Finite Group Databasebeta

← C151×#14312 #50319237

Subgroups — C151×#14312 #50319237

Order 38656.

1766 conjugacy classes of subgroups.

The subgroup lattice has 716 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#394×C151C211yesmaximal, characteristic
2C2×#390×C151C211yesmaximal, characteristic
3C2×#388×C151C212yesmaximal, complemented
4C2×C4×C4⋊C4×C151C211yesmaximal, characteristic, complemented
5#1444×C151C211yesmaximal, characteristic, complemented
6#1441×C151C211yesmaximal, characteristic, complemented
7#1439×C151C212yesmaximal, complemented
8#1439×C151C212yesmaximal, complemented
9#1438×C151C211yesmaximal, characteristic
10#1437×C151C212yesmaximal, complemented
11#1434×C151C211yesmaximal, characteristic, complemented
12C23×D4×C151C2211yescharacteristic
13C22×C4⋊C4×C151C2211yescharacteristic
14C22×C4⋊C4×C151C2211yescharacteristic
15C22×C4⋊C4×C151C2212yes—
16C22×C4⋊C4×C151C2211yescharacteristic
17C22×C22⋊C4×C151C2212yes—
18C22×C22⋊C4×C151C2212yes—
19C22×C22⋊C4×C151C2212yes—
20C22×C22⋊C4×C151C2212yes—
21C22×C22⋊C4×C151C2212yes—
22C22×C22⋊C4×C151C2212yes—
23C22×C42×C151C2211yescharacteristic
24C22×C42×C151C2211yescharacteristic
25C22×C42×C151C2211yescharacteristic
26#394×C151C418yescomplemented
27#390×C151—24no—
28#388×C151—28no—
29C4×C4⋊C4×C151—24no—
30C2×#95×C151C2212yes—
31C2×#95×C151C2211yescharacteristic
32C2×#95×C151C2211yescharacteristic
33C2×#95×C151C2211yescharacteristic
34C2×#95×C151C2212yes—
35C2×#95×C151C2212yes—
36C2×#95×C151C2212yes—
37C2×#95×C151C2212yes—
38C2×#95×C151C2211yescharacteristic
39C25×C151C2312yes—
40C22×D4×C151—22no—
41C22×D4×C151—22no—
42C22×D4×C151—42no—
43C22×D4×C151—42no—
44C22×D4×C151C2×C414yes—
45C23×C4×C151C2312yes—
46C23×C4×C151C2312yes—
47C23×C4×C151C2312yes—
48C23×C4×C151C2311yescharacteristic
49C23×C4×C151C2311yescharacteristic
50C23×C4×C151C2311yescharacteristic
51C23×C4×C151C2311yescharacteristic
52C23×C4×C151C2311yescharacteristic
53C23×C4×C151C2311yescharacteristic
54C23×C4×C151C2311yescharacteristic
55C2×C4⋊C4×C151—22no—
56C2×C4⋊C4×C151—22no—
57C2×C4⋊C4×C151—22no—
58C2×C4⋊C4×C151—22no—
59C2×C4⋊C4×C151—22no—
60C2×C4⋊C4×C151—24no—
61C2×C4⋊C4×C151—22no—
62C2×C4⋊C4×C151—42no—
63C2×C4⋊C4×C151—42no—
64C2×C4⋊C4×C151—42no—
65C2×C4⋊C4×C151C2×C414yes—
66C2×C22⋊C4×C151—24no—
67C2×C22⋊C4×C151—24no—
68C2×C22⋊C4×C151—24no—
69C2×C22⋊C4×C151—24no—
70C2×C22⋊C4×C151—24no—
71C2×C22⋊C4×C151—24no—
72C2×C22⋊C4×C151—24no—
73C2×C22⋊C4×C151—24no—
74C2×C22⋊C4×C151—42no—
75C2×C22⋊C4×C151—42no—
76C2×C22⋊C4×C151—42no—
77C2×C22⋊C4×C151—42no—
78C2×C22⋊C4×C151—42no—
79C2×C22⋊C4×C151—42no—
80C2×C22⋊C4×C151—42no—
81C2×C22⋊C4×C151—42no—
82C2×C22⋊C4×C151C2×C418yes—
83C2×C22⋊C4×C151C2×C418yes—
84C2×C42×C151—22no—
85C2×C42×C151—22no—
86C2×C42×C151—22no—
