Finite Group Databasebeta

← C151×#14551 #50319476

Subgroups — C151×#14551 #50319476

Order 38656.

1642 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×#399×C151C211yesmaximal, characteristic
2C2×#389×C151C212yesmaximal, complemented
3C2×#385×C151C212yesmaximal
4#1445×C151C212yesmaximal, complemented
5#1441×C151C212yesmaximal, complemented
6#1439×C151C211yesmaximal, characteristic
7#1437×C151C212yesmaximal
8#1436×C151C212yesmaximal, complemented
9C22⋊#95×C151C211yesmaximal, characteristic
10C24×C4×C151C2211yescharacteristic
11C22×C4⋊C4×C151C2211yescharacteristic
12C22×C4⋊C4×C151C2212yes—
13C22×C4⋊C4×C151C2212yes—
14C22×C4⋊C4×C151C2211yescharacteristic
15C22×C4⋊C4×C151C2212yes—
16C22×C22⋊C4×C151C2212yes—
17C22×C22⋊C4×C151C2212yes—
18C22×C22⋊C4×C151C2211yescharacteristic
19C22×C22⋊C4×C151C2211yescharacteristic
20C22×C42×C151C2212yes—
21#399×C151C418yescomplemented
22#389×C151—28no—
23#385×C151—28no—
24C2×#95×C151C2212yes—
25C2×#95×C151C2212yes—
26C2×#95×C151C2212yes—
27C2×#95×C151C2212yes—
28C2×#95×C151C2212yes—
29C2×#95×C151C2212yes—
30C2×#95×C151C2212yes—
31C2×#95×C151C2212yes—
32C2×#95×C151C2211yescharacteristic
33C2×#95×C151C2211yescharacteristic
34C25×C151C2311yescharacteristic
35C23×C4×C151—24no—
36C23×C4×C151—22no—
37C23×C4×C151—42no—
38C23×C4×C151—41no—
39C23×C4×C151—41no—
40C23×C4×C151C2312yes—
41C23×C4×C151C2311yescharacteristic
42C23×C4×C151C2312yes—
43C23×C4×C151C2311yescharacteristic
44C23×C4×C151C2312yes—
45C23×C4×C151C2312yes—
46C23×C4×C151C2312yes—
47C23×C4×C151C2312yes—
48C2×C4⋊C4×C151—24no—
49C2×C4⋊C4×C151—24no—
50C2×C4⋊C4×C151—24no—
51C2×C4⋊C4×C151—24no—
52C2×C4⋊C4×C151—24no—
53C2×C4⋊C4×C151—41no—
54C2×C4⋊C4×C151—41no—
55C2×C4⋊C4×C151—42no—
56C2×C4⋊C4×C151—42no—
57C2×C4⋊C4×C151—41no—
58C2×C4⋊C4×C151—42no—
59C2×C4⋊C4×C151C2×C418yescomplemented
60C2×C4⋊C4×C151C2×C414yescomplemented
61C2×C4⋊C4×C151D418yes—
62C2×C22⋊C4×C151—24no—
63C2×C22⋊C4×C151—24no—
64C2×C22⋊C4×C151—24no—
65C2×C22⋊C4×C151—24no—
66C2×C22⋊C4×C151—41no—
67C2×C22⋊C4×C151—41no—
68C2×C22⋊C4×C151—41no—
69C2×C22⋊C4×C151—41no—
70C2×C22⋊C4×C151—42no—
71C2×C22⋊C4×C151C2×C418yes—
72C2×C22⋊C4×C151C2×C414yes—
73C2×C22⋊C4×C151Q814yes—
74C2×C42×C151—24no—
75C2×C42×C151—42no—
76C2×C42×C151—42no—
77#95×C151—24no—
78#95×C151—24no—
79#95×C151—24no—
80#95×C151—24no—
81#95×C151—24no—
82#95×C151—42no—
83#95×C151—42no—
84#95×C151—42no—
85#95×C151—41no—
86#95×C151C2×C414yescomplemented
87C24×C151—22no—
88C24×C151—22no—
