Finite Group Databasebeta

← C151×#24186 #50329111

Subgroups — C151×#24186 #50329111

Order 38656.

1214 conjugacy classes of subgroups.

The subgroup lattice has 584 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#559×C151C211yesmaximal, characteristic, complemented
2C2×#459×C151C211yesmaximal, characteristic
3C2×C4×SD16×C151C211yesmaximal, characteristic, complemented
4#2538×C151C211yesmaximal, characteristic, complemented
5#2042×C151C212yesmaximal, complemented
6#2012×C151C212yesmaximal, complemented
7#1984×C151C211yesmaximal, characteristic, complemented
8#1957×C151C211yesmaximal, characteristic, complemented
9#1879×C151C212yesmaximal, complemented
10#1864×C151C212yesmaximal, complemented
11#1803×C151C211yesmaximal, characteristic, complemented
12C22×SD16×C151C2211yescharacteristic
13C22×D8×C151C2212yes—
14#559×C151—24no—
15#559×C151—24no—
16C2×#127×C151C2211yescharacteristic
17C2×#124×C151—21no—
18C2×#124×C151C2212yes—
19C2×#123×C151—22no—
20C2×C22⋊Q8×C151—21no—
21C2×C4×Q8×C151C2211yescharacteristic
22C2×C4×Q8×C151C2211yescharacteristic
23C2×C4×D4×C151—21no—
24C2×C4×D4×C151C2212yes—
25C2×C4×D4×C151C2211yescharacteristic
26#459×C151—24no—
27C4×SD16×C151—24no—
28C2×#106×C151C2211yescharacteristic
29C2×C4⋊C8×C151C2211yescharacteristic
30C2×#103×C151C2211yescharacteristic
31C2×#103×C151C2212yes—
32C2×#102×C151C2212yes—
33C2×#102×C151C2212yes—
34C2×#102×C151C2211yescharacteristic
35C2×#102×C151C2212yes—
36C2×C4×C8×C151C2211yescharacteristic
37#396×C151—22no—
38#390×C151C2212yes—
39#389×C151C2212yes—
40#384×C151C2211yescharacteristic
41#380×C151—21no—
42#340×C151C2212yes—
43#336×C151C2212yes—
44#336×C151C2212yes—
45C22×Q8×C151D411yescharacteristic
46C22×Q8×C151C2311yescharacteristic
47C22×D4×C151—21no—
48C22×D4×C151—21no—
49C22×D4×C151C2312yes—
50C22×D4×C151C2311yescharacteristic
51C23×C4×C151—22no—
52C23×C4×C151—21no—
53C2×SD16×C151—22no—
54C2×SD16×C151—22no—
55C2×SD16×C151—22no—
56C2×D8×C151—24no—
57C2×D8×C151—24no—
58C2×D8×C151—42no—
59C22×C8×C151C2312yes—
60C22×C8×C151C2311yescharacteristic
61C22×C8×C151C2311yescharacteristic
62#127×C151—22no—
63#127×C151D414yes—
64#124×C151—28no—
65#124×C151—24no—
66#124×C151—24no—
67#123×C151—216no—
68C22⋊Q8×C151—44no—
69C4×Q8×C151—22no—
70C4×Q8×C151—22no—
71C4×Q8×C151—22no—
72C4×Q8×C151D414yes—
73C4×D4×C151—28no—
74C4×D4×C151—24no—
75C4×D4×C151—24no—
76C4×D4×C151—22no—
77C4×D4×C151—22no—
78C2×C4⋊C4×C151—21no—
79C2×C4⋊C4×C151—21no—
80C2×C4⋊C4×C151—22no—
81C2×C4⋊C4×C151—21no—
82C2×C4⋊C4×C151D411yescharacteristic
83C2×C4⋊C4×C151D412yes—
84C2×C4⋊C4×C151C2312yes—
85C2×C4⋊C4×C151C2311yescharacteristic
86C2×C4⋊C4×C151C2311yescharacteristic
87C2×C22⋊C4×C151—22no—
88C2×C22⋊C4×C151—22no—
89C2×C22⋊C4×C151—22no—
90C2×C22⋊C4×C151—22no—
91C2×C22⋊C4×C151—21no—
92C2×C22⋊C4×C151—22no—
93C2×C42×C151—21no—
94C2×C42×C151C2312yes—
95C2×C42×C151C2311yescharacteristic
