Finite Group Databasebeta

← C151×#19748 #50324673

Subgroups — C151×#19748 #50324673

Order 38656.

792 conjugacy classes of subgroups.

The subgroup lattice has 540 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#3184×C151C211yesmaximal, characteristic
2#3182×C151C211yesmaximal, characteristic, complemented
3#3182×C151C211yesmaximal, characteristic, complemented
4#3165×C151C211yesmaximal, characteristic, complemented
5#3152×C151C211yesmaximal, characteristic, complemented
6#3141×C151C211yesmaximal, characteristic, complemented
7#1723×C151C211yesmaximal, characteristic, complemented
8#1722×C151C211yesmaximal, characteristic, complemented
9#1720×C151C211yesmaximal, characteristic, complemented
10#1719×C151C211yesmaximal, characteristic, complemented
11#1715×C151C211yesmaximal, characteristic, complemented
12#1714×C151C211yesmaximal, characteristic, complemented
13#1707×C151C211yesmaximal, characteristic, complemented
14#1706×C151C211yesmaximal, characteristic, complemented
15#1455×C151C211yesmaximal, characteristic, complemented
16C2×#137×C151—22no—
17#533×C151C2211yescharacteristic
18#532×C151C2211yescharacteristic
19#532×C151C2211yescharacteristic
20C2×C4⋊Q8×C151C2211yescharacteristic
21#501×C151—22no—
22#500×C151C2211yescharacteristic
23#500×C151C2211yescharacteristic
24#500×C151C2211yescharacteristic
25#500×C151C2211yescharacteristic
26#498×C151C2211yescharacteristic
27#498×C151C2211yescharacteristic
28#498×C151C2211yescharacteristic
29#497×C151—22no—
30#494×C151C2211yescharacteristic
31#494×C151C2211yescharacteristic
32#493×C151C2211yescharacteristic
33#492×C151C2211yescharacteristic
34#492×C151C2211yescharacteristic
35#492×C151C2211yescharacteristic
36#492×C151C2211yescharacteristic
37#489×C151—22no—
38#487×C151C2211yescharacteristic
39#487×C151C2211yescharacteristic
40#487×C151C2211yescharacteristic
41#487×C151C2211yescharacteristic
42#486×C151C2211yescharacteristic
43#486×C151C2211yescharacteristic
44#486×C151C2211yescharacteristic
45#486×C151C2211yescharacteristic
46#486×C151C2211yescharacteristic
47#486×C151C2211yescharacteristic
48#469×C151—22no—
49#468×C151—22no—
50#468×C151—22no—
51#442×C151—22no—
52#440×C151—22no—
53#440×C151—22no—
54#428×C151—22no—
55#417×C151—22no—
56C4×M16×C151C2211yescharacteristic
57C4×M16×C151C2211yescharacteristic
58C4×M16×C151C2211yescharacteristic
59#322×C151C2211yescharacteristic
60#322×C151C2211yescharacteristic
61#322×C151C2211yescharacteristic
62C82×C151C2211yescharacteristic
63C2×#41×C151—21no—
64C2×#41×C151—21no—
65C22×Q8×C151—21no—
66#137×C151—48no—
67C2×Q16×C151—22no—
68C2×Q16×C151—22no—
69C2×SD16×C151—22no—
70C2×SD16×C151—22no—
71C2×SD16×C151—22no—
72C2×SD16×C151—22no—
73C2×D8×C151—22no—
74C2×M16×C151D412yes—
75C2×M16×C151D412yes—
76C2×M16×C151D412yes—
77C4⋊Q8×C151—21no—
78C4⋊Q8×C151—21no—
79C4⋊Q8×C151—21no—
80C4⋊Q8×C151C2311yescharacteristic
81C4⋊Q8×C151C2311yescharacteristic
82C4⋊Q8×C151C2311yescharacteristic
83C4⋊Q8×C151C2311yescharacteristic
84C4⋊Q8×C151C2311yescharacteristic
85C4⋊Q8×C151C2311yescharacteristic
86#127×C151C2311yescharacteristic
87#127×C151C2311yescharacteristic
88#125×C151—21no—
89#124×C151—21no—
90#124×C151—21no—
91C22⋊Q8×C151—21no—
92C22⋊Q8×C151—21no—
93#121×C151—21no—
94#121×C151—21no—
95#121×C151—21no—
96#121×C151—21no—
97C4×Q8×C151—21no—
98C4×Q8×C151—21no—
99C4×D4×C151—21no—
