Finite Group Databasebeta

← C151×#18580 #50323505

Subgroups — C151×#18580 #50323505

Order 38656.

962 conjugacy classes of subgroups.

The subgroup lattice has 646 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#3523×C151C211yesmaximal, characteristic, complemented
2#3217×C151C211yesmaximal, characteristic
3#3138×C151C211yesmaximal, characteristic, complemented
4C2×#460×C151C211yesmaximal, characteristic, complemented
5#1628×C151C212yesmaximal, complemented
6#1627×C151C212yesmaximal, complemented
7#1626×C151C212yesmaximal, complemented
8#1626×C151C212yesmaximal, complemented
9#1552×C151C211yesmaximal, characteristic, complemented
10#1491×C151C211yesmaximal, characteristic, complemented
11#1483×C151C211yesmaximal, characteristic, complemented
12C22×SD16×C151—21no—
13#557×C151—21no—
14#557×C151C2211yescharacteristic, complemented
15#557×C151C2211yescharacteristic, complemented
16#556×C151—21no—
17#556×C151C2211yescharacteristic, complemented
18#552×C151—22no—
19#552×C151—21no—
20D4×Q8×C151—21no—
21D4×Q8×C151C2211yescharacteristic, complemented
22#541×C151—22no—
23#541×C151—21no—
24#533×C151—21no—
25#533×C151C2211yescharacteristic
26C2×#127×C151C2211yescharacteristic
27#529×C151—21no—
28#529×C151C2211yescharacteristic
29#519×C151—21no—
30C2×C4×Q8×C151C2211yescharacteristic
31#496×C151—21no—
32#490×C151—22no—
33#490×C151—21no—
34#486×C151C2212yes—
35#486×C151C2212yes—
36#460×C151—21no—
37#460×C151—21no—
38#460×C151C2212yes—
39#460×C151C2212yes—
40#460×C151C2212yes—
41#459×C151C2212yes—
42#450×C151—21no—
43#447×C151—21no—
44#432×C151C2211yescharacteristic
45C2×C4⋊C8×C151C2211yescharacteristic
46#418×C151—22no—
47C2×#102×C151—21no—
48C4×M16×C151C2211yescharacteristic
49#332×C151C2212yescomplemented
50#332×C151C2212yescomplemented
51Q8⋊C8×C151C2212yescomplemented
52Q8⋊C8×C151C2212yescomplemented
53Q8⋊C8×C151C2212yescomplemented
54D4⋊C8×C151C2212yescomplemented
55C22×Q8×C151—21no—
56C22×Q8×C151D411yescharacteristic
57C22×D4×C151—21no—
58C22×D4×C151—21no—
59C22×D4×C151—21no—
60C2×SD16×C151—22no—
61C2×SD16×C151—22no—
62C2×SD16×C151—22no—
63C2×SD16×C151—44no—
64C2×D8×C151—22no—
65C2×M16×C151—21no—
66C22×C8×C151—21no—
67C4⋊Q8×C151—22no—
68C4⋊Q8×C151—21no—
69C4⋊Q8×C151—21no—
70C4⋊Q8×C151—21no—
71C4⋊Q8×C151C2311yescharacteristic
72C4⋊Q8×C151C2311yescharacteristic
73#127×C151—21no—
74#127×C151—21no—
75#127×C151—21no—
76#127×C151C2312yes—
77#126×C151—22no—
78#126×C151—22no—
79#126×C151—22no—
80#126×C151—22no—
81#126×C151—21no—
82#125×C151—22no—
83#125×C151—22no—
84#125×C151—22no—
85#125×C151—21no—
86#125×C151—22no—
87#125×C151—22no—
88#125×C151—21no—
89#125×C151D411yescharacteristic
