Finite Group Databasebeta

← C151×#24690 #50329615

Subgroups — C151×#24690 #50329615

Order 38656.

808 conjugacy classes of subgroups.

The subgroup lattice has 622 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#478×C151C211yesmaximal, characteristic
2C2×#440×C151C211yesmaximal, characteristic
3#2565×C151C211yesmaximal, characteristic, complemented
4#2354×C151C211yesmaximal, characteristic
5#2073×C151C211yesmaximal, characteristic
6#2071×C151C211yesmaximal, characteristic
7#2055×C151C211yesmaximal, characteristic
8#2055×C151C211yesmaximal, characteristic
9#1992×C151C211yesmaximal, characteristic, complemented
10#1949×C151C211yesmaximal, characteristic, complemented
11#1947×C151C211yesmaximal, characteristic, complemented
12#1940×C151C211yesmaximal, characteristic, complemented
13#1928×C151C211yesmaximal, characteristic, complemented
14#1927×C151C211yesmaximal, characteristic, complemented
15#1803×C151C211yesmaximal, characteristic, complemented
16C22×SD16×C151C2211yescharacteristic
17C2×#125×C151C2211yescharacteristic
18C2×C4×Q8×C151C2211yescharacteristic
19C2×C4×D4×C151C2211yescharacteristic
20C2×#117×C151—21no—
21#478×C151—24no—
22#440×C151—24no—
23C2×#107×C151C2211yescharacteristic
24C2×#107×C151C2211yescharacteristic
25C2×#106×C151C2211yescharacteristic
26C2×C4⋊C8×C151C2211yescharacteristic
27C2×C4⋊C8×C151C2211yescharacteristic
28C2×C4⋊C8×C151C2211yescharacteristic
29C2×#103×C151C2211yescharacteristic
30C2×#103×C151C2211yescharacteristic
31C2×#103×C151C2211yescharacteristic
32C2×#102×C151C2211yescharacteristic
33C2×#102×C151C2211yescharacteristic
34C2×#102×C151C2211yescharacteristic
35C2×#97×C151C2211yescharacteristic
36#398×C151—21no—
37#398×C151—21no—
38#391×C151C2211yescharacteristic
39#391×C151C2211yescharacteristic
40#390×C151C2211yescharacteristic
41#390×C151C2211yescharacteristic
42#388×C151—21no—
43#388×C151—21no—
44#387×C151—21no—
45#387×C151—21no—
46#384×C151C2211yescharacteristic
47#384×C151C2211yescharacteristic
48#382×C151C2211yescharacteristic
49#380×C151—21no—
50C4×C4⋊C4×C151C2211yescharacteristic
51C4×C4⋊C4×C151C2211yescharacteristic
52C4×C4⋊C4×C151C2211yescharacteristic
53#340×C151C2211yescharacteristic
54#340×C151C2211yescharacteristic
55#340×C151C2211yescharacteristic
56#340×C151C2211yescharacteristic
57#340×C151C2211yescharacteristic
58#340×C151C2211yescharacteristic
59#336×C151C2211yescharacteristic
60#336×C151C2211yescharacteristic
61C22×Q8×C151C2311yescharacteristic
62C22×D4×C151C2311yescharacteristic
63C23×C4×C151—21no—
64C2×SD16×C151—22no—
65C2×SD16×C151—22no—
66C2×SD16×C151—22no—
67C22×C8×C151C2311yescharacteristic
68C22×C8×C151C2311yescharacteristic
69C22×C8×C151C2311yescharacteristic
70C22×C8×C151C2311yescharacteristic
