Finite Group Databasebeta

← C151×#24686 #50329611

Subgroups — C151×#24686 #50329611

Order 38656.

778 conjugacy classes of subgroups.

The subgroup lattice has 616 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#478×C151C211yesmaximal, characteristic
2C2×C4×SD16×C151C211yesmaximal, characteristic
3#2565×C151C211yesmaximal, characteristic, complemented
4#2357×C151C211yesmaximal, characteristic
5#2073×C151C211yesmaximal, characteristic
6#2071×C151C211yesmaximal, characteristic
7#2055×C151C211yesmaximal, characteristic
8#2055×C151C211yesmaximal, characteristic
9#1991×C151C211yesmaximal, characteristic, complemented
10#1949×C151C211yesmaximal, characteristic, complemented
11#1948×C151C211yesmaximal, characteristic, complemented
12#1939×C151C211yesmaximal, characteristic, complemented
13#1928×C151C211yesmaximal, characteristic, complemented
14#1927×C151C211yesmaximal, characteristic, complemented
15#1805×C151C211yesmaximal, characteristic, complemented
16C22×SD16×C151C2211yescharacteristic
17C2×#125×C151C2211yescharacteristic
18C2×C4×Q8×C151C2211yescharacteristic
19C2×C4×D4×C151C2211yescharacteristic
20#478×C151—24no—
21C4×SD16×C151—24no—
22C2×#107×C151C2211yescharacteristic
23C2×#106×C151C2211yescharacteristic
24C2×#106×C151C2211yescharacteristic
25C2×C4⋊C8×C151C2211yescharacteristic
26C2×C4⋊C8×C151C2211yescharacteristic
27C2×C4⋊C8×C151C2211yescharacteristic
28C2×#103×C151C2211yescharacteristic
29C2×#103×C151C2211yescharacteristic
30C2×#103×C151C2211yescharacteristic
31C2×#102×C151C2211yescharacteristic
32C2×#102×C151C2211yescharacteristic
33C2×#102×C151C2211yescharacteristic
34C2×C4×C8×C151C2211yescharacteristic
35#398×C151—21no—
36#398×C151—21no—
37#391×C151C2211yescharacteristic
38#391×C151C2211yescharacteristic
39#390×C151C2211yescharacteristic
40#390×C151C2211yescharacteristic
41#388×C151—21no—
42#388×C151—21no—
43#387×C151—21no—
44#387×C151—21no—
45#384×C151C2211yescharacteristic
46#382×C151C2211yescharacteristic
47#382×C151C2211yescharacteristic
48#381×C151—21no—
49C4×C4⋊C4×C151C2211yescharacteristic
50C4×C4⋊C4×C151C2211yescharacteristic
51C4×C4⋊C4×C151C2211yescharacteristic
52C4×C22⋊C4×C151—21no—
53#340×C151C2211yescharacteristic
54#340×C151C2211yescharacteristic
55#340×C151C2211yescharacteristic
56#340×C151C2211yescharacteristic
57#340×C151C2211yescharacteristic
58#340×C151C2211yescharacteristic
59#336×C151C2211yescharacteristic
60#336×C151C2211yescharacteristic
61C22×Q8×C151C2311yescharacteristic
62C22×D4×C151C2311yescharacteristic
63C23×C4×C151—21no—
64C2×SD16×C151—22no—
65C2×SD16×C151—22no—
66C2×SD16×C151—22no—
67C22×C8×C151C2311yescharacteristic
68C22×C8×C151C2311yescharacteristic
69C22×C8×C151C2311yescharacteristic
70C22×C8×C151C2311yescharacteristic
71#125×C151—22no—
72#125×C151—22no—
73C4×Q8×C151—22no—
74C4×Q8×C151—22no—
75C4×D4×C151—22no—
76C4×D4×C151D414yes—
77C2×C4⋊C4×C151—21no—
78C2×C4⋊C4×C151—21no—
79C2×C4⋊C4×C151—21no—
80C2×C4⋊C4×C151—21no—
81C2×C4⋊C4×C151—21no—
82C2×C4⋊C4×C151D411yescharacteristic
83C2×C4⋊C4×C151D411yescharacteristic
84C2×C4⋊C4×C151C2311yescharacteristic
85C2×C4⋊C4×C151C2311yescharacteristic
86C2×C4⋊C4×C151C2311yescharacteristic
