Finite Group Databasebeta

← C151×#24247 #50329172

Subgroups — C151×#24247 #50329172

Order 38656.

1564 conjugacy classes of subgroups.

The subgroup lattice has 920 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#546×C151C211yesmaximal, characteristic
2C2×#464×C151C211yesmaximal, characteristic, complemented
3C2×#452×C151C211yesmaximal, characteristic, complemented
4C2×#450×C151C211yesmaximal, characteristic, complemented
5C2×C4×SD16×C151C211yesmaximal, characteristic, complemented
6#2536×C151C211yesmaximal, characteristic, complemented
7#2035×C151C211yesmaximal, characteristic, complemented
8#2034×C151C211yesmaximal, characteristic, complemented
9#2001×C151C211yesmaximal, characteristic, complemented
10#2000×C151C211yesmaximal, characteristic, complemented
11#1958×C151C211yesmaximal, characteristic, complemented
12#1954×C151C211yesmaximal, characteristic, complemented
13#1804×C151C211yesmaximal, characteristic, complemented
14#1788×C151C211yesmaximal, characteristic, complemented
15#1786×C151C211yesmaximal, characteristic, complemented
16C22×#41×C151C2211yescharacteristic
17C23×D4×C151C2211yescharacteristic
18C22×Q16×C151C2211yescharacteristic, complemented
19C22×SD16×C151C2211yescharacteristic
20C22×SD16×C151C2211yescharacteristic
21#546×C151—24no—
22#546×C151—24no—
23C2×#124×C151C2211yescharacteristic
24C2×#123×C151—21no—
25C2×C22⋊Q8×C151C2211yescharacteristic
26C2×C22⋊Q8×C151C2211yescharacteristic
27C2×C22⋊Q8×C151C2211yescharacteristic, complemented
28C2×#121×C151—21no—
29C2×#121×C151C2211yescharacteristic
30C2×#120×C151—21no—
31C2×C4×Q8×C151C2211yescharacteristic, complemented
32C2×C4×D4×C151C2211yescharacteristic
33C2×C4×D4×C151C2211yescharacteristic
34C22×C22⋊C4×C151—21no—
35#464×C151—24no—
36#452×C151—24no—
37#450×C151—24no—
38C4×SD16×C151—24no—
39C2×#106×C151C2211yescharacteristic, complemented
40C2×C4⋊C8×C151C2211yescharacteristic, complemented
41C2×#103×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×C22⋊C8×C151C2211yescharacteristic
52C2×C22⋊C8×C151C2211yescharacteristic
53C2×C22⋊C8×C151C2211yescharacteristic, complemented
54C2×C22⋊C8×C151C2211yescharacteristic, complemented
55C2×C4×C8×C151C2211yescharacteristic, complemented
56#398×C151—21no—
57#394×C151—21no—
58#388×C151—21no—
59#388×C151—21no—
60#382×C151C2211yescharacteristic, complemented
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×Q8×C151C2311yescharacteristic
74C22×D4×C151—22no—
75C22×D4×C151—22no—
76C22×D4×C151—21no—
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×C151D411yescharacteristic
84C22×D4×C151C2311yescharacteristic
85C22×D4×C151C2311yescharacteristic
86C23×C4×C151—21no—
87C23×C4×C151—21no—
88C23×C4×C151C2311yescharacteristic
89C23×C4×C151C2311yescharacteristic
90C2×Q16×C151—22no—
91C2×Q16×C151—22no—
92C2×Q16×C151—41no—