71#125×C151—22no—
72#125×C151—22no—
73C4×Q8×C151—22no—
74C4×Q8×C151—22no—
75C4×D4×C151—22no—
76C4×D4×C151D414yes—
77#117×C151—44no—
78C2×C4⋊C4×C151—21no—
79C2×C4⋊C4×C151—21no—
80C2×C4⋊C4×C151—21no—
81C2×C4⋊C4×C151—21no—
82C2×C4⋊C4×C151—21no—
83C2×C4⋊C4×C151—21no—
84C2×C4⋊C4×C151—21no—
85C2×C4⋊C4×C151D411yescharacteristic
86C2×C4⋊C4×C151D411yescharacteristic
87C2×C4⋊C4×C151C2311yescharacteristic
88C2×C4⋊C4×C151C2311yescharacteristic
89C2×C4⋊C4×C151C2311yescharacteristic
90C2×C4⋊C4×C151C2311yescharacteristic
91C2×C4⋊C4×C151C2311yescharacteristic
92C2×C4⋊C4×C151C2311yescharacteristic
93C2×C22⋊C4×C151—21no—
94C2×C22⋊C4×C151—21no—
95C2×C22⋊C4×C151—21no—
96C2×C22⋊C4×C151—21no—
97C2×C22⋊C4×C151—21no—
98C2×C42×C151—21no—
99C2×C42×C151—21no—
100C2×C42×C151—21no—
101C2×C42×C151C2311yescharacteristic
102C2×C42×C151C2311yescharacteristic
103C2×C42×C151C2311yescharacteristic
104#107×C151—22no—
105#107×C151—22no—
106#106×C151—22no—
107C4⋊C8×C151—22no—
108C4⋊C8×C151—22no—
109C4⋊C8×C151—22no—
110#103×C151—22no—
111#103×C151—22no—
112#103×C151—22no—
113#102×C151—22no—
114#102×C151—22no—
115#102×C151—22no—
116#97×C151—22no—
117#95×C151—21no—
118#95×C151—21no—
119#95×C151—21no—
120#95×C151—21no—
121#95×C151—21no—
122#95×C151—21no—
123#95×C151—21no—
124#95×C151—21no—
125#95×C151D411yescharacteristic
126#95×C151D411yescharacteristic
127C24×C151—21no—
128C2×Q8×C151—21no—
129C2×Q8×C151—21no—
130C2×Q8×C151—21no—
131C2×Q8×C151—21no—
132C2×Q8×C151—21no—
133C2×Q8×C151#4112yes—
134C2×D4×C151—21no—
135C2×D4×C151—21no—
136C2×D4×C151—21no—
137C2×D4×C151—21no—
138C2×D4×C151—21no—
139C2×D4×C151C2×D412yes—
140C22×C4×C151—21no—
141C22×C4×C151—21no—
142C22×C4×C151—24no—
143C22×C4×C151—21no—
144C22×C4×C151—21no—
145C22×C4×C151—21no—
146C22×C4×C151—21no—
147C22×C4×C151—21no—
148C22×C4×C151—42no—
149C22×C4×C151—42no—
150C22×C4×C151C2×D411yescharacteristic
151C22×C4×C151C2×D411yescharacteristic
152C22×C4×C151C2×D411yescharacteristic
153C22×C4×C151C2×D411yescharacteristic
154C22×C4×C151C2×D411yescharacteristic
155C22×C4×C151C2×D411yescharacteristic
156C22×C4×C151C2411yescharacteristic
157SD16×C151—28no—
158C2×C8×C151—21no—
159C2×C8×C151—21no—
160C2×C8×C151—21no—
161C2×C8×C151—21no—
162C2×C8×C151—21no—
163C2×C8×C151—21no—
164C2×C8×C151—21no—
165C2×C8×C151—21no—
166C2×C8×C151—21no—
167C2×C8×C151—21no—
168C2×C8×C151—21no—
169C2×C8×C151#4112yes—
170C4⋊C4×C151—22no—
171C4⋊C4×C151—21no—
172C4⋊C4×C151—21no—
173C4⋊C4×C151—21no—
174C4⋊C4×C151—21no—
175C4⋊C4×C151—21no—
176C4⋊C4×C151—21no—
177C4⋊C4×C151—21no—
178C4⋊C4×C151—21no—
179C4⋊C4×C151—21no—
180C4⋊C4×C151—21no—
181C4⋊C4×C151—21no—
182C4⋊C4×C151—41no—
183C4⋊C4×C151—42no—
184C4⋊C4×C151—42no—
185C4⋊C4×C151—42no—
186C4⋊C4×C151—42no—
187C4⋊C4×C151—42no—
188C4⋊C4×C151—42no—
