Finite Group Databasebeta

← C151×#24322 #50329247

Subgroups — C151×#24322 #50329247

Order 38656.

988 conjugacy classes of subgroups.

The subgroup lattice has 606 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#2568×C151C211yesmaximal, characteristic, complemented
5#2061×C151C212yesmaximal, complemented
6#2028×C151C212yesmaximal, complemented
7#1997×C151C211yesmaximal, characteristic, complemented
8#1986×C151C211yesmaximal, characteristic, complemented
9#1882×C151C212yesmaximal
10#1860×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#400×C151—22no—
44#391×C151—22no—
45#391×C151C2212yes—
46#382×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—22no—
109C2×C4⋊C4×C151—21no—
110C2×C4⋊C4×C151—21no—
111C2×C4⋊C4×C151D412yes—
112C2×C4⋊C4×C151C2311yescharacteristic
113C2×C4⋊C4×C151C2312yes—
114C2×C42×C151—21no—
115C2×C42×C151—21no—
116C2×C42×C151C2312yes—
117C2×C42×C151C2311yescharacteristic
118#107×C151—21no—
119#107×C151—22no—
120#106×C151—21no—
121#106×C151—22no—
122C4⋊C8×C151—21no—
123C4⋊C8×C151—21no—
124#104×C151—24no—
125#103×C151—21no—
126#103×C151—21no—
127#103×C151—22no—
128#103×C151—22no—
129#103×C151—21no—
130#102×C151—21no—
131#97×C151—21no—
132C4×C8×C151—21no—
133#95×C151—21no—
134#95×C151—24no—
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—44no—
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—24no—
159C22×C4×C151—21no—
160C22×C4×C151—21no—
161C22×C4×C151—22no—
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—21no—
183C4⋊C4×C151—22no—
184C4⋊C4×C151—22no—
185C4⋊C4×C151—21no—
186C4⋊C4×C151—21no—
187C4⋊C4×C151—21no—
188C4⋊C4×C151—22no—
189C4⋊C4×C151—22no—
190C4⋊C4×C151—22no—
191C4⋊C4×C151—22no—
192C4⋊C4×C151—21no—
193C4⋊C4×C151—21no—
194C4⋊C4×C151—42no—
195C4⋊C4×C151—41no—
196C4⋊C4×C151—41no—
197C4⋊C4×C151C2×D412yes—
198C4⋊C4×C151C2×D411yescharacteristic
199C4⋊C4×C151C2×D412yes—
200C4⋊C4×C151C2×D411yescharacteristic
201C22⋊C4×C151—24no—
202C22⋊C4×C151—21no—
203C22⋊C4×C151—22no—
204C22⋊C4×C151—21no—
205C22⋊C4×C151—21no—
206C42×C151—24no—
207C42×C151—21no—
208C42×C151—21no—
209C42×C151—21no—
210C42×C151—22no—
211C42×C151—22no—
212C42×C151—22no—
213C42×C151—41no—
214C42×C151—41no—
215C42×C151C2×D411yescharacteristic
216C42×C151C2×D411yescharacteristic
217C42×C151C2×D411yescharacteristic
218C42×C151C2×D411yescharacteristic
219C23×C151—21no—
220C23×C151C22×D411yescharacteristic
221Q8×C151—21no—
222Q8×C151—22no—
223Q8×C151—22no—
224Q8×C151—42no—
225Q8×C151—41no—
226Q8×C151—41no—
227Q8×C151—44no—
228Q8×C151—42no—
229Q8×C151—82no—
230Q8×C151—84no—
231Q8×C151C22⋊Q812yes—
232D4×C151—22no—
233D4×C151—22no—
234D4×C151—21no—
235D4×C151C22⋊Q812yes—
236C2×C4×C151—21no—
237C2×C4×C151—22no—
238C2×C4×C151—22no—
239C2×C4×C151—22no—
240C2×C4×C151—21no—
241C2×C4×C151—24no—
242C2×C4×C151—22no—
243C2×C4×C151—22no—
244C2×C4×C151—21no—
