Finite Group Databasebeta

← C151×#15257 #50320182

Subgroups — C151×#15257 #50320182

Order 38656.

4462 conjugacy classes of subgroups.

The subgroup lattice has 1076 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#121×C151C211yesmaximal, characteristic, complemented
2C22×#120×C151C211yesmaximal, characteristic, complemented
3C22×#120×C151C211yesmaximal, characteristic, complemented
4C2×#392×C151C212yesmaximal, complemented
5C2×#386×C151C212yesmaximal, complemented
6C2×#379×C151C211yesmaximal, characteristic, complemented
7#1440×C151C211yesmaximal, characteristic, complemented
8#1439×C151C212yesmaximal, complemented
9#1438×C151C211yesmaximal, characteristic, complemented
10#1438×C151C212yesmaximal, complemented
11#1438×C151C211yesmaximal, characteristic, complemented
12C26×C151C2211yescharacteristic
13C23×D4×C151C2212yes—
14C23×D4×C151C2212yes—
15C23×D4×C151C2211yescharacteristic
16C23×D4×C151C2211yescharacteristic
17C23×D4×C151C2211yescharacteristic, complemented
18C24×C4×C151C2211yescharacteristic, complemented
19C2×#121×C151—24no—
20C2×#121×C151—24no—
21C2×#121×C151—24no—
22C2×#120×C151—28no—
23C2×#120×C151—24no—
24C2×#120×C151—24no—
25C2×#120×C151—28no—
26C22×C4⋊C4×C151C2211yescharacteristic, complemented
27C22×C22⋊C4×C151C2212yes—
28C22×C22⋊C4×C151C2211yescharacteristic
29C22×C22⋊C4×C151C2211yescharacteristic
30C22×C22⋊C4×C151C2212yes—
31C22×C22⋊C4×C151C2212yes—
32C22×C22⋊C4×C151C2212yes—
33C22×C22⋊C4×C151C2211yescharacteristic
34C22×C22⋊C4×C151C2211yescharacteristic
35C22×C22⋊C4×C151C2211yescharacteristic, complemented
36C22×C22⋊C4×C151C2212yescomplemented
37C22×C22⋊C4×C151C2212yescomplemented
38#392×C151—28no—
39#386×C151—28no—
40#379×C151—24no—
41C2×#95×C151C2212yescomplemented
42C2×#95×C151C2212yescomplemented
43C2×#95×C151C2212yescomplemented
44C2×#95×C151C2212yescomplemented
45C25×C151—22no—
46C25×C151—22no—
47C25×C151—22no—
48C25×C151—24no—
49C25×C151—24no—
50C25×C151—24no—
51C25×C151—42no—
52C25×C151—42no—
53C25×C151—42no—
54C25×C151C2311yescharacteristic
55C25×C151C2311yescharacteristic
56C25×C151C2311yescharacteristic
57C25×C151C2312yes—
58C22×D4×C151—24no—
59C22×D4×C151—24no—
60C22×D4×C151—22no—
61C22×D4×C151—24no—
62C22×D4×C151—24no—
63C22×D4×C151—24no—
64C22×D4×C151—24no—
65C22×D4×C151—24no—
66C22×D4×C151—24no—
67C22×D4×C151—22no—
68C22×D4×C151—22no—
69C22×D4×C151—22no—
70C22×D4×C151—22no—
71C22×D4×C151—22no—
72C22×D4×C151—22no—
73C22×D4×C151—24no—
74C22×D4×C151—24no—
75C22×D4×C151—24no—
76C22×D4×C151—24no—
77C22×D4×C151—42no—
78C22×D4×C151—42no—
79C22×D4×C151—42no—
80C22×D4×C151—42no—
81C22×D4×C151—42no—
82C22×D4×C151—42no—
83C22×D4×C151—42no—
84C22×D4×C151D418yescomplemented
85C22×D4×C151D414yescomplemented
86C22×D4×C151D414yescomplemented
87C23×C4×C151—22no—
88C23×C4×C151—22no—
89C23×C4×C151—24no—
90C23×C4×C151—22no—
91C23×C4×C151—42no—
92C23×C4×C151C2312yes—
93C23×C4×C151C2312yes—
94C23×C4×C151C2312yes—
95C23×C4×C151C2311yescharacteristic
96C23×C4×C151C2311yescharacteristic
