Finite Group Databasebeta

← C151×#24118 #50329043

Subgroups — C151×#24118 #50329043

Order 38656.

1218 conjugacy classes of subgroups.

The subgroup lattice has 582 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#554×C151C211yesmaximal, characteristic, complemented
2C2×#476×C151C211yesmaximal, characteristic, complemented
3C2×C4×SD16×C151C211yesmaximal, characteristic, complemented
4#2537×C151C211yesmaximal, characteristic
5#2035×C151C212yesmaximal, complemented
6#2000×C151C212yesmaximal, complemented
7#1990×C151C211yesmaximal, characteristic, complemented
8#1954×C151C211yesmaximal, characteristic, complemented
9#1874×C151C212yesmaximal, complemented
10#1853×C151C212yesmaximal, complemented
11#1803×C151C211yesmaximal, characteristic, complemented
12C22×SD16×C151C2211yescharacteristic
13#554×C151—24no—
14#554×C151—24no—
15C2×C4⋊Q8×C151C2211yescharacteristic
16C2×#125×C151—21no—
17C2×C22⋊Q8×C151—22no—
18C2×C22⋊Q8×C151C2212yes—
19C2×#121×C151—21no—
20C2×#121×C151C2212yes—
21C2×C4×Q8×C151C2211yescharacteristic
22C2×C4×D4×C151—21no—
23C2×C4×D4×C151C2211yescharacteristic
24C2×C4×D4×C151C2211yescharacteristic
25C22×C4⋊C4×C151C2212yes—
26#476×C151—24no—
27C4×SD16×C151—24no—
28C2×#106×C151C2211yescharacteristic
29C2×#106×C151C2212yes—
30C2×C4⋊C8×C151C2211yescharacteristic
31C2×#103×C151C2211yescharacteristic
32C2×#103×C151C2212yes—
33C2×#102×C151C2211yescharacteristic
34C2×#102×C151C2212yes—
35C2×C22⋊C8×C151C2212yes—
36C2×C22⋊C8×C151C2212yes—
37C2×C4×C8×C151C2211yescharacteristic
38#394×C151—22no—
39#384×C151C2211yescharacteristic
40#380×C151—21no—
41#380×C151C2212yes—
42#340×C151C2212yes—
43#340×C151C2212yes—
44#340×C151C2212yes—
45C22×Q8×C151—21no—
46C22×Q8×C151C2311yescharacteristic
47C22×D4×C151—22no—
48C22×D4×C151D411yescharacteristic
49C22×D4×C151C2311yescharacteristic
50C23×C4×C151—21no—
51C23×C4×C151—22no—
52C23×C4×C151C2312yes—
53C2×SD16×C151—22no—
54C2×SD16×C151—22no—
55C2×SD16×C151—22no—
56C22×C8×C151C2311yescharacteristic
57C22×C8×C151C2312yes—
58C22×C8×C151C2311yescharacteristic
59C4⋊Q8×C151—22no—
60C4⋊Q8×C151D414yescomplemented
61#125×C151—28no—
62C22⋊Q8×C151—216no—
63C22⋊Q8×C151—24no—
64C22⋊Q8×C151—24no—
65#121×C151—24no—
66#121×C151—42no—
67#121×C151—44no—
68C4×Q8×C151—22no—
69C4×Q8×C151D414yescomplemented
70C4×D4×C151—28no—
71C4×D4×C151—22no—
72C4×D4×C151—22no—
73C4×D4×C151—22no—
74C4×D4×C151—22no—
75C2×C4⋊C4×C151—22no—
76C2×C4⋊C4×C151—21no—
77C2×C4⋊C4×C151—21no—
78C2×C4⋊C4×C151—22no—
79C2×C4⋊C4×C151—24no—
80C2×C4⋊C4×C151—24no—
81C2×C4⋊C4×C151—21no—
82C2×C4⋊C4×C151—21no—
83C2×C4⋊C4×C151D411yescharacteristic
84C2×C4⋊C4×C151C2312yes—
85C2×C4⋊C4×C151C2311yescharacteristic
86C2×C4⋊C4×C151C2311yescharacteristic
87C2×C4⋊C4×C151C2312yes—
88C2×C22⋊C4×C151—22no—
89C2×C22⋊C4×C151—21no—
90C2×C22⋊C4×C151—22no—
91C2×C22⋊C4×C151—22no—
92C2×C22⋊C4×C151D412yes—
93C2×C42×C151—21no—
