Finite Group Databasebeta

← C151×#24634 #50329559

Subgroups — C151×#24634 #50329559

Order 38656.

952 conjugacy classes of subgroups.

The subgroup lattice has 746 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#463×C151C211yesmaximal, characteristic, complemented
2C2×C4×D8×C151C211yesmaximal, characteristic, complemented
3#2544×C151C211yesmaximal, characteristic, complemented
4#2357×C151C211yesmaximal, characteristic, complemented
5#2055×C151C211yesmaximal, characteristic, complemented
6#2054×C151C211yesmaximal, characteristic, complemented
7#2012×C151C211yesmaximal, characteristic, complemented
8#2011×C151C211yesmaximal, characteristic
9#1983×C151C211yesmaximal, characteristic, complemented
10#1982×C151C211yesmaximal, characteristic, complemented
11#1958×C151C211yesmaximal, characteristic, complemented
12#1939×C151C211yesmaximal, characteristic, complemented
13#1928×C151C211yesmaximal, characteristic, complemented
14#1925×C151C211yesmaximal, characteristic, complemented
15#1804×C151C211yesmaximal, characteristic, complemented
16C22×SD16×C151C2211yescharacteristic
17C22×D8×C151C2211yescharacteristic
18C22×D8×C151C2211yescharacteristic
19C2×#127×C151C2211yescharacteristic
20C2×#124×C151C2211yescharacteristic
21C2×#124×C151C2211yescharacteristic
22C2×C4×D4×C151C2211yescharacteristic
23C2×C4×D4×C151C2211yescharacteristic
24#463×C151—24no—
25C4×D8×C151—24no—
26C2×#107×C151C2211yescharacteristic
27C2×C4⋊C8×C151C2211yescharacteristic
28C2×C4⋊C8×C151C2211yescharacteristic
29C2×C4⋊C8×C151C2211yescharacteristic
30C2×#103×C151C2211yescharacteristic
31C2×#103×C151C2211yescharacteristic
32C2×#103×C151C2211yescharacteristic
33C2×#102×C151C2211yescharacteristic
34C2×#102×C151C2211yescharacteristic
35C2×#102×C151C2211yescharacteristic
36C2×#102×C151C2211yescharacteristic
37C2×#102×C151C2211yescharacteristic
38C2×#102×C151C2211yescharacteristic
39C2×#102×C151C2211yescharacteristic
40C2×C4×C8×C151C2211yescharacteristic
41#394×C151—21no—
42#394×C151—21no—
43#391×C151C2211yescharacteristic
44#390×C151C2211yescharacteristic
45#390×C151C2211yescharacteristic
46#390×C151C2211yescharacteristic
47#388×C151—21no—
48#388×C151—21no—
49#386×C151—21no—
50#386×C151—21no—
51#382×C151C2211yescharacteristic
52#381×C151—21no—
53C4×C4⋊C4×C151C2211yescharacteristic
54C4×C4⋊C4×C151C2211yescharacteristic
55C4×C4⋊C4×C151C2211yescharacteristic
56C4×C22⋊C4×C151—21no—
57#340×C151C2211yescharacteristic
58#340×C151C2211yescharacteristic
59#336×C151C2211yescharacteristic
60#336×C151C2211yescharacteristic
61C22×Q8×C151C2311yescharacteristic
62C22×D4×C151—21no—
63C22×D4×C151—21no—
64C22×D4×C151C2311yescharacteristic
65C22×D4×C151C2311yescharacteristic
66C22×D4×C151C2311yescharacteristic
67C23×C4×C151—21no—
68C23×C4×C151—21no—
69C2×SD16×C151—22no—
70C2×SD16×C151—41no—
71C2×SD16×C151—41no—
72C2×D8×C151—22no—
73C2×D8×C151—22no—
74C2×D8×C151—22no—
75C2×D8×C151—22no—
