Finite Group Databasebeta

← C151×#24296 #50329221

Subgroups — C151×#24296 #50329221

Order 38656.

1270 conjugacy classes of subgroups.

The subgroup lattice has 646 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#578×C151C211yesmaximal, characteristic, complemented
2#3067×C151C211yesmaximal, characteristic, complemented
3#3059×C151C211yesmaximal, characteristic, complemented
4#3020×C151C212yesmaximal, complemented
5#2955×C151C211yesmaximal, characteristic, complemented
6#2049×C151C212yesmaximal, complemented
7#2009×C151C212yesmaximal, complemented
8#1979×C151C211yesmaximal, characteristic, complemented
9#1976×C151C211yesmaximal, characteristic, complemented
10#1814×C151C211yesmaximal, characteristic, complemented
11#1796×C151C212yesmaximal, complemented
12C2×2−1+4×C151C2212yes—
13#578×C151—22no—
14#578×C151—22no—
15#578×C151—22no—
16#578×C151—22no—
17#575×C151C2211yescharacteristic
18#575×C151C2212yes—
19C2×#137×C151—22no—
20C2×#137×C151C2212yes—
21C2×#135×C151—21no—
22C2×#135×C151C2211yescharacteristic
23C22×Q16×C151—21no—
24C22×Q16×C151C2211yescharacteristic
25C2×#131×C151C2211yescharacteristic
26C2×#131×C151C2211yescharacteristic
27#536×C151C2212yes—
28#473×C151—21no—
29#472×C151—21no—
30#471×C151—22no—
31#470×C151—22no—
32#467×C151—22no—
33#456×C151—24no—
34#454×C151—24no—
35#444×C151—22no—
36#443×C151—22no—
37#430×C151C2211yescharacteristic
38C2×#108×C151C2211yescharacteristic
39#427×C151C2211yescharacteristic
40#421×C151C2211yescharacteristic
41#421×C151C2211yescharacteristic
42#421×C151C2212yes—
43#421×C151C2212yes—
44#419×C151C2212yes—
45#419×C151C2212yes—
46#413×C151C2212yes—
47C2×#101×C151C2212yes—
48#410×C151C2212yes—
49#405×C151C2211yescharacteristic
50#344×C151C2212yes—
512−1+4×C151—24no—
522−1+4×C151—24no—
532−1+4×C151—24no—
542−1+4×C151—42no—
55C2×#41×C151—22no—
56C2×#41×C151—22no—
57C2×#41×C151—42no—
58C2×#41×C151C2312yes—
59C2×#41×C151C2311yescharacteristic
60C2×#41×C151C2311yescharacteristic
61C22×Q8×C151—22no—
62C22×Q8×C151—22no—
63C22×Q8×C151C2312yes—
64#137×C151—28no—
65#137×C151—28no—
66#137×C151—24no—
67#137×C151—24no—
68#137×C151—22no—
69#137×C151—22no—
70#137×C151—21no—
71#137×C151D412yes—
72AGL(1,ℤ/8)×C151—21no—
73AGL(1,ℤ/8)×C151—22no—
74AGL(1,ℤ/8)×C151—22no—
75AGL(1,ℤ/8)×C151D412yes—
76#135×C151—24no—
77#135×C151—24no—
78#135×C151—21no—
79#135×C151—21no—
80#135×C151—21no—
81#135×C151—21no—
82#135×C151—22no—
83#135×C151—42no—
84C2×Q16×C151—24no—
85C2×Q16×C151—24no—
86C2×Q16×C151—21no—
87C2×Q16×C151—21no—
88C2×Q16×C151—21no—
89C2×Q16×C151—21no—
90C2×Q16×C151—22no—
91C2×Q16×C151D412yes—
92C2×Q16×C151D412yes—
93C2×Q16×C151D411yescharacteristic
94C2×SD16×C151—22no—
95C2×SD16×C151D412yes—
96C2×D8×C151D411yescharacteristic
97#131×C151—21no—
98#131×C151—21no—
99#131×C151—21no—
100#131×C151—21no—
101#131×C151—21no—
102#131×C151—21no—
103#131×C151D412yes—
104#131×C151D412yes—
105C2×M16×C151—21no—
106C2×M16×C151—21no—
107C2×M16×C151C2312yes—
108C2×M16×C151C2311yescharacteristic
109C2×M16×C151C2311yescharacteristic
