Finite Group Databasebeta

← C151×#18276 #50323201

Subgroups — C151×#18276 #50323201

Order 38656.

966 conjugacy classes of subgroups.

The subgroup lattice has 676 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#3559×C151C211yesmaximal, characteristic, complemented
2#3109×C151C211yesmaximal, characteristic, complemented
3#3105×C151C211yesmaximal, characteristic, complemented
4#2562×C151C211yesmaximal, characteristic, complemented
5#1616×C151C212yesmaximal, complemented
6#1615×C151C212yesmaximal, complemented
7#1598×C151C212yesmaximal, complemented
8#1597×C151C212yesmaximal, complemented
9#1509×C151C211yesmaximal, characteristic, complemented
10#1502×C151C211yesmaximal, characteristic, complemented
11#1470×C151C211yesmaximal, characteristic, complemented
12#563×C151—21no—
13#562×C151—21no—
14#554×C151—21no—
15#553×C151—21no—
16#553×C151—21no—
17#547×C151—22no—
18#547×C151—21no—
19#544×C151—21no—
20#540×C151—21no—
21#539×C151—22no—
22#539×C151C2212yes—
23#537×C151C2212yes—
24#532×C151C2211yescharacteristic
25#529×C151C2211yescharacteristic
26C2×#125×C151C2211yescharacteristic
27C2×C4×D4×C151C2211yescharacteristic
28#484×C151C2211yescharacteristic
29#481×C151C2211yescharacteristic
30#481×C151C2212yes—
31#478×C151—21no—
32#476×C151—21no—
33#463×C151—21no—
34#459×C151—21no—
35#450×C151C2211yescharacteristic
36#447×C151C2211yescharacteristic
37#447×C151C2212yes—
38#442×C151—22no—
39C4×SD16×C151—21no—
40C4×D8×C151—21no—
41#432×C151C2211yescharacteristic
42#431×C151C2211yescharacteristic
43#400×C151C2212yes—
44#394×C151C2212yes—
45#388×C151—22no—
46#380×C151—21no—
47#380×C151—21no—
48C4×C4⋊C4×C151C2211yescharacteristic
49#328×C151C2212yes—
50#327×C151C2212yes—
51#327×C151C2212yes—
52#327×C151C2212yes—
53#324×C151C2212yes—
54#324×C151C2212yes—
55C2×#41×C151—21no—
56C2×#41×C151—22no—
57C22×D4×C151C2311yescharacteristic
58C23×C4×C151—21no—
59C2×SD16×C151—21no—
60C2×D8×C151—21no—
61C2×D8×C151—22no—
62C4⋊Q8×C151—21no—
63C4⋊Q8×C151—22no—
64C4⋊Q8×C151D411yescharacteristic
65#127×C151D411yescharacteristic
66#126×C151—22no—
67#126×C151—22no—
68#126×C151—21no—
69#125×C151—21no—
70#125×C151—22no—
71#125×C151—21no—
72#125×C151—21no—
73#125×C151—21no—
74#125×C151—21no—
75#125×C151D411yescharacteristic
76#124×C151—21no—
77#124×C151D411yescharacteristic
78#123×C151—22no—
79#123×C151—22no—
80#123×C151—22no—
81#123×C151—22no—
82#123×C151—22no—
83#123×C151—21no—
84#123×C151—22no—
85C22⋊Q8×C151—22no—
86C22⋊Q8×C151—22no—
87C22⋊Q8×C151—22no—
88C22⋊Q8×C151—22no—
89C22⋊Q8×C151—22no—
90C22⋊Q8×C151—22no—
91C22⋊Q8×C151C2311yescharacteristic
92#121×C151—21no—
