Finite Group Databasebeta

← C151×#24366 #50329291

Subgroups — C151×#24366 #50329291

Order 38656.

1662 conjugacy classes of subgroups.

The subgroup lattice has 956 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×AGL(1,ℤ/8)×C151C211yesmaximal, characteristic, complemented
2C2×#463×C151C211yesmaximal, characteristic, complemented
3C2×#459×C151C211yesmaximal, characteristic, complemented
4C2×#447×C151C211yesmaximal, characteristic, complemented
5#2431×C151C211yesmaximal, characteristic, complemented
6D4×C22⋊C4×C151C211yesmaximal, characteristic, complemented
7#2055×C151C211yesmaximal, characteristic, complemented
8#2054×C151C211yesmaximal, characteristic, complemented
9#2012×C151C211yesmaximal, characteristic, complemented
10#2011×C151C211yesmaximal, characteristic, complemented
11#1895×C151C211yesmaximal, characteristic, complemented
12#1879×C151C211yesmaximal, characteristic, complemented
13#1877×C151C211yesmaximal, characteristic, complemented
14#1851×C151C211yesmaximal, characteristic, complemented
15#1788×C151C211yesmaximal, characteristic, complemented
16C22×#41×C151C2211yescharacteristic
17C23×D4×C151C2211yescharacteristic
18C2×AGL(1,ℤ/8)×C151—24no—
19C2×AGL(1,ℤ/8)×C151—24no—
20C2×AGL(1,ℤ/8)×C151—24no—
21C22×SD16×C151C2211yescharacteristic
22C22×SD16×C151C2211yescharacteristic
23C22×D8×C151C2211yescharacteristic
24C22×D8×C151C2211yescharacteristic
25C22×D8×C151C2211yescharacteristic
26C22×D8×C151C2211yescharacteristic
27C22×M16×C151C2211yescharacteristic
28C2×#127×C151C2211yescharacteristic, complemented
29C2×#124×C151C2211yescharacteristic, complemented
30C2×#121×C151C2211yescharacteristic
31C2×C4×D4×C151C2211yescharacteristic
32C2×C4×D4×C151C2211yescharacteristic
33C22×C22⋊C4×C151—21no—
34#463×C151—24no—
35#459×C151—24no—
36#447×C151—24no—
37C2×C4⋊C8×C151C2211yescharacteristic, complemented
38C2×C4⋊C8×C151C2211yescharacteristic, complemented
39C2×#103×C151C2211yescharacteristic, complemented
40C2×#103×C151C2211yescharacteristic, complemented
41C2×#102×C151C2211yescharacteristic
42C2×#102×C151C2211yescharacteristic
43C2×#102×C151C2211yescharacteristic, complemented
44C2×#102×C151C2211yescharacteristic, complemented
45C2×#102×C151C2211yescharacteristic, complemented
46C2×#102×C151C2211yescharacteristic, complemented
47C2×C22⋊C8×C151C2211yescharacteristic
48#392×C151—21no—
49#392×C151—21no—
50#391×C151C2211yescharacteristic, complemented
51#390×C151C2211yescharacteristic
52#390×C151C2211yescharacteristic
53#390×C151C2211yescharacteristic, complemented
54#386×C151—21no—
55#386×C151—21no—
56#386×C151—21no—
57#386×C151—21no—
58#380×C151C2211yescharacteristic
59#379×C151—21no—
60C4×C22⋊C4×C151C2211yescharacteristic
61#340×C151C2211yescharacteristic, complemented
62#340×C151C2211yescharacteristic, complemented
63#336×C151C2211yescharacteristic, complemented
