Finite Group Databasebeta

← C151×#9042 #50313967

Subgroups — C151×#9042 #50313967

Order 38656.

966 conjugacy classes of subgroups.

The subgroup lattice has 668 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#450×C151C211yesmaximal, characteristic
2#2329×C151C211yesmaximal, characteristic, complemented
3#1786×C151C211yesmaximal, characteristic
4C2×#328×C151C211yesmaximal, characteristic, complemented
5#1438×C151C211yesmaximal, characteristic
6#1294×C151C211yesmaximal, characteristic, complemented
7#1280×C151C211yesmaximal, characteristic, complemented
8C23×D4×C151C2211yescharacteristic
9C22×SD16×C151—21no—
10C2×C22⋊Q8×C151C2211yescharacteristic
11C22×C22⋊C4×C151—21no—
12C22×C22⋊C4×C151—21no—
13#450×C151—22no—
14#450×C151C414yescomplemented
15C2×#102×C151—21no—
16C2×#102×C151—21no—
17C2×#102×C151—21no—
18C2×C22⋊C8×C151C2211yescharacteristic
19C2×C22⋊C8×C151C2211yescharacteristic
20#391×C151—21no—
21#389×C151—21no—
22#387×C151—21no—
23#387×C151—21no—
24#385×C151—21no—
25#380×C151C2211yescharacteristic
26C4×C22⋊C4×C151—21no—
27C2×#95×C151C2211yescharacteristic
28C2×#95×C151C2211yescharacteristic
29#328×C151—22no—
30C25×C151—21no—
31C22×Q8×C151D411yescharacteristic
32C22×D4×C151—21no—
33C22×D4×C151—21no—
34C22×D4×C151—21no—
35C22×D4×C151—21no—
36C22×D4×C151—21no—
37C22×D4×C151—42no—
38C22×D4×C151—42no—
39C22×D4×C151C2×C412yes—
40C23×C4×C151—21no—
41C23×C4×C151D411yescharacteristic
42C23×C4×C151D411yescharacteristic
43C23×C4×C151C2311yescharacteristic
44C2×SD16×C151—24no—
45C2×SD16×C151—42no—
46C2×SD16×C151—42no—
47C22×C8×C151—21no—
48C22×C8×C151—21no—
49C22⋊Q8×C151—21no—
50C22⋊Q8×C151—21no—
51C22⋊Q8×C151C2×C412yes—
52C22⋊Q8×C151D412yes—
53C2×C4⋊C4×C151—21no—
54C2×C4⋊C4×C151—21no—
55C2×C4⋊C4×C151—21no—
56C2×C4⋊C4×C151D411yescharacteristic
57C2×C4⋊C4×C151D411yescharacteristic
58C2×C4⋊C4×C151D411yescharacteristic
59C2×C22⋊C4×C151—21no—
60C2×C22⋊C4×C151—21no—
61C2×C22⋊C4×C151—42no—
62C2×C22⋊C4×C151—42no—
63C2×C22⋊C4×C151—42no—
64C2×C22⋊C4×C151—42no—
65C2×C22⋊C4×C151—42no—
66C2×C22⋊C4×C151—42no—
67C2×C42×C151—21no—
68C2×C42×C151—21no—
69#102×C151—24no—
70#102×C151—42no—
71#102×C151—42no—
72C22⋊C8×C151—21no—
73C22⋊C8×C151—21no—
74C22⋊C8×C151—21no—
75C22⋊C8×C151C2×C412yes—
76#95×C151—21no—
77#95×C151—21no—
78#95×C151—21no—
79#95×C151—21no—
80#95×C151—21no—
81#95×C151—21no—
82#95×C151—21no—
83#95×C151—21no—
84#95×C151—21no—
85C24×C151—22no—
86C24×C151—22no—
87C24×C151—22no—
88C24×C151—41no—
89C24×C151—41no—
90C24×C151—41no—
91C24×C151—41no—
92C24×C151—41no—
93C24×C151—41no—
