Finite Group Databasebeta

← C151×#18544 #50323469

Subgroups — C151×#18544 #50323469

Order 38656.

954 conjugacy classes of subgroups.

The subgroup lattice has 654 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#3482×C151C211yesmaximal, characteristic
2#3165×C151C211yesmaximal, characteristic, complemented
3#3079×C151C211yesmaximal, characteristic, complemented
4#3039×C151C211yesmaximal, characteristic, complemented
5#1654×C151C212yesmaximal, complemented
6#1653×C151C212yesmaximal, complemented
7#1650×C151C212yesmaximal, complemented
8#1649×C151C212yesmaximal, complemented
9#1561×C151C211yesmaximal, characteristic, complemented
10#1489×C151C211yesmaximal, characteristic, complemented
11#1489×C151C211yesmaximal, characteristic, complemented
12C2×#137×C151—21no—
13#557×C151C2211yescharacteristic
14#556×C151—21no—
15#556×C151C2211yescharacteristic
16#552×C151—22no—
17#552×C151—21no—
18D4×Q8×C151C2211yescharacteristic
19#548×C151—21no—
20#547×C151—21no—
21#547×C151C2211yescharacteristic
22#533×C151—21no—
23#533×C151C2211yescharacteristic
24C2×C4⋊Q8×C151C2211yescharacteristic
25#529×C151—21no—
26#529×C151—22no—
27C4×#41×C151—21no—
28C4×#41×C151C2211yescharacteristic
29C4×#41×C151C2211yescharacteristic
30C2×C4×Q8×C151—21no—
31#501×C151—22no—
32#500×C151C2212yes—
33#498×C151C2212yes—
34#477×C151—21no—
35#476×C151—21no—
36#475×C151C2212yes—
37#474×C151C2212yes—
38#462×C151—21no—
39#462×C151C2212yes—
40#461×C151—21no—
41#461×C151C2212yes—
42#428×C151—22no—
43#428×C151—21no—
44#423×C151C2211yescharacteristic
45#423×C151C2211yescharacteristic
46#419×C151—21no—
47#417×C151—21no—
48C4×M16×C151C2211yescharacteristic
49#332×C151C2212yes—
50#332×C151C2212yes—
51Q8⋊C8×C151C2212yes—
52Q8⋊C8×C151C2212yes—
53D4⋊C8×C151C2212yes—
54D4⋊C8×C151C2212yes—
55C2×#41×C151—21no—
56C2×#41×C151D411yescharacteristic
57C2×#41×C151D411yescharacteristic
58C22×Q8×C151—21no—
59C22×Q8×C151—21no—
60#137×C151—44no—
61C2×Q16×C151—22no—
62C2×SD16×C151—22no—
63C2×M16×C151—21no—
64C2×M16×C151—21no—
65C2×M16×C151—21no—
66C4⋊Q8×C151—21no—
67C4⋊Q8×C151—21no—
68C4⋊Q8×C151—21no—
69C4⋊Q8×C151—21no—
70C4⋊Q8×C151—21no—
71C4⋊Q8×C151C2312yes—
72C4⋊Q8×C151C2311yescharacteristic
73C4⋊Q8×C151C2311yescharacteristic
74#126×C151—22no—
75#126×C151—22no—
76#126×C151—22no—
77#125×C151—22no—
78#125×C151—22no—
79#125×C151—21no—
80#125×C151D412yes—
81#124×C151—22no—
82#124×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—21no—
89C22⋊Q8×C151—22no—
90C22⋊Q8×C151—21no—
91C22⋊Q8×C151—21no—
92C22⋊Q8×C151—21no—
93#121×C151—22no—
94#121×C151—21no—
95C4×Q8×C151—22no—
96C4×Q8×C151—22no—
97C4×Q8×C151—21no—
98C4×Q8×C151—21no—
99C4×Q8×C151—21no—
100C4×Q8×C151—21no—
101C4×Q8×C151—21no—
102C4×Q8×C151D411yescharacteristic
103C4×Q8×C151D411yescharacteristic
104C4×Q8×C151C2311yescharacteristic
105C4×Q8×C151C2311yescharacteristic
106C4×D4×C151—22no—
107C4×D4×C151—22no—
108C4×D4×C151—21no—
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
117#117×C151—22no—
