Finite Group Databasebeta

← C151×#24377 #50329302

Subgroups — C151×#24377 #50329302

Order 38656.

1450 conjugacy classes of subgroups.

The subgroup lattice has 574 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#137×C151C211yesmaximal, characteristic, complemented
2C2×#463×C151C212yesmaximal, complemented
3C2×#449×C151C211yesmaximal, characteristic
4#2436×C151C211yesmaximal, characteristic, complemented
5#2339×C151C211yesmaximal, characteristic, complemented
6#2056×C151C212yesmaximal, complemented
7#2015×C151C212yesmaximal, complemented
8#1895×C151C211yesmaximal, characteristic, complemented
9#1877×C151C212yesmaximal, complemented
10#1851×C151C211yesmaximal, characteristic, complemented
11#1787×C151C211yesmaximal, characteristic, complemented
12C22×#41×C151C2211yescharacteristic
13C23×Q8×C151C2211yescharacteristic
14C2×#137×C151—24no—
15C2×#137×C151—28no—
16C22×Q16×C151C2212yes—
17C22×SD16×C151C2212yes—
18C22×SD16×C151C2211yescharacteristic
19C22×D8×C151C2211yescharacteristic
20C22×M16×C151C2211yescharacteristic
21C2×#124×C151C2212yes—
22C2×#121×C151C2211yescharacteristic
23C2×C4×D4×C151C2212yes—
24#463×C151—28no—
25#449×C151—24no—
26C2×C4⋊C8×C151C2212yes—
27C2×#103×C151C2211yescharacteristic
28C2×#103×C151C2212yes—
29C2×#103×C151C2212yes—
30C2×#102×C151C2211yescharacteristic
31C2×#102×C151C2212yes—
32C2×C22⋊C8×C151C2211yescharacteristic
33#393×C151—21no—
34#393×C151—21no—
35#391×C151C2212yes—
36#391×C151C2212yes—
37#386×C151—22no—
38#386×C151—22no—
39#381×C151—21no—
40#380×C151C2211yescharacteristic
41C4×C22⋊C4×C151C2211yescharacteristic
42C2×#95×C151—21no—
43#340×C151C2212yes—
44#336×C151C2212yes—
45C2×#41×C151—24no—
46C2×#41×C151—22no—
47C2×#41×C151—42no—
48C2×#41×C151D414yes—
49C22×Q8×C151—22no—
50C22×Q8×C151—24no—
51C22×Q8×C151—22no—
52C22×Q8×C151—21no—
53C22×Q8×C151—42no—
54C22×Q8×C151C2311yescharacteristic
55C22×Q8×C151C2312yes—
56C22×D4×C151—21no—
57C22×D4×C151—21no—
58C22×D4×C151C2311yescharacteristic
59C22×D4×C151C2311yescharacteristic
60C23×C4×C151—21no—
61C23×C4×C151—22no—
62C23×C4×C151—21no—
63C23×C4×C151C2311yescharacteristic
64#137×C151—232no—
65C2×Q16×C151—24no—
66C2×Q16×C151—24no—
67C2×Q16×C151—24no—
68C2×SD16×C151—24no—
69C2×SD16×C151—24no—
70C2×SD16×C151—22no—
71C2×SD16×C151—42no—
72C2×SD16×C151D418yescomplemented
73C2×D8×C151—22no—
74C2×D8×C151—24no—
75C2×M16×C151—22no—
76C2×M16×C151—24no—
77C22×C8×C151C2311yescharacteristic
78C22×C8×C151C2311yescharacteristic
79C22×C8×C151C2312yes—
80#124×C151—24no—
81#124×C151—42no—
82#121×C151—22no—
83#121×C151—22no—
84C4×D4×C151—24no—
85C4×D4×C151—42no—
86C2×C4⋊C4×C151C2311yescharacteristic
87C2×C4⋊C4×C151C2312yes—
88C2×C22⋊C4×C151—22no—
89C2×C22⋊C4×C151—22no—
90C2×C22⋊C4×C151—22no—
91C2×C22⋊C4×C151—21no—
92C2×C22⋊C4×C151—21no—
