Finite Group Databasebeta

← C151×#24526 #50329451

Subgroups — C151×#24526 #50329451

Order 38656.

1280 conjugacy classes of subgroups.

The subgroup lattice has 572 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#447×C151C211yesmaximal, characteristic
2C22×#102×C151C211yesmaximal, characteristic, complemented
3#2501×C151C211yesmaximal, characteristic, complemented
4D4×C22⋊C4×C151C211yesmaximal, characteristic, complemented
5#2071×C151C212yesmaximal, complemented
6#2054×C151C212yesmaximal, complemented
7#1893×C151C211yesmaximal, characteristic, complemented
8#1879×C151C212yesmaximal, complemented
9#1850×C151C211yesmaximal, characteristic, complemented
10#1823×C151C211yesmaximal, characteristic, complemented
11#1802×C151C212yesmaximal, complemented
12C23×D4×C151C2211yescharacteristic
13C22×D8×C151C2211yescharacteristic
14C22×D8×C151C2211yescharacteristic
15C23×C8×C151C2211yescharacteristic
16C2×#123×C151—21no—
17C2×#123×C151—21no—
18C2×#121×C151C2211yescharacteristic
19C2×C4×D4×C151C2212yes—
20C22×C4⋊C4×C151C2211yescharacteristic
21C22×C22⋊C4×C151—21no—
22#447×C151—24no—
23C2×C4⋊C8×C151C2212yescomplemented
24C2×#102×C151—24no—
25C2×#102×C151C2212yes—
26C2×#102×C151C2212yes—
27C2×#102×C151C2211yescharacteristic
28C2×#102×C151C2211yescharacteristic
29C2×#102×C151C2212yescomplemented
30C2×C22⋊C8×C151C2211yescharacteristic
31#399×C151—22no—
32#390×C151C2212yes—
33#390×C151C2212yescomplemented
34#386×C151—22no—
35#384×C151C2212yescomplemented
36#380×C151C2211yescharacteristic
37#379×C151—21no—
38C4×C22⋊C4×C151C2211yescharacteristic
39#340×C151C2212yescomplemented
40#340×C151C2212yescomplemented
41#340×C151C2212yescomplemented
42#336×C151C2212yescomplemented
43C25×C151—21no—
44C22×D4×C151—21no—
45C22×D4×C151—22no—
46C22×D4×C151—21no—
47C22×D4×C151—24no—
48C22×D4×C151—42no—
49C22×D4×C151D414yes—
50C22×D4×C151C2311yescharacteristic
51C22×D4×C151C2311yescharacteristic
52C22×D4×C151C2311yescharacteristic
53C23×C4×C151—22no—
54C23×C4×C151—21no—
55C23×C4×C151C2311yescharacteristic
56C2×D8×C151—22no—
57C2×D8×C151—22no—
58C2×D8×C151—24no—
59C2×D8×C151—42no—
60C22×C8×C151—22no—
61C22×C8×C151—42no—
62C22×C8×C151C2311yescharacteristic
63C22×C8×C151C2312yes—
64C22×C8×C151C2311yescharacteristic
65#123×C151—44no—
66#123×C151—44no—
67#121×C151—22no—
68#121×C151—22no—
69C4×D4×C151—24no—
70C4×D4×C151—42no—
71C2×C4⋊C4×C151—22no—
72C2×C4⋊C4×C151—22no—
73C2×C4⋊C4×C151—22no—
74C2×C4⋊C4×C151—22no—
75C2×C4⋊C4×C151—21no—
76C2×C4⋊C4×C151C2312yes—
77C2×C4⋊C4×C151C2311yescharacteristic
78C2×C4⋊C4×C151C2312yes—
79C2×C22⋊C4×C151—22no—
80C2×C22⋊C4×C151—22no—
81C2×C22⋊C4×C151—22no—
82C2×C22⋊C4×C151—22no—
83C2×C22⋊C4×C151—21no—
84C2×C22⋊C4×C151—22no—
85C2×C22⋊C4×C151—21no—
86C2×C22⋊C4×C151—44no—
87C2×C22⋊C4×C151D411yescharacteristic
88C2×C22⋊C4×C151D411yescharacteristic
89C2×C42×C151C2312yes—
90C4⋊C8×C151—42no—
91#102×C151—24no—