87C2×C42×C151—42no—
88C2×C42×C151—42no—
89C2×C42×C151D414yes—
90C2×C42×C151D414yescomplemented
91#95×C151—22no—
92#95×C151—22no—
93#95×C151—24no—
94#95×C151—24no—
95#95×C151—22no—
96#95×C151—42no—
97#95×C151—42no—
98#95×C151—42no—
99#95×C151C2×C414yes—
100C24×C151—22no—
101C24×C151—22no—
102C24×C151—22no—
103C24×C151—22no—
104C24×C151—22no—
105C24×C151—22no—
106C24×C151—22no—
107C24×C151—22no—
108C24×C151—22no—
109C24×C151—22no—
110C24×C151—22no—
111C24×C151—22no—
112C24×C151—22no—
113C24×C151—22no—
114C24×C151C22×C414yes—
115C24×C151C2411yescharacteristic
116C2×D4×C151—28no—
117C2×D4×C151—48no—
118C2×D4×C151—44no—
119C2×D4×C151—44no—
120C2×D4×C151—48no—
121C22×C4×C151—21no—
122C22×C4×C151—21no—
123C22×C4×C151—21no—
124C22×C4×C151—21no—
125C22×C4×C151—22no—
126C22×C4×C151—22no—
127C22×C4×C151—22no—
128C22×C4×C151—22no—
129C22×C4×C151—21no—
130C22×C4×C151—21no—
131C22×C4×C151—21no—
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—22no—
142C22×C4×C151—22no—
143C22×C4×C151—22no—
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—22no—
154C22×C4×C151—22no—
155C22×C4×C151—22no—
156C22×C4×C151—22no—
157C22×C4×C151—22no—
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×C151C22×C414yes—
166C22×C4×C151C22×C412yes—
167C22×C4×C151C22×C412yes—
168C22×C4×C151C22×C412yes—
169C22×C4×C151C2×D412yes—
170C22×C4×C151C2×D412yes—
171C22×C4×C151C2×D412yes—
172C22×C4×C151C2×D412yes—
173C22×C4×C151C2×D412yes—
174C22×C4×C151C2×D412yes—
175C22×C4×C151#4112yes—
176C22×C4×C151#4112yes—
177C22×C4×C151#4112yes—
178C22×C4×C151#4112yes—
179C4⋊C4×C151—28no—
180C4⋊C4×C151—28no—
181C4⋊C4×C151—44no—
182C4⋊C4×C151—48no—
183C22⋊C4×C151—216no—
184C22⋊C4×C151—48no—
185C22⋊C4×C151—48no—
186C22⋊C4×C151—48no—
187C22⋊C4×C151—48no—
188C22⋊C4×C151—48no—
189C42×C151—28no—
190C42×C151—44no—
191C42×C151—44no—
192C23×C151—24no—
193C23×C151—24no—
194C23×C151—24no—
195C23×C151—24no—
196C23×C151—24no—
197C23×C151—24no—
198C23×C151—24no—
199C23×C151—42no—
200C23×C151—42no—
201C23×C151—42no—
202C23×C151—42no—
203C23×C151—42no—
204C23×C151—42no—
205C23×C151—42no—
206C23×C151—42no—
207C23×C151—42no—
208C23×C151—42no—
209C23×C151—42no—
210C23×C151—42no—
211C23×C151—42no—
212C23×C151—42no—
213C23×C151—42no—
214C23×C151—42no—
215C23×C151—42no—
216C23×C151—42no—
217C23×C151—42no—
218C23×C151—42no—
219C23×C151—42no—
220C23×C151—42no—
221C23×C151—42no—
222C23×C151—42no—
223C23×C151—42no—
224C23×C151—42no—
225C23×C151—42no—
226C23×C151—42no—
227C23×C151C23×C411yescharacteristic
228C23×C151C22×D411yescharacteristic
229C23×C151C22×D411yescharacteristic
230C23×C151C2×#4111yescharacteristic
231C23×C151C2×#4111yescharacteristic
232C23×C151C2×#4111yescharacteristic
233C23×C151C2×#4111yescharacteristic
234C23×C151H(5,𝔽2)12yes—
