Finite Group Databasebeta

← C151×#24651 #50329576

Subgroups — C151×#24651 #50329576

Order 38656.

980 conjugacy classes of subgroups.

The subgroup lattice has 588 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#461×C151C211yesmaximal, characteristic, complemented
2C2×#431×C151C211yesmaximal, characteristic, complemented
3#2857×C151C211yesmaximal, characteristic, complemented
4C4×#121×C151C211yesmaximal, characteristic
5#2035×C151C212yesmaximal, complemented
6#2000×C151C212yesmaximal
7#1981×C151C211yesmaximal, characteristic, complemented
8#1968×C151C212yesmaximal, complemented
9#1948×C151C211yesmaximal, characteristic, complemented
10#1933×C151C212yesmaximal, complemented
11#1802×C151C211yesmaximal, characteristic, complemented
12C22×SD16×C151C2212yes—
13C2×C4⋊Q8×C151C2211yescharacteristic
14C2×C22⋊Q8×C151C2212yes—
15C2×#121×C151C2211yescharacteristic
16C2×C4×D4×C151—21no—
17C2×C4×D4×C151C2211yescharacteristic
18C22×C42×C151C2211yescharacteristic
19#461×C151—24no—
20#431×C151—24no—
21C2×#106×C151C2212yes—
22C2×C4⋊C8×C151C2211yescharacteristic
23C2×C4⋊C8×C151C2211yescharacteristic
24C2×#103×C151C2212yes—
25C2×#103×C151C2212yes—
26C2×#103×C151C2212yes—
27C2×#102×C151C2212yes—
28C2×C22⋊C8×C151C2212yes—
29C2×C4×C8×C151C2212yes—
30#391×C151C2212yes—
31#390×C151C2211yescharacteristic
32#389×C151—21no—
33#389×C151—21no—
34#389×C151C2211yescharacteristic
35#388×C151—21no—
36#386×C151—21no—
37#384×C151C2211yescharacteristic
38#380×C151—21no—
39#380×C151—21no—
40#380×C151C2211yescharacteristic
41C4×C4⋊C4×C151C2211yescharacteristic
42C4×C22⋊C4×C151—21no—
43#340×C151C2212yes—
44#340×C151C2212yes—
45C22×Q8×C151C2312yes—
46C22×D4×C151—21no—
47C22×D4×C151C2311yescharacteristic
48C23×C4×C151—21no—
49C23×C4×C151D411yescharacteristic
50C23×C4×C151D411yescharacteristic
51C23×C4×C151C2311yescharacteristic
52C2×SD16×C151—24no—
53C2×SD16×C151—24no—
54C2×SD16×C151—42no—
55C22×C8×C151C2312yes—
56C22×C8×C151C2312yes—
57C4⋊Q8×C151—22no—
58C4⋊Q8×C151—22no—
59C22⋊Q8×C151—42no—
60C22⋊Q8×C151—42no—
61#121×C151—22no—
62#121×C151—22no—
63C4×D4×C151—22no—
64C4×D4×C151—22no—
65C4×D4×C151—44no—
66C2×C4⋊C4×C151—21no—
67C2×C4⋊C4×C151—21no—
68C2×C4⋊C4×C151—21no—
69C2×C4⋊C4×C151—21no—
70C2×C4⋊C4×C151—21no—
71C2×C4⋊C4×C151—22no—
72C2×C4⋊C4×C151C2311yescharacteristic
73C2×C4⋊C4×C151C2312yes—
74C2×C4⋊C4×C151C2311yescharacteristic
75C2×C4⋊C4×C151C2311yescharacteristic
76C2×C22⋊C4×C151—21no—
77C2×C22⋊C4×C151—21no—
78C2×C22⋊C4×C151—21no—
79C2×C22⋊C4×C151—21no—
80C2×C22⋊C4×C151—22no—
81C2×C22⋊C4×C151—21no—
82C2×C42×C151—22no—
83C2×C42×C151—22no—
84C2×C42×C151—21no—
85C2×C42×C151D411yescharacteristic
86C2×C42×C151D411yescharacteristic
87C2×C42×C151C2311yescharacteristic
88C2×C42×C151C2311yescharacteristic
89#106×C151—42no—
90C4⋊C8×C151—22no—
91C4⋊C8×C151D414yescomplemented
92#103×C151—24no—
93#103×C151—24no—
94#103×C151—42no—
95#102×C151—42no—
96C22⋊C8×C151—24no—
97C4×C8×C151—24no—
98#95×C151—21no—