94C2×C42×C151C2311yescharacteristic
95#106×C151—22no—
96#106×C151—24no—
97C4⋊C8×C151—22no—
98#103×C151—22no—
99#103×C151—42no—
100#102×C151—22no—
101#102×C151—24no—
102C22⋊C8×C151—24no—
103C22⋊C8×C151—42no—
104C4×C8×C151—22no—
105#95×C151—22no—
106C24×C151—21no—
107C24×C151C2×D412yes—
108C2×Q8×C151—24no—
109C2×Q8×C151—21no—
110C2×Q8×C151—21no—
111C2×Q8×C151—21no—
112C2×Q8×C151—21no—
113C2×Q8×C151—21no—
114C2×Q8×C151—81no—
115C2×Q8×C151—81no—
116C2×Q8×C151C2×D412yes—
117C2×D4×C151—22no—
118C2×D4×C151—22no—
119C2×D4×C151—21no—
120C2×D4×C151—21no—
121C2×D4×C151—21no—
122C2×D4×C151—21no—
123C2×D4×C151—21no—
124C2×D4×C151—44no—
125C2×D4×C151—44no—
126C2×D4×C151—82no—
127C2×D4×C151SD1614yescomplemented
128C2×D4×C151#4112yes—
129C22×C4×C151—21no—
130C22×C4×C151—21no—
131C22×C4×C151—22no—
132C22×C4×C151—28no—
133C22×C4×C151—22no—
134C22×C4×C151—22no—
135C22×C4×C151—22no—
136C22×C4×C151—22no—
137C22×C4×C151—22no—
138C22×C4×C151—22no—
139C22×C4×C151—21no—
140C22×C4×C151—22no—
141C22×C4×C151—42no—
142C22×C4×C151—42no—
143C22×C4×C151—42no—
144C22×C4×C151—82no—
145C22×C4×C151—82no—
146C22×C4×C151C2×D412yes—
147C22×C4×C151C2×D411yescharacteristic
148C22×C4×C151C2×D411yescharacteristic
149C22×C4×C151C2411yescharacteristic
150SD16×C151—28no—
151C2×C8×C151—21no—
152C2×C8×C151—21no—
153C2×C8×C151—21no—
154C2×C8×C151—22no—
155C2×C8×C151—22no—
156C2×C8×C151—21no—
157C2×C8×C151—22no—
158C2×C8×C151—21no—
159C2×C8×C151#4112yes—
160C4⋊C4×C151—28no—
161C4⋊C4×C151—28no—
162C4⋊C4×C151—24no—
163C4⋊C4×C151—24no—
164C4⋊C4×C151—22no—
165C4⋊C4×C151—21no—
166C4⋊C4×C151—22no—
167C4⋊C4×C151—21no—
168C4⋊C4×C151—21no—
169C4⋊C4×C151—22no—
170C4⋊C4×C151—22no—
171C4⋊C4×C151—42no—
172C4⋊C4×C151—81no—
173C4⋊C4×C151C2×D412yes—
174C4⋊C4×C151C2×D414yes—
175C22⋊C4×C151—28no—
176C22⋊C4×C151—24no—
177C22⋊C4×C151—44no—
178C22⋊C4×C151—44no—
179C22⋊C4×C151—42no—
180C42×C151—24no—
181C42×C151C2×D412yes—
182C42×C151C2×D412yes—
183C23×C151—22no—
184C23×C151—22no—
185C23×C151—22no—
186C23×C151—22no—
187C23×C151—22no—
188C23×C151—22no—
189C23×C151—22no—
190C23×C151—41no—
191C23×C151—41no—
192C23×C151—41no—
193C23×C151—41no—
194C23×C151—41no—
195C23×C151—41no—
196C23×C151C2×SD1614yes—
197C23×C151C22×D411yescharacteristic
198Q8×C151—22no—
199Q8×C151—22no—
200Q8×C151—41no—
201Q8×C151—41no—
202Q8×C151—84no—
203D4×C151—22no—
204D4×C151—22no—
205D4×C151—28no—
206D4×C151—41no—
207D4×C151—41no—
208D4×C151—88no—
209C2×C4×C151—21no—
210C2×C4×C151—21no—
211C2×C4×C151—24no—
212C2×C4×C151—22no—
213C2×C4×C151—22no—
214C2×C4×C151—22no—
215C2×C4×C151—22no—
216C2×C4×C151—22no—
217C2×C4×C151—41no—
218C2×C4×C151—41no—
219C2×C4×C151—42no—
220C2×C4×C151—41no—
221C2×C4×C151—42no—
222C2×C4×C151—41no—
223C2×C4×C151—42no—
224C2×C4×C151—42no—
225C2×C4×C151—42no—
226C2×C4×C151—42no—
227C2×C4×C151—41no—
228C2×C4×C151—42no—
229C2×C4×C151—41no—
230C2×C4×C151—42no—
231C2×C4×C151—41no—
232C2×C4×C151—42no—
