Finite Group Databasebeta

← C151×#18584 #50323509

Subgroups — C151×#18584 #50323509

Order 38656.

882 conjugacy classes of subgroups.

The subgroup lattice has 572 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#3509×C151C211yesmaximal, characteristic, complemented
2#3254×C151C211yesmaximal, characteristic, complemented
3#3141×C151C211yesmaximal, characteristic, complemented
4#3106×C151C211yesmaximal, characteristic
5#1638×C151C212yesmaximal, complemented
6#1636×C151C212yesmaximal, complemented
7#1628×C151C212yesmaximal, complemented
8#1626×C151C212yesmaximal, complemented
9#1549×C151C211yesmaximal, characteristic, complemented
10#1489×C151C211yesmaximal, characteristic, complemented
11#1485×C151C211yesmaximal, characteristic, complemented
12#557×C151—21no—
13#557×C151C2212yes—
14#556×C151—21no—
15#556×C151C2212yes—
16#552×C151—22no—
17#552×C151—22no—
18#541×C151—22no—
19#536×C151—21no—
20#533×C151—21no—
21#533×C151—21no—
22#533×C151C2211yescharacteristic
23#532×C151C2211yescharacteristic
24C2×C4⋊Q8×C151C2211yescharacteristic
25#519×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—
56C2×SD16×C151—21no—
57C2×SD16×C151—22no—
58C2×D8×C151—21no—
59C2×M16×C151—21no—
60C2×M16×C151—21no—
61C4⋊Q8×C151—21no—
62C4⋊Q8×C151—21no—
63C4⋊Q8×C151—22no—
64C4⋊Q8×C151D411yescharacteristic
65C4⋊Q8×C151D412yes—
66C4⋊Q8×C151D411yescharacteristic
67C4⋊Q8×C151C2311yescharacteristic
68C4⋊Q8×C151C2312yes—
69#127×C151C2311yescharacteristic
70#126×C151—24no—
71#126×C151—24no—
72#125×C151—22no—
73#125×C151—24no—
74#125×C151—22no—
75#125×C151—24no—
76#125×C151—21no—
77#124×C151—22no—
78#124×C151—21no—
79#123×C151—24no—
80C22⋊Q8×C151—22no—
81C22⋊Q8×C151—22no—
82C22⋊Q8×C151—22no—
83C22⋊Q8×C151—21no—
84C22⋊Q8×C151—22no—
85C22⋊Q8×C151D412yes—
86#121×C151—21no—
87#121×C151—21no—
88C4×Q8×C151—22no—
89C4×Q8×C151—22no—
90C4×Q8×C151—22no—
91C4×Q8×C151—22no—
92C4×Q8×C151—22no—
93C4×Q8×C151—21no—
94C4×Q8×C151—22no—
95C4×Q8×C151D411yescharacteristic
96C4×Q8×C151C2311yescharacteristic
97C4×Q8×C151C2312yes—
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—24no—
105#117×C151—22no—
106#117×C151—21no—
107#117×C151—22no—
108#117×C151—21no—
109#117×C151D411yescharacteristic
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—41no—
134#41×C151—41no—
135#41×C151—44no—
136C2×Q8×C151—21no—
137C2×Q8×C151—22no—
138C2×Q8×C151—22no—
139C2×Q8×C151—21no—
140C2×Q8×C151—42no—
141C2×Q8×C151—42no—
142C2×Q8×C151C2×D412yes—
143C2×Q8×C151C2×D411yescharacteristic
144C2×D4×C151—21no—
145C2×D4×C151—21no—
146C2×D4×C151—21no—
147C2×D4×C151—21no—
148C2×D4×C151—41no—
149C2×D4×C151C2×D411yescharacteristic
150C22×C4×C151—22no—
151C22×C4×C151—21no—
152C22×C4×C151—21no—
153C22×C4×C151—21no—
154C22×C4×C151—41no—
155C22×C4×C151C2×D411yescharacteristic
156C22×C4×C151C2×D411yescharacteristic
157C22×C4×C151C2×D411yescharacteristic
158SD16×C151—42no—
159SD16×C151—82no—
160D8×C151—42no—
161M16×C151—42no—
162M16×C151—81no—
163C2×C8×C151—21no—
164C2×C8×C151—21no—
165C2×C8×C151—22no—
166C2×C8×C151—22no—
167C4⋊C4×C151—24no—
168C4⋊C4×C151—24no—
169C4⋊C4×C151—24no—