100C4×D4×C151—21no—
101C4×D4×C151—21no—
102C4×D4×C151—21no—
103#117×C151—21no—
104C2×C4⋊C4×C151—21no—
105C2×C4⋊C4×C151—21no—
106C2×C42×C151C2311yescharacteristic
107#107×C151—22no—
108#107×C151—22no—
109#107×C151—22no—
110#107×C151—22no—
111#106×C151—22no—
112#106×C151—22no—
113#106×C151—22no—
114#103×C151—22no—
115#103×C151—22no—
116#103×C151—22no—
117#103×C151—22no—
118#102×C151—22no—
119#102×C151—22no—
120#102×C151—22no—
121#102×C151—22no—
122#102×C151—22no—
123#102×C151—22no—
124#97×C151D412yes—
125#97×C151D412yes—
126#97×C151D412yes—
127C4×C8×C151C2311yescharacteristic
128C4×C8×C151C2311yescharacteristic
129C4×C8×C151C2311yescharacteristic
130C4×C8×C151C2311yescharacteristic
131C4×C8×C151C2311yescharacteristic
132C4×C8×C151C2311yescharacteristic
133#41×C151—44no—
134#41×C151—44no—
135C2×Q8×C151—21no—
136C2×Q8×C151—21no—
137C2×Q8×C151—21no—
138C2×Q8×C151—21no—
139C2×Q8×C151—21no—
140C2×Q8×C151—21no—
141C2×Q8×C151—44no—
142C2×Q8×C151—41no—
143C2×D4×C151—21no—
144C2×D4×C151—21no—
145C2×D4×C151—21no—
146C2×D4×C151—21no—
147C2×D4×C151—21no—
148C2×D4×C151—21no—
149C2×D4×C151—41no—
150C2×D4×C151—41no—
151C22×C4×C151—41no—
152C22×C4×C151—41no—
153C22×C4×C151—41no—
154C22×C4×C151C2×D411yescharacteristic
155C22×C4×C151C2×D411yescharacteristic
156C22×C4×C151C2×D411yescharacteristic
157Q16×C151—44no—
158Q16×C151—44no—
159SD16×C151—44no—
160SD16×C151—44no—
161SD16×C151—44no—
162SD16×C151—44no—
163D8×C151—44no—
164M16×C151—24no—
165M16×C151—24no—
166M16×C151—42no—
167C2×C8×C151C2×D412yes—
168C2×C8×C151C2×D412yes—
169C2×C8×C151C2×D412yes—
170C2×C8×C151C2×D412yes—
171C2×C8×C151C2×D412yes—
172C2×C8×C151C2×D412yes—
173C4⋊C4×C151—21no—
174C4⋊C4×C151—21no—
175C4⋊C4×C151—21no—
176C4⋊C4×C151—21no—
177C4⋊C4×C151—21no—
178C4⋊C4×C151—21no—
179C4⋊C4×C151—21no—
180C4⋊C4×C151—21no—
181C4⋊C4×C151—21no—
182C4⋊C4×C151—21no—
183C4⋊C4×C151—21no—
184C4⋊C4×C151—21no—
185C4⋊C4×C151—41no—
186C4⋊C4×C151—41no—
187C4⋊C4×C151—41no—
188C4⋊C4×C151—41no—
189C22⋊C4×C151—41no—
190C22⋊C4×C151—41no—
191C22⋊C4×C151—41no—
192C22⋊C4×C151—41no—
193C22⋊C4×C151—41no—
194C42×C151—41no—
195C42×C151C2×D411yescharacteristic
196C42×C151C2×D411yescharacteristic
197C42×C151C2×D411yescharacteristic
198C42×C151C2411yescharacteristic
199C23×C151—41no—
200C23×C151—41no—
201C23×C151#12711yescharacteristic
202Q8×C151—42no—
203Q8×C151—42no—
204Q8×C151—42no—
205Q8×C151—42no—
206Q8×C151—42no—
207Q8×C151—42no—
208Q8×C151—82no—
209D4×C151—42no—
210D4×C151—42no—
211D4×C151—42no—
212D4×C151—42no—
213D4×C151—42no—
214D4×C151—42no—
215D4×C151—82no—
216D4×C151—82no—
217C2×C4×C151—22no—
218C2×C4×C151—22no—
219C2×C4×C151—22no—
220C2×C4×C151—41no—
221C2×C4×C151—41no—
222C2×C4×C151—41no—
223C2×C4×C151—41no—
224C2×C4×C151—41no—
225C2×C4×C151—41no—
226C2×C4×C151—82no—
227C2×C4×C151—82no—
228C2×C4×C151—82no—
229C2×C4×C151#12711yescharacteristic
230C2×C4×C151#12711yescharacteristic
231C2×C4×C151#12711yescharacteristic
232C2×C4×C151C22×D411yescharacteristic
233C2×C4×C151C22×D411yescharacteristic
234C2×C4×C151C22×D411yescharacteristic
235C8×C151—22no—
236C8×C151—22no—
237C8×C151—22no—
238C8×C151—22no—
239C8×C151AGL(1,ℤ/8)14yes—
240C8×C151#13714yescomplemented
241C22×C151—21no—
242C22×C151—21no—
243C22×C151—21no—
244C22×C151—81no—
245C22×C151—81no—
246C22×C151—81no—
247C22×C151—81no—
248C22×C151—81no—
249C22×C151—81no—
250C22×C151C2×#12711yescharacteristic
