Finite Group Databasebeta

← C151×#18582 #50323507

Subgroups — C151×#18582 #50323507

Order 38656.

1124 conjugacy classes of subgroups.

The subgroup lattice has 618 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#3499×C151C211yesmaximal, characteristic, complemented
2#3253×C151C211yesmaximal, characteristic, complemented
3#3141×C151C211yesmaximal, characteristic, complemented
4#3106×C151C211yesmaximal, characteristic, complemented
5#1637×C151C212yesmaximal, complemented
6#1635×C151C212yesmaximal, complemented
7#1627×C151C212yesmaximal, complemented
8#1625×C151C212yesmaximal, complemented
9#1549×C151C211yesmaximal, characteristic, complemented
10#1489×C151C211yesmaximal, characteristic, complemented
11#1484×C151C211yesmaximal, characteristic, complemented
12C2×2−1+4×C151—21no—
13D4×Q8×C151—21no—
14D4×Q8×C151C2212yes—
15#547×C151—22no—
16#547×C151—21no—
17#547×C151—22no—
18#547×C151C2212yes—
19#536×C151—22no—
20#536×C151—21no—
21#532×C151—21no—
22#532×C151C2211yescharacteristic
23#532×C151C2211yescharacteristic
24C2×C4⋊Q8×C151—21no—
25C2×C4⋊Q8×C151C2211yescharacteristic
26C4×#41×C151C2211yescharacteristic
27#489×C151—22no—
28#487×C151C2212yes—
29#486×C151C2212yes—
30#482×C151—21no—
31#477×C151C2211yescharacteristic
32#476×C151—21no—
33#476×C151C2211yescharacteristic
34#476×C151C2212yes—
35#469×C151—22no—
36#460×C151C2211yescharacteristic
37#459×C151—21no—
38#459×C151C2211yescharacteristic
39#459×C151C2212yes—
40#449×C151—21no—
41C4×SD16×C151—21no—
42C4×D8×C151—21no—
43#431×C151C2211yescharacteristic
44#423×C151C2211yescharacteristic
45#417×C151—22no—
46C4×M16×C151C2211yescharacteristic
47#332×C151C2212yes—
48#332×C151C2212yes—
49Q8⋊C8×C151C2212yes—
50D4⋊C8×C151C2212yes—
51D4⋊C8×C151C2212yes—
52D4⋊C8×C151C2212yes—
532−1+4×C151—44no—
542−1+4×C151—44no—
55C2×#41×C151—22no—
56C2×#41×C151—24no—
57C2×#41×C151—22no—
58C2×#41×C151—21no—
59C2×#41×C151—21no—
60C2×#41×C151D411yescharacteristic
61C22×Q8×C151—22no—
62C22×Q8×C151—21no—
63C22×Q8×C151—22no—
64C2×SD16×C151—21no—
65C2×D8×C151—21no—
66C2×D8×C151—22no—
67C2×M16×C151—21no—
68C2×M16×C151—21no—
69C4⋊Q8×C151—22no—
70C4⋊Q8×C151—22no—
71C4⋊Q8×C151—22no—
72C4⋊Q8×C151—21no—
73C4⋊Q8×C151—21no—
74C4⋊Q8×C151D411yescharacteristic
75C4⋊Q8×C151D412yes—
76C4⋊Q8×C151C2311yescharacteristic
77C4⋊Q8×C151C2312yes—
78#127×C151D411yescharacteristic
79#127×C151C2311yescharacteristic
80#124×C151—22no—
81#124×C151—21no—
82#124×C151—21no—
83#123×C151—24no—
84#123×C151—24no—
85#123×C151—24no—
86C22⋊Q8×C151—24no—
87C22⋊Q8×C151—24no—
88C22⋊Q8×C151—22no—
89C22⋊Q8×C151—22no—
90#121×C151—22no—
91#121×C151—22no—
92#121×C151—21no—
93#121×C151—21no—
94#121×C151—21no—
95#121×C151D412yes—
96C4×Q8×C151D411yescharacteristic
97C4×Q8×C151C2311yescharacteristic
98C4×D4×C151—22no—
99C4×D4×C151—22no—
100C4×D4×C151—21no—
101C4×D4×C151—21no—
102C4×D4×C151—21no—
103C4×D4×C151—21no—
104C4×D4×C151—21no—
105C4×D4×C151D411yescharacteristic
