Finite Group Databasebeta

← C151×#14872 #50319797

Subgroups — C151×#14872 #50319797

Order 38656.

1426 conjugacy classes of subgroups.

The subgroup lattice has 596 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#395×C151C211yesmaximal, characteristic
2C2×#391×C151C211yesmaximal, characteristic
3C2×#387×C151C211yesmaximal, characteristic
4C2×C4×C4⋊C4×C151C211yesmaximal, characteristic
5#1446×C151C211yesmaximal, characteristic
6#1444×C151C211yesmaximal, characteristic
7#1441×C151C212yesmaximal
8#1441×C151C212yesmaximal
9#1441×C151C211yesmaximal, characteristic
10#1436×C151C212yesmaximal
11C4⋊#95×C151C212yesmaximal
12C23×Q8×C151C2211yescharacteristic
13C22×C4⋊C4×C151C2211yescharacteristic
14C22×C4⋊C4×C151C2212yes—
15C22×C4⋊C4×C151C2211yescharacteristic
16C22×C4⋊C4×C151C2212yes—
17C22×C4⋊C4×C151C2212yes—
18C22×C4⋊C4×C151C2211yescharacteristic
19C22×C42×C151C2212yes—
20C22×C42×C151C2211yescharacteristic
21#395×C151—24no—
22#391×C151—24no—
23#387×C151—24no—
24C4×C4⋊C4×C151—24no—
25C2×#95×C151C2212yes—
26C2×#95×C151C2211yescharacteristic
27C2×#95×C151C2212yes—
28C2×#95×C151C2212yes—
29C2×#95×C151C2212yes—
30C2×#95×C151C2211yescharacteristic
31C2×#95×C151C2211yescharacteristic
32C2×#95×C151C2212yes—
33C2×#95×C151C2211yescharacteristic
34C2×#95×C151C2211yescharacteristic
35C2×#95×C151C2212yes—
36C2×#95×C151C2212yes—
37C2×#95×C151C2212yes—
38C2×#95×C151C2211yescharacteristic
39C22×Q8×C151—22no—
40C22×Q8×C151—24no—
41C22×Q8×C151—22no—
42C22×Q8×C151—22no—
43C22×Q8×C151—42no—
44C23×C4×C151C2311yescharacteristic
45C23×C4×C151C2312yes—
46C23×C4×C151C2311yescharacteristic
47C23×C4×C151C2311yescharacteristic
48C23×C4×C151C2312yes—
49C23×C4×C151C2311yescharacteristic
50C23×C4×C151C2312yes—
51C23×C4×C151C2311yescharacteristic
52C23×C4×C151C2311yescharacteristic
53C23×C4×C151C2311yescharacteristic
54C23×C4×C151C2312yes—
55C2×C4⋊C4×C151—24no—
56C2×C4⋊C4×C151—22no—
57C2×C4⋊C4×C151—24no—
58C2×C4⋊C4×C151—22no—
59C2×C4⋊C4×C151—22no—
60C2×C4⋊C4×C151—22no—
61C2×C4⋊C4×C151—24no—
62C2×C4⋊C4×C151—22no—
63C2×C4⋊C4×C151—24no—
64C2×C4⋊C4×C151—24no—
65C2×C4⋊C4×C151—22no—
66C2×C4⋊C4×C151—42no—
67C2×C4⋊C4×C151—42no—
68C2×C4⋊C4×C151—42no—
69C2×C4⋊C4×C151—42no—
70C2×C4⋊C4×C151Q814yescomplemented
71C2×C4⋊C4×C151Q818yescomplemented
72C2×C42×C151—22no—
73C2×C42×C151—22no—
74C2×C42×C151—24no—
75C2×C42×C151—24no—
76C2×C42×C151—42no—
77C2×C42×C151D414yes—
78#95×C151—22no—
79#95×C151—22no—
80#95×C151—22no—
81#95×C151—22no—
82#95×C151—22no—
83#95×C151—24no—
84#95×C151—24no—
85#95×C151—24no—
86#95×C151—24no—
87#95×C151—24no—
88#95×C151—42no—
89#95×C151—42no—
90#95×C151—42no—
91#95×C151D414yes—
92C24×C151C2411yescharacteristic
93C2×Q8×C151—28no—
