Finite Group Databasebeta

← C151×#23957 #50328882

Subgroups — C151×#23957 #50328882

Order 38656.

1318 conjugacy classes of subgroups.

The subgroup lattice has 752 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#3495×C151C211yesmaximal, characteristic, complemented
2#3003×C151C211yesmaximal, characteristic
3C2×#418×C151C211yesmaximal, characteristic, complemented
4#2435×C151C211yesmaximal, characteristic, complemented
5#2027×C151C212yesmaximal, complemented
6#2003×C151C212yesmaximal, complemented
7#1901×C151C211yesmaximal, characteristic, complemented
8#1888×C151C212yesmaximal, complemented
9#1883×C151C212yesmaximal, complemented
10#1871×C151C211yesmaximal, characteristic, complemented
11#1826×C151C211yesmaximal, characteristic, complemented
12C23×D4×C151C2211yescharacteristic
13C2×AGL(1,ℤ/8)×C151C2212yes—
14C22×M16×C151C2211yescharacteristic
15#556×C151—21no—
16#554×C151—21no—
17#552×C151—21no—
18#552×C151—22no—
19#552×C151—21no—
20#551×C151—22no—
21#544×C151C2211yescharacteristic, complemented
22#542×C151—21no—
23#541×C151—21no—
24#536×C151C2211yescharacteristic, complemented
25#533×C151—21no—
26#529×C151—21no—
27C2×#124×C151C2212yes—
28#525×C151C2211yescharacteristic
29C2×C22⋊Q8×C151C2211yescharacteristic
30#520×C151C2211yescharacteristic, complemented
31#519×C151C2211yescharacteristic, complemented
32C2×#117×C151C2211yescharacteristic
33#450×C151—21no—
34#450×C151—21no—
35#447×C151—21no—
36#447×C151—21no—
37C2×#104×C151C2212yescomplemented
38#418×C151—21no—
39#418×C151—21no—
40#418×C151C2212yes—
41#418×C151C2212yes—
42#418×C151C2212yes—
43C2×#102×C151—21no—
44C2×#102×C151—21no—
45C2×#101×C151C2212yescomplemented
46#407×C151C2211yescharacteristic
47#394×C151—22no—
48#390×C151C2212yes—
49#379×C151—22no—
50C4×C22⋊C4×C151C2211yescharacteristic
51#343×C151C2212yescomplemented
52#339×C151C2212yescomplemented
53#339×C151C2212yescomplemented
54#339×C151C2212yescomplemented
55C25×C151—21no—
56C2×#41×C151C2311yescharacteristic
57C22×Q8×C151C2311yescharacteristic
58C22×D4×C151—21no—
59C22×D4×C151—24no—
60C22×D4×C151—21no—
61C22×D4×C151—21no—
62C22×D4×C151—21no—
63C22×D4×C151—21no—
64C22×D4×C151—42no—
65C22×D4×C151C2312yes—
66C23×C4×C151C2311yescharacteristic
67AGL(1,ℤ/8)×C151—24no—
68AGL(1,ℤ/8)×C151—42no—
69C2×SD16×C151—22no—
70C2×D8×C151—22no—
71C2×M16×C151—21no—
72C2×M16×C151—42no—
73C2×M16×C151C2312yes—
74C2×M16×C151C2312yes—
75C22×C8×C151—21no—
76C4⋊Q8×C151—21no—
77C4⋊Q8×C151—21no—
78C4⋊Q8×C151—21no—
79#126×C151—22no—
80#126×C151—22no—
81#126×C151—22no—
82#126×C151—22no—
83#125×C151—22no—
84#125×C151—22no—