97C23×C4×C151C2311yescharacteristic
98C23×C4×C151C2311yescharacteristic
99#121×C151—232no—
100#120×C151—232no—
101#120×C151—232no—
102C2×C4⋊C4×C151—22no—
103C2×C4⋊C4×C151—22no—
104C2×C4⋊C4×C151—22no—
105C2×C22⋊C4×C151—24no—
106C2×C22⋊C4×C151—24no—
107C2×C22⋊C4×C151—24no—
108C2×C22⋊C4×C151—24no—
109C2×C22⋊C4×C151—24no—
110C2×C22⋊C4×C151—24no—
111C2×C22⋊C4×C151—22no—
112C2×C22⋊C4×C151—22no—
113C2×C22⋊C4×C151—24no—
114C2×C22⋊C4×C151—24no—
115C2×C22⋊C4×C151—24no—
116C2×C22⋊C4×C151—24no—
117C2×C22⋊C4×C151—22no—
118C2×C22⋊C4×C151—22no—
119C2×C22⋊C4×C151—24no—
120C2×C22⋊C4×C151—22no—
121C2×C22⋊C4×C151—22no—
122C2×C22⋊C4×C151—22no—
123C2×C22⋊C4×C151—22no—
124C2×C22⋊C4×C151—24no—
125C2×C22⋊C4×C151—24no—
126C2×C22⋊C4×C151—24no—
127C2×C22⋊C4×C151—42no—
128C2×C22⋊C4×C151—42no—
129C2×C22⋊C4×C151—42no—
130C2×C22⋊C4×C151—42no—
131C2×C22⋊C4×C151—42no—
132C2×C22⋊C4×C151—42no—
133C2×C22⋊C4×C151D414yescomplemented
134C2×C22⋊C4×C151D418yescomplemented
135#95×C151—24no—
136#95×C151—24no—
137#95×C151—24no—
138#95×C151—42no—
139C24×C151—22no—
140C24×C151—22no—
141C24×C151—22no—
142C24×C151—22no—
143C24×C151—22no—
144C24×C151—22no—
145C24×C151—22no—
146C24×C151—22no—
147C24×C151—21no—
148C24×C151—21no—
149C24×C151—22no—
150C24×C151—22no—
151C24×C151—22no—
152C24×C151—22no—
153C24×C151—22no—
154C24×C151—22no—
155C24×C151—22no—
156C24×C151—22no—
157C24×C151—22no—
158C24×C151—22no—
159C24×C151—22no—
160C24×C151—22no—
161C24×C151—22no—
162C24×C151—22no—
163C24×C151—22no—
164C24×C151—28no—
165C24×C151—28no—
166C24×C151—28no—
167C24×C151—21no—
168C24×C151—21no—
169C24×C151—22no—
170C24×C151—22no—
171C24×C151—22no—
172C24×C151—22no—
173C24×C151—22no—
174C24×C151—22no—
175C24×C151—48no—
176C24×C151—48no—
177C24×C151—48no—
178C24×C151—48no—
179C24×C151—48no—
180C24×C151—48no—
181C24×C151—48no—
182C24×C151—48no—
183C24×C151—48no—
184C24×C151—44no—
185C24×C151—44no—
186C24×C151—48no—
187C24×C151—44no—
188C24×C151—48no—
189C24×C151—48no—
190C24×C151—48no—
191C24×C151—44no—
192C24×C151—48no—
193C24×C151C2×D412yes—
194C24×C151C2×D412yes—
195C24×C151C2×D412yes—
196C24×C151C2×D412yes—
197C24×C151C2×D414yes—
198C24×C151C2×D412yes—
199C24×C151C2×D414yes—
200C24×C151C2×D414yes—
201C24×C151#4114yes—
202C24×C151C2411yescharacteristic
203C2×D4×C151—216no—
204C2×D4×C151—28no—
205C2×D4×C151—28no—
206C2×D4×C151—28no—
207C2×D4×C151—216no—
208C2×D4×C151—28no—
209C2×D4×C151—216no—
210C2×D4×C151—28no—
211C2×D4×C151—44no—
212C2×D4×C151—48no—
213C2×D4×C151—44no—
214C2×D4×C151—48no—
215C2×D4×C151—48no—
216C2×D4×C151—48no—
217C2×D4×C151—48no—
218C2×D4×C151—48no—
219C2×D4×C151—48no—
220C2×D4×C151—48no—
221C2×D4×C151—48no—
222C2×D4×C151—48no—
223C2×D4×C151—48no—
224C2×D4×C151—48no—
225C2×D4×C151—48no—
226C2×D4×C151—48no—
227C2×D4×C151—48no—
228C2×D4×C151—44no—
229C2×D4×C151—48no—
230C2×D4×C151—44no—
231C2×D4×C151—48no—
232C22×C4×C151—21no—
233C22×C4×C151—21no—
234C22×C4×C151—22no—
235C22×C4×C151—28no—
236C22×C4×C151—22no—
237C22×C4×C151—22no—
238C22×C4×C151—22no—
239C22×C4×C151—22no—