93C2×SD16×C151—22no—
94C2×SD16×C151—22no—
95C2×SD16×C151—22no—
96C2×SD16×C151—22no—
97C2×SD16×C151—41no—
98C2×SD16×C151D414yescomplemented
99C22×C8×C151C2311yescharacteristic
100C22×C8×C151C2311yescharacteristic
101C22×C8×C151C2311yescharacteristic
102C22×C8×C151C2311yescharacteristic
103#124×C151—22no—
104#124×C151D414yes—
105#123×C151—28no—
106C22⋊Q8×C151—22no—
107C22⋊Q8×C151—22no—
108C22⋊Q8×C151—22no—
109C22⋊Q8×C151—22no—
110C22⋊Q8×C151—41no—
111C22⋊Q8×C151—41no—
112#121×C151—28no—
113#121×C151—22no—
114#121×C151—22no—
115#120×C151—28no—
116C4×Q8×C151—22no—
117C4×Q8×C151—22no—
118C4×D4×C151—22no—
119C4×D4×C151—22no—
120C4×D4×C151—22no—
121C4×D4×C151D414yes—
122C2×C4⋊C4×C151—21no—
123C2×C4⋊C4×C151—21no—
124C2×C4⋊C4×C151—21no—
125C2×C4⋊C4×C151—21no—
126C2×C4⋊C4×C151D411yescharacteristic
127C2×C4⋊C4×C151C2311yescharacteristic
128C2×C4⋊C4×C151C2311yescharacteristic
129C2×C4⋊C4×C151C2311yescharacteristic
130C2×C4⋊C4×C151C2311yescharacteristic
131C2×C22⋊C4×C151—28no—
132C2×C22⋊C4×C151—21no—
133C2×C22⋊C4×C151—21no—
134C2×C22⋊C4×C151—21no—
135C2×C22⋊C4×C151—21no—
136C2×C22⋊C4×C151—21no—
137C2×C22⋊C4×C151—21no—
138C2×C22⋊C4×C151—21no—
139C2×C22⋊C4×C151—21no—
140C2×C22⋊C4×C151—21no—
141C2×C22⋊C4×C151D411yescharacteristic
142C2×C22⋊C4×C151D411yescharacteristic
143C2×C42×C151—21no—
144C2×C42×C151C2311yescharacteristic
145#106×C151—22no—
146C4⋊C8×C151—22no—
147#103×C151—22no—
148#103×C151—22no—
149#103×C151—22no—
150#103×C151—41no—
151#102×C151—22no—
152#102×C151—22no—
153#102×C151—22no—
154#102×C151—22no—
155#102×C151—22no—
156#102×C151—41no—
157C22⋊C8×C151—22no—
158C22⋊C8×C151—22no—
159C22⋊C8×C151—41no—
160C22⋊C8×C151—41no—
161C4×C8×C151—22no—
162#95×C151—21no—
163#95×C151—21no—
164#95×C151—21no—
165#95×C151—21no—
166C24×C151—21no—
167C24×C151—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
176C24×C151C2×D411yescharacteristic
177#41×C151—44no—
178#41×C151—44no—
179#41×C151—44no—
180#41×C151—44no—
181C2×Q8×C151—21no—
182C2×Q8×C151—21no—
183C2×Q8×C151—21no—
184C2×Q8×C151—21no—
185C2×Q8×C151—21no—
186C2×Q8×C151—21no—
187C2×Q8×C151—21no—
188C2×Q8×C151—21no—
189C2×Q8×C151—21no—
190C2×Q8×C151—21no—
191C2×Q8×C151C2×D412yes—
192C2×Q8×C151C2×D412yes—
193C2×D4×C151—24no—
194C2×D4×C151—24no—
195C2×D4×C151—22no—
196C2×D4×C151—24no—
197C2×D4×C151—22no—
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—41no—
207C2×D4×C151—42no—
208C2×D4×C151—42no—
209C2×D4×C151—44no—
210C2×D4×C151—44no—
211C2×D4×C151—44no—
212C2×D4×C151—42no—
213C2×D4×C151—42no—
214C2×D4×C151—44no—
215C2×D4×C151—81no—
216C2×D4×C151—81no—
217C2×D4×C151C2×D412yes—
218C2×D4×C151C2×D412yes—
219C2×D4×C151C2×D412yes—
220C2×D4×C151#4112yes—
221C22×C4×C151—24no—
222C22×C4×C151—21no—
223C22×C4×C151—21no—
224C22×C4×C151—21no—
225C22×C4×C151—21no—
226C22×C4×C151—21no—
227C22×C4×C151—21no—
