Finite Group Databasebeta

← C151×#23972 #50328897

Subgroups — C151×#23972 #50328897

Order 38656.

1516 conjugacy classes of subgroups.

The subgroup lattice has 876 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#547×C151C211yesmaximal, characteristic, complemented
2C2×#449×C151C211yesmaximal, characteristic, complemented
3C2×#417×C151C211yesmaximal, characteristic, complemented
4#2407×C151C211yesmaximal, characteristic, complemented
5#2024×C151C211yesmaximal, characteristic, complemented
6#2023×C151C211yesmaximal, characteristic, complemented
7#2000×C151C211yesmaximal, characteristic, complemented
8#1999×C151C211yesmaximal, characteristic, complemented
9#1895×C151C211yesmaximal, characteristic, complemented
10#1879×C151C211yesmaximal, characteristic, complemented
11#1877×C151C211yesmaximal, characteristic, complemented
12#1874×C151C211yesmaximal, characteristic, complemented
13#1872×C151C211yesmaximal, characteristic, complemented
14#1870×C151C211yesmaximal, characteristic, complemented
15#1824×C151C211yesmaximal, characteristic, complemented
16C22×#41×C151—21no—
17C22×#41×C151C2211yescharacteristic
18C22×SD16×C151C2211yescharacteristic
19C22×D8×C151C2211yescharacteristic
20C22×M16×C151C2211yescharacteristic
21#547×C151—24no—
22#547×C151—24no—
23C2×C4⋊Q8×C151C2211yescharacteristic
24C2×#123×C151—21no—
25C2×#123×C151—21no—
26C2×C22⋊Q8×C151—21no—
27C2×C22⋊Q8×C151C2211yescharacteristic
28C2×#121×C151C2211yescharacteristic
29C2×#121×C151C2211yescharacteristic
30C2×#121×C151C2211yescharacteristic
31C2×C4×D4×C151C2211yescharacteristic
32C2×C4×D4×C151C2211yescharacteristic
33C22×C4⋊C4×C151C2211yescharacteristic
34C22×C4⋊C4×C151C2211yescharacteristic
35#449×C151—24no—
36#417×C151—24no—
37C2×#103×C151C2211yescharacteristic
38C2×#103×C151C2211yescharacteristic
39C2×#103×C151C2211yescharacteristic
40C2×#102×C151C2211yescharacteristic
41C2×#102×C151C2211yescharacteristic
42C2×#102×C151C2211yescharacteristic
43C2×#102×C151C2211yescharacteristic
44C2×#102×C151C2211yescharacteristic
45C2×C22⋊C8×C151C2211yescharacteristic
46C2×C22⋊C8×C151C2211yescharacteristic
47C2×C22⋊C8×C151C2211yescharacteristic
48#394×C151—21no—
49#392×C151—21no—
50#391×C151C2211yescharacteristic
51#390×C151C2211yescharacteristic
52#386×C151—21no—
53#385×C151—21no—
54#380×C151C2211yescharacteristic
55#340×C151C2211yescharacteristic
56#340×C151C2211yescharacteristic
57#340×C151C2211yescharacteristic
58#340×C151C2211yescharacteristic
59#340×C151C2211yescharacteristic
60#340×C151C2211yescharacteristic
61#336×C151C2211yescharacteristic
62#336×C151C2211yescharacteristic
63C2×#41×C151—22no—
64C2×#41×C151—22no—
65C2×#41×C151—28no—
66C2×#41×C151—22no—
