Finite Group Databasebeta

← C151×#19020 #50323945

Subgroups — C151×#19020 #50323945

Order 38656.

960 conjugacy classes of subgroups.

The subgroup lattice has 598 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#3558×C151C211yesmaximal, characteristic
2#3218×C151C211yesmaximal, characteristic, complemented
3#3141×C151C211yesmaximal, characteristic, complemented
4C2×#489×C151C211yesmaximal, characteristic, complemented
5#1662×C151C214yesmaximal, complemented
6#1659×C151C214yesmaximal, complemented
7#1530×C151C211yesmaximal, characteristic, complemented
8#1527×C151C211yesmaximal, characteristic, complemented
9#1524×C151C211yesmaximal, characteristic, complemented
10#562×C151C2212yes—
11H(3,𝔽4)×C151C2212yes—
12#559×C151—21no—
13#548×C151—21no—
14#546×C151—22no—
15#546×C151—21no—
16D42×C151—21no—
17#542×C151—21no—
18#538×C151—22no—
19#538×C151—21no—
20#535×C151—21no—
21#534×C151—21no—
22#532×C151C2211yescharacteristic
23C2×C4⋊Q8×C151C2211yescharacteristic, complemented
24#529×C151C2211yescharacteristic
25C2×#124×C151C2211yescharacteristic
26#497×C151C2212yescomplemented
27#491×C151C2212yescomplemented
28#489×C151—22no—
29#489×C151C2214yescomplemented
30#489×C151C2214yescomplemented
31#487×C151—21no—
32#486×C151—21no—
33#462×C151—21no—
34#461×C151—21no—
35#451×C151—21no—
36#448×C151—21no—
37#432×C151C2211yescharacteristic, complemented
38#417×C151—22no—
39C2×#103×C151—21no—
40C2×#102×C151—21no—
41C4×M16×C151C2211yescharacteristic, complemented
42C2×#97×C151C2211yescharacteristic, complemented
43#330×C151C2212yescomplemented
44#329×C151C2212yescomplemented
45#329×C151C2214yescomplemented
46#329×C151C2214yescomplemented
47C2×#41×C151—21no—
48C2×#41×C151D412yes—
49C22×Q8×C151—21no—
50C22×Q8×C151D411yescharacteristic
51C22×D4×C151—22no—
52C22×D4×C151—21no—
53C22×D4×C151D411yescharacteristic
54C2×Q16×C151—22no—
55C2×SD16×C151—22no—
56C2×M16×C151—21no—
57C22×C8×C151—21no—
58C4⋊Q8×C151—21no—
59C4⋊Q8×C151—21no—
60C4⋊Q8×C151—21no—
61C4⋊Q8×C151D411yescharacteristic
62C4⋊Q8×C151C2312yes—
63#127×C151—21no—
64#127×C151D411yescharacteristic
65#126×C151—22no—
66#126×C151—21no—
67#125×C151C2311yescharacteristic
68#124×C151—21no—
69#124×C151—21no—
70#124×C151—21no—
71#124×C151—22no—
72#124×C151—22no—
73#124×C151—22no—
74#124×C151D412yes—
75#124×C151C2312yes—
76#124×C151C2312yes—
77#124×C151C2311yescharacteristic
78#123×C151—22no—
79#123×C151—22no—
80#123×C151—21no—
81#123×C151—22no—
82#123×C151—22no—
83C22⋊Q8×C151—21no—
84C22⋊Q8×C151—22no—
85C22⋊Q8×C151—22no—
86C22⋊Q8×C151D411yescharacteristic
87#121×C151—22no—
88#121×C151—22no—
89#121×C151—22no—
90#121×C151—21no—
91#121×C151—22no—
92#121×C151—22no—
93#121×C151—21no—
94#121×C151—21no—
95#121×C151D411yescharacteristic
96#120×C151—22no—
97#120×C151—22no—
98#120×C151—22no—
99#120×C151—22no—
100#120×C151—22no—
101C4×Q8×C151—21no—
102C4×Q8×C151D411yescharacteristic
103C4×D4×C151—22no—
