Finite Group Databasebeta

← C151×#24256 #50329181

Subgroups — C151×#24256 #50329181

Order 38656.

1510 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
1C2×#548×C151C211yesmaximal, characteristic, complemented
2C2×#463×C151C211yesmaximal, characteristic, complemented
3C2×#449×C151C211yesmaximal, characteristic, complemented
4C2×#448×C151C211yesmaximal, characteristic, complemented
5C2×#440×C151C211yesmaximal, characteristic, complemented
6#2537×C151C211yesmaximal, characteristic, complemented
7#2036×C151C211yesmaximal, characteristic, complemented
8#2033×C151C211yesmaximal, characteristic, complemented
9#2000×C151C211yesmaximal, characteristic, complemented
10#1999×C151C211yesmaximal, characteristic, complemented
11#1959×C151C211yesmaximal, characteristic, complemented
12#1955×C151C211yesmaximal, characteristic, complemented
13#1803×C151C211yesmaximal, characteristic, complemented
14#1788×C151C211yesmaximal, characteristic, complemented
15#1787×C151C211yesmaximal, characteristic, complemented
16C22×#41×C151C2211yescharacteristic
17C23×Q8×C151C2211yescharacteristic
18C22×SD16×C151C2211yescharacteristic
19C22×SD16×C151C2211yescharacteristic
20C22×D8×C151C2211yescharacteristic
21#548×C151—24no—
22#548×C151—24no—
23C2×#124×C151—21no—
24C2×#124×C151C2211yescharacteristic
25C2×C22⋊Q8×C151—21no—
26C2×C22⋊Q8×C151C2211yescharacteristic
27C2×#121×C151—21no—
28C2×#121×C151—21no—
29C2×#121×C151C2211yescharacteristic
30C2×#121×C151C2211yescharacteristic
31C2×#121×C151C2211yescharacteristic
32C2×C4×Q8×C151C2211yescharacteristic
33C2×C4×D4×C151—21no—
34C2×C4×D4×C151C2211yescharacteristic
35C2×C4×D4×C151C2211yescharacteristic
36#463×C151—24no—
37#449×C151—24no—
38#448×C151—24no—
39#440×C151—24no—
40C2×#107×C151C2211yescharacteristic
41C2×C4⋊C8×C151C2211yescharacteristic
42C2×#103×C151C2211yescharacteristic
43C2×#103×C151C2211yescharacteristic
44C2×#103×C151C2211yescharacteristic
45C2×#103×C151C2211yescharacteristic
46C2×#103×C151C2211yescharacteristic
47C2×#103×C151C2211yescharacteristic
48C2×#102×C151C2211yescharacteristic
49C2×#102×C151C2211yescharacteristic
50C2×#102×C151C2211yescharacteristic
51C2×#102×C151C2211yescharacteristic
52C2×C22⋊C8×C151C2211yescharacteristic
53C2×C22⋊C8×C151C2211yescharacteristic
54C2×C22⋊C8×C151C2211yescharacteristic
55C2×C22⋊C8×C151C2211yescharacteristic
56C2×#97×C151C2211yescharacteristic
57#394×C151—21no—
58#394×C151—21no—
59#384×C151C2211yescharacteristic
60#380×C151—21no—
61#380×C151C2211yescharacteristic
62#380×C151C2211yescharacteristic
63#340×C151C2211yescharacteristic
64#340×C151C2211yescharacteristic
65C2×#41×C151—22no—
66C2×#41×C151—22no—
