Finite Group Databasebeta

← C151×#18883 #50323808

Subgroups — C151×#18883 #50323808

Order 38656.

1096 conjugacy classes of subgroups.

The subgroup lattice has 596 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#3499×C151C211yesmaximal, characteristic
2#3246×C151C211yesmaximal, characteristic, complemented
3#3229×C151C211yesmaximal, characteristic, complemented
4#3076×C151C211yesmaximal, characteristic, complemented
5#1654×C151C212yesmaximal, complemented
6#1651×C151C212yesmaximal, complemented
7#1637×C151C212yesmaximal, complemented
8#1635×C151C212yesmaximal, complemented
9C2×#332×C151C211yesmaximal, characteristic, complemented
10#1480×C151C211yesmaximal, characteristic, complemented
11#1477×C151C211yesmaximal, characteristic, complemented
12C2×2−1+4×C151—21no—
13D4×Q8×C151—21no—
14D4×Q8×C151C2212yes—
15#547×C151—22no—
16#547×C151—21no—
17#547×C151—22no—
18#547×C151C2212yes—
19#536×C151—22no—
20#536×C151—21no—
21#533×C151C2211yescharacteristic
22#532×C151—21no—
23#532×C151C2211yescharacteristic
24C2×C4⋊Q8×C151—21no—
25C2×C4⋊Q8×C151C2211yescharacteristic
26C4×#41×C151C2211yescharacteristic
27#498×C151C2212yes—
28#487×C151C2212yes—
29#483×C151—22no—
30#479×C151—21no—
31#478×C151—21no—
32#477×C151C2211yescharacteristic
33#476×C151C2211yescharacteristic
34#476×C151C2212yes—
35#475×C151—22no—
36#475×C151—21no—
37#475×C151C2211yescharacteristic
38#474×C151C2211yescharacteristic
39#465×C151—22no—
40#461×C151C2212yes—
41#460×C151—21no—
42#431×C151C2211yescharacteristic
43#427×C151—21no—
44C2×C4⋊C8×C151C2211yescharacteristic
45C2×C4⋊C8×C151C2211yescharacteristic
46#416×C151—21no—
47#332×C151C2212yes—
48#332×C151C2212yes—
49Q8⋊C8×C151C2212yes—
50D4⋊C8×C151C2212yes—
51D4⋊C8×C151C2212yes—
52D4⋊C8×C151C2212yes—
532−1+4×C151—44no—
542−1+4×C151—44no—
55C2×#41×C151—22no—
56C2×#41×C151—24no—
57C2×#41×C151—22no—
58C2×#41×C151—21no—
59C2×#41×C151D411yescharacteristic
60C22×Q8×C151—22no—
61C22×Q8×C151—21no—
62C22×Q8×C151—22no—
63C2×SD16×C151—22no—
64C22×C8×C151—21no—
65C22×C8×C151—21no—
66C4⋊Q8×C151—22no—
67C4⋊Q8×C151—22no—
68C4⋊Q8×C151—22no—
69C4⋊Q8×C151—21no—
70C4⋊Q8×C151—21no—
71C4⋊Q8×C151D411yescharacteristic
72C4⋊Q8×C151D412yes—
73C4⋊Q8×C151C2311yescharacteristic
74C4⋊Q8×C151C2311yescharacteristic
75C4⋊Q8×C151C2312yes—
76#127×C151D411yescharacteristic
77#125×C151—21no—
78#124×C151—22no—
79#124×C151—21no—
80#123×C151—24no—
81#123×C151—24no—
82#123×C151—24no—
83C22⋊Q8×C151—24no—
84C22⋊Q8×C151—24no—
85C22⋊Q8×C151—22no—
86C22⋊Q8×C151—22no—
87C22⋊Q8×C151—21no—
88C22⋊Q8×C151—21no—
89#121×C151—22no—
90#121×C151—22no—
91#121×C151—21no—
92#121×C151D412yes—
93C4×Q8×C151—21no—
94C4×Q8×C151—21no—
95C4×Q8×C151D411yescharacteristic
96C4×Q8×C151C2311yescharacteristic
97C4×D4×C151—22no—
98C4×D4×C151—22no—
99C4×D4×C151—21no—
100C4×D4×C151—21no—
101C4×D4×C151—21no—
102C4×D4×C151D411yescharacteristic
103C4×D4×C151C2312yes—