240C22×C4×C151—21no—
241C22×C4×C151—21no—
242C22×C4×C151—22no—
243C22×C4×C151—22no—
244C22×C4×C151—22no—
245C22×C4×C151—22no—
246C22×C4×C151—22no—
247C22×C4×C151—21no—
248C22×C4×C151—21no—
249C22×C4×C151—21no—
250C22×C4×C151—21no—
251C22×C4×C151—22no—
252C22×C4×C151—22no—
253C22×C4×C151—22no—
254C22×C4×C151—22no—
255C22×C4×C151—22no—
256C22×C4×C151—22no—
257C22×C4×C151—22no—
258C22×C4×C151—22no—
259C22×C4×C151—22no—
260C22×C4×C151—22no—
261C22×C4×C151—22no—
262C22×C4×C151—22no—
263C22×C4×C151—22no—
264C22×C4×C151—22no—
265C22×C4×C151—22no—
266C22×C4×C151—22no—
267C22×C4×C151—48no—
268C22×C4×C151—48no—
269C22×C4×C151—44no—
270C22×C4×C151—44no—
271C22×C4×C151C2×D414yes—
272C22×C4×C151C2×D414yes—
273C22×C4×C151C2×D412yes—
274C22×C4×C151C2×D412yes—
275C22×C4×C151C2×D412yes—
276C22×C4×C151C2×D414yes—
277C22×C4×C151C2×D412yes—
278C4⋊C4×C151—28no—
279C22⋊C4×C151—216no—
280C22⋊C4×C151—28no—
281C22⋊C4×C151—28no—
282C22⋊C4×C151—28no—
283C22⋊C4×C151—28no—
284C22⋊C4×C151—216no—
285C22⋊C4×C151—48no—
286C22⋊C4×C151—48no—
287C22⋊C4×C151—48no—
288C22⋊C4×C151—48no—
289C22⋊C4×C151—44no—
290C23×C151—22no—
291C23×C151—22no—
292C23×C151—24no—
293C23×C151—24no—
294C23×C151—22no—
295C23×C151—24no—
296C23×C151—22no—
297C23×C151—24no—
298C23×C151—22no—
299C23×C151—22no—
300C23×C151—24no—
301C23×C151—24no—
302C23×C151—22no—
303C23×C151—22no—
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—24no—
314C23×C151—24no—
315C23×C151—24no—
316C23×C151—24no—
317C23×C151—24no—
318C23×C151—24no—
319C23×C151—24no—
320C23×C151—24no—
321C23×C151—24no—
322C23×C151—24no—
323C23×C151—24no—
324C23×C151—24no—
325C23×C151—24no—
326C23×C151—24no—
327C23×C151—24no—
328C23×C151—24no—
329C23×C151—24no—
330C23×C151—22no—
331C23×C151—22no—
332C23×C151—22no—
333C23×C151—24no—
334C23×C151—24no—
335C23×C151—416no—
336C23×C151—416no—
337C23×C151—416no—
338C23×C151—432no—
339C23×C151—432no—
340C23×C151—432no—
341C23×C151—432no—
342C23×C151—432no—
343C23×C151—432no—
344C23×C151—42no—
345C23×C151—41no—
346C23×C151—42no—
347C23×C151—42no—
348C23×C151—41no—
349C23×C151—42no—
350C23×C151—42no—
351C23×C151—42no—
352C23×C151—42no—
353C23×C151—41no—
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—42no—
363C23×C151—42no—
364C23×C151—42no—
365C23×C151—42no—
366C23×C151—42no—
367C23×C151—42no—
368C23×C151—42no—
369C23×C151—42no—
370C23×C151—42no—
371C23×C151—42no—
372C23×C151—42no—
373C23×C151—42no—
374C23×C151—42no—
375C23×C151—42no—
376C23×C151—42no—
377C23×C151—42no—
378C23×C151—41no—
379C23×C151—42no—
380C23×C151—41no—
381C23×C151—42no—
382C23×C151—41no—
383C23×C151—41no—
384C23×C151—42no—
385C23×C151—42no—
386C23×C151—42no—
387C23×C151—42no—
388C23×C151—42no—
389C23×C151—42no—
390C23×C151—42no—
391C23×C151—42no—
392C23×C151—42no—
393C23×C151—42no—
394C23×C151#12014yes—
395C23×C151#12014yescomplemented
396C23×C151#12118yescomplemented
397C23×C151C22×D411yescharacteristic
398C23×C151C22×D411yescharacteristic
399C23×C151C22×D412yes—
400C23×C151C22×D412yes—
