Finite Group Databasebeta

← C151×#15568 #50320493

Subgroups — C151×#15568 #50320493

Order 38656.

1538 conjugacy classes of subgroups.

The subgroup lattice has 590 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#393×C151C211yesmaximal, characteristic
2C2×#385×C151C211yesmaximal, characteristic
3#1446×C151C212yesmaximal, complemented
4#1442×C151C212yesmaximal, complemented
5#1441×C151C212yesmaximal, complemented
6#1439×C151C212yesmaximal
7#1437×C151C211yesmaximal, characteristic
8#1436×C151C212yesmaximal, complemented
9C22⋊#95×C151C212yesmaximal
10C23×Q8×C151C2211yescharacteristic
11C24×C4×C151C2211yescharacteristic
12C22×C4⋊C4×C151C2212yes—
13C22×C4⋊C4×C151C2212yes—
14C22×C22⋊C4×C151C2211yescharacteristic
15C22×C22⋊C4×C151C2212yes—
16C22×C22⋊C4×C151C2211yescharacteristic
17C22×C22⋊C4×C151C2212yes—
18C22×C42×C151C2211yescharacteristic
19#393×C151—24no—
20#385×C151—24no—
21C2×#95×C151C2212yes—
22C2×#95×C151C2211yescharacteristic
23C2×#95×C151C2212yes—
24C2×#95×C151C2212yes—
25C2×#95×C151C2212yes—
26C2×#95×C151C2212yes—
27C2×#95×C151C2212yes—
28C2×#95×C151C2212yes—
29C2×#95×C151C2212yes—
30C2×#95×C151C2211yescharacteristic
31C2×#95×C151C2212yes—
32C2×#95×C151C2212yes—
33C25×C151C2311yescharacteristic
34C22×Q8×C151—22no—
35C22×Q8×C151—24no—
36C22×Q8×C151—42no—
37C22×Q8×C151—41no—
38C22×Q8×C151—41no—
39C23×C4×C151—24no—
40C23×C4×C151—22no—
41C23×C4×C151—41no—
42C23×C4×C151—41no—
43C23×C4×C151—42no—
44C23×C4×C151C2312yes—
45C23×C4×C151C2311yescharacteristic
46C23×C4×C151C2311yescharacteristic
47C23×C4×C151C2312yes—
48C23×C4×C151C2312yes—
49C23×C4×C151C2312yes—
50C23×C4×C151C2312yes—
51C23×C4×C151C2312yes—
52C2×C4⋊C4×C151—24no—
53C2×C4⋊C4×C151—24no—
54C2×C4⋊C4×C151—24no—
55C2×C4⋊C4×C151—42no—
56C2×C4⋊C4×C151—42no—
57C2×C4⋊C4×C151—42no—
58C2×C22⋊C4×C151—24no—
59C2×C22⋊C4×C151—24no—
60C2×C22⋊C4×C151—22no—
61C2×C22⋊C4×C151—24no—
62C2×C22⋊C4×C151—42no—
63C2×C22⋊C4×C151—42no—
64C2×C22⋊C4×C151—41no—
65C2×C22⋊C4×C151—41no—
66C2×C22⋊C4×C151—42no—
67C2×C22⋊C4×C151D414yes—
68C2×C22⋊C4×C151Q818yescomplemented
69C2×C42×C151—41no—
70C2×C42×C151—42no—
71#95×C151—24no—
72#95×C151—24no—
73#95×C151—22no—
74#95×C151—24no—
75#95×C151—24no—
76#95×C151—24no—
77#95×C151—41no—
78#95×C151—42no—
79#95×C151—42no—
80#95×C151—42no—
81#95×C151—42no—
82#95×C151—42no—
83C24×C151—22no—
84C24×C151—22no—
85C24×C151—22no—
86C24×C151—22no—
87C24×C151—21no—
88C24×C151—21no—
89C24×C151—22no—
90C24×C151C2×D412yes—
91C24×C151C2×Q814yes—
