Finite Group Databasebeta

← C151×#18587 #50323512

Subgroups — C151×#18587 #50323512

Order 38656.

944 conjugacy classes of subgroups.

The subgroup lattice has 652 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#3520×C151C211yesmaximal, characteristic
2#3218×C151C211yesmaximal, characteristic, complemented
3#3165×C151C211yesmaximal, characteristic, complemented
4C2×#474×C151C211yesmaximal, characteristic, complemented
5#1654×C151C212yesmaximal, complemented
6#1652×C151C212yesmaximal, complemented
7#1649×C151C212yesmaximal, complemented
8#1647×C151C212yesmaximal, complemented
9#1552×C151C211yesmaximal, characteristic, complemented
10#1490×C151C211yesmaximal, characteristic, complemented
11#1483×C151C211yesmaximal, characteristic, complemented
12#556×C151C2211yescharacteristic
13#554×C151—21no—
14#552×C151—21no—
15#551×C151—22no—
16D4×Q8×C151C2211yescharacteristic
17#548×C151—21no—
18#547×C151C2211yescharacteristic
19#547×C151C2211yescharacteristic
20#546×C151—21no—
21#542×C151—21no—
22#539×C151—22no—
23#533×C151C2211yescharacteristic
24C2×C4⋊Q8×C151C2211yescharacteristic
25#529×C151C2211yescharacteristic
26#525×C151—21no—
27C2×C22⋊Q8×C151—21no—
28#520×C151—21no—
29C2×C4×D4×C151C2211yescharacteristic
30#501×C151—22no—
31#500×C151C2212yescomplemented
32#498×C151C2212yescomplemented
33#497×C151—21no—
34#491×C151—21no—
35#474×C151—21no—
36#474×C151—21no—
37#474×C151C2212yes—
38#474×C151C2212yes—
39#462×C151C2212yescomplemented
40#461×C151C2212yescomplemented
41#451×C151—21no—
42#448×C151—21no—
43#432×C151C2211yescharacteristic
44#428×C151—22no—
45C2×#107×C151—21no—
46C2×C4⋊C8×C151C2211yescharacteristic
47C2×#102×C151—21no—
48C4×M16×C151C2211yescharacteristic
49#332×C151C2212yescomplemented
50#332×C151C2212yescomplemented
51Q8⋊C8×C151C2212yescomplemented
52D4⋊C8×C151C2212yes—
53D4⋊C8×C151C2212yes—
54D4⋊C8×C151C2212yescomplemented
55C2×#41×C151—21no—
56C2×#41×C151—21no—
57C22×Q8×C151—21no—
58C22×Q8×C151—21no—
59C22×D4×C151D411yescharacteristic
60C23×C4×C151—21no—
61C2×Q16×C151—22no—
62C2×SD16×C151—22no—
63C2×M16×C151—21no—
64C22×C8×C151—21no—
65C4⋊Q8×C151—21no—
66C4⋊Q8×C151—21no—
67C4⋊Q8×C151—21no—
68C4⋊Q8×C151—21no—
69C4⋊Q8×C151C2312yes—
70C4⋊Q8×C151C2311yescharacteristic
71C4⋊Q8×C151C2311yescharacteristic
72#126×C151—22no—
73#126×C151—22no—
74#126×C151—21no—
75#125×C151—22no—
76#125×C151D411yescharacteristic
77#125×C151D412yes—
78#124×C151—22no—
79#124×C151—21no—
80#124×C151D411yescharacteristic
81#123×C151—22no—
82#123×C151—22no—
83#123×C151—21no—
84#123×C151—22no—
85#123×C151—22no—
86C22⋊Q8×C151—22no—
87C22⋊Q8×C151—22no—
88C22⋊Q8×C151—22no—
89C22⋊Q8×C151—21no—
