Finite Group Databasebeta

← C151×#24572 #50329497

Subgroups — C151×#24572 #50329497

Order 38656.

910 conjugacy classes of subgroups.

The subgroup lattice has 600 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#484×C151C211yesmaximal, characteristic, complemented
2#3007×C151C211yesmaximal, characteristic
3C2×#417×C151C211yesmaximal, characteristic
4#2880×C151C211yesmaximal, characteristic
5#2078×C151C212yesmaximal, complemented
6#2052×C151C212yesmaximal, complemented
7#1908×C151C212yesmaximal, complemented
8#1901×C151C211yesmaximal, characteristic, complemented
9#1855×C151C211yesmaximal, characteristic, complemented
10#1821×C151C211yesmaximal, characteristic, complemented
11#1816×C151C212yesmaximal, complemented
12C22×#41×C151C2211yescharacteristic
13C2×#137×C151C2211yescharacteristic
14C2×#137×C151C2211yescharacteristic
15C2×#131×C151C2212yes—
16C22×M16×C151C2211yescharacteristic
17C2×C22⋊Q8×C151C2211yescharacteristic
18C22×C4⋊C4×C151C2211yescharacteristic
19#484×C151—21no—
20#484×C151—21no—
21#484×C151—22no—
22#452×C151—21no—
23#452×C151—21no—
24#451×C151—21no—
25#450×C151—21no—
26C2×#108×C151C2212yescomplemented
27C2×#107×C151C2212yescomplemented
28#417×C151—21no—
29#417×C151—21no—
30#417×C151C2211yescharacteristic
31#417×C151C2212yes—
32#417×C151C2212yes—
33#417×C151C2211yescharacteristic
34C2×#103×C151—21no—
35C2×#103×C151C2212yescomplemented
36C2×#102×C151—21no—
37C2×#101×C151C2212yescomplemented
38#408×C151—22no—
39#408×C151C2212yes—
40#407×C151—21no—
41#407×C151C2211yescharacteristic
42#407×C151C2211yescharacteristic
43C2×C22⋊C8×C151—21no—
44C2×C22⋊C8×C151C2211yescharacteristic
45#343×C151C2212yescomplemented
46#343×C151C2212yescomplemented
47#343×C151C2212yescomplemented
48#341×C151C2212yescomplemented
49C2×#41×C151—24no—
50C2×#41×C151—21no—
51C2×#41×C151—21no—
52C2×#41×C151—42no—
53C2×#41×C151D411yescharacteristic
54C2×#41×C151D411yescharacteristic
55C2×#41×C151C2311yescharacteristic
56C2×#41×C151C2311yescharacteristic
57C22×Q8×C151D411yescharacteristic
58C22×Q8×C151C2311yescharacteristic
59C22×D4×C151—21no—
60C22×D4×C151D411yescharacteristic
61C23×C4×C151—21no—
62C23×C4×C151—21no—
63C23×C4×C151C2311yescharacteristic
64#137×C151—24no—
65#137×C151—42no—
66C2×Q16×C151—21no—
67C2×Q16×C151—21no—
68C2×SD16×C151—21no—
69C2×SD16×C151—21no—
70#131×C151—24no—
71#131×C151—42no—
72C2×M16×C151—21no—
73C2×M16×C151—22no—
74C2×M16×C151—42no—
75C2×M16×C151C2311yescharacteristic
76C2×M16×C151C2312yes—
77C2×M16×C151C2312yes—
78C2×M16×C151C2311yescharacteristic
79C22×C8×C151—21no—
80C22×C8×C151—22no—
81C22×C8×C151C2312yes—
82C22⋊Q8×C151—21no—
83C22⋊Q8×C151—21no—
84C22⋊Q8×C151—21no—
85C22⋊Q8×C151—21no—
86C2×C4⋊C4×C151—21no—
87C2×C4⋊C4×C151—21no—
88C2×C4⋊C4×C151—21no—
89C2×C4⋊C4×C151—21no—
90C2×C4⋊C4×C151—21no—
91C2×C4⋊C4×C151—21no—
92C2×C4⋊C4×C151C2312yes—
93C2×C4⋊C4×C151C2311yescharacteristic
94C2×C22⋊C4×C151—21no—
95#108×C151—42no—
96#107×C151—22no—
97#107×C151—22no—
98#103×C151—22no—
99#103×C151—22no—
100#103×C151—22no—
101#103×C151—22no—
102#103×C151—21no—
103#103×C151—21no—
104#102×C151—22no—
105#102×C151—22no—
106#102×C151—21no—
107#102×C151—21no—
108#101×C151—42no—
109C22⋊C8×C151—21no—
110C22⋊C8×C151—21no—
111C22⋊C8×C151—21no—
112C22⋊C8×C151—21no—
113C22⋊C8×C151—22no—
114C22⋊C8×C151—22no—
115C22⋊C8×C151D411yescharacteristic
116C22⋊C8×C151D411yescharacteristic
117C22⋊C8×C151D412yes—
118C24×C151—21no—
119C24×C151#4111yescharacteristic
