Finite Group Databasebeta

← C151×#24588 #50329513

Subgroups — C151×#24588 #50329513

Order 38656.

800 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×#484×C151C211yesmaximal, characteristic
2C2×#428×C151C211yesmaximal, characteristic
3#2499×C151C211yesmaximal, characteristic
4#2344×C151C211yesmaximal, characteristic
5#2085×C151C211yesmaximal, characteristic, complemented
6#2083×C151C211yesmaximal, characteristic, complemented
7#2068×C151C211yesmaximal, characteristic, complemented
8#2066×C151C211yesmaximal, characteristic, complemented
9#1949×C151C211yesmaximal, characteristic, complemented
10#1947×C151C211yesmaximal, characteristic, complemented
11#1928×C151C211yesmaximal, characteristic, complemented
12#1927×C151C211yesmaximal, characteristic, complemented
13#1894×C151C211yesmaximal, characteristic
14#1851×C151C211yesmaximal, characteristic
15#1825×C151C211yesmaximal, characteristic
16C22×M16×C151C2211yescharacteristic
17C2×C22⋊Q8×C151C2211yescharacteristic
18C2×#117×C151—21no—
19C2×#117×C151C2211yescharacteristic
20C22×C4⋊C4×C151C2211yescharacteristic
21#484×C151—24no—
22#428×C151—24no—
23C2×#107×C151C2211yescharacteristic
24C2×#107×C151C2211yescharacteristic
25C2×#107×C151C2211yescharacteristic
26C2×#107×C151C2211yescharacteristic
27C2×#106×C151C2211yescharacteristic
28C2×#106×C151C2211yescharacteristic
29C2×C4⋊C8×C151C2211yescharacteristic
30C2×C4⋊C8×C151C2211yescharacteristic
31C2×#103×C151C2211yescharacteristic
32C2×#103×C151C2211yescharacteristic
33C2×#103×C151C2211yescharacteristic
34C2×#103×C151C2211yescharacteristic
35C2×C22⋊C8×C151C2211yescharacteristic
36#397×C151—21no—
37#397×C151—21no—
38#391×C151C2211yescharacteristic
39#391×C151C2211yescharacteristic
40#389×C151C2211yescharacteristic
41#389×C151C2211yescharacteristic
42#387×C151—21no—
43#387×C151—21no—
44#387×C151—21no—
45#387×C151—21no—
46#384×C151C2211yescharacteristic
47#382×C151C2211yescharacteristic
48#381×C151—21no—
49#380×C151C2211yescharacteristic
50C4×C4⋊C4×C151C2211yescharacteristic
51C4×C4⋊C4×C151C2211yescharacteristic
52C4×C22⋊C4×C151C2211yescharacteristic
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
62C23×C4×C151—21no—
63C23×C4×C151C2311yescharacteristic
64C2×M16×C151—22no—
65C2×M16×C151—22no—
66C2×M16×C151—22no—
67C22×C8×C151C2311yescharacteristic
68C22×C8×C151C2311yescharacteristic
69C22×C8×C151C2311yescharacteristic
70C22×C8×C151C2311yescharacteristic
71C22⋊Q8×C151—22no—
72C22⋊Q8×C151—22no—
73#117×C151—22no—
74#117×C151—22no—
75#117×C151—44no—
76C2×C4⋊C4×C151—21no—
77C2×C4⋊C4×C151—22no—
78C2×C4⋊C4×C151—21no—
79C2×C4⋊C4×C151—21no—
80C2×C4⋊C4×C151—21no—
81C2×C4⋊C4×C151—21no—
82C2×C4⋊C4×C151—21no—
83C2×C4⋊C4×C151D414yes—
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×C4⋊C4×C151C2311yescharacteristic
91C2×C22⋊C4×C151—21no—
92C2×C22⋊C4×C151—21no—
93C2×C22⋊C4×C151—21no—
94C2×C22⋊C4×C151D411yescharacteristic
95C2×C22⋊C4×C151D411yescharacteristic
96C2×C42×C151—21no—
97C2×C42×C151—21no—
98C2×C42×C151—21no—
99C2×C42×C151C2311yescharacteristic
100C2×C42×C151C2311yescharacteristic
101#107×C151—22no—
102#107×C151—22no—
103#107×C151—22no—
104#107×C151—22no—
105#106×C151—22no—
106#106×C151—22no—
107C4⋊C8×C151—22no—
108C4⋊C8×C151—22no—
109#103×C151—22no—
110#103×C151—22no—
111#103×C151—22no—
112#103×C151—22no—
113C22⋊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×C151—21no—
