Finite Group Databasebeta

← C151×#19842 #50324767

Subgroups — C151×#19842 #50324767

Order 38656.

576 conjugacy classes of subgroups.

The subgroup lattice has 558 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#3372×C151C211yesmaximal, characteristic, complemented
2#3365×C151C211yesmaximal, characteristic, complemented
3#3361×C151C211yesmaximal, characteristic
4#3338×C151C211yesmaximal, characteristic, complemented
5#1719×C151C211yesmaximal, characteristic, complemented
6#1698×C151C211yesmaximal, characteristic, complemented
7#1684×C151C211yesmaximal, characteristic, complemented
8#1681×C151C211yesmaximal, characteristic
9#1676×C151C211yesmaximal, characteristic, complemented
10#1643×C151C211yesmaximal, characteristic, complemented
11#1636×C151C211yesmaximal, characteristic, complemented
12#1630×C151C211yesmaximal, characteristic, complemented
13#1622×C151C211yesmaximal, characteristic
14#1584×C151C211yesmaximal, characteristic, complemented
15SD16⋊C8×C151C211yesmaximal, characteristic, complemented
16#559×C151C2211yescharacteristic
17#557×C151C2211yescharacteristic
18#554×C151C2211yescharacteristic
19#554×C151C2211yescharacteristic
20#500×C151C2211yescharacteristic
21#492×C151C2211yescharacteristic
22#491×C151—21no—
23#488×C151—21no—
24#488×C151—21no—
25#487×C151C2211yescharacteristic
26#487×C151C2211yescharacteristic
27#486×C151C2211yescharacteristic
28#486×C151C2211yescharacteristic
29#484×C151—21no—
30#484×C151—21no—
31#479×C151—21no—
32#478×C151—21no—
33#478×C151—21no—
34#477×C151C2211yescharacteristic
35#477×C151C2211yescharacteristic
36#477×C151C2211yescharacteristic
37#477×C151C2211yescharacteristic
38#475×C151C2211yescharacteristic
39#467×C151—21no—
40#464×C151—21no—
41#463×C151—21no—
42#461×C151—21no—
43#461×C151C2211yescharacteristic
44#460×C151C2211yescharacteristic
45#459×C151C2211yescharacteristic
46#446×C151C2211yescharacteristic
47C8×Q8×C151C2211yescharacteristic
48C8×Q8×C151C2211yescharacteristic
49#440×C151—21no—
50C4×Q16×C151C2211yescharacteristic
51C4×SD16×C151—21no—
52C4×SD16×C151C2211yescharacteristic
53C4×D8×C151—21no—
54C8×D4×C151C2211yescharacteristic
55C2×#107×C151—21no—
56#335×C151C2211yescharacteristic
57#335×C151C2211yescharacteristic
58#333×C151C2211yescharacteristic
59#333×C151C2211yescharacteristic
60#332×C151C2211yescharacteristic
61#331×C151C2211yescharacteristic
62Q8⋊C8×C151C2211yescharacteristic
63Q8⋊C8×C151C2211yescharacteristic
64Q8⋊C8×C151C2211yescharacteristic
65D4⋊C8×C151C2211yescharacteristic
66#322×C151C2211yescharacteristic
67C2×Q16×C151D411yescharacteristic
68C2×SD16×C151—21no—
69C2×SD16×C151—21no—
70C2×SD16×C151—41no—
71C2×SD16×C151D411yescharacteristic
72C2×D8×C151—21no—
73C22×C8×C151—21no—
74C4⋊Q8×C151—21no—
75C4⋊Q8×C151C2311yescharacteristic
76C4⋊Q8×C151C2311yescharacteristic
77C4⋊Q8×C151C2311yescharacteristic
78#127×C151C2311yescharacteristic
79#125×C151—21no—
80#125×C151—21no—
81#125×C151—21no—
82#125×C151—41no—
83#124×C151—21no—
84#124×C151—21no—
85#123×C151—41no—
86C22⋊Q8×C151—21no—
87C22⋊Q8×C151—21no—
88C22⋊Q8×C151—41no—
89C22⋊Q8×C151—41no—
90C4×Q8×C151—21no—
91C4×Q8×C151—21no—
92C4×Q8×C151C2311yescharacteristic
93C4×Q8×C151C2311yescharacteristic
94C4×Q8×C151C2311yescharacteristic
95C4×D4×C151—21no—
96C4×D4×C151—21no—
97C4×D4×C151—21no—
98C4×D4×C151—21no—
99C4×D4×C151C2311yescharacteristic
100C2×C4⋊C4×C151—21no—
101C2×C4⋊C4×C151—21no—