94C24×C151—41no—
95C24×C151—41no—
96C24×C151—41no—
97C24×C151—41no—
98C24×C151—41no—
99C24×C151—41no—
100C24×C151C2×D411yescharacteristic
101C2×Q8×C151—21no—
102C2×Q8×C151—41no—
103C2×Q8×C151—41no—
104C2×Q8×C151C22⋊C412yescomplemented
105C2×D4×C151—22no—
106C2×D4×C151—22no—
107C2×D4×C151—22no—
108C2×D4×C151—22no—
109C2×D4×C151—22no—
110C2×D4×C151—22no—
111C2×D4×C151—41no—
112C2×D4×C151—41no—
113C2×D4×C151—41no—
114C2×D4×C151—41no—
115C2×D4×C151—44no—
116C2×D4×C151—44no—
117C2×D4×C151—44no—
118C2×D4×C151—44no—
119C2×D4×C151—41no—
120C2×D4×C151—41no—
121C22×C4×C151—21no—
122C22×C4×C151—21no—
123C22×C4×C151—21no—
124C22×C4×C151—21no—
125C22×C4×C151—22no—
126C22×C4×C151—21no—
127C22×C4×C151—21no—
128C22×C4×C151—21no—
129C22×C4×C151—21no—
130C22×C4×C151—21no—
131C22×C4×C151—41no—
132C22×C4×C151—41no—
133C22×C4×C151—41no—
134C22×C4×C151—41no—
135C22×C4×C151—41no—
136C22×C4×C151—41no—
137C22×C4×C151—41no—
138C22×C4×C151—41no—
139C22×C4×C151—41no—
140C22×C4×C151—41no—
141C22×C4×C151—41no—
142C22×C4×C151—41no—
143C22×C4×C151SD1612yescomplemented
144C22×C4×C151C22×C411yescharacteristic
145C22×C4×C151C2×D411yescharacteristic
146C22×C4×C151C2×D411yescharacteristic
147C22×C4×C151C2×D411yescharacteristic
148C22×C4×C151#4111yescharacteristic
149C22×C4×C151#4111yescharacteristic
150SD16×C151—48no—
151C2×C8×C151—22no—
152C2×C8×C151—41no—
153C2×C8×C151—41no—
154C2×C8×C151—41no—
155C2×C8×C151—41no—
156C2×C8×C151—41no—
157C4⋊C4×C151—22no—
158C4⋊C4×C151—22no—
159C4⋊C4×C151—21no—
160C4⋊C4×C151—41no—
161C4⋊C4×C151—41no—
162C4⋊C4×C151—81no—
163C4⋊C4×C151—81no—
164C4⋊C4×C151C22⋊C412yescomplemented
165C22⋊C4×C151—22no—
166C22⋊C4×C151—22no—
167C22⋊C4×C151—48no—
168C22⋊C4×C151—48no—
169C22⋊C4×C151—41no—
170C22⋊C4×C151—41no—
171C42×C151—81no—
172C42×C151—81no—
173C23×C151—21no—
174C23×C151—21no—
175C23×C151—21no—
176C23×C151—21no—
177C23×C151—24no—
178C23×C151—42no—
179C23×C151—42no—
180C23×C151—42no—
181C23×C151—42no—
182C23×C151—42no—
183C23×C151—42no—
184C23×C151—42no—
185C23×C151—42no—
186C23×C151—42no—
187C23×C151—42no—
188C23×C151—42no—
189C23×C151—42no—
190C23×C151—42no—
191C23×C151—42no—
192C23×C151—42no—
193C23×C151—42no—
194C23×C151—42no—
195C23×C151—42no—
196C23×C151—81no—
197C23×C151—81no—
198C23×C151—81no—
199C23×C151—81no—
200C23×C151—81no—
201C23×C151—81no—
202C23×C151—81no—
203C23×C151—81no—
204C23×C151—81no—
205C23×C151—81no—
206C23×C151—81no—
207C23×C151—81no—
208C23×C151—81no—
209C23×C151—81no—
210C23×C151—81no—
211C23×C151—81no—
212C23×C151C4×D411yescharacteristic
