Finite Group Databasebeta

← C151×#24687 #50329612

Subgroups — C151×#24687 #50329612

Order 38656.

730 conjugacy classes of subgroups.

The subgroup lattice has 580 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#479×C151C211yesmaximal, characteristic
2C2×C4×Q16×C151C211yesmaximal, characteristic
3#2565×C151C211yesmaximal, characteristic
4#2356×C151C211yesmaximal, characteristic
5#2074×C151C211yesmaximal, characteristic
6#2072×C151C211yesmaximal, characteristic
7#2056×C151C211yesmaximal, characteristic
8#2056×C151C211yesmaximal, characteristic
9#1991×C151C211yesmaximal, characteristic
10#1949×C151C211yesmaximal, characteristic
11#1947×C151C211yesmaximal, characteristic
12#1939×C151C211yesmaximal, characteristic
13#1928×C151C211yesmaximal, characteristic
14#1927×C151C211yesmaximal, characteristic
15#1805×C151C211yesmaximal, characteristic
16C22×Q16×C151C2211yescharacteristic
17C2×#125×C151C2211yescharacteristic
18C2×C4×Q8×C151C2211yescharacteristic
19C2×C4×Q8×C151C2211yescharacteristic
20#479×C151—24no—
21C4×Q16×C151—24no—
22C2×#107×C151C2211yescharacteristic
23C2×#107×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×#103×C151C2211yescharacteristic
32C2×#103×C151C2211yescharacteristic
33C2×#103×C151C2211yescharacteristic
34C2×C4×C8×C151C2211yescharacteristic
35#398×C151—21no—
36#398×C151—21no—
37#391×C151C2211yescharacteristic
38#391×C151C2211yescharacteristic
39#391×C151C2211yescharacteristic
40#391×C151C2211yescharacteristic
41#387×C151—21no—
42#387×C151—21no—
43#387×C151—21no—
44#387×C151—21no—
45#384×C151C2211yescharacteristic
46#383×C151—21no—
47#382×C151C2211yescharacteristic
48#382×C151C2211yescharacteristic
49C4×C4⋊C4×C151C2211yescharacteristic
50C4×C4⋊C4×C151C2211yescharacteristic
51C4×C4⋊C4×C151C2211yescharacteristic
52#376×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×Q8×C151C2311yescharacteristic
63C2×Q16×C151—22no—
64C2×Q16×C151—22no—
65C2×Q16×C151—22no—
66C22×C8×C151C2311yescharacteristic
67C22×C8×C151C2311yescharacteristic
68C22×C8×C151C2311yescharacteristic
69C22×C8×C151C2311yescharacteristic
70#125×C151—22no—
71#125×C151—22no—
72C4×Q8×C151—22no—
73C4×Q8×C151—22no—
74C4×Q8×C151—22no—
75C4×Q8×C151D414yes—
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×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×C42×C151—21no—
91C2×C42×C151—21no—
92C2×C42×C151—21no—
93C2×C42×C151—21no—
94C2×C42×C151C2311yescharacteristic
95C2×C42×C151C2311yescharacteristic
96C2×C42×C151C2311yescharacteristic
97#107×C151—22no—
98#107×C151—22no—
99#106×C151—22no—
100C4⋊C8×C151—22no—
101C4⋊C8×C151—22no—
102C4⋊C8×C151—22no—
103#103×C151—22no—
104#103×C151—22no—
105#103×C151—22no—
106#103×C151—22no—
107#103×C151—22no—
108#103×C151—22no—
109C4×C8×C151—22no—
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×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
126C2×Q8×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—21no—
133C2×Q8×C151—21no—
134C2×Q8×C151—21no—
135C2×Q8×C151—21no—
136C2×Q8×C151C2×D412yes—
137C2×Q8×C151#4112yes—
138C22×C4×C151—21no—
139C22×C4×C151—21no—
140C22×C4×C151—21no—
141C22×C4×C151—21no—
142C22×C4×C151—21no—
143C22×C4×C151—21no—
144C22×C4×C151—21no—
145C22×C4×C151—21no—
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
