Finite Group Databasebeta

← C151×#15100 #50320025

Subgroups — C151×#15100 #50320025

Order 38656.

1378 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×#388×C151C211yesmaximal, characteristic
2C2×C4×C4⋊C4×C151C211yesmaximal, characteristic, complemented
3#1444×C151C211yesmaximal, characteristic, complemented
4#1442×C151C212yesmaximal, complemented
5#1442×C151C211yesmaximal, characteristic, complemented
6#1439×C151C212yesmaximal
7#1439×C151C211yesmaximal, characteristic
8#1439×C151C211yesmaximal, characteristic
9#1437×C151C212yesmaximal
10#1436×C151C212yesmaximal, complemented
11#1434×C151C211yesmaximal, characteristic, complemented
12C22×C4⋊C4×C151C2211yescharacteristic
13C22×C4⋊C4×C151C2211yescharacteristic
14C22×C4⋊C4×C151C2212yes—
15C22×C4⋊C4×C151C2211yescharacteristic
16C22×C22⋊C4×C151C2211yescharacteristic
17C22×C22⋊C4×C151C2212yes—
18C22×C22⋊C4×C151C2211yescharacteristic
19C22×C22⋊C4×C151C2212yes—
20C22×C22⋊C4×C151C2211yescharacteristic
21C22×C42×C151C2211yescharacteristic
22C22×C42×C151C2212yes—
23#388×C151—24no—
24C4×C4⋊C4×C151—24no—
25C2×#95×C151C2212yes—
26C2×#95×C151C2211yescharacteristic
27C2×#95×C151C2212yes—
28C2×#95×C151C2211yescharacteristic
29C2×#95×C151C2211yescharacteristic
30C2×#95×C151C2212yes—
31C2×#95×C151C2212yes—
32C2×#95×C151C2212yes—
33C2×#95×C151C2211yescharacteristic
34C2×#95×C151C2212yes—
35C2×#95×C151C2212yes—
36C2×#95×C151C2212yes—
37C25×C151C2311yescharacteristic
38C23×C4×C151C2312yes—
39C23×C4×C151C2311yescharacteristic
40C23×C4×C151C2311yescharacteristic
41C23×C4×C151C2311yescharacteristic
42C23×C4×C151C2311yescharacteristic
43C23×C4×C151C2312yes—
44C23×C4×C151C2312yes—
45C23×C4×C151C2312yes—
46C23×C4×C151C2311yescharacteristic
47C23×C4×C151C2311yescharacteristic
48C2×C4⋊C4×C151—22no—
49C2×C4⋊C4×C151—22no—
50C2×C4⋊C4×C151—24no—
51C2×C4⋊C4×C151—24no—
52C2×C4⋊C4×C151—22no—
53C2×C4⋊C4×C151—24no—
54C2×C4⋊C4×C151—42no—
55C2×C4⋊C4×C151—42no—
56C2×C4⋊C4×C151—42no—
57C2×C22⋊C4×C151—22no—
58C2×C22⋊C4×C151—22no—
59C2×C22⋊C4×C151—22no—
60C2×C22⋊C4×C151—22no—
61C2×C22⋊C4×C151—24no—
62C2×C22⋊C4×C151—24no—
63C2×C22⋊C4×C151—24no—
64C2×C22⋊C4×C151—22no—
65C2×C22⋊C4×C151—22no—
66C2×C22⋊C4×C151—42no—
67C2×C22⋊C4×C151—42no—
68C2×C22⋊C4×C151—42no—
69C2×C22⋊C4×C151—42no—
70C2×C22⋊C4×C151Q814yes—
71C2×C42×C151—22no—
72C2×C42×C151—22no—
73C2×C42×C151—24no—
74C2×C42×C151—42no—
75C2×C42×C151—42no—
76C2×C42×C151D414yes—
77#95×C151—24no—
78#95×C151—22no—
79#95×C151—22no—
80#95×C151—22no—
81#95×C151—24no—
82#95×C151—24no—
83#95×C151—24no—
84#95×C151—24no—
85#95×C151—22no—
86#95×C151—42no—
87#95×C151—42no—
88#95×C151—42no—
89C24×C151—21no—
90C24×C151—21no—
91C24×C151—22no—
92C24×C151—22no—
93C24×C151—21no—
94C24×C151—21no—
95C24×C151—22no—
96C24×C151—21no—
97C24×C151—21no—
