Finite Group Databasebeta

← C151×#17362 #50322287

Subgroups — C151×#17362 #50322287

Order 38656.

1738 conjugacy classes of subgroups.

The subgroup lattice has 606 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C4×D4×C151C211yesmaximal, characteristic
2C2×#407×C151C212yesmaximal, complemented
3#1465×C151C214yesmaximal, complemented
4#1463×C151C212yesmaximal, complemented
5#1462×C151C212yesmaximal, complemented
6#1459×C151C214yesmaximal, complemented
7C23×D4×C151C411yescharacteristic
8C24×C4×C151C411yescharacteristic
9C24×C4×C151C2211yescharacteristic
10C22×M16×C151—22no—
11C2×C4×D4×C151—22no—
12C2×C4×D4×C151—22no—
13C2×C4×D4×C151—22no—
14C2×C4×D4×C151—22no—
15C2×C4×D4×C151C412yes—
16C2×C4×D4×C151C412yes—
17C2×C4×D4×C151C2212yes—
18C2×C4×D4×C151C2212yes—
19C22×C4⋊C4×C151C2211yescharacteristic
20C22×C22⋊C4×C151C411yescharacteristic
21C22×C22⋊C4×C151C2211yescharacteristic
22C22×C42×C151C411yescharacteristic
23#407×C151—22no—
24#407×C151—22no—
25#407×C151C2214yes—
26#407×C151C2214yescomplemented
27C2×C22⋊C8×C151—22no—
28C2×C22⋊C8×C151C2214yescomplemented
29#324×C151C2218yescomplemented
30#323×C151C2218yescomplemented
31C25×C151C2×C411yescharacteristic
32C25×C151C2×C411yescharacteristic
33C22×D4×C151—28no—
34C22×D4×C151—22no—
35C22×D4×C151—22no—
36C22×D4×C151C2×C412yes—
37C22×D4×C151C2×C412yes—
38C23×C4×C151—21no—
39C23×C4×C151—21no—
40C23×C4×C151—21no—
41C23×C4×C151—21no—
42C23×C4×C151—44no—
43C23×C4×C151—44no—
44C23×C4×C151C2×C411yescharacteristic
45C23×C4×C151C2×C411yescharacteristic
46C23×C4×C151C2×C411yescharacteristic
47C23×C4×C151C2×C411yescharacteristic
48C23×C4×C151C2×C412yes—
49C23×C4×C151C2×C412yes—
50C23×C4×C151C2×C411yescharacteristic
51C23×C4×C151C2×C411yescharacteristic
52C23×C4×C151D412yes—
53C23×C4×C151D412yes—
54C23×C4×C151D412yes—
55C23×C4×C151D412yes—
56C23×C4×C151C2311yescharacteristic
57C23×C4×C151C2311yescharacteristic
58C23×C4×C151C2311yescharacteristic
59C2×M16×C151—24no—
60C2×M16×C151—24no—
61C2×M16×C151—48no—
62C22×C8×C151—24no—
63C4×D4×C151—24no—
64C4×D4×C151—24no—
65C4×D4×C151—24no—
66C4×D4×C151—24no—
67C4×D4×C151—24no—
68C4×D4×C151—24no—
69C4×D4×C151—24no—
70C4×D4×C151—24no—
71C2×C4⋊C4×C151—22no—
72C2×C4⋊C4×C151—22no—
73C2×C4⋊C4×C151C2×C412yes—
74C2×C4⋊C4×C151C2312yes—
75C2×C22⋊C4×C151—22no—
76C2×C22⋊C4×C151—22no—
77C2×C22⋊C4×C151—22no—
78C2×C22⋊C4×C151—22no—
79C2×C22⋊C4×C151C2×C412yes—
80C2×C22⋊C4×C151C2×C412yes—
81C2×C22⋊C4×C151C2×C412yes—
82C2×C22⋊C4×C151C2312yes—
83C2×C42×C151—21no—
84C2×C42×C151—21no—
85C2×C42×C151—21no—
86C2×C42×C151—21no—
87C2×C42×C151C2×C412yes—
88C2×C42×C151C2×C412yes—
89C22⋊C8×C151—24no—
90C22⋊C8×C151—24no—
91C22⋊C8×C151—24no—
92C22⋊C8×C151C2318yes—
93C24×C151—21no—
94C24×C151—21no—
95C24×C151—24no—
96C24×C151—24no—
97C24×C151—42no—
98C24×C151—42no—
