Finite Group Databasebeta

← C151×#22419 #50327344

Subgroups — C151×#22419 #50327344

Order 38656.

1670 conjugacy classes of subgroups.

The subgroup lattice has 904 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#546×C151C211yesmaximal, characteristic
2C2×#435×C151C211yesmaximal, characteristic, complemented
3C2×#417×C151C211yesmaximal, characteristic, complemented
4C22×#102×C151C211yesmaximal, characteristic, complemented
5D4×C4⋊C4×C151C211yesmaximal, characteristic, complemented
6#1983×C151C211yesmaximal, characteristic, complemented
7#1959×C151C211yesmaximal, characteristic, complemented
8#1895×C151C211yesmaximal, characteristic, complemented
9#1892×C151C211yesmaximal, characteristic, complemented
10#1874×C151C211yesmaximal, characteristic, complemented
11#1872×C151C211yesmaximal, characteristic, complemented
12#1802×C151C211yesmaximal, characteristic, complemented
13#1788×C151C211yesmaximal, characteristic, complemented
14#1786×C151C211yesmaximal, characteristic, complemented
15#1762×C151C211yesmaximal, characteristic, complemented
16C22×#41×C151C2211yescharacteristic
17C23×D4×C151C2211yescharacteristic
18C22×M16×C151C2211yescharacteristic, complemented
19C23×C8×C151C2211yescharacteristic
20#546×C151—24no—
21#546×C151C418yescomplemented
22C2×#124×C151C2211yescharacteristic
23C2×#123×C151—21no—
24C2×C22⋊Q8×C151C2211yescharacteristic
25C2×#121×C151—21no—
26C2×#121×C151C2211yescharacteristic
27C2×#120×C151—21no—
28C2×C4×D4×C151—21no—
29C2×C4×D4×C151C2211yescharacteristic
30C2×C4×D4×C151C2211yescharacteristic
31C22×C4⋊C4×C151C2211yescharacteristic
32C22×C4⋊C4×C151C2211yescharacteristic, complemented
33C22×C22⋊C4×C151—21no—
34#435×C151—24no—
35C2×C4⋊C8×C151C2211yescharacteristic, complemented
36#417×C151—24no—
37C2×#103×C151C2211yescharacteristic, complemented
38C2×#103×C151C2211yescharacteristic, complemented
39C2×#103×C151C2211yescharacteristic, complemented
40C2×#103×C151C2211yescharacteristic, complemented
41C2×#102×C151—24no—
42C2×#102×C151C2211yescharacteristic
43C2×#102×C151C2211yescharacteristic
44C2×#102×C151C2211yescharacteristic
45C2×#102×C151C2211yescharacteristic
46C2×#102×C151C2211yescharacteristic
47C2×#102×C151C2211yescharacteristic
48C2×#102×C151C2211yescharacteristic
49C2×#102×C151C2211yescharacteristic
50C2×C22⋊C8×C151C2211yescharacteristic
51C2×C22⋊C8×C151C2211yescharacteristic, complemented
52C2×#97×C151C2211yescharacteristic, complemented
53#389×C151—21no—
54#385×C151—21no—
55#385×C151—21no—
56#384×C151C2211yescharacteristic, complemented
57#380×C151C2211yescharacteristic
58#380×C151C2211yescharacteristic, complemented
59C4×C4⋊C4×C151C2211yescharacteristic, complemented
60#340×C151C2211yescharacteristic, complemented
61#340×C151C2211yescharacteristic, complemented
62#340×C151C2211yescharacteristic, complemented
63#340×C151C2211yescharacteristic, complemented
64C25×C151—21no—
65C2×#41×C151—22no—
66C2×#41×C151—22no—
67C2×#41×C151—22no—
68C2×#41×C151—41no—
69C2×#41×C151—41no—
