Finite Group Databasebeta

← C151×#24367 #50329292

Subgroups — C151×#24367 #50329292

Order 38656.

1604 conjugacy classes of subgroups.

The subgroup lattice has 916 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×AGL(1,ℤ/8)×C151C211yesmaximal, characteristic
2C2×#463×C151C211yesmaximal, characteristic, complemented
3C2×#461×C151C211yesmaximal, characteristic, complemented
4C2×#450×C151C211yesmaximal, characteristic, complemented
5#2432×C151C211yesmaximal, characteristic, complemented
6D4×C22⋊C4×C151C211yesmaximal, characteristic, complemented
7#2055×C151C211yesmaximal, characteristic, complemented
8#2054×C151C211yesmaximal, characteristic, complemented
9#2013×C151C211yesmaximal, characteristic, complemented
10#2012×C151C211yesmaximal, characteristic, complemented
11#1894×C151C211yesmaximal, characteristic, complemented
12#1879×C151C211yesmaximal, characteristic, complemented
13#1877×C151C211yesmaximal, characteristic, complemented
14#1851×C151C211yesmaximal, characteristic, complemented
15#1788×C151C211yesmaximal, characteristic, complemented
16C22×#41×C151C2211yescharacteristic
17C23×D4×C151C2211yescharacteristic
18C2×AGL(1,ℤ/8)×C151—24no—
19C2×AGL(1,ℤ/8)×C151—24no—
20C2×AGL(1,ℤ/8)×C151—24no—
21C22×SD16×C151C2211yescharacteristic
22C22×SD16×C151C2211yescharacteristic
23C22×SD16×C151C2211yescharacteristic
24C22×SD16×C151C2211yescharacteristic
25C22×D8×C151C2211yescharacteristic
26C22×D8×C151C2211yescharacteristic
27C22×M16×C151C2211yescharacteristic
28C2×C4⋊Q8×C151C2211yescharacteristic, complemented
29C2×#124×C151C2211yescharacteristic, complemented
30C2×C22⋊Q8×C151C2211yescharacteristic
31C2×C4×D4×C151C2211yescharacteristic
32C2×C4×D4×C151C2211yescharacteristic
33C22×C22⋊C4×C151—21no—
34#463×C151—24no—
35#461×C151—24no—
36#450×C151—24no—
37C2×C4⋊C8×C151C2211yescharacteristic, complemented
38C2×C4⋊C8×C151C2211yescharacteristic, complemented
39C2×#103×C151C2211yescharacteristic, complemented
40C2×#103×C151C2211yescharacteristic, complemented
41C2×#103×C151C2211yescharacteristic, complemented
42C2×#103×C151C2211yescharacteristic, complemented
43C2×#102×C151C2211yescharacteristic
44C2×#102×C151C2211yescharacteristic
45C2×#102×C151C2211yescharacteristic, complemented
46C2×#102×C151C2211yescharacteristic, complemented
47C2×C22⋊C8×C151C2211yescharacteristic
48#394×C151—21no—
49#394×C151—21no—
50#391×C151C2211yescharacteristic, complemented
51#390×C151C2211yescharacteristic
52#390×C151C2211yescharacteristic
53#390×C151C2211yescharacteristic, complemented
54#386×C151—21no—
55#386×C151—21no—
56#385×C151—21no—
57#385×C151—21no—
58#380×C151C2211yescharacteristic
59#379×C151—21no—
60C4×C22⋊C4×C151C2211yescharacteristic
61#340×C151C2211yescharacteristic, complemented
62#340×C151C2211yescharacteristic, complemented
63#336×C151C2211yescharacteristic, complemented
64#336×C151C2211yescharacteristic, complemented
65C25×C151—21no—
66C2×#41×C151—22no—
67C2×#41×C151—22no—
68C2×#41×C151—22no—