92#102×C151—24no—
93#102×C151—22no—
94#102×C151—22no—
95#102×C151—42no—
96C22⋊C8×C151—22no—
97#95×C151—21no—
98#95×C151D412yes—
99C24×C151—21no—
100C24×C151—21no—
101C24×C151—24no—
102C24×C151—21no—
103C24×C151—44no—
104C24×C151—42no—
105C24×C151—42no—
106C24×C151—82no—
107C24×C151C2×D411yescharacteristic
108C2×D4×C151—28no—
109C2×D4×C151—24no—
110C2×D4×C151—21no—
111C2×D4×C151—21no—
112C2×D4×C151—22no—
113C2×D4×C151—21no—
114C2×D4×C151—21no—
115C2×D4×C151—22no—
116C2×D4×C151—22no—
117C2×D4×C151—22no—
118C2×D4×C151—22no—
119C2×D4×C151—44no—
120C2×D4×C151—48no—
121C2×D4×C151—44no—
122C2×D4×C151—42no—
123C2×D4×C151—42no—
124C2×D4×C151—42no—
125C2×D4×C151C2×D412yes—
126C2×D4×C151C2×D412yes—
127C2×D4×C151#4114yes—
128C22×C4×C151—22no—
129C22×C4×C151—22no—
130C22×C4×C151—22no—
131C22×C4×C151—22no—
132C22×C4×C151—21no—
133C22×C4×C151—44no—
134C22×C4×C151—42no—
135C22×C4×C151—42no—
136C22×C4×C151—42no—
137C22×C4×C151—44no—
138C22×C4×C151—82no—
139C22×C4×C151C2×D412yes—
140C22×C4×C151C2×D411yescharacteristic
141C22×C4×C151C2×D412yes—
142C22×C4×C151C2×D412yes—
143C22×C4×C151#4112yes—
144C22×C4×C151C2411yescharacteristic
145D8×C151—44no—
146D8×C151—44no—
147C2×C8×C151—21no—
148C2×C8×C151—21no—
149C2×C8×C151—22no—
150C2×C8×C151—22no—
151C2×C8×C151—22no—
152C2×C8×C151—22no—
153C2×C8×C151—22no—
154C2×C8×C151—44no—
155C4⋊C4×C151—22no—
156C4⋊C4×C151—21no—
157C4⋊C4×C151—22no—
158C4⋊C4×C151—22no—
159C4⋊C4×C151—21no—
160C4⋊C4×C151—22no—
161C4⋊C4×C151—44no—
162C4⋊C4×C151—42no—
163C4⋊C4×C151—44no—
164C22⋊C4×C151—22no—
165C22⋊C4×C151—44no—
166C22⋊C4×C151—44no—
167C22⋊C4×C151—42no—
168C22⋊C4×C151—42no—
169C22⋊C4×C151—44no—
170C22⋊C4×C151—44no—
171C22⋊C4×C151—82no—
172C22⋊C4×C151D814yescomplemented
173C42×C151—22no—
174C42×C151—22no—
175C23×C151—22no—
176C23×C151—22no—
177C23×C151—22no—
178C23×C151—24no—
179C23×C151—22no—
180C23×C151—48no—
181C23×C151—41no—
182C23×C151—41no—
183C23×C151—42no—
184C23×C151—42no—
185C23×C151—41no—
186C23×C151—41no—
187C23×C151—42no—
188C23×C151—48no—
189C23×C151—41no—
190C23×C151—42no—
191C23×C151—41no—
192C23×C151—41no—
193C23×C151—42no—
194C23×C151—84no—
195C23×C151—88no—
196C23×C151—88no—
197C23×C151#12112yes—
198C23×C151C2×D812yes—
199C23×C151AGL(1,ℤ/8)12yes—
200C23×C151C22×D411yescharacteristic
201D4×C151—22no—
202D4×C151—22no—
203D4×C151—22no—
204D4×C151—24no—
205D4×C151—48no—
206D4×C151—41no—
207D4×C151—41no—
208D4×C151—42no—
209D4×C151—42no—
210D4×C151—84no—
211D4×C151#12314yescomplemented
212C2×C4×C151—22no—
213C2×C4×C151—22no—
214C2×C4×C151—22no—
215C2×C4×C151—22no—
216C2×C4×C151—22no—
217C2×C4×C151—24no—
218C2×C4×C151—22no—
219C2×C4×C151—22no—
220C2×C4×C151—22no—
221C2×C4×C151—41no—
222C2×C4×C151—42no—
223C2×C4×C151—42no—
224C2×C4×C151—42no—
225C2×C4×C151—42no—
226C2×C4×C151—41no—
227C2×C4×C151—42no—
228C2×C4×C151—41no—
229C2×C4×C151—42no—
230C2×C4×C151—88no—
231C2×C4×C151—84no—
232C2×C4×C151#12112yes—
