Finite Group Databasebeta

← C151×#23809 #50328734

Subgroups — C151×#23809 #50328734

Order 38656.

974 conjugacy classes of subgroups.

The subgroup lattice has 604 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#441×C151C211yesmaximal, characteristic, complemented
2C2×#440×C151C211yesmaximal, characteristic
3C2×C4×Q16×C151C211yesmaximal, characteristic, complemented
4C2×C4×SD16×C151C211yesmaximal, characteristic
5#2327×C151C211yesmaximal, characteristic, complemented
6#2326×C151C211yesmaximal, characteristic
7#2097×C151C211yesmaximal, characteristic, complemented
8#2096×C151C211yesmaximal, characteristic, complemented
9#2095×C151C211yesmaximal, characteristic, complemented
10#2092×C151C211yesmaximal, characteristic
11#2016×C151C211yesmaximal, characteristic, complemented
12#2015×C151C211yesmaximal, characteristic
13#2015×C151C211yesmaximal, characteristic
14#2013×C151C211yesmaximal, characteristic
15#1746×C151C211yesmaximal, characteristic, complemented
16C22×Q16×C151C2211yescharacteristic
17C22×Q16×C151C2211yescharacteristic
18C22×SD16×C151C2211yescharacteristic
19C22×SD16×C151C2211yescharacteristic
20C2×C4⋊Q8×C151C2211yescharacteristic
21C2×#124×C151C2211yescharacteristic
22C2×C4×Q8×C151C2211yescharacteristic
23C2×C4×Q8×C151C2211yescharacteristic
24C2×C4×Q8×C151C2211yescharacteristic
25C2×C4×D4×C151C2211yescharacteristic
26#441×C151—24no—
27#440×C151—24no—
28C4×Q16×C151—24no—
29C4×SD16×C151—24no—
30C2×#107×C151C2211yescharacteristic
31C2×#107×C151C2211yescharacteristic
32C2×#106×C151C2211yescharacteristic
33C2×#106×C151C2211yescharacteristic
34C2×#103×C151C2211yescharacteristic
35C2×#103×C151C2211yescharacteristic
36C2×#103×C151C2211yescharacteristic
37C2×#103×C151C2211yescharacteristic
38C2×#103×C151C2211yescharacteristic
39C2×#103×C151C2211yescharacteristic
40C2×#102×C151C2211yescharacteristic
41C2×#102×C151C2211yescharacteristic
42C2×#97×C151C2211yescharacteristic
43C2×C4×C8×C151C2211yescharacteristic
44#391×C151C2211yescharacteristic
45#391×C151C2211yescharacteristic
46#391×C151C2211yescharacteristic
47#390×C151C2211yescharacteristic
48#388×C151—22no—
49#387×C151—22no—
50#387×C151—22no—
51#385×C151—22no—
52#384×C151C2211yescharacteristic
53#382×C151C2211yescharacteristic
54#376×C151C2211yescharacteristic
55#336×C151C2211yescharacteristic
56#336×C151C2211yescharacteristic
57#336×C151C2211yescharacteristic
58#336×C151C2211yescharacteristic
59C22×Q8×C151C2311yescharacteristic
60C22×Q8×C151C2311yescharacteristic
61C22×Q8×C151C2311yescharacteristic
62C22×D4×C151C2311yescharacteristic
63C23×C4×C151—21no—
64C2×Q16×C151—22no—
65C2×Q16×C151—22no—
66C2×Q16×C151—22no—
67C2×Q16×C151—22no—
68C2×Q16×C151—22no—
69C2×Q16×C151—22no—
70C2×SD16×C151—22no—
71C2×SD16×C151—22no—
72C2×SD16×C151—22no—
73C2×SD16×C151—22no—
74C2×SD16×C151—22no—
75C2×SD16×C151—22no—
76C22×C8×C151C2311yescharacteristic
77C22×C8×C151C2311yescharacteristic
78C22×C8×C151C2311yescharacteristic
79C22×C8×C151C2311yescharacteristic
80C4⋊Q8×C151—22no—
81C4⋊Q8×C151—22no—
82#124×C151—22no—
