Finite Group Databasebeta

← C151×#24257 #50329182

Subgroups — C151×#24257 #50329182

Order 38656.

1650 conjugacy classes of subgroups.

The subgroup lattice has 966 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#546×C151C211yesmaximal, characteristic, complemented
2C2×#463×C151C211yesmaximal, characteristic, complemented
3C2×#449×C151C211yesmaximal, characteristic, complemented
4C2×#447×C151C211yesmaximal, characteristic, complemented
5C2×#442×C151C211yesmaximal, characteristic, complemented
6#2537×C151C211yesmaximal, characteristic, complemented
7#2035×C151C211yesmaximal, characteristic, complemented
8#2034×C151C211yesmaximal, characteristic, complemented
9#2000×C151C211yesmaximal, characteristic, complemented
10#1999×C151C211yesmaximal, characteristic, complemented
11#1959×C151C211yesmaximal, characteristic, complemented
12#1955×C151C211yesmaximal, characteristic, complemented
13#1802×C151C211yesmaximal, characteristic, complemented
14#1788×C151C211yesmaximal, characteristic, complemented
15#1786×C151C211yesmaximal, characteristic, complemented
16C22×#41×C151C2211yescharacteristic
17C23×D4×C151C2211yescharacteristic
18C22×SD16×C151C2211yescharacteristic, complemented
19C22×D8×C151C2211yescharacteristic
20C22×D8×C151C2211yescharacteristic
21#546×C151—24no—
22#546×C151—24no—
23C2×#124×C151C2211yescharacteristic
24C2×#123×C151—21no—
25C2×C22⋊Q8×C151C2211yescharacteristic
26C2×#121×C151—21no—
27C2×#121×C151—21no—
28C2×#121×C151C2211yescharacteristic
29C2×#121×C151C2211yescharacteristic
30C2×#121×C151C2211yescharacteristic, complemented
31C2×#120×C151—21no—
32C2×C4×D4×C151C2211yescharacteristic
33C2×C4×D4×C151C2211yescharacteristic
34C2×C4×D4×C151C2211yescharacteristic, complemented
35C22×C22⋊C4×C151—21no—
36#463×C151—24no—
37#449×C151—24no—
38#447×C151—24no—
39#442×C151—24no—
40C2×#106×C151C2211yescharacteristic, complemented
41C2×C4⋊C8×C151C2211yescharacteristic, complemented
42C2×#103×C151C2211yescharacteristic, complemented
43C2×#103×C151C2211yescharacteristic, complemented
44C2×#103×C151C2211yescharacteristic, complemented
45C2×#102×C151C2211yescharacteristic
46C2×#102×C151C2211yescharacteristic
47C2×#102×C151C2211yescharacteristic
48C2×#102×C151C2211yescharacteristic
49C2×#102×C151C2211yescharacteristic
50C2×#102×C151C2211yescharacteristic
51C2×#102×C151C2211yescharacteristic, complemented
52C2×C22⋊C8×C151C2211yescharacteristic
53C2×C22⋊C8×C151C2211yescharacteristic
54C2×C22⋊C8×C151C2211yescharacteristic, complemented
55C2×C22⋊C8×C151C2211yescharacteristic, complemented
56C2×#97×C151C2211yescharacteristic, complemented
57#394×C151—21no—
58#394×C151—21no—
59#384×C151C2211yescharacteristic, complemented
60#380×C151—21no—
61#380×C151C2211yescharacteristic
62#380×C151C2211yescharacteristic, complemented
63#340×C151C2211yescharacteristic, complemented
64#340×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×D4×C151—22no—
74C22×D4×C151—22no—
