Finite Group Databasebeta

← C151×#13083 #50318008

Subgroups — C151×#13083 #50318008

Order 38656.

818 conjugacy classes of subgroups.

The subgroup lattice has 534 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#413×C151C211yesmaximal, characteristic, complemented
2#2404×C151C211yesmaximal, characteristic
3C2×AΣL(1,𝔽16)×C151C212yesmaximal, complemented
4#1782×C151C211yesmaximal, characteristic, complemented
5#1390×C151C212yesmaximal, complemented
6C22×#41×C151C2211yescharacteristic
7C22×M16×C151—21no—
8C2×#120×C151C411yescharacteristic, complemented
9C2×#120×C151C2211yescharacteristic
10C22×C22⋊C4×C151C411yescharacteristic, complemented
11#413×C151—24no—
12C2×#101×C151—21no—
13C2×#100×C151C2212yes—
14C2×#99×C151—21no—
15C2×#99×C151C2212yes—
16#393×C151—21no—
17#392×C151—21no—
18#386×C151—21no—
19#386×C151—21no—
20#386×C151C411yescharacteristic, complemented
21#386×C151C2211yescharacteristic
22#381×C151—21no—
23#381×C151C411yescharacteristic, complemented
24AΣL(1,𝔽16)×C151—24no—
25C25×C151C2×C411yescharacteristic
26C2×#41×C151—22no—
27C2×#41×C151—22no—
28C2×#41×C151—41no—
29C2×#41×C151—41no—
30C2×#41×C151—42no—
31C22×Q8×C151D411yescharacteristic
32C22×D4×C151—21no—
33C22×D4×C151—21no—
34C22×D4×C151C2×C411yescharacteristic
35C22×D4×C151D411yescharacteristic
36C22×D4×C151C2311yescharacteristic
37C23×C4×C151C2×C411yescharacteristic
38C23×C4×C151C2×C411yescharacteristic
39C23×C4×C151D411yescharacteristic
40C23×C4×C151D411yescharacteristic
41C2×M16×C151—24no—
42C2×M16×C151—22no—
43C2×M16×C151—42no—
44C2×M16×C151—41no—
45C22×C8×C151—41no—
46#120×C151—22no—
47#120×C151—22no—
48#120×C151—42no—
49C2×C22⋊C4×C151—21no—
50C2×C22⋊C4×C151—21no—
51C2×C22⋊C4×C151—21no—
52C2×C22⋊C4×C151—21no—
53C2×C22⋊C4×C151—21no—
54C2×C22⋊C4×C151—22no—
55C2×C22⋊C4×C151—21no—
56C2×C22⋊C4×C151—41no—
57C2×C22⋊C4×C151—41no—
58C2×C22⋊C4×C151C2×C411yescharacteristic
59C2×C22⋊C4×C151C2×C411yescharacteristic
60#101×C151—24no—
61#100×C151—22no—
62#100×C151D414yescomplemented
63#99×C151—22no—
64#99×C151—22no—
65#99×C151—42no—
66#95×C151—21no—
67#95×C151—21no—
68#95×C151—21no—
69#95×C151—21no—
70#95×C151—41no—
71#95×C151—41no—
72C24×C151—21no—
73C24×C151—22no—
74C24×C151—41no—
75C24×C151—42no—
76C24×C151—41no—
77C24×C151—81no—
78C24×C151C22⋊C411yescharacteristic
79C24×C151C22×C411yescharacteristic
80C24×C151C2×D411yescharacteristic
81#41×C151—44no—
82#41×C151—44no—
83#41×C151—44no—
84#41×C151—44no—
85C2×Q8×C151—21no—
86C2×Q8×C151—21no—
87C2×Q8×C151—41no—
88C2×Q8×C151—41no—
89C2×D4×C151—22no—
90C2×D4×C151—22no—
91C2×D4×C151—22no—
92C2×D4×C151—22no—
93C2×D4×C151—41no—
94C2×D4×C151—41no—
95C2×D4×C151—41no—
96C2×D4×C151—41no—
97C2×D4×C151—42no—
98C2×D4×C151—42no—
99C2×D4×C151—42no—
100C2×D4×C151—42no—
101C2×D4×C151—81no—
102C2×D4×C151—81no—
103C2×D4×C151C2×D412yes—
104C2×D4×C151#4112yes—
105C22×C4×C151—22no—
106C22×C4×C151—21no—
107C22×C4×C151—21no—
108C22×C4×C151—21no—
109C22×C4×C151—21no—
110C22×C4×C151—22no—
111C22×C4×C151—22no—
112C22×C4×C151—21no—
113C22×C4×C151—21no—
114C22×C4×C151—21no—
115C22×C4×C151—21no—
