Finite Group Databasebeta

← C151×#14879 #50319804

Subgroups — C151×#14879 #50319804

Order 38656.

1634 conjugacy classes of subgroups.

The subgroup lattice has 604 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C4×Q8×C151C211yesmaximal, characteristic
2C2×#398×C151C211yesmaximal, characteristic
3C2×#395×C151C211yesmaximal, characteristic
4C2×#387×C151C211yesmaximal, characteristic
5#1446×C151C211yesmaximal, characteristic
6#1445×C151C211yesmaximal, characteristic
7#1444×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×C151C2212yes—
21C22×C4⋊C4×C151C2211yescharacteristic
22C22×C42×C151C2212yes—
23C22×C42×C151C2211yescharacteristic
24#398×C151—24no—
25#395×C151—24no—
26#387×C151—24no—
27C2×#95×C151C2211yescharacteristic
28C2×#95×C151C2212yes—
29C2×#95×C151C2211yescharacteristic
30C2×#95×C151C2212yes—
31C2×#95×C151C2211yescharacteristic
32C2×#95×C151C2211yescharacteristic
33C2×#95×C151C2212yes—
34C2×#95×C151C2212yes—
35C2×#95×C151C2212yes—
36C2×#95×C151C2211yescharacteristic
37C2×#95×C151C2211yescharacteristic
38C2×#95×C151C2212yes—
39C2×#95×C151C2212yes—
40C2×#95×C151C2212yes—
41C22×Q8×C151—22no—
42C22×Q8×C151—22no—
43C22×Q8×C151—24no—
44C22×Q8×C151—24no—
45C22×Q8×C151D414yes—
46C23×C4×C151C2311yescharacteristic
47C23×C4×C151C2311yescharacteristic
48C23×C4×C151C2312yes—
49C23×C4×C151C2311yescharacteristic
50C23×C4×C151C2312yes—
51C23×C4×C151C2312yes—
52C23×C4×C151C2311yescharacteristic
53C23×C4×C151C2311yescharacteristic
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—22no—
68C2×C4⋊C4×C151—24no—
69C2×C4⋊C4×C151—24no—
70C2×C4⋊C4×C151—22no—
71C2×C4⋊C4×C151—24no—
72C2×C4⋊C4×C151—24no—
73C2×C4⋊C4×C151—24no—
74C2×C4⋊C4×C151—42no—
75C2×C4⋊C4×C151D414yes—
76C2×C42×C151—24no—
77C2×C42×C151—24no—
78C2×C42×C151—24no—
79C2×C42×C151—22no—
80C2×C42×C151—22no—
81C2×C42×C151D414yes—
82#95×C151—22no—
83#95×C151—22no—
84#95×C151—22no—
85#95×C151—22no—
86#95×C151—22no—
87#95×C151—24no—
88#95×C151—22no—
89#95×C151—24no—
90#95×C151—24no—
91#95×C151—24no—
92#95×C151—24no—
93#95×C151—42no—
94#95×C151—42no—
95#95×C151Q818yescomplemented
96C24×C151C2411yescharacteristic
97C2×Q8×C151—28no—
98C2×Q8×C151—28no—
99C2×Q8×C151—216no—
100C2×Q8×C151—28no—
101C2×Q8×C151—216no—
102C22×C4×C151—21no—
103C22×C4×C151—21no—
104C22×C4×C151—22no—
105C22×C4×C151—22no—
106C22×C4×C151—22no—
107C22×C4×C151—22no—
108C22×C4×C151—22no—
109C22×C4×C151—22no—
110C22×C4×C151—22no—
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—21no—
118C22×C4×C151—22no—
119C22×C4×C151—21no—
120C22×C4×C151—21no—
121C22×C4×C151—22no—
122C22×C4×C151—22no—
123C22×C4×C151—22no—
124C22×C4×C151—22no—
125C22×C4×C151—22no—
126C22×C4×C151—21no—
127C22×C4×C151—21no—
