Finite Group Databasebeta

← C151×#24656 #50329581

Subgroups — C151×#24656 #50329581

Order 38656.

986 conjugacy classes of subgroups.

The subgroup lattice has 754 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#463×C151C211yesmaximal, characteristic, complemented
2C2×#432×C151C211yesmaximal, characteristic, complemented
3#2850×C151C211yesmaximal, characteristic, complemented
4C4×#121×C151C211yesmaximal, characteristic, complemented
5#2035×C151C211yesmaximal, characteristic, complemented
6#2033×C151C211yesmaximal, characteristic, complemented
7#2000×C151C211yesmaximal, characteristic, complemented
8#1999×C151C211yesmaximal, characteristic
9#1983×C151C211yesmaximal, characteristic, complemented
10#1973×C151C211yesmaximal, characteristic, complemented
11#1972×C151C211yesmaximal, characteristic, complemented
12#1949×C151C211yesmaximal, characteristic, complemented
13#1936×C151C211yesmaximal, characteristic, complemented
14#1935×C151C211yesmaximal, characteristic, complemented
15#1804×C151C211yesmaximal, characteristic, complemented
16C22×SD16×C151C2211yescharacteristic
17C22×D8×C151C2211yescharacteristic
18C2×#124×C151C2211yescharacteristic
19C2×C22⋊Q8×C151C2211yescharacteristic
20C2×#121×C151C2211yescharacteristic
21C2×#121×C151C2211yescharacteristic
22C2×C4×D4×C151—21no—
23C2×C4×D4×C151C2211yescharacteristic
24C22×C42×C151C2211yescharacteristic
25#463×C151—24no—
26#432×C151—24no—
27C2×#107×C151C2211yescharacteristic
28C2×#106×C151C2211yescharacteristic
29C2×C4⋊C8×C151C2211yescharacteristic
30C2×C4⋊C8×C151C2211yescharacteristic
31C2×#103×C151C2211yescharacteristic
32C2×#103×C151C2211yescharacteristic
33C2×#103×C151C2211yescharacteristic
34C2×#102×C151C2211yescharacteristic
35C2×#102×C151C2211yescharacteristic
36C2×#102×C151C2211yescharacteristic
37C2×#102×C151C2211yescharacteristic
38C2×#102×C151C2211yescharacteristic
39C2×C22⋊C8×C151C2211yescharacteristic
40C2×C22⋊C8×C151C2211yescharacteristic
41C2×#97×C151C2211yescharacteristic
42C2×#97×C151C2211yescharacteristic
43#391×C151C2211yescharacteristic
44#390×C151C2211yescharacteristic
45#390×C151C2211yescharacteristic
46#389×C151C2211yescharacteristic
47#388×C151—21no—
48#388×C151—21no—
49#388×C151—21no—
50#386×C151—21no—
51#386×C151—21no—
52#386×C151—21no—
53#382×C151C2211yescharacteristic
54#380×C151C2211yescharacteristic
55C4×C4⋊C4×C151C2211yescharacteristic
56C4×C22⋊C4×C151—21no—
57#340×C151C2211yescharacteristic
58#340×C151C2211yescharacteristic
59#340×C151C2211yescharacteristic
60#340×C151C2211yescharacteristic
61C22×Q8×C151C2311yescharacteristic
62C22×D4×C151—21no—
63C22×D4×C151—21no—
64C22×D4×C151C2311yescharacteristic
65C22×D4×C151C2311yescharacteristic
66C23×C4×C151—21no—
67C23×C4×C151D411yescharacteristic
