Finite Group Databasebeta

← C151×#19370 #50324295

Subgroups — C151×#19370 #50324295

Order 38656.

678 conjugacy classes of subgroups.

The subgroup lattice has 632 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#3253×C151C211yesmaximal, characteristic, complemented
2#3214×C151C211yesmaximal, characteristic, complemented
3#3184×C151C211yesmaximal, characteristic, complemented
4#2935×C151C211yesmaximal, characteristic, complemented
5#1701×C151C211yesmaximal, characteristic, complemented
6#1697×C151C211yesmaximal, characteristic, complemented
7#1691×C151C211yesmaximal, characteristic, complemented
8#1687×C151C211yesmaximal, characteristic, complemented
9#1681×C151C211yesmaximal, characteristic, complemented
10#1677×C151C211yesmaximal, characteristic, complemented
11#1671×C151C211yesmaximal, characteristic, complemented
12#1667×C151C211yesmaximal, characteristic, complemented
13#1569×C151C211yesmaximal, characteristic, complemented
14#1551×C151C211yesmaximal, characteristic, complemented
15#1547×C151C211yesmaximal, characteristic, complemented
16C2×#131×C151—21no—
17#532×C151C2211yescharacteristic
18#532×C151C2211yescharacteristic
19#532×C151C2211yescharacteristic
20#498×C151C2211yescharacteristic
21#496×C151—21no—
22#493×C151C2211yescharacteristic
23#489×C151—21no—
24#486×C151C2211yescharacteristic
25#486×C151C2211yescharacteristic
26#476×C151—21no—
27#476×C151C2211yescharacteristic
28#476×C151C2211yescharacteristic
29#469×C151—21no—
30#469×C151—21no—
31#469×C151—21no—
32#469×C151—21no—
33#461×C151C2211yescharacteristic
34#461×C151C2211yescharacteristic
35#459×C151—21no—
36#459×C151C2211yescharacteristic
37#459×C151C2211yescharacteristic
38#459×C151C2211yescharacteristic
39#459×C151C2211yescharacteristic
40#449×C151—21no—
41#449×C151—21no—
42#442×C151—21no—
43#442×C151—21no—
44#436×C151C2211yescharacteristic
45#436×C151C2211yescharacteristic
46#435×C151—21no—
47#435×C151—21no—
48C8×D4×C151C2211yescharacteristic
49C8×D4×C151C2211yescharacteristic
50#432×C151C2211yescharacteristic
51#423×C151C2211yescharacteristic
52C2×C4⋊C8×C151C2211yescharacteristic
53#408×C151—21no—
54C4×M16×C151C2211yescharacteristic
55#335×C151C2211yescharacteristic
56#335×C151C2211yescharacteristic
57#334×C151C2211yescharacteristic
58#334×C151C2211yescharacteristic
59#333×C151C2211yescharacteristic
60#333×C151C2211yescharacteristic
61#332×C151C2211yescharacteristic
62#332×C151C2211yescharacteristic
63#331×C151C2211yescharacteristic
64#331×C151C2211yescharacteristic
65#331×C151C2211yescharacteristic
66#331×C151C2211yescharacteristic
67C2×#41×C151—21no—
68C2×#41×C151—21no—
69C2×#41×C151—21no—
70C2×SD16×C151—21no—
71C2×SD16×C151—21no—
72C2×D8×C151—21no—
73C2×D8×C151—21no—
74C2×D8×C151—21no—