64#336×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—21no—
74C22×D4×C151—21no—
75C22×D4×C151—21no—
76C22×D4×C151—22no—
77C22×D4×C151—21no—
78C22×D4×C151—21no—
79C22×D4×C151—22no—
80C22×D4×C151—22no—
81C22×D4×C151—41no—
82C22×D4×C151—41no—
83C22×D4×C151D414yescomplemented
84C22×D4×C151C2311yescharacteristic
85C22×D4×C151C2311yescharacteristic
86C22×D4×C151C2311yescharacteristic
87C22×D4×C151C2311yescharacteristic
88C23×C4×C151—21no—
89C23×C4×C151—21no—
90C23×C4×C151—21no—
91C23×C4×C151C2311yescharacteristic
92AGL(1,ℤ/8)×C151—232no—
93C2×SD16×C151—22no—
94C2×SD16×C151—22no—
95C2×SD16×C151—22no—
96C2×SD16×C151—22no—
97C2×SD16×C151—22no—
98C2×SD16×C151D414yescomplemented
99C2×D8×C151—22no—
100C2×D8×C151—22no—
101C2×D8×C151—22no—
102C2×D8×C151—22no—
103C2×D8×C151—22no—
104C2×D8×C151—22no—
105C2×D8×C151—22no—
106C2×D8×C151—22no—
107C2×D8×C151—22no—
108C2×D8×C151—41no—
109C2×D8×C151—41no—
110C2×D8×C151D414yescomplemented
111C2×M16×C151—22no—
112C2×M16×C151—22no—
113C2×M16×C151—22no—
114C22×C8×C151C2311yescharacteristic
115C22×C8×C151C2311yescharacteristic
116C22×C8×C151C2311yescharacteristic
117C22×C8×C151C2311yescharacteristic
118#127×C151—22no—
119#127×C151—41no—
120#124×C151—22no—
121#124×C151—41no—
122#121×C151—22no—
123#121×C151—22no—
124C4×D4×C151—22no—
125C4×D4×C151—22no—
126C4×D4×C151—41no—
127C4×D4×C151—41no—
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×C151—21no—
140C2×C22⋊C4×C151—21no—
141C2×C22⋊C4×C151—21no—
142C2×C22⋊C4×C151—21no—
143C2×C22⋊C4×C151—44no—
144C2×C22⋊C4×C151D411yescharacteristic
145C2×C22⋊C4×C151D411yescharacteristic
146C2×C42×C151C2311yescharacteristic
147C2×C42×C151C2311yescharacteristic
148C4⋊C8×C151—22no—
149C4⋊C8×C151—22no—
150#103×C151—22no—
151#103×C151—41no—
152#102×C151—22no—
153#102×C151—22no—
154#102×C151—22no—
155#102×C151—22no—
156#102×C151—22no—
157#102×C151—41no—
158C22⋊C8×C151—22no—
159#95×C151—21no—
160#95×C151—21no—
161#95×C151—21no—
162#95×C151D411yescharacteristic
163#95×C151D411yescharacteristic
164C24×C151—21no—
165C24×C151—21no—
166C24×C151—21no—
167C24×C151—24no—
168C24×C151—21no—
169C24×C151—42no—
170C24×C151—42no—
171C24×C151—42no—
172C24×C151—42no—
173C24×C151—81no—
174C24×C151—81no—
175C24×C151C2×D411yescharacteristic
176#41×C151—28no—
177#41×C151—44no—
178#41×C151—44no—
179#41×C151—44no—
180C2×Q8×C151—21no—
181C2×Q8×C151—21no—
182C2×Q8×C151—21no—
183C2×Q8×C151—21no—
184C2×Q8×C151—21no—
185C2×Q8×C151C2×D412yes—
186C2×D4×C151—28no—
187C2×D4×C151—24no—
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—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—44no—
208C2×D4×C151—44no—
209C2×D4×C151—44no—
210C2×D4×C151—42no—
211C2×D4×C151—42no—
212C2×D4×C151—42no—
213C2×D4×C151—42no—
214C2×D4×C151—42no—
215C2×D4×C151—42no—
216C2×D4×C151—42no—
217C2×D4×C151—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×C151C2×D412yes—
