Finite Group Databasebeta

← C151×#23827 #50328752

Subgroups — C151×#23827 #50328752

Order 38656.

738 conjugacy classes of subgroups.

The subgroup lattice has 608 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#2331×C151C211yesmaximal, characteristic, complemented
2#2326×C151C211yesmaximal, characteristic
3#2100×C151C211yesmaximal, characteristic, complemented
4#2099×C151C211yesmaximal, characteristic, complemented
5#2074×C151C211yesmaximal, characteristic, complemented
6#2073×C151C211yesmaximal, characteristic
7#2042×C151C211yesmaximal, characteristic
8#2042×C151C211yesmaximal, characteristic
9#2024×C151C211yesmaximal, characteristic, complemented
10#2023×C151C211yesmaximal, characteristic
11#1763×C151C211yesmaximal, characteristic, complemented
12#1762×C151C211yesmaximal, characteristic
13C4×#103×C151C211yesmaximal, characteristic, complemented
14C4×#102×C151C211yesmaximal, characteristic
15#1746×C151C211yesmaximal, characteristic, complemented
16C2×C4⋊Q8×C151C2211yescharacteristic
17C2×#124×C151C2211yescharacteristic
18C2×C4×Q8×C151C2211yescharacteristic
19C2×C4×D4×C151C2211yescharacteristic
20C2×#103×C151C2211yescharacteristic
21C2×#103×C151C2211yescharacteristic
22C2×#103×C151C2211yescharacteristic
23C2×#103×C151C2211yescharacteristic
24C2×#102×C151C2211yescharacteristic
25C2×#102×C151C2211yescharacteristic
26C2×#102×C151C2211yescharacteristic
27C2×#102×C151C2211yescharacteristic
28C2×#97×C151C2211yescharacteristic
29C2×C4×C8×C151C2211yescharacteristic
30#391×C151—21no—
31#391×C151—21no—
32#391×C151C2211yescharacteristic
33#390×C151C2211yescharacteristic
34#389×C151C2211yescharacteristic
35#389×C151C2211yescharacteristic
36#388×C151—21no—
37#388×C151—21no—
38#387×C151—21no—
39#387×C151—21no—
40#385×C151—21no—
41#385×C151—21no—
42#384×C151C2211yescharacteristic
43#382×C151C2211yescharacteristic
44C4×C4⋊C4×C151C2211yescharacteristic
45C4×C4⋊C4×C151C2211yescharacteristic
46#376×C151C2211yescharacteristic
47#340×C151C2211yescharacteristic
48#340×C151C2211yescharacteristic
49#340×C151C2211yescharacteristic
50#340×C151C2211yescharacteristic
51#340×C151C2211yescharacteristic
52#340×C151C2211yescharacteristic
53#340×C151C2211yescharacteristic
54#340×C151C2211yescharacteristic
55#336×C151C2211yescharacteristic
56#336×C151C2211yescharacteristic
57#336×C151C2211yescharacteristic
58#336×C151C2211yescharacteristic
59C22×Q8×C151—21no—
60C22×Q8×C151C2311yescharacteristic
61C22×D4×C151C2311yescharacteristic
62C23×C4×C151—21no—
63C22×C8×C151C2311yescharacteristic
64C22×C8×C151C2311yescharacteristic
65C22×C8×C151C2311yescharacteristic
66C22×C8×C151C2311yescharacteristic
67C4⋊Q8×C151—22no—
