Finite Group Databasebeta

← C151×#24140 #50329065

Subgroups — C151×#24140 #50329065

Order 38656.

1556 conjugacy classes of subgroups.

The subgroup lattice has 940 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#3505×C151C211yesmaximal, characteristic, complemented
2#2848×C151C211yesmaximal, characteristic, complemented
3#2847×C151C211yesmaximal, characteristic, complemented
4C4×#120×C151C211yesmaximal, characteristic, complemented
5#2044×C151C212yesmaximal, complemented
6#2021×C151C212yesmaximal, complemented
7#1996×C151C211yesmaximal, characteristic, complemented
8#1964×C151C211yesmaximal, characteristic, complemented
9#1889×C151C212yesmaximal, complemented
10#1867×C151C212yesmaximal, complemented
11#1799×C151C211yesmaximal, characteristic, complemented
12C24×C4×C151C2211yescharacteristic
13#553×C151—21no—
14#553×C151—22no—
15#552×C151—21no—
16#551×C151—22no—
17#548×C151—21no—
18#546×C151—21no—
19#539×C151—21no—
20#538×C151—21no—
21#534×C151C2212yes—
22#529×C151—21no—
23#525×C151—21no—
24C2×C22⋊Q8×C151—21no—
25C2×C22⋊Q8×C151C2211yescharacteristic
26C2×#121×C151—21no—
27C2×#121×C151C2211yescharacteristic
28C2×#120×C151C2211yescharacteristic
29C2×#120×C151C2212yes—
30#518×C151C2212yes—
31C2×C4×D4×C151—21no—
32C2×C4×D4×C151C2211yescharacteristic
33C2×#99×C151C2212yes—
34C2×#99×C151C2212yes—
35C2×#99×C151C2212yes—
36#386×C151—22no—
37#386×C151—21no—
38#386×C151C2212yes—
39#386×C151C2211yescharacteristic
40#385×C151—22no—
41#385×C151—21no—
42#385×C151C2212yes—
43#385×C151C2211yescharacteristic
44#380×C151—21no—
45#380×C151—21no—
46#380×C151C2211yescharacteristic
47#380×C151C2211yescharacteristic
48#379×C151C2212yes—
49#379×C151C2211yescharacteristic
50C4×C22⋊C4×C151—21no—
51C4×C22⋊C4×C151C2211yescharacteristic
52#342×C151C2212yes—
53#342×C151C2212yes—
54#342×C151C2212yes—
55C25×C151C2311yescharacteristic
56C2×#41×C151—21no—
57C22×Q8×C151D411yescharacteristic, complemented
58C22×D4×C151—21no—
59C22×D4×C151—22no—
60C22×D4×C151D411yescharacteristic, complemented
61C22×D4×C151C2311yescharacteristic
62C22×D4×C151C2312yes—
63C23×C4×C151—21no—
64C23×C4×C151—21no—
65C23×C4×C151—21no—
66C23×C4×C151—21no—
67C23×C4×C151—21no—
68C23×C4×C151—21no—
69C23×C4×C151—44no—
70C23×C4×C151D411yescharacteristic, complemented
71C23×C4×C151C2311yescharacteristic
72C23×C4×C151C2311yescharacteristic
73#126×C151—22no—
74#126×C151—22no—
75#126×C151—22no—
76#125×C151—21no—
77#125×C151—22no—
78#124×C151—21no—
79#124×C151—22no—
80#123×C151—22no—
81#123×C151—22no—
82#123×C151—22no—
83#123×C151—22no—
84#123×C151—22no—
85C22⋊Q8×C151—21no—
86C22⋊Q8×C151—22no—
87C22⋊Q8×C151—21no—
88C22⋊Q8×C151—21no—
89C22⋊Q8×C151—21no—
90C22⋊Q8×C151—21no—
91C22⋊Q8×C151—44no—
