Finite Group Databasebeta

← C151×#24500 #50329425

Subgroups — C151×#24500 #50329425

Order 38656.

1270 conjugacy classes of subgroups.

The subgroup lattice has 626 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#447×C151C211yesmaximal, characteristic
2C2×#431×C151C211yesmaximal, characteristic, complemented
3#2854×C151C211yesmaximal, characteristic, complemented
4C2×#390×C151C211yesmaximal, characteristic, complemented
5#2067×C151C212yesmaximal, complemented
6#2054×C151C212yesmaximal, complemented
7#1970×C151C212yesmaximal, complemented
8#1934×C151C212yesmaximal, complemented
9#1874×C151C211yesmaximal, characteristic, complemented
10#1852×C151C211yesmaximal, characteristic, complemented
11#1786×C151C211yesmaximal, characteristic, complemented
12C23×D4×C151C2211yescharacteristic
13C22×D8×C151C2212yes—
14C2×#123×C151—21no—
15C2×#121×C151C2211yescharacteristic
16C22×C4⋊C4×C151C2211yescharacteristic
17C22×C22⋊C4×C151—21no—
18C22×C22⋊C4×C151—21no—
19C22×C42×C151C2211yescharacteristic
20#447×C151—24no—
21#431×C151—24no—
22C2×#107×C151C2212yescomplemented
23C2×C4⋊C8×C151C2212yescomplemented
24C2×#102×C151C2212yes—
25C2×#102×C151C2212yes—
26C2×#102×C151C2212yes—
27C2×#102×C151C2212yescomplemented
28C2×C22⋊C8×C151C2211yescharacteristic
29C2×C22⋊C8×C151C2211yescharacteristic
30C2×C4×C8×C151C2212yescomplemented
31#390×C151—21no—
32#390×C151—21no—
33#390×C151C2212yes—
34#390×C151C2212yes—
35#390×C151C2211yescharacteristic, complemented
36#390×C151C2211yescharacteristic, complemented
37#389×C151C2211yescharacteristic, complemented
38#389×C151C2211yescharacteristic, complemented
39#388×C151—21no—
40#388×C151—21no—
41#386×C151—21no—
42#380×C151C2211yescharacteristic
43#340×C151C2212yescomplemented
44#340×C151C2212yescomplemented
45C25×C151—21no—
46C22×D4×C151—24no—
47C22×D4×C151—21no—
48C22×D4×C151—21no—
49C22×D4×C151—22no—
50C22×D4×C151—22no—
51C22×D4×C151—42no—
52C22×D4×C151C2311yescharacteristic
53C22×D4×C151C2312yes—
54C23×C4×C151—21no—
55C23×C4×C151D411yescharacteristic
56C23×C4×C151D411yescharacteristic
57C23×C4×C151C2311yescharacteristic
58C2×D8×C151—24no—
59C2×D8×C151—24no—
60C2×D8×C151—42no—
61C22×C8×C151C2312yes—
62C22×C8×C151C2312yes—
63#123×C151—44no—
64#121×C151—22no—
65#121×C151—22no—
66C2×C4⋊C4×C151—21no—
67C2×C4⋊C4×C151—21no—
68C2×C4⋊C4×C151—21no—
69C2×C4⋊C4×C151—42no—
70C2×C4⋊C4×C151C2311yescharacteristic
71C2×C4⋊C4×C151C2311yescharacteristic
72C2×C4⋊C4×C151C2312yes—
73C2×C4⋊C4×C151C2311yescharacteristic
74C2×C22⋊C4×C151—21no—
75C2×C22⋊C4×C151—21no—
76C2×C22⋊C4×C151—21no—
77C2×C22⋊C4×C151—21no—
78C2×C22⋊C4×C151—21no—
79C2×C22⋊C4×C151—22no—
80C2×C22⋊C4×C151—22no—
81C2×C22⋊C4×C151—22no—
82C2×C22⋊C4×C151—22no—
83C2×C22⋊C4×C151—21no—
84C2×C22⋊C4×C151—44no—
85C2×C22⋊C4×C151—44no—
86C2×C42×C151—22no—
87C2×C42×C151—22no—
88C2×C42×C151D411yescharacteristic
89C2×C42×C151D411yescharacteristic
