Finite Group Databasebeta

← C151×#14725 #50319650

Subgroups — C151×#14725 #50319650

Order 38656.

4034 conjugacy classes of subgroups.

The subgroup lattice has 1034 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#120×C151C211yesmaximal, characteristic
2C23×C22⋊C4×C151C211yesmaximal, characteristic, complemented
3C2×#394×C151C212yesmaximal, complemented
4C2×#386×C151C211yesmaximal, characteristic, complemented
5C2×#386×C151C211yesmaximal, characteristic, complemented
6C2×#380×C151C211yesmaximal, characteristic, complemented
7C2×#379×C151C211yesmaximal, characteristic, complemented
8#1440×C151C212yesmaximal, complemented
9#1439×C151C212yesmaximal, complemented
10#1438×C151C212yesmaximal, complemented
11C22⋊#95×C151C211yesmaximal, characteristic, complemented
12C26×C151C2211yescharacteristic
13C23×D4×C151C2211yescharacteristic
14C23×D4×C151C2212yes—
15C24×C4×C151C2211yescharacteristic
16C24×C4×C151C2211yescharacteristic
17C2×#120×C151—24no—
18C2×#120×C151—24no—
19C2×#120×C151—24no—
20C22×C4⋊C4×C151C2212yescomplemented
21C22×C22⋊C4×C151—24no—
22C22×C22⋊C4×C151—28no—
23C22×C22⋊C4×C151C2212yes—
24C22×C22⋊C4×C151C2212yes—
25C22×C22⋊C4×C151C2212yes—
26C22×C22⋊C4×C151C2211yescharacteristic
27C22×C22⋊C4×C151C2211yescharacteristic
28C22×C22⋊C4×C151C2211yescharacteristic
29C22×C22⋊C4×C151C2212yes—
30C22×C22⋊C4×C151C2212yes—
31C22×C22⋊C4×C151C2211yescharacteristic, complemented
32C22×C22⋊C4×C151C2212yescomplemented
33C22×C22⋊C4×C151C2211yescharacteristic, complemented
34#394×C151—28no—
35#386×C151—24no—
36#386×C151—24no—
37#380×C151—24no—
38#379×C151—24no—
39C2×#95×C151C2212yescomplemented
40C2×#95×C151C2212yescomplemented
41C2×#95×C151C2211yescharacteristic, complemented
42C2×#95×C151C2212yescomplemented
43C2×#95×C151C2211yescharacteristic, complemented
44C2×#95×C151C2212yescomplemented
45C25×C151—24no—
46C25×C151—22no—
47C25×C151—24no—
48C25×C151—22no—
49C25×C151—22no—
50C25×C151—22no—
51C25×C151—22no—
52C25×C151—22no—
53C25×C151—42no—
54C25×C151—42no—
55C25×C151D414yes—
56C25×C151C2311yescharacteristic
57C25×C151C2312yes—
58C25×C151C2311yescharacteristic
59C22×D4×C151—24no—
60C22×D4×C151—22no—
61C22×D4×C151—24no—
62C22×D4×C151—24no—
63C22×D4×C151—22no—
64C22×D4×C151—22no—
65C22×D4×C151—24no—
66C22×D4×C151—22no—
67C22×D4×C151—22no—
68C22×D4×C151—22no—
69C22×D4×C151—24no—
70C22×D4×C151—42no—
71C22×D4×C151—42no—
72C22×D4×C151D414yes—
73C23×C4×C151—24no—
74C23×C4×C151—24no—
75C23×C4×C151—22no—
76C23×C4×C151—22no—
77C23×C4×C151—22no—
78C23×C4×C151—22no—
79C23×C4×C151—22no—
80C23×C4×C151—42no—
81C23×C4×C151—42no—
82C23×C4×C151D414yescomplemented
83C23×C4×C151C2311yescharacteristic
84C23×C4×C151C2311yescharacteristic
85C23×C4×C151C2312yes—
86C23×C4×C151C2311yescharacteristic
87C23×C4×C151C2311yescharacteristic
88C23×C4×C151C2312yes—
89C23×C4×C151C2312yes—
90C23×C4×C151C2311yescharacteristic
91#120×C151—232no—
92C2×C4⋊C4×C151—24no—
93C2×C4⋊C4×C151—24no—
94C2×C4⋊C4×C151—42no—
95C2×C22⋊C4×C151—232no—
