Finite Group Databasebeta

← C151×#24836 #50329761

Subgroups — C151×#24836 #50329761

Order 38656.

988 conjugacy classes of subgroups.

The subgroup lattice has 572 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#476×C151C211yesmaximal, characteristic, complemented
2C22×C4⋊C8×C151C211yesmaximal, characteristic, complemented
3#2857×C151C211yesmaximal, characteristic, complemented
4C4×#121×C151C211yesmaximal, characteristic
5#2088×C151C212yesmaximal, complemented
6#2065×C151C212yesmaximal, complemented
7#1987×C151C211yesmaximal, characteristic, complemented
8#1948×C151C211yesmaximal, characteristic, complemented
9#1893×C151C212yesmaximal
10#1807×C151C212yesmaximal, complemented
11#1802×C151C211yesmaximal, characteristic, complemented
12C23×C8×C151C2212yes—
13C2×C4⋊Q8×C151C2211yescharacteristic
14C2×C22⋊Q8×C151—21no—
15C2×#121×C151C2211yescharacteristic
16C2×C4×D4×C151—21no—
17C2×C4×D4×C151C2211yescharacteristic
18C22×C42×C151C2211yescharacteristic
19#476×C151—24no—
20C2×#106×C151C2212yes—
21C2×#106×C151C2212yes—
22C2×C4⋊C8×C151—24no—
23C2×C4⋊C8×C151C2212yes—
24C2×C4⋊C8×C151C2211yescharacteristic
25C2×C4⋊C8×C151C2211yescharacteristic
26C2×#102×C151C2212yes—
27C2×#102×C151C2212yes—
28#391×C151—21no—
29#390×C151C2211yescharacteristic
30#389×C151—21no—
31#389×C151C2211yescharacteristic
32#389×C151C2212yes—
33#388×C151—21no—
34#386×C151—21no—
35#384×C151C2211yescharacteristic
36#380×C151—21no—
37#380×C151C2212yes—
38#380×C151C2211yescharacteristic
39C4×C4⋊C4×C151C2211yescharacteristic
40C4×C22⋊C4×C151—21no—
41#340×C151C2212yes—
42#340×C151C2212yes—
43#340×C151C2212yes—
44#340×C151C2212yes—
45C22×Q8×C151—21no—
46C22×D4×C151—21no—
47C22×D4×C151C2311yescharacteristic
48C23×C4×C151—21no—
49C23×C4×C151D411yescharacteristic
50C23×C4×C151D411yescharacteristic
51C23×C4×C151C2311yescharacteristic
52C22×C8×C151—24no—
53C22×C8×C151—24no—
54C22×C8×C151—42no—
55C22×C8×C151C2312yes—
56C22×C8×C151C2312yes—
57C4⋊Q8×C151—22no—
58C4⋊Q8×C151—22no—
59C22⋊Q8×C151—44no—
60#121×C151—22no—
61#121×C151Q814yescomplemented
62C4×D4×C151—22no—
63C4×D4×C151—22no—
64C4×D4×C151—44no—
65C2×C4⋊C4×C151—21no—
66C2×C4⋊C4×C151—21no—
67C2×C4⋊C4×C151—21no—
68C2×C4⋊C4×C151—21no—
69C2×C4⋊C4×C151—22no—
70C2×C4⋊C4×C151C2311yescharacteristic
71C2×C4⋊C4×C151C2312yes—
72C2×C4⋊C4×C151C2312yes—
73C2×C4⋊C4×C151C2311yescharacteristic
74C2×C4⋊C4×C151C2311yescharacteristic
75C2×C22⋊C4×C151—21no—
76C2×C22⋊C4×C151—21no—
77C2×C22⋊C4×C151—21no—
78C2×C22⋊C4×C151—21no—
79C2×C22⋊C4×C151—22no—
80C2×C22⋊C4×C151—21no—
81C2×C42×C151—22no—
82C2×C42×C151—22no—
83C2×C42×C151—21no—
84C2×C42×C151D411yescharacteristic
85C2×C42×C151D411yescharacteristic
86C2×C42×C151C2311yescharacteristic
87C2×C42×C151C2311yescharacteristic
88#106×C151—24no—
89#106×C151—42no—
90C4⋊C8×C151—24no—
91C4⋊C8×C151—22no—
92C4⋊C8×C151D414yescomplemented
93#102×C151—24no—
94#102×C151—42no—
95#95×C151—21no—
96#95×C151—21no—
