Finite Group Databasebeta

← C151×#19895 #50324820

Subgroups — C151×#19895 #50324820

Order 38656.

624 conjugacy classes of subgroups.

The subgroup lattice has 574 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#3385×C151C211yesmaximal, characteristic, complemented
2Q8×SD16×C151C211yesmaximal, characteristic, complemented
3#3335×C151C211yesmaximal, characteristic
4#3276×C151C211yesmaximal, characteristic
5#1707×C151C211yesmaximal, characteristic, complemented
6#1695×C151C211yesmaximal, characteristic, complemented
7#1690×C151C211yesmaximal, characteristic, complemented
8#1672×C151C211yesmaximal, characteristic, complemented
9#1671×C151C211yesmaximal, characteristic, complemented
10#1645×C151C211yesmaximal, characteristic, complemented
11#1643×C151C211yesmaximal, characteristic, complemented
12#1637×C151C211yesmaximal, characteristic, complemented
13#1635×C151C211yesmaximal, characteristic
14#1590×C151C211yesmaximal, characteristic, complemented
15C8×SD16×C151C211yesmaximal, characteristic, complemented
16C2×#137×C151—21no—
17Q82×C151C2211yescharacteristic
18#554×C151C2211yescharacteristic
19D4×Q8×C151C2211yescharacteristic
20#547×C151C2211yescharacteristic
21#501×C151—21no—
22#500×C151C2211yescharacteristic
23#498×C151—21no—
24#498×C151C2211yescharacteristic
25#498×C151C2211yescharacteristic
26#494×C151C2211yescharacteristic
27#487×C151C2211yescharacteristic
28#487×C151C2211yescharacteristic
29#483×C151—21no—
30#481×C151—21no—
31#479×C151—21no—
32#477×C151C2211yescharacteristic
33#476×C151—21no—
34#476×C151C2211yescharacteristic
35#476×C151C2211yescharacteristic
36#476×C151C2211yescharacteristic
37#475×C151—21no—
38#475×C151C2211yescharacteristic
39#475×C151C2211yescharacteristic
40#474×C151—21no—
41#470×C151—21no—
42#465×C151—21no—
43#462×C151C2211yescharacteristic
44#461×C151C2211yescharacteristic
45#452×C151—21no—
46#451×C151—21no—
47#446×C151C2211yescharacteristic
48C8×Q8×C151C2211yescharacteristic
49#440×C151—21no—
50C4×SD16×C151—21no—
51C4×SD16×C151C2211yescharacteristic
52C4×SD16×C151C2211yescharacteristic
53#436×C151C2211yescharacteristic
54C8×D4×C151C2211yescharacteristic
55C2×#106×C151—21no—
56#334×C151C2211yescharacteristic
57#334×C151C2211yescharacteristic
58#333×C151C2211yescharacteristic
59#333×C151C2211yescharacteristic
60#332×C151C2211yescharacteristic
61#332×C151C2211yescharacteristic
62Q8⋊C8×C151C2211yescharacteristic
63Q8⋊C8×C151C2211yescharacteristic
64D4⋊C8×C151C2211yescharacteristic
65D4⋊C8×C151C2211yescharacteristic
66C82×C151C2211yescharacteristic
67C2×#41×C151—21no—
68C22×Q8×C151—21no—
69#137×C151—44no—
70C2×Q16×C151—21no—
71C2×Q16×C151—21no—
72C2×Q16×C151—21no—
73C2×SD16×C151—21no—
74C2×SD16×C151D411yescharacteristic
75C2×SD16×C151D411yescharacteristic
76C2×M16×C151—21no—
77C22×C8×C151—21no—
78C4⋊Q8×C151—21no—
79C4⋊Q8×C151—21no—
80C4⋊Q8×C151—21no—
81C4⋊Q8×C151—41no—
82C4⋊Q8×C151C2311yescharacteristic
83C4⋊Q8×C151C2311yescharacteristic
84C4⋊Q8×C151C2311yescharacteristic
85C4⋊Q8×C151C2311yescharacteristic
86#125×C151—21no—
87#123×C151—41no—
88C22⋊Q8×C151—21no—