69C2×#41×C151—22no—
70C2×#41×C151—41no—
71C2×#41×C151—41no—
72C22×Q8×C151C2311yescharacteristic
73C22×Q8×C151C2311yescharacteristic
74C22×D4×C151—21no—
75C22×D4×C151—22no—
76C22×D4×C151—21no—
77C22×D4×C151—22no—
78C22×D4×C151—22no—
79C22×D4×C151—41no—
80C22×D4×C151—41no—
81C22×D4×C151D414yes—
82C22×D4×C151C2311yescharacteristic
83C22×D4×C151C2311yescharacteristic
84C22×D4×C151C2311yescharacteristic
85C23×C4×C151—21no—
86C23×C4×C151—21no—
87C23×C4×C151—21no—
88C23×C4×C151C2311yescharacteristic
89AGL(1,ℤ/8)×C151—232no—
90C2×SD16×C151—22no—
91C2×SD16×C151—22no—
92C2×SD16×C151—22no—
93C2×SD16×C151—22no—
94C2×SD16×C151—22no—
95C2×SD16×C151—22no—
96C2×SD16×C151—22no—
97C2×SD16×C151—22no—
98C2×SD16×C151—22no—
99C2×SD16×C151—41no—
100C2×SD16×C151—41no—
101C2×SD16×C151D414yes—
102C2×D8×C151—22no—
103C2×D8×C151—22no—
104C2×D8×C151—22no—
105C2×D8×C151—22no—
106C2×D8×C151—22no—
107C2×D8×C151D414yes—
108C2×M16×C151—22no—
109C2×M16×C151—22no—
110C2×M16×C151—22no—
111C22×C8×C151C2311yescharacteristic
112C22×C8×C151C2311yescharacteristic
113C22×C8×C151C2311yescharacteristic
114C22×C8×C151C2311yescharacteristic
115C4⋊Q8×C151—22no—
116C4⋊Q8×C151—41no—
117#124×C151—22no—
118#124×C151—41no—
119C22⋊Q8×C151—22no—
120C22⋊Q8×C151—22no—
121C4×D4×C151—22no—
122C4×D4×C151—22no—
123C4×D4×C151—41no—
124C4×D4×C151—41no—
125C2×C4⋊C4×C151—21no—
126C2×C4⋊C4×C151—21no—
127C2×C4⋊C4×C151—21no—
128C2×C4⋊C4×C151C2311yescharacteristic
129C2×C4⋊C4×C151C2311yescharacteristic
130C2×C4⋊C4×C151C2311yescharacteristic
131C2×C22⋊C4×C151—21no—
132C2×C22⋊C4×C151—21no—
133C2×C22⋊C4×C151—21no—
134C2×C22⋊C4×C151—21no—
135C2×C22⋊C4×C151—21no—
136C2×C22⋊C4×C151—21no—
137C2×C22⋊C4×C151—21no—
138C2×C22⋊C4×C151—21no—
139C2×C22⋊C4×C151—21no—
140C2×C22⋊C4×C151—21no—
141C2×C22⋊C4×C151—21no—
142C2×C22⋊C4×C151—21no—
143C2×C22⋊C4×C151—44no—
144C2×C22⋊C4×C151D411yescharacteristic
145C2×C22⋊C4×C151D411yescharacteristic
146C2×C42×C151C2311yescharacteristic
147C2×C42×C151C2311yescharacteristic
148C4⋊C8×C151—22no—
149C4⋊C8×C151—22no—
150#103×C151—22no—
151#103×C151—22no—
152#103×C151—22no—
153#103×C151—41no—
154#102×C151—22no—
155#102×C151—22no—
156#102×C151—22no—
157#102×C151—41no—
158C22⋊C8×C151—22no—
159#95×C151—21no—
160#95×C151—21no—
161#95×C151—21no—
162#95×C151D411yescharacteristic
163#95×C151D411yescharacteristic
164C24×C151—21no—
165C24×C151—21no—
166C24×C151—21no—
167C24×C151—24no—
168C24×C151—42no—
169C24×C151—42no—
170C24×C151—42no—
171C24×C151—42no—
172C24×C151—81no—
173C24×C151—81no—
174C24×C151C2×D411yescharacteristic
175#41×C151—28no—
176#41×C151—44no—
177#41×C151—44no—
178#41×C151—44no—
179C2×Q8×C151—21no—
180C2×Q8×C151—21no—
181C2×Q8×C151—21no—
182C2×Q8×C151—21no—
183C2×Q8×C151—21no—
184C2×Q8×C151—21no—
185C2×Q8×C151—21no—
186C2×Q8×C151—21no—
187C2×Q8×C151—21no—
188C2×Q8×C151—21no—
189C2×Q8×C151—21no—
190C2×Q8×C151C2×D412yes—
191C2×D4×C151—28no—
192C2×D4×C151—24no—
193C2×D4×C151—21no—
194C2×D4×C151—21no—
195C2×D4×C151—21no—