110C2×M16×C151C2311yescharacteristic
111C22×C8×C151—21no—
112C22×C8×C151—21no—
113C22×C8×C151C2311yescharacteristic
114C4⋊Q8×C151—22no—
115#124×C151—22no—
116#123×C151—42no—
117C22⋊Q8×C151—24no—
118#117×C151C2312yes—
119#117×C151C2311yescharacteristic
120#108×C151—22no—
121#108×C151—21no—
122#108×C151—21no—
123#107×C151—21no—
124#106×C151—21no—
125#104×C151—22no—
126#104×C151—24no—
127#104×C151—22no—
128#104×C151—24no—
129#103×C151—24no—
130#103×C151—42no—
131#101×C151—24no—
132#101×C151—22no—
133#100×C151—22no—
134#99×C151—42no—
135#97×C151—21no—
136C4×C8×C151—21no—
137#41×C151—21no—
138#41×C151—21no—
139#41×C151—28no—
140#41×C151—21no—
141#41×C151—22no—
142#41×C151—21no—
143#41×C151—22no—
144#41×C151—22no—
145#41×C151—21no—
146#41×C151—21no—
147#41×C151—22no—
148#41×C151—44no—
149#41×C151—48no—
150#41×C151—44no—
151#41×C151—48no—
152#41×C151—44no—
153#41×C151C2×D412yes—
154#41×C151C2×D412yes—
155C2×Q8×C151—22no—
156C2×Q8×C151—28no—
157C2×Q8×C151—22no—
158C2×Q8×C151—22no—
159C2×Q8×C151—22no—
160C2×Q8×C151—22no—
161C2×Q8×C151—42no—
162C2×Q8×C151—44no—
163C2×Q8×C151—44no—
164C2×Q8×C151—44no—
165C2×Q8×C151C2×D412yes—
166C2×Q8×C151C2×D414yes—
167C2×Q8×C151C2×D411yescharacteristic
168C2×Q8×C151#4111yescharacteristic
169C2×D4×C151—21no—
170C2×D4×C151—22no—
171C2×D4×C151—21no—
172C2×D4×C151—42no—
173C2×D4×C151C2×D412yes—
174C2×D4×C151C2×D411yescharacteristic
175C2×D4×C151#4111yescharacteristic
176C22×C4×C151—21no—
177C22×C4×C151—22no—
178C22×C4×C151—21no—
179C22×C4×C151—22no—
180C22×C4×C151—42no—
181C22×C4×C151—42no—
182C22×C4×C151C2411yescharacteristic
183Q16×C151—28no—
184Q16×C151—22no—
185Q16×C151—21no—
186Q16×C151—22no—
187Q16×C151—21no—
188Q16×C151—22no—
189Q16×C151—22no—
190Q16×C151—22no—
191Q16×C151—42no—
192SD16×C151—28no—
193SD16×C151—22no—
194SD16×C151—22no—
195SD16×C151—22no—
196SD16×C151—22no—
197SD16×C151—42no—
198SD16×C151—42no—
199D8×C151—22no—
200D8×C151—21no—
201D8×C151—21no—
202D8×C151—42no—
203M16×C151—21no—
204M16×C151—21no—
205M16×C151—22no—
206M16×C151—22no—
207M16×C151—21no—
208M16×C151—22no—
209M16×C151—22no—
210M16×C151—21no—
211M16×C151—41no—
212M16×C151—41no—
213M16×C151C2×D412yes—
214M16×C151C2×D412yes—
215C2×C8×C151—21no—
216C2×C8×C151—21no—
217C2×C8×C151—22no—
218C2×C8×C151—22no—
219C2×C8×C151—21no—
220C2×C8×C151—22no—
221C2×C8×C151—41no—
222C2×C8×C151—41no—
223C2×C8×C151C2×D411yescharacteristic
224C2×C8×C151C2×D411yescharacteristic
225C2×C8×C151C2×D411yescharacteristic
226C2×C8×C151C2×D411yescharacteristic
227C2×C8×C151C2×D411yescharacteristic
228C2×C8×C151C2×D411yescharacteristic
229C4⋊C4×C151—22no—
230C4⋊C4×C151—21no—
231C4⋊C4×C151—44no—
232C22⋊C4×C151—21no—
233C22⋊C4×C151—22no—
234C22⋊C4×C151—44no—
235C42×C151—21no—
236C42×C151—22no—
237C23×C151—21no—
238C23×C151—21no—
239C23×C151—22no—
240C23×C151H(5,𝔽2)11yescharacteristic
241Q8×C151—21no—
242Q8×C151—22no—
243Q8×C151—24no—
244Q8×C151—21no—
245Q8×C151—22no—
246Q8×C151—21no—
247Q8×C151—24no—
248Q8×C151—48no—
249Q8×C151—42no—
250Q8×C151—42no—
251Q8×C151#12112yes—
252D4×C151—22no—
253D4×C151—22no—
