Finite Group Databasebeta

← C151×#23984 #50328909

Subgroups — C151×#23984 #50328909

Order 38656.

2810 conjugacy classes of subgroups.

The subgroup lattice has 560 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#3490×C151C211yesmaximal, characteristic, complemented
2#2846×C151C212yesmaximal, complemented
3C2×#379×C151C211yesmaximal, characteristic, complemented
4#2029×C151C212yesmaximal, complemented
5#2021×C151C212yesmaximal, complemented
6#1898×C151C212yesmaximal, complemented
7#1889×C151C214yesmaximal, complemented
8#1819×C151C211yesmaximal, characteristic, complemented
9C26×C151C2211yescharacteristic
10#551×C151—24no—
11#546×C151—24no—
12#543×C151C2211yescharacteristic, complemented
13#538×C151—22no—
14#534×C151C2211yescharacteristic, complemented
15#525×C151—22no—
16C2×#120×C151—24no—
17C2×#120×C151C2214yes—
18C2×#120×C151C2212yes—
19#518×C151C2212yescomplemented
20C22×C22⋊C4×C151—22no—
21C22×C22⋊C4×C151C2211yescharacteristic
22C22×C22⋊C4×C151C2211yescharacteristic
23C2×#99×C151C2214yescomplemented
24#379×C151—24no—
25#379×C151—22no—
26#379×C151C2214yes—
27#379×C151C2212yes—
28#379×C151C2212yes—
29#379×C151C2212yes—
30#342×C151C2212yescomplemented
31#342×C151C2214yescomplemented
32#342×C151C2212yescomplemented
33C25×C151—21no—
34C25×C151—21no—
35C25×C151—24no—
36C25×C151—24no—
37C25×C151—48no—
38C25×C151—42no—
39C25×C151C2312yes—
40C25×C151C2311yescharacteristic
41C2×#41×C151—22no—
42C22×D4×C151—24no—
43C22×D4×C151D414yescomplemented
44C22×D4×C151C2312yes—
45C23×C4×C151—21no—
46C23×C4×C151D412yescomplemented
47#126×C151—24no—
48#124×C151—24no—
49#123×C151—24no—
50#123×C151—24no—
51#123×C151—22no—
52C22⋊Q8×C151—22no—
53C22⋊Q8×C151—22no—
54C22⋊Q8×C151—24no—
55#121×C151—22no—
56#121×C151—24no—
57#121×C151—22no—
58#120×C151—22no—
59#120×C151—22no—
60#120×C151—24no—
61#120×C151—22no—
62#120×C151—28no—
63#120×C151—44no—
64#120×C151—416no—
65C4×D4×C151—24no—
66C4×D4×C151—24no—
67C4×D4×C151—24no—
68#117×C151—22no—
69#117×C151—22no—
70C2×C22⋊C4×C151—24no—
71C2×C22⋊C4×C151—24no—
72C2×C22⋊C4×C151—24no—
73C2×C22⋊C4×C151—28no—
74C2×C22⋊C4×C151—24no—
75C2×C22⋊C4×C151—22no—
76C2×C22⋊C4×C151—21no—
77C2×C22⋊C4×C151—24no—
78C2×C22⋊C4×C151—42no—
79C2×C22⋊C4×C151—48no—
80C2×C22⋊C4×C151D412yescomplemented
81C2×C22⋊C4×C151D414yescomplemented
82C2×C22⋊C4×C151C2314yes—
83C2×C22⋊C4×C151C2312yes—
84C2×C22⋊C4×C151C2311yescharacteristic
85C2×C22⋊C4×C151C2311yescharacteristic
86C2×C22⋊C4×C151C2312yes—
87#99×C151—44no—
88C24×C151—28no—
89C24×C151—24no—
90C24×C151—22no—
91C24×C151—24no—
92C24×C151—22no—
93C24×C151—22no—
94C24×C151—216no—
95C24×C151—24no—
96C24×C151—22no—
97C24×C151—24no—
98C24×C151—48no—
99C24×C151—44no—
100C24×C151—416no—
101C24×C151—42no—
102C24×C151—44no—
103C24×C151—432no—
104C24×C151—48no—
105C24×C151—416no—
106C24×C151—42no—
107C24×C151—48no—
108C24×C151—432no—
109C24×C151—42no—
110C24×C151—42no—
111C24×C151C2×D411yescharacteristic