70C2×#41×C151C2×C414yescomplemented
71C22×Q8×C151C2311yescharacteristic
72C22×D4×C151—21no—
73C22×D4×C151—22no—
74C22×D4×C151—21no—
75C22×D4×C151—21no—
76C22×D4×C151—22no—
77C22×D4×C151—22no—
78C22×D4×C151—41no—
79C22×D4×C151—41no—
80C22×D4×C151C2×C414yescomplemented
81C22×D4×C151D411yescharacteristic
82C22×D4×C151C2311yescharacteristic
83C22×D4×C151C2311yescharacteristic
84C23×C4×C151—21no—
85C23×C4×C151—21no—
86C23×C4×C151—21no—
87C23×C4×C151—21no—
88C23×C4×C151C2311yescharacteristic
89C23×C4×C151C2311yescharacteristic
90C2×M16×C151—22no—
91C2×M16×C151—22no—
92C2×M16×C151—41no—
93C22×C8×C151—22no—
94C22×C8×C151—22no—
95C22×C8×C151—41no—
96C22×C8×C151C2311yescharacteristic
97C22×C8×C151C2311yescharacteristic
98C22×C8×C151C2311yescharacteristic
99C22×C8×C151C2311yescharacteristic
100#124×C151—22no—
101#124×C151C2×C414yescomplemented
102#123×C151—28no—
103C22⋊Q8×C151—22no—
104C22⋊Q8×C151C2×C414yescomplemented
105#121×C151—22no—
106#121×C151—28no—
107#121×C151C2×C414yescomplemented
108#120×C151—28no—
109C4×D4×C151—22no—
110C4×D4×C151—44no—
111C4×D4×C151C2×C414yes—
112C4×D4×C151C2×C414yescomplemented
113C4×D4×C151D414yes—
114C2×C4⋊C4×C151—21no—
115C2×C4⋊C4×C151—22no—
116C2×C4⋊C4×C151—22no—
117C2×C4⋊C4×C151—21no—
118C2×C4⋊C4×C151—21no—
119C2×C4⋊C4×C151—21no—
120C2×C4⋊C4×C151—21no—
121C2×C4⋊C4×C151—41no—
122C2×C4⋊C4×C151—41no—
123C2×C4⋊C4×C151D411yescharacteristic
124C2×C4⋊C4×C151C2311yescharacteristic
125C2×C4⋊C4×C151C2311yescharacteristic
126C2×C4⋊C4×C151C2311yescharacteristic
127C2×C4⋊C4×C151C2311yescharacteristic
128C2×C4⋊C4×C151C2311yescharacteristic
129C2×C22⋊C4×C151—21no—
130C2×C22⋊C4×C151—21no—
131C2×C22⋊C4×C151—21no—
132C2×C22⋊C4×C151—21no—
133C2×C22⋊C4×C151—28no—
134C2×C22⋊C4×C151—21no—
135C2×C22⋊C4×C151—21no—
136C2×C22⋊C4×C151—21no—
137C2×C22⋊C4×C151D411yescharacteristic
138C2×C22⋊C4×C151D411yescharacteristic
139C2×C42×C151—21no—
140C2×C42×C151C2311yescharacteristic
141C4⋊C8×C151—22no—
142#103×C151—22no—
143#103×C151—22no—
144#103×C151—41no—
145#103×C151—41no—
146#102×C151—22no—
147#102×C151—22no—
148#102×C151—22no—
149#102×C151—22no—
150#102×C151—22no—
151#102×C151—41no—
152#102×C151—41no—
153#102×C151D414yescomplemented
154C22⋊C8×C151—22no—
155C22⋊C8×C151—22no—
156#97×C151—22no—
157#95×C151—21no—
158#95×C151—21no—
159#95×C151—21no—
160C24×C151—21no—
161C24×C151—21no—
162C24×C151—24no—
163C24×C151—42no—
164C24×C151—42no—
165C24×C151—42no—
166C24×C151—42no—
167C24×C151—81no—
168C24×C151—81no—
169C24×C151C2×D411yescharacteristic
170C24×C151C2×D411yescharacteristic
171#41×C151—28no—
172#41×C151—44no—
173#41×C151—44no—
174#41×C151—44no—
175C2×Q8×C151—21no—
176C2×Q8×C151—21no—
177C2×Q8×C151—21no—
178C2×Q8×C151—21no—
179C2×Q8×C151—21no—
180C2×Q8×C151C22×C412yes—
181C2×D4×C151—22no—
182C2×D4×C151—22no—
183C2×D4×C151—28no—
184C2×D4×C151—24no—
185C2×D4×C151—24no—
186C2×D4×C151—24no—
187C2×D4×C151—21no—
188C2×D4×C151—21no—
189C2×D4×C151—21no—
190C2×D4×C151—21no—
191C2×D4×C151—21no—
192C2×D4×C151—21no—