90C2×C42×C151C2311yescharacteristic
91C2×C42×C151C2311yescharacteristic
92#107×C151—42no—
93C4⋊C8×C151—24no—
94#102×C151—24no—
95#102×C151—24no—
96#102×C151—42no—
97#102×C151—42no—
98C22⋊C8×C151—22no—
99C22⋊C8×C151D414yes—
100C4×C8×C151—24no—
101#95×C151—21no—
102#95×C151—21no—
103#95×C151—21no—
104C24×C151—24no—
105C24×C151—22no—
106C24×C151—21no—
107C24×C151—42no—
108C24×C151—42no—
109C24×C151—42no—
110C24×C151—42no—
111C24×C151—42no—
112C24×C151—42no—
113C24×C151C2×D411yescharacteristic
114C2×D4×C151—24no—
115C2×D4×C151—22no—
116C2×D4×C151—21no—
117C2×D4×C151—22no—
118C2×D4×C151—22no—
119C2×D4×C151—21no—
120C2×D4×C151—22no—
121C2×D4×C151—22no—
122C2×D4×C151—22no—
123C2×D4×C151—22no—
124C2×D4×C151—48no—
125C2×D4×C151—48no—
126C2×D4×C151—42no—
127C2×D4×C151—42no—
128C2×D4×C151—42no—
129C2×D4×C151—42no—
130C2×D4×C151—42no—
131C2×D4×C151#4114yes—
132C22×C4×C151—22no—
133C22×C4×C151—22no—
134C22×C4×C151—22no—
135C22×C4×C151—22no—
136C22×C4×C151—22no—
137C22×C4×C151—22no—
138C22×C4×C151—21no—
139C22×C4×C151—21no—
140C22×C4×C151—21no—
141C22×C4×C151—22no—
142C22×C4×C151—41no—
143C22×C4×C151—42no—
144C22×C4×C151—42no—
145C22×C4×C151—42no—
146C22×C4×C151D814yescomplemented
147C22×C4×C151C2×D411yescharacteristic
148C22×C4×C151C2×D411yescharacteristic
149C22×C4×C151C2×D412yes—
150C22×C4×C151C2×D411yescharacteristic
151C22×C4×C151C2×D411yescharacteristic
152C22×C4×C151C2×D411yescharacteristic
153C22×C4×C151#4112yes—
154C22×C4×C151C2411yescharacteristic
155D8×C151—48no—
156C2×C8×C151—22no—
157C2×C8×C151—22no—
158C2×C8×C151—22no—
159C2×C8×C151—22no—
160C2×C8×C151—22no—
161C2×C8×C151C2×D414yes—
162C4⋊C4×C151—21no—
163C4⋊C4×C151—22no—
164C4⋊C4×C151—21no—
165C4⋊C4×C151—22no—
166C4⋊C4×C151—22no—
167C4⋊C4×C151—22no—
168C4⋊C4×C151—42no—
169C4⋊C4×C151—42no—
170C4⋊C4×C151—42no—
171C22⋊C4×C151—42no—
172C22⋊C4×C151—44no—
173C22⋊C4×C151—42no—
174C22⋊C4×C151—42no—
175C22⋊C4×C151—44no—
176C22⋊C4×C151—44no—
177C22⋊C4×C151—42no—
178C22⋊C4×C151—42no—
179C22⋊C4×C151—42no—
180C22⋊C4×C151—44no—
181C42×C151—22no—
182C42×C151—22no—
183C42×C151—21no—
184C42×C151—21no—
185C42×C151—21no—
186C42×C151—21no—
187C23×C151—21no—
188C23×C151—21no—
189C23×C151—21no—
190C23×C151—21no—
191C23×C151—24no—
192C23×C151—48no—
193C23×C151—48no—
194C23×C151—48no—
195C23×C151—42no—
196C23×C151—42no—
197C23×C151—42no—
198C23×C151—42no—
199C23×C151—42no—
200C23×C151—42no—
201C23×C151—41no—
202C23×C151—41no—
203C23×C151—41no—
204C23×C151—41no—
205C23×C151—41no—
206C23×C151—41no—
207C23×C151—41no—
208C23×C151—84no—
209C23×C151—84no—
210C23×C151—84no—
211C23×C151—84no—
212C23×C151#12112yes—
213C23×C151C2×D812yes—
214C23×C151#13512yes—
215C23×C151C22×D411yescharacteristic
216D4×C151—24no—
217D4×C151—24no—
218D4×C151—48no—
219D4×C151—42no—
220D4×C151—42no—
221D4×C151—42no—
222D4×C151—42no—
223D4×C151—84no—
224C2×C4×C151—21no—
225C2×C4×C151—21no—
226C2×C4×C151—21no—
