Finite Group Databasebeta

← C151×#24026 #50328951

Subgroups — C151×#24026 #50328951

Order 38656.

1404 conjugacy classes of subgroups.

The subgroup lattice has 820 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#3488×C151C211yesmaximal, characteristic
2#3092×C151C211yesmaximal, characteristic, complemented
3C2×#417×C151C211yesmaximal, characteristic, complemented
4#2501×C151C211yesmaximal, characteristic, complemented
5#2039×C151C212yesmaximal, complemented
6#2037×C151C212yesmaximal, complemented
7#1900×C151C211yesmaximal, characteristic, complemented
8#1871×C151C211yesmaximal, characteristic, complemented
9#1859×C151C212yesmaximal, complemented
10#1792×C151C212yesmaximal, complemented
11#1789×C151C211yesmaximal, characteristic, complemented
12C2×H(5,𝔽2)×C151C2211yescharacteristic
13C22×#41×C151C2211yescharacteristic
14C22×M16×C151C2211yescharacteristic, complemented
15#550×C151—21no—
16#548×C151—21no—
17#546×C151—21no—
18#546×C151—22no—
19D42×C151—22no—
20D42×C151—21no—
21#537×C151—21no—
22#537×C151C2211yescharacteristic
23#535×C151—21no—
24#535×C151C2211yescharacteristic
25#525×C151—21no—
26#525×C151C2211yescharacteristic
27C2×#123×C151—22no—
28C2×#121×C151—21no—
29C2×#121×C151C2211yescharacteristic
30#520×C151C2211yescharacteristic
31C22×C4⋊C4×C151C2211yescharacteristic, complemented
32#484×C151—21no—
33#483×C151—21no—
34#481×C151—21no—
35#480×C151—21no—
36#428×C151C2212yescomplemented
37C2×#104×C151C2212yes—
38C2×#104×C151C2212yescomplemented
39C2×#104×C151C2212yescomplemented
40#417×C151—21no—
41#417×C151—21no—
42#417×C151C2212yes—
43#417×C151C2212yescomplemented
44#417×C151C2212yescomplemented
45C2×#103×C151—21no—
46C2×#102×C151—21no—
47C2×#100×C151C2212yescomplemented
48#407×C151C2211yescharacteristic, complemented
49#399×C151—22no—
50#390×C151C2212yescomplemented
51#384×C151C2212yescomplemented
52C4×C22⋊C4×C151C2211yescharacteristic, complemented
53#343×C151C2212yescomplemented
54#339×C151C2212yescomplemented
55H(5,𝔽2)×C151—24no—
56H(5,𝔽2)×C151—42no—
57C2×#41×C151—24no—
58C2×#41×C151—21no—
59C2×#41×C151—21no—
60C2×#41×C151—21no—
61C2×#41×C151—21no—
62C2×#41×C151—42no—
63C2×#41×C151D411yescharacteristic
64C2×#41×C151D411yescharacteristic
65C2×#41×C151C2311yescharacteristic
66C2×#41×C151C2311yescharacteristic
67C2×#41×C151C2311yescharacteristic
68C22×Q8×C151D411yescharacteristic
69C22×D4×C151—22no—
70C22×D4×C151—21no—
71C22×D4×C151—21no—
72C22×D4×C151—21no—
73C22×D4×C151—22no—
74C22×D4×C151D411yescharacteristic
75C22×D4×C151D412yes—
76C22×D4×C151C2311yescharacteristic
77C23×C4×C151—21no—
78C23×C4×C151—21no—
79C23×C4×C151C2311yescharacteristic
80C2×M16×C151—21no—
81C2×M16×C151—42no—
82C2×M16×C151C2312yes—
83C2×M16×C151C2312yes—
84C22×C8×C151—21no—
85#127×C151—22no—
86#127×C151—21no—
87#124×C151—22no—
88#124×C151—21no—
