Finite Group Databasebeta

← C151×#19737 #50324662

Subgroups — C151×#19737 #50324662

Order 38656.

746 conjugacy classes of subgroups.

The subgroup lattice has 552 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#3231×C151C211yesmaximal, characteristic, complemented
2#3228×C151C211yesmaximal, characteristic, complemented
3#3210×C151C211yesmaximal, characteristic, complemented
4#3208×C151C211yesmaximal, characteristic, complemented
5#3208×C151C211yesmaximal, characteristic, complemented
6#3205×C151C211yesmaximal, characteristic
7#1722×C151C211yesmaximal, characteristic, complemented
8#1720×C151C211yesmaximal, characteristic, complemented
9#1717×C151C211yesmaximal, characteristic, complemented
10#1717×C151C211yesmaximal, characteristic, complemented
11#1715×C151C211yesmaximal, characteristic, complemented
12#1714×C151C211yesmaximal, characteristic, complemented
13#1708×C151C211yesmaximal, characteristic, complemented
14#1706×C151C211yesmaximal, characteristic, complemented
15#1454×C151C211yesmaximal, characteristic, complemented
16#533×C151C2211yescharacteristic
17#533×C151C2211yescharacteristic
18#532×C151C2211yescharacteristic
19C2×#127×C151C2211yescharacteristic
20#500×C151C2211yescharacteristic, complemented
21#500×C151C2211yescharacteristic, complemented
22#498×C151C2211yescharacteristic, complemented
23#498×C151C2211yescharacteristic, complemented
24#494×C151C2211yescharacteristic, complemented
25#493×C151C2211yescharacteristic
26#493×C151C2211yescharacteristic
27#492×C151C2211yescharacteristic
28#492×C151C2211yescharacteristic
29#492×C151C2211yescharacteristic
30#492×C151C2211yescharacteristic
31#492×C151C2211yescharacteristic, complemented
32#487×C151C2211yescharacteristic, complemented
33#487×C151C2211yescharacteristic, complemented
34#487×C151C2211yescharacteristic, complemented
35#486×C151C2211yescharacteristic
36#486×C151C2211yescharacteristic
37#486×C151C2211yescharacteristic
38#486×C151C2211yescharacteristic
39#486×C151C2211yescharacteristic
40#486×C151C2211yescharacteristic
41#486×C151C2211yescharacteristic, complemented
42#486×C151C2211yescharacteristic, complemented
43#486×C151C2211yescharacteristic, complemented
44#485×C151—22no—
45#482×C151—22no—
46#479×C151—22no—
47#478×C151—22no—
48#464×C151—22no—
49#460×C151—22no—
50#460×C151—22no—
51#459×C151—22no—
52#452×C151—22no—
53#450×C151—22no—
54#450×C151—22no—
55#447×C151—22no—
56#431×C151C2211yescharacteristic
57#431×C151C2211yescharacteristic
58#431×C151C2211yescharacteristic
59#322×C151C2211yescharacteristic, complemented
60#322×C151C2211yescharacteristic, complemented
61#322×C151C2211yescharacteristic, complemented
62C82×C151C2211yescharacteristic, complemented
63C2×#41×C151—21no—
64C22×D4×C151—21no—
65C22×D4×C151—21no—
66C22×D4×C151—21no—
67C2×Q16×C151—22no—
68C2×SD16×C151—22no—
69C2×SD16×C151—22no—
70C2×SD16×C151—22no—
71C2×SD16×C151—22no—
72C2×SD16×C151—22no—
73C2×D8×C151—22no—
74C2×D8×C151—22no—
75C4⋊Q8×C151C2311yescharacteristic
76C4⋊Q8×C151C2311yescharacteristic
77C4⋊Q8×C151C2311yescharacteristic
78C4⋊Q8×C151C2311yescharacteristic
79C4⋊Q8×C151C2311yescharacteristic
