Finite Group Databasebeta

← C151×#19861 #50324786

Subgroups — C151×#19861 #50324786

Order 38656.

596 conjugacy classes of subgroups.

The subgroup lattice has 572 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#3380×C151C211yesmaximal, characteristic, complemented
2#3357×C151C211yesmaximal, characteristic, complemented
3#3335×C151C211yesmaximal, characteristic, complemented
4#3303×C151C211yesmaximal, characteristic
5#1723×C151C211yesmaximal, characteristic, complemented
6#1691×C151C211yesmaximal, characteristic, complemented
7#1684×C151C211yesmaximal, characteristic, complemented
8#1675×C151C211yesmaximal, characteristic, complemented
9#1675×C151C211yesmaximal, characteristic, complemented
10#1643×C151C211yesmaximal, characteristic, complemented
11#1635×C151C211yesmaximal, characteristic, complemented
12#1634×C151C211yesmaximal, characteristic, complemented
13#1632×C151C211yesmaximal, characteristic, complemented
14#1581×C151C211yesmaximal, characteristic, complemented
15SD16⋊C8×C151C211yesmaximal, characteristic, complemented
16#555×C151C2211yescharacteristic
17#554×C151C2211yescharacteristic
18#554×C151C2211yescharacteristic
19#547×C151C2211yescharacteristic
20#500×C151C2211yescharacteristic
21#500×C151C2211yescharacteristic
22#499×C151—21no—
23#498×C151C2211yescharacteristic
24#494×C151C2211yescharacteristic
25#487×C151C2211yescharacteristic
26#487×C151C2211yescharacteristic
27#485×C151—21no—
28#485×C151—21no—
29#483×C151—21no—
30#481×C151—21no—
31#480×C151—21no—
32#478×C151—21no—
33#478×C151—21no—
34#477×C151C2211yescharacteristic
35#476×C151C2211yescharacteristic
36#476×C151C2211yescharacteristic
37#476×C151C2211yescharacteristic
38#476×C151C2211yescharacteristic
39#476×C151C2211yescharacteristic
40#475×C151C2211yescharacteristic
41#468×C151—21no—
42#465×C151—21no—
43#465×C151—21no—
44#461×C151C2211yescharacteristic
45#449×C151—21no—
46C8×Q8×C151C2211yescharacteristic
47C4×SD16×C151C2211yescharacteristic
48C4×D8×C151—21no—
49C4×D8×C151C2211yescharacteristic
50#436×C151C2211yescharacteristic
51C8×D4×C151C2211yescharacteristic
52C8×D4×C151C2211yescharacteristic
53#428×C151—21no—
54C2×#106×C151—21no—
55#416×C151—21no—
56#335×C151C2211yescharacteristic
57#335×C151C2211yescharacteristic
58#333×C151C2211yescharacteristic
59#333×C151C2211yescharacteristic
60#333×C151C2211yescharacteristic
61#332×C151C2211yescharacteristic
62Q8⋊C8×C151C2211yescharacteristic
63D4⋊C8×C151C2211yescharacteristic
64D4⋊C8×C151C2211yescharacteristic
65D4⋊C8×C151C2211yescharacteristic
66#322×C151C2211yescharacteristic
67C2×#41×C151—21no—
68C2×Q16×C151—41no—
69C2×SD16×C151—21no—
70C2×SD16×C151D411yescharacteristic
71C2×D8×C151D411yescharacteristic
72C2×M16×C151—21no—
73C22×C8×C151—21no—
74C22×C8×C151—21no—
75C4⋊Q8×C151C2311yescharacteristic
76C4⋊Q8×C151C2311yescharacteristic
77C4⋊Q8×C151C2311yescharacteristic
78C4⋊Q8×C151C2311yescharacteristic
79#125×C151—21no—
80#125×C151—21no—
81#124×C151—41no—
82#123×C151—41no—