189C4⋊C4×C151—81no—
190C4⋊C4×C151C2×D412yes—
191C22⋊C4×C151—24no—
192C22⋊C4×C151—42no—
193C22⋊C4×C151—42no—
194C22⋊C4×C151—81no—
195C22⋊C4×C151—81no—
196C42×C151—21no—
197C42×C151—21no—
198C42×C151—21no—
199C42×C151—21no—
200C42×C151—42no—
201C42×C151—42no—
202C42×C151—42no—
203C42×C151C2×D412yes—
204C42×C151#4112yes—
205C23×C151—22no—
206C23×C151—41no—
207C23×C151—41no—
208C23×C151—41no—
209C23×C151—41no—
210C23×C151—41no—
211C23×C151—41no—
212C23×C151C22×D411yescharacteristic
213Q8×C151—22no—
214Q8×C151—22no—
215Q8×C151—41no—
216Q8×C151—41no—
217D4×C151—22no—
218D4×C151—22no—
219D4×C151—41no—
220D4×C151—41no—
221C2×C4×C151—21no—
222C2×C4×C151—21no—
223C2×C4×C151—21no—
224C2×C4×C151—21no—
225C2×C4×C151—21no—
226C2×C4×C151—21no—
227C2×C4×C151—22no—
228C2×C4×C151—21no—
229C2×C4×C151—21no—
230C2×C4×C151—21no—
231C2×C4×C151—22no—
232C2×C4×C151—21no—
233C2×C4×C151—21no—
234C2×C4×C151—21no—
235C2×C4×C151—21no—
236C2×C4×C151—21no—
237C2×C4×C151—21no—
238C2×C4×C151—48no—
239C2×C4×C151—41no—
240C2×C4×C151—41no—
241C2×C4×C151—41no—
242C2×C4×C151—41no—
243C2×C4×C151—41no—
244C2×C4×C151—41no—
245C2×C4×C151—41no—
246C2×C4×C151—41no—
247C2×C4×C151—41no—
248C2×C4×C151—41no—
249C2×C4×C151—41no—
250C2×C4×C151—41no—
251C2×C4×C151—41no—
252C2×C4×C151—41no—
253C2×C4×C151—41no—
254C2×C4×C151—41no—
255C2×C4×C151—41no—
256C2×C4×C151—41no—
257C2×C4×C151—41no—
258C2×C4×C151#12112yes—
259C2×C4×C151#12112yes—
260C2×C4×C151AGL(1,ℤ/8)12yes—
261C2×C4×C151C22×D411yescharacteristic
262C2×C4×C151C2×#4111yescharacteristic
263C2×C4×C151C2×#4111yescharacteristic
264C2×C4×C151C2×#4111yescharacteristic
265C2×C4×C1512−1+411yescharacteristic
266C2×C4×C1512−1+411yescharacteristic
267C8×C151—22no—
268C8×C151—41no—
269C8×C151—41no—
270C8×C151—41no—
271C22×C151—42no—
272C22×C151—42no—
273C22×C151—42no—
274C22×C151—81no—
275C22×C151—81no—
276C22×C151—81no—
277C22×C151—81no—
278C22×C151C2×#12111yescharacteristic
279C22×C151#54711yescharacteristic
280C22×C151#54811yescharacteristic
281C22×C151C2×AGL(1,ℤ/8)11yescharacteristic
282C22×C151#57511yescharacteristic
283C22×C151#57711yescharacteristic
284C22×C151#57811yescharacteristic
285C4×C151—22no—
286C4×C151—22no—
287C4×C151—22no—
288C4×C151—41no—
289C4×C151—41no—
290C4×C151—41no—
291C4×C151—42no—
292C4×C151—42no—
293C4×C151—81no—
294C4×C151—81no—
295C4×C151—81no—
296C4×C151—81no—
297C4×C151—81no—
298C4×C151#52511yescharacteristic
299C4×C151#53611yescharacteristic
300C4×C151#55211yescharacteristic
301C4×C151#55611yescharacteristic
302C2×C151—82no—
303C2×C151#241511yescharacteristic
304C2×C151#303611yescharacteristic
305C2×C151#304611yescharacteristic
306C2×C151#334311yescharacteristic
307C2×C151#334811yescharacteristic
308C2×C151#336811yescharacteristic