153Q16×C151—28no—
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—
165C2×C8×C151#4112yes—
166C4⋊C4×C151—24no—
167C4⋊C4×C151—22no—
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—21no—
177C4⋊C4×C151—21no—
178C4⋊C4×C151—21no—
179C4⋊C4×C151—41no—
180C4⋊C4×C151—42no—
181C4⋊C4×C151—42no—
182C4⋊C4×C151—42no—
183C4⋊C4×C151—42no—
184C4⋊C4×C151—42no—
185C4⋊C4×C151C2×D412yes—
186C42×C151—24no—
187C42×C151—21no—
188C42×C151—21no—
189C42×C151—21no—
190C42×C151—21no—
191C42×C151—42no—
192C42×C151—42no—
193C42×C151—42no—
194C42×C151C2×D412yes—
195C42×C151#4112yes—
196C23×C151C22×D411yescharacteristic
197Q8×C151—22no—
198Q8×C151—22no—
199Q8×C151—22no—
200Q8×C151—22no—
201Q8×C151—41no—
202Q8×C151—41no—
203Q8×C151—41no—
204Q8×C151—41no—
205C2×C4×C151—21no—
206C2×C4×C151—21no—
207C2×C4×C151—21no—
208C2×C4×C151—21no—
209C2×C4×C151—21no—
210C2×C4×C151—21no—
211C2×C4×C151—22no—
212C2×C4×C151—22no—
213C2×C4×C151—21no—
214C2×C4×C151—21no—
215C2×C4×C151—21no—
216C2×C4×C151—22no—
217C2×C4×C151—21no—
218C2×C4×C151—21no—
219C2×C4×C151—21no—
220C2×C4×C151—21no—
221C2×C4×C151—21no—
222C2×C4×C151—21no—
223C2×C4×C151—41no—
224C2×C4×C151—41no—
225C2×C4×C151—41no—
226C2×C4×C151—41no—
227C2×C4×C151—41no—
228C2×C4×C151—41no—
229C2×C4×C151—41no—
230C2×C4×C151—41no—
231C2×C4×C151—41no—
232C2×C4×C151—41no—
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#12112yes—
245C2×C4×C151#12112yes—
246C2×C4×C151#13512yes—
247C2×C4×C151C22×D411yescharacteristic
248C2×C4×C151C2×#4111yescharacteristic
249C2×C4×C151C2×#4111yescharacteristic
250C2×C4×C151C2×#4111yescharacteristic
251C2×C4×C1512−1+411yescharacteristic
252C2×C4×C1512−1+411yescharacteristic
253C8×C151—22no—
254C8×C151—41no—
255C8×C151—41no—
256C8×C151—41no—
257C22×C151C2×#12111yescharacteristic
258C22×C151#54711yescharacteristic
259C22×C151#54811yescharacteristic
260C22×C151C2×#13511yescharacteristic
261C22×C151#57511yescharacteristic
262C22×C151#57811yescharacteristic
263C22×C151#57811yescharacteristic
264C4×C151—22no—
265C4×C151—22no—
266C4×C151—22no—
267C4×C151—41no—
268C4×C151—41no—
269C4×C151—41no—
270C4×C151—42no—
271C4×C151—42no—
272C4×C151—42no—
273C4×C151—81no—
274C4×C151—81no—
275C4×C151—81no—
276C4×C151—81no—
277C4×C151—81no—
278C4×C151#52511yescharacteristic
279C4×C151#53611yescharacteristic
280C4×C151#55211yescharacteristic
281C4×C151#55611yescharacteristic
282C2×C151#241511yescharacteristic
283C2×C151#303511yescharacteristic
284C2×C151#304411yescharacteristic
285C2×C151#333611yescharacteristic
286C2×C151#335211yescharacteristic
287C2×C151#336411yescharacteristic
288C2×C151#337711yescharacteristic
289#24687C15111yesmaximal, characteristic, direct product factor, Sylow
290C151#2468711yescharacteristic, direct product factor, Sylow
291C2×#479C2×C15111yescharacteristic
292C2×C4×Q16C2×C15111yescharacteristic
293#2565C2×C15111yescharacteristic
294#2356C2×C15111yescharacteristic
295#2074C2×C15111yescharacteristic
296#2072C2×C15111yescharacteristic
297#2056C2×C15111yescharacteristic
298#2056C2×C15111yescharacteristic
299#1991C2×C15111yescharacteristic
300#1949C2×C15111yescharacteristic
301#1947C2×C15111yescharacteristic
302#1939C2×C15111yescharacteristic
303#1928C2×C15111yescharacteristic
304#1927C2×C15111yescharacteristic