93C2×C22⋊C4×C151D412yes—
94C2×C42×C151C2312yes—
95C4⋊C8×C151—24no—
96#103×C151—22no—
97#103×C151—24no—
98#103×C151—42no—
99#102×C151—22no—
100#102×C151—24no—
101C22⋊C8×C151—22no—
102#95×C151—21no—
103#95×C151—22no—
104#95×C151—22no—
105#95×C151—22no—
106#95×C151—22no—
107#95×C151D411yescharacteristic
108#95×C151D411yescharacteristic
109C24×C151—21no—
110C24×C151—21no—
111C24×C151C2×D411yescharacteristic
112#41×C151—28no—
113#41×C151—44no—
114#41×C151—48no—
115C2×Q8×C151—21no—
116C2×Q8×C151—22no—
117C2×Q8×C151—28no—
118C2×Q8×C151—22no—
119C2×Q8×C151—22no—
120C2×Q8×C151—22no—
121C2×Q8×C151—22no—
122C2×Q8×C151—22no—
123C2×Q8×C151—22no—
124C2×Q8×C151—44no—
125C2×Q8×C151—48no—
126C2×Q8×C151—44no—
127C2×Q8×C151—42no—
128C2×Q8×C151C2×D414yes—
129C2×Q8×C151C2×D412yes—
130C2×D4×C151—24no—
131C2×D4×C151—22no—
132C2×D4×C151—21no—
133C2×D4×C151—21no—
134C2×D4×C151—21no—
135C2×D4×C151—22no—
136C2×D4×C151—22no—
137C2×D4×C151—44no—
138C2×D4×C151—44no—
139C2×D4×C151—42no—
140C2×D4×C151C2×D412yes—
141C2×D4×C151C2×D414yes—
142C22×C4×C151—22no—
143C22×C4×C151—22no—
144C22×C4×C151—21no—
145C22×C4×C151—22no—
146C22×C4×C151—24no—
147C22×C4×C151—21no—
148C22×C4×C151—22no—
149C22×C4×C151—44no—
150C22×C4×C151—44no—
151C22×C4×C151—44no—
152C22×C4×C151—44no—
153C22×C4×C151—42no—
154C22×C4×C151—82no—
155C22×C4×C151C2×D412yes—
156C22×C4×C151C2×D412yes—
157C22×C4×C151C2×D411yescharacteristic
158C22×C4×C151C2×D412yes—
159C22×C4×C151#4112yes—
160C22×C4×C151C2411yescharacteristic
161Q16×C151—216no—
162SD16×C151—216no—
163SD16×C151—44no—
164D8×C151—44no—
165M16×C151—28no—
166C2×C8×C151—22no—
167C2×C8×C151—22no—
168C2×C8×C151—21no—
169C2×C8×C151—21no—
170C2×C8×C151—22no—
171C2×C8×C151—22no—
172C2×C8×C151C2×D414yes—
173C4⋊C4×C151—22no—
174C4⋊C4×C151—21no—
175C4⋊C4×C151—21no—
176C4⋊C4×C151—22no—
177C22⋊C4×C151—42no—
178C22⋊C4×C151—44no—
179C22⋊C4×C151—44no—
180C22⋊C4×C151—44no—
181C22⋊C4×C151—42no—
182C22⋊C4×C151—81no—
183C42×C151—22no—
184C42×C151—22no—
185C23×C151—22no—
186C23×C151—24no—
187C23×C151—22no—
188C23×C151—22no—
189C23×C151—21no—
190C23×C151—21no—
191C23×C151—42no—
192C23×C151—41no—
193C23×C151—41no—
194C23×C151—41no—
195C23×C151—42no—
196C23×C151—42no—
197C23×C151—41no—
198C23×C151—41no—
199C23×C151#12112yes—
200C23×C151C22×D411yescharacteristic
201Q8×C151—24no—
202Q8×C151—22no—
203Q8×C151—22no—
204Q8×C151—24no—
205Q8×C151—48no—
206Q8×C151—42no—
207Q8×C151—42no—
208Q8×C151—42no—
209D4×C151—22no—
210D4×C151—24no—
211D4×C151—48no—
212D4×C151—41no—
213D4×C151—41no—
214D4×C151—42no—
215D4×C151—84no—
216D4×C151#12014yes—
217C2×C4×C151—22no—
218C2×C4×C151—22no—
219C2×C4×C151—22no—
220C2×C4×C151—24no—
221C2×C4×C151—22no—
222C2×C4×C151—24no—
223C2×C4×C151—22no—
224C2×C4×C151—22no—
225C2×C4×C151—22no—
