Finite Group Databasebeta

← C151×#9914 #50314839

Subgroups — C151×#9914 #50314839

Order 38656.

1356 conjugacy classes of subgroups.

The subgroup lattice has 662 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#447×C151C211yesmaximal, characteristic, complemented
2#2617×C151C211yesmaximal, characteristic, complemented
3C2×#392×C151C211yesmaximal, characteristic, complemented
4#1786×C151C211yesmaximal, characteristic, complemented
5C2×#327×C151C211yesmaximal, characteristic, complemented
6C2×#323×C151C211yesmaximal, characteristic, complemented
7#1294×C151C211yesmaximal, characteristic, complemented
8C23×D4×C151—21no—
9C23×D4×C151C2211yescharacteristic
10C22×D8×C151—21no—
11C2×#121×C151C2211yescharacteristic
12C2×#120×C151—21no—
13C22×C22⋊C4×C151—21no—
14C22×C22⋊C4×C151C2211yescharacteristic
15#447×C151—22no—
16#447×C151—22no—
17C2×#102×C151—21no—
18C2×#102×C151—22no—
19C2×C22⋊C8×C151C2211yescharacteristic
20C2×C22⋊C8×C151C2211yescharacteristic
21#397×C151—21no—
22#394×C151—22no—
23#392×C151—21no—
24#392×C151—22no—
25#392×C151—22no—
26#386×C151—21no—
27#380×C151C2211yescharacteristic
28C2×#95×C151C2211yescharacteristic
29#327×C151—22no—
30#323×C151—22no—
31C25×C151—21no—
32C25×C151D411yescharacteristic
33C22×D4×C151—24no—
34C22×D4×C151—22no—
35C22×D4×C151—21no—
36C22×D4×C151—21no—
37C22×D4×C151—21no—
38C22×D4×C151—21no—
39C22×D4×C151—21no—
40C22×D4×C151—21no—
41C22×D4×C151—44no—
42C22×D4×C151—44no—
43C22×D4×C151—42no—
44C22×D4×C151—44no—
45C22×D4×C151—42no—
46C22×D4×C151D412yescomplemented
47C22×D4×C151D411yescharacteristic, complemented
48C23×C4×C151—21no—
49C23×C4×C151D411yescharacteristic
50C23×C4×C151C2311yescharacteristic
51C2×D8×C151—24no—
52C2×D8×C151—44no—
53C22×C8×C151—21no—
54C22×C8×C151—21no—
55#121×C151—21no—
56#121×C151—21no—
57#121×C151—21no—
58#121×C151—21no—
59#120×C151—42no—
60#120×C151—42no—
61C2×C4⋊C4×C151D411yescharacteristic, complemented
62C2×C4⋊C4×C151D412yescomplemented
63C2×C22⋊C4×C151—24no—
64C2×C22⋊C4×C151—22no—
65C2×C22⋊C4×C151—21no—
66C2×C22⋊C4×C151—21no—
67C2×C22⋊C4×C151—21no—
68C2×C22⋊C4×C151—21no—
69C2×C22⋊C4×C151—21no—
70C2×C22⋊C4×C151—21no—
71C2×C22⋊C4×C151—21no—
72C2×C22⋊C4×C151—22no—
73C2×C22⋊C4×C151—21no—
74C2×C22⋊C4×C151—44no—
75#102×C151—24no—
76#102×C151—44no—
77C22⋊C8×C151—21no—
78C22⋊C8×C151—21no—
79C22⋊C8×C151—21no—
80C22⋊C8×C151D412yescomplemented
81#95×C151—22no—
82#95×C151—21no—
83#95×C151—21no—
84#95×C151D412yescomplemented
85C24×C151—24no—
86C24×C151—21no—
87C24×C151—22no—
88C24×C151—21no—
89C24×C151—21no—
90C24×C151—21no—
91C24×C151—21no—
92C24×C151—21no—
93C24×C151—21no—
94C24×C151—42no—
95C24×C151—42no—
96C24×C151—42no—
97C24×C151—42no—
98C24×C151—42no—
99C24×C151—41no—
100C24×C151—41no—
101C24×C151—41no—
102C24×C151—41no—
103C24×C151—41no—
104C24×C151—41no—
105C24×C151D812yescomplemented
106C24×C151C2×D411yescharacteristic
107C2×D4×C151—24no—
108C2×D4×C151—24no—
109C2×D4×C151—22no—
110C2×D4×C151—21no—
111C2×D4×C151—22no—
112C2×D4×C151—21no—
113C2×D4×C151—42no—