93#121×C151—22no—
94#121×C151—21no—
95#121×C151—22no—
96#121×C151—22no—
97#121×C151—21no—
98#121×C151—22no—
99#121×C151C2311yescharacteristic
100#121×C151C2312yes—
101C4×Q8×C151D411yescharacteristic
102C4×D4×C151—22no—
103C4×D4×C151—21no—
104C4×D4×C151—21no—
105C4×D4×C151—21no—
106C4×D4×C151—22no—
107C4×D4×C151—21no—
108C4×D4×C151—21no—
109C4×D4×C151—21no—
110C4×D4×C151—21no—
111C4×D4×C151—21no—
112C4×D4×C151D411yescharacteristic
113C4×D4×C151D412yes—
114#117×C151—21no—
115#117×C151—21no—
116C2×C4⋊C4×C151—22no—
117C2×C4⋊C4×C151—21no—
118C2×C4⋊C4×C151—21no—
119C2×C4⋊C4×C151D411yescharacteristic
120C2×C4⋊C4×C151D411yescharacteristic
121C2×C4⋊C4×C151D412yes—
122C2×C4⋊C4×C151C2311yescharacteristic
123C2×C4⋊C4×C151C2312yes—
124C2×C22⋊C4×C151—22no—
125C2×C22⋊C4×C151—21no—
126C2×C22⋊C4×C151—22no—
127C2×C42×C151—21no—
128C2×C42×C151C2311yescharacteristic
129#107×C151—21no—
130#106×C151—21no—
131#106×C151—22no—
132C4⋊C8×C151—21no—
133C4⋊C8×C151—21no—
134#103×C151—21no—
135#102×C151—21no—
136#102×C151—22no—
137#102×C151—21no—
138#102×C151—21no—
139#102×C151—22no—
140C22⋊C8×C151C2311yescharacteristic
141C22⋊C8×C151C2311yescharacteristic
142C22⋊C8×C151C2312yes—
143#97×C151—21no—
144C4×C8×C151—21no—
145#95×C151—22no—
146#95×C151—22no—
147#95×C151C2312yes—
148C24×C151—21no—
149#41×C151—81no—
150#41×C151—81no—
151#41×C151—82no—
152#41×C151—82no—
153C2×Q8×C151—22no—
154C2×Q8×C151—21no—
155C2×Q8×C151C2×D411yescharacteristic
156C2×D4×C151—21no—
157C2×D4×C151—22no—
158C2×D4×C151—22no—
159C2×D4×C151—22no—
160C2×D4×C151—21no—
161C2×D4×C151—21no—
162C2×D4×C151—21no—
163C2×D4×C151—21no—
164C2×D4×C151—42no—
165C2×D4×C151C2×D411yescharacteristic
166C2×D4×C151C2×D412yes—
167C22×C4×C151—22no—
168C22×C4×C151—22no—
169C22×C4×C151—22no—
170C22×C4×C151—21no—
171C22×C4×C151—22no—
172C22×C4×C151—21no—
173C22×C4×C151—22no—
174C22×C4×C151—42no—
175C22×C4×C151—42no—
176C22×C4×C151—41no—
177C22×C4×C151—41no—
178C22×C4×C151C2×D412yes—
179C22×C4×C151C2×D411yescharacteristic
180C22×C4×C151C2×D411yescharacteristic
181C22×C4×C151C2×D412yes—
182C22×C4×C151C2411yescharacteristic
183SD16×C151—42no—
184D8×C151—44no—
185D8×C151—42no—
186C2×C8×C151—21no—
187C2×C8×C151—21no—
188C2×C8×C151—22no—
189C4⋊C4×C151—22no—
190C4⋊C4×C151—22no—
191C4⋊C4×C151—22no—
192C4⋊C4×C151—22no—
193C4⋊C4×C151—21no—
194C4⋊C4×C151—21no—
195C4⋊C4×C151—22no—
196C4⋊C4×C151—21no—
197C4⋊C4×C151—21no—
198C4⋊C4×C151—22no—
199C4⋊C4×C151—21no—
200C4⋊C4×C151—21no—
201C4⋊C4×C151—21no—
202C4⋊C4×C151—21no—
203C4⋊C4×C151—22no—
204C4⋊C4×C151—22no—
205C4⋊C4×C151—21no—
206C4⋊C4×C151—21no—
207C4⋊C4×C151—21no—