226C2×C4×C151—22no—
227C2×C4×C151—22no—
228C2×C4×C151—22no—
229C2×C4×C151—48no—
230C2×C4×C151—48no—
231C2×C4×C151—42no—
232C2×C4×C151—42no—
233C2×C4×C151—42no—
234C2×C4×C151—41no—
235C2×C4×C151—42no—
236C2×C4×C151—42no—
237C2×C4×C151—42no—
238C2×C4×C151—42no—
239C2×C4×C151—88no—
240C2×C4×C151#12112yes—
241C2×C4×C151C22×D411yescharacteristic
242C2×C4×C151C22×D412yes—
243C2×C4×C151C2×#4111yescharacteristic
244C2×C4×C151H(5,𝔽2)12yes—
245C8×C151—24no—
246C8×C151—41no—
247C8×C151—41no—
248C22×C151—22no—
249C22×C151—24no—
250C22×C151—22no—
251C22×C151—22no—
252C22×C151—42no—
253C22×C151—44no—
254C22×C151—44no—
255C22×C151—42no—
256C22×C151—42no—
257C22×C151—42no—
258C22×C151—81no—
259C22×C151—82no—
260C22×C151—82no—
261C22×C151—81no—
262C22×C151—81no—
263C22×C151C2×#12111yescharacteristic
264C22×C151D4212yes—
265C22×C151#57512yes—
266C22×C151#57711yescharacteristic
267C22×C151#57811yescharacteristic
268C4×C151—22no—
269C4×C151—42no—
270C4×C151—44no—
271C4×C151—42no—
272C4×C151—42no—
273C4×C151—82no—
274C4×C151—81no—
275C4×C151C2×#12011yescharacteristic
276C4×C151#53411yescharacteristic
277C4×C151#54612yes—
278C2×C151—42no—
279C2×C151—44no—
280C2×C151—161no—
281C2×C151#241011yescharacteristic
282C2×C151#304011yescharacteristic
283C2×C151#304611yescharacteristic
284C2×C151#326912yes—
285C2×C151#327512yes—
286#24377C15111yesmaximal, characteristic, direct product factor, Sylow
287C151#2437711yescharacteristic, direct product factor, Sylow
288C22×#137C2×C15111yescharacteristic, complemented
289C2×#463C2×C15112yescomplemented
290C2×#449C2×C15111yescharacteristic
291#2436C2×C15111yescharacteristic, complemented
292#2339C2×C15111yescharacteristic, complemented
293#2056C2×C15112yescomplemented
294#2015C2×C15112yescomplemented
295#1895C2×C15111yescharacteristic, complemented
296#1877C2×C15112yescomplemented
297#1851C2×C15111yescharacteristic, complemented
298#1787C2×C15111yescharacteristic, complemented
299C22×#41C22×C15111yescharacteristic
300C23×Q8C22×C15111yescharacteristic
301C2×#137—24no—
302C2×#137—28no—
303C22×Q16C22×C15112yes—
304C22×SD16C22×C15112yes—
305C22×SD16C22×C15111yescharacteristic
306C22×D8C22×C15111yescharacteristic
307C22×M16C22×C15111yescharacteristic
308C2×#124C22×C15112yes—
309C2×#121C22×C15111yescharacteristic
310C2×C4×D4C22×C15112yes—
311#463—28no—
312#449—24no—
313C2×C4⋊C8C22×C15112yes—
314C2×#103C22×C15111yescharacteristic
315C2×#103C22×C15112yes—
316C2×#103C22×C15112yes—
317C2×#102C22×C15111yescharacteristic
318C2×#102C22×C15112yes—
319C2×C22⋊C8C22×C15111yescharacteristic
320#393—21no—
321#393—21no—
322#391C22×C15112yes—
323#391C22×C15112yes—
324#386—22no—
325#386—22no—
326#381—21no—
327#380C22×C15111yescharacteristic
328C4×C22⋊C4C22×C15111yescharacteristic
329C2×#95—21no—