116C22×C4×C151—21no—
117C22×C4×C151—21no—
118C22×C4×C151—21no—
119C22×C4×C151—41no—
120C22×C4×C151—41no—
121C22×C4×C151—41no—
122C22×C4×C151—42no—
123C22×C4×C151—81no—
124C22×C4×C151C22⋊C411yescharacteristic
125C22×C4×C151C22⋊C411yescharacteristic
126C22×C4×C151C22⋊C411yescharacteristic
127C22×C4×C151C2×D411yescharacteristic
128M16×C151—24no—
129M16×C151—44no—
130M16×C151—42no—
131C2×C8×C151—44no—
132C2×C8×C151—42no—
133C22⋊C4×C151—22no—
134C22⋊C4×C151—42no—
135C22⋊C4×C151—42no—
136C22⋊C4×C151—41no—
137C22⋊C4×C151—41no—
138C22⋊C4×C151—41no—
139C22⋊C4×C151—41no—
140C22⋊C4×C151—41no—
141C22⋊C4×C151—42no—
142C22⋊C4×C151—42no—
143C22⋊C4×C151—81no—
144C22⋊C4×C151—81no—
145C23×C151—21no—
146C23×C151—21no—
147C23×C151—21no—
148C23×C151—21no—
149C23×C151—21no—
150C23×C151—21no—
151C23×C151—22no—
152C23×C151—41no—
153C23×C151—41no—
154C23×C151—41no—
155C23×C151—41no—
156C23×C151—41no—
157C23×C151—41no—
158C23×C151—41no—
159C23×C151—41no—
160C23×C151—41no—
161C23×C151—42no—
162C23×C151—42no—
163C23×C151—41no—
164C23×C151—41no—
165C23×C151—41no—
166C23×C151—82no—
167C23×C151—84no—
168C23×C151—84no—
169C23×C151—82no—
170C23×C151#9912yes—
171C23×C151C2×C22⋊C411yescharacteristic
172C23×C151C4×D412yes—
173C23×C151#12112yes—
174Q8×C151—42no—
175Q8×C151—42no—
176D4×C151—42no—
177D4×C151—42no—
178D4×C151—44no—
179D4×C151—44no—
180D4×C151—84no—
181D4×C151—84no—
182C2×C4×C151—22no—
183C2×C4×C151—22no—
184C2×C4×C151—22no—
185C2×C4×C151—22no—
186C2×C4×C151—21no—
187C2×C4×C151—21no—
188C2×C4×C151—21no—
189C2×C4×C151—21no—
190C2×C4×C151—21no—
191C2×C4×C151—21no—
192C2×C4×C151—21no—
193C2×C4×C151—21no—
194C2×C4×C151—21no—
195C2×C4×C151—21no—
196C2×C4×C151—42no—
197C2×C4×C151—42no—
198C2×C4×C151—42no—
199C2×C4×C151—42no—
200C2×C4×C151—41no—
201C2×C4×C151—41no—
202C2×C4×C151—41no—
203C2×C4×C151—41no—
204C2×C4×C151—41no—
205C2×C4×C151—41no—
206C2×C4×C151—41no—
207C2×C4×C151—41no—
208C2×C4×C151—41no—
209C2×C4×C151—82no—
210C2×C4×C151—82no—
211C2×C4×C151—82no—
212C2×C4×C151—82no—
213C2×C4×C151#9911yescharacteristic
214C2×C4×C151#9911yescharacteristic
215C2×C4×C151#12011yescharacteristic
216C2×C4×C151#12311yescharacteristic
217C8×C151—44no—
218C22×C151—21no—
219C22×C151—21no—
220C22×C151—22no—
221C22×C151—22no—
222C22×C151—22no—
223C22×C151—42no—
224C22×C151—42no—
225C22×C151—42no—
226C22×C151—42no—
227C22×C151—42no—
228C22×C151—42no—
229C22×C151—41no—
230C22×C151—41no—
231C22×C151—41no—
232C22×C151—41no—
233C22×C151—41no—
234C22×C151—41no—
235C22×C151—42no—
236C22×C151—81no—
237C22×C151—81no—
238C22×C151—81no—
239C22×C151—81no—
240C22×C151—84no—
241C22×C151—84no—
242C22×C151—81no—
243C22×C151—81no—
244C22×C151#38611yescharacteristic
245C22×C151C2×#9911yescharacteristic
246C22×C151C2×#9911yescharacteristic
247C4×C151—21no—
248C4×C151—21no—
249C4×C151—21no—
250C4×C151—21no—
251C4×C151—41no—
252C4×C151—41no—
253C4×C151—81no—
254C4×C151—81no—
255C4×C151—81no—
256C4×C151—162no—
257C2×C151—21no—
258C2×C151—21no—
259C2×C151—42no—
260C2×C151—42no—
261C2×C151—42no—
262C2×C151—82no—
263C2×C151#189811yescharacteristic