92#121×C151—21no—
93#121×C151—22no—
94#121×C151—21no—
95#121×C151—21no—
96#121×C151—21no—
97#121×C151—21no—
98#121×C151—22no—
99#121×C151—22no—
100#121×C151—44no—
101#120×C151—22no—
102#120×C151—22no—
103#120×C151—22no—
104#120×C151—22no—
105#120×C151—24no—
106#120×C151—42no—
107C4×Q8×C151—21no—
108C4×D4×C151—22no—
109C4×D4×C151—21no—
110C4×D4×C151—21no—
111C4×D4×C151—21no—
112C4×D4×C151—21no—
113C4×D4×C151—21no—
114C4×D4×C151—22no—
115C4×D4×C151—22no—
116C4×D4×C151—22no—
117C4×D4×C151—22no—
118C4×D4×C151—44no—
119#117×C151—21no—
120#117×C151—22no—
121#117×C151—22no—
122C2×C4⋊C4×C151—21no—
123C2×C4⋊C4×C151—21no—
124C2×C4⋊C4×C151—21no—
125C2×C4⋊C4×C151—22no—
126C2×C4⋊C4×C151D411yescharacteristic, complemented
127C2×C4⋊C4×C151D411yescharacteristic, complemented
128C2×C4⋊C4×C151D411yescharacteristic, complemented
129C2×C4⋊C4×C151D412yescomplemented
130C2×C22⋊C4×C151—21no—
131C2×C22⋊C4×C151—21no—
132C2×C22⋊C4×C151—22no—
133C2×C22⋊C4×C151—21no—
134C2×C22⋊C4×C151—22no—
135C2×C22⋊C4×C151—22no—
136C2×C22⋊C4×C151—22no—
137C2×C22⋊C4×C151—21no—
138C2×C22⋊C4×C151—22no—
139C2×C22⋊C4×C151D411yescharacteristic, complemented
140C2×C22⋊C4×C151D412yescomplemented
141C2×C22⋊C4×C151C2312yes—
142C2×C22⋊C4×C151C2311yescharacteristic
143C2×C22⋊C4×C151C2312yes—
144C2×C22⋊C4×C151C2311yescharacteristic
145C2×C22⋊C4×C151C2312yes—
146C2×C22⋊C4×C151C2311yescharacteristic
147C2×C42×C151—21no—
148C2×C42×C151D411yescharacteristic, complemented
149#99×C151—24no—
150#99×C151—42no—
151#99×C151—42no—
152#95×C151—21no—
153#95×C151—21no—
154#95×C151—21no—
155#95×C151—22no—
156#95×C151—22no—
157#95×C151—21no—
158#95×C151—21no—
159C24×C151—21no—
160C24×C151—21no—
161C24×C151—21no—
162C24×C151—21no—
163C24×C151—21no—
164C24×C151—21no—
165C24×C151—42no—
166C24×C151—42no—
167C24×C151C2×D412yes—
168C24×C151C2×D411yescharacteristic
169C24×C151#4112yescomplemented
170C24×C151C2411yescharacteristic
171#41×C151—82no—
172C2×Q8×C151—21no—
173C2×Q8×C151—21no—
174C2×Q8×C151—42no—
175C2×D4×C151—24no—
176C2×D4×C151—21no—
177C2×D4×C151—22no—
178C2×D4×C151—21no—
179C2×D4×C151—22no—
180C2×D4×C151—22no—
181C2×D4×C151—21no—
182C2×D4×C151—21no—
183C2×D4×C151—22no—
184C2×D4×C151—21no—
185C2×D4×C151—22no—
186C2×D4×C151—21no—
187C2×D4×C151—22no—
188C2×D4×C151—22no—
189C2×D4×C151—22no—
190C2×D4×C151—21no—
191C2×D4×C151—21no—
192C2×D4×C151—42no—
193C2×D4×C151—42no—
194C2×D4×C151—42no—
195C2×D4×C151—44no—
196C2×D4×C151—44no—
197C2×D4×C151—44no—
198C22×C4×C151—24no—
199C22×C4×C151—24no—
200C22×C4×C151—24no—
201C22×C4×C151—21no—
202C22×C4×C151—21no—
203C22×C4×C151—21no—
204C22×C4×C151—21no—
205C22×C4×C151—22no—
206C22×C4×C151—22no—
207C22×C4×C151—21no—
208C22×C4×C151—21no—
209C22×C4×C151—21no—