85#125×C151—22no—
86#125×C151—21no—
87#125×C151—21no—
88#124×C151—22no—
89#124×C151—21no—
90#124×C151—24no—
91#124×C151—42no—
92#123×C151—22no—
93#123×C151—22no—
94#123×C151—21no—
95#123×C151—22no—
96C22⋊Q8×C151—22no—
97C22⋊Q8×C151—22no—
98C22⋊Q8×C151—21no—
99C22⋊Q8×C151—21no—
100C22⋊Q8×C151—21no—
101C22⋊Q8×C151—21no—
102C22⋊Q8×C151—22no—
103C22⋊Q8×C151—21no—
104C22⋊Q8×C151—21no—
105C22⋊Q8×C151D411yescharacteristic
106C22⋊Q8×C151D411yescharacteristic
107#121×C151D411yescharacteristic
108#121×C151D411yescharacteristic
109#120×C151—21no—
110C4×Q8×C151—22no—
111C4×Q8×C151—21no—
112C4×Q8×C151—21no—
113C4×Q8×C151—21no—
114C4×Q8×C151—21no—
115C4×Q8×C151—21no—
116C4×D4×C151—22no—
117C4×D4×C151—21no—
118C4×D4×C151—22no—
119C4×D4×C151—21no—
120C4×D4×C151—21no—
121#117×C151—22no—
122#117×C151—22no—
123#117×C151—21no—
124#117×C151—21no—
125#117×C151—22no—
126#117×C151—21no—
127#117×C151D411yescharacteristic
128#117×C151D411yescharacteristic
129#117×C151C2311yescharacteristic
130#117×C151C2311yescharacteristic
131#117×C151C2311yescharacteristic
132C2×C4⋊C4×C151—21no—
133C2×C4⋊C4×C151D412yes—
134C2×C4⋊C4×C151D411yescharacteristic
135C2×C4⋊C4×C151D411yescharacteristic
136C2×C4⋊C4×C151C2311yescharacteristic
137C2×C22⋊C4×C151—24no—
138C2×C22⋊C4×C151—24no—
139C2×C22⋊C4×C151—21no—
140C2×C22⋊C4×C151—21no—
141C2×C22⋊C4×C151D412yes—
142C2×C42×C151—21no—
143C2×C42×C151C2312yes—
144#104×C151—42no—
145#102×C151—22no—
146#102×C151—22no—
147#102×C151—22no—
148#102×C151—22no—
149#102×C151—22no—
150#102×C151—22no—
151#101×C151—42no—
152C22⋊C8×C151—21no—
153C22⋊C8×C151—21no—
154#95×C151—21no—
155C24×C151—22no—
156C24×C151—44no—
157C24×C151—44no—
158C24×C151—41no—
159C24×C151—41no—
160C24×C151—82no—
161C24×C151C2×D411yescharacteristic
162#41×C151—22no—
163#41×C151—22no—
164C2×Q8×C151—22no—
165C2×Q8×C151—21no—
166C2×Q8×C151—21no—
167C2×Q8×C151—22no—
168C2×Q8×C151—22no—
169C2×Q8×C151C2×D411yescharacteristic
170C2×D4×C151—24no—
171C2×D4×C151—24no—
172C2×D4×C151—21no—
173C2×D4×C151—21no—
174C2×D4×C151—21no—
175C2×D4×C151—22no—
176C2×D4×C151—22no—
177C2×D4×C151—22no—
178C2×D4×C151—22no—
179C2×D4×C151—22no—
180C2×D4×C151—44no—
181C2×D4×C151—44no—
182C2×D4×C151—44no—
183C2×D4×C151—42no—
184C2×D4×C151—42no—
185C2×D4×C151—41no—
186C2×D4×C151—41no—
187C2×D4×C151C2×D411yescharacteristic
188C2×D4×C151#4114yes—
189C22×C4×C151—22no—
190C22×C4×C151—22no—
191C22×C4×C151—21no—
192C22×C4×C151—22no—
193C22×C4×C151—21no—
194C22×C4×C151—21no—
195C22×C4×C151—22no—
196C22×C4×C151C2×D412yes—
197C22×C4×C151C2×D411yescharacteristic
198C22×C4×C151C2×D411yescharacteristic