196C2×D4×C151—21no—
197C2×D4×C151—21no—
198C2×D4×C151—21no—
199C2×D4×C151—21no—
200C2×D4×C151—21no—
201C2×D4×C151—21no—
202C2×D4×C151—21no—
203C2×D4×C151—21no—
204C2×D4×C151—21no—
205C2×D4×C151—21no—
206C2×D4×C151—44no—
207C2×D4×C151—44no—
208C2×D4×C151—44no—
209C2×D4×C151—42no—
210C2×D4×C151—42no—
211C2×D4×C151—42no—
212C2×D4×C151—42no—
213C2×D4×C151—42no—
214C2×D4×C151C2×D412yes—
215C2×D4×C151C2×D412yes—
216C2×D4×C151C2×D412yes—
217C2×D4×C151C2×D412yes—
218C2×D4×C151C2×D412yes—
219C22×C4×C151—21no—
220C22×C4×C151—21no—
221C22×C4×C151—21no—
222C22×C4×C151—21no—
223C22×C4×C151—21no—
224C22×C4×C151—21no—
225C22×C4×C151—21no—
226C22×C4×C151—21no—
227C22×C4×C151—21no—
228C22×C4×C151—42no—
229C22×C4×C151—42no—
230C22×C4×C151—42no—
231C22×C4×C151—42no—
232C22×C4×C151—42no—
233C22×C4×C151—42no—
234C22×C4×C151—42no—
235C22×C4×C151—81no—
236C22×C4×C151—81no—
237C22×C4×C151C2×D411yescharacteristic
238C22×C4×C151C2×D411yescharacteristic
239C22×C4×C151C2×D411yescharacteristic
240C22×C4×C151C2×D411yescharacteristic
241C22×C4×C151C2×D412yes—
242C22×C4×C151C2×D411yescharacteristic
243C22×C4×C151#4112yes—
244C22×C4×C151C2411yescharacteristic
245SD16×C151—28no—
246SD16×C151—28no—
247SD16×C151—44no—
248SD16×C151—44no—
249D8×C151—28no—
250D8×C151—28no—
251M16×C151—28no—
252C2×C8×C151—21no—
253C2×C8×C151—21no—
254C2×C8×C151—21no—
255C2×C8×C151—21no—
256C2×C8×C151—21no—
257C2×C8×C151—21no—
258C2×C8×C151—21no—
259C2×C8×C151—21no—
260C2×C8×C151—21no—
261C2×C8×C151—21no—
262C2×C8×C151C2×D412yes—
263C2×C8×C151C2×D412yes—
264C4⋊C4×C151—21no—
265C4⋊C4×C151—21no—
266C4⋊C4×C151—21no—
267C4⋊C4×C151—21no—
268C4⋊C4×C151—21no—
269C4⋊C4×C151—21no—
270C4⋊C4×C151—42no—
271C4⋊C4×C151—42no—
272C4⋊C4×C151—42no—
273C22⋊C4×C151—22no—
274C22⋊C4×C151—41no—
275C22⋊C4×C151—42no—
276C22⋊C4×C151—42no—
277C22⋊C4×C151—42no—
278C22⋊C4×C151—42no—
279C22⋊C4×C151—42no—
280C22⋊C4×C151—42no—
281C22⋊C4×C151—42no—
282C22⋊C4×C151—42no—
283C22⋊C4×C151—42no—
284C22⋊C4×C151—42no—
285C22⋊C4×C151—81no—
286C22⋊C4×C151—81no—
287C42×C151—21no—
288C42×C151—21no—
289C42×C151—21no—
290C42×C151—21no—
291C23×C151—22no—
292C23×C151—22no—
293C23×C151—22no—
294C23×C151—21no—
295C23×C151—21no—
296C23×C151—21no—
297C23×C151—21no—
298C23×C151—21no—
299C23×C151—21no—
300C23×C151—22no—
301C23×C151—22no—
302C23×C151—48no—
303C23×C151—48no—
304C23×C151—41no—
305C23×C151—41no—
306C23×C151—41no—
307C23×C151—41no—
308C23×C151—41no—
309C23×C151—41no—
310C23×C151—41no—
311C23×C151—41no—
312C23×C151—41no—
313C23×C151—41no—
314C23×C151—41no—
315C23×C151—41no—
316C23×C151—41no—
317C23×C151—41no—
318C23×C151—41no—
319C23×C151—41no—
320C23×C151—84no—
321C23×C151—84no—
322C23×C151—84no—
323C23×C151—84no—
324C23×C151—84no—
325C23×C151#12112yes—
326C23×C151C22×D411yescharacteristic
327Q8×C151—22no—
328Q8×C151—22no—
329Q8×C151—41no—
330Q8×C151—41no—
331Q8×C151—41no—
332Q8×C151—41no—
333Q8×C151—41no—
334Q8×C151—41no—
335D4×C151—22no—
336D4×C151—22no—
337D4×C151—22no—
