Finite Group Databasebeta

← C151×#13912 #50318837

Subgroups — C151×#13912 #50318837

Order 38656.

2314 conjugacy classes of subgroups.

The subgroup lattice has 770 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C4×D4×C151C211yesmaximal, characteristic
2C2×#388×C151C212yesmaximal, complemented
3C2×#381×C151C211yesmaximal, characteristic, complemented
4C2×#380×C151C211yesmaximal, characteristic, complemented
5#1441×C151C212yesmaximal, complemented
6#1438×C151C212yesmaximal
7#1437×C151C212yesmaximal, complemented
8#1434×C151C211yesmaximal, characteristic, complemented
9C22⋊#95×C151C211yesmaximal, characteristic, complemented
10C22⋊#95×C151C211yesmaximal, characteristic, complemented
11C4×#95×C151C211yesmaximal, characteristic, complemented
12C23×D4×C151C2211yescharacteristic
13C24×C4×C151C2211yescharacteristic
14C24×C4×C151C2211yescharacteristic
15C2×C4×D4×C151—28no—
16C2×C4×D4×C151C418yescomplemented
17C22×C4⋊C4×C151C2212yes—
18C22×C4⋊C4×C151C2211yescharacteristic
19C22×C22⋊C4×C151C2212yes—
20C22×C22⋊C4×C151C2212yes—
21C22×C22⋊C4×C151C2212yes—
22C22×C22⋊C4×C151C2212yes—
23C22×C22⋊C4×C151C2211yescharacteristic
24C22×C22⋊C4×C151C2211yescharacteristic
25C22×C42×C151C2212yes—
26C22×C42×C151C2211yescharacteristic
27#388×C151—28no—
28#381×C151—24no—
29#380×C151—24no—
30C2×#95×C151C2211yescharacteristic
31C2×#95×C151C2212yes—
32C2×#95×C151C2211yescharacteristic
33C2×#95×C151C2211yescharacteristic
34C2×#95×C151C2212yes—
35C2×#95×C151C2212yes—
36C2×#95×C151C2212yes—
37C2×#95×C151C2212yes—
38C2×#95×C151C2212yes—
39C2×#95×C151C2211yescharacteristic
40C25×C151C2311yescharacteristic
41C25×C151C2311yescharacteristic
42C22×D4×C151—24no—
43C22×D4×C151—24no—
44C22×D4×C151—22no—
45C22×D4×C151—22no—
46C22×D4×C151C2×C414yes—
47C23×C4×C151—22no—
48C23×C4×C151—22no—
49C23×C4×C151—24no—
50C23×C4×C151—22no—
51C23×C4×C151—22no—
52C23×C4×C151—24no—
53C23×C4×C151—42no—
54C23×C4×C151—42no—
55C23×C4×C151C2×C414yes—
56C23×C4×C151C2×C414yes—
57C23×C4×C151C2312yes—
58C23×C4×C151C2312yes—
59C23×C4×C151C2311yescharacteristic
60C23×C4×C151C2312yes—
61C23×C4×C151C2312yes—
62C23×C4×C151C2311yescharacteristic
63C23×C4×C151C2311yescharacteristic
64C23×C4×C151C2311yescharacteristic
65C23×C4×C151C2311yescharacteristic
66C4×D4×C151—232no—
67C2×C4⋊C4×C151—24no—
68C2×C4⋊C4×C151—24no—
69C2×C4⋊C4×C151—24no—
70C2×C4⋊C4×C151—42no—
71C2×C4⋊C4×C151C2×C414yes—
72C2×C22⋊C4×C151—24no—
73C2×C22⋊C4×C151—24no—
74C2×C22⋊C4×C151—24no—
75C2×C22⋊C4×C151—24no—
76C2×C22⋊C4×C151—24no—
77C2×C22⋊C4×C151—24no—
78C2×C22⋊C4×C151—24no—
