Finite Group Databasebeta

← C151×#19545 #50324470

Subgroups — C151×#19545 #50324470

Order 38656.

564 conjugacy classes of subgroups.

The subgroup lattice has 560 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#3233×C151C211yesmaximal, characteristic
2#3229×C151C211yesmaximal, characteristic, complemented
3#3218×C151C211yesmaximal, characteristic
4#2993×C151C211yesmaximal, characteristic
5#1700×C151C211yesmaximal, characteristic, complemented
6#1699×C151C211yesmaximal, characteristic, complemented
7#1692×C151C211yesmaximal, characteristic, complemented
8#1691×C151C211yesmaximal, characteristic, complemented
9#1680×C151C211yesmaximal, characteristic, complemented
10#1679×C151C211yesmaximal, characteristic, complemented
11#1672×C151C211yesmaximal, characteristic, complemented
12#1671×C151C211yesmaximal, characteristic, complemented
13#1572×C151C211yesmaximal, characteristic, complemented
14#1559×C151C211yesmaximal, characteristic, complemented
15#1549×C151C211yesmaximal, characteristic, complemented
16#533×C151C2211yescharacteristic
17C2×C4⋊Q8×C151C2211yescharacteristic
18#529×C151C2211yescharacteristic
19#499×C151—21no—
20#498×C151C2211yescharacteristic
21#498×C151C2211yescharacteristic
22#497×C151—21no—
23#491×C151—21no—
24#488×C151—21no—
25#487×C151C2211yescharacteristic
26#487×C151C2211yescharacteristic
27#485×C151—21no—
28#483×C151—21no—
29#483×C151—21no—
30#482×C151—21no—
31#477×C151C2211yescharacteristic
32#476×C151C2211yescharacteristic
33#475×C151—21no—
34#475×C151—21no—
35#475×C151C2211yescharacteristic
36#474×C151C2211yescharacteristic
37#462×C151C2211yescharacteristic
38#462×C151C2211yescharacteristic
39#461×C151C2211yescharacteristic
40#461×C151C2211yescharacteristic
41#451×C151—21no—
42#448×C151—21no—
43#446×C151C2211yescharacteristic
44C8×Q8×C151C2211yescharacteristic
45#436×C151—21no—
46#436×C151C2211yescharacteristic
47#435×C151—21no—
48C8×D4×C151C2211yescharacteristic
49#433×C151—21no—
50#432×C151C2211yescharacteristic
51#431×C151C2211yescharacteristic
52#431×C151C2211yescharacteristic
53#424×C151—21no—
54#423×C151C2211yescharacteristic
55#335×C151C2211yescharacteristic
56#335×C151C2211yescharacteristic
57#334×C151C2211yescharacteristic
58#334×C151C2211yescharacteristic
59#333×C151C2211yescharacteristic
60#333×C151C2211yescharacteristic
61#332×C151C2211yescharacteristic
62#332×C151C2211yescharacteristic
63#332×C151C2211yescharacteristic
64#332×C151C2211yescharacteristic
65#332×C151C2211yescharacteristic
66#332×C151C2211yescharacteristic
67C22×Q8×C151—21no—
68C2×Q16×C151—21no—
69C2×Q16×C151—21no—
70C2×SD16×C151—21no—
71C2×SD16×C151—21no—
72C2×M16×C151—21no—
73C2×M16×C151—21no—
74C22×C8×C151—21no—
75C4⋊Q8×C151—21no—
76C4⋊Q8×C151—21no—
77C4⋊Q8×C151—21no—
78C4⋊Q8×C151C2311yescharacteristic
79C4⋊Q8×C151C2311yescharacteristic
80C4⋊Q8×C151C2311yescharacteristic
81C4⋊Q8×C151C2311yescharacteristic
82#126×C151—21no—
83#125×C151—21no—
84#125×C151D411yescharacteristic
85#124×C151D411yescharacteristic
86#123×C151—21no—