75C22×D4×C151—21no—
76C22×D4×C151—21no—
77C22×D4×C151—21no—
78C22×D4×C151—21no—
79C22×D4×C151—21no—
80C22×D4×C151—22no—
81C22×D4×C151—22no—
82C22×D4×C151—41no—
83C22×D4×C151—41no—
84C22×D4×C151D411yescharacteristic
85C22×D4×C151C2311yescharacteristic
86C22×D4×C151C2311yescharacteristic
87C22×D4×C151C2311yescharacteristic
88C23×C4×C151—21no—
89C23×C4×C151—21no—
90C23×C4×C151—21no—
91C23×C4×C151C2311yescharacteristic
92C23×C4×C151C2311yescharacteristic
93C2×SD16×C151—22no—
94C2×SD16×C151—22no—
95C2×SD16×C151—41no—
96C2×D8×C151—22no—
97C2×D8×C151—22no—
98C2×D8×C151—22no—
99C2×D8×C151—22no—
100C2×D8×C151—41no—
101C2×D8×C151D414yescomplemented
102C22×C8×C151C2311yescharacteristic
103C22×C8×C151C2311yescharacteristic
104C22×C8×C151C2311yescharacteristic
105C22×C8×C151C2311yescharacteristic
106#124×C151—22no—
107#124×C151D414yescomplemented
108#123×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—
119#120×C151—28no—
120C4×D4×C151—22no—
121C4×D4×C151—22no—
122C4×D4×C151—22no—
123C4×D4×C151—22no—
124C4×D4×C151—22no—
125C4×D4×C151D414yescomplemented
126C2×C4⋊C4×C151—21no—
127C2×C4⋊C4×C151—21no—
128C2×C4⋊C4×C151—21no—
129C2×C4⋊C4×C151D411yescharacteristic
130C2×C4⋊C4×C151C2311yescharacteristic
131C2×C4⋊C4×C151C2311yescharacteristic
132C2×C4⋊C4×C151C2311yescharacteristic
133C2×C4⋊C4×C151C2311yescharacteristic
134C2×C22⋊C4×C151—28no—
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×C151—21no—
145C2×C22⋊C4×C151D411yescharacteristic
146C2×C22⋊C4×C151D411yescharacteristic
147C2×C42×C151C2311yescharacteristic
148#106×C151—22no—
149C4⋊C8×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—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—24no—
169C24×C151—21no—
170C24×C151—21no—
171C24×C151—42no—
172C24×C151—42no—
173C24×C151—42no—
174C24×C151—42no—
175C24×C151—81no—
176C24×C151—81no—
177C24×C151C2×D411yescharacteristic
178C24×C151C2×D411yescharacteristic
179#41×C151—44no—
180#41×C151—44no—
181#41×C151—44no—
182#41×C151—44no—
183C2×Q8×C151—21no—
184C2×Q8×C151—21no—
185C2×Q8×C151—21no—
186C2×Q8×C151—21no—
187C2×Q8×C151—21no—
188C2×Q8×C151C2×D412yes—
189C2×D4×C151—24no—
190C2×D4×C151—24no—
191C2×D4×C151—22no—
192C2×D4×C151—24no—
193C2×D4×C151—22no—
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—21no—
207C2×D4×C151—41no—
208C2×D4×C151—42no—
209C2×D4×C151—42no—
210C2×D4×C151—44no—
211C2×D4×C151—44no—
212C2×D4×C151—44no—
213C2×D4×C151—42no—
214C2×D4×C151—42no—
215C2×D4×C151—44no—
216C2×D4×C151—42no—
217C2×D4×C151—42no—
218C2×D4×C151—42no—
219C2×D4×C151—42no—
220C2×D4×C151—81no—
221C2×D4×C151—81no—
222C2×D4×C151—81no—
223C2×D4×C151—81no—
224C2×D4×C151C2×D412yes—
225C2×D4×C151C2×D412yes—
226C2×D4×C151C2×D412yes—
227C2×D4×C151C2×D412yes—
228C2×D4×C151#4112yes—
229C22×C4×C151—24no—
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—21no—
242C22×C4×C151—21no—
243C22×C4×C151—21no—
244C22×C4×C151—24no—
245C22×C4×C151—21no—
246C22×C4×C151—21no—
