Finite Group Databasebeta

← C151×#24808 #50329733

Subgroups — C151×#24808 #50329733

Order 38656.

820 conjugacy classes of subgroups.

The subgroup lattice has 658 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#3069×C151C211yesmaximal, characteristic, complemented
2#3068×C151C211yesmaximal, characteristic
3C2×#471×C151C211yesmaximal, characteristic, complemented
4C2×#471×C151C211yesmaximal, characteristic, complemented
5#2955×C151C211yesmaximal, characteristic, complemented
6#2916×C151C211yesmaximal, characteristic, complemented
7#2070×C151C211yesmaximal, characteristic, complemented
8#2069×C151C211yesmaximal, characteristic, complemented
9#2049×C151C211yesmaximal, characteristic, complemented
10#2048×C151C211yesmaximal, characteristic, complemented
11#1977×C151C211yesmaximal, characteristic, complemented
12#1953×C151C211yesmaximal, characteristic, complemented
13#1903×C151C211yesmaximal, characteristic, complemented
14#1902×C151C211yesmaximal, characteristic, complemented
15#1813×C151C211yesmaximal, characteristic, complemented
16#575×C151C2211yescharacteristic
17C2×#137×C151C2211yescharacteristic
18C2×#137×C151C2211yescharacteristic
19C2×AGL(1,ℤ/8)×C151C2211yescharacteristic
20C2×AGL(1,ℤ/8)×C151C2211yescharacteristic
21C22×SD16×C151C2211yescharacteristic
22#568×C151C2211yescharacteristic
23#568×C151C2211yescharacteristic
24C2×#131×C151C2211yescharacteristic
25C2×#131×C151C2211yescharacteristic
26#473×C151—22no—
27#472×C151—22no—
28#471×C151—22no—
29#471×C151—22no—
30#471×C151—22no—
31#471×C151—22no—
32#471×C151—22no—
33#471×C151—22no—
34#444×C151—22no—
35#443×C151—22no—
36#430×C151—22no—
37#430×C151C2211yescharacteristic
38#430×C151C2211yescharacteristic
39#430×C151C2211yescharacteristic
40#430×C151C2211yescharacteristic
41#430×C151C2211yescharacteristic
42C2×#108×C151—22no—
43C2×#108×C151C2211yescharacteristic
44C2×#108×C151C2211yescharacteristic
45C2×#108×C151C2211yescharacteristic
46#421×C151C2211yescharacteristic
47#421×C151C2211yescharacteristic
48#419×C151C2211yescharacteristic
49#418×C151C2211yescharacteristic
50#413×C151C2211yescharacteristic
51#413×C151C2211yescharacteristic
52C2×#101×C151C2211yescharacteristic
53C2×#101×C151C2211yescharacteristic
54C2×#101×C151C2211yescharacteristic
55C2×#100×C151C2211yescharacteristic
56C2×#100×C151C2211yescharacteristic
57C2×#100×C151C2211yescharacteristic
58#405×C151C2211yescharacteristic
59#344×C151C2211yescharacteristic
60#344×C151C2211yescharacteristic
61#338×C151C2211yescharacteristic
62#338×C151C2211yescharacteristic
63C2×#41×C151C2311yescharacteristic
64C2×#41×C151C2311yescharacteristic
65C22×Q8×C151C2311yescharacteristic
66C22×D4×C151C2311yescharacteristic
67#137×C151—22no—
68#137×C151—22no—
69#137×C151—22no—
70#137×C151—21no—
71#137×C151—41no—
72#137×C151D412yes—
73AGL(1,ℤ/8)×C151—21no—