102#107×C151—21no—
103#107×C151—21no—
104#107×C151—21no—
105#107×C151—21no—
106#107×C151—21no—
107#107×C151—21no—
108#107×C151D411yescharacteristic
109#106×C151—21no—
110#106×C151D411yescharacteristic
111C4⋊C8×C151—21no—
112C4⋊C8×C151—21no—
113C4⋊C8×C151—21no—
114C4⋊C8×C151C2311yescharacteristic
115C4⋊C8×C151C2311yescharacteristic
116C4⋊C8×C151C2311yescharacteristic
117C4⋊C8×C151C2311yescharacteristic
118#103×C151—21no—
119#103×C151—21no—
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—41no—
127#103×C151D411yescharacteristic
128#103×C151D411yescharacteristic
129#103×C151D411yescharacteristic
130#102×C151—21no—
131#102×C151—21no—
132#102×C151—21no—
133#102×C151—21no—
134#102×C151—21no—
135#102×C151—21no—
136#102×C151D411yescharacteristic
137C22⋊C8×C151—21no—
138#97×C151—21no—
139C4×C8×C151—21no—
140C4×C8×C151—21no—
141C4×C8×C151C2311yescharacteristic
142C4×C8×C151C2311yescharacteristic
143C4×C8×C151C2311yescharacteristic
144C2×Q8×C151—21no—
145C2×Q8×C151—21no—
146C2×Q8×C151—21no—
147C2×Q8×C151C2×D411yescharacteristic
148C2×Q8×C151C2×D411yescharacteristic
149C2×Q8×C151C2×D411yescharacteristic
150C2×D4×C151—21no—
151C2×D4×C151—21no—
152C2×D4×C151—21no—
153C2×D4×C151C2×D411yescharacteristic
154C22×C4×C151—21no—
155C22×C4×C151—41no—
156C22×C4×C151—41no—
157C22×C4×C151—41no—
158Q16×C151—41no—
159SD16×C151—22no—
160SD16×C151—42no—
161SD16×C151—42no—
162SD16×C151—82no—
163D8×C151—42no—
164C2×C8×C151—21no—
165C2×C8×C151—21no—
166C2×C8×C151—21no—
167C2×C8×C151—21no—
168C2×C8×C151—21no—
169C2×C8×C151—42no—
170C2×C8×C151C2×D411yescharacteristic
171C2×C8×C151C2×D411yescharacteristic
172C2×C8×C151C2×D411yescharacteristic
173C2×C8×C151C2×D411yescharacteristic
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—
187C4⋊C4×C151—41no—
188C4⋊C4×C151—41no—
189C4⋊C4×C151—41no—
190C4⋊C4×C151C2×D411yescharacteristic
191C4⋊C4×C151C2×D411yescharacteristic
192C4⋊C4×C151C2×D411yescharacteristic
193C4⋊C4×C151C2×D411yescharacteristic
194C22⋊C4×C151—21no—
195C22⋊C4×C151—41no—
196C22⋊C4×C151—41no—
197C22⋊C4×C151—41no—
198C22⋊C4×C151—41no—
199C22⋊C4×C151—41no—
200C42×C151—21no—
201C42×C151—21no—
202C42×C151—21no—
203C42×C151—41no—
204C42×C151C2411yescharacteristic
205C23×C151—21no—
206C23×C151—41no—
207Q8×C151—21no—
208Q8×C151—21no—
209Q8×C151—21no—
210Q8×C151—21no—
211Q8×C151—21no—
212Q8×C151—21no—
213Q8×C151—41no—
214Q8×C151—41no—
215Q8×C151—81no—
216Q8×C151—81no—
217D4×C151—21no—
218D4×C151—41no—
219D4×C151—41no—
220D4×C151—41no—
221D4×C151—41no—
222D4×C151—81no—
223D4×C151#13512yes—
224C2×C4×C151—21no—
225C2×C4×C151—21no—
226C2×C4×C151—21no—
227C2×C4×C151—21no—
228C2×C4×C151—21no—
229C2×C4×C151—21no—
230C2×C4×C151—21no—
231C2×C4×C151—41no—
232C2×C4×C151—41no—
233C2×C4×C151—41no—
234C2×C4×C151—41no—
235C2×C4×C151—41no—
236C2×C4×C151—161no—
237C2×C4×C151—161no—
238C2×C4×C151—161no—
239C2×C4×C151C22×D411yescharacteristic
240C2×C4×C151C22×D411yescharacteristic
241C2×C4×C151H(5,𝔽2)11yescharacteristic
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—
251C22×C151—22no—
252C22×C151—41no—
253C22×C151—41no—
254C22×C151—81no—
255C22×C151—81no—
256C22×C151—81no—
257C22×C151D4211yescharacteristic
258C4×C151—21no—
259C4×C151—41no—
260C4×C151—41no—
261C4×C151—41no—
262C4×C151—41no—
263C4×C151—41no—
264C4×C151—41no—
265C4×C151—41no—
266C4×C151—81no—
267C4×C151—81no—
268C4×C151—81no—
269C4×C151C2×#13511yescharacteristic
