Finite Group Databasebeta

← C151×#18466 #50323391

Subgroups — C151×#18466 #50323391

Order 38656.

954 conjugacy classes of subgroups.

The subgroup lattice has 668 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#3558×C151C211yesmaximal, characteristic
2#3234×C151C211yesmaximal, characteristic, complemented
3#3232×C151C211yesmaximal, characteristic, complemented
4#2820×C151C211yesmaximal, characteristic, complemented
5#1618×C151C212yesmaximal, complemented
6#1613×C151C212yesmaximal, complemented
7#1612×C151C212yesmaximal, complemented
8#1607×C151C212yesmaximal, complemented
9#1517×C151C211yesmaximal, characteristic, complemented
10#1512×C151C211yesmaximal, characteristic, complemented
11#1469×C151C211yesmaximal, characteristic, complemented
12#562×C151—21no—
13H(3,𝔽4)×C151—21no—
14#559×C151—21no—
15#548×C151—21no—
16#546×C151—21no—
17#546×C151—22no—
18D42×C151—21no—
19#542×C151—21no—
20#538×C151—22no—
21#538×C151C2212yes—
22#535×C151—21no—
23#534×C151C2212yes—
24#532×C151C2211yescharacteristic
25#529×C151C2211yescharacteristic
26C2×#125×C151C2211yescharacteristic, complemented
27C2×#124×C151C2211yescharacteristic
28#501×C151—21no—
29#499×C151—21no—
30#490×C151—21no—
31#488×C151—21no—
32#484×C151C2211yescharacteristic, complemented
33#483×C151C2211yescharacteristic, complemented
34#481×C151C2211yescharacteristic
35#481×C151C2212yescomplemented
36#480×C151C2211yescharacteristic
37#480×C151C2212yescomplemented
38#479×C151—21no—
39#478×C151—21no—
40#478×C151—22no—
41#432×C151C2211yescharacteristic, complemented
42#431×C151C2211yescharacteristic, complemented
43#399×C151C2212yescomplemented
44#397×C151C2212yescomplemented
45#396×C151—22no—
46#395×C151—21no—
47#394×C151—21no—
48#382×C151C2211yescharacteristic, complemented
49#328×C151C2212yescomplemented
50#327×C151C2212yes—
51#327×C151C2212yescomplemented
52#327×C151C2212yescomplemented
53#323×C151C2212yescomplemented
54#323×C151C2212yescomplemented
55C2×#41×C151—21no—
56C2×#41×C151—21no—
57C22×Q8×C151D411yescharacteristic
58C22×D4×C151—21no—
59C22×D4×C151—22no—
60C22×D4×C151D411yescharacteristic
61C4⋊Q8×C151D411yescharacteristic
62#127×C151—21no—
63#127×C151D411yescharacteristic
64#126×C151—22no—
65#126×C151—21no—
66#125×C151—21no—
67#125×C151—21no—
68#125×C151—21no—
69#125×C151—21no—
70#125×C151D411yescharacteristic
71#124×C151—21no—
72#124×C151—22no—
73#124×C151—22no—
74#124×C151—21no—
75#124×C151—21no—
76#124×C151—21no—
77#124×C151—21no—
78#124×C151—21no—
79#124×C151—22no—
80#124×C151D411yescharacteristic
81#123×C151—22no—
82#123×C151—21no—
83#123×C151—22no—
84#123×C151—22no—
85#123×C151—22no—
86C22⋊Q8×C151—22no—
87C22⋊Q8×C151—21no—
88C22⋊Q8×C151—22no—
89C22⋊Q8×C151C2311yescharacteristic
90#121×C151—22no—