87C22⋊Q8×C151—21no—
88C22⋊Q8×C151—21no—
89C22⋊Q8×C151D411yescharacteristic
90#121×C151D411yescharacteristic
91C4×Q8×C151—21no—
92C4×Q8×C151—21no—
93C4×Q8×C151C2311yescharacteristic
94C4×D4×C151—21no—
95C4×D4×C151C2311yescharacteristic
96#117×C151—21no—
97#117×C151—21no—
98C2×C4⋊C4×C151—21no—
99C2×C4⋊C4×C151—21no—
100C2×C42×C151C2311yescharacteristic
101#107×C151—21no—
102#107×C151—21no—
103#106×C151—21no—
104#106×C151—21no—
105#106×C151—21no—
106#106×C151—21no—
107#106×C151—21no—
108#106×C151—21no—
109C4⋊C8×C151—21no—
110C4⋊C8×C151—21no—
111C4⋊C8×C151—21no—
112C4⋊C8×C151D411yescharacteristic
113C4⋊C8×C151D411yescharacteristic
114C4⋊C8×C151C2311yescharacteristic
115C4⋊C8×C151C2311yescharacteristic
116C4⋊C8×C151C2311yescharacteristic
117C4⋊C8×C151C2311yescharacteristic
118C4⋊C8×C151C2311yescharacteristic
119C4⋊C8×C151C2311yescharacteristic
120#103×C151—21no—
121#103×C151—21no—
122#103×C151—21no—
123#103×C151—21no—
124#103×C151—21no—
125#103×C151—21no—
126#103×C151—21no—
127#103×C151—21no—
128#103×C151—21no—
129#103×C151—21no—
130#102×C151—21no—
131#102×C151—21no—
132C22⋊C8×C151—21no—
133C22⋊C8×C151—21no—
134C22⋊C8×C151—21no—
135C22⋊C8×C151—21no—
136C22⋊C8×C151D411yescharacteristic
137C22⋊C8×C151D411yescharacteristic
138#97×C151—21no—
139#97×C151—21no—
140C4×C8×C151—21no—
141C4×C8×C151—21no—
142C4×C8×C151C2311yescharacteristic
143C4×C8×C151C2311yescharacteristic
144C2×Q8×C151—21no—
145C2×Q8×C151—21no—
146C2×Q8×C151—21no—
147C2×Q8×C151—21no—
148C2×Q8×C151—41no—
149C2×Q8×C151—81no—
150C2×Q8×C151—81no—
151C2×Q8×C151C2×D411yescharacteristic
152C2×D4×C151—21no—
153C2×D4×C151C2×D411yescharacteristic
154C22×C4×C151—21no—
155C22×C4×C151—41no—
156C22×C4×C151C2×D411yescharacteristic
157C22×C4×C151C2×D411yescharacteristic
158C22×C4×C151#4111yescharacteristic
159Q16×C151—81no—
160Q16×C151—81no—
161SD16×C151—81no—
162SD16×C151—81no—
163M16×C151—81no—
164M16×C151—81no—
165C2×C8×C151—21no—
166C2×C8×C151—21no—
167C2×C8×C151—21no—
168C2×C8×C151—21no—
169C2×C8×C151—21no—
170C2×C8×C151—21no—
171C2×C8×C151—81no—
172C2×C8×C151C2×D411yescharacteristic
173C2×C8×C151C2×D411yescharacteristic
174C2×C8×C151C2×D411yescharacteristic
175C2×C8×C151C2×D411yescharacteristic
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—21no—
186C4⋊C4×C151—21no—
187C4⋊C4×C151—21no—
188C4⋊C4×C151—41no—
189C4⋊C4×C151—41no—
190C4⋊C4×C151—41no—
191C4⋊C4×C151—41no—
192C4⋊C4×C151C2×D411yescharacteristic
193C4⋊C4×C151C2×D411yescharacteristic
194C22⋊C4×C151—21no—
195C22⋊C4×C151—21no—
196C22⋊C4×C151—21no—
197C22⋊C4×C151—21no—
198C22⋊C4×C151—21no—
199C22⋊C4×C151—41no—
200C42×C151—21no—
201C42×C151—41no—
202C42×C151C2×D411yescharacteristic
203C42×C151C2×D411yescharacteristic
204C42×C151#4111yescharacteristic
205C42×C151C2411yescharacteristic
206C23×C151—21no—
207C23×C151#12111yescharacteristic
208Q8×C151—21no—
209Q8×C151—21no—
210Q8×C151—41no—
211Q8×C151—41no—
212Q8×C151—41no—
213Q8×C151—41no—
214Q8×C151—41no—
215Q8×C151—41no—
216Q8×C151—81no—
217Q8×C151—82no—
218D4×C151—21no—