80#127×C151—21no—
81#127×C151—21no—
82#127×C151—21no—
83#127×C151C2311yescharacteristic
84#127×C151C2311yescharacteristic
85#127×C151C2311yescharacteristic
86#125×C151—21no—
87#125×C151—21no—
88#124×C151—21no—
89C22⋊Q8×C151—21no—
90C22⋊Q8×C151—21no—
91C22⋊Q8×C151—21no—
92C22⋊Q8×C151—21no—
93#121×C151—21no—
94#121×C151—21no—
95C4×Q8×C151—21no—
96C4×Q8×C151—21no—
97C4×Q8×C151—21no—
98C4×Q8×C151—21no—
99C4×D4×C151—21no—
100C4×D4×C151—21no—
101#117×C151—21no—
102#117×C151—21no—
103C2×C42×C151C2311yescharacteristic
104#107×C151—22no—
105#107×C151—22no—
106#106×C151—22no—
107#106×C151—22no—
108C4⋊C8×C151D412yes—
109C4⋊C8×C151D412yes—
110C4⋊C8×C151D412yes—
111#103×C151—22no—
112#103×C151—22no—
113#103×C151—22no—
114#102×C151—22no—
115#102×C151—22no—
116#102×C151—22no—
117#102×C151—22no—
118#102×C151—22no—
119#102×C151—22no—
120#102×C151—22no—
121#102×C151—22no—
122#102×C151—22no—
123C22⋊C8×C151D412yes—
124C22⋊C8×C151D412yes—
125C22⋊C8×C151D412yes—
126C4×C8×C151C2311yescharacteristic
127C4×C8×C151C2311yescharacteristic
128C4×C8×C151C2311yescharacteristic
129C4×C8×C151C2311yescharacteristic
130C4×C8×C151C2311yescharacteristic
131C4×C8×C151C2311yescharacteristic
132C24×C151—41no—
133#41×C151—82no—
134C2×Q8×C151—21no—
135C2×Q8×C151—21no—
136C2×Q8×C151—21no—
137C2×Q8×C151—21no—
138C2×Q8×C151—21no—
139C2×D4×C151—21no—
140C2×D4×C151—21no—
141C2×D4×C151—21no—
142C2×D4×C151—21no—
143C2×D4×C151—21no—
144C2×D4×C151—21no—
145C2×D4×C151—21no—
146C2×D4×C151—21no—
147C2×D4×C151—21no—
148C2×D4×C151—41no—
149C2×D4×C151—41no—
150C2×D4×C151—41no—
151C2×D4×C151—41no—
152C2×D4×C151—82no—
153C2×D4×C151—82no—
154C2×D4×C151—82no—
155C22×C4×C151—41no—
156C22×C4×C151C2×D411yescharacteristic
157C22×C4×C151C2×D411yescharacteristic
158C22×C4×C151C2×D411yescharacteristic
159Q16×C151—82no—
160SD16×C151—82no—
161SD16×C151—82no—
162SD16×C151—82no—
163SD16×C151—82no—
164SD16×C151—82no—
165D8×C151—82no—
166D8×C151—82no—
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—41no—
184C4⋊C4×C151—41no—
185C4⋊C4×C151—41no—
186C4⋊C4×C151—41no—
187C22⋊C4×C151—41no—
188C22⋊C4×C151—41no—
189C22⋊C4×C151—41no—
190C22⋊C4×C151—41no—
191C42×C151—41no—
192C42×C151—41no—
193C42×C151C2×D411yescharacteristic
194C42×C151C2×D411yescharacteristic
195C42×C151C2×D411yescharacteristic
196C42×C151C2411yescharacteristic
197C23×C151—41no—
198C23×C151—41no—
199C23×C151—41no—
200C23×C151—82no—
201C23×C151—82no—
202C23×C151—82no—
203C23×C151#12711yescharacteristic
204Q8×C151—42no—
205Q8×C151—42no—
206Q8×C151—42no—
207Q8×C151—42no—
208Q8×C151—42no—
209D4×C151—42no—
210D4×C151—42no—
211D4×C151—42no—
212D4×C151—42no—
213D4×C151—42no—
214D4×C151—42no—
215D4×C151—42no—
216D4×C151—42no—
217D4×C151—42no—
218D4×C151—82no—
219D4×C151—82no—
220D4×C151—82no—
221D4×C151—82no—
222C2×C4×C151—22no—
223C2×C4×C151—22no—
224C2×C4×C151—22no—
225C2×C4×C151—41no—
226C2×C4×C151—41no—
227C2×C4×C151—41no—
228C2×C4×C151—41no—
229C2×C4×C151—41no—
230C2×C4×C151—82no—
231C2×C4×C151#12711yescharacteristic
232C2×C4×C151#12711yescharacteristic
233C2×C4×C151#12711yescharacteristic
234C2×C4×C151C22×D411yescharacteristic
