Finite Group Databasebeta

← C151×#14824 #50319749

Subgroups — C151×#14824 #50319749

Order 38656.

2238 conjugacy classes of subgroups.

The subgroup lattice has 802 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C4×D4×C151C211yesmaximal, characteristic
2C2×#398×C151C211yesmaximal, characteristic, complemented
3C2×#397×C151C211yesmaximal, characteristic, complemented
4C2×#394×C151C212yesmaximal
5C2×#380×C151C211yesmaximal, characteristic, complemented
6#1441×C151C211yesmaximal, characteristic, complemented
7#1440×C151C212yesmaximal, complemented
8#1439×C151C211yesmaximal, characteristic, complemented
9#1436×C151C212yesmaximal, complemented
10C22⋊#95×C151C211yesmaximal, characteristic, complemented
11C22⋊#95×C151C212yesmaximal, complemented
12C23×D4×C151C2211yescharacteristic
13C24×C4×C151C2211yescharacteristic
14C24×C4×C151C2211yescharacteristic
15C2×C4×D4×C151—24no—
16C2×C4×D4×C151—24no—
17C2×C4×D4×C151—24no—
18C22×C4⋊C4×C151C2212yes—
19C22×C4⋊C4×C151C2211yescharacteristic
20C22×C4⋊C4×C151C2211yescharacteristic
21C22×C4⋊C4×C151C2211yescharacteristic
22C22×C22⋊C4×C151C2212yes—
23C22×C22⋊C4×C151C2212yes—
24C22×C22⋊C4×C151C2211yescharacteristic
25C22×C22⋊C4×C151C2212yes—
26C22×C22⋊C4×C151C2212yes—
27C22×C22⋊C4×C151C2211yescharacteristic
28C22×C42×C151C2211yescharacteristic
29#398×C151—24no—
30#397×C151—24no—
31#394×C151—28no—
32#380×C151—24no—
33C2×#95×C151C2212yes—
34C2×#95×C151C2211yescharacteristic
35C2×#95×C151C2212yes—
36C2×#95×C151C2211yescharacteristic
37C2×#95×C151C2212yes—
38C2×#95×C151C2212yes—
39C2×#95×C151C2212yes—
40C2×#95×C151C2212yes—
41C2×#95×C151C2212yes—
42C25×C151C2311yescharacteristic
43C25×C151C2311yescharacteristic
44C22×D4×C151—22no—
45C22×D4×C151—22no—
46C22×D4×C151—22no—
47C22×D4×C151—22no—
48C22×D4×C151—22no—
49C22×D4×C151—22no—
50C22×D4×C151D414yes—
51C23×C4×C151—22no—
52C23×C4×C151—22no—
53C23×C4×C151—22no—
54C23×C4×C151—22no—
55C23×C4×C151—24no—
56C23×C4×C151—24no—
57C23×C4×C151—22no—
58C23×C4×C151—42no—
59C23×C4×C151—42no—
60C23×C4×C151D414yes—
61C23×C4×C151C2312yes—
62C23×C4×C151C2312yes—
63C23×C4×C151C2312yes—
64C23×C4×C151C2311yescharacteristic
65C23×C4×C151C2311yescharacteristic
66C23×C4×C151C2312yes—
67C23×C4×C151C2311yescharacteristic
68C23×C4×C151C2311yescharacteristic
69C23×C4×C151C2311yescharacteristic
70C4×D4×C151—232no—
71C2×C4⋊C4×C151—22no—
72C2×C4⋊C4×C151—22no—
73C2×C4⋊C4×C151—22no—
74C2×C4⋊C4×C151—22no—
75C2×C4⋊C4×C151—24no—
76C2×C4⋊C4×C151—22no—
77C2×C4⋊C4×C151—22no—
78C2×C4⋊C4×C151—24no—
79C2×C4⋊C4×C151—24no—
80C2×C4⋊C4×C151—42no—
81C2×C4⋊C4×C151D414yes—
82C2×C22⋊C4×C151—22no—
83C2×C22⋊C4×C151—22no—
84C2×C22⋊C4×C151—22no—