125#95×C151D411yescharacteristic
126#95×C151D411yescharacteristic
127C24×C151C2×D411yescharacteristic
128C2×Q8×C151—21no—
129C2×Q8×C151—21no—
130C2×Q8×C151—21no—
131C2×Q8×C151—21no—
132C2×Q8×C151—21no—
133C2×Q8×C151—21no—
134C22×C4×C151—21no—
135C22×C4×C151—21no—
136C22×C4×C151—21no—
137C22×C4×C151—21no—
138C22×C4×C151—24no—
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×C151—21no—
147C22×C4×C151—42no—
148C22×C4×C151—42no—
149C22×C4×C151C2×D411yescharacteristic
150C22×C4×C151C2×D411yescharacteristic
151C22×C4×C151C2×D411yescharacteristic
152C22×C4×C151C2×D411yescharacteristic
153C22×C4×C151C2×D412yes—
154C22×C4×C151C2×D411yescharacteristic
155C22×C4×C151#4112yes—
156C22×C4×C151C2411yescharacteristic
157M16×C151—28no—
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—
169C2×C8×C151#4112yes—
170C4⋊C4×C151—24no—
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—21no—
182C4⋊C4×C151—21no—
183C4⋊C4×C151—42no—
184C4⋊C4×C151—42no—
185C4⋊C4×C151—42no—
186C4⋊C4×C151—42no—
187C4⋊C4×C151—42no—
188C4⋊C4×C151C2×D412yes—
189C4⋊C4×C151C2×D412yes—
190C22⋊C4×C151—22no—
191C22⋊C4×C151—41no—
192C22⋊C4×C151—42no—
193C22⋊C4×C151—42no—
194C22⋊C4×C151—42no—
195C42×C151—21no—
196C42×C151—21no—
197C42×C151—21no—
198C42×C151—21no—
199C42×C151—42no—
200C42×C151—42no—
201C42×C151—42no—
202C23×C151—21no—
203C23×C151—21no—
204C23×C151—21no—
205C23×C151—21no—
206C23×C151—21no—
207C23×C151—21no—
208C23×C151#12112yes—
209C23×C151C22×D411yescharacteristic
210Q8×C151—41no—
211Q8×C151—41no—
212Q8×C151—41no—
213Q8×C151—41no—
214C2×C4×C151—21no—
215C2×C4×C151—21no—
216C2×C4×C151—21no—
217C2×C4×C151—21no—
218C2×C4×C151—22no—
219C2×C4×C151—22no—
220C2×C4×C151—22no—
221C2×C4×C151—22no—
222C2×C4×C151—22no—
223C2×C4×C151—22no—
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—48no—
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—41no—
252C2×C4×C151—41no—
253C2×C4×C151—41no—
254C2×C4×C151—41no—
255C2×C4×C151—41no—
256C2×C4×C151#12112yes—
257C2×C4×C151AGL(1,ℤ/8)12yes—
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—22no—
266C8×C151—41no—
267C8×C151—41no—
268C22×C151—22no—
269C22×C151—22no—
270C22×C151—22no—
271C22×C151—41no—
272C22×C151—41no—
273C22×C151—41no—
274C22×C151—41no—
275C22×C151C2×#12111yescharacteristic
276C22×C151#54711yescharacteristic
277C22×C151#54711yescharacteristic
278C22×C151C2×AGL(1,ℤ/8)11yescharacteristic
279C22×C151#57511yescharacteristic
280C22×C151#57811yescharacteristic
281C22×C151#57811yescharacteristic
282C4×C151—22no—
283C4×C151—22no—
284C4×C151—41no—
285C4×C151—41no—
286C4×C151—41no—
287C4×C151—42no—
288C4×C151—42no—
289C4×C151—81no—
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#55211yescharacteristic
299C2×C151—42no—
300C2×C151#241311yescharacteristic
301C2×C151#303611yescharacteristic
302C2×C151#304411yescharacteristic
303C2×C151#334311yescharacteristic
304C2×C151#334911yescharacteristic
305C2×C151#335211yescharacteristic
306C2×C151#335311yescharacteristic
307#24588C15111yesmaximal, characteristic, direct product factor, Sylow
308C151#2458811yescharacteristic, direct product factor, Sylow
309C2×#484C2×C15111yescharacteristic
310C2×#428C2×C15111yescharacteristic
311#2499C2×C15111yescharacteristic
312#2344C2×C15111yescharacteristic
313#2085C2×C15111yescharacteristic, complemented
314#2083C2×C15111yescharacteristic, complemented