233C2×C4×C151C2×D814yes—
234C2×C4×C151C22×D411yescharacteristic
235C2×C4×C151C2×#4112yes—
236C2×C4×C151C2×#4111yescharacteristic
237C2×C4×C151H(5,𝔽2)12yes—
238C8×C151—41no—
239C8×C151—42no—
240C8×C151—41no—
241C22×C151—22no—
242C22×C151—24no—
243C22×C151—22no—
244C22×C151—24no—
245C22×C151—24no—
246C22×C151—42no—
247C22×C151—44no—
248C22×C151—42no—
249C22×C151—44no—
250C22×C151—42no—
251C22×C151—42no—
252C22×C151—42no—
253C22×C151—816no—
254C22×C151—82no—
255C22×C151—82no—
256C22×C151—81no—
257C22×C151—81no—
258C22×C151—82no—
259C22×C151—81no—
260C22×C151—82no—
261C22×C151#45914yes—
262C22×C151C2×#12111yescharacteristic
263C22×C151#54612yes—
264C22×C151C22×D811yescharacteristic
265C22×C151C2×AGL(1,ℤ/8)11yescharacteristic
266C22×C151#57712yes—
267C4×C151—22no—
268C4×C151—24no—
269C4×C151—42no—
270C4×C151—82no—
271C4×C151—81no—
272C4×C151—82no—
273C4×C151C2×#12311yescharacteristic
274C4×C151#53411yescharacteristic
275C4×C151#55112yes—
276C2×C151—24no—
277C2×C151—44no—
278C2×C151—82no—
279C2×C151—161no—
280C2×C151#241211yescharacteristic
281C2×C151C2×#45911yescharacteristic
282C2×C151#304211yescharacteristic
283C2×C151#329412yes—
284C2×C151#330612yes—
285#24526C15111yesmaximal, characteristic, direct product factor, Sylow
286C151#2452611yescharacteristic, direct product factor, Sylow
287C2×#447C2×C15111yescharacteristic
288C22×#102C2×C15111yescharacteristic, complemented
289#2501C2×C15111yescharacteristic, complemented
290D4×C22⋊C4C2×C15111yescharacteristic, complemented
291#2071C2×C15112yescomplemented
292#2054C2×C15112yescomplemented
293#1893C2×C15111yescharacteristic, complemented
294#1879C2×C15112yescomplemented
295#1850C2×C15111yescharacteristic, complemented
296#1823C2×C15111yescharacteristic, complemented
297#1802C2×C15112yescomplemented
298C23×D4C22×C15111yescharacteristic
299C22×D8C22×C15111yescharacteristic
300C22×D8C22×C15111yescharacteristic
301C23×C8C22×C15111yescharacteristic
302C2×#123—21no—
303C2×#123—21no—
304C2×#121C22×C15111yescharacteristic
305C2×C4×D4C22×C15112yes—
306C22×C4⋊C4C22×C15111yescharacteristic
307C22×C22⋊C4—21no—
308#447—24no—
309C2×C4⋊C8C22×C15112yescomplemented
310C2×#102—24no—
311C2×#102C22×C15112yes—
312C2×#102C22×C15111yescharacteristic
313C2×#102C22×C15112yes—
314C2×#102C22×C15111yescharacteristic
315C2×#102C22×C15112yescomplemented
316C2×C22⋊C8C22×C15111yescharacteristic
317#399—22no—
318#390C22×C15112yes—
319#390C22×C15112yescomplemented
320#386—22no—
321#384C22×C15112yescomplemented
322#380C22×C15111yescharacteristic
323#379—21no—
324C4×C22⋊C4C22×C15111yescharacteristic
325#340C22×C15112yescomplemented
326#340C22×C15112yescomplemented
327#340C22×C15112yescomplemented
328#336C22×C15112yescomplemented
329C25—21no—
330C22×D4—24no—
331C22×D4—21no—
332C22×D4—22no—
333C22×D4—21no—
334C22×D4—42no—
335C22×D4D4×C15114yes—
336C22×D4C23×C15111yescharacteristic