89#123×C151—22no—
90#123×C151—21no—
91#123×C151—48no—
92C22⋊Q8×C151—22no—
93C22⋊Q8×C151—21no—
94C22⋊Q8×C151—21no—
95C22⋊Q8×C151D411yescharacteristic
96C22⋊Q8×C151D411yescharacteristic
97#121×C151—22no—
98#121×C151—22no—
99#121×C151—22no—
100#121×C151—22no—
101#121×C151—22no—
102#121×C151—21no—
103#121×C151—21no—
104#121×C151—21no—
105#121×C151—21no—
106#121×C151—21no—
107#121×C151—21no—
108#121×C151—22no—
109#121×C151—21no—
110#121×C151—21no—
111#121×C151D411yescharacteristic
112#121×C151D411yescharacteristic
113#120×C151—22no—
114#120×C151—22no—
115#120×C151—22no—
116#120×C151—21no—
117#120×C151—22no—
118C4×Q8×C151—21no—
119C4×D4×C151—22no—
120C4×D4×C151—22no—
121C4×D4×C151—21no—
122C4×D4×C151—22no—
123C4×D4×C151—21no—
124C4×D4×C151—21no—
125#117×C151—21no—
126#117×C151C2311yescharacteristic
127C2×C4⋊C4×C151—21no—
128C2×C4⋊C4×C151—21no—
129C2×C4⋊C4×C151—21no—
130C2×C4⋊C4×C151—21no—
131C2×C4⋊C4×C151—21no—
132C2×C4⋊C4×C151—24no—
133C2×C4⋊C4×C151—21no—
134C2×C4⋊C4×C151C2312yes—
135C2×C4⋊C4×C151C2311yescharacteristic
136C2×C22⋊C4×C151—22no—
137C2×C22⋊C4×C151—21no—
138C2×C22⋊C4×C151—24no—
139C2×C22⋊C4×C151D412yes—
140C2×C42×C151C2312yes—
141#107×C151—22no—
142#106×C151—22no—
143#104×C151—24no—
144#104×C151—42no—
145#104×C151—42no—
146#103×C151—22no—
147#103×C151—22no—
148#103×C151—22no—
149#102×C151—22no—
150#102×C151—22no—
151#102×C151—22no—
152#100×C151—42no—
153C22⋊C8×C151—21no—
154C22⋊C8×C151—21no—
155#95×C151—21no—
156C24×C151—22no—
157C24×C151—21no—
158C24×C151C2×D411yescharacteristic
159C24×C151C2×D412yes—
160#41×C151—22no—
161#41×C151—22no—
162#41×C151—22no—
163#41×C151—22no—
164#41×C151—22no—
165#41×C151—22no—
166#41×C151—22no—
167#41×C151—44no—
168#41×C151—41no—
169#41×C151—41no—
170#41×C151—44no—
171#41×C151—44no—
172#41×C151—42no—
173#41×C151—42no—
174#41×C151#4114yes—
175C2×Q8×C151—21no—
176C2×Q8×C151—22no—
177C2×Q8×C151—41no—
178C2×Q8×C151C2×D411yescharacteristic
179C2×Q8×C151C2×D411yescharacteristic
180C2×Q8×C151C2×D411yescharacteristic
181C2×D4×C151—21no—
182C2×D4×C151—22no—
183C2×D4×C151—22no—
184C2×D4×C151—22no—
185C2×D4×C151—22no—
186C2×D4×C151—21no—
187C2×D4×C151—21no—
188C2×D4×C151—21no—
189C2×D4×C151—21no—
190C2×D4×C151—21no—
191C2×D4×C151—22no—
192C2×D4×C151—22no—
193C2×D4×C151—22no—
194C2×D4×C151—21no—
195C2×D4×C151—22no—
196C2×D4×C151—21no—
197C2×D4×C151—21no—
198C2×D4×C151—21no—
199C2×D4×C151—22no—
200C2×D4×C151—22no—
201C2×D4×C151—41no—
202C2×D4×C151—44no—
203C2×D4×C151—44no—
204C2×D4×C151—48no—
205C2×D4×C151—42no—
206C2×D4×C151—42no—
207C2×D4×C151—44no—
208C2×D4×C151—84no—
209C2×D4×C151C2×D411yescharacteristic
210C2×D4×C151C2×D411yescharacteristic
211C2×D4×C151C2×D411yescharacteristic
212C22×C4×C151—21no—
213C22×C4×C151—22no—
214C22×C4×C151—22no—
215C22×C4×C151—22no—
216C22×C4×C151—21no—
217C22×C4×C151—22no—
