Finite Group Databasebeta

← C151×#24214 #50329139

Subgroups — C151×#24214 #50329139

Order 38656.

1566 conjugacy classes of subgroups.

The subgroup lattice has 654 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#532×C151C211yesmaximal, characteristic, complemented
2C2×#463×C151C212yesmaximal, complemented
3C2×#449×C151C212yesmaximal, complemented
4C4×#121×C151C211yesmaximal, characteristic, complemented
5#2043×C151C211yesmaximal, characteristic, complemented
6#2041×C151C211yesmaximal, characteristic, complemented
7#2013×C151C211yesmaximal, characteristic, complemented
8#2011×C151C211yesmaximal, characteristic, complemented
9#1983×C151C212yesmaximal, complemented
10#1797×C151C211yesmaximal, characteristic, complemented
11#1788×C151C212yesmaximal, complemented
12C22×#41×C151C2212yes—
13C22×SD16×C151C2212yes—
14C22×D8×C151C2212yes—
15#532×C151—28no—
16C2×C4⋊Q8×C151C2211yescharacteristic
17C2×#127×C151C2211yescharacteristic
18C2×#124×C151C2212yes—
19C2×#121×C151—21no—
20C2×#121×C151—21no—
21C2×#121×C151C2211yescharacteristic
22C2×C4×D4×C151—21no—
23C2×C4×D4×C151—21no—
24C2×C4×D4×C151—21no—
25C2×C4×D4×C151C2211yescharacteristic
26C22×C42×C151C2211yescharacteristic
27#463×C151—28no—
28#449×C151—28no—
29C2×C4⋊C8×C151C2212yes—
30C2×#103×C151C2212yes—
31C2×#103×C151C2212yes—
32C2×#103×C151C2212yes—
33C2×#102×C151C2212yes—
34C2×#102×C151C2212yes—
35C2×#102×C151C2212yes—
36C2×C22⋊C8×C151C2212yes—
37#390×C151C2211yescharacteristic
38#389×C151C2211yescharacteristic
39#388×C151—21no—
40#386×C151—21no—
41#380×C151C2211yescharacteristic
42C4×C4⋊C4×C151C2211yescharacteristic
43C4×C22⋊C4×C151—21no—
44#336×C151C2211yescharacteristic
45#336×C151C2211yescharacteristic
46C2×#41×C151—24no—
47C2×#41×C151—24no—
48C2×#41×C151—24no—
49C2×#41×C151—24no—
50C2×#41×C151—42no—
51C2×#41×C151—42no—
52C22×Q8×C151C2312yes—
53C22×D4×C151—21no—
54C22×D4×C151—21no—
55C22×D4×C151—21no—
56C22×D4×C151—22no—
57C22×D4×C151C2311yescharacteristic
58C22×D4×C151C2312yes—
59C23×C4×C151—22no—
60C23×C4×C151—21no—
61C23×C4×C151D411yescharacteristic
62C23×C4×C151D411yescharacteristic
63C23×C4×C151C2311yescharacteristic
64C2×SD16×C151—24no—
65C2×SD16×C151—24no—
66C2×SD16×C151—42no—
67C2×D8×C151—24no—
68C2×D8×C151—24no—
69C2×D8×C151—42no—
70C22×C8×C151C2312yes—
71C22×C8×C151C2312yes—
72C4⋊Q8×C151—24no—
73#127×C151—24no—
74#124×C151—24no—
75#124×C151D418yescomplemented
76#121×C151—28no—
77#121×C151—28no—
78#121×C151—22no—
79#121×C151D414yescomplemented
80C4×D4×C151—28no—
81C4×D4×C151—28no—
82C4×D4×C151—24no—
83C4×D4×C151—44no—
84C2×C4⋊C4×C151—21no—
85C2×C4⋊C4×C151—21no—
86C2×C4⋊C4×C151—21no—
