Finite Group Databasebeta

← C151×#22417 #50327342

Subgroups — C151×#22417 #50327342

Order 38656.

1490 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×#547×C151C211yesmaximal, characteristic
2C2×C8×D4×C151C211yesmaximal, characteristic, complemented
3C2×#416×C151C212yesmaximal, complemented
4#2354×C151C211yesmaximal, characteristic, complemented
5#1981×C151C211yesmaximal, characteristic, complemented
6#1956×C151C211yesmaximal, characteristic, complemented
7#1892×C151C212yesmaximal, complemented
8#1873×C151C212yesmaximal, complemented
9#1802×C151C211yesmaximal, characteristic, complemented
10#1788×C151C212yesmaximal, complemented
11C4×#102×C151C211yesmaximal, characteristic, complemented
12C22×#41×C151C2212yes—
13C23×C8×C151C2212yes—
14#547×C151—24no—
15#547×C151C418yescomplemented
16C2×C4⋊Q8×C151C2211yescharacteristic
17C2×#123×C151—22no—
18C2×C22⋊Q8×C151C2212yes—
19C2×#121×C151—21no—
20C2×C4×D4×C151C2211yescharacteristic
21C2×C4×D4×C151C2211yescharacteristic
22C2×#117×C151C2212yes—
23C22×C4⋊C4×C151—21no—
24C8×D4×C151—24no—
25C2×C4⋊C8×C151C2211yescharacteristic
26#416×C151—28no—
27C2×#103×C151C2212yes—
28C2×#103×C151C2212yes—
29C2×#103×C151C2212yes—
30C2×#103×C151C2212yes—
31C2×#102×C151C2212yes—
32C2×#102×C151C2211yescharacteristic
33C2×#102×C151C2211yescharacteristic
34C2×C22⋊C8×C151C2212yes—
35C2×C4×C8×C151C2211yescharacteristic
36#390×C151—21no—
37#388×C151—22no—
38#384×C151C2211yescharacteristic
39#380×C151C2212yes—
40C4×C4⋊C4×C151—21no—
41C4×C4⋊C4×C151C2211yescharacteristic
42#340×C151C2211yescharacteristic
43#340×C151C2212yes—
44#340×C151C2211yescharacteristic
45C2×#41×C151—24no—
46C2×#41×C151—24no—
47C2×#41×C151—24no—
48C2×#41×C151—42no—
49C2×#41×C151—42no—
50C2×#41×C151C2×C418yes—
51C22×Q8×C151C2312yes—
52C22×D4×C151—22no—
53C22×D4×C151D411yescharacteristic
54C22×D4×C151C2311yescharacteristic
55C23×C4×C151—21no—
56C23×C4×C151—22no—
57C23×C4×C151C2312yes—
58C22×C8×C151—24no—
59C22×C8×C151—24no—
60C22×C8×C151—42no—
61C22×C8×C151C2311yescharacteristic
62C22×C8×C151C2312yes—
63C22×C8×C151C2311yescharacteristic
64C4⋊Q8×C151—22no—
65C4⋊Q8×C151C2×C414yes—
66#123×C151—216no—
67C22⋊Q8×C151—24no—
68C22⋊Q8×C151C2×C418yes—
69#121×C151—28no—
70C4×D4×C151—22no—
71C4×D4×C151C2×C414yes—
72C4×D4×C151C2×C414yes—
73C4×D4×C151D414yes—
74#117×C151—24no—
75#117×C151—42no—
76C2×C4⋊C4×C151—21no—
77C2×C4⋊C4×C151—22no—
78C2×C4⋊C4×C151—21no—
79C2×C4⋊C4×C151—28no—
80C2×C4⋊C4×C151—21no—
81C2×C4⋊C4×C151—21no—
