Finite Group Databasebeta

← C151×#23954 #50328879

Subgroups — C151×#23954 #50328879

Order 38656.

1482 conjugacy classes of subgroups.

The subgroup lattice has 788 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#3494×C151C211yesmaximal, characteristic, complemented
2#3003×C151C211yesmaximal, characteristic, complemented
3C2×#418×C151C211yesmaximal, characteristic, complemented
4#2433×C151C211yesmaximal, characteristic, complemented
5#2027×C151C212yesmaximal, complemented
6#2002×C151C212yesmaximal, complemented
7#1900×C151C211yesmaximal, characteristic, complemented
8#1887×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#555×C151—21no—
16#553×C151—21no—
17#553×C151—21no—
18#551×C151—22no—
19#547×C151—21no—
20#546×C151—22no—
21#544×C151C2211yescharacteristic, complemented
22#542×C151—21no—
23#540×C151—21no—
24#535×C151C2211yescharacteristic, complemented
25#532×C151—21no—
26C2×#127×C151C2212yes—
27#529×C151—21no—
28#525×C151C2211yescharacteristic
29C2×#121×C151C2211yescharacteristic
30C2×#120×C151—22no—
31#520×C151C2211yescharacteristic, complemented
32#518×C151C2211yescharacteristic, complemented
33C2×#117×C151C2211yescharacteristic
34#450×C151—21no—
35#450×C151—21no—
36#447×C151—21no—
37#447×C151—21no—
38C2×#104×C151C2212yescomplemented
39#418×C151—21no—
40#418×C151—21no—
41#418×C151C2212yes—
42#418×C151C2212yes—
43#418×C151C2212yes—
44C2×#102×C151—21no—
45C2×#102×C151—21no—
46C2×#100×C151C2212yescomplemented
47#407×C151C2211yescharacteristic
48#392×C151—22no—
49#390×C151C2212yes—
50C4×C22⋊C4×C151C2211yescharacteristic
51#343×C151C2212yescomplemented
52#339×C151C2212yescomplemented
53#339×C151C2212yescomplemented
54#339×C151C2212yescomplemented
55C25×C151—21no—
56C2×#41×C151—22no—
57C2×#41×C151C2311yescharacteristic
58C22×D4×C151—21no—
59C22×D4×C151—24no—
60C22×D4×C151—24no—
61C22×D4×C151—21no—
62C22×D4×C151—21no—
63C22×D4×C151—21no—
64C22×D4×C151—21no—
65C22×D4×C151—42no—
66C22×D4×C151D412yes—
67C22×D4×C151C2312yes—
68C22×D4×C151C2311yescharacteristic
69C23×C4×C151C2311yescharacteristic
70AGL(1,ℤ/8)×C151—24no—
71AGL(1,ℤ/8)×C151—42no—
72C2×SD16×C151—22no—
73C2×D8×C151—22no—
74C2×M16×C151—21no—
75C2×M16×C151—42no—
76C2×M16×C151C2312yes—
77C2×M16×C151C2312yes—
78C22×C8×C151—21no—
79C4⋊Q8×C151—21no—
80C4⋊Q8×C151—21no—
81#127×C151—21no—
82#127×C151—24no—
83#127×C151—42no—
84#126×C151—22no—
85#126×C151—22no—
86#125×C151—21no—
87#125×C151—21no—
88#124×C151—22no—
89#124×C151—22no—
90#124×C151—21no—
91#123×C151—22no—
92#123×C151—22no—
93#123×C151—22no—
94#123×C151—22no—
95#123×C151—21no—
96C22⋊Q8×C151—22no—
97C22⋊Q8×C151—22no—
98C22⋊Q8×C151D411yescharacteristic, complemented
99C22⋊Q8×C151D411yescharacteristic, complemented
100#121×C151—22no—