67C2×#41×C151—22no—
68C2×#41×C151—41no—
69C2×#41×C151—41no—
70C2×#41×C151—44no—
71C2×#41×C151—44no—
72C22×Q8×C151—21no—
73C22×Q8×C151C2311yescharacteristic
74C22×D4×C151—21no—
75C22×D4×C151—21no—
76C22×D4×C151—21no—
77C22×D4×C151—21no—
78C22×D4×C151D411yescharacteristic
79C22×D4×C151C2311yescharacteristic
80C22×D4×C151C2311yescharacteristic
81C23×C4×C151—21no—
82C23×C4×C151—21no—
83C23×C4×C151—21no—
84C23×C4×C151—21no—
85C23×C4×C151C2311yescharacteristic
86C23×C4×C151C2311yescharacteristic
87C2×SD16×C151—22no—
88C2×SD16×C151—22no—
89C2×SD16×C151—41no—
90C2×D8×C151—22no—
91C2×D8×C151—22no—
92C2×D8×C151—41no—
93C2×M16×C151—22no—
94C2×M16×C151—41no—
95C2×M16×C151—41no—
96C22×C8×C151C2311yescharacteristic
97C22×C8×C151C2311yescharacteristic
98C22×C8×C151C2311yescharacteristic
99C22×C8×C151C2311yescharacteristic
100C4⋊Q8×C151—22no—
101C4⋊Q8×C151—22no—
102#123×C151—28no—
103#123×C151—28no—
104C22⋊Q8×C151—28no—
105C22⋊Q8×C151—22no—
106C22⋊Q8×C151—41no—
107#121×C151—22no—
108#121×C151—22no—
109#121×C151—22no—
110#121×C151—22no—
111#121×C151—41no—
112#121×C151D414yescomplemented
113C4×D4×C151—22no—
114C4×D4×C151—22no—
115C4×D4×C151—22no—
116C4×D4×C151—22no—
117C2×C4⋊C4×C151—21no—
118C2×C4⋊C4×C151—21no—
119C2×C4⋊C4×C151—22no—
120C2×C4⋊C4×C151—21no—
121C2×C4⋊C4×C151—22no—
122C2×C4⋊C4×C151—22no—
123C2×C4⋊C4×C151—21no—
124C2×C4⋊C4×C151D411yescharacteristic
125C2×C4⋊C4×C151D414yescomplemented
126C2×C4⋊C4×C151C2311yescharacteristic
127C2×C4⋊C4×C151C2311yescharacteristic
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×C151D411yescharacteristic
140C2×C22⋊C4×C151D411yescharacteristic
141C2×C42×C151C2311yescharacteristic
142#103×C151—22no—
143#103×C151—22no—
144#103×C151—22no—
145#102×C151—22no—
146#102×C151—22no—
147#102×C151—22no—
148#102×C151—41no—
149#102×C151—41no—
150C22⋊C8×C151—22no—
151C22⋊C8×C151—41no—
152C22⋊C8×C151—41no—
153#95×C151—21no—
154#95×C151—21no—
155#95×C151—21no—
156C24×C151—21no—
157C24×C151—21no—
158C24×C151C2×D411yescharacteristic
159C24×C151C2×D411yescharacteristic
160#41×C151—28no—
161#41×C151—44no—
162#41×C151—44no—
163#41×C151—44no—
164#41×C151—432no—
165C2×Q8×C151—24no—
166C2×Q8×C151—21no—
167C2×Q8×C151—21no—
168C2×Q8×C151—21no—
169C2×Q8×C151—21no—
170C2×Q8×C151—21no—
171C2×Q8×C151—42no—
172C2×Q8×C151—42no—
173C2×Q8×C151#4112yescomplemented
174C2×D4×C151—22no—
175C2×D4×C151—22no—
176C2×D4×C151—24no—
177C2×D4×C151—24no—
178C2×D4×C151—22no—
179C2×D4×C151—21no—
180C2×D4×C151—21no—
181C2×D4×C151—21no—
182C2×D4×C151—21no—
183C2×D4×C151—21no—
184C2×D4×C151—21no—
185C2×D4×C151—21no—
186C2×D4×C151—21no—
187C2×D4×C151—21no—
188C2×D4×C151—21no—
189C2×D4×C151—42no—
190C2×D4×C151—42no—