128C22×C4×C151—21no—
129C22×C4×C151—21no—
130C22×C4×C151—22no—
131C22×C4×C151—22no—
132C22×C4×C151—22no—
133C22×C4×C151—22no—
134C22×C4×C151—21no—
135C22×C4×C151—22no—
136C22×C4×C151—22no—
137C22×C4×C151—22no—
138C22×C4×C151—21no—
139C22×C4×C151—21no—
140C22×C4×C151—22no—
141C22×C4×C151—21no—
142C22×C4×C151—22no—
143C22×C4×C151—22no—
144C22×C4×C151—22no—
145C22×C4×C151—21no—
146C22×C4×C151—21no—
147C22×C4×C151—21no—
148C22×C4×C151—21no—
149C22×C4×C151—22no—
150C22×C4×C151—22no—
151C22×C4×C151—22no—
152C22×C4×C151—21no—
153C22×C4×C151—22no—
154C22×C4×C151—21no—
155C22×C4×C151C2×D414yes—
156C22×C4×C151C2×D412yes—
157C22×C4×C151C2×D412yes—
158C22×C4×C151C2×D412yes—
159C22×C4×C151C2×D412yes—
160C22×C4×C151C2×D414yes—
161C22×C4×C151C2×D412yes—
162C22×C4×C151C2×Q814yes—
163C22×C4×C151C2×Q814yes—
164C22×C4×C151C2×Q814yes—
165C22×C4×C151#4112yes—
166C22×C4×C151#4112yes—
167C22×C4×C151#4114yes—
168C22×C4×C151#4114yes—
169C4⋊C4×C151—28no—
170C4⋊C4×C151—216no—
171C4⋊C4×C151—28no—
172C4⋊C4×C151—48no—
173C4⋊C4×C151—44no—
174C4⋊C4×C151—48no—
175C42×C151—216no—
176C42×C151—28no—
177C23×C151C22×D411yescharacteristic
178C23×C151C22×D411yescharacteristic
179C23×C151C22×D411yescharacteristic
180C23×C151C22×Q812yes—
181C23×C151C2×#4112yes—
182C23×C151C2×#4112yes—
183C23×C151C2×#4111yescharacteristic
184C23×C151C2×#4111yescharacteristic
185C23×C151H(5,𝔽2)11yescharacteristic
186C23×C1512−1+412yes—
187C23×C1512−1+411yescharacteristic
188Q8×C151—232no—
189C2×C4×C151—24no—
190C2×C4×C151—22no—
191C2×C4×C151—24no—
192C2×C4×C151—24no—
193C2×C4×C151—22no—
194C2×C4×C151—22no—
195C2×C4×C151—24no—
196C2×C4×C151—24no—
197C2×C4×C151—24no—
198C2×C4×C151—24no—
199C2×C4×C151—24no—
200C2×C4×C151—22no—
201C2×C4×C151—24no—
202C2×C4×C151—24no—
203C2×C4×C151—24no—
204C2×C4×C151—22no—
205C2×C4×C151—22no—
206C2×C4×C151—22no—
207C2×C4×C151—22no—
208C2×C4×C151—24no—
209C2×C4×C151—24no—
210C2×C4×C151—22no—
211C2×C4×C151—22no—
212C2×C4×C151—24no—
213C2×C4×C151—24no—
214C2×C4×C151—22no—
215C2×C4×C151—24no—
216C2×C4×C151—24no—
217C2×C4×C151—24no—
218C2×C4×C151—24no—
219C2×C4×C151—24no—
220C2×C4×C151—41no—
221C2×C4×C151—42no—
222C2×C4×C151—41no—
223C2×C4×C151—42no—
224C2×C4×C151—42no—
225C2×C4×C151—41no—
226C2×C4×C151—41no—
227C2×C4×C151—42no—
228C2×C4×C151—42no—
229C2×C4×C151—42no—
230C2×C4×C151—42no—
231C2×C4×C151—41no—
232C2×C4×C151—41no—
233C2×C4×C151—41no—
234C2×C4×C151—41no—
235C2×C4×C151—42no—
236C2×C4×C151—41no—
237C2×C4×C151—42no—
238C2×C4×C151—41no—
239C2×C4×C151—42no—
240C2×C4×C151—42no—
241C2×C4×C151—42no—
242C2×C4×C151—42no—
243C2×C4×C151—41no—
244C2×C4×C151—42no—
245C2×C4×C151—41no—
246C2×C4×C151—41no—
247C2×C4×C151—42no—
248C2×C4×C151—41no—