96C2×C22⋊C4×C151—24no—
97C2×C22⋊C4×C151—24no—
98C2×C22⋊C4×C151—24no—
99C2×C22⋊C4×C151—24no—
100C2×C22⋊C4×C151—24no—
101C2×C22⋊C4×C151—24no—
102C2×C22⋊C4×C151—22no—
103C2×C22⋊C4×C151—22no—
104C2×C22⋊C4×C151—24no—
105C2×C22⋊C4×C151—24no—
106C2×C22⋊C4×C151—24no—
107C2×C22⋊C4×C151—24no—
108C2×C22⋊C4×C151—22no—
109C2×C22⋊C4×C151—22no—
110C2×C22⋊C4×C151—24no—
111C2×C22⋊C4×C151—24no—
112C2×C22⋊C4×C151—22no—
113C2×C22⋊C4×C151—22no—
114C2×C22⋊C4×C151—22no—
115C2×C22⋊C4×C151—22no—
116C2×C22⋊C4×C151—22no—
117C2×C22⋊C4×C151—24no—
118C2×C22⋊C4×C151—24no—
119C2×C22⋊C4×C151—24no—
120C2×C22⋊C4×C151—22no—
121C2×C22⋊C4×C151—42no—
122C2×C22⋊C4×C151—42no—
123C2×C22⋊C4×C151—42no—
124C2×C22⋊C4×C151—42no—
125C2×C22⋊C4×C151D414yes—
126C2×C22⋊C4×C151D418yescomplemented
127#95×C151—24no—
128#95×C151—22no—
129#95×C151—22no—
130#95×C151—24no—
131#95×C151—24no—
132#95×C151—42no—
133C24×C151—22no—
134C24×C151—22no—
135C24×C151—22no—
136C24×C151—22no—
137C24×C151—28no—
138C24×C151—28no—
139C24×C151—216no—
140C24×C151—216no—
141C24×C151—28no—
142C24×C151—22no—
143C24×C151—22no—
144C24×C151—22no—
145C24×C151—22no—
146C24×C151—22no—
147C24×C151—22no—
148C24×C151—22no—
149C24×C151—22no—
150C24×C151—22no—
151C24×C151—22no—
152C24×C151—22no—
153C24×C151—22no—
154C24×C151—28no—
155C24×C151—28no—
156C24×C151—21no—
157C24×C151—22no—
158C24×C151—21no—
159C24×C151—21no—
160C24×C151—21no—
161C24×C151—21no—
162C24×C151—21no—
163C24×C151—22no—
164C24×C151—22no—
165C24×C151—22no—
166C24×C151—48no—
167C24×C151—48no—
168C24×C151—48no—
169C24×C151—48no—
170C24×C151—48no—
171C24×C151—48no—
172C24×C151—48no—
173C24×C151—48no—
174C24×C151—48no—
175C24×C151—44no—
176C24×C151—44no—
177C24×C151—48no—
178C24×C151—44no—
179C24×C151—44no—
180C24×C151—44no—
181C24×C151—44no—
182C24×C151C2×D412yes—
183C24×C151C2×D414yes—
184C24×C151C2×D414yes—
185C24×C151C2×D412yes—
186C24×C151C2×D412yes—
187C24×C151C2×D412yes—
188C24×C151C2×D412yes—
189C24×C151#4114yes—
190C24×C151#4112yes—
191C24×C151#4112yes—
192C24×C151#4112yes—
193C24×C151C2411yescharacteristic
194C2×D4×C151—216no—
195C2×D4×C151—28no—
196C2×D4×C151—28no—
197C2×D4×C151—28no—
198C2×D4×C151—48no—
199C2×D4×C151—48no—
200C2×D4×C151—48no—
201C2×D4×C151—48no—
202C2×D4×C151—48no—
203C2×D4×C151—48no—
204C2×D4×C151—44no—
205C2×D4×C151—44no—
206C2×D4×C151—44no—
207C2×D4×C151—44no—
208C22×C4×C151—21no—
209C22×C4×C151—21no—
210C22×C4×C151—22no—
211C22×C4×C151—28no—
212C22×C4×C151—28no—
213C22×C4×C151—21no—
214C22×C4×C151—21no—
215C22×C4×C151—22no—
216C22×C4×C151—22no—
217C22×C4×C151—22no—
218C22×C4×C151—22no—
219C22×C4×C151—22no—
220C22×C4×C151—21no—
221C22×C4×C151—21no—
222C22×C4×C151—22no—
223C22×C4×C151—22no—
224C22×C4×C151—21no—
225C22×C4×C151—22no—
226C22×C4×C151—21no—
227C22×C4×C151—21no—
228C22×C4×C151—21no—
229C22×C4×C151—22no—
230C22×C4×C151—22no—
231C22×C4×C151—22no—
232C22×C4×C151—22no—
233C22×C4×C151—22no—
234C22×C4×C151—22no—
235C22×C4×C151—28no—
236C22×C4×C151—21no—
