Finite Group Databasebeta

← C151×#14627 #50319552

Subgroups — C151×#14627 #50319552

Order 38656.

1434 conjugacy classes of subgroups.

The subgroup lattice has 602 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#397×C151C211yesmaximal, characteristic
2C2×#385×C151C212yesmaximal
3#1444×C151C212yesmaximal, complemented
4#1443×C151C212yesmaximal, complemented
5#1442×C151C212yesmaximal, complemented
6#1441×C151C212yesmaximal, complemented
7#1440×C151C212yesmaximal
8#1439×C151C211yesmaximal, characteristic
9C22⋊#95×C151C211yesmaximal, characteristic
10C24×C4×C151C2211yescharacteristic
11C22×C4⋊C4×C151C2212yes—
12C22×C4⋊C4×C151C2212yes—
13C22×C4⋊C4×C151C2211yescharacteristic
14C22×C4⋊C4×C151C2211yescharacteristic
15C22×C22⋊C4×C151C2212yes—
16C22×C22⋊C4×C151C2211yescharacteristic
17C22×C22⋊C4×C151C2212yes—
18C22×C22⋊C4×C151C2211yescharacteristic
19#397×C151C418yescomplemented
20#385×C151—28no—
21C2×#95×C151C2212yes—
22C2×#95×C151C2212yes—
23C2×#95×C151C2212yes—
24C2×#95×C151C2212yes—
25C2×#95×C151C2212yes—
26C2×#95×C151C2211yescharacteristic
27C2×#95×C151C2212yes—
28C2×#95×C151C2212yes—
29C2×#95×C151C2212yes—
30C2×#95×C151C2212yes—
31C2×#95×C151C2211yescharacteristic
32C2×#95×C151C2212yes—
33C25×C151C2311yescharacteristic
34C23×C4×C151—42no—
35C23×C4×C151—42no—
36C23×C4×C151—41no—
37C23×C4×C151—41no—
38C23×C4×C151D414yes—
39C23×C4×C151C2312yes—
40C23×C4×C151C2312yes—
41C23×C4×C151C2312yes—
42C23×C4×C151C2312yes—
43C23×C4×C151C2311yescharacteristic
44C23×C4×C151C2311yescharacteristic
45C23×C4×C151C2312yes—
46C23×C4×C151C2312yes—
47C2×C4⋊C4×C151—24no—
48C2×C4⋊C4×C151—24no—
49C2×C4⋊C4×C151—41no—
50C2×C4⋊C4×C151—41no—
51C2×C4⋊C4×C151—42no—
52C2×C4⋊C4×C151—42no—
53C2×C4⋊C4×C151—42no—
54C2×C4⋊C4×C151—42no—
55C2×C4⋊C4×C151—42no—
56C2×C4⋊C4×C151—41no—
57C2×C4⋊C4×C151C2×C414yescomplemented
58C2×C22⋊C4×C151—24no—
59C2×C22⋊C4×C151—24no—
60C2×C22⋊C4×C151—24no—
61C2×C22⋊C4×C151—22no—
62C2×C22⋊C4×C151—41no—
63C2×C22⋊C4×C151—41no—
64C2×C22⋊C4×C151—41no—
65C2×C22⋊C4×C151—41no—
66C2×C22⋊C4×C151—42no—
67C2×C22⋊C4×C151—42no—
68C2×C22⋊C4×C151C2×C418yes—
69C2×C22⋊C4×C151C2×C414yes—
70#95×C151—24no—
71#95×C151—24no—
72#95×C151—42no—
73#95×C151—42no—
74#95×C151—41no—
75#95×C151—42no—
76#95×C151—42no—
77#95×C151—42no—
78#95×C151—42no—
79#95×C151—42no—
80#95×C151C2×C414yescomplemented
81#95×C151C2×C418yescomplemented
82C24×C151—21no—
83C24×C151—21no—
84C24×C151—22no—
85C24×C151—22no—
86C24×C151—21no—
87C24×C151—22no—
88C24×C151—22no—
89C24×C151—21no—
90C24×C151C22×C412yes—
91C24×C151C2×D412yes—
92C24×C151#4112yes—
93C24×C151C2411yescharacteristic
94C22×C4×C151—22no—
95C22×C4×C151—22no—