68C23×C4×C151D411yescharacteristic
69C23×C4×C151C2311yescharacteristic
70C2×SD16×C151—22no—
71C2×SD16×C151—22no—
72C2×SD16×C151—41no—
73C2×D8×C151—22no—
74C2×D8×C151—22no—
75C2×D8×C151—41no—
76C22×C8×C151C2311yescharacteristic
77C22×C8×C151C2311yescharacteristic
78C22×C8×C151C2311yescharacteristic
79C22×C8×C151C2311yescharacteristic
80#124×C151—22no—
81#124×C151—22no—
82C22⋊Q8×C151—41no—
83C22⋊Q8×C151—41no—
84#121×C151—22no—
85#121×C151—22no—
86#121×C151—41no—
87#121×C151—41no—
88C4×D4×C151—22no—
89C4×D4×C151—22no—
90C4×D4×C151—44no—
91C2×C4⋊C4×C151—21no—
92C2×C4⋊C4×C151—21no—
93C2×C4⋊C4×C151C2311yescharacteristic
94C2×C4⋊C4×C151C2311yescharacteristic
95C2×C4⋊C4×C151C2311yescharacteristic
96C2×C4⋊C4×C151C2311yescharacteristic
97C2×C4⋊C4×C151C2311yescharacteristic
98C2×C22⋊C4×C151—21no—
99C2×C22⋊C4×C151—21no—
100C2×C22⋊C4×C151—21no—
101C2×C22⋊C4×C151—21no—
102C2×C22⋊C4×C151—21no—
103C2×C22⋊C4×C151—21no—
104C2×C22⋊C4×C151—21no—
105C2×C22⋊C4×C151—21no—
106C2×C22⋊C4×C151—21no—
107C2×C22⋊C4×C151—21no—
108C2×C22⋊C4×C151—21no—
109C2×C42×C151—22no—
110C2×C42×C151—22no—
111C2×C42×C151—21no—
112C2×C42×C151D411yescharacteristic
113C2×C42×C151D411yescharacteristic
114C2×C42×C151C2311yescharacteristic
115C2×C42×C151C2311yescharacteristic
116#107×C151—41no—
117#106×C151—41no—
118C4⋊C8×C151—22no—
119C4⋊C8×C151D414yescomplemented
120#103×C151—22no—
121#103×C151—22no—
122#103×C151—41no—
123#102×C151—22no—
124#102×C151—22no—
125#102×C151—41no—
126#102×C151—41no—
127#102×C151—41no—
128C22⋊C8×C151—22no—
129C22⋊C8×C151—22no—
130#97×C151—22no—
131#97×C151—22no—
132#95×C151—21no—
133#95×C151—21no—
134#95×C151—21no—
135#95×C151—21no—
136#95×C151—21no—
137#95×C151—21no—
138#95×C151—21no—
139C24×C151—21no—
140C24×C151—21no—
141C24×C151C2×D411yescharacteristic
142C2×Q8×C151—21no—
143C2×Q8×C151—21no—
144C2×Q8×C151—21no—
145C2×Q8×C151—21no—
146C2×Q8×C151—21no—
147C2×Q8×C151—21no—
148C2×D4×C151—24no—
149C2×D4×C151—21no—
150C2×D4×C151—21no—
151C2×D4×C151—21no—
152C2×D4×C151—21no—
153C2×D4×C151—21no—
154C2×D4×C151—21no—
155C2×D4×C151—21no—
156C2×D4×C151—21no—
157C2×D4×C151—21no—
158C2×D4×C151—21no—
159C2×D4×C151—21no—
160C2×D4×C151—42no—
161C2×D4×C151—42no—
162C2×D4×C151—42no—
163C2×D4×C151—42no—
164C2×D4×C151—42no—
165C2×D4×C151#4112yes—
166C22×C4×C151—22no—
167C22×C4×C151—21no—
168C22×C4×C151—22no—
169C22×C4×C151—22no—
170C22×C4×C151—21no—
171C22×C4×C151—21no—
172C22×C4×C151—21no—
173C22×C4×C151—21no—
174C22×C4×C151—21no—
175C22×C4×C151—21no—
176C22×C4×C151—21no—
177C22×C4×C151—21no—
178C22×C4×C151—21no—
179C22×C4×C151—21no—
180C22×C4×C151—21no—
181C22×C4×C151—41no—
182C22×C4×C151—41no—
183C22×C4×C151—41no—
184C22×C4×C151—42no—
185C22×C4×C151—42no—
186C22×C4×C151—42no—
187C22×C4×C151C2×D411yescharacteristic
