Finite Group Databasebeta

← C151×#24376 #50329301

Subgroups — C151×#24376 #50329301

Order 38656.

1424 conjugacy classes of subgroups.

The subgroup lattice has 556 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#137×C151C211yesmaximal, characteristic
2C2×#461×C151C212yesmaximal, complemented
3C2×#452×C151C211yesmaximal, characteristic
4#2434×C151C211yesmaximal, characteristic, complemented
5#2339×C151C211yesmaximal, characteristic
6#2056×C151C212yesmaximal, complemented
7#2016×C151C212yesmaximal, complemented
8#1894×C151C211yesmaximal, characteristic, complemented
9#1877×C151C212yesmaximal, complemented
10#1851×C151C211yesmaximal, characteristic, complemented
11#1787×C151C211yesmaximal, characteristic, complemented
12C22×#41×C151C2211yescharacteristic
13C23×Q8×C151C2211yescharacteristic
14C2×#137×C151—24no—
15C2×#137×C151—28no—
16C22×Q16×C151C2212yes—
17C22×Q16×C151C2211yescharacteristic
18C22×SD16×C151C2211yescharacteristic
19C22×SD16×C151C2212yes—
20C22×M16×C151C2211yescharacteristic
21C2×C4⋊Q8×C151C2212yes—
22C2×C22⋊Q8×C151C2211yescharacteristic
23C2×C4×D4×C151C2212yes—
24#461×C151—28no—
25#452×C151—24no—
26C2×C4⋊C8×C151C2212yes—
27C2×#103×C151C2212yes—
28C2×#103×C151C2211yescharacteristic
29C2×#103×C151C2212yes—
30C2×#103×C151C2212yes—
31C2×#102×C151C2211yescharacteristic
32C2×C22⋊C8×C151C2211yescharacteristic
33#395×C151—21no—
34#395×C151—21no—
35#391×C151C2212yes—
36#391×C151C2212yes—
37#386×C151—22no—
38#385×C151—22no—
39#381×C151—21no—
40#380×C151C2211yescharacteristic
41C4×C22⋊C4×C151C2211yescharacteristic
42C2×#95×C151—21no—
43#340×C151C2212yes—
44#336×C151C2212yes—
45C2×#41×C151—24no—
46C2×#41×C151—22no—
47C2×#41×C151—42no—
48C2×#41×C151D414yes—
49C22×Q8×C151—22no—
50C22×Q8×C151—24no—
51C22×Q8×C151—22no—
52C22×Q8×C151—21no—
53C22×Q8×C151—42no—
54C22×Q8×C151C2311yescharacteristic
55C22×Q8×C151C2311yescharacteristic
56C22×Q8×C151C2312yes—
57C22×D4×C151—21no—
58C22×D4×C151C2311yescharacteristic
59C23×C4×C151—21no—
60C23×C4×C151—22no—
61C23×C4×C151—21no—
62C23×C4×C151C2311yescharacteristic
63#137×C151—232no—
64C2×Q16×C151—24no—
65C2×Q16×C151—24no—
66C2×Q16×C151—24no—
67C2×Q16×C151—22no—
68C2×Q16×C151—42no—
69C2×SD16×C151—24no—
70C2×SD16×C151—24no—
71C2×SD16×C151—22no—
72C2×SD16×C151—24no—
73C2×SD16×C151D418yes—
74C2×M16×C151—22no—
75C2×M16×C151—24no—
76C22×C8×C151C2311yescharacteristic
77C22×C8×C151C2311yescharacteristic
78C22×C8×C151C2312yes—
79C4⋊Q8×C151—24no—
80C4⋊Q8×C151—42no—
81C22⋊Q8×C151—22no—
82C22⋊Q8×C151—22no—
83C4×D4×C151—24no—
84C4×D4×C151—42no—
85C2×C4⋊C4×C151—22no—
86C2×C4⋊C4×C151—22no—
87C2×C4⋊C4×C151—21no—
88C2×C4⋊C4×C151C2311yescharacteristic
89C2×C4⋊C4×C151C2312yes—