85C2×C22⋊C4×C151—22no—
86C2×C22⋊C4×C151—24no—
87C2×C22⋊C4×C151—24no—
88C2×C22⋊C4×C151—22no—
89C2×C22⋊C4×C151—24no—
90C2×C22⋊C4×C151—24no—
91C2×C22⋊C4×C151—24no—
92C2×C22⋊C4×C151—24no—
93C2×C22⋊C4×C151—24no—
94C2×C22⋊C4×C151—24no—
95C2×C22⋊C4×C151—24no—
96C2×C22⋊C4×C151—24no—
97C2×C22⋊C4×C151—42no—
98C2×C22⋊C4×C151—42no—
99C2×C22⋊C4×C151D414yes—
100C2×C42×C151—22no—
101C2×C42×C151—22no—
102C2×C42×C151—22no—
103#95×C151—24no—
104#95×C151—24no—
105#95×C151—22no—
106#95×C151—24no—
107#95×C151—22no—
108#95×C151—24no—
109#95×C151—24no—
110#95×C151—24no—
111#95×C151—42no—
112C24×C151—21no—
113C24×C151—21no—
114C24×C151—21no—
115C24×C151—21no—
116C24×C151—22no—
117C24×C151—22no—
118C24×C151—22no—
119C24×C151—22no—
120C24×C151—21no—
121C24×C151—21no—
122C24×C151—21no—
123C24×C151—21no—
124C24×C151—22no—
125C24×C151—22no—
126C24×C151—22no—
127C24×C151—22no—
128C24×C151C2×D412yes—
129C24×C151C2×D412yes—
130C24×C151C2×D412yes—
131C24×C151C2×D412yes—
132C24×C151#4112yes—
133C24×C151#4112yes—
134C24×C151C2411yescharacteristic
135C2×D4×C151—28no—
136C2×D4×C151—28no—
137C2×D4×C151—28no—
138C2×D4×C151—28no—
139C2×D4×C151—28no—
140C2×D4×C151—28no—
141C2×D4×C151—28no—
142C22×C4×C151—21no—
143C22×C4×C151—21no—
144C22×C4×C151—21no—
145C22×C4×C151—21no—
146C22×C4×C151—22no—
147C22×C4×C151—21no—
148C22×C4×C151—21no—
149C22×C4×C151—22no—
150C22×C4×C151—22no—
151C22×C4×C151—28no—
152C22×C4×C151—22no—
153C22×C4×C151—21no—
154C22×C4×C151—21no—
155C22×C4×C151—22no—
156C22×C4×C151—21no—
157C22×C4×C151—21no—
158C22×C4×C151—22no—
159C22×C4×C151—22no—
160C22×C4×C151—22no—
161C22×C4×C151—22no—
162C22×C4×C151—22no—
163C22×C4×C151—22no—
164C22×C4×C151—22no—
165C22×C4×C151—22no—
166C22×C4×C151—28no—
167C22×C4×C151—28no—
168C22×C4×C151—22no—
169C22×C4×C151—22no—
170C22×C4×C151—22no—
171C22×C4×C151—22no—
172C22×C4×C151—22no—
173C22×C4×C151—22no—
174C22×C4×C151—22no—
175C22×C4×C151—22no—
176C22×C4×C151—22no—
177C22×C4×C151—22no—
178C22×C4×C151—22no—
179C22×C4×C151—22no—
180C22×C4×C151—22no—
181C22×C4×C151—22no—
182C22×C4×C151—22no—
183C22×C4×C151—22no—
184C22×C4×C151—22no—
185C22×C4×C151—22no—
186C22×C4×C151—22no—
187C22×C4×C151—22no—
188C22×C4×C151—22no—
189C22×C4×C151—44no—
190C22×C4×C151—48no—
191C22×C4×C151—48no—
192C22×C4×C151—48no—
193C22×C4×C151—48no—
194C22×C4×C151—44no—
195C22×C4×C151—44no—
196C22×C4×C151C2×D412yes—
197C22×C4×C151C2×D412yes—
198C22×C4×C151C2×D412yes—
199C22×C4×C151C2×D412yes—
200C22×C4×C151C2×D412yes—
201C22×C4×C151C2×D412yes—
202C22×C4×C151C2×D412yes—
203C22×C4×C151C2×D412yes—
204C22×C4×C151#4114yes—
205C22×C4×C151#4112yes—
206C22×C4×C151#4114yes—
207C4⋊C4×C151—28no—