97#95×C151—21no—
98#95×C151—22no—
99#95×C151—22no—
100C24×C151—21no—
101C24×C151C2×D411yescharacteristic
102C2×Q8×C151—42no—
103C2×Q8×C151—42no—
104C2×Q8×C151—42no—
105C2×D4×C151—24no—
106C2×D4×C151—21no—
107C2×D4×C151—21no—
108C2×D4×C151—21no—
109C2×D4×C151—21no—
110C2×D4×C151—21no—
111C2×D4×C151—42no—
112C2×D4×C151—42no—
113C2×D4×C151C2×Q812yes—
114C22×C4×C151—22no—
115C22×C4×C151—22no—
116C22×C4×C151—21no—
117C22×C4×C151—21no—
118C22×C4×C151—21no—
119C22×C4×C151—21no—
120C22×C4×C151—22no—
121C22×C4×C151—21no—
122C22×C4×C151—22no—
123C22×C4×C151—21no—
124C22×C4×C151—21no—
125C22×C4×C151—22no—
126C22×C4×C151—22no—
127C22×C4×C151—41no—
128C22×C4×C151—42no—
129C22×C4×C151—42no—
130C22×C4×C151—42no—
131C22×C4×C151SD1614yes—
132C22×C4×C151C2×D411yescharacteristic
133C22×C4×C151C2×D411yescharacteristic
134C22×C4×C151C2×D411yescharacteristic
135C22×C4×C151C2×D411yescharacteristic
136C22×C4×C151C2×D411yescharacteristic
137C22×C4×C151C2×Q812yes—
138C22×C4×C151#4112yes—
139C22×C4×C151C2411yescharacteristic
140C2×C8×C151—22no—
141C2×C8×C151—22no—
142C2×C8×C151—22no—
143C2×C8×C151—22no—
144C2×C8×C151—22no—
145C2×C8×C151—48no—
146C2×C8×C151C2×D414yes—
147C4⋊C4×C151—21no—
148C4⋊C4×C151—22no—
149C4⋊C4×C151—21no—
150C4⋊C4×C151—21no—
151C4⋊C4×C151—22no—
152C4⋊C4×C151—22no—
153C4⋊C4×C151—21no—
154C4⋊C4×C151—21no—
155C4⋊C4×C151—22no—
156C4⋊C4×C151—42no—
157C4⋊C4×C151—44no—
158C4⋊C4×C151—42no—
159C4⋊C4×C151—42no—
160C4⋊C4×C151—42no—
161C4⋊C4×C151C2×Q812yes—
162C22⋊C4×C151—24no—
163C22⋊C4×C151—42no—
164C22⋊C4×C151—42no—
165C22⋊C4×C151—44no—
166C22⋊C4×C151—42no—
167C22⋊C4×C151—42no—
168C42×C151—22no—
169C42×C151—22no—
170C42×C151—21no—
171C42×C151—21no—
172C42×C151—42no—
173C42×C151C2×D412yes—
174C42×C151#4112yes—
175C23×C151—21no—
176C23×C151—21no—
177C23×C151—21no—
178C23×C151—21no—
179C23×C151—22no—
180C23×C151—41no—
181C23×C151—41no—
182C23×C151—41no—
183C23×C151—41no—
184C23×C151—41no—
185C23×C151—41no—
186C23×C151C22⋊Q812yes—
187C23×C151C2×SD1612yes—
188C23×C151AGL(1,ℤ/8)12yes—
189C23×C151C22×D411yescharacteristic
190Q8×C151—84no—
191D4×C151—22no—
192D4×C151—22no—
193D4×C151—48no—
194D4×C151—41no—
195D4×C151—41no—
196C2×C4×C151—21no—
197C2×C4×C151—21no—
198C2×C4×C151—21no—
199C2×C4×C151—21no—
200C2×C4×C151—21no—
201C2×C4×C151—21no—
202C2×C4×C151—22no—
203C2×C4×C151—22no—
204C2×C4×C151—22no—
205C2×C4×C151—22no—
206C2×C4×C151—28no—
207C2×C4×C151—21no—
208C2×C4×C151—22no—
209C2×C4×C151—21no—
210C2×C4×C151—21no—
211C2×C4×C151—44no—
212C2×C4×C151—41no—
213C2×C4×C151—41no—
214C2×C4×C151—42no—
215C2×C4×C151—41no—
216C2×C4×C151—41no—
217C2×C4×C151—42no—
218C2×C4×C151—41no—
219C2×C4×C151—41no—
220C2×C4×C151—42no—
221C2×C4×C151—41no—
222C2×C4×C151—42no—
223C2×C4×C151—42no—
224C2×C4×C151—42no—
225C2×C4×C151—41no—
226C2×C4×C151—84no—
227C2×C4×C151#12112yes—
228C2×C4×C151#12112yes—
229C2×C4×C151C22⋊Q812yes—
230C2×C4×C151C2×SD1612yes—
231C2×C4×C151C2×SD1612yes—
