Finite Group Databasebeta

← C151×#24404 #50329329

Subgroups — C151×#24404 #50329329

Order 38656.

2010 conjugacy classes of subgroups.

The subgroup lattice has 1046 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#3484×C151C211yesmaximal, characteristic, complemented
2C2×B(4,𝔽2)×C151C211yesmaximal, characteristic, complemented
3C22×#99×C151C211yesmaximal, characteristic, complemented
4#2410×C151C212yesmaximal, complemented
5#2403×C151C211yesmaximal, characteristic, complemented
6#2044×C151C212yesmaximal, complemented
7#2021×C151C212yesmaximal, complemented
8#1898×C151C212yesmaximal, complemented
9#1889×C151C211yesmaximal, characteristic, complemented
10#1867×C151C211yesmaximal, characteristic, complemented
11#1790×C151C211yesmaximal, characteristic, complemented
12C2×H(5,𝔽2)×C151C2211yescharacteristic
13C23×D4×C151C2211yescharacteristic
14C23×D4×C151C2211yescharacteristic, complemented
15#546×C151—22no—
16#546×C151—22no—
17D42×C151—22no—
18D42×C151—22no—
19#535×C151—21no—
20#534×C151—21no—
21#534×C151C2212yes—
22#525×C151—21no—
23C2×#121×C151—22no—
24C2×#120×C151—21no—
25C2×#120×C151—21no—
26C2×#120×C151C2211yescharacteristic
27C2×#120×C151C2212yes—
28C2×#120×C151C2212yescomplemented
29C2×#120×C151C2211yescharacteristic, complemented
30#518×C151C2211yescharacteristic
31C22×C22⋊C4×C151C2212yescomplemented
32B(4,𝔽2)×C151—24no—
33C2×#99×C151—24no—
34C2×#99×C151C2211yescharacteristic
35C2×#99×C151C2211yescharacteristic
36C2×#99×C151C2212yescomplemented
37C2×#99×C151C2212yescomplemented
38C2×#99×C151C2212yescomplemented
39#394×C151—22no—
40#392×C151—21no—
41#392×C151—21no—
42#392×C151—22no—
43#386×C151—21no—
44#386×C151—22no—
45#386×C151C2211yescharacteristic
46#386×C151C2211yescharacteristic, complemented
47#386×C151C2212yescomplemented
48#385×C151C2212yescomplemented
49#379×C151C2212yescomplemented
50#379×C151C2211yescharacteristic, complemented
51#342×C151C2212yescomplemented
52#342×C151C2212yescomplemented
53C25×C151D411yescharacteristic, complemented
54C25×C151C2311yescharacteristic
55C25×C151C2311yescharacteristic
56H(5,𝔽2)×C151—22no—
57H(5,𝔽2)×C151—22no—
58H(5,𝔽2)×C151—42no—
59C2×#41×C151—21no—
60C2×#41×C151—22no—
61C22×D4×C151—21no—
62C22×D4×C151—21no—
63C22×D4×C151—22no—
64C22×D4×C151—22no—
65C22×D4×C151—21no—
66C22×D4×C151—22no—
67C22×D4×C151—21no—
68C22×D4×C151—22no—
69C22×D4×C151—22no—
70C22×D4×C151—22no—
71C22×D4×C151—21no—
72C22×D4×C151—22no—
73C22×D4×C151—21no—
74C22×D4×C151—21no—
75C22×D4×C151—22no—
76C22×D4×C151—42no—
77C22×D4×C151—44no—
78C22×D4×C151D411yescharacteristic, complemented
79C22×D4×C151D411yescharacteristic, complemented
80C22×D4×C151D412yescomplemented
81C22×D4×C151D412yescomplemented
82C22×D4×C151C2312yes—
83C22×D4×C151C2311yescharacteristic
84C22×D4×C151C2311yescharacteristic
85C23×C4×C151—22no—
86C23×C4×C151D411yescharacteristic, complemented
87C23×C4×C151C2311yescharacteristic
88#127×C151—22no—
89#124×C151—22no—
90#123×C151—22no—
91#123×C151—22no—
92#123×C151—22no—
93C22⋊Q8×C151—21no—
94C22⋊Q8×C151—21no—