245C2×C4×C151—22no—
246C2×C4×C151—41no—
247C2×C4×C151—42no—
248C2×C4×C151—41no—
249C2×C4×C151—41no—
250C2×C4×C151—42no—
251C2×C4×C151—44no—
252C2×C4×C151—42no—
253C2×C4×C151—42no—
254C2×C4×C151—42no—
255C2×C4×C151—41no—
256C2×C4×C151—42no—
257C2×C4×C151—84no—
258C2×C4×C151#12011yescharacteristic
259C2×C4×C151#12011yescharacteristic
260C2×C4×C151#12011yescharacteristic
261C2×C4×C151#12011yescharacteristic
262C2×C4×C151C22×D411yescharacteristic
263C2×C4×C151C22×D411yescharacteristic
264C2×C4×C151C22×Q811yescharacteristic
265C2×C4×C151C2×#4111yescharacteristic
266C2×C4×C1512−1+411yescharacteristic
267C2×C4×C1512−1+411yescharacteristic
268C8×C151—22no—
269C8×C151—41no—
270C8×C151—42no—
271C22×C151—21no—
272C22×C151—21no—
273C22×C151—22no—
274C22×C151—41no—
275C22×C151—41no—
276C22×C151C2×#12011yescharacteristic
277C22×C151#54811yescharacteristic
278C22×C151D4×Q811yescharacteristic
279C4×C151—22no—
280C4×C151—21no—
281C4×C151—21no—
282C4×C151—21no—
283C4×C151—42no—
284C4×C151—41no—
285C4×C151—44no—
286C4×C151—42no—
287C4×C151—41no—
288C4×C151—42no—
289C4×C151—82no—
290C4×C151—81no—
291C4×C151#45512yes—
292C4×C151C2×C22⋊Q811yescharacteristic
293C4×C151#53611yescharacteristic
294C4×C151#54811yescharacteristic
295C4×C151D4×Q811yescharacteristic
296C2×C151—21no—
297C2×C151—21no—
298C2×C151—42no—
299C2×C151#240911yescharacteristic
300C2×C151C2×#45511yescharacteristic
301C2×C151#302011yescharacteristic
302#24322C15111yesmaximal, characteristic, direct product factor, Sylow
303C151#2432211yescharacteristic, direct product factor, Sylow
304#3503C2×C15111yescharacteristic
305#3078C2×C15111yescharacteristic, complemented
306C4×#137C2×C15111yescharacteristic
307#2568C2×C15111yescharacteristic, complemented
308#2061C2×C15112yescomplemented
309#2028C2×C15112yescomplemented
310#1997C2×C15111yescharacteristic, complemented
311#1986C2×C15111yescharacteristic, complemented
312#1882C2×C15112yes—
313#1860C2×C15112yes—
314#1806C2×C15111yescharacteristic
315C2×#137C22×C15111yescharacteristic
316Q82—21no—
317#557—21no—
318#554—21no—
319#554—22no—
320D4×Q8—22no—
321D4×Q8—21no—
322#544—22no—
323#544C22×C15112yes—
324#533—21no—
325#533C22×C15111yescharacteristic
326C2×C4⋊Q8—21no—
327C2×C4⋊Q8C22×C15111yescharacteristic
328#520C22×C15112yes—
329C4×#41C22×C15111yescharacteristic
330C2×C4×Q8C22×C15111yescharacteristic
331#479—22no—
332#477—21no—
333#475—21no—
334#441—21no—
335#440—21no—
336C4×Q16—21no—
337C4×SD16—21no—
338#428C22×C15112yes—
339#428C22×C15111yescharacteristic
340#423C22×C15111yescharacteristic
341C2×#104C22×C15112yes—
342#419C22×C15112yes—
343#419C22×C15111yescharacteristic
344#417C22×C15111yescharacteristic
345C4×M16C22×C15111yescharacteristic
346#400—22no—
347#391—22no—
348#391C22×C15112yes—
349#382C22×C15112yes—
350C4×C4⋊C4C22×C15111yescharacteristic