251C4×C151—21no—
252C4×C151—21no—
253C4×C151—21no—
254C4×C151—81no—
255C4×C151—81no—
256C4×C151—81no—
257C4×C151—81no—
258C4×C151—81no—
259C4×C151—81no—
260C4×C151C2×AGL(1,ℤ/8)12yes—
261C4×C151C2×#13712yes—
262C4×C151#57512yes—
263C2×C151—41no—
264C2×C151—161no—
265C2×C151—161no—
266C2×C151#315111yescharacteristic
267C2×C151#315211yescharacteristic
268C2×C151#315311yescharacteristic
269#19748C15111yesmaximal, characteristic, direct product factor, Sylow
270C151#1974811yescharacteristic, direct product factor, Sylow
271#3184C2×C15111yescharacteristic
272#3182C2×C15111yescharacteristic, complemented
273#3182C2×C15111yescharacteristic, complemented
274#3165C2×C15111yescharacteristic, complemented
275#3152C2×C15111yescharacteristic, complemented
276#3141C2×C15111yescharacteristic, complemented
277#1723C2×C15111yescharacteristic, complemented
278#1722C2×C15111yescharacteristic, complemented
279#1720C2×C15111yescharacteristic, complemented
280#1719C2×C15111yescharacteristic, complemented
281#1715C2×C15111yescharacteristic, complemented
282#1714C2×C15111yescharacteristic, complemented
283#1707C2×C15111yescharacteristic, complemented
284#1706C2×C15111yescharacteristic, complemented
285#1455C2×C15111yescharacteristic, complemented
286C2×#137—22no—
287#533C22×C15111yescharacteristic
288#532C22×C15111yescharacteristic
289#532C22×C15111yescharacteristic
290C2×C4⋊Q8C22×C15111yescharacteristic
291#501—22no—
292#500C22×C15111yescharacteristic
293#500C22×C15111yescharacteristic
294#500C22×C15111yescharacteristic
295#500C22×C15111yescharacteristic
296#498C22×C15111yescharacteristic
297#498C22×C15111yescharacteristic
298#498C22×C15111yescharacteristic
299#497—22no—
300#494C22×C15111yescharacteristic
301#494C22×C15111yescharacteristic
302#493C22×C15111yescharacteristic
303#492C22×C15111yescharacteristic
304#492C22×C15111yescharacteristic
305#492C22×C15111yescharacteristic
306#492C22×C15111yescharacteristic
307#489—22no—
308#487C22×C15111yescharacteristic
309#487C22×C15111yescharacteristic
310#487C22×C15111yescharacteristic
311#487C22×C15111yescharacteristic
312#486C22×C15111yescharacteristic
313#486C22×C15111yescharacteristic
314#486C22×C15111yescharacteristic
315#486C22×C15111yescharacteristic
316#486C22×C15111yescharacteristic
317#486C22×C15111yescharacteristic
318#469—22no—
319#468—22no—
320#468—22no—
321#442—22no—
322#440—22no—
323#440—22no—
324#428—22no—
325#417—22no—
326C4×M16C22×C15111yescharacteristic
327C4×M16C22×C15111yescharacteristic
328C4×M16C22×C15111yescharacteristic
329#322C22×C15111yescharacteristic
330#322C22×C15111yescharacteristic
331#322C22×C15111yescharacteristic
332C82C22×C15111yescharacteristic
333C2×#41—21no—
334C2×#41—21no—
335C22×Q8—21no—
336#137—48no—
337C2×Q16—22no—
338C2×Q16—22no—
339C2×SD16—22no—
340C2×SD16—22no—
341C2×SD16—22no—
342C2×SD16—22no—
343C2×D8—22no—
344C2×M16D4×C15112yes—
345C2×M16D4×C15112yes—
346C2×M16D4×C15112yes—
347C4⋊Q8—21no—
348C4⋊Q8—21no—
349C4⋊Q8—21no—
350C4⋊Q8C23×C15111yescharacteristic
351C4⋊Q8C23×C15111yescharacteristic
352C4⋊Q8C23×C15111yescharacteristic
353C4⋊Q8C23×C15111yescharacteristic
354C4⋊Q8C23×C15111yescharacteristic
355C4⋊Q8C23×C15111yescharacteristic
356#127C23×C15111yescharacteristic
357#127C23×C15111yescharacteristic
358#125—21no—
359#124—21no—
360#124—21no—
361C22⋊Q8—21no—
362C22⋊Q8—21no—
363#121—21no—
