Finite Group Databasebeta

← C151×#19042 #50323967

Subgroups — C151×#19042 #50323967

Order 38656.

1036 conjugacy classes of subgroups.

The subgroup lattice has 674 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#3558×C151C211yesmaximal, characteristic, complemented
2#3213×C151C211yesmaximal, characteristic, complemented
3#3180×C151C211yesmaximal, characteristic, complemented
4#3150×C151C211yesmaximal, characteristic, complemented
5#1661×C151C212yesmaximal, complemented
6#1659×C151C212yesmaximal, complemented
7#1656×C151C212yesmaximal, complemented
8#1655×C151C212yesmaximal, complemented
9#1532×C151C211yesmaximal, characteristic, complemented
10#1530×C151C211yesmaximal, characteristic, complemented
11C2×#329×C151C211yesmaximal, characteristic, complemented
12C2×#135×C151—22no—
13#562×C151C2212yes—
14H(3,𝔽4)×C151C2212yes—
15#559×C151—21no—
16#548×C151—21no—
17#546×C151—22no—
18#546×C151—21no—
19D42×C151—21no—
20#542×C151—21no—
21#538×C151—22no—
22#538×C151—21no—
23#535×C151—21no—
24#534×C151—21no—
25#532×C151C2211yescharacteristic
26#532×C151C2211yescharacteristic, complemented
27#529×C151C2211yescharacteristic
28C2×#124×C151C2211yescharacteristic
29#501×C151C2211yescharacteristic, complemented
30#497×C151—21no—
31#497×C151C2212yescomplemented
32#496×C151—21no—
33#496×C151C2212yescomplemented
34#496×C151C2211yescharacteristic, complemented
35#496×C151C2212yescomplemented
36#490×C151C2211yescharacteristic, complemented
37#489×C151C2211yescharacteristic, complemented
38#489×C151C2212yescomplemented
39#466×C151—21no—
40#465×C151—21no—
41#463×C151—22no—
42#448×C151—21no—
43#447×C151—21no—
44#442×C151—21no—
45#440×C151—21no—
46#432×C151C2211yescharacteristic, complemented
47C2×#97×C151C2211yescharacteristic, complemented
48C2×#97×C151C2211yescharacteristic, complemented
49#330×C151C2212yescomplemented
50#329×C151C2212yescomplemented
51#329×C151C2212yescomplemented
52#329×C151C2212yescomplemented
53#329×C151C2212yescomplemented
54#329×C151C2212yescomplemented
55C2×#41×C151—21no—
56C2×#41×C151—21no—
57C2×#41×C151D412yes—
58C22×Q8×C151D411yescharacteristic
59C22×D4×C151—22no—
60C22×D4×C151—21no—
61C22×D4×C151D411yescharacteristic
62#135×C151—48no—
63C2×Q16×C151—22no—
64C2×SD16×C151—22no—
65C2×SD16×C151—21no—
66C2×SD16×C151—22no—
67C2×SD16×C151—22no—
68C2×D8×C151—21no—
69C2×D8×C151—22no—
70C2×D8×C151—22no—
71C22×C8×C151—21no—
72C22×C8×C151—21no—
73C4⋊Q8×C151D411yescharacteristic
74C4⋊Q8×C151C2311yescharacteristic
75#127×C151—21no—
76#127×C151D411yescharacteristic
77#127×C151C2311yescharacteristic
78#126×C151—22no—
79#126×C151—21no—
80#125×C151C2311yescharacteristic
81#124×C151—21no—
82#124×C151—21no—
83#124×C151—21no—
84#124×C151—21no—
85#124×C151—22no—
86#124×C151—22no—
87#124×C151—22no—
88#124×C151D412yes—
