Finite Group Databasebeta

← C151×#18872 #50323797

Subgroups — C151×#18872 #50323797

Order 38656.

954 conjugacy classes of subgroups.

The subgroup lattice has 586 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#3503×C151C211yesmaximal, characteristic, complemented
2#3246×C151C211yesmaximal, characteristic, complemented
3#3206×C151C211yesmaximal, characteristic, complemented
4#3035×C151C211yesmaximal, characteristic
5#1645×C151C212yesmaximal, complemented
6#1643×C151C212yesmaximal, complemented
7#1623×C151C212yesmaximal, complemented
8#1622×C151C212yesmaximal, complemented
9C2×#333×C151C211yesmaximal, characteristic, complemented
10#1481×C151C211yesmaximal, characteristic, complemented
11#1477×C151C211yesmaximal, characteristic, complemented
12C2×#135×C151—21no—
13Q82×C151C2212yes—
14#557×C151—21no—
15#554×C151—22no—
16#554×C151C2212yes—
17D4×Q8×C151—22no—
18D4×Q8×C151—21no—
19#544×C151—22no—
20#544×C151—21no—
21#533×C151—21no—
22#533×C151C2211yescharacteristic
23#532×C151C2211yescharacteristic
24C2×C4⋊Q8×C151—21no—
25C2×C4⋊Q8×C151C2211yescharacteristic
26#520×C151—21no—
27C4×#41×C151C2211yescharacteristic
28#492×C151C2212yes—
29#487×C151C2212yes—
30#476×C151—21no—
31#475×C151C2212yes—
32#465×C151—22no—
33#464×C151—21no—
34#463×C151—21no—
35#462×C151C2211yescharacteristic
36#461×C151—22no—
37#461×C151—21no—
38#461×C151C2211yescharacteristic
39#460×C151C2212yes—
40#460×C151C2211yescharacteristic
41#459×C151C2211yescharacteristic
42#448×C151—22no—
43#431×C151C2211yescharacteristic
44C2×C4⋊C8×C151C2211yescharacteristic
45C2×C4⋊C8×C151C2211yescharacteristic
46#416×C151—21no—
47#333×C151C2212yes—
48#333×C151C2212yes—
49Q8⋊C8×C151C2212yes—
50Q8⋊C8×C151C2212yes—
51Q8⋊C8×C151C2212yes—
52D4⋊C8×C151C2212yes—
53C2×#41×C151—21no—
54C2×#41×C151D411yescharacteristic
55C22×Q8×C151—22no—
56C22×Q8×C151D412yes—
57#135×C151—44no—
58C2×Q16×C151—21no—
59C2×SD16×C151—21no—
60C2×SD16×C151—21no—
61C2×SD16×C151—24no—
62C2×SD16×C151—22no—
63C2×D8×C151—21no—
64C22×C8×C151—21no—
65C22×C8×C151—21no—
66C4⋊Q8×C151—22no—
67C4⋊Q8×C151—22no—
68C4⋊Q8×C151—22no—
69C4⋊Q8×C151—22no—
70C4⋊Q8×C151—21no—
71C4⋊Q8×C151—21no—
72C4⋊Q8×C151—24no—
73C4⋊Q8×C151D411yescharacteristic
74C4⋊Q8×C151D412yes—
75C4⋊Q8×C151D411yescharacteristic
76C4⋊Q8×C151C2311yescharacteristic
77C4⋊Q8×C151C2312yes—
78#127×C151C2311yescharacteristic
79#125×C151—22no—
80#125×C151—24no—
81#125×C151—22no—
82#125×C151—21no—
83#124×C151—21no—
84C22⋊Q8×C151—22no—
85C22⋊Q8×C151—24no—
86C22⋊Q8×C151—24no—
87C22⋊Q8×C151—21no—
88C22⋊Q8×C151—22no—
89C22⋊Q8×C151—24no—
90C22⋊Q8×C151D412yes—
91#121×C151—21no—
92#121×C151—21no—
93C4×Q8×C151—22no—
94C4×Q8×C151—21no—
95C4×Q8×C151—22no—
96C4×Q8×C151—22no—
97C4×Q8×C151D411yescharacteristic
98C4×Q8×C151C2311yescharacteristic
99C4×Q8×C151C2312yes—
100C4×D4×C151—24no—
101C4×D4×C151—22no—
102C4×D4×C151—21no—