89C24×C151—21no—
90C24×C151—21no—
91C24×C151—21no—
92C24×C151—22no—
93C24×C151—21no—
94C24×C151—22no—
95C24×C151C22×C412yes—
96C24×C151C2×Q812yes—
97C24×C151#4112yes—
98C24×C151C2411yescharacteristic
99C22×C4×C151—22no—
100C22×C4×C151—22no—
101C22×C4×C151—22no—
102C22×C4×C151—22no—
103C22×C4×C151—22no—
104C22×C4×C151—22no—
105C22×C4×C151—22no—
106C22×C4×C151—22no—
107C22×C4×C151—22no—
108C22×C4×C151—22no—
109C22×C4×C151—22no—
110C22×C4×C151—22no—
111C22×C4×C151—22no—
112C22×C4×C151—22no—
113C22×C4×C151—22no—
114C22×C4×C151—22no—
115C22×C4×C151—22no—
116C22×C4×C151—22no—
117C22×C4×C151—21no—
118C22×C4×C151—22no—
119C22×C4×C151—22no—
120C22×C4×C151—22no—
121C22×C4×C151—22no—
122C22×C4×C151—22no—
123C22×C4×C151—22no—
124C22×C4×C151—22no—
125C22×C4×C151—21no—
126C22×C4×C151—21no—
127C22×C4×C151—21no—
128C22×C4×C151—22no—
129C22×C4×C151—22no—
130C22×C4×C151—22no—
131C22×C4×C151—22no—
132C22×C4×C151—22no—
133C22×C4×C151—22no—
134C22×C4×C151—22no—
135C22×C4×C151—22no—
136C22×C4×C151—22no—
137C22×C4×C151—22no—
138C22×C4×C151—22no—
139C22×C4×C151—22no—
140C22×C4×C151—22no—
141C22×C4×C151—22no—
142C22×C4×C151—44no—
143C22×C4×C151—48no—
144C22×C4×C151—48no—
145C22×C4×C151—44no—
146C22×C4×C151—44no—
147C22×C4×C151C22×C412yes—
148C22×C4×C151C22×C414yes—
149C22×C4×C151C22×C412yes—
150C22×C4×C151C22×C414yes—
151C22×C4×C151C2×D414yes—
152C22×C4×C151C2×D414yes—
153C22×C4×C151C2×D414yes—
154C22×C4×C151C2×Q814yes—
155C22×C4×C151#4114yes—
156C4⋊C4×C151—216no—
157C4⋊C4×C151—44no—
158C4⋊C4×C151—48no—
159C4⋊C4×C151—44no—
160C4⋊C4×C151—48no—
161C22⋊C4×C151—216no—
162C22⋊C4×C151—44no—
163C22⋊C4×C151—44no—
164C22⋊C4×C151—48no—
165C42×C151—48no—
166C23×C151—24no—
167C23×C151—22no—
168C23×C151—22no—
169C23×C151—24no—
170C23×C151—22no—
171C23×C151—22no—
172C23×C151—22no—
173C23×C151—22no—
174C23×C151—24no—
175C23×C151—24no—
176C23×C151—24no—
177C23×C151—24no—
178C23×C151—42no—
179C23×C151—42no—
180C23×C151—42no—
181C23×C151—42no—
182C23×C151—41no—
183C23×C151—42no—
184C23×C151—41no—
185C23×C151—41no—
186C23×C151—42no—
187C23×C151—41no—
188C23×C151C4×Q814yes—
189C23×C151C23×C411yescharacteristic
190C23×C151C22×D412yes—
191C23×C151C22×Q811yescharacteristic
192C23×C151C2×#4112yes—
193C23×C151C2×#4111yescharacteristic
194C23×C151H(5,𝔽2)11yescharacteristic
195C23×C151H(5,𝔽2)11yescharacteristic
196C23×C151H(5,𝔽2)11yescharacteristic
197C23×C151H(5,𝔽2)12yes—
198C23×C1512−1+411yescharacteristic
199C23×C1512−1+412yes—