89#124×C151C2312yes—
90#124×C151C2311yescharacteristic
91#124×C151C2312yes—
92#123×C151—22no—
93#123×C151—22no—
94#123×C151—21no—
95#123×C151—22no—
96#123×C151—22no—
97C22⋊Q8×C151—21no—
98C22⋊Q8×C151—22no—
99C22⋊Q8×C151—22no—
100C22⋊Q8×C151D411yescharacteristic
101#121×C151—22no—
102#121×C151—22no—
103#121×C151—22no—
104#121×C151—21no—
105#121×C151—22no—
106#121×C151—22no—
107#121×C151—21no—
108#121×C151—21no—
109#121×C151—21no—
110#121×C151—21no—
111#121×C151D411yescharacteristic
112#120×C151—22no—
113#120×C151—22no—
114#120×C151—22no—
115#120×C151—22no—
116#120×C151—22no—
117C4×Q8×C151—21no—
118C4×Q8×C151D411yescharacteristic
119C4×D4×C151—22no—
120C4×D4×C151—22no—
121C4×D4×C151—21no—
122C4×D4×C151—21no—
123C4×D4×C151—21no—
124C4×D4×C151—21no—
125C4×D4×C151—21no—
126C4×D4×C151—21no—
127C4×D4×C151D411yescharacteristic
128#117×C151—21no—
129C2×C22⋊C4×C151—22no—
130C2×C22⋊C4×C151—21no—
131C2×C22⋊C4×C151—21no—
132C2×C42×C151C2311yescharacteristic
133#107×C151—21no—
134#106×C151—21no—
135C4⋊C8×C151—21no—
136#103×C151—21no—
137#103×C151—22no—
138#102×C151—21no—
139#102×C151—22no—
140#102×C151—21no—
141#102×C151—21no—
142C22⋊C8×C151—21no—
143#97×C151—21no—
144#97×C151—21no—
145#97×C151C2311yescharacteristic
146#97×C151C2312yes—
147#97×C151C2311yescharacteristic
148#97×C151C2312yes—
149C24×C151—22no—
150C24×C151—21no—
151#41×C151—44no—
152#41×C151—44no—
153#41×C151—82no—
154C2×Q8×C151—21no—
155C2×Q8×C151—21no—
156C2×Q8×C151—81no—
157C2×Q8×C151C2×D411yescharacteristic
158C2×Q8×C151C2×D412yes—
159C2×Q8×C151C2×D412yes—
160C2×D4×C151—22no—
161C2×D4×C151—21no—
162C2×D4×C151—22no—
163C2×D4×C151—22no—
164C2×D4×C151—22no—
165C2×D4×C151—22no—
166C2×D4×C151—22no—
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—41no—
174C2×D4×C151—81no—
175C2×D4×C151—82no—
176C2×D4×C151—84no—
177C2×D4×C151C2×D411yescharacteristic
178C2×D4×C151C2×D412yes—
179C2×D4×C151C2×D412yes—
180C22×C4×C151—22no—
181C22×C4×C151—22no—
182C22×C4×C151—21no—
183C22×C4×C151—21no—
184C22×C4×C151—22no—
185C22×C4×C151—41no—
186C22×C4×C151C2×D411yescharacteristic
187C22×C4×C151C2×D411yescharacteristic
188C22×C4×C151C2×D411yescharacteristic
189Q16×C151—44no—
190SD16×C151—42no—
191SD16×C151—44no—
192SD16×C151—44no—
193SD16×C151—82no—
194D8×C151—42no—
195D8×C151—44no—
196D8×C151—82no—
197C2×C8×C151—24no—
198C2×C8×C151—21no—
199C2×C8×C151—22no—
200C2×C8×C151—21no—
201C2×C8×C151—22no—
202C2×C8×C151—42no—
203C4⋊C4×C151—22no—
204C4⋊C4×C151—22no—
205C4⋊C4×C151—21no—
206C4⋊C4×C151—21no—
207C4⋊C4×C151—21no—
208C4⋊C4×C151—21no—
209C4⋊C4×C151—21no—
210C4⋊C4×C151—21no—
211C4⋊C4×C151—21no—
212C4⋊C4×C151—21no—
213C4⋊C4×C151C2×D411yescharacteristic
214C4⋊C4×C151C2×D411yescharacteristic
215C22⋊C4×C151—22no—
216C22⋊C4×C151—22no—
217C22⋊C4×C151—22no—
218C22⋊C4×C151—22no—