193C2×D4×C151—21no—
194C2×D4×C151—21no—
195C2×D4×C151—44no—
196C2×D4×C151—44no—
197C2×D4×C151—44no—
198C2×D4×C151—42no—
199C2×D4×C151—42no—
200C2×D4×C151—42no—
201C2×D4×C151—42no—
202C2×D4×C151—81no—
203C2×D4×C151—81no—
204C2×D4×C151C22⋊C414yes—
205C2×D4×C151C22×C412yes—
206C2×D4×C151C22×C412yes—
207C2×D4×C151C2×D412yes—
208C2×D4×C151#4112yes—
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—24no—
221C22×C4×C151—24no—
222C22×C4×C151—21no—
223C22×C4×C151—21no—
224C22×C4×C151—21no—
225C22×C4×C151—42no—
226C22×C4×C151—42no—
227C22×C4×C151—42no—
228C22×C4×C151—42no—
229C22×C4×C151—42no—
230C22×C4×C151—42no—
231C22×C4×C151—81no—
232C22×C4×C151—81no—
233C22×C4×C151—81no—
234C22×C4×C151—81no—
235C22×C4×C151C22×C412yes—
236C22×C4×C151C22×C412yes—
237C22×C4×C151C2×D411yescharacteristic
238C22×C4×C151C2×D411yescharacteristic
239C22×C4×C151C2×D411yescharacteristic
240C22×C4×C151C2×D411yescharacteristic
241C22×C4×C151C2×D412yes—
242C22×C4×C151C2×D412yes—
243C22×C4×C151C2411yescharacteristic
244M16×C151—44no—
245C2×C8×C151—21no—
246C2×C8×C151—21no—
247C2×C8×C151—21no—
248C2×C8×C151—21no—
249C2×C8×C151—21no—
250C2×C8×C151—21no—
251C2×C8×C151—21no—
252C2×C8×C151—21no—
253C2×C8×C151—21no—
254C2×C8×C151—21no—
255C2×C8×C151—21no—
256C2×C8×C151—44no—
257C2×C8×C151C2×D412yes—
258C4⋊C4×C151—24no—
259C4⋊C4×C151—21no—
260C4⋊C4×C151—21no—
261C4⋊C4×C151—21no—
262C4⋊C4×C151—21no—
263C4⋊C4×C151—21no—
264C4⋊C4×C151—21no—
265C4⋊C4×C151—21no—
266C4⋊C4×C151—21no—
267C4⋊C4×C151—42no—
268C4⋊C4×C151—42no—
269C4⋊C4×C151—42no—
270C4⋊C4×C151—81no—
271C4⋊C4×C151C22⋊C414yes—
272C4⋊C4×C151C22×C412yes—
273C4⋊C4×C151C2×D412yes—
274C22⋊C4×C151—24no—
275C22⋊C4×C151—24no—
276C22⋊C4×C151—24no—
277C22⋊C4×C151—24no—
278C22⋊C4×C151—24no—
279C22⋊C4×C151—42no—
280C22⋊C4×C151—42no—
281C22⋊C4×C151C22⋊C414yes—
282C22⋊C4×C151C22⋊C414yes—
283C42×C151—42no—
284C42×C151C22×C412yes—
285C42×C151C2×D412yes—
286C23×C151—21no—
287C23×C151—21no—
288C23×C151—21no—
289C23×C151—21no—
290C23×C151—22no—
291C23×C151—22no—
292C23×C151—21no—
293C23×C151—22no—
294C23×C151—21no—
295C23×C151—21no—
296C23×C151—21no—
297C23×C151—21no—
298C23×C151—21no—
299C23×C151—22no—
300C23×C151—48no—
301C23×C151—41no—
302C23×C151—41no—
303C23×C151—41no—
304C23×C151—41no—
305C23×C151—41no—
306C23×C151—41no—
307C23×C151—41no—
308C23×C151—41no—
309C23×C151—41no—
310C23×C151—41no—
311C23×C151—48no—
312C23×C151—84no—
313C23×C151—84no—
314C23×C151—84no—
315C23×C151—84no—
316C23×C151—84no—
317C23×C151C2×C22⋊C412yes—
318C23×C151C2×C22⋊C412yes—
319C23×C151AGL(1,ℤ/8)12yes—
320C23×C151#13712yes—
321C23×C151C22×D411yescharacteristic
322Q8×C151—22no—
323Q8×C151—22no—
324Q8×C151—41no—
325Q8×C151—41no—
326D4×C151—28no—
327D4×C151—22no—
328D4×C151—22no—
329D4×C151—22no—
330D4×C151—22no—
331D4×C151—22no—
332D4×C151—48no—
333D4×C151—48no—
334D4×C151—41no—
335D4×C151—41no—
336D4×C151—84no—
337D4×C151C4×D414yescomplemented
338C2×C4×C151—21no—
339C2×C4×C151—21no—
340C2×C4×C151—21no—
341C2×C4×C151—21no—