104C4×D4×C151—22no—
105C4×D4×C151—21no—
106C4×D4×C151—21no—
107C4×D4×C151—21no—
108C4×D4×C151—21no—
109C4×D4×C151D411yescharacteristic
110#117×C151—21no—
111C2×C4⋊C4×C151—21no—
112C2×C4⋊C4×C151—21no—
113C2×C22⋊C4×C151—22no—
114C2×C22⋊C4×C151—21no—
115C2×C22⋊C4×C151—21no—
116C2×C42×C151C2311yescharacteristic
117C4⋊C8×C151—21no—
118#103×C151—22no—
119#103×C151—22no—
120#103×C151—24no—
121#103×C151—24no—
122#102×C151—24no—
123#102×C151—24no—
124C22⋊C8×C151—21no—
125#97×C151—21no—
126#97×C151C2312yes—
127#97×C151C2312yes—
128#97×C151C2312yes—
129C4×C8×C151—21no—
130C24×C151—22no—
131C24×C151—21no—
132#41×C151—44no—
133#41×C151—82no—
134C2×Q8×C151—21no—
135C2×Q8×C151—22no—
136C2×Q8×C151—42no—
137C2×Q8×C151—41no—
138C2×Q8×C151—82no—
139C2×Q8×C151C2×D412yes—
140C2×Q8×C151C2×D412yes—
141C2×Q8×C151C2×D411yescharacteristic
142C2×D4×C151—22no—
143C2×D4×C151—21no—
144C2×D4×C151—22no—
145C2×D4×C151—22no—
146C2×D4×C151—22no—
147C2×D4×C151—22no—
148C2×D4×C151—22no—
149C2×D4×C151—21no—
150C2×D4×C151—21no—
151C2×D4×C151—21no—
152C2×D4×C151—42no—
153C2×D4×C151—82no—
154C2×D4×C151—84no—
155C2×D4×C151C2×D412yes—
156C2×D4×C151C2×D412yes—
157C2×D4×C151C2×D411yescharacteristic
158C22×C4×C151—22no—
159C22×C4×C151—22no—
160C22×C4×C151—21no—
161C22×C4×C151—21no—
162C22×C4×C151—22no—
163C22×C4×C151—41no—
164C22×C4×C151C2×D411yescharacteristic
165C22×C4×C151C2×D411yescharacteristic
166C22×C4×C151C2×D411yescharacteristic
167Q16×C151—82no—
168SD16×C151—82no—
169M16×C151—42no—
170C2×C8×C151—22no—
171C2×C8×C151—22no—
172C2×C8×C151—22no—
173C2×C8×C151—42no—
174C4⋊C4×C151—22no—
175C4⋊C4×C151—22no—
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—22no—
183C4⋊C4×C151—22no—
184C4⋊C4×C151—41no—
185C4⋊C4×C151—41no—
186C4⋊C4×C151C2×D411yescharacteristic
187C4⋊C4×C151C2×D411yescharacteristic
188C22⋊C4×C151—22no—
189C22⋊C4×C151—22no—
190C22⋊C4×C151—22no—
191C22⋊C4×C151—22no—
192C22⋊C4×C151—22no—
193C22⋊C4×C151—21no—
194C22⋊C4×C151—22no—
195C22⋊C4×C151—21no—
196C22⋊C4×C151—22no—
197C22⋊C4×C151—21no—
198C22⋊C4×C151—22no—
199C22⋊C4×C151—22no—
200C22⋊C4×C151—21no—
201C22⋊C4×C151—21no—
202C22⋊C4×C151—22no—
203C22⋊C4×C151—22no—
204C42×C151—22no—
205C42×C151—21no—
206C42×C151C2×D411yescharacteristic
207C42×C151C2×D411yescharacteristic
208C42×C151C2×D411yescharacteristic
209C42×C151C2411yescharacteristic
210C23×C151—21no—
211C23×C151—22no—
212C23×C151—22no—
213C23×C151—42no—
214C23×C151—81no—
215C23×C151—81no—
216C23×C151—82no—
217C23×C151—82no—
218C23×C151—82no—
219C23×C151#12011yescharacteristic
220Q8×C151—42no—
221Q8×C151—42no—
222Q8×C151—41no—
223Q8×C151—42no—
224Q8×C151—42no—
225Q8×C151—42no—
226Q8×C151—82no—
227D4×C151—42no—
228D4×C151—41no—
229D4×C151—42no—
230D4×C151—44no—
231D4×C151—42no—
232D4×C151—42no—
233D4×C151—42no—
234D4×C151—81no—
235D4×C151—82no—
236D4×C151—82no—
237D4×C151—82no—
238D4×C151—82no—
239D4×C151—82no—
240C2×C4×C151—22no—
241C2×C4×C151—22no—