79C2×C22⋊C4×C151—24no—
80C2×C22⋊C4×C151—24no—
81C2×C22⋊C4×C151—42no—
82C2×C22⋊C4×C151—42no—
83C2×C22⋊C4×C151—42no—
84C2×C22⋊C4×C151—42no—
85C2×C22⋊C4×C151C2×C414yes—
86C2×C22⋊C4×C151C2×C414yes—
87C2×C22⋊C4×C151D418yes—
88C2×C42×C151—24no—
89C2×C42×C151—24no—
90C2×C42×C151—24no—
91C2×C42×C151—42no—
92C2×C42×C151C2×C414yes—
93#95×C151—22no—
94#95×C151—24no—
95#95×C151—22no—
96#95×C151—24no—
97#95×C151—24no—
98#95×C151—24no—
99#95×C151—22no—
100#95×C151—24no—
101#95×C151—42no—
102#95×C151D414yescomplemented
103C24×C151—21no—
104C24×C151—21no—
105C24×C151—22no—
106C24×C151—22no—
107C24×C151—22no—
108C24×C151—21no—
109C24×C151—21no—
110C24×C151—22no—
111C24×C151—21no—
112C24×C151—21no—
113C24×C151—22no—
114C24×C151—21no—
115C24×C151—21no—
116C24×C151—22no—
117C24×C151—22no—
118C24×C151—21no—
119C24×C151—21no—
120C24×C151C22×C412yes—
121C24×C151C22×C412yes—
122C24×C151C2×D414yes—
123C24×C151#4112yes—
124C24×C151#4112yes—
125C24×C151C2411yescharacteristic
126C2×D4×C151—216no—
127C2×D4×C151—216no—
128C2×D4×C151—28no—
129C2×D4×C151—28no—
130C2×D4×C151—28no—
131C22×C4×C151—22no—
132C22×C4×C151—22no—
133C22×C4×C151—21no—
134C22×C4×C151—22no—
135C22×C4×C151—21no—
136C22×C4×C151—21no—
137C22×C4×C151—21no—
138C22×C4×C151—21no—
139C22×C4×C151—22no—
140C22×C4×C151—22no—
141C22×C4×C151—21no—
142C22×C4×C151—28no—
143C22×C4×C151—21no—
144C22×C4×C151—22no—
145C22×C4×C151—22no—
146C22×C4×C151—22no—
147C22×C4×C151—22no—
148C22×C4×C151—22no—
149C22×C4×C151—22no—
150C22×C4×C151—22no—
151C22×C4×C151—22no—
152C22×C4×C151—22no—
153C22×C4×C151—21no—
154C22×C4×C151—22no—
155C22×C4×C151—22no—
156C22×C4×C151—22no—
157C22×C4×C151—22no—
158C22×C4×C151—22no—
159C22×C4×C151—28no—
160C22×C4×C151—28no—
161C22×C4×C151—28no—
162C22×C4×C151—22no—
163C22×C4×C151—22no—
164C22×C4×C151—22no—
165C22×C4×C151—22no—
166C22×C4×C151—22no—
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—22no—
176C22×C4×C151—44no—
177C22×C4×C151—44no—
178C22×C4×C151—48no—
179C22×C4×C151—48no—
180C22×C4×C151—48no—
181C22×C4×C151—48no—
182C22×C4×C151C22×C412yes—
183C22×C4×C151C22×C412yes—
184C22×C4×C151C22×C412yes—
185C22×C4×C151C22×C412yes—
186C22×C4×C151C22×C412yes—
187C22×C4×C151C2×D414yes—
188C22×C4×C151C2×D414yes—
189C22×C4×C151C2×D414yes—
190C22×C4×C151C2×D412yes—
191C22×C4×C151#4114yes—
192C22×C4×C151#4114yes—
193C22×C4×C151#4112yes—
194C4⋊C4×C151—28no—
195C4⋊C4×C151—48no—
196C22⋊C4×C151—28no—
197C22⋊C4×C151—48no—
198C22⋊C4×C151—48no—
199C22⋊C4×C151—48no—
200C22⋊C4×C151—48no—
201C22⋊C4×C151C22⋊C4116yescomplemented
202C42×C151—28no—
203C42×C151—48no—