82C2×C4⋊C4×C151D411yescharacteristic
83C2×C4⋊C4×C151C2311yescharacteristic
84C2×C4⋊C4×C151C2312yes—
85C2×C4⋊C4×C151C2311yescharacteristic
86C2×C4⋊C4×C151C2311yescharacteristic
87C2×C22⋊C4×C151—21no—
88C2×C22⋊C4×C151—22no—
89C2×C22⋊C4×C151—22no—
90C2×C22⋊C4×C151—22no—
91C2×C22⋊C4×C151D412yes—
92C2×C42×C151—21no—
93C2×C42×C151—22no—
94C2×C42×C151C2311yescharacteristic
95C4⋊C8×C151—22no—
96#103×C151—24no—
97#103×C151—24no—
98#103×C151—42no—
99#103×C151—42no—
100#102×C151—24no—
101#102×C151—22no—
102#102×C151D414yescomplemented
103C22⋊C8×C151—24no—
104C4×C8×C151—22no—
105#95×C151—22no—
106#95×C151—21no—
107C24×C151—21no—
108C24×C151C2×D412yes—
109#41×C151—216no—
110#41×C151—48no—
111#41×C151—48no—
112#41×C151—48no—
113C2×Q8×C151—22no—
114C2×Q8×C151—22no—
115C2×Q8×C151—22no—
116C2×Q8×C151—22no—
117C2×Q8×C151—22no—
118C2×Q8×C151C22×C414yes—
119C2×D4×C151—28no—
120C2×D4×C151—22no—
121C2×D4×C151—22no—
122C2×D4×C151—21no—
123C2×D4×C151—21no—
124C2×D4×C151—21no—
125C2×D4×C151—44no—
126C2×D4×C151—44no—
127C2×D4×C151C22⋊C414yes—
128C2×D4×C151C22×C412yes—
129C2×D4×C151C2×D412yes—
130C2×D4×C151#4112yes—
131C22×C4×C151—22no—
132C22×C4×C151—22no—
133C22×C4×C151—22no—
134C22×C4×C151—22no—
135C22×C4×C151—21no—
136C22×C4×C151—21no—
137C22×C4×C151—22no—
138C22×C4×C151—24no—
139C22×C4×C151—28no—
140C22×C4×C151—21no—
141C22×C4×C151—22no—
142C22×C4×C151—44no—
143C22×C4×C151—44no—
144C22×C4×C151—42no—
145C22×C4×C151—42no—
146C22×C4×C151C22×C414yes—
147C22×C4×C151C2×D412yes—
148C22×C4×C151C2×D411yescharacteristic
149C22×C4×C151C2×D414yes—
150C22×C4×C151C2×D411yescharacteristic
151C22×C4×C151C2411yescharacteristic
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—21no—
159C2×C8×C151—22no—
160C2×C8×C151—48no—
161C2×C8×C151C2×D412yes—
162C4⋊C4×C151—24no—
163C4⋊C4×C151—28no—
164C4⋊C4×C151—24no—
165C4⋊C4×C151—21no—
166C4⋊C4×C151—21no—
167C4⋊C4×C151—22no—
168C4⋊C4×C151—21no—
169C4⋊C4×C151—21no—
170C4⋊C4×C151—22no—
171C4⋊C4×C151—42no—
172C4⋊C4×C151—81no—
173C4⋊C4×C151C22⋊C414yes—
174C4⋊C4×C151C22×C412yes—
175C4⋊C4×C151C2×D412yes—
176C22⋊C4×C151—28no—
177C22⋊C4×C151—24no—
178C22⋊C4×C151—44no—
179C22⋊C4×C151—82no—
180C22⋊C4×C151C22⋊C418yes—
181C42×C151—44no—
182C42×C151—42no—
183C42×C151C22×C412yes—
184C42×C151C2×D412yes—
185C23×C151—22no—
186C23×C151—22no—
187C23×C151—22no—
188C23×C151—22no—
189C23×C151—22no—
190C23×C151—22no—
191C23×C151—22no—
192C23×C151—22no—
193C23×C151—22no—
194C23×C151—41no—
195C23×C151—41no—
196C23×C151—41no—