83C22⋊Q8×C151—21no—
84C22⋊Q8×C151—21no—
85C22⋊Q8×C151—21no—
86C22⋊Q8×C151—41no—
87C22⋊Q8×C151—41no—
88#121×C151—21no—
89#121×C151—21no—
90#121×C151—21no—
91C4×Q8×C151C2311yescharacteristic
92C4×D4×C151—21no—
93C4×D4×C151—21no—
94C4×D4×C151C2311yescharacteristic
95C4×D4×C151C2311yescharacteristic
96C4×D4×C151C2311yescharacteristic
97#117×C151—21no—
98#117×C151—21no—
99C2×C4⋊C4×C151—21no—
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×C151D411yescharacteristic
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
117C4⋊C8×C151—21no—
118C4⋊C8×C151C2311yescharacteristic
119C4⋊C8×C151C2311yescharacteristic
120C4⋊C8×C151C2311yescharacteristic
121C4⋊C8×C151C2311yescharacteristic
122#103×C151—21no—
123#103×C151—21no—
124#103×C151—21no—
125#103×C151—21no—
126#103×C151—21no—
127#103×C151—41no—
128#103×C151D411yescharacteristic
129#102×C151—21no—
130#102×C151—21no—
131#102×C151—21no—
132#102×C151—21no—
133#102×C151—21no—
134#102×C151D411yescharacteristic
135#102×C151D411yescharacteristic
136#102×C151D411yescharacteristic
137C22⋊C8×C151—21no—
138C22⋊C8×C151—21no—
139C22⋊C8×C151—21no—
140C4×C8×C151—21no—
141C4×C8×C151C2311yescharacteristic
142C4×C8×C151C2311yescharacteristic
143C4×C8×C151C2311yescharacteristic
144#41×C151—42no—
145#41×C151—81no—
146C2×Q8×C151—21no—
147C2×Q8×C151—21no—
148C2×Q8×C151—21no—
149C2×Q8×C151—21no—
150C2×Q8×C151C2×D411yescharacteristic
151C2×D4×C151—41no—
152C2×D4×C151—41no—
153C2×D4×C151C2×D411yescharacteristic
154C2×D4×C151C2×D411yescharacteristic
155C2×D4×C151C2×D411yescharacteristic
156C22×C4×C151—21no—
157C22×C4×C151—21no—
158C22×C4×C151—21no—
159C22×C4×C151—41no—
160C22×C4×C151—41no—
161C22×C4×C151—41no—
162Q16×C151—82no—
163SD16×C151—22no—
164SD16×C151—81no—
165D8×C151—22no—
166M16×C151—42no—
167C2×C8×C151—21no—
168C2×C8×C151—21no—
169C2×C8×C151—21no—
170C2×C8×C151—21no—
171C2×C8×C151—21no—
172C2×C8×C151—42no—
173C2×C8×C151—81no—
174C2×C8×C151C2×D411yescharacteristic
175C2×C8×C151C2×D411yescharacteristic
176C2×C8×C151C2×D411yescharacteristic
177C2×C8×C151C2×D411yescharacteristic
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—41no—
188C4⋊C4×C151—41no—
189C4⋊C4×C151—41no—
190C4⋊C4×C151—41no—
191C4⋊C4×C151—41no—
192C4⋊C4×C151C2×D411yescharacteristic
193C4⋊C4×C151C2×D411yescharacteristic
194C4⋊C4×C151C2×D411yescharacteristic
195C4⋊C4×C151C2×D411yescharacteristic
196C22⋊C4×C151—21no—
197C22⋊C4×C151—21no—
198C22⋊C4×C151—21no—
199C22⋊C4×C151—41no—
200C22⋊C4×C151—41no—
201C22⋊C4×C151—41no—
202C22⋊C4×C151—41no—
203C22⋊C4×C151—41no—
204C42×C151—21no—
205C42×C151—41no—
206C42×C151C2411yescharacteristic
207C23×C151—21no—
208C23×C151—21no—
209C23×C151—21no—
210Q8×C151—21no—
211Q8×C151—21no—
212Q8×C151—41no—
213Q8×C151—41no—
214Q8×C151—81no—
215Q8×C151—81no—
216Q8×C151—81no—
217D4×C151—21no—
218D4×C151—21no—
219D4×C151—21no—
220D4×C151—21no—
221D4×C151—21no—
222D4×C151—82no—
223D4×C151—161no—
224D4×C151#13712yes—
225C2×C4×C151—21no—
226C2×C4×C151—21no—
227C2×C4×C151—21no—
228C2×C4×C151—21no—