228C22×C4×C151—21no—
229C22×C4×C151—21no—
230C22×C4×C151—21no—
231C22×C4×C151—21no—
232C22×C4×C151—21no—
233C22×C4×C151—21no—
234C22×C4×C151—21no—
235C22×C4×C151—21no—
236C22×C4×C151—21no—
237C22×C4×C151—24no—
238C22×C4×C151—21no—
239C22×C4×C151—21no—
240C22×C4×C151—21no—
241C22×C4×C151—42no—
242C22×C4×C151—42no—
243C22×C4×C151—81no—
244C22×C4×C151—81no—
245C22×C4×C151C2×D411yescharacteristic
246C22×C4×C151C2×D411yescharacteristic
247C22×C4×C151C2×D411yescharacteristic
248C22×C4×C151C2×D411yescharacteristic
249C22×C4×C151C2411yescharacteristic
250Q16×C151—44no—
251SD16×C151—28no—
252SD16×C151—44no—
253C2×C8×C151—21no—
254C2×C8×C151—21no—
255C2×C8×C151—21no—
256C2×C8×C151—21no—
257C2×C8×C151—21no—
258C2×C8×C151—21no—
259C2×C8×C151—21no—
260C2×C8×C151—21no—
261C2×C8×C151—21no—
262C2×C8×C151—21no—
263C2×C8×C151—21no—
264C2×C8×C151C2×D412yes—
265C4⋊C4×C151—24no—
266C4⋊C4×C151—22no—
267C4⋊C4×C151—21no—
268C4⋊C4×C151—21no—
269C4⋊C4×C151—21no—
270C4⋊C4×C151—21no—
271C4⋊C4×C151—21no—
272C4⋊C4×C151—21no—
273C4⋊C4×C151—21no—
274C4⋊C4×C151—42no—
275C4⋊C4×C151—42no—
276C4⋊C4×C151—42no—
277C4⋊C4×C151C2×D412yes—
278C22⋊C4×C151—24no—
279C22⋊C4×C151—24no—
280C22⋊C4×C151—22no—
281C22⋊C4×C151—24no—
282C22⋊C4×C151—24no—
283C22⋊C4×C151—24no—
284C22⋊C4×C151—22no—
285C22⋊C4×C151—42no—
286C22⋊C4×C151—42no—
287C22⋊C4×C151—42no—
288C22⋊C4×C151—42no—
289C42×C151—42no—
290C42×C151C2×D412yes—
291C42×C151C2×D412yes—
292C23×C151—21no—
293C23×C151—22no—
294C23×C151—22no—
295C23×C151—21no—
296C23×C151—22no—
297C23×C151—21no—
298C23×C151—21no—
299C23×C151—21no—
300C23×C151—21no—
301C23×C151—22no—
302C23×C151—21no—
303C23×C151—21no—
304C23×C151—21no—
305C23×C151—21no—
306C23×C151—21no—
307C23×C151—21no—
308C23×C151—21no—
309C23×C151—48no—
310C23×C151—48no—
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—84no—
322C23×C151—84no—
323C23×C151—84no—
324C23×C151—84no—
325C23×C151—84no—
326C23×C151#13512yes—
327C23×C151C22×D411yescharacteristic
328Q8×C151—22no—
329Q8×C151—22no—
330Q8×C151—22no—
331Q8×C151—22no—
332Q8×C151—41no—
333Q8×C151—41no—
334Q8×C151—41no—
335Q8×C151—41no—
336D4×C151—22no—
337D4×C151—22no—
338D4×C151—22no—
339D4×C151—22no—
340D4×C151—22no—
341D4×C151—44no—
342D4×C151—48no—
343D4×C151—48no—
344D4×C151—41no—
345D4×C151—41no—
346D4×C151—84no—
347D4×C151#12114yes—
348C2×C4×C151—21no—
349C2×C4×C151—21no—
350C2×C4×C151—21no—
351C2×C4×C151—21no—
352C2×C4×C151—22no—
353C2×C4×C151—22no—
354C2×C4×C151—21no—
355C2×C4×C151—21no—
356C2×C4×C151—22no—
357C2×C4×C151—21no—
358C2×C4×C151—21no—
359C2×C4×C151—21no—
360C2×C4×C151—21no—
361C2×C4×C151—48no—
362C2×C4×C151—41no—
363C2×C4×C151—41no—
364C2×C4×C151—41no—
365C2×C4×C151—41no—
366C2×C4×C151—41no—
367C2×C4×C151—41no—
368C2×C4×C151—41no—
369C2×C4×C151—41no—
370C2×C4×C151—41no—
371C2×C4×C151—41no—
372C2×C4×C151—41no—
