Finite Group Databasebeta

← C151×#24046 #50328971

Subgroups — C151×#24046 #50328971

Order 38656.

1390 conjugacy classes of subgroups.

The subgroup lattice has 642 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#550×C151C211yesmaximal, characteristic
2C2×#480×C151C211yesmaximal, characteristic, complemented
3C2×#417×C151C211yesmaximal, characteristic, complemented
4#2487×C151C211yesmaximal, characteristic, complemented
5#2041×C151C212yesmaximal, complemented
6#2033×C151C212yesmaximal, complemented
7#1895×C151C211yesmaximal, characteristic, complemented
8#1870×C151C211yesmaximal, characteristic, complemented
9#1863×C151C212yesmaximal, complemented
10#1788×C151C211yesmaximal, characteristic, complemented
11#1788×C151C212yesmaximal, complemented
12C22×#41×C151C2211yescharacteristic
13C22×#41×C151C2211yescharacteristic
14C22×M16×C151C2211yescharacteristic
15#550×C151—24no—
16#550×C151—24no—
17C2×#127×C151—21no—
18C2×#127×C151C2211yescharacteristic
19C2×#121×C151—21no—
20C2×#121×C151—21no—
21C2×#121×C151C2211yescharacteristic
22C2×#121×C151C2211yescharacteristic
23C2×C4×Q8×C151C2211yescharacteristic
24C2×C4×D4×C151—21no—
25C2×C4×D4×C151C2211yescharacteristic
26C22×C4⋊C4×C151C2211yescharacteristic
27#480×C151—24no—
28C2×#107×C151C2212yes—
29#417×C151—24no—
30C2×#103×C151C2212yes—
31C2×#103×C151C2212yes—
32C2×#102×C151C2212yes—
33C2×#102×C151C2212yes—
34C2×#102×C151C2212yes—
35C2×#102×C151C2212yes—
36C2×C22⋊C8×C151C2211yescharacteristic
37C2×C22⋊C8×C151C2212yes—
38#400×C151—21no—
39#399×C151—21no—
40#389×C151C2212yes—
41#386×C151—21no—
42#385×C151—21no—
43#380×C151C2211yescharacteristic
44#380×C151C2212yes—
45#340×C151C2212yes—
46#336×C151C2212yes—
47C2×#41×C151—22no—
48C2×#41×C151—22no—
49C2×#41×C151—22no—
50C2×#41×C151—24no—
51C2×#41×C151—24no—
52C2×#41×C151—42no—
53C2×#41×C151—42no—
54C2×#41×C151D414yes—
55C22×Q8×C151C2311yescharacteristic
56C22×D4×C151—21no—
57C22×D4×C151—21no—
58C22×D4×C151—21no—
59C22×D4×C151—21no—
60C22×D4×C151—21no—
61C22×D4×C151—21no—
62C22×D4×C151D411yescharacteristic
63C22×D4×C151C2311yescharacteristic
64C22×D4×C151C2311yescharacteristic
65C23×C4×C151—21no—
66C23×C4×C151—21no—
67C23×C4×C151—21no—
68C23×C4×C151C2311yescharacteristic
69C23×C4×C151C2311yescharacteristic
70C2×M16×C151—22no—
71C2×M16×C151—42no—
72C22×C8×C151C2312yes—
73C22×C8×C151C2312yes—
74#127×C151—28no—
75#127×C151—22no—
76#127×C151—22no—
77#121×C151—28no—
78#121×C151—28no—
79#121×C151—22no—
80#121×C151—22no—
81#121×C151—22no—
82#121×C151D414yes—
83C4×Q8×C151—22no—
84C4×Q8×C151—22no—
85C4×D4×C151—28no—
86C4×D4×C151—22no—
87C4×D4×C151—22no—
88C2×C4⋊C4×C151—21no—
89C2×C4⋊C4×C151—22no—
90C2×C4⋊C4×C151—22no—
91C2×C4⋊C4×C151—21no—
92C2×C4⋊C4×C151—22no—
93C2×C4⋊C4×C151D411yescharacteristic
94C2×C4⋊C4×C151C2312yes—
95C2×C4⋊C4×C151C2312yes—
96C2×C4⋊C4×C151C2311yescharacteristic
97C2×C22⋊C4×C151—21no—
98C2×C22⋊C4×C151—21no—
99C2×C22⋊C4×C151—21no—
100C2×C22⋊C4×C151—22no—