99#95×C151—21no—
100#95×C151—21no—
101#95×C151—22no—
102#95×C151—22no—
103C24×C151—21no—
104C24×C151C2×D411yescharacteristic
105C2×Q8×C151—22no—
106C2×Q8×C151—22no—
107C2×Q8×C151—22no—
108C2×Q8×C151—22no—
109C2×Q8×C151—22no—
110C2×Q8×C151—22no—
111C2×D4×C151—24no—
112C2×D4×C151—21no—
113C2×D4×C151—21no—
114C2×D4×C151—21no—
115C2×D4×C151—21no—
116C2×D4×C151—21no—
117C2×D4×C151—42no—
118C2×D4×C151—42no—
119C2×D4×C151#4112yes—
120C22×C4×C151—22no—
121C22×C4×C151—22no—
122C22×C4×C151—21no—
123C22×C4×C151—22no—
124C22×C4×C151—22no—
125C22×C4×C151—21no—
126C22×C4×C151—21no—
127C22×C4×C151—21no—
128C22×C4×C151—21no—
129C22×C4×C151—21no—
130C22×C4×C151—21no—
131C22×C4×C151—21no—
132C22×C4×C151—21no—
133C22×C4×C151—22no—
134C22×C4×C151—22no—
135C22×C4×C151—41no—
136C22×C4×C151—42no—
137C22×C4×C151—42no—
138C22×C4×C151—42no—
139C22×C4×C151SD1614yescomplemented
140C22×C4×C151C2×D411yescharacteristic
141C22×C4×C151C2×D411yescharacteristic
142C22×C4×C151C2×D411yescharacteristic
143C22×C4×C151C2×D411yescharacteristic
144C22×C4×C151C2×D411yescharacteristic
145C22×C4×C151C2411yescharacteristic
146SD16×C151—48no—
147C2×C8×C151—22no—
148C2×C8×C151—22no—
149C2×C8×C151—22no—
150C2×C8×C151—22no—
151C2×C8×C151—22no—
152C2×C8×C151C2×D414yes—
153C4⋊C4×C151—21no—
154C4⋊C4×C151—21no—
155C4⋊C4×C151—21no—
156C4⋊C4×C151—22no—
157C4⋊C4×C151—21no—
158C4⋊C4×C151—21no—
159C4⋊C4×C151—22no—
160C4⋊C4×C151—42no—
161C4⋊C4×C151—44no—
162C4⋊C4×C151—42no—
163C4⋊C4×C151—42no—
164C4⋊C4×C151—42no—
165C4⋊C4×C151—42no—
166C4⋊C4×C151#4112yes—
167C22⋊C4×C151—24no—
168C22⋊C4×C151—44no—
169C22⋊C4×C151—42no—
170C22⋊C4×C151—42no—
171C22⋊C4×C151—42no—
172C22⋊C4×C151—42no—
173C42×C151—22no—
174C42×C151—22no—
175C42×C151—21no—
176C42×C151—21no—
177C42×C151—42no—
178C42×C151C2×D412yes—
179C42×C151#4112yes—
180C23×C151—21no—
181C23×C151—21no—
182C23×C151—21no—
183C23×C151—21no—
184C23×C151—21no—
185C23×C151—21no—
186C23×C151—22no—
187C23×C151—41no—
188C23×C151—41no—
189C23×C151—41no—
190C23×C151—41no—
191C23×C151—41no—
192C23×C151—41no—
193C23×C151C2×SD1612yes—
194C23×C151C22×D411yescharacteristic
195Q8×C151—42no—
196Q8×C151—42no—
197Q8×C151—42no—
198Q8×C151—42no—
199D4×C151—22no—
200D4×C151—22no—
201D4×C151—48no—
202D4×C151—41no—
203D4×C151—41no—
204C2×C4×C151—21no—
205C2×C4×C151—21no—
206C2×C4×C151—21no—
207C2×C4×C151—21no—
208C2×C4×C151—21no—
209C2×C4×C151—21no—
210C2×C4×C151—28no—
211C2×C4×C151—21no—
212C2×C4×C151—21no—
213C2×C4×C151—22no—
214C2×C4×C151—21no—
215C2×C4×C151—44no—
216C2×C4×C151—41no—
217C2×C4×C151—41no—
218C2×C4×C151—41no—
219C2×C4×C151—41no—
220C2×C4×C151—41no—
221C2×C4×C151—41no—
222C2×C4×C151—42no—
223C2×C4×C151—41no—
224C2×C4×C151—42no—
225C2×C4×C151—42no—
226C2×C4×C151—42no—
227C2×C4×C151—41no—
228C2×C4×C151—41no—
229C2×C4×C151—41no—
230C2×C4×C151—42no—
231C2×C4×C151—41no—
232C2×C4×C151—41no—
233C2×C4×C151—42no—
234C2×C4×C151—84no—
235C2×C4×C151#12112yes—
236C2×C4×C151#12112yes—
237C2×C4×C151C2×SD1612yes—