237C22×C4×C151—22no—
238C22×C4×C151—22no—
239C22×C4×C151—21no—
240C22×C4×C151—22no—
241C22×C4×C151—22no—
242C22×C4×C151—21no—
243C22×C4×C151—21no—
244C22×C4×C151—22no—
245C22×C4×C151—21no—
246C22×C4×C151—22no—
247C22×C4×C151—21no—
248C22×C4×C151—22no—
249C22×C4×C151—22no—
250C22×C4×C151—22no—
251C22×C4×C151—22no—
252C22×C4×C151—22no—
253C22×C4×C151—44no—
254C22×C4×C151—48no—
255C22×C4×C151—48no—
256C22×C4×C151—48no—
257C22×C4×C151—48no—
258C22×C4×C151—44no—
259C22×C4×C151—44no—
260C22×C4×C151C2×D412yes—
261C22×C4×C151C2×D412yes—
262C22×C4×C151C2×D414yes—
263C22×C4×C151C2×D414yes—
264C22×C4×C151C2×D412yes—
265C22×C4×C151C2×D414yes—
266C4⋊C4×C151—48no—
267C22⋊C4×C151—216no—
268C22⋊C4×C151—216no—
269C22⋊C4×C151—28no—
270C22⋊C4×C151—216no—
271C22⋊C4×C151—48no—
272C22⋊C4×C151—44no—
273C22⋊C4×C151—48no—
274C22⋊C4×C151—44no—
275C22⋊C4×C151—48no—
276C22⋊C4×C151—44no—
277C22⋊C4×C151—44no—
278C23×C151—22no—
279C23×C151—24no—
280C23×C151—22no—
281C23×C151—24no—
282C23×C151—24no—
283C23×C151—22no—
284C23×C151—22no—
285C23×C151—24no—
286C23×C151—24no—
287C23×C151—24no—
288C23×C151—24no—
289C23×C151—24no—
290C23×C151—24no—
291C23×C151—24no—
292C23×C151—24no—
293C23×C151—24no—
294C23×C151—232no—
295C23×C151—24no—
296C23×C151—24no—
297C23×C151—24no—
298C23×C151—24no—
299C23×C151—24no—
300C23×C151—24no—
301C23×C151—24no—
302C23×C151—24no—
303C23×C151—24no—
304C23×C151—24no—
305C23×C151—24no—
306C23×C151—24no—
307C23×C151—24no—
308C23×C151—24no—
309C23×C151—24no—
310C23×C151—24no—
311C23×C151—24no—
312C23×C151—24no—
313C23×C151—22no—
314C23×C151—22no—
315C23×C151—22no—
316C23×C151—24no—
317C23×C151—24no—
318C23×C151—432no—
319C23×C151—432no—
320C23×C151—416no—
321C23×C151—416no—
322C23×C151—416no—
323C23×C151—416no—
324C23×C151—432no—
325C23×C151—432no—
326C23×C151—416no—
327C23×C151—42no—
328C23×C151—42no—
329C23×C151—42no—
330C23×C151—42no—
331C23×C151—42no—
332C23×C151—42no—
333C23×C151—42no—
334C23×C151—42no—
335C23×C151—42no—
336C23×C151—42no—
337C23×C151—42no—
338C23×C151—42no—
339C23×C151—42no—
340C23×C151—42no—
341C23×C151—42no—
342C23×C151—42no—
343C23×C151—416no—
344C23×C151—41no—
345C23×C151—41no—
346C23×C151—41no—
347C23×C151—42no—
348C23×C151—41no—
349C23×C151—42no—
350C23×C151—41no—
351C23×C151—41no—
352C23×C151—41no—
353C23×C151—42no—
354C23×C151—41no—
355C23×C151—42no—
356C23×C151—42no—
357C23×C151—42no—
358C23×C151—42no—
359C23×C151—42no—
360C23×C151—42no—
361C23×C151—42no—
362C23×C151#12014yes—
363C23×C151#12118yes—
364C23×C151#12114yes—
365C23×C151#12114yes—
366C23×C151#12114yes—
367C23×C151#12314yes—
368C23×C151#12314yes—
369C23×C151#12414yes—
370C23×C151C22×D411yescharacteristic
371C23×C151C22×D411yescharacteristic
372C23×C151C22×D411yescharacteristic
373C23×C151C22×D412yes—
374C23×C151C22×D411yescharacteristic
375C23×C151C2×#4111yescharacteristic
376C23×C151C2×#4111yescharacteristic
377C23×C151C2×#4111yescharacteristic
378C23×C151C2×#4112yes—
379C23×C151H(5,𝔽2)12yes—
380C23×C151H(5,𝔽2)12yes—
