Finite Group Databasebeta

← C151×#24196 #50329121

Subgroups — C151×#24196 #50329121

Order 38656.

1428 conjugacy classes of subgroups.

The subgroup lattice has 580 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#550×C151C211yesmaximal, characteristic, complemented
2C2×#459×C151C211yesmaximal, characteristic, complemented
3C2×#442×C151C211yesmaximal, characteristic, complemented
4#2580×C151C211yesmaximal, characteristic, complemented
5#2041×C151C212yesmaximal, complemented
6#2011×C151C212yesmaximal, complemented
7#1985×C151C211yesmaximal, characteristic, complemented
8#1961×C151C211yesmaximal, characteristic, complemented
9#1879×C151C212yesmaximal, complemented
10#1864×C151C212yesmaximal, complemented
11#1804×C151C211yesmaximal, characteristic, complemented
12C22×#41×C151—21no—
13C22×D8×C151C2211yescharacteristic
14C22×D8×C151C2212yes—
15#550×C151—24no—
16#550×C151—24no—
17C2×#127×C151C2212yes—
18C2×#127×C151C2211yescharacteristic
19C2×#121×C151—22no—
20C2×#121×C151—21no—
21C2×C4×Q8×C151C2211yescharacteristic
22C2×C4×D4×C151C2212yes—
23C2×C4×D4×C151C2211yescharacteristic
24C2×C4×D4×C151C2211yescharacteristic
25#459×C151—24no—
26#442×C151—24no—
27C2×#106×C151C2211yescharacteristic
28C2×C4⋊C8×C151C2211yescharacteristic
29C2×#102×C151C2212yes—
30C2×#102×C151C2212yes—
31C2×#102×C151C2211yescharacteristic
32C2×#102×C151C2211yescharacteristic
33C2×#102×C151C2212yes—
34C2×#102×C151C2212yes—
35C2×#97×C151C2211yescharacteristic
36#399×C151—21no—
37#393×C151—21no—
38#390×C151C2212yes—
39#389×C151C2212yes—
40#385×C151—22no—
41#382×C151C2211yescharacteristic
42#340×C151C2212yes—
43#336×C151C2212yes—
44#336×C151C2212yes—
45C2×#41×C151—28no—
46C2×#41×C151—48no—
47C22×Q8×C151D411yescharacteristic
48C22×D4×C151—21no—
49C22×D4×C151—22no—
50C22×D4×C151—22no—
51C22×D4×C151—21no—
52C22×D4×C151C2312yes—
53C22×D4×C151C2311yescharacteristic
54C22×D4×C151C2311yescharacteristic
55C23×C4×C151—22no—
56C23×C4×C151—21no—
57C23×C4×C151—21no—
58C2×D8×C151—22no—
59C2×D8×C151—22no—
60C2×D8×C151—24no—
61C2×D8×C151—24no—
62C2×D8×C151—22no—
63C2×D8×C151—42no—
64C22×C8×C151C2312yes—
65C22×C8×C151C2311yescharacteristic
66C22×C8×C151C2311yescharacteristic
67#127×C151—24no—
68#127×C151—24no—
69#127×C151—22no—
70#127×C151D414yes—
71#121×C151—28no—
72#121×C151—216no—
73C4×Q8×C151—22no—
74C4×Q8×C151—22no—
75C4×D4×C151—24no—
76C4×D4×C151—24no—
77C4×D4×C151—22no—
78C4×D4×C151—22no—
79C4×D4×C151—22no—
80C4×D4×C151D414yes—
81C2×C4⋊C4×C151—22no—
82C2×C4⋊C4×C151D412yes—
83C2×C4⋊C4×C151D411yescharacteristic
84C2×C4⋊C4×C151C2312yes—
85C2×C4⋊C4×C151C2311yescharacteristic
86C2×C4⋊C4×C151C2311yescharacteristic
87C2×C22⋊C4×C151—22no—
88C2×C22⋊C4×C151—21no—
89C2×C22⋊C4×C151—22no—
90C2×C22⋊C4×C151—21no—
91C2×C22⋊C4×C151—22no—
92C2×C42×C151C2312yes—
93C2×C42×C151C2311yescharacteristic
94#106×C151—22no—