90C22⋊Q8×C151—21no—
91C22⋊Q8×C151—21no—
92C22⋊Q8×C151—21no—
93C22⋊Q8×C151—22no—
94C22⋊Q8×C151—21no—
95C22⋊Q8×C151—21no—
96C22⋊Q8×C151D411yescharacteristic
97#121×C151—22no—
98#121×C151—21no—
99#121×C151—21no—
100#121×C151D411yescharacteristic
101#120×C151—22no—
102C4×Q8×C151—21no—
103C4×Q8×C151—21no—
104C4×Q8×C151—21no—
105C4×Q8×C151C2311yescharacteristic
106C4×D4×C151—22no—
107C4×D4×C151—22no—
108C4×D4×C151—22no—
109C4×D4×C151—21no—
110C4×D4×C151—21no—
111C4×D4×C151—21no—
112C4×D4×C151—21no—
113C4×D4×C151D411yescharacteristic
114C4×D4×C151D411yescharacteristic
115C4×D4×C151C2311yescharacteristic
116C4×D4×C151C2311yescharacteristic
117C4×D4×C151C2311yescharacteristic
118#117×C151—22no—
119#117×C151—21no—
120#117×C151—21no—
121#117×C151D412yes—
122C2×C4⋊C4×C151—22no—
123C2×C4⋊C4×C151—21no—
124C2×C4⋊C4×C151—21no—
125C2×C4⋊C4×C151—21no—
126C2×C4⋊C4×C151—21no—
127C2×C4⋊C4×C151D411yescharacteristic
128C2×C22⋊C4×C151—22no—
129C2×C22⋊C4×C151—21no—
130C2×C42×C151C2311yescharacteristic
131#107×C151—22no—
132#107×C151—22no—
133#107×C151—24no—
134#106×C151—24no—
135C4⋊C8×C151—21no—
136C4⋊C8×C151C2312yes—
137C4⋊C8×C151C2312yes—
138#103×C151—22no—
139#103×C151—22no—
140#102×C151—22no—
141#102×C151—22no—
142C22⋊C8×C151—21no—
143#97×C151—21no—
144#97×C151—21no—
145C4×C8×C151C2312yes—
146C24×C151—21no—
147#41×C151—42no—
148#41×C151—42no—
149#41×C151—82no—
150C2×Q8×C151—22no—
151C2×Q8×C151—21no—
152C2×Q8×C151—21no—
153C2×Q8×C151—22no—
154C2×Q8×C151—41no—
155C2×Q8×C151—82no—
156C2×Q8×C151—82no—
157C2×Q8×C151C2×D411yescharacteristic
158C2×D4×C151—22no—
159C2×D4×C151—22no—
160C2×D4×C151—21no—
161C2×D4×C151—22no—
162C2×D4×C151—21no—
163C2×D4×C151—41no—
164C2×D4×C151C2×D411yescharacteristic
165C2×D4×C151C2×D411yescharacteristic
166C2×D4×C151C2×D411yescharacteristic
167C22×C4×C151—22no—
168C22×C4×C151—22no—
169C22×C4×C151—22no—
170C22×C4×C151—21no—
171C22×C4×C151—21no—
172C22×C4×C151—21no—
173C22×C4×C151—21no—
174C22×C4×C151—21no—
175C22×C4×C151—21no—
176C22×C4×C151—41no—
177C22×C4×C151—82no—
178C22×C4×C151C2×D411yescharacteristic
179C22×C4×C151C2×D411yescharacteristic
180C22×C4×C151C2×D411yescharacteristic
181Q16×C151—82no—
182SD16×C151—82no—
183M16×C151—24no—
184C2×C8×C151—22no—
185C2×C8×C151—22no—
186C2×C8×C151—22no—
187C2×C8×C151—42no—
188C4⋊C4×C151—22no—
189C4⋊C4×C151—22no—
190C4⋊C4×C151—22no—
191C4⋊C4×C151—22no—
192C4⋊C4×C151—21no—
193C4⋊C4×C151—22no—
194C4⋊C4×C151—21no—
195C4⋊C4×C151—21no—
196C4⋊C4×C151—21no—
197C4⋊C4×C151—22no—
198C4⋊C4×C151—21no—
199C4⋊C4×C151—21no—
200C4⋊C4×C151—21no—
201C4⋊C4×C151—22no—
202C4⋊C4×C151—22no—
203C4⋊C4×C151—41no—
204C4⋊C4×C151—41no—