94C2×Q8×C151—48no—
95C2×Q8×C151—48no—
96C2×Q8×C151—44no—
97C2×Q8×C151—44no—
98C22×C4×C151—21no—
99C22×C4×C151—21no—
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—21no—
107C22×C4×C151—22no—
108C22×C4×C151—22no—
109C22×C4×C151—22no—
110C22×C4×C151—21no—
111C22×C4×C151—21no—
112C22×C4×C151—21no—
113C22×C4×C151—22no—
114C22×C4×C151—22no—
115C22×C4×C151—21no—
116C22×C4×C151—22no—
117C22×C4×C151—22no—
118C22×C4×C151—22no—
119C22×C4×C151—22no—
120C22×C4×C151—22no—
121C22×C4×C151—21no—
122C22×C4×C151—22no—
123C22×C4×C151—21no—
124C22×C4×C151—21no—
125C22×C4×C151—22no—
126C22×C4×C151—22no—
127C22×C4×C151—21no—
128C22×C4×C151—22no—
129C22×C4×C151—22no—
130C22×C4×C151—22no—
131C22×C4×C151—22no—
132C22×C4×C151—21no—
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—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—21no—
148C22×C4×C151—21no—
149C22×C4×C151—22no—
150C22×C4×C151C2×D412yes—
151C22×C4×C151C2×D412yes—
152C22×C4×C151C2×D412yes—
153C22×C4×C151C2×D414yes—
154C22×C4×C151C2×D412yes—
155C22×C4×C151C2×Q812yes—
156C22×C4×C151C2×Q812yes—
157C22×C4×C151C2×Q814yes—
158C22×C4×C151C2×Q812yes—
159C22×C4×C151C2×Q814yes—
160C22×C4×C151C2×Q814yes—
161C22×C4×C151#4114yes—
162C22×C4×C151#4112yes—
163C22×C4×C151#4114yes—
164C22×C4×C151#4112yes—
165C4⋊C4×C151—216no—
166C4⋊C4×C151—28no—
167C4⋊C4×C151—48no—
168C4⋊C4×C151—44no—
169C4⋊C4×C151—48no—
170C4⋊C4×C151—44no—
171C42×C151—28no—
172C42×C151—48no—
173C23×C151C22×D411yescharacteristic
174C23×C151C22×D411yescharacteristic
175C23×C151C22×Q812yes—
176C23×C151C22×Q811yescharacteristic
177C23×C151C2×#4111yescharacteristic
178C23×C151C2×#4111yescharacteristic
179C23×C151C2×#4112yes—
180C23×C151C2×#4112yes—
181C23×C151H(5,𝔽2)12yes—
182C23×C151H(5,𝔽2)11yescharacteristic
183C23×C1512−1+411yescharacteristic
184Q8×C151—416no—
185C2×C4×C151—22no—
186C2×C4×C151—22no—
187C2×C4×C151—24no—
188C2×C4×C151—22no—
189C2×C4×C151—24no—
190C2×C4×C151—22no—
191C2×C4×C151—24no—
192C2×C4×C151—22no—
193C2×C4×C151—22no—
194C2×C4×C151—24no—
195C2×C4×C151—24no—
196C2×C4×C151—22no—
197C2×C4×C151—24no—
198C2×C4×C151—24no—
199C2×C4×C151—22no—
200C2×C4×C151—24no—
201C2×C4×C151—22no—
202C2×C4×C151—22no—
203C2×C4×C151—24no—
204C2×C4×C151—24no—
205C2×C4×C151—22no—
206C2×C4×C151—22no—
207C2×C4×C151—24no—
208C2×C4×C151—24no—
209C2×C4×C151—24no—
210C2×C4×C151—24no—
211C2×C4×C151—22no—
212C2×C4×C151—24no—
213C2×C4×C151—22no—
214C2×C4×C151—24no—
215C2×C4×C151—24no—
216C2×C4×C151—42no—
217C2×C4×C151—41no—
218C2×C4×C151—41no—
219C2×C4×C151—42no—
220C2×C4×C151—42no—
221C2×C4×C151—41no—
222C2×C4×C151—42no—
223C2×C4×C151—41no—
224C2×C4×C151—42no—
225C2×C4×C151—42no—
226C2×C4×C151—42no—
227C2×C4×C151—41no—