233C2×C4×C151—88no—
234C2×C4×C151—84no—
235C2×C4×C151#12012yes—
236C2×C4×C151#12012yes—
237C2×C4×C151C2×SD1612yes—
238C2×C4×C151#13712yes—
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—24no—
249C22×C151—24no—
250C22×C151—24no—
251C22×C151—42no—
252C22×C151—42no—
253C22×C151—42no—
254C22×C151—42no—
255C22×C151—42no—
256C22×C151—42no—
257C22×C151—42no—
258C22×C151—81no—
259C22×C151—81no—
260C22×C151—81no—
261C22×C151—81no—
262C22×C151C2×#12011yescharacteristic
263C22×C151#54611yescharacteristic
264C22×C151#54711yescharacteristic
265C22×C151C22×SD1611yescharacteristic
266C22×C151C2×#13711yescharacteristic
267C22×C151#57611yescharacteristic
268C22×C151#57711yescharacteristic
269C4×C151—22no—
270C4×C151—42no—
271C4×C151—42no—
272C4×C151—42no—
273C4×C151—44no—
274C4×C151—81no—
275C4×C151—82no—
276C4×C151#44814yes—
277C4×C151#52511yescharacteristic
278C4×C151#53711yescharacteristic
279C4×C151#54811yescharacteristic
280C4×C151#55011yescharacteristic
281C2×C151—44no—
282C2×C151—82no—
283C2×C151#240711yescharacteristic
284C2×C151C2×#44811yescharacteristic
285C2×C151#301211yescharacteristic
286C2×C151#329511yescharacteristic
287C2×C151#333111yescharacteristic
288C2×C151#333511yescharacteristic
289C2×C151#335711yescharacteristic
290#24118C15111yesmaximal, characteristic, direct product factor, Sylow
291C151#2411811yescharacteristic, direct product factor, Sylow
292C2×#554C2×C15111yescharacteristic, complemented
293C2×#476C2×C15111yescharacteristic, complemented
294C2×C4×SD16C2×C15111yescharacteristic, complemented
295#2537C2×C15111yescharacteristic
296#2035C2×C15112yescomplemented
297#2000C2×C15112yescomplemented
298#1990C2×C15111yescharacteristic, complemented
299#1954C2×C15111yescharacteristic, complemented
300#1874C2×C15112yescomplemented
301#1853C2×C15112yescomplemented
302#1803C2×C15111yescharacteristic, complemented
303C22×SD16C22×C15111yescharacteristic
304#554—24no—
305#554—24no—
306C2×C4⋊Q8C22×C15111yescharacteristic
307C2×#125—21no—
308C2×C22⋊Q8—22no—
309C2×C22⋊Q8C22×C15112yes—
310C2×#121—21no—
311C2×#121C22×C15112yes—
312C2×C4×Q8C22×C15111yescharacteristic
313C2×C4×D4—21no—
314C2×C4×D4C22×C15111yescharacteristic
315C2×C4×D4C22×C15111yescharacteristic
316C22×C4⋊C4C22×C15112yes—
317#476—24no—
318C4×SD16—24no—
319C2×#106C22×C15111yescharacteristic
320C2×#106C22×C15112yes—
321C2×C4⋊C8C22×C15111yescharacteristic
322C2×#103C22×C15111yescharacteristic
323C2×#103C22×C15112yes—
324C2×#102C22×C15111yescharacteristic
325C2×#102C22×C15112yes—
326C2×C22⋊C8C22×C15112yes—
327C2×C22⋊C8C22×C15112yes—
328C2×C4×C8C22×C15111yescharacteristic
329#394—22no—
330#384C22×C15111yescharacteristic
331#380—21no—
332#380C22×C15112yes—
333#340C22×C15112yes—
334#340C22×C15112yes—
335#340C22×C15112yes—
336C22×Q8—21no—
337C22×Q8C23×C15111yescharacteristic
338C22×D4—22no—
339C22×D4D4×C15111yescharacteristic