227C2×C4×C151—21no—
228C2×C4×C151—21no—
229C2×C4×C151—21no—
230C2×C4×C151—21no—
231C2×C4×C151—21no—
232C2×C4×C151—28no—
233C2×C4×C151—24no—
234C2×C4×C151—24no—
235C2×C4×C151—21no—
236C2×C4×C151—21no—
237C2×C4×C151—21no—
238C2×C4×C151—44no—
239C2×C4×C151—41no—
240C2×C4×C151—41no—
241C2×C4×C151—42no—
242C2×C4×C151—41no—
243C2×C4×C151—41no—
244C2×C4×C151—41no—
245C2×C4×C151—42no—
246C2×C4×C151—41no—
247C2×C4×C151—41no—
248C2×C4×C151—42no—
249C2×C4×C151—41no—
250C2×C4×C151—41no—
251C2×C4×C151—84no—
252C2×C4×C151#12112yes—
253C2×C4×C151C2×D812yes—
254C2×C4×C151C2×D812yes—
255C2×C4×C151AGL(1,ℤ/8)12yes—
256C2×C4×C151C22×D411yescharacteristic
257C2×C4×C151C2×#4112yes—
258C2×C4×C151C2×#4111yescharacteristic
259C2×C4×C151H(5,𝔽2)12yes—
260C8×C151—24no—
261C8×C151—42no—
262C22×C151—22no—
263C22×C151—22no—
264C22×C151—22no—
265C22×C151—22no—
266C22×C151—22no—
267C22×C151—22no—
268C22×C151—44no—
269C22×C151—44no—
270C22×C151—44no—
271C22×C151—816no—
272C22×C151—82no—
273C22×C151—82no—
274C22×C151—82no—
275C22×C151—82no—
276C22×C151—81no—
277C22×C151—81no—
278C22×C151—81no—
279C22×C151—81no—
280C22×C151—81no—
281C22×C151—81no—
282C22×C151—81no—
283C22×C151#46614yes—
284C22×C151C2×#12111yescharacteristic
285C22×C151#52511yescharacteristic
286C22×C151#53511yescharacteristic
287C22×C151C22×D811yescharacteristic
288C22×C151C2×#13511yescharacteristic
289C22×C151C2×AGL(1,ℤ/8)11yescharacteristic
290C22×C151#57511yescharacteristic
291C4×C151—22no—
292C4×C151—22no—
293C4×C151—22no—
294C4×C151—22no—
295C4×C151—41no—
296C4×C151—81no—
297C4×C151—81no—
298C4×C151—82no—
299C4×C151—81no—
300C4×C151#54612yes—
301C4×C151#55112yes—
302C2×C151—24no—
303C2×C151—84no—
304C2×C151—161no—
305C2×C151#241111yescharacteristic
306C2×C151C2×#46611yescharacteristic
307C2×C151#305511yescharacteristic
308C2×C151#310011yescharacteristic
309C2×C151#310511yescharacteristic
310C2×C151#320511yescharacteristic
311C2×C151#321111yescharacteristic
312#24500C15111yesmaximal, characteristic, direct product factor, Sylow
313C151#2450011yescharacteristic, direct product factor, Sylow
314C2×#447C2×C15111yescharacteristic
315C2×#431C2×C15111yescharacteristic, complemented
316#2854C2×C15111yescharacteristic, complemented
317C2×#390C2×C15111yescharacteristic, complemented
318#2067C2×C15112yescomplemented
319#2054C2×C15112yescomplemented
320#1970C2×C15112yescomplemented
321#1934C2×C15112yescomplemented
322#1874C2×C15111yescharacteristic, complemented
323#1852C2×C15111yescharacteristic, complemented
324#1786C2×C15111yescharacteristic, complemented
325C23×D4C22×C15111yescharacteristic
326C22×D8C22×C15112yes—
327C2×#123—21no—
328C2×#121C22×C15111yescharacteristic
329C22×C4⋊C4C22×C15111yescharacteristic
330C22×C22⋊C4—21no—
331C22×C22⋊C4—21no—
332C22×C42C22×C15111yescharacteristic
333#447—24no—
334#431—24no—
335C2×#107C22×C15112yescomplemented
336C2×C4⋊C8C22×C15112yescomplemented