401C23×C151C22×D411yescharacteristic
402C23×C151C2×#4112yes—
403C23×C151H(5,𝔽2)12yes—
404C23×C151H(5,𝔽2)12yes—
405C23×C151H(5,𝔽2)12yes—
406D4×C151—416no—
407D4×C151—416no—
408D4×C151—432no—
409D4×C151—416no—
410D4×C151—432no—
411C2×C4×C151—22no—
412C2×C4×C151—22no—
413C2×C4×C151—24no—
414C2×C4×C151—24no—
415C2×C4×C151—22no—
416C2×C4×C151—22no—
417C2×C4×C151—24no—
418C2×C4×C151—24no—
419C2×C4×C151—22no—
420C2×C4×C151—22no—
421C2×C4×C151—24no—
422C2×C4×C151—24no—
423C2×C4×C151—22no—
424C2×C4×C151—24no—
425C2×C4×C151—24no—
426C2×C4×C151—24no—
427C2×C4×C151—24no—
428C2×C4×C151—416no—
429C2×C4×C151—41no—
430C2×C4×C151—41no—
431C2×C4×C151—42no—
432C2×C4×C151—41no—
433C2×C4×C151—41no—
434C2×C4×C151—42no—
435C2×C4×C151—42no—
436C2×C4×C151—42no—
437C2×C4×C151—42no—
438C2×C4×C151—42no—
439C2×C4×C151—42no—
440C2×C4×C151—42no—
441C2×C4×C151—42no—
442C2×C4×C151—42no—
443C2×C4×C151—42no—
444C2×C4×C151—42no—
445C2×C4×C151—42no—
446C2×C4×C151—42no—
447C2×C4×C151—42no—
448C2×C4×C151—42no—
449C2×C4×C151—42no—
450C2×C4×C151—42no—
451C2×C4×C151—42no—
452C2×C4×C151#12014yescomplemented
453C22×C151—24no—
454C22×C151—24no—
455C22×C151—24no—
456C22×C151—24no—
457C22×C151—28no—
458C22×C151—28no—
459C22×C151—28no—
460C22×C151—28no—
461C22×C151—464no—
462C22×C151—42no—
463C22×C151—44no—
464C22×C151—44no—
465C22×C151—42no—
466C22×C151—44no—
467C22×C151—44no—
468C22×C151—44no—
469C22×C151—44no—
470C22×C151—44no—
471C22×C151—44no—
472C22×C151—44no—
473C22×C151—44no—
474C22×C151—44no—
475C22×C151—44no—
476C22×C151—44no—
477C22×C151—44no—
478C22×C151—44no—
479C22×C151—44no—
480C22×C151—44no—
481C22×C151—44no—
482C22×C151—44no—
483C22×C151—44no—
484C22×C151—44no—
485C22×C151—44no—
486C22×C151—44no—
487C22×C151—42no—
488C22×C151—42no—
489C22×C151—42no—
490C22×C151—44no—
491C22×C151—44no—
492C22×C151—82no—
493C22×C151—82no—
494C22×C151—82no—
495C22×C151—82no—
496C22×C151C2×#12011yescharacteristic
497C22×C151C2×#12011yescharacteristic
498C22×C151C2×#12011yescharacteristic
499C22×C151C2×#12112yes—
500C22×C151#52511yescharacteristic
501C22×C151#53411yescharacteristic
502C22×C151#53411yescharacteristic
503C22×C151#53412yes—
504C22×C151#53511yescharacteristic
505C22×C151#53512yes—
506C22×C151#53812yes—
507C22×C151D4212yes—
508C22×C151D4212yes—
509C22×C151D4212yes—
510C22×C151D4212yes—
511C22×C151D4212yes—
512C22×C151#54612yes—
513C22×C151#54612yes—
514C22×C151#54612yes—
515C22×C151#54612yes—
516C22×C151#56012yes—
517C4×C151—24no—
518C4×C151—42no—
519C4×C151—42no—
520C4×C151—42no—
521C4×C151—44no—
522C4×C151—44no—
523C4×C151—82no—
524C2×C151—44no—
525C2×C151—44no—
526C2×C151—48no—
527C2×C151—82no—
528C2×C151#240311yescharacteristic
529C2×C151#240311yescharacteristic
530C2×C151#240411yescharacteristic
531C2×C151#240812yes—
532C2×C151#241012yes—
533C2×C151#242412yes—
534C2×C151#266812yes—
535C2×C151#266912yes—
536C2×C151#267812yes—
537#15257C15111yesmaximal, characteristic, direct product factor, Sylow
538C151#1525711yescharacteristic, direct product factor, Sylow
