Finite Group Databasebeta

← C151×#14839 #50319764

Subgroups — C151×#14839 #50319764

Order 38656.

1962 conjugacy classes of subgroups.

The subgroup lattice has 764 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#399×C151C211yesmaximal, characteristic, complemented
2C2×#397×C151C212yesmaximal, complemented
3C2×#394×C151C212yesmaximal
4C2×#386×C151C211yesmaximal, characteristic
5C2×#380×C151C211yesmaximal, characteristic, complemented
6C2×C4×C22⋊C4×C151C211yesmaximal, characteristic, complemented
7#1445×C151C211yesmaximal, characteristic, complemented
8#1444×C151C211yesmaximal, characteristic, complemented
9#1439×C151C211yesmaximal, characteristic, complemented
10#1437×C151C212yesmaximal, complemented
11C4⋊#95×C151C212yesmaximal, complemented
12C23×D4×C151C2211yescharacteristic
13C24×C4×C151C2211yescharacteristic
14C22×C4⋊C4×C151C2212yes—
15C22×C4⋊C4×C151C2211yescharacteristic
16C22×C4⋊C4×C151C2212yes—
17C22×C4⋊C4×C151C2211yescharacteristic
18C22×C22⋊C4×C151C2212yes—
19C22×C22⋊C4×C151C2212yes—
20C22×C22⋊C4×C151C2211yescharacteristic
21C22×C22⋊C4×C151C2211yescharacteristic
22C22×C22⋊C4×C151C2211yescharacteristic
23C22×C22⋊C4×C151C2212yes—
24C22×C22⋊C4×C151C2212yes—
25C22×C42×C151C2212yes—
26#399×C151—24no—
27#397×C151—28no—
28#394×C151—28no—
29#386×C151—24no—
30#380×C151—24no—
31C4×C22⋊C4×C151—24no—
32C2×#95×C151C2212yes—
33C2×#95×C151C2212yes—
34C2×#95×C151C2212yes—
35C2×#95×C151C2212yes—
36C2×#95×C151C2211yescharacteristic
37C2×#95×C151C2212yes—
38C2×#95×C151C2211yescharacteristic
39C2×#95×C151C2211yescharacteristic
40C2×#95×C151C2211yescharacteristic
41C25×C151C2311yescharacteristic
42C25×C151C2311yescharacteristic
43C22×D4×C151—22no—
44C22×D4×C151—22no—
45C22×D4×C151—24no—
46C22×D4×C151—22no—
47C22×D4×C151—42no—
48C23×C4×C151—22no—
49C23×C4×C151—22no—
50C23×C4×C151—24no—
51C23×C4×C151—42no—
52C23×C4×C151D414yes—
53C23×C4×C151C2311yescharacteristic
54C23×C4×C151C2312yes—
55C23×C4×C151C2312yes—
56C23×C4×C151C2311yescharacteristic
57C23×C4×C151C2312yes—
58C23×C4×C151C2311yescharacteristic
59C23×C4×C151C2311yescharacteristic
60C23×C4×C151C2312yes—
61C23×C4×C151C2311yescharacteristic
62C2×C4⋊C4×C151—22no—
63C2×C4⋊C4×C151—22no—
64C2×C4⋊C4×C151—24no—
65C2×C4⋊C4×C151—24no—
66C2×C4⋊C4×C151—22no—
67C2×C4⋊C4×C151—24no—
68C2×C4⋊C4×C151—24no—
69C2×C4⋊C4×C151—24no—
70C2×C4⋊C4×C151—22no—
71C2×C4⋊C4×C151—42no—
72C2×C4⋊C4×C151—42no—
73C2×C22⋊C4×C151—24no—
74C2×C22⋊C4×C151—24no—
75C2×C22⋊C4×C151—22no—
76C2×C22⋊C4×C151—22no—
77C2×C22⋊C4×C151—24no—
78C2×C22⋊C4×C151—24no—
79C2×C22⋊C4×C151—22no—
80C2×C22⋊C4×C151—24no—
81C2×C22⋊C4×C151—24no—
82C2×C22⋊C4×C151—22no—
83C2×C22⋊C4×C151—24no—
84C2×C22⋊C4×C151—24no—
85C2×C22⋊C4×C151—22no—
86C2×C22⋊C4×C151—24no—
87C2×C22⋊C4×C151—24no—
88C2×C22⋊C4×C151—24no—
89C2×C22⋊C4×C151—24no—
90C2×C22⋊C4×C151—42no—
91C2×C22⋊C4×C151D418yes—
92C2×C42×C151—24no—
93C2×C42×C151—24no—