87C2×C4⋊C4×C151C2311yescharacteristic
88C2×C4⋊C4×C151C2311yescharacteristic
89C2×C4⋊C4×C151C2311yescharacteristic
90C2×C22⋊C4×C151—21no—
91C2×C22⋊C4×C151—21no—
92C2×C22⋊C4×C151—21no—
93C2×C22⋊C4×C151—21no—
94C2×C22⋊C4×C151—21no—
95C2×C42×C151—21no—
96C2×C42×C151—21no—
97C2×C42×C151—21no—
98C2×C42×C151C2311yescharacteristic
99C2×C42×C151C2311yescharacteristic
100C2×C42×C151C2311yescharacteristic
101#107×C151—22no—
102#106×C151—22no—
103#106×C151—22no—
104C4⋊C8×C151—22no—
105C4⋊C8×C151—22no—
106C4⋊C8×C151—22no—
107#103×C151—22no—
108#103×C151—22no—
109#103×C151—22no—
110#102×C151—22no—
111#102×C151—22no—
112#102×C151—22no—
113C4×C8×C151—22no—
114#95×C151—21no—
115#95×C151—21no—
116#95×C151—21no—
117#95×C151—21no—
118#95×C151—21no—
119#95×C151—21no—
120#95×C151—21no—
121#95×C151—21no—
122#95×C151—21no—
123#95×C151—21no—
124#95×C151D411yescharacteristic
125#95×C151D411yescharacteristic
126C24×C151—21no—
127C2×Q8×C151—21no—
128C2×Q8×C151—21no—
129C2×Q8×C151—21no—
130C2×Q8×C151—21no—
131C2×Q8×C151—21no—
132C2×Q8×C151#4112yes—
133C2×D4×C151—21no—
134C2×D4×C151—21no—
135C2×D4×C151—21no—
136C2×D4×C151—21no—
137C2×D4×C151—21no—
138C2×D4×C151C2×D412yes—
139C22×C4×C151—21no—
140C22×C4×C151—21no—
141C22×C4×C151—24no—
142C22×C4×C151—21no—
143C22×C4×C151—21no—
144C22×C4×C151—21no—
145C22×C4×C151—21no—
146C22×C4×C151—21no—
147C22×C4×C151—81no—
148C22×C4×C151—81no—
149C22×C4×C151C2×D411yescharacteristic
150C22×C4×C151C2×D411yescharacteristic
151C22×C4×C151C2×D411yescharacteristic
152C22×C4×C151C2×D411yescharacteristic
153C22×C4×C151C2×D411yescharacteristic
154C22×C4×C151C2×D411yescharacteristic
155C22×C4×C151C2411yescharacteristic
156SD16×C151—28no—
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—
165C2×C8×C151—21no—
166C2×C8×C151—21no—
167C2×C8×C151—21no—
168C2×C8×C151#4112yes—
169C4⋊C4×C151—22no—
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—21no—
177C4⋊C4×C151—21no—
178C4⋊C4×C151—21no—
179C4⋊C4×C151—21no—
180C4⋊C4×C151—21no—
181C4⋊C4×C151—41no—
182C4⋊C4×C151—42no—
183C4⋊C4×C151—42no—
184C4⋊C4×C151—42no—
185C4⋊C4×C151—42no—
186C4⋊C4×C151—42no—
187C4⋊C4×C151C2×D412yes—
188C22⋊C4×C151—24no—
189C22⋊C4×C151—42no—
190C22⋊C4×C151—42no—
191C22⋊C4×C151—81no—
192C22⋊C4×C151—81no—
193C42×C151—21no—
194C42×C151—21no—
195C42×C151—21no—
196C42×C151—21no—
197C42×C151—42no—
198C42×C151—81no—
199C42×C151—81no—
200C42×C151C2×D412yes—
201C42×C151#4112yes—
202C23×C151—22no—
203C23×C151—41no—
204C23×C151—41no—
205C23×C151—41no—
206C23×C151—41no—
207C23×C151—41no—
208C23×C151—41no—
209C23×C151C22×D411yescharacteristic
210Q8×C151—22no—
211Q8×C151—22no—
212Q8×C151—41no—
213Q8×C151—41no—
214D4×C151—22no—
215D4×C151—22no—
216D4×C151—41no—
217D4×C151—41no—
218C2×C4×C151—21no—
219C2×C4×C151—21no—
220C2×C4×C151—21no—
221C2×C4×C151—21no—
222C2×C4×C151—21no—
223C2×C4×C151—21no—
224C2×C4×C151—22no—
225C2×C4×C151—21no—
226C2×C4×C151—21no—
227C2×C4×C151—21no—
228C2×C4×C151—22no—
229C2×C4×C151—21no—
230C2×C4×C151—21no—
231C2×C4×C151—21no—
232C2×C4×C151—21no—
233C2×C4×C151—21no—
234C2×C4×C151—21no—
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—41no—
252C2×C4×C151—41no—
