Finite Group Databasebeta

← C151×#18687 #50323612

Subgroups — C151×#18687 #50323612

Order 38656.

1010 conjugacy classes of subgroups.

The subgroup lattice has 582 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#3548×C151C211yesmaximal, characteristic, complemented
2#3254×C151C211yesmaximal, characteristic, complemented
3#3253×C151C211yesmaximal, characteristic, complemented
4#3147×C151C211yesmaximal, characteristic, complemented
5#1632×C151C212yesmaximal, complemented
6#1631×C151C212yesmaximal, complemented
7#1622×C151C212yesmaximal, complemented
8#1621×C151C212yesmaximal, complemented
9#1560×C151C211yesmaximal, characteristic, complemented
10#1493×C151C211yesmaximal, characteristic, complemented
11#1492×C151C211yesmaximal, characteristic, complemented
12C2×#135×C151—22no—
13#562×C151—22no—
14#554×C151—21no—
15#554×C151C2212yes—
16#550×C151—21no—
17#550×C151C2212yes—
18#547×C151—21no—
19#547×C151—21no—
20#540×C151—22no—
21#537×C151—22no—
22#537×C151—22no—
23#533×C151C2211yescharacteristic
24#532×C151C2211yescharacteristic
25#532×C151C2211yescharacteristic
26#532×C151C2211yescharacteristic
27#495×C151—22no—
28#494×C151C2211yescharacteristic
29#493×C151C2211yescharacteristic
30#492×C151C2211yescharacteristic
31#492×C151C2211yescharacteristic
32#477×C151C2212yes—
33#476×C151—21no—
34#476×C151C2212yes—
35#474×C151—21no—
36#469×C151—22no—
37#468×C151—22no—
38#461×C151—21no—
39#460×C151C2212yes—
40#459×C151—21no—
41#459×C151C2212yes—
42#423×C151C2211yescharacteristic
43#423×C151C2211yescharacteristic
44C2×C4×C8×C151C2211yescharacteristic
45#333×C151C2212yes—
46#331×C151C2212yes—
47Q8⋊C8×C151C2212yes—
48Q8⋊C8×C151C2212yes—
49D4⋊C8×C151C2212yes—
50D4⋊C8×C151C2212yes—
51C2×#41×C151—21no—
52C2×#41×C151—22no—
53C2×#41×C151—21no—
54C2×#41×C151—22no—
55C2×#41×C151D412yes—
56#135×C151—48no—
57C2×Q16×C151—22no—
58C2×SD16×C151—22no—
59C2×SD16×C151—22no—
60C2×SD16×C151—22no—
61C2×D8×C151—22no—
62C2×D8×C151—22no—
63C2×M16×C151—21no—
64C2×M16×C151—21no—
65C22×C8×C151—21no—
66C4⋊Q8×C151D411yescharacteristic
67C4⋊Q8×C151D411yescharacteristic
68C4⋊Q8×C151D411yescharacteristic
69C4⋊Q8×C151C2311yescharacteristic
70C4⋊Q8×C151C2311yescharacteristic
71#127×C151—22no—
72#127×C151D411yescharacteristic
73#127×C151C2311yescharacteristic
74#127×C151C2311yescharacteristic
75#125×C151—22no—
76#125×C151—21no—
77#124×C151—21no—
78#124×C151—21no—
79#124×C151D412yes—
80#123×C151—24no—
81#123×C151—24no—
82C22⋊Q8×C151—22no—
83C22⋊Q8×C151—24no—
84C22⋊Q8×C151—21no—
85C22⋊Q8×C151—22no—
86C22⋊Q8×C151—24no—
87C22⋊Q8×C151D412yes—
88#121×C151—24no—
89#121×C151—24no—
90#121×C151—22no—
91#121×C151—24no—
92#121×C151—24no—
93#121×C151—21no—
94#121×C151—21no—
95#121×C151—21no—