208C4⋊C4×C151—42no—
209C4⋊C4×C151C2×D412yes—
210C4⋊C4×C151C2×D411yescharacteristic
211C4⋊C4×C151C2×D411yescharacteristic
212C22⋊C4×C151—22no—
213C22⋊C4×C151—22no—
214C22⋊C4×C151—22no—
215C22⋊C4×C151—22no—
216C22⋊C4×C151—22no—
217C22⋊C4×C151—21no—
218C22⋊C4×C151—21no—
219C22⋊C4×C151—21no—
220C22⋊C4×C151—21no—
221C22⋊C4×C151—22no—
222C22⋊C4×C151—21no—
223C22⋊C4×C151—22no—
224C22⋊C4×C151—44no—
225C22⋊C4×C151—41no—
226C22⋊C4×C151—41no—
227C22⋊C4×C151—82no—
228C42×C151—22no—
229C42×C151—21no—
230C42×C151—81no—
231C42×C151C2×D411yescharacteristic
232C42×C151C2×D411yescharacteristic
233C42×C151C2×D411yescharacteristic
234C42×C151C2×D411yescharacteristic
235C23×C151—22no—
236C23×C151—21no—
237C23×C151—22no—
238C23×C151—41no—
239C23×C151—41no—
240C23×C151—41no—
241C23×C151—41no—
242C23×C151—41no—
243C23×C151—41no—
244C23×C151C22×D411yescharacteristic
245Q8×C151—41no—
246Q8×C151—81no—
247Q8×C151—82no—
248D4×C151—22no—
249D4×C151—22no—
250D4×C151—42no—
251D4×C151—41no—
252D4×C151—41no—
253D4×C151—41no—
254D4×C151—42no—
255D4×C151—41no—
256D4×C151—42no—
257D4×C151—41no—
258D4×C151—42no—
259D4×C151—81no—
260D4×C151—82no—
261D4×C151—82no—
262C2×C4×C151—21no—
263C2×C4×C151—21no—
264C2×C4×C151—22no—
265C2×C4×C151—21no—
266C2×C4×C151—22no—
267C2×C4×C151—22no—
268C2×C4×C151—21no—
269C2×C4×C151—21no—
270C2×C4×C151—22no—
271C2×C4×C151—22no—
272C2×C4×C151—22no—
273C2×C4×C151—41no—
274C2×C4×C151—42no—
275C2×C4×C151—42no—
276C2×C4×C151—42no—
277C2×C4×C151—42no—
278C2×C4×C151—41no—
279C2×C4×C151—41no—
280C2×C4×C151—41no—
281C2×C4×C151—42no—
282C2×C4×C151—82no—
283C2×C4×C151—82no—
284C2×C4×C151—82no—
285C2×C4×C151—82no—
286C2×C4×C151—82no—
287C2×C4×C151—82no—
288C2×C4×C151#12011yescharacteristic
289C2×C4×C151#12011yescharacteristic
290C2×C4×C151#12011yescharacteristic
291C2×C4×C151#12011yescharacteristic
292C2×C4×C151C22×D411yescharacteristic
293C2×C4×C151C22×D411yescharacteristic
294C8×C151—42no—
295C8×C151—41no—
296C8×C151—41no—
297C22×C151—21no—
298C22×C151—21no—
299C22×C151—42no—
300C22×C151—42no—
301C22×C151—42no—
302C22×C151—41no—
303C22×C151—41no—
304C22×C151—42no—
305C22×C151—42no—
306C22×C151—42no—
307C22×C151—41no—
308C22×C151—81no—
309C22×C151—81no—
310C22×C151—81no—
311C22×C151—81no—
312C22×C151C2×#12011yescharacteristic
313C22×C151#57611yescharacteristic
314C22×C151#57711yescharacteristic
315C4×C151—21no—
316C4×C151—21no—
317C4×C151—21no—
318C4×C151—21no—
319C4×C151—21no—
320C4×C151—42no—
321C4×C151—42no—
322C4×C151—41no—
323C4×C151—41no—
324C4×C151—42no—
325C4×C151—41no—
326C4×C151—82no—
327C4×C151—81no—
328C4×C151#45412yes—
329C2×C151—21no—