101#121×C151—22no—
102#121×C151—22no—
103#121×C151—21no—
104#121×C151—21no—
105#121×C151—21no—
106#121×C151—21no—
107#121×C151—21no—
108#121×C151—21no—
109#121×C151D411yescharacteristic, complemented
110#121×C151D411yescharacteristic, complemented
111#120×C151—21no—
112#120×C151—22no—
113#120×C151—48no—
114C4×Q8×C151—21no—
115C4×D4×C151—22no—
116C4×D4×C151—22no—
117C4×D4×C151—21no—
118C4×D4×C151—22no—
119C4×D4×C151—21no—
120C4×D4×C151—21no—
121C4×D4×C151—21no—
122C4×D4×C151—21no—
123C4×D4×C151—21no—
124C4×D4×C151—21no—
125#117×C151—22no—
126#117×C151—21no—
127#117×C151—21no—
128#117×C151—21no—
129#117×C151D411yescharacteristic, complemented
130#117×C151D411yescharacteristic, complemented
131#117×C151C2311yescharacteristic
132#117×C151C2311yescharacteristic
133#117×C151C2311yescharacteristic
134C2×C4⋊C4×C151—21no—
135C2×C4⋊C4×C151D411yescharacteristic, complemented
136C2×C4⋊C4×C151D411yescharacteristic, complemented
137C2×C4⋊C4×C151C2311yescharacteristic
138C2×C22⋊C4×C151—24no—
139C2×C22⋊C4×C151—21no—
140C2×C22⋊C4×C151—21no—
141C2×C22⋊C4×C151—22no—
142C2×C22⋊C4×C151D412yes—
143C2×C42×C151—21no—
144C2×C42×C151C2312yes—
145#104×C151—42no—
146#102×C151—22no—
147#102×C151—22no—
148#102×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—44no—
158C24×C151—44no—
159C24×C151—41no—
160C24×C151—41no—
161C24×C151—82no—
162C24×C151C2×D411yescharacteristic
163C24×C151C2×D412yes—
164#41×C151—22no—
165#41×C151—22no—
166#41×C151—84no—
167C2×Q8×C151—22no—
168C2×Q8×C151C2×D411yescharacteristic
169C2×D4×C151—24no—
170C2×D4×C151—24no—
171C2×D4×C151—21no—
172C2×D4×C151—22no—
173C2×D4×C151—21no—
174C2×D4×C151—22no—
175C2×D4×C151—22no—
176C2×D4×C151—21no—
177C2×D4×C151—22no—
178C2×D4×C151—22no—
179C2×D4×C151—22no—
180C2×D4×C151—21no—
181C2×D4×C151—21no—
182C2×D4×C151—22no—
183C2×D4×C151—22no—
184C2×D4×C151—22no—
185C2×D4×C151—22no—
186C2×D4×C151—22no—
187C2×D4×C151—44no—
188C2×D4×C151—44no—
189C2×D4×C151—44no—
190C2×D4×C151—42no—
191C2×D4×C151—42no—
192C2×D4×C151—48no—
193C2×D4×C151—44no—
194C2×D4×C151—48no—
195C2×D4×C151—41no—
196C2×D4×C151—41no—
197C2×D4×C151—84no—
198C2×D4×C151C2×D411yescharacteristic
199C2×D4×C151#4114yescomplemented
200C22×C4×C151—22no—
201C22×C4×C151—22no—
202C22×C4×C151—21no—
203C22×C4×C151—22no—
204C22×C4×C151—22no—
205C22×C4×C151—22no—
206C22×C4×C151—22no—
207C22×C4×C151—21no—
208C22×C4×C151—21no—
209C22×C4×C151C2×D411yescharacteristic
210C22×C4×C151C2×D411yescharacteristic
211C22×C4×C151C2×D411yescharacteristic
212C22×C4×C151C2×D411yescharacteristic
213C22×C4×C151C2×D411yescharacteristic
214C22×C4×C151C2×D412yes—
215C22×C4×C151C2411yescharacteristic
216SD16×C151—44no—
217D8×C151—44no—
218M16×C151—22no—
219M16×C151—22no—