309C2×C151#337711yescharacteristic
310#24690C15111yesmaximal, characteristic, direct product factor, Sylow
311C151#2469011yescharacteristic, direct product factor, Sylow
312C2×#478C2×C15111yescharacteristic
313C2×#440C2×C15111yescharacteristic
314#2565C2×C15111yescharacteristic, complemented
315#2354C2×C15111yescharacteristic
316#2073C2×C15111yescharacteristic
317#2071C2×C15111yescharacteristic
318#2055C2×C15111yescharacteristic
319#2055C2×C15111yescharacteristic
320#1992C2×C15111yescharacteristic, complemented
321#1949C2×C15111yescharacteristic, complemented
322#1947C2×C15111yescharacteristic, complemented
323#1940C2×C15111yescharacteristic, complemented
324#1928C2×C15111yescharacteristic, complemented
325#1927C2×C15111yescharacteristic, complemented
326#1803C2×C15111yescharacteristic, complemented
327C22×SD16C22×C15111yescharacteristic
328C2×#125C22×C15111yescharacteristic
329C2×C4×Q8C22×C15111yescharacteristic
330C2×C4×D4C22×C15111yescharacteristic
331C2×#117—21no—
332#478—24no—
333#440—24no—
334C2×#107C22×C15111yescharacteristic
335C2×#107C22×C15111yescharacteristic
336C2×#106C22×C15111yescharacteristic
337C2×C4⋊C8C22×C15111yescharacteristic
338C2×C4⋊C8C22×C15111yescharacteristic
339C2×C4⋊C8C22×C15111yescharacteristic
340C2×#103C22×C15111yescharacteristic
341C2×#103C22×C15111yescharacteristic
342C2×#103C22×C15111yescharacteristic
343C2×#102C22×C15111yescharacteristic
344C2×#102C22×C15111yescharacteristic
345C2×#102C22×C15111yescharacteristic
346C2×#97C22×C15111yescharacteristic
347#398—21no—
348#398—21no—
349#391C22×C15111yescharacteristic
350#391C22×C15111yescharacteristic
351#390C22×C15111yescharacteristic
352#390C22×C15111yescharacteristic
353#388—21no—
354#388—21no—
355#387—21no—
356#387—21no—
357#384C22×C15111yescharacteristic
358#384C22×C15111yescharacteristic
359#382C22×C15111yescharacteristic
360#380—21no—
361C4×C4⋊C4C22×C15111yescharacteristic
362C4×C4⋊C4C22×C15111yescharacteristic
363C4×C4⋊C4C22×C15111yescharacteristic
364#340C22×C15111yescharacteristic
365#340C22×C15111yescharacteristic
366#340C22×C15111yescharacteristic
367#340C22×C15111yescharacteristic
368#340C22×C15111yescharacteristic
369#340C22×C15111yescharacteristic
370#336C22×C15111yescharacteristic
371#336C22×C15111yescharacteristic
372C22×Q8C23×C15111yescharacteristic
373C22×D4C23×C15111yescharacteristic
374C23×C4—21no—
375C2×SD16—22no—
376C2×SD16—22no—
377C2×SD16—22no—
378C22×C8C23×C15111yescharacteristic
379C22×C8C23×C15111yescharacteristic
380C22×C8C23×C15111yescharacteristic
381C22×C8C23×C15111yescharacteristic
382#125—22no—
383#125—22no—
384C4×Q8—22no—
385C4×Q8—22no—
386C4×D4—22no—
387C4×D4D4×C15114yes—
388#117—44no—
389C2×C4⋊C4—21no—
390C2×C4⋊C4—21no—
391C2×C4⋊C4—21no—
392C2×C4⋊C4—21no—