90#125×C151D412yes—
91#124×C151—21no—
92#124×C151D411yescharacteristic
93#123×C151—22no—
94#123×C151—21no—
95C22⋊Q8×C151—22no—
96C22⋊Q8×C151—22no—
97C22⋊Q8×C151—21no—
98C22⋊Q8×C151—21no—
99C22⋊Q8×C151—22no—
100C22⋊Q8×C151—21no—
101C22⋊Q8×C151—21no—
102C22⋊Q8×C151D411yescharacteristic
103#121×C151D411yescharacteristic
104C4×Q8×C151—22no—
105C4×Q8×C151—22no—
106C4×Q8×C151—21no—
107C4×Q8×C151—21no—
108C4×Q8×C151—21no—
109C4×Q8×C151—21no—
110C4×Q8×C151—21no—
111C4×Q8×C151—21no—
112C4×Q8×C151—21no—
113C4×Q8×C151—21no—
114C4×Q8×C151—21no—
115C4×Q8×C151D411yescharacteristic
116C4×Q8×C151D411yescharacteristic
117C4×Q8×C151C2311yescharacteristic
118C4×Q8×C151C2311yescharacteristic
119C4×Q8×C151C2311yescharacteristic
120C4×D4×C151—22no—
121C4×D4×C151—21no—
122C4×D4×C151—21no—
123C4×D4×C151C2311yescharacteristic
124#117×C151—22no—
125#117×C151—22no—
126#117×C151—22no—
127#117×C151—21no—
128#117×C151—21no—
129#117×C151D412yes—
130C2×C4⋊C4×C151—21no—
131C2×C4⋊C4×C151D411yescharacteristic
132C2×C42×C151—21no—
133C2×C42×C151C2311yescharacteristic
134C4⋊C8×C151—21no—
135C4⋊C8×C151C2312yes—
136C4⋊C8×C151C2312yes—
137#102×C151—22no—
138#102×C151—22no—
139#102×C151—24no—
140#102×C151—24no—
141#102×C151—22no—
142#102×C151—22no—
143C22⋊C8×C151—21no—
144#97×C151—21no—
145#97×C151—21no—
146C4×C8×C151C2312yes—
147C24×C151—41no—
148C2×Q8×C151—22no—
149C2×Q8×C151—21no—
150C2×Q8×C151—21no—
151C2×Q8×C151—21no—
152C2×Q8×C151—22no—
153C2×Q8×C151—41no—
154C2×Q8×C151—42no—
155C2×Q8×C151—42no—
156C2×Q8×C151C2×D411yescharacteristic
157C2×Q8×C151C2×D411yescharacteristic
158C2×Q8×C151C2×D411yescharacteristic
159C2×D4×C151—21no—
160C2×D4×C151—22no—
161C2×D4×C151—22no—
162C2×D4×C151—22no—
163C2×D4×C151—42no—
164C2×D4×C151—44no—
165C2×D4×C151—42no—
166C2×D4×C151—41no—
167C2×D4×C151—41no—
168C2×D4×C151—41no—
169C2×D4×C151—82no—
170C2×D4×C151C2×D411yescharacteristic
171C22×C4×C151—22no—
172C22×C4×C151—21no—
173C22×C4×C151—21no—
174C22×C4×C151—21no—
175C22×C4×C151C2×D411yescharacteristic
176C22×C4×C151C2×D411yescharacteristic
177C22×C4×C151C2×D411yescharacteristic
178SD16×C151—44no—
179SD16×C151—44no—
180SD16×C151—82no—
181D8×C151—82no—
182M16×C151—42no—
183C2×C8×C151—22no—
184C2×C8×C151—22no—
185C2×C8×C151—22no—
186C2×C8×C151—42no—
187C4⋊C4×C151—22no—
188C4⋊C4×C151—22no—
189C4⋊C4×C151—22no—
190C4⋊C4×C151—22no—
191C4⋊C4×C151—22no—
192C4⋊C4×C151—22no—
193C4⋊C4×C151—22no—
194C4⋊C4×C151—22no—
195C4⋊C4×C151—21no—
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—22no—
203C4⋊C4×C151—21no—
204C4⋊C4×C151—21no—
205C4⋊C4×C151—21no—
206C4⋊C4×C151—21no—
207C4⋊C4×C151—21no—
208C4⋊C4×C151C2×D411yescharacteristic
209C4⋊C4×C151C2×D411yescharacteristic