338D4×C151—22no—
339D4×C151—22no—
340D4×C151—22no—
341D4×C151—22no—
342D4×C151—48no—
343D4×C151—48no—
344D4×C151—41no—
345D4×C151—41no—
346D4×C151—41no—
347D4×C151—41no—
348D4×C151#12014yes—
349C2×C4×C151—21no—
350C2×C4×C151—21no—
351C2×C4×C151—21no—
352C2×C4×C151—21no—
353C2×C4×C151—22no—
354C2×C4×C151—22no—
355C2×C4×C151—22no—
356C2×C4×C151—22no—
357C2×C4×C151—22no—
358C2×C4×C151—21no—
359C2×C4×C151—21no—
360C2×C4×C151—21no—
361C2×C4×C151—21no—
362C2×C4×C151—21no—
363C2×C4×C151—21no—
364C2×C4×C151—21no—
365C2×C4×C151—21no—
366C2×C4×C151—21no—
367C2×C4×C151—48no—
368C2×C4×C151—41no—
369C2×C4×C151—41no—
370C2×C4×C151—41no—
371C2×C4×C151—41no—
372C2×C4×C151—41no—
373C2×C4×C151—41no—
374C2×C4×C151—41no—
375C2×C4×C151—41no—
376C2×C4×C151—41no—
377C2×C4×C151—41no—
378C2×C4×C151—41no—
379C2×C4×C151—41no—
380C2×C4×C151—41no—
381C2×C4×C151—41no—
382C2×C4×C151—84no—
383C2×C4×C151—84no—
384C2×C4×C151#12112yes—
385C2×C4×C151AGL(1,ℤ/8)12yescomplemented
386C2×C4×C151C22×D411yescharacteristic
387C2×C4×C151C22×D411yescharacteristic
388C2×C4×C151C22×D411yescharacteristic
389C2×C4×C151C2×#4111yescharacteristic
390C2×C4×C151H(5,𝔽2)11yescharacteristic
391C2×C4×C151H(5,𝔽2)11yescharacteristic
392C8×C151—22no—
393C8×C151—22no—
394C8×C151—41no—
395C8×C151—41no—
396C22×C151—22no—
397C22×C151—24no—
398C22×C151—22no—
399C22×C151—22no—
400C22×C151—42no—
401C22×C151—41no—
402C22×C151—41no—
403C22×C151—42no—
404C22×C151—42no—
405C22×C151—41no—
406C22×C151—41no—
407C22×C151—42no—
408C22×C151—42no—
409C22×C151—42no—
410C22×C151—42no—
411C22×C151—42no—
412C22×C151—42no—
413C22×C151—42no—
414C22×C151—42no—
415C22×C151—42no—
416C22×C151—816no—
417C22×C151—81no—
418C22×C151—81no—
419C22×C151—81no—
420C22×C151—81no—
421C22×C151—81no—
422C22×C151—81no—
423C22×C151—81no—
424C22×C151—81no—
425C22×C151C2×#12111yescharacteristic
426C22×C151D4211yescharacteristic
427C22×C151D4211yescharacteristic
428C22×C151C2×AGL(1,ℤ/8)11yescharacteristic
429C22×C151#57511yescharacteristic
430C22×C151#57711yescharacteristic
431C22×C151#57711yescharacteristic
432C4×C151—22no—
433C4×C151—22no—
434C4×C151—42no—
435C4×C151—41no—
436C4×C151—41no—
437C4×C151—41no—
438C4×C151—81no—
439C4×C151—81no—
440C4×C151—81no—
441C4×C151—81no—
442C4×C151C2×#12011yescharacteristic
443C4×C151#53411yescharacteristic
444C4×C151#54611yescharacteristic
445C4×C151#54611yescharacteristic
446C2×C151—42no—
447C2×C151—44no—
448C2×C151—82no—
449C2×C151—82no—
450C2×C151#241011yescharacteristic
451C2×C151#303611yescharacteristic
452C2×C151#304211yescharacteristic
453C2×C151#326511yescharacteristic
454C2×C151#326711yescharacteristic
455C2×C151#327211yescharacteristic
456C2×C151#327511yescharacteristic
457#24367C15111yesmaximal, characteristic, direct product factor, Sylow
458C151#2436711yescharacteristic, direct product factor, Sylow
459C22×AGL(1,ℤ/8)C2×C15111yescharacteristic
460C2×#463C2×C15111yescharacteristic, complemented
461C2×#461C2×C15111yescharacteristic, complemented
