Finite Group Databasebeta

← C151×#14876 #50319801

Subgroups — C151×#14876 #50319801

Order 38656.

1590 conjugacy classes of subgroups.

The subgroup lattice has 598 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C4×Q8×C151C211yesmaximal, characteristic
2C2×#400×C151C211yesmaximal, characteristic
3C2×#395×C151C211yesmaximal, characteristic
4C2×#387×C151C211yesmaximal, characteristic
5#1446×C151C211yesmaximal, characteristic
6#1445×C151C211yesmaximal, characteristic
7#1442×C151C212yesmaximal
8#1441×C151C212yesmaximal
9#1436×C151C212yesmaximal
10#1436×C151C212yesmaximal
11#1434×C151C211yesmaximal, characteristic
12C23×Q8×C151C2211yescharacteristic
13C2×C4×Q8×C151—24no—
14C2×C4×Q8×C151—24no—
15C2×C4×Q8×C151—24no—
16C22×C4⋊C4×C151C2211yescharacteristic
17C22×C4⋊C4×C151C2212yes—
18C22×C4⋊C4×C151C2212yes—
19C22×C4⋊C4×C151C2211yescharacteristic
20C22×C4⋊C4×C151C2211yescharacteristic
21C22×C42×C151C2212yes—
22C22×C42×C151C2211yescharacteristic
23#400×C151—24no—
24#395×C151—24no—
25#387×C151—24no—
26C2×#95×C151C2211yescharacteristic
27C2×#95×C151C2212yes—
28C2×#95×C151C2211yescharacteristic
29C2×#95×C151C2212yes—
30C2×#95×C151C2212yes—
31C2×#95×C151C2212yes—
32C2×#95×C151C2212yes—
33C2×#95×C151C2211yescharacteristic
34C2×#95×C151C2212yes—
35C2×#95×C151C2212yes—
36C2×#95×C151C2212yes—
37C2×#95×C151C2212yes—
38C2×#95×C151C2211yescharacteristic
39C2×#95×C151C2211yescharacteristic
40C2×#95×C151C2211yescharacteristic
41C22×Q8×C151—22no—
42C22×Q8×C151—22no—
43C22×Q8×C151—24no—
44C22×Q8×C151—24no—
45C22×Q8×C151D414yes—
46C23×C4×C151C2312yes—
47C23×C4×C151C2311yescharacteristic
48C23×C4×C151C2311yescharacteristic
49C23×C4×C151C2312yes—
50C23×C4×C151C2311yescharacteristic
51C23×C4×C151C2311yescharacteristic
52C23×C4×C151C2311yescharacteristic
53C23×C4×C151C2312yes—
54C23×C4×C151C2311yescharacteristic
55C23×C4×C151C2311yescharacteristic
56C23×C4×C151C2312yes—
57C4×Q8×C151—232no—
58C2×C4⋊C4×C151—22no—
59C2×C4⋊C4×C151—24no—
60C2×C4⋊C4×C151—24no—
61C2×C4⋊C4×C151—24no—
62C2×C4⋊C4×C151—22no—
63C2×C4⋊C4×C151—22no—
64C2×C4⋊C4×C151—22no—
65C2×C4⋊C4×C151—22no—
66C2×C4⋊C4×C151—22no—
67C2×C4⋊C4×C151—24no—
68C2×C4⋊C4×C151—22no—
69C2×C4⋊C4×C151—24no—
70C2×C4⋊C4×C151—24no—
71C2×C4⋊C4×C151D414yes—
72C2×C4⋊C4×C151Q814yescomplemented
73C2×C42×C151—24no—
74C2×C42×C151—24no—
75C2×C42×C151—24no—
76C2×C42×C151—22no—
77C2×C42×C151—22no—
78C2×C42×C151D414yes—
79#95×C151—22no—
80#95×C151—22no—
81#95×C151—22no—
82#95×C151—22no—
83#95×C151—22no—
84#95×C151—24no—
85#95×C151—24no—
86#95×C151—22no—
87#95×C151—24no—
88#95×C151—24no—
89#95×C151—24no—
90#95×C151—24no—
91#95×C151—24no—
92#95×C151—24no—
93#95×C151—24no—
94C24×C151C2411yescharacteristic
95C2×Q8×C151—28no—
96C2×Q8×C151—28no—