197C23×C151—41no—
198C23×C151C2×C22⋊C414yes—
199C23×C151C22×D411yescharacteristic
200Q8×C151—24no—
201Q8×C151—24no—
202Q8×C151—42no—
203Q8×C151—42no—
204D4×C151—22no—
205D4×C151—22no—
206D4×C151—22no—
207D4×C151—28no—
208D4×C151—416no—
209D4×C151C4×D414yes—
210C2×C4×C151—22no—
211C2×C4×C151—22no—
212C2×C4×C151—21no—
213C2×C4×C151—21no—
214C2×C4×C151—24no—
215C2×C4×C151—24no—
216C2×C4×C151—24no—
217C2×C4×C151—24no—
218C2×C4×C151—24no—
219C2×C4×C151—22no—
220C2×C4×C151—22no—
221C2×C4×C151—416no—
222C2×C4×C151—42no—
223C2×C4×C151—42no—
224C2×C4×C151—41no—
225C2×C4×C151—41no—
226C2×C4×C151—41no—
227C2×C4×C151—41no—
228C2×C4×C151—48no—
229C2×C4×C151—42no—
230C2×C4×C151—41no—
231C2×C4×C151—41no—
232C2×C4×C151—42no—
233C2×C4×C151—41no—
234C2×C4×C151—42no—
235C2×C4×C151C2×C22⋊C412yes—
236C2×C4×C151C2×C22⋊C414yes—
237C2×C4×C151C2×C22⋊C412yes—
238C2×C4×C151#13512yes—
239C2×C4×C151#13512yes—
240C2×C4×C151C23×C411yescharacteristic
241C2×C4×C151C22×D411yescharacteristic
242C2×C4×C151C22×D411yescharacteristic
243C2×C4×C151C2×#4111yescharacteristic
244C2×C4×C151H(5,𝔽2)11yescharacteristic
245C2×C4×C151H(5,𝔽2)11yescharacteristic
246C8×C151—22no—
247C8×C151—42no—
248C8×C151—41no—
249C22×C151—24no—
250C22×C151—24no—
251C22×C151—24no—
252C22×C151—24no—
253C22×C151—42no—
254C22×C151—42no—
255C22×C151—42no—
256C22×C151—42no—
257C22×C151—42no—
258C22×C151—42no—
259C22×C151—42no—
260C22×C151—42no—
261C22×C151—42no—
262C22×C151—42no—
263C22×C151C22×C22⋊C411yescharacteristic
264C22×C151D4211yescharacteristic
265C22×C151#54611yescharacteristic
266C22×C151C2×#13511yescharacteristic
267C22×C151C2×#13511yescharacteristic
268C22×C151#57711yescharacteristic
269C22×C151#57811yescharacteristic
270C4×C151—24no—
271C4×C151—22no—
272C4×C151—44no—
273C4×C151—42no—
274C4×C151—42no—
275C4×C151—82no—
276C4×C151—81no—
277C4×C151#41614yescomplemented
278C4×C151C2×C4×D411yescharacteristic
279C4×C151#51811yescharacteristic
280C4×C151D4211yescharacteristic
281C4×C151#54611yescharacteristic
282C2×C151—44no—
283C2×C151—44no—
284C2×C151D4×C22⋊C411yescharacteristic
285C2×C151C2×#41611yescharacteristic
286C2×C151#289811yescharacteristic
287C2×C151#328311yescharacteristic
288C2×C151#328411yescharacteristic
289C2×C151#330211yescharacteristic
290C2×C151#330311yescharacteristic
291#22417C15111yesmaximal, characteristic, direct product factor, Sylow
292C151#2241711yescharacteristic, direct product factor, Sylow
293C2×#547C2×C15111yescharacteristic