98C24×C151—22no—
99C24×C151C2×Q812yes—
100C24×C151C2411yescharacteristic
101C22×C4×C151—21no—
102C22×C4×C151—21no—
103C22×C4×C151—22no—
104C22×C4×C151—22no—
105C22×C4×C151—21no—
106C22×C4×C151—21no—
107C22×C4×C151—22no—
108C22×C4×C151—22no—
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—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—21no—
134C22×C4×C151—21no—
135C22×C4×C151—22no—
136C22×C4×C151—22no—
137C22×C4×C151—22no—
138C22×C4×C151—22no—
139C22×C4×C151—22no—
140C22×C4×C151—21no—
141C22×C4×C151—21no—
142C22×C4×C151—22no—
143C22×C4×C151—22no—
144C22×C4×C151—21no—
145C22×C4×C151—22no—
146C22×C4×C151—22no—
147C22×C4×C151—22no—
148C22×C4×C151—22no—
149C22×C4×C151—21no—
150C22×C4×C151C2×D412yes—
151C22×C4×C151C2×D412yes—
152C22×C4×C151C2×D412yes—
153C22×C4×C151C2×Q812yes—
154C22×C4×C151C2×Q812yes—
155C22×C4×C151#4114yes—
156C22×C4×C151#4114yes—
157C22×C4×C151#4114yes—
158C22×C4×C151#4112yes—
159C22×C4×C151#4112yes—
160C22×C4×C151#4112yes—
161C4⋊C4×C151—28no—
162C4⋊C4×C151—28no—
163C4⋊C4×C151—44no—
164C4⋊C4×C151—48no—
165C22⋊C4×C151—28no—
166C22⋊C4×C151—48no—
167C22⋊C4×C151—44no—
168C22⋊C4×C151—48no—
169C22⋊C4×C151—44no—
170C42×C151—28no—
171C42×C151—48no—
172C23×C151—22no—
173C23×C151—24no—
174C23×C151—22no—
175C23×C151—24no—
176C23×C151—22no—
177C23×C151—41no—
178C23×C151—41no—
179C23×C151—41no—
180C23×C151—42no—
181C23×C151—42no—
182C23×C151—42no—
183C23×C151—41no—
184C23×C151—41no—
185C23×C151—41no—
186C23×C151—42no—
187C23×C151—42no—
188C23×C151—42no—
189C23×C151—42no—
190C23×C151—42no—
191C23×C151—41no—
192C23×C151—41no—
193C23×C151—42no—
194C23×C151—42no—
195C23×C151C22×D411yescharacteristic
196C23×C151C22×Q811yescharacteristic
197C23×C151C2×#4111yescharacteristic
198C23×C151C2×#4111yescharacteristic
199C23×C151C2×#4111yescharacteristic
200C23×C151C2×#4112yes—
201C23×C151C2×#4112yes—
202C23×C151C2×#4112yes—
203C23×C151H(5,𝔽2)11yescharacteristic
204C23×C151H(5,𝔽2)11yescharacteristic
205C23×C151H(5,𝔽2)12yes—
206C2×C4×C151—22no—
207C2×C4×C151—22no—
208C2×C4×C151—22no—
209C2×C4×C151—24no—
210C2×C4×C151—24no—
211C2×C4×C151—22no—
212C2×C4×C151—22no—
213C2×C4×C151—22no—
214C2×C4×C151—22no—
215C2×C4×C151—22no—
216C2×C4×C151—22no—
217C2×C4×C151—22no—
218C2×C4×C151—24no—
219C2×C4×C151—24no—
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—24no—
228C2×C4×C151—24no—
229C2×C4×C151—24no—
230C2×C4×C151—41no—
231C2×C4×C151—42no—
232C2×C4×C151—42no—
233C2×C4×C151—42no—
234C2×C4×C151—42no—
235C2×C4×C151—41no—
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—
246C2×C4×C151—42no—
247C2×C4×C151—41no—
248C2×C4×C151—41no—
249C2×C4×C151—42no—
250C2×C4×C151—42no—
251C2×C4×C151—41no—
252C2×C4×C151—41no—
253C2×C4×C151—41no—
254C2×C4×C151—41no—
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#12314yes—