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—42no—
238C22×C4×C151—42no—
239C22×C4×C151—42no—
240C22×C4×C151—42no—
241C22×C4×C151—42no—
242C22×C4×C151—42no—
243C22×C4×C151—42no—
244C22×C4×C151—81no—
245C22×C4×C151—81no—
246C22×C4×C151C2×D411yescharacteristic
247C22×C4×C151C2×D411yescharacteristic
248C22×C4×C151C2×D411yescharacteristic
249C22×C4×C151C2×D411yescharacteristic
250C22×C4×C151C2×D412yes—
251C22×C4×C151C2×D411yescharacteristic
252C22×C4×C151#4112yes—
253C22×C4×C151C2411yescharacteristic
254SD16×C151—28no—
255SD16×C151—28no—
256D8×C151—28no—
257D8×C151—28no—
258D8×C151—44no—
259D8×C151—44no—
260M16×C151—28no—
261C2×C8×C151—21no—
262C2×C8×C151—21no—
263C2×C8×C151—21no—
264C2×C8×C151—21no—
265C2×C8×C151—21no—
266C2×C8×C151—21no—
267C2×C8×C151—21no—
268C2×C8×C151—21no—
269C2×C8×C151—21no—
270C2×C8×C151—21no—
271C2×C8×C151C2×D412yes—
272C2×C8×C151C2×D412yes—
273C4⋊C4×C151—21no—
274C4⋊C4×C151—21no—
275C4⋊C4×C151—21no—
276C4⋊C4×C151—21no—
277C4⋊C4×C151—21no—
278C4⋊C4×C151—21no—
279C22⋊C4×C151—22no—
280C22⋊C4×C151—41no—
281C22⋊C4×C151—42no—
282C22⋊C4×C151—42no—
283C22⋊C4×C151—42no—
284C22⋊C4×C151—42no—
285C22⋊C4×C151—42no—
286C22⋊C4×C151—42no—
287C22⋊C4×C151—42no—
288C22⋊C4×C151—42no—
289C22⋊C4×C151—81no—
290C22⋊C4×C151—81no—
291C22⋊C4×C151—81no—
292C22⋊C4×C151—81no—
293C42×C151—21no—
294C42×C151—21no—
295C42×C151—21no—
296C42×C151—21no—
297C23×C151—22no—
298C23×C151—22no—
299C23×C151—22no—
300C23×C151—21no—
301C23×C151—21no—
302C23×C151—21no—
303C23×C151—21no—
304C23×C151—21no—
305C23×C151—21no—
306C23×C151—22no—
307C23×C151—22no—
308C23×C151—48no—
309C23×C151—48no—
310C23×C151—41no—
311C23×C151—41no—
312C23×C151—41no—
313C23×C151—41no—
314C23×C151—41no—
315C23×C151—41no—
316C23×C151—41no—
317C23×C151—41no—
318C23×C151—41no—
319C23×C151—41no—
320C23×C151—41no—
321C23×C151—41no—
322C23×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—84no—
334C23×C151—84no—
335C23×C151—84no—
336C23×C151—84no—
337C23×C151—84no—
338C23×C151#12112yes—
339C23×C151C22×D411yescharacteristic
340Q8×C151—22no—
341Q8×C151—22no—
342Q8×C151—41no—
343Q8×C151—41no—
344D4×C151—22no—
345D4×C151—22no—
346D4×C151—22no—
347D4×C151—22no—
348D4×C151—22no—
349D4×C151—22no—
350D4×C151—22no—
351D4×C151—48no—
352D4×C151—48no—
353D4×C151—41no—
354D4×C151—41no—
355D4×C151—41no—
356D4×C151—41no—
357D4×C151—41no—
358D4×C151—41no—
359D4×C151—41no—
360D4×C151—41no—
361D4×C151—84no—
362D4×C151—84no—
363D4×C151—84no—
364D4×C151#12014yes—
365C2×C4×C151—21no—
366C2×C4×C151—21no—
367C2×C4×C151—21no—
368C2×C4×C151—21no—
369C2×C4×C151—22no—
370C2×C4×C151—22no—
371C2×C4×C151—22no—
372C2×C4×C151—22no—
373C2×C4×C151—22no—
374C2×C4×C151—21no—
375C2×C4×C151—21no—
376C2×C4×C151—21no—
377C2×C4×C151—21no—
378C2×C4×C151—21no—
379C2×C4×C151—21no—
380C2×C4×C151—21no—
381C2×C4×C151—21no—
382C2×C4×C151—21no—
383C2×C4×C151—48no—
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—84no—