219D4×C151—21no—
220D4×C151—81no—
221C2×C4×C151—21no—
222C2×C4×C151—21no—
223C2×C4×C151—21no—
224C2×C4×C151—21no—
225C2×C4×C151—21no—
226C2×C4×C151—21no—
227C2×C4×C151—21no—
228C2×C4×C151—41no—
229C2×C4×C151—41no—
230C2×C4×C151—41no—
231C2×C4×C151—41no—
232C2×C4×C151—41no—
233C2×C4×C151—41no—
234C2×C4×C151—41no—
235C2×C4×C151—82no—
236C2×C4×C151#12111yescharacteristic
237C2×C4×C151#12111yescharacteristic
238C2×C4×C151#12111yescharacteristic
239C2×C4×C151C22×D411yescharacteristic
240C2×C4×C151C22×D411yescharacteristic
241C2×C4×C151C2×#4111yescharacteristic
242C8×C151—21no—
243C8×C151—21no—
244C8×C151—21no—
245C8×C151—21no—
246C8×C151—41no—
247C8×C151—41no—
248C8×C151—41no—
249C8×C151—41no—
250C8×C151—41no—
251C8×C151—41no—
252C22×C151—21no—
253C22×C151—21no—
254C22×C151—21no—
255C22×C151—41no—
256C22×C151—41no—
257C22×C151—41no—
258C22×C151C2×#12111yescharacteristic
259C4×C151—21no—
260C4×C151—21no—
261C4×C151—21no—
262C4×C151—21no—
263C4×C151—41no—
264C4×C151—41no—
265C4×C151—41no—
266C4×C151—81no—
267C4×C151—81no—
268C4×C151—81no—
269C4×C151—81no—
270C4×C151#57711yescharacteristic
271C4×C151#57711yescharacteristic
272C4×C151#57711yescharacteristic
273C4×C151#57811yescharacteristic
274C2×C151—41no—
275C2×C151—81no—
276C2×C151#304611yescharacteristic
277C2×C151#305711yescharacteristic
278C2×C151#306911yescharacteristic
279#19545C15111yesmaximal, characteristic, direct product factor, Sylow
280C151#1954511yescharacteristic, direct product factor, Sylow
281#3233C2×C15111yescharacteristic
282#3229C2×C15111yescharacteristic, complemented
283#3218C2×C15111yescharacteristic
284#2993C2×C15111yescharacteristic
285#1700C2×C15111yescharacteristic, complemented
286#1699C2×C15111yescharacteristic, complemented
287#1692C2×C15111yescharacteristic, complemented
288#1691C2×C15111yescharacteristic, complemented
289#1680C2×C15111yescharacteristic, complemented
290#1679C2×C15111yescharacteristic, complemented
291#1672C2×C15111yescharacteristic, complemented
292#1671C2×C15111yescharacteristic, complemented
293#1572C2×C15111yescharacteristic, complemented
294#1559C2×C15111yescharacteristic, complemented
295#1549C2×C15111yescharacteristic, complemented
296#533C22×C15111yescharacteristic
297C2×C4⋊Q8C22×C15111yescharacteristic
298#529C22×C15111yescharacteristic
299#499—21no—
300#498C22×C15111yescharacteristic
301#498C22×C15111yescharacteristic
302#497—21no—
303#491—21no—
304#488—21no—
305#487C22×C15111yescharacteristic
306#487C22×C15111yescharacteristic
307#485—21no—
308#483—21no—
309#483—21no—
310#482—21no—
311#477C22×C15111yescharacteristic
312#476C22×C15111yescharacteristic
313#475—21no—
314#475—21no—
315#475C22×C15111yescharacteristic
316#474C22×C15111yescharacteristic
317#462C22×C15111yescharacteristic
318#462C22×C15111yescharacteristic
319#461C22×C15111yescharacteristic
320#461C22×C15111yescharacteristic
321#451—21no—
322#448—21no—
323#446C22×C15111yescharacteristic
324C8×Q8C22×C15111yescharacteristic
325#436—21no—
326#436C22×C15111yescharacteristic