120#41×C151—22no—
121#41×C151—22no—
122#41×C151—22no—
123#41×C151—22no—
124#41×C151—22no—
125#41×C151—44no—
126#41×C151—41no—
127#41×C151—41no—
128#41×C151—44no—
129#41×C151#4114yes—
130C2×Q8×C151—21no—
131C2×Q8×C151—22no—
132C2×Q8×C151—21no—
133C2×Q8×C151—21no—
134C2×Q8×C151—22no—
135C2×Q8×C151—22no—
136C2×Q8×C151—41no—
137C2×Q8×C151C2×D411yescharacteristic
138C2×Q8×C151C2×D411yescharacteristic
139C2×D4×C151—21no—
140C2×D4×C151—22no—
141C2×D4×C151—21no—
142C2×D4×C151—21no—
143C2×D4×C151—21no—
144C2×D4×C151—21no—
145C2×D4×C151—41no—
146C2×D4×C151—44no—
147C2×D4×C151C2×D411yescharacteristic
148C2×D4×C151C2×D411yescharacteristic
149C22×C4×C151—21no—
150C22×C4×C151—22no—
151C22×C4×C151—22no—
152C22×C4×C151—21no—
153C22×C4×C151—21no—
154C22×C4×C151—21no—
155C22×C4×C151—21no—
156C22×C4×C151—21no—
157C22×C4×C151—21no—
158C22×C4×C151—22no—
159C22×C4×C151—44no—
160C22×C4×C151—41no—
161C22×C4×C151—41no—
162C22×C4×C151—82no—
163C22×C4×C151C2×D411yescharacteristic
164C22×C4×C151C2×D411yescharacteristic
165C22×C4×C151C2×D411yescharacteristic
166C22×C4×C151C2×D411yescharacteristic
167C22×C4×C151#4111yescharacteristic
168C22×C4×C151C2411yescharacteristic
169Q16×C151—42no—
170Q16×C151—42no—
171SD16×C151—42no—
172SD16×C151—42no—
173M16×C151—22no—
174M16×C151—22no—
175M16×C151—22no—
176M16×C151—22no—
177M16×C151—22no—
178M16×C151—22no—
179M16×C151—44no—
180M16×C151—42no—
181C2×C8×C151—22no—
182C2×C8×C151—22no—
183C2×C8×C151—22no—
184C2×C8×C151—21no—
185C2×C8×C151—21no—
186C2×C8×C151—22no—
187C2×C8×C151—44no—
188C2×C8×C151—42no—
189C2×C8×C151C2×D412yes—
190C2×C8×C151C2×D412yes—
191C4⋊C4×C151—22no—
192C4⋊C4×C151—21no—
193C4⋊C4×C151—22no—
194C4⋊C4×C151—21no—
195C4⋊C4×C151—41no—
196C4⋊C4×C151—41no—
197C4⋊C4×C151—41no—
198C4⋊C4×C151—41no—
199C22⋊C4×C151—41no—
200C22⋊C4×C151—41no—
201C23×C151—21no—
202C23×C151—22no—
203C23×C151—22no—
204C23×C151—21no—
205C23×C151—41no—
206C23×C151—42no—
207C23×C151—42no—
208C23×C151—81no—
209C23×C151#12111yescharacteristic
210C23×C151#12111yescharacteristic
211C23×C151C2×#4111yescharacteristic
212Q8×C151—21no—
213Q8×C151—21no—
214Q8×C151—21no—
215Q8×C151—42no—
216Q8×C151—41no—
217Q8×C151—41no—
218Q8×C151—42no—
219Q8×C151#12312yes—
220D4×C151—24no—
221D4×C151—21no—
222D4×C151—21no—
223D4×C151—21no—
224D4×C151—42no—
225D4×C151—42no—
226D4×C151—42no—
227D4×C151—42no—
228D4×C151#12312yes—
229C2×C4×C151—21no—
230C2×C4×C151—22no—
231C2×C4×C151—21no—
232C2×C4×C151—21no—
233C2×C4×C151—21no—
234C2×C4×C151—21no—
235C2×C4×C151—24no—
236C2×C4×C151—22no—
237C2×C4×C151—22no—
238C2×C4×C151—21no—
239C2×C4×C151—42no—
240C2×C4×C151—42no—
241C2×C4×C151—42no—
242C2×C4×C151—42no—
243C2×C4×C151—41no—
244C2×C4×C151—41no—
245C2×C4×C151—42no—
246C2×C4×C151—42no—
247C2×C4×C151—82no—
248C2×C4×C151—82no—
249C2×C4×C151—81no—
250C2×C4×C151—82no—
251C2×C4×C151#12111yescharacteristic
252C2×C4×C151#12111yescharacteristic
253C2×C4×C151C22×D411yescharacteristic
254C2×C4×C151C22×D411yescharacteristic
255C2×C4×C151C2×#4112yes—
256C2×C4×C151H(5,𝔽2)12yes—
257C8×C151—22no—
258C8×C151—22no—
259C8×C151—41no—
260C8×C151—42no—
261C8×C151—41no—
262C8×C151—42no—
263C22×C151—21no—
264C22×C151—21no—
265C22×C151—21no—
266C22×C151—21no—
267C22×C151—21no—
268C22×C151—22no—
269C22×C151—21no—
270C22×C151—21no—
271C22×C151—44no—
272C22×C151—41no—
273C22×C151—41no—
274C22×C151—41no—
275C22×C151—41no—
276C22×C151—41no—
277C22×C151—84no—
278C22×C151#47312yes—