337C22×D4C23×C15111yescharacteristic
338C22×D4C23×C15111yescharacteristic
339C23×C4—21no—
340C23×C4—22no—
341C23×C4C23×C15111yescharacteristic
342C2×D8—24no—
343C2×D8—22no—
344C2×D8—22no—
345C2×D8—42no—
346C22×C8—22no—
347C22×C8—42no—
348C22×C8C23×C15112yes—
349C22×C8C23×C15111yescharacteristic
350C22×C8C23×C15111yescharacteristic
351#123—44no—
352#123—44no—
353#121—22no—
354#121—22no—
355C4×D4—24no—
356C4×D4—42no—
357C2×C4⋊C4—22no—
358C2×C4⋊C4—22no—
359C2×C4⋊C4—21no—
360C2×C4⋊C4—22no—
361C2×C4⋊C4—22no—
362C2×C4⋊C4C23×C15112yes—
363C2×C4⋊C4C23×C15112yes—
364C2×C4⋊C4C23×C15111yescharacteristic
365C2×C22⋊C4—21no—
366C2×C22⋊C4—22no—
367C2×C22⋊C4—22no—
368C2×C22⋊C4—21no—
369C2×C22⋊C4—22no—
370C2×C22⋊C4—22no—
371C2×C22⋊C4—22no—
372C2×C22⋊C4—44no—
373C2×C22⋊C4D4×C15111yescharacteristic
374C2×C22⋊C4D4×C15111yescharacteristic
375C2×C42C23×C15112yes—
376C4⋊C8—42no—
377#102—24no—
378#102—24no—
379#102—22no—
380#102—22no—
381#102—42no—
382C22⋊C8—22no—
383#95—21no—
384#95D4×C15112yes—
385C24—21no—
386C24—21no—
387C24—24no—
388C24—21no—
389C24—44no—
390C24—42no—
391C24—42no—
392C24—82no—
393C24C2×D4×C15111yescharacteristic
394C2×D4—28no—
395C2×D4—24no—
396C2×D4—21no—
397C2×D4—21no—
398C2×D4—22no—
399C2×D4—21no—
400C2×D4—21no—
401C2×D4—22no—
402C2×D4—22no—
403C2×D4—22no—
404C2×D4—22no—
405C2×D4—44no—
406C2×D4—48no—
407C2×D4—44no—
408C2×D4—42no—
409C2×D4—42no—
410C2×D4—42no—
411C2×D4C2×D4×C15112yes—
412C2×D4C2×D4×C15112yes—
413C2×D4#41×C15114yes—
414C22×C4—22no—
415C22×C4—22no—
416C22×C4—22no—
417C22×C4—22no—
418C22×C4—21no—
419C22×C4—44no—
420C22×C4—42no—
421C22×C4—42no—
422C22×C4—42no—
423C22×C4—44no—
424C22×C4—82no—
425C22×C4C2×D4×C15112yes—
426C22×C4C2×D4×C15111yescharacteristic
427C22×C4C2×D4×C15112yes—
428C22×C4C2×D4×C15112yes—
429C22×C4#41×C15112yes—
430C22×C4C24×C15111yescharacteristic
431D8—44no—
432D8—44no—
433C2×C8—21no—
434C2×C8—21no—
435C2×C8—22no—
436C2×C8—22no—
437C2×C8—22no—
438C2×C8—22no—
439C2×C8—22no—
440C2×C8—44no—
441C4⋊C4—22no—
442C4⋊C4—21no—
443C4⋊C4—22no—
444C4⋊C4—22no—
445C4⋊C4—21no—
446C4⋊C4—22no—
447C4⋊C4—44no—
448C4⋊C4—42no—
449C4⋊C4—44no—
450C22⋊C4—22no—
451C22⋊C4—44no—
452C22⋊C4—44no—
453C22⋊C4—42no—
454C22⋊C4—42no—
455C22⋊C4—44no—
456C22⋊C4—44no—
457C22⋊C4—82no—
458C22⋊C4D8×C15114yescomplemented
459C42—22no—
460C42—22no—
461C23—22no—
462C23—22no—
463C23—22no—
464C23—24no—
465C23—22no—
466C23—48no—
467C23—41no—
468C23—41no—
469C23—42no—
470C23—48no—
471C23—42no—
472C23—41no—
473C23—41no—
474C23—42no—
475C23—41no—
476C23—42no—
477C23—41no—
478C23—41no—
479C23—42no—
480C23—84no—
481C23—88no—
482C23—88no—
483C23#121×C15112yes—
484C23C2×D8×C15112yes—
485C23AGL(1,ℤ/8)×C15112yes—
486C23C22×D4×C15111yescharacteristic
487D4—22no—
488D4—22no—
489D4—22no—
490D4—24no—
491D4—48no—
492D4—41no—
493D4—41no—
494D4—42no—
495D4—42no—
496D4—84no—
497D4#123×C15114yescomplemented
498C2×C4—22no—
499C2×C4—22no—
500C2×C4—22no—