103C4×D4×C151—21no—
104C4×D4×C151—21no—
105C4×D4×C151—21no—
106C4×D4×C151D411yescharacteristic
107C4×D4×C151C2311yescharacteristic
108#117×C151—22no—
109#117×C151—21no—
110#117×C151—21no—
111#117×C151D411yescharacteristic
112C2×C4⋊C4×C151—22no—
113C2×C4⋊C4×C151—21no—
114C2×C4⋊C4×C151—21no—
115C2×C4⋊C4×C151—22no—
116C2×C42×C151—21no—
117C2×C42×C151C2311yescharacteristic
118#106×C151—22no—
119C4⋊C8×C151—21no—
120C4⋊C8×C151—21no—
121C4⋊C8×C151—21no—
122C4⋊C8×C151C2311yescharacteristic
123C4⋊C8×C151C2311yescharacteristic
124C4⋊C8×C151C2312yes—
125#103×C151—21no—
126#103×C151—21no—
127#103×C151—24no—
128#103×C151—22no—
129#102×C151—21no—
130#102×C151—21no—
131#102×C151—22no—
132C22⋊C8×C151—21no—
133C4×C8×C151C2312yes—
134#41×C151—22no—
135#41×C151—42no—
136#41×C151—42no—
137#41×C151SD1614yescomplemented
138C2×Q8×C151—24no—
139C2×Q8×C151—22no—
140C2×Q8×C151—21no—
141C2×Q8×C151—21no—
142C2×Q8×C151—84no—
143C2×Q8×C151—82no—
144C2×Q8×C151C2×D412yes—
145C2×Q8×C151C2×D411yescharacteristic
146C2×Q8×C151C2×D414yes—
147C2×D4×C151—21no—
148C2×D4×C151—21no—
149C2×D4×C151—21no—
150C2×D4×C151—21no—
151C2×D4×C151—41no—
152C2×D4×C151C2×D411yescharacteristic
153C22×C4×C151—21no—
154C22×C4×C151—24no—
155C22×C4×C151—22no—
156C22×C4×C151—21no—
157C22×C4×C151—21no—
158C22×C4×C151—41no—
159C22×C4×C151C2×D411yescharacteristic
160C22×C4×C151C2×D411yescharacteristic
161C22×C4×C151C2×D411yescharacteristic
162Q16×C151—42no—
163SD16×C151—42no—
164SD16×C151—42no—
165SD16×C151—82no—
166SD16×C151—84no—
167D8×C151—42no—
168C2×C8×C151—22no—
169C2×C8×C151—22no—
170C2×C8×C151—21no—
171C2×C8×C151—21no—
172C2×C8×C151—42no—
173C2×C8×C151—81no—
174C4⋊C4×C151—24no—
175C4⋊C4×C151—24no—
176C4⋊C4×C151—24no—
177C4⋊C4×C151—24no—
178C4⋊C4×C151—21no—
179C4⋊C4×C151—22no—
180C4⋊C4×C151—22no—
181C4⋊C4×C151—21no—
182C4⋊C4×C151—21no—
183C4⋊C4×C151—21no—
184C4⋊C4×C151—22no—
185C4⋊C4×C151—22no—
186C4⋊C4×C151—22no—
187C4⋊C4×C151—21no—
188C4⋊C4×C151—22no—
189C4⋊C4×C151—21no—
190C4⋊C4×C151—21no—
191C4⋊C4×C151C2×D411yescharacteristic
192C4⋊C4×C151C2×D411yescharacteristic
193C4⋊C4×C151C2×D412yes—
194C22⋊C4×C151—24no—
195C22⋊C4×C151—22no—
196C22⋊C4×C151—21no—
197C22⋊C4×C151—21no—
198C22⋊C4×C151—21no—
199C22⋊C4×C151—41no—
200C22⋊C4×C151—41no—
201C42×C151—24no—
202C42×C151—21no—
203C42×C151—21no—
204C42×C151—21no—
205C42×C151—22no—
206C42×C151C2×D411yescharacteristic
207C42×C151C2×D411yescharacteristic
208C42×C151C2×D411yescharacteristic
209C42×C151C2411yescharacteristic
210C23×C151—21no—
211C23×C151—41no—
212C23×C151#12011yescharacteristic
213Q8×C151—21no—
214Q8×C151—22no—
215Q8×C151—22no—
216Q8×C151—44no—
217Q8×C151—44no—
218Q8×C151—42no—
219Q8×C151—41no—
220Q8×C151—41no—
221Q8×C151—84no—
222Q8×C151C2×SD1612yes—
223D4×C151—24no—
224D4×C151—21no—
225D4×C151—42no—
226D4×C151—41no—
227D4×C151—41no—
228D4×C151—41no—
229D4×C151—41no—