462C2×#450C2×C15111yescharacteristic, complemented
463#2432C2×C15111yescharacteristic, complemented
464D4×C22⋊C4C2×C15111yescharacteristic, complemented
465#2055C2×C15111yescharacteristic, complemented
466#2054C2×C15111yescharacteristic, complemented
467#2013C2×C15111yescharacteristic, complemented
468#2012C2×C15111yescharacteristic, complemented
469#1894C2×C15111yescharacteristic, complemented
470#1879C2×C15111yescharacteristic, complemented
471#1877C2×C15111yescharacteristic, complemented
472#1851C2×C15111yescharacteristic, complemented
473#1788C2×C15111yescharacteristic, complemented
474C22×#41C22×C15111yescharacteristic
475C23×D4C22×C15111yescharacteristic
476C2×AGL(1,ℤ/8)—24no—
477C2×AGL(1,ℤ/8)—24no—
478C2×AGL(1,ℤ/8)—24no—
479C22×SD16C22×C15111yescharacteristic
480C22×SD16C22×C15111yescharacteristic
481C22×SD16C22×C15111yescharacteristic
482C22×SD16C22×C15111yescharacteristic
483C22×D8C22×C15111yescharacteristic
484C22×D8C22×C15111yescharacteristic
485C22×M16C22×C15111yescharacteristic
486C2×C4⋊Q8C22×C15111yescharacteristic, complemented
487C2×#124C22×C15111yescharacteristic, complemented
488C2×C22⋊Q8C22×C15111yescharacteristic
489C2×C4×D4C22×C15111yescharacteristic
490C2×C4×D4C22×C15111yescharacteristic
491C22×C22⋊C4—21no—
492#463—24no—
493#461—24no—
494#450—24no—
495C2×C4⋊C8C22×C15111yescharacteristic, complemented
496C2×C4⋊C8C22×C15111yescharacteristic, complemented
497C2×#103C22×C15111yescharacteristic, complemented
498C2×#103C22×C15111yescharacteristic, complemented
499C2×#103C22×C15111yescharacteristic, complemented
500C2×#103C22×C15111yescharacteristic, complemented
501C2×#102C22×C15111yescharacteristic
502C2×#102C22×C15111yescharacteristic
503C2×#102C22×C15111yescharacteristic, complemented
504C2×#102C22×C15111yescharacteristic, complemented
505C2×C22⋊C8C22×C15111yescharacteristic
506#394—21no—
507#394—21no—
508#391C22×C15111yescharacteristic, complemented
509#390C22×C15111yescharacteristic
510#390C22×C15111yescharacteristic
511#390C22×C15111yescharacteristic, complemented
512#386—21no—
513#386—21no—
514#385—21no—
515#385—21no—
516#380C22×C15111yescharacteristic
517#379—21no—
518C4×C22⋊C4C22×C15111yescharacteristic
519#340C22×C15111yescharacteristic, complemented
520#340C22×C15111yescharacteristic, complemented
521#336C22×C15111yescharacteristic, complemented
522#336C22×C15111yescharacteristic, complemented
523C25—21no—
524C2×#41—22no—
525C2×#41—22no—
526C2×#41—22no—
527C2×#41—22no—
528C2×#41—41no—
529C2×#41—41no—
530C22×Q8C23×C15111yescharacteristic
531C22×Q8C23×C15111yescharacteristic
532C22×D4—22no—
533C22×D4—22no—
534C22×D4—21no—
535C22×D4—22no—
536C22×D4—21no—
537C22×D4—41no—
538C22×D4—41no—
539C22×D4D4×C15114yes—
540C22×D4C23×C15111yescharacteristic
541C22×D4C23×C15111yescharacteristic
542C22×D4C23×C15111yescharacteristic
543C23×C4—21no—
544C23×C4—21no—
545C23×C4—21no—
546C23×C4C23×C15111yescharacteristic
547AGL(1,ℤ/8)—232no—
548C2×SD16—22no—
