Finite Group Databasebeta

← C151×#24323 #50329248

Subgroups — C151×#24323 #50329248

Order 38656.

1004 conjugacy classes of subgroups.

The subgroup lattice has 608 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#3503×C151C211yesmaximal, characteristic
2#3078×C151C211yesmaximal, characteristic, complemented
3C4×#137×C151C211yesmaximal, characteristic
4#2567×C151C211yesmaximal, characteristic, complemented
5#2060×C151C212yesmaximal, complemented
6#2028×C151C212yesmaximal, complemented
7#1997×C151C211yesmaximal, characteristic, complemented
8#1986×C151C211yesmaximal, characteristic, complemented
9#1882×C151C212yesmaximal
10#1859×C151C212yesmaximal
11#1806×C151C211yesmaximal, characteristic
12C2×#137×C151C2211yescharacteristic
13Q82×C151—21no—
14#557×C151—21no—
15#554×C151—21no—
16#554×C151—22no—
17D4×Q8×C151—22no—
18D4×Q8×C151—21no—
19#544×C151—22no—
20#544×C151C2212yes—
21#533×C151—21no—
22#533×C151C2211yescharacteristic
23C2×C4⋊Q8×C151—21no—
24C2×C4⋊Q8×C151C2211yescharacteristic
25#520×C151C2212yes—
26C4×#41×C151C2211yescharacteristic
27C2×C4×Q8×C151C2211yescharacteristic
28#479×C151—22no—
29#477×C151—21no—
30#475×C151—21no—
31#441×C151—21no—
32#440×C151—21no—
33C4×Q16×C151—21no—
34C4×SD16×C151—21no—
35#428×C151C2212yes—
36#428×C151C2211yescharacteristic
37#423×C151C2211yescharacteristic
38C2×#104×C151C2212yes—
39#419×C151C2212yes—
40#419×C151C2211yescharacteristic
41#417×C151C2211yescharacteristic
42C4×M16×C151C2211yescharacteristic
43#395×C151—22no—
44#391×C151C2212yes—
45#389×C151—22no—
46#384×C151C2212yes—
47C4×C4⋊C4×C151C2211yescharacteristic
48#343×C151C2212yes—
49#343×C151C2212yes—
50#339×C151C2212yes—
51#339×C151C2212yes—
52#339×C151C2212yes—
53C2×#41×C151C2311yescharacteristic
54C22×Q8×C151—22no—
55C22×Q8×C151D412yes—
56C22×Q8×C151C2311yescharacteristic
57#137×C151—22no—
58#137×C151Q814yescomplemented
59C2×Q16×C151—21no—
60C2×SD16×C151—21no—
61C2×M16×C151C2311yescharacteristic
62C2×M16×C151C2312yes—
63C2×M16×C151C2311yescharacteristic
64C4⋊Q8×C151—22no—
65C4⋊Q8×C151—22no—
66C4⋊Q8×C151—24no—
67C4⋊Q8×C151—22no—
68C4⋊Q8×C151—22no—
69C4⋊Q8×C151—21no—
70C4⋊Q8×C151—21no—
71C4⋊Q8×C151—21no—
72C4⋊Q8×C151—21no—
73C4⋊Q8×C151D411yescharacteristic
74C4⋊Q8×C151D411yescharacteristic
75#125×C151—24no—
76#125×C151—22no—
77#125×C151—22no—
78#125×C151D412yes—
79C22⋊Q8×C151—22no—
80C22⋊Q8×C151—22no—
81C22⋊Q8×C151—24no—
82C22⋊Q8×C151—24no—
83C22⋊Q8×C151—21no—
84C22⋊Q8×C151—21no—
85C22⋊Q8×C151—24no—
