Finite Group Databasebeta

← C151×#18583 #50323508

Subgroups — C151×#18583 #50323508

Order 38656.

916 conjugacy classes of subgroups.

The subgroup lattice has 580 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#3503×C151C211yesmaximal, characteristic, complemented
2#3254×C151C211yesmaximal, characteristic, complemented
3#3141×C151C211yesmaximal, characteristic, complemented
4#3106×C151C211yesmaximal, characteristic
5#1637×C151C212yesmaximal, complemented
6#1636×C151C212yesmaximal, complemented
7#1627×C151C212yesmaximal, complemented
8#1626×C151C212yesmaximal, complemented
9#1546×C151C211yesmaximal, characteristic, complemented
10#1489×C151C211yesmaximal, characteristic, complemented
11#1485×C151C211yesmaximal, characteristic, complemented
12Q82×C151—21no—
13#557×C151C2212yes—
14#554×C151—21no—
15#554×C151—22no—
16D4×Q8×C151—22no—
17D4×Q8×C151C2212yes—
18#544×C151—22no—
19#544×C151—21no—
20#533×C151—21no—
21#533×C151C2211yescharacteristic
22#532×C151C2211yescharacteristic
23C2×C4⋊Q8×C151—21no—
24C2×C4⋊Q8×C151C2211yescharacteristic
25#520×C151—21no—
26C4×#41×C151C2211yescharacteristic
27#489×C151—22no—
28#487×C151C2212yes—
29#486×C151C2212yes—
30#482×C151—21no—
31#477×C151C2211yescharacteristic
32#477×C151C2212yes—
33#476×C151C2211yescharacteristic
34#474×C151—21no—
35#468×C151—22no—
36#461×C151—21no—
37#460×C151C2211yescharacteristic
38#460×C151C2212yes—
39#459×C151C2211yescharacteristic
40#449×C151—21no—
41C4×SD16×C151—21no—
42C4×D8×C151—21no—
43#431×C151C2211yescharacteristic
44#423×C151C2211yescharacteristic
45#417×C151—22no—
46C4×M16×C151C2211yescharacteristic
47#332×C151C2212yes—
48#332×C151C2212yes—
49Q8⋊C8×C151C2212yes—
50Q8⋊C8×C151C2212yes—
51Q8⋊C8×C151C2212yes—
52D4⋊C8×C151C2212yes—
53C2×#41×C151—21no—
54C2×#41×C151D411yescharacteristic
55C22×Q8×C151—21no—
56C22×Q8×C151—22no—
57C2×SD16×C151—21no—
58C2×SD16×C151—22no—
59C2×D8×C151—21no—
60C2×M16×C151—21no—
61C2×M16×C151—21no—
62C4⋊Q8×C151—22no—
63C4⋊Q8×C151—22no—
64C4⋊Q8×C151—24no—
65C4⋊Q8×C151—22no—
66C4⋊Q8×C151—21no—
67C4⋊Q8×C151—21no—
68C4⋊Q8×C151—22no—
69C4⋊Q8×C151D411yescharacteristic
70C4⋊Q8×C151D412yes—
71C4⋊Q8×C151D411yescharacteristic
72C4⋊Q8×C151C2311yescharacteristic
73C4⋊Q8×C151C2312yes—
74#127×C151C2311yescharacteristic
75#125×C151—22no—
76#125×C151—24no—
77#125×C151—22no—
78#125×C151—21no—
79#124×C151—21no—
80C22⋊Q8×C151—22no—
81C22⋊Q8×C151—24no—
82C22⋊Q8×C151—24no—
83C22⋊Q8×C151—21no—
84C22⋊Q8×C151—22no—
85C22⋊Q8×C151—24no—
86C22⋊Q8×C151D412yes—
87#121×C151—21no—
88#121×C151—21no—
89C4×Q8×C151—22no—
90C4×Q8×C151—22no—
91C4×Q8×C151—21no—
92C4×Q8×C151—22no—
93C4×Q8×C151D411yescharacteristic
94C4×Q8×C151C2311yescharacteristic
95C4×Q8×C151C2312yes—
96C4×D4×C151—24no—
