Finite Group Databasebeta

← C151×#19086 #50324011

Subgroups — C151×#19086 #50324011

Order 38656.

964 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#3219×C151C211yesmaximal, characteristic, complemented
3#3214×C151C211yesmaximal, characteristic, complemented
4#3213×C151C211yesmaximal, characteristic, complemented
5#1662×C151C212yesmaximal, complemented
6#1659×C151C212yesmaximal, complemented
7#1656×C151C212yesmaximal, complemented
8#1655×C151C212yesmaximal, complemented
9#1536×C151C211yesmaximal, characteristic, complemented
10#1535×C151C211yesmaximal, characteristic, complemented
11#1533×C151C211yesmaximal, characteristic, complemented
12#562×C151C2212yes—
13H(3,𝔽4)×C151C2212yes—
14#559×C151—21no—
15#548×C151—21no—
16#546×C151—22no—
17#546×C151—21no—
18D42×C151—21no—
19#542×C151—21no—
20#538×C151—22no—
21#538×C151—21no—
22#535×C151—21no—
23#534×C151—21no—
24#532×C151C2211yescharacteristic
25#532×C151C2211yescharacteristic, complemented
26#529×C151C2211yescharacteristic
27C2×#124×C151C2211yescharacteristic
28#497×C151C2211yescharacteristic, complemented
29#496×C151C2211yescharacteristic, complemented
30#496×C151C2212yescomplemented
31#496×C151C2212yescomplemented
32#491×C151C2211yescharacteristic, complemented
33#490×C151C2211yescharacteristic, complemented
34#489×C151C2212yescomplemented
35#489×C151C2212yescomplemented
36#464×C151—21no—
37#463×C151—22no—
38#463×C151—21no—
39#461×C151—21no—
40#459×C151—21no—
41#452×C151—21no—
42#449×C151—22no—
43#449×C151—21no—
44#448×C151—21no—
45#447×C151—21no—
46#432×C151C2211yescharacteristic, complemented
47#432×C151C2211yescharacteristic, complemented
48#432×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
62C2×Q16×C151—21no—
63C2×SD16×C151—21no—
64C2×SD16×C151—22no—
65C2×SD16×C151—22no—
66C2×SD16×C151—21no—
67C2×D8×C151—22no—
68C2×D8×C151—22no—
69C2×D8×C151—21no—
70C4⋊Q8×C151D411yescharacteristic
71C4⋊Q8×C151C2311yescharacteristic
72#127×C151—21no—
73#127×C151D411yescharacteristic
74#127×C151C2311yescharacteristic
75#126×C151—22no—
76#126×C151—21no—
77#125×C151C2311yescharacteristic
78#124×C151—21no—
79#124×C151—21no—
80#124×C151—21no—
81#124×C151—21no—
82#124×C151—22no—
83#124×C151—22no—
84#124×C151—22no—
85#124×C151D412yes—
86#124×C151C2312yes—
87#124×C151C2312yes—
88#124×C151C2311yescharacteristic
89#123×C151—22no—
90#123×C151—22no—
91#123×C151—21no—
92#123×C151—22no—
93#123×C151—22no—
94C22⋊Q8×C151—21no—
95C22⋊Q8×C151—22no—
96C22⋊Q8×C151—22no—
97C22⋊Q8×C151D411yescharacteristic
98#121×C151—22no—
99#121×C151—22no—
100#121×C151—22no—
101#121×C151—21no—
102#121×C151—22no—
103#121×C151—22no—
104#121×C151—21no—
105#121×C151—21no—
106#121×C151—21no—
107#121×C151—21no—
108#121×C151D411yescharacteristic
