Finite Group Databasebeta

← C151×#23649 #50328574

Subgroups — C151×#23649 #50328574

Order 38656.

892 conjugacy classes of subgroups.

The subgroup lattice has 606 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#2905×C151C211yesmaximal, characteristic, complemented
2C2×#421×C151C211yesmaximal, characteristic
3#2896×C151C211yesmaximal, characteristic
4C2×#413×C151C211yesmaximal, characteristic
5#2080×C151C218yesmaximal, complemented
6C2×#344×C151C211yesmaximal, characteristic, complemented
7#1738×C151C211yesmaximal, characteristic, complemented
8C2×H(3,ℤ/4)×C151C211yesmaximal, characteristic, complemented
9C22×#41×C151C2211yescharacteristic
10C22×M16×C151C2211yescharacteristic
11C22×M16×C151C2211yescharacteristic
12C22×M16×C151C2211yescharacteristic
13C22×M16×C151C2211yescharacteristic
14C2×#117×C151C2211yescharacteristic
15C2×#117×C151C2211yescharacteristic
16#424×C151—22no—
17#424×C151C2214yescomplemented
18#423×C151—22no—
19#421×C151—22no—
20#421×C151C2214yes—
21C2×#104×C151—22no—
22#419×C151—21no—
23#418×C151—21no—
24#417×C151—22no—
25#416×C151C2214yes—
26#413×C151—22no—
27#413×C151C2214yes—
28C2×#101×C151—21no—
29C2×#100×C151—21no—
30#344×C151C2214yescomplemented
31#341×C151C2214yescomplemented
32H(3,ℤ/4)×C151C2214yescomplemented
33C2×#41×C151—21no—
34C2×#41×C151—21no—
35C2×#41×C151—21no—
36C2×#41×C151—21no—
37C2×#41×C151—21no—
38C2×#41×C151—21no—
39C2×#41×C151—21no—
40C2×#41×C151—21no—
41C2×#41×C151—21no—
42C2×#41×C151—21no—
43C2×#41×C151D412yes—
44C2×#41×C151C2312yes—
45C22×Q8×C151D411yescharacteristic
46C22×D4×C151—21no—
47C22×D4×C151D411yescharacteristic
48C23×C4×C151—21no—
49C23×C4×C151C2311yescharacteristic
50C2×M16×C151—21no—
51C2×M16×C151—21no—
52C2×M16×C151—21no—
53C2×M16×C151—21no—
54C2×M16×C151—21no—
55C2×M16×C151—21no—
56C2×M16×C151—21no—
57C2×M16×C151—21no—
58C2×M16×C151—21no—
59C2×M16×C151—21no—
60C2×M16×C151—21no—
61C2×M16×C151—21no—
62C2×M16×C151—21no—
63C2×M16×C151—21no—
64C2×M16×C151—21no—
65C2×M16×C151—21no—
66C2×M16×C151—21no—
67C2×M16×C151—21no—
68C2×M16×C151—21no—
69C2×M16×C151—21no—
70C2×M16×C151—21no—
71C2×M16×C151C2312yes—
72C2×M16×C151C2312yes—
73C2×M16×C151C2312yes—
74C22×C8×C151—21no—
75C22×C8×C151—21no—
76C22×C8×C151—21no—
77C22×C8×C151C2312yes—
78#117×C151—21no—
79#117×C151—21no—
80#117×C151—21no—
81#117×C151—21no—
82#117×C151—21no—
83#117×C151D412yes—
84#117×C151C2312yes—
85#117×C151C2312yes—
86C2×C4⋊C4×C151—21no—
87C2×C4⋊C4×C151—21no—
88C2×C22⋊C4×C151—21no—
89C2×C22⋊C4×C151—21no—
90C2×C42×C151—21no—
91C2×C42×C151D412yes—
92C4⋊C8×C151—28no—
93#104×C151—28no—
94#103×C151—24no—
95#102×C151—24no—
96#101×C151—24no—
97#100×C151—24no—
98C24×C151—21no—
99C24×C151#4111yescharacteristic
100#41×C151—22no—
101#41×C151—22no—
102#41×C151—22no—
103#41×C151—22no—
104#41×C151—22no—
105#41×C151—22no—
106#41×C151—22no—
107#41×C151—22no—
108#41×C151—41no—
109#41×C151—41no—
110#41×C151—41no—
111#41×C151—41no—
112#41×C151—41no—
113#41×C151—41no—
114#41×C151—41no—
115#41×C151—41no—
116C2×Q8×C151—21no—
117C2×Q8×C151—21no—
118C2×Q8×C151—21no—
119C2×Q8×C151—21no—
120C2×Q8×C151—21no—