351#343C22×C15112yes—
352#343C22×C15112yes—
353#339C22×C15112yes—
354#339C22×C15112yes—
355#339C22×C15112yes—
356C2×#41C23×C15111yescharacteristic
357C22×Q8—22no—
358C22×Q8D4×C15112yes—
359C22×Q8C23×C15111yescharacteristic
360#137—22no—
361#137Q8×C15114yescomplemented
362C2×Q16—21no—
363C2×SD16—21no—
364C2×M16C23×C15111yescharacteristic
365C2×M16C23×C15112yes—
366C2×M16C23×C15111yescharacteristic
367C4⋊Q8—22no—
368C4⋊Q8—22no—
369C4⋊Q8—24no—
370C4⋊Q8—22no—
371C4⋊Q8—22no—
372C4⋊Q8—21no—
373C4⋊Q8—21no—
374C4⋊Q8—21no—
375C4⋊Q8—21no—
376C4⋊Q8D4×C15111yescharacteristic
377C4⋊Q8D4×C15111yescharacteristic
378#125—24no—
379#125—22no—
380#125—22no—
381#125D4×C15112yes—
382C22⋊Q8—22no—
383C22⋊Q8—22no—
384C22⋊Q8—24no—
385C22⋊Q8—24no—
386C22⋊Q8—21no—
387C22⋊Q8—21no—
388C22⋊Q8—24no—
389C4×Q8—22no—
390C4×Q8—22no—
391C4×Q8—22no—
392C4×Q8—21no—
393C4×Q8—21no—
394C4×Q8—21no—
395C4×Q8—21no—
396C4×Q8—21no—
397C4×Q8—21no—
398C4×Q8D4×C15111yescharacteristic
399C4×Q8D4×C15111yescharacteristic
400C4×D4—22no—
401C4×D4—21no—
402C4×D4—21no—
403C4×D4—24no—
404C4×D4D4×C15111yescharacteristic
405C4×D4D4×C15111yescharacteristic
406#117—22no—
407#117—21no—
408#117C23×C15111yescharacteristic
409#117C23×C15112yes—
410C2×C4⋊C4—22no—
411C2×C4⋊C4—22no—
412C2×C4⋊C4—21no—
413C2×C4⋊C4—21no—
414C2×C4⋊C4D4×C15112yes—
415C2×C4⋊C4C23×C15111yescharacteristic
416C2×C4⋊C4C23×C15112yes—
417C2×C42—21no—
418C2×C42—21no—
419C2×C42C23×C15112yes—
420C2×C42C23×C15111yescharacteristic
421#107—21no—
422#107—22no—
423#106—21no—
424#106—22no—
425C4⋊C8—21no—
426C4⋊C8—21no—
427#104—24no—
428#103—21no—
429#103—21no—
430#103—21no—
431#103—22no—
432#103—22no—
433#102—21no—
434#97—21no—
435C4×C8—21no—
436#95—21no—
437#95—24no—
438#95—24no—
439#41—21no—
440#41—21no—
441#41C2×Q8×C15112yes—
442#41#41×C15112yes—
443C2×Q8—24no—
444C2×Q8—21no—
445C2×Q8—22no—
446C2×Q8—21no—
447C2×Q8—22no—
448C2×Q8—21no—
449C2×Q8—21no—
450C2×Q8—21no—
451C2×Q8—21no—
452C2×Q8—21no—
453C2×Q8—44no—
454C2×Q8—84no—
455C2×Q8C2×D4×C15111yescharacteristic
456C2×Q8C2×Q8×C15112yescomplemented
457C2×D4—21no—
458C2×D4C2×D4×C15111yescharacteristic
459C22×C4—21no—
460C22×C4—21no—
461C22×C4—24no—
462C22×C4—21no—
463C22×C4—21no—
464C22×C4—22no—
465C22×C4—21no—
466C22×C4C2×D4×C15111yescharacteristic
467C22×C4C2×D4×C15114yes—
468C22×C4C2×D4×C15111yescharacteristic
469C22×C4C24×C15111yescharacteristic
470Q16—24no—
471SD16—24no—
472M16—21no—
473M16—22no—
474M16—21no—
475M16—21no—
476M16—22no—
477M16C2×Q8×C15112yescomplemented
478C2×C8—21no—
479C2×C8—21no—
480C2×C8—22no—
481C4⋊C4—24no—
482C4⋊C4—24no—
483C4⋊C4—24no—
484C4⋊C4—24no—
485C4⋊C4—21no—
486C4⋊C4—22no—
487C4⋊C4—22no—
488C4⋊C4—21no—
489C4⋊C4—21no—
490C4⋊C4—21no—
491C4⋊C4—22no—
492C4⋊C4—22no—
493C4⋊C4—22no—
494C4⋊C4—22no—
495C4⋊C4—21no—
496C4⋊C4—21no—
497C4⋊C4—42no—
498C4⋊C4—41no—
499C4⋊C4—41no—