235C23×C151H(5,𝔽2)12yes—
236C23×C151H(5,𝔽2)12yes—
237C23×C1512−1+412yes—
238D4×C151—416no—
239C2×C4×C151—22no—
240C2×C4×C151—22no—
241C2×C4×C151—24no—
242C2×C4×C151—22no—
243C2×C4×C151—22no—
244C2×C4×C151—22no—
245C2×C4×C151—22no—
246C2×C4×C151—22no—
247C2×C4×C151—22no—
248C2×C4×C151—22no—
249C2×C4×C151—22no—
250C2×C4×C151—24no—
251C2×C4×C151—24no—
252C2×C4×C151—24no—
253C2×C4×C151—24no—
254C2×C4×C151—22no—
255C2×C4×C151—24no—
256C2×C4×C151—24no—
257C2×C4×C151—24no—
258C2×C4×C151—22no—
259C2×C4×C151—22no—
260C2×C4×C151—22no—
261C2×C4×C151—22no—
262C2×C4×C151—22no—
263C2×C4×C151—24no—
264C2×C4×C151—24no—
265C2×C4×C151—41no—
266C2×C4×C151—41no—
267C2×C4×C151—42no—
268C2×C4×C151—41no—
269C2×C4×C151—41no—
270C2×C4×C151—41no—
271C2×C4×C151—41no—
272C2×C4×C151—42no—
273C2×C4×C151—42no—
274C2×C4×C151—42no—
275C2×C4×C151—42no—
276C2×C4×C151—42no—
277C2×C4×C151—42no—
278C2×C4×C151—42no—
279C2×C4×C151—42no—
280C2×C4×C151—42no—
281C2×C4×C151—42no—
282C2×C4×C151—42no—
283C2×C4×C151—42no—
284C2×C4×C151—42no—
285C2×C4×C151—42no—
286C2×C4×C151—42no—
287C2×C4×C151—42no—
288C2×C4×C151—42no—
289C2×C4×C151—42no—
290C2×C4×C151—42no—
291C2×C4×C151—42no—
292C2×C4×C151—42no—
293C2×C4×C151—42no—
294C2×C4×C151C4×D414yes—
295C2×C4×C151C4×D414yes—
296C2×C4×C151#12114yes—
297C22×C151—44no—
298C22×C151—44no—
299C22×C151—44no—
300C22×C151—44no—
301C22×C151—44no—
302C22×C151—44no—
303C22×C151—44no—
304C22×C151—82no—
305C22×C151—82no—
306C22×C151—82no—
307C22×C151—82no—
308C22×C151—82no—
309C22×C151—82no—
310C22×C151—82no—
311C22×C151—82no—
312C22×C151C2×C4×D411yescharacteristic
313C22×C151C2×C4×D411yescharacteristic
314C22×C151C4×#4111yescharacteristic
315C22×C151#51812yes—
316C22×C151#52012yes—
317C22×C151C2×#12111yescharacteristic
318C22×C151#52511yescharacteristic
319C22×C151#52911yescharacteristic
320C22×C151#53211yescharacteristic
321C22×C151#53411yescharacteristic
322C22×C151#53511yescharacteristic
323C22×C151#53512yes—
324C22×C151#53511yescharacteristic
325C22×C151#53611yescharacteristic
326C22×C151#53712yes—
327C22×C151#53812yes—
328C22×C151#53812yes—
329C22×C151#53912yes—
330C22×C151#54012yes—
331C22×C151#54012yes—
332C22×C151#54212yes—
333C22×C151#54212yes—
334C22×C151#54212yes—
335C4×C151—24no—
336C4×C151—24no—
337C4×C151—24no—
338C4×C151—42no—
339C4×C151—44no—
340C4×C151—42no—
341C4×C151—42no—
342C4×C151—42no—
343C4×C151—82no—
344C4×C151—82no—
345C2×C151—84no—
346C2×C151C4×#12111yescharacteristic
347C2×C151#232111yescharacteristic
348C2×C151#232412yes—
349C2×C151#232611yescharacteristic
350C2×C151#233512yes—
351C2×C151#261811yescharacteristic
352C2×C151#261911yescharacteristic
353C2×C151#263211yescharacteristic
354C2×C151#263511yescharacteristic
355C2×C151#265112yes—
356C2×C151#266212yes—
