Finite Group Databasebeta

← C151×#24128 #50329053

Subgroups — C151×#24128 #50329053

Order 38656.

1400 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
1C2×#547×C151C211yesmaximal, characteristic, complemented
2C2×#476×C151C211yesmaximal, characteristic, complemented
3C2×#442×C151C211yesmaximal, characteristic, complemented
4#2535×C151C211yesmaximal, characteristic, complemented
5#2034×C151C212yesmaximal, complemented
6#1999×C151C212yesmaximal, complemented
7#1993×C151C211yesmaximal, characteristic, complemented
8#1955×C151C211yesmaximal, characteristic, complemented
9#1874×C151C212yesmaximal, complemented
10#1853×C151C212yesmaximal, complemented
11#1804×C151C211yesmaximal, characteristic, complemented
12C22×#41×C151—21no—
13C22×D8×C151C2211yescharacteristic
14#547×C151—24no—
15#547×C151—24no—
16C2×C4⋊Q8×C151C2211yescharacteristic
17C2×#123×C151—22no—
18C2×C22⋊Q8×C151—21no—
19C2×#121×C151C2212yes—
20C2×#121×C151C2212yes—
21C2×C4×D4×C151C2211yescharacteristic
22C2×C4×D4×C151C2211yescharacteristic
23C2×C4×D4×C151C2211yescharacteristic
24C22×C4⋊C4×C151C2212yes—
25#476×C151—24no—
26#442×C151—24no—
27C2×#106×C151C2211yescharacteristic
28C2×#106×C151C2212yes—
29C2×C4⋊C8×C151C2211yescharacteristic
30C2×#102×C151C2211yescharacteristic
31C2×#102×C151C2212yes—
32C2×#102×C151C2211yescharacteristic
33C2×#102×C151C2212yes—
34C2×C22⋊C8×C151C2212yes—
35C2×C22⋊C8×C151C2212yes—
36C2×#97×C151C2211yescharacteristic
37#397×C151—21no—
38#392×C151—21no—
39#386×C151—22no—
40#382×C151C2211yescharacteristic
41#380×C151C2212yes—
42#340×C151C2212yes—
43#340×C151C2212yes—
44#340×C151C2212yes—
45C2×#41×C151—28no—
46C2×#41×C151—48no—
47C22×Q8×C151—21no—
48C22×D4×C151—22no—
49C22×D4×C151—22no—
50C22×D4×C151D411yescharacteristic
51C22×D4×C151C2311yescharacteristic
52C22×D4×C151C2311yescharacteristic
53C23×C4×C151—21no—
54C23×C4×C151—21no—
55C23×C4×C151—22no—
56C23×C4×C151C2312yes—
57C2×D8×C151—22no—
58C2×D8×C151—22no—
59C2×D8×C151—22no—
60C22×C8×C151C2311yescharacteristic
61C22×C8×C151C2312yes—
62C22×C8×C151C2311yescharacteristic
63C4⋊Q8×C151—22no—
64C4⋊Q8×C151D414yescomplemented
65#123×C151—216no—
66C22⋊Q8×C151—28no—
67#121×C151—24no—
68#121×C151—24no—
69#121×C151—24no—
70#121×C151—42no—
71C4×D4×C151—22no—
72C4×D4×C151—22no—
73C4×D4×C151—22no—
74C4×D4×C151—22no—
75C4×D4×C151—22no—
76C4×D4×C151D414yescomplemented
77C2×C4⋊C4×C151—22no—
78C2×C4⋊C4×C151—21no—
79C2×C4⋊C4×C151—24no—
80C2×C4⋊C4×C151—24no—
81C2×C4⋊C4×C151D411yescharacteristic
82C2×C4⋊C4×C151C2312yes—
83C2×C4⋊C4×C151C2311yescharacteristic
84C2×C4⋊C4×C151C2311yescharacteristic
85C2×C4⋊C4×C151C2312yes—
86C2×C22⋊C4×C151—21no—
87C2×C22⋊C4×C151—22no—
88C2×C22⋊C4×C151—22no—
89C2×C22⋊C4×C151—21no—
90C2×C22⋊C4×C151—22no—
91C2×C22⋊C4×C151D412yes—
92C2×C42×C151C2311yescharacteristic
93#106×C151—22no—
94#106×C151—24no—
95C4⋊C8×C151—22no—
96#102×C151—22no—