228C2×C4×C151—42no—
229C2×C4×C151—42no—
230C2×C4×C151—41no—
231C2×C4×C151—41no—
232C2×C4×C151—41no—
233C2×C4×C151—41no—
234C2×C4×C151—42no—
235C2×C4×C151—42no—
236C2×C4×C151—41no—
237C2×C4×C151—41no—
238C2×C4×C151—41no—
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#12114yes—
249C2×C4×C151C22⋊Q814yes—
250C2×C4×C151C22⋊Q818yes—
251C2×C4×C151C4⋊Q814yes—
252C22×C151C2×#12111yescharacteristic
253C22×C151C2×C22⋊Q811yescharacteristic
254C22×C151C2×C22⋊Q812yes—
255C22×C151#52511yescharacteristic
256C22×C151#52912yes—
257C22×C151C2×C4⋊Q811yescharacteristic
258C22×C151#53211yescharacteristic
259C22×C151#53312yes—
260C22×C151#53312yes—
261C22×C151#53511yescharacteristic
262C22×C151#53711yescharacteristic
263C22×C151#53812yes—
264C22×C151#54212yes—
265C22×C151#54612yes—
266C22×C151#54611yescharacteristic
267C22×C151D4×Q811yescharacteristic
268C22×C151#55112yes—
269C22×C151#55211yescharacteristic
270C22×C151#55412yes—
271C22×C151#55412yes—
272C22×C151#55411yescharacteristic
273C22×C151#55712yes—
274C22×C151Q8212yes—
275C4×C151—24no—
276C4×C151—24no—
277C4×C151—24no—
278C4×C151—28no—
279C4×C151—42no—
280C4×C151—44no—
281C4×C151—42no—
282C4×C151—44no—
283C4×C151—82no—
284C4×C151—81no—
285C4×C151—81no—
286C2×C151#239611yescharacteristic
287C2×C151#241111yescharacteristic
288C2×C151#241711yescharacteristic
289C2×C151#245012yes—
290C2×C151#245112yes—
291C2×C151#252012yes—
292C2×C151#256711yescharacteristic
293C2×C151#258411yescharacteristic
294C2×C151#258612yes—
295C2×C151#266211yescharacteristic
296C2×C151#285711yescharacteristic
297#14872C15111yesmaximal, characteristic, direct product factor, Sylow
298C151#1487211yescharacteristic, direct product factor, Sylow
299C2×#395C2×C15111yescharacteristic
300C2×#391C2×C15111yescharacteristic
301C2×#387C2×C15111yescharacteristic
302C2×C4×C4⋊C4C2×C15111yescharacteristic
303#1446C2×C15111yescharacteristic
304#1444C2×C15111yescharacteristic
305#1441C2×C15111yescharacteristic
306#1441C2×C15112yes—
307#1441C2×C15112yes—
308#1436C2×C15112yes—
309C4⋊#95C2×C15112yes—
310C23×Q8C22×C15111yescharacteristic
311C22×C4⋊C4C22×C15111yescharacteristic
312C22×C4⋊C4C22×C15112yes—
313C22×C4⋊C4C22×C15111yescharacteristic
314C22×C4⋊C4C22×C15112yes—
315C22×C4⋊C4C22×C15112yes—
316C22×C4⋊C4C22×C15111yescharacteristic
317C22×C42C22×C15112yes—
318C22×C42C22×C15111yescharacteristic
319#395—24no—
320#391—24no—
321#387—24no—
322C4×C4⋊C4—24no—
323C2×#95C22×C15112yes—
324C2×#95C22×C15111yescharacteristic
325C2×#95C22×C15112yes—
326C2×#95C22×C15112yes—
327C2×#95C22×C15112yes—
328C2×#95C22×C15111yescharacteristic
329C2×#95C22×C15111yescharacteristic
330C2×#95C22×C15112yes—
331C2×#95C22×C15111yescharacteristic