254D4×C151—22no—
255D4×C151—21no—
256D4×C151—22no—
257D4×C151—21no—
258D4×C151—21no—
259D4×C151—48no—
260D4×C151—42no—
261D4×C151—41no—
262D4×C151—42no—
263D4×C151—41no—
264D4×C151#12112yes—
265C2×C4×C151—21no—
266C2×C4×C151—22no—
267C2×C4×C151—22no—
268C2×C4×C151—24no—
269C2×C4×C151—21no—
270C2×C4×C151—22no—
271C2×C4×C151—48no—
272C2×C4×C151—48no—
273C2×C4×C151—42no—
274C2×C4×C151—42no—
275C2×C4×C151—41no—
276C2×C4×C151—42no—
277C2×C4×C151—42no—
278C2×C4×C151—41no—
279C2×C4×C151—41no—
280C2×C4×C151—42no—
281C2×C4×C151C22×D411yescharacteristic
282C2×C4×C151C22×D411yescharacteristic
283C2×C4×C151C22×D411yescharacteristic
284C2×C4×C151C22×D411yescharacteristic
285C2×C4×C151C2×#4111yescharacteristic
286C2×C4×C151H(5,𝔽2)11yescharacteristic
287C8×C151—22no—
288C8×C151—22no—
289C8×C151—41no—
290C8×C151—42no—
291C8×C151#12011yescharacteristic
292C8×C151#12011yescharacteristic
293C8×C151#12011yescharacteristic
294C8×C151#12011yescharacteristic
295C22×C151—22no—
296C22×C151—41no—
297C22×C151—42no—
298C22×C151—42no—
299C22×C151—42no—
300C22×C151—41no—
301C22×C151—82no—
302C22×C151#53511yescharacteristic
303C22×C151D4211yescharacteristic
304C22×C151#54611yescharacteristic
305C4×C151—22no—
306C4×C151—44no—
307C4×C151—42no—
308C4×C151—41no—
309C4×C151—82no—
310C4×C151—81no—
311C4×C151C2×#12011yescharacteristic
312C4×C151C2×#12111yescharacteristic
313C4×C151D4211yescharacteristic
314C4×C151#54611yescharacteristic
315C2×C151—21no—
316C2×C151—21no—
317C2×C151—21no—
318C2×C151—42no—
319C2×C151—81no—
320C2×C151—82no—
321C2×C151#240811yescharacteristic
322#24296C15111yesmaximal, characteristic, direct product factor, Sylow
323C151#2429611yescharacteristic, direct product factor, Sylow
324C2×#578C2×C15111yescharacteristic, complemented
325#3067C2×C15111yescharacteristic, complemented
326#3059C2×C15111yescharacteristic, complemented
327#3020C2×C15112yescomplemented
328#2955C2×C15111yescharacteristic, complemented
329#2049C2×C15112yescomplemented
330#2009C2×C15112yescomplemented
331#1979C2×C15111yescharacteristic, complemented
332#1976C2×C15111yescharacteristic, complemented
333#1814C2×C15111yescharacteristic, complemented
334#1796C2×C15112yescomplemented
335C2×2−1+4C22×C15112yes—
336#578—22no—
337#578—22no—
338#578—22no—
339#578—22no—
340#575C22×C15111yescharacteristic
341#575C22×C15112yes—
342C2×#137—22no—
343C2×#137C22×C15112yes—
344C2×#135—21no—
345C2×#135C22×C15111yescharacteristic
346C22×Q16—21no—
347C22×Q16C22×C15111yescharacteristic
348C2×#131C22×C15111yescharacteristic
349C2×#131C22×C15111yescharacteristic
350#536C22×C15112yes—
351#473—21no—
352#472—21no—
353#471—22no—
354#470—22no—
355#467—22no—
356#456—24no—
357#454—24no—
358#444—22no—
359#443—22no—
360#430C22×C15111yescharacteristic
361C2×#108C22×C15111yescharacteristic
362#427C22×C15111yescharacteristic
363#421C22×C15112yes—
364#421C22×C15111yescharacteristic
365#421C22×C15112yes—
366#421C22×C15111yescharacteristic
367#419C22×C15112yes—
368#419C22×C15112yes—
369#413C22×C15112yes—
370C2×#101C22×C15112yes—