91#121×C151—22no—
92#121×C151—22no—
93#121×C151—21no—
94#121×C151—22no—
95#121×C151—21no—
96#121×C151—22no—
97#121×C151C2311yescharacteristic
98#121×C151C2312yes—
99#120×C151—22no—
100#120×C151—22no—
101#120×C151—22no—
102#120×C151—22no—
103#120×C151—22no—
104C4×Q8×C151—21no—
105C4×Q8×C151D411yescharacteristic
106C4×D4×C151—22no—
107C4×D4×C151—21no—
108C4×D4×C151—21no—
109C4×D4×C151—22no—
110C4×D4×C151—21no—
111C4×D4×C151D411yescharacteristic
112C4×D4×C151D412yes—
113#117×C151—21no—
114C2×C4⋊C4×C151—21no—
115C2×C4⋊C4×C151—21no—
116C2×C4⋊C4×C151—21no—
117C2×C4⋊C4×C151—22no—
118C2×C4⋊C4×C151C2311yescharacteristic
119C2×C4⋊C4×C151C2311yescharacteristic
120C2×C22⋊C4×C151—22no—
121C2×C22⋊C4×C151—22no—
122C2×C22⋊C4×C151—22no—
123C2×C22⋊C4×C151D412yes—
124C2×C22⋊C4×C151C2312yes—
125C2×C42×C151C2311yescharacteristic
126#107×C151—22no—
127#107×C151—21no—
128#107×C151—21no—
129#106×C151—22no—
130#106×C151—21no—
131#106×C151—21no—
132C4⋊C8×C151—21no—
133C4⋊C8×C151—21no—
134#103×C151—21no—
135#103×C151—21no—
136#102×C151—21no—
137#102×C151—22no—
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—21no—
146#95×C151—22no—
147#95×C151C2312yes—
148C24×C151—22no—
149C24×C151C2×D412yes—
150#41×C151—81no—
151#41×C151—81no—
152#41×C151—82no—
153C2×Q8×C151—21no—
154C2×Q8×C151—21no—
155C2×Q8×C151—21no—
156C2×Q8×C151—81no—
157C2×Q8×C151C2×D411yescharacteristic
158C2×D4×C151—22no—
159C2×D4×C151—21no—
160C2×D4×C151—22no—
161C2×D4×C151—22no—
162C2×D4×C151—22no—
163C2×D4×C151—22no—
164C2×D4×C151—22no—
165C2×D4×C151—21no—
166C2×D4×C151—21no—
167C2×D4×C151—21no—
168C2×D4×C151—21no—
169C2×D4×C151—82no—
170C2×D4×C151—81no—
171C2×D4×C151—82no—
172C2×D4×C151—82no—
173C2×D4×C151C2×D411yescharacteristic
174C2×D4×C151C2×D412yes—
175C22×C4×C151—22no—
176C22×C4×C151—22no—
177C22×C4×C151—21no—
178C22×C4×C151—22no—
179C22×C4×C151—22no—
180C22×C4×C151—21no—
181C22×C4×C151—21no—
182C22×C4×C151C2×D411yescharacteristic
183C22×C4×C151C2×D412yes—
184C22×C4×C151C2×D411yescharacteristic
185C22×C4×C151C2411yescharacteristic
186C2×C8×C151—21no—
187C2×C8×C151—21no—
188C2×C8×C151—22no—
189C4⋊C4×C151—22no—
190C4⋊C4×C151—22no—
191C4⋊C4×C151—21no—
192C4⋊C4×C151—21no—
193C4⋊C4×C151—21no—
194C4⋊C4×C151—21no—
195C4⋊C4×C151—21no—
196C4⋊C4×C151—21no—
197C4⋊C4×C151—21no—
198C4⋊C4×C151—21no—
199C4⋊C4×C151—21no—
200C4⋊C4×C151—41no—
201C4⋊C4×C151—41no—
202C4⋊C4×C151—41no—
203C4⋊C4×C151—41no—
204C4⋊C4×C151—81no—
205C4⋊C4×C151—82no—
206C4⋊C4×C151C2×D412yes—
207C4⋊C4×C151C2×D411yescharacteristic
208C4⋊C4×C151C2×D411yescharacteristic
209C22⋊C4×C151—22no—
210C22⋊C4×C151—22no—
211C22⋊C4×C151—22no—
212C22⋊C4×C151—22no—
213C22⋊C4×C151—22no—
214C22⋊C4×C151—21no—
215C22⋊C4×C151—21no—
216C22⋊C4×C151—22no—
217C22⋊C4×C151—22no—
218C22⋊C4×C151—21no—