92C24×C151C2411yescharacteristic
93C2×Q8×C151—48no—
94C2×Q8×C151—44no—
95C2×Q8×C151—44no—
96C2×Q8×C151—48no—
97C2×Q8×C151—44no—
98C22×C4×C151—22no—
99C22×C4×C151—22no—
100C22×C4×C151—22no—
101C22×C4×C151—22no—
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—22no—
109C22×C4×C151—22no—
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—22no—
117C22×C4×C151—22no—
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—21no—
128C22×C4×C151—22no—
129C22×C4×C151—22no—
130C22×C4×C151—22no—
131C22×C4×C151—21no—
132C22×C4×C151—21no—
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—44no—
144C22×C4×C151—48no—
145C22×C4×C151—48no—
146C22×C4×C151—44no—
147C22×C4×C151—44no—
148C22×C4×C151C2×D412yes—
149C22×C4×C151C2×D412yes—
150C22×C4×C151C2×Q814yes—
151C22×C4×C151C2×Q814yes—
152C22×C4×C151#4114yes—
153C22×C4×C151#4114yes—
154C22×C4×C151#4114yes—
155C4⋊C4×C151—48no—
156C4⋊C4×C151—48no—
157C22⋊C4×C151—28no—
158C22⋊C4×C151—44no—
159C22⋊C4×C151—48no—
160C22⋊C4×C151—48no—
161C42×C151—44no—
162C23×C151—22no—
163C23×C151—24no—
164C23×C151—22no—
165C23×C151—24no—
166C23×C151—24no—
167C23×C151—24no—
168C23×C151—24no—
169C23×C151—24no—
170C23×C151—24no—
171C23×C151—24no—
172C23×C151—42no—
173C23×C151—42no—
174C23×C151—42no—
175C23×C151—42no—
176C23×C151—41no—
177C23×C151—41no—
178C23×C151—42no—
179C23×C151—42no—
180C23×C151—41no—
181C23×C151—41no—
182C23×C151C4⋊Q814yes—
183C23×C151C22×D411yescharacteristic
184C23×C151C22×Q812yes—
185C23×C151C2×#4112yes—
186C23×C151C2×#4112yes—
187C23×C151C2×#4112yes—
188C23×C151H(5,𝔽2)11yescharacteristic
189C23×C151H(5,𝔽2)11yescharacteristic
190C23×C151H(5,𝔽2)12yes—
191C23×C151H(5,𝔽2)12yes—
192Q8×C151—416no—
193C2×C4×C151—24no—
194C2×C4×C151—24no—
195C2×C4×C151—22no—
196C2×C4×C151—22no—
197C2×C4×C151—24no—
198C2×C4×C151—24no—
199C2×C4×C151—24no—
200C2×C4×C151—24no—
201C2×C4×C151—24no—
202C2×C4×C151—24no—
203C2×C4×C151—24no—
204C2×C4×C151—24no—
205C2×C4×C151—24no—
206C2×C4×C151—24no—
207C2×C4×C151—24no—
208C2×C4×C151—24no—
209C2×C4×C151—24no—
210C2×C4×C151—24no—
211C2×C4×C151—24no—
212C2×C4×C151—416no—
213C2×C4×C151—42no—
214C2×C4×C151—42no—
215C2×C4×C151—42no—
216C2×C4×C151—42no—
217C2×C4×C151—42no—
218C2×C4×C151—42no—
219C2×C4×C151—42no—
220C2×C4×C151—42no—
221C2×C4×C151—42no—
222C2×C4×C151—42no—
223C2×C4×C151—42no—
224C2×C4×C151—42no—
225C2×C4×C151—42no—
226C2×C4×C151—42no—
227C2×C4×C151—41no—
228C2×C4×C151—41no—
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—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—
