Finite Group Databasebeta

← C151×#18874 #50323799

Subgroups — C151×#18874 #50323799

Order 38656.

1040 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
1#3508×C151C211yesmaximal, characteristic, complemented
2#3246×C151C211yesmaximal, characteristic, complemented
3#3205×C151C211yesmaximal, characteristic, complemented
4#3035×C151C211yesmaximal, characteristic, complemented
5#1642×C151C212yesmaximal, complemented
6#1640×C151C212yesmaximal, complemented
7#1621×C151C212yesmaximal, complemented
8#1620×C151C212yesmaximal, complemented
9C2×#331×C151C211yesmaximal, characteristic, complemented
10#1481×C151C211yesmaximal, characteristic, complemented
11#1477×C151C211yesmaximal, characteristic, complemented
12C2×#135×C151—21no—
13#559×C151—21no—
14#559×C151C2212yes—
15#550×C151—21no—
16#550×C151C2212yes—
17#546×C151—22no—
18#546×C151—22no—
19#540×C151—22no—
20#535×C151—21no—
21#533×C151C2211yescharacteristic
22#532×C151—21no—
23#532×C151—21no—
24#532×C151C2211yescharacteristic
25C2×#127×C151C2211yescharacteristic
26#518×C151—21no—
27C4×#41×C151C2211yescharacteristic
28#493×C151C2212yes—
29#486×C151C2212yes—
30#476×C151—21no—
31#475×C151C2212yescomplemented
32#465×C151—22no—
33#464×C151—21no—
34#463×C151—21no—
35#462×C151C2211yescharacteristic, complemented
36#461×C151—21no—
37#461×C151C2211yescharacteristic, complemented
38#460×C151C2211yescharacteristic, complemented
39#460×C151C2212yescomplemented
40#459×C151—22no—
41#459×C151C2211yescharacteristic, complemented
42#447×C151—22no—
43#431×C151C2211yescharacteristic
44C2×C4⋊C8×C151C2211yescharacteristic
45C2×C4⋊C8×C151C2211yescharacteristic
46#416×C151—21no—
47#331×C151C2212yes—
48#331×C151C2212yes—
49Q8⋊C8×C151C2212yescomplemented
50Q8⋊C8×C151C2212yescomplemented
51Q8⋊C8×C151C2212yescomplemented
52D4⋊C8×C151C2212yescomplemented
53C2×#41×C151—21no—
54C2×#41×C151—22no—
55C2×#41×C151—22no—
56C2×#41×C151D411yescharacteristic
57C22×D4×C151—21no—
58C22×D4×C151—21no—
59C22×D4×C151D412yes—
60#135×C151—44no—
61C2×Q16×C151—21no—
62C2×SD16×C151—21no—
63C2×SD16×C151—21no—
64C2×SD16×C151—22no—
65C2×D8×C151—21no—
66C2×D8×C151—24no—
67C22×C8×C151—21no—
68C22×C8×C151—21no—
69C4⋊Q8×C151D411yescharacteristic
70C4⋊Q8×C151D411yescharacteristic
71C4⋊Q8×C151C2311yescharacteristic
72#127×C151—22no—
73#127×C151—21no—
74#127×C151—21no—
75#127×C151D412yes—
76#127×C151C2311yescharacteristic
77#127×C151C2312yes—
78#125×C151—21no—
79#124×C151—22no—
80#124×C151—21no—
81#124×C151—22no—
82#124×C151—22no—
83#123×C151—24no—
84#123×C151—24no—
85C22⋊Q8×C151—21no—
86C22⋊Q8×C151D412yes—
87#121×C151—22no—
88#121×C151—22no—
