Finite Group Databasebeta

← C151×#23591 #50328516

Subgroups — C151×#23591 #50328516

Order 38656.

1182 conjugacy classes of subgroups.

The subgroup lattice has 582 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#3460×C151C211yesmaximal, characteristic, complemented
2C4×AGL(1,ℤ/8)×C151C212yesmaximal, complemented
3#2328×C151C211yesmaximal, characteristic, complemented
4#2061×C151C211yesmaximal, characteristic, complemented
5#2040×C151C211yesmaximal, characteristic, complemented
6#2037×C151C212yesmaximal, complemented
7#2027×C151C211yesmaximal, characteristic, complemented
8#2006×C151C211yesmaximal, characteristic, complemented
9#2002×C151C212yesmaximal, complemented
10#1759×C151C212yesmaximal, complemented
11C4×#100×C151C211yesmaximal, characteristic, complemented
12C2×AGL(1,ℤ/8)×C151C2212yes—
13#544×C151C2211yescharacteristic
14#542×C151—22no—
15#540×C151—22no—
16#538×C151—22no—
17#537×C151C2211yescharacteristic
18#535×C151C2212yes—
19#532×C151—22no—
20C2×#127×C151C2211yescharacteristic
21#529×C151—22no—
22#525×C151—22no—
23C4×#41×C151C2212yes—
24C2×C4×D4×C151C2211yescharacteristic
25C2×C4×D4×C151C2211yescharacteristic
26#442×C151—22no—
27#440×C151—22no—
28C4×SD16×C151—22no—
29C4×D8×C151—22no—
30#428×C151C2212yes—
31C2×#104×C151C2212yes—
32C2×#104×C151C2212yes—
33#418×C151C2212yes—
34#417×C151C2212yes—
35C2×#100×C151C2212yes—
36C4×M16×C151C2212yes—
37#390×C151C2211yescharacteristic
38#390×C151C2211yescharacteristic
39#386×C151—22no—
40#386×C151—22no—
41#382×C151C2211yescharacteristic
42#376×C151C2211yescharacteristic
43#343×C151C2211yescharacteristic
44#343×C151C2211yescharacteristic
45#339×C151C2212yes—
46#339×C151C2212yes—
47C2×#41×C151—22no—
48C2×#41×C151C2312yes—
49C22×D4×C151—22no—
50C22×D4×C151C2311yescharacteristic
51C22×D4×C151C2311yescharacteristic
52C23×C4×C151—21no—
53C23×C4×C151D412yes—
54AGL(1,ℤ/8)×C151—24no—
55AGL(1,ℤ/8)×C151—24no—
56C2×SD16×C151—22no—
57C2×D8×C151—22no—
58C2×M16×C151C2312yes—
59C2×M16×C151C2312yes—
60C4⋊Q8×C151—22no—
61#127×C151—22no—
62#127×C151—22no—
63#127×C151—22no—
64#126×C151—24no—
65#125×C151—22no—
66#124×C151—24no—
67#124×C151—22no—
68#123×C151—24no—
69#123×C151—24no—
70C22⋊Q8×C151—22no—
71C22⋊Q8×C151—22no—
72C22⋊Q8×C151—22no—
73#121×C151—22no—
74#121×C151—24no—
75#121×C151—22no—
76#121×C151—22no—
77#121×C151—22no—
78#121×C151—22no—
79#120×C151—24no—
80C4×Q8×C151D412yescomplemented
81C4×Q8×C151D412yescomplemented
82C4×D4×C151—24no—
83C4×D4×C151—22no—
84C4×D4×C151—22no—
85C4×D4×C151—22no—
86C4×D4×C151—22no—
87C4×D4×C151—22no—
88C4×D4×C151—22no—
89C4×D4×C151D412yescomplemented
90C4×D4×C151D412yescomplemented
91#117×C151—22no—
92#117×C151—22no—
93#117×C151C2312yes—
94C2×C4⋊C4×C151C2311yescharacteristic
95C2×C4⋊C4×C151C2311yescharacteristic
96C2×C22⋊C4×C151—21no—
97C2×C22⋊C4×C151—22no—
98C2×C22⋊C4×C151—22no—
99C2×C22⋊C4×C151D412yes—
100C2×C42×C151—22no—
101C2×C42×C151C2311yescharacteristic
102C2×C42×C151C2311yescharacteristic
103C2×C42×C151C2311yescharacteristic
104#107×C151—22no—
105#106×C151—22no—
106#104×C151—24no—
107#104×C151—24no—
108#103×C151—22no—
109#102×C151—22no—
110#102×C151—22no—
111#102×C151—22no—
112#100×C151—24no—
113#97×C151—22no—