188C22×C4×C151C2×D411yescharacteristic
189C22×C4×C151C2×D411yescharacteristic
190C22×C4×C151C2×D411yescharacteristic
191C22×C4×C151C2×D411yescharacteristic
192C22×C4×C151C2411yescharacteristic
193SD16×C151—44no—
194D8×C151—44no—
195C2×C8×C151—21no—
196C2×C8×C151—21no—
197C2×C8×C151—21no—
198C2×C8×C151—21no—
199C2×C8×C151—21no—
200C2×C8×C151—21no—
201C2×C8×C151—21no—
202C2×C8×C151—21no—
203C2×C8×C151—21no—
204C2×C8×C151—21no—
205C2×C8×C151C2×D412yes—
206C2×C8×C151C2×D412yes—
207C4⋊C4×C151—21no—
208C4⋊C4×C151—21no—
209C4⋊C4×C151—21no—
210C4⋊C4×C151—21no—
211C4⋊C4×C151—21no—
212C4⋊C4×C151—21no—
213C4⋊C4×C151—21no—
214C4⋊C4×C151—21no—
215C4⋊C4×C151—21no—
216C4⋊C4×C151—42no—
217C4⋊C4×C151—42no—
218C4⋊C4×C151#4112yes—
219C22⋊C4×C151—24no—
220C22⋊C4×C151—42no—
221C22⋊C4×C151—42no—
222C22⋊C4×C151—42no—
223C22⋊C4×C151—42no—
224C22⋊C4×C151—42no—
225C22⋊C4×C151—42no—
226C22⋊C4×C151—42no—
227C22⋊C4×C151—42no—
228C22⋊C4×C151—42no—
229C22⋊C4×C151—42no—
230C42×C151—22no—
231C42×C151—22no—
232C42×C151—21no—
233C42×C151—21no—
234C42×C151—42no—
235C42×C151C2×D412yes—
236C42×C151#4112yes—
237C23×C151—21no—
238C23×C151—21no—
239C23×C151—21no—
240C23×C151—21no—
241C23×C151—21no—
242C23×C151—21no—
243C23×C151—22no—
244C23×C151—41no—
245C23×C151—41no—
246C23×C151—41no—
247C23×C151—41no—
248C23×C151—41no—
249C23×C151—41no—
250C23×C151—41no—
251C23×C151—41no—
252C23×C151—41no—
253C23×C151—41no—
254C23×C151—41no—
255C23×C151—41no—
256C23×C151—41no—
257C23×C151AGL(1,ℤ/8)12yes—
258C23×C151C22×D411yescharacteristic
259Q8×C151—41no—
260Q8×C151—41no—
261Q8×C151—41no—
262Q8×C151—41no—
263D4×C151—22no—
264D4×C151—22no—
265D4×C151—48no—
266D4×C151—41no—
267D4×C151—41no—
268D4×C151—41no—
269D4×C151—41no—
270D4×C151—41no—
271D4×C151—41no—
272D4×C151—84no—
273C2×C4×C151—21no—
274C2×C4×C151—21no—
275C2×C4×C151—21no—
276C2×C4×C151—21no—
277C2×C4×C151—21no—
278C2×C4×C151—21no—
279C2×C4×C151—21no—
280C2×C4×C151—21no—
281C2×C4×C151—22no—
282C2×C4×C151—21no—
283C2×C4×C151—21no—
284C2×C4×C151—21no—
285C2×C4×C151—21no—
286C2×C4×C151—21no—
287C2×C4×C151—44no—
288C2×C4×C151—44no—
289C2×C4×C151—41no—
290C2×C4×C151—41no—
291C2×C4×C151—41no—
292C2×C4×C151—41no—
293C2×C4×C151—41no—
294C2×C4×C151—41no—
295C2×C4×C151—41no—
296C2×C4×C151—41no—
297C2×C4×C151—41no—
298C2×C4×C151—41no—
299C2×C4×C151—41no—
300C2×C4×C151—41no—
301C2×C4×C151—41no—
302C2×C4×C151—41no—
303C2×C4×C151—41no—
304C2×C4×C151—41no—
305C2×C4×C151—41no—
306C2×C4×C151—41no—
307C2×C4×C151—41no—
308C2×C4×C151—41no—
309C2×C4×C151—41no—
310C2×C4×C151—84no—
311C2×C4×C151#12112yes—
312C2×C4×C151#12112yes—
313C2×C4×C151C22×D411yescharacteristic
314C2×C4×C151C2×#4111yescharacteristic
315C2×C4×C151C2×#4111yescharacteristic
316C2×C4×C151C2×#4111yescharacteristic
317C2×C4×C151H(5,𝔽2)11yescharacteristic