266C22×C151—44no—
267C22×C151—42no—
268C22×C151—44no—
269C22×C151—42no—
270C22×C151—42no—
271C22×C151—82no—
272C22×C151—82no—
273C22×C151—81no—
274C22×C151—81no—
275C22×C151—81no—
276C22×C151—81no—
277C22×C151C2×C22⋊Q811yescharacteristic
278C22×C151C2×#12311yescharacteristic
279C22×C151#52511yescharacteristic
280C22×C151#52511yescharacteristic
281C22×C151#52912yes—
282C22×C151#52912yes—
283C22×C151#52912yes—
284C22×C151#53211yescharacteristic
285C22×C151#53312yes—
286C22×C151#53511yescharacteristic
287C22×C151#53511yescharacteristic
288C22×C151#53812yes—
289C22×C151#53812yes—
290C22×C151#55112yes—
291C22×C151#55312yes—
292C22×C151#55312yes—
293C22×C151#55311yescharacteristic
294C22×C151#55311yescharacteristic
295C22×C151#55411yescharacteristic
296C22×C151#55412yes—
297C22×C151#55411yescharacteristic
298C22×C151#55512yes—
299C22×C151#55912yes—
300C4×C151—24no—
301C4×C151—24no—
302C4×C151—42no—
303C4×C151—44no—
304C4×C151—44no—
305C4×C151—44no—
306C4×C151—42no—
307C4×C151—82no—
308C4×C151—81no—
309C4×C151—81no—
310C2×C151—82no—
311C2×C151#239611yescharacteristic
312C2×C151#248711yescharacteristic
313C2×C151#250011yescharacteristic
314C2×C151#257412yes—
315C2×C151#258011yescharacteristic
316C2×C151#258712yes—
317C2×C151#259312yes—
318C2×C151#259512yes—
319C2×C151#260311yescharacteristic
320C2×C151#263111yescharacteristic
321C2×C151#285311yescharacteristic
322#15100C15111yesmaximal, characteristic, direct product factor, Sylow
323C151#1510011yescharacteristic, direct product factor, Sylow
324C2×#388C2×C15111yescharacteristic
325C2×C4×C4⋊C4C2×C15111yescharacteristic, complemented
326#1444C2×C15111yescharacteristic, complemented
327#1442C2×C15111yescharacteristic, complemented
328#1442C2×C15112yescomplemented
329#1439C2×C15111yescharacteristic
330#1439C2×C15111yescharacteristic
331#1439C2×C15112yes—
332#1437C2×C15112yes—
333#1436C2×C15112yescomplemented
334#1434C2×C15111yescharacteristic, complemented
335C22×C4⋊C4C22×C15111yescharacteristic
336C22×C4⋊C4C22×C15111yescharacteristic
337C22×C4⋊C4C22×C15112yes—
338C22×C4⋊C4C22×C15111yescharacteristic
339C22×C22⋊C4C22×C15111yescharacteristic
340C22×C22⋊C4C22×C15112yes—
341C22×C22⋊C4C22×C15111yescharacteristic
342C22×C22⋊C4C22×C15112yes—
343C22×C22⋊C4C22×C15111yescharacteristic
344C22×C42C22×C15111yescharacteristic
345C22×C42C22×C15112yes—
346#388—24no—
347C4×C4⋊C4—24no—
348C2×#95C22×C15112yes—
349C2×#95C22×C15111yescharacteristic
350C2×#95C22×C15112yes—
351C2×#95C22×C15111yescharacteristic
352C2×#95C22×C15111yescharacteristic
353C2×#95C22×C15112yes—
354C2×#95C22×C15112yes—
355C2×#95C22×C15112yes—
356C2×#95C22×C15111yescharacteristic
357C2×#95C22×C15112yes—
358C2×#95C22×C15112yes—
359C2×#95C22×C15112yes—
360C25C23×C15111yescharacteristic