76C2×D8×C151—41no—
77C2×D8×C151—41no—
78C22×C8×C151C2311yescharacteristic
79C22×C8×C151C2311yescharacteristic
80C22×C8×C151C2311yescharacteristic
81C22×C8×C151C2311yescharacteristic
82#127×C151—22no—
83#127×C151—41no—
84#124×C151—22no—
85#124×C151—22no—
86#124×C151—22no—
87#124×C151—41no—
88C4×D4×C151—22no—
89C4×D4×C151—22no—
90C4×D4×C151—22no—
91C4×D4×C151D414yescomplemented
92C2×C4⋊C4×C151D411yescharacteristic
93C2×C4⋊C4×C151D411yescharacteristic
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×C22⋊C4×C151—21no—
110C2×C42×C151—21no—
111C2×C42×C151—21no—
112C2×C42×C151C2311yescharacteristic
113C2×C42×C151C2311yescharacteristic
114C2×C42×C151C2311yescharacteristic
115#107×C151—22no—
116C4⋊C8×C151—22no—
117C4⋊C8×C151—41no—
118C4⋊C8×C151—41no—
119#103×C151—22no—
120#103×C151—22no—
121#103×C151—41no—
122#102×C151—22no—
123#102×C151—22no—
124#102×C151—22no—
125#102×C151—22no—
126#102×C151—41no—
127#102×C151—41no—
128#102×C151—41no—
129C4×C8×C151—22no—
130#95×C151—21no—
131#95×C151—21no—
132#95×C151—21no—
133#95×C151—21no—
134#95×C151—21no—
135#95×C151—21no—
136#95×C151D411yescharacteristic
137#95×C151D411yescharacteristic
138C24×C151—21no—
139C24×C151—21no—
140C24×C151—21no—
141C2×Q8×C151—21no—
142C2×Q8×C151—21no—
143C2×Q8×C151—21no—
144C2×Q8×C151—21no—
145C2×Q8×C151—21no—
146C2×Q8×C151—21no—
147C2×D4×C151—21no—
148C2×D4×C151—21no—
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—21no—
161C2×D4×C151—21no—
162C2×D4×C151—21no—
163C2×D4×C151—42no—
164C2×D4×C151—42no—
165C2×D4×C151—42no—
166C2×D4×C151—42no—
167C2×D4×C151—81no—
168C2×D4×C151—81no—
169C2×D4×C151C2×D412yes—
170C2×D4×C151#4112yes—
171C22×C4×C151—21no—
172C22×C4×C151—24no—
173C22×C4×C151—21no—
174C22×C4×C151—21no—
175C22×C4×C151—21no—
176C22×C4×C151—21no—
177C22×C4×C151—42no—
178C22×C4×C151—81no—
179C22×C4×C151—81no—
180C22×C4×C151—81no—
181C22×C4×C151—81no—
182C22×C4×C151C2×D411yescharacteristic
183C22×C4×C151C2×D411yescharacteristic
184C22×C4×C151C2×D411yescharacteristic
185C22×C4×C151C2×D411yescharacteristic
186C22×C4×C151C2×D411yescharacteristic
187C22×C4×C151C2×D411yescharacteristic
188C22×C4×C151C2411yescharacteristic
189SD16×C151—44no—
190D8×C151—28no—
191D8×C151—44no—
192C2×C8×C151—21no—
193C2×C8×C151—21no—
194C2×C8×C151—21no—
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#4112yes—
204C4⋊C4×C151—22no—
205C4⋊C4×C151—21no—
206C4⋊C4×C151—21no—
207C4⋊C4×C151—21no—
208C4⋊C4×C151—21no—
209C4⋊C4×C151—21no—
210C4⋊C4×C151—21no—
211C4⋊C4×C151—21no—
212C4⋊C4×C151—41no—
213C4⋊C4×C151C2×D412yes—
214C22⋊C4×C151—24no—
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—81no—
223C22⋊C4×C151—81no—
224C22⋊C4×C151—81no—
225C22⋊C4×C151—81no—
226C42×C151—21no—
227C42×C151—21no—
228C42×C151—21no—
229C42×C151—21no—
230C42×C151—81no—
231C42×C151—81no—
232C42×C151C2×D412yes—
233C42×C151#4112yes—
234C23×C151—22no—
235C23×C151—22no—
236C23×C151—41no—
237C23×C151—41no—