539C22×#121C2×C15111yescharacteristic, complemented
540C22×#120C2×C15111yescharacteristic, complemented
541C22×#120C2×C15111yescharacteristic, complemented
542C2×#392C2×C15112yescomplemented
543C2×#386C2×C15112yescomplemented
544C2×#379C2×C15111yescharacteristic, complemented
545#1440C2×C15111yescharacteristic, complemented
546#1439C2×C15112yescomplemented
547#1438C2×C15112yescomplemented
548#1438C2×C15111yescharacteristic, complemented
549#1438C2×C15111yescharacteristic, complemented
550C26C22×C15111yescharacteristic
551C23×D4C22×C15112yes—
552C23×D4C22×C15112yes—
553C23×D4C22×C15111yescharacteristic
554C23×D4C22×C15111yescharacteristic
555C23×D4C22×C15111yescharacteristic, complemented
556C24×C4C22×C15111yescharacteristic, complemented
557C2×#121—24no—
558C2×#121—24no—
559C2×#121—24no—
560C2×#120—24no—
561C2×#120—24no—
562C2×#120—28no—
563C2×#120—28no—
564C22×C4⋊C4C22×C15111yescharacteristic, complemented
565C22×C22⋊C4C22×C15112yes—
566C22×C22⋊C4C22×C15111yescharacteristic
567C22×C22⋊C4C22×C15111yescharacteristic
568C22×C22⋊C4C22×C15112yes—
569C22×C22⋊C4C22×C15112yes—
570C22×C22⋊C4C22×C15112yes—
571C22×C22⋊C4C22×C15111yescharacteristic
572C22×C22⋊C4C22×C15111yescharacteristic
573C22×C22⋊C4C22×C15111yescharacteristic, complemented
574C22×C22⋊C4C22×C15112yescomplemented
575C22×C22⋊C4C22×C15112yescomplemented
576#392—28no—
577#386—28no—
578#379—24no—
579C2×#95C22×C15112yescomplemented
580C2×#95C22×C15112yescomplemented
581C2×#95C22×C15112yescomplemented
582C2×#95C22×C15112yescomplemented
583C25—24no—
584C25—22no—
585C25—22no—
586C25—24no—
587C25—24no—
588C25—22no—
589C25—42no—
590C25—42no—
591C25—42no—
592C25C23×C15111yescharacteristic
593C25C23×C15112yes—
594C25C23×C15111yescharacteristic
595C25C23×C15111yescharacteristic
596C22×D4—24no—
597C22×D4—24no—
598C22×D4—24no—
599C22×D4—24no—
600C22×D4—24no—
601C22×D4—24no—
602C22×D4—22no—
603C22×D4—22no—
604C22×D4—22no—
605C22×D4—22no—
606C22×D4—22no—
607C22×D4—22no—
608C22×D4—24no—
609C22×D4—24no—
610C22×D4—24no—
611C22×D4—24no—
612C22×D4—24no—
613C22×D4—24no—
614C22×D4—22no—
615C22×D4—42no—
616C22×D4—42no—
617C22×D4—42no—
618C22×D4—42no—
619C22×D4—42no—
620C22×D4—42no—
621C22×D4—42no—
622C22×D4D4×C15114yescomplemented
623C22×D4D4×C15114yescomplemented
624C22×D4D4×C15118yescomplemented
625C23×C4—22no—
626C23×C4—22no—
627C23×C4—22no—
628C23×C4—24no—
629C23×C4—42no—
630C23×C4C23×C15112yes—
631C23×C4C23×C15111yescharacteristic
632C23×C4C23×C15111yescharacteristic
633C23×C4C23×C15111yescharacteristic
634C23×C4C23×C15112yes—
635C23×C4C23×C15112yes—
636C23×C4C23×C15111yescharacteristic
637#121—232no—
638#120—232no—
639#120—232no—
640C2×C4⋊C4—22no—
641C2×C4⋊C4—22no—
642C2×C4⋊C4—22no—
643C2×C22⋊C4—22no—
644C2×C22⋊C4—22no—
645C2×C22⋊C4—24no—
646C2×C22⋊C4—22no—
647C2×C22⋊C4—22no—
648C2×C22⋊C4—22no—
649C2×C22⋊C4—24no—
650C2×C22⋊C4—24no—
651C2×C22⋊C4—24no—
652C2×C22⋊C4—24no—
653C2×C22⋊C4—24no—
654C2×C22⋊C4—24no—
655C2×C22⋊C4—22no—
656C2×C22⋊C4—22no—
657C2×C22⋊C4—22no—
658C2×C22⋊C4—24no—