204C23×C151—22no—
205C23×C151—22no—
206C23×C151—22no—
207C23×C151—22no—
208C23×C151—22no—
209C23×C151—22no—
210C23×C151—22no—
211C23×C151—22no—
212C23×C151—22no—
213C23×C151—22no—
214C23×C151—22no—
215C23×C151—22no—
216C23×C151—24no—
217C23×C151—24no—
218C23×C151—24no—
219C23×C151—24no—
220C23×C151—24no—
221C23×C151—24no—
222C23×C151—24no—
223C23×C151—22no—
224C23×C151—24no—
225C23×C151—22no—
226C23×C151—24no—
227C23×C151—22no—
228C23×C151—22no—
229C23×C151—24no—
230C23×C151—42no—
231C23×C151—42no—
232C23×C151—42no—
233C23×C151—42no—
234C23×C151—42no—
235C23×C151—42no—
236C23×C151—42no—
237C23×C151—42no—
238C23×C151—42no—
239C23×C151—42no—
240C23×C151—41no—
241C23×C151—42no—
242C23×C151—42no—
243C23×C151—41no—
244C23×C151—42no—
245C23×C151—41no—
246C23×C151—41no—
247C23×C151—42no—
248C23×C151C2×C22⋊C414yes—
249C23×C151#11714yes—
250C23×C151C23×C411yescharacteristic
251C23×C151C22×D412yes—
252C23×C151C22×D411yescharacteristic
253C23×C151C2×#4112yes—
254C23×C151C2×#4111yescharacteristic
255C23×C151C2×#4111yescharacteristic
256C23×C151C2×#4111yescharacteristic
257C23×C151C2×#4112yes—
258C23×C151H(5,𝔽2)12yes—
259C23×C151H(5,𝔽2)11yescharacteristic
260C23×C1512−1+411yescharacteristic
261D4×C151—232no—
262C2×C4×C151—22no—
263C2×C4×C151—22no—
264C2×C4×C151—22no—
265C2×C4×C151—22no—
266C2×C4×C151—22no—
267C2×C4×C151—22no—
268C2×C4×C151—22no—
269C2×C4×C151—22no—
270C2×C4×C151—24no—
271C2×C4×C151—24no—
272C2×C4×C151—24no—
273C2×C4×C151—24no—
274C2×C4×C151—24no—
275C2×C4×C151—24no—
276C2×C4×C151—24no—
277C2×C4×C151—24no—
278C2×C4×C151—22no—
279C2×C4×C151—22no—
280C2×C4×C151—22no—
281C2×C4×C151—24no—
282C2×C4×C151—24no—
283C2×C4×C151—24no—
284C2×C4×C151—24no—
285C2×C4×C151—24no—
286C2×C4×C151—24no—
287C2×C4×C151—416no—
288C2×C4×C151—416no—
289C2×C4×C151—42no—
290C2×C4×C151—42no—
291C2×C4×C151—42no—
292C2×C4×C151—42no—
293C2×C4×C151—42no—
294C2×C4×C151—42no—
295C2×C4×C151—42no—
296C2×C4×C151—42no—
297C2×C4×C151—42no—
298C2×C4×C151—42no—
299C2×C4×C151—42no—
300C2×C4×C151—42no—
301C2×C4×C151—42no—
302C2×C4×C151—42no—
303C2×C4×C151—42no—
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×C151C2×C22⋊C414yes—
314C2×C4×C151C2×C22⋊C414yes—
315C2×C4×C151#11714yes—
316C2×C4×C151C4×D414yes—
317C22×C151—24no—
318C22×C151—24no—
319C22×C151—24no—
320C22×C151—24no—
321C22×C151—24no—
322C22×C151—24no—
323C22×C151—42no—
324C22×C151—42no—
325C22×C151—42no—
326C22×C151—42no—
327C22×C151—42no—
328C22×C151—42no—
329C22×C151—44no—
330C22×C151—44no—
331C22×C151—44no—
332C22×C151—44no—
333C22×C151—44no—
334C22×C151—44no—