74AGL(1,ℤ/8)×C151—22no—
75AGL(1,ℤ/8)×C151—22no—
76AGL(1,ℤ/8)×C151—22no—
77AGL(1,ℤ/8)×C151—41no—
78AGL(1,ℤ/8)×C151D412yes—
79#135×C151—22no—
80C2×Q16×C151—21no—
81C2×Q16×C151—21no—
82C2×SD16×C151—21no—
83C2×SD16×C151—21no—
84C2×SD16×C151—21no—
85C2×SD16×C151—21no—
86C2×SD16×C151—21no—
87C2×SD16×C151—21no—
88C2×SD16×C151—21no—
89C2×SD16×C151—21no—
90C2×SD16×C151—21no—
91C2×SD16×C151—21no—
92C2×D8×C151—21no—
93C2×D8×C151—21no—
94#131×C151—21no—
95#131×C151—21no—
96#131×C151—21no—
97#131×C151—21no—
98#131×C151—21no—
99#131×C151—21no—
100#131×C151—22no—
101#131×C151—22no—
102#131×C151—41no—
103#131×C151—41no—
104#131×C151D412yes—
105#131×C151D412yes—
106C2×M16×C151—21no—
107C2×M16×C151—21no—
108C2×M16×C151—22no—
109C2×M16×C151—22no—
110C2×M16×C151C2311yescharacteristic
111C2×M16×C151C2311yescharacteristic
112C2×M16×C151C2311yescharacteristic
113C2×M16×C151C2311yescharacteristic
114C2×M16×C151C2311yescharacteristic
115C2×M16×C151C2311yescharacteristic
116C2×M16×C151C2311yescharacteristic
117C2×M16×C151C2311yescharacteristic
118C2×M16×C151C2311yescharacteristic
119C22×C8×C151—21no—
120C22×C8×C151—21no—
121C22×C8×C151C2311yescharacteristic
122#117×C151C2311yescharacteristic
123#108×C151—22no—
124#108×C151—22no—
125#108×C151—22no—
126#108×C151—22no—
127#108×C151—22no—
128#108×C151—21no—
129#108×C151—21no—
130#108×C151—21no—
131#108×C151—21no—
132#108×C151D412yes—
133#108×C151D412yes—
134#104×C151—22no—
135#104×C151—22no—
136#103×C151—41no—
137#102×C151—41no—
138#101×C151—22no—
139#101×C151—22no—
140#101×C151—22no—
141#101×C151—21no—
142#101×C151—21no—
143#100×C151—21no—
144#100×C151—21no—
145#100×C151—22no—
146#100×C151—22no—
147#100×C151—22no—
148#97×C151—21no—
149C4×C8×C151—21no—
150C24×C151—21no—
151#41×C151—21no—
152#41×C151—21no—
153#41×C151—21no—
154#41×C151—21no—
155#41×C151—21no—
156#41×C151—21no—
157#41×C151C2×D412yes—
158#41×C151C2×D412yes—
159C2×Q8×C151—21no—
160C2×Q8×C151—21no—
161C2×Q8×C151—21no—
162C2×Q8×C151—21no—
163C2×Q8×C151—21no—
164C2×Q8×C151—21no—
165C2×Q8×C151C2×D411yescharacteristic
166C2×Q8×C151#4111yescharacteristic
167C2×D4×C151—21no—
168C2×D4×C151—21no—
169C2×D4×C151—21no—
170C2×D4×C151—21no—
171C2×D4×C151—21no—
172C2×D4×C151—21no—
173C2×D4×C151—21no—
174C2×D4×C151—21no—
175C2×D4×C151C2×D411yescharacteristic
176C2×D4×C151#4111yescharacteristic
177C22×C4×C151—21no—
178C22×C4×C151—21no—
179C22×C4×C151—21no—
180C22×C4×C151C2411yescharacteristic
181Q16×C151—22no—
182Q16×C151—42no—
183Q16×C151—42no—
184SD16×C151—22no—
185SD16×C151—22no—
186SD16×C151—42no—
187SD16×C151—42no—
188SD16×C151—42no—
189SD16×C151—42no—
190SD16×C151—41no—
191SD16×C151—41no—
192SD16×C151—41no—
193SD16×C151—41no—
194D8×C151—22no—
195D8×C151—42no—
196D8×C151—42no—
197M16×C151—21no—
198M16×C151—21no—
199M16×C151—21no—
200M16×C151—21no—
201M16×C151—22no—