170C4⋊C4×C151—24no—
171C4⋊C4×C151—22no—
172C4⋊C4×C151—22no—
173C4⋊C4×C151—21no—
174C4⋊C4×C151—21no—
175C4⋊C4×C151—21no—
176C4⋊C4×C151—21no—
177C4⋊C4×C151—22no—
178C4⋊C4×C151—22no—
179C4⋊C4×C151—21no—
180C4⋊C4×C151—22no—
181C4⋊C4×C151—21no—
182C4⋊C4×C151—21no—
183C4⋊C4×C151C2×D414yes—
184C4⋊C4×C151C2×D411yescharacteristic
185C4⋊C4×C151C2×D412yes—
186C4⋊C4×C151C2×D411yescharacteristic
187C22⋊C4×C151—24no—
188C22⋊C4×C151—24no—
189C22⋊C4×C151—21no—
190C22⋊C4×C151—22no—
191C22⋊C4×C151—21no—
192C22⋊C4×C151—21no—
193C22⋊C4×C151—41no—
194C22⋊C4×C151—41no—
195C42×C151—24no—
196C42×C151—24no—
197C42×C151—21no—
198C42×C151—21no—
199C42×C151—21no—
200C42×C151—22no—
201C42×C151C2×D411yescharacteristic
202C42×C151C2×D411yescharacteristic
203C42×C151C2×D411yescharacteristic
204C42×C151C2411yescharacteristic
205C23×C151—21no—
206C23×C151—41no—
207C23×C151#12011yescharacteristic
208Q8×C151—21no—
209Q8×C151—21no—
210Q8×C151—22no—
211Q8×C151—22no—
212Q8×C151—44no—
213Q8×C151—42no—
214Q8×C151—42no—
215Q8×C151—42no—
216Q8×C151—42no—
217D4×C151—21no—
218D4×C151—21no—
219D4×C151—42no—
220D4×C151—42no—
221D4×C151—41no—
222D4×C151—41no—
223D4×C151—41no—
224D4×C151—41no—
225D4×C151—82no—
226C2×C4×C151—21no—
227C2×C4×C151—21no—
228C2×C4×C151—21no—
229C2×C4×C151—21no—
230C2×C4×C151—22no—
231C2×C4×C151—24no—
232C2×C4×C151—22no—
233C2×C4×C151—22no—
234C2×C4×C151—21no—
235C2×C4×C151—21no—
236C2×C4×C151—21no—
237C2×C4×C151—42no—
238C2×C4×C151—44no—
239C2×C4×C151—41no—
240C2×C4×C151—41no—
241C2×C4×C151—42no—
242C2×C4×C151—41no—
243C2×C4×C151—82no—
244C2×C4×C151#12011yescharacteristic
245C2×C4×C151#12011yescharacteristic
246C2×C4×C151#12011yescharacteristic
247C2×C4×C151C22×D411yescharacteristic
248C2×C4×C151C22×D411yescharacteristic
249C2×C4×C151C22×D411yescharacteristic
250C8×C151—42no—
251C8×C151—41no—
252C8×C151—41no—
253C8×C151—42no—
254C22×C151—21no—
255C22×C151—21no—
256C22×C151—21no—
257C22×C151—41no—
258C22×C151—41no—
259C22×C151—41no—
260C22×C151—81no—
261C22×C151—81no—
262C22×C151—81no—
263C22×C151C2×#12011yescharacteristic
264C4×C151—21no—
265C4×C151—21no—
266C4×C151—21no—
267C4×C151—41no—
268C4×C151—44no—
269C4×C151—41no—
270C4×C151—42no—
271C4×C151—41no—
272C4×C151—42no—
273C4×C151—81no—
274C4×C151#45412yes—
275C4×C151#57511yescharacteristic
276C4×C151#57511yescharacteristic
277C4×C151#57711yescharacteristic
278C4×C151#57811yescharacteristic
279C2×C151—41no—
280C2×C151—81no—
281C2×C151—161no—
282C2×C151#300511yescharacteristic
283C2×C151#301311yescharacteristic
284C2×C151C2×#45411yescharacteristic
285#18584C15111yesmaximal, characteristic, direct product factor, Sylow
286C151#1858411yescharacteristic, direct product factor, Sylow
287#3509C2×C15111yescharacteristic, complemented
288#3254C2×C15111yescharacteristic, complemented
289#3141C2×C15111yescharacteristic, complemented
290#3106C2×C15111yescharacteristic
291#1638C2×C15112yescomplemented
292#1636C2×C15112yescomplemented
293#1628C2×C15112yescomplemented
294#1626C2×C15112yescomplemented
295#1549C2×C15111yescharacteristic, complemented
296#1489C2×C15111yescharacteristic, complemented