199C22×C4×C151C2×D411yescharacteristic
200C22×C4×C151C2×D411yescharacteristic
201C22×C4×C151C2×D411yescharacteristic
202C22×C4×C151C2×D412yes—
203C22×C4×C151C2411yescharacteristic
204SD16×C151—44no—
205D8×C151—44no—
206M16×C151—22no—
207M16×C151—22no—
208M16×C151—22no—
209M16×C151—22no—
210M16×C151—42no—
211C2×C8×C151—22no—
212C2×C8×C151—22no—
213C2×C8×C151—42no—
214C4⋊C4×C151—22no—
215C4⋊C4×C151—22no—
216C4⋊C4×C151—22no—
217C4⋊C4×C151—22no—
218C4⋊C4×C151—22no—
219C4⋊C4×C151—22no—
220C4⋊C4×C151—22no—
221C4⋊C4×C151—22no—
222C4⋊C4×C151—21no—
223C4⋊C4×C151—21no—
224C4⋊C4×C151—22no—
225C4⋊C4×C151—22no—
226C4⋊C4×C151—21no—
227C4⋊C4×C151—21no—
228C4⋊C4×C151—21no—
229C4⋊C4×C151—21no—
230C4⋊C4×C151C2×D411yescharacteristic
231C4⋊C4×C151C2×D411yescharacteristic
232C4⋊C4×C151C2×D411yescharacteristic
233C4⋊C4×C151C2×D411yescharacteristic
234C4⋊C4×C151C2×D411yescharacteristic
235C4⋊C4×C151C2×D411yescharacteristic
236C22⋊C4×C151—22no—
237C22⋊C4×C151—22no—
238C22⋊C4×C151—22no—
239C22⋊C4×C151—21no—
240C22⋊C4×C151—21no—
241C22⋊C4×C151—22no—
242C22⋊C4×C151—22no—
243C22⋊C4×C151—21no—
244C22⋊C4×C151—21no—
245C22⋊C4×C151—21no—
246C22⋊C4×C151—21no—
247C22⋊C4×C151—21no—
248C22⋊C4×C151—21no—
249C22⋊C4×C151—21no—
250C22⋊C4×C151—48no—
251C22⋊C4×C151—42no—
252C22⋊C4×C151—84no—
253C42×C151—22no—
254C42×C151—22no—
255C42×C151—22no—
256C42×C151—21no—
257C42×C151—21no—
258C42×C151—21no—
259C42×C151—21no—
260C42×C151—21no—
261C42×C151—22no—
262C42×C151—22no—
263C23×C151—22no—
264C23×C151—22no—
265C23×C151—21no—
266C23×C151—24no—
267C23×C151—41no—
268C23×C151—44no—
269C23×C151—44no—
270C23×C151—44no—
271C23×C151—44no—
272C23×C151—42no—
273C23×C151—42no—
274C23×C151—82no—
275C23×C151—82no—
276C23×C151—82no—
277C23×C151—816no—
278C23×C151—82no—
279C23×C151#12011yescharacteristic
280C23×C151#12011yescharacteristic
281C23×C151C22×D411yescharacteristic
282Q8×C151—22no—
283Q8×C151—41no—
284Q8×C151—41no—
285Q8×C151—42no—
286Q8×C151—82no—
287D4×C151—24no—
288D4×C151—22no—
289D4×C151—24no—
290D4×C151—44no—
291D4×C151—44no—
292D4×C151—42no—
293D4×C151—42no—
294D4×C151—42no—
295D4×C151—42no—
296D4×C151—81no—
297C2×C4×C151—22no—
298C2×C4×C151—21no—
299C2×C4×C151—21no—
300C2×C4×C151—21no—
301C2×C4×C151—21no—
302C2×C4×C151—22no—
303C2×C4×C151—22no—
304C2×C4×C151—21no—
305C2×C4×C151—22no—
306C2×C4×C151—21no—
307C2×C4×C151—22no—
308C2×C4×C151—21no—
309C2×C4×C151—21no—
310C2×C4×C151—21no—
311C2×C4×C151—21no—
312C2×C4×C151—21no—
313C2×C4×C151—24no—
314C2×C4×C151—42no—
315C2×C4×C151—41no—
316C2×C4×C151—41no—
317C2×C4×C151—42no—
318C2×C4×C151—42no—
319C2×C4×C151—42no—