361C23×C4C23×C15111yescharacteristic
362C23×C4C23×C15111yescharacteristic
363C23×C4C23×C15112yes—
364C23×C4C23×C15111yescharacteristic
365C23×C4C23×C15112yes—
366C23×C4C23×C15112yes—
367C23×C4C23×C15112yes—
368C23×C4C23×C15111yescharacteristic
369C23×C4C23×C15111yescharacteristic
370C23×C4C23×C15111yescharacteristic
371C2×C4⋊C4—24no—
372C2×C4⋊C4—24no—
373C2×C4⋊C4—22no—
374C2×C4⋊C4—22no—
375C2×C4⋊C4—24no—
376C2×C4⋊C4—22no—
377C2×C4⋊C4—42no—
378C2×C4⋊C4—42no—
379C2×C4⋊C4—42no—
380C2×C22⋊C4—22no—
381C2×C22⋊C4—22no—
382C2×C22⋊C4—24no—
383C2×C22⋊C4—24no—
384C2×C22⋊C4—24no—
385C2×C22⋊C4—22no—
386C2×C22⋊C4—22no—
387C2×C22⋊C4—22no—
388C2×C22⋊C4—22no—
389C2×C22⋊C4—42no—
390C2×C22⋊C4—42no—
391C2×C22⋊C4—42no—
392C2×C22⋊C4—42no—
393C2×C22⋊C4Q8×C15114yes—
394C2×C42—22no—
395C2×C42—22no—
396C2×C42—24no—
397C2×C42—42no—
398C2×C42—42no—
399C2×C42D4×C15114yes—
400#95—22no—
401#95—24no—
402#95—24no—
403#95—24no—
404#95—24no—
405#95—22no—
406#95—24no—
407#95—22no—
408#95—22no—
409#95—42no—
410#95—42no—
411#95—42no—
412C24—21no—
413C24—21no—
414C24—22no—
415C24—22no—
416C24—21no—
417C24—21no—
418C24—22no—
419C24—22no—
420C24—21no—
421C24—21no—
422C24C2×Q8×C15112yes—
423C24C24×C15111yescharacteristic
424C22×C4—21no—
425C22×C4—21no—
426C22×C4—22no—
427C22×C4—22no—
428C22×C4—21no—
429C22×C4—21no—
430C22×C4—22no—
431C22×C4—22no—
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—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—22no—
451C22×C4—22no—
452C22×C4—22no—
453C22×C4—22no—
454C22×C4—22no—
455C22×C4—22no—
456C22×C4—21no—
457C22×C4—21no—
458C22×C4—22no—
459C22×C4—22no—
460C22×C4—22no—
461C22×C4—22no—
462C22×C4—22no—
463C22×C4—21no—
464C22×C4—21no—
465C22×C4—22no—
466C22×C4—22no—
467C22×C4—21no—
468C22×C4—22no—
469C22×C4—22no—
470C22×C4—22no—
471C22×C4—22no—
472C22×C4—21no—
473C22×C4C2×D4×C15112yes—
474C22×C4C2×D4×C15112yes—
475C22×C4C2×D4×C15112yes—
476C22×C4C2×Q8×C15112yes—
477C22×C4C2×Q8×C15112yes—
478C22×C4#41×C15114yes—
479C22×C4#41×C15114yes—
480C22×C4#41×C15114yes—
481C22×C4#41×C15112yes—
482C22×C4#41×C15112yes—
483C22×C4#41×C15112yes—
484C4⋊C4—28no—
485C4⋊C4—28no—
486C4⋊C4—44no—
487C4⋊C4—48no—
488C22⋊C4—28no—
489C22⋊C4—48no—
490C22⋊C4—44no—
491C22⋊C4—48no—
492C22⋊C4—44no—
493C42—28no—
494C42—48no—
495C23—22no—
496C23—24no—
497C23—22no—
498C23—22no—
499C23—24no—
500C23—41no—
501C23—41no—
502C23—41no—
503C23—42no—
504C23—42no—
505C23—42no—
506C23—41no—
507C23—41no—
508C23—41no—
509C23—42no—
510C23—42no—
511C23—42no—
512C23—41no—
513C23—41no—
514C23—42no—
515C23—42no—
516C23—42no—
517C23—42no—
518C23C22×D4×C15111yescharacteristic
519C23C22×Q8×C15111yescharacteristic
520C23C2×#41×C15111yescharacteristic
521C23C2×#41×C15111yescharacteristic
522C23C2×#41×C15111yescharacteristic
523C23C2×#41×C15112yes—