95#121×C151—21no—
96#121×C151—21no—
97#121×C151—22no—
98#121×C151—22no—
99#121×C151—22no—
100#121×C151—22no—
101#121×C151—22no—
102#121×C151—22no—
103#121×C151—48no—
104#120×C151—22no—
105#120×C151—22no—
106#120×C151—22no—
107#120×C151—22no—
108#120×C151—22no—
109#120×C151—24no—
110#120×C151—22no—
111#120×C151—22no—
112#120×C151—22no—
113#120×C151—22no—
114#120×C151—22no—
115#120×C151—22no—
116#120×C151—42no—
117#120×C151—42no—
118#120×C151—44no—
119C4×D4×C151—22no—
120C4×D4×C151—22no—
121C4×D4×C151—22no—
122C4×D4×C151—22no—
123#117×C151—21no—
124C2×C4⋊C4×C151—22no—
125C2×C22⋊C4×C151—21no—
126C2×C22⋊C4×C151—21no—
127C2×C22⋊C4×C151—24no—
128C2×C22⋊C4×C151—22no—
129C2×C22⋊C4×C151—21no—
130C2×C22⋊C4×C151—21no—
131C2×C22⋊C4×C151—22no—
132C2×C22⋊C4×C151—22no—
133C2×C22⋊C4×C151—21no—
134C2×C22⋊C4×C151—21no—
135C2×C22⋊C4×C151—21no—
136C2×C22⋊C4×C151—21no—
137C2×C22⋊C4×C151—22no—
138C2×C22⋊C4×C151—22no—
139C2×C22⋊C4×C151—21no—
140C2×C22⋊C4×C151—42no—
141C2×C22⋊C4×C151D412yescomplemented
142C2×C22⋊C4×C151D412yescomplemented
143C2×C22⋊C4×C151C2311yescharacteristic
144C2×C22⋊C4×C151C2311yescharacteristic
145C2×C22⋊C4×C151C2312yes—
146C2×C22⋊C4×C151C2312yes—
147C2×C22⋊C4×C151C2312yes—
148#99×C151—22no—
149#99×C151—24no—
150#99×C151—24no—
151#99×C151—42no—
152#99×C151D414yescomplemented
153#95×C151—22no—
154#95×C151—21no—
155#95×C151—21no—
156#95×C151—22no—
157C24×C151—21no—
158C24×C151—21no—
159C24×C151—22no—
160C24×C151—21no—
161C24×C151—22no—
162C24×C151—21no—
163C24×C151—21no—
164C24×C151—21no—
165C24×C151—22no—
166C24×C151—21no—
167C24×C151—21no—
168C24×C151—22no—
169C24×C151—41no—
170C24×C151—42no—
171C24×C151—42no—
172C24×C151—42no—
173C24×C151—81no—
174C24×C151—81no—
175C24×C151—81no—
176C24×C151C2×D411yescharacteristic
177C24×C151C2×D412yes—
178C24×C151C2×D411yescharacteristic
179C24×C151C2×D412yes—
180C24×C151C2×D412yes—
181C24×C151C2×D411yescharacteristic
182C24×C151C2×D411yescharacteristic
183C24×C151C2411yescharacteristic
184#41×C151—44no—
185#41×C151—44no—
186#41×C151—42no—
187#41×C151—42no—
188C2×Q8×C151—21no—
189C2×D4×C151—22no—
190C2×D4×C151—22no—
191C2×D4×C151—22no—
192C2×D4×C151—24no—
193C2×D4×C151—21no—
194C2×D4×C151—28no—
195C2×D4×C151—22no—
196C2×D4×C151—22no—
197C2×D4×C151—22no—
198C2×D4×C151—22no—
199C2×D4×C151—22no—
200C2×D4×C151—21no—
201C2×D4×C151—22no—
202C2×D4×C151—22no—
203C2×D4×C151—22no—
204C2×D4×C151—22no—
205C2×D4×C151—21no—
206C2×D4×C151—22no—
207C2×D4×C151—22no—
208C2×D4×C151—22no—
209C2×D4×C151—22no—
210C2×D4×C151—22no—
211C2×D4×C151—22no—
212C2×D4×C151—22no—
213C2×D4×C151—22no—
214C2×D4×C151—22no—
215C2×D4×C151—41no—
216C2×D4×C151—41no—
217C2×D4×C151—42no—
218C2×D4×C151—44no—
219C2×D4×C151—44no—
220C2×D4×C151—44no—
221C2×D4×C151—44no—
222C2×D4×C151—44no—
223C2×D4×C151—44no—
224C2×D4×C151—44no—
225C2×D4×C151—44no—
226C2×D4×C151—44no—
227C2×D4×C151—42no—
228C2×D4×C151—42no—
229C2×D4×C151—44no—
230C2×D4×C151—42no—
231C2×D4×C151—41no—
232C2×D4×C151—42no—
233C2×D4×C151—41no—
234C2×D4×C151—42no—
235C2×D4×C151—44no—