340C22×D4C23×C15111yescharacteristic
341C23×C4—22no—
342C23×C4—21no—
343C23×C4C23×C15112yes—
344C2×SD16—22no—
345C2×SD16—22no—
346C2×SD16—22no—
347C22×C8C23×C15111yescharacteristic
348C22×C8C23×C15112yes—
349C22×C8C23×C15111yescharacteristic
350C4⋊Q8—22no—
351C4⋊Q8D4×C15114yescomplemented
352#125—28no—
353C22⋊Q8—216no—
354C22⋊Q8—24no—
355C22⋊Q8—24no—
356#121—24no—
357#121—42no—
358#121—44no—
359C4×Q8—22no—
360C4×Q8D4×C15114yescomplemented
361C4×D4—28no—
362C4×D4—22no—
363C4×D4—22no—
364C4×D4—22no—
365C4×D4—22no—
366C2×C4⋊C4—22no—
367C2×C4⋊C4—21no—
368C2×C4⋊C4—21no—
369C2×C4⋊C4—22no—
370C2×C4⋊C4—24no—
371C2×C4⋊C4—24no—
372C2×C4⋊C4—21no—
373C2×C4⋊C4—21no—
374C2×C4⋊C4D4×C15111yescharacteristic
375C2×C4⋊C4C23×C15111yescharacteristic
376C2×C4⋊C4C23×C15112yes—
377C2×C4⋊C4C23×C15111yescharacteristic
378C2×C4⋊C4C23×C15112yes—
379C2×C22⋊C4—22no—
380C2×C22⋊C4—22no—
381C2×C22⋊C4—21no—
382C2×C22⋊C4—22no—
383C2×C22⋊C4D4×C15112yes—
384C2×C42—21no—
385C2×C42C23×C15111yescharacteristic
386#106—22no—
387#106—24no—
388C4⋊C8—22no—
389#103—22no—
390#103—42no—
391#102—22no—
392#102—24no—
393C22⋊C8—24no—
394C22⋊C8—42no—
395C4×C8—22no—
396#95—22no—
397C24—21no—
398C24C2×D4×C15112yes—
399C2×Q8—24no—
400C2×Q8—21no—
401C2×Q8—21no—
402C2×Q8—21no—
403C2×Q8—21no—
404C2×Q8—21no—
405C2×Q8—81no—
406C2×Q8—81no—
407C2×Q8C2×D4×C15112yes—
408C2×D4—22no—
409C2×D4—22no—
410C2×D4—21no—
411C2×D4—21no—
412C2×D4—21no—
413C2×D4—21no—
414C2×D4—21no—
415C2×D4—44no—
416C2×D4—44no—
417C2×D4—82no—
418C2×D4SD16×C15114yescomplemented
419C2×D4#41×C15112yes—
420C22×C4—21no—
421C22×C4—21no—
422C22×C4—22no—
423C22×C4—28no—
424C22×C4—22no—
425C22×C4—22no—
426C22×C4—22no—
427C22×C4—22no—
428C22×C4—22no—
429C22×C4—22no—
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×C15111yescharacteristic
439C22×C4C2×D4×C15111yescharacteristic
440C22×C4C24×C15111yescharacteristic
441SD16—28no—
442C2×C8—21no—
443C2×C8—21no—
444C2×C8—21no—
445C2×C8—22no—
446C2×C8—22no—
447C2×C8—21no—
448C2×C8—22no—
449C2×C8—21no—
450C2×C8#41×C15112yes—
451C4⋊C4—28no—
452C4⋊C4—28no—
453C4⋊C4—24no—
454C4⋊C4—24no—
455C4⋊C4—22no—
456C4⋊C4—21no—
457C4⋊C4—22no—
458C4⋊C4—21no—
459C4⋊C4—21no—
460C4⋊C4—22no—
461C4⋊C4—22no—
462C4⋊C4—42no—
463C4⋊C4—81no—
464C4⋊C4C2×D4×C15112yes—
465C4⋊C4C2×D4×C15114yes—
466C22⋊C4—28no—
467C22⋊C4—24no—
468C22⋊C4—44no—
469C22⋊C4—44no—
470C22⋊C4—42no—
471C42—24no—
472C42C2×D4×C15112yes—
473C42C2×D4×C15112yes—
474C23—22no—
475C23—22no—
476C23—22no—
477C23—22no—
478C23—22no—
479C23—22no—
480C23—22no—
481C23—41no—
482C23—41no—
483C23—41no—
484C23—41no—
485C23—41no—
486C23—41no—
487C23C2×SD16×C15114yes—
488C23C22×D4×C15111yescharacteristic
489Q8—22no—
490Q8—22no—
491Q8—41no—
492Q8—41no—
493Q8—84no—
494D4—28no—
495D4—22no—
496D4—22no—
497D4—41no—
498D4—41no—
499D4—88no—
500C2×C4—21no—
501C2×C4—21no—
502C2×C4—22no—
503C2×C4—22no—
504C2×C4—22no—
505C2×C4—24no—
506C2×C4—22no—
507C2×C4—22no—