75C2×D8×C151—21no—
76C2×D8×C151—21no—
77C2×D8×C151—21no—
78#131×C151—44no—
79C2×M16×C151—21no—
80C2×M16×C151—21no—
81C2×M16×C151—21no—
82C2×M16×C151D411yescharacteristic
83C2×M16×C151D411yescharacteristic
84C22×C8×C151—21no—
85C22×C8×C151—21no—
86C22×C8×C151—21no—
87C4⋊Q8×C151D411yescharacteristic
88C4⋊Q8×C151C2311yescharacteristic
89C4⋊Q8×C151C2311yescharacteristic
90#127×C151D411yescharacteristic
91#127×C151C2311yescharacteristic
92#127×C151C2311yescharacteristic
93#124×C151—21no—
94#124×C151—21no—
95#124×C151—21no—
96#121×C151—21no—
97#121×C151—21no—
98#121×C151—21no—
99#121×C151—21no—
100#121×C151—21no—
101#121×C151D411yescharacteristic
102#121×C151D411yescharacteristic
103C4×D4×C151—21no—
104C4×D4×C151—21no—
105C4×D4×C151—21no—
106C4×D4×C151—21no—
107C4×D4×C151—21no—
108C4×D4×C151C2311yescharacteristic
109C4×D4×C151C2311yescharacteristic
110C2×C42×C151C2311yescharacteristic
111#106×C151—21no—
112#106×C151—21no—
113#106×C151—21no—
114#106×C151—21no—
115C4⋊C8×C151—21no—
116C4⋊C8×C151—21no—
117C4⋊C8×C151C2311yescharacteristic
118C4⋊C8×C151C2311yescharacteristic
119C4⋊C8×C151C2311yescharacteristic
120C4⋊C8×C151C2311yescharacteristic
121C4⋊C8×C151C2311yescharacteristic
122C4⋊C8×C151C2311yescharacteristic
123#103×C151—21no—
124#103×C151—21no—
125#102×C151—21no—
126#102×C151—21no—
127#102×C151—21no—
128#102×C151—21no—
129#102×C151—21no—
130#102×C151—21no—
131#102×C151—21no—
132#102×C151—21no—
133#102×C151—21no—
134#102×C151—21no—
135C22⋊C8×C151—21no—
136C22⋊C8×C151—21no—
137C22⋊C8×C151—21no—
138C22⋊C8×C151—21no—
139C22⋊C8×C151—21no—
140#97×C151—21no—
141#97×C151D411yescharacteristic
142#97×C151D411yescharacteristic
143C4×C8×C151C2311yescharacteristic
144C4×C8×C151C2311yescharacteristic
145#41×C151—42no—
146#41×C151—42no—
147#41×C151—81no—
148#41×C151—81no—
149#41×C151—82no—
150C2×Q8×C151—21no—
151C2×Q8×C151—21no—
152C2×Q8×C151—21no—
153C2×D4×C151—21no—
154C2×D4×C151—21no—
155C2×D4×C151—21no—
156C2×D4×C151—21no—
157C2×D4×C151—21no—
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×C151—41no—
165C2×D4×C151C2×D411yescharacteristic
166C2×D4×C151C2×D411yescharacteristic
167C22×C4×C151—21no—
168C22×C4×C151—21no—
169C22×C4×C151—41no—
170C22×C4×C151—41no—
171C22×C4×C151C2×D411yescharacteristic
172C22×C4×C151C2×D411yescharacteristic
173C22×C4×C151#4111yescharacteristic
174SD16×C151—81no—
175SD16×C151—81no—
176D8×C151—42no—
177D8×C151—42no—
178D8×C151—81no—
179D8×C151—81no—
180D8×C151—81no—
181D8×C151—81no—
182M16×C151—22no—
183M16×C151—41no—
184M16×C151—42no—
185M16×C151—42no—
186M16×C151—81no—
187C2×C8×C151—21no—
188C2×C8×C151—21no—
189C2×C8×C151—21no—
190C2×C8×C151—21no—
191C2×C8×C151—21no—
192C2×C8×C151—21no—
193C2×C8×C151—42no—
194C2×C8×C151—42no—
195C2×C8×C151—42no—