230D4×C151—82no—
231D4×C151C2×SD1612yes—
232C2×C4×C151—21no—
233C2×C4×C151—21no—
234C2×C4×C151—21no—
235C2×C4×C151—24no—
236C2×C4×C151—21no—
237C2×C4×C151—22no—
238C2×C4×C151—24no—
239C2×C4×C151—22no—
240C2×C4×C151—21no—
241C2×C4×C151—41no—
242C2×C4×C151—42no—
243C2×C4×C151—41no—
244C2×C4×C151—41no—
245C2×C4×C151—41no—
246C2×C4×C151—82no—
247C2×C4×C151—84no—
248C2×C4×C151—82no—
249C2×C4×C151#12011yescharacteristic
250C2×C4×C151#12011yescharacteristic
251C2×C4×C151#12011yescharacteristic
252C2×C4×C151C2×SD1612yes—
253C2×C4×C151#13712yes—
254C2×C4×C151C22×D411yescharacteristic
255C2×C4×C151C22×D411yescharacteristic
256C2×C4×C151C22×D411yescharacteristic
257C8×C151—42no—
258C8×C151—41no—
259C8×C151—41no—
260C8×C151—42no—
261C22×C151—21no—
262C22×C151—21no—
263C22×C151—22no—
264C22×C151—41no—
265C22×C151—41no—
266C22×C151—81no—
267C22×C151—81no—
268C22×C151—81no—
269C22×C151#44812yes—
270C22×C151C2×#12011yescharacteristic
271C4×C151—22no—
272C4×C151—21no—
273C4×C151—21no—
274C4×C151—21no—
275C4×C151—41no—
276C4×C151—42no—
277C4×C151—41no—
278C4×C151—44no—
279C4×C151—42no—
280C4×C151—81no—
281C4×C151#44812yes—
282C4×C151C22×SD1611yescharacteristic
283C4×C151C2×#13711yescharacteristic
284C4×C151#57711yescharacteristic
285C4×C151#57811yescharacteristic
286C2×C151—22no—
287C2×C151—42no—
288C2×C151—161no—
289C2×C151C2×#44811yescharacteristic
290C2×C151#301311yescharacteristic
291C2×C151#301911yescharacteristic
292#18872C15111yesmaximal, characteristic, direct product factor, Sylow
293C151#1887211yescharacteristic, direct product factor, Sylow
294#3503C2×C15111yescharacteristic, complemented
295#3246C2×C15111yescharacteristic, complemented
296#3206C2×C15111yescharacteristic, complemented
297#3035C2×C15111yescharacteristic
298#1645C2×C15112yescomplemented
299#1643C2×C15112yescomplemented
300#1623C2×C15112yescomplemented
301#1622C2×C15112yescomplemented
302C2×#333C2×C15111yescharacteristic, complemented
303#1481C2×C15111yescharacteristic, complemented
304#1477C2×C15111yescharacteristic, complemented
305C2×#135—21no—
306Q82C22×C15112yes—
307#557—21no—
308#554—22no—
309#554C22×C15112yes—
310D4×Q8—22no—
311D4×Q8—21no—
312#544—22no—
313#544—21no—
314#533—21no—
315#533C22×C15111yescharacteristic
316#532C22×C15111yescharacteristic
317C2×C4⋊Q8—21no—
318C2×C4⋊Q8C22×C15111yescharacteristic
319#520—21no—
320C4×#41C22×C15111yescharacteristic
321#492C22×C15112yes—
322#487C22×C15112yes—
323#476—21no—
324#475C22×C15112yes—
325#465—22no—
326#464—21no—
327#463—21no—
328#462C22×C15111yescharacteristic
329#461—22no—
330#461—21no—
331#461C22×C15111yescharacteristic
332#460C22×C15112yes—
333#460C22×C15111yescharacteristic
334#459C22×C15111yescharacteristic
335#448—22no—
336#431C22×C15111yescharacteristic
337C2×C4⋊C8C22×C15111yescharacteristic
338C2×C4⋊C8C22×C15111yescharacteristic
339#416—21no—