86C4×Q8×C151—22no—
87C4×Q8×C151—22no—
88C4×Q8×C151—21no—
89C4×Q8×C151—21no—
90C4×Q8×C151—21no—
91C4×Q8×C151—21no—
92C4×Q8×C151—21no—
93C4×Q8×C151—21no—
94C4×Q8×C151—22no—
95C4×Q8×C151D411yescharacteristic
96C4×Q8×C151D411yescharacteristic
97C4×D4×C151—22no—
98C4×D4×C151—21no—
99C4×D4×C151—21no—
100C4×D4×C151—24no—
101C4×D4×C151D411yescharacteristic
102C4×D4×C151D411yescharacteristic
103#117×C151—22no—
104#117×C151—21no—
105#117×C151C2311yescharacteristic
106#117×C151C2312yes—
107C2×C4⋊C4×C151—22no—
108C2×C4⋊C4×C151—21no—
109C2×C4⋊C4×C151—22no—
110C2×C4⋊C4×C151—21no—
111C2×C4⋊C4×C151—24no—
112C2×C4⋊C4×C151D412yes—
113C2×C4⋊C4×C151C2311yescharacteristic
114C2×C4⋊C4×C151C2312yes—
115C2×C42×C151—21no—
116C2×C42×C151—21no—
117C2×C42×C151C2312yes—
118C2×C42×C151C2311yescharacteristic
119#107×C151—21no—
120#107×C151—22no—
121#106×C151—21no—
122#106×C151—22no—
123C4⋊C8×C151—21no—
124C4⋊C8×C151—21no—
125#104×C151—24no—
126#103×C151—21no—
127#103×C151—21no—
128#103×C151—22no—
129#103×C151—22no—
130#103×C151—21no—
131#102×C151—21no—
132#97×C151—21no—
133C4×C8×C151—21no—
134#95×C151—21no—
135#95×C151—24no—
136#41×C151—21no—
137#41×C151—21no—
138#41×C151C2×Q812yes—
139#41×C151#4112yes—
140C2×Q8×C151—24no—
141C2×Q8×C151—21no—
142C2×Q8×C151—22no—
143C2×Q8×C151—21no—
144C2×Q8×C151—22no—
145C2×Q8×C151—21no—
146C2×Q8×C151—21no—
147C2×Q8×C151—21no—
148C2×Q8×C151—21no—
149C2×Q8×C151—21no—
150C2×Q8×C151—82no—
151C2×Q8×C151—84no—
152C2×Q8×C151C2×D411yescharacteristic
153C2×Q8×C151C2×Q812yescomplemented
154C2×D4×C151—21no—
155C2×D4×C151C2×D411yescharacteristic
156C22×C4×C151—21no—
157C22×C4×C151—21no—
158C22×C4×C151—22no—
159C22×C4×C151—24no—
160C22×C4×C151—21no—
161C22×C4×C151—21no—
162C22×C4×C151—21no—
163C22×C4×C151C2×D411yescharacteristic
164C22×C4×C151C2×D414yes—
165C22×C4×C151C2×D411yescharacteristic
166C22×C4×C151C2411yescharacteristic
167Q16×C151—24no—
168SD16×C151—24no—
169M16×C151—21no—
170M16×C151—22no—
171M16×C151—21no—
172M16×C151—21no—
173M16×C151—22no—
174M16×C151C2×Q812yescomplemented
175C2×C8×C151—21no—
176C2×C8×C151—21no—
177C2×C8×C151—22no—
178C4⋊C4×C151—24no—
179C4⋊C4×C151—24no—
180C4⋊C4×C151—24no—
181C4⋊C4×C151—24no—
182C4⋊C4×C151—24no—
183C4⋊C4×C151—21no—
184C4⋊C4×C151—22no—
185C4⋊C4×C151—22no—
186C4⋊C4×C151—21no—
187C4⋊C4×C151—21no—
188C4⋊C4×C151—21no—
189C4⋊C4×C151—22no—
190C4⋊C4×C151—22no—
191C4⋊C4×C151—22no—
192C4⋊C4×C151—22no—
193C4⋊C4×C151—21no—
194C4⋊C4×C151—21no—
195C4⋊C4×C151—41no—
196C4⋊C4×C151—41no—