87C2×C4⋊C4×C151C2311yescharacteristic
88C2×C4⋊C4×C151C2311yescharacteristic
89C2×C4⋊C4×C151C2311yescharacteristic
90C2×C22⋊C4×C151—21no—
91C2×C22⋊C4×C151—22no—
92C2×C22⋊C4×C151—22no—
93C2×C22⋊C4×C151—21no—
94C2×C22⋊C4×C151—21no—
95C2×C22⋊C4×C151—21no—
96C2×C22⋊C4×C151—21no—
97C2×C42×C151—24no—
98C2×C42×C151—21no—
99C2×C42×C151D411yescharacteristic
100C2×C42×C151D411yescharacteristic
101C2×C42×C151C2311yescharacteristic
102C2×C42×C151C2311yescharacteristic
103C4⋊C8×C151—24no—
104#103×C151—24no—
105#103×C151—24no—
106#103×C151—42no—
107#102×C151—24no—
108#102×C151—24no—
109#102×C151—42no—
110C22⋊C8×C151—24no—
111#95×C151—21no—
112#95×C151—21no—
113#95×C151—21no—
114C24×C151—21no—
115C24×C151—22no—
116C24×C151C2×D411yescharacteristic
117#41×C151—48no—
118#41×C151—48no—
119#41×C151—48no—
120#41×C151—48no—
121C2×Q8×C151—22no—
122C2×Q8×C151—22no—
123C2×Q8×C151—22no—
124C2×Q8×C151—22no—
125C2×Q8×C151—22no—
126C2×Q8×C151C2×D414yes—
127C2×D4×C151—24no—
128C2×D4×C151—24no—
129C2×D4×C151—28no—
130C2×D4×C151—24no—
131C2×D4×C151—22no—
132C2×D4×C151—22no—
133C2×D4×C151—22no—
134C2×D4×C151—22no—
135C2×D4×C151—21no—
136C2×D4×C151—22no—
137C2×D4×C151—22no—
138C2×D4×C151—22no—
139C2×D4×C151—42no—
140C2×D4×C151—42no—
141C2×D4×C151—42no—
142C2×D4×C151—42no—
143C2×D4×C151—44no—
144C2×D4×C151—44no—
145C2×D4×C151—42no—
146C2×D4×C151—42no—
147C2×D4×C151C2×D414yes—
148C2×D4×C151C2×D412yes—
149C22×C4×C151—22no—
150C22×C4×C151—22no—
151C22×C4×C151—28no—
152C22×C4×C151—21no—
153C22×C4×C151—22no—
154C22×C4×C151—22no—
155C22×C4×C151—22no—
156C22×C4×C151—22no—
157C22×C4×C151—22no—
158C22×C4×C151—21no—
159C22×C4×C151—21no—
160C22×C4×C151—41no—
161C22×C4×C151—41no—
162C22×C4×C151—44no—
163C22×C4×C151—42no—
164C22×C4×C151—42no—
165C22×C4×C151—44no—
166C22×C4×C151—42no—
167C22×C4×C151C2×D411yescharacteristic
168C22×C4×C151C2×D411yescharacteristic
169C22×C4×C151C2×D411yescharacteristic
170C22×C4×C151C2×D412yes—
171C22×C4×C151C2×D411yescharacteristic
172C22×C4×C151C2×D411yescharacteristic
173C22×C4×C151#4112yes—
174C22×C4×C151C2411yescharacteristic
175SD16×C151—48no—
176D8×C151—48no—
177C2×C8×C151—22no—
178C2×C8×C151—22no—
179C2×C8×C151—22no—
180C2×C8×C151—22no—
181C2×C8×C151—22no—
182C2×C8×C151—22no—
183C4⋊C4×C151—24no—
184C4⋊C4×C151—24no—
185C4⋊C4×C151—21no—
186C4⋊C4×C151—22no—
187C4⋊C4×C151—22no—
188C4⋊C4×C151—42no—
189C4⋊C4×C151C2×D412yes—
190C22⋊C4×C151—28no—
191C22⋊C4×C151—28no—
192C22⋊C4×C151—24no—
193C22⋊C4×C151—42no—
194C22⋊C4×C151—42no—
195C22⋊C4×C151—42no—
196C22⋊C4×C151—42no—
197C42×C151—22no—
198C42×C151—22no—
199C42×C151—22no—
200C42×C151—42no—
201C42×C151C2×D414yes—
202C23×C151—21no—