396C2×C4×C151—84no—
397C2×C4×C151#12112yes—
398C2×C4×C151AGL(1,ℤ/8)12yescomplemented
399C2×C4×C151C22×D411yescharacteristic
400C2×C4×C151C22×D411yescharacteristic
401C2×C4×C151C22×D411yescharacteristic
402C2×C4×C151C2×#4111yescharacteristic
403C2×C4×C151H(5,𝔽2)11yescharacteristic
404C2×C4×C151H(5,𝔽2)11yescharacteristic
405C8×C151—22no—
406C8×C151—22no—
407C8×C151—41no—
408C8×C151—41no—
409C22×C151—22no—
410C22×C151—24no—
411C22×C151—22no—
412C22×C151—22no—
413C22×C151—42no—
414C22×C151—41no—
415C22×C151—41no—
416C22×C151—42no—
417C22×C151—41no—
418C22×C151—42no—
419C22×C151—42no—
420C22×C151—41no—
421C22×C151—42no—
422C22×C151—42no—
423C22×C151—42no—
424C22×C151—42no—
425C22×C151—42no—
426C22×C151—42no—
427C22×C151—42no—
428C22×C151—42no—
429C22×C151—816no—
430C22×C151—81no—
431C22×C151—81no—
432C22×C151—81no—
433C22×C151—81no—
434C22×C151—81no—
435C22×C151—81no—
436C22×C151—81no—
437C22×C151—81no—
438C22×C151—81no—
439C22×C151—81no—
440C22×C151—81no—
441C22×C151—81no—
442C22×C151—81no—
443C22×C151—81no—
444C22×C151—81no—
445C22×C151C2×#12111yescharacteristic
446C22×C151D4211yescharacteristic
447C22×C151D4211yescharacteristic
448C22×C151C2×AGL(1,ℤ/8)11yescharacteristic
449C22×C151#57511yescharacteristic
450C22×C151#57611yescharacteristic
451C22×C151#57611yescharacteristic
452C4×C151—22no—
453C4×C151—22no—
454C4×C151—42no—
455C4×C151—41no—
456C4×C151—41no—
457C4×C151—41no—
458C4×C151—81no—
459C4×C151—81no—
460C4×C151—81no—
461C4×C151C2×#12011yescharacteristic
462C4×C151#53411yescharacteristic
463C4×C151#54611yescharacteristic
464C4×C151#54611yescharacteristic
465C2×C151—42no—
466C2×C151—44no—
467C2×C151—82no—
468C2×C151—82no—
469C2×C151—161no—
470C2×C151#241011yescharacteristic
471C2×C151#303611yescharacteristic
472C2×C151#304111yescharacteristic
473C2×C151#326411yescharacteristic
474C2×C151#326811yescharacteristic
475C2×C151#327311yescharacteristic
476C2×C151#327411yescharacteristic
477#24366C15111yesmaximal, characteristic, direct product factor, Sylow
478C151#2436611yescharacteristic, direct product factor, Sylow
479C22×AGL(1,ℤ/8)C2×C15111yescharacteristic, complemented
480C2×#463C2×C15111yescharacteristic, complemented
481C2×#459C2×C15111yescharacteristic, complemented
482C2×#447C2×C15111yescharacteristic, complemented
483#2431C2×C15111yescharacteristic, complemented
484D4×C22⋊C4C2×C15111yescharacteristic, complemented
485#2055C2×C15111yescharacteristic, complemented
486#2054C2×C15111yescharacteristic, complemented
487#2012C2×C15111yescharacteristic, complemented
488#2011C2×C15111yescharacteristic, complemented
489#1895C2×C15111yescharacteristic, complemented
490#1879C2×C15111yescharacteristic, complemented
491#1877C2×C15111yescharacteristic, complemented
492#1851C2×C15111yescharacteristic, complemented
493#1788C2×C15111yescharacteristic, complemented