104C4×D4×C151C2311yescharacteristic
105#117×C151—21no—
106#117×C151—21no—
107#117×C151D411yescharacteristic
108C2×C4⋊C4×C151—22no—
109C2×C4⋊C4×C151—21no—
110C2×C4⋊C4×C151—22no—
111C2×C4⋊C4×C151D412yes—
112C2×C42×C151—21no—
113C2×C42×C151C2311yescharacteristic
114#107×C151—21no—
115#107×C151—21no—
116#106×C151—21no—
117#106×C151—21no—
118#106×C151—22no—
119#106×C151—24no—
120C4⋊C8×C151—21no—
121C4⋊C8×C151—21no—
122C4⋊C8×C151—21no—
123C4⋊C8×C151C2312yes—
124C4⋊C8×C151C2311yescharacteristic
125C4⋊C8×C151C2311yescharacteristic
126#103×C151—22no—
127#103×C151—24no—
128#103×C151—21no—
129#103×C151—21no—
130#102×C151—21no—
131#102×C151—21no—
132#102×C151—22no—
133C22⋊C8×C151—21no—
134C4×C8×C151C2312yes—
135#41×C151—22no—
136#41×C151—48no—
137#41×C151—416no—
138#41×C151—44no—
139#41×C151—44no—
140#41×C151—42no—
141#41×C151—42no—
142#41×C151SD1614yescomplemented
143C2×Q8×C151—24no—
144C2×Q8×C151—22no—
145C2×Q8×C151—21no—
146C2×Q8×C151—22no—
147C2×Q8×C151—21no—
148C2×Q8×C151—21no—
149C2×Q8×C151—48no—
150C2×Q8×C151—44no—
151C2×Q8×C151—44no—
152C2×Q8×C151—42no—
153C2×Q8×C151—42no—
154C2×Q8×C151C2×D411yescharacteristic
155C2×D4×C151—21no—
156C2×D4×C151—24no—
157C2×D4×C151—22no—
158C2×D4×C151—21no—
159C2×D4×C151—21no—
160C2×D4×C151C2×D412yes—
161C2×D4×C151C2×D411yescharacteristic
162C22×C4×C151—21no—
163C22×C4×C151—24no—
164C22×C4×C151—24no—
165C22×C4×C151—22no—
166C22×C4×C151—21no—
167C22×C4×C151—21no—
168C22×C4×C151—22no—
169C22×C4×C151C2×D411yescharacteristic
170C22×C4×C151C2×D411yescharacteristic
171C22×C4×C151C2×D411yescharacteristic
172SD16×C151—82no—
173C2×C8×C151—22no—
174C2×C8×C151—21no—
175C2×C8×C151—22no—
176C2×C8×C151—21no—
177C2×C8×C151—42no—
178C2×C8×C151—81no—
179C4⋊C4×C151—24no—
180C4⋊C4×C151—24no—
181C4⋊C4×C151—21no—
182C4⋊C4×C151—22no—
183C4⋊C4×C151—22no—
184C4⋊C4×C151—21no—
185C4⋊C4×C151—22no—
186C4⋊C4×C151—21no—
187C4⋊C4×C151—21no—
188C4⋊C4×C151—21no—
189C4⋊C4×C151—21no—
190C4⋊C4×C151—21no—
191C4⋊C4×C151—41no—
192C4⋊C4×C151—41no—
193C4⋊C4×C151C2×D412yes—
194C4⋊C4×C151C2×D414yes—
195C4⋊C4×C151C2×D411yescharacteristic
196C4⋊C4×C151C2×D411yescharacteristic
197C22⋊C4×C151—24no—
198C22⋊C4×C151—24no—
199C22⋊C4×C151—21no—
200C22⋊C4×C151—21no—
201C22⋊C4×C151—22no—
202C22⋊C4×C151—21no—
203C22⋊C4×C151—22no—
204C22⋊C4×C151—41no—
205C42×C151—21no—
206C42×C151—21no—
207C42×C151—21no—
208C42×C151—41no—
209C42×C151C2×D411yescharacteristic
210C42×C151C2×D411yescharacteristic
211C42×C151C2×D411yescharacteristic
212C42×C151C2411yescharacteristic
213C23×C151—21no—
214C23×C151—22no—
215C23×C151#12011yescharacteristic
216Q8×C151—21no—
217Q8×C151—48no—
218Q8×C151—42no—
219Q8×C151—42no—
220Q8×C151—42no—
221Q8×C151—42no—
222Q8×C151—44no—
223Q8×C151—41no—
224Q8×C151—41no—
225Q8×C151C2×SD1612yes—
226D4×C151—24no—
227D4×C151—21no—
228D4×C151—22no—
229D4×C151—22no—
230D4×C151—42no—
231D4×C151—48no—
232D4×C151—44no—
233D4×C151—42no—