114C4×C8×C151—22no—
115#95×C151—21no—
116#95×C151—21no—
117#95×C151—22no—
118C24×C151—21no—
119C24×C151C2×D412yes—
120#41×C151—22no—
121#41×C151—22no—
122#41×C151—22no—
123#41×C151—22no—
124#41×C151—84no—
125C2×Q8×C151—22no—
126C2×Q8×C151C2×D412yes—
127C2×D4×C151—22no—
128C2×D4×C151—24no—
129C2×D4×C151—24no—
130C2×D4×C151—22no—
131C2×D4×C151—28no—
132C2×D4×C151—22no—
133C2×D4×C151—22no—
134C2×D4×C151—22no—
135C2×D4×C151—22no—
136C2×D4×C151—21no—
137C2×D4×C151—21no—
138C2×D4×C151—21no—
139C2×D4×C151—82no—
140C2×D4×C151—82no—
141C2×D4×C151C2×D412yes—
142C2×D4×C151#4112yescomplemented
143C22×C4×C151—21no—
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—42no—
152C22×C4×C151—82no—
153C22×C4×C151—82no—
154C22×C4×C151C2×D412yes—
155C22×C4×C151C2×D411yescharacteristic
156C22×C4×C151C2×D411yescharacteristic
157C22×C4×C151C2411yescharacteristic
158SD16×C151—28no—
159D8×C151—28no—
160M16×C151—22no—
161M16×C151—22no—
162M16×C151—22no—
163M16×C151#4114yescomplemented
164C2×C8×C151—22no—
165C2×C8×C151—22no—
166C4⋊C4×C151—22no—
167C4⋊C4×C151—22no—
168C4⋊C4×C151—24no—
169C4⋊C4×C151—22no—
170C4⋊C4×C151—22no—
171C4⋊C4×C151—22no—
172C4⋊C4×C151—22no—
173C4⋊C4×C151C2×D412yes—
174C4⋊C4×C151C2×D412yes—
175C22⋊C4×C151—24no—
176C22⋊C4×C151—24no—
177C22⋊C4×C151—24no—
178C22⋊C4×C151—22no—
179C22⋊C4×C151—24no—
180C22⋊C4×C151—22no—
181C22⋊C4×C151—22no—
182C22⋊C4×C151—41no—
183C22⋊C4×C151—41no—
184C22⋊C4×C151—82no—
185C22⋊C4×C151—82no—
186C42×C151—22no—
187C42×C151—22no—
188C42×C151—22no—
189C42×C151—21no—
190C42×C151—22no—
191C42×C151C2×D412yes—
192C42×C151C2×D412yes—
193C42×C151#4112yescomplemented
194C23×C151—22no—
195C23×C151—22no—
196C23×C151—22no—
197C23×C151—22no—
198C23×C151—22no—
199C23×C151—42no—
200C23×C151—42no—
201C23×C151—42no—
202C23×C151—42no—
203C23×C151—41no—
204C23×C151—41no—
205C23×C151C22×D411yescharacteristic
206Q8×C151—22no—
207Q8×C151—22no—
208Q8×C151—82no—
209D4×C151—22no—
210D4×C151—24no—
211D4×C151—22no—
212D4×C151—42no—
213D4×C151—42no—
214D4×C151—42no—
215D4×C151—42no—
216D4×C151—42no—
217D4×C151—82no—
218D4×C151—84no—
219D4×C151—84no—
220D4×C151—88no—
221C2×C4×C151—22no—
222C2×C4×C151—22no—
223C2×C4×C151—22no—
224C2×C4×C151—22no—
225C2×C4×C151—22no—
226C2×C4×C151—41no—
227C2×C4×C151—41no—
228C2×C4×C151—44no—
229C2×C4×C151—44no—
230C2×C4×C151—41no—
231C2×C4×C151—41no—
232C2×C4×C151—42no—
233C2×C4×C151—42no—
234C2×C4×C151—42no—
235C2×C4×C151—41no—
236C2×C4×C151—41no—
237C2×C4×C151—42no—
238C2×C4×C151—41no—
239C2×C4×C151—41no—
240C2×C4×C151—82no—
241C2×C4×C151—82no—
242C2×C4×C151—84no—
243C2×C4×C151#12011yescharacteristic
244C2×C4×C151#12012yes—
245C2×C4×C151#12011yescharacteristic
246C2×C4×C151C22×D412yes—
247C2×C4×C151C2×#4111yescharacteristic
248C2×C4×C151C2×#4112yes—
249C2×C4×C151C2×#4111yescharacteristic
250C8×C151—24no—
251C8×C151—42no—
252C22×C151—21no—
253C22×C151—21no—
254C22×C151—44no—
255C22×C151—44no—
256C22×C151—42no—
257C22×C151—42no—
258C22×C151—42no—
259C22×C151—42no—
260C22×C151—42no—
261C22×C151—42no—
262C22×C151—42no—
263C22×C151—82no—
264C22×C151—82no—
265C22×C151—81no—
266C22×C151—81no—
267C22×C151C2×#12011yescharacteristic
268C22×C151#52511yescharacteristic