67C2×#41×C151—22no—
68C2×#41×C151—22no—
69C2×#41×C151—41no—
70C2×#41×C151—41no—
71C22×Q8×C151—21no—
72C22×Q8×C151—22no—
73C22×Q8×C151—22no—
74C22×Q8×C151—22no—
75C22×Q8×C151—22no—
76C22×Q8×C151—41no—
77C22×Q8×C151—41no—
78C22×Q8×C151C2311yescharacteristic
79C22×Q8×C151C2311yescharacteristic
80C22×D4×C151—21no—
81C22×D4×C151—21no—
82C22×D4×C151—21no—
83C22×D4×C151—21no—
84C22×D4×C151D411yescharacteristic
85C22×D4×C151C2311yescharacteristic
86C22×D4×C151C2311yescharacteristic
87C23×C4×C151—21no—
88C23×C4×C151—21no—
89C23×C4×C151—21no—
90C23×C4×C151C2311yescharacteristic
91C23×C4×C151C2311yescharacteristic
92C2×SD16×C151—22no—
93C2×SD16×C151—22no—
94C2×SD16×C151—22no—
95C2×SD16×C151—22no—
96C2×SD16×C151—41no—
97C2×SD16×C151D414yescomplemented
98C2×D8×C151—22no—
99C2×D8×C151—22no—
100C2×D8×C151—41no—
101C22×C8×C151C2311yescharacteristic
102C22×C8×C151C2311yescharacteristic
103C22×C8×C151C2311yescharacteristic
104C22×C8×C151C2311yescharacteristic
105#124×C151—28no—
106#124×C151—22no—
107#124×C151D414yescomplemented
108C22⋊Q8×C151—28no—
109C22⋊Q8×C151—22no—
110C22⋊Q8×C151—22no—
111#121×C151—28no—
112#121×C151—22no—
113#121×C151—22no—
114#121×C151—22no—
115#121×C151—22no—
116#121×C151—41no—
117#121×C151—41no—
118#121×C151—44no—
119C4×Q8×C151—22no—
120C4×Q8×C151D414yescomplemented
121C4×D4×C151—28no—
122C4×D4×C151—22no—
123C4×D4×C151—22no—
124C4×D4×C151—22no—
125C4×D4×C151—22no—
126C2×C4⋊C4×C151—21no—
127C2×C4⋊C4×C151—21no—
128C2×C4⋊C4×C151—21no—
129C2×C4⋊C4×C151—21no—
130C2×C4⋊C4×C151D411yescharacteristic
131C2×C4⋊C4×C151C2311yescharacteristic
132C2×C4⋊C4×C151C2311yescharacteristic
133C2×C4⋊C4×C151C2311yescharacteristic
134C2×C4⋊C4×C151C2311yescharacteristic
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—21no—
144C2×C22⋊C4×C151D411yescharacteristic
145C2×C22⋊C4×C151D411yescharacteristic
146C2×C42×C151—21no—
147C2×C42×C151C2311yescharacteristic
148#107×C151—22no—
149C4⋊C8×C151—22no—
150#103×C151—22no—
151#103×C151—22no—
152#103×C151—22no—
153#103×C151—22no—
154#103×C151—22no—
155#103×C151—41no—
156#102×C151—22no—
157#102×C151—22no—
158#102×C151—22no—
159#102×C151—41no—
160C22⋊C8×C151—22no—
161C22⋊C8×C151—22no—
162C22⋊C8×C151—41no—
163C22⋊C8×C151—41no—
164#97×C151—22no—
165#95×C151—21no—
166#95×C151—21no—
167C24×C151—21no—
168C24×C151—21no—
169C24×C151C2×D411yescharacteristic
170C24×C151C2×D411yescharacteristic
171#41×C151—44no—
172#41×C151—44no—
173#41×C151—44no—
174#41×C151—44no—
175C2×Q8×C151—24no—
176C2×Q8×C151—21no—
177C2×Q8×C151—21no—
178C2×Q8×C151—21no—
179C2×Q8×C151—21no—
180C2×Q8×C151—21no—
181C2×Q8×C151—21no—
182C2×Q8×C151—21no—
183C2×Q8×C151—21no—
184C2×Q8×C151—42no—