213C23×C151#12011yescharacteristic
214C23×C151#12111yescharacteristic
215C23×C151C2×SD1611yescharacteristic
216C23×C151#13511yescharacteristic
217C23×C151AGL(1,ℤ/8)11yescharacteristic
218C23×C151#13711yescharacteristic
219Q8×C151—42no—
220Q8×C151—81no—
221D4×C151—24no—
222D4×C151—24no—
223D4×C151—42no—
224D4×C151—42no—
225D4×C151—42no—
226D4×C151—42no—
227D4×C151—42no—
228D4×C151—42no—
229C2×C4×C151—21no—
230C2×C4×C151—21no—
231C2×C4×C151—21no—
232C2×C4×C151—21no—
233C2×C4×C151—22no—
234C2×C4×C151—22no—
235C2×C4×C151—22no—
236C2×C4×C151—41no—
237C2×C4×C151—41no—
238C2×C4×C151—41no—
239C2×C4×C151—41no—
240C2×C4×C151—41no—
241C2×C4×C151—41no—
242C2×C4×C151—41no—
243C2×C4×C151—41no—
244C2×C4×C151—41no—
245C2×C4×C151—41no—
246C2×C4×C151—42no—
247C2×C4×C151—42no—
248C2×C4×C151—42no—
249C2×C4×C151—42no—
250C2×C4×C151—42no—
251C2×C4×C151—41no—
252C2×C4×C151—41no—
253C2×C4×C151—41no—
254C2×C4×C151—41no—
255C2×C4×C151—41no—
256C2×C4×C151—41no—
257C2×C4×C151—41no—
258C2×C4×C151—41no—
259C2×C4×C151—41no—
260C2×C4×C151—81no—
261C2×C4×C151—81no—
262C2×C4×C151—81no—
263C2×C4×C151—81no—
264C2×C4×C151—81no—
265C2×C4×C151—81no—
266C2×C4×C151C2×C22⋊C411yescharacteristic
267C2×C4×C151C4×D411yescharacteristic
268C2×C4×C151#12111yescharacteristic
269C2×C4×C151#12311yescharacteristic
270C8×C151—42no—
271C8×C151—81no—
272C22×C151—21no—
273C22×C151—21no—
274C22×C151—21no—
275C22×C151—21no—
276C22×C151—21no—
277C22×C151—21no—
278C22×C151—21no—
279C22×C151—21no—
280C22×C151—21no—
281C22×C151—21no—
282C22×C151—21no—
283C22×C151—21no—
284C22×C151—44no—
285C22×C151—44no—
286C22×C151—44no—
287C22×C151—82no—
288C22×C151—82no—
289C22×C151—82no—
290C22×C151—82no—
291C22×C151—82no—
292C22×C151—82no—
293C22×C151—82no—
294C22×C151—82no—
295C22×C151—82no—
296C22×C151—82no—
297C22×C151—82no—
298C22×C151—82no—
299C22×C151#38611yescharacteristic
300C22×C151C4×SD1611yescharacteristic
301C22×C151#44011yescharacteristic
302C22×C151#44811yescharacteristic
303C22×C151#44911yescharacteristic
304C22×C151#45311yescharacteristic
305C22×C151#45411yescharacteristic
306C22×C151B(4,𝔽2)11yescharacteristic
307C22×C151B(4,𝔽2)11yescharacteristic
308C22×C151#46011yescharacteristic
309C22×C151#46411yescharacteristic
310C4×C151—21no—
311C4×C151—21no—
312C4×C151—21no—
313C4×C151—21no—
314C4×C151—42no—
315C4×C151—42no—
316C4×C151—42no—
317C4×C151—82no—
318C4×C151—81no—
319C4×C151—81no—
320C4×C151—81no—
321C2×C151—21no—
322C2×C151—21no—
323C2×C151—21no—
324C2×C151—21no—
325C2×C151—84no—
326C2×C151#159611yescharacteristic