218C22×C4×C151—22no—
219C22×C4×C151—21no—
220C22×C4×C151—21no—
221C22×C4×C151—21no—
222C22×C4×C151—21no—
223C22×C4×C151—22no—
224C22×C4×C151—44no—
225C22×C4×C151—44no—
226C22×C4×C151—41no—
227C22×C4×C151—41no—
228C22×C4×C151C2×D411yescharacteristic
229C22×C4×C151C2×D411yescharacteristic
230C22×C4×C151C2×D411yescharacteristic
231C22×C4×C151C2×D411yescharacteristic
232C22×C4×C151C2×D411yescharacteristic
233C22×C4×C151C2×D412yes—
234C22×C4×C151C2411yescharacteristic
235M16×C151—22no—
236M16×C151—22no—
237M16×C151—22no—
238M16×C151—22no—
239M16×C151—42no—
240C2×C8×C151—22no—
241C2×C8×C151—22no—
242C2×C8×C151—42no—
243C4⋊C4×C151—22no—
244C4⋊C4×C151—22no—
245C4⋊C4×C151—21no—
246C4⋊C4×C151—21no—
247C4⋊C4×C151—21no—
248C4⋊C4×C151—21no—
249C4⋊C4×C151—22no—
250C4⋊C4×C151—22no—
251C4⋊C4×C151—48no—
252C4⋊C4×C151—41no—
253C4⋊C4×C151—41no—
254C4⋊C4×C151C2×D411yescharacteristic
255C4⋊C4×C151C2×D411yescharacteristic
256C22⋊C4×C151—22no—
257C22⋊C4×C151—22no—
258C22⋊C4×C151—24no—
259C22⋊C4×C151—22no—
260C22⋊C4×C151—22no—
261C22⋊C4×C151—22no—
262C22⋊C4×C151—21no—
263C22⋊C4×C151—21no—
264C22⋊C4×C151—21no—
265C22⋊C4×C151—21no—
266C22⋊C4×C151—22no—
267C22⋊C4×C151—22no—
268C22⋊C4×C151—21no—
269C22⋊C4×C151—48no—
270C42×C151—22no—
271C42×C151—21no—
272C42×C151—22no—
273C42×C151—22no—
274C23×C151—21no—
275C23×C151—22no—
276C23×C151—22no—
277C23×C151—21no—
278C23×C151—22no—
279C23×C151—21no—
280C23×C151—24no—
281C23×C151—41no—
282C23×C151—42no—
283C23×C151—44no—
284C23×C151—42no—
285C23×C151—42no—
286C23×C151—42no—
287C23×C151—81no—
288C23×C151—82no—
289C23×C151—82no—
290C23×C151#12011yescharacteristic
291C23×C151#12011yescharacteristic
292C23×C151C22×D411yescharacteristic
293Q8×C151—21no—
294Q8×C151—21no—
295Q8×C151—21no—
296Q8×C151—22no—
297Q8×C151—42no—
298Q8×C151#12312yescomplemented
299D4×C151—24no—
300D4×C151—21no—
301D4×C151—21no—
302D4×C151—21no—
303D4×C151—22no—
304D4×C151—42no—
305D4×C151—42no—
306D4×C151—44no—
307D4×C151—42no—
308D4×C151—44no—
309D4×C151—42no—
310D4×C151—42no—
311D4×C151—44no—
312D4×C151—42no—
313D4×C151—41no—
314D4×C151—41no—
315D4×C151—42no—
316D4×C151—81no—
317D4×C151—82no—
318D4×C151—82no—
319D4×C151—82no—
320D4×C151—82no—
321D4×C151#12312yescomplemented
322C2×C4×C151—21no—
323C2×C4×C151—22no—
324C2×C4×C151—21no—
325C2×C4×C151—21no—
326C2×C4×C151—21no—
327C2×C4×C151—21no—
328C2×C4×C151—24no—
329C2×C4×C151—22no—
330C2×C4×C151—22no—
331C2×C4×C151—24no—
332C2×C4×C151—21no—
333C2×C4×C151—21no—
334C2×C4×C151—21no—
335C2×C4×C151—22no—
336C2×C4×C151—21no—
337C2×C4×C151—42no—
338C2×C4×C151—42no—
339C2×C4×C151—42no—
340C2×C4×C151—44no—
341C2×C4×C151—42no—
342C2×C4×C151—42no—
343C2×C4×C151—41no—
344C2×C4×C151—41no—
345C2×C4×C151—42no—
346C2×C4×C151—42no—
347C2×C4×C151—44no—
348C2×C4×C151—42no—
349C2×C4×C151—82no—