247C22×C4×C151—21no—
248C22×C4×C151—42no—
249C22×C4×C151—42no—
250C22×C4×C151—42no—
251C22×C4×C151—42no—
252C22×C4×C151—42no—
253C22×C4×C151—81no—
254C22×C4×C151—81no—
255C22×C4×C151C2×D411yescharacteristic
256C22×C4×C151C2×D411yescharacteristic
257C22×C4×C151C2×D411yescharacteristic
258C22×C4×C151C2×D411yescharacteristic
259C22×C4×C151C2411yescharacteristic
260SD16×C151—44no—
261D8×C151—28no—
262D8×C151—44no—
263C2×C8×C151—21no—
264C2×C8×C151—21no—
265C2×C8×C151—21no—
266C2×C8×C151—21no—
267C2×C8×C151—21no—
268C2×C8×C151—21no—
269C2×C8×C151—21no—
270C2×C8×C151—21no—
271C2×C8×C151—21no—
272C2×C8×C151—21no—
273C2×C8×C151—21no—
274C2×C8×C151C2×D412yes—
275C4⋊C4×C151—24no—
276C4⋊C4×C151—22no—
277C4⋊C4×C151—21no—
278C4⋊C4×C151—21no—
279C4⋊C4×C151—21no—
280C4⋊C4×C151—21no—
281C4⋊C4×C151—21no—
282C4⋊C4×C151—21no—
283C4⋊C4×C151—21no—
284C4⋊C4×C151—42no—
285C4⋊C4×C151—81no—
286C4⋊C4×C151C2×D412yes—
287C22⋊C4×C151—24no—
288C22⋊C4×C151—24no—
289C22⋊C4×C151—22no—
290C22⋊C4×C151—24no—
291C22⋊C4×C151—24no—
292C22⋊C4×C151—24no—
293C22⋊C4×C151—22no—
294C22⋊C4×C151—42no—
295C22⋊C4×C151—42no—
296C22⋊C4×C151—42no—
297C22⋊C4×C151—42no—
298C22⋊C4×C151—42no—
299C42×C151C2×D412yes—
300C42×C151C2×D412yes—
301C23×C151—21no—
302C23×C151—22no—
303C23×C151—22no—
304C23×C151—21no—
305C23×C151—22no—
306C23×C151—21no—
307C23×C151—21no—
308C23×C151—21no—
309C23×C151—21no—
310C23×C151—22no—
311C23×C151—21no—
312C23×C151—22no—
313C23×C151—21no—
314C23×C151—21no—
315C23×C151—21no—
316C23×C151—21no—
317C23×C151—21no—
318C23×C151—21no—
319C23×C151—48no—
320C23×C151—48no—
321C23×C151—41no—
322C23×C151—41no—
323C23×C151—41no—
324C23×C151—41no—
325C23×C151—41no—
326C23×C151—41no—
327C23×C151—41no—
328C23×C151—41no—
329C23×C151—41no—
330C23×C151—41no—
331C23×C151—41no—
332C23×C151—41no—
333C23×C151—41no—
334C23×C151—41no—
335C23×C151—41no—
336C23×C151—41no—
337C23×C151—84no—
338C23×C151—84no—
339C23×C151—84no—
340C23×C151—84no—
341C23×C151—84no—
342C23×C151AGL(1,ℤ/8)12yes—
343C23×C151C22×D411yescharacteristic
344Q8×C151—22no—
345Q8×C151—22no—
346Q8×C151—41no—
347Q8×C151—41no—
348D4×C151—22no—
349D4×C151—22no—
350D4×C151—22no—
351D4×C151—22no—
352D4×C151—22no—
353D4×C151—22no—
354D4×C151—22no—
355D4×C151—44no—
356D4×C151—48no—
357D4×C151—48no—
358D4×C151—41no—
359D4×C151—41no—
360D4×C151—41no—
361D4×C151—41no—
362D4×C151—84no—
363D4×C151—84no—
364D4×C151—84no—
365D4×C151#12114yescomplemented
366C2×C4×C151—21no—
367C2×C4×C151—21no—
368C2×C4×C151—21no—
369C2×C4×C151—21no—
370C2×C4×C151—22no—
371C2×C4×C151—22no—
372C2×C4×C151—21no—
373C2×C4×C151—21no—
374C2×C4×C151—21no—
375C2×C4×C151—21no—
376C2×C4×C151—21no—
377C2×C4×C151—21no—
378C2×C4×C151—48no—
379C2×C4×C151—41no—
380C2×C4×C151—41no—
381C2×C4×C151—41no—
382C2×C4×C151—41no—
383C2×C4×C151—41no—
384C2×C4×C151—41no—
385C2×C4×C151—41no—
386C2×C4×C151—41no—
387C2×C4×C151—41no—
388C2×C4×C151—41no—
389C2×C4×C151—41no—
390C2×C4×C151—41no—