96C22×C4×C151—22no—
97C22×C4×C151—22no—
98C22×C4×C151—22no—
99C22×C4×C151—21no—
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—21no—
108C22×C4×C151—21no—
109C22×C4×C151—21no—
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—22no—
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—22no—
126C22×C4×C151—22no—
127C22×C4×C151—22no—
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—44no—
142C22×C4×C151—48no—
143C22×C4×C151—48no—
144C22×C4×C151—44no—
145C22×C4×C151—44no—
146C22×C4×C151C22×C414yes—
147C22×C4×C151C22×C412yes—
148C22×C4×C151C22×C414yes—
149C22×C4×C151C22×C412yes—
150C22×C4×C151C2×D414yes—
151C4⋊C4×C151—44no—
152C4⋊C4×C151—48no—
153C4⋊C4×C151—48no—
154C4⋊C4×C151—44no—
155C22⋊C4×C151—216no—
156C22⋊C4×C151—44no—
157C22⋊C4×C151—48no—
158C22⋊C4×C151—44no—
159C23×C151—22no—
160C23×C151—24no—
161C23×C151—24no—
162C23×C151—22no—
163C23×C151—24no—
164C23×C151—22no—
165C23×C151—24no—
166C23×C151—22no—
167C23×C151—22no—
168C23×C151—24no—
169C23×C151—24no—
170C23×C151—22no—
171C23×C151—42no—
172C23×C151—41no—
173C23×C151—41no—
174C23×C151—42no—
175C23×C151—42no—
176C23×C151—42no—
177C23×C151—41no—
178C23×C151—41no—
179C23×C151—42no—
180C23×C151—42no—
181C23×C151C4×D414yes—
182C23×C151C23×C411yescharacteristic
183C23×C151C22×D411yescharacteristic
184C23×C151C2×#4111yescharacteristic
185C23×C151H(5,𝔽2)11yescharacteristic
186C23×C151H(5,𝔽2)11yescharacteristic
187C23×C151H(5,𝔽2)11yescharacteristic
188C23×C151H(5,𝔽2)12yes—
189C23×C151H(5,𝔽2)12yes—
190C23×C1512−1+412yes—
191C23×C1512−1+412yes—
192C23×C1512−1+411yescharacteristic
193C2×C4×C151—24no—
194C2×C4×C151—24no—
195C2×C4×C151—22no—
196C2×C4×C151—22no—
197C2×C4×C151—24no—
198C2×C4×C151—24no—
199C2×C4×C151—24no—
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—416no—
207C2×C4×C151—42no—
208C2×C4×C151—42no—
209C2×C4×C151—42no—
210C2×C4×C151—42no—
211C2×C4×C151—42no—
212C2×C4×C151—42no—
213C2×C4×C151—42no—
214C2×C4×C151—42no—
215C2×C4×C151—41no—
216C2×C4×C151—42no—
217C2×C4×C151—42no—
218C2×C4×C151—42no—
219C2×C4×C151—41no—
220C2×C4×C151—42no—
221C2×C4×C151—42no—
222C2×C4×C151—42no—
223C2×C4×C151—41no—
224C2×C4×C151—41no—
225C2×C4×C151—42no—
226C2×C4×C151—42no—
227C2×C4×C151—42no—
228C2×C4×C151—42no—
229C2×C4×C151—42no—
230C2×C4×C151—42no—
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—42no—
239C2×C4×C151—42no—
240C2×C4×C151—42no—
241C2×C4×C151—42no—
242C2×C4×C151—42no—
243C2×C4×C151—42no—
244C2×C4×C151—42no—
245C2×C4×C151—42no—
246C22×C151—28no—
247C22×C151—24no—
248C22×C151—42no—
249C22×C151—44no—
250C22×C151—42no—
251C22×C151—42no—
252C22×C151—42no—
253C22×C151—42no—
254C22×C151—44no—