68C4⋊Q8×C151—22no—
69#124×C151—22no—
70#124×C151—22no—
71C4×Q8×C151—22no—
72C4×Q8×C151—22no—
73C4×D4×C151—22no—
74C4×D4×C151—22no—
75C2×C4⋊C4×C151—21no—
76C2×C4⋊C4×C151—21no—
77C2×C4⋊C4×C151—21no—
78C2×C4⋊C4×C151—21no—
79C2×C4⋊C4×C151—21no—
80C2×C4⋊C4×C151—21no—
81C2×C4⋊C4×C151C2311yescharacteristic
82C2×C4⋊C4×C151C2311yescharacteristic
83C2×C4⋊C4×C151C2311yescharacteristic
84C2×C4⋊C4×C151C2311yescharacteristic
85C2×C4⋊C4×C151C2311yescharacteristic
86C2×C4⋊C4×C151C2311yescharacteristic
87C2×C22⋊C4×C151—21no—
88C2×C22⋊C4×C151—21no—
89C2×C22⋊C4×C151—21no—
90C2×C22⋊C4×C151—21no—
91C2×C22⋊C4×C151—21no—
92C2×C42×C151—21no—
93C2×C42×C151—21no—
94C2×C42×C151—21no—
95C2×C42×C151C2311yescharacteristic
96C2×C42×C151C2311yescharacteristic
97C2×C42×C151C2311yescharacteristic
98#103×C151—22no—
99#103×C151—22no—
100#103×C151—22no—
101#103×C151—22no—
102#102×C151—22no—
103#102×C151—22no—
104#102×C151—22no—
105#102×C151—22no—
106#97×C151—22no—
107C4×C8×C151—22no—
108#95×C151—21no—
109#95×C151—21no—
110#95×C151—21no—
111#95×C151—21no—
112#95×C151—21no—
113#95×C151—21no—
114#95×C151—21no—
115#95×C151—21no—
116#95×C151D411yescharacteristic
117#95×C151D411yescharacteristic
118#95×C151D411yescharacteristic
119#95×C151D411yescharacteristic
120C24×C151—21no—
121C2×Q8×C151—24no—
122C2×Q8×C151—21no—
123C2×Q8×C151—21no—
124C2×Q8×C151—21no—
125C2×Q8×C151—21no—
126C2×Q8×C151—21no—
127C2×Q8×C151—81no—
128C2×Q8×C151—81no—
129C2×Q8×C151#4112yes—
130C2×D4×C151—21no—
131C2×D4×C151—21no—
132C2×D4×C151—21no—
133C2×D4×C151—21no—
134C2×D4×C151—21no—
135C2×D4×C151#4112yes—
136C22×C4×C151—21no—
137C22×C4×C151—21no—
138C22×C4×C151—21no—
139C22×C4×C151—21no—
140C22×C4×C151—21no—
141C22×C4×C151—21no—
142C22×C4×C151—21no—
143C22×C4×C151—42no—
144C22×C4×C151—81no—
145C22×C4×C151—81no—
146C22×C4×C151C2×D411yescharacteristic
147C22×C4×C151C2×D411yescharacteristic
148C22×C4×C151C2×D411yescharacteristic
149C22×C4×C151C2×D411yescharacteristic
150C22×C4×C151C2×D411yescharacteristic
151C22×C4×C151C2×D411yescharacteristic
152C22×C4×C151C2411yescharacteristic
153C2×C8×C151—21no—
154C2×C8×C151—21no—
155C2×C8×C151—21no—
156C2×C8×C151—21no—
157C2×C8×C151—21no—
158C2×C8×C151—21no—
159C2×C8×C151—21no—
160C2×C8×C151—21no—
161C2×C8×C151—21no—
162C2×C8×C151—21no—
163C2×C8×C151—21no—
164C2×C8×C151—21no—
165C4⋊C4×C151—24no—
166C4⋊C4×C151—21no—
167C4⋊C4×C151—21no—
168C4⋊C4×C151—21no—
169C4⋊C4×C151—21no—
170C4⋊C4×C151—21no—
171C4⋊C4×C151—21no—
172C4⋊C4×C151—21no—
173C4⋊C4×C151—21no—
174C4⋊C4×C151—21no—
175C4⋊C4×C151—21no—
176C4⋊C4×C151—42no—
177C4⋊C4×C151—81no—
178C4⋊C4×C151—81no—
179C4⋊C4×C151—81no—
180C4⋊C4×C151—81no—
181C4⋊C4×C151#4112yes—
182C4⋊C4×C151#4112yes—