340#333C22×C15112yes—
341#333C22×C15112yes—
342Q8⋊C8C22×C15112yes—
343Q8⋊C8C22×C15112yes—
344Q8⋊C8C22×C15112yes—
345D4⋊C8C22×C15112yes—
346C2×#41—21no—
347C2×#41D4×C15111yescharacteristic
348C22×Q8—22no—
349C22×Q8D4×C15112yes—
350#135—44no—
351C2×Q16—21no—
352C2×SD16—21no—
353C2×SD16—21no—
354C2×SD16—24no—
355C2×SD16—22no—
356C2×D8—21no—
357C22×C8—21no—
358C22×C8—21no—
359C4⋊Q8—22no—
360C4⋊Q8—22no—
361C4⋊Q8—24no—
362C4⋊Q8—22no—
363C4⋊Q8—22no—
364C4⋊Q8—21no—
365C4⋊Q8—21no—
366C4⋊Q8D4×C15112yes—
367C4⋊Q8D4×C15111yescharacteristic
368C4⋊Q8D4×C15111yescharacteristic
369C4⋊Q8C23×C15111yescharacteristic
370C4⋊Q8C23×C15112yes—
371#127C23×C15111yescharacteristic
372#125—22no—
373#125—24no—
374#125—22no—
375#125—21no—
376#124—21no—
377C22⋊Q8—22no—
378C22⋊Q8—24no—
379C22⋊Q8—24no—
380C22⋊Q8—22no—
381C22⋊Q8—24no—
382C22⋊Q8—21no—
383C22⋊Q8D4×C15112yes—
384#121—21no—
385#121—21no—
386C4×Q8—22no—
387C4×Q8—22no—
388C4×Q8—22no—
389C4×Q8—21no—
390C4×Q8D4×C15111yescharacteristic
391C4×Q8C23×C15111yescharacteristic
392C4×Q8C23×C15112yes—
393C4×D4—24no—
394C4×D4—22no—
395C4×D4—21no—
396C4×D4—21no—
397C4×D4—21no—
398C4×D4—21no—
399C4×D4D4×C15111yescharacteristic
400C4×D4C23×C15111yescharacteristic
401#117—22no—
402#117—21no—
403#117—21no—
404#117D4×C15111yescharacteristic
405C2×C4⋊C4—22no—
406C2×C4⋊C4—21no—
407C2×C4⋊C4—21no—
408C2×C4⋊C4—22no—
409C2×C42—21no—
410C2×C42C23×C15111yescharacteristic
411#106—22no—
412C4⋊C8—21no—
413C4⋊C8—21no—
414C4⋊C8—21no—
415C4⋊C8C23×C15112yes—
416C4⋊C8C23×C15111yescharacteristic
417C4⋊C8C23×C15111yescharacteristic
418#103—24no—
419#103—22no—
420#103—21no—
421#103—21no—
422#102—21no—
423#102—21no—
424#102—22no—
425C22⋊C8—21no—
426C4×C8C23×C15112yes—
427#41—22no—
428#41—42no—
429#41—42no—
430#41SD16×C15114yescomplemented
431C2×Q8—24no—
432C2×Q8—22no—
433C2×Q8—21no—
434C2×Q8—21no—
435C2×Q8—84no—
436C2×Q8—82no—
437C2×Q8C2×D4×C15112yes—
438C2×Q8C2×D4×C15111yescharacteristic
439C2×Q8C2×D4×C15114yes—
440C2×D4—21no—
441C2×D4—21no—
442C2×D4—21no—
443C2×D4—21no—
444C2×D4—41no—
445C2×D4C2×D4×C15111yescharacteristic
446C22×C4—21no—
447C22×C4—24no—
448C22×C4—22no—
449C22×C4—21no—
450C22×C4—21no—
451C22×C4—41no—
452C22×C4C2×D4×C15111yescharacteristic
453C22×C4C2×D4×C15111yescharacteristic
454C22×C4C2×D4×C15111yescharacteristic
455Q16—42no—
456SD16—42no—
457SD16—42no—
458SD16—82no—
459SD16—84no—
460D8—42no—
461C2×C8—22no—
462C2×C8—22no—
463C2×C8—21no—
464C2×C8—21no—
465C2×C8—42no—
466C2×C8—81no—
467C4⋊C4—24no—
468C4⋊C4—24no—
469C4⋊C4—24no—
470C4⋊C4—24no—
471C4⋊C4—22no—
472C4⋊C4—21no—
473C4⋊C4—22no—
474C4⋊C4—21no—
475C4⋊C4—21no—
476C4⋊C4—21no—
477C4⋊C4—22no—
478C4⋊C4—22no—
479C4⋊C4—22no—
480C4⋊C4—21no—
481C4⋊C4—22no—
482C4⋊C4—21no—
483C4⋊C4—21no—
484C4⋊C4C2×D4×C15111yescharacteristic
485C4⋊C4C2×D4×C15111yescharacteristic
486C4⋊C4C2×D4×C15112yes—
487C22⋊C4—24no—
488C22⋊C4—22no—