205C4⋊C4×C151C2×D411yescharacteristic
206C4⋊C4×C151C2×D411yescharacteristic
207C4⋊C4×C151C2×D412yes—
208C4⋊C4×C151C2×D411yescharacteristic
209C4⋊C4×C151C2×D411yescharacteristic
210C4⋊C4×C151C2×D412yes—
211C22⋊C4×C151—22no—
212C22⋊C4×C151—22no—
213C22⋊C4×C151—22no—
214C22⋊C4×C151—22no—
215C22⋊C4×C151—22no—
216C22⋊C4×C151—21no—
217C22⋊C4×C151—22no—
218C22⋊C4×C151—21no—
219C22⋊C4×C151—21no—
220C22⋊C4×C151—21no—
221C22⋊C4×C151—21no—
222C22⋊C4×C151—21no—
223C22⋊C4×C151—21no—
224C22⋊C4×C151—21no—
225C22⋊C4×C151—21no—
226C42×C151—22no—
227C42×C151—22no—
228C42×C151—21no—
229C42×C151C2×D411yescharacteristic
230C42×C151C2×D411yescharacteristic
231C42×C151C2×D411yescharacteristic
232C42×C151C2411yescharacteristic
233C23×C151—21no—
234C23×C151—21no—
235C23×C151—21no—
236C23×C151—42no—
237C23×C151—42no—
238C23×C151—81no—
239C23×C151#12011yescharacteristic
240Q8×C151—22no—
241Q8×C151—41no—
242Q8×C151—41no—
243Q8×C151—42no—
244Q8×C151—42no—
245Q8×C151—42no—
246Q8×C151—82no—
247Q8×C151—82no—
248D4×C151—21no—
249D4×C151—21no—
250D4×C151—21no—
251D4×C151—22no—
252D4×C151—42no—
253D4×C151—44no—
254D4×C151—42no—
255D4×C151—82no—
256D4×C151#13712yes—
257C2×C4×C151—22no—
258C2×C4×C151—21no—
259C2×C4×C151—21no—
260C2×C4×C151—22no—
261C2×C4×C151—21no—
262C2×C4×C151—22no—
263C2×C4×C151—21no—
264C2×C4×C151—22no—
265C2×C4×C151—21no—
266C2×C4×C151—21no—
267C2×C4×C151—21no—
268C2×C4×C151—44no—
269C2×C4×C151—41no—
270C2×C4×C151—41no—
271C2×C4×C151—42no—
272C2×C4×C151—42no—
273C2×C4×C151—42no—
274C2×C4×C151—81no—
275C2×C4×C151—81no—
276C2×C4×C151—81no—
277C2×C4×C151—82no—
278C2×C4×C151—82no—
279C2×C4×C151—82no—
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—24no—
287C8×C151—42no—
288C8×C151—42no—
289C22×C151—21no—
290C22×C151—21no—
291C22×C151—22no—
292C22×C151—41no—
293C22×C151—41no—
294C22×C151—41no—
295C22×C151—41no—
296C22×C151—41no—
297C22×C151—41no—
298C22×C151—41no—
299C22×C151—41no—
300C22×C151—84no—
301C22×C151#45612yes—
302C22×C151C2×#12011yescharacteristic
303C4×C151—21no—
304C4×C151—21no—
305C4×C151—21no—
306C4×C151—21no—
307C4×C151—41no—
308C4×C151—42no—
309C4×C151—41no—
310C4×C151—41no—
311C4×C151—42no—
312C4×C151—41no—
313C4×C151—41no—
314C4×C151—82no—
315C4×C151C2×#13711yescharacteristic
316C4×C151#57511yescharacteristic
317C4×C151#57612yes—
318C2×C151—22no—
319C2×C151—42no—
320C2×C151—81no—
321C2×C151—81no—
322C2×C151#300711yescharacteristic
323C2×C151#300811yescharacteristic
324C2×C151C2×#45611yescharacteristic
325#18587C15111yesmaximal, characteristic, direct product factor, Sylow
326C151#1858711yescharacteristic, direct product factor, Sylow
327#3520C2×C15111yescharacteristic