183C22⋊C4×C151—24no—
184C22⋊C4×C151—24no—
185C22⋊C4×C151—42no—
186C22⋊C4×C151—81no—
187C22⋊C4×C151—81no—
188C42×C151—21no—
189C42×C151—21no—
190C42×C151—21no—
191C42×C151—21no—
192C42×C151—42no—
193C42×C151—81no—
194C42×C151—81no—
195C42×C151#4112yes—
196C42×C151#4112yes—
197C23×C151—22no—
198C23×C151—41no—
199C23×C151—41no—
200C23×C151—41no—
201C23×C151—41no—
202C23×C151—41no—
203C23×C151—41no—
204C23×C151C22×D411yescharacteristic
205Q8×C151—22no—
206Q8×C151—22no—
207Q8×C151—41no—
208Q8×C151—41no—
209Q8×C151—84no—
210D4×C151—22no—
211D4×C151—22no—
212D4×C151—41no—
213D4×C151—41no—
214C2×C4×C151—21no—
215C2×C4×C151—21no—
216C2×C4×C151—21no—
217C2×C4×C151—21no—
218C2×C4×C151—21no—
219C2×C4×C151—22no—
220C2×C4×C151—22no—
221C2×C4×C151—22no—
222C2×C4×C151—21no—
223C2×C4×C151—21no—
224C2×C4×C151—21no—
225C2×C4×C151—21no—
226C2×C4×C151—21no—
227C2×C4×C151—21no—
228C2×C4×C151—21no—
229C2×C4×C151—21no—
230C2×C4×C151—21no—
231C2×C4×C151—21no—
232C2×C4×C151—21no—
233C2×C4×C151—41no—
234C2×C4×C151—41no—
235C2×C4×C151—41no—
236C2×C4×C151—41no—
237C2×C4×C151—41no—
238C2×C4×C151—41no—
239C2×C4×C151—41no—
240C2×C4×C151—41no—
241C2×C4×C151—41no—
242C2×C4×C151—41no—
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—41no—
250C2×C4×C151—41no—
251C2×C4×C151—84no—
252C2×C4×C151#12412yes—
253C2×C4×C151#12412yes—
254C2×C4×C151C2×#4111yescharacteristic
255C2×C4×C151C2×#4111yescharacteristic
256C2×C4×C151C2×#4111yescharacteristic
257C2×C4×C151C2×#4111yescharacteristic
258C2×C4×C151C2×#4111yescharacteristic
259C2×C4×C151C2×#4111yescharacteristic
260C8×C151—41no—
261C8×C151—41no—
262C8×C151—41no—
263C8×C151—41no—
264C22×C151—42no—
265C22×C151—42no—
266C22×C151—42no—
267C22×C151—81no—
268C22×C151—81no—
269C22×C151—81no—
270C22×C151—81no—
271C22×C151#52511yescharacteristic
272C22×C151#52511yescharacteristic
273C22×C151C2×#12411yescharacteristic
274C22×C151#57611yescharacteristic
275C22×C151#57711yescharacteristic
276C22×C151#57711yescharacteristic
277C22×C151#57811yescharacteristic
278C4×C151—22no—
279C4×C151—22no—
280C4×C151—41no—
281C4×C151—42no—
282C4×C151—42no—
283C4×C151—41no—
284C4×C151—41no—
285C4×C151—41no—
286C4×C151—42no—
287C4×C151—81no—
288C4×C151—81no—
289C4×C151—81no—
290C4×C151—81no—
291C4×C151#52911yescharacteristic
292C4×C151#52911yescharacteristic
293C4×C151#52911yescharacteristic
294C4×C151#52911yescharacteristic
295C2×C151—82no—
296C2×C151#239811yescharacteristic
297C2×C151#311811yescharacteristic
298C2×C151#312111yescharacteristic
299C2×C151#312411yescharacteristic
300C2×C151#312511yescharacteristic
301C2×C151#313611yescharacteristic
302C2×C151#313711yescharacteristic
