Finite Group Databasebeta

← C151×#24626 #50329551

Subgroups — C151×#24626 #50329551

Order 38656.

1110 conjugacy classes of subgroups.

The subgroup lattice has 598 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#459×C151C211yesmaximal, characteristic, complemented
2C2×C4×D8×C151C211yesmaximal, characteristic, complemented
3#2541×C151C211yesmaximal, characteristic, complemented
4#2354×C151C211yesmaximal, characteristic, complemented
5#2054×C151C212yesmaximal, complemented
6#2011×C151C212yesmaximal, complemented
7#1982×C151C212yesmaximal, complemented
8#1957×C151C211yesmaximal, characteristic, complemented
9#1939×C151C211yesmaximal, characteristic, complemented
10#1925×C151C212yesmaximal, complemented
11#1802×C151C211yesmaximal, characteristic, complemented
12C22×D8×C151C2211yescharacteristic
13C22×D8×C151C2212yes—
14C2×#127×C151C2211yescharacteristic
15C2×#127×C151C2212yes—
16C2×#121×C151—21no—
17C2×#121×C151—21no—
18C2×C4×D4×C151C2211yescharacteristic
19C2×C4×D4×C151C2211yescharacteristic
20C2×#117×C151—21no—
21#459×C151—24no—
22C4×D8×C151—24no—
23C2×#107×C151C2211yescharacteristic
24C2×C4⋊C8×C151C2211yescharacteristic
25C2×C4⋊C8×C151C2212yes—
26C2×#102×C151C2211yescharacteristic
27C2×#102×C151C2211yescharacteristic
28C2×#102×C151C2212yes—
29C2×#102×C151C2212yes—
30C2×#102×C151C2212yes—
31C2×#102×C151C2212yes—
32C2×C4×C8×C151C2211yescharacteristic
33#392×C151—22no—
34#390×C151C2212yes—
35#390×C151C2212yes—
36#388×C151—22no—
37#384×C151C2211yescharacteristic
38#380×C151—21no—
39C4×C4⋊C4×C151C2212yes—
40C4×C4⋊C4×C151C2211yescharacteristic
41#340×C151C2212yes—
42#336×C151C2212yes—
43C22×D4×C151—21no—
44C22×D4×C151—22no—
45C22×D4×C151—22no—
46C22×D4×C151—21no—
47C22×D4×C151C2312yes—
48C22×D4×C151C2311yescharacteristic
49C22×D4×C151C2311yescharacteristic
50C23×C4×C151—21no—
51C23×C4×C151—21no—
52C2×D8×C151—22no—
53C2×D8×C151—22no—
54C2×D8×C151—24no—
55C2×D8×C151—22no—
56C2×D8×C151—42no—
57C2×D8×C151—42no—
58C22×C8×C151C2312yes—
59C22×C8×C151C2311yescharacteristic
60C22×C8×C151C2311yescharacteristic
61#127×C151—24no—
62#127×C151—22no—
63#127×C151—22no—
64#127×C151—42no—
65#121×C151—44no—
66#121×C151—44no—
67C4×D4×C151—22no—
68C4×D4×C151—22no—
69C4×D4×C151—22no—
70C4×D4×C151D414yescomplemented
71#117×C151—44no—
72C2×C4⋊C4×C151—21no—
73C2×C4⋊C4×C151—21no—
74C2×C4⋊C4×C151D411yescharacteristic
75C2×C4⋊C4×C151D411yescharacteristic
76C2×C4⋊C4×C151C2311yescharacteristic
77C2×C4⋊C4×C151C2312yes—
78C2×C4⋊C4×C151C2311yescharacteristic
79C2×C22⋊C4×C151—21no—
80C2×C22⋊C4×C151—22no—
81C2×C22⋊C4×C151—22no—
82C2×C22⋊C4×C151—22no—
83C2×C22⋊C4×C151—21no—
84C2×C22⋊C4×C151—22no—
85C2×C42×C151—22no—
86C2×C42×C151C2312yes—
87C2×C42×C151C2311yescharacteristic
88#107×C151—22no—
89C4⋊C8×C151—22no—
90C4⋊C8×C151—42no—
91#102×C151—22no—
92#102×C151—24no—
93#102×C151—22no—
94#102×C151—24no—
95#102×C151—42no—
96#102×C151—42no—
97C4×C8×C151—22no—
98#95×C151—22no—
99#95×C151D412yes—