320C2×C4×C151—42no—
321C2×C4×C151—81no—
322C2×C4×C151—82no—
323C2×C4×C151#12011yescharacteristic
324C2×C4×C151#12011yescharacteristic
325C2×C4×C151C22×D411yescharacteristic
326C2×C4×C151C22×D411yescharacteristic
327C2×C4×C151C2×#4112yes—
328C2×C4×C151H(5,𝔽2)12yes—
329C8×C151—42no—
330C8×C151—42no—
331C22×C151—21no—
332C22×C151—21no—
333C22×C151—21no—
334C22×C151—21no—
335C22×C151—21no—
336C22×C151—21no—
337C22×C151—21no—
338C22×C151—44no—
339C22×C151—48no—
340C22×C151—41no—
341C22×C151—44no—
342C22×C151—41no—
343C22×C151—41no—
344C22×C151—84no—
345C22×C151—88no—
346C22×C151—88no—
347C22×C151—82no—
348C22×C151—82no—
349C22×C151#45412yes—
350C22×C151C2×#12011yescharacteristic
351C22×C151#54612yes—
352C4×C151—21no—
353C4×C151—21no—
354C4×C151—42no—
355C4×C151—41no—
356C4×C151—41no—
357C4×C151—41no—
358C4×C151—41no—
359C4×C151—42no—
360C4×C151—41no—
361C4×C151—41no—
362C4×C151—41no—
363C4×C151—82no—
364C4×C151#52511yescharacteristic
365C4×C151#53511yescharacteristic
366C4×C151#54612yes—
367C2×C151—22no—
368C2×C151—22no—
369C2×C151—41no—
370C2×C151—81no—
371C2×C151—84no—
372C2×C151#240411yescharacteristic
373C2×C151C2×#45411yescharacteristic
374C2×C151#302111yescharacteristic
375#23957C15111yesmaximal, characteristic, direct product factor, Sylow
376C151#2395711yescharacteristic, direct product factor, Sylow
377#3495C2×C15111yescharacteristic, complemented
378#3003C2×C15111yescharacteristic
379C2×#418C2×C15111yescharacteristic, complemented
380#2435C2×C15111yescharacteristic, complemented
381#2027C2×C15112yescomplemented
382#2003C2×C15112yescomplemented
383#1901C2×C15111yescharacteristic, complemented
384#1888C2×C15112yescomplemented
385#1883C2×C15112yescomplemented
386#1871C2×C15111yescharacteristic, complemented
387#1826C2×C15111yescharacteristic, complemented
388C23×D4C22×C15111yescharacteristic
389C2×AGL(1,ℤ/8)C22×C15112yes—
390C22×M16C22×C15111yescharacteristic
391#556—21no—
392#554—21no—
393#552—21no—
394#552—22no—
395#552—21no—
396#551—22no—
397#544C22×C15111yescharacteristic, complemented
398#542—21no—
399#541—21no—
400#536C22×C15111yescharacteristic, complemented
401#533—21no—
402#529—21no—
403C2×#124C22×C15112yes—
404#525C22×C15111yescharacteristic
405C2×C22⋊Q8C22×C15111yescharacteristic
406#520C22×C15111yescharacteristic, complemented
407#519C22×C15111yescharacteristic, complemented
408C2×#117C22×C15111yescharacteristic
409#450—21no—
410#450—21no—
411#447—21no—
412#447—21no—
413C2×#104C22×C15112yescomplemented
414#418—21no—
415#418—21no—
416#418C22×C15112yes—
417#418C22×C15112yes—
418#418C22×C15112yes—