264C2×C151#212011yescharacteristic
265C2×C151#212211yescharacteristic
266#13083C15111yesmaximal, characteristic, direct product factor, Sylow
267C151#1308311yescharacteristic, direct product factor, Sylow
268C2×#413C2×C15111yescharacteristic, complemented
269#2404C2×C15111yescharacteristic
270C2×AΣL(1,𝔽16)C2×C15112yescomplemented
271#1782C2×C15111yescharacteristic, complemented
272#1390C2×C15112yescomplemented
273C22×#41C22×C15111yescharacteristic
274C22×M16—21no—
275C2×#120C4×C15111yescharacteristic, complemented
276C2×#120C22×C15111yescharacteristic
277C22×C22⋊C4C4×C15111yescharacteristic, complemented
278#413—24no—
279C2×#101—21no—
280C2×#100C22×C15112yes—
281C2×#99—21no—
282C2×#99C22×C15112yes—
283#393—21no—
284#392—21no—
285#386—21no—
286#386—21no—
287#386C4×C15111yescharacteristic, complemented
288#386C22×C15111yescharacteristic
289#381—21no—
290#381C4×C15111yescharacteristic, complemented
291AΣL(1,𝔽16)—24no—
292C25C2×C4×C15111yescharacteristic
293C2×#41—22no—
294C2×#41—22no—
295C2×#41—41no—
296C2×#41—41no—
297C2×#41—42no—
298C22×Q8D4×C15111yescharacteristic
299C22×D4—21no—
300C22×D4—21no—
301C22×D4C2×C4×C15111yescharacteristic
302C22×D4D4×C15111yescharacteristic
303C22×D4C23×C15111yescharacteristic
304C23×C4C2×C4×C15111yescharacteristic
305C23×C4C2×C4×C15111yescharacteristic
306C23×C4D4×C15111yescharacteristic
307C23×C4D4×C15111yescharacteristic
308C2×M16—24no—
309C2×M16—22no—
310C2×M16—42no—
311C2×M16—41no—
312C22×C8—41no—
313#120—22no—
314#120—22no—
315#120—42no—
316C2×C22⋊C4—21no—
317C2×C22⋊C4—21no—
318C2×C22⋊C4—21no—
319C2×C22⋊C4—21no—
320C2×C22⋊C4—22no—
321C2×C22⋊C4—21no—
322C2×C22⋊C4—21no—
323C2×C22⋊C4—41no—
324C2×C22⋊C4—41no—
325C2×C22⋊C4C2×C4×C15111yescharacteristic
326C2×C22⋊C4C2×C4×C15111yescharacteristic
327#101—24no—
328#100—22no—
329#100D4×C15114yescomplemented
330#99—22no—
331#99—22no—
332#99—42no—
333#95—21no—
334#95—21no—
335#95—21no—
336#95—21no—
337#95—41no—
338#95—41no—
339C24—21no—
340C24—22no—
341C24—41no—
342C24—42no—
343C24—41no—
344C24—81no—
345C24C22⋊C4×C15111yescharacteristic
346C24C22×C4×C15111yescharacteristic
347C24C2×D4×C15111yescharacteristic
348#41—44no—
349#41—44no—
350#41—44no—
351#41—44no—
352C2×Q8—21no—
353C2×Q8—21no—
354C2×Q8—41no—
355C2×Q8—41no—
356C2×D4—22no—
357C2×D4—22no—
358C2×D4—22no—
359C2×D4—22no—
360C2×D4—41no—
361C2×D4—41no—
362C2×D4—41no—
363C2×D4—41no—
364C2×D4—42no—
365C2×D4—42no—
366C2×D4—42no—
367C2×D4—42no—
368C2×D4—81no—
369C2×D4—81no—
370C2×D4C2×D4×C15112yes—
371C2×D4#41×C15112yes—
372C22×C4—22no—
373C22×C4—21no—
374C22×C4—21no—
375C22×C4—21no—
376C22×C4—21no—
377C22×C4—22no—
378C22×C4—22no—
379C22×C4—21no—
380C22×C4—21no—
381C22×C4—21no—
382C22×C4—21no—
383C22×C4—21no—
384C22×C4—21no—
385C22×C4—21no—
386C22×C4—41no—
387C22×C4—41no—
388C22×C4—41no—
389C22×C4—42no—
390C22×C4—81no—
391C22×C4C22⋊C4×C15111yescharacteristic
392C22×C4C22⋊C4×C15111yescharacteristic
393C22×C4C22⋊C4×C15111yescharacteristic
394C22×C4C2×D4×C15111yescharacteristic
395M16—24no—
396M16—44no—
397M16—42no—
398C2×C8—44no—
399C2×C8—42no—
400C22⋊C4—22no—
401C22⋊C4—42no—
