Finite Group Databasebeta

← C151×#24521 #50329446

Subgroups — C151×#24521 #50329446

Order 38656.

976 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#3095×C151C211yesmaximal, characteristic, complemented
2C2×#450×C151C211yesmaximal, characteristic
3#2924×C151C211yesmaximal, characteristic, complemented
4C2×#418×C151C211yesmaximal, characteristic
5#2063×C151C212yesmaximal, complemented
6#2046×C151C212yesmaximal, complemented
7#1977×C151C212yesmaximal, complemented
8#1931×C151C212yesmaximal, complemented
9#1901×C151C211yesmaximal, characteristic, complemented
10#1855×C151C211yesmaximal, characteristic, complemented
11#1783×C151C211yesmaximal, characteristic
12C23×D4×C151C2211yescharacteristic
13C22×SD16×C151C2212yes—
14C22×M16×C151C2211yescharacteristic
15C2×C22⋊Q8×C151C2211yescharacteristic
16C2×#117×C151C2211yescharacteristic
17#485×C151—21no—
18#485×C151—21no—
19#484×C151—21no—
20#483×C151—21no—
21#450×C151—21no—
22#450×C151—21no—
23#450×C151—22no—
24#433×C151—22no—
25#432×C151—21no—
26#431×C151—21no—
27C2×#108×C151C2212yescomplemented
28#428×C151C2211yescharacteristic, complemented
29#428×C151C2211yescharacteristic, complemented
30#424×C151C2212yescomplemented
31#419×C151C2211yescharacteristic, complemented
32#419×C151C2211yescharacteristic, complemented
33#418×C151—21no—
34#418×C151—21no—
35#418×C151C2212yes—
36#418×C151C2212yes—
37C2×#102×C151—21no—
38C2×#102×C151—21no—
39C2×#102×C151C2212yes—
40C2×#101×C151C2212yescomplemented
41C2×#100×C151C2212yes—
42C2×#100×C151C2212yes—
43#407×C151C2211yescharacteristic
44#407×C151C2211yescharacteristic
45C2×C22⋊C8×C151C2211yescharacteristic
46#405×C151C2212yescomplemented
47#343×C151C2212yescomplemented
48#341×C151C2212yescomplemented
49C25×C151—21no—
50C22×Q8×C151C2311yescharacteristic
51C22×D4×C151—21no—
52C22×D4×C151—24no—
53C22×D4×C151—21no—
54C22×D4×C151—21no—
55C22×D4×C151—21no—
56C22×D4×C151—21no—
57C22×D4×C151—42no—
58C22×D4×C151C2312yes—
59C23×C4×C151C2311yescharacteristic
60C2×SD16×C151—24no—
61C2×SD16×C151—22no—
62C2×SD16×C151—22no—
63C2×SD16×C151—42no—
64C2×M16×C151—21no—
65C2×M16×C151—42no—
66C2×M16×C151C2311yescharacteristic
67C2×M16×C151C2312yes—
68C2×M16×C151C2312yes—
69C2×M16×C151C2311yescharacteristic
70C22×C8×C151—21no—
71C22×C8×C151C2312yes—
72C22⋊Q8×C151—21no—
73C22⋊Q8×C151—21no—
74C22⋊Q8×C151—21no—
75C22⋊Q8×C151—21no—
76#117×C151—21no—
77#117×C151—21no—
78#117×C151D411yescharacteristic
79#117×C151D411yescharacteristic
80#117×C151C2311yescharacteristic
81#117×C151C2311yescharacteristic
82C2×C4⋊C4×C151—21no—
83C2×C4⋊C4×C151D411yescharacteristic
84C2×C4⋊C4×C151D411yescharacteristic
85C2×C4⋊C4×C151C2311yescharacteristic
86C2×C22⋊C4×C151—21no—
87C2×C22⋊C4×C151—21no—
88C2×C42×C151—21no—
89#108×C151—42no—
90#107×C151—21no—
91#107×C151—21no—
92#106×C151—21no—
93#106×C151—21no—
94C4⋊C8×C151—22no—
95C4⋊C8×C151—22no—
96#103×C151—21no—
97#103×C151—21no—
98#103×C151—21no—
99#103×C151—21no—
100#102×C151—22no—
101#102×C151—22no—
102#102×C151—22no—
103#102×C151—22no—
104#102×C151—22no—
105#102×C151—22no—
106#101×C151—42no—
107#100×C151—24no—
108#100×C151—42no—
109C22⋊C8×C151—21no—
110C22⋊C8×C151—21no—
111C22⋊C8×C151—21no—
112C22⋊C8×C151—21no—
113C22⋊C8×C151D411yescharacteristic
114C22⋊C8×C151D411yescharacteristic
115C22⋊C8×C151D412yes—