208C4⋊C4×C151—44no—
209C4⋊C4×C151—44no—
210C4⋊C4×C151—48no—
211C22⋊C4×C151—28no—
212C22⋊C4×C151—28no—
213C22⋊C4×C151—48no—
214C22⋊C4×C151—48no—
215C22⋊C4×C151—48no—
216C22⋊C4×C151—48no—
217C42×C151—28no—
218C23×C151—22no—
219C23×C151—22no—
220C23×C151—22no—
221C23×C151—22no—
222C23×C151—22no—
223C23×C151—22no—
224C23×C151—22no—
225C23×C151—22no—
226C23×C151—22no—
227C23×C151—22no—
228C23×C151—22no—
229C23×C151—22no—
230C23×C151—22no—
231C23×C151—24no—
232C23×C151—22no—
233C23×C151—22no—
234C23×C151—22no—
235C23×C151—24no—
236C23×C151—24no—
237C23×C151—24no—
238C23×C151—24no—
239C23×C151—24no—
240C23×C151—24no—
241C23×C151—24no—
242C23×C151—24no—
243C23×C151—24no—
244C23×C151—41no—
245C23×C151—42no—
246C23×C151—42no—
247C23×C151—42no—
248C23×C151—41no—
249C23×C151—41no—
250C23×C151—41no—
251C23×C151—42no—
252C23×C151—42no—
253C23×C151—42no—
254C23×C151—42no—
255C23×C151—42no—
256C23×C151—42no—
257C23×C151—42no—
258C23×C151—42no—
259C23×C151—42no—
260C23×C151—42no—
261C23×C151—42no—
262C23×C151#12114yes—
263C23×C151#12114yes—
264C23×C151C22×D411yescharacteristic
265C23×C151C22×D411yescharacteristic
266C23×C151C22×D411yescharacteristic
267C23×C151C22×D411yescharacteristic
268C23×C151C2×#4111yescharacteristic
269C23×C151C2×#4111yescharacteristic
270C23×C151C2×#4111yescharacteristic
271C23×C151C2×#4112yes—
272C23×C151C2×#4112yes—
273C23×C151H(5,𝔽2)12yes—
274C23×C1512−1+412yes—
275D4×C151—232no—
276C2×C4×C151—22no—
277C2×C4×C151—22no—
278C2×C4×C151—22no—
279C2×C4×C151—22no—
280C2×C4×C151—22no—
281C2×C4×C151—22no—
282C2×C4×C151—22no—
283C2×C4×C151—22no—
284C2×C4×C151—22no—
285C2×C4×C151—22no—
286C2×C4×C151—24no—
287C2×C4×C151—24no—
288C2×C4×C151—24no—
289C2×C4×C151—24no—
290C2×C4×C151—22no—
291C2×C4×C151—22no—
292C2×C4×C151—24no—
293C2×C4×C151—24no—
294C2×C4×C151—24no—
295C2×C4×C151—24no—
296C2×C4×C151—24no—
297C2×C4×C151—416no—
298C2×C4×C151—416no—
299C2×C4×C151—42no—
300C2×C4×C151—41no—
301C2×C4×C151—41no—
302C2×C4×C151—41no—
303C2×C4×C151—41no—
304C2×C4×C151—42no—
305C2×C4×C151—42no—
306C2×C4×C151—42no—
307C2×C4×C151—42no—
308C2×C4×C151—42no—
309C2×C4×C151—42no—
310C2×C4×C151—42no—
311C2×C4×C151—42no—
312C2×C4×C151—42no—
313C2×C4×C151—42no—
314C2×C4×C151—42no—
315C2×C4×C151—42no—
316C2×C4×C151—42no—
317C2×C4×C151—42no—
318C2×C4×C151—42no—
319C2×C4×C151—42no—
320C2×C4×C151—42no—
321C2×C4×C151—42no—
322C2×C4×C151—42no—
323C2×C4×C151—42no—
324C2×C4×C151—42no—
325C2×C4×C151—42no—
326C2×C4×C151—42no—
327C2×C4×C151—42no—
328C2×C4×C151—42no—
329C2×C4×C151—42no—
330C2×C4×C151#12014yes—
331C2×C4×C151#12114yes—
332C2×C4×C151#12314yes—
333C22×C151—24no—
334C22×C151—24no—
335C22×C151—28no—
