Finite Group Databasebeta

← C151×#24056 #50328981

Subgroups — C151×#24056 #50328981

Order 38656.

1820 conjugacy classes of subgroups.

The subgroup lattice has 796 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#3484×C151C211yesmaximal, characteristic
2#2849×C151C212yesmaximal, complemented
3C2×#386×C151C211yesmaximal, characteristic, complemented
4#2044×C151C214yesmaximal, complemented
5#1898×C151C212yesmaximal, complemented
6#1867×C151C212yesmaximal, complemented
7#1790×C151C212yesmaximal, complemented
8#1781×C151C211yesmaximal, characteristic, complemented
9C2×H(5,𝔽2)×C151C2211yescharacteristic
10C23×D4×C151C2211yescharacteristic
11C24×C4×C151C2211yescharacteristic, complemented
12#546×C151—22no—
13#546×C151—22no—
14D42×C151—22no—
15D42×C151—22no—
16#535×C151—21no—
17#534×C151—21no—
18#534×C151C2212yes—
19#525×C151—21no—
20C2×#123×C151—22no—
21C2×#120×C151—21no—
22C2×#120×C151C2212yes—
23#518×C151C2211yescharacteristic
24C22×C22⋊C4×C151—21no—
25C22×C22⋊C4×C151C2211yescharacteristic, complemented
26C2×#99×C151C2212yes—
27C2×#99×C151C2214yescomplemented
28C2×#99×C151C2212yescomplemented
29#386×C151—22no—
30#386×C151—21no—
31#386×C151—21no—
32#386×C151C2212yes—
33#386×C151C2214yescomplemented
34#386×C151C2212yescomplemented
35#385×C151—22no—
36#385×C151C2214yescomplemented
37#381×C151—22no—
38#379×C151C2212yescomplemented
39C2×#95×C151—21no—
40#342×C151C2214yescomplemented
41C25×C151D411yescharacteristic
42C25×C151C2311yescharacteristic
43H(5,𝔽2)×C151—24no—
44H(5,𝔽2)×C151—42no—
45C2×#41×C151—21no—
46C2×#41×C151—22no—
47C22×D4×C151—21no—
48C22×D4×C151—21no—
49C22×D4×C151—24no—
50C22×D4×C151—21no—
51C22×D4×C151—22no—
52C22×D4×C151—22no—
53C22×D4×C151—22no—
54C22×D4×C151—42no—
55C22×D4×C151D411yescharacteristic
56C22×D4×C151D411yescharacteristic
57C22×D4×C151D412yes—
58C22×D4×C151D412yes—
59C22×D4×C151C2312yes—
60C22×D4×C151C2311yescharacteristic
61C22×D4×C151C2311yescharacteristic
62C23×C4×C151—21no—
63C23×C4×C151—22no—
64C23×C4×C151—21no—
65C23×C4×C151—22no—
66C23×C4×C151—21no—
67C23×C4×C151—44no—
68C23×C4×C151D411yescharacteristic
69C23×C4×C151C2312yes—
70#127×C151—22no—
71#124×C151—22no—
72#123×C151—22no—
73#123×C151—22no—
74#123×C151—22no—
75#123×C151—48no—
76C22⋊Q8×C151—21no—
77C22⋊Q8×C151—21no—
78#121×C151—21no—
79#121×C151—21no—
80#121×C151—22no—
81#121×C151—22no—
82#121×C151—22no—
83#121×C151—22no—
84#121×C151—22no—
85#121×C151—22no—
86#120×C151—22no—
87#120×C151—22no—
88#120×C151—22no—
89#120×C151—22no—
90#120×C151—22no—