210C22×C4×C151—22no—
211C22×C4×C151—22no—
212C22×C4×C151—42no—
213C22×C4×C151—42no—
214C22×C4×C151—42no—
215C22×C4×C151—42no—
216C22×C4×C151—42no—
217C22×C4×C151—42no—
218C22×C4×C151—42no—
219C22×C4×C151—42no—
220C22×C4×C151—42no—
221C22×C4×C151—42no—
222C22×C4×C151—42no—
223C22×C4×C151—42no—
224C22×C4×C151—41no—
225C22×C4×C151—41no—
226C22×C4×C151—41no—
227C22×C4×C151—41no—
228C22×C4×C151C2×D411yescharacteristic
229C22×C4×C151C2×D412yes—
230C22×C4×C151C2×D411yescharacteristic
231C22×C4×C151C2×D411yescharacteristic
232C22×C4×C151C2×D411yescharacteristic
233C22×C4×C151C2×D411yescharacteristic
234C22×C4×C151C2×D412yes—
235C22×C4×C151C2×D411yescharacteristic
236C22×C4×C151C2×D412yes—
237C22×C4×C151C2×D411yescharacteristic
238C22×C4×C151C2×D411yescharacteristic
239C22×C4×C151C2×D411yescharacteristic
240C4⋊C4×C151—22no—
241C4⋊C4×C151—22no—
242C4⋊C4×C151—22no—
243C4⋊C4×C151—22no—
244C4⋊C4×C151—21no—
245C4⋊C4×C151—22no—
246C4⋊C4×C151—21no—
247C4⋊C4×C151—21no—
248C4⋊C4×C151—21no—
249C4⋊C4×C151—21no—
250C4⋊C4×C151—22no—
251C4⋊C4×C151—21no—
252C4⋊C4×C151—42no—
253C4⋊C4×C151—42no—
254C4⋊C4×C151—42no—
255C4⋊C4×C151—44no—
256C22⋊C4×C151—22no—
257C22⋊C4×C151—22no—
258C22⋊C4×C151—24no—
259C22⋊C4×C151—22no—
260C22⋊C4×C151—22no—
261C22⋊C4×C151—22no—
262C22⋊C4×C151—22no—
263C22⋊C4×C151—21no—
264C22⋊C4×C151—22no—
265C22⋊C4×C151—21no—
266C22⋊C4×C151—22no—
267C22⋊C4×C151—21no—
268C22⋊C4×C151—22no—
269C22⋊C4×C151—21no—
270C22⋊C4×C151—21no—
271C22⋊C4×C151—22no—
272C22⋊C4×C151—22no—
273C22⋊C4×C151—22no—
274C22⋊C4×C151—21no—
275C22⋊C4×C151—22no—
276C22⋊C4×C151—22no—
277C22⋊C4×C151—21no—
278C22⋊C4×C151—44no—
279C22⋊C4×C151—42no—
280C22⋊C4×C151—44no—
281C22⋊C4×C151—44no—
282C22⋊C4×C151—42no—
283C22⋊C4×C151—42no—
284C22⋊C4×C151—44no—
285C22⋊C4×C151#4112yescomplemented
286C42×C151—22no—
287C42×C151—22no—
288C42×C151—21no—
289C42×C151—21no—
290C42×C151—42no—
291C23×C151—22no—
292C23×C151—22no—
293C23×C151—22no—
294C23×C151—22no—
295C23×C151—22no—
296C23×C151—22no—
297C23×C151—22no—
298C23×C151—22no—
299C23×C151—22no—
300C23×C151—21no—
301C23×C151—22no—
302C23×C151—21no—
303C23×C151—21no—
304C23×C151—22no—
305C23×C151—22no—
306C23×C151—44no—
307C23×C151—41no—
308C23×C151—41no—
309C23×C151—41no—
310C23×C151—41no—
311C23×C151—41no—
312C23×C151—44no—
313C23×C151—44no—
314C23×C151—44no—
315C23×C151—41no—
316C23×C151—41no—
317C23×C151—41no—
318C23×C151—41no—
319C23×C151—41no—
320C23×C151—42no—
321C23×C151—42no—
322C23×C151—41no—
323C23×C151—41no—
324C23×C151—41no—
325C23×C151—41no—
326C23×C151C22×D411yescharacteristic
327C23×C151C22×D411yescharacteristic
328C23×C151C22×D411yescharacteristic
329C23×C151C2×#4111yescharacteristic
330C23×C151C2×#4111yescharacteristic