203C23×C151—21no—
204C23×C151—21no—
205C23×C151—21no—
206C23×C151—21no—
207C23×C151—21no—
208C23×C151—24no—
209C23×C151—22no—
210C23×C151—41no—
211C23×C151—42no—
212C23×C151—42no—
213C23×C151—41no—
214C23×C151—41no—
215C23×C151—42no—
216C23×C151—41no—
217C23×C151—42no—
218C23×C151—41no—
219C23×C151—42no—
220C23×C151—42no—
221C23×C151—41no—
222C23×C151#12112yes—
223C23×C151C22×D411yescharacteristic
224Q8×C151—24no—
225Q8×C151—24no—
226Q8×C151—42no—
227Q8×C151—42no—
228D4×C151—24no—
229D4×C151—24no—
230D4×C151—24no—
231D4×C151—48no—
232D4×C151—48no—
233D4×C151—416no—
234D4×C151—48no—
235D4×C151—42no—
236D4×C151—42no—
237D4×C151—42no—
238C2×C4×C151—21no—
239C2×C4×C151—21no—
240C2×C4×C151—21no—
241C2×C4×C151—21no—
242C2×C4×C151—21no—
243C2×C4×C151—21no—
244C2×C4×C151—21no—
245C2×C4×C151—21no—
246C2×C4×C151—21no—
247C2×C4×C151—21no—
248C2×C4×C151—24no—
249C2×C4×C151—24no—
250C2×C4×C151—24no—
251C2×C4×C151—22no—
252C2×C4×C151—44no—
253C2×C4×C151—44no—
254C2×C4×C151—416no—
255C2×C4×C151—42no—
256C2×C4×C151—42no—
257C2×C4×C151—41no—
258C2×C4×C151—41no—
259C2×C4×C151—41no—
260C2×C4×C151—41no—
261C2×C4×C151—41no—
262C2×C4×C151—41no—
263C2×C4×C151—41no—
264C2×C4×C151—41no—
265C2×C4×C151—84no—
266C2×C4×C151#12012yes—
267C2×C4×C151#12012yes—
268C2×C4×C151#12112yes—
269C2×C4×C151#13512yes—
270C2×C4×C151AGL(1,ℤ/8)12yes—
271C2×C4×C151C22×D411yescharacteristic
272C2×C4×C151C22×D412yes—
273C2×C4×C151C2×#4111yescharacteristic
274C2×C4×C151H(5,𝔽2)12yes—
275C8×C151—42no—
276C8×C151—42no—
277C22×C151—22no—
278C22×C151—22no—
279C22×C151—22no—
280C22×C151—41no—
281C22×C151—41no—
282C22×C151—41no—
283C22×C151—41no—
284C22×C151—44no—
285C22×C151—42no—
286C22×C151—44no—
287C22×C151—44no—
288C22×C151—42no—
289C22×C151—42no—
290C22×C151—82no—
291C22×C151—81no—
292C22×C151—82no—
293C22×C151—81no—
294C22×C151—81no—
295C22×C151—81no—
296C22×C151—82no—
297C22×C151—82no—
298C22×C151C2×#12011yescharacteristic
299C22×C151C2×#12111yescharacteristic
300C22×C151#53511yescharacteristic
301C22×C151C2×#13511yescharacteristic
302C22×C151C2×AGL(1,ℤ/8)11yescharacteristic
303C22×C151#57511yescharacteristic
304C22×C151#57511yescharacteristic
305C4×C151—22no—
306C4×C151—22no—
307C4×C151—22no—
308C4×C151—22no—
309C4×C151—22no—
310C4×C151—44no—
311C4×C151—42no—
312C4×C151—81no—
313C4×C151—81no—
314C4×C151D4212yes—
315C4×C151#54612yes—
316C2×C151—42no—
317C2×C151—84no—
318C2×C151—82no—
319C2×C151#240811yescharacteristic
320C2×C151#300211yescharacteristic
321C2×C151#300611yescharacteristic
322C2×C151#303511yescharacteristic
323C2×C151#303611yescharacteristic
324C2×C151#320711yescharacteristic
325C2×C151#321911yescharacteristic