232C2×C4×C151#13512yes—
233C2×C4×C151C22×D411yescharacteristic
234C2×C4×C151C22×Q811yescharacteristic
235C2×C4×C151C2×#4111yescharacteristic
236C2×C4×C151C2×#4111yescharacteristic
237C2×C4×C151H(5,𝔽2)11yescharacteristic
238C2×C4×C1512−1+411yescharacteristic
239C8×C151—24no—
240C8×C151—42no—
241C22×C151—22no—
242C22×C151—22no—
243C22×C151—22no—
244C22×C151—22no—
245C22×C151—22no—
246C22×C151—22no—
247C22×C151—42no—
248C22×C151—42no—
249C22×C151—42no—
250C22×C151—81no—
251C22×C151—81no—
252C22×C151—81no—
253C22×C151—81no—
254C22×C151#47614yescomplemented
255C22×C151C2×#12111yescharacteristic
256C22×C151C2×C22⋊Q811yescharacteristic
257C22×C151#53711yescharacteristic
258C22×C151C22×SD1611yescharacteristic
259C22×C151C2×#13511yescharacteristic
260C22×C151C2×AGL(1,ℤ/8)11yescharacteristic
261C22×C151#57511yescharacteristic
262C4×C151—22no—
263C4×C151—22no—
264C4×C151—22no—
265C4×C151—41no—
266C4×C151—42no—
267C4×C151—81no—
268C4×C151—82no—
269C4×C151—81no—
270C4×C151—82no—
271C4×C151#46514yes—
272C4×C151#54611yescharacteristic
273C4×C151D4×Q811yescharacteristic
274C4×C151#55211yescharacteristic
275C4×C151#55411yescharacteristic
276C2×C151—24no—
277C2×C151—82no—
278C2×C151#241711yescharacteristic
279C2×C151C2×#46511yescharacteristic
280C2×C151#305511yescharacteristic
281C2×C151C2×#47611yescharacteristic
282C2×C151#307611yescharacteristic
283C2×C151#324611yescharacteristic
284C2×C151#324711yescharacteristic
285#24836C15111yesmaximal, characteristic, direct product factor, Sylow
286C151#2483611yescharacteristic, direct product factor, Sylow
287C2×#476C2×C15111yescharacteristic, complemented
288C22×C4⋊C8C2×C15111yescharacteristic, complemented
289#2857C2×C15111yescharacteristic, complemented
290C4×#121C2×C15111yescharacteristic
291#2088C2×C15112yescomplemented
292#2065C2×C15112yescomplemented
293#1987C2×C15111yescharacteristic, complemented
294#1948C2×C15111yescharacteristic, complemented
295#1893C2×C15112yes—
296#1807C2×C15112yescomplemented
297#1802C2×C15111yescharacteristic, complemented
298C23×C8C22×C15112yes—
299C2×C4⋊Q8C22×C15111yescharacteristic
300C2×C22⋊Q8—21no—
301C2×#121C22×C15111yescharacteristic
302C2×C4×D4—21no—
303C2×C4×D4C22×C15111yescharacteristic
304C22×C42C22×C15111yescharacteristic
305#476—24no—
306C2×#106C22×C15112yes—
307C2×#106C22×C15112yes—
308C2×C4⋊C8—24no—
309C2×C4⋊C8C22×C15111yescharacteristic
310C2×C4⋊C8C22×C15112yes—
311C2×C4⋊C8C22×C15111yescharacteristic
312C2×#102C22×C15112yes—
313C2×#102C22×C15112yes—
314#391—21no—
315#390C22×C15111yescharacteristic
316#389—21no—
317#389C22×C15112yes—
318#389C22×C15111yescharacteristic
319#388—21no—
320#386—21no—
321#384C22×C15111yescharacteristic
322#380—21no—
323#380C22×C15111yescharacteristic
324#380C22×C15112yes—
325C4×C4⋊C4C22×C15111yescharacteristic
326C4×C22⋊C4—21no—
327#340C22×C15112yes—
328#340C22×C15112yes—
329#340C22×C15112yes—
330#340C22×C15112yes—