331C23×C151H(5,𝔽2)11yescharacteristic
332C23×C1512−1+411yescharacteristic
333Q8×C151—42no—
334Q8×C151—81no—
335D4×C151—48no—
336D4×C151—42no—
337D4×C151—42no—
338D4×C151—41no—
339D4×C151—41no—
340D4×C151—41no—
341D4×C151—42no—
342D4×C151—42no—
343D4×C151—41no—
344D4×C151—42no—
345D4×C151—81no—
346D4×C151—82no—
347D4×C151—82no—
348D4×C151—88no—
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—21no—
357C2×C4×C151—22no—
358C2×C4×C151—21no—
359C2×C4×C151—21no—
360C2×C4×C151—22no—
361C2×C4×C151—21no—
362C2×C4×C151—22no—
363C2×C4×C151—21no—
364C2×C4×C151—22no—
365C2×C4×C151—22no—
366C2×C4×C151—41no—
367C2×C4×C151—41no—
368C2×C4×C151—41no—
369C2×C4×C151—44no—
370C2×C4×C151—44no—
371C2×C4×C151—44no—
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—42no—
379C2×C4×C151—44no—
380C2×C4×C151—42no—
381C2×C4×C151—41no—
382C2×C4×C151—41no—
383C2×C4×C151—42no—
384C2×C4×C151—41no—
385C2×C4×C151—42no—
386C2×C4×C151—42no—
387C2×C4×C151—42no—
388C2×C4×C151—41no—
389C2×C4×C151—42no—
390C2×C4×C151—41no—
391C2×C4×C151—42no—
392C2×C4×C151—42no—
393C2×C4×C151—81no—
394C2×C4×C151—82no—
395C2×C4×C151—82no—
396C2×C4×C151#12011yescharacteristic
397C2×C4×C151#12011yescharacteristic
398C2×C4×C151#12011yescharacteristic
399C2×C4×C151#12011yescharacteristic
400C22×C151—21no—
401C22×C151—21no—
402C22×C151—21no—
403C22×C151—21no—
404C22×C151—21no—
405C22×C151—21no—
406C22×C151—24no—
407C22×C151—24no—
408C22×C151—24no—
409C22×C151—41no—
410C22×C151—41no—
411C22×C151—41no—
412C22×C151—41no—
413C22×C151—42no—
414C22×C151—42no—
415C22×C151—42no—
416C22×C151—42no—
417C22×C151—42no—
418C22×C151—42no—
419C22×C151—42no—
420C22×C151—42no—
421C22×C151—42no—
422C22×C151—42no—
423C22×C151—42no—
424C22×C151—42no—
425C22×C151—42no—
426C22×C151—41no—
427C22×C151—42no—
428C22×C151—41no—
429C22×C151—42no—
430C22×C151—42no—
431C22×C151—41no—
432C22×C151—82no—
433C22×C151—81no—
434C22×C151—82no—
435C22×C151C2×#12011yescharacteristic
436C22×C151#52511yescharacteristic
437C22×C151#53711yescharacteristic
438C22×C151#54611yescharacteristic
439C22×C151#54711yescharacteristic
440C22×C151#54811yescharacteristic
441C22×C151#55011yescharacteristic
442C4×C151—21no—
443C4×C151—21no—
444C4×C151—21no—
445C4×C151—42no—
446C4×C151—41no—
447C4×C151—42no—
448C4×C151—42no—
449C4×C151—41no—
450C4×C151—42no—
451C4×C151—41no—
452C4×C151—42no—
453C4×C151—82no—
454C4×C151—81no—
455C4×C151—82no—
456C4×C151B(4,𝔽2)12yes—
457C2×C151—21no—
458C2×C151—21no—
459C2×C151—21no—
460C2×C151—21no—
461C2×C151—21no—
462C2×C151—21no—
463C2×C151—44no—
464C2×C151—81no—
465C2×C151—82no—
466C2×C151#240711yescharacteristic
467C2×C151C2×B(4,𝔽2)11yescharacteristic
468C2×C151#302511yescharacteristic