305#1805C2×C15111yescharacteristic
306C22×Q16C22×C15111yescharacteristic
307C2×#125C22×C15111yescharacteristic
308C2×C4×Q8C22×C15111yescharacteristic
309C2×C4×Q8C22×C15111yescharacteristic
310#479—24no—
311C4×Q16—24no—
312C2×#107C22×C15111yescharacteristic
313C2×#107C22×C15111yescharacteristic
314C2×#106C22×C15111yescharacteristic
315C2×C4⋊C8C22×C15111yescharacteristic
316C2×C4⋊C8C22×C15111yescharacteristic
317C2×C4⋊C8C22×C15111yescharacteristic
318C2×#103C22×C15111yescharacteristic
319C2×#103C22×C15111yescharacteristic
320C2×#103C22×C15111yescharacteristic
321C2×#103C22×C15111yescharacteristic
322C2×#103C22×C15111yescharacteristic
323C2×#103C22×C15111yescharacteristic
324C2×C4×C8C22×C15111yescharacteristic
325#398—21no—
326#398—21no—
327#391C22×C15111yescharacteristic
328#391C22×C15111yescharacteristic
329#391C22×C15111yescharacteristic
330#391C22×C15111yescharacteristic
331#387—21no—
332#387—21no—
333#387—21no—
334#387—21no—
335#384C22×C15111yescharacteristic
336#383—21no—
337#382C22×C15111yescharacteristic
338#382C22×C15111yescharacteristic
339C4×C4⋊C4C22×C15111yescharacteristic
340C4×C4⋊C4C22×C15111yescharacteristic
341C4×C4⋊C4C22×C15111yescharacteristic
342#376—21no—
343#340C22×C15111yescharacteristic
344#340C22×C15111yescharacteristic
345#340C22×C15111yescharacteristic
346#340C22×C15111yescharacteristic
347#340C22×C15111yescharacteristic
348#340C22×C15111yescharacteristic
349#336C22×C15111yescharacteristic
350#336C22×C15111yescharacteristic
351C22×Q8C23×C15111yescharacteristic
352C22×Q8C23×C15111yescharacteristic
353C2×Q16—22no—
354C2×Q16—22no—
355C2×Q16—22no—
356C22×C8C23×C15111yescharacteristic
357C22×C8C23×C15111yescharacteristic
358C22×C8C23×C15111yescharacteristic
359C22×C8C23×C15111yescharacteristic
360#125—22no—
361#125—22no—
362C4×Q8—22no—
363C4×Q8—22no—
364C4×Q8—22no—
365C4×Q8D4×C15114yes—
366C2×C4⋊C4—21no—
367C2×C4⋊C4—21no—
368C2×C4⋊C4—21no—
369C2×C4⋊C4—21no—
370C2×C4⋊C4—21no—
371C2×C4⋊C4—21no—
372C2×C4⋊C4D4×C15111yescharacteristic
373C2×C4⋊C4D4×C15111yescharacteristic
374C2×C4⋊C4C23×C15111yescharacteristic
375C2×C4⋊C4C23×C15111yescharacteristic
376C2×C4⋊C4C23×C15111yescharacteristic
377C2×C4⋊C4C23×C15111yescharacteristic
378C2×C4⋊C4C23×C15111yescharacteristic
379C2×C4⋊C4C23×C15111yescharacteristic
380C2×C42—21no—
381C2×C42—21no—
382C2×C42—21no—
383C2×C42—21no—
384C2×C42C23×C15111yescharacteristic
385C2×C42C23×C15111yescharacteristic
386C2×C42C23×C15111yescharacteristic
387#107—22no—
388#107—22no—
389#106—22no—
390C4⋊C8—22no—
391C4⋊C8—22no—
392C4⋊C8—22no—
393#103—22no—
394#103—22no—
395#103—22no—
396#103—22no—
397#103—22no—
398#103—22no—
399C4×C8—22no—
400#95—21no—
401#95—21no—
402#95—21no—
403#95—21no—
404#95—21no—
405#95—21no—
406#95—21no—
407#95—21no—
408#95—21no—
409#95—21no—
410#95—21no—
411#95—21no—
412#95—21no—
413#95—21no—
414#95D4×C15111yescharacteristic
415#95D4×C15111yescharacteristic
416C2×Q8—21no—
417C2×Q8—21no—
418C2×Q8—21no—
419C2×Q8—21no—
420C2×Q8—21no—
421C2×Q8—21no—
422C2×Q8—21no—
423C2×Q8—21no—
424C2×Q8—21no—
425C2×Q8—21no—
426C2×Q8C2×D4×C15112yes—
427C2×Q8#41×C15112yes—
428C22×C4—21no—
429C22×C4—21no—
430C22×C4—21no—
431C22×C4—21no—
432C22×C4—21no—
433C22×C4—21no—
434C22×C4—21no—
435C22×C4—21no—