90C2×C22⋊C4×C151—22no—
91C2×C22⋊C4×C151—21no—
92C2×C22⋊C4×C151—21no—
93C2×C22⋊C4×C151D412yes—
94C2×C42×C151C2312yes—
95C4⋊C8×C151—24no—
96#103×C151—24no—
97#103×C151—22no—
98#103×C151—24no—
99#103×C151—42no—
100#102×C151—22no—
101C22⋊C8×C151—22no—
102#95×C151—21no—
103#95×C151—22no—
104#95×C151—22no—
105#95×C151—22no—
106#95×C151—22no—
107#95×C151D411yescharacteristic
108#95×C151D411yescharacteristic
109C24×C151—21no—
110C24×C151C2×D411yescharacteristic
111#41×C151—28no—
112#41×C151—44no—
113#41×C151—48no—
114C2×Q8×C151—21no—
115C2×Q8×C151—22no—
116C2×Q8×C151—28no—
117C2×Q8×C151—22no—
118C2×Q8×C151—22no—
119C2×Q8×C151—22no—
120C2×Q8×C151—22no—
121C2×Q8×C151—21no—
122C2×Q8×C151—22no—
123C2×Q8×C151—21no—
124C2×Q8×C151—22no—
125C2×Q8×C151—22no—
126C2×Q8×C151—22no—
127C2×Q8×C151—44no—
128C2×Q8×C151—48no—
129C2×Q8×C151—44no—
130C2×Q8×C151—42no—
131C2×Q8×C151C2×D414yes—
132C2×Q8×C151C2×D412yes—
133C2×D4×C151—24no—
134C2×D4×C151—21no—
135C2×D4×C151—22no—
136C2×D4×C151—44no—
137C2×D4×C151C2×D412yes—
138C2×D4×C151C2×D414yes—
139C22×C4×C151—22no—
140C22×C4×C151—22no—
141C22×C4×C151—21no—
142C22×C4×C151—22no—
143C22×C4×C151—24no—
144C22×C4×C151—21no—
145C22×C4×C151—22no—
146C22×C4×C151—21no—
147C22×C4×C151—44no—
148C22×C4×C151—44no—
149C22×C4×C151—44no—
150C22×C4×C151—42no—
151C22×C4×C151—44no—
152C22×C4×C151—82no—
153C22×C4×C151C2×D412yes—
154C22×C4×C151C2×D411yescharacteristic
155C22×C4×C151C2×D412yes—
156C22×C4×C151C2×D412yes—
157C22×C4×C151#4112yes—
158C22×C4×C151C2411yescharacteristic
159Q16×C151—216no—
160Q16×C151—44no—
161SD16×C151—216no—
162SD16×C151—44no—
163M16×C151—28no—
164C2×C8×C151—22no—
165C2×C8×C151—22no—
166C2×C8×C151—21no—
167C2×C8×C151—21no—
168C2×C8×C151—22no—
169C2×C8×C151—22no—
170C2×C8×C151C2×D414yes—
171C4⋊C4×C151—21no—
172C4⋊C4×C151—22no—
173C4⋊C4×C151—21no—
174C4⋊C4×C151—22no—
175C4⋊C4×C151—44no—
176C4⋊C4×C151—44no—
177C4⋊C4×C151—42no—
178C22⋊C4×C151—24no—
179C22⋊C4×C151—44no—
180C22⋊C4×C151—42no—
181C22⋊C4×C151—81no—
182C42×C151—22no—
183C42×C151—22no—
184C23×C151—22no—
185C23×C151—24no—
186C23×C151—22no—
187C23×C151—22no—
188C23×C151—21no—
189C23×C151—21no—
190C23×C151—42no—
191C23×C151—41no—
192C23×C151—41no—
193C23×C151#12112yes—
194C23×C151C22×D411yescharacteristic
195Q8×C151—24no—
196Q8×C151—22no—
197Q8×C151—22no—
198Q8×C151—24no—
199Q8×C151—48no—
200Q8×C151—42no—
201Q8×C151—42no—
202Q8×C151—42no—
203Q8×C151—41no—
204Q8×C151—41no—
205Q8×C151—42no—
206D4×C151—22no—
207D4×C151—24no—
208D4×C151—48no—
209D4×C151#12014yes—
210C2×C4×C151—22no—
211C2×C4×C151—22no—
212C2×C4×C151—22no—
213C2×C4×C151—22no—
214C2×C4×C151—22no—
215C2×C4×C151—24no—
216C2×C4×C151—22no—
217C2×C4×C151—24no—
218C2×C4×C151—22no—