469#24140C15111yesmaximal, characteristic, direct product factor, Sylow
470C151#2414011yescharacteristic, direct product factor, Sylow
471#3505C2×C15111yescharacteristic, complemented
472#2848C2×C15111yescharacteristic, complemented
473#2847C2×C15111yescharacteristic, complemented
474C4×#120C2×C15111yescharacteristic, complemented
475#2044C2×C15112yescomplemented
476#2021C2×C15112yescomplemented
477#1996C2×C15111yescharacteristic, complemented
478#1964C2×C15111yescharacteristic, complemented
479#1889C2×C15112yescomplemented
480#1867C2×C15112yescomplemented
481#1799C2×C15111yescharacteristic, complemented
482C24×C4C22×C15111yescharacteristic
483#553—21no—
484#553—22no—
485#552—21no—
486#551—22no—
487#548—21no—
488#546—21no—
489#539—21no—
490#538—21no—
491#534C22×C15112yes—
492#529—21no—
493#525—21no—
494C2×C22⋊Q8—21no—
495C2×C22⋊Q8C22×C15111yescharacteristic
496C2×#121—21no—
497C2×#121C22×C15111yescharacteristic
498C2×#120C22×C15111yescharacteristic
499C2×#120C22×C15112yes—
500#518C22×C15112yes—
501C2×C4×D4—21no—
502C2×C4×D4C22×C15111yescharacteristic
503C2×#99C22×C15112yes—
504C2×#99C22×C15112yes—
505C2×#99C22×C15112yes—
506#386—22no—
507#386—21no—
508#386C22×C15112yes—
509#386C22×C15111yescharacteristic
510#385—22no—
511#385—21no—
512#385C22×C15112yes—
513#385C22×C15111yescharacteristic
514#380—21no—
515#380—21no—
516#380C22×C15111yescharacteristic
517#380C22×C15111yescharacteristic
518#379C22×C15112yes—
519#379C22×C15111yescharacteristic
520C4×C22⋊C4—21no—
521C4×C22⋊C4C22×C15111yescharacteristic
522#342C22×C15112yes—
523#342C22×C15112yes—
524#342C22×C15112yes—
525C25C23×C15111yescharacteristic
526C2×#41—21no—
527C22×Q8D4×C15111yescharacteristic, complemented
528C22×D4—21no—
529C22×D4—22no—
530C22×D4D4×C15111yescharacteristic, complemented
531C22×D4C23×C15111yescharacteristic
532C22×D4C23×C15112yes—
533C23×C4—21no—
534C23×C4—21no—
535C23×C4—21no—
536C23×C4—21no—
537C23×C4—21no—
538C23×C4—21no—
539C23×C4—44no—
540C23×C4D4×C15111yescharacteristic, complemented
541C23×C4C23×C15111yescharacteristic
542C23×C4C23×C15111yescharacteristic
543#126—22no—
544#126—22no—
545#126—22no—
546#125—21no—
547#125—22no—
548#124—21no—
549#124—22no—
550#123—22no—
551#123—22no—
552#123—22no—
553#123—22no—
554#123—22no—
555C22⋊Q8—21no—
556C22⋊Q8—22no—
557C22⋊Q8—21no—
558C22⋊Q8—21no—
559C22⋊Q8—21no—
560C22⋊Q8—21no—
561C22⋊Q8—44no—
562#121—21no—
563#121—22no—
564#121—21no—
565#121—21no—
566#121—21no—
567#121—21no—
568#121—22no—
569#121—22no—
570#121—44no—
571#120—22no—
572#120—22no—
573#120—22no—
574#120—22no—
575#120—24no—
576#120—42no—
577C4×Q8—21no—
578C4×D4—22no—
579C4×D4—21no—
580C4×D4—21no—
581C4×D4—21no—
582C4×D4—21no—
583C4×D4—21no—
584C4×D4—22no—
585C4×D4—22no—
586C4×D4—22no—