501C2×C4—22no—
502C2×C4—22no—
503C2×C4—24no—
504C2×C4—22no—
505C2×C4—22no—
506C2×C4—22no—
507C2×C4—41no—
508C2×C4—42no—
509C2×C4—42no—
510C2×C4—42no—
511C2×C4—42no—
512C2×C4—41no—
513C2×C4—42no—
514C2×C4—41no—
515C2×C4—42no—
516C2×C4—88no—
517C2×C4—84no—
518C2×C4#121×C15112yes—
519C2×C4C2×D8×C15114yes—
520C2×C4C22×D4×C15111yescharacteristic
521C2×C4C2×#41×C15112yes—
522C2×C4C2×#41×C15111yescharacteristic
523C2×C4H(5,𝔽2)×C15112yes—
524C8—41no—
525C8—42no—
526C8—41no—
527C22—22no—
528C22—24no—
529C22—22no—
530C22—24no—
531C22—24no—
532C22—42no—
533C22—44no—
534C22—42no—
535C22—44no—
536C22—42no—
537C22—42no—
538C22—42no—
539C22—816no—
540C22—82no—
541C22—82no—
542C22—81no—
543C22—81no—
544C22—82no—
545C22—81no—
546C22—82no—
547C22#459×C15114yes—
548C22C2×#121×C15111yescharacteristic
549C22#546×C15112yes—
550C22C22×D8×C15111yescharacteristic
551C22C2×AGL(1,ℤ/8)×C15111yescharacteristic
552C22#577×C15112yes—
553C4—22no—
554C4—24no—
555C4—42no—
556C4—82no—
557C4—81no—
558C4—82no—
559C4C2×#123×C15111yescharacteristic
560C4#534×C15111yescharacteristic
561C4#551×C15112yes—
562C2—24no—
563C2—44no—
564C2—82no—
565C2—161no—
566C2#2412×C15111yescharacteristic
567C2C2×#459×C15111yescharacteristic
568C2#3042×C15111yescharacteristic
569C2#3294×C15112yes—
570C2#3306×C15112yes—
subgroupG/H
center, socleC23×C151C22×D4
commutator, Frattini, cosocleC22×C4C24×C151
prime radicalC2×#447×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
2. C22×#102×C151C2semidirect
3. #2501×C151C2semidirect
4. D4×C22⋊C4×C151C2semidirect
5. #2071×C151C2semidirect
6. #2054×C151C2semidirect
7. #1893×C151C2semidirect
8. #1879×C151C2semidirect
9. #1850×C151C2semidirect
10. #1823×C151C2semidirect
11. #1802×C151C2semidirect
23. C2×C4⋊C8×C151C22semidirect
29. C2×#102×C151C22semidirect
33. #390×C151C22semidirect
35. #384×C151C22semidirect
39. #340×C151C22semidirect
40. #340×C151C22semidirect
41. #340×C151C22semidirect
42. #336×C151C22semidirect
172. C22⋊C4×C151D8semidirect
211. D4×C151#123semidirect
285. #24526C151direct (N × H)
286. C151#24526direct (N × H)
288. C22×#102C2×C151semidirect
289. #2501C2×C151semidirect
290. D4×C22⋊C4C2×C151semidirect
291. #2071C2×C151semidirect
292. #2054C2×C151semidirect
293. #1893C2×C151semidirect
294. #1879C2×C151semidirect
295. #1850C2×C151semidirect
296. #1823C2×C151semidirect
297. #1802C2×C151semidirect
309. C2×C4⋊C8C22×C151semidirect
315. C2×#102C22×C151semidirect
319. #390C22×C151semidirect
321. #384C22×C151semidirect
325. #340C22×C151semidirect
326. #340C22×C151semidirect
327. #340C22×C151semidirect
328. #336C22×C151semidirect
458. C22⋊C4D8×C151semidirect
497. D4#123×C151semidirect

Maximal subgroups

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

subgroupindex
C2×#447×C1512
C22×#102×C1512
#2501×C1512
D4×C22⋊C4×C1512
#2071×C1512
#2054×C1512
#1893×C1512
#1879×C1512
#1850×C1512
#1823×C1512
#1802×C1512
#24526151