494C22×#41C22×C15111yescharacteristic
495C23×D4C22×C15111yescharacteristic
496C2×AGL(1,ℤ/8)—24no—
497C2×AGL(1,ℤ/8)—24no—
498C2×AGL(1,ℤ/8)—24no—
499C22×SD16C22×C15111yescharacteristic
500C22×SD16C22×C15111yescharacteristic
501C22×D8C22×C15111yescharacteristic
502C22×D8C22×C15111yescharacteristic
503C22×D8C22×C15111yescharacteristic
504C22×D8C22×C15111yescharacteristic
505C22×M16C22×C15111yescharacteristic
506C2×#127C22×C15111yescharacteristic, complemented
507C2×#124C22×C15111yescharacteristic, complemented
508C2×#121C22×C15111yescharacteristic
509C2×C4×D4C22×C15111yescharacteristic
510C2×C4×D4C22×C15111yescharacteristic
511C22×C22⋊C4—21no—
512#463—24no—
513#459—24no—
514#447—24no—
515C2×C4⋊C8C22×C15111yescharacteristic, complemented
516C2×C4⋊C8C22×C15111yescharacteristic, complemented
517C2×#103C22×C15111yescharacteristic, complemented
518C2×#103C22×C15111yescharacteristic, complemented
519C2×#102C22×C15111yescharacteristic
520C2×#102C22×C15111yescharacteristic
521C2×#102C22×C15111yescharacteristic, complemented
522C2×#102C22×C15111yescharacteristic, complemented
523C2×#102C22×C15111yescharacteristic, complemented
524C2×#102C22×C15111yescharacteristic, complemented
525C2×C22⋊C8C22×C15111yescharacteristic
526#392—21no—
527#392—21no—
528#391C22×C15111yescharacteristic, complemented
529#390C22×C15111yescharacteristic
530#390C22×C15111yescharacteristic
531#390C22×C15111yescharacteristic, complemented
532#386—21no—
533#386—21no—
534#386—21no—
535#386—21no—
536#380C22×C15111yescharacteristic
537#379—21no—
538C4×C22⋊C4C22×C15111yescharacteristic
539#340C22×C15111yescharacteristic, complemented
540#340C22×C15111yescharacteristic, complemented
541#336C22×C15111yescharacteristic, complemented
542#336C22×C15111yescharacteristic, complemented
543C25—21no—
544C2×#41—22no—
545C2×#41—22no—
546C2×#41—22no—
547C2×#41—22no—
548C2×#41—41no—
549C2×#41—41no—
550C22×Q8C23×C15111yescharacteristic
551C22×D4—22no—
552C22×D4—22no—
553C22×D4—21no—
554C22×D4—21no—
555C22×D4—22no—
556C22×D4—21no—
557C22×D4—21no—
558C22×D4—21no—
559C22×D4—41no—
560C22×D4—41no—
561C22×D4D4×C15114yescomplemented
562C22×D4C23×C15111yescharacteristic
563C22×D4C23×C15111yescharacteristic
564C22×D4C23×C15111yescharacteristic
565C22×D4C23×C15111yescharacteristic
566C23×C4—21no—
567C23×C4—21no—
568C23×C4—21no—
569C23×C4C23×C15111yescharacteristic
570AGL(1,ℤ/8)—232no—
571C2×SD16—22no—
572C2×SD16—22no—
573C2×SD16—22no—
574C2×SD16—22no—
575C2×SD16—22no—
576C2×SD16D4×C15114yescomplemented
577C2×D8—22no—
578C2×D8—22no—
579C2×D8—22no—
580C2×D8—22no—
581C2×D8—22no—
582C2×D8—22no—
583C2×D8—22no—
584C2×D8—22no—
585C2×D8—22no—
586C2×D8—41no—
587C2×D8—41no—
588C2×D8D4×C15114yescomplemented
589C2×M16—22no—
590C2×M16—22no—
591C2×M16—22no—
592C22×C8C23×C15111yescharacteristic
593C22×C8C23×C15111yescharacteristic
594C22×C8C23×C15111yescharacteristic