381D4×C151—432no—
382D4×C151—416no—
383C2×C4×C151—22no—
384C2×C4×C151—22no—
385C2×C4×C151—24no—
386C2×C4×C151—24no—
387C2×C4×C151—24no—
388C2×C4×C151—22no—
389C2×C4×C151—22no—
390C2×C4×C151—24no—
391C2×C4×C151—22no—
392C2×C4×C151—22no—
393C2×C4×C151—22no—
394C2×C4×C151—22no—
395C2×C4×C151—24no—
396C2×C4×C151—24no—
397C2×C4×C151—24no—
398C2×C4×C151—24no—
399C2×C4×C151—416no—
400C2×C4×C151—416no—
401C2×C4×C151—42no—
402C2×C4×C151—41no—
403C2×C4×C151—41no—
404C2×C4×C151—42no—
405C2×C4×C151—41no—
406C2×C4×C151—41no—
407C2×C4×C151—42no—
408C2×C4×C151—42no—
409C2×C4×C151—42no—
410C2×C4×C151—42no—
411C2×C4×C151—42no—
412C2×C4×C151—42no—
413C2×C4×C151—42no—
414C2×C4×C151—42no—
415C2×C4×C151—41no—
416C2×C4×C151—42no—
417C2×C4×C151—41no—
418C2×C4×C151—42no—
419C2×C4×C151—41no—
420C2×C4×C151—42no—
421C2×C4×C151—41no—
422C2×C4×C151—42no—
423C2×C4×C151—42no—
424C2×C4×C151—41no—
425C2×C4×C151—42no—
426C2×C4×C151—41no—
427C2×C4×C151—42no—
428C2×C4×C151—42no—
429C2×C4×C151—42no—
430C2×C4×C151—42no—
431C2×C4×C151—42no—
432C2×C4×C151#12014yescomplemented
433C22×C151—24no—
434C22×C151—24no—
435C22×C151—24no—
436C22×C151—24no—
437C22×C151—28no—
438C22×C151—24no—
439C22×C151—28no—
440C22×C151—28no—
441C22×C151—28no—
442C22×C151—24no—
443C22×C151—28no—
444C22×C151—28no—
445C22×C151—28no—
446C22×C151—464no—
447C22×C151—44no—
448C22×C151—44no—
449C22×C151—44no—
450C22×C151—44no—
451C22×C151—44no—
452C22×C151—44no—
453C22×C151—44no—
454C22×C151—44no—
455C22×C151—44no—
456C22×C151—44no—
457C22×C151—44no—
458C22×C151—44no—
459C22×C151—42no—
460C22×C151—42no—
461C22×C151—44no—
462C22×C151—44no—
463C22×C151—42no—
464C22×C151—81no—
465C22×C151—81no—
466C22×C151—81no—
467C22×C151—81no—
468C22×C151—82no—
469C22×C151—82no—
470C22×C151#39418yescomplemented
471C22×C151C2×#12011yescharacteristic
472C22×C151C2×#12011yescharacteristic
473C22×C151C2×#12111yescharacteristic
474C22×C151C2×#12112yes—
475C22×C151C2×#12111yescharacteristic
476C22×C151C2×#12111yescharacteristic
477C22×C151C2×#12311yescharacteristic
478C22×C151C2×#12311yescharacteristic
479C22×C151#52511yescharacteristic
480C22×C151#52512yes—
481C22×C151C2×#12411yescharacteristic
482C22×C151#53412yes—
483C22×C151#53411yescharacteristic
484C22×C151#53511yescharacteristic
485C22×C151#53812yes—
486C22×C151D4212yes—
487C22×C151D4212yes—
488C22×C151#54612yes—
489C22×C151#54612yes—
490C22×C151#54612yes—
491C22×C151#54612yes—
492C22×C151#55112yes—
493C22×C151#55112yes—
494C4×C151—24no—
495C4×C151—42no—
496C4×C151—44no—
497C4×C151—42no—
498C4×C151—44no—
499C4×C151—81no—
500C4×C151—81no—
501C4×C151—82no—
502C2×C151—28no—
503C2×C151—48no—
504C2×C151—82no—
505C2×C151C2×#39411yescharacteristic
506C2×C151#240811yescharacteristic
507C2×C151#241011yescharacteristic
508C2×C151#241012yes—
509C2×C151#241111yescharacteristic
510C2×C151#241212yes—
511C2×C151#241812yes—
512C2×C151#247212yes—
513C2×C151#253411yescharacteristic
514C2×C151#261711yescharacteristic