350C2×C4×C151—82no—
351C2×C4×C151—82no—
352C2×C4×C151#12011yescharacteristic
353C2×C4×C151#12011yescharacteristic
354C2×C4×C151C22×D411yescharacteristic
355C2×C4×C151C22×D411yescharacteristic
356C2×C4×C151C2×#4112yes—
357C2×C4×C151H(5,𝔽2)12yes—
358C8×C151—42no—
359C8×C151—42no—
360C22×C151—21no—
361C22×C151—21no—
362C22×C151—21no—
363C22×C151—21no—
364C22×C151—21no—
365C22×C151—22no—
366C22×C151—21no—
367C22×C151—21no—
368C22×C151—44no—
369C22×C151—41no—
370C22×C151—41no—
371C22×C151—41no—
372C22×C151—41no—
373C22×C151—42no—
374C22×C151—42no—
375C22×C151—41no—
376C22×C151—41no—
377C22×C151—41no—
378C22×C151—42no—
379C22×C151—41no—
380C22×C151—84no—
381C22×C151—84no—
382C22×C151—164no—
383C22×C151#45312yes—
384C22×C151C2×#12011yescharacteristic
385C22×C151#54612yes—
386C4×C151—21no—
387C4×C151—21no—
388C4×C151—22no—
389C4×C151—44no—
390C4×C151—41no—
391C4×C151—41no—
392C4×C151—42no—
393C4×C151—41no—
394C4×C151—41no—
395C4×C151—82no—
396C4×C151C2×#12311yescharacteristic
397C4×C151#53411yescharacteristic
398C4×C151#54612yes—
399C2×C151—22no—
400C2×C151—22no—
401C2×C151—41no—
402C2×C151—42no—
403C2×C151—81no—
404C2×C151—82no—
405C2×C151—81no—
406C2×C151#240511yescharacteristic
407C2×C151C2×#45311yescharacteristic
408C2×C151#302211yescharacteristic
409#24026C15111yesmaximal, characteristic, direct product factor, Sylow
410C151#2402611yescharacteristic, direct product factor, Sylow
411#3488C2×C15111yescharacteristic
412#3092C2×C15111yescharacteristic, complemented
413C2×#417C2×C15111yescharacteristic, complemented
414#2501C2×C15111yescharacteristic, complemented
415#2039C2×C15112yescomplemented
416#2037C2×C15112yescomplemented
417#1900C2×C15111yescharacteristic, complemented
418#1871C2×C15111yescharacteristic, complemented
419#1859C2×C15112yescomplemented
420#1792C2×C15112yescomplemented
421#1789C2×C15111yescharacteristic, complemented
422C2×H(5,𝔽2)C22×C15111yescharacteristic
423C22×#41C22×C15111yescharacteristic
424C22×M16C22×C15111yescharacteristic, complemented
425#550—21no—
426#548—21no—
427#546—21no—
428#546—22no—
429D42—22no—
430D42—21no—
431#537—21no—
432#537C22×C15111yescharacteristic
433#535—21no—
434#535C22×C15111yescharacteristic
435#525—21no—
436#525C22×C15111yescharacteristic
437C2×#123—22no—
438C2×#121—21no—
439C2×#121C22×C15111yescharacteristic
440#520C22×C15111yescharacteristic
441C22×C4⋊C4C22×C15111yescharacteristic, complemented
442#484—21no—
443#483—21no—
444#481—21no—
445#480—21no—
446#428C22×C15112yescomplemented
447C2×#104C22×C15112yes—
448C2×#104C22×C15112yescomplemented
449C2×#104C22×C15112yescomplemented
450#417—21no—
451#417—21no—
452#417C22×C15112yes—
453#417C22×C15112yescomplemented
454#417C22×C15112yescomplemented
455C2×#103—21no—
456C2×#102—21no—
457C2×#100C22×C15112yescomplemented
458#407C22×C15111yescharacteristic, complemented