303#23827C15111yesmaximal, characteristic, direct product factor, Sylow
304C151#2382711yescharacteristic, direct product factor, Sylow
305#2331C2×C15111yescharacteristic, complemented
306#2326C2×C15111yescharacteristic
307#2100C2×C15111yescharacteristic, complemented
308#2099C2×C15111yescharacteristic, complemented
309#2074C2×C15111yescharacteristic, complemented
310#2073C2×C15111yescharacteristic
311#2042C2×C15111yescharacteristic
312#2042C2×C15111yescharacteristic
313#2024C2×C15111yescharacteristic, complemented
314#2023C2×C15111yescharacteristic
315#1763C2×C15111yescharacteristic, complemented
316#1762C2×C15111yescharacteristic
317C4×#103C2×C15111yescharacteristic, complemented
318C4×#102C2×C15111yescharacteristic
319#1746C2×C15111yescharacteristic, complemented
320C2×C4⋊Q8C22×C15111yescharacteristic
321C2×#124C22×C15111yescharacteristic
322C2×C4×Q8C22×C15111yescharacteristic
323C2×C4×D4C22×C15111yescharacteristic
324C2×#103C22×C15111yescharacteristic
325C2×#103C22×C15111yescharacteristic
326C2×#103C22×C15111yescharacteristic
327C2×#103C22×C15111yescharacteristic
328C2×#102C22×C15111yescharacteristic
329C2×#102C22×C15111yescharacteristic
330C2×#102C22×C15111yescharacteristic
331C2×#102C22×C15111yescharacteristic
332C2×#97C22×C15111yescharacteristic
333C2×C4×C8C22×C15111yescharacteristic
334#391—21no—
335#391—21no—
336#391C22×C15111yescharacteristic
337#390C22×C15111yescharacteristic
338#389C22×C15111yescharacteristic
339#389C22×C15111yescharacteristic
340#388—21no—
341#388—21no—
342#387—21no—
343#387—21no—
344#385—21no—
345#385—21no—
346#384C22×C15111yescharacteristic
347#382C22×C15111yescharacteristic
348C4×C4⋊C4C22×C15111yescharacteristic
349C4×C4⋊C4C22×C15111yescharacteristic
350#376C22×C15111yescharacteristic
351#340C22×C15111yescharacteristic
352#340C22×C15111yescharacteristic
353#340C22×C15111yescharacteristic
354#340C22×C15111yescharacteristic
355#340C22×C15111yescharacteristic
356#340C22×C15111yescharacteristic
357#340C22×C15111yescharacteristic
358#340C22×C15111yescharacteristic
359#336C22×C15111yescharacteristic
360#336C22×C15111yescharacteristic
361#336C22×C15111yescharacteristic
362#336C22×C15111yescharacteristic
363C22×Q8—21no—
364C22×Q8C23×C15111yescharacteristic
365C22×D4C23×C15111yescharacteristic
366C23×C4—21no—
367C22×C8C23×C15111yescharacteristic
368C22×C8C23×C15111yescharacteristic
369C22×C8C23×C15111yescharacteristic
370C22×C8C23×C15111yescharacteristic
371C4⋊Q8—22no—
372C4⋊Q8—22no—
373#124—22no—
374#124—22no—
375C4×Q8—22no—
376C4×Q8—22no—
377C4×D4—22no—
378C4×D4—22no—
379C2×C4⋊C4—21no—
380C2×C4⋊C4—21no—
381C2×C4⋊C4—21no—
382C2×C4⋊C4—21no—
383C2×C4⋊C4—21no—
384C2×C4⋊C4—21no—