83#124×C151—22no—
84C4×Q8×C151—22no—
85C4×Q8×C151—22no—
86C4×Q8×C151—22no—
87C4×Q8×C151—22no—
88C4×Q8×C151—22no—
89C4×Q8×C151—22no—
90C4×D4×C151—22no—
91C4×D4×C151—22no—
92C2×C4⋊C4×C151—22no—
93C2×C4⋊C4×C151—21no—
94C2×C4⋊C4×C151—21no—
95C2×C4⋊C4×C151—21no—
96C2×C4⋊C4×C151—22no—
97C2×C4⋊C4×C151C2311yescharacteristic
98C2×C4⋊C4×C151C2311yescharacteristic
99C2×C4⋊C4×C151C2311yescharacteristic
100C2×C4⋊C4×C151C2311yescharacteristic
101C2×C22⋊C4×C151—22no—
102C2×C22⋊C4×C151—21no—
103C2×C22⋊C4×C151—22no—
104C2×C42×C151—21no—
105C2×C42×C151—21no—
106C2×C42×C151—21no—
107C2×C42×C151C2311yescharacteristic
108C2×C42×C151C2311yescharacteristic
109C2×C42×C151C2311yescharacteristic
110#107×C151—22no—
111#107×C151—22no—
112#106×C151—22no—
113#106×C151—22no—
114#103×C151—22no—
115#103×C151—22no—
116#103×C151—22no—
117#103×C151—22no—
118#103×C151—22no—
119#103×C151—22no—
120#102×C151—22no—
121#102×C151—22no—
122#97×C151D414yes—
123C4×C8×C151D414yes—
124#95×C151—22no—
125#95×C151—22no—
126#95×C151—22no—
127#95×C151—22no—
128#95×C151D412yes—
129#95×C151D412yes—
130C24×C151—21no—
131C2×Q8×C151—21no—
132C2×Q8×C151—21no—
133C2×Q8×C151—21no—
134C2×Q8×C151—21no—
135C2×Q8×C151—21no—
136C2×Q8×C151—21no—
137C2×Q8×C151—21no—
138C2×Q8×C151—21no—
139C2×Q8×C151—21no—
140C2×Q8×C151—21no—
141C2×Q8×C151—21no—
142C2×Q8×C151—21no—
143C2×Q8×C151—21no—
144C2×Q8×C151—21no—
145C2×Q8×C151—21no—
146C2×Q8×C151#4112yes—
147C2×Q8×C151#4112yes—
148C2×Q8×C151#4112yes—
149C2×D4×C151—21no—
150C2×D4×C151—21no—
151C2×D4×C151—21no—
152C2×D4×C151—21no—
153C2×D4×C151—21no—
154C2×D4×C151#4112yes—
155C22×C4×C151—21no—
156C22×C4×C151—21no—
157C22×C4×C151—21no—
158C22×C4×C151—21no—
159C22×C4×C151—21no—
160C22×C4×C151—21no—
161C22×C4×C151—21no—
162C22×C4×C151—42no—
163C22×C4×C151—82no—
164C22×C4×C151C2×D412yes—
165C22×C4×C151C2×D412yes—
166C22×C4×C151C2×D411yescharacteristic
167C22×C4×C151C2×D411yescharacteristic
168C22×C4×C151C2411yescharacteristic
169Q16×C151—28no—
170Q16×C151—28no—
171SD16×C151—28no—
172SD16×C151—28no—
173C2×C8×C151—21no—
174C2×C8×C151—21no—
175C2×C8×C151—21no—
176C2×C8×C151—21no—
177C2×C8×C151—21no—
178C2×C8×C151—21no—
179C2×C8×C151—21no—
180C2×C8×C151—21no—
181C2×C8×C151C2×D412yes—
182C2×C8×C151C2×D412yes—
183C2×C8×C151C2×D412yes—
184C2×C8×C151C2×D412yes—
185C4⋊C4×C151—28no—
186C4⋊C4×C151—21no—
187C4⋊C4×C151—21no—
188C4⋊C4×C151—21no—
189C4⋊C4×C151—21no—
190C4⋊C4×C151—21no—
191C4⋊C4×C151—21no—
192C4⋊C4×C151—21no—
193C4⋊C4×C151—21no—
194C4⋊C4×C151—42no—
195C4⋊C4×C151—42no—
196C4⋊C4×C151—42no—
197C4⋊C4×C151—82no—
198C22⋊C4×C151—28no—
199C22⋊C4×C151—42no—
200C22⋊C4×C151—82no—
201C42×C151—21no—
202C42×C151—21no—
203C42×C151—21no—
204C42×C151—21no—
205C42×C151—42no—
206C42×C151—42no—
207C42×C151—42no—
208C42×C151C2×D412yes—
209C42×C151C2×D412yes—
210C23×C151—22no—
211C23×C151—41no—
212C23×C151—41no—
213C23×C151—42no—
214C23×C151—42no—
215C23×C151C22×D411yescharacteristic
216Q8×C151—22no—
217Q8×C151—22no—
218Q8×C151—22no—
219Q8×C151—22no—
220Q8×C151—22no—
221Q8×C151—22no—
222Q8×C151—41no—