659C2×C22⋊C4—24no—
660C2×C22⋊C4—24no—
661C2×C22⋊C4—24no—
662C2×C22⋊C4—24no—
663C2×C22⋊C4—24no—
664C2×C22⋊C4—24no—
665C2×C22⋊C4—42no—
666C2×C22⋊C4—42no—
667C2×C22⋊C4—42no—
668C2×C22⋊C4—42no—
669C2×C22⋊C4—42no—
670C2×C22⋊C4—42no—
671C2×C22⋊C4D4×C15118yescomplemented
672C2×C22⋊C4D4×C15114yescomplemented
673#95—24no—
674#95—24no—
675#95—24no—
676#95—42no—
677C24—22no—
678C24—22no—
679C24—22no—
680C24—22no—
681C24—22no—
682C24—22no—
683C24—22no—
684C24—22no—
685C24—21no—
686C24—21no—
687C24—22no—
688C24—22no—
689C24—22no—
690C24—22no—
691C24—22no—
692C24—22no—
693C24—22no—
694C24—22no—
695C24—22no—
696C24—22no—
697C24—22no—
698C24—22no—
699C24—22no—
700C24—22no—
701C24—22no—
702C24—28no—
703C24—28no—
704C24—28no—
705C24—21no—
706C24—21no—
707C24—22no—
708C24—22no—
709C24—22no—
710C24—22no—
711C24—22no—
712C24—22no—
713C24—48no—
714C24—48no—
715C24—48no—
716C24—48no—
717C24—48no—
718C24—48no—
719C24—48no—
720C24—48no—
721C24—48no—
722C24—44no—
723C24—44no—
724C24—48no—
725C24—44no—
726C24—48no—
727C24—48no—
728C24—48no—
729C24—44no—
730C24—48no—
731C24C2×D4×C15112yes—
732C24C2×D4×C15112yes—
733C24C2×D4×C15112yes—
734C24C2×D4×C15112yes—
735C24C2×D4×C15114yes—
736C24C2×D4×C15112yes—
737C24C2×D4×C15114yes—
738C24C2×D4×C15114yes—
739C24#41×C15114yes—
740C24C24×C15111yescharacteristic
741C2×D4—216no—
742C2×D4—28no—
743C2×D4—28no—
744C2×D4—28no—
745C2×D4—28no—
746C2×D4—216no—
747C2×D4—216no—
748C2×D4—28no—
749C2×D4—44no—
750C2×D4—48no—
751C2×D4—44no—
752C2×D4—48no—
753C2×D4—48no—
754C2×D4—48no—
755C2×D4—48no—
756C2×D4—48no—
757C2×D4—48no—
758C2×D4—48no—
759C2×D4—48no—
760C2×D4—48no—
761C2×D4—48no—
762C2×D4—48no—
763C2×D4—48no—
764C2×D4—48no—
765C2×D4—48no—
766C2×D4—44no—
767C2×D4—48no—
768C2×D4—44no—
769C2×D4—48no—
770C22×C4—21no—
771C22×C4—21no—
772C22×C4—22no—
773C22×C4—28no—
774C22×C4—22no—
775C22×C4—22no—
776C22×C4—22no—
777C22×C4—22no—
778C22×C4—21no—
779C22×C4—21no—
780C22×C4—22no—
781C22×C4—22no—
782C22×C4—22no—
783C22×C4—22no—
784C22×C4—22no—
785C22×C4—21no—
786C22×C4—21no—
787C22×C4—21no—
788C22×C4—21no—
789C22×C4—22no—
790C22×C4—22no—
791C22×C4—22no—
792C22×C4—22no—
793C22×C4—22no—
794C22×C4—22no—
795C22×C4—22no—
796C22×C4—22no—
797C22×C4—22no—
798C22×C4—22no—
799C22×C4—22no—
800C22×C4—22no—
801C22×C4—22no—
802C22×C4—22no—
803C22×C4—22no—
804C22×C4—22no—
805C22×C4—48no—
806C22×C4—48no—
807C22×C4—44no—
808C22×C4—44no—
809C22×C4C2×D4×C15114yes—
810C22×C4C2×D4×C15114yes—
811C22×C4C2×D4×C15112yes—
812C22×C4C2×D4×C15112yes—
813C22×C4C2×D4×C15112yes—
814C22×C4C2×D4×C15114yes—
815C22×C4C2×D4×C15112yes—
816C4⋊C4—28no—
817C22⋊C4—216no—
818C22⋊C4—28no—
819C22⋊C4—28no—
820C22⋊C4—28no—
821C22⋊C4—28no—
822C22⋊C4—216no—
823C22⋊C4—48no—
824C22⋊C4—48no—
825C22⋊C4—48no—
826C22⋊C4—48no—
827C22⋊C4—44no—
828C23—22no—
829C23—22no—
830C23—24no—
831C23—24no—
832C23—22no—
833C23—24no—
834C23—24no—
835C23—22no—
836C23—22no—
837C23—22no—
838C23—22no—
839C23—24no—
840C23—24no—
841C23—22no—
842C23—24no—
843C23—24no—
844C23—24no—
845C23—24no—