118#117×C151—22no—
119#117×C151—21no—
120#117×C151—21no—
121#117×C151—21no—
122#117×C151D411yescharacteristic
123#117×C151D411yescharacteristic
124#117×C151D412yes—
125C2×C4⋊C4×C151—22no—
126C2×C4⋊C4×C151—21no—
127C2×C4⋊C4×C151—21no—
128C2×C4⋊C4×C151—21no—
129C2×C42×C151—22no—
130C2×C42×C151—21no—
131C2×C42×C151—21no—
132C2×C42×C151C2311yescharacteristic
133#107×C151—22no—
134#107×C151—24no—
135#106×C151—22no—
136#106×C151—24no—
137C4⋊C8×C151—21no—
138C4⋊C8×C151—21no—
139C4⋊C8×C151C2312yes—
140C4⋊C8×C151C2312yes—
141#103×C151—22no—
142#103×C151—22no—
143#103×C151—22no—
144#102×C151—22no—
145#97×C151—21no—
146C4×C8×C151C2312yes—
147#41×C151—22no—
148#41×C151—22no—
149#41×C151—41no—
150#41×C151—41no—
151#41×C151—42no—
152#41×C151—42no—
153C2×Q8×C151—22no—
154C2×Q8×C151—21no—
155C2×Q8×C151—21no—
156C2×Q8×C151—22no—
157C2×Q8×C151—42no—
158C2×Q8×C151—42no—
159C2×Q8×C151—42no—
160C2×Q8×C151—42no—
161C2×Q8×C151—41no—
162C2×Q8×C151C2×D411yescharacteristic
163C2×Q8×C151C2×D411yescharacteristic
164C2×D4×C151—22no—
165C2×D4×C151—21no—
166C2×D4×C151—21no—
167C2×D4×C151C2×D411yescharacteristic
168C2×D4×C151C2×D411yescharacteristic
169C22×C4×C151—22no—
170C22×C4×C151—22no—
171C22×C4×C151—21no—
172C22×C4×C151—21no—
173C22×C4×C151—21no—
174C22×C4×C151—21no—
175C22×C4×C151—21no—
176C22×C4×C151—21no—
177C22×C4×C151—41no—
178C22×C4×C151C2×D411yescharacteristic
179C22×C4×C151C2×D411yescharacteristic
180C22×C4×C151C2×D411yescharacteristic
181Q16×C151—44no—
182SD16×C151—44no—
183M16×C151—24no—
184M16×C151—42no—
185M16×C151—42no—
186C2×C8×C151—22no—
187C2×C8×C151—22no—
188C2×C8×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—22no—
197C4⋊C4×C151—22no—
198C4⋊C4×C151—21no—
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—41no—
206C4⋊C4×C151—41no—
207C4⋊C4×C151C2×D411yescharacteristic
208C4⋊C4×C151C2×D411yescharacteristic
209C4⋊C4×C151C2×D411yescharacteristic
210C4⋊C4×C151C2×D412yes—
211C4⋊C4×C151C2×D411yescharacteristic
212C4⋊C4×C151C2×D412yes—
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—22no—
220C22⋊C4×C151—21no—
221C22⋊C4×C151—21no—
222C22⋊C4×C151—21no—
223C22⋊C4×C151—21no—
224C42×C151—22no—
225C42×C151—22no—
226C42×C151—21no—
227C42×C151—21no—
228C42×C151—21no—
229C42×C151—22no—
230C42×C151—21no—
231C42×C151—21no—
232C42×C151—21no—
233C42×C151C2×D411yescharacteristic
234C42×C151C2×D411yescharacteristic
235C42×C151C2×D411yescharacteristic
236C42×C151C2411yescharacteristic
237C23×C151—21no—
238C23×C151—21no—
239C23×C151#12011yescharacteristic
240Q8×C151—21no—
241Q8×C151—21no—
242Q8×C151—21no—
243Q8×C151—44no—
244Q8×C151—41no—
245Q8×C151—41no—
246Q8×C151—41no—
247Q8×C151—41no—
248Q8×C151—42no—
249Q8×C151—42no—
250Q8×C151—82no—
251Q8×C151AGL(1,ℤ/8)12yes—
252D4×C151—21no—
253D4×C151—21no—
254D4×C151—21no—
255D4×C151—42no—
256D4×C151—42no—
257D4×C151—44no—
258D4×C151#13712yescomplemented
259C2×C4×C151—21no—
260C2×C4×C151—21no—
261C2×C4×C151—21no—
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—21no—