89C22⋊Q8×C151—21no—
90C22⋊Q8×C151—21no—
91C22⋊Q8×C151—41no—
92C22⋊Q8×C151—41no—
93#121×C151—21no—
94C4×Q8×C151—21no—
95C4×Q8×C151—21no—
96C4×Q8×C151C2311yescharacteristic
97C4×Q8×C151C2311yescharacteristic
98C4×D4×C151—21no—
99C4×D4×C151—21no—
100C4×D4×C151C2311yescharacteristic
101C4×D4×C151C2311yescharacteristic
102C2×C4⋊C4×C151—21no—
103C2×C4⋊C4×C151—21no—
104#107×C151—21no—
105#107×C151—21no—
106#107×C151—21no—
107#106×C151—21no—
108#106×C151—21no—
109#106×C151—21no—
110#106×C151—21no—
111#106×C151—21no—
112#106×C151—21no—
113#106×C151—21no—
114#106×C151—21no—
115#106×C151—21no—
116#106×C151D411yescharacteristic
117#106×C151D411yescharacteristic
118C4⋊C8×C151—21no—
119C4⋊C8×C151—21no—
120C4⋊C8×C151C2311yescharacteristic
121C4⋊C8×C151C2311yescharacteristic
122C4⋊C8×C151C2311yescharacteristic
123C4⋊C8×C151C2311yescharacteristic
124#103×C151—21no—
125#103×C151—21no—
126#103×C151—21no—
127#103×C151—21no—
128#103×C151—21no—
129#103×C151—41no—
130#103×C151—41no—
131#103×C151D411yescharacteristic
132#103×C151D411yescharacteristic
133#102×C151—21no—
134#102×C151—21no—
135#102×C151—21no—
136#102×C151D411yescharacteristic
137#102×C151D411yescharacteristic
138C22⋊C8×C151—21no—
139C22⋊C8×C151—21no—
140#97×C151—21no—
141C4×C8×C151—21no—
142C4×C8×C151C2311yescharacteristic
143C4×C8×C151C2311yescharacteristic
144C4×C8×C151C2311yescharacteristic
145#41×C151—42no—
146#41×C151—81no—
147C2×Q8×C151—21no—
148C2×Q8×C151—21no—
149C2×Q8×C151—21no—
150C2×Q8×C151—21no—
151C2×Q8×C151—41no—
152C2×Q8×C151—41no—
153C2×Q8×C151—42no—
154C2×Q8×C151—81no—
155C2×Q8×C151C2×D411yescharacteristic
156C2×Q8×C151C2×D411yescharacteristic
157C2×D4×C151—41no—
158C2×D4×C151C2×D411yescharacteristic
159C2×D4×C151C2×D411yescharacteristic
160C22×C4×C151—21no—
161C22×C4×C151—21no—
162C22×C4×C151—41no—
163C22×C4×C151—41no—
164C22×C4×C151—41no—
165Q16×C151—42no—
166Q16×C151—42no—
167Q16×C151—81no—
168SD16×C151—22no—
169SD16×C151—42no—
170SD16×C151SD1614yescomplemented
171M16×C151—42no—
172C2×C8×C151—21no—
173C2×C8×C151—21no—
174C2×C8×C151—21no—
175C2×C8×C151—21no—
176C2×C8×C151—21no—
177C2×C8×C151—42no—
178C2×C8×C151C2×D411yescharacteristic
179C2×C8×C151C2×D411yescharacteristic
180C2×C8×C151C2×D411yescharacteristic
181C2×C8×C151C2×D411yescharacteristic
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—21no—
189C4⋊C4×C151—21no—
190C4⋊C4×C151—21no—
191C4⋊C4×C151—21no—
192C4⋊C4×C151—41no—
193C4⋊C4×C151—41no—
194C4⋊C4×C151—41no—
195C4⋊C4×C151—41no—
196C4⋊C4×C151—41no—
197C4⋊C4×C151—41no—
198C4⋊C4×C151C2×D411yescharacteristic
199C4⋊C4×C151C2×D411yescharacteristic
200C4⋊C4×C151C2×D411yescharacteristic
201C4⋊C4×C151C2×D411yescharacteristic
202C22⋊C4×C151—21no—
203C22⋊C4×C151—21no—
204C22⋊C4×C151—41no—
205C22⋊C4×C151—41no—
206C22⋊C4×C151—41no—
207C42×C151—21no—
208C42×C151—21no—
209C42×C151—41no—
210C42×C151C2411yescharacteristic
211C23×C151—21no—
212C23×C151—21no—
213Q8×C151—21no—
214Q8×C151—21no—
215Q8×C151—21no—
216Q8×C151—41no—
217Q8×C151—41no—
218Q8×C151—41no—
219Q8×C151—41no—
220Q8×C151—82no—
221Q8×C151—81no—
222Q8×C151—81no—
223Q8×C151—161no—