94C2×C42×C151—42no—
95#95×C151—22no—
96#95×C151—24no—
97#95×C151—22no—
98#95×C151—22no—
99#95×C151—24no—
100#95×C151—24no—
101#95×C151—24no—
102#95×C151—24no—
103#95×C151D414yescomplemented
104C24×C151—21no—
105C24×C151—22no—
106C24×C151—21no—
107C24×C151—22no—
108C24×C151—21no—
109C24×C151—21no—
110C24×C151—22no—
111C24×C151—21no—
112C24×C151—21no—
113C24×C151—21no—
114C24×C151—21no—
115C24×C151—22no—
116C24×C151—22no—
117C24×C151—22no—
118C24×C151—21no—
119C24×C151—21no—
120C24×C151—22no—
121C24×C151—21no—
122C24×C151—21no—
123C24×C151C2×D414yes—
124C24×C151C2×D412yes—
125C24×C151#4112yes—
126C24×C151C2411yescharacteristic
127C2×D4×C151—28no—
128C2×D4×C151—48no—
129C2×D4×C151—48no—
130C2×D4×C151—44no—
131C2×D4×C151—44no—
132C22×C4×C151—21no—
133C22×C4×C151—22no—
134C22×C4×C151—22no—
135C22×C4×C151—21no—
136C22×C4×C151—22no—
137C22×C4×C151—22no—
138C22×C4×C151—22no—
139C22×C4×C151—22no—
140C22×C4×C151—22no—
141C22×C4×C151—21no—
142C22×C4×C151—22no—
143C22×C4×C151—22no—
144C22×C4×C151—22no—
145C22×C4×C151—22no—
146C22×C4×C151—22no—
147C22×C4×C151—21no—
148C22×C4×C151—22no—
149C22×C4×C151—22no—
150C22×C4×C151—22no—
151C22×C4×C151—28no—
152C22×C4×C151—28no—
153C22×C4×C151—22no—
154C22×C4×C151—22no—
155C22×C4×C151—21no—
156C22×C4×C151—22no—
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—21no—
164C22×C4×C151—22no—
165C22×C4×C151—22no—
166C22×C4×C151—21no—
167C22×C4×C151—22no—
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—21no—
176C22×C4×C151—21no—
177C22×C4×C151—44no—
178C22×C4×C151—48no—
179C22×C4×C151—48no—
180C22×C4×C151C2×D414yes—
181C22×C4×C151C2×D412yes—
182C22×C4×C151C2×D414yes—
183C22×C4×C151C2×D412yes—
184C22×C4×C151C2×D414yes—
185C22×C4×C151C2×D412yes—
186C22×C4×C151#4112yes—
187C22×C4×C151#4114yes—
188C22×C4×C151#4112yes—
189C22×C4×C151#4114yes—
190C4⋊C4×C151—48no—
191C4⋊C4×C151—44no—
192C4⋊C4×C151—48no—
193C4⋊C4×C151—44no—
194C22⋊C4×C151—216no—
195C22⋊C4×C151—48no—
196C22⋊C4×C151—48no—
197C22⋊C4×C151—44no—
198C22⋊C4×C151—48no—
199C22⋊C4×C151—44no—
200C22⋊C4×C151—44no—
201C42×C151—48no—
202C23×C151—24no—
203C23×C151—22no—
204C23×C151—22no—
205C23×C151—22no—
206C23×C151—22no—
207C23×C151—24no—
208C23×C151—22no—
209C23×C151—22no—
210C23×C151—24no—
211C23×C151—24no—
212C23×C151—24no—
213C23×C151—24no—
214C23×C151—22no—
215C23×C151—24no—
216C23×C151—24no—
217C23×C151—22no—
218C23×C151—22no—
219C23×C151—42no—
220C23×C151—42no—
221C23×C151—42no—
222C23×C151—42no—
223C23×C151—42no—
224C23×C151—41no—
225C23×C151—41no—
226C23×C151—42no—
227C23×C151—41no—
228C23×C151—41no—
229C23×C151—41no—
230C23×C151—42no—
231C23×C151—41no—
232C23×C151—42no—
233C23×C151—41no—
234C23×C151—41no—
235C23×C151—42no—
236C23×C151—41no—
237C23×C151—41no—
238C23×C151—42no—
239C23×C151—42no—
240C23×C151—42no—
241C23×C151—42no—
242C23×C151—41no—
243C23×C151—42no—
244C23×C151—42no—
245C23×C151—42no—
246C23×C151—41no—