269C22×C151#53211yescharacteristic
270C4×C151—21no—
271C4×C151—21no—
272C4×C151—22no—
273C4×C151—42no—
274C4×C151—42no—
275C4×C151—42no—
276C4×C151—42no—
277C4×C151—42no—
278C4×C151—81no—
279C4×C151—81no—
280C4×C151#52512yes—
281C4×C151#53212yes—
282C2×C151—21no—
283C2×C151—21no—
284C2×C151—82no—
285C2×C151—82no—
286C2×C151—82no—
287C2×C151#238811yescharacteristic
288C2×C151#301911yescharacteristic
289C2×C151#302111yescharacteristic
290#23591C15111yesmaximal, characteristic, direct product factor, Sylow
291C151#2359111yescharacteristic, direct product factor, Sylow
292#3460C2×C15111yescharacteristic, complemented
293C4×AGL(1,ℤ/8)C2×C15112yescomplemented
294#2328C2×C15111yescharacteristic, complemented
295#2061C2×C15111yescharacteristic, complemented
296#2040C2×C15111yescharacteristic, complemented
297#2037C2×C15112yescomplemented
298#2027C2×C15111yescharacteristic, complemented
299#2006C2×C15111yescharacteristic, complemented
300#2002C2×C15112yescomplemented
301#1759C2×C15112yescomplemented
302C4×#100C2×C15111yescharacteristic, complemented
303C2×AGL(1,ℤ/8)C22×C15112yes—
304#544C22×C15111yescharacteristic
305#542—22no—
306#540—22no—
307#538—22no—
308#537C22×C15111yescharacteristic
309#535C22×C15112yes—
310#532—22no—
311C2×#127C22×C15111yescharacteristic
312#529—22no—
313#525—22no—
314C4×#41C22×C15112yes—
315C2×C4×D4C22×C15111yescharacteristic
316C2×C4×D4C22×C15111yescharacteristic
317#442—22no—
318#440—22no—
319C4×SD16—22no—
320C4×D8—22no—
321#428C22×C15112yes—
322C2×#104C22×C15112yes—
323C2×#104C22×C15112yes—
324#418C22×C15112yes—
325#417C22×C15112yes—
326C2×#100C22×C15112yes—
327C4×M16C22×C15112yes—
328#390C22×C15111yescharacteristic
329#390C22×C15111yescharacteristic
330#386—22no—
331#386—22no—
332#382C22×C15111yescharacteristic
333#376C22×C15111yescharacteristic
334#343C22×C15111yescharacteristic
335#343C22×C15111yescharacteristic
336#339C22×C15112yes—
337#339C22×C15112yes—
338C2×#41—22no—
339C2×#41C23×C15112yes—
340C22×D4—22no—
341C22×D4C23×C15111yescharacteristic
342C22×D4C23×C15111yescharacteristic
343C23×C4—21no—
344C23×C4D4×C15112yes—
345AGL(1,ℤ/8)—24no—
346AGL(1,ℤ/8)—24no—
347C2×SD16—22no—
348C2×D8—22no—
349C2×M16C23×C15112yes—
350C2×M16C23×C15112yes—
351C4⋊Q8—22no—
352#127—22no—
353#127—22no—
354#127—22no—
355#126—24no—
356#125—22no—
357#124—24no—
358#124—22no—
359#123—24no—
360#123—24no—
361C22⋊Q8—22no—
362C22⋊Q8—22no—
363C22⋊Q8—22no—
364#121—22no—
365#121—24no—
366#121—22no—
367#121—22no—
368#121—22no—
369#121—22no—
370#120—24no—
371C4×Q8D4×C15112yescomplemented
372C4×Q8D4×C15112yescomplemented
373C4×D4—24no—
374C4×D4—22no—
375C4×D4—22no—
376C4×D4—22no—
377C4×D4—22no—
378C4×D4—22no—
379C4×D4—22no—
380C4×D4D4×C15112yescomplemented
381C4×D4D4×C15112yescomplemented
382#117—22no—
383#117—22no—
384#117C23×C15112yes—
385C2×C4⋊C4C23×C15111yescharacteristic
386C2×C4⋊C4C23×C15111yescharacteristic
387C2×C22⋊C4—21no—
388C2×C22⋊C4—22no—
389C2×C22⋊C4—22no—
390C2×C22⋊C4D4×C15112yes—
391C2×C42—22no—
392C2×C42C23×C15111yescharacteristic
393C2×C42C23×C15111yescharacteristic
394C2×C42C23×C15111yescharacteristic
395#107—22no—
396#106—22no—
397#104—24no—
398#104—24no—
399#103—22no—
400#102—22no—
401#102—22no—