373C2×C4×C151—41no—
374C2×C4×C151—41no—
375C2×C4×C151—41no—
376C2×C4×C151—41no—
377C2×C4×C151—41no—
378C2×C4×C151—41no—
379C2×C4×C151—41no—
380C2×C4×C151—41no—
381C2×C4×C151—41no—
382C2×C4×C151—41no—
383C2×C4×C151—41no—
384C2×C4×C151—41no—
385C2×C4×C151—84no—
386C2×C4×C151#12012yes—
387C2×C4×C151#12012yes—
388C2×C4×C151C22×D411yescharacteristic
389C2×C4×C151C22×D411yescharacteristic
390C2×C4×C151C22×D411yescharacteristic
391C2×C4×C151C2×#4111yescharacteristic
392C2×C4×C151H(5,𝔽2)11yescharacteristic
393C2×C4×C151H(5,𝔽2)11yescharacteristic
394C8×C151—22no—
395C8×C151—41no—
396C8×C151—41no—
397C8×C151—41no—
398C22×C151—24no—
399C22×C151—22no—
400C22×C151—22no—
401C22×C151—22no—
402C22×C151—41no—
403C22×C151—42no—
404C22×C151—42no—
405C22×C151—41no—
406C22×C151—41no—
407C22×C151—42no—
408C22×C151—42no—
409C22×C151—42no—
410C22×C151—41no—
411C22×C151—42no—
412C22×C151—41no—
413C22×C151—42no—
414C22×C151—41no—
415C22×C151—42no—
416C22×C151—41no—
417C22×C151—42no—
418C22×C151—41no—
419C22×C151—41no—
420C22×C151—41no—
421C22×C151—41no—
422C22×C151—816no—
423C22×C151—81no—
424C22×C151—81no—
425C22×C151—81no—
426C22×C151—81no—
427C22×C151C2×#12011yescharacteristic
428C22×C151D4211yescharacteristic
429C22×C151#54611yescharacteristic
430C22×C151C2×#13511yescharacteristic
431C22×C151#57511yescharacteristic
432C22×C151#57711yescharacteristic
433C22×C151#57711yescharacteristic
434C4×C151—22no—
435C4×C151—22no—
436C4×C151—41no—
437C4×C151—41no—
438C4×C151—42no—
439C4×C151—42no—
440C4×C151—42no—
441C4×C151—81no—
442C4×C151—81no—
443C4×C151—81no—
444C4×C151C2×#12111yescharacteristic
445C4×C151#53511yescharacteristic
446C4×C151D4211yescharacteristic
447C4×C151#54611yescharacteristic
448C2×C151—42no—
449C2×C151—44no—
450C2×C151—81no—
451C2×C151—82no—
452C2×C151#240811yescharacteristic
453C2×C151#300211yescharacteristic
454C2×C151#300911yescharacteristic
455C2×C151#327511yescharacteristic
456C2×C151#328211yescharacteristic
457C2×C151#329611yescharacteristic
458C2×C151#332311yescharacteristic
459#24247C15111yesmaximal, characteristic, direct product factor, Sylow
460C151#2424711yescharacteristic, direct product factor, Sylow
461C2×#546C2×C15111yescharacteristic
462C2×#464C2×C15111yescharacteristic, complemented
463C2×#452C2×C15111yescharacteristic, complemented
464C2×#450C2×C15111yescharacteristic, complemented
465C2×C4×SD16C2×C15111yescharacteristic, complemented
466#2536C2×C15111yescharacteristic, complemented
467#2035C2×C15111yescharacteristic, complemented
468#2034C2×C15111yescharacteristic, complemented
469#2001C2×C15111yescharacteristic, complemented
470#2000C2×C15111yescharacteristic, complemented
471#1958C2×C15111yescharacteristic, complemented
472#1954C2×C15111yescharacteristic, complemented
473#1804C2×C15111yescharacteristic, complemented