393C2×C4⋊C4—21no—
394C2×C4⋊C4—21no—
395C2×C4⋊C4—21no—
396C2×C4⋊C4D4×C15111yescharacteristic
397C2×C4⋊C4D4×C15111yescharacteristic
398C2×C4⋊C4C23×C15111yescharacteristic
399C2×C4⋊C4C23×C15111yescharacteristic
400C2×C4⋊C4C23×C15111yescharacteristic
401C2×C4⋊C4C23×C15111yescharacteristic
402C2×C4⋊C4C23×C15111yescharacteristic
403C2×C4⋊C4C23×C15111yescharacteristic
404C2×C22⋊C4—21no—
405C2×C22⋊C4—21no—
406C2×C22⋊C4—21no—
407C2×C22⋊C4—21no—
408C2×C22⋊C4—21no—
409C2×C42—21no—
410C2×C42—21no—
411C2×C42—21no—
412C2×C42C23×C15111yescharacteristic
413C2×C42C23×C15111yescharacteristic
414C2×C42C23×C15111yescharacteristic
415#107—22no—
416#107—22no—
417#106—22no—
418C4⋊C8—22no—
419C4⋊C8—22no—
420C4⋊C8—22no—
421#103—22no—
422#103—22no—
423#103—22no—
424#102—22no—
425#102—22no—
426#102—22no—
427#97—22no—
428#95—21no—
429#95—21no—
430#95—21no—
431#95—21no—
432#95—21no—
433#95—21no—
434#95—21no—
435#95—21no—
436#95D4×C15111yescharacteristic
437#95D4×C15111yescharacteristic
438C24—21no—
439C2×Q8—21no—
440C2×Q8—21no—
441C2×Q8—21no—
442C2×Q8—21no—
443C2×Q8—21no—
444C2×Q8#41×C15112yes—
445C2×D4—21no—
446C2×D4—21no—
447C2×D4—21no—
448C2×D4—21no—
449C2×D4—21no—
450C2×D4C2×D4×C15112yes—
451C22×C4—21no—
452C22×C4—21no—
453C22×C4—24no—
454C22×C4—21no—
455C22×C4—21no—
456C22×C4—21no—
457C22×C4—21no—
458C22×C4—21no—
459C22×C4—42no—
460C22×C4—42no—
461C22×C4C2×D4×C15111yescharacteristic
462C22×C4C2×D4×C15111yescharacteristic
463C22×C4C2×D4×C15111yescharacteristic
464C22×C4C2×D4×C15111yescharacteristic
465C22×C4C2×D4×C15111yescharacteristic
466C22×C4C2×D4×C15111yescharacteristic
467C22×C4C24×C15111yescharacteristic
468SD16—28no—
469C2×C8—21no—
470C2×C8—21no—
471C2×C8—21no—
472C2×C8—21no—
473C2×C8—21no—
474C2×C8—21no—
475C2×C8—21no—
476C2×C8—21no—
477C2×C8—21no—
478C2×C8—21no—
479C2×C8—21no—
480C2×C8#41×C15112yes—
481C4⋊C4—22no—
482C4⋊C4—21no—
483C4⋊C4—21no—
484C4⋊C4—21no—
485C4⋊C4—21no—
486C4⋊C4—21no—
487C4⋊C4—21no—
488C4⋊C4—21no—
489C4⋊C4—21no—
490C4⋊C4—21no—
491C4⋊C4—21no—
492C4⋊C4—21no—
493C4⋊C4—41no—
494C4⋊C4—42no—
495C4⋊C4—42no—
496C4⋊C4—42no—
497C4⋊C4—42no—
498C4⋊C4—42no—
499C4⋊C4—42no—
500C4⋊C4—81no—
501C4⋊C4C2×D4×C15112yes—
502C22⋊C4—24no—
503C22⋊C4—42no—
504C22⋊C4—42no—
505C22⋊C4—81no—
506C22⋊C4—81no—
507C42—21no—
508C42—21no—
509C42—21no—
510C42—21no—
511C42—42no—
512C42—42no—
513C42—42no—
514C42C2×D4×C15112yes—
515C42#41×C15112yes—
516C23—22no—
517C23—41no—
518C23—41no—
519C23—41no—
520C23—41no—
521C23—41no—
522C23—41no—
523C23C22×D4×C15111yescharacteristic
524Q8—22no—
525Q8—22no—
526Q8—41no—
527Q8—41no—
528D4—22no—
529D4—22no—
530D4—41no—
531D4—41no—
532C2×C4—21no—
533C2×C4—21no—
534C2×C4—21no—
535C2×C4—21no—
536C2×C4—21no—
537C2×C4—21no—
538C2×C4—22no—
539C2×C4—21no—
540C2×C4—21no—