357#14312C15111yesmaximal, characteristic, direct product factor, Sylow
358C151#1431211yescharacteristic, direct product factor, Sylow
359C2×#394C2×C15111yescharacteristic
360C2×#390C2×C15111yescharacteristic
361C2×#388C2×C15112yescomplemented
362C2×C4×C4⋊C4C2×C15111yescharacteristic, complemented
363#1444C2×C15111yescharacteristic, complemented
364#1441C2×C15111yescharacteristic, complemented
365#1439C2×C15112yescomplemented
366#1439C2×C15112yescomplemented
367#1438C2×C15111yescharacteristic
368#1437C2×C15112yescomplemented
369#1434C2×C15111yescharacteristic, complemented
370C23×D4C22×C15111yescharacteristic
371C22×C4⋊C4C22×C15111yescharacteristic
372C22×C4⋊C4C22×C15111yescharacteristic
373C22×C4⋊C4C22×C15112yes—
374C22×C4⋊C4C22×C15111yescharacteristic
375C22×C22⋊C4C22×C15112yes—
376C22×C22⋊C4C22×C15112yes—
377C22×C22⋊C4C22×C15112yes—
378C22×C22⋊C4C22×C15112yes—
379C22×C22⋊C4C22×C15112yes—
380C22×C22⋊C4C22×C15112yes—
381C22×C42C22×C15111yescharacteristic
382C22×C42C22×C15111yescharacteristic
383C22×C42C22×C15111yescharacteristic
384#394C4×C15118yescomplemented
385#390—24no—
386#388—28no—
387C4×C4⋊C4—24no—
388C2×#95C22×C15112yes—
389C2×#95C22×C15111yescharacteristic
390C2×#95C22×C15111yescharacteristic
391C2×#95C22×C15111yescharacteristic
392C2×#95C22×C15112yes—
393C2×#95C22×C15112yes—
394C2×#95C22×C15112yes—
395C2×#95C22×C15112yes—
396C2×#95C22×C15111yescharacteristic
397C25C23×C15112yes—
398C22×D4—22no—
399C22×D4—22no—
400C22×D4—42no—
401C22×D4—42no—
402C22×D4C2×C4×C15114yes—
403C23×C4C23×C15112yes—
404C23×C4C23×C15112yes—
405C23×C4C23×C15111yescharacteristic
406C23×C4C23×C15112yes—
407C23×C4C23×C15111yescharacteristic
408C23×C4C23×C15111yescharacteristic
409C23×C4C23×C15111yescharacteristic
410C23×C4C23×C15111yescharacteristic
411C23×C4C23×C15111yescharacteristic
412C23×C4C23×C15111yescharacteristic
413C2×C4⋊C4—22no—
414C2×C4⋊C4—22no—
415C2×C4⋊C4—22no—
416C2×C4⋊C4—22no—
417C2×C4⋊C4—22no—
418C2×C4⋊C4—24no—
419C2×C4⋊C4—22no—
420C2×C4⋊C4—42no—
421C2×C4⋊C4—42no—
422C2×C4⋊C4—42no—
423C2×C4⋊C4C2×C4×C15114yes—
424C2×C22⋊C4—24no—
425C2×C22⋊C4—24no—
426C2×C22⋊C4—24no—
427C2×C22⋊C4—24no—
428C2×C22⋊C4—24no—
429C2×C22⋊C4—24no—
430C2×C22⋊C4—24no—
431C2×C22⋊C4—24no—
432C2×C22⋊C4—42no—
433C2×C22⋊C4—42no—
434C2×C22⋊C4—42no—
435C2×C22⋊C4—42no—
436C2×C22⋊C4—42no—
437C2×C22⋊C4—42no—
438C2×C22⋊C4—42no—
439C2×C22⋊C4—42no—
440C2×C22⋊C4C2×C4×C15118yes—
441C2×C22⋊C4C2×C4×C15118yes—
442C2×C42—22no—
443C2×C42—22no—
444C2×C42—22no—
445C2×C42—42no—
446C2×C42—42no—
447C2×C42D4×C15114yes—
448C2×C42D4×C15114yescomplemented
449#95—22no—
450#95—22no—
451#95—22no—
452#95—24no—
453#95—24no—
454#95—42no—
455#95—42no—
456#95—42no—
457#95C2×C4×C15114yes—
458C24—22no—
459C24—22no—
460C24—22no—
461C24—22no—
462C24—22no—