246C22×C151—24no—
247C22×C151—28no—
248C22×C151—44no—
249C22×C151—44no—
250C22×C151—42no—
251C22×C151—42no—
252C22×C151—44no—
253C22×C151—44no—
254C22×C151—44no—
255C22×C151#52511yescharacteristic
256C22×C151#52912yes—
257C22×C151C2×C4⋊Q811yescharacteristic
258C22×C151#53312yes—
259C22×C151#53411yescharacteristic
260C22×C151#53812yes—
261C22×C151#53812yes—
262C22×C151#53812yes—
263C22×C151#54312yes—
264C22×C151#54612yes—
265C22×C151#54612yes—
266C22×C151#55111yescharacteristic
267C22×C151#55111yescharacteristic
268C22×C151#55412yes—
269C22×C151#55412yes—
270C22×C151#55412yes—
271C22×C151#55412yes—
272C22×C151#55512yes—
273C22×C151#55912yes—
274C22×C151#56011yescharacteristic
275C22×C151H(3,𝔽4)11yescharacteristic
276C4×C151—42no—
277C4×C151—44no—
278C4×C151—42no—
279C4×C151—44no—
280C4×C151—44no—
281C4×C151—44no—
282C4×C151—44no—
283C4×C151—82no—
284C2×C151—44no—
285C2×C151#245912yes—
286C2×C151#254912yes—
287C2×C151#257412yes—
288C2×C151#258311yescharacteristic
289C2×C151#258912yes—
290C2×C151#268411yescharacteristic
291C2×C151#269711yescharacteristic
292C2×C151#278412yes—
293C2×C151#280412yes—
294#15568C15111yesmaximal, characteristic, direct product factor, Sylow
295C151#1556811yescharacteristic, direct product factor, Sylow
296C2×#393C2×C15111yescharacteristic
297C2×#385C2×C15111yescharacteristic
298#1446C2×C15112yescomplemented
299#1442C2×C15112yescomplemented
300#1441C2×C15112yescomplemented
301#1439C2×C15112yes—
302#1437C2×C15111yescharacteristic
303#1436C2×C15112yescomplemented
304C22⋊#95C2×C15112yes—
305C23×Q8C22×C15111yescharacteristic
306C24×C4C22×C15111yescharacteristic
307C22×C4⋊C4C22×C15112yes—
308C22×C4⋊C4C22×C15112yes—
309C22×C22⋊C4C22×C15111yescharacteristic
310C22×C22⋊C4C22×C15112yes—
311C22×C22⋊C4C22×C15111yescharacteristic
312C22×C22⋊C4C22×C15112yes—
313C22×C42C22×C15111yescharacteristic
314#393—24no—
315#385—24no—
316C2×#95C22×C15112yes—
317C2×#95C22×C15111yescharacteristic
318C2×#95C22×C15112yes—
319C2×#95C22×C15112yes—
320C2×#95C22×C15112yes—
321C2×#95C22×C15112yes—
322C2×#95C22×C15112yes—
323C2×#95C22×C15112yes—
324C2×#95C22×C15112yes—
325C2×#95C22×C15111yescharacteristic
326C2×#95C22×C15112yes—
327C2×#95C22×C15112yes—
328C25C23×C15111yescharacteristic
329C22×Q8—24no—
330C22×Q8—22no—
331C22×Q8—42no—
332C22×Q8—41no—
333C22×Q8—41no—
334C23×C4—22no—
335C23×C4—24no—
336C23×C4—41no—
337C23×C4—41no—
338C23×C4—42no—
339C23×C4C23×C15112yes—
340C23×C4C23×C15112yes—
341C23×C4C23×C15112yes—