474#1788C2×C15111yescharacteristic, complemented
475#1786C2×C15111yescharacteristic, complemented
476C22×#41C22×C15111yescharacteristic
477C23×D4C22×C15111yescharacteristic
478C22×Q16C22×C15111yescharacteristic, complemented
479C22×SD16C22×C15111yescharacteristic
480C22×SD16C22×C15111yescharacteristic
481#546—24no—
482#546—24no—
483C2×#124C22×C15111yescharacteristic
484C2×#123—21no—
485C2×C22⋊Q8C22×C15111yescharacteristic
486C2×C22⋊Q8C22×C15111yescharacteristic
487C2×C22⋊Q8C22×C15111yescharacteristic, complemented
488C2×#121—21no—
489C2×#121C22×C15111yescharacteristic
490C2×#120—21no—
491C2×C4×Q8C22×C15111yescharacteristic, complemented
492C2×C4×D4C22×C15111yescharacteristic
493C2×C4×D4C22×C15111yescharacteristic
494C22×C22⋊C4—21no—
495#464—24no—
496#452—24no—
497#450—24no—
498C4×SD16—24no—
499C2×#106C22×C15111yescharacteristic, complemented
500C2×C4⋊C8C22×C15111yescharacteristic, complemented
501C2×#103C22×C15111yescharacteristic, complemented
502C2×#103C22×C15111yescharacteristic, complemented
503C2×#103C22×C15111yescharacteristic, complemented
504C2×#103C22×C15111yescharacteristic, complemented
505C2×#102C22×C15111yescharacteristic
506C2×#102C22×C15111yescharacteristic
507C2×#102C22×C15111yescharacteristic
508C2×#102C22×C15111yescharacteristic
509C2×#102C22×C15111yescharacteristic
510C2×#102C22×C15111yescharacteristic
511C2×C22⋊C8C22×C15111yescharacteristic
512C2×C22⋊C8C22×C15111yescharacteristic
513C2×C22⋊C8C22×C15111yescharacteristic, complemented
514C2×C22⋊C8C22×C15111yescharacteristic, complemented
515C2×C4×C8C22×C15111yescharacteristic, complemented
516#398—21no—
517#394—21no—
518#388—21no—
519#388—21no—
520#382C22×C15111yescharacteristic, complemented
521#380C22×C15111yescharacteristic
522#380C22×C15111yescharacteristic, complemented
523#340C22×C15111yescharacteristic, complemented
524#340C22×C15111yescharacteristic, complemented
525C25—21no—
526C2×#41—22no—
527C2×#41—22no—
528C2×#41—22no—
529C2×#41—22no—
530C2×#41—41no—
531C2×#41—41no—
532C22×Q8C23×C15111yescharacteristic
533C22×Q8C23×C15111yescharacteristic
534C22×D4—21no—
535C22×D4—21no—
536C22×D4—22no—
537C22×D4—22no—
538C22×D4—22no—
539C22×D4—22no—
540C22×D4—21no—
541C22×D4—41no—
542C22×D4—41no—
543C22×D4D4×C15111yescharacteristic
544C22×D4C23×C15111yescharacteristic
545C22×D4C23×C15111yescharacteristic
546C23×C4—21no—
547C23×C4—21no—
548C23×C4C23×C15111yescharacteristic
549C23×C4C23×C15111yescharacteristic
550C2×Q16—22no—
551C2×Q16—22no—
552C2×Q16—41no—
553C2×SD16—22no—
554C2×SD16—22no—
555C2×SD16—22no—
556C2×SD16—22no—
557C2×SD16—41no—
558C2×SD16D4×C15114yescomplemented
559C22×C8C23×C15111yescharacteristic
560C22×C8C23×C15111yescharacteristic
561C22×C8C23×C15111yescharacteristic
562C22×C8C23×C15111yescharacteristic
563#124—22no—
564#124D4×C15114yes—
565#123—28no—
566C22⋊Q8—22no—
