Finite Group Databasebeta

← C151×#24244 #50329169

Subgroups — C151×#24244 #50329169

Order 38656.

1488 conjugacy classes of subgroups.

The subgroup lattice has 910 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×C4×SD16×C151C211yesmaximal, characteristic, complemented
6#2535×C151C211yesmaximal, characteristic, complemented
7#2035×C151C211yesmaximal, characteristic, complemented
8#2034×C151C211yesmaximal, characteristic, complemented
9#2000×C151C211yesmaximal, characteristic, complemented
10#1999×C151C211yesmaximal, characteristic, complemented
11#1958×C151C211yesmaximal, characteristic, complemented
12#1954×C151C211yesmaximal, characteristic, complemented
13#1805×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×C151C2211yescharacteristic
29C2×#121×C151C2211yescharacteristic
30C2×#121×C151C2211yescharacteristic
31C2×C4×Q8×C151C2211yescharacteristic
32C2×C4×D4×C151—21no—
33C2×C4×D4×C151C2211yescharacteristic
34C2×C4×D4×C151C2211yescharacteristic
35#463×C151—24no—
36#449×C151—24no—
37#448×C151—24no—
38C4×SD16×C151—24no—
39C2×#106×C151C2211yescharacteristic
40C2×C4⋊C8×C151C2211yescharacteristic
41C2×#103×C151C2211yescharacteristic
42C2×#103×C151C2211yescharacteristic
43C2×#103×C151C2211yescharacteristic
44C2×#103×C151C2211yescharacteristic
45C2×#103×C151C2211yescharacteristic
46C2×#103×C151C2211yescharacteristic
47C2×#102×C151C2211yescharacteristic
48C2×#102×C151C2211yescharacteristic
49C2×#102×C151C2211yescharacteristic
50C2×#102×C151C2211yescharacteristic
51C2×C22⋊C8×C151C2211yescharacteristic
52C2×C22⋊C8×C151C2211yescharacteristic
53C2×C22⋊C8×C151C2211yescharacteristic
54C2×C22⋊C8×C151C2211yescharacteristic
55C2×C4×C8×C151C2211yescharacteristic
56#397×C151—21no—
57#392×C151—21no—
58#386×C151—21no—
59#386×C151—21no—
60#382×C151C2211yescharacteristic
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—
118C4×Q8×C151—22no—
119C4×Q8×C151D414yescomplemented
120C4×D4×C151—28no—
121C4×D4×C151—22no—
122C4×D4×C151—22no—
123C4×D4×C151—22no—
124C4×D4×C151—22no—
125C2×C4⋊C4×C151—21no—
126C2×C4⋊C4×C151—21no—
127C2×C4⋊C4×C151D411yescharacteristic
128C2×C4⋊C4×C151C2311yescharacteristic
129C2×C4⋊C4×C151C2311yescharacteristic
130C2×C4⋊C4×C151C2311yescharacteristic
131C2×C4⋊C4×C151C2311yescharacteristic
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×C151D411yescharacteristic
142C2×C22⋊C4×C151D411yescharacteristic
143C2×C42×C151—21no—
144C2×C42×C151C2311yescharacteristic
145#106×C151—22no—
146C4⋊C8×C151—22no—
147#103×C151—22no—
148#103×C151—22no—
149#103×C151—22no—
150#103×C151—22no—
151#103×C151—22no—
152#103×C151—41no—
153#102×C151—22no—
154#102×C151—22no—
155#102×C151—22no—
156#102×C151—41no—
157C22⋊C8×C151—22no—
158C22⋊C8×C151—22no—
159C22⋊C8×C151—41no—
160C22⋊C8×C151—41no—
161C4×C8×C151—22no—
162#95×C151—21no—
163#95×C151—21no—
164#95×C151—21no—
165#95×C151—21no—
166C24×C151—21no—
167C24×C151—21no—
168C24×C151C2×D411yescharacteristic