219C22⋊C4×C151—21no—
220C22⋊C4×C151—22no—
221C22⋊C4×C151—22no—
222C22⋊C4×C151—22no—
223C22⋊C4×C151—21no—
224C22⋊C4×C151—22no—
225C22⋊C4×C151—82no—
226C22⋊C4×C151—82no—
227C42×C151—22no—
228C42×C151—21no—
229C42×C151C2×D411yescharacteristic
230C42×C151C2×D411yescharacteristic
231C42×C151C2×D411yescharacteristic
232C42×C151C2×D411yescharacteristic
233C23×C151—21no—
234C23×C151—22no—
235C23×C151—22no—
236C23×C151—22no—
237C23×C151—22no—
238C23×C151—42no—
239C23×C151—42no—
240C23×C151—82no—
241C23×C151—82no—
242C23×C151—82no—
243C23×C151C22×D411yescharacteristic
244Q8×C151—41no—
245Q8×C151—42no—
246Q8×C151—81no—
247Q8×C151—81no—
248D4×C151—42no—
249D4×C151—41no—
250D4×C151—42no—
251D4×C151—42no—
252D4×C151—42no—
253D4×C151—41no—
254D4×C151—42no—
255D4×C151—41no—
256D4×C151—81no—
257D4×C151—81no—
258D4×C151—82no—
259D4×C151—82no—
260D4×C151—82no—
261D4×C151—82no—
262D4×C151—82no—
263C2×C4×C151—21no—
264C2×C4×C151—21no—
265C2×C4×C151—22no—
266C2×C4×C151—22no—
267C2×C4×C151—21no—
268C2×C4×C151—21no—
269C2×C4×C151—21no—
270C2×C4×C151—41no—
271C2×C4×C151—41no—
272C2×C4×C151—42no—
273C2×C4×C151—42no—
274C2×C4×C151—42no—
275C2×C4×C151—42no—
276C2×C4×C151—42no—
277C2×C4×C151—41no—
278C2×C4×C151—41no—
279C2×C4×C151—41no—
280C2×C4×C151—42no—
281C2×C4×C151—41no—
282C2×C4×C151—82no—
283C2×C4×C151—82no—
284C2×C4×C151—82no—
285C2×C4×C151#12011yescharacteristic
286C2×C4×C151#12011yescharacteristic
287C2×C4×C151#12011yescharacteristic
288C2×C4×C151#12011yescharacteristic
289C2×C4×C151C22×D411yescharacteristic
290C2×C4×C151C22×D411yescharacteristic
291C8×C151—42no—
292C8×C151—41no—
293C8×C151—41no—
294C22×C151—21no—
295C22×C151—21no—
296C22×C151—42no—
297C22×C151—42no—
298C22×C151—41no—
299C22×C151—41no—
300C22×C151—42no—
301C22×C151—42no—
302C22×C151—42no—
303C22×C151—41no—
304C22×C151—42no—
305C22×C151—82no—
306C22×C151—82no—
307C22×C151—164no—
308C22×C151C2×#12011yescharacteristic
309C22×C151#57611yescharacteristic
310C22×C151#57711yescharacteristic
311C4×C151—21no—
312C4×C151—21no—
313C4×C151—21no—
314C4×C151—21no—
315C4×C151—21no—
316C4×C151—21no—
317C4×C151—41no—
318C4×C151—42no—
319C4×C151—41no—
320C4×C151—42no—
321C4×C151—41no—
322C4×C151—82no—
323C4×C151—81no—
324C4×C151—81no—
325C2×C151—21no—
326C2×C151—21no—
327C2×C151—82no—
328C2×C151—82no—
329C2×C151—81no—
330C2×C151#301211yescharacteristic
331C2×C151#301911yescharacteristic
332C2×C151#302811yescharacteristic
333#18466C15111yesmaximal, characteristic, direct product factor, Sylow
334C151#1846611yescharacteristic, direct product factor, Sylow
335#3558C2×C15111yescharacteristic
336#3234C2×C15111yescharacteristic, complemented
337#3232C2×C15111yescharacteristic, complemented
338#2820C2×C15111yescharacteristic, complemented