567C22⋊Q8—22no—
568C22⋊Q8—22no—
569C22⋊Q8—22no—
570C22⋊Q8—41no—
571C22⋊Q8—41no—
572#121—28no—
573#121—22no—
574#121—22no—
575#120—28no—
576C4×Q8—22no—
577C4×Q8—22no—
578C4×D4—22no—
579C4×D4—22no—
580C4×D4—22no—
581C4×D4D4×C15114yes—
582C2×C4⋊C4—21no—
583C2×C4⋊C4—21no—
584C2×C4⋊C4—21no—
585C2×C4⋊C4—21no—
586C2×C4⋊C4D4×C15111yescharacteristic
587C2×C4⋊C4C23×C15111yescharacteristic
588C2×C4⋊C4C23×C15111yescharacteristic
589C2×C4⋊C4C23×C15111yescharacteristic
590C2×C4⋊C4C23×C15111yescharacteristic
591C2×C22⋊C4—28no—
592C2×C22⋊C4—21no—
593C2×C22⋊C4—21no—
594C2×C22⋊C4—21no—
595C2×C22⋊C4—21no—
596C2×C22⋊C4—21no—
597C2×C22⋊C4—21no—
598C2×C22⋊C4—21no—
599C2×C22⋊C4—21no—
600C2×C22⋊C4—21no—
601C2×C22⋊C4D4×C15111yescharacteristic
602C2×C22⋊C4D4×C15111yescharacteristic
603C2×C42—21no—
604C2×C42C23×C15111yescharacteristic
605#106—22no—
606C4⋊C8—22no—
607#103—22no—
608#103—22no—
609#103—22no—
610#103—41no—
611#102—22no—
612#102—22no—
613#102—22no—
614#102—22no—
615#102—22no—
616#102—41no—
617C22⋊C8—22no—
618C22⋊C8—22no—
619C22⋊C8—41no—
620C22⋊C8—41no—
621C4×C8—22no—
622#95—21no—
623#95—21no—
624#95—21no—
625#95—21no—
626C24—21no—
627C24—24no—
628C24—21no—
629C24—42no—
630C24—42no—
631C24—42no—
632C24—42no—
633C24—81no—
634C24—81no—
635C24C2×D4×C15111yescharacteristic
636C24C2×D4×C15111yescharacteristic
637#41—44no—
638#41—44no—
639#41—44no—
640#41—44no—
641C2×Q8—21no—
642C2×Q8—21no—
643C2×Q8—21no—
644C2×Q8—21no—
645C2×Q8—21no—
646C2×Q8—21no—
647C2×Q8—21no—
648C2×Q8—21no—
649C2×Q8—21no—
650C2×Q8—21no—
651C2×Q8C2×D4×C15112yes—
652C2×Q8C2×D4×C15112yes—
653C2×D4—24no—
654C2×D4—24no—
655C2×D4—22no—
656C2×D4—24no—
657C2×D4—22no—
658C2×D4—21no—
659C2×D4—21no—
660C2×D4—21no—
661C2×D4—21no—
662C2×D4—21no—
663C2×D4—21no—
664C2×D4—21no—
665C2×D4—21no—
666C2×D4—41no—
667C2×D4—42no—
668C2×D4—42no—
669C2×D4—44no—
670C2×D4—44no—
671C2×D4—44no—
672C2×D4—42no—
673C2×D4—42no—
674C2×D4—44no—
675C2×D4—81no—
676C2×D4—81no—
677C2×D4C2×D4×C15112yes—
678C2×D4C2×D4×C15112yes—
679C2×D4C2×D4×C15112yes—
680C2×D4#41×C15112yes—
681C22×C4—24no—
682C22×C4—21no—
683C22×C4—21no—
684C22×C4—21no—
685C22×C4—21no—
686C22×C4—21no—
687C22×C4—21no—
688C22×C4—21no—
689C22×C4—21no—
690C22×C4—21no—
691C22×C4—21no—
692C22×C4—21no—
693C22×C4—21no—
694C22×C4—21no—
695C22×C4—21no—
696C22×C4—21no—
697C22×C4—24no—
698C22×C4—21no—
699C22×C4—21no—
700C22×C4—21no—
701C22×C4—42no—
702C22×C4—42no—
703C22×C4—81no—
704C22×C4—81no—
705C22×C4C2×D4×C15111yescharacteristic
706C22×C4C2×D4×C15111yescharacteristic
707C22×C4C2×D4×C15111yescharacteristic
708C22×C4C2×D4×C15111yescharacteristic
709C22×C4C24×C15111yescharacteristic
710Q16—44no—
711SD16—28no—
712SD16—44no—
713C2×C8—21no—
714C2×C8—21no—
715C2×C8—21no—
716C2×C8—21no—
717C2×C8—21no—
718C2×C8—21no—
719C2×C8—21no—
720C2×C8—21no—
721C2×C8—21no—
722C2×C8—21no—