330#340C22×C15112yes—
331#336C22×C15112yes—
332C2×#41—22no—
333C2×#41—24no—
334C2×#41—42no—
335C2×#41D4×C15114yes—
336C22×Q8—21no—
337C22×Q8—24no—
338C22×Q8—22no—
339C22×Q8—22no—
340C22×Q8—42no—
341C22×Q8C23×C15112yes—
342C22×Q8C23×C15111yescharacteristic
343C22×D4—21no—
344C22×D4—21no—
345C22×D4C23×C15111yescharacteristic
346C22×D4C23×C15111yescharacteristic
347C23×C4—21no—
348C23×C4—21no—
349C23×C4—22no—
350C23×C4C23×C15111yescharacteristic
351#137—232no—
352C2×Q16—24no—
353C2×Q16—24no—
354C2×Q16—24no—
355C2×SD16—24no—
356C2×SD16—24no—
357C2×SD16—22no—
358C2×SD16—42no—
359C2×SD16D4×C15118yescomplemented
360C2×D8—22no—
361C2×D8—24no—
362C2×M16—22no—
363C2×M16—24no—
364C22×C8C23×C15111yescharacteristic
365C22×C8C23×C15111yescharacteristic
366C22×C8C23×C15112yes—
367#124—24no—
368#124—42no—
369#121—22no—
370#121—22no—
371C4×D4—24no—
372C4×D4—42no—
373C2×C4⋊C4C23×C15112yes—
374C2×C4⋊C4C23×C15111yescharacteristic
375C2×C22⋊C4—22no—
376C2×C22⋊C4—21no—
377C2×C22⋊C4—22no—
378C2×C22⋊C4—22no—
379C2×C22⋊C4—21no—
380C2×C22⋊C4D4×C15112yes—
381C2×C42C23×C15112yes—
382C4⋊C8—24no—
383#103—22no—
384#103—24no—
385#103—42no—
386#102—22no—
387#102—24no—
388C22⋊C8—22no—
389#95—21no—
390#95—22no—
391#95—22no—
392#95—22no—
393#95—22no—
394#95D4×C15111yescharacteristic
395#95D4×C15111yescharacteristic
396C24—21no—
397C24—21no—
398C24C2×D4×C15111yescharacteristic
399#41—28no—
400#41—44no—
401#41—48no—
402C2×Q8—21no—
403C2×Q8—22no—
404C2×Q8—28no—
405C2×Q8—22no—
406C2×Q8—22no—
407C2×Q8—22no—
408C2×Q8—22no—
409C2×Q8—22no—
410C2×Q8—22no—
411C2×Q8—44no—
412C2×Q8—48no—
413C2×Q8—44no—
414C2×Q8—42no—
415C2×Q8C2×D4×C15114yes—
416C2×Q8C2×D4×C15112yes—
417C2×D4—24no—
418C2×D4—22no—
419C2×D4—21no—
420C2×D4—21no—
421C2×D4—21no—
422C2×D4—22no—
423C2×D4—22no—
424C2×D4—44no—
425C2×D4—44no—
426C2×D4—42no—
427C2×D4C2×D4×C15112yes—
428C2×D4C2×D4×C15114yes—
429C22×C4—22no—
430C22×C4—22no—
431C22×C4—21no—
432C22×C4—22no—
433C22×C4—24no—
434C22×C4—21no—
435C22×C4—22no—
436C22×C4—44no—
437C22×C4—44no—
438C22×C4—44no—
439C22×C4—44no—
440C22×C4—42no—
441C22×C4—82no—
442C22×C4C2×D4×C15112yes—
443C22×C4C2×D4×C15112yes—
444C22×C4C2×D4×C15111yescharacteristic
445C22×C4C2×D4×C15112yes—
446C22×C4#41×C15112yes—
447C22×C4C24×C15111yescharacteristic
448Q16—216no—
449SD16—216no—
450SD16—44no—
451D8—44no—
452M16—28no—
453C2×C8—22no—
454C2×C8—22no—
455C2×C8—21no—
456C2×C8—21no—
457C2×C8—22no—
458C2×C8—22no—
459C2×C8C2×D4×C15114yes—
460C4⋊C4—22no—
461C4⋊C4—21no—
462C4⋊C4—21no—
463C4⋊C4—22no—
464C22⋊C4—42no—
465C22⋊C4—44no—
466C22⋊C4—44no—
467C22⋊C4—44no—
468C22⋊C4—42no—
469C22⋊C4—81no—
470C42—22no—
471C42—22no—
472C23—22no—
473C23—24no—
474C23—22no—
475C23—22no—
476C23—21no—
477C23—21no—
478C23—42no—
479C23—41no—
480C23—41no—
481C23—41no—