270C4×C151#57511yescharacteristic
271C4×C151#57811yescharacteristic
272C4×C151#57811yescharacteristic
273C2×C151—42no—
274C2×C151—161no—
275C2×C151#326911yescharacteristic
276C2×C151#328511yescharacteristic
277C2×C151#328811yescharacteristic
278#19842C15111yesmaximal, characteristic, direct product factor, Sylow
279C151#1984211yescharacteristic, direct product factor, Sylow
280#3372C2×C15111yescharacteristic, complemented
281#3365C2×C15111yescharacteristic, complemented
282#3361C2×C15111yescharacteristic
283#3338C2×C15111yescharacteristic, complemented
284#1719C2×C15111yescharacteristic, complemented
285#1698C2×C15111yescharacteristic, complemented
286#1684C2×C15111yescharacteristic, complemented
287#1681C2×C15111yescharacteristic
288#1676C2×C15111yescharacteristic, complemented
289#1643C2×C15111yescharacteristic, complemented
290#1636C2×C15111yescharacteristic, complemented
291#1630C2×C15111yescharacteristic, complemented
292#1622C2×C15111yescharacteristic
293#1584C2×C15111yescharacteristic, complemented
294SD16⋊C8C2×C15111yescharacteristic, complemented
295#559C22×C15111yescharacteristic
296#557C22×C15111yescharacteristic
297#554C22×C15111yescharacteristic
298#554C22×C15111yescharacteristic
299#500C22×C15111yescharacteristic
300#492C22×C15111yescharacteristic
301#491—21no—
302#488—21no—
303#488—21no—
304#487C22×C15111yescharacteristic
305#487C22×C15111yescharacteristic
306#486C22×C15111yescharacteristic
307#486C22×C15111yescharacteristic
308#484—21no—
309#484—21no—
310#479—21no—
311#478—21no—
312#478—21no—
313#477C22×C15111yescharacteristic
314#477C22×C15111yescharacteristic
315#477C22×C15111yescharacteristic
316#477C22×C15111yescharacteristic
317#475C22×C15111yescharacteristic
318#467—21no—
319#464—21no—
320#463—21no—
321#461—21no—
322#461C22×C15111yescharacteristic
323#460C22×C15111yescharacteristic
324#459C22×C15111yescharacteristic
325#446C22×C15111yescharacteristic
326C8×Q8C22×C15111yescharacteristic
327C8×Q8C22×C15111yescharacteristic
328#440—21no—
329C4×Q16C22×C15111yescharacteristic
330C4×SD16—21no—
331C4×SD16C22×C15111yescharacteristic
332C4×D8—21no—
333C8×D4C22×C15111yescharacteristic
334C2×#107—21no—
335#335C22×C15111yescharacteristic
336#335C22×C15111yescharacteristic
337#333C22×C15111yescharacteristic
338#333C22×C15111yescharacteristic
339#332C22×C15111yescharacteristic
340#331C22×C15111yescharacteristic
341Q8⋊C8C22×C15111yescharacteristic
342Q8⋊C8C22×C15111yescharacteristic
343Q8⋊C8C22×C15111yescharacteristic
344D4⋊C8C22×C15111yescharacteristic
345#322C22×C15111yescharacteristic
346C2×Q16D4×C15111yescharacteristic
347C2×SD16—21no—
348C2×SD16—21no—
349C2×SD16—41no—
350C2×SD16D4×C15111yescharacteristic
351C2×D8—21no—
352C22×C8—21no—
353C4⋊Q8—21no—
354C4⋊Q8C23×C15111yescharacteristic
355C4⋊Q8C23×C15111yescharacteristic
356C4⋊Q8C23×C15111yescharacteristic
357#127C23×C15111yescharacteristic
358#125—21no—
359#125—21no—
360#125—21no—
361#125—41no—
362#124—21no—
363#124—21no—
364#123—41no—
365C22⋊Q8—21no—
366C22⋊Q8—21no—
367C22⋊Q8—41no—
368C22⋊Q8—41no—
369C4×Q8—21no—
370C4×Q8—21no—
371C4×Q8C23×C15111yescharacteristic
372C4×Q8C23×C15111yescharacteristic
373C4×Q8C23×C15111yescharacteristic
374C4×D4—21no—
375C4×D4—21no—
376C4×D4—21no—
377C4×D4—21no—
378C4×D4C23×C15111yescharacteristic
379C2×C4⋊C4—21no—
380C2×C4⋊C4—21no—
381#107—21no—
382#107—21no—
383#107—21no—
384#107—21no—
385#107—21no—
386#107—21no—