235C2×C4×C151C22×D411yescharacteristic
236C2×C4×C151C22×D411yescharacteristic
237C8×C151—22no—
238C8×C151—22no—
239C8×C151—22no—
240C8×C151—22no—
241C8×C151—22no—
242C8×C151—22no—
243C22×C151—21no—
244C22×C151—21no—
245C22×C151—21no—
246C22×C151—81no—
247C22×C151—81no—
248C22×C151—81no—
249C22×C151—81no—
250C22×C151—81no—
251C22×C151—81no—
252C22×C151—81no—
253C22×C151—81no—
254C22×C151—81no—
255C22×C151—164no—
256C22×C151C2×#12711yescharacteristic
257C4×C151—21no—
258C4×C151—21no—
259C4×C151—21no—
260C4×C151—81no—
261C4×C151—81no—
262C4×C151—81no—
263C4×C151—81no—
264C4×C151—81no—
265C4×C151#57612yes—
266C4×C151#57712yes—
267C4×C151#57712yes—
268C2×C151—41no—
269C2×C151—161no—
270C2×C151—161no—
271C2×C151—161no—
272C2×C151#315411yescharacteristic
273C2×C151#315411yescharacteristic
274C2×C151#315511yescharacteristic
275#19737C15111yesmaximal, characteristic, direct product factor, Sylow
276C151#1973711yescharacteristic, direct product factor, Sylow
277#3231C2×C15111yescharacteristic, complemented
278#3228C2×C15111yescharacteristic, complemented
279#3210C2×C15111yescharacteristic, complemented
280#3208C2×C15111yescharacteristic, complemented
281#3208C2×C15111yescharacteristic, complemented
282#3205C2×C15111yescharacteristic
283#1722C2×C15111yescharacteristic, complemented
284#1720C2×C15111yescharacteristic, complemented
285#1717C2×C15111yescharacteristic, complemented
286#1717C2×C15111yescharacteristic, complemented
287#1715C2×C15111yescharacteristic, complemented
288#1714C2×C15111yescharacteristic, complemented
289#1708C2×C15111yescharacteristic, complemented
290#1706C2×C15111yescharacteristic, complemented
291#1454C2×C15111yescharacteristic, complemented
292#533C22×C15111yescharacteristic
293#533C22×C15111yescharacteristic
294#532C22×C15111yescharacteristic
295C2×#127C22×C15111yescharacteristic
296#500C22×C15111yescharacteristic, complemented
297#500C22×C15111yescharacteristic, complemented
298#498C22×C15111yescharacteristic, complemented
299#498C22×C15111yescharacteristic, complemented
300#494C22×C15111yescharacteristic, complemented
301#493C22×C15111yescharacteristic
302#493C22×C15111yescharacteristic
303#492C22×C15111yescharacteristic
304#492C22×C15111yescharacteristic
305#492C22×C15111yescharacteristic
306#492C22×C15111yescharacteristic
307#492C22×C15111yescharacteristic, complemented
308#487C22×C15111yescharacteristic, complemented
309#487C22×C15111yescharacteristic, complemented
310#487C22×C15111yescharacteristic, complemented
311#486C22×C15111yescharacteristic
312#486C22×C15111yescharacteristic
313#486C22×C15111yescharacteristic
314#486C22×C15111yescharacteristic
315#486C22×C15111yescharacteristic
316#486C22×C15111yescharacteristic
317#486C22×C15111yescharacteristic, complemented
318#486C22×C15111yescharacteristic, complemented
319#486C22×C15111yescharacteristic, complemented
320#485—22no—
321#482—22no—
322#479—22no—
323#478—22no—
324#464—22no—
325#460—22no—
326#460—22no—
327#459—22no—
328#452—22no—
329#450—22no—
330#450—22no—
331#447—22no—
332#431C22×C15111yescharacteristic
333#431C22×C15111yescharacteristic