116#97×C151—22no—
117C4×C8×C151—22no—
118C24×C151—22no—
119C24×C151—44no—
120C24×C151—41no—
121C24×C151—41no—
122C24×C151—82no—
123C24×C151—82no—
124C24×C151#4111yescharacteristic
125C2×Q8×C151—21no—
126C2×Q8×C151—21no—
127C2×Q8×C151—22no—
128C2×Q8×C151—22no—
129C2×D4×C151—24no—
130C2×D4×C151—24no—
131C2×D4×C151—22no—
132C2×D4×C151—22no—
133C2×D4×C151—22no—
134C2×D4×C151—22no—
135C2×D4×C151—22no—
136C2×D4×C151—44no—
137C2×D4×C151—44no—
138C2×D4×C151—44no—
139C2×D4×C151—42no—
140C2×D4×C151—42no—
141C2×D4×C151—41no—
142C2×D4×C151—41no—
143C2×D4×C151#4114yes—
144C22×C4×C151—22no—
145C22×C4×C151—22no—
146C22×C4×C151—21no—
147C22×C4×C151—21no—
148C22×C4×C151—21no—
149C22×C4×C151—21no—
150C22×C4×C151C2×D411yescharacteristic
151C22×C4×C151C2×D411yescharacteristic
152C22×C4×C151C2×D411yescharacteristic
153C22×C4×C151C2×D411yescharacteristic
154C22×C4×C151#4111yescharacteristic
155C22×C4×C151C2411yescharacteristic
156SD16×C151—44no—
157SD16×C151—44no—
158M16×C151—22no—
159M16×C151—22no—
160M16×C151—22no—
161M16×C151—22no—
162M16×C151—22no—
163M16×C151—22no—
164M16×C151—42no—
165C2×C8×C151—22no—
166C2×C8×C151—22no—
167C2×C8×C151—22no—
168C2×C8×C151—21no—
169C2×C8×C151—21no—
170C2×C8×C151—22no—
171C2×C8×C151—42no—
172C2×C8×C151C2×D412yes—
173C2×C8×C151C2×D412yes—
174C4⋊C4×C151—21no—
175C4⋊C4×C151—21no—
176C4⋊C4×C151—21no—
177C4⋊C4×C151—21no—
178C4⋊C4×C151—41no—
179C4⋊C4×C151—41no—
180C4⋊C4×C151C2×D411yescharacteristic
181C4⋊C4×C151C2×D411yescharacteristic
182C4⋊C4×C151C2×D411yescharacteristic
183C4⋊C4×C151C2×D411yescharacteristic
184C22⋊C4×C151—21no—
185C22⋊C4×C151—21no—
186C22⋊C4×C151—21no—
187C22⋊C4×C151—21no—
188C22⋊C4×C151—41no—
189C22⋊C4×C151—41no—
190C42×C151—21no—
191C42×C151—21no—
192C42×C151—21no—
193C42×C151—21no—
194C23×C151—22no—
195C23×C151—22no—
196C23×C151—24no—
197C23×C151—41no—
198C23×C151—44no—
199C23×C151—44no—
200C23×C151—42no—
201C23×C151—42no—
202C23×C151—82no—
203C23×C151—82no—
204C23×C151—82no—
205C23×C151—82no—
206C23×C151—82no—
207C23×C151—816no—
208C23×C151—82no—
209C23×C151#12111yescharacteristic
210C23×C151#12111yescharacteristic
211C23×C151C2×#4111yescharacteristic
212Q8×C151—41no—
213Q8×C151—41no—
214Q8×C151—42no—
215D4×C151—24no—
216D4×C151—24no—
217D4×C151—44no—
218D4×C151—44no—
219D4×C151—42no—
220D4×C151—42no—
221C2×C4×C151—22no—
222C2×C4×C151—21no—
223C2×C4×C151—21no—
224C2×C4×C151—21no—
225C2×C4×C151—21no—
226C2×C4×C151—22no—
227C2×C4×C151—22no—
228C2×C4×C151—21no—
229C2×C4×C151—21no—
230C2×C4×C151—21no—
231C2×C4×C151—21no—
232C2×C4×C151—42no—
233C2×C4×C151—41no—
234C2×C4×C151—41no—
235C2×C4×C151—42no—
236C2×C4×C151—81no—
237C2×C4×C151—81no—
238C2×C4×C151#12111yescharacteristic
239C2×C4×C151#12111yescharacteristic
240C2×C4×C151C22×D411yescharacteristic
241C2×C4×C151C22×D411yescharacteristic
242C2×C4×C151C2×#4112yes—
243C2×C4×C151H(5,𝔽2)12yes—
244C8×C151—22no—
245C8×C151—22no—
246C8×C151—41no—
247C8×C151—42no—
248C8×C151—41no—
249C8×C151—42no—
250C22×C151—21no—
251C22×C151—21no—
252C22×C151—21no—
253C22×C151—21no—
254C22×C151—21no—
255C22×C151—21no—
256C22×C151—21no—
257C22×C151—44no—
258C22×C151—44no—
259C22×C151—84no—
260C22×C151—84no—
261C22×C151—88no—
262C22×C151—88no—
263C22×C151—82no—
264C22×C151—82no—
265C22×C151#47112yes—
266C22×C151C2×#12111yescharacteristic