169C24×C151C2×D411yescharacteristic
170#41×C151—44no—
171#41×C151—44no—
172#41×C151—44no—
173#41×C151—44no—
174C2×Q8×C151—24no—
175C2×Q8×C151—21no—
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—42no—
184C2×Q8×C151—42no—
185C2×Q8×C151—44no—
186C2×Q8×C151—44no—
187C2×Q8×C151—44no—
188C2×Q8×C151—44no—
189C2×Q8×C151C2×D412yes—
190C2×Q8×C151C2×D412yes—
191C2×Q8×C151C2×D412yes—
192C2×Q8×C151#4112yes—
193C2×D4×C151—24no—
194C2×D4×C151—24no—
195C2×D4×C151—22no—
196C2×D4×C151—22no—
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—21no—
207C2×D4×C151—41no—
208C2×D4×C151—42no—
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—81no—
217C2×D4×C151—81no—
218C2×D4×C151C2×D412yes—
219C2×D4×C151C2×D412yes—
220C22×C4×C151—21no—
221C22×C4×C151—24no—
222C22×C4×C151—24no—
223C22×C4×C151—21no—
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—42no—
241C22×C4×C151—42no—
242C22×C4×C151—42no—
243C22×C4×C151—42no—
244C22×C4×C151—42no—
245C22×C4×C151—81no—
246C22×C4×C151—81no—
247C22×C4×C151C2×D411yescharacteristic
248C22×C4×C151C2×D411yescharacteristic
249C22×C4×C151C2×D411yescharacteristic
250C22×C4×C151C2×D411yescharacteristic
251C22×C4×C151C2411yescharacteristic
252SD16×C151—28no—
253SD16×C151—44no—
254D8×C151—44no—
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×C151—21no—
263C2×C8×C151—21no—
264C2×C8×C151—21no—
265C2×C8×C151—21no—
266C2×C8×C151C2×D412yes—
267C4⋊C4×C151—24no—
268C4⋊C4×C151—24no—
269C4⋊C4×C151—22no—
270C4⋊C4×C151—21no—
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×C151C2×D412yes—
278C22⋊C4×C151—24no—
279C22⋊C4×C151—24no—
280C22⋊C4×C151—24no—
281C22⋊C4×C151—24no—
282C22⋊C4×C151—22no—
283C22⋊C4×C151—22no—
284C22⋊C4×C151—42no—
285C22⋊C4×C151—42no—
286C22⋊C4×C151—42no—
287C22⋊C4×C151—81no—
288C22⋊C4×C151—81no—
289C42×C151—24no—
290C42×C151C2×D412yes—
291C42×C151C2×D412yes—
292C23×C151—21no—
293C23×C151—21no—
294C23×C151—21no—
295C23×C151—21no—
296C23×C151—21no—
297C23×C151—21no—
298C23×C151—22no—
299C23×C151—21no—
300C23×C151—22no—
301C23×C151—21no—
302C23×C151—21no—
303C23×C151—21no—
304C23×C151—21no—
305C23×C151—21no—
306C23×C151—21no—
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#13512yes—
320C23×C151C22×D411yescharacteristic
321Q8×C151—22no—
322Q8×C151—22no—
323Q8×C151—22no—
324Q8×C151—22no—
325Q8×C151—22no—
326Q8×C151—48no—
327Q8×C151—41no—
328Q8×C151—41no—
329Q8×C151#12114yes—
330D4×C151—22no—
331D4×C151—22no—
332D4×C151—22no—
333D4×C151—22no—
334D4×C151—44no—
335D4×C151—48no—
336D4×C151—48no—
337D4×C151—41no—
338D4×C151—41no—
339D4×C151—41no—
340D4×C151—41no—
341D4×C151—84no—
342D4×C151—84no—
343C2×C4×C151—22no—
344C2×C4×C151—22no—
345C2×C4×C151—22no—
346C2×C4×C151—21no—
347C2×C4×C151—21no—
348C2×C4×C151—21no—
349C2×C4×C151—21no—
350C2×C4×C151—21no—
351C2×C4×C151—22no—
352C2×C4×C151—22no—
353C2×C4×C151—21no—
354C2×C4×C151—21no—
355C2×C4×C151—21no—
356C2×C4×C151—21no—
357C2×C4×C151—21no—
358C2×C4×C151—48no—
359C2×C4×C151—48no—
360C2×C4×C151—41no—