419C2×#102—21no—
420C2×#102—21no—
421C2×#101C22×C15112yescomplemented
422#407C22×C15111yescharacteristic
423#394—22no—
424#390C22×C15112yes—
425#379—22no—
426C4×C22⋊C4C22×C15111yescharacteristic
427#343C22×C15112yescomplemented
428#339C22×C15112yescomplemented
429#339C22×C15112yescomplemented
430#339C22×C15112yescomplemented
431C25—21no—
432C2×#41C23×C15111yescharacteristic
433C22×Q8C23×C15111yescharacteristic
434C22×D4—24no—
435C22×D4—21no—
436C22×D4—21no—
437C22×D4—21no—
438C22×D4—21no—
439C22×D4—21no—
440C22×D4—42no—
441C22×D4C23×C15112yes—
442C23×C4C23×C15111yescharacteristic
443AGL(1,ℤ/8)—24no—
444AGL(1,ℤ/8)—42no—
445C2×SD16—22no—
446C2×D8—22no—
447C2×M16—21no—
448C2×M16—42no—
449C2×M16C23×C15112yes—
450C2×M16C23×C15112yes—
451C22×C8—21no—
452C4⋊Q8—21no—
453C4⋊Q8—21no—
454C4⋊Q8—21no—
455#126—22no—
456#126—22no—
457#126—22no—
458#126—22no—
459#125—22no—
460#125—22no—
461#125—22no—
462#125—21no—
463#125—21no—
464#124—22no—
465#124—21no—
466#124—24no—
467#124—42no—
468#123—22no—
469#123—22no—
470#123—21no—
471#123—22no—
472C22⋊Q8—22no—
473C22⋊Q8—22no—
474C22⋊Q8—21no—
475C22⋊Q8—21no—
476C22⋊Q8—21no—
477C22⋊Q8—21no—
478C22⋊Q8—22no—
479C22⋊Q8—21no—
480C22⋊Q8—21no—
481C22⋊Q8D4×C15111yescharacteristic
482C22⋊Q8D4×C15111yescharacteristic
483#121D4×C15111yescharacteristic
484#121D4×C15111yescharacteristic
485#120—21no—
486C4×Q8—22no—
487C4×Q8—21no—
488C4×Q8—21no—
489C4×Q8—21no—
490C4×Q8—21no—
491C4×Q8—21no—
492C4×D4—22no—
493C4×D4—21no—
494C4×D4—22no—
495C4×D4—21no—
496C4×D4—21no—
497#117—22no—
498#117—22no—
499#117—21no—
500#117—21no—
501#117—22no—
502#117—21no—
503#117D4×C15111yescharacteristic
504#117D4×C15111yescharacteristic
505#117C23×C15111yescharacteristic
506#117C23×C15111yescharacteristic
507#117C23×C15111yescharacteristic
508C2×C4⋊C4—21no—
509C2×C4⋊C4D4×C15112yes—
510C2×C4⋊C4D4×C15111yescharacteristic
511C2×C4⋊C4D4×C15111yescharacteristic
512C2×C4⋊C4C23×C15111yescharacteristic
513C2×C22⋊C4—21no—
514C2×C22⋊C4—21no—
515C2×C22⋊C4—24no—
516C2×C22⋊C4—24no—
517C2×C22⋊C4D4×C15112yes—
518C2×C42—21no—
519C2×C42C23×C15112yes—
520#104—42no—
521#102—22no—
522#102—22no—
523#102—22no—
524#102—22no—
525#102—22no—
526#102—22no—
527#101—42no—
528C22⋊C8—21no—
529C22⋊C8—21no—
530#95—21no—
531C24—22no—
532C24—44no—
533C24—44no—
534C24—41no—
535C24—41no—
536C24—82no—
537C24C2×D4×C15111yescharacteristic
538#41—22no—
539#41—22no—
540C2×Q8—22no—
541C2×Q8—21no—
542C2×Q8—21no—
543C2×Q8—22no—
544C2×Q8—22no—
545C2×Q8C2×D4×C15111yescharacteristic
546C2×D4—24no—
547C2×D4—24no—
548C2×D4—21no—
549C2×D4—21no—
550C2×D4—21no—
551C2×D4—22no—