336C22×C151—24no—
337C22×C151—24no—
338C22×C151—42no—
339C22×C151—42no—
340C22×C151—42no—
341C22×C151—42no—
342C22×C151—42no—
343C22×C151—42no—
344C22×C151—44no—
345C22×C151—44no—
346C22×C151—44no—
347C22×C151—42no—
348C22×C151—42no—
349C22×C151—44no—
350C22×C151—44no—
351C22×C151—44no—
352C22×C151—44no—
353C22×C151—42no—
354C22×C151—42no—
355C22×C151C2×#12011yescharacteristic
356C22×C151C2×#12111yescharacteristic
357C22×C151C2×#12111yescharacteristic
358C22×C151C2×#12111yescharacteristic
359C22×C151C2×#12311yescharacteristic
360C22×C151#52511yescharacteristic
361C22×C151#52511yescharacteristic
362C22×C151#52511yescharacteristic
363C22×C151#52912yes—
364C22×C151#52912yes—
365C22×C151#53211yescharacteristic
366C22×C151#53411yescharacteristic
367C22×C151#53611yescharacteristic
368C22×C151#53912yes—
369C22×C151#54212yes—
370C22×C151#54612yes—
371C22×C151#54612yes—
372C22×C151#54612yes—
373C22×C151#54712yes—
374C22×C151#54712yes—
375C22×C151#54812yes—
376C22×C151#55212yes—
377C22×C151#55312yes—
378C4×C151—24no—
379C4×C151—24no—
380C4×C151—24no—
381C4×C151—42no—
382C4×C151—44no—
383C4×C151—42no—
384C4×C151—82no—
385C4×C151—82no—
386C4×C151—82no—
387C2×C151—44no—
388C2×C151—44no—
389C2×C151#239511yescharacteristic
390C2×C151#240511yescharacteristic
391C2×C151#242512yes—
392C2×C151#242712yes—
393C2×C151#243211yescharacteristic
394C2×C151#246012yes—
395C2×C151#246812yes—
396C2×C151#248611yescharacteristic
397C2×C151#254311yescharacteristic
398C2×C151#263811yescharacteristic
399C2×C151#284711yescharacteristic
400#14824C15111yesmaximal, characteristic, direct product factor, Sylow
401C151#1482411yescharacteristic, direct product factor, Sylow
402C22×C4×D4C2×C15111yescharacteristic
403C2×#398C2×C15111yescharacteristic, complemented
404C2×#397C2×C15111yescharacteristic, complemented
405C2×#394C2×C15112yes—
406C2×#380C2×C15111yescharacteristic, complemented
407#1441C2×C15111yescharacteristic, complemented
408#1440C2×C15112yescomplemented
409#1439C2×C15111yescharacteristic, complemented
410#1436C2×C15112yescomplemented
411C22⋊#95C2×C15112yescomplemented
412C22⋊#95C2×C15111yescharacteristic, complemented
413C23×D4C22×C15111yescharacteristic
414C24×C4C22×C15111yescharacteristic
415C24×C4C22×C15111yescharacteristic
416C2×C4×D4—24no—
417C2×C4×D4—24no—
418C2×C4×D4—24no—
419C22×C4⋊C4C22×C15112yes—
420C22×C4⋊C4C22×C15111yescharacteristic
421C22×C4⋊C4C22×C15111yescharacteristic
422C22×C4⋊C4C22×C15111yescharacteristic
423C22×C22⋊C4C22×C15112yes—
424C22×C22⋊C4C22×C15112yes—
425C22×C22⋊C4C22×C15111yescharacteristic
426C22×C22⋊C4C22×C15112yes—
427C22×C22⋊C4C22×C15112yes—