328#3218C2×C15111yescharacteristic, complemented
329#3165C2×C15111yescharacteristic, complemented
330C2×#474C2×C15111yescharacteristic, complemented
331#1654C2×C15112yescomplemented
332#1652C2×C15112yescomplemented
333#1649C2×C15112yescomplemented
334#1647C2×C15112yescomplemented
335#1552C2×C15111yescharacteristic, complemented
336#1490C2×C15111yescharacteristic, complemented
337#1483C2×C15111yescharacteristic, complemented
338#556C22×C15111yescharacteristic
339#554—21no—
340#552—21no—
341#551—22no—
342D4×Q8C22×C15111yescharacteristic
343#548—21no—
344#547C22×C15111yescharacteristic
345#547C22×C15111yescharacteristic
346#546—21no—
347#542—21no—
348#539—22no—
349#533C22×C15111yescharacteristic
350C2×C4⋊Q8C22×C15111yescharacteristic
351#529C22×C15111yescharacteristic
352#525—21no—
353C2×C22⋊Q8—21no—
354#520—21no—
355C2×C4×D4C22×C15111yescharacteristic
356#501—22no—
357#500C22×C15112yescomplemented
358#498C22×C15112yescomplemented
359#497—21no—
360#491—21no—
361#474—21no—
362#474—21no—
363#474C22×C15112yes—
364#474C22×C15112yes—
365#462C22×C15112yescomplemented
366#461C22×C15112yescomplemented
367#451—21no—
368#448—21no—
369#432C22×C15111yescharacteristic
370#428—22no—
371C2×#107—21no—
372C2×C4⋊C8C22×C15111yescharacteristic
373C2×#102—21no—
374C4×M16C22×C15111yescharacteristic
375#332C22×C15112yescomplemented
376#332C22×C15112yescomplemented
377Q8⋊C8C22×C15112yescomplemented
378D4⋊C8C22×C15112yes—
379D4⋊C8C22×C15112yes—
380D4⋊C8C22×C15112yescomplemented
381C2×#41—21no—
382C2×#41—21no—
383C22×Q8—21no—
384C22×Q8—21no—
385C22×D4D4×C15111yescharacteristic
386C23×C4—21no—
387C2×Q16—22no—
388C2×SD16—22no—
389C2×M16—21no—
390C22×C8—21no—
391C4⋊Q8—21no—
392C4⋊Q8—21no—
393C4⋊Q8—21no—
394C4⋊Q8—21no—
395C4⋊Q8C23×C15112yes—
396C4⋊Q8C23×C15111yescharacteristic
397C4⋊Q8C23×C15111yescharacteristic
398#126—22no—
399#126—22no—
400#126—21no—
401#125—22no—
402#125D4×C15111yescharacteristic
403#125D4×C15112yes—
404#124—22no—
405#124—21no—
406#124D4×C15111yescharacteristic
407#123—22no—
408#123—22no—
409#123—21no—
410#123—22no—
411#123—22no—
412C22⋊Q8—22no—
413C22⋊Q8—22no—
414C22⋊Q8—22no—
415C22⋊Q8—21no—
416C22⋊Q8—21no—
417C22⋊Q8—21no—
418C22⋊Q8—21no—
419C22⋊Q8—21no—
420C22⋊Q8—22no—
421C22⋊Q8—21no—
422C22⋊Q8D4×C15111yescharacteristic
423#121—22no—
424#121—21no—
425#121—21no—
426#121D4×C15111yescharacteristic
427#120—22no—
428C4×Q8—21no—
429C4×Q8—21no—
430C4×Q8—21no—
431C4×Q8C23×C15111yescharacteristic
432C4×D4—22no—
433C4×D4—22no—
434C4×D4—22no—
435C4×D4—21no—
436C4×D4—21no—
437C4×D4—21no—
438C4×D4—21no—
439C4×D4D4×C15111yescharacteristic
440C4×D4D4×C15111yescharacteristic
441C4×D4C23×C15111yescharacteristic