267C22×C151#55112yes—
268C4×C151—21no—
269C4×C151—21no—
270C4×C151—41no—
271C4×C151—41no—
272C4×C151—41no—
273C4×C151—41no—
274C4×C151—81no—
275C4×C151—81no—
276C4×C151#52511yescharacteristic
277C4×C151#53511yescharacteristic
278C4×C151#54612yes—
279C2×C151—22no—
280C2×C151—22no—
281C2×C151—41no—
282C2×C151—84no—
283C2×C151#241111yescharacteristic
284C2×C151C2×#47111yescharacteristic
285C2×C151#306811yescharacteristic
286#24521C15111yesmaximal, characteristic, direct product factor, Sylow
287C151#2452111yescharacteristic, direct product factor, Sylow
288#3095C2×C15111yescharacteristic, complemented
289C2×#450C2×C15111yescharacteristic
290#2924C2×C15111yescharacteristic, complemented
291C2×#418C2×C15111yescharacteristic
292#2063C2×C15112yescomplemented
293#2046C2×C15112yescomplemented
294#1977C2×C15112yescomplemented
295#1931C2×C15112yescomplemented
296#1901C2×C15111yescharacteristic, complemented
297#1855C2×C15111yescharacteristic, complemented
298#1783C2×C15111yescharacteristic
299C23×D4C22×C15111yescharacteristic
300C22×SD16C22×C15112yes—
301C22×M16C22×C15111yescharacteristic
302C2×C22⋊Q8C22×C15111yescharacteristic
303C2×#117C22×C15111yescharacteristic
304#485—21no—
305#485—21no—
306#484—21no—
307#483—21no—
308#450—21no—
309#450—21no—
310#450—22no—
311#433—22no—
312#432—21no—
313#431—21no—
314C2×#108C22×C15112yescomplemented
315#428C22×C15111yescharacteristic, complemented
316#428C22×C15111yescharacteristic, complemented
317#424C22×C15112yescomplemented
318#419C22×C15111yescharacteristic, complemented
319#419C22×C15111yescharacteristic, complemented
320#418—21no—
321#418—21no—
322#418C22×C15112yes—
323#418C22×C15112yes—
324C2×#102—21no—
325C2×#102—21no—
326C2×#102C22×C15112yes—
327C2×#101C22×C15112yescomplemented
328C2×#100C22×C15112yes—
329C2×#100C22×C15112yes—
330#407C22×C15111yescharacteristic
331#407C22×C15111yescharacteristic
332C2×C22⋊C8C22×C15111yescharacteristic
333#405C22×C15112yescomplemented
334#343C22×C15112yescomplemented
335#341C22×C15112yescomplemented
336C25—21no—
337C22×Q8C23×C15111yescharacteristic
338C22×D4—24no—
339C22×D4—21no—
340C22×D4—21no—
341C22×D4—21no—
342C22×D4—21no—
343C22×D4—21no—
344C22×D4—42no—
345C22×D4C23×C15112yes—
346C23×C4C23×C15111yescharacteristic
347C2×SD16—24no—
348C2×SD16—22no—
349C2×SD16—22no—
350C2×SD16—42no—
351C2×M16—21no—
352C2×M16—42no—
353C2×M16C23×C15112yes—
354C2×M16C23×C15111yescharacteristic
355C2×M16C23×C15112yes—
356C2×M16C23×C15111yescharacteristic
357C22×C8—21no—
358C22×C8C23×C15112yes—
359C22⋊Q8—21no—
360C22⋊Q8—21no—
361C22⋊Q8—21no—
362C22⋊Q8—21no—
363#117—21no—
364#117—21no—
365#117D4×C15111yescharacteristic
366#117D4×C15111yescharacteristic
367#117C23×C15111yescharacteristic
368#117C23×C15111yescharacteristic
369C2×C4⋊C4—21no—
370C2×C4⋊C4D4×C15111yescharacteristic
371C2×C4⋊C4D4×C15111yescharacteristic
372C2×C4⋊C4C23×C15111yescharacteristic
373C2×C22⋊C4—21no—
374C2×C22⋊C4—21no—
375C2×C42—21no—
376#108—42no—
377#107—21no—
378#107—21no—
379#106—21no—
380#106—21no—
381C4⋊C8—22no—
382C4⋊C8—22no—
383#103—21no—
384#103—21no—
385#103—21no—
386#103—21no—
387#102—22no—
388#102—22no—
389#102—22no—
390#102—22no—
391#102—22no—
392#102—22no—
393#101—42no—
394#100—24no—
395#100—42no—
396C22⋊C8—21no—
397C22⋊C8—21no—
398C22⋊C8—21no—
399C22⋊C8—21no—