339#1618C2×C15112yescomplemented
340#1613C2×C15112yescomplemented
341#1612C2×C15112yescomplemented
342#1607C2×C15112yescomplemented
343#1517C2×C15111yescharacteristic, complemented
344#1512C2×C15111yescharacteristic, complemented
345#1469C2×C15111yescharacteristic, complemented
346#562—21no—
347H(3,𝔽4)—21no—
348#559—21no—
349#548—21no—
350#546—21no—
351#546—22no—
352D42—21no—
353#542—21no—
354#538—22no—
355#538C22×C15112yes—
356#535—21no—
357#534C22×C15112yes—
358#532C22×C15111yescharacteristic
359#529C22×C15111yescharacteristic
360C2×#125C22×C15111yescharacteristic, complemented
361C2×#124C22×C15111yescharacteristic
362#501—21no—
363#499—21no—
364#490—21no—
365#488—21no—
366#484C22×C15111yescharacteristic, complemented
367#483C22×C15111yescharacteristic, complemented
368#481C22×C15111yescharacteristic
369#481C22×C15112yescomplemented
370#480C22×C15111yescharacteristic
371#480C22×C15112yescomplemented
372#479—21no—
373#478—21no—
374#478—22no—
375#432C22×C15111yescharacteristic, complemented
376#431C22×C15111yescharacteristic, complemented
377#399C22×C15112yescomplemented
378#397C22×C15112yescomplemented
379#396—22no—
380#395—21no—
381#394—21no—
382#382C22×C15111yescharacteristic, complemented
383#328C22×C15112yescomplemented
384#327C22×C15112yes—
385#327C22×C15112yescomplemented
386#327C22×C15112yescomplemented
387#323C22×C15112yescomplemented
388#323C22×C15112yescomplemented
389C2×#41—21no—
390C2×#41—21no—
391C22×Q8D4×C15111yescharacteristic
392C22×D4—21no—
393C22×D4—22no—
394C22×D4D4×C15111yescharacteristic
395C4⋊Q8D4×C15111yescharacteristic
396#127—21no—
397#127D4×C15111yescharacteristic
398#126—22no—
399#126—21no—
400#125—21no—
401#125—21no—
402#125—21no—
403#125—21no—
404#125D4×C15111yescharacteristic
405#124—21no—
406#124—22no—
407#124—22no—
408#124—22no—
409#124—21no—
410#124—21no—
411#124—21no—
412#124—21no—
413#124—21no—
414#124D4×C15111yescharacteristic
415#123—22no—
416#123—21no—
417#123—22no—
418#123—22no—
419#123—22no—
420C22⋊Q8—22no—
421C22⋊Q8—21no—
422C22⋊Q8—22no—
423C22⋊Q8C23×C15111yescharacteristic
424#121—22no—
425#121—22no—
426#121—22no—
427#121—21no—
428#121—22no—
429#121—21no—
430#121—22no—
431#121C23×C15111yescharacteristic
432#121C23×C15112yes—
433#120—22no—
434#120—22no—
435#120—22no—
436#120—22no—
437#120—22no—
438C4×Q8—21no—
439C4×Q8D4×C15111yescharacteristic
440C4×D4—22no—
441C4×D4—21no—
442C4×D4—21no—
443C4×D4—22no—
444C4×D4—21no—
445C4×D4D4×C15111yescharacteristic
446C4×D4D4×C15112yes—
447#117—21no—
448C2×C4⋊C4—21no—
449C2×C4⋊C4—21no—
450C2×C4⋊C4—21no—
451C2×C4⋊C4—22no—
452C2×C4⋊C4C23×C15111yescharacteristic
453C2×C4⋊C4C23×C15111yescharacteristic
454C2×C22⋊C4—22no—
455C2×C22⋊C4—22no—
456C2×C22⋊C4—22no—
457C2×C22⋊C4D4×C15112yes—
458C2×C22⋊C4C23×C15112yes—