238C23×C151—41no—
239C23×C151—41no—
240C23×C151—41no—
241C23×C151—41no—
242C23×C151—41no—
243C23×C151—41no—
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×C151C22×D411yescharacteristic
256Q8×C151—41no—
257Q8×C151—41no—
258Q8×C151—41no—
259Q8×C151—41no—
260D4×C151—22no—
261D4×C151—22no—
262D4×C151—22no—
263D4×C151—22no—
264D4×C151—41no—
265D4×C151—41no—
266D4×C151—41no—
267D4×C151—41no—
268D4×C151—41no—
269D4×C151—41no—
270D4×C151—41no—
271D4×C151—41no—
272D4×C151—84no—
273D4×C151—84no—
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—22no—
281C2×C4×C151—21no—
282C2×C4×C151—21no—
283C2×C4×C151—21no—
284C2×C4×C151—21no—
285C2×C4×C151—21no—
286C2×C4×C151—21no—
287C2×C4×C151—21no—
288C2×C4×C151—21no—
289C2×C4×C151—21no—
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—84no—
305C2×C4×C151—84no—
306C2×C4×C151#12112yes—
307C2×C4×C151#12112yes—
308C2×C4×C151#13512yes—
309C2×C4×C151C22×D411yescharacteristic
310C2×C4×C151C2×#4111yescharacteristic
311C2×C4×C151C2×#4111yescharacteristic
312C2×C4×C151C2×#4111yescharacteristic
313C2×C4×C151H(5,𝔽2)11yescharacteristic
314C2×C4×C151H(5,𝔽2)11yescharacteristic
315C8×C151—22no—
316C8×C151—41no—
317C8×C151—41no—
318C8×C151—41no—
319C22×C151—42no—
320C22×C151—42no—
321C22×C151—42no—
322C22×C151—42no—
323C22×C151—42no—
324C22×C151—42no—
325C22×C151—81no—
326C22×C151—81no—
327C22×C151—81no—
328C22×C151—81no—
329C22×C151—81no—
330C22×C151—81no—
331C22×C151—81no—
332C22×C151—81no—
333C22×C151—81no—
334C22×C151—81no—
335C22×C151—81no—
336C22×C151—81no—
337C22×C151—81no—
338C22×C151—81no—
339C22×C151—81no—
340C22×C151C2×#12111yescharacteristic
341C22×C151#54611yescharacteristic
342C22×C151#55011yescharacteristic
343C22×C151C2×#13511yescharacteristic
344C22×C151#57511yescharacteristic
345C22×C151#57611yescharacteristic
346C22×C151#57611yescharacteristic
347C4×C151—22no—
348C4×C151—22no—
349C4×C151—22no—
350C4×C151—42no—
351C4×C151—41no—
352C4×C151—41no—
353C4×C151—41no—
354C4×C151—81no—
355C4×C151—81no—
356C4×C151—81no—
357C4×C151—81no—
358C4×C151#52511yescharacteristic
359C4×C151#53511yescharacteristic
360C4×C151#55311yescharacteristic
361C4×C151#55511yescharacteristic
362C2×C151—82no—
363C2×C151—82no—
364C2×C151—161no—
365C2×C151#241411yescharacteristic
366C2×C151#303511yescharacteristic
367C2×C151#304111yescharacteristic
368C2×C151#329711yescharacteristic
369C2×C151#332211yescharacteristic
370C2×C151#339611yescharacteristic
371C2×C151#340311yescharacteristic
372#24634C15111yesmaximal, characteristic, direct product factor, Sylow
373C151#2463411yescharacteristic, direct product factor, Sylow
374C2×#463C2×C15111yescharacteristic, complemented
375C2×C4×D8C2×C15111yescharacteristic, complemented
376#2544C2×C15111yescharacteristic, complemented
377#2357C2×C15111yescharacteristic, complemented
378#2055C2×C15111yescharacteristic, complemented
379#2054C2×C15111yescharacteristic, complemented