210C4⋊C4×C151C2×D412yes—
211C4⋊C4×C151C2×D412yes—
212C4⋊C4×C151C2×D411yescharacteristic
213C4⋊C4×C151C2×D411yescharacteristic
214C22⋊C4×C151—22no—
215C22⋊C4×C151—22no—
216C22⋊C4×C151—22no—
217C22⋊C4×C151—21no—
218C22⋊C4×C151—22no—
219C22⋊C4×C151—21no—
220C22⋊C4×C151—21no—
221C22⋊C4×C151—21no—
222C22⋊C4×C151—21no—
223C42×C151—22no—
224C42×C151—22no—
225C42×C151—22no—
226C42×C151—21no—
227C42×C151—21no—
228C42×C151—22no—
229C42×C151—21no—
230C42×C151—21no—
231C42×C151—21no—
232C42×C151C2×D411yescharacteristic
233C42×C151C2×D411yescharacteristic
234C42×C151C2×D411yescharacteristic
235C42×C151C2411yescharacteristic
236C23×C151—21no—
237C23×C151—42no—
238C23×C151—82no—
239C23×C151—82no—
240C23×C151—82no—
241C23×C151#12011yescharacteristic
242Q8×C151—21no—
243Q8×C151—21no—
244Q8×C151—21no—
245Q8×C151—22no—
246Q8×C151—42no—
247Q8×C151—44no—
248Q8×C151—41no—
249Q8×C151—41no—
250Q8×C151—42no—
251Q8×C151AGL(1,ℤ/8)12yes—
252D4×C151—22no—
253D4×C151—44no—
254D4×C151—42no—
255D4×C151—42no—
256D4×C151—42no—
257D4×C151—42no—
258D4×C151—42no—
259D4×C151—82no—
260D4×C151—82no—
261D4×C151—82no—
262C2×C4×C151—21no—
263C2×C4×C151—22no—
264C2×C4×C151—21no—
265C2×C4×C151—21no—
266C2×C4×C151—22no—
267C2×C4×C151—21no—
268C2×C4×C151—22no—
269C2×C4×C151—21no—
270C2×C4×C151—22no—
271C2×C4×C151—21no—
272C2×C4×C151—21no—
273C2×C4×C151—21no—
274C2×C4×C151—21no—
275C2×C4×C151—42no—
276C2×C4×C151—44no—
277C2×C4×C151—42no—
278C2×C4×C151—41no—
279C2×C4×C151—41no—
280C2×C4×C151#12011yescharacteristic
281C2×C4×C151#12011yescharacteristic
282C2×C4×C151#12011yescharacteristic
283C2×C4×C151C22×D411yescharacteristic
284C2×C4×C151C22×D411yescharacteristic
285C2×C4×C151C22×D411yescharacteristic
286C8×C151—42no—
287C8×C151—42no—
288C8×C151—42no—
289C22×C151—21no—
290C22×C151—21no—
291C22×C151—41no—
292C22×C151—41no—
293C22×C151—41no—
294C22×C151—82no—
295C22×C151—82no—
296C22×C151—82no—
297C22×C151—164no—
298C22×C151#45412yes—
299C22×C151C2×#12011yescharacteristic
300C4×C151—21no—
301C4×C151—22no—
302C4×C151—21no—
303C4×C151—21no—
304C4×C151—21no—
305C4×C151—41no—
306C4×C151—42no—
307C4×C151—41no—
308C4×C151—41no—
309C4×C151—42no—
310C4×C151—41no—
311C4×C151—41no—
312C4×C151—41no—
313C4×C151C2×AGL(1,ℤ/8)11yescharacteristic
314C4×C151#57511yescharacteristic
315C4×C151#57712yes—
316C2×C151—22no—
317C2×C151—81no—
318C2×C151—162no—
319C2×C151#300611yescharacteristic
320C2×C151#301011yescharacteristic
321C2×C151C2×#45411yescharacteristic
322#18580C15111yesmaximal, characteristic, direct product factor, Sylow
323C151#1858011yescharacteristic, direct product factor, Sylow
324#3523C2×C15111yescharacteristic, complemented