255C22×C151—42no—
256C22×C151—44no—
257C22×C151C2×C4×D411yescharacteristic
258C22×C151#51811yescharacteristic
259C22×C151#52012yes—
260C22×C151#52012yes—
261C22×C151#52011yescharacteristic
262C22×C151#53411yescharacteristic
263C22×C151#53412yes—
264C22×C151#53612yes—
265C22×C151#53711yescharacteristic
266C22×C151#53811yescharacteristic
267C22×C151#53912yes—
268C22×C151#53912yes—
269C22×C151#53911yescharacteristic
270C22×C151#56012yes—
271C22×C151#56011yescharacteristic
272C22×C151H(3,𝔽4)11yescharacteristic
273C22×C151#56212yes—
274C22×C151#56212yes—
275C22×C151#56312yes—
276C22×C151#56311yescharacteristic
277C22×C151#56311yescharacteristic
278C22×C151#56312yes—
279C22×C151#56312yes—
280C4×C151—44no—
281C4×C151—44no—
282C4×C151—42no—
283C4×C151—42no—
284C4×C151—44no—
285C4×C151—82no—
286C4×C151—82no—
287C4×C151—82no—
288C2×C151—44no—
289C2×C151#232212yes—
290C2×C151#232511yescharacteristic
291C2×C151#237611yescharacteristic
292C2×C151#237911yescharacteristic
293C2×C151#238312yes—
294C2×C151#281211yescharacteristic
295C2×C151#281412yes—
296C2×C151#281711yescharacteristic
297C2×C151#282712yes—
298C2×C151#283411yescharacteristic
299C2×C151#283511yescharacteristic
300#14627C15111yesmaximal, characteristic, direct product factor, Sylow
301C151#1462711yescharacteristic, direct product factor, Sylow
302C2×#397C2×C15111yescharacteristic
303C2×#385C2×C15112yes—
304#1444C2×C15112yescomplemented
305#1443C2×C15112yescomplemented
306#1442C2×C15112yescomplemented
307#1441C2×C15112yescomplemented
308#1440C2×C15112yes—
309#1439C2×C15111yescharacteristic
310C22⋊#95C2×C15111yescharacteristic
311C24×C4C22×C15111yescharacteristic
312C22×C4⋊C4C22×C15112yes—
313C22×C4⋊C4C22×C15112yes—
314C22×C4⋊C4C22×C15111yescharacteristic
315C22×C4⋊C4C22×C15111yescharacteristic
316C22×C22⋊C4C22×C15112yes—
317C22×C22⋊C4C22×C15111yescharacteristic
318C22×C22⋊C4C22×C15112yes—
319C22×C22⋊C4C22×C15111yescharacteristic
320#397C4×C15118yescomplemented
321#385—28no—
322C2×#95C22×C15112yes—
323C2×#95C22×C15112yes—
324C2×#95C22×C15112yes—
325C2×#95C22×C15112yes—
326C2×#95C22×C15112yes—
327C2×#95C22×C15111yescharacteristic
328C2×#95C22×C15112yes—
329C2×#95C22×C15112yes—
330C2×#95C22×C15112yes—
331C2×#95C22×C15112yes—
332C2×#95C22×C15111yescharacteristic
333C2×#95C22×C15112yes—
334C25C23×C15111yescharacteristic
335C23×C4—42no—
336C23×C4—42no—
337C23×C4—41no—
338C23×C4—41no—
339C23×C4D4×C15114yes—
340C23×C4C23×C15112yes—
341C23×C4C23×C15112yes—
342C23×C4C23×C15112yes—
343C23×C4C23×C15112yes—
344C23×C4C23×C15112yes—
345C23×C4C23×C15111yescharacteristic
346C23×C4C23×C15111yescharacteristic
347C23×C4C23×C15112yes—
348C2×C4⋊C4—24no—