197C4⋊C4×C151—84no—
198C4⋊C4×C151C2×D412yes—
199C4⋊C4×C151C2×D411yescharacteristic
200C4⋊C4×C151C2×D412yes—
201C4⋊C4×C151C2×D411yescharacteristic
202C22⋊C4×C151—24no—
203C22⋊C4×C151—21no—
204C22⋊C4×C151—22no—
205C22⋊C4×C151—21no—
206C22⋊C4×C151—21no—
207C42×C151—24no—
208C42×C151—21no—
209C42×C151—21no—
210C42×C151—21no—
211C42×C151—22no—
212C42×C151—22no—
213C42×C151—22no—
214C42×C151—41no—
215C42×C151—41no—
216C42×C151C2×D411yescharacteristic
217C42×C151C2×D411yescharacteristic
218C42×C151C2×D411yescharacteristic
219C42×C151C2×D411yescharacteristic
220C23×C151—21no—
221C23×C151C22×D411yescharacteristic
222Q8×C151—21no—
223Q8×C151—22no—
224Q8×C151—22no—
225Q8×C151—44no—
226Q8×C151—42no—
227Q8×C151—41no—
228Q8×C151—41no—
229Q8×C151—42no—
230Q8×C151—82no—
231Q8×C151—84no—
232Q8×C151C22⋊Q812yes—
233D4×C151—22no—
234D4×C151—22no—
235D4×C151—21no—
236D4×C151C22⋊Q812yes—
237C2×C4×C151—21no—
238C2×C4×C151—22no—
239C2×C4×C151—22no—
240C2×C4×C151—22no—
241C2×C4×C151—24no—
242C2×C4×C151—21no—
243C2×C4×C151—24no—
244C2×C4×C151—22no—
245C2×C4×C151—22no—
246C2×C4×C151—21no—
247C2×C4×C151—22no—
248C2×C4×C151—41no—
249C2×C4×C151—42no—
250C2×C4×C151—42no—
251C2×C4×C151—41no—
252C2×C4×C151—41no—
253C2×C4×C151—42no—
254C2×C4×C151—42no—
255C2×C4×C151—44no—
256C2×C4×C151—42no—
257C2×C4×C151—41no—
258C2×C4×C151—84no—
259C2×C4×C151#12011yescharacteristic
260C2×C4×C151#12011yescharacteristic
261C2×C4×C151#12011yescharacteristic
262C2×C4×C151#12011yescharacteristic
263C2×C4×C151C22×D411yescharacteristic
264C2×C4×C151C22×D411yescharacteristic
265C2×C4×C151C22×Q811yescharacteristic
266C2×C4×C151C2×#4111yescharacteristic
267C2×C4×C1512−1+411yescharacteristic
268C2×C4×C1512−1+411yescharacteristic
269C8×C151—22no—
270C8×C151—41no—
271C8×C151—42no—
272C22×C151—21no—
273C22×C151—21no—
274C22×C151—22no—
275C22×C151—41no—
276C22×C151—41no—
277C22×C151C2×#12011yescharacteristic
278C22×C151#54811yescharacteristic
279C22×C151D4×Q811yescharacteristic
280C4×C151—22no—
281C4×C151—21no—
282C4×C151—21no—
283C4×C151—21no—
284C4×C151—44no—
285C4×C151—42no—
286C4×C151—41no—
287C4×C151—42no—
288C4×C151—41no—
289C4×C151—44no—
290C4×C151—42no—
291C4×C151—81no—
292C4×C151#45612yes—
293C4×C151C2×C22⋊Q811yescharacteristic
294C4×C151#53611yescharacteristic
295C4×C151#54811yescharacteristic
296C4×C151D4×Q811yescharacteristic
297C2×C151—21no—
298C2×C151—21no—
299C2×C151—42no—
300C2×C151#240911yescharacteristic
301C2×C151C2×#45611yescharacteristic