332C2×#95C22×C15111yescharacteristic
333C2×#95C22×C15112yes—
334C2×#95C22×C15112yes—
335C2×#95C22×C15112yes—
336C2×#95C22×C15111yescharacteristic
337C22×Q8—24no—
338C22×Q8—22no—
339C22×Q8—22no—
340C22×Q8—22no—
341C22×Q8—42no—
342C23×C4C23×C15111yescharacteristic
343C23×C4C23×C15111yescharacteristic
344C23×C4C23×C15112yes—
345C23×C4C23×C15111yescharacteristic
346C23×C4C23×C15111yescharacteristic
347C23×C4C23×C15112yes—
348C23×C4C23×C15112yes—
349C23×C4C23×C15111yescharacteristic
350C23×C4C23×C15112yes—
351C23×C4C23×C15111yescharacteristic
352C23×C4C23×C15111yescharacteristic
353C2×C4⋊C4—24no—
354C2×C4⋊C4—22no—
355C2×C4⋊C4—24no—
356C2×C4⋊C4—22no—
357C2×C4⋊C4—24no—
358C2×C4⋊C4—24no—
359C2×C4⋊C4—22no—
360C2×C4⋊C4—22no—
361C2×C4⋊C4—22no—
362C2×C4⋊C4—24no—
363C2×C4⋊C4—22no—
364C2×C4⋊C4—42no—
365C2×C4⋊C4—42no—
366C2×C4⋊C4—42no—
367C2×C4⋊C4—42no—
368C2×C4⋊C4Q8×C15114yescomplemented
369C2×C4⋊C4Q8×C15118yescomplemented
370C2×C42—22no—
371C2×C42—22no—
372C2×C42—24no—
373C2×C42—24no—
374C2×C42—42no—
375C2×C42D4×C15114yes—
376#95—24no—
377#95—24no—
378#95—22no—
379#95—22no—
380#95—22no—
381#95—22no—
382#95—22no—
383#95—24no—
384#95—24no—
385#95—24no—
386#95—42no—
387#95—42no—
388#95—42no—
389#95D4×C15114yes—
390C24C24×C15111yescharacteristic
391C2×Q8—28no—
392C2×Q8—48no—
393C2×Q8—48no—
394C2×Q8—44no—
395C2×Q8—44no—
396C22×C4—21no—
397C22×C4—21no—
398C22×C4—21no—
399C22×C4—21no—
400C22×C4—22no—
401C22×C4—22no—
402C22×C4—22no—
403C22×C4—22no—
404C22×C4—21no—
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—21no—
414C22×C4—22no—
415C22×C4—22no—
416C22×C4—22no—
417C22×C4—22no—
418C22×C4—22no—
419C22×C4—21no—
420C22×C4—22no—
421C22×C4—21no—
422C22×C4—21no—
423C22×C4—22no—
424C22×C4—22no—
425C22×C4—21no—
426C22×C4—22no—
427C22×C4—22no—
428C22×C4—22no—
429C22×C4—22no—
430C22×C4—21no—
431C22×C4—21no—
432C22×C4—21no—
433C22×C4—22no—
434C22×C4—21no—
435C22×C4—22no—
436C22×C4—21no—
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—21no—
446C22×C4—21no—
447C22×C4—22no—
448C22×C4C2×D4×C15112yes—
449C22×C4C2×D4×C15112yes—
450C22×C4C2×D4×C15112yes—
451C22×C4C2×D4×C15114yes—
452C22×C4C2×D4×C15112yes—
453C22×C4C2×Q8×C15112yes—
454C22×C4C2×Q8×C15112yes—
455C22×C4C2×Q8×C15114yes—
456C22×C4C2×Q8×C15112yes—
457C22×C4C2×Q8×C15114yes—
458C22×C4C2×Q8×C15114yes—
459C22×C4#41×C15114yes—
460C22×C4#41×C15112yes—
461C22×C4#41×C15114yes—
462C22×C4#41×C15112yes—
463C4⋊C4—216no—
464C4⋊C4—28no—
465C4⋊C4—48no—
466C4⋊C4—44no—
467C4⋊C4—48no—
468C4⋊C4—44no—
469C42—28no—
470C42—48no—
471C23C22×D4×C15111yescharacteristic
472C23C22×D4×C15111yescharacteristic
473C23C22×Q8×C15112yes—
474C23C22×Q8×C15111yescharacteristic
475C23C2×#41×C15111yescharacteristic