327C2×C151#159711yescharacteristic
328C2×C151#159911yescharacteristic
329C2×C151#160011yescharacteristic
330C2×C151#188011yescharacteristic
331C2×C151#188311yescharacteristic
332C2×C151#188911yescharacteristic
333#9042C15111yesmaximal, characteristic, direct product factor, Sylow
334C151#904211yescharacteristic, direct product factor, Sylow
335C2×#450C2×C15111yescharacteristic
336#2329C2×C15111yescharacteristic, complemented
337#1786C2×C15111yescharacteristic
338C2×#328C2×C15111yescharacteristic, complemented
339#1438C2×C15111yescharacteristic
340#1294C2×C15111yescharacteristic, complemented
341#1280C2×C15111yescharacteristic, complemented
342C23×D4C22×C15111yescharacteristic
343C22×SD16—21no—
344C2×C22⋊Q8C22×C15111yescharacteristic
345C22×C22⋊C4—21no—
346C22×C22⋊C4—21no—
347#450—22no—
348#450C4×C15114yescomplemented
349C2×#102—21no—
350C2×#102—21no—
351C2×#102—21no—
352C2×C22⋊C8C22×C15111yescharacteristic
353C2×C22⋊C8C22×C15111yescharacteristic
354#391—21no—
355#389—21no—
356#387—21no—
357#387—21no—
358#385—21no—
359#380C22×C15111yescharacteristic
360C4×C22⋊C4—21no—
361C2×#95C22×C15111yescharacteristic
362C2×#95C22×C15111yescharacteristic
363#328—22no—
364C25—21no—
365C22×Q8D4×C15111yescharacteristic
366C22×D4—21no—
367C22×D4—21no—
368C22×D4—21no—
369C22×D4—21no—
370C22×D4—21no—
371C22×D4—42no—
372C22×D4—42no—
373C22×D4C2×C4×C15112yes—
374C23×C4—21no—
375C23×C4D4×C15111yescharacteristic
376C23×C4D4×C15111yescharacteristic
377C23×C4C23×C15111yescharacteristic
378C2×SD16—24no—
379C2×SD16—42no—
380C2×SD16—42no—
381C22×C8—21no—
382C22×C8—21no—
383C22⋊Q8—21no—
384C22⋊Q8—21no—
385C22⋊Q8C2×C4×C15112yes—
386C22⋊Q8D4×C15112yes—
387C2×C4⋊C4—21no—
388C2×C4⋊C4—21no—
389C2×C4⋊C4—21no—
390C2×C4⋊C4D4×C15111yescharacteristic
391C2×C4⋊C4D4×C15111yescharacteristic
392C2×C4⋊C4D4×C15111yescharacteristic
393C2×C22⋊C4—21no—
394C2×C22⋊C4—21no—
395C2×C22⋊C4—42no—
396C2×C22⋊C4—42no—
397C2×C22⋊C4—42no—
398C2×C22⋊C4—42no—
399C2×C22⋊C4—42no—
400C2×C22⋊C4—42no—
401C2×C42—21no—
402C2×C42—21no—
403#102—24no—
404#102—42no—
405#102—42no—
406C22⋊C8—21no—
407C22⋊C8—21no—
408C22⋊C8—21no—
409C22⋊C8C2×C4×C15112yes—
410#95—21no—
411#95—21no—
412#95—21no—
413#95—21no—
414#95—21no—
415#95—21no—
416#95—21no—
417#95—21no—
418#95—21no—
419C24—22no—
420C24—22no—
421C24—22no—
422C24—41no—
423C24—41no—
424C24—41no—
425C24—41no—
426C24—41no—
427C24—41no—
428C24—41no—
429C24—41no—
430C24—41no—
431C24—41no—
432C24—41no—
433C24—41no—
434C24C2×D4×C15111yescharacteristic
435C2×Q8—21no—
436C2×Q8—41no—
437C2×Q8—41no—