595C22×C8C23×C15111yescharacteristic
596#127—22no—
597#127—41no—
598#124—22no—
599#124—41no—
600#121—22no—
601#121—22no—
602C4×D4—22no—
603C4×D4—22no—
604C4×D4—41no—
605C4×D4—41no—
606C2×C4⋊C4C23×C15111yescharacteristic
607C2×C4⋊C4C23×C15111yescharacteristic
608C2×C4⋊C4C23×C15111yescharacteristic
609C2×C22⋊C4—21no—
610C2×C22⋊C4—21no—
611C2×C22⋊C4—21no—
612C2×C22⋊C4—21no—
613C2×C22⋊C4—21no—
614C2×C22⋊C4—21no—
615C2×C22⋊C4—21no—
616C2×C22⋊C4—21no—
617C2×C22⋊C4—21no—
618C2×C22⋊C4—21no—
619C2×C22⋊C4—21no—
620C2×C22⋊C4—21no—
621C2×C22⋊C4—44no—
622C2×C22⋊C4D4×C15111yescharacteristic
623C2×C22⋊C4D4×C15111yescharacteristic
624C2×C42C23×C15111yescharacteristic
625C2×C42C23×C15111yescharacteristic
626C4⋊C8—22no—
627C4⋊C8—22no—
628#103—22no—
629#103—41no—
630#102—22no—
631#102—22no—
632#102—22no—
633#102—22no—
634#102—22no—
635#102—41no—
636C22⋊C8—22no—
637#95—21no—
638#95—21no—
639#95—21no—
640#95D4×C15111yescharacteristic
641#95D4×C15111yescharacteristic
642C24—21no—
643C24—21no—
644C24—21no—
645C24—24no—
646C24—21no—
647C24—42no—
648C24—42no—
649C24—42no—
650C24—42no—
651C24—81no—
652C24—81no—
653C24C2×D4×C15111yescharacteristic
654#41—28no—
655#41—44no—
656#41—44no—
657#41—44no—
658C2×Q8—21no—
659C2×Q8—21no—
660C2×Q8—21no—
661C2×Q8—21no—
662C2×Q8—21no—
663C2×Q8C2×D4×C15112yes—
664C2×D4—28no—
665C2×D4—24no—
666C2×D4—21no—
667C2×D4—21no—
668C2×D4—21no—
669C2×D4—21no—
670C2×D4—21no—
671C2×D4—21no—
672C2×D4—21no—
673C2×D4—21no—
674C2×D4—21no—
675C2×D4—21no—
676C2×D4—21no—
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—44no—
686C2×D4—44no—
687C2×D4—44no—
688C2×D4—42no—
689C2×D4—42no—
690C2×D4—42no—
691C2×D4—42no—
692C2×D4—42no—
693C2×D4—42no—
694C2×D4—42no—
695C2×D4—42no—
696C2×D4—42no—
697C2×D4—42no—
698C2×D4—81no—
699C2×D4—81no—
700C2×D4—81no—
701C2×D4—81no—
702C2×D4C2×D4×C15112yes—
703C2×D4C2×D4×C15112yes—
704C2×D4C2×D4×C15112yes—
705C2×D4C2×D4×C15112yes—
706C2×D4C2×D4×C15112yes—
707C22×C4—21no—
708C22×C4—21no—
709C22×C4—21no—
710C22×C4—21no—
711C22×C4—21no—
712C22×C4—21no—
713C22×C4—21no—
714C22×C4—21no—
715C22×C4—42no—
716C22×C4—42no—
717C22×C4—42no—
718C22×C4—42no—
719C22×C4—42no—
720C22×C4—42no—
721C22×C4—42no—
722C22×C4—81no—
723C22×C4—81no—
724C22×C4C2×D4×C15111yescharacteristic
725C22×C4C2×D4×C15111yescharacteristic
726C22×C4C2×D4×C15111yescharacteristic
727C22×C4C2×D4×C15111yescharacteristic
728C22×C4C2×D4×C15112yes—
729C22×C4C2×D4×C15111yescharacteristic
730C22×C4#41×C15112yes—
731C22×C4C24×C15111yescharacteristic
732SD16—28no—
733SD16—28no—
734D8—28no—
735D8—28no—
736D8—44no—
737D8—44no—
738M16—28no—
739C2×C8—21no—
740C2×C8—21no—
741C2×C8—21no—
742C2×C8—21no—
743C2×C8—21no—
744C2×C8—21no—
745C2×C8—21no—
746C2×C8—21no—
747C2×C8—21no—
748C2×C8—21no—
749C2×C8C2×D4×C15112yes—
750C2×C8C2×D4×C15112yes—
751C4⋊C4—21no—
752C4⋊C4—21no—
753C4⋊C4—21no—
754C4⋊C4—21no—
755C4⋊C4—21no—
756C4⋊C4—21no—
757C22⋊C4—22no—