463C24—22no—
464C24—22no—
465C24—22no—
466C24—22no—
467C24—22no—
468C24—22no—
469C24—22no—
470C24—22no—
471C24—22no—
472C24C22×C4×C15114yes—
473C24C24×C15111yescharacteristic
474C2×D4—28no—
475C2×D4—48no—
476C2×D4—44no—
477C2×D4—44no—
478C2×D4—48no—
479C22×C4—21no—
480C22×C4—21no—
481C22×C4—21no—
482C22×C4—21no—
483C22×C4—22no—
484C22×C4—22no—
485C22×C4—22no—
486C22×C4—22no—
487C22×C4—21no—
488C22×C4—21no—
489C22×C4—21no—
490C22×C4—22no—
491C22×C4—21no—
492C22×C4—22no—
493C22×C4—21no—
494C22×C4—21no—
495C22×C4—21no—
496C22×C4—21no—
497C22×C4—22no—
498C22×C4—22no—
499C22×C4—22no—
500C22×C4—22no—
501C22×C4—22no—
502C22×C4—22no—
503C22×C4—22no—
504C22×C4—22no—
505C22×C4—22no—
506C22×C4—22no—
507C22×C4—22no—
508C22×C4—22no—
509C22×C4—22no—
510C22×C4—22no—
511C22×C4—22no—
512C22×C4—22no—
513C22×C4—22no—
514C22×C4—22no—
515C22×C4—22no—
516C22×C4—22no—
517C22×C4—22no—
518C22×C4—22no—
519C22×C4—22no—
520C22×C4—22no—
521C22×C4—22no—
522C22×C4—22no—
523C22×C4C22×C4×C15114yes—
524C22×C4C22×C4×C15112yes—
525C22×C4C22×C4×C15112yes—
526C22×C4C22×C4×C15112yes—
527C22×C4C2×D4×C15112yes—
528C22×C4C2×D4×C15112yes—
529C22×C4C2×D4×C15112yes—
530C22×C4C2×D4×C15112yes—
531C22×C4C2×D4×C15112yes—
532C22×C4C2×D4×C15112yes—
533C22×C4#41×C15112yes—
534C22×C4#41×C15112yes—
535C22×C4#41×C15112yes—
536C22×C4#41×C15112yes—
537C4⋊C4—28no—
538C4⋊C4—28no—
539C4⋊C4—44no—
540C4⋊C4—48no—
541C22⋊C4—216no—
542C22⋊C4—48no—
543C22⋊C4—48no—
544C22⋊C4—48no—
545C22⋊C4—48no—
546C22⋊C4—48no—
547C42—28no—
548C42—44no—
549C42—44no—
550C23—24no—
551C23—24no—
552C23—24no—
553C23—24no—
554C23—24no—
555C23—24no—
556C23—24no—
557C23—42no—
558C23—42no—
559C23—42no—
560C23—42no—
561C23—42no—
562C23—42no—
563C23—42no—
564C23—42no—
565C23—42no—
566C23—42no—
567C23—42no—
568C23—42no—
569C23—42no—
570C23—42no—
571C23—42no—
572C23—42no—
573C23—42no—
574C23—42no—
575C23—42no—
576C23—42no—
577C23—42no—
578C23—42no—
579C23—42no—
580C23—42no—
581C23—42no—
582C23—42no—
583C23—42no—
584C23—42no—
585C23C23×C4×C15111yescharacteristic
586C23C22×D4×C15111yescharacteristic
587C23C22×D4×C15111yescharacteristic
588C23C2×#41×C15111yescharacteristic
589C23C2×#41×C15111yescharacteristic
590C23C2×#41×C15111yescharacteristic
591C23C2×#41×C15111yescharacteristic
592C23H(5,𝔽2)×C15112yes—
593C23H(5,𝔽2)×C15112yes—
594C23H(5,𝔽2)×C15112yes—
595C232−1+4×C15112yes—
596D4—416no—
597C2×C4—22no—
598C2×C4—22no—
599C2×C4—24no—
600C2×C4—22no—
601C2×C4—22no—
602C2×C4—22no—
603C2×C4—22no—
604C2×C4—22no—
605C2×C4—22no—
606C2×C4—22no—
607C2×C4—22no—
608C2×C4—24no—
609C2×C4—24no—
610C2×C4—24no—
611C2×C4—24no—
612C2×C4—22no—
613C2×C4—24no—
614C2×C4—24no—
615C2×C4—24no—
616C2×C4—22no—
617C2×C4—22no—
618C2×C4—22no—
619C2×C4—22no—
620C2×C4—22no—
621C2×C4—24no—
622C2×C4—24no—