223Q8×C151—41no—
224Q8×C151—41no—
225Q8×C151—41no—
226Q8×C151—41no—
227Q8×C151—41no—
228D4×C151—22no—
229D4×C151—22no—
230D4×C151—41no—
231D4×C151—41no—
232C2×C4×C151—22no—
233C2×C4×C151—22no—
234C2×C4×C151—22no—
235C2×C4×C151—22no—
236C2×C4×C151—22no—
237C2×C4×C151—22no—
238C2×C4×C151—22no—
239C2×C4×C151—22no—
240C2×C4×C151—22no—
241C2×C4×C151—22no—
242C2×C4×C151—22no—
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—41no—
252C2×C4×C151—41no—
253C2×C4×C151—42no—
254C2×C4×C151—42no—
255C2×C4×C151—42no—
256C2×C4×C151—42no—
257C2×C4×C151—84no—
258C2×C4×C151#12712yes—
259C2×C4×C151#12712yes—
260C2×C4×C151C22×D411yescharacteristic
261C2×C4×C151C22×D411yescharacteristic
262C2×C4×C151C2×#4111yescharacteristic
263C2×C4×C151C2×#4111yescharacteristic
264C2×C4×C151C2×#4111yescharacteristic
265C2×C4×C151C2×#4111yescharacteristic
266C8×C151—22no—
267C8×C151—22no—
268C8×C151—22no—
269C8×C151—22no—
270C22×C151—44no—
271C22×C151—42no—
272C22×C151—82no—
273C22×C151—81no—
274C22×C151—81no—
275C22×C151#52511yescharacteristic
276C22×C151#52511yescharacteristic
277C22×C151C2×#12711yescharacteristic
278C22×C151#57712yes—
279C22×C151#57812yes—
280C4×C151—22no—
281C4×C151—22no—
282C4×C151—42no—
283C4×C151—42no—
284C4×C151—42no—
285C4×C151—42no—
286C4×C151—42no—
287C4×C151—81no—
288C4×C151—81no—
289C4×C151—81no—
290C4×C151—81no—
291C4×C151#52511yescharacteristic
292C4×C151#52511yescharacteristic
293C4×C151#52511yescharacteristic
294C4×C151#52511yescharacteristic
295C2×C151—82no—
296C2×C151#239711yescharacteristic
297C2×C151#312012yes—
298C2×C151#312112yes—
299C2×C151#315411yescharacteristic
300C2×C151#315611yescharacteristic
301#23809C15111yesmaximal, characteristic, direct product factor, Sylow
302C151#2380911yescharacteristic, direct product factor, Sylow
303C2×#441C2×C15111yescharacteristic, complemented
304C2×#440C2×C15111yescharacteristic
305C2×C4×Q16C2×C15111yescharacteristic, complemented
306C2×C4×SD16C2×C15111yescharacteristic
307#2327C2×C15111yescharacteristic, complemented
308#2326C2×C15111yescharacteristic
309#2097C2×C15111yescharacteristic, complemented
310#2096C2×C15111yescharacteristic, complemented
311#2095C2×C15111yescharacteristic, complemented
312#2092C2×C15111yescharacteristic
313#2016C2×C15111yescharacteristic, complemented
314#2015C2×C15111yescharacteristic
315#2015C2×C15111yescharacteristic
316#2013C2×C15111yescharacteristic
317#1746C2×C15111yescharacteristic, complemented
318C22×Q16C22×C15111yescharacteristic
319C22×Q16C22×C15111yescharacteristic
320C22×SD16C22×C15111yescharacteristic
321C22×SD16C22×C15111yescharacteristic
322C2×C4⋊Q8C22×C15111yescharacteristic
323C2×#124C22×C15111yescharacteristic
324C2×C4×Q8C22×C15111yescharacteristic
325C2×C4×Q8C22×C15111yescharacteristic
326C2×C4×Q8C22×C15111yescharacteristic
327C2×C4×D4C22×C15111yescharacteristic
328#441—24no—
329#440—24no—
330C4×Q16—24no—
331C4×SD16—24no—
332C2×#107C22×C15111yescharacteristic
333C2×#107C22×C15111yescharacteristic
334C2×#106C22×C15111yescharacteristic
335C2×#106C22×C15111yescharacteristic