549C2×SD16—22no—
550C2×SD16—22no—
551C2×SD16—22no—
552C2×SD16—22no—
553C2×SD16—22no—
554C2×SD16—22no—
555C2×SD16—22no—
556C2×SD16—22no—
557C2×SD16—41no—
558C2×SD16—41no—
559C2×SD16D4×C15114yes—
560C2×D8—22no—
561C2×D8—22no—
562C2×D8—22no—
563C2×D8—22no—
564C2×D8—22no—
565C2×D8D4×C15114yes—
566C2×M16—22no—
567C2×M16—22no—
568C2×M16—22no—
569C22×C8C23×C15111yescharacteristic
570C22×C8C23×C15111yescharacteristic
571C22×C8C23×C15111yescharacteristic
572C22×C8C23×C15111yescharacteristic
573C4⋊Q8—22no—
574C4⋊Q8—41no—
575#124—22no—
576#124—41no—
577C22⋊Q8—22no—
578C22⋊Q8—22no—
579C4×D4—22no—
580C4×D4—22no—
581C4×D4—41no—
582C4×D4—41no—
583C2×C4⋊C4—21no—
584C2×C4⋊C4—21no—
585C2×C4⋊C4—21no—
586C2×C4⋊C4C23×C15111yescharacteristic
587C2×C4⋊C4C23×C15111yescharacteristic
588C2×C4⋊C4C23×C15111yescharacteristic
589C2×C22⋊C4—21no—
590C2×C22⋊C4—21no—
591C2×C22⋊C4—21no—
592C2×C22⋊C4—21no—
593C2×C22⋊C4—21no—
594C2×C22⋊C4—21no—
595C2×C22⋊C4—21no—
596C2×C22⋊C4—21no—
597C2×C22⋊C4—21no—
598C2×C22⋊C4—21no—
599C2×C22⋊C4—21no—
600C2×C22⋊C4—21no—
601C2×C22⋊C4—44no—
602C2×C22⋊C4D4×C15111yescharacteristic
603C2×C22⋊C4D4×C15111yescharacteristic
604C2×C42C23×C15111yescharacteristic
605C2×C42C23×C15111yescharacteristic
606C4⋊C8—22no—
607C4⋊C8—22no—
608#103—22no—
609#103—22no—
610#103—22no—
611#103—41no—
612#102—22no—
613#102—22no—
614#102—22no—
615#102—41no—
616C22⋊C8—22no—
617#95—21no—
618#95—21no—
619#95—21no—
620#95D4×C15111yescharacteristic
621#95D4×C15111yescharacteristic
622C24—21no—
623C24—21no—
624C24—21no—
625C24—24no—
626C24—42no—
627C24—42no—
628C24—42no—
629C24—42no—
630C24—81no—
631C24—81no—
632C24C2×D4×C15111yescharacteristic
633#41—28no—
634#41—44no—
635#41—44no—
636#41—44no—
637C2×Q8—21no—
638C2×Q8—21no—
639C2×Q8—21no—
640C2×Q8—21no—
641C2×Q8—21no—
642C2×Q8—21no—
643C2×Q8—21no—
644C2×Q8—21no—
645C2×Q8—21no—
646C2×Q8—21no—
647C2×Q8—21no—
648C2×Q8C2×D4×C15112yes—
649C2×D4—28no—
650C2×D4—24no—
651C2×D4—21no—
652C2×D4—21no—
653C2×D4—21no—
654C2×D4—21no—
655C2×D4—21no—
656C2×D4—21no—
657C2×D4—21no—
658C2×D4—21no—
659C2×D4—21no—
660C2×D4—21no—
661C2×D4—21no—
662C2×D4—21no—
663C2×D4—21no—
664C2×D4—44no—
665C2×D4—44no—
666C2×D4—44no—
667C2×D4—42no—
668C2×D4—42no—
669C2×D4—42no—
670C2×D4—42no—
671C2×D4—42no—
672C2×D4C2×D4×C15112yes—
673C2×D4C2×D4×C15112yes—
674C2×D4C2×D4×C15112yes—
675C2×D4C2×D4×C15112yes—
676C2×D4C2×D4×C15112yes—
677C22×C4—21no—
678C22×C4—21no—
679C22×C4—21no—
680C22×C4—21no—
681C22×C4—21no—
682C22×C4—21no—
683C22×C4—21no—
684C22×C4—21no—
685C22×C4—21no—
686C22×C4—42no—
687C22×C4—42no—
688C22×C4—42no—
689C22×C4—42no—
690C22×C4—42no—
691C22×C4—42no—
692C22×C4—42no—
693C22×C4—81no—
694C22×C4—81no—
695C22×C4C2×D4×C15111yescharacteristic
696C22×C4C2×D4×C15111yescharacteristic
697C22×C4C2×D4×C15111yescharacteristic
698C22×C4C2×D4×C15111yescharacteristic
699C22×C4C2×D4×C15112yes—
700C22×C4C2×D4×C15111yescharacteristic
701C22×C4#41×C15112yes—
702C22×C4C24×C15111yescharacteristic