361C2×C4×C151—41no—
362C2×C4×C151—41no—
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—84no—
382C2×C4×C151#12012yes—
383C2×C4×C151#12012yes—
384C2×C4×C151C22×D411yescharacteristic
385C2×C4×C151C22×D411yescharacteristic
386C2×C4×C151C22×D411yescharacteristic
387C2×C4×C151C2×#4111yescharacteristic
388C2×C4×C151H(5,𝔽2)11yescharacteristic
389C2×C4×C151H(5,𝔽2)11yescharacteristic
390C8×C151—22no—
391C8×C151—41no—
392C8×C151—41no—
393C8×C151—41no—
394C22×C151—22no—
395C22×C151—22no—
396C22×C151—22no—
397C22×C151—41no—
398C22×C151—41no—
399C22×C151—41no—
400C22×C151—41no—
401C22×C151—42no—
402C22×C151—41no—
403C22×C151—42no—
404C22×C151—41no—
405C22×C151—42no—
406C22×C151—41no—
407C22×C151—42no—
408C22×C151—41no—
409C22×C151—42no—
410C22×C151—42no—
411C22×C151—41no—
412C22×C151—41no—
413C22×C151—41no—
414C22×C151—81no—
415C22×C151—81no—
416C22×C151—81no—
417C22×C151—81no—
418C22×C151—81no—
419C22×C151—81no—
420C22×C151—81no—
421C22×C151—81no—
422C22×C151C2×#12011yescharacteristic
423C22×C151D4211yescharacteristic
424C22×C151#54611yescharacteristic
425C22×C151C2×#13511yescharacteristic
426C22×C151#57511yescharacteristic
427C22×C151#57711yescharacteristic
428C22×C151#57711yescharacteristic
429C4×C151—24no—
430C4×C151—22no—
431C4×C151—22no—
432C4×C151—41no—
433C4×C151—41no—
434C4×C151—42no—
435C4×C151—42no—
436C4×C151—81no—
437C4×C151—81no—
438C4×C151—81no—
439C4×C151C2×#12111yescharacteristic
440C4×C151#53511yescharacteristic
441C4×C151D4211yescharacteristic
442C4×C151#54611yescharacteristic
443C2×C151—42no—
444C2×C151—81no—
445C2×C151—82no—
446C2×C151—82no—
447C2×C151#240811yescharacteristic
448C2×C151#300211yescharacteristic
449C2×C151#301011yescharacteristic
450C2×C151#327511yescharacteristic
451C2×C151#328211yescharacteristic
452C2×C151#330111yescharacteristic
453C2×C151#332611yescharacteristic
454#24244C15111yesmaximal, characteristic, direct product factor, Sylow
455C151#2424411yescharacteristic, direct product factor, Sylow
456C2×#548C2×C15111yescharacteristic, complemented
457C2×#463C2×C15111yescharacteristic, complemented
458C2×#449C2×C15111yescharacteristic, complemented
459C2×#448C2×C15111yescharacteristic, complemented
460C2×C4×SD16C2×C15111yescharacteristic, complemented
461#2535C2×C15111yescharacteristic, complemented
462#2035C2×C15111yescharacteristic, complemented
463#2034C2×C15111yescharacteristic, complemented
464#2000C2×C15111yescharacteristic, complemented
465#1999C2×C15111yescharacteristic, complemented
466#1958C2×C15111yescharacteristic, complemented
467#1954C2×C15111yescharacteristic, complemented
468#1805C2×C15111yescharacteristic, complemented
469#1788C2×C15111yescharacteristic, complemented
470#1787C2×C15111yescharacteristic, complemented
471C22×#41C22×C15111yescharacteristic
472C23×Q8C22×C15111yescharacteristic
473C22×SD16C22×C15111yescharacteristic
474C22×SD16C22×C15111yescharacteristic
475C22×D8C22×C15111yescharacteristic