101C2×C22⋊C4×C151D411yescharacteristic
102C2×C22⋊C4×C151D411yescharacteristic
103C2×C42×C151—21no—
104C2×C42×C151C2311yescharacteristic
105#107×C151—24no—
106#103×C151—24no—
107#103×C151—24no—
108#102×C151—24no—
109#102×C151—24no—
110#102×C151—42no—
111#102×C151—42no—
112C22⋊C8×C151—22no—
113C22⋊C8×C151—42no—
114#95×C151—22no—
115#95×C151—21no—
116#95×C151—22no—
117C24×C151—21no—
118C24×C151—21no—
119C24×C151C2×D411yescharacteristic
120C24×C151C2×D411yescharacteristic
121#41×C151—28no—
122#41×C151—44no—
123#41×C151—48no—
124#41×C151—48no—
125#41×C151—44no—
126#41×C151—44no—
127C2×Q8×C151—21no—
128C2×Q8×C151—22no—
129C2×Q8×C151C2×D412yes—
130C2×Q8×C151#4114yes—
131C2×D4×C151—24no—
132C2×D4×C151—24no—
133C2×D4×C151—22no—
134C2×D4×C151—24no—
135C2×D4×C151—24no—
136C2×D4×C151—24no—
137C2×D4×C151—24no—
138C2×D4×C151—22no—
139C2×D4×C151—21no—
140C2×D4×C151—21no—
141C2×D4×C151—22no—
142C2×D4×C151—22no—
143C2×D4×C151—22no—
144C2×D4×C151—22no—
145C2×D4×C151—41no—
146C2×D4×C151—44no—
147C2×D4×C151—44no—
148C2×D4×C151—42no—
149C2×D4×C151—42no—
150C2×D4×C151—82no—
151C2×D4×C151—82no—
152C2×D4×C151—82no—
153C2×D4×C151C2×D412yes—
154C2×D4×C151C2×D412yes—
155C22×C4×C151—21no—
156C22×C4×C151—22no—
157C22×C4×C151—22no—
158C22×C4×C151—24no—
159C22×C4×C151—21no—
160C22×C4×C151—24no—
161C22×C4×C151—21no—
162C22×C4×C151—21no—
163C22×C4×C151—22no—
164C22×C4×C151—22no—
165C22×C4×C151—22no—
166C22×C4×C151—22no—
167C22×C4×C151—44no—
168C22×C4×C151—44no—
169C22×C4×C151—42no—
170C22×C4×C151—82no—
171C22×C4×C151C2×D411yescharacteristic
172C22×C4×C151C2×D411yescharacteristic
173C22×C4×C151C2×D411yescharacteristic
174C22×C4×C151C2×D412yes—
175C22×C4×C151C2×D412yes—
176C22×C4×C151C2×D411yescharacteristic
177C22×C4×C151C2411yescharacteristic
178M16×C151—44no—
179C2×C8×C151—22no—
180C2×C8×C151—22no—
181C2×C8×C151—22no—
182C2×C8×C151—22no—
183C2×C8×C151—22no—
184C2×C8×C151—22no—
185C4⋊C4×C151—24no—
186C4⋊C4×C151—22no—
187C4⋊C4×C151—21no—
188C4⋊C4×C151—22no—
189C4⋊C4×C151—22no—
190C4⋊C4×C151—22no—
191C4⋊C4×C151—22no—
192C4⋊C4×C151—42no—
193C4⋊C4×C151—82no—
194C4⋊C4×C151C2×D412yes—
195C22⋊C4×C151—24no—
196C22⋊C4×C151—22no—
197C22⋊C4×C151—24no—
198C22⋊C4×C151—22no—
199C22⋊C4×C151—42no—
200C22⋊C4×C151—82no—
201C42×C151—24no—
202C42×C151—21no—
203C42×C151—21no—
204C23×C151—22no—
205C23×C151—21no—
206C23×C151—21no—
207C23×C151—22no—
208C23×C151—22no—
209C23×C151—22no—
210C23×C151—21no—
211C23×C151—22no—
212C23×C151—21no—
213C23×C151—21no—
214C23×C151—22no—
215C23×C151—42no—
216C23×C151—42no—
217C23×C151—41no—
218C23×C151—41no—
219C23×C151—41no—
220C23×C151—41no—
221C23×C151—42no—
222C23×C151—42no—
223C23×C151#12012yes—
224C23×C151C22×D411yescharacteristic
225Q8×C151—22no—
226Q8×C151—24no—
227Q8×C151#12314yes—
228D4×C151—22no—
229D4×C151—22no—
230D4×C151—24no—
231D4×C151—48no—
232D4×C151—44no—
233D4×C151—48no—
234D4×C151—48no—
235D4×C151—41no—
236D4×C151—41no—
237D4×C151—42no—
238D4×C151—84no—