196C2×C8×C151C2×D411yescharacteristic
197C2×C8×C151C2×D411yescharacteristic
198C2×C8×C151C2×D411yescharacteristic
199C2×C8×C151C2×D411yescharacteristic
200C4⋊C4×C151—21no—
201C4⋊C4×C151—21no—
202C4⋊C4×C151—21no—
203C4⋊C4×C151—21no—
204C4⋊C4×C151—21no—
205C4⋊C4×C151C2×D411yescharacteristic
206C4⋊C4×C151C2×D411yescharacteristic
207C22⋊C4×C151—21no—
208C22⋊C4×C151—21no—
209C22⋊C4×C151—21no—
210C22⋊C4×C151—21no—
211C22⋊C4×C151—41no—
212C22⋊C4×C151—41no—
213C22⋊C4×C151—41no—
214C22⋊C4×C151—41no—
215C42×C151C2×D411yescharacteristic
216C42×C151C2×D411yescharacteristic
217C42×C151#4111yescharacteristic
218C42×C151C2411yescharacteristic
219C23×C151—21no—
220C23×C151—21no—
221C23×C151—41no—
222C23×C151—41no—
223C23×C151#12111yescharacteristic
224Q8×C151—42no—
225Q8×C151—41no—
226Q8×C151—41no—
227Q8×C151—81no—
228D4×C151—21no—
229D4×C151—21no—
230D4×C151—21no—
231D4×C151—21no—
232D4×C151—42no—
233D4×C151—42no—
234D4×C151—42no—
235D4×C151—41no—
236D4×C151—41no—
237D4×C151—41no—
238D4×C151—41no—
239D4×C151—41no—
240D4×C151—41no—
241D4×C151—41no—
242D4×C151—41no—
243D4×C151—81no—
244D4×C151—81no—
245D4×C151—81no—
246D4×C151—82no—
247D4×C151—82no—
248C2×C4×C151—21no—
249C2×C4×C151—21no—
250C2×C4×C151—21no—
251C2×C4×C151—21no—
252C2×C4×C151—21no—
253C2×C4×C151—21no—
254C2×C4×C151—41no—
255C2×C4×C151—41no—
256C2×C4×C151—41no—
257C2×C4×C151—41no—
258C2×C4×C151—41no—
259C2×C4×C151—41no—
260C2×C4×C151—41no—
261C2×C4×C151—82no—
262C2×C4×C151—82no—
263C2×C4×C151#12111yescharacteristic
264C2×C4×C151#12111yescharacteristic
265C2×C4×C151#12111yescharacteristic
266C2×C4×C151C22×D411yescharacteristic
267C2×C4×C151C22×D411yescharacteristic
268C2×C4×C151C2×#4111yescharacteristic
269C8×C151—21no—
270C8×C151—21no—
271C8×C151—21no—
272C8×C151—41no—
273C8×C151—41no—
274C8×C151—41no—
275C8×C151—41no—
276C8×C151—41no—
277C8×C151—41no—
278C8×C151AGL(1,ℤ/8)12yes—
279C22×C151—21no—
280C22×C151—21no—
281C22×C151—21no—
282C22×C151—41no—
283C22×C151—41no—
284C22×C151—41no—
285C22×C151—41no—
286C22×C151—41no—
287C22×C151—41no—
288C22×C151—81no—
289C22×C151—81no—
290C22×C151—81no—
291C22×C151—81no—
292C22×C151—81no—
293C22×C151—81no—
294C22×C151C2×#12111yescharacteristic
295C4×C151—21no—
296C4×C151—21no—
297C4×C151—21no—
298C4×C151—21no—
299C4×C151—41no—
300C4×C151—41no—
301C4×C151—81no—
302C4×C151—81no—
303C4×C151C2×AGL(1,ℤ/8)11yescharacteristic
304C4×C151#57511yescharacteristic
305C4×C151#57611yescharacteristic
306C4×C151#57711yescharacteristic
307C2×C151—41no—
308C2×C151—81no—
309C2×C151—81no—
310C2×C151—161no—
311C2×C151—161no—
312C2×C151#303611yescharacteristic
313C2×C151#306211yescharacteristic
314C2×C151#306811yescharacteristic
315#19370C15111yesmaximal, characteristic, direct product factor, Sylow