238C2×C4×C151C2×SD1612yes—
239C2×C4×C151#13512yes—
240C2×C4×C151#13712yes—
241C2×C4×C151C22×D411yescharacteristic
242C2×C4×C151C2×#4111yescharacteristic
243C2×C4×C151C2×#4111yescharacteristic
244C2×C4×C151C2×#4111yescharacteristic
245C2×C4×C151H(5,𝔽2)11yescharacteristic
246C2×C4×C151H(5,𝔽2)11yescharacteristic
247C8×C151—24no—
248C8×C151—42no—
249C22×C151—22no—
250C22×C151—22no—
251C22×C151—22no—
252C22×C151—41no—
253C22×C151—41no—
254C22×C151—41no—
255C22×C151—41no—
256C22×C151—42no—
257C22×C151—42no—
258C22×C151—42no—
259C22×C151—81no—
260C22×C151—81no—
261C22×C151—81no—
262C22×C151—81no—
263C22×C151C2×#12111yescharacteristic
264C22×C151#52511yescharacteristic
265C22×C151#53511yescharacteristic
266C22×C151C22×SD1611yescharacteristic
267C22×C151C2×#13511yescharacteristic
268C22×C151C2×#13711yescharacteristic
269C22×C151#57511yescharacteristic
270C4×C151—22no—
271C4×C151—22no—
272C4×C151—22no—
273C4×C151—42no—
274C4×C151—41no—
275C4×C151—82no—
276C4×C151—81no—
277C4×C151—82no—
278C4×C151—81no—
279C4×C151#46514yes—
280C4×C151#54611yescharacteristic
281C4×C151#55011yescharacteristic
282C4×C151#55311yescharacteristic
283C4×C151#55511yescharacteristic
284C2×C151—42no—
285C2×C151—82no—
286C2×C151#241411yescharacteristic
287C2×C151C2×#46511yescharacteristic
288C2×C151#305611yescharacteristic
289C2×C151#310111yescharacteristic
290C2×C151#310711yescharacteristic
291C2×C151#320611yescharacteristic
292C2×C151#321211yescharacteristic
293#24651C15111yesmaximal, characteristic, direct product factor, Sylow
294C151#2465111yescharacteristic, direct product factor, Sylow
295C2×#461C2×C15111yescharacteristic, complemented
296C2×#431C2×C15111yescharacteristic, complemented
297#2857C2×C15111yescharacteristic, complemented
298C4×#121C2×C15111yescharacteristic
299#2035C2×C15112yescomplemented
300#2000C2×C15112yes—
301#1981C2×C15111yescharacteristic, complemented
302#1968C2×C15112yescomplemented
303#1948C2×C15111yescharacteristic, complemented
304#1933C2×C15112yescomplemented
305#1802C2×C15111yescharacteristic, complemented
306C22×SD16C22×C15112yes—
307C2×C4⋊Q8C22×C15111yescharacteristic
308C2×C22⋊Q8C22×C15112yes—
309C2×#121C22×C15111yescharacteristic
310C2×C4×D4—21no—
311C2×C4×D4C22×C15111yescharacteristic
312C22×C42C22×C15111yescharacteristic
313#461—24no—
314#431—24no—
315C2×#106C22×C15112yes—
316C2×C4⋊C8C22×C15111yescharacteristic
317C2×C4⋊C8C22×C15111yescharacteristic
318C2×#103C22×C15112yes—
319C2×#103C22×C15112yes—
320C2×#103C22×C15112yes—
321C2×#102C22×C15112yes—
322C2×C22⋊C8C22×C15112yes—
323C2×C4×C8C22×C15112yes—
324#391C22×C15112yes—
325#390C22×C15111yescharacteristic
326#389—21no—
327#389—21no—
328#389C22×C15111yescharacteristic
329#388—21no—
330#386—21no—
331#384C22×C15111yescharacteristic
332#380—21no—
333#380—21no—
334#380C22×C15111yescharacteristic
335C4×C4⋊C4C22×C15111yescharacteristic
336C4×C22⋊C4—21no—
337#340C22×C15112yes—
338#340C22×C15112yes—
339C22×Q8C23×C15112yes—