342C2×C4×C151—21no—
343C2×C4×C151—21no—
344C2×C4×C151—21no—
345C2×C4×C151—21no—
346C2×C4×C151—22no—
347C2×C4×C151—22no—
348C2×C4×C151—22no—
349C2×C4×C151—22no—
350C2×C4×C151—22no—
351C2×C4×C151—22no—
352C2×C4×C151—22no—
353C2×C4×C151—22no—
354C2×C4×C151—22no—
355C2×C4×C151—22no—
356C2×C4×C151—22no—
357C2×C4×C151—48no—
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—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—84no—
374C2×C4×C151—84no—
375C2×C4×C151—84no—
376C2×C4×C151C2×C22⋊C412yes—
377C2×C4×C151C2×C22⋊C412yes—
378C2×C4×C151C2×C22⋊C412yes—
379C2×C4×C151C2×C22⋊C412yes—
380C2×C4×C151C23×C411yescharacteristic
381C2×C4×C151C22×D411yescharacteristic
382C2×C4×C151C22×D411yescharacteristic
383C2×C4×C151C2×#4111yescharacteristic
384C2×C4×C151H(5,𝔽2)11yescharacteristic
385C2×C4×C151H(5,𝔽2)11yescharacteristic
386C8×C151—22no—
387C8×C151—41no—
388C8×C151—41no—
389C8×C151—41no—
390C22×C151—22no—
391C22×C151—22no—
392C22×C151—22no—
393C22×C151—22no—
394C22×C151—22no—
395C22×C151—22no—
396C22×C151—22no—
397C22×C151—24no—
398C22×C151—22no—
399C22×C151—22no—
400C22×C151—42no—
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—42no—
412C22×C151—42no—
413C22×C151—816no—
414C22×C151—81no—
415C22×C151—81no—
416C22×C151—81no—
417C22×C151—81no—
418C22×C151#41714yescomplemented
419C22×C151C22×C22⋊C411yescharacteristic
420C22×C151D4211yescharacteristic
421C22×C151#54611yescharacteristic
422C22×C151C2×AGL(1,ℤ/8)11yescharacteristic
423C22×C151C2×#13711yescharacteristic
424C22×C151#57611yescharacteristic
425C22×C151#57711yescharacteristic
426C4×C151—22no—
427C4×C151—22no—
428C4×C151—22no—
429C4×C151—22no—
430C4×C151—42no—
431C4×C151—42no—
432C4×C151—42no—
433C4×C151—81no—
434C4×C151—81no—
435C4×C151—81no—
436C4×C151C2×C4×D411yescharacteristic
437C4×C151#51811yescharacteristic
438C4×C151D4211yescharacteristic
439C4×C151#54611yescharacteristic
440C2×C151—24no—
441C2×C151—42no—
442C2×C151—44no—
443C2×C151—82no—
444C2×C151D4×C22⋊C411yescharacteristic
445C2×C151C2×#41711yescharacteristic
446C2×C151#289711yescharacteristic
447C2×C151#326411yescharacteristic
448C2×C151#326611yescharacteristic
449C2×C151#330611yescharacteristic
450C2×C151#331411yescharacteristic
451#22419C15111yesmaximal, characteristic, direct product factor, Sylow
452C151#2241911yescharacteristic, direct product factor, Sylow
453C2×#546C2×C15111yescharacteristic
454C2×#435C2×C15111yescharacteristic, complemented
455C2×#417C2×C15111yescharacteristic, complemented
456C22×#102C2×C15111yescharacteristic, complemented
457D4×C4⋊C4C2×C15111yescharacteristic, complemented
458#1983C2×C15111yescharacteristic, complemented
459#1959C2×C15111yescharacteristic, complemented
460#1895C2×C15111yescharacteristic, complemented
461#1892C2×C15111yescharacteristic, complemented
462#1874C2×C15111yescharacteristic, complemented
463#1872C2×C15111yescharacteristic, complemented
464#1802C2×C15111yescharacteristic, complemented
465#1788C2×C15111yescharacteristic, complemented