109#120×C151—22no—
110#120×C151—22no—
111#120×C151—22no—
112#120×C151—22no—
113#120×C151—22no—
114C4×Q8×C151—21no—
115C4×Q8×C151D411yescharacteristic
116C4×D4×C151—22no—
117C4×D4×C151—22no—
118C4×D4×C151—21no—
119C4×D4×C151—21no—
120C4×D4×C151—21no—
121C4×D4×C151—21no—
122C4×D4×C151—21no—
123C4×D4×C151—21no—
124C4×D4×C151D411yescharacteristic
125#117×C151—21no—
126C2×C22⋊C4×C151—22no—
127C2×C22⋊C4×C151—21no—
128C2×C22⋊C4×C151—21no—
129C2×C42×C151C2311yescharacteristic
130C4⋊C8×C151—21no—
131C4⋊C8×C151—21no—
132C4⋊C8×C151—21no—
133#103×C151—21no—
134#103×C151—21no—
135#103×C151—22no—
136#103×C151—22no—
137#102×C151—22no—
138#102×C151—22no—
139#102×C151—21no—
140#102×C151—21no—
141C22⋊C8×C151—21no—
142C22⋊C8×C151—21no—
143C22⋊C8×C151—21no—
144#97×C151C2312yes—
145#97×C151C2312yes—
146#97×C151C2311yescharacteristic
147#97×C151C2311yescharacteristic
148C24×C151—22no—
149C24×C151—21no—
150#41×C151—81no—
151#41×C151—81no—
152#41×C151—82no—
153#41×C151—82no—
154C2×Q8×C151—21no—
155C2×Q8×C151—21no—
156C2×Q8×C151—81no—
157C2×Q8×C151C2×D412yes—
158C2×Q8×C151C2×D412yes—
159C2×Q8×C151C2×D411yescharacteristic
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×D412yes—
178C2×D4×C151C2×D412yes—
179C2×D4×C151C2×D411yescharacteristic
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—81no—
190SD16×C151—81no—
191SD16×C151—82no—
192SD16×C151—82no—
193SD16×C151—81no—
194D8×C151—82no—
195D8×C151—81no—
196D8×C151—82no—
197C2×C8×C151—21no—
198C2×C8×C151—22no—
199C2×C8×C151—22no—
200C2×C8×C151—21no—
201C4⋊C4×C151—22no—
202C4⋊C4×C151—22no—
203C4⋊C4×C151—21no—
204C4⋊C4×C151—21no—
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×C151C2×D411yescharacteristic
212C4⋊C4×C151C2×D411yescharacteristic
213C22⋊C4×C151—22no—
214C22⋊C4×C151—22no—
215C22⋊C4×C151—22no—
216C22⋊C4×C151—22no—
217C22⋊C4×C151—22no—
218C22⋊C4×C151—21no—
219C22⋊C4×C151—22no—
220C22⋊C4×C151—21no—
221C22⋊C4×C151—22no—
222C22⋊C4×C151—21no—
223C22⋊C4×C151—22no—
224C22⋊C4×C151—22no—
225C22⋊C4×C151—21no—
226C22⋊C4×C151—21no—
227C22⋊C4×C151—22no—
228C22⋊C4×C151—22no—
229C22⋊C4×C151—41no—
230C22⋊C4×C151—41no—
231C42×C151—22no—
232C42×C151—21no—
233C42×C151C2×D411yescharacteristic
234C42×C151C2×D411yescharacteristic
235C42×C151C2×D411yescharacteristic
236C42×C151C2411yescharacteristic
237C23×C151—21no—
238C23×C151—22no—
239C23×C151—22no—
240C23×C151—42no—
241C23×C151—41no—
242C23×C151—81no—
243C23×C151—81no—
244C23×C151—82no—
245C23×C151—82no—
246C23×C151—82no—
247C23×C151#12011yescharacteristic
248Q8×C151—42no—
249Q8×C151—42no—
250Q8×C151—41no—
251Q8×C151—42no—
252Q8×C151—41no—
253Q8×C151—41no—
254D4×C151—42no—
255D4×C151—41no—
256D4×C151—42no—
257D4×C151—42no—
258D4×C151—42no—
259D4×C151—41no—
260D4×C151—41no—