459C2×C42C23×C15111yescharacteristic
460#107—22no—
461#107—21no—
462#107—21no—
463#106—22no—
464#106—21no—
465#106—21no—
466C4⋊C8—21no—
467C4⋊C8—21no—
468#103—21no—
469#103—21no—
470#102—21no—
471#102—22no—
472#102—21no—
473#102—22no—
474C22⋊C8C23×C15112yes—
475C22⋊C8C23×C15111yescharacteristic
476C22⋊C8C23×C15111yescharacteristic
477#97—21no—
478C4×C8—21no—
479#95—21no—
480#95—22no—
481#95C23×C15112yes—
482C24—22no—
483C24C2×D4×C15112yes—
484#41—81no—
485#41—81no—
486#41—82no—
487C2×Q8—21no—
488C2×Q8—21no—
489C2×Q8—21no—
490C2×Q8—81no—
491C2×Q8C2×D4×C15111yescharacteristic
492C2×D4—22no—
493C2×D4—21no—
494C2×D4—22no—
495C2×D4—22no—
496C2×D4—22no—
497C2×D4—22no—
498C2×D4—22no—
499C2×D4—21no—
500C2×D4—21no—
501C2×D4—21no—
502C2×D4—21no—
503C2×D4—82no—
504C2×D4—81no—
505C2×D4—82no—
506C2×D4—82no—
507C2×D4C2×D4×C15111yescharacteristic
508C2×D4C2×D4×C15112yes—
509C22×C4—22no—
510C22×C4—22no—
511C22×C4—21no—
512C22×C4—22no—
513C22×C4—22no—
514C22×C4—21no—
515C22×C4—21no—
516C22×C4C2×D4×C15111yescharacteristic
517C22×C4C2×D4×C15112yes—
518C22×C4C2×D4×C15111yescharacteristic
519C22×C4C24×C15111yescharacteristic
520C2×C8—21no—
521C2×C8—21no—
522C2×C8—22no—
523C4⋊C4—22no—
524C4⋊C4—22no—
525C4⋊C4—21no—
526C4⋊C4—21no—
527C4⋊C4—21no—
528C4⋊C4—21no—
529C4⋊C4—21no—
530C4⋊C4—21no—
531C4⋊C4—21no—
532C4⋊C4—21no—
533C4⋊C4—21no—
534C4⋊C4—41no—
535C4⋊C4—41no—
536C4⋊C4—41no—
537C4⋊C4—41no—
538C4⋊C4—81no—
539C4⋊C4—82no—
540C4⋊C4C2×D4×C15112yes—
541C4⋊C4C2×D4×C15111yescharacteristic
542C4⋊C4C2×D4×C15111yescharacteristic
543C22⋊C4—22no—
544C22⋊C4—22no—
545C22⋊C4—22no—
546C22⋊C4—22no—
547C22⋊C4—22no—
548C22⋊C4—21no—
549C22⋊C4—21no—
550C22⋊C4—22no—
551C22⋊C4—22no—
552C22⋊C4—21no—
553C22⋊C4—21no—
554C22⋊C4—22no—
555C22⋊C4—22no—
556C22⋊C4—22no—
557C22⋊C4—21no—
558C22⋊C4—22no—
559C22⋊C4—82no—
560C22⋊C4—82no—
561C42—22no—
562C42—21no—
563C42C2×D4×C15111yescharacteristic
564C42C2×D4×C15111yescharacteristic
565C42C2×D4×C15111yescharacteristic
566C42C2×D4×C15111yescharacteristic
567C23—22no—
568C23—21no—
569C23—22no—
570C23—22no—
571C23—22no—
572C23—42no—
573C23—42no—
574C23—82no—
575C23—82no—
576C23—82no—
577C23C22×D4×C15111yescharacteristic
578Q8—41no—
579Q8—42no—
580Q8—81no—
581Q8—81no—
582D4—42no—
583D4—41no—
584D4—42no—
585D4—42no—
586D4—41no—
587D4—42no—
588D4—41no—
589D4—42no—
590D4—81no—
591D4—81no—
592D4—82no—
593D4—82no—
594D4—82no—
595D4—82no—
596D4—82no—
597C2×C4—21no—
598C2×C4—21no—
599C2×C4—21no—
600C2×C4—22no—
601C2×C4—22no—
602C2×C4—21no—
603C2×C4—21no—
604C2×C4—41no—
605C2×C4—41no—
606C2×C4—42no—
607C2×C4—42no—
608C2×C4—42no—
609C2×C4—42no—
610C2×C4—42no—
611C2×C4—41no—
612C2×C4—41no—
613C2×C4—41no—
614C2×C4—42no—
615C2×C4—41no—
616C2×C4—82no—
617C2×C4—82no—
618C2×C4—82no—