200C2×C4×C151—24no—
201C2×C4×C151—24no—
202C2×C4×C151—24no—
203C2×C4×C151—24no—
204C2×C4×C151—24no—
205C2×C4×C151—24no—
206C2×C4×C151—24no—
207C2×C4×C151—24no—
208C2×C4×C151—24no—
209C2×C4×C151—22no—
210C2×C4×C151—22no—
211C2×C4×C151—24no—
212C2×C4×C151—24no—
213C2×C4×C151—24no—
214C2×C4×C151—24no—
215C2×C4×C151—24no—
216C2×C4×C151—24no—
217C2×C4×C151—24no—
218C2×C4×C151—24no—
219C2×C4×C151—24no—
220C2×C4×C151—24no—
221C2×C4×C151—24no—
222C2×C4×C151—416no—
223C2×C4×C151—42no—
224C2×C4×C151—42no—
225C2×C4×C151—42no—
226C2×C4×C151—42no—
227C2×C4×C151—42no—
228C2×C4×C151—42no—
229C2×C4×C151—42no—
230C2×C4×C151—41no—
231C2×C4×C151—42no—
232C2×C4×C151—42no—
233C2×C4×C151—42no—
234C2×C4×C151—42no—
235C2×C4×C151—42no—
236C2×C4×C151—42no—
237C2×C4×C151—42no—
238C2×C4×C151—41no—
239C2×C4×C151—41no—
240C2×C4×C151—42no—
241C2×C4×C151—42no—
242C2×C4×C151—42no—
243C2×C4×C151—42no—
244C2×C4×C151—41no—
245C2×C4×C151—42no—
246C2×C4×C151—42no—
247C2×C4×C151—42no—
248C2×C4×C151—42no—
249C2×C4×C151—42no—
250C2×C4×C151—42no—
251C2×C4×C151—42no—
252C2×C4×C151C4×D418yes—
253C22×C151—24no—
254C22×C151—28no—
255C22×C151—44no—
256C22×C151—42no—
257C22×C151—42no—
258C22×C151—42no—
259C22×C151—42no—
260C22×C151—44no—
261C22×C151—44no—
262C22×C151—42no—
263C22×C151—42no—
264C22×C151C2×C4×D412yes—
265C22×C151C2×C4×Q811yescharacteristic
266C22×C151#51811yescharacteristic
267C22×C151#52011yescharacteristic
268C22×C151#52012yes—
269C22×C151#53412yes—
270C22×C151#53612yes—
271C22×C151#53811yescharacteristic
272C22×C151#53912yes—
273C22×C151#53912yes—
274C22×C151#53911yescharacteristic
275C22×C151#54311yescharacteristic
276C22×C151#54411yescharacteristic
277C22×C151D4211yescharacteristic
278C22×C151#54612yes—
279C22×C151D4×Q812yes—
280C22×C151#55012yes—
281C22×C151#55212yes—
282C22×C151#55412yes—
283C22×C151#55911yescharacteristic
284C22×C151#56011yescharacteristic
285C22×C151#56212yes—
286C22×C151#56311yescharacteristic
287C4×C151—28no—
288C4×C151—44no—
289C4×C151—42no—
290C4×C151—42no—
291C4×C151—44no—
292C4×C151—44no—
293C4×C151—44no—
294C4×C151—82no—
295C2×C151—44no—
296C2×C151#232212yes—
297C2×C151#232911yescharacteristic
298C2×C151#236012yes—
299C2×C151#236611yescharacteristic
300C2×C151#237611yescharacteristic
301C2×C151#266811yescharacteristic
302C2×C151#267711yescharacteristic
303C2×C151#269412yes—
304C2×C151#273212yes—
305C2×C151#277111yescharacteristic
306C2×C151#280711yescharacteristic