387#107D4×C15111yescharacteristic
388#106—21no—
389#106D4×C15111yescharacteristic
390C4⋊C8—21no—
391C4⋊C8—21no—
392C4⋊C8—21no—
393C4⋊C8C23×C15111yescharacteristic
394C4⋊C8C23×C15111yescharacteristic
395C4⋊C8C23×C15111yescharacteristic
396C4⋊C8C23×C15111yescharacteristic
397#103—21no—
398#103—21no—
399#103—21no—
400#103—21no—
401#103—21no—
402#103—21no—
403#103—21no—
404#103—21no—
405#103—41no—
406#103D4×C15111yescharacteristic
407#103D4×C15111yescharacteristic
408#103D4×C15111yescharacteristic
409#102—21no—
410#102—21no—
411#102—21no—
412#102—21no—
413#102—21no—
414#102—21no—
415#102D4×C15111yescharacteristic
416C22⋊C8—21no—
417#97—21no—
418C4×C8—21no—
419C4×C8—21no—
420C4×C8C23×C15111yescharacteristic
421C4×C8C23×C15111yescharacteristic
422C4×C8C23×C15111yescharacteristic
423C2×Q8—21no—
424C2×Q8—21no—
425C2×Q8—21no—
426C2×Q8C2×D4×C15111yescharacteristic
427C2×Q8C2×D4×C15111yescharacteristic
428C2×Q8C2×D4×C15111yescharacteristic
429C2×D4—21no—
430C2×D4—21no—
431C2×D4—21no—
432C2×D4C2×D4×C15111yescharacteristic
433C22×C4—21no—
434C22×C4—41no—
435C22×C4—41no—
436C22×C4—41no—
437Q16—41no—
438SD16—22no—
439SD16—42no—
440SD16—42no—
441SD16—82no—
442D8—42no—
443C2×C8—21no—
444C2×C8—21no—
445C2×C8—21no—
446C2×C8—21no—
447C2×C8—21no—
448C2×C8—42no—
449C2×C8C2×D4×C15111yescharacteristic
450C2×C8C2×D4×C15111yescharacteristic
451C2×C8C2×D4×C15111yescharacteristic
452C2×C8C2×D4×C15111yescharacteristic
453C4⋊C4—21no—
454C4⋊C4—21no—
455C4⋊C4—21no—
456C4⋊C4—21no—
457C4⋊C4—21no—
458C4⋊C4—21no—
459C4⋊C4—21no—
460C4⋊C4—21no—
461C4⋊C4—21no—
462C4⋊C4—41no—
463C4⋊C4—41no—
464C4⋊C4—41no—
465C4⋊C4—41no—
466C4⋊C4—41no—
467C4⋊C4—41no—
468C4⋊C4—41no—
469C4⋊C4C2×D4×C15111yescharacteristic
470C4⋊C4C2×D4×C15111yescharacteristic
471C4⋊C4C2×D4×C15111yescharacteristic
472C4⋊C4C2×D4×C15111yescharacteristic
473C22⋊C4—21no—
474C22⋊C4—41no—
475C22⋊C4—41no—
476C22⋊C4—41no—
477C22⋊C4—41no—
478C22⋊C4—41no—
479C42—21no—
480C42—21no—
481C42—21no—
482C42—41no—
483C42C24×C15111yescharacteristic
484C23—21no—
485C23—41no—
486Q8—21no—
487Q8—21no—
488Q8—21no—
489Q8—21no—
490Q8—21no—
491Q8—21no—
492Q8—41no—
493Q8—41no—
494Q8—81no—
495Q8—81no—
496D4—21no—
497D4—41no—
498D4—41no—
499D4—41no—
500D4—41no—
501D4—81no—
502D4#135×C15112yes—
503C2×C4—21no—
504C2×C4—21no—
505C2×C4—21no—
506C2×C4—21no—
507C2×C4—21no—
508C2×C4—21no—
509C2×C4—21no—
510C2×C4—41no—
511C2×C4—41no—
512C2×C4—41no—
513C2×C4—41no—
514C2×C4—41no—
515C2×C4—161no—
516C2×C4—161no—
517C2×C4—161no—
518C2×C4C22×D4×C15111yescharacteristic
519C2×C4C22×D4×C15111yescharacteristic
520C2×C4H(5,𝔽2)×C15111yescharacteristic
521C8—21no—
522C8—21no—
523C8—21no—
524C8—21no—
525C8—41no—
526C8—41no—
527C8—41no—
528C8—41no—
529C8—41no—
530C22—22no—
531C22—41no—
532C22—41no—
533C22—81no—
534C22—81no—
535C22—81no—
536C22D42×C15111yescharacteristic
537C4—21no—
538C4—41no—
539C4—41no—
540C4—41no—
541C4—41no—
542C4—41no—
543C4—41no—
544C4—41no—
545C4—81no—
546C4—81no—
547C4—81no—
548C4C2×#135×C15111yescharacteristic
549C4#575×C15111yescharacteristic
550C4#578×C15111yescharacteristic
551C4#578×C15111yescharacteristic
552C2—42no—
553C2—161no—
554C2#3269×C15111yescharacteristic
555C2#3285×C15111yescharacteristic
556C2#3288×C15111yescharacteristic
subgroupG/H
center, socleC22×C151D42
commutator, Frattini, cosocleC42C24×C151
prime radical#459×C151C22
LCSG ▷ C42 ▷ C22 ▷ C1
UCSC1 ◁ C22×C151 ◁ C42×C151 ◁ G