336C2×#103C22×C15111yescharacteristic
337C2×#103C22×C15111yescharacteristic
338C2×#103C22×C15111yescharacteristic
339C2×#103C22×C15111yescharacteristic
340C2×#103C22×C15111yescharacteristic
341C2×#103C22×C15111yescharacteristic
342C2×#102C22×C15111yescharacteristic
343C2×#102C22×C15111yescharacteristic
344C2×#97C22×C15111yescharacteristic
345C2×C4×C8C22×C15111yescharacteristic
346#391C22×C15111yescharacteristic
347#391C22×C15111yescharacteristic
348#391C22×C15111yescharacteristic
349#390C22×C15111yescharacteristic
350#388—22no—
351#387—22no—
352#387—22no—
353#385—22no—
354#384C22×C15111yescharacteristic
355#382C22×C15111yescharacteristic
356#376C22×C15111yescharacteristic
357#336C22×C15111yescharacteristic
358#336C22×C15111yescharacteristic
359#336C22×C15111yescharacteristic
360#336C22×C15111yescharacteristic
361C22×Q8C23×C15111yescharacteristic
362C22×Q8C23×C15111yescharacteristic
363C22×Q8C23×C15111yescharacteristic
364C22×D4C23×C15111yescharacteristic
365C23×C4—21no—
366C2×Q16—22no—
367C2×Q16—22no—
368C2×Q16—22no—
369C2×Q16—22no—
370C2×Q16—22no—
371C2×Q16—22no—
372C2×SD16—22no—
373C2×SD16—22no—
374C2×SD16—22no—
375C2×SD16—22no—
376C2×SD16—22no—
377C2×SD16—22no—
378C22×C8C23×C15111yescharacteristic
379C22×C8C23×C15111yescharacteristic
380C22×C8C23×C15111yescharacteristic
381C22×C8C23×C15111yescharacteristic
382C4⋊Q8—22no—
383C4⋊Q8—22no—
384#124—22no—
385#124—22no—
386C4×Q8—22no—
387C4×Q8—22no—
388C4×Q8—22no—
389C4×Q8—22no—
390C4×Q8—22no—
391C4×Q8—22no—
392C4×D4—22no—
393C4×D4—22no—
394C2×C4⋊C4—22no—
395C2×C4⋊C4—21no—
396C2×C4⋊C4—21no—
397C2×C4⋊C4—21no—
398C2×C4⋊C4—22no—
399C2×C4⋊C4C23×C15111yescharacteristic
400C2×C4⋊C4C23×C15111yescharacteristic
401C2×C4⋊C4C23×C15111yescharacteristic
402C2×C4⋊C4C23×C15111yescharacteristic
403C2×C22⋊C4—22no—
404C2×C22⋊C4—21no—
405C2×C22⋊C4—22no—
406C2×C42—21no—
407C2×C42—21no—
408C2×C42—21no—
409C2×C42C23×C15111yescharacteristic
410C2×C42C23×C15111yescharacteristic
411C2×C42C23×C15111yescharacteristic
412#107—22no—
413#107—22no—
414#106—22no—
415#106—22no—
416#103—22no—
417#103—22no—
418#103—22no—
419#103—22no—
420#103—22no—
421#103—22no—
422#102—22no—
423#102—22no—
424#97D4×C15114yes—
425C4×C8D4×C15114yes—
426#95—22no—
427#95—22no—
428#95—22no—
429#95—22no—
430#95D4×C15112yes—
431#95D4×C15112yes—
432C24—21no—
433C2×Q8—21no—
434C2×Q8—21no—
435C2×Q8—21no—
436C2×Q8—21no—
437C2×Q8—21no—
438C2×Q8—21no—
439C2×Q8—21no—
440C2×Q8—21no—
441C2×Q8—21no—
442C2×Q8—21no—
443C2×Q8—21no—
444C2×Q8—21no—
445C2×Q8—21no—
446C2×Q8—21no—
447C2×Q8—21no—
448C2×Q8#41×C15112yes—
449C2×Q8#41×C15112yes—
450C2×Q8#41×C15112yes—
451C2×D4—21no—
452C2×D4—21no—
453C2×D4—21no—
454C2×D4—21no—
455C2×D4—21no—
456C2×D4#41×C15112yes—
457C22×C4—21no—
458C22×C4—21no—
459C22×C4—21no—
460C22×C4—21no—
461C22×C4—21no—
462C22×C4—21no—
463C22×C4—21no—
464C22×C4—42no—
465C22×C4—82no—
466C22×C4C2×D4×C15112yes—
467C22×C4C2×D4×C15112yes—
468C22×C4C2×D4×C15111yescharacteristic
469C22×C4C2×D4×C15111yescharacteristic
470C22×C4C24×C15111yescharacteristic
471Q16—28no—