380#2012C2×C15111yescharacteristic, complemented
381#2011C2×C15111yescharacteristic
382#1983C2×C15111yescharacteristic, complemented
383#1982C2×C15111yescharacteristic, complemented
384#1958C2×C15111yescharacteristic, complemented
385#1939C2×C15111yescharacteristic, complemented
386#1928C2×C15111yescharacteristic, complemented
387#1925C2×C15111yescharacteristic, complemented
388#1804C2×C15111yescharacteristic, complemented
389C22×SD16C22×C15111yescharacteristic
390C22×D8C22×C15111yescharacteristic
391C22×D8C22×C15111yescharacteristic
392C2×#127C22×C15111yescharacteristic
393C2×#124C22×C15111yescharacteristic
394C2×#124C22×C15111yescharacteristic
395C2×C4×D4C22×C15111yescharacteristic
396C2×C4×D4C22×C15111yescharacteristic
397#463—24no—
398C4×D8—24no—
399C2×#107C22×C15111yescharacteristic
400C2×C4⋊C8C22×C15111yescharacteristic
401C2×C4⋊C8C22×C15111yescharacteristic
402C2×C4⋊C8C22×C15111yescharacteristic
403C2×#103C22×C15111yescharacteristic
404C2×#103C22×C15111yescharacteristic
405C2×#103C22×C15111yescharacteristic
406C2×#102C22×C15111yescharacteristic
407C2×#102C22×C15111yescharacteristic
408C2×#102C22×C15111yescharacteristic
409C2×#102C22×C15111yescharacteristic
410C2×#102C22×C15111yescharacteristic
411C2×#102C22×C15111yescharacteristic
412C2×#102C22×C15111yescharacteristic
413C2×C4×C8C22×C15111yescharacteristic
414#394—21no—
415#394—21no—
416#391C22×C15111yescharacteristic
417#390C22×C15111yescharacteristic
418#390C22×C15111yescharacteristic
419#390C22×C15111yescharacteristic
420#388—21no—
421#388—21no—
422#386—21no—
423#386—21no—
424#382C22×C15111yescharacteristic
425#381—21no—
426C4×C4⋊C4C22×C15111yescharacteristic
427C4×C4⋊C4C22×C15111yescharacteristic
428C4×C4⋊C4C22×C15111yescharacteristic
429C4×C22⋊C4—21no—
430#340C22×C15111yescharacteristic
431#340C22×C15111yescharacteristic
432#336C22×C15111yescharacteristic
433#336C22×C15111yescharacteristic
434C22×Q8C23×C15111yescharacteristic
435C22×D4—21no—
436C22×D4—21no—
437C22×D4C23×C15111yescharacteristic
438C22×D4C23×C15111yescharacteristic
439C22×D4C23×C15111yescharacteristic
440C23×C4—21no—
441C23×C4—21no—
442C2×SD16—22no—
443C2×SD16—41no—
444C2×SD16—41no—
445C2×D8—22no—
446C2×D8—22no—
447C2×D8—22no—
448C2×D8—22no—
449C2×D8—41no—
450C2×D8—41no—
451C22×C8C23×C15111yescharacteristic
452C22×C8C23×C15111yescharacteristic
453C22×C8C23×C15111yescharacteristic
454C22×C8C23×C15111yescharacteristic
455#127—22no—
456#127—41no—
457#124—22no—
458#124—22no—
459#124—22no—
460#124—41no—
461C4×D4—22no—
462C4×D4—22no—
463C4×D4—22no—
464C4×D4D4×C15114yescomplemented
465C2×C4⋊C4D4×C15111yescharacteristic
466C2×C4⋊C4D4×C15111yescharacteristic
467C2×C4⋊C4C23×C15111yescharacteristic
468C2×C4⋊C4C23×C15111yescharacteristic
469C2×C4⋊C4C23×C15111yescharacteristic
470C2×C4⋊C4C23×C15111yescharacteristic
471C2×C22⋊C4—21no—
472C2×C22⋊C4—21no—
473C2×C22⋊C4—21no—
474C2×C22⋊C4—21no—