234D4×C151C2×SD1612yes—
235C2×C4×C151—21no—
236C2×C4×C151—21no—
237C2×C4×C151—21no—
238C2×C4×C151—24no—
239C2×C4×C151—22no—
240C2×C4×C151—24no—
241C2×C4×C151—21no—
242C2×C4×C151—21no—
243C2×C4×C151—41no—
244C2×C4×C151—48no—
245C2×C4×C151—42no—
246C2×C4×C151—48no—
247C2×C4×C151—44no—
248C2×C4×C151—42no—
249C2×C4×C151—42no—
250C2×C4×C151—41no—
251C2×C4×C151—41no—
252C2×C4×C151—41no—
253C2×C4×C151—41no—
254C2×C4×C151#12011yescharacteristic
255C2×C4×C151#12011yescharacteristic
256C2×C4×C151#12011yescharacteristic
257C2×C4×C151C2×SD1612yes—
258C2×C4×C151AGL(1,ℤ/8)12yes—
259C2×C4×C151C22×D411yescharacteristic
260C2×C4×C151C22×D411yescharacteristic
261C2×C4×C151C22×D411yescharacteristic
262C8×C151—42no—
263C8×C151—41no—
264C8×C151—41no—
265C8×C151—42no—
266C22×C151—21no—
267C22×C151—21no—
268C22×C151—22no—
269C22×C151—41no—
270C22×C151—41no—
271C22×C151—42no—
272C22×C151—42no—
273C22×C151—42no—
274C22×C151#45012yes—
275C22×C151C2×#12011yescharacteristic
276C4×C151—22no—
277C4×C151—21no—
278C4×C151—21no—
279C4×C151—21no—
280C4×C151—44no—
281C4×C151—42no—
282C4×C151—41no—
283C4×C151—41no—
284C4×C151—81no—
285C4×C151—81no—
286C4×C151#45012yes—
287C4×C151C22×SD1611yescharacteristic
288C4×C151C2×AGL(1,ℤ/8)11yescharacteristic
289C4×C151#57711yescharacteristic
290C4×C151#57811yescharacteristic
291C2×C151—22no—
292C2×C151—42no—
293C2×C151—82no—
294C2×C151C2×#45011yescharacteristic
295C2×C151#301311yescharacteristic
296C2×C151#302011yescharacteristic
297#18883C15111yesmaximal, characteristic, direct product factor, Sylow
298C151#1888311yescharacteristic, direct product factor, Sylow
299#3499C2×C15111yescharacteristic
300#3246C2×C15111yescharacteristic, complemented
301#3229C2×C15111yescharacteristic, complemented
302#3076C2×C15111yescharacteristic, complemented
303#1654C2×C15112yescomplemented
304#1651C2×C15112yescomplemented
305#1637C2×C15112yescomplemented
306#1635C2×C15112yescomplemented
307C2×#332C2×C15111yescharacteristic, complemented
308#1480C2×C15111yescharacteristic, complemented
309#1477C2×C15111yescharacteristic, complemented
310C2×2−1+4—21no—
311D4×Q8—21no—
312D4×Q8C22×C15112yes—
313#547—22no—
314#547—21no—
315#547—22no—
316#547C22×C15112yes—
317#536—22no—
318#536—21no—
319#533C22×C15111yescharacteristic
320#532—21no—
321#532C22×C15111yescharacteristic
322C2×C4⋊Q8—21no—
323C2×C4⋊Q8C22×C15111yescharacteristic
324C4×#41C22×C15111yescharacteristic
325#498C22×C15112yes—
326#487C22×C15112yes—
327#483—22no—
328#479—21no—
329#478—21no—
330#477C22×C15111yescharacteristic
331#476C22×C15111yescharacteristic
332#476C22×C15112yes—
333#475—22no—
334#475—21no—
335#475C22×C15111yescharacteristic
336#474C22×C15111yescharacteristic
337#465—22no—
338#461C22×C15112yes—
339#460—21no—
340#431C22×C15111yescharacteristic
341#427—21no—
342C2×C4⋊C8C22×C15111yescharacteristic
343C2×C4⋊C8C22×C15111yescharacteristic
344#416—21no—