96#121×C151—22no—
97#121×C151—21no—
98#121×C151—21no—
99#121×C151D412yes—
100C4×Q8×C151—21no—
101C4×Q8×C151C2312yes—
102C4×D4×C151—22no—
103C4×D4×C151—22no—
104C4×D4×C151—21no—
105C4×D4×C151—21no—
106C4×D4×C151—21no—
107C4×D4×C151—21no—
108C4×D4×C151—21no—
109C4×D4×C151C2312yes—
110#117×C151—21no—
111C2×C4⋊C4×C151—22no—
112C2×C4⋊C4×C151—22no—
113C2×C42×C151C2311yescharacteristic
114#107×C151—22no—
115#106×C151—22no—
116C4⋊C8×C151—21no—
117C4⋊C8×C151—21no—
118C4⋊C8×C151C2312yes—
119C4⋊C8×C151C2312yes—
120#103×C151—22no—
121#102×C151—22no—
122#102×C151—22no—
123#102×C151—22no—
124C4×C8×C151—21no—
125C4×C8×C151C2311yescharacteristic
126C4×C8×C151C2311yescharacteristic
127#41×C151—44no—
128#41×C151—44no—
129#41×C151—81no—
130#41×C151—81no—
131#41×C151—82no—
132#41×C151—82no—
133#41×C151—84no—
134C2×Q8×C151—21no—
135C2×Q8×C151—21no—
136C2×Q8×C151—21no—
137C2×Q8×C151C2×D412yes—
138C2×Q8×C151C2×D412yes—
139C2×D4×C151—24no—
140C2×D4×C151—24no—
141C2×D4×C151—22no—
142C2×D4×C151—22no—
143C2×D4×C151—21no—
144C2×D4×C151—21no—
145C2×D4×C151—21no—
146C2×D4×C151—21no—
147C2×D4×C151—21no—
148C2×D4×C151—21no—
149C2×D4×C151—21no—
150C2×D4×C151—41no—
151C2×D4×C151C2×D412yes—
152C2×D4×C151C2×D412yes—
153C22×C4×C151—24no—
154C22×C4×C151—24no—
155C22×C4×C151—22no—
156C22×C4×C151—22no—
157C22×C4×C151—41no—
158C22×C4×C151C2×D411yescharacteristic
159C22×C4×C151C2×D411yescharacteristic
160C22×C4×C151C2×D411yescharacteristic
161Q16×C151—44no—
162SD16×C151—44no—
163SD16×C151—44no—
164SD16×C151—82no—
165D8×C151—44no—
166D8×C151—82no—
167M16×C151—81no—
168M16×C151—81no—
169C2×C8×C151—24no—
170C2×C8×C151—21no—
171C2×C8×C151—21no—
172C2×C8×C151—22no—
173C2×C8×C151—22no—
174C4⋊C4×C151—24no—
175C4⋊C4×C151—24no—
176C4⋊C4×C151—21no—
177C4⋊C4×C151—21no—
178C4⋊C4×C151—21no—
179C4⋊C4×C151—21no—
180C4⋊C4×C151—22no—
181C4⋊C4×C151—21no—
182C4⋊C4×C151—21no—
183C4⋊C4×C151—22no—
184C4⋊C4×C151—21no—
185C4⋊C4×C151—21no—
186C4⋊C4×C151C2×D412yes—
187C4⋊C4×C151C2×D412yes—
188C22⋊C4×C151—24no—
189C22⋊C4×C151—24no—
190C22⋊C4×C151—22no—
191C22⋊C4×C151—22no—
192C22⋊C4×C151—22no—
193C22⋊C4×C151—22no—
194C22⋊C4×C151—22no—
195C22⋊C4×C151—41no—
196C22⋊C4×C151—41no—
197C42×C151—22no—
198C42×C151C2×D411yescharacteristic
199C42×C151C2×D411yescharacteristic
200C42×C151C2×D411yescharacteristic
201C42×C151C2411yescharacteristic
202C23×C151—22no—
203C23×C151—22no—
204C23×C151—41no—
205C23×C151#12011yescharacteristic
206Q8×C151—22no—
207Q8×C151—22no—
208Q8×C151—42no—
209Q8×C151—42no—
210Q8×C151—42no—
211Q8×C151—81no—
212D4×C151—22no—
213D4×C151—22no—
214D4×C151—42no—
215D4×C151—42no—
216D4×C151—41no—
217D4×C151—41no—
218D4×C151—41no—
219D4×C151—41no—
220D4×C151—41no—
221D4×C151—41no—