202M16×C151—22no—
203M16×C151—21no—
204M16×C151—21no—
205M16×C151—21no—
206M16×C151—21no—
207M16×C151—21no—
208M16×C151—21no—
209M16×C151—21no—
210M16×C151—21no—
211M16×C151—21no—
212M16×C151—21no—
213M16×C151—42no—
214M16×C151—42no—
215M16×C151—41no—
216M16×C151—41no—
217M16×C151C2×D412yes—
218M16×C151C2×D412yes—
219M16×C151C2×D412yes—
220M16×C151C2×D412yes—
221C2×C8×C151—21no—
222C2×C8×C151—21no—
223C2×C8×C151—21no—
224C2×C8×C151—21no—
225C2×C8×C151—22no—
226C2×C8×C151—22no—
227C2×C8×C151—21no—
228C2×C8×C151—21no—
229C2×C8×C151—21no—
230C2×C8×C151—21no—
231C2×C8×C151—21no—
232C2×C8×C151—42no—
233C2×C8×C151—42no—
234C2×C8×C151—41no—
235C2×C8×C151—41no—
236C2×C8×C151C2×D411yescharacteristic
237C2×C8×C151C2×D411yescharacteristic
238C2×C8×C151C2×D411yescharacteristic
239C2×C8×C151C2×D411yescharacteristic
240C2×C8×C151#4111yescharacteristic
241C2×C8×C151#4111yescharacteristic
242C4⋊C4×C151—21no—
243C22⋊C4×C151—21no—
244C42×C151—21no—
245C23×C151—21no—
246C23×C151—21no—
247C23×C151—41no—
248C23×C151—41no—
249C23×C151—41no—
250C23×C151—161no—
251C23×C1512−1+411yescharacteristic
252Q8×C151—21no—
253Q8×C151—21no—
254Q8×C151—21no—
255Q8×C151—41no—
256Q8×C151—41no—
257Q8×C151—41no—
258Q8×C151—41no—
259Q8×C151#12112yes—
260D4×C151—22no—
261D4×C151—22no—
262D4×C151—21no—
263D4×C151—21no—
264D4×C151—21no—
265D4×C151—41no—
266D4×C151—41no—
267D4×C151—41no—
268D4×C151—41no—
269D4×C151—41no—
270D4×C151—41no—
271D4×C151#12112yes—
272C2×C4×C151—21no—
273C2×C4×C151—22no—
274C2×C4×C151—22no—
275C2×C4×C151—21no—
276C2×C4×C151—41no—
277C2×C4×C151—41no—
278C2×C4×C151—41no—
279C2×C4×C151—41no—
280C2×C4×C151—41no—
281C2×C4×C151—41no—
282C2×C4×C151C22×D411yescharacteristic
283C2×C4×C151C22×D411yescharacteristic
284C2×C4×C151C22×D411yescharacteristic
285C2×C4×C151C2×#4111yescharacteristic
286C2×C4×C151C2×#4111yescharacteristic
287C2×C4×C151H(5,𝔽2)11yescharacteristic
288C8×C151—22no—
289C8×C151—22no—
290C8×C151—22no—
291C8×C151—22no—
292C8×C151—41no—
293C8×C151—41no—
294C8×C151—41no—
295C8×C151—41no—
296C8×C151—41no—
297C8×C151#12111yescharacteristic
298C8×C151#12111yescharacteristic
299C8×C151#12111yescharacteristic
300C8×C151#12111yescharacteristic
301C22×C151—22no—
302C22×C151—41no—
303C22×C151—41no—
304C22×C151—81no—
305C22×C151—81no—
306C22×C151—81no—
307C22×C151—161no—
308C22×C151—161no—
309C22×C151—161no—
310C22×C151#53711yescharacteristic
311C22×C151#54711yescharacteristic
312C22×C151#54811yescharacteristic
313C4×C151—22no—
314C4×C151—41no—
315C4×C151—81no—
316C4×C151—81no—
317C4×C151C2×#12111yescharacteristic
318C4×C151C2×#12111yescharacteristic
319C4×C151D4211yescharacteristic
320C4×C151#55311yescharacteristic
321C2×C151—21no—
322C2×C151—21no—
323C2×C151—21no—
324C2×C151—42no—
325C2×C151—81no—
326C2×C151—161no—
327C2×C151#241611yescharacteristic