89#121×C151—22no—
90#121×C151—24no—
91#121×C151—24no—
92#121×C151—22no—
93#121×C151—21no—
94#121×C151—21no—
95#120×C151—24no—
96C4×Q8×C151—21no—
97C4×Q8×C151D411yescharacteristic
98C4×Q8×C151C2311yescharacteristic
99C4×Q8×C151C2312yes—
100C4×D4×C151—22no—
101C4×D4×C151—22no—
102C4×D4×C151—22no—
103C4×D4×C151—21no—
104C4×D4×C151—21no—
105C4×D4×C151—22no—
106C4×D4×C151—22no—
107C4×D4×C151—22no—
108C4×D4×C151—21no—
109C4×D4×C151—21no—
110C4×D4×C151D411yescharacteristic
111C4×D4×C151C2311yescharacteristic
112#117×C151—21no—
113#117×C151—21no—
114#117×C151D411yescharacteristic
115C2×C22⋊C4×C151—24no—
116C2×C42×C151—21no—
117C2×C42×C151C2311yescharacteristic
118#106×C151—22no—
119C4⋊C8×C151—21no—
120C4⋊C8×C151—21no—
121C4⋊C8×C151—21no—
122C4⋊C8×C151C2311yescharacteristic
123C4⋊C8×C151C2311yescharacteristic
124C4⋊C8×C151C2312yes—
125#103×C151—21no—
126#103×C151—21no—
127#103×C151—22no—
128#102×C151—24no—
129#102×C151—21no—
130#102×C151—21no—
131#102×C151—22no—
132C22⋊C8×C151—21no—
133C4×C8×C151C2312yes—
134C24×C151—22no—
135#41×C151—22no—
136#41×C151—22no—
137#41×C151—42no—
138#41×C151—42no—
139#41×C151—82no—
140#41×C151—82no—
141#41×C151—84no—
142C2×Q8×C151—21no—
143C2×Q8×C151—21no—
144C2×Q8×C151C2×D412yes—
145C2×Q8×C151C2×D411yescharacteristic
146C2×D4×C151—21no—
147C2×D4×C151—24no—
148C2×D4×C151—24no—
149C2×D4×C151—22no—
150C2×D4×C151—22no—
151C2×D4×C151—22no—
152C2×D4×C151—22no—
153C2×D4×C151—22no—
154C2×D4×C151—21no—
155C2×D4×C151—21no—
156C2×D4×C151—21no—
157C2×D4×C151—41no—
158C2×D4×C151—42no—
159C2×D4×C151—42no—
160C2×D4×C151—81no—
161C2×D4×C151—81no—
162C2×D4×C151—82no—
163C2×D4×C151C2×D411yescharacteristic
164C2×D4×C151C2×D414yes—
165C22×C4×C151—24no—
166C22×C4×C151—24no—
167C22×C4×C151—21no—
168C22×C4×C151—21no—
169C22×C4×C151—21no—
170C22×C4×C151—41no—
171C22×C4×C151C2×D411yescharacteristic
172C22×C4×C151C2×D411yescharacteristic
173C22×C4×C151C2×D411yescharacteristic
174Q16×C151—42no—
175SD16×C151—42no—
176SD16×C151—42no—
177SD16×C151—82no—
178D8×C151—42no—
179D8×C151—84no—
180C2×C8×C151—22no—
181C2×C8×C151—22no—
182C2×C8×C151—21no—
183C2×C8×C151—21no—
184C2×C8×C151—42no—
185C2×C8×C151—81no—
186C4⋊C4×C151—21no—
187C4⋊C4×C151—21no—
188C4⋊C4×C151—21no—
189C4⋊C4×C151—21no—
190C4⋊C4×C151—22no—
191C4⋊C4×C151—21no—
192C4⋊C4×C151—22no—
193C4⋊C4×C151—21no—
194C4⋊C4×C151—21no—
195C4⋊C4×C151C2×D411yescharacteristic
196C4⋊C4×C151C2×D411yescharacteristic
197C4⋊C4×C151C2×D412yes—
198C22⋊C4×C151—24no—
199C22⋊C4×C151—24no—
200C22⋊C4×C151—24no—
201C22⋊C4×C151—24no—
202C22⋊C4×C151—21no—
203C22⋊C4×C151—22no—
204C22⋊C4×C151—21no—