442C4×D4C23×C15111yescharacteristic
443C4×D4C23×C15111yescharacteristic
444#117—22no—
445#117—21no—
446#117—21no—
447#117D4×C15112yes—
448C2×C4⋊C4—22no—
449C2×C4⋊C4—21no—
450C2×C4⋊C4—21no—
451C2×C4⋊C4—21no—
452C2×C4⋊C4—21no—
453C2×C4⋊C4D4×C15111yescharacteristic
454C2×C22⋊C4—22no—
455C2×C22⋊C4—21no—
456C2×C42C23×C15111yescharacteristic
457#107—22no—
458#107—22no—
459#107—24no—
460#106—24no—
461C4⋊C8—21no—
462C4⋊C8C23×C15112yes—
463C4⋊C8C23×C15112yes—
464#103—22no—
465#103—22no—
466#102—22no—
467#102—22no—
468C22⋊C8—21no—
469#97—21no—
470#97—21no—
471C4×C8C23×C15112yes—
472C24—21no—
473#41—42no—
474#41—42no—
475#41—82no—
476C2×Q8—22no—
477C2×Q8—21no—
478C2×Q8—21no—
479C2×Q8—22no—
480C2×Q8—41no—
481C2×Q8—82no—
482C2×Q8—82no—
483C2×Q8C2×D4×C15111yescharacteristic
484C2×D4—22no—
485C2×D4—22no—
486C2×D4—21no—
487C2×D4—22no—
488C2×D4—21no—
489C2×D4—41no—
490C2×D4C2×D4×C15111yescharacteristic
491C2×D4C2×D4×C15111yescharacteristic
492C2×D4C2×D4×C15111yescharacteristic
493C22×C4—22no—
494C22×C4—22no—
495C22×C4—22no—
496C22×C4—21no—
497C22×C4—21no—
498C22×C4—21no—
499C22×C4—21no—
500C22×C4—21no—
501C22×C4—21no—
502C22×C4—41no—
503C22×C4—82no—
504C22×C4C2×D4×C15111yescharacteristic
505C22×C4C2×D4×C15111yescharacteristic
506C22×C4C2×D4×C15111yescharacteristic
507Q16—82no—
508SD16—82no—
509M16—24no—
510C2×C8—22no—
511C2×C8—22no—
512C2×C8—22no—
513C2×C8—42no—
514C4⋊C4—22no—
515C4⋊C4—22no—
516C4⋊C4—22no—
517C4⋊C4—22no—
518C4⋊C4—21no—
519C4⋊C4—22no—
520C4⋊C4—21no—
521C4⋊C4—21no—
522C4⋊C4—21no—
523C4⋊C4—22no—
524C4⋊C4—21no—
525C4⋊C4—21no—
526C4⋊C4—21no—
527C4⋊C4—22no—
528C4⋊C4—22no—
529C4⋊C4—41no—
530C4⋊C4—41no—
531C4⋊C4C2×D4×C15111yescharacteristic
532C4⋊C4C2×D4×C15111yescharacteristic
533C4⋊C4C2×D4×C15112yes—
534C4⋊C4C2×D4×C15111yescharacteristic
535C4⋊C4C2×D4×C15111yescharacteristic
536C4⋊C4C2×D4×C15112yes—
537C22⋊C4—22no—
538C22⋊C4—22no—
539C22⋊C4—22no—
540C22⋊C4—22no—
541C22⋊C4—22no—
542C22⋊C4—21no—
543C22⋊C4—22no—
544C22⋊C4—21no—
545C22⋊C4—21no—
546C22⋊C4—21no—
547C22⋊C4—21no—
548C22⋊C4—21no—
549C22⋊C4—21no—
550C22⋊C4—21no—
551C22⋊C4—21no—
552C42—22no—
553C42—22no—
554C42—21no—
555C42C2×D4×C15111yescharacteristic
556C42C2×D4×C15111yescharacteristic
557C42C2×D4×C15111yescharacteristic
558C42C24×C15111yescharacteristic
559C23—21no—
560C23—21no—
561C23—21no—
562C23—42no—
563C23—42no—
564C23—81no—
565C23#120×C15111yescharacteristic
566Q8—22no—
567Q8—41no—
568Q8—41no—
569Q8—42no—
570Q8—42no—
571Q8—42no—
572Q8—82no—
573Q8—82no—
574D4—21no—
575D4—21no—
576D4—21no—
577D4—22no—
578D4—42no—
579D4—44no—
580D4—42no—
581D4—82no—
582D4#137×C15112yes—
583C2×C4—22no—
584C2×C4—21no—
585C2×C4—21no—