515C2×C151#284711yescharacteristic
516#14725C15111yesmaximal, characteristic, direct product factor, Sylow
517C151#1472511yescharacteristic, direct product factor, Sylow
518C22×#120C2×C15111yescharacteristic
519C23×C22⋊C4C2×C15111yescharacteristic, complemented
520C2×#394C2×C15112yescomplemented
521C2×#386C2×C15111yescharacteristic, complemented
522C2×#386C2×C15111yescharacteristic, complemented
523C2×#380C2×C15111yescharacteristic, complemented
524C2×#379C2×C15111yescharacteristic, complemented
525#1440C2×C15112yescomplemented
526#1439C2×C15112yescomplemented
527#1438C2×C15112yescomplemented
528C22⋊#95C2×C15111yescharacteristic, complemented
529C26C22×C15111yescharacteristic
530C23×D4C22×C15111yescharacteristic
531C23×D4C22×C15112yes—
532C24×C4C22×C15111yescharacteristic
533C24×C4C22×C15111yescharacteristic
534C2×#120—24no—
535C2×#120—24no—
536C2×#120—24no—
537C22×C4⋊C4C22×C15112yescomplemented
538C22×C22⋊C4—24no—
539C22×C22⋊C4—28no—
540C22×C22⋊C4C22×C15112yes—
541C22×C22⋊C4C22×C15112yes—
542C22×C22⋊C4C22×C15112yes—
543C22×C22⋊C4C22×C15111yescharacteristic
544C22×C22⋊C4C22×C15111yescharacteristic
545C22×C22⋊C4C22×C15111yescharacteristic
546C22×C22⋊C4C22×C15112yes—
547C22×C22⋊C4C22×C15112yes—
548C22×C22⋊C4C22×C15111yescharacteristic, complemented
549C22×C22⋊C4C22×C15112yescomplemented
550C22×C22⋊C4C22×C15111yescharacteristic, complemented
551#394—28no—
552#386—24no—
553#386—24no—
554#380—24no—
555#379—24no—
556C2×#95C22×C15112yescomplemented
557C2×#95C22×C15112yescomplemented
558C2×#95C22×C15111yescharacteristic, complemented
559C2×#95C22×C15112yescomplemented
560C2×#95C22×C15111yescharacteristic, complemented
561C2×#95C22×C15112yescomplemented
562C25—24no—
563C25—22no—
564C25—24no—
565C25—22no—
566C25—22no—
567C25—22no—
568C25—22no—
569C25—22no—
570C25—42no—
571C25—42no—
572C25D4×C15114yes—
573C25C23×C15111yescharacteristic
574C25C23×C15112yes—
575C25C23×C15111yescharacteristic
576C22×D4—22no—
577C22×D4—22no—
578C22×D4—22no—
579C22×D4—24no—
580C22×D4—24no—
581C22×D4—22no—
582C22×D4—22no—
583C22×D4—22no—
584C22×D4—24no—
585C22×D4—24no—
586C22×D4—24no—
587C22×D4—42no—
588C22×D4—42no—
589C22×D4D4×C15114yes—
590C23×C4—22no—
591C23×C4—22no—
592C23×C4—22no—
593C23×C4—24no—
594C23×C4—24no—
595C23×C4—22no—
596C23×C4—22no—
597C23×C4—42no—
598C23×C4—42no—
599C23×C4D4×C15114yescomplemented
600C23×C4C23×C15112yes—
601C23×C4C23×C15111yescharacteristic
602C23×C4C23×C15111yescharacteristic
603C23×C4C23×C15111yescharacteristic
604C23×C4C23×C15112yes—
605C23×C4C23×C15112yes—
606C23×C4C23×C15111yescharacteristic
607C23×C4C23×C15111yescharacteristic
608#120—232no—
609C2×C4⋊C4—24no—
610C2×C4⋊C4—24no—
611C2×C4⋊C4—42no—
612C2×C22⋊C4—232no—
613C2×C22⋊C4—24no—
614C2×C22⋊C4—24no—
615C2×C22⋊C4—22no—
616C2×C22⋊C4—22no—
617C2×C22⋊C4—24no—
618C2×C22⋊C4—24no—
619C2×C22⋊C4—24no—
620C2×C22⋊C4—24no—
621C2×C22⋊C4—24no—
622C2×C22⋊C4—24no—
623C2×C22⋊C4—24no—
624C2×C22⋊C4—22no—
625C2×C22⋊C4—24no—
626C2×C22⋊C4—22no—
627C2×C22⋊C4—24no—