97C2×Q8×C151—216no—
98C2×Q8×C151—28no—
99C2×Q8×C151—216no—
100C22×C4×C151—21no—
101C22×C4×C151—21no—
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—21no—
109C22×C4×C151—21no—
110C22×C4×C151—21no—
111C22×C4×C151—22no—
112C22×C4×C151—21no—
113C22×C4×C151—21no—
114C22×C4×C151—21no—
115C22×C4×C151—22no—
116C22×C4×C151—21no—
117C22×C4×C151—22no—
118C22×C4×C151—21no—
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—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—21no—
137C22×C4×C151—22no—
138C22×C4×C151—21no—
139C22×C4×C151—21no—
140C22×C4×C151—21no—
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—21no—
150C22×C4×C151—21no—
151C22×C4×C151—22no—
152C22×C4×C151—22no—
153C22×C4×C151C2×D414yes—
154C22×C4×C151C2×D412yes—
155C22×C4×C151C2×D412yes—
156C22×C4×C151C2×D412yes—
157C22×C4×C151C2×D412yes—
158C22×C4×C151C2×D412yes—
159C22×C4×C151C2×D414yes—
160C22×C4×C151C2×Q812yes—
161C22×C4×C151C2×Q812yes—
162C22×C4×C151C2×Q812yes—
163C22×C4×C151#4114yes—
164C22×C4×C151#4112yes—
165C22×C4×C151#4114yes—
166C22×C4×C151#4114yes—
167C4⋊C4×C151—216no—
168C4⋊C4×C151—28no—
169C4⋊C4×C151—28no—
170C4⋊C4×C151—44no—
171C4⋊C4×C151—48no—
172C42×C151—216no—
173C42×C151—28no—
174C23×C151C22×D411yescharacteristic
175C23×C151C22×D411yescharacteristic
176C23×C151C22×D411yescharacteristic
177C23×C151C22×Q811yescharacteristic
178C23×C151C2×#4111yescharacteristic
179C23×C151C2×#4112yes—
180C23×C151C2×#4112yes—
181C23×C151C2×#4112yes—
182C23×C1512−1+412yes—
183C23×C1512−1+411yescharacteristic
184C23×C1512−1+411yescharacteristic
185Q8×C151—232no—
186C2×C4×C151—24no—
187C2×C4×C151—22no—
188C2×C4×C151—24no—
189C2×C4×C151—24no—
190C2×C4×C151—22no—
191C2×C4×C151—22no—
192C2×C4×C151—24no—
193C2×C4×C151—24no—
194C2×C4×C151—24no—
195C2×C4×C151—24no—
196C2×C4×C151—24no—
197C2×C4×C151—22no—
198C2×C4×C151—22no—
199C2×C4×C151—22no—
200C2×C4×C151—22no—
201C2×C4×C151—22no—
202C2×C4×C151—24no—
203C2×C4×C151—22no—
204C2×C4×C151—22no—
205C2×C4×C151—22no—
206C2×C4×C151—24no—
207C2×C4×C151—22no—
208C2×C4×C151—24no—
209C2×C4×C151—22no—
210C2×C4×C151—24no—
211C2×C4×C151—24no—
212C2×C4×C151—24no—
213C2×C4×C151—22no—
214C2×C4×C151—22no—
215C2×C4×C151—24no—
216C2×C4×C151—41no—
217C2×C4×C151—42no—
218C2×C4×C151—41no—
219C2×C4×C151—42no—
220C2×C4×C151—41no—
221C2×C4×C151—42no—
222C2×C4×C151—41no—
223C2×C4×C151—42no—
224C2×C4×C151—42no—
225C2×C4×C151—42no—
226C2×C4×C151—41no—
227C2×C4×C151—41no—
228C2×C4×C151—42no—
229C2×C4×C151—42no—
230C2×C4×C151—42no—
231C2×C4×C151—42no—
232C2×C4×C151—42no—
233C2×C4×C151—41no—
234C2×C4×C151—42no—
235C2×C4×C151—41no—
236C2×C4×C151—41no—
237C2×C4×C151—42no—
238C2×C4×C151—41no—
239C2×C4×C151—42no—
240C2×C4×C151—42no—
241C2×C4×C151—41no—