222D4×C151—41no—
223D4×C151—41no—
224D4×C151—42no—
225D4×C151—81no—
226D4×C151—82no—
227D4×C151—82no—
228D4×C151—84no—
229D4×C151—84no—
230D4×C151—82no—
231C2×C4×C151—21no—
232C2×C4×C151—21no—
233C2×C4×C151—21no—
234C2×C4×C151—21no—
235C2×C4×C151—22no—
236C2×C4×C151—22no—
237C2×C4×C151—22no—
238C2×C4×C151—22no—
239C2×C4×C151—22no—
240C2×C4×C151—42no—
241C2×C4×C151—42no—
242C2×C4×C151—44no—
243C2×C4×C151—41no—
244C2×C4×C151—84no—
245C2×C4×C151—84no—
246C2×C4×C151—82no—
247C2×C4×C151#12011yescharacteristic
248C2×C4×C151#12011yescharacteristic
249C2×C4×C151#12011yescharacteristic
250C2×C4×C151C22×D411yescharacteristic
251C2×C4×C151C22×D411yescharacteristic
252C2×C4×C151C22×D411yescharacteristic
253C8×C151—22no—
254C8×C151—22no—
255C8×C151—42no—
256C8×C151—42no—
257C22×C151—21no—
258C22×C151—21no—
259C22×C151—21no—
260C22×C151—42no—
261C22×C151—42no—
262C22×C151—42no—
263C22×C151—42no—
264C22×C151—42no—
265C22×C151—42no—
266C22×C151—81no—
267C22×C151—81no—
268C22×C151—81no—
269C22×C151C2×#12011yescharacteristic
270C4×C151—21no—
271C4×C151—21no—
272C4×C151—21no—
273C4×C151—42no—
274C4×C151—42no—
275C4×C151—42no—
276C4×C151—42no—
277C4×C151—81no—
278C4×C151#45312yes—
279C4×C151#57611yescharacteristic
280C4×C151#57711yescharacteristic
281C4×C151#57711yescharacteristic
282C4×C151#57811yescharacteristic
283C2×C151—41no—
284C2×C151—82no—
285C2×C151—82no—
286C2×C151—161no—
287C2×C151#301211yescharacteristic
288C2×C151#301311yescharacteristic
289C2×C151C2×#45311yescharacteristic
290#18687C15111yesmaximal, characteristic, direct product factor, Sylow
291C151#1868711yescharacteristic, direct product factor, Sylow
292#3548C2×C15111yescharacteristic, complemented
293#3254C2×C15111yescharacteristic, complemented
294#3253C2×C15111yescharacteristic, complemented
295#3147C2×C15111yescharacteristic, complemented
296#1632C2×C15112yescomplemented
297#1631C2×C15112yescomplemented
298#1622C2×C15112yescomplemented
299#1621C2×C15112yescomplemented
300#1560C2×C15111yescharacteristic, complemented
301#1493C2×C15111yescharacteristic, complemented
302#1492C2×C15111yescharacteristic, complemented
303C2×#135—22no—
304#562—22no—
305#554—21no—
306#554C22×C15112yes—
307#550—21no—
308#550C22×C15112yes—
309#547—21no—
310#547—21no—
311#540—22no—
312#537—22no—
313#537—22no—
314#533C22×C15111yescharacteristic
315#532C22×C15111yescharacteristic
316#532C22×C15111yescharacteristic
317#532C22×C15111yescharacteristic
318#495—22no—
319#494C22×C15111yescharacteristic
320#493C22×C15111yescharacteristic
321#492C22×C15111yescharacteristic
322#492C22×C15111yescharacteristic
323#477C22×C15112yes—
324#476—21no—
325#476C22×C15112yes—
326#474—21no—
327#469—22no—
328#468—22no—
329#461—21no—