703SD16—28no—
704SD16—28no—
705SD16—44no—
706SD16—44no—
707D8—28no—
708D8—28no—
709M16—28no—
710C2×C8—21no—
711C2×C8—21no—
712C2×C8—21no—
713C2×C8—21no—
714C2×C8—21no—
715C2×C8—21no—
716C2×C8—21no—
717C2×C8—21no—
718C2×C8—21no—
719C2×C8—21no—
720C2×C8C2×D4×C15112yes—
721C2×C8C2×D4×C15112yes—
722C4⋊C4—21no—
723C4⋊C4—21no—
724C4⋊C4—21no—
725C4⋊C4—21no—
726C4⋊C4—21no—
727C4⋊C4—21no—
728C4⋊C4—42no—
729C4⋊C4—42no—
730C4⋊C4—42no—
731C22⋊C4—22no—
732C22⋊C4—41no—
733C22⋊C4—42no—
734C22⋊C4—42no—
735C22⋊C4—42no—
736C22⋊C4—42no—
737C22⋊C4—42no—
738C22⋊C4—42no—
739C22⋊C4—42no—
740C22⋊C4—42no—
741C22⋊C4—42no—
742C22⋊C4—42no—
743C22⋊C4—81no—
744C22⋊C4—81no—
745C42—21no—
746C42—21no—
747C42—21no—
748C42—21no—
749C23—22no—
750C23—22no—
751C23—22no—
752C23—21no—
753C23—21no—
754C23—21no—
755C23—21no—
756C23—21no—
757C23—21no—
758C23—22no—
759C23—22no—
760C23—48no—
761C23—48no—
762C23—41no—
763C23—41no—
764C23—41no—
765C23—41no—
766C23—41no—
767C23—41no—
768C23—41no—
769C23—41no—
770C23—41no—
771C23—41no—
772C23—41no—
773C23—41no—
774C23—41no—
775C23—41no—
776C23—41no—
777C23—41no—
778C23—84no—
779C23—84no—
780C23—84no—
781C23—84no—
782C23—84no—
783C23#121×C15112yes—
784C23C22×D4×C15111yescharacteristic
785Q8—22no—
786Q8—22no—
787Q8—41no—
788Q8—41no—
789Q8—41no—
790Q8—41no—
791Q8—41no—
792Q8—41no—
793D4—22no—
794D4—22no—
795D4—22no—
796D4—22no—
797D4—22no—
798D4—22no—
799D4—22no—
800D4—48no—
801D4—48no—
802D4—41no—
803D4—41no—
804D4—41no—
805D4—41no—
806D4#120×C15114yes—
807C2×C4—21no—
808C2×C4—21no—
809C2×C4—21no—
810C2×C4—21no—
811C2×C4—22no—
812C2×C4—22no—
813C2×C4—22no—
814C2×C4—22no—
815C2×C4—21no—
816C2×C4—21no—
817C2×C4—21no—
818C2×C4—22no—
819C2×C4—21no—
820C2×C4—21no—
821C2×C4—21no—
822C2×C4—21no—
823C2×C4—21no—
824C2×C4—21no—
825C2×C4—48no—
826C2×C4—41no—
827C2×C4—41no—
828C2×C4—41no—
829C2×C4—41no—
830C2×C4—41no—
831C2×C4—41no—
832C2×C4—41no—
833C2×C4—41no—
834C2×C4—41no—
835C2×C4—41no—
836C2×C4—41no—
837C2×C4—41no—
838C2×C4—41no—
839C2×C4—41no—
840C2×C4—84no—
841C2×C4—84no—
842C2×C4#121×C15112yes—
843C2×C4AGL(1,ℤ/8)×C15112yescomplemented
844C2×C4C22×D4×C15111yescharacteristic
845C2×C4C22×D4×C15111yescharacteristic
846C2×C4C22×D4×C15111yescharacteristic
847C2×C4C2×#41×C15111yescharacteristic
848C2×C4H(5,𝔽2)×C15111yescharacteristic
849C2×C4H(5,𝔽2)×C15111yescharacteristic
850C8—22no—
851C8—22no—
852C8—41no—
853C8—41no—
854C22—22no—
855C22—24no—
856C22—22no—
857C22—22no—
858C22—42no—
859C22—41no—
860C22—41no—
861C22—42no—
862C22—42no—
863C22—41no—
864C22—41no—
865C22—42no—
866C22—42no—
867C22—42no—
868C22—42no—
869C22—42no—
870C22—42no—
871C22—42no—
872C22—42no—
873C22—42no—
874C22—816no—
875C22—81no—
876C22—81no—
877C22—81no—
878C22—81no—
879C22—81no—
880C22—81no—
881C22—81no—
882C22—81no—
883C22C2×#121×C15111yescharacteristic
884C22D42×C15111yescharacteristic
885C22D42×C15111yescharacteristic
886C22C2×AGL(1,ℤ/8)×C15111yescharacteristic
887C22#575×C15111yescharacteristic