185C2×Q8×C151—42no—
186C2×Q8×C151—44no—
187C2×Q8×C151—44no—
188C2×Q8×C151—44no—
189C2×Q8×C151—44no—
190C2×Q8×C151C2×D412yes—
191C2×Q8×C151C2×D412yes—
192C2×Q8×C151C2×D412yes—
193C2×Q8×C151#4112yes—
194C2×D4×C151—24no—
195C2×D4×C151—24no—
196C2×D4×C151—22no—
197C2×D4×C151—22no—
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—21no—
207C2×D4×C151—21no—
208C2×D4×C151—41no—
209C2×D4×C151—42no—
210C2×D4×C151—42no—
211C2×D4×C151—42no—
212C2×D4×C151—42no—
213C2×D4×C151—42no—
214C2×D4×C151—42no—
215C2×D4×C151—42no—
216C2×D4×C151—42no—
217C2×D4×C151—81no—
218C2×D4×C151—81no—
219C2×D4×C151C2×D412yes—
220C2×D4×C151C2×D412yes—
221C22×C4×C151—21no—
222C22×C4×C151—24no—
223C22×C4×C151—24no—
224C22×C4×C151—21no—
225C22×C4×C151—21no—
226C22×C4×C151—21no—
227C22×C4×C151—21no—
228C22×C4×C151—21no—
229C22×C4×C151—21no—
230C22×C4×C151—21no—
231C22×C4×C151—21no—
232C22×C4×C151—21no—
233C22×C4×C151—21no—
234C22×C4×C151—21no—
235C22×C4×C151—21no—
236C22×C4×C151—21no—
237C22×C4×C151—21no—
238C22×C4×C151—21no—
239C22×C4×C151—21no—
240C22×C4×C151—21no—
241C22×C4×C151—42no—
242C22×C4×C151—42no—
243C22×C4×C151—42no—
244C22×C4×C151—42no—
245C22×C4×C151—42no—
246C22×C4×C151—42no—
247C22×C4×C151—42no—
248C22×C4×C151C2×D411yescharacteristic
249C22×C4×C151C2×D411yescharacteristic
250C22×C4×C151C2×D411yescharacteristic
251C22×C4×C151C2×D411yescharacteristic
252C22×C4×C151C2411yescharacteristic
253SD16×C151—28no—
254SD16×C151—44no—
255D8×C151—44no—
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×C151—21no—
263C2×C8×C151—21no—
264C2×C8×C151—21no—
265C2×C8×C151—21no—
266C2×C8×C151—21no—
267C2×C8×C151C2×D412yes—
268C4⋊C4×C151—24no—
269C4⋊C4×C151—24no—
270C4⋊C4×C151—22no—
271C4⋊C4×C151—21no—
272C4⋊C4×C151—21no—
273C4⋊C4×C151—21no—
274C4⋊C4×C151—21no—
275C4⋊C4×C151—21no—
276C4⋊C4×C151—21no—
277C4⋊C4×C151—21no—
278C4⋊C4×C151—42no—
279C4⋊C4×C151—81no—
280C4⋊C4×C151C2×D412yes—
281C22⋊C4×C151—24no—
282C22⋊C4×C151—24no—
283C22⋊C4×C151—24no—
284C22⋊C4×C151—24no—
285C22⋊C4×C151—22no—
286C22⋊C4×C151—22no—
287C22⋊C4×C151—42no—
288C22⋊C4×C151—42no—
289C22⋊C4×C151—42no—
290C22⋊C4×C151—42no—
291C22⋊C4×C151—42no—
292C42×C151—24no—
293C42×C151C2×D412yes—
294C42×C151C2×D412yes—
295C23×C151—21no—
296C23×C151—21no—
297C23×C151—21no—
298C23×C151—21no—
299C23×C151—21no—
300C23×C151—21no—
301C23×C151—22no—
302C23×C151—21no—
303C23×C151—22no—
304C23×C151—21no—
305C23×C151—21no—
306C23×C151—21no—
307C23×C151—21no—
308C23×C151—21no—
309C23×C151—21no—
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—41no—
321C23×C151—41no—
322C23×C151AGL(1,ℤ/8)12yes—
323C23×C151C22×D411yescharacteristic
324Q8×C151—22no—
325Q8×C151—22no—