224Q8×C151C2×SD1612yes—
225D4×C151—21no—
226D4×C151—21no—
227D4×C151—21no—
228D4×C151—82no—
229D4×C151C2×SD1612yes—
230C2×C4×C151—21no—
231C2×C4×C151—21no—
232C2×C4×C151—21no—
233C2×C4×C151—21no—
234C2×C4×C151—21no—
235C2×C4×C151—21no—
236C2×C4×C151—41no—
237C2×C4×C151—41no—
238C2×C4×C151—41no—
239C2×C4×C151—41no—
240C2×C4×C151—41no—
241C2×C4×C151—41no—
242C2×C4×C151—41no—
243C2×C4×C151—41no—
244C2×C4×C151—82no—
245C2×C4×C151—82no—
246C2×C4×C151—161no—
247C2×C4×C151C22×D411yescharacteristic
248C2×C4×C151C22×D411yescharacteristic
249C2×C4×C151H(5,𝔽2)11yescharacteristic
250C8×C151—21no—
251C8×C151—21no—
252C8×C151—41no—
253C8×C151—41no—
254C8×C151—41no—
255C8×C151—41no—
256C8×C151—41no—
257C8×C151C2×SD1612yes—
258C8×C151#13712yescomplemented
259C22×C151—22no—
260C22×C151—41no—
261C22×C151—41no—
262C22×C151—41no—
263C22×C151—41no—
264C22×C151—41no—
265C22×C151D4211yescharacteristic
266C4×C151—22no—
267C4×C151—21no—
268C4×C151—41no—
269C4×C151—41no—
270C4×C151—41no—
271C4×C151—41no—
272C4×C151—41no—
273C4×C151—81no—
274C4×C151—81no—
275C4×C151—81no—
276C4×C151—81no—
277C4×C151C22×SD1611yescharacteristic
278C4×C151C2×#13711yescharacteristic
279C4×C151#57711yescharacteristic
280C4×C151#57811yescharacteristic
281C2×C151—42no—
282C2×C151—81no—
283C2×C151#327611yescharacteristic
284C2×C151D4×SD1611yescharacteristic
285C2×C151#329011yescharacteristic
286#19895C15111yesmaximal, characteristic, direct product factor, Sylow
287C151#1989511yescharacteristic, direct product factor, Sylow
288#3385C2×C15111yescharacteristic, complemented
289Q8×SD16C2×C15111yescharacteristic, complemented
290#3335C2×C15111yescharacteristic
291#3276C2×C15111yescharacteristic
292#1707C2×C15111yescharacteristic, complemented
293#1695C2×C15111yescharacteristic, complemented
294#1690C2×C15111yescharacteristic, complemented
295#1672C2×C15111yescharacteristic, complemented
296#1671C2×C15111yescharacteristic, complemented
297#1645C2×C15111yescharacteristic, complemented
298#1643C2×C15111yescharacteristic, complemented
299#1637C2×C15111yescharacteristic, complemented
300#1635C2×C15111yescharacteristic
301#1590C2×C15111yescharacteristic, complemented
302C8×SD16C2×C15111yescharacteristic, complemented
303C2×#137—21no—
304Q82C22×C15111yescharacteristic
305#554C22×C15111yescharacteristic
306D4×Q8C22×C15111yescharacteristic
307#547C22×C15111yescharacteristic
308#501—21no—
309#500C22×C15111yescharacteristic
310#498—21no—
311#498C22×C15111yescharacteristic
312#498C22×C15111yescharacteristic
313#494C22×C15111yescharacteristic
314#487C22×C15111yescharacteristic
315#487C22×C15111yescharacteristic
316#483—21no—
317#481—21no—
318#479—21no—
319#477C22×C15111yescharacteristic
320#476—21no—
321#476C22×C15111yescharacteristic
322#476C22×C15111yescharacteristic
323#476C22×C15111yescharacteristic
324#475—21no—
325#475C22×C15111yescharacteristic
326#475C22×C15111yescharacteristic
327#474—21no—
328#470—21no—
329#465—21no—
330#462C22×C15111yescharacteristic
331#461C22×C15111yescharacteristic
332#452—21no—
333#451—21no—
334#446C22×C15111yescharacteristic
