Finite Group Databasebeta

← C151×#13082 #50318007

Subgroups — C151×#13082 #50318007

Order 38656.

1088 conjugacy classes of subgroups.

The subgroup lattice has 644 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#100×C151C211yesmaximal, characteristic, complemented
2#2403×C151C211yesmaximal, characteristic
3C2×AΣL(1,𝔽16)×C151C212yesmaximal, complemented
4#1781×C151C211yesmaximal, characteristic, complemented
5#1390×C151C212yesmaximal, complemented
6C23×D4×C151C411yescharacteristic, complemented
7C23×D4×C151C2211yescharacteristic
8C22×M16×C151—21no—
9C2×#120×C151—21no—
10C2×#120×C151C411yescharacteristic, complemented
11C2×#120×C151C2211yescharacteristic
12C2×#100×C151—21no—
13C2×#100×C151—24no—
14C2×#100×C151C2212yes—
15C2×#99×C151—21no—
16C2×#99×C151C2212yes—
17#392×C151—21no—
18#392×C151—21no—
19#386×C151—21no—
20#386×C151C411yescharacteristic, complemented
21#386×C151C2211yescharacteristic
22#379×C151—21no—
23#379×C151C411yescharacteristic, complemented
24AΣL(1,𝔽16)×C151—24no—
25C25×C151C2×C411yescharacteristic
26C25×C151C2×C411yescharacteristic
27C25×C151D411yescharacteristic
28C22×D4×C151—22no—
29C22×D4×C151—22no—
30C22×D4×C151—21no—
31C22×D4×C151—21no—
32C22×D4×C151—21no—
33C22×D4×C151—21no—
34C22×D4×C151—41no—
35C22×D4×C151—41no—
36C22×D4×C151—41no—
37C22×D4×C151—41no—
38C22×D4×C151—42no—
39C22×D4×C151—44no—
40C22×D4×C151C2×C411yescharacteristic
41C22×D4×C151D411yescharacteristic
42C22×D4×C151D411yescharacteristic
43C22×D4×C151C2311yescharacteristic
44C23×C4×C151C2×C411yescharacteristic
45C23×C4×C151D411yescharacteristic
46C2×M16×C151—24no—
47C2×M16×C151—22no—
48C2×M16×C151—41no—
49C2×M16×C151—42no—
50C22×C8×C151—41no—
51#120×C151—22no—
52#120×C151—22no—
53#120×C151—44no—
54#120×C151—42no—
55C2×C22⋊C4×C151—21no—
56C2×C22⋊C4×C151—21no—
57C2×C22⋊C4×C151—21no—
58C2×C22⋊C4×C151—21no—
59C2×C22⋊C4×C151—21no—
60C2×C22⋊C4×C151—21no—
61C2×C22⋊C4×C151—22no—
62C2×C22⋊C4×C151—41no—
63C2×C22⋊C4×C151—41no—
64C2×C22⋊C4×C151C2×C411yescharacteristic
65C2×C22⋊C4×C151C2×C411yescharacteristic
66#100×C151—24no—
67#100×C151—22no—
68#100×C151D414yescomplemented
69#99×C151—22no—
70#99×C151—22no—
71#99×C151—42no—
72#95×C151—21no—
73#95×C151—21no—
74C24×C151—21no—
75C24×C151—21no—
76C24×C151—21no—
77C24×C151—21no—
78C24×C151—21no—
79C24×C151—22no—
80C24×C151—22no—
81C24×C151—22no—
82C24×C151—41no—
83C24×C151—41no—
84C24×C151—42no—
85C24×C151—41no—
86C24×C151—42no—
87C24×C151—42no—
88C24×C151—41no—
89C24×C151—81no—
90C24×C151—81no—
91C24×C151—81no—
92C24×C151C22⋊C411yescharacteristic
93C24×C151C22⋊C411yescharacteristic
94C24×C151C22⋊C411yescharacteristic
95C24×C151C22×C411yescharacteristic
96C24×C151C2×D411yescharacteristic
97C2×D4×C151—24no—
98C2×D4×C151—22no—
99C2×D4×C151—22no—
100C2×D4×C151—22no—
101C2×D4×C151—22no—
102C2×D4×C151—21no—
103C2×D4×C151—21no—