219C22⋊C4×C151—22no—
220C22⋊C4×C151—21no—
221C22⋊C4×C151—22no—
222C22⋊C4×C151—21no—
223C22⋊C4×C151—22no—
224C22⋊C4×C151—21no—
225C22⋊C4×C151—22no—
226C22⋊C4×C151—22no—
227C22⋊C4×C151—21no—
228C22⋊C4×C151—21no—
229C22⋊C4×C151—22no—
230C22⋊C4×C151—22no—
231C22⋊C4×C151—41no—
232C22⋊C4×C151—41no—
233C42×C151—22no—
234C42×C151—21no—
235C42×C151C2×D411yescharacteristic
236C42×C151C2×D411yescharacteristic
237C42×C151C2×D411yescharacteristic
238C42×C151C2411yescharacteristic
239C23×C151—22no—
240C23×C151—21no—
241C23×C151—22no—
242C23×C151—42no—
243C23×C151—41no—
244C23×C151—81no—
245C23×C151—81no—
246C23×C151—82no—
247C23×C151—82no—
248C23×C151—82no—
249C23×C151#12011yescharacteristic
250Q8×C151—42no—
251Q8×C151—42no—
252Q8×C151—41no—
253Q8×C151—42no—
254Q8×C151—42no—
255D4×C151—42no—
256D4×C151—41no—
257D4×C151—42no—
258D4×C151—42no—
259D4×C151—42no—
260D4×C151—42no—
261D4×C151—41no—
262D4×C151—42no—
263D4×C151—41no—
264D4×C151—44no—
265D4×C151—42no—
266D4×C151—81no—
267D4×C151—82no—
268D4×C151—82no—
269D4×C151—82no—
270D4×C151—82no—
271D4×C151—82no—
272D4×C151—82no—
273C2×C4×C151—22no—
274C2×C4×C151—22no—
275C2×C4×C151—21no—
276C2×C4×C151—22no—
277C2×C4×C151—21no—
278C2×C4×C151—21no—
279C2×C4×C151—41no—
280C2×C4×C151—41no—
281C2×C4×C151—42no—
282C2×C4×C151—41no—
283C2×C4×C151—82no—
284C2×C4×C151—82no—
285C2×C4×C151—81no—
286C2×C4×C151—82no—
287C2×C4×C151—82no—
288C2×C4×C151#12011yescharacteristic
289C2×C4×C151#12011yescharacteristic
290C2×C4×C151#12011yescharacteristic
291C2×C4×C151C22×D411yescharacteristic
292C2×C4×C151C22×D411yescharacteristic
293C2×C4×C151C22×D411yescharacteristic
294C8×C151—24no—
295C8×C151—22no—
296C8×C151—41no—
297C8×C151—42no—
298C22×C151—21no—
299C22×C151—21no—
300C22×C151—42no—
301C22×C151—42no—
302C22×C151—41no—
303C22×C151—41no—
304C22×C151—42no—
305C22×C151—42no—
306C22×C151—41no—
307C22×C151—42no—
308C22×C151—42no—
309C22×C151—81no—
310C22×C151—81no—
311C22×C151—81no—
312C22×C151—162no—
313C22×C151—164no—
314C22×C151#45312yes—
315C22×C151C2×#12011yescharacteristic
316C4×C151—21no—
317C4×C151—21no—
318C4×C151—21no—
319C4×C151—21no—
320C4×C151—21no—
321C4×C151—21no—
322C4×C151—41no—
323C4×C151—42no—
324C4×C151—41no—
325C4×C151—41no—
326C4×C151—42no—
327C4×C151—81no—
328C2×C151—22no—
329C2×C151—82no—
330C2×C151—82no—
331C2×C151—81no—
332C2×C151—161no—
333C2×C151C2×#45311yescharacteristic
334C2×C151#301811yescharacteristic
335C2×C151#301911yescharacteristic
336#19042C15111yesmaximal, characteristic, direct product factor, Sylow
337C151#1904211yescharacteristic, direct product factor, Sylow
338#3558C2×C15111yescharacteristic, complemented
339#3213C2×C15111yescharacteristic, complemented
340#3180C2×C15111yescharacteristic, complemented
341#3150C2×C15111yescharacteristic, complemented