279C22×C151C2×#12111yescharacteristic
280C22×C151#55112yes—
281C4×C151—21no—
282C4×C151—21no—
283C4×C151—22no—
284C4×C151—41no—
285C4×C151—81no—
286C4×C151—81no—
287C4×C151—82no—
288C4×C151C2×#12311yescharacteristic
289C4×C151#53411yescharacteristic
290C4×C151#54612yes—
291C2×C151—22no—
292C2×C151—22no—
293C2×C151—41no—
294C2×C151—42no—
295C2×C151—81no—
296C2×C151#241211yescharacteristic
297C2×C151C2×#47311yescharacteristic
298C2×C151#306811yescharacteristic
299#24572C15111yesmaximal, characteristic, direct product factor, Sylow
300C151#2457211yescharacteristic, direct product factor, Sylow
301C2×#484C2×C15111yescharacteristic, complemented
302#3007C2×C15111yescharacteristic
303C2×#417C2×C15111yescharacteristic
304#2880C2×C15111yescharacteristic
305#2078C2×C15112yescomplemented
306#2052C2×C15112yescomplemented
307#1908C2×C15112yescomplemented
308#1901C2×C15111yescharacteristic, complemented
309#1855C2×C15111yescharacteristic, complemented
310#1821C2×C15111yescharacteristic, complemented
311#1816C2×C15112yescomplemented
312C22×#41C22×C15111yescharacteristic
313C2×#137C22×C15111yescharacteristic
314C2×#137C22×C15111yescharacteristic
315C2×#131C22×C15112yes—
316C22×M16C22×C15111yescharacteristic
317C2×C22⋊Q8C22×C15111yescharacteristic
318C22×C4⋊C4C22×C15111yescharacteristic
319#484—21no—
320#484—21no—
321#484—22no—
322#452—21no—
323#452—21no—
324#451—21no—
325#450—21no—
326C2×#108C22×C15112yescomplemented
327C2×#107C22×C15112yescomplemented
328#417—21no—
329#417—21no—
330#417C22×C15112yes—
331#417C22×C15111yescharacteristic
332#417C22×C15112yes—
333#417C22×C15111yescharacteristic
334C2×#103—21no—
335C2×#103C22×C15112yescomplemented
336C2×#102—21no—
337C2×#101C22×C15112yescomplemented
338#408—22no—
339#408C22×C15112yes—
340#407—21no—
341#407C22×C15111yescharacteristic
342#407C22×C15111yescharacteristic
343C2×C22⋊C8—21no—
344C2×C22⋊C8C22×C15111yescharacteristic
345#343C22×C15112yescomplemented
346#343C22×C15112yescomplemented
347#343C22×C15112yescomplemented
348#341C22×C15112yescomplemented
349C2×#41—21no—
350C2×#41—21no—
351C2×#41—24no—
352C2×#41—42no—
353C2×#41D4×C15111yescharacteristic
354C2×#41D4×C15111yescharacteristic
355C2×#41C23×C15111yescharacteristic
356C2×#41C23×C15111yescharacteristic
357C22×Q8D4×C15111yescharacteristic
358C22×Q8C23×C15111yescharacteristic
359C22×D4—21no—
360C22×D4D4×C15111yescharacteristic
361C23×C4—21no—
362C23×C4—21no—
363C23×C4C23×C15111yescharacteristic
364#137—24no—
365#137—42no—
366C2×Q16—21no—
367C2×Q16—21no—
368C2×SD16—21no—
369C2×SD16—21no—
370#131—24no—
371#131—42no—
372C2×M16—21no—
373C2×M16—22no—
374C2×M16—42no—
375C2×M16C23×C15112yes—
376C2×M16C23×C15112yes—
377C2×M16C23×C15111yescharacteristic
378C2×M16C23×C15111yescharacteristic
379C22×C8—21no—
380C22×C8—22no—
381C22×C8C23×C15112yes—
382C22⋊Q8—21no—
383C22⋊Q8—21no—
384C22⋊Q8—21no—
385C22⋊Q8—21no—
386C2×C4⋊C4—21no—
387C2×C4⋊C4—21no—
388C2×C4⋊C4—21no—
389C2×C4⋊C4—21no—
390C2×C4⋊C4—21no—
391C2×C4⋊C4—21no—
392C2×C4⋊C4C23×C15112yes—
393C2×C4⋊C4C23×C15111yescharacteristic
394C2×C22⋊C4—21no—
395#108—42no—
396#107—22no—
397#107—22no—
398#103—22no—
399#103—22no—
400#103—21no—
401#103—21no—
402#103—22no—
403#103—22no—
404#102—22no—
405#102—22no—
406#102—21no—
407#102—21no—
408#101—42no—
409C22⋊C8—21no—
410C22⋊C8—21no—
411C22⋊C8—21no—
412C22⋊C8—21no—
413C22⋊C8—22no—
414C22⋊C8—22no—
415C22⋊C8D4×C15111yescharacteristic
416C22⋊C8D4×C15111yescharacteristic