326Q8×C151—22no—
327Q8×C151—22no—
328Q8×C151—22no—
329Q8×C151—48no—
330Q8×C151—41no—
331Q8×C151—41no—
332Q8×C151#12114yescomplemented
333D4×C151—22no—
334D4×C151—22no—
335D4×C151—22no—
336D4×C151—22no—
337D4×C151—44no—
338D4×C151—48no—
339D4×C151—48no—
340D4×C151—41no—
341D4×C151—41no—
342D4×C151—41no—
343D4×C151—41no—
344D4×C151—84no—
345D4×C151—84no—
346C2×C4×C151—22no—
347C2×C4×C151—22no—
348C2×C4×C151—22no—
349C2×C4×C151—21no—
350C2×C4×C151—21no—
351C2×C4×C151—21no—
352C2×C4×C151—21no—
353C2×C4×C151—21no—
354C2×C4×C151—22no—
355C2×C4×C151—22no—
356C2×C4×C151—21no—
357C2×C4×C151—21no—
358C2×C4×C151—21no—
359C2×C4×C151—21no—
360C2×C4×C151—21no—
361C2×C4×C151—48no—
362C2×C4×C151—48no—
363C2×C4×C151—41no—
364C2×C4×C151—41no—
365C2×C4×C151—41no—
366C2×C4×C151—41no—
367C2×C4×C151—41no—
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—41no—
383C2×C4×C151—41no—
384C2×C4×C151—84no—
385C2×C4×C151#12012yes—
386C2×C4×C151#12012yes—
387C2×C4×C151C22×D411yescharacteristic
388C2×C4×C151C22×D411yescharacteristic
389C2×C4×C151C22×D411yescharacteristic
390C2×C4×C151C2×#4111yescharacteristic
391C2×C4×C151H(5,𝔽2)11yescharacteristic
392C2×C4×C151H(5,𝔽2)11yescharacteristic
393C8×C151—22no—
394C8×C151—41no—
395C8×C151—41no—
396C8×C151—41no—
397C22×C151—22no—
398C22×C151—22no—
399C22×C151—22no—
400C22×C151—41no—
401C22×C151—41no—
402C22×C151—41no—
403C22×C151—41no—
404C22×C151—42no—
405C22×C151—41no—
406C22×C151—42no—
407C22×C151—41no—
408C22×C151—42no—
409C22×C151—41no—
410C22×C151—42no—
411C22×C151—41no—
412C22×C151—42no—
413C22×C151—41no—
414C22×C151—42no—
415C22×C151—41no—
416C22×C151—41no—
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×#12011yescharacteristic
426C22×C151D4211yescharacteristic
427C22×C151#54611yescharacteristic
428C22×C151C2×AGL(1,ℤ/8)11yescharacteristic
429C22×C151#57511yescharacteristic
430C22×C151#57711yescharacteristic
431C22×C151#57811yescharacteristic
432C4×C151—24no—
433C4×C151—22no—
434C4×C151—22no—
435C4×C151—41no—
436C4×C151—41no—
437C4×C151—42no—
438C4×C151—42no—
439C4×C151—81no—
440C4×C151—81no—
441C4×C151—81no—
442C4×C151C2×#12111yescharacteristic
443C4×C151#53511yescharacteristic
444C4×C151D4211yescharacteristic
445C4×C151#54611yescharacteristic
446C2×C151—42no—
447C2×C151—81no—
448C2×C151—82no—
449C2×C151—82no—
450C2×C151#240811yescharacteristic
451C2×C151#300611yescharacteristic
452C2×C151#301311yescharacteristic
453C2×C151#326511yescharacteristic
454C2×C151#326911yescharacteristic
455C2×C151#330811yescharacteristic
456C2×C151#332111yescharacteristic
457#24256C15111yesmaximal, characteristic, direct product factor, Sylow