219C2×C4×C151—22no—
220C2×C4×C151—22no—
221C2×C4×C151—48no—
222C2×C4×C151—48no—
223C2×C4×C151—42no—
224C2×C4×C151—42no—
225C2×C4×C151—42no—
226C2×C4×C151—41no—
227C2×C4×C151—41no—
228C2×C4×C151—42no—
229C2×C4×C151—42no—
230C2×C4×C151—42no—
231C2×C4×C151—42no—
232C2×C4×C151—41no—
233C2×C4×C151—41no—
234C2×C4×C151—88no—
235C2×C4×C151#12112yes—
236C2×C4×C151#13714yescomplemented
237C2×C4×C151C22×D411yescharacteristic
238C2×C4×C151C22×D412yes—
239C2×C4×C151C2×#4111yescharacteristic
240C2×C4×C151H(5,𝔽2)12yes—
241C8×C151—24no—
242C8×C151—41no—
243C8×C151—41no—
244C22×C151—22no—
245C22×C151—24no—
246C22×C151—22no—
247C22×C151—22no—
248C22×C151—44no—
249C22×C151—42no—
250C22×C151—42no—
251C22×C151—44no—
252C22×C151—42no—
253C22×C151—42no—
254C22×C151C2×#12111yescharacteristic
255C22×C151D4212yes—
256C22×C151C2×#13712yes—
257C22×C151#57711yescharacteristic
258C22×C151#57811yescharacteristic
259C4×C151—22no—
260C4×C151—24no—
261C4×C151—42no—
262C4×C151—44no—
263C4×C151—42no—
264C4×C151—81no—
265C4×C151—82no—
266C4×C151—81no—
267C4×C151C2×#12011yescharacteristic
268C4×C151#53411yescharacteristic
269C4×C151#54612yes—
270C2×C151—42no—
271C2×C151—44no—
272C2×C151#241011yescharacteristic
273C2×C151#303911yescharacteristic
274C2×C151#304611yescharacteristic
275C2×C151#326612yes—
276C2×C151#327612yes—
277#24376C15111yesmaximal, characteristic, direct product factor, Sylow
278C151#2437611yescharacteristic, direct product factor, Sylow
279C22×#137C2×C15111yescharacteristic
280C2×#461C2×C15112yescomplemented
281C2×#452C2×C15111yescharacteristic
282#2434C2×C15111yescharacteristic, complemented
283#2339C2×C15111yescharacteristic
284#2056C2×C15112yescomplemented
285#2016C2×C15112yescomplemented
286#1894C2×C15111yescharacteristic, complemented
287#1877C2×C15112yescomplemented
288#1851C2×C15111yescharacteristic, complemented
289#1787C2×C15111yescharacteristic, complemented
290C22×#41C22×C15111yescharacteristic
291C23×Q8C22×C15111yescharacteristic
292C2×#137—24no—
293C2×#137—28no—
294C22×Q16C22×C15112yes—
295C22×Q16C22×C15111yescharacteristic
296C22×SD16C22×C15111yescharacteristic
297C22×SD16C22×C15112yes—
298C22×M16C22×C15111yescharacteristic
299C2×C4⋊Q8C22×C15112yes—
300C2×C22⋊Q8C22×C15111yescharacteristic
301C2×C4×D4C22×C15112yes—
302#461—28no—
303#452—24no—
304C2×C4⋊C8C22×C15112yes—
305C2×#103C22×C15111yescharacteristic
306C2×#103C22×C15112yes—
307C2×#103C22×C15112yes—
308C2×#103C22×C15112yes—
309C2×#102C22×C15111yescharacteristic
310C2×C22⋊C8C22×C15111yescharacteristic
311#395—21no—
312#395—21no—
313#391C22×C15112yes—
314#391C22×C15112yes—
315#386—22no—
316#385—22no—
317#381—21no—
318#380C22×C15111yescharacteristic