476#548—24no—
477#548—24no—
478C2×#124—21no—
479C2×#124C22×C15111yescharacteristic
480C2×C22⋊Q8—21no—
481C2×C22⋊Q8C22×C15111yescharacteristic
482C2×#121—21no—
483C2×#121C22×C15111yescharacteristic
484C2×#121C22×C15111yescharacteristic
485C2×#121C22×C15111yescharacteristic
486C2×C4×Q8C22×C15111yescharacteristic
487C2×C4×D4—21no—
488C2×C4×D4C22×C15111yescharacteristic
489C2×C4×D4C22×C15111yescharacteristic
490#463—24no—
491#449—24no—
492#448—24no—
493C4×SD16—24no—
494C2×#106C22×C15111yescharacteristic
495C2×C4⋊C8C22×C15111yescharacteristic
496C2×#103C22×C15111yescharacteristic
497C2×#103C22×C15111yescharacteristic
498C2×#103C22×C15111yescharacteristic
499C2×#103C22×C15111yescharacteristic
500C2×#103C22×C15111yescharacteristic
501C2×#103C22×C15111yescharacteristic
502C2×#102C22×C15111yescharacteristic
503C2×#102C22×C15111yescharacteristic
504C2×#102C22×C15111yescharacteristic
505C2×#102C22×C15111yescharacteristic
506C2×C22⋊C8C22×C15111yescharacteristic
507C2×C22⋊C8C22×C15111yescharacteristic
508C2×C22⋊C8C22×C15111yescharacteristic
509C2×C22⋊C8C22×C15111yescharacteristic
510C2×C4×C8C22×C15111yescharacteristic
511#397—21no—
512#392—21no—
513#386—21no—
514#386—21no—
515#382C22×C15111yescharacteristic
516#380C22×C15111yescharacteristic
517#380C22×C15111yescharacteristic
518#340C22×C15111yescharacteristic
519#340C22×C15111yescharacteristic
520C2×#41—22no—
521C2×#41—22no—
522C2×#41—22no—
523C2×#41—22no—
524C2×#41—41no—
525C2×#41—41no—
526C22×Q8—22no—
527C22×Q8—22no—
528C22×Q8—21no—
529C22×Q8—22no—
530C22×Q8—22no—
531C22×Q8—41no—
532C22×Q8—41no—
533C22×Q8C23×C15111yescharacteristic
534C22×Q8C23×C15111yescharacteristic
535C22×D4—21no—
536C22×D4—21no—
537C22×D4—21no—
538C22×D4—21no—
539C22×D4D4×C15111yescharacteristic
540C22×D4C23×C15111yescharacteristic
541C22×D4C23×C15111yescharacteristic
542C23×C4—21no—
543C23×C4—21no—
544C23×C4—21no—
545C23×C4C23×C15111yescharacteristic
546C23×C4C23×C15111yescharacteristic
547C2×SD16—22no—
548C2×SD16—22no—
549C2×SD16—22no—
550C2×SD16—22no—
551C2×SD16—41no—
552C2×SD16D4×C15114yescomplemented
553C2×D8—22no—
554C2×D8—22no—
555C2×D8—41no—
556C22×C8C23×C15111yescharacteristic
557C22×C8C23×C15111yescharacteristic
558C22×C8C23×C15111yescharacteristic
559C22×C8C23×C15111yescharacteristic
560#124—28no—
561#124—22no—
562#124D4×C15114yescomplemented
563C22⋊Q8—28no—
564C22⋊Q8—22no—
565C22⋊Q8—22no—
566#121—28no—
567#121—22no—
568#121—22no—
569#121—22no—
570#121—22no—
571#121—41no—
572#121—41no—
573C4×Q8—22no—
574C4×Q8D4×C15114yescomplemented
575C4×D4—28no—
576C4×D4—22no—
577C4×D4—22no—
578C4×D4—22no—
579C4×D4—22no—
580C2×C4⋊C4—21no—
581C2×C4⋊C4—21no—
582C2×C4⋊C4D4×C15111yescharacteristic
583C2×C4⋊C4C23×C15111yescharacteristic
584C2×C4⋊C4C23×C15111yescharacteristic
585C2×C4⋊C4C23×C15111yescharacteristic
586C2×C4⋊C4C23×C15111yescharacteristic
587C2×C22⋊C4—21no—
588C2×C22⋊C4—21no—
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⋊C4D4×C15111yescharacteristic