236C2×D4×C151—42no—
237C2×D4×C151—42no—
238C2×D4×C151—42no—
239C2×D4×C151—44no—
240C2×D4×C151—42no—
241C2×D4×C151—82no—
242C2×D4×C151—82no—
243C2×D4×C151—81no—
244C2×D4×C151—81no—
245C2×D4×C151—82no—
246C2×D4×C151—82no—
247C2×D4×C151C2×D412yes—
248C2×D4×C151#4112yes—
249C22×C4×C151—21no—
250C22×C4×C151—22no—
251C22×C4×C151—21no—
252C22×C4×C151—21no—
253C22×C4×C151—21no—
254C22×C4×C151—22no—
255C22×C4×C151—22no—
256C22×C4×C151—21no—
257C22×C4×C151—21no—
258C22×C4×C151—22no—
259C22×C4×C151—22no—
260C22×C4×C151—21no—
261C22×C4×C151—21no—
262C22×C4×C151—42no—
263C22×C4×C151—41no—
264C22×C4×C151—44no—
265C22×C4×C151—44no—
266C22×C4×C151—82no—
267C22×C4×C151C2×D412yes—
268C22×C4×C151C2×D411yescharacteristic
269C22×C4×C151C2×D411yescharacteristic
270C22×C4×C151C2×D412yes—
271C22×C4×C151C2×D412yes—
272C4⋊C4×C151—21no—
273C4⋊C4×C151—21no—
274C4⋊C4×C151—22no—
275C4⋊C4×C151—22no—
276C4⋊C4×C151—44no—
277C22⋊C4×C151—22no—
278C22⋊C4×C151—22no—
279C22⋊C4×C151—22no—
280C22⋊C4×C151—22no—
281C22⋊C4×C151—22no—
282C22⋊C4×C151—22no—
283C22⋊C4×C151—22no—
284C22⋊C4×C151—22no—
285C22⋊C4×C151—22no—
286C22⋊C4×C151—22no—
287C22⋊C4×C151—22no—
288C22⋊C4×C151—22no—
289C22⋊C4×C151—22no—
290C22⋊C4×C151—21no—
291C22⋊C4×C151—21no—
292C22⋊C4×C151—22no—
293C22⋊C4×C151—22no—
294C22⋊C4×C151—44no—
295C22⋊C4×C151—44no—
296C22⋊C4×C151—42no—
297C22⋊C4×C151—42no—
298C22⋊C4×C151—42no—
299C22⋊C4×C151—44no—
300C22⋊C4×C151—42no—
301C22⋊C4×C151—44no—
302C22⋊C4×C151—42no—
303C22⋊C4×C151—82no—
304C22⋊C4×C151—81no—
305C22⋊C4×C151C2×D414yescomplemented
306C42×C151—22no—
307C23×C151—21no—
308C23×C151—21no—
309C23×C151—21no—
310C23×C151—22no—
311C23×C151—22no—
312C23×C151—22no—
313C23×C151—24no—
314C23×C151—21no—
315C23×C151—21no—
316C23×C151—21no—
317C23×C151—22no—
318C23×C151—22no—
319C23×C151—24no—
320C23×C151—22no—
321C23×C151—21no—
322C23×C151—22no—
323C23×C151—21no—
324C23×C151—21no—
325C23×C151—22no—
326C23×C151—22no—
327C23×C151—41no—
328C23×C151—41no—
329C23×C151—41no—
330C23×C151—42no—
331C23×C151—42no—
332C23×C151—41no—
333C23×C151—41no—
334C23×C151—42no—
335C23×C151—42no—
336C23×C151—42no—
337C23×C151—41no—
338C23×C151—41no—
339C23×C151—41no—
340C23×C151—41no—
341C23×C151—42no—
342C23×C151—41no—
343C23×C151—42no—
344C23×C151—42no—
345C23×C151—41no—
346C23×C151—41no—
347C23×C151—42no—
348C23×C151—42no—
349C23×C151—42no—
350C23×C151—42no—
351C23×C151—41no—
352C23×C151—41no—
353C23×C151—41no—
354C23×C151—42no—
355C23×C151—42no—
356C23×C151—42no—
357C23×C151—81no—
358C23×C151—81no—
359C23×C151—82no—
360C23×C151—82no—
361C23×C151—82no—
362C23×C151—82no—
363C23×C151—84no—
364C23×C151—84no—
365C23×C151—81no—
366C23×C151—81no—
367C23×C151—84no—
368C23×C151—84no—
369C23×C151#12011yescharacteristic
370C23×C151#12012yes—
371C23×C151#12011yescharacteristic
372C23×C151#12112yescomplemented
373C23×C151C22×D411yescharacteristic
374C23×C151C22×D412yes—
375C23×C151C22×D411yescharacteristic
376C23×C151C2×#4111yescharacteristic
377C23×C151H(5,𝔽2)12yes—
378Q8×C151—42no—
379D4×C151—24no—