319C4×C22⋊C4C22×C15111yescharacteristic
320C2×#95—21no—
321#340C22×C15112yes—
322#336C22×C15112yes—
323C2×#41—22no—
324C2×#41—24no—
325C2×#41—42no—
326C2×#41D4×C15114yes—
327C22×Q8—21no—
328C22×Q8—24no—
329C22×Q8—22no—
330C22×Q8—22no—
331C22×Q8—42no—
332C22×Q8C23×C15111yescharacteristic
333C22×Q8C23×C15112yes—
334C22×Q8C23×C15111yescharacteristic
335C22×D4—21no—
336C22×D4C23×C15111yescharacteristic
337C23×C4—21no—
338C23×C4—21no—
339C23×C4—22no—
340C23×C4C23×C15111yescharacteristic
341#137—232no—
342C2×Q16—24no—
343C2×Q16—24no—
344C2×Q16—22no—
345C2×Q16—24no—
346C2×Q16—42no—
347C2×SD16—24no—
348C2×SD16—24no—
349C2×SD16—22no—
350C2×SD16—24no—
351C2×SD16D4×C15118yes—
352C2×M16—22no—
353C2×M16—24no—
354C22×C8C23×C15111yescharacteristic
355C22×C8C23×C15111yescharacteristic
356C22×C8C23×C15112yes—
357C4⋊Q8—24no—
358C4⋊Q8—42no—
359C22⋊Q8—22no—
360C22⋊Q8—22no—
361C4×D4—24no—
362C4×D4—42no—
363C2×C4⋊C4—21no—
364C2×C4⋊C4—22no—
365C2×C4⋊C4—22no—
366C2×C4⋊C4C23×C15112yes—
367C2×C4⋊C4C23×C15111yescharacteristic
368C2×C22⋊C4—21no—
369C2×C22⋊C4—22no—
370C2×C22⋊C4—21no—
371C2×C22⋊C4D4×C15112yes—
372C2×C42C23×C15112yes—
373C4⋊C8—24no—
374#103—22no—
375#103—24no—
376#103—24no—
377#103—42no—
378#102—22no—
379C22⋊C8—22no—
380#95—21no—
381#95—22no—
382#95—22no—
383#95—22no—
384#95—22no—
385#95D4×C15111yescharacteristic
386#95D4×C15111yescharacteristic
387C24—21no—
388C24C2×D4×C15111yescharacteristic
389#41—28no—
390#41—44no—
391#41—48no—
392C2×Q8—21no—
393C2×Q8—22no—
394C2×Q8—28no—
395C2×Q8—22no—
396C2×Q8—22no—
397C2×Q8—22no—
398C2×Q8—22no—
399C2×Q8—21no—
400C2×Q8—22no—
401C2×Q8—21no—
402C2×Q8—22no—
403C2×Q8—22no—
404C2×Q8—22no—
405C2×Q8—44no—
406C2×Q8—48no—
407C2×Q8—44no—
408C2×Q8—42no—
409C2×Q8C2×D4×C15114yes—
410C2×Q8C2×D4×C15112yes—
411C2×D4—24no—
412C2×D4—21no—
413C2×D4—22no—
414C2×D4—44no—
415C2×D4C2×D4×C15112yes—
416C2×D4C2×D4×C15114yes—
417C22×C4—22no—
418C22×C4—22no—
419C22×C4—21no—
420C22×C4—22no—
421C22×C4—24no—
422C22×C4—21no—
423C22×C4—22no—
424C22×C4—21no—
425C22×C4—44no—
426C22×C4—44no—
427C22×C4—44no—
428C22×C4—42no—
429C22×C4—44no—
430C22×C4—82no—
431C22×C4C2×D4×C15112yes—
432C22×C4C2×D4×C15111yescharacteristic
433C22×C4C2×D4×C15112yes—
434C22×C4C2×D4×C15112yes—
435C22×C4#41×C15112yes—
436C22×C4C24×C15111yescharacteristic
437Q16—216no—
438Q16—44no—
439SD16—216no—
440SD16—44no—
441M16—28no—
442C2×C8—22no—
443C2×C8—22no—
444C2×C8—21no—
445C2×C8—21no—
446C2×C8—22no—
447C2×C8—22no—
448C2×C8C2×D4×C15114yes—
449C4⋊C4—21no—
450C4⋊C4—22no—
451C4⋊C4—21no—
452C4⋊C4—22no—
453C4⋊C4—44no—
454C4⋊C4—44no—
455C4⋊C4—42no—
456C22⋊C4—24no—
457C22⋊C4—44no—
458C22⋊C4—42no—
459C22⋊C4—81no—
460C42—22no—
461C42—22no—
462C23—22no—
463C23—24no—