229C2×C4×C151—21no—
230C2×C4×C151—41no—
231C2×C4×C151—41no—
232C2×C4×C151—41no—
233C2×C4×C151—41no—
234C2×C4×C151—41no—
235C2×C4×C151—41no—
236C2×C4×C151—41no—
237C2×C4×C151—41no—
238C2×C4×C151—41no—
239C2×C4×C151—41no—
240C2×C4×C151—82no—
241C2×C4×C151—161no—
242C2×C4×C151—161no—
243C2×C4×C151C22×D411yescharacteristic
244C2×C4×C151C22×D411yescharacteristic
245C2×C4×C151H(5,𝔽2)11yescharacteristic
246C8×C151—21no—
247C8×C151—21no—
248C8×C151—21no—
249C8×C151—41no—
250C8×C151—41no—
251C8×C151—41no—
252C8×C151—41no—
253C8×C151—41no—
254C8×C151#13512yes—
255C22×C151—22no—
256C22×C151—41no—
257C22×C151—41no—
258C22×C151—41no—
259C22×C151—41no—
260C22×C151—41no—
261C22×C151—41no—
262C22×C151—41no—
263C22×C151—41no—
264C22×C151D4211yescharacteristic
265C4×C151—21no—
266C4×C151—41no—
267C4×C151—41no—
268C4×C151—41no—
269C4×C151—41no—
270C4×C151—41no—
271C4×C151—81no—
272C4×C151—81no—
273C4×C151—81no—
274C4×C151—81no—
275C4×C151C2×#13511yescharacteristic
276C4×C151C2×#13711yescharacteristic
277C4×C151#57711yescharacteristic
278C4×C151#57811yescharacteristic
279C2×C151—42no—
280C2×C151—81no—
281C2×C151—81no—
282C2×C151#326611yescharacteristic
283C2×C151#328311yescharacteristic
284C2×C151#328811yescharacteristic
285#19861C15111yesmaximal, characteristic, direct product factor, Sylow
286C151#1986111yescharacteristic, direct product factor, Sylow
287#3380C2×C15111yescharacteristic, complemented
288#3357C2×C15111yescharacteristic, complemented
289#3335C2×C15111yescharacteristic, complemented
290#3303C2×C15111yescharacteristic
291#1723C2×C15111yescharacteristic, complemented
292#1691C2×C15111yescharacteristic, complemented
293#1684C2×C15111yescharacteristic, complemented
294#1675C2×C15111yescharacteristic, complemented
295#1675C2×C15111yescharacteristic, complemented
296#1643C2×C15111yescharacteristic, complemented
297#1635C2×C15111yescharacteristic, complemented
298#1634C2×C15111yescharacteristic, complemented
299#1632C2×C15111yescharacteristic, complemented
300#1581C2×C15111yescharacteristic, complemented
301SD16⋊C8C2×C15111yescharacteristic, complemented
302#555C22×C15111yescharacteristic
303#554C22×C15111yescharacteristic
304#554C22×C15111yescharacteristic
305#547C22×C15111yescharacteristic
306#500C22×C15111yescharacteristic
307#500C22×C15111yescharacteristic
308#499—21no—
309#498C22×C15111yescharacteristic
310#494C22×C15111yescharacteristic
311#487C22×C15111yescharacteristic
312#487C22×C15111yescharacteristic
313#485—21no—
314#485—21no—
315#483—21no—
316#481—21no—
317#480—21no—
318#478—21no—
319#478—21no—
320#477C22×C15111yescharacteristic
321#476C22×C15111yescharacteristic
322#476C22×C15111yescharacteristic
323#476C22×C15111yescharacteristic
324#476C22×C15111yescharacteristic
325#476C22×C15111yescharacteristic
326#475C22×C15111yescharacteristic
327#468—21no—
328#465—21no—
329#465—21no—
330#461C22×C15111yescharacteristic
331#449—21no—
332C8×Q8C22×C15111yescharacteristic
333C4×SD16C22×C15111yescharacteristic
334C4×D8—21no—