325#3217C2×C15111yescharacteristic
326#3138C2×C15111yescharacteristic, complemented
327C2×#460C2×C15111yescharacteristic, complemented
328#1628C2×C15112yescomplemented
329#1627C2×C15112yescomplemented
330#1626C2×C15112yescomplemented
331#1626C2×C15112yescomplemented
332#1552C2×C15111yescharacteristic, complemented
333#1491C2×C15111yescharacteristic, complemented
334#1483C2×C15111yescharacteristic, complemented
335C22×SD16—21no—
336#557—21no—
337#557C22×C15111yescharacteristic, complemented
338#557C22×C15111yescharacteristic, complemented
339#556—21no—
340#556C22×C15111yescharacteristic, complemented
341#552—22no—
342#552—21no—
343D4×Q8—21no—
344D4×Q8C22×C15111yescharacteristic, complemented
345#541—22no—
346#541—21no—
347#533—21no—
348#533C22×C15111yescharacteristic
349C2×#127C22×C15111yescharacteristic
350#529—21no—
351#529C22×C15111yescharacteristic
352#519—21no—
353C2×C4×Q8C22×C15111yescharacteristic
354#496—21no—
355#490—22no—
356#490—21no—
357#486C22×C15112yes—
358#486C22×C15112yes—
359#460—21no—
360#460—21no—
361#460C22×C15112yes—
362#460C22×C15112yes—
363#460C22×C15112yes—
364#459C22×C15112yes—
365#450—21no—
366#447—21no—
367#432C22×C15111yescharacteristic
368C2×C4⋊C8C22×C15111yescharacteristic
369#418—22no—
370C2×#102—21no—
371C4×M16C22×C15111yescharacteristic
372#332C22×C15112yescomplemented
373#332C22×C15112yescomplemented
374Q8⋊C8C22×C15112yescomplemented
375Q8⋊C8C22×C15112yescomplemented
376Q8⋊C8C22×C15112yescomplemented
377D4⋊C8C22×C15112yescomplemented
378C22×Q8—21no—
379C22×Q8D4×C15111yescharacteristic
380C22×D4—21no—
381C22×D4—21no—
382C22×D4—21no—
383C2×SD16—22no—
384C2×SD16—22no—
385C2×SD16—22no—
386C2×SD16—44no—
387C2×D8—22no—
388C2×M16—21no—
389C22×C8—21no—
390C4⋊Q8—22no—
391C4⋊Q8—21no—
392C4⋊Q8—21no—
393C4⋊Q8—21no—
394C4⋊Q8C23×C15111yescharacteristic
395C4⋊Q8C23×C15111yescharacteristic
396#127—21no—
397#127—21no—
398#127—21no—
399#127C23×C15112yes—
400#126—22no—
401#126—22no—
402#126—22no—
403#126—22no—
404#126—21no—
405#125—22no—
406#125—22no—
407#125—22no—
408#125—21no—
409#125—22no—
410#125—22no—
411#125—21no—
412#125D4×C15111yescharacteristic
413#125D4×C15112yes—
414#124—21no—
415#124D4×C15111yescharacteristic
416#123—22no—
417#123—21no—
418C22⋊Q8—22no—
419C22⋊Q8—22no—
420C22⋊Q8—21no—
421C22⋊Q8—21no—
422C22⋊Q8—21no—
423C22⋊Q8—21no—
424C22⋊Q8—22no—
425C22⋊Q8D4×C15111yescharacteristic
426#121D4×C15111yescharacteristic
427C4×Q8—22no—
428C4×Q8—22no—
429C4×Q8—21no—
430C4×Q8—21no—
431C4×Q8—21no—
432C4×Q8—21no—
433C4×Q8—21no—
434C4×Q8—21no—
435C4×Q8—21no—
436C4×Q8—21no—
437C4×Q8—21no—
438C4×Q8D4×C15111yescharacteristic
439C4×Q8D4×C15111yescharacteristic
440C4×Q8C23×C15111yescharacteristic