316C151#1937011yescharacteristic, direct product factor, Sylow
317#3253C2×C15111yescharacteristic, complemented
318#3214C2×C15111yescharacteristic, complemented
319#3184C2×C15111yescharacteristic, complemented
320#2935C2×C15111yescharacteristic, complemented
321#1701C2×C15111yescharacteristic, complemented
322#1697C2×C15111yescharacteristic, complemented
323#1691C2×C15111yescharacteristic, complemented
324#1687C2×C15111yescharacteristic, complemented
325#1681C2×C15111yescharacteristic, complemented
326#1677C2×C15111yescharacteristic, complemented
327#1671C2×C15111yescharacteristic, complemented
328#1667C2×C15111yescharacteristic, complemented
329#1569C2×C15111yescharacteristic, complemented
330#1551C2×C15111yescharacteristic, complemented
331#1547C2×C15111yescharacteristic, complemented
332C2×#131—21no—
333#532C22×C15111yescharacteristic
334#532C22×C15111yescharacteristic
335#532C22×C15111yescharacteristic
336#498C22×C15111yescharacteristic
337#496—21no—
338#493C22×C15111yescharacteristic
339#489—21no—
340#486C22×C15111yescharacteristic
341#486C22×C15111yescharacteristic
342#476—21no—
343#476C22×C15111yescharacteristic
344#476C22×C15111yescharacteristic
345#469—21no—
346#469—21no—
347#469—21no—
348#469—21no—
349#461C22×C15111yescharacteristic
350#461C22×C15111yescharacteristic
351#459—21no—
352#459C22×C15111yescharacteristic
353#459C22×C15111yescharacteristic
354#459C22×C15111yescharacteristic
355#459C22×C15111yescharacteristic
356#449—21no—
357#449—21no—
358#442—21no—
359#442—21no—
360#436C22×C15111yescharacteristic
361#436C22×C15111yescharacteristic
362#435—21no—
363#435—21no—
364C8×D4C22×C15111yescharacteristic
365C8×D4C22×C15111yescharacteristic
366#432C22×C15111yescharacteristic
367#423C22×C15111yescharacteristic
368C2×C4⋊C8C22×C15111yescharacteristic
369#408—21no—
370C4×M16C22×C15111yescharacteristic
371#335C22×C15111yescharacteristic
372#335C22×C15111yescharacteristic
373#334C22×C15111yescharacteristic
374#334C22×C15111yescharacteristic
375#333C22×C15111yescharacteristic
376#333C22×C15111yescharacteristic
377#332C22×C15111yescharacteristic
378#332C22×C15111yescharacteristic
379#331C22×C15111yescharacteristic
380#331C22×C15111yescharacteristic
381#331C22×C15111yescharacteristic
382#331C22×C15111yescharacteristic
383C2×#41—21no—
384C2×#41—21no—
385C2×#41—21no—
386C2×SD16—21no—
387C2×SD16—21no—
388C2×D8—21no—
389C2×D8—21no—
390C2×D8—21no—
391C2×D8—21no—
392C2×D8—21no—
393C2×D8—21no—
394#131—44no—
395C2×M16—21no—
396C2×M16—21no—
397C2×M16—21no—
398C2×M16D4×C15111yescharacteristic
399C2×M16D4×C15111yescharacteristic
400C22×C8—21no—
401C22×C8—21no—
402C22×C8—21no—
403C4⋊Q8D4×C15111yescharacteristic
404C4⋊Q8C23×C15111yescharacteristic
405C4⋊Q8C23×C15111yescharacteristic