112C24×C151C2×D414yes—
113C24×C151C2×D412yes—
114C24×C151C2×D411yescharacteristic
115C24×C151#4114yescomplemented
116C24×C151C2411yescharacteristic
117#41×C151—84no—
118C2×Q8×C151—22no—
119C2×D4×C151—24no—
120C2×D4×C151—22no—
121C2×D4×C151—22no—
122C2×D4×C151—24no—
123C2×D4×C151—24no—
124C2×D4×C151—22no—
125C2×D4×C151—24no—
126C2×D4×C151—48no—
127C2×D4×C151—48no—
128C2×D4×C151—416no—
129C22×C4×C151—22no—
130C22×C4×C151—24no—
131C22×C4×C151—22no—
132C22×C4×C151—22no—
133C22×C4×C151—24no—
134C22×C4×C151—44no—
135C22×C4×C151—44no—
136C22×C4×C151—42no—
137C22×C4×C151C2×D412yes—
138C22×C4×C151C2×D412yes—
139C22×C4×C151C2×D414yes—
140C22×C4×C151C2×D412yes—
141C4⋊C4×C151—24no—
142C4⋊C4×C151—22no—
143C4⋊C4×C151—22no—
144C4⋊C4×C151—24no—
145C22⋊C4×C151—24no—
146C22⋊C4×C151—24no—
147C22⋊C4×C151—24no—
148C22⋊C4×C151—24no—
149C22⋊C4×C151—24no—
150C22⋊C4×C151—22no—
151C22⋊C4×C151—22no—
152C22⋊C4×C151—22no—
153C22⋊C4×C151—22no—
154C22⋊C4×C151—24no—
155C22⋊C4×C151—24no—
156C22⋊C4×C151—24no—
157C22⋊C4×C151—48no—
158C22⋊C4×C151—48no—
159C22⋊C4×C151—48no—
160C22⋊C4×C151—42no—
161C22⋊C4×C151—416no—
162C22⋊C4×C151—48no—
163C42×C151—24no—
164C23×C151—21no—
165C23×C151—21no—
166C23×C151—24no—
167C23×C151—216no—
168C23×C151—28no—
169C23×C151—216no—
170C23×C151—21no—
171C23×C151—24no—
172C23×C151—21no—
173C23×C151—28no—
174C23×C151—28no—
175C23×C151—28no—
176C23×C151—22no—
177C23×C151—24no—
178C23×C151—42no—
179C23×C151—44no—
180C23×C151—48no—
181C23×C151—42no—
182C23×C151—48no—
183C23×C151—416no—
184C23×C151—48no—
185C23×C151—48no—
186C23×C151—48no—
187C23×C151—44no—
188C23×C151—48no—
189C23×C151—48no—
190C23×C151—416no—
191C23×C151—464no—
192C23×C151—48no—
193C23×C151—416no—
194C23×C151—48no—
195C23×C151—416no—
196C23×C151—44no—
197C23×C151—464no—
198C23×C151—416no—
199C23×C151—42no—
200C23×C151—42no—
201C23×C151—44no—
202C23×C151—48no—
203C23×C151#12012yes—
204C23×C151#12012yes—
205C23×C151C22×D411yescharacteristic
206C23×C151C22×D412yes—
207C23×C151C2×#4112yes—
208C23×C151H(5,𝔽2)12yes—
209Q8×C151—82no—
210D4×C151—42no—
211D4×C151—42no—
212D4×C151—44no—
213D4×C151—48no—
214D4×C151—84no—
215D4×C151—82no—
216D4×C151—816no—
217C2×C4×C151—24no—
218C2×C4×C151—22no—
219C2×C4×C151—22no—
220C2×C4×C151—22no—
221C2×C4×C151—24no—
222C2×C4×C151—44no—
223C2×C4×C151—42no—
224C2×C4×C151—42no—
225C2×C4×C151—44no—
226C2×C4×C151—44no—
227C2×C4×C151—48no—
228C2×C4×C151—42no—
229C2×C4×C151—44no—
230C2×C4×C151—82no—
231C2×C4×C151—84no—
232C2×C4×C151—84no—
233C22×C151—24no—
234C22×C151—24no—
235C22×C151—22no—
236C22×C151—22no—
237C22×C151—24no—
238C22×C151—22no—
239C22×C151—216no—
240C22×C151—28no—
241C22×C151—22no—
242C22×C151—24no—
243C22×C151—42no—
244C22×C151—42no—
245C22×C151—416no—
246C22×C151—48no—
247C22×C151—42no—
248C22×C151—416no—
249C22×C151—48no—
250C22×C151—42no—
251C22×C151—44no—
252C22×C151—432no—
253C22×C151—432no—
254C22×C151—44no—