104C2×D4×C151—41no—
105C2×D4×C151—41no—
106C2×D4×C151—41no—
107C2×D4×C151—41no—
108C2×D4×C151—41no—
109C2×D4×C151—41no—
110C2×D4×C151—44no—
111C2×D4×C151—44no—
112C2×D4×C151—44no—
113C2×D4×C151—44no—
114C2×D4×C151—42no—
115C2×D4×C151—42no—
116C2×D4×C151—42no—
117C2×D4×C151—42no—
118C2×D4×C151—44no—
119C2×D4×C151—44no—
120C2×D4×C151—44no—
121C2×D4×C151—41no—
122C2×D4×C151—41no—
123C2×D4×C151—44no—
124C2×D4×C151—42no—
125C2×D4×C151—42no—
126C2×D4×C151—42no—
127C2×D4×C151—42no—
128C2×D4×C151—81no—
129C2×D4×C151—81no—
130C2×D4×C151C2×D412yes—
131C2×D4×C151#4112yes—
132C22×C4×C151—21no—
133C22×C4×C151—21no—
134C22×C4×C151—22no—
135C22×C4×C151—21no—
136C22×C4×C151—21no—
137C22×C4×C151—21no—
138C22×C4×C151—21no—
139C22×C4×C151—21no—
140C22×C4×C151—42no—
141C22×C4×C151—41no—
142C22×C4×C151—42no—
143C22×C4×C151C22⋊C411yescharacteristic
144C22×C4×C151C2×D411yescharacteristic
145M16×C151—24no—
146M16×C151—44no—
147M16×C151—42no—
148C2×C8×C151—44no—
149C2×C8×C151—42no—
150C22⋊C4×C151—22no—
151C22⋊C4×C151—42no—
152C22⋊C4×C151—42no—
153C22⋊C4×C151—42no—
154C22⋊C4×C151—42no—
155C22⋊C4×C151—41no—
156C22⋊C4×C151—41no—
157C22⋊C4×C151—41no—
158C22⋊C4×C151—42no—
159C22⋊C4×C151—42no—
160C22⋊C4×C151—81no—
161C22⋊C4×C151—82no—
162C22⋊C4×C151—82no—
163C23×C151—22no—
164C23×C151—21no—
165C23×C151—21no—
166C23×C151—21no—
167C23×C151—21no—
168C23×C151—21no—
169C23×C151—21no—
170C23×C151—22no—
171C23×C151—21no—
172C23×C151—21no—
173C23×C151—21no—
174C23×C151—21no—
175C23×C151—21no—
176C23×C151—21no—
177C23×C151—41no—
178C23×C151—42no—
179C23×C151—42no—
180C23×C151—42no—
181C23×C151—42no—
182C23×C151—41no—
183C23×C151—41no—
184C23×C151—41no—
185C23×C151—41no—
186C23×C151—41no—
187C23×C151—41no—
188C23×C151—41no—
189C23×C151—42no—
190C23×C151—42no—
191C23×C151—41no—
192C23×C151—41no—
193C23×C151—41no—
194C23×C151—41no—
195C23×C151—42no—
196C23×C151—42no—
197C23×C151—42no—
198C23×C151—42no—
199C23×C151—41no—
200C23×C151—41no—
201C23×C151—41no—
202C23×C151—81no—
203C23×C151—81no—
204C23×C151—81no—
205C23×C151—81no—
206C23×C151—82no—
207C23×C151—84no—
208C23×C151—84no—
209C23×C151—84no—
210C23×C151—84no—
211C23×C151—84no—
212C23×C151—84no—
213C23×C151—82no—
214C23×C151#9911yescharacteristic
215C23×C151#9911yescharacteristic
216C23×C151C2×C22⋊C411yescharacteristic
217C23×C151C4×D412yes—
218C23×C151#12112yes—
219D4×C151—42no—
220D4×C151—42no—
221D4×C151—44no—
222D4×C151—44no—
223D4×C151—42no—
224D4×C151—42no—
225D4×C151—44no—
226D4×C151—48no—
227D4×C151—44no—
228D4×C151—84no—
229D4×C151—84no—
230C2×C4×C151—22no—
231C2×C4×C151—22no—
232C2×C4×C151—22no—
233C2×C4×C151—22no—
234C2×C4×C151—21no—
235C2×C4×C151—21no—
236C2×C4×C151—21no—
237C2×C4×C151—21no—
238C2×C4×C151—22no—
239C2×C4×C151—41no—
240C2×C4×C151—42no—
241C2×C4×C151—41no—
242C2×C4×C151—42no—
243C2×C4×C151—41no—
244C2×C4×C151—41no—