95C4⋊C8×C151—22no—
96#102×C151—22no—
97#102×C151—24no—
98#102×C151—24no—
99#102×C151—22no—
100#102×C151—42no—
101#102×C151—42no—
102#97×C151—22no—
103#95×C151—21no—
104#95×C151—21no—
105#95×C151—22no—
106C24×C151—21no—
107C24×C151—22no—
108C24×C151—21no—
109#41×C151—432no—
110C2×Q8×C151—22no—
111C2×Q8×C151—24no—
112C2×D4×C151—28no—
113C2×D4×C151—28no—
114C2×D4×C151—24no—
115C2×D4×C151—24no—
116C2×D4×C151—21no—
117C2×D4×C151—21no—
118C2×D4×C151—22no—
119C2×D4×C151—21no—
120C2×D4×C151—22no—
121C2×D4×C151—21no—
122C2×D4×C151—22no—
123C2×D4×C151—21no—
124C2×D4×C151—21no—
125C2×D4×C151—21no—
126C2×D4×C151—22no—
127C2×D4×C151—21no—
128C2×D4×C151—21no—
129C2×D4×C151—22no—
130C2×D4×C151—21no—
131C2×D4×C151—44no—
132C2×D4×C151—44no—
133C2×D4×C151—44no—
134C2×D4×C151—82no—
135C2×D4×C151—82no—
136C2×D4×C151—82no—
137C2×D4×C151C2×D414yes—
138C2×D4×C151C2×D412yes—
139C2×D4×C151#4112yescomplemented
140C22×C4×C151—28no—
141C22×C4×C151—21no—
142C22×C4×C151—24no—
143C22×C4×C151—22no—
144C22×C4×C151—21no—
145C22×C4×C151—44no—
146C22×C4×C151—44no—
147C22×C4×C151—44no—
148C22×C4×C151—42no—
149C22×C4×C151—82no—
150C22×C4×C151C2×D412yes—
151C22×C4×C151C2×D411yescharacteristic
152C22×C4×C151C2×D411yescharacteristic
153C22×C4×C151C2×D412yes—
154C22×C4×C151C2411yescharacteristic
155D8×C151—28no—
156D8×C151—48no—
157C2×C8×C151—21no—
158C2×C8×C151—21no—
159C2×C8×C151—21no—
160C2×C8×C151—22no—
161C2×C8×C151—22no—
162C2×C8×C151—21no—
163C2×C8×C151—22no—
164C2×C8×C151—21no—
165C2×C8×C151#4112yescomplemented
166C4⋊C4×C151—24no—
167C4⋊C4×C151—22no—
168C4⋊C4×C151—21no—
169C4⋊C4×C151—21no—
170C4⋊C4×C151—21no—
171C4⋊C4×C151—22no—
172C4⋊C4×C151—22no—
173C4⋊C4×C151—82no—
174C4⋊C4×C151C2×D412yes—
175C22⋊C4×C151—28no—
176C22⋊C4×C151—24no—
177C22⋊C4×C151—42no—
178C22⋊C4×C151—44no—
179C22⋊C4×C151—82no—
180C42×C151—22no—
181C42×C151—22no—
182C42×C151C2×D412yes—
183C42×C151C2×D412yes—
184C23×C151—24no—
185C23×C151—22no—
186C23×C151—22no—
187C23×C151—41no—
188C23×C151—41no—
189C23×C151—42no—
190C23×C151—41no—
191C23×C151—42no—
192C23×C151—41no—
193C23×C151—42no—
194C23×C151—42no—
195C23×C151—42no—
196C23×C151—42no—
197C23×C151—42no—
198C23×C151—42no—
199C23×C151—42no—
200C23×C151—42no—
201C23×C151C22×D411yescharacteristic
202Q8×C151—28no—
203D4×C151—22no—
204D4×C151—22no—
205D4×C151—22no—
206D4×C151—22no—
207D4×C151—24no—
208D4×C151—24no—
209D4×C151—48no—
210D4×C151—416no—
211D4×C151—42no—
212D4×C151—41no—
213D4×C151—42no—
214D4×C151—41no—
215D4×C151—41no—
216D4×C151—41no—
217D4×C151—84no—
218D4×C151—88no—
219C2×C4×C151—22no—
220C2×C4×C151—22no—
221C2×C4×C151—22no—
222C2×C4×C151—22no—
223C2×C4×C151—22no—
224C2×C4×C151—22no—
225C2×C4×C151—22no—
226C2×C4×C151—22no—
227C2×C4×C151—48no—
228C2×C4×C151—416no—
229C2×C4×C151—42no—
230C2×C4×C151—41no—
231C2×C4×C151—42no—
232C2×C4×C151—42no—
233C2×C4×C151—42no—
