Finite Group Databasebeta

← C151×#15045 #50319970

Subgroups — C151×#15045 #50319970

Order 38656.

1486 conjugacy classes of subgroups.

The subgroup lattice has 646 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#389×C151C211yesmaximal, characteristic, complemented
2C2×C4×C22⋊C4×C151C211yesmaximal, characteristic
3#1442×C151C211yesmaximal, characteristic, complemented
4#1442×C151C212yesmaximal, complemented
5#1442×C151C211yesmaximal, characteristic, complemented
6#1439×C151C212yesmaximal
7#1439×C151C211yesmaximal, characteristic
8#1439×C151C211yesmaximal, characteristic
9#1434×C151C211yesmaximal, characteristic, complemented
10#1434×C151C212yesmaximal, complemented
11C22⋊#95×C151C212yesmaximal
12C24×C4×C151C2211yescharacteristic
13C22×C4⋊C4×C151C2211yescharacteristic
14C22×C4⋊C4×C151C2211yescharacteristic
15C22×C4⋊C4×C151C2212yes—
16C22×C22⋊C4×C151C2211yescharacteristic
17C22×C22⋊C4×C151C2212yes—
18C22×C22⋊C4×C151C2211yescharacteristic
19C22×C22⋊C4×C151C2212yes—
20C22×C42×C151C2211yescharacteristic
21C22×C42×C151C2211yescharacteristic
22#389×C151—24no—
23C4×C22⋊C4×C151—24no—
24C2×#95×C151C2212yes—
25C2×#95×C151C2212yes—
26C2×#95×C151C2212yes—
27C2×#95×C151C2211yescharacteristic
28C2×#95×C151C2211yescharacteristic
29C2×#95×C151C2212yes—
30C2×#95×C151C2212yes—
31C2×#95×C151C2211yescharacteristic
32C2×#95×C151C2211yescharacteristic
33C2×#95×C151C2212yes—
34C2×#95×C151C2212yes—
35C2×#95×C151C2212yes—
36C2×#95×C151C2212yes—
37C25×C151C2311yescharacteristic
38C23×C4×C151—22no—
39C23×C4×C151—22no—
40C23×C4×C151—24no—
41C23×C4×C151—22no—
42C23×C4×C151—42no—
43C23×C4×C151C2312yes—
44C23×C4×C151C2312yes—
45C23×C4×C151C2312yes—
46C23×C4×C151C2311yescharacteristic
47C23×C4×C151C2311yescharacteristic
48C23×C4×C151C2311yescharacteristic
49C23×C4×C151C2311yescharacteristic
50C23×C4×C151C2312yes—
51C23×C4×C151C2311yescharacteristic
52C23×C4×C151C2311yescharacteristic
53C2×C4⋊C4×C151—22no—
54C2×C4⋊C4×C151—24no—
55C2×C4⋊C4×C151—24no—
56C2×C4⋊C4×C151—22no—
57C2×C4⋊C4×C151—42no—
58C2×C4⋊C4×C151—42no—
59C2×C4⋊C4×C151—42no—
60C2×C22⋊C4×C151—22no—
61C2×C22⋊C4×C151—22no—
62C2×C22⋊C4×C151—22no—
63C2×C22⋊C4×C151—22no—
64C2×C22⋊C4×C151—24no—
65C2×C22⋊C4×C151—22no—
66C2×C22⋊C4×C151—24no—
67C2×C22⋊C4×C151—24no—
68C2×C22⋊C4×C151—42no—
69C2×C22⋊C4×C151—42no—
70C2×C22⋊C4×C151—42no—
71C2×C22⋊C4×C151Q814yes—
72C2×C42×C151—22no—
73C2×C42×C151—24no—
74C2×C42×C151—42no—
75C2×C42×C151D414yes—
76#95×C151—22no—
77#95×C151—22no—
78#95×C151—24no—
79#95×C151—24no—
80#95×C151—24no—
81#95×C151—24no—
82#95×C151—22no—
83#95×C151—22no—
84#95×C151—24no—
85#95×C151—42no—
86#95×C151—42no—
87#95×C151—42no—
88#95×C151—42no—
89C24×C151—21no—
90C24×C151—21no—
91C24×C151—21no—
92C24×C151—22no—
93C24×C151—21no—
94C24×C151—22no—
95C24×C151—22no—
96C24×C151—22no—
97C24×C151C2×Q812yes—
98C24×C151#4112yes—
99C24×C151#4112yes—
100C24×C151C2411yescharacteristic