335C22×C151—44no—
336C22×C151—44no—
337C22×C151—42no—
338C22×C151—42no—
339C22×C151C22×C22⋊C411yescharacteristic
340C22×C151C2×#11711yescharacteristic
341C22×C151C2×#11711yescharacteristic
342C22×C151C2×C4×D411yescharacteristic
343C22×C151C4×#4111yescharacteristic
344C22×C151#51811yescharacteristic
345C22×C151#52011yescharacteristic
346C22×C151#52512yes—
347C22×C151#52512yes—
348C22×C151#52912yes—
349C22×C151#53212yes—
350C22×C151#54012yes—
351C22×C151#54212yes—
352C22×C151D4212yes—
353C22×C151#54612yes—
354C22×C151#54612yes—
355C22×C151#54611yescharacteristic
356C22×C151#54712yes—
357C22×C151#54811yescharacteristic
358C22×C151#55112yes—
359C22×C151#55211yescharacteristic
360C22×C151#55311yescharacteristic
361C22×C151#55312yes—
362C4×C151—24no—
363C4×C151—24no—
364C4×C151—24no—
365C4×C151—24no—
366C4×C151—42no—
367C4×C151—44no—
368C4×C151—44no—
369C4×C151—82no—
370C4×C151—82no—
371C2×C151—44no—
372C2×C151—44no—
373C2×C151#228011yescharacteristic
374C2×C151#229311yescharacteristic
375C2×C151#231911yescharacteristic
376C2×C151D4×C22⋊C411yescharacteristic
377C2×C151#233911yescharacteristic
378C2×C151#235211yescharacteristic
379C2×C151#235311yescharacteristic
380C2×C151#245712yes—
381C2×C151#246112yes—
382C2×C151#246412yes—
383C2×C151#246812yes—
384#13912C15111yesmaximal, characteristic, direct product factor, Sylow
385C151#1391211yescharacteristic, direct product factor, Sylow
386C22×C4×D4C2×C15111yescharacteristic
387C2×#388C2×C15112yescomplemented
388C2×#381C2×C15111yescharacteristic, complemented
389C2×#380C2×C15111yescharacteristic, complemented
390#1441C2×C15112yescomplemented
391#1438C2×C15112yes—
392#1437C2×C15112yescomplemented
393#1434C2×C15111yescharacteristic, complemented
394C22⋊#95C2×C15111yescharacteristic, complemented
395C22⋊#95C2×C15111yescharacteristic, complemented
396C4×#95C2×C15111yescharacteristic, complemented
397C23×D4C22×C15111yescharacteristic
398C24×C4C22×C15111yescharacteristic
399C24×C4C22×C15111yescharacteristic
400C2×C4×D4—28no—
401C2×C4×D4C4×C15118yescomplemented
402C22×C4⋊C4C22×C15112yes—
403C22×C4⋊C4C22×C15111yescharacteristic
404C22×C22⋊C4C22×C15112yes—
405C22×C22⋊C4C22×C15112yes—
406C22×C22⋊C4C22×C15112yes—
407C22×C22⋊C4C22×C15112yes—
408C22×C22⋊C4C22×C15111yescharacteristic
409C22×C22⋊C4C22×C15111yescharacteristic
410C22×C42C22×C15112yes—
411C22×C42C22×C15111yescharacteristic
412#388—28no—
413#381—24no—
414#380—24no—
415C2×#95C22×C15111yescharacteristic
416C2×#95C22×C15112yes—
417C2×#95C22×C15111yescharacteristic
418C2×#95C22×C15111yescharacteristic