337C2×#102C22×C15112yes—
338C2×#102C22×C15112yes—
339C2×#102C22×C15112yes—
340C2×#102C22×C15112yescomplemented
341C2×C22⋊C8C22×C15111yescharacteristic
342C2×C22⋊C8C22×C15111yescharacteristic
343C2×C4×C8C22×C15112yescomplemented
344#390—21no—
345#390—21no—
346#390C22×C15112yes—
347#390C22×C15112yes—
348#390C22×C15111yescharacteristic, complemented
349#390C22×C15111yescharacteristic, complemented
350#389C22×C15111yescharacteristic, complemented
351#389C22×C15111yescharacteristic, complemented
352#388—21no—
353#388—21no—
354#386—21no—
355#380C22×C15111yescharacteristic
356#340C22×C15112yescomplemented
357#340C22×C15112yescomplemented
358C25—21no—
359C22×D4—24no—
360C22×D4—21no—
361C22×D4—22no—
362C22×D4—21no—
363C22×D4—22no—
364C22×D4—42no—
365C22×D4C23×C15111yescharacteristic
366C22×D4C23×C15112yes—
367C23×C4—21no—
368C23×C4D4×C15111yescharacteristic
369C23×C4D4×C15111yescharacteristic
370C23×C4C23×C15111yescharacteristic
371C2×D8—24no—
372C2×D8—24no—
373C2×D8—42no—
374C22×C8C23×C15112yes—
375C22×C8C23×C15112yes—
376#123—44no—
377#121—22no—
378#121—22no—
379C2×C4⋊C4—21no—
380C2×C4⋊C4—21no—
381C2×C4⋊C4—21no—
382C2×C4⋊C4—42no—
383C2×C4⋊C4C23×C15112yes—
384C2×C4⋊C4C23×C15111yescharacteristic
385C2×C4⋊C4C23×C15111yescharacteristic
386C2×C4⋊C4C23×C15111yescharacteristic
387C2×C22⋊C4—21no—
388C2×C22⋊C4—22no—
389C2×C22⋊C4—22no—
390C2×C22⋊C4—22no—
391C2×C22⋊C4—22no—
392C2×C22⋊C4—21no—
393C2×C22⋊C4—21no—
394C2×C22⋊C4—21no—
395C2×C22⋊C4—21no—
396C2×C22⋊C4—21no—
397C2×C22⋊C4—44no—
398C2×C22⋊C4—44no—
399C2×C42—22no—
400C2×C42—22no—
401C2×C42D4×C15111yescharacteristic
402C2×C42D4×C15111yescharacteristic
403C2×C42C23×C15111yescharacteristic
404C2×C42C23×C15111yescharacteristic
405#107—42no—
406C4⋊C8—24no—
407#102—24no—
408#102—24no—
409#102—42no—
410#102—42no—
411C22⋊C8—22no—
412C22⋊C8D4×C15114yes—
413C4×C8—24no—
414#95—21no—
415#95—21no—
416#95—21no—
417C24—24no—
418C24—22no—
419C24—21no—
420C24—42no—
421C24—42no—
422C24—42no—
423C24—42no—
424C24—42no—
425C24—42no—
426C24C2×D4×C15111yescharacteristic
427C2×D4—24no—
428C2×D4—22no—
429C2×D4—21no—
430C2×D4—22no—
431C2×D4—22no—
432C2×D4—21no—
433C2×D4—22no—
434C2×D4—22no—
435C2×D4—22no—
436C2×D4—22no—
437C2×D4—48no—
438C2×D4—48no—
439C2×D4—42no—
440C2×D4—42no—
441C2×D4—42no—
442C2×D4—42no—
443C2×D4—42no—
444C2×D4#41×C15114yes—
445C22×C4—22no—
446C22×C4—22no—
447C22×C4—22no—
448C22×C4—22no—
449C22×C4—22no—
450C22×C4—22no—
451C22×C4—21no—
452C22×C4—21no—
453C22×C4—21no—
454C22×C4—22no—
455C22×C4—41no—
456C22×C4—42no—
457C22×C4—42no—
458C22×C4—42no—
459C22×C4D8×C15114yescomplemented
460C22×C4C2×D4×C15111yescharacteristic
461C22×C4C2×D4×C15111yescharacteristic
462C22×C4C2×D4×C15112yes—
463C22×C4C2×D4×C15111yescharacteristic
464C22×C4C2×D4×C15111yescharacteristic
465C22×C4C2×D4×C15111yescharacteristic
466C22×C4#41×C15112yes—
467C22×C4C24×C15111yescharacteristic
468D8—48no—