294C2×C8×D4C2×C15111yescharacteristic, complemented
295C2×#416C2×C15112yescomplemented
296#2354C2×C15111yescharacteristic, complemented
297#1981C2×C15111yescharacteristic, complemented
298#1956C2×C15111yescharacteristic, complemented
299#1892C2×C15112yescomplemented
300#1873C2×C15112yescomplemented
301#1802C2×C15111yescharacteristic, complemented
302#1788C2×C15112yescomplemented
303C4×#102C2×C15111yescharacteristic, complemented
304C22×#41C22×C15112yes—
305C23×C8C22×C15112yes—
306#547—24no—
307#547C4×C15118yescomplemented
308C2×C4⋊Q8C22×C15111yescharacteristic
309C2×#123—22no—
310C2×C22⋊Q8C22×C15112yes—
311C2×#121—21no—
312C2×C4×D4C22×C15111yescharacteristic
313C2×C4×D4C22×C15111yescharacteristic
314C2×#117C22×C15112yes—
315C22×C4⋊C4—21no—
316C8×D4—24no—
317C2×C4⋊C8C22×C15111yescharacteristic
318#416—28no—
319C2×#103C22×C15112yes—
320C2×#103C22×C15112yes—
321C2×#103C22×C15112yes—
322C2×#103C22×C15112yes—
323C2×#102C22×C15112yes—
324C2×#102C22×C15111yescharacteristic
325C2×#102C22×C15111yescharacteristic
326C2×C22⋊C8C22×C15112yes—
327C2×C4×C8C22×C15111yescharacteristic
328#390—21no—
329#388—22no—
330#384C22×C15111yescharacteristic
331#380C22×C15112yes—
332C4×C4⋊C4—21no—
333C4×C4⋊C4C22×C15111yescharacteristic
334#340C22×C15112yes—
335#340C22×C15111yescharacteristic
336#340C22×C15111yescharacteristic
337C2×#41—24no—
338C2×#41—24no—
339C2×#41—24no—
340C2×#41—42no—
341C2×#41—42no—
342C2×#41C2×C4×C15118yes—
343C22×Q8C23×C15112yes—
344C22×D4—22no—
345C22×D4D4×C15111yescharacteristic
346C22×D4C23×C15111yescharacteristic
347C23×C4—21no—
348C23×C4—22no—
349C23×C4C23×C15112yes—
350C22×C8—24no—
351C22×C8—24no—
352C22×C8—42no—
353C22×C8C23×C15112yes—
354C22×C8C23×C15111yescharacteristic
355C22×C8C23×C15111yescharacteristic
356C4⋊Q8—22no—
357C4⋊Q8C2×C4×C15114yes—
358#123—216no—
359C22⋊Q8—24no—
360C22⋊Q8C2×C4×C15118yes—
361#121—28no—
362C4×D4—22no—
363C4×D4C2×C4×C15114yes—
364C4×D4C2×C4×C15114yes—
365C4×D4D4×C15114yes—
366#117—24no—
367#117—42no—
368C2×C4⋊C4—21no—
369C2×C4⋊C4—22no—
370C2×C4⋊C4—21no—
371C2×C4⋊C4—28no—
372C2×C4⋊C4—21no—
373C2×C4⋊C4—21no—
374C2×C4⋊C4D4×C15111yescharacteristic
375C2×C4⋊C4C23×C15112yes—
376C2×C4⋊C4C23×C15111yescharacteristic
377C2×C4⋊C4C23×C15111yescharacteristic
378C2×C4⋊C4C23×C15111yescharacteristic
379C2×C22⋊C4—22no—
380C2×C22⋊C4—21no—
381C2×C22⋊C4—22no—
382C2×C22⋊C4—22no—
383C2×C22⋊C4D4×C15112yes—
384C2×C42—22no—
385C2×C42—21no—
386C2×C42C23×C15111yescharacteristic
387C4⋊C8—22no—
388#103—24no—