628C2×C22⋊C4—22no—
629C2×C22⋊C4—22no—
630C2×C22⋊C4—22no—
631C2×C22⋊C4—22no—
632C2×C22⋊C4—24no—
633C2×C22⋊C4—24no—
634C2×C22⋊C4—22no—
635C2×C22⋊C4—22no—
636C2×C22⋊C4—24no—
637C2×C22⋊C4—24no—
638C2×C22⋊C4—42no—
639C2×C22⋊C4—42no—
640C2×C22⋊C4—42no—
641C2×C22⋊C4—42no—
642C2×C22⋊C4D4×C15114yes—
643C2×C22⋊C4D4×C15118yescomplemented
644#95—24no—
645#95—22no—
646#95—22no—
647#95—24no—
648#95—24no—
649#95—42no—
650C24—22no—
651C24—22no—
652C24—22no—
653C24—22no—
654C24—28no—
655C24—216no—
656C24—28no—
657C24—216no—
658C24—28no—
659C24—22no—
660C24—22no—
661C24—22no—
662C24—22no—
663C24—22no—
664C24—22no—
665C24—22no—
666C24—22no—
667C24—22no—
668C24—22no—
669C24—22no—
670C24—22no—
671C24—28no—
672C24—28no—
673C24—21no—
674C24—22no—
675C24—21no—
676C24—21no—
677C24—21no—
678C24—21no—
679C24—21no—
680C24—22no—
681C24—22no—
682C24—22no—
683C24—48no—
684C24—48no—
685C24—48no—
686C24—48no—
687C24—48no—
688C24—48no—
689C24—48no—
690C24—48no—
691C24—48no—
692C24—44no—
693C24—44no—
694C24—48no—
695C24—44no—
696C24—44no—
697C24—44no—
698C24—44no—
699C24C2×D4×C15112yes—
700C24C2×D4×C15114yes—
701C24C2×D4×C15114yes—
702C24C2×D4×C15112yes—
703C24C2×D4×C15112yes—
704C24C2×D4×C15112yes—
705C24C2×D4×C15112yes—
706C24#41×C15114yes—
707C24#41×C15112yes—
708C24#41×C15112yes—
709C24#41×C15112yes—
710C24C24×C15111yescharacteristic
711C2×D4—216no—
712C2×D4—28no—
713C2×D4—28no—
714C2×D4—28no—
715C2×D4—48no—
716C2×D4—48no—
717C2×D4—48no—
718C2×D4—48no—
719C2×D4—48no—
720C2×D4—48no—
721C2×D4—44no—
722C2×D4—44no—
723C2×D4—44no—
724C2×D4—44no—
725C22×C4—21no—
726C22×C4—21no—
727C22×C4—22no—
728C22×C4—28no—
729C22×C4—28no—
730C22×C4—21no—
731C22×C4—21no—
732C22×C4—22no—
733C22×C4—22no—
734C22×C4—22no—
735C22×C4—22no—
736C22×C4—22no—
737C22×C4—21no—
738C22×C4—21no—
739C22×C4—22no—
740C22×C4—22no—
741C22×C4—21no—
742C22×C4—22no—
743C22×C4—21no—
744C22×C4—21no—
745C22×C4—21no—
746C22×C4—22no—
747C22×C4—22no—
748C22×C4—22no—
749C22×C4—22no—
750C22×C4—22no—
751C22×C4—22no—
752C22×C4—28no—
753C22×C4—21no—
754C22×C4—22no—
755C22×C4—22no—
756C22×C4—21no—
757C22×C4—22no—
758C22×C4—22no—
759C22×C4—21no—
760C22×C4—21no—
761C22×C4—22no—
762C22×C4—21no—
763C22×C4—22no—
764C22×C4—21no—
765C22×C4—22no—
766C22×C4—22no—
767C22×C4—22no—
768C22×C4—22no—
769C22×C4—22no—
770C22×C4—44no—
771C22×C4—48no—
772C22×C4—48no—
773C22×C4—48no—
774C22×C4—48no—
775C22×C4—44no—
776C22×C4—44no—
777C22×C4C2×D4×C15112yes—
778C22×C4C2×D4×C15112yes—
779C22×C4C2×D4×C15114yes—
780C22×C4C2×D4×C15114yes—
781C22×C4C2×D4×C15112yes—
782C22×C4C2×D4×C15114yes—
783C4⋊C4—48no—
784C22⋊C4—216no—
785C22⋊C4—216no—
786C22⋊C4—28no—
787C22⋊C4—216no—
788C22⋊C4—48no—
789C22⋊C4—44no—
790C22⋊C4—48no—
791C22⋊C4—44no—
792C22⋊C4—48no—
793C22⋊C4—44no—
794C22⋊C4—44no—
795C23—22no—
796C23—24no—
797C23—24no—
798C23—22no—
799C23—22no—
800C23—24no—
801C23—22no—
802C23—24no—
803C23—24no—
804C23—24no—
805C23—24no—
806C23—24no—
807C23—24no—
808C23—24no—
809C23—24no—
810C23—24no—