205C22⋊C4×C151—21no—
206C22⋊C4×C151—41no—
207C22⋊C4×C151—41no—
208C42×C151—21no—
209C42×C151—21no—
210C42×C151—21no—
211C42×C151—22no—
212C42×C151C2×D411yescharacteristic
213C42×C151C2×D411yescharacteristic
214C42×C151C2×D411yescharacteristic
215C42×C151C2411yescharacteristic
216C23×C151—24no—
217C23×C151—21no—
218C23×C151—44no—
219C23×C151—41no—
220C23×C151—82no—
221C23×C151—82no—
222C23×C151#12011yescharacteristic
223Q8×C151—21no—
224Q8×C151—21no—
225Q8×C151—22no—
226Q8×C151—22no—
227Q8×C151—42no—
228Q8×C151—41no—
229Q8×C151—41no—
230D4×C151—21no—
231D4×C151—21no—
232D4×C151—44no—
233D4×C151—44no—
234D4×C151—42no—
235D4×C151—42no—
236D4×C151—42no—
237D4×C151—41no—
238D4×C151—42no—
239D4×C151—41no—
240D4×C151—42no—
241D4×C151—41no—
242D4×C151—42no—
243D4×C151—41no—
244D4×C151—44no—
245D4×C151—82no—
246D4×C151—84no—
247D4×C151—84no—
248D4×C151—82no—
249C2×C4×C151—21no—
250C2×C4×C151—21no—
251C2×C4×C151—22no—
252C2×C4×C151—21no—
253C2×C4×C151—22no—
254C2×C4×C151—21no—
255C2×C4×C151—21no—
256C2×C4×C151—41no—
257C2×C4×C151—42no—
258C2×C4×C151—41no—
259C2×C4×C151—41no—
260C2×C4×C151—42no—
261C2×C4×C151—41no—
262C2×C4×C151—84no—
263C2×C4×C151—84no—
264C2×C4×C151—82no—
265C2×C4×C151#12011yescharacteristic
266C2×C4×C151#12011yescharacteristic
267C2×C4×C151#12011yescharacteristic
268C2×C4×C151#13512yes—
269C2×C4×C151AGL(1,ℤ/8)12yes—
270C2×C4×C151C22×D411yescharacteristic
271C2×C4×C151C22×D411yescharacteristic
272C2×C4×C151C22×D411yescharacteristic
273C8×C151—42no—
274C8×C151—41no—
275C8×C151—41no—
276C8×C151—42no—
277C22×C151—21no—
278C22×C151—21no—
279C22×C151—41no—
280C22×C151—44no—
281C22×C151—41no—
282C22×C151—44no—
283C22×C151—41no—
284C22×C151—44no—
285C22×C151—81no—
286C22×C151—81no—
287C22×C151—81no—
288C22×C151—164no—
289C22×C151#44912yes—
290C22×C151C2×#12011yescharacteristic
291C4×C151—21no—
292C4×C151—21no—
293C4×C151—21no—
294C4×C151—41no—
295C4×C151—41no—
296C4×C151—42no—
297C4×C151—41no—
298C4×C151—42no—
299C4×C151—81no—
300C4×C151#44912yes—
301C4×C151C2×#13511yescharacteristic
302C4×C151C2×AGL(1,ℤ/8)11yescharacteristic
303C4×C151#57611yescharacteristic
304C4×C151#57711yescharacteristic
305C2×C151—22no—
306C2×C151—81no—
307C2×C151—84no—
308C2×C151—161no—
309C2×C151C2×#44911yescharacteristic
310C2×C151#301211yescharacteristic
311C2×C151#301911yescharacteristic
312#18874C15111yesmaximal, characteristic, direct product factor, Sylow
313C151#1887411yescharacteristic, direct product factor, Sylow
314#3508C2×C15111yescharacteristic, complemented
315#3246C2×C15111yescharacteristic, complemented
316#3205C2×C15111yescharacteristic, complemented