335C8×Q8C22×C15111yescharacteristic
336#440—21no—
337C4×SD16—21no—
338C4×SD16C22×C15111yescharacteristic
339C4×SD16C22×C15111yescharacteristic
340#436C22×C15111yescharacteristic
341C8×D4C22×C15111yescharacteristic
342C2×#106—21no—
343#334C22×C15111yescharacteristic
344#334C22×C15111yescharacteristic
345#333C22×C15111yescharacteristic
346#333C22×C15111yescharacteristic
347#332C22×C15111yescharacteristic
348#332C22×C15111yescharacteristic
349Q8⋊C8C22×C15111yescharacteristic
350Q8⋊C8C22×C15111yescharacteristic
351D4⋊C8C22×C15111yescharacteristic
352D4⋊C8C22×C15111yescharacteristic
353C82C22×C15111yescharacteristic
354C2×#41—21no—
355C22×Q8—21no—
356#137—44no—
357C2×Q16—21no—
358C2×Q16—21no—
359C2×Q16—21no—
360C2×SD16—21no—
361C2×SD16D4×C15111yescharacteristic
362C2×SD16D4×C15111yescharacteristic
363C2×M16—21no—
364C22×C8—21no—
365C4⋊Q8—21no—
366C4⋊Q8—21no—
367C4⋊Q8—21no—
368C4⋊Q8—41no—
369C4⋊Q8C23×C15111yescharacteristic
370C4⋊Q8C23×C15111yescharacteristic
371C4⋊Q8C23×C15111yescharacteristic
372C4⋊Q8C23×C15111yescharacteristic
373#125—21no—
374#123—41no—
375C22⋊Q8—21no—
376C22⋊Q8—21no—
377C22⋊Q8—21no—
378C22⋊Q8—41no—
379C22⋊Q8—41no—
380#121—21no—
381C4×Q8—21no—
382C4×Q8—21no—
383C4×Q8C23×C15111yescharacteristic
384C4×Q8C23×C15111yescharacteristic
385C4×D4—21no—
386C4×D4—21no—
387C4×D4C23×C15111yescharacteristic
388C4×D4C23×C15111yescharacteristic
389C2×C4⋊C4—21no—
390C2×C4⋊C4—21no—
391#107—21no—
392#107—21no—
393#107—21no—
394#106—21no—
395#106—21no—
396#106—21no—
397#106—21no—
398#106—21no—
399#106—21no—
400#106—21no—
401#106—21no—
402#106—21no—
403#106D4×C15111yescharacteristic
404#106D4×C15111yescharacteristic
405C4⋊C8—21no—
406C4⋊C8—21no—
407C4⋊C8C23×C15111yescharacteristic
408C4⋊C8C23×C15111yescharacteristic
409C4⋊C8C23×C15111yescharacteristic
410C4⋊C8C23×C15111yescharacteristic
411#103—21no—
412#103—21no—
413#103—21no—
414#103—21no—
415#103—21no—
416#103—41no—
417#103—41no—
418#103D4×C15111yescharacteristic
419#103D4×C15111yescharacteristic
420#102—21no—
421#102—21no—
422#102—21no—
423#102D4×C15111yescharacteristic
424#102D4×C15111yescharacteristic
425C22⋊C8—21no—
426C22⋊C8—21no—
427#97—21no—
428C4×C8—21no—
429C4×C8C23×C15111yescharacteristic
430C4×C8C23×C15111yescharacteristic
431C4×C8C23×C15111yescharacteristic
432#41—42no—
433#41—81no—
434C2×Q8—21no—
435C2×Q8—21no—
436C2×Q8—21no—
437C2×Q8—21no—
438C2×Q8—41no—
439C2×Q8—41no—
440C2×Q8—42no—
441C2×Q8—81no—
442C2×Q8C2×D4×C15111yescharacteristic
443C2×Q8C2×D4×C15111yescharacteristic
444C2×D4—41no—
445C2×D4C2×D4×C15111yescharacteristic
446C2×D4C2×D4×C15111yescharacteristic
447C22×C4—21no—
448C22×C4—21no—
449C22×C4—41no—
450C22×C4—41no—
451C22×C4—41no—
452Q16—42no—
453Q16—42no—
454Q16—81no—
455SD16—22no—
456SD16—42no—
457SD16SD16×C15114yescomplemented
458M16—42no—
459C2×C8—21no—
460C2×C8—21no—
461C2×C8—21no—
462C2×C8—21no—
463C2×C8—21no—
464C2×C8—42no—
465C2×C8C2×D4×C15111yescharacteristic
466C2×C8C2×D4×C15111yescharacteristic
467C2×C8C2×D4×C15111yescharacteristic
468C2×C8C2×D4×C15111yescharacteristic
469C4⋊C4—21no—
470C4⋊C4—21no—
471C4⋊C4—21no—