220M16×C151—22no—
221M16×C151—22no—
222M16×C151—42no—
223C2×C8×C151—22no—
224C2×C8×C151—22no—
225C2×C8×C151—42no—
226C4⋊C4×C151—22no—
227C4⋊C4×C151—22no—
228C4⋊C4×C151—22no—
229C4⋊C4×C151—22no—
230C4⋊C4×C151—21no—
231C4⋊C4×C151—21no—
232C4⋊C4×C151—21no—
233C4⋊C4×C151—21no—
234C4⋊C4×C151—21no—
235C4⋊C4×C151—21no—
236C4⋊C4×C151C2×D411yescharacteristic
237C4⋊C4×C151C2×D411yescharacteristic
238C4⋊C4×C151C2×D411yescharacteristic
239C4⋊C4×C151C2×D411yescharacteristic
240C4⋊C4×C151C2×D411yescharacteristic
241C4⋊C4×C151C2×D411yescharacteristic
242C22⋊C4×C151—22no—
243C22⋊C4×C151—22no—
244C22⋊C4×C151—24no—
245C22⋊C4×C151—22no—
246C22⋊C4×C151—22no—
247C22⋊C4×C151—22no—
248C22⋊C4×C151—21no—
249C22⋊C4×C151—21no—
250C22⋊C4×C151—21no—
251C22⋊C4×C151—21no—
252C22⋊C4×C151—21no—
253C22⋊C4×C151—21no—
254C22⋊C4×C151—21no—
255C22⋊C4×C151—22no—
256C22⋊C4×C151—22no—
257C22⋊C4×C151—21no—
258C22⋊C4×C151—21no—
259C22⋊C4×C151—48no—
260C42×C151—22no—
261C42×C151—21no—
262C42×C151—21no—
263C42×C151—21no—
264C42×C151—21no—
265C42×C151—21no—
266C42×C151—22no—
267C42×C151—22no—
268C23×C151—22no—
269C23×C151—22no—
270C23×C151—22no—
271C23×C151—21no—
272C23×C151—24no—
273C23×C151—24no—
274C23×C151—41no—
275C23×C151—44no—
276C23×C151—44no—
277C23×C151—44no—
278C23×C151—44no—
279C23×C151—42no—
280C23×C151—42no—
281C23×C151—42no—
282C23×C151—42no—
283C23×C151—82no—
284C23×C151—82no—
285C23×C151—82no—
286C23×C151—816no—
287C23×C151—82no—
288C23×C151#12011yescharacteristic
289C23×C151#12011yescharacteristic
290C23×C151C22×D411yescharacteristic
291Q8×C151—22no—
292Q8×C151—82no—
293D4×C151—24no—
294D4×C151—22no—
295D4×C151—24no—
296D4×C151—44no—
297D4×C151—44no—
298D4×C151—42no—
299D4×C151—42no—
300D4×C151—44no—
301D4×C151—41no—
302D4×C151—41no—
303D4×C151—42no—
304D4×C151—42no—
305D4×C151—42no—
306D4×C151—81no—
307D4×C151—82no—
308D4×C151—82no—
309D4×C151—82no—
310D4×C151—816no—
311C2×C4×C151—22no—
312C2×C4×C151—21no—
313C2×C4×C151—21no—
314C2×C4×C151—21no—
315C2×C4×C151—21no—
316C2×C4×C151—22no—
317C2×C4×C151—22no—
318C2×C4×C151—24no—
319C2×C4×C151—21no—
320C2×C4×C151—21no—
321C2×C4×C151—22no—
322C2×C4×C151—21no—
323C2×C4×C151—21no—
324C2×C4×C151—21no—
325C2×C4×C151—21no—
326C2×C4×C151—21no—
327C2×C4×C151—42no—
328C2×C4×C151—42no—
329C2×C4×C151—42no—
330C2×C4×C151—41no—
331C2×C4×C151—41no—
332C2×C4×C151—42no—
333C2×C4×C151—81no—
334C2×C4×C151—82no—
335C2×C4×C151—82no—
336C2×C4×C151—82no—
337C2×C4×C151#12011yescharacteristic
338C2×C4×C151#12011yescharacteristic
339C2×C4×C151C22×D411yescharacteristic
340C2×C4×C151C22×D411yescharacteristic
341C2×C4×C151C2×#4112yes—
342C2×C4×C151H(5,𝔽2)12yes—
343C8×C151—42no—
344C8×C151—42no—
345C22×C151—21no—
346C22×C151—21no—
347C22×C151—21no—