380D4×C151—24no—
381D4×C151—44no—
382D4×C151—42no—
383D4×C151—44no—
384D4×C151—44no—
385D4×C151—48no—
386D4×C151—44no—
387D4×C151—44no—
388D4×C151—42no—
389D4×C151—42no—
390D4×C151—42no—
391D4×C151—42no—
392D4×C151—42no—
393D4×C151—42no—
394D4×C151—44no—
395D4×C151—44no—
396D4×C151—82no—
397D4×C151—82no—
398D4×C151—82no—
399D4×C151—82no—
400D4×C151—88no—
401D4×C151—84no—
402D4×C151—84no—
403C2×C4×C151—21no—
404C2×C4×C151—21no—
405C2×C4×C151—22no—
406C2×C4×C151—24no—
407C2×C4×C151—22no—
408C2×C4×C151—22no—
409C2×C4×C151—22no—
410C2×C4×C151—21no—
411C2×C4×C151—21no—
412C2×C4×C151—21no—
413C2×C4×C151—22no—
414C2×C4×C151—24no—
415C2×C4×C151—22no—
416C2×C4×C151—42no—
417C2×C4×C151—42no—
418C2×C4×C151—44no—
419C2×C4×C151—42no—
420C2×C4×C151—42no—
421C2×C4×C151—42no—
422C2×C4×C151—41no—
423C2×C4×C151—42no—
424C2×C4×C151—41no—
425C2×C4×C151—42no—
426C2×C4×C151—42no—
427C2×C4×C151—42no—
428C2×C4×C151—41no—
429C2×C4×C151—41no—
430C2×C4×C151—42no—
431C2×C4×C151—41no—
432C2×C4×C151—41no—
433C2×C4×C151—41no—
434C2×C4×C151—41no—
435C2×C4×C151—42no—
436C2×C4×C151—81no—
437C2×C4×C151—81no—
438C2×C4×C151—88no—
439C2×C4×C151#12112yescomplemented
440C22×C151—21no—
441C22×C151—22no—
442C22×C151—21no—
443C22×C151—22no—
444C22×C151—21no—
445C22×C151—21no—
446C22×C151—21no—
447C22×C151—22no—
448C22×C151—22no—
449C22×C151—22no—
450C22×C151—21no—
451C22×C151—21no—
452C22×C151—22no—
453C22×C151—41no—
454C22×C151—41no—
455C22×C151—42no—
456C22×C151—44no—
457C22×C151—44no—
458C22×C151—42no—
459C22×C151—42no—
460C22×C151—42no—
461C22×C151—44no—
462C22×C151—42no—
463C22×C151—42no—
464C22×C151—42no—
465C22×C151—44no—
466C22×C151—41no—
467C22×C151—41no—
468C22×C151—42no—
469C22×C151—41no—
470C22×C151—42no—
471C22×C151—42no—
472C22×C151—41no—
473C22×C151—42no—
474C22×C151—41no—
475C22×C151—82no—
476C22×C151—81no—
477C22×C151—81no—
478C22×C151—81no—
479C22×C151—82no—
480C22×C151—84no—
481C22×C151—82no—
482C22×C151—82no—
483C22×C151—81no—
484C22×C151—82no—
485C22×C151—81no—
486C22×C151—81no—
487C22×C151—82no—
488C22×C151—84no—
489C22×C151—81no—
490C22×C151—81no—
491C22×C151—162no—
492C22×C151B(4,𝔽2)12yescomplemented
493C22×C151C2×#12011yescharacteristic
494C22×C151C2×#12111yescharacteristic
495C22×C151#53411yescharacteristic
496C22×C151D4212yes—
497C22×C151#54612yes—
498C4×C151—22no—
499C4×C151—44no—
500C4×C151—41no—
501C4×C151—42no—
502C4×C151—42no—
503C4×C151—42no—
504C4×C151—42no—
505C4×C151—82no—
506C4×C151—81no—
507C4×C151—81no—
508C2×C151—22no—
509C2×C151—21no—
510C2×C151—21no—
511C2×C151—22no—
512C2×C151—22no—
513C2×C151—42no—
514C2×C151—41no—
515C2×C151—42no—
516C2×C151—82no—
517C2×C151—81no—
518C2×C151—82no—
519C2×C151#241011yescharacteristic
520C2×C151C2×B(4,𝔽2)11yescharacteristic
521C2×C151#302611yescharacteristic
522#24404C15111yesmaximal, characteristic, direct product factor, Sylow
523C151#2440411yescharacteristic, direct product factor, Sylow
524#3484C2×C15111yescharacteristic, complemented
525C2×B(4,𝔽2)C2×C15111yescharacteristic, complemented