466#1786C2×C15111yescharacteristic, complemented
467#1762C2×C15111yescharacteristic, complemented
468C22×#41C22×C15111yescharacteristic
469C23×D4C22×C15111yescharacteristic
470C22×M16C22×C15111yescharacteristic, complemented
471C23×C8C22×C15111yescharacteristic
472#546—24no—
473#546C4×C15118yescomplemented
474C2×#124C22×C15111yescharacteristic
475C2×#123—21no—
476C2×C22⋊Q8C22×C15111yescharacteristic
477C2×#121—21no—
478C2×#121C22×C15111yescharacteristic
479C2×#120—21no—
480C2×C4×D4—21no—
481C2×C4×D4C22×C15111yescharacteristic
482C2×C4×D4C22×C15111yescharacteristic
483C22×C4⋊C4C22×C15111yescharacteristic
484C22×C4⋊C4C22×C15111yescharacteristic, complemented
485C22×C22⋊C4—21no—
486#435—24no—
487C2×C4⋊C8C22×C15111yescharacteristic, complemented
488#417—24no—
489C2×#103C22×C15111yescharacteristic, complemented
490C2×#103C22×C15111yescharacteristic, complemented
491C2×#103C22×C15111yescharacteristic, complemented
492C2×#103C22×C15111yescharacteristic, complemented
493C2×#102—24no—
494C2×#102C22×C15111yescharacteristic
495C2×#102C22×C15111yescharacteristic
496C2×#102C22×C15111yescharacteristic
497C2×#102C22×C15111yescharacteristic
498C2×#102C22×C15111yescharacteristic
499C2×#102C22×C15111yescharacteristic
500C2×#102C22×C15111yescharacteristic
501C2×#102C22×C15111yescharacteristic
502C2×C22⋊C8C22×C15111yescharacteristic
503C2×C22⋊C8C22×C15111yescharacteristic, complemented
504C2×#97C22×C15111yescharacteristic, complemented
505#389—21no—
506#385—21no—
507#385—21no—
508#384C22×C15111yescharacteristic, complemented
509#380C22×C15111yescharacteristic
510#380C22×C15111yescharacteristic, complemented
511C4×C4⋊C4C22×C15111yescharacteristic, complemented
512#340C22×C15111yescharacteristic, complemented
513#340C22×C15111yescharacteristic, complemented
514#340C22×C15111yescharacteristic, complemented
515#340C22×C15111yescharacteristic, complemented
516C25—21no—
517C2×#41—22no—
518C2×#41—22no—
519C2×#41—22no—
520C2×#41—41no—
521C2×#41—41no—
522C2×#41C2×C4×C15114yescomplemented
523C22×Q8C23×C15111yescharacteristic
524C22×D4—22no—
525C22×D4—22no—
526C22×D4—21no—
527C22×D4—21no—
528C22×D4—21no—
529C22×D4—22no—
530C22×D4—41no—
531C22×D4—41no—
532C22×D4C2×C4×C15114yescomplemented
533C22×D4D4×C15111yescharacteristic
534C22×D4C23×C15111yescharacteristic
535C22×D4C23×C15111yescharacteristic
536C23×C4—21no—
537C23×C4—21no—
538C23×C4—21no—
539C23×C4—21no—
540C23×C4C23×C15111yescharacteristic
541C23×C4C23×C15111yescharacteristic
542C2×M16—22no—
543C2×M16—22no—
544C2×M16—41no—
545C22×C8—22no—
546C22×C8—22no—
547C22×C8—41no—
548C22×C8C23×C15111yescharacteristic
549C22×C8C23×C15111yescharacteristic
550C22×C8C23×C15111yescharacteristic
551C22×C8C23×C15111yescharacteristic
552#124—22no—
553#124C2×C4×C15114yescomplemented
554#123—28no—
555C22⋊Q8—22no—
556C22⋊Q8C2×C4×C15114yescomplemented
557#121—22no—
558#121—28no—
559#121C2×C4×C15114yescomplemented
560#120—28no—
561C4×D4—22no—
562C4×D4—44no—
563C4×D4C2×C4×C15114yes—
564C4×D4C2×C4×C15114yescomplemented