315#2068C2×C15111yescharacteristic, complemented
316#2066C2×C15111yescharacteristic, complemented
317#1949C2×C15111yescharacteristic, complemented
318#1947C2×C15111yescharacteristic, complemented
319#1928C2×C15111yescharacteristic, complemented
320#1927C2×C15111yescharacteristic, complemented
321#1894C2×C15111yescharacteristic
322#1851C2×C15111yescharacteristic
323#1825C2×C15111yescharacteristic
324C22×M16C22×C15111yescharacteristic
325C2×C22⋊Q8C22×C15111yescharacteristic
326C2×#117—21no—
327C2×#117C22×C15111yescharacteristic
328C22×C4⋊C4C22×C15111yescharacteristic
329#484—24no—
330#428—24no—
331C2×#107C22×C15111yescharacteristic
332C2×#107C22×C15111yescharacteristic
333C2×#107C22×C15111yescharacteristic
334C2×#107C22×C15111yescharacteristic
335C2×#106C22×C15111yescharacteristic
336C2×#106C22×C15111yescharacteristic
337C2×C4⋊C8C22×C15111yescharacteristic
338C2×C4⋊C8C22×C15111yescharacteristic
339C2×#103C22×C15111yescharacteristic
340C2×#103C22×C15111yescharacteristic
341C2×#103C22×C15111yescharacteristic
342C2×#103C22×C15111yescharacteristic
343C2×C22⋊C8C22×C15111yescharacteristic
344#397—21no—
345#397—21no—
346#391C22×C15111yescharacteristic
347#391C22×C15111yescharacteristic
348#389C22×C15111yescharacteristic
349#389C22×C15111yescharacteristic
350#387—21no—
351#387—21no—
352#387—21no—
353#387—21no—
354#384C22×C15111yescharacteristic
355#382C22×C15111yescharacteristic
356#381—21no—
357#380C22×C15111yescharacteristic
358C4×C4⋊C4C22×C15111yescharacteristic
359C4×C4⋊C4C22×C15111yescharacteristic
360C4×C22⋊C4C22×C15111yescharacteristic
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
370C23×C4—21no—
371C23×C4C23×C15111yescharacteristic
372C2×M16—22no—
373C2×M16—22no—
374C2×M16—22no—
375C22×C8C23×C15111yescharacteristic
376C22×C8C23×C15111yescharacteristic
377C22×C8C23×C15111yescharacteristic
378C22×C8C23×C15111yescharacteristic
379C22⋊Q8—22no—
380C22⋊Q8—22no—
381#117—22no—
382#117—22no—
383#117—44no—
384C2×C4⋊C4—22no—
385C2×C4⋊C4—21no—
386C2×C4⋊C4—21no—
387C2×C4⋊C4—21no—
388C2×C4⋊C4—21no—
389C2×C4⋊C4—21no—
390C2×C4⋊C4—21no—
391C2×C4⋊C4D4×C15114yes—
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×C4⋊C4C23×C15111yescharacteristic
399C2×C22⋊C4—21no—
400C2×C22⋊C4—21no—
401C2×C22⋊C4—21no—
402C2×C22⋊C4D4×C15111yescharacteristic
403C2×C22⋊C4D4×C15111yescharacteristic
404C2×C42—21no—
405C2×C42—21no—
406C2×C42—21no—
407C2×C42C23×C15111yescharacteristic
408C2×C42C23×C15111yescharacteristic
409#107—22no—
410#107—22no—
411#107—22no—
412#107—22no—
413#106—22no—
414#106—22no—
415C4⋊C8—22no—
416C4⋊C8—22no—
417#103—22no—
418#103—22no—
419#103—22no—
420#103—22no—
421C22⋊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#95—21no—
433#95D4×C15111yescharacteristic
434#95D4×C15111yescharacteristic
435C24C2×D4×C15111yescharacteristic
436C2×Q8—21no—
437C2×Q8—21no—
438C2×Q8—21no—
439C2×Q8—21no—
440C2×Q8—21no—
441C2×Q8—21no—
442C22×C4—21no—
443C22×C4—21no—
444C22×C4—21no—
445C22×C4—21no—
446C22×C4—24no—
447C22×C4—21no—
448C22×C4—21no—
449C22×C4—21no—
450C22×C4—21no—
451C22×C4—21no—
452C22×C4—21no—
453C22×C4—21no—
454C22×C4—21no—
455C22×C4—42no—
456C22×C4—42no—
457C22×C4C2×D4×C15111yescharacteristic
458C22×C4C2×D4×C15111yescharacteristic
459C22×C4C2×D4×C15111yescharacteristic
460C22×C4C2×D4×C15111yescharacteristic
461C22×C4C2×D4×C15112yes—