97C4×D4×C151—22no—
98C4×D4×C151—21no—
99C4×D4×C151—21no—
100C4×D4×C151—21no—
101C4×D4×C151—21no—
102C4×D4×C151D411yescharacteristic
103C4×D4×C151C2311yescharacteristic
104#117×C151—22no—
105#117×C151—21no—
106#117×C151—21no—
107#117×C151D411yescharacteristic
108C2×C4⋊C4×C151—22no—
109C2×C4⋊C4×C151—22no—
110C2×C4⋊C4×C151—21no—
111C2×C4⋊C4×C151D412yes—
112C2×C42×C151—21no—
113C2×C42×C151C2311yescharacteristic
114#107×C151—21no—
115#107×C151—22no—
116#106×C151—21no—
117C4⋊C8×C151—21no—
118C4⋊C8×C151C2312yes—
119C4⋊C8×C151C2311yescharacteristic
120C4⋊C8×C151C2311yescharacteristic
121#103×C151—24no—
122#103×C151—21no—
123#103×C151—22no—
124#102×C151—21no—
125#102×C151—24no—
126#102×C151—21no—
127#102×C151—21no—
128#102×C151—22no—
129C22⋊C8×C151—21no—
130#97×C151—21no—
131C4×C8×C151—21no—
132C4×C8×C151C2312yes—
133#41×C151—22no—
134#41×C151—22no—
135#41×C151—44no—
136C2×Q8×C151—24no—
137C2×Q8×C151—21no—
138C2×Q8×C151—22no—
139C2×Q8×C151—22no—
140C2×Q8×C151—21no—
141C2×Q8×C151—81no—
142C2×Q8×C151—81no—
143C2×Q8×C151—82no—
144C2×Q8×C151—82no—
145C2×Q8×C151C2×D412yes—
146C2×Q8×C151C2×D411yescharacteristic
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
162SD16×C151—42no—
163SD16×C151—82no—
164D8×C151—42no—
165M16×C151—42no—
166M16×C151—81no—
167C2×C8×C151—21no—
168C2×C8×C151—21no—
169C2×C8×C151—22no—
170C2×C8×C151—22no—
171C4⋊C4×C151—24no—
172C4⋊C4×C151—24no—
173C4⋊C4×C151—24no—
174C4⋊C4×C151—24no—
175C4⋊C4×C151—22no—
176C4⋊C4×C151—21no—
177C4⋊C4×C151—21no—
178C4⋊C4×C151—22no—
179C4⋊C4×C151—21no—
180C4⋊C4×C151—21no—
181C4⋊C4×C151—22no—
182C4⋊C4×C151—22no—
183C4⋊C4×C151—21no—
184C4⋊C4×C151—22no—
185C4⋊C4×C151—21no—
186C4⋊C4×C151—21no—
187C4⋊C4×C151C2×D414yes—
188C4⋊C4×C151C2×D411yescharacteristic
189C4⋊C4×C151C2×D411yescharacteristic
190C4⋊C4×C151C2×D412yes—
191C22⋊C4×C151—24no—
192C22⋊C4×C151—22no—
193C22⋊C4×C151—21no—
194C22⋊C4×C151—21no—
195C22⋊C4×C151—21no—
196C22⋊C4×C151—41no—
197C22⋊C4×C151—41no—
198C42×C151—24no—
199C42×C151—21no—
200C42×C151—21no—
201C42×C151—21no—
202C42×C151—22no—
203C42×C151C2×D411yescharacteristic
204C42×C151C2×D411yescharacteristic
205C42×C151C2×D411yescharacteristic
206C42×C151C2411yescharacteristic
207C23×C151—21no—
208C23×C151—41no—
209C23×C151#12011yescharacteristic
210Q8×C151—21no—
211Q8×C151—22no—
212Q8×C151—22no—
213Q8×C151—42no—
214Q8×C151—42no—
215Q8×C151—42no—
216Q8×C151—42no—
217Q8×C151—82no—
218Q8×C151—84no—
219Q8×C151#13712yes—
220D4×C151—24no—
221D4×C151—21no—
222D4×C151—42no—
223D4×C151—41no—
224D4×C151—41no—
225D4×C151—41no—
226D4×C151—41no—
227D4×C151—82no—
228D4×C151#13712yes—
229C2×C4×C151—24no—
230C2×C4×C151—21no—
231C2×C4×C151—21no—
232C2×C4×C151—21no—
233C2×C4×C151—21no—
234C2×C4×C151—21no—