469C2×C8—22no—
470C2×C8—22no—
471C2×C8—22no—
472C2×C8—22no—
473C2×C8—22no—
474C2×C8C2×D4×C15114yes—
475C4⋊C4—21no—
476C4⋊C4—22no—
477C4⋊C4—21no—
478C4⋊C4—22no—
479C4⋊C4—22no—
480C4⋊C4—22no—
481C4⋊C4—42no—
482C4⋊C4—42no—
483C4⋊C4—42no—
484C22⋊C4—44no—
485C22⋊C4—42no—
486C22⋊C4—42no—
487C22⋊C4—42no—
488C22⋊C4—44no—
489C22⋊C4—44no—
490C22⋊C4—42no—
491C22⋊C4—42no—
492C22⋊C4—44no—
493C22⋊C4—42no—
494C42—22no—
495C42—22no—
496C42—21no—
497C42—21no—
498C42—21no—
499C42—21no—
500C23—21no—
501C23—21no—
502C23—21no—
503C23—21no—
504C23—24no—
505C23—48no—
506C23—48no—
507C23—48no—
508C23—42no—
509C23—42no—
510C23—42no—
511C23—42no—
512C23—42no—
513C23—42no—
514C23—41no—
515C23—41no—
516C23—41no—
517C23—41no—
518C23—41no—
519C23—41no—
520C23—41no—
521C23—84no—
522C23—84no—
523C23—84no—
524C23—84no—
525C23#121×C15112yes—
526C23C2×D8×C15112yes—
527C23#135×C15112yes—
528C23C22×D4×C15111yescharacteristic
529D4—24no—
530D4—24no—
531D4—48no—
532D4—42no—
533D4—42no—
534D4—42no—
535D4—42no—
536D4—84no—
537C2×C4—28no—
538C2×C4—21no—
539C2×C4—21no—
540C2×C4—21no—
541C2×C4—21no—
542C2×C4—21no—
543C2×C4—21no—
544C2×C4—21no—
545C2×C4—21no—
546C2×C4—24no—
547C2×C4—24no—
548C2×C4—21no—
549C2×C4—21no—
550C2×C4—21no—
551C2×C4—44no—
552C2×C4—41no—
553C2×C4—41no—
554C2×C4—42no—
555C2×C4—41no—
556C2×C4—41no—
557C2×C4—41no—
558C2×C4—42no—
559C2×C4—41no—
560C2×C4—41no—
561C2×C4—42no—
562C2×C4—41no—
563C2×C4—41no—
564C2×C4—84no—
565C2×C4#121×C15112yes—
566C2×C4C2×D8×C15112yes—
567C2×C4C2×D8×C15112yes—
568C2×C4AGL(1,ℤ/8)×C15112yes—
569C2×C4C22×D4×C15111yescharacteristic
570C2×C4C2×#41×C15112yes—
571C2×C4C2×#41×C15111yescharacteristic
572C2×C4H(5,𝔽2)×C15112yes—
573C8—24no—
574C8—42no—
575C22—22no—
576C22—22no—
577C22—22no—
578C22—22no—
579C22—22no—
580C22—22no—
581C22—44no—
582C22—44no—
583C22—44no—
584C22—816no—
585C22—82no—
586C22—82no—
587C22—82no—
588C22—82no—
589C22—81no—
590C22—81no—
591C22—81no—
592C22—81no—
593C22—81no—
594C22—81no—
595C22—81no—
596C22#466×C15114yes—
597C22C2×#121×C15111yescharacteristic
598C22#525×C15111yescharacteristic
599C22#535×C15111yescharacteristic
600C22C22×D8×C15111yescharacteristic
601C22C2×#135×C15111yescharacteristic
602C22C2×AGL(1,ℤ/8)×C15111yescharacteristic
603C22#575×C15111yescharacteristic
604C4—22no—
605C4—22no—
606C4—22no—
607C4—22no—
608C4—41no—
609C4—81no—
610C4—82no—
611C4—81no—
612C4—81no—
613C4#546×C15112yes—
614C4#551×C15112yes—
615C2—24no—
616C2—84no—
617C2—161no—
618C2#2411×C15111yescharacteristic
619C2C2×#466×C15111yescharacteristic
620C2#3055×C15111yescharacteristic
621C2#3100×C15111yescharacteristic
622C2#3105×C15111yescharacteristic
623C2#3205×C15111yescharacteristic
624C2#3211×C15111yescharacteristic
subgroupG/H
center, socleC23×C151C22×D4
commutator, Frattini, cosocleC22×C4C24×C151
prime radicalC2×#447×C151C2
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C151 ◁ C22×C42×C151 ◁ G