302C2×C151#301911yescharacteristic
303#24323C15111yesmaximal, characteristic, direct product factor, Sylow
304C151#2432311yescharacteristic, direct product factor, Sylow
305#3503C2×C15111yescharacteristic
306#3078C2×C15111yescharacteristic, complemented
307C4×#137C2×C15111yescharacteristic
308#2567C2×C15111yescharacteristic, complemented
309#2060C2×C15112yescomplemented
310#2028C2×C15112yescomplemented
311#1997C2×C15111yescharacteristic, complemented
312#1986C2×C15111yescharacteristic, complemented
313#1882C2×C15112yes—
314#1859C2×C15112yes—
315#1806C2×C15111yescharacteristic
316C2×#137C22×C15111yescharacteristic
317Q82—21no—
318#557—21no—
319#554—21no—
320#554—22no—
321D4×Q8—22no—
322D4×Q8—21no—
323#544—22no—
324#544C22×C15112yes—
325#533—21no—
326#533C22×C15111yescharacteristic
327C2×C4⋊Q8—21no—
328C2×C4⋊Q8C22×C15111yescharacteristic
329#520C22×C15112yes—
330C4×#41C22×C15111yescharacteristic
331C2×C4×Q8C22×C15111yescharacteristic
332#479—22no—
333#477—21no—
334#475—21no—
335#441—21no—
336#440—21no—
337C4×Q16—21no—
338C4×SD16—21no—
339#428C22×C15112yes—
340#428C22×C15111yescharacteristic
341#423C22×C15111yescharacteristic
342C2×#104C22×C15112yes—
343#419C22×C15112yes—
344#419C22×C15111yescharacteristic
345#417C22×C15111yescharacteristic
346C4×M16C22×C15111yescharacteristic
347#395—22no—
348#391C22×C15112yes—
349#389—22no—
350#384C22×C15112yes—
351C4×C4⋊C4C22×C15111yescharacteristic
352#343C22×C15112yes—
353#343C22×C15112yes—
354#339C22×C15112yes—
355#339C22×C15112yes—
356#339C22×C15112yes—
357C2×#41C23×C15111yescharacteristic
358C22×Q8—22no—
359C22×Q8D4×C15112yes—
360C22×Q8C23×C15111yescharacteristic
361#137—22no—
362#137Q8×C15114yescomplemented
363C2×Q16—21no—
364C2×SD16—21no—
365C2×M16C23×C15111yescharacteristic
366C2×M16C23×C15112yes—
367C2×M16C23×C15111yescharacteristic
368C4⋊Q8—22no—
369C4⋊Q8—22no—
370C4⋊Q8—24no—
371C4⋊Q8—22no—
372C4⋊Q8—22no—
373C4⋊Q8—21no—
374C4⋊Q8—21no—
375C4⋊Q8—21no—
376C4⋊Q8—21no—
377C4⋊Q8D4×C15111yescharacteristic
378C4⋊Q8D4×C15111yescharacteristic
379#125—24no—
380#125—22no—
381#125—22no—
382#125D4×C15112yes—
383C22⋊Q8—22no—
384C22⋊Q8—22no—
385C22⋊Q8—24no—
386C22⋊Q8—24no—
387C22⋊Q8—21no—
388C22⋊Q8—21no—
389C22⋊Q8—24no—
390C4×Q8—22no—
391C4×Q8—22no—
392C4×Q8—22no—
393C4×Q8—21no—
394C4×Q8—21no—
395C4×Q8—21no—
396C4×Q8—21no—
397C4×Q8—21no—
398C4×Q8—21no—
399C4×Q8D4×C15111yescharacteristic
400C4×Q8D4×C15111yescharacteristic
401C4×D4—22no—
402C4×D4—21no—
403C4×D4—21no—
404C4×D4—24no—