330#460C22×C15112yes—
331#459—21no—
332#459C22×C15112yes—
333#423C22×C15111yescharacteristic
334#423C22×C15111yescharacteristic
335C2×C4×C8C22×C15111yescharacteristic
336#333C22×C15112yes—
337#331C22×C15112yes—
338Q8⋊C8C22×C15112yes—
339Q8⋊C8C22×C15112yes—
340D4⋊C8C22×C15112yes—
341D4⋊C8C22×C15112yes—
342C2×#41—22no—
343C2×#41—22no—
344C2×#41—21no—
345C2×#41—21no—
346C2×#41D4×C15112yes—
347#135—48no—
348C2×Q16—22no—
349C2×SD16—22no—
350C2×SD16—22no—
351C2×SD16—22no—
352C2×D8—22no—
353C2×D8—22no—
354C2×M16—21no—
355C2×M16—21no—
356C22×C8—21no—
357C4⋊Q8D4×C15111yescharacteristic
358C4⋊Q8D4×C15111yescharacteristic
359C4⋊Q8D4×C15111yescharacteristic
360C4⋊Q8C23×C15111yescharacteristic
361C4⋊Q8C23×C15111yescharacteristic
362#127—22no—
363#127D4×C15111yescharacteristic
364#127C23×C15111yescharacteristic
365#127C23×C15111yescharacteristic
366#125—22no—
367#125—21no—
368#124—21no—
369#124—21no—
370#124D4×C15112yes—
371#123—24no—
372#123—24no—
373C22⋊Q8—22no—
374C22⋊Q8—24no—
375C22⋊Q8—22no—
376C22⋊Q8—24no—
377C22⋊Q8—21no—
378C22⋊Q8D4×C15112yes—
379#121—24no—
380#121—24no—
381#121—22no—
382#121—24no—
383#121—24no—
384#121—21no—
385#121—21no—
386#121—21no—
387#121—22no—
388#121—21no—
389#121—21no—
390#121D4×C15112yes—
391C4×Q8—21no—
392C4×Q8C23×C15112yes—
393C4×D4—22no—
394C4×D4—22no—
395C4×D4—21no—
396C4×D4—21no—
397C4×D4—21no—
398C4×D4—21no—
399C4×D4—21no—
400C4×D4C23×C15112yes—
401#117—21no—
402C2×C4⋊C4—22no—
403C2×C4⋊C4—22no—
404C2×C42C23×C15111yescharacteristic
405#107—22no—
406#106—22no—
407C4⋊C8—21no—
408C4⋊C8—21no—
409C4⋊C8C23×C15112yes—
410C4⋊C8C23×C15112yes—
411#103—22no—
412#102—22no—
413#102—22no—
414#102—22no—
415C4×C8—21no—
416C4×C8C23×C15111yescharacteristic
417C4×C8C23×C15111yescharacteristic
418#41—44no—
419#41—44no—
420#41—81no—
421#41—81no—
422#41—82no—
423#41—82no—
424#41—84no—
425C2×Q8—21no—
426C2×Q8—21no—
427C2×Q8—21no—
428C2×Q8C2×D4×C15112yes—
429C2×Q8C2×D4×C15112yes—
430C2×D4—24no—
431C2×D4—24no—
432C2×D4—22no—
433C2×D4—22no—
434C2×D4—21no—
435C2×D4—21no—
436C2×D4—21no—
437C2×D4—21no—
438C2×D4—21no—
439C2×D4—21no—
440C2×D4—21no—
441C2×D4—41no—
442C2×D4C2×D4×C15112yes—
443C2×D4C2×D4×C15112yes—
444C22×C4—24no—
445C22×C4—24no—
446C22×C4—22no—
447C22×C4—22no—
448C22×C4—41no—
449C22×C4C2×D4×C15111yescharacteristic
450C22×C4C2×D4×C15111yescharacteristic
451C22×C4C2×D4×C15111yescharacteristic
452Q16—44no—
453SD16—44no—
454SD16—44no—
455SD16—82no—
456D8—44no—
457D8—82no—
458M16—81no—
459M16—81no—
460C2×C8—24no—
461C2×C8—21no—
462C2×C8—21no—
463C2×C8—22no—
464C2×C8—22no—
465C4⋊C4—24no—
466C4⋊C4—24no—
467C4⋊C4—21no—
468C4⋊C4—21no—
469C4⋊C4—21no—
470C4⋊C4—21no—
471C4⋊C4—22no—
472C4⋊C4—21no—
473C4⋊C4—21no—
474C4⋊C4—22no—