428C22×C22⋊C4C22×C15111yescharacteristic
429C22×C42C22×C15111yescharacteristic
430#398—24no—
431#397—24no—
432#394—28no—
433#380—24no—
434C2×#95C22×C15112yes—
435C2×#95C22×C15111yescharacteristic
436C2×#95C22×C15112yes—
437C2×#95C22×C15111yescharacteristic
438C2×#95C22×C15112yes—
439C2×#95C22×C15112yes—
440C2×#95C22×C15112yes—
441C2×#95C22×C15112yes—
442C2×#95C22×C15112yes—
443C25C23×C15111yescharacteristic
444C25C23×C15111yescharacteristic
445C22×D4—22no—
446C22×D4—22no—
447C22×D4—22no—
448C22×D4—22no—
449C22×D4—22no—
450C22×D4—22no—
451C22×D4D4×C15114yes—
452C23×C4—22no—
453C23×C4—24no—
454C23×C4—22no—
455C23×C4—22no—
456C23×C4—22no—
457C23×C4—22no—
458C23×C4—24no—
459C23×C4—42no—
460C23×C4—42no—
461C23×C4D4×C15114yes—
462C23×C4C23×C15112yes—
463C23×C4C23×C15112yes—
464C23×C4C23×C15112yes—
465C23×C4C23×C15112yes—
466C23×C4C23×C15111yescharacteristic
467C23×C4C23×C15111yescharacteristic
468C23×C4C23×C15111yescharacteristic
469C23×C4C23×C15111yescharacteristic
470C23×C4C23×C15111yescharacteristic
471C4×D4—232no—
472C2×C4⋊C4—22no—
473C2×C4⋊C4—22no—
474C2×C4⋊C4—24no—
475C2×C4⋊C4—22no—
476C2×C4⋊C4—22no—
477C2×C4⋊C4—24no—
478C2×C4⋊C4—22no—
479C2×C4⋊C4—22no—
480C2×C4⋊C4—24no—
481C2×C4⋊C4—42no—
482C2×C4⋊C4D4×C15114yes—
483C2×C22⋊C4—22no—
484C2×C22⋊C4—22no—
485C2×C22⋊C4—22no—
486C2×C22⋊C4—22no—
487C2×C22⋊C4—22no—
488C2×C22⋊C4—24no—
489C2×C22⋊C4—24no—
490C2×C22⋊C4—24no—
491C2×C22⋊C4—24no—
492C2×C22⋊C4—24no—
493C2×C22⋊C4—24no—
494C2×C22⋊C4—24no—
495C2×C22⋊C4—24no—
496C2×C22⋊C4—24no—
497C2×C22⋊C4—24no—
498C2×C22⋊C4—42no—
499C2×C22⋊C4—42no—
500C2×C22⋊C4D4×C15114yes—
501C2×C42—22no—
502C2×C42—22no—
503C2×C42—22no—
504#95—24no—
505#95—24no—
506#95—24no—
507#95—24no—
508#95—22no—
509#95—24no—
510#95—22no—
511#95—24no—
512#95—42no—
513C24—21no—
514C24—21no—
515C24—21no—
516C24—21no—
517C24—22no—
518C24—22no—
519C24—22no—
520C24—22no—
521C24—21no—
522C24—21no—
523C24—21no—
524C24—21no—
525C24—22no—
526C24—22no—
527C24—22no—
528C24—22no—
529C24C2×D4×C15112yes—
530C24C2×D4×C15112yes—
531C24C2×D4×C15112yes—
532C24C2×D4×C15112yes—
533C24#41×C15112yes—
534C24#41×C15112yes—
535C24C24×C15111yescharacteristic
536C2×D4—28no—
537C2×D4—28no—
538C2×D4—28no—
539C2×D4—28no—
540C2×D4—28no—
541C2×D4—28no—
542C2×D4—28no—
543C22×C4—21no—
544C22×C4—21no—
545C22×C4—21no—
546C22×C4—21no—
547C22×C4—22no—
548C22×C4—21no—
549C22×C4—21no—
550C22×C4—22no—
551C22×C4—22no—
552C22×C4—28no—
553C22×C4—22no—
554C22×C4—21no—
555C22×C4—21no—
556C22×C4—22no—
557C22×C4—21no—
558C22×C4—21no—
559C22×C4—22no—
560C22×C4—22no—
561C22×C4—22no—
562C22×C4—22no—
563C22×C4—22no—
564C22×C4—22no—
565C22×C4—22no—
566C22×C4—22no—
567C22×C4—28no—