406#127D4×C15111yescharacteristic
407#127C23×C15111yescharacteristic
408#127C23×C15111yescharacteristic
409#124—21no—
410#124—21no—
411#124—21no—
412#121—21no—
413#121—21no—
414#121—21no—
415#121—21no—
416#121—21no—
417#121D4×C15111yescharacteristic
418#121D4×C15111yescharacteristic
419C4×D4—21no—
420C4×D4—21no—
421C4×D4—21no—
422C4×D4—21no—
423C4×D4—21no—
424C4×D4C23×C15111yescharacteristic
425C4×D4C23×C15111yescharacteristic
426C2×C42C23×C15111yescharacteristic
427#106—21no—
428#106—21no—
429#106—21no—
430#106—21no—
431C4⋊C8—21no—
432C4⋊C8—21no—
433C4⋊C8C23×C15111yescharacteristic
434C4⋊C8C23×C15111yescharacteristic
435C4⋊C8C23×C15111yescharacteristic
436C4⋊C8C23×C15111yescharacteristic
437C4⋊C8C23×C15111yescharacteristic
438C4⋊C8C23×C15111yescharacteristic
439#103—21no—
440#103—21no—
441#102—21no—
442#102—21no—
443#102—21no—
444#102—21no—
445#102—21no—
446#102—21no—
447#102—21no—
448#102—21no—
449#102—21no—
450#102—21no—
451C22⋊C8—21no—
452C22⋊C8—21no—
453C22⋊C8—21no—
454C22⋊C8—21no—
455C22⋊C8—21no—
456#97—21no—
457#97D4×C15111yescharacteristic
458#97D4×C15111yescharacteristic
459C4×C8C23×C15111yescharacteristic
460C4×C8C23×C15111yescharacteristic
461#41—42no—
462#41—42no—
463#41—81no—
464#41—81no—
465#41—82no—
466C2×Q8—21no—
467C2×Q8—21no—
468C2×Q8—21no—
469C2×D4—21no—
470C2×D4—21no—
471C2×D4—21no—
472C2×D4—21no—
473C2×D4—21no—
474C2×D4—21no—
475C2×D4—21no—
476C2×D4—21no—
477C2×D4—21no—
478C2×D4—21no—
479C2×D4—41no—
480C2×D4—41no—
481C2×D4C2×D4×C15111yescharacteristic
482C2×D4C2×D4×C15111yescharacteristic
483C22×C4—21no—
484C22×C4—21no—
485C22×C4—41no—
486C22×C4—41no—
487C22×C4C2×D4×C15111yescharacteristic
488C22×C4C2×D4×C15111yescharacteristic
489C22×C4#41×C15111yescharacteristic
490SD16—81no—
491SD16—81no—
492D8—42no—
493D8—42no—
494D8—81no—
495D8—81no—
496D8—81no—
497D8—81no—
498M16—22no—
499M16—41no—
500M16—42no—
501M16—42no—
502M16—81no—
503C2×C8—21no—
504C2×C8—21no—
505C2×C8—21no—
506C2×C8—21no—
507C2×C8—21no—
508C2×C8—21no—
509C2×C8—42no—
510C2×C8—42no—
511C2×C8—42no—
512C2×C8C2×D4×C15111yescharacteristic
513C2×C8C2×D4×C15111yescharacteristic
514C2×C8C2×D4×C15111yescharacteristic
515C2×C8C2×D4×C15111yescharacteristic
516C4⋊C4—21no—
517C4⋊C4—21no—
518C4⋊C4—21no—
519C4⋊C4—21no—
520C4⋊C4—21no—
521C4⋊C4C2×D4×C15111yescharacteristic
522C4⋊C4C2×D4×C15111yescharacteristic
523C22⋊C4—21no—
524C22⋊C4—21no—
525C22⋊C4—21no—
526C22⋊C4—21no—
527C22⋊C4—41no—
528C22⋊C4—41no—
529C22⋊C4—41no—
530C22⋊C4—41no—
531C42C2×D4×C15111yescharacteristic
532C42C2×D4×C15111yescharacteristic
533C42#41×C15111yescharacteristic
534C42C24×C15111yescharacteristic
535C23—21no—
536C23—21no—
537C23—41no—
538C23—41no—
539C23#121×C15111yescharacteristic
540Q8—42no—
541Q8—41no—
542Q8—41no—
543Q8—81no—