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×C42—21no—
484C2×C42—21no—
485C2×C42C23×C15111yescharacteristic
486C2×C42C23×C15111yescharacteristic
487C2×C42C23×C15111yescharacteristic
488#107—22no—
489C4⋊C8—22no—
490C4⋊C8—41no—
491C4⋊C8—41no—
492#103—22no—
493#103—22no—
494#103—41no—
495#102—22no—
496#102—22no—
497#102—22no—
498#102—22no—
499#102—41no—
500#102—41no—
501#102—41no—
502C4×C8—22no—
503#95—21no—
504#95—21no—
505#95—21no—
506#95—21no—
507#95—21no—
508#95—21no—
509#95D4×C15111yescharacteristic
510#95D4×C15111yescharacteristic
511C24—21no—
512C24—21no—
513C24—21no—
514C2×Q8—21no—
515C2×Q8—21no—
516C2×Q8—21no—
517C2×Q8—21no—
518C2×Q8—21no—
519C2×Q8—21no—
520C2×D4—21no—
521C2×D4—21no—
522C2×D4—21no—
523C2×D4—21no—
524C2×D4—21no—
525C2×D4—21no—
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—42no—
537C2×D4—42no—
538C2×D4—42no—
539C2×D4—42no—
540C2×D4—81no—
541C2×D4—81no—
542C2×D4C2×D4×C15112yes—
543C2×D4#41×C15112yes—
544C22×C4—21no—
545C22×C4—24no—
546C22×C4—21no—
547C22×C4—21no—
548C22×C4—21no—
549C22×C4—21no—
550C22×C4—42no—
551C22×C4—81no—
552C22×C4—81no—
553C22×C4—81no—
554C22×C4—81no—
555C22×C4C2×D4×C15111yescharacteristic
556C22×C4C2×D4×C15111yescharacteristic
557C22×C4C2×D4×C15111yescharacteristic
558C22×C4C2×D4×C15111yescharacteristic
559C22×C4C2×D4×C15111yescharacteristic
560C22×C4C2×D4×C15111yescharacteristic
561C22×C4C24×C15111yescharacteristic
562SD16—44no—
563D8—28no—
564D8—44no—
565C2×C8—21no—
566C2×C8—21no—
567C2×C8—21no—
568C2×C8—21no—
569C2×C8—21no—
570C2×C8—21no—
571C2×C8—21no—
572C2×C8—21no—
573C2×C8—21no—
574C2×C8—21no—
575C2×C8—21no—
576C2×C8#41×C15112yes—
577C4⋊C4—22no—
578C4⋊C4—21no—
579C4⋊C4—21no—
580C4⋊C4—21no—
581C4⋊C4—21no—
582C4⋊C4—21no—
583C4⋊C4—21no—
584C4⋊C4—21no—
585C4⋊C4—41no—
586C4⋊C4C2×D4×C15112yes—
587C22⋊C4—24no—
588C22⋊C4—42no—
589C22⋊C4—42no—
590C22⋊C4—42no—
591C22⋊C4—42no—
592C22⋊C4—42no—
593C22⋊C4—42no—
594C22⋊C4—42no—
595C22⋊C4—81no—
596C22⋊C4—81no—
597C22⋊C4—81no—
598C22⋊C4—81no—
599C42—21no—
600C42—21no—
601C42—21no—
602C42—21no—
603C42—81no—
604C42—81no—
605C42C2×D4×C15112yes—
606C42#41×C15112yes—
607C23—22no—
608C23—22no—
609C23—41no—
610C23—41no—
611C23—41no—
612C23—41no—
613C23—41no—
614C23—41no—
615C23—41no—
616C23—41no—
617C23—41no—
618C23—41no—
619C23—41no—
620C23—41no—
621C23—41no—
622C23—41no—
623C23—41no—
624C23—41no—
625C23—41no—
626C23—41no—
627C23—41no—
628C23C22×D4×C15111yescharacteristic
629Q8—41no—
630Q8—41no—
631Q8—41no—
632Q8—41no—
633D4—22no—
634D4—22no—
635D4—22no—
636D4—22no—
637D4—41no—
638D4—41no—
639D4—41no—
640D4—41no—
641D4—41no—
642D4—41no—
643D4—41no—
644D4—41no—
645D4—84no—
646D4—84no—
647C2×C4—21no—
648C2×C4—21no—
649C2×C4—21no—
650C2×C4—21no—
651C2×C4—21no—
652C2×C4—21no—
653C2×C4—22no—
654C2×C4—21no—
655C2×C4—21no—
656C2×C4—21no—
657C2×C4—21no—
658C2×C4—21no—
659C2×C4—21no—
660C2×C4—21no—
661C2×C4—21no—
662C2×C4—21no—
663C2×C4—41no—