345#332C22×C15112yes—
346#332C22×C15112yes—
347Q8⋊C8C22×C15112yes—
348D4⋊C8C22×C15112yes—
349D4⋊C8C22×C15112yes—
350D4⋊C8C22×C15112yes—
3512−1+4—44no—
3522−1+4—44no—
353C2×#41—22no—
354C2×#41—24no—
355C2×#41—22no—
356C2×#41—21no—
357C2×#41D4×C15111yescharacteristic
358C22×Q8—22no—
359C22×Q8—22no—
360C22×Q8—21no—
361C2×SD16—22no—
362C22×C8—21no—
363C22×C8—21no—
364C4⋊Q8—22no—
365C4⋊Q8—22no—
366C4⋊Q8—22no—
367C4⋊Q8—21no—
368C4⋊Q8—21no—
369C4⋊Q8D4×C15111yescharacteristic
370C4⋊Q8D4×C15112yes—
371C4⋊Q8C23×C15111yescharacteristic
372C4⋊Q8C23×C15111yescharacteristic
373C4⋊Q8C23×C15112yes—
374#127D4×C15111yescharacteristic
375#125—21no—
376#124—22no—
377#124—21no—
378#123—24no—
379#123—24no—
380#123—24no—
381C22⋊Q8—24no—
382C22⋊Q8—22no—
383C22⋊Q8—24no—
384C22⋊Q8—22no—
385C22⋊Q8—21no—
386C22⋊Q8—21no—
387#121—22no—
388#121—22no—
389#121—21no—
390#121D4×C15112yes—
391C4×Q8—21no—
392C4×Q8—21no—
393C4×Q8D4×C15111yescharacteristic
394C4×Q8C23×C15111yescharacteristic
395C4×D4—22no—
396C4×D4—22no—
397C4×D4—21no—
398C4×D4—21no—
399C4×D4—21no—
400C4×D4D4×C15111yescharacteristic
401C4×D4C23×C15111yescharacteristic
402C4×D4C23×C15112yes—
403#117—21no—
404#117—21no—
405#117D4×C15111yescharacteristic
406C2×C4⋊C4—22no—
407C2×C4⋊C4—21no—
408C2×C4⋊C4—22no—
409C2×C4⋊C4D4×C15112yes—
410C2×C42—21no—
411C2×C42C23×C15111yescharacteristic
412#107—21no—
413#107—21no—
414#106—21no—
415#106—21no—
416#106—22no—
417#106—24no—
418C4⋊C8—21no—
419C4⋊C8—21no—
420C4⋊C8—21no—
421C4⋊C8C23×C15111yescharacteristic
422C4⋊C8C23×C15111yescharacteristic
423C4⋊C8C23×C15112yes—
424#103—21no—
425#103—21no—
426#103—22no—
427#103—24no—
428#102—21no—
429#102—21no—
430#102—22no—
431C22⋊C8—21no—
432C4×C8C23×C15112yes—
433#41—22no—
434#41—48no—
435#41—416no—
436#41—44no—
437#41—44no—
438#41—42no—
439#41—42no—
440#41SD16×C15114yescomplemented
441C2×Q8—24no—
442C2×Q8—22no—
443C2×Q8—21no—
444C2×Q8—22no—
445C2×Q8—21no—
446C2×Q8—21no—
447C2×Q8—48no—
448C2×Q8—44no—
449C2×Q8—44no—
450C2×Q8—42no—
451C2×Q8—42no—
452C2×Q8C2×D4×C15111yescharacteristic
453C2×D4—21no—
454C2×D4—24no—
455C2×D4—22no—
456C2×D4—21no—
457C2×D4—21no—
458C2×D4C2×D4×C15112yes—
459C2×D4C2×D4×C15111yescharacteristic
460C22×C4—21no—
461C22×C4—24no—
462C22×C4—24no—
463C22×C4—22no—
464C22×C4—21no—
465C22×C4—21no—
466C22×C4—22no—
467C22×C4C2×D4×C15111yescharacteristic
468C22×C4C2×D4×C15111yescharacteristic
469C22×C4C2×D4×C15111yescharacteristic
470SD16—82no—
471C2×C8—22no—
472C2×C8—21no—
473C2×C8—22no—
474C2×C8—21no—
475C2×C8—42no—
476C2×C8—81no—
477C4⋊C4—24no—
478C4⋊C4—24no—
479C4⋊C4—21no—
480C4⋊C4—22no—
481C4⋊C4—22no—
482C4⋊C4—21no—
483C4⋊C4—22no—
484C4⋊C4—21no—
485C4⋊C4—21no—
486C4⋊C4—21no—
487C4⋊C4—21no—
488C4⋊C4—21no—
489C4⋊C4—41no—
490C4⋊C4—41no—
491C4⋊C4C2×D4×C15112yes—
492C4⋊C4C2×D4×C15114yes—
493C4⋊C4C2×D4×C15111yescharacteristic
494C4⋊C4C2×D4×C15111yescharacteristic
495C22⋊C4—24no—
496C22⋊C4—24no—
497C22⋊C4—21no—