106C4×D4×C151C2311yescharacteristic
107C4×D4×C151C2312yes—
108#117×C151—21no—
109#117×C151D411yescharacteristic
110C2×C4⋊C4×C151—22no—
111C2×C4⋊C4×C151—21no—
112C2×C4⋊C4×C151—22no—
113C2×C4⋊C4×C151D412yes—
114C2×C42×C151—21no—
115C2×C42×C151C2311yescharacteristic
116#107×C151—21no—
117#106×C151—21no—
118#106×C151—22no—
119C4⋊C8×C151—21no—
120C4⋊C8×C151C2312yes—
121C4⋊C8×C151C2311yescharacteristic
122C4⋊C8×C151C2311yescharacteristic
123#103×C151—24no—
124#103×C151—21no—
125#102×C151—21no—
126#102×C151—22no—
127#102×C151—24no—
128#102×C151—21no—
129#102×C151—21no—
130#102×C151—22no—
131C22⋊C8×C151—21no—
132#97×C151—21no—
133C4×C8×C151—21no—
134C4×C8×C151C2312yes—
135#41×C151—22no—
136#41×C151—22no—
137#41×C151—48no—
138#41×C151—42no—
139#41×C151—42no—
140#41×C151—44no—
141#41×C151—416no—
142#41×C151—44no—
143#41×C151—44no—
144C2×Q8×C151—24no—
145C2×Q8×C151—22no—
146C2×Q8×C151—21no—
147C2×Q8×C151—22no—
148C2×Q8×C151—21no—
149C2×Q8×C151—48no—
150C2×Q8×C151—42no—
151C2×Q8×C151—42no—
152C2×Q8×C151—44no—
153C2×Q8×C151—44no—
154C2×Q8×C151C2×D411yescharacteristic
155C2×D4×C151—21no—
156C2×D4×C151—24no—
157C2×D4×C151—22no—
158C2×D4×C151—21no—
159C2×D4×C151—21no—
160C2×D4×C151—21no—
161C2×D4×C151—21no—
162C2×D4×C151—21no—
163C2×D4×C151—41no—
164C2×D4×C151C2×D412yes—
165C2×D4×C151C2×D411yescharacteristic
166C22×C4×C151—21no—
167C22×C4×C151—24no—
168C22×C4×C151—24no—
169C22×C4×C151—22no—
170C22×C4×C151—21no—
171C22×C4×C151—21no—
172C22×C4×C151—22no—
173C22×C4×C151—41no—
174C22×C4×C151C2×D411yescharacteristic
175C22×C4×C151C2×D411yescharacteristic
176C22×C4×C151C2×D411yescharacteristic
177SD16×C151—42no—
178D8×C151—42no—
179D8×C151—82no—
180M16×C151—42no—
181M16×C151—81no—
182C2×C8×C151—21no—
183C2×C8×C151—21no—
184C2×C8×C151—22no—
185C2×C8×C151—22no—
186C4⋊C4×C151—24no—
187C4⋊C4×C151—24no—
188C4⋊C4×C151—21no—
189C4⋊C4×C151—22no—
190C4⋊C4×C151—22no—
191C4⋊C4×C151—21no—
192C4⋊C4×C151—22no—
193C4⋊C4×C151—21no—
194C4⋊C4×C151—21no—
195C4⋊C4×C151—21no—
196C4⋊C4×C151C2×D414yes—
197C4⋊C4×C151C2×D412yes—
198C4⋊C4×C151C2×D411yescharacteristic
199C4⋊C4×C151C2×D411yescharacteristic
200C22⋊C4×C151—24no—
201C22⋊C4×C151—24no—
202C22⋊C4×C151—21no—
203C22⋊C4×C151—21no—
204C22⋊C4×C151—22no—
205C22⋊C4×C151—21no—
206C22⋊C4×C151—22no—
207C22⋊C4×C151—41no—
208C22⋊C4×C151—41no—
209C42×C151—21no—
210C42×C151—21no—
211C42×C151—21no—
212C42×C151C2×D411yescharacteristic
213C42×C151C2×D411yescharacteristic
214C42×C151C2×D411yescharacteristic
215C42×C151C2411yescharacteristic
216C23×C151—21no—
217C23×C151—22no—
218C23×C151—41no—
219C23×C151#12011yescharacteristic
220Q8×C151—21no—
221Q8×C151—44no—
222Q8×C151—42no—
223Q8×C151—48no—
224Q8×C151—42no—
225Q8×C151—42no—
226Q8×C151—42no—
227Q8×C151AGL(1,ℤ/8)12yes—
228D4×C151—24no—
229D4×C151—21no—
230D4×C151—22no—
231D4×C151—22no—
232D4×C151—42no—
233D4×C151—42no—
234D4×C151—44no—
235D4×C151—48no—
236D4×C151—41no—
237D4×C151—41no—