328#24808C15111yesmaximal, characteristic, direct product factor, Sylow
329C151#2480811yescharacteristic, direct product factor, Sylow
330#3069C2×C15111yescharacteristic, complemented
331#3068C2×C15111yescharacteristic
332C2×#471C2×C15111yescharacteristic, complemented
333C2×#471C2×C15111yescharacteristic, complemented
334#2955C2×C15111yescharacteristic, complemented
335#2916C2×C15111yescharacteristic, complemented
336#2070C2×C15111yescharacteristic, complemented
337#2069C2×C15111yescharacteristic, complemented
338#2049C2×C15111yescharacteristic, complemented
339#2048C2×C15111yescharacteristic, complemented
340#1977C2×C15111yescharacteristic, complemented
341#1953C2×C15111yescharacteristic, complemented
342#1903C2×C15111yescharacteristic, complemented
343#1902C2×C15111yescharacteristic, complemented
344#1813C2×C15111yescharacteristic, complemented
345#575C22×C15111yescharacteristic
346C2×#137C22×C15111yescharacteristic
347C2×#137C22×C15111yescharacteristic
348C2×AGL(1,ℤ/8)C22×C15111yescharacteristic
349C2×AGL(1,ℤ/8)C22×C15111yescharacteristic
350C22×SD16C22×C15111yescharacteristic
351#568C22×C15111yescharacteristic
352#568C22×C15111yescharacteristic
353C2×#131C22×C15111yescharacteristic
354C2×#131C22×C15111yescharacteristic
355#473—22no—
356#472—22no—
357#471—22no—
358#471—22no—
359#471—22no—
360#471—22no—
361#471—22no—
362#471—22no—
363#444—22no—
364#443—22no—
365#430—22no—
366#430C22×C15111yescharacteristic
367#430C22×C15111yescharacteristic
368#430C22×C15111yescharacteristic
369#430C22×C15111yescharacteristic
370#430C22×C15111yescharacteristic
371C2×#108—22no—
372C2×#108C22×C15111yescharacteristic
373C2×#108C22×C15111yescharacteristic
374C2×#108C22×C15111yescharacteristic
375#421C22×C15111yescharacteristic
376#421C22×C15111yescharacteristic
377#419C22×C15111yescharacteristic
378#418C22×C15111yescharacteristic
379#413C22×C15111yescharacteristic
380#413C22×C15111yescharacteristic
381C2×#101C22×C15111yescharacteristic
382C2×#101C22×C15111yescharacteristic
383C2×#101C22×C15111yescharacteristic
384C2×#100C22×C15111yescharacteristic
385C2×#100C22×C15111yescharacteristic
386C2×#100C22×C15111yescharacteristic
387#405C22×C15111yescharacteristic
388#344C22×C15111yescharacteristic
389#344C22×C15111yescharacteristic
390#338C22×C15111yescharacteristic
391#338C22×C15111yescharacteristic
392C2×#41C23×C15111yescharacteristic
393C2×#41C23×C15111yescharacteristic
394C22×Q8C23×C15111yescharacteristic
395C22×D4C23×C15111yescharacteristic
396#137—21no—
397#137—22no—
398#137—22no—
399#137—22no—
400#137—41no—
401#137D4×C15112yes—
402AGL(1,ℤ/8)—21no—
403AGL(1,ℤ/8)—22no—
404AGL(1,ℤ/8)—22no—
405AGL(1,ℤ/8)—22no—
406AGL(1,ℤ/8)—41no—
407AGL(1,ℤ/8)D4×C15112yes—
408#135—22no—
409C2×Q16—21no—
410C2×Q16—21no—
411C2×SD16—21no—
412C2×SD16—21no—
413C2×SD16—21no—
414C2×SD16—21no—
415C2×SD16—21no—
416C2×SD16—21no—