247C23×C151#12714yes—
248C23×C151C22×D411yescharacteristic
249C23×C151C22×D411yescharacteristic
250C23×C151C22×D412yes—
251C23×C151C2×#4112yes—
252C23×C151C2×#4111yescharacteristic
253C23×C151C2×#4112yes—
254C23×C151C2×#4111yescharacteristic
255C23×C151C2×#4111yescharacteristic
256C23×C151H(5,𝔽2)12yes—
257C23×C1512−1+411yescharacteristic
258C23×C1512−1+411yescharacteristic
259D4×C151—416no—
260C2×C4×C151—22no—
261C2×C4×C151—22no—
262C2×C4×C151—24no—
263C2×C4×C151—22no—
264C2×C4×C151—22no—
265C2×C4×C151—24no—
266C2×C4×C151—24no—
267C2×C4×C151—24no—
268C2×C4×C151—24no—
269C2×C4×C151—24no—
270C2×C4×C151—24no—
271C2×C4×C151—24no—
272C2×C4×C151—24no—
273C2×C4×C151—24no—
274C2×C4×C151—24no—
275C2×C4×C151—22no—
276C2×C4×C151—24no—
277C2×C4×C151—24no—
278C2×C4×C151—24no—
279C2×C4×C151—416no—
280C2×C4×C151—42no—
281C2×C4×C151—41no—
282C2×C4×C151—41no—
283C2×C4×C151—42no—
284C2×C4×C151—42no—
285C2×C4×C151—42no—
286C2×C4×C151—42no—
287C2×C4×C151—41no—
288C2×C4×C151—42no—
289C2×C4×C151—42no—
290C2×C4×C151—42no—
291C2×C4×C151—42no—
292C2×C4×C151—41no—
293C2×C4×C151—42no—
294C2×C4×C151—42no—
295C2×C4×C151—41no—
296C2×C4×C151—41no—
297C2×C4×C151—42no—
298C2×C4×C151—41no—
299C2×C4×C151—42no—
300C2×C4×C151—42no—
301C2×C4×C151—42no—
302C2×C4×C151—42no—
303C2×C4×C151—42no—
304C2×C4×C151—41no—
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#12118yes—
312C2×C4×C151#12114yes—
313C2×C4×C151#12314yes—
314C22×C151—24no—
315C22×C151—24no—
316C22×C151—24no—
317C22×C151—42no—
318C22×C151—42no—
319C22×C151—42no—
320C22×C151—42no—
321C22×C151—44no—
322C22×C151—44no—
323C22×C151—44no—
324C22×C151—44no—
325C22×C151—42no—
326C22×C151—42no—
327C22×C151—44no—
328C22×C151—42no—
329C22×C151—44no—
330C22×C151—81no—
331C22×C151—81no—
332C22×C151—81no—
333C22×C151—82no—
334C22×C151—81no—
335C22×C151—82no—
336C22×C151C2×#12111yescharacteristic
337C22×C151C2×#12112yes—
338C22×C151C2×#12311yescharacteristic
339C22×C151#52511yescharacteristic
340C22×C151#52912yes—
341C22×C151#52912yes—
342C22×C151C2×#12711yescharacteristic
343C22×C151#53211yescharacteristic
344C22×C151#53212yes—
345C22×C151#53411yescharacteristic
346C22×C151#53611yescharacteristic
347C22×C151#53912yes—
348C22×C151#54212yes—
349C22×C151#54612yes—
350C22×C151#54612yes—
351C22×C151#54612yes—
352C22×C151#54711yescharacteristic
353C22×C151#54712yes—
354C22×C151#54712yes—
355C22×C151#54811yescharacteristic
356C22×C151#55112yes—
357C22×C151#55211yescharacteristic
358C22×C151#55611yescharacteristic
359C4×C151—24no—
360C4×C151—24no—
361C4×C151—28no—
362C4×C151—44no—
363C4×C151—42no—
364C4×C151—81no—
365C4×C151—82no—
366C4×C151—81no—
367C4×C151—82no—
368C2×C151—44no—
369C2×C151—82no—
370C2×C151#239511yescharacteristic
371C2×C151#241211yescharacteristic
372C2×C151#241511yescharacteristic
373C2×C151#242512yes—
374C2×C151#242712yes—
375C2×C151#250111yescharacteristic
376C2×C151#252112yes—