587C4×D4—22no—
588C4×D4—44no—
589#117—21no—
590#117—22no—
591#117—22no—
592C2×C4⋊C4—21no—
593C2×C4⋊C4—21no—
594C2×C4⋊C4—21no—
595C2×C4⋊C4—22no—
596C2×C4⋊C4D4×C15111yescharacteristic, complemented
597C2×C4⋊C4D4×C15111yescharacteristic, complemented
598C2×C4⋊C4D4×C15111yescharacteristic, complemented
599C2×C4⋊C4D4×C15112yescomplemented
600C2×C22⋊C4—22no—
601C2×C22⋊C4—21no—
602C2×C22⋊C4—21no—
603C2×C22⋊C4—22no—
604C2×C22⋊C4—21no—
605C2×C22⋊C4—22no—
606C2×C22⋊C4—22no—
607C2×C22⋊C4—21no—
608C2×C22⋊C4—22no—
609C2×C22⋊C4D4×C15111yescharacteristic, complemented
610C2×C22⋊C4D4×C15112yescomplemented
611C2×C22⋊C4C23×C15112yes—
612C2×C22⋊C4C23×C15111yescharacteristic
613C2×C22⋊C4C23×C15112yes—
614C2×C22⋊C4C23×C15111yescharacteristic
615C2×C22⋊C4C23×C15112yes—
616C2×C22⋊C4C23×C15111yescharacteristic
617C2×C42—21no—
618C2×C42D4×C15111yescharacteristic, complemented
619#99—24no—
620#99—42no—
621#99—42no—
622#95—21no—
623#95—21no—
624#95—21no—
625#95—22no—
626#95—22no—
627#95—21no—
628#95—21no—
629C24—21no—
630C24—21no—
631C24—21no—
632C24—21no—
633C24—21no—
634C24—21no—
635C24—42no—
636C24—42no—
637C24C2×D4×C15112yes—
638C24C2×D4×C15111yescharacteristic
639C24#41×C15112yescomplemented
640C24C24×C15111yescharacteristic
641#41—82no—
642C2×Q8—21no—
643C2×Q8—21no—
644C2×Q8—42no—
645C2×D4—24no—
646C2×D4—21no—
647C2×D4—22no—
648C2×D4—21no—
649C2×D4—22no—
650C2×D4—22no—
651C2×D4—21no—
652C2×D4—21no—
653C2×D4—22no—
654C2×D4—21no—
655C2×D4—22no—
656C2×D4—21no—
657C2×D4—22no—
658C2×D4—22no—
659C2×D4—22no—
660C2×D4—21no—
661C2×D4—21no—
662C2×D4—42no—
663C2×D4—42no—
664C2×D4—42no—
665C2×D4—44no—
666C2×D4—44no—
667C2×D4—44no—
668C22×C4—24no—
669C22×C4—24no—
670C22×C4—24no—
671C22×C4—21no—
672C22×C4—21no—
673C22×C4—21no—
674C22×C4—21no—
675C22×C4—22no—
676C22×C4—22no—
677C22×C4—21no—
678C22×C4—21no—
679C22×C4—21no—
680C22×C4—22no—
681C22×C4—22no—
682C22×C4—42no—
683C22×C4—42no—
684C22×C4—42no—
685C22×C4—42no—
686C22×C4—42no—
687C22×C4—42no—
688C22×C4—42no—
689C22×C4—42no—
690C22×C4—42no—
691C22×C4—42no—
692C22×C4—42no—
693C22×C4—42no—
694C22×C4—41no—
695C22×C4—41no—
696C22×C4—41no—
697C22×C4—41no—
698C22×C4C2×D4×C15111yescharacteristic
699C22×C4C2×D4×C15112yes—
700C22×C4C2×D4×C15111yescharacteristic
701C22×C4C2×D4×C15111yescharacteristic
702C22×C4C2×D4×C15111yescharacteristic
703C22×C4C2×D4×C15111yescharacteristic
704C22×C4C2×D4×C15112yes—
705C22×C4C2×D4×C15111yescharacteristic
706C22×C4C2×D4×C15112yes—
707C22×C4C2×D4×C15111yescharacteristic
708C22×C4C2×D4×C15111yescharacteristic
709C22×C4C2×D4×C15111yescharacteristic
710C4⋊C4—22no—
711C4⋊C4—22no—
712C4⋊C4—22no—
713C4⋊C4—22no—
714C4⋊C4—21no—
715C4⋊C4—22no—
716C4⋊C4—21no—
717C4⋊C4—21no—
718C4⋊C4—21no—
719C4⋊C4—21no—