888C22#577×C15111yescharacteristic
889C22#577×C15111yescharacteristic
890C4—22no—
891C4—22no—
892C4—42no—
893C4—41no—
894C4—41no—
895C4—41no—
896C4—81no—
897C4—81no—
898C4—81no—
899C4—81no—
900C4C2×#120×C15111yescharacteristic
901C4#534×C15111yescharacteristic
902C4#546×C15111yescharacteristic
903C4#546×C15111yescharacteristic
904C2—42no—
905C2—44no—
906C2—82no—
907C2—82no—
908C2#2410×C15111yescharacteristic
909C2#3036×C15111yescharacteristic
910C2#3042×C15111yescharacteristic
911C2#3265×C15111yescharacteristic
912C2#3267×C15111yescharacteristic
913C2#3272×C15111yescharacteristic
914C2#3275×C15111yescharacteristic
subgroupG/H
center, socleC23×C151C22×D4
commutator, Frattini, cosocleC22×C4C24×C151
prime radicalC22×AGL(1,ℤ/8)×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. C2×#463×C151C2semidirect
3. C2×#461×C151C2semidirect
4. C2×#450×C151C2semidirect
5. #2432×C151C2semidirect
6. D4×C22⋊C4×C151C2semidirect
7. #2055×C151C2semidirect
8. #2054×C151C2semidirect
9. #2013×C151C2semidirect
10. #2012×C151C2semidirect
11. #1894×C151C2semidirect
12. #1879×C151C2semidirect
13. #1877×C151C2semidirect
14. #1851×C151C2semidirect
15. #1788×C151C2semidirect
28. C2×C4⋊Q8×C151C22semidirect
29. C2×#124×C151C22semidirect
37. C2×C4⋊C8×C151C22semidirect
38. C2×C4⋊C8×C151C22semidirect
39. C2×#103×C151C22semidirect
40. C2×#103×C151C22semidirect
41. C2×#103×C151C22semidirect
42. C2×#103×C151C22semidirect
45. C2×#102×C151C22semidirect
46. C2×#102×C151C22semidirect
50. #391×C151C22semidirect
53. #390×C151C22semidirect
61. #340×C151C22semidirect
62. #340×C151C22semidirect
63. #336×C151C22semidirect
64. #336×C151C22semidirect
385. C2×C4×C151AGL(1,ℤ/8)semidirect
457. #24367C151direct (N × H)
458. C151#24367direct (N × H)
460. C2×#463C2×C151semidirect
461. C2×#461C2×C151semidirect
462. C2×#450C2×C151semidirect
463. #2432C2×C151semidirect
464. D4×C22⋊C4C2×C151semidirect
465. #2055C2×C151semidirect
466. #2054C2×C151semidirect
467. #2013C2×C151semidirect
468. #2012C2×C151semidirect
469. #1894C2×C151semidirect
470. #1879C2×C151semidirect
471. #1877C2×C151semidirect
472. #1851C2×C151semidirect
473. #1788C2×C151semidirect
486. C2×C4⋊Q8C22×C151semidirect
487. C2×#124C22×C151semidirect
495. C2×C4⋊C8C22×C151semidirect
496. C2×C4⋊C8C22×C151semidirect
497. C2×#103C22×C151semidirect
498. C2×#103C22×C151semidirect
499. C2×#103C22×C151semidirect
500. C2×#103C22×C151semidirect
503. C2×#102C22×C151semidirect
504. C2×#102C22×C151semidirect
508. #391C22×C151semidirect
511. #390C22×C151semidirect
519. #340C22×C151semidirect
520. #340C22×C151semidirect
521. #336C22×C151semidirect
522. #336C22×C151semidirect
843. C2×C4AGL(1,ℤ/8)×C151semidirect

Maximal subgroups

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

subgroupindex
C22×AGL(1,ℤ/8)×C1512
C2×#463×C1512
C2×#461×C1512
C2×#450×C1512
#2432×C1512
D4×C22⋊C4×C1512
#2055×C1512
#2054×C1512
#2013×C1512
#2012×C1512
#1894×C1512
#1879×C1512
#1877×C1512
#1851×C1512
#1788×C1512
#24367151