191C2×D4×C151—42no—
192C2×D4×C151—42no—
193C2×D4×C151—42no—
194C2×D4×C151—42no—
195C2×D4×C151—42no—
196C2×D4×C151—42no—
197C2×D4×C151—42no—
198C2×D4×C151—81no—
199C2×D4×C151C2×D412yes—
200C2×D4×C151#4112yescomplemented
201C22×C4×C151—21no—
202C22×C4×C151—21no—
203C22×C4×C151—21no—
204C22×C4×C151—21no—
205C22×C4×C151—24no—
206C22×C4×C151—24no—
207C22×C4×C151—24no—
208C22×C4×C151—21no—
209C22×C4×C151—21no—
210C22×C4×C151—21no—
211C22×C4×C151—21no—
212C22×C4×C151—21no—
213C22×C4×C151—21no—
214C22×C4×C151—21no—
215C22×C4×C151—21no—
216C22×C4×C151—21no—
217C22×C4×C151—21no—
218C22×C4×C151—21no—
219C22×C4×C151—21no—
220C22×C4×C151—42no—
221C22×C4×C151—42no—
222C22×C4×C151—42no—
223C22×C4×C151—42no—
224C22×C4×C151—42no—
225C22×C4×C151—42no—
226C22×C4×C151—42no—
227C22×C4×C151—42no—
228C22×C4×C151—42no—
229C22×C4×C151C2×D411yescharacteristic
230C22×C4×C151C2×D411yescharacteristic
231C22×C4×C151C2×D411yescharacteristic
232C22×C4×C151C2×D412yes—
233C22×C4×C151C2×D412yes—
234C22×C4×C151C2×D411yescharacteristic
235C22×C4×C151C2411yescharacteristic
236SD16×C151—44no—
237D8×C151—44no—
238M16×C151—44no—
239C2×C8×C151—21no—
240C2×C8×C151—21no—
241C2×C8×C151—21no—
242C2×C8×C151—21no—
243C2×C8×C151—21no—
244C2×C8×C151—21no—
245C2×C8×C151—21no—
246C2×C8×C151—21no—
247C2×C8×C151—21no—
248C2×C8×C151—21no—
249C2×C8×C151—21no—
250C2×C8×C151—21no—
251C4⋊C4×C151—24no—
252C4⋊C4×C151—24no—
253C4⋊C4×C151—24no—
254C4⋊C4×C151—22no—
255C4⋊C4×C151—21no—
256C4⋊C4×C151—21no—
257C4⋊C4×C151—21no—
258C4⋊C4×C151—21no—
259C4⋊C4×C151—21no—
260C4⋊C4×C151—21no—
261C4⋊C4×C151—21no—
262C4⋊C4×C151—42no—
263C4⋊C4×C151C2×D412yes—
264C4⋊C4×C151C2×D412yes—
265C4⋊C4×C151C2×D412yes—
266C22⋊C4×C151—24no—
267C22⋊C4×C151—24no—
268C22⋊C4×C151—22no—
269C22⋊C4×C151—24no—
270C22⋊C4×C151—22no—
271C22⋊C4×C151—42no—
272C22⋊C4×C151—42no—
273C22⋊C4×C151—42no—
274C22⋊C4×C151—81no—
275C22⋊C4×C151—81no—
276C42×C151—21no—
277C42×C151—21no—
278C23×C151—21no—
279C23×C151—21no—
280C23×C151—21no—
281C23×C151—21no—
282C23×C151—21no—
283C23×C151—21no—
284C23×C151—21no—
285C23×C151—21no—
286C23×C151—21no—
287C23×C151—21no—
288C23×C151—21no—
289C23×C151—21no—
290C23×C151—22no—
291C23×C151—22no—
292C23×C151—41no—
293C23×C151—41no—
294C23×C151—41no—
295C23×C151—41no—
296C23×C151—41no—
297C23×C151—41no—
298C23×C151—41no—
299C23×C151—41no—
300C23×C151—41no—
301C23×C151—41no—
302C23×C151—41no—
303C23×C151—41no—
304C23×C151#12012yes—
305C23×C151AGL(1,ℤ/8)12yes—
306C23×C151C22×D411yescharacteristic
307Q8×C151—22no—
308Q8×C151—22no—
309Q8×C151—48no—
310Q8×C151—41no—
311Q8×C151—41no—
312D4×C151—28no—
313D4×C151—22no—
314D4×C151—22no—
315D4×C151—22no—
316D4×C151—22no—
317D4×C151—48no—