720C4⋊C4—22no—
721C4⋊C4—21no—
722C4⋊C4—42no—
723C4⋊C4—42no—
724C4⋊C4—42no—
725C4⋊C4—44no—
726C22⋊C4—22no—
727C22⋊C4—22no—
728C22⋊C4—24no—
729C22⋊C4—22no—
730C22⋊C4—22no—
731C22⋊C4—22no—
732C22⋊C4—22no—
733C22⋊C4—21no—
734C22⋊C4—22no—
735C22⋊C4—21no—
736C22⋊C4—22no—
737C22⋊C4—21no—
738C22⋊C4—22no—
739C22⋊C4—21no—
740C22⋊C4—21no—
741C22⋊C4—22no—
742C22⋊C4—22no—
743C22⋊C4—22no—
744C22⋊C4—21no—
745C22⋊C4—22no—
746C22⋊C4—22no—
747C22⋊C4—21no—
748C22⋊C4—44no—
749C22⋊C4—42no—
750C22⋊C4—44no—
751C22⋊C4—42no—
752C22⋊C4—44no—
753C22⋊C4—44no—
754C22⋊C4—42no—
755C22⋊C4#41×C15112yescomplemented
756C42—22no—
757C42—22no—
758C42—21no—
759C42—21no—
760C42—42no—
761C23—22no—
762C23—22no—
763C23—22no—
764C23—22no—
765C23—22no—
766C23—22no—
767C23—22no—
768C23—22no—
769C23—22no—
770C23—21no—
771C23—22no—
772C23—21no—
773C23—21no—
774C23—22no—
775C23—22no—
776C23—41no—
777C23—44no—
778C23—41no—
779C23—41no—
780C23—41no—
781C23—41no—
782C23—41no—
783C23—41no—
784C23—41no—
785C23—44no—
786C23—44no—
787C23—44no—
788C23—41no—
789C23—41no—
790C23—42no—
791C23—42no—
792C23—41no—
793C23—41no—
794C23—41no—
795C23—41no—
796C23C22×D4×C15111yescharacteristic
797C23C22×D4×C15111yescharacteristic
798C23C22×D4×C15111yescharacteristic
799C23C2×#41×C15111yescharacteristic
800C23C2×#41×C15111yescharacteristic
801C23H(5,𝔽2)×C15111yescharacteristic
802C232−1+4×C15111yescharacteristic
803Q8—42no—
804Q8—81no—
805D4—48no—
806D4—42no—
807D4—42no—
808D4—41no—
809D4—41no—
810D4—41no—
811D4—42no—
812D4—42no—
813D4—41no—
814D4—42no—
815D4—81no—
816D4—82no—
817D4—82no—
818D4—88no—
819C2×C4—22no—
820C2×C4—22no—
821C2×C4—22no—
822C2×C4—22no—
823C2×C4—22no—
824C2×C4—22no—
825C2×C4—21no—
826C2×C4—22no—
827C2×C4—21no—
828C2×C4—21no—
829C2×C4—22no—
830C2×C4—22no—
831C2×C4—21no—
832C2×C4—22no—
833C2×C4—21no—
834C2×C4—22no—
835C2×C4—22no—
836C2×C4—41no—
837C2×C4—41no—
838C2×C4—41no—
839C2×C4—44no—
840C2×C4—44no—
841C2×C4—44no—
842C2×C4—41no—
843C2×C4—41no—
844C2×C4—41no—
845C2×C4—41no—
846C2×C4—41no—
847C2×C4—41no—
848C2×C4—44no—
849C2×C4—42no—
850C2×C4—41no—
851C2×C4—42no—
852C2×C4—41no—
853C2×C4—42no—
854C2×C4—41no—
855C2×C4—42no—
856C2×C4—42no—
857C2×C4—42no—
858C2×C4—41no—
859C2×C4—42no—
860C2×C4—41no—
861C2×C4—42no—
862C2×C4—42no—
863C2×C4—81no—
864C2×C4—82no—
865C2×C4—82no—
866C2×C4#120×C15111yescharacteristic
867C2×C4#120×C15111yescharacteristic
868C2×C4#120×C15111yescharacteristic
869C2×C4#120×C15111yescharacteristic
870C22—21no—
871C22—21no—
872C22—21no—
873C22—21no—
874C22—21no—
875C22—21no—
876C22—24no—
877C22—24no—
878C22—24no—
879C22—41no—
880C22—41no—
881C22—41no—
882C22—41no—
883C22—42no—
884C22—42no—
885C22—42no—
886C22—42no—
887C22—42no—
888C22—42no—
889C22—42no—