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—21no—
275C2×C4×C151—22no—
276C2×C4×C151—21no—
277C2×C4×C151—21no—
278C2×C4×C151—41no—
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—42no—
295C8×C151—42no—
296C8×C151—41no—
297C8×C151—41no—
298C22×C151—21no—
299C22×C151—21no—
300C22×C151—21no—
301C22×C151—41no—
302C22×C151—42no—
303C22×C151—42no—
304C22×C151—42no—
305C22×C151—42no—
306C22×C151—41no—
307C22×C151—41no—
308C22×C151—42no—
309C22×C151—42no—
310C22×C151—81no—
311C22×C151—81no—
312C22×C151—81no—
313C22×C151—162no—
314C22×C151—164no—
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—41no—
324C4×C151—42no—
325C4×C151—42no—
326C4×C151—41no—
327C4×C151—81no—
328C2×C151—41no—
329C2×C151—82no—
330C2×C151—81no—
331C2×C151—82no—
332C2×C151—161no—
333C2×C151#301911yescharacteristic
334C2×C151#301911yescharacteristic
335C2×C151#302111yescharacteristic
336#19086C15111yesmaximal, characteristic, direct product factor, Sylow
337C151#1908611yescharacteristic, direct product factor, Sylow
338#3558C2×C15111yescharacteristic, complemented
339#3219C2×C15111yescharacteristic, complemented
340#3214C2×C15111yescharacteristic, complemented
341#3213C2×C15111yescharacteristic, complemented
342#1662C2×C15112yescomplemented
343#1659C2×C15112yescomplemented
344#1656C2×C15112yescomplemented
345#1655C2×C15112yescomplemented
346#1536C2×C15111yescharacteristic, complemented
347#1535C2×C15111yescharacteristic, complemented
348#1533C2×C15111yescharacteristic, complemented
349#562C22×C15112yes—
350H(3,𝔽4)C22×C15112yes—
351#559—21no—
352#548—21no—
353#546—22no—
354#546—21no—
355D42—21no—
356#542—21no—
357#538—22no—
358#538—21no—
359#535—21no—
360#534—21no—
361#532C22×C15111yescharacteristic
362#532C22×C15111yescharacteristic, complemented
363#529C22×C15111yescharacteristic
364C2×#124C22×C15111yescharacteristic
365#497C22×C15111yescharacteristic, complemented
366#496C22×C15111yescharacteristic, complemented
367#496C22×C15112yescomplemented
368#496C22×C15112yescomplemented
369#491C22×C15111yescharacteristic, complemented
370#490C22×C15111yescharacteristic, complemented
371#489C22×C15112yescomplemented
372#489C22×C15112yescomplemented
373#464—21no—
374#463—22no—
375#463—21no—
376#461—21no—
377#459—21no—
378#452—21no—
379#449—22no—
380#449—21no—
381#448—21no—
382#447—21no—
383#432C22×C15111yescharacteristic, complemented
384#432C22×C15111yescharacteristic, complemented
385#432C22×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
399C2×Q16—21no—
400C2×SD16—22no—
401C2×SD16—22no—
402C2×SD16—21no—
403C2×SD16—21no—
404C2×D8—22no—
405C2×D8—22no—
406C2×D8—21no—
407C4⋊Q8D4×C15111yescharacteristic
408C4⋊Q8C23×C15111yescharacteristic
409#127—21no—
410#127D4×C15111yescharacteristic