846C23—24no—
847C23—24no—
848C23—24no—
849C23—24no—
850C23—24no—
851C23—24no—
852C23—24no—
853C23—24no—
854C23—24no—
855C23—24no—
856C23—24no—
857C23—24no—
858C23—24no—
859C23—24no—
860C23—24no—
861C23—24no—
862C23—24no—
863C23—24no—
864C23—24no—
865C23—24no—
866C23—24no—
867C23—24no—
868C23—22no—
869C23—22no—
870C23—22no—
871C23—24no—
872C23—24no—
873C23—416no—
874C23—416no—
875C23—416no—
876C23—432no—
877C23—432no—
878C23—432no—
879C23—432no—
880C23—432no—
881C23—432no—
882C23—41no—
883C23—42no—
884C23—42no—
885C23—42no—
886C23—41no—
887C23—41no—
888C23—42no—
889C23—42no—
890C23—42no—
891C23—42no—
892C23—42no—
893C23—42no—
894C23—42no—
895C23—41no—
896C23—42no—
897C23—42no—
898C23—42no—
899C23—42no—
900C23—42no—
901C23—42no—
902C23—42no—
903C23—42no—
904C23—42no—
905C23—42no—
906C23—42no—
907C23—42no—
908C23—42no—
909C23—42no—
910C23—42no—
911C23—42no—
912C23—42no—
913C23—42no—
914C23—42no—
915C23—42no—
916C23—41no—
917C23—42no—
918C23—41no—
919C23—42no—
920C23—41no—
921C23—42no—
922C23—41no—
923C23—42no—
924C23—42no—
925C23—42no—
926C23—42no—
927C23—42no—
928C23—42no—
929C23—42no—
930C23—42no—
931C23—42no—
932C23#120×C15114yes—
933C23#120×C15114yescomplemented
934C23#121×C15118yescomplemented
935C23C22×D4×C15111yescharacteristic
936C23C22×D4×C15111yescharacteristic
937C23C22×D4×C15112yes—
938C23C22×D4×C15112yes—
939C23C22×D4×C15111yescharacteristic
940C23C2×#41×C15112yes—
941C23H(5,𝔽2)×C15112yes—
942C23H(5,𝔽2)×C15112yes—
943C23H(5,𝔽2)×C15112yes—
944D4—416no—
945D4—416no—
946D4—432no—
947D4—416no—
948D4—432no—
949C2×C4—22no—
950C2×C4—22no—
951C2×C4—24no—
952C2×C4—24no—
953C2×C4—22no—
954C2×C4—22no—
955C2×C4—24no—
956C2×C4—24no—
957C2×C4—22no—
958C2×C4—22no—
959C2×C4—24no—
960C2×C4—24no—
961C2×C4—22no—
962C2×C4—24no—
963C2×C4—24no—
964C2×C4—24no—
965C2×C4—24no—
966C2×C4—416no—
967C2×C4—41no—
968C2×C4—41no—
969C2×C4—42no—
970C2×C4—41no—
971C2×C4—41no—
972C2×C4—42no—
973C2×C4—42no—
974C2×C4—42no—
975C2×C4—42no—
976C2×C4—42no—
977C2×C4—42no—
978C2×C4—42no—
979C2×C4—42no—
980C2×C4—42no—
981C2×C4—42no—
982C2×C4—42no—
983C2×C4—42no—
984C2×C4—42no—
985C2×C4—42no—
986C2×C4—42no—
987C2×C4—42no—
988C2×C4—42no—
989C2×C4—42no—
990C2×C4#120×C15114yescomplemented
991C22—24no—
992C22—24no—
993C22—24no—
994C22—24no—
995C22—28no—
996C22—28no—
997C22—28no—
998C22—28no—
999C22—464no—
1000C22—42no—
1001C22—44no—
1002C22—44no—
1003C22—44no—
1004C22—42no—
1005C22—44no—
1006C22—44no—
1007C22—44no—
1008C22—44no—
1009C22—44no—
1010C22—44no—
1011C22—44no—
1012C22—44no—
1013C22—44no—
1014C22—44no—
1015C22—44no—
1016C22—44no—
1017C22—44no—
1018C22—44no—
1019C22—44no—
1020C22—44no—
1021C22—44no—
1022C22—44no—
1023C22—44no—
1024C22—44no—
1025C22—42no—
1026C22—42no—
1027C22—42no—
1028C22—44no—
1029C22—44no—
1030C22—82no—
1031C22—82no—
1032C22—82no—
1033C22—82no—
1034C22C2×#120×C15111yescharacteristic
1035C22C2×#120×C15111yescharacteristic
1036C22C2×#120×C15111yescharacteristic
1037C22C2×#121×C15112yes—
1038C22#525×C15111yescharacteristic