349C2×C4⋊C4—24no—
350C2×C4⋊C4—41no—
351C2×C4⋊C4—41no—
352C2×C4⋊C4—42no—
353C2×C4⋊C4—42no—
354C2×C4⋊C4—42no—
355C2×C4⋊C4—42no—
356C2×C4⋊C4—42no—
357C2×C4⋊C4—41no—
358C2×C4⋊C4C2×C4×C15114yescomplemented
359C2×C22⋊C4—24no—
360C2×C22⋊C4—24no—
361C2×C22⋊C4—22no—
362C2×C22⋊C4—24no—
363C2×C22⋊C4—41no—
364C2×C22⋊C4—41no—
365C2×C22⋊C4—41no—
366C2×C22⋊C4—41no—
367C2×C22⋊C4—42no—
368C2×C22⋊C4—42no—
369C2×C22⋊C4C2×C4×C15118yes—
370C2×C22⋊C4C2×C4×C15114yes—
371#95—24no—
372#95—24no—
373#95—42no—
374#95—42no—
375#95—41no—
376#95—42no—
377#95—42no—
378#95—42no—
379#95—42no—
380#95—42no—
381#95C2×C4×C15114yescomplemented
382#95C2×C4×C15118yescomplemented
383C24—21no—
384C24—21no—
385C24—22no—
386C24—22no—
387C24—21no—
388C24—22no—
389C24—22no—
390C24—21no—
391C24C22×C4×C15112yes—
392C24C2×D4×C15112yes—
393C24#41×C15112yes—
394C24C24×C15111yescharacteristic
395C22×C4—22no—
396C22×C4—22no—
397C22×C4—22no—
398C22×C4—22no—
399C22×C4—22no—
400C22×C4—21no—
401C22×C4—22no—
402C22×C4—22no—
403C22×C4—22no—
404C22×C4—22no—
405C22×C4—22no—
406C22×C4—22no—
407C22×C4—22no—
408C22×C4—21no—
409C22×C4—21no—
410C22×C4—21no—
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—22no—
426C22×C4—22no—
427C22×C4—22no—
428C22×C4—22no—
429C22×C4—22no—
430C22×C4—22no—
431C22×C4—22no—
432C22×C4—22no—
433C22×C4—22no—
434C22×C4—22no—
435C22×C4—22no—
436C22×C4—22no—
437C22×C4—22no—
438C22×C4—22no—
439C22×C4—22no—
440C22×C4—22no—
441C22×C4—22no—
442C22×C4—44no—
443C22×C4—48no—
444C22×C4—44no—
445C22×C4—48no—
446C22×C4—44no—
447C22×C4C22×C4×C15114yes—
448C22×C4C22×C4×C15112yes—
449C22×C4C22×C4×C15114yes—
450C22×C4C22×C4×C15112yes—
451C22×C4C2×D4×C15114yes—
452C4⋊C4—44no—
453C4⋊C4—48no—
454C4⋊C4—48no—
455C4⋊C4—44no—
456C22⋊C4—216no—
457C22⋊C4—44no—
458C22⋊C4—48no—
459C22⋊C4—44no—
460C23—22no—
461C23—24no—
462C23—24no—
463C23—22no—
464C23—24no—
465C23—22no—
466C23—24no—
467C23—22no—
468C23—22no—
469C23—24no—
470C23—24no—
471C23—22no—
472C23—41no—
473C23—42no—
474C23—41no—
475C23—42no—
476C23—42no—
477C23—41no—
478C23—41no—
479C23—42no—
480C23—42no—
481C23—42no—
482C23C4×D4×C15114yes—
483C23C23×C4×C15111yescharacteristic
484C23C22×D4×C15111yescharacteristic
485C23C2×#41×C15111yescharacteristic
486C23H(5,𝔽2)×C15111yescharacteristic
487C23H(5,𝔽2)×C15111yescharacteristic
488C23H(5,𝔽2)×C15111yescharacteristic
489C23H(5,𝔽2)×C15112yes—
490C23H(5,𝔽2)×C15112yes—
491C232−1+4×C15112yes—
492C232−1+4×C15112yes—
493C232−1+4×C15111yescharacteristic
494C2×C4—24no—
495C2×C4—24no—
496C2×C4—22no—
497C2×C4—22no—
498C2×C4—24no—
499C2×C4—24no—
500C2×C4—24no—
501C2×C4—24no—
502C2×C4—24no—
503C2×C4—24no—
504C2×C4—24no—
505C2×C4—24no—