97#102×C151—22no—
98#102×C151—24no—
99#102×C151—42no—
100C22⋊C8×C151—24no—
101C22⋊C8×C151—42no—
102#97×C151—22no—
103#95×C151—22no—
104#95×C151—21no—
105#95×C151—21no—
106C24×C151—21no—
107C24×C151—21no—
108C24×C151C2×D412yes—
109#41×C151—432no—
110C2×Q8×C151—24no—
111C2×Q8×C151—44no—
112C2×D4×C151—24no—
113C2×D4×C151—28no—
114C2×D4×C151—22no—
115C2×D4×C151—21no—
116C2×D4×C151—21no—
117C2×D4×C151—21no—
118C2×D4×C151—21no—
119C2×D4×C151—21no—
120C2×D4×C151—21no—
121C2×D4×C151—21no—
122C2×D4×C151—21no—
123C2×D4×C151—21no—
124C2×D4×C151—21no—
125C2×D4×C151—44no—
126C2×D4×C151—44no—
127C2×D4×C151—44no—
128C2×D4×C151—44no—
129C2×D4×C151—82no—
130C2×D4×C151C2×D412yes—
131C2×D4×C151#4112yescomplemented
132C22×C4×C151—28no—
133C22×C4×C151—21no—
134C22×C4×C151—22no—
135C22×C4×C151—24no—
136C22×C4×C151—22no—
137C22×C4×C151—22no—
138C22×C4×C151—22no—
139C22×C4×C151—22no—
140C22×C4×C151—22no—
141C22×C4×C151—22no—
142C22×C4×C151—22no—
143C22×C4×C151—21no—
144C22×C4×C151—44no—
145C22×C4×C151—44no—
146C22×C4×C151—44no—
147C22×C4×C151—42no—
148C22×C4×C151—82no—
149C22×C4×C151C2×D412yes—
150C22×C4×C151C2×D411yescharacteristic
151C22×C4×C151C2×D411yescharacteristic
152C22×C4×C151C2411yescharacteristic
153D8×C151—28no—
154C2×C8×C151—21no—
155C2×C8×C151—21no—
156C2×C8×C151—21no—
157C2×C8×C151—22no—
158C2×C8×C151—22no—
159C2×C8×C151—21no—
160C2×C8×C151—22no—
161C2×C8×C151—21no—
162C2×C8×C151#4112yescomplemented
163C4⋊C4×C151—28no—
164C4⋊C4×C151—24no—
165C4⋊C4×C151—22no—
166C4⋊C4×C151—21no—
167C4⋊C4×C151—22no—
168C4⋊C4×C151—21no—
169C4⋊C4×C151—21no—
170C4⋊C4×C151—22no—
171C4⋊C4×C151—22no—
172C4⋊C4×C151C2×D412yes—
173C4⋊C4×C151C2×D414yes—
174C22⋊C4×C151—28no—
175C22⋊C4×C151—24no—
176C22⋊C4×C151—24no—
177C22⋊C4×C151—44no—
178C22⋊C4×C151—42no—
179C22⋊C4×C151—82no—
180C42×C151C2×D412yes—
181C42×C151C2×D412yes—
182C23×C151—22no—
183C23×C151—22no—
184C23×C151—22no—
185C23×C151—22no—
186C23×C151—22no—
187C23×C151—22no—
188C23×C151—22no—
189C23×C151—22no—
190C23×C151—41no—
191C23×C151—41no—
192C23×C151—41no—
193C23×C151—41no—
194C23×C151—42no—
195C23×C151—42no—
196C23×C151—42no—
197C23×C151—42no—
198C23×C151AGL(1,ℤ/8)14yes—
199C23×C151C22×D411yescharacteristic
200Q8×C151—48no—
201D4×C151—28no—
202D4×C151—22no—
203D4×C151—22no—
204D4×C151—22no—
205D4×C151—22no—
206D4×C151—416no—
207D4×C151—41no—
208D4×C151—41no—
209D4×C151—41no—
210D4×C151—41no—
211D4×C151—88no—
212C2×C4×C151—22no—
213C2×C4×C151—22no—
214C2×C4×C151—24no—
215C2×C4×C151—22no—
216C2×C4×C151—22no—
217C2×C4×C151—22no—
218C2×C4×C151—22no—
219C2×C4×C151—48no—
220C2×C4×C151—416no—
221C2×C4×C151—42no—
222C2×C4×C151—42no—
223C2×C4×C151—42no—
224C2×C4×C151—42no—
225C2×C4×C151—42no—
226C2×C4×C151—42no—
227C2×C4×C151—42no—
228C2×C4×C151—41no—
229C2×C4×C151—42no—
230C2×C4×C151—42no—
231C2×C4×C151—42no—
232C2×C4×C151—42no—
233C2×C4×C151—84no—