342#1661C2×C15112yescomplemented
343#1659C2×C15112yescomplemented
344#1656C2×C15112yescomplemented
345#1655C2×C15112yescomplemented
346#1532C2×C15111yescharacteristic, complemented
347#1530C2×C15111yescharacteristic, complemented
348C2×#329C2×C15111yescharacteristic, complemented
349C2×#135—22no—
350#562C22×C15112yes—
351H(3,𝔽4)C22×C15112yes—
352#559—21no—
353#548—21no—
354#546—22no—
355#546—21no—
356D42—21no—
357#542—21no—
358#538—22no—
359#538—21no—
360#535—21no—
361#534—21no—
362#532C22×C15111yescharacteristic
363#532C22×C15111yescharacteristic, complemented
364#529C22×C15111yescharacteristic
365C2×#124C22×C15111yescharacteristic
366#501C22×C15111yescharacteristic, complemented
367#497—21no—
368#497C22×C15112yescomplemented
369#496—21no—
370#496C22×C15112yescomplemented
371#496C22×C15111yescharacteristic, complemented
372#496C22×C15112yescomplemented
373#490C22×C15111yescharacteristic, complemented
374#489C22×C15111yescharacteristic, complemented
375#489C22×C15112yescomplemented
376#466—21no—
377#465—21no—
378#463—22no—
379#448—21no—
380#447—21no—
381#442—21no—
382#440—21no—
383#432C22×C15111yescharacteristic, complemented
384C2×#97C22×C15111yescharacteristic, complemented
385C2×#97C22×C15111yescharacteristic, complemented
386#330C22×C15112yescomplemented
387#329C22×C15112yescomplemented
388#329C22×C15112yescomplemented
389#329C22×C15112yescomplemented
390#329C22×C15112yescomplemented
391#329C22×C15112yescomplemented
392C2×#41—21no—
393C2×#41—21no—
394C2×#41D4×C15112yes—
395C22×Q8D4×C15111yescharacteristic
396C22×D4—22no—
397C22×D4—21no—
398C22×D4D4×C15111yescharacteristic
399#135—48no—
400C2×Q16—22no—
401C2×SD16—22no—
402C2×SD16—21no—
403C2×SD16—22no—
404C2×SD16—22no—
405C2×D8—22no—
406C2×D8—21no—
407C2×D8—22no—
408C22×C8—21no—
409C22×C8—21no—
410C4⋊Q8D4×C15111yescharacteristic
411C4⋊Q8C23×C15111yescharacteristic
412#127—21no—
413#127D4×C15111yescharacteristic
414#127C23×C15111yescharacteristic
415#126—22no—
416#126—21no—
417#125C23×C15111yescharacteristic
418#124—21no—
419#124—22no—
420#124—22no—
421#124—22no—
422#124—21no—
423#124—21no—
424#124—21no—
425#124D4×C15112yes—
426#124C23×C15112yes—
427#124C23×C15111yescharacteristic
428#124C23×C15112yes—
429#123—22no—
430#123—22no—
431#123—21no—
432#123—22no—
433#123—22no—
434C22⋊Q8—21no—
435C22⋊Q8—22no—
436C22⋊Q8—22no—
437C22⋊Q8D4×C15111yescharacteristic
438#121—22no—
439#121—22no—
440#121—22no—
441#121—21no—
442#121—22no—
443#121—22no—
444#121—21no—
445#121—21no—
446#121—21no—
447#121—21no—
448#121D4×C15111yescharacteristic
449#120—22no—
450#120—22no—
451#120—22no—
452#120—22no—
453#120—22no—
454C4×Q8—21no—
455C4×Q8D4×C15111yescharacteristic
456C4×D4—22no—
457C4×D4—22no—
458C4×D4—21no—
459C4×D4—21no—
460C4×D4—21no—
461C4×D4—21no—
462C4×D4—21no—