472C4⋊C4—21no—
473C4⋊C4—21no—
474C4⋊C4—21no—
475C4⋊C4—21no—
476C4⋊C4—21no—
477C4⋊C4—21no—
478C4⋊C4—21no—
479C4⋊C4—41no—
480C4⋊C4—41no—
481C4⋊C4—41no—
482C4⋊C4—41no—
483C4⋊C4—41no—
484C4⋊C4—41no—
485C4⋊C4C2×D4×C15111yescharacteristic
486C4⋊C4C2×D4×C15111yescharacteristic
487C4⋊C4C2×D4×C15111yescharacteristic
488C4⋊C4C2×D4×C15111yescharacteristic
489C22⋊C4—21no—
490C22⋊C4—21no—
491C22⋊C4—41no—
492C22⋊C4—41no—
493C22⋊C4—41no—
494C42—21no—
495C42—21no—
496C42—41no—
497C42C24×C15111yescharacteristic
498C23—21no—
499C23—21no—
500Q8—21no—
501Q8—21no—
502Q8—21no—
503Q8—41no—
504Q8—41no—
505Q8—41no—
506Q8—41no—
507Q8—82no—
508Q8—81no—
509Q8—81no—
510Q8—161no—
511Q8C2×SD16×C15112yes—
512D4—21no—
513D4—21no—
514D4—21no—
515D4—82no—
516D4C2×SD16×C15112yes—
517C2×C4—21no—
518C2×C4—21no—
519C2×C4—21no—
520C2×C4—21no—
521C2×C4—21no—
522C2×C4—21no—
523C2×C4—41no—
524C2×C4—41no—
525C2×C4—41no—
526C2×C4—41no—
527C2×C4—41no—
528C2×C4—41no—
529C2×C4—41no—
530C2×C4—41no—
531C2×C4—82no—
532C2×C4—82no—
533C2×C4—161no—
534C2×C4C22×D4×C15111yescharacteristic
535C2×C4C22×D4×C15111yescharacteristic
536C2×C4H(5,𝔽2)×C15111yescharacteristic
537C8—21no—
538C8—21no—
539C8—41no—
540C8—41no—
541C8—41no—
542C8—41no—
543C8—41no—
544C8C2×SD16×C15112yes—
545C8#137×C15112yescomplemented
546C22—22no—
547C22—41no—
548C22—41no—
549C22—41no—
550C22—41no—
551C22—41no—
552C22D42×C15111yescharacteristic
553C4—22no—
554C4—21no—
555C4—41no—
556C4—41no—
557C4—41no—
558C4—41no—
559C4—41no—
560C4—81no—
561C4—81no—
562C4—81no—
563C4—81no—
564C4C22×SD16×C15111yescharacteristic
565C4C2×#137×C15111yescharacteristic
566C4#577×C15111yescharacteristic
567C4#578×C15111yescharacteristic
568C2—42no—
569C2—81no—
570C2#3276×C15111yescharacteristic
571C2D4×SD16×C15111yescharacteristic
572C2#3290×C15111yescharacteristic
subgroupG/H
center, socleC22×C151D42
commutator, Frattini, cosocleC42C24×C151
prime radical#547×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. #3385×C151C2semidirect
2. Q8×SD16×C151C2semidirect
5. #1707×C151C2semidirect
6. #1695×C151C2semidirect
7. #1690×C151C2semidirect
8. #1672×C151C2semidirect
9. #1671×C151C2semidirect
10. #1645×C151C2semidirect
11. #1643×C151C2semidirect
12. #1637×C151C2semidirect
14. #1590×C151C2semidirect
15. C8×SD16×C151C2semidirect
170. SD16×C151SD16semidirect
258. C8×C151#137semidirect
286. #19895C151direct (N × H)
287. C151#19895direct (N × H)
288. #3385C2×C151semidirect
289. Q8×SD16C2×C151semidirect
292. #1707C2×C151semidirect
293. #1695C2×C151semidirect
294. #1690C2×C151semidirect
295. #1672C2×C151semidirect
296. #1671C2×C151semidirect
297. #1645C2×C151semidirect
298. #1643C2×C151semidirect
299. #1637C2×C151semidirect
301. #1590C2×C151semidirect
302. C8×SD16C2×C151semidirect
457. SD16SD16×C151semidirect
545. C8#137×C151semidirect

Maximal subgroups

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

subgroupindex
#3385×C1512
Q8×SD16×C1512
#3335×C1512
#3276×C1512
#1707×C1512
#1695×C1512
#1690×C1512
#1672×C1512
#1671×C1512
#1645×C1512
#1643×C1512
#1637×C1512
#1635×C1512
#1590×C1512
C8×SD16×C1512
#19895151