239D4×C151—84no—
240D4×C151—84no—
241C2×C4×C151—22no—
242C2×C4×C151—21no—
243C2×C4×C151—24no—
244C2×C4×C151—22no—
245C2×C4×C151—21no—
246C2×C4×C151—22no—
247C2×C4×C151—22no—
248C2×C4×C151—24no—
249C2×C4×C151—21no—
250C2×C4×C151—22no—
251C2×C4×C151—21no—
252C2×C4×C151—22no—
253C2×C4×C151—22no—
254C2×C4×C151—48no—
255C2×C4×C151—48no—
256C2×C4×C151—42no—
257C2×C4×C151—41no—
258C2×C4×C151—41no—
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—84no—
267C2×C4×C151#12012yes—
268C2×C4×C151#13712yes—
269C2×C4×C151C22×D411yescharacteristic
270C2×C4×C151C22×D411yescharacteristic
271C2×C4×C151C2×#4112yes—
272C2×C4×C151H(5,𝔽2)12yes—
273C8×C151—42no—
274C8×C151—42no—
275C22×C151—22no—
276C22×C151—22no—
277C22×C151—22no—
278C22×C151—42no—
279C22×C151—42no—
280C22×C151—42no—
281C22×C151—42no—
282C22×C151—42no—
283C22×C151—41no—
284C22×C151—41no—
285C22×C151—42no—
286C22×C151—42no—
287C22×C151—41no—
288C22×C151—42no—
289C22×C151—42no—
290C22×C151—42no—
291C22×C151—82no—
292C22×C151—82no—
293C22×C151—82no—
294C22×C151—82no—
295C22×C151C2×#12011yescharacteristic
296C22×C151#54612yes—
297C22×C151C2×#13711yescharacteristic
298C22×C151#57511yescharacteristic
299C22×C151#57612yes—
300C4×C151—22no—
301C4×C151—24no—
302C4×C151—22no—
303C4×C151—41no—
304C4×C151—41no—
305C4×C151—42no—
306C4×C151—82no—
307C4×C151—82no—
308C4×C151C2×#12311yescharacteristic
309C4×C151#53411yescharacteristic
310C4×C151#54612yes—
311C2×C151—42no—
312C2×C151—81no—
313C2×C151—82no—
314C2×C151—82no—
315C2×C151#240511yescharacteristic
316C2×C151#300711yescharacteristic
317C2×C151#300811yescharacteristic
318C2×C151#330912yes—
319C2×C151#333312yes—
320#24046C15111yesmaximal, characteristic, direct product factor, Sylow
321C151#2404611yescharacteristic, direct product factor, Sylow
322C2×#550C2×C15111yescharacteristic
323C2×#480C2×C15111yescharacteristic, complemented
324C2×#417C2×C15111yescharacteristic, complemented
325#2487C2×C15111yescharacteristic, complemented
326#2041C2×C15112yescomplemented
327#2033C2×C15112yescomplemented
328#1895C2×C15111yescharacteristic, complemented
329#1870C2×C15111yescharacteristic, complemented
330#1863C2×C15112yescomplemented
331#1788C2×C15112yescomplemented
332#1788C2×C15111yescharacteristic, complemented
333C22×#41C22×C15111yescharacteristic
334C22×#41C22×C15111yescharacteristic
335C22×M16C22×C15111yescharacteristic
336#550—24no—
337#550—24no—
338C2×#127—21no—
339C2×#127C22×C15111yescharacteristic
340C2×#121—21no—
341C2×#121—21no—
342C2×#121C22×C15111yescharacteristic
343C2×#121C22×C15111yescharacteristic
344C2×C4×Q8C22×C15111yescharacteristic
345C2×C4×D4—21no—
346C2×C4×D4C22×C15111yescharacteristic
347C22×C4⋊C4C22×C15111yescharacteristic
348#480—24no—
349C2×#107C22×C15112yes—
350#417—24no—
351C2×#103C22×C15112yes—
352C2×#103C22×C15112yes—
353C2×#102C22×C15112yes—
354C2×#102C22×C15112yes—
355C2×#102C22×C15112yes—
356C2×#102C22×C15112yes—
357C2×C22⋊C8C22×C15111yescharacteristic