91#120×C151—22no—
92#120×C151—22no—
93#120×C151—22no—
94#120×C151—22no—
95C4×D4×C151—22no—
96C4×D4×C151—22no—
97C4×D4×C151—22no—
98C4×D4×C151—22no—
99#117×C151—21no—
100C2×C4⋊C4×C151—24no—
101C2×C22⋊C4×C151—21no—
102C2×C22⋊C4×C151—21no—
103C2×C22⋊C4×C151—21no—
104C2×C22⋊C4×C151—22no—
105C2×C22⋊C4×C151—22no—
106C2×C22⋊C4×C151—21no—
107C2×C22⋊C4×C151—22no—
108C2×C22⋊C4×C151—22no—
109C2×C22⋊C4×C151—24no—
110C2×C22⋊C4×C151—42no—
111C2×C22⋊C4×C151—44no—
112C2×C22⋊C4×C151D412yes—
113C2×C22⋊C4×C151D412yes—
114C2×C22⋊C4×C151C2312yes—
115C2×C22⋊C4×C151C2314yes—
116C2×C22⋊C4×C151C2312yes—
117#99×C151—24no—
118#99×C151—42no—
119#99×C151—44no—
120#95×C151—22no—
121#95×C151—22no—
122#95×C151—24no—
123#95×C151—24no—
124C24×C151—22no—
125C24×C151—22no—
126C24×C151—21no—
127C24×C151—22no—
128C24×C151—21no—
129C24×C151—21no—
130C24×C151—42no—
131C24×C151—42no—
132C24×C151—41no—
133C24×C151—42no—
134C24×C151—42no—
135C24×C151C2×D411yescharacteristic
136C24×C151C2×D412yes—
137C24×C151C2×D412yes—
138C24×C151C2×D411yescharacteristic
139C24×C151C2×D412yes—
140C24×C151C2×D411yescharacteristic
141C24×C151C2×D411yescharacteristic
142C24×C151C2411yescharacteristic
143#41×C151—48no—
144#41×C151—42no—
145#41×C151—42no—
146C2×Q8×C151—21no—
147C2×D4×C151—22no—
148C2×D4×C151—22no—
149C2×D4×C151—22no—
150C2×D4×C151—21no—
151C2×D4×C151—22no—
152C2×D4×C151—22no—
153C2×D4×C151—22no—
154C2×D4×C151—22no—
155C2×D4×C151—22no—
156C2×D4×C151—22no—
157C2×D4×C151—22no—
158C2×D4×C151—22no—
159C2×D4×C151—22no—
160C2×D4×C151—24no—
161C2×D4×C151—22no—
162C2×D4×C151—24no—
163C2×D4×C151—22no—
164C2×D4×C151—22no—
165C2×D4×C151—22no—
166C2×D4×C151—22no—
167C2×D4×C151—22no—
168C2×D4×C151—41no—
169C2×D4×C151—41no—
170C2×D4×C151—48no—
171C2×D4×C151—48no—
172C2×D4×C151—48no—
173C2×D4×C151—42no—
174C2×D4×C151—42no—
175C2×D4×C151—44no—
176C2×D4×C151—44no—
177C2×D4×C151—82no—
178C2×D4×C151—82no—
179C2×D4×C151#4114yes—
180C22×C4×C151—21no—
181C22×C4×C151—24no—
182C22×C4×C151—22no—
183C22×C4×C151—28no—
184C22×C4×C151—21no—
185C22×C4×C151—21no—
186C22×C4×C151—22no—
187C22×C4×C151—24no—
188C22×C4×C151—21no—
189C22×C4×C151—21no—
190C22×C4×C151—22no—
191C22×C4×C151—24no—
192C22×C4×C151—22no—
193C22×C4×C151—44no—
194C22×C4×C151—41no—
195C22×C4×C151—44no—
196C22×C4×C151—48no—
197C22×C4×C151—42no—
198C22×C4×C151—44no—
199C22×C4×C151—42no—
200C22×C4×C151—41no—
201C22×C4×C151—41no—
202C22×C4×C151—42no—
203C22×C4×C151—42no—
204C22×C4×C151—42no—
205C22×C4×C151C2×D412yes—
206C22×C4×C151C2×D411yescharacteristic