459#399—22no—
460#390C22×C15112yescomplemented
461#384C22×C15112yescomplemented
462C4×C22⋊C4C22×C15111yescharacteristic, complemented
463#343C22×C15112yescomplemented
464#339C22×C15112yescomplemented
465H(5,𝔽2)—24no—
466H(5,𝔽2)—42no—
467C2×#41—21no—
468C2×#41—21no—
469C2×#41—21no—
470C2×#41—21no—
471C2×#41—24no—
472C2×#41—42no—
473C2×#41D4×C15111yescharacteristic
474C2×#41D4×C15111yescharacteristic
475C2×#41C23×C15111yescharacteristic
476C2×#41C23×C15111yescharacteristic
477C2×#41C23×C15111yescharacteristic
478C22×Q8D4×C15111yescharacteristic
479C22×D4—21no—
480C22×D4—22no—
481C22×D4—22no—
482C22×D4—21no—
483C22×D4—21no—
484C22×D4D4×C15111yescharacteristic
485C22×D4D4×C15112yes—
486C22×D4C23×C15111yescharacteristic
487C23×C4—21no—
488C23×C4—21no—
489C23×C4C23×C15111yescharacteristic
490C2×M16—21no—
491C2×M16—42no—
492C2×M16C23×C15112yes—
493C2×M16C23×C15112yes—
494C22×C8—21no—
495#127—22no—
496#127—21no—
497#124—22no—
498#124—21no—
499#123—22no—
500#123—21no—
501#123—48no—
502C22⋊Q8—22no—
503C22⋊Q8—21no—
504C22⋊Q8—21no—
505C22⋊Q8D4×C15111yescharacteristic
506C22⋊Q8D4×C15111yescharacteristic
507#121—22no—
508#121—22no—
509#121—22no—
510#121—22no—
511#121—22no—
512#121—21no—
513#121—21no—
514#121—21no—
515#121—21no—
516#121—21no—
517#121—21no—
518#121—22no—
519#121—21no—
520#121—21no—
521#121D4×C15111yescharacteristic
522#121D4×C15111yescharacteristic
523#120—22no—
524#120—22no—
525#120—22no—
526#120—21no—
527#120—22no—
528C4×Q8—21no—
529C4×D4—22no—
530C4×D4—22no—
531C4×D4—21no—
532C4×D4—22no—
533C4×D4—21no—
534C4×D4—21no—
535#117—21no—
536#117C23×C15111yescharacteristic
537C2×C4⋊C4—21no—
538C2×C4⋊C4—21no—
539C2×C4⋊C4—21no—
540C2×C4⋊C4—21no—
541C2×C4⋊C4—21no—
542C2×C4⋊C4—21no—
543C2×C4⋊C4—24no—
544C2×C4⋊C4C23×C15112yes—
545C2×C4⋊C4C23×C15111yescharacteristic
546C2×C22⋊C4—22no—
547C2×C22⋊C4—21no—
548C2×C22⋊C4—24no—
549C2×C22⋊C4D4×C15112yes—
550C2×C42C23×C15112yes—
551#107—22no—
552#106—22no—
553#104—24no—
554#104—42no—
555#104—42no—
556#103—22no—
557#103—22no—
558#103—22no—
559#102—22no—
560#102—22no—
561#102—22no—
562#100—42no—
563C22⋊C8—21no—
564C22⋊C8—21no—
565#95—21no—
566C24—22no—
567C24—21no—
568C24C2×D4×C15111yescharacteristic
569C24C2×D4×C15112yes—
570#41—22no—
571#41—22no—
572#41—22no—
573#41—22no—
574#41—22no—
575#41—22no—
576#41—22no—
577#41—44no—
578#41—41no—
579#41—41no—
580#41—44no—
581#41—44no—
582#41—42no—
583#41—42no—
584#41#41×C15114yes—
585C2×Q8—21no—
586C2×Q8—22no—
587C2×Q8—41no—
588C2×Q8C2×D4×C15111yescharacteristic
589C2×Q8C2×D4×C15111yescharacteristic
590C2×Q8C2×D4×C15111yescharacteristic
591C2×D4—21no—
592C2×D4—22no—
593C2×D4—22no—
594C2×D4—22no—
595C2×D4—22no—
596C2×D4—21no—
597C2×D4—21no—
598C2×D4—21no—
599C2×D4—21no—
600C2×D4—21no—
601C2×D4—22no—
602C2×D4—22no—
603C2×D4—22no—
604C2×D4—21no—