411#127C23×C15111yescharacteristic
412#126—22no—
413#126—21no—
414#125C23×C15111yescharacteristic
415#124—21no—
416#124—22no—
417#124—22no—
418#124—22no—
419#124—21no—
420#124—21no—
421#124—21no—
422#124D4×C15112yes—
423#124C23×C15112yes—
424#124C23×C15111yescharacteristic
425#124C23×C15112yes—
426#123—22no—
427#123—22no—
428#123—21no—
429#123—22no—
430#123—22no—
431C22⋊Q8—21no—
432C22⋊Q8—22no—
433C22⋊Q8—22no—
434C22⋊Q8D4×C15111yescharacteristic
435#121—22no—
436#121—22no—
437#121—22no—
438#121—21no—
439#121—22no—
440#121—22no—
441#121—21no—
442#121—21no—
443#121—21no—
444#121—21no—
445#121D4×C15111yescharacteristic
446#120—22no—
447#120—22no—
448#120—22no—
449#120—22no—
450#120—22no—
451C4×Q8—21no—
452C4×Q8D4×C15111yescharacteristic
453C4×D4—22no—
454C4×D4—22no—
455C4×D4—21no—
456C4×D4—21no—
457C4×D4—21no—
458C4×D4—21no—
459C4×D4—21no—
460C4×D4—21no—
461C4×D4D4×C15111yescharacteristic
462#117—21no—
463C2×C22⋊C4—22no—
464C2×C22⋊C4—21no—
465C2×C22⋊C4—21no—
466C2×C42C23×C15111yescharacteristic
467C4⋊C8—21no—
468C4⋊C8—21no—
469C4⋊C8—21no—
470#103—22no—
471#103—22no—
472#103—21no—
473#103—21no—
474#102—22no—
475#102—22no—
476#102—21no—
477#102—21no—
478C22⋊C8—21no—
479C22⋊C8—21no—
480C22⋊C8—21no—
481#97C23×C15111yescharacteristic
482#97C23×C15111yescharacteristic
483#97C23×C15112yes—
484#97C23×C15112yes—
485C24—22no—
486C24—21no—
487#41—81no—
488#41—81no—
489#41—82no—
490#41—82no—
491C2×Q8—21no—
492C2×Q8—21no—
493C2×Q8—81no—
494C2×Q8C2×D4×C15112yes—
495C2×Q8C2×D4×C15112yes—
496C2×Q8C2×D4×C15111yescharacteristic
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×C15112yes—
515C2×D4C2×D4×C15112yes—
516C2×D4C2×D4×C15111yescharacteristic
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—81no—
527SD16—82no—
528SD16—82no—
529SD16—81no—
530SD16—81no—
531D8—81no—
532D8—82no—
533D8—82no—
534C2×C8—21no—
535C2×C8—22no—
536C2×C8—22no—
537C2×C8—21no—
538C4⋊C4—22no—
539C4⋊C4—22no—
540C4⋊C4—21no—
541C4⋊C4—21no—
542C4⋊C4—21no—
543C4⋊C4—21no—
544C4⋊C4—21no—
545C4⋊C4—21no—
546C4⋊C4—21no—
547C4⋊C4—21no—
548C4⋊C4C2×D4×C15111yescharacteristic
549C4⋊C4C2×D4×C15111yescharacteristic
550C22⋊C4—22no—
551C22⋊C4—22no—
552C22⋊C4—22no—
553C22⋊C4—22no—
554C22⋊C4—22no—
555C22⋊C4—21no—
556C22⋊C4—22no—
557C22⋊C4—21no—
558C22⋊C4—22no—
559C22⋊C4—21no—
560C22⋊C4—22no—
561C22⋊C4—22no—
562C22⋊C4—21no—
563C22⋊C4—21no—
564C22⋊C4—22no—
565C22⋊C4—22no—
566C22⋊C4—41no—
567C22⋊C4—41no—
568C42—22no—
569C42—21no—
570C42C2×D4×C15111yescharacteristic
571C42C2×D4×C15111yescharacteristic
572C42C2×D4×C15111yescharacteristic
573C42C24×C15111yescharacteristic
574C23—21no—
575C23—22no—
576C23—22no—
577C23—42no—
578C23—41no—
579C23—81no—
580C23—81no—
581C23—82no—
582C23—82no—
583C23—82no—
584C23#120×C15111yescharacteristic