417C2×SD16—21no—
418C2×SD16—21no—
419C2×SD16—21no—
420C2×SD16—21no—
421C2×D8—21no—
422C2×D8—21no—
423#131—21no—
424#131—21no—
425#131—22no—
426#131—22no—
427#131—21no—
428#131—21no—
429#131—21no—
430#131—21no—
431#131—41no—
432#131—41no—
433#131D4×C15112yes—
434#131D4×C15112yes—
435C2×M16—21no—
436C2×M16—21no—
437C2×M16—22no—
438C2×M16—22no—
439C2×M16C23×C15111yescharacteristic
440C2×M16C23×C15111yescharacteristic
441C2×M16C23×C15111yescharacteristic
442C2×M16C23×C15111yescharacteristic
443C2×M16C23×C15111yescharacteristic
444C2×M16C23×C15111yescharacteristic
445C2×M16C23×C15111yescharacteristic
446C2×M16C23×C15111yescharacteristic
447C2×M16C23×C15111yescharacteristic
448C22×C8—21no—
449C22×C8—21no—
450C22×C8C23×C15111yescharacteristic
451#117C23×C15111yescharacteristic
452#108—22no—
453#108—22no—
454#108—22no—
455#108—22no—
456#108—22no—
457#108—21no—
458#108—21no—
459#108—21no—
460#108—21no—
461#108D4×C15112yes—
462#108D4×C15112yes—
463#104—22no—
464#104—22no—
465#103—41no—
466#102—41no—
467#101—21no—
468#101—21no—
469#101—22no—
470#101—22no—
471#101—22no—
472#100—21no—
473#100—21no—
474#100—22no—
475#100—22no—
476#100—22no—
477#97—21no—
478C4×C8—21no—
479C24—21no—
480#41—21no—
481#41—21no—
482#41—21no—
483#41—21no—
484#41—21no—
485#41—21no—
486#41C2×D4×C15112yes—
487#41C2×D4×C15112yes—
488C2×Q8—21no—
489C2×Q8—21no—
490C2×Q8—21no—
491C2×Q8—21no—
492C2×Q8—21no—
493C2×Q8—21no—
494C2×Q8C2×D4×C15111yescharacteristic
495C2×Q8#41×C15111yescharacteristic
496C2×D4—21no—
497C2×D4—21no—
498C2×D4—21no—
499C2×D4—21no—
500C2×D4—21no—
501C2×D4—21no—
502C2×D4—21no—
503C2×D4—21no—
504C2×D4C2×D4×C15111yescharacteristic
505C2×D4#41×C15111yescharacteristic
506C22×C4—21no—
507C22×C4—21no—
508C22×C4—21no—
509C22×C4C24×C15111yescharacteristic
510Q16—22no—
511Q16—42no—
512Q16—42no—
513SD16—22no—
514SD16—22no—
515SD16—42no—
516SD16—42no—
517SD16—42no—
518SD16—42no—
519SD16—41no—
520SD16—41no—
521SD16—41no—
522SD16—41no—
523D8—22no—
524D8—42no—
525D8—42no—
526M16—21no—
527M16—21no—
528M16—21no—
529M16—21no—
530M16—22no—
531M16—22no—
532M16—21no—
533M16—21no—
534M16—21no—
535M16—21no—
536M16—21no—
537M16—21no—
538M16—21no—
539M16—21no—
540M16—21no—
541M16—21no—
542M16—42no—
543M16—42no—
544M16—41no—
545M16—41no—
546M16C2×D4×C15112yes—
547M16C2×D4×C15112yes—
548M16C2×D4×C15112yes—
549M16C2×D4×C15112yes—
550C2×C8—21no—
551C2×C8—21no—
552C2×C8—21no—
553C2×C8—21no—
554C2×C8—22no—
555C2×C8—22no—
556C2×C8—21no—
557C2×C8—21no—
558C2×C8—21no—
559C2×C8—21no—
560C2×C8—21no—
561C2×C8—42no—
562C2×C8—42no—
563C2×C8—41no—
564C2×C8—41no—
565C2×C8C2×D4×C15111yescharacteristic
566C2×C8C2×D4×C15111yescharacteristic
567C2×C8C2×D4×C15111yescharacteristic
568C2×C8C2×D4×C15111yescharacteristic
569C2×C8#41×C15111yescharacteristic
570C2×C8#41×C15111yescharacteristic
571C4⋊C4—21no—
572C22⋊C4—21no—