331C22×Q8—21no—
332C22×D4—21no—
333C22×D4C23×C15111yescharacteristic
334C23×C4—21no—
335C23×C4D4×C15111yescharacteristic
336C23×C4D4×C15111yescharacteristic
337C23×C4C23×C15111yescharacteristic
338C22×C8—24no—
339C22×C8—24no—
340C22×C8—42no—
341C22×C8C23×C15112yes—
342C22×C8C23×C15112yes—
343C4⋊Q8—22no—
344C4⋊Q8—22no—
345C22⋊Q8—44no—
346#121—22no—
347#121Q8×C15114yescomplemented
348C4×D4—22no—
349C4×D4—22no—
350C4×D4—44no—
351C2×C4⋊C4—21no—
352C2×C4⋊C4—21no—
353C2×C4⋊C4—22no—
354C2×C4⋊C4—21no—
355C2×C4⋊C4—21no—
356C2×C4⋊C4C23×C15111yescharacteristic
357C2×C4⋊C4C23×C15112yes—
358C2×C4⋊C4C23×C15111yescharacteristic
359C2×C4⋊C4C23×C15112yes—
360C2×C4⋊C4C23×C15111yescharacteristic
361C2×C22⋊C4—21no—
362C2×C22⋊C4—21no—
363C2×C22⋊C4—22no—
364C2×C22⋊C4—21no—
365C2×C22⋊C4—21no—
366C2×C22⋊C4—21no—
367C2×C42—22no—
368C2×C42—22no—
369C2×C42—21no—
370C2×C42D4×C15111yescharacteristic
371C2×C42D4×C15111yescharacteristic
372C2×C42C23×C15111yescharacteristic
373C2×C42C23×C15111yescharacteristic
374#106—24no—
375#106—42no—
376C4⋊C8—24no—
377C4⋊C8—22no—
378C4⋊C8D4×C15114yescomplemented
379#102—24no—
380#102—42no—
381#95—21no—
382#95—21no—
383#95—21no—
384#95—22no—
385#95—22no—
386C24—21no—
387C24C2×D4×C15111yescharacteristic
388C2×Q8—42no—
389C2×Q8—42no—
390C2×Q8—42no—
391C2×D4—24no—
392C2×D4—21no—
393C2×D4—21no—
394C2×D4—21no—
395C2×D4—21no—
396C2×D4—21no—
397C2×D4—42no—
398C2×D4—42no—
399C2×D4C2×Q8×C15112yes—
400C22×C4—22no—
401C22×C4—22no—
402C22×C4—21no—
403C22×C4—21no—
404C22×C4—21no—
405C22×C4—21no—
406C22×C4—22no—
407C22×C4—21no—
408C22×C4—22no—
409C22×C4—21no—
410C22×C4—21no—
411C22×C4—22no—
412C22×C4—22no—
413C22×C4—41no—
414C22×C4—42no—
415C22×C4—42no—
416C22×C4—42no—
417C22×C4SD16×C15114yes—
418C22×C4C2×D4×C15111yescharacteristic
419C22×C4C2×D4×C15111yescharacteristic
420C22×C4C2×D4×C15111yescharacteristic
421C22×C4C2×D4×C15111yescharacteristic
422C22×C4C2×D4×C15111yescharacteristic
423C22×C4C2×Q8×C15112yes—
424C22×C4#41×C15112yes—
425C22×C4C24×C15111yescharacteristic
426C2×C8—22no—
427C2×C8—22no—
428C2×C8—22no—
429C2×C8—22no—
430C2×C8—22no—
431C2×C8—48no—
432C2×C8C2×D4×C15114yes—
433C4⋊C4—21no—
434C4⋊C4—22no—
435C4⋊C4—21no—
436C4⋊C4—21no—
437C4⋊C4—22no—
438C4⋊C4—22no—
439C4⋊C4—21no—
440C4⋊C4—21no—
441C4⋊C4—22no—
442C4⋊C4—42no—
443C4⋊C4—44no—
444C4⋊C4—42no—
445C4⋊C4—42no—
446C4⋊C4—42no—
447C4⋊C4C2×Q8×C15112yes—
448C22⋊C4—24no—
449C22⋊C4—42no—
450C22⋊C4—42no—
451C22⋊C4—44no—
452C22⋊C4—42no—
453C22⋊C4—42no—
454C42—22no—
455C42—22no—
456C42—21no—
457C42—21no—
458C42—42no—
459C42C2×D4×C15112yes—
460C42#41×C15112yes—
461C23—21no—
462C23—21no—
463C23—21no—
464C23—21no—
465C23—22no—
466C23—41no—
467C23—41no—
468C23—41no—
469C23—41no—
470C23—41no—
471C23—41no—
472C23C22⋊Q8×C15112yes—
473C23C2×SD16×C15112yes—
474C23AGL(1,ℤ/8)×C15112yes—
475C23C22×D4×C15111yescharacteristic
476Q8—84no—
477D4—22no—
478D4—22no—
479D4—48no—
480D4—41no—
481D4—41no—