253C2×C4×C151—41no—
254C2×C4×C151—84no—
255C2×C4×C151#12112yes—
256C2×C4×C151#12112yes—
257C2×C4×C151#13512yes—
258C2×C4×C151C22×D411yescharacteristic
259C2×C4×C151C2×#4111yescharacteristic
260C2×C4×C151C2×#4111yescharacteristic
261C2×C4×C151C2×#4111yescharacteristic
262C2×C4×C1512−1+411yescharacteristic
263C2×C4×C1512−1+411yescharacteristic
264C8×C151—22no—
265C8×C151—41no—
266C8×C151—41no—
267C8×C151—41no—
268C22×C151—42no—
269C22×C151—42no—
270C22×C151—42no—
271C22×C151—81no—
272C22×C151—81no—
273C22×C151—81no—
274C22×C151—81no—
275C22×C151C2×#12111yescharacteristic
276C22×C151#54711yescharacteristic
277C22×C151#54811yescharacteristic
278C22×C151C2×#13511yescharacteristic
279C22×C151#57511yescharacteristic
280C22×C151#57711yescharacteristic
281C22×C151#57711yescharacteristic
282C4×C151—22no—
283C4×C151—22no—
284C4×C151—22no—
285C4×C151—41no—
286C4×C151—41no—
287C4×C151—41no—
288C4×C151—42no—
289C4×C151—42no—
290C4×C151—81no—
291C4×C151—81no—
292C4×C151—81no—
293C4×C151—81no—
294C4×C151—81no—
295C4×C151#52511yescharacteristic
296C4×C151#53611yescharacteristic
297C4×C151#55211yescharacteristic
298C4×C151#55611yescharacteristic
299C2×C151—82no—
300C2×C151#241511yescharacteristic
301C2×C151#303511yescharacteristic
302C2×C151#304211yescharacteristic
303C2×C151#333711yescharacteristic
304C2×C151#335111yescharacteristic
305C2×C151#336511yescharacteristic
306C2×C151#337111yescharacteristic
307#24686C15111yesmaximal, characteristic, direct product factor, Sylow
308C151#2468611yescharacteristic, direct product factor, Sylow
309C2×#478C2×C15111yescharacteristic
310C2×C4×SD16C2×C15111yescharacteristic
311#2565C2×C15111yescharacteristic, complemented
312#2357C2×C15111yescharacteristic
313#2073C2×C15111yescharacteristic
314#2071C2×C15111yescharacteristic
315#2055C2×C15111yescharacteristic
316#2055C2×C15111yescharacteristic
317#1991C2×C15111yescharacteristic, complemented
318#1949C2×C15111yescharacteristic, complemented
319#1948C2×C15111yescharacteristic, complemented
320#1939C2×C15111yescharacteristic, complemented
321#1928C2×C15111yescharacteristic, complemented
322#1927C2×C15111yescharacteristic, complemented
323#1805C2×C15111yescharacteristic, complemented
324C22×SD16C22×C15111yescharacteristic
325C2×#125C22×C15111yescharacteristic
326C2×C4×Q8C22×C15111yescharacteristic
327C2×C4×D4C22×C15111yescharacteristic
328#478—24no—
329C4×SD16—24no—
330C2×#107C22×C15111yescharacteristic
331C2×#106C22×C15111yescharacteristic
332C2×#106C22×C15111yescharacteristic
333C2×C4⋊C8C22×C15111yescharacteristic
334C2×C4⋊C8C22×C15111yescharacteristic
335C2×C4⋊C8C22×C15111yescharacteristic
336C2×#103C22×C15111yescharacteristic
337C2×#103C22×C15111yescharacteristic
338C2×#103C22×C15111yescharacteristic
339C2×#102C22×C15111yescharacteristic
340C2×#102C22×C15111yescharacteristic
341C2×#102C22×C15111yescharacteristic
342C2×C4×C8C22×C15111yescharacteristic
343#398—21no—
344#398—21no—
345#391C22×C15111yescharacteristic
346#391C22×C15111yescharacteristic
347#390C22×C15111yescharacteristic
348#390C22×C15111yescharacteristic
349#388—21no—
350#388—21no—
351#387—21no—
352#387—21no—