664C2×C4—41no—
665C2×C4—41no—
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—84no—
678C2×C4—84no—
679C2×C4#121×C15112yes—
680C2×C4#121×C15112yes—
681C2×C4#135×C15112yes—
682C2×C4C22×D4×C15111yescharacteristic
683C2×C4C2×#41×C15111yescharacteristic
684C2×C4C2×#41×C15111yescharacteristic
685C2×C4C2×#41×C15111yescharacteristic
686C2×C4H(5,𝔽2)×C15111yescharacteristic
687C2×C4H(5,𝔽2)×C15111yescharacteristic
688C8—22no—
689C8—41no—
690C8—41no—
691C8—41no—
692C22—42no—
693C22—42no—
694C22—42no—
695C22—42no—
696C22—42no—
697C22—42no—
698C22—81no—
699C22—81no—
700C22—81no—
701C22—81no—
702C22—81no—
703C22—81no—
704C22—81no—
705C22—81no—
706C22—81no—
707C22—81no—
708C22—81no—
709C22—81no—
710C22—81no—
711C22—81no—
712C22—81no—
713C22C2×#121×C15111yescharacteristic
714C22#546×C15111yescharacteristic
715C22#550×C15111yescharacteristic
716C22C2×#135×C15111yescharacteristic
717C22#575×C15111yescharacteristic
718C22#576×C15111yescharacteristic
719C22#576×C15111yescharacteristic
720C4—22no—
721C4—22no—
722C4—22no—
723C4—42no—
724C4—41no—
725C4—41no—
726C4—41no—
727C4—81no—
728C4—81no—
729C4—81no—
730C4—81no—
731C4#525×C15111yescharacteristic
732C4#535×C15111yescharacteristic
733C4#553×C15111yescharacteristic
734C4#555×C15111yescharacteristic
735C2—82no—
736C2—82no—
737C2—161no—
738C2#2414×C15111yescharacteristic
739C2#3035×C15111yescharacteristic
740C2#3041×C15111yescharacteristic
741C2#3297×C15111yescharacteristic
742C2#3322×C15111yescharacteristic
743C2#3396×C15111yescharacteristic
744C2#3403×C15111yescharacteristic
subgroupG/H
center, socleC23×C151C22×D4
commutator, Frattini, cosocleC22×C4C24×C151
prime radical#2011×C151C2
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C151 ◁ C4×C4⋊C4×C151 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×#463×C151C2semidirect
2. C2×C4×D8×C151C2semidirect
3. #2544×C151C2semidirect
4. #2357×C151C2semidirect
5. #2055×C151C2semidirect
6. #2054×C151C2semidirect
7. #2012×C151C2semidirect
9. #1983×C151C2semidirect
10. #1982×C151C2semidirect
11. #1958×C151C2semidirect
12. #1939×C151C2semidirect
13. #1928×C151C2semidirect
14. #1925×C151C2semidirect
15. #1804×C151C2semidirect
91. C4×D4×C151D4semidirect
372. #24634C151direct (N × H)
373. C151#24634direct (N × H)
374. C2×#463C2×C151semidirect
375. C2×C4×D8C2×C151semidirect
376. #2544C2×C151semidirect
377. #2357C2×C151semidirect
378. #2055C2×C151semidirect
379. #2054C2×C151semidirect
380. #2012C2×C151semidirect
382. #1983C2×C151semidirect
383. #1982C2×C151semidirect
384. #1958C2×C151semidirect
385. #1939C2×C151semidirect
386. #1928C2×C151semidirect
387. #1925C2×C151semidirect
388. #1804C2×C151semidirect
464. C4×D4D4×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×C4×D8×C1512
#2544×C1512
#2357×C1512
#2055×C1512
#2054×C1512
#2012×C1512
#2011×C1512
#1983×C1512
#1982×C1512
#1958×C1512
#1939×C1512
#1928×C1512
#1925×C1512
#1804×C1512
#24634151