318D4×C151—48no—
319D4×C151—48no—
320D4×C151—41no—
321D4×C151—41no—
322D4×C151—41no—
323D4×C151—41no—
324D4×C151—84no—
325C2×C4×C151—21no—
326C2×C4×C151—21no—
327C2×C4×C151—21no—
328C2×C4×C151—21no—
329C2×C4×C151—22no—
330C2×C4×C151—22no—
331C2×C4×C151—22no—
332C2×C4×C151—22no—
333C2×C4×C151—22no—
334C2×C4×C151—22no—
335C2×C4×C151—21no—
336C2×C4×C151—21no—
337C2×C4×C151—22no—
338C2×C4×C151—22no—
339C2×C4×C151—21no—
340C2×C4×C151—21no—
341C2×C4×C151—21no—
342C2×C4×C151—21no—
343C2×C4×C151—48no—
344C2×C4×C151—48no—
345C2×C4×C151—48no—
346C2×C4×C151—48no—
347C2×C4×C151—41no—
348C2×C4×C151—41no—
349C2×C4×C151—41no—
350C2×C4×C151—41no—
351C2×C4×C151—41no—
352C2×C4×C151—41no—
353C2×C4×C151—41no—
354C2×C4×C151—41no—
355C2×C4×C151—41no—
356C2×C4×C151—41no—
357C2×C4×C151—41no—
358C2×C4×C151—41no—
359C2×C4×C151—41no—
360C2×C4×C151—41no—
361C2×C4×C151—41no—
362C2×C4×C151—41no—
363C2×C4×C151—41no—
364C2×C4×C151—41no—
365C2×C4×C151#12012yes—
366C2×C4×C151AGL(1,ℤ/8)12yes—
367C2×C4×C151C22×D411yescharacteristic
368C2×C4×C151C22×D411yescharacteristic
369C2×C4×C151C2×#4111yescharacteristic
370C2×C4×C151C2×#4111yescharacteristic
371C2×C4×C151H(5,𝔽2)11yescharacteristic
372C2×C4×C151H(5,𝔽2)11yescharacteristic
373C8×C151—41no—
374C8×C151—41no—
375C8×C151—41no—
376C8×C151—41no—
377C22×C151—22no—
378C22×C151—22no—
379C22×C151—22no—
380C22×C151—22no—
381C22×C151—22no—
382C22×C151—22no—
383C22×C151—41no—
384C22×C151—41no—
385C22×C151—41no—
386C22×C151—41no—
387C22×C151—41no—
388C22×C151—41no—
389C22×C151—41no—
390C22×C151—41no—
391C22×C151—42no—
392C22×C151—42no—
393C22×C151—42no—
394C22×C151—42no—
395C22×C151—42no—
396C22×C151—42no—
397C22×C151—81no—
398C22×C151—81no—
399C22×C151—81no—
400C22×C151—81no—
401C22×C151—81no—
402C22×C151—81no—
403C22×C151—81no—
404C22×C151—81no—
405C22×C151C2×#12011yescharacteristic
406C22×C151#54611yescharacteristic
407C22×C151#54611yescharacteristic
408C22×C151C2×AGL(1,ℤ/8)11yescharacteristic
409C22×C151C2×AGL(1,ℤ/8)11yescharacteristic
410C22×C151#57711yescharacteristic
411C22×C151#57811yescharacteristic
412C4×C151—22no—
413C4×C151—22no—
414C4×C151—41no—
415C4×C151—42no—
416C4×C151—42no—
417C4×C151—42no—
418C4×C151—42no—
419C4×C151—41no—
420C4×C151—81no—
421C4×C151—81no—
422C4×C151#52511yescharacteristic
423C4×C151#53511yescharacteristic
424C4×C151#54611yescharacteristic
425C4×C151#54611yescharacteristic
426C2×C151—42no—
427C2×C151—42no—
428C2×C151—82no—
429C2×C151—82no—
430C2×C151#240411yescharacteristic
431C2×C151#300311yescharacteristic
432C2×C151#301311yescharacteristic
433C2×C151#330611yescharacteristic
434C2×C151#330811yescharacteristic
435C2×C151#333011yescharacteristic
436C2×C151#333211yescharacteristic