508C2×C4—41no—
509C2×C4—41no—
510C2×C4—41no—
511C2×C4—42no—
512C2×C4—41no—
513C2×C4—42no—
514C2×C4—42no—
515C2×C4—42no—
516C2×C4—42no—
517C2×C4—42no—
518C2×C4—41no—
519C2×C4—42no—
520C2×C4—41no—
521C2×C4—42no—
522C2×C4—41no—
523C2×C4—42no—
524C2×C4—88no—
525C2×C4—84no—
526C2×C4#120×C15112yes—
527C2×C4#120×C15112yes—
528C2×C4C2×SD16×C15112yes—
529C2×C4#137×C15112yes—
530C2×C4C22×D4×C15111yescharacteristic
531C2×C4C22×D4×C15111yescharacteristic
532C2×C4C2×#41×C15111yescharacteristic
533C2×C4C2×#41×C15111yescharacteristic
534C2×C4H(5,𝔽2)×C15111yescharacteristic
535C2×C42−1+4×C15111yescharacteristic
536C8—22no—
537C8—41no—
538C8—42no—
539C22—24no—
540C22—24no—
541C22—24no—
542C22—42no—
543C22—42no—
544C22—42no—
545C22—42no—
546C22—42no—
547C22—42no—
548C22—42no—
549C22—81no—
550C22—81no—
551C22—81no—
552C22—81no—
553C22C2×#120×C15111yescharacteristic
554C22#546×C15111yescharacteristic
555C22#547×C15111yescharacteristic
556C22C22×SD16×C15111yescharacteristic
557C22C2×#137×C15111yescharacteristic
558C22#576×C15111yescharacteristic
559C22#577×C15111yescharacteristic
560C4—22no—
561C4—42no—
562C4—42no—
563C4—42no—
564C4—44no—
565C4—81no—
566C4—82no—
567C4#448×C15114yes—
568C4#525×C15111yescharacteristic
569C4#537×C15111yescharacteristic
570C4#548×C15111yescharacteristic
571C4#550×C15111yescharacteristic
572C2—44no—
573C2—82no—
574C2#2407×C15111yescharacteristic
575C2C2×#448×C15111yescharacteristic
576C2#3012×C15111yescharacteristic
577C2#3295×C15111yescharacteristic
578C2#3331×C15111yescharacteristic
579C2#3335×C15111yescharacteristic
580C2#3357×C15111yescharacteristic
subgroupG/H
center, socleC23×C151C22×D4
commutator, Frattini, cosocleC22×C4C24×C151
prime radical#2537×C151C2
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C151 ◁ C2×C4×D4×C151 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×#554×C151C2semidirect
2. C2×#476×C151C2semidirect
3. C2×C4×SD16×C151C2semidirect
5. #2035×C151C2semidirect
6. #2000×C151C2semidirect
7. #1990×C151C2semidirect
8. #1954×C151C2semidirect
9. #1874×C151C2semidirect
10. #1853×C151C2semidirect
11. #1803×C151C2semidirect
60. C4⋊Q8×C151D4semidirect
69. C4×Q8×C151D4semidirect
127. C2×D4×C151SD16semidirect
290. #24118C151direct (N × H)
291. C151#24118direct (N × H)
292. C2×#554C2×C151semidirect
293. C2×#476C2×C151semidirect
294. C2×C4×SD16C2×C151semidirect
296. #2035C2×C151semidirect
297. #2000C2×C151semidirect
298. #1990C2×C151semidirect
299. #1954C2×C151semidirect
300. #1874C2×C151semidirect
301. #1853C2×C151semidirect
302. #1803C2×C151semidirect
351. C4⋊Q8D4×C151semidirect
360. C4×Q8D4×C151semidirect
418. C2×D4SD16×C151semidirect

Maximal subgroups

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

subgroupindex
C2×#554×C1512
C2×#476×C1512
C2×C4×SD16×C1512
#2537×C1512
#2035×C1512
#2000×C1512
#1990×C1512
#1954×C1512
#1874×C1512
#1853×C1512
#1803×C1512
#24118151