114C2×D4×C151—42no—
115C2×D4×C151—48no—
116C2×D4×C151—42no—
117C2×D4×C151—44no—
118C2×D4×C151—44no—
119C2×D4×C151—44no—
120C2×D4×C151—44no—
121C2×D4×C151—48no—
122C2×D4×C151—48no—
123C2×D4×C151—416no—
124C2×D4×C151—416no—
125C2×D4×C151—44no—
126C2×D4×C151—41no—
127C2×D4×C151—41no—
128C2×D4×C151—41no—
129C2×D4×C151—41no—
130C2×D4×C151—41no—
131C2×D4×C151—41no—
132C2×D4×C151—41no—
133C2×D4×C151—41no—
134C2×D4×C151—82no—
135C2×D4×C151—82no—
136C22×C4×C151—24no—
137C22×C4×C151—22no—
138C22×C4×C151—21no—
139C22×C4×C151—21no—
140C22×C4×C151—21no—
141C22×C4×C151—22no—
142C22×C4×C151—21no—
143C22×C4×C151—42no—
144C22×C4×C151—42no—
145C22×C4×C151—41no—
146C22×C4×C151—41no—
147C22×C4×C151—42no—
148C22×C4×C151C2×D411yescharacteristic
149C22×C4×C151C2×D411yescharacteristic
150C22×C4×C151C2×D411yescharacteristic
151C22×C4×C151C2×D411yescharacteristic
152C22×C4×C151C2×D411yescharacteristic
153C22×C4×C151#4111yescharacteristic
154D8×C151—48no—
155C2×C8×C151—22no—
156C2×C8×C151—42no—
157C2×C8×C151—42no—
158C2×C8×C151—41no—
159C4⋊C4×C151—21no—
160C4⋊C4×C151—21no—
161C4⋊C4×C151—42no—
162C22⋊C4×C151—48no—
163C22⋊C4×C151—44no—
164C22⋊C4×C151—41no—
165C22⋊C4×C151—41no—
166C22⋊C4×C151—41no—
167C22⋊C4×C151—41no—
168C22⋊C4×C151—41no—
169C22⋊C4×C151—41no—
170C22⋊C4×C151—41no—
171C22⋊C4×C151—41no—
172C22⋊C4×C151—82no—
173C23×C151—22no—
174C23×C151—22no—
175C23×C151—24no—
176C23×C151—22no—
177C23×C151—22no—
178C23×C151—22no—
179C23×C151—44no—
180C23×C151—44no—
181C23×C151—44no—
182C23×C151—42no—
183C23×C151—44no—
184C23×C151—44no—
185C23×C151—44no—
186C23×C151—42no—
187C23×C151—42no—
188C23×C151—42no—
189C23×C151—42no—
190C23×C151—44no—
191C23×C151—41no—
192C23×C151—42no—
193C23×C151—42no—
194C23×C151—41no—
195C23×C151—41no—
196C23×C151—42no—
197C23×C151—42no—
198C23×C151—44no—
199C23×C151—42no—
200C23×C151—41no—
201C23×C151—41no—
202C23×C151—41no—
203C23×C151—41no—
204C23×C151—42no—
205C23×C151—42no—
206C23×C151—82no—
207C23×C151—82no—
208C23×C151—81no—
209C23×C151—81no—
210C23×C151—82no—
211C23×C151—82no—
212C23×C151—82no—
213C23×C151—82no—
214C23×C151—82no—
215C23×C151—81no—
216C23×C151—81no—
217C23×C151—82no—
218C23×C151—81no—
219C23×C151—81no—
220C23×C151#12011yescharacteristic
221C23×C151#12011yescharacteristic
222C23×C151#12111yescharacteristic
223C23×C151C2×D811yescharacteristic
224C23×C151#13511yescharacteristic
225C23×C151AGL(1,ℤ/8)11yescharacteristic
226C23×C151AGL(1,ℤ/8)11yescharacteristic
227D4×C151—24no—
228D4×C151—24no—
229D4×C151—42no—
230D4×C151—44no—
231D4×C151—42no—
232D4×C151—44no—
233D4×C151—42no—
234D4×C151—432no—
235D4×C151—81no—
236D4×C151—88no—
237D4×C151—81no—
238D4×C151—81no—
239D4×C151—81no—
240D4×C151—81no—
241C2×C4×C151—22no—
242C2×C4×C151—22no—
243C2×C4×C151—24no—
244C2×C4×C151—41no—
245C2×C4×C151—41no—
246C2×C4×C151—41no—
247C2×C4×C151—41no—
248C2×C4×C151—44no—
249C2×C4×C151—44no—
250C2×C4×C151—42no—
251C2×C4×C151—42no—
252C2×C4×C151—42no—
253C2×C4×C151—41no—
254C2×C4×C151—41no—
255C2×C4×C151—42no—
256C2×C4×C151—41no—