402#102—22no—
403#100—24no—
404#97—22no—
405C4×C8—22no—
406#95—21no—
407#95—21no—
408#95—22no—
409C24—21no—
410C24C2×D4×C15112yes—
411#41—22no—
412#41—22no—
413#41—22no—
414#41—22no—
415#41—84no—
416C2×Q8—22no—
417C2×Q8C2×D4×C15112yes—
418C2×D4—22no—
419C2×D4—24no—
420C2×D4—24no—
421C2×D4—22no—
422C2×D4—28no—
423C2×D4—22no—
424C2×D4—22no—
425C2×D4—22no—
426C2×D4—22no—
427C2×D4—21no—
428C2×D4—21no—
429C2×D4—21no—
430C2×D4—82no—
431C2×D4—82no—
432C2×D4C2×D4×C15112yes—
433C2×D4#41×C15112yescomplemented
434C22×C4—21no—
435C22×C4—22no—
436C22×C4—22no—
437C22×C4—22no—
438C22×C4—22no—
439C22×C4—22no—
440C22×C4—21no—
441C22×C4—21no—
442C22×C4—42no—
443C22×C4—82no—
444C22×C4—82no—
445C22×C4C2×D4×C15112yes—
446C22×C4C2×D4×C15111yescharacteristic
447C22×C4C2×D4×C15111yescharacteristic
448C22×C4C24×C15111yescharacteristic
449SD16—28no—
450D8—28no—
451M16—22no—
452M16—22no—
453M16—22no—
454M16#41×C15114yescomplemented
455C2×C8—22no—
456C2×C8—22no—
457C4⋊C4—22no—
458C4⋊C4—22no—
459C4⋊C4—24no—
460C4⋊C4—22no—
461C4⋊C4—22no—
462C4⋊C4—22no—
463C4⋊C4—22no—
464C4⋊C4C2×D4×C15112yes—
465C4⋊C4C2×D4×C15112yes—
466C22⋊C4—24no—
467C22⋊C4—24no—
468C22⋊C4—24no—
469C22⋊C4—22no—
470C22⋊C4—24no—
471C22⋊C4—22no—
472C22⋊C4—22no—
473C22⋊C4—41no—
474C22⋊C4—41no—
475C22⋊C4—82no—
476C22⋊C4—82no—
477C42—22no—
478C42—22no—
479C42—22no—
480C42—21no—
481C42—22no—
482C42C2×D4×C15112yes—
483C42C2×D4×C15112yes—
484C42#41×C15112yescomplemented
485C23—22no—
486C23—22no—
487C23—22no—
488C23—22no—
489C23—22no—
490C23—42no—
491C23—42no—
492C23—42no—
493C23—42no—
494C23—41no—
495C23—41no—
496C23C22×D4×C15111yescharacteristic
497Q8—22no—
498Q8—22no—
499Q8—82no—
500D4—22no—
501D4—24no—
502D4—22no—
503D4—42no—
504D4—42no—
505D4—42no—
506D4—42no—
507D4—42no—
508D4—88no—
509D4—82no—
510D4—84no—
511D4—84no—
512C2×C4—22no—
513C2×C4—22no—
514C2×C4—22no—
515C2×C4—22no—
516C2×C4—22no—
517C2×C4—41no—
518C2×C4—41no—
519C2×C4—44no—
520C2×C4—44no—
521C2×C4—41no—
522C2×C4—41no—
523C2×C4—42no—
524C2×C4—42no—
525C2×C4—42no—
526C2×C4—41no—
527C2×C4—41no—
528C2×C4—42no—
529C2×C4—41no—
530C2×C4—41no—
531C2×C4—82no—
532C2×C4—82no—
533C2×C4—84no—
534C2×C4#120×C15111yescharacteristic
535C2×C4#120×C15112yes—
536C2×C4#120×C15111yescharacteristic
537C2×C4C22×D4×C15112yes—
538C2×C4C2×#41×C15111yescharacteristic
539C2×C4C2×#41×C15112yes—
540C2×C4C2×#41×C15111yescharacteristic
541C8—24no—
542C8—42no—
543C22—21no—
544C22—21no—
545C22—44no—
546C22—44no—
547C22—42no—
548C22—42no—
549C22—42no—
550C22—42no—
551C22—42no—
552C22—42no—
553C22—42no—
554C22—82no—
555C22—82no—
556C22—81no—
557C22—81no—
558C22C2×#120×C15111yescharacteristic
559C22#525×C15111yescharacteristic
560C22#532×C15111yescharacteristic
561C4—21no—
562C4—21no—
563C4—22no—
564C4—42no—
565C4—42no—
566C4—42no—
567C4—42no—
568C4—42no—
569C4—81no—
570C4—81no—
571C4#525×C15112yes—
572C4#532×C15112yes—
573C2—21no—
574C2—21no—
575C2—82no—
576C2—82no—
577C2—82no—
578C2#2388×C15111yescharacteristic
579C2#3019×C15111yescharacteristic
580C2#3021×C15111yescharacteristic
subgroupG/H
center, socleC22×C151C2×#120
commutator, Frattini, cosocleC22×C4C24×C151
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C151 ◁ C2×C42×C151 ◁ G