364#121—21no—
365#121—21no—
366#121—21no—
367C4×Q8—21no—
368C4×Q8—21no—
369C4×D4—21no—
370C4×D4—21no—
371C4×D4—21no—
372C4×D4—21no—
373#117—21no—
374C2×C4⋊C4—21no—
375C2×C4⋊C4—21no—
376C2×C42C23×C15111yescharacteristic
377#107—22no—
378#107—22no—
379#107—22no—
380#107—22no—
381#106—22no—
382#106—22no—
383#106—22no—
384#103—22no—
385#103—22no—
386#103—22no—
387#103—22no—
388#102—22no—
389#102—22no—
390#102—22no—
391#102—22no—
392#102—22no—
393#102—22no—
394#97D4×C15112yes—
395#97D4×C15112yes—
396#97D4×C15112yes—
397C4×C8C23×C15111yescharacteristic
398C4×C8C23×C15111yescharacteristic
399C4×C8C23×C15111yescharacteristic
400C4×C8C23×C15111yescharacteristic
401C4×C8C23×C15111yescharacteristic
402C4×C8C23×C15111yescharacteristic
403#41—44no—
404#41—44no—
405C2×Q8—21no—
406C2×Q8—21no—
407C2×Q8—21no—
408C2×Q8—21no—
409C2×Q8—21no—
410C2×Q8—21no—
411C2×Q8—44no—
412C2×Q8—41no—
413C2×D4—21no—
414C2×D4—21no—
415C2×D4—21no—
416C2×D4—21no—
417C2×D4—21no—
418C2×D4—21no—
419C2×D4—41no—
420C2×D4—41no—
421C22×C4—41no—
422C22×C4—41no—
423C22×C4—41no—
424C22×C4C2×D4×C15111yescharacteristic
425C22×C4C2×D4×C15111yescharacteristic
426C22×C4C2×D4×C15111yescharacteristic
427Q16—44no—
428Q16—44no—
429SD16—44no—
430SD16—44no—
431SD16—44no—
432SD16—44no—
433D8—44no—
434M16—24no—
435M16—24no—
436M16—42no—
437C2×C8C2×D4×C15112yes—
438C2×C8C2×D4×C15112yes—
439C2×C8C2×D4×C15112yes—
440C2×C8C2×D4×C15112yes—
441C2×C8C2×D4×C15112yes—
442C2×C8C2×D4×C15112yes—
443C4⋊C4—21no—
444C4⋊C4—21no—
445C4⋊C4—21no—
446C4⋊C4—21no—
447C4⋊C4—21no—
448C4⋊C4—21no—
449C4⋊C4—21no—
450C4⋊C4—21no—
451C4⋊C4—21no—
452C4⋊C4—21no—
453C4⋊C4—21no—
454C4⋊C4—21no—
455C4⋊C4—41no—
456C4⋊C4—41no—
457C4⋊C4—41no—
458C4⋊C4—41no—
459C22⋊C4—41no—
460C22⋊C4—41no—
461C22⋊C4—41no—
462C22⋊C4—41no—
463C22⋊C4—41no—
464C42—41no—
465C42C2×D4×C15111yescharacteristic
466C42C2×D4×C15111yescharacteristic
467C42C2×D4×C15111yescharacteristic
468C42C24×C15111yescharacteristic
469C23—41no—
470C23—41no—
471C23#127×C15111yescharacteristic
472Q8—42no—
473Q8—42no—
474Q8—42no—
475Q8—42no—
476Q8—42no—
477Q8—42no—
478Q8—82no—
479D4—42no—
480D4—42no—
481D4—42no—
482D4—42no—
483D4—42no—
484D4—42no—
485D4—82no—
486D4—82no—
487C2×C4—22no—
488C2×C4—22no—
489C2×C4—22no—
490C2×C4—41no—
491C2×C4—41no—
492C2×C4—41no—
493C2×C4—41no—
494C2×C4—41no—
495C2×C4—41no—
496C2×C4—82no—
497C2×C4—82no—
498C2×C4—82no—
499C2×C4#127×C15111yescharacteristic
500C2×C4#127×C15111yescharacteristic
501C2×C4#127×C15111yescharacteristic
502C2×C4C22×D4×C15111yescharacteristic
503C2×C4C22×D4×C15111yescharacteristic
504C2×C4C22×D4×C15111yescharacteristic
505C8—22no—
506C8—22no—
507C8—22no—
508C8—22no—
509C8AGL(1,ℤ/8)×C15114yes—
510C8#137×C15114yescomplemented
511C22—21no—
512C22—21no—
513C22—21no—
514C22—81no—
515C22—81no—
516C22—81no—
517C22—81no—
518C22—81no—
519C22—81no—
520C22C2×#127×C15111yescharacteristic
521C4—21no—
522C4—21no—
523C4—21no—
524C4—81no—
525C4—81no—
526C4—81no—
527C4—81no—
528C4—81no—
529C4—81no—
530C4C2×AGL(1,ℤ/8)×C15112yes—
531C4C2×#137×C15112yes—
532C4#575×C15112yes—
533C2—41no—
534C2—161no—
535C2—161no—
536C2#3151×C15111yescharacteristic
537C2#3152×C15111yescharacteristic
538C2#3153×C15111yescharacteristic
subgroupG/H
center, socleC22×C151C2×#127
commutator, Frattini, cosocleC42C24×C151
prime radical#3184×C151C2
LCSG ▷ C42 ▷ C22 ▷ C1
UCSC1 ◁ C22×C151 ◁ C2×C42×C151 ◁ G