476C23C2×#41×C15111yescharacteristic
477C23C2×#41×C15112yes—
478C23C2×#41×C15112yes—
479C23H(5,𝔽2)×C15112yes—
480C23H(5,𝔽2)×C15111yescharacteristic
481C232−1+4×C15111yescharacteristic
482Q8—416no—
483C2×C4—22no—
484C2×C4—22no—
485C2×C4—24no—
486C2×C4—22no—
487C2×C4—24no—
488C2×C4—22no—
489C2×C4—24no—
490C2×C4—22no—
491C2×C4—22no—
492C2×C4—24no—
493C2×C4—22no—
494C2×C4—24no—
495C2×C4—24no—
496C2×C4—24no—
497C2×C4—22no—
498C2×C4—24no—
499C2×C4—22no—
500C2×C4—22no—
501C2×C4—24no—
502C2×C4—24no—
503C2×C4—22no—
504C2×C4—22no—
505C2×C4—24no—
506C2×C4—24no—
507C2×C4—24no—
508C2×C4—24no—
509C2×C4—22no—
510C2×C4—24no—
511C2×C4—22no—
512C2×C4—24no—
513C2×C4—24no—
514C2×C4—41no—
515C2×C4—42no—
516C2×C4—41no—
517C2×C4—42no—
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—42no—
527C2×C4—42no—
528C2×C4—41no—
529C2×C4—41no—
530C2×C4—41no—
531C2×C4—41no—
532C2×C4—42no—
533C2×C4—42no—
534C2×C4—41no—
535C2×C4—41no—
536C2×C4—41no—
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#121×C15114yes—
547C2×C4C22⋊Q8×C15114yes—
548C2×C4C22⋊Q8×C15118yes—
549C2×C4C4⋊Q8×C15114yes—
550C22C2×#121×C15111yescharacteristic
551C22C2×C22⋊Q8×C15112yes—
552C22C2×C22⋊Q8×C15111yescharacteristic
553C22#525×C15111yescharacteristic
554C22#529×C15112yes—
555C22C2×C4⋊Q8×C15111yescharacteristic
556C22#532×C15111yescharacteristic
557C22#533×C15112yes—
558C22#533×C15112yes—
559C22#535×C15111yescharacteristic
560C22#537×C15111yescharacteristic
561C22#538×C15112yes—
562C22#542×C15112yes—
563C22#546×C15112yes—
564C22#546×C15111yescharacteristic
565C22D4×Q8×C15111yescharacteristic
566C22#551×C15112yes—
567C22#552×C15111yescharacteristic
568C22#554×C15111yescharacteristic
569C22#554×C15112yes—
570C22#554×C15112yes—
571C22#557×C15112yes—
572C22Q82×C15112yes—
573C4—24no—
574C4—24no—
575C4—24no—
576C4—28no—
577C4—42no—
578C4—44no—
579C4—42no—
580C4—44no—
581C4—82no—
582C4—81no—
583C4—81no—
584C2#2396×C15111yescharacteristic
585C2#2411×C15111yescharacteristic
586C2#2417×C15111yescharacteristic
587C2#2450×C15112yes—
588C2#2451×C15112yes—
589C2#2520×C15112yes—
590C2#2567×C15111yescharacteristic
591C2#2584×C15111yescharacteristic
592C2#2586×C15112yes—
593C2#2662×C15111yescharacteristic
594C2#2857×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
70. C2×C4⋊C4×C151Q8semidirect
71. C2×C4⋊C4×C151Q8semidirect
297. #14872C151direct (N × H)
298. C151#14872direct (N × H)
368. C2×C4⋊C4Q8×C151semidirect
369. C2×C4⋊C4Q8×C151semidirect

Maximal subgroups

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

subgroupindex
C2×#395×C1512
C2×#391×C1512
C2×#387×C1512
C2×C4×C4⋊C4×C1512
#1446×C1512
#1444×C1512
#1441×C1512
#1436×C1512
C4⋊#95×C1512
#14872151