99C24×C151—42no—
100C24×C151—42no—
101C24×C151C22⋊C412yes—
102C24×C151C22⋊C412yes—
103C24×C151C22×C411yescharacteristic
104C24×C151C22×C411yescharacteristic
105C24×C151C22×C412yes—
106C24×C151C22×C411yescharacteristic
107C2×D4×C151—216no—
108C2×D4×C151—216no—
109C2×D4×C151—24no—
110C2×D4×C151—24no—
111C2×D4×C151—24no—
112C2×D4×C151—24no—
113C2×D4×C151—24no—
114C2×D4×C151M1618yescomplemented
115C22×C4×C151—21no—
116C22×C4×C151—21no—
117C22×C4×C151—28no—
118C22×C4×C151—24no—
119C22×C4×C151—24no—
120C22×C4×C151—21no—
121C22×C4×C151—21no—
122C22×C4×C151—21no—
123C22×C4×C151—21no—
124C22×C4×C151—22no—
125C22×C4×C151—22no—
126C22×C4×C151—22no—
127C22×C4×C151—22no—
128C22×C4×C151—42no—
129C22×C4×C151—42no—
130C22×C4×C151—44no—
131C22×C4×C151—44no—
132C22×C4×C151—42no—
133C22×C4×C151—42no—
134C22×C4×C151—44no—
135C22×C4×C151—42no—
136C22×C4×C151—44no—
137C22×C4×C151—44no—
138C22×C4×C151—44no—
139C22×C4×C151—44no—
140C22×C4×C151—44no—
141C22×C4×C151—44no—
142C22×C4×C151—42no—
143C22×C4×C151—42no—
144C22×C4×C151C22⋊C411yescharacteristic
145C22×C4×C151C22⋊C411yescharacteristic
146C22×C4×C151C22⋊C412yes—
147C22×C4×C151C22⋊C411yescharacteristic
148C22×C4×C151C22⋊C412yes—
149C22×C4×C151C22⋊C412yes—
150C22×C4×C151C22⋊C412yes—
151C22×C4×C151C22⋊C411yescharacteristic
152C22×C4×C151C22×C411yescharacteristic
153C22×C4×C151C22×C411yescharacteristic
154C22×C4×C151C22×C412yes—
155C22×C4×C151C22×C412yes—
156C22×C4×C151C22×C412yes—
157C22×C4×C151C22×C411yescharacteristic
158C22×C4×C151C2×D412yes—
159C22×C4×C151C2×D412yes—
160C22×C4×C151C2×D412yes—
161C22×C4×C151C2×D412yes—
162C22×C4×C151C2×D412yes—
163C22×C4×C151C2×D412yes—
164C22×C4×C151C2411yescharacteristic
165M16×C151—48no—
166M16×C151—48no—
167C2×C8×C151—28no—
168C2×C8×C151—48no—
169C4⋊C4×C151—24no—
170C4⋊C4×C151—24no—
171C22⋊C4×C151—24no—
172C22⋊C4×C151—24no—
173C22⋊C4×C151—24no—
174C22⋊C4×C151—24no—
175C42×C151—22no—
176C42×C151—22no—
177C42×C151—22no—
178C42×C151—22no—
179C23×C151—22no—
180C23×C151—22no—
181C23×C151—22no—
182C23×C151—24no—
183C23×C151—24no—
184C23×C151—22no—
185C23×C151—22no—
186C23×C151—22no—
187C23×C151—24no—
188C23×C151—24no—
189C23×C151—24no—
190C23×C151—24no—
191C23×C151—42no—
192C23×C151—42no—
193C23×C151—41no—
194C23×C151—41no—
195C23×C151—41no—
196C23×C151—41no—
197C23×C151—42no—
198C23×C151—42no—
199C23×C151—416no—
200C23×C151—416no—
201C23×C151—42no—
202C23×C151—42no—
203C23×C151—42no—
204C23×C151—42no—
205C23×C151C2×C22⋊C412yes—
206C23×C151C2×C22⋊C412yes—
207C23×C151C2×C22⋊C411yescharacteristic
208C23×C151C2×C22⋊C411yescharacteristic
209C23×C151C2×M1614yes—
210C23×C151C2×M1614yescomplemented
211C23×C151C23×C411yescharacteristic
212D4×C151—216no—
213D4×C151—216no—
214C2×C4×C151—24no—
215C2×C4×C151—24no—
216C2×C4×C151—22no—
217C2×C4×C151—22no—
218C2×C4×C151—24no—