327#435—21no—
328C8×D4C22×C15111yescharacteristic
329#433—21no—
330#432C22×C15111yescharacteristic
331#431C22×C15111yescharacteristic
332#431C22×C15111yescharacteristic
333#424—21no—
334#423C22×C15111yescharacteristic
335#335C22×C15111yescharacteristic
336#335C22×C15111yescharacteristic
337#334C22×C15111yescharacteristic
338#334C22×C15111yescharacteristic
339#333C22×C15111yescharacteristic
340#333C22×C15111yescharacteristic
341#332C22×C15111yescharacteristic
342#332C22×C15111yescharacteristic
343#332C22×C15111yescharacteristic
344#332C22×C15111yescharacteristic
345#332C22×C15111yescharacteristic
346#332C22×C15111yescharacteristic
347C22×Q8—21no—
348C2×Q16—21no—
349C2×Q16—21no—
350C2×SD16—21no—
351C2×SD16—21no—
352C2×M16—21no—
353C2×M16—21no—
354C22×C8—21no—
355C4⋊Q8—21no—
356C4⋊Q8—21no—
357C4⋊Q8—21no—
358C4⋊Q8C23×C15111yescharacteristic
359C4⋊Q8C23×C15111yescharacteristic
360C4⋊Q8C23×C15111yescharacteristic
361C4⋊Q8C23×C15111yescharacteristic
362#126—21no—
363#125—21no—
364#125D4×C15111yescharacteristic
365#124D4×C15111yescharacteristic
366#123—21no—
367C22⋊Q8—21no—
368C22⋊Q8—21no—
369C22⋊Q8D4×C15111yescharacteristic
370#121D4×C15111yescharacteristic
371C4×Q8—21no—
372C4×Q8—21no—
373C4×Q8C23×C15111yescharacteristic
374C4×D4—21no—
375C4×D4C23×C15111yescharacteristic
376#117—21no—
377#117—21no—
378C2×C4⋊C4—21no—
379C2×C4⋊C4—21no—
380C2×C42C23×C15111yescharacteristic
381#107—21no—
382#107—21no—
383#106—21no—
384#106—21no—
385#106—21no—
386#106—21no—
387#106—21no—
388#106—21no—
389C4⋊C8—21no—
390C4⋊C8—21no—
391C4⋊C8—21no—
392C4⋊C8D4×C15111yescharacteristic
393C4⋊C8D4×C15111yescharacteristic
394C4⋊C8C23×C15111yescharacteristic
395C4⋊C8C23×C15111yescharacteristic
396C4⋊C8C23×C15111yescharacteristic
397C4⋊C8C23×C15111yescharacteristic
398C4⋊C8C23×C15111yescharacteristic
399C4⋊C8C23×C15111yescharacteristic
400#103—21no—
401#103—21no—
402#103—21no—
403#103—21no—
404#103—21no—
405#103—21no—
406#103—21no—
407#103—21no—
408#103—21no—
409#103—21no—
410#102—21no—
411#102—21no—
412C22⋊C8—21no—
413C22⋊C8—21no—
414C22⋊C8—21no—
415C22⋊C8—21no—
416C22⋊C8D4×C15111yescharacteristic
417C22⋊C8D4×C15111yescharacteristic
418#97—21no—
419#97—21no—
420C4×C8—21no—
421C4×C8—21no—
422C4×C8C23×C15111yescharacteristic
423C4×C8C23×C15111yescharacteristic
424C2×Q8—21no—
425C2×Q8—21no—
426C2×Q8—21no—
427C2×Q8—21no—
428C2×Q8—41no—
429C2×Q8—81no—
430C2×Q8—81no—
431C2×Q8C2×D4×C15111yescharacteristic
432C2×D4—21no—
433C2×D4C2×D4×C15111yescharacteristic
434C22×C4—21no—
435C22×C4—41no—
436C22×C4C2×D4×C15111yescharacteristic
437C22×C4C2×D4×C15111yescharacteristic
438C22×C4#41×C15111yescharacteristic
439Q16—81no—
440Q16—81no—
441SD16—81no—
442SD16—81no—
443M16—81no—
444M16—81no—
445C2×C8—21no—
446C2×C8—21no—
447C2×C8—21no—
448C2×C8—21no—
449C2×C8—21no—
450C2×C8—21no—
451C2×C8—81no—
452C2×C8C2×D4×C15111yescharacteristic
453C2×C8C2×D4×C15111yescharacteristic
454C2×C8C2×D4×C15111yescharacteristic
455C2×C8C2×D4×C15111yescharacteristic
456C4⋊C4—21no—
457C4⋊C4—21no—
458C4⋊C4—21no—