255C22×C151—48no—
256C22×C151—42no—
257C22×C151—44no—
258C22×C151—84no—
259C22×C151B(4,𝔽2)14yes—
260C22×C151C2×#12011yescharacteristic
261C22×C151#52511yescharacteristic
262C22×C151#53511yescharacteristic
263C22×C151#54614yes—
264C4×C151—42no—
265C4×C151—42no—
266C4×C151—42no—
267C4×C151—44no—
268C4×C151—82no—
269C4×C151—84no—
270C2×C151—21no—
271C2×C151—24no—
272C2×C151—21no—
273C2×C151—24no—
274C2×C151—48no—
275C2×C151—42no—
276C2×C151—82no—
277C2×C151#240411yescharacteristic
278C2×C151C2×B(4,𝔽2)12yes—
279#23984C15111yesmaximal, characteristic, direct product factor, Sylow
280C151#2398411yescharacteristic, direct product factor, Sylow
281#3490C2×C15111yescharacteristic, complemented
282#2846C2×C15112yescomplemented
283C2×#379C2×C15111yescharacteristic, complemented
284#2029C2×C15112yescomplemented
285#2021C2×C15112yescomplemented
286#1898C2×C15112yescomplemented
287#1889C2×C15114yescomplemented
288#1819C2×C15111yescharacteristic, complemented
289C26C22×C15111yescharacteristic
290#551—24no—
291#546—24no—
292#543C22×C15111yescharacteristic, complemented
293#538—22no—
294#534C22×C15111yescharacteristic, complemented
295#525—22no—
296C2×#120—24no—
297C2×#120C22×C15114yes—
298C2×#120C22×C15112yes—
299#518C22×C15112yescomplemented
300C22×C22⋊C4—22no—
301C22×C22⋊C4C22×C15111yescharacteristic
302C22×C22⋊C4C22×C15111yescharacteristic
303C2×#99C22×C15114yescomplemented
304#379—24no—
305#379—22no—
306#379C22×C15112yes—
307#379C22×C15114yes—
308#379C22×C15112yes—
309#379C22×C15112yes—
310#342C22×C15112yescomplemented
311#342C22×C15112yescomplemented
312#342C22×C15114yescomplemented
313C25—21no—
314C25—24no—
315C25—24no—
316C25—21no—
317C25—48no—
318C25—42no—
319C25C23×C15112yes—
320C25C23×C15111yescharacteristic
321C2×#41—22no—
322C22×D4—24no—
323C22×D4D4×C15114yescomplemented
324C22×D4C23×C15112yes—
325C23×C4—21no—
326C23×C4D4×C15112yescomplemented
327#126—24no—
328#124—24no—
329#123—24no—
330#123—24no—
331#123—22no—
332C22⋊Q8—22no—
333C22⋊Q8—22no—
334C22⋊Q8—24no—
335#121—22no—
336#121—24no—
337#121—22no—
338#120—22no—
339#120—22no—
340#120—24no—
341#120—22no—
342#120—28no—
343#120—44no—
344#120—416no—
345C4×D4—24no—
346C4×D4—24no—
347C4×D4—24no—
348#117—22no—
349#117—22no—
350C2×C22⋊C4—24no—
351C2×C22⋊C4—22no—
352C2×C22⋊C4—21no—
353C2×C22⋊C4—24no—
354C2×C22⋊C4—24no—
355C2×C22⋊C4—24no—
356C2×C22⋊C4—28no—
357C2×C22⋊C4—24no—
358C2×C22⋊C4—42no—
359C2×C22⋊C4—48no—
360C2×C22⋊C4D4×C15112yescomplemented
361C2×C22⋊C4D4×C15114yescomplemented
362C2×C22⋊C4C23×C15112yes—
363C2×C22⋊C4C23×C15114yes—
364C2×C22⋊C4C23×C15111yescharacteristic
365C2×C22⋊C4C23×C15111yescharacteristic
366C2×C22⋊C4C23×C15112yes—
367#99—44no—
368C24—28no—
369C24—24no—
370C24—22no—
371C24—24no—
372C24—22no—
373C24—22no—
374C24—216no—
375C24—24no—
376C24—22no—
377C24—24no—
378C24—44no—
379C24—48no—
380C24—416no—
381C24—44no—
382C24—42no—
383C24—48no—
384C24—416no—
385C24—432no—