605C2×D4—22no—
606C2×D4—21no—
607C2×D4—21no—
608C2×D4—21no—
609C2×D4—22no—
610C2×D4—22no—
611C2×D4—41no—
612C2×D4—44no—
613C2×D4—44no—
614C2×D4—48no—
615C2×D4—42no—
616C2×D4—42no—
617C2×D4—44no—
618C2×D4—84no—
619C2×D4C2×D4×C15111yescharacteristic
620C2×D4C2×D4×C15111yescharacteristic
621C2×D4C2×D4×C15111yescharacteristic
622C22×C4—21no—
623C22×C4—22no—
624C22×C4—22no—
625C22×C4—22no—
626C22×C4—21no—
627C22×C4—22no—
628C22×C4—22no—
629C22×C4—21no—
630C22×C4—21no—
631C22×C4—21no—
632C22×C4—21no—
633C22×C4—22no—
634C22×C4—44no—
635C22×C4—44no—
636C22×C4—41no—
637C22×C4—41no—
638C22×C4C2×D4×C15111yescharacteristic
639C22×C4C2×D4×C15111yescharacteristic
640C22×C4C2×D4×C15111yescharacteristic
641C22×C4C2×D4×C15111yescharacteristic
642C22×C4C2×D4×C15111yescharacteristic
643C22×C4C2×D4×C15112yes—
644C22×C4C24×C15111yescharacteristic
645M16—22no—
646M16—22no—
647M16—22no—
648M16—22no—
649M16—42no—
650C2×C8—22no—
651C2×C8—22no—
652C2×C8—42no—
653C4⋊C4—22no—
654C4⋊C4—22no—
655C4⋊C4—21no—
656C4⋊C4—21no—
657C4⋊C4—21no—
658C4⋊C4—21no—
659C4⋊C4—22no—
660C4⋊C4—22no—
661C4⋊C4—48no—
662C4⋊C4—41no—
663C4⋊C4—41no—
664C4⋊C4C2×D4×C15111yescharacteristic
665C4⋊C4C2×D4×C15111yescharacteristic
666C22⋊C4—22no—
667C22⋊C4—22no—
668C22⋊C4—24no—
669C22⋊C4—22no—
670C22⋊C4—22no—
671C22⋊C4—22no—
672C22⋊C4—21no—
673C22⋊C4—21no—
674C22⋊C4—21no—
675C22⋊C4—21no—
676C22⋊C4—22no—
677C22⋊C4—22no—
678C22⋊C4—21no—
679C22⋊C4—48no—
680C42—22no—
681C42—21no—
682C42—22no—
683C42—22no—
684C23—22no—
685C23—21no—
686C23—22no—
687C23—22no—
688C23—21no—
689C23—21no—
690C23—24no—
691C23—41no—
692C23—42no—
693C23—44no—
694C23—42no—
695C23—42no—
696C23—42no—
697C23—81no—
698C23—82no—
699C23—82no—
700C23#120×C15111yescharacteristic
701C23#120×C15111yescharacteristic
702C23C22×D4×C15111yescharacteristic
703Q8—21no—
704Q8—21no—
705Q8—21no—
706Q8—22no—
707Q8—42no—
708Q8#123×C15112yescomplemented
709D4—24no—
710D4—21no—
711D4—21no—
712D4—21no—
713D4—22no—
714D4—42no—
715D4—42no—
716D4—44no—
717D4—42no—
718D4—44no—
719D4—44no—
720D4—42no—
721D4—42no—
722D4—42no—
723D4—41no—
724D4—41no—
725D4—42no—
726D4—82no—
727D4—81no—
728D4—82no—
729D4—82no—
730D4—82no—
731D4#123×C15112yescomplemented
732C2×C4—21no—
733C2×C4—22no—
734C2×C4—21no—
735C2×C4—21no—
736C2×C4—21no—
737C2×C4—21no—
738C2×C4—22no—
739C2×C4—22no—
740C2×C4—24no—
741C2×C4—24no—
742C2×C4—21no—
743C2×C4—22no—
744C2×C4—21no—
745C2×C4—21no—
746C2×C4—21no—
747C2×C4—42no—
748C2×C4—42no—
749C2×C4—42no—
750C2×C4—44no—
751C2×C4—42no—
752C2×C4—42no—
753C2×C4—41no—
754C2×C4—41no—
755C2×C4—42no—
756C2×C4—42no—
757C2×C4—44no—
758C2×C4—42no—
759C2×C4—82no—
760C2×C4—82no—
761C2×C4—82no—
762C2×C4#120×C15111yescharacteristic
763C2×C4#120×C15111yescharacteristic
764C2×C4C22×D4×C15111yescharacteristic
765C2×C4C22×D4×C15111yescharacteristic