441C4×Q8C23×C15111yescharacteristic
442C4×Q8C23×C15111yescharacteristic
443C4×D4—22no—
444C4×D4—21no—
445C4×D4—21no—
446C4×D4C23×C15111yescharacteristic
447#117—22no—
448#117—22no—
449#117—22no—
450#117—21no—
451#117—21no—
452#117D4×C15112yes—
453C2×C4⋊C4—21no—
454C2×C4⋊C4D4×C15111yescharacteristic
455C2×C42—21no—
456C2×C42C23×C15111yescharacteristic
457C4⋊C8—21no—
458C4⋊C8C23×C15112yes—
459C4⋊C8C23×C15112yes—
460#102—22no—
461#102—22no—
462#102—24no—
463#102—24no—
464#102—22no—
465#102—22no—
466C22⋊C8—21no—
467#97—21no—
468#97—21no—
469C4×C8C23×C15112yes—
470C24—41no—
471C2×Q8—22no—
472C2×Q8—21no—
473C2×Q8—21no—
474C2×Q8—21no—
475C2×Q8—22no—
476C2×Q8—41no—
477C2×Q8—42no—
478C2×Q8—42no—
479C2×Q8C2×D4×C15111yescharacteristic
480C2×Q8C2×D4×C15111yescharacteristic
481C2×Q8C2×D4×C15111yescharacteristic
482C2×D4—21no—
483C2×D4—22no—
484C2×D4—22no—
485C2×D4—22no—
486C2×D4—42no—
487C2×D4—44no—
488C2×D4—42no—
489C2×D4—41no—
490C2×D4—41no—
491C2×D4—41no—
492C2×D4—82no—
493C2×D4C2×D4×C15111yescharacteristic
494C22×C4—22no—
495C22×C4—21no—
496C22×C4—21no—
497C22×C4—21no—
498C22×C4C2×D4×C15111yescharacteristic
499C22×C4C2×D4×C15111yescharacteristic
500C22×C4C2×D4×C15111yescharacteristic
501SD16—44no—
502SD16—44no—
503SD16—82no—
504D8—82no—
505M16—42no—
506C2×C8—22no—
507C2×C8—22no—
508C2×C8—22no—
509C2×C8—42no—
510C4⋊C4—22no—
511C4⋊C4—22no—
512C4⋊C4—22no—
513C4⋊C4—22no—
514C4⋊C4—22no—
515C4⋊C4—22no—
516C4⋊C4—22no—
517C4⋊C4—22no—
518C4⋊C4—21no—
519C4⋊C4—21no—
520C4⋊C4—21no—
521C4⋊C4—22no—
522C4⋊C4—21no—
523C4⋊C4—21no—
524C4⋊C4—21no—
525C4⋊C4—22no—
526C4⋊C4—21no—
527C4⋊C4—21no—
528C4⋊C4—21no—
529C4⋊C4—21no—
530C4⋊C4—21no—
531C4⋊C4C2×D4×C15111yescharacteristic
532C4⋊C4C2×D4×C15111yescharacteristic
533C4⋊C4C2×D4×C15112yes—
534C4⋊C4C2×D4×C15112yes—
535C4⋊C4C2×D4×C15111yescharacteristic
536C4⋊C4C2×D4×C15111yescharacteristic
537C22⋊C4—22no—
538C22⋊C4—22no—
539C22⋊C4—22no—
540C22⋊C4—21no—
541C22⋊C4—22no—
542C22⋊C4—21no—
543C22⋊C4—21no—
544C22⋊C4—21no—
545C22⋊C4—21no—
546C42—22no—
547C42—22no—
548C42—22no—
549C42—21no—
550C42—21no—
551C42—22no—
552C42—21no—
553C42—21no—
554C42—21no—
555C42C2×D4×C15111yescharacteristic
556C42C2×D4×C15111yescharacteristic
557C42C2×D4×C15111yescharacteristic
558C42C24×C15111yescharacteristic
559C23—21no—
560C23—42no—
561C23—82no—
562C23—82no—
563C23—82no—
564C23#120×C15111yescharacteristic
565Q8—21no—
566Q8—21no—
567Q8—21no—
568Q8—22no—
569Q8—42no—
570Q8—44no—
571Q8—41no—
572Q8—41no—
573Q8—42no—
574Q8AGL(1,ℤ/8)×C15112yes—
575D4—22no—
576D4—44no—
577D4—42no—
578D4—42no—
579D4—42no—
580D4—42no—
581D4—42no—
582D4—82no—
583D4—82no—
584D4—82no—
585C2×C4—22no—
586C2×C4—21no—