257C2×C4×C151—41no—
258C2×C4×C151—42no—
259C2×C4×C151—42no—
260C2×C4×C151—42no—
261C2×C4×C151—81no—
262C2×C4×C151#12011yescharacteristic
263C2×C4×C151#12111yescharacteristic
264C2×C4×C151#12111yescharacteristic
265C2×C4×C151#12711yescharacteristic
266C8×C151—42no—
267C8×C151—81no—
268C22×C151—22no—
269C22×C151—22no—
270C22×C151—22no—
271C22×C151—22no—
272C22×C151—21no—
273C22×C151—21no—
274C22×C151—21no—
275C22×C151—21no—
276C22×C151—44no—
277C22×C151—44no—
278C22×C151—44no—
279C22×C151—44no—
280C22×C151—42no—
281C22×C151—44no—
282C22×C151—82no—
283C22×C151—82no—
284C22×C151—82no—
285C22×C151—82no—
286C22×C151—84no—
287C22×C151—82no—
288C22×C151—84no—
289C22×C151—84no—
290C22×C151—82no—
291C22×C151—84no—
292C22×C151—82no—
293C22×C151—81no—
294C22×C151—82no—
295C22×C151—81no—
296C22×C151—82no—
297C22×C151—82no—
298C22×C151—81no—
299C22×C151—81no—
300C22×C151—81no—
301C22×C151#39211yescharacteristic
302C22×C151#44711yescharacteristic
303C22×C151#44711yescharacteristic
304C22×C151#44911yescharacteristic
305C22×C151#44911yescharacteristic
306C22×C151#45312yes—
307C22×C151B(4,𝔽2)12yes—
308C22×C151#46611yescharacteristic
309C22×C151#46911yescharacteristic
310C4×C151—21no—
311C4×C151—21no—
312C4×C151—21no—
313C4×C151—21no—
314C4×C151—44no—
315C4×C151—82no—
316C4×C151—81no—
317C4×C151—81no—
318C2×C151—21no—
319C2×C151—21no—
320C2×C151—21no—
321C2×C151—21no—
322C2×C151—82no—
323C2×C151—84no—
324C2×C151—161no—
325C2×C151#159512yes—
326C2×C151#160012yes—
327C2×C151#199911yescharacteristic
328C2×C151#200211yescharacteristic
329C2×C151#202111yescharacteristic
330#9914C15111yesmaximal, characteristic, direct product factor, Sylow
331C151#991411yescharacteristic, direct product factor, Sylow
332C2×#447C2×C15111yescharacteristic, complemented
333#2617C2×C15111yescharacteristic, complemented
334C2×#392C2×C15111yescharacteristic, complemented
335#1786C2×C15111yescharacteristic, complemented
336C2×#327C2×C15111yescharacteristic, complemented
337C2×#323C2×C15111yescharacteristic, complemented
338#1294C2×C15111yescharacteristic, complemented
339C23×D4—21no—
340C23×D4C22×C15111yescharacteristic
341C22×D8—21no—
342C2×#121C22×C15111yescharacteristic
343C2×#120—21no—
344C22×C22⋊C4—21no—
345C22×C22⋊C4C22×C15111yescharacteristic
346#447—22no—
347#447—22no—
348C2×#102—21no—
349C2×#102—22no—
350C2×C22⋊C8C22×C15111yescharacteristic
351C2×C22⋊C8C22×C15111yescharacteristic
352#397—21no—
353#394—22no—
354#392—21no—
355#392—22no—
356#392—22no—
357#386—21no—
358#380C22×C15111yescharacteristic
359C2×#95C22×C15111yescharacteristic
360#327—22no—
361#323—22no—
362C25—21no—
363C25D4×C15111yescharacteristic
364C22×D4—24no—
365C22×D4—21no—
366C22×D4—22no—
367C22×D4—21no—
368C22×D4—21no—
369C22×D4—21no—
370C22×D4—21no—
371C22×D4—21no—
372C22×D4—44no—
373C22×D4—44no—
374C22×D4—44no—
375C22×D4—42no—
376C22×D4—42no—
377C22×D4D4×C15111yescharacteristic, complemented
378C22×D4D4×C15112yescomplemented
379C23×C4—21no—
380C23×C4D4×C15111yescharacteristic