544D4—21no—
545D4—21no—
546D4—21no—
547D4—21no—
548D4—42no—
549D4—42no—
550D4—42no—
551D4—41no—
552D4—41no—
553D4—41no—
554D4—41no—
555D4—41no—
556D4—41no—
557D4—41no—
558D4—41no—
559D4—81no—
560D4—81no—
561D4—81no—
562D4—82no—
563D4—82no—
564C2×C4—21no—
565C2×C4—21no—
566C2×C4—21no—
567C2×C4—21no—
568C2×C4—21no—
569C2×C4—21no—
570C2×C4—41no—
571C2×C4—41no—
572C2×C4—41no—
573C2×C4—41no—
574C2×C4—41no—
575C2×C4—41no—
576C2×C4—41no—
577C2×C4—82no—
578C2×C4—82no—
579C2×C4#121×C15111yescharacteristic
580C2×C4#121×C15111yescharacteristic
581C2×C4#121×C15111yescharacteristic
582C2×C4C22×D4×C15111yescharacteristic
583C2×C4C22×D4×C15111yescharacteristic
584C2×C4C2×#41×C15111yescharacteristic
585C8—21no—
586C8—21no—
587C8—21no—
588C8—41no—
589C8—41no—
590C8—41no—
591C8—41no—
592C8—41no—
593C8—41no—
594C8AGL(1,ℤ/8)×C15112yes—
595C22—21no—
596C22—21no—
597C22—21no—
598C22—41no—
599C22—41no—
600C22—41no—
601C22—41no—
602C22—41no—
603C22—41no—
604C22—81no—
605C22—81no—
606C22—81no—
607C22—81no—
608C22—81no—
609C22—81no—
610C22C2×#121×C15111yescharacteristic
611C4—21no—
612C4—21no—
613C4—21no—
614C4—21no—
615C4—41no—
616C4—41no—
617C4—81no—
618C4—81no—
619C4C2×AGL(1,ℤ/8)×C15111yescharacteristic
620C4#575×C15111yescharacteristic
621C4#576×C15111yescharacteristic
622C4#577×C15111yescharacteristic
623C2—41no—
624C2—81no—
625C2—81no—
626C2—161no—
627C2—161no—
628C2#3036×C15111yescharacteristic
629C2#3062×C15111yescharacteristic
630C2#3068×C15111yescharacteristic
subgroupG/H
center, socleC22×C151C2×#121
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. #3253×C151C2semidirect
2. #3214×C151C2semidirect
3. #3184×C151C2semidirect
4. #2935×C151C2semidirect
5. #1701×C151C2semidirect
6. #1697×C151C2semidirect
7. #1691×C151C2semidirect
8. #1687×C151C2semidirect
9. #1681×C151C2semidirect
10. #1677×C151C2semidirect
11. #1671×C151C2semidirect
12. #1667×C151C2semidirect
13. #1569×C151C2semidirect
14. #1551×C151C2semidirect
15. #1547×C151C2semidirect
315. #19370C151direct (N × H)
316. C151#19370direct (N × H)
317. #3253C2×C151semidirect
318. #3214C2×C151semidirect
319. #3184C2×C151semidirect
320. #2935C2×C151semidirect
321. #1701C2×C151semidirect
322. #1697C2×C151semidirect
323. #1691C2×C151semidirect
324. #1687C2×C151semidirect
325. #1681C2×C151semidirect
326. #1677C2×C151semidirect
327. #1671C2×C151semidirect
328. #1667C2×C151semidirect
329. #1569C2×C151semidirect
330. #1551C2×C151semidirect
331. #1547C2×C151semidirect

Maximal subgroups

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

subgroupindex
#3253×C1512
#3214×C1512
#3184×C1512
#2935×C1512
#1701×C1512
#1697×C1512
#1691×C1512
#1687×C1512
#1681×C1512
#1677×C1512
#1671×C1512
#1667×C1512
#1569×C1512
#1551×C1512
#1547×C1512
#19370151