541C2×C4—21no—
542C2×C4—22no—
543C2×C4—21no—
544C2×C4—21no—
545C2×C4—21no—
546C2×C4—21no—
547C2×C4—21no—
548C2×C4—21no—
549C2×C4—48no—
550C2×C4—41no—
551C2×C4—41no—
552C2×C4—41no—
553C2×C4—41no—
554C2×C4—41no—
555C2×C4—41no—
556C2×C4—41no—
557C2×C4—41no—
558C2×C4—41no—
559C2×C4—41no—
560C2×C4—41no—
561C2×C4—41no—
562C2×C4—41no—
563C2×C4—41no—
564C2×C4—41no—
565C2×C4—41no—
566C2×C4—41no—
567C2×C4—41no—
568C2×C4—41no—
569C2×C4#121×C15112yes—
570C2×C4#121×C15112yes—
571C2×C4AGL(1,ℤ/8)×C15112yes—
572C2×C4C22×D4×C15111yescharacteristic
573C2×C4C2×#41×C15111yescharacteristic
574C2×C4C2×#41×C15111yescharacteristic
575C2×C4C2×#41×C15111yescharacteristic
576C2×C42−1+4×C15111yescharacteristic
577C2×C42−1+4×C15111yescharacteristic
578C8—22no—
579C8—41no—
580C8—41no—
581C8—41no—
582C22—42no—
583C22—42no—
584C22—42no—
585C22—81no—
586C22—81no—
587C22—81no—
588C22—81no—
589C22C2×#121×C15111yescharacteristic
590C22#547×C15111yescharacteristic
591C22#548×C15111yescharacteristic
592C22C2×AGL(1,ℤ/8)×C15111yescharacteristic
593C22#575×C15111yescharacteristic
594C22#577×C15111yescharacteristic
595C22#578×C15111yescharacteristic
596C4—22no—
597C4—22no—
598C4—22no—
599C4—42no—
600C4—42no—
601C4—41no—
602C4—41no—
603C4—41no—
604C4—81no—
605C4—81no—
606C4—81no—
607C4—81no—
608C4—81no—
609C4#525×C15111yescharacteristic
610C4#536×C15111yescharacteristic
611C4#552×C15111yescharacteristic
612C4#556×C15111yescharacteristic
613C2—82no—
614C2#2415×C15111yescharacteristic
615C2#3036×C15111yescharacteristic
616C2#3046×C15111yescharacteristic
617C2#3343×C15111yescharacteristic
618C2#3348×C15111yescharacteristic
619C2#3368×C15111yescharacteristic
620C2#3377×C15111yescharacteristic
subgroupG/H
center, socleC23×C151C22×D4
commutator, Frattini, cosocleC22×C4C24×C151
prime radicalC22×D4×C151C23
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C151 ◁ C4×C4⋊C4×C151 ◁ G

Complements

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

NH ≅ G/Ntype
3. #2565×C151C2semidirect
9. #1992×C151C2semidirect
10. #1949×C151C2semidirect
11. #1947×C151C2semidirect
12. #1940×C151C2semidirect
13. #1928×C151C2semidirect
14. #1927×C151C2semidirect
15. #1803×C151C2semidirect
310. #24690C151direct (N × H)
311. C151#24690direct (N × H)
314. #2565C2×C151semidirect
320. #1992C2×C151semidirect
321. #1949C2×C151semidirect
322. #1947C2×C151semidirect
323. #1940C2×C151semidirect
324. #1928C2×C151semidirect
325. #1927C2×C151semidirect
326. #1803C2×C151semidirect

Maximal subgroups

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

subgroupindex
C2×#478×C1512
C2×#440×C1512
#2565×C1512
#2354×C1512
#2073×C1512
#2071×C1512
#2055×C1512
#1992×C1512
#1949×C1512
#1947×C1512
#1940×C1512
#1928×C1512
#1927×C1512
#1803×C1512
#24690151