242C2×C4×C151—22no—
243C2×C4×C151—21no—
244C2×C4×C151—22no—
245C2×C4×C151—21no—
246C2×C4×C151—21no—
247C2×C4×C151—41no—
248C2×C4×C151—42no—
249C2×C4×C151—42no—
250C2×C4×C151—82no—
251C2×C4×C151—81no—
252C2×C4×C151—82no—
253C2×C4×C151—82no—
254C2×C4×C151—82no—
255C2×C4×C151#12011yescharacteristic
256C2×C4×C151#12011yescharacteristic
257C2×C4×C151#12011yescharacteristic
258C2×C4×C151C22×D411yescharacteristic
259C2×C4×C151C22×D411yescharacteristic
260C2×C4×C151C22×D411yescharacteristic
261C8×C151—42no—
262C8×C151—42no—
263C8×C151—42no—
264C22×C151—21no—
265C22×C151—21no—
266C22×C151—41no—
267C22×C151—42no—
268C22×C151—42no—
269C22×C151—42no—
270C22×C151—42no—
271C22×C151—41no—
272C22×C151—41no—
273C22×C151—42no—
274C22×C151—42no—
275C22×C151—162no—
276C22×C151—164no—
277C22×C151#45512yes—
278C22×C151C2×#12011yescharacteristic
279C4×C151—21no—
280C4×C151—21no—
281C4×C151—21no—
282C4×C151—21no—
283C4×C151—21no—
284C4×C151—41no—
285C4×C151—41no—
286C4×C151—42no—
287C4×C151—42no—
288C4×C151—41no—
289C4×C151—82no—
290C4×C151#45512yes—
291C2×C151—22no—
292C2×C151—82no—
293C2×C151—81no—
294C2×C151—82no—
295C2×C151C2×#45511yescharacteristic
296C2×C151C2×#45511yescharacteristic
297C2×C151#302111yescharacteristic
298#19020C15111yesmaximal, characteristic, direct product factor, Sylow
299C151#1902011yescharacteristic, direct product factor, Sylow
300#3558C2×C15111yescharacteristic
301#3218C2×C15111yescharacteristic, complemented
302#3141C2×C15111yescharacteristic, complemented
303C2×#489C2×C15111yescharacteristic, complemented
304#1662C2×C15114yescomplemented
305#1659C2×C15114yescomplemented
306#1530C2×C15111yescharacteristic, complemented
307#1527C2×C15111yescharacteristic, complemented
308#1524C2×C15111yescharacteristic, complemented
309#562C22×C15112yes—
310H(3,𝔽4)C22×C15112yes—
311#559—21no—
312#548—21no—
313#546—22no—
314#546—21no—
315D42—21no—
316#542—21no—
317#538—22no—
318#538—21no—
319#535—21no—
320#534—21no—
321#532C22×C15111yescharacteristic
322C2×C4⋊Q8C22×C15111yescharacteristic, complemented
323#529C22×C15111yescharacteristic
324C2×#124C22×C15111yescharacteristic
325#497C22×C15112yescomplemented
326#491C22×C15112yescomplemented
327#489—22no—
328#489C22×C15114yescomplemented
329#489C22×C15114yescomplemented
330#487—21no—
331#486—21no—
332#462—21no—
333#461—21no—
334#451—21no—
335#448—21no—
336#432C22×C15111yescharacteristic, complemented
337#417—22no—
338C2×#103—21no—
339C2×#102—21no—
340C4×M16C22×C15111yescharacteristic, complemented
341C2×#97C22×C15111yescharacteristic, complemented
342#330C22×C15112yescomplemented
343#329C22×C15112yescomplemented
344#329C22×C15114yescomplemented
345#329C22×C15114yescomplemented
346C2×#41—21no—
347C2×#41D4×C15112yes—
348C22×Q8—21no—
349C22×Q8D4×C15111yescharacteristic
350C22×D4—22no—
351C22×D4—21no—
352C22×D4D4×C15111yescharacteristic
353C2×Q16—22no—
354C2×SD16—22no—
355C2×M16—21no—
356C22×C8—21no—