245C2×C4×C151—41no—
246C2×C4×C151—41no—
247C2×C4×C151—41no—
248C2×C4×C151—41no—
249C2×C4×C151—82no—
250C2×C4×C151—82no—
251C2×C4×C151—82no—
252C2×C4×C151#9912yes—
253C2×C4×C151#12011yescharacteristic
254C2×C4×C151#12311yescharacteristic
255C8×C151—44no—
256C22×C151—21no—
257C22×C151—21no—
258C22×C151—21no—
259C22×C151—21no—
260C22×C151—21no—
261C22×C151—21no—
262C22×C151—21no—
263C22×C151—22no—
264C22×C151—22no—
265C22×C151—42no—
266C22×C151—42no—
267C22×C151—42no—
268C22×C151—42no—
269C22×C151—42no—
270C22×C151—42no—
271C22×C151—42no—
272C22×C151—42no—
273C22×C151—41no—
274C22×C151—41no—
275C22×C151—41no—
276C22×C151—41no—
277C22×C151—42no—
278C22×C151—41no—
279C22×C151—41no—
280C22×C151—41no—
281C22×C151—41no—
282C22×C151—41no—
283C22×C151—41no—
284C22×C151—81no—
285C22×C151—84no—
286C22×C151—84no—
287C22×C151—81no—
288C22×C151—81no—
289C22×C151—81no—
290C22×C151—81no—
291C22×C151—81no—
292C22×C151—84no—
293C22×C151—84no—
294C22×C151—84no—
295C22×C151—84no—
296C22×C151—81no—
297C22×C151—81no—
298C22×C151AΣL(1,𝔽16)12yescomplemented
299C22×C151#38611yescharacteristic
300C22×C151C2×#9911yescharacteristic
301C22×C151C2×#9911yescharacteristic
302C4×C151—21no—
303C4×C151—22no—
304C4×C151—21no—
305C4×C151—42no—
306C4×C151—81no—
307C4×C151—81no—
308C4×C151—162no—
309C2×C151—21no—
310C2×C151—21no—
311C2×C151—22no—
312C2×C151—42no—
313C2×C151—41no—
314C2×C151—42no—
315C2×C151—81no—
316C2×C151—82no—
317C2×C151—81no—
318C2×C151#189811yescharacteristic
319C2×C151C2×AΣL(1,𝔽16)11yescharacteristic
320C2×C151#212111yescharacteristic
321#13082C15111yesmaximal, characteristic, direct product factor, Sylow
322C151#1308211yescharacteristic, direct product factor, Sylow
323C22×#100C2×C15111yescharacteristic, complemented
324#2403C2×C15111yescharacteristic
325C2×AΣL(1,𝔽16)C2×C15112yescomplemented
326#1781C2×C15111yescharacteristic, complemented
327#1390C2×C15112yescomplemented
328C23×D4C4×C15111yescharacteristic, complemented
329C23×D4C22×C15111yescharacteristic
330C22×M16—21no—
331C2×#120—21no—
332C2×#120C4×C15111yescharacteristic, complemented
333C2×#120C22×C15111yescharacteristic
334C2×#100—21no—
335C2×#100—24no—
336C2×#100C22×C15112yes—
337C2×#99—21no—
338C2×#99C22×C15112yes—
339#392—21no—
340#392—21no—
341#386—21no—
342#386C4×C15111yescharacteristic, complemented
343#386C22×C15111yescharacteristic
344#379—21no—
345#379C4×C15111yescharacteristic, complemented
346AΣL(1,𝔽16)—24no—
347C25C2×C4×C15111yescharacteristic
348C25C2×C4×C15111yescharacteristic
349C25D4×C15111yescharacteristic
350C22×D4—21no—
351C22×D4—22no—
352C22×D4—22no—
353C22×D4—21no—
354C22×D4—21no—
355C22×D4—21no—
356C22×D4—42no—
357C22×D4—41no—
358C22×D4—41no—
359C22×D4—44no—
360C22×D4—41no—
361C22×D4—41no—
362C22×D4C2×C4×C15111yescharacteristic
363C22×D4D4×C15111yescharacteristic
364C22×D4D4×C15111yescharacteristic