386C24—48no—
387C24—42no—
388C24—432no—
389C24—42no—
390C24—42no—
391C24C2×D4×C15111yescharacteristic
392C24C2×D4×C15114yes—
393C24C2×D4×C15112yes—
394C24C2×D4×C15111yescharacteristic
395C24#41×C15114yescomplemented
396C24C24×C15111yescharacteristic
397#41—84no—
398C2×Q8—22no—
399C2×D4—24no—
400C2×D4—22no—
401C2×D4—22no—
402C2×D4—24no—
403C2×D4—24no—
404C2×D4—22no—
405C2×D4—24no—
406C2×D4—48no—
407C2×D4—48no—
408C2×D4—416no—
409C22×C4—22no—
410C22×C4—24no—
411C22×C4—22no—
412C22×C4—22no—
413C22×C4—24no—
414C22×C4—44no—
415C22×C4—44no—
416C22×C4—42no—
417C22×C4C2×D4×C15112yes—
418C22×C4C2×D4×C15112yes—
419C22×C4C2×D4×C15114yes—
420C22×C4C2×D4×C15112yes—
421C4⋊C4—24no—
422C4⋊C4—22no—
423C4⋊C4—22no—
424C4⋊C4—24no—
425C22⋊C4—24no—
426C22⋊C4—24no—
427C22⋊C4—24no—
428C22⋊C4—24no—
429C22⋊C4—24no—
430C22⋊C4—22no—
431C22⋊C4—22no—
432C22⋊C4—22no—
433C22⋊C4—22no—
434C22⋊C4—24no—
435C22⋊C4—24no—
436C22⋊C4—24no—
437C22⋊C4—48no—
438C22⋊C4—48no—
439C22⋊C4—48no—
440C22⋊C4—42no—
441C22⋊C4—416no—
442C22⋊C4—48no—
443C42—24no—
444C23—24no—
445C23—21no—
446C23—21no—
447C23—28no—
448C23—216no—
449C23—216no—
450C23—28no—
451C23—24no—
452C23—21no—
453C23—21no—
454C23—28no—
455C23—28no—
456C23—22no—
457C23—24no—
458C23—48no—
459C23—42no—
460C23—42no—
461C23—44no—
462C23—48no—
463C23—416no—
464C23—48no—
465C23—48no—
466C23—48no—
467C23—44no—
468C23—48no—
469C23—48no—
470C23—416no—
471C23—464no—
472C23—48no—
473C23—416no—
474C23—48no—
475C23—416no—
476C23—44no—
477C23—464no—
478C23—416no—
479C23—48no—
480C23—42no—
481C23—42no—
482C23—44no—
483C23#120×C15112yes—
484C23#120×C15112yes—
485C23C22×D4×C15111yescharacteristic
486C23C22×D4×C15112yes—
487C23C2×#41×C15112yes—
488C23H(5,𝔽2)×C15112yes—
489Q8—82no—
490D4—48no—
491D4—42no—
492D4—42no—
493D4—44no—
494D4—84no—
495D4—82no—
496D4—816no—
497C2×C4—22no—
498C2×C4—22no—
499C2×C4—24no—
500C2×C4—22no—
501C2×C4—24no—
502C2×C4—44no—
503C2×C4—42no—
504C2×C4—42no—
505C2×C4—44no—
506C2×C4—44no—
507C2×C4—48no—
508C2×C4—42no—
509C2×C4—44no—
510C2×C4—82no—
511C2×C4—84no—
512C2×C4—84no—
513C22—24no—
514C22—24no—
515C22—22no—
516C22—22no—
517C22—24no—
518C22—22no—
519C22—216no—
520C22—28no—
521C22—22no—
522C22—24no—
523C22—42no—
524C22—42no—
525C22—416no—
526C22—48no—
527C22—42no—
528C22—416no—
529C22—48no—
530C22—44no—
531C22—42no—
532C22—432no—
533C22—432no—
534C22—44no—
535C22—48no—
536C22—42no—
537C22—44no—
538C22—84no—
539C22B(4,𝔽2)×C15114yes—
540C22C2×#120×C15111yescharacteristic
541C22#525×C15111yescharacteristic
542C22#535×C15111yescharacteristic
543C22#546×C15114yes—
544C4—42no—
545C4—42no—
546C4—42no—
547C4—44no—
548C4—82no—
549C4—84no—
550C2—21no—
551C2—24no—
552C2—21no—
553C2—24no—
554C2—48no—
555C2—42no—
556C2—82no—
557C2#2404×C15111yescharacteristic
558C2C2×B(4,𝔽2)×C15112yes—
subgroupG/H
center, socleC22×C151C2×#120
commutator, Frattini, cosocleC24C24×C151
LCSG ▷ C24 ▷ C2 ▷ C1
UCSC1 ◁ C22×C151 ◁ C25×C151 ◁ G