317#3035C2×C15111yescharacteristic, complemented
318#1642C2×C15112yescomplemented
319#1640C2×C15112yescomplemented
320#1621C2×C15112yescomplemented
321#1620C2×C15112yescomplemented
322C2×#331C2×C15111yescharacteristic, complemented
323#1481C2×C15111yescharacteristic, complemented
324#1477C2×C15111yescharacteristic, complemented
325C2×#135—21no—
326#559—21no—
327#559C22×C15112yes—
328#550—21no—
329#550C22×C15112yes—
330#546—22no—
331#546—22no—
332#540—22no—
333#535—21no—
334#533C22×C15111yescharacteristic
335#532—21no—
336#532—21no—
337#532C22×C15111yescharacteristic
338C2×#127C22×C15111yescharacteristic
339#518—21no—
340C4×#41C22×C15111yescharacteristic
341#493C22×C15112yes—
342#486C22×C15112yes—
343#476—21no—
344#475C22×C15112yescomplemented
345#465—22no—
346#464—21no—
347#463—21no—
348#462C22×C15111yescharacteristic, complemented
349#461—21no—
350#461C22×C15111yescharacteristic, complemented
351#460C22×C15111yescharacteristic, complemented
352#460C22×C15112yescomplemented
353#459—22no—
354#459C22×C15111yescharacteristic, complemented
355#447—22no—
356#431C22×C15111yescharacteristic
357C2×C4⋊C8C22×C15111yescharacteristic
358C2×C4⋊C8C22×C15111yescharacteristic
359#416—21no—
360#331C22×C15112yes—
361#331C22×C15112yes—
362Q8⋊C8C22×C15112yescomplemented
363Q8⋊C8C22×C15112yescomplemented
364Q8⋊C8C22×C15112yescomplemented
365D4⋊C8C22×C15112yescomplemented
366C2×#41—22no—
367C2×#41—22no—
368C2×#41—21no—
369C2×#41D4×C15111yescharacteristic
370C22×D4—21no—
371C22×D4—21no—
372C22×D4D4×C15112yes—
373#135—44no—
374C2×Q16—21no—
375C2×SD16—21no—
376C2×SD16—21no—
377C2×SD16—22no—
378C2×D8—21no—
379C2×D8—24no—
380C22×C8—21no—
381C22×C8—21no—
382C4⋊Q8D4×C15111yescharacteristic
383C4⋊Q8D4×C15111yescharacteristic
384C4⋊Q8C23×C15111yescharacteristic
385#127—22no—
386#127—21no—
387#127—21no—
388#127D4×C15112yes—
389#127C23×C15111yescharacteristic
390#127C23×C15112yes—
391#125—21no—
392#124—22no—
393#124—22no—
394#124—22no—
395#124—21no—
396#123—24no—
397#123—24no—
398C22⋊Q8—21no—
399C22⋊Q8D4×C15112yes—
400#121—22no—
401#121—22no—
402#121—22no—
403#121—24no—
404#121—24no—
405#121—22no—
406#121—21no—
407#121—21no—
408#120—24no—
409C4×Q8—21no—
410C4×Q8D4×C15111yescharacteristic
411C4×Q8C23×C15111yescharacteristic
412C4×Q8C23×C15112yes—
413C4×D4—22no—
414C4×D4—22no—
415C4×D4—22no—
416C4×D4—21no—
417C4×D4—21no—
418C4×D4—22no—
419C4×D4—22no—
420C4×D4—22no—
421C4×D4—21no—
422C4×D4—21no—
423C4×D4D4×C15111yescharacteristic
424C4×D4C23×C15111yescharacteristic
425#117—21no—
426#117—21no—
427#117D4×C15111yescharacteristic
428C2×C22⋊C4—24no—