334#431C22×C15111yescharacteristic
335#322C22×C15111yescharacteristic, complemented
336#322C22×C15111yescharacteristic, complemented
337#322C22×C15111yescharacteristic, complemented
338C82C22×C15111yescharacteristic, complemented
339C2×#41—21no—
340C22×D4—21no—
341C22×D4—21no—
342C22×D4—21no—
343C2×Q16—22no—
344C2×SD16—22no—
345C2×SD16—22no—
346C2×SD16—22no—
347C2×SD16—22no—
348C2×SD16—22no—
349C2×D8—22no—
350C2×D8—22no—
351C4⋊Q8C23×C15111yescharacteristic
352C4⋊Q8C23×C15111yescharacteristic
353C4⋊Q8C23×C15111yescharacteristic
354C4⋊Q8C23×C15111yescharacteristic
355C4⋊Q8C23×C15111yescharacteristic
356#127—21no—
357#127—21no—
358#127—21no—
359#127C23×C15111yescharacteristic
360#127C23×C15111yescharacteristic
361#127C23×C15111yescharacteristic
362#125—21no—
363#125—21no—
364#124—21no—
365C22⋊Q8—21no—
366C22⋊Q8—21no—
367C22⋊Q8—21no—
368C22⋊Q8—21no—
369#121—21no—
370#121—21no—
371C4×Q8—21no—
372C4×Q8—21no—
373C4×Q8—21no—
374C4×Q8—21no—
375C4×D4—21no—
376C4×D4—21no—
377#117—21no—
378#117—21no—
379C2×C42C23×C15111yescharacteristic
380#107—22no—
381#107—22no—
382#106—22no—
383#106—22no—
384C4⋊C8D4×C15112yes—
385C4⋊C8D4×C15112yes—
386C4⋊C8D4×C15112yes—
387#103—22no—
388#103—22no—
389#103—22no—
390#102—22no—
391#102—22no—
392#102—22no—
393#102—22no—
394#102—22no—
395#102—22no—
396#102—22no—
397#102—22no—
398#102—22no—
399C22⋊C8D4×C15112yes—
400C22⋊C8D4×C15112yes—
401C22⋊C8D4×C15112yes—
402C4×C8C23×C15111yescharacteristic
403C4×C8C23×C15111yescharacteristic
404C4×C8C23×C15111yescharacteristic
405C4×C8C23×C15111yescharacteristic
406C4×C8C23×C15111yescharacteristic
407C4×C8C23×C15111yescharacteristic
408C24—41no—
409#41—82no—
410C2×Q8—21no—
411C2×Q8—21no—
412C2×Q8—21no—
413C2×Q8—21no—
414C2×Q8—21no—
415C2×D4—21no—
416C2×D4—21no—
417C2×D4—21no—
418C2×D4—21no—
419C2×D4—21no—
420C2×D4—21no—
421C2×D4—21no—
422C2×D4—21no—
423C2×D4—21no—
424C2×D4—41no—
425C2×D4—41no—
426C2×D4—41no—
427C2×D4—41no—
428C2×D4—82no—
429C2×D4—82no—
430C2×D4—82no—
431C22×C4—41no—
432C22×C4C2×D4×C15111yescharacteristic
433C22×C4C2×D4×C15111yescharacteristic
434C22×C4C2×D4×C15111yescharacteristic
435Q16—82no—
436SD16—82no—
437SD16—82no—
438SD16—82no—
439SD16—82no—
440SD16—82no—
441D8—82no—
442D8—82no—
443C2×C8C2×D4×C15112yes—
444C2×C8C2×D4×C15112yes—
445C2×C8C2×D4×C15112yes—
446C2×C8C2×D4×C15112yes—
447C2×C8C2×D4×C15112yes—
448C2×C8C2×D4×C15112yes—
449C4⋊C4—21no—
450C4⋊C4—21no—
451C4⋊C4—21no—
452C4⋊C4—21no—
453C4⋊C4—21no—
454C4⋊C4—21no—
455C4⋊C4—21no—
456C4⋊C4—21no—
457C4⋊C4—21no—
458C4⋊C4—21no—
459C4⋊C4—41no—
460C4⋊C4—41no—
461C4⋊C4—41no—
462C4⋊C4—41no—
463C22⋊C4—41no—
464C22⋊C4—41no—
465C22⋊C4—41no—
466C22⋊C4—41no—
467C42—41no—
468C42—41no—
469C42C2×D4×C15111yescharacteristic
470C42C2×D4×C15111yescharacteristic
471C42C2×D4×C15111yescharacteristic
472C42C24×C15111yescharacteristic
473C23—41no—
474C23—41no—
475C23—41no—
476C23—82no—
477C23—82no—
478C23—82no—
479C23#127×C15111yescharacteristic
480Q8—42no—
481Q8—42no—
482Q8—42no—
483Q8—42no—
484Q8—42no—
485D4—42no—
486D4—42no—
487D4—42no—
488D4—42no—
489D4—42no—
490D4—42no—
491D4—42no—
492D4—42no—
493D4—42no—
494D4—82no—
495D4—82no—