391C2×C4×C151—41no—
392C2×C4×C151—41no—
393C2×C4×C151—41no—
394C2×C4×C151—41no—
395C2×C4×C151—41no—
396C2×C4×C151—41no—
397C2×C4×C151—41no—
398C2×C4×C151—41no—
399C2×C4×C151—41no—
400C2×C4×C151—84no—
401C2×C4×C151—84no—
402C2×C4×C151#12012yes—
403C2×C4×C151#12012yes—
404C2×C4×C151C22×D411yescharacteristic
405C2×C4×C151C22×D411yescharacteristic
406C2×C4×C151C22×D411yescharacteristic
407C2×C4×C151C2×#4111yescharacteristic
408C2×C4×C151H(5,𝔽2)11yescharacteristic
409C2×C4×C151H(5,𝔽2)11yescharacteristic
410C8×C151—22no—
411C8×C151—41no—
412C8×C151—41no—
413C8×C151—41no—
414C22×C151—24no—
415C22×C151—22no—
416C22×C151—22no—
417C22×C151—22no—
418C22×C151—41no—
419C22×C151—42no—
420C22×C151—42no—
421C22×C151—41no—
422C22×C151—42no—
423C22×C151—42no—
424C22×C151—41no—
425C22×C151—42no—
426C22×C151—41no—
427C22×C151—42no—
428C22×C151—41no—
429C22×C151—42no—
430C22×C151—42no—
431C22×C151—41no—
432C22×C151—42no—
433C22×C151—41no—
434C22×C151—42no—
435C22×C151—41no—
436C22×C151—42no—
437C22×C151—41no—
438C22×C151—42no—
439C22×C151—41no—
440C22×C151—41no—
441C22×C151—816no—
442C22×C151—81no—
443C22×C151—81no—
444C22×C151—81no—
445C22×C151—81no—
446C22×C151—81no—
447C22×C151—81no—
448C22×C151—81no—
449C22×C151—81no—
450C22×C151C2×#12011yescharacteristic
451C22×C151D4211yescharacteristic
452C22×C151#54611yescharacteristic
453C22×C151C2×AGL(1,ℤ/8)11yescharacteristic
454C22×C151#57511yescharacteristic
455C22×C151#57611yescharacteristic
456C22×C151#57711yescharacteristic
457C4×C151—22no—
458C4×C151—22no—
459C4×C151—41no—
460C4×C151—41no—
461C4×C151—42no—
462C4×C151—42no—
463C4×C151—81no—
464C4×C151—81no—
465C4×C151—81no—
466C4×C151C2×#12111yescharacteristic
467C4×C151#53511yescharacteristic
468C4×C151D4211yescharacteristic
469C4×C151#54611yescharacteristic
470C2×C151—42no—
471C2×C151—44no—
472C2×C151—81no—
473C2×C151—82no—
474C2×C151—82no—
475C2×C151#240811yescharacteristic
476C2×C151#300611yescharacteristic
477C2×C151#301211yescharacteristic
478C2×C151#326411yescharacteristic
479C2×C151#326711yescharacteristic
480C2×C151#330611yescharacteristic
481C2×C151#331911yescharacteristic
482#24257C15111yesmaximal, characteristic, direct product factor, Sylow
483C151#2425711yescharacteristic, direct product factor, Sylow
484C2×#546C2×C15111yescharacteristic, complemented
485C2×#463C2×C15111yescharacteristic, complemented
486C2×#449C2×C15111yescharacteristic, complemented
487C2×#447C2×C15111yescharacteristic, complemented
488C2×#442C2×C15111yescharacteristic, complemented
489#2537C2×C15111yescharacteristic, complemented
490#2035C2×C15111yescharacteristic, complemented
491#2034C2×C15111yescharacteristic, complemented
492#2000C2×C15111yescharacteristic, complemented
493#1999C2×C15111yescharacteristic, complemented
494#1959C2×C15111yescharacteristic, complemented
495#1955C2×C15111yescharacteristic, complemented
496#1802C2×C15111yescharacteristic, complemented