297#1485C2×C15111yescharacteristic, complemented
298#557—21no—
299#557C22×C15112yes—
300#556—21no—
301#556C22×C15112yes—
302#552—22no—
303#552—22no—
304#541—22no—
305#536—21no—
306#533—21no—
307#533—21no—
308#533C22×C15111yescharacteristic
309#532C22×C15111yescharacteristic
310C2×C4⋊Q8C22×C15111yescharacteristic
311#519—21no—
312C4×#41C22×C15111yescharacteristic
313#489—22no—
314#487C22×C15112yes—
315#486C22×C15112yes—
316#482—21no—
317#477C22×C15111yescharacteristic
318#477C22×C15112yes—
319#476C22×C15111yescharacteristic
320#474—21no—
321#468—22no—
322#461—21no—
323#460C22×C15111yescharacteristic
324#460C22×C15112yes—
325#459C22×C15111yescharacteristic
326#449—21no—
327C4×SD16—21no—
328C4×D8—21no—
329#431C22×C15111yescharacteristic
330#423C22×C15111yescharacteristic
331#417—22no—
332C4×M16C22×C15111yescharacteristic
333#332C22×C15112yes—
334#332C22×C15112yes—
335Q8⋊C8C22×C15112yes—
336Q8⋊C8C22×C15112yes—
337Q8⋊C8C22×C15112yes—
338D4⋊C8C22×C15112yes—
339C2×#41—21no—
340C2×#41D4×C15111yescharacteristic
341C22×Q8—21no—
342C2×SD16—21no—
343C2×SD16—22no—
344C2×D8—21no—
345C2×M16—21no—
346C2×M16—21no—
347C4⋊Q8—22no—
348C4⋊Q8—21no—
349C4⋊Q8—21no—
350C4⋊Q8D4×C15111yescharacteristic
351C4⋊Q8D4×C15112yes—
352C4⋊Q8D4×C15111yescharacteristic
353C4⋊Q8C23×C15111yescharacteristic
354C4⋊Q8C23×C15112yes—
355#127C23×C15111yescharacteristic
356#126—24no—
357#126—24no—
358#125—22no—
359#125—24no—
360#125—22no—
361#125—24no—
362#125—21no—
363#124—22no—
364#124—21no—
365#123—24no—
366C22⋊Q8—22no—
367C22⋊Q8—22no—
368C22⋊Q8—22no—
369C22⋊Q8—22no—
370C22⋊Q8—21no—
371C22⋊Q8D4×C15112yes—
372#121—21no—
373#121—21no—
374C4×Q8—22no—
375C4×Q8—22no—
376C4×Q8—22no—
377C4×Q8—22no—
378C4×Q8—22no—
379C4×Q8—22no—
380C4×Q8—21no—
381C4×Q8D4×C15111yescharacteristic
382C4×Q8C23×C15111yescharacteristic
383C4×Q8C23×C15112yes—
384C4×D4—21no—
385C4×D4—21no—
386C4×D4—21no—
387C4×D4—21no—
388C4×D4D4×C15111yescharacteristic
389C4×D4C23×C15111yescharacteristic
390#117—24no—
391#117—22no—
392#117—21no—
393#117—22no—
394#117—21no—
395#117D4×C15111yescharacteristic
396C2×C4⋊C4—21no—
397C2×C4⋊C4D4×C15112yes—
398C2×C42—21no—
399C2×C42C23×C15111yescharacteristic
400#107—21no—
401#107—22no—
402#106—21no—
403C4⋊C8—21no—
404C4⋊C8C23×C15112yes—
405C4⋊C8C23×C15111yescharacteristic
406C4⋊C8C23×C15111yescharacteristic
407#103—21no—
408#103—22no—
409#103—24no—
410#102—21no—
411#102—24no—
412#102—21no—
413#102—21no—
414#102—22no—
415C22⋊C8—21no—
416#97—21no—
417C4×C8—21no—
418C4×C8C23×C15112yes—
419#41—41no—
420#41—41no—
421#41—44no—
422C2×Q8—21no—
423C2×Q8—22no—
424C2×Q8—22no—
425C2×Q8—21no—
426C2×Q8—42no—
427C2×Q8—42no—
428C2×Q8C2×D4×C15112yes—
429C2×Q8C2×D4×C15111yescharacteristic
430C2×D4—21no—
431C2×D4—21no—
432C2×D4—21no—
433C2×D4—21no—
434C2×D4—41no—
435C2×D4C2×D4×C15111yescharacteristic
436C22×C4—22no—
437C22×C4—21no—
438C22×C4—21no—
439C22×C4—21no—
440C22×C4—41no—
441C22×C4C2×D4×C15111yescharacteristic
442C22×C4C2×D4×C15111yescharacteristic
443C22×C4C2×D4×C15111yescharacteristic
444SD16—42no—
445SD16—82no—
446D8—42no—