318C2×C4×C151H(5,𝔽2)11yescharacteristic
319C8×C151—22no—
320C8×C151—22no—
321C8×C151—41no—
322C8×C151—41no—
323C22×C151—22no—
324C22×C151—22no—
325C22×C151—22no—
326C22×C151—41no—
327C22×C151—41no—
328C22×C151—41no—
329C22×C151—41no—
330C22×C151—42no—
331C22×C151—42no—
332C22×C151—42no—
333C22×C151—81no—
334C22×C151—81no—
335C22×C151—81no—
336C22×C151—81no—
337C22×C151—81no—
338C22×C151—81no—
339C22×C151—81no—
340C22×C151—81no—
341C22×C151—81no—
342C22×C151—81no—
343C22×C151—81no—
344C22×C151C2×#12111yescharacteristic
345C22×C151#52511yescharacteristic
346C22×C151#53511yescharacteristic
347C22×C151C2×AGL(1,ℤ/8)11yescharacteristic
348C22×C151#57511yescharacteristic
349C22×C151#57511yescharacteristic
350C22×C151#57511yescharacteristic
351C4×C151—22no—
352C4×C151—22no—
353C4×C151—42no—
354C4×C151—41no—
355C4×C151—41no—
356C4×C151—41no—
357C4×C151—81no—
358C4×C151—81no—
359C4×C151—81no—
360C4×C151—81no—
361C4×C151—81no—
362C4×C151#54611yescharacteristic
363C4×C151#55011yescharacteristic
364C4×C151#55311yescharacteristic
365C4×C151#55511yescharacteristic
366C2×C151—42no—
367C2×C151—82no—
368C2×C151—161no—
369C2×C151#241411yescharacteristic
370C2×C151#305411yescharacteristic
371C2×C151#305511yescharacteristic
372C2×C151#311111yescharacteristic
373C2×C151#311411yescharacteristic
374C2×C151#321311yescharacteristic
375C2×C151#321911yescharacteristic
376#24656C15111yesmaximal, characteristic, direct product factor, Sylow
377C151#2465611yescharacteristic, direct product factor, Sylow
378C2×#463C2×C15111yescharacteristic, complemented
379C2×#432C2×C15111yescharacteristic, complemented
380#2850C2×C15111yescharacteristic, complemented
381C4×#121C2×C15111yescharacteristic, complemented
382#2035C2×C15111yescharacteristic, complemented
383#2033C2×C15111yescharacteristic, complemented
384#2000C2×C15111yescharacteristic, complemented
385#1999C2×C15111yescharacteristic
386#1983C2×C15111yescharacteristic, complemented
387#1973C2×C15111yescharacteristic, complemented
388#1972C2×C15111yescharacteristic, complemented
389#1949C2×C15111yescharacteristic, complemented
390#1936C2×C15111yescharacteristic, complemented
391#1935C2×C15111yescharacteristic, complemented
392#1804C2×C15111yescharacteristic, complemented
393C22×SD16C22×C15111yescharacteristic
394C22×D8C22×C15111yescharacteristic
395C2×#124C22×C15111yescharacteristic
396C2×C22⋊Q8C22×C15111yescharacteristic
397C2×#121C22×C15111yescharacteristic
398C2×#121C22×C15111yescharacteristic
399C2×C4×D4—21no—
400C2×C4×D4C22×C15111yescharacteristic
401C22×C42C22×C15111yescharacteristic
402#463—24no—
403#432—24no—
404C2×#107C22×C15111yescharacteristic
405C2×#106C22×C15111yescharacteristic
406C2×C4⋊C8C22×C15111yescharacteristic
407C2×C4⋊C8C22×C15111yescharacteristic