326#24214C15111yesmaximal, characteristic, direct product factor, Sylow
327C151#2421411yescharacteristic, direct product factor, Sylow
328C2×#532C2×C15111yescharacteristic, complemented
329C2×#463C2×C15112yescomplemented
330C2×#449C2×C15112yescomplemented
331C4×#121C2×C15111yescharacteristic, complemented
332#2043C2×C15111yescharacteristic, complemented
333#2041C2×C15111yescharacteristic, complemented
334#2013C2×C15111yescharacteristic, complemented
335#2011C2×C15111yescharacteristic, complemented
336#1983C2×C15112yescomplemented
337#1797C2×C15111yescharacteristic, complemented
338#1788C2×C15112yescomplemented
339C22×#41C22×C15112yes—
340C22×SD16C22×C15112yes—
341C22×D8C22×C15112yes—
342#532—28no—
343C2×C4⋊Q8C22×C15111yescharacteristic
344C2×#127C22×C15111yescharacteristic
345C2×#124C22×C15112yes—
346C2×#121—21no—
347C2×#121—21no—
348C2×#121C22×C15111yescharacteristic
349C2×C4×D4—21no—
350C2×C4×D4—21no—
351C2×C4×D4—21no—
352C2×C4×D4C22×C15111yescharacteristic
353C22×C42C22×C15111yescharacteristic
354#463—28no—
355#449—28no—
356C2×C4⋊C8C22×C15112yes—
357C2×#103C22×C15112yes—
358C2×#103C22×C15112yes—
359C2×#103C22×C15112yes—
360C2×#102C22×C15112yes—
361C2×#102C22×C15112yes—
362C2×#102C22×C15112yes—
363C2×C22⋊C8C22×C15112yes—
364#390C22×C15111yescharacteristic
365#389C22×C15111yescharacteristic
366#388—21no—
367#386—21no—
368#380C22×C15111yescharacteristic
369C4×C4⋊C4C22×C15111yescharacteristic
370C4×C22⋊C4—21no—
371#336C22×C15111yescharacteristic
372#336C22×C15111yescharacteristic
373C2×#41—24no—
374C2×#41—24no—
375C2×#41—24no—
376C2×#41—24no—
377C2×#41—42no—
378C2×#41—42no—
379C22×Q8C23×C15112yes—
380C22×D4—21no—
381C22×D4—22no—
382C22×D4—21no—
383C22×D4—21no—
384C22×D4C23×C15111yescharacteristic
385C22×D4C23×C15112yes—
386C23×C4—22no—
387C23×C4—21no—
388C23×C4D4×C15111yescharacteristic
389C23×C4D4×C15111yescharacteristic
390C23×C4C23×C15111yescharacteristic
391C2×SD16—24no—
392C2×SD16—24no—
393C2×SD16—42no—
394C2×D8—24no—
395C2×D8—24no—
396C2×D8—42no—
397C22×C8C23×C15112yes—
398C22×C8C23×C15112yes—
399C4⋊Q8—24no—
400#127—24no—
401#124—24no—
402#124D4×C15118yescomplemented
403#121—28no—
404#121—28no—
405#121—22no—
406#121D4×C15114yescomplemented
407C4×D4—28no—
408C4×D4—28no—
409C4×D4—24no—
410C4×D4—44no—
411C2×C4⋊C4—21no—
412C2×C4⋊C4—21no—
413C2×C4⋊C4—21no—
414C2×C4⋊C4C23×C15111yescharacteristic
415C2×C4⋊C4C23×C15111yescharacteristic
416C2×C4⋊C4C23×C15111yescharacteristic
417C2×C22⋊C4—22no—
418C2×C22⋊C4—22no—
419C2×C22⋊C4—21no—
420C2×C22⋊C4—21no—
421C2×C22⋊C4—21no—
422C2×C22⋊C4—21no—
423C2×C22⋊C4—21no—
424C2×C42—24no—
425C2×C42—21no—