458C151#2425611yescharacteristic, direct product factor, Sylow
459C2×#548C2×C15111yescharacteristic, complemented
460C2×#463C2×C15111yescharacteristic, complemented
461C2×#449C2×C15111yescharacteristic, complemented
462C2×#448C2×C15111yescharacteristic, complemented
463C2×#440C2×C15111yescharacteristic, complemented
464#2537C2×C15111yescharacteristic, complemented
465#2036C2×C15111yescharacteristic, complemented
466#2033C2×C15111yescharacteristic, complemented
467#2000C2×C15111yescharacteristic, complemented
468#1999C2×C15111yescharacteristic, complemented
469#1959C2×C15111yescharacteristic, complemented
470#1955C2×C15111yescharacteristic, complemented
471#1803C2×C15111yescharacteristic, complemented
472#1788C2×C15111yescharacteristic, complemented
473#1787C2×C15111yescharacteristic, complemented
474C22×#41C22×C15111yescharacteristic
475C23×Q8C22×C15111yescharacteristic
476C22×SD16C22×C15111yescharacteristic
477C22×SD16C22×C15111yescharacteristic
478C22×D8C22×C15111yescharacteristic
479#548—24no—
480#548—24no—
481C2×#124—21no—
482C2×#124C22×C15111yescharacteristic
483C2×C22⋊Q8—21no—
484C2×C22⋊Q8C22×C15111yescharacteristic
485C2×#121—21no—
486C2×#121—21no—
487C2×#121C22×C15111yescharacteristic
488C2×#121C22×C15111yescharacteristic
489C2×#121C22×C15111yescharacteristic
490C2×C4×Q8C22×C15111yescharacteristic
491C2×C4×D4—21no—
492C2×C4×D4C22×C15111yescharacteristic
493C2×C4×D4C22×C15111yescharacteristic
494#463—24no—
495#449—24no—
496#448—24no—
497#440—24no—
498C2×#107C22×C15111yescharacteristic
499C2×C4⋊C8C22×C15111yescharacteristic
500C2×#103C22×C15111yescharacteristic
501C2×#103C22×C15111yescharacteristic
502C2×#103C22×C15111yescharacteristic
503C2×#103C22×C15111yescharacteristic
504C2×#103C22×C15111yescharacteristic
505C2×#103C22×C15111yescharacteristic
506C2×#102C22×C15111yescharacteristic
507C2×#102C22×C15111yescharacteristic
508C2×#102C22×C15111yescharacteristic
509C2×#102C22×C15111yescharacteristic
510C2×C22⋊C8C22×C15111yescharacteristic
511C2×C22⋊C8C22×C15111yescharacteristic
512C2×C22⋊C8C22×C15111yescharacteristic
513C2×C22⋊C8C22×C15111yescharacteristic
514C2×#97C22×C15111yescharacteristic
515#394—21no—
516#394—21no—
517#384C22×C15111yescharacteristic
518#380—21no—
519#380C22×C15111yescharacteristic
520#380C22×C15111yescharacteristic
521#340C22×C15111yescharacteristic
522#340C22×C15111yescharacteristic
523C2×#41—22no—
524C2×#41—22no—
525C2×#41—22no—
526C2×#41—22no—
527C2×#41—41no—
528C2×#41—41no—
529C22×Q8—22no—
530C22×Q8—22no—
531C22×Q8—21no—
532C22×Q8—22no—
533C22×Q8—22no—
534C22×Q8—41no—
535C22×Q8—41no—
536C22×Q8C23×C15111yescharacteristic
537C22×Q8C23×C15111yescharacteristic
538C22×D4—21no—