234C2×C4×C151—42no—
235C2×C4×C151—84no—
236C2×C4×C151#12012yes—
237C2×C4×C151#12012yes—
238C2×C4×C151AGL(1,ℤ/8)14yes—
239C2×C4×C151C22×D411yescharacteristic
240C2×C4×C151C22×D411yescharacteristic
241C2×C4×C151C2×#4111yescharacteristic
242C2×C4×C151C2×#4111yescharacteristic
243C2×C4×C151H(5,𝔽2)11yescharacteristic
244C2×C4×C1512−1+411yescharacteristic
245C8×C151—22no—
246C8×C151—41no—
247C8×C151—42no—
248C22×C151—44no—
249C22×C151—42no—
250C22×C151—42no—
251C22×C151—44no—
252C22×C151—42no—
253C22×C151—44no—
254C22×C151—44no—
255C22×C151—42no—
256C22×C151—82no—
257C22×C151—82no—
258C22×C151—82no—
259C22×C151—82no—
260C22×C151—82no—
261C22×C151—82no—
262C22×C151—82no—
263C22×C151—81no—
264C22×C151—81no—
265C22×C151C2×#12011yescharacteristic
266C22×C151#54811yescharacteristic
267C22×C151#55011yescharacteristic
268C22×C151C2×AGL(1,ℤ/8)12yes—
269C22×C151#57612yes—
270C4×C151—22no—
271C4×C151—24no—
272C4×C151—22no—
273C4×C151—42no—
274C4×C151—42no—
275C4×C151—82no—
276C4×C151—81no—
277C4×C151#52511yescharacteristic
278C4×C151#53711yescharacteristic
279C4×C151#54611yescharacteristic
280C4×C151#54711yescharacteristic
281C2×C151—82no—
282C2×C151—82no—
283C2×C151—84no—
284C2×C151#240711yescharacteristic
285C2×C151#300311yescharacteristic
286C2×C151#300811yescharacteristic
287C2×C151#336612yes—
288C2×C151#339912yes—
289#24196C15111yesmaximal, characteristic, direct product factor, Sylow
290C151#2419611yescharacteristic, direct product factor, Sylow
291C2×#550C2×C15111yescharacteristic, complemented
292C2×#459C2×C15111yescharacteristic, complemented
293C2×#442C2×C15111yescharacteristic, complemented
294#2580C2×C15111yescharacteristic, complemented
295#2041C2×C15112yescomplemented
296#2011C2×C15112yescomplemented
297#1985C2×C15111yescharacteristic, complemented
298#1961C2×C15111yescharacteristic, complemented
299#1879C2×C15112yescomplemented
300#1864C2×C15112yescomplemented
301#1804C2×C15111yescharacteristic, complemented
302C22×#41—21no—
303C22×D8C22×C15111yescharacteristic
304C22×D8C22×C15112yes—
305#550—24no—
306#550—24no—
307C2×#127C22×C15112yes—
308C2×#127C22×C15111yescharacteristic
309C2×#121—22no—
310C2×#121—21no—
311C2×C4×Q8C22×C15111yescharacteristic
312C2×C4×D4C22×C15111yescharacteristic
313C2×C4×D4C22×C15112yes—
314C2×C4×D4C22×C15111yescharacteristic
315#459—24no—
316#442—24no—
317C2×#106C22×C15111yescharacteristic
318C2×C4⋊C8C22×C15111yescharacteristic
319C2×#102C22×C15112yes—
320C2×#102C22×C15112yes—
321C2×#102C22×C15111yescharacteristic
322C2×#102C22×C15111yescharacteristic
323C2×#102C22×C15112yes—
324C2×#102C22×C15112yes—
325C2×#97C22×C15111yescharacteristic
326#399—21no—
327#393—21no—
328#390C22×C15112yes—
329#389C22×C15112yes—
330#385—22no—
331#382C22×C15111yescharacteristic
332#340C22×C15112yes—
333#336C22×C15112yes—
334#336C22×C15112yes—