586C2×C4—22no—
587C2×C4—21no—
588C2×C4—22no—
589C2×C4—21no—
590C2×C4—21no—
591C2×C4—22no—
592C2×C4—21no—
593C2×C4—21no—
594C2×C4—44no—
595C2×C4—41no—
596C2×C4—41no—
597C2×C4—42no—
598C2×C4—42no—
599C2×C4—42no—
600C2×C4—81no—
601C2×C4—81no—
602C2×C4—81no—
603C2×C4—82no—
604C2×C4—82no—
605C2×C4—82no—
606C2×C4#120×C15111yescharacteristic
607C2×C4#120×C15111yescharacteristic
608C2×C4#120×C15111yescharacteristic
609C2×C4C22×D4×C15111yescharacteristic
610C2×C4C22×D4×C15111yescharacteristic
611C2×C4C22×D4×C15111yescharacteristic
612C8—24no—
613C8—42no—
614C8—42no—
615C22—21no—
616C22—21no—
617C22—22no—
618C22—41no—
619C22—41no—
620C22—41no—
621C22—41no—
622C22—41no—
623C22—41no—
624C22—41no—
625C22—41no—
626C22—84no—
627C22#456×C15112yes—
628C22C2×#120×C15111yescharacteristic
629C4—21no—
630C4—21no—
631C4—21no—
632C4—21no—
633C4—41no—
634C4—42no—
635C4—41no—
636C4—41no—
637C4—42no—
638C4—41no—
639C4—41no—
640C4—82no—
641C4C2×#137×C15111yescharacteristic
642C4#575×C15111yescharacteristic
643C4#576×C15112yes—
644C2—22no—
645C2—42no—
646C2—81no—
647C2—81no—
648C2#3007×C15111yescharacteristic
649C2#3008×C15111yescharacteristic
650C2C2×#456×C15111yescharacteristic
subgroupG/H
center, socleC22×C151C2×#120
commutator, Frattini, cosocleC42C24×C151
prime radical#3520×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
2. #3218×C151C2semidirect
3. #3165×C151C2semidirect
4. C2×#474×C151C2semidirect
5. #1654×C151C2semidirect
6. #1652×C151C2semidirect
7. #1649×C151C2semidirect
8. #1647×C151C2semidirect
9. #1552×C151C2semidirect
10. #1490×C151C2semidirect
11. #1483×C151C2semidirect
31. #500×C151C22semidirect
32. #498×C151C22semidirect
39. #462×C151C22semidirect
40. #461×C151C22semidirect
49. #332×C151C22semidirect
50. #332×C151C22semidirect
51. Q8⋊C8×C151C22semidirect
54. D4⋊C8×C151C22semidirect
325. #18587C151direct (N × H)
326. C151#18587direct (N × H)
328. #3218C2×C151semidirect
329. #3165C2×C151semidirect
330. C2×#474C2×C151semidirect
331. #1654C2×C151semidirect
332. #1652C2×C151semidirect
333. #1649C2×C151semidirect
334. #1647C2×C151semidirect
335. #1552C2×C151semidirect
336. #1490C2×C151semidirect
337. #1483C2×C151semidirect
357. #500C22×C151semidirect
358. #498C22×C151semidirect
365. #462C22×C151semidirect
366. #461C22×C151semidirect
375. #332C22×C151semidirect
376. #332C22×C151semidirect
377. Q8⋊C8C22×C151semidirect
380. D4⋊C8C22×C151semidirect

Maximal subgroups

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

subgroupindex
#3520×C1512
#3218×C1512
#3165×C1512
C2×#474×C1512
#1654×C1512
#1652×C1512
#1649×C1512
#1647×C1512
#1552×C1512
#1490×C1512
#1483×C1512
#18587151