101C22×C4×C151—22no—
102C22×C4×C151—21no—
103C22×C4×C151—21no—
104C22×C4×C151—22no—
105C22×C4×C151—22no—
106C22×C4×C151—28no—
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—21no—
116C22×C4×C151—21no—
117C22×C4×C151—21no—
118C22×C4×C151—21no—
119C22×C4×C151—22no—
120C22×C4×C151—22no—
121C22×C4×C151—21no—
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—22no—
142C22×C4×C151—22no—
143C22×C4×C151—22no—
144C22×C4×C151—22no—
145C22×C4×C151—22no—
146C22×C4×C151—22no—
147C22×C4×C151—22no—
148C22×C4×C151—22no—
149C22×C4×C151—22no—
150C22×C4×C151—48no—
151C22×C4×C151—48no—
152C22×C4×C151—44no—
153C22×C4×C151—44no—
154C22×C4×C151C2×D412yes—
155C22×C4×C151C2×D412yes—
156C22×C4×C151C2×D412yes—
157C22×C4×C151C2×Q812yes—
158C22×C4×C151C2×Q812yes—
159C22×C4×C151#4112yes—
160C22×C4×C151#4112yes—
161C22×C4×C151#4114yes—
162C22×C4×C151#4112yes—
163C22×C4×C151#4114yes—
164C4⋊C4×C151—28no—
165C4⋊C4×C151—44no—
166C4⋊C4×C151—48no—
167C22⋊C4×C151—28no—
168C22⋊C4×C151—28no—
169C22⋊C4×C151—48no—
170C22⋊C4×C151—48no—
171C42×C151—44no—
172C42×C151—44no—
173C23×C151—22no—
174C23×C151—22no—
175C23×C151—22no—
176C23×C151—22no—
177C23×C151—22no—
178C23×C151—24no—
179C23×C151—22no—
180C23×C151—24no—
181C23×C151—24no—
182C23×C151—24no—
183C23×C151—24no—
184C23×C151—24no—
185C23×C151—41no—
186C23×C151—41no—
187C23×C151—42no—
188C23×C151—41no—
189C23×C151—41no—
190C23×C151—42no—
191C23×C151—42no—
192C23×C151—42no—
193C23×C151—42no—
194C23×C151—42no—
195C23×C151#12514yes—
196C23×C151C22×D411yescharacteristic
197C23×C151C22×Q811yescharacteristic
198C23×C151C2×#4111yescharacteristic
199C23×C151C2×#4111yescharacteristic
200C23×C151C2×#4111yescharacteristic
201C23×C151C2×#4111yescharacteristic
202C23×C151C2×#4112yes—
203C23×C151C2×#4111yescharacteristic
204C23×C151C2×#4112yes—
205C23×C151H(5,𝔽2)12yes—
206C23×C151H(5,𝔽2)12yes—
207C2×C4×C151—22no—
208C2×C4×C151—22no—
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—22no—
216C2×C4×C151—22no—
217C2×C4×C151—22no—
218C2×C4×C151—24no—
219C2×C4×C151—22no—
220C2×C4×C151—24no—
221C2×C4×C151—22no—
222C2×C4×C151—22no—
223C2×C4×C151—24no—
224C2×C4×C151—24no—
225C2×C4×C151—24no—
226C2×C4×C151—24no—
227C2×C4×C151—416no—
228C2×C4×C151—42no—
229C2×C4×C151—41no—
230C2×C4×C151—41no—
231C2×C4×C151—41no—
232C2×C4×C151—41no—
233C2×C4×C151—42no—
234C2×C4×C151—41no—
235C2×C4×C151—42no—
236C2×C4×C151—41no—
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—
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×C151—42no—
253C2×C4×C151—42no—
254C2×C4×C151—42no—
255C2×C4×C151—42no—
256C2×C4×C151—42no—
257C2×C4×C151—42no—
258C2×C4×C151—42no—
259C2×C4×C151—42no—
260C2×C4×C151—42no—
261C2×C4×C151—42no—
262C2×C4×C151—42no—
263C2×C4×C151—42no—
264C2×C4×C151C22⋊Q814yes—
265C2×C4×C151#12414yes—
266C22×C151—24no—
267C22×C151—28no—
268C22×C151—42no—
269C22×C151—42no—
270C22×C151—42no—
271C22×C151—42no—
272C22×C151—42no—
273C22×C151—42no—