437#23972C15111yesmaximal, characteristic, direct product factor, Sylow
438C151#2397211yescharacteristic, direct product factor, Sylow
439C2×#547C2×C15111yescharacteristic, complemented
440C2×#449C2×C15111yescharacteristic, complemented
441C2×#417C2×C15111yescharacteristic, complemented
442#2407C2×C15111yescharacteristic, complemented
443#2024C2×C15111yescharacteristic, complemented
444#2023C2×C15111yescharacteristic, complemented
445#2000C2×C15111yescharacteristic, complemented
446#1999C2×C15111yescharacteristic, complemented
447#1895C2×C15111yescharacteristic, complemented
448#1879C2×C15111yescharacteristic, complemented
449#1877C2×C15111yescharacteristic, complemented
450#1874C2×C15111yescharacteristic, complemented
451#1872C2×C15111yescharacteristic, complemented
452#1870C2×C15111yescharacteristic, complemented
453#1824C2×C15111yescharacteristic, complemented
454C22×#41—21no—
455C22×#41C22×C15111yescharacteristic
456C22×SD16C22×C15111yescharacteristic
457C22×D8C22×C15111yescharacteristic
458C22×M16C22×C15111yescharacteristic
459#547—24no—
460#547—24no—
461C2×C4⋊Q8C22×C15111yescharacteristic
462C2×#123—21no—
463C2×#123—21no—
464C2×C22⋊Q8—21no—
465C2×C22⋊Q8C22×C15111yescharacteristic
466C2×#121C22×C15111yescharacteristic
467C2×#121C22×C15111yescharacteristic
468C2×#121C22×C15111yescharacteristic
469C2×C4×D4C22×C15111yescharacteristic
470C2×C4×D4C22×C15111yescharacteristic
471C22×C4⋊C4C22×C15111yescharacteristic
472C22×C4⋊C4C22×C15111yescharacteristic
473#449—24no—
474#417—24no—
475C2×#103C22×C15111yescharacteristic
476C2×#103C22×C15111yescharacteristic
477C2×#103C22×C15111yescharacteristic
478C2×#102C22×C15111yescharacteristic
479C2×#102C22×C15111yescharacteristic
480C2×#102C22×C15111yescharacteristic
481C2×#102C22×C15111yescharacteristic
482C2×#102C22×C15111yescharacteristic
483C2×C22⋊C8C22×C15111yescharacteristic
484C2×C22⋊C8C22×C15111yescharacteristic
485C2×C22⋊C8C22×C15111yescharacteristic
486#394—21no—
487#392—21no—
488#391C22×C15111yescharacteristic
489#390C22×C15111yescharacteristic
490#386—21no—
491#385—21no—
492#380C22×C15111yescharacteristic
493#340C22×C15111yescharacteristic
494#340C22×C15111yescharacteristic
495#340C22×C15111yescharacteristic
496#340C22×C15111yescharacteristic
497#340C22×C15111yescharacteristic
498#340C22×C15111yescharacteristic
499#336C22×C15111yescharacteristic
500#336C22×C15111yescharacteristic
501C2×#41—28no—
502C2×#41—22no—
503C2×#41—22no—
504C2×#41—22no—
505C2×#41—22no—
506C2×#41—41no—
507C2×#41—41no—
508C2×#41—44no—
509C2×#41—44no—
510C22×Q8—21no—
511C22×Q8C23×C15111yescharacteristic
512C22×D4—21no—
513C22×D4—21no—
514C22×D4—21no—
515C22×D4—21no—