539C22×D4—21no—
540C22×D4—21no—
541C22×D4—21no—
542C22×D4D4×C15111yescharacteristic
543C22×D4C23×C15111yescharacteristic
544C22×D4C23×C15111yescharacteristic
545C23×C4—21no—
546C23×C4—21no—
547C23×C4—21no—
548C23×C4C23×C15111yescharacteristic
549C23×C4C23×C15111yescharacteristic
550C2×SD16—22no—
551C2×SD16—22no—
552C2×SD16—22no—
553C2×SD16—22no—
554C2×SD16—41no—
555C2×SD16D4×C15114yescomplemented
556C2×D8—22no—
557C2×D8—22no—
558C2×D8—41no—
559C22×C8C23×C15111yescharacteristic
560C22×C8C23×C15111yescharacteristic
561C22×C8C23×C15111yescharacteristic
562C22×C8C23×C15111yescharacteristic
563#124—28no—
564#124—22no—
565#124D4×C15114yescomplemented
566C22⋊Q8—28no—
567C22⋊Q8—22no—
568C22⋊Q8—22no—
569#121—28no—
570#121—22no—
571#121—22no—
572#121—22no—
573#121—22no—
574#121—41no—
575#121—41no—
576#121—44no—
577C4×Q8—22no—
578C4×Q8D4×C15114yescomplemented
579C4×D4—28no—
580C4×D4—22no—
581C4×D4—22no—
582C4×D4—22no—
583C4×D4—22no—
584C2×C4⋊C4—21no—
585C2×C4⋊C4—21no—
586C2×C4⋊C4—21no—
587C2×C4⋊C4—21no—
588C2×C4⋊C4D4×C15111yescharacteristic
589C2×C4⋊C4C23×C15111yescharacteristic
590C2×C4⋊C4C23×C15111yescharacteristic
591C2×C4⋊C4C23×C15111yescharacteristic
592C2×C4⋊C4C23×C15111yescharacteristic
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—21no—
602C2×C22⋊C4D4×C15111yescharacteristic
603C2×C22⋊C4D4×C15111yescharacteristic
604C2×C42—21no—
605C2×C42C23×C15111yescharacteristic
606#107—22no—
607C4⋊C8—22no—
608#103—22no—
609#103—22no—
610#103—22no—
611#103—22no—
612#103—22no—
613#103—41no—
614#102—22no—
615#102—22no—
616#102—22no—
617#102—41no—
618C22⋊C8—22no—
619C22⋊C8—22no—
620C22⋊C8—41no—
621C22⋊C8—41no—
622#97—22no—
623#95—21no—
624#95—21no—
625C24—21no—
626C24—21no—
627C24C2×D4×C15111yescharacteristic
628C24C2×D4×C15111yescharacteristic
629#41—44no—
630#41—44no—
631#41—44no—
632#41—44no—
633C2×Q8—24no—
634C2×Q8—21no—
635C2×Q8—21no—
636C2×Q8—21no—
637C2×Q8—21no—
638C2×Q8—21no—
639C2×Q8—21no—
640C2×Q8—21no—
641C2×Q8—21no—
642C2×Q8—42no—
643C2×Q8—42no—
644C2×Q8—44no—
645C2×Q8—44no—
646C2×Q8—44no—
647C2×Q8—44no—
648C2×Q8C2×D4×C15112yes—
649C2×Q8C2×D4×C15112yes—
650C2×Q8C2×D4×C15112yes—
651C2×Q8#41×C15112yes—
652C2×D4—24no—
653C2×D4—24no—
654C2×D4—22no—
655C2×D4—22no—
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—21no—
665C2×D4—21no—
666C2×D4—41no—
667C2×D4—42no—
668C2×D4—42no—
669C2×D4—42no—
670C2×D4—42no—
671C2×D4—42no—
672C2×D4—42no—
673C2×D4—42no—
674C2×D4—42no—
675C2×D4—81no—
676C2×D4—81no—
677C2×D4C2×D4×C15112yes—
678C2×D4C2×D4×C15112yes—
679C22×C4—21no—
680C22×C4—24no—
681C22×C4—24no—
682C22×C4—21no—
683C22×C4—21no—
684C22×C4—21no—
685C22×C4—21no—
686C22×C4—21no—