242C2×C4×C151—41no—
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#12014yes—
251C2×C4×C151C22⋊Q814yes—
252C2×C4×C151#12318yes—
253C22×C151C2×#12011yescharacteristic
254C22×C151C2×C22⋊Q811yescharacteristic
255C22×C151C2×#12312yes—
256C22×C151#52511yescharacteristic
257C22×C151#52511yescharacteristic
258C22×C151#52512yes—
259C22×C151#52912yes—
260C22×C151#53211yescharacteristic
261C22×C151#53312yes—
262C22×C151#53611yescharacteristic
263C22×C151#53611yescharacteristic
264C22×C151#54112yes—
265C22×C151#54112yes—
266C22×C151#54712yes—
267C22×C151#54811yescharacteristic
268C22×C151#54811yescharacteristic
269C22×C151#54812yes—
270C22×C151D4×Q811yescharacteristic
271C22×C151D4×Q811yescharacteristic
272C22×C151#55212yes—
273C22×C151#55612yes—
274C22×C151#55612yes—
275C22×C151#55712yes—
276C4×C151—24no—
277C4×C151—28no—
278C4×C151—24no—
279C4×C151—42no—
280C4×C151—42no—
281C4×C151—44no—
282C4×C151—42no—
283C4×C151—44no—
284C4×C151—81no—
285C4×C151—81no—
286C4×C151—82no—
287C2×C151#239611yescharacteristic
288C2×C151#240911yescharacteristic
289C2×C151#242112yes—
290C2×C151#243211yescharacteristic
291C2×C151#244612yes—
292C2×C151#246212yes—
293C2×C151#246912yes—
294C2×C151#258111yescharacteristic
295C2×C151#260411yescharacteristic
296C2×C151#263411yescharacteristic
297C2×C151#284911yescharacteristic
298#14876C15111yesmaximal, characteristic, direct product factor, Sylow
299C151#1487611yescharacteristic, direct product factor, Sylow
300C22×C4×Q8C2×C15111yescharacteristic
301C2×#400C2×C15111yescharacteristic
302C2×#395C2×C15111yescharacteristic
303C2×#387C2×C15111yescharacteristic
304#1446C2×C15111yescharacteristic
305#1445C2×C15111yescharacteristic
306#1442C2×C15112yes—
307#1441C2×C15112yes—
308#1436C2×C15112yes—
309#1436C2×C15112yes—
310#1434C2×C15111yescharacteristic
311C23×Q8C22×C15111yescharacteristic
312C2×C4×Q8—24no—
313C2×C4×Q8—24no—
314C2×C4×Q8—24no—
315C22×C4⋊C4C22×C15111yescharacteristic
316C22×C4⋊C4C22×C15112yes—
317C22×C4⋊C4C22×C15112yes—
318C22×C4⋊C4C22×C15111yescharacteristic
319C22×C4⋊C4C22×C15111yescharacteristic
320C22×C42C22×C15112yes—
321C22×C42C22×C15111yescharacteristic
322#400—24no—
323#395—24no—
324#387—24no—
325C2×#95C22×C15111yescharacteristic
326C2×#95C22×C15112yes—
327C2×#95C22×C15111yescharacteristic
328C2×#95C22×C15112yes—
329C2×#95C22×C15112yes—
330C2×#95C22×C15112yes—
331C2×#95C22×C15112yes—
332C2×#95C22×C15111yescharacteristic
333C2×#95C22×C15112yes—
334C2×#95C22×C15112yes—
335C2×#95C22×C15112yes—
336C2×#95C22×C15112yes—
337C2×#95C22×C15111yescharacteristic
338C2×#95C22×C15111yescharacteristic
339C2×#95C22×C15111yescharacteristic
340C22×Q8—24no—
341C22×Q8—24no—
342C22×Q8—22no—
343C22×Q8—22no—
344C22×Q8D4×C15114yes—