489C22⋊C4—21no—
490C22⋊C4—21no—
491C22⋊C4—21no—
492C22⋊C4—41no—
493C22⋊C4—41no—
494C42—24no—
495C42—21no—
496C42—21no—
497C42—21no—
498C42—22no—
499C42C2×D4×C15111yescharacteristic
500C42C2×D4×C15111yescharacteristic
501C42C2×D4×C15111yescharacteristic
502C42C24×C15111yescharacteristic
503C23—21no—
504C23—41no—
505C23#120×C15111yescharacteristic
506Q8—21no—
507Q8—22no—
508Q8—22no—
509Q8—44no—
510Q8—44no—
511Q8—42no—
512Q8—41no—
513Q8—41no—
514Q8—84no—
515Q8C2×SD16×C15112yes—
516D4—24no—
517D4—21no—
518D4—42no—
519D4—41no—
520D4—41no—
521D4—41no—
522D4—41no—
523D4—82no—
524D4C2×SD16×C15112yes—
525C2×C4—21no—
526C2×C4—24no—
527C2×C4—21no—
528C2×C4—21no—
529C2×C4—22no—
530C2×C4—21no—
531C2×C4—21no—
532C2×C4—24no—
533C2×C4—22no—
534C2×C4—41no—
535C2×C4—42no—
536C2×C4—41no—
537C2×C4—41no—
538C2×C4—41no—
539C2×C4—82no—
540C2×C4—84no—
541C2×C4—82no—
542C2×C4#120×C15111yescharacteristic
543C2×C4#120×C15111yescharacteristic
544C2×C4#120×C15111yescharacteristic
545C2×C4C2×SD16×C15112yes—
546C2×C4#137×C15112yes—
547C2×C4C22×D4×C15111yescharacteristic
548C2×C4C22×D4×C15111yescharacteristic
549C2×C4C22×D4×C15111yescharacteristic
550C8—42no—
551C8—41no—
552C8—41no—
553C8—42no—
554C22—21no—
555C22—21no—
556C22—22no—
557C22—41no—
558C22—41no—
559C22—81no—
560C22—81no—
561C22—81no—
562C22#448×C15112yes—
563C22C2×#120×C15111yescharacteristic
564C4—22no—
565C4—21no—
566C4—21no—
567C4—21no—
568C4—41no—
569C4—42no—
570C4—41no—
571C4—44no—
572C4—42no—
573C4—81no—
574C4#448×C15112yes—
575C4C22×SD16×C15111yescharacteristic
576C4C2×#137×C15111yescharacteristic
577C4#577×C15111yescharacteristic
578C4#578×C15111yescharacteristic
579C2—22no—
580C2—42no—
581C2—161no—
582C2C2×#448×C15111yescharacteristic
583C2#3013×C15111yescharacteristic
584C2#3019×C15111yescharacteristic
subgroupG/H
center, socleC22×C151C2×#120
commutator, Frattini, cosocleC42C24×C151
prime radical#3035×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. #3503×C151C2semidirect
2. #3246×C151C2semidirect
3. #3206×C151C2semidirect
5. #1645×C151C2semidirect
6. #1643×C151C2semidirect
7. #1623×C151C2semidirect
8. #1622×C151C2semidirect
9. C2×#333×C151C2semidirect
10. #1481×C151C2semidirect
11. #1477×C151C2semidirect
137. #41×C151SD16semidirect
292. #18872C151direct (N × H)
293. C151#18872direct (N × H)
294. #3503C2×C151semidirect
295. #3246C2×C151semidirect
296. #3206C2×C151semidirect
298. #1645C2×C151semidirect
299. #1643C2×C151semidirect
300. #1623C2×C151semidirect
301. #1622C2×C151semidirect
302. C2×#333C2×C151semidirect
303. #1481C2×C151semidirect
304. #1477C2×C151semidirect
430. #41SD16×C151semidirect

Maximal subgroups

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

subgroupindex
#3503×C1512
#3246×C1512
#3206×C1512
#3035×C1512
#1645×C1512
#1643×C1512
#1623×C1512
#1622×C1512
C2×#333×C1512
#1481×C1512
#1477×C1512
#18872151