506C2×C4—24no—
507C2×C4—416no—
508C2×C4—42no—
509C2×C4—42no—
510C2×C4—42no—
511C2×C4—42no—
512C2×C4—42no—
513C2×C4—42no—
514C2×C4—42no—
515C2×C4—42no—
516C2×C4—42no—
517C2×C4—42no—
518C2×C4—42no—
519C2×C4—41no—
520C2×C4—41no—
521C2×C4—42no—
522C2×C4—42no—
523C2×C4—42no—
524C2×C4—41no—
525C2×C4—41no—
526C2×C4—42no—
527C2×C4—42no—
528C2×C4—42no—
529C2×C4—42no—
530C2×C4—42no—
531C2×C4—42no—
532C2×C4—42no—
533C2×C4—42no—
534C2×C4—42no—
535C2×C4—42no—
536C2×C4—42no—
537C2×C4—42no—
538C2×C4—42no—
539C2×C4—42no—
540C2×C4—42no—
541C2×C4—42no—
542C2×C4—42no—
543C2×C4—42no—
544C2×C4—42no—
545C2×C4—42no—
546C2×C4—42no—
547C22—28no—
548C22—24no—
549C22—42no—
550C22—42no—
551C22—44no—
552C22—42no—
553C22—44no—
554C22—42no—
555C22—44no—
556C22—42no—
557C22—42no—
558C22C2×C4×D4×C15111yescharacteristic
559C22#518×C15111yescharacteristic
560C22#520×C15112yes—
561C22#520×C15112yes—
562C22#520×C15111yescharacteristic
563C22#534×C15112yes—
564C22#534×C15111yescharacteristic
565C22#536×C15112yes—
566C22#537×C15111yescharacteristic
567C22#538×C15111yescharacteristic
568C22#539×C15112yes—
569C22#539×C15112yes—
570C22#539×C15111yescharacteristic
571C22#560×C15111yescharacteristic
572C22#560×C15112yes—
573C22H(3,𝔽4)×C15111yescharacteristic
574C22#562×C15112yes—
575C22#562×C15112yes—
576C22#563×C15111yescharacteristic
577C22#563×C15111yescharacteristic
578C22#563×C15112yes—
579C22#563×C15112yes—
580C22#563×C15112yes—
581C4—42no—
582C4—42no—
583C4—44no—
584C4—44no—
585C4—44no—
586C4—82no—
587C4—82no—
588C4—82no—
589C2—44no—
590C2#2322×C15112yes—
591C2#2325×C15111yescharacteristic
592C2#2376×C15111yescharacteristic
593C2#2379×C15111yescharacteristic
594C2#2383×C15112yes—
595C2#2812×C15111yescharacteristic
596C2#2814×C15112yes—
597C2#2817×C15111yescharacteristic
598C2#2827×C15112yes—
599C2#2834×C15111yescharacteristic
600C2#2835×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
3. #1444×C151C2semidirect
4. #1443×C151C2semidirect
5. #1442×C151C2semidirect
6. #1441×C151C2semidirect
19. #397×C151C4semidirect
57. C2×C4⋊C4×C151C2×C4semidirect
80. #95×C151C2×C4semidirect
81. #95×C151C2×C4semidirect
300. #14627C151direct (N × H)
301. C151#14627direct (N × H)
304. #1444C2×C151semidirect
305. #1443C2×C151semidirect
306. #1442C2×C151semidirect
307. #1441C2×C151semidirect
320. #397C4×C151semidirect
358. C2×C4⋊C4C2×C4×C151semidirect
381. #95C2×C4×C151semidirect
382. #95C2×C4×C151semidirect

Maximal subgroups

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

subgroupindex
C2×#397×C1512
C2×#385×C1512
#1444×C1512
#1443×C1512
#1442×C1512
#1441×C1512
#1440×C1512
#1439×C1512
C22⋊#95×C1512
#14627151