516C22×D4D4×C15111yescharacteristic
517C22×D4C23×C15111yescharacteristic
518C22×D4C23×C15111yescharacteristic
519C23×C4—21no—
520C23×C4—21no—
521C23×C4—21no—
522C23×C4—21no—
523C23×C4C23×C15111yescharacteristic
524C23×C4C23×C15111yescharacteristic
525C2×SD16—22no—
526C2×SD16—22no—
527C2×SD16—41no—
528C2×D8—22no—
529C2×D8—22no—
530C2×D8—41no—
531C2×M16—22no—
532C2×M16—41no—
533C2×M16—41no—
534C22×C8C23×C15111yescharacteristic
535C22×C8C23×C15111yescharacteristic
536C22×C8C23×C15111yescharacteristic
537C22×C8C23×C15111yescharacteristic
538C4⋊Q8—22no—
539C4⋊Q8—22no—
540#123—28no—
541#123—28no—
542C22⋊Q8—28no—
543C22⋊Q8—22no—
544C22⋊Q8—41no—
545#121—22no—
546#121—22no—
547#121—22no—
548#121—22no—
549#121—41no—
550#121D4×C15114yescomplemented
551C4×D4—22no—
552C4×D4—22no—
553C4×D4—22no—
554C4×D4—22no—
555C2×C4⋊C4—21no—
556C2×C4⋊C4—21no—
557C2×C4⋊C4—22no—
558C2×C4⋊C4—21no—
559C2×C4⋊C4—22no—
560C2×C4⋊C4—22no—
561C2×C4⋊C4—21no—
562C2×C4⋊C4D4×C15111yescharacteristic
563C2×C4⋊C4D4×C15114yescomplemented
564C2×C4⋊C4C23×C15111yescharacteristic
565C2×C4⋊C4C23×C15111yescharacteristic
566C2×C4⋊C4C23×C15111yescharacteristic
567C2×C4⋊C4C23×C15111yescharacteristic
568C2×C4⋊C4C23×C15111yescharacteristic
569C2×C22⋊C4—21no—
570C2×C22⋊C4—21no—
571C2×C22⋊C4—21no—
572C2×C22⋊C4—21no—
573C2×C22⋊C4—21no—
574C2×C22⋊C4—21no—
575C2×C22⋊C4—21no—
576C2×C22⋊C4—21no—
577C2×C22⋊C4D4×C15111yescharacteristic
578C2×C22⋊C4D4×C15111yescharacteristic
579C2×C42C23×C15111yescharacteristic
580#103—22no—
581#103—22no—
582#103—22no—
583#102—22no—
584#102—22no—
585#102—22no—
586#102—41no—
587#102—41no—
588C22⋊C8—22no—
589C22⋊C8—41no—
590C22⋊C8—41no—
591#95—21no—
592#95—21no—
593#95—21no—
594C24—21no—
595C24—21no—
596C24C2×D4×C15111yescharacteristic
597C24C2×D4×C15111yescharacteristic
598#41—28no—
599#41—44no—
600#41—44no—
601#41—44no—
602#41—432no—
603C2×Q8—24no—
604C2×Q8—21no—
605C2×Q8—21no—
606C2×Q8—21no—
607C2×Q8—21no—
608C2×Q8—21no—
609C2×Q8—42no—
610C2×Q8—42no—
611C2×Q8#41×C15112yescomplemented
612C2×D4—22no—
613C2×D4—22no—
614C2×D4—24no—
615C2×D4—24no—
616C2×D4—22no—
617C2×D4—21no—
618C2×D4—21no—
619C2×D4—21no—
620C2×D4—21no—
621C2×D4—21no—
622C2×D4—21no—
623C2×D4—21no—
624C2×D4—21no—
625C2×D4—21no—
626C2×D4—21no—
627C2×D4—42no—
628C2×D4—42no—
629C2×D4—42no—
630C2×D4—42no—
631C2×D4—42no—
632C2×D4—42no—
633C2×D4—42no—
634C2×D4—42no—
635C2×D4—42no—
636C2×D4—81no—
637C2×D4C2×D4×C15112yes—
638C2×D4#41×C15112yescomplemented
639C22×C4—21no—
640C22×C4—21no—
641C22×C4—21no—
642C22×C4—21no—
643C22×C4—24no—
644C22×C4—24no—
645C22×C4—24no—
646C22×C4—21no—
647C22×C4—21no—
648C22×C4—21no—
649C22×C4—21no—
650C22×C4—21no—
651C22×C4—21no—
652C22×C4—21no—
653C22×C4—21no—