100C24×C151—21no—
101C24×C151—21no—
102C24×C151—22no—
103C2×D4×C151—21no—
104C2×D4×C151—22no—
105C2×D4×C151—21no—
106C2×D4×C151—21no—
107C2×D4×C151—21no—
108C2×D4×C151—21no—
109C2×D4×C151—21no—
110C2×D4×C151—22no—
111C2×D4×C151—22no—
112C2×D4×C151—22no—
113C2×D4×C151—21no—
114C2×D4×C151—21no—
115C2×D4×C151—21no—
116C2×D4×C151—21no—
117C2×D4×C151—22no—
118C2×D4×C151—22no—
119C2×D4×C151—44no—
120C2×D4×C151—44no—
121C2×D4×C151—44no—
122C2×D4×C151—42no—
123C2×D4×C151—42no—
124C2×D4×C151—44no—
125C2×D4×C151—42no—
126C2×D4×C151—42no—
127C2×D4×C151—81no—
128C2×D4×C151—82no—
129C2×D4×C151—81no—
130C2×D4×C151—82no—
131C2×D4×C151C2×D412yes—
132C2×D4×C151#4112yes—
133C22×C4×C151—21no—
134C22×C4×C151—24no—
135C22×C4×C151—22no—
136C22×C4×C151—21no—
137C22×C4×C151—42no—
138C22×C4×C151—42no—
139C22×C4×C151—42no—
140C22×C4×C151—42no—
141C22×C4×C151—42no—
142C22×C4×C151C2×D412yes—
143C22×C4×C151C2×D411yescharacteristic
144C22×C4×C151C2×D412yes—
145C22×C4×C151C2×D411yescharacteristic
146C22×C4×C151C2411yescharacteristic
147D8×C151—28no—
148D8×C151—48no—
149C2×C8×C151—21no—
150C2×C8×C151—21no—
151C2×C8×C151—21no—
152C2×C8×C151—22no—
153C2×C8×C151—21no—
154C2×C8×C151—22no—
155C2×C8×C151—21no—
156C2×C8×C151—22no—
157C2×C8×C151#4112yes—
158C4⋊C4×C151—22no—
159C4⋊C4×C151—21no—
160C4⋊C4×C151—21no—
161C4⋊C4×C151—22no—
162C4⋊C4×C151—21no—
163C4⋊C4×C151—22no—
164C4⋊C4×C151—42no—
165C4⋊C4×C151—81no—
166C4⋊C4×C151D814yescomplemented
167C4⋊C4×C151C2×D412yes—
168C22⋊C4×C151—24no—
169C22⋊C4×C151—44no—
170C22⋊C4×C151—42no—
171C22⋊C4×C151—44no—
172C22⋊C4×C151—44no—
173C22⋊C4×C151—82no—
174C42×C151—22no—
175C42×C151—22no—
176C42×C151—44no—
177C42×C151C2×D412yes—
178C42×C151#4112yes—
179C23×C151—22no—
180C23×C151—22no—
181C23×C151—41no—
182C23×C151—41no—
183C23×C151—41no—
184C23×C151—41no—
185C23×C151—41no—
186C23×C151—41no—
187C23×C151—41no—
188C23×C151—41no—
189C23×C151—41no—
190C23×C151—41no—
191C23×C151—41no—
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×C151C22×D411yescharacteristic
201D4×C151—22no—
202D4×C151—22no—
203D4×C151—22no—
204D4×C151—22no—
205D4×C151—42no—
206D4×C151—41no—
207D4×C151—42no—
208D4×C151—41no—
209D4×C151—42no—
210D4×C151—41no—
211D4×C151—41no—
212D4×C151—42no—
213D4×C151—88no—
214D4×C151—84no—
215D4×C151—88no—
216D4×C151—84no—
217C2×C4×C151—22no—
218C2×C4×C151—21no—
219C2×C4×C151—22no—
220C2×C4×C151—21no—
221C2×C4×C151—22no—
222C2×C4×C151—22no—
223C2×C4×C151—22no—
224C2×C4×C151—22no—
225C2×C4×C151—41no—
226C2×C4×C151—41no—
227C2×C4×C151—48no—
228C2×C4×C151—41no—
229C2×C4×C151—42no—
230C2×C4×C151—42no—
231C2×C4×C151—41no—
232C2×C4×C151—41no—
233C2×C4×C151—42no—
234C2×C4×C151—84no—
235C2×C4×C151#12112yes—
236C2×C4×C151#12112yes—
237C2×C4×C151C2×D814yes—
238C2×C4×C151C2×D812yes—
239C2×C4×C151AGL(1,ℤ/8)12yes—
240C2×C4×C151C22×D411yescharacteristic
241C2×C4×C151C2×#4111yescharacteristic
242C2×C4×C151C2×#4111yescharacteristic
243C2×C4×C151C2×#4111yescharacteristic