417C22⋊C8D4×C15112yes—
418C24—21no—
419C24#41×C15111yescharacteristic
420#41—22no—
421#41—22no—
422#41—22no—
423#41—22no—
424#41—22no—
425#41—44no—
426#41—41no—
427#41—41no—
428#41—44no—
429#41#41×C15114yes—
430C2×Q8—21no—
431C2×Q8—22no—
432C2×Q8—21no—
433C2×Q8—21no—
434C2×Q8—22no—
435C2×Q8—22no—
436C2×Q8—41no—
437C2×Q8C2×D4×C15111yescharacteristic
438C2×Q8C2×D4×C15111yescharacteristic
439C2×D4—21no—
440C2×D4—22no—
441C2×D4—21no—
442C2×D4—21no—
443C2×D4—21no—
444C2×D4—21no—
445C2×D4—41no—
446C2×D4—44no—
447C2×D4C2×D4×C15111yescharacteristic
448C2×D4C2×D4×C15111yescharacteristic
449C22×C4—21no—
450C22×C4—22no—
451C22×C4—22no—
452C22×C4—21no—
453C22×C4—21no—
454C22×C4—21no—
455C22×C4—21no—
456C22×C4—21no—
457C22×C4—21no—
458C22×C4—22no—
459C22×C4—44no—
460C22×C4—41no—
461C22×C4—41no—
462C22×C4—82no—
463C22×C4C2×D4×C15111yescharacteristic
464C22×C4C2×D4×C15111yescharacteristic
465C22×C4C2×D4×C15111yescharacteristic
466C22×C4C2×D4×C15111yescharacteristic
467C22×C4#41×C15111yescharacteristic
468C22×C4C24×C15111yescharacteristic
469Q16—42no—
470Q16—42no—
471SD16—42no—
472SD16—42no—
473M16—22no—
474M16—22no—
475M16—22no—
476M16—22no—
477M16—22no—
478M16—22no—
479M16—44no—
480M16—42no—
481C2×C8—22no—
482C2×C8—22no—
483C2×C8—22no—
484C2×C8—21no—
485C2×C8—21no—
486C2×C8—22no—
487C2×C8—44no—
488C2×C8—42no—
489C2×C8C2×D4×C15112yes—
490C2×C8C2×D4×C15112yes—
491C4⋊C4—22no—
492C4⋊C4—21no—
493C4⋊C4—22no—
494C4⋊C4—21no—
495C4⋊C4—41no—
496C4⋊C4—41no—
497C4⋊C4—41no—
498C4⋊C4—41no—
499C22⋊C4—41no—
500C22⋊C4—41no—
501C23—22no—
502C23—21no—
503C23—22no—
504C23—21no—
505C23—41no—
506C23—42no—
507C23—42no—
508C23—81no—
509C23#121×C15111yescharacteristic
510C23#121×C15111yescharacteristic
511C23C2×#41×C15111yescharacteristic
512Q8—21no—
513Q8—21no—
514Q8—21no—
515Q8—42no—
516Q8—41no—
517Q8—41no—
518Q8—42no—
519Q8#123×C15112yes—
520D4—24no—
521D4—21no—
522D4—21no—
523D4—21no—
524D4—42no—
525D4—42no—
526D4—42no—
527D4—42no—
528D4#123×C15112yes—
529C2×C4—21no—
530C2×C4—22no—
531C2×C4—21no—
532C2×C4—21no—
533C2×C4—21no—
534C2×C4—21no—
535C2×C4—24no—
536C2×C4—22no—
537C2×C4—22no—
538C2×C4—21no—
539C2×C4—42no—
540C2×C4—42no—
541C2×C4—42no—
542C2×C4—42no—
543C2×C4—41no—
544C2×C4—41no—
545C2×C4—42no—
546C2×C4—42no—
547C2×C4—82no—
548C2×C4—82no—
549C2×C4—82no—
550C2×C4—81no—
551C2×C4#121×C15111yescharacteristic
552C2×C4#121×C15111yescharacteristic
553C2×C4C22×D4×C15111yescharacteristic
554C2×C4C22×D4×C15111yescharacteristic
555C2×C4C2×#41×C15112yes—
556C2×C4H(5,𝔽2)×C15112yes—
557C8—22no—
558C8—22no—
559C8—41no—
560C8—42no—
561C8—41no—
562C8—42no—
563C22—21no—
564C22—21no—
565C22—21no—
566C22—21no—
567C22—21no—
568C22—22no—
569C22—21no—
570C22—21no—
571C22—44no—
572C22—41no—
573C22—41no—
574C22—41no—
575C22—41no—
576C22—41no—
577C22—84no—
578C22#473×C15112yes—
579C22C2×#121×C15111yescharacteristic
580C22#551×C15112yes—
581C4—21no—
582C4—21no—
583C4—22no—
584C4—41no—
585C4—81no—
586C4—82no—
587C4—81no—
588C4C2×#123×C15111yescharacteristic
589C4#534×C15111yescharacteristic
590C4#546×C15112yes—
591C2—22no—
592C2—22no—
593C2—41no—
594C2—42no—
595C2—81no—
596C2#2412×C15111yescharacteristic
597C2C2×#473×C15111yescharacteristic
598C2#3068×C15111yescharacteristic
subgroupG/H
center, socleC22×C151C2×#121
commutator, Frattini, cosocleC22×C4C24×C151
prime radicalC22×#41×C151C22
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C151 ◁ C23×C4×C151 ◁ G