587C2×C4—21no—
588C2×C4—21no—
589C2×C4—22no—
590C2×C4—21no—
591C2×C4—21no—
592C2×C4—22no—
593C2×C4—21no—
594C2×C4—21no—
595C2×C4—21no—
596C2×C4—21no—
597C2×C4—22no—
598C2×C4—42no—
599C2×C4—44no—
600C2×C4—42no—
601C2×C4—41no—
602C2×C4—41no—
603C2×C4#120×C15111yescharacteristic
604C2×C4#120×C15111yescharacteristic
605C2×C4#120×C15111yescharacteristic
606C2×C4C22×D4×C15111yescharacteristic
607C2×C4C22×D4×C15111yescharacteristic
608C2×C4C22×D4×C15111yescharacteristic
609C8—42no—
610C8—42no—
611C8—42no—
612C22—21no—
613C22—21no—
614C22—41no—
615C22—41no—
616C22—41no—
617C22—82no—
618C22—82no—
619C22—82no—
620C22—164no—
621C22#454×C15112yes—
622C22C2×#120×C15111yescharacteristic
623C4—21no—
624C4—22no—
625C4—21no—
626C4—21no—
627C4—21no—
628C4—41no—
629C4—42no—
630C4—41no—
631C4—41no—
632C4—42no—
633C4—41no—
634C4—41no—
635C4—41no—
636C4C2×AGL(1,ℤ/8)×C15111yescharacteristic
637C4#575×C15111yescharacteristic
638C4#577×C15112yes—
639C2—22no—
640C2—81no—
641C2—162no—
642C2#3006×C15111yescharacteristic
643C2#3010×C15111yescharacteristic
644C2C2×#454×C15111yescharacteristic
subgroupG/H
center, socleC22×C151C2×#120
commutator, Frattini, cosocleC42C24×C151
prime radical#3217×C151C2
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. #3523×C151C2semidirect
3. #3138×C151C2semidirect
4. C2×#460×C151C2semidirect
5. #1628×C151C2semidirect
6. #1627×C151C2semidirect
7. #1626×C151C2semidirect
8. #1626×C151C2semidirect
9. #1552×C151C2semidirect
10. #1491×C151C2semidirect
11. #1483×C151C2semidirect
14. #557×C151C22semidirect
15. #557×C151C22semidirect
17. #556×C151C22semidirect
21. D4×Q8×C151C22semidirect
49. #332×C151C22semidirect
50. #332×C151C22semidirect
51. Q8⋊C8×C151C22semidirect
52. Q8⋊C8×C151C22semidirect
53. Q8⋊C8×C151C22semidirect
54. D4⋊C8×C151C22semidirect
322. #18580C151direct (N × H)
323. C151#18580direct (N × H)
324. #3523C2×C151semidirect
326. #3138C2×C151semidirect
327. C2×#460C2×C151semidirect
328. #1628C2×C151semidirect
329. #1627C2×C151semidirect
330. #1626C2×C151semidirect
331. #1626C2×C151semidirect
332. #1552C2×C151semidirect
333. #1491C2×C151semidirect
334. #1483C2×C151semidirect
337. #557C22×C151semidirect
338. #557C22×C151semidirect
340. #556C22×C151semidirect
344. D4×Q8C22×C151semidirect
372. #332C22×C151semidirect
373. #332C22×C151semidirect
374. Q8⋊C8C22×C151semidirect
375. Q8⋊C8C22×C151semidirect
376. Q8⋊C8C22×C151semidirect
377. D4⋊C8C22×C151semidirect

Maximal subgroups

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

subgroupindex
#3523×C1512
#3217×C1512
#3138×C1512
C2×#460×C1512
#1628×C1512
#1627×C1512
#1626×C1512
#1552×C1512
#1491×C1512
#1483×C1512
#18580151