385C2×C4⋊C4C23×C15111yescharacteristic
386C2×C4⋊C4C23×C15111yescharacteristic
387C2×C4⋊C4C23×C15111yescharacteristic
388C2×C4⋊C4C23×C15111yescharacteristic
389C2×C4⋊C4C23×C15111yescharacteristic
390C2×C4⋊C4C23×C15111yescharacteristic
391C2×C22⋊C4—21no—
392C2×C22⋊C4—21no—
393C2×C22⋊C4—21no—
394C2×C22⋊C4—21no—
395C2×C22⋊C4—21no—
396C2×C42—21no—
397C2×C42—21no—
398C2×C42—21no—
399C2×C42C23×C15111yescharacteristic
400C2×C42C23×C15111yescharacteristic
401C2×C42C23×C15111yescharacteristic
402#103—22no—
403#103—22no—
404#103—22no—
405#103—22no—
406#102—22no—
407#102—22no—
408#102—22no—
409#102—22no—
410#97—22no—
411C4×C8—22no—
412#95—21no—
413#95—21no—
414#95—21no—
415#95—21no—
416#95—21no—
417#95—21no—
418#95—21no—
419#95—21no—
420#95D4×C15111yescharacteristic
421#95D4×C15111yescharacteristic
422#95D4×C15111yescharacteristic
423#95D4×C15111yescharacteristic
424C24—21no—
425C2×Q8—24no—
426C2×Q8—21no—
427C2×Q8—21no—
428C2×Q8—21no—
429C2×Q8—21no—
430C2×Q8—21no—
431C2×Q8—81no—
432C2×Q8—81no—
433C2×Q8#41×C15112yes—
434C2×D4—21no—
435C2×D4—21no—
436C2×D4—21no—
437C2×D4—21no—
438C2×D4—21no—
439C2×D4#41×C15112yes—
440C22×C4—21no—
441C22×C4—21no—
442C22×C4—21no—
443C22×C4—21no—
444C22×C4—21no—
445C22×C4—21no—
446C22×C4—21no—
447C22×C4—42no—
448C22×C4—81no—
449C22×C4—81no—
450C22×C4C2×D4×C15111yescharacteristic
451C22×C4C2×D4×C15111yescharacteristic
452C22×C4C2×D4×C15111yescharacteristic
453C22×C4C2×D4×C15111yescharacteristic
454C22×C4C2×D4×C15111yescharacteristic
455C22×C4C2×D4×C15111yescharacteristic
456C22×C4C24×C15111yescharacteristic
457C2×C8—21no—
458C2×C8—21no—
459C2×C8—21no—
460C2×C8—21no—
461C2×C8—21no—
462C2×C8—21no—
463C2×C8—21no—
464C2×C8—21no—
465C2×C8—21no—
466C2×C8—21no—
467C2×C8—21no—
468C2×C8—21no—
469C4⋊C4—24no—
470C4⋊C4—21no—
471C4⋊C4—21no—
472C4⋊C4—21no—
473C4⋊C4—21no—
474C4⋊C4—21no—
475C4⋊C4—21no—
476C4⋊C4—21no—
477C4⋊C4—21no—
478C4⋊C4—21no—
479C4⋊C4—21no—
480C4⋊C4—42no—
481C4⋊C4—81no—
482C4⋊C4—81no—
483C4⋊C4—81no—
484C4⋊C4—81no—
485C4⋊C4#41×C15112yes—
486C4⋊C4#41×C15112yes—
487C22⋊C4—24no—
488C22⋊C4—24no—
489C22⋊C4—42no—
490C22⋊C4—81no—
491C22⋊C4—81no—
492C42—21no—
493C42—21no—
494C42—21no—
495C42—21no—
496C42—42no—
497C42—81no—
498C42—81no—
499C42#41×C15112yes—
500C42#41×C15112yes—
501C23—22no—
502C23—41no—
503C23—41no—
504C23—41no—
505C23—41no—
506C23—41no—
507C23—41no—
508C23C22×D4×C15111yescharacteristic
509Q8—22no—
510Q8—22no—
511Q8—41no—
512Q8—41no—
513Q8—84no—
514D4—22no—
515D4—22no—
516D4—41no—
517D4—41no—
518C2×C4—21no—
519C2×C4—21no—
520C2×C4—21no—
521C2×C4—21no—
522C2×C4—21no—
523C2×C4—21no—
524C2×C4—21no—
525C2×C4—21no—
526C2×C4—22no—
527C2×C4—22no—
528C2×C4—22no—
529C2×C4—21no—