1039C22#534×C15111yescharacteristic
1040C22#534×C15111yescharacteristic
1041C22#534×C15112yes—
1042C22#535×C15111yescharacteristic
1043C22#535×C15112yes—
1044C22#538×C15112yes—
1045C22D42×C15112yes—
1046C22D42×C15112yes—
1047C22D42×C15112yes—
1048C22D42×C15112yes—
1049C22D42×C15112yes—
1050C22#546×C15112yes—
1051C22#546×C15112yes—
1052C22#546×C15112yes—
1053C22#546×C15112yes—
1054C22#560×C15112yes—
1055C4—24no—
1056C4—42no—
1057C4—42no—
1058C4—42no—
1059C4—44no—
1060C4—44no—
1061C4—82no—
1062C2—44no—
1063C2—48no—
1064C2—44no—
1065C2—82no—
1066C2#2403×C15111yescharacteristic
1067C2#2403×C15111yescharacteristic
1068C2#2404×C15111yescharacteristic
1069C2#2408×C15112yes—
1070C2#2410×C15112yes—
1071C2#2424×C15112yes—
1072C2#2668×C15112yes—
1073C2#2669×C15112yes—
1074C2#2678×C15112yes—
subgroupG/H
center, socleC24×C151C24
commutator, Frattini, cosocleC24C24×C151
LCSG ▷ C24 ▷ C1
UCSC1 ◁ C24×C151 ◁ G

Complements

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

NH ≅ G/Ntype
1. C22×#121×C151C2semidirect
2. C22×#120×C151C2semidirect
3. C22×#120×C151C2semidirect
4. C2×#392×C151C2semidirect
5. C2×#386×C151C2semidirect
6. C2×#379×C151C2semidirect
7. #1440×C151C2semidirect
8. #1439×C151C2semidirect
9. #1438×C151C2semidirect
10. #1438×C151C2semidirect
11. #1438×C151C2semidirect
17. C23×D4×C151C22semidirect
18. C24×C4×C151C22semidirect
26. C22×C4⋊C4×C151C22semidirect
35. C22×C22⋊C4×C151C22semidirect
36. C22×C22⋊C4×C151C22semidirect
37. C22×C22⋊C4×C151C22semidirect
41. C2×#95×C151C22semidirect
42. C2×#95×C151C22semidirect
43. C2×#95×C151C22semidirect
44. C2×#95×C151C22semidirect
84. C22×D4×C151D4semidirect
85. C22×D4×C151D4semidirect
86. C22×D4×C151D4semidirect
133. C2×C22⋊C4×C151D4semidirect
134. C2×C22⋊C4×C151D4semidirect
395. C23×C151#120semidirect
396. C23×C151#121semidirect
452. C2×C4×C151#120semidirect
537. #15257C151direct (N × H)
538. C151#15257direct (N × H)
539. C22×#121C2×C151semidirect
540. C22×#120C2×C151semidirect
541. C22×#120C2×C151semidirect
542. C2×#392C2×C151semidirect
543. C2×#386C2×C151semidirect
544. C2×#379C2×C151semidirect
545. #1440C2×C151semidirect
546. #1439C2×C151semidirect
547. #1438C2×C151semidirect
548. #1438C2×C151semidirect
549. #1438C2×C151semidirect
555. C23×D4C22×C151semidirect
556. C24×C4C22×C151semidirect
564. C22×C4⋊C4C22×C151semidirect
573. C22×C22⋊C4C22×C151semidirect
574. C22×C22⋊C4C22×C151semidirect
575. C22×C22⋊C4C22×C151semidirect
579. C2×#95C22×C151semidirect
580. C2×#95C22×C151semidirect
581. C2×#95C22×C151semidirect
582. C2×#95C22×C151semidirect
622. C22×D4D4×C151semidirect
623. C22×D4D4×C151semidirect
624. C22×D4D4×C151semidirect
671. C2×C22⋊C4D4×C151semidirect
672. C2×C22⋊C4D4×C151semidirect
933. C23#120×C151semidirect
934. C23#121×C151semidirect
990. C2×C4#120×C151semidirect

Maximal subgroups

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

subgroupindex
C22×#121×C1512
C22×#120×C1512
C2×#392×C1512
C2×#386×C1512
C2×#379×C1512
#1440×C1512
#1439×C1512
#1438×C1512
#15257151