419C2×#95C22×C15112yes—
420C2×#95C22×C15112yes—
421C2×#95C22×C15112yes—
422C2×#95C22×C15112yes—
423C2×#95C22×C15112yes—
424C2×#95C22×C15111yescharacteristic
425C25C23×C15111yescharacteristic
426C25C23×C15111yescharacteristic
427C22×D4—22no—
428C22×D4—22no—
429C22×D4—24no—
430C22×D4—24no—
431C22×D4C2×C4×C15114yes—
432C23×C4—24no—
433C23×C4—22no—
434C23×C4—22no—
435C23×C4—24no—
436C23×C4—22no—
437C23×C4—22no—
438C23×C4—42no—
439C23×C4—42no—
440C23×C4C2×C4×C15114yes—
441C23×C4C2×C4×C15114yes—
442C23×C4C23×C15112yes—
443C23×C4C23×C15112yes—
444C23×C4C23×C15112yes—
445C23×C4C23×C15111yescharacteristic
446C23×C4C23×C15112yes—
447C23×C4C23×C15111yescharacteristic
448C23×C4C23×C15111yescharacteristic
449C23×C4C23×C15111yescharacteristic
450C23×C4C23×C15111yescharacteristic
451C4×D4—232no—
452C2×C4⋊C4—24no—
453C2×C4⋊C4—24no—
454C2×C4⋊C4—24no—
455C2×C4⋊C4—42no—
456C2×C4⋊C4C2×C4×C15114yes—
457C2×C22⋊C4—24no—
458C2×C22⋊C4—24no—
459C2×C22⋊C4—24no—
460C2×C22⋊C4—24no—
461C2×C22⋊C4—24no—
462C2×C22⋊C4—24no—
463C2×C22⋊C4—24no—
464C2×C22⋊C4—24no—
465C2×C22⋊C4—24no—
466C2×C22⋊C4—42no—
467C2×C22⋊C4—42no—
468C2×C22⋊C4—42no—
469C2×C22⋊C4—42no—
470C2×C22⋊C4C2×C4×C15114yes—
471C2×C22⋊C4C2×C4×C15114yes—
472C2×C22⋊C4D4×C15118yes—
473C2×C42—24no—
474C2×C42—24no—
475C2×C42—24no—
476C2×C42—42no—
477C2×C42C2×C4×C15114yes—
478#95—24no—
479#95—22no—
480#95—24no—
481#95—22no—
482#95—24no—
483#95—22no—
484#95—24no—
485#95—24no—
486#95—42no—
487#95D4×C15114yescomplemented
488C24—21no—
489C24—21no—
490C24—22no—
491C24—22no—
492C24—22no—
493C24—21no—
494C24—21no—
495C24—22no—
496C24—22no—
497C24—21no—
498C24—21no—
499C24—21no—
500C24—21no—
501C24—22no—
502C24—22no—
503C24—21no—
504C24—21no—
505C24C22×C4×C15112yes—
506C24C22×C4×C15112yes—
507C24C2×D4×C15114yes—
508C24#41×C15112yes—
509C24#41×C15112yes—
510C24C24×C15111yescharacteristic
511C2×D4—216no—
512C2×D4—216no—
513C2×D4—28no—
514C2×D4—28no—
515C2×D4—28no—
516C22×C4—22no—
517C22×C4—22no—
518C22×C4—21no—
519C22×C4—22no—
520C22×C4—21no—
521C22×C4—21no—
522C22×C4—21no—
523C22×C4—21no—
524C22×C4—22no—
525C22×C4—22no—
526C22×C4—21no—
527C22×C4—28no—
528C22×C4—21no—
529C22×C4—22no—
530C22×C4—22no—
531C22×C4—22no—
532C22×C4—22no—
533C22×C4—22no—
534C22×C4—22no—
535C22×C4—22no—
536C22×C4—22no—
537C22×C4—22no—
538C22×C4—21no—
539C22×C4—22no—
540C22×C4—22no—
541C22×C4—22no—
542C22×C4—22no—
543C22×C4—22no—
544C22×C4—28no—
545C22×C4—28no—
546C22×C4—28no—
547C22×C4—22no—
548C22×C4—22no—
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—22no—
558C22×C4—22no—
559C22×C4—22no—