219C2×C4×C151—22no—
220C2×C4×C151—24no—
221C2×C4×C151—24no—
222C2×C4×C151—22no—
223C2×C4×C151—22no—
224C2×C4×C151—22no—
225C2×C4×C151—22no—
226C2×C4×C151—24no—
227C2×C4×C151—24no—
228C2×C4×C151—22no—
229C2×C4×C151—22no—
230C2×C4×C151—42no—
231C2×C4×C151—42no—
232C2×C4×C151—41no—
233C2×C4×C151—42no—
234C2×C4×C151—42no—
235C2×C4×C151—42no—
236C2×C4×C151—41no—
237C2×C4×C151—44no—
238C2×C4×C151—44no—
239C2×C4×C151—42no—
240C2×C4×C151—42no—
241C2×C4×C151—42no—
242C2×C4×C151—42no—
243C2×C4×C151—44no—
244C2×C4×C151—44no—
245C2×C4×C151—42no—
246C2×C4×C151—42no—
247C2×C4×C151#9914yes—
248C2×C4×C151C2×C22⋊C411yescharacteristic
249C2×C4×C151C2×C22⋊C411yescharacteristic
250C2×C4×C151C2×C22⋊C412yes—
251C2×C4×C151C2×C22⋊C411yescharacteristic
252C2×C4×C151C2×C22⋊C411yescharacteristic
253C2×C4×C151C2×M1614yescomplemented
254C2×C4×C151C22×D412yes—
255C8×C151—48no—
256C22×C151—28no—
257C22×C151—21no—
258C22×C151—21no—
259C22×C151—21no—
260C22×C151—21no—
261C22×C151—22no—
262C22×C151—21no—
263C22×C151—21no—
264C22×C151—22no—
265C22×C151—22no—
266C22×C151—24no—
267C22×C151—22no—
268C22×C151—22no—
269C22×C151—44no—
270C22×C151—48no—
271C22×C151—48no—
272C22×C151—44no—
273C22×C151—44no—
274C22×C151—44no—
275C22×C151—48no—
276C22×C151—48no—
277C22×C151—42no—
278C22×C151—42no—
279C22×C151#40714yes—
280C22×C151C2×#9912yes—
281C22×C151#41312yes—
282C22×C151C22×C22⋊C411yescharacteristic
283C22×C151C22×M1612yes—
284C4×C151—24no—
285C4×C151—22no—
286C4×C151—21no—
287C4×C151—21no—
288C4×C151—22no—
289C4×C151—42no—
290C4×C151—42no—
291C4×C151C2×#9912yes—
292C4×C151C2×#9912yes—
293C2×C151—22no—
294C2×C151—22no—
295C2×C151—22no—
296C2×C151—24no—
297C2×C151—42no—
298C2×C151—44no—
299C2×C151C2×#40711yescharacteristic
300C2×C151C22×#9911yescharacteristic
301C2×C151C2×#41311yescharacteristic
302#17362C15111yesmaximal, characteristic, direct product factor, Sylow
303C151#1736211yescharacteristic, direct product factor, Sylow
304C22×C4×D4C2×C15111yescharacteristic
305C2×#407C2×C15112yescomplemented
306#1465C2×C15114yescomplemented
307#1463C2×C15112yescomplemented
308#1462C2×C15112yescomplemented
309#1459C2×C15114yescomplemented
310C23×D4C4×C15111yescharacteristic
311C24×C4C4×C15111yescharacteristic
312C24×C4C22×C15111yescharacteristic
313C22×M16—22no—
314C2×C4×D4—22no—
315C2×C4×D4—22no—
316C2×C4×D4—22no—
317C2×C4×D4—22no—
318C2×C4×D4C4×C15112yes—
319C2×C4×D4C4×C15112yes—
320C2×C4×D4C22×C15112yes—
321C2×C4×D4C22×C15112yes—
322C22×C4⋊C4C22×C15111yescharacteristic
323C22×C22⋊C4C4×C15111yescharacteristic
324C22×C22⋊C4C22×C15111yescharacteristic
325C22×C42C4×C15111yescharacteristic
326#407—22no—
327#407—22no—
328#407C22×C15114yes—
329#407C22×C15114yescomplemented
330C2×C22⋊C8—22no—
331C2×C22⋊C8C22×C15114yescomplemented
332#324C22×C15118yescomplemented