400C22⋊C8D4×C15111yescharacteristic
401C22⋊C8D4×C15111yescharacteristic
402C22⋊C8D4×C15112yes—
403#97—22no—
404C4×C8—22no—
405C24—22no—
406C24—44no—
407C24—41no—
408C24—41no—
409C24—82no—
410C24—82no—
411C24#41×C15111yescharacteristic
412C2×Q8—21no—
413C2×Q8—21no—
414C2×Q8—22no—
415C2×Q8—22no—
416C2×D4—24no—
417C2×D4—24no—
418C2×D4—22no—
419C2×D4—22no—
420C2×D4—22no—
421C2×D4—22no—
422C2×D4—22no—
423C2×D4—44no—
424C2×D4—44no—
425C2×D4—44no—
426C2×D4—42no—
427C2×D4—42no—
428C2×D4—41no—
429C2×D4—41no—
430C2×D4#41×C15114yes—
431C22×C4—22no—
432C22×C4—22no—
433C22×C4—21no—
434C22×C4—21no—
435C22×C4—21no—
436C22×C4—21no—
437C22×C4C2×D4×C15111yescharacteristic
438C22×C4C2×D4×C15111yescharacteristic
439C22×C4C2×D4×C15111yescharacteristic
440C22×C4C2×D4×C15111yescharacteristic
441C22×C4#41×C15111yescharacteristic
442C22×C4C24×C15111yescharacteristic
443SD16—44no—
444SD16—44no—
445M16—22no—
446M16—22no—
447M16—22no—
448M16—22no—
449M16—22no—
450M16—22no—
451M16—42no—
452C2×C8—22no—
453C2×C8—22no—
454C2×C8—22no—
455C2×C8—21no—
456C2×C8—21no—
457C2×C8—22no—
458C2×C8—42no—
459C2×C8C2×D4×C15112yes—
460C2×C8C2×D4×C15112yes—
461C4⋊C4—21no—
462C4⋊C4—21no—
463C4⋊C4—21no—
464C4⋊C4—21no—
465C4⋊C4—41no—
466C4⋊C4—41no—
467C4⋊C4C2×D4×C15111yescharacteristic
468C4⋊C4C2×D4×C15111yescharacteristic
469C4⋊C4C2×D4×C15111yescharacteristic
470C4⋊C4C2×D4×C15111yescharacteristic
471C22⋊C4—21no—
472C22⋊C4—21no—
473C22⋊C4—21no—
474C22⋊C4—21no—
475C22⋊C4—41no—
476C22⋊C4—41no—
477C42—21no—
478C42—21no—
479C42—21no—
480C42—21no—
481C23—22no—
482C23—22no—
483C23—24no—
484C23—41no—
485C23—44no—
486C23—44no—
487C23—42no—
488C23—42no—
489C23—82no—
490C23—82no—
491C23—82no—
492C23—82no—
493C23—82no—
494C23—816no—
495C23—82no—
496C23#121×C15111yescharacteristic
497C23#121×C15111yescharacteristic
498C23C2×#41×C15111yescharacteristic
499Q8—41no—
500Q8—41no—
501Q8—42no—
502D4—24no—
503D4—24no—
504D4—44no—
505D4—44no—
506D4—42no—
507D4—42no—
508C2×C4—22no—
509C2×C4—21no—
510C2×C4—21no—
511C2×C4—21no—
512C2×C4—21no—
513C2×C4—22no—
514C2×C4—22no—
515C2×C4—21no—
516C2×C4—21no—
517C2×C4—21no—
518C2×C4—21no—
519C2×C4—42no—
520C2×C4—41no—
521C2×C4—41no—
522C2×C4—42no—
523C2×C4—81no—
524C2×C4—81no—
525C2×C4#121×C15111yescharacteristic
526C2×C4#121×C15111yescharacteristic
527C2×C4C22×D4×C15111yescharacteristic
528C2×C4C22×D4×C15111yescharacteristic
529C2×C4C2×#41×C15112yes—
530C2×C4H(5,𝔽2)×C15112yes—
531C8—22no—
532C8—22no—
533C8—41no—
534C8—42no—
535C8—41no—
536C8—42no—
537C22—21no—
538C22—21no—
539C22—21no—
540C22—21no—
541C22—21no—
542C22—21no—
543C22—21no—
544C22—44no—
545C22—44no—
546C22—84no—
547C22—88no—
548C22—84no—
549C22—88no—
550C22—82no—
551C22—82no—
552C22#471×C15112yes—
553C22C2×#121×C15111yescharacteristic
554C22#551×C15112yes—
555C4—21no—
556C4—21no—
557C4—41no—
558C4—41no—
559C4—41no—
560C4—41no—
561C4—81no—
562C4—81no—
563C4#525×C15111yescharacteristic
564C4#535×C15111yescharacteristic
565C4#546×C15112yes—
566C2—22no—
567C2—22no—
568C2—41no—
569C2—84no—
570C2#2411×C15111yescharacteristic
571C2C2×#471×C15111yescharacteristic
572C2#3068×C15111yescharacteristic
subgroupG/H
center, socleC22×C151C2×#121
commutator, Frattini, cosocleC22×C4C24×C151
prime radicalC23×D4×C151C22
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C151 ◁ C23×C4×C151 ◁ G