811C23—232no—
812C23—24no—
813C23—24no—
814C23—24no—
815C23—24no—
816C23—24no—
817C23—24no—
818C23—24no—
819C23—24no—
820C23—24no—
821C23—24no—
822C23—24no—
823C23—24no—
824C23—24no—
825C23—24no—
826C23—24no—
827C23—24no—
828C23—24no—
829C23—24no—
830C23—22no—
831C23—22no—
832C23—22no—
833C23—24no—
834C23—24no—
835C23—432no—
836C23—432no—
837C23—416no—
838C23—416no—
839C23—416no—
840C23—416no—
841C23—432no—
842C23—432no—
843C23—416no—
844C23—416no—
845C23—42no—
846C23—42no—
847C23—42no—
848C23—42no—
849C23—42no—
850C23—42no—
851C23—42no—
852C23—42no—
853C23—42no—
854C23—42no—
855C23—42no—
856C23—42no—
857C23—42no—
858C23—42no—
859C23—42no—
860C23—42no—
861C23—41no—
862C23—41no—
863C23—41no—
864C23—42no—
865C23—41no—
866C23—42no—
867C23—41no—
868C23—41no—
869C23—41no—
870C23—42no—
871C23—41no—
872C23—42no—
873C23—42no—
874C23—42no—
875C23—42no—
876C23—42no—
877C23—42no—
878C23—42no—
879C23#120×C15114yes—
880C23#121×C15118yes—
881C23#121×C15114yes—
882C23#121×C15114yes—
883C23#121×C15114yes—
884C23#123×C15114yes—
885C23#123×C15114yes—
886C23#124×C15114yes—
887C23C22×D4×C15111yescharacteristic
888C23C22×D4×C15111yescharacteristic
889C23C22×D4×C15111yescharacteristic
890C23C22×D4×C15112yes—
891C23C22×D4×C15111yescharacteristic
892C23C2×#41×C15111yescharacteristic
893C23C2×#41×C15111yescharacteristic
894C23C2×#41×C15111yescharacteristic
895C23C2×#41×C15112yes—
896C23H(5,𝔽2)×C15112yes—
897C23H(5,𝔽2)×C15112yes—
898D4—432no—
899D4—416no—
900C2×C4—22no—
901C2×C4—22no—
902C2×C4—24no—
903C2×C4—24no—
904C2×C4—24no—
905C2×C4—22no—
906C2×C4—22no—
907C2×C4—24no—
908C2×C4—22no—
909C2×C4—22no—
910C2×C4—22no—
911C2×C4—22no—
912C2×C4—24no—
913C2×C4—24no—
914C2×C4—24no—
915C2×C4—24no—
916C2×C4—416no—
917C2×C4—416no—
918C2×C4—42no—
919C2×C4—41no—
920C2×C4—41no—
921C2×C4—42no—
922C2×C4—41no—
923C2×C4—41no—
924C2×C4—42no—
925C2×C4—42no—
926C2×C4—42no—
927C2×C4—42no—
928C2×C4—42no—
929C2×C4—42no—
930C2×C4—42no—
931C2×C4—42no—
932C2×C4—41no—
933C2×C4—42no—
934C2×C4—41no—
935C2×C4—42no—
936C2×C4—41no—
937C2×C4—42no—
938C2×C4—41no—
939C2×C4—42no—
940C2×C4—42no—
941C2×C4—41no—
942C2×C4—42no—
943C2×C4—41no—
944C2×C4—42no—
945C2×C4—42no—
946C2×C4—42no—
947C2×C4—42no—
948C2×C4—42no—
949C2×C4#120×C15114yescomplemented
950C22—24no—
951C22—24no—
952C22—24no—
953C22—24no—
954C22—28no—
955C22—24no—
956C22—28no—
957C22—28no—
958C22—28no—
959C22—24no—
960C22—28no—
961C22—28no—
962C22—28no—
963C22—464no—
964C22—44no—
965C22—44no—
966C22—44no—
967C22—44no—
968C22—44no—
969C22—44no—
970C22—44no—
971C22—44no—
972C22—44no—
973C22—44no—
974C22—44no—
975C22—44no—
976C22—42no—
977C22—42no—
978C22—44no—
979C22—44no—
980C22—42no—
981C22—81no—
982C22—81no—
983C22—81no—
984C22—81no—
985C22—82no—
986C22—82no—
987C22#394×C15118yescomplemented
988C22C2×#120×C15111yescharacteristic
989C22C2×#120×C15111yescharacteristic
990C22C2×#121×C15111yescharacteristic
991C22C2×#121×C15112yes—
992C22C2×#121×C15111yescharacteristic