472Q16—28no—
473SD16—28no—
474SD16—28no—
475C2×C8—21no—
476C2×C8—21no—
477C2×C8—21no—
478C2×C8—21no—
479C2×C8—21no—
480C2×C8—21no—
481C2×C8—21no—
482C2×C8—21no—
483C2×C8C2×D4×C15112yes—
484C2×C8C2×D4×C15112yes—
485C2×C8C2×D4×C15112yes—
486C2×C8C2×D4×C15112yes—
487C4⋊C4—28no—
488C4⋊C4—21no—
489C4⋊C4—21no—
490C4⋊C4—21no—
491C4⋊C4—21no—
492C4⋊C4—21no—
493C4⋊C4—21no—
494C4⋊C4—21no—
495C4⋊C4—21no—
496C4⋊C4—42no—
497C4⋊C4—42no—
498C4⋊C4—42no—
499C4⋊C4—82no—
500C22⋊C4—28no—
501C22⋊C4—42no—
502C22⋊C4—82no—
503C42—21no—
504C42—21no—
505C42—21no—
506C42—21no—
507C42—42no—
508C42—42no—
509C42—42no—
510C42C2×D4×C15112yes—
511C42C2×D4×C15112yes—
512C23—22no—
513C23—41no—
514C23—41no—
515C23—42no—
516C23—42no—
517C23C22×D4×C15111yescharacteristic
518Q8—22no—
519Q8—22no—
520Q8—22no—
521Q8—22no—
522Q8—22no—
523Q8—22no—
524Q8—41no—
525Q8—41no—
526Q8—41no—
527Q8—41no—
528Q8—41no—
529Q8—41no—
530D4—22no—
531D4—22no—
532D4—41no—
533D4—41no—
534C2×C4—22no—
535C2×C4—22no—
536C2×C4—22no—
537C2×C4—22no—
538C2×C4—22no—
539C2×C4—22no—
540C2×C4—22no—
541C2×C4—22no—
542C2×C4—22no—
543C2×C4—22no—
544C2×C4—22no—
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—42no—
556C2×C4—42no—
557C2×C4—42no—
558C2×C4—42no—
559C2×C4—84no—
560C2×C4#127×C15112yes—
561C2×C4#127×C15112yes—
562C2×C4C22×D4×C15111yescharacteristic
563C2×C4C22×D4×C15111yescharacteristic
564C2×C4C2×#41×C15111yescharacteristic
565C2×C4C2×#41×C15111yescharacteristic
566C2×C4C2×#41×C15111yescharacteristic
567C2×C4C2×#41×C15111yescharacteristic
568C8—22no—
569C8—22no—
570C8—22no—
571C8—22no—
572C22—44no—
573C22—42no—
574C22—82no—
575C22—81no—
576C22—81no—
577C22#525×C15111yescharacteristic
578C22#525×C15111yescharacteristic
579C22C2×#127×C15111yescharacteristic
580C22#577×C15112yes—
581C22#578×C15112yes—
582C4—22no—
583C4—22no—
584C4—42no—
585C4—42no—
586C4—42no—
587C4—42no—
588C4—42no—
589C4—81no—
590C4—81no—
591C4—81no—
592C4—81no—
593C4#525×C15111yescharacteristic
594C4#525×C15111yescharacteristic
595C4#525×C15111yescharacteristic
596C4#525×C15111yescharacteristic
597C2—82no—
598C2#2397×C15111yescharacteristic
599C2#3120×C15112yes—
600C2#3121×C15112yes—
601C2#3154×C15111yescharacteristic
602C2#3156×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. C2×#441×C151C2semidirect
3. C2×C4×Q16×C151C2semidirect
5. #2327×C151C2semidirect
7. #2097×C151C2semidirect
8. #2096×C151C2semidirect
9. #2095×C151C2semidirect
11. #2016×C151C2semidirect
15. #1746×C151C2semidirect
301. #23809C151direct (N × H)
302. C151#23809direct (N × H)
303. C2×#441C2×C151semidirect
305. C2×C4×Q16C2×C151semidirect
307. #2327C2×C151semidirect
309. #2097C2×C151semidirect
310. #2096C2×C151semidirect
311. #2095C2×C151semidirect
313. #2016C2×C151semidirect
317. #1746C2×C151semidirect

Maximal subgroups

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

subgroupindex
C2×#441×C1512
C2×#440×C1512
C2×C4×Q16×C1512
C2×C4×SD16×C1512
#2327×C1512
#2326×C1512
#2097×C1512
#2096×C1512
#2095×C1512
#2092×C1512
#2016×C1512
#2015×C1512
#2013×C1512
#1746×C1512
#23809151