389#103—24no—
390#103—42no—
391#103—42no—
392#102—22no—
393#102—24no—
394#102D4×C15114yescomplemented
395C22⋊C8—24no—
396C4×C8—22no—
397#95—22no—
398#95—21no—
399C24—21no—
400C24C2×D4×C15112yes—
401#41—216no—
402#41—48no—
403#41—48no—
404#41—48no—
405C2×Q8—22no—
406C2×Q8—22no—
407C2×Q8—22no—
408C2×Q8—22no—
409C2×Q8—22no—
410C2×Q8C22×C4×C15114yes—
411C2×D4—28no—
412C2×D4—22no—
413C2×D4—22no—
414C2×D4—21no—
415C2×D4—21no—
416C2×D4—21no—
417C2×D4—44no—
418C2×D4—44no—
419C2×D4C22⋊C4×C15114yes—
420C2×D4C22×C4×C15112yes—
421C2×D4C2×D4×C15112yes—
422C2×D4#41×C15112yes—
423C22×C4—22no—
424C22×C4—22no—
425C22×C4—22no—
426C22×C4—22no—
427C22×C4—21no—
428C22×C4—21no—
429C22×C4—22no—
430C22×C4—24no—
431C22×C4—28no—
432C22×C4—21no—
433C22×C4—22no—
434C22×C4—44no—
435C22×C4—44no—
436C22×C4—42no—
437C22×C4—42no—
438C22×C4C22×C4×C15114yes—
439C22×C4C2×D4×C15112yes—
440C22×C4C2×D4×C15111yescharacteristic
441C22×C4C2×D4×C15114yes—
442C22×C4C2×D4×C15111yescharacteristic
443C22×C4C24×C15111yescharacteristic
444C2×C8—21no—
445C2×C8—21no—
446C2×C8—21no—
447C2×C8—22no—
448C2×C8—22no—
449C2×C8—21no—
450C2×C8—21no—
451C2×C8—22no—
452C2×C8—48no—
453C2×C8C2×D4×C15112yes—
454C4⋊C4—24no—
455C4⋊C4—28no—
456C4⋊C4—24no—
457C4⋊C4—21no—
458C4⋊C4—21no—
459C4⋊C4—22no—
460C4⋊C4—21no—
461C4⋊C4—21no—
462C4⋊C4—22no—
463C4⋊C4—42no—
464C4⋊C4—81no—
465C4⋊C4C22⋊C4×C15114yes—
466C4⋊C4C22×C4×C15112yes—
467C4⋊C4C2×D4×C15112yes—
468C22⋊C4—28no—
469C22⋊C4—24no—
470C22⋊C4—44no—
471C22⋊C4—82no—
472C22⋊C4C22⋊C4×C15118yes—
473C42—44no—
474C42—42no—
475C42C22×C4×C15112yes—
476C42C2×D4×C15112yes—
477C23—22no—
478C23—22no—
479C23—22no—
480C23—22no—
481C23—22no—
482C23—22no—
483C23—22no—
484C23—22no—
485C23—22no—
486C23—41no—
487C23—41no—
488C23—41no—
489C23—41no—
490C23C2×C22⋊C4×C15114yes—
491C23C22×D4×C15111yescharacteristic
492Q8—24no—
493Q8—24no—
494Q8—42no—
495Q8—42no—
496D4—28no—
497D4—22no—
498D4—22no—
499D4—22no—
500D4—416no—
501D4C4×D4×C15114yes—
502C2×C4—22no—
503C2×C4—22no—
504C2×C4—21no—
505C2×C4—21no—
506C2×C4—24no—
507C2×C4—24no—
508C2×C4—24no—
509C2×C4—24no—
510C2×C4—22no—
511C2×C4—24no—
512C2×C4—22no—
513C2×C4—416no—
514C2×C4—42no—
515C2×C4—42no—
516C2×C4—41no—
517C2×C4—41no—
518C2×C4—41no—
519C2×C4—41no—
520C2×C4—48no—
521C2×C4—42no—
522C2×C4—41no—
523C2×C4—41no—
524C2×C4—42no—
525C2×C4—41no—
526C2×C4—42no—
527C2×C4C2×C22⋊C4×C15112yes—
528C2×C4C2×C22⋊C4×C15114yes—
529C2×C4C2×C22⋊C4×C15112yes—
530C2×C4#135×C15112yes—
531C2×C4#135×C15112yes—