654C22×C4—21no—
655C22×C4—21no—
656C22×C4—21no—
657C22×C4—21no—
658C22×C4—42no—
659C22×C4—42no—
660C22×C4—42no—
661C22×C4—42no—
662C22×C4—42no—
663C22×C4—42no—
664C22×C4—42no—
665C22×C4—42no—
666C22×C4—42no—
667C22×C4C2×D4×C15111yescharacteristic
668C22×C4C2×D4×C15111yescharacteristic
669C22×C4C2×D4×C15111yescharacteristic
670C22×C4C2×D4×C15112yes—
671C22×C4C2×D4×C15112yes—
672C22×C4C2×D4×C15111yescharacteristic
673C22×C4C24×C15111yescharacteristic
674SD16—44no—
675D8—44no—
676M16—44no—
677C2×C8—21no—
678C2×C8—21no—
679C2×C8—21no—
680C2×C8—21no—
681C2×C8—21no—
682C2×C8—21no—
683C2×C8—21no—
684C2×C8—21no—
685C2×C8—21no—
686C2×C8—21no—
687C2×C8—21no—
688C2×C8—21no—
689C4⋊C4—24no—
690C4⋊C4—24no—
691C4⋊C4—24no—
692C4⋊C4—22no—
693C4⋊C4—21no—
694C4⋊C4—21no—
695C4⋊C4—21no—
696C4⋊C4—21no—
697C4⋊C4—21no—
698C4⋊C4—21no—
699C4⋊C4—21no—
700C4⋊C4—42no—
701C4⋊C4C2×D4×C15112yes—
702C4⋊C4C2×D4×C15112yes—
703C4⋊C4C2×D4×C15112yes—
704C22⋊C4—24no—
705C22⋊C4—24no—
706C22⋊C4—22no—
707C22⋊C4—24no—
708C22⋊C4—22no—
709C22⋊C4—42no—
710C22⋊C4—42no—
711C22⋊C4—42no—
712C22⋊C4—81no—
713C22⋊C4—81no—
714C42—21no—
715C42—21no—
716C23—21no—
717C23—21no—
718C23—21no—
719C23—21no—
720C23—21no—
721C23—21no—
722C23—21no—
723C23—21no—
724C23—21no—
725C23—21no—
726C23—21no—
727C23—21no—
728C23—22no—
729C23—22no—
730C23—41no—
731C23—41no—
732C23—41no—
733C23—41no—
734C23—41no—
735C23—41no—
736C23—41no—
737C23—41no—
738C23—41no—
739C23—41no—
740C23—41no—
741C23—41no—
742C23#120×C15112yes—
743C23AGL(1,ℤ/8)×C15112yes—
744C23C22×D4×C15111yescharacteristic
745Q8—22no—
746Q8—22no—
747Q8—48no—
748Q8—41no—
749Q8—41no—
750D4—28no—
751D4—22no—
752D4—22no—
753D4—22no—
754D4—22no—
755D4—48no—
756D4—48no—
757D4—48no—
758D4—41no—
759D4—41no—
760D4—41no—
761D4—41no—
762D4—84no—
763C2×C4—21no—
764C2×C4—21no—
765C2×C4—21no—
766C2×C4—21no—
767C2×C4—22no—
768C2×C4—22no—
769C2×C4—22no—
770C2×C4—22no—
771C2×C4—21no—
772C2×C4—21no—
773C2×C4—22no—
774C2×C4—22no—
775C2×C4—22no—
776C2×C4—21no—
777C2×C4—22no—
778C2×C4—21no—
779C2×C4—21no—
780C2×C4—21no—
781C2×C4—48no—
782C2×C4—48no—
783C2×C4—48no—
784C2×C4—48no—
785C2×C4—41no—
786C2×C4—41no—
787C2×C4—41no—
788C2×C4—41no—
789C2×C4—41no—
790C2×C4—41no—
791C2×C4—41no—
792C2×C4—41no—
793C2×C4—41no—
794C2×C4—41no—
795C2×C4—41no—
796C2×C4—41no—
797C2×C4—41no—
798C2×C4—41no—
799C2×C4—41no—
800C2×C4—41no—
801C2×C4—41no—
802C2×C4—41no—
803C2×C4#120×C15112yes—
804C2×C4AGL(1,ℤ/8)×C15112yes—
805C2×C4C22×D4×C15111yescharacteristic
806C2×C4C22×D4×C15111yescharacteristic
807C2×C4C2×#41×C15111yescharacteristic
808C2×C4C2×#41×C15111yescharacteristic
809C2×C4H(5,𝔽2)×C15111yescharacteristic
810C2×C4H(5,𝔽2)×C15111yescharacteristic