524C23C2×#41×C15112yes—
525C23C2×#41×C15112yes—
526C23H(5,𝔽2)×C15111yescharacteristic
527C23H(5,𝔽2)×C15111yescharacteristic
528C23H(5,𝔽2)×C15112yes—
529C2×C4—22no—
530C2×C4—22no—
531C2×C4—22no—
532C2×C4—24no—
533C2×C4—24no—
534C2×C4—22no—
535C2×C4—22no—
536C2×C4—22no—
537C2×C4—22no—
538C2×C4—22no—
539C2×C4—22no—
540C2×C4—22no—
541C2×C4—24no—
542C2×C4—24no—
543C2×C4—24no—
544C2×C4—22no—
545C2×C4—22no—
546C2×C4—24no—
547C2×C4—24no—
548C2×C4—24no—
549C2×C4—24no—
550C2×C4—24no—
551C2×C4—24no—
552C2×C4—24no—
553C2×C4—41no—
554C2×C4—42no—
555C2×C4—42no—
556C2×C4—42no—
557C2×C4—42no—
558C2×C4—41no—
559C2×C4—42no—
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—41no—
571C2×C4—41no—
572C2×C4—42no—
573C2×C4—42no—
574C2×C4—41no—
575C2×C4—41no—
576C2×C4—41no—
577C2×C4—41no—
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#123×C15114yes—
589C22—42no—
590C22—42no—
591C22—44no—
592C22—42no—
593C22—44no—
594C22—82no—
595C22—82no—
596C22—81no—
597C22—81no—
598C22—81no—
599C22—81no—
600C22C2×C22⋊Q8×C15111yescharacteristic
601C22C2×#123×C15111yescharacteristic
602C22#525×C15111yescharacteristic
603C22#525×C15111yescharacteristic
604C22#529×C15112yes—
605C22#529×C15112yes—
606C22#529×C15112yes—
607C22#532×C15111yescharacteristic
608C22#533×C15112yes—
609C22#535×C15111yescharacteristic
610C22#535×C15111yescharacteristic
611C22#538×C15112yes—
612C22#538×C15112yes—
613C22#551×C15112yes—
614C22#553×C15111yescharacteristic
615C22#553×C15112yes—
616C22#553×C15111yescharacteristic
617C22#553×C15112yes—
618C22#554×C15111yescharacteristic
619C22#554×C15111yescharacteristic
620C22#554×C15112yes—
621C22#555×C15112yes—
622C22#559×C15112yes—
623C4—24no—
624C4—24no—
625C4—44no—
626C4—44no—
627C4—44no—
628C4—42no—
629C4—42no—
630C4—82no—
631C4—81no—
632C4—81no—
633C2—82no—
634C2#2396×C15111yescharacteristic
635C2#2487×C15111yescharacteristic
636C2#2500×C15111yescharacteristic
637C2#2574×C15112yes—
638C2#2580×C15111yescharacteristic
639C2#2587×C15112yes—
640C2#2593×C15112yes—
641C2#2595×C15112yes—
642C2#2603×C15111yescharacteristic
643C2#2631×C15111yescharacteristic
644C2#2853×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
2. C2×C4×C4⋊C4×C151C2semidirect
3. #1444×C151C2semidirect
4. #1442×C151C2semidirect
5. #1442×C151C2semidirect
10. #1436×C151C2semidirect
11. #1434×C151C2semidirect
322. #15100C151direct (N × H)
323. C151#15100direct (N × H)
325. C2×C4×C4⋊C4C2×C151semidirect
326. #1444C2×C151semidirect
327. #1442C2×C151semidirect
328. #1442C2×C151semidirect
333. #1436C2×C151semidirect
334. #1434C2×C151semidirect

Maximal subgroups

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

subgroupindex
C2×#388×C1512
C2×C4×C4⋊C4×C1512
#1444×C1512
#1442×C1512
#1439×C1512
#1437×C1512
#1436×C1512
#1434×C1512
#15100151