Complements

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

NH ≅ G/Ntype
2. C2×#431×C151C2semidirect
3. #2854×C151C2semidirect
4. C2×#390×C151C2semidirect
5. #2067×C151C2semidirect
6. #2054×C151C2semidirect
7. #1970×C151C2semidirect
8. #1934×C151C2semidirect
9. #1874×C151C2semidirect
10. #1852×C151C2semidirect
11. #1786×C151C2semidirect
22. C2×#107×C151C22semidirect
23. C2×C4⋊C8×C151C22semidirect
27. C2×#102×C151C22semidirect
30. C2×C4×C8×C151C22semidirect
35. #390×C151C22semidirect
36. #390×C151C22semidirect
37. #389×C151C22semidirect
38. #389×C151C22semidirect
43. #340×C151C22semidirect
44. #340×C151C22semidirect
146. C22×C4×C151D8semidirect
312. #24500C151direct (N × H)
313. C151#24500direct (N × H)
315. C2×#431C2×C151semidirect
316. #2854C2×C151semidirect
317. C2×#390C2×C151semidirect
318. #2067C2×C151semidirect
319. #2054C2×C151semidirect
320. #1970C2×C151semidirect
321. #1934C2×C151semidirect
322. #1874C2×C151semidirect
323. #1852C2×C151semidirect
324. #1786C2×C151semidirect
335. C2×#107C22×C151semidirect
336. C2×C4⋊C8C22×C151semidirect
340. C2×#102C22×C151semidirect
343. C2×C4×C8C22×C151semidirect
348. #390C22×C151semidirect
349. #390C22×C151semidirect
350. #389C22×C151semidirect
351. #389C22×C151semidirect
356. #340C22×C151semidirect
357. #340C22×C151semidirect
459. C22×C4D8×C151semidirect

Maximal subgroups

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

subgroupindex
C2×#447×C1512
C2×#431×C1512
#2854×C1512
C2×#390×C1512
#2067×C1512
#2054×C1512
#1970×C1512
#1934×C1512
#1874×C1512
#1852×C1512
#1786×C1512
#24500151