Complements

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

NH ≅ G/Ntype
1. #3095×C151C2semidirect
3. #2924×C151C2semidirect
5. #2063×C151C2semidirect
6. #2046×C151C2semidirect
7. #1977×C151C2semidirect
8. #1931×C151C2semidirect
9. #1901×C151C2semidirect
10. #1855×C151C2semidirect
27. C2×#108×C151C22semidirect
28. #428×C151C22semidirect
29. #428×C151C22semidirect
30. #424×C151C22semidirect
31. #419×C151C22semidirect
32. #419×C151C22semidirect
40. C2×#101×C151C22semidirect
46. #405×C151C22semidirect
47. #343×C151C22semidirect
48. #341×C151C22semidirect
286. #24521C151direct (N × H)
287. C151#24521direct (N × H)
288. #3095C2×C151semidirect
290. #2924C2×C151semidirect
292. #2063C2×C151semidirect
293. #2046C2×C151semidirect
294. #1977C2×C151semidirect
295. #1931C2×C151semidirect
296. #1901C2×C151semidirect
297. #1855C2×C151semidirect
314. C2×#108C22×C151semidirect
315. #428C22×C151semidirect
316. #428C22×C151semidirect
317. #424C22×C151semidirect
318. #419C22×C151semidirect
319. #419C22×C151semidirect
327. C2×#101C22×C151semidirect
333. #405C22×C151semidirect
334. #343C22×C151semidirect
335. #341C22×C151semidirect

Maximal subgroups

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

subgroupindex
#3095×C1512
C2×#450×C1512
#2924×C1512
C2×#418×C1512
#2063×C1512
#2046×C1512
#1977×C1512
#1931×C1512
#1901×C1512
#1855×C1512
#1783×C1512
#24521151