408C2×#103C22×C15111yescharacteristic
409C2×#103C22×C15111yescharacteristic
410C2×#103C22×C15111yescharacteristic
411C2×#102C22×C15111yescharacteristic
412C2×#102C22×C15111yescharacteristic
413C2×#102C22×C15111yescharacteristic
414C2×#102C22×C15111yescharacteristic
415C2×#102C22×C15111yescharacteristic
416C2×C22⋊C8C22×C15111yescharacteristic
417C2×C22⋊C8C22×C15111yescharacteristic
418C2×#97C22×C15111yescharacteristic
419C2×#97C22×C15111yescharacteristic
420#391C22×C15111yescharacteristic
421#390C22×C15111yescharacteristic
422#390C22×C15111yescharacteristic
423#389C22×C15111yescharacteristic
424#388—21no—
425#388—21no—
426#388—21no—
427#386—21no—
428#386—21no—
429#386—21no—
430#382C22×C15111yescharacteristic
431#380C22×C15111yescharacteristic
432C4×C4⋊C4C22×C15111yescharacteristic
433C4×C22⋊C4—21no—
434#340C22×C15111yescharacteristic
435#340C22×C15111yescharacteristic
436#340C22×C15111yescharacteristic
437#340C22×C15111yescharacteristic
438C22×Q8C23×C15111yescharacteristic
439C22×D4—21no—
440C22×D4—21no—
441C22×D4C23×C15111yescharacteristic
442C22×D4C23×C15111yescharacteristic
443C23×C4—21no—
444C23×C4D4×C15111yescharacteristic
445C23×C4D4×C15111yescharacteristic
446C23×C4C23×C15111yescharacteristic
447C2×SD16—22no—
448C2×SD16—22no—
449C2×SD16—41no—
450C2×D8—22no—
451C2×D8—22no—
452C2×D8—41no—
453C22×C8C23×C15111yescharacteristic
454C22×C8C23×C15111yescharacteristic
455C22×C8C23×C15111yescharacteristic
456C22×C8C23×C15111yescharacteristic
457#124—22no—
458#124—22no—
459C22⋊Q8—41no—
460C22⋊Q8—41no—
461#121—22no—
462#121—22no—
463#121—41no—
464#121—41no—
465C4×D4—22no—
466C4×D4—22no—
467C4×D4—44no—
468C2×C4⋊C4—21no—
469C2×C4⋊C4—21no—
470C2×C4⋊C4C23×C15111yescharacteristic
471C2×C4⋊C4C23×C15111yescharacteristic
472C2×C4⋊C4C23×C15111yescharacteristic
473C2×C4⋊C4C23×C15111yescharacteristic
474C2×C4⋊C4C23×C15111yescharacteristic
475C2×C22⋊C4—21no—
476C2×C22⋊C4—21no—
477C2×C22⋊C4—21no—
478C2×C22⋊C4—21no—
479C2×C22⋊C4—21no—
480C2×C22⋊C4—21no—
481C2×C22⋊C4—21no—
482C2×C22⋊C4—21no—
483C2×C22⋊C4—21no—
484C2×C22⋊C4—21no—
485C2×C22⋊C4—21no—
486C2×C42—22no—
487C2×C42—22no—
488C2×C42—21no—
489C2×C42D4×C15111yescharacteristic
490C2×C42D4×C15111yescharacteristic
491C2×C42C23×C15111yescharacteristic
492C2×C42C23×C15111yescharacteristic
493#107—41no—
494#106—41no—
495C4⋊C8—22no—
496C4⋊C8D4×C15114yescomplemented
497#103—22no—
498#103—22no—
499#103—41no—
500#102—22no—
501#102—22no—
502#102—41no—
503#102—41no—
504#102—41no—
505C22⋊C8—22no—
506C22⋊C8—22no—
507#97—22no—
508#97—22no—
509#95—21no—
510#95—21no—
511#95—21no—
512#95—21no—
513#95—21no—
514#95—21no—
515#95—21no—
516C24—21no—
517C24—21no—
518C24C2×D4×C15111yescharacteristic
519C2×Q8—21no—
520C2×Q8—21no—
521C2×Q8—21no—
522C2×Q8—21no—