426C2×C42D4×C15111yescharacteristic
427C2×C42D4×C15111yescharacteristic
428C2×C42C23×C15111yescharacteristic
429C2×C42C23×C15111yescharacteristic
430C4⋊C8—24no—
431#103—24no—
432#103—24no—
433#103—42no—
434#102—24no—
435#102—24no—
436#102—42no—
437C22⋊C8—24no—
438#95—21no—
439#95—21no—
440#95—21no—
441C24—21no—
442C24—22no—
443C24C2×D4×C15111yescharacteristic
444#41—48no—
445#41—48no—
446#41—48no—
447#41—48no—
448C2×Q8—22no—
449C2×Q8—22no—
450C2×Q8—22no—
451C2×Q8—22no—
452C2×Q8—22no—
453C2×Q8C2×D4×C15114yes—
454C2×D4—24no—
455C2×D4—24no—
456C2×D4—28no—
457C2×D4—24no—
458C2×D4—22no—
459C2×D4—22no—
460C2×D4—22no—
461C2×D4—22no—
462C2×D4—21no—
463C2×D4—22no—
464C2×D4—22no—
465C2×D4—22no—
466C2×D4—42no—
467C2×D4—42no—
468C2×D4—42no—
469C2×D4—44no—
470C2×D4—42no—
471C2×D4—44no—
472C2×D4—42no—
473C2×D4—42no—
474C2×D4C2×D4×C15114yes—
475C2×D4C2×D4×C15112yes—
476C22×C4—22no—
477C22×C4—22no—
478C22×C4—28no—
479C22×C4—21no—
480C22×C4—22no—
481C22×C4—22no—
482C22×C4—22no—
483C22×C4—22no—
484C22×C4—22no—
485C22×C4—21no—
486C22×C4—21no—
487C22×C4—41no—
488C22×C4—41no—
489C22×C4—44no—
490C22×C4—42no—
491C22×C4—42no—
492C22×C4—44no—
493C22×C4—42no—
494C22×C4C2×D4×C15111yescharacteristic
495C22×C4C2×D4×C15111yescharacteristic
496C22×C4C2×D4×C15111yescharacteristic
497C22×C4C2×D4×C15112yes—
498C22×C4C2×D4×C15111yescharacteristic
499C22×C4C2×D4×C15111yescharacteristic
500C22×C4#41×C15112yes—
501C22×C4C24×C15111yescharacteristic
502SD16—48no—
503D8—48no—
504C2×C8—22no—
505C2×C8—22no—
506C2×C8—22no—
507C2×C8—22no—
508C2×C8—22no—
509C2×C8—22no—
510C4⋊C4—24no—
511C4⋊C4—24no—
512C4⋊C4—21no—
513C4⋊C4—22no—
514C4⋊C4—22no—
515C4⋊C4—42no—
516C4⋊C4C2×D4×C15112yes—
517C22⋊C4—28no—
518C22⋊C4—28no—
519C22⋊C4—24no—
520C22⋊C4—42no—
521C22⋊C4—42no—
522C22⋊C4—42no—
523C22⋊C4—42no—
524C42—22no—
525C42—22no—
526C42—22no—
527C42—42no—
528C42C2×D4×C15114yes—
529C23—21no—
530C23—21no—
531C23—21no—
532C23—21no—
533C23—21no—
534C23—21no—
535C23—24no—
536C23—22no—
537C23—41no—
538C23—42no—
539C23—42no—
540C23—41no—
541C23—41no—
542C23—42no—
543C23—41no—
544C23—42no—
545C23—41no—
546C23—42no—
547C23—42no—
548C23—41no—
549C23#121×C15112yes—
550C23C22×D4×C15111yescharacteristic
551Q8—24no—
552Q8—24no—
553Q8—42no—
554Q8—42no—
555D4—24no—
556D4—24no—
557D4—24no—
558D4—48no—
559D4—48no—
560D4—416no—
561D4—48no—
562D4—42no—
563D4—42no—
564D4—42no—
565C2×C4—21no—
566C2×C4—21no—
567C2×C4—21no—
568C2×C4—21no—
569C2×C4—21no—
570C2×C4—21no—
571C2×C4—21no—
572C2×C4—21no—
573C2×C4—21no—
574C2×C4—21no—
575C2×C4—24no—
576C2×C4—24no—
577C2×C4—24no—
578C2×C4—22no—
579C2×C4—44no—
580C2×C4—44no—
581C2×C4—416no—
582C2×C4—42no—
583C2×C4—42no—