207C22×C4×C151C2×D411yescharacteristic
208C22×C4×C151C2×D412yes—
209C22×C4×C151C2×D412yes—
210C4⋊C4×C151—21no—
211C4⋊C4×C151—21no—
212C4⋊C4×C151—22no—
213C4⋊C4×C151—22no—
214C4⋊C4×C151—48no—
215C22⋊C4×C151—22no—
216C22⋊C4×C151—22no—
217C22⋊C4×C151—22no—
218C22⋊C4×C151—22no—
219C22⋊C4×C151—22no—
220C22⋊C4×C151—22no—
221C22⋊C4×C151—22no—
222C22⋊C4×C151—22no—
223C22⋊C4×C151—22no—
224C22⋊C4×C151—22no—
225C22⋊C4×C151—22no—
226C22⋊C4×C151—24no—
227C22⋊C4×C151—24no—
228C22⋊C4×C151—24no—
229C22⋊C4×C151—44no—
230C22⋊C4×C151—44no—
231C22⋊C4×C151—48no—
232C22⋊C4×C151—44no—
233C22⋊C4×C151—42no—
234C22⋊C4×C151—44no—
235C42×C151—22no—
236C23×C151—21no—
237C23×C151—21no—
238C23×C151—22no—
239C23×C151—22no—
240C23×C151—21no—
241C23×C151—21no—
242C23×C151—21no—
243C23×C151—24no—
244C23×C151—24no—
245C23×C151—24no—
246C23×C151—24no—
247C23×C151—21no—
248C23×C151—21no—
249C23×C151—22no—
250C23×C151—21no—
251C23×C151—21no—
252C23×C151—24no—
253C23×C151—42no—
254C23×C151—41no—
255C23×C151—42no—
256C23×C151—41no—
257C23×C151—41no—
258C23×C151—41no—
259C23×C151—42no—
260C23×C151—42no—
261C23×C151—48no—
262C23×C151—48no—
263C23×C151—41no—
264C23×C151—41no—
265C23×C151—41no—
266C23×C151—41no—
267C23×C151—48no—
268C23×C151—42no—
269C23×C151—42no—
270C23×C151—42no—
271C23×C151—42no—
272C23×C151—42no—
273C23×C151—81no—
274C23×C151—81no—
275C23×C151—84no—
276C23×C151—81no—
277C23×C151—81no—
278C23×C151#12012yes—
279C23×C151#12011yescharacteristic
280C23×C151#12011yescharacteristic
281C23×C151#12312yescomplemented
282C23×C151C22×D411yescharacteristic
283C23×C151C22×D412yes—
284C23×C151C2×#4112yes—
285C23×C151H(5,𝔽2)12yes—
286Q8×C151—42no—
287D4×C151—28no—
288D4×C151—44no—
289D4×C151—42no—
290D4×C151—44no—
291D4×C151—44no—
292D4×C151—42no—
293D4×C151—42no—
294D4×C151—44no—
295D4×C151—44no—
296D4×C151—44no—
297D4×C151—44no—
298D4×C151—82no—
299D4×C151—82no—
300D4×C151—82no—
301D4×C151—82no—
302C2×C4×C151—21no—
303C2×C4×C151—21no—
304C2×C4×C151—24no—
305C2×C4×C151—28no—
306C2×C4×C151—22no—
307C2×C4×C151—22no—
308C2×C4×C151—22no—
309C2×C4×C151—21no—
310C2×C4×C151—21no—
311C2×C4×C151—21no—
312C2×C4×C151—24no—
313C2×C4×C151—42no—
314C2×C4×C151—42no—
315C2×C4×C151—44no—
316C2×C4×C151—42no—
317C2×C4×C151—44no—
318C2×C4×C151—42no—
319C2×C4×C151—44no—
320C2×C4×C151—48no—
321C2×C4×C151—42no—
322C2×C4×C151—44no—
323C2×C4×C151—42no—
324C2×C4×C151—42no—
325C2×C4×C151—44no—
326C2×C4×C151—42no—
327C2×C4×C151—44no—
328C2×C4×C151—42no—
329C2×C4×C151—42no—
330C2×C4×C151—44no—