353#384C22×C15111yescharacteristic
354#382C22×C15111yescharacteristic
355#382C22×C15111yescharacteristic
356#381—21no—
357C4×C4⋊C4C22×C15111yescharacteristic
358C4×C4⋊C4C22×C15111yescharacteristic
359C4×C4⋊C4C22×C15111yescharacteristic
360C4×C22⋊C4—21no—
361#340C22×C15111yescharacteristic
362#340C22×C15111yescharacteristic
363#340C22×C15111yescharacteristic
364#340C22×C15111yescharacteristic
365#340C22×C15111yescharacteristic
366#340C22×C15111yescharacteristic
367#336C22×C15111yescharacteristic
368#336C22×C15111yescharacteristic
369C22×Q8C23×C15111yescharacteristic
370C22×D4C23×C15111yescharacteristic
371C23×C4—21no—
372C2×SD16—22no—
373C2×SD16—22no—
374C2×SD16—22no—
375C22×C8C23×C15111yescharacteristic
376C22×C8C23×C15111yescharacteristic
377C22×C8C23×C15111yescharacteristic
378C22×C8C23×C15111yescharacteristic
379#125—22no—
380#125—22no—
381C4×Q8—22no—
382C4×Q8—22no—
383C4×D4—22no—
384C4×D4D4×C15114yes—
385C2×C4⋊C4—21no—
386C2×C4⋊C4—21no—
387C2×C4⋊C4—21no—
388C2×C4⋊C4—21no—
389C2×C4⋊C4—21no—
390C2×C4⋊C4D4×C15111yescharacteristic
391C2×C4⋊C4D4×C15111yescharacteristic
392C2×C4⋊C4C23×C15111yescharacteristic
393C2×C4⋊C4C23×C15111yescharacteristic
394C2×C4⋊C4C23×C15111yescharacteristic
395C2×C4⋊C4C23×C15111yescharacteristic
396C2×C4⋊C4C23×C15111yescharacteristic
397C2×C4⋊C4C23×C15111yescharacteristic
398C2×C22⋊C4—21no—
399C2×C22⋊C4—21no—
400C2×C22⋊C4—21no—
401C2×C22⋊C4—21no—
402C2×C22⋊C4—21no—
403C2×C42—21no—
404C2×C42—21no—
405C2×C42—21no—
406C2×C42C23×C15111yescharacteristic
407C2×C42C23×C15111yescharacteristic
408C2×C42C23×C15111yescharacteristic
409#107—22no—
410#106—22no—
411#106—22no—
412C4⋊C8—22no—
413C4⋊C8—22no—
414C4⋊C8—22no—
415#103—22no—
416#103—22no—
417#103—22no—
418#102—22no—
419#102—22no—
420#102—22no—
421C4×C8—22no—
422#95—21no—
423#95—21no—
424#95—21no—
425#95—21no—
426#95—21no—
427#95—21no—
428#95—21no—
429#95—21no—
430#95—21no—
431#95—21no—
432#95D4×C15111yescharacteristic
433#95D4×C15111yescharacteristic
434C24—21no—
435C2×Q8—21no—
436C2×Q8—21no—
437C2×Q8—21no—
438C2×Q8—21no—
439C2×Q8—21no—
440C2×Q8#41×C15112yes—
441C2×D4—21no—
442C2×D4—21no—
443C2×D4—21no—
444C2×D4—21no—
445C2×D4—21no—
446C2×D4C2×D4×C15112yes—
447C22×C4—21no—
448C22×C4—21no—
449C22×C4—24no—
450C22×C4—21no—
451C22×C4—21no—
452C22×C4—21no—
453C22×C4—21no—
454C22×C4—21no—
455C22×C4—81no—
456C22×C4—81no—
457C22×C4C2×D4×C15111yescharacteristic
458C22×C4C2×D4×C15111yescharacteristic
459C22×C4C2×D4×C15111yescharacteristic
460C22×C4C2×D4×C15111yescharacteristic
461C22×C4C2×D4×C15111yescharacteristic
462C22×C4C2×D4×C15111yescharacteristic
463C22×C4C24×C15111yescharacteristic
464SD16—28no—
465C2×C8—21no—
466C2×C8—21no—
467C2×C8—21no—
468C2×C8—21no—
469C2×C8—21no—
470C2×C8—21no—
471C2×C8—21no—
472C2×C8—21no—
473C2×C8—21no—
474C2×C8—21no—
475C2×C8—21no—
476C2×C8#41×C15112yes—
477C4⋊C4—22no—
478C4⋊C4—21no—
479C4⋊C4—21no—
480C4⋊C4—21no—
481C4⋊C4—21no—
482C4⋊C4—21no—
483C4⋊C4—21no—
484C4⋊C4—21no—
485C4⋊C4—21no—
486C4⋊C4—21no—
487C4⋊C4—21no—
488C4⋊C4—21no—
489C4⋊C4—41no—
490C4⋊C4—42no—
491C4⋊C4—42no—
492C4⋊C4—42no—
493C4⋊C4—42no—
494C4⋊C4—42no—
495C4⋊C4C2×D4×C15112yes—
496C22⋊C4—24no—
497C22⋊C4—42no—