271C2×C4×C151—21no—
272C2×C4×C151—42no—
273C2×C4×C151—42no—
274C2×C4×C151—44no—
275C2×C4×C151—44no—
276C2×C4×C151—41no—
277C2×C4×C151—41no—
278C2×C4×C151—41no—
279C2×C4×C151—41no—
280C2×C4×C151—42no—
281C2×C4×C151—42no—
282C2×C4×C151—42no—
283C2×C4×C151—82no—
284C2×C4×C151#12011yescharacteristic
285C2×C4×C151#12011yescharacteristic
286C2×C4×C151#12011yescharacteristic
287C2×C4×C151C22×D411yescharacteristic
288C2×C4×C151C22×D411yescharacteristic
289C2×C4×C151C22×D411yescharacteristic
290C8×C151—24no—
291C8×C151—42no—
292C8×C151—42no—
293C22×C151—21no—
294C22×C151—21no—
295C22×C151—22no—
296C22×C151—21no—
297C22×C151—41no—
298C22×C151—41no—
299C22×C151—41no—
300C22×C151—41no—
301C22×C151—41no—
302C22×C151C2×#12011yescharacteristic
303C4×C151—21no—
304C4×C151—22no—
305C4×C151—21no—
306C4×C151—21no—
307C4×C151—42no—
308C4×C151—41no—
309C4×C151—41no—
310C4×C151—41no—
311C4×C151—42no—
312C4×C151—41no—
313C4×C151—41no—
314C4×C151—82no—
315C4×C151#45612yes—
316C4×C151C2×AGL(1,ℤ/8)11yescharacteristic
317C4×C151C2×#13711yescharacteristic
318C4×C151#57511yescharacteristic
319C4×C151#57511yescharacteristic
320C2×C151—41no—
321C2×C151—42no—
322C2×C151—81no—
323C2×C151#300611yescharacteristic
324C2×C151#300711yescharacteristic
325C2×C151C2×#45611yescharacteristic
326#18544C15111yesmaximal, characteristic, direct product factor, Sylow
327C151#1854411yescharacteristic, direct product factor, Sylow
328#3482C2×C15111yescharacteristic
329#3165C2×C15111yescharacteristic, complemented
330#3079C2×C15111yescharacteristic, complemented
331#3039C2×C15111yescharacteristic, complemented
332#1654C2×C15112yescomplemented
333#1653C2×C15112yescomplemented
334#1650C2×C15112yescomplemented
335#1649C2×C15112yescomplemented
336#1561C2×C15111yescharacteristic, complemented
337#1489C2×C15111yescharacteristic, complemented
338#1489C2×C15111yescharacteristic, complemented
339C2×#137—21no—
340#557C22×C15111yescharacteristic
341#556—21no—
342#556C22×C15111yescharacteristic
343#552—22no—
344#552—21no—
345D4×Q8C22×C15111yescharacteristic
346#548—21no—
347#547—21no—
348#547C22×C15111yescharacteristic
349#533—21no—
350#533C22×C15111yescharacteristic
351C2×C4⋊Q8C22×C15111yescharacteristic
352#529—21no—
353#529—22no—
354C4×#41—21no—
355C4×#41C22×C15111yescharacteristic
356C4×#41C22×C15111yescharacteristic
357C2×C4×Q8—21no—
358#501—22no—
359#500C22×C15112yes—
360#498C22×C15112yes—
361#477—21no—
362#476—21no—
363#475C22×C15112yes—
364#474C22×C15112yes—
365#462—21no—
366#462C22×C15112yes—
367#461—21no—
368#461C22×C15112yes—
369#428—21no—
370#428—22no—
371#423C22×C15111yescharacteristic
372#423C22×C15111yescharacteristic
373#419—21no—
374#417—21no—
375C4×M16C22×C15111yescharacteristic
376#332C22×C15112yes—
377#332C22×C15112yes—
378Q8⋊C8C22×C15112yes—
379Q8⋊C8C22×C15112yes—
380D4⋊C8C22×C15112yes—
381D4⋊C8C22×C15112yes—
382C2×#41—21no—
383C2×#41D4×C15111yescharacteristic
384C2×#41D4×C15111yescharacteristic
385C22×Q8—21no—
386C22×Q8—21no—
387#137—44no—