335C4×D8C22×C15111yescharacteristic
336#436C22×C15111yescharacteristic
337C8×D4C22×C15111yescharacteristic
338C8×D4C22×C15111yescharacteristic
339#428—21no—
340C2×#106—21no—
341#416—21no—
342#335C22×C15111yescharacteristic
343#335C22×C15111yescharacteristic
344#333C22×C15111yescharacteristic
345#333C22×C15111yescharacteristic
346#333C22×C15111yescharacteristic
347#332C22×C15111yescharacteristic
348Q8⋊C8C22×C15111yescharacteristic
349D4⋊C8C22×C15111yescharacteristic
350D4⋊C8C22×C15111yescharacteristic
351D4⋊C8C22×C15111yescharacteristic
352#322C22×C15111yescharacteristic
353C2×#41—21no—
354C2×Q16—41no—
355C2×SD16—21no—
356C2×SD16D4×C15111yescharacteristic
357C2×D8D4×C15111yescharacteristic
358C2×M16—21no—
359C22×C8—21no—
360C22×C8—21no—
361C4⋊Q8C23×C15111yescharacteristic
362C4⋊Q8C23×C15111yescharacteristic
363C4⋊Q8C23×C15111yescharacteristic
364C4⋊Q8C23×C15111yescharacteristic
365#125—21no—
366#125—21no—
367#124—41no—
368#123—41no—
369C22⋊Q8—21no—
370C22⋊Q8—21no—
371C22⋊Q8—21no—
372C22⋊Q8—41no—
373C22⋊Q8—41no—
374#121—21no—
375#121—21no—
376#121—21no—
377C4×Q8C23×C15111yescharacteristic
378C4×D4—21no—
379C4×D4—21no—
380C4×D4C23×C15111yescharacteristic
381C4×D4C23×C15111yescharacteristic
382C4×D4C23×C15111yescharacteristic
383#117—21no—
384#117—21no—
385C2×C4⋊C4—21no—
386C2×C4⋊C4—21no—
387C2×C4⋊C4—21no—
388#107—21no—
389#107—21no—
390#107—21no—
391#107—21no—
392#107—21no—
393#107D4×C15111yescharacteristic
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#106D4×C15111yescharacteristic
403C4⋊C8—21no—
404C4⋊C8C23×C15111yescharacteristic
405C4⋊C8C23×C15111yescharacteristic
406C4⋊C8C23×C15111yescharacteristic
407C4⋊C8C23×C15111yescharacteristic
408#103—21no—
409#103—21no—
410#103—21no—
411#103—21no—
412#103—21no—
413#103—41no—
414#103D4×C15111yescharacteristic
415#102—21no—
416#102—21no—
417#102—21no—
418#102—21no—
419#102—21no—
420#102D4×C15111yescharacteristic
421#102D4×C15111yescharacteristic
422#102D4×C15111yescharacteristic
423C22⋊C8—21no—
424C22⋊C8—21no—
425C22⋊C8—21no—
426C4×C8—21no—
427C4×C8C23×C15111yescharacteristic
428C4×C8C23×C15111yescharacteristic
429C4×C8C23×C15111yescharacteristic
430#41—42no—
431#41—81no—
432C2×Q8—21no—
433C2×Q8—21no—
434C2×Q8—21no—
435C2×Q8—21no—
436C2×Q8C2×D4×C15111yescharacteristic
437C2×D4—41no—
438C2×D4—41no—
439C2×D4C2×D4×C15111yescharacteristic
440C2×D4C2×D4×C15111yescharacteristic
441C2×D4C2×D4×C15111yescharacteristic
442C22×C4—21no—
443C22×C4—21no—
444C22×C4—21no—
445C22×C4—41no—
446C22×C4—41no—
447C22×C4—41no—
448Q16—82no—
449SD16—22no—
450SD16—81no—
451D8—22no—
452M16—42no—
453C2×C8—21no—
454C2×C8—21no—
455C2×C8—21no—
456C2×C8—21no—
457C2×C8—21no—
458C2×C8—42no—
459C2×C8—81no—
460C2×C8C2×D4×C15111yescharacteristic
461C2×C8C2×D4×C15111yescharacteristic
462C2×C8C2×D4×C15111yescharacteristic
463C2×C8C2×D4×C15111yescharacteristic
464C4⋊C4—21no—
465C4⋊C4—21no—
466C4⋊C4—21no—
467C4⋊C4—21no—
468C4⋊C4—21no—
469C4⋊C4—21no—
470C4⋊C4—21no—
471C4⋊C4—21no—
472C4⋊C4—21no—