121C2×Q8×C151C2×D412yes—
122C2×D4×C151—22no—
123C2×D4×C151—22no—
124C2×D4×C151—21no—
125C2×D4×C151—21no—
126C2×D4×C151—21no—
127C2×D4×C151—21no—
128C2×D4×C151—21no—
129C2×D4×C151—41no—
130C2×D4×C151—41no—
131C2×D4×C151—41no—
132C2×D4×C151—41no—
133C2×D4×C151C2×D412yes—
134C22×C4×C151—21no—
135C22×C4×C151—22no—
136C22×C4×C151—22no—
137C22×C4×C151—22no—
138C22×C4×C151—41no—
139C22×C4×C151—41no—
140C22×C4×C151—41no—
141C22×C4×C151—41no—
142C22×C4×C151—41no—
143C22×C4×C151C2×D411yescharacteristic
144C22×C4×C151C2×D411yescharacteristic
145C22×C4×C151C2×D411yescharacteristic
146C22×C4×C151C2×D411yescharacteristic
147C22×C4×C151#4111yescharacteristic
148C22×C4×C151#4111yescharacteristic
149C22×C4×C151#4111yescharacteristic
150C22×C4×C151#4111yescharacteristic
151C22×C4×C151#4111yescharacteristic
152C22×C4×C151#4111yescharacteristic
153C22×C4×C151#4111yescharacteristic
154C22×C4×C151#4111yescharacteristic
155C22×C4×C151#4111yescharacteristic
156C22×C4×C151C2411yescharacteristic
157M16×C151—22no—
158M16×C151—22no—
159M16×C151—22no—
160M16×C151—22no—
161M16×C151—22no—
162M16×C151—22no—
163M16×C151—41no—
164M16×C151—41no—
165M16×C151—41no—
166M16×C151—41no—
167M16×C151—41no—
168M16×C151—41no—
169M16×C151—41no—
170M16×C151—41no—
171M16×C151—41no—
172M16×C151—41no—
173C2×C8×C151—22no—
174C2×C8×C151—22no—
175C2×C8×C151—22no—
176C2×C8×C151—22no—
177C2×C8×C151—22no—
178C2×C8×C151—22no—
179C2×C8×C151—41no—
180C2×C8×C151—41no—
181C2×C8×C151—41no—
182C2×C8×C151—41no—
183C2×C8×C151—41no—
184C2×C8×C151—41no—
185C4⋊C4×C151—22no—
186C4⋊C4×C151—22no—
187C4⋊C4×C151—22no—
188C4⋊C4×C151—41no—
189C22⋊C4×C151—22no—
190C22⋊C4×C151—22no—
191C22⋊C4×C151—22no—
192C22⋊C4×C151—41no—
193C42×C151—22no—
194C42×C151—22no—
195C42×C151—41no—
196C42×C151C2×D414yes—
197C23×C151—22no—
198C23×C151—41no—
199C23×C151—41no—
200C23×C151—81no—
201C23×C151—82no—
202C23×C151#12311yescharacteristic
203C23×C151#12311yescharacteristic
204C23×C151#12311yescharacteristic
205C23×C151#12311yescharacteristic
206C23×C151#12611yescharacteristic
207C23×C151#12611yescharacteristic
208C23×C151C2×#4111yescharacteristic
209Q8×C151—22no—
210Q8×C151—22no—
211Q8×C151—41no—
212Q8×C151—41no—
213D4×C151—22no—
214D4×C151—22no—
215D4×C151—42no—
216D4×C151—42no—
217D4×C151—42no—
218D4×C151—42no—
219D4×C151—41no—
220D4×C151—41no—
221C2×C4×C151—22no—
222C2×C4×C151—24no—
223C2×C4×C151—41no—
224C2×C4×C151—41no—
225C2×C4×C151—42no—
226C2×C4×C151—42no—
227C2×C4×C151—42no—
228C2×C4×C151—42no—
229C2×C4×C151—42no—
230C2×C4×C151—82no—
231C2×C4×C151—82no—
232C2×C4×C151#12111yescharacteristic
233C2×C4×C151#12111yescharacteristic
234C2×C4×C151#12111yescharacteristic
235C2×C4×C151#12111yescharacteristic
236C2×C4×C151#12311yescharacteristic
237C2×C4×C151#12311yescharacteristic
238C2×C4×C151#12311yescharacteristic
239C2×C4×C151#12311yescharacteristic
240C2×C4×C151#12311yescharacteristic
241C2×C4×C151#12311yescharacteristic
242C2×C4×C151#12311yescharacteristic
243C2×C4×C151#12311yescharacteristic
244C2×C4×C151#12411yescharacteristic
245C2×C4×C151#12411yescharacteristic
246C2×C4×C151#12411yescharacteristic