238D4×C151—41no—
239D4×C151—41no—
240D4×C151—42no—
241D4×C151—82no—
242D4×C151AGL(1,ℤ/8)12yes—
243C2×C4×C151—24no—
244C2×C4×C151—21no—
245C2×C4×C151—21no—
246C2×C4×C151—21no—
247C2×C4×C151—21no—
248C2×C4×C151—21no—
249C2×C4×C151—22no—
250C2×C4×C151—22no—
251C2×C4×C151—24no—
252C2×C4×C151—21no—
253C2×C4×C151—21no—
254C2×C4×C151—48no—
255C2×C4×C151—44no—
256C2×C4×C151—48no—
257C2×C4×C151—42no—
258C2×C4×C151—42no—
259C2×C4×C151—41no—
260C2×C4×C151—41no—
261C2×C4×C151—42no—
262C2×C4×C151—41no—
263C2×C4×C151—82no—
264C2×C4×C151#12011yescharacteristic
265C2×C4×C151#12011yescharacteristic
266C2×C4×C151#12011yescharacteristic
267C2×C4×C151C22×D411yescharacteristic
268C2×C4×C151C22×D411yescharacteristic
269C2×C4×C151C22×D411yescharacteristic
270C8×C151—42no—
271C8×C151—41no—
272C8×C151—41no—
273C8×C151—42no—
274C22×C151—21no—
275C22×C151—22no—
276C22×C151—21no—
277C22×C151—21no—
278C22×C151—41no—
279C22×C151—41no—
280C22×C151—42no—
281C22×C151—42no—
282C22×C151—42no—
283C22×C151—81no—
284C22×C151—81no—
285C22×C151—81no—
286C22×C151C2×#12011yescharacteristic
287C4×C151—21no—
288C4×C151—22no—
289C4×C151—21no—
290C4×C151—21no—
291C4×C151—44no—
292C4×C151—42no—
293C4×C151—41no—
294C4×C151—41no—
295C4×C151—81no—
296C4×C151#45412yes—
297C4×C151C2×AGL(1,ℤ/8)11yescharacteristic
298C4×C151C2×AGL(1,ℤ/8)11yescharacteristic
299C4×C151#57711yescharacteristic
300C4×C151#57811yescharacteristic
301C2×C151—41no—
302C2×C151—42no—
303C2×C151—82no—
304C2×C151—161no—
305C2×C151#300311yescharacteristic
306C2×C151#301311yescharacteristic
307C2×C151C2×#45411yescharacteristic
308#18582C15111yesmaximal, characteristic, direct product factor, Sylow
309C151#1858211yescharacteristic, direct product factor, Sylow
310#3499C2×C15111yescharacteristic, complemented
311#3253C2×C15111yescharacteristic, complemented
312#3141C2×C15111yescharacteristic, complemented
313#3106C2×C15111yescharacteristic, complemented
314#1637C2×C15112yescomplemented
315#1635C2×C15112yescomplemented
316#1627C2×C15112yescomplemented
317#1625C2×C15112yescomplemented
318#1549C2×C15111yescharacteristic, complemented
319#1489C2×C15111yescharacteristic, complemented
320#1484C2×C15111yescharacteristic, complemented
321C2×2−1+4—21no—
322D4×Q8—21no—
323D4×Q8C22×C15112yes—
324#547—22no—
325#547—21no—
326#547—22no—
327#547C22×C15112yes—
328#536—22no—
329#536—21no—
330#532—21no—
331#532C22×C15111yescharacteristic
332#532C22×C15111yescharacteristic
333C2×C4⋊Q8—21no—
334C2×C4⋊Q8C22×C15111yescharacteristic
335C4×#41C22×C15111yescharacteristic
336#489—22no—
337#487C22×C15112yes—
338#486C22×C15112yes—
339#482—21no—
340#477C22×C15111yescharacteristic
341#476—21no—
342#476C22×C15111yescharacteristic
343#476C22×C15112yes—
344#469—22no—
345#460C22×C15111yescharacteristic
346#459—21no—
347#459C22×C15111yescharacteristic
348#459C22×C15112yes—
349#449—21no—
350C4×SD16—21no—
351C4×D8—21no—
352#431C22×C15111yescharacteristic