307#14551C15111yesmaximal, characteristic, direct product factor, Sylow
308C151#1455111yescharacteristic, direct product factor, Sylow
309C2×#399C2×C15111yescharacteristic
310C2×#389C2×C15112yescomplemented
311C2×#385C2×C15112yes—
312#1445C2×C15112yescomplemented
313#1441C2×C15112yescomplemented
314#1439C2×C15111yescharacteristic
315#1437C2×C15112yes—
316#1436C2×C15112yescomplemented
317C22⋊#95C2×C15111yescharacteristic
318C24×C4C22×C15111yescharacteristic
319C22×C4⋊C4C22×C15111yescharacteristic
320C22×C4⋊C4C22×C15112yes—
321C22×C4⋊C4C22×C15112yes—
322C22×C4⋊C4C22×C15111yescharacteristic
323C22×C4⋊C4C22×C15112yes—
324C22×C22⋊C4C22×C15112yes—
325C22×C22⋊C4C22×C15112yes—
326C22×C22⋊C4C22×C15111yescharacteristic
327C22×C22⋊C4C22×C15111yescharacteristic
328C22×C42C22×C15112yes—
329#399C4×C15118yescomplemented
330#389—28no—
331#385—28no—
332C2×#95C22×C15112yes—
333C2×#95C22×C15112yes—
334C2×#95C22×C15112yes—
335C2×#95C22×C15112yes—
336C2×#95C22×C15112yes—
337C2×#95C22×C15112yes—
338C2×#95C22×C15112yes—
339C2×#95C22×C15112yes—
340C2×#95C22×C15111yescharacteristic
341C2×#95C22×C15111yescharacteristic
342C25C23×C15111yescharacteristic
343C23×C4—22no—
344C23×C4—24no—
345C23×C4—42no—
346C23×C4—41no—
347C23×C4—41no—
348C23×C4C23×C15112yes—
349C23×C4C23×C15112yes—
350C23×C4C23×C15112yes—
351C23×C4C23×C15111yescharacteristic
352C23×C4C23×C15111yescharacteristic
353C23×C4C23×C15112yes—
354C23×C4C23×C15112yes—
355C23×C4C23×C15112yes—
356C2×C4⋊C4—24no—
357C2×C4⋊C4—24no—
358C2×C4⋊C4—24no—
359C2×C4⋊C4—24no—
360C2×C4⋊C4—24no—
361C2×C4⋊C4—41no—
362C2×C4⋊C4—41no—
363C2×C4⋊C4—42no—
364C2×C4⋊C4—42no—
365C2×C4⋊C4—41no—
366C2×C4⋊C4—42no—
367C2×C4⋊C4C2×C4×C15118yescomplemented
368C2×C4⋊C4C2×C4×C15114yescomplemented
369C2×C4⋊C4D4×C15118yes—
370C2×C22⋊C4—24no—
371C2×C22⋊C4—24no—
372C2×C22⋊C4—24no—
373C2×C22⋊C4—24no—
374C2×C22⋊C4—41no—
375C2×C22⋊C4—41no—
376C2×C22⋊C4—41no—
377C2×C22⋊C4—41no—
378C2×C22⋊C4—42no—
379C2×C22⋊C4C2×C4×C15118yes—
380C2×C22⋊C4C2×C4×C15114yes—
381C2×C22⋊C4Q8×C15114yes—
382C2×C42—24no—
383C2×C42—42no—
384C2×C42—42no—
385#95—24no—
386#95—24no—
387#95—24no—
388#95—24no—
389#95—24no—
390#95—42no—
391#95—42no—
392#95—42no—
393#95—41no—
394#95C2×C4×C15114yescomplemented
395C24—22no—
396C24—22no—
397C24—21no—
398C24—21no—
399C24—21no—
400C24—22no—
401C24—21no—
402C24—22no—
403C24C22×C4×C15112yes—
404C24C2×Q8×C15112yes—
405C24#41×C15112yes—
406C24C24×C15111yescharacteristic
407C22×C4—22no—
408C22×C4—22no—