Complements

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

NH ≅ G/Ntype
2. #3182×C151C2semidirect
3. #3182×C151C2semidirect
4. #3165×C151C2semidirect
5. #3152×C151C2semidirect
6. #3141×C151C2semidirect
7. #1723×C151C2semidirect
8. #1722×C151C2semidirect
9. #1720×C151C2semidirect
10. #1719×C151C2semidirect
11. #1715×C151C2semidirect
12. #1714×C151C2semidirect
13. #1707×C151C2semidirect
14. #1706×C151C2semidirect
15. #1455×C151C2semidirect
240. C8×C151#137semidirect
269. #19748C151direct (N × H)
270. C151#19748direct (N × H)
272. #3182C2×C151semidirect
273. #3182C2×C151semidirect
274. #3165C2×C151semidirect
275. #3152C2×C151semidirect
276. #3141C2×C151semidirect
277. #1723C2×C151semidirect
278. #1722C2×C151semidirect
279. #1720C2×C151semidirect
280. #1719C2×C151semidirect
281. #1715C2×C151semidirect
282. #1714C2×C151semidirect
283. #1707C2×C151semidirect
284. #1706C2×C151semidirect
285. #1455C2×C151semidirect
510. C8#137×C151semidirect

Maximal subgroups

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

subgroupindex
#3184×C1512
#3182×C1512
#3165×C1512
#3152×C1512
#3141×C1512
#1723×C1512
#1722×C1512
#1720×C1512
#1719×C1512
#1715×C1512
#1714×C1512
#1707×C1512
#1706×C1512
#1455×C1512
#19748151