811C8—41no—
812C8—41no—
813C8—41no—
814C8—41no—
815C22—22no—
816C22—22no—
817C22—22no—
818C22—22no—
819C22—22no—
820C22—22no—
821C22—41no—
822C22—41no—
823C22—41no—
824C22—41no—
825C22—41no—
826C22—41no—
827C22—41no—
828C22—41no—
829C22—42no—
830C22—42no—
831C22—42no—
832C22—42no—
833C22—42no—
834C22—42no—
835C22—81no—
836C22—81no—
837C22—81no—
838C22—81no—
839C22—81no—
840C22—81no—
841C22—81no—
842C22—81no—
843C22C2×#120×C15111yescharacteristic
844C22#546×C15111yescharacteristic
845C22#546×C15111yescharacteristic
846C22C2×AGL(1,ℤ/8)×C15111yescharacteristic
847C22C2×AGL(1,ℤ/8)×C15111yescharacteristic
848C22#577×C15111yescharacteristic
849C22#578×C15111yescharacteristic
850C4—22no—
851C4—22no—
852C4—41no—
853C4—42no—
854C4—42no—
855C4—42no—
856C4—42no—
857C4—41no—
858C4—81no—
859C4—81no—
860C4#525×C15111yescharacteristic
861C4#535×C15111yescharacteristic
862C4#546×C15111yescharacteristic
863C4#546×C15111yescharacteristic
864C2—42no—
865C2—42no—
866C2—82no—
867C2—82no—
868C2#2404×C15111yescharacteristic
869C2#3003×C15111yescharacteristic
870C2#3013×C15111yescharacteristic
871C2#3306×C15111yescharacteristic
872C2#3308×C15111yescharacteristic
873C2#3330×C15111yescharacteristic
874C2#3332×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×#547×C151C2semidirect
2. C2×#449×C151C2semidirect
3. C2×#417×C151C2semidirect
4. #2407×C151C2semidirect
5. #2024×C151C2semidirect
6. #2023×C151C2semidirect
7. #2000×C151C2semidirect
8. #1999×C151C2semidirect
9. #1895×C151C2semidirect
10. #1879×C151C2semidirect
11. #1877×C151C2semidirect
12. #1874×C151C2semidirect
13. #1872×C151C2semidirect
14. #1870×C151C2semidirect
15. #1824×C151C2semidirect
112. #121×C151D4semidirect
125. C2×C4⋊C4×C151D4semidirect
173. C2×Q8×C151#41semidirect
200. C2×D4×C151#41semidirect
437. #23972C151direct (N × H)
438. C151#23972direct (N × H)
439. C2×#547C2×C151semidirect
440. C2×#449C2×C151semidirect
441. C2×#417C2×C151semidirect
442. #2407C2×C151semidirect
443. #2024C2×C151semidirect
444. #2023C2×C151semidirect
445. #2000C2×C151semidirect
446. #1999C2×C151semidirect
447. #1895C2×C151semidirect
448. #1879C2×C151semidirect
449. #1877C2×C151semidirect
450. #1874C2×C151semidirect
451. #1872C2×C151semidirect
452. #1870C2×C151semidirect
453. #1824C2×C151semidirect
550. #121D4×C151semidirect
563. C2×C4⋊C4D4×C151semidirect
611. C2×Q8#41×C151semidirect
638. C2×D4#41×C151semidirect

Maximal subgroups

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

subgroupindex
C2×#547×C1512
C2×#449×C1512
C2×#417×C1512
#2407×C1512
#2024×C1512
#2023×C1512
#2000×C1512
#1999×C1512
#1895×C1512
#1879×C1512
#1877×C1512
#1874×C1512
#1872×C1512
#1870×C1512
#1824×C1512
#23972151