462C22×C4C2×D4×C15111yescharacteristic
463C22×C4#41×C15112yes—
464C22×C4C24×C15111yescharacteristic
465M16—28no—
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—
477C2×C8#41×C15112yes—
478C4⋊C4—24no—
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—21no—
490C4⋊C4—21no—
491C4⋊C4—42no—
492C4⋊C4—42no—
493C4⋊C4—42no—
494C4⋊C4—42no—
495C4⋊C4—42no—
496C4⋊C4C2×D4×C15112yes—
497C4⋊C4C2×D4×C15112yes—
498C22⋊C4—22no—
499C22⋊C4—41no—
500C22⋊C4—42no—
501C22⋊C4—42no—
502C22⋊C4—42no—
503C42—21no—
504C42—21no—
505C42—21no—
506C42—21no—
507C42—42no—
508C42—42no—
509C42—42no—
510C23—21no—
511C23—21no—
512C23—21no—
513C23—21no—
514C23—21no—
515C23—21no—
516C23#121×C15112yes—
517C23C22×D4×C15111yescharacteristic
518Q8—41no—
519Q8—41no—
520Q8—41no—
521Q8—41no—
522C2×C4—21no—
523C2×C4—21no—
524C2×C4—21no—
525C2×C4—21no—
526C2×C4—22no—
527C2×C4—22no—
528C2×C4—22no—
529C2×C4—22no—
530C2×C4—22no—
531C2×C4—22no—
532C2×C4—21no—
533C2×C4—21no—
534C2×C4—21no—
535C2×C4—21no—
536C2×C4—21no—
537C2×C4—21no—
538C2×C4—21no—
539C2×C4—21no—
540C2×C4—21no—
541C2×C4—48no—
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—41no—
556C2×C4—41no—
557C2×C4—41no—
558C2×C4—41no—
559C2×C4—41no—
560C2×C4—41no—
561C2×C4—41no—
562C2×C4—41no—
563C2×C4—41no—
564C2×C4#121×C15112yes—
565C2×C4AGL(1,ℤ/8)×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—22no—
574C8—41no—
575C8—41no—
576C22—22no—
577C22—22no—
578C22—22no—
579C22—41no—
580C22—41no—
581C22—41no—
582C22—41no—
583C22C2×#121×C15111yescharacteristic
584C22#547×C15111yescharacteristic
585C22#547×C15111yescharacteristic
586C22C2×AGL(1,ℤ/8)×C15111yescharacteristic
587C22#575×C15111yescharacteristic
588C22#578×C15111yescharacteristic
589C22#578×C15111yescharacteristic
590C4—22no—
591C4—22no—
592C4—42no—
593C4—42no—
594C4—41no—
595C4—41no—
596C4—41no—
597C4—81no—
598C4—81no—
599C4—81no—
600C4—81no—
601C4—81no—
602C4—81no—
603C4#525×C15111yescharacteristic
604C4#536×C15111yescharacteristic
605C4#552×C15111yescharacteristic
606C4#552×C15111yescharacteristic
607C2—42no—
608C2#2413×C15111yescharacteristic
609C2#3036×C15111yescharacteristic
610C2#3044×C15111yescharacteristic
611C2#3343×C15111yescharacteristic
612C2#3349×C15111yescharacteristic
613C2#3352×C15111yescharacteristic
614C2#3353×C15111yescharacteristic
subgroupG/H
center, socleC23×C151C22×D4
commutator, Frattini, cosocleC22×C4C24×C151
prime radicalC24×C151C2×D4
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C151 ◁ C4×C22⋊C4×C151 ◁ G

Complements

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

NH ≅ G/Ntype
5. #2085×C151C2semidirect
6. #2083×C151C2semidirect
7. #2068×C151C2semidirect
8. #2066×C151C2semidirect
9. #1949×C151C2semidirect
10. #1947×C151C2semidirect
11. #1928×C151C2semidirect
12. #1927×C151C2semidirect
307. #24588C151direct (N × H)
308. C151#24588direct (N × H)
313. #2085C2×C151semidirect
314. #2083C2×C151semidirect
315. #2068C2×C151semidirect
316. #2066C2×C151semidirect
317. #1949C2×C151semidirect
318. #1947C2×C151semidirect
319. #1928C2×C151semidirect
320. #1927C2×C151semidirect

Maximal subgroups

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

subgroupindex
C2×#484×C1512
C2×#428×C1512
#2499×C1512
#2344×C1512
#2085×C1512
#2083×C1512
#2068×C1512
#2066×C1512
#1949×C1512
#1947×C1512
#1928×C1512
#1927×C1512
#1894×C1512
#1851×C1512
#1825×C1512
#24588151