371#410C22×C15112yes—
372#405C22×C15111yescharacteristic
373#344C22×C15112yes—
3742−1+4—24no—
3752−1+4—24no—
3762−1+4—24no—
3772−1+4—42no—
378C2×#41—22no—
379C2×#41—22no—
380C2×#41—42no—
381C2×#41C23×C15111yescharacteristic
382C2×#41C23×C15111yescharacteristic
383C2×#41C23×C15112yes—
384C22×Q8—22no—
385C22×Q8—22no—
386C22×Q8C23×C15112yes—
387#137—28no—
388#137—28no—
389#137—21no—
390#137—24no—
391#137—22no—
392#137—22no—
393#137—24no—
394#137D4×C15112yes—
395AGL(1,ℤ/8)—21no—
396AGL(1,ℤ/8)—22no—
397AGL(1,ℤ/8)—22no—
398AGL(1,ℤ/8)D4×C15112yes—
399#135—24no—
400#135—24no—
401#135—22no—
402#135—21no—
403#135—21no—
404#135—21no—
405#135—21no—
406#135—42no—
407C2×Q16—24no—
408C2×Q16—24no—
409C2×Q16—22no—
410C2×Q16—21no—
411C2×Q16—21no—
412C2×Q16—21no—
413C2×Q16—21no—
414C2×Q16D4×C15111yescharacteristic
415C2×Q16D4×C15112yes—
416C2×Q16D4×C15112yes—
417C2×SD16—22no—
418C2×SD16D4×C15112yes—
419C2×D8D4×C15111yescharacteristic
420#131—21no—
421#131—21no—
422#131—21no—
423#131—21no—
424#131—21no—
425#131—21no—
426#131D4×C15112yes—
427#131D4×C15112yes—
428C2×M16—21no—
429C2×M16—21no—
430C2×M16C23×C15111yescharacteristic
431C2×M16C23×C15112yes—
432C2×M16C23×C15111yescharacteristic
433C2×M16C23×C15111yescharacteristic
434C22×C8—21no—
435C22×C8—21no—
436C22×C8C23×C15111yescharacteristic
437C4⋊Q8—22no—
438#124—22no—
439#123—42no—
440C22⋊Q8—24no—
441#117C23×C15112yes—
442#117C23×C15111yescharacteristic
443#108—22no—
444#108—21no—
445#108—21no—
446#107—21no—
447#106—21no—
448#104—22no—
449#104—24no—
450#104—22no—
451#104—24no—
452#103—24no—
453#103—42no—
454#101—22no—
455#101—24no—
456#100—22no—
457#99—42no—
458#97—21no—
459C4×C8—21no—
460#41—21no—
461#41—21no—
462#41—28no—
463#41—21no—
464#41—22no—
465#41—21no—
466#41—22no—
467#41—22no—
468#41—21no—
469#41—21no—
470#41—22no—
471#41—44no—
472#41—48no—
473#41—44no—
474#41—48no—
475#41—44no—
476#41C2×D4×C15112yes—
477#41C2×D4×C15112yes—
478C2×Q8—22no—
479C2×Q8—28no—
480C2×Q8—22no—
481C2×Q8—22no—
482C2×Q8—22no—
483C2×Q8—22no—
484C2×Q8—42no—
485C2×Q8—44no—
486C2×Q8—44no—
487C2×Q8—44no—
488C2×Q8C2×D4×C15112yes—
489C2×Q8C2×D4×C15114yes—
490C2×Q8C2×D4×C15111yescharacteristic
491C2×Q8#41×C15111yescharacteristic
492C2×D4—21no—
493C2×D4—22no—
494C2×D4—21no—
495C2×D4—42no—
496C2×D4C2×D4×C15112yes—
497C2×D4C2×D4×C15111yescharacteristic
498C2×D4#41×C15111yescharacteristic
499C22×C4—21no—
500C22×C4—22no—
501C22×C4—21no—
502C22×C4—22no—
503C22×C4—42no—
504C22×C4—42no—
505C22×C4C24×C15111yescharacteristic
506Q16—28no—
507Q16—22no—
508Q16—21no—
509Q16—22no—
510Q16—21no—
511Q16—22no—
512Q16—22no—
513Q16—22no—
514Q16—42no—
515SD16—28no—
516SD16—22no—
517SD16—22no—
518SD16—22no—
519SD16—22no—
520SD16—42no—
521SD16—42no—
522D8—22no—
523D8—21no—
524D8—21no—
525D8—42no—
526M16—21no—
527M16—21no—
528M16—22no—
529M16—22no—
530M16—21no—
531M16—22no—
532M16—22no—
533M16—21no—
534M16—41no—
535M16—41no—
536M16C2×D4×C15112yes—
537M16C2×D4×C15112yes—
538C2×C8—21no—
539C2×C8—21no—
540C2×C8—22no—
541C2×C8—22no—
542C2×C8—21no—
543C2×C8—22no—
544C2×C8—41no—