436C22×C4C2×D4×C15111yescharacteristic
437C22×C4C2×D4×C15111yescharacteristic
438C22×C4C2×D4×C15111yescharacteristic
439C22×C4C2×D4×C15111yescharacteristic
440C22×C4C2×D4×C15111yescharacteristic
441C22×C4C2×D4×C15111yescharacteristic
442C22×C4C24×C15111yescharacteristic
443Q16—28no—
444C2×C8—21no—
445C2×C8—21no—
446C2×C8—21no—
447C2×C8—21no—
448C2×C8—21no—
449C2×C8—21no—
450C2×C8—21no—
451C2×C8—21no—
452C2×C8—21no—
453C2×C8—21no—
454C2×C8—21no—
455C2×C8#41×C15112yes—
456C4⋊C4—24no—
457C4⋊C4—22no—
458C4⋊C4—21no—
459C4⋊C4—21no—
460C4⋊C4—21no—
461C4⋊C4—21no—
462C4⋊C4—21no—
463C4⋊C4—21no—
464C4⋊C4—21no—
465C4⋊C4—21no—
466C4⋊C4—21no—
467C4⋊C4—21no—
468C4⋊C4—21no—
469C4⋊C4—41no—
470C4⋊C4—42no—
471C4⋊C4—42no—
472C4⋊C4—42no—
473C4⋊C4—42no—
474C4⋊C4—42no—
475C4⋊C4C2×D4×C15112yes—
476C42—24no—
477C42—21no—
478C42—21no—
479C42—21no—
480C42—21no—
481C42—42no—
482C42—42no—
483C42—42no—
484C42C2×D4×C15112yes—
485C42#41×C15112yes—
486C23C22×D4×C15111yescharacteristic
487Q8—22no—
488Q8—22no—
489Q8—22no—
490Q8—22no—
491Q8—41no—
492Q8—41no—
493Q8—41no—
494Q8—41no—
495C2×C4—21no—
496C2×C4—21no—
497C2×C4—21no—
498C2×C4—21no—
499C2×C4—21no—
500C2×C4—21no—
501C2×C4—22no—
502C2×C4—22no—
503C2×C4—21no—
504C2×C4—21no—
505C2×C4—21no—
506C2×C4—22no—
507C2×C4—21no—
508C2×C4—21no—
509C2×C4—21no—
510C2×C4—21no—
511C2×C4—21no—
512C2×C4—21no—
513C2×C4—41no—
514C2×C4—41no—
515C2×C4—41no—
516C2×C4—41no—
517C2×C4—41no—
518C2×C4—41no—
519C2×C4—41no—
520C2×C4—41no—
521C2×C4—41no—
522C2×C4—41no—
523C2×C4—41no—
524C2×C4—41no—
525C2×C4—41no—
526C2×C4—41no—
527C2×C4—41no—
528C2×C4—41no—
529C2×C4—41no—
530C2×C4—41no—
531C2×C4—41no—
532C2×C4—41no—
533C2×C4—41no—
534C2×C4#121×C15112yes—
535C2×C4#121×C15112yes—
536C2×C4#135×C15112yes—
537C2×C4C22×D4×C15111yescharacteristic
538C2×C4C2×#41×C15111yescharacteristic
539C2×C4C2×#41×C15111yescharacteristic
540C2×C4C2×#41×C15111yescharacteristic
541C2×C42−1+4×C15111yescharacteristic
542C2×C42−1+4×C15111yescharacteristic
543C8—22no—
544C8—41no—
545C8—41no—
546C8—41no—
547C22C2×#121×C15111yescharacteristic
548C22#547×C15111yescharacteristic
549C22#548×C15111yescharacteristic
550C22C2×#135×C15111yescharacteristic
551C22#575×C15111yescharacteristic
552C22#578×C15111yescharacteristic
553C22#578×C15111yescharacteristic
554C4—22no—
555C4—22no—
556C4—22no—
557C4—42no—
558C4—42no—
559C4—42no—
560C4—41no—
561C4—41no—
562C4—41no—
563C4—81no—
564C4—81no—
565C4—81no—
566C4—81no—
567C4—81no—
568C4#525×C15111yescharacteristic
569C4#536×C15111yescharacteristic
570C4#552×C15111yescharacteristic
571C4#556×C15111yescharacteristic
572C2#2415×C15111yescharacteristic
573C2#3035×C15111yescharacteristic
574C2#3044×C15111yescharacteristic
575C2#3336×C15111yescharacteristic
576C2#3352×C15111yescharacteristic
577C2#3364×C15111yescharacteristic
578C2#3377×C15111yescharacteristic
subgroupG/H
center, socle, prime radicalC23×C151C22×D4
commutator, Frattini, cosocleC22×C4C24×C151
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
289. #24687C151direct (N × H)
290. C151#24687direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#479×C1512
C2×C4×Q16×C1512
#2565×C1512
#2356×C1512
#2074×C1512
#2072×C1512
#2056×C1512
#1991×C1512
#1949×C1512
#1947×C1512
#1939×C1512
#1928×C1512
#1927×C1512
#1805×C1512
#24687151