560C22×C4—22no—
561C22×C4—44no—
562C22×C4—44no—
563C22×C4—48no—
564C22×C4—48no—
565C22×C4—48no—
566C22×C4—48no—
567C22×C4C22×C4×C15112yes—
568C22×C4C22×C4×C15112yes—
569C22×C4C22×C4×C15112yes—
570C22×C4C22×C4×C15112yes—
571C22×C4C22×C4×C15112yes—
572C22×C4C2×D4×C15114yes—
573C22×C4C2×D4×C15114yes—
574C22×C4C2×D4×C15114yes—
575C22×C4C2×D4×C15112yes—
576C22×C4#41×C15114yes—
577C22×C4#41×C15114yes—
578C22×C4#41×C15112yes—
579C4⋊C4—28no—
580C4⋊C4—48no—
581C22⋊C4—28no—
582C22⋊C4—48no—
583C22⋊C4—48no—
584C22⋊C4—48no—
585C22⋊C4—48no—
586C22⋊C4C22⋊C4×C151116yescomplemented
587C42—28no—
588C42—48no—
589C23—22no—
590C23—22no—
591C23—22no—
592C23—22no—
593C23—22no—
594C23—22no—
595C23—22no—
596C23—22no—
597C23—22no—
598C23—22no—
599C23—22no—
600C23—22no—
601C23—24no—
602C23—24no—
603C23—24no—
604C23—24no—
605C23—24no—
606C23—22no—
607C23—24no—
608C23—24no—
609C23—24no—
610C23—22no—
611C23—24no—
612C23—22no—
613C23—22no—
614C23—24no—
615C23—42no—
616C23—42no—
617C23—42no—
618C23—42no—
619C23—42no—
620C23—42no—
621C23—42no—
622C23—42no—
623C23—42no—
624C23—42no—
625C23—42no—
626C23—41no—
627C23—42no—
628C23—41no—
629C23—42no—
630C23—41no—
631C23—41no—
632C23—42no—
633C23C2×C22⋊C4×C15114yes—
634C23#117×C15114yes—
635C23C23×C4×C15111yescharacteristic
636C23C22×D4×C15112yes—
637C23C22×D4×C15111yescharacteristic
638C23C2×#41×C15112yes—
639C23C2×#41×C15111yescharacteristic
640C23C2×#41×C15111yescharacteristic
641C23C2×#41×C15111yescharacteristic
642C23C2×#41×C15112yes—
643C23H(5,𝔽2)×C15112yes—
644C23H(5,𝔽2)×C15111yescharacteristic
645C232−1+4×C15111yescharacteristic
646D4—232no—
647C2×C4—22no—
648C2×C4—22no—
649C2×C4—22no—
650C2×C4—22no—
651C2×C4—22no—
652C2×C4—22no—
653C2×C4—22no—
654C2×C4—22no—
655C2×C4—24no—
656C2×C4—24no—
657C2×C4—24no—
658C2×C4—24no—
659C2×C4—24no—
660C2×C4—24no—
661C2×C4—24no—
662C2×C4—24no—
663C2×C4—22no—
664C2×C4—22no—
665C2×C4—22no—
666C2×C4—24no—
667C2×C4—24no—
668C2×C4—24no—
669C2×C4—24no—
670C2×C4—24no—
671C2×C4—24no—
672C2×C4—416no—
673C2×C4—416no—
674C2×C4—42no—
675C2×C4—42no—
676C2×C4—42no—
677C2×C4—42no—
678C2×C4—42no—
679C2×C4—42no—
680C2×C4—42no—
681C2×C4—42no—
682C2×C4—42no—
683C2×C4—42no—
684C2×C4—42no—
685C2×C4—42no—
686C2×C4—42no—
687C2×C4—42no—
688C2×C4—42no—
689C2×C4—42no—
690C2×C4—42no—
691C2×C4—42no—
692C2×C4—42no—
693C2×C4—42no—
694C2×C4—42no—
695C2×C4—42no—
696C2×C4—42no—
697C2×C4—42no—
698C2×C4C2×C22⋊C4×C15114yes—
699C2×C4C2×C22⋊C4×C15114yes—
700C2×C4#117×C15114yes—
701C2×C4C4×D4×C15114yes—
702C22—24no—
703C22—24no—
704C22—24no—
705C22—24no—
706C22—24no—