249C2×C4×C151—41no—
250C2×C4×C151—41no—
251C2×C4×C151—42no—
252C2×C4×C151—42no—
253C2×C4×C151#12014yes—
254C2×C4×C151#12318yes—
255C2×C4×C151C4⋊Q814yes—
256C22×C151C2×#12011yescharacteristic
257C22×C151C2×#12312yes—
258C22×C151#52511yescharacteristic
259C22×C151#52511yescharacteristic
260C22×C151#52512yes—
261C22×C151#52511yescharacteristic
262C22×C151C2×C4⋊Q811yescharacteristic
263C22×C151#53312yes—
264C22×C151#53312yes—
265C22×C151#53611yescharacteristic
266C22×C151#53711yescharacteristic
267C22×C151#54112yes—
268C22×C151#54212yes—
269C22×C151#54611yescharacteristic
270C22×C151#54711yescharacteristic
271C22×C151#54811yescharacteristic
272C22×C151D4×Q812yes—
273C22×C151D4×Q812yes—
274C22×C151#55011yescharacteristic
275C22×C151#55212yes—
276C22×C151#55412yes—
277C22×C151#55612yes—
278C22×C151#55712yes—
279C4×C151—24no—
280C4×C151—28no—
281C4×C151—24no—
282C4×C151—42no—
283C4×C151—42no—
284C4×C151—44no—
285C4×C151—42no—
286C4×C151—44no—
287C4×C151—44no—
288C4×C151—81no—
289C4×C151—81no—
290C2×C151#239911yescharacteristic
291C2×C151#240711yescharacteristic
292C2×C151#242312yes—
293C2×C151#243411yescharacteristic
294C2×C151#244612yes—
295C2×C151#246212yes—
296C2×C151#246512yes—
297C2×C151#258411yescharacteristic
298C2×C151#259911yescharacteristic
299C2×C151#263711yescharacteristic
300C2×C151#284911yescharacteristic
301#14879C15111yesmaximal, characteristic, direct product factor, Sylow
302C151#1487911yescharacteristic, direct product factor, Sylow
303C22×C4×Q8C2×C15111yescharacteristic
304C2×#398C2×C15111yescharacteristic
305C2×#395C2×C15111yescharacteristic
306C2×#387C2×C15111yescharacteristic
307#1446C2×C15111yescharacteristic
308#1445C2×C15111yescharacteristic
309#1444C2×C15112yes—
310#1441C2×C15112yes—
311#1436C2×C15112yes—
312#1436C2×C15112yes—
313#1434C2×C15111yescharacteristic
314C23×Q8C22×C15111yescharacteristic
315C2×C4×Q8—24no—
316C2×C4×Q8—24no—
317C2×C4×Q8—24no—
318C22×C4⋊C4C22×C15111yescharacteristic
319C22×C4⋊C4C22×C15112yes—
320C22×C4⋊C4C22×C15112yes—
321C22×C4⋊C4C22×C15111yescharacteristic
322C22×C4⋊C4C22×C15112yes—
323C22×C4⋊C4C22×C15111yescharacteristic
324C22×C42C22×C15112yes—
325C22×C42C22×C15111yescharacteristic
326#398—24no—
327#395—24no—
328#387—24no—
329C2×#95C22×C15111yescharacteristic
330C2×#95C22×C15112yes—
331C2×#95C22×C15111yescharacteristic
332C2×#95C22×C15112yes—
333C2×#95C22×C15111yescharacteristic
334C2×#95C22×C15111yescharacteristic
335C2×#95C22×C15112yes—
336C2×#95C22×C15112yes—
337C2×#95C22×C15112yes—
338C2×#95C22×C15111yescharacteristic
339C2×#95C22×C15111yescharacteristic
340C2×#95C22×C15112yes—
341C2×#95C22×C15112yes—
342C2×#95C22×C15112yes—
343C22×Q8—24no—
344C22×Q8—24no—