552C2×D4—22no—
553C2×D4—22no—
554C2×D4—22no—
555C2×D4—22no—
556C2×D4—44no—
557C2×D4—44no—
558C2×D4—44no—
559C2×D4—42no—
560C2×D4—42no—
561C2×D4—41no—
562C2×D4—41no—
563C2×D4C2×D4×C15111yescharacteristic
564C2×D4#41×C15114yes—
565C22×C4—22no—
566C22×C4—22no—
567C22×C4—21no—
568C22×C4—22no—
569C22×C4—21no—
570C22×C4—21no—
571C22×C4—22no—
572C22×C4C2×D4×C15112yes—
573C22×C4C2×D4×C15111yescharacteristic
574C22×C4C2×D4×C15111yescharacteristic
575C22×C4C2×D4×C15111yescharacteristic
576C22×C4C2×D4×C15111yescharacteristic
577C22×C4C2×D4×C15111yescharacteristic
578C22×C4C2×D4×C15112yes—
579C22×C4C24×C15111yescharacteristic
580SD16—44no—
581D8—44no—
582M16—22no—
583M16—22no—
584M16—22no—
585M16—22no—
586M16—42no—
587C2×C8—22no—
588C2×C8—22no—
589C2×C8—42no—
590C4⋊C4—22no—
591C4⋊C4—22no—
592C4⋊C4—22no—
593C4⋊C4—22no—
594C4⋊C4—22no—
595C4⋊C4—22no—
596C4⋊C4—22no—
597C4⋊C4—22no—
598C4⋊C4—21no—
599C4⋊C4—21no—
600C4⋊C4—22no—
601C4⋊C4—22no—
602C4⋊C4—21no—
603C4⋊C4—21no—
604C4⋊C4—21no—
605C4⋊C4—21no—
606C4⋊C4C2×D4×C15111yescharacteristic
607C4⋊C4C2×D4×C15111yescharacteristic
608C4⋊C4C2×D4×C15111yescharacteristic
609C4⋊C4C2×D4×C15111yescharacteristic
610C4⋊C4C2×D4×C15111yescharacteristic
611C4⋊C4C2×D4×C15111yescharacteristic
612C22⋊C4—22no—
613C22⋊C4—22no—
614C22⋊C4—22no—
615C22⋊C4—21no—
616C22⋊C4—21no—
617C22⋊C4—22no—
618C22⋊C4—22no—
619C22⋊C4—21no—
620C22⋊C4—21no—
621C22⋊C4—21no—
622C22⋊C4—21no—
623C22⋊C4—21no—
624C22⋊C4—21no—
625C22⋊C4—21no—
626C22⋊C4—48no—
627C22⋊C4—42no—
628C22⋊C4—84no—
629C42—22no—
630C42—22no—
631C42—22no—
632C42—21no—
633C42—21no—
634C42—21no—
635C42—21no—
636C42—21no—
637C42—22no—
638C42—22no—
639C23—22no—
640C23—22no—
641C23—21no—
642C23—24no—
643C23—41no—
644C23—44no—
645C23—44no—
646C23—44no—
647C23—44no—
648C23—42no—
649C23—42no—
650C23—82no—
651C23—82no—
652C23—82no—
653C23—816no—
654C23—82no—
655C23#120×C15111yescharacteristic
656C23#120×C15111yescharacteristic
657C23C22×D4×C15111yescharacteristic
658Q8—22no—
659Q8—41no—
660Q8—41no—
661Q8—42no—
662Q8—82no—
663D4—24no—
664D4—22no—
665D4—24no—
666D4—44no—
667D4—44no—
668D4—42no—
669D4—42no—
670D4—42no—
671D4—42no—
672D4—81no—
673C2×C4—22no—
674C2×C4—21no—
675C2×C4—21no—
676C2×C4—21no—
677C2×C4—21no—
678C2×C4—22no—
679C2×C4—22no—
680C2×C4—21no—
681C2×C4—21no—
682C2×C4—21no—
683C2×C4—21no—
684C2×C4—21no—
685C2×C4—22no—
686C2×C4—21no—
687C2×C4—21no—
688C2×C4—22no—
689C2×C4—24no—
690C2×C4—42no—
691C2×C4—41no—
692C2×C4—41no—
693C2×C4—42no—
694C2×C4—42no—
695C2×C4—42no—
696C2×C4—42no—
697C2×C4—81no—
698C2×C4—82no—
699C2×C4#120×C15111yescharacteristic