585Q8—41no—
586Q8—42no—
587Q8—42no—
588Q8—42no—
589Q8—41no—
590Q8—41no—
591D4—41no—
592D4—42no—
593D4—42no—
594D4—42no—
595D4—42no—
596D4—41no—
597D4—42no—
598D4—41no—
599D4—41no—
600D4—41no—
601D4—42no—
602D4—44no—
603D4—81no—
604D4—82no—
605D4—82no—
606D4—82no—
607D4—82no—
608D4—82no—
609D4—82no—
610C2×C4—21no—
611C2×C4—22no—
612C2×C4—22no—
613C2×C4—21no—
614C2×C4—21no—
615C2×C4—41no—
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—42no—
632C8—42no—
633C8—41no—
634C8—41no—
635C22—21no—
636C22—21no—
637C22—21no—
638C22—41no—
639C22—42no—
640C22—42no—
641C22—42no—
642C22—42no—
643C22—41no—
644C22—41no—
645C22—42no—
646C22—42no—
647C22—81no—
648C22—81no—
649C22—81no—
650C22—162no—
651C22—164no—
652C22C2×#120×C15111yescharacteristic
653C4—21no—
654C4—21no—
655C4—21no—
656C4—21no—
657C4—21no—
658C4—21no—
659C4—41no—
660C4—41no—
661C4—42no—
662C4—42no—
663C4—41no—
664C4—81no—
665C2—41no—
666C2—81no—
667C2—82no—
668C2—82no—
669C2—161no—
670C2#3019×C15111yescharacteristic
671C2#3019×C15111yescharacteristic
672C2#3021×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. #3219×C151C2semidirect
3. #3214×C151C2semidirect
4. #3213×C151C2semidirect
5. #1662×C151C2semidirect
6. #1659×C151C2semidirect
7. #1656×C151C2semidirect
8. #1655×C151C2semidirect
9. #1536×C151C2semidirect
10. #1535×C151C2semidirect
11. #1533×C151C2semidirect
25. #532×C151C22semidirect
28. #497×C151C22semidirect
29. #496×C151C22semidirect
30. #496×C151C22semidirect
31. #496×C151C22semidirect
32. #491×C151C22semidirect
33. #490×C151C22semidirect
34. #489×C151C22semidirect
35. #489×C151C22semidirect
46. #432×C151C22semidirect
47. #432×C151C22semidirect
48. #432×C151C22semidirect
49. #330×C151C22semidirect
50. #329×C151C22semidirect
51. #329×C151C22semidirect
52. #329×C151C22semidirect
53. #329×C151C22semidirect
54. #329×C151C22semidirect
336. #19086C151direct (N × H)
337. C151#19086direct (N × H)
338. #3558C2×C151semidirect
339. #3219C2×C151semidirect
340. #3214C2×C151semidirect
341. #3213C2×C151semidirect
342. #1662C2×C151semidirect
343. #1659C2×C151semidirect
344. #1656C2×C151semidirect
345. #1655C2×C151semidirect
346. #1536C2×C151semidirect
347. #1535C2×C151semidirect
348. #1533C2×C151semidirect
362. #532C22×C151semidirect
365. #497C22×C151semidirect
366. #496C22×C151semidirect
367. #496C22×C151semidirect
368. #496C22×C151semidirect
369. #491C22×C151semidirect
370. #490C22×C151semidirect
371. #489C22×C151semidirect
372. #489C22×C151semidirect
383. #432C22×C151semidirect
384. #432C22×C151semidirect
385. #432C22×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
#3219×C1512
#3214×C1512
#3213×C1512
#1662×C1512
#1659×C1512
#1656×C1512
#1655×C1512
#1536×C1512
#1535×C1512
#1533×C1512
#19086151