526C22×#99C2×C15111yescharacteristic, complemented
527#2410C2×C15112yescomplemented
528#2403C2×C15111yescharacteristic, complemented
529#2044C2×C15112yescomplemented
530#2021C2×C15112yescomplemented
531#1898C2×C15112yescomplemented
532#1889C2×C15111yescharacteristic, complemented
533#1867C2×C15111yescharacteristic, complemented
534#1790C2×C15111yescharacteristic, complemented
535C2×H(5,𝔽2)C22×C15111yescharacteristic
536C23×D4C22×C15111yescharacteristic
537C23×D4C22×C15111yescharacteristic, complemented
538#546—22no—
539#546—22no—
540D42—22no—
541D42—22no—
542#535—21no—
543#534—21no—
544#534C22×C15112yes—
545#525—21no—
546C2×#121—22no—
547C2×#120—21no—
548C2×#120—21no—
549C2×#120C22×C15111yescharacteristic
550C2×#120C22×C15112yes—
551C2×#120C22×C15112yescomplemented
552C2×#120C22×C15111yescharacteristic, complemented
553#518C22×C15111yescharacteristic
554C22×C22⋊C4C22×C15112yescomplemented
555B(4,𝔽2)—24no—
556C2×#99—24no—
557C2×#99C22×C15111yescharacteristic
558C2×#99C22×C15111yescharacteristic
559C2×#99C22×C15112yescomplemented
560C2×#99C22×C15112yescomplemented
561C2×#99C22×C15112yescomplemented
562#394—22no—
563#392—21no—
564#392—21no—
565#392—22no—
566#386—21no—
567#386—22no—
568#386C22×C15111yescharacteristic
569#386C22×C15111yescharacteristic, complemented
570#386C22×C15112yescomplemented
571#385C22×C15112yescomplemented
572#379C22×C15112yescomplemented
573#379C22×C15111yescharacteristic, complemented
574#342C22×C15112yescomplemented
575#342C22×C15112yescomplemented
576C25D4×C15111yescharacteristic, complemented
577C25C23×C15111yescharacteristic
578C25C23×C15111yescharacteristic
579H(5,𝔽2)—22no—
580H(5,𝔽2)—22no—
581H(5,𝔽2)—42no—
582C2×#41—21no—
583C2×#41—22no—
584C22×D4—21no—
585C22×D4—21no—
586C22×D4—22no—
587C22×D4—22no—
588C22×D4—22no—
589C22×D4—22no—
590C22×D4—21no—
591C22×D4—21no—
592C22×D4—22no—
593C22×D4—22no—
594C22×D4—21no—
595C22×D4—22no—
596C22×D4—21no—
597C22×D4—21no—
598C22×D4—22no—
599C22×D4—44no—
600C22×D4—42no—
601C22×D4D4×C15111yescharacteristic, complemented
602C22×D4D4×C15111yescharacteristic, complemented
603C22×D4D4×C15112yescomplemented
604C22×D4D4×C15112yescomplemented
605C22×D4C23×C15112yes—
606C22×D4C23×C15111yescharacteristic
607C22×D4C23×C15111yescharacteristic
608C23×C4—22no—
609C23×C4D4×C15111yescharacteristic, complemented
610C23×C4C23×C15111yescharacteristic
611#127—22no—
612#124—22no—
613#123—22no—
614#123—22no—
615#123—22no—
616C22⋊Q8—21no—
617C22⋊Q8—21no—
618#121—21no—
619#121—21no—
620#121—22no—
621#121—22no—
622#121—22no—
623#121—22no—
624#121—22no—
625#121—22no—
626#121—48no—
627#120—22no—
628#120—22no—
629#120—22no—
630#120—22no—
631#120—22no—
632#120—22no—
633#120—22no—
634#120—22no—
635#120—22no—
636#120—22no—
637#120—22no—
638#120—24no—
639#120—42no—
640#120—42no—
641#120—44no—
642C4×D4—22no—
643C4×D4—22no—
644C4×D4—22no—
645C4×D4—22no—
646#117—21no—
647C2×C4⋊C4—22no—
648C2×C22⋊C4—21no—
649C2×C22⋊C4—21no—
650C2×C22⋊C4—21no—
651C2×C22⋊C4—24no—
652C2×C22⋊C4—22no—
653C2×C22⋊C4—21no—
654C2×C22⋊C4—21no—