96#106×C151—22no—
97C4⋊C8×C151—22no—
98#103×C151—22no—
99#103×C151—42no—
100#102×C151—24no—
101#102×C151—24no—
102#102×C151—22no—
103#102×C151—42no—
104C4×C8×C151—22no—
105#95×C151—22no—
106C24×C151—21no—
107C24×C151—22no—
108C2×Q8×C151—22no—
109C2×Q8×C151—22no—
110C2×Q8×C151—22no—
111C2×Q8×C151—21no—
112C2×Q8×C151—21no—
113C2×Q8×C151—21no—
114C2×Q8×C151—21no—
115C2×Q8×C151—21no—
116C2×Q8×C151C2×D412yes—
117C2×D4×C151—24no—
118C2×D4×C151—24no—
119C2×D4×C151—21no—
120C2×D4×C151—21no—
121C2×D4×C151—22no—
122C2×D4×C151—22no—
123C2×D4×C151—22no—
124C2×D4×C151—21no—
125C2×D4×C151—22no—
126C2×D4×C151—21no—
127C2×D4×C151—22no—
128C2×D4×C151—21no—
129C2×D4×C151—42no—
130C2×D4×C151—42no—
131C2×D4×C151—81no—
132C2×D4×C151—81no—
133C2×D4×C151C2×D414yes—
134C2×D4×C151#4112yes—
135C22×C4×C151—21no—
136C22×C4×C151—21no—
137C22×C4×C151—28no—
138C22×C4×C151—21no—
139C22×C4×C151—22no—
140C22×C4×C151—42no—
141C22×C4×C151—42no—
142C22×C4×C151—42no—
143C22×C4×C151—82no—
144C22×C4×C151—82no—
145C22×C4×C151C2×D412yes—
146C22×C4×C151C2×D412yes—
147C22×C4×C151C2×D411yescharacteristic
148C22×C4×C151C2×D411yescharacteristic
149C22×C4×C151C2411yescharacteristic
150SD16×C151—28no—
151D8×C151—48no—
152C2×C8×C151—21no—
153C2×C8×C151—21no—
154C2×C8×C151—21no—
155C2×C8×C151—22no—
156C2×C8×C151—22no—
157C2×C8×C151—21no—
158C2×C8×C151—22no—
159C2×C8×C151—21no—
160C2×C8×C151#4112yes—
161C4⋊C4×C151—24no—
162C4⋊C4×C151—22no—
163C4⋊C4×C151—24no—
164C4⋊C4×C151—21no—
165C4⋊C4×C151—21no—
166C4⋊C4×C151—21no—
167C4⋊C4×C151—22no—
168C4⋊C4×C151—22no—
169C4⋊C4×C151—44no—
170C4⋊C4×C151—42no—
171C4⋊C4×C151—81no—
172C4⋊C4×C151C2×D412yes—
173C22⋊C4×C151—28no—
174C22⋊C4×C151—28no—
175C22⋊C4×C151—28no—
176C22⋊C4×C151—44no—
177C22⋊C4×C151—42no—
178C22⋊C4×C151—82no—
179C42×C151—24no—
180C42×C151—22no—
181C42×C151—22no—
182C42×C151C2×D412yes—
183C42×C151C2×D412yes—
184C23×C151—24no—
185C23×C151—22no—
186C23×C151—41no—
187C23×C151—42no—
188C23×C151—41no—
189C23×C151—42no—
190C23×C151—41no—
191C23×C151—42no—
192C23×C151—41no—
193C23×C151—42no—
194C23×C151—41no—
195C23×C151—42no—
196C23×C151—41no—
197C23×C151—42no—
198C23×C151C22×D411yescharacteristic
199Q8×C151—22no—
200Q8×C151—22no—
201Q8×C151—41no—
202Q8×C151—41no—
203Q8×C151—44no—
204D4×C151—22no—
205D4×C151—22no—
206D4×C151—24no—
207D4×C151—24no—
208D4×C151—42no—
209D4×C151—41no—
210D4×C151—42no—
211D4×C151—41no—
212D4×C151—48no—
213D4×C151—84no—
214C2×C4×C151—21no—
215C2×C4×C151—21no—
216C2×C4×C151—22no—
217C2×C4×C151—22no—
218C2×C4×C151—22no—
219C2×C4×C151—22no—
220C2×C4×C151—22no—
221C2×C4×C151—22no—
222C2×C4×C151—22no—
223C2×C4×C151—22no—
224C2×C4×C151—41no—
225C2×C4×C151—41no—
226C2×C4×C151—41no—
227C2×C4×C151—41no—
228C2×C4×C151—41no—
229C2×C4×C151—42no—
230C2×C4×C151—41no—
231C2×C4×C151—42no—
232C2×C4×C151—41no—
233C2×C4×C151—42no—
234C2×C4×C151—88no—
235C2×C4×C151—84no—