523C2×Q8—21no—
524C2×Q8—21no—
525C2×D4—24no—
526C2×D4—21no—
527C2×D4—21no—
528C2×D4—21no—
529C2×D4—21no—
530C2×D4—21no—
531C2×D4—21no—
532C2×D4—21no—
533C2×D4—21no—
534C2×D4—21no—
535C2×D4—21no—
536C2×D4—21no—
537C2×D4—42no—
538C2×D4—42no—
539C2×D4—42no—
540C2×D4—42no—
541C2×D4—42no—
542C2×D4#41×C15112yes—
543C22×C4—22no—
544C22×C4—21no—
545C22×C4—22no—
546C22×C4—22no—
547C22×C4—21no—
548C22×C4—21no—
549C22×C4—21no—
550C22×C4—21no—
551C22×C4—21no—
552C22×C4—21no—
553C22×C4—21no—
554C22×C4—21no—
555C22×C4—21no—
556C22×C4—21no—
557C22×C4—21no—
558C22×C4—41no—
559C22×C4—41no—
560C22×C4—41no—
561C22×C4—42no—
562C22×C4—42no—
563C22×C4—42no—
564C22×C4C2×D4×C15111yescharacteristic
565C22×C4C2×D4×C15111yescharacteristic
566C22×C4C2×D4×C15111yescharacteristic
567C22×C4C2×D4×C15111yescharacteristic
568C22×C4C2×D4×C15111yescharacteristic
569C22×C4C24×C15111yescharacteristic
570SD16—44no—
571D8—44no—
572C2×C8—21no—
573C2×C8—21no—
574C2×C8—21no—
575C2×C8—21no—
576C2×C8—21no—
577C2×C8—21no—
578C2×C8—21no—
579C2×C8—21no—
580C2×C8—21no—
581C2×C8—21no—
582C2×C8C2×D4×C15112yes—
583C2×C8C2×D4×C15112yes—
584C4⋊C4—21no—
585C4⋊C4—21no—
586C4⋊C4—21no—
587C4⋊C4—21no—
588C4⋊C4—21no—
589C4⋊C4—21no—
590C4⋊C4—21no—
591C4⋊C4—21no—
592C4⋊C4—21no—
593C4⋊C4—42no—
594C4⋊C4—42no—
595C4⋊C4#41×C15112yes—
596C22⋊C4—24no—
597C22⋊C4—42no—
598C22⋊C4—42no—
599C22⋊C4—42no—
600C22⋊C4—42no—
601C22⋊C4—42no—
602C22⋊C4—42no—
603C22⋊C4—42no—
604C22⋊C4—42no—
605C22⋊C4—42no—
606C22⋊C4—42no—
607C42—22no—
608C42—22no—
609C42—21no—
610C42—21no—
611C42—42no—
612C42C2×D4×C15112yes—
613C42#41×C15112yes—
614C23—21no—
615C23—21no—
616C23—21no—
617C23—21no—
618C23—21no—
619C23—21no—
620C23—22no—
621C23—41no—
622C23—41no—
623C23—41no—
624C23—41no—
625C23—41no—
626C23—41no—
627C23—41no—
628C23—41no—
629C23—41no—
630C23—41no—
631C23—41no—
632C23—41no—
633C23—41no—
634C23AGL(1,ℤ/8)×C15112yes—
635C23C22×D4×C15111yescharacteristic
636Q8—41no—
637Q8—41no—
638Q8—41no—
639Q8—41no—
640D4—22no—
641D4—22no—
642D4—48no—
643D4—41no—
644D4—41no—
645D4—41no—
646D4—41no—
647D4—41no—
648D4—41no—
649D4—84no—
650C2×C4—21no—
651C2×C4—21no—
652C2×C4—21no—
653C2×C4—21no—
654C2×C4—21no—
655C2×C4—21no—
656C2×C4—21no—
657C2×C4—21no—
658C2×C4—22no—
659C2×C4—21no—
660C2×C4—21no—
661C2×C4—21no—
662C2×C4—21no—
663C2×C4—21no—
664C2×C4—44no—
665C2×C4—44no—
666C2×C4—41no—
667C2×C4—41no—
668C2×C4—41no—
669C2×C4—41no—
670C2×C4—41no—
671C2×C4—41no—
672C2×C4—41no—
673C2×C4—41no—
674C2×C4—41no—
675C2×C4—41no—
676C2×C4—41no—
677C2×C4—41no—
678C2×C4—41no—
679C2×C4—41no—
680C2×C4—41no—
681C2×C4—41no—
682C2×C4—41no—
683C2×C4—41no—
684C2×C4—41no—
685C2×C4—41no—
686C2×C4—41no—
687C2×C4—84no—
688C2×C4#121×C15112yes—
689C2×C4#121×C15112yes—
690C2×C4C22×D4×C15111yescharacteristic
