4—22no—
414C2×C4⋊C4D4×C15111yescharacteristic
415C2×C4⋊C4C23×C15112yes—
416C2×C4⋊C4C23×C15112yes—
417C2×C4⋊C4C23×C15111yescharacteristic
418C2×C22⋊C4—28no—
419C2×C22⋊C4—21no—
420C2×C22⋊C4—21no—
421C2×C22⋊C4—21no—
422C2×C22⋊C4—21no—
423C2×C22⋊C4—21no—
424C2×C22⋊C4—21no—
425C2×C22⋊C4—22no—
426C2×C22⋊C4D4×C15111yescharacteristic
427C2×C22⋊C4D4×C15111yescharacteristic
428C2×C42C23×C15111yescharacteristic
429#107—24no—
430#103—24no—
431#103—42no—
432#102—24no—
433#102—24no—
434#102—24no—
435#102—42no—
436C22⋊C8—22no—
437C22⋊C8—42no—
438#95—21no—
439#95—22no—
440#95—22no—
441C24—21no—
442C24—21no—
443C24—24no—
444C24—44no—
445C24—42no—
446C24—42no—
447C24—82no—
448C24C2×D4×C15111yescharacteristic
449C24C2×D4×C15111yescharacteristic
450#41—48no—
451#41—44no—
452#41—44no—
453C2×Q8—21no—
454C2×Q8—22no—
455C2×Q8—22no—
456C2×Q8C2×D4×C15112yes—
457C2×D4—28no—
458C2×D4—24no—
459C2×D4—22no—
460C2×D4—22no—
461C2×D4—22no—
462C2×D4—24no—
463C2×D4—24no—
464C2×D4—21no—
465C2×D4—21no—
466C2×D4—22no—
467C2×D4—22no—
468C2×D4—22no—
469C2×D4—44no—
470C2×D4—48no—
471C2×D4—44no—
472C2×D4—44no—
473C2×D4—82no—
474C2×D4C2×D4×C15112yes—
475C2×D4C2×D4×C15112yes—
476C2×D4#41×C15114yes—
477C22×C4—22no—
478C22×C4—22no—
479C22×C4—24no—
480C22×C4—21no—
481C22×C4—21no—
482C22×C4—24no—
483C22×C4—21no—
484C22×C4—21no—
485C22×C4—22no—
486C22×C4—22no—
487C22×C4—22no—
488C22×C4—22no—
489C22×C4—44no—
490C22×C4—42no—
491C22×C4—82no—
492C22×C4—82no—
493C22×C4C2×D4×C15111yescharacteristic
494C22×C4C2×D4×C15111yescharacteristic
495C22×C4C2×D4×C15111yescharacteristic
496C22×C4C2×D4×C15111yescharacteristic
497C22×C4C2×D4×C15112yes—
498C22×C4C2×D4×C15112yes—
499C22×C4C24×C15111yescharacteristic
500C2×C8—22no—
501C2×C8—22no—
502C2×C8—22no—
503C2×C8—22no—
504C2×C8—22no—
505C2×C8—22no—
506C2×C8—44no—
507C4⋊C4—24no—
508C4⋊C4—22no—
509C4⋊C4—21no—
510C4⋊C4—22no—
511C4⋊C4—22no—
512C4⋊C4—22no—
513C4⋊C4—22no—
514C4⋊C4—42no—
515C4⋊C4—82no—
516C4⋊C4C2×D4×C15112yes—
517C22⋊C4—24no—
518C22⋊C4—24no—
519C22⋊C4—24no—
520C22⋊C4—24no—
521C22⋊C4—22no—
522C22⋊C4—24no—
523C22⋊C4—22no—
524C22⋊C4—42no—
525C22⋊C4—82no—
526C42—21no—
527C42—21no—
528C23—22no—
529C23—22no—
530C23—22no—
531C23—24no—
532C23—22no—
533C23—21no—
534C23—22no—
535C23—21no—
536C23—21no—
537C23—22no—
538C23—48no—
539C23—41no—
540C23—41no—
541C23—42no—
542C23—48no—
543C23—42no—
544C23—41no—
545C23—41no—
546C23—42no—
547C23—84no—
548C23—88no—
549C23—88no—
550C23#120×C15112yes—
551C23#135×C15112yes—
552C23#137×C15112yes—
553C23C22×D4×C15111yescharacteristic
554Q8—24no—
555Q8—41no—
556Q8—41no—
557D4—22no—
558D4—22no—
559D4—22no—
560D4—24no—
561D4—48no—
562D4—48no—
563D4—44no—
564D4—42no—
565D4—84no—
566D4#123×C15114yes—
567C2×C4—22no—
568C2×C4—22no—
569C2×C4—22no—
570C2×C4—24no—
571C2×C4—21no—
572C2×C4—21no—
573C2×C4—22no—
574C2×C4—21no—
575C2×C4—22no—
576C2×C4—22no—
577C2×C4—21no—
578C2×C4—21no—
579C2×C4—22no—
580C2×C4—48no—
581C2×C4—42no—
582C2×C4—42no—
583C2×C4—41no—
584C2×C4—41no—
585C2×C4—42no—
586C2×C4—42no—
587C2×C4—42no—
588C2×C4—42no—
589C2×C4—42no—
590C2×C4—42no—
591C2×C4—42no—
592C2×C4—84no—
593C2×C4—84no—
594C2×C4#120×C15112yes—
595C2×C4C22×D4×C15111yescharacteristic
596C2×C4C22×D4×C15111yescharacteristic
597C2×C4C2×#41×C15112yes—
598C2×C4H(5,𝔽2)×C15112yes—
599C8—42no—
600C8—42no—
601C22—22no—
602C22—22no—
603C22—24no—
604C22—24no—
605C22—24no—
606C22—42no—
607C22—42no—
608C22—44no—
609C22—44no—
610C22—41no—
611C22—42no—
612C22—41no—
613C22—42no—
614C22—41no—
615C22—42no—
616C22—42no—
617C22—42no—
618C22—816no—
619C22—82no—
620C22—82no—
621C22#452×C15114yes—
622C22C2×#120×C15111yescharacteristic
623C22#546×C15112yes—
624C22C2×#135×C15111yescharacteristic
625C22C2×#137×C15111yescharacteristic
626C22#576×C15112yes—
627C4—22no—
628C4—41no—
629C4—42no—
630C4—41no—
631C4—41no—
632C4—42no—
633C4—82no—
634C4—82no—
635C4C2×#123×C15111yescharacteristic
636C4#534×C15111yescharacteristic
637C4#546×C15112yes—
638C2—24no—
639C2—44no—
640C2—81no—
641C2—82no—
642C2#2405×C15111yescharacteristic
643C2C2×#452×C15111yescharacteristic
644C2#3008×C15111yescharacteristic
645C2#3297×C15112yes—
646C2#3314×C15112yes—
subgroupG/H
center, socleC23×C151C22×D4
commutator, Frattini, cosocleC22×C4C24×C151
prime radicalC2×#546×C151C2
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C151 ◁ C2×C4×D4×C151 ◁ G