623C2×C4—41no—
624C2×C4—41no—
625C2×C4—42no—
626C2×C4—41no—
627C2×C4—41no—
628C2×C4—41no—
629C2×C4—41no—
630C2×C4—42no—
631C2×C4—42no—
632C2×C4—42no—
633C2×C4—42no—
634C2×C4—42no—
635C2×C4—42no—
636C2×C4—42no—
637C2×C4—42no—
638C2×C4—42no—
639C2×C4—42no—
640C2×C4—42no—
641C2×C4—42no—
642C2×C4—42no—
643C2×C4—42no—
644C2×C4—42no—
645C2×C4—42no—
646C2×C4—42no—
647C2×C4—42no—
648C2×C4—42no—
649C2×C4—42no—
650C2×C4—42no—
651C2×C4—42no—
652C2×C4C4×D4×C15114yes—
653C2×C4C4×D4×C15114yes—
654C2×C4#121×C15114yes—
655C22—44no—
656C22—44no—
657C22—44no—
658C22—44no—
659C22—44no—
660C22—44no—
661C22—44no—
662C22—82no—
663C22—82no—
664C22—82no—
665C22—82no—
666C22—82no—
667C22—82no—
668C22—82no—
669C22—82no—
670C22C2×C4×D4×C15111yescharacteristic
671C22C2×C4×D4×C15111yescharacteristic
672C22C4×#41×C15111yescharacteristic
673C22#518×C15112yes—
674C22#520×C15112yes—
675C22C2×#121×C15111yescharacteristic
676C22#525×C15111yescharacteristic
677C22#529×C15111yescharacteristic
678C22#532×C15111yescharacteristic
679C22#534×C15111yescharacteristic
680C22#535×C15111yescharacteristic
681C22#535×C15111yescharacteristic
682C22#535×C15112yes—
683C22#536×C15111yescharacteristic
684C22#537×C15112yes—
685C22#538×C15112yes—
686C22#538×C15112yes—
687C22#539×C15112yes—
688C22#540×C15112yes—
689C22#540×C15112yes—
690C22#542×C15112yes—
691C22#542×C15112yes—
692C22#542×C15112yes—
693C4—24no—
694C4—24no—
695C4—24no—
696C4—42no—
697C4—42no—
698C4—42no—
699C4—42no—
700C4—44no—
701C4—82no—
702C4—82no—
703C2—84no—
704C2C4×#121×C15111yescharacteristic
705C2#2321×C15111yescharacteristic
706C2#2324×C15112yes—
707C2#2326×C15111yescharacteristic
708C2#2335×C15112yes—
709C2#2618×C15111yescharacteristic
710C2#2619×C15111yescharacteristic
711C2#2632×C15111yescharacteristic
712C2#2635×C15111yescharacteristic
713C2#2651×C15112yes—
714C2#2662×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
3. C2×#388×C151C2semidirect
4. C2×C4×C4⋊C4×C151C2semidirect
5. #1444×C151C2semidirect
6. #1441×C151C2semidirect
7. #1439×C151C2semidirect
8. #1439×C151C2semidirect
10. #1437×C151C2semidirect
11. #1434×C151C2semidirect
26. #394×C151C4semidirect
90. C2×C42×C151D4semidirect
357. #14312C151direct (N × H)
358. C151#14312direct (N × H)
361. C2×#388C2×C151semidirect
362. C2×C4×C4⋊C4C2×C151semidirect
363. #1444C2×C151semidirect
364. #1441C2×C151semidirect
365. #1439C2×C151semidirect
366. #1439C2×C151semidirect
368. #1437C2×C151semidirect
369. #1434C2×C151semidirect
384. #394C4×C151semidirect
448. C2×C42D4×C151semidirect

Maximal subgroups

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

subgroupindex
C2×#394×C1512
C2×#390×C1512
C2×#388×C1512
C2×C4×C4⋊C4×C1512
#1444×C1512
#1441×C1512
#1439×C1512
#1438×C1512
#1437×C1512
#1434×C1512
#14312151