429C2×C42—21no—
430C2×C42C23×C15111yescharacteristic
431#106—22no—
432C4⋊C8—21no—
433C4⋊C8—21no—
434C4⋊C8—21no—
435C4⋊C8C23×C15112yes—
436C4⋊C8C23×C15111yescharacteristic
437C4⋊C8C23×C15111yescharacteristic
438#103—22no—
439#103—21no—
440#103—21no—
441#102—24no—
442#102—21no—
443#102—21no—
444#102—22no—
445C22⋊C8—21no—
446C4×C8C23×C15112yes—
447C24—22no—
448#41—22no—
449#41—22no—
450#41—42no—
451#41—42no—
452#41—82no—
453#41—82no—
454#41—84no—
455C2×Q8—21no—
456C2×Q8—21no—
457C2×Q8C2×D4×C15112yes—
458C2×Q8C2×D4×C15111yescharacteristic
459C2×D4—21no—
460C2×D4—24no—
461C2×D4—24no—
462C2×D4—22no—
463C2×D4—22no—
464C2×D4—22no—
465C2×D4—22no—
466C2×D4—22no—
467C2×D4—21no—
468C2×D4—21no—
469C2×D4—21no—
470C2×D4—41no—
471C2×D4—42no—
472C2×D4—42no—
473C2×D4—81no—
474C2×D4—81no—
475C2×D4—82no—
476C2×D4C2×D4×C15111yescharacteristic
477C2×D4C2×D4×C15114yes—
478C22×C4—24no—
479C22×C4—24no—
480C22×C4—21no—
481C22×C4—21no—
482C22×C4—21no—
483C22×C4—41no—
484C22×C4C2×D4×C15111yescharacteristic
485C22×C4C2×D4×C15111yescharacteristic
486C22×C4C2×D4×C15111yescharacteristic
487Q16—42no—
488SD16—42no—
489SD16—42no—
490SD16—82no—
491D8—42no—
492D8—84no—
493C2×C8—22no—
494C2×C8—22no—
495C2×C8—21no—
496C2×C8—21no—
497C2×C8—42no—
498C2×C8—81no—
499C4⋊C4—21no—
500C4⋊C4—21no—
501C4⋊C4—21no—
502C4⋊C4—21no—
503C4⋊C4—22no—
504C4⋊C4—21no—
505C4⋊C4—22no—
506C4⋊C4—21no—
507C4⋊C4—21no—
508C4⋊C4C2×D4×C15111yescharacteristic
509C4⋊C4C2×D4×C15111yescharacteristic
510C4⋊C4C2×D4×C15112yes—
511C22⋊C4—24no—
512C22⋊C4—24no—
513C22⋊C4—24no—
514C22⋊C4—24no—
515C22⋊C4—21no—
516C22⋊C4—22no—
517C22⋊C4—21no—
518C22⋊C4—21no—
519C22⋊C4—41no—
520C22⋊C4—41no—
521C42—21no—
522C42—21no—
523C42—21no—
524C42—22no—
525C42C2×D4×C15111yescharacteristic
526C42C2×D4×C15111yescharacteristic
527C42C2×D4×C15111yescharacteristic
528C42C24×C15111yescharacteristic
529C23—24no—
530C23—21no—
531C23—44no—
532C23—41no—
533C23—82no—
534C23—82no—
535C23#120×C15111yescharacteristic
536Q8—21no—
537Q8—21no—
538Q8—22no—
539Q8—22no—
540Q8—42no—
541Q8—41no—
542Q8—41no—
543D4—21no—
544D4—21no—
545D4—44no—
546D4—44no—
547D4—42no—
548D4—42no—
549D4—44no—
550D4—42no—
551D4—41no—
552D4—42no—
553D4—41no—
554D4—42no—
555D4—41no—
556D4—42no—
557D4—41no—
558D4—82no—
559D4—84no—
560D4—84no—
561D4—82no—
562C2×C4—21no—
563C2×C4—21no—
564C2×C4—21no—
565C2×C4—21no—
566C2×C4—21no—
567C2×C4—22no—
568C2×C4—22no—
569C2×C4—41no—
570C2×C4—42no—
571C2×C4—42no—
572C2×C4—41no—
573C2×C4—41no—
574C2×C4—41no—
575C2×C4—84no—
576C2×C4—84no—
577C2×C4—82no—
578C2×C4#120×C15111yescharacteristic
579C2×C4#120×C15111yescharacteristic