236C2×C4×C151#12012yes—
237C2×C4×C151#12012yes—
238C2×C4×C151#13512yes—
239C2×C4×C151AGL(1,ℤ/8)12yes—
240C2×C4×C151C22×D411yescharacteristic
241C2×C4×C151C22×D411yescharacteristic
242C2×C4×C151C2×#4111yescharacteristic
243C2×C4×C151C2×#4111yescharacteristic
244C2×C4×C151H(5,𝔽2)11yescharacteristic
245C2×C4×C1512−1+411yescharacteristic
246C8×C151—22no—
247C8×C151—41no—
248C8×C151—42no—
249C22×C151—42no—
250C22×C151—42no—
251C22×C151—42no—
252C22×C151—44no—
253C22×C151—44no—
254C22×C151—44no—
255C22×C151—82no—
256C22×C151—82no—
257C22×C151—81no—
258C22×C151—82no—
259C22×C151—81no—
260C22×C151—82no—
261C22×C151—81no—
262C22×C151—81no—
263C22×C151C2×#12011yescharacteristic
264C22×C151#54811yescharacteristic
265C22×C151#55011yescharacteristic
266C22×C151C2×#13511yescharacteristic
267C22×C151C2×AGL(1,ℤ/8)11yescharacteristic
268C22×C151#57611yescharacteristic
269C22×C151#57711yescharacteristic
270C4×C151—22no—
271C4×C151—42no—
272C4×C151—42no—
273C4×C151—42no—
274C4×C151—42no—
275C4×C151—82no—
276C4×C151—81no—
277C4×C151#44914yes—
278C4×C151#52511yescharacteristic
279C4×C151#53711yescharacteristic
280C4×C151#54611yescharacteristic
281C4×C151#54711yescharacteristic
282C2×C151—82no—
283C2×C151—84no—
284C2×C151#240711yescharacteristic
285C2×C151C2×#44911yescharacteristic
286C2×C151#301211yescharacteristic
287C2×C151#336111yescharacteristic
288C2×C151#337311yescharacteristic
289C2×C151#339411yescharacteristic
290C2×C151#339911yescharacteristic
291#24186C15111yesmaximal, characteristic, direct product factor, Sylow
292C151#2418611yescharacteristic, direct product factor, Sylow
293C2×#559C2×C15111yescharacteristic, complemented
294C2×#459C2×C15111yescharacteristic
295C2×C4×SD16C2×C15111yescharacteristic, complemented
296#2538C2×C15111yescharacteristic, complemented
297#2042C2×C15112yescomplemented
298#2012C2×C15112yescomplemented
299#1984C2×C15111yescharacteristic, complemented
300#1957C2×C15111yescharacteristic, complemented
301#1879C2×C15112yescomplemented
302#1864C2×C15112yescomplemented
303#1803C2×C15111yescharacteristic, complemented
304C22×SD16C22×C15111yescharacteristic
305C22×D8C22×C15112yes—
306#559—24no—
307#559—24no—
308C2×#127C22×C15111yescharacteristic
309C2×#124—21no—
310C2×#124C22×C15112yes—
311C2×#123—22no—
312C2×C22⋊Q8—21no—
313C2×C4×Q8C22×C15111yescharacteristic
314C2×C4×Q8C22×C15111yescharacteristic
315C2×C4×D4—21no—
316C2×C4×D4C22×C15112yes—
317C2×C4×D4C22×C15111yescharacteristic
318#459—24no—
319C4×SD16—24no—
320C2×#106C22×C15111yescharacteristic
321C2×C4⋊C8C22×C15111yescharacteristic
322C2×#103C22×C15111yescharacteristic
323C2×#103C22×C15112yes—
324C2×#102C22×C15112yes—
325C2×#102C22×C15112yes—
326C2×#102C22×C15111yescharacteristic
327C2×#102C22×C15112yes—
328C2×C4×C8C22×C15111yescharacteristic
329#396—22no—
330#390C22×C15112yes—
331#389C22×C15112yes—
332#384C22×C15111yescharacteristic
333#380—21no—