655C2×C22⋊C4—21no—
656C2×C22⋊C4—22no—
657C2×C22⋊C4—21no—
658C2×C22⋊C4—21no—
659C2×C22⋊C4—22no—
660C2×C22⋊C4—22no—
661C2×C22⋊C4—21no—
662C2×C22⋊C4—22no—
663C2×C22⋊C4—42no—
664C2×C22⋊C4D4×C15112yescomplemented
665C2×C22⋊C4D4×C15112yescomplemented
666C2×C22⋊C4C23×C15112yes—
667C2×C22⋊C4C23×C15111yescharacteristic
668C2×C22⋊C4C23×C15111yescharacteristic
669C2×C22⋊C4C23×C15112yes—
670C2×C22⋊C4C23×C15112yes—
671#99—22no—
672#99—24no—
673#99—24no—
674#99—42no—
675#99D4×C15114yescomplemented
676#95—22no—
677#95—21no—
678#95—21no—
679#95—22no—
680C24—21no—
681C24—21no—
682C24—22no—
683C24—21no—
684C24—22no—
685C24—21no—
686C24—21no—
687C24—21no—
688C24—22no—
689C24—21no—
690C24—21no—
691C24—22no—
692C24—41no—
693C24—42no—
694C24—42no—
695C24—42no—
696C24—81no—
697C24—81no—
698C24—81no—
699C24C2×D4×C15111yescharacteristic
700C24C2×D4×C15112yes—
701C24C2×D4×C15111yescharacteristic
702C24C2×D4×C15112yes—
703C24C2×D4×C15112yes—
704C24C2×D4×C15111yescharacteristic
705C24C2×D4×C15111yescharacteristic
706C24C24×C15111yescharacteristic
707#41—44no—
708#41—44no—
709#41—42no—
710#41—42no—
711C2×Q8—21no—
712C2×D4—22no—
713C2×D4—22no—
714C2×D4—22no—
715C2×D4—24no—
716C2×D4—21no—
717C2×D4—28no—
718C2×D4—22no—
719C2×D4—22no—
720C2×D4—22no—
721C2×D4—22no—
722C2×D4—22no—
723C2×D4—21no—
724C2×D4—22no—
725C2×D4—22no—
726C2×D4—22no—
727C2×D4—22no—
728C2×D4—21no—
729C2×D4—22no—
730C2×D4—22no—
731C2×D4—22no—
732C2×D4—22no—
733C2×D4—22no—
734C2×D4—22no—
735C2×D4—22no—
736C2×D4—22no—
737C2×D4—22no—
738C2×D4—41no—
739C2×D4—41no—
740C2×D4—42no—
741C2×D4—44no—
742C2×D4—44no—
743C2×D4—44no—
744C2×D4—44no—
745C2×D4—44no—
746C2×D4—44no—
747C2×D4—44no—
748C2×D4—44no—
749C2×D4—44no—
750C2×D4—42no—
751C2×D4—42no—
752C2×D4—44no—
753C2×D4—42no—
754C2×D4—41no—
755C2×D4—42no—
756C2×D4—41no—
757C2×D4—42no—
758C2×D4—44no—
759C2×D4—42no—
760C2×D4—42no—
761C2×D4—42no—
762C2×D4—44no—
763C2×D4—42no—
764C2×D4—82no—
765C2×D4—82no—
766C2×D4—81no—
767C2×D4—81no—
768C2×D4—82no—
769C2×D4—82no—
770C2×D4C2×D4×C15112yes—
771C2×D4#41×C15112yes—
772C22×C4—21no—
773C22×C4—22no—
774C22×C4—21no—
775C22×C4—21no—
776C22×C4—21no—
777C22×C4—22no—
778C22×C4—22no—
779C22×C4—21no—
780C22×C4—21no—
781C22×C4—22no—
782C22×C4—22no—
783C22×C4—21no—
784C22×C4—21no—
785C22×C4—42no—
786C22×C4—41no—
787C22×C4—44no—
788C22×C4—44no—
789C22×C4—82no—
790C22×C4C2×D4×C15112yes—
791C22×C4C2×D4×C15111yescharacteristic
792C22×C4C2×D4×C15111yescharacteristic
793C22×C4C2×D4×C15112yes—
794C22×C4C2×D4×C15112yes—
795C4⋊C4—21no—
796C4⋊C4—21no—
797C4⋊C4—22no—
798C4⋊C4—22no—
799C4⋊C4—44no—
800C22⋊C4—22no—
801C22⋊C4—22no—
802C22⋊C4—22no—
803C22⋊C4—22no—
804C22⋊C4—22no—
805C22⋊C4—22no—
806C22⋊C4—22no—
807C22⋊C4—22no—
808C22⋊C4—22no—
809C22⋊C4—22no—
810C22⋊C4—22no—
811C22⋊C4—22no—
812C22⋊C4—22no—
813C22⋊C4—21no—
814C22⋊C4—21no—
815C22⋊C4—22no—
816C22⋊C4—22no—
817C22⋊C4—44no—
818C22⋊C4—44no—
819C22⋊C4—42no—
820C22⋊C4—42no—
821C22⋊C4—42no—
822C22⋊C4—44no—
823C22⋊C4—42no—
824C22⋊C4—44no—
825C22⋊C4—42no—
826C22⋊C4—82no—
827C22⋊C4—81no—