766C2×C4C2×#41×C15112yes—
767C2×C4H(5,𝔽2)×C15112yes—
768C8—42no—
769C8—42no—
770C22—21no—
771C22—21no—
772C22—21no—
773C22—21no—
774C22—21no—
775C22—22no—
776C22—21no—
777C22—21no—
778C22—44no—
779C22—41no—
780C22—41no—
781C22—41no—
782C22—41no—
783C22—42no—
784C22—42no—
785C22—41no—
786C22—41no—
787C22—41no—
788C22—42no—
789C22—41no—
790C22—84no—
791C22—84no—
792C22—164no—
793C22#453×C15112yes—
794C22C2×#120×C15111yescharacteristic
795C22#546×C15112yes—
796C4—21no—
797C4—21no—
798C4—22no—
799C4—44no—
800C4—41no—
801C4—41no—
802C4—42no—
803C4—41no—
804C4—41no—
805C4—82no—
806C4C2×#123×C15111yescharacteristic
807C4#534×C15111yescharacteristic
808C4#546×C15112yes—
809C2—22no—
810C2—22no—
811C2—41no—
812C2—42no—
813C2—81no—
814C2—82no—
815C2—81no—
816C2#2405×C15111yescharacteristic
817C2C2×#453×C15111yescharacteristic
818C2#3022×C15111yescharacteristic
subgroupG/H
center, socleC22×C151C2×#120
commutator, Frattini, cosocleC22×C4C24×C151
prime radical#3488×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
2. #3092×C151C2semidirect
3. C2×#417×C151C2semidirect
4. #2501×C151C2semidirect
5. #2039×C151C2semidirect
6. #2037×C151C2semidirect
7. #1900×C151C2semidirect
8. #1871×C151C2semidirect
9. #1859×C151C2semidirect
10. #1792×C151C2semidirect
11. #1789×C151C2semidirect
14. C22×M16×C151C22semidirect
31. C22×C4⋊C4×C151C22semidirect
36. #428×C151C22semidirect
38. C2×#104×C151C22semidirect
39. C2×#104×C151C22semidirect
43. #417×C151C22semidirect
44. #417×C151C22semidirect
47. C2×#100×C151C22semidirect
48. #407×C151C22semidirect
50. #390×C151C22semidirect
51. #384×C151C22semidirect
52. C4×C22⋊C4×C151C22semidirect
53. #343×C151C22semidirect
54. #339×C151C22semidirect
298. Q8×C151#123semidirect
321. D4×C151#123semidirect
409. #24026C151direct (N × H)
410. C151#24026direct (N × H)
412. #3092C2×C151semidirect
413. C2×#417C2×C151semidirect
414. #2501C2×C151semidirect
415. #2039C2×C151semidirect
416. #2037C2×C151semidirect
417. #1900C2×C151semidirect
418. #1871C2×C151semidirect
419. #1859C2×C151semidirect
420. #1792C2×C151semidirect
421. #1789C2×C151semidirect
424. C22×M16C22×C151semidirect
441. C22×C4⋊C4C22×C151semidirect
446. #428C22×C151semidirect
448. C2×#104C22×C151semidirect
449. C2×#104C22×C151semidirect
453. #417C22×C151semidirect
454. #417C22×C151semidirect
457. C2×#100C22×C151semidirect
458. #407C22×C151semidirect
460. #390C22×C151semidirect
461. #384C22×C151semidirect
462. C4×C22⋊C4C22×C151semidirect
463. #343C22×C151semidirect
464. #339C22×C151semidirect
708. Q8#123×C151semidirect
731. D4#123×C151semidirect

Maximal subgroups

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

subgroupindex
#3488×C1512
#3092×C1512
C2×#417×C1512
#2501×C1512
#2039×C1512
#2037×C1512
#1900×C1512
#1871×C1512
#1859×C1512
#1792×C1512
#1789×C1512
#24026151