234C2×C4×C151#12012yes—
235C2×C4×C151#12012yes—
236C2×C4×C151C22×D411yescharacteristic
237C2×C4×C151C22×D411yescharacteristic
238C2×C4×C151C2×#4111yescharacteristic
239C2×C4×C151C2×#4111yescharacteristic
240C2×C4×C151H(5,𝔽2)11yescharacteristic
241C2×C4×C1512−1+411yescharacteristic
242C8×C151—22no—
243C8×C151—41no—
244C8×C151—42no—
245C22×C151—24no—
246C22×C151—24no—
247C22×C151—24no—
248C22×C151—42no—
249C22×C151—42no—
250C22×C151—42no—
251C22×C151—42no—
252C22×C151—42no—
253C22×C151—42no—
254C22×C151—42no—
255C22×C151—42no—
256C22×C151—44no—
257C22×C151—82no—
258C22×C151—82no—
259C22×C151—81no—
260C22×C151—81no—
261C22×C151—82no—
262C22×C151C2×#12011yescharacteristic
263C22×C151#54611yescharacteristic
264C22×C151#54711yescharacteristic
265C22×C151C2×AGL(1,ℤ/8)12yes—
266C22×C151#57712yes—
267C4×C151—22no—
268C4×C151—22no—
269C4×C151—42no—
270C4×C151—42no—
271C4×C151—44no—
272C4×C151—81no—
273C4×C151—82no—
274C4×C151#52511yescharacteristic
275C4×C151#53711yescharacteristic
276C4×C151#54811yescharacteristic
277C4×C151#55011yescharacteristic
278C2×C151—44no—
279C2×C151—82no—
280C2×C151—82no—
281C2×C151#240711yescharacteristic
282C2×C151#300311yescharacteristic
283C2×C151#301011yescharacteristic
284C2×C151#330612yes—
285C2×C151#334512yes—
286#24128C15111yesmaximal, characteristic, direct product factor, Sylow
287C151#2412811yescharacteristic, direct product factor, Sylow
288C2×#547C2×C15111yescharacteristic, complemented
289C2×#476C2×C15111yescharacteristic, complemented
290C2×#442C2×C15111yescharacteristic, complemented
291#2535C2×C15111yescharacteristic, complemented
292#2034C2×C15112yescomplemented
293#1999C2×C15112yescomplemented
294#1993C2×C15111yescharacteristic, complemented
295#1955C2×C15111yescharacteristic, complemented
296#1874C2×C15112yescomplemented
297#1853C2×C15112yescomplemented
298#1804C2×C15111yescharacteristic, complemented
299C22×#41—21no—
300C22×D8C22×C15111yescharacteristic
301#547—24no—
302#547—24no—
303C2×C4⋊Q8C22×C15111yescharacteristic
304C2×#123—22no—
305C2×C22⋊Q8—21no—
306C2×#121C22×C15112yes—
307C2×#121C22×C15112yes—
308C2×C4×D4C22×C15111yescharacteristic
309C2×C4×D4C22×C15111yescharacteristic
310C2×C4×D4C22×C15111yescharacteristic
311C22×C4⋊C4C22×C15112yes—
312#476—24no—
313#442—24no—
314C2×#106C22×C15111yescharacteristic
315C2×#106C22×C15112yes—
316C2×C4⋊C8C22×C15111yescharacteristic
317C2×#102C22×C15111yescharacteristic
318C2×#102C22×C15112yes—
319C2×#102C22×C15111yescharacteristic
320C2×#102C22×C15112yes—
321C2×C22⋊C8C22×C15112yes—
322C2×C22⋊C8C22×C15112yes—
323C2×#97C22×C15111yescharacteristic
324#397—21no—
325#392—21no—
326#386—22no—
327#382C22×C15111yescharacteristic
328#380C22×C15112yes—
329#340C22×C15112yes—
330#340C22×C15112yes—
331#340C22×C15112yes—
332C2×#41—28no—
333C2×#41—48no—
334C22×Q8—21no—
335C22×D4—22no—
336C22×D4—22no—