274C22×C151—44no—
275C22×C151—44no—
276C22×C151—44no—
277C22×C151C2×C22⋊Q811yescharacteristic
278C22×C151#52511yescharacteristic
279C22×C151#52511yescharacteristic
280C22×C151#52511yescharacteristic
281C22×C151C2×#12411yescharacteristic
282C22×C151C2×#12511yescharacteristic
283C22×C151#52911yescharacteristic
284C22×C151#52911yescharacteristic
285C22×C151#52912yes—
286C22×C151#52912yes—
287C22×C151#53311yescharacteristic
288C22×C151#53411yescharacteristic
289C22×C151#53511yescharacteristic
290C22×C151#53812yes—
291C22×C151#54012yes—
292C22×C151#55112yes—
293C22×C151#55112yes—
294C22×C151#55112yes—
295C22×C151#55312yes—
296C22×C151#55312yes—
297C22×C151#55412yes—
298C22×C151#55412yes—
299C22×C151#55512yes—
300C4×C151—24no—
301C4×C151—24no—
302C4×C151—42no—
303C4×C151—42no—
304C4×C151—44no—
305C4×C151—42no—
306C4×C151—42no—
307C4×C151—82no—
308C4×C151—82no—
309C4×C151—82no—
310C2×C151—44no—
311C2×C151#239811yescharacteristic
312C2×C151#250512yes—
313C2×C151#251812yes—
314C2×C151#252212yes—
315C2×C151#252612yes—
316C2×C151#256111yescharacteristic
317C2×C151#256311yescharacteristic
318C2×C151#257911yescharacteristic
319C2×C151#259811yescharacteristic
320C2×C151#263511yescharacteristic
321C2×C151#285111yescharacteristic
322#15045C15111yesmaximal, characteristic, direct product factor, Sylow
323C151#1504511yescharacteristic, direct product factor, Sylow
324C2×#389C2×C15111yescharacteristic, complemented
325C2×C4×C22⋊C4C2×C15111yescharacteristic
326#1442C2×C15111yescharacteristic, complemented
327#1442C2×C15112yescomplemented
328#1442C2×C15111yescharacteristic, complemented
329#1439C2×C15112yes—
330#1439C2×C15111yescharacteristic
331#1439C2×C15111yescharacteristic
332#1434C2×C15111yescharacteristic, complemented
333#1434C2×C15112yescomplemented
334C22⋊#95C2×C15112yes—
335C24×C4C22×C15111yescharacteristic
336C22×C4⋊C4C22×C15111yescharacteristic
337C22×C4⋊C4C22×C15111yescharacteristic
338C22×C4⋊C4C22×C15112yes—
339C22×C22⋊C4C22×C15111yescharacteristic
340C22×C22⋊C4C22×C15112yes—
341C22×C22⋊C4C22×C15111yescharacteristic
342C22×C22⋊C4C22×C15112yes—
343C22×C42C22×C15111yescharacteristic
344C22×C42C22×C15111yescharacteristic
345#389—24no—
346C4×C22⋊C4—24no—
347C2×#95C22×C15112yes—
348C2×#95C22×C15112yes—
349C2×#95C22×C15112yes—
350C2×#95C22×C15112yes—
351C2×#95C22×C15111yescharacteristic
352C2×#95C22×C15111yescharacteristic
353C2×#95C22×C15112yes—
354C2×#95C22×C15111yescharacteristic
355C2×#95C22×C15111yescharacteristic
356C2×#95C22×C15112yes—
357C2×#95C22×C15112yes—
358C2×#95C22×C15112yes—
359C2×#95C22×C15112yes—
360C25C23×C15111yescharacteristic
361C23×C4—22no—
362C23×C4—22no—
363C23×C4—22no—
364C23×C4—24no—
365C23×C4—42no—
366C23×C4C23×C15112yes—
367C23×C4C23×C15112yes—
368C23×C4C23×C15112yes—
369C23×C4C23×C15111yescharacteristic
370C23×C4C23×C15112yes—
371C23×C4C23×C15111yescharacteristic
372C23×C4C23×C15111yescharacteristic