330C2×C151—21no—
331C2×C151—81no—
332C2×C151—82no—
333C2×C151—82no—
334C2×C151#301211yescharacteristic
335C2×C151C2×#45411yescharacteristic
336C2×C151#302511yescharacteristic
337#18276C15111yesmaximal, characteristic, direct product factor, Sylow
338C151#1827611yescharacteristic, direct product factor, Sylow
339#3559C2×C15111yescharacteristic, complemented
340#3109C2×C15111yescharacteristic, complemented
341#3105C2×C15111yescharacteristic, complemented
342#2562C2×C15111yescharacteristic, complemented
343#1616C2×C15112yescomplemented
344#1615C2×C15112yescomplemented
345#1598C2×C15112yescomplemented
346#1597C2×C15112yescomplemented
347#1509C2×C15111yescharacteristic, complemented
348#1502C2×C15111yescharacteristic, complemented
349#1470C2×C15111yescharacteristic, complemented
350#563—21no—
351#562—21no—
352#554—21no—
353#553—21no—
354#553—21no—
355#547—22no—
356#547—21no—
357#544—21no—
358#540—21no—
359#539—22no—
360#539C22×C15112yes—
361#537C22×C15112yes—
362#532C22×C15111yescharacteristic
363#529C22×C15111yescharacteristic
364C2×#125C22×C15111yescharacteristic
365C2×C4×D4C22×C15111yescharacteristic
366#484C22×C15111yescharacteristic
367#481C22×C15111yescharacteristic
368#481C22×C15112yes—
369#478—21no—
370#476—21no—
371#463—21no—
372#459—21no—
373#450C22×C15111yescharacteristic
374#447C22×C15111yescharacteristic
375#447C22×C15112yes—
376#442—22no—
377C4×SD16—21no—
378C4×D8—21no—
379#432C22×C15111yescharacteristic
380#431C22×C15111yescharacteristic
381#400C22×C15112yes—
382#394C22×C15112yes—
383#388—22no—
384#380—21no—
385#380—21no—
386C4×C4⋊C4C22×C15111yescharacteristic
387#328C22×C15112yes—
388#327C22×C15112yes—
389#327C22×C15112yes—
390#327C22×C15112yes—
391#324C22×C15112yes—
392#324C22×C15112yes—
393C2×#41—21no—
394C2×#41—22no—
395C22×D4C23×C15111yescharacteristic
396C23×C4—21no—
397C2×SD16—21no—
398C2×D8—21no—
399C2×D8—22no—
400C4⋊Q8—21no—
401C4⋊Q8—22no—
402C4⋊Q8D4×C15111yescharacteristic
403#127D4×C15111yescharacteristic
404#126—22no—
405#126—22no—
406#126—21no—
407#125—21no—
408#125—22no—
409#125—21no—
410#125—21no—
411#125—21no—
412#125—21no—
413#125D4×C15111yescharacteristic
414#124—21no—
415#124D4×C15111yescharacteristic
416#123—22no—
417#123—22no—
418#123—22no—
419#123—22no—
420#123—22no—
421#123—21no—
422#123—22no—
423C22⋊Q8—22no—
424C22⋊Q8—22no—
425C22⋊Q8—22no—
426C22⋊Q8—22no—
427C22⋊Q8—22no—
428C22⋊Q8—22no—
429C22⋊Q8C23×C15111yescharacteristic
430#121—21no—
431#121—22no—
432#121—21no—
433#121—22no—
434#121—22no—
435#121—21no—
436#121—22no—
437#121C23×C15111yescharacteristic
438#121C23×C15112yes—
439C4×Q8D4×C15111yescharacteristic