568C22×C4—28no—
569C22×C4—22no—
570C22×C4—22no—
571C22×C4—22no—
572C22×C4—22no—
573C22×C4—22no—
574C22×C4—22no—
575C22×C4—22no—
576C22×C4—22no—
577C22×C4—22no—
578C22×C4—22no—
579C22×C4—22no—
580C22×C4—22no—
581C22×C4—22no—
582C22×C4—22no—
583C22×C4—22no—
584C22×C4—22no—
585C22×C4—22no—
586C22×C4—22no—
587C22×C4—22no—
588C22×C4—22no—
589C22×C4—22no—
590C22×C4—44no—
591C22×C4—48no—
592C22×C4—48no—
593C22×C4—48no—
594C22×C4—48no—
595C22×C4—44no—
596C22×C4—44no—
597C22×C4C2×D4×C15112yes—
598C22×C4C2×D4×C15112yes—
599C22×C4C2×D4×C15112yes—
600C22×C4C2×D4×C15112yes—
601C22×C4C2×D4×C15112yes—
602C22×C4C2×D4×C15112yes—
603C22×C4C2×D4×C15112yes—
604C22×C4C2×D4×C15112yes—
605C22×C4#41×C15114yes—
606C22×C4#41×C15112yes—
607C22×C4#41×C15114yes—
608C4⋊C4—28no—
609C4⋊C4—44no—
610C4⋊C4—44no—
611C4⋊C4—48no—
612C22⋊C4—28no—
613C22⋊C4—28no—
614C22⋊C4—48no—
615C22⋊C4—48no—
616C22⋊C4—48no—
617C22⋊C4—48no—
618C42—28no—
619C23—22no—
620C23—22no—
621C23—22no—
622C23—22no—
623C23—22no—
624C23—22no—
625C23—22no—
626C23—22no—
627C23—22no—
628C23—22no—
629C23—22no—
630C23—22no—
631C23—22no—
632C23—24no—
633C23—22no—
634C23—22no—
635C23—22no—
636C23—24no—
637C23—24no—
638C23—24no—
639C23—24no—
640C23—24no—
641C23—24no—
642C23—24no—
643C23—24no—
644C23—24no—
645C23—41no—
646C23—42no—
647C23—42no—
648C23—42no—
649C23—41no—
650C23—41no—
651C23—41no—
652C23—42no—
653C23—42no—
654C23—42no—
655C23—42no—
656C23—42no—
657C23—42no—
658C23—42no—
659C23—42no—
660C23—42no—
661C23—42no—
662C23—42no—
663C23#121×C15114yes—
664C23#121×C15114yes—
665C23C22×D4×C15111yescharacteristic
666C23C22×D4×C15111yescharacteristic
667C23C22×D4×C15111yescharacteristic
668C23C22×D4×C15111yescharacteristic
669C23C2×#41×C15111yescharacteristic
670C23C2×#41×C15111yescharacteristic
671C23C2×#41×C15111yescharacteristic
672C23C2×#41×C15112yes—
673C23C2×#41×C15112yes—
674C23H(5,𝔽2)×C15112yes—
675C232−1+4×C15112yes—
676D4—232no—
677C2×C4—22no—
678C2×C4—22no—
679C2×C4—22no—
680C2×C4—22no—
681C2×C4—22no—
682C2×C4—22no—
683C2×C4—22no—
684C2×C4—22no—
685C2×C4—22no—
686C2×C4—22no—
687C2×C4—24no—
688C2×C4—24no—
689C2×C4—24no—
690C2×C4—24no—
691C2×C4—22no—
692C2×C4—22no—
693C2×C4—24no—
694C2×C4—24no—
695C2×C4—24no—
696C2×C4—24no—
697C2×C4—24no—
698C2×C4—416no—
699C2×C4—416no—
700C2×C4—42no—
701C2×C4—41no—
702C2×C4—41no—
703C2×C4—41no—
704C2×C4—41no—
705C2×C4—42no—
706C2×C4—42no—
707C2×C4—42no—
708C2×C4—42no—
709C2×C4—42no—
710C2×C4—42no—
711C2×C4—42no—
712C2×C4—42no—
713C2×C4—42no—
714C2×C4—42no—
715C2×C4—42no—
716C2×C4—42no—
717C2×C4—42no—
718C2×C4—42no—
719C2×C4—42no—
720C2×C4—42no—
721C2×C4—42no—
722C2×C4—42no—
723C2×C4—42no—