373C23×C4C23×C15111yescharacteristic
374C23×C4C23×C15111yescharacteristic
375C23×C4C23×C15111yescharacteristic
376C2×C4⋊C4—24no—
377C2×C4⋊C4—22no—
378C2×C4⋊C4—24no—
379C2×C4⋊C4—22no—
380C2×C4⋊C4—42no—
381C2×C4⋊C4—42no—
382C2×C4⋊C4—42no—
383C2×C22⋊C4—22no—
384C2×C22⋊C4—22no—
385C2×C22⋊C4—22no—
386C2×C22⋊C4—22no—
387C2×C22⋊C4—22no—
388C2×C22⋊C4—24no—
389C2×C22⋊C4—24no—
390C2×C22⋊C4—24no—
391C2×C22⋊C4—42no—
392C2×C22⋊C4—42no—
393C2×C22⋊C4—42no—
394C2×C22⋊C4Q8×C15114yes—
395C2×C42—24no—
396C2×C42—22no—
397C2×C42—42no—
398C2×C42D4×C15114yes—
399#95—24no—
400#95—24no—
401#95—24no—
402#95—22no—
403#95—22no—
404#95—24no—
405#95—22no—
406#95—22no—
407#95—24no—
408#95—42no—
409#95—42no—
410#95—42no—
411#95—42no—
412C24—21no—
413C24—21no—
414C24—21no—
415C24—22no—
416C24—21no—
417C24—22no—
418C24—22no—
419C24—22no—
420C24C2×Q8×C15112yes—
421C24#41×C15112yes—
422C24#41×C15112yes—
423C24C24×C15111yescharacteristic
424C22×C4—22no—
425C22×C4—21no—
426C22×C4—21no—
427C22×C4—22no—
428C22×C4—22no—
429C22×C4—28no—
430C22×C4—21no—
431C22×C4—21no—
432C22×C4—21no—
433C22×C4—22no—
434C22×C4—22no—
435C22×C4—22no—
436C22×C4—22no—
437C22×C4—22no—
438C22×C4—21no—
439C22×C4—21no—
440C22×C4—21no—
441C22×C4—21no—
442C22×C4—22no—
443C22×C4—22no—
444C22×C4—21no—
445C22×C4—22no—
446C22×C4—22no—
447C22×C4—22no—
448C22×C4—22no—
449C22×C4—22no—
450C22×C4—22no—
451C22×C4—22no—
452C22×C4—22no—
453C22×C4—22no—
454C22×C4—22no—
455C22×C4—22no—
456C22×C4—22no—
457C22×C4—22no—
458C22×C4—22no—
459C22×C4—22no—
460C22×C4—22no—
461C22×C4—22no—
462C22×C4—22no—
463C22×C4—22no—
464C22×C4—22no—
465C22×C4—22no—
466C22×C4—22no—
467C22×C4—22no—
468C22×C4—22no—
469C22×C4—22no—
470C22×C4—22no—
471C22×C4—22no—
472C22×C4—22no—
473C22×C4—48no—
474C22×C4—48no—
475C22×C4—44no—
476C22×C4—44no—
477C22×C4C2×D4×C15112yes—
478C22×C4C2×D4×C15112yes—
479C22×C4C2×D4×C15112yes—
480C22×C4C2×Q8×C15112yes—
481C22×C4C2×Q8×C15112yes—
482C22×C4#41×C15112yes—
483C22×C4#41×C15112yes—
484C22×C4#41×C15114yes—
485C22×C4#41×C15112yes—
486C22×C4#41×C15114yes—
487C4⋊C4—28no—
488C4⋊C4—44no—
489C4⋊C4—48no—
490C22⋊C4—28no—
491C22⋊C4—28no—
492C22⋊C4—48no—
493C22⋊C4—48no—
494C42—44no—
495C42—44no—
496C23—22no—
497C23—22no—
498C23—22no—
499C23—22no—
500C23—22no—
501C23—24no—
502C23—22no—
503C23—24no—
504C23—24no—
505C23—24no—
506C23—24no—
507C23—24no—
508C23—41no—
509C23—41no—
510C23—42no—
511C23—41no—
512C23—41no—
513C23—42no—
514C23—42no—
515C23—42no—
516C23—42no—
517C23—42no—
518C23#125×C15114yes—
519C23C22×D4×C15111yescharacteristic
520C23C22×Q8×C15111yescharacteristic
521C23C2×#41×C15111yescharacteristic
522C23C2×#41×C15111yescharacteristic
523C23C2×#41×C15111yescharacteristic
524C23C2×#41×C15111yescharacteristic
525C23C2×#41×C15112yes—
526C23C2×#41×C15111yescharacteristic
527C23C2×#41×C15112yes—
528C23H(5,𝔽2)×C15112yes—
529C23H(5,𝔽2)×C15112yes—
530C2×C4—22no—
531C2×C4—22no—
532C2×C4—22no—
533C2×C4—22no—