440C4×D4—22no—
441C4×D4—21no—
442C4×D4—21no—
443C4×D4—21no—
444C4×D4—22no—
445C4×D4—21no—
446C4×D4—21no—
447C4×D4—21no—
448C4×D4—21no—
449C4×D4—21no—
450C4×D4D4×C15111yescharacteristic
451C4×D4D4×C15112yes—
452#117—21no—
453#117—21no—
454C2×C4⋊C4—22no—
455C2×C4⋊C4—21no—
456C2×C4⋊C4—21no—
457C2×C4⋊C4D4×C15111yescharacteristic
458C2×C4⋊C4D4×C15112yes—
459C2×C4⋊C4D4×C15111yescharacteristic
460C2×C4⋊C4C23×C15111yescharacteristic
461C2×C4⋊C4C23×C15112yes—
462C2×C22⋊C4—21no—
463C2×C22⋊C4—22no—
464C2×C22⋊C4—22no—
465C2×C42—21no—
466C2×C42C23×C15111yescharacteristic
467#107—21no—
468#106—21no—
469#106—22no—
470C4⋊C8—21no—
471C4⋊C8—21no—
472#103—21no—
473#102—21no—
474#102—22no—
475#102—21no—
476#102—21no—
477#102—22no—
478C22⋊C8C23×C15111yescharacteristic
479C22⋊C8C23×C15111yescharacteristic
480C22⋊C8C23×C15112yes—
481#97—21no—
482C4×C8—21no—
483#95—22no—
484#95—22no—
485#95C23×C15112yes—
486C24—21no—
487#41—81no—
488#41—81no—
489#41—82no—
490#41—82no—
491C2×Q8—22no—
492C2×Q8—21no—
493C2×Q8C2×D4×C15111yescharacteristic
494C2×D4—21no—
495C2×D4—22no—
496C2×D4—22no—
497C2×D4—22no—
498C2×D4—21no—
499C2×D4—21no—
500C2×D4—21no—
501C2×D4—21no—
502C2×D4—42no—
503C2×D4C2×D4×C15111yescharacteristic
504C2×D4C2×D4×C15112yes—
505C22×C4—22no—
506C22×C4—22no—
507C22×C4—22no—
508C22×C4—21no—
509C22×C4—22no—
510C22×C4—21no—
511C22×C4—22no—
512C22×C4—42no—
513C22×C4—42no—
514C22×C4—41no—
515C22×C4—41no—
516C22×C4C2×D4×C15112yes—
517C22×C4C2×D4×C15111yescharacteristic
518C22×C4C2×D4×C15111yescharacteristic
519C22×C4C2×D4×C15112yes—
520C22×C4C24×C15111yescharacteristic
521SD16—42no—
522D8—44no—
523D8—42no—
524C2×C8—21no—
525C2×C8—21no—
526C2×C8—22no—
527C4⋊C4—22no—
528C4⋊C4—22no—
529C4⋊C4—22no—
530C4⋊C4—22no—
531C4⋊C4—21no—
532C4⋊C4—21no—
533C4⋊C4—22no—
534C4⋊C4—21no—
535C4⋊C4—21no—
536C4⋊C4—22no—
537C4⋊C4—21no—
538C4⋊C4—21no—
539C4⋊C4—21no—
540C4⋊C4—21no—
541C4⋊C4—22no—
542C4⋊C4—22no—
543C4⋊C4—21no—
544C4⋊C4—21no—
545C4⋊C4—21no—
546C4⋊C4—42no—
547C4⋊C4C2×D4×C15112yes—
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—21no—
557C22⋊C4—21no—
558C22⋊C4—21no—
559C22⋊C4—22no—
560C22⋊C4—21no—
561C22⋊C4—22no—
562C22⋊C4—44no—
563C22⋊C4—41no—
564C22⋊C4—41no—
565C22⋊C4—82no—
566C42—22no—
567C42—21no—
568C42—81no—
569C42C2×D4×C15111yescharacteristic
570C42C2×D4×C15111yescharacteristic
571C42C2×D4×C15111yescharacteristic
572C42C2×D4×C15111yescharacteristic
573C23—22no—
574C23—21no—
575C23—22no—
576C23—41no—
577C23—41no—
578C23—41no—
579C23—41no—
580C23—41no—
581C23—41no—
582C23C22×D4×C15111yescharacteristic
583Q8—41no—
584Q8—81no—
585Q8—82no—