335C2×#41—28no—
336C2×#41—48no—
337C22×Q8D4×C15111yescharacteristic
338C22×D4—21no—
339C22×D4—22no—
340C22×D4—22no—
341C22×D4—21no—
342C22×D4C23×C15111yescharacteristic
343C22×D4C23×C15112yes—
344C22×D4C23×C15111yescharacteristic
345C23×C4—22no—
346C23×C4—21no—
347C23×C4—21no—
348C2×D8—22no—
349C2×D8—22no—
350C2×D8—24no—
351C2×D8—24no—
352C2×D8—22no—
353C2×D8—42no—
354C22×C8C23×C15112yes—
355C22×C8C23×C15111yescharacteristic
356C22×C8C23×C15111yescharacteristic
357#127—24no—
358#127—24no—
359#127—22no—
360#127D4×C15114yes—
361#121—28no—
362#121—216no—
363C4×Q8—22no—
364C4×Q8—22no—
365C4×D4—24no—
366C4×D4—24no—
367C4×D4—22no—
368C4×D4—22no—
369C4×D4—22no—
370C4×D4D4×C15114yes—
371C2×C4⋊C4—22no—
372C2×C4⋊C4D4×C15112yes—
373C2×C4⋊C4D4×C15111yescharacteristic
374C2×C4⋊C4C23×C15111yescharacteristic
375C2×C4⋊C4C23×C15112yes—
376C2×C4⋊C4C23×C15111yescharacteristic
377C2×C22⋊C4—22no—
378C2×C22⋊C4—21no—
379C2×C22⋊C4—21no—
380C2×C22⋊C4—22no—
381C2×C22⋊C4—22no—
382C2×C42C23×C15112yes—
383C2×C42C23×C15111yescharacteristic
384#106—22no—
385C4⋊C8—22no—
386#102—22no—
387#102—24no—
388#102—24no—
389#102—22no—
390#102—42no—
391#102—42no—
392#97—22no—
393#95—21no—
394#95—21no—
395#95—22no—
396C24—21no—
397C24—22no—
398C24—21no—
399#41—432no—
400C2×Q8—22no—
401C2×Q8—24no—
402C2×D4—28no—
403C2×D4—28no—
404C2×D4—24no—
405C2×D4—24no—
406C2×D4—21no—
407C2×D4—21no—
408C2×D4—22no—
409C2×D4—21no—
410C2×D4—22no—
411C2×D4—21no—
412C2×D4—22no—
413C2×D4—21no—
414C2×D4—21no—
415C2×D4—21no—
416C2×D4—22no—
417C2×D4—21no—
418C2×D4—21no—
419C2×D4—22no—
420C2×D4—21no—
421C2×D4—44no—
422C2×D4—44no—
423C2×D4—44no—
424C2×D4—82no—
425C2×D4—82no—
426C2×D4—82no—
427C2×D4C2×D4×C15114yes—
428C2×D4C2×D4×C15112yes—
429C2×D4#41×C15112yescomplemented
430C22×C4—28no—
431C22×C4—21no—
432C22×C4—24no—
433C22×C4—22no—
434C22×C4—21no—
435C22×C4—44no—
436C22×C4—44no—
437C22×C4—44no—
438C22×C4—42no—
439C22×C4—82no—
440C22×C4C2×D4×C15112yes—
441C22×C4C2×D4×C15111yescharacteristic
442C22×C4C2×D4×C15111yescharacteristic
443C22×C4C2×D4×C15112yes—
444C22×C4C24×C15111yescharacteristic
445D8—28no—
446D8—48no—
447C2×C8—21no—
448C2×C8—21no—
449C2×C8—21no—
450C2×C8—22no—
451C2×C8—22no—
452C2×C8—21no—
453C2×C8—22no—
454C2×C8—21no—
455C2×C8#41×C15112yescomplemented
456C4⋊C4—24no—
457C4⋊C4—22no—
458C4⋊C4—21no—
459C4⋊C4—21no—
460C4⋊C4—21no—
461C4⋊C4—22no—
462C4⋊C4—22no—
463C4⋊C4—82no—
464C4⋊C4C2×D4×C15112yes—
465C22⋊C4—28no—
466C22⋊C4—24no—
467C22⋊C4—42no—
468C22⋊C4—44no—
469C22⋊C4—82no—
470C42—22no—
471C42—22no—
472C42C2×D4×C15112yes—
473C42C2×D4×C15112yes—
474C23—24no—
475C23—22no—
476C23—22no—
477C23—41no—
478C23—41no—
479C23—42no—
480C23—42no—
481C23—41no—
482C23—41no—
483C23—42no—
484C23—42no—
485C23—42no—
486C23—42no—
487C23—42no—
488C23—42no—
489C23—42no—
490C23—42no—
491C23C22×D4×C15111yescharacteristic
492Q8—28no—