993C22C2×#121×C15111yescharacteristic
994C22C2×#123×C15111yescharacteristic
995C22C2×#123×C15111yescharacteristic
996C22#525×C15111yescharacteristic
997C22#525×C15112yes—
998C22C2×#124×C15111yescharacteristic
999C22#534×C15112yes—
1000C22#534×C15111yescharacteristic
1001C22#535×C15111yescharacteristic
1002C22#538×C15112yes—
1003C22D42×C15112yes—
1004C22D42×C15112yes—
1005C22#546×C15112yes—
1006C22#546×C15112yes—
1007C22#546×C15112yes—
1008C22#546×C15112yes—
1009C22#551×C15112yes—
1010C22#551×C15112yes—
1011C4—24no—
1012C4—42no—
1013C4—44no—
1014C4—42no—
1015C4—44no—
1016C4—81no—
1017C4—81no—
1018C4—82no—
1019C2—28no—
1020C2—48no—
1021C2—82no—
1022C2C2×#394×C15111yescharacteristic
1023C2#2408×C15111yescharacteristic
1024C2#2410×C15111yescharacteristic
1025C2#2410×C15112yes—
1026C2#2411×C15111yescharacteristic
1027C2#2412×C15112yes—
1028C2#2418×C15112yes—
1029C2#2472×C15112yes—
1030C2#2534×C15111yescharacteristic
1031C2#2617×C15111yescharacteristic
1032C2#2847×C15111yescharacteristic
subgroupG/H
center, socleC24×C151C24
commutator, Frattini, cosocleC24C24×C151
prime radicalC22×#120×C151C2
LCSG ▷ C24 ▷ C1
UCSC1 ◁ C24×C151 ◁ G

Complements

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

NH ≅ G/Ntype
2. C23×C22⋊C4×C151C2semidirect
3. C2×#394×C151C2semidirect
4. C2×#386×C151C2semidirect
5. C2×#386×C151C2semidirect
6. C2×#380×C151C2semidirect
7. C2×#379×C151C2semidirect
8. #1440×C151C2semidirect
9. #1439×C151C2semidirect
10. #1438×C151C2semidirect
11. C22⋊#95×C151C2semidirect
20. C22×C4⋊C4×C151C22semidirect
31. C22×C22⋊C4×C151C22semidirect
32. C22×C22⋊C4×C151C22semidirect
33. C22×C22⋊C4×C151C22semidirect
39. C2×#95×C151C22semidirect
40. C2×#95×C151C22semidirect
41. C2×#95×C151C22semidirect
42. C2×#95×C151C22semidirect
43. C2×#95×C151C22semidirect
44. C2×#95×C151C22semidirect
82. C23×C4×C151D4semidirect
126. C2×C22⋊C4×C151D4semidirect
432. C2×C4×C151#120semidirect
470. C22×C151#394semidirect
516. #14725C151direct (N × H)
517. C151#14725direct (N × H)
519. C23×C22⋊C4C2×C151semidirect
520. C2×#394C2×C151semidirect
521. C2×#386C2×C151semidirect
522. C2×#386C2×C151semidirect
523. C2×#380C2×C151semidirect
524. C2×#379C2×C151semidirect
525. #1440C2×C151semidirect
526. #1439C2×C151semidirect
527. #1438C2×C151semidirect
528. C22⋊#95C2×C151semidirect
537. C22×C4⋊C4C22×C151semidirect
548. C22×C22⋊C4C22×C151semidirect
549. C22×C22⋊C4C22×C151semidirect
550. C22×C22⋊C4C22×C151semidirect
556. C2×#95C22×C151semidirect
557. C2×#95C22×C151semidirect
558. C2×#95C22×C151semidirect
559. C2×#95C22×C151semidirect
560. C2×#95C22×C151semidirect
561. C2×#95C22×C151semidirect
599. C23×C4D4×C151semidirect
643. C2×C22⋊C4D4×C151semidirect
949. C2×C4#120×C151semidirect
987. C22#394×C151semidirect

Maximal subgroups

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

subgroupindex
C22×#120×C1512
C23×C22⋊C4×C1512
C2×#394×C1512
C2×#386×C1512
C2×#380×C1512
C2×#379×C1512
#1440×C1512
#1439×C1512
#1438×C1512
C22⋊#95×C1512
#14725151