388C2×Q16—22no—
389C2×SD16—22no—
390C2×M16—21no—
391C2×M16—21no—
392C2×M16—21no—
393C4⋊Q8—21no—
394C4⋊Q8—21no—
395C4⋊Q8—21no—
396C4⋊Q8—21no—
397C4⋊Q8—21no—
398C4⋊Q8C23×C15112yes—
399C4⋊Q8C23×C15111yescharacteristic
400C4⋊Q8C23×C15111yescharacteristic
401#126—22no—
402#126—22no—
403#126—22no—
404#125—22no—
405#125—22no—
406#125—21no—
407#125D4×C15112yes—
408#124—22no—
409#124—21no—
410#123—22no—
411#123—22no—
412#123—22no—
413C22⋊Q8—22no—
414C22⋊Q8—21no—
415C22⋊Q8—21no—
416C22⋊Q8—21no—
417C22⋊Q8—21no—
418C22⋊Q8—22no—
419C22⋊Q8—21no—
420#121—22no—
421#121—21no—
422C4×Q8—22no—
423C4×Q8—22no—
424C4×Q8—21no—
425C4×Q8—21no—
426C4×Q8—21no—
427C4×Q8—21no—
428C4×Q8—21no—
429C4×Q8D4×C15111yescharacteristic
430C4×Q8D4×C15111yescharacteristic
431C4×Q8C23×C15111yescharacteristic
432C4×Q8C23×C15111yescharacteristic
433C4×D4—22no—
434C4×D4—22no—
435C4×D4—21no—
436C4×D4—21no—
437C4×D4—21no—
438C4×D4—21no—
439C4×D4—21no—
440C4×D4D4×C15111yescharacteristic
441C4×D4D4×C15111yescharacteristic
442C4×D4C23×C15111yescharacteristic
443C4×D4C23×C15111yescharacteristic
444#117—22no—
445#117—22no—
446#117—21no—
447#117—21no—
448#117—21no—
449#117D4×C15111yescharacteristic
450#117D4×C15111yescharacteristic
451#117D4×C15112yes—
452C2×C4⋊C4—22no—
453C2×C4⋊C4—21no—
454C2×C4⋊C4—21no—
455C2×C4⋊C4—21no—
456C2×C42—22no—
457C2×C42—21no—
458C2×C42—21no—
459C2×C42C23×C15111yescharacteristic
460#107—22no—
461#107—24no—
462#106—22no—
463#106—24no—
464C4⋊C8—21no—
465C4⋊C8—21no—
466C4⋊C8C23×C15112yes—
467C4⋊C8C23×C15112yes—
468#103—22no—
469#103—22no—
470#103—22no—
471#102—22no—
472#97—21no—
473C4×C8C23×C15112yes—
474#41—22no—
475#41—22no—
476#41—41no—
477#41—41no—
478#41—42no—
479#41—42no—
480C2×Q8—22no—
481C2×Q8—21no—
482C2×Q8—21no—
483C2×Q8—22no—
484C2×Q8—42no—
485C2×Q8—42no—
486C2×Q8—42no—
487C2×Q8—42no—
488C2×Q8—41no—
489C2×Q8C2×D4×C15111yescharacteristic
490C2×Q8C2×D4×C15111yescharacteristic
491C2×D4—22no—
492C2×D4—21no—
493C2×D4—21no—
494C2×D4C2×D4×C15111yescharacteristic
495C2×D4C2×D4×C15111yescharacteristic
496C22×C4—22no—
497C22×C4—22no—
498C22×C4—21no—
499C22×C4—21no—
500C22×C4—21no—
501C22×C4—21no—
502C22×C4—21no—
503C22×C4—21no—
504C22×C4—41no—
505C22×C4C2×D4×C15111yescharacteristic
506C22×C4C2×D4×C15111yescharacteristic
507C22×C4C2×D4×C15111yescharacteristic
508Q16—44no—
509SD16—44no—
510M16—24no—
511M16—42no—
512M16—42no—
513C2×C8—22no—
514C2×C8—22no—
515C2×C8—22no—
516C4⋊C4—22no—
517C4⋊C4—22no—
518C4⋊C4—22no—
519C4⋊C4—22no—
520C4⋊C4—22no—
521C4⋊C4—22no—
522C4⋊C4—21no—
523C4⋊C4—22no—
524C4⋊C4—22no—
525C4⋊C4—21no—
526C4⋊C4—21no—
527C4⋊C4—21no—
528C4⋊C4—21no—
529C4⋊C4—21no—
530C4⋊C4—22no—
531C4⋊C4—22no—
532C4⋊C4—41no—
533C4⋊C4—41no—
534C4⋊C4C2×D4×C15111yescharacteristic
535C4⋊C4C2×D4×C15111yescharacteristic
536C4⋊C4C2×D4×C15111yescharacteristic
537C4⋊C4C2×D4×C15112yes—
538C4⋊C4C2×D4×C15111yescharacteristic
539C4⋊C4C2×D4×C15112yes—
540C22⋊C4—22no—
541C22⋊C4—22no—
542C22⋊C4—22no—
543C22⋊C4—22no—
544C22⋊C4—21no—
545C22⋊C4—21no—