247C2×C4×C151#12411yescharacteristic
248C2×C4×C151#12611yescharacteristic
249C2×C4×C151#12611yescharacteristic
250C2×C4×C151#12611yescharacteristic
251C2×C4×C151#12611yescharacteristic
252C2×C4×C151#12611yescharacteristic
253C2×C4×C151#12611yescharacteristic
254C2×C4×C151C22×D411yescharacteristic
255C2×C4×C151C22×D411yescharacteristic
256C2×C4×C151C2×#4111yescharacteristic
257C2×C4×C151C2×#4111yescharacteristic
258C2×C4×C151C2×#4111yescharacteristic
259C2×C4×C151C2×#4111yescharacteristic
260C8×C151—42no—
261C8×C151—42no—
262C8×C151—42no—
263C8×C151—42no—
264C22×C151—41no—
265C22×C151—41no—
266C22×C151—41no—
267C22×C151—41no—
268C22×C151—41no—
269C22×C151—41no—
270C22×C151—41no—
271C22×C151—42no—
272C22×C151—82no—
273C22×C151—82no—
274C22×C151—82no—
275C22×C151#39711yescharacteristic
276C22×C151#39711yescharacteristic
277C22×C151#39711yescharacteristic
278C22×C151#39711yescharacteristic
279C22×C151C2×#12311yescharacteristic
280C22×C151C2×#12311yescharacteristic
281C22×C151C2×#12611yescharacteristic
282C4×C151—44no—
283C4×C151—42no—
284C4×C151—82no—
285C4×C151#39711yescharacteristic
286C4×C151#39711yescharacteristic
287C4×C151#39711yescharacteristic
288C4×C151#39711yescharacteristic
289C4×C151C2×#12111yescharacteristic
290C4×C151C2×#12311yescharacteristic
291C4×C151C2×#12411yescharacteristic
292C4×C151C2×#12611yescharacteristic
293C2×C151—21no—
294C2×C151—21no—
295C2×C151—21no—
296C2×C151—21no—
297C2×C151—21no—
298C2×C151—21no—
299C2×C151—21no—
300C2×C151—82no—
301C2×C151C2×#39711yescharacteristic
302#23649C15111yesmaximal, characteristic, direct product factor, Sylow
303C151#2364911yescharacteristic, direct product factor, Sylow
304#2905C2×C15111yescharacteristic, complemented
305C2×#421C2×C15111yescharacteristic
306#2896C2×C15111yescharacteristic
307C2×#413C2×C15111yescharacteristic
308#2080C2×C15118yescomplemented
309C2×#344C2×C15111yescharacteristic, complemented
310#1738C2×C15111yescharacteristic, complemented
311C2×H(3,ℤ/4)C2×C15111yescharacteristic, complemented
312C22×#41C22×C15111yescharacteristic
313C22×M16C22×C15111yescharacteristic
314C22×M16C22×C15111yescharacteristic
315C22×M16C22×C15111yescharacteristic
316C22×M16C22×C15111yescharacteristic
317C2×#117C22×C15111yescharacteristic
318C2×#117C22×C15111yescharacteristic
319#424—22no—
320#424C22×C15114yescomplemented
321#423—22no—
322#421—22no—
323#421C22×C15114yes—
324C2×#104—22no—
325#419—21no—
326#418—21no—
327#417—22no—
328#416C22×C15114yes—
329#413—22no—
330#413C22×C15114yes—
331C2×#101—21no—
332C2×#100—21no—
333#344C22×C15114yescomplemented
334#341C22×C15114yescomplemented
335H(3,ℤ/4)C22×C15114yescomplemented
336C2×#41—21no—
337C2×#41—21no—
338C2×#41—21no—
339C2×#41—21no—
340C2×#41—21no—
341C2×#41—21no—
342C2×#41—21no—
343C2×#41—21no—
344C2×#41—21no—
345C2×#41—21no—
346C2×#41D4×C15112yes—
347C2×#41C23×C15112yes—
348C22×Q8D4×C15111yescharacteristic
349C22×D4—21no—
350C22×D4D4×C15111yescharacteristic
351C23×C4—21no—
352C23×C4C23×C15111yescharacteristic
353C2×M16—21no—
354C2×M16—21no—
355C2×M16—21no—
356C2×M16—21no—
357C2×M16—21no—
358C2×M16—21no—