357C4⋊Q8—21no—
358C4⋊Q8—21no—
359C4⋊Q8—21no—
360C4⋊Q8D4×C15111yescharacteristic
361C4⋊Q8C23×C15112yes—
362#127—21no—
363#127D4×C15111yescharacteristic
364#126—22no—
365#126—21no—
366#125C23×C15111yescharacteristic
367#124—21no—
368#124—22no—
369#124—22no—
370#124—22no—
371#124—21no—
372#124—21no—
373#124D4×C15112yes—
374#124C23×C15112yes—
375#124C23×C15111yescharacteristic
376#124C23×C15112yes—
377#123—22no—
378#123—22no—
379#123—21no—
380#123—22no—
381#123—22no—
382C22⋊Q8—21no—
383C22⋊Q8—22no—
384C22⋊Q8—22no—
385C22⋊Q8D4×C15111yescharacteristic
386#121—22no—
387#121—22no—
388#121—22no—
389#121—21no—
390#121—22no—
391#121—22no—
392#121—21no—
393#121—21no—
394#121D4×C15111yescharacteristic
395#120—22no—
396#120—22no—
397#120—22no—
398#120—22no—
399#120—22no—
400C4×Q8—21no—
401C4×Q8D4×C15111yescharacteristic
402C4×D4—22no—
403C4×D4—22no—
404C4×D4—21no—
405C4×D4—21no—
406C4×D4—21no—
407C4×D4—21no—
408C4×D4D4×C15111yescharacteristic
409#117—21no—
410C2×C4⋊C4—21no—
411C2×C4⋊C4—21no—
412C2×C22⋊C4—22no—
413C2×C22⋊C4—21no—
414C2×C22⋊C4—21no—
415C2×C42C23×C15111yescharacteristic
416C4⋊C8—21no—
417#103—24no—
418#103—24no—
419#103—22no—
420#103—22no—
421#102—24no—
422#102—24no—
423C22⋊C8—21no—
424#97—21no—
425#97C23×C15112yes—
426#97C23×C15112yes—
427#97C23×C15112yes—
428C4×C8—21no—
429C24—22no—
430C24—21no—
431#41—44no—
432#41—82no—
433C2×Q8—21no—
434C2×Q8—22no—
435C2×Q8—42no—
436C2×Q8—41no—
437C2×Q8—82no—
438C2×Q8C2×D4×C15112yes—
439C2×Q8C2×D4×C15112yes—
440C2×Q8C2×D4×C15111yescharacteristic
441C2×D4—22no—
442C2×D4—21no—
443C2×D4—22no—
444C2×D4—22no—
445C2×D4—22no—
446C2×D4—22no—
447C2×D4—22no—
448C2×D4—21no—
449C2×D4—21no—
450C2×D4—21no—
451C2×D4—42no—
452C2×D4—82no—
453C2×D4—84no—
454C2×D4C2×D4×C15112yes—
455C2×D4C2×D4×C15112yes—
456C2×D4C2×D4×C15111yescharacteristic
457C22×C4—22no—
458C22×C4—22no—
459C22×C4—21no—
460C22×C4—21no—
461C22×C4—22no—
462C22×C4—41no—
463C22×C4C2×D4×C15111yescharacteristic
464C22×C4C2×D4×C15111yescharacteristic
465C22×C4C2×D4×C15111yescharacteristic
466Q16—82no—
467SD16—82no—
468M16—42no—
469C2×C8—22no—
470C2×C8—22no—
471C2×C8—22no—
472C2×C8—42no—
473C4⋊C4—22no—
474C4⋊C4—22no—
475C4⋊C4—21no—
476C4⋊C4—21no—
477C4⋊C4—21no—
478C4⋊C4—21no—
479C4⋊C4—21no—
480C4⋊C4—21no—
481C4⋊C4—22no—
482C4⋊C4—22no—
483C4⋊C4—41no—
484C4⋊C4—41no—
485C4⋊C4C2×D4×C15111yescharacteristic
486C4⋊C4C2×D4×C15111yescharacteristic
487C22⋊C4—22no—
488C22⋊C4—22no—
489C22⋊C4—22no—
490C22⋊C4—22no—
491C22⋊C4—22no—
492C22⋊C4—21no—
493C22⋊C4—22no—
494C22⋊C4—21no—
495C22⋊C4—22no—
496C22⋊C4—21no—
497C22⋊C4—22no—
498C22⋊C4—22no—
499C22⋊C4—21no—
500C22⋊C4—21no—
501C22⋊C4—22no—
502C22⋊C4—22no—
503C42—22no—
504C42—21no—
505C42C2×D4×C15111yescharacteristic
506C42C2×D4×C15111yescharacteristic
507C42C2×D4×C15111yescharacteristic
508C42C24×C15111yescharacteristic
509C23—21no—
510C23—22no—
511C23—22no—
512C23—42no—
513C23—81no—
514C23—81no—