758C22⋊C4—41no—
759C22⋊C4—42no—
760C22⋊C4—42no—
761C22⋊C4—42no—
762C22⋊C4—42no—
763C22⋊C4—42no—
764C22⋊C4—42no—
765C22⋊C4—42no—
766C22⋊C4—42no—
767C22⋊C4—81no—
768C22⋊C4—81no—
769C22⋊C4—81no—
770C22⋊C4—81no—
771C42—21no—
772C42—21no—
773C42—21no—
774C42—21no—
775C23—22no—
776C23—22no—
777C23—22no—
778C23—21no—
779C23—21no—
780C23—21no—
781C23—21no—
782C23—21no—
783C23—21no—
784C23—22no—
785C23—22no—
786C23—48no—
787C23—48no—
788C23—41no—
789C23—41no—
790C23—41no—
791C23—41no—
792C23—41no—
793C23—41no—
794C23—41no—
795C23—41no—
796C23—41no—
797C23—41no—
798C23—41no—
799C23—41no—
800C23—41no—
801C23—41no—
802C23—41no—
803C23—41no—
804C23—41no—
805C23—41no—
806C23—41no—
807C23—41no—
808C23—41no—
809C23—41no—
810C23—41no—
811C23—84no—
812C23—84no—
813C23—84no—
814C23—84no—
815C23—84no—
816C23#121×C15112yes—
817C23C22×D4×C15111yescharacteristic
818Q8—22no—
819Q8—22no—
820Q8—41no—
821Q8—41no—
822D4—22no—
823D4—22no—
824D4—22no—
825D4—22no—
826D4—22no—
827D4—22no—
828D4—22no—
829D4—48no—
830D4—48no—
831D4—41no—
832D4—41no—
833D4—41no—
834D4—41no—
835D4—41no—
836D4—41no—
837D4—41no—
838D4—41no—
839D4—84no—
840D4—84no—
841D4—84no—
842D4#120×C15114yes—
843C2×C4—21no—
844C2×C4—21no—
845C2×C4—21no—
846C2×C4—21no—
847C2×C4—22no—
848C2×C4—22no—
849C2×C4—22no—
850C2×C4—22no—
851C2×C4—21no—
852C2×C4—21no—
853C2×C4—21no—
854C2×C4—22no—
855C2×C4—21no—
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—84no—
874C2×C4—84no—
875C2×C4#121×C15112yes—
876C2×C4AGL(1,ℤ/8)×C15112yescomplemented
877C2×C4C22×D4×C15111yescharacteristic
878C2×C4C22×D4×C15111yescharacteristic
879C2×C4C22×D4×C15111yescharacteristic
880C2×C4C2×#41×C15111yescharacteristic
881C2×C4H(5,𝔽2)×C15111yescharacteristic
882C2×C4H(5,𝔽2)×C15111yescharacteristic
883C8—22no—
884C8—22no—
885C8—41no—
886C8—41no—
887C22—22no—
888C22—24no—
889C22—22no—
890C22—22no—
891C22—42no—
892C22—41no—
893C22—41no—
894C22—42no—
895C22—41no—
896C22—42no—
897C22—42no—
898C22—41no—
899C22—42no—
900C22—42no—
901C22—42no—
902C22—42no—
903C22—42no—
904C22—42no—
905C22—42no—
906C22—42no—
907C22—816no—
908C22—81no—
909C22—81no—
910C22—81no—
911C22—81no—
912C22—81no—
913C22—81no—
914C22—81no—
915C22—81no—
916C22—81no—
917C22—81no—
918C22—81no—
919C22—81no—
920C22—81no—
921C22—81no—
922C22—81no—
923C22C2×#121×C15111yescharacteristic
924C22D42×C15111yescharacteristic
925C22D42×C15111yescharacteristic
926C22C2×AGL(1,ℤ/8)×C15111yescharacteristic
927C22#575×C15111yescharacteristic
928C22#576×C15111yescharacteristic
929C22#576×C15111yescharacteristic
930C4—22no—
931C4—22no—
932C4—42no—
933C4—41no—
934C4—41no—
935C4—41no—
936C4—81no—
937C4—81no—
938C4—81no—
939C4C2×#120×C15111yescharacteristic
940C4#534×C15111yescharacteristic
941C4#546×C15111yescharacteristic
942C4#546×C15111yescharacteristic
943C2—42no—
944C2—44no—
945C2—82no—
946C2—82no—
947C2—161no—
948C2#2410×C15111yescharacteristic