244C2×C4×C151H(5,𝔽2)11yescharacteristic
245C2×C4×C151H(5,𝔽2)11yescharacteristic
246C8×C151—22no—
247C8×C151—41no—
248C8×C151—42no—
249C22×C151—42no—
250C22×C151—42no—
251C22×C151—42no—
252C22×C151—42no—
253C22×C151—42no—
254C22×C151—42no—
255C22×C151—81no—
256C22×C151—81no—
257C22×C151—81no—
258C22×C151—81no—
259C22×C151—81no—
260C22×C151—81no—
261C22×C151—81no—
262C22×C151—81no—
263C22×C151—82no—
264C22×C151—82no—
265C22×C151—82no—
266C22×C151—82no—
267C22×C151—82no—
268C22×C151—82no—
269C22×C151—82no—
270C22×C151C2×#12111yescharacteristic
271C22×C151#54611yescharacteristic
272C22×C151#55011yescharacteristic
273C22×C151C22×D811yescharacteristic
274C22×C151C2×AGL(1,ℤ/8)11yescharacteristic
275C22×C151#57611yescharacteristic
276C22×C151#57711yescharacteristic
277C4×C151—24no—
278C4×C151—22no—
279C4×C151—42no—
280C4×C151—42no—
281C4×C151—82no—
282C4×C151—81no—
283C4×C151#45914yes—
284C4×C151#52511yescharacteristic
285C4×C151#53511yescharacteristic
286C4×C151#55311yescharacteristic
287C4×C151#55511yescharacteristic
288C2×C151—82no—
289C2×C151—82no—
290C2×C151—162no—
291C2×C151#241411yescharacteristic
292C2×C151C2×#45911yescharacteristic
293C2×C151#304511yescharacteristic
294C2×C151#329411yescharacteristic
295C2×C151#332511yescharacteristic
296C2×C151#339111yescharacteristic
297C2×C151#339711yescharacteristic
298#24626C15111yesmaximal, characteristic, direct product factor, Sylow
299C151#2462611yescharacteristic, direct product factor, Sylow
300C2×#459C2×C15111yescharacteristic, complemented
301C2×C4×D8C2×C15111yescharacteristic, complemented
302#2541C2×C15111yescharacteristic, complemented
303#2354C2×C15111yescharacteristic, complemented
304#2054C2×C15112yescomplemented
305#2011C2×C15112yescomplemented
306#1982C2×C15112yescomplemented
307#1957C2×C15111yescharacteristic, complemented
308#1939C2×C15111yescharacteristic, complemented
309#1925C2×C15112yescomplemented
310#1802C2×C15111yescharacteristic, complemented
311C22×D8C22×C15111yescharacteristic
312C22×D8C22×C15112yes—
313C2×#127C22×C15111yescharacteristic
314C2×#127C22×C15112yes—
315C2×#121—21no—
316C2×#121—21no—
317C2×C4×D4C22×C15111yescharacteristic
318C2×C4×D4C22×C15111yescharacteristic
319C2×#117—21no—
320#459—24no—
321C4×D8—24no—
322C2×#107C22×C15111yescharacteristic
323C2×C4⋊C8C22×C15111yescharacteristic
324C2×C4⋊C8C22×C15112yes—
325C2×#102C22×C15111yescharacteristic
326C2×#102C22×C15111yescharacteristic
327C2×#102C22×C15112yes—
328C2×#102C22×C15112yes—
329C2×#102C22×C15112yes—
330C2×#102C22×C15112yes—
331C2×C4×C8C22×C15111yescharacteristic
332#392—22no—
333#390C22×C15112yes—
334#390C22×C15112yes—
335#388—22no—
336#384C22×C15111yescharacteristic
337#380—21no—
338C4×C4⋊C4C22×C15112yes—
339C4×C4⋊C4C22×C15111yescharacteristic
340#340C22×C15112yes—
341#336C22×C15112yes—
342C22×D4—21no—
343C22×D4—22no—
344C22×D4—22no—
345C22×D4—21no—
346C22×D4C23×C15112yes—
347C22×D4C23×C15111yescharacteristic