Complements

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

NH ≅ G/Ntype
2. C2×#484×C151C2semidirect
3. C22×#102×C151C2semidirect
4. #2487×C151C2semidirect
5. #2042×C151C2semidirect
6. #2033×C151C2semidirect
7. #1892×C151C2semidirect
8. #1869×C151C2semidirect
9. #1862×C151C2semidirect
10. #1788×C151C2semidirect
11. #1786×C151C2semidirect
28. C2×#107×C151C22semidirect
29. C2×#103×C151C22semidirect
30. C2×#103×C151C22semidirect
37. C2×C22⋊C8×C151C22semidirect
40. #389×C151C22semidirect
44. #380×C151C22semidirect
45. #340×C151C22semidirect
46. #336×C151C22semidirect
323. #24039C151direct (N × H)
324. C151#24039direct (N × H)
326. C2×#484C2×C151semidirect
327. C22×#102C2×C151semidirect
328. #2487C2×C151semidirect
329. #2042C2×C151semidirect
330. #2033C2×C151semidirect
331. #1892C2×C151semidirect
332. #1869C2×C151semidirect
333. #1862C2×C151semidirect
334. #1788C2×C151semidirect
335. #1786C2×C151semidirect
352. C2×#107C22×C151semidirect
353. C2×#103C22×C151semidirect
354. C2×#103C22×C151semidirect
361. C2×C22⋊C8C22×C151semidirect
364. #389C22×C151semidirect
368. #380C22×C151semidirect
369. #340C22×C151semidirect
370. #336C22×C151semidirect

Maximal subgroups

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

subgroupindex
C2×#546×C1512
C2×#484×C1512
C22×#102×C1512
#2487×C1512
#2042×C1512
#2033×C1512
#1892×C1512
#1869×C1512
#1862×C1512
#1788×C1512
#1786×C1512
#24039151