459C4⋊C4—21no—
460C4⋊C4—21no—
461C4⋊C4—21no—
462C4⋊C4—21no—
463C4⋊C4—21no—
464C4⋊C4—21no—
465C4⋊C4—21no—
466C4⋊C4—21no—
467C4⋊C4—21no—
468C4⋊C4—41no—
469C4⋊C4—41no—
470C4⋊C4—41no—
471C4⋊C4—41no—
472C4⋊C4C2×D4×C15111yescharacteristic
473C4⋊C4C2×D4×C15111yescharacteristic
474C22⋊C4—21no—
475C22⋊C4—21no—
476C22⋊C4—21no—
477C22⋊C4—21no—
478C22⋊C4—21no—
479C22⋊C4—41no—
480C42—21no—
481C42—41no—
482C42C2×D4×C15111yescharacteristic
483C42C2×D4×C15111yescharacteristic
484C42#41×C15111yescharacteristic
485C42C24×C15111yescharacteristic
486C23—21no—
487C23#121×C15111yescharacteristic
488Q8—21no—
489Q8—21no—
490Q8—41no—
491Q8—41no—
492Q8—41no—
493Q8—41no—
494Q8—41no—
495Q8—41no—
496Q8—81no—
497Q8—82no—
498D4—21no—
499D4—21no—
500D4—81no—
501C2×C4—21no—
502C2×C4—21no—
503C2×C4—21no—
504C2×C4—21no—
505C2×C4—21no—
506C2×C4—21no—
507C2×C4—21no—
508C2×C4—41no—
509C2×C4—41no—
510C2×C4—41no—
511C2×C4—41no—
512C2×C4—41no—
513C2×C4—41no—
514C2×C4—41no—
515C2×C4—82no—
516C2×C4#121×C15111yescharacteristic
517C2×C4#121×C15111yescharacteristic
518C2×C4#121×C15111yescharacteristic
519C2×C4C22×D4×C15111yescharacteristic
520C2×C4C22×D4×C15111yescharacteristic
521C2×C4C2×#41×C15111yescharacteristic
522C8—21no—
523C8—21no—
524C8—21no—
525C8—21no—
526C8—41no—
527C8—41no—
528C8—41no—
529C8—41no—
530C8—41no—
531C8—41no—
532C22—21no—
533C22—21no—
534C22—21no—
535C22—41no—
536C22—41no—
537C22—41no—
538C22C2×#121×C15111yescharacteristic
539C4—21no—
540C4—21no—
541C4—21no—
542C4—21no—
543C4—41no—
544C4—41no—
545C4—41no—
546C4—81no—
547C4—81no—
548C4—81no—
549C4—81no—
550C4#577×C15111yescharacteristic
551C4#577×C15111yescharacteristic
552C4#577×C15111yescharacteristic
553C4#578×C15111yescharacteristic
554C2—41no—
555C2—81no—
556C2#3046×C15111yescharacteristic
557C2#3057×C15111yescharacteristic
558C2#3069×C15111yescharacteristic
subgroupG/H
center, socleC22×C151C2×#121
commutator, Frattini, cosocleC42C24×C151
prime radical#121×C151D4
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. #3229×C151C2semidirect
5. #1700×C151C2semidirect
6. #1699×C151C2semidirect
7. #1692×C151C2semidirect
8. #1691×C151C2semidirect
9. #1680×C151C2semidirect
10. #1679×C151C2semidirect
11. #1672×C151C2semidirect
12. #1671×C151C2semidirect
13. #1572×C151C2semidirect
14. #1559×C151C2semidirect
15. #1549×C151C2semidirect
279. #19545C151direct (N × H)
280. C151#19545direct (N × H)
282. #3229C2×C151semidirect
285. #1700C2×C151semidirect
286. #1699C2×C151semidirect
287. #1692C2×C151semidirect
288. #1691C2×C151semidirect
289. #1680C2×C151semidirect
290. #1679C2×C151semidirect
291. #1672C2×C151semidirect
292. #1671C2×C151semidirect
293. #1572C2×C151semidirect
294. #1559C2×C151semidirect
295. #1549C2×C151semidirect

Maximal subgroups

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

subgroupindex
#3233×C1512
#3229×C1512
#3218×C1512
#2993×C1512
#1700×C1512
#1699×C1512
#1692×C1512
#1691×C1512
#1680×C1512
#1679×C1512
#1672×C1512
#1671×C1512
#1572×C1512
#1559×C1512
#1549×C1512
#19545151