353#423C22×C15111yescharacteristic
354#417—22no—
355C4×M16C22×C15111yescharacteristic
356#332C22×C15112yes—
357#332C22×C15112yes—
358Q8⋊C8C22×C15112yes—
359D4⋊C8C22×C15112yes—
360D4⋊C8C22×C15112yes—
361D4⋊C8C22×C15112yes—
3622−1+4—44no—
3632−1+4—44no—
364C2×#41—22no—
365C2×#41—24no—
366C2×#41—22no—
367C2×#41—21no—
368C2×#41—21no—
369C2×#41D4×C15111yescharacteristic
370C22×Q8—22no—
371C22×Q8—22no—
372C22×Q8—21no—
373C2×SD16—21no—
374C2×D8—21no—
375C2×D8—22no—
376C2×M16—21no—
377C2×M16—21no—
378C4⋊Q8—22no—
379C4⋊Q8—22no—
380C4⋊Q8—22no—
381C4⋊Q8—21no—
382C4⋊Q8—21no—
383C4⋊Q8D4×C15111yescharacteristic
384C4⋊Q8D4×C15112yes—
385C4⋊Q8C23×C15111yescharacteristic
386C4⋊Q8C23×C15112yes—
387#127D4×C15111yescharacteristic
388#127C23×C15111yescharacteristic
389#124—22no—
390#124—21no—
391#124—21no—
392#123—24no—
393#123—24no—
394#123—24no—
395C22⋊Q8—24no—
396C22⋊Q8—22no—
397C22⋊Q8—24no—
398C22⋊Q8—22no—
399#121—22no—
400#121—22no—
401#121—21no—
402#121—21no—
403#121—21no—
404#121D4×C15112yes—
405C4×Q8D4×C15111yescharacteristic
406C4×Q8C23×C15111yescharacteristic
407C4×D4—22no—
408C4×D4—22no—
409C4×D4—21no—
410C4×D4—21no—
411C4×D4—21no—
412C4×D4—21no—
413C4×D4—21no—
414C4×D4D4×C15111yescharacteristic
415C4×D4C23×C15111yescharacteristic
416C4×D4C23×C15112yes—
417#117—21no—
418#117D4×C15111yescharacteristic
419C2×C4⋊C4—22no—
420C2×C4⋊C4—21no—
421C2×C4⋊C4—22no—
422C2×C4⋊C4D4×C15112yes—
423C2×C42—21no—
424C2×C42C23×C15111yescharacteristic
425#107—21no—
426#106—21no—
427#106—22no—
428C4⋊C8—21no—
429C4⋊C8C23×C15111yescharacteristic
430C4⋊C8C23×C15111yescharacteristic
431C4⋊C8C23×C15112yes—
432#103—21no—
433#103—24no—
434#102—21no—
435#102—22no—
436#102—24no—
437#102—21no—
438#102—21no—
439#102—22no—
440C22⋊C8—21no—
441#97—21no—
442C4×C8—21no—
443C4×C8C23×C15112yes—
444#41—22no—
445#41—22no—
446#41—48no—
447#41—42no—
448#41—42no—
449#41—44no—
450#41—416no—
451#41—44no—
452#41—44no—
453C2×Q8—24no—
454C2×Q8—22no—
455C2×Q8—21no—
456C2×Q8—22no—
457C2×Q8—21no—
458C2×Q8—48no—
459C2×Q8—42no—
460C2×Q8—42no—
461C2×Q8—44no—
462C2×Q8—44no—
463C2×Q8C2×D4×C15111yescharacteristic
464C2×D4—21no—
465C2×D4—24no—
466C2×D4—22no—
467C2×D4—21no—
468C2×D4—21no—
469C2×D4—21no—
470C2×D4—21no—
471C2×D4—21no—
472C2×D4—41no—
473C2×D4C2×D4×C15112yes—
474C2×D4C2×D4×C15111yescharacteristic
475C22×C4—21no—
476C22×C4—24no—
477C22×C4—24no—
478C22×C4—22no—
479C22×C4—21no—
480C22×C4—21no—
481C22×C4—22no—
482C22×C4—41no—
483C22×C4C2×D4×C15111yescharacteristic
484C22×C4C2×D4×C15111yescharacteristic
485C22×C4C2×D4×C15111yescharacteristic
486SD16—42no—
487D8—42no—
488D8—82no—
489M16—42no—
490M16—81no—
491C2×C8—21no—
492C2×C8—21no—
493C2×C8—22no—
494C2×C8—22no—
495C4⋊C4—24no—
496C4⋊C4—24no—
497C4⋊C4—21no—
498C4⋊C4—22no—
499C4⋊C4—22no—
500C4⋊C4—21no—
501C4⋊C4—22no—
502C4⋊C4—21no—
503C4⋊C4—21no—
504C4⋊C4—21no—
505C4⋊C4C2×D4×C15114yes—
506C4⋊C4C2×D4×C15112yes—
507C4⋊C4C2×D4×C15111yescharacteristic