515C23—82no—
516C23—82no—
517C23—82no—
518C23#120×C15111yescharacteristic
519Q8—41no—
520Q8—42no—
521Q8—42no—
522Q8—42no—
523Q8—42no—
524Q8—42no—
525Q8—82no—
526D4—41no—
527D4—42no—
528D4—42no—
529D4—42no—
530D4—44no—
531D4—42no—
532D4—42no—
533D4—81no—
534D4—82no—
535D4—82no—
536D4—82no—
537D4—82no—
538D4—82no—
539C2×C4—22no—
540C2×C4—22no—
541C2×C4—21no—
542C2×C4—22no—
543C2×C4—22no—
544C2×C4—21no—
545C2×C4—21no—
546C2×C4—41no—
547C2×C4—42no—
548C2×C4—42no—
549C2×C4—82no—
550C2×C4—81no—
551C2×C4—82no—
552C2×C4—82no—
553C2×C4—82no—
554C2×C4#120×C15111yescharacteristic
555C2×C4#120×C15111yescharacteristic
556C2×C4#120×C15111yescharacteristic
557C2×C4C22×D4×C15111yescharacteristic
558C2×C4C22×D4×C15111yescharacteristic
559C2×C4C22×D4×C15111yescharacteristic
560C8—42no—
561C8—42no—
562C8—42no—
563C22—21no—
564C22—21no—
565C22—41no—
566C22—42no—
567C22—42no—
568C22—42no—
569C22—42no—
570C22—41no—
571C22—41no—
572C22—42no—
573C22—42no—
574C22—162no—
575C22—164no—
576C22#455×C15112yes—
577C22C2×#120×C15111yescharacteristic
578C4—21no—
579C4—21no—
580C4—21no—
581C4—21no—
582C4—21no—
583C4—41no—
584C4—41no—
585C4—42no—
586C4—42no—
587C4—41no—
588C4—82no—
589C4#455×C15112yes—
590C2—22no—
591C2—81no—
592C2—82no—
593C2—82no—
594C2C2×#455×C15111yescharacteristic
595C2C2×#455×C15111yescharacteristic
596C2#3021×C15111yescharacteristic
subgroupG/H
center, socleC22×C151C2×#120
commutator, Frattini, cosocleC42C24×C151
prime radical#3558×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
2. #3218×C151C2semidirect
3. #3141×C151C2semidirect
4. C2×#489×C151C2semidirect
5. #1662×C151C2semidirect
6. #1659×C151C2semidirect
7. #1530×C151C2semidirect
8. #1527×C151C2semidirect
9. #1524×C151C2semidirect
23. C2×C4⋊Q8×C151C22semidirect
26. #497×C151C22semidirect
27. #491×C151C22semidirect
29. #489×C151C22semidirect
30. #489×C151C22semidirect
37. #432×C151C22semidirect
41. C4×M16×C151C22semidirect
42. C2×#97×C151C22semidirect
43. #330×C151C22semidirect
44. #329×C151C22semidirect
45. #329×C151C22semidirect
46. #329×C151C22semidirect
298. #19020C151direct (N × H)
299. C151#19020direct (N × H)
301. #3218C2×C151semidirect
302. #3141C2×C151semidirect
303. C2×#489C2×C151semidirect
304. #1662C2×C151semidirect
305. #1659C2×C151semidirect
306. #1530C2×C151semidirect
307. #1527C2×C151semidirect
308. #1524C2×C151semidirect
322. C2×C4⋊Q8C22×C151semidirect
325. #497C22×C151semidirect
326. #491C22×C151semidirect
328. #489C22×C151semidirect
329. #489C22×C151semidirect
336. #432C22×C151semidirect
340. C4×M16C22×C151semidirect
341. C2×#97C22×C151semidirect
342. #330C22×C151semidirect
343. #329C22×C151semidirect
344. #329C22×C151semidirect
345. #329C22×C151semidirect

Maximal subgroups

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

subgroupindex
#3558×C1512
#3218×C1512
#3141×C1512
C2×#489×C1512
#1662×C1512
#1659×C1512
#1530×C1512
#1527×C1512
#1524×C1512
#19020151