949C2#3036×C15111yescharacteristic
950C2#3041×C15111yescharacteristic
951C2#3264×C15111yescharacteristic
952C2#3268×C15111yescharacteristic
953C2#3273×C15111yescharacteristic
954C2#3274×C15111yescharacteristic
subgroupG/H
center, socleC23×C151C22×D4
commutator, Frattini, cosocleC22×C4C24×C151
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C151 ◁ C4×C22⋊C4×C151 ◁ G

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
1. C22×AGL(1,ℤ/8)×C151C2semidirect
2. C2×#463×C151C2semidirect
3. C2×#459×C151C2semidirect
4. C2×#447×C151C2semidirect
5. #2431×C151C2semidirect
6. D4×C22⋊C4×C151C2semidirect
7. #2055×C151C2semidirect
8. #2054×C151C2semidirect
9. #2012×C151C2semidirect
10. #2011×C151C2semidirect
11. #1895×C151C2semidirect
12. #1879×C151C2semidirect
13. #1877×C151C2semidirect
14. #1851×C151C2semidirect
15. #1788×C151C2semidirect
28. C2×#127×C151C22semidirect
29. C2×#124×C151C22semidirect
37. C2×C4⋊C8×C151C22semidirect
38. C2×C4⋊C8×C151C22semidirect
39. C2×#103×C151C22semidirect
40. C2×#103×C151C22semidirect
43. C2×#102×C151C22semidirect
44. C2×#102×C151C22semidirect
45. C2×#102×C151C22semidirect
46. C2×#102×C151C22semidirect
50. #391×C151C22semidirect
53. #390×C151C22semidirect
61. #340×C151C22semidirect
62. #340×C151C22semidirect
63. #336×C151C22semidirect
64. #336×C151C22semidirect
83. C22×D4×C151D4semidirect
98. C2×SD16×C151D4semidirect
110. C2×D8×C151D4semidirect
398. C2×C4×C151AGL(1,ℤ/8)semidirect
477. #24366C151direct (N × H)
478. C151#24366direct (N × H)
479. C22×AGL(1,ℤ/8)C2×C151semidirect
480. C2×#463C2×C151semidirect
481. C2×#459C2×C151semidirect
482. C2×#447C2×C151semidirect
483. #2431C2×C151semidirect
484. D4×C22⋊C4C2×C151semidirect
485. #2055C2×C151semidirect
486. #2054C2×C151semidirect
487. #2012C2×C151semidirect
488. #2011C2×C151semidirect
489. #1895C2×C151semidirect
490. #1879C2×C151semidirect
491. #1877C2×C151semidirect
492. #1851C2×C151semidirect
493. #1788C2×C151semidirect
506. C2×#127C22×C151semidirect
507. C2×#124C22×C151semidirect
515. C2×C4⋊C8C22×C151semidirect
516. C2×C4⋊C8C22×C151semidirect
517. C2×#103C22×C151semidirect
518. C2×#103C22×C151semidirect
521. C2×#102C22×C151semidirect
522. C2×#102C22×C151semidirect
523. C2×#102C22×C151semidirect
524. C2×#102C22×C151semidirect
528. #391C22×C151semidirect
531. #390C22×C151semidirect
539. #340C22×C151semidirect
540. #340C22×C151semidirect
541. #336C22×C151semidirect
542. #336C22×C151semidirect
561. C22×D4D4×C151semidirect
576. C2×SD16D4×C151semidirect
588. C2×D8D4×C151semidirect
876. C2×C4AGL(1,ℤ/8)×C151semidirect

Maximal subgroups

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

subgroupindex
C22×AGL(1,ℤ/8)×C1512
C2×#463×C1512
C2×#459×C1512
C2×#447×C1512
#2431×C1512
D4×C22⋊C4×C1512
#2055×C1512
#2054×C1512
#2012×C1512
#2011×C1512
#1895×C1512
#1879×C1512
#1877×C1512
#1851×C1512
#1788×C1512
#24366151