337C22×D4D4×C15111yescharacteristic
338C22×D4C23×C15111yescharacteristic
339C22×D4C23×C15111yescharacteristic
340C23×C4—22no—
341C23×C4—21no—
342C23×C4—21no—
343C23×C4C23×C15112yes—
344C2×D8—22no—
345C2×D8—22no—
346C2×D8—22no—
347C22×C8C23×C15111yescharacteristic
348C22×C8C23×C15112yes—
349C22×C8C23×C15111yescharacteristic
350C4⋊Q8—22no—
351C4⋊Q8D4×C15114yescomplemented
352#123—216no—
353C22⋊Q8—28no—
354#121—24no—
355#121—24no—
356#121—24no—
357#121—42no—
358C4×D4—22no—
359C4×D4—22no—
360C4×D4—22no—
361C4×D4—22no—
362C4×D4—22no—
363C4×D4D4×C15114yescomplemented
364C2×C4⋊C4—22no—
365C2×C4⋊C4—21no—
366C2×C4⋊C4—24no—
367C2×C4⋊C4—24no—
368C2×C4⋊C4D4×C15111yescharacteristic
369C2×C4⋊C4C23×C15111yescharacteristic
370C2×C4⋊C4C23×C15112yes—
371C2×C4⋊C4C23×C15111yescharacteristic
372C2×C4⋊C4C23×C15112yes—
373C2×C22⋊C4—21no—
374C2×C22⋊C4—22no—
375C2×C22⋊C4—21no—
376C2×C22⋊C4—22no—
377C2×C22⋊C4—22no—
378C2×C22⋊C4D4×C15112yes—
379C2×C42C23×C15111yescharacteristic
380#106—22no—
381#106—24no—
382C4⋊C8—22no—
383#102—22no—
384#102—22no—
385#102—24no—
386#102—42no—
387C22⋊C8—24no—
388C22⋊C8—42no—
389#97—22no—
390#95—22no—
391#95—21no—
392#95—21no—
393C24—21no—
394C24—21no—
395C24C2×D4×C15112yes—
396#41—432no—
397C2×Q8—24no—
398C2×Q8—44no—
399C2×D4—24no—
400C2×D4—28no—
401C2×D4—22no—
402C2×D4—21no—
403C2×D4—21no—
404C2×D4—21no—
405C2×D4—21no—
406C2×D4—21no—
407C2×D4—21no—
408C2×D4—21no—
409C2×D4—21no—
410C2×D4—21no—
411C2×D4—21no—
412C2×D4—44no—
413C2×D4—44no—
414C2×D4—44no—
415C2×D4—44no—
416C2×D4—82no—
417C2×D4C2×D4×C15112yes—
418C2×D4#41×C15112yescomplemented
419C22×C4—28no—
420C22×C4—21no—
421C22×C4—22no—
422C22×C4—24no—
423C22×C4—22no—
424C22×C4—22no—
425C22×C4—22no—
426C22×C4—22no—
427C22×C4—22no—
428C22×C4—22no—
429C22×C4—22no—
430C22×C4—21no—
431C22×C4—44no—
432C22×C4—44no—
433C22×C4—44no—
434C22×C4—42no—
435C22×C4—82no—
436C22×C4C2×D4×C15112yes—
437C22×C4C2×D4×C15111yescharacteristic
438C22×C4C2×D4×C15111yescharacteristic
439C22×C4C24×C15111yescharacteristic
440D8—28no—
441C2×C8—21no—
442C2×C8—21no—
443C2×C8—21no—
444C2×C8—22no—
445C2×C8—22no—
446C2×C8—21no—
447C2×C8—22no—
448C2×C8—21no—
449C2×C8#41×C15112yescomplemented
450C4⋊C4—28no—
451C4⋊C4—24no—
452C4⋊C4—22no—
453C4⋊C4—21no—
454C4⋊C4—22no—
455C4⋊C4—21no—
456C4⋊C4—21no—
457C4⋊C4—22no—
458C4⋊C4—22no—
459C4⋊C4C2×D4×C15112yes—
460C4⋊C4C2×D4×C15114yes—
461C22⋊C4—28no—
462C22⋊C4—24no—
463C22⋊C4—24no—
464C22⋊C4—44no—
465C22⋊C4—42no—
466C22⋊C4—82no—
467C42C2×D4×C15112yes—
468C42C2×D4×C15112yes—
469C23—22no—
470C23—22no—
471C23—22no—
472C23—22no—
473C23—22no—
474C23—22no—
475C23—22no—
476C23—22no—
477C23—41no—
478C23—41no—
479C23—41no—
480C23—41no—
481C23—42no—
482C23—42no—
483C23—42no—
484C23—42no—
485C23AGL(1,ℤ/8)×C15114yes—
486C23C22×D4×C15111yescharacteristic
487Q8—48no—
488D4—28no—
489D4—22no—
490D4—22no—
491D4—22no—
492D4—22no—
493D4—416no—
494D4—41no—