493D4—22no—
494D4—22no—
495D4—22no—
496D4—22no—
497D4—24no—
498D4—24no—
499D4—48no—
500D4—416no—
501D4—42no—
502D4—41no—
503D4—42no—
504D4—41no—
505D4—41no—
506D4—41no—
507D4—84no—
508D4—88no—
509C2×C4—22no—
510C2×C4—22no—
511C2×C4—22no—
512C2×C4—22no—
513C2×C4—22no—
514C2×C4—22no—
515C2×C4—22no—
516C2×C4—22no—
517C2×C4—48no—
518C2×C4—416no—
519C2×C4—42no—
520C2×C4—41no—
521C2×C4—42no—
522C2×C4—42no—
523C2×C4—42no—
524C2×C4—42no—
525C2×C4—84no—
526C2×C4#120×C15112yes—
527C2×C4#120×C15112yes—
528C2×C4AGL(1,ℤ/8)×C15114yes—
529C2×C4C22×D4×C15111yescharacteristic
530C2×C4C22×D4×C15111yescharacteristic
531C2×C4C2×#41×C15111yescharacteristic
532C2×C4C2×#41×C15111yescharacteristic
533C2×C4H(5,𝔽2)×C15111yescharacteristic
534C2×C42−1+4×C15111yescharacteristic
535C8—22no—
536C8—41no—
537C8—42no—
538C22—44no—
539C22—42no—
540C22—42no—
541C22—44no—
542C22—42no—
543C22—44no—
544C22—44no—
545C22—42no—
546C22—82no—
547C22—82no—
548C22—82no—
549C22—82no—
550C22—82no—
551C22—82no—
552C22—82no—
553C22—81no—
554C22—81no—
555C22C2×#120×C15111yescharacteristic
556C22#548×C15111yescharacteristic
557C22#550×C15111yescharacteristic
558C22C2×AGL(1,ℤ/8)×C15112yes—
559C22#576×C15112yes—
560C4—22no—
561C4—24no—
562C4—22no—
563C4—42no—
564C4—42no—
565C4—82no—
566C4—81no—
567C4#525×C15111yescharacteristic
568C4#537×C15111yescharacteristic
569C4#546×C15111yescharacteristic
570C4#547×C15111yescharacteristic
571C2—82no—
572C2—82no—
573C2—84no—
574C2#2407×C15111yescharacteristic
575C2#3003×C15111yescharacteristic
576C2#3008×C15111yescharacteristic
577C2#3366×C15112yes—
578C2#3399×C15112yes—
subgroupG/H
center, socleC23×C151C22×D4
commutator, Frattini, cosocleC22×C4C24×C151
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C151 ◁ C2×C4×Q8×C151 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×#550×C151C2semidirect
2. C2×#459×C151C2semidirect
3. C2×#442×C151C2semidirect
4. #2580×C151C2semidirect
5. #2041×C151C2semidirect
6. #2011×C151C2semidirect
7. #1985×C151C2semidirect
8. #1961×C151C2semidirect
9. #1879×C151C2semidirect
10. #1864×C151C2semidirect
11. #1804×C151C2semidirect
139. C2×D4×C151#41semidirect
165. C2×C8×C151#41semidirect
289. #24196C151direct (N × H)
290. C151#24196direct (N × H)
291. C2×#550C2×C151semidirect
292. C2×#459C2×C151semidirect
293. C2×#442C2×C151semidirect
294. #2580C2×C151semidirect
295. #2041C2×C151semidirect
296. #2011C2×C151semidirect
297. #1985C2×C151semidirect
298. #1961C2×C151semidirect
299. #1879C2×C151semidirect
300. #1864C2×C151semidirect
301. #1804C2×C151semidirect
429. C2×D4#41×C151semidirect
455. C2×C8#41×C151semidirect

Maximal subgroups

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

subgroupindex
C2×#550×C1512
C2×#459×C1512
C2×#442×C1512
#2580×C1512
#2041×C1512
#2011×C1512
#1985×C1512
#1961×C1512
#1879×C1512
#1864×C1512
#1804×C1512
#24196151