235C2×C4×C151—22no—
236C2×C4×C151—21no—
237C2×C4×C151—24no—
238C2×C4×C151—22no—
239C2×C4×C151—22no—
240C2×C4×C151—21no—
241C2×C4×C151—41no—
242C2×C4×C151—41no—
243C2×C4×C151—42no—
244C2×C4×C151—41no—
245C2×C4×C151—82no—
246C2×C4×C151—84no—
247C2×C4×C151—82no—
248C2×C4×C151#12011yescharacteristic
249C2×C4×C151#12011yescharacteristic
250C2×C4×C151#12011yescharacteristic
251C2×C4×C151C22×D411yescharacteristic
252C2×C4×C151C22×D411yescharacteristic
253C2×C4×C151C22×D411yescharacteristic
254C8×C151—42no—
255C8×C151—41no—
256C8×C151—41no—
257C8×C151—42no—
258C22×C151—21no—
259C22×C151—22no—
260C22×C151—21no—
261C22×C151—21no—
262C22×C151—41no—
263C22×C151—41no—
264C22×C151—81no—
265C22×C151—81no—
266C22×C151—81no—
267C22×C151C2×#12011yescharacteristic
268C4×C151—21no—
269C4×C151—22no—
270C4×C151—21no—
271C4×C151—21no—
272C4×C151—41no—
273C4×C151—42no—
274C4×C151—44no—
275C4×C151—41no—
276C4×C151—42no—
277C4×C151—81no—
278C4×C151#45412yes—
279C4×C151C2×#13711yescharacteristic
280C4×C151C2×#13711yescharacteristic
281C4×C151#57611yescharacteristic
282C4×C151#57711yescharacteristic
283C2×C151—41no—
284C2×C151—42no—
285C2×C151—161no—
286C2×C151#300411yescharacteristic
287C2×C151#301211yescharacteristic
288C2×C151C2×#45411yescharacteristic
289#18583C15111yesmaximal, characteristic, direct product factor, Sylow
290C151#1858311yescharacteristic, direct product factor, Sylow
291#3503C2×C15111yescharacteristic, complemented
292#3254C2×C15111yescharacteristic, complemented
293#3141C2×C15111yescharacteristic, complemented
294#3106C2×C15111yescharacteristic
295#1637C2×C15112yescomplemented
296#1636C2×C15112yescomplemented
297#1627C2×C15112yescomplemented
298#1626C2×C15112yescomplemented
299#1546C2×C15111yescharacteristic, complemented
300#1489C2×C15111yescharacteristic, complemented
301#1485C2×C15111yescharacteristic, complemented
302Q82—21no—
303#557C22×C15112yes—
304#554—21no—
305#554—22no—
306D4×Q8—22no—
307D4×Q8C22×C15112yes—
308#544—22no—
309#544—21no—
310#533—21no—
311#533C22×C15111yescharacteristic
312#532C22×C15111yescharacteristic
313C2×C4⋊Q8—21no—
314C2×C4⋊Q8C22×C15111yescharacteristic
315#520—21no—
316C4×#41C22×C15111yescharacteristic
317#489—22no—
318#487C22×C15112yes—
319#486C22×C15112yes—
320#482—21no—
321#477C22×C15111yescharacteristic
322#477C22×C15112yes—
323#476C22×C15111yescharacteristic
324#474—21no—
325#468—22no—
326#461—21no—
327#460C22×C15111yescharacteristic
328#460C22×C15112yes—
329#459C22×C15111yescharacteristic
330#449—21no—
331C4×SD16—21no—
332C4×D8—21no—
333#431C22×C15111yescharacteristic
334#423C22×C15111yescharacteristic
335#417—22no—
336C4×M16C22×C15111yescharacteristic
337#332C22×C15112yes—
338#332C22×C15112yes—
339Q8⋊C8C22×C15112yes—