333#323C22×C15118yescomplemented
334C25C2×C4×C15111yescharacteristic
335C25C2×C4×C15111yescharacteristic
336C22×D4—22no—
337C22×D4—22no—
338C22×D4—28no—
339C22×D4C2×C4×C15112yes—
340C22×D4C2×C4×C15112yes—
341C23×C4—21no—
342C23×C4—21no—
343C23×C4—21no—
344C23×C4—21no—
345C23×C4—44no—
346C23×C4—44no—
347C23×C4C2×C4×C15111yescharacteristic
348C23×C4C2×C4×C15111yescharacteristic
349C23×C4C2×C4×C15111yescharacteristic
350C23×C4C2×C4×C15111yescharacteristic
351C23×C4C2×C4×C15112yes—
352C23×C4C2×C4×C15112yes—
353C23×C4C2×C4×C15111yescharacteristic
354C23×C4C2×C4×C15111yescharacteristic
355C23×C4D4×C15112yes—
356C23×C4D4×C15112yes—
357C23×C4D4×C15112yes—
358C23×C4D4×C15112yes—
359C23×C4C23×C15111yescharacteristic
360C23×C4C23×C15111yescharacteristic
361C23×C4C23×C15111yescharacteristic
362C2×M16—24no—
363C2×M16—24no—
364C2×M16—48no—
365C22×C8—24no—
366C4×D4—24no—
367C4×D4—24no—
368C4×D4—24no—
369C4×D4—24no—
370C4×D4—24no—
371C4×D4—24no—
372C4×D4—24no—
373C4×D4—24no—
374C2×C4⋊C4—22no—
375C2×C4⋊C4—22no—
376C2×C4⋊C4C2×C4×C15112yes—
377C2×C4⋊C4C23×C15112yes—
378C2×C22⋊C4—22no—
379C2×C22⋊C4—22no—
380C2×C22⋊C4—22no—
381C2×C22⋊C4—22no—
382C2×C22⋊C4C2×C4×C15112yes—
383C2×C22⋊C4C2×C4×C15112yes—
384C2×C22⋊C4C2×C4×C15112yes—
385C2×C22⋊C4C23×C15112yes—
386C2×C42—21no—
387C2×C42—21no—
388C2×C42—21no—
389C2×C42—21no—
390C2×C42C2×C4×C15112yes—
391C2×C42C2×C4×C15112yes—
392C22⋊C8—24no—
393C22⋊C8—24no—
394C22⋊C8—24no—
395C22⋊C8C23×C15118yes—
396C24—21no—
397C24—21no—
398C24—24no—
399C24—24no—
400C24—42no—
401C24—42no—
402C24—42no—
403C24—42no—
404C24C22⋊C4×C15112yes—
405C24C22⋊C4×C15112yes—
406C24C22×C4×C15111yescharacteristic
407C24C22×C4×C15111yescharacteristic
408C24C22×C4×C15112yes—
409C24C22×C4×C15111yescharacteristic
410C2×D4—216no—
411C2×D4—216no—
412C2×D4—24no—
413C2×D4—24no—
414C2×D4—24no—
415C2×D4—24no—
416C2×D4—24no—
417C2×D4M16×C15118yescomplemented
418C22×C4—21no—
419C22×C4—21no—
420C22×C4—28no—
421C22×C4—24no—
422C22×C4—24no—
423C22×C4—21no—
424C22×C4—21no—
425C22×C4—21no—
426C22×C4—21no—
427C22×C4—22no—
428C22×C4—22no—
429C22×C4—22no—
430C22×C4—22no—
431C22×C4—42no—
432C22×C4—42no—
433C22×C4—44no—
434C22×C4—44no—
435C22×C4—42no—
436C22×C4—42no—
437C22×C4—44no—
438C22×C4—42no—
439C22×C4—44no—
440C22×C4—44no—
441C22×C4—44no—
442C22×C4—44no—
443C22×C4—44no—
444C22×C4—44no—
445C22×C4—42no—
446C22×C4—42no—
447C22×C4C22⋊C4×C15111yescharacteristic
448C22×C4C22⋊C4×C15111yescharacteristic
449C22×C4C22⋊C4×C15111yescharacteristic
450C22×C4C22⋊C4×C15112yes—
451C22×C4C22⋊C4×C15112yes—
452C22×C4C22⋊C4×C15112yes—
453C22×C4C22⋊C4×C15112yes—
454C22×C4C22⋊C4×C15111yescharacteristic
455C22×C4C22×C4×C15111yescharacteristic
456C22×C4C22×C4×C15111yescharacteristic
457C22×C4C22×C4×C15112yes—
458C22×C4C22×C4×C15112yes—
459C22×C4C22×C4×C15112yes—