687C22×C4—21no—
688C22×C4—21no—
689C22×C4—21no—
690C22×C4—21no—
691C22×C4—21no—
692C22×C4—21no—
693C22×C4—21no—
694C22×C4—21no—
695C22×C4—21no—
696C22×C4—21no—
697C22×C4—21no—
698C22×C4—21no—
699C22×C4—42no—
700C22×C4—42no—
701C22×C4—42no—
702C22×C4—42no—
703C22×C4—42no—
704C22×C4—42no—
705C22×C4—42no—
706C22×C4C2×D4×C15111yescharacteristic
707C22×C4C2×D4×C15111yescharacteristic
708C22×C4C2×D4×C15111yescharacteristic
709C22×C4C2×D4×C15111yescharacteristic
710C22×C4C24×C15111yescharacteristic
711SD16—28no—
712SD16—44no—
713D8—44no—
714C2×C8—21no—
715C2×C8—21no—
716C2×C8—21no—
717C2×C8—21no—
718C2×C8—21no—
719C2×C8—21no—
720C2×C8—21no—
721C2×C8—21no—
722C2×C8—21no—
723C2×C8—21no—
724C2×C8—21no—
725C2×C8C2×D4×C15112yes—
726C4⋊C4—24no—
727C4⋊C4—24no—
728C4⋊C4—22no—
729C4⋊C4—21no—
730C4⋊C4—21no—
731C4⋊C4—21no—
732C4⋊C4—21no—
733C4⋊C4—21no—
734C4⋊C4—21no—
735C4⋊C4—21no—
736C4⋊C4—42no—
737C4⋊C4—81no—
738C4⋊C4C2×D4×C15112yes—
739C22⋊C4—24no—
740C22⋊C4—24no—
741C22⋊C4—24no—
742C22⋊C4—24no—
743C22⋊C4—22no—
744C22⋊C4—22no—
745C22⋊C4—42no—
746C22⋊C4—42no—
747C22⋊C4—42no—
748C22⋊C4—42no—
749C22⋊C4—42no—
750C42—24no—
751C42C2×D4×C15112yes—
752C42C2×D4×C15112yes—
753C23—21no—
754C23—21no—
755C23—21no—
756C23—21no—
757C23—21no—
758C23—21no—
759C23—21no—
760C23—22no—
761C23—22no—
762C23—21no—
763C23—21no—
764C23—21no—
765C23—21no—
766C23—21no—
767C23—21no—
768C23—41no—
769C23—41no—
770C23—41no—
771C23—41no—
772C23—41no—
773C23—41no—
774C23—41no—
775C23—41no—
776C23—41no—
777C23—41no—
778C23—41no—
779C23—41no—
780C23AGL(1,ℤ/8)×C15112yes—
781C23C22×D4×C15111yescharacteristic
782Q8—22no—
783Q8—22no—
784Q8—22no—
785Q8—22no—
786Q8—22no—
787Q8—48no—
788Q8—41no—
789Q8—41no—
790Q8#121×C15114yescomplemented
791D4—22no—
792D4—22no—
793D4—22no—
794D4—22no—
795D4—44no—
796D4—48no—
797D4—48no—
798D4—41no—
799D4—41no—
800D4—41no—
801D4—41no—
802D4—84no—
803D4—84no—
804C2×C4—22no—
805C2×C4—22no—
806C2×C4—22no—
807C2×C4—21no—
808C2×C4—21no—
809C2×C4—21no—
810C2×C4—21no—
811C2×C4—22no—
812C2×C4—22no—
813C2×C4—21no—
814C2×C4—21no—
815C2×C4—21no—
816C2×C4—21no—
817C2×C4—21no—
818C2×C4—21no—
819C2×C4—48no—
820C2×C4—48no—
821C2×C4—41no—
822C2×C4—41no—
823C2×C4—41no—
824C2×C4—41no—
825C2×C4—41no—
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—41no—
841C2×C4—41no—
842C2×C4—84no—
843C2×C4#120×C15112yes—
844C2×C4#120×C15112yes—
845C2×C4C22×D4×C15111yescharacteristic
846C2×C4C22×D4×C15111yescharacteristic
847C2×C4C22×D4×C15111yescharacteristic
848C2×C4C2×#41×C15111yescharacteristic
849C2×C4H(5,𝔽2)×C15111yescharacteristic
850C2×C4H(5,𝔽2)×C15111yescharacteristic
851C8—22no—
852C8—41no—
853C8—41no—
854C8—41no—