377C2×C151#253911yescharacteristic
378C2×C151#255312yes—
379C2×C151#266311yescharacteristic
380C2×C151#285611yescharacteristic
381#14839C15111yesmaximal, characteristic, direct product factor, Sylow
382C151#1483911yescharacteristic, direct product factor, Sylow
383C2×#399C2×C15111yescharacteristic, complemented
384C2×#397C2×C15112yescomplemented
385C2×#394C2×C15112yes—
386C2×#386C2×C15111yescharacteristic
387C2×#380C2×C15111yescharacteristic, complemented
388C2×C4×C22⋊C4C2×C15111yescharacteristic, complemented
389#1445C2×C15111yescharacteristic, complemented
390#1444C2×C15111yescharacteristic, complemented
391#1439C2×C15111yescharacteristic, complemented
392#1437C2×C15112yescomplemented
393C4⋊#95C2×C15112yescomplemented
394C23×D4C22×C15111yescharacteristic
395C24×C4C22×C15111yescharacteristic
396C22×C4⋊C4C22×C15112yes—
397C22×C4⋊C4C22×C15111yescharacteristic
398C22×C4⋊C4C22×C15112yes—
399C22×C4⋊C4C22×C15111yescharacteristic
400C22×C22⋊C4C22×C15112yes—
401C22×C22⋊C4C22×C15112yes—
402C22×C22⋊C4C22×C15111yescharacteristic
403C22×C22⋊C4C22×C15111yescharacteristic
404C22×C22⋊C4C22×C15111yescharacteristic
405C22×C22⋊C4C22×C15112yes—
406C22×C22⋊C4C22×C15112yes—
407C22×C42C22×C15112yes—
408#399—24no—
409#397—28no—
410#394—28no—
411#386—24no—
412#380—24no—
413C4×C22⋊C4—24no—
414C2×#95C22×C15112yes—
415C2×#95C22×C15112yes—
416C2×#95C22×C15112yes—
417C2×#95C22×C15112yes—
418C2×#95C22×C15111yescharacteristic
419C2×#95C22×C15112yes—
420C2×#95C22×C15111yescharacteristic
421C2×#95C22×C15111yescharacteristic
422C2×#95C22×C15111yescharacteristic
423C25C23×C15111yescharacteristic
424C25C23×C15111yescharacteristic
425C22×D4—22no—
426C22×D4—22no—
427C22×D4—24no—
428C22×D4—22no—
429C22×D4—42no—
430C23×C4—22no—
431C23×C4—24no—
432C23×C4—22no—
433C23×C4—42no—
434C23×C4D4×C15114yes—
435C23×C4C23×C15112yes—
436C23×C4C23×C15112yes—
437C23×C4C23×C15111yescharacteristic
438C23×C4C23×C15111yescharacteristic
439C23×C4C23×C15111yescharacteristic
440C23×C4C23×C15112yes—
441C23×C4C23×C15111yescharacteristic
442C23×C4C23×C15112yes—
443C23×C4C23×C15111yescharacteristic
444C2×C4⋊C4—24no—
445C2×C4⋊C4—24no—
446C2×C4⋊C4—22no—
447C2×C4⋊C4—22no—
448C2×C4⋊C4—22no—
449C2×C4⋊C4—24no—
450C2×C4⋊C4—24no—
451C2×C4⋊C4—22no—
452C2×C4⋊C4—24no—
453C2×C4⋊C4—42no—
454C2×C4⋊C4—42no—
455C2×C22⋊C4—24no—
456C2×C22⋊C4—24no—
457C2×C22⋊C4—24no—
458C2×C22⋊C4—24no—
459C2×C22⋊C4—22no—
460C2×C22⋊C4—24no—
461C2×C22⋊C4—24no—
462C2×C22⋊C4—24no—
463C2×C22⋊C4—24no—
464C2×C22⋊C4—22no—
465C2×C22⋊C4—24no—
466C2×C22⋊C4—22no—
467C2×C22⋊C4—22no—
468C2×C22⋊C4—24no—
469C2×C22⋊C4—24no—
470C2×C22⋊C4—22no—
471C2×C22⋊C4—24no—
472C2×C22⋊C4—42no—
473C2×C22⋊C4D4×C15118yes—
474C2×C42—24no—
475C2×C42—24no—
476C2×C42—42no—
477#95—22no—
478#95—24no—
479#95—22no—
480#95—22no—
481#95—24no—
482#95—24no—
483#95—24no—
484#95—24no—
485#95D4×C15114yescomplemented
486C24—21no—
487C24—22no—
488C24—21no—
489C24—22no—