381C23×C4C23×C15111yescharacteristic
382C2×D8—24no—
383C2×D8—44no—
384C22×C8—21no—
385C22×C8—21no—
386#121—21no—
387#121—21no—
388#121—21no—
389#121—21no—
390#120—42no—
391#120—42no—
392C2×C4⋊C4D4×C15111yescharacteristic, complemented
393C2×C4⋊C4D4×C15112yescomplemented
394C2×C22⋊C4—24no—
395C2×C22⋊C4—22no—
396C2×C22⋊C4—21no—
397C2×C22⋊C4—21no—
398C2×C22⋊C4—21no—
399C2×C22⋊C4—21no—
400C2×C22⋊C4—21no—
401C2×C22⋊C4—21no—
402C2×C22⋊C4—21no—
403C2×C22⋊C4—21no—
404C2×C22⋊C4—22no—
405C2×C22⋊C4—44no—
406#102—24no—
407#102—44no—
408C22⋊C8—21no—
409C22⋊C8—21no—
410C22⋊C8—21no—
411C22⋊C8D4×C15112yescomplemented
412#95—22no—
413#95—21no—
414#95—21no—
415#95D4×C15112yescomplemented
416C24—24no—
417C24—21no—
418C24—21no—
419C24—22no—
420C24—21no—
421C24—21no—
422C24—21no—
423C24—21no—
424C24—21no—
425C24—42no—
426C24—42no—
427C24—42no—
428C24—42no—
429C24—42no—
430C24—41no—
431C24—41no—
432C24—41no—
433C24—41no—
434C24—41no—
435C24—41no—
436C24D8×C15112yescomplemented
437C24C2×D4×C15111yescharacteristic
438C2×D4—24no—
439C2×D4—24no—
440C2×D4—22no—
441C2×D4—21no—
442C2×D4—22no—
443C2×D4—21no—
444C2×D4—42no—
445C2×D4—42no—
446C2×D4—48no—
447C2×D4—42no—
448C2×D4—44no—
449C2×D4—44no—
450C2×D4—44no—
451C2×D4—44no—
452C2×D4—48no—
453C2×D4—48no—
454C2×D4—416no—
455C2×D4—416no—
456C2×D4—44no—
457C2×D4—41no—
458C2×D4—41no—
459C2×D4—41no—
460C2×D4—41no—
461C2×D4—41no—
462C2×D4—41no—
463C2×D4—41no—
464C2×D4—41no—
465C2×D4—82no—
466C2×D4—82no—
467C22×C4—24no—
468C22×C4—22no—
469C22×C4—21no—
470C22×C4—21no—
471C22×C4—22no—
472C22×C4—21no—
473C22×C4—21no—
474C22×C4—42no—
475C22×C4—42no—
476C22×C4—41no—
477C22×C4—41no—
478C22×C4—42no—
479C22×C4C2×D4×C15111yescharacteristic
480C22×C4C2×D4×C15111yescharacteristic
481C22×C4C2×D4×C15111yescharacteristic
482C22×C4C2×D4×C15111yescharacteristic
483C22×C4C2×D4×C15111yescharacteristic
484C22×C4#41×C15111yescharacteristic
485D8—48no—
486C2×C8—22no—
487C2×C8—42no—
488C2×C8—42no—
489C2×C8—41no—
490C4⋊C4—21no—
491C4⋊C4—21no—
492C4⋊C4—42no—
493C22⋊C4—48no—
494C22⋊C4—44no—
495C22⋊C4—41no—
496C22⋊C4—41no—
497C22⋊C4—41no—
498C22⋊C4—41no—
499C22⋊C4—41no—
500C22⋊C4—41no—
501C22⋊C4—41no—
502C22⋊C4—41no—
503C22⋊C4—82no—
504C23—22no—
505C23—22no—
506C23—24no—
507C23—22no—
508C23—22no—
509C23—22no—
510C23—44no—
511C23—42no—
512C23—44no—
513C23—44no—
514C23—44no—
515C23—42no—
516C23—42no—
517C23—42no—
518C23—42no—
519C23—44no—
520C23—44no—
521C23—44no—
522C23—41no—
523C23—42no—
524C23—42no—
525C23—41no—
526C23—41no—
527C23—42no—
528C23—42no—
529C23—44no—
530C23—42no—
531C23—41no—
532C23—41no—
533C23—41no—
534C23—41no—
535C23—42no—
536C23—42no—
537C23—82no—
538C23—82no—
539C23—81no—
540C23—81no—
541C23—82no—
542C23—82no—
543C23—82no—
544C23—82no—
545C23—82no—
546C23—81no—
547C23—81no—
548C23—82no—
549C23—81no—
550C23—81no—
551C23#120×C15111yescharacteristic
552C23#120×C15111yescharacteristic
553C23#121×C15111yescharacteristic
554C23C2×D8×C15111yescharacteristic
555C23#135×C15111yescharacteristic
556C23AGL(1,ℤ/8)×C15111yescharacteristic