545C2×C8—41no—
546C2×C8C2×D4×C15111yescharacteristic
547C2×C8C2×D4×C15111yescharacteristic
548C2×C8C2×D4×C15111yescharacteristic
549C2×C8C2×D4×C15111yescharacteristic
550C2×C8C2×D4×C15111yescharacteristic
551C2×C8C2×D4×C15111yescharacteristic
552C4⋊C4—22no—
553C4⋊C4—21no—
554C4⋊C4—44no—
555C22⋊C4—21no—
556C22⋊C4—22no—
557C22⋊C4—44no—
558C42—21no—
559C42—22no—
560C23—21no—
561C23—21no—
562C23—22no—
563C23H(5,𝔽2)×C15111yescharacteristic
564Q8—21no—
565Q8—24no—
566Q8—22no—
567Q8—21no—
568Q8—21no—
569Q8—22no—
570Q8—24no—
571Q8—48no—
572Q8—42no—
573Q8—42no—
574Q8#121×C15112yes—
575D4—22no—
576D4—22no—
577D4—22no—
578D4—21no—
579D4—21no—
580D4—22no—
581D4—21no—
582D4—48no—
583D4—42no—
584D4—41no—
585D4—42no—
586D4—41no—
587D4#121×C15112yes—
588C2×C4—21no—
589C2×C4—22no—
590C2×C4—22no—
591C2×C4—24no—
592C2×C4—21no—
593C2×C4—22no—
594C2×C4—48no—
595C2×C4—48no—
596C2×C4—42no—
597C2×C4—42no—
598C2×C4—41no—
599C2×C4—42no—
600C2×C4—42no—
601C2×C4—41no—
602C2×C4—41no—
603C2×C4—42no—
604C2×C4C22×D4×C15111yescharacteristic
605C2×C4C22×D4×C15111yescharacteristic
606C2×C4C22×D4×C15111yescharacteristic
607C2×C4C22×D4×C15111yescharacteristic
608C2×C4C2×#41×C15111yescharacteristic
609C2×C4H(5,𝔽2)×C15111yescharacteristic
610C8—22no—
611C8—22no—
612C8—41no—
613C8—42no—
614C8#120×C15111yescharacteristic
615C8#120×C15111yescharacteristic
616C8#120×C15111yescharacteristic
617C8#120×C15111yescharacteristic
618C22—22no—
619C22—41no—
620C22—42no—
621C22—42no—
622C22—42no—
623C22—41no—
624C22—82no—
625C22#535×C15111yescharacteristic
626C22D42×C15111yescharacteristic
627C22#546×C15111yescharacteristic
628C4—22no—
629C4—44no—
630C4—42no—
631C4—41no—
632C4—82no—
633C4—81no—
634C4C2×#120×C15111yescharacteristic
635C4C2×#121×C15111yescharacteristic
636C4D42×C15111yescharacteristic
637C4#546×C15111yescharacteristic
638C2—21no—
639C2—21no—
640C2—21no—
641C2—42no—
642C2—81no—
643C2—82no—
644C2#2408×C15111yescharacteristic
subgroupG/H
center, socleC2×C151#2408
commutator, Frattini, cosocleC22×C4C24×C151
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C2×C151 ◁ C22×C4×C151 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×#578×C151C2semidirect
2. #3067×C151C2semidirect
3. #3059×C151C2semidirect
4. #3020×C151C2semidirect
5. #2955×C151C2semidirect
6. #2049×C151C2semidirect
7. #2009×C151C2semidirect
8. #1979×C151C2semidirect
9. #1976×C151C2semidirect
10. #1814×C151C2semidirect
11. #1796×C151C2semidirect
322. #24296C151direct (N × H)
323. C151#24296direct (N × H)
324. C2×#578C2×C151semidirect
325. #3067C2×C151semidirect
326. #3059C2×C151semidirect
327. #3020C2×C151semidirect
328. #2955C2×C151semidirect
329. #2049C2×C151semidirect
330. #2009C2×C151semidirect
331. #1979C2×C151semidirect
332. #1976C2×C151semidirect
333. #1814C2×C151semidirect
334. #1796C2×C151semidirect

Maximal subgroups

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

subgroupindex
C2×#578×C1512
#3067×C1512
#3059×C1512
#3020×C1512
#2955×C1512
#2049×C1512
#2009×C1512
#1979×C1512
#1976×C1512
#1814×C1512
#1796×C1512
#24296151