546C22⋊C4—22no—
547C22⋊C4—21no—
548C22⋊C4—21no—
549C22⋊C4—21no—
550C22⋊C4—21no—
551C42—22no—
552C42—22no—
553C42—21no—
554C42—21no—
555C42—21no—
556C42—22no—
557C42—21no—
558C42—21no—
559C42—21no—
560C42C2×D4×C15111yescharacteristic
561C42C2×D4×C15111yescharacteristic
562C42C2×D4×C15111yescharacteristic
563C42C24×C15111yescharacteristic
564C23—21no—
565C23—21no—
566C23#120×C15111yescharacteristic
567Q8—21no—
568Q8—21no—
569Q8—21no—
570Q8—44no—
571Q8—41no—
572Q8—41no—
573Q8—41no—
574Q8—41no—
575Q8—42no—
576Q8—42no—
577Q8—82no—
578Q8AGL(1,ℤ/8)×C15112yes—
579D4—21no—
580D4—21no—
581D4—21no—
582D4—42no—
583D4—42no—
584D4—44no—
585D4#137×C15112yescomplemented
586C2×C4—21no—
587C2×C4—22no—
588C2×C4—21no—
589C2×C4—21no—
590C2×C4—21no—
591C2×C4—21no—
592C2×C4—21no—
593C2×C4—21no—
594C2×C4—21no—
595C2×C4—22no—
596C2×C4—21no—
597C2×C4—21no—
598C2×C4—22no—
599C2×C4—42no—
600C2×C4—42no—
601C2×C4—44no—
602C2×C4—44no—
603C2×C4—42no—
604C2×C4—42no—
605C2×C4—41no—
606C2×C4—41no—
607C2×C4—41no—
608C2×C4—41no—
609C2×C4—42no—
610C2×C4—82no—
611C2×C4#120×C15111yescharacteristic
612C2×C4#120×C15111yescharacteristic
613C2×C4#120×C15111yescharacteristic
614C2×C4C22×D4×C15111yescharacteristic
615C2×C4C22×D4×C15111yescharacteristic
616C2×C4C22×D4×C15111yescharacteristic
617C8—24no—
618C8—42no—
619C8—42no—
620C22—21no—
621C22—21no—
622C22—22no—
623C22—21no—
624C22—41no—
625C22—41no—
626C22—41no—
627C22—41no—
628C22—41no—
629C22C2×#120×C15111yescharacteristic
630C4—21no—
631C4—22no—
632C4—21no—
633C4—21no—
634C4—42no—
635C4—41no—
636C4—41no—
637C4—41no—
638C4—42no—
639C4—41no—
640C4—41no—
641C4—82no—
642C4#456×C15112yes—
643C4C2×AGL(1,ℤ/8)×C15111yescharacteristic
644C4C2×#137×C15111yescharacteristic
645C4#575×C15111yescharacteristic
646C4#575×C15111yescharacteristic
647C2—41no—
648C2—42no—
649C2—81no—
650C2#3006×C15111yescharacteristic
651C2#3007×C15111yescharacteristic
652C2C2×#456×C15111yescharacteristic
subgroupG/H
center, socleC22×C151C2×#120
commutator, Frattini, cosocleC42C24×C151
prime radical#3482×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. #3165×C151C2semidirect
3. #3079×C151C2semidirect
4. #3039×C151C2semidirect
5. #1654×C151C2semidirect
6. #1653×C151C2semidirect
7. #1650×C151C2semidirect
8. #1649×C151C2semidirect
9. #1561×C151C2semidirect
10. #1489×C151C2semidirect
11. #1489×C151C2semidirect
258. D4×C151#137semidirect
326. #18544C151direct (N × H)
327. C151#18544direct (N × H)
329. #3165C2×C151semidirect
330. #3079C2×C151semidirect
331. #3039C2×C151semidirect
332. #1654C2×C151semidirect
333. #1653C2×C151semidirect
334. #1650C2×C151semidirect
335. #1649C2×C151semidirect
336. #1561C2×C151semidirect
337. #1489C2×C151semidirect
338. #1489C2×C151semidirect
585. D4#137×C151semidirect

Maximal subgroups

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

subgroupindex
#3482×C1512
#3165×C1512
#3079×C1512
#3039×C1512
#1654×C1512
#1653×C1512
#1650×C1512
#1649×C1512
#1561×C1512
#1489×C1512
#18544151