409C22×C4—22no—
410C22×C4—22no—
411C22×C4—22no—
412C22×C4—22no—
413C22×C4—22no—
414C22×C4—22no—
415C22×C4—22no—
416C22×C4—22no—
417C22×C4—22no—
418C22×C4—22no—
419C22×C4—22no—
420C22×C4—22no—
421C22×C4—22no—
422C22×C4—22no—
423C22×C4—22no—
424C22×C4—22no—
425C22×C4—21no—
426C22×C4—22no—
427C22×C4—22no—
428C22×C4—22no—
429C22×C4—22no—
430C22×C4—22no—
431C22×C4—22no—
432C22×C4—22no—
433C22×C4—21no—
434C22×C4—21no—
435C22×C4—21no—
436C22×C4—22no—
437C22×C4—22no—
438C22×C4—22no—
439C22×C4—22no—
440C22×C4—22no—
441C22×C4—22no—
442C22×C4—22no—
443C22×C4—22no—
444C22×C4—22no—
445C22×C4—22no—
446C22×C4—22no—
447C22×C4—22no—
448C22×C4—22no—
449C22×C4—22no—
450C22×C4—44no—
451C22×C4—48no—
452C22×C4—48no—
453C22×C4—44no—
454C22×C4—44no—
455C22×C4C22×C4×C15112yes—
456C22×C4C22×C4×C15114yes—
457C22×C4C22×C4×C15112yes—
458C22×C4C22×C4×C15114yes—
459C22×C4C2×D4×C15114yes—
460C22×C4C2×D4×C15114yes—
461C22×C4C2×D4×C15114yes—
462C22×C4C2×Q8×C15114yes—
463C22×C4#41×C15114yes—
464C4⋊C4—216no—
465C4⋊C4—44no—
466C4⋊C4—48no—
467C4⋊C4—44no—
468C4⋊C4—48no—
469C22⋊C4—216no—
470C22⋊C4—44no—
471C22⋊C4—44no—
472C22⋊C4—48no—
473C42—48no—
474C23—24no—
475C23—22no—
476C23—24no—
477C23—22no—
478C23—22no—
479C23—22no—
480C23—22no—
481C23—22no—
482C23—24no—
483C23—24no—
484C23—24no—
485C23—24no—
486C23—42no—
487C23—42no—
488C23—42no—
489C23—42no—
490C23—41no—
491C23—42no—
492C23—41no—
493C23—41no—
494C23—42no—
495C23—41no—
496C23C4×Q8×C15114yes—
497C23C23×C4×C15111yescharacteristic
498C23C22×D4×C15112yes—
499C23C22×Q8×C15111yescharacteristic
500C23C2×#41×C15112yes—
501C23C2×#41×C15111yescharacteristic
502C23H(5,𝔽2)×C15111yescharacteristic
503C23H(5,𝔽2)×C15111yescharacteristic
504C23H(5,𝔽2)×C15111yescharacteristic
505C23H(5,𝔽2)×C15112yes—
506C232−1+4×C15111yescharacteristic
507C232−1+4×C15112yes—
508C2×C4—24no—
509C2×C4—24no—
510C2×C4—24no—
511C2×C4—24no—
512C2×C4—24no—
513C2×C4—24no—
514C2×C4—24no—
515C2×C4—24no—
516C2×C4—24no—
517C2×C4—22no—
518C2×C4—22no—
519C2×C4—24no—
520C2×C4—24no—
521C2×C4—24no—
522C2×C4—24no—
523C2×C4—24no—
524C2×C4—24no—
525C2×C4—24no—
526C2×C4—24no—
527C2×C4—24no—
528C2×C4—24no—
529C2×C4—24no—
530C2×C4—416no—
531C2×C4—42no—
532C2×C4—42no—
533C2×C4—42no—
534C2×C4—42no—
535C2×C4—42no—
536C2×C4—42no—
537C2×C4—42no—
538C2×C4—41no—
539C2×C4—42no—
540C2×C4—42no—
541C2×C4—42no—
542C2×C4—42no—
543C2×C4—42no—
544C2×C4—42no—
545C2×C4—42no—
546C2×C4—41no—
547C2×C4—42no—
548C2×C4—41no—
549C2×C4—42no—