342C23×C4C23×C15112yes—
343C23×C4C23×C15112yes—
344C23×C4C23×C15112yes—
345C23×C4C23×C15111yescharacteristic
346C23×C4C23×C15111yescharacteristic
347C2×C4⋊C4—24no—
348C2×C4⋊C4—24no—
349C2×C4⋊C4—24no—
350C2×C4⋊C4—42no—
351C2×C4⋊C4—42no—
352C2×C4⋊C4—42no—
353C2×C22⋊C4—22no—
354C2×C22⋊C4—24no—
355C2×C22⋊C4—24no—
356C2×C22⋊C4—24no—
357C2×C22⋊C4—41no—
358C2×C22⋊C4—41no—
359C2×C22⋊C4—42no—
360C2×C22⋊C4—42no—
361C2×C22⋊C4—42no—
362C2×C22⋊C4D4×C15114yes—
363C2×C22⋊C4Q8×C15118yescomplemented
364C2×C42—41no—
365C2×C42—42no—
366#95—24no—
367#95—24no—
368#95—24no—
369#95—24no—
370#95—24no—
371#95—22no—
372#95—41no—
373#95—42no—
374#95—42no—
375#95—42no—
376#95—42no—
377#95—42no—
378C24—22no—
379C24—22no—
380C24—22no—
381C24—22no—
382C24—21no—
383C24—21no—
384C24—22no—
385C24C2×D4×C15112yes—
386C24C2×Q8×C15114yes—
387C24C24×C15111yescharacteristic
388C2×Q8—48no—
389C2×Q8—44no—
390C2×Q8—44no—
391C2×Q8—48no—
392C2×Q8—44no—
393C22×C4—22no—
394C22×C4—22no—
395C22×C4—22no—
396C22×C4—22no—
397C22×C4—22no—
398C22×C4—22no—
399C22×C4—22no—
400C22×C4—22no—
401C22×C4—22no—
402C22×C4—22no—
403C22×C4—22no—
404C22×C4—22no—
405C22×C4—22no—
406C22×C4—22no—
407C22×C4—22no—
408C22×C4—22no—
409C22×C4—22no—
410C22×C4—21no—
411C22×C4—22no—
412C22×C4—22no—
413C22×C4—22no—
414C22×C4—22no—
415C22×C4—22no—
416C22×C4—22no—
417C22×C4—22no—
418C22×C4—22no—
419C22×C4—22no—
420C22×C4—22no—
421C22×C4—22no—
422C22×C4—21no—
423C22×C4—22no—
424C22×C4—22no—
425C22×C4—22no—
426C22×C4—21no—
427C22×C4—21no—
428C22×C4—22no—
429C22×C4—22no—
430C22×C4—22no—
431C22×C4—22no—
432C22×C4—22no—
433C22×C4—22no—
434C22×C4—22no—
435C22×C4—22no—
436C22×C4—22no—
437C22×C4—22no—
438C22×C4—44no—
439C22×C4—48no—
440C22×C4—48no—
441C22×C4—44no—
442C22×C4—44no—
443C22×C4C2×D4×C15112yes—
444C22×C4C2×D4×C15112yes—
445C22×C4C2×Q8×C15114yes—
446C22×C4C2×Q8×C15114yes—
447C22×C4#41×C15114yes—
448C22×C4#41×C15114yes—
449C22×C4#41×C15114yes—
450C4⋊C4—48no—
451C4⋊C4—48no—
452C22⋊C4—28no—
453C22⋊C4—44no—
454C22⋊C4—48no—
455C22⋊C4—48no—
456C42—44no—
457C23—22no—
458C23—24no—
459C23—22no—
460C23—24no—
461C23—24no—
462C23—24no—
463C23—24no—
464C23—24no—
465C23—24no—
466C23—24no—
467C23—42no—
468C23—42no—
469C23—42no—
470C23—42no—
471C23—41no—
472C23—41no—
473C23—42no—
474C23—42no—
475C23—41no—
476C23—41no—
477C23C4⋊Q8×C15114yes—
478C23C22×D4×C15111yescharacteristic
479C23C22×Q8×C15112yes—
480C23C2×#41×C15112yes—
481C23C2×#41×C15112yes—
482C23C2×#41×C15112yes—
483C23H(5,𝔽2)×C15111yescharacteristic