Complements

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

NH ≅ G/Ntype
1. #3490×C151C2semidirect
2. #2846×C151C2semidirect
3. C2×#379×C151C2semidirect
4. #2029×C151C2semidirect
5. #2021×C151C2semidirect
6. #1898×C151C2semidirect
7. #1889×C151C2semidirect
8. #1819×C151C2semidirect
12. #543×C151C22semidirect
14. #534×C151C22semidirect
19. #518×C151C22semidirect
23. C2×#99×C151C22semidirect
30. #342×C151C22semidirect
31. #342×C151C22semidirect
32. #342×C151C22semidirect
43. C22×D4×C151D4semidirect
46. C23×C4×C151D4semidirect
80. C2×C22⋊C4×C151D4semidirect
81. C2×C22⋊C4×C151D4semidirect
115. C24×C151#41semidirect
279. #23984C151direct (N × H)
280. C151#23984direct (N × H)
281. #3490C2×C151semidirect
282. #2846C2×C151semidirect
283. C2×#379C2×C151semidirect
284. #2029C2×C151semidirect
285. #2021C2×C151semidirect
286. #1898C2×C151semidirect
287. #1889C2×C151semidirect
288. #1819C2×C151semidirect
292. #543C22×C151semidirect
294. #534C22×C151semidirect
299. #518C22×C151semidirect
303. C2×#99C22×C151semidirect
310. #342C22×C151semidirect
311. #342C22×C151semidirect
312. #342C22×C151semidirect
323. C22×D4D4×C151semidirect
326. C23×C4D4×C151semidirect
360. C2×C22⋊C4D4×C151semidirect
361. C2×C22⋊C4D4×C151semidirect
395. C24#41×C151semidirect

Maximal subgroups

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

subgroupindex
#3490×C1512
#2846×C1512
C2×#379×C1512
#2029×C1512
#2021×C1512
#1898×C1512
#1889×C1512
#1819×C1512
#23984151