497#1788C2×C15111yescharacteristic, complemented
498#1786C2×C15111yescharacteristic, complemented
499C22×#41C22×C15111yescharacteristic
500C23×D4C22×C15111yescharacteristic
501C22×SD16C22×C15111yescharacteristic, complemented
502C22×D8C22×C15111yescharacteristic
503C22×D8C22×C15111yescharacteristic
504#546—24no—
505#546—24no—
506C2×#124C22×C15111yescharacteristic
507C2×#123—21no—
508C2×C22⋊Q8C22×C15111yescharacteristic
509C2×#121—21no—
510C2×#121—21no—
511C2×#121C22×C15111yescharacteristic
512C2×#121C22×C15111yescharacteristic
513C2×#121C22×C15111yescharacteristic, complemented
514C2×#120—21no—
515C2×C4×D4C22×C15111yescharacteristic
516C2×C4×D4C22×C15111yescharacteristic
517C2×C4×D4C22×C15111yescharacteristic, complemented
518C22×C22⋊C4—21no—
519#463—24no—
520#449—24no—
521#447—24no—
522#442—24no—
523C2×#106C22×C15111yescharacteristic, complemented
524C2×C4⋊C8C22×C15111yescharacteristic, complemented
525C2×#103C22×C15111yescharacteristic, complemented
526C2×#103C22×C15111yescharacteristic, complemented
527C2×#103C22×C15111yescharacteristic, complemented
528C2×#102C22×C15111yescharacteristic
529C2×#102C22×C15111yescharacteristic
530C2×#102C22×C15111yescharacteristic
531C2×#102C22×C15111yescharacteristic
532C2×#102C22×C15111yescharacteristic
533C2×#102C22×C15111yescharacteristic
534C2×#102C22×C15111yescharacteristic, complemented
535C2×C22⋊C8C22×C15111yescharacteristic
536C2×C22⋊C8C22×C15111yescharacteristic
537C2×C22⋊C8C22×C15111yescharacteristic, complemented
538C2×C22⋊C8C22×C15111yescharacteristic, complemented
539C2×#97C22×C15111yescharacteristic, complemented
540#394—21no—
541#394—21no—
542#384C22×C15111yescharacteristic, complemented
543#380—21no—
544#380C22×C15111yescharacteristic
545#380C22×C15111yescharacteristic, complemented
546#340C22×C15111yescharacteristic, complemented
547#340C22×C15111yescharacteristic, complemented
548C25—21no—
549C2×#41—22no—
550C2×#41—22no—
551C2×#41—22no—
552C2×#41—22no—
553C2×#41—41no—
554C2×#41—41no—
555C22×Q8C23×C15111yescharacteristic
556C22×D4—21no—
557C22×D4—21no—
558C22×D4—22no—
559C22×D4—22no—
560C22×D4—22no—
561C22×D4—22no—
562C22×D4—21no—
563C22×D4—21no—
564C22×D4—21no—
565C22×D4—41no—
566C22×D4—41no—
567C22×D4D4×C15111yescharacteristic
568C22×D4C23×C15111yescharacteristic
569C22×D4C23×C15111yescharacteristic
570C22×D4C23×C15111yescharacteristic
571C23×C4—21no—
572C23×C4—21no—
573C23×C4—21no—
574C23×C4C23×C15111yescharacteristic
575C23×C4C23×C15111yescharacteristic
576C2×SD16—22no—
577C2×SD16—22no—
578C2×SD16—41no—
579C2×D8—22no—
580C2×D8—22no—
581C2×D8—22no—
582C2×D8—22no—
583C2×D8—41no—
584C2×D8D4×C15114yescomplemented
585C22×C8C23×C15111yescharacteristic
586C22×C8C23×C15111yescharacteristic
587C22×C8C23×C15111yescharacteristic
588C22×C8C23×C15111yescharacteristic
589#124—22no—
590#124D4×C15114yescomplemented
591#123—28no—
592C22⋊Q8—22no—
593C22⋊Q8—22no—
594#121—28no—
595#121—22no—
596#121—22no—
597#121—22no—
598#121—22no—