565C4×D4D4×C15114yes—
566C2×C4⋊C4—21no—
567C2×C4⋊C4—22no—
568C2×C4⋊C4—22no—
569C2×C4⋊C4—21no—
570C2×C4⋊C4—21no—
571C2×C4⋊C4—21no—
572C2×C4⋊C4—21no—
573C2×C4⋊C4—41no—
574C2×C4⋊C4—41no—
575C2×C4⋊C4D4×C15111yescharacteristic
576C2×C4⋊C4C23×C15111yescharacteristic
577C2×C4⋊C4C23×C15111yescharacteristic
578C2×C4⋊C4C23×C15111yescharacteristic
579C2×C4⋊C4C23×C15111yescharacteristic
580C2×C4⋊C4C23×C15111yescharacteristic
581C2×C22⋊C4—21no—
582C2×C22⋊C4—21no—
583C2×C22⋊C4—21no—
584C2×C22⋊C4—21no—
585C2×C22⋊C4—21no—
586C2×C22⋊C4—28no—
587C2×C22⋊C4—21no—
588C2×C22⋊C4—21no—
589C2×C22⋊C4D4×C15111yescharacteristic
590C2×C22⋊C4D4×C15111yescharacteristic
591C2×C42—21no—
592C2×C42C23×C15111yescharacteristic
593C4⋊C8—22no—
594#103—22no—
595#103—22no—
596#103—41no—
597#103—41no—
598#102—22no—
599#102—22no—
600#102—22no—
601#102—22no—
602#102—22no—
603#102—41no—
604#102—41no—
605#102D4×C15114yescomplemented
606C22⋊C8—22no—
607C22⋊C8—22no—
608#97—22no—
609#95—21no—
610#95—21no—
611#95—21no—
612C24—21no—
613C24—21no—
614C24—24no—
615C24—42no—
616C24—42no—
617C24—42no—
618C24—42no—
619C24—81no—
620C24—81no—
621C24C2×D4×C15111yescharacteristic
622C24C2×D4×C15111yescharacteristic
623#41—28no—
624#41—44no—
625#41—44no—
626#41—44no—
627C2×Q8—21no—
628C2×Q8—21no—
629C2×Q8—21no—
630C2×Q8—21no—
631C2×Q8—21no—
632C2×Q8C22×C4×C15112yes—
633C2×D4—22no—
634C2×D4—22no—
635C2×D4—28no—
636C2×D4—24no—
637C2×D4—24no—
638C2×D4—24no—
639C2×D4—21no—
640C2×D4—21no—
641C2×D4—21no—
642C2×D4—21no—
643C2×D4—21no—
644C2×D4—21no—
645C2×D4—21no—
646C2×D4—21no—
647C2×D4—44no—
648C2×D4—44no—
649C2×D4—44no—
650C2×D4—42no—
651C2×D4—42no—
652C2×D4—42no—
653C2×D4—42no—
654C2×D4—81no—
655C2×D4—81no—
656C2×D4C22⋊C4×C15114yes—
657C2×D4C22×C4×C15112yes—
658C2×D4C22×C4×C15112yes—
659C2×D4C2×D4×C15112yes—
660C2×D4#41×C15112yes—
661C22×C4—21no—
662C22×C4—21no—
663C22×C4—21no—
664C22×C4—21no—
665C22×C4—21no—
666C22×C4—21no—
667C22×C4—21no—
668C22×C4—21no—
669C22×C4—21no—
670C22×C4—21no—
671C22×C4—21no—
672C22×C4—24no—
673C22×C4—24no—
674C22×C4—21no—
675C22×C4—21no—
676C22×C4—21no—
677C22×C4—42no—
678C22×C4—42no—
679C22×C4—42no—
680C22×C4—42no—
681C22×C4—42no—
682C22×C4—42no—
683C22×C4—81no—
684C22×C4—81no—
685C22×C4—81no—
686C22×C4—81no—
687C22×C4C22×C4×C15112yes—
688C22×C4C22×C4×C15112yes—
689C22×C4C2×D4×C15111yescharacteristic
690C22×C4C2×D4×C15111yescharacteristic
691C22×C4C2×D4×C15111yescharacteristic
692C22×C4C2×D4×C15111yescharacteristic
693C22×C4C2×D4×C15112yes—
694C22×C4C2×D4×C15112yes—
695C22×C4C24×C15111yescharacteristic
696M16—44no—
697C2×C8—21no—
698C2×C8—21no—
699C2×C8—21no—
700C2×C8—21no—
701C2×C8—21no—
702C2×C8—21no—
703C2×C8—21no—
704C2×C8—21no—
705C2×C8—21no—
706C2×C8—21no—
707C2×C8—21no—
708C2×C8—44no—
709C2×C8C2×D4×C15112yes—
710C4⋊C4—24no—
711C4⋊C4—21no—
712C4⋊C4—21no—
713C4⋊C4—21no—
714C4⋊C4—21no—
715C4⋊C4—21no—
716C4⋊C4—21no—
717C4⋊C4—21no—
718C4⋊C4—21no—
719C4⋊C4—42no—
720C4⋊C4—42no—
721C4⋊C4—42no—
722C4⋊C4—81no—
723C4⋊C4C22⋊C4×C15114yes—