890C22—42no—
891C22—42no—
892C22—42no—
893C22—42no—
894C22—42no—
895C22—42no—
896C22—41no—
897C22—42no—
898C22—41no—
899C22—42no—
900C22—42no—
901C22—41no—
902C22—82no—
903C22—81no—
904C22—82no—
905C22C2×#120×C15111yescharacteristic
906C22#525×C15111yescharacteristic
907C22#537×C15111yescharacteristic
908C22#546×C15111yescharacteristic
909C22#547×C15111yescharacteristic
910C22#548×C15111yescharacteristic
911C22#550×C15111yescharacteristic
912C4—21no—
913C4—21no—
914C4—21no—
915C4—42no—
916C4—41no—
917C4—42no—
918C4—42no—
919C4—41no—
920C4—42no—
921C4—41no—
922C4—42no—
923C4—82no—
924C4—82no—
925C4—81no—
926C4B(4,𝔽2)×C15112yes—
927C2—21no—
928C2—21no—
929C2—21no—
930C2—21no—
931C2—21no—
932C2—21no—
933C2—44no—
934C2—81no—
935C2—82no—
936C2#2407×C15111yescharacteristic
937C2C2×B(4,𝔽2)×C15111yescharacteristic
938C2#3025×C15111yescharacteristic
subgroupG/H
center, socleC22×C151C2×#120
commutator, Frattini, cosocleC24C24×C151
LCSG ▷ C24 ▷ C2 ▷ C1
UCSC1 ◁ C22×C151 ◁ C23×C4×C151 ◁ G

Complements

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

NH ≅ G/Ntype
1. #3505×C151C2semidirect
2. #2848×C151C2semidirect
3. #2847×C151C2semidirect
4. C4×#120×C151C2semidirect
5. #2044×C151C2semidirect
6. #2021×C151C2semidirect
7. #1996×C151C2semidirect
8. #1964×C151C2semidirect
9. #1889×C151C2semidirect
10. #1867×C151C2semidirect
11. #1799×C151C2semidirect
57. C22×Q8×C151D4semidirect
60. C22×D4×C151D4semidirect
70. C23×C4×C151D4semidirect
126. C2×C4⋊C4×C151D4semidirect
127. C2×C4⋊C4×C151D4semidirect
128. C2×C4⋊C4×C151D4semidirect
129. C2×C4⋊C4×C151D4semidirect
139. C2×C22⋊C4×C151D4semidirect
140. C2×C22⋊C4×C151D4semidirect
148. C2×C42×C151D4semidirect
169. C24×C151#41semidirect
285. C22⋊C4×C151#41semidirect
469. #24140C151direct (N × H)
470. C151#24140direct (N × H)
471. #3505C2×C151semidirect
472. #2848C2×C151semidirect
473. #2847C2×C151semidirect
474. C4×#120C2×C151semidirect
475. #2044C2×C151semidirect
476. #2021C2×C151semidirect
477. #1996C2×C151semidirect
478. #1964C2×C151semidirect
479. #1889C2×C151semidirect
480. #1867C2×C151semidirect
481. #1799C2×C151semidirect
527. C22×Q8D4×C151semidirect
530. C22×D4D4×C151semidirect
540. C23×C4D4×C151semidirect
596. C2×C4⋊C4D4×C151semidirect
597. C2×C4⋊C4D4×C151semidirect
598. C2×C4⋊C4D4×C151semidirect
599. C2×C4⋊C4D4×C151semidirect
609. C2×C22⋊C4D4×C151semidirect
610. C2×C22⋊C4D4×C151semidirect
618. C2×C42D4×C151semidirect
639. C24#41×C151semidirect
755. C22⋊C4#41×C151semidirect

Maximal subgroups

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

subgroupindex
#3505×C1512
#2848×C1512
#2847×C1512
C4×#120×C1512
#2044×C1512
#2021×C1512
#1996×C1512
#1964×C1512
#1889×C1512
#1867×C1512
#1799×C1512
#24140151