331C2×C4×C151—81no—
332C2×C4×C151—81no—
333C2×C4×C151—84no—
334C2×C4×C151#12312yescomplemented
335C22×C151—24no—
336C22×C151—24no—
337C22×C151—21no—
338C22×C151—21no—
339C22×C151—22no—
340C22×C151—21no—
341C22×C151—21no—
342C22×C151—22no—
343C22×C151—21no—
344C22×C151—21no—
345C22×C151—22no—
346C22×C151—22no—
347C22×C151—22no—
348C22×C151—22no—
349C22×C151—42no—
350C22×C151—42no—
351C22×C151—48no—
352C22×C151—48no—
353C22×C151—42no—
354C22×C151—42no—
355C22×C151—42no—
356C22×C151—42no—
357C22×C151—41no—
358C22×C151—41no—
359C22×C151—42no—
360C22×C151—41no—
361C22×C151—42no—
362C22×C151—41no—
363C22×C151—42no—
364C22×C151—41no—
365C22×C151—81no—
366C22×C151—84no—
367C22×C151—84no—
368C22×C151—84no—
369C22×C151—81no—
370C22×C151—162no—
371C22×C151B(4,𝔽2)12yes—
372C22×C151#45812yes—
373C22×C151C2×#12011yescharacteristic
374C22×C151C2×#12311yescharacteristic
375C22×C151#53411yescharacteristic
376C22×C151#54614yes—
377C4×C151—22no—
378C4×C151—41no—
379C4×C151—42no—
380C4×C151—44no—
381C4×C151—42no—
382C4×C151—42no—
383C4×C151—84no—
384C4×C151—82no—
385C2×C151—21no—
386C2×C151—24no—
387C2×C151—21no—
388C2×C151—22no—
389C2×C151—22no—
390C2×C151—42no—
391C2×C151—42no—
392C2×C151—81no—
393C2×C151—82no—
394C2×C151#240511yescharacteristic
395C2×C151C2×B(4,𝔽2)11yescharacteristic
396C2×C151C2×#45811yescharacteristic
397#24056C15111yesmaximal, characteristic, direct product factor, Sylow
398C151#2405611yescharacteristic, direct product factor, Sylow
399#3484C2×C15111yescharacteristic
400#2849C2×C15112yescomplemented
401C2×#386C2×C15111yescharacteristic, complemented
402#2044C2×C15114yescomplemented
403#1898C2×C15112yescomplemented
404#1867C2×C15112yescomplemented
405#1790C2×C15112yescomplemented
406#1781C2×C15111yescharacteristic, complemented
407C2×H(5,𝔽2)C22×C15111yescharacteristic
408C23×D4C22×C15111yescharacteristic
409C24×C4C22×C15111yescharacteristic, complemented
410#546—22no—
411#546—22no—
412D42—22no—
413D42—22no—
414#535—21no—
415#534—21no—
416#534C22×C15112yes—
417#525—21no—
418C2×#123—22no—
419C2×#120—21no—
420C2×#120C22×C15112yes—
421#518C22×C15111yescharacteristic
422C22×C22⋊C4—21no—
423C22×C22⋊C4C22×C15111yescharacteristic, complemented
424C2×#99C22×C15112yes—
425C2×#99C22×C15114yescomplemented
426C2×#99C22×C15112yescomplemented
427#386—22no—
428#386—21no—
429#386—21no—
430#386C22×C15112yes—
431#386C22×C15114yescomplemented
432#386C22×C15112yescomplemented
433#385—22no—
434#385C22×C15114yescomplemented
435#381—22no—
436#379C22×C15112yescomplemented