530C2×C4—21no—
531C2×C4—21no—
532C2×C4—21no—
533C2×C4—21no—
534C2×C4—21no—
535C2×C4—21no—
536C2×C4—21no—
537C2×C4—41no—
538C2×C4—41no—
539C2×C4—41no—
540C2×C4—41no—
541C2×C4—41no—
542C2×C4—41no—
543C2×C4—41no—
544C2×C4—41no—
545C2×C4—41no—
546C2×C4—41no—
547C2×C4—41no—
548C2×C4—41no—
549C2×C4—41no—
550C2×C4—41no—
551C2×C4—41no—
552C2×C4—41no—
553C2×C4—41no—
554C2×C4—41no—
555C2×C4—84no—
556C2×C4#124×C15112yes—
557C2×C4#124×C15112yes—
558C2×C4C2×#41×C15111yescharacteristic
559C2×C4C2×#41×C15111yescharacteristic
560C2×C4C2×#41×C15111yescharacteristic
561C2×C4C2×#41×C15111yescharacteristic
562C2×C4C2×#41×C15111yescharacteristic
563C2×C4C2×#41×C15111yescharacteristic
564C8—41no—
565C8—41no—
566C8—41no—
567C8—41no—
568C22—42no—
569C22—42no—
570C22—42no—
571C22—81no—
572C22—81no—
573C22—81no—
574C22—81no—
575C22#525×C15111yescharacteristic
576C22#525×C15111yescharacteristic
577C22C2×#124×C15111yescharacteristic
578C22#576×C15111yescharacteristic
579C22#577×C15111yescharacteristic
580C22#577×C15111yescharacteristic
581C22#578×C15111yescharacteristic
582C4—22no—
583C4—22no—
584C4—41no—
585C4—42no—
586C4—42no—
587C4—41no—
588C4—41no—
589C4—41no—
590C4—42no—
591C4—81no—
592C4—81no—
593C4—81no—
594C4—81no—
595C4#529×C15111yescharacteristic
596C4#529×C15111yescharacteristic
597C4#529×C15111yescharacteristic
598C4#529×C15111yescharacteristic
599C2—82no—
600C2#2398×C15111yescharacteristic
601C2#3118×C15111yescharacteristic
602C2#3121×C15111yescharacteristic
603C2#3124×C15111yescharacteristic
604C2#3125×C15111yescharacteristic
605C2#3136×C15111yescharacteristic
606C2#3137×C15111yescharacteristic
subgroupG/H
center, socleC23×C151C22×D4
commutator, Frattini, cosocleC22×C4C24×C151
prime radicalC22×D4×C151C23
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C151 ◁ #376×C151 ◁ G

Complements

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

NH ≅ G/Ntype
1. #2331×C151C2semidirect
3. #2100×C151C2semidirect
4. #2099×C151C2semidirect
5. #2074×C151C2semidirect
9. #2024×C151C2semidirect
11. #1763×C151C2semidirect
13. C4×#103×C151C2semidirect
15. #1746×C151C2semidirect
303. #23827C151direct (N × H)
304. C151#23827direct (N × H)
305. #2331C2×C151semidirect
307. #2100C2×C151semidirect
308. #2099C2×C151semidirect
309. #2074C2×C151semidirect
313. #2024C2×C151semidirect
315. #1763C2×C151semidirect
317. C4×#103C2×C151semidirect
319. #1746C2×C151semidirect

Maximal subgroups

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

subgroupindex
#2331×C1512
#2326×C1512
#2100×C1512
#2099×C1512
#2074×C1512
#2073×C1512
#2042×C1512
#2024×C1512
#2023×C1512
#1763×C1512
#1762×C1512
C4×#103×C1512
C4×#102×C1512
#1746×C1512
#23827151