584C2×C4—41no—
585C2×C4—41no—
586C2×C4—41no—
587C2×C4—41no—
588C2×C4—41no—
589C2×C4—41no—
590C2×C4—41no—
591C2×C4—41no—
592C2×C4—84no—
593C2×C4#120×C15112yes—
594C2×C4#120×C15112yes—
595C2×C4#121×C15112yes—
596C2×C4#135×C15112yes—
597C2×C4AGL(1,ℤ/8)×C15112yes—
598C2×C4C22×D4×C15111yescharacteristic
599C2×C4C22×D4×C15112yes—
600C2×C4C2×#41×C15111yescharacteristic
601C2×C4H(5,𝔽2)×C15112yes—
602C8—42no—
603C8—42no—
604C22—22no—
605C22—22no—
606C22—22no—
607C22—41no—
608C22—41no—
609C22—41no—
610C22—41no—
611C22—44no—
612C22—42no—
613C22—44no—
614C22—44no—
615C22—42no—
616C22—42no—
617C22—82no—
618C22—81no—
619C22—82no—
620C22—81no—
621C22—81no—
622C22—81no—
623C22—82no—
624C22—82no—
625C22C2×#120×C15111yescharacteristic
626C22C2×#121×C15111yescharacteristic
627C22#535×C15111yescharacteristic
628C22C2×#135×C15111yescharacteristic
629C22C2×AGL(1,ℤ/8)×C15111yescharacteristic
630C22#575×C15111yescharacteristic
631C22#575×C15111yescharacteristic
632C4—22no—
633C4—22no—
634C4—22no—
635C4—22no—
636C4—22no—
637C4—44no—
638C4—42no—
639C4—81no—
640C4—81no—
641C4D42×C15112yes—
642C4#546×C15112yes—
643C2—42no—
644C2—84no—
645C2—82no—
646C2#2408×C15111yescharacteristic
647C2#3002×C15111yescharacteristic
648C2#3006×C15111yescharacteristic
649C2#3035×C15111yescharacteristic
650C2#3036×C15111yescharacteristic
651C2#3207×C15111yescharacteristic
652C2#3219×C15111yescharacteristic
subgroupG/H
center, socleC23×C151C22×D4
commutator, Frattini, cosocleC22×C4C24×C151
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C151 ◁ C22×C42×C151 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×#532×C151C2semidirect
2. C2×#463×C151C2semidirect
3. C2×#449×C151C2semidirect
4. C4×#121×C151C2semidirect
5. #2043×C151C2semidirect
6. #2041×C151C2semidirect
7. #2013×C151C2semidirect
8. #2011×C151C2semidirect
9. #1983×C151C2semidirect
10. #1797×C151C2semidirect
11. #1788×C151C2semidirect
75. #124×C151D4semidirect
79. #121×C151D4semidirect
326. #24214C151direct (N × H)
327. C151#24214direct (N × H)
328. C2×#532C2×C151semidirect
329. C2×#463C2×C151semidirect
330. C2×#449C2×C151semidirect
331. C4×#121C2×C151semidirect
332. #2043C2×C151semidirect
333. #2041C2×C151semidirect
334. #2013C2×C151semidirect
335. #2011C2×C151semidirect
336. #1983C2×C151semidirect
337. #1797C2×C151semidirect
338. #1788C2×C151semidirect
402. #124D4×C151semidirect
406. #121D4×C151semidirect

Maximal subgroups

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

subgroupindex
C2×#532×C1512
C2×#463×C1512
C2×#449×C1512
C4×#121×C1512
#2043×C1512
#2041×C1512
#2013×C1512
#2011×C1512
#1983×C1512
#1797×C1512
#1788×C1512
#24214151