437C2×#95—21no—
438#342C22×C15114yescomplemented
439C25D4×C15111yescharacteristic
440C25C23×C15111yescharacteristic
441H(5,𝔽2)—24no—
442H(5,𝔽2)—42no—
443C2×#41—21no—
444C2×#41—22no—
445C22×D4—21no—
446C22×D4—22no—
447C22×D4—22no—
448C22×D4—22no—
449C22×D4—21no—
450C22×D4—21no—
451C22×D4—24no—
452C22×D4—42no—
453C22×D4D4×C15111yescharacteristic
454C22×D4D4×C15111yescharacteristic
455C22×D4D4×C15112yes—
456C22×D4D4×C15112yes—
457C22×D4C23×C15112yes—
458C22×D4C23×C15111yescharacteristic
459C22×D4C23×C15111yescharacteristic
460C23×C4—21no—
461C23×C4—22no—
462C23×C4—21no—
463C23×C4—22no—
464C23×C4—21no—
465C23×C4—44no—
466C23×C4D4×C15111yescharacteristic
467C23×C4C23×C15112yes—
468#127—22no—
469#124—22no—
470#123—22no—
471#123—22no—
472#123—22no—
473#123—48no—
474C22⋊Q8—21no—
475C22⋊Q8—21no—
476#121—21no—
477#121—21no—
478#121—22no—
479#121—22no—
480#121—22no—
481#121—22no—
482#121—22no—
483#121—22no—
484#120—22no—
485#120—22no—
486#120—22no—
487#120—22no—
488#120—22no—
489#120—22no—
490#120—22no—
491#120—22no—
492#120—22no—
493C4×D4—22no—
494C4×D4—22no—
495C4×D4—22no—
496C4×D4—22no—
497#117—21no—
498C2×C4⋊C4—24no—
499C2×C22⋊C4—21no—
500C2×C22⋊C4—21no—
501C2×C22⋊C4—21no—
502C2×C22⋊C4—22no—
503C2×C22⋊C4—22no—
504C2×C22⋊C4—21no—
505C2×C22⋊C4—22no—
506C2×C22⋊C4—24no—
507C2×C22⋊C4—22no—
508C2×C22⋊C4—42no—
509C2×C22⋊C4—44no—
510C2×C22⋊C4D4×C15112yes—
511C2×C22⋊C4D4×C15112yes—
512C2×C22⋊C4C23×C15112yes—
513C2×C22⋊C4C23×C15114yes—
514C2×C22⋊C4C23×C15112yes—
515#99—24no—
516#99—42no—
517#99—44no—
518#95—22no—
519#95—22no—
520#95—24no—
521#95—24no—
522C24—22no—
523C24—22no—
524C24—21no—
525C24—22no—
526C24—21no—
527C24—21no—
528C24—42no—
529C24—42no—
530C24—41no—
531C24—42no—
532C24—42no—
533C24C2×D4×C15111yescharacteristic
534C24C2×D4×C15112yes—
535C24C2×D4×C15112yes—
536C24C2×D4×C15111yescharacteristic
537C24C2×D4×C15112yes—
538C24C2×D4×C15111yescharacteristic
539C24C2×D4×C15111yescharacteristic
540C24C24×C15111yescharacteristic
541#41—48no—
542#41—42no—
543#41—42no—
544C2×Q8—21no—
545C2×D4—22no—
546C2×D4—22no—
547C2×D4—22no—
548C2×D4—21no—
549C2×D4—22no—
550C2×D4—22no—
551C2×D4—22no—
552C2×D4—22no—
553C2×D4—22no—
554C2×D4—22no—
555C2×D4—22no—
556C2×D4—22no—
557C2×D4—22no—
558C2×D4—24no—
559C2×D4—22no—
560C2×D4—24no—
561C2×D4—22no—
562C2×D4—22no—
563C2×D4—22no—
564C2×D4—22no—
565C2×D4—22no—
566C2×D4—41no—
567C2×D4—41no—
568C2×D4—48no—
569C2×D4—48no—
570C2×D4—48no—
571C2×D4—42no—
572C2×D4—42no—
573C2×D4—44no—
574C2×D4—44no—
575C2×D4—82no—