438C2×Q8C22⋊C4×C15112yescomplemented
439C2×D4—22no—
440C2×D4—22no—
441C2×D4—22no—
442C2×D4—22no—
443C2×D4—22no—
444C2×D4—22no—
445C2×D4—41no—
446C2×D4—41no—
447C2×D4—41no—
448C2×D4—41no—
449C2×D4—44no—
450C2×D4—44no—
451C2×D4—44no—
452C2×D4—44no—
453C2×D4—41no—
454C2×D4—41no—
455C22×C4—21no—
456C22×C4—21no—
457C22×C4—21no—
458C22×C4—21no—
459C22×C4—22no—
460C22×C4—21no—
461C22×C4—21no—
462C22×C4—21no—
463C22×C4—21no—
464C22×C4—21no—
465C22×C4—41no—
466C22×C4—41no—
467C22×C4—41no—
468C22×C4—41no—
469C22×C4—41no—
470C22×C4—41no—
471C22×C4—41no—
472C22×C4—41no—
473C22×C4—41no—
474C22×C4—41no—
475C22×C4—41no—
476C22×C4—41no—
477C22×C4SD16×C15112yescomplemented
478C22×C4C22×C4×C15111yescharacteristic
479C22×C4C2×D4×C15111yescharacteristic
480C22×C4C2×D4×C15111yescharacteristic
481C22×C4C2×D4×C15111yescharacteristic
482C22×C4#41×C15111yescharacteristic
483C22×C4#41×C15111yescharacteristic
484SD16—48no—
485C2×C8—22no—
486C2×C8—41no—
487C2×C8—41no—
488C2×C8—41no—
489C2×C8—41no—
490C2×C8—41no—
491C4⋊C4—22no—
492C4⋊C4—22no—
493C4⋊C4—21no—
494C4⋊C4—41no—
495C4⋊C4—41no—
496C4⋊C4—81no—
497C4⋊C4—81no—
498C4⋊C4C22⋊C4×C15112yescomplemented
499C22⋊C4—22no—
500C22⋊C4—22no—
501C22⋊C4—48no—
502C22⋊C4—48no—
503C22⋊C4—41no—
504C22⋊C4—41no—
505C42—81no—
506C42—81no—
507C23—21no—
508C23—21no—
509C23—21no—
510C23—21no—
511C23—24no—
512C23—42no—
513C23—42no—
514C23—42no—
515C23—42no—
516C23—42no—
517C23—42no—
518C23—42no—
519C23—42no—
520C23—42no—
521C23—42no—
522C23—42no—
523C23—42no—
524C23—42no—
525C23—42no—
526C23—42no—
527C23—42no—
528C23—42no—
529C23—42no—
530C23—81no—
531C23—81no—
532C23—81no—
533C23—81no—
534C23—81no—
535C23—81no—
536C23—81no—
537C23—81no—
538C23—81no—
539C23—81no—
540C23—81no—
541C23—81no—
542C23—81no—
543C23—81no—
544C23—81no—
545C23—81no—
546C23C4×D4×C15111yescharacteristic
547C23#120×C15111yescharacteristic
548C23#121×C15111yescharacteristic
549C23C2×SD16×C15111yescharacteristic
550C23#135×C15111yescharacteristic
551C23AGL(1,ℤ/8)×C15111yescharacteristic
552C23#137×C15111yescharacteristic
553Q8—42no—
554Q8—81no—
555D4—24no—
556D4—24no—
557D4—42no—
558D4—42no—
559D4—42no—
560D4—42no—
561D4—42no—
562D4—42no—
563C2×C4—21no—
564C2×C4—21no—
565C2×C4—21no—
566C2×C4—21no—
567C2×C4—22no—
568C2×C4—22no—
569C2×C4—22no—
570C2×C4—41no—
571C2×C4—41no—
572C2×C4—41no—
573C2×C4—41no—
574C2×C4—41no—
575C2×C4—41no—
576C2×C4—41no—
577C2×C4—41no—
578C2×C4—41no—
579C2×C4—41no—
580C2×C4—42no—
581C2×C4—42no—
582C2×C4—42no—
583C2×C4—42no—
584C2×C4—42no—
585C2×C4—41no—
586C2×C4—41no—
587C2×C4—41no—