340Q8⋊C8C22×C15112yes—
341Q8⋊C8C22×C15112yes—
342D4⋊C8C22×C15112yes—
343C2×#41—21no—
344C2×#41D4×C15111yescharacteristic
345C22×Q8—22no—
346C22×Q8—21no—
347C2×SD16—21no—
348C2×SD16—22no—
349C2×D8—21no—
350C2×M16—21no—
351C2×M16—21no—
352C4⋊Q8—22no—
353C4⋊Q8—22no—
354C4⋊Q8—24no—
355C4⋊Q8—22no—
356C4⋊Q8—22no—
357C4⋊Q8—21no—
358C4⋊Q8—21no—
359C4⋊Q8D4×C15111yescharacteristic
360C4⋊Q8D4×C15112yes—
361C4⋊Q8D4×C15111yescharacteristic
362C4⋊Q8C23×C15111yescharacteristic
363C4⋊Q8C23×C15112yes—
364#127C23×C15111yescharacteristic
365#125—22no—
366#125—24no—
367#125—22no—
368#125—21no—
369#124—21no—
370C22⋊Q8—22no—
371C22⋊Q8—24no—
372C22⋊Q8—24no—
373C22⋊Q8—21no—
374C22⋊Q8—22no—
375C22⋊Q8—24no—
376C22⋊Q8D4×C15112yes—
377#121—21no—
378#121—21no—
379C4×Q8—22no—
380C4×Q8—22no—
381C4×Q8—22no—
382C4×Q8—21no—
383C4×Q8D4×C15111yescharacteristic
384C4×Q8C23×C15111yescharacteristic
385C4×Q8C23×C15112yes—
386C4×D4—24no—
387C4×D4—22no—
388C4×D4—21no—
389C4×D4—21no—
390C4×D4—21no—
391C4×D4—21no—
392C4×D4D4×C15111yescharacteristic
393C4×D4C23×C15111yescharacteristic
394#117—22no—
395#117—21no—
396#117—21no—
397#117D4×C15111yescharacteristic
398C2×C4⋊C4—22no—
399C2×C4⋊C4—22no—
400C2×C4⋊C4—21no—
401C2×C4⋊C4D4×C15112yes—
402C2×C42—21no—
403C2×C42C23×C15111yescharacteristic
404#107—21no—
405#107—22no—
406#106—21no—
407C4⋊C8—21no—
408C4⋊C8C23×C15112yes—
409C4⋊C8C23×C15111yescharacteristic
410C4⋊C8C23×C15111yescharacteristic
411#103—21no—
412#103—22no—
413#103—24no—
414#102—21no—
415#102—24no—
416#102—21no—
417#102—21no—
418#102—22no—
419C22⋊C8—21no—
420#97—21no—
421C4×C8—21no—
422C4×C8C23×C15112yes—
423#41—22no—
424#41—22no—
425#41—44no—
426C2×Q8—24no—
427C2×Q8—21no—
428C2×Q8—22no—
429C2×Q8—22no—
430C2×Q8—21no—
431C2×Q8—81no—
432C2×Q8—81no—
433C2×Q8—82no—
434C2×Q8—82no—
435C2×Q8C2×D4×C15112yes—
436C2×Q8C2×D4×C15111yescharacteristic
437C2×D4—21no—
438C2×D4—21no—
439C2×D4—21no—
440C2×D4—21no—
441C2×D4—41no—
442C2×D4C2×D4×C15111yescharacteristic
443C22×C4—21no—
444C22×C4—24no—
445C22×C4—22no—
446C22×C4—21no—
447C22×C4—21no—
448C22×C4—41no—
449C22×C4C2×D4×C15111yescharacteristic
450C22×C4C2×D4×C15111yescharacteristic
451C22×C4C2×D4×C15111yescharacteristic
452SD16—42no—
453SD16—82no—
454D8—42no—
455M16—42no—
456M16—81no—
457C2×C8—21no—
458C2×C8—21no—
459C2×C8—22no—
460C2×C8—22no—
461C4⋊C4—24no—
462C4⋊C4—24no—
463C4⋊C4—24no—
464C4⋊C4—24no—
465C4⋊C4—21no—
466C4⋊C4—22no—
467C4⋊C4—21no—
468C4⋊C4—22no—
469C4⋊C4—21no—
470C4⋊C4—21no—
471C4⋊C4—22no—
472C4⋊C4—22no—
473C4⋊C4—21no—
474C4⋊C4—22no—
475C4⋊C4—21no—
476C4⋊C4—21no—
477C4⋊C4C2×D4×C15114yes—
478C4⋊C4C2×D4×C15111yescharacteristic
479C4⋊C4C2×D4×C15111yescharacteristic
480C4⋊C4C2×D4×C15112yes—
481C22⋊C4—24no—
482C22⋊C4—22no—