482C2×C4—21no—
483C2×C4—21no—
484C2×C4—21no—
485C2×C4—21no—
486C2×C4—21no—
487C2×C4—21no—
488C2×C4—28no—
489C2×C4—22no—
490C2×C4—22no—
491C2×C4—22no—
492C2×C4—22no—
493C2×C4—21no—
494C2×C4—22no—
495C2×C4—21no—
496C2×C4—21no—
497C2×C4—44no—
498C2×C4—41no—
499C2×C4—41no—
500C2×C4—41no—
501C2×C4—42no—
502C2×C4—41no—
503C2×C4—42no—
504C2×C4—41no—
505C2×C4—41no—
506C2×C4—42no—
507C2×C4—41no—
508C2×C4—42no—
509C2×C4—42no—
510C2×C4—41no—
511C2×C4—42no—
512C2×C4—84no—
513C2×C4#121×C15112yes—
514C2×C4#121×C15112yes—
515C2×C4C22⋊Q8×C15112yes—
516C2×C4C2×SD16×C15112yes—
517C2×C4C2×SD16×C15112yes—
518C2×C4#135×C15112yes—
519C2×C4C22×D4×C15111yescharacteristic
520C2×C4C22×Q8×C15111yescharacteristic
521C2×C4C2×#41×C15111yescharacteristic
522C2×C4C2×#41×C15111yescharacteristic
523C2×C4H(5,𝔽2)×C15111yescharacteristic
524C2×C42−1+4×C15111yescharacteristic
525C8—24no—
526C8—42no—
527C22—22no—
528C22—22no—
529C22—22no—
530C22—22no—
531C22—22no—
532C22—22no—
533C22—42no—
534C22—42no—
535C22—42no—
536C22—81no—
537C22—81no—
538C22—81no—
539C22—81no—
540C22#476×C15114yescomplemented
541C22C2×#121×C15111yescharacteristic
542C22C2×C22⋊Q8×C15111yescharacteristic
543C22#537×C15111yescharacteristic
544C22C22×SD16×C15111yescharacteristic
545C22C2×#135×C15111yescharacteristic
546C22C2×AGL(1,ℤ/8)×C15111yescharacteristic
547C22#575×C15111yescharacteristic
548C4—22no—
549C4—22no—
550C4—22no—
551C4—41no—
552C4—42no—
553C4—81no—
554C4—82no—
555C4—81no—
556C4—82no—
557C4#465×C15114yes—
558C4#546×C15111yescharacteristic
559C4D4×Q8×C15111yescharacteristic
560C4#552×C15111yescharacteristic
561C4#554×C15111yescharacteristic
562C2—24no—
563C2—82no—
564C2#2417×C15111yescharacteristic
565C2C2×#465×C15111yescharacteristic
566C2#3055×C15111yescharacteristic
567C2C2×#476×C15111yescharacteristic
568C2#3076×C15111yescharacteristic
569C2#3246×C15111yescharacteristic
570C2#3247×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×#476×C151C2semidirect
2. C22×C4⋊C8×C151C2semidirect
3. #2857×C151C2semidirect
5. #2088×C151C2semidirect
6. #2065×C151C2semidirect
7. #1987×C151C2semidirect
8. #1948×C151C2semidirect
10. #1807×C151C2semidirect
11. #1802×C151C2semidirect
61. #121×C151Q8semidirect
92. C4⋊C8×C151D4semidirect
254. C22×C151#476semidirect
285. #24836C151direct (N × H)
286. C151#24836direct (N × H)
287. C2×#476C2×C151semidirect
288. C22×C4⋊C8C2×C151semidirect
289. #2857C2×C151semidirect
291. #2088C2×C151semidirect
292. #2065C2×C151semidirect
293. #1987C2×C151semidirect
294. #1948C2×C151semidirect
296. #1807C2×C151semidirect
297. #1802C2×C151semidirect
347. #121Q8×C151semidirect
378. C4⋊C8D4×C151semidirect
540. C22#476×C151semidirect

Maximal subgroups

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

subgroupindex
C2×#476×C1512
C22×C4⋊C8×C1512
#2857×C1512
C4×#121×C1512
#2088×C1512
#2065×C1512
#1987×C1512
#1948×C1512
#1893×C1512
#1807×C1512
#1802×C1512
#24836151