724C4⋊C4C22×C4×C15112yes—
725C4⋊C4C2×D4×C15112yes—
726C22⋊C4—24no—
727C22⋊C4—24no—
728C22⋊C4—24no—
729C22⋊C4—24no—
730C22⋊C4—24no—
731C22⋊C4—42no—
732C22⋊C4—42no—
733C22⋊C4C22⋊C4×C15114yes—
734C22⋊C4C22⋊C4×C15114yes—
735C42—42no—
736C42C22×C4×C15112yes—
737C42C2×D4×C15112yes—
738C23—21no—
739C23—21no—
740C23—21no—
741C23—21no—
742C23—22no—
743C23—21no—
744C23—22no—
745C23—21no—
746C23—22no—
747C23—21no—
748C23—21no—
749C23—21no—
750C23—21no—
751C23—22no—
752C23—48no—
753C23—41no—
754C23—41no—
755C23—41no—
756C23—41no—
757C23—48no—
758C23—41no—
759C23—41no—
760C23—41no—
761C23—41no—
762C23—41no—
763C23—41no—
764C23—84no—
765C23—84no—
766C23—84no—
767C23—84no—
768C23—84no—
769C23C2×C22⋊C4×C15112yes—
770C23C2×C22⋊C4×C15112yes—
771C23AGL(1,ℤ/8)×C15112yes—
772C23#137×C15112yes—
773C23C22×D4×C15111yescharacteristic
774Q8—22no—
775Q8—22no—
776Q8—41no—
777Q8—41no—
778D4—28no—
779D4—22no—
780D4—22no—
781D4—22no—
782D4—22no—
783D4—22no—
784D4—48no—
785D4—48no—
786D4—41no—
787D4—41no—
788D4—84no—
789D4C4×D4×C15114yescomplemented
790C2×C4—21no—
791C2×C4—21no—
792C2×C4—21no—
793C2×C4—21no—
794C2×C4—21no—
795C2×C4—21no—
796C2×C4—21no—
797C2×C4—21no—
798C2×C4—22no—
799C2×C4—22no—
800C2×C4—22no—
801C2×C4—22no—
802C2×C4—22no—
803C2×C4—22no—
804C2×C4—22no—
805C2×C4—22no—
806C2×C4—22no—
807C2×C4—22no—
808C2×C4—22no—
809C2×C4—48no—
810C2×C4—41no—
811C2×C4—41no—
812C2×C4—41no—
813C2×C4—41no—
814C2×C4—41no—
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—84no—
826C2×C4—84no—
827C2×C4—84no—
828C2×C4C2×C22⋊C4×C15112yes—
829C2×C4C2×C22⋊C4×C15112yes—
830C2×C4C2×C22⋊C4×C15112yes—
831C2×C4C2×C22⋊C4×C15112yes—
832C2×C4C23×C4×C15111yescharacteristic
833C2×C4C22×D4×C15111yescharacteristic
834C2×C4C22×D4×C15111yescharacteristic
835C2×C4C2×#41×C15111yescharacteristic
836C2×C4H(5,𝔽2)×C15111yescharacteristic
837C2×C4H(5,𝔽2)×C15111yescharacteristic
838C8—22no—
839C8—41no—
840C8—41no—
841C8—41no—
842C22—22no—
843C22—22no—
844C22—22no—
845C22—22no—
846C22—22no—
847C22—22no—
848C22—22no—
849C22—24no—
850C22—22no—
851C22—22no—
852C22—42no—
853C22—42no—
854C22—41no—
855C22—42no—
856C22—41no—
857C22—42no—
858C22—41no—
859C22—42no—
860C22—41no—
861C22—42no—
862C22—42no—
863C22—42no—
864C22—42no—
865C22—816no—
866C22—81no—
867C22—81no—
868C22—81no—
869C22—81no—
870C22#417×C15114yescomplemented
871C22C22×C22⋊C4×C15111yescharacteristic
872C22D42×C15111yescharacteristic
873C22#546×C15111yescharacteristic
874C22C2×AGL(1,ℤ/8)×C15111yescharacteristic
875C22C2×#137×C15111yescharacteristic
876C22#576×C15111yescharacteristic
877C22#577×C15111yescharacteristic
878C4—22no—
879C4—22no—
880C4—22no—
881C4—22no—
882C4—42no—
883C4—42no—
884C4—42no—
885C4—81no—
886C4—81no—
887C4—81no—
888C4C2×C4×D4×C15111yescharacteristic
889C4#518×C15111yescharacteristic
890C4D42×C15111yescharacteristic
891C4#546×C15111yescharacteristic
892C2—24no—
893C2—42no—
894C2—44no—
895C2—82no—
896C2D4×C22⋊C4×C15111yescharacteristic
897C2C2×#417×C15111yescharacteristic