Complements

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

NH ≅ G/Ntype
1. #3460×C151C2semidirect
2. C4×AGL(1,ℤ/8)×C151C2semidirect
3. #2328×C151C2semidirect
4. #2061×C151C2semidirect
5. #2040×C151C2semidirect
6. #2037×C151C2semidirect
7. #2027×C151C2semidirect
8. #2006×C151C2semidirect
9. #2002×C151C2semidirect
10. #1759×C151C2semidirect
11. C4×#100×C151C2semidirect
80. C4×Q8×C151D4semidirect
81. C4×Q8×C151D4semidirect
89. C4×D4×C151D4semidirect
90. C4×D4×C151D4semidirect
142. C2×D4×C151#41semidirect
163. M16×C151#41semidirect
193. C42×C151#41semidirect
290. #23591C151direct (N × H)
291. C151#23591direct (N × H)
292. #3460C2×C151semidirect
293. C4×AGL(1,ℤ/8)C2×C151semidirect
294. #2328C2×C151semidirect
295. #2061C2×C151semidirect
296. #2040C2×C151semidirect
297. #2037C2×C151semidirect
298. #2027C2×C151semidirect
299. #2006C2×C151semidirect
300. #2002C2×C151semidirect
301. #1759C2×C151semidirect
302. C4×#100C2×C151semidirect
371. C4×Q8D4×C151semidirect
372. C4×Q8D4×C151semidirect
380. C4×D4D4×C151semidirect
381. C4×D4D4×C151semidirect
433. C2×D4#41×C151semidirect
454. M16#41×C151semidirect
484. C42#41×C151semidirect

Maximal subgroups

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

subgroupindex
#3460×C1512
C4×AGL(1,ℤ/8)×C1512
#2328×C1512
#2061×C1512
#2040×C1512
#2037×C1512
#2027×C1512
#2006×C1512
#2002×C1512
#1759×C1512
C4×#100×C1512
#23591151