586D4—22no—
587D4—22no—
588D4—42no—
589D4—41no—
590D4—41no—
591D4—41no—
592D4—42no—
593D4—41no—
594D4—42no—
595D4—41no—
596D4—42no—
597D4—81no—
598D4—82no—
599D4—82no—
600C2×C4—21no—
601C2×C4—21no—
602C2×C4—22no—
603C2×C4—21no—
604C2×C4—21no—
605C2×C4—22no—
606C2×C4—22no—
607C2×C4—21no—
608C2×C4—22no—
609C2×C4—22no—
610C2×C4—22no—
611C2×C4—41no—
612C2×C4—42no—
613C2×C4—42no—
614C2×C4—42no—
615C2×C4—42no—
616C2×C4—41no—
617C2×C4—41no—
618C2×C4—41no—
619C2×C4—42no—
620C2×C4—82no—
621C2×C4—82no—
622C2×C4—82no—
623C2×C4—82no—
624C2×C4—82no—
625C2×C4—82no—
626C2×C4#120×C15111yescharacteristic
627C2×C4#120×C15111yescharacteristic
628C2×C4#120×C15111yescharacteristic
629C2×C4#120×C15111yescharacteristic
630C2×C4C22×D4×C15111yescharacteristic
631C2×C4C22×D4×C15111yescharacteristic
632C8—42no—
633C8—41no—
634C8—41no—
635C22—21no—
636C22—21no—
637C22—42no—
638C22—42no—
639C22—42no—
640C22—41no—
641C22—41no—
642C22—42no—
643C22—42no—
644C22—42no—
645C22—41no—
646C22—81no—
647C22—81no—
648C22—81no—
649C22—81no—
650C22C2×#120×C15111yescharacteristic
651C22#576×C15111yescharacteristic
652C22#577×C15111yescharacteristic
653C4—21no—
654C4—21no—
655C4—21no—
656C4—21no—
657C4—21no—
658C4—42no—
659C4—42no—
660C4—41no—
661C4—41no—
662C4—42no—
663C4—41no—
664C4—82no—
665C4—81no—
666C4#454×C15112yes—
667C2—21no—
668C2—21no—
669C2—82no—
670C2—81no—
671C2—82no—
672C2#3012×C15111yescharacteristic
673C2C2×#454×C15111yescharacteristic
674C2#3025×C15111yescharacteristic
subgroupG/H
center, socleC22×C151C2×#120
commutator, Frattini, cosocleC22×C4C24×C151
LCSG ▷ C22×C4 ▷ C22 ▷ C1
UCSC1 ◁ C22×C151 ◁ C2×C42×C151 ◁ G

Complements

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

NH ≅ G/Ntype
1. #3559×C151C2semidirect
2. #3109×C151C2semidirect
3. #3105×C151C2semidirect
4. #2562×C151C2semidirect
5. #1616×C151C2semidirect
6. #1615×C151C2semidirect
7. #1598×C151C2semidirect
8. #1597×C151C2semidirect
9. #1509×C151C2semidirect
10. #1502×C151C2semidirect
11. #1470×C151C2semidirect
337. #18276C151direct (N × H)
338. C151#18276direct (N × H)
339. #3559C2×C151semidirect
340. #3109C2×C151semidirect
341. #3105C2×C151semidirect
342. #2562C2×C151semidirect
343. #1616C2×C151semidirect
344. #1615C2×C151semidirect
345. #1598C2×C151semidirect
346. #1597C2×C151semidirect
347. #1509C2×C151semidirect
348. #1502C2×C151semidirect
349. #1470C2×C151semidirect

Maximal subgroups

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

subgroupindex
#3559×C1512
#3109×C1512
#3105×C1512
#2562×C1512
#1616×C1512
#1615×C1512
#1598×C1512
#1597×C1512
#1509×C1512
#1502×C1512
#1470×C1512
#18276151