447M16—42no—
448M16—81no—
449C2×C8—21no—
450C2×C8—21no—
451C2×C8—22no—
452C2×C8—22no—
453C4⋊C4—24no—
454C4⋊C4—24no—
455C4⋊C4—24no—
456C4⋊C4—24no—
457C4⋊C4—22no—
458C4⋊C4—22no—
459C4⋊C4—21no—
460C4⋊C4—21no—
461C4⋊C4—21no—
462C4⋊C4—21no—
463C4⋊C4—22no—
464C4⋊C4—22no—
465C4⋊C4—21no—
466C4⋊C4—22no—
467C4⋊C4—21no—
468C4⋊C4—21no—
469C4⋊C4C2×D4×C15114yes—
470C4⋊C4C2×D4×C15111yescharacteristic
471C4⋊C4C2×D4×C15112yes—
472C4⋊C4C2×D4×C15111yescharacteristic
473C22⋊C4—24no—
474C22⋊C4—24no—
475C22⋊C4—21no—
476C22⋊C4—22no—
477C22⋊C4—21no—
478C22⋊C4—21no—
479C22⋊C4—41no—
480C22⋊C4—41no—
481C42—24no—
482C42—24no—
483C42—21no—
484C42—21no—
485C42—21no—
486C42—22no—
487C42C2×D4×C15111yescharacteristic
488C42C2×D4×C15111yescharacteristic
489C42C2×D4×C15111yescharacteristic
490C42C24×C15111yescharacteristic
491C23—21no—
492C23—41no—
493C23#120×C15111yescharacteristic
494Q8—21no—
495Q8—21no—
496Q8—22no—
497Q8—22no—
498Q8—44no—
499Q8—42no—
500Q8—42no—
501Q8—42no—
502Q8—42no—
503D4—21no—
504D4—21no—
505D4—42no—
506D4—42no—
507D4—41no—
508D4—41no—
509D4—41no—
510D4—41no—
511D4—82no—
512C2×C4—22no—
513C2×C4—21no—
514C2×C4—21no—
515C2×C4—21no—
516C2×C4—21no—
517C2×C4—21no—
518C2×C4—21no—
519C2×C4—22no—
520C2×C4—22no—
521C2×C4—24no—
522C2×C4—21no—
523C2×C4—42no—
524C2×C4—44no—
525C2×C4—42no—
526C2×C4—41no—
527C2×C4—41no—
528C2×C4—41no—
529C2×C4—82no—
530C2×C4#120×C15111yescharacteristic
531C2×C4#120×C15111yescharacteristic
532C2×C4#120×C15111yescharacteristic
533C2×C4C22×D4×C15111yescharacteristic
534C2×C4C22×D4×C15111yescharacteristic
535C2×C4C22×D4×C15111yescharacteristic
536C8—42no—
537C8—41no—
538C8—41no—
539C8—42no—
540C22—21no—
541C22—21no—
542C22—21no—
543C22—41no—
544C22—41no—
545C22—41no—
546C22—81no—
547C22—81no—
548C22—81no—
549C22C2×#120×C15111yescharacteristic
550C4—21no—
551C4—21no—
552C4—21no—
553C4—41no—
554C4—44no—
555C4—41no—
556C4—42no—
557C4—41no—
558C4—42no—
559C4—81no—
560C4#454×C15112yes—
561C4#575×C15111yescharacteristic
562C4#575×C15111yescharacteristic
563C4#577×C15111yescharacteristic
564C4#578×C15111yescharacteristic
565C2—41no—
566C2—81no—
567C2—161no—
568C2#3005×C15111yescharacteristic
569C2#3013×C15111yescharacteristic
570C2C2×#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. #3509×C151C2semidirect
2. #3254×C151C2semidirect
3. #3141×C151C2semidirect
5. #1638×C151C2semidirect
6. #1636×C151C2semidirect
7. #1628×C151C2semidirect
8. #1626×C151C2semidirect
9. #1549×C151C2semidirect
10. #1489×C151C2semidirect
11. #1485×C151C2semidirect
285. #18584C151direct (N × H)
286. C151#18584direct (N × H)
287. #3509C2×C151semidirect
288. #3254C2×C151semidirect
289. #3141C2×C151semidirect
291. #1638C2×C151semidirect
292. #1636C2×C151semidirect
293. #1628C2×C151semidirect
294. #1626C2×C151semidirect
295. #1549C2×C151semidirect
296. #1489C2×C151semidirect
297. #1485C2×C151semidirect

Maximal subgroups

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

subgroupindex
#3509×C1512
#3254×C1512
#3141×C1512
#3106×C1512
#1638×C1512
#1636×C1512
#1628×C1512
#1626×C1512
#1549×C1512
#1489×C1512
#1485×C1512
#18584151