348C22×C151—21no—
349C22×C151—21no—
350C22×C151—21no—
351C22×C151—21no—
352C22×C151—44no—
353C22×C151—48no—
354C22×C151—41no—
355C22×C151—44no—
356C22×C151—42no—
357C22×C151—41no—
358C22×C151—42no—
359C22×C151—42no—
360C22×C151—41no—
361C22×C151—84no—
362C22×C151—84no—
363C22×C151—88no—
364C22×C151—88no—
365C22×C151—82no—
366C22×C151—82no—
367C22×C151#45312yes—
368C22×C151C2×#12011yescharacteristic
369C22×C151#54612yes—
370C4×C151—21no—
371C4×C151—21no—
372C4×C151—44no—
373C4×C151—41no—
374C4×C151—41no—
375C4×C151—41no—
376C4×C151—42no—
377C4×C151—41no—
378C4×C151—41no—
379C4×C151—41no—
380C4×C151—41no—
381C4×C151#52511yescharacteristic
382C4×C151#53511yescharacteristic
383C4×C151#54612yes—
384C2×C151—22no—
385C2×C151—22no—
386C2×C151—41no—
387C2×C151—81no—
388C2×C151—82no—
389C2×C151—84no—
390C2×C151#240411yescharacteristic
391C2×C151C2×#45311yescharacteristic
392C2×C151#302111yescharacteristic
393#23954C15111yesmaximal, characteristic, direct product factor, Sylow
394C151#2395411yescharacteristic, direct product factor, Sylow
395#3494C2×C15111yescharacteristic, complemented
396#3003C2×C15111yescharacteristic, complemented
397C2×#418C2×C15111yescharacteristic, complemented
398#2433C2×C15111yescharacteristic, complemented
399#2027C2×C15112yescomplemented
400#2002C2×C15112yescomplemented
401#1900C2×C15111yescharacteristic, complemented
402#1887C2×C15112yescomplemented
403#1883C2×C15112yescomplemented
404#1871C2×C15111yescharacteristic, complemented
405#1826C2×C15111yescharacteristic, complemented
406C23×D4C22×C15111yescharacteristic
407C2×AGL(1,ℤ/8)C22×C15112yes—
408C22×M16C22×C15111yescharacteristic
409#555—21no—
410#553—21no—
411#553—21no—
412#551—22no—
413#547—21no—
414#546—22no—
415#544C22×C15111yescharacteristic, complemented
416#542—21no—
417#540—21no—
418#535C22×C15111yescharacteristic, complemented
419#532—21no—
420C2×#127C22×C15112yes—
421#529—21no—
422#525C22×C15111yescharacteristic
423C2×#121C22×C15111yescharacteristic
424C2×#120—22no—
425#520C22×C15111yescharacteristic, complemented
426#518C22×C15111yescharacteristic, complemented
427C2×#117C22×C15111yescharacteristic
428#450—21no—
429#450—21no—
430#447—21no—
431#447—21no—
432C2×#104C22×C15112yescomplemented
433#418—21no—
434#418—21no—
435#418C22×C15112yes—
436#418C22×C15112yes—
437#418C22×C15112yes—
438C2×#102—21no—
439C2×#102—21no—
440C2×#100C22×C15112yescomplemented
441#407C22×C15111yescharacteristic
442#392—22no—
443#390C22×C15112yes—
444C4×C22⋊C4C22×C15111yescharacteristic
445#343C22×C15112yescomplemented
446#339C22×C15112yescomplemented
447#339C22×C15112yescomplemented
448#339C22×C15112yescomplemented
449C25—21no—
450C2×#41—22no—
451C2×#41C23×C15111yescharacteristic
452C22×D4—24no—