597C2×C22⋊C4D4×C15111yescharacteristic
598C2×C42—21no—
599C2×C42C23×C15111yescharacteristic
600#106—22no—
601C4⋊C8—22no—
602#103—22no—
603#103—22no—
604#103—22no—
605#103—22no—
606#103—22no—
607#103—41no—
608#102—22no—
609#102—22no—
610#102—22no—
611#102—41no—
612C22⋊C8—22no—
613C22⋊C8—22no—
614C22⋊C8—41no—
615C22⋊C8—41no—
616C4×C8—22no—
617#95—21no—
618#95—21no—
619#95—21no—
620#95—21no—
621C24—21no—
622C24—21no—
623C24C2×D4×C15111yescharacteristic
624C24C2×D4×C15111yescharacteristic
625#41—44no—
626#41—44no—
627#41—44no—
628#41—44no—
629C2×Q8—24no—
630C2×Q8—21no—
631C2×Q8—21no—
632C2×Q8—21no—
633C2×Q8—21no—
634C2×Q8—21no—
635C2×Q8—21no—
636C2×Q8—21no—
637C2×Q8—21no—
638C2×Q8—42no—
639C2×Q8—42no—
640C2×Q8—44no—
641C2×Q8—44no—
642C2×Q8—44no—
643C2×Q8—44no—
644C2×Q8C2×D4×C15112yes—
645C2×Q8C2×D4×C15112yes—
646C2×Q8C2×D4×C15112yes—
647C2×Q8#41×C15112yes—
648C2×D4—24no—
649C2×D4—24no—
650C2×D4—22no—
651C2×D4—22no—
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—41no—
663C2×D4—42no—
664C2×D4—42no—
665C2×D4—42no—
666C2×D4—42no—
667C2×D4—42no—
668C2×D4—42no—
669C2×D4—42no—
670C2×D4—42no—
671C2×D4—81no—
672C2×D4—81no—
673C2×D4C2×D4×C15112yes—
674C2×D4C2×D4×C15112yes—
675C22×C4—21no—
676C22×C4—24no—
677C22×C4—24no—
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—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—42no—
696C22×C4—42no—
697C22×C4—42no—
698C22×C4—42no—
699C22×C4—42no—
700C22×C4—81no—
701C22×C4—81no—
702C22×C4C2×D4×C15111yescharacteristic
703C22×C4C2×D4×C15111yescharacteristic
704C22×C4C2×D4×C15111yescharacteristic
705C22×C4C2×D4×C15111yescharacteristic
706C22×C4C24×C15111yescharacteristic
707SD16—28no—
708SD16—44no—
709D8—44no—
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×C8—21no—
721C2×C8C2×D4×C15112yes—
722C4⋊C4—24no—
723C4⋊C4—24no—
724C4⋊C4—22no—
725C4⋊C4—21no—
726C4⋊C4—21no—
727C4⋊C4—21no—
728C4⋊C4—21no—
729C4⋊C4—21no—
730C4⋊C4—21no—
731C4⋊C4—21no—
732C4⋊C4C2×D4×C15112yes—
733C22⋊C4—24no—
734C22⋊C4—24no—
735C22⋊C4—24no—
736C22⋊C4—24no—
737C22⋊C4—22no—
738C22⋊C4—22no—
739C22⋊C4—42no—
740C22⋊C4—42no—
741C22⋊C4—42no—
742C22⋊C4—81no—
743C22⋊C4—81no—
744C42—24no—
745C42C2×D4×C15112yes—
746C42C2×D4×C15112yes—
747C23—21no—
748C23—21no—
749C23—21no—
750C23—21no—
751C23—21no—
752C23—21no—
753C23—21no—
754C23—22no—
755C23—22no—
756C23—21no—
757C23—21no—
758C23—21no—
759C23—21no—
760C23—21no—
761C23—21no—
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#135×C15112yes—
775C23C22×D4×C15111yescharacteristic
776Q8—22no—
777Q8—22no—
778Q8—22no—
779Q8—22no—
780Q8—22no—
781Q8—48no—
782Q8—41no—
783Q8—41no—
784Q8#121×C15114yes—
785D4—22no—
786D4—22no—
787D4—22no—
788D4—22no—
789D4—44no—
790D4—48no—
791D4—48no—
792D4—41no—
793D4—41no—
794D4—41no—
795D4—41no—
796D4—84no—
797D4—84no—
798C2×C4—22no—
799C2×C4—22no—
800C2×C4—22no—
801C2×C4—21no—
802C2×C4—21no—
803C2×C4—21no—
804C2×C4—21no—
805C2×C4—22no—
806C2×C4—22no—
807C2×C4—21no—