345C22×Q8—22no—
346C22×Q8—22no—
347C22×Q8D4×C15114yes—
348C23×C4C23×C15111yescharacteristic
349C23×C4C23×C15111yescharacteristic
350C23×C4C23×C15112yes—
351C23×C4C23×C15112yes—
352C23×C4C23×C15111yescharacteristic
353C23×C4C23×C15111yescharacteristic
354C23×C4C23×C15112yes—
355C23×C4C23×C15111yescharacteristic
356C23×C4C23×C15111yescharacteristic
357C23×C4C23×C15112yes—
358C23×C4C23×C15111yescharacteristic
359C4×Q8—232no—
360C2×C4⋊C4—22no—
361C2×C4⋊C4—22no—
362C2×C4⋊C4—24no—
363C2×C4⋊C4—24no—
364C2×C4⋊C4—24no—
365C2×C4⋊C4—22no—
366C2×C4⋊C4—22no—
367C2×C4⋊C4—22no—
368C2×C4⋊C4—24no—
369C2×C4⋊C4—24no—
370C2×C4⋊C4—24no—
371C2×C4⋊C4—22no—
372C2×C4⋊C4—22no—
373C2×C4⋊C4—24no—
374C2×C4⋊C4—24no—
375C2×C4⋊C4—22no—
376C2×C4⋊C4—42no—
377C2×C4⋊C4D4×C15114yes—
378C2×C42—24no—
379C2×C42—24no—
380C2×C42—24no—
381C2×C42—22no—
382C2×C42—22no—
383C2×C42D4×C15114yes—
384#95—24no—
385#95—24no—
386#95—24no—
387#95—22no—
388#95—22no—
389#95—22no—
390#95—22no—
391#95—22no—
392#95—24no—
393#95—22no—
394#95—24no—
395#95—42no—
396#95—42no—
397#95Q8×C15118yescomplemented
398C24C24×C15111yescharacteristic
399C2×Q8—28no—
400C2×Q8—28no—
401C2×Q8—216no—
402C2×Q8—28no—
403C2×Q8—216no—
404C22×C4—21no—
405C22×C4—21no—
406C22×C4—22no—
407C22×C4—22no—
408C22×C4—22no—
409C22×C4—22no—
410C22×C4—22no—
411C22×C4—22no—
412C22×C4—22no—
413C22×C4—21no—
414C22×C4—21no—
415C22×C4—22no—
416C22×C4—22no—
417C22×C4—21no—
418C22×C4—22no—
419C22×C4—21no—
420C22×C4—22no—
421C22×C4—21no—
422C22×C4—21no—
423C22×C4—22no—
424C22×C4—22no—
425C22×C4—22no—
426C22×C4—22no—
427C22×C4—22no—
428C22×C4—21no—
429C22×C4—21no—
430C22×C4—21no—
431C22×C4—21no—
432C22×C4—22no—
433C22×C4—22no—
434C22×C4—22no—
435C22×C4—22no—
436C22×C4—21no—
437C22×C4—22no—
438C22×C4—22no—
439C22×C4—22no—
440C22×C4—21no—
441C22×C4—21no—
442C22×C4—22no—
443C22×C4—21no—
444C22×C4—22no—
445C22×C4—22no—
446C22×C4—22no—
447C22×C4—21no—
448C22×C4—21no—
449C22×C4—21no—
450C22×C4—21no—
451C22×C4—22no—
452C22×C4—22no—
453C22×C4—22no—
454C22×C4—21no—
455C22×C4—22no—
456C22×C4—21no—
457C22×C4C2×D4×C15114yes—
458C22×C4C2×D4×C15112yes—
459C22×C4C2×D4×C15112yes—
460C22×C4C2×D4×C15112yes—
461C22×C4C2×D4×C15112yes—
462C22×C4C2×D4×C15114yes—
463C22×C4C2×D4×C15112yes—
464C22×C4C2×Q8×C15114yes—
465C22×C4C2×Q8×C15114yes—
466C22×C4C2×Q8×C15114yes—
467C22×C4#41×C15112yes—
468C22×C4#41×C15112yes—
469C22×C4#41×C15114yes—
470C22×C4#41×C15114yes—
471C4⋊C4—216no—
472C4⋊C4—28no—
473C4⋊C4—28no—
474C4⋊C4—48no—
475C4⋊C4—44no—
476C4⋊C4—48no—
477C42—216no—
478C42—28no—
479C23C22×D4×C15111yescharacteristic
480C23C22×D4×C15111yescharacteristic
481C23C22×D4×C15111yescharacteristic
482C23C22×Q8×C15112yes—
483C23C2×#41×C15112yes—