532C2×C4C23×C4×C15111yescharacteristic
533C2×C4C22×D4×C15111yescharacteristic
534C2×C4C22×D4×C15111yescharacteristic
535C2×C4C2×#41×C15111yescharacteristic
536C2×C4H(5,𝔽2)×C15111yescharacteristic
537C2×C4H(5,𝔽2)×C15111yescharacteristic
538C8—22no—
539C8—42no—
540C8—41no—
541C22—24no—
542C22—24no—
543C22—24no—
544C22—24no—
545C22—42no—
546C22—42no—
547C22—42no—
548C22—42no—
549C22—42no—
550C22—42no—
551C22—42no—
552C22—42no—
553C22—42no—
554C22—42no—
555C22C22×C22⋊C4×C15111yescharacteristic
556C22D42×C15111yescharacteristic
557C22#546×C15111yescharacteristic
558C22C2×#135×C15111yescharacteristic
559C22C2×#135×C15111yescharacteristic
560C22#577×C15111yescharacteristic
561C22#578×C15111yescharacteristic
562C4—24no—
563C4—22no—
564C4—44no—
565C4—42no—
566C4—42no—
567C4—82no—
568C4—81no—
569C4#416×C15114yescomplemented
570C4C2×C4×D4×C15111yescharacteristic
571C4#518×C15111yescharacteristic
572C4D42×C15111yescharacteristic
573C4#546×C15111yescharacteristic
574C2—44no—
575C2—44no—
576C2D4×C22⋊C4×C15111yescharacteristic
577C2C2×#416×C15111yescharacteristic
578C2#2898×C15111yescharacteristic
579C2#3283×C15111yescharacteristic
580C2#3284×C15111yescharacteristic
581C2#3302×C15111yescharacteristic
582C2#3303×C15111yescharacteristic
subgroupG/H
center, socleC23×C151C22×D4
commutatorC2×C4C23×C4×C151
Frattini, cosocleC22×C4C24×C151
prime radicalC2×#547×C151C2
LCSG ▷ C2×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
2. C2×C8×D4×C151C2semidirect
3. C2×#416×C151C2semidirect
4. #2354×C151C2semidirect
5. #1981×C151C2semidirect
6. #1956×C151C2semidirect
7. #1892×C151C2semidirect
8. #1873×C151C2semidirect
9. #1802×C151C2semidirect
10. #1788×C151C2semidirect
11. C4×#102×C151C2semidirect
15. #547×C151C4semidirect
102. #102×C151D4semidirect
277. C4×C151#416semidirect
291. #22417C151direct (N × H)
292. C151#22417direct (N × H)
294. C2×C8×D4C2×C151semidirect
295. C2×#416C2×C151semidirect
296. #2354C2×C151semidirect
297. #1981C2×C151semidirect
298. #1956C2×C151semidirect
299. #1892C2×C151semidirect
300. #1873C2×C151semidirect
301. #1802C2×C151semidirect
302. #1788C2×C151semidirect
303. C4×#102C2×C151semidirect
307. #547C4×C151semidirect
394. #102D4×C151semidirect
569. C4#416×C151semidirect

Maximal subgroups

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

subgroupindex
C2×#547×C1512
C2×C8×D4×C1512
C2×#416×C1512
#2354×C1512
#1981×C1512
#1956×C1512
#1892×C1512
#1873×C1512
#1802×C1512
#1788×C1512
C4×#102×C1512
#22417151