808C2×C4—21no—
809C2×C4—21no—
810C2×C4—21no—
811C2×C4—21no—
812C2×C4—21no—
813C2×C4—48no—
814C2×C4—48no—
815C2×C4—41no—
816C2×C4—41no—
817C2×C4—41no—
818C2×C4—41no—
819C2×C4—41no—
820C2×C4—41no—
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—84no—
837C2×C4#120×C15112yes—
838C2×C4#120×C15112yes—
839C2×C4C22×D4×C15111yescharacteristic
840C2×C4C22×D4×C15111yescharacteristic
841C2×C4C22×D4×C15111yescharacteristic
842C2×C4C2×#41×C15111yescharacteristic
843C2×C4H(5,𝔽2)×C15111yescharacteristic
844C2×C4H(5,𝔽2)×C15111yescharacteristic
845C8—22no—
846C8—41no—
847C8—41no—
848C8—41no—
849C22—22no—
850C22—22no—
851C22—22no—
852C22—41no—
853C22—41no—
854C22—41no—
855C22—41no—
856C22—42no—
857C22—41no—
858C22—42no—
859C22—41no—
860C22—42no—
861C22—41no—
862C22—42no—
863C22—41no—
864C22—42no—
865C22—42no—
866C22—41no—
867C22—41no—
868C22—41no—
869C22—81no—
870C22—81no—
871C22—81no—
872C22—81no—
873C22—81no—
874C22—81no—
875C22—81no—
876C22—81no—
877C22C2×#120×C15111yescharacteristic
878C22D42×C15111yescharacteristic
879C22#546×C15111yescharacteristic
880C22C2×#135×C15111yescharacteristic
881C22#575×C15111yescharacteristic
882C22#577×C15111yescharacteristic
883C22#577×C15111yescharacteristic
884C4—24no—
885C4—22no—
886C4—22no—
887C4—41no—
888C4—41no—
889C4—42no—
890C4—42no—
891C4—81no—
892C4—81no—
893C4—81no—
894C4C2×#121×C15111yescharacteristic
895C4#535×C15111yescharacteristic
896C4D42×C15111yescharacteristic
897C4#546×C15111yescharacteristic
898C2—42no—
899C2—81no—
900C2—82no—
901C2—82no—
902C2#2408×C15111yescharacteristic
903C2#3002×C15111yescharacteristic
904C2#3010×C15111yescharacteristic
905C2#3275×C15111yescharacteristic
906C2#3282×C15111yescharacteristic
907C2#3301×C15111yescharacteristic
908C2#3326×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×C4×SD16×C151C2semidirect
6. #2535×C151C2semidirect
7. #2035×C151C2semidirect
8. #2034×C151C2semidirect
9. #2000×C151C2semidirect
10. #1999×C151C2semidirect
11. #1958×C151C2semidirect
12. #1954×C151C2semidirect
13. #1805×C151C2semidirect
14. #1788×C151C2semidirect
15. #1787×C151C2semidirect
97. C2×SD16×C151D4semidirect
107. #124×C151D4semidirect
119. C4×Q8×C151D4semidirect
454. #24244C151direct (N × H)
455. C151#24244direct (N × H)
456. C2×#548C2×C151semidirect
457. C2×#463C2×C151semidirect
458. C2×#449C2×C151semidirect
459. C2×#448C2×C151semidirect
460. C2×C4×SD16C2×C151semidirect
461. #2535C2×C151semidirect
462. #2035C2×C151semidirect
463. #2034C2×C151semidirect
464. #2000C2×C151semidirect
465. #1999C2×C151semidirect
466. #1958C2×C151semidirect
467. #1954C2×C151semidirect
468. #1805C2×C151semidirect
469. #1788C2×C151semidirect
470. #1787C2×C151semidirect
552. C2×SD16D4×C151semidirect
562. #124D4×C151semidirect
574. C4×Q8D4×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×C4×SD16×C1512
#2535×C1512
#2035×C1512
#2034×C1512
#2000×C1512
#1999×C1512
#1958×C1512
#1954×C1512
#1805×C1512
#1788×C1512
#1787×C1512
#24244151