475C4⋊C4—21no—
476C4⋊C4—21no—
477C4⋊C4C2×D4×C15112yes—
478C4⋊C4C2×D4×C15112yes—
479C22⋊C4—24no—
480C22⋊C4—24no—
481C22⋊C4—22no—
482C22⋊C4—22no—
483C22⋊C4—22no—
484C22⋊C4—22no—
485C22⋊C4—22no—
486C22⋊C4—41no—
487C22⋊C4—41no—
488C42—22no—
489C42C2×D4×C15111yescharacteristic
490C42C2×D4×C15111yescharacteristic
491C42C2×D4×C15111yescharacteristic
492C42C24×C15111yescharacteristic
493C23—22no—
494C23—22no—
495C23—41no—
496C23#120×C15111yescharacteristic
497Q8—22no—
498Q8—22no—
499Q8—42no—
500Q8—42no—
501Q8—42no—
502Q8—81no—
503D4—22no—
504D4—22no—
505D4—42no—
506D4—42no—
507D4—42no—
508D4—41no—
509D4—41no—
510D4—41no—
511D4—41no—
512D4—41no—
513D4—41no—
514D4—41no—
515D4—41no—
516D4—81no—
517D4—82no—
518D4—82no—
519D4—84no—
520D4—84no—
521D4—82no—
522C2×C4—22no—
523C2×C4—21no—
524C2×C4—21no—
525C2×C4—21no—
526C2×C4—21no—
527C2×C4—22no—
528C2×C4—22no—
529C2×C4—22no—
530C2×C4—22no—
531C2×C4—44no—
532C2×C4—42no—
533C2×C4—42no—
534C2×C4—41no—
535C2×C4—84no—
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—22no—
545C8—22no—
546C8—42no—
547C8—42no—
548C22—21no—
549C22—21no—
550C22—21no—
551C22—42no—
552C22—42no—
553C22—42no—
554C22—42no—
555C22—42no—
556C22—42no—
557C22—81no—
558C22—81no—
559C22—81no—
560C22C2×#120×C15111yescharacteristic
561C4—21no—
562C4—21no—
563C4—21no—
564C4—42no—
565C4—42no—
566C4—42no—
567C4—42no—
568C4—81no—
569C4#453×C15112yes—
570C4#576×C15111yescharacteristic
571C4#577×C15111yescharacteristic
572C4#577×C15111yescharacteristic
573C4#578×C15111yescharacteristic
574C2—41no—
575C2—82no—
576C2—82no—
577C2—161no—
578C2#3012×C15111yescharacteristic
579C2#3013×C15111yescharacteristic
580C2C2×#453×C15111yescharacteristic
subgroupG/H
center, socleC22×C151C2×#120
commutator, Frattini, cosocleC42C24×C151
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. #3548×C151C2semidirect
2. #3254×C151C2semidirect
3. #3253×C151C2semidirect
4. #3147×C151C2semidirect
5. #1632×C151C2semidirect
6. #1631×C151C2semidirect
7. #1622×C151C2semidirect
8. #1621×C151C2semidirect
9. #1560×C151C2semidirect
10. #1493×C151C2semidirect
11. #1492×C151C2semidirect
290. #18687C151direct (N × H)
291. C151#18687direct (N × H)
292. #3548C2×C151semidirect
293. #3254C2×C151semidirect
294. #3253C2×C151semidirect
295. #3147C2×C151semidirect
296. #1632C2×C151semidirect
297. #1631C2×C151semidirect
298. #1622C2×C151semidirect
299. #1621C2×C151semidirect
300. #1560C2×C151semidirect
301. #1493C2×C151semidirect
302. #1492C2×C151semidirect

Maximal subgroups

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

subgroupindex
#3548×C1512
#3254×C1512
#3253×C1512
#3147×C1512
#1632×C1512
#1631×C1512
#1622×C1512
#1621×C1512
#1560×C1512
#1493×C1512
#1492×C1512
#18687151