348C22×D4C23×C15111yescharacteristic
349C23×C4—21no—
350C23×C4—21no—
351C2×D8—22no—
352C2×D8—22no—
353C2×D8—24no—
354C2×D8—22no—
355C2×D8—42no—
356C2×D8—42no—
357C22×C8C23×C15112yes—
358C22×C8C23×C15111yescharacteristic
359C22×C8C23×C15111yescharacteristic
360#127—24no—
361#127—22no—
362#127—22no—
363#127—42no—
364#121—44no—
365#121—44no—
366C4×D4—22no—
367C4×D4—22no—
368C4×D4—22no—
369C4×D4D4×C15114yescomplemented
370#117—44no—
371C2×C4⋊C4—21no—
372C2×C4⋊C4—21no—
373C2×C4⋊C4D4×C15111yescharacteristic
374C2×C4⋊C4D4×C15111yescharacteristic
375C2×C4⋊C4C23×C15111yescharacteristic
376C2×C4⋊C4C23×C15112yes—
377C2×C4⋊C4C23×C15111yescharacteristic
378C2×C22⋊C4—21no—
379C2×C22⋊C4—22no—
380C2×C22⋊C4—21no—
381C2×C22⋊C4—22no—
382C2×C22⋊C4—22no—
383C2×C22⋊C4—22no—
384C2×C42—22no—
385C2×C42C23×C15112yes—
386C2×C42C23×C15111yescharacteristic
387#107—22no—
388C4⋊C8—22no—
389C4⋊C8—42no—
390#102—22no—
391#102—24no—
392#102—22no—
393#102—24no—
394#102—42no—
395#102—42no—
396C4×C8—22no—
397#95—22no—
398#95D4×C15112yes—
399C24—21no—
400C24—21no—
401C24—22no—
402C2×D4—21no—
403C2×D4—22no—
404C2×D4—21no—
405C2×D4—21no—
406C2×D4—21no—
407C2×D4—21no—
408C2×D4—21no—
409C2×D4—22no—
410C2×D4—22no—
411C2×D4—22no—
412C2×D4—21no—
413C2×D4—21no—
414C2×D4—21no—
415C2×D4—21no—
416C2×D4—22no—
417C2×D4—22no—
418C2×D4—44no—
419C2×D4—44no—
420C2×D4—44no—
421C2×D4—42no—
422C2×D4—42no—
423C2×D4—44no—
424C2×D4—42no—
425C2×D4—42no—
426C2×D4—81no—
427C2×D4—82no—
428C2×D4—81no—
429C2×D4—82no—
430C2×D4C2×D4×C15112yes—
431C2×D4#41×C15112yes—
432C22×C4—21no—
433C22×C4—24no—
434C22×C4—22no—
435C22×C4—21no—
436C22×C4—42no—
437C22×C4—42no—
438C22×C4—42no—
439C22×C4—42no—
440C22×C4—42no—
441C22×C4C2×D4×C15112yes—
442C22×C4C2×D4×C15111yescharacteristic
443C22×C4C2×D4×C15112yes—
444C22×C4C2×D4×C15111yescharacteristic
445C22×C4C24×C15111yescharacteristic
446D8—28no—
447D8—48no—
448C2×C8—21no—
449C2×C8—21no—
450C2×C8—21no—
451C2×C8—22no—
452C2×C8—21no—
453C2×C8—22no—
454C2×C8—21no—
455C2×C8—22no—
456C2×C8#41×C15112yes—
457C4⋊C4—22no—
458C4⋊C4—21no—
459C4⋊C4—21no—
460C4⋊C4—22no—
461C4⋊C4—21no—
462C4⋊C4—22no—
463C4⋊C4—42no—
464C4⋊C4—81no—
465C4⋊C4D8×C15114yescomplemented
466C4⋊C4C2×D4×C15112yes—
467C22⋊C4—24no—
468C22⋊C4—44no—
469C22⋊C4—42no—
470C22⋊C4—44no—
471C22⋊C4—44no—
472C22⋊C4—82no—
473C42—22no—
474C42—22no—
475C42—44no—
476C42C2×D4×C15112yes—
477C42#41×C15112yes—
478C23—22no—
479C23—22no—
480C23—41no—
481C23—41no—
482C23—41no—
483C23—41no—
484C23—41no—
485C23—41no—
486C23—41no—
487C23—41no—
488C23—41no—
489C23—41no—
490C23—41no—
491C23—41no—
492C23—42no—
493C23—42no—
494C23—42no—
495C23—42no—
496C23—42no—
497C23—42no—
498C23—42no—
499C23C22×D4×C15111yescharacteristic
500D4—22no—
501D4—22no—
502D4—22no—
503D4—22no—
504D4—42no—
505D4—41no—
506D4—42no—
507D4—41no—
508D4—42no—
509D4—41no—
510D4—41no—
511D4—42no—
512D4—88no—
513D4—84no—
514D4—88no—
515D4—84no—
516C2×C4—22no—
517C2×C4—21no—