496D4—82no—
497D4—82no—
498C2×C4—22no—
499C2×C4—22no—
500C2×C4—22no—
501C2×C4—41no—
502C2×C4—41no—
503C2×C4—41no—
504C2×C4—41no—
505C2×C4—41no—
506C2×C4—82no—
507C2×C4#127×C15111yescharacteristic
508C2×C4#127×C15111yescharacteristic
509C2×C4#127×C15111yescharacteristic
510C2×C4C22×D4×C15111yescharacteristic
511C2×C4C22×D4×C15111yescharacteristic
512C2×C4C22×D4×C15111yescharacteristic
513C8—22no—
514C8—22no—
515C8—22no—
516C8—22no—
517C8—22no—
518C8—22no—
519C22—21no—
520C22—21no—
521C22—21no—
522C22—81no—
523C22—81no—
524C22—81no—
525C22—81no—
526C22—81no—
527C22—81no—
528C22—81no—
529C22—81no—
530C22—81no—
531C22—164no—
532C22C2×#127×C15111yescharacteristic
533C4—21no—
534C4—21no—
535C4—21no—
536C4—81no—
537C4—81no—
538C4—81no—
539C4—81no—
540C4—81no—
541C4#576×C15112yes—
542C4#577×C15112yes—
543C4#577×C15112yes—
544C2—41no—
545C2—161no—
546C2—161no—
547C2—161no—
548C2#3154×C15111yescharacteristic
549C2#3154×C15111yescharacteristic
550C2#3155×C15111yescharacteristic
subgroupG/H
center, socleC22×C151C2×#127
commutator, Frattini, cosocleC42C24×C151
prime radical#3205×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
1. #3231×C151C2semidirect
2. #3228×C151C2semidirect
3. #3210×C151C2semidirect
4. #3208×C151C2semidirect
5. #3208×C151C2semidirect
7. #1722×C151C2semidirect
8. #1720×C151C2semidirect
9. #1717×C151C2semidirect
10. #1717×C151C2semidirect
11. #1715×C151C2semidirect
12. #1714×C151C2semidirect
13. #1708×C151C2semidirect
14. #1706×C151C2semidirect
15. #1454×C151C2semidirect
20. #500×C151C22semidirect
21. #500×C151C22semidirect
22. #498×C151C22semidirect
23. #498×C151C22semidirect
24. #494×C151C22semidirect
31. #492×C151C22semidirect
32. #487×C151C22semidirect
33. #487×C151C22semidirect
34. #487×C151C22semidirect
41. #486×C151C22semidirect
42. #486×C151C22semidirect
43. #486×C151C22semidirect
59. #322×C151C22semidirect
60. #322×C151C22semidirect
61. #322×C151C22semidirect
62. C82×C151C22semidirect
275. #19737C151direct (N × H)
276. C151#19737direct (N × H)
277. #3231C2×C151semidirect
278. #3228C2×C151semidirect
279. #3210C2×C151semidirect
280. #3208C2×C151semidirect
281. #3208C2×C151semidirect
283. #1722C2×C151semidirect
284. #1720C2×C151semidirect
285. #1717C2×C151semidirect
286. #1717C2×C151semidirect
287. #1715C2×C151semidirect
288. #1714C2×C151semidirect
289. #1708C2×C151semidirect
290. #1706C2×C151semidirect
291. #1454C2×C151semidirect
296. #500C22×C151semidirect
297. #500C22×C151semidirect
298. #498C22×C151semidirect
299. #498C22×C151semidirect
300. #494C22×C151semidirect
307. #492C22×C151semidirect
308. #487C22×C151semidirect
309. #487C22×C151semidirect
310. #487C22×C151semidirect
317. #486C22×C151semidirect
318. #486C22×C151semidirect
319. #486C22×C151semidirect
335. #322C22×C151semidirect
336. #322C22×C151semidirect
337. #322C22×C151semidirect
338. C82C22×C151semidirect

Maximal subgroups

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

subgroupindex
#3231×C1512
#3228×C1512
#3210×C1512
#3208×C1512
#3205×C1512
#1722×C1512
#1720×C1512
#1717×C1512
#1715×C1512
#1714×C1512
#1708×C1512
#1706×C1512
#1454×C1512
#19737151