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
1. C2×#484×C151C2semidirect
5. #2078×C151C2semidirect
6. #2052×C151C2semidirect
7. #1908×C151C2semidirect
8. #1901×C151C2semidirect
9. #1855×C151C2semidirect
10. #1821×C151C2semidirect
11. #1816×C151C2semidirect
26. C2×#108×C151C22semidirect
27. C2×#107×C151C22semidirect
35. C2×#103×C151C22semidirect
37. C2×#101×C151C22semidirect
45. #343×C151C22semidirect
46. #343×C151C22semidirect
47. #343×C151C22semidirect
48. #341×C151C22semidirect
299. #24572C151direct (N × H)
300. C151#24572direct (N × H)
301. C2×#484C2×C151semidirect
305. #2078C2×C151semidirect
306. #2052C2×C151semidirect
307. #1908C2×C151semidirect
308. #1901C2×C151semidirect
309. #1855C2×C151semidirect
310. #1821C2×C151semidirect
311. #1816C2×C151semidirect
326. C2×#108C22×C151semidirect
327. C2×#107C22×C151semidirect
335. C2×#103C22×C151semidirect
337. C2×#101C22×C151semidirect
345. #343C22×C151semidirect
346. #343C22×C151semidirect
347. #343C22×C151semidirect
348. #341C22×C151semidirect

Maximal subgroups

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

subgroupindex
C2×#484×C1512
#3007×C1512
C2×#417×C1512
#2880×C1512
#2078×C1512
#2052×C1512
#1908×C1512
#1901×C1512
#1855×C1512
#1821×C1512
#1816×C1512
#24572151