576C2×D4—82no—
577C2×D4#41×C15114yes—
578C22×C4—21no—
579C22×C4—24no—
580C22×C4—22no—
581C22×C4—28no—
582C22×C4—21no—
583C22×C4—21no—
584C22×C4—22no—
585C22×C4—24no—
586C22×C4—21no—
587C22×C4—21no—
588C22×C4—22no—
589C22×C4—24no—
590C22×C4—22no—
591C22×C4—44no—
592C22×C4—41no—
593C22×C4—44no—
594C22×C4—48no—
595C22×C4—42no—
596C22×C4—44no—
597C22×C4—42no—
598C22×C4—41no—
599C22×C4—41no—
600C22×C4—42no—
601C22×C4—42no—
602C22×C4—42no—
603C22×C4C2×D4×C15112yes—
604C22×C4C2×D4×C15111yescharacteristic
605C22×C4C2×D4×C15111yescharacteristic
606C22×C4C2×D4×C15112yes—
607C22×C4C2×D4×C15112yes—
608C4⋊C4—21no—
609C4⋊C4—21no—
610C4⋊C4—22no—
611C4⋊C4—22no—
612C4⋊C4—48no—
613C22⋊C4—22no—
614C22⋊C4—22no—
615C22⋊C4—22no—
616C22⋊C4—22no—
617C22⋊C4—22no—
618C22⋊C4—22no—
619C22⋊C4—22no—
620C22⋊C4—22no—
621C22⋊C4—22no—
622C22⋊C4—22no—
623C22⋊C4—22no—
624C22⋊C4—24no—
625C22⋊C4—24no—
626C22⋊C4—24no—
627C22⋊C4—44no—
628C22⋊C4—44no—
629C22⋊C4—48no—
630C22⋊C4—42no—
631C22⋊C4—44no—
632C22⋊C4—44no—
633C42—22no—
634C23—22no—
635C23—22no—
636C23—21no—
637C23—21no—
638C23—24no—
639C23—24no—
640C23—21no—
641C23—21no—
642C23—21no—
643C23—24no—
644C23—24no—
645C23—21no—
646C23—21no—
647C23—22no—
648C23—21no—
649C23—21no—
650C23—24no—
651C23—41no—
652C23—42no—
653C23—41no—
654C23—41no—
655C23—42no—
656C23—41no—
657C23—42no—
658C23—42no—
659C23—48no—
660C23—48no—
661C23—41no—
662C23—41no—
663C23—41no—
664C23—41no—
665C23—48no—
666C23—42no—
667C23—42no—
668C23—42no—
669C23—42no—
670C23—42no—
671C23—81no—
672C23—81no—
673C23—84no—
674C23—81no—
675C23—81no—
676C23#120×C15112yes—
677C23#120×C15111yescharacteristic
678C23#120×C15111yescharacteristic
679C23#123×C15112yescomplemented
680C23C22×D4×C15111yescharacteristic
681C23C22×D4×C15112yes—
682C23C2×#41×C15112yes—
683C23H(5,𝔽2)×C15112yes—
684Q8—42no—
685D4—28no—
686D4—44no—
687D4—42no—
688D4—44no—
689D4—44no—
690D4—44no—
691D4—44no—
692D4—42no—
693D4—42no—
694D4—44no—
695D4—44no—
696D4—82no—
697D4—82no—
698D4—82no—
699D4—82no—
700C2×C4—21no—
701C2×C4—21no—
702C2×C4—24no—
703C2×C4—28no—
704C2×C4—22no—
705C2×C4—22no—
706C2×C4—22no—
707C2×C4—21no—
708C2×C4—21no—
709C2×C4—21no—
710C2×C4—24no—
711C2×C4—42no—
712C2×C4—42no—
713C2×C4—44no—
714C2×C4—44no—
715C2×C4—42no—
716C2×C4—44no—
717C2×C4—48no—
718C2×C4—42no—
719C2×C4—44no—
720C2×C4—42no—
721C2×C4—42no—
722C2×C4—42no—
723C2×C4—44no—
724C2×C4—42no—
725C2×C4—44no—
726C2×C4—42no—
727C2×C4—42no—
728C2×C4—44no—
729C2×C4—81no—
730C2×C4—81no—
731C2×C4—84no—
732C2×C4#123×C15112yescomplemented