365C22×D4C23×C15111yescharacteristic
366C23×C4C2×C4×C15111yescharacteristic
367C23×C4D4×C15111yescharacteristic
368C2×M16—24no—
369C2×M16—22no—
370C2×M16—41no—
371C2×M16—42no—
372C22×C8—41no—
373#120—22no—
374#120—22no—
375#120—44no—
376#120—42no—
377C2×C22⋊C4—21no—
378C2×C22⋊C4—21no—
379C2×C22⋊C4—21no—
380C2×C22⋊C4—21no—
381C2×C22⋊C4—21no—
382C2×C22⋊C4—22no—
383C2×C22⋊C4—21no—
384C2×C22⋊C4—41no—
385C2×C22⋊C4—41no—
386C2×C22⋊C4C2×C4×C15111yescharacteristic
387C2×C22⋊C4C2×C4×C15111yescharacteristic
388#100—24no—
389#100—22no—
390#100D4×C15114yescomplemented
391#99—22no—
392#99—22no—
393#99—42no—
394#95—21no—
395#95—21no—
396C24—21no—
397C24—21no—
398C24—21no—
399C24—21no—
400C24—21no—
401C24—22no—
402C24—22no—
403C24—22no—
404C24—41no—
405C24—41no—
406C24—42no—
407C24—41no—
408C24—42no—
409C24—42no—
410C24—41no—
411C24—81no—
412C24—81no—
413C24—81no—
414C24C22⋊C4×C15111yescharacteristic
415C24C22⋊C4×C15111yescharacteristic
416C24C22⋊C4×C15111yescharacteristic
417C24C22×C4×C15111yescharacteristic
418C24C2×D4×C15111yescharacteristic
419C2×D4—24no—
420C2×D4—22no—
421C2×D4—22no—
422C2×D4—22no—
423C2×D4—22no—
424C2×D4—21no—
425C2×D4—21no—
426C2×D4—41no—
427C2×D4—41no—
428C2×D4—41no—
429C2×D4—41no—
430C2×D4—41no—
431C2×D4—41no—
432C2×D4—44no—
433C2×D4—44no—
434C2×D4—44no—
435C2×D4—44no—
436C2×D4—42no—
437C2×D4—42no—
438C2×D4—42no—
439C2×D4—42no—
440C2×D4—44no—
441C2×D4—44no—
442C2×D4—44no—
443C2×D4—41no—
444C2×D4—41no—
445C2×D4—44no—
446C2×D4—42no—
447C2×D4—42no—
448C2×D4—42no—
449C2×D4—42no—
450C2×D4—81no—
451C2×D4—81no—
452C2×D4C2×D4×C15112yes—
453C2×D4#41×C15112yes—
454C22×C4—21no—
455C22×C4—21no—
456C22×C4—22no—
457C22×C4—21no—
458C22×C4—21no—
459C22×C4—21no—
460C22×C4—21no—
461C22×C4—21no—
462C22×C4—42no—
463C22×C4—41no—
464C22×C4—42no—
465C22×C4C22⋊C4×C15111yescharacteristic
466C22×C4C2×D4×C15111yescharacteristic
467M16—24no—
468M16—44no—
469M16—42no—
470C2×C8—44no—
471C2×C8—42no—
472C22⋊C4—22no—
473C22⋊C4—42no—
474C22⋊C4—42no—
475C22⋊C4—42no—
476C22⋊C4—42no—
477C22⋊C4—41no—
478C22⋊C4—41no—
479C22⋊C4—41no—
480C22⋊C4—42no—
481C22⋊C4—42no—
482C22⋊C4—81no—
483C22⋊C4—82no—
484C22⋊C4—82no—
485C23—22no—
486C23—21no—
487C23—21no—
488C23—21no—
489C23—21no—
490C23—21no—
491C23—21no—
492C23—22no—
493C23—21no—
494C23—21no—
495C23—21no—
496C23—21no—
497C23—21no—
498C23—21no—
499C23—41no—
500C23—42no—
501C23—42no—
502C23—42no—
503C23—42no—
504C23—41no—
505C23—41no—
506C23—41no—
507C23—41no—
508C23—41no—
509C23—41no—
510C23—42no—
511C23—41no—
512C23—42no—
513C23—41no—
514C23—41no—
515C23—41no—
516C23—41no—
517C23—42no—
518C23—42no—
519C23—42no—
520C23—42no—
521C23—41no—
522C23—41no—
523C23—41no—
524C23—81no—
525C23—81no—
526C23—81no—
527C23—81no—
528C23—82no—
529C23—84no—
530C23—84no—
531C23—84no—
532C23—84no—
533C23—84no—
534C23—84no—
535C23—82no—