495D4—41no—
496D4—41no—
497D4—41no—
498D4—88no—
499C2×C4—22no—
500C2×C4—22no—
501C2×C4—22no—
502C2×C4—22no—
503C2×C4—24no—
504C2×C4—22no—
505C2×C4—22no—
506C2×C4—48no—
507C2×C4—416no—
508C2×C4—42no—
509C2×C4—42no—
510C2×C4—42no—
511C2×C4—42no—
512C2×C4—42no—
513C2×C4—42no—
514C2×C4—42no—
515C2×C4—41no—
516C2×C4—42no—
517C2×C4—42no—
518C2×C4—42no—
519C2×C4—42no—
520C2×C4—84no—
521C2×C4#120×C15112yes—
522C2×C4#120×C15112yes—
523C2×C4C22×D4×C15111yescharacteristic
524C2×C4C22×D4×C15111yescharacteristic
525C2×C4C2×#41×C15111yescharacteristic
526C2×C4C2×#41×C15111yescharacteristic
527C2×C4H(5,𝔽2)×C15111yescharacteristic
528C2×C42−1+4×C15111yescharacteristic
529C8—22no—
530C8—41no—
531C8—42no—
532C22—24no—
533C22—24no—
534C22—24no—
535C22—42no—
536C22—42no—
537C22—42no—
538C22—42no—
539C22—42no—
540C22—42no—
541C22—42no—
542C22—42no—
543C22—44no—
544C22—81no—
545C22—81no—
546C22—82no—
547C22—82no—
548C22—82no—
549C22C2×#120×C15111yescharacteristic
550C22#546×C15111yescharacteristic
551C22#547×C15111yescharacteristic
552C22C2×AGL(1,ℤ/8)×C15112yes—
553C22#577×C15112yes—
554C4—22no—
555C4—22no—
556C4—42no—
557C4—42no—
558C4—44no—
559C4—81no—
560C4—82no—
561C4#525×C15111yescharacteristic
562C4#537×C15111yescharacteristic
563C4#548×C15111yescharacteristic
564C4#550×C15111yescharacteristic
565C2—44no—
566C2—82no—
567C2—82no—
568C2#2407×C15111yescharacteristic
569C2#3003×C15111yescharacteristic
570C2#3010×C15111yescharacteristic
571C2#3306×C15112yes—
572C2#3345×C15112yes—
subgroupG/H
center, socleC23×C151C22×D4
commutator, Frattini, cosocleC22×C4C24×C151
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C151 ◁ C2×C4×D4×C151 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×#547×C151C2semidirect
2. C2×#476×C151C2semidirect
3. C2×#442×C151C2semidirect
4. #2535×C151C2semidirect
5. #2034×C151C2semidirect
6. #1999×C151C2semidirect
7. #1993×C151C2semidirect
8. #1955×C151C2semidirect
9. #1874×C151C2semidirect
10. #1853×C151C2semidirect
11. #1804×C151C2semidirect
64. C4⋊Q8×C151D4semidirect
76. C4×D4×C151D4semidirect
131. C2×D4×C151#41semidirect
162. C2×C8×C151#41semidirect
286. #24128C151direct (N × H)
287. C151#24128direct (N × H)
288. C2×#547C2×C151semidirect
289. C2×#476C2×C151semidirect
290. C2×#442C2×C151semidirect
291. #2535C2×C151semidirect
292. #2034C2×C151semidirect
293. #1999C2×C151semidirect
294. #1993C2×C151semidirect
295. #1955C2×C151semidirect
296. #1874C2×C151semidirect
297. #1853C2×C151semidirect
298. #1804C2×C151semidirect
351. C4⋊Q8D4×C151semidirect
363. C4×D4D4×C151semidirect
418. C2×D4#41×C151semidirect
449. C2×C8#41×C151semidirect

Maximal subgroups

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

subgroupindex
C2×#547×C1512
C2×#476×C1512
C2×#442×C1512
#2535×C1512
#2034×C1512
#1999×C1512
#1993×C1512
#1955×C1512
#1874×C1512
#1853×C1512
#1804×C1512
#24128151