898C2#2897×C15111yescharacteristic
899C2#3264×C15111yescharacteristic
900C2#3266×C15111yescharacteristic
901C2#3306×C15111yescharacteristic
902C2#3314×C15111yescharacteristic
subgroupG/H
center, socleC23×C151C22×D4
commutatorC2×C4C23×C4×C151
Frattini, cosocleC22×C4C24×C151
prime radicalC2×#546×C151C2
LCSG ▷ C2×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
2. C2×#435×C151C2semidirect
3. C2×#417×C151C2semidirect
4. C22×#102×C151C2semidirect
5. D4×C4⋊C4×C151C2semidirect
6. #1983×C151C2semidirect
7. #1959×C151C2semidirect
8. #1895×C151C2semidirect
9. #1892×C151C2semidirect
10. #1874×C151C2semidirect
11. #1872×C151C2semidirect
12. #1802×C151C2semidirect
13. #1788×C151C2semidirect
14. #1786×C151C2semidirect
15. #1762×C151C2semidirect
18. C22×M16×C151C22semidirect
21. #546×C151C4semidirect
32. C22×C4⋊C4×C151C22semidirect
35. C2×C4⋊C8×C151C22semidirect
37. C2×#103×C151C22semidirect
38. C2×#103×C151C22semidirect
39. C2×#103×C151C22semidirect
40. C2×#103×C151C22semidirect
51. C2×C22⋊C8×C151C22semidirect
52. C2×#97×C151C22semidirect
56. #384×C151C22semidirect
58. #380×C151C22semidirect
59. C4×C4⋊C4×C151C22semidirect
60. #340×C151C22semidirect
61. #340×C151C22semidirect
62. #340×C151C22semidirect
63. #340×C151C22semidirect
70. C2×#41×C151C2×C4semidirect
80. C22×D4×C151C2×C4semidirect
101. #124×C151C2×C4semidirect
104. C22⋊Q8×C151C2×C4semidirect
107. #121×C151C2×C4semidirect
112. C4×D4×C151C2×C4semidirect
153. #102×C151D4semidirect
337. D4×C151C4×D4semidirect
418. C22×C151#417semidirect
451. #22419C151direct (N × H)
452. C151#22419direct (N × H)
454. C2×#435C2×C151semidirect
455. C2×#417C2×C151semidirect
456. C22×#102C2×C151semidirect
457. D4×C4⋊C4C2×C151semidirect
458. #1983C2×C151semidirect
459. #1959C2×C151semidirect
460. #1895C2×C151semidirect
461. #1892C2×C151semidirect
462. #1874C2×C151semidirect
463. #1872C2×C151semidirect
464. #1802C2×C151semidirect
465. #1788C2×C151semidirect
466. #1786C2×C151semidirect
467. #1762C2×C151semidirect
470. C22×M16C22×C151semidirect
473. #546C4×C151semidirect
484. C22×C4⋊C4C22×C151semidirect
487. C2×C4⋊C8C22×C151semidirect
489. C2×#103C22×C151semidirect
490. C2×#103C22×C151semidirect
491. C2×#103C22×C151semidirect
492. C2×#103C22×C151semidirect
503. C2×C22⋊C8C22×C151semidirect
504. C2×#97C22×C151semidirect
508. #384C22×C151semidirect
510. #380C22×C151semidirect
511. C4×C4⋊C4C22×C151semidirect
512. #340C22×C151semidirect
513. #340C22×C151semidirect
514. #340C22×C151semidirect
515. #340C22×C151semidirect
522. C2×#41C2×C4×C151semidirect
532. C22×D4C2×C4×C151semidirect
553. #124C2×C4×C151semidirect
556. C22⋊Q8C2×C4×C151semidirect
559. #121C2×C4×C151semidirect
564. C4×D4C2×C4×C151semidirect
605. #102D4×C151semidirect
789. D4C4×D4×C151semidirect
870. C22#417×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×#435×C1512
C2×#417×C1512
C22×#102×C1512
D4×C4⋊C4×C1512
#1983×C1512
#1959×C1512
#1895×C1512
#1892×C1512
#1874×C1512
#1872×C1512
#1802×C1512
#1788×C1512
#1786×C1512
#1762×C1512
#22419151