473C4⋊C4—41no—
474C4⋊C4—41no—
475C4⋊C4—41no—
476C4⋊C4—41no—
477C4⋊C4—41no—
478C4⋊C4C2×D4×C15111yescharacteristic
479C4⋊C4C2×D4×C15111yescharacteristic
480C4⋊C4C2×D4×C15111yescharacteristic
481C4⋊C4C2×D4×C15111yescharacteristic
482C22⋊C4—21no—
483C22⋊C4—21no—
484C22⋊C4—21no—
485C22⋊C4—41no—
486C22⋊C4—41no—
487C22⋊C4—41no—
488C22⋊C4—41no—
489C22⋊C4—41no—
490C42—21no—
491C42—41no—
492C42C24×C15111yescharacteristic
493C23—21no—
494C23—21no—
495C23—21no—
496Q8—21no—
497Q8—21no—
498Q8—41no—
499Q8—41no—
500Q8—81no—
501Q8—81no—
502Q8—81no—
503D4—21no—
504D4—21no—
505D4—21no—
506D4—21no—
507D4—21no—
508D4—82no—
509D4—161no—
510D4#137×C15112yes—
511C2×C4—21no—
512C2×C4—21no—
513C2×C4—21no—
514C2×C4—21no—
515C2×C4—21no—
516C2×C4—41no—
517C2×C4—41no—
518C2×C4—41no—
519C2×C4—41no—
520C2×C4—41no—
521C2×C4—41no—
522C2×C4—41no—
523C2×C4—41no—
524C2×C4—41no—
525C2×C4—41no—
526C2×C4—82no—
527C2×C4—161no—
528C2×C4—161no—
529C2×C4C22×D4×C15111yescharacteristic
530C2×C4C22×D4×C15111yescharacteristic
531C2×C4H(5,𝔽2)×C15111yescharacteristic
532C8—21no—
533C8—21no—
534C8—21no—
535C8—41no—
536C8—41no—
537C8—41no—
538C8—41no—
539C8—41no—
540C8#135×C15112yes—
541C22—22no—
542C22—41no—
543C22—41no—
544C22—41no—
545C22—41no—
546C22—41no—
547C22—41no—
548C22—41no—
549C22—41no—
550C22D42×C15111yescharacteristic
551C4—21no—
552C4—41no—
553C4—41no—
554C4—41no—
555C4—41no—
556C4—41no—
557C4—81no—
558C4—81no—
559C4—81no—
560C4—81no—
561C4C2×#135×C15111yescharacteristic
562C4C2×#137×C15111yescharacteristic
563C4#577×C15111yescharacteristic
564C4#578×C15111yescharacteristic
565C2—42no—
566C2—81no—
567C2—81no—
568C2#3266×C15111yescharacteristic
569C2#3283×C15111yescharacteristic
570C2#3288×C15111yescharacteristic
subgroupG/H
center, socleC22×C151D42
commutator, Frattini, cosocleC42C24×C151
prime radical#3303×C151C2
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. #3380×C151C2semidirect
2. #3357×C151C2semidirect
3. #3335×C151C2semidirect
5. #1723×C151C2semidirect
6. #1691×C151C2semidirect
7. #1684×C151C2semidirect
8. #1675×C151C2semidirect
9. #1675×C151C2semidirect
10. #1643×C151C2semidirect
11. #1635×C151C2semidirect
12. #1634×C151C2semidirect
13. #1632×C151C2semidirect
14. #1581×C151C2semidirect
15. SD16⋊C8×C151C2semidirect
285. #19861C151direct (N × H)
286. C151#19861direct (N × H)
287. #3380C2×C151semidirect
288. #3357C2×C151semidirect
289. #3335C2×C151semidirect
291. #1723C2×C151semidirect
292. #1691C2×C151semidirect
293. #1684C2×C151semidirect
294. #1675C2×C151semidirect
295. #1675C2×C151semidirect
296. #1643C2×C151semidirect
297. #1635C2×C151semidirect
298. #1634C2×C151semidirect
299. #1632C2×C151semidirect
300. #1581C2×C151semidirect
301. SD16⋊C8C2×C151semidirect

Maximal subgroups

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

subgroupindex
#3380×C1512
#3357×C1512
#3335×C1512
#3303×C1512
#1723×C1512
#1691×C1512
#1684×C1512
#1675×C1512
#1643×C1512
#1635×C1512
#1634×C1512
#1632×C1512
#1581×C1512
SD16⋊C8×C1512
#19861151