534C2×C4—24no—
535C2×C4—24no—
536C2×C4—24no—
537C2×C4—24no—
538C2×C4—22no—
539C2×C4—22no—
540C2×C4—22no—
541C2×C4—24no—
542C2×C4—22no—
543C2×C4—24no—
544C2×C4—22no—
545C2×C4—22no—
546C2×C4—24no—
547C2×C4—24no—
548C2×C4—24no—
549C2×C4—24no—
550C2×C4—416no—
551C2×C4—42no—
552C2×C4—41no—
553C2×C4—41no—
554C2×C4—41no—
555C2×C4—41no—
556C2×C4—42no—
557C2×C4—41no—
558C2×C4—42no—
559C2×C4—41no—
560C2×C4—42no—
561C2×C4—42no—
562C2×C4—42no—
563C2×C4—42no—
564C2×C4—42no—
565C2×C4—42no—
566C2×C4—42no—
567C2×C4—42no—
568C2×C4—42no—
569C2×C4—42no—
570C2×C4—42no—
571C2×C4—42no—
572C2×C4—42no—
573C2×C4—42no—
574C2×C4—42no—
575C2×C4—42no—
576C2×C4—42no—
577C2×C4—42no—
578C2×C4—42no—
579C2×C4—42no—
580C2×C4—42no—
581C2×C4—42no—
582C2×C4—42no—
583C2×C4—42no—
584C2×C4—42no—
585C2×C4—42no—
586C2×C4—42no—
587C2×C4C22⋊Q8×C15114yes—
588C2×C4#124×C15114yes—
589C22—24no—
590C22—28no—
591C22—42no—
592C22—42no—
593C22—42no—
594C22—44no—
595C22—44no—
596C22—44no—
597C22—42no—
598C22—42no—
599C22—42no—
600C22C2×C22⋊Q8×C15111yescharacteristic
601C22#525×C15111yescharacteristic
602C22#525×C15111yescharacteristic
603C22#525×C15111yescharacteristic
604C22C2×#124×C15111yescharacteristic
605C22C2×#125×C15111yescharacteristic
606C22#529×C15111yescharacteristic
607C22#529×C15111yescharacteristic
608C22#529×C15112yes—
609C22#529×C15112yes—
610C22#533×C15111yescharacteristic
611C22#534×C15111yescharacteristic
612C22#535×C15111yescharacteristic
613C22#538×C15112yes—
614C22#540×C15112yes—
615C22#551×C15112yes—
616C22#551×C15112yes—
617C22#551×C15112yes—
618C22#553×C15112yes—
619C22#553×C15112yes—
620C22#554×C15112yes—
621C22#554×C15112yes—
622C22#555×C15112yes—
623C4—24no—
624C4—24no—
625C4—44no—
626C4—42no—
627C4—42no—
628C4—42no—
629C4—42no—
630C4—82no—
631C4—82no—
632C4—82no—
633C2—44no—
634C2#2398×C15111yescharacteristic
635C2#2505×C15112yes—
636C2#2518×C15112yes—
637C2#2522×C15112yes—
638C2#2526×C15112yes—
639C2#2561×C15111yescharacteristic
640C2#2563×C15111yescharacteristic
641C2#2579×C15111yescharacteristic
642C2#2598×C15111yescharacteristic
643C2#2635×C15111yescharacteristic
644C2#2851×C15111yescharacteristic
subgroupG/H
center, socleC24×C151C24
commutator, Frattini, cosocleC24C24×C151
prime radicalC25×C151C23
LCSG ▷ C24 ▷ C1
UCSC1 ◁ C24×C151 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×#389×C151C2semidirect
3. #1442×C151C2semidirect
4. #1442×C151C2semidirect
5. #1442×C151C2semidirect
9. #1434×C151C2semidirect
10. #1434×C151C2semidirect
322. #15045C151direct (N × H)
323. C151#15045direct (N × H)
324. C2×#389C2×C151semidirect
326. #1442C2×C151semidirect
327. #1442C2×C151semidirect
328. #1442C2×C151semidirect
332. #1434C2×C151semidirect
333. #1434C2×C151semidirect

Maximal subgroups

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

subgroupindex
C2×#389×C1512
C2×C4×C22⋊C4×C1512
#1442×C1512
#1439×C1512
#1434×C1512
C22⋊#95×C1512
#15045151