345C23×C4C23×C15111yescharacteristic
346C23×C4C23×C15112yes—
347C23×C4C23×C15111yescharacteristic
348C23×C4C23×C15111yescharacteristic
349C23×C4C23×C15111yescharacteristic
350C23×C4C23×C15112yes—
351C23×C4C23×C15112yes—
352C23×C4C23×C15111yescharacteristic
353C23×C4C23×C15111yescharacteristic
354C23×C4C23×C15112yes—
355C23×C4C23×C15111yescharacteristic
356C4×Q8—232no—
357C2×C4⋊C4—22no—
358C2×C4⋊C4—24no—
359C2×C4⋊C4—24no—
360C2×C4⋊C4—24no—
361C2×C4⋊C4—22no—
362C2×C4⋊C4—22no—
363C2×C4⋊C4—22no—
364C2×C4⋊C4—24no—
365C2×C4⋊C4—24no—
366C2×C4⋊C4—22no—
367C2×C4⋊C4—22no—
368C2×C4⋊C4—24no—
369C2×C4⋊C4—22no—
370C2×C4⋊C4D4×C15114yes—
371C2×C4⋊C4Q8×C15114yescomplemented
372C2×C42—24no—
373C2×C42—24no—
374C2×C42—24no—
375C2×C42—22no—
376C2×C42—22no—
377C2×C42D4×C15114yes—
378#95—24no—
379#95—24no—
380#95—24no—
381#95—24no—
382#95—24no—
383#95—24no—
384#95—22no—
385#95—22no—
386#95—22no—
387#95—22no—
388#95—22no—
389#95—24no—
390#95—24no—
391#95—22no—
392#95—24no—
393C24C24×C15111yescharacteristic
394C2×Q8—28no—
395C2×Q8—28no—
396C2×Q8—216no—
397C2×Q8—28no—
398C2×Q8—216no—
399C22×C4—21no—
400C22×C4—21no—
401C22×C4—22no—
402C22×C4—22no—
403C22×C4—22no—
404C22×C4—22no—
405C22×C4—22no—
406C22×C4—22no—
407C22×C4—21no—
408C22×C4—21no—
409C22×C4—21no—
410C22×C4—22no—
411C22×C4—21no—
412C22×C4—21no—
413C22×C4—21no—
414C22×C4—22no—
415C22×C4—21no—
416C22×C4—22no—
417C22×C4—21no—
418C22×C4—22no—
419C22×C4—22no—
420C22×C4—22no—
421C22×C4—22no—
422C22×C4—22no—
423C22×C4—22no—
424C22×C4—21no—
425C22×C4—21no—
426C22×C4—22no—
427C22×C4—22no—
428C22×C4—22no—
429C22×C4—22no—
430C22×C4—22no—
431C22×C4—22no—
432C22×C4—21no—
433C22×C4—21no—
434C22×C4—22no—
435C22×C4—21no—
436C22×C4—22no—
437C22×C4—21no—
438C22×C4—21no—
439C22×C4—21no—
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—21no—
449C22×C4—21no—
450C22×C4—22no—
451C22×C4—22no—
452C22×C4C2×D4×C15114yes—
453C22×C4C2×D4×C15112yes—
454C22×C4C2×D4×C15112yes—
455C22×C4C2×D4×C15112yes—
456C22×C4C2×D4×C15112yes—
457C22×C4C2×D4×C15112yes—
458C22×C4C2×D4×C15114yes—
459C22×C4C2×Q8×C15112yes—
460C22×C4C2×Q8×C15112yes—
461C22×C4C2×Q8×C15112yes—
462C22×C4#41×C15114yes—
463C22×C4#41×C15112yes—
464C22×C4#41×C15114yes—
465C22×C4#41×C15114yes—
466C4⋊C4—216no—
467C4⋊C4—28no—
468C4⋊C4—28no—
469C4⋊C4—44no—
470C4⋊C4—48no—
471C42—216no—
472C42—28no—
473C23C22×D4×C15111yescharacteristic
474C23C22×D4×C15111yescharacteristic
475C23C22×D4×C15111yescharacteristic
476C23C22×Q8×C15111yescharacteristic
477C23C2×#41×C15111yescharacteristic
478C23C2×#41×C15112yes—
479C23C2×#41×C15112yes—
480C23C2×#41×C15112yes—
481C232−1+4×C15112yes—
482C232−1+4×C15111yescharacteristic
483C232−1+4×C15111yescharacteristic
484Q8—232no—
485C2×C4—22no—
486C2×C4—24no—