464C23—22no—
465C23—22no—
466C23—21no—
467C23—21no—
468C23—42no—
469C23—41no—
470C23—41no—
471C23#121×C15112yes—
472C23C22×D4×C15111yescharacteristic
473Q8—24no—
474Q8—22no—
475Q8—22no—
476Q8—24no—
477Q8—48no—
478Q8—42no—
479Q8—42no—
480Q8—42no—
481Q8—41no—
482Q8—41no—
483Q8—42no—
484D4—22no—
485D4—24no—
486D4—48no—
487D4#120×C15114yes—
488C2×C4—22no—
489C2×C4—22no—
490C2×C4—22no—
491C2×C4—22no—
492C2×C4—22no—
493C2×C4—24no—
494C2×C4—22no—
495C2×C4—22no—
496C2×C4—24no—
497C2×C4—22no—
498C2×C4—22no—
499C2×C4—48no—
500C2×C4—48no—
501C2×C4—42no—
502C2×C4—42no—
503C2×C4—42no—
504C2×C4—41no—
505C2×C4—41no—
506C2×C4—42no—
507C2×C4—42no—
508C2×C4—42no—
509C2×C4—42no—
510C2×C4—41no—
511C2×C4—41no—
512C2×C4—88no—
513C2×C4#121×C15112yes—
514C2×C4#137×C15114yescomplemented
515C2×C4C22×D4×C15111yescharacteristic
516C2×C4C22×D4×C15112yes—
517C2×C4C2×#41×C15111yescharacteristic
518C2×C4H(5,𝔽2)×C15112yes—
519C8—24no—
520C8—41no—
521C8—41no—
522C22—22no—
523C22—24no—
524C22—22no—
525C22—22no—
526C22—44no—
527C22—42no—
528C22—42no—
529C22—44no—
530C22—42no—
531C22—42no—
532C22C2×#121×C15111yescharacteristic
533C22D42×C15112yes—
534C22C2×#137×C15112yes—
535C22#577×C15111yescharacteristic
536C22#578×C15111yescharacteristic
537C4—22no—
538C4—24no—
539C4—42no—
540C4—44no—
541C4—42no—
542C4—81no—
543C4—82no—
544C4—81no—
545C4C2×#120×C15111yescharacteristic
546C4#534×C15111yescharacteristic
547C4#546×C15112yes—
548C2—42no—
549C2—44no—
550C2#2410×C15111yescharacteristic
551C2#3039×C15111yescharacteristic
552C2#3046×C15111yescharacteristic
553C2#3266×C15112yes—
554C2#3276×C15112yes—
subgroupG/H
center, socleC23×C151C22×D4
commutator, Frattini, cosocleC22×C4C24×C151
prime radicalC22×#41×C151C22
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C151 ◁ C4×C22⋊C4×C151 ◁ G

Complements

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

NH ≅ G/Ntype
2. C2×#461×C151C2semidirect
4. #2434×C151C2semidirect
6. #2056×C151C2semidirect
7. #2016×C151C2semidirect
8. #1894×C151C2semidirect
9. #1877×C151C2semidirect
10. #1851×C151C2semidirect
11. #1787×C151C2semidirect
236. C2×C4×C151#137semidirect
277. #24376C151direct (N × H)
278. C151#24376direct (N × H)
280. C2×#461C2×C151semidirect
282. #2434C2×C151semidirect
284. #2056C2×C151semidirect
285. #2016C2×C151semidirect
286. #1894C2×C151semidirect
287. #1877C2×C151semidirect
288. #1851C2×C151semidirect
289. #1787C2×C151semidirect
514. C2×C4#137×C151semidirect

Maximal subgroups

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

subgroupindex
C22×#137×C1512
C2×#461×C1512
C2×#452×C1512
#2434×C1512
#2339×C1512
#2056×C1512
#2016×C1512
#1894×C1512
#1877×C1512
#1851×C1512
#1787×C1512
#24376151