588C2×C4—41no—
589C2×C4—41no—
590C2×C4—41no—
591C2×C4—41no—
592C2×C4—41no—
593C2×C4—41no—
594C2×C4—81no—
595C2×C4—81no—
596C2×C4—81no—
597C2×C4—81no—
598C2×C4—81no—
599C2×C4—81no—
600C2×C4C2×C22⋊C4×C15111yescharacteristic
601C2×C4C4×D4×C15111yescharacteristic
602C2×C4#121×C15111yescharacteristic
603C2×C4#123×C15111yescharacteristic
604C8—42no—
605C8—81no—
606C22—21no—
607C22—21no—
608C22—21no—
609C22—21no—
610C22—21no—
611C22—21no—
612C22—21no—
613C22—21no—
614C22—21no—
615C22—21no—
616C22—21no—
617C22—21no—
618C22—44no—
619C22—44no—
620C22—44no—
621C22—82no—
622C22—82no—
623C22—82no—
624C22—82no—
625C22—82no—
626C22—82no—
627C22—82no—
628C22—82no—
629C22—82no—
630C22—82no—
631C22—82no—
632C22—82no—
633C22#386×C15111yescharacteristic
634C22C4×SD16×C15111yescharacteristic
635C22#440×C15111yescharacteristic
636C22#448×C15111yescharacteristic
637C22#449×C15111yescharacteristic
638C22#453×C15111yescharacteristic
639C22#454×C15111yescharacteristic
640C22B(4,𝔽2)×C15111yescharacteristic
641C22B(4,𝔽2)×C15111yescharacteristic
642C22#460×C15111yescharacteristic
643C22#464×C15111yescharacteristic
644C4—21no—
645C4—21no—
646C4—21no—
647C4—21no—
648C4—42no—
649C4—42no—
650C4—42no—
651C4—82no—
652C4—81no—
653C4—81no—
654C4—81no—
655C2—21no—
656C2—21no—
657C2—21no—
658C2—21no—
659C2—84no—
660C2#1596×C15111yescharacteristic
661C2#1597×C15111yescharacteristic
662C2#1599×C15111yescharacteristic
663C2#1600×C15111yescharacteristic
664C2#1880×C15111yescharacteristic
665C2#1883×C15111yescharacteristic
666C2#1889×C15111yescharacteristic
subgroupG/H
center, socleC23×C151#120
commutatorC22×C4C22×C4×C151
Frattini, cosocleC23×C4C23×C151
prime radicalC23×D4×C151C22
LCSG ▷ C22×C4 ▷ C22 ▷ C1
UCSC1 ◁ C23×C151 ◁ C23×C4×C151 ◁ G

Complements

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

NH ≅ G/Ntype
2. #2329×C151C2semidirect
4. C2×#328×C151C2semidirect
6. #1294×C151C2semidirect
7. #1280×C151C2semidirect
14. #450×C151C4semidirect
104. C2×Q8×C151C22⋊C4semidirect
143. C22×C4×C151SD16semidirect
164. C4⋊C4×C151C22⋊C4semidirect
333. #9042C151direct (N × H)
334. C151#9042direct (N × H)
336. #2329C2×C151semidirect
338. C2×#328C2×C151semidirect
340. #1294C2×C151semidirect
341. #1280C2×C151semidirect
348. #450C4×C151semidirect
438. C2×Q8C22⋊C4×C151semidirect
477. C22×C4SD16×C151semidirect
498. C4⋊C4C22⋊C4×C151semidirect

Maximal subgroups

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

subgroupindex
C2×#450×C1512
#2329×C1512
#1786×C1512
C2×#328×C1512
#1438×C1512
#1294×C1512
#1280×C1512
#9042151