599#121—41no—
600#121—41no—
601#121—44no—
602#120—28no—
603C4×D4—22no—
604C4×D4—22no—
605C4×D4—22no—
606C4×D4—22no—
607C4×D4—22no—
608C4×D4D4×C15114yescomplemented
609C2×C4⋊C4—21no—
610C2×C4⋊C4—21no—
611C2×C4⋊C4—21no—
612C2×C4⋊C4D4×C15111yescharacteristic
613C2×C4⋊C4C23×C15111yescharacteristic
614C2×C4⋊C4C23×C15111yescharacteristic
615C2×C4⋊C4C23×C15111yescharacteristic
616C2×C4⋊C4C23×C15111yescharacteristic
617C2×C22⋊C4—28no—
618C2×C22⋊C4—21no—
619C2×C22⋊C4—21no—
620C2×C22⋊C4—21no—
621C2×C22⋊C4—21no—
622C2×C22⋊C4—21no—
623C2×C22⋊C4—21no—
624C2×C22⋊C4—21no—
625C2×C22⋊C4—21no—
626C2×C22⋊C4—21no—
627C2×C22⋊C4—21no—
628C2×C22⋊C4D4×C15111yescharacteristic
629C2×C22⋊C4D4×C15111yescharacteristic
630C2×C42C23×C15111yescharacteristic
631#106—22no—
632C4⋊C8—22no—
633#103—22no—
634#103—22no—
635#103—41no—
636#102—22no—
637#102—22no—
638#102—22no—
639#102—22no—
640#102—22no—
641#102—22no—
642#102—41no—
643C22⋊C8—22no—
644C22⋊C8—22no—
645C22⋊C8—41no—
646C22⋊C8—41no—
647#97—22no—
648#95—21no—
649#95—21no—
650C24—21no—
651C24—24no—
652C24—21no—
653C24—21no—
654C24—42no—
655C24—42no—
656C24—42no—
657C24—42no—
658C24—81no—
659C24—81no—
660C24C2×D4×C15111yescharacteristic
661C24C2×D4×C15111yescharacteristic
662#41—44no—
663#41—44no—
664#41—44no—
665#41—44no—
666C2×Q8—21no—
667C2×Q8—21no—
668C2×Q8—21no—
669C2×Q8—21no—
670C2×Q8—21no—
671C2×Q8C2×D4×C15112yes—
672C2×D4—24no—
673C2×D4—24no—
674C2×D4—22no—
675C2×D4—24no—
676C2×D4—22no—
677C2×D4—21no—
678C2×D4—21no—
679C2×D4—21no—
680C2×D4—21no—
681C2×D4—21no—
682C2×D4—21no—
683C2×D4—21no—
684C2×D4—21no—
685C2×D4—21no—
686C2×D4—21no—
687C2×D4—21no—
688C2×D4—21no—
689C2×D4—21no—
690C2×D4—41no—
691C2×D4—42no—
692C2×D4—42no—
693C2×D4—44no—
694C2×D4—44no—
695C2×D4—44no—
696C2×D4—42no—
697C2×D4—42no—
698C2×D4—44no—
699C2×D4—42no—
700C2×D4—42no—
701C2×D4—42no—
702C2×D4—42no—
703C2×D4—81no—
704C2×D4—81no—
705C2×D4—81no—
706C2×D4—81no—
707C2×D4C2×D4×C15112yes—
708C2×D4C2×D4×C15112yes—
709C2×D4C2×D4×C15112yes—
710C2×D4C2×D4×C15112yes—
711C2×D4#41×C15112yes—
712C22×C4—24no—
713C22×C4—21no—
714C22×C4—21no—
715C22×C4—21no—
716C22×C4—21no—
717C22×C4—21no—
718C22×C4—21no—
719C22×C4—21no—
720C22×C4—21no—
721C22×C4—21no—
722C22×C4—21no—
723C22×C4—21no—
724C22×C4—21no—
725C22×C4—21no—
726C22×C4—21no—
727C22×C4—24no—
728C22×C4—21no—
729C22×C4—21no—
730C22×C4—21no—
731C22×C4—42no—
732C22×C4—42no—
733C22×C4—42no—
734C22×C4—42no—
735C22×C4—42no—
736C22×C4—81no—
737C22×C4—81no—
738C22×C4C2×D4×C15111yescharacteristic
739C22×C4C2×D4×C15111yescharacteristic
740C22×C4C2×D4×C15111yescharacteristic
741C22×C4C2×D4×C15111yescharacteristic
742C22×C4C24×C15111yescharacteristic
743SD16—44no—
744D8—28no—
745D8—44no—
746C2×C8—21no—
747C2×C8—21no—
748C2×C8—21no—
749C2×C8—21no—
750C2×C8—21no—
751C2×C8—21no—
752C2×C8—21no—
753C2×C8—21no—
754C2×C8—21no—
755C2×C8—21no—
756C2×C8—21no—
757C2×C8C2×D4×C15112yes—
758C4⋊C4—24no—
759C4⋊C4—22no—
760C4⋊C4—21no—