358C2×C22⋊C8C22×C15112yes—
359#400—21no—
360#399—21no—
361#389C22×C15112yes—
362#386—21no—
363#385—21no—
364#380C22×C15111yescharacteristic
365#380C22×C15112yes—
366#340C22×C15112yes—
367#336C22×C15112yes—
368C2×#41—22no—
369C2×#41—22no—
370C2×#41—22no—
371C2×#41—24no—
372C2×#41—24no—
373C2×#41—42no—
374C2×#41—42no—
375C2×#41D4×C15114yes—
376C22×Q8C23×C15111yescharacteristic
377C22×D4—21no—
378C22×D4—21no—
379C22×D4—21no—
380C22×D4—21no—
381C22×D4—21no—
382C22×D4—21no—
383C22×D4D4×C15111yescharacteristic
384C22×D4C23×C15111yescharacteristic
385C22×D4C23×C15111yescharacteristic
386C23×C4—21no—
387C23×C4—21no—
388C23×C4—21no—
389C23×C4C23×C15111yescharacteristic
390C23×C4C23×C15111yescharacteristic
391C2×M16—22no—
392C2×M16—42no—
393C22×C8C23×C15112yes—
394C22×C8C23×C15112yes—
395#127—28no—
396#127—22no—
397#127—22no—
398#121—28no—
399#121—28no—
400#121—22no—
401#121—22no—
402#121—22no—
403#121D4×C15114yes—
404C4×Q8—22no—
405C4×Q8—22no—
406C4×D4—28no—
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—21no—
419C2×C22⋊C4—21no—
420C2×C22⋊C4—21no—
421C2×C22⋊C4—22no—
422C2×C22⋊C4D4×C15111yescharacteristic
423C2×C22⋊C4D4×C15111yescharacteristic
424C2×C42—21no—
425C2×C42C23×C15111yescharacteristic
426#107—24no—
427#103—24no—
428#103—24no—
429#102—24no—
430#102—24no—
431#102—42no—
432#102—42no—
433C22⋊C8—22no—
434C22⋊C8—42no—
435#95—22no—
436#95—21no—
437#95—22no—
438C24—21no—
439C24—21no—
440C24C2×D4×C15111yescharacteristic
441C24C2×D4×C15111yescharacteristic
442#41—28no—
443#41—44no—
444#41—48no—
445#41—48no—
446#41—44no—
447#41—44no—
448C2×Q8—21no—
449C2×Q8—22no—
450C2×Q8C2×D4×C15112yes—
451C2×Q8#41×C15114yes—
452C2×D4—24no—
453C2×D4—24no—
454C2×D4—22no—
455C2×D4—24no—
456C2×D4—24no—
457C2×D4—24no—
458C2×D4—24no—
459C2×D4—22no—
460C2×D4—21no—
461C2×D4—21no—
462C2×D4—22no—
463C2×D4—22no—
464C2×D4—22no—
465C2×D4—22no—
466C2×D4—41no—
467C2×D4—44no—
468C2×D4—44no—
469C2×D4—42no—
470C2×D4—42no—
471C2×D4—82no—
472C2×D4—82no—
473C2×D4—82no—
474C2×D4C2×D4×C15112yes—
475C2×D4C2×D4×C15112yes—
476C22×C4—21no—
477C22×C4—22no—
478C22×C4—22no—
479C22×C4—24no—
480C22×C4—21no—
481C22×C4—24no—
482C22×C4—21no—
483C22×C4—21no—
484C22×C4—22no—
485C22×C4—22no—
486C22×C4—22no—
487C22×C4—22no—
488C22×C4—44no—
489C22×C4—44no—
490C22×C4—42no—
491C22×C4—82no—
492C22×C4C2×D4×C15111yescharacteristic
493C22×C4C2×D4×C15111yescharacteristic
494C22×C4C2×D4×C15111yescharacteristic
495C22×C4C2×D4×C15112yes—
496C22×C4C2×D4×C15112yes—
497C22×C4C2×D4×C15111yescharacteristic
498C22×C4C24×C15111yescharacteristic
499M16—44no—
500C2×C8—22no—
501C2×C8—22no—
502C2×C8—22no—
503C2×C8—22no—
504C2×C8—22no—
505C2×C8—22no—
506C4⋊C4—24no—
507C4⋊C4—22no—
508C4⋊C4—21no—
509C4⋊C4—22no—
510C4⋊C4—22no—
511C4⋊C4—22no—
512C4⋊C4—22no—
513C4⋊C4—42no—
514C4⋊C4—82no—
515C4⋊C4C2×D4×C15112yes—
516C22⋊C4—24no—
517C22⋊C4—22no—
518C22⋊C4—24no—
519C22⋊C4—22no—
520C22⋊C4—42no—
521C22⋊C4—82no—
522C42—24no—
523C42—21no—