463C4×D4—21no—
464C4×D4D4×C15111yescharacteristic
465#117—21no—
466C2×C22⋊C4—22no—
467C2×C22⋊C4—21no—
468C2×C22⋊C4—21no—
469C2×C42C23×C15111yescharacteristic
470#107—21no—
471#106—21no—
472C4⋊C8—21no—
473#103—21no—
474#103—22no—
475#102—21no—
476#102—22no—
477#102—21no—
478#102—21no—
479C22⋊C8—21no—
480#97—21no—
481#97—21no—
482#97C23×C15111yescharacteristic
483#97C23×C15111yescharacteristic
484#97C23×C15112yes—
485#97C23×C15112yes—
486C24—22no—
487C24—21no—
488#41—44no—
489#41—44no—
490#41—82no—
491C2×Q8—21no—
492C2×Q8—21no—
493C2×Q8—81no—
494C2×Q8C2×D4×C15111yescharacteristic
495C2×Q8C2×D4×C15112yes—
496C2×Q8C2×D4×C15112yes—
497C2×D4—22no—
498C2×D4—21no—
499C2×D4—22no—
500C2×D4—22no—
501C2×D4—22no—
502C2×D4—22no—
503C2×D4—22no—
504C2×D4—21no—
505C2×D4—21no—
506C2×D4—21no—
507C2×D4—21no—
508C2×D4—21no—
509C2×D4—21no—
510C2×D4—41no—
511C2×D4—81no—
512C2×D4—82no—
513C2×D4—84no—
514C2×D4C2×D4×C15111yescharacteristic
515C2×D4C2×D4×C15112yes—
516C2×D4C2×D4×C15112yes—
517C22×C4—22no—
518C22×C4—22no—
519C22×C4—21no—
520C22×C4—21no—
521C22×C4—22no—
522C22×C4—41no—
523C22×C4C2×D4×C15111yescharacteristic
524C22×C4C2×D4×C15111yescharacteristic
525C22×C4C2×D4×C15111yescharacteristic
526Q16—44no—
527SD16—44no—
528SD16—44no—
529SD16—42no—
530SD16—82no—
531D8—44no—
532D8—42no—
533D8—82no—
534C2×C8—24no—
535C2×C8—21no—
536C2×C8—22no—
537C2×C8—21no—
538C2×C8—22no—
539C2×C8—42no—
540C4⋊C4—22no—
541C4⋊C4—22no—
542C4⋊C4—21no—
543C4⋊C4—21no—
544C4⋊C4—21no—
545C4⋊C4—21no—
546C4⋊C4—21no—
547C4⋊C4—21no—
548C4⋊C4—21no—
549C4⋊C4—21no—
550C4⋊C4C2×D4×C15111yescharacteristic
551C4⋊C4C2×D4×C15111yescharacteristic
552C22⋊C4—22no—
553C22⋊C4—22no—
554C22⋊C4—22no—
555C22⋊C4—22no—
556C22⋊C4—22no—
557C22⋊C4—21no—
558C22⋊C4—22no—
559C22⋊C4—21no—
560C22⋊C4—22no—
561C22⋊C4—21no—
562C22⋊C4—22no—
563C22⋊C4—22no—
564C22⋊C4—21no—
565C22⋊C4—21no—
566C22⋊C4—22no—
567C22⋊C4—22no—
568C22⋊C4—41no—
569C22⋊C4—41no—
570C42—22no—
571C42—21no—
572C42C2×D4×C15111yescharacteristic
573C42C2×D4×C15111yescharacteristic
574C42C2×D4×C15111yescharacteristic
575C42C24×C15111yescharacteristic
576C23—22no—
577C23—21no—
578C23—22no—
579C23—42no—
580C23—41no—
581C23—81no—
582C23—81no—
583C23—82no—
584C23—82no—
585C23—82no—
586C23#120×C15111yescharacteristic
587Q8—42no—
588Q8—41no—
589Q8—42no—
590Q8—42no—
591Q8—42no—
592D4—42no—
593D4—41no—
594D4—42no—
595D4—42no—
596D4—42no—
597D4—42no—
598D4—41no—
599D4—42no—
600D4—41no—
601D4—42no—
602D4—44no—
603D4—81no—
604D4—82no—
605D4—82no—
606D4—82no—
607D4—82no—
608D4—82no—
609D4—82no—
610C2×C4—22no—
611C2×C4—21no—
612C2×C4—22no—
613C2×C4—22no—
614C2×C4—21no—
615C2×C4—21no—
616C2×C4—41no—
617C2×C4—41no—
618C2×C4—42no—
619C2×C4—41no—
620C2×C4—82no—
621C2×C4—82no—
622C2×C4—81no—
623C2×C4—82no—
624C2×C4—82no—
625C2×C4#120×C15111yescharacteristic