580C2×C4#120×C15111yescharacteristic
581C2×C4#135×C15112yes—
582C2×C4AGL(1,ℤ/8)×C15112yes—
583C2×C4C22×D4×C15111yescharacteristic
584C2×C4C22×D4×C15111yescharacteristic
585C2×C4C22×D4×C15111yescharacteristic
586C8—42no—
587C8—41no—
588C8—41no—
589C8—42no—
590C22—21no—
591C22—21no—
592C22—41no—
593C22—44no—
594C22—41no—
595C22—44no—
596C22—41no—
597C22—44no—
598C22—81no—
599C22—81no—
600C22—81no—
601C22—164no—
602C22#449×C15112yes—
603C22C2×#120×C15111yescharacteristic
604C4—21no—
605C4—21no—
606C4—21no—
607C4—41no—
608C4—41no—
609C4—42no—
610C4—41no—
611C4—42no—
612C4—81no—
613C4#449×C15112yes—
614C4C2×#135×C15111yescharacteristic
615C4C2×AGL(1,ℤ/8)×C15111yescharacteristic
616C4#576×C15111yescharacteristic
617C4#577×C15111yescharacteristic
618C2—22no—
619C2—84no—
620C2—81no—
621C2—161no—
622C2C2×#449×C15111yescharacteristic
623C2#3012×C15111yescharacteristic
624C2#3019×C15111yescharacteristic
subgroupG/H
center, socleC22×C151C2×#120
commutator, Frattini, cosocleC42C24×C151
LCSG ▷ C42 ▷ C22 ▷ C1
UCSC1 ◁ C22×C151 ◁ C2×C42×C151 ◁ G

Complements

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

NH ≅ G/Ntype
1. #3508×C151C2semidirect
2. #3246×C151C2semidirect
3. #3205×C151C2semidirect
4. #3035×C151C2semidirect
5. #1642×C151C2semidirect
6. #1640×C151C2semidirect
7. #1621×C151C2semidirect
8. #1620×C151C2semidirect
9. C2×#331×C151C2semidirect
10. #1481×C151C2semidirect
11. #1477×C151C2semidirect
31. #475×C151C22semidirect
35. #462×C151C22semidirect
37. #461×C151C22semidirect
38. #460×C151C22semidirect
39. #460×C151C22semidirect
41. #459×C151C22semidirect
49. Q8⋊C8×C151C22semidirect
50. Q8⋊C8×C151C22semidirect
51. Q8⋊C8×C151C22semidirect
52. D4⋊C8×C151C22semidirect
312. #18874C151direct (N × H)
313. C151#18874direct (N × H)
314. #3508C2×C151semidirect
315. #3246C2×C151semidirect
316. #3205C2×C151semidirect
317. #3035C2×C151semidirect
318. #1642C2×C151semidirect
319. #1640C2×C151semidirect
320. #1621C2×C151semidirect
321. #1620C2×C151semidirect
322. C2×#331C2×C151semidirect
323. #1481C2×C151semidirect
324. #1477C2×C151semidirect
344. #475C22×C151semidirect
348. #462C22×C151semidirect
350. #461C22×C151semidirect
351. #460C22×C151semidirect
352. #460C22×C151semidirect
354. #459C22×C151semidirect
362. Q8⋊C8C22×C151semidirect
363. Q8⋊C8C22×C151semidirect
364. Q8⋊C8C22×C151semidirect
365. D4⋊C8C22×C151semidirect

Maximal subgroups

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

subgroupindex
#3508×C1512
#3246×C1512
#3205×C1512
#3035×C1512
#1642×C1512
#1640×C1512
#1621×C1512
#1620×C1512
C2×#331×C1512
#1481×C1512
#1477×C1512
#18874151