334#340C22×C15112yes—
335#336C22×C15112yes—
336#336C22×C15112yes—
337C22×Q8D4×C15111yescharacteristic
338C22×Q8C23×C15111yescharacteristic
339C22×D4—21no—
340C22×D4—21no—
341C22×D4C23×C15111yescharacteristic
342C22×D4C23×C15112yes—
343C23×C4—22no—
344C23×C4—21no—
345C2×SD16—22no—
346C2×SD16—22no—
347C2×SD16—22no—
348C2×D8—24no—
349C2×D8—24no—
350C2×D8—42no—
351C22×C8C23×C15112yes—
352C22×C8C23×C15111yescharacteristic
353C22×C8C23×C15111yescharacteristic
354#127—22no—
355#127D4×C15114yes—
356#124—28no—
357#124—24no—
358#124—24no—
359#123—216no—
360C22⋊Q8—44no—
361C4×Q8—22no—
362C4×Q8—22no—
363C4×Q8—22no—
364C4×Q8D4×C15114yes—
365C4×D4—28no—
366C4×D4—24no—
367C4×D4—24no—
368C4×D4—22no—
369C4×D4—22no—
370C2×C4⋊C4—21no—
371C2×C4⋊C4—21no—
372C2×C4⋊C4—22no—
373C2×C4⋊C4—21no—
374C2×C4⋊C4D4×C15111yescharacteristic
375C2×C4⋊C4D4×C15112yes—
376C2×C4⋊C4C23×C15111yescharacteristic
377C2×C4⋊C4C23×C15112yes—
378C2×C4⋊C4C23×C15111yescharacteristic
379C2×C22⋊C4—22no—
380C2×C22⋊C4—22no—
381C2×C22⋊C4—22no—
382C2×C22⋊C4—21no—
383C2×C22⋊C4—22no—
384C2×C22⋊C4—22no—
385C2×C42—21no—
386C2×C42C23×C15112yes—
387C2×C42C23×C15111yescharacteristic
388#106—22no—
389C4⋊C8—22no—
390#103—22no—
391#103—42no—
392#102—24no—
393#102—24no—
394#102—22no—
395#102—42no—
396C4×C8—22no—
397#95—22no—
398C24—21no—
399C24—22no—
400C2×Q8—22no—
401C2×Q8—22no—
402C2×Q8—22no—
403C2×Q8—21no—
404C2×Q8—21no—
405C2×Q8—21no—
406C2×Q8—21no—
407C2×Q8—21no—
408C2×Q8C2×D4×C15112yes—
409C2×D4—24no—
410C2×D4—24no—
411C2×D4—21no—
412C2×D4—21no—
413C2×D4—22no—
414C2×D4—22no—
415C2×D4—22no—
416C2×D4—21no—
417C2×D4—22no—
418C2×D4—21no—
419C2×D4—22no—
420C2×D4—21no—
421C2×D4—42no—
422C2×D4—42no—
423C2×D4—81no—
424C2×D4—81no—
425C2×D4C2×D4×C15114yes—
426C2×D4#41×C15112yes—
427C22×C4—21no—
428C22×C4—21no—
429C22×C4—28no—
430C22×C4—21no—
431C22×C4—22no—
432C22×C4—42no—
433C22×C4—42no—
434C22×C4—42no—
435C22×C4—82no—
436C22×C4—82no—
437C22×C4C2×D4×C15112yes—
438C22×C4C2×D4×C15112yes—
439C22×C4C2×D4×C15111yescharacteristic
440C22×C4C2×D4×C15111yescharacteristic
441C22×C4C24×C15111yescharacteristic
442SD16—28no—
443D8—48no—
444C2×C8—21no—
445C2×C8—21no—
446C2×C8—21no—
447C2×C8—22no—
448C2×C8—22no—
449C2×C8—21no—
450C2×C8—22no—
451C2×C8—21no—
452C2×C8#41×C15112yes—
453C4⋊C4—24no—
454C4⋊C4—22no—
455C4⋊C4—24no—
456C4⋊C4—21no—
457C4⋊C4—21no—
458C4⋊C4—21no—
459C4⋊C4—22no—
460C4⋊C4—22no—
461C4⋊C4—44no—
462C4⋊C4—42no—
463C4⋊C4—81no—
464C4⋊C4C2×D4×C15112yes—
465C22⋊C4—28no—
466C22⋊C4—28no—
467C22⋊C4—28no—
468C22⋊C4—44no—
469C22⋊C4—42no—
470C22⋊C4—82no—
471C42—24no—
472C42—22no—
473C42—22no—
474C42C2×D4×C15112yes—
475C42C2×D4×C15112yes—
476C23—24no—
477C23—22no—
478C23—41no—
479C23—42no—
480C23—42no—
481C23—41no—
482C23—41no—
483C23—42no—
484C23—41no—
485C23—42no—
486C23—41no—
487C23—42no—
488C23—42no—
489C23—41no—
490C23C22×D4×C15111yescharacteristic
491Q8—22no—