536C23#99×C15111yescharacteristic
537C23#99×C15111yescharacteristic
538C23C2×C22⋊C4×C15111yescharacteristic
539C23C4×D4×C15112yes—
540C23#121×C15112yes—
541D4—42no—
542D4—42no—
543D4—44no—
544D4—44no—
545D4—42no—
546D4—42no—
547D4—44no—
548D4—48no—
549D4—44no—
550D4—84no—
551D4—84no—
552C2×C4—22no—
553C2×C4—22no—
554C2×C4—22no—
555C2×C4—22no—
556C2×C4—21no—
557C2×C4—21no—
558C2×C4—21no—
559C2×C4—21no—
560C2×C4—22no—
561C2×C4—41no—
562C2×C4—42no—
563C2×C4—41no—
564C2×C4—42no—
565C2×C4—41no—
566C2×C4—41no—
567C2×C4—41no—
568C2×C4—41no—
569C2×C4—41no—
570C2×C4—41no—
571C2×C4—82no—
572C2×C4—82no—
573C2×C4—82no—
574C2×C4#99×C15112yes—
575C2×C4#120×C15111yescharacteristic
576C2×C4#123×C15111yescharacteristic
577C8—44no—
578C22—21no—
579C22—21no—
580C22—21no—
581C22—21no—
582C22—21no—
583C22—21no—
584C22—21no—
585C22—22no—
586C22—22no—
587C22—42no—
588C22—42no—
589C22—42no—
590C22—42no—
591C22—42no—
592C22—42no—
593C22—42no—
594C22—42no—
595C22—41no—
596C22—41no—
597C22—41no—
598C22—41no—
599C22—42no—
600C22—41no—
601C22—41no—
602C22—41no—
603C22—41no—
604C22—41no—
605C22—41no—
606C22—81no—
607C22—84no—
608C22—84no—
609C22—81no—
610C22—81no—
611C22—81no—
612C22—81no—
613C22—81no—
614C22—84no—
615C22—84no—
616C22—84no—
617C22—84no—
618C22—81no—
619C22—81no—
620C22AΣL(1,𝔽16)×C15112yescomplemented
621C22#386×C15111yescharacteristic
622C22C2×#99×C15111yescharacteristic
623C22C2×#99×C15111yescharacteristic
624C4—21no—
625C4—22no—
626C4—21no—
627C4—42no—
628C4—81no—
629C4—81no—
630C4—162no—
631C2—21no—
632C2—21no—
633C2—22no—
634C2—42no—
635C2—41no—
636C2—42no—
637C2—81no—
638C2—82no—
639C2—81no—
640C2#1898×C15111yescharacteristic
641C2C2×AΣL(1,𝔽16)×C15111yescharacteristic
642C2#2121×C15111yescharacteristic
subgroupG/H
center, socleC22×C151C2×#99
commutatorC24C22×C4×C151
Frattini, cosocleC22×D4C23×C151
prime radical#2403×C151C2
LCSG ▷ C24 ▷ C22 ▷ C2 ▷ C1
UCSC1 ◁ C22×C151 ◁ C24×C151 ◁ C23×D4×C151 ◁ G

Complements

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

NH ≅ G/Ntype
1. C22×#100×C151C2semidirect
3. C2×AΣL(1,𝔽16)×C151C2semidirect
4. #1781×C151C2semidirect
5. #1390×C151C2semidirect
6. C23×D4×C151C4semidirect
10. C2×#120×C151C4semidirect
20. #386×C151C4semidirect
23. #379×C151C4semidirect
68. #100×C151D4semidirect
298. C22×C151AΣL(1,𝔽16)semidirect
321. #13082C151direct (N × H)
322. C151#13082direct (N × H)
323. C22×#100C2×C151semidirect
325. C2×AΣL(1,𝔽16)C2×C151semidirect
326. #1781C2×C151semidirect
327. #1390C2×C151semidirect
328. C23×D4C4×C151semidirect
332. C2×#120C4×C151semidirect
342. #386C4×C151semidirect
345. #379C4×C151semidirect
390. #100D4×C151semidirect
620. C22AΣL(1,𝔽16)×C151semidirect

Maximal subgroups

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

subgroupindex
C22×#100×C1512
#2403×C1512
C2×AΣL(1,𝔽16)×C1512
#1781×C1512
#1390×C1512
#13082151