508C4⋊C4C2×D4×C15111yescharacteristic
509C22⋊C4—24no—
510C22⋊C4—24no—
511C22⋊C4—21no—
512C22⋊C4—21no—
513C22⋊C4—22no—
514C22⋊C4—21no—
515C22⋊C4—22no—
516C22⋊C4—41no—
517C22⋊C4—41no—
518C42—21no—
519C42—21no—
520C42—21no—
521C42C2×D4×C15111yescharacteristic
522C42C2×D4×C15111yescharacteristic
523C42C2×D4×C15111yescharacteristic
524C42C24×C15111yescharacteristic
525C23—21no—
526C23—22no—
527C23—41no—
528C23#120×C15111yescharacteristic
529Q8—21no—
530Q8—44no—
531Q8—42no—
532Q8—48no—
533Q8—42no—
534Q8—42no—
535Q8—42no—
536Q8AGL(1,ℤ/8)×C15112yes—
537D4—24no—
538D4—21no—
539D4—22no—
540D4—22no—
541D4—42no—
542D4—42no—
543D4—44no—
544D4—48no—
545D4—42no—
546D4—41no—
547D4—41no—
548D4—41no—
549D4—41no—
550D4—82no—
551D4AGL(1,ℤ/8)×C15112yes—
552C2×C4—24no—
553C2×C4—21no—
554C2×C4—22no—
555C2×C4—21no—
556C2×C4—21no—
557C2×C4—21no—
558C2×C4—21no—
559C2×C4—21no—
560C2×C4—21no—
561C2×C4—24no—
562C2×C4—22no—
563C2×C4—48no—
564C2×C4—44no—
565C2×C4—48no—
566C2×C4—42no—
567C2×C4—42no—
568C2×C4—42no—
569C2×C4—41no—
570C2×C4—41no—
571C2×C4—41no—
572C2×C4—82no—
573C2×C4#120×C15111yescharacteristic
574C2×C4#120×C15111yescharacteristic
575C2×C4#120×C15111yescharacteristic
576C2×C4C22×D4×C15111yescharacteristic
577C2×C4C22×D4×C15111yescharacteristic
578C2×C4C22×D4×C15111yescharacteristic
579C8—42no—
580C8—41no—
581C8—41no—
582C8—42no—
583C22—21no—
584C22—22no—
585C22—21no—
586C22—21no—
587C22—41no—
588C22—41no—
589C22—42no—
590C22—42no—
591C22—42no—
592C22—81no—
593C22—81no—
594C22—81no—
595C22C2×#120×C15111yescharacteristic
596C4—21no—
597C4—22no—
598C4—21no—
599C4—21no—
600C4—44no—
601C4—42no—
602C4—41no—
603C4—41no—
604C4—81no—
605C4#454×C15112yes—
606C4C2×AGL(1,ℤ/8)×C15111yescharacteristic
607C4C2×AGL(1,ℤ/8)×C15111yescharacteristic
608C4#577×C15111yescharacteristic
609C4#578×C15111yescharacteristic
610C2—41no—
611C2—42no—
612C2—82no—
613C2—161no—
614C2#3003×C15111yescharacteristic
615C2#3013×C15111yescharacteristic
616C2C2×#454×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. #3499×C151C2semidirect
2. #3253×C151C2semidirect
3. #3141×C151C2semidirect
4. #3106×C151C2semidirect
5. #1637×C151C2semidirect
6. #1635×C151C2semidirect
7. #1627×C151C2semidirect
8. #1625×C151C2semidirect
9. #1549×C151C2semidirect
10. #1489×C151C2semidirect
11. #1484×C151C2semidirect
308. #18582C151direct (N × H)
309. C151#18582direct (N × H)
310. #3499C2×C151semidirect
311. #3253C2×C151semidirect
312. #3141C2×C151semidirect
313. #3106C2×C151semidirect
314. #1637C2×C151semidirect
315. #1635C2×C151semidirect
316. #1627C2×C151semidirect
317. #1625C2×C151semidirect
318. #1549C2×C151semidirect
319. #1489C2×C151semidirect
320. #1484C2×C151semidirect

Maximal subgroups

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

subgroupindex
#3499×C1512
#3253×C1512
#3141×C1512
#3106×C1512
#1637×C1512
#1635×C1512
#1627×C1512
#1625×C1512
#1549×C1512
#1489×C1512
#1484×C1512
#18582151