724C2×C4—42no—
725C2×C4—42no—
726C2×C4—42no—
727C2×C4—42no—
728C2×C4—42no—
729C2×C4—42no—
730C2×C4—42no—
731C2×C4#120×C15114yes—
732C2×C4#121×C15114yes—
733C2×C4#123×C15114yes—
734C22—24no—
735C22—24no—
736C22—28no—
737C22—24no—
738C22—24no—
739C22—42no—
740C22—42no—
741C22—42no—
742C22—42no—
743C22—42no—
744C22—42no—
745C22—44no—
746C22—44no—
747C22—44no—
748C22—42no—
749C22—42no—
750C22—44no—
751C22—44no—
752C22—44no—
753C22—44no—
754C22—42no—
755C22—42no—
756C22C2×#120×C15111yescharacteristic
757C22C2×#121×C15111yescharacteristic
758C22C2×#121×C15111yescharacteristic
759C22C2×#121×C15111yescharacteristic
760C22C2×#123×C15111yescharacteristic
761C22#525×C15111yescharacteristic
762C22#525×C15111yescharacteristic
763C22#525×C15111yescharacteristic
764C22#529×C15112yes—
765C22#529×C15112yes—
766C22#532×C15111yescharacteristic
767C22#534×C15111yescharacteristic
768C22#536×C15111yescharacteristic
769C22#539×C15112yes—
770C22#542×C15112yes—
771C22#546×C15112yes—
772C22#546×C15112yes—
773C22#546×C15112yes—
774C22#547×C15112yes—
775C22#547×C15112yes—
776C22#548×C15112yes—
777C22#552×C15112yes—
778C22#553×C15112yes—
779C4—24no—
780C4—24no—
781C4—24no—
782C4—42no—
783C4—44no—
784C4—42no—
785C4—82no—
786C4—82no—
787C4—82no—
788C2—44no—
789C2—44no—
790C2#2395×C15111yescharacteristic
791C2#2405×C15111yescharacteristic
792C2#2425×C15112yes—
793C2#2427×C15112yes—
794C2#2432×C15111yescharacteristic
795C2#2460×C15112yes—
796C2#2468×C15112yes—
797C2#2486×C15111yescharacteristic
798C2#2543×C15111yescharacteristic
799C2#2638×C15111yescharacteristic
800C2#2847×C15111yescharacteristic
subgroupG/H
center, socleC24×C151C24
commutator, Frattini, cosocleC24C24×C151
prime radicalC23×D4×C151C22
LCSG ▷ C24 ▷ C1
UCSC1 ◁ C24×C151 ◁ G

Complements

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

NH ≅ G/Ntype
2. C2×#398×C151C2semidirect
3. C2×#397×C151C2semidirect
5. C2×#380×C151C2semidirect
6. #1441×C151C2semidirect
7. #1440×C151C2semidirect
8. #1439×C151C2semidirect
9. #1436×C151C2semidirect
10. C22⋊#95×C151C2semidirect
11. C22⋊#95×C151C2semidirect
400. #14824C151direct (N × H)
401. C151#14824direct (N × H)
403. C2×#398C2×C151semidirect
404. C2×#397C2×C151semidirect
406. C2×#380C2×C151semidirect
407. #1441C2×C151semidirect
408. #1440C2×C151semidirect
409. #1439C2×C151semidirect
410. #1436C2×C151semidirect
411. C22⋊#95C2×C151semidirect
412. C22⋊#95C2×C151semidirect

Maximal subgroups

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

subgroupindex
C22×C4×D4×C1512
C2×#398×C1512
C2×#397×C1512
C2×#394×C1512
C2×#380×C1512
#1441×C1512
#1440×C1512
#1439×C1512
#1436×C1512
C22⋊#95×C1512
#14824151