402C22⋊C4—42no—
403C22⋊C4—41no—
404C22⋊C4—41no—
405C22⋊C4—41no—
406C22⋊C4—41no—
407C22⋊C4—41no—
408C22⋊C4—42no—
409C22⋊C4—42no—
410C22⋊C4—81no—
411C22⋊C4—81no—
412C23—21no—
413C23—21no—
414C23—21no—
415C23—21no—
416C23—21no—
417C23—21no—
418C23—22no—
419C23—41no—
420C23—41no—
421C23—41no—
422C23—41no—
423C23—41no—
424C23—41no—
425C23—41no—
426C23—41no—
427C23—41no—
428C23—42no—
429C23—42no—
430C23—41no—
431C23—41no—
432C23—41no—
433C23—82no—
434C23—84no—
435C23—84no—
436C23—82no—
437C23#99×C15112yes—
438C23C2×C22⋊C4×C15111yescharacteristic
439C23C4×D4×C15112yes—
440C23#121×C15112yes—
441Q8—42no—
442Q8—42no—
443D4—42no—
444D4—42no—
445D4—44no—
446D4—44no—
447D4—84no—
448D4—84no—
449C2×C4—22no—
450C2×C4—22no—
451C2×C4—22no—
452C2×C4—22no—
453C2×C4—21no—
454C2×C4—21no—
455C2×C4—21no—
456C2×C4—21no—
457C2×C4—21no—
458C2×C4—21no—
459C2×C4—21no—
460C2×C4—21no—
461C2×C4—21no—
462C2×C4—21no—
463C2×C4—42no—
464C2×C4—42no—
465C2×C4—42no—
466C2×C4—42no—
467C2×C4—41no—
468C2×C4—41no—
469C2×C4—41no—
470C2×C4—41no—
471C2×C4—41no—
472C2×C4—41no—
473C2×C4—41no—
474C2×C4—41no—
475C2×C4—41no—
476C2×C4—82no—
477C2×C4—82no—
478C2×C4—82no—
479C2×C4—82no—
480C2×C4#99×C15111yescharacteristic
481C2×C4#99×C15111yescharacteristic
482C2×C4#120×C15111yescharacteristic
483C2×C4#123×C15111yescharacteristic
484C8—44no—
485C22—21no—
486C22—21no—
487C22—22no—
488C22—22no—
489C22—22no—
490C22—42no—
491C22—42no—
492C22—42no—
493C22—42no—
494C22—42no—
495C22—42no—
496C22—41no—
497C22—41no—
498C22—41no—
499C22—41no—
500C22—41no—
501C22—41no—
502C22—42no—
503C22—81no—
504C22—81no—
505C22—81no—
506C22—81no—
507C22—84no—
508C22—84no—
509C22—81no—
510C22—81no—
511C22#386×C15111yescharacteristic
512C22C2×#99×C15111yescharacteristic
513C22C2×#99×C15111yescharacteristic
514C4—21no—
515C4—21no—
516C4—21no—
517C4—21no—
518C4—41no—
519C4—41no—
520C4—81no—
521C4—81no—
522C4—81no—
523C4—162no—
524C2—21no—
525C2—21no—
526C2—42no—
527C2—42no—
528C2—42no—
529C2—82no—
530C2#1898×C15111yescharacteristic
531C2#2120×C15111yescharacteristic
532C2#2122×C15111yescharacteristic
subgroupG/H
center, socleC22×C151C2×#99
commutatorC24C22×C4×C151
Frattini, cosocleC22×D4C23×C151
prime radical#2404×C151C2
LCSG ▷ C24 ▷ C22 ▷ C2 ▷ C1
UCSC1 ◁ C22×C151 ◁ C22×C4×C151 ◁ C22×#41×C151 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×#413×C151C2semidirect
3. C2×AΣL(1,𝔽16)×C151C2semidirect
4. #1782×C151C2semidirect
5. #1390×C151C2semidirect
8. C2×#120×C151C4semidirect
10. C22×C22⋊C4×C151C4semidirect
20. #386×C151C4semidirect
23. #381×C151C4semidirect
62. #100×C151D4semidirect
266. #13083C151direct (N × H)
267. C151#13083direct (N × H)
268. C2×#413C2×C151semidirect
270. C2×AΣL(1,𝔽16)C2×C151semidirect
271. #1782C2×C151semidirect
272. #1390C2×C151semidirect
275. C2×#120C4×C151semidirect
277. C22×C22⋊C4C4×C151semidirect
287. #386C4×C151semidirect
290. #381C4×C151semidirect
329. #100D4×C151semidirect

Maximal subgroups

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

subgroupindex
C2×#413×C1512
#2404×C1512
C2×AΣL(1,𝔽16)×C1512
#1782×C1512
#1390×C1512
#13083151