359C2×M16—21no—
360C2×M16—21no—
361C2×M16—21no—
362C2×M16—21no—
363C2×M16—21no—
364C2×M16—21no—
365C2×M16—21no—
366C2×M16—21no—
367C2×M16—21no—
368C2×M16—21no—
369C2×M16—21no—
370C2×M16—21no—
371C2×M16—21no—
372C2×M16—21no—
373C2×M16—21no—
374C2×M16C23×C15112yes—
375C2×M16C23×C15112yes—
376C2×M16C23×C15112yes—
377C22×C8—21no—
378C22×C8—21no—
379C22×C8—21no—
380C22×C8C23×C15112yes—
381#117—21no—
382#117—21no—
383#117—21no—
384#117—21no—
385#117—21no—
386#117D4×C15112yes—
387#117C23×C15112yes—
388#117C23×C15112yes—
389C2×C4⋊C4—21no—
390C2×C4⋊C4—21no—
391C2×C22⋊C4—21no—
392C2×C22⋊C4—21no—
393C2×C42—21no—
394C2×C42D4×C15112yes—
395C4⋊C8—28no—
396#104—28no—
397#103—24no—
398#102—24no—
399#101—24no—
400#100—24no—
401C24—21no—
402C24#41×C15111yescharacteristic
403#41—22no—
404#41—22no—
405#41—22no—
406#41—22no—
407#41—22no—
408#41—22no—
409#41—22no—
410#41—22no—
411#41—41no—
412#41—41no—
413#41—41no—
414#41—41no—
415#41—41no—
416#41—41no—
417#41—41no—
418#41—41no—
419C2×Q8—21no—
420C2×Q8—21no—
421C2×Q8—21no—
422C2×Q8—21no—
423C2×Q8—21no—
424C2×Q8C2×D4×C15112yes—
425C2×D4—22no—
426C2×D4—22no—
427C2×D4—21no—
428C2×D4—21no—
429C2×D4—21no—
430C2×D4—21no—
431C2×D4—21no—
432C2×D4—41no—
433C2×D4—41no—
434C2×D4—41no—
435C2×D4—41no—
436C2×D4C2×D4×C15112yes—
437C22×C4—21no—
438C22×C4—22no—
439C22×C4—22no—
440C22×C4—22no—
441C22×C4—41no—
442C22×C4—41no—
443C22×C4—41no—
444C22×C4—41no—
445C22×C4—41no—
446C22×C4C2×D4×C15111yescharacteristic
447C22×C4C2×D4×C15111yescharacteristic
448C22×C4C2×D4×C15111yescharacteristic
449C22×C4C2×D4×C15111yescharacteristic
450C22×C4#41×C15111yescharacteristic
451C22×C4#41×C15111yescharacteristic
452C22×C4#41×C15111yescharacteristic
453C22×C4#41×C15111yescharacteristic
454C22×C4#41×C15111yescharacteristic
455C22×C4#41×C15111yescharacteristic
456C22×C4#41×C15111yescharacteristic
457C22×C4#41×C15111yescharacteristic
458C22×C4#41×C15111yescharacteristic
459C22×C4C24×C15111yescharacteristic
460M16—22no—
461M16—22no—
462M16—22no—
463M16—22no—
464M16—22no—
465M16—22no—
466M16—41no—
467M16—41no—
468M16—41no—
469M16—41no—
470M16—41no—
471M16—41no—
472M16—41no—
473M16—41no—
474M16—41no—
475M16—41no—
476C2×C8—22no—
477C2×C8—22no—
478C2×C8—22no—
479C2×C8—22no—
480C2×C8—22no—
481C2×C8—22no—
482C2×C8—41no—
483C2×C8—41no—
484C2×C8—41no—
485C2×C8—41no—
486C2×C8—41no—
487C2×C8—41no—
488C4⋊C4—22no—
489C4⋊C4—22no—
490C4⋊C4—22no—
491C4⋊C4—41no—
492C22⋊C4—22no—
493C22⋊C4—22no—
494C22⋊C4—22no—
495C22⋊C4—41no—
496C42—22no—
497C42—22no—
498C42—41no—
499C42C2×D4×C15114yes—
500C23—22no—
501C23—41no—
502C23—41no—
503C23—81no—
504C23—82no—
505C23#123×C15111yescharacteristic
506C23#123×C15111yescharacteristic
507C23#123×C15111yescharacteristic
508C23#123×C15111yescharacteristic
509C23#126×C15111yescharacteristic
510C23#126×C15111yescharacteristic
511C23C2×#41×C15111yescharacteristic
512Q8—22no—
513Q8—22no—
514Q8—41no—
515Q8—41no—
516D4—22no—
517D4—22no—
518D4—42no—
519D4—42no—
520D4—42no—
521D4—42no—
522D4—41no—
523D4—41no—
524C2×C4—24no—
525C2×C4—22no—
526C2×C4—41no—
527C2×C4—41no—
528C2×C4—42no—
529C2×C4—42no—
530C2×C4—42no—