619C2×C4#120×C15111yescharacteristic
620C2×C4#120×C15111yescharacteristic
621C2×C4#120×C15111yescharacteristic
622C2×C4#120×C15111yescharacteristic
623C2×C4C22×D4×C15111yescharacteristic
624C2×C4C22×D4×C15111yescharacteristic
625C8—42no—
626C8—41no—
627C8—41no—
628C22—21no—
629C22—21no—
630C22—42no—
631C22—42no—
632C22—41no—
633C22—41no—
634C22—42no—
635C22—42no—
636C22—42no—
637C22—41no—
638C22—42no—
639C22—82no—
640C22—82no—
641C22—164no—
642C22C2×#120×C15111yescharacteristic
643C22#576×C15111yescharacteristic
644C22#577×C15111yescharacteristic
645C4—21no—
646C4—21no—
647C4—21no—
648C4—21no—
649C4—21no—
650C4—21no—
651C4—41no—
652C4—42no—
653C4—41no—
654C4—42no—
655C4—41no—
656C4—82no—
657C4—81no—
658C4—81no—
659C2—21no—
660C2—21no—
661C2—82no—
662C2—81no—
663C2—82no—
664C2#3012×C15111yescharacteristic
665C2#3019×C15111yescharacteristic
666C2#3028×C15111yescharacteristic
subgroupG/H
center, socleC22×C151C2×#120
commutator, Frattini, cosocleC22×C4C24×C151
prime radical#3558×C151C2
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
2. #3234×C151C2semidirect
3. #3232×C151C2semidirect
4. #2820×C151C2semidirect
5. #1618×C151C2semidirect
6. #1613×C151C2semidirect
7. #1612×C151C2semidirect
8. #1607×C151C2semidirect
9. #1517×C151C2semidirect
10. #1512×C151C2semidirect
11. #1469×C151C2semidirect
26. C2×#125×C151C22semidirect
32. #484×C151C22semidirect
33. #483×C151C22semidirect
35. #481×C151C22semidirect
37. #480×C151C22semidirect
41. #432×C151C22semidirect
42. #431×C151C22semidirect
43. #399×C151C22semidirect
44. #397×C151C22semidirect
48. #382×C151C22semidirect
49. #328×C151C22semidirect
51. #327×C151C22semidirect
52. #327×C151C22semidirect
53. #323×C151C22semidirect
54. #323×C151C22semidirect
333. #18466C151direct (N × H)
334. C151#18466direct (N × H)
336. #3234C2×C151semidirect
337. #3232C2×C151semidirect
338. #2820C2×C151semidirect
339. #1618C2×C151semidirect
340. #1613C2×C151semidirect
341. #1612C2×C151semidirect
342. #1607C2×C151semidirect
343. #1517C2×C151semidirect
344. #1512C2×C151semidirect
345. #1469C2×C151semidirect
360. C2×#125C22×C151semidirect
366. #484C22×C151semidirect
367. #483C22×C151semidirect
369. #481C22×C151semidirect
371. #480C22×C151semidirect
375. #432C22×C151semidirect
376. #431C22×C151semidirect
377. #399C22×C151semidirect
378. #397C22×C151semidirect
382. #382C22×C151semidirect
383. #328C22×C151semidirect
385. #327C22×C151semidirect
386. #327C22×C151semidirect
387. #323C22×C151semidirect
388. #323C22×C151semidirect

Maximal subgroups

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

subgroupindex
#3558×C1512
#3234×C1512
#3232×C1512
#2820×C1512
#1618×C1512
#1613×C1512
#1612×C1512
#1607×C1512
#1517×C1512
#1512×C1512
#1469×C1512
#18466151