524C42—21no—
525C23—22no—
526C23—21no—
527C23—21no—
528C23—22no—
529C23—21no—
530C23—22no—
531C23—22no—
532C23—22no—
533C23—21no—
534C23—21no—
535C23—22no—
536C23—42no—
537C23—42no—
538C23—41no—
539C23—41no—
540C23—41no—
541C23—41no—
542C23—42no—
543C23—42no—
544C23#120×C15112yes—
545C23C22×D4×C15111yescharacteristic
546Q8—22no—
547Q8—24no—
548Q8#123×C15114yes—
549D4—22no—
550D4—22no—
551D4—24no—
552D4—44no—
553D4—48no—
554D4—48no—
555D4—48no—
556D4—41no—
557D4—41no—
558D4—42no—
559D4—84no—
560D4—84no—
561D4—84no—
562C2×C4—21no—
563C2×C4—22no—
564C2×C4—22no—
565C2×C4—24no—
566C2×C4—21no—
567C2×C4—22no—
568C2×C4—22no—
569C2×C4—24no—
570C2×C4—21no—
571C2×C4—22no—
572C2×C4—21no—
573C2×C4—22no—
574C2×C4—22no—
575C2×C4—48no—
576C2×C4—48no—
577C2×C4—42no—
578C2×C4—41no—
579C2×C4—41no—
580C2×C4—42no—
581C2×C4—42no—
582C2×C4—42no—
583C2×C4—42no—
584C2×C4—42no—
585C2×C4—42no—
586C2×C4—42no—
587C2×C4—84no—
588C2×C4#120×C15112yes—
589C2×C4#137×C15112yes—
590C2×C4C22×D4×C15111yescharacteristic
591C2×C4C22×D4×C15111yescharacteristic
592C2×C4C2×#41×C15112yes—
593C2×C4H(5,𝔽2)×C15112yes—
594C8—42no—
595C8—42no—
596C22—22no—
597C22—22no—
598C22—22no—
599C22—42no—
600C22—42no—
601C22—42no—
602C22—42no—
603C22—41no—
604C22—41no—
605C22—42no—
606C22—42no—
607C22—41no—
608C22—42no—
609C22—42no—
610C22—42no—
611C22—42no—
612C22—82no—
613C22—82no—
614C22—82no—
615C22—82no—
616C22C2×#120×C15111yescharacteristic
617C22#546×C15112yes—
618C22C2×#137×C15111yescharacteristic
619C22#575×C15111yescharacteristic
620C22#576×C15112yes—
621C4—22no—
622C4—24no—
623C4—22no—
624C4—41no—
625C4—41no—
626C4—42no—
627C4—82no—
628C4—82no—
629C4C2×#123×C15111yescharacteristic
630C4#534×C15111yescharacteristic
631C4#546×C15112yes—
632C2—42no—
633C2—81no—
634C2—82no—
635C2—82no—
636C2#2405×C15111yescharacteristic
637C2#3007×C15111yescharacteristic
638C2#3008×C15111yescharacteristic
639C2#3309×C15112yes—
640C2#3333×C15112yes—
subgroupG/H
center, socleC23×C151C22×D4
commutator, Frattini, cosocleC22×C4C24×C151
prime radicalC2×#550×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×#480×C151C2semidirect
3. C2×#417×C151C2semidirect
4. #2487×C151C2semidirect
5. #2041×C151C2semidirect
6. #2033×C151C2semidirect
7. #1895×C151C2semidirect
8. #1870×C151C2semidirect
9. #1863×C151C2semidirect
10. #1788×C151C2semidirect
11. #1788×C151C2semidirect
320. #24046C151direct (N × H)
321. C151#24046direct (N × H)
323. C2×#480C2×C151semidirect
324. C2×#417C2×C151semidirect
325. #2487C2×C151semidirect
326. #2041C2×C151semidirect
327. #2033C2×C151semidirect
328. #1895C2×C151semidirect
329. #1870C2×C151semidirect
330. #1863C2×C151semidirect
331. #1788C2×C151semidirect
332. #1788C2×C151semidirect

Maximal subgroups

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

subgroupindex
C2×#550×C1512
C2×#480×C1512
C2×#417×C1512
#2487×C1512
#2041×C1512
#2033×C1512
#1895×C1512
#1870×C1512
#1863×C1512
#1788×C1512
#24046151