460C22×C4C22×C4×C15111yescharacteristic
461C22×C4C2×D4×C15112yes—
462C22×C4C2×D4×C15112yes—
463C22×C4C2×D4×C15112yes—
464C22×C4C2×D4×C15112yes—
465C22×C4C2×D4×C15112yes—
466C22×C4C2×D4×C15112yes—
467C22×C4C24×C15111yescharacteristic
468M16—48no—
469M16—48no—
470C2×C8—28no—
471C2×C8—48no—
472C4⋊C4—24no—
473C4⋊C4—24no—
474C22⋊C4—24no—
475C22⋊C4—24no—
476C22⋊C4—24no—
477C22⋊C4—24no—
478C42—22no—
479C42—22no—
480C42—22no—
481C42—22no—
482C23—22no—
483C23—22no—
484C23—22no—
485C23—24no—
486C23—24no—
487C23—24no—
488C23—24no—
489C23—24no—
490C23—24no—
491C23—22no—
492C23—22no—
493C23—22no—
494C23—42no—
495C23—41no—
496C23—41no—
497C23—42no—
498C23—41no—
499C23—41no—
500C23—42no—
501C23—42no—
502C23—42no—
503C23—416no—
504C23—416no—
505C23—42no—
506C23—42no—
507C23—42no—
508C23C2×C22⋊C4×C15112yes—
509C23C2×C22⋊C4×C15112yes—
510C23C2×C22⋊C4×C15111yescharacteristic
511C23C2×C22⋊C4×C15111yescharacteristic
512C23C2×M16×C15114yes—
513C23C2×M16×C15114yescomplemented
514C23C23×C4×C15111yescharacteristic
515D4—216no—
516D4—216no—
517C2×C4—24no—
518C2×C4—24no—
519C2×C4—24no—
520C2×C4—22no—
521C2×C4—22no—
522C2×C4—22no—
523C2×C4—24no—
524C2×C4—24no—
525C2×C4—22no—
526C2×C4—22no—
527C2×C4—22no—
528C2×C4—22no—
529C2×C4—24no—
530C2×C4—24no—
531C2×C4—22no—
532C2×C4—22no—
533C2×C4—41no—
534C2×C4—42no—
535C2×C4—42no—
536C2×C4—41no—
537C2×C4—42no—
538C2×C4—42no—
539C2×C4—42no—
540C2×C4—44no—
541C2×C4—44no—
542C2×C4—42no—
543C2×C4—42no—
544C2×C4—42no—
545C2×C4—42no—
546C2×C4—44no—
547C2×C4—44no—
548C2×C4—42no—
549C2×C4—42no—
550C2×C4#99×C15114yes—
551C2×C4C2×C22⋊C4×C15111yescharacteristic
552C2×C4C2×C22⋊C4×C15111yescharacteristic
553C2×C4C2×C22⋊C4×C15112yes—
554C2×C4C2×C22⋊C4×C15111yescharacteristic
555C2×C4C2×C22⋊C4×C15111yescharacteristic
556C2×C4C2×M16×C15114yescomplemented
557C2×C4C22×D4×C15112yes—
558C8—48no—
559C22—28no—
560C22—21no—
561C22—21no—
562C22—21no—
563C22—21no—
564C22—22no—
565C22—21no—
566C22—21no—
567C22—22no—
568C22—22no—
569C22—24no—
570C22—22no—
571C22—22no—
572C22—44no—
573C22—48no—
574C22—48no—
575C22—44no—
576C22—48no—
577C22—48no—
578C22—44no—
579C22—44no—
580C22—42no—
581C22—42no—
582C22#407×C15114yes—
583C22C2×#99×C15112yes—
584C22#413×C15112yes—
585C22C22×C22⋊C4×C15111yescharacteristic
586C22C22×M16×C15112yes—
587C4—24no—
588C4—22no—
589C4—21no—
590C4—21no—
591C4—22no—
592C4—42no—
593C4—42no—
594C4C2×#99×C15112yes—
595C4C2×#99×C15112yes—
596C2—22no—
597C2—22no—
598C2—22no—
599C2—24no—
600C2—42no—
601C2—44no—
602C2C2×#407×C15111yescharacteristic
603C2C22×#99×C15111yescharacteristic
604C2C2×#413×C15111yescharacteristic
subgroupG/H
centerC2×C4×C151C2×C22⋊C4
commutatorC23C23×C4×C151
Frattini, cosocleC22×C4C24×C151
socleC22×C151C22×C22⋊C4
prime radicalC23×D4×C151C4
LCSG ▷ C23 ▷ C2 ▷ C1
UCSC1 ◁ C2×C4×C151 ◁ C24×C4×C151 ◁ G