484C23C2×#41×C15112yes—
485C23C2×#41×C15111yescharacteristic
486C23C2×#41×C15111yescharacteristic
487C23H(5,𝔽2)×C15111yescharacteristic
488C232−1+4×C15112yes—
489C232−1+4×C15111yescharacteristic
490Q8—232no—
491C2×C4—22no—
492C2×C4—24no—
493C2×C4—24no—
494C2×C4—24no—
495C2×C4—24no—
496C2×C4—24no—
497C2×C4—24no—
498C2×C4—24no—
499C2×C4—22no—
500C2×C4—22no—
501C2×C4—24no—
502C2×C4—22no—
503C2×C4—24no—
504C2×C4—24no—
505C2×C4—24no—
506C2×C4—22no—
507C2×C4—22no—
508C2×C4—22no—
509C2×C4—22no—
510C2×C4—24no—
511C2×C4—24no—
512C2×C4—22no—
513C2×C4—22no—
514C2×C4—24no—
515C2×C4—24no—
516C2×C4—22no—
517C2×C4—24no—
518C2×C4—24no—
519C2×C4—24no—
520C2×C4—24no—
521C2×C4—24no—
522C2×C4—41no—
523C2×C4—42no—
524C2×C4—41no—
525C2×C4—42no—
526C2×C4—42no—
527C2×C4—41no—
528C2×C4—41no—
529C2×C4—42no—
530C2×C4—42no—
531C2×C4—42no—
532C2×C4—42no—
533C2×C4—41no—
534C2×C4—41no—
535C2×C4—41no—
536C2×C4—41no—
537C2×C4—42no—
538C2×C4—41no—
539C2×C4—42no—
540C2×C4—41no—
541C2×C4—42no—
542C2×C4—42no—
543C2×C4—42no—
544C2×C4—42no—
545C2×C4—41no—
546C2×C4—42no—
547C2×C4—41no—
548C2×C4—41no—
549C2×C4—42no—
550C2×C4—41no—
551C2×C4—41no—
552C2×C4—41no—
553C2×C4—42no—
554C2×C4—42no—
555C2×C4#120×C15114yes—
556C2×C4#123×C15118yes—
557C2×C4C4⋊Q8×C15114yes—
558C22C2×#120×C15111yescharacteristic
559C22C2×#123×C15112yes—
560C22#525×C15111yescharacteristic
561C22#525×C15111yescharacteristic
562C22#525×C15112yes—
563C22#525×C15111yescharacteristic
564C22C2×C4⋊Q8×C15111yescharacteristic
565C22#533×C15112yes—
566C22#533×C15112yes—
567C22#536×C15111yescharacteristic
568C22#537×C15111yescharacteristic
569C22#541×C15112yes—
570C22#542×C15112yes—
571C22#546×C15111yescharacteristic
572C22#547×C15111yescharacteristic
573C22#548×C15111yescharacteristic
574C22D4×Q8×C15112yes—
575C22D4×Q8×C15112yes—
576C22#550×C15111yescharacteristic
577C22#552×C15112yes—
578C22#554×C15112yes—
579C22#556×C15112yes—
580C22#557×C15112yes—
581C4—24no—
582C4—28no—
583C4—24no—
584C4—42no—
585C4—42no—
586C4—44no—
587C4—42no—
588C4—44no—
589C4—44no—
590C4—81no—
591C4—81no—
592C2#2399×C15111yescharacteristic
593C2#2407×C15111yescharacteristic
594C2#2423×C15112yes—
595C2#2434×C15111yescharacteristic
596C2#2446×C15112yes—
597C2#2462×C15112yes—
598C2#2465×C15112yes—
599C2#2584×C15111yescharacteristic
600C2#2599×C15111yescharacteristic
601C2#2637×C15111yescharacteristic
602C2#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
95. #95×C151Q8semidirect
301. #14879C151direct (N × H)
302. C151#14879direct (N × H)
397. #95Q8×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×#398×C1512
C2×#395×C1512
C2×#387×C1512
#1446×C1512
#1445×C1512
#1444×C1512
#1441×C1512
#1436×C1512
#1434×C1512
#14879151