723C2×C8—21no—
724C2×C8C2×D4×C15112yes—
725C4⋊C4—24no—
726C4⋊C4—22no—
727C4⋊C4—21no—
728C4⋊C4—21no—
729C4⋊C4—21no—
730C4⋊C4—21no—
731C4⋊C4—21no—
732C4⋊C4—21no—
733C4⋊C4—21no—
734C4⋊C4—42no—
735C4⋊C4—42no—
736C4⋊C4—42no—
737C4⋊C4C2×D4×C15112yes—
738C22⋊C4—24no—
739C22⋊C4—24no—
740C22⋊C4—22no—
741C22⋊C4—24no—
742C22⋊C4—24no—
743C22⋊C4—24no—
744C22⋊C4—22no—
745C22⋊C4—42no—
746C22⋊C4—42no—
747C22⋊C4—42no—
748C22⋊C4—42no—
749C42—42no—
750C42C2×D4×C15112yes—
751C42C2×D4×C15112yes—
752C23—21no—
753C23—22no—
754C23—21no—
755C23—22no—
756C23—21no—
757C23—22no—
758C23—21no—
759C23—21no—
760C23—21no—
761C23—22no—
762C23—21no—
763C23—21no—
764C23—21no—
765C23—21no—
766C23—21no—
767C23—21no—
768C23—21no—
769C23—48no—
770C23—48no—
771C23—41no—
772C23—41no—
773C23—41no—
774C23—41no—
775C23—41no—
776C23—41no—
777C23—41no—
778C23—41no—
779C23—41no—
780C23—41no—
781C23—84no—
782C23—84no—
783C23—84no—
784C23—84no—
785C23—84no—
786C23#135×C15112yes—
787C23C22×D4×C15111yescharacteristic
788Q8—22no—
789Q8—22no—
790Q8—22no—
791Q8—22no—
792Q8—41no—
793Q8—41no—
794Q8—41no—
795Q8—41no—
796D4—22no—
797D4—22no—
798D4—22no—
799D4—22no—
800D4—22no—
801D4—44no—
802D4—48no—
803D4—48no—
804D4—41no—
805D4—41no—
806D4—84no—
807D4#121×C15114yes—
808C2×C4—21no—
809C2×C4—21no—
810C2×C4—21no—
811C2×C4—21no—
812C2×C4—22no—
813C2×C4—21no—
814C2×C4—22no—
815C2×C4—21no—
816C2×C4—22no—
817C2×C4—21no—
818C2×C4—21no—
819C2×C4—21no—
820C2×C4—21no—
821C2×C4—48no—
822C2×C4—41no—
823C2×C4—41no—
824C2×C4—41no—
825C2×C4—41no—
826C2×C4—41no—
827C2×C4—41no—
828C2×C4—41no—
829C2×C4—41no—
830C2×C4—41no—
831C2×C4—41no—
832C2×C4—41no—
833C2×C4—41no—
834C2×C4—41no—
835C2×C4—41no—
836C2×C4—41no—
837C2×C4—41no—
838C2×C4—41no—
839C2×C4—41no—
840C2×C4—41no—
841C2×C4—41no—
842C2×C4—41no—
843C2×C4—41no—
844C2×C4—41no—
845C2×C4—84no—
846C2×C4#120×C15112yes—
847C2×C4#120×C15112yes—
848C2×C4C22×D4×C15111yescharacteristic
849C2×C4C22×D4×C15111yescharacteristic
850C2×C4C22×D4×C15111yescharacteristic
851C2×C4C2×#41×C15111yescharacteristic
852C2×C4H(5,𝔽2)×C15111yescharacteristic
853C2×C4H(5,𝔽2)×C15111yescharacteristic
854C8—22no—
855C8—41no—
856C8—41no—
857C8—41no—
858C22—24no—
859C22—22no—
860C22—22no—
861C22—22no—
862C22—41no—
863C22—42no—
864C22—42no—
865C22—41no—
866C22—41no—
867C22—42no—
868C22—42no—
869C22—42no—
870C22—41no—
871C22—42no—
872C22—41no—
873C22—42no—
874C22—41no—
875C22—42no—
876C22—41no—
877C22—42no—
878C22—41no—
879C22—41no—
880C22—41no—
881C22—41no—
882C22—816no—
883C22—81no—
884C22—81no—
885C22—81no—
886C22—81no—
887C22C2×#120×C15111yescharacteristic
888C22D42×C15111yescharacteristic
889C22#546×C15111yescharacteristic
890C22C2×#135×C15111yescharacteristic
891C22#575×C15111yescharacteristic
892C22#577×C15111yescharacteristic
893C22#577×C15111yescharacteristic
894C4—22no—
895C4—22no—