340C22×D4—21no—
341C22×D4C23×C15111yescharacteristic
342C23×C4—21no—
343C23×C4D4×C15111yescharacteristic
344C23×C4D4×C15111yescharacteristic
345C23×C4C23×C15111yescharacteristic
346C2×SD16—24no—
347C2×SD16—24no—
348C2×SD16—42no—
349C22×C8C23×C15112yes—
350C22×C8C23×C15112yes—
351C4⋊Q8—22no—
352C4⋊Q8—22no—
353C22⋊Q8—42no—
354C22⋊Q8—42no—
355#121—22no—
356#121—22no—
357C4×D4—22no—
358C4×D4—22no—
359C4×D4—44no—
360C2×C4⋊C4—21no—
361C2×C4⋊C4—22no—
362C2×C4⋊C4—21no—
363C2×C4⋊C4—21no—
364C2×C4⋊C4—21no—
365C2×C4⋊C4—21no—
366C2×C4⋊C4C23×C15111yescharacteristic
367C2×C4⋊C4C23×C15112yes—
368C2×C4⋊C4C23×C15111yescharacteristic
369C2×C4⋊C4C23×C15111yescharacteristic
370C2×C22⋊C4—21no—
371C2×C22⋊C4—21no—
372C2×C22⋊C4—22no—
373C2×C22⋊C4—21no—
374C2×C22⋊C4—21no—
375C2×C22⋊C4—21no—
376C2×C42—22no—
377C2×C42—22no—
378C2×C42—21no—
379C2×C42D4×C15111yescharacteristic
380C2×C42D4×C15111yescharacteristic
381C2×C42C23×C15111yescharacteristic
382C2×C42C23×C15111yescharacteristic
383#106—42no—
384C4⋊C8—22no—
385C4⋊C8D4×C15114yescomplemented
386#103—24no—
387#103—24no—
388#103—42no—
389#102—42no—
390C22⋊C8—24no—
391C4×C8—24no—
392#95—21no—
393#95—21no—
394#95—21no—
395#95—22no—
396#95—22no—
397C24—21no—
398C24C2×D4×C15111yescharacteristic
399C2×Q8—22no—
400C2×Q8—22no—
401C2×Q8—22no—
402C2×Q8—22no—
403C2×Q8—22no—
404C2×Q8—22no—
405C2×D4—24no—
406C2×D4—21no—
407C2×D4—21no—
408C2×D4—21no—
409C2×D4—21no—
410C2×D4—21no—
411C2×D4—42no—
412C2×D4—42no—
413C2×D4#41×C15112yes—
414C22×C4—22no—
415C22×C4—22no—
416C22×C4—21no—
417C22×C4—22no—
418C22×C4—22no—
419C22×C4—21no—
420C22×C4—21no—
421C22×C4—21no—
422C22×C4—21no—
423C22×C4—21no—
424C22×C4—21no—
425C22×C4—21no—
426C22×C4—21no—
427C22×C4—22no—
428C22×C4—22no—
429C22×C4—41no—
430C22×C4—42no—
431C22×C4—42no—
432C22×C4—42no—
433C22×C4SD16×C15114yescomplemented
434C22×C4C2×D4×C15111yescharacteristic
435C22×C4C2×D4×C15111yescharacteristic
436C22×C4C2×D4×C15111yescharacteristic
437C22×C4C2×D4×C15111yescharacteristic
438C22×C4C2×D4×C15111yescharacteristic
439C22×C4C24×C15111yescharacteristic
440SD16—48no—
441C2×C8—22no—
442C2×C8—22no—
443C2×C8—22no—
444C2×C8—22no—
445C2×C8—22no—
446C2×C8C2×D4×C15114yes—
447C4⋊C4—21no—
448C4⋊C4—21no—
449C4⋊C4—21no—
450C4⋊C4—22no—
451C4⋊C4—21no—
452C4⋊C4—21no—
453C4⋊C4—22no—
454C4⋊C4—44no—
455C4⋊C4—42no—
456C4⋊C4—42no—
457C4⋊C4—42no—
458C4⋊C4—42no—
459C4⋊C4—42no—
460C4⋊C4#41×C15112yes—
461C22⋊C4—24no—
462C22⋊C4—44no—
463C22⋊C4—42no—
464C22⋊C4—42no—
465C22⋊C4—42no—
466C22⋊C4—42no—
467C42—22no—
468C42—22no—
469C42—21no—
470C42—21no—
471C42—42no—
472C42C2×D4×C15112yes—
473C42#41×C15112yes—
474C23—21no—
475C23—21no—
476C23—21no—
477C23—21no—
478C23—21no—
479C23—21no—
480C23—22no—
481C23—41no—
482C23—41no—
483C23—41no—
484C23—41no—
485C23—41no—
486C23—41no—
487C23C2×SD16×C15112yes—
488C23C22×D4×C15111yescharacteristic
489Q8—42no—
490Q8—42no—
491Q8—42no—
492Q8—42no—
493D4—22no—
494D4—22no—
495D4—48no—
496D4—41no—
497D4—41no—