550C2×C4—42no—
551C2×C4—42no—
552C2×C4—41no—
553C2×C4—42no—
554C2×C4—42no—
555C2×C4—42no—
556C2×C4—42no—
557C2×C4—42no—
558C2×C4—42no—
559C2×C4—42no—
560C2×C4C4×D4×C15118yes—
561C22—28no—
562C22—24no—
563C22—42no—
564C22—42no—
565C22—42no—
566C22—42no—
567C22—44no—
568C22—44no—
569C22—42no—
570C22—42no—
571C22—44no—
572C22C2×C4×D4×C15112yes—
573C22C2×C4×Q8×C15111yescharacteristic
574C22#518×C15111yescharacteristic
575C22#520×C15112yes—
576C22#520×C15111yescharacteristic
577C22#534×C15112yes—
578C22#536×C15112yes—
579C22#538×C15111yescharacteristic
580C22#539×C15111yescharacteristic
581C22#539×C15112yes—
582C22#539×C15112yes—
583C22#543×C15111yescharacteristic
584C22#544×C15111yescharacteristic
585C22D42×C15111yescharacteristic
586C22#546×C15112yes—
587C22D4×Q8×C15112yes—
588C22#550×C15112yes—
589C22#552×C15112yes—
590C22#554×C15112yes—
591C22#559×C15111yescharacteristic
592C22#560×C15111yescharacteristic
593C22#562×C15112yes—
594C22#563×C15111yescharacteristic
595C4—28no—
596C4—44no—
597C4—42no—
598C4—42no—
599C4—44no—
600C4—44no—
601C4—44no—
602C4—82no—
603C2—44no—
604C2#2322×C15112yes—
605C2#2329×C15111yescharacteristic
606C2#2360×C15112yes—
607C2#2366×C15111yescharacteristic
608C2#2376×C15111yescharacteristic
609C2#2668×C15111yescharacteristic
610C2#2677×C15111yescharacteristic
611C2#2694×C15112yes—
612C2#2732×C15112yes—
613C2#2771×C15111yescharacteristic
614C2#2807×C15111yescharacteristic
subgroupG/H
center, socleC24×C151C24
commutatorC23C23×C4×C151
Frattini, cosocleC24C24×C151
prime radicalC25×C151C23
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C24×C151 ◁ G

Complements

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

NH ≅ G/Ntype
2. C2×#389×C151C2semidirect
4. #1445×C151C2semidirect
5. #1441×C151C2semidirect
8. #1436×C151C2semidirect
21. #399×C151C4semidirect
59. C2×C4⋊C4×C151C2×C4semidirect
60. C2×C4⋊C4×C151C2×C4semidirect
86. #95×C151C2×C4semidirect
307. #14551C151direct (N × H)
308. C151#14551direct (N × H)
310. C2×#389C2×C151semidirect
312. #1445C2×C151semidirect
313. #1441C2×C151semidirect
316. #1436C2×C151semidirect
329. #399C4×C151semidirect
367. C2×C4⋊C4C2×C4×C151semidirect
368. C2×C4⋊C4C2×C4×C151semidirect
394. #95C2×C4×C151semidirect

Maximal subgroups

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

subgroupindex
C2×#399×C1512
C2×#389×C1512
C2×#385×C1512
#1445×C1512
#1441×C1512
#1439×C1512
#1437×C1512
#1436×C1512
C22⋊#95×C1512
#14551151