896C4—41no—
897C4—41no—
898C4—42no—
899C4—42no—
900C4—42no—
901C4—81no—
902C4—81no—
903C4—81no—
904C4C2×#121×C15111yescharacteristic
905C4#535×C15111yescharacteristic
906C4D42×C15111yescharacteristic
907C4#546×C15111yescharacteristic
908C2—42no—
909C2—44no—
910C2—81no—
911C2—82no—
912C2#2408×C15111yescharacteristic
913C2#3002×C15111yescharacteristic
914C2#3009×C15111yescharacteristic
915C2#3275×C15111yescharacteristic
916C2#3282×C15111yescharacteristic
917C2#3296×C15111yescharacteristic
918C2#3323×C15111yescharacteristic
subgroupG/H
center, socleC23×C151C22×D4
commutator, Frattini, cosocleC22×C4C24×C151
prime radicalC2×#546×C151C2
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
2. C2×#464×C151C2semidirect
3. C2×#452×C151C2semidirect
4. C2×#450×C151C2semidirect
5. C2×C4×SD16×C151C2semidirect
6. #2536×C151C2semidirect
7. #2035×C151C2semidirect
8. #2034×C151C2semidirect
9. #2001×C151C2semidirect
10. #2000×C151C2semidirect
11. #1958×C151C2semidirect
12. #1954×C151C2semidirect
13. #1804×C151C2semidirect
14. #1788×C151C2semidirect
15. #1786×C151C2semidirect
18. C22×Q16×C151C22semidirect
27. C2×C22⋊Q8×C151C22semidirect
31. C2×C4×Q8×C151C22semidirect
39. C2×#106×C151C22semidirect
40. C2×C4⋊C8×C151C22semidirect
41. C2×#103×C151C22semidirect
42. C2×#103×C151C22semidirect
43. C2×#103×C151C22semidirect
44. C2×#103×C151C22semidirect
53. C2×C22⋊C8×C151C22semidirect
54. C2×C22⋊C8×C151C22semidirect
55. C2×C4×C8×C151C22semidirect
60. #382×C151C22semidirect
62. #380×C151C22semidirect
63. #340×C151C22semidirect
64. #340×C151C22semidirect
98. C2×SD16×C151D4semidirect
459. #24247C151direct (N × H)
460. C151#24247direct (N × H)
462. C2×#464C2×C151semidirect
463. C2×#452C2×C151semidirect
464. C2×#450C2×C151semidirect
465. C2×C4×SD16C2×C151semidirect
466. #2536C2×C151semidirect
467. #2035C2×C151semidirect
468. #2034C2×C151semidirect
469. #2001C2×C151semidirect
470. #2000C2×C151semidirect
471. #1958C2×C151semidirect
472. #1954C2×C151semidirect
473. #1804C2×C151semidirect
474. #1788C2×C151semidirect
475. #1786C2×C151semidirect
478. C22×Q16C22×C151semidirect
487. C2×C22⋊Q8C22×C151semidirect
491. C2×C4×Q8C22×C151semidirect
499. C2×#106C22×C151semidirect
500. C2×C4⋊C8C22×C151semidirect
501. C2×#103C22×C151semidirect
502. C2×#103C22×C151semidirect
503. C2×#103C22×C151semidirect
504. C2×#103C22×C151semidirect
513. C2×C22⋊C8C22×C151semidirect
514. C2×C22⋊C8C22×C151semidirect
515. C2×C4×C8C22×C151semidirect
520. #382C22×C151semidirect
522. #380C22×C151semidirect
523. #340C22×C151semidirect
524. #340C22×C151semidirect
558. C2×SD16D4×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×#464×C1512
C2×#452×C1512
C2×#450×C1512
C2×C4×SD16×C1512
#2536×C1512
#2035×C1512
#2034×C1512
#2001×C1512
#2000×C1512
#1958×C1512
#1954×C1512
#1804×C1512
#1788×C1512
#1786×C1512
#24247151