Complements

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

NH ≅ G/Ntype
1. #3372×C151C2semidirect
2. #3365×C151C2semidirect
4. #3338×C151C2semidirect
5. #1719×C151C2semidirect
6. #1698×C151C2semidirect
7. #1684×C151C2semidirect
9. #1676×C151C2semidirect
10. #1643×C151C2semidirect
11. #1636×C151C2semidirect
12. #1630×C151C2semidirect
14. #1584×C151C2semidirect
15. SD16⋊C8×C151C2semidirect
278. #19842C151direct (N × H)
279. C151#19842direct (N × H)
280. #3372C2×C151semidirect
281. #3365C2×C151semidirect
283. #3338C2×C151semidirect
284. #1719C2×C151semidirect
285. #1698C2×C151semidirect
286. #1684C2×C151semidirect
288. #1676C2×C151semidirect
289. #1643C2×C151semidirect
290. #1636C2×C151semidirect
291. #1630C2×C151semidirect
293. #1584C2×C151semidirect
294. SD16⋊C8C2×C151semidirect

Maximal subgroups

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

subgroupindex
#3372×C1512
#3365×C1512
#3361×C1512
#3338×C1512
#1719×C1512
#1698×C1512
#1684×C1512
#1681×C1512
#1676×C1512
#1643×C1512
#1636×C1512
#1630×C1512
#1622×C1512
#1584×C1512
SD16⋊C8×C1512
#19842151