626C2×C4#120×C15111yescharacteristic
627C2×C4#120×C15111yescharacteristic
628C2×C4C22×D4×C15111yescharacteristic
629C2×C4C22×D4×C15111yescharacteristic
630C2×C4C22×D4×C15111yescharacteristic
631C8—24no—
632C8—22no—
633C8—41no—
634C8—42no—
635C22—21no—
636C22—21no—
637C22—42no—
638C22—42no—
639C22—41no—
640C22—41no—
641C22—42no—
642C22—42no—
643C22—41no—
644C22—42no—
645C22—42no—
646C22—81no—
647C22—81no—
648C22—81no—
649C22—162no—
650C22—164no—
651C22#453×C15112yes—
652C22C2×#120×C15111yescharacteristic
653C4—21no—
654C4—21no—
655C4—21no—
656C4—21no—
657C4—21no—
658C4—21no—
659C4—41no—
660C4—42no—
661C4—41no—
662C4—41no—
663C4—42no—
664C4—81no—
665C2—22no—
666C2—82no—
667C2—81no—
668C2—82no—
669C2—161no—
670C2C2×#453×C15111yescharacteristic
671C2#3018×C15111yescharacteristic
672C2#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. #3558×C151C2semidirect
2. #3213×C151C2semidirect
3. #3180×C151C2semidirect
4. #3150×C151C2semidirect
5. #1661×C151C2semidirect
6. #1659×C151C2semidirect
7. #1656×C151C2semidirect
8. #1655×C151C2semidirect
9. #1532×C151C2semidirect
10. #1530×C151C2semidirect
11. C2×#329×C151C2semidirect
26. #532×C151C22semidirect
29. #501×C151C22semidirect
31. #497×C151C22semidirect
33. #496×C151C22semidirect
34. #496×C151C22semidirect
35. #496×C151C22semidirect
36. #490×C151C22semidirect
37. #489×C151C22semidirect
38. #489×C151C22semidirect
46. #432×C151C22semidirect
47. C2×#97×C151C22semidirect
48. C2×#97×C151C22semidirect
49. #330×C151C22semidirect
50. #329×C151C22semidirect
51. #329×C151C22semidirect
52. #329×C151C22semidirect
53. #329×C151C22semidirect
54. #329×C151C22semidirect
336. #19042C151direct (N × H)
337. C151#19042direct (N × H)
338. #3558C2×C151semidirect
339. #3213C2×C151semidirect
340. #3180C2×C151semidirect
341. #3150C2×C151semidirect
342. #1661C2×C151semidirect
343. #1659C2×C151semidirect
344. #1656C2×C151semidirect
345. #1655C2×C151semidirect
346. #1532C2×C151semidirect
347. #1530C2×C151semidirect
348. C2×#329C2×C151semidirect
363. #532C22×C151semidirect
366. #501C22×C151semidirect
368. #497C22×C151semidirect
370. #496C22×C151semidirect
371. #496C22×C151semidirect
372. #496C22×C151semidirect
373. #490C22×C151semidirect
374. #489C22×C151semidirect
375. #489C22×C151semidirect
383. #432C22×C151semidirect
384. C2×#97C22×C151semidirect
385. C2×#97C22×C151semidirect
386. #330C22×C151semidirect
387. #329C22×C151semidirect
388. #329C22×C151semidirect
389. #329C22×C151semidirect
390. #329C22×C151semidirect
391. #329C22×C151semidirect

Maximal subgroups

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

subgroupindex
#3558×C1512
#3213×C1512
#3180×C1512
#3150×C1512
#1661×C1512
#1659×C1512
#1656×C1512
#1655×C1512
#1532×C1512
#1530×C1512
C2×#329×C1512
#19042151