531C2×C4—42no—
532C2×C4—42no—
533C2×C4—82no—
534C2×C4—82no—
535C2×C4#121×C15111yescharacteristic
536C2×C4#121×C15111yescharacteristic
537C2×C4#121×C15111yescharacteristic
538C2×C4#121×C15111yescharacteristic
539C2×C4#123×C15111yescharacteristic
540C2×C4#123×C15111yescharacteristic
541C2×C4#123×C15111yescharacteristic
542C2×C4#123×C15111yescharacteristic
543C2×C4#123×C15111yescharacteristic
544C2×C4#123×C15111yescharacteristic
545C2×C4#123×C15111yescharacteristic
546C2×C4#123×C15111yescharacteristic
547C2×C4#124×C15111yescharacteristic
548C2×C4#124×C15111yescharacteristic
549C2×C4#124×C15111yescharacteristic
550C2×C4#124×C15111yescharacteristic
551C2×C4#126×C15111yescharacteristic
552C2×C4#126×C15111yescharacteristic
553C2×C4#126×C15111yescharacteristic
554C2×C4#126×C15111yescharacteristic
555C2×C4#126×C15111yescharacteristic
556C2×C4#126×C15111yescharacteristic
557C2×C4C22×D4×C15111yescharacteristic
558C2×C4C22×D4×C15111yescharacteristic
559C2×C4C2×#41×C15111yescharacteristic
560C2×C4C2×#41×C15111yescharacteristic
561C2×C4C2×#41×C15111yescharacteristic
562C2×C4C2×#41×C15111yescharacteristic
563C8—42no—
564C8—42no—
565C8—42no—
566C8—42no—
567C22—41no—
568C22—41no—
569C22—41no—
570C22—41no—
571C22—41no—
572C22—41no—
573C22—41no—
574C22—42no—
575C22—82no—
576C22—82no—
577C22—82no—
578C22#397×C15111yescharacteristic
579C22#397×C15111yescharacteristic
580C22#397×C15111yescharacteristic
581C22#397×C15111yescharacteristic
582C22C2×#123×C15111yescharacteristic
583C22C2×#123×C15111yescharacteristic
584C22C2×#126×C15111yescharacteristic
585C4—44no—
586C4—42no—
587C4—82no—
588C4#397×C15111yescharacteristic
589C4#397×C15111yescharacteristic
590C4#397×C15111yescharacteristic
591C4#397×C15111yescharacteristic
592C4C2×#121×C15111yescharacteristic
593C4C2×#123×C15111yescharacteristic
594C4C2×#124×C15111yescharacteristic
595C4C2×#126×C15111yescharacteristic
596C2—21no—
597C2—21no—
598C2—21no—
599C2—21no—
600C2—21no—
601C2—21no—
602C2—21no—
603C2—82no—
604C2C2×#397×C15111yescharacteristic
subgroupG/H
centerC4×C151C2×#124
commutator, Frattini, cosocleC22×C4C24×C151
socleC2×C151C2×#397
prime radicalC22×#41×C151C22
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C4×C151 ◁ C23×C4×C151 ◁ G

Complements

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

NH ≅ G/Ntype
1. #2905×C151C2semidirect
5. #2080×C151C2semidirect
6. C2×#344×C151C2semidirect
7. #1738×C151C2semidirect
8. C2×H(3,ℤ/4)×C151C2semidirect
17. #424×C151C22semidirect
30. #344×C151C22semidirect
31. #341×C151C22semidirect
32. H(3,ℤ/4)×C151C22semidirect
302. #23649C151direct (N × H)
303. C151#23649direct (N × H)
304. #2905C2×C151semidirect
308. #2080C2×C151semidirect
309. C2×#344C2×C151semidirect
310. #1738C2×C151semidirect
311. C2×H(3,ℤ/4)C2×C151semidirect
320. #424C22×C151semidirect
333. #344C22×C151semidirect
334. #341C22×C151semidirect
335. H(3,ℤ/4)C22×C151semidirect

Maximal subgroups

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

subgroupindex
#2905×C1512
C2×#421×C1512
#2896×C1512
C2×#413×C1512
#2080×C1512
C2×#344×C1512
#1738×C1512
C2×H(3,ℤ/4)×C1512
#23649151