498C22⋊C4—42no—
499C22⋊C4—81no—
500C22⋊C4—81no—
501C42—21no—
502C42—21no—
503C42—21no—
504C42—21no—
505C42—42no—
506C42—81no—
507C42—81no—
508C42C2×D4×C15112yes—
509C42#41×C15112yes—
510C23—22no—
511C23—41no—
512C23—41no—
513C23—41no—
514C23—41no—
515C23—41no—
516C23—41no—
517C23C22×D4×C15111yescharacteristic
518Q8—22no—
519Q8—22no—
520Q8—41no—
521Q8—41no—
522D4—22no—
523D4—22no—
524D4—41no—
525D4—41no—
526C2×C4—21no—
527C2×C4—21no—
528C2×C4—21no—
529C2×C4—21no—
530C2×C4—21no—
531C2×C4—21no—
532C2×C4—22no—
533C2×C4—21no—
534C2×C4—21no—
535C2×C4—21no—
536C2×C4—22no—
537C2×C4—21no—
538C2×C4—21no—
539C2×C4—21no—
540C2×C4—21no—
541C2×C4—21no—
542C2×C4—21no—
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—41no—
556C2×C4—41no—
557C2×C4—41no—
558C2×C4—41no—
559C2×C4—41no—
560C2×C4—41no—
561C2×C4—41no—
562C2×C4—84no—
563C2×C4#121×C15112yes—
564C2×C4#121×C15112yes—
565C2×C4#135×C15112yes—
566C2×C4C22×D4×C15111yescharacteristic
567C2×C4C2×#41×C15111yescharacteristic
568C2×C4C2×#41×C15111yescharacteristic
569C2×C4C2×#41×C15111yescharacteristic
570C2×C42−1+4×C15111yescharacteristic
571C2×C42−1+4×C15111yescharacteristic
572C8—22no—
573C8—41no—
574C8—41no—
575C8—41no—
576C22—42no—
577C22—42no—
578C22—42no—
579C22—81no—
580C22—81no—
581C22—81no—
582C22—81no—
583C22C2×#121×C15111yescharacteristic
584C22#547×C15111yescharacteristic
585C22#548×C15111yescharacteristic
586C22C2×#135×C15111yescharacteristic
587C22#575×C15111yescharacteristic
588C22#577×C15111yescharacteristic
589C22#577×C15111yescharacteristic
590C4—22no—
591C4—22no—
592C4—22no—
593C4—42no—
594C4—42no—
595C4—41no—
596C4—41no—
597C4—41no—
598C4—81no—
599C4—81no—
600C4—81no—
601C4—81no—
602C4—81no—
603C4#525×C15111yescharacteristic
604C4#536×C15111yescharacteristic
605C4#552×C15111yescharacteristic
606C4#556×C15111yescharacteristic
607C2—82no—
608C2#2415×C15111yescharacteristic
609C2#3035×C15111yescharacteristic
610C2#3042×C15111yescharacteristic
611C2#3337×C15111yescharacteristic
612C2#3351×C15111yescharacteristic
613C2#3365×C15111yescharacteristic
614C2#3371×C15111yescharacteristic
subgroupG/H
center, socleC23×C151C22×D4
commutator, Frattini, cosocleC22×C4C24×C151
prime radicalC22×D4×C151C23
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C151 ◁ C4×C4⋊C4×C151 ◁ G

Complements

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

NH ≅ G/Ntype
3. #2565×C151C2semidirect
9. #1991×C151C2semidirect
10. #1949×C151C2semidirect
11. #1948×C151C2semidirect
12. #1939×C151C2semidirect
13. #1928×C151C2semidirect
14. #1927×C151C2semidirect
15. #1805×C151C2semidirect
307. #24686C151direct (N × H)
308. C151#24686direct (N × H)
311. #2565C2×C151semidirect
317. #1991C2×C151semidirect
318. #1949C2×C151semidirect
319. #1948C2×C151semidirect
320. #1939C2×C151semidirect
321. #1928C2×C151semidirect
322. #1927C2×C151semidirect
323. #1805C2×C151semidirect

Maximal subgroups

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

subgroupindex
C2×#478×C1512
C2×C4×SD16×C1512
#2565×C1512
#2357×C1512
#2073×C1512
#2071×C1512
#2055×C1512
#1991×C1512
#1949×C1512
#1948×C1512
#1939×C1512
#1928×C1512
#1927×C1512
#1805×C1512
#24686151