518C2×C4—22no—
519C2×C4—21no—
520C2×C4—22no—
521C2×C4—22no—
522C2×C4—22no—
523C2×C4—22no—
524C2×C4—41no—
525C2×C4—41no—
526C2×C4—48no—
527C2×C4—41no—
528C2×C4—42no—
529C2×C4—42no—
530C2×C4—41no—
531C2×C4—41no—
532C2×C4—42no—
533C2×C4—84no—
534C2×C4#121×C15112yes—
535C2×C4#121×C15112yes—
536C2×C4C2×D8×C15114yes—
537C2×C4C2×D8×C15112yes—
538C2×C4AGL(1,ℤ/8)×C15112yes—
539C2×C4C22×D4×C15111yescharacteristic
540C2×C4C2×#41×C15111yescharacteristic
541C2×C4C2×#41×C15111yescharacteristic
542C2×C4C2×#41×C15111yescharacteristic
543C2×C4H(5,𝔽2)×C15111yescharacteristic
544C2×C4H(5,𝔽2)×C15111yescharacteristic
545C8—22no—
546C8—42no—
547C8—41no—
548C22—42no—
549C22—42no—
550C22—42no—
551C22—42no—
552C22—42no—
553C22—42no—
554C22—81no—
555C22—81no—
556C22—81no—
557C22—81no—
558C22—81no—
559C22—81no—
560C22—81no—
561C22—81no—
562C22—82no—
563C22—82no—
564C22—82no—
565C22—82no—
566C22—82no—
567C22—82no—
568C22—82no—
569C22C2×#121×C15111yescharacteristic
570C22#546×C15111yescharacteristic
571C22#550×C15111yescharacteristic
572C22C22×D8×C15111yescharacteristic
573C22C2×AGL(1,ℤ/8)×C15111yescharacteristic
574C22#576×C15111yescharacteristic
575C22#577×C15111yescharacteristic
576C4—24no—
577C4—22no—
578C4—42no—
579C4—42no—
580C4—82no—
581C4—81no—
582C4#459×C15114yes—
583C4#525×C15111yescharacteristic
584C4#535×C15111yescharacteristic
585C4#553×C15111yescharacteristic
586C4#555×C15111yescharacteristic
587C2—82no—
588C2—82no—
589C2—162no—
590C2#2414×C15111yescharacteristic
591C2C2×#459×C15111yescharacteristic
592C2#3045×C15111yescharacteristic
593C2#3294×C15111yescharacteristic
594C2#3325×C15111yescharacteristic
595C2#3391×C15111yescharacteristic
596C2#3397×C15111yescharacteristic
subgroupG/H
center, socleC23×C151C22×D4
commutator, Frattini, cosocleC22×C4C24×C151
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C151 ◁ C4×C4⋊C4×C151 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×#459×C151C2semidirect
2. C2×C4×D8×C151C2semidirect
3. #2541×C151C2semidirect
4. #2354×C151C2semidirect
5. #2054×C151C2semidirect
6. #2011×C151C2semidirect
7. #1982×C151C2semidirect
8. #1957×C151C2semidirect
9. #1939×C151C2semidirect
10. #1925×C151C2semidirect
11. #1802×C151C2semidirect
70. C4×D4×C151D4semidirect
166. C4⋊C4×C151D8semidirect
298. #24626C151direct (N × H)
299. C151#24626direct (N × H)
300. C2×#459C2×C151semidirect
301. C2×C4×D8C2×C151semidirect
302. #2541C2×C151semidirect
303. #2354C2×C151semidirect
304. #2054C2×C151semidirect
305. #2011C2×C151semidirect
306. #1982C2×C151semidirect
307. #1957C2×C151semidirect
308. #1939C2×C151semidirect
309. #1925C2×C151semidirect
310. #1802C2×C151semidirect
369. C4×D4D4×C151semidirect
465. C4⋊C4D8×C151semidirect

Maximal subgroups

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

subgroupindex
C2×#459×C1512
C2×C4×D8×C1512
#2541×C1512
#2354×C1512
#2054×C1512
#2011×C1512
#1982×C1512
#1957×C1512
#1939×C1512
#1925×C1512
#1802×C1512
#24626151