490C24—21no—
491C24—21no—
492C24—22no—
493C24—21no—
494C24—21no—
495C24—21no—
496C24—21no—
497C24—22no—
498C24—22no—
499C24—22no—
500C24—21no—
501C24—21no—
502C24—22no—
503C24—21no—
504C24—21no—
505C24C2×D4×C15114yes—
506C24C2×D4×C15112yes—
507C24#41×C15112yes—
508C24C24×C15111yescharacteristic
509C2×D4—28no—
510C2×D4—48no—
511C2×D4—48no—
512C2×D4—44no—
513C2×D4—44no—
514C22×C4—21no—
515C22×C4—22no—
516C22×C4—22no—
517C22×C4—21no—
518C22×C4—22no—
519C22×C4—22no—
520C22×C4—22no—
521C22×C4—22no—
522C22×C4—22no—
523C22×C4—21no—
524C22×C4—22no—
525C22×C4—22no—
526C22×C4—22no—
527C22×C4—22no—
528C22×C4—22no—
529C22×C4—21no—
530C22×C4—22no—
531C22×C4—22no—
532C22×C4—22no—
533C22×C4—28no—
534C22×C4—28no—
535C22×C4—22no—
536C22×C4—22no—
537C22×C4—21no—
538C22×C4—22no—
539C22×C4—21no—
540C22×C4—22no—
541C22×C4—22no—
542C22×C4—22no—
543C22×C4—22no—
544C22×C4—22no—
545C22×C4—21no—
546C22×C4—22no—
547C22×C4—22no—
548C22×C4—21no—
549C22×C4—22no—
550C22×C4—22no—
551C22×C4—22no—
552C22×C4—22no—
553C22×C4—22no—
554C22×C4—22no—
555C22×C4—22no—
556C22×C4—22no—
557C22×C4—21no—
558C22×C4—21no—
559C22×C4—44no—
560C22×C4—48no—
561C22×C4—48no—
562C22×C4C2×D4×C15114yes—
563C22×C4C2×D4×C15112yes—
564C22×C4C2×D4×C15114yes—
565C22×C4C2×D4×C15112yes—
566C22×C4C2×D4×C15114yes—
567C22×C4C2×D4×C15112yes—
568C22×C4#41×C15112yes—
569C22×C4#41×C15114yes—
570C22×C4#41×C15112yes—
571C22×C4#41×C15114yes—
572C4⋊C4—48no—
573C4⋊C4—44no—
574C4⋊C4—48no—
575C4⋊C4—44no—
576C22⋊C4—216no—
577C22⋊C4—48no—
578C22⋊C4—48no—
579C22⋊C4—44no—
580C22⋊C4—48no—
581C22⋊C4—44no—
582C22⋊C4—44no—
583C42—48no—
584C23—24no—
585C23—22no—
586C23—22no—
587C23—22no—
588C23—22no—
589C23—24no—
590C23—22no—
591C23—22no—
592C23—24no—
593C23—24no—
594C23—24no—
595C23—24no—
596C23—22no—
597C23—24no—
598C23—24no—
599C23—22no—
600C23—22no—
601C23—42no—
602C23—42no—
603C23—42no—
604C23—42no—
605C23—42no—
606C23—41no—
607C23—41no—
608C23—42no—
609C23—41no—
610C23—41no—
611C23—41no—
612C23—42no—
613C23—41no—
614C23—42no—
615C23—41no—
616C23—41no—
617C23—42no—
618C23—41no—
619C23—41no—
620C23—42no—
621C23—42no—
622C23—42no—
623C23—42no—
624C23—41no—
625C23—42no—
626C23—42no—
627C23—42no—
628C23—41no—
629C23#127×C15114yes—
630C23C22×D4×C15111yescharacteristic
631C23C22×D4×C15111yescharacteristic
632C23C22×D4×C15112yes—
633C23C2×#41×C15112yes—
634C23C2×#41×C15111yescharacteristic
635C23C2×#41×C15112yes—
636C23C2×#41×C15111yescharacteristic
637C23C2×#41×C15111yescharacteristic
638C23H(5,𝔽2)×C15112yes—
639C232−1+4×C15111yescharacteristic
640C232−1+4×C15111yescharacteristic
641D4—416no—
642C2×C4—22no—
643C2×C4—22no—
644C2×C4—24no—
645C2×C4—22no—
646C2×C4—22no—
647C2×C4—24no—
648C2×C4—24no—
649C2×C4—24no—
650C2×C4—24no—
651C2×C4—24no—
652C2×C4—24no—
653C2×C4—24no—
654C2×C4—24no—
655C2×C4—24no—
656C2×C4—24no—
657C2×C4—22no—
658C2×C4—24no—
659C2×C4—24no—
660C2×C4—24no—
661C2×C4—416no—