453C22×D4—24no—
454C22×D4—21no—
455C22×D4—21no—
456C22×D4—21no—
457C22×D4—21no—
458C22×D4—21no—
459C22×D4—42no—
460C22×D4D4×C15112yes—
461C22×D4C23×C15111yescharacteristic
462C22×D4C23×C15112yes—
463C23×C4C23×C15111yescharacteristic
464AGL(1,ℤ/8)—24no—
465AGL(1,ℤ/8)—42no—
466C2×SD16—22no—
467C2×D8—22no—
468C2×M16—21no—
469C2×M16—42no—
470C2×M16C23×C15112yes—
471C2×M16C23×C15112yes—
472C22×C8—21no—
473C4⋊Q8—21no—
474C4⋊Q8—21no—
475#127—21no—
476#127—24no—
477#127—42no—
478#126—22no—
479#126—22no—
480#125—21no—
481#125—21no—
482#124—22no—
483#124—22no—
484#124—21no—
485#123—22no—
486#123—22no—
487#123—22no—
488#123—22no—
489#123—21no—
490C22⋊Q8—22no—
491C22⋊Q8—22no—
492C22⋊Q8D4×C15111yescharacteristic, complemented
493C22⋊Q8D4×C15111yescharacteristic, complemented
494#121—22no—
495#121—22no—
496#121—22no—
497#121—21no—
498#121—21no—
499#121—21no—
500#121—21no—
501#121—21no—
502#121—21no—
503#121D4×C15111yescharacteristic, complemented
504#121D4×C15111yescharacteristic, complemented
505#120—21no—
506#120—22no—
507#120—48no—
508C4×Q8—21no—
509C4×D4—22no—
510C4×D4—22no—
511C4×D4—21no—
512C4×D4—22no—
513C4×D4—21no—
514C4×D4—21no—
515C4×D4—21no—
516C4×D4—21no—
517C4×D4—21no—
518C4×D4—21no—
519#117—22no—
520#117—21no—
521#117—21no—
522#117—21no—
523#117D4×C15111yescharacteristic, complemented
524#117D4×C15111yescharacteristic, complemented
525#117C23×C15111yescharacteristic
526#117C23×C15111yescharacteristic
527#117C23×C15111yescharacteristic
528C2×C4⋊C4—21no—
529C2×C4⋊C4D4×C15111yescharacteristic, complemented
530C2×C4⋊C4D4×C15111yescharacteristic, complemented
531C2×C4⋊C4C23×C15111yescharacteristic
532C2×C22⋊C4—21no—
533C2×C22⋊C4—22no—
534C2×C22⋊C4—21no—
535C2×C22⋊C4—24no—
536C2×C22⋊C4D4×C15112yes—
537C2×C42—21no—
538C2×C42C23×C15112yes—
539#104—42no—
540#102—22no—
541#102—22no—
542#102—22no—
543#102—22no—
544#102—22no—
545#102—22no—
546#100—42no—
547C22⋊C8—21no—
548C22⋊C8—21no—
549#95—21no—
550C24—22no—
551C24—44no—
552C24—44no—
553C24—41no—
554C24—41no—
555C24—82no—
556C24C2×D4×C15111yescharacteristic
557C24C2×D4×C15112yes—
558#41—22no—
559#41—22no—
560#41—84no—
561C2×Q8—22no—
562C2×Q8C2×D4×C15111yescharacteristic
563C2×D4—24no—
564C2×D4—24no—
565C2×D4—21no—
566C2×D4—22no—
567C2×D4—21no—
568C2×D4—22no—
569C2×D4—22no—
570C2×D4—21no—
571C2×D4—22no—
572C2×D4—22no—
573C2×D4—22no—
574C2×D4—21no—
575C2×D4—21no—
576C2×D4—22no—
577C2×D4—22no—
578C2×D4—22no—
579C2×D4—22no—
580C2×D4—22no—
581C2×D4—44no—
582C2×D4—44no—
583C2×D4—44no—
584C2×D4—42no—
585C2×D4—42no—
586C2×D4—48no—
587C2×D4—44no—
588C2×D4—48no—
589C2×D4—41no—
590C2×D4—41no—
591C2×D4—84no—
592C2×D4C2×D4×C15111yescharacteristic
593C2×D4#41×C15114yescomplemented
594C22×C4—22no—
595C22×C4—22no—