484C23H(5,𝔽2)×C15111yescharacteristic
485C23H(5,𝔽2)×C15112yes—
486C23H(5,𝔽2)×C15112yes—
487Q8—416no—
488C2×C4—24no—
489C2×C4—24no—
490C2×C4—22no—
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—24no—
500C2×C4—24no—
501C2×C4—24no—
502C2×C4—24no—
503C2×C4—24no—
504C2×C4—24no—
505C2×C4—24no—
506C2×C4—24no—
507C2×C4—416no—
508C2×C4—42no—
509C2×C4—42no—
510C2×C4—42no—
511C2×C4—42no—
512C2×C4—42no—
513C2×C4—42no—
514C2×C4—42no—
515C2×C4—42no—
516C2×C4—42no—
517C2×C4—42no—
518C2×C4—42no—
519C2×C4—42no—
520C2×C4—42no—
521C2×C4—42no—
522C2×C4—41no—
523C2×C4—41no—
524C2×C4—42no—
525C2×C4—42no—
526C2×C4—42no—
527C2×C4—42no—
528C2×C4—41no—
529C2×C4—42no—
530C2×C4—42no—
531C2×C4—41no—
532C2×C4—42no—
533C2×C4—42no—
534C2×C4—42no—
535C2×C4—42no—
536C2×C4—42no—
537C2×C4—42no—
538C2×C4—42no—
539C2×C4—42no—
540C2×C4—42no—
541C22—28no—
542C22—24no—
543C22—44no—
544C22—42no—
545C22—42no—
546C22—44no—
547C22—44no—
548C22—44no—
549C22—44no—
550C22#525×C15111yescharacteristic
551C22#529×C15112yes—
552C22C2×C4⋊Q8×C15111yescharacteristic
553C22#533×C15112yes—
554C22#534×C15111yescharacteristic
555C22#538×C15112yes—
556C22#538×C15112yes—
557C22#538×C15112yes—
558C22#543×C15112yes—
559C22#546×C15112yes—
560C22#546×C15112yes—
561C22#551×C15111yescharacteristic
562C22#551×C15111yescharacteristic
563C22#554×C15112yes—
564C22#554×C15112yes—
565C22#554×C15112yes—
566C22#554×C15112yes—
567C22#555×C15112yes—
568C22#559×C15112yes—
569C22#560×C15111yescharacteristic
570C22H(3,𝔽4)×C15111yescharacteristic
571C4—44no—
572C4—42no—
573C4—42no—
574C4—44no—
575C4—44no—
576C4—44no—
577C4—44no—
578C4—82no—
579C2—44no—
580C2#2459×C15112yes—
581C2#2549×C15112yes—
582C2#2574×C15112yes—
583C2#2583×C15111yescharacteristic
584C2#2589×C15112yes—
585C2#2684×C15111yescharacteristic
586C2#2697×C15111yescharacteristic
587C2#2784×C15112yes—
588C2#2804×C15112yes—
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
3. #1446×C151C2semidirect
4. #1442×C151C2semidirect
5. #1441×C151C2semidirect
8. #1436×C151C2semidirect
68. C2×C22⋊C4×C151Q8semidirect
294. #15568C151direct (N × H)
295. C151#15568direct (N × H)
298. #1446C2×C151semidirect
299. #1442C2×C151semidirect
300. #1441C2×C151semidirect
303. #1436C2×C151semidirect
363. C2×C22⋊C4Q8×C151semidirect

Maximal subgroups

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

subgroupindex
C2×#393×C1512
C2×#385×C1512
#1446×C1512
#1442×C1512
#1441×C1512
#1439×C1512
#1437×C1512
#1436×C1512
C22⋊#95×C1512
#15568151