500C4⋊C4C2×D4×C15112yes—
501C4⋊C4C2×D4×C15111yescharacteristic
502C4⋊C4C2×D4×C15112yes—
503C4⋊C4C2×D4×C15111yescharacteristic
504C22⋊C4—24no—
505C22⋊C4—22no—
506C22⋊C4—21no—
507C22⋊C4—21no—
508C22⋊C4—21no—
509C42—24no—
510C42—21no—
511C42—21no—
512C42—21no—
513C42—22no—
514C42—22no—
515C42—22no—
516C42—41no—
517C42—41no—
518C42C2×D4×C15111yescharacteristic
519C42C2×D4×C15111yescharacteristic
520C42C2×D4×C15111yescharacteristic
521C42C2×D4×C15111yescharacteristic
522C23—21no—
523C23C22×D4×C15111yescharacteristic
524Q8—21no—
525Q8—22no—
526Q8—22no—
527Q8—42no—
528Q8—44no—
529Q8—42no—
530Q8—41no—
531Q8—41no—
532Q8—82no—
533Q8—84no—
534Q8C22⋊Q8×C15112yes—
535D4—22no—
536D4—22no—
537D4—21no—
538D4C22⋊Q8×C15112yes—
539C2×C4—21no—
540C2×C4—22no—
541C2×C4—22no—
542C2×C4—22no—
543C2×C4—22no—
544C2×C4—21no—
545C2×C4—21no—
546C2×C4—24no—
547C2×C4—22no—
548C2×C4—22no—
549C2×C4—41no—
550C2×C4—42no—
551C2×C4—41no—
552C2×C4—41no—
553C2×C4—42no—
554C2×C4—44no—
555C2×C4—42no—
556C2×C4—42no—
557C2×C4—42no—
558C2×C4—41no—
559C2×C4—42no—
560C2×C4—84no—
561C2×C4#120×C15111yescharacteristic
562C2×C4#120×C15111yescharacteristic
563C2×C4#120×C15111yescharacteristic
564C2×C4#120×C15111yescharacteristic
565C2×C4C22×D4×C15111yescharacteristic
566C2×C4C22×D4×C15111yescharacteristic
567C2×C4C22×Q8×C15111yescharacteristic
568C2×C4C2×#41×C15111yescharacteristic
569C2×C42−1+4×C15111yescharacteristic
570C2×C42−1+4×C15111yescharacteristic
571C8—22no—
572C8—41no—
573C8—42no—
574C22—21no—
575C22—21no—
576C22—22no—
577C22—41no—
578C22—41no—
579C22C2×#120×C15111yescharacteristic
580C22#548×C15111yescharacteristic
581C22D4×Q8×C15111yescharacteristic
582C4—22no—
583C4—21no—
584C4—21no—
585C4—21no—
586C4—42no—
587C4—41no—
588C4—44no—
589C4—42no—
590C4—41no—
591C4—42no—
592C4—82no—
593C4—81no—
594C4#455×C15112yes—
595C4C2×C22⋊Q8×C15111yescharacteristic
596C4#536×C15111yescharacteristic
597C4#548×C15111yescharacteristic
598C4D4×Q8×C15111yescharacteristic
599C2—21no—
600C2—21no—
601C2—42no—
602C2#2409×C15111yescharacteristic
603C2C2×#455×C15111yescharacteristic
604C2#3020×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. #2568×C151C2semidirect
5. #2061×C151C2semidirect
6. #2028×C151C2semidirect
7. #1997×C151C2semidirect
8. #1986×C151C2semidirect
58. #137×C151Q8semidirect
153. C2×Q8×C151C2×Q8semidirect
174. M16×C151C2×Q8semidirect
302. #24322C151direct (N × H)
303. C151#24322direct (N × H)
305. #3078C2×C151semidirect
307. #2568C2×C151semidirect
308. #2061C2×C151semidirect
309. #2028C2×C151semidirect
310. #1997C2×C151semidirect
311. #1986C2×C151semidirect
361. #137Q8×C151semidirect
456. C2×Q8C2×Q8×C151semidirect
477. 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
#2568×C1512
#2061×C1512
#2028×C1512
#1997×C1512
#1986×C1512
#1882×C1512
#1860×C1512
#1806×C1512
#24322151