596C22×C4—21no—
597C22×C4—22no—
598C22×C4—22no—
599C22×C4—22no—
600C22×C4—22no—
601C22×C4—21no—
602C22×C4—21no—
603C22×C4C2×D4×C15111yescharacteristic
604C22×C4C2×D4×C15111yescharacteristic
605C22×C4C2×D4×C15111yescharacteristic
606C22×C4C2×D4×C15111yescharacteristic
607C22×C4C2×D4×C15111yescharacteristic
608C22×C4C2×D4×C15112yes—
609C22×C4C24×C15111yescharacteristic
610SD16—44no—
611D8—44no—
612M16—22no—
613M16—22no—
614M16—22no—
615M16—22no—
616M16—42no—
617C2×C8—22no—
618C2×C8—22no—
619C2×C8—42no—
620C4⋊C4—22no—
621C4⋊C4—22no—
622C4⋊C4—22no—
623C4⋊C4—22no—
624C4⋊C4—21no—
625C4⋊C4—21no—
626C4⋊C4—21no—
627C4⋊C4—21no—
628C4⋊C4—21no—
629C4⋊C4—21no—
630C4⋊C4C2×D4×C15111yescharacteristic
631C4⋊C4C2×D4×C15111yescharacteristic
632C4⋊C4C2×D4×C15111yescharacteristic
633C4⋊C4C2×D4×C15111yescharacteristic
634C4⋊C4C2×D4×C15111yescharacteristic
635C4⋊C4C2×D4×C15111yescharacteristic
636C22⋊C4—22no—
637C22⋊C4—22no—
638C22⋊C4—24no—
639C22⋊C4—22no—
640C22⋊C4—22no—
641C22⋊C4—22no—
642C22⋊C4—21no—
643C22⋊C4—21no—
644C22⋊C4—21no—
645C22⋊C4—21no—
646C22⋊C4—21no—
647C22⋊C4—21no—
648C22⋊C4—21no—
649C22⋊C4—22no—
650C22⋊C4—22no—
651C22⋊C4—21no—
652C22⋊C4—21no—
653C22⋊C4—48no—
654C42—22no—
655C42—21no—
656C42—21no—
657C42—21no—
658C42—21no—
659C42—21no—
660C42—22no—
661C42—22no—
662C23—22no—
663C23—22no—
664C23—22no—
665C23—21no—
666C23—24no—
667C23—24no—
668C23—41no—
669C23—44no—
670C23—44no—
671C23—44no—
672C23—44no—
673C23—42no—
674C23—42no—
675C23—42no—
676C23—42no—
677C23—82no—
678C23—82no—
679C23—82no—
680C23—816no—
681C23—82no—
682C23#120×C15111yescharacteristic
683C23#120×C15111yescharacteristic
684C23C22×D4×C15111yescharacteristic
685Q8—22no—
686Q8—82no—
687D4—24no—
688D4—22no—
689D4—24no—
690D4—44no—
691D4—44no—
692D4—44no—
693D4—42no—
694D4—42no—
695D4—41no—
696D4—42no—
697D4—41no—
698D4—42no—
699D4—42no—
700D4—82no—
701D4—81no—
702D4—82no—
703D4—82no—
704D4—816no—
705C2×C4—22no—
706C2×C4—21no—
707C2×C4—21no—
708C2×C4—21no—
709C2×C4—21no—
710C2×C4—22no—
711C2×C4—22no—
712C2×C4—24no—
713C2×C4—21no—
714C2×C4—21no—
715C2×C4—21no—
716C2×C4—21no—
717C2×C4—21no—
718C2×C4—21no—
719C2×C4—21no—
720C2×C4—22no—
721C2×C4—42no—
722C2×C4—42no—
723C2×C4—42no—
724C2×C4—41no—
725C2×C4—41no—
726C2×C4—42no—
727C2×C4—81no—
728C2×C4—82no—
729C2×C4—82no—
730C2×C4—82no—
731C2×C4#120×C15111yescharacteristic
732C2×C4#120×C15111yescharacteristic
733C2×C4C22×D4×C15111yescharacteristic
734C2×C4C22×D4×C15111yescharacteristic
735C2×C4C2×#41×C15112yes—
736C2×C4H(5,𝔽2)×C15112yes—
737C8—42no—
738C8—42no—
739C22—21no—
740C22—21no—
741C22—21no—
742C22—21no—
743C22—21no—
744C22—21no—
745C22—21no—
746C22—44no—
747C22—48no—
748C22—41no—
749C22—44no—
750C22—42no—
751C22—41no—
752C22—42no—