828C22⋊C4C2×D4×C15114yescomplemented
829C42—22no—
830C23—22no—
831C23—24no—
832C23—21no—
833C23—21no—
834C23—21no—
835C23—22no—
836C23—22no—
837C23—21no—
838C23—21no—
839C23—21no—
840C23—22no—
841C23—22no—
842C23—24no—
843C23—22no—
844C23—21no—
845C23—22no—
846C23—21no—
847C23—21no—
848C23—22no—
849C23—22no—
850C23—41no—
851C23—42no—
852C23—41no—
853C23—41no—
854C23—41no—
855C23—42no—
856C23—41no—
857C23—42no—
858C23—42no—
859C23—42no—
860C23—41no—
861C23—41no—
862C23—41no—
863C23—41no—
864C23—42no—
865C23—42no—
866C23—41no—
867C23—42no—
868C23—41no—
869C23—41no—
870C23—42no—
871C23—42no—
872C23—42no—
873C23—42no—
874C23—42no—
875C23—41no—
876C23—41no—
877C23—41no—
878C23—42no—
879C23—42no—
880C23—81no—
881C23—81no—
882C23—82no—
883C23—82no—
884C23—82no—
885C23—82no—
886C23—84no—
887C23—84no—
888C23—81no—
889C23—81no—
890C23—84no—
891C23—84no—
892C23#120×C15111yescharacteristic
893C23#120×C15112yes—
894C23#120×C15111yescharacteristic
895C23#121×C15112yescomplemented
896C23C22×D4×C15111yescharacteristic
897C23C22×D4×C15112yes—
898C23C22×D4×C15111yescharacteristic
899C23C2×#41×C15111yescharacteristic
900C23H(5,𝔽2)×C15112yes—
901Q8—42no—
902D4—24no—
903D4—24no—
904D4—44no—
905D4—42no—
906D4—44no—
907D4—48no—
908D4—44no—
909D4—44no—
910D4—44no—
911D4—44no—
912D4—44no—
913D4—42no—
914D4—42no—
915D4—42no—
916D4—42no—
917D4—42no—
918D4—42no—
919D4—82no—
920D4—82no—
921D4—82no—
922D4—82no—
923D4—88no—
924D4—84no—
925D4—84no—
926C2×C4—21no—
927C2×C4—21no—
928C2×C4—22no—
929C2×C4—24no—
930C2×C4—22no—
931C2×C4—22no—
932C2×C4—22no—
933C2×C4—21no—
934C2×C4—21no—
935C2×C4—21no—
936C2×C4—24no—
937C2×C4—22no—
938C2×C4—22no—
939C2×C4—42no—
940C2×C4—42no—
941C2×C4—44no—
942C2×C4—42no—
943C2×C4—42no—
944C2×C4—41no—
945C2×C4—42no—
946C2×C4—42no—
947C2×C4—41no—
948C2×C4—42no—
949C2×C4—42no—
950C2×C4—42no—
951C2×C4—41no—
952C2×C4—41no—
953C2×C4—42no—
954C2×C4—41no—
955C2×C4—41no—
956C2×C4—41no—
957C2×C4—41no—
958C2×C4—42no—
959C2×C4—81no—
960C2×C4—81no—
961C2×C4—88no—
962C2×C4#121×C15112yescomplemented
963C22—21no—
964C22—22no—
965C22—21no—
966C22—22no—
967C22—21no—
968C22—21no—
969C22—21no—
970C22—22no—
971C22—22no—
972C22—22no—
973C22—21no—
974C22—21no—
975C22—22no—
976C22—41no—
977C22—41no—
978C22—42no—
979C22—44no—
980C22—42no—
981C22—42no—
982C22—44no—
983C22—42no—
984C22—44no—
985C22—42no—
986C22—42no—
987C22—42no—
988C22—44no—
989C22—41no—
990C22—41no—
991C22—42no—
992C22—41no—
993C22—42no—
994C22—42no—
995C22—41no—
996C22—42no—
997C22—41no—
998C22—82no—
999C22—81no—
1000C22—81no—
1001C22—81no—
1002C22—82no—
1003C22—84no—
1004C22—82no—
1005C22—81no—
1006C22—82no—
1007C22—82no—
1008C22—81no—
1009C22—81no—
1010C22—82no—
1011C22—84no—
1012C22—81no—
1013C22—81no—
1014C22—162no—
1015C22B(4,𝔽2)×C15112yescomplemented
1016C22C2×#120×C15111yescharacteristic
1017C22C2×#121×C15111yescharacteristic
1018C22#534×C15111yescharacteristic
1019C22D42×C15112yes—
1020C22#546×C15112yes—
1021C4—22no—
1022C4—44no—
1023C4—41no—
1024C4—42no—
1025C4—42no—
1026C4—42no—
1027C4—42no—