761C4⋊C4—21no—
762C4⋊C4—21no—
763C4⋊C4—21no—
764C4⋊C4—21no—
765C4⋊C4—21no—
766C4⋊C4—21no—
767C4⋊C4—42no—
768C4⋊C4—81no—
769C4⋊C4C2×D4×C15112yes—
770C22⋊C4—24no—
771C22⋊C4—24no—
772C22⋊C4—22no—
773C22⋊C4—24no—
774C22⋊C4—24no—
775C22⋊C4—24no—
776C22⋊C4—22no—
777C22⋊C4—42no—
778C22⋊C4—42no—
779C22⋊C4—42no—
780C22⋊C4—42no—
781C22⋊C4—42no—
782C42C2×D4×C15112yes—
783C42C2×D4×C15112yes—
784C23—21no—
785C23—22no—
786C23—21no—
787C23—22no—
788C23—21no—
789C23—22no—
790C23—21no—
791C23—21no—
792C23—21no—
793C23—22no—
794C23—21no—
795C23—22no—
796C23—21no—
797C23—21no—
798C23—21no—
799C23—21no—
800C23—21no—
801C23—21no—
802C23—48no—
803C23—48no—
804C23—41no—
805C23—41no—
806C23—41no—
807C23—41no—
808C23—41no—
809C23—41no—
810C23—41no—
811C23—41no—
812C23—41no—
813C23—41no—
814C23—41no—
815C23—41no—
816C23—41no—
817C23—41no—
818C23—41no—
819C23—41no—
820C23—84no—
821C23—84no—
822C23—84no—
823C23—84no—
824C23—84no—
825C23AGL(1,ℤ/8)×C15112yes—
826C23C22×D4×C15111yescharacteristic
827Q8—22no—
828Q8—22no—
829Q8—41no—
830Q8—41no—
831D4—22no—
832D4—22no—
833D4—22no—
834D4—22no—
835D4—22no—
836D4—22no—
837D4—22no—
838D4—44no—
839D4—48no—
840D4—48no—
841D4—41no—
842D4—41no—
843D4—41no—
844D4—41no—
845D4—84no—
846D4—84no—
847D4—84no—
848D4#121×C15114yescomplemented
849C2×C4—21no—
850C2×C4—21no—
851C2×C4—21no—
852C2×C4—21no—
853C2×C4—22no—
854C2×C4—21no—
855C2×C4—22no—
856C2×C4—21no—
857C2×C4—21no—
858C2×C4—21no—
859C2×C4—21no—
860C2×C4—21no—
861C2×C4—48no—
862C2×C4—41no—
863C2×C4—41no—
864C2×C4—41no—
865C2×C4—41no—
866C2×C4—41no—
867C2×C4—41no—
868C2×C4—41no—
869C2×C4—41no—
870C2×C4—41no—
871C2×C4—41no—
872C2×C4—41no—
873C2×C4—41no—
874C2×C4—41no—
875C2×C4—41no—
876C2×C4—41no—
877C2×C4—41no—
878C2×C4—41no—
879C2×C4—41no—
880C2×C4—41no—
881C2×C4—41no—
882C2×C4—41no—
883C2×C4—84no—
884C2×C4—84no—
885C2×C4#120×C15112yes—
886C2×C4#120×C15112yes—
887C2×C4C22×D4×C15111yescharacteristic
888C2×C4C22×D4×C15111yescharacteristic
889C2×C4C22×D4×C15111yescharacteristic
890C2×C4C2×#41×C15111yescharacteristic
891C2×C4H(5,𝔽2)×C15111yescharacteristic
892C2×C4H(5,𝔽2)×C15111yescharacteristic
893C8—22no—
894C8—41no—
895C8—41no—
896C8—41no—
897C22—24no—
898C22—22no—
899C22—22no—
900C22—22no—
901C22—41no—
902C22—42no—
903C22—42no—
904C22—41no—
905C22—42no—
906C22—42no—
907C22—41no—
908C22—42no—
909C22—41no—
910C22—42no—
911C22—41no—
912C22—42no—
913C22—42no—
914C22—41no—
915C22—42no—
916C22—41no—
917C22—42no—
918C22—41no—
919C22—42no—
920C22—41no—
921C22—42no—
922C22—41no—
923C22—41no—
924C22—816no—
925C22—81no—
926C22—81no—
927C22—81no—
928C22—81no—
929C22—81no—
930C22—81no—
931C22—81no—
932C22—81no—
933C22C2×#120×C15111yescharacteristic
934C22D42×C15111yescharacteristic
935C22#546×C15111yescharacteristic
936C22C2×AGL(1,ℤ/8)×C15111yescharacteristic
937C22#575×C15111yescharacteristic
938C22#576×C15111yescharacteristic
939C22#577×C15111yescharacteristic
940C4—22no—
941C4—22no—
942C4—41no—
943C4—41no—