483C22⋊C4—21no—
484C22⋊C4—21no—
485C22⋊C4—21no—
486C22⋊C4—41no—
487C22⋊C4—41no—
488C42—24no—
489C42—21no—
490C42—21no—
491C42—21no—
492C42—22no—
493C42C2×D4×C15111yescharacteristic
494C42C2×D4×C15111yescharacteristic
495C42C2×D4×C15111yescharacteristic
496C42C24×C15111yescharacteristic
497C23—21no—
498C23—41no—
499C23#120×C15111yescharacteristic
500Q8—21no—
501Q8—22no—
502Q8—22no—
503Q8—42no—
504Q8—42no—
505Q8—42no—
506Q8—42no—
507Q8—82no—
508Q8—84no—
509Q8#137×C15112yes—
510D4—24no—
511D4—21no—
512D4—42no—
513D4—41no—
514D4—41no—
515D4—41no—
516D4—41no—
517D4—82no—
518D4#137×C15112yes—
519C2×C4—24no—
520C2×C4—21no—
521C2×C4—22no—
522C2×C4—21no—
523C2×C4—21no—
524C2×C4—21no—
525C2×C4—21no—
526C2×C4—22no—
527C2×C4—21no—
528C2×C4—21no—
529C2×C4—22no—
530C2×C4—24no—
531C2×C4—42no—
532C2×C4—41no—
533C2×C4—41no—
534C2×C4—41no—
535C2×C4—82no—
536C2×C4—84no—
537C2×C4—82no—
538C2×C4#120×C15111yescharacteristic
539C2×C4#120×C15111yescharacteristic
540C2×C4#120×C15111yescharacteristic
541C2×C4C22×D4×C15111yescharacteristic
542C2×C4C22×D4×C15111yescharacteristic
543C2×C4C22×D4×C15111yescharacteristic
544C8—42no—
545C8—41no—
546C8—41no—
547C8—42no—
548C22—21no—
549C22—22no—
550C22—21no—
551C22—21no—
552C22—41no—
553C22—41no—
554C22—81no—
555C22—81no—
556C22—81no—
557C22C2×#120×C15111yescharacteristic
558C4—21no—
559C4—22no—
560C4—21no—
561C4—21no—
562C4—41no—
563C4—42no—
564C4—44no—
565C4—41no—
566C4—42no—
567C4—81no—
568C4#454×C15112yes—
569C4C2×#137×C15111yescharacteristic
570C4C2×#137×C15111yescharacteristic
571C4#576×C15111yescharacteristic
572C4#577×C15111yescharacteristic
573C2—41no—
574C2—42no—
575C2—161no—
576C2#3004×C15111yescharacteristic
577C2#3012×C15111yescharacteristic
578C2C2×#454×C15111yescharacteristic
subgroupG/H
center, socleC22×C151C2×#120
commutator, Frattini, cosocleC42C24×C151
prime radical#3106×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. #3254×C151C2semidirect
3. #3141×C151C2semidirect
5. #1637×C151C2semidirect
6. #1636×C151C2semidirect
7. #1627×C151C2semidirect
8. #1626×C151C2semidirect
9. #1546×C151C2semidirect
10. #1489×C151C2semidirect
11. #1485×C151C2semidirect
289. #18583C151direct (N × H)
290. C151#18583direct (N × H)
291. #3503C2×C151semidirect
292. #3254C2×C151semidirect
293. #3141C2×C151semidirect
295. #1637C2×C151semidirect
296. #1636C2×C151semidirect
297. #1627C2×C151semidirect
298. #1626C2×C151semidirect
299. #1546C2×C151semidirect
300. #1489C2×C151semidirect
301. #1485C2×C151semidirect

Maximal subgroups

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

subgroupindex
#3503×C1512
#3254×C1512
#3141×C1512
#3106×C1512
#1637×C1512
#1636×C1512
#1627×C1512
#1626×C1512
#1546×C1512
#1489×C1512
#1485×C1512
#18583151