733C22—24no—
734C22—24no—
735C22—21no—
736C22—21no—
737C22—22no—
738C22—21no—
739C22—21no—
740C22—22no—
741C22—21no—
742C22—21no—
743C22—22no—
744C22—22no—
745C22—22no—
746C22—22no—
747C22—42no—
748C22—42no—
749C22—48no—
750C22—48no—
751C22—42no—
752C22—42no—
753C22—42no—
754C22—42no—
755C22—41no—
756C22—41no—
757C22—42no—
758C22—41no—
759C22—42no—
760C22—41no—
761C22—42no—
762C22—41no—
763C22—81no—
764C22—84no—
765C22—84no—
766C22—81no—
767C22—84no—
768C22—162no—
769C22B(4,𝔽2)×C15112yes—
770C22#458×C15112yes—
771C22C2×#120×C15111yescharacteristic
772C22C2×#123×C15111yescharacteristic
773C22#534×C15111yescharacteristic
774C22#546×C15114yes—
775C4—22no—
776C4—41no—
777C4—42no—
778C4—44no—
779C4—42no—
780C4—42no—
781C4—82no—
782C4—84no—
783C2—21no—
784C2—24no—
785C2—21no—
786C2—22no—
787C2—22no—
788C2—42no—
789C2—42no—
790C2—81no—
791C2—82no—
792C2#2405×C15111yescharacteristic
793C2C2×B(4,𝔽2)×C15111yescharacteristic
794C2C2×#458×C15111yescharacteristic
subgroupG/H
center, socleC22×C151C2×#120
commutator, Frattini, cosocleC24C24×C151
prime radical#3484×C151C2
LCSG ▷ C24 ▷ C2 ▷ C1
UCSC1 ◁ C22×C151 ◁ C25×C151 ◁ G

Complements

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

NH ≅ G/Ntype
2. #2849×C151C2semidirect
3. C2×#386×C151C2semidirect
4. #2044×C151C2semidirect
5. #1898×C151C2semidirect
6. #1867×C151C2semidirect
7. #1790×C151C2semidirect
8. #1781×C151C2semidirect
11. C24×C4×C151C22semidirect
25. C22×C22⋊C4×C151C22semidirect
27. C2×#99×C151C22semidirect
28. C2×#99×C151C22semidirect
33. #386×C151C22semidirect
34. #386×C151C22semidirect
36. #385×C151C22semidirect
38. #379×C151C22semidirect
40. #342×C151C22semidirect
281. C23×C151#123semidirect
334. C2×C4×C151#123semidirect
397. #24056C151direct (N × H)
398. C151#24056direct (N × H)
400. #2849C2×C151semidirect
401. C2×#386C2×C151semidirect
402. #2044C2×C151semidirect
403. #1898C2×C151semidirect
404. #1867C2×C151semidirect
405. #1790C2×C151semidirect
406. #1781C2×C151semidirect
409. C24×C4C22×C151semidirect
423. C22×C22⋊C4C22×C151semidirect
425. C2×#99C22×C151semidirect
426. C2×#99C22×C151semidirect
431. #386C22×C151semidirect
432. #386C22×C151semidirect
434. #385C22×C151semidirect
436. #379C22×C151semidirect
438. #342C22×C151semidirect
679. C23#123×C151semidirect
732. C2×C4#123×C151semidirect

Maximal subgroups

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

subgroupindex
#3484×C1512
#2849×C1512
C2×#386×C1512
#2044×C1512
#1898×C1512
#1867×C1512
#1790×C1512
#1781×C1512
#24056151