944C4—42no—
945C4—42no—
946C4—81no—
947C4—81no—
948C4—81no—
949C4C2×#121×C15111yescharacteristic
950C4#535×C15111yescharacteristic
951C4D42×C15111yescharacteristic
952C4#546×C15111yescharacteristic
953C2—42no—
954C2—44no—
955C2—81no—
956C2—82no—
957C2—82no—
958C2#2408×C15111yescharacteristic
959C2#3006×C15111yescharacteristic
960C2#3012×C15111yescharacteristic
961C2#3264×C15111yescharacteristic
962C2#3267×C15111yescharacteristic
963C2#3306×C15111yescharacteristic
964C2#3319×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×#546×C151C2semidirect
2. C2×#463×C151C2semidirect
3. C2×#449×C151C2semidirect
4. C2×#447×C151C2semidirect
5. C2×#442×C151C2semidirect
6. #2537×C151C2semidirect
7. #2035×C151C2semidirect
8. #2034×C151C2semidirect
9. #2000×C151C2semidirect
10. #1999×C151C2semidirect
11. #1959×C151C2semidirect
12. #1955×C151C2semidirect
13. #1802×C151C2semidirect
14. #1788×C151C2semidirect
15. #1786×C151C2semidirect
18. C22×SD16×C151C22semidirect
30. C2×#121×C151C22semidirect
34. C2×C4×D4×C151C22semidirect
40. C2×#106×C151C22semidirect
41. C2×C4⋊C8×C151C22semidirect
42. C2×#103×C151C22semidirect
43. C2×#103×C151C22semidirect
44. C2×#103×C151C22semidirect
51. C2×#102×C151C22semidirect
54. C2×C22⋊C8×C151C22semidirect
55. C2×C22⋊C8×C151C22semidirect
56. C2×#97×C151C22semidirect
59. #384×C151C22semidirect
62. #380×C151C22semidirect
63. #340×C151C22semidirect
64. #340×C151C22semidirect
101. C2×D8×C151D4semidirect
107. #124×C151D4semidirect
125. C4×D4×C151D4semidirect
365. D4×C151#121semidirect
482. #24257C151direct (N × H)
483. C151#24257direct (N × H)
484. C2×#546C2×C151semidirect
485. C2×#463C2×C151semidirect
486. C2×#449C2×C151semidirect
487. C2×#447C2×C151semidirect
488. C2×#442C2×C151semidirect
489. #2537C2×C151semidirect
490. #2035C2×C151semidirect
491. #2034C2×C151semidirect
492. #2000C2×C151semidirect
493. #1999C2×C151semidirect
494. #1959C2×C151semidirect
495. #1955C2×C151semidirect
496. #1802C2×C151semidirect
497. #1788C2×C151semidirect
498. #1786C2×C151semidirect
501. C22×SD16C22×C151semidirect
513. C2×#121C22×C151semidirect
517. C2×C4×D4C22×C151semidirect
523. C2×#106C22×C151semidirect
524. C2×C4⋊C8C22×C151semidirect
525. C2×#103C22×C151semidirect
526. C2×#103C22×C151semidirect
527. C2×#103C22×C151semidirect
534. C2×#102C22×C151semidirect
537. C2×C22⋊C8C22×C151semidirect
538. C2×C22⋊C8C22×C151semidirect
539. C2×#97C22×C151semidirect
542. #384C22×C151semidirect
545. #380C22×C151semidirect
546. #340C22×C151semidirect
547. #340C22×C151semidirect
584. C2×D8D4×C151semidirect
590. #124D4×C151semidirect
608. C4×D4D4×C151semidirect
848. D4#121×C151semidirect

Maximal subgroups

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

subgroupindex
C2×#546×C1512
C2×#463×C1512
C2×#449×C1512
C2×#447×C1512
C2×#442×C1512
#2537×C1512
#2035×C1512
#2034×C1512
#2000×C1512
#1999×C1512
#1959×C1512
#1955×C1512
#1802×C1512
#1788×C1512
#1786×C1512
#24257151