405C4×D4D4×C15111yescharacteristic
406C4×D4D4×C15111yescharacteristic
407#117—22no—
408#117—21no—
409#117C23×C15111yescharacteristic
410#117C23×C15112yes—
411C2×C4⋊C4—22no—
412C2×C4⋊C4—21no—
413C2×C4⋊C4—22no—
414C2×C4⋊C4—21no—
415C2×C4⋊C4—24no—
416C2×C4⋊C4D4×C15112yes—
417C2×C4⋊C4C23×C15111yescharacteristic
418C2×C4⋊C4C23×C15112yes—
419C2×C42—21no—
420C2×C42—21no—
421C2×C42C23×C15112yes—
422C2×C42C23×C15111yescharacteristic
423#107—21no—
424#107—22no—
425#106—21no—
426#106—22no—
427C4⋊C8—21no—
428C4⋊C8—21no—
429#104—24no—
430#103—21no—
431#103—21no—
432#103—21no—
433#103—22no—
434#103—22no—
435#102—21no—
436#97—21no—
437C4×C8—21no—
438#95—21no—
439#95—24no—
440#41—21no—
441#41—21no—
442#41C2×Q8×C15112yes—
443#41#41×C15112yes—
444C2×Q8—24no—
445C2×Q8—21no—
446C2×Q8—22no—
447C2×Q8—21no—
448C2×Q8—22no—
449C2×Q8—21no—
450C2×Q8—21no—
451C2×Q8—21no—
452C2×Q8—21no—
453C2×Q8—21no—
454C2×Q8—82no—
455C2×Q8—84no—
456C2×Q8C2×D4×C15111yescharacteristic
457C2×Q8C2×Q8×C15112yescomplemented
458C2×D4—21no—
459C2×D4C2×D4×C15111yescharacteristic
460C22×C4—21no—
461C22×C4—21no—
462C22×C4—22no—
463C22×C4—24no—
464C22×C4—21no—
465C22×C4—21no—
466C22×C4—21no—
467C22×C4C2×D4×C15111yescharacteristic
468C22×C4C2×D4×C15114yes—
469C22×C4C2×D4×C15111yescharacteristic
470C22×C4C24×C15111yescharacteristic
471Q16—24no—
472SD16—24no—
473M16—21no—
474M16—22no—
475M16—21no—
476M16—21no—
477M16—22no—
478M16C2×Q8×C15112yescomplemented
479C2×C8—21no—
480C2×C8—21no—
481C2×C8—22no—
482C4⋊C4—24no—
483C4⋊C4—24no—
484C4⋊C4—24no—
485C4⋊C4—24no—
486C4⋊C4—24no—
487C4⋊C4—21no—
488C4⋊C4—22no—
489C4⋊C4—22no—
490C4⋊C4—21no—
491C4⋊C4—21no—
492C4⋊C4—21no—
493C4⋊C4—22no—
494C4⋊C4—22no—
495C4⋊C4—22no—
496C4⋊C4—22no—
497C4⋊C4—21no—
498C4⋊C4—21no—
499C4⋊C4—41no—
500C4⋊C4—41no—
501C4⋊C4—84no—
502C4⋊C4C2×D4×C15112yes—
503C4⋊C4C2×D4×C15111yescharacteristic
504C4⋊C4C2×D4×C15112yes—
505C4⋊C4C2×D4×C15111yescharacteristic
506C22⋊C4—24no—
507C22⋊C4—22no—
508C22⋊C4—21no—
509C22⋊C4—21no—
510C22⋊C4—21no—
511C42—24no—
512C42—21no—
513C42—21no—
514C42—21no—
515C42—22no—
516C42—22no—
517C42—22no—
518C42—41no—
519C42—41no—
520C42C2×D4×C15111yescharacteristic
521C42C2×D4×C15111yescharacteristic
522C42C2×D4×C15111yescharacteristic
523C42C2×D4×C15111yescharacteristic
524C23—21no—
525C23C22×D4×C15111yescharacteristic
526Q8—21no—
527Q8—22no—
528Q8—22no—
529Q8—44no—
530Q8—42no—
531Q8—42no—
532Q8—41no—
533Q8—41no—
534Q8—82no—
535Q8—84no—
536Q8C22⋊Q8×C15112yes—
537D4—22no—