753C22—42no—
754C22—41no—
755C22—84no—
756C22—84no—
757C22—88no—
758C22—88no—
759C22—82no—
760C22—82no—
761C22#453×C15112yes—
762C22C2×#120×C15111yescharacteristic
763C22#546×C15112yes—
764C4—21no—
765C4—21no—
766C4—44no—
767C4—41no—
768C4—41no—
769C4—41no—
770C4—42no—
771C4—41no—
772C4—41no—
773C4—41no—
774C4—41no—
775C4#525×C15111yescharacteristic
776C4#535×C15111yescharacteristic
777C4#546×C15112yes—
778C2—22no—
779C2—22no—
780C2—41no—
781C2—84no—
782C2—82no—
783C2—81no—
784C2#2404×C15111yescharacteristic
785C2C2×#453×C15111yescharacteristic
786C2#3021×C15111yescharacteristic
subgroupG/H
center, socleC22×C151C2×#120
commutator, Frattini, cosocleC22×C4C24×C151
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. #3494×C151C2semidirect
2. #3003×C151C2semidirect
3. C2×#418×C151C2semidirect
4. #2433×C151C2semidirect
5. #2027×C151C2semidirect
6. #2002×C151C2semidirect
7. #1900×C151C2semidirect
8. #1887×C151C2semidirect
9. #1883×C151C2semidirect
10. #1871×C151C2semidirect
11. #1826×C151C2semidirect
21. #544×C151C22semidirect
24. #535×C151C22semidirect
31. #520×C151C22semidirect
32. #518×C151C22semidirect
38. C2×#104×C151C22semidirect
46. C2×#100×C151C22semidirect
51. #343×C151C22semidirect
52. #339×C151C22semidirect
53. #339×C151C22semidirect
54. #339×C151C22semidirect
98. C22⋊Q8×C151D4semidirect
99. C22⋊Q8×C151D4semidirect
109. #121×C151D4semidirect
110. #121×C151D4semidirect
129. #117×C151D4semidirect
130. #117×C151D4semidirect
135. C2×C4⋊C4×C151D4semidirect
136. C2×C4⋊C4×C151D4semidirect
199. C2×D4×C151#41semidirect
393. #23954C151direct (N × H)
394. C151#23954direct (N × H)
395. #3494C2×C151semidirect
396. #3003C2×C151semidirect
397. C2×#418C2×C151semidirect
398. #2433C2×C151semidirect
399. #2027C2×C151semidirect
400. #2002C2×C151semidirect
401. #1900C2×C151semidirect
402. #1887C2×C151semidirect
403. #1883C2×C151semidirect
404. #1871C2×C151semidirect
405. #1826C2×C151semidirect
415. #544C22×C151semidirect
418. #535C22×C151semidirect
425. #520C22×C151semidirect
426. #518C22×C151semidirect
432. C2×#104C22×C151semidirect
440. C2×#100C22×C151semidirect
445. #343C22×C151semidirect
446. #339C22×C151semidirect
447. #339C22×C151semidirect
448. #339C22×C151semidirect
492. C22⋊Q8D4×C151semidirect
493. C22⋊Q8D4×C151semidirect
503. #121D4×C151semidirect
504. #121D4×C151semidirect
523. #117D4×C151semidirect
524. #117D4×C151semidirect
529. C2×C4⋊C4D4×C151semidirect
530. C2×C4⋊C4D4×C151semidirect
593. C2×D4#41×C151semidirect

Maximal subgroups

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

subgroupindex
#3494×C1512
#3003×C1512
C2×#418×C1512
#2433×C1512
#2027×C1512
#2002×C1512
#1900×C1512
#1887×C1512
#1883×C1512
#1871×C1512
#1826×C1512
#23954151