1028C4—82no—
1029C4—81no—
1030C4—81no—
1031C2—22no—
1032C2—21no—
1033C2—21no—
1034C2—22no—
1035C2—22no—
1036C2—41no—
1037C2—42no—
1038C2—42no—
1039C2—82no—
1040C2—81no—
1041C2—82no—
1042C2#2410×C15111yescharacteristic
1043C2C2×B(4,𝔽2)×C15111yescharacteristic
1044C2#3026×C15111yescharacteristic
subgroupG/H
center, socleC22×C151C2×#120
commutator, Frattini, cosocleC24C24×C151
LCSG ▷ C24 ▷ C2 ▷ C1
UCSC1 ◁ C22×C151 ◁ C25×C151 ◁ G

Complements

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

NH ≅ G/Ntype
1. #3484×C151C2semidirect
2. C2×B(4,𝔽2)×C151C2semidirect
3. C22×#99×C151C2semidirect
4. #2410×C151C2semidirect
5. #2403×C151C2semidirect
6. #2044×C151C2semidirect
7. #2021×C151C2semidirect
8. #1898×C151C2semidirect
9. #1889×C151C2semidirect
10. #1867×C151C2semidirect
11. #1790×C151C2semidirect
14. C23×D4×C151C22semidirect
28. C2×#120×C151C22semidirect
29. C2×#120×C151C22semidirect
31. C22×C22⋊C4×C151C22semidirect
36. C2×#99×C151C22semidirect
37. C2×#99×C151C22semidirect
38. C2×#99×C151C22semidirect
46. #386×C151C22semidirect
47. #386×C151C22semidirect
48. #385×C151C22semidirect
49. #379×C151C22semidirect
50. #379×C151C22semidirect
51. #342×C151C22semidirect
52. #342×C151C22semidirect
53. C25×C151D4semidirect
78. C22×D4×C151D4semidirect
79. C22×D4×C151D4semidirect
80. C22×D4×C151D4semidirect
81. C22×D4×C151D4semidirect
86. C23×C4×C151D4semidirect
141. C2×C22⋊C4×C151D4semidirect
142. C2×C22⋊C4×C151D4semidirect
152. #99×C151D4semidirect
305. C22⋊C4×C151C2×D4semidirect
372. C23×C151#121semidirect
439. C2×C4×C151#121semidirect
492. C22×C151B(4,𝔽2)semidirect
522. #24404C151direct (N × H)
523. C151#24404direct (N × H)
524. #3484C2×C151semidirect
525. C2×B(4,𝔽2)C2×C151semidirect
526. C22×#99C2×C151semidirect
527. #2410C2×C151semidirect
528. #2403C2×C151semidirect
529. #2044C2×C151semidirect
530. #2021C2×C151semidirect
531. #1898C2×C151semidirect
532. #1889C2×C151semidirect
533. #1867C2×C151semidirect
534. #1790C2×C151semidirect
537. C23×D4C22×C151semidirect
551. C2×#120C22×C151semidirect
552. C2×#120C22×C151semidirect
554. C22×C22⋊C4C22×C151semidirect
559. C2×#99C22×C151semidirect
560. C2×#99C22×C151semidirect
561. C2×#99C22×C151semidirect
569. #386C22×C151semidirect
570. #386C22×C151semidirect
571. #385C22×C151semidirect
572. #379C22×C151semidirect
573. #379C22×C151semidirect
574. #342C22×C151semidirect
575. #342C22×C151semidirect
576. C25D4×C151semidirect
601. C22×D4D4×C151semidirect
602. C22×D4D4×C151semidirect
603. C22×D4D4×C151semidirect
604. C22×D4D4×C151semidirect
609. C23×C4D4×C151semidirect
664. C2×C22⋊C4D4×C151semidirect
665. C2×C22⋊C4D4×C151semidirect
675. #99D4×C151semidirect
828. C22⋊C4C2×D4×C151semidirect
895. C23#121×C151semidirect
962. C2×C4#121×C151semidirect
1015. C22B(4,𝔽2)×C151semidirect

Maximal subgroups

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

subgroupindex
#3484×C1512
C2×B(4,𝔽2)×C1512
C22×#99×C1512
#2410×C1512
#2403×C1512
#2044×C1512
#2021×C1512
#1898×C1512
#1889×C1512
#1867×C1512
#1790×C1512
#24404151