482C23—42no—
483C23—42no—
484C23—41no—
485C23—41no—
486C23#121×C15112yes—
487C23C22×D4×C15111yescharacteristic
488Q8—24no—
489Q8—22no—
490Q8—22no—
491Q8—24no—
492Q8—48no—
493Q8—42no—
494Q8—42no—
495Q8—42no—
496D4—22no—
497D4—24no—
498D4—48no—
499D4—41no—
500D4—41no—
501D4—42no—
502D4—84no—
503D4#120×C15114yes—
504C2×C4—22no—
505C2×C4—22no—
506C2×C4—22no—
507C2×C4—24no—
508C2×C4—22no—
509C2×C4—22no—
510C2×C4—22no—
511C2×C4—24no—
512C2×C4—22no—
513C2×C4—22no—
514C2×C4—22no—
515C2×C4—22no—
516C2×C4—48no—
517C2×C4—48no—
518C2×C4—42no—
519C2×C4—42no—
520C2×C4—42no—
521C2×C4—41no—
522C2×C4—42no—
523C2×C4—42no—
524C2×C4—42no—
525C2×C4—42no—
526C2×C4—88no—
527C2×C4#121×C15112yes—
528C2×C4C22×D4×C15111yescharacteristic
529C2×C4C22×D4×C15112yes—
530C2×C4C2×#41×C15111yescharacteristic
531C2×C4H(5,𝔽2)×C15112yes—
532C8—24no—
533C8—41no—
534C8—41no—
535C22—22no—
536C22—24no—
537C22—22no—
538C22—22no—
539C22—42no—
540C22—44no—
541C22—44no—
542C22—42no—
543C22—42no—
544C22—42no—
545C22—81no—
546C22—82no—
547C22—82no—
548C22—81no—
549C22—81no—
550C22C2×#121×C15111yescharacteristic
551C22D42×C15112yes—
552C22#575×C15112yes—
553C22#577×C15111yescharacteristic
554C22#578×C15111yescharacteristic
555C4—22no—
556C4—42no—
557C4—44no—
558C4—42no—
559C4—42no—
560C4—82no—
561C4—81no—
562C4C2×#120×C15111yescharacteristic
563C4#534×C15111yescharacteristic
564C4#546×C15112yes—
565C2—42no—
566C2—44no—
567C2—161no—
568C2#2410×C15111yescharacteristic
569C2#3040×C15111yescharacteristic
570C2#3046×C15111yescharacteristic
571C2#3269×C15112yes—
572C2#3275×C15112yes—
subgroupG/H
center, socleC23×C151C22×D4
commutator, Frattini, cosocleC22×C4C24×C151
prime radicalC2×#449×C151C2
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C151 ◁ C4×C22⋊C4×C151 ◁ G

Complements

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

NH ≅ G/Ntype
1. C22×#137×C151C2semidirect
2. C2×#463×C151C2semidirect
4. #2436×C151C2semidirect
5. #2339×C151C2semidirect
6. #2056×C151C2semidirect
7. #2015×C151C2semidirect
8. #1895×C151C2semidirect
9. #1877×C151C2semidirect
10. #1851×C151C2semidirect
11. #1787×C151C2semidirect
72. C2×SD16×C151D4semidirect
286. #24377C151direct (N × H)
287. C151#24377direct (N × H)
288. C22×#137C2×C151semidirect
289. C2×#463C2×C151semidirect
291. #2436C2×C151semidirect
292. #2339C2×C151semidirect
293. #2056C2×C151semidirect
294. #2015C2×C151semidirect
295. #1895C2×C151semidirect
296. #1877C2×C151semidirect
297. #1851C2×C151semidirect
298. #1787C2×C151semidirect
359. C2×SD16D4×C151semidirect

Maximal subgroups

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

subgroupindex
C22×#137×C1512
C2×#463×C1512
C2×#449×C1512
#2436×C1512
#2339×C1512
#2056×C1512
#2015×C1512
#1895×C1512
#1877×C1512
#1851×C1512
#1787×C1512
#24377151