662C2×C4—42no—
663C2×C4—41no—
664C2×C4—41no—
665C2×C4—42no—
666C2×C4—42no—
667C2×C4—42no—
668C2×C4—42no—
669C2×C4—41no—
670C2×C4—42no—
671C2×C4—42no—
672C2×C4—42no—
673C2×C4—42no—
674C2×C4—41no—
675C2×C4—42no—
676C2×C4—42no—
677C2×C4—41no—
678C2×C4—41no—
679C2×C4—42no—
680C2×C4—41no—
681C2×C4—42no—
682C2×C4—42no—
683C2×C4—42no—
684C2×C4—42no—
685C2×C4—42no—
686C2×C4—41no—
687C2×C4—42no—
688C2×C4—42no—
689C2×C4—42no—
690C2×C4—42no—
691C2×C4—42no—
692C2×C4—42no—
693C2×C4#121×C15118yes—
694C2×C4#121×C15114yes—
695C2×C4#123×C15114yes—
696C22—24no—
697C22—24no—
698C22—24no—
699C22—42no—
700C22—42no—
701C22—42no—
702C22—42no—
703C22—44no—
704C22—44no—
705C22—44no—
706C22—44no—
707C22—42no—
708C22—42no—
709C22—44no—
710C22—42no—
711C22—44no—
712C22—81no—
713C22—81no—
714C22—81no—
715C22—82no—
716C22—81no—
717C22—82no—
718C22C2×#121×C15111yescharacteristic
719C22C2×#121×C15112yes—
720C22C2×#123×C15111yescharacteristic
721C22#525×C15111yescharacteristic
722C22#529×C15112yes—
723C22#529×C15112yes—
724C22C2×#127×C15111yescharacteristic
725C22#532×C15111yescharacteristic
726C22#532×C15112yes—
727C22#534×C15111yescharacteristic
728C22#536×C15111yescharacteristic
729C22#539×C15112yes—
730C22#542×C15112yes—
731C22#546×C15112yes—
732C22#546×C15112yes—
733C22#546×C15112yes—
734C22#547×C15111yescharacteristic
735C22#547×C15112yes—
736C22#547×C15112yes—
737C22#548×C15111yescharacteristic
738C22#551×C15112yes—
739C22#552×C15111yescharacteristic
740C22#556×C15111yescharacteristic
741C4—24no—
742C4—24no—
743C4—28no—
744C4—44no—
745C4—42no—
746C4—81no—
747C4—82no—
748C4—81no—
749C4—82no—
750C2—44no—
751C2—82no—
752C2#2395×C15111yescharacteristic
753C2#2412×C15111yescharacteristic
754C2#2415×C15111yescharacteristic
755C2#2425×C15112yes—
756C2#2427×C15112yes—
757C2#2501×C15111yescharacteristic
758C2#2521×C15112yes—
759C2#2539×C15111yescharacteristic
760C2#2553×C15112yes—
761C2#2663×C15111yescharacteristic
762C2#2856×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
1. C2×#399×C151C2semidirect
2. C2×#397×C151C2semidirect
5. C2×#380×C151C2semidirect
6. C2×C4×C22⋊C4×C151C2semidirect
7. #1445×C151C2semidirect
8. #1444×C151C2semidirect
9. #1439×C151C2semidirect
10. #1437×C151C2semidirect
11. C4⋊#95×C151C2semidirect
103. #95×C151D4semidirect
381. #14839C151direct (N × H)
382. C151#14839direct (N × H)
383. C2×#399C2×C151semidirect
384. C2×#397C2×C151semidirect
387. C2×#380C2×C151semidirect
388. C2×C4×C22⋊C4C2×C151semidirect
389. #1445C2×C151semidirect
390. #1444C2×C151semidirect
391. #1439C2×C151semidirect
392. #1437C2×C151semidirect
393. C4⋊#95C2×C151semidirect
485. #95D4×C151semidirect

Maximal subgroups

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

subgroupindex
C2×#399×C1512
C2×#397×C1512
C2×#394×C1512
C2×#386×C1512
C2×#380×C1512
C2×C4×C22⋊C4×C1512
#1445×C1512
#1444×C1512
#1439×C1512
#1437×C1512
C4⋊#95×C1512
#14839151