538D4—22no—
539D4—21no—
540D4C22⋊Q8×C15112yes—
541C2×C4—21no—
542C2×C4—22no—
543C2×C4—22no—
544C2×C4—22no—
545C2×C4—24no—
546C2×C4—22no—
547C2×C4—21no—
548C2×C4—21no—
549C2×C4—24no—
550C2×C4—22no—
551C2×C4—22no—
552C2×C4—41no—
553C2×C4—42no—
554C2×C4—42no—
555C2×C4—41no—
556C2×C4—42no—
557C2×C4—41no—
558C2×C4—42no—
559C2×C4—44no—
560C2×C4—42no—
561C2×C4—41no—
562C2×C4—84no—
563C2×C4#120×C15111yescharacteristic
564C2×C4#120×C15111yescharacteristic
565C2×C4#120×C15111yescharacteristic
566C2×C4#120×C15111yescharacteristic
567C2×C4C22×D4×C15111yescharacteristic
568C2×C4C22×D4×C15111yescharacteristic
569C2×C4C22×Q8×C15111yescharacteristic
570C2×C4C2×#41×C15111yescharacteristic
571C2×C42−1+4×C15111yescharacteristic
572C2×C42−1+4×C15111yescharacteristic
573C8—22no—
574C8—41no—
575C8—42no—
576C22—21no—
577C22—21no—
578C22—22no—
579C22—41no—
580C22—41no—
581C22C2×#120×C15111yescharacteristic
582C22#548×C15111yescharacteristic
583C22D4×Q8×C15111yescharacteristic
584C4—22no—
585C4—21no—
586C4—21no—
587C4—21no—
588C4—44no—
589C4—42no—
590C4—41no—
591C4—42no—
592C4—41no—
593C4—44no—
594C4—42no—
595C4—81no—
596C4#456×C15112yes—
597C4C2×C22⋊Q8×C15111yescharacteristic
598C4#536×C15111yescharacteristic
599C4#548×C15111yescharacteristic
600C4D4×Q8×C15111yescharacteristic
601C2—21no—
602C2—21no—
603C2—42no—
604C2#2409×C15111yescharacteristic
605C2C2×#456×C15111yescharacteristic
606C2#3019×C15111yescharacteristic
subgroupG/H
center, socleC22×C151C2×#120
commutator, Frattini, cosocleC22×C4C24×C151
prime radicalC2×#41×C151C23
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C151 ◁ C2×C42×C151 ◁ G

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
2. #3078×C151C2semidirect
4. #2567×C151C2semidirect
5. #2060×C151C2semidirect
6. #2028×C151C2semidirect
7. #1997×C151C2semidirect
8. #1986×C151C2semidirect
58. #137×C151Q8semidirect
153. C2×Q8×C151C2×Q8semidirect
174. M16×C151C2×Q8semidirect
303. #24323C151direct (N × H)
304. C151#24323direct (N × H)
306. #3078C2×C151semidirect
308. #2567C2×C151semidirect
309. #2060C2×C151semidirect
310. #2028C2×C151semidirect
311. #1997C2×C151semidirect
312. #1986C2×C151semidirect
362. #137Q8×C151semidirect
457. C2×Q8C2×Q8×C151semidirect
478. M16C2×Q8×C151semidirect

Maximal subgroups

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

subgroupindex
#3503×C1512
#3078×C1512
C4×#137×C1512
#2567×C1512
#2060×C1512
#2028×C1512
#1997×C1512
#1986×C1512
#1882×C1512
#1859×C1512
#1806×C1512
#24323151