492Q8—22no—
493Q8—44no—
494Q8—41no—
495Q8—41no—
496D4—22no—
497D4—22no—
498D4—24no—
499D4—24no—
500D4—48no—
501D4—42no—
502D4—41no—
503D4—42no—
504D4—41no—
505D4—84no—
506C2×C4—21no—
507C2×C4—21no—
508C2×C4—22no—
509C2×C4—22no—
510C2×C4—22no—
511C2×C4—22no—
512C2×C4—22no—
513C2×C4—22no—
514C2×C4—22no—
515C2×C4—22no—
516C2×C4—41no—
517C2×C4—41no—
518C2×C4—41no—
519C2×C4—41no—
520C2×C4—41no—
521C2×C4—42no—
522C2×C4—41no—
523C2×C4—42no—
524C2×C4—41no—
525C2×C4—42no—
526C2×C4—88no—
527C2×C4—84no—
528C2×C4#120×C15112yes—
529C2×C4#120×C15112yes—
530C2×C4#135×C15112yes—
531C2×C4AGL(1,ℤ/8)×C15112yes—
532C2×C4C22×D4×C15111yescharacteristic
533C2×C4C22×D4×C15111yescharacteristic
534C2×C4C2×#41×C15111yescharacteristic
535C2×C4C2×#41×C15111yescharacteristic
536C2×C4H(5,𝔽2)×C15111yescharacteristic
537C2×C42−1+4×C15111yescharacteristic
538C8—22no—
539C8—41no—
540C8—42no—
541C22—42no—
542C22—42no—
543C22—42no—
544C22—44no—
545C22—44no—
546C22—44no—
547C22—82no—
548C22—82no—
549C22—81no—
550C22—82no—
551C22—81no—
552C22—82no—
553C22—81no—
554C22—81no—
555C22C2×#120×C15111yescharacteristic
556C22#548×C15111yescharacteristic
557C22#550×C15111yescharacteristic
558C22C2×#135×C15111yescharacteristic
559C22C2×AGL(1,ℤ/8)×C15111yescharacteristic
560C22#576×C15111yescharacteristic
561C22#577×C15111yescharacteristic
562C4—22no—
563C4—42no—
564C4—42no—
565C4—42no—
566C4—42no—
567C4—82no—
568C4—81no—
569C4#449×C15114yes—
570C4#525×C15111yescharacteristic
571C4#537×C15111yescharacteristic
572C4#546×C15111yescharacteristic
573C4#547×C15111yescharacteristic
574C2—82no—
575C2—84no—
576C2#2407×C15111yescharacteristic
577C2C2×#449×C15111yescharacteristic
578C2#3012×C15111yescharacteristic
579C2#3361×C15111yescharacteristic
580C2#3373×C15111yescharacteristic
581C2#3394×C15111yescharacteristic
582C2#3399×C15111yescharacteristic
subgroupG/H
center, socleC23×C151C22×D4
commutator, Frattini, cosocleC22×C4C24×C151
prime radicalC2×#459×C151C2
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×#559×C151C2semidirect
3. C2×C4×SD16×C151C2semidirect
4. #2538×C151C2semidirect
5. #2042×C151C2semidirect
6. #2012×C151C2semidirect
7. #1984×C151C2semidirect
8. #1957×C151C2semidirect
9. #1879×C151C2semidirect
10. #1864×C151C2semidirect
11. #1803×C151C2semidirect
291. #24186C151direct (N × H)
292. C151#24186direct (N × H)
293. C2×#559C2×C151semidirect
295. C2×C4×SD16C2×C151semidirect
296. #2538C2×C151semidirect
297. #2042C2×C151semidirect
298. #2012C2×C151semidirect
299. #1984C2×C151semidirect
300. #1957C2×C151semidirect
301. #1879C2×C151semidirect
302. #1864C2×C151semidirect
303. #1803C2×C151semidirect

Maximal subgroups

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

subgroupindex
C2×#559×C1512
C2×#459×C1512
C2×C4×SD16×C1512
#2538×C1512
#2042×C1512
#2012×C1512
#1984×C1512
#1957×C1512
#1879×C1512
#1864×C1512
#1803×C1512
#24186151