707C22—24no—
708C22—42no—
709C22—42no—
710C22—42no—
711C22—42no—
712C22—44no—
713C22—44no—
714C22—44no—
715C22—44no—
716C22—44no—
717C22—44no—
718C22—44no—
719C22—44no—
720C22—42no—
721C22—42no—
722C22—42no—
723C22—42no—
724C22C22×C22⋊C4×C15111yescharacteristic
725C22C2×#117×C15111yescharacteristic
726C22C2×#117×C15111yescharacteristic
727C22C2×C4×D4×C15111yescharacteristic
728C22C4×#41×C15111yescharacteristic
729C22#518×C15111yescharacteristic
730C22#520×C15111yescharacteristic
731C22#525×C15112yes—
732C22#525×C15112yes—
733C22#529×C15112yes—
734C22#532×C15112yes—
735C22#540×C15112yes—
736C22#542×C15112yes—
737C22D42×C15112yes—
738C22#546×C15112yes—
739C22#546×C15112yes—
740C22#546×C15111yescharacteristic
741C22#547×C15112yes—
742C22#548×C15111yescharacteristic
743C22#551×C15112yes—
744C22#552×C15111yescharacteristic
745C22#553×C15111yescharacteristic
746C22#553×C15112yes—
747C4—24no—
748C4—24no—
749C4—24no—
750C4—24no—
751C4—42no—
752C4—44no—
753C4—44no—
754C4—82no—
755C4—82no—
756C2—44no—
757C2—44no—
758C2#2280×C15111yescharacteristic
759C2#2293×C15111yescharacteristic
760C2#2319×C15111yescharacteristic
761C2D4×C22⋊C4×C15111yescharacteristic
762C2#2339×C15111yescharacteristic
763C2#2352×C15111yescharacteristic
764C2#2353×C15111yescharacteristic
765C2#2457×C15112yes—
766C2#2461×C15112yes—
767C2#2464×C15112yes—
768C2#2468×C15112yes—
subgroupG/H
center, socleC24×C151C24
commutatorC23C23×C4×C151
Frattini, cosocleC24C24×C151
prime radicalC23×D4×C151C22
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C24×C151 ◁ G

Complements

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

NH ≅ G/Ntype
2. C2×#388×C151C2semidirect
3. C2×#381×C151C2semidirect
4. C2×#380×C151C2semidirect
5. #1441×C151C2semidirect
7. #1437×C151C2semidirect
8. #1434×C151C2semidirect
9. C22⋊#95×C151C2semidirect
10. C22⋊#95×C151C2semidirect
11. C4×#95×C151C2semidirect
16. C2×C4×D4×C151C4semidirect
102. #95×C151D4semidirect
201. C22⋊C4×C151C22⋊C4semidirect
384. #13912C151direct (N × H)
385. C151#13912direct (N × H)
387. C2×#388C2×C151semidirect
388. C2×#381C2×C151semidirect
389. C2×#380C2×C151semidirect
390. #1441C2×C151semidirect
392. #1437C2×C151semidirect
393. #1434C2×C151semidirect
394. C22⋊#95C2×C151semidirect
395. C22⋊#95C2×C151semidirect
396. C4×#95C2×C151semidirect
401. C2×C4×D4C4×C151semidirect
487. #95D4×C151semidirect
586. C22⋊C4C22⋊C4×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×#388×C1512
C2×#381×C1512
C2×#380×C1512
#1441×C1512
#1438×C1512
#1437×C1512
#1434×C1512
C22⋊#95×C1512
C4×#95×C1512
#13912151