Complements

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

NH ≅ G/Ntype
2. C2×#407×C151C2semidirect
3. #1465×C151C2semidirect
4. #1463×C151C2semidirect
5. #1462×C151C2semidirect
6. #1459×C151C2semidirect
26. #407×C151C22semidirect
28. C2×C22⋊C8×C151C22semidirect
29. #324×C151C22semidirect
30. #323×C151C22semidirect
114. C2×D4×C151M16semidirect
210. C23×C151C2×M16semidirect
253. C2×C4×C151C2×M16semidirect
302. #17362C151direct (N × H)
303. C151#17362direct (N × H)
305. C2×#407C2×C151semidirect
306. #1465C2×C151semidirect
307. #1463C2×C151semidirect
308. #1462C2×C151semidirect
309. #1459C2×C151semidirect
329. #407C22×C151semidirect
331. C2×C22⋊C8C22×C151semidirect
332. #324C22×C151semidirect
333. #323C22×C151semidirect
417. C2×D4M16×C151semidirect
513. C23C2×M16×C151semidirect
556. C2×C4C2×M16×C151semidirect

Maximal subgroups

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

subgroupindex
C22×C4×D4×C1512
C2×#407×C1512
#1465×C1512
#1463×C1512
#1462×C1512
#1459×C1512
#17362151