700C2×C4#120×C15111yescharacteristic
701C2×C4C22×D4×C15111yescharacteristic
702C2×C4C22×D4×C15111yescharacteristic
703C2×C4C2×#41×C15112yes—
704C2×C4H(5,𝔽2)×C15112yes—
705C8—42no—
706C8—42no—
707C22—21no—
708C22—21no—
709C22—21no—
710C22—21no—
711C22—21no—
712C22—21no—
713C22—21no—
714C22—44no—
715C22—48no—
716C22—41no—
717C22—44no—
718C22—41no—
719C22—41no—
720C22—84no—
721C22—88no—
722C22—88no—
723C22—82no—
724C22—82no—
725C22#454×C15112yes—
726C22C2×#120×C15111yescharacteristic
727C22#546×C15112yes—
728C4—21no—
729C4—21no—
730C4—42no—
731C4—41no—
732C4—41no—
733C4—41no—
734C4—41no—
735C4—42no—
736C4—41no—
737C4—41no—
738C4—41no—
739C4—82no—
740C4#525×C15111yescharacteristic
741C4#535×C15111yescharacteristic
742C4#546×C15112yes—
743C2—22no—
744C2—22no—
745C2—41no—
746C2—84no—
747C2—81no—
748C2#2404×C15111yescharacteristic
749C2C2×#454×C15111yescharacteristic
750C2#3021×C15111yescharacteristic
subgroupG/H
center, socleC22×C151C2×#120
commutator, Frattini, cosocleC22×C4C24×C151
prime radical#3003×C151C2
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C151 ◁ C23×C4×C151 ◁ G

Complements

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

NH ≅ G/Ntype
1. #3495×C151C2semidirect
3. C2×#418×C151C2semidirect
4. #2435×C151C2semidirect
5. #2027×C151C2semidirect
6. #2003×C151C2semidirect
7. #1901×C151C2semidirect
8. #1888×C151C2semidirect
9. #1883×C151C2semidirect
10. #1871×C151C2semidirect
11. #1826×C151C2semidirect
21. #544×C151C22semidirect
24. #536×C151C22semidirect
30. #520×C151C22semidirect
31. #519×C151C22semidirect
37. C2×#104×C151C22semidirect
45. C2×#101×C151C22semidirect
51. #343×C151C22semidirect
52. #339×C151C22semidirect
53. #339×C151C22semidirect
54. #339×C151C22semidirect
375. #23957C151direct (N × H)
376. C151#23957direct (N × H)
377. #3495C2×C151semidirect
379. C2×#418C2×C151semidirect
380. #2435C2×C151semidirect
381. #2027C2×C151semidirect
382. #2003C2×C151semidirect
383. #1901C2×C151semidirect
384. #1888C2×C151semidirect
385. #1883C2×C151semidirect
386. #1871C2×C151semidirect
387. #1826C2×C151semidirect
397. #544C22×C151semidirect
400. #536C22×C151semidirect
406. #520C22×C151semidirect
407. #519C22×C151semidirect
413. C2×#104C22×C151semidirect
421. C2×#101C22×C151semidirect
427. #343C22×C151semidirect
428. #339C22×C151semidirect
429. #339C22×C151semidirect
430. #339C22×C151semidirect

Maximal subgroups

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

subgroupindex
#3495×C1512
#3003×C1512
C2×#418×C1512
#2435×C1512
#2027×C1512
#2003×C1512
#1901×C1512
#1888×C1512
#1883×C1512
#1871×C1512
#1826×C1512
#23957151