691C2×C4C2×#41×C15111yescharacteristic
692C2×C4C2×#41×C15111yescharacteristic
693C2×C4C2×#41×C15111yescharacteristic
694C2×C4H(5,𝔽2)×C15111yescharacteristic
695C2×C4H(5,𝔽2)×C15111yescharacteristic
696C8—22no—
697C8—22no—
698C8—41no—
699C8—41no—
700C22—22no—
701C22—22no—
702C22—22no—
703C22—41no—
704C22—41no—
705C22—41no—
706C22—41no—
707C22—42no—
708C22—42no—
709C22—42no—
710C22—81no—
711C22—81no—
712C22—81no—
713C22—81no—
714C22—81no—
715C22—81no—
716C22—81no—
717C22—81no—
718C22—81no—
719C22—81no—
720C22—81no—
721C22C2×#121×C15111yescharacteristic
722C22#525×C15111yescharacteristic
723C22#535×C15111yescharacteristic
724C22C2×AGL(1,ℤ/8)×C15111yescharacteristic
725C22#575×C15111yescharacteristic
726C22#575×C15111yescharacteristic
727C22#575×C15111yescharacteristic
728C4—22no—
729C4—22no—
730C4—42no—
731C4—41no—
732C4—41no—
733C4—41no—
734C4—81no—
735C4—81no—
736C4—81no—
737C4—81no—
738C4—81no—
739C4#546×C15111yescharacteristic
740C4#550×C15111yescharacteristic
741C4#553×C15111yescharacteristic
742C4#555×C15111yescharacteristic
743C2—42no—
744C2—82no—
745C2—161no—
746C2#2414×C15111yescharacteristic
747C2#3054×C15111yescharacteristic
748C2#3055×C15111yescharacteristic
749C2#3111×C15111yescharacteristic
750C2#3114×C15111yescharacteristic
751C2#3213×C15111yescharacteristic
752C2#3219×C15111yescharacteristic
subgroupG/H
center, socleC23×C151C22×D4
commutator, Frattini, cosocleC22×C4C24×C151
prime radical#1999×C151C2
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C151 ◁ C22×C42×C151 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×#463×C151C2semidirect
2. C2×#432×C151C2semidirect
3. #2850×C151C2semidirect
4. C4×#121×C151C2semidirect
5. #2035×C151C2semidirect
6. #2033×C151C2semidirect
7. #2000×C151C2semidirect
9. #1983×C151C2semidirect
10. #1973×C151C2semidirect
11. #1972×C151C2semidirect
12. #1949×C151C2semidirect
13. #1936×C151C2semidirect
14. #1935×C151C2semidirect
15. #1804×C151C2semidirect
119. C4⋊C8×C151D4semidirect
376. #24656C151direct (N × H)
377. C151#24656direct (N × H)
378. C2×#463C2×C151semidirect
379. C2×#432C2×C151semidirect
380. #2850C2×C151semidirect
381. C4×#121C2×C151semidirect
382. #2035C2×C151semidirect
383. #2033C2×C151semidirect
384. #2000C2×C151semidirect
386. #1983C2×C151semidirect
387. #1973C2×C151semidirect
388. #1972C2×C151semidirect
389. #1949C2×C151semidirect
390. #1936C2×C151semidirect
391. #1935C2×C151semidirect
392. #1804C2×C151semidirect
496. C4⋊C8D4×C151semidirect

Maximal subgroups

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

subgroupindex
C2×#463×C1512
C2×#432×C1512
#2850×C1512
C4×#121×C1512
#2035×C1512
#2033×C1512
#2000×C1512
#1999×C1512
#1983×C1512
#1973×C1512
#1972×C1512
#1949×C1512
#1936×C1512
#1935×C1512
#1804×C1512
#24656151