573C42—21no—
574C23—21no—
575C23—21no—
576C23—41no—
577C23—41no—
578C23—41no—
579C23—161no—
580C232−1+4×C15111yescharacteristic
581Q8—21no—
582Q8—21no—
583Q8—21no—
584Q8—41no—
585Q8—41no—
586Q8—41no—
587Q8—41no—
588Q8#121×C15112yes—
589D4—22no—
590D4—22no—
591D4—21no—
592D4—21no—
593D4—21no—
594D4—41no—
595D4—41no—
596D4—41no—
597D4—41no—
598D4—41no—
599D4—41no—
600D4#121×C15112yes—
601C2×C4—21no—
602C2×C4—22no—
603C2×C4—22no—
604C2×C4—21no—
605C2×C4—41no—
606C2×C4—41no—
607C2×C4—41no—
608C2×C4—41no—
609C2×C4—41no—
610C2×C4—41no—
611C2×C4C22×D4×C15111yescharacteristic
612C2×C4C22×D4×C15111yescharacteristic
613C2×C4C22×D4×C15111yescharacteristic
614C2×C4C2×#41×C15111yescharacteristic
615C2×C4C2×#41×C15111yescharacteristic
616C2×C4H(5,𝔽2)×C15111yescharacteristic
617C8—22no—
618C8—22no—
619C8—22no—
620C8—22no—
621C8—41no—
622C8—41no—
623C8—41no—
624C8—41no—
625C8—41no—
626C8#121×C15111yescharacteristic
627C8#121×C15111yescharacteristic
628C8#121×C15111yescharacteristic
629C8#121×C15111yescharacteristic
630C22—22no—
631C22—41no—
632C22—41no—
633C22—81no—
634C22—81no—
635C22—81no—
636C22—161no—
637C22—161no—
638C22—161no—
639C22#537×C15111yescharacteristic
640C22#547×C15111yescharacteristic
641C22#548×C15111yescharacteristic
642C4—22no—
643C4—41no—
644C4—81no—
645C4—81no—
646C4C2×#121×C15111yescharacteristic
647C4C2×#121×C15111yescharacteristic
648C4D42×C15111yescharacteristic
649C4#553×C15111yescharacteristic
650C2—21no—
651C2—21no—
652C2—21no—
653C2—42no—
654C2—81no—
655C2—161no—
656C2#2416×C15111yescharacteristic
subgroupG/H
center, socleC2×C151#2416
commutator, Frattini, cosocleC22×C4C24×C151
prime radical#3068×C151C2
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. #3069×C151C2semidirect
3. C2×#471×C151C2semidirect
4. C2×#471×C151C2semidirect
5. #2955×C151C2semidirect
6. #2916×C151C2semidirect
7. #2070×C151C2semidirect
8. #2069×C151C2semidirect
9. #2049×C151C2semidirect
10. #2048×C151C2semidirect
11. #1977×C151C2semidirect
12. #1953×C151C2semidirect
13. #1903×C151C2semidirect
14. #1902×C151C2semidirect
15. #1813×C151C2semidirect
328. #24808C151direct (N × H)
329. C151#24808direct (N × H)
330. #3069C2×C151semidirect
332. C2×#471C2×C151semidirect
333. C2×#471C2×C151semidirect
334. #2955C2×C151semidirect
335. #2916C2×C151semidirect
336. #2070C2×C151semidirect
337. #2069C2×C151semidirect
338. #2049C2×C151semidirect
339. #2048C2×C151semidirect
340. #1977C2×C151semidirect
341. #1953C2×C151semidirect
342. #1903C2×C151semidirect
343. #1902C2×C151semidirect
344. #1813C2×C151semidirect

Maximal subgroups

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

subgroupindex
#3069×C1512
#3068×C1512
C2×#471×C1512
#2955×C1512
#2916×C1512
#2070×C1512
#2069×C1512
#2049×C1512
#2048×C1512
#1977×C1512
#1953×C1512
#1903×C1512
#1902×C1512
#1813×C1512
#24808151