557C23AGL(1,ℤ/8)×C15111yescharacteristic
558D4—24no—
559D4—24no—
560D4—42no—
561D4—44no—
562D4—42no—
563D4—44no—
564D4—42no—
565D4—432no—
566D4—81no—
567D4—88no—
568D4—81no—
569D4—81no—
570D4—81no—
571D4—81no—
572C2×C4—22no—
573C2×C4—22no—
574C2×C4—24no—
575C2×C4—41no—
576C2×C4—41no—
577C2×C4—41no—
578C2×C4—41no—
579C2×C4—44no—
580C2×C4—44no—
581C2×C4—42no—
582C2×C4—42no—
583C2×C4—42no—
584C2×C4—41no—
585C2×C4—41no—
586C2×C4—42no—
587C2×C4—41no—
588C2×C4—41no—
589C2×C4—42no—
590C2×C4—42no—
591C2×C4—42no—
592C2×C4—81no—
593C2×C4#120×C15111yescharacteristic
594C2×C4#121×C15111yescharacteristic
595C2×C4#121×C15111yescharacteristic
596C2×C4#127×C15111yescharacteristic
597C8—42no—
598C8—81no—
599C22—22no—
600C22—22no—
601C22—22no—
602C22—22no—
603C22—21no—
604C22—21no—
605C22—21no—
606C22—21no—
607C22—44no—
608C22—44no—
609C22—44no—
610C22—44no—
611C22—42no—
612C22—44no—
613C22—82no—
614C22—82no—
615C22—82no—
616C22—82no—
617C22—84no—
618C22—82no—
619C22—84no—
620C22—84no—
621C22—82no—
622C22—84no—
623C22—82no—
624C22—81no—
625C22—82no—
626C22—81no—
627C22—82no—
628C22—82no—
629C22—81no—
630C22—81no—
631C22—81no—
632C22#392×C15111yescharacteristic
633C22#447×C15111yescharacteristic
634C22#447×C15111yescharacteristic
635C22#449×C15111yescharacteristic
636C22#449×C15111yescharacteristic
637C22#453×C15112yes—
638C22B(4,𝔽2)×C15112yes—
639C22#466×C15111yescharacteristic
640C22#469×C15111yescharacteristic
641C4—21no—
642C4—21no—
643C4—21no—
644C4—21no—
645C4—44no—
646C4—82no—
647C4—81no—
648C4—81no—
649C2—21no—
650C2—21no—
651C2—21no—
652C2—21no—
653C2—82no—
654C2—84no—
655C2—161no—
656C2#1595×C15112yes—
657C2#1600×C15112yes—
658C2#1999×C15111yescharacteristic
659C2#2002×C15111yescharacteristic
660C2#2021×C15111yescharacteristic
subgroupG/H
center, socleC23×C151#120
commutator, Frattini, cosocleC23×C4C23×C151
LCSG ▷ C23×C4 ▷ C22 ▷ C1
UCSC1 ◁ C23×C151 ◁ C23×C4×C151 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×#447×C151C2semidirect
2. #2617×C151C2semidirect
3. C2×#392×C151C2semidirect
4. #1786×C151C2semidirect
5. C2×#327×C151C2semidirect
6. C2×#323×C151C2semidirect
7. #1294×C151C2semidirect
46. C22×D4×C151D4semidirect
47. C22×D4×C151D4semidirect
61. C2×C4⋊C4×C151D4semidirect
62. C2×C4⋊C4×C151D4semidirect
80. C22⋊C8×C151D4semidirect
84. #95×C151D4semidirect
105. C24×C151D8semidirect
330. #9914C151direct (N × H)
331. C151#9914direct (N × H)
332. C2×#447C2×C151semidirect
333. #2617C2×C151semidirect
334. C2×#392C2×C151semidirect
335. #1786C2×C151semidirect
336. C2×#327C2×C151semidirect
337. C2×#323C2×C151semidirect
338. #1294C2×C151semidirect
377. C22×D4D4×C151semidirect
378. C22×D4D4×C151semidirect
392. C2×C4⋊C4D4×C151semidirect
393. C2×C4⋊C4D4×C151semidirect
411. C22⋊C8D4×C151semidirect
415. #95D4×C151semidirect
436. C24D8×C151semidirect

Maximal subgroups

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

subgroupindex
C2×#447×C1512
#2617×C1512
C2×#392×C1512
#1786×C1512
C2×#327×C1512
C2×#323×C1512
#1294×C1512
#9914151