498C2×C4—21no—
499C2×C4—21no—
500C2×C4—21no—
501C2×C4—21no—
502C2×C4—21no—
503C2×C4—21no—
504C2×C4—28no—
505C2×C4—21no—
506C2×C4—21no—
507C2×C4—22no—
508C2×C4—21no—
509C2×C4—44no—
510C2×C4—41no—
511C2×C4—41no—
512C2×C4—41no—
513C2×C4—41no—
514C2×C4—41no—
515C2×C4—41no—
516C2×C4—41no—
517C2×C4—42no—
518C2×C4—42no—
519C2×C4—42no—
520C2×C4—42no—
521C2×C4—41no—
522C2×C4—41no—
523C2×C4—41no—
524C2×C4—42no—
525C2×C4—41no—
526C2×C4—41no—
527C2×C4—42no—
528C2×C4—84no—
529C2×C4#121×C15112yes—
530C2×C4#121×C15112yes—
531C2×C4C2×SD16×C15112yes—
532C2×C4C2×SD16×C15112yes—
533C2×C4#135×C15112yes—
534C2×C4#137×C15112yes—
535C2×C4C22×D4×C15111yescharacteristic
536C2×C4C2×#41×C15111yescharacteristic
537C2×C4C2×#41×C15111yescharacteristic
538C2×C4C2×#41×C15111yescharacteristic
539C2×C4H(5,𝔽2)×C15111yescharacteristic
540C2×C4H(5,𝔽2)×C15111yescharacteristic
541C8—24no—
542C8—42no—
543C22—22no—
544C22—22no—
545C22—22no—
546C22—41no—
547C22—41no—
548C22—41no—
549C22—41no—
550C22—42no—
551C22—42no—
552C22—42no—
553C22—81no—
554C22—81no—
555C22—81no—
556C22—81no—
557C22C2×#121×C15111yescharacteristic
558C22#525×C15111yescharacteristic
559C22#535×C15111yescharacteristic
560C22C22×SD16×C15111yescharacteristic
561C22C2×#135×C15111yescharacteristic
562C22C2×#137×C15111yescharacteristic
563C22#575×C15111yescharacteristic
564C4—22no—
565C4—22no—
566C4—22no—
567C4—42no—
568C4—41no—
569C4—82no—
570C4—81no—
571C4—82no—
572C4—81no—
573C4#465×C15114yes—
574C4#546×C15111yescharacteristic
575C4#550×C15111yescharacteristic
576C4#553×C15111yescharacteristic
577C4#555×C15111yescharacteristic
578C2—42no—
579C2—82no—
580C2#2414×C15111yescharacteristic
581C2C2×#465×C15111yescharacteristic
582C2#3056×C15111yescharacteristic
583C2#3101×C15111yescharacteristic
584C2#3107×C15111yescharacteristic
585C2#3206×C15111yescharacteristic
586C2#3212×C15111yescharacteristic
subgroupG/H
center, socleC23×C151C22×D4
commutator, Frattini, cosocleC22×C4C24×C151
prime radicalC2×#121×C151C22
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×#461×C151C2semidirect
2. C2×#431×C151C2semidirect
3. #2857×C151C2semidirect
5. #2035×C151C2semidirect
7. #1981×C151C2semidirect
8. #1968×C151C2semidirect
9. #1948×C151C2semidirect
10. #1933×C151C2semidirect
11. #1802×C151C2semidirect
91. C4⋊C8×C151D4semidirect
139. C22×C4×C151SD16semidirect
293. #24651C151direct (N × H)
294. C151#24651direct (N × H)
295. C2×#461C2×C151semidirect
296. C2×#431C2×C151semidirect
297. #2857C2×C151semidirect
299. #2035C2×C151semidirect
301. #1981C2×C151semidirect
302. #1968C2×C151semidirect
303. #1948C2×C151semidirect
304. #1933C2×C151semidirect
305. #1802C2×C151semidirect
385. C4⋊C8D4×C151semidirect
433. C22×C4SD16×C151semidirect

Maximal subgroups

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

subgroupindex
C2×#461×C1512
C2×#431×C1512
#2857×C1512
C4×#121×C1512
#2035×C1512
#2000×C1512
#1981×C1512
#1968×C1512
#1948×C1512
#1933×C1512
#1802×C1512
#24651151