498C22⋊C4—21no—
499C22⋊C4—22no—
500C22⋊C4—21no—
501C22⋊C4—22no—
502C22⋊C4—41no—
503C42—21no—
504C42—21no—
505C42—21no—
506C42—41no—
507C42C2×D4×C15111yescharacteristic
508C42C2×D4×C15111yescharacteristic
509C42C2×D4×C15111yescharacteristic
510C42C24×C15111yescharacteristic
511C23—21no—
512C23—22no—
513C23#120×C15111yescharacteristic
514Q8—21no—
515Q8—48no—
516Q8—42no—
517Q8—42no—
518Q8—44no—
519Q8—42no—
520Q8—42no—
521Q8—41no—
522Q8—41no—
523Q8C2×SD16×C15112yes—
524D4—24no—
525D4—21no—
526D4—22no—
527D4—22no—
528D4—42no—
529D4—48no—
530D4—44no—
531D4—42no—
532D4C2×SD16×C15112yes—
533C2×C4—21no—
534C2×C4—24no—
535C2×C4—21no—
536C2×C4—21no—
537C2×C4—21no—
538C2×C4—21no—
539C2×C4—24no—
540C2×C4—22no—
541C2×C4—41no—
542C2×C4—48no—
543C2×C4—42no—
544C2×C4—48no—
545C2×C4—44no—
546C2×C4—42no—
547C2×C4—42no—
548C2×C4—41no—
549C2×C4—41no—
550C2×C4—41no—
551C2×C4—41no—
552C2×C4#120×C15111yescharacteristic
553C2×C4#120×C15111yescharacteristic
554C2×C4#120×C15111yescharacteristic
555C2×C4C2×SD16×C15112yes—
556C2×C4AGL(1,ℤ/8)×C15112yes—
557C2×C4C22×D4×C15111yescharacteristic
558C2×C4C22×D4×C15111yescharacteristic
559C2×C4C22×D4×C15111yescharacteristic
560C8—42no—
561C8—41no—
562C8—41no—
563C8—42no—
564C22—21no—
565C22—21no—
566C22—22no—
567C22—41no—
568C22—41no—
569C22—42no—
570C22—42no—
571C22—42no—
572C22#450×C15112yes—
573C22C2×#120×C15111yescharacteristic
574C4—22no—
575C4—21no—
576C4—21no—
577C4—21no—
578C4—44no—
579C4—42no—
580C4—41no—
581C4—41no—
582C4—81no—
583C4—81no—
584C4#450×C15112yes—
585C4C22×SD16×C15111yescharacteristic
586C4C2×AGL(1,ℤ/8)×C15111yescharacteristic
587C4#577×C15111yescharacteristic
588C4#578×C15111yescharacteristic
589C2—22no—
590C2—42no—
591C2—82no—
592C2C2×#450×C15111yescharacteristic
593C2#3013×C15111yescharacteristic
594C2#3020×C15111yescharacteristic
subgroupG/H
center, socleC22×C151C2×#120
commutator, Frattini, cosocleC42C24×C151
prime radical#3499×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
2. #3246×C151C2semidirect
3. #3229×C151C2semidirect
4. #3076×C151C2semidirect
5. #1654×C151C2semidirect
6. #1651×C151C2semidirect
7. #1637×C151C2semidirect
8. #1635×C151C2semidirect
9. C2×#332×C151C2semidirect
10. #1480×C151C2semidirect
11. #1477×C151C2semidirect
142. #41×C151SD16semidirect
297. #18883C151direct (N × H)
298. C151#18883direct (N × H)
300. #3246C2×C151semidirect
301. #3229C2×C151semidirect
302. #3076C2×C151semidirect
303. #1654C2×C151semidirect
304. #1651C2×C151semidirect
305. #1637C2×C151semidirect
306. #1635C2×C151semidirect
307. C2×#332C2×C151semidirect
308. #1480C2×C151semidirect
309. #1477C2×C151semidirect
440. #41SD16×C151semidirect

Maximal subgroups

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

subgroupindex
#3499×C1512
#3246×C1512
#3229×C1512
#3076×C1512
#1654×C1512
#1651×C1512
#1637×C1512
#1635×C1512
C2×#332×C1512
#1480×C1512
#1477×C1512
#18883151