855C22—22no—
856C22—22no—
857C22—22no—
858C22—41no—
859C22—41no—
860C22—41no—
861C22—41no—
862C22—42no—
863C22—41no—
864C22—42no—
865C22—41no—
866C22—42no—
867C22—41no—
868C22—42no—
869C22—41no—
870C22—42no—
871C22—41no—
872C22—42no—
873C22—41no—
874C22—41no—
875C22—81no—
876C22—81no—
877C22—81no—
878C22—81no—
879C22—81no—
880C22—81no—
881C22—81no—
882C22—81no—
883C22C2×#120×C15111yescharacteristic
884C22D42×C15111yescharacteristic
885C22#546×C15111yescharacteristic
886C22C2×AGL(1,ℤ/8)×C15111yescharacteristic
887C22#575×C15111yescharacteristic
888C22#577×C15111yescharacteristic
889C22#578×C15111yescharacteristic
890C4—24no—
891C4—22no—
892C4—22no—
893C4—41no—
894C4—41no—
895C4—42no—
896C4—42no—
897C4—81no—
898C4—81no—
899C4—81no—
900C4C2×#121×C15111yescharacteristic
901C4#535×C15111yescharacteristic
902C4D42×C15111yescharacteristic
903C4#546×C15111yescharacteristic
904C2—42no—
905C2—81no—
906C2—82no—
907C2—82no—
908C2#2408×C15111yescharacteristic
909C2#3006×C15111yescharacteristic
910C2#3013×C15111yescharacteristic
911C2#3265×C15111yescharacteristic
912C2#3269×C15111yescharacteristic
913C2#3308×C15111yescharacteristic
914C2#3321×C15111yescharacteristic
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×#548×C151C2semidirect
2. C2×#463×C151C2semidirect
3. C2×#449×C151C2semidirect
4. C2×#448×C151C2semidirect
5. C2×#440×C151C2semidirect
6. #2537×C151C2semidirect
7. #2036×C151C2semidirect
8. #2033×C151C2semidirect
9. #2000×C151C2semidirect
10. #1999×C151C2semidirect
11. #1959×C151C2semidirect
12. #1955×C151C2semidirect
13. #1803×C151C2semidirect
14. #1788×C151C2semidirect
15. #1787×C151C2semidirect
97. C2×SD16×C151D4semidirect
107. #124×C151D4semidirect
120. C4×Q8×C151D4semidirect
332. Q8×C151#121semidirect
457. #24256C151direct (N × H)
458. C151#24256direct (N × H)
459. C2×#548C2×C151semidirect
460. C2×#463C2×C151semidirect
461. C2×#449C2×C151semidirect
462. C2×#448C2×C151semidirect
463. C2×#440C2×C151semidirect
464. #2537C2×C151semidirect
465. #2036C2×C151semidirect
466. #2033C2×C151semidirect
467. #2000C2×C151semidirect
468. #1999C2×C151semidirect
469. #1959C2×C151semidirect
470. #1955C2×C151semidirect
471. #1803C2×C151semidirect
472. #1788C2×C151semidirect
473. #1787C2×C151semidirect
555. C2×SD16D4×C151semidirect
565. #124D4×C151semidirect
578. C4×Q8D4×C151semidirect
790. Q8#121×C151semidirect

Maximal subgroups

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

subgroupindex
C2×#548×C1512
C2×#463×C1512
C2×#449×C1512
C2×#448×C1512
C2×#440×C1512
#2537×C1512
#2036×C1512
#2033×C1512
#2000×C1512
#1999×C1512
#1959×C1512
#1955×C1512
#1803×C1512
#1788×C1512
#1787×C1512
#24256151