487C2×C4—24no—
488C2×C4—24no—
489C2×C4—24no—
490C2×C4—24no—
491C2×C4—24no—
492C2×C4—24no—
493C2×C4—22no—
494C2×C4—22no—
495C2×C4—24no—
496C2×C4—22no—
497C2×C4—22no—
498C2×C4—22no—
499C2×C4—22no—
500C2×C4—22no—
501C2×C4—24no—
502C2×C4—22no—
503C2×C4—22no—
504C2×C4—22no—
505C2×C4—24no—
506C2×C4—22no—
507C2×C4—24no—
508C2×C4—22no—
509C2×C4—24no—
510C2×C4—24no—
511C2×C4—24no—
512C2×C4—22no—
513C2×C4—22no—
514C2×C4—24no—
515C2×C4—41no—
516C2×C4—42no—
517C2×C4—41no—
518C2×C4—42no—
519C2×C4—41no—
520C2×C4—42no—
521C2×C4—41no—
522C2×C4—42no—
523C2×C4—42no—
524C2×C4—42no—
525C2×C4—41no—
526C2×C4—41no—
527C2×C4—42no—
528C2×C4—42no—
529C2×C4—42no—
530C2×C4—42no—
531C2×C4—42no—
532C2×C4—41no—
533C2×C4—42no—
534C2×C4—41no—
535C2×C4—41no—
536C2×C4—42no—
537C2×C4—41no—
538C2×C4—42no—
539C2×C4—42no—
540C2×C4—41no—
541C2×C4—41no—
542C2×C4—42no—
543C2×C4—42no—
544C2×C4—42no—
545C2×C4—42no—
546C2×C4—42no—
547C2×C4—42no—
548C2×C4—42no—
549C2×C4#120×C15114yes—
550C2×C4C22⋊Q8×C15114yes—
551C2×C4#123×C15118yes—
552C22C2×#120×C15111yescharacteristic
553C22C2×C22⋊Q8×C15111yescharacteristic
554C22C2×#123×C15112yes—
555C22#525×C15111yescharacteristic
556C22#525×C15111yescharacteristic
557C22#525×C15112yes—
558C22#529×C15112yes—
559C22#532×C15111yescharacteristic
560C22#533×C15112yes—
561C22#536×C15111yescharacteristic
562C22#536×C15111yescharacteristic
563C22#541×C15112yes—
564C22#541×C15112yes—
565C22#547×C15112yes—
566C22#548×C15111yescharacteristic
567C22#548×C15111yescharacteristic
568C22#548×C15112yes—
569C22D4×Q8×C15111yescharacteristic
570C22D4×Q8×C15111yescharacteristic
571C22#552×C15112yes—
572C22#556×C15112yes—
573C22#556×C15112yes—
574C22#557×C15112yes—
575C4—24no—
576C4—28no—
577C4—24no—
578C4—42no—
579C4—42no—
580C4—44no—
581C4—42no—
582C4—44no—
583C4—81no—
584C4—81no—
585C4—82no—
586C2#2396×C15111yescharacteristic
587C2#2409×C15111yescharacteristic
588C2#2421×C15112yes—
589C2#2432×C15111yescharacteristic
590C2#2446×C15112yes—
591C2#2462×C15112yes—
592C2#2469×C15112yes—
593C2#2581×C15111yescharacteristic
594C2#2604×C15111yescharacteristic
595C2#2634×C15111yescharacteristic
596C2#2849×C15111yescharacteristic
subgroupG/H
center, socle, prime radicalC24×C151C24
commutator, Frattini, cosocleC24C24×C151
LCSG ▷ C24 ▷ C1
UCSC1 ◁ C24×C151 ◁ G

Complements

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

NH ≅ G/Ntype
72. C2×C4⋊C4×C151Q8semidirect
298. #14876C151direct (N × H)
299. C151#14876direct (N × H)
371. C2×C4⋊C4Q8×C151semidirect

Maximal subgroups

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

subgroupindex
C22×C4×Q8×C1512
C2×#400×C1512
C2×#395×C1512
C2×#387×C1512
#1446×C1512
#1445×C1512
#1442×C1512
#1441×C1512
#1436×C1512
#1434×C1512
#14876151